LMFDB - Embedded newform 935.2.a.i.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [935,2,Mod(1,935)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(935, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("935.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 935 = 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	935.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:	$7.46601258899$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 10x^{7} + 31x^{6} + 29x^{5} - 97x^{4} - 19x^{3} + 94x^{2} - 10x - 9 $ x^9 - 3x^8 - 10x^7 + 31x^6 + 29x^5 - 97x^4 - 19x^3 + 94x^2 - 10x - 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.82213$ of defining polynomial
Character	$\chi$	$=$	935.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.82213 q^{2} -2.88880 q^{3} +1.32016 q^{4} -1.00000 q^{5} +5.26377 q^{6} +5.06716 q^{7} +1.23876 q^{8} +5.34517 q^{9} +O(q^{10})$	\(q-1.82213 q^{2} -2.88880 q^{3} +1.32016 q^{4} -1.00000 q^{5} +5.26377 q^{6} +5.06716 q^{7} +1.23876 q^{8} +5.34517 q^{9} +1.82213 q^{10} +1.00000 q^{11} -3.81368 q^{12} +6.98651 q^{13} -9.23303 q^{14} +2.88880 q^{15} -4.89750 q^{16} -1.00000 q^{17} -9.73960 q^{18} -2.97265 q^{19} -1.32016 q^{20} -14.6380 q^{21} -1.82213 q^{22} +4.46920 q^{23} -3.57853 q^{24} +1.00000 q^{25} -12.7303 q^{26} -6.77473 q^{27} +6.68946 q^{28} -7.16142 q^{29} -5.26377 q^{30} +10.0398 q^{31} +6.44636 q^{32} -2.88880 q^{33} +1.82213 q^{34} -5.06716 q^{35} +7.05647 q^{36} -1.09232 q^{37} +5.41656 q^{38} -20.1827 q^{39} -1.23876 q^{40} +6.24623 q^{41} +26.6724 q^{42} -1.59304 q^{43} +1.32016 q^{44} -5.34517 q^{45} -8.14346 q^{46} -6.87199 q^{47} +14.1479 q^{48} +18.6761 q^{49} -1.82213 q^{50} +2.88880 q^{51} +9.22331 q^{52} +11.2736 q^{53} +12.3444 q^{54} -1.00000 q^{55} +6.27700 q^{56} +8.58740 q^{57} +13.0490 q^{58} -7.62548 q^{59} +3.81368 q^{60} -9.78595 q^{61} -18.2938 q^{62} +27.0849 q^{63} -1.95111 q^{64} -6.98651 q^{65} +5.26377 q^{66} +1.45320 q^{67} -1.32016 q^{68} -12.9106 q^{69} +9.23303 q^{70} -8.24819 q^{71} +6.62138 q^{72} +4.24422 q^{73} +1.99036 q^{74} -2.88880 q^{75} -3.92437 q^{76} +5.06716 q^{77} +36.7754 q^{78} -4.32806 q^{79} +4.89750 q^{80} +3.53534 q^{81} -11.3815 q^{82} +4.77036 q^{83} -19.3245 q^{84} +1.00000 q^{85} +2.90273 q^{86} +20.6879 q^{87} +1.23876 q^{88} -2.28487 q^{89} +9.73960 q^{90} +35.4018 q^{91} +5.90005 q^{92} -29.0030 q^{93} +12.5217 q^{94} +2.97265 q^{95} -18.6223 q^{96} +3.05884 q^{97} -34.0304 q^{98} +5.34517 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 3 q^{2} + 3 q^{3} + 11 q^{4} - 9 q^{5} + 9 q^{6} + 8 q^{7} + 12 q^{8} + 8 q^{9}+O(q^{10}) $ 9 * q + 3 * q^2 + 3 * q^3 + 11 * q^4 - 9 * q^5 + 9 * q^6 + 8 * q^7 + 12 * q^8 + 8 * q^9	\( 9 q + 3 q^{2} + 3 q^{3} + 11 q^{4} - 9 q^{5} + 9 q^{6} + 8 q^{7} + 12 q^{8} + 8 q^{9} - 3 q^{10} + 9 q^{11} + 12 q^{12} + 23 q^{13} - 16 q^{14} - 3 q^{15} + 15 q^{16} - 9 q^{17} - q^{18} + 12 q^{19} - 11 q^{20} - 4 q^{21} + 3 q^{22} - q^{23} - q^{24} + 9 q^{25} + 16 q^{26} + 12 q^{27} + 4 q^{28} - 19 q^{29} - 9 q^{30} + 14 q^{31} + 42 q^{32} + 3 q^{33} - 3 q^{34} - 8 q^{35} + 12 q^{36} + 15 q^{37} + 6 q^{38} - 4 q^{39} - 12 q^{40} - 7 q^{41} + 8 q^{42} + 33 q^{43} + 11 q^{44} - 8 q^{45} - 14 q^{46} - 10 q^{47} + 38 q^{48} + 37 q^{49} + 3 q^{50} - 3 q^{51} + 44 q^{52} + 18 q^{53} + 43 q^{54} - 9 q^{55} - 16 q^{56} + 2 q^{57} - 38 q^{58} - 7 q^{59} - 12 q^{60} + 13 q^{61} - 16 q^{62} + 28 q^{63} + 38 q^{64} - 23 q^{65} + 9 q^{66} + 8 q^{67} - 11 q^{68} - 48 q^{69} + 16 q^{70} - 16 q^{71} - 44 q^{72} + 30 q^{73} - 36 q^{74} + 3 q^{75} + 24 q^{76} + 8 q^{77} + 42 q^{78} - 21 q^{79} - 15 q^{80} + 21 q^{81} - 19 q^{82} + 33 q^{83} - 76 q^{84} + 9 q^{85} + 3 q^{86} + 8 q^{87} + 12 q^{88} - 11 q^{89} + q^{90} - 31 q^{92} - 40 q^{94} - 12 q^{95} + 34 q^{96} + 27 q^{97} + 47 q^{98} + 8 q^{99}+O(q^{100}) \) 9 * q + 3 * q^2 + 3 * q^3 + 11 * q^4 - 9 * q^5 + 9 * q^6 + 8 * q^7 + 12 * q^8 + 8 * q^9 - 3 * q^10 + 9 * q^11 + 12 * q^12 + 23 * q^13 - 16 * q^14 - 3 * q^15 + 15 * q^16 - 9 * q^17 - q^18 + 12 * q^19 - 11 * q^20 - 4 * q^21 + 3 * q^22 - q^23 - q^24 + 9 * q^25 + 16 * q^26 + 12 * q^27 + 4 * q^28 - 19 * q^29 - 9 * q^30 + 14 * q^31 + 42 * q^32 + 3 * q^33 - 3 * q^34 - 8 * q^35 + 12 * q^36 + 15 * q^37 + 6 * q^38 - 4 * q^39 - 12 * q^40 - 7 * q^41 + 8 * q^42 + 33 * q^43 + 11 * q^44 - 8 * q^45 - 14 * q^46 - 10 * q^47 + 38 * q^48 + 37 * q^49 + 3 * q^50 - 3 * q^51 + 44 * q^52 + 18 * q^53 + 43 * q^54 - 9 * q^55 - 16 * q^56 + 2 * q^57 - 38 * q^58 - 7 * q^59 - 12 * q^60 + 13 * q^61 - 16 * q^62 + 28 * q^63 + 38 * q^64 - 23 * q^65 + 9 * q^66 + 8 * q^67 - 11 * q^68 - 48 * q^69 + 16 * q^70 - 16 * q^71 - 44 * q^72 + 30 * q^73 - 36 * q^74 + 3 * q^75 + 24 * q^76 + 8 * q^77 + 42 * q^78 - 21 * q^79 - 15 * q^80 + 21 * q^81 - 19 * q^82 + 33 * q^83 - 76 * q^84 + 9 * q^85 + 3 * q^86 + 8 * q^87 + 12 * q^88 - 11 * q^89 + q^90 - 31 * q^92 - 40 * q^94 - 12 * q^95 + 34 * q^96 + 27 * q^97 + 47 * q^98 + 8 * 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 $

$2$	−1.82213	−1.28844	−0.644220	−	0.764840i	$-0.722818\pi$
$2$	−1.82213	−1.28844	−0.644220	+	0.764840i	$0.722818\pi$
$3$	−2.88880	−1.66785	−0.833925	−	0.551878i	$-0.813911\pi$
$3$	−2.88880	−1.66785	−0.833925	+	0.551878i	$0.813911\pi$
$4$	1.32016	0.660079
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	5.26377	2.14893
$7$	5.06716	1.91521	0.957604	−	0.288088i	$-0.0930196\pi$
$7$	5.06716	1.91521	0.957604	+	0.288088i	$0.0930196\pi$
$8$	1.23876	0.437968
$9$	5.34517	1.78172
$10$	1.82213	0.576208
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−3.81368	−1.10091
$13$	6.98651	1.93771	0.968855	−	0.247628i	$-0.0796510\pi$
$13$	6.98651	1.93771	0.968855	+	0.247628i	$0.0796510\pi$
$14$	−9.23303	−2.46763
$15$	2.88880	0.745885
$16$	−4.89750	−1.22437
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−9.73960	−2.29565
$19$	−2.97265	−0.681973	−0.340986	−	0.940068i	$-0.610761\pi$
$19$	−2.97265	−0.681973	−0.340986	+	0.940068i	$0.610761\pi$
$20$	−1.32016	−0.295196
$21$	−14.6380	−3.19428
$22$	−1.82213	−0.388479
$23$	4.46920	0.931892	0.465946	−	0.884813i	$-0.345714\pi$
$23$	4.46920	0.931892	0.465946	+	0.884813i	$0.345714\pi$
$24$	−3.57853	−0.730464
$25$	1.00000	0.200000
$26$	−12.7303	−2.49663
$27$	−6.77473	−1.30380
$28$	6.68946	1.26419
$29$	−7.16142	−1.32984	−0.664921	−	0.746914i	$-0.731535\pi$
$29$	−7.16142	−1.32984	−0.664921	+	0.746914i	$0.731535\pi$
$30$	−5.26377	−0.961029
$31$	10.0398	1.80320	0.901602	−	0.432567i	$-0.142392\pi$
$31$	10.0398	1.80320	0.901602	+	0.432567i	$0.142392\pi$
$32$	6.44636	1.13957
$33$	−2.88880	−0.502876
$34$	1.82213	0.312493
$35$	−5.06716	−0.856507
$36$	7.05647	1.17608
$37$	−1.09232	−0.179577	−0.0897884	−	0.995961i	$-0.528619\pi$
$37$	−1.09232	−0.179577	−0.0897884	+	0.995961i	$0.528619\pi$
$38$	5.41656	0.878682
$39$	−20.1827	−3.23181
$40$	−1.23876	−0.195865
$41$	6.24623	0.975498	0.487749	−	0.872984i	$-0.337818\pi$
$41$	6.24623	0.975498	0.487749	+	0.872984i	$0.337818\pi$
$42$	26.6724	4.11564
$43$	−1.59304	−0.242936	−0.121468	−	0.992595i	$-0.538760\pi$
$43$	−1.59304	−0.242936	−0.121468	+	0.992595i	$0.538760\pi$
$44$	1.32016	0.199021
$45$	−5.34517	−0.796811
$46$	−8.14346	−1.20069
$47$	−6.87199	−1.00238	−0.501191	−	0.865337i	$-0.667105\pi$
$47$	−6.87199	−1.00238	−0.501191	+	0.865337i	$0.667105\pi$
$48$	14.1479	2.04207
$49$	18.6761	2.66802
$50$	−1.82213	−0.257688
$51$	2.88880	0.404513
$52$	9.22331	1.27904
$53$	11.2736	1.54855	0.774277	−	0.632847i	$-0.218114\pi$
$53$	11.2736	1.54855	0.774277	+	0.632847i	$0.218114\pi$
$54$	12.3444	1.67987
$55$	−1.00000	−0.134840
$56$	6.27700	0.838799
$57$	8.58740	1.13743
$58$	13.0490	1.71342
$59$	−7.62548	−0.992753	−0.496376	−	0.868107i	$-0.665336\pi$
$59$	−7.62548	−0.992753	−0.496376	+	0.868107i	$0.665336\pi$
$60$	3.81368	0.492343
$61$	−9.78595	−1.25296	−0.626481	−	0.779436i	$-0.715506\pi$
$61$	−9.78595	−1.25296	−0.626481	+	0.779436i	$0.715506\pi$
$62$	−18.2938	−2.32332
$63$	27.0849	3.41237
$64$	−1.95111	−0.243889
$65$	−6.98651	−0.866570
$66$	5.26377	0.647925
$67$	1.45320	0.177536	0.0887681	−	0.996052i	$-0.471707\pi$
$67$	1.45320	0.177536	0.0887681	+	0.996052i	$0.471707\pi$
$68$	−1.32016	−0.160093
$69$	−12.9106	−1.55426
$70$	9.23303	1.10356
$71$	−8.24819	−0.978880	−0.489440	−	0.872037i	$-0.662799\pi$
$71$	−8.24819	−0.978880	−0.489440	+	0.872037i	$0.662799\pi$
$72$	6.62138	0.780337
$73$	4.24422	0.496748	0.248374	−	0.968664i	$-0.420104\pi$
$73$	4.24422	0.496748	0.248374	+	0.968664i	$0.420104\pi$
$74$	1.99036	0.231374
$75$	−2.88880	−0.333570
$76$	−3.92437	−0.450156
$77$	5.06716	0.577457
$78$	36.7754	4.16400
$79$	−4.32806	−0.486945	−0.243473	−	0.969908i	$-0.578287\pi$
$79$	−4.32806	−0.486945	−0.243473	+	0.969908i	$0.578287\pi$
$80$	4.89750	0.547557
$81$	3.53534	0.392815
$82$	−11.3815	−1.25687
$83$	4.77036	0.523615	0.261807	−	0.965120i	$-0.415681\pi$
$83$	4.77036	0.523615	0.261807	+	0.965120i	$0.415681\pi$
$84$	−19.3245	−2.10848
$85$	1.00000	0.108465
$86$	2.90273	0.313009
$87$	20.6879	2.21798
$88$	1.23876	0.132052
$89$	−2.28487	−0.242196	−0.121098	−	0.992641i	$-0.538642\pi$
$89$	−2.28487	−0.242196	−0.121098	+	0.992641i	$0.538642\pi$
$90$	9.73960	1.02664
$91$	35.4018	3.71112
$92$	5.90005	0.615123
$93$	−29.0030	−3.00747
$94$	12.5217	1.29151
$95$	2.97265	0.304988
$96$	−18.6223	−1.90063
$97$	3.05884	0.310578	0.155289	−	0.987869i	$-0.450369\pi$
$97$	3.05884	0.310578	0.155289	+	0.987869i	$0.450369\pi$
$98$	−34.0304	−3.43759
$99$	5.34517	0.537210
$100$	1.32016	0.132016
$101$	15.1734	1.50981	0.754906	−	0.655832i	$-0.227682\pi$
$101$	15.1734	1.50981	0.754906	+	0.655832i	$0.227682\pi$
$102$	−5.26377	−0.521191
$103$	−5.37325	−0.529442	−0.264721	−	0.964325i	$-0.585280\pi$
$103$	−5.37325	−0.529442	−0.264721	+	0.964325i	$0.585280\pi$
$104$	8.65461	0.848654
$105$	14.6380	1.42853
$106$	−20.5420	−1.99522
$107$	−5.65457	−0.546648	−0.273324	−	0.961922i	$-0.588123\pi$
$107$	−5.65457	−0.546648	−0.273324	+	0.961922i	$0.588123\pi$
$108$	−8.94372	−0.860610
$109$	0.980781	0.0939417	0.0469709	−	0.998896i	$-0.485043\pi$
$109$	0.980781	0.0939417	0.0469709	+	0.998896i	$0.485043\pi$
$110$	1.82213	0.173733
$111$	3.15550	0.299507
$112$	−24.8164	−2.34493
$113$	0.111447	0.0104841	0.00524203	−	0.999986i	$-0.498331\pi$
$113$	0.111447	0.0104841	0.00524203	+	0.999986i	$0.498331\pi$
$114$	−15.6474	−1.46551
$115$	−4.46920	−0.416755
$116$	−9.45421	−0.877801
$117$	37.3441	3.45246
$118$	13.8946	1.27910
$119$	−5.06716	−0.464506
$120$	3.57853	0.326674
$121$	1.00000	0.0909091
$122$	17.8313	1.61437
$123$	−18.0441	−1.62698
$124$	13.2541	1.19026
$125$	−1.00000	−0.0894427
$126$	−49.3521	−4.39664
$127$	2.63769	0.234057	0.117029	−	0.993129i	$-0.462663\pi$
$127$	2.63769	0.234057	0.117029	+	0.993129i	$0.462663\pi$
$128$	−9.33754	−0.825330
$129$	4.60198	0.405181
$130$	12.7303	1.11652
$131$	−6.64479	−0.580558	−0.290279	−	0.956942i	$-0.593748\pi$
$131$	−6.64479	−0.580558	−0.290279	+	0.956942i	$0.593748\pi$
$132$	−3.81368	−0.331938
$133$	−15.0629	−1.30612
$134$	−2.64791	−0.228745
$135$	6.77473	0.583076
$136$	−1.23876	−0.106223
$137$	−1.32377	−0.113098	−0.0565488	−	0.998400i	$-0.518010\pi$
$137$	−1.32377	−0.113098	−0.0565488	+	0.998400i	$0.518010\pi$
$138$	23.5248	2.00257
$139$	−6.13446	−0.520318	−0.260159	−	0.965566i	$-0.583775\pi$
$139$	−6.13446	−0.520318	−0.260159	+	0.965566i	$0.583775\pi$
$140$	−6.68946	−0.565363
$141$	19.8518	1.67182
$142$	15.0293	1.26123
$143$	6.98651	0.584242
$144$	−26.1780	−2.18150
$145$	7.16142	0.594723
$146$	−7.73351	−0.640030
$147$	−53.9517	−4.44986
$148$	−1.44204	−0.118535
$149$	7.09646	0.581365	0.290682	−	0.956820i	$-0.406118\pi$
$149$	7.09646	0.581365	0.290682	+	0.956820i	$0.406118\pi$
$150$	5.26377	0.429785
$151$	15.2568	1.24158	0.620791	−	0.783976i	$-0.286812\pi$
$151$	15.2568	1.24158	0.620791	+	0.783976i	$0.286812\pi$
$152$	−3.68240	−0.298682
$153$	−5.34517	−0.432131
$154$	−9.23303	−0.744019
$155$	−10.0398	−0.806417
$156$	−26.6443	−2.13325
$157$	9.11124	0.727156	0.363578	−	0.931564i	$-0.381555\pi$
$157$	9.11124	0.727156	0.363578	+	0.931564i	$0.381555\pi$
$158$	7.88630	0.627400
$159$	−32.5673	−2.58275
$160$	−6.44636	−0.509630
$161$	22.6462	1.78477
$162$	−6.44185	−0.506119
$163$	−9.35424	−0.732680	−0.366340	−	0.930481i	$-0.619389\pi$
$163$	−9.35424	−0.732680	−0.366340	+	0.930481i	$0.619389\pi$
$164$	8.24602	0.643906
$165$	2.88880	0.224893
$166$	−8.69221	−0.674647
$167$	11.4960	0.889589	0.444795	−	0.895633i	$-0.353277\pi$
$167$	11.4960	0.889589	0.444795	+	0.895633i	$0.353277\pi$
$168$	−18.1330	−1.39899
$169$	35.8114	2.75472
$170$	−1.82213	−0.139751
$171$	−15.8893	−1.21509
$172$	−2.10307	−0.160357
$173$	4.87944	0.370977	0.185488	−	0.982646i	$-0.440613\pi$
$173$	4.87944	0.370977	0.185488	+	0.982646i	$0.440613\pi$
$174$	−37.6961	−2.85773
$175$	5.06716	0.383042
$176$	−4.89750	−0.369163
$177$	22.0285	1.65576
$178$	4.16334	0.312055
$179$	−4.77850	−0.357162	−0.178581	−	0.983925i	$-0.557151\pi$
$179$	−4.77850	−0.357162	−0.178581	+	0.983925i	$0.557151\pi$
$180$	−7.05647	−0.525958
$181$	17.6096	1.30891	0.654455	−	0.756101i	$-0.272898\pi$
$181$	17.6096	1.30891	0.654455	+	0.756101i	$0.272898\pi$
$182$	−64.5067	−4.78156
$183$	28.2697	2.08975
$184$	5.53626	0.408139
$185$	1.09232	0.0803092
$186$	52.8473	3.87495
$187$	−1.00000	−0.0731272
$188$	−9.07211	−0.661652
$189$	−34.3287	−2.49704
$190$	−5.41656	−0.392958
$191$	21.6696	1.56796	0.783978	−	0.620788i	$-0.213187\pi$
$191$	21.6696	1.56796	0.783978	+	0.620788i	$0.213187\pi$
$192$	5.63638	0.406770
$193$	−9.04009	−0.650720	−0.325360	−	0.945590i	$-0.605485\pi$
$193$	−9.04009	−0.650720	−0.325360	+	0.945590i	$0.605485\pi$
$194$	−5.57361	−0.400162
$195$	20.1827	1.44531
$196$	24.6555	1.76111
$197$	0.945816	0.0673866	0.0336933	−	0.999432i	$-0.489273\pi$
$197$	0.945816	0.0673866	0.0336933	+	0.999432i	$0.489273\pi$
$198$	−9.73960	−0.692163
$199$	−25.2911	−1.79284	−0.896418	−	0.443209i	$-0.853840\pi$
$199$	−25.2911	−1.79284	−0.896418	+	0.443209i	$0.853840\pi$
$200$	1.23876	0.0875935
$201$	−4.19800	−0.296104
$202$	−27.6480	−1.94530
$203$	−36.2881	−2.54692
$204$	3.81368	0.267011
$205$	−6.24623	−0.436256
$206$	9.79076	0.682154
$207$	23.8886	1.66037
$208$	−34.2164	−2.37248
$209$	−2.97265	−0.205623
$210$	−26.6724	−1.84057
$211$	−13.8545	−0.953784	−0.476892	−	0.878962i	$-0.658237\pi$
$211$	−13.8545	−0.953784	−0.476892	+	0.878962i	$0.658237\pi$
$212$	14.8830	1.02217
$213$	23.8274	1.63262
$214$	10.3034	0.704324
$215$	1.59304	0.108644
$216$	−8.39226	−0.571021
$217$	50.8734	3.45351
$218$	−1.78711	−0.121038
$219$	−12.2607	−0.828501
$220$	−1.32016	−0.0890051
$221$	−6.98651	−0.469964
$222$	−5.74974	−0.385897
$223$	17.4530	1.16874	0.584371	−	0.811487i	$-0.301341\pi$
$223$	17.4530	1.16874	0.584371	+	0.811487i	$0.301341\pi$
$224$	32.6648	2.18251
$225$	5.34517	0.356345
$226$	−0.203071	−0.0135081
$227$	7.13841	0.473793	0.236897	−	0.971535i	$-0.423870\pi$
$227$	7.13841	0.473793	0.236897	+	0.971535i	$0.423870\pi$
$228$	11.3367	0.750793
$229$	−1.35045	−0.0892406	−0.0446203	−	0.999004i	$-0.514208\pi$
$229$	−1.35045	−0.0892406	−0.0446203	+	0.999004i	$0.514208\pi$
$230$	8.14346	0.536964
$231$	−14.6380	−0.963111
$232$	−8.87127	−0.582428
$233$	−28.0721	−1.83906	−0.919532	−	0.393014i	$-0.871432\pi$
$233$	−28.0721	−1.83906	−0.919532	+	0.393014i	$0.871432\pi$
$234$	−68.0458	−4.44830
$235$	6.87199	0.448279
$236$	−10.0668	−0.655296
$237$	12.5029	0.812152
$238$	9.23303	0.598489
$239$	0.369603	0.0239076	0.0119538	−	0.999929i	$-0.496195\pi$
$239$	0.369603	0.0239076	0.0119538	+	0.999929i	$0.496195\pi$
$240$	−14.1479	−0.913243
$241$	−7.83858	−0.504927	−0.252464	−	0.967606i	$-0.581241\pi$
$241$	−7.83858	−0.504927	−0.252464	+	0.967606i	$0.581241\pi$
$242$	−1.82213	−0.117131
$243$	10.1113	0.648641
$244$	−12.9190	−0.827055
$245$	−18.6761	−1.19318
$246$	32.8788	2.09627
$247$	−20.7685	−1.32147
$248$	12.4369	0.789745
$249$	−13.7806	−0.873311
$250$	1.82213	0.115242
$251$	−5.83935	−0.368577	−0.184288	−	0.982872i	$-0.558998\pi$
$251$	−5.83935	−0.368577	−0.184288	+	0.982872i	$0.558998\pi$
$252$	35.7563	2.25244
$253$	4.46920	0.280976
$254$	−4.80621	−0.301569
$255$	−2.88880	−0.180904
$256$	20.9164	1.30728
$257$	−10.1375	−0.632360	−0.316180	−	0.948699i	$-0.602400\pi$
$257$	−10.1375	−0.632360	−0.316180	+	0.948699i	$0.602400\pi$
$258$	−8.38540	−0.522052
$259$	−5.53498	−0.343927
$260$	−9.22331	−0.572005
$261$	−38.2790	−2.36941
$262$	12.1077	0.748014
$263$	−6.95183	−0.428668	−0.214334	−	0.976760i	$-0.568758\pi$
$263$	−6.95183	−0.428668	−0.214334	+	0.976760i	$0.568758\pi$
$264$	−3.57853	−0.220243
$265$	−11.2736	−0.692534
$266$	27.4466	1.68286
$267$	6.60054	0.403947
$268$	1.91845	0.117188
$269$	14.1502	0.862752	0.431376	−	0.902172i	$-0.358028\pi$
$269$	14.1502	0.862752	0.431376	+	0.902172i	$0.358028\pi$
$270$	−12.3444	−0.751259
$271$	−7.60243	−0.461815	−0.230907	−	0.972976i	$-0.574169\pi$
$271$	−7.60243	−0.461815	−0.230907	+	0.972976i	$0.574169\pi$
$272$	4.89750	0.296954
$273$	−102.269	−6.18959
$274$	2.41209	0.145719
$275$	1.00000	0.0603023
$276$	−17.0441	−1.02593
$277$	12.3436	0.741653	0.370826	−	0.928702i	$-0.379075\pi$
$277$	12.3436	0.741653	0.370826	+	0.928702i	$0.379075\pi$
$278$	11.1778	0.670399
$279$	53.6645	3.21281
$280$	−6.27700	−0.375122
$281$	12.6098	0.752239	0.376119	−	0.926571i	$-0.377258\pi$
$281$	12.6098	0.752239	0.376119	+	0.926571i	$0.377258\pi$
$282$	−36.1726	−2.15405
$283$	−3.71094	−0.220592	−0.110296	−	0.993899i	$-0.535180\pi$
$283$	−3.71094	−0.220592	−0.110296	+	0.993899i	$0.535180\pi$
$284$	−10.8889	−0.646138
$285$	−8.58740	−0.508673
$286$	−12.7303	−0.752761
$287$	31.6507	1.86828
$288$	34.4569	2.03039
$289$	1.00000	0.0588235
$290$	−13.0490	−0.766266
$291$	−8.83638	−0.517998
$292$	5.60304	0.327893
$293$	3.10252	0.181251	0.0906254	−	0.995885i	$-0.471113\pi$
$293$	3.10252	0.181251	0.0906254	+	0.995885i	$0.471113\pi$
$294$	98.3070	5.73338
$295$	7.62548	0.443973
$296$	−1.35313	−0.0786489
$297$	−6.77473	−0.393110
$298$	−12.9307	−0.749054
$299$	31.2241	1.80574
$300$	−3.81368	−0.220183
$301$	−8.07219	−0.465274
$302$	−27.7999	−1.59970
$303$	−43.8330	−2.51814
$304$	14.5586	0.834990
$305$	9.78595	0.560342
$306$	9.73960	0.556776
$307$	15.7041	0.896281	0.448140	−	0.893963i	$-0.352086\pi$
$307$	15.7041	0.896281	0.448140	+	0.893963i	$0.352086\pi$
$308$	6.68946	0.381167
$309$	15.5222	0.883029
$310$	18.2938	1.03902
$311$	10.1521	0.575674	0.287837	−	0.957679i	$-0.407064\pi$
$311$	10.1521	0.575674	0.287837	+	0.957679i	$0.407064\pi$
$312$	−25.0014	−1.41543
$313$	20.2199	1.14289	0.571447	−	0.820639i	$-0.306382\pi$
$313$	20.2199	1.14289	0.571447	+	0.820639i	$0.306382\pi$
$314$	−16.6019	−0.936897
$315$	−27.0849	−1.52606
$316$	−5.71373	−0.321423
$317$	22.0725	1.23972	0.619858	−	0.784714i	$-0.287190\pi$
$317$	22.0725	1.23972	0.619858	+	0.784714i	$0.287190\pi$
$318$	59.3419	3.32773
$319$	−7.16142	−0.400962
$320$	1.95111	0.109071
$321$	16.3349	0.911727
$322$	−41.2643	−2.29957
$323$	2.97265	0.165403
$324$	4.66721	0.259289
$325$	6.98651	0.387542
$326$	17.0446	0.944015
$327$	−2.83328	−0.156681
$328$	7.73758	0.427237
$329$	−34.8215	−1.91977
$330$	−5.26377	−0.289761
$331$	−33.6762	−1.85101	−0.925505	−	0.378735i	$-0.876359\pi$
$331$	−33.6762	−1.85101	−0.925505	+	0.378735i	$0.876359\pi$
$332$	6.29763	0.345627
$333$	−5.83866	−0.319956
$334$	−20.9473	−1.14618
$335$	−1.45320	−0.0793966
$336$	71.6897	3.91099
$337$	−7.80402	−0.425112	−0.212556	−	0.977149i	$-0.568179\pi$
$337$	−7.80402	−0.425112	−0.212556	+	0.977149i	$0.568179\pi$
$338$	−65.2530	−3.54930
$339$	−0.321949	−0.0174858
$340$	1.32016	0.0715957
$341$	10.0398	0.543686
$342$	28.9524	1.56557
$343$	59.1649	3.19461
$344$	−1.97339	−0.106398
$345$	12.9106	0.695085
$346$	−8.89097	−0.477981
$347$	−16.4596	−0.883597	−0.441799	−	0.897114i	$-0.645659\pi$
$347$	−16.4596	−0.883597	−0.441799	+	0.897114i	$0.645659\pi$
$348$	27.3113	1.46404
$349$	−15.2500	−0.816313	−0.408156	−	0.912912i	$-0.633828\pi$
$349$	−15.2500	−0.816313	−0.408156	+	0.912912i	$0.633828\pi$
$350$	−9.23303	−0.493526
$351$	−47.3318	−2.52638
$352$	6.44636	0.343592
$353$	7.12551	0.379253	0.189626	−	0.981856i	$-0.439272\pi$
$353$	7.12551	0.379253	0.189626	+	0.981856i	$0.439272\pi$
$354$	−40.1388	−2.13335
$355$	8.24819	0.437768
$356$	−3.01639	−0.159869
$357$	14.6380	0.774727
$358$	8.70705	0.460182
$359$	−6.23353	−0.328993	−0.164497	−	0.986378i	$-0.552600\pi$
$359$	−6.23353	−0.328993	−0.164497	+	0.986378i	$0.552600\pi$
$360$	−6.62138	−0.348977
$361$	−10.1633	−0.534913
$362$	−32.0870	−1.68645
$363$	−2.88880	−0.151623
$364$	46.7360	2.44963
$365$	−4.24422	−0.222152
$366$	−51.5110	−2.69252
$367$	−23.6762	−1.23589	−0.617943	−	0.786223i	$-0.712034\pi$
$367$	−23.6762	−1.23589	−0.617943	+	0.786223i	$0.712034\pi$
$368$	−21.8879	−1.14099
$369$	33.3872	1.73807
$370$	−1.99036	−0.103474
$371$	57.1254	2.96580
$372$	−38.2886	−1.98517
$373$	26.0524	1.34894	0.674472	−	0.738301i	$-0.264371\pi$
$373$	26.0524	1.34894	0.674472	+	0.738301i	$0.264371\pi$
$374$	1.82213	0.0942201
$375$	2.88880	0.149177
$376$	−8.51274	−0.439011
$377$	−50.0334	−2.57685
$378$	62.5513	3.21729
$379$	0.496177	0.0254869	0.0127434	−	0.999919i	$-0.495944\pi$
$379$	0.496177	0.0254869	0.0127434	+	0.999919i	$0.495944\pi$
$380$	3.92437	0.201316
$381$	−7.61976	−0.390372
$382$	−39.4848	−2.02022
$383$	11.9554	0.610894	0.305447	−	0.952209i	$-0.401194\pi$
$383$	11.9554	0.610894	0.305447	+	0.952209i	$0.401194\pi$
$384$	26.9743	1.37653
$385$	−5.06716	−0.258247
$386$	16.4722	0.838414
$387$	−8.51507	−0.432845
$388$	4.03816	0.205006
$389$	−21.1673	−1.07322	−0.536612	−	0.843829i	$-0.680296\pi$
$389$	−21.1673	−1.07322	−0.536612	+	0.843829i	$0.680296\pi$
$390$	−36.7754	−1.86220
$391$	−4.46920	−0.226017
$392$	23.1353	1.16851
$393$	19.1955	0.968283
$394$	−1.72340	−0.0868236
$395$	4.32806	0.217769
$396$	7.05647	0.354601
$397$	33.9824	1.70553	0.852763	−	0.522298i	$-0.174925\pi$
$397$	33.9824	1.70553	0.852763	+	0.522298i	$0.174925\pi$
$398$	46.0836	2.30996
$399$	43.5137	2.17841
$400$	−4.89750	−0.244875
$401$	27.4666	1.37161	0.685807	−	0.727783i	$-0.259449\pi$
$401$	27.4666	1.37161	0.685807	+	0.727783i	$0.259449\pi$
$402$	7.64930	0.381512
$403$	70.1433	3.49409
$404$	20.0313	0.996596
$405$	−3.53534	−0.175672
$406$	66.1216	3.28156
$407$	−1.09232	−0.0541445
$408$	3.57853	0.177164
$409$	28.9425	1.43112	0.715558	−	0.698553i	$-0.246173\pi$
$409$	28.9425	1.43112	0.715558	+	0.698553i	$0.246173\pi$
$410$	11.3815	0.562090
$411$	3.82412	0.188630
$412$	−7.09354	−0.349474
$413$	−38.6396	−1.90133
$414$	−43.5282	−2.13929
$415$	−4.77036	−0.234168
$416$	45.0376	2.20815
$417$	17.7212	0.867813
$418$	5.41656	0.264932
$419$	−24.9346	−1.21814	−0.609068	−	0.793118i	$-0.708456\pi$
$419$	−24.9346	−1.21814	−0.609068	+	0.793118i	$0.708456\pi$
$420$	19.3245	0.942940
$421$	11.5387	0.562363	0.281182	−	0.959655i	$-0.409274\pi$
$421$	11.5387	0.562363	0.281182	+	0.959655i	$0.409274\pi$
$422$	25.2447	1.22889
$423$	−36.7319	−1.78597
$424$	13.9653	0.678216
$425$	−1.00000	−0.0485071
$426$	−43.4166	−2.10354
$427$	−49.5870	−2.39968
$428$	−7.46493	−0.360831
$429$	−20.1827	−0.974428
$430$	−2.90273	−0.139982
$431$	−8.24827	−0.397305	−0.198653	−	0.980070i	$-0.563657\pi$
$431$	−8.24827	−0.397305	−0.198653	+	0.980070i	$0.563657\pi$
$432$	33.1792	1.59634
$433$	19.1861	0.922024	0.461012	−	0.887394i	$-0.347487\pi$
$433$	19.1861	0.922024	0.461012	+	0.887394i	$0.347487\pi$
$434$	−92.6979	−4.44964
$435$	−20.6879	−0.991909
$436$	1.29479	0.0620090
$437$	−13.2854	−0.635525
$438$	22.3406	1.06747
$439$	24.7626	1.18186	0.590928	−	0.806724i	$-0.298762\pi$
$439$	24.7626	1.18186	0.590928	+	0.806724i	$0.298762\pi$
$440$	−1.23876	−0.0590555
$441$	99.8272	4.75368
$442$	12.7303	0.605521
$443$	−24.9739	−1.18655	−0.593274	−	0.805001i	$-0.702165\pi$
$443$	−24.9739	−1.18655	−0.593274	+	0.805001i	$0.702165\pi$
$444$	4.16577	0.197699
$445$	2.28487	0.108313
$446$	−31.8017	−1.50585
$447$	−20.5003	−0.969629
$448$	−9.88661	−0.467098
$449$	−26.7551	−1.26265	−0.631325	−	0.775519i	$-0.717488\pi$
$449$	−26.7551	−1.26265	−0.631325	+	0.775519i	$0.717488\pi$
$450$	−9.73960	−0.459129
$451$	6.24623	0.294124
$452$	0.147128	0.00692031
$453$	−44.0739	−2.07077
$454$	−13.0071	−0.610454
$455$	−35.4018	−1.65966
$456$	10.6377	0.498157
$457$	−0.154328	−0.00721916	−0.00360958	−	0.999993i	$-0.501149\pi$
$457$	−0.154328	−0.00721916	−0.00360958	+	0.999993i	$0.501149\pi$
$458$	2.46070	0.114981
$459$	6.77473	0.316217
$460$	−5.90005	−0.275091
$461$	5.91809	0.275633	0.137816	−	0.990458i	$-0.455992\pi$
$461$	5.91809	0.275633	0.137816	+	0.990458i	$0.455992\pi$
$462$	26.6724	1.24091
$463$	20.7414	0.963937	0.481968	−	0.876189i	$-0.339922\pi$
$463$	20.7414	0.963937	0.481968	+	0.876189i	$0.339922\pi$
$464$	35.0730	1.62822
$465$	29.0030	1.34498
$466$	51.1510	2.36953
$467$	36.4153	1.68510	0.842550	−	0.538618i	$-0.181053\pi$
$467$	36.4153	1.68510	0.842550	+	0.538618i	$0.181053\pi$
$468$	49.3002	2.27890
$469$	7.36359	0.340019
$470$	−12.5217	−0.577581
$471$	−26.3205	−1.21279
$472$	−9.44614	−0.434794
$473$	−1.59304	−0.0732481
$474$	−22.7819	−1.04641
$475$	−2.97265	−0.136395
$476$	−6.68946	−0.306611
$477$	60.2595	2.75909
$478$	−0.673464	−0.0308035
$479$	14.9332	0.682315	0.341158	−	0.940006i	$-0.389181\pi$
$479$	14.9332	0.682315	0.341158	+	0.940006i	$0.389181\pi$
$480$	18.6223	0.849986
$481$	−7.63153	−0.347968
$482$	14.2829	0.650569
$483$	−65.4203	−2.97672
$484$	1.32016	0.0600072
$485$	−3.05884	−0.138895
$486$	−18.4241	−0.835735
$487$	1.52612	0.0691553	0.0345777	−	0.999402i	$-0.488991\pi$
$487$	1.52612	0.0691553	0.0345777	+	0.999402i	$0.488991\pi$
$488$	−12.1224	−0.548757
$489$	27.0225	1.22200
$490$	34.0304	1.53734
$491$	−23.0102	−1.03844	−0.519218	−	0.854642i	$-0.673777\pi$
$491$	−23.0102	−1.03844	−0.519218	+	0.854642i	$0.673777\pi$
$492$	−23.8211	−1.07394
$493$	7.16142	0.322534
$494$	37.8429	1.70263
$495$	−5.34517	−0.240248
$496$	−49.1700	−2.20780
$497$	−41.7949	−1.87476
$498$	25.1101	1.12521
$499$	−20.0524	−0.897668	−0.448834	−	0.893615i	$-0.648161\pi$
$499$	−20.0524	−0.897668	−0.448834	+	0.893615i	$0.648161\pi$
$500$	−1.32016	−0.0590393
$501$	−33.2097	−1.48370
$502$	10.6401	0.474889
$503$	−14.7651	−0.658341	−0.329171	−	0.944270i	$-0.606769\pi$
$503$	−14.7651	−0.658341	−0.329171	+	0.944270i	$0.606769\pi$
$504$	33.5516	1.49451
$505$	−15.1734	−0.675209
$506$	−8.14346	−0.362021
$507$	−103.452	−4.59446
$508$	3.48217	0.154496
$509$	20.1225	0.891913	0.445957	−	0.895055i	$-0.352864\pi$
$509$	20.1225	0.891913	0.445957	+	0.895055i	$0.352864\pi$
$510$	5.26377	0.233084
$511$	21.5061	0.951375
$512$	−19.4374	−0.859020
$513$	20.1389	0.889155
$514$	18.4719	0.814758
$515$	5.37325	0.236774
$516$	6.07534	0.267452
$517$	−6.87199	−0.302230
$518$	10.0855	0.443130
$519$	−14.0957	−0.618733
$520$	−8.65461	−0.379530
$521$	31.8275	1.39439	0.697195	−	0.716881i	$-0.254431\pi$
$521$	31.8275	1.39439	0.697195	+	0.716881i	$0.254431\pi$
$522$	69.7493	3.05285
$523$	3.69253	0.161463	0.0807316	−	0.996736i	$-0.474274\pi$
$523$	3.69253	0.161463	0.0807316	+	0.996736i	$0.474274\pi$
$524$	−8.77217	−0.383214
$525$	−14.6380	−0.638856
$526$	12.6671	0.552313
$527$	−10.0398	−0.437341
$528$	14.1479	0.615708
$529$	−3.02626	−0.131577
$530$	20.5420	0.892289
$531$	−40.7595	−1.76881
$532$	−19.8854	−0.862143
$533$	43.6394	1.89023
$534$	−12.0270	−0.520461
$535$	5.65457	0.244468
$536$	1.80016	0.0777551
$537$	13.8041	0.595692
$538$	−25.7835	−1.11160
$539$	18.6761	0.804439
$540$	8.94372	0.384876
$541$	−0.859204	−0.0369401	−0.0184700	−	0.999829i	$-0.505880\pi$
$541$	−0.859204	−0.0369401	−0.0184700	+	0.999829i	$0.505880\pi$
$542$	13.8526	0.595021
$543$	−50.8706	−2.18307
$544$	−6.44636	−0.276385
$545$	−0.980781	−0.0420120
$546$	186.347	7.97492
$547$	−34.1095	−1.45842	−0.729209	−	0.684291i	$-0.760112\pi$
$547$	−34.1095	−1.45842	−0.729209	+	0.684291i	$0.760112\pi$
$548$	−1.74759	−0.0746533
$549$	−52.3076	−2.23243
$550$	−1.82213	−0.0776959
$551$	21.2884	0.906916
$552$	−15.9932	−0.680714
$553$	−21.9310	−0.932602
$554$	−22.4916	−0.955575
$555$	−3.15550	−0.133944
$556$	−8.09847	−0.343451
$557$	20.1344	0.853124	0.426562	−	0.904458i	$-0.359725\pi$
$557$	20.1344	0.853124	0.426562	+	0.904458i	$0.359725\pi$
$558$	−97.7837	−4.13952
$559$	−11.1298	−0.470740
$560$	24.8164	1.04869
$561$	2.88880	0.121965
$562$	−22.9767	−0.969215
$563$	44.4992	1.87542	0.937709	−	0.347422i	$-0.112943\pi$
$563$	44.4992	1.87542	0.937709	+	0.347422i	$0.112943\pi$
$564$	26.2075	1.10354
$565$	−0.111447	−0.00468862
$566$	6.76182	0.284220
$567$	17.9141	0.752323
$568$	−10.2175	−0.428718
$569$	−33.5537	−1.40665	−0.703323	−	0.710870i	$-0.748301\pi$
$569$	−33.5537	−1.40665	−0.703323	+	0.710870i	$0.748301\pi$
$570$	15.6474	0.655396
$571$	−2.48576	−0.104026	−0.0520129	−	0.998646i	$-0.516564\pi$
$571$	−2.48576	−0.104026	−0.0520129	+	0.998646i	$0.516564\pi$
$572$	9.22331	0.385646
$573$	−62.5991	−2.61512
$574$	−57.6717	−2.40717
$575$	4.46920	0.186378
$576$	−10.4290	−0.434543
$577$	−35.2730	−1.46843	−0.734217	−	0.678915i	$-0.762451\pi$
$577$	−35.2730	−1.46843	−0.734217	+	0.678915i	$0.762451\pi$
$578$	−1.82213	−0.0757906
$579$	26.1150	1.08530
$580$	9.45421	0.392565
$581$	24.1722	1.00283
$582$	16.1010	0.667410
$583$	11.2736	0.466906
$584$	5.25756	0.217559
$585$	−37.3441	−1.54399
$586$	−5.65319	−0.233531
$587$	−1.40975	−0.0581865	−0.0290933	−	0.999577i	$-0.509262\pi$
$587$	−1.40975	−0.0581865	−0.0290933	+	0.999577i	$0.509262\pi$
$588$	−71.2248	−2.93726
$589$	−29.8449	−1.22974
$590$	−13.8946	−0.572032
$591$	−2.73227	−0.112391
$592$	5.34965	0.219869
$593$	35.5298	1.45904	0.729518	−	0.683962i	$-0.239745\pi$
$593$	35.5298	1.45904	0.729518	+	0.683962i	$0.239745\pi$
$594$	12.3444	0.506499
$595$	5.06716	0.207733
$596$	9.36845	0.383747
$597$	73.0609	2.99018
$598$	−56.8944	−2.32659
$599$	13.3523	0.545562	0.272781	−	0.962076i	$-0.412057\pi$
$599$	13.3523	0.545562	0.272781	+	0.962076i	$0.412057\pi$
$600$	−3.57853	−0.146093
$601$	−19.4156	−0.791977	−0.395989	−	0.918255i	$-0.629598\pi$
$601$	−19.4156	−0.791977	−0.395989	+	0.918255i	$0.629598\pi$
$602$	14.7086	0.599477
$603$	7.76758	0.316320
$604$	20.1414	0.819543
$605$	−1.00000	−0.0406558
$606$	79.8695	3.24448
$607$	−39.0238	−1.58393	−0.791964	−	0.610568i	$-0.790941\pi$
$607$	−39.0238	−1.58393	−0.791964	+	0.610568i	$0.790941\pi$
$608$	−19.1628	−0.777153
$609$	104.829	4.24789
$610$	−17.8313	−0.721967
$611$	−48.0112	−1.94233
$612$	−7.05647	−0.285241
$613$	15.5615	0.628521	0.314261	−	0.949337i	$-0.398243\pi$
$613$	15.5615	0.628521	0.314261	+	0.949337i	$0.398243\pi$
$614$	−28.6149	−1.15480
$615$	18.0441	0.727609
$616$	6.27700	0.252907
$617$	−24.3137	−0.978832	−0.489416	−	0.872050i	$-0.662790\pi$
$617$	−24.3137	−0.978832	−0.489416	+	0.872050i	$0.662790\pi$
$618$	−28.2835	−1.13773
$619$	−29.9680	−1.20452	−0.602258	−	0.798302i	$-0.705732\pi$
$619$	−29.9680	−1.20452	−0.602258	+	0.798302i	$0.705732\pi$
$620$	−13.2541	−0.532299
$621$	−30.2776	−1.21500
$622$	−18.4985	−0.741722
$623$	−11.5778	−0.463856
$624$	98.8445	3.95695
$625$	1.00000	0.0400000
$626$	−36.8432	−1.47255
$627$	8.58740	0.342948
$628$	12.0283	0.479981
$629$	1.09232	0.0435538
$630$	49.3521	1.96624
$631$	26.7450	1.06470	0.532351	−	0.846524i	$-0.321309\pi$
$631$	26.7450	1.06470	0.532351	+	0.846524i	$0.321309\pi$
$632$	−5.36143	−0.213266
$633$	40.0229	1.59077
$634$	−40.2190	−1.59730
$635$	−2.63769	−0.104674
$636$	−42.9940	−1.70482
$637$	130.481	5.16985
$638$	13.0490	0.516616
$639$	−44.0880	−1.74409
$640$	9.33754	0.369099
$641$	−38.2407	−1.51042	−0.755209	−	0.655484i	$-0.772464\pi$
$641$	−38.2407	−1.51042	−0.755209	+	0.655484i	$0.772464\pi$
$642$	−29.7644	−1.17471
$643$	−34.0856	−1.34421	−0.672103	−	0.740457i	$-0.734609\pi$
$643$	−34.0856	−1.34421	−0.672103	+	0.740457i	$0.734609\pi$
$644$	29.8965	1.17809
$645$	−4.60198	−0.181203
$646$	−5.41656	−0.213112
$647$	−25.0135	−0.983381	−0.491690	−	0.870770i	$-0.663621\pi$
$647$	−25.0135	−0.983381	−0.491690	+	0.870770i	$0.663621\pi$
$648$	4.37943	0.172040
$649$	−7.62548	−0.299326
$650$	−12.7303	−0.499325
$651$	−146.963	−5.75994
$652$	−12.3491	−0.483627
$653$	−0.703057	−0.0275127	−0.0137564	−	0.999905i	$-0.504379\pi$
$653$	−0.703057	−0.0275127	−0.0137564	+	0.999905i	$0.504379\pi$
$654$	5.16261	0.201874
$655$	6.64479	0.259633
$656$	−30.5909	−1.19437
$657$	22.6861	0.885067
$658$	63.4493	2.47351
$659$	35.3400	1.37665	0.688325	−	0.725403i	$-0.258346\pi$
$659$	35.3400	1.37665	0.688325	+	0.725403i	$0.258346\pi$
$660$	3.81368	0.148447
$661$	−47.8220	−1.86006	−0.930029	−	0.367485i	$-0.880219\pi$
$661$	−47.8220	−1.86006	−0.930029	+	0.367485i	$0.880219\pi$
$662$	61.3624	2.38492
$663$	20.1827	0.783829
$664$	5.90933	0.229326
$665$	15.0629	0.584114
$666$	10.6388	0.412245
$667$	−32.0058	−1.23927
$668$	15.1766	0.587199
$669$	−50.4184	−1.94929
$670$	2.64791	0.102298
$671$	−9.78595	−0.377782
$672$	−94.3620	−3.64009
$673$	11.3006	0.435604	0.217802	−	0.975993i	$-0.430111\pi$
$673$	11.3006	0.435604	0.217802	+	0.975993i	$0.430111\pi$
$674$	14.2199	0.547732
$675$	−6.77473	−0.260760
$676$	47.2767	1.81834
$677$	27.8329	1.06970	0.534852	−	0.844946i	$-0.320367\pi$
$677$	27.8329	1.06970	0.534852	+	0.844946i	$0.320367\pi$
$678$	0.586632	0.0225295
$679$	15.4997	0.594822
$680$	1.23876	0.0475043
$681$	−20.6215	−0.790216
$682$	−18.2938	−0.700508
$683$	−20.7316	−0.793272	−0.396636	−	0.917976i	$-0.629822\pi$
$683$	−20.7316	−0.793272	−0.396636	+	0.917976i	$0.629822\pi$
$684$	−20.9764	−0.802054
$685$	1.32377	0.0505787
$686$	−107.806	−4.11606
$687$	3.90119	0.148840
$688$	7.80191	0.297445
$689$	78.7634	3.00065
$690$	−23.5248	−0.895575
$691$	−13.0085	−0.494867	−0.247434	−	0.968905i	$-0.579587\pi$
$691$	−13.0085	−0.494867	−0.247434	+	0.968905i	$0.579587\pi$
$692$	6.44163	0.244874
$693$	27.0849	1.02887
$694$	29.9915	1.13846
$695$	6.13446	0.232693
$696$	25.6273	0.971402
$697$	−6.24623	−0.236593
$698$	27.7874	1.05177
$699$	81.0947	3.06728
$700$	6.68946	0.252838
$701$	−13.7697	−0.520075	−0.260037	−	0.965599i	$-0.583735\pi$
$701$	−13.7697	−0.520075	−0.260037	+	0.965599i	$0.583735\pi$
$702$	86.2446	3.25509
$703$	3.24710	0.122467
$704$	−1.95111	−0.0735353
$705$	−19.8518	−0.747662
$706$	−12.9836	−0.488645
$707$	76.8863	2.89161
$708$	29.0811	1.09293
$709$	−6.60669	−0.248119	−0.124060	−	0.992275i	$-0.539591\pi$
$709$	−6.60669	−0.248119	−0.124060	+	0.992275i	$0.539591\pi$
$710$	−15.0293	−0.564039
$711$	−23.1342	−0.867602
$712$	−2.83041	−0.106074
$713$	44.8699	1.68039
$714$	−26.6724	−0.998189
$715$	−6.98651	−0.261281
$716$	−6.30838	−0.235755
$717$	−1.06771	−0.0398743
$718$	11.3583	0.423888
$719$	−10.7591	−0.401248	−0.200624	−	0.979668i	$-0.564297\pi$
$719$	−10.7591	−0.401248	−0.200624	+	0.979668i	$0.564297\pi$
$720$	26.1780	0.975595
$721$	−27.2271	−1.01399
$722$	18.5189	0.689204
$723$	22.6441	0.842143
$724$	23.2475	0.863985
$725$	−7.16142	−0.265968
$726$	5.26377	0.195357
$727$	3.42750	0.127119	0.0635595	−	0.997978i	$-0.479755\pi$
$727$	3.42750	0.127119	0.0635595	+	0.997978i	$0.479755\pi$
$728$	43.8543	1.62535
$729$	−39.8156	−1.47465
$730$	7.73351	0.286230
$731$	1.59304	0.0589207
$732$	37.3204	1.37940
$733$	3.42141	0.126373	0.0631863	−	0.998002i	$-0.479874\pi$
$733$	3.42141	0.126373	0.0631863	+	0.998002i	$0.479874\pi$
$734$	43.1411	1.59237
$735$	53.9517	1.99004
$736$	28.8101	1.06195
$737$	1.45320	0.0535292
$738$	−60.8358	−2.23940
$739$	10.7900	0.396917	0.198458	−	0.980109i	$-0.436407\pi$
$739$	10.7900	0.396917	0.198458	+	0.980109i	$0.436407\pi$
$740$	1.44204	0.0530105
$741$	59.9960	2.20401
$742$	−104.090	−3.82126
$743$	19.4446	0.713352	0.356676	−	0.934228i	$-0.383910\pi$
$743$	19.4446	0.713352	0.356676	+	0.934228i	$0.383910\pi$
$744$	−35.9278	−1.31718
$745$	−7.09646	−0.259994
$746$	−47.4709	−1.73803
$747$	25.4984	0.932937
$748$	−1.32016	−0.0482698
$749$	−28.6526	−1.04694
$750$	−5.26377	−0.192206
$751$	−29.1694	−1.06441	−0.532203	−	0.846617i	$-0.678636\pi$
$751$	−29.1694	−1.06441	−0.532203	+	0.846617i	$0.678636\pi$
$752$	33.6555	1.22729
$753$	16.8687	0.614731
$754$	91.1673	3.32012
$755$	−15.2568	−0.555252
$756$	−45.3193	−1.64825
$757$	−23.3808	−0.849790	−0.424895	−	0.905243i	$-0.639689\pi$
$757$	−23.3808	−0.849790	−0.424895	+	0.905243i	$0.639689\pi$
$758$	−0.904099	−0.0328384
$759$	−12.9106	−0.468626
$760$	3.68240	0.133575
$761$	−24.9504	−0.904451	−0.452225	−	0.891904i	$-0.649370\pi$
$761$	−24.9504	−0.904451	−0.452225	+	0.891904i	$0.649370\pi$
$762$	13.8842	0.502971
$763$	4.96978	0.179918
$764$	28.6073	1.03498
$765$	5.34517	0.193255
$766$	−21.7844	−0.787101
$767$	−53.2755	−1.92367
$768$	−60.4234	−2.18034
$769$	23.7826	0.857622	0.428811	−	0.903394i	$-0.358933\pi$
$769$	23.7826	0.857622	0.428811	+	0.903394i	$0.358933\pi$
$770$	9.23303	0.332735
$771$	29.2852	1.05468
$772$	−11.9343	−0.429527
$773$	−0.480311	−0.0172756	−0.00863779	−	0.999963i	$-0.502750\pi$
$773$	−0.480311	−0.0172756	−0.00863779	+	0.999963i	$0.502750\pi$
$774$	15.5156	0.557696
$775$	10.0398	0.360641
$776$	3.78917	0.136023
$777$	15.9895	0.573619
$778$	38.5695	1.38278
$779$	−18.5679	−0.665263
$780$	26.6443	0.954019
$781$	−8.24819	−0.295143
$782$	8.14346	0.291210
$783$	48.5167	1.73384
$784$	−91.4664	−3.26666
$785$	−9.11124	−0.325194
$786$	−34.9766	−1.24758
$787$	5.81639	0.207332	0.103666	−	0.994612i	$-0.466943\pi$
$787$	5.81639	0.207332	0.103666	+	0.994612i	$0.466943\pi$
$788$	1.24863	0.0444805
$789$	20.0825	0.714954
$790$	−7.88630	−0.280582
$791$	0.564721	0.0200792
$792$	6.62138	0.235281
$793$	−68.3697	−2.42788
$794$	−61.9203	−2.19747
$795$	32.5673	1.15504
$796$	−33.3882	−1.18341
$797$	36.7865	1.30304	0.651522	−	0.758630i	$-0.274131\pi$
$797$	36.7865	1.30304	0.651522	+	0.758630i	$0.274131\pi$
$798$	−79.2877	−2.80675
$799$	6.87199	0.243113
$800$	6.44636	0.227913
$801$	−12.2130	−0.431526
$802$	−50.0477	−1.76724
$803$	4.24422	0.149775
$804$	−5.54202	−0.195452
$805$	−22.6462	−0.798172
$806$	−127.810	−4.50192
$807$	−40.8771	−1.43894
$808$	18.7962	0.661249
$809$	−7.02564	−0.247008	−0.123504	−	0.992344i	$-0.539413\pi$
$809$	−7.02564	−0.247008	−0.123504	+	0.992344i	$0.539413\pi$
$810$	6.44185	0.226343
$811$	34.5536	1.21334	0.606670	−	0.794954i	$-0.292505\pi$
$811$	34.5536	1.21334	0.606670	+	0.794954i	$0.292505\pi$
$812$	−47.9060	−1.68117
$813$	21.9619	0.770238
$814$	1.99036	0.0697619
$815$	9.35424	0.327665
$816$	−14.1479	−0.495275
$817$	4.73555	0.165676
$818$	−52.7371	−1.84391
$819$	189.229	6.61219
$820$	−8.24602	−0.287964
$821$	−8.55727	−0.298651	−0.149325	−	0.988788i	$-0.547710\pi$
$821$	−8.55727	−0.298651	−0.149325	+	0.988788i	$0.547710\pi$
$822$	−6.96804	−0.243038
$823$	−18.8917	−0.658522	−0.329261	−	0.944239i	$-0.606800\pi$
$823$	−18.8917	−0.658522	−0.329261	+	0.944239i	$0.606800\pi$
$824$	−6.65616	−0.231878
$825$	−2.88880	−0.100575
$826$	70.4063	2.44975
$827$	2.36780	0.0823365	0.0411683	−	0.999152i	$-0.486892\pi$
$827$	2.36780	0.0823365	0.0411683	+	0.999152i	$0.486892\pi$
$828$	31.5368	1.09598
$829$	−43.6463	−1.51590	−0.757950	−	0.652313i	$-0.773799\pi$
$829$	−43.6463	−1.51590	−0.757950	+	0.652313i	$0.773799\pi$
$830$	8.69221	0.301711
$831$	−35.6581	−1.23697
$832$	−13.6315	−0.472586
$833$	−18.6761	−0.647090
$834$	−32.2904	−1.11813
$835$	−11.4960	−0.397836
$836$	−3.92437	−0.135727
$837$	−68.0170	−2.35101
$838$	45.4341	1.56950
$839$	47.3095	1.63330	0.816652	−	0.577130i	$-0.195828\pi$
$839$	47.3095	1.63330	0.816652	+	0.577130i	$0.195828\pi$
$840$	18.1330	0.625648
$841$	22.2859	0.768479
$842$	−21.0251	−0.724572
$843$	−36.4273	−1.25462
$844$	−18.2902	−0.629573
$845$	−35.8114	−1.23195
$846$	66.9304	2.30111
$847$	5.06716	0.174110
$848$	−55.2126	−1.89601
$849$	10.7202	0.367915
$850$	1.82213	0.0624986
$851$	−4.88181	−0.167346
$852$	31.4559	1.07766
$853$	−11.7180	−0.401216	−0.200608	−	0.979672i	$-0.564292\pi$
$853$	−11.7180	−0.401216	−0.200608	+	0.979672i	$0.564292\pi$
$854$	90.3540	3.09185
$855$	15.8893	0.543403
$856$	−7.00466	−0.239414
$857$	23.1665	0.791351	0.395676	−	0.918390i	$-0.370510\pi$
$857$	23.1665	0.791351	0.395676	+	0.918390i	$0.370510\pi$
$858$	36.7754	1.25549
$859$	−27.3657	−0.933707	−0.466854	−	0.884335i	$-0.654613\pi$
$859$	−27.3657	−0.933707	−0.466854	+	0.884335i	$0.654613\pi$
$860$	2.10307	0.0717139
$861$	−91.4326	−3.11601
$862$	15.0294	0.511904
$863$	−22.6931	−0.772482	−0.386241	−	0.922398i	$-0.626227\pi$
$863$	−22.6931	−0.772482	−0.386241	+	0.922398i	$0.626227\pi$
$864$	−43.6724	−1.48576
$865$	−4.87944	−0.165906
$866$	−34.9595	−1.18797
$867$	−2.88880	−0.0981088
$868$	67.1609	2.27959
$869$	−4.32806	−0.146820
$870$	37.6961	1.27802
$871$	10.1528	0.344014
$872$	1.21495	0.0411434
$873$	16.3500	0.553365
$874$	24.2077	0.818837
$875$	−5.06716	−0.171301
$876$	−16.1861	−0.546876
$877$	31.1090	1.05048	0.525238	−	0.850955i	$-0.323976\pi$
$877$	31.1090	1.05048	0.525238	+	0.850955i	$0.323976\pi$
$878$	−45.1207	−1.52275
$879$	−8.96255	−0.302299
$880$	4.89750	0.165095
$881$	29.8066	1.00421	0.502106	−	0.864806i	$-0.332559\pi$
$881$	29.8066	1.00421	0.502106	+	0.864806i	$0.332559\pi$
$882$	−181.898	−6.12483
$883$	−41.3913	−1.39293	−0.696464	−	0.717592i	$-0.745244\pi$
$883$	−41.3913	−1.39293	−0.696464	+	0.717592i	$0.745244\pi$
$884$	−9.22331	−0.310213
$885$	−22.0285	−0.740480
$886$	45.5057	1.52880
$887$	10.8136	0.363084	0.181542	−	0.983383i	$-0.441891\pi$
$887$	10.8136	0.363084	0.181542	+	0.983383i	$0.441891\pi$
$888$	3.90891	0.131174
$889$	13.3656	0.448268
$890$	−4.16334	−0.139555
$891$	3.53534	0.118438
$892$	23.0408	0.771462
$893$	20.4280	0.683597
$894$	37.3541	1.24931
$895$	4.77850	0.159728
$896$	−47.3148	−1.58068
$897$	−90.2003	−3.01170
$898$	48.7512	1.62685
$899$	−71.8993	−2.39798
$900$	7.05647	0.235216
$901$	−11.2736	−0.375579
$902$	−11.3815	−0.378961
$903$	23.3190	0.776006
$904$	0.138056	0.00459168
$905$	−17.6096	−0.585363
$906$	80.3084	2.66807
$907$	−21.3836	−0.710031	−0.355015	−	0.934860i	$-0.615524\pi$
$907$	−21.3836	−0.710031	−0.355015	+	0.934860i	$0.615524\pi$
$908$	9.42384	0.312741
$909$	81.1046	2.69007
$910$	64.5067	2.13838
$911$	5.61200	0.185934	0.0929669	−	0.995669i	$-0.470365\pi$
$911$	5.61200	0.185934	0.0929669	+	0.995669i	$0.470365\pi$
$912$	−42.0568	−1.39264
$913$	4.77036	0.157876
$914$	0.281206	0.00930146
$915$	−28.2697	−0.934566
$916$	−1.78281	−0.0589058
$917$	−33.6702	−1.11189
$918$	−12.3444	−0.407427
$919$	−55.9183	−1.84458	−0.922288	−	0.386504i	$-0.873683\pi$
$919$	−55.9183	−1.84458	−0.922288	+	0.386504i	$0.873683\pi$
$920$	−5.53626	−0.182525
$921$	−45.3660	−1.49486
$922$	−10.7835	−0.355137
$923$	−57.6261	−1.89679
$924$	−19.3245	−0.635730
$925$	−1.09232	−0.0359154
$926$	−37.7936	−1.24198
$927$	−28.7209	−0.943319
$928$	−46.1651	−1.51544
$929$	13.6062	0.446406	0.223203	−	0.974772i	$-0.428349\pi$
$929$	13.6062	0.446406	0.223203	+	0.974772i	$0.428349\pi$
$930$	−52.8473	−1.73293
$931$	−55.5177	−1.81952
$932$	−37.0596	−1.21393
$933$	−29.3275	−0.960138
$934$	−66.3535	−2.17115
$935$	1.00000	0.0327035
$936$	46.2604	1.51207
$937$	−12.3186	−0.402432	−0.201216	−	0.979547i	$-0.564489\pi$
$937$	−12.3186	−0.402432	−0.201216	+	0.979547i	$0.564489\pi$
$938$	−13.4174	−0.438094
$939$	−58.4112	−1.90618
$940$	9.07211	0.295900
$941$	−44.8005	−1.46045	−0.730227	−	0.683204i	$-0.760586\pi$
$941$	−44.8005	−1.46045	−0.730227	+	0.683204i	$0.760586\pi$
$942$	47.9595	1.56260
$943$	27.9157	0.909059
$944$	37.3458	1.21550
$945$	34.3287	1.11671
$946$	2.90273	0.0943758
$947$	−21.5480	−0.700215	−0.350107	−	0.936710i	$-0.613855\pi$
$947$	−21.5480	−0.700215	−0.350107	+	0.936710i	$0.613855\pi$
$948$	16.5058	0.536085
$949$	29.6523	0.962553
$950$	5.41656	0.175736
$951$	−63.7632	−2.06766
$952$	−6.27700	−0.203439
$953$	−20.8667	−0.675939	−0.337970	−	0.941157i	$-0.609740\pi$
$953$	−20.8667	−0.675939	−0.337970	+	0.941157i	$0.609740\pi$
$954$	−109.801	−3.55493
$955$	−21.6696	−0.701211
$956$	0.487934	0.0157809
$957$	20.6879	0.668745
$958$	−27.2102	−0.879123
$959$	−6.70777	−0.216605
$960$	−5.63638	−0.181913
$961$	69.7979	2.25154
$962$	13.9056	0.448336
$963$	−30.2247	−0.973976
$964$	−10.3482	−0.333292
$965$	9.04009	0.291011
$966$	119.204	3.83533
$967$	6.79399	0.218480	0.109240	−	0.994015i	$-0.465158\pi$
$967$	6.79399	0.218480	0.109240	+	0.994015i	$0.465158\pi$
$968$	1.23876	0.0398152
$969$	−8.58740	−0.275867
$970$	5.57361	0.178958
$971$	14.1812	0.455097	0.227549	−	0.973767i	$-0.426929\pi$
$971$	14.1812	0.455097	0.227549	+	0.973767i	$0.426929\pi$
$972$	13.3485	0.428154
$973$	−31.0843	−0.996518
$974$	−2.78080	−0.0891025
$975$	−20.1827	−0.646362
$976$	47.9267	1.53410
$977$	30.3222	0.970094	0.485047	−	0.874488i	$-0.338802\pi$
$977$	30.3222	0.970094	0.485047	+	0.874488i	$0.338802\pi$
$978$	−49.2386	−1.57448
$979$	−2.28487	−0.0730248
$980$	−24.6555	−0.787590
$981$	5.24244	0.167378
$982$	41.9276	1.33796
$983$	−18.4787	−0.589381	−0.294690	−	0.955593i	$-0.595216\pi$
$983$	−18.4787	−0.589381	−0.294690	+	0.955593i	$0.595216\pi$
$984$	−22.3523	−0.712566
$985$	−0.945816	−0.0301362
$986$	−13.0490	−0.415566
$987$	100.592	3.20189
$988$	−27.4177	−0.872272
$989$	−7.11961	−0.226391
$990$	9.73960	0.309545
$991$	−21.2105	−0.673775	−0.336887	−	0.941545i	$-0.609374\pi$
$991$	−21.2105	−0.673775	−0.336887	+	0.941545i	$0.609374\pi$
$992$	64.7203	2.05487
$993$	97.2838	3.08721
$994$	76.1558	2.41551
$995$	25.2911	0.801781
$996$	−18.1926	−0.576454
$997$	−23.2649	−0.736808	−0.368404	−	0.929666i	$-0.620096\pi$
$997$	−23.2649	−0.736808	−0.368404	+	0.929666i	$0.620096\pi$
$998$	36.5381	1.15659
$999$	7.40020	0.234132

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	935.2.a.i.1.2	✓	9
3.2	odd	2		8415.2.a.bt.1.8		9
5.4	even	2		4675.2.a.bi.1.8		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
935.2.a.i.1.2	✓	9	1.1	even	1	trivial
4675.2.a.bi.1.8		9	5.4	even	2
8415.2.a.bt.1.8		9	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 935 = 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	935.a (trivial)

\(f(q)\)	\(=\)	\(q-1.82213 q^{2} -2.88880 q^{3} +1.32016 q^{4} -1.00000 q^{5} +5.26377 q^{6} +5.06716 q^{7} +1.23876 q^{8} +5.34517 q^{9} +O(q^{10})\)	\(q-1.82213 q^{2} -2.88880 q^{3} +1.32016 q^{4} -1.00000 q^{5} +5.26377 q^{6} +5.06716 q^{7} +1.23876 q^{8} +5.34517 q^{9} +1.82213 q^{10} +1.00000 q^{11} -3.81368 q^{12} +6.98651 q^{13} -9.23303 q^{14} +2.88880 q^{15} -4.89750 q^{16} -1.00000 q^{17} -9.73960 q^{18} -2.97265 q^{19} -1.32016 q^{20} -14.6380 q^{21} -1.82213 q^{22} +4.46920 q^{23} -3.57853 q^{24} +1.00000 q^{25} -12.7303 q^{26} -6.77473 q^{27} +6.68946 q^{28} -7.16142 q^{29} -5.26377 q^{30} +10.0398 q^{31} +6.44636 q^{32} -2.88880 q^{33} +1.82213 q^{34} -5.06716 q^{35} +7.05647 q^{36} -1.09232 q^{37} +5.41656 q^{38} -20.1827 q^{39} -1.23876 q^{40} +6.24623 q^{41} +26.6724 q^{42} -1.59304 q^{43} +1.32016 q^{44} -5.34517 q^{45} -8.14346 q^{46} -6.87199 q^{47} +14.1479 q^{48} +18.6761 q^{49} -1.82213 q^{50} +2.88880 q^{51} +9.22331 q^{52} +11.2736 q^{53} +12.3444 q^{54} -1.00000 q^{55} +6.27700 q^{56} +8.58740 q^{57} +13.0490 q^{58} -7.62548 q^{59} +3.81368 q^{60} -9.78595 q^{61} -18.2938 q^{62} +27.0849 q^{63} -1.95111 q^{64} -6.98651 q^{65} +5.26377 q^{66} +1.45320 q^{67} -1.32016 q^{68} -12.9106 q^{69} +9.23303 q^{70} -8.24819 q^{71} +6.62138 q^{72} +4.24422 q^{73} +1.99036 q^{74} -2.88880 q^{75} -3.92437 q^{76} +5.06716 q^{77} +36.7754 q^{78} -4.32806 q^{79} +4.89750 q^{80} +3.53534 q^{81} -11.3815 q^{82} +4.77036 q^{83} -19.3245 q^{84} +1.00000 q^{85} +2.90273 q^{86} +20.6879 q^{87} +1.23876 q^{88} -2.28487 q^{89} +9.73960 q^{90} +35.4018 q^{91} +5.90005 q^{92} -29.0030 q^{93} +12.5217 q^{94} +2.97265 q^{95} -18.6223 q^{96} +3.05884 q^{97} -34.0304 q^{98} +5.34517 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 3 q^{2} + 3 q^{3} + 11 q^{4} - 9 q^{5} + 9 q^{6} + 8 q^{7} + 12 q^{8} + 8 q^{9}+O(q^{10}) \) 9 * q + 3 * q^2 + 3 * q^3 + 11 * q^4 - 9 * q^5 + 9 * q^6 + 8 * q^7 + 12 * q^8 + 8 * q^9	\( 9 q + 3 q^{2} + 3 q^{3} + 11 q^{4} - 9 q^{5} + 9 q^{6} + 8 q^{7} + 12 q^{8} + 8 q^{9} - 3 q^{10} + 9 q^{11} + 12 q^{12} + 23 q^{13} - 16 q^{14} - 3 q^{15} + 15 q^{16} - 9 q^{17} - q^{18} + 12 q^{19} - 11 q^{20} - 4 q^{21} + 3 q^{22} - q^{23} - q^{24} + 9 q^{25} + 16 q^{26} + 12 q^{27} + 4 q^{28} - 19 q^{29} - 9 q^{30} + 14 q^{31} + 42 q^{32} + 3 q^{33} - 3 q^{34} - 8 q^{35} + 12 q^{36} + 15 q^{37} + 6 q^{38} - 4 q^{39} - 12 q^{40} - 7 q^{41} + 8 q^{42} + 33 q^{43} + 11 q^{44} - 8 q^{45} - 14 q^{46} - 10 q^{47} + 38 q^{48} + 37 q^{49} + 3 q^{50} - 3 q^{51} + 44 q^{52} + 18 q^{53} + 43 q^{54} - 9 q^{55} - 16 q^{56} + 2 q^{57} - 38 q^{58} - 7 q^{59} - 12 q^{60} + 13 q^{61} - 16 q^{62} + 28 q^{63} + 38 q^{64} - 23 q^{65} + 9 q^{66} + 8 q^{67} - 11 q^{68} - 48 q^{69} + 16 q^{70} - 16 q^{71} - 44 q^{72} + 30 q^{73} - 36 q^{74} + 3 q^{75} + 24 q^{76} + 8 q^{77} + 42 q^{78} - 21 q^{79} - 15 q^{80} + 21 q^{81} - 19 q^{82} + 33 q^{83} - 76 q^{84} + 9 q^{85} + 3 q^{86} + 8 q^{87} + 12 q^{88} - 11 q^{89} + q^{90} - 31 q^{92} - 40 q^{94} - 12 q^{95} + 34 q^{96} + 27 q^{97} + 47 q^{98} + 8 q^{99}+O(q^{100}) \) 9 * q + 3 * q^2 + 3 * q^3 + 11 * q^4 - 9 * q^5 + 9 * q^6 + 8 * q^7 + 12 * q^8 + 8 * q^9 - 3 * q^10 + 9 * q^11 + 12 * q^12 + 23 * q^13 - 16 * q^14 - 3 * q^15 + 15 * q^16 - 9 * q^17 - q^18 + 12 * q^19 - 11 * q^20 - 4 * q^21 + 3 * q^22 - q^23 - q^24 + 9 * q^25 + 16 * q^26 + 12 * q^27 + 4 * q^28 - 19 * q^29 - 9 * q^30 + 14 * q^31 + 42 * q^32 + 3 * q^33 - 3 * q^34 - 8 * q^35 + 12 * q^36 + 15 * q^37 + 6 * q^38 - 4 * q^39 - 12 * q^40 - 7 * q^41 + 8 * q^42 + 33 * q^43 + 11 * q^44 - 8 * q^45 - 14 * q^46 - 10 * q^47 + 38 * q^48 + 37 * q^49 + 3 * q^50 - 3 * q^51 + 44 * q^52 + 18 * q^53 + 43 * q^54 - 9 * q^55 - 16 * q^56 + 2 * q^57 - 38 * q^58 - 7 * q^59 - 12 * q^60 + 13 * q^61 - 16 * q^62 + 28 * q^63 + 38 * q^64 - 23 * q^65 + 9 * q^66 + 8 * q^67 - 11 * q^68 - 48 * q^69 + 16 * q^70 - 16 * q^71 - 44 * q^72 + 30 * q^73 - 36 * q^74 + 3 * q^75 + 24 * q^76 + 8 * q^77 + 42 * q^78 - 21 * q^79 - 15 * q^80 + 21 * q^81 - 19 * q^82 + 33 * q^83 - 76 * q^84 + 9 * q^85 + 3 * q^86 + 8 * q^87 + 12 * q^88 - 11 * q^89 + q^90 - 31 * q^92 - 40 * q^94 - 12 * q^95 + 34 * q^96 + 27 * q^97 + 47 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more