LMFDB - Embedded newform 1226.2.a.e.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1226,2,Mod(1,1226)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1226, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1226.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1226 = 2 \cdot 613 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1226.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:	$9.78965928781$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 4 x^{16} - 28 x^{15} + 120 x^{14} + 291 x^{13} - 1382 x^{12} - 1398 x^{11} + 7700 x^{10} + \cdots - 320 $ x^17 - 4x^16 - 28x^15 + 120x^14 + 291x^13 - 1382x^12 - 1398x^11 + 7700x^10 + 3456x^9 - 21974x^8 - 6336x^7 + 33062x^6 + 9753x^5 - 24446x^4 - 8368x^3 + 7000x^2 + 2384x - 320
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$0.722845$ of defining polynomial
Character	$\chi$	$=$	1226.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.722845 q^{3} +1.00000 q^{4} -2.20965 q^{5} -0.722845 q^{6} +2.70732 q^{7} -1.00000 q^{8} -2.47750 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.722845 q^{3} +1.00000 q^{4} -2.20965 q^{5} -0.722845 q^{6} +2.70732 q^{7} -1.00000 q^{8} -2.47750 q^{9} +2.20965 q^{10} +0.0954648 q^{11} +0.722845 q^{12} +5.13120 q^{13} -2.70732 q^{14} -1.59723 q^{15} +1.00000 q^{16} -2.27819 q^{17} +2.47750 q^{18} -0.433314 q^{19} -2.20965 q^{20} +1.95697 q^{21} -0.0954648 q^{22} +6.23208 q^{23} -0.722845 q^{24} -0.117460 q^{25} -5.13120 q^{26} -3.95938 q^{27} +2.70732 q^{28} -2.96351 q^{29} +1.59723 q^{30} +1.12156 q^{31} -1.00000 q^{32} +0.0690062 q^{33} +2.27819 q^{34} -5.98222 q^{35} -2.47750 q^{36} +11.2895 q^{37} +0.433314 q^{38} +3.70906 q^{39} +2.20965 q^{40} +10.8248 q^{41} -1.95697 q^{42} -1.62571 q^{43} +0.0954648 q^{44} +5.47439 q^{45} -6.23208 q^{46} +1.72925 q^{47} +0.722845 q^{48} +0.329577 q^{49} +0.117460 q^{50} -1.64678 q^{51} +5.13120 q^{52} +4.89772 q^{53} +3.95938 q^{54} -0.210943 q^{55} -2.70732 q^{56} -0.313219 q^{57} +2.96351 q^{58} -9.52455 q^{59} -1.59723 q^{60} +6.62100 q^{61} -1.12156 q^{62} -6.70737 q^{63} +1.00000 q^{64} -11.3381 q^{65} -0.0690062 q^{66} +6.93040 q^{67} -2.27819 q^{68} +4.50483 q^{69} +5.98222 q^{70} -1.38975 q^{71} +2.47750 q^{72} +15.2603 q^{73} -11.2895 q^{74} -0.0849052 q^{75} -0.433314 q^{76} +0.258454 q^{77} -3.70906 q^{78} +4.89981 q^{79} -2.20965 q^{80} +4.57047 q^{81} -10.8248 q^{82} +9.26623 q^{83} +1.95697 q^{84} +5.03400 q^{85} +1.62571 q^{86} -2.14216 q^{87} -0.0954648 q^{88} -5.15290 q^{89} -5.47439 q^{90} +13.8918 q^{91} +6.23208 q^{92} +0.810716 q^{93} -1.72925 q^{94} +0.957471 q^{95} -0.722845 q^{96} -9.79802 q^{97} -0.329577 q^{98} -0.236514 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 17 q^{2} + 4 q^{3} + 17 q^{4} - 5 q^{5} - 4 q^{6} + 7 q^{7} - 17 q^{8} + 21 q^{9}+O(q^{10}) $ 17 * q - 17 * q^2 + 4 * q^3 + 17 * q^4 - 5 * q^5 - 4 * q^6 + 7 * q^7 - 17 * q^8 + 21 * q^9	\( 17 q - 17 q^{2} + 4 q^{3} + 17 q^{4} - 5 q^{5} - 4 q^{6} + 7 q^{7} - 17 q^{8} + 21 q^{9} + 5 q^{10} + 8 q^{11} + 4 q^{12} + 9 q^{13} - 7 q^{14} - 4 q^{15} + 17 q^{16} - q^{17} - 21 q^{18} + 32 q^{19} - 5 q^{20} + 6 q^{21} - 8 q^{22} - 5 q^{23} - 4 q^{24} + 30 q^{25} - 9 q^{26} + 16 q^{27} + 7 q^{28} + 3 q^{29} + 4 q^{30} + 27 q^{31} - 17 q^{32} - 14 q^{33} + q^{34} + 25 q^{35} + 21 q^{36} + 7 q^{37} - 32 q^{38} + 27 q^{39} + 5 q^{40} - 2 q^{41} - 6 q^{42} + 36 q^{43} + 8 q^{44} - q^{45} + 5 q^{46} - 3 q^{47} + 4 q^{48} + 52 q^{49} - 30 q^{50} + 40 q^{51} + 9 q^{52} - 20 q^{53} - 16 q^{54} + 48 q^{55} - 7 q^{56} + 12 q^{57} - 3 q^{58} + 34 q^{59} - 4 q^{60} + 49 q^{61} - 27 q^{62} + 27 q^{63} + 17 q^{64} - 6 q^{65} + 14 q^{66} + 36 q^{67} - q^{68} + 18 q^{69} - 25 q^{70} - q^{71} - 21 q^{72} + 24 q^{73} - 7 q^{74} + 35 q^{75} + 32 q^{76} - 6 q^{77} - 27 q^{78} + 43 q^{79} - 5 q^{80} + 37 q^{81} + 2 q^{82} + 10 q^{83} + 6 q^{84} + 16 q^{85} - 36 q^{86} + 28 q^{87} - 8 q^{88} - 12 q^{89} + q^{90} + 42 q^{91} - 5 q^{92} + 3 q^{93} + 3 q^{94} - 10 q^{95} - 4 q^{96} + 26 q^{97} - 52 q^{98} + 34 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 4 * q^3 + 17 * q^4 - 5 * q^5 - 4 * q^6 + 7 * q^7 - 17 * q^8 + 21 * q^9 + 5 * q^10 + 8 * q^11 + 4 * q^12 + 9 * q^13 - 7 * q^14 - 4 * q^15 + 17 * q^16 - q^17 - 21 * q^18 + 32 * q^19 - 5 * q^20 + 6 * q^21 - 8 * q^22 - 5 * q^23 - 4 * q^24 + 30 * q^25 - 9 * q^26 + 16 * q^27 + 7 * q^28 + 3 * q^29 + 4 * q^30 + 27 * q^31 - 17 * q^32 - 14 * q^33 + q^34 + 25 * q^35 + 21 * q^36 + 7 * q^37 - 32 * q^38 + 27 * q^39 + 5 * q^40 - 2 * q^41 - 6 * q^42 + 36 * q^43 + 8 * q^44 - q^45 + 5 * q^46 - 3 * q^47 + 4 * q^48 + 52 * q^49 - 30 * q^50 + 40 * q^51 + 9 * q^52 - 20 * q^53 - 16 * q^54 + 48 * q^55 - 7 * q^56 + 12 * q^57 - 3 * q^58 + 34 * q^59 - 4 * q^60 + 49 * q^61 - 27 * q^62 + 27 * q^63 + 17 * q^64 - 6 * q^65 + 14 * q^66 + 36 * q^67 - q^68 + 18 * q^69 - 25 * q^70 - q^71 - 21 * q^72 + 24 * q^73 - 7 * q^74 + 35 * q^75 + 32 * q^76 - 6 * q^77 - 27 * q^78 + 43 * q^79 - 5 * q^80 + 37 * q^81 + 2 * q^82 + 10 * q^83 + 6 * q^84 + 16 * q^85 - 36 * q^86 + 28 * q^87 - 8 * q^88 - 12 * q^89 + q^90 + 42 * q^91 - 5 * q^92 + 3 * q^93 + 3 * q^94 - 10 * q^95 - 4 * q^96 + 26 * q^97 - 52 * q^98 + 34 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.722845	0.417335	0.208667	−	0.977987i	$-0.433087\pi$
$3$	0.722845	0.417335	0.208667	+	0.977987i	$0.433087\pi$
$4$	1.00000	0.500000
$5$	−2.20965	−0.988184	−0.494092	−	0.869410i	$-0.664499\pi$
$5$	−2.20965	−0.988184	−0.494092	+	0.869410i	$0.664499\pi$
$6$	−0.722845	−0.295100
$7$	2.70732	1.02327	0.511635	−	0.859203i	$-0.329040\pi$
$7$	2.70732	1.02327	0.511635	+	0.859203i	$0.329040\pi$
$8$	−1.00000	−0.353553
$9$	−2.47750	−0.825832
$10$	2.20965	0.698752
$11$	0.0954648	0.0287837	0.0143919	−	0.999896i	$-0.495419\pi$
$11$	0.0954648	0.0287837	0.0143919	+	0.999896i	$0.495419\pi$
$12$	0.722845	0.208667
$13$	5.13120	1.42314	0.711569	−	0.702616i	$-0.247985\pi$
$13$	5.13120	1.42314	0.711569	+	0.702616i	$0.247985\pi$
$14$	−2.70732	−0.723561
$15$	−1.59723	−0.412404
$16$	1.00000	0.250000
$17$	−2.27819	−0.552543	−0.276271	−	0.961080i	$-0.589099\pi$
$17$	−2.27819	−0.552543	−0.276271	+	0.961080i	$0.589099\pi$
$18$	2.47750	0.583951
$19$	−0.433314	−0.0994090	−0.0497045	−	0.998764i	$-0.515828\pi$
$19$	−0.433314	−0.0994090	−0.0497045	+	0.998764i	$0.515828\pi$
$20$	−2.20965	−0.494092
$21$	1.95697	0.427046
$22$	−0.0954648	−0.0203532
$23$	6.23208	1.29948	0.649739	−	0.760157i	$-0.274878\pi$
$23$	6.23208	1.29948	0.649739	+	0.760157i	$0.274878\pi$
$24$	−0.722845	−0.147550
$25$	−0.117460	−0.0234920
$26$	−5.13120	−1.00631
$27$	−3.95938	−0.761983
$28$	2.70732	0.511635
$29$	−2.96351	−0.550311	−0.275155	−	0.961400i	$-0.588729\pi$
$29$	−2.96351	−0.550311	−0.275155	+	0.961400i	$0.588729\pi$
$30$	1.59723	0.291613
$31$	1.12156	0.201439	0.100719	−	0.994915i	$-0.467886\pi$
$31$	1.12156	0.201439	0.100719	+	0.994915i	$0.467886\pi$
$32$	−1.00000	−0.176777
$33$	0.0690062	0.0120124
$34$	2.27819	0.390707
$35$	−5.98222	−1.01118
$36$	−2.47750	−0.412916
$37$	11.2895	1.85597	0.927987	−	0.372612i	$-0.121538\pi$
$37$	11.2895	1.85597	0.927987	+	0.372612i	$0.121538\pi$
$38$	0.433314	0.0702928
$39$	3.70906	0.593925
$40$	2.20965	0.349376
$41$	10.8248	1.69056	0.845278	−	0.534327i	$-0.179435\pi$
$41$	10.8248	1.69056	0.845278	+	0.534327i	$0.179435\pi$
$42$	−1.95697	−0.301967
$43$	−1.62571	−0.247918	−0.123959	−	0.992287i	$-0.539559\pi$
$43$	−1.62571	−0.247918	−0.123959	+	0.992287i	$0.539559\pi$
$44$	0.0954648	0.0143919
$45$	5.47439	0.816074
$46$	−6.23208	−0.918870
$47$	1.72925	0.252237	0.126119	−	0.992015i	$-0.459748\pi$
$47$	1.72925	0.252237	0.126119	+	0.992015i	$0.459748\pi$
$48$	0.722845	0.104334
$49$	0.329577	0.0470824
$50$	0.117460	0.0166113
$51$	−1.64678	−0.230595
$52$	5.13120	0.711569
$53$	4.89772	0.672754	0.336377	−	0.941727i	$-0.390798\pi$
$53$	4.89772	0.672754	0.336377	+	0.941727i	$0.390798\pi$
$54$	3.95938	0.538803
$55$	−0.210943	−0.0284436
$56$	−2.70732	−0.361781
$57$	−0.313219	−0.0414868
$58$	2.96351	0.389129
$59$	−9.52455	−1.23999	−0.619995	−	0.784606i	$-0.712865\pi$
$59$	−9.52455	−1.23999	−0.619995	+	0.784606i	$0.712865\pi$
$60$	−1.59723	−0.206202
$61$	6.62100	0.847732	0.423866	−	0.905725i	$-0.360673\pi$
$61$	6.62100	0.847732	0.423866	+	0.905725i	$0.360673\pi$
$62$	−1.12156	−0.142439
$63$	−6.70737	−0.845049
$64$	1.00000	0.125000
$65$	−11.3381	−1.40632
$66$	−0.0690062	−0.00849408
$67$	6.93040	0.846683	0.423342	−	0.905970i	$-0.360857\pi$
$67$	6.93040	0.846683	0.423342	+	0.905970i	$0.360857\pi$
$68$	−2.27819	−0.276271
$69$	4.50483	0.542317
$70$	5.98222	0.715012
$71$	−1.38975	−0.164933	−0.0824663	−	0.996594i	$-0.526280\pi$
$71$	−1.38975	−0.164933	−0.0824663	+	0.996594i	$0.526280\pi$
$72$	2.47750	0.291976
$73$	15.2603	1.78608	0.893040	−	0.449977i	$-0.148568\pi$
$73$	15.2603	1.78608	0.893040	+	0.449977i	$0.148568\pi$
$74$	−11.2895	−1.31237
$75$	−0.0849052	−0.00980401
$76$	−0.433314	−0.0497045
$77$	0.258454	0.0294535
$78$	−3.70906	−0.419969
$79$	4.89981	0.551272	0.275636	−	0.961262i	$-0.411112\pi$
$79$	4.89981	0.551272	0.275636	+	0.961262i	$0.411112\pi$
$80$	−2.20965	−0.247046
$81$	4.57047	0.507830
$82$	−10.8248	−1.19540
$83$	9.26623	1.01710	0.508551	−	0.861032i	$-0.330181\pi$
$83$	9.26623	1.01710	0.508551	+	0.861032i	$0.330181\pi$
$84$	1.95697	0.213523
$85$	5.03400	0.546014
$86$	1.62571	0.175305
$87$	−2.14216	−0.229664
$88$	−0.0954648	−0.0101766
$89$	−5.15290	−0.546206	−0.273103	−	0.961985i	$-0.588050\pi$
$89$	−5.15290	−0.546206	−0.273103	+	0.961985i	$0.588050\pi$
$90$	−5.47439	−0.577051
$91$	13.8918	1.45626
$92$	6.23208	0.649739
$93$	0.810716	0.0840674
$94$	−1.72925	−0.178359
$95$	0.957471	0.0982344
$96$	−0.722845	−0.0737750
$97$	−9.79802	−0.994838	−0.497419	−	0.867510i	$-0.665719\pi$
$97$	−9.79802	−0.994838	−0.497419	+	0.867510i	$0.665719\pi$
$98$	−0.329577	−0.0332923
$99$	−0.236514	−0.0237705
$100$	−0.117460	−0.0117460
$101$	−5.40495	−0.537812	−0.268906	−	0.963166i	$-0.586662\pi$
$101$	−5.40495	−0.537812	−0.268906	+	0.963166i	$0.586662\pi$
$102$	1.64678	0.163055
$103$	10.6321	1.04761	0.523804	−	0.851839i	$-0.324513\pi$
$103$	10.6321	1.04761	0.523804	+	0.851839i	$0.324513\pi$
$104$	−5.13120	−0.503156
$105$	−4.32422	−0.422000
$106$	−4.89772	−0.475709
$107$	7.30886	0.706574	0.353287	−	0.935515i	$-0.385064\pi$
$107$	7.30886	0.706574	0.353287	+	0.935515i	$0.385064\pi$
$108$	−3.95938	−0.380991
$109$	11.5354	1.10490	0.552448	−	0.833548i	$-0.313694\pi$
$109$	11.5354	1.10490	0.552448	+	0.833548i	$0.313694\pi$
$110$	0.210943	0.0201127
$111$	8.16052	0.774563
$112$	2.70732	0.255818
$113$	−9.89094	−0.930461	−0.465231	−	0.885189i	$-0.654029\pi$
$113$	−9.89094	−0.930461	−0.465231	+	0.885189i	$0.654029\pi$
$114$	0.313219	0.0293356
$115$	−13.7707	−1.28412
$116$	−2.96351	−0.275155
$117$	−12.7125	−1.17527
$118$	9.52455	0.876805
$119$	−6.16779	−0.565401
$120$	1.59723	0.145807
$121$	−10.9909	−0.999171
$122$	−6.62100	−0.599437
$123$	7.82468	0.705528
$124$	1.12156	0.100719
$125$	11.3078	1.01140
$126$	6.70737	0.597540
$127$	−11.3089	−1.00350	−0.501752	−	0.865011i	$-0.667311\pi$
$127$	−11.3089	−1.00350	−0.501752	+	0.865011i	$0.667311\pi$
$128$	−1.00000	−0.0883883
$129$	−1.17514	−0.103465
$130$	11.3381	0.994421
$131$	5.58159	0.487666	0.243833	−	0.969817i	$-0.421595\pi$
$131$	5.58159	0.487666	0.243833	+	0.969817i	$0.421595\pi$
$132$	0.0690062	0.00600622
$133$	−1.17312	−0.101722
$134$	−6.93040	−0.598695
$135$	8.74883	0.752979
$136$	2.27819	0.195353
$137$	18.6944	1.59717	0.798585	−	0.601882i	$-0.205582\pi$
$137$	18.6944	1.59717	0.798585	+	0.601882i	$0.205582\pi$
$138$	−4.50483	−0.383476
$139$	−18.3919	−1.55998	−0.779990	−	0.625792i	$-0.784776\pi$
$139$	−18.3919	−1.55998	−0.779990	+	0.625792i	$0.784776\pi$
$140$	−5.98222	−0.505590
$141$	1.24998	0.105267
$142$	1.38975	0.116625
$143$	0.489849	0.0409632
$144$	−2.47750	−0.206458
$145$	6.54832	0.543809
$146$	−15.2603	−1.26295
$147$	0.238233	0.0196491
$148$	11.2895	0.927987
$149$	2.68792	0.220203	0.110102	−	0.993920i	$-0.464882\pi$
$149$	2.68792	0.220203	0.110102	+	0.993920i	$0.464882\pi$
$150$	0.0849052	0.00693248
$151$	−14.4711	−1.17764	−0.588820	−	0.808264i	$-0.700407\pi$
$151$	−14.4711	−1.17764	−0.588820	+	0.808264i	$0.700407\pi$
$152$	0.433314	0.0351464
$153$	5.64421	0.456307
$154$	−0.258454	−0.0208268
$155$	−2.47826	−0.199059
$156$	3.70906	0.296963
$157$	13.2808	1.05992	0.529962	−	0.848021i	$-0.322206\pi$
$157$	13.2808	1.05992	0.529962	+	0.848021i	$0.322206\pi$
$158$	−4.89981	−0.389808
$159$	3.54029	0.280764
$160$	2.20965	0.174688
$161$	16.8722	1.32972
$162$	−4.57047	−0.359090
$163$	9.33126	0.730880	0.365440	−	0.930835i	$-0.380918\pi$
$163$	9.33126	0.730880	0.365440	+	0.930835i	$0.380918\pi$
$164$	10.8248	0.845278
$165$	−0.152479	−0.0118705
$166$	−9.26623	−0.719199
$167$	7.49526	0.580001	0.290000	−	0.957027i	$-0.406345\pi$
$167$	7.49526	0.580001	0.290000	+	0.957027i	$0.406345\pi$
$168$	−1.95697	−0.150984
$169$	13.3292	1.02532
$170$	−5.03400	−0.386090
$171$	1.07353	0.0820951
$172$	−1.62571	−0.123959
$173$	7.74353	0.588730	0.294365	−	0.955693i	$-0.404892\pi$
$173$	7.74353	0.588730	0.294365	+	0.955693i	$0.404892\pi$
$174$	2.14216	0.162397
$175$	−0.318001	−0.0240386
$176$	0.0954648	0.00719593
$177$	−6.88477	−0.517491
$178$	5.15290	0.386226
$179$	1.64290	0.122796	0.0613981	−	0.998113i	$-0.480444\pi$
$179$	1.64290	0.122796	0.0613981	+	0.998113i	$0.480444\pi$
$180$	5.47439	0.408037
$181$	−1.40631	−0.104530	−0.0522650	−	0.998633i	$-0.516644\pi$
$181$	−1.40631	−0.104530	−0.0522650	+	0.998633i	$0.516644\pi$
$182$	−13.8918	−1.02973
$183$	4.78595	0.353788
$184$	−6.23208	−0.459435
$185$	−24.9457	−1.83405
$186$	−0.810716	−0.0594446
$187$	−0.217487	−0.0159042
$188$	1.72925	0.126119
$189$	−10.7193	−0.779715
$190$	−0.957471	−0.0694622
$191$	19.8210	1.43420	0.717098	−	0.696972i	$-0.245470\pi$
$191$	19.8210	1.43420	0.717098	+	0.696972i	$0.245470\pi$
$192$	0.722845	0.0521668
$193$	−8.33663	−0.600084	−0.300042	−	0.953926i	$-0.597001\pi$
$193$	−8.33663	−0.600084	−0.300042	+	0.953926i	$0.597001\pi$
$194$	9.79802	0.703457
$195$	−8.19572	−0.586907
$196$	0.329577	0.0235412
$197$	−19.2362	−1.37052	−0.685261	−	0.728298i	$-0.740312\pi$
$197$	−19.2362	−1.37052	−0.685261	+	0.728298i	$0.740312\pi$
$198$	0.236514	0.0168083
$199$	14.3078	1.01425	0.507126	−	0.861872i	$-0.330708\pi$
$199$	14.3078	1.01425	0.507126	+	0.861872i	$0.330708\pi$
$200$	0.117460	0.00830566
$201$	5.00960	0.353350
$202$	5.40495	0.380291
$203$	−8.02318	−0.563117
$204$	−1.64678	−0.115298
$205$	−23.9191	−1.67058
$206$	−10.6321	−0.740770
$207$	−15.4399	−1.07315
$208$	5.13120	0.355785
$209$	−0.0413662	−0.00286136
$210$	4.32422	0.298399
$211$	9.72412	0.669436	0.334718	−	0.942318i	$-0.391359\pi$
$211$	9.72412	0.669436	0.334718	+	0.942318i	$0.391359\pi$
$212$	4.89772	0.336377
$213$	−1.00457	−0.0688321
$214$	−7.30886	−0.499623
$215$	3.59224	0.244989
$216$	3.95938	0.269402
$217$	3.03643	0.206126
$218$	−11.5354	−0.781279
$219$	11.0308	0.745393
$220$	−0.210943	−0.0142218
$221$	−11.6899	−0.786345
$222$	−8.16052	−0.547699
$223$	−17.5023	−1.17204	−0.586019	−	0.810297i	$-0.699306\pi$
$223$	−17.5023	−1.17204	−0.586019	+	0.810297i	$0.699306\pi$
$224$	−2.70732	−0.180890
$225$	0.291006	0.0194004
$226$	9.89094	0.657936
$227$	−12.8140	−0.850493	−0.425247	−	0.905077i	$-0.639813\pi$
$227$	−12.8140	−0.850493	−0.425247	+	0.905077i	$0.639813\pi$
$228$	−0.313219	−0.0207434
$229$	−13.4292	−0.887425	−0.443713	−	0.896169i	$-0.646339\pi$
$229$	−13.4292	−0.887425	−0.443713	+	0.896169i	$0.646339\pi$
$230$	13.7707	0.908013
$231$	0.186822	0.0122920
$232$	2.96351	0.194564
$233$	−12.2322	−0.801359	−0.400680	−	0.916218i	$-0.631226\pi$
$233$	−12.2322	−0.801359	−0.400680	+	0.916218i	$0.631226\pi$
$234$	12.7125	0.831044
$235$	−3.82104	−0.249257
$236$	−9.52455	−0.619995
$237$	3.54180	0.230065
$238$	6.16779	0.399799
$239$	−15.0343	−0.972489	−0.486245	−	0.873823i	$-0.661634\pi$
$239$	−15.0343	−0.972489	−0.486245	+	0.873823i	$0.661634\pi$
$240$	−1.59723	−0.103101
$241$	26.2394	1.69023	0.845115	−	0.534585i	$-0.179532\pi$
$241$	26.2394	1.69023	0.845115	+	0.534585i	$0.179532\pi$
$242$	10.9909	0.706521
$243$	15.1819	0.973918
$244$	6.62100	0.423866
$245$	−0.728249	−0.0465261
$246$	−7.82468	−0.498883
$247$	−2.22342	−0.141473
$248$	−1.12156	−0.0712193
$249$	6.69805	0.424472
$250$	−11.3078	−0.715167
$251$	−21.9914	−1.38809	−0.694043	−	0.719933i	$-0.744172\pi$
$251$	−21.9914	−1.38809	−0.694043	+	0.719933i	$0.744172\pi$
$252$	−6.70737	−0.422525
$253$	0.594944	0.0374038
$254$	11.3089	0.709585
$255$	3.63880	0.227871
$256$	1.00000	0.0625000
$257$	9.27410	0.578503	0.289251	−	0.957253i	$-0.406594\pi$
$257$	9.27410	0.578503	0.289251	+	0.957253i	$0.406594\pi$
$258$	1.17514	0.0731607
$259$	30.5642	1.89916
$260$	−11.3381	−0.703162
$261$	7.34209	0.454464
$262$	−5.58159	−0.344832
$263$	−13.9420	−0.859699	−0.429850	−	0.902900i	$-0.641433\pi$
$263$	−13.9420	−0.859699	−0.429850	+	0.902900i	$0.641433\pi$
$264$	−0.0690062	−0.00424704
$265$	−10.8222	−0.664805
$266$	1.17312	0.0719285
$267$	−3.72475	−0.227951
$268$	6.93040	0.423342
$269$	−6.89727	−0.420534	−0.210267	−	0.977644i	$-0.567433\pi$
$269$	−6.89727	−0.420534	−0.210267	+	0.977644i	$0.567433\pi$
$270$	−8.74883	−0.532437
$271$	−28.2386	−1.71537	−0.857685	−	0.514175i	$-0.828098\pi$
$271$	−28.2386	−1.71537	−0.857685	+	0.514175i	$0.828098\pi$
$272$	−2.27819	−0.138136
$273$	10.0416	0.607746
$274$	−18.6944	−1.12937
$275$	−0.0112133	−0.000676186 0
$276$	4.50483	0.271159
$277$	−19.8581	−1.19316	−0.596578	−	0.802555i	$-0.703473\pi$
$277$	−19.8581	−1.19316	−0.596578	+	0.802555i	$0.703473\pi$
$278$	18.3919	1.10307
$279$	−2.77867	−0.166354
$280$	5.98222	0.357506
$281$	−23.9424	−1.42829	−0.714143	−	0.700000i	$-0.753183\pi$
$281$	−23.9424	−1.42829	−0.714143	+	0.700000i	$0.753183\pi$
$282$	−1.24998	−0.0744353
$283$	−13.9986	−0.832131	−0.416065	−	0.909335i	$-0.636591\pi$
$283$	−13.9986	−0.832131	−0.416065	+	0.909335i	$0.636591\pi$
$284$	−1.38975	−0.0824663
$285$	0.692103	0.0409966
$286$	−0.489849	−0.0289654
$287$	29.3063	1.72990
$288$	2.47750	0.145988
$289$	−11.8098	−0.694697
$290$	−6.54832	−0.384531
$291$	−7.08245	−0.415180
$292$	15.2603	0.893040
$293$	−26.1274	−1.52638	−0.763189	−	0.646175i	$-0.776368\pi$
$293$	−26.1274	−1.52638	−0.763189	+	0.646175i	$0.776368\pi$
$294$	−0.238233	−0.0138940
$295$	21.0459	1.22534
$296$	−11.2895	−0.656186
$297$	−0.377981	−0.0219327
$298$	−2.68792	−0.155707
$299$	31.9780	1.84934
$300$	−0.0849052	−0.00490200
$301$	−4.40131	−0.253687
$302$	14.4711	0.832717
$303$	−3.90694	−0.224448
$304$	−0.433314	−0.0248523
$305$	−14.6301	−0.837715
$306$	−5.64421	−0.322658
$307$	7.81564	0.446062	0.223031	−	0.974811i	$-0.428405\pi$
$307$	7.81564	0.446062	0.223031	+	0.974811i	$0.428405\pi$
$308$	0.258454	0.0147268
$309$	7.68533	0.437203
$310$	2.47826	0.140756
$311$	17.7029	1.00384	0.501919	−	0.864915i	$-0.332628\pi$
$311$	17.7029	1.00384	0.501919	+	0.864915i	$0.332628\pi$
$312$	−3.70906	−0.209984
$313$	−0.771609	−0.0436139	−0.0218070	−	0.999762i	$-0.506942\pi$
$313$	−0.771609	−0.0436139	−0.0218070	+	0.999762i	$0.506942\pi$
$314$	−13.2808	−0.749480
$315$	14.8209	0.835064
$316$	4.89981	0.275636
$317$	1.00025	0.0561797	0.0280899	−	0.999605i	$-0.491058\pi$
$317$	1.00025	0.0561797	0.0280899	+	0.999605i	$0.491058\pi$
$318$	−3.54029	−0.198530
$319$	−0.282911	−0.0158400
$320$	−2.20965	−0.123523
$321$	5.28317	0.294878
$322$	−16.8722	−0.940252
$323$	0.987172	0.0549277
$324$	4.57047	0.253915
$325$	−0.602709	−0.0334323
$326$	−9.33126	−0.516811
$327$	8.33834	0.461111
$328$	−10.8248	−0.597702
$329$	4.68164	0.258107
$330$	0.152479	0.00839371
$331$	2.23138	0.122648	0.0613239	−	0.998118i	$-0.480468\pi$
$331$	2.23138	0.122648	0.0613239	+	0.998118i	$0.480468\pi$
$332$	9.26623	0.508551
$333$	−27.9696	−1.53272
$334$	−7.49526	−0.410122
$335$	−15.3137	−0.836679
$336$	1.95697	0.106762
$337$	−14.7441	−0.803161	−0.401580	−	0.915824i	$-0.631539\pi$
$337$	−14.7441	−0.803161	−0.401580	+	0.915824i	$0.631539\pi$
$338$	−13.3292	−0.725014
$339$	−7.14962	−0.388314
$340$	5.03400	0.273007
$341$	0.107070	0.00579815
$342$	−1.07353	−0.0580500
$343$	−18.0590	−0.975092
$344$	1.62571	0.0876523
$345$	−9.95408	−0.535909
$346$	−7.74353	−0.416295
$347$	12.5914	0.675944	0.337972	−	0.941156i	$-0.390259\pi$
$347$	12.5914	0.675944	0.337972	+	0.941156i	$0.390259\pi$
$348$	−2.14216	−0.114832
$349$	−25.4548	−1.36257	−0.681283	−	0.732020i	$-0.738578\pi$
$349$	−25.4548	−1.36257	−0.681283	+	0.732020i	$0.738578\pi$
$350$	0.318001	0.0169979
$351$	−20.3164	−1.08441
$352$	−0.0954648	−0.00508829
$353$	−16.4143	−0.873645	−0.436823	−	0.899548i	$-0.643896\pi$
$353$	−16.4143	−0.873645	−0.436823	+	0.899548i	$0.643896\pi$
$354$	6.88477	0.365921
$355$	3.07085	0.162984
$356$	−5.15290	−0.273103
$357$	−4.45836	−0.235961
$358$	−1.64290	−0.0868300
$359$	19.0909	1.00758	0.503790	−	0.863826i	$-0.331939\pi$
$359$	19.0909	1.00758	0.503790	+	0.863826i	$0.331939\pi$
$360$	−5.47439	−0.288526
$361$	−18.8122	−0.990118
$362$	1.40631	0.0739138
$363$	−7.94471	−0.416989
$364$	13.8918	0.728128
$365$	−33.7198	−1.76498
$366$	−4.78595	−0.250166
$367$	−25.1588	−1.31328	−0.656641	−	0.754204i	$-0.728023\pi$
$367$	−25.1588	−1.31328	−0.656641	+	0.754204i	$0.728023\pi$
$368$	6.23208	0.324870
$369$	−26.8185	−1.39611
$370$	24.9457	1.29687
$371$	13.2597	0.688409
$372$	0.810716	0.0420337
$373$	8.50076	0.440153	0.220076	−	0.975483i	$-0.429369\pi$
$373$	8.50076	0.440153	0.220076	+	0.975483i	$0.429369\pi$
$374$	0.217487	0.0112460
$375$	8.17377	0.422092
$376$	−1.72925	−0.0891793
$377$	−15.2064	−0.783169
$378$	10.7193	0.551341
$379$	−6.98190	−0.358636	−0.179318	−	0.983791i	$-0.557389\pi$
$379$	−6.98190	−0.358636	−0.179318	+	0.983791i	$0.557389\pi$
$380$	0.957471	0.0491172
$381$	−8.17460	−0.418797
$382$	−19.8210	−1.01413
$383$	12.0379	0.615107	0.307553	−	0.951531i	$-0.400490\pi$
$383$	12.0379	0.615107	0.307553	+	0.951531i	$0.400490\pi$
$384$	−0.722845	−0.0368875
$385$	−0.571091	−0.0291055
$386$	8.33663	0.424323
$387$	4.02769	0.204739
$388$	−9.79802	−0.497419
$389$	−4.11805	−0.208793	−0.104397	−	0.994536i	$-0.533291\pi$
$389$	−4.11805	−0.208793	−0.104397	+	0.994536i	$0.533291\pi$
$390$	8.19572	0.415006
$391$	−14.1979	−0.718017
$392$	−0.329577	−0.0166462
$393$	4.03463	0.203520
$394$	19.2362	0.969105
$395$	−10.8269	−0.544758
$396$	−0.236514	−0.0118853
$397$	2.51013	0.125980	0.0629900	−	0.998014i	$-0.479936\pi$
$397$	2.51013	0.125980	0.0629900	+	0.998014i	$0.479936\pi$
$398$	−14.3078	−0.717184
$399$	−0.847983	−0.0424522
$400$	−0.117460	−0.00587299
$401$	7.69520	0.384280	0.192140	−	0.981368i	$-0.438457\pi$
$401$	7.69520	0.384280	0.192140	+	0.981368i	$0.438457\pi$
$402$	−5.00960	−0.249856
$403$	5.75496	0.286675
$404$	−5.40495	−0.268906
$405$	−10.0991	−0.501829
$406$	8.02318	0.398184
$407$	1.07775	0.0534218
$408$	1.64678	0.0815277
$409$	−28.4726	−1.40788	−0.703940	−	0.710259i	$-0.748578\pi$
$409$	−28.4726	−1.40788	−0.703940	+	0.710259i	$0.748578\pi$
$410$	23.9191	1.18128
$411$	13.5132	0.666555
$412$	10.6321	0.523804
$413$	−25.7860	−1.26885
$414$	15.4399	0.758832
$415$	−20.4751	−1.00508
$416$	−5.13120	−0.251578
$417$	−13.2945	−0.651034
$418$	0.0413662	0.00202329
$419$	34.1972	1.67064	0.835321	−	0.549762i	$-0.185282\pi$
$419$	34.1972	1.67064	0.835321	+	0.549762i	$0.185282\pi$
$420$	−4.32422	−0.211000
$421$	27.6168	1.34596	0.672980	−	0.739661i	$-0.265014\pi$
$421$	27.6168	1.34596	0.672980	+	0.739661i	$0.265014\pi$
$422$	−9.72412	−0.473363
$423$	−4.28421	−0.208306
$424$	−4.89772	−0.237854
$425$	0.267596	0.0129803
$426$	1.00457	0.0486717
$427$	17.9252	0.867459
$428$	7.30886	0.353287
$429$	0.354085	0.0170954
$430$	−3.59224	−0.173233
$431$	5.85931	0.282233	0.141117	−	0.989993i	$-0.454931\pi$
$431$	5.85931	0.282233	0.141117	+	0.989993i	$0.454931\pi$
$432$	−3.95938	−0.190496
$433$	−12.8382	−0.616965	−0.308482	−	0.951230i	$-0.599821\pi$
$433$	−12.8382	−0.616965	−0.308482	+	0.951230i	$0.599821\pi$
$434$	−3.03643	−0.145753
$435$	4.73342	0.226950
$436$	11.5354	0.552448
$437$	−2.70045	−0.129180
$438$	−11.0308	−0.527073
$439$	41.0869	1.96097	0.980485	−	0.196596i	$-0.0629886\pi$
$439$	41.0869	1.96097	0.980485	+	0.196596i	$0.0629886\pi$
$440$	0.210943	0.0100563
$441$	−0.816526	−0.0388822
$442$	11.6899	0.556030
$443$	−2.79376	−0.132735	−0.0663677	−	0.997795i	$-0.521141\pi$
$443$	−2.79376	−0.132735	−0.0663677	+	0.997795i	$0.521141\pi$
$444$	8.16052	0.387281
$445$	11.3861	0.539752
$446$	17.5023	0.828757
$447$	1.94295	0.0918985
$448$	2.70732	0.127909
$449$	−9.95840	−0.469966	−0.234983	−	0.971999i	$-0.575503\pi$
$449$	−9.95840	−0.469966	−0.234983	+	0.971999i	$0.575503\pi$
$450$	−0.291006	−0.0137182
$451$	1.03339	0.0486605
$452$	−9.89094	−0.465231
$453$	−10.4603	−0.491470
$454$	12.8140	0.601390
$455$	−30.6960	−1.43905
$456$	0.313219	0.0146678
$457$	−5.49311	−0.256957	−0.128478	−	0.991712i	$-0.541009\pi$
$457$	−5.49311	−0.256957	−0.128478	+	0.991712i	$0.541009\pi$
$458$	13.4292	0.627504
$459$	9.02023	0.421028
$460$	−13.7707	−0.642062
$461$	−19.2302	−0.895642	−0.447821	−	0.894123i	$-0.647800\pi$
$461$	−19.2302	−0.895642	−0.447821	+	0.894123i	$0.647800\pi$
$462$	−0.186822	−0.00869174
$463$	9.97182	0.463430	0.231715	−	0.972784i	$-0.425566\pi$
$463$	9.97182	0.463430	0.231715	+	0.972784i	$0.425566\pi$
$464$	−2.96351	−0.137578
$465$	−1.79140	−0.0830740
$466$	12.2322	0.566646
$467$	−14.0167	−0.648616	−0.324308	−	0.945952i	$-0.605131\pi$
$467$	−14.0167	−0.648616	−0.324308	+	0.945952i	$0.605131\pi$
$468$	−12.7125	−0.587637
$469$	18.7628	0.866386
$470$	3.82104	0.176251
$471$	9.59997	0.442343
$472$	9.52455	0.438403
$473$	−0.155198	−0.00713601
$474$	−3.54180	−0.162680
$475$	0.0508969	0.00233531
$476$	−6.16779	−0.282700
$477$	−12.1341	−0.555582
$478$	15.0343	0.687654
$479$	2.51841	0.115069	0.0575346	−	0.998344i	$-0.481676\pi$
$479$	2.51841	0.115069	0.0575346	+	0.998344i	$0.481676\pi$
$480$	1.59723	0.0729033
$481$	57.9284	2.64131
$482$	−26.2394	−1.19517
$483$	12.1960	0.554937
$484$	−10.9909	−0.499586
$485$	21.6502	0.983083
$486$	−15.1819	−0.688664
$487$	−8.73952	−0.396025	−0.198013	−	0.980199i	$-0.563449\pi$
$487$	−8.73952	−0.396025	−0.198013	+	0.980199i	$0.563449\pi$
$488$	−6.62100	−0.299718
$489$	6.74505	0.305022
$490$	0.728249	0.0328989
$491$	19.4042	0.875699	0.437850	−	0.899048i	$-0.355740\pi$
$491$	19.4042	0.875699	0.437850	+	0.899048i	$0.355740\pi$
$492$	7.82468	0.352764
$493$	6.75145	0.304070
$494$	2.22342	0.100036
$495$	0.522611	0.0234896
$496$	1.12156	0.0503597
$497$	−3.76249	−0.168771
$498$	−6.69805	−0.300147
$499$	23.6544	1.05892	0.529459	−	0.848335i	$-0.322395\pi$
$499$	23.6544	1.05892	0.529459	+	0.848335i	$0.322395\pi$
$500$	11.3078	0.505699
$501$	5.41791	0.242054
$502$	21.9914	0.981526
$503$	−20.3413	−0.906973	−0.453486	−	0.891263i	$-0.649820\pi$
$503$	−20.3413	−0.906973	−0.453486	+	0.891263i	$0.649820\pi$
$504$	6.70737	0.298770
$505$	11.9430	0.531458
$506$	−0.594944	−0.0264485
$507$	9.63495	0.427903
$508$	−11.3089	−0.501752
$509$	4.25914	0.188783	0.0943915	−	0.995535i	$-0.469909\pi$
$509$	4.25914	0.188783	0.0943915	+	0.995535i	$0.469909\pi$
$510$	−3.63880	−0.161129
$511$	41.3144	1.82764
$512$	−1.00000	−0.0441942
$513$	1.71565	0.0757480
$514$	−9.27410	−0.409063
$515$	−23.4931	−1.03523
$516$	−1.17514	−0.0517324
$517$	0.165083	0.00726032
$518$	−30.5642	−1.34291
$519$	5.59737	0.245697
$520$	11.3381	0.497210
$521$	22.7493	0.996664	0.498332	−	0.866986i	$-0.333946\pi$
$521$	22.7493	0.996664	0.498332	+	0.866986i	$0.333946\pi$
$522$	−7.34209	−0.321355
$523$	40.3329	1.76363	0.881816	−	0.471593i	$-0.156321\pi$
$523$	40.3329	1.76363	0.881816	+	0.471593i	$0.156321\pi$
$524$	5.58159	0.243833
$525$	−0.229865	−0.0100321
$526$	13.9420	0.607899
$527$	−2.55514	−0.111303
$528$	0.0690062	0.00300311
$529$	15.8388	0.688644
$530$	10.8222	0.470088
$531$	23.5970	1.02402
$532$	−1.17312	−0.0508611
$533$	55.5444	2.40590
$534$	3.72475	0.161185
$535$	−16.1500	−0.698225
$536$	−6.93040	−0.299348
$537$	1.18756	0.0512471
$538$	6.89727	0.297362
$539$	0.0314630	0.00135521
$540$	8.74883	0.376490
$541$	14.0183	0.602693	0.301346	−	0.953515i	$-0.402564\pi$
$541$	14.0183	0.602693	0.301346	+	0.953515i	$0.402564\pi$
$542$	28.2386	1.21295
$543$	−1.01654	−0.0436240
$544$	2.27819	0.0976767
$545$	−25.4893	−1.09184
$546$	−10.0416	−0.429741
$547$	43.5774	1.86324	0.931618	−	0.363439i	$-0.118397\pi$
$547$	43.5774	1.86324	0.931618	+	0.363439i	$0.118397\pi$
$548$	18.6944	0.798585
$549$	−16.4035	−0.700084
$550$	0.0112133	0.000478135 0
$551$	1.28413	0.0547059
$552$	−4.50483	−0.191738
$553$	13.2654	0.564100
$554$	19.8581	0.843688
$555$	−18.0319	−0.765411
$556$	−18.3919	−0.779990
$557$	9.14658	0.387553	0.193777	−	0.981046i	$-0.437926\pi$
$557$	9.14658	0.387553	0.193777	+	0.981046i	$0.437926\pi$
$558$	2.77867	0.117630
$559$	−8.34184	−0.352822
$560$	−5.98222	−0.252795
$561$	−0.157209	−0.00663739
$562$	23.9424	1.00995
$563$	8.81420	0.371474	0.185737	−	0.982599i	$-0.440533\pi$
$563$	8.81420	0.371474	0.185737	+	0.982599i	$0.440533\pi$
$564$	1.24998	0.0526337
$565$	21.8555	0.919467
$566$	13.9986	0.588405
$567$	12.3737	0.519647
$568$	1.38975	0.0583125
$569$	−5.55128	−0.232722	−0.116361	−	0.993207i	$-0.537123\pi$
$569$	−5.55128	−0.232722	−0.116361	+	0.993207i	$0.537123\pi$
$570$	−0.692103	−0.0289890
$571$	29.8341	1.24852	0.624260	−	0.781217i	$-0.285401\pi$
$571$	29.8341	1.24852	0.624260	+	0.781217i	$0.285401\pi$
$572$	0.489849	0.0204816
$573$	14.3275	0.598540
$574$	−29.3063	−1.22322
$575$	−0.732018	−0.0305273
$576$	−2.47750	−0.103229
$577$	−20.3859	−0.848676	−0.424338	−	0.905504i	$-0.639493\pi$
$577$	−20.3859	−0.848676	−0.424338	+	0.905504i	$0.639493\pi$
$578$	11.8098	0.491225
$579$	−6.02609	−0.250436
$580$	6.54832	0.271904
$581$	25.0866	1.04077
$582$	7.08245	0.293577
$583$	0.467560	0.0193644
$584$	−15.2603	−0.631475
$585$	28.0902	1.16139
$586$	26.1274	1.07931
$587$	−21.3161	−0.879809	−0.439904	−	0.898045i	$-0.644988\pi$
$587$	−21.3161	−0.879809	−0.439904	+	0.898045i	$0.644988\pi$
$588$	0.238233	0.00982457
$589$	−0.485989	−0.0200248
$590$	−21.0459	−0.866445
$591$	−13.9048	−0.571966
$592$	11.2895	0.463994
$593$	34.1151	1.40094	0.700469	−	0.713683i	$-0.252974\pi$
$593$	34.1151	1.40094	0.700469	+	0.713683i	$0.252974\pi$
$594$	0.377981	0.0155088
$595$	13.6286	0.558720
$596$	2.68792	0.110102
$597$	10.3423	0.423282
$598$	−31.9780	−1.30768
$599$	44.0228	1.79872	0.899361	−	0.437207i	$-0.144032\pi$
$599$	44.0228	1.79872	0.899361	+	0.437207i	$0.144032\pi$
$600$	0.0849052	0.00346624
$601$	8.44957	0.344665	0.172333	−	0.985039i	$-0.444870\pi$
$601$	8.44957	0.344665	0.172333	+	0.985039i	$0.444870\pi$
$602$	4.40131	0.179384
$603$	−17.1700	−0.699218
$604$	−14.4711	−0.588820
$605$	24.2860	0.987366
$606$	3.90694	0.158708
$607$	−39.0086	−1.58331	−0.791655	−	0.610969i	$-0.790780\pi$
$607$	−39.0086	−1.58331	−0.791655	+	0.610969i	$0.790780\pi$
$608$	0.433314	0.0175732
$609$	−5.79951	−0.235008
$610$	14.6301	0.592354
$611$	8.87313	0.358969
$612$	5.64421	0.228154
$613$	1.00000	0.0403896
$613$	1.00000	0.0403896
$614$	−7.81564	−0.315414
$615$	−17.2898	−0.697191
$616$	−0.258454	−0.0104134
$617$	−29.3158	−1.18021	−0.590106	−	0.807326i	$-0.700914\pi$
$617$	−29.3158	−1.18021	−0.590106	+	0.807326i	$0.700914\pi$
$618$	−7.68533	−0.309149
$619$	−20.2381	−0.813438	−0.406719	−	0.913553i	$-0.633327\pi$
$619$	−20.2381	−0.813438	−0.406719	+	0.913553i	$0.633327\pi$
$620$	−2.47826	−0.0995293
$621$	−24.6752	−0.990180
$622$	−17.7029	−0.709820
$623$	−13.9505	−0.558916
$624$	3.70906	0.148481
$625$	−24.3989	−0.975956
$626$	0.771609	0.0308397
$627$	−0.0299013	−0.00119414
$628$	13.2808	0.529962
$629$	−25.7195	−1.02551
$630$	−14.8209	−0.590480
$631$	−47.5460	−1.89278	−0.946388	−	0.323031i	$-0.895298\pi$
$631$	−47.5460	−1.89278	−0.946388	+	0.323031i	$0.895298\pi$
$632$	−4.89981	−0.194904
$633$	7.02903	0.279379
$634$	−1.00025	−0.0397251
$635$	24.9887	0.991648
$636$	3.54029	0.140382
$637$	1.69113	0.0670048
$638$	0.282911	0.0112006
$639$	3.44309	0.136207
$640$	2.20965	0.0873440
$641$	−3.53153	−0.139487	−0.0697435	−	0.997565i	$-0.522218\pi$
$641$	−3.53153	−0.139487	−0.0697435	+	0.997565i	$0.522218\pi$
$642$	−5.28317	−0.208510
$643$	34.4058	1.35683	0.678415	−	0.734679i	$-0.262667\pi$
$643$	34.4058	1.35683	0.678415	+	0.734679i	$0.262667\pi$
$644$	16.8722	0.664859
$645$	2.59663	0.102242
$646$	−0.987172	−0.0388398
$647$	−0.616646	−0.0242429	−0.0121214	−	0.999927i	$-0.503858\pi$
$647$	−0.616646	−0.0242429	−0.0121214	+	0.999927i	$0.503858\pi$
$648$	−4.57047	−0.179545
$649$	−0.909259	−0.0356915
$650$	0.602709	0.0236402
$651$	2.19487	0.0860236
$652$	9.33126	0.365440
$653$	−17.1098	−0.669559	−0.334780	−	0.942296i	$-0.608662\pi$
$653$	−17.1098	−0.669559	−0.334780	+	0.942296i	$0.608662\pi$
$654$	−8.33834	−0.326055
$655$	−12.3334	−0.481904
$656$	10.8248	0.422639
$657$	−37.8073	−1.47500
$658$	−4.68164	−0.182509
$659$	21.6160	0.842039	0.421020	−	0.907052i	$-0.361672\pi$
$659$	21.6160	0.842039	0.421020	+	0.907052i	$0.361672\pi$
$660$	−0.152479	−0.00593525
$661$	37.3889	1.45426	0.727131	−	0.686499i	$-0.240853\pi$
$661$	37.3889	1.45426	0.727131	+	0.686499i	$0.240853\pi$
$662$	−2.23138	−0.0867250
$663$	−8.44995	−0.328169
$664$	−9.26623	−0.359600
$665$	2.59218	0.100520
$666$	27.9696	1.08380
$667$	−18.4689	−0.715117
$668$	7.49526	0.290000
$669$	−12.6514	−0.489132
$670$	15.3137	0.591621
$671$	0.632072	0.0244009
$672$	−1.95697	−0.0754918
$673$	2.75526	0.106208	0.0531038	−	0.998589i	$-0.483089\pi$
$673$	2.75526	0.106208	0.0531038	+	0.998589i	$0.483089\pi$
$674$	14.7441	0.567920
$675$	0.465068	0.0179005
$676$	13.3292	0.512662
$677$	−3.49071	−0.134159	−0.0670795	−	0.997748i	$-0.521368\pi$
$677$	−3.49071	−0.134159	−0.0670795	+	0.997748i	$0.521368\pi$
$678$	7.14962	0.274579
$679$	−26.5264	−1.01799
$680$	−5.03400	−0.193045
$681$	−9.26252	−0.354940
$682$	−0.107070	−0.00409991
$683$	5.12462	0.196088	0.0980441	−	0.995182i	$-0.468741\pi$
$683$	5.12462	0.196088	0.0980441	+	0.995182i	$0.468741\pi$
$684$	1.07353	0.0410476
$685$	−41.3080	−1.57830
$686$	18.0590	0.689494
$687$	−9.70721	−0.370353
$688$	−1.62571	−0.0619796
$689$	25.1312	0.957422
$690$	9.95408	0.378945
$691$	−32.3559	−1.23087	−0.615437	−	0.788186i	$-0.711021\pi$
$691$	−32.3559	−1.23087	−0.615437	+	0.788186i	$0.711021\pi$
$692$	7.74353	0.294365
$693$	−0.640318	−0.0243237
$694$	−12.5914	−0.477965
$695$	40.6396	1.54155
$696$	2.14216	0.0811984
$697$	−24.6611	−0.934104
$698$	25.4548	0.963479
$699$	−8.84199	−0.334435
$700$	−0.318001	−0.0120193
$701$	−25.6398	−0.968401	−0.484201	−	0.874957i	$-0.660890\pi$
$701$	−25.6398	−0.968401	−0.484201	+	0.874957i	$0.660890\pi$
$702$	20.3164	0.766792
$703$	−4.89188	−0.184501
$704$	0.0954648	0.00359796
$705$	−2.76202	−0.104024
$706$	16.4143	0.617761
$707$	−14.6329	−0.550327
$708$	−6.88477	−0.258745
$709$	31.9112	1.19845	0.599226	−	0.800580i	$-0.295475\pi$
$709$	31.9112	1.19845	0.599226	+	0.800580i	$0.295475\pi$
$710$	−3.07085	−0.115247
$711$	−12.1393	−0.455258
$712$	5.15290	0.193113
$713$	6.98967	0.261765
$714$	4.45836	0.166850
$715$	−1.08239	−0.0404792
$716$	1.64290	0.0613981
$717$	−10.8675	−0.405853
$718$	−19.0909	−0.712466
$719$	−7.95947	−0.296838	−0.148419	−	0.988925i	$-0.547418\pi$
$719$	−7.95947	−0.296838	−0.148419	+	0.988925i	$0.547418\pi$
$720$	5.47439	0.204018
$721$	28.7844	1.07199
$722$	18.8122	0.700119
$723$	18.9670	0.705391
$724$	−1.40631	−0.0522650
$725$	0.348094	0.0129279
$726$	7.94471	0.294856
$727$	−34.7447	−1.28861	−0.644306	−	0.764768i	$-0.722853\pi$
$727$	−34.7447	−1.28861	−0.644306	+	0.764768i	$0.722853\pi$
$728$	−13.8918	−0.514864
$729$	−2.73726	−0.101380
$730$	33.7198	1.24803
$731$	3.70368	0.136985
$732$	4.78595	0.176894
$733$	−11.1010	−0.410026	−0.205013	−	0.978759i	$-0.565724\pi$
$733$	−11.1010	−0.410026	−0.205013	+	0.978759i	$0.565724\pi$
$734$	25.1588	0.928630
$735$	−0.526411	−0.0194170
$736$	−6.23208	−0.229717
$737$	0.661609	0.0243707
$738$	26.8185	0.987202
$739$	−22.2318	−0.817809	−0.408905	−	0.912577i	$-0.634089\pi$
$739$	−22.2318	−0.817809	−0.408905	+	0.912577i	$0.634089\pi$
$740$	−24.9457	−0.917023
$741$	−1.60719	−0.0590415
$742$	−13.2597	−0.486779
$743$	−47.9440	−1.75889	−0.879447	−	0.475998i	$-0.842087\pi$
$743$	−47.9440	−1.75889	−0.879447	+	0.475998i	$0.842087\pi$
$744$	−0.810716	−0.0297223
$745$	−5.93936	−0.217601
$746$	−8.50076	−0.311235
$747$	−22.9570	−0.839954
$748$	−0.217487	−0.00795211
$749$	19.7874	0.723016
$750$	−8.17377	−0.298464
$751$	27.5659	1.00589	0.502946	−	0.864318i	$-0.332249\pi$
$751$	27.5659	1.00589	0.502946	+	0.864318i	$0.332249\pi$
$752$	1.72925	0.0630593
$753$	−15.8964	−0.579297
$754$	15.2064	0.553784
$755$	31.9760	1.16373
$756$	−10.7193	−0.389857
$757$	9.34875	0.339786	0.169893	−	0.985463i	$-0.445658\pi$
$757$	9.34875	0.339786	0.169893	+	0.985463i	$0.445658\pi$
$758$	6.98190	0.253594
$759$	0.430052	0.0156099
$760$	−0.957471	−0.0347311
$761$	42.1640	1.52844	0.764221	−	0.644954i	$-0.223124\pi$
$761$	42.1640	1.52844	0.764221	+	0.644954i	$0.223124\pi$
$762$	8.17460	0.296134
$763$	31.2301	1.13061
$764$	19.8210	0.717098
$765$	−12.4717	−0.450916
$766$	−12.0379	−0.434946
$767$	−48.8723	−1.76468
$768$	0.722845	0.0260834
$769$	−34.8666	−1.25732	−0.628662	−	0.777679i	$-0.716397\pi$
$769$	−34.8666	−1.25732	−0.628662	+	0.777679i	$0.716397\pi$
$770$	0.571091	0.0205807
$771$	6.70374	0.241429
$772$	−8.33663	−0.300042
$773$	28.7933	1.03562	0.517811	−	0.855495i	$-0.326747\pi$
$773$	28.7933	1.03562	0.517811	+	0.855495i	$0.326747\pi$
$774$	−4.02769	−0.144772
$775$	−0.131739	−0.00473219
$776$	9.79802	0.351728
$777$	22.0931	0.792587
$778$	4.11805	0.147639
$779$	−4.69055	−0.168056
$780$	−8.19572	−0.293454
$781$	−0.132672	−0.00474737
$782$	14.1979	0.507715
$783$	11.7337	0.419327
$784$	0.329577	0.0117706
$785$	−29.3459	−1.04740
$786$	−4.03463	−0.143910
$787$	32.4720	1.15750	0.578750	−	0.815505i	$-0.303541\pi$
$787$	32.4720	1.15750	0.578750	+	0.815505i	$0.303541\pi$
$788$	−19.2362	−0.685261
$789$	−10.0779	−0.358782
$790$	10.8269	0.385202
$791$	−26.7779	−0.952114
$792$	0.236514	0.00840414
$793$	33.9737	1.20644
$794$	−2.51013	−0.0890813
$795$	−7.82280	−0.277446
$796$	14.3078	0.507126
$797$	−50.1997	−1.77816	−0.889082	−	0.457747i	$-0.848656\pi$
$797$	−50.1997	−1.77816	−0.889082	+	0.457747i	$0.848656\pi$
$798$	0.847983	0.0300183
$799$	−3.93957	−0.139372
$800$	0.117460	0.00415283
$801$	12.7663	0.451074
$802$	−7.69520	−0.271727
$803$	1.45682	0.0514100
$804$	5.00960	0.176675
$805$	−37.2817	−1.31401
$806$	−5.75496	−0.202710
$807$	−4.98566	−0.175503
$808$	5.40495	0.190145
$809$	5.89320	0.207194	0.103597	−	0.994619i	$-0.466965\pi$
$809$	5.89320	0.207194	0.103597	+	0.994619i	$0.466965\pi$
$810$	10.0991	0.354847
$811$	44.5075	1.56287	0.781435	−	0.623986i	$-0.214488\pi$
$811$	44.5075	1.56287	0.781435	+	0.623986i	$0.214488\pi$
$812$	−8.02318	−0.281558
$813$	−20.4121	−0.715884
$814$	−1.07775	−0.0377750
$815$	−20.6188	−0.722245
$816$	−1.64678	−0.0576488
$817$	0.704442	0.0246453
$818$	28.4726	0.995522
$819$	−34.4169	−1.20262
$820$	−23.9191	−0.835290
$821$	−28.0640	−0.979441	−0.489721	−	0.871879i	$-0.662901\pi$
$821$	−28.0640	−0.979441	−0.489721	+	0.871879i	$0.662901\pi$
$822$	−13.5132	−0.471325
$823$	20.8731	0.727589	0.363795	−	0.931479i	$-0.381481\pi$
$823$	20.8731	0.727589	0.363795	+	0.931479i	$0.381481\pi$
$824$	−10.6321	−0.370385
$825$	−0.00810545	−0.000282196 0
$826$	25.7860	0.897209
$827$	16.6810	0.580057	0.290028	−	0.957018i	$-0.406335\pi$
$827$	16.6810	0.580057	0.290028	+	0.957018i	$0.406335\pi$
$828$	−15.4399	−0.536575
$829$	−13.7682	−0.478190	−0.239095	−	0.970996i	$-0.576851\pi$
$829$	−13.7682	−0.478190	−0.239095	+	0.970996i	$0.576851\pi$
$830$	20.4751	0.710701
$831$	−14.3543	−0.497945
$832$	5.13120	0.177892
$833$	−0.750840	−0.0260151
$834$	13.2945	0.460350
$835$	−16.5619	−0.573148
$836$	−0.0413662	−0.00143068
$837$	−4.44069	−0.153493
$838$	−34.1972	−1.18132
$839$	−3.59376	−0.124070	−0.0620352	−	0.998074i	$-0.519759\pi$
$839$	−3.59376	−0.124070	−0.0620352	+	0.998074i	$0.519759\pi$
$840$	4.32422	0.149200
$841$	−20.2176	−0.697158
$842$	−27.6168	−0.951737
$843$	−17.3067	−0.596073
$844$	9.72412	0.334718
$845$	−29.4529	−1.01321
$846$	4.28421	0.147294
$847$	−29.7558	−1.02242
$848$	4.89772	0.168188
$849$	−10.1188	−0.347277
$850$	−0.267596	−0.00917846
$851$	70.3568	2.41180
$852$	−1.00457	−0.0344161
$853$	43.8394	1.50103	0.750517	−	0.660852i	$-0.229805\pi$
$853$	43.8394	1.50103	0.750517	+	0.660852i	$0.229805\pi$
$854$	−17.9252	−0.613386
$855$	−2.37213	−0.0811251
$856$	−7.30886	−0.249812
$857$	14.9512	0.510723	0.255361	−	0.966846i	$-0.417806\pi$
$857$	14.9512	0.510723	0.255361	+	0.966846i	$0.417806\pi$
$858$	−0.354085	−0.0120883
$859$	−3.11965	−0.106441	−0.0532206	−	0.998583i	$-0.516949\pi$
$859$	−3.11965	−0.106441	−0.0532206	+	0.998583i	$0.516949\pi$
$860$	3.59224	0.122494
$861$	21.1839	0.721945
$862$	−5.85931	−0.199569
$863$	−19.7069	−0.670832	−0.335416	−	0.942070i	$-0.608877\pi$
$863$	−19.7069	−0.670832	−0.335416	+	0.942070i	$0.608877\pi$
$864$	3.95938	0.134701
$865$	−17.1105	−0.581774
$866$	12.8382	0.436260
$867$	−8.53668	−0.289921
$868$	3.03643	0.103063
$869$	0.467759	0.0158676
$870$	−4.73342	−0.160478
$871$	35.5613	1.20495
$872$	−11.5354	−0.390639
$873$	24.2745	0.821569
$874$	2.70045	0.0913439
$875$	30.6138	1.03493
$876$	11.0308	0.372697
$877$	1.45677	0.0491916	0.0245958	−	0.999697i	$-0.492170\pi$
$877$	1.45677	0.0491916	0.0245958	+	0.999697i	$0.492170\pi$
$878$	−41.0869	−1.38661
$879$	−18.8861	−0.637011
$880$	−0.210943	−0.00711090
$881$	45.9054	1.54659	0.773297	−	0.634044i	$-0.218606\pi$
$881$	45.9054	1.54659	0.773297	+	0.634044i	$0.218606\pi$
$882$	0.816526	0.0274938
$883$	22.7903	0.766956	0.383478	−	0.923550i	$-0.374726\pi$
$883$	22.7903	0.766956	0.383478	+	0.923550i	$0.374726\pi$
$884$	−11.6899	−0.393172
$885$	15.2129	0.511376
$886$	2.79376	0.0938581
$887$	13.0221	0.437239	0.218620	−	0.975810i	$-0.429845\pi$
$887$	13.0221	0.437239	0.218620	+	0.975810i	$0.429845\pi$
$888$	−8.16052	−0.273849
$889$	−30.6169	−1.02686
$890$	−11.3861	−0.381662
$891$	0.436319	0.0146172
$892$	−17.5023	−0.586019
$893$	−0.749309	−0.0250747
$894$	−1.94295	−0.0649820
$895$	−3.63023	−0.121345
$896$	−2.70732	−0.0904452
$897$	23.1152	0.771793
$898$	9.95840	0.332316
$899$	−3.32377	−0.110854
$900$	0.291006	0.00970020
$901$	−11.1580	−0.371725
$902$	−1.03339	−0.0344081
$903$	−3.18147	−0.105873
$904$	9.89094	0.328968
$905$	3.10744	0.103295
$906$	10.4603	0.347522
$907$	27.0298	0.897511	0.448756	−	0.893655i	$-0.351867\pi$
$907$	27.0298	0.897511	0.448756	+	0.893655i	$0.351867\pi$
$908$	−12.8140	−0.425247
$909$	13.3907	0.444142
$910$	30.6960	1.01756
$911$	13.3141	0.441115	0.220557	−	0.975374i	$-0.429212\pi$
$911$	13.3141	0.441115	0.220557	+	0.975374i	$0.429212\pi$
$912$	−0.313219	−0.0103717
$913$	0.884599	0.0292759
$914$	5.49311	0.181696
$915$	−10.5753	−0.349608
$916$	−13.4292	−0.443713
$917$	15.1112	0.499014
$918$	−9.02023	−0.297712
$919$	−52.0711	−1.71767	−0.858834	−	0.512254i	$-0.828810\pi$
$919$	−52.0711	−1.71767	−0.858834	+	0.512254i	$0.828810\pi$
$920$	13.7707	0.454006
$921$	5.64949	0.186157
$922$	19.2302	0.633315
$923$	−7.13107	−0.234722
$924$	0.186822	0.00614599
$925$	−1.32606	−0.0436005
$926$	−9.97182	−0.327694
$927$	−26.3409	−0.865147
$928$	2.96351	0.0972821
$929$	21.2324	0.696613	0.348307	−	0.937381i	$-0.386757\pi$
$929$	21.2324	0.696613	0.348307	+	0.937381i	$0.386757\pi$
$930$	1.79140	0.0587422
$931$	−0.142810	−0.00468042
$932$	−12.2322	−0.400680
$933$	12.7964	0.418936
$934$	14.0167	0.458641
$935$	0.480570	0.0157163
$936$	12.7125	0.415522
$937$	−49.8748	−1.62934	−0.814669	−	0.579926i	$-0.803081\pi$
$937$	−49.8748	−1.62934	−0.814669	+	0.579926i	$0.803081\pi$
$938$	−18.7628	−0.612627
$939$	−0.557753	−0.0182016
$940$	−3.82104	−0.124628
$941$	−15.9752	−0.520775	−0.260388	−	0.965504i	$-0.583850\pi$
$941$	−15.9752	−0.520775	−0.260388	+	0.965504i	$0.583850\pi$
$942$	−9.59997	−0.312784
$943$	67.4612	2.19684
$944$	−9.52455	−0.309998
$945$	23.6859	0.770502
$946$	0.155198	0.00504592
$947$	15.5634	0.505741	0.252870	−	0.967500i	$-0.418625\pi$
$947$	15.5634	0.505741	0.252870	+	0.967500i	$0.418625\pi$
$948$	3.54180	0.115032
$949$	78.3035	2.54184
$950$	−0.0508969	−0.00165131
$951$	0.723027	0.0234458
$952$	6.16779	0.199899
$953$	−21.9246	−0.710209	−0.355104	−	0.934827i	$-0.615555\pi$
$953$	−21.9246	−0.710209	−0.355104	+	0.934827i	$0.615555\pi$
$954$	12.1341	0.392855
$955$	−43.7974	−1.41725
$956$	−15.0343	−0.486245
$957$	−0.204501	−0.00661058
$958$	−2.51841	−0.0813662
$959$	50.6117	1.63434
$960$	−1.59723	−0.0515504
$961$	−29.7421	−0.959422
$962$	−57.9284	−1.86769
$963$	−18.1077	−0.583511
$964$	26.2394	0.845115
$965$	18.4210	0.592993
$966$	−12.1960	−0.392400
$967$	30.3454	0.975843	0.487921	−	0.872888i	$-0.337755\pi$
$967$	30.3454	0.975843	0.487921	+	0.872888i	$0.337755\pi$
$968$	10.9909	0.353260
$969$	0.713572	0.0229232
$970$	−21.6502	−0.695145
$971$	−1.55791	−0.0499956	−0.0249978	−	0.999688i	$-0.507958\pi$
$971$	−1.55791	−0.0499956	−0.0249978	+	0.999688i	$0.507958\pi$
$972$	15.1819	0.486959
$973$	−49.7927	−1.59628
$974$	8.73952	0.280032
$975$	−0.435665	−0.0139525
$976$	6.62100	0.211933
$977$	−50.1870	−1.60562	−0.802812	−	0.596232i	$-0.796664\pi$
$977$	−50.1870	−1.60562	−0.802812	+	0.596232i	$0.796664\pi$
$978$	−6.74505	−0.215683
$979$	−0.491920	−0.0157218
$980$	−0.728249	−0.0232631
$981$	−28.5790	−0.912458
$982$	−19.4042	−0.619213
$983$	32.6643	1.04183	0.520915	−	0.853609i	$-0.325591\pi$
$983$	32.6643	1.04183	0.520915	+	0.853609i	$0.325591\pi$
$984$	−7.82468	−0.249442
$985$	42.5052	1.35433
$986$	−6.75145	−0.215010
$987$	3.38410	0.107717
$988$	−2.22342	−0.0707364
$989$	−10.1315	−0.322164
$990$	−0.522611	−0.0166097
$991$	−11.3590	−0.360830	−0.180415	−	0.983591i	$-0.557744\pi$
$991$	−11.3590	−0.360830	−0.180415	+	0.983591i	$0.557744\pi$
$992$	−1.12156	−0.0356097
$993$	1.61294	0.0511851
$994$	3.76249	0.119339
$995$	−31.6151	−1.00227
$996$	6.69805	0.212236
$997$	5.44346	0.172396	0.0861980	−	0.996278i	$-0.472528\pi$
$997$	5.44346	0.172396	0.0861980	+	0.996278i	$0.472528\pi$
$998$	−23.6544	−0.748769
$999$	−44.6992	−1.41422

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1226.2.a.e.1.10	✓	17
4.3	odd	2		9808.2.a.f.1.8		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1226.2.a.e.1.10	✓	17	1.1	even	1	trivial
9808.2.a.f.1.8		17	4.3	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:	\( N \)	\(=\)	\( 1226 = 2 \cdot 613 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1226.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.722845 q^{3} +1.00000 q^{4} -2.20965 q^{5} -0.722845 q^{6} +2.70732 q^{7} -1.00000 q^{8} -2.47750 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.722845 q^{3} +1.00000 q^{4} -2.20965 q^{5} -0.722845 q^{6} +2.70732 q^{7} -1.00000 q^{8} -2.47750 q^{9} +2.20965 q^{10} +0.0954648 q^{11} +0.722845 q^{12} +5.13120 q^{13} -2.70732 q^{14} -1.59723 q^{15} +1.00000 q^{16} -2.27819 q^{17} +2.47750 q^{18} -0.433314 q^{19} -2.20965 q^{20} +1.95697 q^{21} -0.0954648 q^{22} +6.23208 q^{23} -0.722845 q^{24} -0.117460 q^{25} -5.13120 q^{26} -3.95938 q^{27} +2.70732 q^{28} -2.96351 q^{29} +1.59723 q^{30} +1.12156 q^{31} -1.00000 q^{32} +0.0690062 q^{33} +2.27819 q^{34} -5.98222 q^{35} -2.47750 q^{36} +11.2895 q^{37} +0.433314 q^{38} +3.70906 q^{39} +2.20965 q^{40} +10.8248 q^{41} -1.95697 q^{42} -1.62571 q^{43} +0.0954648 q^{44} +5.47439 q^{45} -6.23208 q^{46} +1.72925 q^{47} +0.722845 q^{48} +0.329577 q^{49} +0.117460 q^{50} -1.64678 q^{51} +5.13120 q^{52} +4.89772 q^{53} +3.95938 q^{54} -0.210943 q^{55} -2.70732 q^{56} -0.313219 q^{57} +2.96351 q^{58} -9.52455 q^{59} -1.59723 q^{60} +6.62100 q^{61} -1.12156 q^{62} -6.70737 q^{63} +1.00000 q^{64} -11.3381 q^{65} -0.0690062 q^{66} +6.93040 q^{67} -2.27819 q^{68} +4.50483 q^{69} +5.98222 q^{70} -1.38975 q^{71} +2.47750 q^{72} +15.2603 q^{73} -11.2895 q^{74} -0.0849052 q^{75} -0.433314 q^{76} +0.258454 q^{77} -3.70906 q^{78} +4.89981 q^{79} -2.20965 q^{80} +4.57047 q^{81} -10.8248 q^{82} +9.26623 q^{83} +1.95697 q^{84} +5.03400 q^{85} +1.62571 q^{86} -2.14216 q^{87} -0.0954648 q^{88} -5.15290 q^{89} -5.47439 q^{90} +13.8918 q^{91} +6.23208 q^{92} +0.810716 q^{93} -1.72925 q^{94} +0.957471 q^{95} -0.722845 q^{96} -9.79802 q^{97} -0.329577 q^{98} -0.236514 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 17 q^{2} + 4 q^{3} + 17 q^{4} - 5 q^{5} - 4 q^{6} + 7 q^{7} - 17 q^{8} + 21 q^{9}+O(q^{10}) \) 17 * q - 17 * q^2 + 4 * q^3 + 17 * q^4 - 5 * q^5 - 4 * q^6 + 7 * q^7 - 17 * q^8 + 21 * q^9	\( 17 q - 17 q^{2} + 4 q^{3} + 17 q^{4} - 5 q^{5} - 4 q^{6} + 7 q^{7} - 17 q^{8} + 21 q^{9} + 5 q^{10} + 8 q^{11} + 4 q^{12} + 9 q^{13} - 7 q^{14} - 4 q^{15} + 17 q^{16} - q^{17} - 21 q^{18} + 32 q^{19} - 5 q^{20} + 6 q^{21} - 8 q^{22} - 5 q^{23} - 4 q^{24} + 30 q^{25} - 9 q^{26} + 16 q^{27} + 7 q^{28} + 3 q^{29} + 4 q^{30} + 27 q^{31} - 17 q^{32} - 14 q^{33} + q^{34} + 25 q^{35} + 21 q^{36} + 7 q^{37} - 32 q^{38} + 27 q^{39} + 5 q^{40} - 2 q^{41} - 6 q^{42} + 36 q^{43} + 8 q^{44} - q^{45} + 5 q^{46} - 3 q^{47} + 4 q^{48} + 52 q^{49} - 30 q^{50} + 40 q^{51} + 9 q^{52} - 20 q^{53} - 16 q^{54} + 48 q^{55} - 7 q^{56} + 12 q^{57} - 3 q^{58} + 34 q^{59} - 4 q^{60} + 49 q^{61} - 27 q^{62} + 27 q^{63} + 17 q^{64} - 6 q^{65} + 14 q^{66} + 36 q^{67} - q^{68} + 18 q^{69} - 25 q^{70} - q^{71} - 21 q^{72} + 24 q^{73} - 7 q^{74} + 35 q^{75} + 32 q^{76} - 6 q^{77} - 27 q^{78} + 43 q^{79} - 5 q^{80} + 37 q^{81} + 2 q^{82} + 10 q^{83} + 6 q^{84} + 16 q^{85} - 36 q^{86} + 28 q^{87} - 8 q^{88} - 12 q^{89} + q^{90} + 42 q^{91} - 5 q^{92} + 3 q^{93} + 3 q^{94} - 10 q^{95} - 4 q^{96} + 26 q^{97} - 52 q^{98} + 34 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 4 * q^3 + 17 * q^4 - 5 * q^5 - 4 * q^6 + 7 * q^7 - 17 * q^8 + 21 * q^9 + 5 * q^10 + 8 * q^11 + 4 * q^12 + 9 * q^13 - 7 * q^14 - 4 * q^15 + 17 * q^16 - q^17 - 21 * q^18 + 32 * q^19 - 5 * q^20 + 6 * q^21 - 8 * q^22 - 5 * q^23 - 4 * q^24 + 30 * q^25 - 9 * q^26 + 16 * q^27 + 7 * q^28 + 3 * q^29 + 4 * q^30 + 27 * q^31 - 17 * q^32 - 14 * q^33 + q^34 + 25 * q^35 + 21 * q^36 + 7 * q^37 - 32 * q^38 + 27 * q^39 + 5 * q^40 - 2 * q^41 - 6 * q^42 + 36 * q^43 + 8 * q^44 - q^45 + 5 * q^46 - 3 * q^47 + 4 * q^48 + 52 * q^49 - 30 * q^50 + 40 * q^51 + 9 * q^52 - 20 * q^53 - 16 * q^54 + 48 * q^55 - 7 * q^56 + 12 * q^57 - 3 * q^58 + 34 * q^59 - 4 * q^60 + 49 * q^61 - 27 * q^62 + 27 * q^63 + 17 * q^64 - 6 * q^65 + 14 * q^66 + 36 * q^67 - q^68 + 18 * q^69 - 25 * q^70 - q^71 - 21 * q^72 + 24 * q^73 - 7 * q^74 + 35 * q^75 + 32 * q^76 - 6 * q^77 - 27 * q^78 + 43 * q^79 - 5 * q^80 + 37 * q^81 + 2 * q^82 + 10 * q^83 + 6 * q^84 + 16 * q^85 - 36 * q^86 + 28 * q^87 - 8 * q^88 - 12 * q^89 + q^90 + 42 * q^91 - 5 * q^92 + 3 * q^93 + 3 * q^94 - 10 * q^95 - 4 * q^96 + 26 * q^97 - 52 * q^98 + 34 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more