LMFDB - Embedded newform 1183.2.c.j.337.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(337,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("1183.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.c (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			337.4
Character	$\chi$	$=$	1183.337
Dual form			1183.2.c.j.337.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.23724i q^{2} +3.02592 q^{3} -3.00523 q^{4} +3.28547i q^{5} -6.76971i q^{6} +1.00000i q^{7} +2.24893i q^{8} +6.15622 q^{9} +O(q^{10})$	\(q-2.23724i q^{2} +3.02592 q^{3} -3.00523 q^{4} +3.28547i q^{5} -6.76971i q^{6} +1.00000i q^{7} +2.24893i q^{8} +6.15622 q^{9} +7.35037 q^{10} +3.69978i q^{11} -9.09359 q^{12} +2.23724 q^{14} +9.94158i q^{15} -0.979066 q^{16} -0.705252 q^{17} -13.7729i q^{18} -0.911595i q^{19} -9.87358i q^{20} +3.02592i q^{21} +8.27729 q^{22} +3.01033 q^{23} +6.80509i q^{24} -5.79431 q^{25} +9.55048 q^{27} -3.00523i q^{28} +6.55076 q^{29} +22.2417 q^{30} +9.55811i q^{31} +6.68826i q^{32} +11.1953i q^{33} +1.57782i q^{34} -3.28547 q^{35} -18.5008 q^{36} -7.26452i q^{37} -2.03945 q^{38} -7.38879 q^{40} -0.884807i q^{41} +6.76971 q^{42} -0.536043 q^{43} -11.1187i q^{44} +20.2261i q^{45} -6.73483i q^{46} -11.4085i q^{47} -2.96258 q^{48} -1.00000 q^{49} +12.9633i q^{50} -2.13404 q^{51} +3.77189 q^{53} -21.3667i q^{54} -12.1555 q^{55} -2.24893 q^{56} -2.75842i q^{57} -14.6556i q^{58} -7.40281i q^{59} -29.8767i q^{60} -1.81991 q^{61} +21.3838 q^{62} +6.15622i q^{63} +13.0051 q^{64} +25.0465 q^{66} -6.41024i q^{67} +2.11944 q^{68} +9.10904 q^{69} +7.35037i q^{70} -10.7248i q^{71} +13.8449i q^{72} +9.72504i q^{73} -16.2524 q^{74} -17.5332 q^{75} +2.73955i q^{76} -3.69978 q^{77} -7.00757 q^{79} -3.21669i q^{80} +10.4304 q^{81} -1.97952 q^{82} +2.31514i q^{83} -9.09359i q^{84} -2.31709i q^{85} +1.19925i q^{86} +19.8221 q^{87} -8.32055 q^{88} -2.23203i q^{89} +45.2505 q^{90} -9.04673 q^{92} +28.9221i q^{93} -25.5235 q^{94} +2.99502 q^{95} +20.2382i q^{96} -8.79590i q^{97} +2.23724i q^{98} +22.7767i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 16 q^{3} - 30 q^{4} + 52 q^{9}+O(q^{10}) $ 24 * q + 16 * q^3 - 30 * q^4 + 52 * q^9	$ 24 q + 16 q^{3} - 30 q^{4} + 52 q^{9} + 12 q^{10} - 26 q^{12} + 6 q^{14} + 26 q^{16} - 62 q^{17} - 8 q^{22} - 36 q^{23} - 64 q^{25} + 64 q^{27} + 30 q^{29} + 20 q^{30} - 8 q^{35} - 98 q^{36} - 90 q^{38} - 40 q^{40} + 4 q^{42} + 44 q^{43} + 22 q^{48} - 24 q^{49} - 36 q^{51} + 106 q^{53} - 52 q^{55} - 24 q^{56} + 44 q^{61} - 38 q^{62} - 4 q^{64} - 68 q^{66} + 68 q^{68} - 6 q^{69} - 80 q^{74} - 30 q^{75} - 24 q^{77} + 4 q^{79} + 72 q^{81} + 64 q^{82} + 54 q^{87} + 96 q^{88} + 52 q^{90} + 104 q^{92} - 88 q^{94} - 58 q^{95}+O(q^{100}) $ 24 * q + 16 * q^3 - 30 * q^4 + 52 * q^9 + 12 * q^10 - 26 * q^12 + 6 * q^14 + 26 * q^16 - 62 * q^17 - 8 * q^22 - 36 * q^23 - 64 * q^25 + 64 * q^27 + 30 * q^29 + 20 * q^30 - 8 * q^35 - 98 * q^36 - 90 * q^38 - 40 * q^40 + 4 * q^42 + 44 * q^43 + 22 * q^48 - 24 * q^49 - 36 * q^51 + 106 * q^53 - 52 * q^55 - 24 * q^56 + 44 * q^61 - 38 * q^62 - 4 * q^64 - 68 * q^66 + 68 * q^68 - 6 * q^69 - 80 * q^74 - 30 * q^75 - 24 * q^77 + 4 * q^79 + 72 * q^81 + 64 * q^82 + 54 * q^87 + 96 * q^88 + 52 * q^90 + 104 * q^92 - 88 * q^94 - 58 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$	− 2.23724i	− 1.58197i	−0.611839	−	0.790983i	$-0.709570\pi$
$2$	− 2.23724i	− 1.58197i	0.611839	−	0.790983i	$-0.290430\pi$
$3$	3.02592	1.74702	0.873509	−	0.486808i	$-0.161839\pi$
$3$	3.02592	1.74702	0.873509	+	0.486808i	$0.161839\pi$
$4$	−3.00523	−1.50261
$5$	3.28547i	1.46931i	0.678443	+	0.734653i	$0.262655\pi$
$5$	3.28547i	1.46931i	−0.678443	+	0.734653i	$0.737345\pi$
$6$	− 6.76971i	− 2.76372i
$7$	1.00000i	0.377964i
$7$	1.00000i	0.377964i
$8$	2.24893i	0.795117i
$9$	6.15622	2.05207
$10$	7.35037	2.32439
$11$	3.69978i	1.11553i	0.830000	+	0.557763i	$0.188340\pi$
$11$	3.69978i	1.11553i	−0.830000	+	0.557763i	$0.811660\pi$
$12$	−9.09359	−2.62509
$13$	0	0
$13$	0	0
$14$	2.23724	0.597927
$15$	9.94158i	2.56691i
$16$	−0.979066	−0.244766
$17$	−0.705252	−0.171049	−0.0855244	−	0.996336i	$-0.527257\pi$
$17$	−0.705252	−0.171049	−0.0855244	+	0.996336i	$0.527257\pi$
$18$	− 13.7729i	− 3.24631i
$19$	− 0.911595i	− 0.209134i	−0.994518	−	0.104567i	$-0.966654\pi$
$19$	− 0.911595i	− 0.209134i	0.994518	−	0.104567i	$-0.0333457\pi$
$20$	− 9.87358i	− 2.20780i
$21$	3.02592i	0.660311i
$22$	8.27729	1.76472
$23$	3.01033	0.627698	0.313849	−	0.949473i	$-0.398381\pi$
$23$	3.01033	0.627698	0.313849	+	0.949473i	$0.398381\pi$
$24$	6.80509i	1.38908i
$25$	−5.79431	−1.15886
$26$	0	0
$27$	9.55048	1.83799
$28$	− 3.00523i	− 0.567934i
$29$	6.55076	1.21645	0.608223	−	0.793767i	$-0.291883\pi$
$29$	6.55076	1.21645	0.608223	+	0.793767i	$0.291883\pi$
$30$	22.2417	4.06076
$31$	9.55811i	1.71669i	0.513075	+	0.858344i	$0.328506\pi$
$31$	9.55811i	1.71669i	−0.513075	+	0.858344i	$0.671494\pi$
$32$	6.68826i	1.18233i
$33$	11.1953i	1.94885i
$34$	1.57782i	0.270593i
$35$	−3.28547	−0.555346
$36$	−18.5008	−3.08347
$37$	− 7.26452i	− 1.19428i	−0.802137	−	0.597140i	$-0.796304\pi$
$37$	− 7.26452i	− 1.19428i	0.802137	−	0.597140i	$-0.203696\pi$
$38$	−2.03945	−0.330843
$39$	0	0
$40$	−7.38879	−1.16827
$41$	− 0.884807i	− 0.138184i	−0.997610	−	0.0690918i	$-0.977990\pi$
$41$	− 0.884807i	− 0.138184i	0.997610	−	0.0690918i	$-0.0220101\pi$
$42$	6.76971	1.04459
$43$	−0.536043	−0.0817458	−0.0408729	−	0.999164i	$-0.513014\pi$
$43$	−0.536043	−0.0817458	−0.0408729	+	0.999164i	$0.513014\pi$
$44$	− 11.1187i	− 1.67621i
$45$	20.2261i	3.01512i
$46$	− 6.73483i	− 0.992996i
$47$	− 11.4085i	− 1.66410i	−0.554700	−	0.832050i	$-0.687167\pi$
$47$	− 11.4085i	− 1.66410i	0.554700	−	0.832050i	$-0.312833\pi$
$48$	−2.96258	−0.427611
$49$	−1.00000	−0.142857
$50$	12.9633i	1.83328i
$51$	−2.13404	−0.298825
$52$	0	0
$53$	3.77189	0.518109	0.259054	−	0.965863i	$-0.416589\pi$
$53$	3.77189	0.518109	0.259054	+	0.965863i	$0.416589\pi$
$54$	− 21.3667i	− 2.90764i
$55$	−12.1555	−1.63905
$56$	−2.24893	−0.300526
$57$	− 2.75842i	− 0.365361i
$58$	− 14.6556i	− 1.92437i
$59$	− 7.40281i	− 0.963764i	−0.876236	−	0.481882i	$-0.839953\pi$
$59$	− 7.40281i	− 0.963764i	0.876236	−	0.481882i	$-0.160047\pi$
$60$	− 29.8767i	− 3.85707i
$61$	−1.81991	−0.233015	−0.116508	−	0.993190i	$-0.537170\pi$
$61$	−1.81991	−0.233015	−0.116508	+	0.993190i	$0.537170\pi$
$62$	21.3838	2.71574
$63$	6.15622i	0.775611i
$64$	13.0051	1.62564
$65$	0	0
$66$	25.0465	3.08301
$67$	− 6.41024i	− 0.783135i	−0.920149	−	0.391568i	$-0.871933\pi$
$67$	− 6.41024i	− 0.783135i	0.920149	−	0.391568i	$-0.128067\pi$
$68$	2.11944	0.257020
$69$	9.10904	1.09660
$70$	7.35037i	0.878538i
$71$	− 10.7248i	− 1.27280i	−0.771357	−	0.636402i	$-0.780422\pi$
$71$	− 10.7248i	− 1.27280i	0.771357	−	0.636402i	$-0.219578\pi$
$72$	13.8449i	1.63164i
$73$	9.72504i	1.13823i	0.822258	+	0.569115i	$0.192714\pi$
$73$	9.72504i	1.13823i	−0.822258	+	0.569115i	$0.807286\pi$
$74$	−16.2524	−1.88931
$75$	−17.5332	−2.02455
$76$	2.73955i	0.314248i
$77$	−3.69978	−0.421630
$78$	0	0
$79$	−7.00757	−0.788414	−0.394207	−	0.919022i	$-0.628981\pi$
$79$	−7.00757	−0.788414	−0.394207	+	0.919022i	$0.628981\pi$
$80$	− 3.21669i	− 0.359637i
$81$	10.4304	1.15893
$82$	−1.97952	−0.218602
$83$	2.31514i	0.254120i	0.991895	+	0.127060i	$0.0405540\pi$
$83$	2.31514i	0.254120i	−0.991895	+	0.127060i	$0.959446\pi$
$84$	− 9.09359i	− 0.992192i
$85$	− 2.31709i	− 0.251323i
$86$	1.19925i	0.129319i
$87$	19.8221	2.12515
$88$	−8.32055	−0.886974
$89$	− 2.23203i	− 0.236595i	−0.992978	−	0.118297i	$-0.962256\pi$
$89$	− 2.23203i	− 0.236595i	0.992978	−	0.118297i	$-0.0377436\pi$
$90$	45.2505	4.76982
$91$	0	0
$92$	−9.04673	−0.943187
$93$	28.9221i	2.99908i
$94$	−25.5235	−2.63255
$95$	2.99502	0.307283
$96$	20.2382i	2.06555i
$97$	− 8.79590i	− 0.893088i	−0.894762	−	0.446544i	$-0.852655\pi$
$97$	− 8.79590i	− 0.893088i	0.894762	−	0.446544i	$-0.147345\pi$
$98$	2.23724i	0.225995i
$99$	22.7767i	2.28914i
$100$	17.4132	1.74132
$101$	−8.54632	−0.850391	−0.425195	−	0.905102i	$-0.639795\pi$
$101$	−8.54632	−0.850391	−0.425195	+	0.905102i	$0.639795\pi$
$102$	4.77435i	0.472731i
$103$	13.7298	1.35284	0.676420	−	0.736516i	$-0.263531\pi$
$103$	13.7298	1.35284	0.676420	+	0.736516i	$0.263531\pi$
$104$	0	0
$105$	−9.94158	−0.970199
$106$	− 8.43860i	− 0.819630i
$107$	−17.4965	−1.69145	−0.845725	−	0.533620i	$-0.820831\pi$
$107$	−17.4965	−1.69145	−0.845725	+	0.533620i	$0.820831\pi$
$108$	−28.7013	−2.76179
$109$	− 6.94941i	− 0.665633i	−0.942992	−	0.332816i	$-0.892001\pi$
$109$	− 6.94941i	− 0.665633i	0.942992	−	0.332816i	$-0.107999\pi$
$110$	27.1948i	2.59292i
$111$	− 21.9819i	− 2.08643i
$112$	− 0.979066i	− 0.0925130i
$113$	−2.83036	−0.266258	−0.133129	−	0.991099i	$-0.542502\pi$
$113$	−2.83036	−0.266258	−0.133129	+	0.991099i	$0.542502\pi$
$114$	−6.17123	−0.577989
$115$	9.89036i	0.922281i
$116$	−19.6865	−1.82785
$117$	0	0
$118$	−16.5618	−1.52464
$119$	− 0.705252i	− 0.0646504i
$120$	−22.3579	−2.04099
$121$	−2.68840	−0.244400
$122$	4.07156i	0.368622i
$123$	− 2.67736i	− 0.241409i
$124$	− 28.7243i	− 2.57952i
$125$	− 2.60969i	− 0.233418i
$126$	13.7729	1.22699
$127$	−3.59346	−0.318868	−0.159434	−	0.987209i	$-0.550967\pi$
$127$	−3.59346	−0.318868	−0.159434	+	0.987209i	$0.550967\pi$
$128$	− 15.7189i	− 1.38937i
$129$	−1.62202	−0.142811
$130$	0	0
$131$	1.05865	0.0924943	0.0462471	−	0.998930i	$-0.485274\pi$
$131$	1.05865	0.0924943	0.0462471	+	0.998930i	$0.485274\pi$
$132$	− 33.6443i	− 2.92836i
$133$	0.911595	0.0790454
$134$	−14.3412	−1.23889
$135$	31.3778i	2.70057i
$136$	− 1.58606i	− 0.136004i
$137$	− 8.29848i	− 0.708987i	−0.935058	−	0.354494i	$-0.884653\pi$
$137$	− 8.29848i	− 0.708987i	0.935058	−	0.354494i	$-0.115347\pi$
$138$	− 20.3791i	− 1.73478i
$139$	−7.02640	−0.595971	−0.297986	−	0.954570i	$-0.596315\pi$
$139$	−7.02640	−0.595971	−0.297986	+	0.954570i	$0.596315\pi$
$140$	9.87358	0.834470
$141$	− 34.5213i	− 2.90721i
$142$	−23.9940	−2.01353
$143$	0	0
$144$	−6.02734	−0.502278
$145$	21.5223i	1.78733i
$146$	21.7572	1.80064
$147$	−3.02592	−0.249574
$148$	21.8315i	1.79454i
$149$	7.93264i	0.649867i	0.945737	+	0.324934i	$0.105342\pi$
$149$	7.93264i	0.649867i	−0.945737	+	0.324934i	$0.894658\pi$
$150$	39.2258i	3.20277i
$151$	21.1019i	1.71725i	0.512604	+	0.858625i	$0.328681\pi$
$151$	21.1019i	1.71725i	−0.512604	+	0.858625i	$0.671319\pi$
$152$	2.05011	0.166286
$153$	−4.34169	−0.351005
$154$	8.27729i	0.667003i
$155$	−31.4029	−2.52234
$156$	0	0
$157$	4.49489	0.358732	0.179366	−	0.983782i	$-0.442595\pi$
$157$	4.49489	0.358732	0.179366	+	0.983782i	$0.442595\pi$
$158$	15.6776i	1.24724i
$159$	11.4134	0.905145
$160$	−21.9741	−1.73720
$161$	3.01033i	0.237247i
$162$	− 23.3352i	− 1.83339i
$163$	2.10111i	0.164572i	0.996609	+	0.0822860i	$0.0262221\pi$
$163$	2.10111i	0.164572i	−0.996609	+	0.0822860i	$0.973778\pi$
$164$	2.65904i	0.207637i
$165$	−36.7817	−2.86345
$166$	5.17951	0.402008
$167$	12.6092i	0.975727i	0.872920	+	0.487863i	$0.162224\pi$
$167$	12.6092i	0.975727i	−0.872920	+	0.487863i	$0.837776\pi$
$168$	−6.80509	−0.525024
$169$	0	0
$170$	−5.18387	−0.397584
$171$	− 5.61198i	− 0.429159i
$172$	1.61093	0.122832
$173$	−3.96895	−0.301754	−0.150877	−	0.988553i	$-0.548210\pi$
$173$	−3.96895	−0.301754	−0.150877	+	0.988553i	$0.548210\pi$
$174$	− 44.3467i	− 3.36192i
$175$	− 5.79431i	− 0.438009i
$176$	− 3.62233i	− 0.273044i
$177$	− 22.4003i	− 1.68371i
$178$	−4.99357	−0.374284
$179$	−23.6790	−1.76985	−0.884926	−	0.465731i	$-0.845791\pi$
$179$	−23.6790	−1.76985	−0.884926	+	0.465731i	$0.845791\pi$
$180$	− 60.7839i	− 4.53057i
$181$	24.6397	1.83145	0.915727	−	0.401801i	$-0.131616\pi$
$181$	24.6397	1.83145	0.915727	+	0.401801i	$0.131616\pi$
$182$	0	0
$183$	−5.50690	−0.407082
$184$	6.77003i	0.499093i
$185$	23.8674	1.75476
$186$	64.7056	4.74445
$187$	− 2.60928i	− 0.190810i
$188$	34.2851i	2.50050i
$189$	9.55048i	0.694695i
$190$	− 6.70057i	− 0.486110i
$191$	2.98048	0.215660	0.107830	−	0.994169i	$-0.465610\pi$
$191$	2.98048	0.215660	0.107830	+	0.994169i	$0.465610\pi$
$192$	39.3524	2.84002
$193$	− 17.5119i	− 1.26053i	−0.776379	−	0.630266i	$-0.782946\pi$
$193$	− 17.5119i	− 1.26053i	0.776379	−	0.630266i	$-0.217054\pi$
$194$	−19.6785	−1.41283
$195$	0	0
$196$	3.00523	0.214659
$197$	− 19.6212i	− 1.39795i	−0.715145	−	0.698976i	$-0.753639\pi$
$197$	− 19.6212i	− 1.39795i	0.715145	−	0.698976i	$-0.246361\pi$
$198$	50.9568	3.62134
$199$	24.8307	1.76020	0.880102	−	0.474784i	$-0.157474\pi$
$199$	24.8307	1.76020	0.880102	+	0.474784i	$0.157474\pi$
$200$	− 13.0310i	− 0.921431i
$201$	− 19.3969i	− 1.36815i
$202$	19.1201i	1.34529i
$203$	6.55076i	0.459773i
$204$	6.41327	0.449019
$205$	2.90701	0.203034
$206$	− 30.7169i	− 2.14014i
$207$	18.5323	1.28808
$208$	0	0
$209$	3.37271	0.233295
$210$	22.2417i	1.53482i
$211$	−1.39982	−0.0963674	−0.0481837	−	0.998838i	$-0.515343\pi$
$211$	−1.39982	−0.0963674	−0.0481837	+	0.998838i	$0.515343\pi$
$212$	−11.3354	−0.778517
$213$	− 32.4526i	− 2.22361i
$214$	39.1438i	2.67581i
$215$	− 1.76115i	− 0.120110i
$216$	21.4783i	1.46142i
$217$	−9.55811	−0.648847
$218$	−15.5475	−1.05301
$219$	29.4272i	1.98851i
$220$	36.5301	2.46286
$221$	0	0
$222$	−49.1787	−3.30066
$223$	− 9.68552i	− 0.648591i	−0.945956	−	0.324295i	$-0.894873\pi$
$223$	− 9.68552i	− 0.648591i	0.945956	−	0.324295i	$-0.105127\pi$
$224$	−6.68826	−0.446878
$225$	−35.6711	−2.37807
$226$	6.33219i	0.421211i
$227$	− 23.2669i	− 1.54428i	−0.635454	−	0.772139i	$-0.719187\pi$
$227$	− 23.2669i	− 1.54428i	0.635454	−	0.772139i	$-0.280813\pi$
$228$	8.28967i	0.548997i
$229$	20.5801i	1.35997i	0.733224	+	0.679987i	$0.238015\pi$
$229$	20.5801i	1.35997i	−0.733224	+	0.679987i	$0.761985\pi$
$230$	22.1271	1.45902
$231$	−11.1953	−0.736594
$232$	14.7322i	0.967216i
$233$	−27.2955	−1.78819	−0.894094	−	0.447880i	$-0.852179\pi$
$233$	−27.2955	−1.78819	−0.894094	+	0.447880i	$0.852179\pi$
$234$	0	0
$235$	37.4823	2.44507
$236$	22.2471i	1.44816i
$237$	−21.2044	−1.37737
$238$	−1.57782	−0.102275
$239$	− 22.9752i	− 1.48614i	−0.669214	−	0.743070i	$-0.733369\pi$
$239$	− 22.9752i	− 1.48614i	0.669214	−	0.743070i	$-0.266631\pi$
$240$	− 9.73346i	− 0.628292i
$241$	− 10.7263i	− 0.690939i	−0.938430	−	0.345469i	$-0.887720\pi$
$241$	− 10.7263i	− 0.690939i	0.938430	−	0.345469i	$-0.112280\pi$
$242$	6.01459i	0.386633i
$243$	2.91006	0.186680
$244$	5.46923	0.350132
$245$	− 3.28547i	− 0.209901i
$246$	−5.98988	−0.381901
$247$	0	0
$248$	−21.4955	−1.36497
$249$	7.00544i	0.443951i
$250$	−5.83850	−0.369259
$251$	−7.34076	−0.463345	−0.231672	−	0.972794i	$-0.574420\pi$
$251$	−7.34076	−0.463345	−0.231672	+	0.972794i	$0.574420\pi$
$252$	− 18.5008i	− 1.16544i
$253$	11.1376i	0.700214i
$254$	8.03942i	0.504438i
$255$	− 7.01132i	− 0.439066i
$256$	−9.15680	−0.572300
$257$	−14.9907	−0.935092	−0.467546	−	0.883969i	$-0.654862\pi$
$257$	−14.9907	−0.935092	−0.467546	+	0.883969i	$0.654862\pi$
$258$	3.62885i	0.225923i
$259$	7.26452	0.451395
$260$	0	0
$261$	40.3279	2.49623
$262$	− 2.36844i	− 0.146323i
$263$	8.05245	0.496535	0.248268	−	0.968692i	$-0.420139\pi$
$263$	8.05245	0.496535	0.248268	+	0.968692i	$0.420139\pi$
$264$	−25.1774	−1.54956
$265$	12.3924i	0.761261i
$266$	− 2.03945i	− 0.125047i
$267$	− 6.75395i	− 0.413335i
$268$	19.2642i	1.17675i
$269$	−2.52431	−0.153910	−0.0769549	−	0.997035i	$-0.524520\pi$
$269$	−2.52431	−0.153910	−0.0769549	+	0.997035i	$0.524520\pi$
$270$	70.1996	4.27221
$271$	− 0.785036i	− 0.0476875i	−0.999716	−	0.0238438i	$-0.992410\pi$
$271$	− 0.785036i	− 0.0476875i	0.999716	−	0.0238438i	$-0.00759042\pi$
$272$	0.690488	0.0418670
$273$	0	0
$274$	−18.5657	−1.12159
$275$	− 21.4377i	− 1.29274i
$276$	−27.3747	−1.64777
$277$	−21.4193	−1.28696	−0.643482	−	0.765462i	$-0.722511\pi$
$277$	−21.4193	−1.28696	−0.643482	+	0.765462i	$0.722511\pi$
$278$	15.7197i	0.942806i
$279$	58.8418i	3.52277i
$280$	− 7.38879i	− 0.441565i
$281$	22.3710i	1.33454i	0.744816	+	0.667270i	$0.232537\pi$
$281$	22.3710i	1.33454i	−0.744816	+	0.667270i	$0.767463\pi$
$282$	−77.2322	−4.59911
$283$	24.8797	1.47895	0.739473	−	0.673186i	$-0.235075\pi$
$283$	24.8797	1.47895	0.739473	+	0.673186i	$0.235075\pi$
$284$	32.2306i	1.91253i
$285$	9.06270	0.536828
$286$	0	0
$287$	0.884807	0.0522285
$288$	41.1744i	2.42622i
$289$	−16.5026	−0.970742
$290$	48.1505	2.82750
$291$	− 26.6157i	− 1.56024i
$292$	− 29.2259i	− 1.71032i
$293$	11.7686i	0.687528i	0.939056	+	0.343764i	$0.111702\pi$
$293$	11.7686i	0.687528i	−0.939056	+	0.343764i	$0.888298\pi$
$294$	6.76971i	0.394817i
$295$	24.3217	1.41607
$296$	16.3374	0.949591
$297$	35.3347i	2.05033i
$298$	17.7472	1.02807
$299$	0	0
$300$	52.6911	3.04212
$301$	− 0.536043i	− 0.0308970i
$302$	47.2100	2.71663
$303$	−25.8605	−1.48565
$304$	0.892512i	0.0511891i
$305$	− 5.97925i	− 0.342371i
$306$	9.71338i	0.555277i
$307$	20.3861i	1.16350i	0.813368	+	0.581749i	$0.197631\pi$
$307$	20.3861i	1.16350i	−0.813368	+	0.581749i	$0.802369\pi$
$308$	11.1187	0.633546
$309$	41.5454	2.36344
$310$	70.2557i	3.99026i
$311$	11.6036	0.657979	0.328990	−	0.944334i	$-0.393292\pi$
$311$	11.6036	0.657979	0.328990	+	0.944334i	$0.393292\pi$
$312$	0	0
$313$	6.91958	0.391118	0.195559	−	0.980692i	$-0.437348\pi$
$313$	6.91958	0.391118	0.195559	+	0.980692i	$0.437348\pi$
$314$	− 10.0561i	− 0.567501i
$315$	−20.2261	−1.13961
$316$	21.0593	1.18468
$317$	− 21.6606i	− 1.21658i	−0.793715	−	0.608290i	$-0.791856\pi$
$317$	− 21.6606i	− 1.21658i	0.793715	−	0.608290i	$-0.208144\pi$
$318$	− 25.5346i	− 1.43191i
$319$	24.2364i	1.35698i
$320$	42.7278i	2.38856i
$321$	−52.9430	−2.95499
$322$	6.73483	0.375317
$323$	0.642905i	0.0357722i
$324$	−31.3456	−1.74142
$325$	0	0
$326$	4.70069	0.260347
$327$	− 21.0284i	− 1.16287i
$328$	1.98987	0.109872
$329$	11.4085	0.628971
$330$	82.2894i	4.52988i
$331$	23.6068i	1.29755i	0.760981	+	0.648774i	$0.224718\pi$
$331$	23.6068i	1.29755i	−0.760981	+	0.648774i	$0.775282\pi$
$332$	− 6.95752i	− 0.381843i
$333$	− 44.7219i	− 2.45075i
$334$	28.2097	1.54357
$335$	21.0607	1.15067
$336$	− 2.96258i	− 0.161622i
$337$	3.99359	0.217544	0.108772	−	0.994067i	$-0.465308\pi$
$337$	3.99359	0.217544	0.108772	+	0.994067i	$0.465308\pi$
$338$	0	0
$339$	−8.56446	−0.465158
$340$	6.96337i	0.377642i
$341$	−35.3630	−1.91501
$342$	−12.5553	−0.678914
$343$	− 1.00000i	− 0.0539949i
$344$	− 1.20552i	− 0.0649974i
$345$	29.9275i	1.61124i
$346$	8.87948i	0.477364i
$347$	28.5043	1.53019	0.765095	−	0.643917i	$-0.222692\pi$
$347$	28.5043	1.53019	0.765095	+	0.643917i	$0.222692\pi$
$348$	−59.5699	−3.19328
$349$	− 3.99439i	− 0.213815i	−0.994269	−	0.106907i	$-0.965905\pi$
$349$	− 3.99439i	− 0.213815i	0.994269	−	0.106907i	$-0.0340948\pi$
$350$	−12.9633	−0.692915
$351$	0	0
$352$	−24.7451	−1.31892
$353$	24.1725i	1.28657i	0.765627	+	0.643285i	$0.222429\pi$
$353$	24.1725i	1.28657i	−0.765627	+	0.643285i	$0.777571\pi$
$354$	−50.1149	−2.66358
$355$	35.2361	1.87014
$356$	6.70775i	0.355510i
$357$	− 2.13404i	− 0.112945i
$358$	52.9755i	2.79984i
$359$	− 13.5039i	− 0.712709i	−0.934351	−	0.356355i	$-0.884019\pi$
$359$	− 13.5039i	− 0.712709i	0.934351	−	0.356355i	$-0.115981\pi$
$360$	−45.4870	−2.39738
$361$	18.1690	0.956263
$362$	− 55.1248i	− 2.89730i
$363$	−8.13490	−0.426972
$364$	0	0
$365$	−31.9513	−1.67241
$366$	12.3202i	0.643989i
$367$	15.9888	0.834611	0.417306	−	0.908766i	$-0.362975\pi$
$367$	15.9888	0.834611	0.417306	+	0.908766i	$0.362975\pi$
$368$	−2.94731	−0.153639
$369$	− 5.44706i	− 0.283563i
$370$	− 53.3969i	− 2.77597i
$371$	3.77189i	0.195827i
$372$	− 86.9176i	− 4.50647i
$373$	24.5970	1.27358	0.636791	−	0.771036i	$-0.280261\pi$
$373$	24.5970	1.27358	0.636791	+	0.771036i	$0.280261\pi$
$374$	−5.83758	−0.301854
$375$	− 7.89674i	− 0.407786i
$376$	25.6569	1.32315
$377$	0	0
$378$	21.3667	1.09898
$379$	8.07743i	0.414910i	0.978245	+	0.207455i	$0.0665180\pi$
$379$	8.07743i	0.414910i	−0.978245	+	0.207455i	$0.933482\pi$
$380$	−9.00071	−0.461727
$381$	−10.8735	−0.557068
$382$	− 6.66804i	− 0.341167i
$383$	− 3.45536i	− 0.176561i	−0.996096	−	0.0882803i	$-0.971863\pi$
$383$	− 3.45536i	− 0.176561i	0.996096	−	0.0882803i	$-0.0281371\pi$
$384$	− 47.5643i	− 2.42726i
$385$	− 12.1555i	− 0.619503i
$386$	−39.1782	−1.99412
$387$	−3.30000	−0.167748
$388$	26.4337i	1.34197i
$389$	23.6133	1.19724	0.598620	−	0.801033i	$-0.295716\pi$
$389$	23.6133	1.19724	0.598620	+	0.801033i	$0.295716\pi$
$390$	0	0
$391$	−2.12304	−0.107367
$392$	− 2.24893i	− 0.113588i
$393$	3.20338	0.161589
$394$	−43.8972	−2.21151
$395$	− 23.0232i	− 1.15842i
$396$	− 68.4491i	− 3.43970i
$397$	− 5.84404i	− 0.293304i	−0.989188	−	0.146652i	$-0.953150\pi$
$397$	− 5.84404i	− 0.293304i	0.989188	−	0.146652i	$-0.0468498\pi$
$398$	− 55.5522i	− 2.78458i
$399$	2.75842	0.138094
$400$	5.67301	0.283651
$401$	− 25.0841i	− 1.25264i	−0.779566	−	0.626320i	$-0.784560\pi$
$401$	− 25.0841i	− 1.25264i	0.779566	−	0.626320i	$-0.215440\pi$
$402$	−43.3955	−2.16437
$403$	0	0
$404$	25.6836	1.27781
$405$	34.2686i	1.70282i
$406$	14.6556	0.727345
$407$	26.8771	1.33225
$408$	− 4.79931i	− 0.237601i
$409$	− 0.157493i	− 0.00778752i	−0.999992	−	0.00389376i	$-0.998761\pi$
$409$	− 0.157493i	− 0.00778752i	0.999992	−	0.00389376i	$-0.00123943\pi$
$410$	− 6.50366i	− 0.321193i
$411$	− 25.1106i	− 1.23861i
$412$	−41.2612	−2.03279
$413$	7.40281	0.364269
$414$	− 41.4611i	− 2.03770i
$415$	−7.60632	−0.373380
$416$	0	0
$417$	−21.2614	−1.04117
$418$	− 7.54554i	− 0.369064i
$419$	−6.94332	−0.339203	−0.169602	−	0.985513i	$-0.554248\pi$
$419$	−6.94332	−0.339203	−0.169602	+	0.985513i	$0.554248\pi$
$420$	29.8767	1.45783
$421$	18.2428i	0.889100i	0.895754	+	0.444550i	$0.146636\pi$
$421$	18.2428i	0.889100i	−0.895754	+	0.444550i	$0.853364\pi$
$422$	3.13172i	0.152450i
$423$	− 70.2332i	− 3.41486i
$424$	8.48271i	0.411957i
$425$	4.08645	0.198222
$426$	−72.6040	−3.51768
$427$	− 1.81991i	− 0.0880715i
$428$	52.5809	2.54159
$429$	0	0
$430$	−3.94011	−0.190009
$431$	24.6803i	1.18881i	0.804167	+	0.594404i	$0.202612\pi$
$431$	24.6803i	1.18881i	−0.804167	+	0.594404i	$0.797388\pi$
$432$	−9.35054	−0.449878
$433$	8.18788	0.393485	0.196742	−	0.980455i	$-0.436964\pi$
$433$	8.18788	0.393485	0.196742	+	0.980455i	$0.436964\pi$
$434$	21.3838i	1.02645i
$435$	65.1249i	3.12250i
$436$	20.8846i	1.00019i
$437$	− 2.74421i	− 0.131273i
$438$	65.8357	3.14575
$439$	−28.8065	−1.37486	−0.687429	−	0.726252i	$-0.741261\pi$
$439$	−28.8065	−1.37486	−0.687429	+	0.726252i	$0.741261\pi$
$440$	− 27.3369i	− 1.30324i
$441$	−6.15622	−0.293153
$442$	0	0
$443$	15.6483	0.743472	0.371736	−	0.928338i	$-0.378763\pi$
$443$	15.6483	0.743472	0.371736	+	0.928338i	$0.378763\pi$
$444$	66.0605i	3.13509i
$445$	7.33326	0.347630
$446$	−21.6688	−1.02605
$447$	24.0036i	1.13533i
$448$	13.0051i	0.614433i
$449$	18.0140i	0.850131i	0.905163	+	0.425066i	$0.139749\pi$
$449$	18.0140i	0.850131i	−0.905163	+	0.425066i	$0.860251\pi$
$450$	79.8046i	3.76202i
$451$	3.27359	0.154148
$452$	8.50588	0.400083
$453$	63.8528i	3.00007i
$454$	−52.0535	−2.44299
$455$	0	0
$456$	6.20349	0.290505
$457$	− 9.21009i	− 0.430830i	−0.976523	−	0.215415i	$-0.930890\pi$
$457$	− 9.21009i	− 0.430830i	0.976523	−	0.215415i	$-0.0691104\pi$
$458$	46.0426	2.15143
$459$	−6.73549	−0.314386
$460$	− 29.7228i	− 1.38583i
$461$	17.2980i	0.805648i	0.915278	+	0.402824i	$0.131971\pi$
$461$	17.2980i	0.805648i	−0.915278	+	0.402824i	$0.868029\pi$
$462$	25.0465i	1.16527i
$463$	− 17.9458i	− 0.834011i	−0.908904	−	0.417005i	$-0.863080\pi$
$463$	− 17.9458i	− 0.834011i	0.908904	−	0.417005i	$-0.136920\pi$
$464$	−6.41362	−0.297745
$465$	−95.0228	−4.40658
$466$	61.0665i	2.82885i
$467$	−14.8415	−0.686783	−0.343391	−	0.939192i	$-0.611576\pi$
$467$	−14.8415	−0.686783	−0.343391	+	0.939192i	$0.611576\pi$
$468$	0	0
$469$	6.41024	0.295997
$470$	− 83.8567i	− 3.86802i
$471$	13.6012	0.626711
$472$	16.6484	0.766305
$473$	− 1.98324i	− 0.0911896i
$474$	47.4392i	2.17896i
$475$	5.28207i	0.242358i
$476$	2.11944i	0.0971445i
$477$	23.2206	1.06320
$478$	−51.4009	−2.35102
$479$	4.23377i	0.193446i	0.995311	+	0.0967229i	$0.0308360\pi$
$479$	4.23377i	0.193446i	−0.995311	+	0.0967229i	$0.969164\pi$
$480$	−66.4919	−3.03493
$481$	0	0
$482$	−23.9972	−1.09304
$483$	9.10904i	0.414476i
$484$	8.07926	0.367239
$485$	28.8987	1.31222
$486$	− 6.51049i	− 0.295322i
$487$	− 2.98273i	− 0.135160i	−0.997714	−	0.0675802i	$-0.978472\pi$
$487$	− 2.98273i	− 0.135160i	0.997714	−	0.0675802i	$-0.0215279\pi$
$488$	− 4.09284i	− 0.185274i
$489$	6.35781i	0.287510i
$490$	−7.35037	−0.332056
$491$	7.33211	0.330894	0.165447	−	0.986219i	$-0.447093\pi$
$491$	7.33211	0.330894	0.165447	+	0.986219i	$0.447093\pi$
$492$	8.04607i	0.362745i
$493$	−4.61994	−0.208071
$494$	0	0
$495$	−74.8321	−3.36345
$496$	− 9.35802i	− 0.420188i
$497$	10.7248	0.481075
$498$	15.6728	0.702316
$499$	15.6355i	0.699939i	0.936761	+	0.349970i	$0.113808\pi$
$499$	15.6355i	0.699939i	−0.936761	+	0.349970i	$0.886192\pi$
$500$	7.84272i	0.350737i
$501$	38.1544i	1.70461i
$502$	16.4230i	0.732995i
$503$	27.1014	1.20839	0.604196	−	0.796836i	$-0.293494\pi$
$503$	27.1014	1.20839	0.604196	+	0.796836i	$0.293494\pi$
$504$	−13.8449	−0.616701
$505$	− 28.0787i	− 1.24949i
$506$	24.9174	1.10771
$507$	0	0
$508$	10.7992	0.479135
$509$	− 44.3319i	− 1.96498i	−0.186321	−	0.982489i	$-0.559656\pi$
$509$	− 44.3319i	− 1.96498i	0.186321	−	0.982489i	$-0.440344\pi$
$510$	−15.6860	−0.694587
$511$	−9.72504	−0.430210
$512$	− 10.9519i	− 0.484012i
$513$	− 8.70617i	− 0.384387i
$514$	33.5376i	1.47928i
$515$	45.1089i	1.98774i
$516$	4.87455	0.214590
$517$	42.2090	1.85635
$518$	− 16.2524i	− 0.714091i
$519$	−12.0097	−0.527169
$520$	0	0
$521$	−2.24230	−0.0982371	−0.0491186	−	0.998793i	$-0.515641\pi$
$521$	−2.24230	−0.0982371	−0.0491186	+	0.998793i	$0.515641\pi$
$522$	− 90.2230i	− 3.94895i
$523$	−41.8877	−1.83162	−0.915810	−	0.401612i	$-0.868450\pi$
$523$	−41.8877	−1.83162	−0.915810	+	0.401612i	$0.868450\pi$
$524$	−3.18147	−0.138983
$525$	− 17.5332i	− 0.765210i
$526$	− 18.0152i	− 0.785501i
$527$	− 6.74088i	− 0.293637i
$528$	− 10.9609i	− 0.477012i
$529$	−13.9379	−0.605995
$530$	27.7248	1.20429
$531$	− 45.5733i	− 1.97771i
$532$	−2.73955	−0.118775
$533$	0	0
$534$	−15.1102	−0.653881
$535$	− 57.4842i	− 2.48526i
$536$	14.4162	0.622684
$537$	−71.6509	−3.09196
$538$	5.64747i	0.243480i
$539$	− 3.69978i	− 0.159361i
$540$	− 94.2974i	− 4.05791i
$541$	− 13.4214i	− 0.577032i	−0.957475	−	0.288516i	$-0.906838\pi$
$541$	− 13.4214i	− 0.577032i	0.957475	−	0.288516i	$-0.0931619\pi$
$542$	−1.75631	−0.0754400
$543$	74.5579	3.19958
$544$	− 4.71691i	− 0.202236i
$545$	22.8321	0.978019
$546$	0	0
$547$	29.3951	1.25684	0.628422	−	0.777873i	$-0.283701\pi$
$547$	29.3951	1.25684	0.628422	+	0.777873i	$0.283701\pi$
$548$	24.9388i	1.06533i
$549$	−11.2037	−0.478164
$550$	−47.9612	−2.04507
$551$	− 5.97164i	− 0.254400i
$552$	20.4856i	0.871925i
$553$	− 7.00757i	− 0.297992i
$554$	47.9201i	2.03593i
$555$	72.2208	3.06560
$556$	21.1159	0.895515
$557$	− 38.9882i	− 1.65198i	−0.563683	−	0.825991i	$-0.690616\pi$
$557$	− 38.9882i	− 1.65198i	0.563683	−	0.825991i	$-0.309384\pi$
$558$	131.643	5.57290
$559$	0	0
$560$	3.21669	0.135930
$561$	− 7.89549i	− 0.333348i
$562$	50.0492	2.11120
$563$	3.99187	0.168237	0.0841186	−	0.996456i	$-0.473193\pi$
$563$	3.99187	0.168237	0.0841186	+	0.996456i	$0.473193\pi$
$564$	103.744i	4.36842i
$565$	− 9.29907i	− 0.391215i
$566$	− 55.6618i	− 2.33964i
$567$	10.4304i	0.438034i
$568$	24.1194	1.01203
$569$	−18.8465	−0.790087	−0.395043	−	0.918663i	$-0.629270\pi$
$569$	−18.8465	−0.790087	−0.395043	+	0.918663i	$0.629270\pi$
$570$	− 20.2754i	− 0.849243i
$571$	−12.1859	−0.509965	−0.254983	−	0.966946i	$-0.582070\pi$
$571$	−12.1859	−0.509965	−0.254983	+	0.966946i	$0.582070\pi$
$572$	0	0
$573$	9.01871	0.376762
$574$	− 1.97952i	− 0.0826236i
$575$	−17.4428	−0.727416
$576$	80.0622	3.33592
$577$	23.1257i	0.962736i	0.876519	+	0.481368i	$0.159860\pi$
$577$	23.1257i	0.962736i	−0.876519	+	0.481368i	$0.840140\pi$
$578$	36.9203i	1.53568i
$579$	− 52.9896i	− 2.20217i
$580$	− 64.6794i	− 2.68567i
$581$	−2.31514	−0.0960482
$582$	−59.5456	−2.46825
$583$	13.9552i	0.577964i
$584$	−21.8709	−0.905026
$585$	0	0
$586$	26.3291	1.08765
$587$	42.2460i	1.74368i	0.489790	+	0.871840i	$0.337073\pi$
$587$	42.2460i	1.74368i	−0.489790	+	0.871840i	$0.662927\pi$
$588$	9.09359	0.375013
$589$	8.71313	0.359018
$590$	− 54.4134i	− 2.24017i
$591$	− 59.3722i	− 2.44225i
$592$	7.11244i	0.292319i
$593$	− 12.3223i	− 0.506017i	−0.967464	−	0.253008i	$-0.918580\pi$
$593$	− 12.3223i	− 0.506017i	0.967464	−	0.253008i	$-0.0814200\pi$
$594$	79.0521	3.24355
$595$	2.31709	0.0949912
$596$	− 23.8394i	− 0.976499i
$597$	75.1359	3.07511
$598$	0	0
$599$	−13.3578	−0.545785	−0.272893	−	0.962045i	$-0.587980\pi$
$599$	−13.3578	−0.545785	−0.272893	+	0.962045i	$0.587980\pi$
$600$	− 39.4308i	− 1.60976i
$601$	−15.9766	−0.651700	−0.325850	−	0.945421i	$-0.605651\pi$
$601$	−15.9766	−0.651700	−0.325850	+	0.945421i	$0.605651\pi$
$602$	−1.19925	−0.0488780
$603$	− 39.4628i	− 1.60705i
$604$	− 63.4161i	− 2.58036i
$605$	− 8.83266i	− 0.359099i
$606$	57.8561i	2.35024i
$607$	−27.4273	−1.11324	−0.556619	−	0.830768i	$-0.687902\pi$
$607$	−27.4273	−1.11324	−0.556619	+	0.830768i	$0.687902\pi$
$608$	6.09699	0.247266
$609$	19.8221i	0.803232i
$610$	−13.3770	−0.541619
$611$	0	0
$612$	13.0478	0.527424
$613$	18.2538i	0.737262i	0.929576	+	0.368631i	$0.120173\pi$
$613$	18.2538i	0.737262i	−0.929576	+	0.368631i	$0.879827\pi$
$614$	45.6086	1.84061
$615$	8.79638	0.354704
$616$	− 8.32055i	− 0.335245i
$617$	− 27.9970i	− 1.12712i	−0.826076	−	0.563558i	$-0.809432\pi$
$617$	− 27.9970i	− 1.12712i	0.826076	−	0.563558i	$-0.190568\pi$
$618$	− 92.9469i	− 3.73887i
$619$	4.93459i	0.198338i	0.995071	+	0.0991689i	$0.0316184\pi$
$619$	4.93459i	0.198338i	−0.995071	+	0.0991689i	$0.968382\pi$
$620$	94.3728	3.79010
$621$	28.7501	1.15370
$622$	− 25.9600i	− 1.04090i
$623$	2.23203	0.0894243
$624$	0	0
$625$	−20.3975	−0.815900
$626$	− 15.4807i	− 0.618735i
$627$	10.2056	0.407571
$628$	−13.5082	−0.539035
$629$	5.12332i	0.204280i
$630$	45.2505i	1.80282i
$631$	24.1702i	0.962199i	0.876666	+	0.481100i	$0.159763\pi$
$631$	24.1702i	0.962199i	−0.876666	+	0.481100i	$0.840237\pi$
$632$	− 15.7595i	− 0.626881i
$633$	−4.23574	−0.168356
$634$	−48.4599	−1.92459
$635$	− 11.8062i	− 0.468515i
$636$	−34.3000	−1.36008
$637$	0	0
$638$	54.2225	2.14669
$639$	− 66.0245i	− 2.61189i
$640$	51.6441	2.04141
$641$	−23.0926	−0.912103	−0.456052	−	0.889953i	$-0.650737\pi$
$641$	−23.0926	−0.912103	−0.456052	+	0.889953i	$0.650737\pi$
$642$	118.446i	4.67469i
$643$	3.73802i	0.147413i	0.997280	+	0.0737065i	$0.0234828\pi$
$643$	3.73802i	0.147413i	−0.997280	+	0.0737065i	$0.976517\pi$
$644$	− 9.04673i	− 0.356491i
$645$	− 5.32911i	− 0.209834i
$646$	1.43833	0.0565903
$647$	21.3102	0.837789	0.418895	−	0.908035i	$-0.362418\pi$
$647$	21.3102	0.837789	0.418895	+	0.908035i	$0.362418\pi$
$648$	23.4572i	0.921484i
$649$	27.3888	1.07510
$650$	0	0
$651$	−28.9221	−1.13355
$652$	− 6.31432i	− 0.247288i
$653$	−13.2897	−0.520067	−0.260034	−	0.965600i	$-0.583734\pi$
$653$	−13.2897	−0.520067	−0.260034	+	0.965600i	$0.583734\pi$
$654$	−47.0455	−1.83962
$655$	3.47815i	0.135902i
$656$	0.866284i	0.0338227i
$657$	59.8695i	2.33573i
$658$	− 25.5235i	− 0.995010i
$659$	−47.9835	−1.86917	−0.934586	−	0.355737i	$-0.884230\pi$
$659$	−47.9835	−1.86917	−0.934586	+	0.355737i	$0.884230\pi$
$660$	110.537	4.30266
$661$	− 34.2025i	− 1.33032i	−0.746700	−	0.665161i	$-0.768363\pi$
$661$	− 34.2025i	− 1.33032i	0.746700	−	0.665161i	$-0.231637\pi$
$662$	52.8141	2.05268
$663$	0	0
$664$	−5.20659	−0.202055
$665$	2.99502i	0.116142i
$666$	−100.054	−3.87700
$667$	19.7200	0.763560
$668$	− 37.8934i	− 1.46614i
$669$	− 29.3077i	− 1.13310i
$670$	− 47.1177i	− 1.82031i
$671$	− 6.73326i	− 0.259935i
$672$	−20.2382	−0.780704
$673$	−19.0820	−0.735556	−0.367778	−	0.929914i	$-0.619881\pi$
$673$	−19.0820	−0.735556	−0.367778	+	0.929914i	$0.619881\pi$
$674$	− 8.93459i	− 0.344148i
$675$	−55.3385	−2.12998
$676$	0	0
$677$	36.3983	1.39890	0.699451	−	0.714681i	$-0.253428\pi$
$677$	36.3983	1.39890	0.699451	+	0.714681i	$0.253428\pi$
$678$	19.1607i	0.735863i
$679$	8.79590	0.337555
$680$	5.21096	0.199831
$681$	− 70.4039i	− 2.69788i
$682$	79.1153i	3.02948i
$683$	− 38.5512i	− 1.47512i	−0.675282	−	0.737560i	$-0.735978\pi$
$683$	− 38.5512i	− 1.47512i	0.675282	−	0.737560i	$-0.264022\pi$
$684$	16.8653i	0.644860i
$685$	27.2644	1.04172
$686$	−2.23724	−0.0854181
$687$	62.2739i	2.37590i
$688$	0.524821	0.0200086
$689$	0	0
$690$	66.9548	2.54893
$691$	25.7213i	0.978483i	0.872148	+	0.489241i	$0.162726\pi$
$691$	25.7213i	0.978483i	−0.872148	+	0.489241i	$0.837274\pi$
$692$	11.9276	0.453419
$693$	−22.7767	−0.865214
$694$	− 63.7708i	− 2.42071i
$695$	− 23.0850i	− 0.875665i
$696$	44.5785i	1.68974i
$697$	0.624012i	0.0236361i
$698$	−8.93639	−0.338247
$699$	−82.5941	−3.12400
$700$	17.4132i	0.658158i
$701$	20.7378	0.783255	0.391627	−	0.920124i	$-0.371912\pi$
$701$	20.7378	0.783255	0.391627	+	0.920124i	$0.371912\pi$
$702$	0	0
$703$	−6.62230	−0.249765
$704$	48.1160i	1.81344i
$705$	113.419	4.27159
$706$	54.0795	2.03531
$707$	− 8.54632i	− 0.321418i
$708$	67.3181i	2.52997i
$709$	19.1426i	0.718915i	0.933161	+	0.359458i	$0.117038\pi$
$709$	19.1426i	0.718915i	−0.933161	+	0.359458i	$0.882962\pi$
$710$	− 78.8316i	− 2.95850i
$711$	−43.1401	−1.61788
$712$	5.01968	0.188120
$713$	28.7731i	1.07756i
$714$	−4.77435	−0.178676
$715$	0	0
$716$	71.1608	2.65940
$717$	− 69.5211i	− 2.59631i
$718$	−30.2115	−1.12748
$719$	−24.2544	−0.904538	−0.452269	−	0.891882i	$-0.649385\pi$
$719$	−24.2544	−0.904538	−0.452269	+	0.891882i	$0.649385\pi$
$720$	− 19.8027i	− 0.738001i
$721$	13.7298i	0.511325i
$722$	− 40.6483i	− 1.51277i
$723$	− 32.4568i	− 1.20708i
$724$	−74.0479	−2.75197
$725$	−37.9571	−1.40969
$726$	18.1997i	0.675454i
$727$	−45.3677	−1.68260	−0.841298	−	0.540572i	$-0.818208\pi$
$727$	−45.3677	−1.68260	−0.841298	+	0.540572i	$0.818208\pi$
$728$	0	0
$729$	−22.4855	−0.832795
$730$	71.4827i	2.64569i
$731$	0.378045	0.0139825
$732$	16.5495	0.611687
$733$	− 1.81036i	− 0.0668671i	−0.999441	−	0.0334336i	$-0.989356\pi$
$733$	− 1.81036i	− 0.0668671i	0.999441	−	0.0334336i	$-0.0106442\pi$
$734$	− 35.7708i	− 1.32033i
$735$	− 9.94158i	− 0.366701i
$736$	20.1339i	0.742145i
$737$	23.7165	0.873609
$738$	−12.1864	−0.448586
$739$	41.5849i	1.52973i	0.644193	+	0.764863i	$0.277193\pi$
$739$	41.5849i	1.52973i	−0.644193	+	0.764863i	$0.722807\pi$
$740$	−71.7268	−2.63673
$741$	0	0
$742$	8.43860	0.309791
$743$	15.0289i	0.551357i	0.961250	+	0.275678i	$0.0889025\pi$
$743$	15.0289i	0.551357i	−0.961250	+	0.275678i	$0.911098\pi$
$744$	−65.0438	−2.38462
$745$	−26.0625	−0.954854
$746$	− 55.0292i	− 2.01476i
$747$	14.2525i	0.521472i
$748$	7.84148i	0.286713i
$749$	− 17.4965i	− 0.639308i
$750$	−17.6669	−0.645103
$751$	20.1839	0.736522	0.368261	−	0.929723i	$-0.379953\pi$
$751$	20.1839	0.736522	0.368261	+	0.929723i	$0.379953\pi$
$752$	11.1697i	0.407316i
$753$	−22.2126	−0.809472
$754$	0	0
$755$	−69.3297	−2.52317
$756$	− 28.7013i	− 1.04386i
$757$	−17.7415	−0.644824	−0.322412	−	0.946599i	$-0.604494\pi$
$757$	−17.7415	−0.644824	−0.322412	+	0.946599i	$0.604494\pi$
$758$	18.0711	0.656373
$759$	33.7015i	1.22329i
$760$	6.73559i	0.244325i
$761$	29.2075i	1.05877i	0.848381	+	0.529386i	$0.177578\pi$
$761$	29.2075i	1.05877i	−0.848381	+	0.529386i	$0.822422\pi$
$762$	24.3267i	0.881262i
$763$	6.94941	0.251586
$764$	−8.95703	−0.324054
$765$	− 14.2645i	− 0.515733i
$766$	−7.73045	−0.279313
$767$	0	0
$768$	−27.7078	−0.999819
$769$	12.5419i	0.452271i	0.974096	+	0.226136i	$0.0726093\pi$
$769$	12.5419i	0.452271i	−0.974096	+	0.226136i	$0.927391\pi$
$770$	−27.1948	−0.980032
$771$	−45.3606	−1.63362
$772$	52.6272i	1.89409i
$773$	− 34.4451i	− 1.23891i	−0.785034	−	0.619453i	$-0.787355\pi$
$773$	− 34.4451i	− 1.23891i	0.785034	−	0.619453i	$-0.212645\pi$
$774$	7.38287i	0.265372i
$775$	− 55.3827i	− 1.98941i
$776$	19.7814	0.710109
$777$	21.9819	0.788595
$778$	− 52.8285i	− 1.89399i
$779$	−0.806586	−0.0288989
$780$	0	0
$781$	39.6796	1.41985
$782$	4.74975i	0.169851i
$783$	62.5628	2.23581
$784$	0.979066	0.0349666
$785$	14.7678i	0.527087i
$786$	− 7.16672i	− 0.255628i
$787$	− 0.728879i	− 0.0259817i	−0.999916	−	0.0129909i	$-0.995865\pi$
$787$	− 0.728879i	− 0.0259817i	0.999916	−	0.0129909i	$-0.00413524\pi$
$788$	58.9661i	2.10058i
$789$	24.3661	0.867456
$790$	−51.5083	−1.83258
$791$	− 2.83036i	− 0.100636i
$792$	−51.2231	−1.82014
$793$	0	0
$794$	−13.0745	−0.463997
$795$	37.4985i	1.32994i
$796$	−74.6220	−2.64491
$797$	26.0339	0.922167	0.461084	−	0.887357i	$-0.347461\pi$
$797$	26.0339	0.922167	0.461084	+	0.887357i	$0.347461\pi$
$798$	− 6.17123i	− 0.218459i
$799$	8.04587i	0.284642i
$800$	− 38.7539i	− 1.37016i
$801$	− 13.7409i	− 0.485509i
$802$	−56.1190	−1.98163
$803$	−35.9805	−1.26973
$804$	58.2921i	2.05580i
$805$	−9.89036	−0.348589
$806$	0	0
$807$	−7.63836	−0.268883
$808$	− 19.2201i	− 0.676160i
$809$	15.0861	0.530398	0.265199	−	0.964194i	$-0.414562\pi$
$809$	15.0861	0.530398	0.265199	+	0.964194i	$0.414562\pi$
$810$	76.6671	2.69381
$811$	6.89347i	0.242062i	0.992649	+	0.121031i	$0.0386201\pi$
$811$	6.89347i	0.242062i	−0.992649	+	0.121031i	$0.961380\pi$
$812$	− 19.6865i	− 0.690861i
$813$	− 2.37546i	− 0.0833110i
$814$	− 60.1305i	− 2.10757i
$815$	−6.90315	−0.241807
$816$	2.08937	0.0731424
$817$	0.488654i	0.0170958i
$818$	−0.352349	−0.0123196
$819$	0	0
$820$	−8.73621	−0.305082
$821$	14.8223i	0.517301i	0.965971	+	0.258650i	$0.0832778\pi$
$821$	14.8223i	0.517301i	−0.965971	+	0.258650i	$0.916722\pi$
$822$	−56.1783	−1.95944
$823$	7.29232	0.254194	0.127097	−	0.991890i	$-0.459434\pi$
$823$	7.29232	0.254194	0.127097	+	0.991890i	$0.459434\pi$
$824$	30.8774i	1.07567i
$825$	− 64.8689i	− 2.25844i
$826$	− 16.5618i	− 0.576260i
$827$	− 20.3151i	− 0.706424i	−0.935543	−	0.353212i	$-0.885089\pi$
$827$	− 20.3151i	− 0.706424i	0.935543	−	0.353212i	$-0.114911\pi$
$828$	−55.6937	−1.93549
$829$	−16.4470	−0.571227	−0.285614	−	0.958345i	$-0.592197\pi$
$829$	−16.4470	−0.571227	−0.285614	+	0.958345i	$0.592197\pi$
$830$	17.0171i	0.590673i
$831$	−64.8133	−2.24835
$832$	0	0
$833$	0.705252	0.0244355
$834$	47.5667i	1.64710i
$835$	−41.4271	−1.43364
$836$	−10.1357	−0.350552
$837$	91.2845i	3.15525i
$838$	15.5338i	0.536608i
$839$	24.0612i	0.830687i	0.909665	+	0.415343i	$0.136339\pi$
$839$	24.0612i	0.830687i	−0.909665	+	0.415343i	$0.863661\pi$
$840$	− 22.3579i	− 0.771422i
$841$	13.9124	0.479739
$842$	40.8135	1.40653
$843$	67.6929i	2.33147i
$844$	4.20677	0.144803
$845$	0	0
$846$	−157.128	−5.40218
$847$	− 2.68840i	− 0.0923746i
$848$	−3.69293	−0.126816
$849$	75.2842	2.58375
$850$	− 9.14236i	− 0.313580i
$851$	− 21.8686i	− 0.749646i
$852$	97.5273i	3.34123i
$853$	20.1772i	0.690854i	0.938446	+	0.345427i	$0.112266\pi$
$853$	20.1772i	0.690854i	−0.938446	+	0.345427i	$0.887734\pi$
$854$	−4.07156	−0.139326
$855$	18.4380	0.630566
$856$	− 39.3484i	− 1.34490i
$857$	−35.6705	−1.21848	−0.609241	−	0.792985i	$-0.708526\pi$
$857$	−35.6705	−1.21848	−0.609241	+	0.792985i	$0.708526\pi$
$858$	0	0
$859$	18.8085	0.641738	0.320869	−	0.947124i	$-0.396025\pi$
$859$	18.8085	0.641738	0.320869	+	0.947124i	$0.396025\pi$
$860$	5.29266i	0.180478i
$861$	2.67736	0.0912441
$862$	55.2157	1.88065
$863$	19.3191i	0.657631i	0.944394	+	0.328815i	$0.106649\pi$
$863$	19.3191i	0.657631i	−0.944394	+	0.328815i	$0.893351\pi$
$864$	63.8761i	2.17311i
$865$	− 13.0399i	− 0.443369i
$866$	− 18.3182i	− 0.622479i
$867$	−49.9357	−1.69590
$868$	28.7243	0.974966
$869$	− 25.9265i	− 0.879497i
$870$	145.700	4.93969
$871$	0	0
$872$	15.6287	0.529256
$873$	− 54.1494i	− 1.83268i
$874$	−6.13944	−0.207670
$875$	2.60969	0.0882238
$876$	− 88.4355i	− 2.98796i
$877$	45.9401i	1.55129i	0.631171	+	0.775644i	$0.282575\pi$
$877$	45.9401i	1.55129i	−0.631171	+	0.775644i	$0.717425\pi$
$878$	64.4469i	2.17498i
$879$	35.6108i	1.20112i
$880$	11.9011	0.401185
$881$	36.3751	1.22551	0.612755	−	0.790273i	$-0.290061\pi$
$881$	36.3751	1.22551	0.612755	+	0.790273i	$0.290061\pi$
$882$	13.7729i	0.463758i
$883$	33.5090	1.12767	0.563834	−	0.825888i	$-0.309326\pi$
$883$	33.5090	1.12767	0.563834	+	0.825888i	$0.309326\pi$
$884$	0	0
$885$	73.5957	2.47389
$886$	− 35.0089i	− 1.17615i
$887$	0.246789	0.00828635	0.00414318	−	0.999991i	$-0.498681\pi$
$887$	0.246789	0.00828635	0.00414318	+	0.999991i	$0.498681\pi$
$888$	49.4357	1.65895
$889$	− 3.59346i	− 0.120521i
$890$	− 16.4062i	− 0.549938i
$891$	38.5901i	1.29282i
$892$	29.1072i	0.974581i
$893$	−10.3999	−0.348021
$894$	53.7017	1.79605
$895$	− 77.7967i	− 2.60046i
$896$	15.7189	0.525133
$897$	0	0
$898$	40.3015	1.34488
$899$	62.6129i	2.08826i
$900$	107.200	3.57332
$901$	−2.66013	−0.0886218
$902$	− 7.32380i	− 0.243856i
$903$	− 1.62202i	− 0.0539776i
$904$	− 6.36529i	− 0.211706i
$905$	80.9530i	2.69097i
$906$	142.854	4.74600
$907$	−45.4657	−1.50966	−0.754831	−	0.655919i	$-0.772281\pi$
$907$	−45.4657	−1.50966	−0.754831	+	0.655919i	$0.772281\pi$
$908$	69.9223i	2.32045i
$909$	−52.6130	−1.74506
$910$	0	0
$911$	−41.7848	−1.38439	−0.692195	−	0.721710i	$-0.743356\pi$
$911$	−41.7848	−1.38439	−0.692195	+	0.721710i	$0.743356\pi$
$912$	2.70067i	0.0894282i
$913$	−8.56552	−0.283477
$914$	−20.6051	−0.681558
$915$	− 18.0928i	− 0.598128i
$916$	− 61.8480i	− 2.04351i
$917$	1.05865i	0.0349595i
$918$	15.0689i	0.497348i
$919$	−31.3491	−1.03411	−0.517056	−	0.855951i	$-0.672972\pi$
$919$	−31.3491	−1.03411	−0.517056	+	0.855951i	$0.672972\pi$
$920$	−22.2427	−0.733321
$921$	61.6869i	2.03265i
$922$	38.6997	1.27451
$923$	0	0
$924$	33.6443	1.10682
$925$	42.0929i	1.38401i
$926$	−40.1489	−1.31938
$927$	84.5238	2.77612
$928$	43.8132i	1.43824i
$929$	− 46.7428i	− 1.53358i	−0.641896	−	0.766791i	$-0.721852\pi$
$929$	− 46.7428i	− 1.53358i	0.641896	−	0.766791i	$-0.278148\pi$
$930$	212.588i	6.97105i
$931$	0.911595i	0.0298763i
$932$	82.0292	2.68695
$933$	35.1116	1.14950
$934$	33.2039i	1.08647i
$935$	8.57271	0.280358
$936$	0	0
$937$	46.2840	1.51203	0.756016	−	0.654553i	$-0.227143\pi$
$937$	46.2840	1.51203	0.756016	+	0.654553i	$0.227143\pi$
$938$	− 14.3412i	− 0.468257i
$939$	20.9381	0.683290
$940$	−112.643	−3.67400
$941$	12.0118i	0.391574i	0.980646	+	0.195787i	$0.0627262\pi$
$941$	12.0118i	0.391574i	−0.980646	+	0.195787i	$0.937274\pi$
$942$	− 30.4291i	− 0.991434i
$943$	− 2.66356i	− 0.0867375i
$944$	7.24784i	0.235897i
$945$	−31.3778	−1.02072
$946$	−4.43698	−0.144259
$947$	− 22.5259i	− 0.731993i	−0.930616	−	0.365997i	$-0.880728\pi$
$947$	− 22.5259i	− 0.731993i	0.930616	−	0.365997i	$-0.119272\pi$
$948$	63.7240	2.06966
$949$	0	0
$950$	11.8172	0.383402
$951$	− 65.5433i	− 2.12539i
$952$	1.58606	0.0514046
$953$	−46.1823	−1.49599	−0.747995	−	0.663704i	$-0.768983\pi$
$953$	−46.1823	−1.49599	−0.747995	+	0.663704i	$0.768983\pi$
$954$	− 51.9499i	− 1.68194i
$955$	9.79229i	0.316871i
$956$	69.0456i	2.23309i
$957$	73.3375i	2.37066i
$958$	9.47194	0.306024
$959$	8.29848	0.267972
$960$	129.291i	4.17286i
$961$	−60.3575	−1.94702
$962$	0	0
$963$	−107.712	−3.47098
$964$	32.2348i	1.03821i
$965$	57.5348	1.85211
$966$	20.3791	0.655686
$967$	1.04412i	0.0335765i	0.999859	+	0.0167882i	$0.00534412\pi$
$967$	1.04412i	0.0335765i	−0.999859	+	0.0167882i	$0.994656\pi$
$968$	− 6.04603i	− 0.194327i
$969$	1.94538i	0.0624946i
$970$	− 64.6531i	− 2.07589i
$971$	−6.88771	−0.221037	−0.110519	−	0.993874i	$-0.535251\pi$
$971$	−6.88771	−0.221037	−0.110519	+	0.993874i	$0.535251\pi$
$972$	−8.74539	−0.280508
$973$	− 7.02640i	− 0.225256i
$974$	−6.67308	−0.213819
$975$	0	0
$976$	1.78181	0.0570343
$977$	− 14.2731i	− 0.456637i	−0.973586	−	0.228319i	$-0.926677\pi$
$977$	− 14.2731i	− 0.456637i	0.973586	−	0.228319i	$-0.0733228\pi$
$978$	14.2239	0.454831
$979$	8.25802	0.263928
$980$	9.87358i	0.315400i
$981$	− 42.7821i	− 1.36593i
$982$	− 16.4037i	− 0.523462i
$983$	− 8.84698i	− 0.282175i	−0.989997	−	0.141087i	$-0.954940\pi$
$983$	− 8.84698i	− 0.282175i	0.989997	−	0.141087i	$-0.0450599\pi$
$984$	6.02119	0.191949
$985$	64.4648	2.05402
$986$	10.3359i	0.329162i
$987$	34.5213	1.09882
$988$	0	0
$989$	−1.61367	−0.0513116
$990$	167.417i	5.32086i
$991$	−35.7187	−1.13464	−0.567321	−	0.823497i	$-0.692020\pi$
$991$	−35.7187	−1.13464	−0.567321	+	0.823497i	$0.692020\pi$
$992$	−63.9272	−2.02969
$993$	71.4325i	2.26684i
$994$	− 23.9940i	− 0.761044i
$995$	81.5806i	2.58628i
$996$	− 21.0529i	− 0.667087i
$997$	43.5743	1.38001	0.690006	−	0.723804i	$-0.257608\pi$
$997$	43.5743	1.38001	0.690006	+	0.723804i	$0.257608\pi$
$998$	34.9802	1.10728
$999$	− 69.3796i	− 2.19507i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.c.j.337.4		24
13.5	odd	4		1183.2.a.q.1.3	✓	12
13.8	odd	4		1183.2.a.r.1.10	yes	12
13.12	even	2	inner	1183.2.c.j.337.21		24
91.34	even	4		8281.2.a.cq.1.10		12
91.83	even	4		8281.2.a.cn.1.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.a.q.1.3	✓	12	13.5	odd	4
1183.2.a.r.1.10	yes	12	13.8	odd	4
1183.2.c.j.337.4		24	1.1	even	1	trivial
1183.2.c.j.337.21		24	13.12	even	2	inner
8281.2.a.cn.1.3		12	91.83	even	4
8281.2.a.cq.1.10		12	91.34	even	4

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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.23724i q^{2} +3.02592 q^{3} -3.00523 q^{4} +3.28547i q^{5} -6.76971i q^{6} +1.00000i q^{7} +2.24893i q^{8} +6.15622 q^{9} +O(q^{10})\)	\(q-2.23724i q^{2} +3.02592 q^{3} -3.00523 q^{4} +3.28547i q^{5} -6.76971i q^{6} +1.00000i q^{7} +2.24893i q^{8} +6.15622 q^{9} +7.35037 q^{10} +3.69978i q^{11} -9.09359 q^{12} +2.23724 q^{14} +9.94158i q^{15} -0.979066 q^{16} -0.705252 q^{17} -13.7729i q^{18} -0.911595i q^{19} -9.87358i q^{20} +3.02592i q^{21} +8.27729 q^{22} +3.01033 q^{23} +6.80509i q^{24} -5.79431 q^{25} +9.55048 q^{27} -3.00523i q^{28} +6.55076 q^{29} +22.2417 q^{30} +9.55811i q^{31} +6.68826i q^{32} +11.1953i q^{33} +1.57782i q^{34} -3.28547 q^{35} -18.5008 q^{36} -7.26452i q^{37} -2.03945 q^{38} -7.38879 q^{40} -0.884807i q^{41} +6.76971 q^{42} -0.536043 q^{43} -11.1187i q^{44} +20.2261i q^{45} -6.73483i q^{46} -11.4085i q^{47} -2.96258 q^{48} -1.00000 q^{49} +12.9633i q^{50} -2.13404 q^{51} +3.77189 q^{53} -21.3667i q^{54} -12.1555 q^{55} -2.24893 q^{56} -2.75842i q^{57} -14.6556i q^{58} -7.40281i q^{59} -29.8767i q^{60} -1.81991 q^{61} +21.3838 q^{62} +6.15622i q^{63} +13.0051 q^{64} +25.0465 q^{66} -6.41024i q^{67} +2.11944 q^{68} +9.10904 q^{69} +7.35037i q^{70} -10.7248i q^{71} +13.8449i q^{72} +9.72504i q^{73} -16.2524 q^{74} -17.5332 q^{75} +2.73955i q^{76} -3.69978 q^{77} -7.00757 q^{79} -3.21669i q^{80} +10.4304 q^{81} -1.97952 q^{82} +2.31514i q^{83} -9.09359i q^{84} -2.31709i q^{85} +1.19925i q^{86} +19.8221 q^{87} -8.32055 q^{88} -2.23203i q^{89} +45.2505 q^{90} -9.04673 q^{92} +28.9221i q^{93} -25.5235 q^{94} +2.99502 q^{95} +20.2382i q^{96} -8.79590i q^{97} +2.23724i q^{98} +22.7767i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 16 q^{3} - 30 q^{4} + 52 q^{9}+O(q^{10}) \) 24 * q + 16 * q^3 - 30 * q^4 + 52 * q^9	\( 24 q + 16 q^{3} - 30 q^{4} + 52 q^{9} + 12 q^{10} - 26 q^{12} + 6 q^{14} + 26 q^{16} - 62 q^{17} - 8 q^{22} - 36 q^{23} - 64 q^{25} + 64 q^{27} + 30 q^{29} + 20 q^{30} - 8 q^{35} - 98 q^{36} - 90 q^{38} - 40 q^{40} + 4 q^{42} + 44 q^{43} + 22 q^{48} - 24 q^{49} - 36 q^{51} + 106 q^{53} - 52 q^{55} - 24 q^{56} + 44 q^{61} - 38 q^{62} - 4 q^{64} - 68 q^{66} + 68 q^{68} - 6 q^{69} - 80 q^{74} - 30 q^{75} - 24 q^{77} + 4 q^{79} + 72 q^{81} + 64 q^{82} + 54 q^{87} + 96 q^{88} + 52 q^{90} + 104 q^{92} - 88 q^{94} - 58 q^{95}+O(q^{100}) \) 24 * q + 16 * q^3 - 30 * q^4 + 52 * q^9 + 12 * q^10 - 26 * q^12 + 6 * q^14 + 26 * q^16 - 62 * q^17 - 8 * q^22 - 36 * q^23 - 64 * q^25 + 64 * q^27 + 30 * q^29 + 20 * q^30 - 8 * q^35 - 98 * q^36 - 90 * q^38 - 40 * q^40 + 4 * q^42 + 44 * q^43 + 22 * q^48 - 24 * q^49 - 36 * q^51 + 106 * q^53 - 52 * q^55 - 24 * q^56 + 44 * q^61 - 38 * q^62 - 4 * q^64 - 68 * q^66 + 68 * q^68 - 6 * q^69 - 80 * q^74 - 30 * q^75 - 24 * q^77 + 4 * q^79 + 72 * q^81 + 64 * q^82 + 54 * q^87 + 96 * q^88 + 52 * q^90 + 104 * q^92 - 88 * q^94 - 58 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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