LMFDB - Embedded newform 1445.2.d.j.866.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1445,2,Mod(866,1445)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1445, 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("1445.866");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1445 = 5 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1445.d (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:	$11.5383830921$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			866.14
Character	$\chi$	$=$	1445.866
Dual form			1445.2.d.j.866.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.962871 q^{2} +2.64897i q^{3} -1.07288 q^{4} +1.00000i q^{5} +2.55062i q^{6} +3.09463i q^{7} -2.95879 q^{8} -4.01706 q^{9} +0.962871i q^{10} +6.13071i q^{11} -2.84203i q^{12} +1.16017 q^{13} +2.97973i q^{14} -2.64897 q^{15} -0.703170 q^{16} -3.86791 q^{18} +5.42585 q^{19} -1.07288i q^{20} -8.19759 q^{21} +5.90308i q^{22} -3.11745i q^{23} -7.83775i q^{24} -1.00000 q^{25} +1.11710 q^{26} -2.69417i q^{27} -3.32016i q^{28} -4.99698i q^{29} -2.55062 q^{30} -3.72804i q^{31} +5.24051 q^{32} -16.2401 q^{33} -3.09463 q^{35} +4.30982 q^{36} +0.396716i q^{37} +5.22439 q^{38} +3.07327i q^{39} -2.95879i q^{40} +1.70263i q^{41} -7.89322 q^{42} +0.0268304 q^{43} -6.57751i q^{44} -4.01706i q^{45} -3.00170i q^{46} -5.43715 q^{47} -1.86268i q^{48} -2.57672 q^{49} -0.962871 q^{50} -1.24473 q^{52} -0.345087 q^{53} -2.59413i q^{54} -6.13071 q^{55} -9.15634i q^{56} +14.3729i q^{57} -4.81144i q^{58} -4.06060 q^{59} +2.84203 q^{60} +12.4424i q^{61} -3.58962i q^{62} -12.4313i q^{63} +6.45228 q^{64} +1.16017i q^{65} -15.6371 q^{66} +5.62508 q^{67} +8.25804 q^{69} -2.97973 q^{70} -10.7794i q^{71} +11.8856 q^{72} +1.65433i q^{73} +0.381986i q^{74} -2.64897i q^{75} -5.82128 q^{76} -18.9723 q^{77} +2.95916i q^{78} -5.27290i q^{79} -0.703170i q^{80} -4.91441 q^{81} +1.63941i q^{82} +12.4258 q^{83} +8.79502 q^{84} +0.0258342 q^{86} +13.2369 q^{87} -18.1394i q^{88} -3.22930 q^{89} -3.86791i q^{90} +3.59031i q^{91} +3.34465i q^{92} +9.87549 q^{93} -5.23528 q^{94} +5.42585i q^{95} +13.8820i q^{96} +12.9349i q^{97} -2.48105 q^{98} -24.6274i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8} - 24 q^{9} - 16 q^{13} + 16 q^{15} + 24 q^{16} + 8 q^{18} + 32 q^{21} - 24 q^{25} - 32 q^{26} - 16 q^{30} + 56 q^{32} - 32 q^{35} - 24 q^{36} - 48 q^{38} + 32 q^{43}+ \cdots - 120 q^{98}+O(q^{100}) $ 24 * q + 8 * q^2 + 24 * q^4 + 24 * q^8 - 24 * q^9 - 16 * q^13 + 16 * q^15 + 24 * q^16 + 8 * q^18 + 32 * q^21 - 24 * q^25 - 32 * q^26 - 16 * q^30 + 56 * q^32 - 32 * q^35 - 24 * q^36 - 48 * q^38 + 32 * q^43 - 64 * q^47 - 40 * q^49 - 8 * q^50 - 48 * q^52 - 32 * q^55 - 16 * q^59 + 32 * q^60 + 72 * q^64 - 80 * q^66 - 16 * q^67 + 96 * q^69 - 32 * q^70 + 24 * q^72 - 32 * q^76 - 48 * q^77 + 72 * q^81 + 80 * q^83 + 64 * q^84 - 16 * q^86 + 64 * q^87 + 16 * q^89 - 48 * q^93 + 32 * q^94 - 120 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1445\mathbb{Z}\right)^\times$.

$n$	$581$	$1157$
$\chi(n)$	$-1$	$1$

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 $

$2$	0.962871	0.680853	0.340426	−	0.940271i	$-0.389429\pi$
$2$	0.962871	0.680853	0.340426	+	0.940271i	$0.389429\pi$
$3$	2.64897i	1.52939i	0.644395	+	0.764693i	$0.277109\pi$
$3$	2.64897i	1.52939i	−0.644395	+	0.764693i	$0.722891\pi$
$4$	−1.07288	−0.536440
$5$	1.00000i	0.447214i
$5$	1.00000i	0.447214i
$6$	2.55062i	1.04129i
$7$	3.09463i	1.16966i	0.811156	+	0.584830i	$0.198839\pi$
$7$	3.09463i	1.16966i	−0.811156	+	0.584830i	$0.801161\pi$
$8$	−2.95879	−1.04609
$9$	−4.01706	−1.33902
$10$	0.962871i	0.304487i
$11$	6.13071i	1.84848i	0.381815	+	0.924239i	$0.375299\pi$
$11$	6.13071i	1.84848i	−0.381815	+	0.924239i	$0.624701\pi$
$12$	− 2.84203i	− 0.820423i
$13$	1.16017	0.321775	0.160887	−	0.986973i	$-0.448564\pi$
$13$	1.16017	0.321775	0.160887	+	0.986973i	$0.448564\pi$
$14$	2.97973i	0.796366i
$15$	−2.64897	−0.683962
$16$	−0.703170	−0.175793
$17$	0	0
$17$	0	0
$18$	−3.86791	−0.911675
$19$	5.42585	1.24477	0.622387	−	0.782709i	$-0.286163\pi$
$19$	5.42585	1.24477	0.622387	+	0.782709i	$0.286163\pi$
$20$	− 1.07288i	− 0.239903i
$21$	−8.19759	−1.78886
$22$	5.90308i	1.25854i
$23$	− 3.11745i	− 0.650033i	−0.945708	−	0.325017i	$-0.894630\pi$
$23$	− 3.11745i	− 0.650033i	0.945708	−	0.325017i	$-0.105370\pi$
$24$	− 7.83775i	− 1.59987i
$25$	−1.00000	−0.200000
$26$	1.11710	0.219081
$27$	− 2.69417i	− 0.518492i
$28$	− 3.32016i	− 0.627452i
$29$	− 4.99698i	− 0.927915i	−0.885857	−	0.463958i	$-0.846429\pi$
$29$	− 4.99698i	− 0.927915i	0.885857	−	0.463958i	$-0.153571\pi$
$30$	−2.55062	−0.465677
$31$	− 3.72804i	− 0.669576i	−0.942293	−	0.334788i	$-0.891335\pi$
$31$	− 3.72804i	− 0.669576i	0.942293	−	0.334788i	$-0.108665\pi$
$32$	5.24051	0.926400
$33$	−16.2401	−2.82703
$34$	0	0
$35$	−3.09463	−0.523088
$36$	4.30982	0.718304
$37$	0.396716i	0.0652197i	0.999468	+	0.0326098i	$0.0103819\pi$
$37$	0.396716i	0.0652197i	−0.999468	+	0.0326098i	$0.989618\pi$
$38$	5.22439	0.847508
$39$	3.07327i	0.492117i
$40$	− 2.95879i	− 0.467825i
$41$	1.70263i	0.265906i	0.991122	+	0.132953i	$0.0424460\pi$
$41$	1.70263i	0.265906i	−0.991122	+	0.132953i	$0.957554\pi$
$42$	−7.89322	−1.21795
$43$	0.0268304	0.00409160	0.00204580	−	0.999998i	$-0.499349\pi$
$43$	0.0268304	0.00409160	0.00204580	+	0.999998i	$0.499349\pi$
$44$	− 6.57751i	− 0.991597i
$45$	− 4.01706i	− 0.598828i
$46$	− 3.00170i	− 0.442577i
$47$	−5.43715	−0.793090	−0.396545	−	0.918015i	$-0.629791\pi$
$47$	−5.43715	−0.793090	−0.396545	+	0.918015i	$0.629791\pi$
$48$	− 1.86268i	− 0.268855i
$49$	−2.57672	−0.368103
$50$	−0.962871	−0.136171
$51$	0	0
$52$	−1.24473	−0.172613
$53$	−0.345087	−0.0474014	−0.0237007	−	0.999719i	$-0.507545\pi$
$53$	−0.345087	−0.0474014	−0.0237007	+	0.999719i	$0.507545\pi$
$54$	− 2.59413i	− 0.353017i
$55$	−6.13071	−0.826664
$56$	− 9.15634i	− 1.22357i
$57$	14.3729i	1.90374i
$58$	− 4.81144i	− 0.631773i
$59$	−4.06060	−0.528645	−0.264322	−	0.964434i	$-0.585148\pi$
$59$	−4.06060	−0.528645	−0.264322	+	0.964434i	$0.585148\pi$
$60$	2.84203	0.366904
$61$	12.4424i	1.59308i	0.604584	+	0.796541i	$0.293339\pi$
$61$	12.4424i	1.59308i	−0.604584	+	0.796541i	$0.706661\pi$
$62$	− 3.58962i	− 0.455883i
$63$	− 12.4313i	− 1.56620i
$64$	6.45228	0.806534
$65$	1.16017i	0.143902i
$66$	−15.6371	−1.92479
$67$	5.62508	0.687213	0.343607	−	0.939114i	$-0.388351\pi$
$67$	5.62508	0.687213	0.343607	+	0.939114i	$0.388351\pi$
$68$	0	0
$69$	8.25804	0.994152
$70$	−2.97973	−0.356146
$71$	− 10.7794i	− 1.27928i	−0.768674	−	0.639640i	$-0.779083\pi$
$71$	− 10.7794i	− 1.27928i	0.768674	−	0.639640i	$-0.220917\pi$
$72$	11.8856	1.40073
$73$	1.65433i	0.193624i	0.995303	+	0.0968121i	$0.0308646\pi$
$73$	1.65433i	0.193624i	−0.995303	+	0.0968121i	$0.969135\pi$
$74$	0.381986i	0.0444050i
$75$	− 2.64897i	− 0.305877i
$76$	−5.82128	−0.667747
$77$	−18.9723	−2.16209
$78$	2.95916i	0.335059i
$79$	− 5.27290i	− 0.593248i	−0.954994	−	0.296624i	$-0.904139\pi$
$79$	− 5.27290i	− 0.593248i	0.954994	−	0.296624i	$-0.0958608\pi$
$80$	− 0.703170i	− 0.0786168i
$81$	−4.91441	−0.546045
$82$	1.63941i	0.181043i
$83$	12.4258	1.36391	0.681955	−	0.731394i	$-0.261130\pi$
$83$	12.4258	1.36391	0.681955	+	0.731394i	$0.261130\pi$
$84$	8.79502	0.959616
$85$	0	0
$86$	0.0258342	0.00278577
$87$	13.2369	1.41914
$88$	− 18.1394i	− 1.93367i
$89$	−3.22930	−0.342305	−0.171152	−	0.985245i	$-0.554749\pi$
$89$	−3.22930	−0.342305	−0.171152	+	0.985245i	$0.554749\pi$
$90$	− 3.86791i	− 0.407714i
$91$	3.59031i	0.376367i
$92$	3.34465i	0.348704i
$93$	9.87549	1.02404
$94$	−5.23528	−0.539978
$95$	5.42585i	0.556680i
$96$	13.8820i	1.41682i
$97$	12.9349i	1.31334i	0.754180	+	0.656668i	$0.228035\pi$
$97$	12.9349i	1.31334i	−0.754180	+	0.656668i	$0.771965\pi$
$98$	−2.48105	−0.250624
$99$	− 24.6274i	− 2.47515i
$100$	1.07288	0.107288
$101$	−1.46947	−0.146218	−0.0731088	−	0.997324i	$-0.523292\pi$
$101$	−1.46947	−0.146218	−0.0731088	+	0.997324i	$0.523292\pi$
$102$	0	0
$103$	9.80978	0.966586	0.483293	−	0.875459i	$-0.339441\pi$
$103$	9.80978	0.966586	0.483293	+	0.875459i	$0.339441\pi$
$104$	−3.43271	−0.336605
$105$	− 8.19759i	− 0.800003i
$106$	−0.332275	−0.0322734
$107$	2.88742i	0.279137i	0.990212	+	0.139569i	$0.0445716\pi$
$107$	2.88742i	0.279137i	−0.990212	+	0.139569i	$0.955428\pi$
$108$	2.89052i	0.278140i
$109$	5.76330i	0.552024i	0.961154	+	0.276012i	$0.0890130\pi$
$109$	5.76330i	0.552024i	−0.961154	+	0.276012i	$0.910987\pi$
$110$	−5.90308	−0.562836
$111$	−1.05089	−0.0997460
$112$	− 2.17605i	− 0.205617i
$113$	− 9.02043i	− 0.848571i	−0.905529	−	0.424285i	$-0.860525\pi$
$113$	− 9.02043i	− 0.848571i	0.905529	−	0.424285i	$-0.139475\pi$
$114$	13.8393i	1.29617i
$115$	3.11745	0.290704
$116$	5.36115i	0.497771i
$117$	−4.66049	−0.430863
$118$	−3.90983	−0.359929
$119$	0	0
$120$	7.83775	0.715485
$121$	−26.5856	−2.41687
$122$	11.9804i	1.08465i
$123$	−4.51022	−0.406673
$124$	3.99974i	0.359187i
$125$	− 1.00000i	− 0.0894427i
$126$	− 11.9697i	− 1.06635i
$127$	13.9992	1.24223	0.621114	−	0.783720i	$-0.286681\pi$
$127$	13.9992	1.24223	0.621114	+	0.783720i	$0.286681\pi$
$128$	−4.26831	−0.377269
$129$	0.0710730i	0.00625763i
$130$	1.11710i	0.0979760i
$131$	12.6704i	1.10702i	0.832843	+	0.553509i	$0.186712\pi$
$131$	12.6704i	1.10702i	−0.832843	+	0.553509i	$0.813288\pi$
$132$	17.4236	1.51653
$133$	16.7910i	1.45596i
$134$	5.41623	0.467891
$135$	2.69417	0.231877
$136$	0	0
$137$	2.97888	0.254503	0.127251	−	0.991870i	$-0.459384\pi$
$137$	2.97888	0.254503	0.127251	+	0.991870i	$0.459384\pi$
$138$	7.95143	0.676871
$139$	− 19.6413i	− 1.66595i	−0.553308	−	0.832977i	$-0.686635\pi$
$139$	− 19.6413i	− 1.66595i	0.553308	−	0.832977i	$-0.313365\pi$
$140$	3.32016	0.280605
$141$	− 14.4029i	− 1.21294i
$142$	− 10.3792i	− 0.871002i
$143$	7.11269i	0.594793i
$144$	2.82468	0.235390
$145$	4.99698	0.414976
$146$	1.59290i	0.131830i
$147$	− 6.82567i	− 0.562972i
$148$	− 0.425628i	− 0.0349864i
$149$	2.95573	0.242143	0.121072	−	0.992644i	$-0.461367\pi$
$149$	2.95573	0.242143	0.121072	+	0.992644i	$0.461367\pi$
$150$	− 2.55062i	− 0.208257i
$151$	−22.0403	−1.79361	−0.896807	−	0.442422i	$-0.854119\pi$
$151$	−22.0403	−1.79361	−0.896807	+	0.442422i	$0.854119\pi$
$152$	−16.0539	−1.30214
$153$	0	0
$154$	−18.2678	−1.47206
$155$	3.72804	0.299444
$156$	− 3.29725i	− 0.263991i
$157$	12.8666	1.02686	0.513432	−	0.858130i	$-0.328374\pi$
$157$	12.8666	1.02686	0.513432	+	0.858130i	$0.328374\pi$
$158$	− 5.07713i	− 0.403914i
$159$	− 0.914127i	− 0.0724950i
$160$	5.24051i	0.414299i
$161$	9.64735	0.760318
$162$	−4.73194	−0.371776
$163$	19.2925i	1.51110i	0.655089	+	0.755551i	$0.272631\pi$
$163$	19.2925i	1.51110i	−0.655089	+	0.755551i	$0.727369\pi$
$164$	− 1.82672i	− 0.142643i
$165$	− 16.2401i	− 1.26429i
$166$	11.9645	0.928622
$167$	− 18.8591i	− 1.45936i	−0.683787	−	0.729681i	$-0.739668\pi$
$167$	− 18.8591i	− 1.45936i	0.683787	−	0.729681i	$-0.260332\pi$
$168$	24.2549	1.87131
$169$	−11.6540	−0.896461
$170$	0	0
$171$	−21.7960	−1.66678
$172$	−0.0287858	−0.00219490
$173$	22.5770i	1.71650i	0.513233	+	0.858249i	$0.328448\pi$
$173$	22.5770i	1.71650i	−0.513233	+	0.858249i	$0.671552\pi$
$174$	12.7454	0.966225
$175$	− 3.09463i	− 0.233932i
$176$	− 4.31093i	− 0.324949i
$177$	− 10.7564i	− 0.808502i
$178$	−3.10940	−0.233059
$179$	−1.96068	−0.146548	−0.0732740	−	0.997312i	$-0.523345\pi$
$179$	−1.96068	−0.146548	−0.0732740	+	0.997312i	$0.523345\pi$
$180$	4.30982i	0.321235i
$181$	− 0.711719i	− 0.0529016i	−0.999650	−	0.0264508i	$-0.991579\pi$
$181$	− 0.711719i	− 0.0529016i	0.999650	−	0.0264508i	$-0.00842054\pi$
$182$	3.45700i	0.256250i
$183$	−32.9595	−2.43644
$184$	9.22387i	0.679993i
$185$	−0.396716	−0.0291671
$186$	9.50882	0.697220
$187$	0	0
$188$	5.83341	0.425445
$189$	8.33744	0.606460
$190$	5.22439i	0.379017i
$191$	−5.26341	−0.380847	−0.190423	−	0.981702i	$-0.560986\pi$
$191$	−5.26341	−0.380847	−0.190423	+	0.981702i	$0.560986\pi$
$192$	17.0919i	1.23350i
$193$	14.9301i	1.07469i	0.843361	+	0.537347i	$0.180574\pi$
$193$	14.9301i	1.07469i	−0.843361	+	0.537347i	$0.819426\pi$
$194$	12.4546i	0.894188i
$195$	−3.07327	−0.220082
$196$	2.76451	0.197465
$197$	− 6.33014i	− 0.451004i	−0.974243	−	0.225502i	$-0.927598\pi$
$197$	− 6.33014i	− 0.451004i	0.974243	−	0.225502i	$-0.0724022\pi$
$198$	− 23.7130i	− 1.68521i
$199$	− 14.9149i	− 1.05729i	−0.848843	−	0.528645i	$-0.822700\pi$
$199$	− 14.9149i	− 1.05729i	0.848843	−	0.528645i	$-0.177300\pi$
$200$	2.95879	0.209218
$201$	14.9007i	1.05101i
$202$	−1.41491	−0.0995526
$203$	15.4638	1.08534
$204$	0	0
$205$	−1.70263	−0.118917
$206$	9.44555	0.658103
$207$	12.5230i	0.870408i
$208$	−0.815800	−0.0565656
$209$	33.2643i	2.30094i
$210$	− 7.89322i	− 0.544684i
$211$	13.3987i	0.922404i	0.887295	+	0.461202i	$0.152582\pi$
$211$	13.3987i	0.922404i	−0.887295	+	0.461202i	$0.847418\pi$
$212$	0.370237	0.0254280
$213$	28.5544	1.95651
$214$	2.78021i	0.190051i
$215$	0.0268304i	0.00182982i
$216$	7.97146i	0.542389i
$217$	11.5369	0.783176
$218$	5.54932i	0.375847i
$219$	−4.38227	−0.296126
$220$	6.57751	0.443456
$221$	0	0
$222$	−1.01187	−0.0679123
$223$	2.11298	0.141496	0.0707478	−	0.997494i	$-0.477461\pi$
$223$	2.11298	0.141496	0.0707478	+	0.997494i	$0.477461\pi$
$224$	16.2174i	1.08357i
$225$	4.01706	0.267804
$226$	− 8.68551i	− 0.577752i
$227$	14.5595i	0.966348i	0.875524	+	0.483174i	$0.160516\pi$
$227$	14.5595i	0.966348i	−0.875524	+	0.483174i	$0.839484\pi$
$228$	− 15.4204i	− 1.02124i
$229$	2.65040	0.175143	0.0875716	−	0.996158i	$-0.472089\pi$
$229$	2.65040	0.175143	0.0875716	+	0.996158i	$0.472089\pi$
$230$	3.00170	0.197926
$231$	− 50.2570i	− 3.30667i
$232$	14.7850i	0.970682i
$233$	− 3.13924i	− 0.205658i	−0.994699	−	0.102829i	$-0.967210\pi$
$233$	− 3.13924i	− 0.205658i	0.994699	−	0.102829i	$-0.0327895\pi$
$234$	−4.48745	−0.293354
$235$	− 5.43715i	− 0.354681i
$236$	4.35653	0.283586
$237$	13.9678	0.907305
$238$	0	0
$239$	13.7090	0.886760	0.443380	−	0.896334i	$-0.353779\pi$
$239$	13.7090	0.886760	0.443380	+	0.896334i	$0.353779\pi$
$240$	1.86268	0.120235
$241$	12.4877i	0.804404i	0.915551	+	0.402202i	$0.131755\pi$
$241$	12.4877i	0.804404i	−0.915551	+	0.402202i	$0.868245\pi$
$242$	−25.5985	−1.64553
$243$	− 21.1006i	− 1.35361i
$244$	− 13.3492i	− 0.854593i
$245$	− 2.57672i	− 0.164621i
$246$	−4.34276	−0.276884
$247$	6.29493	0.400537
$248$	11.0305i	0.700436i
$249$	32.9157i	2.08595i
$250$	− 0.962871i	− 0.0608973i
$251$	17.4413	1.10088	0.550441	−	0.834874i	$-0.314459\pi$
$251$	17.4413	1.10088	0.550441	+	0.834874i	$0.314459\pi$
$252$	13.3373i	0.840171i
$253$	19.1122	1.20157
$254$	13.4794	0.845774
$255$	0	0
$256$	−17.0144	−1.06340
$257$	−6.88101	−0.429226	−0.214613	−	0.976699i	$-0.568849\pi$
$257$	−6.88101	−0.429226	−0.214613	+	0.976699i	$0.568849\pi$
$258$	0.0684341i	0.00426052i
$259$	−1.22769	−0.0762848
$260$	− 1.24473i	− 0.0771947i
$261$	20.0732i	1.24250i
$262$	12.2000i	0.753716i
$263$	−6.23809	−0.384657	−0.192329	−	0.981331i	$-0.561604\pi$
$263$	−6.23809	−0.384657	−0.192329	+	0.981331i	$0.561604\pi$
$264$	48.0509	2.95733
$265$	− 0.345087i	− 0.0211986i
$266$	16.1675i	0.991296i
$267$	− 8.55432i	− 0.523516i
$268$	−6.03504	−0.368648
$269$	1.29087i	0.0787059i	0.999225	+	0.0393530i	$0.0125297\pi$
$269$	1.29087i	0.0787059i	−0.999225	+	0.0393530i	$0.987470\pi$
$270$	2.59413	0.157874
$271$	10.2849	0.624764	0.312382	−	0.949957i	$-0.398873\pi$
$271$	10.2849	0.624764	0.312382	+	0.949957i	$0.398873\pi$
$272$	0	0
$273$	−9.51063	−0.575610
$274$	2.86828	0.173279
$275$	− 6.13071i	− 0.369695i
$276$	−8.85989	−0.533302
$277$	− 25.3802i	− 1.52495i	−0.647019	−	0.762474i	$-0.723985\pi$
$277$	− 25.3802i	− 1.52495i	0.647019	−	0.762474i	$-0.276015\pi$
$278$	− 18.9120i	− 1.13427i
$279$	14.9758i	0.896576i
$280$	9.15634	0.547196
$281$	−5.89557	−0.351700	−0.175850	−	0.984417i	$-0.556267\pi$
$281$	−5.89557	−0.351700	−0.175850	+	0.984417i	$0.556267\pi$
$282$	− 13.8681i	− 0.825834i
$283$	18.4663i	1.09771i	0.835918	+	0.548854i	$0.184936\pi$
$283$	18.4663i	1.09771i	−0.835918	+	0.548854i	$0.815064\pi$
$284$	11.5650i	0.686257i
$285$	−14.3729	−0.851378
$286$	6.84860i	0.404966i
$287$	−5.26901	−0.311020
$288$	−21.0514	−1.24047
$289$	0	0
$290$	4.81144	0.282538
$291$	−34.2641	−2.00860
$292$	− 1.77489i	− 0.103868i
$293$	8.31894	0.485998	0.242999	−	0.970027i	$-0.421869\pi$
$293$	8.31894	0.485998	0.242999	+	0.970027i	$0.421869\pi$
$294$	− 6.57224i	− 0.383301i
$295$	− 4.06060i	− 0.236417i
$296$	− 1.17380i	− 0.0682256i
$297$	16.5171	0.958422
$298$	2.84599	0.164864
$299$	− 3.61679i	− 0.209164i
$300$	2.84203i	0.164085i
$301$	0.0830301i	0.00478577i
$302$	−21.2220	−1.22119
$303$	− 3.89258i	− 0.223623i
$304$	−3.81529	−0.218822
$305$	−12.4424	−0.712448
$306$	0	0
$307$	−12.2369	−0.698398	−0.349199	−	0.937049i	$-0.613546\pi$
$307$	−12.2369	−0.698398	−0.349199	+	0.937049i	$0.613546\pi$
$308$	20.3549	1.15983
$309$	25.9858i	1.47828i
$310$	3.58962	0.203877
$311$	32.6368i	1.85066i	0.379160	+	0.925331i	$0.376213\pi$
$311$	32.6368i	1.85066i	−0.379160	+	0.925331i	$0.623787\pi$
$312$	− 9.09315i	− 0.514799i
$313$	− 13.4290i	− 0.759053i	−0.925181	−	0.379526i	$-0.876087\pi$
$313$	− 13.4290i	− 0.759053i	0.925181	−	0.379526i	$-0.123913\pi$
$314$	12.3889	0.699143
$315$	12.4313	0.700425
$316$	5.65719i	0.318242i
$317$	9.87357i	0.554555i	0.960790	+	0.277278i	$0.0894322\pi$
$317$	9.87357i	0.554555i	−0.960790	+	0.277278i	$0.910568\pi$
$318$	− 0.880187i	− 0.0493584i
$319$	30.6350	1.71523
$320$	6.45228i	0.360693i
$321$	−7.64869	−0.426909
$322$	9.28915	0.517664
$323$	0	0
$324$	5.27257	0.292920
$325$	−1.16017	−0.0643549
$326$	18.5762i	1.02884i
$327$	−15.2668	−0.844258
$328$	− 5.03772i	− 0.278162i
$329$	− 16.8260i	− 0.927646i
$330$	− 15.6371i	− 0.860794i
$331$	5.64305	0.310170	0.155085	−	0.987901i	$-0.450435\pi$
$331$	5.64305	0.310170	0.155085	+	0.987901i	$0.450435\pi$
$332$	−13.3314	−0.731656
$333$	− 1.59363i	− 0.0873304i
$334$	− 18.1589i	− 0.993611i
$335$	5.62508i	0.307331i
$336$	5.76430	0.314468
$337$	16.5925i	0.903853i	0.892055	+	0.451927i	$0.149263\pi$
$337$	16.5925i	0.903853i	−0.892055	+	0.451927i	$0.850737\pi$
$338$	−11.2213	−0.610358
$339$	23.8949	1.29779
$340$	0	0
$341$	22.8555	1.23770
$342$	−20.9867	−1.13483
$343$	13.6884i	0.739104i
$344$	−0.0793854	−0.00428017
$345$	8.25804i	0.444598i
$346$	21.7387i	1.16868i
$347$	9.24424i	0.496257i	0.968727	+	0.248129i	$0.0798155\pi$
$347$	9.24424i	0.496257i	−0.968727	+	0.248129i	$0.920184\pi$
$348$	−14.2016	−0.761283
$349$	−26.9273	−1.44139	−0.720694	−	0.693254i	$-0.756177\pi$
$349$	−26.9273	−1.44139	−0.720694	+	0.693254i	$0.756177\pi$
$350$	− 2.97973i	− 0.159273i
$351$	− 3.12570i	− 0.166838i
$352$	32.1280i	1.71243i
$353$	−22.9722	−1.22269	−0.611343	−	0.791366i	$-0.709370\pi$
$353$	−22.9722	−1.22269	−0.611343	+	0.791366i	$0.709370\pi$
$354$	− 10.3570i	− 0.550470i
$355$	10.7794	0.572112
$356$	3.46465	0.183626
$357$	0	0
$358$	−1.88788	−0.0997775
$359$	−34.1089	−1.80020	−0.900101	−	0.435682i	$-0.856507\pi$
$359$	−34.1089	−1.80020	−0.900101	+	0.435682i	$0.856507\pi$
$360$	11.8856i	0.626427i
$361$	10.4398	0.549463
$362$	− 0.685293i	− 0.0360182i
$363$	− 70.4244i	− 3.69632i
$364$	− 3.85197i	− 0.201898i
$365$	−1.65433	−0.0865914
$366$	−31.7358	−1.65885
$367$	− 9.27610i	− 0.484209i	−0.970250	−	0.242104i	$-0.922162\pi$
$367$	− 9.27610i	− 0.484209i	0.970250	−	0.242104i	$-0.0778376\pi$
$368$	2.19210i	0.114271i
$369$	− 6.83957i	− 0.356054i
$370$	−0.381986	−0.0198585
$371$	− 1.06792i	− 0.0554435i
$372$	−10.5952	−0.549336
$373$	−3.06857	−0.158884	−0.0794422	−	0.996839i	$-0.525314\pi$
$373$	−3.06857	−0.158884	−0.0794422	+	0.996839i	$0.525314\pi$
$374$	0	0
$375$	2.64897	0.136792
$376$	16.0874	0.829643
$377$	− 5.79736i	− 0.298579i
$378$	8.02788	0.412910
$379$	− 36.5339i	− 1.87662i	−0.345795	−	0.938310i	$-0.612391\pi$
$379$	− 36.5339i	− 1.87662i	0.345795	−	0.938310i	$-0.387609\pi$
$380$	− 5.82128i	− 0.298625i
$381$	37.0835i	1.89984i
$382$	−5.06798	−0.259301
$383$	9.32150	0.476306	0.238153	−	0.971228i	$-0.423458\pi$
$383$	9.32150	0.476306	0.238153	+	0.971228i	$0.423458\pi$
$384$	− 11.3066i	− 0.576990i
$385$	− 18.9723i	− 0.966916i
$386$	14.3758i	0.731709i
$387$	−0.107779	−0.00547873
$388$	− 13.8775i	− 0.704525i
$389$	−33.1623	−1.68139	−0.840697	−	0.541507i	$-0.817854\pi$
$389$	−33.1623	−1.68139	−0.840697	+	0.541507i	$0.817854\pi$
$390$	−2.95916	−0.149843
$391$	0	0
$392$	7.62397	0.385069
$393$	−33.5636	−1.69306
$394$	− 6.09511i	− 0.307067i
$395$	5.27290	0.265309
$396$	26.4223i	1.32777i
$397$	− 8.82540i	− 0.442934i	−0.975168	−	0.221467i	$-0.928915\pi$
$397$	− 8.82540i	− 0.442934i	0.975168	−	0.221467i	$-0.0710846\pi$
$398$	− 14.3611i	− 0.719859i
$399$	−44.4789	−2.22673
$400$	0.703170	0.0351585
$401$	− 19.5190i	− 0.974732i	−0.873198	−	0.487366i	$-0.837958\pi$
$401$	− 19.5190i	− 0.974732i	0.873198	−	0.487366i	$-0.162042\pi$
$402$	14.3474i	0.715585i
$403$	− 4.32518i	− 0.215453i
$404$	1.57656	0.0784369
$405$	− 4.91441i	− 0.244199i
$406$	14.8896	0.738960
$407$	−2.43215	−0.120557
$408$	0	0
$409$	10.4152	0.514998	0.257499	−	0.966279i	$-0.417102\pi$
$409$	10.4152	0.514998	0.257499	+	0.966279i	$0.417102\pi$
$410$	−1.63941	−0.0809649
$411$	7.89097i	0.389233i
$412$	−10.5247	−0.518515
$413$	− 12.5660i	− 0.618334i
$414$	12.0580i	0.592619i
$415$	12.4258i	0.609959i
$416$	6.07991	0.298092
$417$	52.0293	2.54789
$418$	32.0292i	1.56660i
$419$	− 35.3206i	− 1.72552i	−0.505610	−	0.862762i	$-0.668733\pi$
$419$	− 35.3206i	− 1.72552i	0.505610	−	0.862762i	$-0.331267\pi$
$420$	8.79502i	0.429153i
$421$	−15.0205	−0.732052	−0.366026	−	0.930605i	$-0.619282\pi$
$421$	−15.0205	−0.732052	−0.366026	+	0.930605i	$0.619282\pi$
$422$	12.9012i	0.628021i
$423$	21.8414	1.06196
$424$	1.02104	0.0495861
$425$	0	0
$426$	27.4942	1.33210
$427$	−38.5045	−1.86336
$428$	− 3.09785i	− 0.149740i
$429$	−18.8413	−0.909668
$430$	0.0258342i	0.00124584i
$431$	− 23.3518i	− 1.12481i	−0.826860	−	0.562407i	$-0.809875\pi$
$431$	− 23.3518i	− 1.12481i	0.826860	−	0.562407i	$-0.190125\pi$
$432$	1.89446i	0.0911471i
$433$	18.3077	0.879811	0.439906	−	0.898044i	$-0.355012\pi$
$433$	18.3077	0.879811	0.439906	+	0.898044i	$0.355012\pi$
$434$	11.1086	0.533228
$435$	13.2369i	0.634659i
$436$	− 6.18333i	− 0.296128i
$437$	− 16.9148i	− 0.809145i
$438$	−4.21956	−0.201618
$439$	20.2697i	0.967421i	0.875228	+	0.483711i	$0.160711\pi$
$439$	20.2697i	0.967421i	−0.875228	+	0.483711i	$0.839289\pi$
$440$	18.1394	0.864764
$441$	10.3509	0.492898
$442$	0	0
$443$	29.3849	1.39612	0.698058	−	0.716041i	$-0.254048\pi$
$443$	29.3849	1.39612	0.698058	+	0.716041i	$0.254048\pi$
$444$	1.12748	0.0535077
$445$	− 3.22930i	− 0.153083i
$446$	2.03453	0.0963376
$447$	7.82966i	0.370330i
$448$	19.9674i	0.943371i
$449$	− 32.6419i	− 1.54047i	−0.637761	−	0.770234i	$-0.720139\pi$
$449$	− 32.6419i	− 1.54047i	0.637761	−	0.770234i	$-0.279861\pi$
$450$	3.86791	0.182335
$451$	−10.4383	−0.491522
$452$	9.67784i	0.455207i
$453$	− 58.3842i	− 2.74313i
$454$	14.0189i	0.657940i
$455$	−3.59031	−0.168316
$456$	− 42.5264i	− 1.99148i
$457$	8.45112	0.395327	0.197663	−	0.980270i	$-0.436665\pi$
$457$	8.45112	0.395327	0.197663	+	0.980270i	$0.436665\pi$
$458$	2.55199	0.119247
$459$	0	0
$460$	−3.34465	−0.155945
$461$	38.2583	1.78187	0.890933	−	0.454134i	$-0.150051\pi$
$461$	38.2583	1.78187	0.890933	+	0.454134i	$0.150051\pi$
$462$	− 48.3910i	− 2.25135i
$463$	27.1761	1.26298	0.631491	−	0.775383i	$-0.282443\pi$
$463$	27.1761	1.26298	0.631491	+	0.775383i	$0.282443\pi$
$464$	3.51373i	0.163121i
$465$	9.87549i	0.457965i
$466$	− 3.02268i	− 0.140023i
$467$	−3.44525	−0.159427	−0.0797136	−	0.996818i	$-0.525401\pi$
$467$	−3.44525	−0.159427	−0.0797136	+	0.996818i	$0.525401\pi$
$468$	5.00015	0.231132
$469$	17.4075i	0.803805i
$470$	− 5.23528i	− 0.241485i
$471$	34.0832i	1.57047i
$472$	12.0144	0.553009
$473$	0.164489i	0.00756322i
$474$	13.4492	0.617741
$475$	−5.42585	−0.248955
$476$	0	0
$477$	1.38624	0.0634714
$478$	13.2000	0.603753
$479$	− 15.3593i	− 0.701785i	−0.936416	−	0.350893i	$-0.885878\pi$
$479$	− 15.3593i	− 0.701785i	0.936416	−	0.350893i	$-0.114122\pi$
$480$	−13.8820	−0.633622
$481$	0.460260i	0.0209860i
$482$	12.0241i	0.547681i
$483$	25.5556i	1.16282i
$484$	28.5231	1.29650
$485$	−12.9349	−0.587341
$486$	− 20.3172i	− 0.921606i
$487$	26.3095i	1.19220i	0.802911	+	0.596099i	$0.203283\pi$
$487$	26.3095i	1.19220i	−0.802911	+	0.596099i	$0.796717\pi$
$488$	− 36.8143i	− 1.66651i
$489$	−51.1052	−2.31106
$490$	− 2.48105i	− 0.112083i
$491$	29.0366	1.31040	0.655202	−	0.755454i	$-0.272583\pi$
$491$	29.0366	1.31040	0.655202	+	0.755454i	$0.272583\pi$
$492$	4.83893	0.218156
$493$	0	0
$494$	6.06120	0.272706
$495$	24.6274	1.10692
$496$	2.62145i	0.117707i
$497$	33.3583	1.49632
$498$	31.6935i	1.42022i
$499$	32.5905i	1.45895i	0.684007	+	0.729475i	$0.260236\pi$
$499$	32.5905i	1.45895i	−0.684007	+	0.729475i	$0.739764\pi$
$500$	1.07288i	0.0479806i
$501$	49.9573	2.23193
$502$	16.7937	0.749539
$503$	− 23.5391i	− 1.04956i	−0.851239	−	0.524779i	$-0.824148\pi$
$503$	− 23.5391i	− 1.04956i	0.851239	−	0.524779i	$-0.175852\pi$
$504$	36.7816i	1.63838i
$505$	− 1.46947i	− 0.0653905i
$506$	18.4026	0.818093
$507$	− 30.8711i	− 1.37103i
$508$	−15.0194	−0.666380
$509$	−17.5818	−0.779300	−0.389650	−	0.920963i	$-0.627404\pi$
$509$	−17.5818	−0.779300	−0.389650	+	0.920963i	$0.627404\pi$
$510$	0	0
$511$	−5.11953	−0.226474
$512$	−7.84603	−0.346749
$513$	− 14.6181i	− 0.645406i
$514$	−6.62553	−0.292239
$515$	9.80978i	0.432271i
$516$	− 0.0762528i	− 0.00335684i
$517$	− 33.3336i	− 1.46601i
$518$	−1.18210	−0.0519387
$519$	−59.8059	−2.62519
$520$	− 3.43271i	− 0.150534i
$521$	20.5061i	0.898388i	0.893434	+	0.449194i	$0.148289\pi$
$521$	20.5061i	0.898388i	−0.893434	+	0.449194i	$0.851711\pi$
$522$	19.3279i	0.845957i
$523$	9.19853	0.402224	0.201112	−	0.979568i	$-0.435545\pi$
$523$	9.19853	0.402224	0.201112	+	0.979568i	$0.435545\pi$
$524$	− 13.5938i	− 0.593849i
$525$	8.19759	0.357772
$526$	−6.00648	−0.261895
$527$	0	0
$528$	11.4195	0.496972
$529$	13.2815	0.577457
$530$	− 0.332275i	− 0.0144331i
$531$	16.3117	0.707866
$532$	− 18.0147i	− 0.781036i
$533$	1.97535i	0.0855618i
$534$	− 8.23671i	− 0.356437i
$535$	−2.88742	−0.124834
$536$	−16.6434	−0.718886
$537$	− 5.19378i	− 0.224128i
$538$	1.24294i	0.0535871i
$539$	− 15.7971i	− 0.680431i
$540$	−2.89052	−0.124388
$541$	− 14.2880i	− 0.614291i	−0.951663	−	0.307145i	$-0.900626\pi$
$541$	− 14.2880i	− 0.614291i	0.951663	−	0.307145i	$-0.0993738\pi$
$542$	9.90305	0.425372
$543$	1.88532	0.0809070
$544$	0	0
$545$	−5.76330	−0.246873
$546$	−9.15751	−0.391905
$547$	− 23.7010i	− 1.01338i	−0.862128	−	0.506691i	$-0.830869\pi$
$547$	− 23.7010i	− 1.01338i	0.862128	−	0.506691i	$-0.169131\pi$
$548$	−3.19598	−0.136525
$549$	− 49.9818i	− 2.13317i
$550$	− 5.90308i	− 0.251708i
$551$	− 27.1128i	− 1.15505i
$552$	−24.4338	−1.03997
$553$	16.3177	0.693898
$554$	− 24.4378i	− 1.03826i
$555$	− 1.05089i	− 0.0446078i
$556$	21.0728i	0.893684i
$557$	0.399812	0.0169406	0.00847028	−	0.999964i	$-0.497304\pi$
$557$	0.399812	0.0169406	0.00847028	+	0.999964i	$0.497304\pi$
$558$	14.4197i	0.610436i
$559$	0.0311279	0.00131657
$560$	2.17605	0.0919549
$561$	0	0
$562$	−5.67668	−0.239456
$563$	−9.26358	−0.390413	−0.195207	−	0.980762i	$-0.562538\pi$
$563$	−9.26358	−0.390413	−0.195207	+	0.980762i	$0.562538\pi$
$564$	15.4525i	0.650670i
$565$	9.02043	0.379492
$566$	17.7807i	0.747377i
$567$	− 15.2083i	− 0.638687i
$568$	31.8940i	1.33824i
$569$	−5.75650	−0.241325	−0.120662	−	0.992694i	$-0.538502\pi$
$569$	−5.75650	−0.241325	−0.120662	+	0.992694i	$0.538502\pi$
$570$	−13.8393	−0.579663
$571$	13.9987i	0.585825i	0.956139	+	0.292913i	$0.0946245\pi$
$571$	13.9987i	0.585825i	−0.956139	+	0.292913i	$0.905375\pi$
$572$	− 7.63106i	− 0.319071i
$573$	− 13.9426i	− 0.582462i
$574$	−5.07337	−0.211759
$575$	3.11745i	0.130007i
$576$	−25.9192	−1.07997
$577$	18.4417	0.767736	0.383868	−	0.923388i	$-0.374592\pi$
$577$	18.4417	0.767736	0.383868	+	0.923388i	$0.374592\pi$
$578$	0	0
$579$	−39.5495	−1.64362
$580$	−5.36115	−0.222610
$581$	38.4533i	1.59531i
$582$	−32.9919	−1.36756
$583$	− 2.11563i	− 0.0876204i
$584$	− 4.89480i	− 0.202548i
$585$	− 4.66049i	− 0.192688i
$586$	8.01007	0.330893
$587$	−4.03167	−0.166405	−0.0832024	−	0.996533i	$-0.526515\pi$
$587$	−4.03167	−0.166405	−0.0832024	+	0.996533i	$0.526515\pi$
$588$	7.32312i	0.302001i
$589$	− 20.2278i	− 0.833471i
$590$	− 3.90983i	− 0.160965i
$591$	16.7684	0.689758
$592$	− 0.278959i	− 0.0114651i
$593$	6.52416	0.267915	0.133958	−	0.990987i	$-0.457231\pi$
$593$	6.52416	0.267915	0.133958	+	0.990987i	$0.457231\pi$
$594$	15.9039	0.652544
$595$	0	0
$596$	−3.17114	−0.129895
$597$	39.5092	1.61700
$598$	− 3.48250i	− 0.142410i
$599$	6.81189	0.278326	0.139163	−	0.990269i	$-0.455559\pi$
$599$	6.81189	0.278326	0.139163	+	0.990269i	$0.455559\pi$
$600$	7.83775i	0.319975i
$601$	38.1591i	1.55654i	0.627927	+	0.778272i	$0.283904\pi$
$601$	38.1591i	1.55654i	−0.627927	+	0.778272i	$0.716096\pi$
$602$	0.0799473i	0.00325841i
$603$	−22.5963	−0.920192
$604$	23.6466	0.962166
$605$	− 26.5856i	− 1.08086i
$606$	− 3.74805i	− 0.152254i
$607$	− 27.1567i	− 1.10226i	−0.834420	−	0.551129i	$-0.814197\pi$
$607$	− 27.1567i	− 1.10226i	0.834420	−	0.551129i	$-0.185803\pi$
$608$	28.4342	1.15316
$609$	40.9632i	1.65991i
$610$	−11.9804	−0.485072
$611$	−6.30805	−0.255196
$612$	0	0
$613$	2.48591	0.100405	0.0502025	−	0.998739i	$-0.484013\pi$
$613$	2.48591	0.100405	0.0502025	+	0.998739i	$0.484013\pi$
$614$	−11.7826	−0.475506
$615$	− 4.51022i	− 0.181870i
$616$	56.1349	2.26174
$617$	− 43.1941i	− 1.73893i	−0.493994	−	0.869465i	$-0.664464\pi$
$617$	− 43.1941i	− 1.73893i	0.493994	−	0.869465i	$-0.335536\pi$
$618$	25.0210i	1.00649i
$619$	− 1.37692i	− 0.0553430i	−0.999617	−	0.0276715i	$-0.991191\pi$
$619$	− 1.37692i	− 0.0553430i	0.999617	−	0.0276715i	$-0.00880923\pi$
$620$	−3.99974	−0.160633
$621$	−8.39893	−0.337037
$622$	31.4250i	1.26003i
$623$	− 9.99347i	− 0.400380i
$624$	− 2.16103i	− 0.0865106i
$625$	1.00000	0.0400000
$626$	− 12.9304i	− 0.516803i
$627$	−88.1162	−3.51902
$628$	−13.8043	−0.550851
$629$	0	0
$630$	11.9697	0.476886
$631$	32.4351	1.29122	0.645611	−	0.763667i	$-0.276603\pi$
$631$	32.4351	1.29122	0.645611	+	0.763667i	$0.276603\pi$
$632$	15.6014i	0.620590i
$633$	−35.4928	−1.41071
$634$	9.50698i	0.377570i
$635$	13.9992i	0.555541i
$636$	0.980749i	0.0388892i
$637$	−2.98945	−0.118446
$638$	29.4975	1.16782
$639$	43.3015i	1.71298i
$640$	− 4.26831i	− 0.168720i
$641$	22.2992i	0.880764i	0.897811	+	0.440382i	$0.145157\pi$
$641$	22.2992i	0.880764i	−0.897811	+	0.440382i	$0.854843\pi$
$642$	−7.36471	−0.290662
$643$	− 11.7260i	− 0.462430i	−0.972903	−	0.231215i	$-0.925730\pi$
$643$	− 11.7260i	− 0.462430i	0.972903	−	0.231215i	$-0.0742701\pi$
$644$	−10.3504	−0.407865
$645$	−0.0710730	−0.00279850
$646$	0	0
$647$	−37.3217	−1.46727	−0.733634	−	0.679544i	$-0.762177\pi$
$647$	−37.3217	−1.46727	−0.733634	+	0.679544i	$0.762177\pi$
$648$	14.5407	0.571212
$649$	− 24.8943i	− 0.977188i
$650$	−1.11710	−0.0438162
$651$	30.5610i	1.19778i
$652$	− 20.6985i	− 0.810616i
$653$	− 1.75573i	− 0.0687071i	−0.999410	−	0.0343535i	$-0.989063\pi$
$653$	− 1.75573i	− 0.0687071i	0.999410	−	0.0343535i	$-0.0109372\pi$
$654$	−14.7000	−0.574815
$655$	−12.6704	−0.495074
$656$	− 1.19724i	− 0.0467443i
$657$	− 6.64553i	− 0.259267i
$658$	− 16.2012i	− 0.631590i
$659$	6.02834	0.234831	0.117415	−	0.993083i	$-0.462539\pi$
$659$	6.02834	0.234831	0.117415	+	0.993083i	$0.462539\pi$
$660$	17.4236i	0.678215i
$661$	−32.0199	−1.24543	−0.622715	−	0.782449i	$-0.713970\pi$
$661$	−32.0199	−1.24543	−0.622715	+	0.782449i	$0.713970\pi$
$662$	5.43353	0.211180
$663$	0	0
$664$	−36.7653	−1.42677
$665$	−16.7910	−0.651126
$666$	− 1.53446i	− 0.0594592i
$667$	−15.5778	−0.603176
$668$	20.2336i	0.782860i
$669$	5.59723i	0.216401i
$670$	5.41623i	0.209247i
$671$	−76.2805	−2.94478
$672$	−42.9595	−1.65720
$673$	39.5902i	1.52609i	0.646346	+	0.763044i	$0.276296\pi$
$673$	39.5902i	1.52609i	−0.646346	+	0.763044i	$0.723704\pi$
$674$	15.9765i	0.615391i
$675$	2.69417i	0.103698i
$676$	12.5033	0.480897
$677$	6.99467i	0.268827i	0.990925	+	0.134413i	$0.0429150\pi$
$677$	6.99467i	0.268827i	−0.990925	+	0.134413i	$0.957085\pi$
$678$	23.0077	0.883605
$679$	−40.0286	−1.53616
$680$	0	0
$681$	−38.5677	−1.47792
$682$	22.0069	0.842689
$683$	− 37.2155i	− 1.42401i	−0.702174	−	0.712005i	$-0.747787\pi$
$683$	− 37.2155i	− 1.42401i	0.702174	−	0.712005i	$-0.252213\pi$
$684$	23.3844	0.894126
$685$	2.97888i	0.113817i
$686$	13.1802i	0.503221i
$687$	7.02084i	0.267862i
$688$	−0.0188663	−0.000719272 0
$689$	−0.400362	−0.0152526
$690$	7.95143i	0.302706i
$691$	15.6482i	0.595286i	0.954677	+	0.297643i	$0.0962005\pi$
$691$	15.6482i	0.595286i	−0.954677	+	0.297643i	$0.903800\pi$
$692$	− 24.2224i	− 0.920798i
$693$	76.2127	2.89508
$694$	8.90101i	0.337878i
$695$	19.6413	0.745037
$696$	−39.1650	−1.48455
$697$	0	0
$698$	−25.9276	−0.981372
$699$	8.31576	0.314531
$700$	3.32016i	0.125490i
$701$	−6.08551	−0.229847	−0.114923	−	0.993374i	$-0.536662\pi$
$701$	−6.08551	−0.229847	−0.114923	+	0.993374i	$0.536662\pi$
$702$	− 3.00965i	− 0.113592i
$703$	2.15252i	0.0811838i
$704$	39.5570i	1.49086i
$705$	14.4029	0.542444
$706$	−22.1193	−0.832469
$707$	− 4.54746i	− 0.171025i
$708$	11.5403i	0.433712i
$709$	19.7081i	0.740154i	0.929001	+	0.370077i	$0.120669\pi$
$709$	19.7081i	0.740154i	−0.929001	+	0.370077i	$0.879331\pi$
$710$	10.3792	0.389524
$711$	21.1816i	0.794371i
$712$	9.55480	0.358081
$713$	−11.6220	−0.435247
$714$	0	0
$715$	−7.11269	−0.266000
$716$	2.10357	0.0786141
$717$	36.3147i	1.35620i
$718$	−32.8425	−1.22567
$719$	15.9164i	0.593583i	0.954942	+	0.296791i	$0.0959166\pi$
$719$	15.9164i	0.593583i	−0.954942	+	0.296791i	$0.904083\pi$
$720$	2.82468i	0.105270i
$721$	30.3576i	1.13058i
$722$	10.0522	0.374104
$723$	−33.0796	−1.23024
$724$	0.763588i	0.0283785i
$725$	4.99698i	0.185583i
$726$	− 67.8096i	− 2.51665i
$727$	22.2643	0.825736	0.412868	−	0.910791i	$-0.364527\pi$
$727$	22.2643	0.825736	0.412868	+	0.910791i	$0.364527\pi$
$728$	− 10.6230i	− 0.393713i
$729$	41.1518	1.52414
$730$	−1.59290	−0.0589560
$731$	0	0
$732$	35.3616	1.30700
$733$	5.67351	0.209556	0.104778	−	0.994496i	$-0.466587\pi$
$733$	5.67351	0.209556	0.104778	+	0.994496i	$0.466587\pi$
$734$	− 8.93169i	− 0.329675i
$735$	6.82567	0.251769
$736$	− 16.3370i	− 0.602191i
$737$	34.4857i	1.27030i
$738$	− 6.58562i	− 0.242420i
$739$	39.7975	1.46397	0.731987	−	0.681319i	$-0.238593\pi$
$739$	39.7975	1.46397	0.731987	+	0.681319i	$0.238593\pi$
$740$	0.425628	0.0156464
$741$	16.6751i	0.612575i
$742$	− 1.02827i	− 0.0377488i
$743$	− 10.6500i	− 0.390709i	−0.980733	−	0.195355i	$-0.937414\pi$
$743$	− 10.6500i	− 0.390709i	0.980733	−	0.195355i	$-0.0625858\pi$
$744$	−29.2195	−1.07124
$745$	2.95573i	0.108290i
$746$	−2.95464	−0.108177
$747$	−49.9153	−1.82630
$748$	0	0
$749$	−8.93549	−0.326496
$750$	2.55062	0.0931355
$751$	− 18.1195i	− 0.661190i	−0.943773	−	0.330595i	$-0.892751\pi$
$751$	− 18.1195i	− 0.661190i	0.943773	−	0.330595i	$-0.107249\pi$
$752$	3.82324	0.139419
$753$	46.2014i	1.68367i
$754$	− 5.58211i	− 0.203289i
$755$	− 22.0403i	− 0.802128i
$756$	−8.94507	−0.325329
$757$	17.0771	0.620676	0.310338	−	0.950626i	$-0.399558\pi$
$757$	17.0771	0.620676	0.310338	+	0.950626i	$0.399558\pi$
$758$	− 35.1774i	− 1.27770i
$759$	50.6276i	1.83767i
$760$	− 16.0539i	− 0.582337i
$761$	−31.9719	−1.15898	−0.579491	−	0.814979i	$-0.696749\pi$
$761$	−31.9719	−1.15898	−0.579491	+	0.814979i	$0.696749\pi$
$762$	35.7066i	1.29351i
$763$	−17.8353	−0.645681
$764$	5.64701	0.204301
$765$	0	0
$766$	8.97540	0.324294
$767$	−4.71100	−0.170104
$768$	− 45.0707i	− 1.62635i
$769$	−34.9147	−1.25906	−0.629529	−	0.776977i	$-0.716752\pi$
$769$	−34.9147	−1.25906	−0.629529	+	0.776977i	$0.716752\pi$
$770$	− 18.2678i	− 0.658327i
$771$	− 18.2276i	− 0.656452i
$772$	− 16.0182i	− 0.576509i
$773$	−4.49160	−0.161552	−0.0807758	−	0.996732i	$-0.525740\pi$
$773$	−4.49160	−0.161552	−0.0807758	+	0.996732i	$0.525740\pi$
$774$	−0.103778	−0.00373021
$775$	3.72804i	0.133915i
$776$	− 38.2715i	− 1.37387i
$777$	− 3.25211i	− 0.116669i
$778$	−31.9310	−1.14478
$779$	9.23821i	0.330993i
$780$	3.29725	0.118061
$781$	66.0854	2.36472
$782$	0	0
$783$	−13.4627	−0.481117
$784$	1.81188	0.0647098
$785$	12.8666i	0.459228i
$786$	−32.3174	−1.15272
$787$	8.65141i	0.308390i	0.988040	+	0.154195i	$0.0492783\pi$
$787$	8.65141i	0.308390i	−0.988040	+	0.154195i	$0.950722\pi$
$788$	6.79148i	0.241936i
$789$	− 16.5245i	− 0.588289i
$790$	5.07713	0.180636
$791$	27.9149	0.992539
$792$	72.8673i	2.58923i
$793$	14.4353i	0.512613i
$794$	− 8.49772i	− 0.301573i
$795$	0.914127	0.0324208
$796$	16.0019i	0.567173i
$797$	−19.0137	−0.673500	−0.336750	−	0.941594i	$-0.609328\pi$
$797$	−19.0137	−0.673500	−0.336750	+	0.941594i	$0.609328\pi$
$798$	−42.8274	−1.51607
$799$	0	0
$800$	−5.24051	−0.185280
$801$	12.9723	0.458353
$802$	− 18.7943i	− 0.663649i
$803$	−10.1422	−0.357910
$804$	− 15.9866i	− 0.563806i
$805$	9.64735i	0.340024i
$806$	− 4.16459i	− 0.146691i
$807$	−3.41949	−0.120372
$808$	4.34784	0.152957
$809$	22.6712i	0.797077i	0.917152	+	0.398538i	$0.130482\pi$
$809$	22.6712i	0.797077i	−0.917152	+	0.398538i	$0.869518\pi$
$810$	− 4.73194i	− 0.166263i
$811$	− 24.1167i	− 0.846850i	−0.905931	−	0.423425i	$-0.860828\pi$
$811$	− 24.1167i	− 0.846850i	0.905931	−	0.423425i	$-0.139172\pi$
$812$	−16.5908	−0.582222
$813$	27.2445i	0.955505i
$814$	−2.34184	−0.0820816
$815$	−19.2925	−0.675786
$816$	0	0
$817$	0.145578	0.00509311
$818$	10.0285	0.350638
$819$	− 14.4225i	− 0.503963i
$820$	1.82672	0.0637917
$821$	0.114687i	0.00400260i	0.999998	+	0.00200130i	$0.000637035\pi$
$821$	0.114687i	0.00400260i	−0.999998	+	0.00200130i	$0.999363\pi$
$822$	7.59799i	0.265010i
$823$	− 33.8610i	− 1.18032i	−0.807286	−	0.590161i	$-0.799064\pi$
$823$	− 33.8610i	− 1.18032i	0.807286	−	0.590161i	$-0.200936\pi$
$824$	−29.0250	−1.01114
$825$	16.2401	0.565407
$826$	− 12.0995i	− 0.420995i
$827$	20.5646i	0.715102i	0.933894	+	0.357551i	$0.116388\pi$
$827$	20.5646i	0.715102i	−0.933894	+	0.357551i	$0.883612\pi$
$828$	− 13.4357i	− 0.466921i
$829$	26.7935	0.930576	0.465288	−	0.885159i	$-0.345951\pi$
$829$	26.7935	0.930576	0.465288	+	0.885159i	$0.345951\pi$
$830$	11.9645i	0.415292i
$831$	67.2314	2.33223
$832$	7.48577	0.259522
$833$	0	0
$834$	50.0975	1.73473
$835$	18.8591	0.652647
$836$	− 35.6886i	− 1.23431i
$837$	−10.0440	−0.347170
$838$	− 34.0092i	− 1.17483i
$839$	13.8332i	0.477575i	0.971072	+	0.238788i	$0.0767500\pi$
$839$	13.8332i	0.477575i	−0.971072	+	0.238788i	$0.923250\pi$
$840$	24.2549i	0.836874i
$841$	4.03023	0.138973
$842$	−14.4628	−0.498419
$843$	− 15.6172i	− 0.537886i
$844$	− 14.3752i	− 0.494814i
$845$	− 11.6540i	− 0.400910i
$846$	21.0304	0.723041
$847$	− 82.2724i	− 2.82691i
$848$	0.242655	0.00833281
$849$	−48.9168	−1.67882
$850$	0	0
$851$	1.23674	0.0423950
$852$	−30.6354	−1.04955
$853$	− 12.7815i	− 0.437631i	−0.975766	−	0.218816i	$-0.929781\pi$
$853$	− 12.7815i	− 0.437631i	0.975766	−	0.218816i	$-0.0702193\pi$
$854$	−37.0749	−1.26868
$855$	− 21.7960i	− 0.745406i
$856$	− 8.54325i	− 0.292002i
$857$	6.31557i	0.215736i	0.994165	+	0.107868i	$0.0344023\pi$
$857$	6.31557i	0.215736i	−0.994165	+	0.107868i	$0.965598\pi$
$858$	−18.1418	−0.619350
$859$	35.1334	1.19874	0.599369	−	0.800473i	$-0.295418\pi$
$859$	35.1334	1.19874	0.599369	+	0.800473i	$0.295418\pi$
$860$	− 0.0287858i	0 0.000981587i
$861$	− 13.9575i	− 0.475669i
$862$	− 22.4847i	− 0.765833i
$863$	−44.2102	−1.50493	−0.752466	−	0.658632i	$-0.771136\pi$
$863$	−44.2102	−1.50493	−0.752466	+	0.658632i	$0.771136\pi$
$864$	− 14.1188i	− 0.480331i
$865$	−22.5770	−0.767641
$866$	17.6279	0.599022
$867$	0	0
$868$	−12.3777	−0.420127
$869$	32.3266	1.09661
$870$	12.7454i	0.432109i
$871$	6.52608	0.221128
$872$	− 17.0524i	− 0.577467i
$873$	− 51.9601i	− 1.75858i
$874$	− 16.2868i	− 0.550908i
$875$	3.09463	0.104618
$876$	4.70164	0.158854
$877$	− 23.6073i	− 0.797164i	−0.917133	−	0.398582i	$-0.869503\pi$
$877$	− 23.6073i	− 0.797164i	0.917133	−	0.398582i	$-0.130497\pi$
$878$	19.5171i	0.658671i
$879$	22.0367i	0.743278i
$880$	4.31093	0.145321
$881$	− 33.0624i	− 1.11390i	−0.830546	−	0.556950i	$-0.811971\pi$
$881$	− 33.0624i	− 1.11390i	0.830546	−	0.556950i	$-0.188029\pi$
$882$	9.96654	0.335591
$883$	58.1141	1.95569	0.977847	−	0.209320i	$-0.0671251\pi$
$883$	58.1141	1.95569	0.977847	+	0.209320i	$0.0671251\pi$
$884$	0	0
$885$	10.7564	0.361573
$886$	28.2938	0.950550
$887$	28.0097i	0.940474i	0.882540	+	0.470237i	$0.155832\pi$
$887$	28.0097i	0.940474i	−0.882540	+	0.470237i	$0.844168\pi$
$888$	3.10936	0.104343
$889$	43.3223i	1.45298i
$890$	− 3.10940i	− 0.104227i
$891$	− 30.1288i	− 1.00935i
$892$	−2.26697	−0.0759039
$893$	−29.5012	−0.987219
$894$	7.53895i	0.252140i
$895$	− 1.96068i	− 0.0655382i
$896$	− 13.2088i	− 0.441276i
$897$	9.58077	0.319893
$898$	− 31.4300i	− 1.04883i
$899$	−18.6289	−0.621310
$900$	−4.30982	−0.143661
$901$	0	0
$902$	−10.0508	−0.334654
$903$	−0.219944	−0.00731929
$904$	26.6895i	0.887680i
$905$	0.711719	0.0236583
$906$	− 56.2164i	− 1.86766i
$907$	49.9204i	1.65758i	0.559560	+	0.828790i	$0.310970\pi$
$907$	49.9204i	1.65758i	−0.559560	+	0.828790i	$0.689030\pi$
$908$	− 15.6206i	− 0.518387i
$909$	5.90294	0.195788
$910$	−3.45700	−0.114599
$911$	21.8797i	0.724908i	0.932002	+	0.362454i	$0.118061\pi$
$911$	21.8797i	0.724908i	−0.932002	+	0.362454i	$0.881939\pi$
$912$	− 10.1066i	− 0.334663i
$913$	76.1790i	2.52116i
$914$	8.13734	0.269159
$915$	− 32.9595i	− 1.08961i
$916$	−2.84356	−0.0939538
$917$	−39.2102	−1.29483
$918$	0	0
$919$	−11.0529	−0.364600	−0.182300	−	0.983243i	$-0.558354\pi$
$919$	−11.0529	−0.364600	−0.182300	+	0.983243i	$0.558354\pi$
$920$	−9.22387	−0.304102
$921$	− 32.4153i	− 1.06812i
$922$	36.8378	1.21319
$923$	− 12.5060i	− 0.411640i
$924$	53.9197i	1.77383i
$925$	− 0.396716i	− 0.0130439i
$926$	26.1671	0.859905
$927$	−39.4065	−1.29428
$928$	− 26.1867i	− 0.859621i
$929$	− 33.1333i	− 1.08707i	−0.839387	−	0.543534i	$-0.817086\pi$
$929$	− 33.1333i	− 1.08707i	0.839387	−	0.543534i	$-0.182914\pi$
$930$	9.50882i	0.311806i
$931$	−13.9809	−0.458206
$932$	3.36803i	0.110323i
$933$	−86.4540	−2.83038
$934$	−3.31733	−0.108546
$935$	0	0
$936$	13.7894	0.450721
$937$	58.3815	1.90724	0.953621	−	0.301011i	$-0.0973241\pi$
$937$	58.3815	1.90724	0.953621	+	0.301011i	$0.0973241\pi$
$938$	16.7612i	0.547273i
$939$	35.5731	1.16088
$940$	5.83341i	0.190265i
$941$	− 6.09945i	− 0.198836i	−0.995046	−	0.0994181i	$-0.968302\pi$
$941$	− 6.09945i	− 0.198836i	0.995046	−	0.0994181i	$-0.0316981\pi$
$942$	32.8177i	1.06926i
$943$	5.30787	0.172848
$944$	2.85529	0.0929318
$945$	8.33744i	0.271217i
$946$	0.158382i	0.00514944i
$947$	47.1485i	1.53212i	0.642769	+	0.766060i	$0.277785\pi$
$947$	47.1485i	1.53212i	−0.642769	+	0.766060i	$0.722215\pi$
$948$	−14.9857	−0.486714
$949$	1.91931i	0.0623034i
$950$	−5.22439	−0.169502
$951$	−26.1548	−0.848129
$952$	0	0
$953$	26.8459	0.869625	0.434812	−	0.900521i	$-0.356815\pi$
$953$	26.8459	0.869625	0.434812	+	0.900521i	$0.356815\pi$
$954$	1.33477	0.0432147
$955$	− 5.26341i	− 0.170320i
$956$	−14.7081	−0.475694
$957$	81.1513i	2.62325i
$958$	− 14.7890i	− 0.477812i
$959$	9.21852i	0.297682i
$960$	−17.0919	−0.551639
$961$	17.1017	0.551668
$962$	0.443171i	0.0142884i
$963$	− 11.5989i	− 0.373770i
$964$	− 13.3978i	− 0.431514i
$965$	−14.9301	−0.480618
$966$	24.6067i	0.791708i
$967$	34.1142	1.09704	0.548519	−	0.836138i	$-0.315192\pi$
$967$	34.1142	1.09704	0.548519	+	0.836138i	$0.315192\pi$
$968$	78.6610	2.52826
$969$	0	0
$970$	−12.4546	−0.399893
$971$	−22.9516	−0.736551	−0.368276	−	0.929717i	$-0.620052\pi$
$971$	−22.9516	−0.736551	−0.368276	+	0.929717i	$0.620052\pi$
$972$	22.6384i	0.726128i
$973$	60.7825	1.94860
$974$	25.3327i	0.811711i
$975$	− 3.07327i	− 0.0984235i
$976$	− 8.74911i	− 0.280052i
$977$	−19.8739	−0.635823	−0.317912	−	0.948120i	$-0.602982\pi$
$977$	−19.8739	−0.635823	−0.317912	+	0.948120i	$0.602982\pi$
$978$	−49.2077	−1.57349
$979$	− 19.7979i	− 0.632743i
$980$	2.76451i	0.0883092i
$981$	− 23.1515i	− 0.739172i
$982$	27.9585	0.892192
$983$	− 59.0708i	− 1.88407i	−0.335518	−	0.942034i	$-0.608911\pi$
$983$	− 59.0708i	− 1.88407i	0.335518	−	0.942034i	$-0.391089\pi$
$984$	13.3448	0.425416
$985$	6.33014	0.201695
$986$	0	0
$987$	44.5715	1.41873
$988$	−6.75370	−0.214864
$989$	− 0.0836424i	− 0.00265967i
$990$	23.7130	0.753649
$991$	10.5941i	0.336534i	0.985741	+	0.168267i	$0.0538171\pi$
$991$	10.5941i	0.336534i	−0.985741	+	0.168267i	$0.946183\pi$
$992$	− 19.5368i	− 0.620296i
$993$	14.9483i	0.474370i
$994$	32.1197	1.01878
$995$	14.9149	0.472835
$996$	− 35.3145i	− 1.11898i
$997$	− 40.7864i	− 1.29172i	−0.763456	−	0.645860i	$-0.776499\pi$
$997$	− 40.7864i	− 1.29172i	0.763456	−	0.645860i	$-0.223501\pi$
$998$	31.3804i	0.993331i
$999$	1.06882	0.0338159

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1445.2.d.j.866.14		24
17.3	odd	16		85.2.l.a.76.4	yes	24
17.4	even	4		1445.2.a.p.1.6		12
17.11	odd	16		85.2.l.a.66.4	✓	24
17.13	even	4		1445.2.a.q.1.6		12
17.16	even	2	inner	1445.2.d.j.866.13		24
51.11	even	16		765.2.be.b.406.3		24
51.20	even	16		765.2.be.b.586.3		24
85.3	even	16		425.2.n.c.399.3		24
85.4	even	4		7225.2.a.bs.1.7		12
85.28	even	16		425.2.n.f.49.4		24
85.37	even	16		425.2.n.f.399.4		24
85.54	odd	16		425.2.m.b.76.3		24
85.62	even	16		425.2.n.c.49.3		24
85.64	even	4		7225.2.a.bq.1.7		12
85.79	odd	16		425.2.m.b.151.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.66.4	✓	24	17.11	odd	16
85.2.l.a.76.4	yes	24	17.3	odd	16
425.2.m.b.76.3		24	85.54	odd	16
425.2.m.b.151.3		24	85.79	odd	16
425.2.n.c.49.3		24	85.62	even	16
425.2.n.c.399.3		24	85.3	even	16
425.2.n.f.49.4		24	85.28	even	16
425.2.n.f.399.4		24	85.37	even	16
765.2.be.b.406.3		24	51.11	even	16
765.2.be.b.586.3		24	51.20	even	16
1445.2.a.p.1.6		12	17.4	even	4
1445.2.a.q.1.6		12	17.13	even	4
1445.2.d.j.866.13		24	17.16	even	2	inner
1445.2.d.j.866.14		24	1.1	even	1	trivial
7225.2.a.bq.1.7		12	85.64	even	4
7225.2.a.bs.1.7		12	85.4	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:	\( N \)	\(=\)	\( 1445 = 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1445.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+0.962871 q^{2} +2.64897i q^{3} -1.07288 q^{4} +1.00000i q^{5} +2.55062i q^{6} +3.09463i q^{7} -2.95879 q^{8} -4.01706 q^{9} +0.962871i q^{10} +6.13071i q^{11} -2.84203i q^{12} +1.16017 q^{13} +2.97973i q^{14} -2.64897 q^{15} -0.703170 q^{16} -3.86791 q^{18} +5.42585 q^{19} -1.07288i q^{20} -8.19759 q^{21} +5.90308i q^{22} -3.11745i q^{23} -7.83775i q^{24} -1.00000 q^{25} +1.11710 q^{26} -2.69417i q^{27} -3.32016i q^{28} -4.99698i q^{29} -2.55062 q^{30} -3.72804i q^{31} +5.24051 q^{32} -16.2401 q^{33} -3.09463 q^{35} +4.30982 q^{36} +0.396716i q^{37} +5.22439 q^{38} +3.07327i q^{39} -2.95879i q^{40} +1.70263i q^{41} -7.89322 q^{42} +0.0268304 q^{43} -6.57751i q^{44} -4.01706i q^{45} -3.00170i q^{46} -5.43715 q^{47} -1.86268i q^{48} -2.57672 q^{49} -0.962871 q^{50} -1.24473 q^{52} -0.345087 q^{53} -2.59413i q^{54} -6.13071 q^{55} -9.15634i q^{56} +14.3729i q^{57} -4.81144i q^{58} -4.06060 q^{59} +2.84203 q^{60} +12.4424i q^{61} -3.58962i q^{62} -12.4313i q^{63} +6.45228 q^{64} +1.16017i q^{65} -15.6371 q^{66} +5.62508 q^{67} +8.25804 q^{69} -2.97973 q^{70} -10.7794i q^{71} +11.8856 q^{72} +1.65433i q^{73} +0.381986i q^{74} -2.64897i q^{75} -5.82128 q^{76} -18.9723 q^{77} +2.95916i q^{78} -5.27290i q^{79} -0.703170i q^{80} -4.91441 q^{81} +1.63941i q^{82} +12.4258 q^{83} +8.79502 q^{84} +0.0258342 q^{86} +13.2369 q^{87} -18.1394i q^{88} -3.22930 q^{89} -3.86791i q^{90} +3.59031i q^{91} +3.34465i q^{92} +9.87549 q^{93} -5.23528 q^{94} +5.42585i q^{95} +13.8820i q^{96} +12.9349i q^{97} -2.48105 q^{98} -24.6274i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8} - 24 q^{9} - 16 q^{13} + 16 q^{15} + 24 q^{16} + 8 q^{18} + 32 q^{21} - 24 q^{25} - 32 q^{26} - 16 q^{30} + 56 q^{32} - 32 q^{35} - 24 q^{36} - 48 q^{38} + 32 q^{43}+ \cdots - 120 q^{98}+O(q^{100}) \) 24 * q + 8 * q^2 + 24 * q^4 + 24 * q^8 - 24 * q^9 - 16 * q^13 + 16 * q^15 + 24 * q^16 + 8 * q^18 + 32 * q^21 - 24 * q^25 - 32 * q^26 - 16 * q^30 + 56 * q^32 - 32 * q^35 - 24 * q^36 - 48 * q^38 + 32 * q^43 - 64 * q^47 - 40 * q^49 - 8 * q^50 - 48 * q^52 - 32 * q^55 - 16 * q^59 + 32 * q^60 + 72 * q^64 - 80 * q^66 - 16 * q^67 + 96 * q^69 - 32 * q^70 + 24 * q^72 - 32 * q^76 - 48 * q^77 + 72 * q^81 + 80 * q^83 + 64 * q^84 - 16 * q^86 + 64 * q^87 + 16 * q^89 - 48 * q^93 + 32 * q^94 - 120 * q^98

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