LMFDB - Embedded newform 1445.2.d.f.866.1

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:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			866.1
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1445.866
Dual form			1445.2.d.f.866.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.414214 q^{2} -3.41421i q^{3} -1.82843 q^{4} -1.00000i q^{5} +1.41421i q^{6} +0.585786i q^{7} +1.58579 q^{8} -8.65685 q^{9} +0.414214i q^{10} +2.58579i q^{11} +6.24264i q^{12} -2.82843 q^{13} -0.242641i q^{14} -3.41421 q^{15} +3.00000 q^{16} +3.58579 q^{18} +2.82843 q^{19} +1.82843i q^{20} +2.00000 q^{21} -1.07107i q^{22} +3.41421i q^{23} -5.41421i q^{24} -1.00000 q^{25} +1.17157 q^{26} +19.3137i q^{27} -1.07107i q^{28} -4.82843i q^{29} +1.41421 q^{30} +4.24264i q^{31} -4.41421 q^{32} +8.82843 q^{33} +0.585786 q^{35} +15.8284 q^{36} +6.48528i q^{37} -1.17157 q^{38} +9.65685i q^{39} -1.58579i q^{40} +6.48528i q^{41} -0.828427 q^{42} -7.65685 q^{43} -4.72792i q^{44} +8.65685i q^{45} -1.41421i q^{46} -4.82843 q^{47} -10.2426i q^{48} +6.65685 q^{49} +0.414214 q^{50} +5.17157 q^{52} -0.343146 q^{53} -8.00000i q^{54} +2.58579 q^{55} +0.928932i q^{56} -9.65685i q^{57} +2.00000i q^{58} +9.17157 q^{59} +6.24264 q^{60} -7.65685i q^{61} -1.75736i q^{62} -5.07107i q^{63} -4.17157 q^{64} +2.82843i q^{65} -3.65685 q^{66} -3.17157 q^{67} +11.6569 q^{69} -0.242641 q^{70} -4.24264i q^{71} -13.7279 q^{72} -4.82843i q^{73} -2.68629i q^{74} +3.41421i q^{75} -5.17157 q^{76} -1.51472 q^{77} -4.00000i q^{78} -5.41421i q^{79} -3.00000i q^{80} +39.9706 q^{81} -2.68629i q^{82} -9.31371 q^{83} -3.65685 q^{84} +3.17157 q^{86} -16.4853 q^{87} +4.10051i q^{88} -2.34315 q^{89} -3.58579i q^{90} -1.65685i q^{91} -6.24264i q^{92} +14.4853 q^{93} +2.00000 q^{94} -2.82843i q^{95} +15.0711i q^{96} +3.65685i q^{97} -2.75736 q^{98} -22.3848i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{4} + 12 q^{8} - 12 q^{9} - 8 q^{15} + 12 q^{16} + 20 q^{18} + 8 q^{21} - 4 q^{25} + 16 q^{26} - 12 q^{32} + 24 q^{33} + 8 q^{35} + 52 q^{36} - 16 q^{38} + 8 q^{42} - 8 q^{43} - 8 q^{47}+ \cdots - 28 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^4 + 12 * q^8 - 12 * q^9 - 8 * q^15 + 12 * q^16 + 20 * q^18 + 8 * q^21 - 4 * q^25 + 16 * q^26 - 12 * q^32 + 24 * q^33 + 8 * q^35 + 52 * q^36 - 16 * q^38 + 8 * q^42 - 8 * q^43 - 8 * q^47 + 4 * q^49 - 4 * q^50 + 32 * q^52 - 24 * q^53 + 16 * q^55 + 48 * q^59 + 8 * q^60 - 28 * q^64 + 8 * q^66 - 24 * q^67 + 24 * q^69 + 16 * q^70 - 4 * q^72 - 32 * q^76 - 40 * q^77 + 92 * q^81 + 8 * q^83 + 8 * q^84 + 24 * q^86 - 32 * q^87 - 32 * q^89 + 24 * q^93 + 8 * q^94 - 28 * 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 $

$2$	−0.414214	−0.292893	−0.146447	−	0.989219i	$-0.546784\pi$
$2$	−0.414214	−0.292893	−0.146447	+	0.989219i	$0.546784\pi$
$3$	− 3.41421i	− 1.97120i	−0.169102	−	0.985599i	$-0.554087\pi$
$3$	− 3.41421i	− 1.97120i	0.169102	−	0.985599i	$-0.445913\pi$
$4$	−1.82843	−0.914214
$5$	− 1.00000i	− 0.447214i
$5$	− 1.00000i	− 0.447214i
$6$	1.41421i	0.577350i
$7$	0.585786i	0.221406i	0.993854	+	0.110703i	$0.0353103\pi$
$7$	0.585786i	0.221406i	−0.993854	+	0.110703i	$0.964690\pi$
$8$	1.58579	0.560660
$9$	−8.65685	−2.88562
$10$	0.414214i	0.130986i
$11$	2.58579i	0.779644i	0.920890	+	0.389822i	$0.127463\pi$
$11$	2.58579i	0.779644i	−0.920890	+	0.389822i	$0.872537\pi$
$12$	6.24264i	1.80210i
$13$	−2.82843	−0.784465	−0.392232	−	0.919866i	$-0.628297\pi$
$13$	−2.82843	−0.784465	−0.392232	+	0.919866i	$0.628297\pi$
$14$	− 0.242641i	− 0.0648485i
$15$	−3.41421	−0.881546
$16$	3.00000	0.750000
$17$	0	0
$17$	0	0
$18$	3.58579	0.845178
$19$	2.82843	0.648886	0.324443	−	0.945905i	$-0.394823\pi$
$19$	2.82843	0.648886	0.324443	+	0.945905i	$0.394823\pi$
$20$	1.82843i	0.408849i
$21$	2.00000	0.436436
$22$	− 1.07107i	− 0.228352i
$23$	3.41421i	0.711913i	0.934503	+	0.355956i	$0.115845\pi$
$23$	3.41421i	0.711913i	−0.934503	+	0.355956i	$0.884155\pi$
$24$	− 5.41421i	− 1.10517i
$25$	−1.00000	−0.200000
$26$	1.17157	0.229764
$27$	19.3137i	3.71692i
$28$	− 1.07107i	− 0.202413i
$29$	− 4.82843i	− 0.896616i	−0.893879	−	0.448308i	$-0.852027\pi$
$29$	− 4.82843i	− 0.896616i	0.893879	−	0.448308i	$-0.147973\pi$
$30$	1.41421	0.258199
$31$	4.24264i	0.762001i	0.924575	+	0.381000i	$0.124420\pi$
$31$	4.24264i	0.762001i	−0.924575	+	0.381000i	$0.875580\pi$
$32$	−4.41421	−0.780330
$33$	8.82843	1.53683
$34$	0	0
$35$	0.585786	0.0990160
$36$	15.8284	2.63807
$37$	6.48528i	1.06617i	0.846061	+	0.533087i	$0.178968\pi$
$37$	6.48528i	1.06617i	−0.846061	+	0.533087i	$0.821032\pi$
$38$	−1.17157	−0.190054
$39$	9.65685i	1.54633i
$40$	− 1.58579i	− 0.250735i
$41$	6.48528i	1.01283i	0.862290	+	0.506415i	$0.169030\pi$
$41$	6.48528i	1.01283i	−0.862290	+	0.506415i	$0.830970\pi$
$42$	−0.828427	−0.127829
$43$	−7.65685	−1.16766	−0.583830	−	0.811876i	$-0.698446\pi$
$43$	−7.65685	−1.16766	−0.583830	+	0.811876i	$0.698446\pi$
$44$	− 4.72792i	− 0.712761i
$45$	8.65685i	1.29049i
$46$	− 1.41421i	− 0.208514i
$47$	−4.82843	−0.704298	−0.352149	−	0.935944i	$-0.614549\pi$
$47$	−4.82843	−0.704298	−0.352149	+	0.935944i	$0.614549\pi$
$48$	− 10.2426i	− 1.47840i
$49$	6.65685	0.950979
$50$	0.414214	0.0585786
$51$	0	0
$52$	5.17157	0.717168
$53$	−0.343146	−0.0471347	−0.0235673	−	0.999722i	$-0.507502\pi$
$53$	−0.343146	−0.0471347	−0.0235673	+	0.999722i	$0.507502\pi$
$54$	− 8.00000i	− 1.08866i
$55$	2.58579	0.348667
$56$	0.928932i	0.124134i
$57$	− 9.65685i	− 1.27908i
$58$	2.00000i	0.262613i
$59$	9.17157	1.19404	0.597019	−	0.802227i	$-0.296352\pi$
$59$	9.17157	1.19404	0.597019	+	0.802227i	$0.296352\pi$
$60$	6.24264	0.805921
$61$	− 7.65685i	− 0.980360i	−0.871621	−	0.490180i	$-0.836931\pi$
$61$	− 7.65685i	− 0.980360i	0.871621	−	0.490180i	$-0.163069\pi$
$62$	− 1.75736i	− 0.223185i
$63$	− 5.07107i	− 0.638894i
$64$	−4.17157	−0.521447
$65$	2.82843i	0.350823i
$66$	−3.65685	−0.450128
$67$	−3.17157	−0.387469	−0.193735	−	0.981054i	$-0.562060\pi$
$67$	−3.17157	−0.387469	−0.193735	+	0.981054i	$0.562060\pi$
$68$	0	0
$69$	11.6569	1.40332
$70$	−0.242641	−0.0290011
$71$	− 4.24264i	− 0.503509i	−0.967791	−	0.251754i	$-0.918992\pi$
$71$	− 4.24264i	− 0.503509i	0.967791	−	0.251754i	$-0.0810075\pi$
$72$	−13.7279	−1.61785
$73$	− 4.82843i	− 0.565125i	−0.959249	−	0.282562i	$-0.908816\pi$
$73$	− 4.82843i	− 0.565125i	0.959249	−	0.282562i	$-0.0911844\pi$
$74$	− 2.68629i	− 0.312275i
$75$	3.41421i	0.394239i
$76$	−5.17157	−0.593220
$77$	−1.51472	−0.172618
$78$	− 4.00000i	− 0.452911i
$79$	− 5.41421i	− 0.609147i	−0.952489	−	0.304573i	$-0.901486\pi$
$79$	− 5.41421i	− 0.609147i	0.952489	−	0.304573i	$-0.0985139\pi$
$80$	− 3.00000i	− 0.335410i
$81$	39.9706	4.44117
$82$	− 2.68629i	− 0.296651i
$83$	−9.31371	−1.02231	−0.511156	−	0.859488i	$-0.670783\pi$
$83$	−9.31371	−1.02231	−0.511156	+	0.859488i	$0.670783\pi$
$84$	−3.65685	−0.398996
$85$	0	0
$86$	3.17157	0.341999
$87$	−16.4853	−1.76741
$88$	4.10051i	0.437115i
$89$	−2.34315	−0.248373	−0.124186	−	0.992259i	$-0.539632\pi$
$89$	−2.34315	−0.248373	−0.124186	+	0.992259i	$0.539632\pi$
$90$	− 3.58579i	− 0.377975i
$91$	− 1.65685i	− 0.173686i
$92$	− 6.24264i	− 0.650840i
$93$	14.4853	1.50205
$94$	2.00000	0.206284
$95$	− 2.82843i	− 0.290191i
$96$	15.0711i	1.53818i
$97$	3.65685i	0.371297i	0.982616	+	0.185649i	$0.0594386\pi$
$97$	3.65685i	0.371297i	−0.982616	+	0.185649i	$0.940561\pi$
$98$	−2.75736	−0.278535
$99$	− 22.3848i	− 2.24975i
$100$	1.82843	0.182843
$101$	−8.00000	−0.796030	−0.398015	−	0.917379i	$-0.630301\pi$
$101$	−8.00000	−0.796030	−0.398015	+	0.917379i	$0.630301\pi$
$102$	0	0
$103$	−0.828427	−0.0816274	−0.0408137	−	0.999167i	$-0.512995\pi$
$103$	−0.828427	−0.0816274	−0.0408137	+	0.999167i	$0.512995\pi$
$104$	−4.48528	−0.439818
$105$	− 2.00000i	− 0.195180i
$106$	0.142136	0.0138054
$107$	11.8995i	1.15037i	0.818024	+	0.575184i	$0.195069\pi$
$107$	11.8995i	1.15037i	−0.818024	+	0.575184i	$0.804931\pi$
$108$	− 35.3137i	− 3.39806i
$109$	17.3137i	1.65835i	0.558987	+	0.829176i	$0.311190\pi$
$109$	17.3137i	1.65835i	−0.558987	+	0.829176i	$0.688810\pi$
$110$	−1.07107	−0.102122
$111$	22.1421	2.10164
$112$	1.75736i	0.166055i
$113$	3.17157i	0.298356i	0.988810	+	0.149178i	$0.0476628\pi$
$113$	3.17157i	0.298356i	−0.988810	+	0.149178i	$0.952337\pi$
$114$	4.00000i	0.374634i
$115$	3.41421	0.318377
$116$	8.82843i	0.819699i
$117$	24.4853	2.26367
$118$	−3.79899	−0.349725
$119$	0	0
$120$	−5.41421	−0.494248
$121$	4.31371	0.392155
$122$	3.17157i	0.287141i
$123$	22.1421	1.99649
$124$	− 7.75736i	− 0.696631i
$125$	1.00000i	0.0894427i
$126$	2.10051i	0.187128i
$127$	17.3137	1.53634	0.768172	−	0.640244i	$-0.221167\pi$
$127$	17.3137	1.53634	0.768172	+	0.640244i	$0.221167\pi$
$128$	10.5563	0.933058
$129$	26.1421i	2.30169i
$130$	− 1.17157i	− 0.102754i
$131$	− 13.8995i	− 1.21440i	−0.794547	−	0.607202i	$-0.792292\pi$
$131$	− 13.8995i	− 1.21440i	0.794547	−	0.607202i	$-0.207708\pi$
$132$	−16.1421	−1.40499
$133$	1.65685i	0.143667i
$134$	1.31371	0.113487
$135$	19.3137	1.66226
$136$	0	0
$137$	1.17157	0.100094	0.0500471	−	0.998747i	$-0.484063\pi$
$137$	1.17157	0.100094	0.0500471	+	0.998747i	$0.484063\pi$
$138$	−4.82843	−0.411023
$139$	17.8995i	1.51822i	0.650965	+	0.759108i	$0.274364\pi$
$139$	17.8995i	1.51822i	−0.650965	+	0.759108i	$0.725636\pi$
$140$	−1.07107	−0.0905218
$141$	16.4853i	1.38831i
$142$	1.75736i	0.147474i
$143$	− 7.31371i	− 0.611603i
$144$	−25.9706	−2.16421
$145$	−4.82843	−0.400979
$146$	2.00000i	0.165521i
$147$	− 22.7279i	− 1.87457i
$148$	− 11.8579i	− 0.974710i
$149$	2.00000	0.163846	0.0819232	−	0.996639i	$-0.473894\pi$
$149$	2.00000	0.163846	0.0819232	+	0.996639i	$0.473894\pi$
$150$	− 1.41421i	− 0.115470i
$151$	−7.51472	−0.611539	−0.305770	−	0.952106i	$-0.598914\pi$
$151$	−7.51472	−0.611539	−0.305770	+	0.952106i	$0.598914\pi$
$152$	4.48528	0.363804
$153$	0	0
$154$	0.627417	0.0505587
$155$	4.24264	0.340777
$156$	− 17.6569i	− 1.41368i
$157$	−21.3137	−1.70102	−0.850510	−	0.525960i	$-0.823706\pi$
$157$	−21.3137	−1.70102	−0.850510	+	0.525960i	$0.823706\pi$
$158$	2.24264i	0.178415i
$159$	1.17157i	0.0929118i
$160$	4.41421i	0.348974i
$161$	−2.00000	−0.157622
$162$	−16.5563	−1.30079
$163$	− 0.585786i	− 0.0458823i	−0.999737	−	0.0229412i	$-0.992697\pi$
$163$	− 0.585786i	− 0.0458823i	0.999737	−	0.0229412i	$-0.00730304\pi$
$164$	− 11.8579i	− 0.925944i
$165$	− 8.82843i	− 0.687292i
$166$	3.85786	0.299428
$167$	2.24264i	0.173541i	0.996228	+	0.0867704i	$0.0276546\pi$
$167$	2.24264i	0.173541i	−0.996228	+	0.0867704i	$0.972345\pi$
$168$	3.17157	0.244692
$169$	−5.00000	−0.384615
$170$	0	0
$171$	−24.4853	−1.87244
$172$	14.0000	1.06749
$173$	12.8284i	0.975327i	0.873032	+	0.487664i	$0.162151\pi$
$173$	12.8284i	0.975327i	−0.873032	+	0.487664i	$0.837849\pi$
$174$	6.82843	0.517662
$175$	− 0.585786i	− 0.0442813i
$176$	7.75736i	0.584733i
$177$	− 31.3137i	− 2.35368i
$178$	0.970563	0.0727468
$179$	6.82843	0.510381	0.255190	−	0.966891i	$-0.417862\pi$
$179$	6.82843	0.510381	0.255190	+	0.966891i	$0.417862\pi$
$180$	− 15.8284i	− 1.17978i
$181$	− 2.48528i	− 0.184730i	−0.995725	−	0.0923648i	$-0.970557\pi$
$181$	− 2.48528i	− 0.184730i	0.995725	−	0.0923648i	$-0.0294426\pi$
$182$	0.686292i	0.0508713i
$183$	−26.1421	−1.93248
$184$	5.41421i	0.399141i
$185$	6.48528	0.476807
$186$	−6.00000	−0.439941
$187$	0	0
$188$	8.82843	0.643879
$189$	−11.3137	−0.822951
$190$	1.17157i	0.0849948i
$191$	12.0000	0.868290	0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000	0.868290	0.434145	+	0.900843i	$0.357051\pi$
$192$	14.2426i	1.02787i
$193$	20.8284i	1.49926i	0.661855	+	0.749631i	$0.269769\pi$
$193$	20.8284i	1.49926i	−0.661855	+	0.749631i	$0.730231\pi$
$194$	− 1.51472i	− 0.108750i
$195$	9.65685	0.691542
$196$	−12.1716	−0.869398
$197$	− 12.8284i	− 0.913988i	−0.889470	−	0.456994i	$-0.848926\pi$
$197$	− 12.8284i	− 0.913988i	0.889470	−	0.456994i	$-0.151074\pi$
$198$	9.27208i	0.658938i
$199$	24.2426i	1.71852i	0.511543	+	0.859258i	$0.329074\pi$
$199$	24.2426i	1.71852i	−0.511543	+	0.859258i	$0.670926\pi$
$200$	−1.58579	−0.112132
$201$	10.8284i	0.763778i
$202$	3.31371	0.233152
$203$	2.82843	0.198517
$204$	0	0
$205$	6.48528	0.452952
$206$	0.343146	0.0239081
$207$	− 29.5563i	− 2.05431i
$208$	−8.48528	−0.588348
$209$	7.31371i	0.505900i
$210$	0.828427i	0.0571669i
$211$	2.10051i	0.144605i	0.997383	+	0.0723024i	$0.0230347\pi$
$211$	2.10051i	0.144605i	−0.997383	+	0.0723024i	$0.976965\pi$
$212$	0.627417	0.0430912
$213$	−14.4853	−0.992515
$214$	− 4.92893i	− 0.336935i
$215$	7.65685i	0.522193i
$216$	30.6274i	2.08393i
$217$	−2.48528	−0.168712
$218$	− 7.17157i	− 0.485720i
$219$	−16.4853	−1.11397
$220$	−4.72792	−0.318756
$221$	0	0
$222$	−9.17157	−0.615556
$223$	−6.00000	−0.401790	−0.200895	−	0.979613i	$-0.564385\pi$
$223$	−6.00000	−0.401790	−0.200895	+	0.979613i	$0.564385\pi$
$224$	− 2.58579i	− 0.172770i
$225$	8.65685	0.577124
$226$	− 1.31371i	− 0.0873866i
$227$	22.7279i	1.50851i	0.656584	+	0.754253i	$0.272001\pi$
$227$	22.7279i	1.50851i	−0.656584	+	0.754253i	$0.727999\pi$
$228$	17.6569i	1.16935i
$229$	0.686292	0.0453514	0.0226757	−	0.999743i	$-0.492781\pi$
$229$	0.686292	0.0453514	0.0226757	+	0.999743i	$0.492781\pi$
$230$	−1.41421	−0.0932505
$231$	5.17157i	0.340265i
$232$	− 7.65685i	− 0.502697i
$233$	9.31371i	0.610161i	0.952327	+	0.305081i	$0.0986834\pi$
$233$	9.31371i	0.610161i	−0.952327	+	0.305081i	$0.901317\pi$
$234$	−10.1421	−0.663012
$235$	4.82843i	0.314972i
$236$	−16.7696	−1.09160
$237$	−18.4853	−1.20075
$238$	0	0
$239$	20.0000	1.29369	0.646846	−	0.762620i	$-0.276088\pi$
$239$	20.0000	1.29369	0.646846	+	0.762620i	$0.276088\pi$
$240$	−10.2426	−0.661160
$241$	12.8284i	0.826352i	0.910651	+	0.413176i	$0.135581\pi$
$241$	12.8284i	0.826352i	−0.910651	+	0.413176i	$0.864419\pi$
$242$	−1.78680	−0.114860
$243$	− 78.5269i	− 5.03750i
$244$	14.0000i	0.896258i
$245$	− 6.65685i	− 0.425291i
$246$	−9.17157	−0.584758
$247$	−8.00000	−0.509028
$248$	6.72792i	0.427223i
$249$	31.7990i	2.01518i
$250$	− 0.414214i	− 0.0261972i
$251$	−12.0000	−0.757433	−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000	−0.757433	−0.378717	+	0.925513i	$0.623635\pi$
$252$	9.27208i	0.584086i
$253$	−8.82843	−0.555038
$254$	−7.17157	−0.449985
$255$	0	0
$256$	3.97056	0.248160
$257$	2.82843	0.176432	0.0882162	−	0.996101i	$-0.471883\pi$
$257$	2.82843	0.176432	0.0882162	+	0.996101i	$0.471883\pi$
$258$	− 10.8284i	− 0.674148i
$259$	−3.79899	−0.236058
$260$	− 5.17157i	− 0.320727i
$261$	41.7990i	2.58729i
$262$	5.75736i	0.355691i
$263$	−9.31371	−0.574308	−0.287154	−	0.957884i	$-0.592709\pi$
$263$	−9.31371	−0.574308	−0.287154	+	0.957884i	$0.592709\pi$
$264$	14.0000	0.861640
$265$	0.343146i	0.0210793i
$266$	− 0.686292i	− 0.0420792i
$267$	8.00000i	0.489592i
$268$	5.79899	0.354230
$269$	18.9706i	1.15666i	0.815804	+	0.578328i	$0.196295\pi$
$269$	18.9706i	1.15666i	−0.815804	+	0.578328i	$0.803705\pi$
$270$	−8.00000	−0.486864
$271$	−13.6569	−0.829595	−0.414797	−	0.909914i	$-0.636148\pi$
$271$	−13.6569	−0.829595	−0.414797	+	0.909914i	$0.636148\pi$
$272$	0	0
$273$	−5.65685	−0.342368
$274$	−0.485281	−0.0293169
$275$	− 2.58579i	− 0.155929i
$276$	−21.3137	−1.28293
$277$	− 10.0000i	− 0.600842i	−0.953807	−	0.300421i	$-0.902873\pi$
$277$	− 10.0000i	− 0.600842i	0.953807	−	0.300421i	$-0.0971271\pi$
$278$	− 7.41421i	− 0.444675i
$279$	− 36.7279i	− 2.19884i
$280$	0.928932	0.0555143
$281$	4.34315	0.259090	0.129545	−	0.991574i	$-0.458648\pi$
$281$	4.34315	0.259090	0.129545	+	0.991574i	$0.458648\pi$
$282$	− 6.82843i	− 0.406627i
$283$	− 14.2426i	− 0.846637i	−0.905981	−	0.423319i	$-0.860865\pi$
$283$	− 14.2426i	− 0.846637i	0.905981	−	0.423319i	$-0.139135\pi$
$284$	7.75736i	0.460315i
$285$	−9.65685	−0.572023
$286$	3.02944i	0.179134i
$287$	−3.79899	−0.224247
$288$	38.2132	2.25173
$289$	0	0
$290$	2.00000	0.117444
$291$	12.4853	0.731900
$292$	8.82843i	0.516645i
$293$	18.0000	1.05157	0.525786	−	0.850617i	$-0.323771\pi$
$293$	18.0000	1.05157	0.525786	+	0.850617i	$0.323771\pi$
$294$	9.41421i	0.549048i
$295$	− 9.17157i	− 0.533990i
$296$	10.2843i	0.597761i
$297$	−49.9411	−2.89788
$298$	−0.828427	−0.0479895
$299$	− 9.65685i	− 0.558470i
$300$	− 6.24264i	− 0.360419i
$301$	− 4.48528i	− 0.258527i
$302$	3.11270	0.179116
$303$	27.3137i	1.56913i
$304$	8.48528	0.486664
$305$	−7.65685	−0.438430
$306$	0	0
$307$	−16.8284	−0.960449	−0.480225	−	0.877146i	$-0.659445\pi$
$307$	−16.8284	−0.960449	−0.480225	+	0.877146i	$0.659445\pi$
$308$	2.76955	0.157810
$309$	2.82843i	0.160904i
$310$	−1.75736	−0.0998113
$311$	15.0711i	0.854602i	0.904109	+	0.427301i	$0.140536\pi$
$311$	15.0711i	0.854602i	−0.904109	+	0.427301i	$0.859464\pi$
$312$	15.3137i	0.866968i
$313$	5.79899i	0.327778i	0.986479	+	0.163889i	$0.0524039\pi$
$313$	5.79899i	0.327778i	−0.986479	+	0.163889i	$0.947596\pi$
$314$	8.82843	0.498217
$315$	−5.07107	−0.285722
$316$	9.89949i	0.556890i
$317$	21.3137i	1.19710i	0.801087	+	0.598549i	$0.204256\pi$
$317$	21.3137i	1.19710i	−0.801087	+	0.598549i	$0.795744\pi$
$318$	− 0.485281i	− 0.0272132i
$319$	12.4853	0.699042
$320$	4.17157i	0.233198i
$321$	40.6274	2.26760
$322$	0.828427	0.0461664
$323$	0	0
$324$	−73.0833	−4.06018
$325$	2.82843	0.156893
$326$	0.242641i	0.0134386i
$327$	59.1127	3.26894
$328$	10.2843i	0.567854i
$329$	− 2.82843i	− 0.155936i
$330$	3.65685i	0.201303i
$331$	−26.8284	−1.47462	−0.737312	−	0.675553i	$-0.763905\pi$
$331$	−26.8284	−1.47462	−0.737312	+	0.675553i	$0.763905\pi$
$332$	17.0294	0.934612
$333$	− 56.1421i	− 3.07657i
$334$	− 0.928932i	− 0.0508289i
$335$	3.17157i	0.173282i
$336$	6.00000	0.327327
$337$	− 20.6274i	− 1.12365i	−0.827257	−	0.561824i	$-0.810100\pi$
$337$	− 20.6274i	− 1.12365i	0.827257	−	0.561824i	$-0.189900\pi$
$338$	2.07107	0.112651
$339$	10.8284	0.588119
$340$	0	0
$341$	−10.9706	−0.594089
$342$	10.1421	0.548424
$343$	8.00000i	0.431959i
$344$	−12.1421	−0.654660
$345$	− 11.6569i	− 0.627584i
$346$	− 5.31371i	− 0.285667i
$347$	23.6985i	1.27220i	0.771606	+	0.636101i	$0.219454\pi$
$347$	23.6985i	1.27220i	−0.771606	+	0.636101i	$0.780546\pi$
$348$	30.1421	1.61579
$349$	−31.6569	−1.69455	−0.847276	−	0.531152i	$-0.821759\pi$
$349$	−31.6569	−1.69455	−0.847276	+	0.531152i	$0.821759\pi$
$350$	0.242641i	0.0129697i
$351$	− 54.6274i	− 2.91580i
$352$	− 11.4142i	− 0.608380i
$353$	−27.6569	−1.47203	−0.736013	−	0.676967i	$-0.763294\pi$
$353$	−27.6569	−1.47203	−0.736013	+	0.676967i	$0.763294\pi$
$354$	12.9706i	0.689378i
$355$	−4.24264	−0.225176
$356$	4.28427	0.227066
$357$	0	0
$358$	−2.82843	−0.149487
$359$	31.7990	1.67829	0.839143	−	0.543910i	$-0.183057\pi$
$359$	31.7990	1.67829	0.839143	+	0.543910i	$0.183057\pi$
$360$	13.7279i	0.723525i
$361$	−11.0000	−0.578947
$362$	1.02944i	0.0541060i
$363$	− 14.7279i	− 0.773015i
$364$	3.02944i	0.158786i
$365$	−4.82843	−0.252731
$366$	10.8284	0.566011
$367$	14.2426i	0.743460i	0.928341	+	0.371730i	$0.121235\pi$
$367$	14.2426i	0.743460i	−0.928341	+	0.371730i	$0.878765\pi$
$368$	10.2426i	0.533935i
$369$	− 56.1421i	− 2.92264i
$370$	−2.68629	−0.139654
$371$	− 0.201010i	− 0.0104359i
$372$	−26.4853	−1.37320
$373$	11.7990	0.610929	0.305464	−	0.952204i	$-0.401188\pi$
$373$	11.7990	0.610929	0.305464	+	0.952204i	$0.401188\pi$
$374$	0	0
$375$	3.41421	0.176309
$376$	−7.65685	−0.394872
$377$	13.6569i	0.703364i
$378$	4.68629	0.241037
$379$	− 26.8701i	− 1.38022i	−0.723703	−	0.690111i	$-0.757562\pi$
$379$	− 26.8701i	− 1.38022i	0.723703	−	0.690111i	$-0.242438\pi$
$380$	5.17157i	0.265296i
$381$	− 59.1127i	− 3.02844i
$382$	−4.97056	−0.254316
$383$	34.2843	1.75184	0.875922	−	0.482452i	$-0.160254\pi$
$383$	34.2843	1.75184	0.875922	+	0.482452i	$0.160254\pi$
$384$	− 36.0416i	− 1.83924i
$385$	1.51472i	0.0771972i
$386$	− 8.62742i	− 0.439124i
$387$	66.2843	3.36942
$388$	− 6.68629i	− 0.339445i
$389$	16.0000	0.811232	0.405616	−	0.914044i	$-0.367057\pi$
$389$	16.0000	0.811232	0.405616	+	0.914044i	$0.367057\pi$
$390$	−4.00000	−0.202548
$391$	0	0
$392$	10.5563	0.533176
$393$	−47.4558	−2.39383
$394$	5.31371i	0.267701i
$395$	−5.41421	−0.272419
$396$	40.9289i	2.05676i
$397$	− 13.3137i	− 0.668196i	−0.942538	−	0.334098i	$-0.891568\pi$
$397$	− 13.3137i	− 0.668196i	0.942538	−	0.334098i	$-0.108432\pi$
$398$	− 10.0416i	− 0.503341i
$399$	5.65685	0.283197
$400$	−3.00000	−0.150000
$401$	16.3431i	0.816138i	0.912951	+	0.408069i	$0.133798\pi$
$401$	16.3431i	0.816138i	−0.912951	+	0.408069i	$0.866202\pi$
$402$	− 4.48528i	− 0.223706i
$403$	− 12.0000i	− 0.597763i
$404$	14.6274	0.727741
$405$	− 39.9706i	− 1.98615i
$406$	−1.17157	−0.0581442
$407$	−16.7696	−0.831236
$408$	0	0
$409$	−6.00000	−0.296681	−0.148340	−	0.988936i	$-0.547393\pi$
$409$	−6.00000	−0.296681	−0.148340	+	0.988936i	$0.547393\pi$
$410$	−2.68629	−0.132666
$411$	− 4.00000i	− 0.197305i
$412$	1.51472	0.0746248
$413$	5.37258i	0.264368i
$414$	12.2426i	0.601693i
$415$	9.31371i	0.457192i
$416$	12.4853	0.612141
$417$	61.1127	2.99270
$418$	− 3.02944i	− 0.148175i
$419$	− 12.2426i	− 0.598092i	−0.954239	−	0.299046i	$-0.903332\pi$
$419$	− 12.2426i	− 0.598092i	0.954239	−	0.299046i	$-0.0966684\pi$
$420$	3.65685i	0.178436i
$421$	−28.9706	−1.41194	−0.705969	−	0.708242i	$-0.749488\pi$
$421$	−28.9706	−1.41194	−0.705969	+	0.708242i	$0.749488\pi$
$422$	− 0.870058i	− 0.0423537i
$423$	41.7990	2.03234
$424$	−0.544156	−0.0264265
$425$	0	0
$426$	6.00000	0.290701
$427$	4.48528	0.217058
$428$	− 21.7574i	− 1.05168i
$429$	−24.9706	−1.20559
$430$	− 3.17157i	− 0.152947i
$431$	− 1.41421i	− 0.0681203i	−0.999420	−	0.0340601i	$-0.989156\pi$
$431$	− 1.41421i	− 0.0681203i	0.999420	−	0.0340601i	$-0.0108438\pi$
$432$	57.9411i	2.78769i
$433$	−2.82843	−0.135926	−0.0679628	−	0.997688i	$-0.521650\pi$
$433$	−2.82843	−0.135926	−0.0679628	+	0.997688i	$0.521650\pi$
$434$	1.02944	0.0494146
$435$	16.4853i	0.790409i
$436$	− 31.6569i	− 1.51609i
$437$	9.65685i	0.461950i
$438$	6.82843	0.326275
$439$	5.41421i	0.258406i	0.991618	+	0.129203i	$0.0412419\pi$
$439$	5.41421i	0.258406i	−0.991618	+	0.129203i	$0.958758\pi$
$440$	4.10051	0.195484
$441$	−57.6274	−2.74416
$442$	0	0
$443$	−14.4853	−0.688216	−0.344108	−	0.938930i	$-0.611819\pi$
$443$	−14.4853	−0.688216	−0.344108	+	0.938930i	$0.611819\pi$
$444$	−40.4853	−1.92135
$445$	2.34315i	0.111076i
$446$	2.48528	0.117681
$447$	− 6.82843i	− 0.322974i
$448$	− 2.44365i	− 0.115452i
$449$	26.4853i	1.24992i	0.780658	+	0.624959i	$0.214884\pi$
$449$	26.4853i	1.24992i	−0.780658	+	0.624959i	$0.785116\pi$
$450$	−3.58579	−0.169036
$451$	−16.7696	−0.789647
$452$	− 5.79899i	− 0.272762i
$453$	25.6569i	1.20546i
$454$	− 9.41421i	− 0.441831i
$455$	−1.65685	−0.0776745
$456$	− 15.3137i	− 0.717130i
$457$	−39.1127	−1.82961	−0.914807	−	0.403890i	$-0.867658\pi$
$457$	−39.1127	−1.82961	−0.914807	+	0.403890i	$0.867658\pi$
$458$	−0.284271	−0.0132831
$459$	0	0
$460$	−6.24264	−0.291065
$461$	−41.5980	−1.93741	−0.968706	−	0.248213i	$-0.920157\pi$
$461$	−41.5980	−1.93741	−0.968706	+	0.248213i	$0.920157\pi$
$462$	− 2.14214i	− 0.0996612i
$463$	−3.17157	−0.147395	−0.0736977	−	0.997281i	$-0.523480\pi$
$463$	−3.17157	−0.147395	−0.0736977	+	0.997281i	$0.523480\pi$
$464$	− 14.4853i	− 0.672462i
$465$	− 14.4853i	− 0.671739i
$466$	− 3.85786i	− 0.178712i
$467$	0.343146	0.0158789	0.00793945	−	0.999968i	$-0.497473\pi$
$467$	0.343146	0.0158789	0.00793945	+	0.999968i	$0.497473\pi$
$468$	−44.7696	−2.06947
$469$	− 1.85786i	− 0.0857882i
$470$	− 2.00000i	− 0.0922531i
$471$	72.7696i	3.35304i
$472$	14.5442	0.669449
$473$	− 19.7990i	− 0.910359i
$474$	7.65685	0.351691
$475$	−2.82843	−0.129777
$476$	0	0
$477$	2.97056	0.136013
$478$	−8.28427	−0.378914
$479$	− 15.7574i	− 0.719972i	−0.932958	−	0.359986i	$-0.882781\pi$
$479$	− 15.7574i	− 0.719972i	0.932958	−	0.359986i	$-0.117219\pi$
$480$	15.0711	0.687897
$481$	− 18.3431i	− 0.836375i
$482$	− 5.31371i	− 0.242033i
$483$	6.82843i	0.310704i
$484$	−7.88730	−0.358514
$485$	3.65685	0.166049
$486$	32.5269i	1.47545i
$487$	3.89949i	0.176703i	0.996089	+	0.0883515i	$0.0281599\pi$
$487$	3.89949i	0.176703i	−0.996089	+	0.0883515i	$0.971840\pi$
$488$	− 12.1421i	− 0.549649i
$489$	−2.00000	−0.0904431
$490$	2.75736i	0.124565i
$491$	16.4853	0.743970	0.371985	−	0.928239i	$-0.378677\pi$
$491$	16.4853	0.743970	0.371985	+	0.928239i	$0.378677\pi$
$492$	−40.4853	−1.82522
$493$	0	0
$494$	3.31371	0.149091
$495$	−22.3848	−1.00612
$496$	12.7279i	0.571501i
$497$	2.48528	0.111480
$498$	− 13.1716i	− 0.590232i
$499$	− 12.2426i	− 0.548056i	−0.961722	−	0.274028i	$-0.911644\pi$
$499$	− 12.2426i	− 0.548056i	0.961722	−	0.274028i	$-0.0883561\pi$
$500$	− 1.82843i	− 0.0817697i
$501$	7.65685	0.342083
$502$	4.97056	0.221847
$503$	− 31.6985i	− 1.41337i	−0.707531	−	0.706683i	$-0.750191\pi$
$503$	− 31.6985i	− 1.41337i	0.707531	−	0.706683i	$-0.249809\pi$
$504$	− 8.04163i	− 0.358203i
$505$	8.00000i	0.355995i
$506$	3.65685	0.162567
$507$	17.0711i	0.758153i
$508$	−31.6569	−1.40455
$509$	20.6274	0.914294	0.457147	−	0.889391i	$-0.348871\pi$
$509$	20.6274	0.914294	0.457147	+	0.889391i	$0.348871\pi$
$510$	0	0
$511$	2.82843	0.125122
$512$	−22.7574	−1.00574
$513$	54.6274i	2.41186i
$514$	−1.17157	−0.0516759
$515$	0.828427i	0.0365049i
$516$	− 47.7990i	− 2.10423i
$517$	− 12.4853i	− 0.549102i
$518$	1.57359	0.0691397
$519$	43.7990	1.92256
$520$	4.48528i	0.196693i
$521$	6.00000i	0.262865i	0.991325	+	0.131432i	$0.0419576\pi$
$521$	6.00000i	0.262865i	−0.991325	+	0.131432i	$0.958042\pi$
$522$	− 17.3137i	− 0.757800i
$523$	−0.142136	−0.00621516	−0.00310758	−	0.999995i	$-0.500989\pi$
$523$	−0.142136	−0.00621516	−0.00310758	+	0.999995i	$0.500989\pi$
$524$	25.4142i	1.11023i
$525$	−2.00000	−0.0872872
$526$	3.85786	0.168211
$527$	0	0
$528$	26.4853	1.15262
$529$	11.3431	0.493180
$530$	− 0.142136i	− 0.00617398i
$531$	−79.3970	−3.44554
$532$	− 3.02944i	− 0.131343i
$533$	− 18.3431i	− 0.794530i
$534$	− 3.31371i	− 0.143398i
$535$	11.8995	0.514460
$536$	−5.02944	−0.217239
$537$	− 23.3137i	− 1.00606i
$538$	− 7.85786i	− 0.338777i
$539$	17.2132i	0.741425i
$540$	−35.3137	−1.51966
$541$	− 42.7696i	− 1.83881i	−0.393316	−	0.919403i	$-0.628672\pi$
$541$	− 42.7696i	− 1.83881i	0.393316	−	0.919403i	$-0.371328\pi$
$542$	5.65685	0.242983
$543$	−8.48528	−0.364138
$544$	0	0
$545$	17.3137	0.741638
$546$	2.34315	0.100277
$547$	7.21320i	0.308414i	0.988039	+	0.154207i	$0.0492823\pi$
$547$	7.21320i	0.308414i	−0.988039	+	0.154207i	$0.950718\pi$
$548$	−2.14214	−0.0915075
$549$	66.2843i	2.82894i
$550$	1.07107i	0.0456705i
$551$	− 13.6569i	− 0.581802i
$552$	18.4853	0.786786
$553$	3.17157	0.134869
$554$	4.14214i	0.175982i
$555$	− 22.1421i	− 0.939881i
$556$	− 32.7279i	− 1.38797i
$557$	26.8284	1.13676	0.568378	−	0.822767i	$-0.307571\pi$
$557$	26.8284	1.13676	0.568378	+	0.822767i	$0.307571\pi$
$558$	15.2132i	0.644026i
$559$	21.6569	0.915987
$560$	1.75736	0.0742620
$561$	0	0
$562$	−1.79899	−0.0758858
$563$	20.3431	0.857361	0.428681	−	0.903456i	$-0.358979\pi$
$563$	20.3431	0.857361	0.428681	+	0.903456i	$0.358979\pi$
$564$	− 30.1421i	− 1.26921i
$565$	3.17157	0.133429
$566$	5.89949i	0.247974i
$567$	23.4142i	0.983305i
$568$	− 6.72792i	− 0.282297i
$569$	26.2843	1.10189	0.550947	−	0.834540i	$-0.314267\pi$
$569$	26.2843	1.10189	0.550947	+	0.834540i	$0.314267\pi$
$570$	4.00000	0.167542
$571$	4.44365i	0.185961i	0.995668	+	0.0929805i	$0.0296394\pi$
$571$	4.44365i	0.185961i	−0.995668	+	0.0929805i	$0.970361\pi$
$572$	13.3726i	0.559136i
$573$	− 40.9706i	− 1.71157i
$574$	1.57359	0.0656805
$575$	− 3.41421i	− 0.142383i
$576$	36.1127	1.50470
$577$	22.8284	0.950360	0.475180	−	0.879889i	$-0.342383\pi$
$577$	22.8284	0.950360	0.475180	+	0.879889i	$0.342383\pi$
$578$	0	0
$579$	71.1127	2.95534
$580$	8.82843	0.366580
$581$	− 5.45584i	− 0.226347i
$582$	−5.17157	−0.214369
$583$	− 0.887302i	− 0.0367483i
$584$	− 7.65685i	− 0.316843i
$585$	− 24.4853i	− 1.01234i
$586$	−7.45584	−0.307998
$587$	−28.6274	−1.18158	−0.590790	−	0.806825i	$-0.701184\pi$
$587$	−28.6274	−1.18158	−0.590790	+	0.806825i	$0.701184\pi$
$588$	41.5563i	1.71375i
$589$	12.0000i	0.494451i
$590$	3.79899i	0.156402i
$591$	−43.7990	−1.80165
$592$	19.4558i	0.799630i
$593$	−30.0000	−1.23195	−0.615976	−	0.787765i	$-0.711238\pi$
$593$	−30.0000	−1.23195	−0.615976	+	0.787765i	$0.711238\pi$
$594$	20.6863	0.848769
$595$	0	0
$596$	−3.65685	−0.149791
$597$	82.7696	3.38753
$598$	4.00000i	0.163572i
$599$	45.9411	1.87710	0.938552	−	0.345139i	$-0.112168\pi$
$599$	45.9411	1.87710	0.938552	+	0.345139i	$0.112168\pi$
$600$	5.41421i	0.221034i
$601$	25.7990i	1.05236i	0.850372	+	0.526181i	$0.176377\pi$
$601$	25.7990i	1.05236i	−0.850372	+	0.526181i	$0.823623\pi$
$602$	1.85786i	0.0757209i
$603$	27.4558	1.11809
$604$	13.7401	0.559077
$605$	− 4.31371i	− 0.175377i
$606$	− 11.3137i	− 0.459588i
$607$	− 4.58579i	− 0.186131i	−0.995660	−	0.0930657i	$-0.970333\pi$
$607$	− 4.58579i	− 0.186131i	0.995660	−	0.0930657i	$-0.0296667\pi$
$608$	−12.4853	−0.506345
$609$	− 9.65685i	− 0.391315i
$610$	3.17157	0.128413
$611$	13.6569	0.552497
$612$	0	0
$613$	−46.9706	−1.89712	−0.948562	−	0.316593i	$-0.897461\pi$
$613$	−46.9706	−1.89712	−0.948562	+	0.316593i	$0.897461\pi$
$614$	6.97056	0.281309
$615$	− 22.1421i	− 0.892857i
$616$	−2.40202	−0.0967802
$617$	25.5147i	1.02718i	0.858035	+	0.513592i	$0.171685\pi$
$617$	25.5147i	1.02718i	−0.858035	+	0.513592i	$0.828315\pi$
$618$	− 1.17157i	− 0.0471276i
$619$	16.9289i	0.680431i	0.940347	+	0.340216i	$0.110500\pi$
$619$	16.9289i	0.680431i	−0.940347	+	0.340216i	$0.889500\pi$
$620$	−7.75736	−0.311543
$621$	−65.9411	−2.64613
$622$	− 6.24264i	− 0.250307i
$623$	− 1.37258i	− 0.0549914i
$624$	28.9706i	1.15975i
$625$	1.00000	0.0400000
$626$	− 2.40202i	− 0.0960040i
$627$	24.9706	0.997228
$628$	38.9706	1.55509
$629$	0	0
$630$	2.10051	0.0836861
$631$	15.7990	0.628948	0.314474	−	0.949266i	$-0.398172\pi$
$631$	15.7990	0.628948	0.314474	+	0.949266i	$0.398172\pi$
$632$	− 8.58579i	− 0.341524i
$633$	7.17157	0.285044
$634$	− 8.82843i	− 0.350622i
$635$	− 17.3137i	− 0.687074i
$636$	− 2.14214i	− 0.0849412i
$637$	−18.8284	−0.746009
$638$	−5.17157	−0.204745
$639$	36.7279i	1.45293i
$640$	− 10.5563i	− 0.417276i
$641$	28.1421i	1.11155i	0.831334	+	0.555774i	$0.187578\pi$
$641$	28.1421i	1.11155i	−0.831334	+	0.555774i	$0.812422\pi$
$642$	−16.8284	−0.664165
$643$	− 47.6985i	− 1.88104i	−0.339732	−	0.940522i	$-0.610336\pi$
$643$	− 47.6985i	− 1.88104i	0.339732	−	0.940522i	$-0.389664\pi$
$644$	3.65685	0.144100
$645$	26.1421	1.02935
$646$	0	0
$647$	−20.8284	−0.818850	−0.409425	−	0.912344i	$-0.634271\pi$
$647$	−20.8284	−0.818850	−0.409425	+	0.912344i	$0.634271\pi$
$648$	63.3848	2.48999
$649$	23.7157i	0.930924i
$650$	−1.17157	−0.0459529
$651$	8.48528i	0.332564i
$652$	1.07107i	0.0419463i
$653$	− 18.4853i	− 0.723385i	−0.932297	−	0.361692i	$-0.882199\pi$
$653$	− 18.4853i	− 0.723385i	0.932297	−	0.361692i	$-0.117801\pi$
$654$	−24.4853	−0.957450
$655$	−13.8995	−0.543098
$656$	19.4558i	0.759623i
$657$	41.7990i	1.63073i
$658$	1.17157i	0.0456727i
$659$	−4.68629	−0.182552	−0.0912760	−	0.995826i	$-0.529095\pi$
$659$	−4.68629	−0.182552	−0.0912760	+	0.995826i	$0.529095\pi$
$660$	16.1421i	0.628332i
$661$	−13.3137	−0.517843	−0.258922	−	0.965898i	$-0.583367\pi$
$661$	−13.3137	−0.517843	−0.258922	+	0.965898i	$0.583367\pi$
$662$	11.1127	0.431907
$663$	0	0
$664$	−14.7696	−0.573170
$665$	1.65685	0.0642501
$666$	23.2548i	0.901107i
$667$	16.4853	0.638313
$668$	− 4.10051i	− 0.158653i
$669$	20.4853i	0.792007i
$670$	− 1.31371i	− 0.0507530i
$671$	19.7990	0.764332
$672$	−8.82843	−0.340564
$673$	28.1421i	1.08480i	0.840120	+	0.542400i	$0.182484\pi$
$673$	28.1421i	1.08480i	−0.840120	+	0.542400i	$0.817516\pi$
$674$	8.54416i	0.329109i
$675$	− 19.3137i	− 0.743385i
$676$	9.14214	0.351621
$677$	4.62742i	0.177846i	0.996038	+	0.0889230i	$0.0283425\pi$
$677$	4.62742i	0.177846i	−0.996038	+	0.0889230i	$0.971657\pi$
$678$	−4.48528	−0.172256
$679$	−2.14214	−0.0822076
$680$	0	0
$681$	77.5980	2.97356
$682$	4.54416	0.174005
$683$	− 14.7279i	− 0.563548i	−0.959481	−	0.281774i	$-0.909077\pi$
$683$	− 14.7279i	− 0.563548i	0.959481	−	0.281774i	$-0.0909229\pi$
$684$	44.7696	1.71181
$685$	− 1.17157i	− 0.0447635i
$686$	− 3.31371i	− 0.126518i
$687$	− 2.34315i	− 0.0893966i
$688$	−22.9706	−0.875744
$689$	0.970563	0.0369755
$690$	4.82843i	0.183815i
$691$	17.2132i	0.654821i	0.944882	+	0.327411i	$0.106176\pi$
$691$	17.2132i	0.654821i	−0.944882	+	0.327411i	$0.893824\pi$
$692$	− 23.4558i	− 0.891657i
$693$	13.1127	0.498110
$694$	− 9.81623i	− 0.372619i
$695$	17.8995	0.678967
$696$	−26.1421	−0.990915
$697$	0	0
$698$	13.1127	0.496323
$699$	31.7990	1.20275
$700$	1.07107i	0.0404826i
$701$	30.3431	1.14604	0.573022	−	0.819540i	$-0.305771\pi$
$701$	30.3431	1.14604	0.573022	+	0.819540i	$0.305771\pi$
$702$	22.6274i	0.854017i
$703$	18.3431i	0.691825i
$704$	− 10.7868i	− 0.406543i
$705$	16.4853	0.620872
$706$	11.4558	0.431146
$707$	− 4.68629i	− 0.176246i
$708$	57.2548i	2.15177i
$709$	25.7990i	0.968901i	0.874819	+	0.484451i	$0.160981\pi$
$709$	25.7990i	0.968901i	−0.874819	+	0.484451i	$0.839019\pi$
$710$	1.75736	0.0659525
$711$	46.8701i	1.75776i
$712$	−3.71573	−0.139253
$713$	−14.4853	−0.542478
$714$	0	0
$715$	−7.31371	−0.273517
$716$	−12.4853	−0.466597
$717$	− 68.2843i	− 2.55012i
$718$	−13.1716	−0.491559
$719$	− 53.4975i	− 1.99512i	−0.0698205	−	0.997560i	$-0.522243\pi$
$719$	− 53.4975i	− 1.99512i	0.0698205	−	0.997560i	$-0.477757\pi$
$720$	25.9706i	0.967866i
$721$	− 0.485281i	− 0.0180728i
$722$	4.55635	0.169570
$723$	43.7990	1.62890
$724$	4.54416i	0.168882i
$725$	4.82843i	0.179323i
$726$	6.10051i	0.226411i
$727$	11.4558	0.424874	0.212437	−	0.977175i	$-0.431860\pi$
$727$	11.4558	0.424874	0.212437	+	0.977175i	$0.431860\pi$
$728$	− 2.62742i	− 0.0973786i
$729$	−148.196	−5.48874
$730$	2.00000	0.0740233
$731$	0	0
$732$	47.7990	1.76670
$733$	−46.2843	−1.70955	−0.854774	−	0.519000i	$-0.826304\pi$
$733$	−46.2843	−1.70955	−0.854774	+	0.519000i	$0.826304\pi$
$734$	− 5.89949i	− 0.217754i
$735$	−22.7279	−0.838332
$736$	− 15.0711i	− 0.555527i
$737$	− 8.20101i	− 0.302088i
$738$	23.2548i	0.856022i
$739$	−27.7990	−1.02260	−0.511301	−	0.859402i	$-0.670836\pi$
$739$	−27.7990	−1.02260	−0.511301	+	0.859402i	$0.670836\pi$
$740$	−11.8579	−0.435904
$741$	27.3137i	1.00339i
$742$	0.0832611i	0.00305661i
$743$	14.0416i	0.515137i	0.966260	+	0.257569i	$0.0829214\pi$
$743$	14.0416i	0.515137i	−0.966260	+	0.257569i	$0.917079\pi$
$744$	22.9706	0.842142
$745$	− 2.00000i	− 0.0732743i
$746$	−4.88730	−0.178937
$747$	80.6274	2.95000
$748$	0	0
$749$	−6.97056	−0.254699
$750$	−1.41421	−0.0516398
$751$	− 46.1838i	− 1.68527i	−0.538485	−	0.842635i	$-0.681003\pi$
$751$	− 46.1838i	− 1.68527i	0.538485	−	0.842635i	$-0.318997\pi$
$752$	−14.4853	−0.528224
$753$	40.9706i	1.49305i
$754$	− 5.65685i	− 0.206010i
$755$	7.51472i	0.273489i
$756$	20.6863	0.752353
$757$	−41.1716	−1.49641	−0.748203	−	0.663470i	$-0.769083\pi$
$757$	−41.1716	−1.49641	−0.748203	+	0.663470i	$0.769083\pi$
$758$	11.1299i	0.404258i
$759$	30.1421i	1.09409i
$760$	− 4.48528i	− 0.162698i
$761$	12.6863	0.459878	0.229939	−	0.973205i	$-0.426147\pi$
$761$	12.6863	0.459878	0.229939	+	0.973205i	$0.426147\pi$
$762$	24.4853i	0.887008i
$763$	−10.1421	−0.367170
$764$	−21.9411	−0.793802
$765$	0	0
$766$	−14.2010	−0.513103
$767$	−25.9411	−0.936680
$768$	− 13.5563i	− 0.489173i
$769$	−34.3431	−1.23845	−0.619223	−	0.785215i	$-0.712552\pi$
$769$	−34.3431	−1.23845	−0.619223	+	0.785215i	$0.712552\pi$
$770$	− 0.627417i	− 0.0226105i
$771$	− 9.65685i	− 0.347783i
$772$	− 38.0833i	− 1.37065i
$773$	−27.1127	−0.975176	−0.487588	−	0.873074i	$-0.662123\pi$
$773$	−27.1127	−0.975176	−0.487588	+	0.873074i	$0.662123\pi$
$774$	−27.4558	−0.986880
$775$	− 4.24264i	− 0.152400i
$776$	5.79899i	0.208172i
$777$	12.9706i	0.465316i
$778$	−6.62742	−0.237604
$779$	18.3431i	0.657211i
$780$	−17.6569	−0.632217
$781$	10.9706	0.392558
$782$	0	0
$783$	93.2548	3.33266
$784$	19.9706	0.713234
$785$	21.3137i	0.760719i
$786$	19.6569	0.701137
$787$	− 31.2132i	− 1.11263i	−0.830971	−	0.556315i	$-0.812215\pi$
$787$	− 31.2132i	− 1.11263i	0.830971	−	0.556315i	$-0.187785\pi$
$788$	23.4558i	0.835580i
$789$	31.7990i	1.13207i
$790$	2.24264	0.0797896
$791$	−1.85786	−0.0660581
$792$	− 35.4975i	− 1.26135i
$793$	21.6569i	0.769057i
$794$	5.51472i	0.195710i
$795$	1.17157	0.0415514
$796$	− 44.3259i	− 1.57109i
$797$	36.6274	1.29741	0.648705	−	0.761040i	$-0.275311\pi$
$797$	36.6274	1.29741	0.648705	+	0.761040i	$0.275311\pi$
$798$	−2.34315	−0.0829465
$799$	0	0
$800$	4.41421	0.156066
$801$	20.2843	0.716709
$802$	− 6.76955i	− 0.239041i
$803$	12.4853	0.440596
$804$	− 19.7990i	− 0.698257i
$805$	2.00000i	0.0704907i
$806$	4.97056i	0.175081i
$807$	64.7696	2.28000
$808$	−12.6863	−0.446302
$809$	31.6569i	1.11300i	0.830849	+	0.556498i	$0.187855\pi$
$809$	31.6569i	1.11300i	−0.830849	+	0.556498i	$0.812145\pi$
$810$	16.5563i	0.581731i
$811$	18.5858i	0.652635i	0.945260	+	0.326318i	$0.105808\pi$
$811$	18.5858i	0.652635i	−0.945260	+	0.326318i	$0.894192\pi$
$812$	−5.17157	−0.181487
$813$	46.6274i	1.63529i
$814$	6.94618	0.243463
$815$	−0.585786	−0.0205192
$816$	0	0
$817$	−21.6569	−0.757677
$818$	2.48528	0.0868958
$819$	14.3431i	0.501190i
$820$	−11.8579	−0.414095
$821$	36.6274i	1.27831i	0.769080	+	0.639153i	$0.220715\pi$
$821$	36.6274i	1.27831i	−0.769080	+	0.639153i	$0.779285\pi$
$822$	1.65685i	0.0577894i
$823$	25.0711i	0.873922i	0.899480	+	0.436961i	$0.143945\pi$
$823$	25.0711i	0.873922i	−0.899480	+	0.436961i	$0.856055\pi$
$824$	−1.31371	−0.0457652
$825$	−8.82843	−0.307366
$826$	− 2.22540i	− 0.0774315i
$827$	29.5563i	1.02777i	0.857858	+	0.513887i	$0.171795\pi$
$827$	29.5563i	1.02777i	−0.857858	+	0.513887i	$0.828205\pi$
$828$	54.0416i	1.87808i
$829$	39.9411	1.38721	0.693606	−	0.720354i	$-0.256021\pi$
$829$	39.9411	1.38721	0.693606	+	0.720354i	$0.256021\pi$
$830$	− 3.85786i	− 0.133908i
$831$	−34.1421	−1.18438
$832$	11.7990	0.409056
$833$	0	0
$834$	−25.3137	−0.876542
$835$	2.24264	0.0776098
$836$	− 13.3726i	− 0.462500i
$837$	−81.9411	−2.83230
$838$	5.07107i	0.175177i
$839$	− 42.1838i	− 1.45635i	−0.685394	−	0.728173i	$-0.740370\pi$
$839$	− 42.1838i	− 1.45635i	0.685394	−	0.728173i	$-0.259630\pi$
$840$	− 3.17157i	− 0.109430i
$841$	5.68629	0.196079
$842$	12.0000	0.413547
$843$	− 14.8284i	− 0.510718i
$844$	− 3.84062i	− 0.132200i
$845$	5.00000i	0.172005i
$846$	−17.3137	−0.595258
$847$	2.52691i	0.0868257i
$848$	−1.02944	−0.0353510
$849$	−48.6274	−1.66889
$850$	0	0
$851$	−22.1421	−0.759023
$852$	26.4853	0.907371
$853$	− 31.1716i	− 1.06729i	−0.845707	−	0.533647i	$-0.820821\pi$
$853$	− 31.1716i	− 1.06729i	0.845707	−	0.533647i	$-0.179179\pi$
$854$	−1.85786	−0.0635748
$855$	24.4853i	0.837379i
$856$	18.8701i	0.644965i
$857$	− 13.5147i	− 0.461654i	−0.972995	−	0.230827i	$-0.925857\pi$
$857$	− 13.5147i	− 0.461654i	0.972995	−	0.230827i	$-0.0741431\pi$
$858$	10.3431	0.353109
$859$	−36.7696	−1.25456	−0.627280	−	0.778793i	$-0.715832\pi$
$859$	−36.7696	−1.25456	−0.627280	+	0.778793i	$0.715832\pi$
$860$	− 14.0000i	− 0.477396i
$861$	12.9706i	0.442036i
$862$	0.585786i	0.0199520i
$863$	6.48528	0.220762	0.110381	−	0.993889i	$-0.464793\pi$
$863$	6.48528	0.220762	0.110381	+	0.993889i	$0.464793\pi$
$864$	− 85.2548i	− 2.90043i
$865$	12.8284	0.436180
$866$	1.17157	0.0398117
$867$	0	0
$868$	4.54416	0.154239
$869$	14.0000	0.474917
$870$	− 6.82843i	− 0.231505i
$871$	8.97056	0.303956
$872$	27.4558i	0.929772i
$873$	− 31.6569i	− 1.07142i
$874$	− 4.00000i	− 0.135302i
$875$	−0.585786	−0.0198032
$876$	30.1421	1.01841
$877$	2.28427i	0.0771344i	0.999256	+	0.0385672i	$0.0122794\pi$
$877$	2.28427i	0.0771344i	−0.999256	+	0.0385672i	$0.987721\pi$
$878$	− 2.24264i	− 0.0756855i
$879$	− 61.4558i	− 2.07285i
$880$	7.75736	0.261501
$881$	48.1421i	1.62195i	0.585081	+	0.810975i	$0.301063\pi$
$881$	48.1421i	1.62195i	−0.585081	+	0.810975i	$0.698937\pi$
$882$	23.8701	0.803747
$883$	15.1716	0.510564	0.255282	−	0.966867i	$-0.417832\pi$
$883$	15.1716	0.510564	0.255282	+	0.966867i	$0.417832\pi$
$884$	0	0
$885$	−31.3137	−1.05260
$886$	6.00000	0.201574
$887$	− 14.9289i	− 0.501264i	−0.968082	−	0.250632i	$-0.919362\pi$
$887$	− 14.9289i	− 0.501264i	0.968082	−	0.250632i	$-0.0806385\pi$
$888$	35.1127	1.17831
$889$	10.1421i	0.340156i
$890$	− 0.970563i	− 0.0325333i
$891$	103.355i	3.46253i
$892$	10.9706	0.367322
$893$	−13.6569	−0.457009
$894$	2.82843i	0.0945968i
$895$	− 6.82843i	− 0.228249i
$896$	6.18377i	0.206585i
$897$	−32.9706	−1.10086
$898$	− 10.9706i	− 0.366092i
$899$	20.4853	0.683222
$900$	−15.8284	−0.527614
$901$	0	0
$902$	6.94618	0.231282
$903$	−15.3137	−0.509608
$904$	5.02944i	0.167277i
$905$	−2.48528	−0.0826135
$906$	− 10.6274i	− 0.353072i
$907$	6.72792i	0.223397i	0.993742	+	0.111698i	$0.0356291\pi$
$907$	6.72792i	0.223397i	−0.993742	+	0.111698i	$0.964371\pi$
$908$	− 41.5563i	− 1.37910i
$909$	69.2548	2.29704
$910$	0.686292	0.0227503
$911$	− 12.2426i	− 0.405617i	−0.979218	−	0.202808i	$-0.934993\pi$
$911$	− 12.2426i	− 0.405617i	0.979218	−	0.202808i	$-0.0650069\pi$
$912$	− 28.9706i	− 0.959311i
$913$	− 24.0833i	− 0.797040i
$914$	16.2010	0.535882
$915$	26.1421i	0.864232i
$916$	−1.25483	−0.0414609
$917$	8.14214	0.268877
$918$	0	0
$919$	40.9706	1.35149	0.675747	−	0.737134i	$-0.263821\pi$
$919$	40.9706	1.35149	0.675747	+	0.737134i	$0.263821\pi$
$920$	5.41421	0.178501
$921$	57.4558i	1.89323i
$922$	17.2304	0.567455
$923$	12.0000i	0.394985i
$924$	− 9.45584i	− 0.311074i
$925$	− 6.48528i	− 0.213235i
$926$	1.31371	0.0431711
$927$	7.17157	0.235545
$928$	21.3137i	0.699657i
$929$	− 35.4558i	− 1.16327i	−0.813450	−	0.581634i	$-0.802414\pi$
$929$	− 35.4558i	− 1.16327i	0.813450	−	0.581634i	$-0.197586\pi$
$930$	6.00000i	0.196748i
$931$	18.8284	0.617077
$932$	− 17.0294i	− 0.557818i
$933$	51.4558	1.68459
$934$	−0.142136	−0.00465082
$935$	0	0
$936$	38.8284	1.26915
$937$	−34.2843	−1.12002	−0.560009	−	0.828486i	$-0.689202\pi$
$937$	−34.2843	−1.12002	−0.560009	+	0.828486i	$0.689202\pi$
$938$	0.769553i	0.0251268i
$939$	19.7990	0.646116
$940$	− 8.82843i	− 0.287952i
$941$	3.45584i	0.112657i	0.998412	+	0.0563286i	$0.0179395\pi$
$941$	3.45584i	0.112657i	−0.998412	+	0.0563286i	$0.982061\pi$
$942$	− 30.1421i	− 0.982084i
$943$	−22.1421	−0.721047
$944$	27.5147	0.895528
$945$	11.3137i	0.368035i
$946$	8.20101i	0.266638i
$947$	− 35.8995i	− 1.16658i	−0.812265	−	0.583288i	$-0.801766\pi$
$947$	− 35.8995i	− 1.16658i	0.812265	−	0.583288i	$-0.198234\pi$
$948$	33.7990	1.09774
$949$	13.6569i	0.443320i
$950$	1.17157	0.0380108
$951$	72.7696	2.35971
$952$	0	0
$953$	−21.8579	−0.708046	−0.354023	−	0.935237i	$-0.615186\pi$
$953$	−21.8579	−0.708046	−0.354023	+	0.935237i	$0.615186\pi$
$954$	−1.23045	−0.0398372
$955$	− 12.0000i	− 0.388311i
$956$	−36.5685	−1.18271
$957$	− 42.6274i	− 1.37795i
$958$	6.52691i	0.210875i
$959$	0.686292i	0.0221615i
$960$	14.2426	0.459679
$961$	13.0000	0.419355
$962$	7.59798i	0.244969i
$963$	− 103.012i	− 3.31952i
$964$	− 23.4558i	− 0.755462i
$965$	20.8284	0.670491
$966$	− 2.82843i	− 0.0910032i
$967$	1.02944	0.0331045	0.0165522	−	0.999863i	$-0.494731\pi$
$967$	1.02944	0.0331045	0.0165522	+	0.999863i	$0.494731\pi$
$968$	6.84062	0.219866
$969$	0	0
$970$	−1.51472	−0.0486347
$971$	8.20101	0.263183	0.131591	−	0.991304i	$-0.457991\pi$
$971$	8.20101	0.263183	0.131591	+	0.991304i	$0.457991\pi$
$972$	143.581i	4.60535i
$973$	−10.4853	−0.336143
$974$	− 1.61522i	− 0.0517551i
$975$	− 9.65685i	− 0.309267i
$976$	− 22.9706i	− 0.735270i
$977$	−59.2548	−1.89573	−0.947865	−	0.318672i	$-0.896763\pi$
$977$	−59.2548	−1.89573	−0.947865	+	0.318672i	$0.896763\pi$
$978$	0.828427	0.0264902
$979$	− 6.05887i	− 0.193642i
$980$	12.1716i	0.388807i
$981$	− 149.882i	− 4.78537i
$982$	−6.82843	−0.217904
$983$	− 41.3553i	− 1.31903i	−0.751691	−	0.659515i	$-0.770762\pi$
$983$	− 41.3553i	− 1.31903i	0.751691	−	0.659515i	$-0.229238\pi$
$984$	35.1127	1.11935
$985$	−12.8284	−0.408748
$986$	0	0
$987$	−9.65685	−0.307381
$988$	14.6274	0.465360
$989$	− 26.1421i	− 0.831272i
$990$	9.27208	0.294686
$991$	33.4142i	1.06144i	0.847548	+	0.530719i	$0.178078\pi$
$991$	33.4142i	1.06144i	−0.847548	+	0.530719i	$0.821922\pi$
$992$	− 18.7279i	− 0.594612i
$993$	91.5980i	2.90677i
$994$	−1.02944	−0.0326518
$995$	24.2426	0.768543
$996$	− 58.1421i	− 1.84230i
$997$	− 40.1421i	− 1.27131i	−0.771972	−	0.635657i	$-0.780729\pi$
$997$	− 40.1421i	− 1.27131i	0.771972	−	0.635657i	$-0.219271\pi$
$998$	5.07107i	0.160522i
$999$	−125.255	−3.96289

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1445.2.d.f.866.1		4
17.4	even	4		85.2.a.b.1.2	✓	2
17.13	even	4		1445.2.a.f.1.2		2
17.16	even	2	inner	1445.2.d.f.866.2		4
51.38	odd	4		765.2.a.i.1.1		2
68.55	odd	4		1360.2.a.o.1.2		2
85.4	even	4		425.2.a.f.1.1		2
85.38	odd	4		425.2.b.e.324.2		4
85.64	even	4		7225.2.a.o.1.1		2
85.72	odd	4		425.2.b.e.324.3		4
119.55	odd	4		4165.2.a.q.1.2		2
136.21	even	4		5440.2.a.bm.1.2		2
136.123	odd	4		5440.2.a.ba.1.1		2
255.89	odd	4		3825.2.a.p.1.2		2
340.259	odd	4		6800.2.a.ba.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.a.b.1.2	✓	2	17.4	even	4
425.2.a.f.1.1		2	85.4	even	4
425.2.b.e.324.2		4	85.38	odd	4
425.2.b.e.324.3		4	85.72	odd	4
765.2.a.i.1.1		2	51.38	odd	4
1360.2.a.o.1.2		2	68.55	odd	4
1445.2.a.f.1.2		2	17.13	even	4
1445.2.d.f.866.1		4	1.1	even	1	trivial
1445.2.d.f.866.2		4	17.16	even	2	inner
3825.2.a.p.1.2		2	255.89	odd	4
4165.2.a.q.1.2		2	119.55	odd	4
5440.2.a.ba.1.1		2	136.123	odd	4
5440.2.a.bm.1.2		2	136.21	even	4
6800.2.a.ba.1.1		2	340.259	odd	4
7225.2.a.o.1.1		2	85.64	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)

\(f(q)\)	\(=\)	\(q-0.414214 q^{2} -3.41421i q^{3} -1.82843 q^{4} -1.00000i q^{5} +1.41421i q^{6} +0.585786i q^{7} +1.58579 q^{8} -8.65685 q^{9} +0.414214i q^{10} +2.58579i q^{11} +6.24264i q^{12} -2.82843 q^{13} -0.242641i q^{14} -3.41421 q^{15} +3.00000 q^{16} +3.58579 q^{18} +2.82843 q^{19} +1.82843i q^{20} +2.00000 q^{21} -1.07107i q^{22} +3.41421i q^{23} -5.41421i q^{24} -1.00000 q^{25} +1.17157 q^{26} +19.3137i q^{27} -1.07107i q^{28} -4.82843i q^{29} +1.41421 q^{30} +4.24264i q^{31} -4.41421 q^{32} +8.82843 q^{33} +0.585786 q^{35} +15.8284 q^{36} +6.48528i q^{37} -1.17157 q^{38} +9.65685i q^{39} -1.58579i q^{40} +6.48528i q^{41} -0.828427 q^{42} -7.65685 q^{43} -4.72792i q^{44} +8.65685i q^{45} -1.41421i q^{46} -4.82843 q^{47} -10.2426i q^{48} +6.65685 q^{49} +0.414214 q^{50} +5.17157 q^{52} -0.343146 q^{53} -8.00000i q^{54} +2.58579 q^{55} +0.928932i q^{56} -9.65685i q^{57} +2.00000i q^{58} +9.17157 q^{59} +6.24264 q^{60} -7.65685i q^{61} -1.75736i q^{62} -5.07107i q^{63} -4.17157 q^{64} +2.82843i q^{65} -3.65685 q^{66} -3.17157 q^{67} +11.6569 q^{69} -0.242641 q^{70} -4.24264i q^{71} -13.7279 q^{72} -4.82843i q^{73} -2.68629i q^{74} +3.41421i q^{75} -5.17157 q^{76} -1.51472 q^{77} -4.00000i q^{78} -5.41421i q^{79} -3.00000i q^{80} +39.9706 q^{81} -2.68629i q^{82} -9.31371 q^{83} -3.65685 q^{84} +3.17157 q^{86} -16.4853 q^{87} +4.10051i q^{88} -2.34315 q^{89} -3.58579i q^{90} -1.65685i q^{91} -6.24264i q^{92} +14.4853 q^{93} +2.00000 q^{94} -2.82843i q^{95} +15.0711i q^{96} +3.65685i q^{97} -2.75736 q^{98} -22.3848i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{4} + 12 q^{8} - 12 q^{9} - 8 q^{15} + 12 q^{16} + 20 q^{18} + 8 q^{21} - 4 q^{25} + 16 q^{26} - 12 q^{32} + 24 q^{33} + 8 q^{35} + 52 q^{36} - 16 q^{38} + 8 q^{42} - 8 q^{43} - 8 q^{47}+ \cdots - 28 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^4 + 12 * q^8 - 12 * q^9 - 8 * q^15 + 12 * q^16 + 20 * q^18 + 8 * q^21 - 4 * q^25 + 16 * q^26 - 12 * q^32 + 24 * q^33 + 8 * q^35 + 52 * q^36 - 16 * q^38 + 8 * q^42 - 8 * q^43 - 8 * q^47 + 4 * q^49 - 4 * q^50 + 32 * q^52 - 24 * q^53 + 16 * q^55 + 48 * q^59 + 8 * q^60 - 28 * q^64 + 8 * q^66 - 24 * q^67 + 24 * q^69 + 16 * q^70 - 4 * q^72 - 32 * q^76 - 40 * q^77 + 92 * q^81 + 8 * q^83 + 8 * q^84 + 24 * q^86 - 32 * q^87 - 32 * q^89 + 24 * q^93 + 8 * q^94 - 28 * q^98

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