LMFDB - Embedded newform 1600.2.s.d.207.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1600,2,Mod(207,1600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1600, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 1]))

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

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

chi := DirichletCharacter("1600.207");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1600 = 2^{6} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1600.s (of order $4$, degree $2$, 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:	$12.7760643234$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{15} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			207.5
Root			$-1.37691 - 0.322680i$ of defining polynomial
Character	$\chi$	$=$	1600.207
Dual form			1600.2.s.d.943.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.614566 q^{3} +(2.83610 + 2.83610i) q^{7} -2.62231 q^{9} +O(q^{10})$	$q+0.614566 q^{3} +(2.83610 + 2.83610i) q^{7} -2.62231 q^{9} +(-1.95928 + 1.95928i) q^{11} -2.05493i q^{13} +(4.06774 + 4.06774i) q^{17} +(0.683479 - 0.683479i) q^{19} +(1.74297 + 1.74297i) q^{21} +(-4.95014 + 4.95014i) q^{23} -3.45528 q^{27} +(0.835439 + 0.835439i) q^{29} -2.35978i q^{31} +(-1.20411 + 1.20411i) q^{33} +4.54384i q^{37} -1.26289i q^{39} +5.07255i q^{41} +0.849753i q^{43} +(-2.72646 + 2.72646i) q^{47} +9.08690i q^{49} +(2.49989 + 2.49989i) q^{51} -5.17605 q^{53} +(0.420043 - 0.420043i) q^{57} +(4.16328 + 4.16328i) q^{59} +(5.55706 - 5.55706i) q^{61} +(-7.43712 - 7.43712i) q^{63} -1.73609i q^{67} +(-3.04219 + 3.04219i) q^{69} -2.33526 q^{71} +(4.39686 + 4.39686i) q^{73} -11.1134 q^{77} -14.0993 q^{79} +5.74343 q^{81} -2.75725 q^{83} +(0.513433 + 0.513433i) q^{87} +11.6448 q^{89} +(5.82797 - 5.82797i) q^{91} -1.45024i q^{93} +(3.52933 + 3.52933i) q^{97} +(5.13783 - 5.13783i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{7} + 10 q^{9}+O(q^{10}) $ 18 * q + 2 * q^7 + 10 * q^9	$ 18 q + 2 q^{7} + 10 q^{9} + 2 q^{11} + 6 q^{17} + 2 q^{19} - 16 q^{21} - 2 q^{23} - 24 q^{27} + 14 q^{29} + 8 q^{33} + 38 q^{47} - 8 q^{51} - 12 q^{53} + 24 q^{57} - 10 q^{59} + 14 q^{61} - 6 q^{63} - 32 q^{69} - 24 q^{71} + 14 q^{73} + 44 q^{77} + 16 q^{79} + 2 q^{81} + 40 q^{83} + 24 q^{87} + 12 q^{89} - 18 q^{97} - 22 q^{99}+O(q^{100}) $ 18 * q + 2 * q^7 + 10 * q^9 + 2 * q^11 + 6 * q^17 + 2 * q^19 - 16 * q^21 - 2 * q^23 - 24 * q^27 + 14 * q^29 + 8 * q^33 + 38 * q^47 - 8 * q^51 - 12 * q^53 + 24 * q^57 - 10 * q^59 + 14 * q^61 - 6 * q^63 - 32 * q^69 - 24 * q^71 + 14 * q^73 + 44 * q^77 + 16 * q^79 + 2 * q^81 + 40 * q^83 + 24 * q^87 + 12 * q^89 - 18 * q^97 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1151$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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			0
$2$		0			0
$3$	0.614566			0.354820			0.177410	−	0.984137i	$-0.443228\pi$
$3$	0.614566			0.354820			0.177410	+	0.984137i	$0.443228\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.83610	+	2.83610i	1.07194	+	1.07194i	0.997203	+	0.0747413i	$0.0238131\pi$
$7$	2.83610	+	2.83610i	1.07194	+	1.07194i	0.0747413	+	0.997203i	$0.476187\pi$
$8$		0			0
$9$	−2.62231			−0.874103
$10$		0			0
$11$	−1.95928	+	1.95928i	−0.590745	+	0.590745i	−0.937833	−	0.347088i	$-0.887171\pi$
$11$	−1.95928	+	1.95928i	−0.590745	+	0.590745i	0.347088	+	0.937833i	$0.387171\pi$
$12$		0			0
$13$		−	2.05493i		−	0.569934i	−0.958537	−	0.284967i	$-0.908017\pi$
$13$		−	2.05493i		−	0.569934i	0.958537	−	0.284967i	$-0.0919826\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	4.06774	+	4.06774i	0.986571	+	0.986571i	0.999911	−	0.0133401i	$-0.00424641\pi$
$17$	4.06774	+	4.06774i	0.986571	+	0.986571i	−0.0133401	+	0.999911i	$0.504246\pi$
$18$		0			0
$19$	0.683479	−	0.683479i	0.156801	−	0.156801i	−0.624347	−	0.781147i	$-0.714635\pi$
$19$	0.683479	−	0.683479i	0.156801	−	0.156801i	0.781147	+	0.624347i	$0.214635\pi$
$20$		0			0
$21$	1.74297	+	1.74297i	0.380347	+	0.380347i
$22$		0			0
$23$	−4.95014	+	4.95014i	−1.03218	+	1.03218i	−0.0327113	+	0.999465i	$0.510414\pi$
$23$	−4.95014	+	4.95014i	−1.03218	+	1.03218i	−0.999465	+	0.0327113i	$0.989586\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−3.45528			−0.664969
$28$		0			0
$29$	0.835439	+	0.835439i	0.155137	+	0.155137i	0.780408	−	0.625271i	$-0.215011\pi$
$29$	0.835439	+	0.835439i	0.155137	+	0.155137i	−0.625271	+	0.780408i	$0.715011\pi$
$30$		0			0
$31$		−	2.35978i		−	0.423829i	−0.977288	−	0.211915i	$-0.932030\pi$
$31$		−	2.35978i		−	0.423829i	0.977288	−	0.211915i	$-0.0679698\pi$
$32$		0			0
$33$	−1.20411	+	1.20411i	−0.209608	+	0.209608i
$34$		0			0
$35$		0			0
$36$		0			0
$37$			4.54384i			0.747002i	0.927630	+	0.373501i	$0.121843\pi$
$37$			4.54384i			0.747002i	−0.927630	+	0.373501i	$0.878157\pi$
$38$		0			0
$39$		−	1.26289i		−	0.202224i
$40$		0			0
$41$			5.07255i			0.792199i	0.918208	+	0.396100i	$0.129636\pi$
$41$			5.07255i			0.792199i	−0.918208	+	0.396100i	$0.870364\pi$
$42$		0			0
$43$			0.849753i			0.129586i	0.997899	+	0.0647930i	$0.0206387\pi$
$43$			0.849753i			0.129586i	−0.997899	+	0.0647930i	$0.979361\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.72646	+	2.72646i	−0.397696	+	0.397696i	−0.877419	−	0.479724i	$-0.840737\pi$
$47$	−2.72646	+	2.72646i	−0.397696	+	0.397696i	0.479724	+	0.877419i	$0.340737\pi$
$48$		0			0
$49$			9.08690i			1.29813i
$50$		0			0
$51$	2.49989	+	2.49989i	0.350055	+	0.350055i
$52$		0			0
$53$	−5.17605			−0.710985			−0.355492	−	0.934679i	$-0.615687\pi$
$53$	−5.17605			−0.710985			−0.355492	+	0.934679i	$0.615687\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	0.420043	−	0.420043i	0.0556360	−	0.0556360i
$58$		0			0
$59$	4.16328	+	4.16328i	0.542013	+	0.542013i	0.924119	−	0.382105i	$-0.124801\pi$
$59$	4.16328	+	4.16328i	0.542013	+	0.542013i	−0.382105	+	0.924119i	$0.624801\pi$
$60$		0			0
$61$	5.55706	−	5.55706i	0.711509	−	0.711509i	−0.255342	−	0.966851i	$-0.582188\pi$
$61$	5.55706	−	5.55706i	0.711509	−	0.711509i	0.966851	+	0.255342i	$0.0821880\pi$
$62$		0			0
$63$	−7.43712	−	7.43712i	−0.936990	−	0.936990i
$64$		0			0
$65$		0			0
$66$		0			0
$67$		−	1.73609i		−	0.212097i	−0.994361	−	0.106048i	$-0.966180\pi$
$67$		−	1.73609i		−	0.212097i	0.994361	−	0.106048i	$-0.0338198\pi$
$68$		0			0
$69$	−3.04219	+	3.04219i	−0.366237	+	0.366237i
$70$		0			0
$71$	−2.33526			−0.277144			−0.138572	−	0.990352i	$-0.544251\pi$
$71$	−2.33526			−0.277144			−0.138572	+	0.990352i	$0.544251\pi$
$72$		0			0
$73$	4.39686	+	4.39686i	0.514613	+	0.514613i	0.915936	−	0.401323i	$-0.131450\pi$
$73$	4.39686	+	4.39686i	0.514613	+	0.514613i	−0.401323	+	0.915936i	$0.631450\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−11.1134			−1.26649
$78$		0			0
$79$	−14.0993			−1.58629			−0.793146	−	0.609032i	$-0.791558\pi$
$79$	−14.0993			−1.58629			−0.793146	+	0.609032i	$0.791558\pi$
$80$		0			0
$81$	5.74343			0.638159
$82$		0			0
$83$	−2.75725			−0.302648			−0.151324	−	0.988484i	$-0.548354\pi$
$83$	−2.75725			−0.302648			−0.151324	+	0.988484i	$0.548354\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	0.513433	+	0.513433i	0.0550458	+	0.0550458i
$88$		0			0
$89$	11.6448			1.23435			0.617173	−	0.786828i	$-0.288278\pi$
$89$	11.6448			1.23435			0.617173	+	0.786828i	$0.288278\pi$
$90$		0			0
$91$	5.82797	−	5.82797i	0.610937	−	0.610937i
$92$		0			0
$93$		−	1.45024i		−	0.150383i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	3.52933	+	3.52933i	0.358349	+	0.358349i	0.863204	−	0.504855i	$-0.168454\pi$
$97$	3.52933	+	3.52933i	0.358349	+	0.358349i	−0.504855	+	0.863204i	$0.668454\pi$
$98$		0			0
$99$	5.13783	−	5.13783i	0.516372	−	0.516372i
$100$		0			0
$101$	7.39467	+	7.39467i	0.735797	+	0.735797i	0.971762	−	0.235964i	$-0.0758249\pi$
$101$	7.39467	+	7.39467i	0.735797	+	0.735797i	−0.235964	+	0.971762i	$0.575825\pi$
$102$		0			0
$103$	3.72605	−	3.72605i	0.367139	−	0.367139i	−0.499294	−	0.866433i	$-0.666407\pi$
$103$	3.72605	−	3.72605i	0.367139	−	0.367139i	0.866433	+	0.499294i	$0.166407\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	16.4605			1.59130			0.795649	−	0.605758i	$-0.207130\pi$
$107$	16.4605			1.59130			0.795649	+	0.605758i	$0.207130\pi$
$108$		0			0
$109$	−12.8554	−	12.8554i	−1.23133	−	1.23133i	−0.963455	−	0.267870i	$-0.913680\pi$
$109$	−12.8554	−	12.8554i	−1.23133	−	1.23133i	−0.267870	−	0.963455i	$-0.586320\pi$
$110$		0			0
$111$			2.79249i			0.265051i
$112$		0			0
$113$	−0.863630	+	0.863630i	−0.0812435	+	0.0812435i	−0.746561	−	0.665317i	$-0.768296\pi$
$113$	−0.863630	+	0.863630i	−0.0812435	+	0.0812435i	0.665317	+	0.746561i	$0.268296\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$			5.38865i			0.498181i
$118$		0			0
$119$			23.0730i			2.11510i
$120$		0			0
$121$			3.32246i			0.302042i
$122$		0			0
$123$			3.11742i			0.281088i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−11.7944	+	11.7944i	−1.04659	+	1.04659i	−0.0477265	+	0.998860i	$0.515198\pi$
$127$	−11.7944	+	11.7944i	−1.04659	+	1.04659i	−0.998860	+	0.0477265i	$0.984802\pi$
$128$		0			0
$129$			0.522229i			0.0459797i
$130$		0			0
$131$	15.9756	+	15.9756i	1.39579	+	1.39579i	0.811659	+	0.584132i	$0.198565\pi$
$131$	15.9756	+	15.9756i	1.39579	+	1.39579i	0.584132	+	0.811659i	$0.301435\pi$
$132$		0			0
$133$	3.87683			0.336163
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.29423	+	1.29423i	−0.110573	+	0.110573i	−0.760229	−	0.649655i	$-0.774913\pi$
$137$	−1.29423	+	1.29423i	−0.110573	+	0.110573i	0.649655	+	0.760229i	$0.274913\pi$
$138$		0			0
$139$	−8.61413	−	8.61413i	−0.730641	−	0.730641i	0.240106	−	0.970747i	$-0.422818\pi$
$139$	−8.61413	−	8.61413i	−0.730641	−	0.730641i	−0.970747	+	0.240106i	$0.922818\pi$
$140$		0			0
$141$	−1.67559	+	1.67559i	−0.141110	+	0.141110i
$142$		0			0
$143$	4.02617	+	4.02617i	0.336685	+	0.336685i
$144$		0			0
$145$		0			0
$146$		0			0
$147$			5.58450i			0.460602i
$148$		0			0
$149$	0.0806133	−	0.0806133i	0.00660410	−	0.00660410i	−0.703797	−	0.710401i	$-0.748514\pi$
$149$	0.0806133	−	0.0806133i	0.00660410	−	0.00660410i	0.710401	+	0.703797i	$0.248514\pi$
$150$		0			0
$151$	3.25198			0.264643			0.132321	−	0.991207i	$-0.457757\pi$
$151$	3.25198			0.264643			0.132321	+	0.991207i	$0.457757\pi$
$152$		0			0
$153$	−10.6669	−	10.6669i	−0.862364	−	0.862364i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	9.06652			0.723587			0.361793	−	0.932258i	$-0.382165\pi$
$157$	9.06652			0.723587			0.361793	+	0.932258i	$0.382165\pi$
$158$		0			0
$159$	−3.18102			−0.252271
$160$		0			0
$161$	−28.0782			−2.21287
$162$		0			0
$163$	3.93313			0.308067			0.154033	−	0.988066i	$-0.450774\pi$
$163$	3.93313			0.308067			0.154033	+	0.988066i	$0.450774\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	8.13216	+	8.13216i	0.629285	+	0.629285i	0.947888	−	0.318603i	$-0.103214\pi$
$167$	8.13216	+	8.13216i	0.629285	+	0.629285i	−0.318603	+	0.947888i	$0.603214\pi$
$168$		0			0
$169$	8.77728			0.675175
$170$		0			0
$171$	−1.79229	+	1.79229i	−0.137060	+	0.137060i
$172$		0			0
$173$			6.86735i			0.522115i	0.965323	+	0.261057i	$0.0840712\pi$
$173$			6.86735i			0.522115i	−0.965323	+	0.261057i	$0.915929\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	2.55861	+	2.55861i	0.192317	+	0.192317i
$178$		0			0
$179$	15.7117	−	15.7117i	1.17435	−	1.17435i	0.193183	−	0.981163i	$-0.438119\pi$
$179$	15.7117	−	15.7117i	1.17435	−	1.17435i	0.981163	−	0.193183i	$-0.0618811\pi$
$180$		0			0
$181$	−13.9112	−	13.9112i	−1.03401	−	1.03401i	−0.999401	−	0.0346142i	$-0.988980\pi$
$181$	−13.9112	−	13.9112i	−1.03401	−	1.03401i	−0.0346142	−	0.999401i	$-0.511020\pi$
$182$		0			0
$183$	3.41518	−	3.41518i	0.252458	−	0.252458i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−15.9397			−1.16562
$188$		0			0
$189$	−9.79951	−	9.79951i	−0.712810	−	0.712810i
$190$		0			0
$191$		−	10.3393i		−	0.748123i	−0.927404	−	0.374061i	$-0.877965\pi$
$191$		−	10.3393i		−	0.748123i	0.927404	−	0.374061i	$-0.122035\pi$
$192$		0			0
$193$	−13.2080	+	13.2080i	−0.950734	+	0.950734i	−0.998842	−	0.0481079i	$-0.984681\pi$
$193$	−13.2080	+	13.2080i	−0.950734	+	0.950734i	0.0481079	+	0.998842i	$0.484681\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	15.2437i		−	1.08607i	−0.839709	−	0.543036i	$-0.817275\pi$
$197$		−	15.2437i		−	1.08607i	0.839709	−	0.543036i	$-0.182725\pi$
$198$		0			0
$199$		−	4.98761i		−	0.353562i	−0.984250	−	0.176781i	$-0.943432\pi$
$199$		−	4.98761i		−	0.353562i	0.984250	−	0.176781i	$-0.0565684\pi$
$200$		0			0
$201$		−	1.06694i		−	0.0752561i
$202$		0			0
$203$			4.73878i			0.332597i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	12.9808	−	12.9808i	0.902228	−	0.902228i
$208$		0			0
$209$			2.67825i			0.185258i
$210$		0			0
$211$	−10.3803	−	10.3803i	−0.714608	−	0.714608i	0.252887	−	0.967496i	$-0.418620\pi$
$211$	−10.3803	−	10.3803i	−0.714608	−	0.714608i	−0.967496	+	0.252887i	$0.918620\pi$
$212$		0			0
$213$	−1.43517			−0.0983362
$214$		0			0
$215$		0			0
$216$		0			0
$217$	6.69257	−	6.69257i	0.454321	−	0.454321i
$218$		0			0
$219$	2.70216	+	2.70216i	0.182595	+	0.182595i
$220$		0			0
$221$	8.35890	−	8.35890i	0.562280	−	0.562280i
$222$		0			0
$223$	1.49853	+	1.49853i	0.100349	+	0.100349i	0.755499	−	0.655150i	$-0.227395\pi$
$223$	1.49853	+	1.49853i	0.100349	+	0.100349i	−0.655150	+	0.755499i	$0.727395\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		−	15.6346i		−	1.03771i	−0.854864	−	0.518853i	$-0.826359\pi$
$227$		−	15.6346i		−	1.03771i	0.854864	−	0.518853i	$-0.173641\pi$
$228$		0			0
$229$	9.74097	−	9.74097i	0.643702	−	0.643702i	−0.307762	−	0.951463i	$-0.599580\pi$
$229$	9.74097	−	9.74097i	0.643702	−	0.643702i	0.951463	+	0.307762i	$0.0995800\pi$
$230$		0			0
$231$	−6.82992			−0.449376
$232$		0			0
$233$	0.509123	+	0.509123i	0.0333538	+	0.0333538i	0.723587	−	0.690233i	$-0.242492\pi$
$233$	0.509123	+	0.509123i	0.0333538	+	0.0333538i	−0.690233	+	0.723587i	$0.742492\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−8.66493			−0.562848
$238$		0			0
$239$	8.19486			0.530081			0.265041	−	0.964237i	$-0.414615\pi$
$239$	8.19486			0.530081			0.265041	+	0.964237i	$0.414615\pi$
$240$		0			0
$241$	5.66775			0.365092			0.182546	−	0.983197i	$-0.441566\pi$
$241$	5.66775			0.365092			0.182546	+	0.983197i	$0.441566\pi$
$242$		0			0
$243$	13.8956			0.891400
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−1.40450	−	1.40450i	−0.0893661	−	0.0893661i
$248$		0			0
$249$	−1.69451			−0.107385
$250$		0			0
$251$	−14.7484	+	14.7484i	−0.930911	+	0.930911i	−0.997763	−	0.0668521i	$-0.978704\pi$
$251$	−14.7484	+	14.7484i	−0.930911	+	0.930911i	0.0668521	+	0.997763i	$0.478704\pi$
$252$		0			0
$253$		−	19.3974i		−	1.21951i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−3.61143	−	3.61143i	−0.225275	−	0.225275i	0.585440	−	0.810715i	$-0.300922\pi$
$257$	−3.61143	−	3.61143i	−0.225275	−	0.225275i	−0.810715	+	0.585440i	$0.800922\pi$
$258$		0			0
$259$	−12.8868	+	12.8868i	−0.800745	+	0.800745i
$260$		0			0
$261$	−2.19078	−	2.19078i	−0.135606	−	0.135606i
$262$		0			0
$263$	−6.80041	+	6.80041i	−0.419331	+	0.419331i	−0.884973	−	0.465642i	$-0.845823\pi$
$263$	−6.80041	+	6.80041i	−0.419331	+	0.419331i	0.465642	+	0.884973i	$0.345823\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	7.15650			0.437970
$268$		0			0
$269$	1.20010	+	1.20010i	0.0731711	+	0.0731711i	0.742745	−	0.669574i	$-0.233523\pi$
$269$	1.20010	+	1.20010i	0.0731711	+	0.0731711i	−0.669574	+	0.742745i	$0.733523\pi$
$270$		0			0
$271$		−	2.79591i		−	0.169840i	−0.996388	−	0.0849199i	$-0.972937\pi$
$271$		−	2.79591i		−	0.169840i	0.996388	−	0.0849199i	$-0.0270634\pi$
$272$		0			0
$273$	3.58167	−	3.58167i	0.216773	−	0.216773i
$274$		0			0
$275$		0			0
$276$		0			0
$277$		−	13.8115i		−	0.829852i	−0.909855	−	0.414926i	$-0.863807\pi$
$277$		−	13.8115i		−	0.829852i	0.909855	−	0.414926i	$-0.136193\pi$
$278$		0			0
$279$			6.18807i			0.370470i
$280$		0			0
$281$		−	7.21718i		−	0.430541i	−0.976554	−	0.215270i	$-0.930937\pi$
$281$		−	7.21718i		−	0.430541i	0.976554	−	0.215270i	$-0.0690633\pi$
$282$		0			0
$283$		−	25.2988i		−	1.50386i	−0.659243	−	0.751930i	$-0.729123\pi$
$283$		−	25.2988i		−	1.50386i	0.659243	−	0.751930i	$-0.270877\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−14.3862	+	14.3862i	−0.849193	+	0.849193i
$288$		0			0
$289$			16.0930i			0.946644i
$290$		0			0
$291$	2.16901	+	2.16901i	0.127149	+	0.127149i
$292$		0			0
$293$	14.1276			0.825344			0.412672	−	0.910880i	$-0.364596\pi$
$293$	14.1276			0.825344			0.412672	+	0.910880i	$0.364596\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	6.76985	−	6.76985i	0.392827	−	0.392827i
$298$		0			0
$299$	10.1722	+	10.1722i	0.588272	+	0.588272i
$300$		0			0
$301$	−2.40998	+	2.40998i	−0.138909	+	0.138909i
$302$		0			0
$303$	4.54451	+	4.54451i	0.261076	+	0.261076i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	22.6081i		−	1.29031i	−0.764051	−	0.645156i	$-0.776792\pi$
$307$		−	22.6081i		−	1.29031i	0.764051	−	0.645156i	$-0.223208\pi$
$308$		0			0
$309$	2.28990	−	2.28990i	0.130268	−	0.130268i
$310$		0			0
$311$	10.7903			0.611859			0.305929	−	0.952054i	$-0.401033\pi$
$311$	10.7903			0.611859			0.305929	+	0.952054i	$0.401033\pi$
$312$		0			0
$313$	20.6842	+	20.6842i	1.16914	+	1.16914i	0.982412	+	0.186727i	$0.0597879\pi$
$313$	20.6842	+	20.6842i	1.16914	+	1.16914i	0.186727	+	0.982412i	$0.440212\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−23.8207			−1.33791			−0.668953	−	0.743305i	$-0.733257\pi$
$317$	−23.8207			−1.33791			−0.668953	+	0.743305i	$0.733257\pi$
$318$		0			0
$319$	−3.27372			−0.183293
$320$		0			0
$321$	10.1161			0.564624
$322$		0			0
$323$	5.56042			0.309390
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−7.90050	−	7.90050i	−0.436899	−	0.436899i
$328$		0			0
$329$	−15.4650			−0.852615
$330$		0			0
$331$	19.7688	−	19.7688i	1.08659	−	1.08659i	0.0907155	−	0.995877i	$-0.471085\pi$
$331$	19.7688	−	19.7688i	1.08659	−	1.08659i	0.995877	−	0.0907155i	$-0.0289154\pi$
$332$		0			0
$333$		−	11.9153i		−	0.652957i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−7.26955	−	7.26955i	−0.395998	−	0.395998i	0.480821	−	0.876819i	$-0.340339\pi$
$337$	−7.26955	−	7.26955i	−0.395998	−	0.395998i	−0.876819	+	0.480821i	$0.840339\pi$
$338$		0			0
$339$	−0.530758	+	0.530758i	−0.0288268	+	0.0288268i
$340$		0			0
$341$	4.62347	+	4.62347i	0.250375	+	0.250375i
$342$		0			0
$343$	−5.91866	+	5.91866i	−0.319578	+	0.319578i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−23.4667			−1.25976			−0.629880	−	0.776692i	$-0.716896\pi$
$347$	−23.4667			−1.25976			−0.629880	+	0.776692i	$0.716896\pi$
$348$		0			0
$349$	23.2089	+	23.2089i	1.24234	+	1.24234i	0.959027	+	0.283315i	$0.0914342\pi$
$349$	23.2089	+	23.2089i	1.24234	+	1.24234i	0.283315	+	0.959027i	$0.408566\pi$
$350$		0			0
$351$			7.10035i			0.378988i
$352$		0			0
$353$	13.3220	−	13.3220i	0.709059	−	0.709059i	−0.257278	−	0.966337i	$-0.582826\pi$
$353$	13.3220	−	13.3220i	0.709059	−	0.709059i	0.966337	+	0.257278i	$0.0828256\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$			14.1799i			0.750479i
$358$		0			0
$359$		−	26.9902i		−	1.42449i	−0.701932	−	0.712244i	$-0.747679\pi$
$359$		−	26.9902i		−	1.42449i	0.701932	−	0.712244i	$-0.252321\pi$
$360$		0			0
$361$			18.0657i			0.950827i
$362$		0			0
$363$			2.04187i			0.107170i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	19.4758	−	19.4758i	1.01663	−	1.01663i	0.0167684	−	0.999859i	$-0.494662\pi$
$367$	19.4758	−	19.4758i	1.01663	−	1.01663i	0.999859	−	0.0167684i	$-0.00533781\pi$
$368$		0			0
$369$		−	13.3018i		−	0.692464i
$370$		0			0
$371$	−14.6798	−	14.6798i	−0.762136	−	0.762136i
$372$		0			0
$373$	−4.87069			−0.252195			−0.126097	−	0.992018i	$-0.540245\pi$
$373$	−4.87069			−0.252195			−0.126097	+	0.992018i	$0.540245\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	1.71677	−	1.71677i	0.0884180	−	0.0884180i
$378$		0			0
$379$	2.54450	+	2.54450i	0.130702	+	0.130702i	0.769432	−	0.638729i	$-0.220540\pi$
$379$	2.54450	+	2.54450i	0.130702	+	0.130702i	−0.638729	+	0.769432i	$0.720540\pi$
$380$		0			0
$381$	−7.24846	+	7.24846i	−0.371350	+	0.371350i
$382$		0			0
$383$	−0.193238	−	0.193238i	−0.00987399	−	0.00987399i	0.702153	−	0.712027i	$-0.252222\pi$
$383$	−0.193238	−	0.193238i	−0.00987399	−	0.00987399i	−0.712027	+	0.702153i	$0.752222\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		−	2.22831i		−	0.113272i
$388$		0			0
$389$	−2.01528	+	2.01528i	−0.102179	+	0.102179i	−0.756348	−	0.654169i	$-0.773018\pi$
$389$	−2.01528	+	2.01528i	−0.102179	+	0.102179i	0.654169	+	0.756348i	$0.273018\pi$
$390$		0			0
$391$	−40.2718			−2.03663
$392$		0			0
$393$	9.81803	+	9.81803i	0.495254	+	0.495254i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	21.5509			1.08161			0.540804	−	0.841149i	$-0.318120\pi$
$397$	21.5509			1.08161			0.540804	+	0.841149i	$0.318120\pi$
$398$		0			0
$399$	2.38257			0.119277
$400$		0			0
$401$	−10.3965			−0.519176			−0.259588	−	0.965719i	$-0.583587\pi$
$401$	−10.3965			−0.519176			−0.259588	+	0.965719i	$0.583587\pi$
$402$		0			0
$403$	−4.84917			−0.241555
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−8.90264	−	8.90264i	−0.441288	−	0.441288i
$408$		0			0
$409$	0.330732			0.0163536			0.00817682	−	0.999967i	$-0.497397\pi$
$409$	0.330732			0.0163536			0.00817682	+	0.999967i	$0.497397\pi$
$410$		0			0
$411$	−0.795389	+	0.795389i	−0.0392337	+	0.0392337i
$412$		0			0
$413$			23.6150i			1.16202i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−5.29395	−	5.29395i	−0.259246	−	0.259246i
$418$		0			0
$419$	−6.71354	+	6.71354i	−0.327978	+	0.327978i	−0.851817	−	0.523839i	$-0.824499\pi$
$419$	−6.71354	+	6.71354i	−0.327978	+	0.327978i	0.523839	+	0.851817i	$0.324499\pi$
$420$		0			0
$421$	2.99831	+	2.99831i	0.146129	+	0.146129i	0.776386	−	0.630258i	$-0.217051\pi$
$421$	2.99831	+	2.99831i	0.146129	+	0.146129i	−0.630258	+	0.776386i	$0.717051\pi$
$422$		0			0
$423$	7.14963	−	7.14963i	0.347627	−	0.347627i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	31.5208			1.52540
$428$		0			0
$429$	2.47435	+	2.47435i	0.119463	+	0.119463i
$430$		0			0
$431$		−	19.9548i		−	0.961191i	−0.876942	−	0.480596i	$-0.840420\pi$
$431$		−	19.9548i		−	0.961191i	0.876942	−	0.480596i	$-0.159580\pi$
$432$		0			0
$433$	16.1910	−	16.1910i	0.778092	−	0.778092i	−0.201414	−	0.979506i	$-0.564554\pi$
$433$	16.1910	−	16.1910i	0.778092	−	0.778092i	0.979506	+	0.201414i	$0.0645537\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$			6.76664i			0.323692i
$438$		0			0
$439$		−	29.3734i		−	1.40191i	−0.713204	−	0.700957i	$-0.752757\pi$
$439$		−	29.3734i		−	1.40191i	0.713204	−	0.700957i	$-0.247243\pi$
$440$		0			0
$441$		−	23.8287i		−	1.13470i
$442$		0			0
$443$			19.8713i			0.944115i	0.881568	+	0.472057i	$0.156489\pi$
$443$			19.8713i			0.944115i	−0.881568	+	0.472057i	$0.843511\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	0.0495422	−	0.0495422i	0.00234326	−	0.00234326i
$448$		0			0
$449$		−	16.7577i		−	0.790844i	−0.918500	−	0.395422i	$-0.870598\pi$
$449$		−	16.7577i		−	0.790844i	0.918500	−	0.395422i	$-0.129402\pi$
$450$		0			0
$451$	−9.93854	−	9.93854i	−0.467987	−	0.467987i
$452$		0			0
$453$	1.99856			0.0939005
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−5.00267	+	5.00267i	−0.234015	+	0.234015i	−0.814366	−	0.580351i	$-0.802915\pi$
$457$	−5.00267	+	5.00267i	−0.234015	+	0.234015i	0.580351	+	0.814366i	$0.302915\pi$
$458$		0			0
$459$	−14.0552	−	14.0552i	−0.656039	−	0.656039i
$460$		0			0
$461$	2.71518	−	2.71518i	0.126459	−	0.126459i	−0.641045	−	0.767503i	$-0.721499\pi$
$461$	2.71518	−	2.71518i	0.126459	−	0.126459i	0.767503	+	0.641045i	$0.221499\pi$
$462$		0			0
$463$	−9.18551	−	9.18551i	−0.426887	−	0.426887i	0.460680	−	0.887566i	$-0.347606\pi$
$463$	−9.18551	−	9.18551i	−0.426887	−	0.426887i	−0.887566	+	0.460680i	$0.847606\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	1.06405i		−	0.0492385i	−0.999697	−	0.0246193i	$-0.992163\pi$
$467$		−	1.06405i		−	0.0492385i	0.999697	−	0.0246193i	$-0.00783735\pi$
$468$		0			0
$469$	4.92371	−	4.92371i	0.227356	−	0.227356i
$470$		0			0
$471$	5.57197			0.256743
$472$		0			0
$473$	−1.66490	−	1.66490i	−0.0765523	−	0.0765523i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	13.5732			0.621474
$478$		0			0
$479$	15.8658			0.724926			0.362463	−	0.931998i	$-0.381936\pi$
$479$	15.8658			0.724926			0.362463	+	0.931998i	$0.381936\pi$
$480$		0			0
$481$	9.33725			0.425742
$482$		0			0
$483$	−17.2559			−0.785170
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−13.7947	−	13.7947i	−0.625099	−	0.625099i	0.321732	−	0.946831i	$-0.395735\pi$
$487$	−13.7947	−	13.7947i	−0.625099	−	0.625099i	−0.946831	+	0.321732i	$0.895735\pi$
$488$		0			0
$489$	2.41717			0.109308
$490$		0			0
$491$	−19.4471	+	19.4471i	−0.877637	+	0.877637i	−0.993290	−	0.115652i	$-0.963104\pi$
$491$	−19.4471	+	19.4471i	−0.877637	+	0.877637i	0.115652	+	0.993290i	$0.463104\pi$
$492$		0			0
$493$			6.79669i			0.306108i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−6.62302	−	6.62302i	−0.297083	−	0.297083i
$498$		0			0
$499$	23.0141	−	23.0141i	1.03025	−	1.03025i	0.0307258	−	0.999528i	$-0.490218\pi$
$499$	23.0141	−	23.0141i	1.03025	−	1.03025i	0.999528	−	0.0307258i	$-0.00978185\pi$
$500$		0			0
$501$	4.99775	+	4.99775i	0.223283	+	0.223283i
$502$		0			0
$503$	6.63364	−	6.63364i	0.295780	−	0.295780i	−0.543579	−	0.839358i	$-0.682931\pi$
$503$	6.63364	−	6.63364i	0.295780	−	0.295780i	0.839358	+	0.543579i	$0.182931\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	5.39422			0.239566
$508$		0			0
$509$	−8.04140	−	8.04140i	−0.356429	−	0.356429i	0.506066	−	0.862495i	$-0.331099\pi$
$509$	−8.04140	−	8.04140i	−0.356429	−	0.356429i	−0.862495	+	0.506066i	$0.831099\pi$
$510$		0			0
$511$			24.9398i			1.10327i
$512$		0			0
$513$	−2.36161	+	2.36161i	−0.104268	+	0.104268i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		−	10.6838i		−	0.469873i
$518$		0			0
$519$			4.22044i			0.185257i
$520$		0			0
$521$		−	32.8549i		−	1.43940i	−0.694285	−	0.719700i	$-0.744279\pi$
$521$		−	32.8549i		−	1.43940i	0.694285	−	0.719700i	$-0.255721\pi$
$522$		0			0
$523$			2.46341i			0.107717i	0.998549	+	0.0538587i	$0.0171521\pi$
$523$			2.46341i			0.107717i	−0.998549	+	0.0538587i	$0.982848\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	9.59896	−	9.59896i	0.418137	−	0.418137i
$528$		0			0
$529$		−	26.0078i		−	1.13078i
$530$		0			0
$531$	−10.9174	−	10.9174i	−0.473775	−	0.473775i
$532$		0			0
$533$	10.4237			0.451501
$534$		0			0
$535$		0			0
$536$		0			0
$537$	9.65586	−	9.65586i	0.416681	−	0.416681i
$538$		0			0
$539$	−17.8038	−	17.8038i	−0.766863	−	0.766863i
$540$		0			0
$541$	−18.0772	+	18.0772i	−0.777198	+	0.777198i	−0.979353	−	0.202156i	$-0.935205\pi$
$541$	−18.0772	+	18.0772i	−0.777198	+	0.777198i	0.202156	+	0.979353i	$0.435205\pi$
$542$		0			0
$543$	−8.54938	−	8.54938i	−0.366889	−	0.366889i
$544$		0			0
$545$		0			0
$546$		0			0
$547$			43.6742i			1.86738i	0.358089	+	0.933688i	$0.383428\pi$
$547$			43.6742i			1.86738i	−0.358089	+	0.933688i	$0.616572\pi$
$548$		0			0
$549$	−14.5723	+	14.5723i	−0.621932	+	0.621932i
$550$		0			0
$551$	1.14201			0.0486513
$552$		0			0
$553$	−39.9869	−	39.9869i	−1.70042	−	1.70042i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	5.18948			0.219885			0.109943	−	0.993938i	$-0.464933\pi$
$557$	5.18948			0.219885			0.109943	+	0.993938i	$0.464933\pi$
$558$		0			0
$559$	1.74618			0.0738555
$560$		0			0
$561$	−9.79597			−0.413586
$562$		0			0
$563$	11.3756			0.479423			0.239711	−	0.970844i	$-0.422947\pi$
$563$	11.3756			0.479423			0.239711	+	0.970844i	$0.422947\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	16.2889	+	16.2889i	0.684071	+	0.684071i
$568$		0			0
$569$	7.51787			0.315165			0.157583	−	0.987506i	$-0.449630\pi$
$569$	7.51787			0.315165			0.157583	+	0.987506i	$0.449630\pi$
$570$		0			0
$571$	7.76889	−	7.76889i	0.325118	−	0.325118i	−0.525609	−	0.850726i	$-0.676162\pi$
$571$	7.76889	−	7.76889i	0.325118	−	0.325118i	0.850726	+	0.525609i	$0.176162\pi$
$572$		0			0
$573$		−	6.35416i		−	0.265449i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	9.84819	+	9.84819i	0.409986	+	0.409986i	0.881733	−	0.471748i	$-0.156377\pi$
$577$	9.84819	+	9.84819i	0.409986	+	0.409986i	−0.471748	+	0.881733i	$0.656377\pi$
$578$		0			0
$579$	−8.11720	+	8.11720i	−0.337339	+	0.337339i
$580$		0			0
$581$	−7.81984	−	7.81984i	−0.324421	−	0.324421i
$582$		0			0
$583$	10.1413	−	10.1413i	0.420010	−	0.420010i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−33.0447			−1.36390			−0.681951	−	0.731398i	$-0.738868\pi$
$587$	−33.0447			−1.36390			−0.681951	+	0.731398i	$0.738868\pi$
$588$		0			0
$589$	−1.61286	−	1.61286i	−0.0664567	−	0.0664567i
$590$		0			0
$591$		−	9.36829i		−	0.385360i
$592$		0			0
$593$	−18.5424	+	18.5424i	−0.761445	+	0.761445i	−0.976584	−	0.215139i	$-0.930980\pi$
$593$	−18.5424	+	18.5424i	−0.761445	+	0.761445i	0.215139	+	0.976584i	$0.430980\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		−	3.06521i		−	0.125451i
$598$		0			0
$599$			28.3117i			1.15678i	0.815759	+	0.578392i	$0.196319\pi$
$599$			28.3117i			1.15678i	−0.815759	+	0.578392i	$0.803681\pi$
$600$		0			0
$601$			41.7630i			1.70355i	0.523909	+	0.851774i	$0.324473\pi$
$601$			41.7630i			1.70355i	−0.523909	+	0.851774i	$0.675527\pi$
$602$		0			0
$603$			4.55255i			0.185394i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−4.01973	+	4.01973i	−0.163156	+	0.163156i	−0.783963	−	0.620807i	$-0.786805\pi$
$607$	−4.01973	+	4.01973i	−0.163156	+	0.163156i	0.620807	+	0.783963i	$0.286805\pi$
$608$		0			0
$609$			2.91229i			0.118012i
$610$		0			0
$611$	5.60268	+	5.60268i	0.226660	+	0.226660i
$612$		0			0
$613$	−21.5230			−0.869305			−0.434652	−	0.900598i	$-0.643129\pi$
$613$	−21.5230			−0.869305			−0.434652	+	0.900598i	$0.643129\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−26.4655	+	26.4655i	−1.06546	+	1.06546i	−0.0677580	+	0.997702i	$0.521585\pi$
$617$	−26.4655	+	26.4655i	−1.06546	+	1.06546i	−0.997702	+	0.0677580i	$0.978415\pi$
$618$		0			0
$619$	21.7935	+	21.7935i	0.875955	+	0.875955i	0.993113	−	0.117158i	$-0.0373784\pi$
$619$	21.7935	+	21.7935i	0.875955	+	0.875955i	−0.117158	+	0.993113i	$0.537378\pi$
$620$		0			0
$621$	17.1041	−	17.1041i	0.686365	−	0.686365i
$622$		0			0
$623$	33.0258	+	33.0258i	1.32315	+	1.32315i
$624$		0			0
$625$		0			0
$626$		0			0
$627$			1.64596i			0.0657334i
$628$		0			0
$629$	−18.4831	+	18.4831i	−0.736971	+	0.736971i
$630$		0			0
$631$	42.7412			1.70150			0.850751	−	0.525570i	$-0.176148\pi$
$631$	42.7412			1.70150			0.850751	+	0.525570i	$0.176148\pi$
$632$		0			0
$633$	−6.37937	−	6.37937i	−0.253557	−	0.253557i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	18.6729			0.739848
$638$		0			0
$639$	6.12376			0.242252
$640$		0			0
$641$	45.4930			1.79687			0.898433	−	0.439110i	$-0.144706\pi$
$641$	45.4930			1.79687			0.898433	+	0.439110i	$0.144706\pi$
$642$		0			0
$643$	−31.3531			−1.23645			−0.618224	−	0.786002i	$-0.712147\pi$
$643$	−31.3531			−1.23645			−0.618224	+	0.786002i	$0.712147\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−24.0355	−	24.0355i	−0.944932	−	0.944932i	0.0536292	−	0.998561i	$-0.482921\pi$
$647$	−24.0355	−	24.0355i	−0.944932	−	0.944932i	−0.998561	+	0.0536292i	$0.982921\pi$
$648$		0			0
$649$	−16.3141			−0.640383
$650$		0			0
$651$	4.11303	−	4.11303i	0.161202	−	0.161202i
$652$		0			0
$653$			15.4153i			0.603248i	0.953427	+	0.301624i	$0.0975288\pi$
$653$			15.4153i			0.603248i	−0.953427	+	0.301624i	$0.902471\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−11.5299	−	11.5299i	−0.449825	−	0.449825i
$658$		0			0
$659$	−30.4355	+	30.4355i	−1.18560	+	1.18560i	−0.207327	+	0.978272i	$0.566476\pi$
$659$	−30.4355	+	30.4355i	−1.18560	+	1.18560i	−0.978272	+	0.207327i	$0.933524\pi$
$660$		0			0
$661$	−11.2208	−	11.2208i	−0.436437	−	0.436437i	0.454374	−	0.890811i	$-0.349863\pi$
$661$	−11.2208	−	11.2208i	−0.436437	−	0.436437i	−0.890811	+	0.454374i	$0.849863\pi$
$662$		0			0
$663$	5.13709	−	5.13709i	0.199508	−	0.199508i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−8.27109			−0.320258
$668$		0			0
$669$	0.920946	+	0.920946i	0.0356058	+	0.0356058i
$670$		0			0
$671$			21.7757i			0.840640i
$672$		0			0
$673$	29.2965	−	29.2965i	1.12930	−	1.12930i	0.139006	−	0.990291i	$-0.455609\pi$
$673$	29.2965	−	29.2965i	1.12930	−	1.12930i	0.990291	−	0.139006i	$-0.0443908\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		−	2.74511i		−	0.105503i	−0.998608	−	0.0527516i	$-0.983201\pi$
$677$		−	2.74511i		−	0.105503i	0.998608	−	0.0527516i	$-0.0167991\pi$
$678$		0			0
$679$			20.0191i			0.768261i
$680$		0			0
$681$		−	9.60850i		−	0.368199i
$682$		0			0
$683$			33.0796i			1.26576i	0.774251	+	0.632878i	$0.218127\pi$
$683$			33.0796i			1.26576i	−0.774251	+	0.632878i	$0.781873\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	5.98647	−	5.98647i	0.228398	−	0.228398i
$688$		0			0
$689$			10.6364i			0.405214i
$690$		0			0
$691$	30.8216	+	30.8216i	1.17251	+	1.17251i	0.981610	+	0.190899i	$0.0611404\pi$
$691$	30.8216	+	30.8216i	1.17251	+	1.17251i	0.190899	+	0.981610i	$0.438860\pi$
$692$		0			0
$693$	29.1428			1.10704
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−20.6338	+	20.6338i	−0.781561	+	0.781561i
$698$		0			0
$699$	0.312890	+	0.312890i	0.0118346	+	0.0118346i
$700$		0			0
$701$	−22.1242	+	22.1242i	−0.835619	+	0.835619i	−0.988279	−	0.152660i	$-0.951216\pi$
$701$	−22.1242	+	22.1242i	−0.835619	+	0.835619i	0.152660	+	0.988279i	$0.451216\pi$
$702$		0			0
$703$	3.10562	+	3.10562i	0.117131	+	0.117131i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			41.9440i			1.57747i
$708$		0			0
$709$	7.09244	−	7.09244i	0.266362	−	0.266362i	−0.561270	−	0.827632i	$-0.689687\pi$
$709$	7.09244	−	7.09244i	0.266362	−	0.266362i	0.827632	+	0.561270i	$0.189687\pi$
$710$		0			0
$711$	36.9726			1.38658
$712$		0			0
$713$	11.6812	+	11.6812i	0.437466	+	0.437466i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	5.03628			0.188083
$718$		0			0
$719$	30.2949			1.12981			0.564905	−	0.825156i	$-0.308913\pi$
$719$	30.2949			1.12981			0.564905	+	0.825156i	$0.308913\pi$
$720$		0			0
$721$	21.1349			0.787104
$722$		0			0
$723$	3.48320			0.129542
$724$		0			0
$725$		0			0
$726$		0			0
$727$	15.9503	+	15.9503i	0.591566	+	0.591566i	0.938054	−	0.346489i	$-0.112626\pi$
$727$	15.9503	+	15.9503i	0.591566	+	0.591566i	−0.346489	+	0.938054i	$0.612626\pi$
$728$		0			0
$729$	−8.69055			−0.321872
$730$		0			0
$731$	−3.45657	+	3.45657i	−0.127846	+	0.127846i
$732$		0			0
$733$			35.8535i			1.32428i	0.749380	+	0.662140i	$0.230352\pi$
$733$			35.8535i			1.32428i	−0.749380	+	0.662140i	$0.769648\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	3.40147	+	3.40147i	0.125295	+	0.125295i
$738$		0			0
$739$	−21.4532	+	21.4532i	−0.789168	+	0.789168i	−0.981358	−	0.192190i	$-0.938441\pi$
$739$	−21.4532	+	21.4532i	−0.789168	+	0.789168i	0.192190	+	0.981358i	$0.438441\pi$
$740$		0			0
$741$	−0.863157	−	0.863157i	−0.0317089	−	0.0317089i
$742$		0			0
$743$	13.0311	−	13.0311i	0.478063	−	0.478063i	−0.426449	−	0.904512i	$-0.640235\pi$
$743$	13.0311	−	13.0311i	0.478063	−	0.478063i	0.904512	+	0.426449i	$0.140235\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	7.23036			0.264545
$748$		0			0
$749$	46.6836	+	46.6836i	1.70578	+	1.70578i
$750$		0			0
$751$			22.4879i			0.820595i	0.911952	+	0.410297i	$0.134575\pi$
$751$			22.4879i			0.820595i	−0.911952	+	0.410297i	$0.865425\pi$
$752$		0			0
$753$	−9.06387	+	9.06387i	−0.330306	+	0.330306i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	15.8781i		−	0.577100i	−0.957465	−	0.288550i	$-0.906827\pi$
$757$		−	15.8781i		−	0.577100i	0.957465	−	0.288550i	$-0.0931731\pi$
$758$		0			0
$759$		−	11.9210i		−	0.432705i
$760$		0			0
$761$			19.5227i			0.707696i	0.935303	+	0.353848i	$0.115127\pi$
$761$			19.5227i			0.707696i	−0.935303	+	0.353848i	$0.884873\pi$
$762$		0			0
$763$		−	72.9184i		−	2.63982i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	8.55524	−	8.55524i	0.308912	−	0.308912i
$768$		0			0
$769$		−	8.03843i		−	0.289873i	−0.989441	−	0.144937i	$-0.953702\pi$
$769$		−	8.03843i		−	0.289873i	0.989441	−	0.144937i	$-0.0462978\pi$
$770$		0			0
$771$	−2.21946	−	2.21946i	−0.0799320	−	0.0799320i
$772$		0			0
$773$	−40.5118			−1.45711			−0.728554	−	0.684988i	$-0.759807\pi$
$773$	−40.5118			−1.45711			−0.728554	+	0.684988i	$0.759807\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−7.91977	+	7.91977i	−0.284120	+	0.284120i
$778$		0			0
$779$	3.46698	+	3.46698i	0.124217	+	0.124217i
$780$		0			0
$781$	4.57542	−	4.57542i	0.163721	−	0.163721i
$782$		0			0
$783$	−2.88668	−	2.88668i	−0.103161	−	0.103161i
$784$		0			0
$785$		0			0
$786$		0			0
$787$			15.8333i			0.564396i	0.959356	+	0.282198i	$0.0910635\pi$
$787$			15.8333i			0.564396i	−0.959356	+	0.282198i	$0.908937\pi$
$788$		0			0
$789$	−4.17930	+	4.17930i	−0.148787	+	0.148787i
$790$		0			0
$791$	−4.89868			−0.174177
$792$		0			0
$793$	−11.4194	−	11.4194i	−0.405513	−	0.405513i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	10.2670			0.363674			0.181837	−	0.983329i	$-0.441796\pi$
$797$	10.2670			0.363674			0.181837	+	0.983329i	$0.441796\pi$
$798$		0			0
$799$	−22.1811			−0.784710
$800$		0			0
$801$	−30.5362			−1.07895
$802$		0			0
$803$	−17.2293			−0.608010
$804$		0			0
$805$		0			0
$806$		0			0
$807$	0.737538	+	0.737538i	0.0259626	+	0.0259626i
$808$		0			0
$809$	9.16442			0.322204			0.161102	−	0.986938i	$-0.448495\pi$
$809$	9.16442			0.322204			0.161102	+	0.986938i	$0.448495\pi$
$810$		0			0
$811$	22.1702	−	22.1702i	0.778502	−	0.778502i	−0.201074	−	0.979576i	$-0.564443\pi$
$811$	22.1702	−	22.1702i	0.778502	−	0.778502i	0.979576	+	0.201074i	$0.0644432\pi$
$812$		0			0
$813$		−	1.71827i		−	0.0602625i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	0.580788	+	0.580788i	0.0203192	+	0.0203192i
$818$		0			0
$819$	−15.2827	+	15.2827i	−0.534022	+	0.534022i
$820$		0			0
$821$	13.3258	+	13.3258i	0.465074	+	0.465074i	0.900314	−	0.435240i	$-0.143337\pi$
$821$	13.3258	+	13.3258i	0.465074	+	0.465074i	−0.435240	+	0.900314i	$0.643337\pi$
$822$		0			0
$823$	−34.7796	+	34.7796i	−1.21234	+	1.21234i	−0.242084	+	0.970255i	$0.577831\pi$
$823$	−34.7796	+	34.7796i	−1.21234	+	1.21234i	−0.970255	+	0.242084i	$0.922169\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	16.5717			0.576253			0.288127	−	0.957592i	$-0.406968\pi$
$827$	16.5717			0.576253			0.288127	+	0.957592i	$0.406968\pi$
$828$		0			0
$829$	11.9869	+	11.9869i	0.416321	+	0.416321i	0.883933	−	0.467613i	$-0.154886\pi$
$829$	11.9869	+	11.9869i	0.416321	+	0.416321i	−0.467613	+	0.883933i	$0.654886\pi$
$830$		0			0
$831$		−	8.48807i		−	0.294448i
$832$		0			0
$833$	−36.9631	+	36.9631i	−1.28070	+	1.28070i
$834$		0			0
$835$		0			0
$836$		0			0
$837$			8.15370i			0.281833i
$838$		0			0
$839$		−	4.44215i		−	0.153360i	−0.997056	−	0.0766800i	$-0.975568\pi$
$839$		−	4.44215i		−	0.153360i	0.997056	−	0.0766800i	$-0.0244320\pi$
$840$		0			0
$841$		−	27.6041i		−	0.951865i
$842$		0			0
$843$		−	4.43543i		−	0.152764i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−9.42281	+	9.42281i	−0.323772	+	0.323772i
$848$		0			0
$849$		−	15.5478i		−	0.533599i
$850$		0			0
$851$	−22.4926	−	22.4926i	−0.771038	−	0.771038i
$852$		0			0
$853$	−35.6748			−1.22148			−0.610742	−	0.791830i	$-0.709129\pi$
$853$	−35.6748			−1.22148			−0.610742	+	0.791830i	$0.709129\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−13.8568	+	13.8568i	−0.473340	+	0.473340i	−0.902994	−	0.429654i	$-0.858636\pi$
$857$	−13.8568	+	13.8568i	−0.473340	+	0.473340i	0.429654	+	0.902994i	$0.358636\pi$
$858$		0			0
$859$	−19.4217	−	19.4217i	−0.662660	−	0.662660i	0.293346	−	0.956006i	$-0.405231\pi$
$859$	−19.4217	−	19.4217i	−0.662660	−	0.662660i	−0.956006	+	0.293346i	$0.905231\pi$
$860$		0			0
$861$	−8.84130	+	8.84130i	−0.301311	+	0.301311i
$862$		0			0
$863$	−9.22041	−	9.22041i	−0.313866	−	0.313866i	0.532539	−	0.846405i	$-0.321238\pi$
$863$	−9.22041	−	9.22041i	−0.313866	−	0.313866i	−0.846405	+	0.532539i	$0.821238\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$			9.89018i			0.335888i
$868$		0			0
$869$	27.6244	−	27.6244i	0.937093	−	0.937093i
$870$		0			0
$871$	−3.56753			−0.120881
$872$		0			0
$873$	−9.25500	−	9.25500i	−0.313234	−	0.313234i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−10.4267			−0.352084			−0.176042	−	0.984383i	$-0.556330\pi$
$877$	−10.4267			−0.352084			−0.176042	+	0.984383i	$0.556330\pi$
$878$		0			0
$879$	8.68236			0.292849
$880$		0			0
$881$	−12.7405			−0.429239			−0.214619	−	0.976698i	$-0.568851\pi$
$881$	−12.7405			−0.429239			−0.214619	+	0.976698i	$0.568851\pi$
$882$		0			0
$883$	27.9073			0.939156			0.469578	−	0.882891i	$-0.344406\pi$
$883$	27.9073			0.939156			0.469578	+	0.882891i	$0.344406\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	41.7449	+	41.7449i	1.40166	+	1.40166i	0.794846	+	0.606811i	$0.207552\pi$
$887$	41.7449	+	41.7449i	1.40166	+	1.40166i	0.606811	+	0.794846i	$0.292448\pi$
$888$		0			0
$889$	−66.9004			−2.24377
$890$		0			0
$891$	−11.2530	+	11.2530i	−0.376989	+	0.376989i
$892$		0			0
$893$			3.72696i			0.124718i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	6.25148	+	6.25148i	0.208731	+	0.208731i
$898$		0			0
$899$	1.97145	−	1.97145i	0.0657516	−	0.0657516i
$900$		0			0
$901$	−21.0548	−	21.0548i	−0.701437	−	0.701437i
$902$		0			0
$903$	−1.48109	+	1.48109i	−0.0492877	+	0.0492877i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	26.7614			0.888597			0.444298	−	0.895879i	$-0.353453\pi$
$907$	26.7614			0.888597			0.444298	+	0.895879i	$0.353453\pi$
$908$		0			0
$909$	−19.3911	−	19.3911i	−0.643163	−	0.643163i
$910$		0			0
$911$			19.2403i			0.637459i	0.947846	+	0.318729i	$0.103256\pi$
$911$			19.2403i			0.637459i	−0.947846	+	0.318729i	$0.896744\pi$
$912$		0			0
$913$	5.40222	−	5.40222i	0.178787	−	0.178787i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			90.6165i			2.99242i
$918$		0			0
$919$		−	42.6903i		−	1.40822i	−0.710090	−	0.704111i	$-0.751346\pi$
$919$		−	42.6903i		−	1.40822i	0.710090	−	0.704111i	$-0.248654\pi$
$920$		0			0
$921$		−	13.8942i		−	0.457828i
$922$		0			0
$923$			4.79878i			0.157954i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−9.77085	+	9.77085i	−0.320917	+	0.320917i
$928$		0			0
$929$			5.58037i			0.183086i	0.995801	+	0.0915430i	$0.0291799\pi$
$929$			5.58037i			0.183086i	−0.995801	+	0.0915430i	$0.970820\pi$
$930$		0			0
$931$	6.21070	+	6.21070i	0.203548	+	0.203548i
$932$		0			0
$933$	6.63132			0.217100
$934$		0			0
$935$		0			0
$936$		0			0
$937$	41.0680	−	41.0680i	1.34163	−	1.34163i	0.447197	−	0.894435i	$-0.352422\pi$
$937$	41.0680	−	41.0680i	1.34163	−	1.34163i	0.894435	−	0.447197i	$-0.147578\pi$
$938$		0			0
$939$	12.7118	+	12.7118i	0.414834	+	0.414834i
$940$		0			0
$941$	−31.5476	+	31.5476i	−1.02842	+	1.02842i	−0.0288377	+	0.999584i	$0.509181\pi$
$941$	−31.5476	+	31.5476i	−1.02842	+	1.02842i	−0.999584	+	0.0288377i	$0.990819\pi$
$942$		0			0
$943$	−25.1098	−	25.1098i	−0.817689	−	0.817689i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	34.7892i		−	1.13050i	−0.824921	−	0.565248i	$-0.808780\pi$
$947$		−	34.7892i		−	1.13050i	0.824921	−	0.565248i	$-0.191220\pi$
$948$		0			0
$949$	9.03522	−	9.03522i	0.293296	−	0.293296i
$950$		0			0
$951$	−14.6394			−0.474715
$952$		0			0
$953$	26.7047	+	26.7047i	0.865050	+	0.865050i	0.991919	−	0.126870i	$-0.0404931\pi$
$953$	26.7047	+	26.7047i	0.865050	+	0.865050i	−0.126870	+	0.991919i	$0.540493\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−2.01191			−0.0650360
$958$		0			0
$959$	−7.34112			−0.237057
$960$		0			0
$961$	25.4314			0.820369
$962$		0			0
$963$	−43.1645			−1.39096
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−12.8711	−	12.8711i	−0.413906	−	0.413906i	0.469191	−	0.883097i	$-0.344546\pi$
$967$	−12.8711	−	12.8711i	−0.413906	−	0.413906i	−0.883097	+	0.469191i	$0.844546\pi$
$968$		0			0
$969$	3.41725			0.109778
$970$		0			0
$971$	23.9028	−	23.9028i	0.767078	−	0.767078i	−0.210513	−	0.977591i	$-0.567513\pi$
$971$	23.9028	−	23.9028i	0.767078	−	0.767078i	0.977591	+	0.210513i	$0.0675134\pi$
$972$		0			0
$973$		−	48.8610i		−	1.56641i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−2.71449	−	2.71449i	−0.0868441	−	0.0868441i	0.662350	−	0.749194i	$-0.269559\pi$
$977$	−2.71449	−	2.71449i	−0.0868441	−	0.0868441i	−0.749194	+	0.662350i	$0.769559\pi$
$978$		0			0
$979$	−22.8154	+	22.8154i	−0.729183	+	0.729183i
$980$		0			0
$981$	33.7109	+	33.7109i	1.07630	+	1.07630i
$982$		0			0
$983$	−13.7542	+	13.7542i	−0.438692	+	0.438692i	−0.891572	−	0.452880i	$-0.850397\pi$
$983$	−13.7542	+	13.7542i	−0.438692	+	0.438692i	0.452880	+	0.891572i	$0.350397\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−9.50428			−0.302525
$988$		0			0
$989$	−4.20640	−	4.20640i	−0.133756	−	0.133756i
$990$		0			0
$991$			26.5971i			0.844883i	0.906390	+	0.422442i	$0.138827\pi$
$991$			26.5971i			0.844883i	−0.906390	+	0.422442i	$0.861173\pi$
$992$		0			0
$993$	12.1492	−	12.1492i	0.385545	−	0.385545i
$994$		0			0
$995$		0			0
$996$		0			0
$997$			25.4590i			0.806295i	0.915135	+	0.403148i	$0.132084\pi$
$997$			25.4590i			0.806295i	−0.915135	+	0.403148i	$0.867916\pi$
$998$		0			0
$999$		−	15.7002i		−	0.496733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.s.d.207.5		18
4.3	odd	2		400.2.s.d.107.7		18
5.2	odd	4		320.2.j.b.143.5		18
5.3	odd	4		1600.2.j.d.143.5		18
5.4	even	2		320.2.s.b.207.5		18
16.3	odd	4		1600.2.j.d.1007.5		18
16.13	even	4		400.2.j.d.307.3		18
20.3	even	4		400.2.j.d.43.3		18
20.7	even	4		80.2.j.b.43.7	✓	18
20.19	odd	2		80.2.s.b.27.3	yes	18
40.19	odd	2		640.2.s.d.287.5		18
40.27	even	4		640.2.j.d.543.5		18
40.29	even	2		640.2.s.c.287.5		18
40.37	odd	4		640.2.j.c.543.5		18
60.47	odd	4		720.2.bd.g.523.3		18
60.59	even	2		720.2.z.g.667.7		18
80.3	even	4	inner	1600.2.s.d.943.5		18
80.13	odd	4		400.2.s.d.243.7		18
80.19	odd	4		320.2.j.b.47.5		18
80.27	even	4		640.2.s.c.223.5		18
80.29	even	4		80.2.j.b.67.7	yes	18
80.37	odd	4		640.2.s.d.223.5		18
80.59	odd	4		640.2.j.c.607.5		18
80.67	even	4		320.2.s.b.303.5		18
80.69	even	4		640.2.j.d.607.5		18
80.77	odd	4		80.2.s.b.3.3	yes	18
240.29	odd	4		720.2.bd.g.307.3		18
240.77	even	4		720.2.z.g.163.7		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.7	✓	18	20.7	even	4
80.2.j.b.67.7	yes	18	80.29	even	4
80.2.s.b.3.3	yes	18	80.77	odd	4
80.2.s.b.27.3	yes	18	20.19	odd	2
320.2.j.b.47.5		18	80.19	odd	4
320.2.j.b.143.5		18	5.2	odd	4
320.2.s.b.207.5		18	5.4	even	2
320.2.s.b.303.5		18	80.67	even	4
400.2.j.d.43.3		18	20.3	even	4
400.2.j.d.307.3		18	16.13	even	4
400.2.s.d.107.7		18	4.3	odd	2
400.2.s.d.243.7		18	80.13	odd	4
640.2.j.c.543.5		18	40.37	odd	4
640.2.j.c.607.5		18	80.59	odd	4
640.2.j.d.543.5		18	40.27	even	4
640.2.j.d.607.5		18	80.69	even	4
640.2.s.c.223.5		18	80.27	even	4
640.2.s.c.287.5		18	40.29	even	2
640.2.s.d.223.5		18	80.37	odd	4
640.2.s.d.287.5		18	40.19	odd	2
720.2.z.g.163.7		18	240.77	even	4
720.2.z.g.667.7		18	60.59	even	2
720.2.bd.g.307.3		18	240.29	odd	4
720.2.bd.g.523.3		18	60.47	odd	4
1600.2.j.d.143.5		18	5.3	odd	4
1600.2.j.d.1007.5		18	16.3	odd	4
1600.2.s.d.207.5		18	1.1	even	1	trivial
1600.2.s.d.943.5		18	80.3	even	4	inner

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:	\( N \)	\(=\)	\( 1600 = 2^{6} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1600.s (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.614566 q^{3} +(2.83610 + 2.83610i) q^{7} -2.62231 q^{9} +O(q^{10})\)	\(q+0.614566 q^{3} +(2.83610 + 2.83610i) q^{7} -2.62231 q^{9} +(-1.95928 + 1.95928i) q^{11} -2.05493i q^{13} +(4.06774 + 4.06774i) q^{17} +(0.683479 - 0.683479i) q^{19} +(1.74297 + 1.74297i) q^{21} +(-4.95014 + 4.95014i) q^{23} -3.45528 q^{27} +(0.835439 + 0.835439i) q^{29} -2.35978i q^{31} +(-1.20411 + 1.20411i) q^{33} +4.54384i q^{37} -1.26289i q^{39} +5.07255i q^{41} +0.849753i q^{43} +(-2.72646 + 2.72646i) q^{47} +9.08690i q^{49} +(2.49989 + 2.49989i) q^{51} -5.17605 q^{53} +(0.420043 - 0.420043i) q^{57} +(4.16328 + 4.16328i) q^{59} +(5.55706 - 5.55706i) q^{61} +(-7.43712 - 7.43712i) q^{63} -1.73609i q^{67} +(-3.04219 + 3.04219i) q^{69} -2.33526 q^{71} +(4.39686 + 4.39686i) q^{73} -11.1134 q^{77} -14.0993 q^{79} +5.74343 q^{81} -2.75725 q^{83} +(0.513433 + 0.513433i) q^{87} +11.6448 q^{89} +(5.82797 - 5.82797i) q^{91} -1.45024i q^{93} +(3.52933 + 3.52933i) q^{97} +(5.13783 - 5.13783i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{7} + 10 q^{9}+O(q^{10}) \) 18 * q + 2 * q^7 + 10 * q^9	\( 18 q + 2 q^{7} + 10 q^{9} + 2 q^{11} + 6 q^{17} + 2 q^{19} - 16 q^{21} - 2 q^{23} - 24 q^{27} + 14 q^{29} + 8 q^{33} + 38 q^{47} - 8 q^{51} - 12 q^{53} + 24 q^{57} - 10 q^{59} + 14 q^{61} - 6 q^{63} - 32 q^{69} - 24 q^{71} + 14 q^{73} + 44 q^{77} + 16 q^{79} + 2 q^{81} + 40 q^{83} + 24 q^{87} + 12 q^{89} - 18 q^{97} - 22 q^{99}+O(q^{100}) \) 18 * q + 2 * q^7 + 10 * q^9 + 2 * q^11 + 6 * q^17 + 2 * q^19 - 16 * q^21 - 2 * q^23 - 24 * q^27 + 14 * q^29 + 8 * q^33 + 38 * q^47 - 8 * q^51 - 12 * q^53 + 24 * q^57 - 10 * q^59 + 14 * q^61 - 6 * q^63 - 32 * q^69 - 24 * q^71 + 14 * q^73 + 44 * q^77 + 16 * q^79 + 2 * q^81 + 40 * q^83 + 24 * q^87 + 12 * q^89 - 18 * q^97 - 22 * q^99

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