LMFDB - Embedded newform 1600.2.j.d.143.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1600,2,Mod(143,1600)]

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, 3]))

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

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

chi := DirichletCharacter("1600.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1600 = 2^{6} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1600.j (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			143.6
Root			$-0.635486 - 1.26339i$ of defining polynomial
Character	$\chi$	$=$	1600.143
Dual form			1600.2.j.d.1007.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.692712i q^{3} +(-0.343872 + 0.343872i) q^{7} +2.52015 q^{9} +O(q^{10})$	$q+0.692712i q^{3} +(-0.343872 + 0.343872i) q^{7} +2.52015 q^{9} +(-0.843672 + 0.843672i) q^{11} +3.68390 q^{13} +(-0.412137 + 0.412137i) q^{17} +(5.37721 - 5.37721i) q^{19} +(-0.238204 - 0.238204i) q^{21} +(-3.08788 - 3.08788i) q^{23} +3.82387i q^{27} +(-4.22969 - 4.22969i) q^{29} +8.75966i q^{31} +(-0.584422 - 0.584422i) q^{33} +5.41752 q^{37} +2.55188i q^{39} -2.54777i q^{41} +4.30732 q^{43} +(4.56972 + 4.56972i) q^{47} +6.76350i q^{49} +(-0.285492 - 0.285492i) q^{51} -6.07536i q^{53} +(3.72486 + 3.72486i) q^{57} +(7.33694 + 7.33694i) q^{59} +(-4.81576 + 4.81576i) q^{61} +(-0.866609 + 0.866609i) q^{63} +14.3626 q^{67} +(2.13901 - 2.13901i) q^{69} +2.97605 q^{71} +(6.87152 - 6.87152i) q^{73} -0.580231i q^{77} -10.1654 q^{79} +4.91161 q^{81} -7.15276i q^{83} +(2.92996 - 2.92996i) q^{87} +1.10953 q^{89} +(-1.26679 + 1.26679i) q^{91} -6.06792 q^{93} +(-7.15920 + 7.15920i) q^{97} +(-2.12618 + 2.12618i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 14 q^{29} + 8 q^{33} - 8 q^{37} - 44 q^{43} - 38 q^{47} - 8 q^{51} - 24 q^{57} + 10 q^{59} + 14 q^{61} + 6 q^{63} + 12 q^{67} + 32 q^{69} - 24 q^{71} - 14 q^{73} - 16 q^{79} + 2 q^{81} + 24 q^{87} - 12 q^{89} - 16 q^{93} - 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 - 14 * q^29 + 8 * q^33 - 8 * q^37 - 44 * q^43 - 38 * q^47 - 8 * q^51 - 24 * q^57 + 10 * q^59 + 14 * q^61 + 6 * q^63 + 12 * q^67 + 32 * q^69 - 24 * q^71 - 14 * q^73 - 16 * q^79 + 2 * q^81 + 24 * q^87 - 12 * q^89 - 16 * q^93 - 18 * q^97 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$577$	$901$	$1151$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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
$3$			0.692712i			0.399937i	0.979802	+	0.199969i	$0.0640841\pi$
$3$			0.692712i			0.399937i	−0.979802	+	0.199969i	$0.935916\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.343872	+	0.343872i	−0.129971	+	0.129971i	−0.769100	−	0.639129i	$-0.779295\pi$
$7$	−0.343872	+	0.343872i	−0.129971	+	0.129971i	0.639129	+	0.769100i	$0.279295\pi$
$8$		0			0
$9$	2.52015			0.840050
$10$		0			0
$11$	−0.843672	+	0.843672i	−0.254377	+	0.254377i	−0.822762	−	0.568386i	$-0.807568\pi$
$11$	−0.843672	+	0.843672i	−0.254377	+	0.254377i	0.568386	+	0.822762i	$0.307568\pi$
$12$		0			0
$13$	3.68390			1.02173			0.510865	−	0.859661i	$-0.329325\pi$
$13$	3.68390			1.02173			0.510865	+	0.859661i	$0.329325\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.412137	+	0.412137i	−0.0999579	+	0.0999579i	−0.755317	−	0.655359i	$-0.772517\pi$
$17$	−0.412137	+	0.412137i	−0.0999579	+	0.0999579i	0.655359	+	0.755317i	$0.272517\pi$
$18$		0			0
$19$	5.37721	−	5.37721i	1.23362	−	1.23362i	0.271052	−	0.962565i	$-0.412629\pi$
$19$	5.37721	−	5.37721i	1.23362	−	1.23362i	0.962565	−	0.271052i	$-0.0873714\pi$
$20$		0			0
$21$	−0.238204	−	0.238204i	−0.0519804	−	0.0519804i
$22$		0			0
$23$	−3.08788	−	3.08788i	−0.643868	−	0.643868i	0.307636	−	0.951504i	$-0.400462\pi$
$23$	−3.08788	−	3.08788i	−0.643868	−	0.643868i	−0.951504	+	0.307636i	$0.900462\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			3.82387i			0.735905i
$28$		0			0
$29$	−4.22969	−	4.22969i	−0.785434	−	0.785434i	0.195308	−	0.980742i	$-0.437429\pi$
$29$	−4.22969	−	4.22969i	−0.785434	−	0.785434i	−0.980742	+	0.195308i	$0.937429\pi$
$30$		0			0
$31$			8.75966i			1.57328i	0.617411	+	0.786641i	$0.288182\pi$
$31$			8.75966i			1.57328i	−0.617411	+	0.786641i	$0.711818\pi$
$32$		0			0
$33$	−0.584422	−	0.584422i	−0.101735	−	0.101735i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	5.41752			0.890634			0.445317	−	0.895373i	$-0.353091\pi$
$37$	5.41752			0.890634			0.445317	+	0.895373i	$0.353091\pi$
$38$		0			0
$39$			2.55188i			0.408628i
$40$		0			0
$41$		−	2.54777i		−	0.397895i	−0.980010	−	0.198948i	$-0.936248\pi$
$41$		−	2.54777i		−	0.397895i	0.980010	−	0.198948i	$-0.0637524\pi$
$42$		0			0
$43$	4.30732			0.656861			0.328430	−	0.944528i	$-0.393480\pi$
$43$	4.30732			0.656861			0.328430	+	0.944528i	$0.393480\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.56972	+	4.56972i	0.666562	+	0.666562i	0.956919	−	0.290356i	$-0.0937738\pi$
$47$	4.56972	+	4.56972i	0.666562	+	0.666562i	−0.290356	+	0.956919i	$0.593774\pi$
$48$		0			0
$49$			6.76350i			0.966215i
$50$		0			0
$51$	−0.285492	−	0.285492i	−0.0399769	−	0.0399769i
$52$		0			0
$53$		−	6.07536i		−	0.834515i	−0.908788	−	0.417257i	$-0.862991\pi$
$53$		−	6.07536i		−	0.834515i	0.908788	−	0.417257i	$-0.137009\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	3.72486	+	3.72486i	0.493369	+	0.493369i
$58$		0			0
$59$	7.33694	+	7.33694i	0.955189	+	0.955189i	0.999038	−	0.0438495i	$-0.0139622\pi$
$59$	7.33694	+	7.33694i	0.955189	+	0.955189i	−0.0438495	+	0.999038i	$0.513962\pi$
$60$		0			0
$61$	−4.81576	+	4.81576i	−0.616595	+	0.616595i	−0.944656	−	0.328062i	$-0.893605\pi$
$61$	−4.81576	+	4.81576i	−0.616595	+	0.616595i	0.328062	+	0.944656i	$0.393605\pi$
$62$		0			0
$63$	−0.866609	+	0.866609i	−0.109183	+	0.109183i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	14.3626			1.75467			0.877334	−	0.479880i	$-0.159320\pi$
$67$	14.3626			1.75467			0.877334	+	0.479880i	$0.159320\pi$
$68$		0			0
$69$	2.13901	−	2.13901i	0.257507	−	0.257507i
$70$		0			0
$71$	2.97605			0.353193			0.176596	−	0.984283i	$-0.443491\pi$
$71$	2.97605			0.353193			0.176596	+	0.984283i	$0.443491\pi$
$72$		0			0
$73$	6.87152	−	6.87152i	0.804250	−	0.804250i	−0.179507	−	0.983757i	$-0.557450\pi$
$73$	6.87152	−	6.87152i	0.804250	−	0.804250i	0.983757	+	0.179507i	$0.0574501\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		−	0.580231i		−	0.0661234i
$78$		0			0
$79$	−10.1654			−1.14369			−0.571847	−	0.820360i	$-0.693773\pi$
$79$	−10.1654			−1.14369			−0.571847	+	0.820360i	$0.693773\pi$
$80$		0			0
$81$	4.91161			0.545734
$82$		0			0
$83$		−	7.15276i		−	0.785118i	−0.919727	−	0.392559i	$-0.871590\pi$
$83$		−	7.15276i		−	0.785118i	0.919727	−	0.392559i	$-0.128410\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	2.92996	−	2.92996i	0.314124	−	0.314124i
$88$		0			0
$89$	1.10953			0.117610			0.0588050	−	0.998269i	$-0.481271\pi$
$89$	1.10953			0.117610			0.0588050	+	0.998269i	$0.481271\pi$
$90$		0			0
$91$	−1.26679	+	1.26679i	−0.132796	+	0.132796i
$92$		0			0
$93$	−6.06792			−0.629214
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−7.15920	+	7.15920i	−0.726906	+	0.726906i	−0.970002	−	0.243096i	$-0.921837\pi$
$97$	−7.15920	+	7.15920i	−0.726906	+	0.726906i	0.243096	+	0.970002i	$0.421837\pi$
$98$		0			0
$99$	−2.12618	+	2.12618i	−0.213689	+	0.213689i
$100$		0			0
$101$	0.953394	+	0.953394i	0.0948663	+	0.0948663i	0.752947	−	0.658081i	$-0.228632\pi$
$101$	0.953394	+	0.953394i	0.0948663	+	0.0948663i	−0.658081	+	0.752947i	$0.728632\pi$
$102$		0			0
$103$	9.59425	+	9.59425i	0.945350	+	0.945350i	0.998582	−	0.0532322i	$-0.0169524\pi$
$103$	9.59425	+	9.59425i	0.945350	+	0.945350i	−0.0532322	+	0.998582i	$0.516952\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			5.28201i			0.510631i	0.966858	+	0.255316i	$0.0821794\pi$
$107$			5.28201i			0.510631i	−0.966858	+	0.255316i	$0.917821\pi$
$108$		0			0
$109$	1.53980	+	1.53980i	0.147486	+	0.147486i	0.776994	−	0.629508i	$-0.216744\pi$
$109$	1.53980	+	1.53980i	0.147486	+	0.147486i	−0.629508	+	0.776994i	$0.716744\pi$
$110$		0			0
$111$			3.75278i			0.356198i
$112$		0			0
$113$	2.99656	+	2.99656i	0.281893	+	0.281893i	0.833863	−	0.551971i	$-0.186124\pi$
$113$	2.99656	+	2.99656i	0.281893	+	0.281893i	−0.551971	+	0.833863i	$0.686124\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	9.28399			0.858305
$118$		0			0
$119$		−	0.283445i		−	0.0259833i
$120$		0			0
$121$			9.57643i			0.870585i
$122$		0			0
$123$	1.76487			0.159133
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−10.5522	−	10.5522i	−0.936360	−	0.936360i	0.0617330	−	0.998093i	$-0.480337\pi$
$127$	−10.5522	−	10.5522i	−0.936360	−	0.936360i	−0.998093	+	0.0617330i	$0.980337\pi$
$128$		0			0
$129$			2.98373i			0.262703i
$130$		0			0
$131$	0.850513	+	0.850513i	0.0743096	+	0.0743096i	0.743285	−	0.668975i	$-0.233267\pi$
$131$	0.850513	+	0.850513i	0.0743096	+	0.0743096i	−0.668975	+	0.743285i	$0.733267\pi$
$132$		0			0
$133$			3.69814i			0.320670i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	5.50145	+	5.50145i	0.470021	+	0.470021i	0.901921	−	0.431901i	$-0.142157\pi$
$137$	5.50145	+	5.50145i	0.470021	+	0.470021i	−0.431901	+	0.901921i	$0.642157\pi$
$138$		0			0
$139$	−3.03517	−	3.03517i	−0.257440	−	0.257440i	0.566572	−	0.824012i	$-0.308269\pi$
$139$	−3.03517	−	3.03517i	−0.257440	−	0.257440i	−0.824012	+	0.566572i	$0.808269\pi$
$140$		0			0
$141$	−3.16550	+	3.16550i	−0.266583	+	0.266583i
$142$		0			0
$143$	−3.10801	+	3.10801i	−0.259905	+	0.259905i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−4.68516			−0.386425
$148$		0			0
$149$	11.1571	−	11.1571i	0.914023	−	0.914023i	−0.0825625	−	0.996586i	$-0.526310\pi$
$149$	11.1571	−	11.1571i	0.914023	−	0.914023i	0.996586	+	0.0825625i	$0.0263104\pi$
$150$		0			0
$151$	−3.18265			−0.259000			−0.129500	−	0.991579i	$-0.541337\pi$
$151$	−3.18265			−0.259000			−0.129500	+	0.991579i	$0.541337\pi$
$152$		0			0
$153$	−1.03865	+	1.03865i	−0.0839696	+	0.0839696i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		−	7.05454i		−	0.563014i	−0.959559	−	0.281507i	$-0.909166\pi$
$157$		−	7.05454i		−	0.563014i	0.959559	−	0.281507i	$-0.0908342\pi$
$158$		0			0
$159$	4.20847			0.333754
$160$		0			0
$161$	2.12367			0.167369
$162$		0			0
$163$		−	16.0208i		−	1.25484i	−0.778680	−	0.627422i	$-0.784110\pi$
$163$		−	16.0208i		−	1.25484i	0.778680	−	0.627422i	$-0.215890\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−16.6023	+	16.6023i	−1.28473	+	1.28473i	−0.346780	+	0.937946i	$0.612725\pi$
$167$	−16.6023	+	16.6023i	−1.28473	+	1.28473i	−0.937946	+	0.346780i	$0.887275\pi$
$168$		0			0
$169$	0.571141			0.0439339
$170$		0			0
$171$	13.5514	−	13.5514i	1.03630	−	1.03630i
$172$		0			0
$173$	−14.9958			−1.14011			−0.570054	−	0.821607i	$-0.693078\pi$
$173$	−14.9958			−1.14011			−0.570054	+	0.821607i	$0.693078\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−5.08239	+	5.08239i	−0.382016	+	0.382016i
$178$		0			0
$179$	9.91310	−	9.91310i	0.740940	−	0.740940i	−0.231819	−	0.972759i	$-0.574468\pi$
$179$	9.91310	−	9.91310i	0.740940	−	0.740940i	0.972759	+	0.231819i	$0.0744678\pi$
$180$		0			0
$181$	1.04015	+	1.04015i	0.0773139	+	0.0773139i	0.744706	−	0.667392i	$-0.232590\pi$
$181$	1.04015	+	1.04015i	0.0773139	+	0.0773139i	−0.667392	+	0.744706i	$0.732590\pi$
$182$		0			0
$183$	−3.33593	−	3.33593i	−0.246599	−	0.246599i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		−	0.695417i		−	0.0508539i
$188$		0			0
$189$	−1.31492	−	1.31492i	−0.0956466	−	0.0956466i
$190$		0			0
$191$		−	3.08419i		−	0.223164i	−0.993755	−	0.111582i	$-0.964408\pi$
$191$		−	3.08419i		−	0.223164i	0.993755	−	0.111582i	$-0.0355918\pi$
$192$		0			0
$193$	12.0915	+	12.0915i	0.870368	+	0.870368i	0.992512	−	0.122144i	$-0.0389770\pi$
$193$	12.0915	+	12.0915i	0.870368	+	0.870368i	−0.122144	+	0.992512i	$0.538977\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−13.0186			−0.927540			−0.463770	−	0.885956i	$-0.653504\pi$
$197$	−13.0186			−0.927540			−0.463770	+	0.885956i	$0.653504\pi$
$198$		0			0
$199$		−	10.6279i		−	0.753395i	−0.926336	−	0.376697i	$-0.877060\pi$
$199$		−	10.6279i		−	0.753395i	0.926336	−	0.376697i	$-0.122940\pi$
$200$		0			0
$201$			9.94913i			0.701758i
$202$		0			0
$203$	2.90894			0.204168
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−7.78192	−	7.78192i	−0.540881	−	0.540881i
$208$		0			0
$209$			9.07320i			0.627607i
$210$		0			0
$211$	−11.4801	−	11.4801i	−0.790321	−	0.790321i	0.191225	−	0.981546i	$-0.438754\pi$
$211$	−11.4801	−	11.4801i	−0.790321	−	0.790321i	−0.981546	+	0.191225i	$0.938754\pi$
$212$		0			0
$213$			2.06155i			0.141255i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−3.01220	−	3.01220i	−0.204482	−	0.204482i
$218$		0			0
$219$	4.75998	+	4.75998i	0.321650	+	0.321650i
$220$		0			0
$221$	−1.51827	+	1.51827i	−0.102130	+	0.102130i
$222$		0			0
$223$	2.17863	−	2.17863i	0.145892	−	0.145892i	−0.630388	−	0.776280i	$-0.717104\pi$
$223$	2.17863	−	2.17863i	0.145892	−	0.145892i	0.776280	+	0.630388i	$0.217104\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	9.32318			0.618801			0.309401	−	0.950932i	$-0.399872\pi$
$227$	9.32318			0.618801			0.309401	+	0.950932i	$0.399872\pi$
$228$		0			0
$229$	−2.72259	+	2.72259i	−0.179914	+	0.179914i	−0.791318	−	0.611404i	$-0.790605\pi$
$229$	−2.72259	+	2.72259i	−0.179914	+	0.179914i	0.611404	+	0.791318i	$0.290605\pi$
$230$		0			0
$231$	0.401933			0.0264452
$232$		0			0
$233$	−12.3897	+	12.3897i	−0.811679	+	0.811679i	−0.984886	−	0.173206i	$-0.944587\pi$
$233$	−12.3897	+	12.3897i	−0.811679	+	0.811679i	0.173206	+	0.984886i	$0.444587\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		−	7.04168i		−	0.457406i
$238$		0			0
$239$	−25.2180			−1.63122			−0.815609	−	0.578604i	$-0.803598\pi$
$239$	−25.2180			−1.63122			−0.815609	+	0.578604i	$0.803598\pi$
$240$		0			0
$241$	12.0218			0.774391			0.387195	−	0.921998i	$-0.373444\pi$
$241$	12.0218			0.774391			0.387195	+	0.921998i	$0.373444\pi$
$242$		0			0
$243$			14.8740i			0.954164i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	19.8091	−	19.8091i	1.26042	−	1.26042i
$248$		0			0
$249$	4.95480			0.313998
$250$		0			0
$251$	−7.48911	+	7.48911i	−0.472709	+	0.472709i	−0.902790	−	0.430081i	$-0.858485\pi$
$251$	−7.48911	+	7.48911i	−0.472709	+	0.472709i	0.430081	+	0.902790i	$0.358485\pi$
$252$		0			0
$253$	5.21032			0.327570
$254$		0			0
$255$		0			0
$256$		0			0
$257$	10.0809	−	10.0809i	0.628832	−	0.628832i	−0.318942	−	0.947774i	$-0.603328\pi$
$257$	10.0809	−	10.0809i	0.628832	−	0.628832i	0.947774	+	0.318942i	$0.103328\pi$
$258$		0			0
$259$	−1.86293	+	1.86293i	−0.115757	+	0.115757i
$260$		0			0
$261$	−10.6595	−	10.6595i	−0.659804	−	0.659804i
$262$		0			0
$263$	−3.83599	−	3.83599i	−0.236537	−	0.236537i	0.578877	−	0.815415i	$-0.303491\pi$
$263$	−3.83599	−	3.83599i	−0.236537	−	0.236537i	−0.815415	+	0.578877i	$0.803491\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			0.768585i			0.0470367i
$268$		0			0
$269$	−13.4250	−	13.4250i	−0.818539	−	0.818539i	0.167357	−	0.985896i	$-0.446477\pi$
$269$	−13.4250	−	13.4250i	−0.818539	−	0.818539i	−0.985896	+	0.167357i	$0.946477\pi$
$270$		0			0
$271$		−	12.3519i		−	0.750326i	−0.926959	−	0.375163i	$-0.877587\pi$
$271$		−	12.3519i		−	0.750326i	0.926959	−	0.375163i	$-0.122413\pi$
$272$		0			0
$273$	−0.877522	−	0.877522i	−0.0531100	−	0.0531100i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	6.78804			0.407854			0.203927	−	0.978986i	$-0.434630\pi$
$277$	6.78804			0.407854			0.203927	+	0.978986i	$0.434630\pi$
$278$		0			0
$279$			22.0757i			1.32164i
$280$		0			0
$281$		−	21.5509i		−	1.28562i	−0.766026	−	0.642810i	$-0.777768\pi$
$281$		−	21.5509i		−	1.28562i	0.766026	−	0.642810i	$-0.222232\pi$
$282$		0			0
$283$	−9.86809			−0.586597			−0.293299	−	0.956021i	$-0.594753\pi$
$283$	−9.86809			−0.586597			−0.293299	+	0.956021i	$0.594753\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.876108	+	0.876108i	0.0517150	+	0.0517150i
$288$		0			0
$289$			16.6603i			0.980017i
$290$		0			0
$291$	−4.95926	−	4.95926i	−0.290717	−	0.290717i
$292$		0			0
$293$		−	14.1972i		−	0.829410i	−0.909956	−	0.414705i	$-0.863885\pi$
$293$		−	14.1972i		−	0.829410i	0.909956	−	0.414705i	$-0.136115\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−3.22610	−	3.22610i	−0.187197	−	0.187197i
$298$		0			0
$299$	−11.3755	−	11.3755i	−0.657859	−	0.657859i
$300$		0			0
$301$	−1.48117	+	1.48117i	−0.0853731	+	0.0853731i
$302$		0			0
$303$	−0.660428	+	0.660428i	−0.0379406	+	0.0379406i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−20.4161			−1.16521			−0.582604	−	0.812756i	$-0.697966\pi$
$307$	−20.4161			−1.16521			−0.582604	+	0.812756i	$0.697966\pi$
$308$		0			0
$309$	−6.64605	+	6.64605i	−0.378081	+	0.378081i
$310$		0			0
$311$	6.81074			0.386202			0.193101	−	0.981179i	$-0.438146\pi$
$311$	6.81074			0.386202			0.193101	+	0.981179i	$0.438146\pi$
$312$		0			0
$313$	1.20933	−	1.20933i	0.0683555	−	0.0683555i	−0.672103	−	0.740458i	$-0.734609\pi$
$313$	1.20933	−	1.20933i	0.0683555	−	0.0683555i	0.740458	+	0.672103i	$0.234609\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	3.44178i		−	0.193310i	−0.995318	−	0.0966548i	$-0.969186\pi$
$317$		−	3.44178i		−	0.193310i	0.995318	−	0.0966548i	$-0.0308143\pi$
$318$		0			0
$319$	7.13694			0.399592
$320$		0			0
$321$	−3.65891			−0.204221
$322$		0			0
$323$			4.43229i			0.246619i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−1.06664	+	1.06664i	−0.0589852	+	0.0589852i
$328$		0			0
$329$	−3.14280			−0.173268
$330$		0			0
$331$	1.48462	−	1.48462i	0.0816019	−	0.0816019i	−0.665128	−	0.746730i	$-0.731623\pi$
$331$	1.48462	−	1.48462i	0.0816019	−	0.0816019i	0.746730	+	0.665128i	$0.231623\pi$
$332$		0			0
$333$	13.6530			0.748177
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−6.21211	+	6.21211i	−0.338395	+	0.338395i	−0.855763	−	0.517368i	$-0.826912\pi$
$337$	−6.21211	+	6.21211i	−0.338395	+	0.338395i	0.517368	+	0.855763i	$0.326912\pi$
$338$		0			0
$339$	−2.07575	+	2.07575i	−0.112739	+	0.112739i
$340$		0			0
$341$	−7.39028	−	7.39028i	−0.400206	−	0.400206i
$342$		0			0
$343$	−4.73288	−	4.73288i	−0.255552	−	0.255552i
$344$		0			0
$345$		0			0
$346$		0			0
$347$		−	10.1502i		−	0.544889i	−0.962171	−	0.272445i	$-0.912168\pi$
$347$		−	10.1502i		−	0.544889i	0.962171	−	0.272445i	$-0.0878321\pi$
$348$		0			0
$349$	−3.99595	−	3.99595i	−0.213898	−	0.213898i	0.592023	−	0.805921i	$-0.298329\pi$
$349$	−3.99595	−	3.99595i	−0.213898	−	0.213898i	−0.805921	+	0.592023i	$0.798329\pi$
$350$		0			0
$351$			14.0868i			0.751897i
$352$		0			0
$353$	−22.6637	−	22.6637i	−1.20627	−	1.20627i	−0.972226	−	0.234043i	$-0.924804\pi$
$353$	−22.6637	−	22.6637i	−1.20627	−	1.20627i	−0.234043	−	0.972226i	$-0.575196\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	0.196346			0.0103917
$358$		0			0
$359$			4.31874i			0.227934i	0.993485	+	0.113967i	$0.0363559\pi$
$359$			4.31874i			0.227934i	−0.993485	+	0.113967i	$0.963644\pi$
$360$		0			0
$361$		−	38.8288i		−	2.04362i
$362$		0			0
$363$	−6.63371			−0.348180
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−6.46940	−	6.46940i	−0.337700	−	0.337700i	0.517801	−	0.855501i	$-0.326751\pi$
$367$	−6.46940	−	6.46940i	−0.337700	−	0.337700i	−0.855501	+	0.517801i	$0.826751\pi$
$368$		0			0
$369$		−	6.42077i		−	0.334252i
$370$		0			0
$371$	2.08915	+	2.08915i	0.108463	+	0.108463i
$372$		0			0
$373$			16.7831i			0.868995i	0.900673	+	0.434497i	$0.143074\pi$
$373$			16.7831i			0.868995i	−0.900673	+	0.434497i	$0.856926\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−15.5818	−	15.5818i	−0.802502	−	0.802502i
$378$		0			0
$379$	7.31046	+	7.31046i	0.375513	+	0.375513i	0.869480	−	0.493967i	$-0.164454\pi$
$379$	7.31046	+	7.31046i	0.375513	+	0.375513i	−0.493967	+	0.869480i	$0.664454\pi$
$380$		0			0
$381$	7.30966	−	7.30966i	0.374485	−	0.374485i
$382$		0			0
$383$	−5.31492	+	5.31492i	−0.271580	+	0.271580i	−0.829736	−	0.558156i	$-0.811509\pi$
$383$	−5.31492	+	5.31492i	−0.271580	+	0.271580i	0.558156	+	0.829736i	$0.311509\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	10.8551			0.551796
$388$		0			0
$389$	−1.28845	+	1.28845i	−0.0653271	+	0.0653271i	−0.739016	−	0.673688i	$-0.764709\pi$
$389$	−1.28845	+	1.28845i	−0.0653271	+	0.0653271i	0.673688	+	0.739016i	$0.264709\pi$
$390$		0			0
$391$	2.54526			0.128719
$392$		0			0
$393$	−0.589160	+	0.589160i	−0.0297192	+	0.0297192i
$394$		0			0
$395$		0			0
$396$		0			0
$397$			9.53832i			0.478715i	0.970932	+	0.239357i	$0.0769367\pi$
$397$			9.53832i			0.478715i	−0.970932	+	0.239357i	$0.923063\pi$
$398$		0			0
$399$	−2.56175			−0.128248
$400$		0			0
$401$	−24.6103			−1.22898			−0.614491	−	0.788924i	$-0.710638\pi$
$401$	−24.6103			−1.22898			−0.614491	+	0.788924i	$0.710638\pi$
$402$		0			0
$403$			32.2697i			1.60747i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−4.57061	+	4.57061i	−0.226557	+	0.226557i
$408$		0			0
$409$	−16.9457			−0.837911			−0.418955	−	0.908007i	$-0.637604\pi$
$409$	−16.9457			−0.837911			−0.418955	+	0.908007i	$0.637604\pi$
$410$		0			0
$411$	−3.81092	+	3.81092i	−0.187979	+	0.187979i
$412$		0			0
$413$	−5.04594			−0.248294
$414$		0			0
$415$		0			0
$416$		0			0
$417$	2.10250	−	2.10250i	0.102960	−	0.102960i
$418$		0			0
$419$	6.56956	−	6.56956i	0.320944	−	0.320944i	−0.528185	−	0.849129i	$-0.677127\pi$
$419$	6.56956	−	6.56956i	0.320944	−	0.320944i	0.849129	+	0.528185i	$0.177127\pi$
$420$		0			0
$421$	13.8805	+	13.8805i	0.676493	+	0.676493i	0.959205	−	0.282712i	$-0.0912341\pi$
$421$	13.8805	+	13.8805i	0.676493	+	0.676493i	−0.282712	+	0.959205i	$0.591234\pi$
$422$		0			0
$423$	11.5164	+	11.5164i	0.559946	+	0.559946i
$424$		0			0
$425$		0			0
$426$		0			0
$427$		−	3.31201i		−	0.160279i
$428$		0			0
$429$	−2.15295	−	2.15295i	−0.103946	−	0.103946i
$430$		0			0
$431$		−	12.3740i		−	0.596035i	−0.954560	−	0.298017i	$-0.903675\pi$
$431$		−	12.3740i		−	0.596035i	0.954560	−	0.298017i	$-0.0963254\pi$
$432$		0			0
$433$	0.145326	+	0.145326i	0.00698392	+	0.00698392i	0.710590	−	0.703606i	$-0.248428\pi$
$433$	0.145326	+	0.145326i	0.00698392	+	0.00698392i	−0.703606	+	0.710590i	$0.748428\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−33.2084			−1.58857
$438$		0			0
$439$		−	3.65842i		−	0.174607i	−0.996182	−	0.0873035i	$-0.972175\pi$
$439$		−	3.65842i		−	0.174607i	0.996182	−	0.0873035i	$-0.0278250\pi$
$440$		0			0
$441$			17.0450i			0.811669i
$442$		0			0
$443$	3.94027			0.187208			0.0936039	−	0.995610i	$-0.470161\pi$
$443$	3.94027			0.187208			0.0936039	+	0.995610i	$0.470161\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	7.72864	+	7.72864i	0.365552	+	0.365552i
$448$		0			0
$449$		−	38.0014i		−	1.79340i	−0.442642	−	0.896698i	$-0.645959\pi$
$449$		−	38.0014i		−	1.79340i	0.442642	−	0.896698i	$-0.354041\pi$
$450$		0			0
$451$	2.14949	+	2.14949i	0.101215	+	0.101215i
$452$		0			0
$453$		−	2.20466i		−	0.103584i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−18.1142	−	18.1142i	−0.847348	−	0.847348i	0.142454	−	0.989801i	$-0.454501\pi$
$457$	−18.1142	−	18.1142i	−0.847348	−	0.847348i	−0.989801	+	0.142454i	$0.954501\pi$
$458$		0			0
$459$	−1.57596	−	1.57596i	−0.0735595	−	0.0735595i
$460$		0			0
$461$	12.4144	−	12.4144i	0.578197	−	0.578197i	−0.356209	−	0.934406i	$-0.615931\pi$
$461$	12.4144	−	12.4144i	0.578197	−	0.578197i	0.934406	+	0.356209i	$0.115931\pi$
$462$		0			0
$463$	−8.56578	+	8.56578i	−0.398085	+	0.398085i	−0.877557	−	0.479472i	$-0.840828\pi$
$463$	−8.56578	+	8.56578i	−0.398085	+	0.398085i	0.479472	+	0.877557i	$0.340828\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−34.3465			−1.58937			−0.794684	−	0.607023i	$-0.792364\pi$
$467$	−34.3465			−1.58937			−0.794684	+	0.607023i	$0.792364\pi$
$468$		0			0
$469$	−4.93889	+	4.93889i	−0.228057	+	0.228057i
$470$		0			0
$471$	4.88677			0.225170
$472$		0			0
$473$	−3.63397	+	3.63397i	−0.167090	+	0.167090i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		−	15.3108i		−	0.701034i
$478$		0			0
$479$	23.4504			1.07148			0.535738	−	0.844384i	$-0.320034\pi$
$479$	23.4504			1.07148			0.535738	+	0.844384i	$0.320034\pi$
$480$		0			0
$481$	19.9576			0.909988
$482$		0			0
$483$			1.47109i			0.0669370i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−5.31215	+	5.31215i	−0.240716	+	0.240716i	−0.817146	−	0.576430i	$-0.804445\pi$
$487$	−5.31215	+	5.31215i	−0.240716	+	0.240716i	0.576430	+	0.817146i	$0.304445\pi$
$488$		0			0
$489$	11.0978			0.501859
$490$		0			0
$491$	3.71980	−	3.71980i	0.167872	−	0.167872i	−0.618171	−	0.786044i	$-0.712126\pi$
$491$	3.71980	−	3.71980i	0.167872	−	0.167872i	0.786044	+	0.618171i	$0.212126\pi$
$492$		0			0
$493$	3.48642			0.157021
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.02338	+	1.02338i	−0.0459050	+	0.0459050i
$498$		0			0
$499$	−13.6065	+	13.6065i	−0.609111	+	0.609111i	−0.942714	−	0.333603i	$-0.891736\pi$
$499$	−13.6065	+	13.6065i	−0.609111	+	0.609111i	0.333603	+	0.942714i	$0.391736\pi$
$500$		0			0
$501$	−11.5006	−	11.5006i	−0.513810	−	0.513810i
$502$		0			0
$503$	−9.31208	−	9.31208i	−0.415205	−	0.415205i	0.468342	−	0.883547i	$-0.344852\pi$
$503$	−9.31208	−	9.31208i	−0.415205	−	0.415205i	−0.883547	+	0.468342i	$0.844852\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$			0.395636i			0.0175708i
$508$		0			0
$509$	7.94836	+	7.94836i	0.352305	+	0.352305i	0.860966	−	0.508662i	$-0.169860\pi$
$509$	7.94836	+	7.94836i	0.352305	+	0.352305i	−0.508662	+	0.860966i	$0.669860\pi$
$510$		0			0
$511$			4.72585i			0.209059i
$512$		0			0
$513$	20.5618	+	20.5618i	0.907824	+	0.907824i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−7.71069			−0.339116
$518$		0			0
$519$		−	10.3878i		−	0.455972i
$520$		0			0
$521$			29.3979i			1.28795i	0.765048	+	0.643974i	$0.222715\pi$
$521$			29.3979i			1.28795i	−0.765048	+	0.643974i	$0.777285\pi$
$522$		0			0
$523$	−19.5121			−0.853205			−0.426602	−	0.904439i	$-0.640290\pi$
$523$	−19.5121			−0.853205			−0.426602	+	0.904439i	$0.640290\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−3.61018	−	3.61018i	−0.157262	−	0.157262i
$528$		0			0
$529$		−	3.92999i		−	0.170869i
$530$		0			0
$531$	18.4902	+	18.4902i	0.802406	+	0.802406i
$532$		0			0
$533$		−	9.38575i		−	0.406542i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	6.86692	+	6.86692i	0.296329	+	0.296329i
$538$		0			0
$539$	−5.70618	−	5.70618i	−0.245783	−	0.245783i
$540$		0			0
$541$	8.47183	−	8.47183i	0.364232	−	0.364232i	−0.501136	−	0.865369i	$-0.667084\pi$
$541$	8.47183	−	8.47183i	0.364232	−	0.364232i	0.865369	+	0.501136i	$0.167084\pi$
$542$		0			0
$543$	−0.720526	+	0.720526i	−0.0309207	+	0.0309207i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	9.97988			0.426709			0.213355	−	0.976975i	$-0.431561\pi$
$547$	9.97988			0.426709			0.213355	+	0.976975i	$0.431561\pi$
$548$		0			0
$549$	−12.1364	+	12.1364i	−0.517971	+	0.517971i
$550$		0			0
$551$	−45.4879			−1.93785
$552$		0			0
$553$	3.49559	−	3.49559i	0.148648	−	0.148648i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			13.4866i			0.571445i	0.958312	+	0.285722i	$0.0922335\pi$
$557$			13.4866i			0.571445i	−0.958312	+	0.285722i	$0.907766\pi$
$558$		0			0
$559$	15.8678			0.671135
$560$		0			0
$561$	0.481724			0.0203384
$562$		0			0
$563$		−	20.3451i		−	0.857445i	−0.903436	−	0.428723i	$-0.858964\pi$
$563$		−	20.3451i		−	0.857445i	0.903436	−	0.428723i	$-0.141036\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−1.68896	+	1.68896i	−0.0709298	+	0.0709298i
$568$		0			0
$569$	−17.1460			−0.718797			−0.359399	−	0.933184i	$-0.617018\pi$
$569$	−17.1460			−0.718797			−0.359399	+	0.933184i	$0.617018\pi$
$570$		0			0
$571$	−6.24329	+	6.24329i	−0.261274	+	0.261274i	−0.825571	−	0.564298i	$-0.809147\pi$
$571$	−6.24329	+	6.24329i	−0.261274	+	0.261274i	0.564298	+	0.825571i	$0.309147\pi$
$572$		0			0
$573$	2.13645			0.0892516
$574$		0			0
$575$		0			0
$576$		0			0
$577$	10.0373	−	10.0373i	0.417859	−	0.417859i	−0.466606	−	0.884465i	$-0.654523\pi$
$577$	10.0373	−	10.0373i	0.417859	−	0.417859i	0.884465	+	0.466606i	$0.154523\pi$
$578$		0			0
$579$	−8.37596	+	8.37596i	−0.348093	+	0.348093i
$580$		0			0
$581$	2.45963	+	2.45963i	0.102043	+	0.102043i
$582$		0			0
$583$	5.12561	+	5.12561i	0.212281	+	0.212281i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	30.6857i		−	1.26654i	−0.773933	−	0.633268i	$-0.781713\pi$
$587$		−	30.6857i		−	1.26654i	0.773933	−	0.633268i	$-0.218287\pi$
$588$		0			0
$589$	47.1025	+	47.1025i	1.94083	+	1.94083i
$590$		0			0
$591$		−	9.01817i		−	0.370958i
$592$		0			0
$593$	2.10671	+	2.10671i	0.0865123	+	0.0865123i	0.749039	−	0.662526i	$-0.230516\pi$
$593$	2.10671	+	2.10671i	0.0865123	+	0.0865123i	−0.662526	+	0.749039i	$0.730516\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	7.36210			0.301311
$598$		0			0
$599$		−	32.1322i		−	1.31289i	−0.754375	−	0.656444i	$-0.772060\pi$
$599$		−	32.1322i		−	1.31289i	0.754375	−	0.656444i	$-0.227940\pi$
$600$		0			0
$601$		−	14.9811i		−	0.611091i	−0.952177	−	0.305546i	$-0.901161\pi$
$601$		−	14.9811i		−	0.611091i	0.952177	−	0.305546i	$-0.0988388\pi$
$602$		0			0
$603$	36.1959			1.47401
$604$		0			0
$605$		0			0
$606$		0			0
$607$	27.3357	+	27.3357i	1.10952	+	1.10952i	0.993213	+	0.116310i	$0.0371067\pi$
$607$	27.3357	+	27.3357i	1.10952	+	1.10952i	0.116310	+	0.993213i	$0.462893\pi$
$608$		0			0
$609$			2.01506i			0.0816544i
$610$		0			0
$611$	16.8344	+	16.8344i	0.681047	+	0.681047i
$612$		0			0
$613$			48.3829i			1.95417i	0.212859	+	0.977083i	$0.431723\pi$
$613$			48.3829i			1.95417i	−0.212859	+	0.977083i	$0.568277\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	31.1565	+	31.1565i	1.25432	+	1.25432i	0.953766	+	0.300549i	$0.0971699\pi$
$617$	31.1565	+	31.1565i	1.25432	+	1.25432i	0.300549	+	0.953766i	$0.402830\pi$
$618$		0			0
$619$	−0.198272	−	0.198272i	−0.00796922	−	0.00796922i	0.703111	−	0.711080i	$-0.251794\pi$
$619$	−0.198272	−	0.198272i	−0.00796922	−	0.00796922i	−0.711080	+	0.703111i	$0.751794\pi$
$620$		0			0
$621$	11.8077	−	11.8077i	0.473825	−	0.473825i
$622$		0			0
$623$	−0.381537	+	0.381537i	−0.0152859	+	0.0152859i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−6.28512			−0.251003
$628$		0			0
$629$	−2.23276	+	2.23276i	−0.0890259	+	0.0890259i
$630$		0			0
$631$	32.3314			1.28709			0.643547	−	0.765407i	$-0.277462\pi$
$631$	32.3314			1.28709			0.643547	+	0.765407i	$0.277462\pi$
$632$		0			0
$633$	7.95239	−	7.95239i	0.316079	−	0.316079i
$634$		0			0
$635$		0			0
$636$		0			0
$637$			24.9161i			0.987212i
$638$		0			0
$639$	7.50010			0.296700
$640$		0			0
$641$	−46.5662			−1.83926			−0.919628	−	0.392790i	$-0.871510\pi$
$641$	−46.5662			−1.83926			−0.919628	+	0.392790i	$0.871510\pi$
$642$		0			0
$643$		−	40.2247i		−	1.58631i	−0.609021	−	0.793154i	$-0.708437\pi$
$643$		−	40.2247i		−	1.58631i	0.609021	−	0.793154i	$-0.291563\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−10.7938	+	10.7938i	−0.424349	+	0.424349i	−0.886698	−	0.462349i	$-0.847007\pi$
$647$	−10.7938	+	10.7938i	−0.424349	+	0.424349i	0.462349	+	0.886698i	$0.347007\pi$
$648$		0			0
$649$	−12.3799			−0.485956
$650$		0			0
$651$	2.08659	−	2.08659i	0.0817799	−	0.0817799i
$652$		0			0
$653$	3.92443			0.153575			0.0767875	−	0.997047i	$-0.475534\pi$
$653$	3.92443			0.153575			0.0767875	+	0.997047i	$0.475534\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	17.3173	−	17.3173i	0.675610	−	0.675610i
$658$		0			0
$659$	−34.6142	+	34.6142i	−1.34838	+	1.34838i	−0.460952	+	0.887425i	$0.652492\pi$
$659$	−34.6142	+	34.6142i	−1.34838	+	1.34838i	−0.887425	+	0.460952i	$0.847508\pi$
$660$		0			0
$661$	21.7641	+	21.7641i	0.846525	+	0.846525i	0.989698	−	0.143173i	$-0.0457304\pi$
$661$	21.7641	+	21.7641i	0.846525	+	0.846525i	−0.143173	+	0.989698i	$0.545730\pi$
$662$		0			0
$663$	−1.05173	−	1.05173i	−0.0408456	−	0.0408456i
$664$		0			0
$665$		0			0
$666$		0			0
$667$			26.1216i			1.01143i
$668$		0			0
$669$	1.50917	+	1.50917i	0.0583477	+	0.0583477i
$670$		0			0
$671$		−	8.12584i		−	0.313695i
$672$		0			0
$673$	−29.4450	−	29.4450i	−1.13502	−	1.13502i	−0.989330	−	0.145691i	$-0.953459\pi$
$673$	−29.4450	−	29.4450i	−1.13502	−	1.13502i	−0.145691	−	0.989330i	$-0.546541\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	34.7351			1.33498			0.667490	−	0.744619i	$-0.267369\pi$
$677$	34.7351			1.33498			0.667490	+	0.744619i	$0.267369\pi$
$678$		0			0
$679$		−	4.92370i		−	0.188954i
$680$		0			0
$681$			6.45828i			0.247482i
$682$		0			0
$683$	−22.2693			−0.852110			−0.426055	−	0.904697i	$-0.640097\pi$
$683$	−22.2693			−0.852110			−0.426055	+	0.904697i	$0.640097\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−1.88597	−	1.88597i	−0.0719543	−	0.0719543i
$688$		0			0
$689$		−	22.3810i		−	0.852650i
$690$		0			0
$691$	−15.7043	−	15.7043i	−0.597420	−	0.597420i	0.342205	−	0.939625i	$-0.388826\pi$
$691$	−15.7043	−	15.7043i	−0.597420	−	0.597420i	−0.939625	+	0.342205i	$0.888826\pi$
$692$		0			0
$693$		−	1.46227i		−	0.0555470i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	1.05003	+	1.05003i	0.0397728	+	0.0397728i
$698$		0			0
$699$	−8.58253	−	8.58253i	−0.324621	−	0.324621i
$700$		0			0
$701$	−21.5588	+	21.5588i	−0.814266	+	0.814266i	−0.985270	−	0.171004i	$-0.945299\pi$
$701$	−21.5588	+	21.5588i	−0.814266	+	0.814266i	0.171004	+	0.985270i	$0.445299\pi$
$702$		0			0
$703$	29.1311	−	29.1311i	1.09870	−	1.09870i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−0.655691			−0.0246598
$708$		0			0
$709$	−2.96687	+	2.96687i	−0.111423	+	0.111423i	−0.760620	−	0.649197i	$-0.775105\pi$
$709$	−2.96687	+	2.96687i	−0.111423	+	0.111423i	0.649197	+	0.760620i	$0.275105\pi$
$710$		0			0
$711$	−25.6183			−0.960760
$712$		0			0
$713$	27.0488	−	27.0488i	1.01299	−	1.01299i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		−	17.4688i		−	0.652385i
$718$		0			0
$719$	25.8357			0.963509			0.481755	−	0.876306i	$-0.340000\pi$
$719$	25.8357			0.963509			0.481755	+	0.876306i	$0.340000\pi$
$720$		0			0
$721$	−6.59839			−0.245737
$722$		0			0
$723$			8.32763i			0.309708i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	28.9620	−	28.9620i	1.07414	−	1.07414i	0.0771198	−	0.997022i	$-0.475428\pi$
$727$	28.9620	−	28.9620i	1.07414	−	1.07414i	0.997022	−	0.0771198i	$-0.0245724\pi$
$728$		0			0
$729$	4.43146			0.164128
$730$		0			0
$731$	−1.77521	+	1.77521i	−0.0656584	+	0.0656584i
$732$		0			0
$733$	−21.1673			−0.781832			−0.390916	−	0.920426i	$-0.627842\pi$
$733$	−21.1673			−0.781832			−0.390916	+	0.920426i	$0.627842\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−12.1173	+	12.1173i	−0.446347	+	0.446347i
$738$		0			0
$739$	−2.23302	+	2.23302i	−0.0821431	+	0.0821431i	−0.746985	−	0.664841i	$-0.768499\pi$
$739$	−2.23302	+	2.23302i	−0.0821431	+	0.0821431i	0.664841	+	0.746985i	$0.268499\pi$
$740$		0			0
$741$	13.7220	+	13.7220i	0.504091	+	0.504091i
$742$		0			0
$743$	−18.4514	−	18.4514i	−0.676915	−	0.676915i	0.282386	−	0.959301i	$-0.408874\pi$
$743$	−18.4514	−	18.4514i	−0.676915	−	0.676915i	−0.959301	+	0.282386i	$0.908874\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		−	18.0260i		−	0.659538i
$748$		0			0
$749$	−1.81634	−	1.81634i	−0.0663675	−	0.0663675i
$750$		0			0
$751$		−	42.4243i		−	1.54808i	−0.633134	−	0.774042i	$-0.718232\pi$
$751$		−	42.4243i		−	1.54808i	0.633134	−	0.774042i	$-0.281768\pi$
$752$		0			0
$753$	−5.18780	−	5.18780i	−0.189054	−	0.189054i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	19.7595			0.718170			0.359085	−	0.933305i	$-0.383089\pi$
$757$	19.7595			0.718170			0.359085	+	0.933305i	$0.383089\pi$
$758$		0			0
$759$			3.60925i			0.131007i
$760$		0			0
$761$			48.0351i			1.74127i	0.491928	+	0.870636i	$0.336292\pi$
$761$			48.0351i			1.74127i	−0.491928	+	0.870636i	$0.663708\pi$
$762$		0			0
$763$	−1.05899			−0.0383379
$764$		0			0
$765$		0			0
$766$		0			0
$767$	27.0286	+	27.0286i	0.975946	+	0.975946i
$768$		0			0
$769$		−	24.0184i		−	0.866127i	−0.901363	−	0.433064i	$-0.857433\pi$
$769$		−	24.0184i		−	0.866127i	0.901363	−	0.433064i	$-0.142567\pi$
$770$		0			0
$771$	6.98319	+	6.98319i	0.251493	+	0.251493i
$772$		0			0
$773$		−	22.4630i		−	0.807937i	−0.914773	−	0.403969i	$-0.867630\pi$
$773$		−	22.4630i		−	0.807937i	0.914773	−	0.403969i	$-0.132370\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−1.29048	−	1.29048i	−0.0462956	−	0.0462956i
$778$		0			0
$779$	−13.6999	−	13.6999i	−0.490850	−	0.490850i
$780$		0			0
$781$	−2.51081	+	2.51081i	−0.0898440	+	0.0898440i
$782$		0			0
$783$	16.1738	−	16.1738i	0.578005	−	0.578005i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	26.1054			0.930556			0.465278	−	0.885165i	$-0.345954\pi$
$787$	26.1054			0.930556			0.465278	+	0.885165i	$0.345954\pi$
$788$		0			0
$789$	2.65724	−	2.65724i	0.0946001	−	0.0946001i
$790$		0			0
$791$	−2.06087			−0.0732759
$792$		0			0
$793$	−17.7408	+	17.7408i	−0.629994	+	0.629994i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			43.4888i			1.54045i	0.637770	+	0.770227i	$0.279857\pi$
$797$			43.4888i			1.54045i	−0.637770	+	0.770227i	$0.720143\pi$
$798$		0			0
$799$	−3.76670			−0.133256
$800$		0			0
$801$	2.79618			0.0987983
$802$		0			0
$803$			11.5946i			0.409165i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	9.29969	−	9.29969i	0.327364	−	0.327364i
$808$		0			0
$809$	36.6271			1.28774			0.643870	−	0.765135i	$-0.277328\pi$
$809$	36.6271			1.28774			0.643870	+	0.765135i	$0.277328\pi$
$810$		0			0
$811$	−18.7904	+	18.7904i	−0.659821	+	0.659821i	−0.955338	−	0.295516i	$-0.904508\pi$
$811$	−18.7904	+	18.7904i	−0.659821	+	0.659821i	0.295516	+	0.955338i	$0.404508\pi$
$812$		0			0
$813$	8.55633			0.300084
$814$		0			0
$815$		0			0
$816$		0			0
$817$	23.1614	−	23.1614i	0.810314	−	0.810314i
$818$		0			0
$819$	−3.19250	+	3.19250i	−0.111555	+	0.111555i
$820$		0			0
$821$	3.91048	+	3.91048i	0.136477	+	0.136477i	0.772045	−	0.635568i	$-0.219234\pi$
$821$	3.91048	+	3.91048i	0.136477	+	0.136477i	−0.635568	+	0.772045i	$0.719234\pi$
$822$		0			0
$823$	35.4412	+	35.4412i	1.23540	+	1.23540i	0.961860	+	0.273542i	$0.0881952\pi$
$823$	35.4412	+	35.4412i	1.23540	+	1.23540i	0.273542	+	0.961860i	$0.411805\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			44.0700i			1.53246i	0.642565	+	0.766232i	$0.277870\pi$
$827$			44.0700i			1.53246i	−0.642565	+	0.766232i	$0.722130\pi$
$828$		0			0
$829$	15.1609	+	15.1609i	0.526561	+	0.526561i	0.919545	−	0.392984i	$-0.128557\pi$
$829$	15.1609	+	15.1609i	0.526561	+	0.526561i	−0.392984	+	0.919545i	$0.628557\pi$
$830$		0			0
$831$			4.70216i			0.163116i
$832$		0			0
$833$	−2.78749	−	2.78749i	−0.0965808	−	0.0965808i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−33.4958			−1.15779
$838$		0			0
$839$			40.3143i			1.39180i	0.718137	+	0.695901i	$0.244995\pi$
$839$			40.3143i			1.39180i	−0.718137	+	0.695901i	$0.755005\pi$
$840$		0			0
$841$			6.78056i			0.233812i
$842$		0			0
$843$	14.9286			0.514168
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−3.29307	−	3.29307i	−0.113151	−	0.113151i
$848$		0			0
$849$		−	6.83575i		−	0.234602i
$850$		0			0
$851$	−16.7286	−	16.7286i	−0.573450	−	0.573450i
$852$		0			0
$853$		−	28.6203i		−	0.979941i	−0.871739	−	0.489971i	$-0.837008\pi$
$853$		−	28.6203i		−	0.979941i	0.871739	−	0.489971i	$-0.162992\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	7.19794	+	7.19794i	0.245877	+	0.245877i	0.819276	−	0.573399i	$-0.194376\pi$
$857$	7.19794	+	7.19794i	0.245877	+	0.245877i	−0.573399	+	0.819276i	$0.694376\pi$
$858$		0			0
$859$	18.8135	+	18.8135i	0.641910	+	0.641910i	0.951025	−	0.309115i	$-0.100033\pi$
$859$	18.8135	+	18.8135i	0.641910	+	0.641910i	−0.309115	+	0.951025i	$0.600033\pi$
$860$		0			0
$861$	−0.606890	+	0.606890i	−0.0206828	+	0.0206828i
$862$		0			0
$863$	19.2328	−	19.2328i	0.654691	−	0.654691i	−0.299428	−	0.954119i	$-0.596796\pi$
$863$	19.2328	−	19.2328i	0.654691	−	0.654691i	0.954119	+	0.299428i	$0.0967958\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−11.5408			−0.391945
$868$		0			0
$869$	8.57624	−	8.57624i	0.290929	−	0.290929i
$870$		0			0
$871$	52.9103			1.79280
$872$		0			0
$873$	−18.0423	+	18.0423i	−0.610638	+	0.610638i
$874$		0			0
$875$		0			0
$876$		0			0
$877$			35.4397i			1.19671i	0.801229	+	0.598357i	$0.204180\pi$
$877$			35.4397i			1.19671i	−0.801229	+	0.598357i	$0.795820\pi$
$878$		0			0
$879$	9.83458			0.331712
$880$		0			0
$881$	30.2010			1.01750			0.508748	−	0.860915i	$-0.330108\pi$
$881$	30.2010			1.01750			0.508748	+	0.860915i	$0.330108\pi$
$882$		0			0
$883$			28.9931i			0.975696i	0.872928	+	0.487848i	$0.162218\pi$
$883$			28.9931i			0.975696i	−0.872928	+	0.487848i	$0.837782\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	5.33418	−	5.33418i	0.179104	−	0.179104i	−0.611861	−	0.790965i	$-0.709579\pi$
$887$	5.33418	−	5.33418i	0.179104	−	0.179104i	0.790965	+	0.611861i	$0.209579\pi$
$888$		0			0
$889$	7.25724			0.243400
$890$		0			0
$891$	−4.14379	+	4.14379i	−0.138822	+	0.138822i
$892$		0			0
$893$	49.1447			1.64456
$894$		0			0
$895$		0			0
$896$		0			0
$897$	7.87991	−	7.87991i	0.263103	−	0.263103i
$898$		0			0
$899$	37.0507	−	37.0507i	1.23571	−	1.23571i
$900$		0			0
$901$	2.50388	+	2.50388i	0.0834163	+	0.0834163i
$902$		0			0
$903$	−1.02602	−	1.02602i	−0.0341439	−	0.0341439i
$904$		0			0
$905$		0			0
$906$		0			0
$907$		−	26.2683i		−	0.872226i	−0.899892	−	0.436113i	$-0.856355\pi$
$907$		−	26.2683i		−	0.872226i	0.899892	−	0.436113i	$-0.143645\pi$
$908$		0			0
$909$	2.40270	+	2.40270i	0.0796924	+	0.0796924i
$910$		0			0
$911$			33.5196i			1.11055i	0.831665	+	0.555277i	$0.187388\pi$
$911$			33.5196i			1.11055i	−0.831665	+	0.555277i	$0.812612\pi$
$912$		0			0
$913$	6.03459	+	6.03459i	0.199716	+	0.199716i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−0.584935			−0.0193163
$918$		0			0
$919$		−	25.7545i		−	0.849564i	−0.905296	−	0.424782i	$-0.860351\pi$
$919$		−	25.7545i		−	0.849564i	0.905296	−	0.424782i	$-0.139649\pi$
$920$		0			0
$921$		−	14.1425i		−	0.466011i
$922$		0			0
$923$	10.9635			0.360868
$924$		0			0
$925$		0			0
$926$		0			0
$927$	24.1790	+	24.1790i	0.794141	+	0.794141i
$928$		0			0
$929$		−	9.06425i		−	0.297388i	−0.988883	−	0.148694i	$-0.952493\pi$
$929$		−	9.06425i		−	0.297388i	0.988883	−	0.148694i	$-0.0475070\pi$
$930$		0			0
$931$	36.3688	+	36.3688i	1.19194	+	1.19194i
$932$		0			0
$933$			4.71788i			0.154456i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	3.38621	+	3.38621i	0.110623	+	0.110623i	0.760251	−	0.649629i	$-0.225076\pi$
$937$	3.38621	+	3.38621i	0.110623	+	0.110623i	−0.649629	+	0.760251i	$0.725076\pi$
$938$		0			0
$939$	0.837719	+	0.837719i	0.0273379	+	0.0273379i
$940$		0			0
$941$	−16.9347	+	16.9347i	−0.552054	+	0.552054i	−0.927033	−	0.374979i	$-0.877650\pi$
$941$	−16.9347	+	16.9347i	−0.552054	+	0.552054i	0.374979	+	0.927033i	$0.377650\pi$
$942$		0			0
$943$	−7.86722	+	7.86722i	−0.256192	+	0.256192i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.08633			−0.0353011			−0.0176505	−	0.999844i	$-0.505619\pi$
$947$	−1.08633			−0.0353011			−0.0176505	+	0.999844i	$0.505619\pi$
$948$		0			0
$949$	25.3140	−	25.3140i	0.821727	−	0.821727i
$950$		0			0
$951$	2.38416			0.0773117
$952$		0			0
$953$	−10.7914	+	10.7914i	−0.349567	+	0.349567i	−0.859948	−	0.510381i	$-0.829504\pi$
$953$	−10.7914	+	10.7914i	−0.349567	+	0.349567i	0.510381	+	0.859948i	$0.329504\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			4.94385i			0.159812i
$958$		0			0
$959$	−3.78359			−0.122178
$960$		0			0
$961$	−45.7317			−1.47522
$962$		0			0
$963$			13.3115i			0.428956i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−31.4724	+	31.4724i	−1.01208	+	1.01208i	−0.0121587	+	0.999926i	$0.503870\pi$
$967$	−31.4724	+	31.4724i	−1.01208	+	1.01208i	−0.999926	+	0.0121587i	$0.996130\pi$
$968$		0			0
$969$	−3.07030			−0.0986323
$970$		0			0
$971$	23.1234	−	23.1234i	0.742066	−	0.742066i	−0.230909	−	0.972975i	$-0.574170\pi$
$971$	23.1234	−	23.1234i	0.742066	−	0.742066i	0.972975	+	0.230909i	$0.0741700\pi$
$972$		0			0
$973$	2.08742			0.0669196
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−15.3820	+	15.3820i	−0.492114	+	0.492114i	−0.908972	−	0.416858i	$-0.863131\pi$
$977$	−15.3820	+	15.3820i	−0.492114	+	0.492114i	0.416858	+	0.908972i	$0.363131\pi$
$978$		0			0
$979$	−0.936080	+	0.936080i	−0.0299173	+	0.0299173i
$980$		0			0
$981$	3.88052	+	3.88052i	0.123896	+	0.123896i
$982$		0			0
$983$	−38.5198	−	38.5198i	−1.22859	−	1.22859i	−0.964497	−	0.264093i	$-0.914927\pi$
$983$	−38.5198	−	38.5198i	−1.22859	−	1.22859i	−0.264093	−	0.964497i	$-0.585073\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		−	2.17705i		−	0.0692964i
$988$		0			0
$989$	−13.3005	−	13.3005i	−0.422931	−	0.422931i
$990$		0			0
$991$			22.0556i			0.700619i	0.936634	+	0.350310i	$0.113924\pi$
$991$			22.0556i			0.700619i	−0.936634	+	0.350310i	$0.886076\pi$
$992$		0			0
$993$	1.02841	+	1.02841i	0.0326356	+	0.0326356i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−0.840040			−0.0266043			−0.0133022	−	0.999912i	$-0.504234\pi$
$997$	−0.840040			−0.0266043			−0.0133022	+	0.999912i	$0.504234\pi$
$998$		0			0
$999$			20.7159i			0.655422i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.j.d.143.6		18
4.3	odd	2		400.2.j.d.43.7		18
5.2	odd	4		1600.2.s.d.207.6		18
5.3	odd	4		320.2.s.b.207.4		18
5.4	even	2		320.2.j.b.143.4		18
16.3	odd	4		1600.2.s.d.943.6		18
16.13	even	4		400.2.s.d.243.3		18
20.3	even	4		80.2.s.b.27.7	yes	18
20.7	even	4		400.2.s.d.107.3		18
20.19	odd	2		80.2.j.b.43.3	✓	18
40.3	even	4		640.2.s.d.287.4		18
40.13	odd	4		640.2.s.c.287.6		18
40.19	odd	2		640.2.j.d.543.4		18
40.29	even	2		640.2.j.c.543.6		18
60.23	odd	4		720.2.z.g.667.3		18
60.59	even	2		720.2.bd.g.523.7		18
80.3	even	4		320.2.j.b.47.6		18
80.13	odd	4		80.2.j.b.67.3	yes	18
80.19	odd	4		320.2.s.b.303.4		18
80.29	even	4		80.2.s.b.3.7	yes	18
80.43	even	4		640.2.j.c.607.4		18
80.53	odd	4		640.2.j.d.607.6		18
80.59	odd	4		640.2.s.c.223.6		18
80.67	even	4	inner	1600.2.j.d.1007.4		18
80.69	even	4		640.2.s.d.223.4		18
80.77	odd	4		400.2.j.d.307.7		18
240.29	odd	4		720.2.z.g.163.3		18
240.173	even	4		720.2.bd.g.307.7		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.3	✓	18	20.19	odd	2
80.2.j.b.67.3	yes	18	80.13	odd	4
80.2.s.b.3.7	yes	18	80.29	even	4
80.2.s.b.27.7	yes	18	20.3	even	4
320.2.j.b.47.6		18	80.3	even	4
320.2.j.b.143.4		18	5.4	even	2
320.2.s.b.207.4		18	5.3	odd	4
320.2.s.b.303.4		18	80.19	odd	4
400.2.j.d.43.7		18	4.3	odd	2
400.2.j.d.307.7		18	80.77	odd	4
400.2.s.d.107.3		18	20.7	even	4
400.2.s.d.243.3		18	16.13	even	4
640.2.j.c.543.6		18	40.29	even	2
640.2.j.c.607.4		18	80.43	even	4
640.2.j.d.543.4		18	40.19	odd	2
640.2.j.d.607.6		18	80.53	odd	4
640.2.s.c.223.6		18	80.59	odd	4
640.2.s.c.287.6		18	40.13	odd	4
640.2.s.d.223.4		18	80.69	even	4
640.2.s.d.287.4		18	40.3	even	4
720.2.z.g.163.3		18	240.29	odd	4
720.2.z.g.667.3		18	60.23	odd	4
720.2.bd.g.307.7		18	240.173	even	4
720.2.bd.g.523.7		18	60.59	even	2
1600.2.j.d.143.6		18	1.1	even	1	trivial
1600.2.j.d.1007.4		18	80.67	even	4	inner
1600.2.s.d.207.6		18	5.2	odd	4
1600.2.s.d.943.6		18	16.3	odd	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:	\( N \)	\(=\)	\( 1600 = 2^{6} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1600.j (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.692712i q^{3} +(-0.343872 + 0.343872i) q^{7} +2.52015 q^{9} +O(q^{10})\)	\(q+0.692712i q^{3} +(-0.343872 + 0.343872i) q^{7} +2.52015 q^{9} +(-0.843672 + 0.843672i) q^{11} +3.68390 q^{13} +(-0.412137 + 0.412137i) q^{17} +(5.37721 - 5.37721i) q^{19} +(-0.238204 - 0.238204i) q^{21} +(-3.08788 - 3.08788i) q^{23} +3.82387i q^{27} +(-4.22969 - 4.22969i) q^{29} +8.75966i q^{31} +(-0.584422 - 0.584422i) q^{33} +5.41752 q^{37} +2.55188i q^{39} -2.54777i q^{41} +4.30732 q^{43} +(4.56972 + 4.56972i) q^{47} +6.76350i q^{49} +(-0.285492 - 0.285492i) q^{51} -6.07536i q^{53} +(3.72486 + 3.72486i) q^{57} +(7.33694 + 7.33694i) q^{59} +(-4.81576 + 4.81576i) q^{61} +(-0.866609 + 0.866609i) q^{63} +14.3626 q^{67} +(2.13901 - 2.13901i) q^{69} +2.97605 q^{71} +(6.87152 - 6.87152i) q^{73} -0.580231i q^{77} -10.1654 q^{79} +4.91161 q^{81} -7.15276i q^{83} +(2.92996 - 2.92996i) q^{87} +1.10953 q^{89} +(-1.26679 + 1.26679i) q^{91} -6.06792 q^{93} +(-7.15920 + 7.15920i) q^{97} +(-2.12618 + 2.12618i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{7} - 10 q^{9}+O(q^{10}) \) 18 * q + 2 * q^7 - 10 * q^9	\( 18 q + 2 q^{7} - 10 q^{9} + 2 q^{11} + 6 q^{17} - 2 q^{19} - 16 q^{21} - 2 q^{23} - 14 q^{29} + 8 q^{33} - 8 q^{37} - 44 q^{43} - 38 q^{47} - 8 q^{51} - 24 q^{57} + 10 q^{59} + 14 q^{61} + 6 q^{63} + 12 q^{67} + 32 q^{69} - 24 q^{71} - 14 q^{73} - 16 q^{79} + 2 q^{81} + 24 q^{87} - 12 q^{89} - 16 q^{93} - 18 q^{97} + 22 q^{99}+O(q^{100}) \) 18 * q + 2 * q^7 - 10 * q^9 + 2 * q^11 + 6 * q^17 - 2 * q^19 - 16 * q^21 - 2 * q^23 - 14 * q^29 + 8 * q^33 - 8 * q^37 - 44 * q^43 - 38 * q^47 - 8 * q^51 - 24 * q^57 + 10 * q^59 + 14 * q^61 + 6 * q^63 + 12 * q^67 + 32 * q^69 - 24 * q^71 - 14 * q^73 - 16 * q^79 + 2 * q^81 + 24 * q^87 - 12 * q^89 - 16 * q^93 - 18 * q^97 + 22 * q^99

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