LMFDB - Embedded newform 2100.2.q.l.1201.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(1201,2100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("2100.1201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2100.q (of order $3$, degree $2$, 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:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.17819046144.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 10x^{6} + 8x^{5} + 38x^{4} - 4x^{3} + 16x^{2} + 4x + 4 $ x^8 - 2x^7 + 10x^6 + 8x^5 + 38x^4 - 4x^3 + 16x^2 + 4*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1201.4
Root			$-0.868255 + 1.50386i$ of defining polynomial
Character	$\chi$	$=$	2100.1201
Dual form			2100.2.q.l.1801.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{3} +(2.61250 + 0.418148i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{3} +(2.61250 + 0.418148i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(0.292387 - 0.506430i) q^{11} -1.75198 q^{13} +(3.11250 - 5.39101i) q^{17} +(3.48075 + 6.02884i) q^{19} +(-1.66838 + 2.05342i) q^{21} +(-1.37599 - 2.38328i) q^{23} +1.00000 q^{27} +3.24047 q^{29} +(1.25198 - 2.16849i) q^{31} +(0.292387 + 0.506430i) q^{33} +(-1.94412 - 3.36732i) q^{37} +(0.875989 - 1.51726i) q^{39} +4.58477 q^{41} -0.754325 q^{43} +(0.727603 + 1.26025i) q^{47} +(6.65030 + 2.18482i) q^{49} +(3.11250 + 5.39101i) q^{51} +(-0.263490 + 0.456378i) q^{53} -6.96151 q^{57} +(5.05327 - 8.75253i) q^{59} +(-4.07704 - 7.06164i) q^{61} +(-0.944123 - 2.47156i) q^{63} +(-7.34901 + 12.7289i) q^{67} +2.75198 q^{69} +13.3561 q^{71} +(3.37716 - 5.84942i) q^{73} +(0.975625 - 1.20079i) q^{77} +(4.04771 + 7.01085i) q^{79} +(-0.500000 + 0.866025i) q^{81} +5.72895 q^{83} +(-1.62023 + 2.80633i) q^{87} +(8.50192 + 14.7258i) q^{89} +(-4.57704 - 0.732586i) q^{91} +(1.25198 + 2.16849i) q^{93} -11.1132 q^{97} -0.584775 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} - 2 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 - 2 * q^7 - 4 * q^9	$ 8 q - 4 q^{3} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{13} + 2 q^{17} - 4 q^{19} - 2 q^{21} - 6 q^{23} + 8 q^{27} - 12 q^{29} - 4 q^{33} - 4 q^{37} + 2 q^{39} + 24 q^{41} + 32 q^{43} - 2 q^{47} - 4 q^{49} + 2 q^{51} - 20 q^{53} + 8 q^{57} + 14 q^{59} - 16 q^{61} + 4 q^{63} - 18 q^{67} + 12 q^{69} - 28 q^{71} + 8 q^{73} + 10 q^{77} + 8 q^{79} - 4 q^{81} - 20 q^{83} + 6 q^{87} + 8 q^{89} - 20 q^{91} - 20 q^{97} + 8 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^13 + 2 * q^17 - 4 * q^19 - 2 * q^21 - 6 * q^23 + 8 * q^27 - 12 * q^29 - 4 * q^33 - 4 * q^37 + 2 * q^39 + 24 * q^41 + 32 * q^43 - 2 * q^47 - 4 * q^49 + 2 * q^51 - 20 * q^53 + 8 * q^57 + 14 * q^59 - 16 * q^61 + 4 * q^63 - 18 * q^67 + 12 * q^69 - 28 * q^71 + 8 * q^73 + 10 * q^77 + 8 * q^79 - 4 * q^81 - 20 * q^83 + 6 * q^87 + 8 * q^89 - 20 * q^91 - 20 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.61250	+	0.418148i	0.987432	+	0.158045i
$7$	2.61250	+	0.418148i	0.987432	+	0.158045i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	0.292387	−	0.506430i	0.0881581	−	0.152694i	−0.818574	−	0.574400i	$-0.805235\pi$
$11$	0.292387	−	0.506430i	0.0881581	−	0.152694i	0.906733	+	0.421706i	$0.138569\pi$
$12$		0			0
$13$	−1.75198			−0.485911			−0.242956	−	0.970037i	$-0.578117\pi$
$13$	−1.75198			−0.485911			−0.242956	+	0.970037i	$0.578117\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.11250	−	5.39101i	0.754892	−	1.30751i	−0.190536	−	0.981680i	$-0.561023\pi$
$17$	3.11250	−	5.39101i	0.754892	−	1.30751i	0.945428	−	0.325831i	$-0.105644\pi$
$18$		0			0
$19$	3.48075	+	6.02884i	0.798540	+	1.38311i	0.920567	+	0.390585i	$0.127727\pi$
$19$	3.48075	+	6.02884i	0.798540	+	1.38311i	−0.122027	+	0.992527i	$0.538940\pi$
$20$		0			0
$21$	−1.66838	+	2.05342i	−0.364070	+	0.448092i
$22$		0			0
$23$	−1.37599	−	2.38328i	−0.286914	−	0.496949i	0.686158	−	0.727453i	$-0.259296\pi$
$23$	−1.37599	−	2.38328i	−0.286914	−	0.496949i	−0.973071	+	0.230504i	$0.925963\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	3.24047			0.601739			0.300870	−	0.953665i	$-0.402723\pi$
$29$	3.24047			0.601739			0.300870	+	0.953665i	$0.402723\pi$
$30$		0			0
$31$	1.25198	−	2.16849i	0.224862	−	0.389472i	−0.731416	−	0.681931i	$-0.761140\pi$
$31$	1.25198	−	2.16849i	0.224862	−	0.389472i	0.956278	+	0.292459i	$0.0944736\pi$
$32$		0			0
$33$	0.292387	+	0.506430i	0.0508981	+	0.0881581i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.94412	−	3.36732i	−0.319612	−	0.553584i	0.660795	−	0.750566i	$-0.270219\pi$
$37$	−1.94412	−	3.36732i	−0.319612	−	0.553584i	−0.980407	+	0.196982i	$0.936886\pi$
$38$		0			0
$39$	0.875989	−	1.51726i	0.140271	−	0.242956i
$40$		0			0
$41$	4.58477			0.716022			0.358011	−	0.933717i	$-0.383455\pi$
$41$	4.58477			0.716022			0.358011	+	0.933717i	$0.383455\pi$
$42$		0			0
$43$	−0.754325			−0.115033			−0.0575167	−	0.998345i	$-0.518318\pi$
$43$	−0.754325			−0.115033			−0.0575167	+	0.998345i	$0.518318\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.727603	+	1.26025i	0.106132	+	0.183826i	0.914200	−	0.405263i	$-0.132820\pi$
$47$	0.727603	+	1.26025i	0.106132	+	0.183826i	−0.808068	+	0.589089i	$0.799487\pi$
$48$		0			0
$49$	6.65030	+	2.18482i	0.950043	+	0.312118i
$50$		0			0
$51$	3.11250	+	5.39101i	0.435837	+	0.754892i
$52$		0			0
$53$	−0.263490	+	0.456378i	−0.0361931	+	0.0626883i	−0.883555	−	0.468328i	$-0.844856\pi$
$53$	−0.263490	+	0.456378i	−0.0361931	+	0.0626883i	0.847361	+	0.531017i	$0.178190\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−6.96151			−0.922074
$58$		0			0
$59$	5.05327	−	8.75253i	0.657880	−	1.13948i	−0.323283	−	0.946302i	$-0.604787\pi$
$59$	5.05327	−	8.75253i	0.657880	−	1.13948i	0.981163	−	0.193180i	$-0.0618800\pi$
$60$		0			0
$61$	−4.07704	−	7.06164i	−0.522012	−	0.904151i	−0.999672	−	0.0256061i	$-0.991848\pi$
$61$	−4.07704	−	7.06164i	−0.522012	−	0.904151i	0.477660	−	0.878545i	$-0.341485\pi$
$62$		0			0
$63$	−0.944123	−	2.47156i	−0.118948	−	0.311388i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−7.34901	+	12.7289i	−0.897824	+	1.55508i	−0.0675547	+	0.997716i	$0.521520\pi$
$67$	−7.34901	+	12.7289i	−0.897824	+	1.55508i	−0.830270	+	0.557362i	$0.811814\pi$
$68$		0			0
$69$	2.75198			0.331299
$70$		0			0
$71$	13.3561			1.58507			0.792536	−	0.609825i	$-0.208760\pi$
$71$	13.3561			1.58507			0.792536	+	0.609825i	$0.208760\pi$
$72$		0			0
$73$	3.37716	−	5.84942i	0.395267	−	0.684622i	−0.597868	−	0.801594i	$-0.703985\pi$
$73$	3.37716	−	5.84942i	0.395267	−	0.684622i	0.993135	+	0.116972i	$0.0373187\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.975625	−	1.20079i	0.111183	−	0.136842i
$78$		0			0
$79$	4.04771	+	7.01085i	0.455403	+	0.788782i	0.998711	−	0.0507516i	$-0.0161617\pi$
$79$	4.04771	+	7.01085i	0.455403	+	0.788782i	−0.543308	+	0.839534i	$0.682828\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	5.72895			0.628834			0.314417	−	0.949285i	$-0.398191\pi$
$83$	5.72895			0.628834			0.314417	+	0.949285i	$0.398191\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−1.62023	+	2.80633i	−0.173707	+	0.300870i
$88$		0			0
$89$	8.50192	+	14.7258i	0.901202	+	1.56093i	0.825936	+	0.563763i	$0.190647\pi$
$89$	8.50192	+	14.7258i	0.901202	+	1.56093i	0.0752651	+	0.997164i	$0.476020\pi$
$90$		0			0
$91$	−4.57704	−	0.732586i	−0.479804	−	0.0767959i
$92$		0			0
$93$	1.25198	+	2.16849i	0.129824	+	0.224862i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−11.1132			−1.12838			−0.564189	−	0.825645i	$-0.690811\pi$
$97$	−11.1132			−1.12838			−0.564189	+	0.825645i	$0.690811\pi$
$98$		0			0
$99$	−0.584775			−0.0587721
$100$		0			0
$101$	−8.67803	+	15.0308i	−0.863496	+	1.49562i	0.00503661	+	0.999987i	$0.498397\pi$
$101$	−8.67803	+	15.0308i	−0.863496	+	1.49562i	−0.868533	+	0.495632i	$0.834937\pi$
$102$		0			0
$103$	−6.68063	−	11.5712i	−0.658262	−	1.14014i	−0.981065	−	0.193678i	$-0.937958\pi$
$103$	−6.68063	−	11.5712i	−0.658262	−	1.14014i	0.322803	−	0.946466i	$-0.395375\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.06361	−	1.84223i	−0.102823	−	0.178095i	0.810024	−	0.586397i	$-0.199454\pi$
$107$	−1.06361	−	1.84223i	−0.102823	−	0.178095i	−0.912847	+	0.408302i	$0.866121\pi$
$108$		0			0
$109$	−1.14400	+	1.98147i	−0.109575	+	0.189790i	−0.915598	−	0.402094i	$-0.868282\pi$
$109$	−1.14400	+	1.98147i	−0.109575	+	0.189790i	0.806023	+	0.591884i	$0.201616\pi$
$110$		0			0
$111$	3.88825			0.369056
$112$		0			0
$113$	11.7765			1.10784			0.553920	−	0.832570i	$-0.313132\pi$
$113$	11.7765			1.10784			0.553920	+	0.832570i	$0.313132\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.875989	+	1.51726i	0.0809852	+	0.140271i
$118$		0			0
$119$	10.3856	−	12.7825i	0.952050	−	1.17177i
$120$		0			0
$121$	5.32902	+	9.23013i	0.484456	+	0.839103i
$122$		0			0
$123$	−2.29239	+	3.97053i	−0.206698	+	0.358011i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	15.2606			1.35416			0.677081	−	0.735909i	$-0.263245\pi$
$127$	15.2606			1.35416			0.677081	+	0.735909i	$0.263245\pi$
$128$		0			0
$129$	0.377162	−	0.653265i	0.0332073	−	0.0575167i
$130$		0			0
$131$	−4.00891	−	6.94363i	−0.350260	−	0.606668i	0.636035	−	0.771660i	$-0.280573\pi$
$131$	−4.00891	−	6.94363i	−0.350260	−	0.606668i	−0.986295	+	0.164992i	$0.947240\pi$
$132$		0			0
$133$	6.57252	+	17.2058i	0.569910	+	1.49193i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	7.34641	−	12.7243i	0.627646	−	1.08711i	−0.360377	−	0.932807i	$-0.617352\pi$
$137$	7.34641	−	12.7243i	0.627646	−	1.08711i	0.988023	−	0.154308i	$-0.0493147\pi$
$138$		0			0
$139$	19.1080			1.62072			0.810361	−	0.585931i	$-0.199271\pi$
$139$	19.1080			1.62072			0.810361	+	0.585931i	$0.199271\pi$
$140$		0			0
$141$	−1.45521			−0.122550
$142$		0			0
$143$	−0.512256	+	0.887254i	−0.0428370	+	0.0741959i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−5.21726	+	4.66692i	−0.430313	+	0.384921i
$148$		0			0
$149$	0.912621	+	1.58071i	0.0747648	+	0.129496i	0.900984	−	0.433852i	$-0.142846\pi$
$149$	0.912621	+	1.58071i	0.0747648	+	0.129496i	−0.826219	+	0.563349i	$0.809513\pi$
$150$		0			0
$151$	2.41379	−	4.18081i	0.196432	−	0.340230i	−0.750937	−	0.660374i	$-0.770398\pi$
$151$	2.41379	−	4.18081i	0.196432	−	0.340230i	0.947369	+	0.320144i	$0.103731\pi$
$152$		0			0
$153$	−6.22500			−0.503261
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−7.24281	+	12.5449i	−0.578039	+	1.00119i	0.417665	+	0.908601i	$0.362849\pi$
$157$	−7.24281	+	12.5449i	−0.578039	+	1.00119i	−0.995704	+	0.0925924i	$0.970485\pi$
$158$		0			0
$159$	−0.263490	−	0.456378i	−0.0208961	−	0.0361931i
$160$		0			0
$161$	−2.59820	−	6.80169i	−0.204767	−	0.536048i
$162$		0			0
$163$	5.80977	+	10.0628i	0.455057	+	0.788181i	0.998691	−	0.0511407i	$-0.0162857\pi$
$163$	5.80977	+	10.0628i	0.455057	+	0.788181i	−0.543635	+	0.839322i	$0.682952\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	21.2998			1.64822			0.824112	−	0.566427i	$-0.191675\pi$
$167$	21.2998			1.64822			0.824112	+	0.566427i	$0.191675\pi$
$168$		0			0
$169$	−9.93057			−0.763890
$170$		0			0
$171$	3.48075	−	6.02884i	0.266180	−	0.461037i
$172$		0			0
$173$	−5.99109	−	10.3769i	−0.455494	−	0.788939i	0.543222	−	0.839589i	$-0.317204\pi$
$173$	−5.99109	−	10.3769i	−0.455494	−	0.788939i	−0.998716	+	0.0506497i	$0.983871\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	5.05327	+	8.75253i	0.379827	+	0.657880i
$178$		0			0
$179$	−10.2095	+	17.6834i	−0.763096	+	1.32172i	0.178151	+	0.984003i	$0.442988\pi$
$179$	−10.2095	+	17.6834i	−0.763096	+	1.32172i	−0.941247	+	0.337718i	$0.890345\pi$
$180$		0			0
$181$	19.8276			1.47377			0.736887	−	0.676016i	$-0.236295\pi$
$181$	19.8276			1.47377			0.736887	+	0.676016i	$0.236295\pi$
$182$		0			0
$183$	8.15408			0.602767
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−1.82011	−	3.15253i	−0.133100	−	0.230536i
$188$		0			0
$189$	2.61250	+	0.418148i	0.190031	+	0.0304158i
$190$		0			0
$191$	1.39976	+	2.42445i	0.101283	+	0.175427i	0.912213	−	0.409715i	$-0.134372\pi$
$191$	1.39976	+	2.42445i	0.101283	+	0.175427i	−0.810931	+	0.585142i	$0.801039\pi$
$192$		0			0
$193$	−10.5289	+	18.2366i	−0.757887	+	1.31270i	0.186040	+	0.982542i	$0.440435\pi$
$193$	−10.5289	+	18.2366i	−0.757887	+	1.31270i	−0.943926	+	0.330156i	$0.892899\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	7.18416			0.511850			0.255925	−	0.966697i	$-0.417620\pi$
$197$	7.18416			0.511850			0.255925	+	0.966697i	$0.417620\pi$
$198$		0			0
$199$	5.54771	−	9.60892i	0.393267	−	0.681159i	−0.599611	−	0.800291i	$-0.704678\pi$
$199$	5.54771	−	9.60892i	0.393267	−	0.681159i	0.992878	+	0.119133i	$0.0380115\pi$
$200$		0			0
$201$	−7.34901	−	12.7289i	−0.518359	−	0.897824i
$202$		0			0
$203$	8.46572	+	1.35499i	0.594177	+	0.0951020i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−1.37599	+	2.38328i	−0.0956378	+	0.165650i
$208$		0			0
$209$	4.07092			0.281591
$210$		0			0
$211$	12.2340			0.842226			0.421113	−	0.907008i	$-0.361640\pi$
$211$	12.2340			0.842226			0.421113	+	0.907008i	$0.361640\pi$
$212$		0			0
$213$	−6.67803	+	11.5667i	−0.457571	+	0.792536i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	4.17754	−	5.14166i	0.283590	−	0.349039i
$218$		0			0
$219$	3.37716	+	5.84942i	0.228207	+	0.395267i
$220$		0			0
$221$	−5.45303	+	9.44493i	−0.366810	+	0.635334i
$222$		0			0
$223$	−11.8074			−0.790684			−0.395342	−	0.918534i	$-0.629374\pi$
$223$	−11.8074			−0.790684			−0.395342	+	0.918534i	$0.629374\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	13.0984	−	22.6871i	0.869370	−	1.50579i	0.00672884	−	0.999977i	$-0.497858\pi$
$227$	13.0984	−	22.6871i	0.869370	−	1.50579i	0.862641	−	0.505816i	$-0.168809\pi$
$228$		0			0
$229$	−4.97067	−	8.60946i	−0.328471	−	0.568929i	0.653737	−	0.756721i	$-0.273200\pi$
$229$	−4.97067	−	8.60946i	−0.328471	−	0.568929i	−0.982209	+	0.187792i	$0.939867\pi$
$230$		0			0
$231$	0.552099	+	1.44531i	0.0363255	+	0.0950944i
$232$		0			0
$233$	−7.68241	−	13.3063i	−0.503292	−	0.871727i	−0.999993	−	0.00380503i	$-0.998789\pi$
$233$	−7.68241	−	13.3063i	−0.503292	−	0.871727i	0.496701	−	0.867922i	$-0.334545\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−8.09543			−0.525855
$238$		0			0
$239$	−15.2183			−0.984390			−0.492195	−	0.870485i	$-0.663805\pi$
$239$	−15.2183			−0.984390			−0.492195	+	0.870485i	$0.663805\pi$
$240$		0			0
$241$	−13.3730	+	23.1626i	−0.861428	+	1.49204i	0.00912311	+	0.999958i	$0.497096\pi$
$241$	−13.3730	+	23.1626i	−0.861428	+	1.49204i	−0.870551	+	0.492078i	$0.836237\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−6.09820	−	10.5624i	−0.388019	−	0.672069i
$248$		0			0
$249$	−2.86448	+	4.96142i	−0.181529	+	0.314417i
$250$		0			0
$251$	8.05310			0.508307			0.254154	−	0.967164i	$-0.418203\pi$
$251$	8.05310			0.508307			0.254154	+	0.967164i	$0.418203\pi$
$252$		0			0
$253$	−1.60929			−0.101175
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−7.98514	−	13.8307i	−0.498099	−	0.862733i	0.501898	−	0.864927i	$-0.332635\pi$
$257$	−7.98514	−	13.8307i	−0.498099	−	0.862733i	−0.999998	+	0.00219336i	$0.999302\pi$
$258$		0			0
$259$	−3.67098	−	9.61005i	−0.228104	−	0.597139i
$260$		0			0
$261$	−1.62023	−	2.80633i	−0.100290	−	0.173707i
$262$		0			0
$263$	−11.7454	+	20.3437i	−0.724253	+	1.25444i	0.235027	+	0.971989i	$0.424482\pi$
$263$	−11.7454	+	20.3437i	−0.724253	+	1.25444i	−0.959281	+	0.282455i	$0.908851\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−17.0038			−1.04062
$268$		0			0
$269$	−6.56831	+	11.3766i	−0.400477	+	0.693647i	−0.993783	−	0.111330i	$-0.964489\pi$
$269$	−6.56831	+	11.3766i	−0.400477	+	0.693647i	0.593306	+	0.804977i	$0.297822\pi$
$270$		0			0
$271$	−2.69275	−	4.66398i	−0.163573	−	0.283317i	0.772575	−	0.634924i	$-0.218969\pi$
$271$	−2.69275	−	4.66398i	−0.163573	−	0.283317i	−0.936148	+	0.351607i	$0.885635\pi$
$272$		0			0
$273$	2.92296	−	3.59754i	0.176906	−	0.217733i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−5.03285	+	8.71716i	−0.302395	+	0.523763i	−0.976678	−	0.214710i	$-0.931119\pi$
$277$	−5.03285	+	8.71716i	−0.302395	+	0.523763i	0.674283	+	0.738473i	$0.264453\pi$
$278$		0			0
$279$	−2.50396			−0.149908
$280$		0			0
$281$	−26.8822			−1.60366			−0.801828	−	0.597555i	$-0.796139\pi$
$281$	−26.8822			−1.60366			−0.801828	+	0.597555i	$0.796139\pi$
$282$		0			0
$283$	5.92865	−	10.2687i	0.352422	−	0.610413i	−0.634251	−	0.773127i	$-0.718692\pi$
$283$	5.92865	−	10.2687i	0.352422	−	0.610413i	0.986673	+	0.162714i	$0.0520249\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	11.9777	+	1.91711i	0.707023	+	0.113164i
$288$		0			0
$289$	−10.8753	−	18.8366i	−0.639724	−	1.10803i
$290$		0			0
$291$	5.55662	−	9.62435i	0.325735	−	0.564189i
$292$		0			0
$293$	−16.3879			−0.957388			−0.478694	−	0.877982i	$-0.658890\pi$
$293$	−16.3879			−0.957388			−0.478694	+	0.877982i	$0.658890\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	0.292387	−	0.506430i	0.0169660	−	0.0293860i
$298$		0			0
$299$	2.41070	+	4.17546i	0.139415	+	0.241473i
$300$		0			0
$301$	−1.97067	−	0.315420i	−0.113588	−	0.0181805i
$302$		0			0
$303$	−8.67803	−	15.0308i	−0.498540	−	0.863496i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−20.0141			−1.14226			−0.571132	−	0.820858i	$-0.693496\pi$
$307$	−20.0141			−1.14226			−0.571132	+	0.820858i	$0.693496\pi$
$308$		0			0
$309$	13.3613			0.760096
$310$		0			0
$311$	14.3183	−	24.7999i	0.811914	−	1.40628i	−0.0996095	−	0.995027i	$-0.531759\pi$
$311$	14.3183	−	24.7999i	0.811914	−	1.40628i	0.911523	−	0.411249i	$-0.134907\pi$
$312$		0			0
$313$	−13.6806	−	23.6956i	−0.773275	−	1.33935i	−0.935759	−	0.352641i	$-0.885284\pi$
$313$	−13.6806	−	23.6956i	−0.773275	−	1.33935i	0.162484	−	0.986711i	$-0.448049\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	4.00830	+	6.94258i	0.225129	+	0.389934i	0.956358	−	0.292197i	$-0.0943864\pi$
$317$	4.00830	+	6.94258i	0.225129	+	0.389934i	−0.731229	+	0.682132i	$0.761053\pi$
$318$		0			0
$319$	0.947472	−	1.64107i	0.0530482	−	0.0918822i
$320$		0			0
$321$	2.12722			0.118730
$322$		0			0
$323$	43.3354			2.41125
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−1.14400	−	1.98147i	−0.0632634	−	0.109575i
$328$		0			0
$329$	1.37389	+	3.59664i	0.0757452	+	0.198289i
$330$		0			0
$331$	−4.98849	−	8.64032i	−0.274192	−	0.474915i	0.695739	−	0.718295i	$-0.255077\pi$
$331$	−4.98849	−	8.64032i	−0.274192	−	0.474915i	−0.969931	+	0.243380i	$0.921744\pi$
$332$		0			0
$333$	−1.94412	+	3.36732i	−0.106537	+	0.184528i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.936640			0.0510220			0.0255110	−	0.999675i	$-0.491879\pi$
$337$	0.936640			0.0510220			0.0255110	+	0.999675i	$0.491879\pi$
$338$		0			0
$339$	−5.88825	+	10.1987i	−0.319806	+	0.553920i
$340$		0			0
$341$	−0.732125	−	1.26808i	−0.0396468	−	0.0686703i
$342$		0			0
$343$	16.4603	+	8.48866i	0.888775	+	0.458345i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	0.0887310	−	0.153687i	0.00476333	−	0.00825033i	−0.863634	−	0.504119i	$-0.831817\pi$
$347$	0.0887310	−	0.153687i	0.00476333	−	0.00825033i	0.868397	+	0.495869i	$0.165150\pi$
$348$		0			0
$349$	−31.6891			−1.69628			−0.848139	−	0.529774i	$-0.822277\pi$
$349$	−31.6891			−1.69628			−0.848139	+	0.529774i	$0.822277\pi$
$350$		0			0
$351$	−1.75198			−0.0935137
$352$		0			0
$353$	12.2323	−	21.1870i	0.651060	−	1.12767i	−0.331806	−	0.943348i	$-0.607658\pi$
$353$	12.2323	−	21.1870i	0.651060	−	1.12767i	0.982866	−	0.184321i	$-0.0590086\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	5.87716	+	15.3855i	0.311052	+	0.814286i
$358$		0			0
$359$	−8.01243	−	13.8779i	−0.422880	−	0.732450i	0.573340	−	0.819318i	$-0.305648\pi$
$359$	−8.01243	−	13.8779i	−0.422880	−	0.732450i	−0.996220	+	0.0868679i	$0.972314\pi$
$360$		0			0
$361$	−14.7313	+	25.5154i	−0.775332	+	1.34291i
$362$		0			0
$363$	−10.6580			−0.559402
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−7.67029	+	13.2853i	−0.400386	+	0.693489i	−0.993772	−	0.111429i	$-0.964457\pi$
$367$	−7.67029	+	13.2853i	−0.400386	+	0.693489i	0.593386	+	0.804918i	$0.297791\pi$
$368$		0			0
$369$	−2.29239	−	3.97053i	−0.119337	−	0.206698i
$370$		0			0
$371$	−0.879200	+	1.08211i	−0.0456458	+	0.0561803i
$372$		0			0
$373$	1.82054	+	3.15327i	0.0942640	+	0.163270i	0.909301	−	0.416139i	$-0.136617\pi$
$373$	1.82054	+	3.15327i	0.0942640	+	0.163270i	−0.815037	+	0.579409i	$0.803284\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−5.67723			−0.292392
$378$		0			0
$379$	4.08959			0.210068			0.105034	−	0.994469i	$-0.466505\pi$
$379$	4.08959			0.210068			0.105034	+	0.994469i	$0.466505\pi$
$380$		0			0
$381$	−7.63031	+	13.2161i	−0.390913	+	0.677081i
$382$		0			0
$383$	−3.96002	−	6.85895i	−0.202348	−	0.350476i	0.746937	−	0.664895i	$-0.231524\pi$
$383$	−3.96002	−	6.85895i	−0.202348	−	0.350476i	−0.949284	+	0.314419i	$0.898190\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	0.377162	+	0.653265i	0.0191722	+	0.0332073i
$388$		0			0
$389$	11.3028	−	19.5770i	0.573074	−	0.992593i	−0.423174	−	0.906048i	$-0.639084\pi$
$389$	11.3028	−	19.5770i	0.573074	−	0.992593i	0.996248	−	0.0865447i	$-0.0275825\pi$
$390$		0			0
$391$	−17.1311			−0.866355
$392$		0			0
$393$	8.01781			0.404445
$394$		0			0
$395$		0			0
$396$		0			0
$397$	11.1484	+	19.3097i	0.559524	+	0.969125i	0.997536	+	0.0701554i	$0.0223495\pi$
$397$	11.1484	+	19.3097i	0.559524	+	0.969125i	−0.438012	+	0.898969i	$0.644317\pi$
$398$		0			0
$399$	−18.1869	−	2.91094i	−0.910486	−	0.145729i
$400$		0			0
$401$	3.52177	+	6.09989i	0.175869	+	0.304614i	0.940462	−	0.339900i	$-0.110393\pi$
$401$	3.52177	+	6.09989i	0.175869	+	0.304614i	−0.764593	+	0.644514i	$0.777060\pi$
$402$		0			0
$403$	−2.19344	+	3.79915i	−0.109263	+	0.189249i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−2.27375			−0.112706
$408$		0			0
$409$	−4.62957	+	8.01865i	−0.228917	+	0.396497i	−0.957488	−	0.288475i	$-0.906852\pi$
$409$	−4.62957	+	8.01865i	−0.228917	+	0.396497i	0.728570	+	0.684971i	$0.240185\pi$
$410$		0			0
$411$	7.34641	+	12.7243i	0.362371	+	0.627646i
$412$		0			0
$413$	16.8615	−	20.7529i	0.829701	−	1.02119i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−9.55402	+	16.5480i	−0.467862	+	0.810361i
$418$		0			0
$419$	−11.9183			−0.582248			−0.291124	−	0.956685i	$-0.594029\pi$
$419$	−11.9183			−0.582248			−0.291124	+	0.956685i	$0.594029\pi$
$420$		0			0
$421$	−5.68576			−0.277107			−0.138553	−	0.990355i	$-0.544245\pi$
$421$	−5.68576			−0.277107			−0.138553	+	0.990355i	$0.544245\pi$
$422$		0			0
$423$	0.727603	−	1.26025i	0.0353773	−	0.0612752i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−7.69845	−	20.1533i	−0.372554	−	0.975289i
$428$		0			0
$429$	−0.512256	−	0.887254i	−0.0247320	−	0.0428370i
$430$		0			0
$431$	6.85866	−	11.8796i	0.330370	−	0.572218i	−0.652214	−	0.758035i	$-0.726160\pi$
$431$	6.85866	−	11.8796i	0.330370	−	0.572218i	0.982584	+	0.185817i	$0.0594931\pi$
$432$		0			0
$433$	22.8294			1.09711			0.548556	−	0.836114i	$-0.315178\pi$
$433$	22.8294			1.09711			0.548556	+	0.836114i	$0.315178\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	9.57896	−	16.5912i	0.458224	−	0.793667i
$438$		0			0
$439$	−19.6966	−	34.1155i	−0.940067	−	1.62824i	−0.765340	−	0.643627i	$-0.777429\pi$
$439$	−19.6966	−	34.1155i	−0.940067	−	1.62824i	−0.174727	−	0.984617i	$-0.555904\pi$
$440$		0			0
$441$	−1.43304	−	6.85174i	−0.0682400	−	0.326274i
$442$		0			0
$443$	−2.58342	−	4.47462i	−0.122742	−	0.212596i	0.798106	−	0.602517i	$-0.205835\pi$
$443$	−2.58342	−	4.47462i	−0.122742	−	0.212596i	−0.920848	+	0.389921i	$0.872502\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−1.82524			−0.0863309
$448$		0			0
$449$	−36.7384			−1.73379			−0.866895	−	0.498491i	$-0.833888\pi$
$449$	−36.7384			−1.73379			−0.866895	+	0.498491i	$0.833888\pi$
$450$		0			0
$451$	1.34053	−	2.32187i	0.0631231	−	0.109332i
$452$		0			0
$453$	2.41379	+	4.18081i	0.113410	+	0.196432i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.597031	−	1.03409i	−0.0279280	−	0.0483726i	0.851724	−	0.523991i	$-0.175558\pi$
$457$	−0.597031	−	1.03409i	−0.0279280	−	0.0483726i	−0.879652	+	0.475619i	$0.842224\pi$
$458$		0			0
$459$	3.11250	−	5.39101i	0.145279	−	0.251631i
$460$		0			0
$461$	−14.5340			−0.676917			−0.338459	−	0.940981i	$-0.609906\pi$
$461$	−14.5340			−0.676917			−0.338459	+	0.940981i	$0.609906\pi$
$462$		0			0
$463$	−32.2762			−1.50000			−0.750001	−	0.661436i	$-0.769947\pi$
$463$	−32.2762			−1.50000			−0.750001	+	0.661436i	$0.769947\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−6.15174	−	10.6551i	−0.284668	−	0.493060i	0.687860	−	0.725843i	$-0.258550\pi$
$467$	−6.15174	−	10.6551i	−0.284668	−	0.493060i	−0.972529	+	0.232783i	$0.925217\pi$
$468$		0			0
$469$	−24.5218	+	30.1812i	−1.13231	+	1.39364i
$470$		0			0
$471$	−7.24281	−	12.5449i	−0.333731	−	0.578039i
$472$		0			0
$473$	−0.220555	+	0.382013i	−0.0101411	+	0.0175650i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.526980			0.0241287
$478$		0			0
$479$	11.5196	−	19.9525i	0.526342	−	0.911651i	−0.473187	−	0.880962i	$-0.656896\pi$
$479$	11.5196	−	19.9525i	0.526342	−	0.911651i	0.999529	−	0.0306893i	$-0.00977024\pi$
$480$		0			0
$481$	3.40606	+	5.89947i	0.155303	+	0.268993i
$482$		0			0
$483$	7.18954	+	1.15073i	0.327135	+	0.0523602i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−8.80507	+	15.2508i	−0.398996	+	0.691081i	−0.993602	−	0.112936i	$-0.963975\pi$
$487$	−8.80507	+	15.2508i	−0.398996	+	0.691081i	0.594606	+	0.804017i	$0.297308\pi$
$488$		0			0
$489$	−11.6195			−0.525454
$490$		0			0
$491$	−18.7403			−0.845740			−0.422870	−	0.906190i	$-0.638977\pi$
$491$	−18.7403			−0.845740			−0.422870	+	0.906190i	$0.638977\pi$
$492$		0			0
$493$	10.0859	−	17.4694i	0.454248	−	0.786781i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	34.8927	+	5.58481i	1.56515	+	0.250513i
$498$		0			0
$499$	14.0063	+	24.2596i	0.627008	+	1.08601i	0.988149	+	0.153499i	$0.0490541\pi$
$499$	14.0063	+	24.2596i	0.627008	+	1.08601i	−0.361141	+	0.932511i	$0.617613\pi$
$500$		0			0
$501$	−10.6499	+	18.4461i	−0.475801	+	0.824112i
$502$		0			0
$503$	−16.7178			−0.745412			−0.372706	−	0.927950i	$-0.621570\pi$
$503$	−16.7178			−0.745412			−0.372706	+	0.927950i	$0.621570\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	4.96529	−	8.60013i	0.220516	−	0.381945i
$508$		0			0
$509$	−0.131059	−	0.227000i	−0.00580907	−	0.0100616i	0.863106	−	0.505022i	$-0.168516\pi$
$509$	−0.131059	−	0.227000i	−0.00580907	−	0.0100616i	−0.868915	+	0.494961i	$0.835182\pi$
$510$		0			0
$511$	11.2688	−	13.8694i	0.498500	−	0.613548i
$512$		0			0
$513$	3.48075	+	6.02884i	0.153679	+	0.266180i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	0.850968			0.0374255
$518$		0			0
$519$	11.9822			0.525960
$520$		0			0
$521$	19.1710	−	33.2052i	0.839898	−	1.45475i	−0.0500804	−	0.998745i	$-0.515948\pi$
$521$	19.1710	−	33.2052i	0.839898	−	1.45475i	0.889979	−	0.456002i	$-0.150719\pi$
$522$		0			0
$523$	−1.79603	−	3.11081i	−0.0785348	−	0.136026i	0.824083	−	0.566469i	$-0.191691\pi$
$523$	−1.79603	−	3.11081i	−0.0785348	−	0.136026i	−0.902618	+	0.430443i	$0.858358\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−7.79356	−	13.4988i	−0.339493	−	0.588019i
$528$		0			0
$529$	7.71331	−	13.3598i	0.335361	−	0.580863i
$530$		0			0
$531$	−10.1065			−0.438587
$532$		0			0
$533$	−8.03242			−0.347923
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−10.2095	−	17.6834i	−0.440574	−	0.763096i
$538$		0			0
$539$	3.05093	−	2.72910i	0.131413	−	0.117551i
$540$		0			0
$541$	−8.48602	−	14.6982i	−0.364843	−	0.631926i	0.623908	−	0.781498i	$-0.285544\pi$
$541$	−8.48602	−	14.6982i	−0.364843	−	0.631926i	−0.988751	+	0.149572i	$0.952211\pi$
$542$		0			0
$543$	−9.91379	+	17.1712i	−0.425442	+	0.736887i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	29.0926			1.24391			0.621954	−	0.783054i	$-0.286339\pi$
$547$	29.0926			1.24391			0.621954	+	0.783054i	$0.286339\pi$
$548$		0			0
$549$	−4.07704	+	7.06164i	−0.174004	+	0.301384i
$550$		0			0
$551$	11.2793	+	19.5363i	0.480513	+	0.832273i
$552$		0			0
$553$	7.64308	+	20.0084i	0.325017	+	0.850843i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−0.705437	+	1.22185i	−0.0298903	+	0.0517716i	−0.880584	−	0.473891i	$-0.842849\pi$
$557$	−0.705437	+	1.22185i	−0.0298903	+	0.0517716i	0.850693	+	0.525662i	$0.176182\pi$
$558$		0			0
$559$	1.32156			0.0558961
$560$		0			0
$561$	3.64022			0.153690
$562$		0			0
$563$	−4.39455	+	7.61158i	−0.185208	+	0.320790i	−0.943647	−	0.330955i	$-0.892629\pi$
$563$	−4.39455	+	7.61158i	−0.185208	+	0.320790i	0.758439	+	0.651745i	$0.225963\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−1.66838	+	2.05342i	−0.0700652	+	0.0862354i
$568$		0			0
$569$	−15.0534	−	26.0733i	−0.631072	−	1.09305i	−0.987333	−	0.158662i	$-0.949282\pi$
$569$	−15.0534	−	26.0733i	−0.631072	−	1.09305i	0.356261	−	0.934386i	$-0.384051\pi$
$570$		0			0
$571$	13.0025	−	22.5210i	0.544139	−	0.942476i	−0.454522	−	0.890736i	$-0.650190\pi$
$571$	13.0025	−	22.5210i	0.544139	−	0.942476i	0.998661	−	0.0517403i	$-0.0164768\pi$
$572$		0			0
$573$	−2.79951			−0.116951
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−12.6370	+	21.8879i	−0.526086	+	0.911207i	0.473452	+	0.880819i	$0.343008\pi$
$577$	−12.6370	+	21.8879i	−0.526086	+	0.911207i	−0.999538	+	0.0303878i	$0.990326\pi$
$578$		0			0
$579$	−10.5289	−	18.2366i	−0.437566	−	0.757887i
$580$		0			0
$581$	14.9669	+	2.39555i	0.620931	+	0.0993842i
$582$		0			0
$583$	0.154082	+	0.266878i	0.00638143	+	0.0110530i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	5.75719			0.237625			0.118812	−	0.992917i	$-0.462091\pi$
$587$	5.75719			0.237625			0.118812	+	0.992917i	$0.462091\pi$
$588$		0			0
$589$	17.4313			0.718245
$590$		0			0
$591$	−3.59208	+	6.22167i	−0.147758	+	0.255925i
$592$		0			0
$593$	−7.98514	−	13.8307i	−0.327910	−	0.567957i	0.654187	−	0.756333i	$-0.273011\pi$
$593$	−7.98514	−	13.8307i	−0.327910	−	0.567957i	−0.982097	+	0.188376i	$0.939678\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	5.54771	+	9.60892i	0.227053	+	0.393267i
$598$		0			0
$599$	−13.0976	+	22.6858i	−0.535155	+	0.926916i	0.464001	+	0.885835i	$0.346413\pi$
$599$	−13.0976	+	22.6858i	−0.535155	+	0.926916i	−0.999156	+	0.0410809i	$0.986920\pi$
$600$		0			0
$601$	−21.8615			−0.891749			−0.445875	−	0.895095i	$-0.647107\pi$
$601$	−21.8615			−0.891749			−0.445875	+	0.895095i	$0.647107\pi$
$602$		0			0
$603$	14.6980			0.598550
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−4.30026	−	7.44827i	−0.174542	−	0.302316i	0.765461	−	0.643483i	$-0.222511\pi$
$607$	−4.30026	−	7.44827i	−0.174542	−	0.302316i	−0.940003	+	0.341167i	$0.889178\pi$
$608$		0			0
$609$	−5.40632	+	6.65403i	−0.219075	+	0.269635i
$610$		0			0
$611$	−1.27474	−	2.20792i	−0.0515706	−	0.0893229i
$612$		0			0
$613$	−22.1251	+	38.3217i	−0.893623	+	1.54780i	−0.0581239	+	0.998309i	$0.518512\pi$
$613$	−22.1251	+	38.3217i	−0.893623	+	1.54780i	−0.835499	+	0.549491i	$0.814821\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	32.3683			1.30310			0.651550	−	0.758606i	$-0.274119\pi$
$617$	32.3683			1.30310			0.651550	+	0.758606i	$0.274119\pi$
$618$		0			0
$619$	−21.0233	+	36.4134i	−0.844996	+	1.46358i	0.0406284	+	0.999174i	$0.487064\pi$
$619$	−21.0233	+	36.4134i	−0.844996	+	1.46358i	−0.885625	+	0.464402i	$0.846269\pi$
$620$		0			0
$621$	−1.37599	−	2.38328i	−0.0552165	−	0.0956378i
$622$		0			0
$623$	16.0537	+	42.0261i	0.643178	+	1.68374i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−2.03546	+	3.52552i	−0.0812884	+	0.140796i
$628$		0			0
$629$	−24.2043			−0.965090
$630$		0			0
$631$	3.74086			0.148921			0.0744607	−	0.997224i	$-0.476276\pi$
$631$	3.74086			0.148921			0.0744607	+	0.997224i	$0.476276\pi$
$632$		0			0
$633$	−6.11702	+	10.5950i	−0.243130	+	0.421113i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−11.6512	−	3.82776i	−0.461637	−	0.151661i
$638$		0			0
$639$	−6.67803	−	11.5667i	−0.264179	−	0.457571i
$640$		0			0
$641$	−17.4004	+	30.1384i	−0.687275	+	1.19040i	0.285441	+	0.958396i	$0.407860\pi$
$641$	−17.4004	+	30.1384i	−0.687275	+	1.19040i	−0.972716	+	0.231999i	$0.925473\pi$
$642$		0			0
$643$	−22.9864			−0.906494			−0.453247	−	0.891385i	$-0.649734\pi$
$643$	−22.9864			−0.906494			−0.453247	+	0.891385i	$0.649734\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−3.31312	+	5.73850i	−0.130252	+	0.225604i	−0.923774	−	0.382939i	$-0.874912\pi$
$647$	−3.31312	+	5.73850i	−0.130252	+	0.225604i	0.793521	+	0.608542i	$0.208245\pi$
$648$		0			0
$649$	−2.95503	−	5.11826i	−0.115995	−	0.200909i
$650$		0			0
$651$	2.36404	+	6.18869i	0.0926541	+	0.242554i
$652$		0			0
$653$	5.24207	+	9.07953i	0.205138	+	0.355309i	0.950177	−	0.311712i	$-0.100902\pi$
$653$	5.24207	+	9.07953i	0.205138	+	0.355309i	−0.745039	+	0.667021i	$0.767569\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−6.75432			−0.263511
$658$		0			0
$659$	13.2344			0.515539			0.257770	−	0.966206i	$-0.417012\pi$
$659$	13.2344			0.515539			0.257770	+	0.966206i	$0.417012\pi$
$660$		0			0
$661$	6.75450	−	11.6991i	0.262720	−	0.455044i	−0.704244	−	0.709958i	$-0.748714\pi$
$661$	6.75450	−	11.6991i	0.262720	−	0.455044i	0.966964	+	0.254914i	$0.0820472\pi$
$662$		0			0
$663$	−5.45303	−	9.44493i	−0.211778	−	0.366810i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−4.45885	−	7.72295i	−0.172647	−	0.299034i
$668$		0			0
$669$	5.90371	−	10.2255i	0.228251	−	0.395342i
$670$		0			0
$671$	−4.76830			−0.184078
$672$		0			0
$673$	14.8059			0.570727			0.285363	−	0.958419i	$-0.407886\pi$
$673$	14.8059			0.570727			0.285363	+	0.958419i	$0.407886\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−21.4531	−	37.1578i	−0.824509	−	1.42809i	−0.902294	−	0.431122i	$-0.858118\pi$
$677$	−21.4531	−	37.1578i	−0.824509	−	1.42809i	0.0777847	−	0.996970i	$-0.475215\pi$
$678$		0			0
$679$	−29.0333	−	4.64698i	−1.11420	−	0.178335i
$680$		0			0
$681$	13.0984	+	22.6871i	0.501931	+	0.869370i
$682$		0			0
$683$	−23.8824	+	41.3656i	−0.913836	+	1.58281i	−0.105239	+	0.994447i	$0.533561\pi$
$683$	−23.8824	+	41.3656i	−0.913836	+	1.58281i	−0.808597	+	0.588363i	$0.799773\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	9.94135			0.379286
$688$		0			0
$689$	0.461628	−	0.799564i	0.0175866	−	0.0304609i
$690$		0			0
$691$	10.4948	+	18.1775i	0.399241	+	0.691505i	0.993632	−	0.112671i	$-0.0359405\pi$
$691$	10.4948	+	18.1775i	0.399241	+	0.691505i	−0.594392	+	0.804176i	$0.702607\pi$
$692$		0			0
$693$	−1.52772	−	0.244523i	−0.0580334	−	0.00928864i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	14.2701	−	24.7166i	0.540519	−	0.936206i
$698$		0			0
$699$	15.3648			0.581151
$700$		0			0
$701$	−33.1194			−1.25090			−0.625452	−	0.780263i	$-0.715085\pi$
$701$	−33.1194			−1.25090			−0.625452	+	0.780263i	$0.715085\pi$
$702$		0			0
$703$	13.5340	−	23.4416i	0.510446	−	0.884118i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−28.9564	+	35.6392i	−1.08902	+	1.34035i
$708$		0			0
$709$	16.7366	+	28.9886i	0.628555	+	1.08869i	0.987842	+	0.155462i	$0.0496866\pi$
$709$	16.7366	+	28.9886i	0.628555	+	1.08869i	−0.359287	+	0.933227i	$0.616980\pi$
$710$		0			0
$711$	4.04771	−	7.01085i	0.151801	−	0.262927i
$712$		0			0
$713$	−6.89083			−0.258064
$714$		0			0
$715$		0			0
$716$		0			0
$717$	7.60915	−	13.1794i	0.284169	−	0.492195i
$718$		0			0
$719$	−7.43588	−	12.8793i	−0.277312	−	0.480318i	0.693404	−	0.720549i	$-0.256110\pi$
$719$	−7.43588	−	12.8793i	−0.277312	−	0.480318i	−0.970716	+	0.240231i	$0.922777\pi$
$720$		0			0
$721$	−12.6147	−	33.0232i	−0.469795	−	1.22985i
$722$		0			0
$723$	−13.3730	−	23.1626i	−0.497346	−	0.861428i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	11.9682			0.443876			0.221938	−	0.975061i	$-0.428762\pi$
$727$	11.9682			0.443876			0.221938	+	0.975061i	$0.428762\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−2.34784	+	4.06657i	−0.0868378	+	0.150408i
$732$		0			0
$733$	−12.8474	−	22.2524i	−0.474530	−	0.821909i	0.525045	−	0.851074i	$-0.324048\pi$
$733$	−12.8474	−	22.2524i	−0.474530	−	0.821909i	−0.999575	+	0.0291651i	$0.990715\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	4.29752	+	7.44352i	0.158301	+	0.274185i
$738$		0			0
$739$	2.38298	−	4.12744i	0.0876593	−	0.151830i	−0.818862	−	0.573990i	$-0.805395\pi$
$739$	2.38298	−	4.12744i	0.0876593	−	0.151830i	0.906521	+	0.422160i	$0.138728\pi$
$740$		0			0
$741$	12.1964			0.448046
$742$		0			0
$743$	27.9703			1.02613			0.513065	−	0.858350i	$-0.328510\pi$
$743$	27.9703			1.02613			0.513065	+	0.858350i	$0.328510\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−2.86448	−	4.96142i	−0.104806	−	0.181529i
$748$		0			0
$749$	−2.00836	−	5.25757i	−0.0733838	−	0.192107i
$750$		0			0
$751$	−10.8613	−	18.8123i	−0.396333	−	0.686469i	0.596937	−	0.802288i	$-0.296384\pi$
$751$	−10.8613	−	18.8123i	−0.396333	−	0.686469i	−0.993270	+	0.115819i	$0.963051\pi$
$752$		0			0
$753$	−4.02655	+	6.97419i	−0.146736	+	0.254154i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	10.2574			0.372812			0.186406	−	0.982473i	$-0.440316\pi$
$757$	10.2574			0.372812			0.186406	+	0.982473i	$0.440316\pi$
$758$		0			0
$759$	0.804644	−	1.39368i	0.0292067	−	0.0505875i
$760$		0			0
$761$	15.1717	+	26.2782i	0.549975	+	0.952584i	0.998276	+	0.0587013i	$0.0186960\pi$
$761$	15.1717	+	26.2782i	0.549975	+	0.952584i	−0.448301	+	0.893883i	$0.647971\pi$
$762$		0			0
$763$	−3.81725	+	4.69822i	−0.138194	+	0.170087i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−8.85322	+	15.3342i	−0.319671	+	0.553687i
$768$		0			0
$769$	33.8125			1.21931			0.609655	−	0.792667i	$-0.291308\pi$
$769$	33.8125			1.21931			0.609655	+	0.792667i	$0.291308\pi$
$770$		0			0
$771$	15.9703			0.575156
$772$		0			0
$773$	−7.52017	+	13.0253i	−0.270482	+	0.468488i	−0.968985	−	0.247119i	$-0.920516\pi$
$773$	−7.52017	+	13.0253i	−0.270482	+	0.468488i	0.698504	+	0.715607i	$0.253850\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	10.1580	+	1.62586i	0.364418	+	0.0583275i
$778$		0			0
$779$	15.9585	+	27.6409i	0.571772	+	0.990338i
$780$		0			0
$781$	3.90514	−	6.76391i	0.139737	−	0.242032i
$782$		0			0
$783$	3.24047			0.115805
$784$		0			0
$785$		0			0
$786$		0			0
$787$	0.911269	−	1.57836i	0.0324832	−	0.0562626i	−0.849327	−	0.527867i	$-0.822992\pi$
$787$	0.911269	−	1.57836i	0.0324832	−	0.0562626i	0.881810	+	0.471605i	$0.156325\pi$
$788$		0			0
$789$	−11.7454	−	20.3437i	−0.418148	−	0.724253i
$790$		0			0
$791$	30.7661	+	4.92432i	1.09392	+	0.175089i
$792$		0			0
$793$	7.14289	+	12.3718i	0.253651	+	0.439337i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−26.7990			−0.949270			−0.474635	−	0.880183i	$-0.657420\pi$
$797$	−26.7990			−0.949270			−0.474635	+	0.880183i	$0.657420\pi$
$798$		0			0
$799$	9.05865			0.320472
$800$		0			0
$801$	8.50192	−	14.7258i	0.300401	−	0.520309i
$802$		0			0
$803$	−1.97488	−	3.42059i	−0.0696920	−	0.120710i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−6.56831	−	11.3766i	−0.231216	−	0.400477i
$808$		0			0
$809$	1.01125	−	1.75154i	0.0355538	−	0.0615810i	−0.847701	−	0.530474i	$-0.822014\pi$
$809$	1.01125	−	1.75154i	0.0355538	−	0.0615810i	0.883255	+	0.468893i	$0.155347\pi$
$810$		0			0
$811$	−0.357073			−0.0125385			−0.00626927	−	0.999980i	$-0.501996\pi$
$811$	−0.357073			−0.0125385			−0.00626927	+	0.999980i	$0.501996\pi$
$812$		0			0
$813$	5.38550			0.188878
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−2.62562	−	4.54771i	−0.0918588	−	0.159104i
$818$		0			0
$819$	1.65408	+	4.33013i	0.0577983	+	0.151307i
$820$		0			0
$821$	−2.37963	−	4.12164i	−0.0830496	−	0.143846i	0.821509	−	0.570196i	$-0.193133\pi$
$821$	−2.37963	−	4.12164i	−0.0830496	−	0.143846i	−0.904558	+	0.426350i	$0.859799\pi$
$822$		0			0
$823$	11.3679	−	19.6898i	0.396260	−	0.686342i	−0.597002	−	0.802240i	$-0.703641\pi$
$823$	11.3679	−	19.6898i	0.396260	−	0.686342i	0.993261	+	0.115898i	$0.0369747\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−6.46781			−0.224908			−0.112454	−	0.993657i	$-0.535871\pi$
$827$	−6.46781			−0.224908			−0.112454	+	0.993657i	$0.535871\pi$
$828$		0			0
$829$	−1.18015	+	2.04407i	−0.0409882	+	0.0709936i	−0.885792	−	0.464083i	$-0.846384\pi$
$829$	−1.18015	+	2.04407i	−0.0409882	+	0.0709936i	0.844804	+	0.535077i	$0.179717\pi$
$830$		0			0
$831$	−5.03285	−	8.71716i	−0.174588	−	0.302395i
$832$		0			0
$833$	32.4775	−	29.0516i	1.12528	−	1.00658i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	1.25198	−	2.16849i	0.0432747	−	0.0749540i
$838$		0			0
$839$	31.3590			1.08263			0.541317	−	0.840819i	$-0.317926\pi$
$839$	31.3590			1.08263			0.541317	+	0.840819i	$0.317926\pi$
$840$		0			0
$841$	−18.4994			−0.637910
$842$		0			0
$843$	13.4411	−	23.2806i	0.462936	−	0.801828i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	10.0625	+	26.3420i	0.345751	+	0.905123i
$848$		0			0
$849$	5.92865	+	10.2687i	0.203471	+	0.352422i
$850$		0			0
$851$	−5.35018	+	9.26679i	−0.183402	+	0.317661i
$852$		0			0
$853$	−17.4278			−0.596718			−0.298359	−	0.954454i	$-0.596439\pi$
$853$	−17.4278			−0.596718			−0.298359	+	0.954454i	$0.596439\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−2.35161	+	4.07311i	−0.0803296	+	0.139135i	−0.903392	−	0.428817i	$-0.858931\pi$
$857$	−2.35161	+	4.07311i	−0.0803296	+	0.139135i	0.823062	+	0.567952i	$0.192264\pi$
$858$		0			0
$859$	−3.99708	−	6.92315i	−0.136379	−	0.236215i	0.789745	−	0.613436i	$-0.210213\pi$
$859$	−3.99708	−	6.92315i	−0.136379	−	0.236215i	−0.926123	+	0.377221i	$0.876880\pi$
$860$		0			0
$861$	−7.64913	+	9.41445i	−0.260682	+	0.320844i
$862$		0			0
$863$	−10.3547	−	17.9349i	−0.352478	−	0.610510i	0.634205	−	0.773165i	$-0.281328\pi$
$863$	−10.3547	−	17.9349i	−0.352478	−	0.610510i	−0.986683	+	0.162655i	$0.947994\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	21.7506			0.738689
$868$		0			0
$869$	4.73400			0.160590
$870$		0			0
$871$	12.8753	−	22.3007i	0.436263	−	0.755630i
$872$		0			0
$873$	5.55662	+	9.62435i	0.188063	+	0.325735i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	8.15174	+	14.1192i	0.275265	+	0.476772i	0.970202	−	0.242298i	$-0.0779012\pi$
$877$	8.15174	+	14.1192i	0.275265	+	0.476772i	−0.694937	+	0.719070i	$0.744568\pi$
$878$		0			0
$879$	8.19393	−	14.1923i	0.276374	−	0.478694i
$880$		0			0
$881$	8.44801			0.284621			0.142310	−	0.989822i	$-0.454547\pi$
$881$	8.44801			0.284621			0.142310	+	0.989822i	$0.454547\pi$
$882$		0			0
$883$	40.6622			1.36839			0.684197	−	0.729298i	$-0.260153\pi$
$883$	40.6622			1.36839			0.684197	+	0.729298i	$0.260153\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	10.8781	+	18.8414i	0.365250	+	0.632632i	0.988816	−	0.149139i	$-0.0476501\pi$
$887$	10.8781	+	18.8414i	0.365250	+	0.632632i	−0.623566	+	0.781771i	$0.714317\pi$
$888$		0			0
$889$	39.8684	+	6.38120i	1.33714	+	0.214019i
$890$		0			0
$891$	0.292387	+	0.506430i	0.00979535	+	0.0169660i
$892$		0			0
$893$	−5.06521	+	8.77321i	−0.169501	+	0.293584i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−4.82140			−0.160982
$898$		0			0
$899$	4.05699	−	7.02692i	0.135308	−	0.234361i
$900$		0			0
$901$	1.64022	+	2.84095i	0.0546438	+	0.0946458i
$902$		0			0
$903$	1.25850	−	1.54894i	0.0418802	−	0.0515456i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−12.5598	+	21.7543i	−0.417042	+	0.722339i	−0.995640	−	0.0932742i	$-0.970267\pi$
$907$	−12.5598	+	21.7543i	−0.417042	+	0.722339i	0.578598	+	0.815613i	$0.303600\pi$
$908$		0			0
$909$	17.3561			0.575664
$910$		0			0
$911$	−9.33526			−0.309291			−0.154646	−	0.987970i	$-0.549424\pi$
$911$	−9.33526			−0.309291			−0.154646	+	0.987970i	$0.549424\pi$
$912$		0			0
$913$	1.67507	−	2.90131i	0.0554369	−	0.0960195i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−7.56980	−	19.8165i	−0.249977	−	0.654400i
$918$		0			0
$919$	−10.5657	−	18.3003i	−0.348531	−	0.603673i	0.637458	−	0.770485i	$-0.279986\pi$
$919$	−10.5657	−	18.3003i	−0.348531	−	0.603673i	−0.985989	+	0.166812i	$0.946653\pi$
$920$		0			0
$921$	10.0070	−	17.3327i	0.329743	−	0.571132i
$922$		0			0
$923$	−23.3995			−0.770205
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−6.68063	+	11.5712i	−0.219421	+	0.380048i
$928$		0			0
$929$	28.4611	+	49.2960i	0.933778	+	1.61735i	0.776799	+	0.629748i	$0.216842\pi$
$929$	28.4611	+	49.2960i	0.933778	+	1.61735i	0.156979	+	0.987602i	$0.449825\pi$
$930$		0			0
$931$	9.97612	+	47.6985i	0.326954	+	1.56325i
$932$		0			0
$933$	14.3183	+	24.7999i	0.468759	+	0.811914i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	11.1734			0.365019			0.182509	−	0.983204i	$-0.441578\pi$
$937$	11.1734			0.365019			0.182509	+	0.983204i	$0.441578\pi$
$938$		0			0
$939$	27.3613			0.892901
$940$		0			0
$941$	−14.9941	+	25.9706i	−0.488794	+	0.846616i	−0.999917	−	0.0128918i	$-0.995896\pi$
$941$	−14.9941	+	25.9706i	−0.488794	+	0.846616i	0.511123	+	0.859508i	$0.329230\pi$
$942$		0			0
$943$	−6.30860	−	10.9268i	−0.205436	−	0.355826i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	19.8297	+	34.3460i	0.644378	+	1.11610i	0.984445	+	0.175694i	$0.0562170\pi$
$947$	19.8297	+	34.3460i	0.644378	+	1.11610i	−0.340067	+	0.940401i	$0.610450\pi$
$948$		0			0
$949$	−5.91671	+	10.2480i	−0.192065	+	0.332666i
$950$		0			0
$951$	−8.01660			−0.259956
$952$		0			0
$953$	17.9334			0.580921			0.290460	−	0.956887i	$-0.406192\pi$
$953$	17.9334			0.580921			0.290460	+	0.956887i	$0.406192\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	0.947472	+	1.64107i	0.0306274	+	0.0530482i
$958$		0			0
$959$	24.5131	−	30.1705i	0.791571	−	0.974255i
$960$		0			0
$961$	12.3651	+	21.4170i	0.398874	+	0.690870i
$962$		0			0
$963$	−1.06361	+	1.84223i	−0.0342744	+	0.0593650i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−10.2432			−0.329398			−0.164699	−	0.986344i	$-0.552665\pi$
$967$	−10.2432			−0.329398			−0.164699	+	0.986344i	$0.552665\pi$
$968$		0			0
$969$	−21.6677	+	37.5295i	−0.696066	+	1.20562i
$970$		0			0
$971$	10.3547	+	17.9349i	0.332298	+	0.575558i	0.982962	−	0.183808i	$-0.0588426\pi$
$971$	10.3547	+	17.9349i	0.332298	+	0.575558i	−0.650664	+	0.759366i	$0.725509\pi$
$972$		0			0
$973$	49.9197	+	7.98999i	1.60035	+	0.256147i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−18.1674	+	31.4669i	−0.581228	+	1.00672i	0.414107	+	0.910228i	$0.364094\pi$
$977$	−18.1674	+	31.4669i	−0.581228	+	1.00672i	−0.995334	+	0.0964874i	$0.969239\pi$
$978$		0			0
$979$	9.94342			0.317793
$980$		0			0
$981$	2.28800			0.0730503
$982$		0			0
$983$	15.9387	−	27.6067i	0.508367	−	0.880517i	−0.491586	−	0.870829i	$-0.663583\pi$
$983$	15.9387	−	27.6067i	0.508367	−	0.880517i	0.999953	−	0.00968816i	$-0.00308388\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−3.80172	−	0.608492i	−0.121010	−	0.0193685i
$988$		0			0
$989$	1.03794	+	1.79777i	0.0330047	+	0.0571658i
$990$		0			0
$991$	−5.30365	+	9.18619i	−0.168476	+	0.291809i	−0.937884	−	0.346948i	$-0.887218\pi$
$991$	−5.30365	+	9.18619i	−0.168476	+	0.291809i	0.769408	+	0.638757i	$0.220551\pi$
$992$		0			0
$993$	9.97698			0.316610
$994$		0			0
$995$		0			0
$996$		0			0
$997$	10.8248	−	18.7491i	0.342825	−	0.593791i	−0.642131	−	0.766595i	$-0.721949\pi$
$997$	10.8248	−	18.7491i	0.342825	−	0.593791i	0.984956	+	0.172804i	$0.0552828\pi$
$998$		0			0
$999$	−1.94412	−	3.36732i	−0.0615093	−	0.106537i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.q.l.1201.4		8
5.2	odd	4		420.2.bb.a.109.8	yes	16
5.3	odd	4		420.2.bb.a.109.2	✓	16
5.4	even	2		2100.2.q.m.1201.1		8
7.2	even	3	inner	2100.2.q.l.1801.4		8
15.2	even	4		1260.2.bm.c.109.1		16
15.8	even	4		1260.2.bm.c.109.6		16
20.3	even	4		1680.2.di.e.529.6		16
20.7	even	4		1680.2.di.e.529.4		16
35.2	odd	12		420.2.bb.a.289.2	yes	16
35.3	even	12		2940.2.k.g.589.3		8
35.9	even	6		2100.2.q.m.1801.1		8
35.12	even	12		2940.2.bb.i.1549.7		16
35.13	even	4		2940.2.bb.i.949.7		16
35.17	even	12		2940.2.k.g.589.7		8
35.18	odd	12		2940.2.k.f.589.6		8
35.23	odd	12		420.2.bb.a.289.8	yes	16
35.27	even	4		2940.2.bb.i.949.1		16
35.32	odd	12		2940.2.k.f.589.2		8
35.33	even	12		2940.2.bb.i.1549.1		16
105.2	even	12		1260.2.bm.c.289.6		16
105.23	even	12		1260.2.bm.c.289.1		16
140.23	even	12		1680.2.di.e.289.4		16
140.107	even	12		1680.2.di.e.289.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bb.a.109.2	✓	16	5.3	odd	4
420.2.bb.a.109.8	yes	16	5.2	odd	4
420.2.bb.a.289.2	yes	16	35.2	odd	12
420.2.bb.a.289.8	yes	16	35.23	odd	12
1260.2.bm.c.109.1		16	15.2	even	4
1260.2.bm.c.109.6		16	15.8	even	4
1260.2.bm.c.289.1		16	105.23	even	12
1260.2.bm.c.289.6		16	105.2	even	12
1680.2.di.e.289.4		16	140.23	even	12
1680.2.di.e.289.6		16	140.107	even	12
1680.2.di.e.529.4		16	20.7	even	4
1680.2.di.e.529.6		16	20.3	even	4
2100.2.q.l.1201.4		8	1.1	even	1	trivial
2100.2.q.l.1801.4		8	7.2	even	3	inner
2100.2.q.m.1201.1		8	5.4	even	2
2100.2.q.m.1801.1		8	35.9	even	6
2940.2.k.f.589.2		8	35.32	odd	12
2940.2.k.f.589.6		8	35.18	odd	12
2940.2.k.g.589.3		8	35.3	even	12
2940.2.k.g.589.7		8	35.17	even	12
2940.2.bb.i.949.1		16	35.27	even	4
2940.2.bb.i.949.7		16	35.13	even	4
2940.2.bb.i.1549.1		16	35.33	even	12
2940.2.bb.i.1549.7		16	35.12	even	12

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:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +(2.61250 + 0.418148i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{3} +(2.61250 + 0.418148i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(0.292387 - 0.506430i) q^{11} -1.75198 q^{13} +(3.11250 - 5.39101i) q^{17} +(3.48075 + 6.02884i) q^{19} +(-1.66838 + 2.05342i) q^{21} +(-1.37599 - 2.38328i) q^{23} +1.00000 q^{27} +3.24047 q^{29} +(1.25198 - 2.16849i) q^{31} +(0.292387 + 0.506430i) q^{33} +(-1.94412 - 3.36732i) q^{37} +(0.875989 - 1.51726i) q^{39} +4.58477 q^{41} -0.754325 q^{43} +(0.727603 + 1.26025i) q^{47} +(6.65030 + 2.18482i) q^{49} +(3.11250 + 5.39101i) q^{51} +(-0.263490 + 0.456378i) q^{53} -6.96151 q^{57} +(5.05327 - 8.75253i) q^{59} +(-4.07704 - 7.06164i) q^{61} +(-0.944123 - 2.47156i) q^{63} +(-7.34901 + 12.7289i) q^{67} +2.75198 q^{69} +13.3561 q^{71} +(3.37716 - 5.84942i) q^{73} +(0.975625 - 1.20079i) q^{77} +(4.04771 + 7.01085i) q^{79} +(-0.500000 + 0.866025i) q^{81} +5.72895 q^{83} +(-1.62023 + 2.80633i) q^{87} +(8.50192 + 14.7258i) q^{89} +(-4.57704 - 0.732586i) q^{91} +(1.25198 + 2.16849i) q^{93} -11.1132 q^{97} -0.584775 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} - 2 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 - 2 * q^7 - 4 * q^9	\( 8 q - 4 q^{3} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{13} + 2 q^{17} - 4 q^{19} - 2 q^{21} - 6 q^{23} + 8 q^{27} - 12 q^{29} - 4 q^{33} - 4 q^{37} + 2 q^{39} + 24 q^{41} + 32 q^{43} - 2 q^{47} - 4 q^{49} + 2 q^{51} - 20 q^{53} + 8 q^{57} + 14 q^{59} - 16 q^{61} + 4 q^{63} - 18 q^{67} + 12 q^{69} - 28 q^{71} + 8 q^{73} + 10 q^{77} + 8 q^{79} - 4 q^{81} - 20 q^{83} + 6 q^{87} + 8 q^{89} - 20 q^{91} - 20 q^{97} + 8 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^13 + 2 * q^17 - 4 * q^19 - 2 * q^21 - 6 * q^23 + 8 * q^27 - 12 * q^29 - 4 * q^33 - 4 * q^37 + 2 * q^39 + 24 * q^41 + 32 * q^43 - 2 * q^47 - 4 * q^49 + 2 * q^51 - 20 * q^53 + 8 * q^57 + 14 * q^59 - 16 * q^61 + 4 * q^63 - 18 * q^67 + 12 * q^69 - 28 * q^71 + 8 * q^73 + 10 * q^77 + 8 * q^79 - 4 * q^81 - 20 * q^83 + 6 * q^87 + 8 * q^89 - 20 * q^91 - 20 * q^97 + 8 * q^99

Introduction

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