LMFDB - Embedded newform 2352.2.bl.q.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2352,2,Mod(31,2352)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2352, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 0, 1]))

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

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

chi := DirichletCharacter("2352.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2352 = 2^{4} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2352.bl (of order $6$, 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:	$18.7808145554$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.339738624.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 $ x^8 - 4x^6 + 14x^4 - 8*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.1
Root			$-0.662827 + 0.382683i$ of defining polynomial
Character	$\chi$	$=$	2352.31
Dual form			2352.2.bl.q.607.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{3} +(-3.72153 + 2.14862i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(4.38435 + 2.53131i) q^{11} -3.37849i q^{13} -4.29725i q^{15} +(2.39587 + 1.38326i) q^{17} +(-2.35159 - 4.07308i) q^{19} +(4.18394 - 2.41560i) q^{23} +(6.73317 - 11.6622i) q^{25} +1.00000 q^{27} +2.46054 q^{29} +(2.84882 - 4.93430i) q^{31} +(-4.38435 + 2.53131i) q^{33} +(1.16765 + 2.02243i) q^{37} +(2.92586 + 1.68925i) q^{39} +5.14822i q^{41} +13.0199i q^{43} +(3.72153 + 2.14862i) q^{45} +(-2.67725 - 4.63713i) q^{47} +(-2.39587 + 1.38326i) q^{51} +(2.11185 - 3.65784i) q^{53} -21.7553 q^{55} +4.70319 q^{57} +(-4.80249 + 8.31815i) q^{59} +(3.35757 - 1.93849i) q^{61} +(7.25911 + 12.5732i) q^{65} +(-4.12524 - 2.38171i) q^{67} +4.83120i q^{69} -12.3181i q^{71} +(9.96809 + 5.75508i) q^{73} +(6.73317 + 11.6622i) q^{75} +(-12.0521 + 6.95830i) q^{79} +(-0.500000 + 0.866025i) q^{81} +7.32191 q^{83} -11.8884 q^{85} +(-1.23027 + 2.13089i) q^{87} +(12.1631 - 7.02239i) q^{89} +(2.84882 + 4.93430i) q^{93} +(17.5030 + 10.1054i) q^{95} +14.5716i q^{97} -5.06262i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} - 4 q^{9} + 24 q^{23} + 12 q^{25} + 8 q^{27} + 16 q^{29} + 16 q^{31} + 8 q^{47} - 8 q^{53} - 64 q^{55} - 24 q^{59} + 48 q^{61} + 8 q^{65} - 48 q^{67} + 48 q^{73} + 12 q^{75} - 24 q^{79} - 4 q^{81}+ \cdots + 72 q^{95}+O(q^{100}) $ 8 * q - 4 * q^3 - 4 * q^9 + 24 * q^23 + 12 * q^25 + 8 * q^27 + 16 * q^29 + 16 * q^31 + 8 * q^47 - 8 * q^53 - 64 * q^55 - 24 * q^59 + 48 * q^61 + 8 * q^65 - 48 * q^67 + 48 * q^73 + 12 * q^75 - 24 * q^79 - 4 * q^81 - 64 * q^85 - 8 * q^87 + 48 * q^89 + 16 * q^93 + 72 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times$.

$n$	$785$	$1471$	$1765$	$2257$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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
$5$	−3.72153	+	2.14862i	−1.66432	+	0.960894i	−0.693701	+	0.720264i	$0.744021\pi$
$5$	−3.72153	+	2.14862i	−1.66432	+	0.960894i	−0.970617	+	0.240630i	$0.922646\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	4.38435	+	2.53131i	1.32193	+	0.763218i	0.984037	−	0.177966i	$-0.0569516\pi$
$11$	4.38435	+	2.53131i	1.32193	+	0.763218i	0.337896	+	0.941184i	$0.390285\pi$
$12$		0			0
$13$		−	3.37849i		−	0.937025i	−0.883457	−	0.468513i	$-0.844790\pi$
$13$		−	3.37849i		−	0.937025i	0.883457	−	0.468513i	$-0.155210\pi$
$14$		0			0
$15$		−	4.29725i		−	1.10954i
$16$		0			0
$17$	2.39587	+	1.38326i	0.581084	+	0.335489i	0.761564	−	0.648089i	$-0.224432\pi$
$17$	2.39587	+	1.38326i	0.581084	+	0.335489i	−0.180480	+	0.983579i	$0.557765\pi$
$18$		0			0
$19$	−2.35159	−	4.07308i	−0.539492	−	0.934428i	−0.998931	−	0.0462188i	$-0.985283\pi$
$19$	−2.35159	−	4.07308i	−0.539492	−	0.934428i	0.459439	−	0.888209i	$-0.348050\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.18394	−	2.41560i	0.872412	−	0.503687i	0.00426301	−	0.999991i	$-0.498643\pi$
$23$	4.18394	−	2.41560i	0.872412	−	0.503687i	0.868149	+	0.496304i	$0.165310\pi$
$24$		0			0
$25$	6.73317	−	11.6622i	1.34663	−	2.33244i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	2.46054			0.456912			0.228456	−	0.973554i	$-0.426632\pi$
$29$	2.46054			0.456912			0.228456	+	0.973554i	$0.426632\pi$
$30$		0			0
$31$	2.84882	−	4.93430i	0.511663	−	0.886227i	−0.488245	−	0.872706i	$-0.662363\pi$
$31$	2.84882	−	4.93430i	0.511663	−	0.886227i	0.999909	−	0.0135202i	$-0.00430375\pi$
$32$		0			0
$33$	−4.38435	+	2.53131i	−0.763218	+	0.440644i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.16765	+	2.02243i	0.191961	+	0.332486i	0.945900	−	0.324458i	$-0.105182\pi$
$37$	1.16765	+	2.02243i	0.191961	+	0.332486i	−0.753939	+	0.656944i	$0.771849\pi$
$38$		0			0
$39$	2.92586	+	1.68925i	0.468513	+	0.270496i
$40$		0			0
$41$			5.14822i			0.804018i	0.915636	+	0.402009i	$0.131688\pi$
$41$			5.14822i			0.804018i	−0.915636	+	0.402009i	$0.868312\pi$
$42$		0			0
$43$			13.0199i			1.98552i	0.120117	+	0.992760i	$0.461673\pi$
$43$			13.0199i			1.98552i	−0.120117	+	0.992760i	$0.538327\pi$
$44$		0			0
$45$	3.72153	+	2.14862i	0.554772	+	0.320298i
$46$		0			0
$47$	−2.67725	−	4.63713i	−0.390517	−	0.676395i	0.602001	−	0.798495i	$-0.294370\pi$
$47$	−2.67725	−	4.63713i	−0.390517	−	0.676395i	−0.992518	+	0.122101i	$0.961037\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−2.39587	+	1.38326i	−0.335489	+	0.193695i
$52$		0			0
$53$	2.11185	−	3.65784i	0.290085	−	0.502443i	−0.683744	−	0.729722i	$-0.739650\pi$
$53$	2.11185	−	3.65784i	0.290085	−	0.502443i	0.973830	+	0.227279i	$0.0729830\pi$
$54$		0			0
$55$	−21.7553			−2.93349
$56$		0			0
$57$	4.70319			0.622952
$58$		0			0
$59$	−4.80249	+	8.31815i	−0.625231	+	1.08293i	0.363265	+	0.931686i	$0.381662\pi$
$59$	−4.80249	+	8.31815i	−0.625231	+	1.08293i	−0.988496	+	0.151246i	$0.951672\pi$
$60$		0			0
$61$	3.35757	−	1.93849i	0.429892	−	0.248198i	−0.269408	−	0.963026i	$-0.586828\pi$
$61$	3.35757	−	1.93849i	0.429892	−	0.248198i	0.699301	+	0.714828i	$0.253495\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	7.25911	+	12.5732i	0.900382	+	1.55951i
$66$		0			0
$67$	−4.12524	−	2.38171i	−0.503978	−	0.290972i	0.226377	−	0.974040i	$-0.427312\pi$
$67$	−4.12524	−	2.38171i	−0.503978	−	0.290972i	−0.730355	+	0.683068i	$0.760645\pi$
$68$		0			0
$69$			4.83120i			0.581608i
$70$		0			0
$71$		−	12.3181i		−	1.46189i	−0.682437	−	0.730944i	$-0.739080\pi$
$71$		−	12.3181i		−	1.46189i	0.682437	−	0.730944i	$-0.260920\pi$
$72$		0			0
$73$	9.96809	+	5.75508i	1.16668	+	0.673581i	0.952895	−	0.303300i	$-0.0980886\pi$
$73$	9.96809	+	5.75508i	1.16668	+	0.673581i	0.213782	+	0.976881i	$0.431422\pi$
$74$		0			0
$75$	6.73317	+	11.6622i	0.777480	+	1.34663i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−12.0521	+	6.95830i	−1.35597	+	0.782870i	−0.989078	−	0.147393i	$-0.952912\pi$
$79$	−12.0521	+	6.95830i	−1.35597	+	0.782870i	−0.366893	+	0.930263i	$0.619578\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	7.32191			0.803685			0.401842	−	0.915709i	$-0.368370\pi$
$83$	7.32191			0.803685			0.401842	+	0.915709i	$0.368370\pi$
$84$		0			0
$85$	−11.8884			−1.28948
$86$		0			0
$87$	−1.23027	+	2.13089i	−0.131899	+	0.228456i
$88$		0			0
$89$	12.1631	−	7.02239i	1.28929	−	0.744372i	0.310762	−	0.950488i	$-0.399416\pi$
$89$	12.1631	−	7.02239i	1.28929	−	0.744372i	0.978528	+	0.206116i	$0.0660823\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	2.84882	+	4.93430i	0.295409	+	0.511663i
$94$		0			0
$95$	17.5030	+	10.1054i	1.79577	+	1.03679i
$96$		0			0
$97$			14.5716i			1.47952i	0.672868	+	0.739762i	$0.265062\pi$
$97$			14.5716i			1.47952i	−0.672868	+	0.739762i	$0.734938\pi$
$98$		0			0
$99$		−	5.06262i		−	0.508812i
$100$		0			0
$101$	11.3524	+	6.55434i	1.12961	+	0.652181i	0.943837	−	0.330412i	$-0.107188\pi$
$101$	11.3524	+	6.55434i	1.12961	+	0.652181i	0.185773	+	0.982593i	$0.440521\pi$
$102$		0			0
$103$	−0.104849	−	0.181604i	−0.0103311	−	0.0178939i	0.860814	−	0.508920i	$-0.169955\pi$
$103$	−0.104849	−	0.181604i	−0.0103311	−	0.0178939i	−0.871145	+	0.491026i	$0.836622\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.56558	+	3.21329i	−0.538044	+	0.310640i	−0.744286	−	0.667861i	$-0.767210\pi$
$107$	−5.56558	+	3.21329i	−0.538044	+	0.310640i	0.206242	+	0.978501i	$0.433877\pi$
$108$		0			0
$109$	−0.470012	+	0.814084i	−0.0450190	+	0.0779751i	−0.887657	−	0.460506i	$-0.847668\pi$
$109$	−0.470012	+	0.814084i	−0.0450190	+	0.0779751i	0.842638	+	0.538481i	$0.181001\pi$
$110$		0			0
$111$	−2.33530			−0.221657
$112$		0			0
$113$	1.09821			0.103311			0.0516554	−	0.998665i	$-0.483550\pi$
$113$	1.09821			0.103311			0.0516554	+	0.998665i	$0.483550\pi$
$114$		0			0
$115$	−10.3804	+	17.9794i	−0.967980	+	1.67659i
$116$		0			0
$117$	−2.92586	+	1.68925i	−0.270496	+	0.156171i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	7.31504	+	12.6700i	0.665004	+	1.15182i
$122$		0			0
$123$	−4.45849	−	2.57411i	−0.402009	−	0.232100i
$124$		0			0
$125$			36.3820i			3.25411i
$126$		0			0
$127$		−	5.22625i		−	0.463755i	−0.972745	−	0.231877i	$-0.925513\pi$
$127$		−	5.22625i		−	0.463755i	0.972745	−	0.231877i	$-0.0744868\pi$
$128$		0			0
$129$	−11.2756	−	6.50996i	−0.992760	−	0.573170i
$130$		0			0
$131$	−0.437508	−	0.757785i	−0.0382252	−	0.0662080i	0.846280	−	0.532739i	$-0.178837\pi$
$131$	−0.437508	−	0.757785i	−0.0382252	−	0.0662080i	−0.884505	+	0.466531i	$0.845504\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−3.72153	+	2.14862i	−0.320298	+	0.184924i
$136$		0			0
$137$	−0.118419	+	0.205108i	−0.0101172	+	0.0175235i	−0.871040	−	0.491213i	$-0.836554\pi$
$137$	−0.118419	+	0.205108i	−0.0101172	+	0.0175235i	0.860922	+	0.508736i	$0.169887\pi$
$138$		0			0
$139$	−3.00555			−0.254927			−0.127464	−	0.991843i	$-0.540684\pi$
$139$	−3.00555			−0.254927			−0.127464	+	0.991843i	$0.540684\pi$
$140$		0			0
$141$	5.35449			0.450930
$142$		0			0
$143$	8.55201	−	14.8125i	0.715155	−	1.23868i
$144$		0			0
$145$	−9.15698	+	5.28679i	−0.760446	+	0.439044i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	7.40083	+	12.8186i	0.606299	+	1.05014i	0.991845	+	0.127452i	$0.0406799\pi$
$149$	7.40083	+	12.8186i	0.606299	+	1.05014i	−0.385545	+	0.922689i	$0.625987\pi$
$150$		0			0
$151$	−10.7087	−	6.18269i	−0.871464	−	0.503140i	−0.00362965	−	0.999993i	$-0.501155\pi$
$151$	−10.7087	−	6.18269i	−0.871464	−	0.503140i	−0.867835	+	0.496853i	$0.834489\pi$
$152$		0			0
$153$		−	2.76652i		−	0.223659i
$154$		0			0
$155$			24.4842i			1.96662i
$156$		0			0
$157$	9.43153	+	5.44530i	0.752718	+	0.434582i	0.826675	−	0.562679i	$-0.190229\pi$
$157$	9.43153	+	5.44530i	0.752718	+	0.434582i	−0.0739569	+	0.997261i	$0.523563\pi$
$158$		0			0
$159$	2.11185	+	3.65784i	0.167481	+	0.290085i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−1.30791	+	0.755120i	−0.102443	+	0.0591455i	−0.550346	−	0.834937i	$-0.685504\pi$
$163$	−1.30791	+	0.755120i	−0.102443	+	0.0591455i	0.447903	+	0.894082i	$0.352171\pi$
$164$		0			0
$165$	10.8777	−	18.8407i	0.846825	−	1.46674i
$166$		0			0
$167$	10.3333			0.799612			0.399806	−	0.916600i	$-0.369078\pi$
$167$	10.3333			0.799612			0.399806	+	0.916600i	$0.369078\pi$
$168$		0			0
$169$	1.58579			0.121984
$170$		0			0
$171$	−2.35159	+	4.07308i	−0.179831	+	0.311476i
$172$		0			0
$173$	2.90674	−	1.67821i	0.220996	−	0.127592i	−0.385416	−	0.922743i	$-0.625942\pi$
$173$	2.90674	−	1.67821i	0.220996	−	0.127592i	0.606411	+	0.795151i	$0.292609\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−4.80249	−	8.31815i	−0.360977	−	0.625231i
$178$		0			0
$179$	11.4826	+	6.62946i	0.858247	+	0.495509i	0.863425	−	0.504477i	$-0.168315\pi$
$179$	11.4826	+	6.62946i	0.858247	+	0.495509i	−0.00517789	+	0.999987i	$0.501648\pi$
$180$		0			0
$181$		−	11.8519i		−	0.880946i	−0.897766	−	0.440473i	$-0.854811\pi$
$181$		−	11.8519i		−	0.880946i	0.897766	−	0.440473i	$-0.145189\pi$
$182$		0			0
$183$			3.87698i			0.286595i
$184$		0			0
$185$	−8.69089	−	5.01769i	−0.638967	−	0.368908i
$186$		0			0
$187$	7.00290	+	12.1294i	0.512103	+	0.886988i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1.16619	−	0.673302i	0.0843828	−	0.0487184i	−0.457215	−	0.889356i	$-0.651153\pi$
$191$	1.16619	−	0.673302i	0.0843828	−	0.0487184i	0.541598	+	0.840638i	$0.317820\pi$
$192$		0			0
$193$	13.0577	−	22.6166i	0.939912	−	1.62798i	0.174281	−	0.984696i	$-0.444240\pi$
$193$	13.0577	−	22.6166i	0.939912	−	1.62798i	0.765631	−	0.643280i	$-0.222427\pi$
$194$		0			0
$195$	−14.5182			−1.03967
$196$		0			0
$197$	−7.49083			−0.533699			−0.266850	−	0.963738i	$-0.585983\pi$
$197$	−7.49083			−0.533699			−0.266850	+	0.963738i	$0.585983\pi$
$198$		0			0
$199$	−2.24674	+	3.89147i	−0.159267	+	0.275859i	−0.934605	−	0.355688i	$-0.884247\pi$
$199$	−2.24674	+	3.89147i	−0.159267	+	0.275859i	0.775337	+	0.631547i	$0.217580\pi$
$200$		0			0
$201$	4.12524	−	2.38171i	0.290972	−	0.167993i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−11.0616	−	19.1593i	−0.772576	−	1.33814i
$206$		0			0
$207$	−4.18394	−	2.41560i	−0.290804	−	0.167896i
$208$		0			0
$209$		−	23.8104i		−	1.64700i
$210$		0			0
$211$		−	5.93122i		−	0.408322i	−0.978937	−	0.204161i	$-0.934553\pi$
$211$		−	5.93122i		−	0.408322i	0.978937	−	0.204161i	$-0.0654466\pi$
$212$		0			0
$213$	10.6678	+	6.15905i	0.730944	+	0.422011i
$214$		0			0
$215$	−27.9749	−	48.4540i	−1.90787	−	3.30453i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−9.96809	+	5.75508i	−0.673581	+	0.388892i
$220$		0			0
$221$	4.67333	−	8.09444i	0.314362	−	0.544491i
$222$		0			0
$223$	20.6163			1.38057			0.690286	−	0.723537i	$-0.257485\pi$
$223$	20.6163			1.38057			0.690286	+	0.723537i	$0.257485\pi$
$224$		0			0
$225$	−13.4663			−0.897756
$226$		0			0
$227$	−10.2455	+	17.7458i	−0.680021	+	1.17783i	0.294954	+	0.955512i	$0.404696\pi$
$227$	−10.2455	+	17.7458i	−0.680021	+	1.17783i	−0.974974	+	0.222318i	$0.928638\pi$
$228$		0			0
$229$	−25.1502	+	14.5205i	−1.66197	+	0.959539i	−0.690197	+	0.723622i	$0.742476\pi$
$229$	−25.1502	+	14.5205i	−1.66197	+	0.959539i	−0.971773	+	0.235917i	$0.924191\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−8.86819	−	15.3602i	−0.580975	−	1.00628i	−0.995364	−	0.0961779i	$-0.969338\pi$
$233$	−8.86819	−	15.3602i	−0.580975	−	1.00628i	0.414390	−	0.910100i	$-0.363995\pi$
$234$		0			0
$235$	19.9269	+	11.5048i	1.29989	+	0.750490i
$236$		0			0
$237$		−	13.9166i		−	0.903981i
$238$		0			0
$239$			20.4248i			1.32117i	0.750750	+	0.660586i	$0.229692\pi$
$239$			20.4248i			1.32117i	−0.750750	+	0.660586i	$0.770308\pi$
$240$		0			0
$241$	−2.82101	−	1.62871i	−0.181717	−	0.104915i	0.406382	−	0.913703i	$-0.366790\pi$
$241$	−2.82101	−	1.62871i	−0.181717	−	0.104915i	−0.588099	+	0.808789i	$0.700124\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−13.7609	+	7.94484i	−0.875583	+	0.505518i
$248$		0			0
$249$	−3.66096	+	6.34096i	−0.232004	+	0.401842i
$250$		0			0
$251$	3.95633			0.249721			0.124861	−	0.992174i	$-0.460152\pi$
$251$	3.95633			0.249721			0.124861	+	0.992174i	$0.460152\pi$
$252$		0			0
$253$	24.4585			1.53769
$254$		0			0
$255$	5.94420	−	10.2957i	0.372240	−	0.644739i
$256$		0			0
$257$	−4.45849	+	2.57411i	−0.278113	+	0.160569i	−0.632569	−	0.774504i	$-0.717999\pi$
$257$	−4.45849	+	2.57411i	−0.278113	+	0.160569i	0.354456	+	0.935073i	$0.384666\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−1.23027	−	2.13089i	−0.0761519	−	0.131899i
$262$		0			0
$263$	0.0679848	+	0.0392511i	0.00419212	+	0.00242032i	0.502095	−	0.864813i	$-0.332563\pi$
$263$	0.0679848	+	0.0392511i	0.00419212	+	0.00242032i	−0.497902	+	0.867233i	$0.665896\pi$
$264$		0			0
$265$			18.1503i			1.11497i
$266$		0			0
$267$			14.0448i			0.859527i
$268$		0			0
$269$	0.764956	+	0.441648i	0.0466402	+	0.0269277i	0.523139	−	0.852247i	$-0.324761\pi$
$269$	0.764956	+	0.441648i	0.0466402	+	0.0269277i	−0.476499	+	0.879175i	$0.658094\pi$
$270$		0			0
$271$	9.65421	+	16.7216i	0.586451	+	1.01576i	0.994693	+	0.102890i	$0.0328089\pi$
$271$	9.65421	+	16.7216i	0.586451	+	1.01576i	−0.408241	+	0.912874i	$0.633858\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	59.0412	−	34.0875i	3.56032	−	2.05555i
$276$		0			0
$277$	−8.46635	+	14.6641i	−0.508694	+	0.881083i	0.491256	+	0.871015i	$0.336538\pi$
$277$	−8.46635	+	14.6641i	−0.508694	+	0.881083i	−0.999949	+	0.0100677i	$0.996795\pi$
$278$		0			0
$279$	−5.69764			−0.341109
$280$		0			0
$281$	5.05417			0.301507			0.150753	−	0.988571i	$-0.451830\pi$
$281$	5.05417			0.301507			0.150753	+	0.988571i	$0.451830\pi$
$282$		0			0
$283$	9.55781	−	16.5546i	0.568153	−	0.984069i	−0.428596	−	0.903496i	$-0.640992\pi$
$283$	9.55781	−	16.5546i	0.568153	−	0.984069i	0.996749	−	0.0805731i	$-0.0256750\pi$
$284$		0			0
$285$	−17.5030	+	10.1054i	−1.03679	+	0.598591i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−4.67320	−	8.09421i	−0.274894	−	0.476130i
$290$		0			0
$291$	−12.6194	−	7.28581i	−0.739762	−	0.427102i
$292$		0			0
$293$			2.37837i			0.138946i	0.997584	+	0.0694730i	$0.0221318\pi$
$293$			2.37837i			0.138946i	−0.997584	+	0.0694730i	$0.977868\pi$
$294$		0			0
$295$		−	41.2750i		−	2.40312i
$296$		0			0
$297$	4.38435	+	2.53131i	0.254406	+	0.146881i
$298$		0			0
$299$	−8.16109	−	14.1354i	−0.471968	−	0.817472i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−11.3524	+	6.55434i	−0.652181	+	0.376537i
$304$		0			0
$305$	−8.33018	+	14.4283i	−0.476985	+	0.826162i
$306$		0			0
$307$	4.89599			0.279429			0.139714	−	0.990192i	$-0.455382\pi$
$307$	4.89599			0.279429			0.139714	+	0.990192i	$0.455382\pi$
$308$		0			0
$309$	0.209698			0.0119293
$310$		0			0
$311$	−5.24000	+	9.07594i	−0.297133	+	0.514649i	−0.975479	−	0.220093i	$-0.929364\pi$
$311$	−5.24000	+	9.07594i	−0.297133	+	0.514649i	0.678346	+	0.734743i	$0.262697\pi$
$312$		0			0
$313$	−8.31534	+	4.80086i	−0.470011	+	0.271361i	−0.716244	−	0.697850i	$-0.754140\pi$
$313$	−8.31534	+	4.80086i	−0.470011	+	0.271361i	0.246234	+	0.969211i	$0.420807\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	8.39672	+	14.5435i	0.471607	+	0.816847i	0.999472	−	0.0324809i	$-0.0103408\pi$
$317$	8.39672	+	14.5435i	0.471607	+	0.816847i	−0.527865	+	0.849328i	$0.677007\pi$
$318$		0			0
$319$	10.7879	+	6.22840i	0.604006	+	0.348723i
$320$		0			0
$321$		−	6.42657i		−	0.358696i
$322$		0			0
$323$		−	13.0114i		−	0.723976i
$324$		0			0
$325$	−39.4007	−	22.7480i	−2.18556	−	1.26183i
$326$		0			0
$327$	−0.470012	−	0.814084i	−0.0259917	−	0.0450190i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	23.2409	−	13.4181i	1.27743	−	0.737526i	0.301057	−	0.953606i	$-0.402660\pi$
$331$	23.2409	−	13.4181i	1.27743	−	0.737526i	0.976376	+	0.216080i	$0.0693271\pi$
$332$		0			0
$333$	1.16765	−	2.02243i	0.0639869	−	0.110829i
$334$		0			0
$335$	20.4696			1.11837
$336$		0			0
$337$	23.0827			1.25739			0.628697	−	0.777651i	$-0.283589\pi$
$337$	23.0827			1.25739			0.628697	+	0.777651i	$0.283589\pi$
$338$		0			0
$339$	−0.549104	+	0.951076i	−0.0298232	+	0.0516554i
$340$		0			0
$341$	24.9805	−	14.4225i	1.35277	−	0.781021i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−10.3804	−	17.9794i	−0.558864	−	0.967980i
$346$		0			0
$347$	1.13181	+	0.653449i	0.0607586	+	0.0350790i	0.530072	−	0.847953i	$-0.322165\pi$
$347$	1.13181	+	0.653449i	0.0607586	+	0.0350790i	−0.469313	+	0.883032i	$0.655498\pi$
$348$		0			0
$349$		−	26.5489i		−	1.42113i	−0.703633	−	0.710564i	$-0.748440\pi$
$349$		−	26.5489i		−	1.42113i	0.703633	−	0.710564i	$-0.251560\pi$
$350$		0			0
$351$		−	3.37849i		−	0.180331i
$352$		0			0
$353$	14.6266	+	8.44466i	0.778494	+	0.449464i	0.835896	−	0.548887i	$-0.184948\pi$
$353$	14.6266	+	8.44466i	0.778494	+	0.449464i	−0.0574020	+	0.998351i	$0.518282\pi$
$354$		0			0
$355$	26.4670	+	45.8421i	1.40472	+	2.43305i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−29.0899	+	16.7950i	−1.53530	+	0.886408i	−0.536200	+	0.844091i	$0.680141\pi$
$359$	−29.0899	+	16.7950i	−1.53530	+	0.886408i	−0.999104	+	0.0423171i	$0.986526\pi$
$360$		0			0
$361$	−1.55998	+	2.70196i	−0.0821040	+	0.142208i
$362$		0			0
$363$	−14.6301			−0.767880
$364$		0			0
$365$	−49.4620			−2.58896
$366$		0			0
$367$	3.67989	−	6.37376i	0.192089	−	0.332708i	−0.753854	−	0.657043i	$-0.771807\pi$
$367$	3.67989	−	6.37376i	0.192089	−	0.332708i	0.945942	+	0.324335i	$0.105141\pi$
$368$		0			0
$369$	4.45849	−	2.57411i	0.232100	−	0.134003i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−1.81504	−	3.14374i	−0.0939791	−	0.162777i	0.815203	−	0.579175i	$-0.196625\pi$
$373$	−1.81504	−	3.14374i	−0.0939791	−	0.162777i	−0.909182	+	0.416399i	$0.863292\pi$
$374$		0			0
$375$	−31.5077	−	18.1910i	−1.62705	−	0.939379i
$376$		0			0
$377$		−	8.31293i		−	0.428138i
$378$		0			0
$379$		−	13.6647i		−	0.701908i	−0.936393	−	0.350954i	$-0.885857\pi$
$379$		−	13.6647i		−	0.701908i	0.936393	−	0.350954i	$-0.114143\pi$
$380$		0			0
$381$	4.52607	+	2.61313i	0.231877	+	0.133874i
$382$		0			0
$383$	6.82843	+	11.8272i	0.348916	+	0.604341i	0.986057	−	0.166407i	$-0.0532164\pi$
$383$	6.82843	+	11.8272i	0.348916	+	0.604341i	−0.637141	+	0.770747i	$0.719883\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	11.2756	−	6.50996i	0.573170	−	0.330920i
$388$		0			0
$389$	−13.4540	+	23.3030i	−0.682144	+	1.18151i	0.292181	+	0.956363i	$0.405619\pi$
$389$	−13.4540	+	23.3030i	−0.682144	+	1.18151i	−0.974325	+	0.225145i	$0.927714\pi$
$390$		0			0
$391$	13.3656			0.675927
$392$		0			0
$393$	0.875015			0.0441387
$394$		0			0
$395$	29.9016	−	51.7910i	1.50451	−	2.60589i
$396$		0			0
$397$	31.8041	−	18.3621i	1.59620	−	0.921568i	0.603994	−	0.796989i	$-0.293575\pi$
$397$	31.8041	−	18.3621i	1.59620	−	0.921568i	0.992210	−	0.124579i	$-0.0397581\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	13.8408	+	23.9730i	0.691176	+	1.19715i	0.971453	+	0.237233i	$0.0762405\pi$
$401$	13.8408	+	23.9730i	0.691176	+	1.19715i	−0.280276	+	0.959919i	$0.590426\pi$
$402$		0			0
$403$	−16.6705	−	9.62472i	−0.830417	−	0.479441i
$404$		0			0
$405$		−	4.29725i		−	0.213532i
$406$		0			0
$407$			11.8227i			0.586032i
$408$		0			0
$409$	−7.29903	−	4.21410i	−0.360914	−	0.208374i	0.308568	−	0.951202i	$-0.400150\pi$
$409$	−7.29903	−	4.21410i	−0.360914	−	0.208374i	−0.669482	+	0.742829i	$0.733484\pi$
$410$		0			0
$411$	−0.118419	−	0.205108i	−0.00584118	−	0.0101172i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−27.2487	+	15.7320i	−1.33759	+	0.772256i
$416$		0			0
$417$	1.50277	−	2.60288i	0.0735911	−	0.127464i
$418$		0			0
$419$	−18.3029			−0.894154			−0.447077	−	0.894495i	$-0.647535\pi$
$419$	−18.3029			−0.894154			−0.447077	+	0.894495i	$0.647535\pi$
$420$		0			0
$421$	22.6274			1.10279			0.551396	−	0.834243i	$-0.314095\pi$
$421$	22.6274			1.10279			0.551396	+	0.834243i	$0.314095\pi$
$422$		0			0
$423$	−2.67725	+	4.63713i	−0.130172	+	0.225465i
$424$		0			0
$425$	32.2636	−	18.6274i	1.56502	−	0.903563i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	8.55201	+	14.8125i	0.412895	+	0.715155i
$430$		0			0
$431$	−3.85300	−	2.22453i	−0.185592	−	0.107152i	0.404325	−	0.914615i	$-0.367506\pi$
$431$	−3.85300	−	2.22453i	−0.185592	−	0.107152i	−0.589918	+	0.807464i	$0.700840\pi$
$432$		0			0
$433$			1.66205i			0.0798730i	0.999202	+	0.0399365i	$0.0127156\pi$
$433$			1.66205i			0.0798730i	−0.999202	+	0.0399365i	$0.987284\pi$
$434$		0			0
$435$		−	10.5736i		−	0.506964i
$436$		0			0
$437$	−19.6779	−	11.3610i	−0.941319	−	0.543471i
$438$		0			0
$439$	−9.37753	−	16.2424i	−0.447565	−	0.775206i	0.550662	−	0.834728i	$-0.314375\pi$
$439$	−9.37753	−	16.2424i	−0.447565	−	0.775206i	−0.998227	+	0.0595229i	$0.981042\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	28.6060	−	16.5157i	1.35911	−	0.784684i	0.369609	−	0.929187i	$-0.379492\pi$
$443$	28.6060	−	16.5157i	1.35911	−	0.784684i	0.989504	+	0.144503i	$0.0461584\pi$
$444$		0			0
$445$	−30.1770	+	52.2680i	−1.43053	+	2.47774i
$446$		0			0
$447$	−14.8017			−0.700094
$448$		0			0
$449$	9.29441			0.438630			0.219315	−	0.975654i	$-0.429618\pi$
$449$	9.29441			0.438630			0.219315	+	0.975654i	$0.429618\pi$
$450$		0			0
$451$	−13.0317	+	22.5716i	−0.613641	+	1.06286i
$452$		0			0
$453$	10.7087	−	6.18269i	0.503140	−	0.290488i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	13.7224	+	23.7679i	0.641906	+	1.11181i	0.985007	+	0.172515i	$0.0551893\pi$
$457$	13.7224	+	23.7679i	0.641906	+	1.11181i	−0.343101	+	0.939298i	$0.611477\pi$
$458$		0			0
$459$	2.39587	+	1.38326i	0.111830	+	0.0645649i
$460$		0			0
$461$			4.28209i			0.199437i	0.995016	+	0.0997183i	$0.0317942\pi$
$461$			4.28209i			0.199437i	−0.995016	+	0.0997183i	$0.968206\pi$
$462$		0			0
$463$			16.1278i			0.749521i	0.927122	+	0.374760i	$0.122275\pi$
$463$			16.1278i			0.749521i	−0.927122	+	0.374760i	$0.877725\pi$
$464$		0			0
$465$	−21.2039	−	12.2421i	−0.983308	−	0.567713i
$466$		0			0
$467$	−13.7702	−	23.8506i	−0.637207	−	1.10368i	−0.986043	−	0.166491i	$-0.946756\pi$
$467$	−13.7702	−	23.8506i	−0.637207	−	1.10368i	0.348836	−	0.937184i	$-0.386577\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−9.43153	+	5.44530i	−0.434582	+	0.250906i
$472$		0			0
$473$	−32.9574	+	57.0839i	−1.51538	+	2.62472i
$474$		0			0
$475$	−63.3347			−2.90600
$476$		0			0
$477$	−4.22371			−0.193390
$478$		0			0
$479$	9.77545	−	16.9316i	0.446652	−	0.773624i	−0.551514	−	0.834166i	$-0.685950\pi$
$479$	9.77545	−	16.9316i	0.446652	−	0.773624i	0.998166	+	0.0605420i	$0.0192829\pi$
$480$		0			0
$481$	6.83277	−	3.94490i	0.311548	−	0.179872i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−31.3089	−	54.2287i	−1.42167	−	2.46240i
$486$		0			0
$487$	−32.7285	−	18.8958i	−1.48307	−	0.856252i	−0.483257	−	0.875479i	$-0.660546\pi$
$487$	−32.7285	−	18.8958i	−1.48307	−	0.856252i	−0.999815	+	0.0192268i	$0.993880\pi$
$488$		0			0
$489$		−	1.51024i		−	0.0682954i
$490$		0			0
$491$			29.2605i			1.32051i	0.751042	+	0.660254i	$0.229551\pi$
$491$			29.2605i			1.32051i	−0.751042	+	0.660254i	$0.770449\pi$
$492$		0			0
$493$	5.89515	+	3.40357i	0.265504	+	0.153289i
$494$		0			0
$495$	10.8777	+	18.8407i	0.488914	+	0.846825i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	10.9485	−	6.32111i	0.490122	−	0.282972i	−0.234503	−	0.972115i	$-0.575346\pi$
$499$	10.9485	−	6.32111i	0.490122	−	0.282972i	0.724625	+	0.689143i	$0.242013\pi$
$500$		0			0
$501$	−5.16663	+	8.94887i	−0.230828	+	0.399806i
$502$		0			0
$503$	27.0714			1.20706			0.603528	−	0.797342i	$-0.293761\pi$
$503$	27.0714			1.20706			0.603528	+	0.797342i	$0.293761\pi$
$504$		0			0
$505$	−56.3312			−2.50671
$506$		0			0
$507$	−0.792893	+	1.37333i	−0.0352136	+	0.0609918i
$508$		0			0
$509$	10.1311	−	5.84917i	0.449051	−	0.259260i	−0.258378	−	0.966044i	$-0.583188\pi$
$509$	10.1311	−	5.84917i	0.449051	−	0.259260i	0.707429	+	0.706784i	$0.249855\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−2.35159	−	4.07308i	−0.103825	−	0.179831i
$514$		0			0
$515$	0.780396	+	0.450562i	0.0343884	+	0.0198541i
$516$		0			0
$517$		−	27.1077i		−	1.19220i
$518$		0			0
$519$			3.35642i			0.147330i
$520$		0			0
$521$	6.24095	+	3.60322i	0.273421	+	0.157860i	0.630441	−	0.776237i	$-0.282874\pi$
$521$	6.24095	+	3.60322i	0.273421	+	0.157860i	−0.357020	+	0.934097i	$0.616207\pi$
$522$		0			0
$523$	8.85727	+	15.3412i	0.387301	+	0.670825i	0.992086	−	0.125564i	$-0.0400740\pi$
$523$	8.85727	+	15.3412i	0.387301	+	0.670825i	−0.604784	+	0.796389i	$0.706741\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	13.6508	−	7.88130i	0.594639	−	0.343315i
$528$		0			0
$529$	0.170243	−	0.294869i	0.00740185	−	0.0128204i
$530$		0			0
$531$	9.60498			0.416821
$532$		0			0
$533$	17.3932			0.753385
$534$		0			0
$535$	13.8083	−	23.9167i	0.596984	−	1.03401i
$536$		0			0
$537$	−11.4826	+	6.62946i	−0.495509	+	0.286082i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−11.5590	−	20.0208i	−0.496961	−	0.860761i	0.503033	−	0.864267i	$-0.332217\pi$
$541$	−11.5590	−	20.0208i	−0.496961	−	0.860761i	−0.999994	+	0.00350600i	$0.998884\pi$
$542$		0			0
$543$	10.2641	+	5.92596i	0.440473	+	0.254307i
$544$		0			0
$545$		−	4.03951i		−	0.173034i
$546$		0			0
$547$		−	16.0524i		−	0.686351i	−0.939271	−	0.343176i	$-0.888497\pi$
$547$		−	16.0524i		−	0.686351i	0.939271	−	0.343176i	$-0.111503\pi$
$548$		0			0
$549$	−3.35757	−	1.93849i	−0.143297	−	0.0827328i
$550$		0			0
$551$	−5.78620	−	10.0220i	−0.246500	−	0.426951i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	8.69089	−	5.01769i	0.368908	−	0.212989i
$556$		0			0
$557$	6.29041	−	10.8953i	0.266533	−	0.461649i	−0.701431	−	0.712738i	$-0.747455\pi$
$557$	6.29041	−	10.8953i	0.266533	−	0.461649i	0.967964	+	0.251088i	$0.0807884\pi$
$558$		0			0
$559$	43.9877			1.86048
$560$		0			0
$561$	−14.0058			−0.591325
$562$		0			0
$563$	−18.2974	+	31.6921i	−0.771144	+	1.33566i	0.165792	+	0.986161i	$0.446982\pi$
$563$	−18.2974	+	31.6921i	−0.771144	+	1.33566i	−0.936936	+	0.349500i	$0.886351\pi$
$564$		0			0
$565$	−4.08701	+	2.35964i	−0.171942	+	0.0992707i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	12.2495	+	21.2167i	0.513524	+	0.889450i	0.999877	+	0.0156875i	$0.00499368\pi$
$569$	12.2495	+	21.2167i	0.513524	+	0.889450i	−0.486353	+	0.873763i	$0.661673\pi$
$570$		0			0
$571$	−28.3990	−	16.3962i	−1.18846	−	0.686159i	−0.230506	−	0.973071i	$-0.574038\pi$
$571$	−28.3990	−	16.3962i	−1.18846	−	0.686159i	−0.957957	+	0.286912i	$0.907371\pi$
$572$		0			0
$573$			1.34660i			0.0562552i
$574$		0			0
$575$		−	65.0586i		−	2.71313i
$576$		0			0
$577$	16.6398	+	9.60699i	0.692724	+	0.399944i	0.804632	−	0.593774i	$-0.202363\pi$
$577$	16.6398	+	9.60699i	0.692724	+	0.399944i	−0.111908	+	0.993719i	$0.535696\pi$
$578$		0			0
$579$	13.0577	+	22.6166i	0.542659	+	0.939912i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	18.5182	−	10.6915i	0.766946	−	0.442797i
$584$		0			0
$585$	7.25911	−	12.5732i	0.300127	−	0.519836i
$586$		0			0
$587$	24.1451			0.996573			0.498286	−	0.867012i	$-0.333963\pi$
$587$	24.1451			0.996573			0.498286	+	0.867012i	$0.333963\pi$
$588$		0			0
$589$	−26.7971			−1.10415
$590$		0			0
$591$	3.74541	−	6.48725i	0.154066	−	0.266850i
$592$		0			0
$593$	2.20475	−	1.27291i	0.0905380	−	0.0522722i	−0.454047	−	0.890978i	$-0.650020\pi$
$593$	2.20475	−	1.27291i	0.0905380	−	0.0522722i	0.544585	+	0.838705i	$0.316687\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−2.24674	−	3.89147i	−0.0919531	−	0.159267i
$598$		0			0
$599$	−12.9816	−	7.49493i	−0.530414	−	0.306234i	0.210771	−	0.977535i	$-0.432402\pi$
$599$	−12.9816	−	7.49493i	−0.530414	−	0.306234i	−0.741185	+	0.671301i	$0.765736\pi$
$600$		0			0
$601$		−	24.3343i		−	0.992618i	−0.868146	−	0.496309i	$-0.834688\pi$
$601$		−	24.3343i		−	0.992618i	0.868146	−	0.496309i	$-0.165312\pi$
$602$		0			0
$603$			4.76342i			0.193981i
$604$		0			0
$605$	−54.4462	−	31.4345i	−2.21355	−	1.27800i
$606$		0			0
$607$	−4.45644	−	7.71878i	−0.180881	−	0.313296i	0.761300	−	0.648400i	$-0.224562\pi$
$607$	−4.45644	−	7.71878i	−0.180881	−	0.313296i	−0.942181	+	0.335105i	$0.891228\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−15.6665	+	9.04506i	−0.633799	+	0.365924i
$612$		0			0
$613$	8.58741	−	14.8738i	0.346842	−	0.600748i	−0.638844	−	0.769336i	$-0.720587\pi$
$613$	8.58741	−	14.8738i	0.346842	−	0.600748i	0.985687	+	0.168588i	$0.0539206\pi$
$614$		0			0
$615$	22.1232			0.892094
$616$		0			0
$617$	35.9980			1.44922			0.724612	−	0.689157i	$-0.242019\pi$
$617$	35.9980			1.44922			0.724612	+	0.689157i	$0.242019\pi$
$618$		0			0
$619$	2.05562	−	3.56043i	0.0826222	−	0.143106i	−0.821753	−	0.569843i	$-0.807004\pi$
$619$	2.05562	−	3.56043i	0.0826222	−	0.143106i	0.904376	+	0.426738i	$0.140337\pi$
$620$		0			0
$621$	4.18394	−	2.41560i	0.167896	−	0.0969347i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−44.5054	−	77.0856i	−1.78022	−	3.08342i
$626$		0			0
$627$	20.6204	+	11.9052i	0.823501	+	0.475448i
$628$		0			0
$629$			6.46065i			0.257603i
$630$		0			0
$631$			34.8970i			1.38923i	0.719383	+	0.694613i	$0.244425\pi$
$631$			34.8970i			1.38923i	−0.719383	+	0.694613i	$0.755575\pi$
$632$		0			0
$633$	5.13659	+	2.96561i	0.204161	+	0.117872i
$634$		0			0
$635$	11.2293	+	19.4496i	0.445619	+	0.771835i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−10.6678	+	6.15905i	−0.422011	+	0.243648i
$640$		0			0
$641$	−3.66368	+	6.34567i	−0.144707	+	0.250639i	−0.929263	−	0.369418i	$-0.879557\pi$
$641$	−3.66368	+	6.34567i	−0.144707	+	0.250639i	0.784557	+	0.620057i	$0.212890\pi$
$642$		0			0
$643$	9.24275			0.364498			0.182249	−	0.983252i	$-0.441662\pi$
$643$	9.24275			0.364498			0.182249	+	0.983252i	$0.441662\pi$
$644$		0			0
$645$	55.9498			2.20302
$646$		0			0
$647$	7.59013	−	13.1465i	0.298399	−	0.516842i	−0.677371	−	0.735642i	$-0.736881\pi$
$647$	7.59013	−	13.1465i	0.298399	−	0.516842i	0.975770	+	0.218800i	$0.0702141\pi$
$648$		0			0
$649$	−42.1116	+	24.3132i	−1.65303	+	0.954375i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.06425	+	1.84333i	0.0416471	+	0.0721349i	0.886098	−	0.463499i	$-0.153406\pi$
$653$	1.06425	+	1.84333i	0.0416471	+	0.0721349i	−0.844450	+	0.535634i	$0.820073\pi$
$654$		0			0
$655$	3.25639	+	1.88008i	0.127238	+	0.0734608i
$656$		0			0
$657$		−	11.5102i		−	0.449054i
$658$		0			0
$659$		−	13.0520i		−	0.508436i	−0.967147	−	0.254218i	$-0.918182\pi$
$659$		−	13.0520i		−	0.508436i	0.967147	−	0.254218i	$-0.0818180\pi$
$660$		0			0
$661$	16.6958	+	9.63931i	0.649390	+	0.374926i	0.788223	−	0.615390i	$-0.211002\pi$
$661$	16.6958	+	9.63931i	0.649390	+	0.374926i	−0.138832	+	0.990316i	$0.544335\pi$
$662$		0			0
$663$	4.67333	+	8.09444i	0.181497	+	0.314362i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	10.2948	−	5.94369i	0.398615	−	0.230141i
$668$		0			0
$669$	−10.3082	+	17.8543i	−0.398537	+	0.690286i
$670$		0			0
$671$	19.6277			0.757718
$672$		0			0
$673$	−7.08216			−0.272997			−0.136499	−	0.990640i	$-0.543585\pi$
$673$	−7.08216			−0.272997			−0.136499	+	0.990640i	$0.543585\pi$
$674$		0			0
$675$	6.73317	−	11.6622i	0.259160	−	0.448878i
$676$		0			0
$677$	−31.6135	+	18.2521i	−1.21501	+	0.701485i	−0.963846	−	0.266461i	$-0.914146\pi$
$677$	−31.6135	+	18.2521i	−1.21501	+	0.701485i	−0.251161	+	0.967945i	$0.580812\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−10.2455	−	17.7458i	−0.392610	−	0.680021i
$682$		0			0
$683$	26.0852	+	15.0603i	0.998124	+	0.576267i	0.907693	−	0.419636i	$-0.137842\pi$
$683$	26.0852	+	15.0603i	0.998124	+	0.576267i	0.0904313	+	0.995903i	$0.471175\pi$
$684$		0			0
$685$		−	1.01775i		−	0.0388863i
$686$		0			0
$687$		−	29.0409i		−	1.10798i
$688$		0			0
$689$	−12.3580	−	7.13488i	−0.470801	−	0.271817i
$690$		0			0
$691$	−19.9057	−	34.4776i	−0.757247	−	1.31159i	−0.944249	−	0.329231i	$-0.893211\pi$
$691$	−19.9057	−	34.4776i	−0.757247	−	1.31159i	0.187002	−	0.982359i	$-0.440123\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	11.1852	−	6.45779i	0.424280	−	0.244958i
$696$		0			0
$697$	−7.12132	+	12.3345i	−0.269739	+	0.467202i
$698$		0			0
$699$	17.7364			0.670852
$700$		0			0
$701$	28.0795			1.06055			0.530275	−	0.847826i	$-0.322089\pi$
$701$	28.0795			1.06055			0.530275	+	0.847826i	$0.322089\pi$
$702$		0			0
$703$	5.49168	−	9.51187i	0.207123	−	0.358747i
$704$		0			0
$705$	−19.9269	+	11.5048i	−0.750490	+	0.433296i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	18.4738	+	31.9975i	0.693797	+	1.20169i	0.970585	+	0.240761i	$0.0773969\pi$
$709$	18.4738	+	31.9975i	0.693797	+	1.20169i	−0.276787	+	0.960931i	$0.589270\pi$
$710$		0			0
$711$	12.0521	+	6.95830i	0.451990	+	0.260957i
$712$		0			0
$713$		−	27.5264i		−	1.03087i
$714$		0			0
$715$			73.5002i			2.74875i
$716$		0			0
$717$	−17.6884	−	10.2124i	−0.660586	−	0.381389i
$718$		0			0
$719$	−9.35449	−	16.2025i	−0.348864	−	0.604250i	0.637184	−	0.770712i	$-0.280099\pi$
$719$	−9.35449	−	16.2025i	−0.348864	−	0.604250i	−0.986048	+	0.166462i	$0.946766\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	2.82101	−	1.62871i	0.104915	−	0.0605724i
$724$		0			0
$725$	16.5673	−	28.6954i	0.615293	−	1.06572i
$726$		0			0
$727$	−31.2078			−1.15743			−0.578716	−	0.815529i	$-0.696446\pi$
$727$	−31.2078			−1.15743			−0.578716	+	0.815529i	$0.696446\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−18.0099	+	31.1941i	−0.666120	+	1.15375i
$732$		0			0
$733$	3.52383	−	2.03449i	0.130156	−	0.0751455i	−0.433508	−	0.901150i	$-0.642725\pi$
$733$	3.52383	−	2.03449i	0.130156	−	0.0751455i	0.563664	+	0.826004i	$0.309391\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−12.0577	−	20.8845i	−0.444150	−	0.769291i
$738$		0			0
$739$	−34.5566	−	19.9513i	−1.27119	−	0.733919i	−0.295974	−	0.955196i	$-0.595644\pi$
$739$	−34.5566	−	19.9513i	−1.27119	−	0.733919i	−0.975211	+	0.221277i	$0.928978\pi$
$740$		0			0
$741$		−	15.8897i		−	0.583722i
$742$		0			0
$743$			41.7530i			1.53177i	0.642979	+	0.765884i	$0.277698\pi$
$743$			41.7530i			1.53177i	−0.642979	+	0.765884i	$0.722302\pi$
$744$		0			0
$745$	−55.0847	−	31.8032i	−2.01815	−	1.16518i
$746$		0			0
$747$	−3.66096	−	6.34096i	−0.133947	−	0.232004i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−7.88020	+	4.54963i	−0.287552	+	0.166019i	−0.636838	−	0.770998i	$-0.719758\pi$
$751$	−7.88020	+	4.54963i	−0.287552	+	0.166019i	0.349285	+	0.937017i	$0.386424\pi$
$752$		0			0
$753$	−1.97816	+	3.42628i	−0.0720883	+	0.124861i
$754$		0			0
$755$	53.1371			1.93386
$756$		0			0
$757$	−0.902155			−0.0327894			−0.0163947	−	0.999866i	$-0.505219\pi$
$757$	−0.902155			−0.0327894			−0.0163947	+	0.999866i	$0.505219\pi$
$758$		0			0
$759$	−12.2293	+	21.1817i	−0.443894	+	0.768847i
$760$		0			0
$761$	−20.5924	+	11.8891i	−0.746475	+	0.430978i	−0.824419	−	0.565980i	$-0.808498\pi$
$761$	−20.5924	+	11.8891i	−0.746475	+	0.430978i	0.0779436	+	0.996958i	$0.475165\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	5.94420	+	10.2957i	0.214913	+	0.372240i
$766$		0			0
$767$	28.1028	+	16.2252i	1.01473	+	0.585857i
$768$		0			0
$769$		−	16.3028i		−	0.587895i	−0.955822	−	0.293948i	$-0.905031\pi$
$769$		−	16.3028i		−	0.587895i	0.955822	−	0.293948i	$-0.0949691\pi$
$770$		0			0
$771$		−	5.14822i		−	0.185409i
$772$		0			0
$773$	21.7270	+	12.5441i	0.781465	+	0.451179i	0.836949	−	0.547281i	$-0.184337\pi$
$773$	21.7270	+	12.5441i	0.781465	+	0.451179i	−0.0554845	+	0.998460i	$0.517670\pi$
$774$		0			0
$775$	−38.3632	−	66.4470i	−1.37805	−	2.38685i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	20.9691	−	12.1065i	0.751297	−	0.433761i
$780$		0			0
$781$	31.1809	−	54.0069i	1.11574	−	1.93252i
$782$		0			0
$783$	2.46054			0.0879327
$784$		0			0
$785$	−46.7996			−1.67035
$786$		0			0
$787$	2.23565	−	3.87226i	0.0796924	−	0.138031i	−0.823425	−	0.567425i	$-0.807940\pi$
$787$	2.23565	−	3.87226i	0.0796924	−	0.138031i	0.903117	+	0.429394i	$0.141273\pi$
$788$		0			0
$789$	−0.0679848	+	0.0392511i	−0.00242032	+	0.00139737i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−6.54918	−	11.3435i	−0.232568	−	0.402820i
$794$		0			0
$795$	−15.7186	−	9.07516i	−0.557483	−	0.321863i
$796$		0			0
$797$		−	6.62320i		−	0.234606i	−0.993096	−	0.117303i	$-0.962575\pi$
$797$		−	6.62320i		−	0.234606i	0.993096	−	0.117303i	$-0.0374248\pi$
$798$		0			0
$799$		−	14.8133i		−	0.524056i
$800$		0			0
$801$	−12.1631	−	7.02239i	−0.429763	−	0.248124i
$802$		0			0
$803$	29.1358	+	50.4646i	1.02818	+	1.78086i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−0.764956	+	0.441648i	−0.0269277	+	0.0155467i
$808$		0			0
$809$	4.18522	−	7.24901i	0.147144	−	0.254862i	−0.783027	−	0.621988i	$-0.786325\pi$
$809$	4.18522	−	7.24901i	0.147144	−	0.254862i	0.930171	+	0.367127i	$0.119658\pi$
$810$		0			0
$811$	−1.20944			−0.0424692			−0.0212346	−	0.999775i	$-0.506760\pi$
$811$	−1.20944			−0.0424692			−0.0212346	+	0.999775i	$0.506760\pi$
$812$		0			0
$813$	−19.3084			−0.677176
$814$		0			0
$815$	3.24494	−	5.62040i	0.113665	−	0.196874i
$816$		0			0
$817$	53.0312	−	30.6176i	1.85533	−	1.07117i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−25.6260	−	44.3855i	−0.894353	−	1.54906i	−0.834604	−	0.550851i	$-0.814303\pi$
$821$	−25.6260	−	44.3855i	−0.894353	−	1.54906i	−0.0597490	−	0.998213i	$-0.519030\pi$
$822$		0			0
$823$	27.3271	+	15.7773i	0.952563	+	0.549962i	0.893876	−	0.448314i	$-0.147975\pi$
$823$	27.3271	+	15.7773i	0.952563	+	0.549962i	0.0586866	+	0.998276i	$0.481309\pi$
$824$		0			0
$825$			68.1749i			2.37355i
$826$		0			0
$827$			23.4800i			0.816480i	0.912875	+	0.408240i	$0.133857\pi$
$827$			23.4800i			0.816480i	−0.912875	+	0.408240i	$0.866143\pi$
$828$		0			0
$829$	14.9510	+	8.63194i	0.519268	+	0.299800i	0.736635	−	0.676290i	$-0.236413\pi$
$829$	14.9510	+	8.63194i	0.519268	+	0.299800i	−0.217367	+	0.976090i	$0.569747\pi$
$830$		0			0
$831$	−8.46635	−	14.6641i	−0.293694	−	0.508694i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−38.4555	+	22.2023i	−1.33081	+	0.768342i
$836$		0			0
$837$	2.84882	−	4.93430i	0.0984696	−	0.170554i
$838$		0			0
$839$	−37.4781			−1.29389			−0.646943	−	0.762538i	$-0.723953\pi$
$839$	−37.4781			−1.29389			−0.646943	+	0.762538i	$0.723953\pi$
$840$		0			0
$841$	−22.9457			−0.791232
$842$		0			0
$843$	−2.52709	+	4.37704i	−0.0870375	+	0.150753i
$844$		0			0
$845$	−5.90155	+	3.40726i	−0.203019	+	0.117213i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	9.55781	+	16.5546i	0.328023	+	0.568153i
$850$		0			0
$851$	9.77077	+	5.64116i	0.334938	+	0.193376i
$852$		0			0
$853$		−	9.50115i		−	0.325313i	−0.986683	−	0.162657i	$-0.947994\pi$
$853$		−	9.50115i		−	0.325313i	0.986683	−	0.162657i	$-0.0520063\pi$
$854$		0			0
$855$		−	20.2108i		−	0.691193i
$856$		0			0
$857$	28.3880	+	16.3898i	0.969717	+	0.559866i	0.899150	−	0.437641i	$-0.144186\pi$
$857$	28.3880	+	16.3898i	0.969717	+	0.559866i	0.0705668	+	0.997507i	$0.477519\pi$
$858$		0			0
$859$	−2.68653	−	4.65321i	−0.0916633	−	0.158765i	0.816548	−	0.577278i	$-0.195885\pi$
$859$	−2.68653	−	4.65321i	−0.0916633	−	0.158765i	−0.908211	+	0.418512i	$0.862552\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−25.7057	+	14.8412i	−0.875031	+	0.505200i	−0.869017	−	0.494782i	$-0.835248\pi$
$863$	−25.7057	+	14.8412i	−0.875031	+	0.505200i	−0.00601431	+	0.999982i	$0.501914\pi$
$864$		0			0
$865$	−7.21169	+	12.4910i	−0.245205	+	0.424707i
$866$		0			0
$867$	9.34639			0.317420
$868$		0			0
$869$	−70.4544			−2.39000
$870$		0			0
$871$	−8.04659	+	13.9371i	−0.272648	+	0.472241i
$872$		0			0
$873$	12.6194	−	7.28581i	0.427102	−	0.246587i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	15.1621	+	26.2615i	0.511988	+	0.886789i	0.999903	+	0.0138982i	$0.00442409\pi$
$877$	15.1621	+	26.2615i	0.511988	+	0.886789i	−0.487915	+	0.872891i	$0.662243\pi$
$878$		0			0
$879$	−2.05973	−	1.18919i	−0.0694730	−	0.0401103i
$880$		0			0
$881$		−	16.5012i		−	0.555939i	−0.960590	−	0.277969i	$-0.910339\pi$
$881$		−	16.5012i		−	0.555939i	0.960590	−	0.277969i	$-0.0896614\pi$
$882$		0			0
$883$			22.5909i			0.760245i	0.924936	+	0.380122i	$0.124118\pi$
$883$			22.5909i			0.760245i	−0.924936	+	0.380122i	$0.875882\pi$
$884$		0			0
$885$	35.7452	+	20.6375i	1.20156	+	0.693722i
$886$		0			0
$887$	19.3018	+	33.4317i	0.648090	+	1.12253i	0.983578	+	0.180481i	$0.0577654\pi$
$887$	19.3018	+	33.4317i	0.648090	+	1.12253i	−0.335488	+	0.942044i	$0.608901\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−4.38435	+	2.53131i	−0.146881	+	0.0848020i
$892$		0			0
$893$	−12.5916	+	21.8093i	−0.421361	+	0.729819i
$894$		0			0
$895$	−56.9769			−1.90453
$896$		0			0
$897$	16.3222			0.544981
$898$		0			0
$899$	7.00965	−	12.1411i	0.233785	−	0.404927i
$900$		0			0
$901$	10.1195	−	5.84247i	0.337128	−	0.194641i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	25.4653	+	44.1072i	0.846496	+	1.46617i
$906$		0			0
$907$	−31.7609	−	18.3371i	−1.05460	−	0.608875i	−0.130668	−	0.991426i	$-0.541712\pi$
$907$	−31.7609	−	18.3371i	−1.05460	−	0.608875i	−0.923934	+	0.382551i	$0.875046\pi$
$908$		0			0
$909$		−	13.1087i		−	0.434787i
$910$		0			0
$911$		−	52.6835i		−	1.74548i	−0.488185	−	0.872740i	$-0.662341\pi$
$911$		−	52.6835i		−	1.74548i	0.488185	−	0.872740i	$-0.337659\pi$
$912$		0			0
$913$	32.1019	+	18.5340i	1.06242	+	0.613387i
$914$		0			0
$915$	−8.33018	−	14.4283i	−0.275387	−	0.476985i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	4.43074	−	2.55809i	0.146157	−	0.0843836i	−0.425138	−	0.905128i	$-0.639775\pi$
$919$	4.43074	−	2.55809i	0.146157	−	0.0843836i	0.571295	+	0.820745i	$0.306441\pi$
$920$		0			0
$921$	−2.44799	+	4.24005i	−0.0806642	+	0.139714i
$922$		0			0
$923$	−41.6166			−1.36983
$924$		0			0
$925$	31.4480			1.03400
$926$		0			0
$927$	−0.104849	+	0.181604i	−0.00344369	+	0.00596465i
$928$		0			0
$929$	−30.6308	+	17.6847i	−1.00496	+	0.580217i	−0.909713	−	0.415237i	$-0.863699\pi$
$929$	−30.6308	+	17.6847i	−1.00496	+	0.580217i	−0.0952512	+	0.995453i	$0.530365\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−5.24000	−	9.07594i	−0.171550	−	0.297133i
$934$		0			0
$935$	−52.1230	−	30.0932i	−1.70460	−	0.984153i
$936$		0			0
$937$			23.6290i			0.771924i	0.922515	+	0.385962i	$0.126130\pi$
$937$			23.6290i			0.771924i	−0.922515	+	0.385962i	$0.873870\pi$
$938$		0			0
$939$		−	9.60172i		−	0.313340i
$940$		0			0
$941$	−16.6438	−	9.60933i	−0.542574	−	0.313255i	0.203548	−	0.979065i	$-0.434753\pi$
$941$	−16.6438	−	9.60933i	−0.542574	−	0.313255i	−0.746121	+	0.665810i	$0.768086\pi$
$942$		0			0
$943$	12.4360	+	21.5399i	0.404973	+	0.701435i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−24.0892	+	13.9079i	−0.782795	+	0.451947i	−0.837420	−	0.546560i	$-0.815937\pi$
$947$	−24.0892	+	13.9079i	−0.782795	+	0.451947i	0.0546249	+	0.998507i	$0.482604\pi$
$948$		0			0
$949$	19.4435	−	33.6771i	0.631162	−	1.09321i
$950$		0			0
$951$	−16.7934			−0.544565
$952$		0			0
$953$	56.8087			1.84021			0.920107	−	0.391668i	$-0.128102\pi$
$953$	56.8087			1.84021			0.920107	+	0.391668i	$0.128102\pi$
$954$		0			0
$955$	−2.89335	+	5.01142i	−0.0936264	+	0.162166i
$956$		0			0
$957$	−10.7879	+	6.22840i	−0.348723	+	0.201335i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.731549	−	1.26708i	−0.0235984	−	0.0408736i
$962$		0			0
$963$	5.56558	+	3.21329i	0.179348	+	0.103547i
$964$		0			0
$965$			112.224i			3.61262i
$966$		0			0
$967$			20.3860i			0.655570i	0.944752	+	0.327785i	$0.106302\pi$
$967$			20.3860i			0.655570i	−0.944752	+	0.327785i	$0.893698\pi$
$968$		0			0
$969$	11.2682	+	6.50572i	0.361988	+	0.208994i
$970$		0			0
$971$	−5.61437	−	9.72437i	−0.180174	−	0.312070i	0.761766	−	0.647852i	$-0.224333\pi$
$971$	−5.61437	−	9.72437i	−0.180174	−	0.312070i	−0.941940	+	0.335782i	$0.890999\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	39.4007	−	22.7480i	1.26183	−	0.728518i
$976$		0			0
$977$	6.09164	−	10.5510i	0.194889	−	0.337557i	−0.751975	−	0.659191i	$-0.770899\pi$
$977$	6.09164	−	10.5510i	0.194889	−	0.337557i	0.946864	+	0.321634i	$0.104232\pi$
$978$		0			0
$979$	71.1033			2.27247
$980$		0			0
$981$	0.940024			0.0300126
$982$		0			0
$983$	4.53187	−	7.84943i	0.144544	−	0.250358i	−0.784659	−	0.619928i	$-0.787162\pi$
$983$	4.53187	−	7.84943i	0.144544	−	0.250358i	0.929203	+	0.369570i	$0.120495\pi$
$984$		0			0
$985$	27.8773	−	16.0950i	0.888245	−	0.512829i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	31.4509	+	54.4746i	1.00008	+	1.73219i
$990$		0			0
$991$	4.65193	+	2.68579i	0.147773	+	0.0853170i	0.572064	−	0.820209i	$-0.306143\pi$
$991$	4.65193	+	2.68579i	0.147773	+	0.0853170i	−0.424290	+	0.905526i	$0.639476\pi$
$992$		0			0
$993$			26.8362i			0.851622i
$994$		0			0
$995$		−	19.3096i		−	0.612157i
$996$		0			0
$997$	−12.4222	−	7.17199i	−0.393417	−	0.227139i	0.290223	−	0.956959i	$-0.406271\pi$
$997$	−12.4222	−	7.17199i	−0.393417	−	0.227139i	−0.683639	+	0.729820i	$0.739604\pi$
$998$		0			0
$999$	1.16765	+	2.02243i	0.0369429	+	0.0639869i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2352.2.bl.q.31.1		8
4.3	odd	2		2352.2.bl.r.31.1		8
7.2	even	3		2352.2.bl.o.607.4		8
7.3	odd	6		2352.2.b.k.1567.8	yes	8
7.4	even	3		2352.2.b.l.1567.1	yes	8
7.5	odd	6		2352.2.bl.r.607.1		8
7.6	odd	2		2352.2.bl.t.31.4		8
21.11	odd	6		7056.2.b.w.1567.8		8
21.17	even	6		7056.2.b.x.1567.1		8
28.3	even	6		2352.2.b.l.1567.8	yes	8
28.11	odd	6		2352.2.b.k.1567.1	✓	8
28.19	even	6	inner	2352.2.bl.q.607.1		8
28.23	odd	6		2352.2.bl.t.607.4		8
28.27	even	2		2352.2.bl.o.31.4		8
84.11	even	6		7056.2.b.x.1567.8		8
84.59	odd	6		7056.2.b.w.1567.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2352.2.b.k.1567.1	✓	8	28.11	odd	6
2352.2.b.k.1567.8	yes	8	7.3	odd	6
2352.2.b.l.1567.1	yes	8	7.4	even	3
2352.2.b.l.1567.8	yes	8	28.3	even	6
2352.2.bl.o.31.4		8	28.27	even	2
2352.2.bl.o.607.4		8	7.2	even	3
2352.2.bl.q.31.1		8	1.1	even	1	trivial
2352.2.bl.q.607.1		8	28.19	even	6	inner
2352.2.bl.r.31.1		8	4.3	odd	2
2352.2.bl.r.607.1		8	7.5	odd	6
2352.2.bl.t.31.4		8	7.6	odd	2
2352.2.bl.t.607.4		8	28.23	odd	6
7056.2.b.w.1567.1		8	84.59	odd	6
7056.2.b.w.1567.8		8	21.11	odd	6
7056.2.b.x.1567.1		8	21.17	even	6
7056.2.b.x.1567.8		8	84.11	even	6

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:	\( N \)	\(=\)	\( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2352.bl (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +(-3.72153 + 2.14862i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(4.38435 + 2.53131i) q^{11} -3.37849i q^{13} -4.29725i q^{15} +(2.39587 + 1.38326i) q^{17} +(-2.35159 - 4.07308i) q^{19} +(4.18394 - 2.41560i) q^{23} +(6.73317 - 11.6622i) q^{25} +1.00000 q^{27} +2.46054 q^{29} +(2.84882 - 4.93430i) q^{31} +(-4.38435 + 2.53131i) q^{33} +(1.16765 + 2.02243i) q^{37} +(2.92586 + 1.68925i) q^{39} +5.14822i q^{41} +13.0199i q^{43} +(3.72153 + 2.14862i) q^{45} +(-2.67725 - 4.63713i) q^{47} +(-2.39587 + 1.38326i) q^{51} +(2.11185 - 3.65784i) q^{53} -21.7553 q^{55} +4.70319 q^{57} +(-4.80249 + 8.31815i) q^{59} +(3.35757 - 1.93849i) q^{61} +(7.25911 + 12.5732i) q^{65} +(-4.12524 - 2.38171i) q^{67} +4.83120i q^{69} -12.3181i q^{71} +(9.96809 + 5.75508i) q^{73} +(6.73317 + 11.6622i) q^{75} +(-12.0521 + 6.95830i) q^{79} +(-0.500000 + 0.866025i) q^{81} +7.32191 q^{83} -11.8884 q^{85} +(-1.23027 + 2.13089i) q^{87} +(12.1631 - 7.02239i) q^{89} +(2.84882 + 4.93430i) q^{93} +(17.5030 + 10.1054i) q^{95} +14.5716i q^{97} -5.06262i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} - 4 q^{9} + 24 q^{23} + 12 q^{25} + 8 q^{27} + 16 q^{29} + 16 q^{31} + 8 q^{47} - 8 q^{53} - 64 q^{55} - 24 q^{59} + 48 q^{61} + 8 q^{65} - 48 q^{67} + 48 q^{73} + 12 q^{75} - 24 q^{79} - 4 q^{81}+ \cdots + 72 q^{95}+O(q^{100}) \) 8 * q - 4 * q^3 - 4 * q^9 + 24 * q^23 + 12 * q^25 + 8 * q^27 + 16 * q^29 + 16 * q^31 + 8 * q^47 - 8 * q^53 - 64 * q^55 - 24 * q^59 + 48 * q^61 + 8 * q^65 - 48 * q^67 + 48 * q^73 + 12 * q^75 - 24 * q^79 - 4 * q^81 - 64 * q^85 - 8 * q^87 + 48 * q^89 + 16 * q^93 + 72 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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