LMFDB - Embedded newform 1408.2.i.b.351.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1408,2,Mod(351,1408)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1408, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

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

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

chi := DirichletCharacter("1408.351");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1408 = 2^{7} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1408.i (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.2429366046$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 176)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			351.18
Character	$\chi$	$=$	1408.351
Dual form			1408.2.i.b.1055.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.64229 - 1.64229i) q^{3} +(-1.97065 + 1.97065i) q^{5} +1.30445i q^{7} -2.39422i q^{9} +O(q^{10})$	\(q+(1.64229 - 1.64229i) q^{3} +(-1.97065 + 1.97065i) q^{5} +1.30445i q^{7} -2.39422i q^{9} +(-1.98269 - 2.65875i) q^{11} +(3.45212 - 3.45212i) q^{13} +6.47274i q^{15} -6.16050i q^{17} +(4.15098 + 4.15098i) q^{19} +(2.14228 + 2.14228i) q^{21} -2.00639 q^{23} -2.76691i q^{25} +(0.994862 + 0.994862i) q^{27} +(4.66521 - 4.66521i) q^{29} -6.42706i q^{31} +(-7.62258 - 1.11028i) q^{33} +(-2.57060 - 2.57060i) q^{35} +(1.08623 - 1.08623i) q^{37} -11.3387i q^{39} +4.81907 q^{41} +(5.77453 - 5.77453i) q^{43} +(4.71817 + 4.71817i) q^{45} +4.74805i q^{47} +5.29842 q^{49} +(-10.1173 - 10.1173i) q^{51} +(3.23296 - 3.23296i) q^{53} +(9.14664 + 1.33227i) q^{55} +13.6342 q^{57} +(-1.19357 - 1.19357i) q^{59} +(-1.81748 + 1.81748i) q^{61} +3.12313 q^{63} +13.6058i q^{65} +(-1.51245 + 1.51245i) q^{67} +(-3.29507 + 3.29507i) q^{69} -10.1099 q^{71} +5.86346 q^{73} +(-4.54406 - 4.54406i) q^{75} +(3.46819 - 2.58631i) q^{77} +8.60673 q^{79} +10.4504 q^{81} +(-6.28852 - 6.28852i) q^{83} +(12.1402 + 12.1402i) q^{85} -15.3232i q^{87} -6.63409i q^{89} +(4.50310 + 4.50310i) q^{91} +(-10.5551 - 10.5551i) q^{93} -16.3603 q^{95} -14.4459 q^{97} +(-6.36563 + 4.74700i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 4 q^{3} + 4 q^{5}+O(q^{10}) $ 44 * q + 4 * q^3 + 4 * q^5	$ 44 q + 4 q^{3} + 4 q^{5} + 6 q^{11} - 24 q^{23} - 8 q^{27} - 4 q^{33} + 20 q^{37} - 28 q^{45} - 28 q^{49} - 12 q^{53} - 36 q^{55} + 20 q^{59} - 36 q^{67} + 16 q^{69} - 40 q^{71} - 60 q^{75} - 4 q^{77} - 20 q^{81} - 56 q^{91} - 8 q^{93} - 8 q^{97} + 42 q^{99}+O(q^{100}) $ 44 * q + 4 * q^3 + 4 * q^5 + 6 * q^11 - 24 * q^23 - 8 * q^27 - 4 * q^33 + 20 * q^37 - 28 * q^45 - 28 * q^49 - 12 * q^53 - 36 * q^55 + 20 * q^59 - 36 * q^67 + 16 * q^69 - 40 * q^71 - 60 * q^75 - 4 * q^77 - 20 * q^81 - 56 * q^91 - 8 * q^93 - 8 * q^97 + 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1408\mathbb{Z}\right)^\times$.

$n$	$133$	$639$	$1025$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.64229	−	1.64229i	0.948176	−	0.948176i	−0.0505461	−	0.998722i	$-0.516096\pi$
$3$	1.64229	−	1.64229i	0.948176	−	0.948176i	0.998722	+	0.0505461i	$0.0160962\pi$
$4$		0			0
$5$	−1.97065	+	1.97065i	−0.881301	+	0.881301i	−0.993667	−	0.112366i	$-0.964157\pi$
$5$	−1.97065	+	1.97065i	−0.881301	+	0.881301i	0.112366	+	0.993667i	$0.464157\pi$
$6$		0			0
$7$			1.30445i			0.493034i	0.969138	+	0.246517i	$0.0792862\pi$
$7$			1.30445i			0.493034i	−0.969138	+	0.246517i	$0.920714\pi$
$8$		0			0
$9$		−	2.39422i		−	0.798074i
$10$		0			0
$11$	−1.98269	−	2.65875i	−0.597804	−	0.801643i
$11$	−1.98269	−	2.65875i	−0.597804	−	0.801643i
$12$		0			0
$13$	3.45212	−	3.45212i	0.957445	−	0.957445i	−0.0416860	−	0.999131i	$-0.513273\pi$
$13$	3.45212	−	3.45212i	0.957445	−	0.957445i	0.999131	+	0.0416860i	$0.0132729\pi$
$14$		0			0
$15$			6.47274i			1.67126i
$16$		0			0
$17$		−	6.16050i		−	1.49414i	−0.664745	−	0.747070i	$-0.731460\pi$
$17$		−	6.16050i		−	1.49414i	0.664745	−	0.747070i	$-0.268540\pi$
$18$		0			0
$19$	4.15098	+	4.15098i	0.952301	+	0.952301i	0.998913	−	0.0466123i	$-0.0148425\pi$
$19$	4.15098	+	4.15098i	0.952301	+	0.952301i	−0.0466123	+	0.998913i	$0.514843\pi$
$20$		0			0
$21$	2.14228	+	2.14228i	0.467483	+	0.467483i
$22$		0			0
$23$	−2.00639			−0.418361			−0.209181	−	0.977877i	$-0.567080\pi$
$23$	−2.00639			−0.418361			−0.209181	+	0.977877i	$0.567080\pi$
$24$		0			0
$25$		−	2.76691i		−	0.553381i
$26$		0			0
$27$	0.994862	+	0.994862i	0.191461	+	0.191461i
$28$		0			0
$29$	4.66521	−	4.66521i	0.866307	−	0.866307i	−0.125754	−	0.992061i	$-0.540135\pi$
$29$	4.66521	−	4.66521i	0.866307	−	0.866307i	0.992061	+	0.125754i	$0.0401351\pi$
$30$		0			0
$31$		−	6.42706i		−	1.15433i	−0.816626	−	0.577167i	$-0.804158\pi$
$31$		−	6.42706i		−	1.15433i	0.816626	−	0.577167i	$-0.195842\pi$
$32$		0			0
$33$	−7.62258	−	1.11028i	−1.32692	−	0.193275i
$34$		0			0
$35$	−2.57060	−	2.57060i	−0.434511	−	0.434511i
$36$		0			0
$37$	1.08623	−	1.08623i	0.178576	−	0.178576i	−0.612159	−	0.790735i	$-0.709699\pi$
$37$	1.08623	−	1.08623i	0.178576	−	0.178576i	0.790735	+	0.612159i	$0.209699\pi$
$38$		0			0
$39$		−	11.3387i		−	1.81565i
$40$		0			0
$41$	4.81907			0.752612			0.376306	−	0.926495i	$-0.377194\pi$
$41$	4.81907			0.752612			0.376306	+	0.926495i	$0.377194\pi$
$42$		0			0
$43$	5.77453	−	5.77453i	0.880607	−	0.880607i	−0.112989	−	0.993596i	$-0.536042\pi$
$43$	5.77453	−	5.77453i	0.880607	−	0.880607i	0.993596	+	0.112989i	$0.0360425\pi$
$44$		0			0
$45$	4.71817	+	4.71817i	0.703343	+	0.703343i
$46$		0			0
$47$			4.74805i			0.692574i	0.938129	+	0.346287i	$0.112558\pi$
$47$			4.74805i			0.692574i	−0.938129	+	0.346287i	$0.887442\pi$
$48$		0			0
$49$	5.29842			0.756917
$50$		0			0
$51$	−10.1173	−	10.1173i	−1.41671	−	1.41671i
$52$		0			0
$53$	3.23296	−	3.23296i	0.444081	−	0.444081i	−0.449300	−	0.893381i	$-0.648327\pi$
$53$	3.23296	−	3.23296i	0.444081	−	0.444081i	0.893381	+	0.449300i	$0.148327\pi$
$54$		0			0
$55$	9.14664	+	1.33227i	1.23333	+	0.179643i
$56$		0			0
$57$	13.6342			1.80590
$58$		0			0
$59$	−1.19357	−	1.19357i	−0.155389	−	0.155389i	0.625131	−	0.780520i	$-0.285046\pi$
$59$	−1.19357	−	1.19357i	−0.155389	−	0.155389i	−0.780520	+	0.625131i	$0.785046\pi$
$60$		0			0
$61$	−1.81748	+	1.81748i	−0.232704	+	0.232704i	−0.813821	−	0.581116i	$-0.802616\pi$
$61$	−1.81748	+	1.81748i	−0.232704	+	0.232704i	0.581116	+	0.813821i	$0.302616\pi$
$62$		0			0
$63$	3.12313			0.393478
$64$		0			0
$65$			13.6058i			1.68759i
$66$		0			0
$67$	−1.51245	+	1.51245i	−0.184775	+	0.184775i	−0.793433	−	0.608658i	$-0.791708\pi$
$67$	−1.51245	+	1.51245i	−0.184775	+	0.184775i	0.608658	+	0.793433i	$0.291708\pi$
$68$		0			0
$69$	−3.29507	+	3.29507i	−0.396680	+	0.396680i
$70$		0			0
$71$	−10.1099			−1.19982			−0.599911	−	0.800067i	$-0.704797\pi$
$71$	−10.1099			−1.19982			−0.599911	+	0.800067i	$0.704797\pi$
$72$		0			0
$73$	5.86346			0.686266			0.343133	−	0.939287i	$-0.388512\pi$
$73$	5.86346			0.686266			0.343133	+	0.939287i	$0.388512\pi$
$74$		0			0
$75$	−4.54406	−	4.54406i	−0.524703	−	0.524703i
$76$		0			0
$77$	3.46819	−	2.58631i	0.395237	−	0.294738i
$78$		0			0
$79$	8.60673			0.968333			0.484166	−	0.874976i	$-0.339123\pi$
$79$	8.60673			0.968333			0.484166	+	0.874976i	$0.339123\pi$
$80$		0			0
$81$	10.4504			1.16115
$82$		0			0
$83$	−6.28852	−	6.28852i	−0.690255	−	0.690255i	0.272033	−	0.962288i	$-0.412304\pi$
$83$	−6.28852	−	6.28852i	−0.690255	−	0.690255i	−0.962288	+	0.272033i	$0.912304\pi$
$84$		0			0
$85$	12.1402	+	12.1402i	1.31679	+	1.31679i
$86$		0			0
$87$		−	15.3232i		−	1.64282i
$88$		0			0
$89$		−	6.63409i		−	0.703212i	−0.936148	−	0.351606i	$-0.885636\pi$
$89$		−	6.63409i		−	0.703212i	0.936148	−	0.351606i	$-0.114364\pi$
$90$		0			0
$91$	4.50310	+	4.50310i	0.472053	+	0.472053i
$92$		0			0
$93$	−10.5551	−	10.5551i	−1.09451	−	1.09451i
$94$		0			0
$95$	−16.3603			−1.67853
$96$		0			0
$97$	−14.4459			−1.46676			−0.733381	−	0.679818i	$-0.762059\pi$
$97$	−14.4459			−1.46676			−0.733381	+	0.679818i	$0.762059\pi$
$98$		0			0
$99$	−6.36563	+	4.74700i	−0.639770	+	0.477092i
$100$		0			0
$101$	0.718720	+	0.718720i	0.0715153	+	0.0715153i	0.741960	−	0.670444i	$-0.233897\pi$
$101$	0.718720	+	0.718720i	0.0715153	+	0.0715153i	−0.670444	+	0.741960i	$0.733897\pi$
$102$		0			0
$103$	−5.45098			−0.537101			−0.268551	−	0.963266i	$-0.586545\pi$
$103$	−5.45098			−0.537101			−0.268551	+	0.963266i	$0.586545\pi$
$104$		0			0
$105$	−8.44335			−0.823986
$106$		0			0
$107$	−4.21540	+	4.21540i	−0.407518	+	0.407518i	−0.880872	−	0.473354i	$-0.843043\pi$
$107$	−4.21540	+	4.21540i	−0.407518	+	0.407518i	0.473354	+	0.880872i	$0.343043\pi$
$108$		0			0
$109$	−11.6029	+	11.6029i	−1.11135	+	1.11135i	−0.118386	+	0.992968i	$0.537772\pi$
$109$	−11.6029	+	11.6029i	−1.11135	+	1.11135i	−0.992968	+	0.118386i	$0.962228\pi$
$110$		0			0
$111$		−	3.56782i		−	0.338642i
$112$		0			0
$113$	7.78670			0.732511			0.366256	−	0.930514i	$-0.380640\pi$
$113$	7.78670			0.732511			0.366256	+	0.930514i	$0.380640\pi$
$114$		0			0
$115$	3.95389	−	3.95389i	0.368702	−	0.368702i
$116$		0			0
$117$	−8.26513	−	8.26513i	−0.764112	−	0.764112i
$118$		0			0
$119$	8.03604			0.736663
$120$		0			0
$121$	−3.13788	+	10.5429i	−0.285262	+	0.958450i
$122$		0			0
$123$	7.91430	−	7.91430i	0.713608	−	0.713608i
$124$		0			0
$125$	−4.40064	−	4.40064i	−0.393605	−	0.393605i
$126$		0			0
$127$	−1.23830			−0.109882			−0.0549408	−	0.998490i	$-0.517497\pi$
$127$	−1.23830			−0.109882			−0.0549408	+	0.998490i	$0.517497\pi$
$128$		0			0
$129$		−	18.9669i		−	1.66994i
$130$		0			0
$131$	−4.75753	−	4.75753i	−0.415668	−	0.415668i	0.468040	−	0.883707i	$-0.344960\pi$
$131$	−4.75753	−	4.75753i	−0.415668	−	0.415668i	−0.883707	+	0.468040i	$0.844960\pi$
$132$		0			0
$133$	−5.41473	+	5.41473i	−0.469517	+	0.469517i
$134$		0			0
$135$	−3.92105			−0.337470
$136$		0			0
$137$			16.0454i			1.37085i	0.728143	+	0.685425i	$0.240384\pi$
$137$			16.0454i			1.37085i	−0.728143	+	0.685425i	$0.759616\pi$
$138$		0			0
$139$	−10.1344	+	10.1344i	−0.859585	+	0.859585i	−0.991289	−	0.131704i	$-0.957955\pi$
$139$	−10.1344	+	10.1344i	−0.859585	+	0.859585i	0.131704	+	0.991289i	$0.457955\pi$
$140$		0			0
$141$	7.79766	+	7.79766i	0.656682	+	0.656682i
$142$		0			0
$143$	−16.0228	−	2.33383i	−1.33989	−	0.195165i
$144$		0			0
$145$			18.3870i			1.52695i
$146$		0			0
$147$	8.70153	−	8.70153i	0.717690	−	0.717690i
$148$		0			0
$149$	−14.9286	−	14.9286i	−1.22300	−	1.22300i	−0.966559	−	0.256443i	$-0.917450\pi$
$149$	−14.9286	−	14.9286i	−1.22300	−	1.22300i	−0.256443	−	0.966559i	$-0.582550\pi$
$150$		0			0
$151$		−	5.18799i		−	0.422193i	−0.977465	−	0.211096i	$-0.932297\pi$
$151$		−	5.18799i		−	0.422193i	0.977465	−	0.211096i	$-0.0677034\pi$
$152$		0			0
$153$	−14.7496			−1.19243
$154$		0			0
$155$	12.6655	+	12.6655i	1.01732	+	1.01732i
$156$		0			0
$157$	2.57565	+	2.57565i	0.205559	+	0.205559i	0.802377	−	0.596818i	$-0.203568\pi$
$157$	2.57565	+	2.57565i	0.205559	+	0.205559i	−0.596818	+	0.802377i	$0.703568\pi$
$158$		0			0
$159$		−	10.6189i		−	0.842133i
$160$		0			0
$161$		−	2.61723i		−	0.206266i
$162$		0			0
$163$	−17.6194	+	17.6194i	−1.38006	+	1.38006i	−0.535559	+	0.844498i	$0.679899\pi$
$163$	−17.6194	+	17.6194i	−1.38006	+	1.38006i	−0.844498	+	0.535559i	$0.820101\pi$
$164$		0			0
$165$	17.2094	−	12.8334i	1.33975	−	0.999082i
$166$		0			0
$167$			21.1682i			1.63804i	0.573763	+	0.819021i	$0.305483\pi$
$167$			21.1682i			1.63804i	−0.573763	+	0.819021i	$0.694517\pi$
$168$		0			0
$169$		−	10.8342i		−	0.833401i
$170$		0			0
$171$	9.93837	−	9.93837i	0.760006	−	0.760006i
$172$		0			0
$173$	14.3344	−	14.3344i	1.08982	−	1.08982i	0.0942746	−	0.995546i	$-0.469947\pi$
$173$	14.3344	−	14.3344i	1.08982	−	1.08982i	0.995546	−	0.0942746i	$-0.0300532\pi$
$174$		0			0
$175$	3.60928			0.272836
$176$		0			0
$177$	−3.92037			−0.294673
$178$		0			0
$179$	−0.0982140	+	0.0982140i	−0.00734086	+	0.00734086i	−0.710768	−	0.703427i	$-0.751652\pi$
$179$	−0.0982140	+	0.0982140i	−0.00734086	+	0.00734086i	0.703427	+	0.710768i	$0.251652\pi$
$180$		0			0
$181$	9.76036	−	9.76036i	0.725482	−	0.725482i	−0.244234	−	0.969716i	$-0.578537\pi$
$181$	9.76036	−	9.76036i	0.725482	−	0.725482i	0.969716	+	0.244234i	$0.0785366\pi$
$182$		0			0
$183$			5.96965i			0.441289i
$184$		0			0
$185$			4.28117i			0.314758i
$186$		0			0
$187$	−16.3792	+	12.2144i	−1.19777	+	0.893203i
$188$		0			0
$189$	−1.29774	+	1.29774i	−0.0943970	+	0.0943970i
$190$		0			0
$191$		−	4.98765i		−	0.360894i	−0.983585	−	0.180447i	$-0.942246\pi$
$191$		−	4.98765i		−	0.360894i	0.983585	−	0.180447i	$-0.0577544\pi$
$192$		0			0
$193$		−	0.237674i		−	0.0171081i	−0.999963	−	0.00855406i	$-0.997277\pi$
$193$		−	0.237674i		−	0.0171081i	0.999963	−	0.00855406i	$-0.00272287\pi$
$194$		0			0
$195$	22.3447	+	22.3447i	1.60013	+	1.60013i
$196$		0			0
$197$	15.6379	+	15.6379i	1.11416	+	1.11416i	0.992583	+	0.121573i	$0.0387937\pi$
$197$	15.6379	+	15.6379i	1.11416	+	1.11416i	0.121573	+	0.992583i	$0.461206\pi$
$198$		0			0
$199$	−3.70867			−0.262900			−0.131450	−	0.991323i	$-0.541963\pi$
$199$	−3.70867			−0.262900			−0.131450	+	0.991323i	$0.541963\pi$
$200$		0			0
$201$			4.96776i			0.350399i
$202$		0			0
$203$	6.08551	+	6.08551i	0.427119	+	0.427119i
$204$		0			0
$205$	−9.49669	+	9.49669i	−0.663277	+	0.663277i
$206$		0			0
$207$			4.80374i			0.333883i
$208$		0			0
$209$	2.80630	−	19.2665i	0.194116	−	1.33269i
$210$		0			0
$211$	19.1238	+	19.1238i	1.31653	+	1.31653i	0.916500	+	0.400034i	$0.131002\pi$
$211$	19.1238	+	19.1238i	1.31653	+	1.31653i	0.400034	+	0.916500i	$0.368998\pi$
$212$		0			0
$213$	−16.6033	+	16.6033i	−1.13764	+	1.13764i
$214$		0			0
$215$			22.7591i			1.55216i
$216$		0			0
$217$	8.38376			0.569127
$218$		0			0
$219$	9.62949	−	9.62949i	0.650701	−	0.650701i
$220$		0			0
$221$	−21.2668	−	21.2668i	−1.43056	−	1.43056i
$222$		0			0
$223$		−	1.73302i		−	0.116051i	−0.998315	−	0.0580257i	$-0.981519\pi$
$223$		−	1.73302i		−	0.116051i	0.998315	−	0.0580257i	$-0.0184805\pi$
$224$		0			0
$225$	−6.62459			−0.441639
$226$		0			0
$227$	−0.474965	−	0.474965i	−0.0315245	−	0.0315245i	0.691169	−	0.722693i	$-0.257096\pi$
$227$	−0.474965	−	0.474965i	−0.0315245	−	0.0315245i	−0.722693	+	0.691169i	$0.757096\pi$
$228$		0			0
$229$	15.6441	−	15.6441i	1.03379	−	1.03379i	0.0343851	−	0.999409i	$-0.489053\pi$
$229$	15.6441	−	15.6441i	1.03379	−	1.03379i	0.999409	−	0.0343851i	$-0.0109473\pi$
$230$		0			0
$231$	1.44830	−	9.94324i	0.0952913	−	0.654217i
$232$		0			0
$233$	4.71321			0.308772			0.154386	−	0.988011i	$-0.450660\pi$
$233$	4.71321			0.308772			0.154386	+	0.988011i	$0.450660\pi$
$234$		0			0
$235$	−9.35673	−	9.35673i	−0.610366	−	0.610366i
$236$		0			0
$237$	14.1347	−	14.1347i	0.918150	−	0.918150i
$238$		0			0
$239$	5.38153			0.348102			0.174051	−	0.984737i	$-0.444314\pi$
$239$	5.38153			0.348102			0.174051	+	0.984737i	$0.444314\pi$
$240$		0			0
$241$			12.9397i			0.833518i	0.909017	+	0.416759i	$0.136834\pi$
$241$			12.9397i			0.833518i	−0.909017	+	0.416759i	$0.863166\pi$
$242$		0			0
$243$	14.1779	−	14.1779i	0.909515	−	0.909515i
$244$		0			0
$245$	−10.4413	+	10.4413i	−0.667071	+	0.667071i
$246$		0			0
$247$	28.6593			1.82355
$248$		0			0
$249$	−20.6551			−1.30897
$250$		0			0
$251$	5.06373	+	5.06373i	0.319620	+	0.319620i	0.848621	−	0.529001i	$-0.177433\pi$
$251$	5.06373	+	5.06373i	0.319620	+	0.319620i	−0.529001	+	0.848621i	$0.677433\pi$
$252$		0			0
$253$	3.97805	+	5.33448i	0.250098	+	0.335376i
$254$		0			0
$255$	39.8753			2.49709
$256$		0			0
$257$	1.00113			0.0624489			0.0312245	−	0.999512i	$-0.490059\pi$
$257$	1.00113			0.0624489			0.0312245	+	0.999512i	$0.490059\pi$
$258$		0			0
$259$	1.41693	+	1.41693i	0.0880440	+	0.0880440i
$260$		0			0
$261$	−11.1695	−	11.1695i	−0.691377	−	0.691377i
$262$		0			0
$263$		−	9.72228i		−	0.599501i	−0.954018	−	0.299751i	$-0.903096\pi$
$263$		−	9.72228i		−	0.599501i	0.954018	−	0.299751i	$-0.0969035\pi$
$264$		0			0
$265$			12.7420i			0.782737i
$266$		0			0
$267$	−10.8951	−	10.8951i	−0.666769	−	0.666769i
$268$		0			0
$269$	13.4756	+	13.4756i	0.821623	+	0.821623i	0.986341	−	0.164717i	$-0.0526712\pi$
$269$	13.4756	+	13.4756i	0.821623	+	0.821623i	−0.164717	+	0.986341i	$0.552671\pi$
$270$		0			0
$271$	10.1811			0.618460			0.309230	−	0.950987i	$-0.399929\pi$
$271$	10.1811			0.618460			0.309230	+	0.950987i	$0.399929\pi$
$272$		0			0
$273$	14.7908			0.895179
$274$		0			0
$275$	−7.35650	+	5.48592i	−0.443614	+	0.330813i
$276$		0			0
$277$	8.92325	+	8.92325i	0.536146	+	0.536146i	0.922395	−	0.386248i	$-0.126229\pi$
$277$	8.92325	+	8.92325i	0.536146	+	0.536146i	−0.386248	+	0.922395i	$0.626229\pi$
$278$		0			0
$279$	−15.3878			−0.921245
$280$		0			0
$281$	5.65654			0.337441			0.168720	−	0.985664i	$-0.446037\pi$
$281$	5.65654			0.337441			0.168720	+	0.985664i	$0.446037\pi$
$282$		0			0
$283$	11.7276	−	11.7276i	0.697133	−	0.697133i	−0.266658	−	0.963791i	$-0.585919\pi$
$283$	11.7276	−	11.7276i	0.697133	−	0.697133i	0.963791	+	0.266658i	$0.0859194\pi$
$284$		0			0
$285$	−26.8682	+	26.8682i	−1.59154	+	1.59154i
$286$		0			0
$287$			6.28622i			0.371064i
$288$		0			0
$289$	−20.9518			−1.23246
$290$		0			0
$291$	−23.7244	+	23.7244i	−1.39075	+	1.39075i
$292$		0			0
$293$	−18.5738	−	18.5738i	−1.08510	−	1.08510i	−0.996025	−	0.0890706i	$-0.971610\pi$
$293$	−18.5738	−	18.5738i	−1.08510	−	1.08510i	−0.0890706	−	0.996025i	$-0.528390\pi$
$294$		0			0
$295$	4.70421			0.273889
$296$		0			0
$297$	0.672584	−	4.61759i	0.0390273	−	0.267940i
$298$		0			0
$299$	−6.92629	+	6.92629i	−0.400558	+	0.400558i
$300$		0			0
$301$	7.53256	+	7.53256i	0.434170	+	0.434170i
$302$		0			0
$303$	2.36069			0.135618
$304$		0			0
$305$		−	7.16323i		−	0.410165i
$306$		0			0
$307$	3.27417	+	3.27417i	0.186867	+	0.186867i	0.794340	−	0.607473i	$-0.207817\pi$
$307$	3.27417	+	3.27417i	0.186867	+	0.186867i	−0.607473	+	0.794340i	$0.707817\pi$
$308$		0			0
$309$	−8.95208	+	8.95208i	−0.509266	+	0.509266i
$310$		0			0
$311$	−3.88550			−0.220326			−0.110163	−	0.993914i	$-0.535137\pi$
$311$	−3.88550			−0.220326			−0.110163	+	0.993914i	$0.535137\pi$
$312$		0			0
$313$		−	24.4120i		−	1.37985i	−0.723882	−	0.689924i	$-0.757644\pi$
$313$		−	24.4120i		−	1.37985i	0.723882	−	0.689924i	$-0.242356\pi$
$314$		0			0
$315$	−6.15460	+	6.15460i	−0.346772	+	0.346772i
$316$		0			0
$317$	−0.667694	−	0.667694i	−0.0375014	−	0.0375014i	0.688107	−	0.725609i	$-0.258442\pi$
$317$	−0.667694	−	0.667694i	−0.0375014	−	0.0375014i	−0.725609	+	0.688107i	$0.758442\pi$
$318$		0			0
$319$	−21.6533	−	3.15395i	−1.21235	−	0.176587i
$320$		0			0
$321$			13.8458i			0.772797i
$322$		0			0
$323$	25.5721	−	25.5721i	1.42287	−	1.42287i
$324$		0			0
$325$	−9.55168	−	9.55168i	−0.529832	−	0.529832i
$326$		0			0
$327$			38.1105i			2.10752i
$328$		0			0
$329$	−6.19357			−0.341463
$330$		0			0
$331$	−17.6579	−	17.6579i	−0.970567	−	0.970567i	0.0290123	−	0.999579i	$-0.490764\pi$
$331$	−17.6579	−	17.6579i	−0.970567	−	0.970567i	−0.999579	+	0.0290123i	$0.990764\pi$
$332$		0			0
$333$	−2.60069	−	2.60069i	−0.142517	−	0.142517i
$334$		0			0
$335$		−	5.96101i		−	0.325685i
$336$		0			0
$337$		−	4.75055i		−	0.258779i	−0.991594	−	0.129389i	$-0.958698\pi$
$337$		−	4.75055i		−	0.258779i	0.991594	−	0.129389i	$-0.0413017\pi$
$338$		0			0
$339$	12.7880	−	12.7880i	0.694549	−	0.694549i
$340$		0			0
$341$	−17.0879	+	12.7429i	−0.925364	+	0.690065i
$342$		0			0
$343$			16.0426i			0.866220i
$344$		0			0
$345$		−	12.9868i		−	0.699188i
$346$		0			0
$347$	−23.3539	+	23.3539i	−1.25370	+	1.25370i	−0.299656	+	0.954047i	$0.596872\pi$
$347$	−23.3539	+	23.3539i	−1.25370	+	1.25370i	−0.954047	+	0.299656i	$0.903128\pi$
$348$		0			0
$349$	7.94784	−	7.94784i	0.425438	−	0.425438i	−0.461633	−	0.887071i	$-0.652736\pi$
$349$	7.94784	−	7.94784i	0.425438	−	0.425438i	0.887071	+	0.461633i	$0.152736\pi$
$350$		0			0
$351$	6.86876			0.366627
$352$		0			0
$353$	30.8181			1.64028			0.820141	−	0.572162i	$-0.193895\pi$
$353$	30.8181			1.64028			0.820141	+	0.572162i	$0.193895\pi$
$354$		0			0
$355$	19.9230	−	19.9230i	1.05740	−	1.05740i
$356$		0			0
$357$	13.1975	−	13.1975i	0.698486	−	0.698486i
$358$		0			0
$359$		−	2.41968i		−	0.127706i	−0.997959	−	0.0638529i	$-0.979661\pi$
$359$		−	2.41968i		−	0.127706i	0.997959	−	0.0638529i	$-0.0203388\pi$
$360$		0			0
$361$			15.4613i			0.813753i
$362$		0			0
$363$	12.1613	+	22.4679i	0.638300	+	1.17926i
$364$		0			0
$365$	−11.5548	+	11.5548i	−0.604806	+	0.604806i
$366$		0			0
$367$			33.6337i			1.75567i	0.478966	+	0.877833i	$0.341012\pi$
$367$			33.6337i			1.75567i	−0.478966	+	0.877833i	$0.658988\pi$
$368$		0			0
$369$		−	11.5379i		−	0.600640i
$370$		0			0
$371$	4.21722	+	4.21722i	0.218947	+	0.218947i
$372$		0			0
$373$	5.01540	+	5.01540i	0.259687	+	0.259687i	0.824927	−	0.565239i	$-0.191216\pi$
$373$	5.01540	+	5.01540i	0.259687	+	0.259687i	−0.565239	+	0.824927i	$0.691216\pi$
$374$		0			0
$375$	−14.4542			−0.746414
$376$		0			0
$377$		−	32.2097i		−	1.65888i
$378$		0			0
$379$	−10.3593	−	10.3593i	−0.532124	−	0.532124i	0.389080	−	0.921204i	$-0.372793\pi$
$379$	−10.3593	−	10.3593i	−0.532124	−	0.532124i	−0.921204	+	0.389080i	$0.872793\pi$
$380$		0			0
$381$	−2.03365	+	2.03365i	−0.104187	+	0.104187i
$382$		0			0
$383$			5.81851i			0.297312i	0.988889	+	0.148656i	$0.0474947\pi$
$383$			5.81851i			0.297312i	−0.988889	+	0.148656i	$0.952505\pi$
$384$		0			0
$385$	−1.73788	+	11.9313i	−0.0885703	+	0.608075i
$386$		0			0
$387$	−13.8255	−	13.8255i	−0.702790	−	0.702790i
$388$		0			0
$389$	−16.6717	+	16.6717i	−0.845291	+	0.845291i	−0.989541	−	0.144250i	$-0.953923\pi$
$389$	−16.6717	+	16.6717i	−0.845291	+	0.845291i	0.144250	+	0.989541i	$0.453923\pi$
$390$		0			0
$391$			12.3604i			0.625090i
$392$		0			0
$393$	−15.6265			−0.788252
$394$		0			0
$395$	−16.9608	+	16.9608i	−0.853392	+	0.853392i
$396$		0			0
$397$	26.1152	+	26.1152i	1.31068	+	1.31068i	0.920912	+	0.389771i	$0.127446\pi$
$397$	26.1152	+	26.1152i	1.31068	+	1.31068i	0.389771	+	0.920912i	$0.372554\pi$
$398$		0			0
$399$			17.7851i			0.890369i
$400$		0			0
$401$	−26.8371			−1.34018			−0.670091	−	0.742279i	$-0.733745\pi$
$401$	−26.8371			−1.34018			−0.670091	+	0.742279i	$0.733745\pi$
$402$		0			0
$403$	−22.1870	−	22.1870i	−1.10521	−	1.10521i
$404$		0			0
$405$	−20.5940	+	20.5940i	−1.02332	+	1.02332i
$406$		0			0
$407$	−5.04169	−	0.734356i	−0.249907	−	0.0364007i
$408$		0			0
$409$	−19.5286			−0.965629			−0.482814	−	0.875723i	$-0.660385\pi$
$409$	−19.5286			−0.965629			−0.482814	+	0.875723i	$0.660385\pi$
$410$		0			0
$411$	26.3512	+	26.3512i	1.29981	+	1.29981i
$412$		0			0
$413$	1.55695	−	1.55695i	0.0766123	−	0.0766123i
$414$		0			0
$415$	24.7849			1.21664
$416$		0			0
$417$			33.2871i			1.63007i
$418$		0			0
$419$	−4.72707	+	4.72707i	−0.230933	+	0.230933i	−0.813082	−	0.582149i	$-0.802212\pi$
$419$	−4.72707	+	4.72707i	−0.230933	+	0.230933i	0.582149	+	0.813082i	$0.302212\pi$
$420$		0			0
$421$	7.25561	−	7.25561i	0.353617	−	0.353617i	−0.507837	−	0.861453i	$-0.669555\pi$
$421$	7.25561	−	7.25561i	0.353617	−	0.353617i	0.861453	+	0.507837i	$0.169555\pi$
$422$		0			0
$423$	11.3679			0.552725
$424$		0			0
$425$	−17.0455			−0.826829
$426$		0			0
$427$	−2.37081	−	2.37081i	−0.114731	−	0.114731i
$428$		0			0
$429$	−30.1468	+	22.4812i	−1.45550	+	1.08540i
$430$		0			0
$431$	−26.5369			−1.27824			−0.639120	−	0.769107i	$-0.720701\pi$
$431$	−26.5369			−1.27824			−0.639120	+	0.769107i	$0.720701\pi$
$432$		0			0
$433$	6.04854			0.290674			0.145337	−	0.989382i	$-0.453573\pi$
$433$	6.04854			0.290674			0.145337	+	0.989382i	$0.453573\pi$
$434$		0			0
$435$	30.1967	+	30.1967i	1.44782	+	1.44782i
$436$		0			0
$437$	−8.32849	−	8.32849i	−0.398406	−	0.398406i
$438$		0			0
$439$		−	18.4030i		−	0.878326i	−0.898407	−	0.439163i	$-0.855275\pi$
$439$		−	18.4030i		−	0.878326i	0.898407	−	0.439163i	$-0.144725\pi$
$440$		0			0
$441$		−	12.6856i		−	0.604076i
$442$		0			0
$443$	−11.0759	−	11.0759i	−0.526231	−	0.526231i	0.393215	−	0.919447i	$-0.371363\pi$
$443$	−11.0759	−	11.0759i	−0.526231	−	0.526231i	−0.919447	+	0.393215i	$0.871363\pi$
$444$		0			0
$445$	13.0735	+	13.0735i	0.619741	+	0.619741i
$446$		0			0
$447$	−49.0343			−2.31924
$448$		0			0
$449$	−17.6597			−0.833412			−0.416706	−	0.909041i	$-0.636816\pi$
$449$	−17.6597			−0.833412			−0.416706	+	0.909041i	$0.636816\pi$
$450$		0			0
$451$	−9.55472	−	12.8127i	−0.449914	−	0.603326i
$452$		0			0
$453$	−8.52017	−	8.52017i	−0.400313	−	0.400313i
$454$		0			0
$455$	−17.7480			−0.832041
$456$		0			0
$457$	6.02919			0.282034			0.141017	−	0.990007i	$-0.454963\pi$
$457$	6.02919			0.282034			0.141017	+	0.990007i	$0.454963\pi$
$458$		0			0
$459$	6.12885	−	6.12885i	0.286070	−	0.286070i
$460$		0			0
$461$	−13.1018	+	13.1018i	−0.610210	+	0.610210i	−0.943001	−	0.332791i	$-0.892010\pi$
$461$	−13.1018	+	13.1018i	−0.610210	+	0.610210i	0.332791	+	0.943001i	$0.392010\pi$
$462$		0			0
$463$			10.3093i			0.479114i	0.970882	+	0.239557i	$0.0770023\pi$
$463$			10.3093i			0.479114i	−0.970882	+	0.239557i	$0.922998\pi$
$464$		0			0
$465$	41.6007			1.92919
$466$		0			0
$467$	−20.2742	+	20.2742i	−0.938177	+	0.938177i	−0.998197	−	0.0600206i	$-0.980883\pi$
$467$	−20.2742	+	20.2742i	−0.938177	+	0.938177i	0.0600206	+	0.998197i	$0.480883\pi$
$468$		0			0
$469$	−1.97291	−	1.97291i	−0.0911005	−	0.0911005i
$470$		0			0
$471$	8.45992			0.389813
$472$		0			0
$473$	−26.8021	−	3.90391i	−1.23236	−	0.179502i
$474$		0			0
$475$	11.4854	−	11.4854i	0.526985	−	0.526985i
$476$		0			0
$477$	−7.74041	−	7.74041i	−0.354409	−	0.354409i
$478$		0			0
$479$	13.3943			0.612003			0.306001	−	0.952031i	$-0.401009\pi$
$479$	13.3943			0.612003			0.306001	+	0.952031i	$0.401009\pi$
$480$		0			0
$481$		−	7.49961i		−	0.341953i
$482$		0			0
$483$	−4.29824	−	4.29824i	−0.195577	−	0.195577i
$484$		0			0
$485$	28.4678	−	28.4678i	1.29266	−	1.29266i
$486$		0			0
$487$	12.4795			0.565499			0.282750	−	0.959194i	$-0.408753\pi$
$487$	12.4795			0.565499			0.282750	+	0.959194i	$0.408753\pi$
$488$		0			0
$489$			57.8722i			2.61707i
$490$		0			0
$491$	9.00419	−	9.00419i	0.406353	−	0.406353i	−0.474112	−	0.880465i	$-0.657231\pi$
$491$	9.00419	−	9.00419i	0.406353	−	0.406353i	0.880465	+	0.474112i	$0.157231\pi$
$492$		0			0
$493$	−28.7400	−	28.7400i	−1.29438	−	1.29438i
$494$		0			0
$495$	3.18975	−	21.8991i	0.143369	−	0.984291i
$496$		0			0
$497$		−	13.1878i		−	0.591553i
$498$		0			0
$499$	−19.7586	+	19.7586i	−0.884516	+	0.884516i	−0.993990	−	0.109474i	$-0.965083\pi$
$499$	−19.7586	+	19.7586i	−0.884516	+	0.884516i	0.109474	+	0.993990i	$0.465083\pi$
$500$		0			0
$501$	34.7642	+	34.7642i	1.55315	+	1.55315i
$502$		0			0
$503$		−	7.75362i		−	0.345717i	−0.984947	−	0.172858i	$-0.944700\pi$
$503$		−	7.75362i		−	0.345717i	0.984947	−	0.172858i	$-0.0553003\pi$
$504$		0			0
$505$	−2.83269			−0.126053
$506$		0			0
$507$	−17.7929	−	17.7929i	−0.790210	−	0.790210i
$508$		0			0
$509$	10.3440	+	10.3440i	0.458491	+	0.458491i	0.898160	−	0.439669i	$-0.144904\pi$
$509$	10.3440	+	10.3440i	0.458491	+	0.458491i	−0.439669	+	0.898160i	$0.644904\pi$
$510$		0			0
$511$			7.64857i			0.338353i
$512$		0			0
$513$			8.25931i			0.364657i
$514$		0			0
$515$	10.7420	−	10.7420i	0.473348	−	0.473348i
$516$		0			0
$517$	12.6239	−	9.41391i	0.555197	−	0.414023i
$518$		0			0
$519$		−	47.0823i		−	2.06668i
$520$		0			0
$521$		−	0.00381204i		−	0.000167008i	−1.00000		8.35042e-5i	$-0.999973\pi$
$521$		−	0.00381204i		−	0.000167008i	1.00000		8.35042e-5i	$-2.65802e-5\pi$
$522$		0			0
$523$	1.75317	−	1.75317i	0.0766607	−	0.0766607i	−0.667737	−	0.744397i	$-0.732737\pi$
$523$	1.75317	−	1.75317i	0.0766607	−	0.0766607i	0.744397	+	0.667737i	$0.232737\pi$
$524$		0			0
$525$	5.92748	−	5.92748i	0.258696	−	0.258696i
$526$		0			0
$527$	−39.5939			−1.72474
$528$		0			0
$529$	−18.9744			−0.824974
$530$		0			0
$531$	−2.85767	+	2.85767i	−0.124012	+	0.124012i
$532$		0			0
$533$	16.6360	−	16.6360i	0.720584	−	0.720584i
$534$		0			0
$535$		−	16.6141i		−	0.718292i
$536$		0			0
$537$			0.322591i			0.0139208i
$538$		0			0
$539$	−10.5051	−	14.0872i	−0.452488	−	0.606777i
$540$		0			0
$541$	11.9799	−	11.9799i	0.515057	−	0.515057i	−0.401014	−	0.916072i	$-0.631342\pi$
$541$	11.9799	−	11.9799i	0.515057	−	0.515057i	0.916072	+	0.401014i	$0.131342\pi$
$542$		0			0
$543$		−	32.0587i		−	1.37577i
$544$		0			0
$545$		−	45.7304i		−	1.95887i
$546$		0			0
$547$	10.1405	+	10.1405i	0.433578	+	0.433578i	0.889844	−	0.456265i	$-0.150813\pi$
$547$	10.1405	+	10.1405i	0.433578	+	0.433578i	−0.456265	+	0.889844i	$0.650813\pi$
$548$		0			0
$549$	4.35145	+	4.35145i	0.185715	+	0.185715i
$550$		0			0
$551$	38.7304			1.64997
$552$		0			0
$553$			11.2270i			0.477421i
$554$		0			0
$555$	7.03091	+	7.03091i	0.298446	+	0.298446i
$556$		0			0
$557$	14.6308	−	14.6308i	0.619929	−	0.619929i	−0.325584	−	0.945513i	$-0.605561\pi$
$557$	14.6308	−	14.6308i	0.619929	−	0.619929i	0.945513	+	0.325584i	$0.105561\pi$
$558$		0			0
$559$		−	39.8687i		−	1.68627i
$560$		0			0
$561$	−6.83989	+	46.9589i	−0.288780	+	1.98261i
$562$		0			0
$563$	−4.09572	−	4.09572i	−0.172614	−	0.172614i	0.615513	−	0.788127i	$-0.288949\pi$
$563$	−4.09572	−	4.09572i	−0.172614	−	0.172614i	−0.788127	+	0.615513i	$0.788949\pi$
$564$		0			0
$565$	−15.3448	+	15.3448i	−0.645563	+	0.645563i
$566$		0			0
$567$			13.6319i			0.572488i
$568$		0			0
$569$	17.5021			0.733727			0.366864	−	0.930275i	$-0.380432\pi$
$569$	17.5021			0.733727			0.366864	+	0.930275i	$0.380432\pi$
$570$		0			0
$571$	16.4386	−	16.4386i	0.687934	−	0.687934i	−0.273841	−	0.961775i	$-0.588294\pi$
$571$	16.4386	−	16.4386i	0.687934	−	0.687934i	0.961775	+	0.273841i	$0.0882941\pi$
$572$		0			0
$573$	−8.19116	−	8.19116i	−0.342190	−	0.342190i
$574$		0			0
$575$			5.55149i			0.231513i
$576$		0			0
$577$	−36.6527			−1.52587			−0.762936	−	0.646474i	$-0.776243\pi$
$577$	−36.6527			−1.52587			−0.762936	+	0.646474i	$0.776243\pi$
$578$		0			0
$579$	−0.390328	−	0.390328i	−0.0162215	−	0.0162215i
$580$		0			0
$581$	8.20304	−	8.20304i	0.340319	−	0.340319i
$582$		0			0
$583$	−15.0056	−	2.18566i	−0.621467	−	0.0905209i
$584$		0			0
$585$	32.5753			1.34682
$586$		0			0
$587$	4.90163	+	4.90163i	0.202312	+	0.202312i	0.800990	−	0.598678i	$-0.204307\pi$
$587$	4.90163	+	4.90163i	0.202312	+	0.202312i	−0.598678	+	0.800990i	$0.704307\pi$
$588$		0			0
$589$	26.6786	−	26.6786i	1.09927	−	1.09927i
$590$		0			0
$591$	51.3639			2.11283
$592$		0			0
$593$			12.3403i			0.506753i	0.967368	+	0.253377i	$0.0815412\pi$
$593$			12.3403i			0.506753i	−0.967368	+	0.253377i	$0.918459\pi$
$594$		0			0
$595$	−15.8362	+	15.8362i	−0.649221	+	0.649221i
$596$		0			0
$597$	−6.09070	+	6.09070i	−0.249276	+	0.249276i
$598$		0			0
$599$	18.1281			0.740693			0.370347	−	0.928894i	$-0.379239\pi$
$599$	18.1281			0.740693			0.370347	+	0.928894i	$0.379239\pi$
$600$		0			0
$601$	26.7091			1.08949			0.544743	−	0.838603i	$-0.316627\pi$
$601$	26.7091			1.08949			0.544743	+	0.838603i	$0.316627\pi$
$602$		0			0
$603$	3.62114	+	3.62114i	0.147464	+	0.147464i
$604$		0			0
$605$	−14.5928	−	26.9601i	−0.593281	−	1.09608i
$606$		0			0
$607$	−29.4573			−1.19563			−0.597817	−	0.801633i	$-0.703965\pi$
$607$	−29.4573			−1.19563			−0.597817	+	0.801633i	$0.703965\pi$
$608$		0			0
$609$	19.9883			0.809968
$610$		0			0
$611$	16.3908	+	16.3908i	0.663101	+	0.663101i
$612$		0			0
$613$	1.91963	+	1.91963i	0.0775330	+	0.0775330i	0.744810	−	0.667277i	$-0.232540\pi$
$613$	1.91963	+	1.91963i	0.0775330	+	0.0775330i	−0.667277	+	0.744810i	$0.732540\pi$
$614$		0			0
$615$			31.1926i			1.25781i
$616$		0			0
$617$			14.7427i			0.593520i	0.954952	+	0.296760i	$0.0959061\pi$
$617$			14.7427i			0.593520i	−0.954952	+	0.296760i	$0.904094\pi$
$618$		0			0
$619$	26.1174	+	26.1174i	1.04975	+	1.04975i	0.998696	+	0.0510496i	$0.0162567\pi$
$619$	26.1174	+	26.1174i	1.04975	+	1.04975i	0.0510496	+	0.998696i	$0.483743\pi$
$620$		0			0
$621$	−1.99608	−	1.99608i	−0.0801000	−	0.0801000i
$622$		0			0
$623$	8.65381			0.346708
$624$		0			0
$625$	31.1788			1.24715
$626$		0			0
$627$	−27.0324	−	36.2500i	−1.07957	−	1.44768i
$628$		0			0
$629$	−6.69174	−	6.69174i	−0.266817	−	0.266817i
$630$		0			0
$631$	12.0275			0.478806			0.239403	−	0.970920i	$-0.423048\pi$
$631$	12.0275			0.478806			0.239403	+	0.970920i	$0.423048\pi$
$632$		0			0
$633$	62.8135			2.49661
$634$		0			0
$635$	2.44026	−	2.44026i	0.0968387	−	0.0968387i
$636$		0			0
$637$	18.2908	−	18.2908i	0.724706	−	0.724706i
$638$		0			0
$639$			24.2053i			0.957547i
$640$		0			0
$641$	1.23887			0.0489324			0.0244662	−	0.999701i	$-0.492211\pi$
$641$	1.23887			0.0489324			0.0244662	+	0.999701i	$0.492211\pi$
$642$		0			0
$643$	5.69281	−	5.69281i	0.224503	−	0.224503i	−0.585889	−	0.810391i	$-0.699254\pi$
$643$	5.69281	−	5.69281i	0.224503	−	0.224503i	0.810391	+	0.585889i	$0.199254\pi$
$644$		0			0
$645$	37.3770	+	37.3770i	1.47172	+	1.47172i
$646$		0			0
$647$	−34.1044			−1.34078			−0.670392	−	0.742007i	$-0.733874\pi$
$647$	−34.1044			−1.34078			−0.670392	+	0.742007i	$0.733874\pi$
$648$		0			0
$649$	−0.806921	+	5.53987i	−0.0316744	+	0.217459i
$650$		0			0
$651$	13.7685	−	13.7685i	0.539632	−	0.539632i
$652$		0			0
$653$	27.8809	+	27.8809i	1.09106	+	1.09106i	0.995415	+	0.0956489i	$0.0304926\pi$
$653$	27.8809	+	27.8809i	1.09106	+	1.09106i	0.0956489	+	0.995415i	$0.469507\pi$
$654$		0			0
$655$	18.7508			0.732656
$656$		0			0
$657$		−	14.0384i		−	0.547691i
$658$		0			0
$659$	−25.9362	−	25.9362i	−1.01033	−	1.01033i	−0.999946	−	0.0103856i	$-0.996694\pi$
$659$	−25.9362	−	25.9362i	−1.01033	−	1.01033i	−0.0103856	−	0.999946i	$-0.503306\pi$
$660$		0			0
$661$	−5.45717	+	5.45717i	−0.212259	+	0.212259i	−0.805227	−	0.592967i	$-0.797956\pi$
$661$	−5.45717	+	5.45717i	−0.212259	+	0.212259i	0.592967	+	0.805227i	$0.297956\pi$
$662$		0			0
$663$	−69.8523			−2.71284
$664$		0			0
$665$		−	21.3411i		−	0.827571i
$666$		0			0
$667$	−9.36022	+	9.36022i	−0.362429	+	0.362429i
$668$		0			0
$669$	−2.84611	−	2.84611i	−0.110037	−	0.110037i
$670$		0			0
$671$	8.43572	+	1.22872i	0.325657	+	0.0474342i
$672$		0			0
$673$		−	28.8506i		−	1.11211i	−0.831146	−	0.556054i	$-0.812315\pi$
$673$		−	28.8506i		−	1.11211i	0.831146	−	0.556054i	$-0.187685\pi$
$674$		0			0
$675$	2.75269	−	2.75269i	0.105951	−	0.105951i
$676$		0			0
$677$	−2.41911	−	2.41911i	−0.0929738	−	0.0929738i	0.659090	−	0.752064i	$-0.270942\pi$
$677$	−2.41911	−	2.41911i	−0.0929738	−	0.0929738i	−0.752064	+	0.659090i	$0.770942\pi$
$678$		0			0
$679$		−	18.8439i		−	0.723164i
$680$		0			0
$681$	−1.56006			−0.0597816
$682$		0			0
$683$	19.9142	+	19.9142i	0.761997	+	0.761997i	0.976683	−	0.214686i	$-0.0688728\pi$
$683$	19.9142	+	19.9142i	0.761997	+	0.761997i	−0.214686	+	0.976683i	$0.568873\pi$
$684$		0			0
$685$	−31.6198	−	31.6198i	−1.20813	−	1.20813i
$686$		0			0
$687$		−	51.3844i		−	1.96044i
$688$		0			0
$689$		−	22.3211i		−	0.850365i
$690$		0			0
$691$	2.04357	−	2.04357i	0.0777410	−	0.0777410i	−0.667167	−	0.744908i	$-0.732493\pi$
$691$	2.04357	−	2.04357i	0.0777410	−	0.0777410i	0.744908	+	0.667167i	$0.232493\pi$
$692$		0			0
$693$	−6.19221	−	8.30362i	−0.235222	−	0.315429i
$694$		0			0
$695$		−	39.9425i		−	1.51511i
$696$		0			0
$697$		−	29.6879i		−	1.12451i
$698$		0			0
$699$	7.74045	−	7.74045i	0.292771	−	0.292771i
$700$		0			0
$701$	14.8981	−	14.8981i	0.562694	−	0.562694i	−0.367378	−	0.930072i	$-0.619744\pi$
$701$	14.8981	−	14.8981i	0.562694	−	0.562694i	0.930072	+	0.367378i	$0.119744\pi$
$702$		0			0
$703$	9.01788			0.340116
$704$		0			0
$705$	−30.7329			−1.15747
$706$		0			0
$707$	−0.937531	+	0.937531i	−0.0352595	+	0.0352595i
$708$		0			0
$709$	−11.9614	+	11.9614i	−0.449221	+	0.449221i	−0.895095	−	0.445875i	$-0.852893\pi$
$709$	−11.9614	+	11.9614i	−0.449221	+	0.449221i	0.445875	+	0.895095i	$0.352893\pi$
$710$		0			0
$711$		−	20.6064i		−	0.772801i
$712$		0			0
$713$			12.8952i			0.482929i
$714$		0			0
$715$	36.1744	−	26.9761i	1.35285	−	1.00885i
$716$		0			0
$717$	8.83803	−	8.83803i	0.330062	−	0.330062i
$718$		0			0
$719$			40.0730i			1.49447i	0.664560	+	0.747235i	$0.268619\pi$
$719$			40.0730i			1.49447i	−0.664560	+	0.747235i	$0.731381\pi$
$720$		0			0
$721$		−	7.11051i		−	0.264809i
$722$		0			0
$723$	21.2507	+	21.2507i	0.790322	+	0.790322i
$724$		0			0
$725$	−12.9082	−	12.9082i	−0.479398	−	0.479398i
$726$		0			0
$727$	−5.31823			−0.197242			−0.0986210	−	0.995125i	$-0.531443\pi$
$727$	−5.31823			−0.197242			−0.0986210	+	0.995125i	$0.531443\pi$
$728$		0			0
$729$		−	15.2174i		−	0.563607i
$730$		0			0
$731$	−35.5740	−	35.5740i	−1.31575	−	1.31575i
$732$		0			0
$733$	−33.6126	+	33.6126i	−1.24151	+	1.24151i	−0.282133	+	0.959375i	$0.591042\pi$
$733$	−33.6126	+	33.6126i	−1.24151	+	1.24151i	−0.959375	+	0.282133i	$0.908958\pi$
$734$		0			0
$735$			34.2953i			1.26500i
$736$		0			0
$737$	7.01994	+	1.02250i	0.258583	+	0.0376644i
$738$		0			0
$739$	6.49563	+	6.49563i	0.238946	+	0.238946i	0.816413	−	0.577468i	$-0.195959\pi$
$739$	6.49563	+	6.49563i	0.238946	+	0.238946i	−0.577468	+	0.816413i	$0.695959\pi$
$740$		0			0
$741$	47.0669	−	47.0669i	1.72905	−	1.72905i
$742$		0			0
$743$		−	1.44314i		−	0.0529438i	−0.999650	−	0.0264719i	$-0.991573\pi$
$743$		−	1.44314i		−	0.0529438i	0.999650	−	0.0264719i	$-0.00842726\pi$
$744$		0			0
$745$	58.8382			2.15566
$746$		0			0
$747$	−15.0561	+	15.0561i	−0.550874	+	0.550874i
$748$		0			0
$749$	−5.49876	−	5.49876i	−0.200920	−	0.200920i
$750$		0			0
$751$		−	22.3587i		−	0.815882i	−0.913008	−	0.407941i	$-0.866247\pi$
$751$		−	22.3587i		−	0.815882i	0.913008	−	0.407941i	$-0.133753\pi$
$752$		0			0
$753$	16.6322			0.606111
$754$		0			0
$755$	10.2237	+	10.2237i	0.372078	+	0.372078i
$756$		0			0
$757$	−11.6495	+	11.6495i	−0.423409	+	0.423409i	−0.886376	−	0.462967i	$-0.846785\pi$
$757$	−11.6495	+	11.6495i	−0.423409	+	0.423409i	0.462967	+	0.886376i	$0.346785\pi$
$758$		0			0
$759$	15.2939	+	2.22766i	0.555132	+	0.0808588i
$760$		0			0
$761$	−47.3332			−1.71583			−0.857913	−	0.513795i	$-0.828239\pi$
$761$	−47.3332			−1.71583			−0.857913	+	0.513795i	$0.828239\pi$
$762$		0			0
$763$	−15.1353	−	15.1353i	−0.547936	−	0.547936i
$764$		0			0
$765$	29.0663	−	29.0663i	1.05089	−	1.05089i
$766$		0			0
$767$	−8.24067			−0.297553
$768$		0			0
$769$			0.596251i			0.0215014i	0.999942	+	0.0107507i	$0.00342212\pi$
$769$			0.596251i			0.0215014i	−0.999942	+	0.0107507i	$0.996578\pi$
$770$		0			0
$771$	1.64415	−	1.64415i	0.0592126	−	0.0592126i
$772$		0			0
$773$	−24.2603	+	24.2603i	−0.872583	+	0.872583i	−0.992753	−	0.120170i	$-0.961656\pi$
$773$	−24.2603	+	24.2603i	−0.872583	+	0.872583i	0.120170	+	0.992753i	$0.461656\pi$
$774$		0			0
$775$	−17.7831			−0.638787
$776$		0			0
$777$	4.65403			0.166962
$778$		0			0
$779$	20.0039	+	20.0039i	0.716713	+	0.716713i
$780$		0			0
$781$	20.0448	+	26.8796i	0.717258	+	0.961828i
$782$		0			0
$783$	9.28247			0.331729
$784$		0			0
$785$	−10.1514			−0.362319
$786$		0			0
$787$	10.0469	+	10.0469i	0.358134	+	0.358134i	0.863125	−	0.504991i	$-0.168504\pi$
$787$	10.0469	+	10.0469i	0.358134	+	0.358134i	−0.504991	+	0.863125i	$0.668504\pi$
$788$		0			0
$789$	−15.9668	−	15.9668i	−0.568433	−	0.568433i
$790$		0			0
$791$			10.1573i			0.361153i
$792$		0			0
$793$			12.5483i			0.445603i
$794$		0			0
$795$	20.9261	+	20.9261i	0.742172	+	0.742172i
$796$		0			0
$797$	−15.8157	−	15.8157i	−0.560221	−	0.560221i	0.369149	−	0.929370i	$-0.379649\pi$
$797$	−15.8157	−	15.8157i	−0.560221	−	0.560221i	−0.929370	+	0.369149i	$0.879649\pi$
$798$		0			0
$799$	29.2503			1.03480
$800$		0			0
$801$	−15.8835			−0.561215
$802$		0			0
$803$	−11.6254	−	15.5895i	−0.410252	−	0.550140i
$804$		0			0
$805$	5.15763	+	5.15763i	0.181783	+	0.181783i
$806$		0			0
$807$	44.2617			1.55809
$808$		0			0
$809$	28.7672			1.01140			0.505701	−	0.862709i	$-0.331234\pi$
$809$	28.7672			1.01140			0.505701	+	0.862709i	$0.331234\pi$
$810$		0			0
$811$	−3.78394	+	3.78394i	−0.132872	+	0.132872i	−0.770415	−	0.637543i	$-0.779951\pi$
$811$	−3.78394	+	3.78394i	−0.132872	+	0.132872i	0.637543	+	0.770415i	$0.279951\pi$
$812$		0			0
$813$	16.7204	−	16.7204i	0.586409	−	0.586409i
$814$		0			0
$815$		−	69.4432i		−	2.43249i
$816$		0			0
$817$	47.9399			1.67721
$818$		0			0
$819$	10.7814	−	10.7814i	0.376733	−	0.376733i
$820$		0			0
$821$	23.5237	+	23.5237i	0.820981	+	0.820981i	0.986249	−	0.165267i	$-0.0528487\pi$
$821$	23.5237	+	23.5237i	0.820981	+	0.820981i	−0.165267	+	0.986249i	$0.552849\pi$
$822$		0			0
$823$	−0.0375878			−0.00131023			−0.000655114	−	1.00000i	$-0.500209\pi$
$823$	−0.0375878			−0.00131023			−0.000655114		1.00000i	$0.500209\pi$
$824$		0			0
$825$	−3.07204	+	21.0910i	−0.106955	+	0.734293i
$826$		0			0
$827$	−21.5923	+	21.5923i	−0.750840	+	0.750840i	−0.974636	−	0.223796i	$-0.928155\pi$
$827$	−21.5923	+	21.5923i	−0.750840	+	0.750840i	0.223796	+	0.974636i	$0.428155\pi$
$828$		0			0
$829$	−15.3107	−	15.3107i	−0.531763	−	0.531763i	0.389334	−	0.921097i	$-0.372705\pi$
$829$	−15.3107	−	15.3107i	−0.531763	−	0.531763i	−0.921097	+	0.389334i	$0.872705\pi$
$830$		0			0
$831$	29.3091			1.01672
$832$		0			0
$833$		−	32.6409i		−	1.13094i
$834$		0			0
$835$	−41.7150	−	41.7150i	−1.44361	−	1.44361i
$836$		0			0
$837$	6.39404	−	6.39404i	0.221010	−	0.221010i
$838$		0			0
$839$	27.3563			0.944444			0.472222	−	0.881480i	$-0.343452\pi$
$839$	27.3563			0.944444			0.472222	+	0.881480i	$0.343452\pi$
$840$		0			0
$841$		−	14.5283i		−	0.500976i
$842$		0			0
$843$	9.28966	−	9.28966i	0.319953	−	0.319953i
$844$		0			0
$845$	21.3504	+	21.3504i	0.734477	+	0.734477i
$846$		0			0
$847$	−13.7527	−	4.09319i	−0.472549	−	0.140644i
$848$		0			0
$849$		−	38.5202i		−	1.32201i
$850$		0			0
$851$	−2.17941	+	2.17941i	−0.0747092	+	0.0747092i
$852$		0			0
$853$	−15.7430	−	15.7430i	−0.539028	−	0.539028i	0.384215	−	0.923244i	$-0.374472\pi$
$853$	−15.7430	−	15.7430i	−0.539028	−	0.539028i	−0.923244	+	0.384215i	$0.874472\pi$
$854$		0			0
$855$			39.1701i			1.33959i
$856$		0			0
$857$	42.9438			1.46693			0.733467	−	0.679726i	$-0.237901\pi$
$857$	42.9438			1.46693			0.733467	+	0.679726i	$0.237901\pi$
$858$		0			0
$859$	1.85075	+	1.85075i	0.0631467	+	0.0631467i	0.737975	−	0.674828i	$-0.235782\pi$
$859$	1.85075	+	1.85075i	0.0631467	+	0.0631467i	−0.674828	+	0.737975i	$0.735782\pi$
$860$		0			0
$861$	10.3238	+	10.3238i	0.351833	+	0.351833i
$862$		0			0
$863$			25.6935i			0.874617i	0.899311	+	0.437309i	$0.144068\pi$
$863$			25.6935i			0.874617i	−0.899311	+	0.437309i	$0.855932\pi$
$864$		0			0
$865$			56.4959i			1.92092i
$866$		0			0
$867$	−34.4088	+	34.4088i	−1.16859	+	1.16859i
$868$		0			0
$869$	−17.0645	−	22.8831i	−0.578873	−	0.776257i
$870$		0			0
$871$			10.4423i			0.353824i
$872$		0			0
$873$			34.5868i			1.17058i
$874$		0			0
$875$	5.74040	−	5.74040i	0.194061	−	0.194061i
$876$		0			0
$877$	9.81791	−	9.81791i	0.331527	−	0.331527i	−0.521639	−	0.853166i	$-0.674679\pi$
$877$	9.81791	−	9.81791i	0.331527	−	0.331527i	0.853166	+	0.521639i	$0.174679\pi$
$878$		0			0
$879$	−61.0072			−2.05772
$880$		0			0
$881$	−19.9836			−0.673263			−0.336632	−	0.941636i	$-0.609288\pi$
$881$	−19.9836			−0.673263			−0.336632	+	0.941636i	$0.609288\pi$
$882$		0			0
$883$	−10.5999	+	10.5999i	−0.356715	+	0.356715i	−0.862601	−	0.505885i	$-0.831166\pi$
$883$	−10.5999	+	10.5999i	−0.356715	+	0.356715i	0.505885	+	0.862601i	$0.331166\pi$
$884$		0			0
$885$	7.72566	−	7.72566i	0.259695	−	0.259695i
$886$		0			0
$887$			5.83965i			0.196076i	0.995183	+	0.0980382i	$0.0312567\pi$
$887$			5.83965i			0.196076i	−0.995183	+	0.0980382i	$0.968743\pi$
$888$		0			0
$889$		−	1.61530i		−	0.0541754i
$890$		0			0
$891$	−20.7198	−	27.7849i	−0.694141	−	0.930829i
$892$		0			0
$893$	−19.7091	+	19.7091i	−0.659539	+	0.659539i
$894$		0			0
$895$		−	0.387090i		−	0.0129390i
$896$		0			0
$897$			22.7499i			0.759598i
$898$		0			0
$899$	−29.9836	−	29.9836i	−1.00001	−	1.00001i
$900$		0			0
$901$	−19.9166	−	19.9166i	−0.663519	−	0.663519i
$902$		0			0
$903$	24.7413			0.823338
$904$		0			0
$905$			38.4685i			1.27874i
$906$		0			0
$907$	19.0573	+	19.0573i	0.632786	+	0.632786i	0.948766	−	0.315980i	$-0.102333\pi$
$907$	19.0573	+	19.0573i	0.632786	+	0.632786i	−0.315980	+	0.948766i	$0.602333\pi$
$908$		0			0
$909$	1.72077	−	1.72077i	0.0570745	−	0.0570745i
$910$		0			0
$911$			27.4739i			0.910249i	0.890428	+	0.455125i	$0.150405\pi$
$911$			27.4739i			0.910249i	−0.890428	+	0.455125i	$0.849595\pi$
$912$		0			0
$913$	−4.25140	+	29.1878i	−0.140701	+	0.965975i
$914$		0			0
$915$	−11.7641	−	11.7641i	−0.388909	−	0.388909i
$916$		0			0
$917$	6.20595	−	6.20595i	0.204938	−	0.204938i
$918$		0			0
$919$			0.114331i			0.00377143i	0.999998	+	0.00188571i	$0.000600242\pi$
$919$			0.114331i			0.00377143i	−0.999998	+	0.00188571i	$0.999400\pi$
$920$		0			0
$921$	10.7543			0.354365
$922$		0			0
$923$	−34.9005	+	34.9005i	−1.14876	+	1.14876i
$924$		0			0
$925$	−3.00551	−	3.00551i	−0.0988205	−	0.0988205i
$926$		0			0
$927$			13.0509i			0.428646i
$928$		0			0
$929$	6.61693			0.217095			0.108547	−	0.994091i	$-0.465380\pi$
$929$	6.61693			0.217095			0.108547	+	0.994091i	$0.465380\pi$
$930$		0			0
$931$	21.9937	+	21.9937i	0.720813	+	0.720813i
$932$		0			0
$933$	−6.38110	+	6.38110i	−0.208908	+	0.208908i
$934$		0			0
$935$	8.20746	−	56.3479i	0.268412	−	1.84277i
$936$		0			0
$937$	−50.8045			−1.65971			−0.829855	−	0.557979i	$-0.811577\pi$
$937$	−50.8045			−1.65971			−0.829855	+	0.557979i	$0.811577\pi$
$938$		0			0
$939$	−40.0915	−	40.0915i	−1.30834	−	1.30834i
$940$		0			0
$941$	6.59961	−	6.59961i	0.215141	−	0.215141i	−0.591306	−	0.806447i	$-0.701387\pi$
$941$	6.59961	−	6.59961i	0.215141	−	0.215141i	0.806447	+	0.591306i	$0.201387\pi$
$942$		0			0
$943$	−9.66893			−0.314864
$944$		0			0
$945$		−	5.11479i		−	0.166384i
$946$		0			0
$947$	−15.4716	+	15.4716i	−0.502758	+	0.502758i	−0.912294	−	0.409536i	$-0.865691\pi$
$947$	−15.4716	+	15.4716i	−0.502758	+	0.502758i	0.409536	+	0.912294i	$0.365691\pi$
$948$		0			0
$949$	20.2413	−	20.2413i	0.657062	−	0.657062i
$950$		0			0
$951$	−2.19309			−0.0711159
$952$		0			0
$953$	−26.8866			−0.870943			−0.435472	−	0.900202i	$-0.643418\pi$
$953$	−26.8866			−0.870943			−0.435472	+	0.900202i	$0.643418\pi$
$954$		0			0
$955$	9.82890	+	9.82890i	0.318056	+	0.318056i
$956$		0			0
$957$	−40.7406	+	30.3812i	−1.31696	+	0.982085i
$958$		0			0
$959$	−20.9304			−0.675877
$960$		0			0
$961$	−10.3071			−0.332489
$962$		0			0
$963$	10.0926	+	10.0926i	0.325230	+	0.325230i
$964$		0			0
$965$	0.468371	+	0.468371i	0.0150774	+	0.0150774i
$966$		0			0
$967$		−	28.3815i		−	0.912688i	−0.889803	−	0.456344i	$-0.849159\pi$
$967$		−	28.3815i		−	0.912688i	0.889803	−	0.456344i	$-0.150841\pi$
$968$		0			0
$969$		−	83.9936i		−	2.69826i
$970$		0			0
$971$	−26.5193	−	26.5193i	−0.851044	−	0.851044i	0.139217	−	0.990262i	$-0.455541\pi$
$971$	−26.5193	−	26.5193i	−0.851044	−	0.851044i	−0.990262	+	0.139217i	$0.955541\pi$
$972$		0			0
$973$	−13.2197	−	13.2197i	−0.423805	−	0.423805i
$974$		0			0
$975$	−31.3732			−1.00475
$976$		0			0
$977$	−4.50491			−0.144125			−0.0720625	−	0.997400i	$-0.522958\pi$
$977$	−4.50491			−0.144125			−0.0720625	+	0.997400i	$0.522958\pi$
$978$		0			0
$979$	−17.6384	+	13.1533i	−0.563725	+	0.420383i
$980$		0			0
$981$	27.7799	+	27.7799i	0.886943	+	0.886943i
$982$		0			0
$983$	−36.3939			−1.16079			−0.580393	−	0.814337i	$-0.697101\pi$
$983$	−36.3939			−1.16079			−0.580393	+	0.814337i	$0.697101\pi$
$984$		0			0
$985$	−61.6336			−1.96381
$986$		0			0
$987$	−10.1716	+	10.1716i	−0.323767	+	0.323767i
$988$		0			0
$989$	−11.5860	+	11.5860i	−0.368412	+	0.368412i
$990$		0			0
$991$			8.86453i			0.281591i	0.990039	+	0.140796i	$0.0449660\pi$
$991$			8.86453i			0.281591i	−0.990039	+	0.140796i	$0.955034\pi$
$992$		0			0
$993$	−57.9988			−1.84054
$994$		0			0
$995$	7.30848	−	7.30848i	0.231694	−	0.231694i
$996$		0			0
$997$	19.6285	+	19.6285i	0.621641	+	0.621641i	0.945951	−	0.324310i	$-0.105132\pi$
$997$	19.6285	+	19.6285i	0.621641	+	0.621641i	−0.324310	+	0.945951i	$0.605132\pi$
$998$		0			0
$999$	2.16131			0.0683807

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1408.2.i.b.351.18		44
4.3	odd	2		1408.2.i.a.351.6		44
8.3	odd	2		704.2.i.a.175.17		44
8.5	even	2		176.2.i.a.131.21	yes	44
11.10	odd	2	inner	1408.2.i.b.351.17		44
16.3	odd	4		176.2.i.a.43.2	✓	44
16.5	even	4		1408.2.i.a.1055.5		44
16.11	odd	4	inner	1408.2.i.b.1055.17		44
16.13	even	4		704.2.i.a.527.17		44
44.43	even	2		1408.2.i.a.351.5		44
88.21	odd	2		176.2.i.a.131.2	yes	44
88.43	even	2		704.2.i.a.175.18		44
176.21	odd	4		1408.2.i.a.1055.6		44
176.43	even	4	inner	1408.2.i.b.1055.18		44
176.109	odd	4		704.2.i.a.527.18		44
176.131	even	4		176.2.i.a.43.21	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
176.2.i.a.43.2	✓	44	16.3	odd	4
176.2.i.a.43.21	yes	44	176.131	even	4
176.2.i.a.131.2	yes	44	88.21	odd	2
176.2.i.a.131.21	yes	44	8.5	even	2
704.2.i.a.175.17		44	8.3	odd	2
704.2.i.a.175.18		44	88.43	even	2
704.2.i.a.527.17		44	16.13	even	4
704.2.i.a.527.18		44	176.109	odd	4
1408.2.i.a.351.5		44	44.43	even	2
1408.2.i.a.351.6		44	4.3	odd	2
1408.2.i.a.1055.5		44	16.5	even	4
1408.2.i.a.1055.6		44	176.21	odd	4
1408.2.i.b.351.17		44	11.10	odd	2	inner
1408.2.i.b.351.18		44	1.1	even	1	trivial
1408.2.i.b.1055.17		44	16.11	odd	4	inner
1408.2.i.b.1055.18		44	176.43	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1408 = 2^{7} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1408.i (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.64229 - 1.64229i) q^{3} +(-1.97065 + 1.97065i) q^{5} +1.30445i q^{7} -2.39422i q^{9} +O(q^{10})\)	\(q+(1.64229 - 1.64229i) q^{3} +(-1.97065 + 1.97065i) q^{5} +1.30445i q^{7} -2.39422i q^{9} +(-1.98269 - 2.65875i) q^{11} +(3.45212 - 3.45212i) q^{13} +6.47274i q^{15} -6.16050i q^{17} +(4.15098 + 4.15098i) q^{19} +(2.14228 + 2.14228i) q^{21} -2.00639 q^{23} -2.76691i q^{25} +(0.994862 + 0.994862i) q^{27} +(4.66521 - 4.66521i) q^{29} -6.42706i q^{31} +(-7.62258 - 1.11028i) q^{33} +(-2.57060 - 2.57060i) q^{35} +(1.08623 - 1.08623i) q^{37} -11.3387i q^{39} +4.81907 q^{41} +(5.77453 - 5.77453i) q^{43} +(4.71817 + 4.71817i) q^{45} +4.74805i q^{47} +5.29842 q^{49} +(-10.1173 - 10.1173i) q^{51} +(3.23296 - 3.23296i) q^{53} +(9.14664 + 1.33227i) q^{55} +13.6342 q^{57} +(-1.19357 - 1.19357i) q^{59} +(-1.81748 + 1.81748i) q^{61} +3.12313 q^{63} +13.6058i q^{65} +(-1.51245 + 1.51245i) q^{67} +(-3.29507 + 3.29507i) q^{69} -10.1099 q^{71} +5.86346 q^{73} +(-4.54406 - 4.54406i) q^{75} +(3.46819 - 2.58631i) q^{77} +8.60673 q^{79} +10.4504 q^{81} +(-6.28852 - 6.28852i) q^{83} +(12.1402 + 12.1402i) q^{85} -15.3232i q^{87} -6.63409i q^{89} +(4.50310 + 4.50310i) q^{91} +(-10.5551 - 10.5551i) q^{93} -16.3603 q^{95} -14.4459 q^{97} +(-6.36563 + 4.74700i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{3} + 4 q^{5}+O(q^{10}) \) 44 * q + 4 * q^3 + 4 * q^5	\( 44 q + 4 q^{3} + 4 q^{5} + 6 q^{11} - 24 q^{23} - 8 q^{27} - 4 q^{33} + 20 q^{37} - 28 q^{45} - 28 q^{49} - 12 q^{53} - 36 q^{55} + 20 q^{59} - 36 q^{67} + 16 q^{69} - 40 q^{71} - 60 q^{75} - 4 q^{77} - 20 q^{81} - 56 q^{91} - 8 q^{93} - 8 q^{97} + 42 q^{99}+O(q^{100}) \) 44 * q + 4 * q^3 + 4 * q^5 + 6 * q^11 - 24 * q^23 - 8 * q^27 - 4 * q^33 + 20 * q^37 - 28 * q^45 - 28 * q^49 - 12 * q^53 - 36 * q^55 + 20 * q^59 - 36 * q^67 + 16 * q^69 - 40 * q^71 - 60 * q^75 - 4 * q^77 - 20 * q^81 - 56 * q^91 - 8 * q^93 - 8 * q^97 + 42 * q^99

Introduction

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