LMFDB - Embedded newform 448.2.m.d.113.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [448,2,Mod(113,448)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(448, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("448.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	448.m (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:	$3.57729801055$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.20138089353117696.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3x^{10} - 2x^{9} + 2x^{8} + 4x^{7} + 2x^{6} + 8x^{5} + 8x^{4} - 16x^{3} - 48x^{2} + 64 $ x^12 - 3x^10 - 2x^9 + 2x^8 + 4x^7 + 2x^6 + 8x^5 + 8x^4 - 16x^3 - 48*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			113.1
Root			$1.35309 - 0.411286i$ of defining polynomial
Character	$\chi$	$=$	448.113
Dual form			448.2.m.d.337.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.21570 + 2.21570i) q^{3} +(-0.393125 - 0.393125i) q^{5} -1.00000i q^{7} -6.81864i q^{9} +O(q^{10})$	\(q+(-2.21570 + 2.21570i) q^{3} +(-0.393125 - 0.393125i) q^{5} -1.00000i q^{7} -6.81864i q^{9} +(-2.22602 - 2.22602i) q^{11} +(-3.16316 + 3.16316i) q^{13} +1.74209 q^{15} +0.980951 q^{17} +(5.26429 - 5.26429i) q^{19} +(2.21570 + 2.21570i) q^{21} -1.25951i q^{23} -4.69090i q^{25} +(8.46094 + 8.46094i) q^{27} +(3.17349 - 3.17349i) q^{29} +4.43140 q^{31} +9.86440 q^{33} +(-0.393125 + 0.393125i) q^{35} +(0.645145 + 0.645145i) q^{37} -14.0172i q^{39} -1.21375i q^{41} +(-0.966515 - 0.966515i) q^{43} +(-2.68058 + 2.68058i) q^{45} -9.97147 q^{47} -1.00000 q^{49} +(-2.17349 + 2.17349i) q^{51} +(-8.07814 - 8.07814i) q^{53} +1.75021i q^{55} +23.3282i q^{57} +(-1.81385 - 1.81385i) q^{59} +(-2.58783 + 2.58783i) q^{61} -6.81864 q^{63} +2.48704 q^{65} +(1.59261 - 1.59261i) q^{67} +(2.79069 + 2.79069i) q^{69} +0.934634i q^{71} -0.710511i q^{73} +(10.3936 + 10.3936i) q^{75} +(-2.22602 + 2.22602i) q^{77} -11.8644 q^{79} -17.0379 q^{81} +(6.77482 - 6.77482i) q^{83} +(-0.385637 - 0.385637i) q^{85} +14.0630i q^{87} -10.2082i q^{89} +(3.16316 + 3.16316i) q^{91} +(-9.81864 + 9.81864i) q^{93} -4.13906 q^{95} -3.03684 q^{97} +(-15.1784 + 15.1784i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{3} + 4 q^{5}+O(q^{10}) $ 12 * q - 4 * q^3 + 4 * q^5	$ 12 q - 4 q^{3} + 4 q^{5} + 24 q^{15} - 8 q^{17} + 4 q^{21} - 4 q^{27} - 4 q^{29} + 8 q^{31} + 4 q^{35} - 20 q^{37} - 16 q^{43} + 40 q^{45} - 16 q^{47} - 12 q^{49} + 16 q^{51} + 4 q^{53} + 16 q^{59} - 20 q^{61} - 12 q^{63} + 32 q^{65} - 24 q^{67} - 4 q^{69} + 40 q^{75} - 24 q^{79} - 44 q^{81} + 20 q^{83} - 8 q^{85} - 48 q^{93} + 48 q^{97} - 32 q^{99}+O(q^{100}) $ 12 * q - 4 * q^3 + 4 * q^5 + 24 * q^15 - 8 * q^17 + 4 * q^21 - 4 * q^27 - 4 * q^29 + 8 * q^31 + 4 * q^35 - 20 * q^37 - 16 * q^43 + 40 * q^45 - 16 * q^47 - 12 * q^49 + 16 * q^51 + 4 * q^53 + 16 * q^59 - 20 * q^61 - 12 * q^63 + 32 * q^65 - 24 * q^67 - 4 * q^69 + 40 * q^75 - 24 * q^79 - 44 * q^81 + 20 * q^83 - 8 * q^85 - 48 * q^93 + 48 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	−2.21570	+	2.21570i	−1.27923	+	1.27923i	−0.338137	+	0.941097i	$0.609797\pi$
$3$	−2.21570	+	2.21570i	−1.27923	+	1.27923i	−0.941097	+	0.338137i	$0.890203\pi$
$4$		0			0
$5$	−0.393125	−	0.393125i	−0.175811	−	0.175811i	0.613716	−	0.789527i	$-0.289674\pi$
$5$	−0.393125	−	0.393125i	−0.175811	−	0.175811i	−0.789527	+	0.613716i	$0.789674\pi$
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		0			0
$9$		−	6.81864i		−	2.27288i
$10$		0			0
$11$	−2.22602	−	2.22602i	−0.671172	−	0.671172i	0.286815	−	0.957986i	$-0.407404\pi$
$11$	−2.22602	−	2.22602i	−0.671172	−	0.671172i	−0.957986	+	0.286815i	$0.907404\pi$
$12$		0			0
$13$	−3.16316	+	3.16316i	−0.877304	+	0.877304i	−0.993255	−	0.115951i	$-0.963008\pi$
$13$	−3.16316	+	3.16316i	−0.877304	+	0.877304i	0.115951	+	0.993255i	$0.463008\pi$
$14$		0			0
$15$	1.74209			0.449807
$16$		0			0
$17$	0.980951			0.237915			0.118958	−	0.992899i	$-0.462045\pi$
$17$	0.980951			0.237915			0.118958	+	0.992899i	$0.462045\pi$
$18$		0			0
$19$	5.26429	−	5.26429i	1.20771	−	1.20771i	0.235946	−	0.971766i	$-0.424181\pi$
$19$	5.26429	−	5.26429i	1.20771	−	1.20771i	0.971766	−	0.235946i	$-0.0758188\pi$
$20$		0			0
$21$	2.21570	+	2.21570i	0.483505	+	0.483505i
$22$		0			0
$23$		−	1.25951i		−	0.262626i	−0.991341	−	0.131313i	$-0.958081\pi$
$23$		−	1.25951i		−	0.262626i	0.991341	−	0.131313i	$-0.0419192\pi$
$24$		0			0
$25$		−	4.69090i		−	0.938181i
$26$		0			0
$27$	8.46094	+	8.46094i	1.62831	+	1.62831i
$28$		0			0
$29$	3.17349	−	3.17349i	0.589302	−	0.589302i	−0.348140	−	0.937443i	$-0.613187\pi$
$29$	3.17349	−	3.17349i	0.589302	−	0.589302i	0.937443	+	0.348140i	$0.113187\pi$
$30$		0			0
$31$	4.43140			0.795902			0.397951	−	0.917407i	$-0.369721\pi$
$31$	4.43140			0.795902			0.397951	+	0.917407i	$0.369721\pi$
$32$		0			0
$33$	9.86440			1.71717
$34$		0			0
$35$	−0.393125	+	0.393125i	−0.0664503	+	0.0664503i
$36$		0			0
$37$	0.645145	+	0.645145i	0.106061	+	0.106061i	0.758146	−	0.652085i	$-0.226105\pi$
$37$	0.645145	+	0.645145i	0.106061	+	0.106061i	−0.652085	+	0.758146i	$0.726105\pi$
$38$		0			0
$39$		−	14.0172i		−	2.24455i
$40$		0			0
$41$		−	1.21375i		−	0.189556i	−0.995498	−	0.0947779i	$-0.969786\pi$
$41$		−	1.21375i		−	0.189556i	0.995498	−	0.0947779i	$-0.0302141\pi$
$42$		0			0
$43$	−0.966515	−	0.966515i	−0.147392	−	0.147392i	0.629560	−	0.776952i	$-0.283235\pi$
$43$	−0.966515	−	0.966515i	−0.147392	−	0.147392i	−0.776952	+	0.629560i	$0.783235\pi$
$44$		0			0
$45$	−2.68058	+	2.68058i	−0.399597	+	0.399597i
$46$		0			0
$47$	−9.97147			−1.45449			−0.727244	−	0.686379i	$-0.759199\pi$
$47$	−9.97147			−1.45449			−0.727244	+	0.686379i	$0.759199\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	−2.17349	+	2.17349i	−0.304350	+	0.304350i
$52$		0			0
$53$	−8.07814	−	8.07814i	−1.10962	−	1.10962i	−0.993200	−	0.116418i	$-0.962859\pi$
$53$	−8.07814	−	8.07814i	−1.10962	−	1.10962i	−0.116418	−	0.993200i	$-0.537141\pi$
$54$		0			0
$55$			1.75021i			0.235999i
$56$		0			0
$57$			23.3282i			3.08989i
$58$		0			0
$59$	−1.81385	−	1.81385i	−0.236143	−	0.236143i	0.579108	−	0.815251i	$-0.303401\pi$
$59$	−1.81385	−	1.81385i	−0.236143	−	0.236143i	−0.815251	+	0.579108i	$0.803401\pi$
$60$		0			0
$61$	−2.58783	+	2.58783i	−0.331337	+	0.331337i	−0.853094	−	0.521757i	$-0.825277\pi$
$61$	−2.58783	+	2.58783i	−0.331337	+	0.331337i	0.521757	+	0.853094i	$0.325277\pi$
$62$		0			0
$63$	−6.81864			−0.859067
$64$		0			0
$65$	2.48704			0.308479
$66$		0			0
$67$	1.59261	−	1.59261i	0.194568	−	0.194568i	−0.603098	−	0.797667i	$-0.706067\pi$
$67$	1.59261	−	1.59261i	0.194568	−	0.194568i	0.797667	+	0.603098i	$0.206067\pi$
$68$		0			0
$69$	2.79069	+	2.79069i	0.335960	+	0.335960i
$70$		0			0
$71$			0.934634i			0.110921i	0.998461	+	0.0554603i	$0.0176626\pi$
$71$			0.934634i			0.110921i	−0.998461	+	0.0554603i	$0.982337\pi$
$72$		0			0
$73$		−	0.710511i		−	0.0831591i	−0.999135	−	0.0415795i	$-0.986761\pi$
$73$		−	0.710511i		−	0.0831591i	0.999135	−	0.0415795i	$-0.0132390\pi$
$74$		0			0
$75$	10.3936	+	10.3936i	1.20015	+	1.20015i
$76$		0			0
$77$	−2.22602	+	2.22602i	−0.253679	+	0.253679i
$78$		0			0
$79$	−11.8644			−1.33485			−0.667424	−	0.744678i	$-0.732603\pi$
$79$	−11.8644			−1.33485			−0.667424	+	0.744678i	$0.732603\pi$
$80$		0			0
$81$	−17.0379			−1.89310
$82$		0			0
$83$	6.77482	−	6.77482i	0.743634	−	0.743634i	−0.229642	−	0.973275i	$-0.573755\pi$
$83$	6.77482	−	6.77482i	0.743634	−	0.743634i	0.973275	+	0.229642i	$0.0737554\pi$
$84$		0			0
$85$	−0.385637	−	0.385637i	−0.0418282	−	0.0418282i
$86$		0			0
$87$			14.0630i			1.50771i
$88$		0			0
$89$		−	10.2082i		−	1.08206i	−0.841002	−	0.541032i	$-0.818034\pi$
$89$		−	10.2082i		−	1.08206i	0.841002	−	0.541032i	$-0.181966\pi$
$90$		0			0
$91$	3.16316	+	3.16316i	0.331590	+	0.331590i
$92$		0			0
$93$	−9.81864	+	9.81864i	−1.01815	+	1.01815i
$94$		0			0
$95$	−4.13906			−0.424658
$96$		0			0
$97$	−3.03684			−0.308344			−0.154172	−	0.988044i	$-0.549271\pi$
$97$	−3.03684			−0.308344			−0.154172	+	0.988044i	$0.549271\pi$
$98$		0			0
$99$	−15.1784	+	15.1784i	−1.52549	+	1.52549i
$100$		0			0
$101$	−10.1648	−	10.1648i	−1.01143	−	1.01143i	−0.999934	−	0.0114982i	$-0.996340\pi$
$101$	−10.1648	−	10.1648i	−1.01143	−	1.01143i	−0.0114982	−	0.999934i	$-0.503660\pi$
$102$		0			0
$103$			6.05520i			0.596636i	0.954466	+	0.298318i	$0.0964256\pi$
$103$			6.05520i			0.596636i	−0.954466	+	0.298318i	$0.903574\pi$
$104$		0			0
$105$		−	1.74209i		−	0.170011i
$106$		0			0
$107$	−12.4973	−	12.4973i	−1.20816	−	1.20816i	−0.971624	−	0.236533i	$-0.923989\pi$
$107$	−12.4973	−	12.4973i	−1.20816	−	1.20816i	−0.236533	−	0.971624i	$-0.576011\pi$
$108$		0			0
$109$	10.0575	−	10.0575i	0.963333	−	0.963333i	−0.0360181	−	0.999351i	$-0.511467\pi$
$109$	10.0575	−	10.0575i	0.963333	−	0.963333i	0.999351	+	0.0360181i	$0.0114674\pi$
$110$		0			0
$111$	−2.85889			−0.271354
$112$		0			0
$113$	5.01929			0.472175			0.236088	−	0.971732i	$-0.424135\pi$
$113$	5.01929			0.472175			0.236088	+	0.971732i	$0.424135\pi$
$114$		0			0
$115$	−0.495145	+	0.495145i	−0.0461725	+	0.0461725i
$116$		0			0
$117$	21.5685	+	21.5685i	1.99401	+	1.99401i
$118$		0			0
$119$		−	0.980951i		−	0.0899236i
$120$		0			0
$121$		−	1.08963i		−	0.0990575i
$122$		0			0
$123$	2.68930	+	2.68930i	0.242486	+	0.242486i
$124$		0			0
$125$	−3.80974	+	3.80974i	−0.340754	+	0.340754i
$126$		0			0
$127$	19.3869			1.72031			0.860156	−	0.510031i	$-0.170366\pi$
$127$	19.3869			1.72031			0.860156	+	0.510031i	$0.170366\pi$
$128$		0			0
$129$	4.28301			0.377098
$130$		0			0
$131$	−8.29224	+	8.29224i	−0.724496	+	0.724496i	−0.969518	−	0.245021i	$-0.921205\pi$
$131$	−8.29224	+	8.29224i	−0.724496	+	0.724496i	0.245021	+	0.969518i	$0.421205\pi$
$132$		0			0
$133$	−5.26429	−	5.26429i	−0.456472	−	0.456472i
$134$		0			0
$135$		−	6.65242i		−	0.572549i
$136$		0			0
$137$			10.3723i			0.886168i	0.896480	+	0.443084i	$0.146116\pi$
$137$			10.3723i			0.886168i	−0.896480	+	0.443084i	$0.853884\pi$
$138$		0			0
$139$	4.83290	+	4.83290i	0.409921	+	0.409921i	0.881711	−	0.471790i	$-0.156392\pi$
$139$	4.83290	+	4.83290i	0.409921	+	0.409921i	−0.471790	+	0.881711i	$0.656392\pi$
$140$		0			0
$141$	22.0938	−	22.0938i	1.86063	−	1.86063i
$142$		0			0
$143$	14.0826			1.17764
$144$		0			0
$145$	−2.49516			−0.207212
$146$		0			0
$147$	2.21570	−	2.21570i	0.182748	−	0.182748i
$148$		0			0
$149$	1.74049	+	1.74049i	0.142587	+	0.142587i	0.774797	−	0.632210i	$-0.217852\pi$
$149$	1.74049	+	1.74049i	0.142587	+	0.142587i	−0.632210	+	0.774797i	$0.717852\pi$
$150$		0			0
$151$			20.8131i			1.69374i	0.531798	+	0.846871i	$0.321517\pi$
$151$			20.8131i			1.69374i	−0.531798	+	0.846871i	$0.678483\pi$
$152$		0			0
$153$		−	6.68874i		−	0.540753i
$154$		0			0
$155$	−1.74209	−	1.74209i	−0.139928	−	0.139928i
$156$		0			0
$157$	−10.1441	+	10.1441i	−0.809588	+	0.809588i	−0.984571	−	0.174983i	$-0.944013\pi$
$157$	−10.1441	+	10.1441i	−0.809588	+	0.809588i	0.174983	+	0.984571i	$0.444013\pi$
$158$		0			0
$159$	35.7975			2.83892
$160$		0			0
$161$	−1.25951			−0.0992632
$162$		0			0
$163$	11.8882	−	11.8882i	0.931152	−	0.931152i	−0.0666257	−	0.997778i	$-0.521223\pi$
$163$	11.8882	−	11.8882i	0.931152	−	0.931152i	0.997778	+	0.0666257i	$0.0212233\pi$
$164$		0			0
$165$	−3.87794	−	3.87794i	−0.301898	−	0.301898i
$166$		0			0
$167$			1.10868i			0.0857923i	0.999080	+	0.0428962i	$0.0136585\pi$
$167$			1.10868i			0.0857923i	−0.999080	+	0.0428962i	$0.986342\pi$
$168$		0			0
$169$		−	7.01121i		−	0.539324i
$170$		0			0
$171$	−35.8953	−	35.8953i	−2.74498	−	2.74498i
$172$		0			0
$173$	−7.23971	+	7.23971i	−0.550425	+	0.550425i	−0.926563	−	0.376139i	$-0.877252\pi$
$173$	−7.23971	+	7.23971i	−0.550425	+	0.550425i	0.376139	+	0.926563i	$0.377252\pi$
$174$		0			0
$175$	−4.69090			−0.354599
$176$		0			0
$177$	8.03789			0.604164
$178$		0			0
$179$	−9.93959	+	9.93959i	−0.742920	+	0.742920i	−0.973139	−	0.230219i	$-0.926056\pi$
$179$	−9.93959	+	9.93959i	−0.742920	+	0.742920i	0.230219	+	0.973139i	$0.426056\pi$
$180$		0			0
$181$	7.35342	+	7.35342i	0.546576	+	0.546576i	0.925449	−	0.378873i	$-0.123688\pi$
$181$	7.35342	+	7.35342i	0.546576	+	0.546576i	−0.378873	+	0.925449i	$0.623688\pi$
$182$		0			0
$183$		−	11.4677i		−	0.847715i
$184$		0			0
$185$		−	0.507246i		−	0.0372935i
$186$		0			0
$187$	−2.18362	−	2.18362i	−0.159682	−	0.159682i
$188$		0			0
$189$	8.46094	−	8.46094i	0.615443	−	0.615443i
$190$		0			0
$191$	−3.54684			−0.256640			−0.128320	−	0.991733i	$-0.540958\pi$
$191$	−3.54684			−0.256640			−0.128320	+	0.991733i	$0.540958\pi$
$192$		0			0
$193$	2.99394			0.215509			0.107754	−	0.994178i	$-0.465634\pi$
$193$	2.99394			0.215509			0.107754	+	0.994178i	$0.465634\pi$
$194$		0			0
$195$	−5.51053	+	5.51053i	−0.394617	+	0.394617i
$196$		0			0
$197$	3.55345	+	3.55345i	0.253173	+	0.253173i	0.822270	−	0.569097i	$-0.192707\pi$
$197$	3.55345	+	3.55345i	0.253173	+	0.253173i	−0.569097	+	0.822270i	$0.692707\pi$
$198$		0			0
$199$		−	1.80109i		−	0.127676i	−0.997960	−	0.0638380i	$-0.979666\pi$
$199$		−	1.80109i		−	0.127676i	0.997960	−	0.0638380i	$-0.0203341\pi$
$200$		0			0
$201$			7.05749i			0.497797i
$202$		0			0
$203$	−3.17349	−	3.17349i	−0.222735	−	0.222735i
$204$		0			0
$205$	−0.477156	+	0.477156i	−0.0333260	+	0.0333260i
$206$		0			0
$207$	−8.58813			−0.596916
$208$		0			0
$209$	−23.4369			−1.62116
$210$		0			0
$211$	15.1022	−	15.1022i	1.03968	−	1.03968i	0.0404953	−	0.999180i	$-0.487106\pi$
$211$	15.1022	−	15.1022i	1.03968	−	1.03968i	0.999180	−	0.0404953i	$-0.0128936\pi$
$212$		0			0
$213$	−2.07087	−	2.07087i	−0.141893	−	0.141893i
$214$		0			0
$215$			0.759924i			0.0518264i
$216$		0			0
$217$		−	4.43140i		−	0.300823i
$218$		0			0
$219$	1.57428	+	1.57428i	0.106380	+	0.106380i
$220$		0			0
$221$	−3.10291	+	3.10291i	−0.208724	+	0.208724i
$222$		0			0
$223$	−7.11258			−0.476294			−0.238147	−	0.971229i	$-0.576540\pi$
$223$	−7.11258			−0.476294			−0.238147	+	0.971229i	$0.576540\pi$
$224$		0			0
$225$	−31.9856			−2.13237
$226$		0			0
$227$	12.1687	−	12.1687i	0.807665	−	0.807665i	−0.176615	−	0.984280i	$-0.556515\pi$
$227$	12.1687	−	12.1687i	0.807665	−	0.807665i	0.984280	+	0.176615i	$0.0565147\pi$
$228$		0			0
$229$	−0.621484	−	0.621484i	−0.0410688	−	0.0410688i	0.686274	−	0.727343i	$-0.259245\pi$
$229$	−0.621484	−	0.621484i	−0.0410688	−	0.0410688i	−0.727343	+	0.686274i	$0.759245\pi$
$230$		0			0
$231$		−	9.86440i		−	0.649030i
$232$		0			0
$233$		−	4.85688i		−	0.318185i	−0.987264	−	0.159093i	$-0.949143\pi$
$233$		−	4.85688i		−	0.318185i	0.987264	−	0.159093i	$-0.0508568\pi$
$234$		0			0
$235$	3.92004	+	3.92004i	0.255715	+	0.255715i
$236$		0			0
$237$	26.2879	−	26.2879i	1.70758	−	1.70758i
$238$		0			0
$239$	−4.91033			−0.317623			−0.158811	−	0.987309i	$-0.550766\pi$
$239$	−4.91033			−0.317623			−0.158811	+	0.987309i	$0.550766\pi$
$240$		0			0
$241$	10.8591			0.699498			0.349749	−	0.936843i	$-0.386267\pi$
$241$	10.8591			0.699498			0.349749	+	0.936843i	$0.386267\pi$
$242$		0			0
$243$	12.3680	−	12.3680i	0.793406	−	0.793406i
$244$		0			0
$245$	0.393125	+	0.393125i	0.0251159	+	0.0251159i
$246$		0			0
$247$			33.3037i			2.11906i
$248$		0			0
$249$			30.0219i			1.90256i
$250$		0			0
$251$	−8.18516	−	8.18516i	−0.516643	−	0.516643i	0.399911	−	0.916554i	$-0.369041\pi$
$251$	−8.18516	−	8.18516i	−0.516643	−	0.516643i	−0.916554	+	0.399911i	$0.869041\pi$
$252$		0			0
$253$	−2.80370	+	2.80370i	−0.176267	+	0.176267i
$254$		0			0
$255$	1.70891			0.107016
$256$		0			0
$257$	20.6130			1.28580			0.642902	−	0.765948i	$-0.277730\pi$
$257$	20.6130			1.28580			0.642902	+	0.765948i	$0.277730\pi$
$258$		0			0
$259$	0.645145	−	0.645145i	0.0400874	−	0.0400874i
$260$		0			0
$261$	−21.6389	−	21.6389i	−1.33941	−	1.33941i
$262$		0			0
$263$		−	13.6297i		−	0.840444i	−0.907421	−	0.420222i	$-0.861952\pi$
$263$		−	13.6297i		−	0.840444i	0.907421	−	0.420222i	$-0.138048\pi$
$264$		0			0
$265$			6.35145i			0.390166i
$266$		0			0
$267$	22.6182	+	22.6182i	1.38421	+	1.38421i
$268$		0			0
$269$	4.42999	−	4.42999i	0.270101	−	0.270101i	−0.559040	−	0.829141i	$-0.688830\pi$
$269$	4.42999	−	4.42999i	0.270101	−	0.270101i	0.829141	+	0.559040i	$0.188830\pi$
$270$		0			0
$271$	−12.6851			−0.770564			−0.385282	−	0.922799i	$-0.625896\pi$
$271$	−12.6851			−0.770564			−0.385282	+	0.922799i	$0.625896\pi$
$272$		0			0
$273$	−14.0172			−0.848362
$274$		0			0
$275$	−10.4421	+	10.4421i	−0.629680	+	0.629680i
$276$		0			0
$277$	17.0842	+	17.0842i	1.02649	+	1.02649i	0.999639	+	0.0268508i	$0.00854789\pi$
$277$	17.0842	+	17.0842i	1.02649	+	1.02649i	0.0268508	+	0.999639i	$0.491452\pi$
$278$		0			0
$279$		−	30.2161i		−	1.80899i
$280$		0			0
$281$			12.8628i			0.767330i	0.923472	+	0.383665i	$0.125338\pi$
$281$			12.8628i			0.767330i	−0.923472	+	0.383665i	$0.874662\pi$
$282$		0			0
$283$	0.879091	+	0.879091i	0.0522565	+	0.0522565i	0.732752	−	0.680496i	$-0.238235\pi$
$283$	0.879091	+	0.879091i	0.0522565	+	0.0522565i	−0.680496	+	0.732752i	$0.738235\pi$
$284$		0			0
$285$	9.17090	−	9.17090i	0.543237	−	0.543237i
$286$		0			0
$287$	−1.21375			−0.0716454
$288$		0			0
$289$	−16.0377			−0.943396
$290$		0			0
$291$	6.72872	−	6.72872i	0.394445	−	0.394445i
$292$		0			0
$293$	−17.9935	−	17.9935i	−1.05119	−	1.05119i	−0.998617	−	0.0525765i	$-0.983257\pi$
$293$	−17.9935	−	17.9935i	−1.05119	−	1.05119i	−0.0525765	−	0.998617i	$-0.516743\pi$
$294$		0			0
$295$			1.42614i			0.0830331i
$296$		0			0
$297$		−	37.6685i		−	2.18575i
$298$		0			0
$299$	3.98403	+	3.98403i	0.230403	+	0.230403i
$300$		0			0
$301$	−0.966515	+	0.966515i	−0.0557090	+	0.0557090i
$302$		0			0
$303$	45.0441			2.58772
$304$		0			0
$305$	2.03468			0.116505
$306$		0			0
$307$	1.74987	−	1.74987i	0.0998702	−	0.0998702i	−0.655406	−	0.755277i	$-0.727503\pi$
$307$	1.74987	−	1.74987i	0.0998702	−	0.0998702i	0.755277	+	0.655406i	$0.227503\pi$
$308$		0			0
$309$	−13.4165	−	13.4165i	−0.763237	−	0.763237i
$310$		0			0
$311$		−	17.4288i		−	0.988296i	−0.869378	−	0.494148i	$-0.835480\pi$
$311$		−	17.4288i		−	0.988296i	0.869378	−	0.494148i	$-0.164520\pi$
$312$		0			0
$313$			28.3430i			1.60204i	0.598637	+	0.801021i	$0.295709\pi$
$313$			28.3430i			1.60204i	−0.598637	+	0.801021i	$0.704291\pi$
$314$		0			0
$315$	2.68058	+	2.68058i	0.151033	+	0.151033i
$316$		0			0
$317$	8.24397	−	8.24397i	0.463028	−	0.463028i	−0.436619	−	0.899647i	$-0.643824\pi$
$317$	8.24397	−	8.24397i	0.463028	−	0.463028i	0.899647	+	0.436619i	$0.143824\pi$
$318$		0			0
$319$	−14.1285			−0.791046
$320$		0			0
$321$	55.3803			3.09103
$322$		0			0
$323$	5.16401	−	5.16401i	0.287333	−	0.287333i
$324$		0			0
$325$	14.8381	+	14.8381i	0.823070	+	0.823070i
$326$		0			0
$327$			44.5687i			2.46466i
$328$		0			0
$329$			9.97147i			0.549745i
$330$		0			0
$331$	−0.235462	−	0.235462i	−0.0129422	−	0.0129422i	0.700606	−	0.713548i	$-0.252913\pi$
$331$	−0.235462	−	0.235462i	−0.0129422	−	0.0129422i	−0.713548	+	0.700606i	$0.752913\pi$
$332$		0			0
$333$	4.39901	−	4.39901i	0.241064	−	0.241064i
$334$		0			0
$335$	−1.25219			−0.0684146
$336$		0			0
$337$	9.22099			0.502299			0.251150	−	0.967948i	$-0.419191\pi$
$337$	9.22099			0.502299			0.251150	+	0.967948i	$0.419191\pi$
$338$		0			0
$339$	−11.1212	+	11.1212i	−0.604023	+	0.604023i
$340$		0			0
$341$	−9.86440	−	9.86440i	−0.534187	−	0.534187i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$		−	2.19418i		−	0.118131i
$346$		0			0
$347$	8.02721	+	8.02721i	0.430923	+	0.430923i	0.888942	−	0.458019i	$-0.151441\pi$
$347$	8.02721	+	8.02721i	0.430923	+	0.430923i	−0.458019	+	0.888942i	$0.651441\pi$
$348$		0			0
$349$	11.5879	−	11.5879i	0.620287	−	0.620287i	−0.325318	−	0.945605i	$-0.605471\pi$
$349$	11.5879	−	11.5879i	0.620287	−	0.620287i	0.945605	+	0.325318i	$0.105471\pi$
$350$		0			0
$351$	−53.5267			−2.85704
$352$		0			0
$353$	18.9481			1.00850			0.504252	−	0.863557i	$-0.331768\pi$
$353$	18.9481			1.00850			0.504252	+	0.863557i	$0.331768\pi$
$354$		0			0
$355$	0.367428	−	0.367428i	0.0195011	−	0.0195011i
$356$		0			0
$357$	2.17349	+	2.17349i	0.115033	+	0.115033i
$358$		0			0
$359$			3.54172i			0.186925i	0.995623	+	0.0934624i	$0.0297935\pi$
$359$			3.54172i			0.186925i	−0.995623	+	0.0934624i	$0.970207\pi$
$360$		0			0
$361$		−	36.4256i		−	1.91714i
$362$		0			0
$363$	2.41430	+	2.41430i	0.126718	+	0.126718i
$364$		0			0
$365$	−0.279320	+	0.279320i	−0.0146203	+	0.0146203i
$366$		0			0
$367$	−11.1874			−0.583979			−0.291989	−	0.956422i	$-0.594317\pi$
$367$	−11.1874			−0.583979			−0.291989	+	0.956422i	$0.594317\pi$
$368$		0			0
$369$	−8.27611			−0.430837
$370$		0			0
$371$	−8.07814	+	8.07814i	−0.419396	+	0.419396i
$372$		0			0
$373$	13.8071	+	13.8071i	0.714907	+	0.714907i	0.967558	−	0.252651i	$-0.0813023\pi$
$373$	13.8071	+	13.8071i	0.714907	+	0.714907i	−0.252651	+	0.967558i	$0.581302\pi$
$374$		0			0
$375$		−	16.8825i		−	0.871807i
$376$		0			0
$377$			20.0765i			1.03399i
$378$		0			0
$379$	10.9875	+	10.9875i	0.564391	+	0.564391i	0.930552	−	0.366161i	$-0.119328\pi$
$379$	10.9875	+	10.9875i	0.564391	+	0.564391i	−0.366161	+	0.930552i	$0.619328\pi$
$380$		0			0
$381$	−42.9556	+	42.9556i	−2.20068	+	2.20068i
$382$		0			0
$383$	4.83945			0.247284			0.123642	−	0.992327i	$-0.460542\pi$
$383$	4.83945			0.247284			0.123642	+	0.992327i	$0.460542\pi$
$384$		0			0
$385$	1.75021			0.0891991
$386$		0			0
$387$	−6.59032	+	6.59032i	−0.335005	+	0.335005i
$388$		0			0
$389$	12.4807	+	12.4807i	0.632795	+	0.632795i	0.948768	−	0.315973i	$-0.102331\pi$
$389$	12.4807	+	12.4807i	0.632795	+	0.632795i	−0.315973	+	0.948768i	$0.602331\pi$
$390$		0			0
$391$		−	1.23552i		−	0.0624827i
$392$		0			0
$393$		−	36.7462i		−	1.85360i
$394$		0			0
$395$	4.66419	+	4.66419i	0.234681	+	0.234681i
$396$		0			0
$397$	−11.7543	+	11.7543i	−0.589931	+	0.589931i	−0.937613	−	0.347682i	$-0.886969\pi$
$397$	−11.7543	+	11.7543i	−0.589931	+	0.589931i	0.347682	+	0.937613i	$0.386969\pi$
$398$		0			0
$399$	23.3282			1.16787
$400$		0			0
$401$	−25.5823			−1.27752			−0.638760	−	0.769406i	$-0.720552\pi$
$401$	−25.5823			−1.27752			−0.638760	+	0.769406i	$0.720552\pi$
$402$		0			0
$403$	−14.0172	+	14.0172i	−0.698248	+	0.698248i
$404$		0			0
$405$	6.69803	+	6.69803i	0.332828	+	0.332828i
$406$		0			0
$407$		−	2.87222i		−	0.142371i
$408$		0			0
$409$		−	19.2126i		−	0.950001i	−0.879985	−	0.475001i	$-0.842448\pi$
$409$		−	19.2126i		−	0.950001i	0.879985	−	0.475001i	$-0.157552\pi$
$410$		0			0
$411$	−22.9820	−	22.9820i	−1.13362	−	1.13362i
$412$		0			0
$413$	−1.81385	+	1.81385i	−0.0892537	+	0.0892537i
$414$		0			0
$415$	−5.32671			−0.261478
$416$		0			0
$417$	−21.4165			−1.04877
$418$		0			0
$419$	−11.2764	+	11.2764i	−0.550888	+	0.550888i	−0.926697	−	0.375809i	$-0.877365\pi$
$419$	−11.2764	+	11.2764i	−0.550888	+	0.550888i	0.375809	+	0.926697i	$0.377365\pi$
$420$		0			0
$421$	27.1033	+	27.1033i	1.32094	+	1.32094i	0.913019	+	0.407918i	$0.133745\pi$
$421$	27.1033	+	27.1033i	1.32094	+	1.32094i	0.407918	+	0.913019i	$0.366255\pi$
$422$		0			0
$423$			67.9918i			3.30588i
$424$		0			0
$425$		−	4.60155i		−	0.223208i
$426$		0			0
$427$	2.58783	+	2.58783i	0.125234	+	0.125234i
$428$		0			0
$429$	−31.2027	+	31.2027i	−1.50648	+	1.50648i
$430$		0			0
$431$	14.7618			0.711053			0.355526	−	0.934666i	$-0.384302\pi$
$431$	14.7618			0.711053			0.355526	+	0.934666i	$0.384302\pi$
$432$		0			0
$433$	−30.0057			−1.44198			−0.720991	−	0.692944i	$-0.756313\pi$
$433$	−30.0057			−1.44198			−0.720991	+	0.692944i	$0.756313\pi$
$434$		0			0
$435$	5.52852	−	5.52852i	0.265072	−	0.265072i
$436$		0			0
$437$	−6.63043	−	6.63043i	−0.317176	−	0.317176i
$438$		0			0
$439$		−	33.7523i		−	1.61091i	−0.592659	−	0.805454i	$-0.701922\pi$
$439$		−	33.7523i		−	1.61091i	0.592659	−	0.805454i	$-0.298078\pi$
$440$		0			0
$441$			6.81864i			0.324697i
$442$		0			0
$443$	−5.22020	−	5.22020i	−0.248019	−	0.248019i	0.572138	−	0.820157i	$-0.306114\pi$
$443$	−5.22020	−	5.22020i	−0.248019	−	0.248019i	−0.820157	+	0.572138i	$0.806114\pi$
$444$		0			0
$445$	−4.01309	+	4.01309i	−0.190239	+	0.190239i
$446$		0			0
$447$	−7.71281			−0.364803
$448$		0			0
$449$	−1.59006			−0.0750395			−0.0375197	−	0.999296i	$-0.511946\pi$
$449$	−1.59006			−0.0750395			−0.0375197	+	0.999296i	$0.511946\pi$
$450$		0			0
$451$	−2.70184	+	2.70184i	−0.127224	+	0.127224i
$452$		0			0
$453$	−46.1154	−	46.1154i	−2.16669	−	2.16669i
$454$		0			0
$455$		−	2.48704i		−	0.116594i
$456$		0			0
$457$		−	2.14917i		−	0.100534i	−0.998736	−	0.0502671i	$-0.983993\pi$
$457$		−	2.14917i		−	0.100534i	0.998736	−	0.0502671i	$-0.0160072\pi$
$458$		0			0
$459$	8.29977	+	8.29977i	0.387400	+	0.387400i
$460$		0			0
$461$	−26.7406	+	26.7406i	−1.24543	+	1.24543i	−0.287719	+	0.957715i	$0.592897\pi$
$461$	−26.7406	+	26.7406i	−1.24543	+	1.24543i	−0.957715	+	0.287719i	$0.907103\pi$
$462$		0			0
$463$	−16.2686			−0.756065			−0.378033	−	0.925792i	$-0.623399\pi$
$463$	−16.2686			−0.756065			−0.378033	+	0.925792i	$0.623399\pi$
$464$		0			0
$465$	7.71991			0.358002
$466$		0			0
$467$	−17.9285	+	17.9285i	−0.829632	+	0.829632i	−0.987466	−	0.157834i	$-0.949549\pi$
$467$	−17.9285	+	17.9285i	−0.829632	+	0.829632i	0.157834	+	0.987466i	$0.449549\pi$
$468$		0			0
$469$	−1.59261	−	1.59261i	−0.0735400	−	0.0735400i
$470$		0			0
$471$		−	44.9526i		−	2.07131i
$472$		0			0
$473$			4.30297i			0.197851i
$474$		0			0
$475$	−24.6943	−	24.6943i	−1.13305	−	1.13305i
$476$		0			0
$477$	−55.0819	+	55.0819i	−2.52203	+	2.52203i
$478$		0			0
$479$	16.9860			0.776112			0.388056	−	0.921636i	$-0.373147\pi$
$479$	16.9860			0.776112			0.388056	+	0.921636i	$0.373147\pi$
$480$		0			0
$481$	−4.08140			−0.186096
$482$		0			0
$483$	2.79069	−	2.79069i	0.126981	−	0.126981i
$484$		0			0
$485$	1.19386	+	1.19386i	0.0542103	+	0.0542103i
$486$		0			0
$487$		−	39.0342i		−	1.76881i	−0.466722	−	0.884404i	$-0.654565\pi$
$487$		−	39.0342i		−	1.76881i	0.466722	−	0.884404i	$-0.345435\pi$
$488$		0			0
$489$			52.6811i			2.38232i
$490$		0			0
$491$	26.8828	+	26.8828i	1.21320	+	1.21320i	0.969967	+	0.243238i	$0.0782097\pi$
$491$	26.8828	+	26.8828i	1.21320	+	1.21320i	0.243238	+	0.969967i	$0.421790\pi$
$492$		0			0
$493$	3.11304	−	3.11304i	0.140204	−	0.140204i
$494$		0			0
$495$	11.9341			0.536396
$496$		0			0
$497$	0.934634			0.0419241
$498$		0			0
$499$	−4.52969	+	4.52969i	−0.202777	+	0.202777i	−0.801189	−	0.598412i	$-0.795799\pi$
$499$	−4.52969	+	4.52969i	−0.202777	+	0.202777i	0.598412	+	0.801189i	$0.295799\pi$
$500$		0			0
$501$	−2.45650	−	2.45650i	−0.109748	−	0.109748i
$502$		0			0
$503$			35.6215i			1.58829i	0.607731	+	0.794143i	$0.292080\pi$
$503$			35.6215i			1.58829i	−0.607731	+	0.794143i	$0.707920\pi$
$504$		0			0
$505$			7.99206i			0.355642i
$506$		0			0
$507$	15.5347	+	15.5347i	0.689922	+	0.689922i
$508$		0			0
$509$	18.0304	−	18.0304i	0.799183	−	0.799183i	−0.183783	−	0.982967i	$-0.558835\pi$
$509$	18.0304	−	18.0304i	0.799183	−	0.799183i	0.982967	+	0.183783i	$0.0588345\pi$
$510$		0			0
$511$	−0.710511			−0.0314312
$512$		0			0
$513$	89.0818			3.93306
$514$		0			0
$515$	2.38045	−	2.38045i	0.104895	−	0.104895i
$516$		0			0
$517$	22.1967	+	22.1967i	0.976212	+	0.976212i
$518$		0			0
$519$		−	32.0820i		−	1.40824i
$520$		0			0
$521$		−	15.5300i		−	0.680380i	−0.940357	−	0.340190i	$-0.889509\pi$
$521$		−	15.5300i		−	0.680380i	0.940357	−	0.340190i	$-0.110491\pi$
$522$		0			0
$523$	−7.58074	−	7.58074i	−0.331483	−	0.331483i	0.521667	−	0.853149i	$-0.325310\pi$
$523$	−7.58074	−	7.58074i	−0.331483	−	0.331483i	−0.853149	+	0.521667i	$0.825310\pi$
$524$		0			0
$525$	10.3936	−	10.3936i	0.453615	−	0.453615i
$526$		0			0
$527$	4.34698			0.189357
$528$		0			0
$529$	21.4136			0.931028
$530$		0			0
$531$	−12.3680	+	12.3680i	−0.536725	+	0.536725i
$532$		0			0
$533$	3.83929	+	3.83929i	0.166298	+	0.166298i
$534$		0			0
$535$			9.82598i			0.424814i
$536$		0			0
$537$		−	44.0463i		−	1.90074i
$538$		0			0
$539$	2.22602	+	2.22602i	0.0958817	+	0.0958817i
$540$		0			0
$541$	16.7920	−	16.7920i	0.721944	−	0.721944i	−0.247057	−	0.969001i	$-0.579463\pi$
$541$	16.7920	−	16.7920i	0.721944	−	0.721944i	0.969001	+	0.247057i	$0.0794634\pi$
$542$		0			0
$543$	−32.5859			−1.39840
$544$		0			0
$545$	−7.90771			−0.338729
$546$		0			0
$547$	28.9159	−	28.9159i	1.23636	−	1.23636i	0.274875	−	0.961480i	$-0.411363\pi$
$547$	28.9159	−	28.9159i	1.23636	−	1.23636i	0.961480	−	0.274875i	$-0.0886366\pi$
$548$		0			0
$549$	17.6454	+	17.6454i	0.753089	+	0.753089i
$550$		0			0
$551$		−	33.4124i		−	1.42342i
$552$		0			0
$553$			11.8644i			0.504525i
$554$		0			0
$555$	1.12390	+	1.12390i	0.0477071	+	0.0477071i
$556$		0			0
$557$	11.8756	−	11.8756i	0.503184	−	0.503184i	−0.409242	−	0.912426i	$-0.634207\pi$
$557$	11.8756	−	11.8756i	0.503184	−	0.503184i	0.912426	+	0.409242i	$0.134207\pi$
$558$		0			0
$559$	6.11449			0.258616
$560$		0			0
$561$	9.67648			0.408541
$562$		0			0
$563$	2.51935	−	2.51935i	0.106178	−	0.106178i	−0.652022	−	0.758200i	$-0.726079\pi$
$563$	2.51935	−	2.51935i	0.106178	−	0.106178i	0.758200	+	0.652022i	$0.226079\pi$
$564$		0			0
$565$	−1.97321	−	1.97321i	−0.0830137	−	0.0830137i
$566$		0			0
$567$			17.0379i			0.715524i
$568$		0			0
$569$		−	1.90395i		−	0.0798176i	−0.999203	−	0.0399088i	$-0.987293\pi$
$569$		−	1.90395i		−	0.0798176i	0.999203	−	0.0399088i	$-0.0127067\pi$
$570$		0			0
$571$	−1.94546	−	1.94546i	−0.0814148	−	0.0814148i	0.665227	−	0.746641i	$-0.268335\pi$
$571$	−1.94546	−	1.94546i	−0.0814148	−	0.0814148i	−0.746641	+	0.665227i	$0.768335\pi$
$572$		0			0
$573$	7.85872	−	7.85872i	0.328303	−	0.328303i
$574$		0			0
$575$	−5.90824			−0.246390
$576$		0			0
$577$	−0.270046			−0.0112422			−0.00562108	−	0.999984i	$-0.501789\pi$
$577$	−0.270046			−0.0112422			−0.00562108	+	0.999984i	$0.501789\pi$
$578$		0			0
$579$	−6.63367	+	6.63367i	−0.275686	+	0.275686i
$580$		0			0
$581$	−6.77482	−	6.77482i	−0.281067	−	0.281067i
$582$		0			0
$583$			35.9643i			1.48949i
$584$		0			0
$585$		−	16.9582i		−	0.701136i
$586$		0			0
$587$	22.4556	+	22.4556i	0.926842	+	0.926842i	0.997501	−	0.0706582i	$-0.0225100\pi$
$587$	22.4556	+	22.4556i	0.926842	+	0.926842i	−0.0706582	+	0.997501i	$0.522510\pi$
$588$		0			0
$589$	23.3282	−	23.3282i	0.961221	−	0.961221i
$590$		0			0
$591$	−15.7468			−0.647735
$592$		0			0
$593$	−36.0626			−1.48091			−0.740456	−	0.672105i	$-0.765390\pi$
$593$	−36.0626			−1.48091			−0.740456	+	0.672105i	$0.765390\pi$
$594$		0			0
$595$	−0.385637	+	0.385637i	−0.0158096	+	0.0158096i
$596$		0			0
$597$	3.99067	+	3.99067i	0.163327	+	0.163327i
$598$		0			0
$599$			10.7292i			0.438381i	0.975682	+	0.219191i	$0.0703417\pi$
$599$			10.7292i			0.438381i	−0.975682	+	0.219191i	$0.929658\pi$
$600$		0			0
$601$		−	36.0677i		−	1.47123i	−0.677399	−	0.735616i	$-0.736893\pi$
$601$		−	36.0677i		−	1.47123i	0.677399	−	0.735616i	$-0.263107\pi$
$602$		0			0
$603$	−10.8594	−	10.8594i	−0.442230	−	0.442230i
$604$		0			0
$605$	−0.428362	+	0.428362i	−0.0174154	+	0.0174154i
$606$		0			0
$607$	−6.98617			−0.283560			−0.141780	−	0.989898i	$-0.545283\pi$
$607$	−6.98617			−0.283560			−0.141780	+	0.989898i	$0.545283\pi$
$608$		0			0
$609$	14.0630			0.569861
$610$		0			0
$611$	31.5414	−	31.5414i	1.27603	−	1.27603i
$612$		0			0
$613$	−23.3560	−	23.3560i	−0.943340	−	0.943340i	0.0551389	−	0.998479i	$-0.482440\pi$
$613$	−23.3560	−	23.3560i	−0.943340	−	0.943340i	−0.998479	+	0.0551389i	$0.982440\pi$
$614$		0			0
$615$		−	2.11447i		−	0.0852635i
$616$		0			0
$617$		−	41.5107i		−	1.67116i	−0.549370	−	0.835579i	$-0.685132\pi$
$617$		−	41.5107i		−	1.67116i	0.549370	−	0.835579i	$-0.314868\pi$
$618$		0			0
$619$	19.3546	+	19.3546i	0.777929	+	0.777929i	0.979478	−	0.201550i	$-0.0645978\pi$
$619$	19.3546	+	19.3546i	0.777929	+	0.777929i	−0.201550	+	0.979478i	$0.564598\pi$
$620$		0			0
$621$	10.6566	−	10.6566i	0.427636	−	0.427636i
$622$		0			0
$623$	−10.2082			−0.408982
$624$		0			0
$625$	−20.4591			−0.818365
$626$		0			0
$627$	51.9291	−	51.9291i	2.07385	−	2.07385i
$628$		0			0
$629$	0.632856	+	0.632856i	0.0252336	+	0.0252336i
$630$		0			0
$631$		−	2.56032i		−	0.101925i	−0.998701	−	0.0509624i	$-0.983771\pi$
$631$		−	2.56032i		−	0.101925i	0.998701	−	0.0509624i	$-0.0162289\pi$
$632$		0			0
$633$			66.9236i			2.65997i
$634$		0			0
$635$	−7.62149	−	7.62149i	−0.302450	−	0.302450i
$636$		0			0
$637$	3.16316	−	3.16316i	0.125329	−	0.125329i
$638$		0			0
$639$	6.37293			0.252109
$640$		0			0
$641$	−0.654189			−0.0258389			−0.0129195	−	0.999917i	$-0.504113\pi$
$641$	−0.654189			−0.0258389			−0.0129195	+	0.999917i	$0.504113\pi$
$642$		0			0
$643$	−3.21708	+	3.21708i	−0.126869	+	0.126869i	−0.767690	−	0.640821i	$-0.778594\pi$
$643$	−3.21708	+	3.21708i	−0.126869	+	0.126869i	0.640821	+	0.767690i	$0.278594\pi$
$644$		0			0
$645$	−1.68376	−	1.68376i	−0.0662980	−	0.0662980i
$646$		0			0
$647$		−	39.4069i		−	1.54925i	−0.632423	−	0.774623i	$-0.717939\pi$
$647$		−	39.4069i		−	1.54925i	0.632423	−	0.774623i	$-0.282061\pi$
$648$		0			0
$649$			8.07535i			0.316985i
$650$		0			0
$651$	9.81864	+	9.81864i	0.384823	+	0.384823i
$652$		0			0
$653$	25.4270	−	25.4270i	0.995034	−	0.995034i	−0.00495338	−	0.999988i	$-0.501577\pi$
$653$	25.4270	−	25.4270i	0.995034	−	0.995034i	0.999988	+	0.00495338i	$0.00157672\pi$
$654$		0			0
$655$	6.51978			0.254749
$656$		0			0
$657$	−4.84472			−0.189010
$658$		0			0
$659$	−31.8006	+	31.8006i	−1.23877	+	1.23877i	−0.278272	+	0.960502i	$0.589762\pi$
$659$	−31.8006	+	31.8006i	−1.23877	+	1.23877i	−0.960502	+	0.278272i	$0.910238\pi$
$660$		0			0
$661$	−5.45506	−	5.45506i	−0.212177	−	0.212177i	0.593015	−	0.805192i	$-0.297938\pi$
$661$	−5.45506	−	5.45506i	−0.212177	−	0.212177i	−0.805192	+	0.593015i	$0.797938\pi$
$662$		0			0
$663$		−	13.7502i		−	0.534014i
$664$		0			0
$665$			4.13906i			0.160506i
$666$		0			0
$667$	−3.99704	−	3.99704i	−0.154766	−	0.154766i
$668$		0			0
$669$	15.7593	−	15.7593i	0.609291	−	0.609291i
$670$		0			0
$671$	11.5211			0.444768
$672$		0			0
$673$	−28.3929			−1.09446			−0.547232	−	0.836981i	$-0.684319\pi$
$673$	−28.3929			−1.09446			−0.547232	+	0.836981i	$0.684319\pi$
$674$		0			0
$675$	39.6895	−	39.6895i	1.52765	−	1.52765i
$676$		0			0
$677$	7.58622	+	7.58622i	0.291562	+	0.291562i	0.837697	−	0.546135i	$-0.183901\pi$
$677$	7.58622	+	7.58622i	0.291562	+	0.291562i	−0.546135	+	0.837697i	$0.683901\pi$
$678$		0			0
$679$			3.03684i			0.116543i
$680$		0			0
$681$			53.9243i			2.06639i
$682$		0			0
$683$	10.6493	+	10.6493i	0.407485	+	0.407485i	0.880861	−	0.473376i	$-0.156965\pi$
$683$	10.6493	+	10.6493i	0.407485	+	0.407485i	−0.473376	+	0.880861i	$0.656965\pi$
$684$		0			0
$685$	4.07763	−	4.07763i	0.155798	−	0.155798i
$686$		0			0
$687$	2.75404			0.105073
$688$		0			0
$689$	51.1050			1.94695
$690$		0			0
$691$	−1.31805	+	1.31805i	−0.0501409	+	0.0501409i	−0.731733	−	0.681592i	$-0.761288\pi$
$691$	−1.31805	+	1.31805i	−0.0501409	+	0.0501409i	0.681592	+	0.731733i	$0.261288\pi$
$692$		0			0
$693$	15.1784	+	15.1784i	0.576582	+	0.576582i
$694$		0			0
$695$		−	3.79987i		−	0.144137i
$696$		0			0
$697$		−	1.19063i		−	0.0450983i
$698$		0			0
$699$	10.7614	+	10.7614i	0.407033	+	0.407033i
$700$		0			0
$701$	5.77893	−	5.77893i	0.218267	−	0.218267i	−0.589501	−	0.807768i	$-0.700675\pi$
$701$	5.77893	−	5.77893i	0.218267	−	0.218267i	0.807768	+	0.589501i	$0.200675\pi$
$702$		0			0
$703$	6.79247			0.256183
$704$		0			0
$705$	−17.3712			−0.654239
$706$		0			0
$707$	−10.1648	+	10.1648i	−0.382285	+	0.382285i
$708$		0			0
$709$	−27.5392	−	27.5392i	−1.03426	−	1.03426i	−0.999392	−	0.0348642i	$-0.988900\pi$
$709$	−27.5392	−	27.5392i	−1.03426	−	1.03426i	−0.0348642	−	0.999392i	$-0.511100\pi$
$710$		0			0
$711$			80.8990i			3.03395i
$712$		0			0
$713$		−	5.58138i		−	0.209024i
$714$		0			0
$715$	−5.53621	−	5.53621i	−0.207043	−	0.207043i
$716$		0			0
$717$	10.8798	−	10.8798i	0.406314	−	0.406314i
$718$		0			0
$719$	3.79808			0.141645			0.0708223	−	0.997489i	$-0.477438\pi$
$719$	3.79808			0.141645			0.0708223	+	0.997489i	$0.477438\pi$
$720$		0			0
$721$	6.05520			0.225507
$722$		0			0
$723$	−24.0605	+	24.0605i	−0.894821	+	0.894821i
$724$		0			0
$725$	−14.8865	−	14.8865i	−0.552872	−	0.552872i
$726$		0			0
$727$		−	25.5053i		−	0.945937i	−0.881079	−	0.472969i	$-0.843182\pi$
$727$		−	25.5053i		−	0.945937i	0.881079	−	0.472969i	$-0.156818\pi$
$728$		0			0
$729$			3.69376i			0.136806i
$730$		0			0
$731$	−0.948104	−	0.948104i	−0.0350669	−	0.0350669i
$732$		0			0
$733$	−29.0147	+	29.0147i	−1.07168	+	1.07168i	−0.0744582	+	0.997224i	$0.523723\pi$
$733$	−29.0147	+	29.0147i	−1.07168	+	1.07168i	−0.997224	+	0.0744582i	$0.976277\pi$
$734$		0			0
$735$	−1.74209			−0.0642581
$736$		0			0
$737$	−7.09038			−0.261178
$738$		0			0
$739$	−1.66971	+	1.66971i	−0.0614213	+	0.0614213i	−0.737150	−	0.675729i	$-0.763829\pi$
$739$	−1.66971	+	1.66971i	−0.0614213	+	0.0614213i	0.675729	+	0.737150i	$0.263829\pi$
$740$		0			0
$741$	−73.7909	−	73.7909i	−2.71077	−	2.71077i
$742$		0			0
$743$			24.1373i			0.885513i	0.896642	+	0.442756i	$0.145999\pi$
$743$			24.1373i			0.885513i	−0.896642	+	0.442756i	$0.854001\pi$
$744$		0			0
$745$		−	1.36846i		−	0.0501366i
$746$		0			0
$747$	−46.1951	−	46.1951i	−1.69019	−	1.69019i
$748$		0			0
$749$	−12.4973	+	12.4973i	−0.456640	+	0.456640i
$750$		0			0
$751$	−17.6703			−0.644797			−0.322398	−	0.946604i	$-0.604489\pi$
$751$	−17.6703			−0.644797			−0.322398	+	0.946604i	$0.604489\pi$
$752$		0			0
$753$	36.2717			1.32181
$754$		0			0
$755$	8.18214	−	8.18214i	0.297779	−	0.297779i
$756$		0			0
$757$	−14.3436	−	14.3436i	−0.521327	−	0.521327i	0.396645	−	0.917972i	$-0.370174\pi$
$757$	−14.3436	−	14.3436i	−0.521327	−	0.521327i	−0.917972	+	0.396645i	$0.870174\pi$
$758$		0			0
$759$		−	12.4243i		−	0.450973i
$760$		0			0
$761$		−	13.4406i		−	0.487220i	−0.969873	−	0.243610i	$-0.921668\pi$
$761$		−	13.4406i		−	0.487220i	0.969873	−	0.243610i	$-0.0783317\pi$
$762$		0			0
$763$	−10.0575	−	10.0575i	−0.364106	−	0.364106i
$764$		0			0
$765$	−2.62952	+	2.62952i	−0.0950703	+	0.0950703i
$766$		0			0
$767$	11.4750			0.414338
$768$		0			0
$769$	−42.7134			−1.54029			−0.770143	−	0.637871i	$-0.779815\pi$
$769$	−42.7134			−1.54029			−0.770143	+	0.637871i	$0.779815\pi$
$770$		0			0
$771$	−45.6722	+	45.6722i	−1.64484	+	1.64484i
$772$		0			0
$773$	17.6239	+	17.6239i	0.633886	+	0.633886i	0.949040	−	0.315154i	$-0.102056\pi$
$773$	17.6239	+	17.6239i	0.633886	+	0.633886i	−0.315154	+	0.949040i	$0.602056\pi$
$774$		0			0
$775$		−	20.7873i		−	0.746700i
$776$		0			0
$777$			2.85889i			0.102562i
$778$		0			0
$779$	−6.38953	−	6.38953i	−0.228929	−	0.228929i
$780$		0			0
$781$	2.08052	−	2.08052i	0.0744468	−	0.0744468i
$782$		0			0
$783$	53.7014			1.91913
$784$		0			0
$785$	7.97582			0.284669
$786$		0			0
$787$	−27.4590	+	27.4590i	−0.978807	+	0.978807i	−0.999780	−	0.0209726i	$-0.993324\pi$
$787$	−27.4590	+	27.4590i	−0.978807	+	0.978807i	0.0209726	+	0.999780i	$0.493324\pi$
$788$		0			0
$789$	30.1993	+	30.1993i	1.07512	+	1.07512i
$790$		0			0
$791$		−	5.01929i		−	0.178466i
$792$		0			0
$793$		−	16.3714i		−	0.581367i
$794$		0			0
$795$	−14.0729	−	14.0729i	−0.499114	−	0.499114i
$796$		0			0
$797$	37.2933	−	37.2933i	1.32100	−	1.32100i	0.408024	−	0.912971i	$-0.366218\pi$
$797$	37.2933	−	37.2933i	1.32100	−	1.32100i	0.912971	−	0.408024i	$-0.133782\pi$
$798$		0			0
$799$	−9.78152			−0.346045
$800$		0			0
$801$	−69.6058			−2.45940
$802$		0			0
$803$	−1.58162	+	1.58162i	−0.0558140	+	0.0558140i
$804$		0			0
$805$	0.495145	+	0.495145i	0.0174516	+	0.0174516i
$806$		0			0
$807$			19.6310i			0.691045i
$808$		0			0
$809$			44.3124i			1.55794i	0.627061	+	0.778970i	$0.284258\pi$
$809$			44.3124i			1.55794i	−0.627061	+	0.778970i	$0.715742\pi$
$810$		0			0
$811$	−9.44442	−	9.44442i	−0.331639	−	0.331639i	0.521570	−	0.853209i	$-0.325347\pi$
$811$	−9.44442	−	9.44442i	−0.331639	−	0.331639i	−0.853209	+	0.521570i	$0.825347\pi$
$812$		0			0
$813$	28.1063	−	28.1063i	0.985731	−	0.985731i
$814$		0			0
$815$	−9.34707			−0.327414
$816$		0			0
$817$	−10.1760			−0.356015
$818$		0			0
$819$	21.5685	−	21.5685i	0.753663	−	0.753663i
$820$		0			0
$821$	35.3404	+	35.3404i	1.23339	+	1.23339i	0.962654	+	0.270734i	$0.0872663\pi$
$821$	35.3404	+	35.3404i	1.23339	+	1.23339i	0.270734	+	0.962654i	$0.412734\pi$
$822$		0			0
$823$		−	23.7136i		−	0.826605i	−0.910594	−	0.413302i	$-0.864375\pi$
$823$		−	23.7136i		−	0.826605i	0.910594	−	0.413302i	$-0.135625\pi$
$824$		0			0
$825$		−	46.2729i		−	1.61102i
$826$		0			0
$827$	−34.8453	−	34.8453i	−1.21169	−	1.21169i	−0.970471	−	0.241218i	$-0.922453\pi$
$827$	−34.8453	−	34.8453i	−1.21169	−	1.21169i	−0.241218	−	0.970471i	$-0.577547\pi$
$828$		0			0
$829$	11.9866	−	11.9866i	0.416313	−	0.416313i	−0.467618	−	0.883931i	$-0.654888\pi$
$829$	11.9866	−	11.9866i	0.416313	−	0.416313i	0.883931	+	0.467618i	$0.154888\pi$
$830$		0			0
$831$	−75.7069			−2.62624
$832$		0			0
$833$	−0.980951			−0.0339879
$834$		0			0
$835$	0.435851	−	0.435851i	0.0150832	−	0.0150832i
$836$		0			0
$837$	37.4938	+	37.4938i	1.29598	+	1.29598i
$838$		0			0
$839$		−	1.32175i		−	0.0456320i	−0.999740	−	0.0228160i	$-0.992737\pi$
$839$		−	1.32175i		−	0.0456320i	0.999740	−	0.0228160i	$-0.00726318\pi$
$840$		0			0
$841$			8.85792i			0.305445i
$842$		0			0
$843$	−28.5001	−	28.5001i	−0.981594	−	0.981594i
$844$		0			0
$845$	−2.75629	+	2.75629i	−0.0948191	+	0.0948191i
$846$		0			0
$847$	−1.08963			−0.0374402
$848$		0			0
$849$	−3.89560			−0.133697
$850$		0			0
$851$	0.812566	−	0.812566i	0.0278544	−	0.0278544i
$852$		0			0
$853$	33.7981	+	33.7981i	1.15722	+	1.15722i	0.985070	+	0.172153i	$0.0550725\pi$
$853$	33.7981	+	33.7981i	1.15722	+	1.15722i	0.172153	+	0.985070i	$0.444928\pi$
$854$		0			0
$855$			28.2227i			0.965196i
$856$		0			0
$857$			12.2024i			0.416826i	0.978041	+	0.208413i	$0.0668297\pi$
$857$			12.2024i			0.416826i	−0.978041	+	0.208413i	$0.933170\pi$
$858$		0			0
$859$	9.62063	+	9.62063i	0.328252	+	0.328252i	0.851921	−	0.523670i	$-0.175437\pi$
$859$	9.62063	+	9.62063i	0.328252	+	0.328252i	−0.523670	+	0.851921i	$0.675437\pi$
$860$		0			0
$861$	2.68930	−	2.68930i	0.0916512	−	0.0916512i
$862$		0			0
$863$	48.5092			1.65127			0.825636	−	0.564204i	$-0.190817\pi$
$863$	48.5092			1.65127			0.825636	+	0.564204i	$0.190817\pi$
$864$		0			0
$865$	5.69222			0.193541
$866$		0			0
$867$	35.5348	−	35.5348i	1.20682	−	1.20682i
$868$		0			0
$869$	26.4104	+	26.4104i	0.895913	+	0.895913i
$870$		0			0
$871$			10.0754i			0.341391i
$872$		0			0
$873$			20.7071i			0.700829i
$874$		0			0
$875$	3.80974	+	3.80974i	0.128793	+	0.128793i
$876$		0			0
$877$	−15.6211	+	15.6211i	−0.527487	+	0.527487i	−0.919822	−	0.392336i	$-0.871667\pi$
$877$	−15.6211	+	15.6211i	−0.527487	+	0.527487i	0.392336	+	0.919822i	$0.371667\pi$
$878$		0			0
$879$	79.7365			2.68944
$880$		0			0
$881$	22.7269			0.765688			0.382844	−	0.923813i	$-0.374945\pi$
$881$	22.7269			0.765688			0.382844	+	0.923813i	$0.374945\pi$
$882$		0			0
$883$	30.2833	−	30.2833i	1.01912	−	1.01912i	0.0193019	−	0.999814i	$-0.493856\pi$
$883$	30.2833	−	30.2833i	1.01912	−	1.01912i	0.999814	−	0.0193019i	$-0.00614437\pi$
$884$		0			0
$885$	−3.15990	−	3.15990i	−0.106219	−	0.106219i
$886$		0			0
$887$			38.7161i			1.29996i	0.759951	+	0.649980i	$0.225223\pi$
$887$			38.7161i			1.29996i	−0.759951	+	0.649980i	$0.774777\pi$
$888$		0			0
$889$		−	19.3869i		−	0.650217i
$890$		0			0
$891$	37.9267	+	37.9267i	1.27059	+	1.27059i
$892$		0			0
$893$	−52.4928	+	52.4928i	−1.75660	+	1.75660i
$894$		0			0
$895$	7.81501			0.261227
$896$		0			0
$897$	−17.6548			−0.589478
$898$		0			0
$899$	14.0630	−	14.0630i	0.469027	−	0.469027i
$900$		0			0
$901$	−7.92426	−	7.92426i	−0.263995	−	0.263995i
$902$		0			0
$903$		−	4.28301i		−	0.142530i
$904$		0			0
$905$		−	5.78163i		−	0.192188i
$906$		0			0
$907$	25.4724	+	25.4724i	0.845799	+	0.845799i	0.989606	−	0.143807i	$-0.0459345\pi$
$907$	25.4724	+	25.4724i	0.845799	+	0.845799i	−0.143807	+	0.989606i	$0.545935\pi$
$908$		0			0
$909$	−69.3098	+	69.3098i	−2.29886	+	2.29886i
$910$		0			0
$911$	52.6922			1.74577			0.872886	−	0.487924i	$-0.162246\pi$
$911$	52.6922			1.74577			0.872886	+	0.487924i	$0.162246\pi$
$912$		0			0
$913$	−30.1618			−0.998212
$914$		0			0
$915$	−4.50824	+	4.50824i	−0.149038	+	0.149038i
$916$		0			0
$917$	8.29224	+	8.29224i	0.273834	+	0.273834i
$918$		0			0
$919$			25.5116i			0.841549i	0.907165	+	0.420775i	$0.138242\pi$
$919$			25.5116i			0.841549i	−0.907165	+	0.420775i	$0.861758\pi$
$920$		0			0
$921$			7.75436i			0.255515i
$922$		0			0
$923$	−2.95640	−	2.95640i	−0.0973111	−	0.0973111i
$924$		0			0
$925$	3.02632	−	3.02632i	0.0995046	−	0.0995046i
$926$		0			0
$927$	41.2882			1.35608
$928$		0			0
$929$	49.1998			1.61419			0.807097	−	0.590419i	$-0.201038\pi$
$929$	49.1998			1.61419			0.807097	+	0.590419i	$0.201038\pi$
$930$		0			0
$931$	−5.26429	+	5.26429i	−0.172530	+	0.172530i
$932$		0			0
$933$	38.6169	+	38.6169i	1.26426	+	1.26426i
$934$		0			0
$935$			1.71687i			0.0561477i
$936$		0			0
$937$		−	44.3522i		−	1.44892i	−0.689315	−	0.724462i	$-0.742088\pi$
$937$		−	44.3522i		−	1.44892i	0.689315	−	0.724462i	$-0.257912\pi$
$938$		0			0
$939$	−62.7995	−	62.7995i	−2.04939	−	2.04939i
$940$		0			0
$941$	14.0676	−	14.0676i	0.458591	−	0.458591i	−0.439602	−	0.898193i	$-0.644880\pi$
$941$	14.0676	−	14.0676i	0.458591	−	0.458591i	0.898193	+	0.439602i	$0.144880\pi$
$942$		0			0
$943$	−1.52873			−0.0497822
$944$		0			0
$945$	−6.65242			−0.216403
$946$		0			0
$947$	22.2829	−	22.2829i	0.724098	−	0.724098i	−0.245340	−	0.969437i	$-0.578899\pi$
$947$	22.2829	−	22.2829i	0.724098	−	0.724098i	0.969437	+	0.245340i	$0.0788995\pi$
$948$		0			0
$949$	2.24746	+	2.24746i	0.0729558	+	0.0729558i
$950$		0			0
$951$			36.5323i			1.18464i
$952$		0			0
$953$			52.5006i			1.70066i	0.526250	+	0.850330i	$0.323598\pi$
$953$			52.5006i			1.70066i	−0.526250	+	0.850330i	$0.676402\pi$
$954$		0			0
$955$	1.39435	+	1.39435i	0.0451202	+	0.0451202i
$956$		0			0
$957$	31.3046	−	31.3046i	1.01193	−	1.01193i
$958$		0			0
$959$	10.3723			0.334940
$960$		0			0
$961$	−11.3627			−0.366540
$962$		0			0
$963$	−85.2143	+	85.2143i	−2.74599	+	2.74599i
$964$		0			0
$965$	−1.17699	−	1.17699i	−0.0378888	−	0.0378888i
$966$		0			0
$967$		−	22.7183i		−	0.730572i	−0.930895	−	0.365286i	$-0.880971\pi$
$967$		−	22.7183i		−	0.730572i	0.930895	−	0.365286i	$-0.119029\pi$
$968$		0			0
$969$			22.8838i			0.735133i
$970$		0			0
$971$	8.51367	+	8.51367i	0.273217	+	0.273217i	0.830394	−	0.557177i	$-0.188116\pi$
$971$	8.51367	+	8.51367i	0.273217	+	0.273217i	−0.557177	+	0.830394i	$0.688116\pi$
$972$		0			0
$973$	4.83290	−	4.83290i	0.154936	−	0.154936i
$974$		0			0
$975$	−65.7535			−2.10580
$976$		0			0
$977$	−37.7274			−1.20701			−0.603503	−	0.797361i	$-0.706229\pi$
$977$	−37.7274			−1.20701			−0.603503	+	0.797361i	$0.706229\pi$
$978$		0			0
$979$	−22.7236	+	22.7236i	−0.726250	+	0.726250i
$980$		0			0
$981$	−68.5784	−	68.5784i	−2.18954	−	2.18954i
$982$		0			0
$983$		−	45.1569i		−	1.44028i	−0.693828	−	0.720141i	$-0.744077\pi$
$983$		−	45.1569i		−	1.44028i	0.693828	−	0.720141i	$-0.255923\pi$
$984$		0			0
$985$		−	2.79390i		−	0.0890212i
$986$		0			0
$987$	−22.0938	−	22.0938i	−0.703253	−	0.703253i
$988$		0			0
$989$	−1.21733	+	1.21733i	−0.0387090	+	0.0387090i
$990$		0			0
$991$	46.2280			1.46848			0.734240	−	0.678890i	$-0.237538\pi$
$991$	46.2280			1.46848			0.734240	+	0.678890i	$0.237538\pi$
$992$		0			0
$993$	1.04343			0.0331121
$994$		0			0
$995$	−0.708054	+	0.708054i	−0.0224468	+	0.0224468i
$996$		0			0
$997$	−27.2458	−	27.2458i	−0.862885	−	0.862885i	0.128788	−	0.991672i	$-0.458891\pi$
$997$	−27.2458	−	27.2458i	−0.862885	−	0.862885i	−0.991672	+	0.128788i	$0.958891\pi$
$998$		0			0
$999$			10.9171i			0.345401i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.2.m.d.113.1		12
4.3	odd	2		112.2.m.d.85.2	yes	12
8.3	odd	2		896.2.m.g.225.1		12
8.5	even	2		896.2.m.h.225.6		12
16.3	odd	4		112.2.m.d.29.2	✓	12
16.5	even	4		896.2.m.h.673.6		12
16.11	odd	4		896.2.m.g.673.1		12
16.13	even	4	inner	448.2.m.d.337.1		12
28.3	even	6		784.2.x.m.373.3		24
28.11	odd	6		784.2.x.l.373.3		24
28.19	even	6		784.2.x.m.165.6		24
28.23	odd	6		784.2.x.l.165.6		24
28.27	even	2		784.2.m.h.197.2		12
32.3	odd	8		7168.2.a.bj.1.12		12
32.13	even	8		7168.2.a.bi.1.12		12
32.19	odd	8		7168.2.a.bj.1.1		12
32.29	even	8		7168.2.a.bi.1.1		12
112.3	even	12		784.2.x.m.765.6		24
112.19	even	12		784.2.x.m.557.3		24
112.51	odd	12		784.2.x.l.557.3		24
112.67	odd	12		784.2.x.l.765.6		24
112.83	even	4		784.2.m.h.589.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.m.d.29.2	✓	12	16.3	odd	4
112.2.m.d.85.2	yes	12	4.3	odd	2
448.2.m.d.113.1		12	1.1	even	1	trivial
448.2.m.d.337.1		12	16.13	even	4	inner
784.2.m.h.197.2		12	28.27	even	2
784.2.m.h.589.2		12	112.83	even	4
784.2.x.l.165.6		24	28.23	odd	6
784.2.x.l.373.3		24	28.11	odd	6
784.2.x.l.557.3		24	112.51	odd	12
784.2.x.l.765.6		24	112.67	odd	12
784.2.x.m.165.6		24	28.19	even	6
784.2.x.m.373.3		24	28.3	even	6
784.2.x.m.557.3		24	112.19	even	12
784.2.x.m.765.6		24	112.3	even	12
896.2.m.g.225.1		12	8.3	odd	2
896.2.m.g.673.1		12	16.11	odd	4
896.2.m.h.225.6		12	8.5	even	2
896.2.m.h.673.6		12	16.5	even	4
7168.2.a.bi.1.1		12	32.29	even	8
7168.2.a.bi.1.12		12	32.13	even	8
7168.2.a.bj.1.1		12	32.19	odd	8
7168.2.a.bj.1.12		12	32.3	odd	8

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:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	448.m (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.21570 + 2.21570i) q^{3} +(-0.393125 - 0.393125i) q^{5} -1.00000i q^{7} -6.81864i q^{9} +O(q^{10})\)	\(q+(-2.21570 + 2.21570i) q^{3} +(-0.393125 - 0.393125i) q^{5} -1.00000i q^{7} -6.81864i q^{9} +(-2.22602 - 2.22602i) q^{11} +(-3.16316 + 3.16316i) q^{13} +1.74209 q^{15} +0.980951 q^{17} +(5.26429 - 5.26429i) q^{19} +(2.21570 + 2.21570i) q^{21} -1.25951i q^{23} -4.69090i q^{25} +(8.46094 + 8.46094i) q^{27} +(3.17349 - 3.17349i) q^{29} +4.43140 q^{31} +9.86440 q^{33} +(-0.393125 + 0.393125i) q^{35} +(0.645145 + 0.645145i) q^{37} -14.0172i q^{39} -1.21375i q^{41} +(-0.966515 - 0.966515i) q^{43} +(-2.68058 + 2.68058i) q^{45} -9.97147 q^{47} -1.00000 q^{49} +(-2.17349 + 2.17349i) q^{51} +(-8.07814 - 8.07814i) q^{53} +1.75021i q^{55} +23.3282i q^{57} +(-1.81385 - 1.81385i) q^{59} +(-2.58783 + 2.58783i) q^{61} -6.81864 q^{63} +2.48704 q^{65} +(1.59261 - 1.59261i) q^{67} +(2.79069 + 2.79069i) q^{69} +0.934634i q^{71} -0.710511i q^{73} +(10.3936 + 10.3936i) q^{75} +(-2.22602 + 2.22602i) q^{77} -11.8644 q^{79} -17.0379 q^{81} +(6.77482 - 6.77482i) q^{83} +(-0.385637 - 0.385637i) q^{85} +14.0630i q^{87} -10.2082i q^{89} +(3.16316 + 3.16316i) q^{91} +(-9.81864 + 9.81864i) q^{93} -4.13906 q^{95} -3.03684 q^{97} +(-15.1784 + 15.1784i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{3} + 4 q^{5}+O(q^{10}) \) 12 * q - 4 * q^3 + 4 * q^5	\( 12 q - 4 q^{3} + 4 q^{5} + 24 q^{15} - 8 q^{17} + 4 q^{21} - 4 q^{27} - 4 q^{29} + 8 q^{31} + 4 q^{35} - 20 q^{37} - 16 q^{43} + 40 q^{45} - 16 q^{47} - 12 q^{49} + 16 q^{51} + 4 q^{53} + 16 q^{59} - 20 q^{61} - 12 q^{63} + 32 q^{65} - 24 q^{67} - 4 q^{69} + 40 q^{75} - 24 q^{79} - 44 q^{81} + 20 q^{83} - 8 q^{85} - 48 q^{93} + 48 q^{97} - 32 q^{99}+O(q^{100}) \) 12 * q - 4 * q^3 + 4 * q^5 + 24 * q^15 - 8 * q^17 + 4 * q^21 - 4 * q^27 - 4 * q^29 + 8 * q^31 + 4 * q^35 - 20 * q^37 - 16 * q^43 + 40 * q^45 - 16 * q^47 - 12 * q^49 + 16 * q^51 + 4 * q^53 + 16 * q^59 - 20 * q^61 - 12 * q^63 + 32 * q^65 - 24 * q^67 - 4 * q^69 + 40 * q^75 - 24 * q^79 - 44 * q^81 + 20 * q^83 - 8 * q^85 - 48 * q^93 + 48 * q^97 - 32 * q^99

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