LMFDB - Embedded newform 1456.2.cc.e.673.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1456,2,Mod(225,1456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1456, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1456.225");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.cc (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.6262185343$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.58891012706304.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 $ x^12 - 5x^10 - 2x^9 + 15x^8 + 2x^7 - 30x^6 + 4x^5 + 60x^4 - 16x^3 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 728)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			673.4
Root			$1.34408 - 0.439820i$ of defining polynomial
Character	$\chi$	$=$	1456.673
Dual form			1456.2.cc.e.225.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.439820 + 0.761791i) q^{3} +3.76784i q^{5} +(-0.866025 - 0.500000i) q^{7} +(1.11312 - 1.92797i) q^{9} +O(q^{10})$	\(q+(0.439820 + 0.761791i) q^{3} +3.76784i q^{5} +(-0.866025 - 0.500000i) q^{7} +(1.11312 - 1.92797i) q^{9} +(-2.30533 + 1.33098i) q^{11} +(-3.12338 - 1.80124i) q^{13} +(-2.87031 + 1.65717i) q^{15} +(-2.54109 + 4.40130i) q^{17} +(-6.23758 - 3.60127i) q^{19} -0.879640i q^{21} +(-2.28339 - 3.95494i) q^{23} -9.19662 q^{25} +4.59720 q^{27} +(3.57505 + 6.19217i) q^{29} -4.83511i q^{31} +(-2.02786 - 1.17079i) q^{33} +(1.88392 - 3.26304i) q^{35} +(5.38259 - 3.10764i) q^{37} +(-0.00155628 - 3.17159i) q^{39} +(-10.2695 + 5.92910i) q^{41} +(-0.870305 + 1.50741i) q^{43} +(7.26430 + 4.19404i) q^{45} +5.21495i q^{47} +(0.500000 + 0.866025i) q^{49} -4.47049 q^{51} +6.77640 q^{53} +(-5.01493 - 8.68611i) q^{55} -6.33565i q^{57} +(-6.68825 - 3.86146i) q^{59} +(-1.12213 + 1.94358i) q^{61} +(-1.92797 + 1.11312i) q^{63} +(6.78680 - 11.7684i) q^{65} +(1.79592 - 1.03687i) q^{67} +(2.00856 - 3.47893i) q^{69} +(-8.37953 - 4.83792i) q^{71} -8.61224i q^{73} +(-4.04486 - 7.00590i) q^{75} +2.66197 q^{77} +10.6616 q^{79} +(-1.31741 - 2.28182i) q^{81} +14.9655i q^{83} +(-16.5834 - 9.57442i) q^{85} +(-3.14476 + 5.44688i) q^{87} +(-0.0725747 + 0.0419010i) q^{89} +(1.80431 + 3.12161i) q^{91} +(3.68334 - 2.12658i) q^{93} +(13.5690 - 23.5022i) q^{95} +(-9.76920 - 5.64025i) q^{97} +5.92616i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{3} + 4 q^{9}+O(q^{10}) $ 12 * q + 2 * q^3 + 4 * q^9	$ 12 q + 2 q^{3} + 4 q^{9} + 2 q^{13} - 12 q^{15} + 2 q^{17} - 12 q^{19} + 6 q^{23} + 4 q^{25} - 4 q^{27} + 20 q^{29} + 6 q^{33} + 4 q^{35} - 6 q^{37} - 26 q^{39} - 12 q^{41} + 12 q^{43} + 18 q^{45} + 6 q^{49} - 16 q^{51} + 20 q^{53} - 24 q^{55} + 12 q^{59} - 4 q^{61} + 8 q^{65} + 6 q^{67} - 36 q^{71} + 10 q^{75} + 20 q^{77} + 20 q^{79} + 18 q^{81} - 36 q^{85} - 32 q^{87} - 36 q^{89} - 2 q^{91} - 42 q^{93} + 26 q^{95} - 6 q^{97}+O(q^{100}) $ 12 * q + 2 * q^3 + 4 * q^9 + 2 * q^13 - 12 * q^15 + 2 * q^17 - 12 * q^19 + 6 * q^23 + 4 * q^25 - 4 * q^27 + 20 * q^29 + 6 * q^33 + 4 * q^35 - 6 * q^37 - 26 * q^39 - 12 * q^41 + 12 * q^43 + 18 * q^45 + 6 * q^49 - 16 * q^51 + 20 * q^53 - 24 * q^55 + 12 * q^59 - 4 * q^61 + 8 * q^65 + 6 * q^67 - 36 * q^71 + 10 * q^75 + 20 * q^77 + 20 * q^79 + 18 * q^81 - 36 * q^85 - 32 * q^87 - 36 * q^89 - 2 * q^91 - 42 * q^93 + 26 * q^95 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$.

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

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
$3$	0.439820	+	0.761791i	0.253930	+	0.439820i	0.964604	−	0.263701i	$-0.0849433\pi$
$3$	0.439820	+	0.761791i	0.253930	+	0.439820i	−0.710674	+	0.703521i	$0.751610\pi$
$4$		0			0
$5$			3.76784i			1.68503i	0.538674	+	0.842515i	$0.318926\pi$
$5$			3.76784i			1.68503i	−0.538674	+	0.842515i	$0.681074\pi$
$6$		0			0
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$		0			0
$9$	1.11312	−	1.92797i	0.371039	−	0.642658i
$10$		0			0
$11$	−2.30533	+	1.33098i	−0.695083	+	0.401307i	−0.805514	−	0.592577i	$-0.798110\pi$
$11$	−2.30533	+	1.33098i	−0.695083	+	0.401307i	0.110430	+	0.993884i	$0.464777\pi$
$12$		0			0
$13$	−3.12338	−	1.80124i	−0.866271	−	0.499575i
$13$	−3.12338	−	1.80124i	−0.866271	−	0.499575i
$14$		0			0
$15$	−2.87031	+	1.65717i	−0.741110	+	0.427880i
$16$		0			0
$17$	−2.54109	+	4.40130i	−0.616305	+	1.06747i	0.373849	+	0.927490i	$0.378038\pi$
$17$	−2.54109	+	4.40130i	−0.616305	+	1.06747i	−0.990154	+	0.139982i	$0.955295\pi$
$18$		0			0
$19$	−6.23758	−	3.60127i	−1.43100	−	0.826188i	−0.433803	−	0.901008i	$-0.642829\pi$
$19$	−6.23758	−	3.60127i	−1.43100	−	0.826188i	−0.997197	+	0.0748195i	$0.976162\pi$
$20$		0			0
$21$		−	0.879640i		−	0.191953i
$22$		0			0
$23$	−2.28339	−	3.95494i	−0.476119	−	0.824663i	0.523506	−	0.852022i	$-0.324624\pi$
$23$	−2.28339	−	3.95494i	−0.476119	−	0.824663i	−0.999626	+	0.0273590i	$0.991290\pi$
$24$		0			0
$25$	−9.19662			−1.83932
$26$		0			0
$27$	4.59720			0.884732
$28$		0			0
$29$	3.57505	+	6.19217i	0.663870	+	1.14986i	0.979590	+	0.201004i	$0.0644205\pi$
$29$	3.57505	+	6.19217i	0.663870	+	1.14986i	−0.315721	+	0.948852i	$0.602246\pi$
$30$		0			0
$31$		−	4.83511i		−	0.868411i	−0.900814	−	0.434206i	$-0.857029\pi$
$31$		−	4.83511i		−	0.868411i	0.900814	−	0.434206i	$-0.142971\pi$
$32$		0			0
$33$	−2.02786	−	1.17079i	−0.353005	−	0.203808i
$34$		0			0
$35$	1.88392	−	3.26304i	0.318441	−	0.551555i
$36$		0			0
$37$	5.38259	−	3.10764i	0.884893	−	0.510893i	0.0126245	−	0.999920i	$-0.495981\pi$
$37$	5.38259	−	3.10764i	0.884893	−	0.510893i	0.872269	+	0.489027i	$0.162648\pi$
$38$		0			0
$39$	−0.00155628	−	3.17159i	−0.000249204	−	0.507860i
$40$		0			0
$41$	−10.2695	+	5.92910i	−1.60383	+	0.925970i	−0.613114	+	0.789994i	$0.710083\pi$
$41$	−10.2695	+	5.92910i	−1.60383	+	0.925970i	−0.990712	+	0.135975i	$0.956583\pi$
$42$		0			0
$43$	−0.870305	+	1.50741i	−0.132720	+	0.229878i	−0.924724	−	0.380638i	$-0.875705\pi$
$43$	−0.870305	+	1.50741i	−0.132720	+	0.229878i	0.792004	+	0.610516i	$0.209038\pi$
$44$		0			0
$45$	7.26430	+	4.19404i	1.08290	+	0.625211i
$46$		0			0
$47$			5.21495i			0.760678i	0.924847	+	0.380339i	$0.124193\pi$
$47$			5.21495i			0.760678i	−0.924847	+	0.380339i	$0.875807\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$		0			0
$51$	−4.47049			−0.625994
$52$		0			0
$53$	6.77640			0.930810			0.465405	−	0.885098i	$-0.345909\pi$
$53$	6.77640			0.930810			0.465405	+	0.885098i	$0.345909\pi$
$54$		0			0
$55$	−5.01493	−	8.68611i	−0.676213	−	1.17124i
$56$		0			0
$57$		−	6.33565i		−	0.839177i
$58$		0			0
$59$	−6.68825	−	3.86146i	−0.870736	−	0.502720i	−0.00314310	−	0.999995i	$-0.501000\pi$
$59$	−6.68825	−	3.86146i	−0.870736	−	0.502720i	−0.867593	+	0.497276i	$0.834334\pi$
$60$		0			0
$61$	−1.12213	+	1.94358i	−0.143674	+	0.248851i	−0.928877	−	0.370387i	$-0.879225\pi$
$61$	−1.12213	+	1.94358i	−0.143674	+	0.248851i	0.785204	+	0.619238i	$0.212558\pi$
$62$		0			0
$63$	−1.92797	+	1.11312i	−0.242902	+	0.140240i
$64$		0			0
$65$	6.78680	−	11.7684i	0.841798	−	1.45969i
$66$		0			0
$67$	1.79592	−	1.03687i	0.219406	−	0.126674i	−0.386269	−	0.922386i	$-0.626236\pi$
$67$	1.79592	−	1.03687i	0.219406	−	0.126674i	0.605675	+	0.795712i	$0.292903\pi$
$68$		0			0
$69$	2.00856	−	3.47893i	0.241802	−	0.418814i
$70$		0			0
$71$	−8.37953	−	4.83792i	−0.994467	−	0.574156i	−0.0878607	−	0.996133i	$-0.528003\pi$
$71$	−8.37953	−	4.83792i	−0.994467	−	0.574156i	−0.906607	+	0.421977i	$0.861336\pi$
$72$		0			0
$73$		−	8.61224i		−	1.00799i	−0.863708	−	0.503993i	$-0.831864\pi$
$73$		−	8.61224i		−	1.00799i	0.863708	−	0.503993i	$-0.168136\pi$
$74$		0			0
$75$	−4.04486	−	7.00590i	−0.467060	−	0.808971i
$76$		0			0
$77$	2.66197			0.303359
$78$		0			0
$79$	10.6616			1.19953			0.599763	−	0.800178i	$-0.295261\pi$
$79$	10.6616			1.19953			0.599763	+	0.800178i	$0.295261\pi$
$80$		0			0
$81$	−1.31741	−	2.28182i	−0.146379	−	0.253535i
$82$		0			0
$83$			14.9655i			1.64268i	0.570442	+	0.821338i	$0.306772\pi$
$83$			14.9655i			1.64268i	−0.570442	+	0.821338i	$0.693228\pi$
$84$		0			0
$85$	−16.5834	−	9.57442i	−1.79872	−	1.03849i
$86$		0			0
$87$	−3.14476	+	5.44688i	−0.337153	+	0.583967i
$88$		0			0
$89$	−0.0725747	+	0.0419010i	−0.00769290	+	0.00444150i	−0.503842	−	0.863796i	$-0.668080\pi$
$89$	−0.0725747	+	0.0419010i	−0.00769290	+	0.00444150i	0.496149	+	0.868238i	$0.334747\pi$
$90$		0			0
$91$	1.80431	+	3.12161i	0.189143	+	0.327234i
$92$		0			0
$93$	3.68334	−	2.12658i	0.381945	−	0.220516i
$94$		0			0
$95$	13.5690	−	23.5022i	1.39215	−	2.41128i
$96$		0			0
$97$	−9.76920	−	5.64025i	−0.991911	−	0.572680i	−0.0860664	−	0.996289i	$-0.527430\pi$
$97$	−9.76920	−	5.64025i	−0.991911	−	0.572680i	−0.905845	+	0.423609i	$0.860763\pi$
$98$		0			0
$99$			5.92616i			0.595601i
$100$		0			0
$101$	7.69182	+	13.3226i	0.765365	+	1.32565i	0.940054	+	0.341027i	$0.110775\pi$
$101$	7.69182	+	13.3226i	0.765365	+	1.32565i	−0.174689	+	0.984624i	$0.555892\pi$
$102$		0			0
$103$	−15.5446			−1.53165			−0.765827	−	0.643047i	$-0.777670\pi$
$103$	−15.5446			−1.53165			−0.765827	+	0.643047i	$0.777670\pi$
$104$		0			0
$105$	3.31434			0.323447
$106$		0			0
$107$	0.751179	+	1.30108i	0.0726192	+	0.125780i	0.900048	−	0.435790i	$-0.143531\pi$
$107$	0.751179	+	1.30108i	0.0726192	+	0.125780i	−0.827429	+	0.561570i	$0.810198\pi$
$108$		0			0
$109$		−	4.05793i		−	0.388679i	−0.980934	−	0.194340i	$-0.937744\pi$
$109$		−	4.05793i		−	0.388679i	0.980934	−	0.194340i	$-0.0622564\pi$
$110$		0			0
$111$	4.73475	+	2.73361i	0.449402	+	0.259463i
$112$		0			0
$113$	−1.85116	+	3.20631i	−0.174143	+	0.301624i	−0.939864	−	0.341548i	$-0.889049\pi$
$113$	−1.85116	+	3.20631i	−0.174143	+	0.301624i	0.765722	+	0.643172i	$0.222382\pi$
$114$		0			0
$115$	14.9016	−	8.60344i	1.38958	−	0.802275i
$116$		0			0
$117$	−6.94944	+	4.01681i	−0.642476	+	0.371354i
$118$		0			0
$119$	4.40130	−	2.54109i	0.403466	−	0.232941i
$120$		0			0
$121$	−1.95697	+	3.38957i	−0.177906	+	0.308143i
$122$		0			0
$123$	−9.03346	−	5.21547i	−0.814520	−	0.470263i
$124$		0			0
$125$		−	15.8122i		−	1.41428i
$126$		0			0
$127$	5.64814	+	9.78286i	0.501191	+	0.868088i	0.999999	+	0.00137586i	$0.000437949\pi$
$127$	5.64814	+	9.78286i	0.501191	+	0.868088i	−0.498808	+	0.866713i	$0.666229\pi$
$128$		0			0
$129$	−1.53111			−0.134807
$130$		0			0
$131$	1.43411			0.125299			0.0626495	−	0.998036i	$-0.480045\pi$
$131$	1.43411			0.125299			0.0626495	+	0.998036i	$0.480045\pi$
$132$		0			0
$133$	3.60127	+	6.23758i	0.312270	+	0.540867i
$134$		0			0
$135$			17.3215i			1.49080i
$136$		0			0
$137$	−11.8392	−	6.83534i	−1.01149	−	0.583982i	−0.0998604	−	0.995001i	$-0.531840\pi$
$137$	−11.8392	−	6.83534i	−1.01149	−	0.583982i	−0.911627	+	0.411019i	$0.865173\pi$
$138$		0			0
$139$	−8.91523	+	15.4416i	−0.756180	+	1.30974i	0.188606	+	0.982053i	$0.439603\pi$
$139$	−8.91523	+	15.4416i	−0.756180	+	1.30974i	−0.944786	+	0.327689i	$0.893730\pi$
$140$		0			0
$141$	−3.97270	+	2.29364i	−0.334561	+	0.193159i
$142$		0			0
$143$	9.59785	−	0.00470961i	0.802613	−	0.000393838i
$144$		0			0
$145$	−23.3311	+	13.4702i	−1.93754	+	1.11864i
$146$		0			0
$147$	−0.439820	+	0.761791i	−0.0362757	+	0.0628314i
$148$		0			0
$149$	−5.15235	−	2.97471i	−0.422097	−	0.243698i	0.273877	−	0.961765i	$-0.411694\pi$
$149$	−5.15235	−	2.97471i	−0.422097	−	0.243698i	−0.695974	+	0.718067i	$0.745027\pi$
$150$		0			0
$151$			0.729583i			0.0593727i	0.999559	+	0.0296863i	$0.00945084\pi$
$151$			0.729583i			0.0593727i	−0.999559	+	0.0296863i	$0.990549\pi$
$152$		0			0
$153$	5.65706	+	9.79832i	0.457346	+	0.792147i
$154$		0			0
$155$	18.2179			1.46330
$156$		0			0
$157$	−19.7648			−1.57740			−0.788700	−	0.614779i	$-0.789245\pi$
$157$	−19.7648			−1.57740			−0.788700	+	0.614779i	$0.789245\pi$
$158$		0			0
$159$	2.98040	+	5.16220i	0.236361	+	0.409389i
$160$		0			0
$161$			4.56678i			0.359912i
$162$		0			0
$163$	1.07087	+	0.618268i	0.0838772	+	0.0484265i	0.541352	−	0.840796i	$-0.317913\pi$
$163$	1.07087	+	0.618268i	0.0838772	+	0.0484265i	−0.457475	+	0.889223i	$0.651246\pi$
$164$		0			0
$165$	4.41133	−	7.64066i	0.343422	−	0.594824i
$166$		0			0
$167$	−13.3322	+	7.69734i	−1.03168	+	0.595638i	−0.917464	−	0.397818i	$-0.869767\pi$
$167$	−13.3322	+	7.69734i	−1.03168	+	0.595638i	−0.114211	+	0.993456i	$0.536434\pi$
$168$		0			0
$169$	6.51105	+	11.2519i	0.500850	+	0.865534i
$170$		0			0
$171$	−13.8863	+	8.01727i	−1.06191	+	0.613096i
$172$		0			0
$173$	5.06567	−	8.77400i	0.385136	−	0.667075i	−0.606652	−	0.794967i	$-0.707488\pi$
$173$	5.06567	−	8.77400i	0.385136	−	0.667075i	0.991788	+	0.127892i	$0.0408212\pi$
$174$		0			0
$175$	7.96450	+	4.59831i	0.602060	+	0.347599i
$176$		0			0
$177$		−	6.79339i		−	0.510623i
$178$		0			0
$179$	5.70842	+	9.88728i	0.426667	+	0.739010i	0.996575	−	0.0826995i	$-0.0263542\pi$
$179$	5.70842	+	9.88728i	0.426667	+	0.739010i	−0.569907	+	0.821709i	$0.693021\pi$
$180$		0			0
$181$	12.8724			0.956800			0.478400	−	0.878142i	$-0.341217\pi$
$181$	12.8724			0.956800			0.478400	+	0.878142i	$0.341217\pi$
$182$		0			0
$183$	−1.97414			−0.145933
$184$		0			0
$185$	11.7091	+	20.2808i	0.860870	+	1.49107i
$186$		0			0
$187$		−	13.5286i		−	0.989309i
$188$		0			0
$189$	−3.98130	−	2.29860i	−0.289597	−	0.167199i
$190$		0			0
$191$	−9.61660	+	16.6564i	−0.695833	+	1.20522i	0.274067	+	0.961711i	$0.411631\pi$
$191$	−9.61660	+	16.6564i	−0.695833	+	1.20522i	−0.969899	+	0.243507i	$0.921702\pi$
$192$		0			0
$193$	4.18645	−	2.41705i	0.301347	−	0.173983i	−0.341701	−	0.939809i	$-0.611003\pi$
$193$	4.18645	−	2.41705i	0.301347	−	0.173983i	0.643048	+	0.765826i	$0.277670\pi$
$194$		0			0
$195$	11.9500	−	0.00586381i	0.855760	−	0.000419916i
$196$		0			0
$197$	19.5337	−	11.2778i	1.39172	−	0.803511i	0.398216	−	0.917292i	$-0.369629\pi$
$197$	19.5337	−	11.2778i	1.39172	−	0.803511i	0.993506	+	0.113781i	$0.0362961\pi$
$198$		0			0
$199$	6.21577	−	10.7660i	0.440625	−	0.763184i	−0.557111	−	0.830438i	$-0.688090\pi$
$199$	6.21577	−	10.7660i	0.440625	−	0.763184i	0.997736	+	0.0672537i	$0.0214237\pi$
$200$		0			0
$201$	1.57976	+	0.912076i	0.111428	+	0.0643328i
$202$		0			0
$203$		−	7.15010i		−	0.501838i
$204$		0			0
$205$	−22.3399	−	38.6938i	−1.56029	−	2.70249i
$206$		0			0
$207$	−10.1667			−0.706635
$208$		0			0
$209$	19.1729			1.32622
$210$		0			0
$211$	5.01865	+	8.69256i	0.345498	+	0.598421i	0.985444	−	0.169999i	$-0.0543765\pi$
$211$	5.01865	+	8.69256i	0.345498	+	0.598421i	−0.639946	+	0.768420i	$0.721043\pi$
$212$		0			0
$213$		−	8.51126i		−	0.583182i
$214$		0			0
$215$	−5.67969	−	3.27917i	−0.387352	−	0.223638i
$216$		0			0
$217$	−2.41755	+	4.18733i	−0.164114	+	0.284254i
$218$		0			0
$219$	6.56072	−	3.78784i	0.443333	−	0.255958i
$220$		0			0
$221$	15.8646	−	9.16982i	1.06717	−	0.616829i
$222$		0			0
$223$	2.02549	−	1.16942i	0.135637	−	0.0783100i	−0.430646	−	0.902521i	$-0.641714\pi$
$223$	2.02549	−	1.16942i	0.135637	−	0.0783100i	0.566283	+	0.824211i	$0.308381\pi$
$224$		0			0
$225$	−10.2369	+	17.7308i	−0.682460	+	1.18206i
$226$		0			0
$227$	−13.8592	−	8.00163i	−0.919870	−	0.531087i	−0.0362761	−	0.999342i	$-0.511550\pi$
$227$	−13.8592	−	8.00163i	−0.919870	−	0.531087i	−0.883593	+	0.468255i	$0.844883\pi$
$228$		0			0
$229$		−	2.74697i		−	0.181525i	−0.995873	−	0.0907624i	$-0.971070\pi$
$229$		−	2.74697i		−	0.181525i	0.995873	−	0.0907624i	$-0.0289304\pi$
$230$		0			0
$231$	1.17079	+	2.02786i	0.0770321	+	0.133423i
$232$		0			0
$233$	−9.74094			−0.638150			−0.319075	−	0.947729i	$-0.603372\pi$
$233$	−9.74094			−0.638150			−0.319075	+	0.947729i	$0.603372\pi$
$234$		0			0
$235$	−19.6491			−1.28176
$236$		0			0
$237$	4.68920	+	8.12193i	0.304596	+	0.527576i
$238$		0			0
$239$			28.6495i			1.85318i	0.376070	+	0.926591i	$0.377275\pi$
$239$			28.6495i			1.85318i	−0.376070	+	0.926591i	$0.622725\pi$
$240$		0			0
$241$	7.61747	+	4.39795i	0.490684	+	0.283297i	0.724858	−	0.688898i	$-0.241905\pi$
$241$	7.61747	+	4.39795i	0.490684	+	0.283297i	−0.234174	+	0.972195i	$0.575239\pi$
$242$		0			0
$243$	8.05465	−	13.9511i	0.516706	−	0.894961i
$244$		0			0
$245$	−3.26304	+	1.88392i	−0.208468	+	0.120359i
$246$		0			0
$247$	12.9956	+	22.4836i	0.826890	+	1.43059i
$248$		0			0
$249$	−11.4006	+	6.58212i	−0.722482	+	0.417125i
$250$		0			0
$251$	−8.19738	+	14.1983i	−0.517414	+	0.896188i	0.482381	+	0.875961i	$0.339772\pi$
$251$	−8.19738	+	14.1983i	−0.517414	+	0.896188i	−0.999795	+	0.0202264i	$0.993561\pi$
$252$		0			0
$253$	10.5279	+	6.07830i	0.661885	+	0.382139i
$254$		0			0
$255$		−	16.8441i		−	1.05482i
$256$		0			0
$257$	−5.02643	−	8.70603i	−0.313540	−	0.543067i	0.665586	−	0.746321i	$-0.268182\pi$
$257$	−5.02643	−	8.70603i	−0.313540	−	0.543067i	−0.979126	+	0.203254i	$0.934848\pi$
$258$		0			0
$259$	−6.21529			−0.386199
$260$		0			0
$261$	15.9178			0.985286
$262$		0			0
$263$	−13.6710	−	23.6789i	−0.842992	−	1.46010i	−0.887354	−	0.461089i	$-0.847459\pi$
$263$	−13.6710	−	23.6789i	−0.842992	−	1.46010i	0.0443619	−	0.999016i	$-0.485875\pi$
$264$		0			0
$265$			25.5324i			1.56844i
$266$		0			0
$267$	−0.0638396	−	0.0368578i	−0.00390692	−	0.00225566i
$268$		0			0
$269$	7.74432	−	13.4136i	0.472179	−	0.817839i	−0.527314	−	0.849671i	$-0.676801\pi$
$269$	7.74432	−	13.4136i	0.472179	−	0.817839i	0.999493	+	0.0318319i	$0.0101341\pi$
$270$		0			0
$271$	25.8784	−	14.9409i	1.57200	−	0.907596i	0.576079	−	0.817394i	$-0.304582\pi$
$271$	25.8784	−	14.9409i	1.57200	−	0.907596i	0.995923	−	0.0902021i	$-0.0287513\pi$
$272$		0			0
$273$	−1.58445	+	2.74745i	−0.0958950	+	0.166283i
$274$		0			0
$275$	21.2012	−	12.2405i	1.27848	−	0.738132i
$276$		0			0
$277$	−6.14368	+	10.6412i	−0.369138	+	0.639366i	−0.989431	−	0.145004i	$-0.953680\pi$
$277$	−6.14368	+	10.6412i	−0.369138	+	0.639366i	0.620293	+	0.784370i	$0.287014\pi$
$278$		0			0
$279$	−9.32197	−	5.38204i	−0.558092	−	0.322214i
$280$		0			0
$281$		−	15.2595i		−	0.910303i	−0.890414	−	0.455152i	$-0.849585\pi$
$281$		−	15.2595i		−	0.910303i	0.890414	−	0.455152i	$-0.150415\pi$
$282$		0			0
$283$	12.4442	+	21.5540i	0.739732	+	1.28125i	0.952616	+	0.304176i	$0.0983809\pi$
$283$	12.4442	+	21.5540i	0.739732	+	1.28125i	−0.212884	+	0.977077i	$0.568286\pi$
$284$		0			0
$285$	23.8717			1.41404
$286$		0			0
$287$	11.8582			0.699967
$288$		0			0
$289$	−4.41429	−	7.64577i	−0.259664	−	0.449751i
$290$		0			0
$291$		−	9.92278i		−	0.581683i
$292$		0			0
$293$	4.95801	+	2.86251i	0.289650	+	0.167230i	0.637784	−	0.770215i	$-0.279851\pi$
$293$	4.95801	+	2.86251i	0.289650	+	0.167230i	−0.348134	+	0.937445i	$0.613185\pi$
$294$		0			0
$295$	14.5494	−	25.2002i	0.847097	−	1.46722i
$296$		0			0
$297$	−10.5981	+	6.11880i	−0.614963	+	0.355049i
$298$		0			0
$299$	0.00807965	+	16.4657i	0.000467258	+	0.952238i
$300$		0			0
$301$	1.50741	−	0.870305i	0.0868858	−	0.0501636i
$302$		0			0
$303$	−6.76603	+	11.7191i	−0.388698	+	0.673246i
$304$		0			0
$305$	−7.32312	−	4.22800i	−0.419320	−	0.242095i
$306$		0			0
$307$			16.2893i			0.929677i	0.885395	+	0.464839i	$0.153888\pi$
$307$			16.2893i			0.929677i	−0.885395	+	0.464839i	$0.846112\pi$
$308$		0			0
$309$	−6.83682	−	11.8417i	−0.388933	−	0.673652i
$310$		0			0
$311$	2.11831			0.120118			0.0600592	−	0.998195i	$-0.480871\pi$
$311$	2.11831			0.120118			0.0600592	+	0.998195i	$0.480871\pi$
$312$		0			0
$313$	16.0702			0.908342			0.454171	−	0.890914i	$-0.349935\pi$
$313$	16.0702			0.908342			0.454171	+	0.890914i	$0.349935\pi$
$314$		0			0
$315$	−4.19404	−	7.26430i	−0.236308	−	0.409297i
$316$		0			0
$317$			20.6923i			1.16220i	0.813834	+	0.581098i	$0.197377\pi$
$317$			20.6923i			1.16220i	−0.813834	+	0.581098i	$0.802623\pi$
$318$		0			0
$319$	−16.4833	−	9.51666i	−0.922890	−	0.532831i
$320$		0			0
$321$	−0.660767	+	1.14448i	−0.0368804	+	0.0638788i
$322$		0			0
$323$	31.7005	−	18.3023i	1.76387	−	1.01837i
$324$		0			0
$325$	28.7246	+	16.5653i	1.59335	+	0.918880i
$326$		0			0
$327$	3.09129	−	1.78476i	0.170949	−	0.0986974i
$328$		0			0
$329$	2.60747	−	4.51628i	0.143755	−	0.248990i
$330$		0			0
$331$	−1.06308	−	0.613767i	−0.0584319	−	0.0337357i	0.470499	−	0.882400i	$-0.344074\pi$
$331$	−1.06308	−	0.613767i	−0.0584319	−	0.0337357i	−0.528931	+	0.848665i	$0.677407\pi$
$332$		0			0
$333$		−	13.8367i		−	0.758245i
$334$		0			0
$335$	3.90677	+	6.76673i	0.213450	+	0.369706i
$336$		0			0
$337$	0.153885			0.00838268			0.00419134	−	0.999991i	$-0.498666\pi$
$337$	0.153885			0.00838268			0.00419134	+	0.999991i	$0.498666\pi$
$338$		0			0
$339$	−3.25671			−0.176880
$340$		0			0
$341$	6.43545	+	11.1465i	0.348499	+	0.603618i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$		0			0
$345$	13.1080	+	7.56793i	0.705713	+	0.407444i
$346$		0			0
$347$	6.83070	−	11.8311i	0.366691	−	0.635128i	−0.622355	−	0.782735i	$-0.713824\pi$
$347$	6.83070	−	11.8311i	0.366691	−	0.635128i	0.989046	+	0.147607i	$0.0471572\pi$
$348$		0			0
$349$	−20.3397	+	11.7431i	−1.08876	+	0.628595i	−0.933246	−	0.359238i	$-0.883036\pi$
$349$	−20.3397	+	11.7431i	−1.08876	+	0.628595i	−0.155513	+	0.987834i	$0.549703\pi$
$350$		0			0
$351$	−14.3588	−	8.28068i	−0.766418	−	0.441990i
$352$		0			0
$353$	−18.5928	+	10.7346i	−0.989598	+	0.571344i	−0.905154	−	0.425084i	$-0.860245\pi$
$353$	−18.5928	+	10.7346i	−0.989598	+	0.571344i	−0.0844436	+	0.996428i	$0.526911\pi$
$354$		0			0
$355$	18.2285	−	31.5727i	0.967470	−	1.67571i
$356$		0			0
$357$	3.87156	+	2.23525i	0.204905	+	0.118302i
$358$		0			0
$359$			0.830313i			0.0438222i	0.999760	+	0.0219111i	$0.00697508\pi$
$359$			0.830313i			0.0438222i	−0.999760	+	0.0219111i	$0.993025\pi$
$360$		0			0
$361$	16.4383	+	28.4720i	0.865174	+	1.49853i
$362$		0			0
$363$	−3.44286			−0.180703
$364$		0			0
$365$	32.4495			1.69849
$366$		0			0
$367$	4.39215	+	7.60743i	0.229269	+	0.397105i	0.957592	−	0.288129i	$-0.0930333\pi$
$367$	4.39215	+	7.60743i	0.229269	+	0.397105i	−0.728323	+	0.685234i	$0.759700\pi$
$368$		0			0
$369$			26.3991i			1.37428i
$370$		0			0
$371$	−5.86853	−	3.38820i	−0.304679	−	0.175907i
$372$		0			0
$373$	−1.86849	+	3.23632i	−0.0967467	+	0.167570i	−0.910336	−	0.413869i	$-0.864177\pi$
$373$	−1.86849	+	3.23632i	−0.0967467	+	0.167570i	0.813590	+	0.581440i	$0.197510\pi$
$374$		0			0
$375$	12.0456	−	6.95451i	0.622030	−	0.359129i
$376$		0			0
$377$	−0.0126501	−	25.7800i	−0.000651514	−	1.32774i
$378$		0			0
$379$	−17.2889	+	9.98174i	−0.888070	+	0.512728i	−0.873311	−	0.487164i	$-0.838032\pi$
$379$	−17.2889	+	9.98174i	−0.888070	+	0.512728i	−0.0147594	+	0.999891i	$0.504698\pi$
$380$		0			0
$381$	−4.96833	+	8.60540i	−0.254535	+	0.440868i
$382$		0			0
$383$	17.7216	+	10.2316i	0.905530	+	0.522808i	0.878990	−	0.476840i	$-0.158218\pi$
$383$	17.7216	+	10.2316i	0.905530	+	0.522808i	0.0265399	+	0.999648i	$0.491551\pi$
$384$		0			0
$385$			10.0299i			0.511169i
$386$		0			0
$387$	1.93750	+	3.35585i	0.0984888	+	0.170588i
$388$		0			0
$389$	−23.0038			−1.16634			−0.583169	−	0.812351i	$-0.698187\pi$
$389$	−23.0038			−1.16634			−0.583169	+	0.812351i	$0.698187\pi$
$390$		0			0
$391$	23.2092			1.17374
$392$		0			0
$393$	0.630752	+	1.09249i	0.0318172	+	0.0551090i
$394$		0			0
$395$			40.1713i			2.02124i
$396$		0			0
$397$	−6.20868	−	3.58459i	−0.311605	−	0.179905i	0.336040	−	0.941848i	$-0.390912\pi$
$397$	−6.20868	−	3.58459i	−0.311605	−	0.179905i	−0.647644	+	0.761943i	$0.724246\pi$
$398$		0			0
$399$	−3.16782	+	5.48683i	−0.158589	+	0.274685i
$400$		0			0
$401$	−16.6051	+	9.58695i	−0.829219	+	0.478750i	−0.853585	−	0.520954i	$-0.825576\pi$
$401$	−16.6051	+	9.58695i	−0.829219	+	0.478750i	0.0243665	+	0.999703i	$0.492243\pi$
$402$		0			0
$403$	−8.70921	+	15.1019i	−0.433837	+	0.752279i
$404$		0			0
$405$	8.59752	−	4.96378i	0.427214	−	0.246652i
$406$		0			0
$407$	−8.27244	+	14.3283i	−0.410050	+	0.710227i
$408$		0			0
$409$	6.86690	+	3.96461i	0.339547	+	0.196037i	0.660072	−	0.751203i	$-0.270526\pi$
$409$	6.86690	+	3.96461i	0.339547	+	0.196037i	−0.320525	+	0.947240i	$0.603859\pi$
$410$		0			0
$411$		−	12.0253i		−	0.593163i
$412$		0			0
$413$	3.86146	+	6.68825i	0.190010	+	0.329107i
$414$		0			0
$415$	−56.3875			−2.76796
$416$		0			0
$417$	−15.6844			−0.768068
$418$		0			0
$419$	−7.87090	−	13.6328i	−0.384519	−	0.666006i	0.607184	−	0.794562i	$-0.292299\pi$
$419$	−7.87090	−	13.6328i	−0.384519	−	0.666006i	−0.991702	+	0.128556i	$0.958966\pi$
$420$		0			0
$421$		−	0.690252i		−	0.0336408i	−0.999859	−	0.0168204i	$-0.994646\pi$
$421$		−	0.690252i		−	0.0336408i	0.999859	−	0.0168204i	$-0.00535435\pi$
$422$		0			0
$423$	10.0543	+	5.80484i	0.488856	+	0.282241i
$424$		0			0
$425$	23.3694	−	40.4771i	1.13358	−	1.96343i
$426$		0			0
$427$	1.94358	−	1.12213i	0.0940567	−	0.0543036i
$428$		0			0
$429$	4.22492	+	7.30948i	0.203981	+	0.352905i
$430$		0			0
$431$	−7.91413	+	4.56922i	−0.381210	+	0.220092i	−0.678345	−	0.734744i	$-0.737302\pi$
$431$	−7.91413	+	4.56922i	−0.381210	+	0.220092i	0.297135	+	0.954836i	$0.403969\pi$
$432$		0			0
$433$	4.62366	−	8.00841i	0.222199	−	0.384860i	−0.733277	−	0.679930i	$-0.762010\pi$
$433$	4.62366	−	8.00841i	0.222199	−	0.384860i	0.955475	+	0.295071i	$0.0953433\pi$
$434$		0			0
$435$	−20.5230	−	11.8489i	−0.984001	−	0.568113i
$436$		0			0
$437$			32.8924i			1.57346i
$438$		0			0
$439$	11.3013	+	19.5745i	0.539383	+	0.934239i	0.998937	+	0.0460892i	$0.0146759\pi$
$439$	11.3013	+	19.5745i	0.539383	+	0.934239i	−0.459554	+	0.888150i	$0.651991\pi$
$440$		0			0
$441$	2.22623			0.106011
$442$		0			0
$443$	3.04790			0.144810			0.0724051	−	0.997375i	$-0.476933\pi$
$443$	3.04790			0.144810			0.0724051	+	0.997375i	$0.476933\pi$
$444$		0			0
$445$	−0.157876	−	0.273450i	−0.00748405	−	0.0129628i
$446$		0			0
$447$		−	5.23335i		−	0.247529i
$448$		0			0
$449$	25.1756	+	14.5351i	1.18811	+	0.685954i	0.957876	−	0.287182i	$-0.0927183\pi$
$449$	25.1756	+	14.5351i	1.18811	+	0.685954i	0.230232	+	0.973136i	$0.426052\pi$
$450$		0			0
$451$	15.7831	−	27.3371i	0.743195	−	1.28725i
$452$		0			0
$453$	−0.555790	+	0.320885i	−0.0261133	+	0.0150765i
$454$		0			0
$455$	−11.7617	+	6.79834i	−0.551399	+	0.318711i
$456$		0			0
$457$	3.44229	−	1.98741i	0.161024	−	0.0929670i	−0.417323	−	0.908758i	$-0.637032\pi$
$457$	3.44229	−	1.98741i	0.161024	−	0.0929670i	0.578346	+	0.815791i	$0.303698\pi$
$458$		0			0
$459$	−11.6819	+	20.2337i	−0.545265	+	0.944427i
$460$		0			0
$461$	22.3723	+	12.9167i	1.04198	+	0.601589i	0.920394	−	0.390992i	$-0.127868\pi$
$461$	22.3723	+	12.9167i	1.04198	+	0.601589i	0.121588	+	0.992581i	$0.461201\pi$
$462$		0			0
$463$			29.8415i			1.38685i	0.720527	+	0.693427i	$0.243900\pi$
$463$			29.8415i			1.38685i	−0.720527	+	0.693427i	$0.756100\pi$
$464$		0			0
$465$	8.01261	+	13.8782i	0.371576	+	0.643588i
$466$		0			0
$467$	−31.2977			−1.44828			−0.724142	−	0.689651i	$-0.757764\pi$
$467$	−31.2977			−1.44828			−0.724142	+	0.689651i	$0.757764\pi$
$468$		0			0
$469$	−2.07375			−0.0957567
$470$		0			0
$471$	−8.69294	−	15.0566i	−0.400549	−	0.693772i
$472$		0			0
$473$		−	4.63345i		−	0.213046i
$474$		0			0
$475$	57.3647	+	33.1195i	2.63207	+	1.51963i
$476$		0			0
$477$	7.54292	−	13.0647i	0.345367	−	0.598193i
$478$		0			0
$479$	23.8492	−	13.7693i	1.08970	−	0.629137i	0.156201	−	0.987725i	$-0.450075\pi$
$479$	23.8492	−	13.7693i	1.08970	−	0.629137i	0.933496	+	0.358589i	$0.116742\pi$
$480$		0			0
$481$	−22.4095	+	0.0109962i	−1.02179	+	0.000501385i
$482$		0			0
$483$	−3.47893	+	2.00856i	−0.158297	+	0.0913926i
$484$		0			0
$485$	21.2515	−	36.8088i	0.964983	−	1.67140i
$486$		0			0
$487$	−17.3426	−	10.0127i	−0.785866	−	0.453720i	0.0526392	−	0.998614i	$-0.483237\pi$
$487$	−17.3426	−	10.0127i	−0.785866	−	0.453720i	−0.838505	+	0.544894i	$0.816570\pi$
$488$		0			0
$489$			1.08771i			0.0491878i
$490$		0			0
$491$	−16.0224	−	27.7516i	−0.723080	−	1.25241i	−0.959759	−	0.280824i	$-0.909392\pi$
$491$	−16.0224	−	27.7516i	−0.723080	−	1.25241i	0.236679	−	0.971588i	$-0.423941\pi$
$492$		0			0
$493$	−36.3381			−1.63659
$494$		0			0
$495$	−22.3288			−1.00361
$496$		0			0
$497$	4.83792	+	8.37953i	0.217011	+	0.375873i
$498$		0			0
$499$		−	2.24255i		−	0.100390i	−0.998739	−	0.0501951i	$-0.984016\pi$
$499$		−	2.24255i		−	0.100390i	0.998739	−	0.0501951i	$-0.0159843\pi$
$500$		0			0
$501$	−11.7275	−	6.77089i	−0.523947	−	0.302501i
$502$		0			0
$503$	9.28358	−	16.0796i	0.413934	−	0.716955i	−0.581382	−	0.813631i	$-0.697488\pi$
$503$	9.28358	−	16.0796i	0.413934	−	0.716955i	0.995316	+	0.0966759i	$0.0308210\pi$
$504$		0			0
$505$	−50.1975	+	28.9815i	−2.23376	+	1.28966i
$506$		0			0
$507$	−5.70794	+	9.90889i	−0.253498	+	0.440069i
$508$		0			0
$509$	25.2235	−	14.5628i	1.11801	−	0.645483i	0.177118	−	0.984190i	$-0.443323\pi$
$509$	25.2235	−	14.5628i	1.11801	−	0.645483i	0.940892	+	0.338706i	$0.109989\pi$
$510$		0			0
$511$	−4.30612	+	7.45842i	−0.190492	+	0.329941i
$512$		0			0
$513$	−28.6755	−	16.5558i	−1.26605	−	0.730956i
$514$		0			0
$515$		−	58.5695i		−	2.58088i
$516$		0			0
$517$	−6.94101	−	12.0222i	−0.305265	−	0.528735i
$518$		0			0
$519$	8.91194			0.391191
$520$		0			0
$521$	28.7485			1.25950			0.629748	−	0.776800i	$-0.283158\pi$
$521$	28.7485			1.25950			0.629748	+	0.776800i	$0.283158\pi$
$522$		0			0
$523$	−15.4373	−	26.7382i	−0.675026	−	1.16918i	−0.976461	−	0.215693i	$-0.930799\pi$
$523$	−15.4373	−	26.7382i	−0.675026	−	1.16918i	0.301435	−	0.953487i	$-0.402534\pi$
$524$		0			0
$525$			8.08971i			0.353064i
$526$		0			0
$527$	21.2808	+	12.2865i	0.927005	+	0.535206i
$528$		0			0
$529$	1.07228	−	1.85725i	0.0466209	−	0.0807498i
$530$		0			0
$531$	−14.8896	+	8.59652i	−0.646154	+	0.373057i
$532$		0			0
$533$	42.7553	−	0.0209798i	1.85194	−	0.000908736i
$534$		0			0
$535$	−4.90226	+	2.83032i	−0.211943	+	0.122365i
$536$		0			0
$537$	−5.02136	+	8.69724i	−0.216688	+	0.375314i
$538$		0			0
$539$	−2.30533	−	1.33098i	−0.0992976	−	0.0573295i
$540$		0			0
$541$			15.7868i			0.678729i	0.940655	+	0.339365i	$0.110212\pi$
$541$			15.7868i			0.678729i	−0.940655	+	0.339365i	$0.889788\pi$
$542$		0			0
$543$	5.66155	+	9.80609i	0.242960	+	0.420820i
$544$		0			0
$545$	15.2896			0.654936
$546$		0			0
$547$	−3.93885			−0.168413			−0.0842065	−	0.996448i	$-0.526836\pi$
$547$	−3.93885			−0.168413			−0.0842065	+	0.996448i	$0.526836\pi$
$548$		0			0
$549$	2.49812	+	4.32687i	0.106617	+	0.184666i
$550$		0			0
$551$		−	51.4989i		−	2.19393i
$552$		0			0
$553$	−9.23324	−	5.33081i	−0.392637	−	0.226689i
$554$		0			0
$555$	−10.2998	+	17.8398i	−0.437202	+	0.757256i
$556$		0			0
$557$	−17.0550	+	9.84672i	−0.722644	+	0.417219i	−0.815725	−	0.578440i	$-0.803662\pi$
$557$	−17.0550	+	9.84672i	−0.722644	+	0.417219i	0.0930808	+	0.995659i	$0.470329\pi$
$558$		0			0
$559$	5.43351	−	3.14060i	0.229813	−	0.132833i
$560$		0			0
$561$	10.3060	−	5.95015i	0.435118	−	0.251215i
$562$		0			0
$563$	2.05119	−	3.55276i	0.0864472	−	0.149731i	−0.819560	−	0.572994i	$-0.805782\pi$
$563$	2.05119	−	3.55276i	0.0864472	−	0.149731i	0.906007	+	0.423263i	$0.139115\pi$
$564$		0			0
$565$	−12.0808	−	6.97488i	−0.508245	−	0.293435i
$566$		0			0
$567$			2.63481i			0.110652i
$568$		0			0
$569$	−16.9981	−	29.4415i	−0.712596	−	1.23425i	−0.963880	−	0.266339i	$-0.914186\pi$
$569$	−16.9981	−	29.4415i	−0.712596	−	1.23425i	0.251284	−	0.967913i	$-0.419147\pi$
$570$		0			0
$571$	24.3599			1.01943			0.509716	−	0.860343i	$-0.329750\pi$
$571$	24.3599			1.01943			0.509716	+	0.860343i	$0.329750\pi$
$572$		0			0
$573$	−16.9183			−0.706772
$574$		0			0
$575$	20.9994	+	36.3721i	0.875737	+	1.51682i
$576$		0			0
$577$		−	44.2528i		−	1.84227i	−0.389247	−	0.921134i	$-0.627265\pi$
$577$		−	44.2528i		−	1.84227i	0.389247	−	0.921134i	$-0.372735\pi$
$578$		0			0
$579$	3.68257	+	2.12613i	0.153042	+	0.0883590i
$580$		0			0
$581$	7.48274	−	12.9605i	0.310436	−	0.537692i
$582$		0			0
$583$	−15.6218	+	9.01927i	−0.646990	+	0.373540i
$584$		0			0
$585$	−15.1347	−	26.1844i	−0.625743	−	1.08259i
$586$		0			0
$587$	12.6213	−	7.28694i	0.520939	−	0.300764i	−0.216380	−	0.976309i	$-0.569425\pi$
$587$	12.6213	−	7.28694i	0.520939	−	0.300764i	0.737319	+	0.675545i	$0.236092\pi$
$588$		0			0
$589$	−17.4125	+	30.1594i	−0.717471	+	1.24270i
$590$		0			0
$591$	17.1827	+	9.92042i	0.706801	+	0.408071i
$592$		0			0
$593$		−	22.8573i		−	0.938635i	−0.883030	−	0.469317i	$-0.844500\pi$
$593$		−	22.8573i		−	0.938635i	0.883030	−	0.469317i	$-0.155500\pi$
$594$		0			0
$595$	9.57442	+	16.5834i	0.392513	+	0.679853i
$596$		0			0
$597$	10.9353			0.447552
$598$		0			0
$599$	10.0426			0.410331			0.205165	−	0.978727i	$-0.434227\pi$
$599$	10.0426			0.410331			0.205165	+	0.978727i	$0.434227\pi$
$600$		0			0
$601$	2.67428	+	4.63198i	0.109086	+	0.188942i	0.915400	−	0.402545i	$-0.131874\pi$
$601$	2.67428	+	4.63198i	0.109086	+	0.188942i	−0.806314	+	0.591487i	$0.798541\pi$
$602$		0			0
$603$		−	4.61664i		−	0.188004i
$604$		0			0
$605$	−12.7713	−	7.37354i	−0.519229	−	0.299777i
$606$		0			0
$607$	15.6078	−	27.0335i	0.633500	−	1.09725i	−0.353331	−	0.935498i	$-0.614951\pi$
$607$	15.6078	−	27.0335i	0.633500	−	1.09725i	0.986831	−	0.161756i	$-0.0517156\pi$
$608$		0			0
$609$	5.44688	−	3.14476i	0.220719	−	0.127432i
$610$		0			0
$611$	9.39339	−	16.2883i	0.380016	−	0.658953i
$612$		0			0
$613$	2.21957	−	1.28147i	0.0896476	−	0.0517581i	−0.454506	−	0.890744i	$-0.650184\pi$
$613$	2.21957	−	1.28147i	0.0896476	−	0.0517581i	0.544154	+	0.838986i	$0.316851\pi$
$614$		0			0
$615$	19.6511	−	34.0366i	0.792407	−	1.37249i
$616$		0			0
$617$	−25.5938	−	14.7766i	−1.03037	−	0.594883i	−0.113277	−	0.993563i	$-0.536135\pi$
$617$	−25.5938	−	14.7766i	−1.03037	−	0.594883i	−0.917090	+	0.398681i	$0.869468\pi$
$618$		0			0
$619$			35.8019i			1.43900i	0.694492	+	0.719501i	$0.255629\pi$
$619$			35.8019i			1.43900i	−0.694492	+	0.719501i	$0.744371\pi$
$620$		0			0
$621$	−10.4972	−	18.1817i	−0.421238	−	0.729606i
$622$		0			0
$623$	0.0838020			0.00335746
$624$		0			0
$625$	13.5947			0.543786
$626$		0			0
$627$	8.43264	+	14.6058i	0.336767	+	0.583298i
$628$		0			0
$629$			31.5872i			1.25946i
$630$		0			0
$631$	19.5514	+	11.2880i	0.778330	+	0.449369i	0.835838	−	0.548976i	$-0.184982\pi$
$631$	19.5514	+	11.2880i	0.778330	+	0.449369i	−0.0575078	+	0.998345i	$0.518315\pi$
$632$		0			0
$633$	−4.41461	+	7.64633i	−0.175465	+	0.303914i
$634$		0			0
$635$	−36.8602	+	21.2813i	−1.46275	+	0.844522i
$636$		0			0
$637$	−0.00176922	−	3.60555i	−7.00992e−5	−	0.142857i
$638$		0			0
$639$	−18.6548	+	10.7703i	−0.737972	+	0.426068i
$640$		0			0
$641$	−4.03387	+	6.98686i	−0.159328	+	0.275964i	−0.934627	−	0.355631i	$-0.884266\pi$
$641$	−4.03387	+	6.98686i	−0.159328	+	0.275964i	0.775298	+	0.631595i	$0.217599\pi$
$642$		0			0
$643$	28.1150	+	16.2322i	1.10875	+	0.640136i	0.938505	−	0.345266i	$-0.112211\pi$
$643$	28.1150	+	16.2322i	1.10875	+	0.640136i	0.170244	+	0.985402i	$0.445545\pi$
$644$		0			0
$645$		−	5.76898i		−	0.227153i
$646$		0			0
$647$	6.22214	+	10.7771i	0.244618	+	0.423690i	0.962024	−	0.272965i	$-0.0880042\pi$
$647$	6.22214	+	10.7771i	0.244618	+	0.423690i	−0.717406	+	0.696655i	$0.754671\pi$
$648$		0			0
$649$	20.5582			0.806978
$650$		0			0
$651$	−4.25316			−0.166694
$652$		0			0
$653$	18.1043	+	31.3576i	0.708477	+	1.22712i	0.965422	+	0.260693i	$0.0839510\pi$
$653$	18.1043	+	31.3576i	0.708477	+	1.22712i	−0.256944	+	0.966426i	$0.582716\pi$
$654$		0			0
$655$			5.40351i			0.211133i
$656$		0			0
$657$	−16.6042	−	9.58643i	−0.647791	−	0.374002i
$658$		0			0
$659$	4.74883	−	8.22522i	0.184988	−	0.320409i	−0.758584	−	0.651575i	$-0.774109\pi$
$659$	4.74883	−	8.22522i	0.184988	−	0.320409i	0.943573	+	0.331166i	$0.107442\pi$
$660$		0			0
$661$	−0.717581	+	0.414295i	−0.0279107	+	0.0161142i	−0.513890	−	0.857856i	$-0.671796\pi$
$661$	−0.717581	+	0.414295i	−0.0279107	+	0.0161142i	0.485980	+	0.873970i	$0.338463\pi$
$662$		0			0
$663$	13.9631	+	8.05244i	0.542280	+	0.312731i
$664$		0			0
$665$	−23.5022	+	13.5690i	−0.911377	+	0.526184i
$666$		0			0
$667$	16.3264	−	28.2782i	0.632162	−	1.09494i
$668$		0			0
$669$	1.78170	+	1.02867i	0.0688846	+	0.0397705i
$670$		0			0
$671$		−	5.97414i		−	0.230629i
$672$		0			0
$673$	22.3644	+	38.7362i	0.862083	+	1.49317i	0.869914	+	0.493203i	$0.164174\pi$
$673$	22.3644	+	38.7362i	0.862083	+	1.49317i	−0.00783098	+	0.999969i	$0.502493\pi$
$674$		0			0
$675$	−42.2787			−1.62731
$676$		0			0
$677$	−30.3991			−1.16833			−0.584167	−	0.811634i	$-0.698579\pi$
$677$	−30.3991			−1.16833			−0.584167	+	0.811634i	$0.698579\pi$
$678$		0			0
$679$	5.64025	+	9.76920i	0.216453	+	0.374907i
$680$		0			0
$681$		−	14.0771i		−	0.539436i
$682$		0			0
$683$	−21.2209	−	12.2519i	−0.811995	−	0.468806i	0.0356530	−	0.999364i	$-0.488649\pi$
$683$	−21.2209	−	12.2519i	−0.811995	−	0.468806i	−0.847648	+	0.530559i	$0.821982\pi$
$684$		0			0
$685$	25.7545	−	44.6080i	0.984027	−	1.70439i
$686$		0			0
$687$	2.09261	−	1.20817i	0.0798382	−	0.0460946i
$688$		0			0
$689$	−21.1653	−	12.2059i	−0.806333	−	0.465009i
$690$		0			0
$691$	−37.1787	+	21.4651i	−1.41434	+	0.816572i	−0.995794	−	0.0916213i	$-0.970795\pi$
$691$	−37.1787	+	21.4651i	−1.41434	+	0.816572i	−0.418551	+	0.908193i	$0.637462\pi$
$692$		0			0
$693$	2.96308	−	5.13220i	0.112558	−	0.194956i
$694$		0			0
$695$	−58.1816	−	33.5911i	−2.20695	−	1.27418i
$696$		0			0
$697$		−	60.2655i		−	2.28272i
$698$		0			0
$699$	−4.28426	−	7.42056i	−0.162046	−	0.280671i
$700$		0			0
$701$	−12.1568			−0.459155			−0.229578	−	0.973290i	$-0.573735\pi$
$701$	−12.1568			−0.459155			−0.229578	+	0.973290i	$0.573735\pi$
$702$		0			0
$703$	−44.7659			−1.68838
$704$		0			0
$705$	−8.64206	−	14.9685i	−0.325479	−	0.563746i
$706$		0			0
$707$		−	15.3836i		−	0.578561i
$708$		0			0
$709$	−8.62242	−	4.97815i	−0.323822	−	0.186959i	0.329273	−	0.944235i	$-0.393196\pi$
$709$	−8.62242	−	4.97815i	−0.323822	−	0.186959i	−0.653095	+	0.757276i	$0.726530\pi$
$710$		0			0
$711$	11.8676	−	20.5553i	0.445071	−	0.770885i
$712$		0			0
$713$	−19.1226	+	11.0404i	−0.716146	+	0.413467i
$714$		0			0
$715$	0.0177451	+	36.1632i	0.000663628	+	1.35243i
$716$		0			0
$717$	−21.8249	+	12.6006i	−0.815067	+	0.470579i
$718$		0			0
$719$	−8.74282	+	15.1430i	−0.326052	+	0.564739i	−0.981725	−	0.190306i	$-0.939052\pi$
$719$	−8.74282	+	15.1430i	−0.326052	+	0.564739i	0.655673	+	0.755045i	$0.272385\pi$
$720$		0			0
$721$	13.4620	+	7.77229i	0.501351	+	0.289455i
$722$		0			0
$723$			7.73722i			0.287750i
$724$		0			0
$725$	−32.8783	−	56.9470i	−1.22107	−	2.11496i
$726$		0			0
$727$	−38.7903			−1.43865			−0.719326	−	0.694673i	$-0.755549\pi$
$727$	−38.7903			−1.43865			−0.719326	+	0.694673i	$0.755549\pi$
$728$		0			0
$729$	6.26594			0.232072
$730$		0			0
$731$	−4.42305	−	7.66095i	−0.163592	−	0.283350i
$732$		0			0
$733$			0.490451i			0.0181152i	0.999959	+	0.00905760i	$0.00288316\pi$
$733$			0.490451i			0.0181152i	−0.999959	+	0.00905760i	$0.997117\pi$
$734$		0			0
$735$	−2.87031	−	1.65717i	−0.105873	−	0.0611257i
$736$		0			0
$737$	−2.76012	+	4.78067i	−0.101670	+	0.176098i
$738$		0			0
$739$	−23.4381	+	13.5320i	−0.862186	+	0.497783i	−0.864744	−	0.502213i	$-0.832519\pi$
$739$	−23.4381	+	13.5320i	−0.862186	+	0.497783i	0.00255776	+	0.999997i	$0.499186\pi$
$740$		0			0
$741$	−11.4120	+	19.7886i	−0.419232	+	0.726954i
$742$		0			0
$743$	12.0184	−	6.93882i	0.440912	−	0.254560i	−0.263073	−	0.964776i	$-0.584736\pi$
$743$	12.0184	−	6.93882i	0.440912	−	0.254560i	0.703984	+	0.710216i	$0.251403\pi$
$744$		0			0
$745$	11.2082	−	19.4132i	0.410638	−	0.711246i
$746$		0			0
$747$	28.8531	+	16.6583i	1.05568	+	0.609496i
$748$		0			0
$749$		−	1.50236i		−	0.0548950i
$750$		0			0
$751$	−20.1247	−	34.8570i	−0.734362	−	1.27195i	−0.955003	−	0.296597i	$-0.904148\pi$
$751$	−20.1247	−	34.8570i	−0.734362	−	1.27195i	0.220641	−	0.975355i	$-0.429185\pi$
$752$		0			0
$753$	−14.4215			−0.525549
$754$		0			0
$755$	−2.74895			−0.100045
$756$		0			0
$757$	−20.5916	−	35.6657i	−0.748414	−	1.29629i	−0.948583	−	0.316530i	$-0.897482\pi$
$757$	−20.5916	−	35.6657i	−0.748414	−	1.29629i	0.200169	−	0.979761i	$-0.435851\pi$
$758$		0			0
$759$			10.6934i			0.388147i
$760$		0			0
$761$	−1.10282	−	0.636713i	−0.0399772	−	0.0230808i	0.479878	−	0.877335i	$-0.340681\pi$
$761$	−1.10282	−	0.636713i	−0.0399772	−	0.0230808i	−0.519855	+	0.854254i	$0.674014\pi$
$762$		0			0
$763$	−2.02896	+	3.51427i	−0.0734534	+	0.127225i
$764$		0			0
$765$	−36.9185	+	21.3149i	−1.33479	+	0.770642i
$766$		0			0
$767$	13.9345	+	24.1080i	0.503147	+	0.870489i
$768$		0			0
$769$	−20.0765	+	11.5912i	−0.723978	+	0.417989i	−0.816215	−	0.577748i	$-0.803932\pi$
$769$	−20.0765	+	11.5912i	−0.723978	+	0.417989i	0.0922371	+	0.995737i	$0.470598\pi$
$770$		0			0
$771$	4.42145	−	7.65818i	0.159235	−	0.275802i
$772$		0			0
$773$	28.5556	+	16.4866i	1.02707	+	0.592980i	0.916144	−	0.400848i	$-0.131285\pi$
$773$	28.5556	+	16.4866i	1.02707	+	0.592980i	0.110927	+	0.993829i	$0.464618\pi$
$774$		0			0
$775$			44.4666i			1.59729i
$776$		0			0
$777$	−2.73361	−	4.73475i	−0.0980676	−	0.169858i
$778$		0			0
$779$	85.4092			3.06010
$780$		0			0
$781$	25.7568			0.921650
$782$		0			0
$783$	16.4352	+	28.4667i	0.587347	+	1.01732i
$784$		0			0
$785$		−	74.4704i		−	2.65796i
$786$		0			0
$787$	12.3988	+	7.15842i	0.441968	+	0.255170i	0.704432	−	0.709772i	$-0.251202\pi$
$787$	12.3988	+	7.15842i	0.441968	+	0.255170i	−0.262464	+	0.964942i	$0.584535\pi$
$788$		0			0
$789$	12.0256	−	20.8289i	0.428122	−	0.741529i
$790$		0			0
$791$	3.20631	−	1.85116i	0.114003	−	0.0658197i
$792$		0			0
$793$	7.00571	−	4.04933i	0.248780	−	0.143796i
$794$		0			0
$795$	−19.4503	+	11.2297i	−0.689832	+	0.398275i
$796$		0			0
$797$	0.204305	−	0.353866i	0.00723684	−	0.0125346i	−0.862384	−	0.506254i	$-0.831030\pi$
$797$	0.204305	−	0.353866i	0.00723684	−	0.0125346i	0.869621	+	0.493720i	$0.164363\pi$
$798$		0			0
$799$	−22.9525	−	13.2517i	−0.812002	−	0.468810i
$800$		0			0
$801$			0.186563i			0.00659187i
$802$		0			0
$803$	11.4627	+	19.8541i	0.404512	+	0.700635i
$804$		0			0
$805$	−17.2069			−0.606463
$806$		0			0
$807$	13.6244			0.479602
$808$		0			0
$809$	12.8080	+	22.1841i	0.450305	+	0.779951i	0.998405	−	0.0564617i	$-0.0179819\pi$
$809$	12.8080	+	22.1841i	0.450305	+	0.779951i	−0.548100	+	0.836413i	$0.684649\pi$
$810$		0			0
$811$			17.8876i			0.628119i	0.949403	+	0.314060i	$0.101689\pi$
$811$			17.8876i			0.628119i	−0.949403	+	0.314060i	$0.898311\pi$
$812$		0			0
$813$	22.7637	+	13.1426i	0.798358	+	0.460932i
$814$		0			0
$815$	−2.32954	+	4.03487i	−0.0816001	+	0.141335i
$816$		0			0
$817$	10.8572	−	6.26841i	0.379845	−	0.219304i
$818$		0			0
$819$	8.02680	−	0.00393870i	0.280479	−	0.000137629i
$820$		0			0
$821$	−13.5704	+	7.83489i	−0.473611	+	0.273440i	−0.717750	−	0.696301i	$-0.754828\pi$
$821$	−13.5704	+	7.83489i	−0.473611	+	0.273440i	0.244139	+	0.969740i	$0.421495\pi$
$822$		0			0
$823$	−0.954821	+	1.65380i	−0.0332830	+	0.0576478i	−0.882187	−	0.470899i	$-0.843930\pi$
$823$	−0.954821	+	1.65380i	−0.0332830	+	0.0576478i	0.848904	+	0.528547i	$0.177263\pi$
$824$		0			0
$825$	18.6495	+	10.7673i	0.649291	+	0.374868i
$826$		0			0
$827$		−	35.2014i		−	1.22407i	−0.790829	−	0.612037i	$-0.790350\pi$
$827$		−	35.2014i		−	1.22407i	0.790829	−	0.612037i	$-0.209650\pi$
$828$		0			0
$829$	1.93166	+	3.34573i	0.0670894	+	0.116202i	0.897619	−	0.440772i	$-0.145295\pi$
$829$	1.93166	+	3.34573i	0.0670894	+	0.116202i	−0.830530	+	0.556975i	$0.811962\pi$
$830$		0			0
$831$	−10.8085			−0.374941
$832$		0			0
$833$	−5.08218			−0.176087
$834$		0			0
$835$	−29.0023	−	50.2335i	−1.00367	−	1.73840i
$836$		0			0
$837$		−	22.2280i		−	0.768312i
$838$		0			0
$839$	−3.66402	−	2.11542i	−0.126496	−	0.0730325i	0.435417	−	0.900229i	$-0.356601\pi$
$839$	−3.66402	−	2.11542i	−0.126496	−	0.0730325i	−0.561913	+	0.827196i	$0.689934\pi$
$840$		0			0
$841$	−11.0619	+	19.1599i	−0.381446	+	0.660685i
$842$		0			0
$843$	11.6245	−	6.71142i	0.400370	−	0.231153i
$844$		0			0
$845$	−42.3955	+	24.5326i	−1.45845	+	0.843946i
$846$		0			0
$847$	3.38957	−	1.95697i	0.116467	−	0.0672422i
$848$		0			0
$849$	−10.9464	+	18.9598i	−0.375680	+	0.650698i
$850$		0			0
$851$	−24.5811	−	14.1919i	−0.842629	−	0.486492i
$852$		0			0
$853$			35.8134i			1.22623i	0.789994	+	0.613114i	$0.210083\pi$
$853$			35.8134i			1.22623i	−0.789994	+	0.613114i	$0.789917\pi$
$854$		0			0
$855$	−30.2078	−	52.3214i	−1.03308	−	1.78935i
$856$		0			0
$857$	−27.0000			−0.922302			−0.461151	−	0.887322i	$-0.652563\pi$
$857$	−27.0000			−0.922302			−0.461151	+	0.887322i	$0.652563\pi$
$858$		0			0
$859$	3.27849			0.111861			0.0559303	−	0.998435i	$-0.482188\pi$
$859$	3.27849			0.111861			0.0559303	+	0.998435i	$0.482188\pi$
$860$		0			0
$861$	5.21547	+	9.03346i	0.177743	+	0.307860i
$862$		0			0
$863$		−	26.0340i		−	0.886207i	−0.896470	−	0.443104i	$-0.853877\pi$
$863$		−	26.0340i		−	0.886207i	0.896470	−	0.443104i	$-0.146123\pi$
$864$		0			0
$865$	33.0590	+	19.0866i	1.12404	+	0.648965i
$866$		0			0
$867$	3.88299	−	6.72553i	0.131873	−	0.228411i
$868$		0			0
$869$	−24.5786	+	14.1904i	−0.833771	+	0.481378i
$870$		0			0
$871$	−7.47700	+	0.00366892i	−0.253348	+	0.000124317i
$872$		0			0
$873$	−21.7485	+	12.5565i	−0.736075	+	0.424973i
$874$		0			0
$875$	−7.90609	+	13.6937i	−0.267275	+	0.462933i
$876$		0			0
$877$	−40.3523	−	23.2974i	−1.36260	−	0.786698i	−0.372631	−	0.927980i	$-0.621544\pi$
$877$	−40.3523	−	23.2974i	−1.36260	−	0.786698i	−0.989969	+	0.141282i	$0.954878\pi$
$878$		0			0
$879$			5.03596i			0.169859i
$880$		0			0
$881$	8.92730	+	15.4625i	0.300768	+	0.520946i	0.976310	−	0.216375i	$-0.0694235\pi$
$881$	8.92730	+	15.4625i	0.300768	+	0.520946i	−0.675542	+	0.737322i	$0.736090\pi$
$882$		0			0
$883$	7.96539			0.268057			0.134028	−	0.990977i	$-0.457209\pi$
$883$	7.96539			0.268057			0.134028	+	0.990977i	$0.457209\pi$
$884$		0			0
$885$	25.5964			0.860414
$886$		0			0
$887$	−11.8692	−	20.5580i	−0.398528	−	0.690272i	0.595016	−	0.803714i	$-0.297146\pi$
$887$	−11.8692	−	20.5580i	−0.398528	−	0.690272i	−0.993545	+	0.113442i	$0.963812\pi$
$888$		0			0
$889$		−	11.2963i		−	0.378865i
$890$		0			0
$891$	6.07412	+	3.50689i	0.203491	+	0.117485i
$892$		0			0
$893$	18.7804	−	32.5287i	0.628463	−	1.08853i
$894$		0			0
$895$	−37.2537	+	21.5084i	−1.24525	+	0.718947i
$896$		0			0
$897$	−12.5399	+	7.24812i	−0.418695	+	0.242008i
$898$		0			0
$899$	29.9398	−	17.2858i	0.998548	−	0.576512i
$900$		0			0
$901$	−17.2194	+	29.8250i	−0.573663	+	0.993613i
$902$		0			0
$903$	1.32598	+	0.765555i	0.0441259	+	0.0254761i
$904$		0			0
$905$			48.5012i			1.61224i
$906$		0			0
$907$	−12.4509	−	21.5657i	−0.413427	−	0.716076i	0.581835	−	0.813307i	$-0.302335\pi$
$907$	−12.4509	−	21.5657i	−0.413427	−	0.716076i	−0.995262	+	0.0972306i	$0.969002\pi$
$908$		0			0
$909$	34.2476			1.13592
$910$		0			0
$911$	−49.5060			−1.64021			−0.820104	−	0.572215i	$-0.806084\pi$
$911$	−49.5060			−1.64021			−0.820104	+	0.572215i	$0.806084\pi$
$912$		0			0
$913$	−19.9188	−	34.5004i	−0.659216	−	1.14180i
$914$		0			0
$915$		−	7.43824i		−	0.245901i
$916$		0			0
$917$	−1.24198	−	0.717057i	−0.0410137	−	0.0236793i
$918$		0			0
$919$	1.47735	−	2.55885i	0.0487334	−	0.0844087i	−0.840630	−	0.541610i	$-0.817815\pi$
$919$	1.47735	−	2.55885i	0.0487334	−	0.0844087i	0.889363	+	0.457202i	$0.151148\pi$
$920$		0			0
$921$	−12.4090	+	7.16435i	−0.408891	+	0.236073i
$922$		0			0
$923$	17.4582	+	30.2043i	0.574644	+	0.994185i
$924$		0			0
$925$	−49.5017	+	28.5798i	−1.62760	+	0.939698i
$926$		0			0
$927$	−17.3029	+	29.9696i	−0.568303	+	0.984330i
$928$		0			0
$929$	−31.2688	−	18.0531i	−1.02590	−	0.592302i	−0.110090	−	0.993922i	$-0.535114\pi$
$929$	−31.2688	−	18.0531i	−1.02590	−	0.592302i	−0.915806	+	0.401620i	$0.868447\pi$
$930$		0			0
$931$		−	7.20254i		−	0.236054i
$932$		0			0
$933$	0.931675	+	1.61371i	0.0305017	+	0.0528305i
$934$		0			0
$935$	50.9736			1.66701
$936$		0			0
$937$	−9.04136			−0.295368			−0.147684	−	0.989035i	$-0.547182\pi$
$937$	−9.04136			−0.295368			−0.147684	+	0.989035i	$0.547182\pi$
$938$		0			0
$939$	7.06800	+	12.2421i	0.230656	+	0.399507i
$940$		0			0
$941$		−	6.29095i		−	0.205079i	−0.994729	−	0.102539i	$-0.967303\pi$
$941$		−	6.29095i		−	0.205079i	0.994729	−	0.102539i	$-0.0326968\pi$
$942$		0			0
$943$	46.8985	+	27.0769i	1.52723	+	0.881744i
$944$		0			0
$945$	8.66076	−	15.0009i	0.281735	−	0.487979i
$946$		0			0
$947$	−46.0987	+	26.6151i	−1.49801	+	0.864875i	−0.999997	−	0.00229604i	$-0.999269\pi$
$947$	−46.0987	+	26.6151i	−1.49801	+	0.864875i	−0.498010	+	0.867171i	$0.665936\pi$
$948$		0			0
$949$	−15.5127	+	26.8993i	−0.503565	+	0.873189i
$950$		0			0
$951$	−15.7632	+	9.10089i	−0.511157	+	0.295116i
$952$		0			0
$953$	2.40153	−	4.15957i	0.0777932	−	0.134742i	−0.824504	−	0.565856i	$-0.808546\pi$
$953$	2.40153	−	4.15957i	0.0777932	−	0.134742i	0.902298	+	0.431114i	$0.141879\pi$
$954$		0			0
$955$	−62.7588	−	36.2338i	−2.03083	−	1.17250i
$956$		0			0
$957$		−	16.7425i		−	0.541207i
$958$		0			0
$959$	6.83534	+	11.8392i	0.220725	+	0.382306i
$960$		0			0
$961$	7.62171			0.245862
$962$		0			0
$963$	3.34460			0.107778
$964$		0			0
$965$	9.10704	+	15.7739i	0.293166	+	0.507779i
$966$		0			0
$967$			51.7214i			1.66325i	0.555339	+	0.831624i	$0.312588\pi$
$967$			51.7214i			1.66325i	−0.555339	+	0.831624i	$0.687412\pi$
$968$		0			0
$969$	27.8851	+	16.0995i	0.895797	+	0.517189i
$970$		0			0
$971$	−3.46649	+	6.00414i	−0.111245	+	0.192682i	−0.916272	−	0.400556i	$-0.868817\pi$
$971$	−3.46649	+	6.00414i	−0.111245	+	0.192682i	0.805028	+	0.593237i	$0.202150\pi$
$972$		0			0
$973$	15.4416	−	8.91523i	0.495036	−	0.285809i
$974$		0			0
$975$	0.0143125	+	29.1679i	0.000458367	+	0.934119i
$976$		0			0
$977$	14.2638	−	8.23521i	0.456339	−	0.263468i	−0.254164	−	0.967161i	$-0.581800\pi$
$977$	14.2638	−	8.23521i	0.456339	−	0.263468i	0.710504	+	0.703693i	$0.248467\pi$
$978$		0			0
$979$	0.111539	−	0.193191i	0.00356480	−	0.00617442i
$980$		0			0
$981$	−7.82358	−	4.51695i	−0.249788	−	0.144215i
$982$		0			0
$983$		−	33.1142i		−	1.05618i	−0.849189	−	0.528089i	$-0.822909\pi$
$983$		−	33.1142i		−	1.05618i	0.849189	−	0.528089i	$-0.177091\pi$
$984$		0			0
$985$	42.4930	+	73.6000i	1.35394	+	2.34509i
$986$		0			0
$987$	4.58728			0.146015
$988$		0			0
$989$	7.94898			0.252763
$990$		0			0
$991$	−13.3777	−	23.1709i	−0.424958	−	0.736049i	0.571459	−	0.820631i	$-0.306378\pi$
$991$	−13.3777	−	23.1709i	−0.424958	−	0.736049i	−0.996417	+	0.0845822i	$0.973044\pi$
$992$		0			0
$993$		−	1.07979i		−	0.0342660i
$994$		0			0
$995$	40.5647	+	23.4200i	1.28599	+	0.742465i
$996$		0			0
$997$	15.8330	−	27.4236i	0.501437	−	0.868515i	−0.498561	−	0.866854i	$-0.666138\pi$
$997$	15.8330	−	27.4236i	0.501437	−	0.868515i	0.999999	−	0.00166049i	$-0.000528549\pi$
$998$		0			0
$999$	24.7449	−	14.2865i	0.782894	−	0.452004i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.cc.e.673.4		12
4.3	odd	2		728.2.bm.b.673.3	yes	12
13.4	even	6	inner	1456.2.cc.e.225.4		12
52.11	even	12		9464.2.a.bf.1.4		6
52.15	even	12		9464.2.a.bg.1.4		6
52.43	odd	6		728.2.bm.b.225.3	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.bm.b.225.3	✓	12	52.43	odd	6
728.2.bm.b.673.3	yes	12	4.3	odd	2
1456.2.cc.e.225.4		12	13.4	even	6	inner
1456.2.cc.e.673.4		12	1.1	even	1	trivial
9464.2.a.bf.1.4		6	52.11	even	12
9464.2.a.bg.1.4		6	52.15	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.439820 + 0.761791i) q^{3} +3.76784i q^{5} +(-0.866025 - 0.500000i) q^{7} +(1.11312 - 1.92797i) q^{9} +O(q^{10})\)	\(q+(0.439820 + 0.761791i) q^{3} +3.76784i q^{5} +(-0.866025 - 0.500000i) q^{7} +(1.11312 - 1.92797i) q^{9} +(-2.30533 + 1.33098i) q^{11} +(-3.12338 - 1.80124i) q^{13} +(-2.87031 + 1.65717i) q^{15} +(-2.54109 + 4.40130i) q^{17} +(-6.23758 - 3.60127i) q^{19} -0.879640i q^{21} +(-2.28339 - 3.95494i) q^{23} -9.19662 q^{25} +4.59720 q^{27} +(3.57505 + 6.19217i) q^{29} -4.83511i q^{31} +(-2.02786 - 1.17079i) q^{33} +(1.88392 - 3.26304i) q^{35} +(5.38259 - 3.10764i) q^{37} +(-0.00155628 - 3.17159i) q^{39} +(-10.2695 + 5.92910i) q^{41} +(-0.870305 + 1.50741i) q^{43} +(7.26430 + 4.19404i) q^{45} +5.21495i q^{47} +(0.500000 + 0.866025i) q^{49} -4.47049 q^{51} +6.77640 q^{53} +(-5.01493 - 8.68611i) q^{55} -6.33565i q^{57} +(-6.68825 - 3.86146i) q^{59} +(-1.12213 + 1.94358i) q^{61} +(-1.92797 + 1.11312i) q^{63} +(6.78680 - 11.7684i) q^{65} +(1.79592 - 1.03687i) q^{67} +(2.00856 - 3.47893i) q^{69} +(-8.37953 - 4.83792i) q^{71} -8.61224i q^{73} +(-4.04486 - 7.00590i) q^{75} +2.66197 q^{77} +10.6616 q^{79} +(-1.31741 - 2.28182i) q^{81} +14.9655i q^{83} +(-16.5834 - 9.57442i) q^{85} +(-3.14476 + 5.44688i) q^{87} +(-0.0725747 + 0.0419010i) q^{89} +(1.80431 + 3.12161i) q^{91} +(3.68334 - 2.12658i) q^{93} +(13.5690 - 23.5022i) q^{95} +(-9.76920 - 5.64025i) q^{97} +5.92616i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{3} + 4 q^{9}+O(q^{10}) \) 12 * q + 2 * q^3 + 4 * q^9	\( 12 q + 2 q^{3} + 4 q^{9} + 2 q^{13} - 12 q^{15} + 2 q^{17} - 12 q^{19} + 6 q^{23} + 4 q^{25} - 4 q^{27} + 20 q^{29} + 6 q^{33} + 4 q^{35} - 6 q^{37} - 26 q^{39} - 12 q^{41} + 12 q^{43} + 18 q^{45} + 6 q^{49} - 16 q^{51} + 20 q^{53} - 24 q^{55} + 12 q^{59} - 4 q^{61} + 8 q^{65} + 6 q^{67} - 36 q^{71} + 10 q^{75} + 20 q^{77} + 20 q^{79} + 18 q^{81} - 36 q^{85} - 32 q^{87} - 36 q^{89} - 2 q^{91} - 42 q^{93} + 26 q^{95} - 6 q^{97}+O(q^{100}) \) 12 * q + 2 * q^3 + 4 * q^9 + 2 * q^13 - 12 * q^15 + 2 * q^17 - 12 * q^19 + 6 * q^23 + 4 * q^25 - 4 * q^27 + 20 * q^29 + 6 * q^33 + 4 * q^35 - 6 * q^37 - 26 * q^39 - 12 * q^41 + 12 * q^43 + 18 * q^45 + 6 * q^49 - 16 * q^51 + 20 * q^53 - 24 * q^55 + 12 * q^59 - 4 * q^61 + 8 * q^65 + 6 * q^67 - 36 * q^71 + 10 * q^75 + 20 * q^77 + 20 * q^79 + 18 * q^81 - 36 * q^85 - 32 * q^87 - 36 * q^89 - 2 * q^91 - 42 * q^93 + 26 * q^95 - 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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