LMFDB - Embedded newform 1920.2.w.i.127.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1920,2,Mod(127,1920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1920, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 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("1920.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1920 = 2^{7} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1920.w (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.3312771881$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 14x^{10} + 71x^{8} + 158x^{6} + 149x^{4} + 52x^{2} + 4 $ x^12 + 14x^10 + 71x^8 + 158x^6 + 149x^4 + 52*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.3
Root			$-2.27943i$ of defining polynomial
Character	$\chi$	$=$	1920.127
Dual form			1920.2.w.i.1663.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{3} +(1.92741 + 1.13362i) q^{5} +(-0.497835 + 0.497835i) q^{7} +1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{3} +(1.92741 + 1.13362i) q^{5} +(-0.497835 + 0.497835i) q^{7} +1.00000i q^{9} -1.29595i q^{11} +(-2.60318 + 2.60318i) q^{13} +(-0.561294 - 2.16447i) q^{15} +(-0.0443160 - 0.0443160i) q^{17} -1.31802 q^{19} +0.704045 q^{21} +(0.631215 + 0.631215i) q^{23} +(2.42981 + 4.36990i) q^{25} +(0.707107 - 0.707107i) q^{27} +10.3020i q^{29} +2.02439i q^{31} +(-0.916378 + 0.916378i) q^{33} +(-1.52389 + 0.395177i) q^{35} +(-1.03999 - 1.03999i) q^{37} +3.68145 q^{39} +1.24951 q^{41} +(-2.55886 - 2.55886i) q^{43} +(-1.13362 + 1.92741i) q^{45} +(4.03931 - 4.03931i) q^{47} +6.50432i q^{49} +0.0626722i q^{51} +(0.557751 - 0.557751i) q^{53} +(1.46912 - 2.49784i) q^{55} +(0.931979 + 0.931979i) q^{57} -12.2776 q^{59} -6.87187 q^{61} +(-0.497835 - 0.497835i) q^{63} +(-7.96841 + 2.06638i) q^{65} +(-9.36291 + 9.36291i) q^{67} -0.892673i q^{69} +9.62237i q^{71} +(2.88834 - 2.88834i) q^{73} +(1.37185 - 4.80812i) q^{75} +(0.645172 + 0.645172i) q^{77} +13.9340 q^{79} -1.00000 q^{81} +(-4.29163 - 4.29163i) q^{83} +(-0.0351776 - 0.135652i) q^{85} +(7.28463 - 7.28463i) q^{87} -1.94393i q^{89} -2.59191i q^{91} +(1.43146 - 1.43146i) q^{93} +(-2.54036 - 1.49413i) q^{95} +(3.03479 + 3.03479i) q^{97} +1.29595 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q+O(q^{10}) $ 12 * q	$ 12 q - 4 q^{13} - 4 q^{15} - 20 q^{17} + 8 q^{19} + 8 q^{21} - 4 q^{25} + 8 q^{35} - 20 q^{37} - 8 q^{39} + 16 q^{41} + 16 q^{43} + 4 q^{45} + 40 q^{47} + 4 q^{53} - 24 q^{55} - 16 q^{57} + 16 q^{61} - 12 q^{65} - 8 q^{67} + 4 q^{73} + 16 q^{75} - 48 q^{77} - 16 q^{79} - 12 q^{81} - 40 q^{83} - 28 q^{85} + 8 q^{87} + 16 q^{93} - 72 q^{95} - 52 q^{97} + 16 q^{99}+O(q^{100}) $ 12 * q - 4 * q^13 - 4 * q^15 - 20 * q^17 + 8 * q^19 + 8 * q^21 - 4 * q^25 + 8 * q^35 - 20 * q^37 - 8 * q^39 + 16 * q^41 + 16 * q^43 + 4 * q^45 + 40 * q^47 + 4 * q^53 - 24 * q^55 - 16 * q^57 + 16 * q^61 - 12 * q^65 - 8 * q^67 + 4 * q^73 + 16 * q^75 - 48 * q^77 - 16 * q^79 - 12 * q^81 - 40 * q^83 - 28 * q^85 + 8 * q^87 + 16 * q^93 - 72 * q^95 - 52 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times$.

$n$	$511$	$641$	$901$	$1537$
$\chi(n)$	$-1$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$		0			0
$5$	1.92741	+	1.13362i	0.861964	+	0.506970i
$5$	1.92741	+	1.13362i	0.861964	+	0.506970i
$6$		0			0
$7$	−0.497835	+	0.497835i	−0.188164	+	0.188164i	−0.794902	−	0.606738i	$-0.792478\pi$
$7$	−0.497835	+	0.497835i	−0.188164	+	0.188164i	0.606738	+	0.794902i	$0.292478\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$		−	1.29595i		−	0.390745i	−0.980729	−	0.195373i	$-0.937408\pi$
$11$		−	1.29595i		−	0.390745i	0.980729	−	0.195373i	$-0.0625916\pi$
$12$		0			0
$13$	−2.60318	+	2.60318i	−0.721992	+	0.721992i	−0.969011	−	0.247019i	$-0.920549\pi$
$13$	−2.60318	+	2.60318i	−0.721992	+	0.721992i	0.247019	+	0.969011i	$0.420549\pi$
$14$		0			0
$15$	−0.561294	−	2.16447i	−0.144926	−	0.558865i
$16$		0			0
$17$	−0.0443160	−	0.0443160i	−0.0107482	−	0.0107482i	0.701712	−	0.712460i	$-0.252419\pi$
$17$	−0.0443160	−	0.0443160i	−0.0107482	−	0.0107482i	−0.712460	+	0.701712i	$0.752419\pi$
$18$		0			0
$19$	−1.31802			−0.302374			−0.151187	−	0.988505i	$-0.548310\pi$
$19$	−1.31802			−0.302374			−0.151187	+	0.988505i	$0.548310\pi$
$20$		0			0
$21$	0.704045			0.153635
$22$		0			0
$23$	0.631215	+	0.631215i	0.131617	+	0.131617i	0.769847	−	0.638229i	$-0.220333\pi$
$23$	0.631215	+	0.631215i	0.131617	+	0.131617i	−0.638229	+	0.769847i	$0.720333\pi$
$24$		0			0
$25$	2.42981	+	4.36990i	0.485963	+	0.873980i
$26$		0			0
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$			10.3020i			1.91304i	0.291670	+	0.956519i	$0.405789\pi$
$29$			10.3020i			1.91304i	−0.291670	+	0.956519i	$0.594211\pi$
$30$		0			0
$31$			2.02439i			0.363590i	0.983336	+	0.181795i	$0.0581908\pi$
$31$			2.02439i			0.363590i	−0.983336	+	0.181795i	$0.941809\pi$
$32$		0			0
$33$	−0.916378	+	0.916378i	−0.159521	+	0.159521i
$34$		0			0
$35$	−1.52389	+	0.395177i	−0.257584	+	0.0667970i
$36$		0			0
$37$	−1.03999	−	1.03999i	−0.170973	−	0.170973i	0.616434	−	0.787407i	$-0.288577\pi$
$37$	−1.03999	−	1.03999i	−0.170973	−	0.170973i	−0.787407	+	0.616434i	$0.788577\pi$
$38$		0			0
$39$	3.68145			0.589504
$40$		0			0
$41$	1.24951			0.195140			0.0975701	−	0.995229i	$-0.468893\pi$
$41$	1.24951			0.195140			0.0975701	+	0.995229i	$0.468893\pi$
$42$		0			0
$43$	−2.55886	−	2.55886i	−0.390223	−	0.390223i	0.484544	−	0.874767i	$-0.338986\pi$
$43$	−2.55886	−	2.55886i	−0.390223	−	0.390223i	−0.874767	+	0.484544i	$0.838986\pi$
$44$		0			0
$45$	−1.13362	+	1.92741i	−0.168990	+	0.287321i
$46$		0			0
$47$	4.03931	−	4.03931i	0.589193	−	0.589193i	−0.348220	−	0.937413i	$-0.613214\pi$
$47$	4.03931	−	4.03931i	0.589193	−	0.589193i	0.937413	+	0.348220i	$0.113214\pi$
$48$		0			0
$49$			6.50432i			0.929189i
$50$		0			0
$51$			0.0626722i			0.00877587i
$52$		0			0
$53$	0.557751	−	0.557751i	0.0766130	−	0.0766130i	−0.667762	−	0.744375i	$-0.732748\pi$
$53$	0.557751	−	0.557751i	0.0766130	−	0.0766130i	0.744375	+	0.667762i	$0.232748\pi$
$54$		0			0
$55$	1.46912	−	2.49784i	0.198096	−	0.336808i
$56$		0			0
$57$	0.931979	+	0.931979i	0.123444	+	0.123444i
$58$		0			0
$59$	−12.2776			−1.59841			−0.799206	−	0.601057i	$-0.794747\pi$
$59$	−12.2776			−1.59841			−0.799206	+	0.601057i	$0.794747\pi$
$60$		0			0
$61$	−6.87187			−0.879853			−0.439927	−	0.898034i	$-0.644996\pi$
$61$	−6.87187			−0.879853			−0.439927	+	0.898034i	$0.644996\pi$
$62$		0			0
$63$	−0.497835	−	0.497835i	−0.0627213	−	0.0627213i
$64$		0			0
$65$	−7.96841	+	2.06638i	−0.988360	+	0.256303i
$66$		0			0
$67$	−9.36291	+	9.36291i	−1.14386	+	1.14386i	−0.156123	+	0.987738i	$0.549900\pi$
$67$	−9.36291	+	9.36291i	−1.14386	+	1.14386i	−0.987738	+	0.156123i	$0.950100\pi$
$68$		0			0
$69$		−	0.892673i		−	0.107465i
$70$		0			0
$71$			9.62237i			1.14196i	0.820962	+	0.570982i	$0.193438\pi$
$71$			9.62237i			1.14196i	−0.820962	+	0.570982i	$0.806562\pi$
$72$		0			0
$73$	2.88834	−	2.88834i	0.338055	−	0.338055i	−0.517580	−	0.855635i	$-0.673167\pi$
$73$	2.88834	−	2.88834i	0.338055	−	0.338055i	0.855635	+	0.517580i	$0.173167\pi$
$74$		0			0
$75$	1.37185	−	4.80812i	0.158407	−	0.555194i
$76$		0			0
$77$	0.645172	+	0.645172i	0.0735242	+	0.0735242i
$78$		0			0
$79$	13.9340			1.56770			0.783850	−	0.620951i	$-0.213253\pi$
$79$	13.9340			1.56770			0.783850	+	0.620951i	$0.213253\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−4.29163	−	4.29163i	−0.471067	−	0.471067i	0.431193	−	0.902260i	$-0.358093\pi$
$83$	−4.29163	−	4.29163i	−0.471067	−	0.471067i	−0.902260	+	0.431193i	$0.858093\pi$
$84$		0			0
$85$	−0.0351776	−	0.135652i	−0.00381554	−	0.0147136i
$86$		0			0
$87$	7.28463	−	7.28463i	0.780995	−	0.780995i
$88$		0			0
$89$		−	1.94393i		−	0.206056i	−0.994678	−	0.103028i	$-0.967147\pi$
$89$		−	1.94393i		−	0.206056i	0.994678	−	0.103028i	$-0.0328532\pi$
$90$		0			0
$91$		−	2.59191i		−	0.271706i
$92$		0			0
$93$	1.43146	−	1.43146i	0.148435	−	0.148435i
$94$		0			0
$95$	−2.54036	−	1.49413i	−0.260635	−	0.153294i
$96$		0			0
$97$	3.03479	+	3.03479i	0.308136	+	0.308136i	0.844186	−	0.536050i	$-0.180084\pi$
$97$	3.03479	+	3.03479i	0.308136	+	0.308136i	−0.536050	+	0.844186i	$0.680084\pi$
$98$		0			0
$99$	1.29595			0.130248
$100$		0			0
$101$	13.1703			1.31050			0.655248	−	0.755414i	$-0.272564\pi$
$101$	13.1703			1.31050			0.655248	+	0.755414i	$0.272564\pi$
$102$		0			0
$103$	7.39051	+	7.39051i	0.728208	+	0.728208i	0.970263	−	0.242054i	$-0.0778212\pi$
$103$	7.39051	+	7.39051i	0.728208	+	0.728208i	−0.242054	+	0.970263i	$0.577821\pi$
$104$		0			0
$105$	1.35698	+	0.798119i	0.132428	+	0.0778885i
$106$		0			0
$107$	−12.6589	+	12.6589i	−1.22378	+	1.22378i	−0.257500	+	0.966278i	$0.582899\pi$
$107$	−12.6589	+	12.6589i	−1.22378	+	1.22378i	−0.966278	+	0.257500i	$0.917101\pi$
$108$		0			0
$109$			11.3665i			1.08871i	0.838854	+	0.544356i	$0.183226\pi$
$109$			11.3665i			1.08871i	−0.838854	+	0.544356i	$0.816774\pi$
$110$		0			0
$111$			1.47076i			0.139599i
$112$		0			0
$113$	−9.78874	+	9.78874i	−0.920847	+	0.920847i	−0.997089	−	0.0762421i	$-0.975708\pi$
$113$	−9.78874	+	9.78874i	−0.920847	+	0.920847i	0.0762421	+	0.997089i	$0.475708\pi$
$114$		0			0
$115$	0.501052	+	1.93217i	0.0467234	+	0.180176i
$116$		0			0
$117$	−2.60318	−	2.60318i	−0.240664	−	0.240664i
$118$		0			0
$119$	0.0441241			0.00404485
$120$		0			0
$121$	9.32050			0.847318
$122$		0			0
$123$	−0.883534	−	0.883534i	−0.0796656	−	0.0796656i
$124$		0			0
$125$	−0.270555	+	11.1771i	−0.0241992	+	0.999707i
$126$		0			0
$127$	6.85138	−	6.85138i	0.607962	−	0.607962i	−0.334451	−	0.942413i	$-0.608551\pi$
$127$	6.85138	−	6.85138i	0.607962	−	0.607962i	0.942413	+	0.334451i	$0.108551\pi$
$128$		0			0
$129$			3.61878i			0.318616i
$130$		0			0
$131$			10.1559i			0.887324i	0.896194	+	0.443662i	$0.146321\pi$
$131$			10.1559i			0.887324i	−0.896194	+	0.443662i	$0.853679\pi$
$132$		0			0
$133$	0.656155	−	0.656155i	0.0568959	−	0.0568959i
$134$		0			0
$135$	2.16447	−	0.561294i	0.186288	−	0.0483085i
$136$		0			0
$137$	−7.08343	−	7.08343i	−0.605178	−	0.605178i	0.336504	−	0.941682i	$-0.390756\pi$
$137$	−7.08343	−	7.08343i	−0.605178	−	0.605178i	−0.941682	+	0.336504i	$0.890756\pi$
$138$		0			0
$139$	19.2860			1.63582			0.817910	−	0.575346i	$-0.195133\pi$
$139$	19.2860			1.63582			0.817910	+	0.575346i	$0.195133\pi$
$140$		0			0
$141$	−5.71244			−0.481074
$142$		0			0
$143$	3.37360	+	3.37360i	0.282115	+	0.282115i
$144$		0			0
$145$	−11.6786	+	19.8562i	−0.969853	+	1.64897i
$146$		0			0
$147$	4.59925	−	4.59925i	0.379340	−	0.379340i
$148$		0			0
$149$			4.31039i			0.353121i	0.984290	+	0.176560i	$0.0564970\pi$
$149$			4.31039i			0.353121i	−0.984290	+	0.176560i	$0.943503\pi$
$150$		0			0
$151$		−	9.92313i		−	0.807533i	−0.914862	−	0.403766i	$-0.867701\pi$
$151$		−	9.92313i		−	0.807533i	0.914862	−	0.403766i	$-0.132299\pi$
$152$		0			0
$153$	0.0443160	−	0.0443160i	0.00358273	−	0.00358273i
$154$		0			0
$155$	−2.29488	+	3.90182i	−0.184329	+	0.313402i
$156$		0			0
$157$	−8.11359	−	8.11359i	−0.647535	−	0.647535i	0.304862	−	0.952397i	$-0.401390\pi$
$157$	−8.11359	−	8.11359i	−0.647535	−	0.647535i	−0.952397	+	0.304862i	$0.901390\pi$
$158$		0			0
$159$	−0.788780			−0.0625543
$160$		0			0
$161$	−0.628482			−0.0495313
$162$		0			0
$163$	−12.5589	−	12.5589i	−0.983686	−	0.983686i	0.0161829	−	0.999869i	$-0.494849\pi$
$163$	−12.5589	−	12.5589i	−0.983686	−	0.983686i	−0.999869	+	0.0161829i	$0.994849\pi$
$164$		0			0
$165$	−2.80506	+	0.727412i	−0.218374	+	0.0566289i
$166$		0			0
$167$	−7.40357	+	7.40357i	−0.572906	+	0.572906i	−0.932939	−	0.360034i	$-0.882765\pi$
$167$	−7.40357	+	7.40357i	−0.572906	+	0.572906i	0.360034	+	0.932939i	$0.382765\pi$
$168$		0			0
$169$		−	0.553093i		−	0.0425456i
$170$		0			0
$171$		−	1.31802i		−	0.100791i
$172$		0			0
$173$	0.337923	−	0.337923i	0.0256918	−	0.0256918i	−0.694144	−	0.719836i	$-0.744217\pi$
$173$	0.337923	−	0.337923i	0.0256918	−	0.0256918i	0.719836	+	0.694144i	$0.244217\pi$
$174$		0			0
$175$	−3.38514	−	0.965842i	−0.255892	−	0.0730108i
$176$		0			0
$177$	8.68160	+	8.68160i	0.652549	+	0.652549i
$178$		0			0
$179$	16.3264			1.22029			0.610147	−	0.792288i	$-0.291111\pi$
$179$	16.3264			1.22029			0.610147	+	0.792288i	$0.291111\pi$
$180$		0			0
$181$	20.7305			1.54088			0.770441	−	0.637511i	$-0.220036\pi$
$181$	20.7305			1.54088			0.770441	+	0.637511i	$0.220036\pi$
$182$		0			0
$183$	4.85915	+	4.85915i	0.359199	+	0.359199i
$184$		0			0
$185$	−0.825531	−	3.18343i	−0.0606942	−	0.234050i
$186$		0			0
$187$	−0.0574315	+	0.0574315i	−0.00419981	+	0.00419981i
$188$		0			0
$189$			0.704045i			0.0512118i
$190$		0			0
$191$			21.9680i			1.58955i	0.606904	+	0.794775i	$0.292411\pi$
$191$			21.9680i			1.58955i	−0.606904	+	0.794775i	$0.707589\pi$
$192$		0			0
$193$	−5.74797	+	5.74797i	−0.413748	+	0.413748i	−0.883042	−	0.469294i	$-0.844508\pi$
$193$	−5.74797	+	5.74797i	−0.413748	+	0.413748i	0.469294	+	0.883042i	$0.344508\pi$
$194$		0			0
$195$	7.09567	+	4.17337i	0.508131	+	0.298861i
$196$		0			0
$197$	8.07856	+	8.07856i	0.575574	+	0.575574i	0.933681	−	0.358107i	$-0.116578\pi$
$197$	8.07856	+	8.07856i	0.575574	+	0.575574i	−0.358107	+	0.933681i	$0.616578\pi$
$198$		0			0
$199$	−7.95046			−0.563593			−0.281797	−	0.959474i	$-0.590930\pi$
$199$	−7.95046			−0.563593			−0.281797	+	0.959474i	$0.590930\pi$
$200$		0			0
$201$	13.2411			0.933959
$202$		0			0
$203$	−5.12871	−	5.12871i	−0.359965	−	0.359965i
$204$		0			0
$205$	2.40831	+	1.41646i	0.168204	+	0.0989302i
$206$		0			0
$207$	−0.631215	+	0.631215i	−0.0438725	+	0.0438725i
$208$		0			0
$209$			1.70809i			0.118151i
$210$		0			0
$211$		−	21.9708i		−	1.51254i	−0.654262	−	0.756268i	$-0.727021\pi$
$211$		−	21.9708i		−	1.51254i	0.654262	−	0.756268i	$-0.272979\pi$
$212$		0			0
$213$	6.80404	−	6.80404i	0.466205	−	0.466205i
$214$		0			0
$215$	−2.03120	−	7.83276i	−0.138527	−	0.534190i
$216$		0			0
$217$	−1.00781	−	1.00781i	−0.0684146	−	0.0684146i
$218$		0			0
$219$	−4.08473			−0.276021
$220$		0			0
$221$	0.230725			0.0155202
$222$		0			0
$223$	5.34929	+	5.34929i	0.358215	+	0.358215i	0.863155	−	0.504940i	$-0.168485\pi$
$223$	5.34929	+	5.34929i	0.358215	+	0.358215i	−0.504940	+	0.863155i	$0.668485\pi$
$224$		0			0
$225$	−4.36990	+	2.42981i	−0.291327	+	0.161988i
$226$		0			0
$227$	−15.1937	+	15.1937i	−1.00844	+	1.00844i	−0.00847965	+	0.999964i	$0.502699\pi$
$227$	−15.1937	+	15.1937i	−1.00844	+	1.00844i	−0.999964	+	0.00847965i	$0.997301\pi$
$228$		0			0
$229$		−	7.51752i		−	0.496772i	−0.968661	−	0.248386i	$-0.920100\pi$
$229$		−	7.51752i		−	0.496772i	0.968661	−	0.248386i	$-0.0799001\pi$
$230$		0			0
$231$		−	0.912411i		−	0.0600322i
$232$		0			0
$233$	18.0217	−	18.0217i	1.18064	−	1.18064i	0.201060	−	0.979579i	$-0.435561\pi$
$233$	18.0217	−	18.0217i	1.18064	−	1.18064i	0.979579	−	0.201060i	$-0.0644386\pi$
$234$		0			0
$235$	12.3644	−	3.20636i	0.806567	−	0.209160i
$236$		0			0
$237$	−9.85284	−	9.85284i	−0.640011	−	0.640011i
$238$		0			0
$239$	−21.9950			−1.42274			−0.711368	−	0.702819i	$-0.751924\pi$
$239$	−21.9950			−1.42274			−0.711368	+	0.702819i	$0.751924\pi$
$240$		0			0
$241$	4.00000			0.257663			0.128831	−	0.991667i	$-0.458877\pi$
$241$	4.00000			0.257663			0.128831	+	0.991667i	$0.458877\pi$
$242$		0			0
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$		0			0
$245$	−7.37342	+	12.5365i	−0.471071	+	0.800927i
$246$		0			0
$247$	3.43103	−	3.43103i	0.218312	−	0.218312i
$248$		0			0
$249$			6.06927i			0.384625i
$250$		0			0
$251$			5.90001i			0.372405i	0.982511	+	0.186203i	$0.0596181\pi$
$251$			5.90001i			0.372405i	−0.982511	+	0.186203i	$0.940382\pi$
$252$		0			0
$253$	0.818026	−	0.818026i	0.0514289	−	0.0514289i
$254$		0			0
$255$	−0.0710465	+	0.120795i	−0.00444910	+	0.00756448i
$256$		0			0
$257$	−14.1089	−	14.1089i	−0.880092	−	0.880092i	0.113452	−	0.993543i	$-0.463809\pi$
$257$	−14.1089	−	14.1089i	−0.880092	−	0.880092i	−0.993543	+	0.113452i	$0.963809\pi$
$258$		0			0
$259$	1.03548			0.0643418
$260$		0			0
$261$	−10.3020			−0.637679
$262$		0			0
$263$	−0.117239	−	0.117239i	−0.00722928	−	0.00722928i	0.703483	−	0.710712i	$-0.251627\pi$
$263$	−0.117239	−	0.117239i	−0.00722928	−	0.00722928i	−0.710712	+	0.703483i	$0.751627\pi$
$264$		0			0
$265$	1.70729	−	0.442737i	0.104878	−	0.0271971i
$266$		0			0
$267$	−1.37457	+	1.37457i	−0.0841221	+	0.0841221i
$268$		0			0
$269$			20.2054i			1.23195i	0.787767	+	0.615973i	$0.211237\pi$
$269$			20.2054i			1.23195i	−0.787767	+	0.615973i	$0.788763\pi$
$270$		0			0
$271$		−	8.27633i		−	0.502751i	−0.967890	−	0.251376i	$-0.919117\pi$
$271$		−	8.27633i		−	0.502751i	0.967890	−	0.251376i	$-0.0808830\pi$
$272$		0			0
$273$	−1.83276	+	1.83276i	−0.110923	+	0.110923i
$274$		0			0
$275$	5.66319	−	3.14893i	0.341503	−	0.189888i
$276$		0			0
$277$	−13.1707	−	13.1707i	−0.791351	−	0.791351i	0.190363	−	0.981714i	$-0.439034\pi$
$277$	−13.1707	−	13.1707i	−0.791351	−	0.791351i	−0.981714	+	0.190363i	$0.939034\pi$
$278$		0			0
$279$	−2.02439			−0.121197
$280$		0			0
$281$	−0.324088			−0.0193335			−0.00966674	−	0.999953i	$-0.503077\pi$
$281$	−0.324088			−0.0193335			−0.00966674	+	0.999953i	$0.503077\pi$
$282$		0			0
$283$	16.2477	+	16.2477i	0.965826	+	0.965826i	0.999435	−	0.0336094i	$-0.0107002\pi$
$283$	16.2477	+	16.2477i	0.965826	+	0.965826i	−0.0336094	+	0.999435i	$0.510700\pi$
$284$		0			0
$285$	0.739795	+	2.85281i	0.0438217	+	0.168986i
$286$		0			0
$287$	−0.622048	+	0.622048i	−0.0367184	+	0.0367184i
$288$		0			0
$289$		−	16.9961i		−	0.999769i
$290$		0			0
$291$		−	4.29184i		−	0.251592i
$292$		0			0
$293$	16.9985	−	16.9985i	0.993064	−	0.993064i	−0.00691168	−	0.999976i	$-0.502200\pi$
$293$	16.9985	−	16.9985i	0.993064	−	0.993064i	0.999976	+	0.00691168i	$0.00220007\pi$
$294$		0			0
$295$	−23.6640	−	13.9182i	−1.37777	−	0.810347i
$296$		0			0
$297$	−0.916378	−	0.916378i	−0.0531737	−	0.0531737i
$298$		0			0
$299$	−3.28633			−0.190054
$300$		0			0
$301$	2.54779			0.146852
$302$		0			0
$303$	−9.31282	−	9.31282i	−0.535007	−	0.535007i
$304$		0			0
$305$	−13.2449	−	7.79009i	−0.758402	−	0.446059i
$306$		0			0
$307$	9.16935	−	9.16935i	0.523322	−	0.523322i	−0.395251	−	0.918573i	$-0.629342\pi$
$307$	9.16935	−	9.16935i	0.523322	−	0.523322i	0.918573	+	0.395251i	$0.129342\pi$
$308$		0			0
$309$		−	10.4518i		−	0.594580i
$310$		0			0
$311$			11.4077i			0.646872i	0.946250	+	0.323436i	$0.104838\pi$
$311$			11.4077i			0.646872i	−0.946250	+	0.323436i	$0.895162\pi$
$312$		0			0
$313$	19.9731	−	19.9731i	1.12895	−	1.12895i	0.138600	−	0.990348i	$-0.455740\pi$
$313$	19.9731	−	19.9731i	1.12895	−	1.12895i	0.990348	−	0.138600i	$-0.0442601\pi$
$314$		0			0
$315$	−0.395177	−	1.52389i	−0.0222657	−	0.0858614i
$316$		0			0
$317$	−11.1176	−	11.1176i	−0.624425	−	0.624425i	0.322234	−	0.946660i	$-0.395566\pi$
$317$	−11.1176	−	11.1176i	−0.624425	−	0.624425i	−0.946660	+	0.322234i	$0.895566\pi$
$318$		0			0
$319$	13.3510			0.747510
$320$		0			0
$321$	17.9023			0.999211
$322$		0			0
$323$	0.0584092	+	0.0584092i	0.00324997	+	0.00324997i
$324$		0			0
$325$	−17.7009	−	5.05039i	−0.981868	−	0.280145i
$326$		0			0
$327$	8.03732	−	8.03732i	0.444465	−	0.444465i
$328$		0			0
$329$			4.02182i			0.221730i
$330$		0			0
$331$		−	25.2957i		−	1.39037i	−0.718829	−	0.695187i	$-0.755321\pi$
$331$		−	25.2957i		−	1.39037i	0.718829	−	0.695187i	$-0.244679\pi$
$332$		0			0
$333$	1.03999	−	1.03999i	0.0569909	−	0.0569909i
$334$		0			0
$335$	−28.6601	+	7.43218i	−1.56587	+	0.406063i
$336$		0			0
$337$	−7.49825	−	7.49825i	−0.408456	−	0.408456i	0.472744	−	0.881200i	$-0.343263\pi$
$337$	−7.49825	−	7.49825i	−0.408456	−	0.408456i	−0.881200	+	0.472744i	$0.843263\pi$
$338$		0			0
$339$	13.8434			0.751869
$340$		0			0
$341$	2.62351			0.142071
$342$		0			0
$343$	−6.72293	−	6.72293i	−0.363004	−	0.363004i
$344$		0			0
$345$	1.01195	−	1.72055i	0.0544816	−	0.0926311i
$346$		0			0
$347$	−18.1546	+	18.1546i	−0.974591	+	0.974591i	−0.999685	−	0.0250941i	$-0.992011\pi$
$347$	−18.1546	+	18.1546i	−0.974591	+	0.974591i	0.0250941	+	0.999685i	$0.492011\pi$
$348$		0			0
$349$			11.5709i			0.619378i	0.950838	+	0.309689i	$0.100225\pi$
$349$			11.5709i			0.619378i	−0.950838	+	0.309689i	$0.899775\pi$
$350$		0			0
$351$			3.68145i			0.196501i
$352$		0			0
$353$	6.93419	−	6.93419i	0.369069	−	0.369069i	−0.498068	−	0.867138i	$-0.665957\pi$
$353$	6.93419	−	6.93419i	0.369069	−	0.369069i	0.867138	+	0.498068i	$0.165957\pi$
$354$		0			0
$355$	−10.9081	+	18.5462i	−0.578942	+	0.984332i
$356$		0			0
$357$	−0.0312005	−	0.0312005i	−0.00165130	−	0.00165130i
$358$		0			0
$359$	−0.207103			−0.0109305			−0.00546524	−	0.999985i	$-0.501740\pi$
$359$	−0.207103			−0.0109305			−0.00546524	+	0.999985i	$0.501740\pi$
$360$		0			0
$361$	−17.2628			−0.908570
$362$		0			0
$363$	−6.59059	−	6.59059i	−0.345916	−	0.345916i
$364$		0			0
$365$	8.84130	−	2.29274i	0.462775	−	0.120007i
$366$		0			0
$367$	9.25495	−	9.25495i	0.483104	−	0.483104i	−0.423017	−	0.906122i	$-0.639029\pi$
$367$	9.25495	−	9.25495i	0.483104	−	0.483104i	0.906122	+	0.423017i	$0.139029\pi$
$368$		0			0
$369$			1.24951i			0.0650467i
$370$		0			0
$371$			0.555337i			0.0288316i
$372$		0			0
$373$	13.6272	−	13.6272i	0.705592	−	0.705592i	−0.260013	−	0.965605i	$-0.583727\pi$
$373$	13.6272	−	13.6272i	0.705592	−	0.705592i	0.965605	+	0.260013i	$0.0837268\pi$
$374$		0			0
$375$	8.09469	−	7.71207i	0.418008	−	0.398249i
$376$		0			0
$377$	−26.8180	−	26.8180i	−1.38120	−	1.38120i
$378$		0			0
$379$	18.0342			0.926355			0.463178	−	0.886266i	$-0.346709\pi$
$379$	18.0342			0.926355			0.463178	+	0.886266i	$0.346709\pi$
$380$		0			0
$381$	−9.68932			−0.496399
$382$		0			0
$383$	−12.4015	−	12.4015i	−0.633685	−	0.633685i	0.315305	−	0.948990i	$-0.397893\pi$
$383$	−12.4015	−	12.4015i	−0.633685	−	0.633685i	−0.948990	+	0.315305i	$0.897893\pi$
$384$		0			0
$385$	0.512131	+	1.97489i	0.0261006	+	0.100650i
$386$		0			0
$387$	2.55886	−	2.55886i	0.130074	−	0.130074i
$388$		0			0
$389$		−	25.7012i		−	1.30310i	−0.758604	−	0.651552i	$-0.774118\pi$
$389$		−	25.7012i		−	1.30310i	0.758604	−	0.651552i	$-0.225882\pi$
$390$		0			0
$391$		−	0.0559458i		−	0.00282930i
$392$		0			0
$393$	7.18129	−	7.18129i	0.362248	−	0.362248i
$394$		0			0
$395$	26.8566	+	15.7959i	1.35130	+	0.794777i
$396$		0			0
$397$	−22.7752	−	22.7752i	−1.14305	−	1.14305i	−0.987889	−	0.155163i	$-0.950410\pi$
$397$	−22.7752	−	22.7752i	−1.14305	−	1.14305i	−0.155163	−	0.987889i	$-0.549590\pi$
$398$		0			0
$399$	−0.927944			−0.0464553
$400$		0			0
$401$	21.9756			1.09741			0.548704	−	0.836017i	$-0.315121\pi$
$401$	21.9756			1.09741			0.548704	+	0.836017i	$0.315121\pi$
$402$		0			0
$403$	−5.26984	−	5.26984i	−0.262510	−	0.262510i
$404$		0			0
$405$	−1.92741	−	1.13362i	−0.0957737	−	0.0563300i
$406$		0			0
$407$	−1.34778	+	1.34778i	−0.0668067	+	0.0668067i
$408$		0			0
$409$			14.9242i			0.737956i	0.929438	+	0.368978i	$0.120292\pi$
$409$			14.9242i			0.737956i	−0.929438	+	0.368978i	$0.879708\pi$
$410$		0			0
$411$			10.0175i			0.494126i
$412$		0			0
$413$	6.11224	−	6.11224i	0.300764	−	0.300764i
$414$		0			0
$415$	−3.40665	−	13.1368i	−0.167226	−	0.644860i
$416$		0			0
$417$	−13.6373	−	13.6373i	−0.667821	−	0.667821i
$418$		0			0
$419$	−19.8701			−0.970720			−0.485360	−	0.874314i	$-0.661312\pi$
$419$	−19.8701			−0.970720			−0.485360	+	0.874314i	$0.661312\pi$
$420$		0			0
$421$	10.6819			0.520606			0.260303	−	0.965527i	$-0.416178\pi$
$421$	10.6819			0.520606			0.260303	+	0.965527i	$0.416178\pi$
$422$		0			0
$423$	4.03931	+	4.03931i	0.196398	+	0.196398i
$424$		0			0
$425$	0.0859767	−	0.301336i	0.00417048	−	0.0146169i
$426$		0			0
$427$	3.42106	−	3.42106i	0.165557	−	0.165557i
$428$		0			0
$429$		−	4.77100i		−	0.230346i
$430$		0			0
$431$			13.0578i			0.628972i	0.949262	+	0.314486i	$0.101832\pi$
$431$			13.0578i			0.628972i	−0.949262	+	0.314486i	$0.898168\pi$
$432$		0			0
$433$	15.1148	−	15.1148i	0.726369	−	0.726369i	−0.243525	−	0.969894i	$-0.578304\pi$
$433$	15.1148	−	15.1148i	0.726369	−	0.726369i	0.969894	+	0.243525i	$0.0783040\pi$
$434$		0			0
$435$	22.2985	−	5.78247i	1.06913	−	0.277248i
$436$		0			0
$437$	−0.831952	−	0.831952i	−0.0397977	−	0.0397977i
$438$		0			0
$439$	−30.2133			−1.44200			−0.721001	−	0.692934i	$-0.756318\pi$
$439$	−30.2133			−1.44200			−0.721001	+	0.692934i	$0.756318\pi$
$440$		0			0
$441$	−6.50432			−0.309730
$442$		0			0
$443$	−9.36619	−	9.36619i	−0.445001	−	0.445001i	0.448688	−	0.893689i	$-0.351892\pi$
$443$	−9.36619	−	9.36619i	−0.445001	−	0.445001i	−0.893689	+	0.448688i	$0.851892\pi$
$444$		0			0
$445$	2.20368	−	3.74675i	0.104464	−	0.177613i
$446$		0			0
$447$	3.04790	−	3.04790i	0.144161	−	0.144161i
$448$		0			0
$449$		−	31.9264i		−	1.50670i	−0.657619	−	0.753350i	$-0.728436\pi$
$449$		−	31.9264i		−	1.50670i	0.657619	−	0.753350i	$-0.271564\pi$
$450$		0			0
$451$		−	1.61930i		−	0.0762500i
$452$		0			0
$453$	−7.01671	+	7.01671i	−0.329674	+	0.329674i
$454$		0			0
$455$	2.93824	−	4.99567i	0.137747	−	0.234201i
$456$		0			0
$457$	−13.1817	−	13.1817i	−0.616615	−	0.616615i	0.328047	−	0.944661i	$-0.393610\pi$
$457$	−13.1817	−	13.1817i	−0.616615	−	0.616615i	−0.944661	+	0.328047i	$0.893610\pi$
$458$		0			0
$459$	−0.0626722			−0.00292529
$460$		0			0
$461$	5.04893			0.235152			0.117576	−	0.993064i	$-0.462488\pi$
$461$	5.04893			0.235152			0.117576	+	0.993064i	$0.462488\pi$
$462$		0			0
$463$	26.7581	+	26.7581i	1.24355	+	1.24355i	0.958517	+	0.285036i	$0.0920055\pi$
$463$	26.7581	+	26.7581i	1.24355	+	1.24355i	0.285036	+	0.958517i	$0.407994\pi$
$464$		0			0
$465$	4.38173	−	1.13628i	0.203198	−	0.0526936i
$466$		0			0
$467$	23.3602	−	23.3602i	1.08098	−	1.08098i	0.0845632	−	0.996418i	$-0.473051\pi$
$467$	23.3602	−	23.3602i	1.08098	−	1.08098i	0.996418	−	0.0845632i	$-0.0269495\pi$
$468$		0			0
$469$		−	9.32237i		−	0.430467i
$470$		0			0
$471$			11.4743i			0.528710i
$472$		0			0
$473$	−3.31617	+	3.31617i	−0.152478	+	0.152478i
$474$		0			0
$475$	−3.20254	−	5.75960i	−0.146942	−	0.264268i
$476$		0			0
$477$	0.557751	+	0.557751i	0.0255377	+	0.0255377i
$478$		0			0
$479$	−40.4867			−1.84989			−0.924943	−	0.380106i	$-0.875887\pi$
$479$	−40.4867			−1.84989			−0.924943	+	0.380106i	$0.875887\pi$
$480$		0			0
$481$	5.41454			0.246882
$482$		0			0
$483$	0.444404	+	0.444404i	0.0202211	+	0.0202211i
$484$		0			0
$485$	2.40898	+	9.28957i	0.109386	+	0.421818i
$486$		0			0
$487$	−4.51912	+	4.51912i	−0.204781	+	0.204781i	−0.802045	−	0.597264i	$-0.796255\pi$
$487$	−4.51912	+	4.51912i	−0.204781	+	0.204781i	0.597264	+	0.802045i	$0.296255\pi$
$488$		0			0
$489$			17.7609i			0.803176i
$490$		0			0
$491$		−	26.5364i		−	1.19757i	−0.800909	−	0.598786i	$-0.795650\pi$
$491$		−	26.5364i		−	1.19757i	0.800909	−	0.598786i	$-0.204350\pi$
$492$		0			0
$493$	0.456544	−	0.456544i	0.0205617	−	0.0205617i
$494$		0			0
$495$	2.49784	+	1.46912i	0.112269	+	0.0660320i
$496$		0			0
$497$	−4.79035	−	4.79035i	−0.214877	−	0.214877i
$498$		0			0
$499$	29.4486			1.31830			0.659151	−	0.752011i	$-0.270916\pi$
$499$	29.4486			1.31830			0.659151	+	0.752011i	$0.270916\pi$
$500$		0			0
$501$	10.4702			0.467775
$502$		0			0
$503$	11.1983	+	11.1983i	0.499306	+	0.499306i	0.911222	−	0.411916i	$-0.135140\pi$
$503$	11.1983	+	11.1983i	0.499306	+	0.499306i	−0.411916	+	0.911222i	$0.635140\pi$
$504$		0			0
$505$	25.3846	+	14.9301i	1.12960	+	0.664382i
$506$		0			0
$507$	−0.391095	+	0.391095i	−0.0173692	+	0.0173692i
$508$		0			0
$509$			1.20339i			0.0533394i	0.999644	+	0.0266697i	$0.00849024\pi$
$509$			1.20339i			0.0533394i	−0.999644	+	0.0266697i	$0.991510\pi$
$510$		0			0
$511$			2.87584i			0.127220i
$512$		0			0
$513$	−0.931979	+	0.931979i	−0.0411479	+	0.0411479i
$514$		0			0
$515$	5.86651	+	22.6226i	0.258509	+	0.996869i
$516$		0			0
$517$	−5.23476	−	5.23476i	−0.230224	−	0.230224i
$518$		0			0
$519$	−0.477896			−0.0209773
$520$		0			0
$521$	3.34008			0.146332			0.0731658	−	0.997320i	$-0.476690\pi$
$521$	3.34008			0.146332			0.0731658	+	0.997320i	$0.476690\pi$
$522$		0			0
$523$	24.8561	+	24.8561i	1.08688	+	1.08688i	0.995848	+	0.0910337i	$0.0290171\pi$
$523$	24.8561	+	24.8561i	1.08688	+	1.08688i	0.0910337	+	0.995848i	$0.470983\pi$
$524$		0			0
$525$	1.71070	+	3.07661i	0.0746610	+	0.134274i
$526$		0			0
$527$	0.0897126	−	0.0897126i	0.00390794	−	0.00390794i
$528$		0			0
$529$		−	22.2031i		−	0.965354i
$530$		0			0
$531$		−	12.2776i		−	0.532804i
$532$		0			0
$533$	−3.25269	+	3.25269i	−0.140890	+	0.140890i
$534$		0			0
$535$	−38.7491	+	10.0485i	−1.67527	+	0.434433i
$536$		0			0
$537$	−11.5445	−	11.5445i	−0.498183	−	0.498183i
$538$		0			0
$539$	8.42930			0.363076
$540$		0			0
$541$	26.8547			1.15458			0.577288	−	0.816541i	$-0.304111\pi$
$541$	26.8547			1.15458			0.577288	+	0.816541i	$0.304111\pi$
$542$		0			0
$543$	−14.6586	−	14.6586i	−0.629063	−	0.629063i
$544$		0			0
$545$	−12.8853	+	21.9079i	−0.551945	+	0.938431i
$546$		0			0
$547$	−28.5864	+	28.5864i	−1.22227	+	1.22227i	−0.255442	+	0.966824i	$0.582221\pi$
$547$	−28.5864	+	28.5864i	−1.22227	+	1.22227i	−0.966824	+	0.255442i	$0.917779\pi$
$548$		0			0
$549$		−	6.87187i		−	0.293284i
$550$		0			0
$551$		−	13.5782i		−	0.578453i
$552$		0			0
$553$	−6.93684	+	6.93684i	−0.294985	+	0.294985i
$554$		0			0
$555$	−1.66729	+	2.83476i	−0.0707723	+	0.120329i
$556$		0			0
$557$	−2.23619	−	2.23619i	−0.0947503	−	0.0947503i	0.658143	−	0.752893i	$-0.271342\pi$
$557$	−2.23619	−	2.23619i	−0.0947503	−	0.0947503i	−0.752893	+	0.658143i	$0.771342\pi$
$558$		0			0
$559$	13.3224			0.563476
$560$		0			0
$561$	0.0812204			0.00342913
$562$		0			0
$563$	8.69968	+	8.69968i	0.366648	+	0.366648i	0.866253	−	0.499605i	$-0.166522\pi$
$563$	8.69968	+	8.69968i	0.366648	+	0.366648i	−0.499605	+	0.866253i	$0.666522\pi$
$564$		0			0
$565$	−29.9636	+	7.77020i	−1.26058	+	0.326895i
$566$		0			0
$567$	0.497835	−	0.497835i	0.0209071	−	0.0209071i
$568$		0			0
$569$			22.8686i			0.958703i	0.877623	+	0.479351i	$0.159128\pi$
$569$			22.8686i			0.958703i	−0.877623	+	0.479351i	$0.840872\pi$
$570$		0			0
$571$			4.03649i			0.168922i	0.996427	+	0.0844610i	$0.0269168\pi$
$571$			4.03649i			0.168922i	−0.996427	+	0.0844610i	$0.973083\pi$
$572$		0			0
$573$	15.5337	−	15.5337i	0.648931	−	0.648931i
$574$		0			0
$575$	−1.22461	+	4.29208i	−0.0510698	+	0.178992i
$576$		0			0
$577$	20.0370	+	20.0370i	0.834153	+	0.834153i	0.988082	−	0.153929i	$-0.0491928\pi$
$577$	20.0370	+	20.0370i	0.834153	+	0.834153i	−0.153929	+	0.988082i	$0.549193\pi$
$578$		0			0
$579$	8.12886			0.337824
$580$		0			0
$581$	4.27304			0.177276
$582$		0			0
$583$	−0.722821	−	0.722821i	−0.0299362	−	0.0299362i
$584$		0			0
$585$	−2.06638	−	7.96841i	−0.0854342	−	0.329453i
$586$		0			0
$587$	11.2589	−	11.2589i	0.464705	−	0.464705i	−0.435489	−	0.900194i	$-0.643425\pi$
$587$	11.2589	−	11.2589i	0.464705	−	0.464705i	0.900194	+	0.435489i	$0.143425\pi$
$588$		0			0
$589$		−	2.66817i		−	0.109940i
$590$		0			0
$591$		−	11.4248i		−	0.469954i
$592$		0			0
$593$	1.63591	−	1.63591i	0.0671786	−	0.0671786i	−0.672719	−	0.739898i	$-0.734874\pi$
$593$	1.63591	−	1.63591i	0.0671786	−	0.0671786i	0.739898	+	0.672719i	$0.234874\pi$
$594$		0			0
$595$	0.0850452	+	0.0500199i	0.00348651	+	0.00205062i
$596$		0			0
$597$	5.62183	+	5.62183i	0.230086	+	0.230086i
$598$		0			0
$599$	−17.8538			−0.729487			−0.364743	−	0.931108i	$-0.618843\pi$
$599$	−17.8538			−0.729487			−0.364743	+	0.931108i	$0.618843\pi$
$600$		0			0
$601$	1.53165			0.0624774			0.0312387	−	0.999512i	$-0.490055\pi$
$601$	1.53165			0.0624774			0.0312387	+	0.999512i	$0.490055\pi$
$602$		0			0
$603$	−9.36291	−	9.36291i	−0.381287	−	0.381287i
$604$		0			0
$605$	17.9644	+	10.5659i	0.730358	+	0.429565i
$606$		0			0
$607$	9.73762	−	9.73762i	0.395238	−	0.395238i	−0.481312	−	0.876550i	$-0.659839\pi$
$607$	9.73762	−	9.73762i	0.395238	−	0.395238i	0.876550	+	0.481312i	$0.159839\pi$
$608$		0			0
$609$			7.25309i			0.293910i
$610$		0			0
$611$			21.0301i			0.850786i
$612$		0			0
$613$	−28.9908	+	28.9908i	−1.17093	+	1.17093i	−0.188938	+	0.981989i	$0.560505\pi$
$613$	−28.9908	+	28.9908i	−1.17093	+	1.17093i	−0.981989	+	0.188938i	$0.939495\pi$
$614$		0			0
$615$	−0.701341	−	2.70452i	−0.0282808	−	0.109057i
$616$		0			0
$617$	−13.7163	−	13.7163i	−0.552197	−	0.552197i	0.374877	−	0.927075i	$-0.377685\pi$
$617$	−13.7163	−	13.7163i	−0.552197	−	0.552197i	−0.927075	+	0.374877i	$0.877685\pi$
$618$		0			0
$619$	7.99970			0.321535			0.160768	−	0.986992i	$-0.448603\pi$
$619$	7.99970			0.321535			0.160768	+	0.986992i	$0.448603\pi$
$620$		0			0
$621$	0.892673			0.0358217
$622$		0			0
$623$	0.967757	+	0.967757i	0.0387724	+	0.0387724i
$624$		0			0
$625$	−13.1920	+	21.2361i	−0.527680	+	0.849443i
$626$		0			0
$627$	1.20780	−	1.20780i	0.0482350	−	0.0482350i
$628$		0			0
$629$			0.0921760i			0.00367530i
$630$		0			0
$631$			36.4507i			1.45108i	0.688180	+	0.725540i	$0.258410\pi$
$631$			36.4507i			1.45108i	−0.688180	+	0.725540i	$0.741590\pi$
$632$		0			0
$633$	−15.5357	+	15.5357i	−0.617490	+	0.617490i
$634$		0			0
$635$	20.9723	−	5.43856i	0.832259	−	0.215823i
$636$		0			0
$637$	−16.9319	−	16.9319i	−0.670867	−	0.670867i
$638$		0			0
$639$	−9.62237			−0.380655
$640$		0			0
$641$	6.24546			0.246681			0.123340	−	0.992364i	$-0.460639\pi$
$641$	6.24546			0.246681			0.123340	+	0.992364i	$0.460639\pi$
$642$		0			0
$643$	9.02997	+	9.02997i	0.356107	+	0.356107i	0.862376	−	0.506268i	$-0.168976\pi$
$643$	9.02997	+	9.02997i	0.356107	+	0.356107i	−0.506268	+	0.862376i	$0.668976\pi$
$644$		0			0
$645$	−4.10232	+	6.97487i	−0.161529	+	0.274635i
$646$		0			0
$647$	21.5611	−	21.5611i	0.847654	−	0.847654i	−0.142186	−	0.989840i	$-0.545413\pi$
$647$	21.5611	−	21.5611i	0.847654	−	0.847654i	0.989840	+	0.142186i	$0.0454131\pi$
$648$		0			0
$649$			15.9113i			0.624572i
$650$		0			0
$651$			1.42526i			0.0558603i
$652$		0			0
$653$	32.2913	−	32.2913i	1.26366	−	1.26366i	0.314347	−	0.949308i	$-0.398214\pi$
$653$	32.2913	−	32.2913i	1.26366	−	1.26366i	0.949308	−	0.314347i	$-0.101786\pi$
$654$		0			0
$655$	−11.5129	+	19.5745i	−0.449846	+	0.764841i
$656$		0			0
$657$	2.88834	+	2.88834i	0.112685	+	0.112685i
$658$		0			0
$659$	7.28376			0.283735			0.141867	−	0.989886i	$-0.454689\pi$
$659$	7.28376			0.283735			0.141867	+	0.989886i	$0.454689\pi$
$660$		0			0
$661$	33.8338			1.31598			0.657991	−	0.753026i	$-0.271407\pi$
$661$	33.8338			1.31598			0.657991	+	0.753026i	$0.271407\pi$
$662$		0			0
$663$	−0.163147	−	0.163147i	−0.00633611	−	0.00633611i
$664$		0			0
$665$	2.00851	−	0.520849i	0.0778867	−	0.0201977i
$666$		0			0
$667$	−6.50279	+	6.50279i	−0.251789	+	0.251789i
$668$		0			0
$669$		−	7.56503i		−	0.292481i
$670$		0			0
$671$			8.90564i			0.343798i
$672$		0			0
$673$	20.0728	−	20.0728i	0.773750	−	0.773750i	−0.205010	−	0.978760i	$-0.565723\pi$
$673$	20.0728	−	20.0728i	0.773750	−	0.773750i	0.978760	+	0.205010i	$0.0657225\pi$
$674$		0			0
$675$	4.80812	+	1.37185i	0.185065	+	0.0528024i
$676$		0			0
$677$	11.6171	+	11.6171i	0.446483	+	0.446483i	0.894184	−	0.447700i	$-0.147757\pi$
$677$	11.6171	+	11.6171i	0.446483	+	0.446483i	−0.447700	+	0.894184i	$0.647757\pi$
$678$		0			0
$679$	−3.02165			−0.115960
$680$		0			0
$681$	21.4872			0.823391
$682$		0			0
$683$	−16.7302	−	16.7302i	−0.640162	−	0.640162i	0.310433	−	0.950595i	$-0.399526\pi$
$683$	−16.7302	−	16.7302i	−0.640162	−	0.640162i	−0.950595	+	0.310433i	$0.899526\pi$
$684$		0			0
$685$	−5.62276	−	21.6826i	−0.214835	−	0.828449i
$686$		0			0
$687$	−5.31569	+	5.31569i	−0.202806	+	0.202806i
$688$		0			0
$689$			2.90385i			0.110628i
$690$		0			0
$691$		−	29.3660i		−	1.11714i	−0.829459	−	0.558568i	$-0.811351\pi$
$691$		−	29.3660i		−	1.11714i	0.829459	−	0.558568i	$-0.188649\pi$
$692$		0			0
$693$	−0.645172	+	0.645172i	−0.0245081	+	0.0245081i
$694$		0			0
$695$	37.1721	+	21.8630i	1.41002	+	0.829312i
$696$		0			0
$697$	−0.0553731	−	0.0553731i	−0.00209741	−	0.00209741i
$698$		0			0
$699$	−25.4865			−0.963988
$700$		0			0
$701$	−8.17508			−0.308769			−0.154384	−	0.988011i	$-0.549339\pi$
$701$	−8.17508			−0.308769			−0.154384	+	0.988011i	$0.549339\pi$
$702$		0			0
$703$	1.37072	+	1.37072i	0.0516977	+	0.0516977i
$704$		0			0
$705$	−11.0102	−	6.47573i	−0.414669	−	0.243890i
$706$		0			0
$707$	−6.55665	+	6.55665i	−0.246588	+	0.246588i
$708$		0			0
$709$			12.4019i			0.465762i	0.972505	+	0.232881i	$0.0748153\pi$
$709$			12.4019i			0.465762i	−0.972505	+	0.232881i	$0.925185\pi$
$710$		0			0
$711$			13.9340i			0.522566i
$712$		0			0
$713$	−1.27782	+	1.27782i	−0.0478548	+	0.0478548i
$714$		0			0
$715$	2.67793	+	10.3267i	0.100149	+	0.386197i
$716$		0			0
$717$	15.5528	+	15.5528i	0.580830	+	0.580830i
$718$		0			0
$719$	17.5828			0.655729			0.327865	−	0.944725i	$-0.393671\pi$
$719$	17.5828			0.655729			0.327865	+	0.944725i	$0.393671\pi$
$720$		0			0
$721$	−7.35851			−0.274045
$722$		0			0
$723$	−2.82843	−	2.82843i	−0.105190	−	0.105190i
$724$		0			0
$725$	−45.0188	+	25.0320i	−1.67196	+	0.929665i
$726$		0			0
$727$	5.46814	−	5.46814i	0.202802	−	0.202802i	−0.598397	−	0.801199i	$-0.704196\pi$
$727$	5.46814	−	5.46814i	0.202802	−	0.202802i	0.801199	+	0.598397i	$0.204196\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$			0.226797i			0.00838839i
$732$		0			0
$733$	27.3113	−	27.3113i	1.00877	−	1.00877i	0.00880605	−	0.999961i	$-0.497197\pi$
$733$	27.3113	−	27.3113i	1.00877	−	1.00877i	0.999961	−	0.00880605i	$-0.00280309\pi$
$734$		0			0
$735$	14.0784	−	3.65084i	0.519291	−	0.134663i
$736$		0			0
$737$	12.1339	+	12.1339i	0.446958	+	0.446958i
$738$		0			0
$739$	−43.1910			−1.58881			−0.794404	−	0.607390i	$-0.792216\pi$
$739$	−43.1910			−1.58881			−0.794404	+	0.607390i	$0.792216\pi$
$740$		0			0
$741$	−4.85222			−0.178251
$742$		0			0
$743$	6.43997	+	6.43997i	0.236259	+	0.236259i	0.815299	−	0.579040i	$-0.196572\pi$
$743$	6.43997	+	6.43997i	0.236259	+	0.236259i	−0.579040	+	0.815299i	$0.696572\pi$
$744$		0			0
$745$	−4.88634	+	8.30788i	−0.179022	+	0.304377i
$746$		0			0
$747$	4.29163	−	4.29163i	0.157022	−	0.157022i
$748$		0			0
$749$		−	12.6041i		−	0.460542i
$750$		0			0
$751$		−	30.9736i		−	1.13024i	−0.825008	−	0.565120i	$-0.808830\pi$
$751$		−	30.9736i		−	1.13024i	0.825008	−	0.565120i	$-0.191170\pi$
$752$		0			0
$753$	4.17193	−	4.17193i	0.152034	−	0.152034i
$754$		0			0
$755$	11.2491	−	19.1259i	0.409395	−	0.696064i
$756$		0			0
$757$	0.745659	+	0.745659i	0.0271014	+	0.0271014i	0.720528	−	0.693426i	$-0.243900\pi$
$757$	0.745659	+	0.745659i	0.0271014	+	0.0271014i	−0.693426	+	0.720528i	$0.743900\pi$
$758$		0			0
$759$	−1.15686			−0.0419915
$760$		0			0
$761$	−16.8010			−0.609036			−0.304518	−	0.952507i	$-0.598495\pi$
$761$	−16.8010			−0.609036			−0.304518	+	0.952507i	$0.598495\pi$
$762$		0			0
$763$	−5.65864	−	5.65864i	−0.204857	−	0.204857i
$764$		0			0
$765$	0.135652	−	0.0351776i	0.00490453	−	0.00127185i
$766$		0			0
$767$	31.9609	−	31.9609i	1.15404	−	1.15404i
$768$		0			0
$769$		−	1.86682i		−	0.0673192i	−0.999433	−	0.0336596i	$-0.989284\pi$
$769$		−	1.86682i		−	0.0673192i	0.999433	−	0.0336596i	$-0.0107162\pi$
$770$		0			0
$771$			19.9531i			0.718592i
$772$		0			0
$773$	−27.1527	+	27.1527i	−0.976613	+	0.976613i	−0.999733	−	0.0231192i	$-0.992640\pi$
$773$	−27.1527	+	27.1527i	−0.976613	+	0.976613i	0.0231192	+	0.999733i	$0.492640\pi$
$774$		0			0
$775$	−8.84636	+	4.91888i	−0.317771	+	0.176691i
$776$		0			0
$777$	−0.732198	−	0.732198i	−0.0262674	−	0.0262674i
$778$		0			0
$779$	−1.64687			−0.0590053
$780$		0			0
$781$	12.4702			0.446217
$782$		0			0
$783$	7.28463	+	7.28463i	0.260332	+	0.260332i
$784$		0			0
$785$	−6.44049	−	24.8359i	−0.229871	−	0.886433i
$786$		0			0
$787$	−17.6728	+	17.6728i	−0.629968	+	0.629968i	−0.948060	−	0.318092i	$-0.896958\pi$
$787$	−17.6728	+	17.6728i	−0.629968	+	0.629968i	0.318092	+	0.948060i	$0.396958\pi$
$788$		0			0
$789$			0.165801i			0.00590268i
$790$		0			0
$791$		−	9.74636i		−	0.346541i
$792$		0			0
$793$	17.8887	−	17.8887i	0.635247	−	0.635247i
$794$		0			0
$795$	−1.52030	−	0.894176i	−0.0539195	−	0.0317132i
$796$		0			0
$797$	−13.2811	−	13.2811i	−0.470441	−	0.470441i	0.431616	−	0.902057i	$-0.357943\pi$
$797$	−13.2811	−	13.2811i	−0.470441	−	0.470441i	−0.902057	+	0.431616i	$0.857943\pi$
$798$		0			0
$799$	−0.358012			−0.0126655
$800$		0			0
$801$	1.94393			0.0686854
$802$		0			0
$803$	−3.74316	−	3.74316i	−0.132093	−	0.132093i
$804$		0			0
$805$	−1.21134	−	0.712460i	−0.0426942	−	0.0251109i
$806$		0			0
$807$	14.2874	−	14.2874i	0.502940	−	0.502940i
$808$		0			0
$809$			36.1968i			1.27261i	0.771437	+	0.636305i	$0.219538\pi$
$809$			36.1968i			1.27261i	−0.771437	+	0.636305i	$0.780462\pi$
$810$		0			0
$811$		−	17.7922i		−	0.624769i	−0.949956	−	0.312385i	$-0.898872\pi$
$811$		−	17.7922i		−	0.624769i	0.949956	−	0.312385i	$-0.101128\pi$
$812$		0			0
$813$	−5.85225	+	5.85225i	−0.205247	+	0.205247i
$814$		0			0
$815$	−9.96910	−	38.4430i	−0.349202	−	1.34660i
$816$		0			0
$817$	3.37263	+	3.37263i	0.117993	+	0.117993i
$818$		0			0
$819$	2.59191			0.0905686
$820$		0			0
$821$	2.81859			0.0983693			0.0491847	−	0.998790i	$-0.484338\pi$
$821$	2.81859			0.0983693			0.0491847	+	0.998790i	$0.484338\pi$
$822$		0			0
$823$	29.3448	+	29.3448i	1.02290	+	1.02290i	0.999732	+	0.0231652i	$0.00737438\pi$
$823$	29.3448	+	29.3448i	1.02290	+	1.02290i	0.0231652	+	0.999732i	$0.492626\pi$
$824$		0			0
$825$	−6.23111	−	1.77785i	−0.216939	−	0.0618968i
$826$		0			0
$827$	−34.5161	+	34.5161i	−1.20024	+	1.20024i	−0.226150	+	0.974093i	$0.572614\pi$
$827$	−34.5161	+	34.5161i	−1.20024	+	1.20024i	−0.974093	+	0.226150i	$0.927386\pi$
$828$		0			0
$829$			43.5050i			1.51099i	0.655153	+	0.755496i	$0.272604\pi$
$829$			43.5050i			1.51099i	−0.655153	+	0.755496i	$0.727396\pi$
$830$		0			0
$831$			18.6262i			0.646135i
$832$		0			0
$833$	0.288245	−	0.288245i	0.00998711	−	0.00998711i
$834$		0			0
$835$	−22.6625	+	5.87688i	−0.784270	+	0.203378i
$836$		0			0
$837$	1.43146	+	1.43146i	0.0494784	+	0.0494784i
$838$		0			0
$839$	26.7040			0.921924			0.460962	−	0.887420i	$-0.347504\pi$
$839$	26.7040			0.921924			0.460962	+	0.887420i	$0.347504\pi$
$840$		0			0
$841$	−77.1317			−2.65972
$842$		0			0
$843$	0.229165	+	0.229165i	0.00789286	+	0.00789286i
$844$		0			0
$845$	0.626996	−	1.06604i	0.0215693	−	0.0366727i
$846$		0			0
$847$	−4.64007	+	4.64007i	−0.159435	+	0.159435i
$848$		0			0
$849$		−	22.9777i		−	0.788593i
$850$		0			0
$851$		−	1.31291i		−	0.0450060i
$852$		0			0
$853$	−39.0644	+	39.0644i	−1.33754	+	1.33754i	−0.439101	+	0.898438i	$0.644703\pi$
$853$	−39.0644	+	39.0644i	−1.33754	+	1.33754i	−0.898438	+	0.439101i	$0.855297\pi$
$854$		0			0
$855$	1.49413	−	2.54036i	0.0510981	−	0.0868784i
$856$		0			0
$857$	−2.48615	−	2.48615i	−0.0849253	−	0.0849253i	0.663368	−	0.748293i	$-0.269126\pi$
$857$	−2.48615	−	2.48615i	−0.0849253	−	0.0849253i	−0.748293	+	0.663368i	$0.769126\pi$
$858$		0			0
$859$	5.23229			0.178524			0.0892618	−	0.996008i	$-0.471549\pi$
$859$	5.23229			0.178524			0.0892618	+	0.996008i	$0.471549\pi$
$860$		0			0
$861$	0.879709			0.0299804
$862$		0			0
$863$	3.69832	+	3.69832i	0.125892	+	0.125892i	0.767246	−	0.641353i	$-0.221627\pi$
$863$	3.69832	+	3.69832i	0.125892	+	0.125892i	−0.641353	+	0.767246i	$0.721627\pi$
$864$		0			0
$865$	1.03439	−	0.268240i	0.0351704	−	0.00912044i
$866$		0			0
$867$	−12.0180	+	12.0180i	−0.408154	+	0.408154i
$868$		0			0
$869$		−	18.0579i		−	0.612571i
$870$		0			0
$871$		−	48.7467i		−	1.65172i
$872$		0			0
$873$	−3.03479	+	3.03479i	−0.102712	+	0.102712i
$874$		0			0
$875$	−5.42965	−	5.69903i	−0.183556	−	0.192662i
$876$		0			0
$877$	6.11469	+	6.11469i	0.206478	+	0.206478i	0.802769	−	0.596290i	$-0.203359\pi$
$877$	6.11469	+	6.11469i	0.206478	+	0.206478i	−0.596290	+	0.802769i	$0.703359\pi$
$878$		0			0
$879$	−24.0395			−0.810834
$880$		0			0
$881$	50.1700			1.69027			0.845135	−	0.534553i	$-0.179520\pi$
$881$	50.1700			1.69027			0.845135	+	0.534553i	$0.179520\pi$
$882$		0			0
$883$	−15.9781	−	15.9781i	−0.537707	−	0.537707i	0.385148	−	0.922855i	$-0.374150\pi$
$883$	−15.9781	−	15.9781i	−0.537707	−	0.537707i	−0.922855	+	0.385148i	$0.874150\pi$
$884$		0			0
$885$	6.89137	+	26.5746i	0.231651	+	0.893297i
$886$		0			0
$887$	0.977167	−	0.977167i	0.0328100	−	0.0328100i	−0.690511	−	0.723321i	$-0.742614\pi$
$887$	0.977167	−	0.977167i	0.0328100	−	0.0328100i	0.723321	+	0.690511i	$0.242614\pi$
$888$		0			0
$889$			6.82172i			0.228793i
$890$		0			0
$891$			1.29595i			0.0434161i
$892$		0			0
$893$	−5.32387	+	5.32387i	−0.178157	+	0.178157i
$894$		0			0
$895$	31.4677	+	18.5079i	1.05185	+	0.618652i
$896$		0			0
$897$	2.32379	+	2.32379i	0.0775890	+	0.0775890i
$898$		0			0
$899$	−20.8553			−0.695563
$900$		0			0
$901$	−0.0494346			−0.00164691
$902$		0			0
$903$	−1.80156	−	1.80156i	−0.0599520	−	0.0599520i
$904$		0			0
$905$	39.9561	+	23.5005i	1.32819	+	0.781181i
$906$		0			0
$907$	15.4983	−	15.4983i	0.514612	−	0.514612i	−0.401324	−	0.915936i	$-0.631450\pi$
$907$	15.4983	−	15.4983i	0.514612	−	0.514612i	0.915936	+	0.401324i	$0.131450\pi$
$908$		0			0
$909$			13.1703i			0.436832i
$910$		0			0
$911$			5.09146i			0.168688i	0.996437	+	0.0843438i	$0.0268794\pi$
$911$			5.09146i			0.168688i	−0.996437	+	0.0843438i	$0.973121\pi$
$912$		0			0
$913$	−5.56175	+	5.56175i	−0.184067	+	0.184067i
$914$		0			0
$915$	3.85714	+	14.8740i	0.127513	+	0.491719i
$916$		0			0
$917$	−5.05596	−	5.05596i	−0.166962	−	0.166962i
$918$		0			0
$919$	5.20340			0.171644			0.0858221	−	0.996310i	$-0.472648\pi$
$919$	5.20340			0.171644			0.0858221	+	0.996310i	$0.472648\pi$
$920$		0			0
$921$	−12.9674			−0.427291
$922$		0			0
$923$	−25.0488	−	25.0488i	−0.824490	−	0.824490i
$924$		0			0
$925$	2.01766	−	7.07161i	0.0663403	−	0.232513i
$926$		0			0
$927$	−7.39051	+	7.39051i	−0.242736	+	0.242736i
$928$		0			0
$929$			31.5196i			1.03413i	0.855947	+	0.517063i	$0.172975\pi$
$929$			31.5196i			1.03413i	−0.855947	+	0.517063i	$0.827025\pi$
$930$		0			0
$931$		−	8.57280i		−	0.280962i
$932$		0			0
$933$	8.06647	−	8.06647i	0.264084	−	0.264084i
$934$		0			0
$935$	−0.175799	+	0.0455885i	−0.00574926	+	0.00149090i
$936$		0			0
$937$	−21.8065	−	21.8065i	−0.712387	−	0.712387i	0.254647	−	0.967034i	$-0.418041\pi$
$937$	−21.8065	−	21.8065i	−0.712387	−	0.712387i	−0.967034	+	0.254647i	$0.918041\pi$
$938$		0			0
$939$	−28.2463			−0.921782
$940$		0			0
$941$	−18.8633			−0.614925			−0.307463	−	0.951560i	$-0.599480\pi$
$941$	−18.8633			−0.614925			−0.307463	+	0.951560i	$0.599480\pi$
$942$		0			0
$943$	0.788707	+	0.788707i	0.0256838	+	0.0256838i
$944$		0			0
$945$	−0.798119	+	1.35698i	−0.0259628	+	0.0441427i
$946$		0			0
$947$	35.9995	−	35.9995i	1.16983	−	1.16983i	0.187577	−	0.982250i	$-0.439936\pi$
$947$	35.9995	−	35.9995i	1.16983	−	1.16983i	0.982250	−	0.187577i	$-0.0600635\pi$
$948$		0			0
$949$			15.0378i			0.488146i
$950$		0			0
$951$			15.7226i			0.509841i
$952$		0			0
$953$	−26.8455	+	26.8455i	−0.869609	+	0.869609i	−0.992429	−	0.122820i	$-0.960806\pi$
$953$	−26.8455	+	26.8455i	−0.869609	+	0.869609i	0.122820	+	0.992429i	$0.460806\pi$
$954$		0			0
$955$	−24.9034	+	42.3414i	−0.805854	+	1.37013i
$956$		0			0
$957$	−9.44055	−	9.44055i	−0.305170	−	0.305170i
$958$		0			0
$959$	7.05276			0.227746
$960$		0			0
$961$	26.9019			0.867802
$962$		0			0
$963$	−12.6589	−	12.6589i	−0.407926	−	0.407926i
$964$		0			0
$965$	−17.5947	+	4.56268i	−0.566394	+	0.146878i
$966$		0			0
$967$	−9.09081	+	9.09081i	−0.292341	+	0.292341i	−0.838004	−	0.545664i	$-0.816278\pi$
$967$	−9.09081	+	9.09081i	−0.292341	+	0.292341i	0.545664	+	0.838004i	$0.316278\pi$
$968$		0			0
$969$		−	0.0826031i		−	0.00265359i
$970$		0			0
$971$		−	0.336247i		−	0.0107907i	−0.999985	−	0.00539534i	$-0.998283\pi$
$971$		−	0.336247i		−	0.0107907i	0.999985	−	0.00539534i	$-0.00171740\pi$
$972$		0			0
$973$	−9.60127	+	9.60127i	−0.307803	+	0.307803i
$974$		0			0
$975$	8.94524	+	16.0876i	0.286477	+	0.515215i
$976$		0			0
$977$	14.3570	+	14.3570i	0.459322	+	0.459322i	0.898433	−	0.439111i	$-0.144706\pi$
$977$	14.3570	+	14.3570i	0.459322	+	0.459322i	−0.439111	+	0.898433i	$0.644706\pi$
$978$		0			0
$979$	−2.51925			−0.0805154
$980$		0			0
$981$	−11.3665			−0.362904
$982$		0			0
$983$	−33.3583	−	33.3583i	−1.06396	−	1.06396i	−0.997809	−	0.0661546i	$-0.978927\pi$
$983$	−33.3583	−	33.3583i	−1.06396	−	1.06396i	−0.0661546	−	0.997809i	$-0.521073\pi$
$984$		0			0
$985$	6.41268	+	24.7287i	0.204325	+	0.787922i
$986$		0			0
$987$	2.84385	−	2.84385i	0.0905209	−	0.0905209i
$988$		0			0
$989$		−	3.23039i		−	0.102720i
$990$		0			0
$991$		−	17.9160i		−	0.569119i	−0.958658	−	0.284560i	$-0.908153\pi$
$991$		−	17.9160i		−	0.569119i	0.958658	−	0.284560i	$-0.0918474\pi$
$992$		0			0
$993$	−17.8867	+	17.8867i	−0.567618	+	0.567618i
$994$		0			0
$995$	−15.3238	−	9.01280i	−0.485797	−	0.285725i
$996$		0			0
$997$	36.7719	+	36.7719i	1.16458	+	1.16458i	0.983462	+	0.181116i	$0.0579708\pi$
$997$	36.7719	+	36.7719i	1.16458	+	1.16458i	0.181116	+	0.983462i	$0.442029\pi$
$998$		0			0
$999$	−1.47076			−0.0465329

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1920.2.w.i.127.3	✓	12
4.3	odd	2		1920.2.w.j.127.6	yes	12
5.3	odd	4		1920.2.w.j.1663.6	yes	12
8.3	odd	2		1920.2.w.l.127.1	yes	12
8.5	even	2		1920.2.w.k.127.4	yes	12
20.3	even	4	inner	1920.2.w.i.1663.3	yes	12
40.3	even	4		1920.2.w.k.1663.4	yes	12
40.13	odd	4		1920.2.w.l.1663.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1920.2.w.i.127.3	✓	12	1.1	even	1	trivial
1920.2.w.i.1663.3	yes	12	20.3	even	4	inner
1920.2.w.j.127.6	yes	12	4.3	odd	2
1920.2.w.j.1663.6	yes	12	5.3	odd	4
1920.2.w.k.127.4	yes	12	8.5	even	2
1920.2.w.k.1663.4	yes	12	40.3	even	4
1920.2.w.l.127.1	yes	12	8.3	odd	2
1920.2.w.l.1663.1	yes	12	40.13	odd	4

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:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1920.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{3} +(1.92741 + 1.13362i) q^{5} +(-0.497835 + 0.497835i) q^{7} +1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{3} +(1.92741 + 1.13362i) q^{5} +(-0.497835 + 0.497835i) q^{7} +1.00000i q^{9} -1.29595i q^{11} +(-2.60318 + 2.60318i) q^{13} +(-0.561294 - 2.16447i) q^{15} +(-0.0443160 - 0.0443160i) q^{17} -1.31802 q^{19} +0.704045 q^{21} +(0.631215 + 0.631215i) q^{23} +(2.42981 + 4.36990i) q^{25} +(0.707107 - 0.707107i) q^{27} +10.3020i q^{29} +2.02439i q^{31} +(-0.916378 + 0.916378i) q^{33} +(-1.52389 + 0.395177i) q^{35} +(-1.03999 - 1.03999i) q^{37} +3.68145 q^{39} +1.24951 q^{41} +(-2.55886 - 2.55886i) q^{43} +(-1.13362 + 1.92741i) q^{45} +(4.03931 - 4.03931i) q^{47} +6.50432i q^{49} +0.0626722i q^{51} +(0.557751 - 0.557751i) q^{53} +(1.46912 - 2.49784i) q^{55} +(0.931979 + 0.931979i) q^{57} -12.2776 q^{59} -6.87187 q^{61} +(-0.497835 - 0.497835i) q^{63} +(-7.96841 + 2.06638i) q^{65} +(-9.36291 + 9.36291i) q^{67} -0.892673i q^{69} +9.62237i q^{71} +(2.88834 - 2.88834i) q^{73} +(1.37185 - 4.80812i) q^{75} +(0.645172 + 0.645172i) q^{77} +13.9340 q^{79} -1.00000 q^{81} +(-4.29163 - 4.29163i) q^{83} +(-0.0351776 - 0.135652i) q^{85} +(7.28463 - 7.28463i) q^{87} -1.94393i q^{89} -2.59191i q^{91} +(1.43146 - 1.43146i) q^{93} +(-2.54036 - 1.49413i) q^{95} +(3.03479 + 3.03479i) q^{97} +1.29595 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q+O(q^{10}) \) 12 * q	\( 12 q - 4 q^{13} - 4 q^{15} - 20 q^{17} + 8 q^{19} + 8 q^{21} - 4 q^{25} + 8 q^{35} - 20 q^{37} - 8 q^{39} + 16 q^{41} + 16 q^{43} + 4 q^{45} + 40 q^{47} + 4 q^{53} - 24 q^{55} - 16 q^{57} + 16 q^{61} - 12 q^{65} - 8 q^{67} + 4 q^{73} + 16 q^{75} - 48 q^{77} - 16 q^{79} - 12 q^{81} - 40 q^{83} - 28 q^{85} + 8 q^{87} + 16 q^{93} - 72 q^{95} - 52 q^{97} + 16 q^{99}+O(q^{100}) \) 12 * q - 4 * q^13 - 4 * q^15 - 20 * q^17 + 8 * q^19 + 8 * q^21 - 4 * q^25 + 8 * q^35 - 20 * q^37 - 8 * q^39 + 16 * q^41 + 16 * q^43 + 4 * q^45 + 40 * q^47 + 4 * q^53 - 24 * q^55 - 16 * q^57 + 16 * q^61 - 12 * q^65 - 8 * q^67 + 4 * q^73 + 16 * q^75 - 48 * q^77 - 16 * q^79 - 12 * q^81 - 40 * q^83 - 28 * q^85 + 8 * q^87 + 16 * q^93 - 72 * q^95 - 52 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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