LMFDB - Embedded newform 960.2.v.c.257.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [960,2,Mod(257,960)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("960.257"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(960, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.v (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-4,0,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.66563859404$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			257.1
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	960.257
Dual form			960.2.v.c.833.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.70711 + 0.292893i) q^{3} +(0.707107 - 2.12132i) q^{5} +(1.00000 + 1.00000i) q^{7} +(2.82843 - 1.00000i) q^{9} -1.41421i q^{11} +(-0.585786 + 3.82843i) q^{15} +(1.41421 - 1.41421i) q^{17} +4.00000i q^{19} +(-2.00000 - 1.41421i) q^{21} +(-2.82843 - 2.82843i) q^{23} +(-4.00000 - 3.00000i) q^{25} +(-4.53553 + 2.53553i) q^{27} +7.07107 q^{29} +2.00000 q^{31} +(0.414214 + 2.41421i) q^{33} +(2.82843 - 1.41421i) q^{35} +(-6.00000 - 6.00000i) q^{37} -5.65685i q^{41} +(6.00000 - 6.00000i) q^{43} +(-0.121320 - 6.70711i) q^{45} -5.00000i q^{49} +(-2.00000 + 2.82843i) q^{51} +(2.82843 + 2.82843i) q^{53} +(-3.00000 - 1.00000i) q^{55} +(-1.17157 - 6.82843i) q^{57} +9.89949 q^{59} +6.00000 q^{61} +(3.82843 + 1.82843i) q^{63} +(-4.00000 - 4.00000i) q^{67} +(5.65685 + 4.00000i) q^{69} -14.1421i q^{71} +(-5.00000 + 5.00000i) q^{73} +(7.70711 + 3.94975i) q^{75} +(1.41421 - 1.41421i) q^{77} -6.00000i q^{79} +(7.00000 - 5.65685i) q^{81} +(-8.48528 - 8.48528i) q^{83} +(-2.00000 - 4.00000i) q^{85} +(-12.0711 + 2.07107i) q^{87} +2.82843 q^{89} +(-3.41421 + 0.585786i) q^{93} +(8.48528 + 2.82843i) q^{95} +(3.00000 + 3.00000i) q^{97} +(-1.41421 - 4.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} + 4 q^{7} - 8 q^{15} - 8 q^{21} - 16 q^{25} - 4 q^{27} + 8 q^{31} - 4 q^{33} - 24 q^{37} + 24 q^{43} + 8 q^{45} - 8 q^{51} - 12 q^{55} - 16 q^{57} + 24 q^{61} + 4 q^{63} - 16 q^{67} - 20 q^{73}+ \cdots + 12 q^{97}+O(q^{100}) $ 4 * q - 4 * q^3 + 4 * q^7 - 8 * q^15 - 8 * q^21 - 16 * q^25 - 4 * q^27 + 8 * q^31 - 4 * q^33 - 24 * q^37 + 24 * q^43 + 8 * q^45 - 8 * q^51 - 12 * q^55 - 16 * q^57 + 24 * q^61 + 4 * q^63 - 16 * q^67 - 20 * q^73 + 28 * q^75 + 28 * q^81 - 8 * q^85 - 20 * q^87 - 8 * q^93 + 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.70711	+	0.292893i	−0.985599	+	0.169102i
$3$	−1.70711	+	0.292893i	−0.985599	+	0.169102i
$4$		0			0
$5$	0.707107	−	2.12132i	0.316228	−	0.948683i
$5$	0.707107	−	2.12132i	0.316228	−	0.948683i
$6$		0			0
$7$	1.00000	+	1.00000i	0.377964	+	0.377964i	0.870367	−	0.492403i	$-0.163881\pi$
$7$	1.00000	+	1.00000i	0.377964	+	0.377964i	−0.492403	+	0.870367i	$0.663881\pi$
$8$		0			0
$9$	2.82843	−	1.00000i	0.942809	−	0.333333i
$10$		0			0
$11$		−	1.41421i		−	0.426401i	−0.977008	−	0.213201i	$-0.931611\pi$
$11$		−	1.41421i		−	0.426401i	0.977008	−	0.213201i	$-0.0683888\pi$
$12$		0			0
$13$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$13$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$14$		0			0
$15$	−0.585786	+	3.82843i	−0.151249	+	0.988496i
$16$		0			0
$17$	1.41421	−	1.41421i	0.342997	−	0.342997i	−0.514496	−	0.857493i	$-0.672021\pi$
$17$	1.41421	−	1.41421i	0.342997	−	0.342997i	0.857493	+	0.514496i	$0.172021\pi$
$18$		0			0
$19$			4.00000i			0.917663i	0.888523	+	0.458831i	$0.151732\pi$
$19$			4.00000i			0.917663i	−0.888523	+	0.458831i	$0.848268\pi$
$20$		0			0
$21$	−2.00000	−	1.41421i	−0.436436	−	0.308607i
$22$		0			0
$23$	−2.82843	−	2.82843i	−0.589768	−	0.589768i	0.347801	−	0.937568i	$-0.386929\pi$
$23$	−2.82843	−	2.82843i	−0.589768	−	0.589768i	−0.937568	+	0.347801i	$0.886929\pi$
$24$		0			0
$25$	−4.00000	−	3.00000i	−0.800000	−	0.600000i
$26$		0			0
$27$	−4.53553	+	2.53553i	−0.872864	+	0.487964i
$28$		0			0
$29$	7.07107			1.31306			0.656532	−	0.754298i	$-0.272023\pi$
$29$	7.07107			1.31306			0.656532	+	0.754298i	$0.272023\pi$
$30$		0			0
$31$	2.00000			0.359211			0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000			0.359211			0.179605	+	0.983739i	$0.442518\pi$
$32$		0			0
$33$	0.414214	+	2.41421i	0.0721053	+	0.420261i
$34$		0			0
$35$	2.82843	−	1.41421i	0.478091	−	0.239046i
$36$		0			0
$37$	−6.00000	−	6.00000i	−0.986394	−	0.986394i	0.0135147	−	0.999909i	$-0.495698\pi$
$37$	−6.00000	−	6.00000i	−0.986394	−	0.986394i	−0.999909	+	0.0135147i	$0.995698\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		−	5.65685i		−	0.883452i	−0.897150	−	0.441726i	$-0.854366\pi$
$41$		−	5.65685i		−	0.883452i	0.897150	−	0.441726i	$-0.145634\pi$
$42$		0			0
$43$	6.00000	−	6.00000i	0.914991	−	0.914991i	−0.0816682	−	0.996660i	$-0.526025\pi$
$43$	6.00000	−	6.00000i	0.914991	−	0.914991i	0.996660	+	0.0816682i	$0.0260248\pi$
$44$		0			0
$45$	−0.121320	−	6.70711i	−0.0180854	−	0.999836i
$46$		0			0
$47$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$47$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$48$		0			0
$49$		−	5.00000i		−	0.714286i
$50$		0			0
$51$	−2.00000	+	2.82843i	−0.280056	+	0.396059i
$52$		0			0
$53$	2.82843	+	2.82843i	0.388514	+	0.388514i	0.874157	−	0.485643i	$-0.161414\pi$
$53$	2.82843	+	2.82843i	0.388514	+	0.388514i	−0.485643	+	0.874157i	$0.661414\pi$
$54$		0			0
$55$	−3.00000	−	1.00000i	−0.404520	−	0.134840i
$56$		0			0
$57$	−1.17157	−	6.82843i	−0.155179	−	0.904447i
$58$		0			0
$59$	9.89949			1.28880			0.644402	−	0.764687i	$-0.277106\pi$
$59$	9.89949			1.28880			0.644402	+	0.764687i	$0.277106\pi$
$60$		0			0
$61$	6.00000			0.768221			0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000			0.768221			0.384111	+	0.923287i	$0.374508\pi$
$62$		0			0
$63$	3.82843	+	1.82843i	0.482336	+	0.230360i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−4.00000	−	4.00000i	−0.488678	−	0.488678i	0.419211	−	0.907889i	$-0.362307\pi$
$67$	−4.00000	−	4.00000i	−0.488678	−	0.488678i	−0.907889	+	0.419211i	$0.862307\pi$
$68$		0			0
$69$	5.65685	+	4.00000i	0.681005	+	0.481543i
$70$		0			0
$71$		−	14.1421i		−	1.67836i	−0.543852	−	0.839181i	$-0.683035\pi$
$71$		−	14.1421i		−	1.67836i	0.543852	−	0.839181i	$-0.316965\pi$
$72$		0			0
$73$	−5.00000	+	5.00000i	−0.585206	+	0.585206i	−0.936329	−	0.351123i	$-0.885800\pi$
$73$	−5.00000	+	5.00000i	−0.585206	+	0.585206i	0.351123	+	0.936329i	$0.385800\pi$
$74$		0			0
$75$	7.70711	+	3.94975i	0.889940	+	0.456078i
$76$		0			0
$77$	1.41421	−	1.41421i	0.161165	−	0.161165i
$78$		0			0
$79$		−	6.00000i		−	0.675053i	−0.941316	−	0.337526i	$-0.890410\pi$
$79$		−	6.00000i		−	0.675053i	0.941316	−	0.337526i	$-0.109590\pi$
$80$		0			0
$81$	7.00000	−	5.65685i	0.777778	−	0.628539i
$82$		0			0
$83$	−8.48528	−	8.48528i	−0.931381	−	0.931381i	0.0664117	−	0.997792i	$-0.478845\pi$
$83$	−8.48528	−	8.48528i	−0.931381	−	0.931381i	−0.997792	+	0.0664117i	$0.978845\pi$
$84$		0			0
$85$	−2.00000	−	4.00000i	−0.216930	−	0.433861i
$86$		0			0
$87$	−12.0711	+	2.07107i	−1.29415	+	0.222042i
$88$		0			0
$89$	2.82843			0.299813			0.149906	−	0.988700i	$-0.452103\pi$
$89$	2.82843			0.299813			0.149906	+	0.988700i	$0.452103\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−3.41421	+	0.585786i	−0.354037	+	0.0607432i
$94$		0			0
$95$	8.48528	+	2.82843i	0.870572	+	0.290191i
$96$		0			0
$97$	3.00000	+	3.00000i	0.304604	+	0.304604i	0.842812	−	0.538208i	$-0.180899\pi$
$97$	3.00000	+	3.00000i	0.304604	+	0.304604i	−0.538208	+	0.842812i	$0.680899\pi$
$98$		0			0
$99$	−1.41421	−	4.00000i	−0.142134	−	0.402015i
$100$		0			0
$101$		−	9.89949i		−	0.985037i	−0.870302	−	0.492518i	$-0.836076\pi$
$101$		−	9.89949i		−	0.985037i	0.870302	−	0.492518i	$-0.163924\pi$
$102$		0			0
$103$	−1.00000	+	1.00000i	−0.0985329	+	0.0985329i	−0.754655	−	0.656122i	$-0.772196\pi$
$103$	−1.00000	+	1.00000i	−0.0985329	+	0.0985329i	0.656122	+	0.754655i	$0.272196\pi$
$104$		0			0
$105$	−4.41421	+	3.24264i	−0.430783	+	0.316449i
$106$		0			0
$107$	−2.82843	+	2.82843i	−0.273434	+	0.273434i	−0.830481	−	0.557047i	$-0.811934\pi$
$107$	−2.82843	+	2.82843i	−0.273434	+	0.273434i	0.557047	+	0.830481i	$0.311934\pi$
$108$		0			0
$109$			10.0000i			0.957826i	0.877862	+	0.478913i	$0.158969\pi$
$109$			10.0000i			0.957826i	−0.877862	+	0.478913i	$0.841031\pi$
$110$		0			0
$111$	12.0000	+	8.48528i	1.13899	+	0.805387i
$112$		0			0
$113$	9.89949	+	9.89949i	0.931266	+	0.931266i	0.997785	−	0.0665190i	$-0.0211893\pi$
$113$	9.89949	+	9.89949i	0.931266	+	0.931266i	−0.0665190	+	0.997785i	$0.521189\pi$
$114$		0			0
$115$	−8.00000	+	4.00000i	−0.746004	+	0.373002i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	2.82843			0.259281
$120$		0			0
$121$	9.00000			0.818182
$122$		0			0
$123$	1.65685	+	9.65685i	0.149394	+	0.870729i
$124$		0			0
$125$	−9.19239	+	6.36396i	−0.822192	+	0.569210i
$126$		0			0
$127$	7.00000	+	7.00000i	0.621150	+	0.621150i	0.945825	−	0.324676i	$-0.105255\pi$
$127$	7.00000	+	7.00000i	0.621150	+	0.621150i	−0.324676	+	0.945825i	$0.605255\pi$
$128$		0			0
$129$	−8.48528	+	12.0000i	−0.747087	+	1.05654i
$130$		0			0
$131$		−	18.3848i		−	1.60629i	−0.595787	−	0.803143i	$-0.703160\pi$
$131$		−	18.3848i		−	1.60629i	0.595787	−	0.803143i	$-0.296840\pi$
$132$		0			0
$133$	−4.00000	+	4.00000i	−0.346844	+	0.346844i
$134$		0			0
$135$	2.17157	+	11.4142i	0.186899	+	0.982379i
$136$		0			0
$137$	−4.24264	+	4.24264i	−0.362473	+	0.362473i	−0.864723	−	0.502249i	$-0.832506\pi$
$137$	−4.24264	+	4.24264i	−0.362473	+	0.362473i	0.502249	+	0.864723i	$0.332506\pi$
$138$		0			0
$139$			8.00000i			0.678551i	0.940687	+	0.339276i	$0.110182\pi$
$139$			8.00000i			0.678551i	−0.940687	+	0.339276i	$0.889818\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$		0			0
$145$	5.00000	−	15.0000i	0.415227	−	1.24568i
$146$		0			0
$147$	1.46447	+	8.53553i	0.120787	+	0.703999i
$148$		0			0
$149$	−12.7279			−1.04271			−0.521356	−	0.853339i	$-0.674574\pi$
$149$	−12.7279			−1.04271			−0.521356	+	0.853339i	$0.674574\pi$
$150$		0			0
$151$	−16.0000			−1.30206			−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000			−1.30206			−0.651031	+	0.759051i	$0.725663\pi$
$152$		0			0
$153$	2.58579	−	5.41421i	0.209048	−	0.437713i
$154$		0			0
$155$	1.41421	−	4.24264i	0.113592	−	0.340777i
$156$		0			0
$157$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$157$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$158$		0			0
$159$	−5.65685	−	4.00000i	−0.448618	−	0.317221i
$160$		0			0
$161$		−	5.65685i		−	0.445823i
$162$		0			0
$163$	−4.00000	+	4.00000i	−0.313304	+	0.313304i	−0.846188	−	0.532884i	$-0.821108\pi$
$163$	−4.00000	+	4.00000i	−0.313304	+	0.313304i	0.532884	+	0.846188i	$0.321108\pi$
$164$		0			0
$165$	5.41421	+	0.828427i	0.421496	+	0.0644930i
$166$		0			0
$167$	5.65685	−	5.65685i	0.437741	−	0.437741i	−0.453510	−	0.891251i	$-0.649829\pi$
$167$	5.65685	−	5.65685i	0.437741	−	0.437741i	0.891251	+	0.453510i	$0.149829\pi$
$168$		0			0
$169$			13.0000i			1.00000i
$170$		0			0
$171$	4.00000	+	11.3137i	0.305888	+	0.865181i
$172$		0			0
$173$	1.41421	+	1.41421i	0.107521	+	0.107521i	0.758820	−	0.651300i	$-0.225776\pi$
$173$	1.41421	+	1.41421i	0.107521	+	0.107521i	−0.651300	+	0.758820i	$0.725776\pi$
$174$		0			0
$175$	−1.00000	−	7.00000i	−0.0755929	−	0.529150i
$176$		0			0
$177$	−16.8995	+	2.89949i	−1.27024	+	0.217939i
$178$		0			0
$179$	−18.3848			−1.37414			−0.687071	−	0.726590i	$-0.741104\pi$
$179$	−18.3848			−1.37414			−0.687071	+	0.726590i	$0.741104\pi$
$180$		0			0
$181$	22.0000			1.63525			0.817624	−	0.575753i	$-0.195291\pi$
$181$	22.0000			1.63525			0.817624	+	0.575753i	$0.195291\pi$
$182$		0			0
$183$	−10.2426	+	1.75736i	−0.757158	+	0.129908i
$184$		0			0
$185$	−16.9706	+	8.48528i	−1.24770	+	0.623850i
$186$		0			0
$187$	−2.00000	−	2.00000i	−0.146254	−	0.146254i
$188$		0			0
$189$	−7.07107	−	2.00000i	−0.514344	−	0.145479i
$190$		0			0
$191$			2.82843i			0.204658i	0.994751	+	0.102329i	$0.0326294\pi$
$191$			2.82843i			0.204658i	−0.994751	+	0.102329i	$0.967371\pi$
$192$		0			0
$193$	−15.0000	+	15.0000i	−1.07972	+	1.07972i	−0.0831899	+	0.996534i	$0.526511\pi$
$193$	−15.0000	+	15.0000i	−1.07972	+	1.07972i	−0.996534	+	0.0831899i	$0.973489\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−16.9706	+	16.9706i	−1.20910	+	1.20910i	−0.237785	+	0.971318i	$0.576421\pi$
$197$	−16.9706	+	16.9706i	−1.20910	+	1.20910i	−0.971318	+	0.237785i	$0.923579\pi$
$198$		0			0
$199$			24.0000i			1.70131i	0.525720	+	0.850657i	$0.323796\pi$
$199$			24.0000i			1.70131i	−0.525720	+	0.850657i	$0.676204\pi$
$200$		0			0
$201$	8.00000	+	5.65685i	0.564276	+	0.399004i
$202$		0			0
$203$	7.07107	+	7.07107i	0.496292	+	0.496292i
$204$		0			0
$205$	−12.0000	−	4.00000i	−0.838116	−	0.279372i
$206$		0			0
$207$	−10.8284	−	5.17157i	−0.752628	−	0.359449i
$208$		0			0
$209$	5.65685			0.391293
$210$		0			0
$211$	8.00000			0.550743			0.275371	−	0.961338i	$-0.411199\pi$
$211$	8.00000			0.550743			0.275371	+	0.961338i	$0.411199\pi$
$212$		0			0
$213$	4.14214	+	24.1421i	0.283814	+	1.65419i
$214$		0			0
$215$	−8.48528	−	16.9706i	−0.578691	−	1.15738i
$216$		0			0
$217$	2.00000	+	2.00000i	0.135769	+	0.135769i
$218$		0			0
$219$	7.07107	−	10.0000i	0.477818	−	0.675737i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	9.00000	−	9.00000i	0.602685	−	0.602685i	−0.338340	−	0.941024i	$-0.609865\pi$
$223$	9.00000	−	9.00000i	0.602685	−	0.602685i	0.941024	+	0.338340i	$0.109865\pi$
$224$		0			0
$225$	−14.3137	−	4.48528i	−0.954247	−	0.299019i
$226$		0			0
$227$	15.5563	−	15.5563i	1.03251	−	1.03251i	0.0330577	−	0.999453i	$-0.489475\pi$
$227$	15.5563	−	15.5563i	1.03251	−	1.03251i	0.999453	−	0.0330577i	$-0.0105245\pi$
$228$		0			0
$229$			6.00000i			0.396491i	0.980152	+	0.198246i	$0.0635244\pi$
$229$			6.00000i			0.396491i	−0.980152	+	0.198246i	$0.936476\pi$
$230$		0			0
$231$	−2.00000	+	2.82843i	−0.131590	+	0.186097i
$232$		0			0
$233$	−12.7279	−	12.7279i	−0.833834	−	0.833834i	0.154205	−	0.988039i	$-0.450718\pi$
$233$	−12.7279	−	12.7279i	−0.833834	−	0.833834i	−0.988039	+	0.154205i	$0.950718\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	1.75736	+	10.2426i	0.114153	+	0.665331i
$238$		0			0
$239$	8.48528			0.548867			0.274434	−	0.961606i	$-0.411510\pi$
$239$	8.48528			0.548867			0.274434	+	0.961606i	$0.411510\pi$
$240$		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
$243$	−10.2929	+	11.7071i	−0.660289	+	0.751011i
$244$		0			0
$245$	−10.6066	−	3.53553i	−0.677631	−	0.225877i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	16.9706	+	12.0000i	1.07547	+	0.760469i
$250$		0			0
$251$			12.7279i			0.803379i	0.915776	+	0.401690i	$0.131577\pi$
$251$			12.7279i			0.803379i	−0.915776	+	0.401690i	$0.868423\pi$
$252$		0			0
$253$	−4.00000	+	4.00000i	−0.251478	+	0.251478i
$254$		0			0
$255$	4.58579	+	6.24264i	0.287173	+	0.390929i
$256$		0			0
$257$	−9.89949	+	9.89949i	−0.617514	+	0.617514i	−0.944893	−	0.327379i	$-0.893834\pi$
$257$	−9.89949	+	9.89949i	−0.617514	+	0.617514i	0.327379	+	0.944893i	$0.393834\pi$
$258$		0			0
$259$		−	12.0000i		−	0.745644i
$260$		0			0
$261$	20.0000	−	7.07107i	1.23797	−	0.437688i
$262$		0			0
$263$	−5.65685	−	5.65685i	−0.348817	−	0.348817i	0.510852	−	0.859669i	$-0.329330\pi$
$263$	−5.65685	−	5.65685i	−0.348817	−	0.348817i	−0.859669	+	0.510852i	$0.829330\pi$
$264$		0			0
$265$	8.00000	−	4.00000i	0.491436	−	0.245718i
$266$		0			0
$267$	−4.82843	+	0.828427i	−0.295495	+	0.0506989i
$268$		0			0
$269$	15.5563			0.948487			0.474244	−	0.880394i	$-0.342722\pi$
$269$	15.5563			0.948487			0.474244	+	0.880394i	$0.342722\pi$
$270$		0			0
$271$		0			0			−	1.00000i	$-0.5\pi$
$271$		0			0				1.00000i	$0.5\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−4.24264	+	5.65685i	−0.255841	+	0.341121i
$276$		0			0
$277$	6.00000	+	6.00000i	0.360505	+	0.360505i	0.863999	−	0.503494i	$-0.167952\pi$
$277$	6.00000	+	6.00000i	0.360505	+	0.360505i	−0.503494	+	0.863999i	$0.667952\pi$
$278$		0			0
$279$	5.65685	−	2.00000i	0.338667	−	0.119737i
$280$		0			0
$281$			8.48528i			0.506189i	0.967442	+	0.253095i	$0.0814484\pi$
$281$			8.48528i			0.506189i	−0.967442	+	0.253095i	$0.918552\pi$
$282$		0			0
$283$	20.0000	−	20.0000i	1.18888	−	1.18888i	0.211498	−	0.977378i	$-0.432166\pi$
$283$	20.0000	−	20.0000i	1.18888	−	1.18888i	0.977378	−	0.211498i	$-0.0678343\pi$
$284$		0			0
$285$	−15.3137	−	2.34315i	−0.907106	−	0.138796i
$286$		0			0
$287$	5.65685	−	5.65685i	0.333914	−	0.333914i
$288$		0			0
$289$			13.0000i			0.764706i
$290$		0			0
$291$	−6.00000	−	4.24264i	−0.351726	−	0.248708i
$292$		0			0
$293$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$293$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$294$		0			0
$295$	7.00000	−	21.0000i	0.407556	−	1.22267i
$296$		0			0
$297$	3.58579	+	6.41421i	0.208068	+	0.372190i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	12.0000			0.691669
$302$		0			0
$303$	2.89949	+	16.8995i	0.166572	+	0.970851i
$304$		0			0
$305$	4.24264	−	12.7279i	0.242933	−	0.728799i
$306$		0			0
$307$	18.0000	+	18.0000i	1.02731	+	1.02731i	0.999616	+	0.0276979i	$0.00881765\pi$
$307$	18.0000	+	18.0000i	1.02731	+	1.02731i	0.0276979	+	0.999616i	$0.491182\pi$
$308$		0			0
$309$	1.41421	−	2.00000i	0.0804518	−	0.113776i
$310$		0			0
$311$			19.7990i			1.12270i	0.827579	+	0.561349i	$0.189717\pi$
$311$			19.7990i			1.12270i	−0.827579	+	0.561349i	$0.810283\pi$
$312$		0			0
$313$	9.00000	−	9.00000i	0.508710	−	0.508710i	−0.405420	−	0.914130i	$-0.632875\pi$
$313$	9.00000	−	9.00000i	0.508710	−	0.508710i	0.914130	+	0.405420i	$0.132875\pi$
$314$		0			0
$315$	6.58579	−	6.82843i	0.371067	−	0.384738i
$316$		0			0
$317$	12.7279	−	12.7279i	0.714871	−	0.714871i	−0.252679	−	0.967550i	$-0.581312\pi$
$317$	12.7279	−	12.7279i	0.714871	−	0.714871i	0.967550	+	0.252679i	$0.0813116\pi$
$318$		0			0
$319$		−	10.0000i		−	0.559893i
$320$		0			0
$321$	4.00000	−	5.65685i	0.223258	−	0.315735i
$322$		0			0
$323$	5.65685	+	5.65685i	0.314756	+	0.314756i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−2.92893	−	17.0711i	−0.161970	−	0.944032i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−8.00000			−0.439720			−0.219860	−	0.975531i	$-0.570560\pi$
$331$	−8.00000			−0.439720			−0.219860	+	0.975531i	$0.570560\pi$
$332$		0			0
$333$	−22.9706	−	10.9706i	−1.25878	−	0.601183i
$334$		0			0
$335$	−11.3137	+	5.65685i	−0.618134	+	0.309067i
$336$		0			0
$337$	−9.00000	−	9.00000i	−0.490261	−	0.490261i	0.418127	−	0.908388i	$-0.362687\pi$
$337$	−9.00000	−	9.00000i	−0.490261	−	0.490261i	−0.908388	+	0.418127i	$0.862687\pi$
$338$		0			0
$339$	−19.7990	−	14.0000i	−1.07533	−	0.760376i
$340$		0			0
$341$		−	2.82843i		−	0.153168i
$342$		0			0
$343$	12.0000	−	12.0000i	0.647939	−	0.647939i
$344$		0			0
$345$	12.4853	−	9.17157i	0.672185	−	0.493781i
$346$		0			0
$347$	9.89949	−	9.89949i	0.531433	−	0.531433i	−0.389566	−	0.920999i	$-0.627375\pi$
$347$	9.89949	−	9.89949i	0.531433	−	0.531433i	0.920999	+	0.389566i	$0.127375\pi$
$348$		0			0
$349$			2.00000i			0.107058i	0.998566	+	0.0535288i	$0.0170469\pi$
$349$			2.00000i			0.107058i	−0.998566	+	0.0535288i	$0.982953\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	12.7279	+	12.7279i	0.677439	+	0.677439i	0.959420	−	0.281981i	$-0.0909915\pi$
$353$	12.7279	+	12.7279i	0.677439	+	0.677439i	−0.281981	+	0.959420i	$0.590992\pi$
$354$		0			0
$355$	−30.0000	−	10.0000i	−1.59223	−	0.530745i
$356$		0			0
$357$	−4.82843	+	0.828427i	−0.255547	+	0.0438450i
$358$		0			0
$359$	−11.3137			−0.597115			−0.298557	−	0.954392i	$-0.596505\pi$
$359$	−11.3137			−0.597115			−0.298557	+	0.954392i	$0.596505\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$		0			0
$363$	−15.3640	+	2.63604i	−0.806399	+	0.138356i
$364$		0			0
$365$	7.07107	+	14.1421i	0.370117	+	0.740233i
$366$		0			0
$367$	19.0000	+	19.0000i	0.991792	+	0.991792i	0.999967	−	0.00817466i	$-0.00260210\pi$
$367$	19.0000	+	19.0000i	0.991792	+	0.991792i	−0.00817466	+	0.999967i	$0.502602\pi$
$368$		0			0
$369$	−5.65685	−	16.0000i	−0.294484	−	0.832927i
$370$		0			0
$371$			5.65685i			0.293689i
$372$		0			0
$373$	−4.00000	+	4.00000i	−0.207112	+	0.207112i	−0.803039	−	0.595927i	$-0.796785\pi$
$373$	−4.00000	+	4.00000i	−0.207112	+	0.207112i	0.595927	+	0.803039i	$0.296785\pi$
$374$		0			0
$375$	13.8284	−	13.5563i	0.714097	−	0.700047i
$376$		0			0
$377$		0			0
$378$		0			0
$379$			16.0000i			0.821865i	0.911666	+	0.410932i	$0.134797\pi$
$379$			16.0000i			0.821865i	−0.911666	+	0.410932i	$0.865203\pi$
$380$		0			0
$381$	−14.0000	−	9.89949i	−0.717242	−	0.507166i
$382$		0			0
$383$	16.9706	+	16.9706i	0.867155	+	0.867155i	0.992157	−	0.125001i	$-0.0398935\pi$
$383$	16.9706	+	16.9706i	0.867155	+	0.867155i	−0.125001	+	0.992157i	$0.539894\pi$
$384$		0			0
$385$	−2.00000	−	4.00000i	−0.101929	−	0.203859i
$386$		0			0
$387$	10.9706	−	22.9706i	0.557665	−	1.16766i
$388$		0			0
$389$	−4.24264			−0.215110			−0.107555	−	0.994199i	$-0.534302\pi$
$389$	−4.24264			−0.215110			−0.107555	+	0.994199i	$0.534302\pi$
$390$		0			0
$391$	−8.00000			−0.404577
$392$		0			0
$393$	5.38478	+	31.3848i	0.271626	+	1.58315i
$394$		0			0
$395$	−12.7279	−	4.24264i	−0.640411	−	0.213470i
$396$		0			0
$397$	−22.0000	−	22.0000i	−1.10415	−	1.10415i	−0.993905	−	0.110244i	$-0.964837\pi$
$397$	−22.0000	−	22.0000i	−1.10415	−	1.10415i	−0.110244	−	0.993905i	$-0.535163\pi$
$398$		0			0
$399$	5.65685	−	8.00000i	0.283197	−	0.400501i
$400$		0			0
$401$		−	8.48528i		−	0.423735i	−0.977298	−	0.211867i	$-0.932046\pi$
$401$		−	8.48528i		−	0.423735i	0.977298	−	0.211867i	$-0.0679545\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−7.05025	−	18.8492i	−0.350330	−	0.936626i
$406$		0			0
$407$	−8.48528	+	8.48528i	−0.420600	+	0.420600i
$408$		0			0
$409$		0			0		1.00000			$0$
$409$		0			0		−1.00000			$\pi$
$410$		0			0
$411$	6.00000	−	8.48528i	0.295958	−	0.418548i
$412$		0			0
$413$	9.89949	+	9.89949i	0.487122	+	0.487122i
$414$		0			0
$415$	−24.0000	+	12.0000i	−1.17811	+	0.589057i
$416$		0			0
$417$	−2.34315	−	13.6569i	−0.114744	−	0.668779i
$418$		0			0
$419$	21.2132			1.03633			0.518166	−	0.855280i	$-0.326615\pi$
$419$	21.2132			1.03633			0.518166	+	0.855280i	$0.326615\pi$
$420$		0			0
$421$	−14.0000			−0.682318			−0.341159	−	0.940006i	$-0.610819\pi$
$421$	−14.0000			−0.682318			−0.341159	+	0.940006i	$0.610819\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−9.89949	+	1.41421i	−0.480196	+	0.0685994i
$426$		0			0
$427$	6.00000	+	6.00000i	0.290360	+	0.290360i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	11.3137i		−	0.544962i	−0.962161	−	0.272481i	$-0.912156\pi$
$431$		−	11.3137i		−	0.544962i	0.962161	−	0.272481i	$-0.0878442\pi$
$432$		0			0
$433$	−1.00000	+	1.00000i	−0.0480569	+	0.0480569i	−0.730727	−	0.682670i	$-0.760819\pi$
$433$	−1.00000	+	1.00000i	−0.0480569	+	0.0480569i	0.682670	+	0.730727i	$0.260819\pi$
$434$		0			0
$435$	−4.14214	+	27.0711i	−0.198600	+	1.29796i
$436$		0			0
$437$	11.3137	−	11.3137i	0.541208	−	0.541208i
$438$		0			0
$439$			16.0000i			0.763638i	0.924237	+	0.381819i	$0.124702\pi$
$439$			16.0000i			0.763638i	−0.924237	+	0.381819i	$0.875298\pi$
$440$		0			0
$441$	−5.00000	−	14.1421i	−0.238095	−	0.673435i
$442$		0			0
$443$	−4.24264	−	4.24264i	−0.201574	−	0.201574i	0.599100	−	0.800674i	$-0.295525\pi$
$443$	−4.24264	−	4.24264i	−0.201574	−	0.201574i	−0.800674	+	0.599100i	$0.795525\pi$
$444$		0			0
$445$	2.00000	−	6.00000i	0.0948091	−	0.284427i
$446$		0			0
$447$	21.7279	−	3.72792i	1.02770	−	0.176325i
$448$		0			0
$449$	14.1421			0.667409			0.333704	−	0.942678i	$-0.391701\pi$
$449$	14.1421			0.667409			0.333704	+	0.942678i	$0.391701\pi$
$450$		0			0
$451$	−8.00000			−0.376705
$452$		0			0
$453$	27.3137	−	4.68629i	1.28331	−	0.220181i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−15.0000	−	15.0000i	−0.701670	−	0.701670i	0.263099	−	0.964769i	$-0.415256\pi$
$457$	−15.0000	−	15.0000i	−0.701670	−	0.701670i	−0.964769	+	0.263099i	$0.915256\pi$
$458$		0			0
$459$	−2.82843	+	10.0000i	−0.132020	+	0.466760i
$460$		0			0
$461$		−	7.07107i		−	0.329332i	−0.986349	−	0.164666i	$-0.947345\pi$
$461$		−	7.07107i		−	0.329332i	0.986349	−	0.164666i	$-0.0526547\pi$
$462$		0			0
$463$	−5.00000	+	5.00000i	−0.232370	+	0.232370i	−0.813681	−	0.581311i	$-0.802540\pi$
$463$	−5.00000	+	5.00000i	−0.232370	+	0.232370i	0.581311	+	0.813681i	$0.302540\pi$
$464$		0			0
$465$	−1.17157	+	7.65685i	−0.0543304	+	0.355078i
$466$		0			0
$467$	−19.7990	+	19.7990i	−0.916188	+	0.916188i	−0.996750	−	0.0805616i	$-0.974329\pi$
$467$	−19.7990	+	19.7990i	−0.916188	+	0.916188i	0.0805616	+	0.996750i	$0.474329\pi$
$468$		0			0
$469$		−	8.00000i		−	0.369406i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−8.48528	−	8.48528i	−0.390154	−	0.390154i
$474$		0			0
$475$	12.0000	−	16.0000i	0.550598	−	0.734130i
$476$		0			0
$477$	10.8284	+	5.17157i	0.495800	+	0.236790i
$478$		0			0
$479$	−31.1127			−1.42158			−0.710788	−	0.703407i	$-0.751661\pi$
$479$	−31.1127			−1.42158			−0.710788	+	0.703407i	$0.751661\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	1.65685	+	9.65685i	0.0753895	+	0.439402i
$484$		0			0
$485$	8.48528	−	4.24264i	0.385297	−	0.192648i
$486$		0			0
$487$	−9.00000	−	9.00000i	−0.407829	−	0.407829i	0.473152	−	0.880981i	$-0.343116\pi$
$487$	−9.00000	−	9.00000i	−0.407829	−	0.407829i	−0.880981	+	0.473152i	$0.843116\pi$
$488$		0			0
$489$	5.65685	−	8.00000i	0.255812	−	0.361773i
$490$		0			0
$491$			26.8701i			1.21263i	0.795225	+	0.606314i	$0.207353\pi$
$491$			26.8701i			1.21263i	−0.795225	+	0.606314i	$0.792647\pi$
$492$		0			0
$493$	10.0000	−	10.0000i	0.450377	−	0.450377i
$494$		0			0
$495$	−9.48528	+	0.171573i	−0.426332	+	0.00771163i
$496$		0			0
$497$	14.1421	−	14.1421i	0.634361	−	0.634361i
$498$		0			0
$499$			20.0000i			0.895323i	0.894203	+	0.447661i	$0.147743\pi$
$499$			20.0000i			0.895323i	−0.894203	+	0.447661i	$0.852257\pi$
$500$		0			0
$501$	−8.00000	+	11.3137i	−0.357414	+	0.505459i
$502$		0			0
$503$	−8.48528	−	8.48528i	−0.378340	−	0.378340i	0.492163	−	0.870503i	$-0.336206\pi$
$503$	−8.48528	−	8.48528i	−0.378340	−	0.378340i	−0.870503	+	0.492163i	$0.836206\pi$
$504$		0			0
$505$	−21.0000	−	7.00000i	−0.934488	−	0.311496i
$506$		0			0
$507$	−3.80761	−	22.1924i	−0.169102	−	0.985599i
$508$		0			0
$509$	24.0416			1.06563			0.532813	−	0.846233i	$-0.321135\pi$
$509$	24.0416			1.06563			0.532813	+	0.846233i	$0.321135\pi$
$510$		0			0
$511$	−10.0000			−0.442374
$512$		0			0
$513$	−10.1421	−	18.1421i	−0.447786	−	0.800995i
$514$		0			0
$515$	1.41421	+	2.82843i	0.0623177	+	0.124635i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−2.82843	−	2.00000i	−0.124154	−	0.0877903i
$520$		0			0
$521$		−	25.4558i		−	1.11524i	−0.830096	−	0.557620i	$-0.811714\pi$
$521$		−	25.4558i		−	1.11524i	0.830096	−	0.557620i	$-0.188286\pi$
$522$		0			0
$523$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$523$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$524$		0			0
$525$	3.75736	+	11.6569i	0.163985	+	0.508747i
$526$		0			0
$527$	2.82843	−	2.82843i	0.123208	−	0.123208i
$528$		0			0
$529$		−	7.00000i		−	0.304348i
$530$		0			0
$531$	28.0000	−	9.89949i	1.21510	−	0.429601i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	4.00000	+	8.00000i	0.172935	+	0.345870i
$536$		0			0
$537$	31.3848	−	5.38478i	1.35435	−	0.232370i
$538$		0			0
$539$	−7.07107			−0.304572
$540$		0			0
$541$	2.00000			0.0859867			0.0429934	−	0.999075i	$-0.486311\pi$
$541$	2.00000			0.0859867			0.0429934	+	0.999075i	$0.486311\pi$
$542$		0			0
$543$	−37.5563	+	6.44365i	−1.61170	+	0.276524i
$544$		0			0
$545$	21.2132	+	7.07107i	0.908674	+	0.302891i
$546$		0			0
$547$	6.00000	+	6.00000i	0.256541	+	0.256541i	0.823646	−	0.567104i	$-0.191936\pi$
$547$	6.00000	+	6.00000i	0.256541	+	0.256541i	−0.567104	+	0.823646i	$0.691936\pi$
$548$		0			0
$549$	16.9706	−	6.00000i	0.724286	−	0.256074i
$550$		0			0
$551$			28.2843i			1.20495i
$552$		0			0
$553$	6.00000	−	6.00000i	0.255146	−	0.255146i
$554$		0			0
$555$	26.4853	−	19.4558i	1.12424	−	0.825855i
$556$		0			0
$557$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$557$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	4.00000	+	2.82843i	0.168880	+	0.119416i
$562$		0			0
$563$	21.2132	+	21.2132i	0.894030	+	0.894030i	0.994900	−	0.100870i	$-0.0321625\pi$
$563$	21.2132	+	21.2132i	0.894030	+	0.894030i	−0.100870	+	0.994900i	$0.532163\pi$
$564$		0			0
$565$	28.0000	−	14.0000i	1.17797	−	0.588984i
$566$		0			0
$567$	12.6569	+	1.34315i	0.531538	+	0.0564068i
$568$		0			0
$569$	−14.1421			−0.592869			−0.296435	−	0.955053i	$-0.595798\pi$
$569$	−14.1421			−0.592869			−0.296435	+	0.955053i	$0.595798\pi$
$570$		0			0
$571$	−40.0000			−1.67395			−0.836974	−	0.547243i	$-0.815677\pi$
$571$	−40.0000			−1.67395			−0.836974	+	0.547243i	$0.815677\pi$
$572$		0			0
$573$	−0.828427	−	4.82843i	−0.0346080	−	0.201710i
$574$		0			0
$575$	2.82843	+	19.7990i	0.117954	+	0.825675i
$576$		0			0
$577$	13.0000	+	13.0000i	0.541197	+	0.541197i	0.923880	−	0.382683i	$-0.125000\pi$
$577$	13.0000	+	13.0000i	0.541197	+	0.541197i	−0.382683	+	0.923880i	$0.625000\pi$
$578$		0			0
$579$	21.2132	−	30.0000i	0.881591	−	1.24676i
$580$		0			0
$581$		−	16.9706i		−	0.704058i
$582$		0			0
$583$	4.00000	−	4.00000i	0.165663	−	0.165663i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−25.4558	+	25.4558i	−1.05068	+	1.05068i	−0.0520296	+	0.998646i	$0.516569\pi$
$587$	−25.4558	+	25.4558i	−1.05068	+	1.05068i	−0.998646	+	0.0520296i	$0.983431\pi$
$588$		0			0
$589$			8.00000i			0.329634i
$590$		0			0
$591$	24.0000	−	33.9411i	0.987228	−	1.39615i
$592$		0			0
$593$	15.5563	+	15.5563i	0.638823	+	0.638823i	0.950265	−	0.311442i	$-0.100812\pi$
$593$	15.5563	+	15.5563i	0.638823	+	0.638823i	−0.311442	+	0.950265i	$0.600812\pi$
$594$		0			0
$595$	2.00000	−	6.00000i	0.0819920	−	0.245976i
$596$		0			0
$597$	−7.02944	−	40.9706i	−0.287696	−	1.67681i
$598$		0			0
$599$	45.2548			1.84906			0.924531	−	0.381106i	$-0.124457\pi$
$599$	45.2548			1.84906			0.924531	+	0.381106i	$0.124457\pi$
$600$		0			0
$601$	−10.0000			−0.407909			−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000			−0.407909			−0.203954	+	0.978980i	$0.565379\pi$
$602$		0			0
$603$	−15.3137	−	7.31371i	−0.623622	−	0.297837i
$604$		0			0
$605$	6.36396	−	19.0919i	0.258732	−	0.776195i
$606$		0			0
$607$	−3.00000	−	3.00000i	−0.121766	−	0.121766i	0.643598	−	0.765364i	$-0.277441\pi$
$607$	−3.00000	−	3.00000i	−0.121766	−	0.121766i	−0.765364	+	0.643598i	$0.777441\pi$
$608$		0			0
$609$	−14.1421	−	10.0000i	−0.573068	−	0.405220i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−18.0000	+	18.0000i	−0.727013	+	0.727013i	−0.970024	−	0.243011i	$-0.921865\pi$
$613$	−18.0000	+	18.0000i	−0.727013	+	0.727013i	0.243011	+	0.970024i	$0.421865\pi$
$614$		0			0
$615$	21.6569	+	3.31371i	0.873289	+	0.133622i
$616$		0			0
$617$	21.2132	−	21.2132i	0.854011	−	0.854011i	−0.136613	−	0.990624i	$-0.543622\pi$
$617$	21.2132	−	21.2132i	0.854011	−	0.854011i	0.990624	+	0.136613i	$0.0436217\pi$
$618$		0			0
$619$			24.0000i			0.964641i	0.875995	+	0.482321i	$0.160206\pi$
$619$			24.0000i			0.964641i	−0.875995	+	0.482321i	$0.839794\pi$
$620$		0			0
$621$	20.0000	+	5.65685i	0.802572	+	0.227002i
$622$		0			0
$623$	2.82843	+	2.82843i	0.113319	+	0.113319i
$624$		0			0
$625$	7.00000	+	24.0000i	0.280000	+	0.960000i
$626$		0			0
$627$	−9.65685	+	1.65685i	−0.385658	+	0.0661684i
$628$		0			0
$629$	−16.9706			−0.676661
$630$		0			0
$631$	14.0000			0.557331			0.278666	−	0.960388i	$-0.410108\pi$
$631$	14.0000			0.557331			0.278666	+	0.960388i	$0.410108\pi$
$632$		0			0
$633$	−13.6569	+	2.34315i	−0.542811	+	0.0931317i
$634$		0			0
$635$	19.7990	−	9.89949i	0.785699	−	0.392849i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−14.1421	−	40.0000i	−0.559454	−	1.58238i
$640$		0			0
$641$			5.65685i			0.223432i	0.993740	+	0.111716i	$0.0356347\pi$
$641$			5.65685i			0.223432i	−0.993740	+	0.111716i	$0.964365\pi$
$642$		0			0
$643$	24.0000	−	24.0000i	0.946468	−	0.946468i	−0.0521706	−	0.998638i	$-0.516614\pi$
$643$	24.0000	−	24.0000i	0.946468	−	0.946468i	0.998638	+	0.0521706i	$0.0166140\pi$
$644$		0			0
$645$	19.4558	+	26.4853i	0.766073	+	1.04286i
$646$		0			0
$647$	−19.7990	+	19.7990i	−0.778379	+	0.778379i	−0.979555	−	0.201176i	$-0.935524\pi$
$647$	−19.7990	+	19.7990i	−0.778379	+	0.778379i	0.201176	+	0.979555i	$0.435524\pi$
$648$		0			0
$649$		−	14.0000i		−	0.549548i
$650$		0			0
$651$	−4.00000	−	2.82843i	−0.156772	−	0.110855i
$652$		0			0
$653$	−4.24264	−	4.24264i	−0.166027	−	0.166027i	0.619203	−	0.785231i	$-0.287456\pi$
$653$	−4.24264	−	4.24264i	−0.166027	−	0.166027i	−0.785231	+	0.619203i	$0.787456\pi$
$654$		0			0
$655$	−39.0000	−	13.0000i	−1.52386	−	0.507952i
$656$		0			0
$657$	−9.14214	+	19.1421i	−0.356669	+	0.746806i
$658$		0			0
$659$	−35.3553			−1.37725			−0.688624	−	0.725118i	$-0.741785\pi$
$659$	−35.3553			−1.37725			−0.688624	+	0.725118i	$0.741785\pi$
$660$		0			0
$661$	−50.0000			−1.94477			−0.972387	−	0.233373i	$-0.925024\pi$
$661$	−50.0000			−1.94477			−0.972387	+	0.233373i	$0.925024\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	5.65685	+	11.3137i	0.219363	+	0.438727i
$666$		0			0
$667$	−20.0000	−	20.0000i	−0.774403	−	0.774403i
$668$		0			0
$669$	−12.7279	+	18.0000i	−0.492090	+	0.695920i
$670$		0			0
$671$		−	8.48528i		−	0.327571i
$672$		0			0
$673$	13.0000	−	13.0000i	0.501113	−	0.501113i	−0.410671	−	0.911784i	$-0.634705\pi$
$673$	13.0000	−	13.0000i	0.501113	−	0.501113i	0.911784	+	0.410671i	$0.134705\pi$
$674$		0			0
$675$	25.7487	+	3.46447i	0.991069	+	0.133347i
$676$		0			0
$677$	−18.3848	+	18.3848i	−0.706584	+	0.706584i	−0.965815	−	0.259231i	$-0.916531\pi$
$677$	−18.3848	+	18.3848i	−0.706584	+	0.706584i	0.259231	+	0.965815i	$0.416531\pi$
$678$		0			0
$679$			6.00000i			0.230259i
$680$		0			0
$681$	−22.0000	+	31.1127i	−0.843042	+	1.19224i
$682$		0			0
$683$	−25.4558	−	25.4558i	−0.974041	−	0.974041i	0.0256307	−	0.999671i	$-0.491841\pi$
$683$	−25.4558	−	25.4558i	−0.974041	−	0.974041i	−0.999671	+	0.0256307i	$0.991841\pi$
$684$		0			0
$685$	6.00000	+	12.0000i	0.229248	+	0.458496i
$686$		0			0
$687$	−1.75736	−	10.2426i	−0.0670474	−	0.390781i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	12.0000			0.456502			0.228251	−	0.973602i	$-0.426699\pi$
$691$	12.0000			0.456502			0.228251	+	0.973602i	$0.426699\pi$
$692$		0			0
$693$	2.58579	−	5.41421i	0.0982259	−	0.205669i
$694$		0			0
$695$	16.9706	+	5.65685i	0.643730	+	0.214577i
$696$		0			0
$697$	−8.00000	−	8.00000i	−0.303022	−	0.303022i
$698$		0			0
$699$	25.4558	+	18.0000i	0.962828	+	0.680823i
$700$		0			0
$701$			26.8701i			1.01487i	0.861691	+	0.507434i	$0.169406\pi$
$701$			26.8701i			1.01487i	−0.861691	+	0.507434i	$0.830594\pi$
$702$		0			0
$703$	24.0000	−	24.0000i	0.905177	−	0.905177i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	9.89949	−	9.89949i	0.372309	−	0.372309i
$708$		0			0
$709$		−	10.0000i		−	0.375558i	−0.982211	−	0.187779i	$-0.939871\pi$
$709$		−	10.0000i		−	0.375558i	0.982211	−	0.187779i	$-0.0601289\pi$
$710$		0			0
$711$	−6.00000	−	16.9706i	−0.225018	−	0.636446i
$712$		0			0
$713$	−5.65685	−	5.65685i	−0.211851	−	0.211851i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−14.4853	+	2.48528i	−0.540963	+	0.0928145i
$718$		0			0
$719$	−22.6274			−0.843860			−0.421930	−	0.906628i	$-0.638647\pi$
$719$	−22.6274			−0.843860			−0.421930	+	0.906628i	$0.638647\pi$
$720$		0			0
$721$	−2.00000			−0.0744839
$722$		0			0
$723$	−6.82843	+	1.17157i	−0.253952	+	0.0435713i
$724$		0			0
$725$	−28.2843	−	21.2132i	−1.05045	−	0.787839i
$726$		0			0
$727$	3.00000	+	3.00000i	0.111264	+	0.111264i	0.760547	−	0.649283i	$-0.224931\pi$
$727$	3.00000	+	3.00000i	0.111264	+	0.111264i	−0.649283	+	0.760547i	$0.724931\pi$
$728$		0			0
$729$	14.1421	−	23.0000i	0.523783	−	0.851852i
$730$		0			0
$731$		−	16.9706i		−	0.627679i
$732$		0			0
$733$	26.0000	−	26.0000i	0.960332	−	0.960332i	−0.0389108	−	0.999243i	$-0.512389\pi$
$733$	26.0000	−	26.0000i	0.960332	−	0.960332i	0.999243	+	0.0389108i	$0.0123888\pi$
$734$		0			0
$735$	19.1421	+	2.92893i	0.706068	+	0.108035i
$736$		0			0
$737$	−5.65685	+	5.65685i	−0.208373	+	0.208373i
$738$		0			0
$739$		−	40.0000i		−	1.47142i	−0.677295	−	0.735712i	$-0.736848\pi$
$739$		−	40.0000i		−	1.47142i	0.677295	−	0.735712i	$-0.263152\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	36.7696	+	36.7696i	1.34894	+	1.34894i	0.886810	+	0.462134i	$0.152916\pi$
$743$	36.7696	+	36.7696i	1.34894	+	1.34894i	0.462134	+	0.886810i	$0.347084\pi$
$744$		0			0
$745$	−9.00000	+	27.0000i	−0.329734	+	0.989203i
$746$		0			0
$747$	−32.4853	−	15.5147i	−1.18857	−	0.567654i
$748$		0			0
$749$	−5.65685			−0.206697
$750$		0			0
$751$	30.0000			1.09472			0.547358	−	0.836899i	$-0.315634\pi$
$751$	30.0000			1.09472			0.547358	+	0.836899i	$0.315634\pi$
$752$		0			0
$753$	−3.72792	−	21.7279i	−0.135853	−	0.791809i
$754$		0			0
$755$	−11.3137	+	33.9411i	−0.411748	+	1.23524i
$756$		0			0
$757$	30.0000	+	30.0000i	1.09037	+	1.09037i	0.995489	+	0.0948798i	$0.0302467\pi$
$757$	30.0000	+	30.0000i	1.09037	+	1.09037i	0.0948798	+	0.995489i	$0.469753\pi$
$758$		0			0
$759$	5.65685	−	8.00000i	0.205331	−	0.290382i
$760$		0			0
$761$			36.7696i			1.33290i	0.745552	+	0.666448i	$0.232186\pi$
$761$			36.7696i			1.33290i	−0.745552	+	0.666448i	$0.767814\pi$
$762$		0			0
$763$	−10.0000	+	10.0000i	−0.362024	+	0.362024i
$764$		0			0
$765$	−9.65685	−	9.31371i	−0.349144	−	0.336738i
$766$		0			0
$767$		0			0
$768$		0			0
$769$		−	22.0000i		−	0.793340i	−0.917961	−	0.396670i	$-0.870166\pi$
$769$		−	22.0000i		−	0.793340i	0.917961	−	0.396670i	$-0.129834\pi$
$770$		0			0
$771$	14.0000	−	19.7990i	0.504198	−	0.713043i
$772$		0			0
$773$	−29.6985	−	29.6985i	−1.06818	−	1.06818i	−0.997499	−	0.0706813i	$-0.977483\pi$
$773$	−29.6985	−	29.6985i	−1.06818	−	1.06818i	−0.0706813	−	0.997499i	$-0.522517\pi$
$774$		0			0
$775$	−8.00000	−	6.00000i	−0.287368	−	0.215526i
$776$		0			0
$777$	3.51472	+	20.4853i	0.126090	+	0.734905i
$778$		0			0
$779$	22.6274			0.810711
$780$		0			0
$781$	−20.0000			−0.715656
$782$		0			0
$783$	−32.0711	+	17.9289i	−1.14613	+	0.640728i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	28.0000	+	28.0000i	0.998092	+	0.998092i	0.999998	−	0.00190598i	$-0.000606691\pi$
$787$	28.0000	+	28.0000i	0.998092	+	0.998092i	−0.00190598	+	0.999998i	$0.500607\pi$
$788$		0			0
$789$	11.3137	+	8.00000i	0.402779	+	0.284808i
$790$		0			0
$791$			19.7990i			0.703971i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−12.4853	+	9.17157i	−0.442807	+	0.325282i
$796$		0			0
$797$	−12.7279	+	12.7279i	−0.450846	+	0.450846i	−0.895635	−	0.444789i	$-0.853279\pi$
$797$	−12.7279	+	12.7279i	−0.450846	+	0.450846i	0.444789	+	0.895635i	$0.353279\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	8.00000	−	2.82843i	0.282666	−	0.0999376i
$802$		0			0
$803$	7.07107	+	7.07107i	0.249533	+	0.249533i
$804$		0			0
$805$	−12.0000	−	4.00000i	−0.422944	−	0.140981i
$806$		0			0
$807$	−26.5563	+	4.55635i	−0.934828	+	0.160391i
$808$		0			0
$809$	−22.6274			−0.795538			−0.397769	−	0.917486i	$-0.630215\pi$
$809$	−22.6274			−0.795538			−0.397769	+	0.917486i	$0.630215\pi$
$810$		0			0
$811$	−4.00000			−0.140459			−0.0702295	−	0.997531i	$-0.522373\pi$
$811$	−4.00000			−0.140459			−0.0702295	+	0.997531i	$0.522373\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	5.65685	+	11.3137i	0.198151	+	0.396302i
$816$		0			0
$817$	24.0000	+	24.0000i	0.839654	+	0.839654i
$818$		0			0
$819$		0			0
$820$		0			0
$821$			43.8406i			1.53005i	0.644002	+	0.765024i	$0.277273\pi$
$821$			43.8406i			1.53005i	−0.644002	+	0.765024i	$0.722727\pi$
$822$		0			0
$823$	25.0000	−	25.0000i	0.871445	−	0.871445i	−0.121185	−	0.992630i	$-0.538669\pi$
$823$	25.0000	−	25.0000i	0.871445	−	0.871445i	0.992630	+	0.121185i	$0.0386693\pi$
$824$		0			0
$825$	5.58579	−	10.8995i	0.194472	−	0.379472i
$826$		0			0
$827$	−12.7279	+	12.7279i	−0.442593	+	0.442593i	−0.892883	−	0.450289i	$-0.851321\pi$
$827$	−12.7279	+	12.7279i	−0.442593	+	0.442593i	0.450289	+	0.892883i	$0.351321\pi$
$828$		0			0
$829$		−	14.0000i		−	0.486240i	−0.969996	−	0.243120i	$-0.921829\pi$
$829$		−	14.0000i		−	0.486240i	0.969996	−	0.243120i	$-0.0781709\pi$
$830$		0			0
$831$	−12.0000	−	8.48528i	−0.416275	−	0.294351i
$832$		0			0
$833$	−7.07107	−	7.07107i	−0.244998	−	0.244998i
$834$		0			0
$835$	−8.00000	−	16.0000i	−0.276851	−	0.553703i
$836$		0			0
$837$	−9.07107	+	5.07107i	−0.313542	+	0.175282i
$838$		0			0
$839$	5.65685			0.195296			0.0976481	−	0.995221i	$-0.468868\pi$
$839$	5.65685			0.195296			0.0976481	+	0.995221i	$0.468868\pi$
$840$		0			0
$841$	21.0000			0.724138
$842$		0			0
$843$	−2.48528	−	14.4853i	−0.0855976	−	0.498900i
$844$		0			0
$845$	27.5772	+	9.19239i	0.948683	+	0.316228i
$846$		0			0
$847$	9.00000	+	9.00000i	0.309244	+	0.309244i
$848$		0			0
$849$	−28.2843	+	40.0000i	−0.970714	+	1.37280i
$850$		0			0
$851$			33.9411i			1.16349i
$852$		0			0
$853$	2.00000	−	2.00000i	0.0684787	−	0.0684787i	−0.672038	−	0.740517i	$-0.734581\pi$
$853$	2.00000	−	2.00000i	0.0684787	−	0.0684787i	0.740517	+	0.672038i	$0.234581\pi$
$854$		0			0
$855$	26.8284	−	0.485281i	0.917513	−	0.0165963i
$856$		0			0
$857$	−38.1838	+	38.1838i	−1.30433	+	1.30433i	−0.378892	+	0.925441i	$0.623695\pi$
$857$	−38.1838	+	38.1838i	−1.30433	+	1.30433i	−0.925441	+	0.378892i	$0.876305\pi$
$858$		0			0
$859$			32.0000i			1.09183i	0.837842	+	0.545913i	$0.183817\pi$
$859$			32.0000i			1.09183i	−0.837842	+	0.545913i	$0.816183\pi$
$860$		0			0
$861$	−8.00000	+	11.3137i	−0.272639	+	0.385570i
$862$		0			0
$863$	−36.7696	−	36.7696i	−1.25165	−	1.25165i	−0.954980	−	0.296670i	$-0.904124\pi$
$863$	−36.7696	−	36.7696i	−1.25165	−	1.25165i	−0.296670	−	0.954980i	$-0.595876\pi$
$864$		0			0
$865$	4.00000	−	2.00000i	0.136004	−	0.0680020i
$866$		0			0
$867$	−3.80761	−	22.1924i	−0.129313	−	0.753693i
$868$		0			0
$869$	−8.48528			−0.287843
$870$		0			0
$871$		0			0
$872$		0			0
$873$	11.4853	+	5.48528i	0.388718	+	0.185649i
$874$		0			0
$875$	−15.5563	−	2.82843i	−0.525901	−	0.0956183i
$876$		0			0
$877$	36.0000	+	36.0000i	1.21563	+	1.21563i	0.969146	+	0.246488i	$0.0792765\pi$
$877$	36.0000	+	36.0000i	1.21563	+	1.21563i	0.246488	+	0.969146i	$0.420724\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			19.7990i			0.667045i	0.942742	+	0.333522i	$0.108237\pi$
$881$			19.7990i			0.667045i	−0.942742	+	0.333522i	$0.891763\pi$
$882$		0			0
$883$	4.00000	−	4.00000i	0.134611	−	0.134611i	−0.636591	−	0.771202i	$-0.719656\pi$
$883$	4.00000	−	4.00000i	0.134611	−	0.134611i	0.771202	+	0.636591i	$0.219656\pi$
$884$		0			0
$885$	−5.79899	+	37.8995i	−0.194931	+	1.27398i
$886$		0			0
$887$	−8.48528	+	8.48528i	−0.284908	+	0.284908i	−0.835063	−	0.550155i	$-0.814569\pi$
$887$	−8.48528	+	8.48528i	−0.284908	+	0.284908i	0.550155	+	0.835063i	$0.314569\pi$
$888$		0			0
$889$			14.0000i			0.469545i
$890$		0			0
$891$	−8.00000	−	9.89949i	−0.268010	−	0.331646i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	−13.0000	+	39.0000i	−0.434542	+	1.30363i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	14.1421			0.471667
$900$		0			0
$901$	8.00000			0.266519
$902$		0			0
$903$	−20.4853	+	3.51472i	−0.681707	+	0.116963i
$904$		0			0
$905$	15.5563	−	46.6690i	0.517111	−	1.55133i
$906$		0			0
$907$	22.0000	+	22.0000i	0.730498	+	0.730498i	0.970718	−	0.240220i	$-0.0772197\pi$
$907$	22.0000	+	22.0000i	0.730498	+	0.730498i	−0.240220	+	0.970718i	$0.577220\pi$
$908$		0			0
$909$	−9.89949	−	28.0000i	−0.328346	−	0.928701i
$910$		0			0
$911$		−	39.5980i		−	1.31194i	−0.754787	−	0.655970i	$-0.772260\pi$
$911$		−	39.5980i		−	1.31194i	0.754787	−	0.655970i	$-0.227740\pi$
$912$		0			0
$913$	−12.0000	+	12.0000i	−0.397142	+	0.397142i
$914$		0			0
$915$	−3.51472	+	22.9706i	−0.116193	+	0.759383i
$916$		0			0
$917$	18.3848	−	18.3848i	0.607119	−	0.607119i
$918$		0			0
$919$			34.0000i			1.12156i	0.827966	+	0.560778i	$0.189498\pi$
$919$			34.0000i			1.12156i	−0.827966	+	0.560778i	$0.810502\pi$
$920$		0			0
$921$	−36.0000	−	25.4558i	−1.18624	−	0.838799i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	6.00000	+	42.0000i	0.197279	+	1.38095i
$926$		0			0
$927$	−1.82843	+	3.82843i	−0.0600534	+	0.125742i
$928$		0			0
$929$	−2.82843			−0.0927977			−0.0463988	−	0.998923i	$-0.514775\pi$
$929$	−2.82843			−0.0927977			−0.0463988	+	0.998923i	$0.514775\pi$
$930$		0			0
$931$	20.0000			0.655474
$932$		0			0
$933$	−5.79899	−	33.7990i	−0.189850	−	1.10653i
$934$		0			0
$935$	−5.65685	+	2.82843i	−0.184999	+	0.0924995i
$936$		0			0
$937$	−5.00000	−	5.00000i	−0.163343	−	0.163343i	0.620703	−	0.784046i	$-0.286847\pi$
$937$	−5.00000	−	5.00000i	−0.163343	−	0.163343i	−0.784046	+	0.620703i	$0.786847\pi$
$938$		0			0
$939$	−12.7279	+	18.0000i	−0.415360	+	0.587408i
$940$		0			0
$941$			12.7279i			0.414918i	0.978244	+	0.207459i	$0.0665194\pi$
$941$			12.7279i			0.414918i	−0.978244	+	0.207459i	$0.933481\pi$
$942$		0			0
$943$	−16.0000	+	16.0000i	−0.521032	+	0.521032i
$944$		0			0
$945$	−9.24264	+	13.5858i	−0.300663	+	0.441946i
$946$		0			0
$947$	−18.3848	+	18.3848i	−0.597425	+	0.597425i	−0.939627	−	0.342202i	$-0.888827\pi$
$947$	−18.3848	+	18.3848i	−0.597425	+	0.597425i	0.342202	+	0.939627i	$0.388827\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−18.0000	+	25.4558i	−0.583690	+	0.825462i
$952$		0			0
$953$	−4.24264	−	4.24264i	−0.137433	−	0.137433i	0.635044	−	0.772476i	$-0.280982\pi$
$953$	−4.24264	−	4.24264i	−0.137433	−	0.137433i	−0.772476	+	0.635044i	$0.780982\pi$
$954$		0			0
$955$	6.00000	+	2.00000i	0.194155	+	0.0647185i
$956$		0			0
$957$	2.92893	+	17.0711i	0.0946789	+	0.551829i
$958$		0			0
$959$	−8.48528			−0.274004
$960$		0			0
$961$	−27.0000			−0.870968
$962$		0			0
$963$	−5.17157	+	10.8284i	−0.166652	+	0.348941i
$964$		0			0
$965$	21.2132	+	42.4264i	0.682877	+	1.36575i
$966$		0			0
$967$	−19.0000	−	19.0000i	−0.610999	−	0.610999i	0.332208	−	0.943206i	$-0.392207\pi$
$967$	−19.0000	−	19.0000i	−0.610999	−	0.610999i	−0.943206	+	0.332208i	$0.892207\pi$
$968$		0			0
$969$	−11.3137	−	8.00000i	−0.363449	−	0.256997i
$970$		0			0
$971$		−	41.0122i		−	1.31614i	−0.752955	−	0.658072i	$-0.771372\pi$
$971$		−	41.0122i		−	1.31614i	0.752955	−	0.658072i	$-0.228628\pi$
$972$		0			0
$973$	−8.00000	+	8.00000i	−0.256468	+	0.256468i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	4.24264	−	4.24264i	0.135734	−	0.135734i	−0.635975	−	0.771709i	$-0.719402\pi$
$977$	4.24264	−	4.24264i	0.135734	−	0.135734i	0.771709	+	0.635975i	$0.219402\pi$
$978$		0			0
$979$		−	4.00000i		−	0.127841i
$980$		0			0
$981$	10.0000	+	28.2843i	0.319275	+	0.903047i
$982$		0			0
$983$	−14.1421	−	14.1421i	−0.451064	−	0.451064i	0.444644	−	0.895708i	$-0.353330\pi$
$983$	−14.1421	−	14.1421i	−0.451064	−	0.451064i	−0.895708	+	0.444644i	$0.853330\pi$
$984$		0			0
$985$	24.0000	+	48.0000i	0.764704	+	1.52941i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−33.9411			−1.07927
$990$		0			0
$991$	−40.0000			−1.27064			−0.635321	−	0.772248i	$-0.719132\pi$
$991$	−40.0000			−1.27064			−0.635321	+	0.772248i	$0.719132\pi$
$992$		0			0
$993$	13.6569	−	2.34315i	0.433387	−	0.0743575i
$994$		0			0
$995$	50.9117	+	16.9706i	1.61401	+	0.538003i
$996$		0			0
$997$	8.00000	+	8.00000i	0.253363	+	0.253363i	0.822348	−	0.568985i	$-0.192664\pi$
$997$	8.00000	+	8.00000i	0.253363	+	0.253363i	−0.568985	+	0.822348i	$0.692664\pi$
$998$		0			0
$999$	42.4264	+	12.0000i	1.34231	+	0.379663i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.v.c.257.1		4
3.2	odd	2	inner	960.2.v.c.257.2		4
4.3	odd	2		960.2.v.k.257.2		4
5.3	odd	4	inner	960.2.v.c.833.2		4
8.3	odd	2		30.2.e.a.17.2	yes	4
8.5	even	2		240.2.v.e.17.2		4
12.11	even	2		960.2.v.k.257.1		4
15.8	even	4	inner	960.2.v.c.833.1		4
20.3	even	4		960.2.v.k.833.1		4
24.5	odd	2		240.2.v.e.17.1		4
24.11	even	2		30.2.e.a.17.1	✓	4
40.3	even	4		30.2.e.a.23.1	yes	4
40.13	odd	4		240.2.v.e.113.1		4
40.19	odd	2		150.2.e.a.107.1		4
40.27	even	4		150.2.e.a.143.2		4
40.29	even	2		1200.2.v.b.257.1		4
40.37	odd	4		1200.2.v.b.593.2		4
60.23	odd	4		960.2.v.k.833.2		4
72.11	even	6		810.2.m.f.377.2		8
72.43	odd	6		810.2.m.f.377.1		8
72.59	even	6		810.2.m.f.107.1		8
72.67	odd	6		810.2.m.f.107.2		8
120.29	odd	2		1200.2.v.b.257.2		4
120.53	even	4		240.2.v.e.113.2		4
120.59	even	2		150.2.e.a.107.2		4
120.77	even	4		1200.2.v.b.593.1		4
120.83	odd	4		30.2.e.a.23.2	yes	4
120.107	odd	4		150.2.e.a.143.1		4
360.43	even	12		810.2.m.f.53.1		8
360.83	odd	12		810.2.m.f.53.2		8
360.203	odd	12		810.2.m.f.593.1		8
360.283	even	12		810.2.m.f.593.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.2.e.a.17.1	✓	4	24.11	even	2
30.2.e.a.17.2	yes	4	8.3	odd	2
30.2.e.a.23.1	yes	4	40.3	even	4
30.2.e.a.23.2	yes	4	120.83	odd	4
150.2.e.a.107.1		4	40.19	odd	2
150.2.e.a.107.2		4	120.59	even	2
150.2.e.a.143.1		4	120.107	odd	4
150.2.e.a.143.2		4	40.27	even	4
240.2.v.e.17.1		4	24.5	odd	2
240.2.v.e.17.2		4	8.5	even	2
240.2.v.e.113.1		4	40.13	odd	4
240.2.v.e.113.2		4	120.53	even	4
810.2.m.f.53.1		8	360.43	even	12
810.2.m.f.53.2		8	360.83	odd	12
810.2.m.f.107.1		8	72.59	even	6
810.2.m.f.107.2		8	72.67	odd	6
810.2.m.f.377.1		8	72.43	odd	6
810.2.m.f.377.2		8	72.11	even	6
810.2.m.f.593.1		8	360.203	odd	12
810.2.m.f.593.2		8	360.283	even	12
960.2.v.c.257.1		4	1.1	even	1	trivial
960.2.v.c.257.2		4	3.2	odd	2	inner
960.2.v.c.833.1		4	15.8	even	4	inner
960.2.v.c.833.2		4	5.3	odd	4	inner
960.2.v.k.257.1		4	12.11	even	2
960.2.v.k.257.2		4	4.3	odd	2
960.2.v.k.833.1		4	20.3	even	4
960.2.v.k.833.2		4	60.23	odd	4
1200.2.v.b.257.1		4	40.29	even	2
1200.2.v.b.257.2		4	120.29	odd	2
1200.2.v.b.593.1		4	120.77	even	4
1200.2.v.b.593.2		4	40.37	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.v (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.70711 + 0.292893i) q^{3} +(0.707107 - 2.12132i) q^{5} +(1.00000 + 1.00000i) q^{7} +(2.82843 - 1.00000i) q^{9} -1.41421i q^{11} +(-0.585786 + 3.82843i) q^{15} +(1.41421 - 1.41421i) q^{17} +4.00000i q^{19} +(-2.00000 - 1.41421i) q^{21} +(-2.82843 - 2.82843i) q^{23} +(-4.00000 - 3.00000i) q^{25} +(-4.53553 + 2.53553i) q^{27} +7.07107 q^{29} +2.00000 q^{31} +(0.414214 + 2.41421i) q^{33} +(2.82843 - 1.41421i) q^{35} +(-6.00000 - 6.00000i) q^{37} -5.65685i q^{41} +(6.00000 - 6.00000i) q^{43} +(-0.121320 - 6.70711i) q^{45} -5.00000i q^{49} +(-2.00000 + 2.82843i) q^{51} +(2.82843 + 2.82843i) q^{53} +(-3.00000 - 1.00000i) q^{55} +(-1.17157 - 6.82843i) q^{57} +9.89949 q^{59} +6.00000 q^{61} +(3.82843 + 1.82843i) q^{63} +(-4.00000 - 4.00000i) q^{67} +(5.65685 + 4.00000i) q^{69} -14.1421i q^{71} +(-5.00000 + 5.00000i) q^{73} +(7.70711 + 3.94975i) q^{75} +(1.41421 - 1.41421i) q^{77} -6.00000i q^{79} +(7.00000 - 5.65685i) q^{81} +(-8.48528 - 8.48528i) q^{83} +(-2.00000 - 4.00000i) q^{85} +(-12.0711 + 2.07107i) q^{87} +2.82843 q^{89} +(-3.41421 + 0.585786i) q^{93} +(8.48528 + 2.82843i) q^{95} +(3.00000 + 3.00000i) q^{97} +(-1.41421 - 4.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 4 q^{7} - 8 q^{15} - 8 q^{21} - 16 q^{25} - 4 q^{27} + 8 q^{31} - 4 q^{33} - 24 q^{37} + 24 q^{43} + 8 q^{45} - 8 q^{51} - 12 q^{55} - 16 q^{57} + 24 q^{61} + 4 q^{63} - 16 q^{67} - 20 q^{73}+ \cdots + 12 q^{97}+O(q^{100}) \) 4 * q - 4 * q^3 + 4 * q^7 - 8 * q^15 - 8 * q^21 - 16 * q^25 - 4 * q^27 + 8 * q^31 - 4 * q^33 - 24 * q^37 + 24 * q^43 + 8 * q^45 - 8 * q^51 - 12 * q^55 - 16 * q^57 + 24 * q^61 + 4 * q^63 - 16 * q^67 - 20 * q^73 + 28 * q^75 + 28 * q^81 - 8 * q^85 - 20 * q^87 - 8 * q^93 + 12 * q^97

Introduction

L-functions

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