LMFDB - Embedded newform 1680.2.cz.d.97.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1680,2,Mod(97,1680)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1680, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 2]))

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

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

chi := DirichletCharacter("1680.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1680.cz (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.4148675396$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 6x^{12} - 12x^{10} + 33x^{8} - 48x^{6} + 96x^{4} - 256x^{2} + 256 $ x^16 - 4x^14 + 6x^12 - 12x^10 + 33x^8 - 48x^6 + 96x^4 - 256*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			97.7
Root			$-1.36166 + 0.381939i$ of defining polynomial
Character	$\chi$	$=$	1680.97
Dual form			1680.2.cz.d.433.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{3} +(1.03649 - 1.98133i) q^{5} +(-0.614060 - 2.57351i) q^{7} +1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{3} +(1.03649 - 1.98133i) q^{5} +(-0.614060 - 2.57351i) q^{7} +1.00000i q^{9} +3.85136 q^{11} +(3.66816 + 3.66816i) q^{13} +(2.13393 - 0.668102i) q^{15} +(-1.49007 + 1.49007i) q^{17} +0.0697674 q^{19} +(1.38554 - 2.25395i) q^{21} +(0.534176 - 0.534176i) q^{23} +(-2.85136 - 4.10728i) q^{25} +(-0.707107 + 0.707107i) q^{27} +2.77107i q^{29} -2.39674i q^{31} +(2.72332 + 2.72332i) q^{33} +(-5.73544 - 1.45077i) q^{35} +(6.18757 + 6.18757i) q^{37} +5.18757i q^{39} -8.68077i q^{41} +(2.77107 - 2.77107i) q^{43} +(1.98133 + 1.03649i) q^{45} +(5.49042 - 5.49042i) q^{47} +(-6.24586 + 3.16057i) q^{49} -2.10728 q^{51} +(6.13823 - 6.13823i) q^{53} +(3.99191 - 7.63083i) q^{55} +(0.0493330 + 0.0493330i) q^{57} -6.97440 q^{59} -14.3107i q^{61} +(2.57351 - 0.614060i) q^{63} +(11.0699 - 3.46582i) q^{65} +(-0.416491 - 0.416491i) q^{67} +0.755439 q^{69} +8.12783 q^{71} +(-9.55210 - 9.55210i) q^{73} +(0.888068 - 4.92050i) q^{75} +(-2.36497 - 9.91150i) q^{77} +9.86329i q^{79} -1.00000 q^{81} +(1.63570 + 1.63570i) q^{83} +(1.40788 + 4.49678i) q^{85} +(-1.95945 + 1.95945i) q^{87} +5.05313 q^{89} +(7.18757 - 11.6925i) q^{91} +(1.69475 - 1.69475i) q^{93} +(0.0723134 - 0.138232i) q^{95} +(-6.85851 + 6.85851i) q^{97} +3.85136i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{7}+O(q^{10}) $ 16 * q + 8 * q^7	$ 16 q + 8 q^{7} + 16 q^{11} - 8 q^{15} + 8 q^{21} + 40 q^{23} + 8 q^{35} + 32 q^{37} + 16 q^{43} + 16 q^{51} + 24 q^{53} + 8 q^{57} - 8 q^{63} + 40 q^{65} + 32 q^{67} - 64 q^{71} - 24 q^{77} - 16 q^{81} + 48 q^{85} + 48 q^{91} + 24 q^{93} + 72 q^{95}+O(q^{100}) $ 16 * q + 8 * q^7 + 16 * q^11 - 8 * q^15 + 8 * q^21 + 40 * q^23 + 8 * q^35 + 32 * q^37 + 16 * q^43 + 16 * q^51 + 24 * q^53 + 8 * q^57 - 8 * q^63 + 40 * q^65 + 32 * q^67 - 64 * q^71 - 24 * q^77 - 16 * q^81 + 48 * q^85 + 48 * q^91 + 24 * q^93 + 72 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$421$	$1121$	$1471$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$		0			0
$5$	1.03649	−	1.98133i	0.463534	−	0.886079i
$5$	1.03649	−	1.98133i	0.463534	−	0.886079i
$6$		0			0
$7$	−0.614060	−	2.57351i	−0.232093	−	0.972694i
$7$	−0.614060	−	2.57351i	−0.232093	−	0.972694i
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	3.85136			1.16123			0.580615	−	0.814179i	$-0.302812\pi$
$11$	3.85136			1.16123			0.580615	+	0.814179i	$0.302812\pi$
$12$		0			0
$13$	3.66816	+	3.66816i	1.01737	+	1.01737i	0.999847	+	0.0175187i	$0.00557667\pi$
$13$	3.66816	+	3.66816i	1.01737	+	1.01737i	0.0175187	+	0.999847i	$0.494423\pi$
$14$		0			0
$15$	2.13393	−	0.668102i	0.550977	−	0.172503i
$16$		0			0
$17$	−1.49007	+	1.49007i	−0.361395	+	0.361395i	−0.864326	−	0.502931i	$-0.832255\pi$
$17$	−1.49007	+	1.49007i	−0.361395	+	0.361395i	0.502931	+	0.864326i	$0.332255\pi$
$18$		0			0
$19$	0.0697674			0.0160057			0.00800286	−	0.999968i	$-0.497453\pi$
$19$	0.0697674			0.0160057			0.00800286	+	0.999968i	$0.497453\pi$
$20$		0			0
$21$	1.38554	−	2.25395i	0.302349	−	0.491852i
$22$		0			0
$23$	0.534176	−	0.534176i	0.111383	−	0.111383i	−0.649218	−	0.760602i	$-0.724904\pi$
$23$	0.534176	−	0.534176i	0.111383	−	0.111383i	0.760602	+	0.649218i	$0.224904\pi$
$24$		0			0
$25$	−2.85136	−	4.10728i	−0.570272	−	0.821456i
$26$		0			0
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		0			0
$29$			2.77107i			0.514576i	0.966335	+	0.257288i	$0.0828288\pi$
$29$			2.77107i			0.514576i	−0.966335	+	0.257288i	$0.917171\pi$
$30$		0			0
$31$		−	2.39674i		−	0.430467i	−0.976563	−	0.215233i	$-0.930949\pi$
$31$		−	2.39674i		−	0.430467i	0.976563	−	0.215233i	$-0.0690512\pi$
$32$		0			0
$33$	2.72332	+	2.72332i	0.474070	+	0.474070i
$34$		0			0
$35$	−5.73544	−	1.45077i	−0.969466	−	0.245224i
$36$		0			0
$37$	6.18757	+	6.18757i	1.01723	+	1.01723i	0.999849	+	0.0173805i	$0.00553267\pi$
$37$	6.18757	+	6.18757i	1.01723	+	1.01723i	0.0173805	+	0.999849i	$0.494467\pi$
$38$		0			0
$39$			5.18757i			0.830675i
$40$		0			0
$41$		−	8.68077i		−	1.35571i	−0.735196	−	0.677854i	$-0.762910\pi$
$41$		−	8.68077i		−	1.35571i	0.735196	−	0.677854i	$-0.237090\pi$
$42$		0			0
$43$	2.77107	−	2.77107i	0.422585	−	0.422585i	−0.463508	−	0.886093i	$-0.653409\pi$
$43$	2.77107	−	2.77107i	0.422585	−	0.422585i	0.886093	+	0.463508i	$0.153409\pi$
$44$		0			0
$45$	1.98133	+	1.03649i	0.295360	+	0.154511i
$46$		0			0
$47$	5.49042	−	5.49042i	0.800860	−	0.800860i	−0.182370	−	0.983230i	$-0.558377\pi$
$47$	5.49042	−	5.49042i	0.800860	−	0.800860i	0.983230	+	0.182370i	$0.0583768\pi$
$48$		0			0
$49$	−6.24586	+	3.16057i	−0.892266	+	0.451510i
$50$		0			0
$51$	−2.10728			−0.295078
$52$		0			0
$53$	6.13823	−	6.13823i	0.843151	−	0.843151i	−0.146116	−	0.989267i	$-0.546677\pi$
$53$	6.13823	−	6.13823i	0.843151	−	0.843151i	0.989267	+	0.146116i	$0.0466774\pi$
$54$		0			0
$55$	3.99191	−	7.63083i	0.538269	−	1.02894i
$56$		0			0
$57$	0.0493330	+	0.0493330i	0.00653431	+	0.00653431i
$58$		0			0
$59$	−6.97440			−0.907990			−0.453995	−	0.891004i	$-0.650002\pi$
$59$	−6.97440			−0.907990			−0.453995	+	0.891004i	$0.650002\pi$
$60$		0			0
$61$		−	14.3107i		−	1.83230i	−0.400835	−	0.916150i	$-0.631280\pi$
$61$		−	14.3107i		−	1.83230i	0.400835	−	0.916150i	$-0.368720\pi$
$62$		0			0
$63$	2.57351	−	0.614060i	0.324231	−	0.0773643i
$64$		0			0
$65$	11.0699	−	3.46582i	1.37305	−	0.429883i
$66$		0			0
$67$	−0.416491	−	0.416491i	−0.0508824	−	0.0508824i	0.681208	−	0.732090i	$-0.261455\pi$
$67$	−0.416491	−	0.416491i	−0.0508824	−	0.0508824i	−0.732090	+	0.681208i	$0.761455\pi$
$68$		0			0
$69$	0.755439			0.0909442
$70$		0			0
$71$	8.12783			0.964595			0.482298	−	0.876007i	$-0.339802\pi$
$71$	8.12783			0.964595			0.482298	+	0.876007i	$0.339802\pi$
$72$		0			0
$73$	−9.55210	−	9.55210i	−1.11799	−	1.11799i	−0.992036	−	0.125953i	$-0.959801\pi$
$73$	−9.55210	−	9.55210i	−1.11799	−	1.11799i	−0.125953	−	0.992036i	$-0.540199\pi$
$74$		0			0
$75$	0.888068	−	4.92050i	0.102545	−	0.568171i
$76$		0			0
$77$	−2.36497	−	9.91150i	−0.269513	−	1.12952i
$78$		0			0
$79$			9.86329i			1.10971i	0.831948	+	0.554854i	$0.187226\pi$
$79$			9.86329i			1.10971i	−0.831948	+	0.554854i	$0.812774\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	1.63570	+	1.63570i	0.179541	+	0.179541i	0.791156	−	0.611615i	$-0.209480\pi$
$83$	1.63570	+	1.63570i	0.179541	+	0.179541i	−0.611615	+	0.791156i	$0.709480\pi$
$84$		0			0
$85$	1.40788	+	4.49678i	0.152706	+	0.487744i
$86$		0			0
$87$	−1.95945	+	1.95945i	−0.210075	+	0.210075i
$88$		0			0
$89$	5.05313			0.535631			0.267815	−	0.963470i	$-0.413698\pi$
$89$	5.05313			0.535631			0.267815	+	0.963470i	$0.413698\pi$
$90$		0			0
$91$	7.18757	−	11.6925i	0.753462	−	1.22571i
$92$		0			0
$93$	1.69475	−	1.69475i	0.175737	−	0.175737i
$94$		0			0
$95$	0.0723134	−	0.138232i	0.00741920	−	0.0141823i
$96$		0			0
$97$	−6.85851	+	6.85851i	−0.696376	+	0.696376i	−0.963627	−	0.267251i	$-0.913885\pi$
$97$	−6.85851	+	6.85851i	−0.696376	+	0.696376i	0.267251	+	0.963627i	$0.413885\pi$
$98$		0			0
$99$			3.85136i			0.387076i
$100$		0			0
$101$			19.1953i			1.91000i	0.296605	+	0.955000i	$0.404145\pi$
$101$			19.1953i			1.91000i	−0.296605	+	0.955000i	$0.595855\pi$
$102$		0			0
$103$	2.33825	+	2.33825i	0.230394	+	0.230394i	0.812857	−	0.582463i	$-0.197911\pi$
$103$	2.33825	+	2.33825i	0.230394	+	0.230394i	−0.582463	+	0.812857i	$0.697911\pi$
$104$		0			0
$105$	−3.02972	−	5.08142i	−0.295671	−	0.495895i
$106$		0			0
$107$	6.39747	+	6.39747i	0.618467	+	0.618467i	0.945138	−	0.326671i	$-0.105927\pi$
$107$	6.39747	+	6.39747i	0.618467	+	0.618467i	−0.326671	+	0.945138i	$0.605927\pi$
$108$		0			0
$109$		−	2.16057i		−	0.206945i	−0.994632	−	0.103473i	$-0.967005\pi$
$109$		−	2.16057i		−	0.206945i	0.994632	−	0.103473i	$-0.0329954\pi$
$110$		0			0
$111$			8.75054i			0.830564i
$112$		0			0
$113$	−4.13823	+	4.13823i	−0.389292	+	0.389292i	−0.874435	−	0.485143i	$-0.838768\pi$
$113$	−4.13823	+	4.13823i	−0.389292	+	0.389292i	0.485143	+	0.874435i	$0.338768\pi$
$114$		0			0
$115$	−0.504711	−	1.61205i	−0.0470645	−	0.150325i
$116$		0			0
$117$	−3.66816	+	3.66816i	−0.339122	+	0.339122i
$118$		0			0
$119$	4.74970	+	2.91971i	0.435404	+	0.267650i
$120$		0			0
$121$	3.83298			0.348453
$122$		0			0
$123$	6.13823	−	6.13823i	0.553466	−	0.553466i
$124$		0			0
$125$	−11.0933	+	1.39233i	−0.992215	+	0.124533i
$126$		0			0
$127$	4.83298	+	4.83298i	0.428858	+	0.428858i	0.888239	−	0.459381i	$-0.151929\pi$
$127$	4.83298	+	4.83298i	0.428858	+	0.428858i	−0.459381	+	0.888239i	$0.651929\pi$
$128$		0			0
$129$	3.91889			0.345039
$130$		0			0
$131$			0.647499i			0.0565722i	0.999600	+	0.0282861i	$0.00900495\pi$
$131$			0.647499i			0.0565722i	−0.999600	+	0.0282861i	$0.990995\pi$
$132$		0			0
$133$	−0.0428413	−	0.179547i	−0.00371481	−	0.0155687i
$134$		0			0
$135$	0.668102	+	2.13393i	0.0575011	+	0.183659i
$136$		0			0
$137$	10.2369	+	10.2369i	0.874597	+	0.874597i	0.992969	−	0.118372i	$-0.0377676\pi$
$137$	10.2369	+	10.2369i	0.874597	+	0.874597i	−0.118372	+	0.992969i	$0.537768\pi$
$138$		0			0
$139$	−22.1663			−1.88012			−0.940060	−	0.341009i	$-0.889231\pi$
$139$	−22.1663			−1.88012			−0.940060	+	0.341009i	$0.889231\pi$
$140$		0			0
$141$	7.76463			0.653900
$142$		0			0
$143$	14.1274	+	14.1274i	1.18139	+	1.18139i
$144$		0			0
$145$	5.49042	+	2.87220i	0.455955	+	0.238523i
$146$		0			0
$147$	−6.65135	−	2.18163i	−0.548594	−	0.179938i
$148$		0			0
$149$		−	11.0475i		−	0.905050i	−0.891752	−	0.452525i	$-0.850523\pi$
$149$		−	11.0475i		−	0.905050i	0.891752	−	0.452525i	$-0.149477\pi$
$150$		0			0
$151$	−18.3990			−1.49729			−0.748645	−	0.662972i	$-0.769295\pi$
$151$	−18.3990			−1.49729			−0.748645	+	0.662972i	$0.769295\pi$
$152$		0			0
$153$	−1.49007	−	1.49007i	−0.120465	−	0.120465i
$154$		0			0
$155$	−4.74873	−	2.48420i	−0.381428	−	0.199536i
$156$		0			0
$157$	1.04994	−	1.04994i	0.0837946	−	0.0837946i	−0.663967	−	0.747762i	$-0.731129\pi$
$157$	1.04994	−	1.04994i	0.0837946	−	0.0837946i	0.747762	+	0.663967i	$0.231129\pi$
$158$		0			0
$159$	8.68077			0.688430
$160$		0			0
$161$	−1.70272	−	1.04669i	−0.134193	−	0.0824907i
$162$		0			0
$163$	−5.50539	+	5.50539i	−0.431215	+	0.431215i	−0.889042	−	0.457826i	$-0.848628\pi$
$163$	−5.50539	+	5.50539i	−0.431215	+	0.431215i	0.457826	+	0.889042i	$0.348628\pi$
$164$		0			0
$165$	8.21852	−	2.57310i	0.639811	−	0.200316i
$166$		0			0
$167$	1.88968	−	1.88968i	0.146228	−	0.146228i	−0.630203	−	0.776431i	$-0.717028\pi$
$167$	1.88968	−	1.88968i	0.146228	−	0.146228i	0.776431	+	0.630203i	$0.217028\pi$
$168$		0			0
$169$			13.9108i			1.07006i
$170$		0			0
$171$			0.0697674i			0.00533524i
$172$		0			0
$173$	4.90751	+	4.90751i	0.373111	+	0.373111i	0.868609	−	0.495498i	$-0.165014\pi$
$173$	4.90751	+	4.90751i	0.373111	+	0.373111i	−0.495498	+	0.868609i	$0.665014\pi$
$174$		0			0
$175$	−8.81920	+	9.86011i	−0.666669	+	0.745354i
$176$		0			0
$177$	−4.93165	−	4.93165i	−0.370685	−	0.370685i
$178$		0			0
$179$		−	18.5857i		−	1.38916i	−0.719416	−	0.694579i	$-0.755591\pi$
$179$		−	18.5857i		−	1.38916i	0.719416	−	0.694579i	$-0.244409\pi$
$180$		0			0
$181$		−	8.48528i		−	0.630706i	−0.948974	−	0.315353i	$-0.897877\pi$
$181$		−	8.48528i		−	0.630706i	0.948974	−	0.315353i	$-0.102123\pi$
$182$		0			0
$183$	10.1192	−	10.1192i	0.748034	−	0.748034i
$184$		0			0
$185$	18.6730	−	5.84625i	1.37287	−	0.429825i
$186$		0			0
$187$	−5.73880	+	5.73880i	−0.419663	+	0.419663i
$188$		0			0
$189$	2.25395	+	1.38554i	0.163951	+	0.100783i
$190$		0			0
$191$	5.39351			0.390261			0.195130	−	0.980777i	$-0.437487\pi$
$191$	5.39351			0.390261			0.195130	+	0.980777i	$0.437487\pi$
$192$		0			0
$193$	−4.80599	+	4.80599i	−0.345943	+	0.345943i	−0.858596	−	0.512653i	$-0.828663\pi$
$193$	−4.80599	+	4.80599i	−0.345943	+	0.345943i	0.512653	+	0.858596i	$0.328663\pi$
$194$		0			0
$195$	10.2783	+	5.37688i	0.736044	+	0.385046i
$196$		0			0
$197$	12.6739	+	12.6739i	0.902981	+	0.902981i	0.995693	−	0.0927124i	$-0.0295537\pi$
$197$	12.6739	+	12.6739i	0.902981	+	0.902981i	−0.0927124	+	0.995693i	$0.529554\pi$
$198$		0			0
$199$	−2.67111			−0.189350			−0.0946750	−	0.995508i	$-0.530181\pi$
$199$	−2.67111			−0.189350			−0.0946750	+	0.995508i	$0.530181\pi$
$200$		0			0
$201$		−	0.589007i		−	0.0415453i
$202$		0			0
$203$	7.13138	−	1.70161i	0.500524	−	0.119429i
$204$		0			0
$205$	−17.1995	−	8.99757i	−1.20127	−	0.628417i
$206$		0			0
$207$	0.534176	+	0.534176i	0.0371278	+	0.0371278i
$208$		0			0
$209$	0.268699			0.0185863
$210$		0			0
$211$	12.0239			0.827757			0.413879	−	0.910332i	$-0.364174\pi$
$211$	12.0239			0.827757			0.413879	+	0.910332i	$0.364174\pi$
$212$		0			0
$213$	5.74724	+	5.74724i	0.393794	+	0.393794i
$214$		0			0
$215$	−2.61822	−	8.36262i	−0.178561	−	0.570326i
$216$		0			0
$217$	−6.16802	+	1.47174i	−0.418712	+	0.0999082i
$218$		0			0
$219$		−	13.5087i		−	0.912834i
$220$		0			0
$221$	−10.9316			−0.735342
$222$		0			0
$223$	−11.6925	−	11.6925i	−0.782988	−	0.782988i	0.197346	−	0.980334i	$-0.436768\pi$
$223$	−11.6925	−	11.6925i	−0.782988	−	0.782988i	−0.980334	+	0.197346i	$0.936768\pi$
$224$		0			0
$225$	4.10728	−	2.85136i	0.273819	−	0.190091i
$226$		0			0
$227$	1.10518	−	1.10518i	0.0733535	−	0.0733535i	−0.669478	−	0.742832i	$-0.733482\pi$
$227$	1.10518	−	1.10518i	0.0733535	−	0.0733535i	0.742832	+	0.669478i	$0.233482\pi$
$228$		0			0
$229$	−7.83309			−0.517625			−0.258812	−	0.965928i	$-0.583331\pi$
$229$	−7.83309			−0.517625			−0.258812	+	0.965928i	$0.583331\pi$
$230$		0			0
$231$	5.33620	−	8.68077i	0.351096	−	0.571153i
$232$		0			0
$233$	1.00797	−	1.00797i	0.0660345	−	0.0660345i	−0.673318	−	0.739353i	$-0.735132\pi$
$233$	1.00797	−	1.00797i	0.0660345	−	0.0660345i	0.739353	+	0.673318i	$0.235132\pi$
$234$		0			0
$235$	−5.18757	−	16.5691i	−0.338399	−	1.08085i
$236$		0			0
$237$	−6.97440	+	6.97440i	−0.453036	+	0.453036i
$238$		0			0
$239$			20.2805i			1.31183i	0.754833	+	0.655917i	$0.227718\pi$
$239$			20.2805i			1.31183i	−0.754833	+	0.655917i	$0.772282\pi$
$240$		0			0
$241$		−	2.76994i		−	0.178427i	−0.996013	−	0.0892136i	$-0.971565\pi$
$241$		−	2.76994i		−	0.178427i	0.996013	−	0.0892136i	$-0.0284354\pi$
$242$		0			0
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$		0			0
$245$	−0.211650	+	15.6510i	−0.0135218	+	0.999909i
$246$		0			0
$247$	0.255918	+	0.255918i	0.0162837	+	0.0162837i
$248$		0			0
$249$			2.31322i			0.146595i
$250$		0			0
$251$		−	6.09982i		−	0.385017i	−0.981295	−	0.192509i	$-0.938338\pi$
$251$		−	6.09982i		−	0.385017i	0.981295	−	0.192509i	$-0.0616623\pi$
$252$		0			0
$253$	2.05731	−	2.05731i	0.129342	−	0.129342i
$254$		0			0
$255$	−2.18418	+	4.17522i	−0.136779	+	0.261463i
$256$		0			0
$257$	2.01843	−	2.01843i	0.125906	−	0.125906i	−0.641346	−	0.767252i	$-0.721624\pi$
$257$	2.01843	−	2.01843i	0.125906	−	0.125906i	0.767252	+	0.641346i	$0.221624\pi$
$258$		0			0
$259$	12.1242	−	19.7233i	0.753361	−	1.22554i
$260$		0			0
$261$	−2.77107			−0.171525
$262$		0			0
$263$	−16.7686	+	16.7686i	−1.03400	+	1.03400i	−0.0345941	+	0.999401i	$0.511014\pi$
$263$	−16.7686	+	16.7686i	−1.03400	+	1.03400i	−0.999401	+	0.0345941i	$0.988986\pi$
$264$		0			0
$265$	−5.79964	−	18.5241i	−0.356269	−	1.13793i
$266$		0			0
$267$	3.57310	+	3.57310i	0.218670	+	0.218670i
$268$		0			0
$269$	−24.7351			−1.50813			−0.754064	−	0.656801i	$-0.771909\pi$
$269$	−24.7351			−1.50813			−0.754064	+	0.656801i	$0.771909\pi$
$270$		0			0
$271$			4.13470i			0.251165i	0.992083	+	0.125583i	$0.0400800\pi$
$271$			4.13470i			0.251165i	−0.992083	+	0.125583i	$0.959920\pi$
$272$		0			0
$273$	13.3502	−	3.18548i	0.807993	−	0.192794i
$274$		0			0
$275$	−10.9816	−	15.8186i	−0.662217	−	0.953898i
$276$		0			0
$277$	−12.1128	−	12.1128i	−0.727786	−	0.727786i	0.242393	−	0.970178i	$-0.422068\pi$
$277$	−12.1128	−	12.1128i	−0.727786	−	0.727786i	−0.970178	+	0.242393i	$0.922068\pi$
$278$		0			0
$279$	2.39674			0.143489
$280$		0			0
$281$	5.25279			0.313355			0.156678	−	0.987650i	$-0.449922\pi$
$281$	5.25279			0.313355			0.156678	+	0.987650i	$0.449922\pi$
$282$		0			0
$283$	−1.66729	−	1.66729i	−0.0991101	−	0.0991101i	0.655813	−	0.754923i	$-0.272326\pi$
$283$	−1.66729	−	1.66729i	−0.0991101	−	0.0991101i	−0.754923	+	0.655813i	$0.772326\pi$
$284$		0			0
$285$	0.148878	−	0.0466117i	0.00881879	−	0.00276104i
$286$		0			0
$287$	−22.3400	+	5.33051i	−1.31869	+	0.314650i
$288$		0			0
$289$			12.5594i			0.738787i
$290$		0			0
$291$	−9.69940			−0.568589
$292$		0			0
$293$	15.2556	+	15.2556i	0.891240	+	0.891240i	0.994640	−	0.103400i	$-0.0329722\pi$
$293$	15.2556	+	15.2556i	0.891240	+	0.891240i	−0.103400	+	0.994640i	$0.532972\pi$
$294$		0			0
$295$	−7.22893	+	13.8186i	−0.420884	+	0.804551i
$296$		0			0
$297$	−2.72332	+	2.72332i	−0.158023	+	0.158023i
$298$		0			0
$299$	3.91889			0.226635
$300$		0			0
$301$	−8.83298	−	5.42977i	−0.509125	−	0.312967i
$302$		0			0
$303$	−13.5731	+	13.5731i	−0.779754	+	0.779754i
$304$		0			0
$305$	−28.3543	−	14.8330i	−1.62356	−	0.849334i
$306$		0			0
$307$	−14.6198	+	14.6198i	−0.834394	+	0.834394i	−0.988114	−	0.153721i	$-0.950874\pi$
$307$	−14.6198	+	14.6198i	−0.834394	+	0.834394i	0.153721	+	0.988114i	$0.450874\pi$
$308$		0			0
$309$			3.30678i			0.188116i
$310$		0			0
$311$			2.86218i			0.162299i	0.996702	+	0.0811497i	$0.0258592\pi$
$311$			2.86218i			0.162299i	−0.996702	+	0.0811497i	$0.974141\pi$
$312$		0			0
$313$	9.41824	+	9.41824i	0.532350	+	0.532350i	0.921271	−	0.388921i	$-0.127152\pi$
$313$	9.41824	+	9.41824i	0.532350	+	0.532350i	−0.388921	+	0.921271i	$0.627152\pi$
$314$		0			0
$315$	1.45077	−	5.73544i	0.0817414	−	0.323155i
$316$		0			0
$317$	7.38310	+	7.38310i	0.414676	+	0.414676i	0.883364	−	0.468688i	$-0.155273\pi$
$317$	7.38310	+	7.38310i	0.414676	+	0.414676i	−0.468688	+	0.883364i	$0.655273\pi$
$318$		0			0
$319$			10.6724i			0.597540i
$320$		0			0
$321$			9.04739i			0.504976i
$322$		0			0
$323$	−0.103958	+	0.103958i	−0.00578440	+	0.00578440i
$324$		0			0
$325$	4.60691	−	25.5254i	0.255545	−	1.41590i
$326$		0			0
$327$	1.52776	−	1.52776i	0.0844851	−	0.0844851i
$328$		0			0
$329$	−17.5011	−	10.7582i	−0.964866	−	0.593118i
$330$		0			0
$331$	−23.6200			−1.29827			−0.649136	−	0.760672i	$-0.724870\pi$
$331$	−23.6200			−1.29827			−0.649136	+	0.760672i	$0.724870\pi$
$332$		0			0
$333$	−6.18757	+	6.18757i	−0.339076	+	0.339076i
$334$		0			0
$335$	−1.25690	+	0.393517i	−0.0686716	+	0.0215001i
$336$		0			0
$337$	−4.93809	−	4.93809i	−0.268995	−	0.268995i	0.559700	−	0.828695i	$-0.310916\pi$
$337$	−4.93809	−	4.93809i	−0.268995	−	0.268995i	−0.828695	+	0.559700i	$0.810916\pi$
$338$		0			0
$339$	−5.85234			−0.317856
$340$		0			0
$341$		−	9.23070i		−	0.499870i
$342$		0			0
$343$	11.9691	+	14.1330i	0.646270	+	0.763109i
$344$		0			0
$345$	0.783008	−	1.49678i	0.0421558	−	0.0805838i
$346$		0			0
$347$	−5.83694	−	5.83694i	−0.313343	−	0.313343i	0.532860	−	0.846203i	$-0.321117\pi$
$347$	−5.83694	−	5.83694i	−0.313343	−	0.313343i	−0.846203	+	0.532860i	$0.821117\pi$
$348$		0			0
$349$	16.9121			0.905282			0.452641	−	0.891693i	$-0.350482\pi$
$349$	16.9121			0.905282			0.452641	+	0.891693i	$0.350482\pi$
$350$		0			0
$351$	−5.18757			−0.276892
$352$		0			0
$353$	11.1265	+	11.1265i	0.592202	+	0.592202i	0.938226	−	0.346024i	$-0.112468\pi$
$353$	11.1265	+	11.1265i	0.592202	+	0.592202i	−0.346024	+	0.938226i	$0.612468\pi$
$354$		0			0
$355$	8.42444	−	16.1039i	0.447123	−	0.854708i
$356$		0			0
$357$	1.29400	+	5.42309i	0.0684855	+	0.287021i
$358$		0			0
$359$			8.14864i			0.430069i	0.976606	+	0.215034i	$0.0689864\pi$
$359$			8.14864i			0.430069i	−0.976606	+	0.215034i	$0.931014\pi$
$360$		0			0
$361$	−18.9951			−0.999744
$362$		0			0
$363$	2.71033	+	2.71033i	0.142255	+	0.142255i
$364$		0			0
$365$	−28.8266	+	9.02520i	−1.50885	+	0.472401i
$366$		0			0
$367$	14.7480	−	14.7480i	0.769840	−	0.769840i	−0.208238	−	0.978078i	$-0.566773\pi$
$367$	14.7480	−	14.7480i	0.769840	−	0.769840i	0.978078	+	0.208238i	$0.0667728\pi$
$368$		0			0
$369$	8.68077			0.451903
$370$		0			0
$371$	−19.5660	−	12.0275i	−1.01582	−	0.624438i
$372$		0			0
$373$	1.49461	−	1.49461i	0.0773880	−	0.0773880i	−0.667353	−	0.744741i	$-0.732573\pi$
$373$	1.49461	−	1.49461i	0.0773880	−	0.0773880i	0.744741	+	0.667353i	$0.232573\pi$
$374$		0			0
$375$	−8.82867	−	6.85963i	−0.455911	−	0.354230i
$376$		0			0
$377$	−10.1648	+	10.1648i	−0.523511	+	0.523511i
$378$		0			0
$379$			18.7135i			0.961248i	0.876927	+	0.480624i	$0.159590\pi$
$379$			18.7135i			0.961248i	−0.876927	+	0.480624i	$0.840410\pi$
$380$		0			0
$381$			6.83487i			0.350161i
$382$		0			0
$383$	20.9354	+	20.9354i	1.06975	+	1.06975i	0.997378	+	0.0723706i	$0.0230564\pi$
$383$	20.9354	+	20.9354i	1.06975	+	1.06975i	0.0723706	+	0.997378i	$0.476944\pi$
$384$		0			0
$385$	−22.0893	−	5.58742i	−1.12577	−	0.284761i
$386$		0			0
$387$	2.77107	+	2.77107i	0.140862	+	0.140862i
$388$		0			0
$389$		−	25.6611i		−	1.30107i	−0.759477	−	0.650535i	$-0.774545\pi$
$389$		−	25.6611i		−	1.30107i	0.759477	−	0.650535i	$-0.225455\pi$
$390$		0			0
$391$			1.59192i			0.0805069i
$392$		0			0
$393$	−0.457851	+	0.457851i	−0.0230955	+	0.0230955i
$394$		0			0
$395$	19.5425	+	10.2232i	0.983288	+	0.514387i
$396$		0			0
$397$	−6.73585	+	6.73585i	−0.338063	+	0.338063i	−0.855638	−	0.517575i	$-0.826835\pi$
$397$	−6.73585	+	6.73585i	−0.338063	+	0.338063i	0.517575	+	0.855638i	$0.326835\pi$
$398$		0			0
$399$	0.0966653	−	0.157252i	0.00483932	−	0.00787245i
$400$		0			0
$401$	14.7503			0.736593			0.368296	−	0.929708i	$-0.379941\pi$
$401$	14.7503			0.736593			0.368296	+	0.929708i	$0.379941\pi$
$402$		0			0
$403$	8.79162	−	8.79162i	0.437942	−	0.437942i
$404$		0			0
$405$	−1.03649	+	1.98133i	−0.0515038	+	0.0984532i
$406$		0			0
$407$	23.8305	+	23.8305i	1.18124	+	1.18124i
$408$		0			0
$409$	−10.5604			−0.522180			−0.261090	−	0.965315i	$-0.584082\pi$
$409$	−10.5604			−0.522180			−0.261090	+	0.965315i	$0.584082\pi$
$410$		0			0
$411$			14.4772i			0.714106i
$412$		0			0
$413$	4.28270	+	17.9487i	0.210738	+	0.883196i
$414$		0			0
$415$	4.93625	−	1.54547i	0.242311	−	0.0758641i
$416$		0			0
$417$	−15.6739	−	15.6739i	−0.767556	−	0.767556i
$418$		0			0
$419$	15.5472			0.759532			0.379766	−	0.925083i	$-0.376004\pi$
$419$	15.5472			0.759532			0.379766	+	0.925083i	$0.376004\pi$
$420$		0			0
$421$	3.29886			0.160776			0.0803882	−	0.996764i	$-0.474384\pi$
$421$	3.29886			0.160776			0.0803882	+	0.996764i	$0.474384\pi$
$422$		0			0
$423$	5.49042	+	5.49042i	0.266953	+	0.266953i
$424$		0			0
$425$	10.3689	+	1.87141i	0.502964	+	0.0907766i
$426$		0			0
$427$	−36.8287	+	8.78764i	−1.78227	+	0.425264i
$428$		0			0
$429$			19.9792i			0.964604i
$430$		0			0
$431$	14.0911			0.678743			0.339371	−	0.940652i	$-0.389786\pi$
$431$	14.0911			0.678743			0.339371	+	0.940652i	$0.389786\pi$
$432$		0			0
$433$	1.72650	+	1.72650i	0.0829702	+	0.0829702i	0.747374	−	0.664404i	$-0.231314\pi$
$433$	1.72650	+	1.72650i	0.0829702	+	0.0829702i	−0.664404	+	0.747374i	$0.731314\pi$
$434$		0			0
$435$	1.85136	+	5.91327i	0.0887660	+	0.283519i
$436$		0			0
$437$	0.0372681	−	0.0372681i	0.00178277	−	0.00178277i
$438$		0			0
$439$	−27.1172			−1.29423			−0.647116	−	0.762392i	$-0.724025\pi$
$439$	−27.1172			−1.29423			−0.647116	+	0.762392i	$0.724025\pi$
$440$		0			0
$441$	−3.16057	−	6.24586i	−0.150503	−	0.297422i
$442$		0			0
$443$	24.1502	−	24.1502i	1.14741	−	1.14741i	0.160349	−	0.987060i	$-0.448738\pi$
$443$	24.1502	−	24.1502i	1.14741	−	1.14741i	0.987060	−	0.160349i	$-0.0512618\pi$
$444$		0			0
$445$	5.23754	−	10.0119i	0.248283	−	0.474611i
$446$		0			0
$447$	7.81179	−	7.81179i	0.369485	−	0.369485i
$448$		0			0
$449$			9.80267i			0.462617i	0.972881	+	0.231308i	$0.0743006\pi$
$449$			9.80267i			0.462617i	−0.972881	+	0.231308i	$0.925699\pi$
$450$		0			0
$451$		−	33.4328i		−	1.57429i
$452$		0			0
$453$	−13.0101	−	13.0101i	−0.611266	−	0.611266i
$454$		0			0
$455$	−15.7169	−	26.3602i	−0.736819	−	1.23578i
$456$		0			0
$457$	0.550071	+	0.550071i	0.0257312	+	0.0257312i	0.719855	−	0.694124i	$-0.244208\pi$
$457$	0.550071	+	0.550071i	0.0257312	+	0.0257312i	−0.694124	+	0.719855i	$0.744208\pi$
$458$		0			0
$459$		−	2.10728i		−	0.0983594i
$460$		0			0
$461$		−	0.831786i		−	0.0387401i	−0.999812	−	0.0193701i	$-0.993834\pi$
$461$		−	0.831786i		−	0.0387401i	0.999812	−	0.0193701i	$-0.00616607\pi$
$462$		0			0
$463$	−5.45140	+	5.45140i	−0.253348	+	0.253348i	−0.822342	−	0.568994i	$-0.807333\pi$
$463$	−5.45140	+	5.45140i	−0.253348	+	0.253348i	0.568994	+	0.822342i	$0.307333\pi$
$464$		0			0
$465$	−1.60127	−	5.11446i	−0.0742569	−	0.237177i
$466$		0			0
$467$	−23.2827	+	23.2827i	−1.07740	+	1.07740i	−0.0806551	+	0.996742i	$0.525701\pi$
$467$	−23.2827	+	23.2827i	−1.07740	+	1.07740i	−0.996742	+	0.0806551i	$0.974299\pi$
$468$		0			0
$469$	−0.816091	+	1.32759i	−0.0376836	+	0.0613025i
$470$		0			0
$471$	1.48484			0.0684180
$472$		0			0
$473$	10.6724	−	10.6724i	0.490718	−	0.490718i
$474$		0			0
$475$	−0.198932	−	0.286554i	−0.00912762	−	0.0131480i
$476$		0			0
$477$	6.13823	+	6.13823i	0.281050	+	0.281050i
$478$		0			0
$479$	−40.4319			−1.84738			−0.923691	−	0.383138i	$-0.874843\pi$
$479$	−40.4319			−1.84738			−0.923691	+	0.383138i	$0.874843\pi$
$480$		0			0
$481$			45.3940i			2.06979i
$482$		0			0
$483$	−0.463885	−	1.94413i	−0.0211075	−	0.0884609i
$484$		0			0
$485$	6.48019	+	20.6978i	0.294250	+	0.939839i
$486$		0			0
$487$	7.22893	+	7.22893i	0.327574	+	0.327574i	0.851663	−	0.524089i	$-0.175594\pi$
$487$	7.22893	+	7.22893i	0.327574	+	0.327574i	−0.524089	+	0.851663i	$0.675594\pi$
$488$		0			0
$489$	−7.78580			−0.352086
$490$		0			0
$491$	−20.1040			−0.907279			−0.453639	−	0.891185i	$-0.649875\pi$
$491$	−20.1040			−0.907279			−0.453639	+	0.891185i	$0.649875\pi$
$492$		0			0
$493$	−4.12910	−	4.12910i	−0.185965	−	0.185965i
$494$		0			0
$495$	7.63083	+	3.99191i	0.342980	+	0.179423i
$496$		0			0
$497$	−4.99097	−	20.9170i	−0.223876	−	0.938256i
$498$		0			0
$499$			15.4227i			0.690414i	0.938527	+	0.345207i	$0.112191\pi$
$499$			15.4227i			0.690414i	−0.938527	+	0.345207i	$0.887809\pi$
$500$		0			0
$501$	2.67241			0.119394
$502$		0			0
$503$	25.9985	+	25.9985i	1.15922	+	1.15922i	0.984644	+	0.174573i	$0.0558546\pi$
$503$	25.9985	+	25.9985i	1.15922	+	1.15922i	0.174573	+	0.984644i	$0.444145\pi$
$504$		0			0
$505$	38.0322	+	19.8958i	1.69241	+	0.885350i
$506$		0			0
$507$	−9.83645	+	9.83645i	−0.436852	+	0.436852i
$508$		0			0
$509$	−37.1271			−1.64563			−0.822816	−	0.568309i	$-0.807598\pi$
$509$	−37.1271			−1.64563			−0.822816	+	0.568309i	$0.807598\pi$
$510$		0			0
$511$	−18.7168	+	30.4479i	−0.827983	+	1.34694i
$512$		0			0
$513$	−0.0493330	+	0.0493330i	−0.00217810	+	0.00217810i
$514$		0			0
$515$	7.05642	−	2.20927i	0.310943	−	0.0973519i
$516$		0			0
$517$	21.1456	−	21.1456i	0.929982	−	0.929982i
$518$		0			0
$519$			6.94026i			0.304644i
$520$		0			0
$521$			2.59132i			0.113528i	0.998388	+	0.0567639i	$0.0180782\pi$
$521$			2.59132i			0.113528i	−0.998388	+	0.0567639i	$0.981922\pi$
$522$		0			0
$523$	−6.08854	−	6.08854i	−0.266233	−	0.266233i	0.561347	−	0.827581i	$-0.310283\pi$
$523$	−6.08854	−	6.08854i	−0.266233	−	0.266233i	−0.827581	+	0.561347i	$0.810283\pi$
$524$		0			0
$525$	−13.2083	+	0.736034i	−0.576456	+	0.0321232i
$526$		0			0
$527$	3.57131	+	3.57131i	0.155569	+	0.155569i
$528$		0			0
$529$			22.4293i			0.975187i
$530$		0			0
$531$		−	6.97440i		−	0.302663i
$532$		0			0
$533$	31.8425	−	31.8425i	1.37925	−	1.37925i
$534$		0			0
$535$	19.3065	−	6.04458i	0.834691	−	0.261330i
$536$		0			0
$537$	13.1421	−	13.1421i	0.567122	−	0.567122i
$538$		0			0
$539$	−24.0551	+	12.1725i	−1.03613	+	0.524307i
$540$		0			0
$541$	−33.4638			−1.43872			−0.719360	−	0.694638i	$-0.755565\pi$
$541$	−33.4638			−1.43872			−0.719360	+	0.694638i	$0.755565\pi$
$542$		0			0
$543$	6.00000	−	6.00000i	0.257485	−	0.257485i
$544$		0			0
$545$	−4.28081	−	2.23942i	−0.183370	−	0.0959262i
$546$		0			0
$547$	0.828381	+	0.828381i	0.0354190	+	0.0354190i	0.724594	−	0.689175i	$-0.242027\pi$
$547$	0.828381	+	0.828381i	0.0354190	+	0.0354190i	−0.689175	+	0.724594i	$0.742027\pi$
$548$		0			0
$549$	14.3107			0.610767
$550$		0			0
$551$			0.193331i			0.00823616i
$552$		0			0
$553$	25.3832	−	6.05665i	1.07941	−	0.257555i
$554$		0			0
$555$	17.3377	+	9.06988i	0.735946	+	0.384995i
$556$		0			0
$557$	14.7120	+	14.7120i	0.623366	+	0.623366i	0.946391	−	0.323024i	$-0.104700\pi$
$557$	14.7120	+	14.7120i	0.623366	+	0.623366i	−0.323024	+	0.946391i	$0.604700\pi$
$558$		0			0
$559$	20.3295			0.859846
$560$		0			0
$561$	−8.11589			−0.342653
$562$		0			0
$563$	−23.9693	−	23.9693i	−1.01019	−	1.01019i	−0.999948	−	0.0102391i	$-0.996741\pi$
$563$	−23.9693	−	23.9693i	−1.01019	−	1.01019i	−0.0102391	−	0.999948i	$-0.503259\pi$
$564$		0			0
$565$	3.90996	+	12.4885i	0.164493	+	0.525394i
$566$		0			0
$567$	0.614060	+	2.57351i	0.0257881	+	0.108077i
$568$		0			0
$569$		−	15.6660i		−	0.656751i	−0.944547	−	0.328376i	$-0.893499\pi$
$569$		−	15.6660i		−	0.656751i	0.944547	−	0.328376i	$-0.106501\pi$
$570$		0			0
$571$	−36.9887			−1.54793			−0.773964	−	0.633229i	$-0.781729\pi$
$571$	−36.9887			−1.54793			−0.773964	+	0.633229i	$0.781729\pi$
$572$		0			0
$573$	3.81379	+	3.81379i	0.159323	+	0.159323i
$574$		0			0
$575$	−3.71714	−	0.670882i	−0.155015	−	0.0279777i
$576$		0			0
$577$	−15.5587	+	15.5587i	−0.647717	+	0.647717i	−0.952441	−	0.304724i	$-0.901436\pi$
$577$	−15.5587	+	15.5587i	−0.647717	+	0.647717i	0.304724	+	0.952441i	$0.401436\pi$
$578$		0			0
$579$	−6.79669			−0.282461
$580$		0			0
$581$	3.20506	−	5.21389i	0.132968	−	0.216309i
$582$		0			0
$583$	23.6405	−	23.6405i	0.979091	−	0.979091i
$584$		0			0
$585$	3.46582	+	11.0699i	0.143294	+	0.457683i
$586$		0			0
$587$	−15.7111	+	15.7111i	−0.648468	+	0.648468i	−0.952623	−	0.304155i	$-0.901626\pi$
$587$	−15.7111	+	15.7111i	−0.648468	+	0.648468i	0.304155	+	0.952623i	$0.401626\pi$
$588$		0			0
$589$		−	0.167214i		−	0.00688993i
$590$		0			0
$591$			17.9237i			0.737281i
$592$		0			0
$593$	1.85199	+	1.85199i	0.0760523	+	0.0760523i	0.744110	−	0.668057i	$-0.232874\pi$
$593$	1.85199	+	1.85199i	0.0760523	+	0.0760523i	−0.668057	+	0.744110i	$0.732874\pi$
$594$		0			0
$595$	10.7080	−	6.38447i	0.438984	−	0.261738i
$596$		0			0
$597$	−1.88876	−	1.88876i	−0.0773018	−	0.0773018i
$598$		0			0
$599$		−	47.3151i		−	1.93324i	−0.256208	−	0.966622i	$-0.582473\pi$
$599$		−	47.3151i		−	1.93324i	0.256208	−	0.966622i	$-0.417527\pi$
$600$		0			0
$601$			11.0819i			0.452041i	0.974123	+	0.226021i	$0.0725717\pi$
$601$			11.0819i			0.452041i	−0.974123	+	0.226021i	$0.927428\pi$
$602$		0			0
$603$	0.416491	−	0.416491i	0.0169608	−	0.0169608i
$604$		0			0
$605$	3.97286	−	7.59441i	0.161520	−	0.308757i
$606$		0			0
$607$	7.54653	−	7.54653i	0.306304	−	0.306304i	−0.537170	−	0.843474i	$-0.680507\pi$
$607$	7.54653	−	7.54653i	0.306304	−	0.306304i	0.843474	+	0.537170i	$0.180507\pi$
$608$		0			0
$609$	6.24586	+	3.83943i	0.253095	+	0.155581i
$610$		0			0
$611$	40.2795			1.62953
$612$		0			0
$613$	−2.62487	+	2.62487i	−0.106017	+	0.106017i	−0.758126	−	0.652108i	$-0.773885\pi$
$613$	−2.62487	+	2.62487i	−0.106017	+	0.106017i	0.652108	+	0.758126i	$0.273885\pi$
$614$		0			0
$615$	−5.79964	−	18.5241i	−0.233864	−	0.746965i
$616$		0			0
$617$	11.3212	+	11.3212i	0.455774	+	0.455774i	0.897266	−	0.441491i	$-0.145550\pi$
$617$	11.3212	+	11.3212i	0.455774	+	0.455774i	−0.441491	+	0.897266i	$0.645550\pi$
$618$		0			0
$619$	−9.06771			−0.364462			−0.182231	−	0.983256i	$-0.558332\pi$
$619$	−9.06771			−0.364462			−0.182231	+	0.983256i	$0.558332\pi$
$620$		0			0
$621$			0.755439i			0.0303147i
$622$		0			0
$623$	−3.10292	−	13.0043i	−0.124316	−	0.521005i
$624$		0			0
$625$	−8.73948	+	23.4227i	−0.349579	+	0.936907i
$626$		0			0
$627$	0.189999	+	0.189999i	0.00758783	+	0.00758783i
$628$		0			0
$629$	−18.4398			−0.735244
$630$		0			0
$631$	9.67260			0.385060			0.192530	−	0.981291i	$-0.438331\pi$
$631$	9.67260			0.385060			0.192530	+	0.981291i	$0.438331\pi$
$632$		0			0
$633$	8.50216	+	8.50216i	0.337930	+	0.337930i
$634$		0			0
$635$	14.5851	−	4.56639i	0.578792	−	0.181212i
$636$		0			0
$637$	−34.5043	−	11.3173i	−1.36711	−	0.448409i
$638$		0			0
$639$			8.12783i			0.321532i
$640$		0			0
$641$	−40.5847			−1.60300			−0.801500	−	0.597995i	$-0.795964\pi$
$641$	−40.5847			−1.60300			−0.801500	+	0.597995i	$0.795964\pi$
$642$		0			0
$643$	3.89544	+	3.89544i	0.153621	+	0.153621i	0.779733	−	0.626112i	$-0.215355\pi$
$643$	3.89544	+	3.89544i	0.153621	+	0.153621i	−0.626112	+	0.779733i	$0.715355\pi$
$644$		0			0
$645$	4.06191	−	7.76463i	0.159937	−	0.305732i
$646$		0			0
$647$	16.8414	−	16.8414i	0.662104	−	0.662104i	−0.293772	−	0.955876i	$-0.594911\pi$
$647$	16.8414	−	16.8414i	0.662104	−	0.662104i	0.955876	+	0.293772i	$0.0949106\pi$
$648$		0			0
$649$	−26.8609			−1.05438
$650$		0			0
$651$	−5.40212	−	3.32077i	−0.211726	−	0.130151i
$652$		0			0
$653$	−22.9951	+	22.9951i	−0.899867	+	0.899867i	−0.995424	−	0.0955569i	$-0.969537\pi$
$653$	−22.9951	+	22.9951i	−0.899867	+	0.899867i	0.0955569	+	0.995424i	$0.469537\pi$
$654$		0			0
$655$	1.28291	+	0.671128i	0.0501275	+	0.0262232i
$656$		0			0
$657$	9.55210	−	9.55210i	0.372663	−	0.372663i
$658$		0			0
$659$		−	32.7543i		−	1.27593i	−0.770067	−	0.637963i	$-0.779777\pi$
$659$		−	32.7543i		−	1.27593i	0.770067	−	0.637963i	$-0.220223\pi$
$660$		0			0
$661$		−	32.5174i		−	1.26478i	−0.774650	−	0.632391i	$-0.782074\pi$
$661$		−	32.5174i		−	1.26478i	0.774650	−	0.632391i	$-0.217926\pi$
$662$		0			0
$663$	−7.72984	−	7.72984i	−0.300202	−	0.300202i
$664$		0			0
$665$	−0.400147	−	0.101216i	−0.0155170	−	0.00392499i
$666$		0			0
$667$	1.48024	+	1.48024i	0.0573152	+	0.0573152i
$668$		0			0
$669$		−	16.5357i		−	0.639307i
$670$		0			0
$671$		−	55.1158i		−	2.12772i
$672$		0			0
$673$	−16.7534	+	16.7534i	−0.645796	+	0.645796i	−0.951974	−	0.306179i	$-0.900950\pi$
$673$	−16.7534	+	16.7534i	−0.645796	+	0.645796i	0.306179	+	0.951974i	$0.400950\pi$
$674$		0			0
$675$	4.92050	+	0.888068i	0.189390	+	0.0341818i
$676$		0			0
$677$	6.85568	−	6.85568i	0.263485	−	0.263485i	−0.562983	−	0.826468i	$-0.690346\pi$
$677$	6.85568	−	6.85568i	0.263485	−	0.263485i	0.826468	+	0.562983i	$0.190346\pi$
$678$		0			0
$679$	21.8620	+	13.4389i	0.838985	+	0.515737i
$680$		0			0
$681$	1.56296			0.0598929
$682$		0			0
$683$	−23.2345	+	23.2345i	−0.889042	+	0.889042i	−0.994431	−	0.105389i	$-0.966391\pi$
$683$	−23.2345	+	23.2345i	−0.889042	+	0.889042i	0.105389	+	0.994431i	$0.466391\pi$
$684$		0			0
$685$	30.8932	−	9.67222i	1.18037	−	0.369557i
$686$		0			0
$687$	−5.53883	−	5.53883i	−0.211319	−	0.211319i
$688$		0			0
$689$	45.0321			1.71559
$690$		0			0
$691$			42.4714i			1.61569i	0.589395	+	0.807845i	$0.299366\pi$
$691$			42.4714i			1.61569i	−0.589395	+	0.807845i	$0.700634\pi$
$692$		0			0
$693$	9.91150	−	2.36497i	0.376507	−	0.0898376i
$694$		0			0
$695$	−22.9752	+	43.9188i	−0.871500	+	1.66594i
$696$		0			0
$697$	12.9350	+	12.9350i	0.489947	+	0.489947i
$698$		0			0
$699$	1.42549			0.0539169
$700$		0			0
$701$	17.0793			0.645077			0.322539	−	0.946556i	$-0.395464\pi$
$701$	17.0793			0.645077			0.322539	+	0.946556i	$0.395464\pi$
$702$		0			0
$703$	0.431690	+	0.431690i	0.0162815	+	0.0162815i
$704$		0			0
$705$	8.04799	−	15.3843i	0.303105	−	0.579407i
$706$		0			0
$707$	49.3991	−	11.7870i	1.85785	−	0.443297i
$708$		0			0
$709$			32.6742i			1.22710i	0.789654	+	0.613552i	$0.210260\pi$
$709$			32.6742i			1.22710i	−0.789654	+	0.613552i	$0.789740\pi$
$710$		0			0
$711$	−9.86329			−0.369902
$712$		0			0
$713$	−1.28028	−	1.28028i	−0.0479469	−	0.0479469i
$714$		0			0
$715$	42.6341	−	13.3481i	1.59443	−	0.499192i
$716$		0			0
$717$	−14.3405	+	14.3405i	−0.535554	+	0.535554i
$718$		0			0
$719$	−19.3248			−0.720693			−0.360346	−	0.932819i	$-0.617341\pi$
$719$	−19.3248			−0.720693			−0.360346	+	0.932819i	$0.617341\pi$
$720$		0			0
$721$	4.58166	−	7.45331i	0.170630	−	0.277576i
$722$		0			0
$723$	1.95864	−	1.95864i	0.0728426	−	0.0728426i
$724$		0			0
$725$	11.3816	−	7.90133i	0.422701	−	0.293448i
$726$		0			0
$727$	2.71795	−	2.71795i	0.100803	−	0.100803i	−0.654907	−	0.755710i	$-0.727292\pi$
$727$	2.71795	−	2.71795i	0.100803	−	0.100803i	0.755710	+	0.654907i	$0.227292\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$			8.25820i			0.305440i
$732$		0			0
$733$	2.38437	+	2.38437i	0.0880686	+	0.0880686i	0.749769	−	0.661700i	$-0.230165\pi$
$733$	2.38437	+	2.38437i	0.0880686	+	0.0880686i	−0.661700	+	0.749769i	$0.730165\pi$
$734$		0			0
$735$	−11.2166	+	10.9173i	−0.413731	+	0.402691i
$736$		0			0
$737$	−1.60406	−	1.60406i	−0.0590862	−	0.0590862i
$738$		0			0
$739$		−	4.95679i		−	0.182339i	−0.995835	−	0.0911693i	$-0.970940\pi$
$739$		−	4.95679i		−	0.182339i	0.995835	−	0.0911693i	$-0.0290605\pi$
$740$		0			0
$741$			0.361923i			0.0132956i
$742$		0			0
$743$	−15.6556	+	15.6556i	−0.574347	+	0.574347i	−0.933340	−	0.358993i	$-0.883120\pi$
$743$	−15.6556	+	15.6556i	−0.574347	+	0.574347i	0.358993	+	0.933340i	$0.383120\pi$
$744$		0			0
$745$	−21.8889	−	11.4507i	−0.801946	−	0.419521i
$746$		0			0
$747$	−1.63570	+	1.63570i	−0.0598470	+	0.0598470i
$748$		0			0
$749$	12.5355	−	20.3924i	0.458037	−	0.745120i
$750$		0			0
$751$	11.1909			0.408361			0.204181	−	0.978933i	$-0.434547\pi$
$751$	11.1909			0.408361			0.204181	+	0.978933i	$0.434547\pi$
$752$		0			0
$753$	4.31322	−	4.31322i	0.157183	−	0.157183i
$754$		0			0
$755$	−19.0704	+	36.4545i	−0.694045	+	1.32672i
$756$		0			0
$757$	29.4977	+	29.4977i	1.07211	+	1.07211i	0.997189	+	0.0749214i	$0.0238706\pi$
$757$	29.4977	+	29.4977i	1.07211	+	1.07211i	0.0749214	+	0.997189i	$0.476129\pi$
$758$		0			0
$759$	2.90947			0.105607
$760$		0			0
$761$		−	28.1175i		−	1.01926i	−0.860395	−	0.509629i	$-0.829783\pi$
$761$		−	28.1175i		−	1.01926i	0.860395	−	0.509629i	$-0.170217\pi$
$762$		0			0
$763$	−5.56025	+	1.32672i	−0.201294	+	0.0480305i
$764$		0			0
$765$	−4.49678	+	1.40788i	−0.162581	+	0.0509019i
$766$		0			0
$767$	−25.5832	−	25.5832i	−0.923757	−	0.923757i
$768$		0			0
$769$	−6.61248			−0.238452			−0.119226	−	0.992867i	$-0.538041\pi$
$769$	−6.61248			−0.238452			−0.119226	+	0.992867i	$0.538041\pi$
$770$		0			0
$771$	2.85449			0.102802
$772$		0			0
$773$	−31.7247	−	31.7247i	−1.14106	−	1.14106i	−0.988257	−	0.152800i	$-0.951171\pi$
$773$	−31.7247	−	31.7247i	−1.14106	−	1.14106i	−0.152800	−	0.988257i	$-0.548829\pi$
$774$		0			0
$775$	−9.84407	+	6.83396i	−0.353609	+	0.245483i
$776$		0			0
$777$	22.5196	−	5.37335i	0.807885	−	0.192768i
$778$		0			0
$779$		−	0.605634i		−	0.0216991i
$780$		0			0
$781$	31.3032			1.12012
$782$		0			0
$783$	−1.95945	−	1.95945i	−0.0700249	−	0.0700249i
$784$		0			0
$785$	−0.992027	−	3.16855i	−0.0354070	−	0.113090i
$786$		0			0
$787$	22.4472	−	22.4472i	0.800155	−	0.800155i	−0.182964	−	0.983120i	$-0.558569\pi$
$787$	22.4472	−	22.4472i	0.800155	−	0.800155i	0.983120	+	0.182964i	$0.0585693\pi$
$788$		0			0
$789$	−23.7144			−0.844254
$790$		0			0
$791$	13.1909	+	8.10864i	0.469014	+	0.288310i
$792$		0			0
$793$	52.4941	−	52.4941i	1.86412	−	1.86412i
$794$		0			0
$795$	8.99757	−	17.1995i	0.319111	−	0.610003i
$796$		0			0
$797$	−5.14677	+	5.14677i	−0.182308	+	0.182308i	−0.792361	−	0.610053i	$-0.791148\pi$
$797$	−5.14677	+	5.14677i	−0.182308	+	0.182308i	0.610053	+	0.792361i	$0.291148\pi$
$798$		0			0
$799$			16.3622i			0.578854i
$800$		0			0
$801$			5.05313i			0.178544i
$802$		0			0
$803$	−36.7886	−	36.7886i	−1.29824	−	1.29824i
$804$		0			0
$805$	−3.83870	+	2.28877i	−0.135296	+	0.0806686i
$806$		0			0
$807$	−17.4904	−	17.4904i	−0.615691	−	0.615691i
$808$		0			0
$809$			22.5215i			0.791815i	0.918290	+	0.395907i	$0.129570\pi$
$809$			22.5215i			0.791815i	−0.918290	+	0.395907i	$0.870430\pi$
$810$		0			0
$811$		−	34.9145i		−	1.22602i	−0.790077	−	0.613008i	$-0.789960\pi$
$811$		−	34.9145i		−	1.22602i	0.790077	−	0.613008i	$-0.210040\pi$
$812$		0			0
$813$	−2.92367	+	2.92367i	−0.102538	+	0.102538i
$814$		0			0
$815$	5.20171	+	16.6143i	0.182208	+	0.581974i
$816$		0			0
$817$	0.193331	−	0.193331i	0.00676378	−	0.00676378i
$818$		0			0
$819$	11.6925	+	7.18757i	0.408569	+	0.251154i
$820$		0			0
$821$	8.52640			0.297573			0.148787	−	0.988869i	$-0.452463\pi$
$821$	8.52640			0.297573			0.148787	+	0.988869i	$0.452463\pi$
$822$		0			0
$823$	33.9044	−	33.9044i	1.18183	−	1.18183i	0.202564	−	0.979269i	$-0.435073\pi$
$823$	33.9044	−	33.9044i	1.18183	−	1.18183i	0.979269	−	0.202564i	$-0.0649273\pi$
$824$		0			0
$825$	3.42027	−	18.9506i	0.119079	−	0.659776i
$826$		0			0
$827$	37.8440	+	37.8440i	1.31597	+	1.31597i	0.916940	+	0.399025i	$0.130651\pi$
$827$	37.8440	+	37.8440i	1.31597	+	1.31597i	0.399025	+	0.916940i	$0.369349\pi$
$828$		0			0
$829$	33.7140			1.17094			0.585469	−	0.810695i	$-0.300911\pi$
$829$	33.7140			1.17094			0.585469	+	0.810695i	$0.300911\pi$
$830$		0			0
$831$		−	17.1300i		−	0.594234i
$832$		0			0
$833$	4.59730	−	14.0163i	0.159287	−	0.485635i
$834$		0			0
$835$	−1.78544	−	5.70272i	−0.0617878	−	0.197351i
$836$		0			0
$837$	1.69475	+	1.69475i	0.0585791	+	0.0585791i
$838$		0			0
$839$	−16.0665			−0.554679			−0.277339	−	0.960772i	$-0.589453\pi$
$839$	−16.0665			−0.554679			−0.277339	+	0.960772i	$0.589453\pi$
$840$		0			0
$841$	21.3211			0.735212
$842$		0			0
$843$	3.71429	+	3.71429i	0.127927	+	0.127927i
$844$		0			0
$845$	27.5620	+	14.4185i	0.948161	+	0.496011i
$846$		0			0
$847$	−2.35368	−	9.86420i	−0.0808734	−	0.338938i
$848$		0			0
$849$		−	2.35790i		−	0.0809231i
$850$		0			0
$851$	6.61050			0.226605
$852$		0			0
$853$	−5.14393	−	5.14393i	−0.176125	−	0.176125i	0.613539	−	0.789664i	$-0.289745\pi$
$853$	−5.14393	−	5.14393i	−0.176125	−	0.176125i	−0.789664	+	0.613539i	$0.789745\pi$
$854$		0			0
$855$	0.138232	+	0.0723134i	0.00472745	+	0.00247307i
$856$		0			0
$857$	5.65076	−	5.65076i	0.193026	−	0.193026i	−0.603976	−	0.797002i	$-0.706418\pi$
$857$	5.65076	−	5.65076i	0.193026	−	0.193026i	0.797002	+	0.603976i	$0.206418\pi$
$858$		0			0
$859$	42.0801			1.43575			0.717877	−	0.696170i	$-0.245114\pi$
$859$	42.0801			1.43575			0.717877	+	0.696170i	$0.245114\pi$
$860$		0			0
$861$	−19.5660	−	12.0275i	−0.666808	−	0.409897i
$862$		0			0
$863$	11.9777	−	11.9777i	0.407724	−	0.407724i	−0.473220	−	0.880944i	$-0.656908\pi$
$863$	11.9777	−	11.9777i	0.407724	−	0.407724i	0.880944	+	0.473220i	$0.156908\pi$
$864$		0			0
$865$	14.8100	−	4.63680i	0.503555	−	0.157656i
$866$		0			0
$867$	−8.88082	+	8.88082i	−0.301608	+	0.301608i
$868$		0			0
$869$			37.9871i			1.28862i
$870$		0			0
$871$		−	3.05551i		−	0.103532i
$872$		0			0
$873$	−6.85851	−	6.85851i	−0.232125	−	0.232125i
$874$		0			0
$875$	10.3951	+	27.6937i	0.351419	+	0.936218i
$876$		0			0
$877$	−11.5817	−	11.5817i	−0.391085	−	0.391085i	0.483989	−	0.875074i	$-0.339187\pi$
$877$	−11.5817	−	11.5817i	−0.391085	−	0.391085i	−0.875074	+	0.483989i	$0.839187\pi$
$878$		0			0
$879$			21.5746i			0.727694i
$880$		0			0
$881$		−	8.72058i		−	0.293804i	−0.989151	−	0.146902i	$-0.953070\pi$
$881$		−	8.72058i		−	0.293804i	0.989151	−	0.146902i	$-0.0469301\pi$
$882$		0			0
$883$	−17.0876	+	17.0876i	−0.575044	+	0.575044i	−0.933534	−	0.358490i	$-0.883292\pi$
$883$	−17.0876	+	17.0876i	−0.575044	+	0.575044i	0.358490	+	0.933534i	$0.383292\pi$
$884$		0			0
$885$	−14.8829	+	4.65961i	−0.500282	+	0.156631i
$886$		0			0
$887$	26.4024	−	26.4024i	0.886507	−	0.886507i	−0.107679	−	0.994186i	$-0.534342\pi$
$887$	26.4024	−	26.4024i	0.886507	−	0.886507i	0.994186	+	0.107679i	$0.0343419\pi$
$888$		0			0
$889$	9.46996	−	15.4054i	0.317612	−	0.516682i
$890$		0			0
$891$	−3.85136			−0.129025
$892$		0			0
$893$	0.383052	−	0.383052i	0.0128184	−	0.0128184i
$894$		0			0
$895$	−36.8244	−	19.2639i	−1.23090	−	0.643922i
$896$		0			0
$897$	2.77107	+	2.77107i	0.0925235	+	0.0925235i
$898$		0			0
$899$	6.64154			0.221508
$900$		0			0
$901$			18.2928i			0.609422i
$902$		0			0
$903$	−2.40643	−	10.0853i	−0.0800811	−	0.335617i
$904$		0			0
$905$	−16.8122	−	8.79494i	−0.558855	−	0.292354i
$906$		0			0
$907$	23.6454	+	23.6454i	0.785133	+	0.785133i	0.980692	−	0.195559i	$-0.0626521\pi$
$907$	23.6454	+	23.6454i	0.785133	+	0.785133i	−0.195559	+	0.980692i	$0.562652\pi$
$908$		0			0
$909$	−19.1953			−0.636667
$910$		0			0
$911$	17.8226			0.590490			0.295245	−	0.955422i	$-0.404599\pi$
$911$	17.8226			0.590490			0.295245	+	0.955422i	$0.404599\pi$
$912$		0			0
$913$	6.29966	+	6.29966i	0.208488	+	0.208488i
$914$		0			0
$915$	−9.56103	−	30.5380i	−0.316078	−	1.00956i
$916$		0			0
$917$	1.66634	−	0.397603i	0.0550274	−	0.0131300i
$918$		0			0
$919$		−	21.5752i		−	0.711701i	−0.934543	−	0.355850i	$-0.884191\pi$
$919$		−	21.5752i		−	0.711701i	0.934543	−	0.355850i	$-0.115809\pi$
$920$		0			0
$921$	−20.6755			−0.681280
$922$		0			0
$923$	29.8142	+	29.8142i	0.981346	+	0.981346i
$924$		0			0
$925$	7.77107	−	43.0570i	0.255511	−	1.41571i
$926$		0			0
$927$	−2.33825	+	2.33825i	−0.0767980	+	0.0767980i
$928$		0			0
$929$	−38.3070			−1.25681			−0.628405	−	0.777886i	$-0.716292\pi$
$929$	−38.3070			−1.25681			−0.628405	+	0.777886i	$0.716292\pi$
$930$		0			0
$931$	−0.435757	+	0.220505i	−0.0142814	+	0.00722675i
$932$		0			0
$933$	−2.02387	+	2.02387i	−0.0662584	+	0.0662584i
$934$		0			0
$935$	5.42225	+	17.3187i	0.177326	+	0.566382i
$936$		0			0
$937$	−13.2317	+	13.2317i	−0.432262	+	0.432262i	−0.889397	−	0.457135i	$-0.848875\pi$
$937$	−13.2317	+	13.2317i	−0.432262	+	0.432262i	0.457135	+	0.889397i	$0.348875\pi$
$938$		0			0
$939$			13.3194i			0.434662i
$940$		0			0
$941$			2.58095i			0.0841366i	0.999115	+	0.0420683i	$0.0133947\pi$
$941$			2.58095i			0.0841366i	−0.999115	+	0.0420683i	$0.986605\pi$
$942$		0			0
$943$	−4.63706	−	4.63706i	−0.151004	−	0.151004i
$944$		0			0
$945$	5.08142	−	3.02972i	0.165298	−	0.0985569i
$946$		0			0
$947$	−4.94205	−	4.94205i	−0.160595	−	0.160595i	0.622235	−	0.782830i	$-0.286225\pi$
$947$	−4.94205	−	4.94205i	−0.160595	−	0.160595i	−0.782830	+	0.622235i	$0.786225\pi$
$948$		0			0
$949$		−	70.0773i		−	2.27481i
$950$		0			0
$951$			10.4413i			0.338582i
$952$		0			0
$953$	−16.3558	+	16.3558i	−0.529818	+	0.529818i	−0.920518	−	0.390700i	$-0.872233\pi$
$953$	−16.3558	+	16.3558i	−0.529818	+	0.529818i	0.390700	+	0.920518i	$0.372233\pi$
$954$		0			0
$955$	5.59034	−	10.6863i	0.180899	−	0.345802i
$956$		0			0
$957$	−7.54653	+	7.54653i	−0.243945	+	0.243945i
$958$		0			0
$959$	20.0586	−	32.6308i	0.647727	−	1.05370i
$960$		0			0
$961$	25.2557			0.814698
$962$		0			0
$963$	−6.39747	+	6.39747i	−0.206156	+	0.206156i
$964$		0			0
$965$	4.54089	+	14.5036i	0.146176	+	0.466889i
$966$		0			0
$967$	−8.66781	−	8.66781i	−0.278738	−	0.278738i	0.553867	−	0.832605i	$-0.313152\pi$
$967$	−8.66781	−	8.66781i	−0.278738	−	0.278738i	−0.832605	+	0.553867i	$0.813152\pi$
$968$		0			0
$969$	−0.147019			−0.00472294
$970$		0			0
$971$		−	13.1861i		−	0.423163i	−0.977360	−	0.211582i	$-0.932139\pi$
$971$		−	13.1861i		−	0.423163i	0.977360	−	0.211582i	$-0.0678614\pi$
$972$		0			0
$973$	13.6114	+	57.0451i	0.436362	+	1.82878i
$974$		0			0
$975$	21.3068	−	14.7916i	0.682363	−	0.473711i
$976$		0			0
$977$	−24.4925	−	24.4925i	−0.783586	−	0.783586i	0.196848	−	0.980434i	$-0.436929\pi$
$977$	−24.4925	−	24.4925i	−0.783586	−	0.783586i	−0.980434	+	0.196848i	$0.936929\pi$
$978$		0			0
$979$	19.4614			0.621990
$980$		0			0
$981$	2.16057			0.0689818
$982$		0			0
$983$	15.7362	+	15.7362i	0.501907	+	0.501907i	0.912030	−	0.410123i	$-0.134514\pi$
$983$	15.7362	+	15.7362i	0.501907	+	0.501907i	−0.410123	+	0.912030i	$0.634514\pi$
$984$		0			0
$985$	38.2477	−	11.9748i	1.21867	−	0.381550i
$986$		0			0
$987$	−4.76795	−	19.9823i	−0.151765	−	0.636044i
$988$		0			0
$989$		−	2.96048i		−	0.0941379i
$990$		0			0
$991$	30.1031			0.956257			0.478128	−	0.878290i	$-0.341315\pi$
$991$	30.1031			0.956257			0.478128	+	0.878290i	$0.341315\pi$
$992$		0			0
$993$	−16.7019	−	16.7019i	−0.530018	−	0.530018i
$994$		0			0
$995$	−2.76859	+	5.29236i	−0.0877702	+	0.167779i
$996$		0			0
$997$	22.8721	−	22.8721i	0.724367	−	0.724367i	−0.245125	−	0.969491i	$-0.578829\pi$
$997$	22.8721	−	22.8721i	0.724367	−	0.724367i	0.969491	+	0.245125i	$0.0788290\pi$
$998$		0			0
$999$	−8.75054			−0.276855

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1680.2.cz.d.97.7		16
4.3	odd	2		105.2.m.a.97.5	yes	16
5.3	odd	4	inner	1680.2.cz.d.433.2		16
7.6	odd	2	inner	1680.2.cz.d.97.2		16
12.11	even	2		315.2.p.e.307.3		16
20.3	even	4		105.2.m.a.13.6	yes	16
20.7	even	4		525.2.m.b.118.3		16
20.19	odd	2		525.2.m.b.307.4		16
28.3	even	6		735.2.v.a.607.4		32
28.11	odd	6		735.2.v.a.607.3		32
28.19	even	6		735.2.v.a.472.5		32
28.23	odd	6		735.2.v.a.472.6		32
28.27	even	2		105.2.m.a.97.6	yes	16
35.13	even	4	inner	1680.2.cz.d.433.7		16
60.23	odd	4		315.2.p.e.118.4		16
84.83	odd	2		315.2.p.e.307.4		16
140.3	odd	12		735.2.v.a.313.6		32
140.23	even	12		735.2.v.a.178.4		32
140.27	odd	4		525.2.m.b.118.4		16
140.83	odd	4		105.2.m.a.13.5	✓	16
140.103	odd	12		735.2.v.a.178.3		32
140.123	even	12		735.2.v.a.313.5		32
140.139	even	2		525.2.m.b.307.3		16
420.83	even	4		315.2.p.e.118.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.m.a.13.5	✓	16	140.83	odd	4
105.2.m.a.13.6	yes	16	20.3	even	4
105.2.m.a.97.5	yes	16	4.3	odd	2
105.2.m.a.97.6	yes	16	28.27	even	2
315.2.p.e.118.3		16	420.83	even	4
315.2.p.e.118.4		16	60.23	odd	4
315.2.p.e.307.3		16	12.11	even	2
315.2.p.e.307.4		16	84.83	odd	2
525.2.m.b.118.3		16	20.7	even	4
525.2.m.b.118.4		16	140.27	odd	4
525.2.m.b.307.3		16	140.139	even	2
525.2.m.b.307.4		16	20.19	odd	2
735.2.v.a.178.3		32	140.103	odd	12
735.2.v.a.178.4		32	140.23	even	12
735.2.v.a.313.5		32	140.123	even	12
735.2.v.a.313.6		32	140.3	odd	12
735.2.v.a.472.5		32	28.19	even	6
735.2.v.a.472.6		32	28.23	odd	6
735.2.v.a.607.3		32	28.11	odd	6
735.2.v.a.607.4		32	28.3	even	6
1680.2.cz.d.97.2		16	7.6	odd	2	inner
1680.2.cz.d.97.7		16	1.1	even	1	trivial
1680.2.cz.d.433.2		16	5.3	odd	4	inner
1680.2.cz.d.433.7		16	35.13	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1680.cz (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{3} +(1.03649 - 1.98133i) q^{5} +(-0.614060 - 2.57351i) q^{7} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{3} +(1.03649 - 1.98133i) q^{5} +(-0.614060 - 2.57351i) q^{7} +1.00000i q^{9} +3.85136 q^{11} +(3.66816 + 3.66816i) q^{13} +(2.13393 - 0.668102i) q^{15} +(-1.49007 + 1.49007i) q^{17} +0.0697674 q^{19} +(1.38554 - 2.25395i) q^{21} +(0.534176 - 0.534176i) q^{23} +(-2.85136 - 4.10728i) q^{25} +(-0.707107 + 0.707107i) q^{27} +2.77107i q^{29} -2.39674i q^{31} +(2.72332 + 2.72332i) q^{33} +(-5.73544 - 1.45077i) q^{35} +(6.18757 + 6.18757i) q^{37} +5.18757i q^{39} -8.68077i q^{41} +(2.77107 - 2.77107i) q^{43} +(1.98133 + 1.03649i) q^{45} +(5.49042 - 5.49042i) q^{47} +(-6.24586 + 3.16057i) q^{49} -2.10728 q^{51} +(6.13823 - 6.13823i) q^{53} +(3.99191 - 7.63083i) q^{55} +(0.0493330 + 0.0493330i) q^{57} -6.97440 q^{59} -14.3107i q^{61} +(2.57351 - 0.614060i) q^{63} +(11.0699 - 3.46582i) q^{65} +(-0.416491 - 0.416491i) q^{67} +0.755439 q^{69} +8.12783 q^{71} +(-9.55210 - 9.55210i) q^{73} +(0.888068 - 4.92050i) q^{75} +(-2.36497 - 9.91150i) q^{77} +9.86329i q^{79} -1.00000 q^{81} +(1.63570 + 1.63570i) q^{83} +(1.40788 + 4.49678i) q^{85} +(-1.95945 + 1.95945i) q^{87} +5.05313 q^{89} +(7.18757 - 11.6925i) q^{91} +(1.69475 - 1.69475i) q^{93} +(0.0723134 - 0.138232i) q^{95} +(-6.85851 + 6.85851i) q^{97} +3.85136i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{7}+O(q^{10}) \) 16 * q + 8 * q^7	\( 16 q + 8 q^{7} + 16 q^{11} - 8 q^{15} + 8 q^{21} + 40 q^{23} + 8 q^{35} + 32 q^{37} + 16 q^{43} + 16 q^{51} + 24 q^{53} + 8 q^{57} - 8 q^{63} + 40 q^{65} + 32 q^{67} - 64 q^{71} - 24 q^{77} - 16 q^{81} + 48 q^{85} + 48 q^{91} + 24 q^{93} + 72 q^{95}+O(q^{100}) \) 16 * q + 8 * q^7 + 16 * q^11 - 8 * q^15 + 8 * q^21 + 40 * q^23 + 8 * q^35 + 32 * q^37 + 16 * q^43 + 16 * q^51 + 24 * q^53 + 8 * q^57 - 8 * q^63 + 40 * q^65 + 32 * q^67 - 64 * q^71 - 24 * q^77 - 16 * q^81 + 48 * q^85 + 48 * q^91 + 24 * q^93 + 72 * q^95

Introduction

L-functions

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