LMFDB - Embedded newform 1860.2.s.a.433.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1860,2,Mod(433,1860)] 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("1860.433"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1860, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1860 = 2^{2} \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1860.s (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$14.8521747760$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			433.9
Character	$\chi$	$=$	1860.433
Dual form			1860.2.s.a.1177.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{3} +(1.94432 + 1.10436i) q^{5} +(-1.30181 + 1.30181i) q^{7} -1.00000i q^{9} -0.348868i q^{11} +(3.81091 - 3.81091i) q^{13} +(-2.15575 + 0.593939i) q^{15} +(0.867057 + 0.867057i) q^{17} +3.13612i q^{19} -1.84104i q^{21} +(3.18948 - 3.18948i) q^{23} +(2.56076 + 4.29447i) q^{25} +(0.707107 + 0.707107i) q^{27} +3.05666 q^{29} +(1.80830 - 5.26593i) q^{31} +(0.246687 + 0.246687i) q^{33} +(-3.96880 + 1.09346i) q^{35} +(2.25742 + 2.25742i) q^{37} +5.38944i q^{39} +8.13560 q^{41} +(-1.78149 + 1.78149i) q^{43} +(1.10436 - 1.94432i) q^{45} +(-3.54328 + 3.54328i) q^{47} +3.61059i q^{49} -1.22620 q^{51} +(1.20645 - 1.20645i) q^{53} +(0.385277 - 0.678310i) q^{55} +(-2.21757 - 2.21757i) q^{57} +3.43227i q^{59} +0.764936i q^{61} +(1.30181 + 1.30181i) q^{63} +(11.6183 - 3.20099i) q^{65} +(-0.999024 + 0.999024i) q^{67} +4.51061i q^{69} -7.35363 q^{71} +(-6.15668 + 6.15668i) q^{73} +(-4.84738 - 1.22592i) q^{75} +(0.454159 + 0.454159i) q^{77} +10.7589 q^{79} -1.00000 q^{81} +(-5.99917 + 5.99917i) q^{83} +(0.728290 + 2.64338i) q^{85} +(-2.16139 + 2.16139i) q^{87} -7.46314 q^{89} +9.92214i q^{91} +(2.44491 + 5.00224i) q^{93} +(-3.46342 + 6.09762i) q^{95} +(-1.18994 + 1.18994i) q^{97} -0.348868 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{7} + 16 q^{25} + 8 q^{31} - 8 q^{33} + 24 q^{35} + 16 q^{41} + 56 q^{47} + 8 q^{63} - 32 q^{67} - 16 q^{71} - 64 q^{81} - 32 q^{87} - 32 q^{95} + 64 q^{97}+O(q^{100}) $ 64 * q - 8 * q^7 + 16 * q^25 + 8 * q^31 - 8 * q^33 + 24 * q^35 + 16 * q^41 + 56 * q^47 + 8 * q^63 - 32 * q^67 - 16 * q^71 - 64 * q^81 - 32 * q^87 - 32 * q^95 + 64 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1860\mathbb{Z}\right)^\times$.

$n$	$931$	$1117$	$1241$	$1801$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$		0			0
$5$	1.94432	+	1.10436i	0.869526	+	0.493887i
$5$	1.94432	+	1.10436i	0.869526	+	0.493887i
$6$		0			0
$7$	−1.30181	+	1.30181i	−0.492037	+	0.492037i	−0.908948	−	0.416910i	$-0.863113\pi$
$7$	−1.30181	+	1.30181i	−0.492037	+	0.492037i	0.416910	+	0.908948i	$0.363113\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$		−	0.348868i		−	0.105188i	−0.998616	−	0.0525938i	$-0.983251\pi$
$11$		−	0.348868i		−	0.105188i	0.998616	−	0.0525938i	$-0.0167488\pi$
$12$		0			0
$13$	3.81091	−	3.81091i	1.05696	−	1.05696i	0.0586785	−	0.998277i	$-0.481311\pi$
$13$	3.81091	−	3.81091i	1.05696	−	1.05696i	0.998277	−	0.0586785i	$-0.0186887\pi$
$14$		0			0
$15$	−2.15575	+	0.593939i	−0.556611	+	0.153354i
$16$		0			0
$17$	0.867057	+	0.867057i	0.210292	+	0.210292i	0.804392	−	0.594099i	$-0.202491\pi$
$17$	0.867057	+	0.867057i	0.210292	+	0.210292i	−0.594099	+	0.804392i	$0.702491\pi$
$18$		0			0
$19$			3.13612i			0.719475i	0.933054	+	0.359737i	$0.117134\pi$
$19$			3.13612i			0.719475i	−0.933054	+	0.359737i	$0.882866\pi$
$20$		0			0
$21$		−	1.84104i		−	0.401747i
$22$		0			0
$23$	3.18948	−	3.18948i	0.665054	−	0.665054i	−0.291513	−	0.956567i	$-0.594159\pi$
$23$	3.18948	−	3.18948i	0.665054	−	0.665054i	0.956567	+	0.291513i	$0.0941587\pi$
$24$		0			0
$25$	2.56076	+	4.29447i	0.512152	+	0.858895i
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$	3.05666			0.567608			0.283804	−	0.958882i	$-0.408403\pi$
$29$	3.05666			0.567608			0.283804	+	0.958882i	$0.408403\pi$
$30$		0			0
$31$	1.80830	−	5.26593i	0.324781	−	0.945789i
$31$	1.80830	−	5.26593i	0.324781	−	0.945789i
$32$		0			0
$33$	0.246687	+	0.246687i	0.0429426	+	0.0429426i
$34$		0			0
$35$	−3.96880	+	1.09346i	−0.670850	+	0.184829i
$36$		0			0
$37$	2.25742	+	2.25742i	0.371117	+	0.371117i	0.867884	−	0.496767i	$-0.165480\pi$
$37$	2.25742	+	2.25742i	0.371117	+	0.371117i	−0.496767	+	0.867884i	$0.665480\pi$
$38$		0			0
$39$			5.38944i			0.863000i
$40$		0			0
$41$	8.13560			1.27057			0.635284	−	0.772279i	$-0.280883\pi$
$41$	8.13560			1.27057			0.635284	+	0.772279i	$0.280883\pi$
$42$		0			0
$43$	−1.78149	+	1.78149i	−0.271674	+	0.271674i	−0.829774	−	0.558100i	$-0.811531\pi$
$43$	−1.78149	+	1.78149i	−0.271674	+	0.271674i	0.558100	+	0.829774i	$0.311531\pi$
$44$		0			0
$45$	1.10436	−	1.94432i	0.164629	−	0.289842i
$46$		0			0
$47$	−3.54328	+	3.54328i	−0.516840	+	0.516840i	−0.916614	−	0.399774i	$-0.869089\pi$
$47$	−3.54328	+	3.54328i	−0.516840	+	0.516840i	0.399774	+	0.916614i	$0.369089\pi$
$48$		0			0
$49$			3.61059i			0.515798i
$50$		0			0
$51$	−1.22620			−0.171703
$52$		0			0
$53$	1.20645	−	1.20645i	0.165719	−	0.165719i	−0.619376	−	0.785095i	$-0.712614\pi$
$53$	1.20645	−	1.20645i	0.165719	−	0.165719i	0.785095	+	0.619376i	$0.212614\pi$
$54$		0			0
$55$	0.385277	−	0.678310i	0.0519507	−	0.0914633i
$56$		0			0
$57$	−2.21757	−	2.21757i	−0.293724	−	0.293724i
$58$		0			0
$59$			3.43227i			0.446844i	0.974722	+	0.223422i	$0.0717228\pi$
$59$			3.43227i			0.446844i	−0.974722	+	0.223422i	$0.928277\pi$
$60$		0			0
$61$			0.764936i			0.0979400i	0.998800	+	0.0489700i	$0.0155939\pi$
$61$			0.764936i			0.0979400i	−0.998800	+	0.0489700i	$0.984406\pi$
$62$		0			0
$63$	1.30181	+	1.30181i	0.164012	+	0.164012i
$64$		0			0
$65$	11.6183	−	3.20099i	1.44107	−	0.397035i
$66$		0			0
$67$	−0.999024	+	0.999024i	−0.122050	+	0.122050i	−0.765494	−	0.643443i	$-0.777505\pi$
$67$	−0.999024	+	0.999024i	−0.122050	+	0.122050i	0.643443	+	0.765494i	$0.277505\pi$
$68$		0			0
$69$			4.51061i			0.543014i
$70$		0			0
$71$	−7.35363			−0.872716			−0.436358	−	0.899773i	$-0.643732\pi$
$71$	−7.35363			−0.872716			−0.436358	+	0.899773i	$0.643732\pi$
$72$		0			0
$73$	−6.15668	+	6.15668i	−0.720585	+	0.720585i	−0.968724	−	0.248139i	$-0.920181\pi$
$73$	−6.15668	+	6.15668i	−0.720585	+	0.720585i	0.248139	+	0.968724i	$0.420181\pi$
$74$		0			0
$75$	−4.84738	−	1.22592i	−0.559728	−	0.141557i
$76$		0			0
$77$	0.454159	+	0.454159i	0.0517562	+	0.0517562i
$78$		0			0
$79$	10.7589			1.21047			0.605234	−	0.796048i	$-0.293080\pi$
$79$	10.7589			1.21047			0.605234	+	0.796048i	$0.293080\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−5.99917	+	5.99917i	−0.658494	+	0.658494i	−0.955024	−	0.296530i	$-0.904171\pi$
$83$	−5.99917	+	5.99917i	−0.658494	+	0.658494i	0.296530	+	0.955024i	$0.404171\pi$
$84$		0			0
$85$	0.728290	+	2.64338i	0.0789941	+	0.286715i
$86$		0			0
$87$	−2.16139	+	2.16139i	−0.231725	+	0.231725i
$88$		0			0
$89$	−7.46314			−0.791091			−0.395546	−	0.918446i	$-0.629445\pi$
$89$	−7.46314			−0.791091			−0.395546	+	0.918446i	$0.629445\pi$
$90$		0			0
$91$			9.92214i			1.04012i
$92$		0			0
$93$	2.44491	+	5.00224i	0.253526	+	0.518708i
$94$		0			0
$95$	−3.46342	+	6.09762i	−0.355339	+	0.625602i
$96$		0			0
$97$	−1.18994	+	1.18994i	−0.120820	+	0.120820i	−0.764932	−	0.644111i	$-0.777227\pi$
$97$	−1.18994	+	1.18994i	−0.120820	+	0.120820i	0.644111	+	0.764932i	$0.277227\pi$
$98$		0			0
$99$	−0.348868			−0.0350625
$100$		0			0
$101$	19.4720			1.93753			0.968766	−	0.247975i	$-0.0797650\pi$
$101$	19.4720			1.93753			0.968766	+	0.247975i	$0.0797650\pi$
$102$		0			0
$103$	−3.31073	−	3.31073i	−0.326216	−	0.326216i	0.524930	−	0.851146i	$-0.324092\pi$
$103$	−3.31073	−	3.31073i	−0.326216	−	0.326216i	−0.851146	+	0.524930i	$0.824092\pi$
$104$		0			0
$105$	2.03317	−	3.57956i	0.198417	−	0.349330i
$106$		0			0
$107$	−11.6067	+	11.6067i	−1.12206	+	1.12206i	−0.130631	+	0.991431i	$0.541700\pi$
$107$	−11.6067	+	11.6067i	−1.12206	+	1.12206i	−0.991431	+	0.130631i	$0.958300\pi$
$108$		0			0
$109$		−	6.18632i		−	0.592542i	−0.955104	−	0.296271i	$-0.904257\pi$
$109$		−	6.18632i		−	0.592542i	0.955104	−	0.296271i	$-0.0957432\pi$
$110$		0			0
$111$	−3.19247			−0.303016
$112$		0			0
$113$	−3.20541	−	3.20541i	−0.301539	−	0.301539i	0.540077	−	0.841616i	$-0.318395\pi$
$113$	−3.20541	−	3.20541i	−0.301539	−	0.301539i	−0.841616	+	0.540077i	$0.818395\pi$
$114$		0			0
$115$	9.72373	−	2.67903i	0.906743	−	0.249821i
$116$		0			0
$117$	−3.81091	−	3.81091i	−0.352318	−	0.352318i
$118$		0			0
$119$	−2.25749			−0.206943
$120$		0			0
$121$	10.8783			0.988936
$122$		0			0
$123$	−5.75274	+	5.75274i	−0.518707	+	0.518707i
$124$		0			0
$125$	0.236278	+	11.1778i	0.0211333	+	0.999777i
$126$		0			0
$127$	5.46519	+	5.46519i	0.484957	+	0.484957i	0.906711	−	0.421754i	$-0.138585\pi$
$127$	5.46519	+	5.46519i	0.484957	+	0.484957i	−0.421754	+	0.906711i	$0.638585\pi$
$128$		0			0
$129$		−	2.51940i		−	0.221821i
$130$		0			0
$131$	19.1279			1.67121			0.835607	−	0.549327i	$-0.185116\pi$
$131$	19.1279			1.67121			0.835607	+	0.549327i	$0.185116\pi$
$132$		0			0
$133$	−4.08263	−	4.08263i	−0.354009	−	0.354009i
$134$		0			0
$135$	0.593939	+	2.15575i	0.0511181	+	0.185537i
$136$		0			0
$137$	−11.5636	−	11.5636i	−0.987946	−	0.987946i	0.0119821	−	0.999928i	$-0.496186\pi$
$137$	−11.5636	−	11.5636i	−0.987946	−	0.987946i	−0.999928	+	0.0119821i	$0.996186\pi$
$138$		0			0
$139$	12.8328			1.08846			0.544230	−	0.838936i	$-0.316822\pi$
$139$	12.8328			1.08846			0.544230	+	0.838936i	$0.316822\pi$
$140$		0			0
$141$		−	5.01095i		−	0.421998i
$142$		0			0
$143$	−1.32950	−	1.32950i	−0.111179	−	0.111179i
$144$		0			0
$145$	5.94313	+	3.37567i	0.493550	+	0.280334i
$146$		0			0
$147$	−2.55307	−	2.55307i	−0.210574	−	0.210574i
$148$		0			0
$149$			5.28719i			0.433144i	0.976267	+	0.216572i	$0.0694876\pi$
$149$			5.28719i			0.433144i	−0.976267	+	0.216572i	$0.930512\pi$
$150$		0			0
$151$			0.693754i			0.0564569i	0.999601	+	0.0282285i	$0.00898659\pi$
$151$			0.693754i			0.0564569i	−0.999601	+	0.0282285i	$0.991013\pi$
$152$		0			0
$153$	0.867057	−	0.867057i	0.0700974	−	0.0700974i
$154$		0			0
$155$	9.33142	−	8.24163i	0.749518	−	0.661984i
$156$		0			0
$157$	0.0925744	−	0.0925744i	0.00738824	−	0.00738824i	−0.703403	−	0.710791i	$-0.748337\pi$
$157$	0.0925744	−	0.0925744i	0.00738824	−	0.00738824i	0.710791	+	0.703403i	$0.248337\pi$
$158$		0			0
$159$			1.70618i			0.135309i
$160$		0			0
$161$			8.30420i			0.654463i
$162$		0			0
$163$	13.6251	+	13.6251i	1.06720	+	1.06720i	0.997573	+	0.0696232i	$0.0221797\pi$
$163$	13.6251	+	13.6251i	1.06720	+	1.06720i	0.0696232	+	0.997573i	$0.477820\pi$
$164$		0			0
$165$	0.207206	+	0.752070i	0.0161310	+	0.0585485i
$166$		0			0
$167$	−3.02965	−	3.02965i	−0.234441	−	0.234441i	0.580102	−	0.814544i	$-0.303013\pi$
$167$	−3.02965	−	3.02965i	−0.234441	−	0.234441i	−0.814544	+	0.580102i	$0.803013\pi$
$168$		0			0
$169$		−	16.0460i		−	1.23431i
$170$		0			0
$171$	3.13612			0.239825
$172$		0			0
$173$	−8.02143	−	8.02143i	−0.609858	−	0.609858i	0.333051	−	0.942909i	$-0.391922\pi$
$173$	−8.02143	−	8.02143i	−0.609858	−	0.609858i	−0.942909	+	0.333051i	$0.891922\pi$
$174$		0			0
$175$	−8.92420	−	2.25696i	−0.674606	−	0.170610i
$176$		0			0
$177$	−2.42698	−	2.42698i	−0.182423	−	0.182423i
$178$		0			0
$179$	−12.2755			−0.917512			−0.458756	−	0.888562i	$-0.651705\pi$
$179$	−12.2755			−0.917512			−0.458756	+	0.888562i	$0.651705\pi$
$180$		0			0
$181$			5.12980i			0.381295i	0.981659	+	0.190648i	$0.0610588\pi$
$181$			5.12980i			0.381295i	−0.981659	+	0.190648i	$0.938941\pi$
$182$		0			0
$183$	−0.540891	−	0.540891i	−0.0399838	−	0.0399838i
$184$		0			0
$185$	1.89613	+	6.88215i	0.139406	+	0.505986i
$186$		0			0
$187$	0.302488	−	0.302488i	0.0221201	−	0.0221201i
$188$		0			0
$189$	−1.84104			−0.133916
$190$		0			0
$191$	−6.50562			−0.470730			−0.235365	−	0.971907i	$-0.575629\pi$
$191$	−6.50562			−0.470730			−0.235365	+	0.971907i	$0.575629\pi$
$192$		0			0
$193$	15.4749	+	15.4749i	1.11391	+	1.11391i	0.992617	+	0.121291i	$0.0387034\pi$
$193$	15.4749	+	15.4749i	1.11391	+	1.11391i	0.121291	+	0.992617i	$0.461297\pi$
$194$		0			0
$195$	−5.95190	+	10.4788i	−0.426224	+	0.750402i
$196$		0			0
$197$	−4.59069	−	4.59069i	−0.327073	−	0.327073i	0.524399	−	0.851473i	$-0.324290\pi$
$197$	−4.59069	−	4.59069i	−0.327073	−	0.327073i	−0.851473	+	0.524399i	$0.824290\pi$
$198$		0			0
$199$	21.7917			1.54477			0.772386	−	0.635153i	$-0.219063\pi$
$199$	21.7917			1.54477			0.772386	+	0.635153i	$0.219063\pi$
$200$		0			0
$201$		−	1.41283i		−	0.0996536i
$202$		0			0
$203$	−3.97919	+	3.97919i	−0.279284	+	0.279284i
$204$		0			0
$205$	15.8182	+	8.98466i	1.10479	+	0.627516i
$206$		0			0
$207$	−3.18948	−	3.18948i	−0.221685	−	0.221685i
$208$		0			0
$209$	1.09409			0.0756798
$210$		0			0
$211$	10.4225			0.717512			0.358756	−	0.933431i	$-0.383201\pi$
$211$	10.4225			0.717512			0.358756	+	0.933431i	$0.383201\pi$
$212$		0			0
$213$	5.19980	−	5.19980i	0.356285	−	0.356285i
$214$		0			0
$215$	−5.43119	+	1.49637i	−0.370404	+	0.102052i
$216$		0			0
$217$	4.50117	+	9.20930i	0.305560	+	0.625168i
$218$		0			0
$219$		−	8.70687i		−	0.588356i
$220$		0			0
$221$	6.60855			0.444539
$222$		0			0
$223$	−8.06725	+	8.06725i	−0.540223	+	0.540223i	−0.923594	−	0.383371i	$-0.874763\pi$
$223$	−8.06725	+	8.06725i	−0.540223	+	0.540223i	0.383371	+	0.923594i	$0.374763\pi$
$224$		0			0
$225$	4.29447	−	2.56076i	0.286298	−	0.170717i
$226$		0			0
$227$	−4.97666	+	4.97666i	−0.330312	+	0.330312i	−0.852705	−	0.522393i	$-0.825040\pi$
$227$	−4.97666	+	4.97666i	−0.330312	+	0.330312i	0.522393	+	0.852705i	$0.325040\pi$
$228$		0			0
$229$	11.9227			0.787876			0.393938	−	0.919137i	$-0.371113\pi$
$229$	11.9227			0.787876			0.393938	+	0.919137i	$0.371113\pi$
$230$		0			0
$231$	−0.642278			−0.0422588
$232$		0			0
$233$	−1.09023	−	1.09023i	−0.0714234	−	0.0714234i	0.670493	−	0.741916i	$-0.266083\pi$
$233$	−1.09023	−	1.09023i	−0.0714234	−	0.0714234i	−0.741916	+	0.670493i	$0.766083\pi$
$234$		0			0
$235$	−10.8023	+	2.97620i	−0.704666	+	0.194146i
$236$		0			0
$237$	−7.60767	+	7.60767i	−0.494171	+	0.494171i
$238$		0			0
$239$	−29.3174			−1.89638			−0.948192	−	0.317699i	$-0.897090\pi$
$239$	−29.3174			−1.89638			−0.948192	+	0.317699i	$0.897090\pi$
$240$		0			0
$241$			12.9784i			0.836015i	0.908444	+	0.418007i	$0.137271\pi$
$241$			12.9784i			0.836015i	−0.908444	+	0.418007i	$0.862729\pi$
$242$		0			0
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$		0			0
$245$	−3.98740	+	7.02014i	−0.254746	+	0.448500i
$246$		0			0
$247$	11.9515	+	11.9515i	0.760453	+	0.760453i
$248$		0			0
$249$		−	8.48410i		−	0.537658i
$250$		0			0
$251$		−	15.6400i		−	0.987187i	−0.869693	−	0.493594i	$-0.835683\pi$
$251$		−	15.6400i		−	0.987187i	0.869693	−	0.493594i	$-0.164317\pi$
$252$		0			0
$253$	−1.11271	−	1.11271i	−0.0699554	−	0.0699554i
$254$		0			0
$255$	−2.38413	−	1.35418i	−0.149300	−	0.0848017i
$256$		0			0
$257$	12.0640	−	12.0640i	0.752532	−	0.752532i	−0.222419	−	0.974951i	$-0.571395\pi$
$257$	12.0640	−	12.0640i	0.752532	−	0.752532i	0.974951	+	0.222419i	$0.0713953\pi$
$258$		0			0
$259$	−5.87745			−0.365207
$260$		0			0
$261$		−	3.05666i		−	0.189203i
$262$		0			0
$263$	7.77183	−	7.77183i	0.479232	−	0.479232i	−0.425654	−	0.904886i	$-0.639956\pi$
$263$	7.77183	−	7.77183i	0.479232	−	0.479232i	0.904886	+	0.425654i	$0.139956\pi$
$264$		0			0
$265$	3.67809	−	1.01337i	0.225943	−	0.0622507i
$266$		0			0
$267$	5.27724	−	5.27724i	0.322962	−	0.322962i
$268$		0			0
$269$	−19.4976			−1.18879			−0.594394	−	0.804174i	$-0.702608\pi$
$269$	−19.4976			−1.18879			−0.594394	+	0.804174i	$0.702608\pi$
$270$		0			0
$271$		−	8.35693i		−	0.507647i	−0.967251	−	0.253824i	$-0.918312\pi$
$271$		−	8.35693i		−	0.507647i	0.967251	−	0.253824i	$-0.0816883\pi$
$272$		0			0
$273$	−7.01602	−	7.01602i	−0.424629	−	0.424629i
$274$		0			0
$275$	1.49820	−	0.893367i	0.0903450	−	0.0538720i
$276$		0			0
$277$	9.34364	+	9.34364i	0.561405	+	0.561405i	0.929706	−	0.368302i	$-0.120061\pi$
$277$	9.34364	+	9.34364i	0.561405	+	0.561405i	−0.368302	+	0.929706i	$0.620061\pi$
$278$		0			0
$279$	−5.26593	−	1.80830i	−0.315263	−	0.108260i
$280$		0			0
$281$	−5.67863			−0.338759			−0.169379	−	0.985551i	$-0.554176\pi$
$281$	−5.67863			−0.338759			−0.169379	+	0.985551i	$0.554176\pi$
$282$		0			0
$283$	−23.6450	−	23.6450i	−1.40555	−	1.40555i	−0.780934	−	0.624614i	$-0.785256\pi$
$283$	−23.6450	−	23.6450i	−1.40555	−	1.40555i	−0.624614	−	0.780934i	$-0.714744\pi$
$284$		0			0
$285$	−1.86266	−	6.76067i	−0.110335	−	0.400468i
$286$		0			0
$287$	−10.5910	+	10.5910i	−0.625167	+	0.625167i
$288$		0			0
$289$		−	15.4964i		−	0.911554i
$290$		0			0
$291$		−	1.68283i		−	0.0986493i
$292$		0			0
$293$	−10.2310	−	10.2310i	−0.597699	−	0.597699i	0.342001	−	0.939700i	$-0.388895\pi$
$293$	−10.2310	−	10.2310i	−0.597699	−	0.597699i	−0.939700	+	0.342001i	$0.888895\pi$
$294$		0			0
$295$	−3.79048	+	6.67344i	−0.220690	+	0.388543i
$296$		0			0
$297$	0.246687	−	0.246687i	0.0143142	−	0.0143142i
$298$		0			0
$299$		−	24.3097i		−	1.40586i
$300$		0			0
$301$		−	4.63831i		−	0.267348i
$302$		0			0
$303$	−13.7688	+	13.7688i	−0.790995	+	0.790995i
$304$		0			0
$305$	−0.844767	+	1.48728i	−0.0483712	+	0.0851614i
$306$		0			0
$307$	6.28012	−	6.28012i	0.358425	−	0.358425i	−0.504807	−	0.863232i	$-0.668436\pi$
$307$	6.28012	−	6.28012i	0.358425	−	0.358425i	0.863232	+	0.504807i	$0.168436\pi$
$308$		0			0
$309$	4.68208			0.266354
$310$		0			0
$311$	−6.38003			−0.361778			−0.180889	−	0.983504i	$-0.557898\pi$
$311$	−6.38003			−0.361778			−0.180889	+	0.983504i	$0.557898\pi$
$312$		0			0
$313$	14.3766	−	14.3766i	0.812613	−	0.812613i	−0.172412	−	0.985025i	$-0.555156\pi$
$313$	14.3766	−	14.3766i	0.812613	−	0.812613i	0.985025	+	0.172412i	$0.0551560\pi$
$314$		0			0
$315$	1.09346	+	3.96880i	0.0616096	+	0.223617i
$316$		0			0
$317$	−12.0154	+	12.0154i	−0.674854	+	0.674854i	−0.958831	−	0.283977i	$-0.908346\pi$
$317$	−12.0154	+	12.0154i	−0.674854	+	0.674854i	0.283977	+	0.958831i	$0.408346\pi$
$318$		0			0
$319$		−	1.06637i		−	0.0597053i
$320$		0			0
$321$		−	16.4143i		−	0.916160i
$322$		0			0
$323$	−2.71919	+	2.71919i	−0.151300	+	0.151300i
$324$		0			0
$325$	26.1247	+	6.60702i	1.44914	+	0.366491i
$326$		0			0
$327$	4.37439	+	4.37439i	0.241904	+	0.241904i
$328$		0			0
$329$		−	9.22534i		−	0.508609i
$330$		0			0
$331$		−	9.37198i		−	0.515131i	−0.966261	−	0.257565i	$-0.917080\pi$
$331$		−	9.37198i		−	0.515131i	0.966261	−	0.257565i	$-0.0829202\pi$
$332$		0			0
$333$	2.25742	−	2.25742i	0.123706	−	0.123706i
$334$		0			0
$335$	−3.04571	+	0.839136i	−0.166405	+	0.0458469i
$336$		0			0
$337$	−11.6769	−	11.6769i	−0.636080	−	0.636080i	0.313506	−	0.949586i	$-0.398496\pi$
$337$	−11.6769	−	11.6769i	−0.636080	−	0.636080i	−0.949586	+	0.313506i	$0.898496\pi$
$338$		0			0
$339$	4.53313			0.246206
$340$		0			0
$341$	−1.83711	−	0.630858i	−0.0994853	−	0.0341629i
$342$		0			0
$343$	−13.8130	−	13.8130i	−0.745830	−	0.745830i
$344$		0			0
$345$	−4.98136	+	8.77007i	−0.268187	+	0.472165i
$346$		0			0
$347$	−9.03788	−	9.03788i	−0.485179	−	0.485179i	0.421602	−	0.906781i	$-0.361468\pi$
$347$	−9.03788	−	9.03788i	−0.485179	−	0.485179i	−0.906781	+	0.421602i	$0.861468\pi$
$348$		0			0
$349$		−	30.2184i		−	1.61755i	−0.588116	−	0.808776i	$-0.700130\pi$
$349$		−	30.2184i		−	1.61755i	0.588116	−	0.808776i	$-0.299870\pi$
$350$		0			0
$351$	5.38944			0.287667
$352$		0			0
$353$	16.9052	−	16.9052i	0.899775	−	0.899775i	−0.0956412	−	0.995416i	$-0.530490\pi$
$353$	16.9052	−	16.9052i	0.899775	−	0.899775i	0.995416	+	0.0956412i	$0.0304901\pi$
$354$		0			0
$355$	−14.2978	−	8.12109i	−0.758849	−	0.431023i
$356$		0			0
$357$	1.59628	−	1.59628i	0.0844843	−	0.0844843i
$358$		0			0
$359$		−	11.6863i		−	0.616780i	−0.951260	−	0.308390i	$-0.900210\pi$
$359$		−	11.6863i		−	0.616780i	0.951260	−	0.308390i	$-0.0997902\pi$
$360$		0			0
$361$	9.16476			0.482356
$362$		0			0
$363$	−7.69211	+	7.69211i	−0.403731	+	0.403731i
$364$		0			0
$365$	−18.7698	+	5.17135i	−0.982455	+	0.270681i
$366$		0			0
$367$	4.54775	+	4.54775i	0.237391	+	0.237391i	0.815769	−	0.578378i	$-0.196314\pi$
$367$	4.54775	+	4.54775i	0.237391	+	0.237391i	−0.578378	+	0.815769i	$0.696314\pi$
$368$		0			0
$369$		−	8.13560i		−	0.423522i
$370$		0			0
$371$			3.14114i			0.163080i
$372$		0			0
$373$	−15.8547	−	15.8547i	−0.820924	−	0.820924i	0.165317	−	0.986241i	$-0.447135\pi$
$373$	−15.8547	−	15.8547i	−0.820924	−	0.820924i	−0.986241	+	0.165317i	$0.947135\pi$
$374$		0			0
$375$	−8.07100	−	7.73685i	−0.416785	−	0.399529i
$376$		0			0
$377$	11.6487	−	11.6487i	0.599936	−	0.599936i
$378$		0			0
$379$		−	19.7777i		−	1.01591i	−0.861383	−	0.507956i	$-0.830401\pi$
$379$		−	19.7777i		−	1.01591i	0.861383	−	0.507956i	$-0.169599\pi$
$380$		0			0
$381$	−7.72894			−0.395966
$382$		0			0
$383$	−1.91240	+	1.91240i	−0.0977190	+	0.0977190i	−0.754276	−	0.656557i	$-0.772012\pi$
$383$	−1.91240	+	1.91240i	−0.0977190	+	0.0977190i	0.656557	+	0.754276i	$0.272012\pi$
$384$		0			0
$385$	0.381474	+	1.38459i	0.0194417	+	0.0705651i
$386$		0			0
$387$	1.78149	+	1.78149i	0.0905581	+	0.0905581i
$388$		0			0
$389$	−16.7272			−0.848101			−0.424051	−	0.905638i	$-0.639392\pi$
$389$	−16.7272			−0.848101			−0.424051	+	0.905638i	$0.639392\pi$
$390$		0			0
$391$	5.53093			0.279711
$392$		0			0
$393$	−13.5255	+	13.5255i	−0.682271	+	0.682271i
$394$		0			0
$395$	20.9187	+	11.8817i	1.05253	+	0.597833i
$396$		0			0
$397$	17.0764	−	17.0764i	0.857042	−	0.857042i	−0.133947	−	0.990989i	$-0.542765\pi$
$397$	17.0764	−	17.0764i	0.857042	−	0.857042i	0.990989	+	0.133947i	$0.0427651\pi$
$398$		0			0
$399$	5.77371			0.289047
$400$		0			0
$401$			16.2324i			0.810607i	0.914182	+	0.405303i	$0.132834\pi$
$401$			16.2324i			0.810607i	−0.914182	+	0.405303i	$0.867166\pi$
$402$		0			0
$403$	−13.1767	−	26.9592i	−0.656378	−	1.34294i
$404$		0			0
$405$	−1.94432	−	1.10436i	−0.0966140	−	0.0548763i
$406$		0			0
$407$	0.787540	−	0.787540i	0.0390369	−	0.0390369i
$408$		0			0
$409$	−38.7463			−1.91588			−0.957942	−	0.286963i	$-0.907354\pi$
$409$	−38.7463			−1.91588			−0.957942	+	0.286963i	$0.907354\pi$
$410$		0			0
$411$	16.3534			0.806655
$412$		0			0
$413$	−4.46816	−	4.46816i	−0.219864	−	0.219864i
$414$		0			0
$415$	−18.2896	+	5.03904i	−0.897799	+	0.247357i
$416$		0			0
$417$	−9.07413	+	9.07413i	−0.444362	+	0.444362i
$418$		0			0
$419$			10.0792i			0.492401i	0.969219	+	0.246201i	$0.0791822\pi$
$419$			10.0792i			0.492401i	−0.969219	+	0.246201i	$0.920818\pi$
$420$		0			0
$421$	−1.02447			−0.0499298			−0.0249649	−	0.999688i	$-0.507947\pi$
$421$	−1.02447			−0.0499298			−0.0249649	+	0.999688i	$0.507947\pi$
$422$		0			0
$423$	3.54328	+	3.54328i	0.172280	+	0.172280i
$424$		0			0
$425$	−1.50323	+	5.94388i	−0.0729173	+	0.288321i
$426$		0			0
$427$	−0.995800	−	0.995800i	−0.0481901	−	0.0481901i
$428$		0			0
$429$	1.88020			0.0907769
$430$		0			0
$431$	10.5957			0.510378			0.255189	−	0.966891i	$-0.417862\pi$
$431$	10.5957			0.510378			0.255189	+	0.966891i	$0.417862\pi$
$432$		0			0
$433$	−22.1124	+	22.1124i	−1.06265	+	1.06265i	−0.0647524	+	0.997901i	$0.520626\pi$
$433$	−22.1124	+	22.1124i	−1.06265	+	1.06265i	−0.997901	+	0.0647524i	$0.979374\pi$
$434$		0			0
$435$	−6.58939	+	1.81547i	−0.315937	+	0.0870452i
$436$		0			0
$437$	10.0026	+	10.0026i	0.478489	+	0.478489i
$438$		0			0
$439$		−	2.34169i		−	0.111763i	−0.998437	−	0.0558813i	$-0.982203\pi$
$439$		−	2.34169i		−	0.111763i	0.998437	−	0.0558813i	$-0.0177969\pi$
$440$		0			0
$441$	3.61059			0.171933
$442$		0			0
$443$	−11.9067	−	11.9067i	−0.565705	−	0.565705i	0.365217	−	0.930922i	$-0.380995\pi$
$443$	−11.9067	−	11.9067i	−0.565705	−	0.565705i	−0.930922	+	0.365217i	$0.880995\pi$
$444$		0			0
$445$	−14.5107	−	8.24202i	−0.687875	−	0.390709i
$446$		0			0
$447$	−3.73861	−	3.73861i	−0.176830	−	0.176830i
$448$		0			0
$449$	5.92002			0.279383			0.139692	−	0.990195i	$-0.455389\pi$
$449$	5.92002			0.279383			0.139692	+	0.990195i	$0.455389\pi$
$450$		0			0
$451$		−	2.83825i		−	0.133648i
$452$		0			0
$453$	−0.490558	−	0.490558i	−0.0230484	−	0.0230484i
$454$		0			0
$455$	−10.9577	+	19.2918i	−0.513703	+	0.904415i
$456$		0			0
$457$	−2.39647	−	2.39647i	−0.112102	−	0.112102i	0.648831	−	0.760933i	$-0.275258\pi$
$457$	−2.39647	−	2.39647i	−0.112102	−	0.112102i	−0.760933	+	0.648831i	$0.775258\pi$
$458$		0			0
$459$			1.22620i			0.0572343i
$460$		0			0
$461$		−	36.7775i		−	1.71290i	−0.516230	−	0.856450i	$-0.672665\pi$
$461$		−	36.7775i		−	1.71290i	0.516230	−	0.856450i	$-0.327335\pi$
$462$		0			0
$463$	6.01752	−	6.01752i	0.279658	−	0.279658i	−0.553314	−	0.832972i	$-0.686637\pi$
$463$	6.01752	−	6.01752i	0.279658	−	0.279658i	0.832972	+	0.553314i	$0.186637\pi$
$464$		0			0
$465$	−0.770598	+	12.4260i	−0.0357356	+	0.576243i
$466$		0			0
$467$	10.1040	−	10.1040i	0.467556	−	0.467556i	−0.433566	−	0.901122i	$-0.642745\pi$
$467$	10.1040	−	10.1040i	0.467556	−	0.467556i	0.901122	+	0.433566i	$0.142745\pi$
$468$		0			0
$469$		−	2.60108i		−	0.120107i
$470$		0			0
$471$			0.130920i			0.00603247i
$472$		0			0
$473$	0.621503	+	0.621503i	0.0285767	+	0.0285767i
$474$		0			0
$475$	−13.4680	+	8.03085i	−0.617953	+	0.368481i
$476$		0			0
$477$	−1.20645	−	1.20645i	−0.0552397	−	0.0552397i
$478$		0			0
$479$		−	9.08899i		−	0.415286i	−0.978205	−	0.207643i	$-0.933421\pi$
$479$		−	9.08899i		−	0.415286i	0.978205	−	0.207643i	$-0.0665793\pi$
$480$		0			0
$481$	17.2056			0.784509
$482$		0			0
$483$	−5.87196	−	5.87196i	−0.267183	−	0.267183i
$484$		0			0
$485$	−3.62775	+	0.999498i	−0.164728	+	0.0453849i
$486$		0			0
$487$	19.9178	+	19.9178i	0.902563	+	0.902563i	0.995657	−	0.0930941i	$-0.0296757\pi$
$487$	19.9178	+	19.9178i	0.902563	+	0.902563i	−0.0930941	+	0.995657i	$0.529676\pi$
$488$		0			0
$489$	−19.2687			−0.871362
$490$		0			0
$491$			17.7634i			0.801652i	0.916154	+	0.400826i	$0.131277\pi$
$491$			17.7634i			0.801652i	−0.916154	+	0.400826i	$0.868723\pi$
$492$		0			0
$493$	2.65030	+	2.65030i	0.119364	+	0.119364i
$494$		0			0
$495$	−0.678310	−	0.385277i	−0.0304878	−	0.0173169i
$496$		0			0
$497$	9.57303	−	9.57303i	0.429409	−	0.429409i
$498$		0			0
$499$	43.1597			1.93210			0.966048	−	0.258364i	$-0.0831834\pi$
$499$	43.1597			1.93210			0.966048	+	0.258364i	$0.0831834\pi$
$500$		0			0
$501$	4.28457			0.191421
$502$		0			0
$503$	3.03688	+	3.03688i	0.135408	+	0.135408i	0.771562	−	0.636154i	$-0.219476\pi$
$503$	3.03688	+	3.03688i	0.135408	+	0.135408i	−0.636154	+	0.771562i	$0.719476\pi$
$504$		0			0
$505$	37.8597	+	21.5041i	1.68474	+	0.956921i
$506$		0			0
$507$	11.3463	+	11.3463i	0.503905	+	0.503905i
$508$		0			0
$509$	−21.1512			−0.937511			−0.468756	−	0.883328i	$-0.655297\pi$
$509$	−21.1512			−0.937511			−0.468756	+	0.883328i	$0.655297\pi$
$510$		0			0
$511$		−	16.0297i		−	0.709110i
$512$		0			0
$513$	−2.21757	+	2.21757i	−0.0979081	+	0.0979081i
$514$		0			0
$515$	−2.78087	−	10.0934i	−0.122540	−	0.444767i
$516$		0			0
$517$	1.23613	+	1.23613i	0.0543651	+	0.0543651i
$518$		0			0
$519$	11.3440			0.497947
$520$		0			0
$521$	−1.41037			−0.0617894			−0.0308947	−	0.999523i	$-0.509836\pi$
$521$	−1.41037			−0.0617894			−0.0308947	+	0.999523i	$0.509836\pi$
$522$		0			0
$523$	−15.5265	+	15.5265i	−0.678925	+	0.678925i	−0.959757	−	0.280832i	$-0.909390\pi$
$523$	−15.5265	+	15.5265i	−0.678925	+	0.678925i	0.280832	+	0.959757i	$0.409390\pi$
$524$		0			0
$525$	7.90628	−	4.71445i	0.345058	−	0.205756i
$526$		0			0
$527$	6.13377	−	2.99796i	0.267191	−	0.130593i
$528$		0			0
$529$			2.65437i			0.115408i
$530$		0			0
$531$	3.43227			0.148948
$532$		0			0
$533$	31.0040	−	31.0040i	1.34293	−	1.34293i
$534$		0			0
$535$	−35.3852	+	9.74912i	−1.52983	+	0.421491i
$536$		0			0
$537$	8.68007	−	8.68007i	0.374573	−	0.374573i
$538$		0			0
$539$	1.25962			0.0542556
$540$		0			0
$541$	26.4422			1.13684			0.568420	−	0.822738i	$-0.307555\pi$
$541$	26.4422			1.13684			0.568420	+	0.822738i	$0.307555\pi$
$542$		0			0
$543$	−3.62732	−	3.62732i	−0.155663	−	0.155663i
$544$		0			0
$545$	6.83195	−	12.0282i	0.292649	−	0.515231i
$546$		0			0
$547$	−3.76122	+	3.76122i	−0.160818	+	0.160818i	−0.782929	−	0.622111i	$-0.786275\pi$
$547$	−3.76122	+	3.76122i	−0.160818	+	0.160818i	0.622111	+	0.782929i	$0.286275\pi$
$548$		0			0
$549$	0.764936			0.0326467
$550$		0			0
$551$			9.58606i			0.408380i
$552$		0			0
$553$	−14.0060	+	14.0060i	−0.595595	+	0.595595i
$554$		0			0
$555$	−6.20718	−	3.52565i	−0.263480	−	0.149655i
$556$		0			0
$557$	−14.6279	−	14.6279i	−0.619804	−	0.619804i	0.325677	−	0.945481i	$-0.394408\pi$
$557$	−14.6279	−	14.6279i	−0.619804	−	0.619804i	−0.945481	+	0.325677i	$0.894408\pi$
$558$		0			0
$559$			13.5782i			0.574295i
$560$		0			0
$561$			0.427783i			0.0180610i
$562$		0			0
$563$	−23.5630	−	23.5630i	−0.993064	−	0.993064i	0.00691209	−	0.999976i	$-0.497800\pi$
$563$	−23.5630	−	23.5630i	−0.993064	−	0.993064i	−0.999976	+	0.00691209i	$0.997800\pi$
$564$		0			0
$565$	−2.69240	−	9.77227i	−0.113270	−	0.411123i
$566$		0			0
$567$	1.30181	−	1.30181i	0.0546708	−	0.0546708i
$568$		0			0
$569$	15.9609			0.669114			0.334557	−	0.942376i	$-0.391413\pi$
$569$	15.9609			0.669114			0.334557	+	0.942376i	$0.391413\pi$
$570$		0			0
$571$		−	39.4110i		−	1.64930i	−0.565644	−	0.824650i	$-0.691372\pi$
$571$		−	39.4110i		−	1.64930i	0.565644	−	0.824650i	$-0.308628\pi$
$572$		0			0
$573$	4.60017	−	4.60017i	0.192175	−	0.192175i
$574$		0			0
$575$	21.8647	+	5.52965i	0.911820	+	0.230602i
$576$		0			0
$577$	−24.5914	+	24.5914i	−1.02375	+	1.02375i	−0.0240404	+	0.999711i	$0.507653\pi$
$577$	−24.5914	+	24.5914i	−1.02375	+	1.02375i	−0.999711	+	0.0240404i	$0.992347\pi$
$578$		0			0
$579$	−21.8848			−0.909502
$580$		0			0
$581$		−	15.6195i		−	0.648008i
$582$		0			0
$583$	−0.420892	−	0.420892i	−0.0174316	−	0.0174316i
$584$		0			0
$585$	−3.20099	−	11.6183i	−0.132345	−	0.480356i
$586$		0			0
$587$	−2.23731	−	2.23731i	−0.0923437	−	0.0923437i	0.659426	−	0.751770i	$-0.270799\pi$
$587$	−2.23731	−	2.23731i	−0.0923437	−	0.0923437i	−0.751770	+	0.659426i	$0.770799\pi$
$588$		0			0
$589$	16.5146	+	5.67105i	0.680472	+	0.233672i
$590$		0			0
$591$	6.49222			0.267054
$592$		0			0
$593$	10.7112	+	10.7112i	0.439855	+	0.439855i	0.891963	−	0.452108i	$-0.149328\pi$
$593$	10.7112	+	10.7112i	0.439855	+	0.439855i	−0.452108	+	0.891963i	$0.649328\pi$
$594$		0			0
$595$	−4.38927	−	2.49309i	−0.179943	−	0.102207i
$596$		0			0
$597$	−15.4091	+	15.4091i	−0.630651	+	0.630651i
$598$		0			0
$599$			33.9293i			1.38631i	0.720788	+	0.693156i	$0.243780\pi$
$599$			33.9293i			1.38631i	−0.720788	+	0.693156i	$0.756220\pi$
$600$		0			0
$601$			1.15894i			0.0472740i	0.999721	+	0.0236370i	$0.00752458\pi$
$601$			1.15894i			0.0472740i	−0.999721	+	0.0236370i	$0.992475\pi$
$602$		0			0
$603$	0.999024	+	0.999024i	0.0406834	+	0.0406834i
$604$		0			0
$605$	21.1509	+	12.0136i	0.859906	+	0.488422i
$606$		0			0
$607$	−3.61903	+	3.61903i	−0.146892	+	0.146892i	−0.776728	−	0.629836i	$-0.783122\pi$
$607$	−3.61903	+	3.61903i	−0.146892	+	0.146892i	0.629836	+	0.776728i	$0.283122\pi$
$608$		0			0
$609$		−	5.62743i		−	0.228035i
$610$		0			0
$611$			27.0062i			1.09255i
$612$		0			0
$613$	−27.4579	+	27.4579i	−1.10901	+	1.10901i	−0.115732	+	0.993280i	$0.536922\pi$
$613$	−27.4579	+	27.4579i	−1.10901	+	1.10901i	−0.993280	+	0.115732i	$0.963078\pi$
$614$		0			0
$615$	−17.5383	+	4.83205i	−0.707212	+	0.194847i
$616$		0			0
$617$	−17.7030	+	17.7030i	−0.712697	+	0.712697i	−0.967099	−	0.254402i	$-0.918121\pi$
$617$	−17.7030	+	17.7030i	−0.712697	+	0.712697i	0.254402	+	0.967099i	$0.418121\pi$
$618$		0			0
$619$	−13.2075			−0.530853			−0.265427	−	0.964131i	$-0.585513\pi$
$619$	−13.2075			−0.530853			−0.265427	+	0.964131i	$0.585513\pi$
$620$		0			0
$621$	4.51061			0.181005
$622$		0			0
$623$	9.71558	−	9.71558i	0.389247	−	0.389247i
$624$		0			0
$625$	−11.8850	+	21.9942i	−0.475400	+	0.879770i
$626$		0			0
$627$	−0.773639	+	0.773639i	−0.0308961	+	0.0308961i
$628$		0			0
$629$			3.91462i			0.156086i
$630$		0			0
$631$			19.1048i			0.760550i	0.924873	+	0.380275i	$0.124171\pi$
$631$			19.1048i			0.760550i	−0.924873	+	0.380275i	$0.875829\pi$
$632$		0			0
$633$	−7.36980	+	7.36980i	−0.292923	+	0.292923i
$634$		0			0
$635$	4.59052	+	16.6616i	0.182169	+	0.661197i
$636$		0			0
$637$	13.7596	+	13.7596i	0.545176	+	0.545176i
$638$		0			0
$639$			7.35363i			0.290905i
$640$		0			0
$641$			15.3696i			0.607064i	0.952821	+	0.303532i	$0.0981660\pi$
$641$			15.3696i			0.607064i	−0.952821	+	0.303532i	$0.901834\pi$
$642$		0			0
$643$	4.53851	−	4.53851i	0.178981	−	0.178981i	−0.611930	−	0.790912i	$-0.709607\pi$
$643$	4.53851	−	4.53851i	0.178981	−	0.178981i	0.790912	+	0.611930i	$0.209607\pi$
$644$		0			0
$645$	2.78234	−	4.89853i	0.109554	−	0.192879i
$646$		0			0
$647$	−0.909934	−	0.909934i	−0.0357732	−	0.0357732i	0.688994	−	0.724767i	$-0.258053\pi$
$647$	−0.909934	−	0.909934i	−0.0357732	−	0.0357732i	−0.724767	+	0.688994i	$0.758053\pi$
$648$		0			0
$649$	1.19741			0.0470024
$650$		0			0
$651$	−9.69477	−	3.32915i	−0.379968	−	0.130480i
$652$		0			0
$653$	9.87258	+	9.87258i	0.386344	+	0.386344i	0.873381	−	0.487037i	$-0.161922\pi$
$653$	9.87258	+	9.87258i	0.386344	+	0.386344i	−0.487037	+	0.873381i	$0.661922\pi$
$654$		0			0
$655$	37.1908	+	21.1242i	1.45317	+	0.825390i
$656$		0			0
$657$	6.15668	+	6.15668i	0.240195	+	0.240195i
$658$		0			0
$659$		−	14.2874i		−	0.556559i	−0.960500	−	0.278279i	$-0.910236\pi$
$659$		−	14.2874i		−	0.556559i	0.960500	−	0.278279i	$-0.0897641\pi$
$660$		0			0
$661$	−5.44398			−0.211746			−0.105873	−	0.994380i	$-0.533764\pi$
$661$	−5.44398			−0.211746			−0.105873	+	0.994380i	$0.533764\pi$
$662$		0			0
$663$	−4.67295	+	4.67295i	−0.181482	+	0.181482i
$664$		0			0
$665$	−3.42923	−	12.4466i	−0.132980	−	0.482660i
$666$		0			0
$667$	9.74918	−	9.74918i	0.377490	−	0.377490i
$668$		0			0
$669$		−	11.4088i		−	0.441090i
$670$		0			0
$671$	0.266861			0.0103021
$672$		0			0
$673$	−5.58983	+	5.58983i	−0.215472	+	0.215472i	−0.806587	−	0.591115i	$-0.798688\pi$
$673$	−5.58983	+	5.58983i	−0.215472	+	0.215472i	0.591115	+	0.806587i	$0.298688\pi$
$674$		0			0
$675$	−1.22592	+	4.84738i	−0.0471857	+	0.186576i
$676$		0			0
$677$	−9.65893	−	9.65893i	−0.371223	−	0.371223i	0.496700	−	0.867922i	$-0.334545\pi$
$677$	−9.65893	−	9.65893i	−0.371223	−	0.371223i	−0.867922	+	0.496700i	$0.834545\pi$
$678$		0			0
$679$		−	3.09815i		−	0.118896i
$680$		0			0
$681$		−	7.03806i		−	0.269699i
$682$		0			0
$683$	−11.8201	−	11.8201i	−0.452285	−	0.452285i	0.443827	−	0.896112i	$-0.353620\pi$
$683$	−11.8201	−	11.8201i	−0.452285	−	0.452285i	−0.896112	+	0.443827i	$0.853620\pi$
$684$		0			0
$685$	−9.71293	−	35.2538i	−0.371112	−	1.34698i
$686$		0			0
$687$	−8.43064	+	8.43064i	−0.321649	+	0.321649i
$688$		0			0
$689$		−	9.19536i		−	0.350315i
$690$		0			0
$691$	20.1495			0.766521			0.383261	−	0.923640i	$-0.374801\pi$
$691$	20.1495			0.766521			0.383261	+	0.923640i	$0.374801\pi$
$692$		0			0
$693$	0.454159	−	0.454159i	0.0172521	−	0.0172521i
$694$		0			0
$695$	24.9510	+	14.1720i	0.946445	+	0.537576i
$696$		0			0
$697$	7.05403	+	7.05403i	0.267190	+	0.267190i
$698$		0			0
$699$	1.54182			0.0583169
$700$		0			0
$701$	30.3732			1.14718			0.573589	−	0.819143i	$-0.305551\pi$
$701$	30.3732			1.14718			0.573589	+	0.819143i	$0.305551\pi$
$702$		0			0
$703$	−7.07953	+	7.07953i	−0.267009	+	0.267009i
$704$		0			0
$705$	5.53391	−	9.74289i	0.208419	−	0.366938i
$706$		0			0
$707$	−25.3488	+	25.3488i	−0.953339	+	0.953339i
$708$		0			0
$709$	−24.3199			−0.913354			−0.456677	−	0.889632i	$-0.650961\pi$
$709$	−24.3199			−0.913354			−0.456677	+	0.889632i	$0.650961\pi$
$710$		0			0
$711$		−	10.7589i		−	0.403489i
$712$		0			0
$713$	−11.0281	−	22.5632i	−0.413004	−	0.844997i
$714$		0			0
$715$	−1.11672	−	4.05323i	−0.0417631	−	0.151582i
$716$		0			0
$717$	20.7305	−	20.7305i	0.774195	−	0.774195i
$718$		0			0
$719$	−3.80962			−0.142075			−0.0710374	−	0.997474i	$-0.522631\pi$
$719$	−3.80962			−0.142075			−0.0710374	+	0.997474i	$0.522631\pi$
$720$		0			0
$721$	8.61987			0.321021
$722$		0			0
$723$	−9.17714	−	9.17714i	−0.341302	−	0.341302i
$724$		0			0
$725$	7.82738	+	13.1268i	0.290702	+	0.487516i
$726$		0			0
$727$	−8.15383	+	8.15383i	−0.302409	+	0.302409i	−0.841956	−	0.539547i	$-0.818596\pi$
$727$	−8.15383	+	8.15383i	−0.302409	+	0.302409i	0.539547	+	0.841956i	$0.318596\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−3.08930			−0.114262
$732$		0			0
$733$	−5.56049	−	5.56049i	−0.205381	−	0.205381i	0.596920	−	0.802301i	$-0.296391\pi$
$733$	−5.56049	−	5.56049i	−0.205381	−	0.205381i	−0.802301	+	0.596920i	$0.796391\pi$
$734$		0			0
$735$	−2.14447	−	7.78351i	−0.0790999	−	0.287099i
$736$		0			0
$737$	0.348527	+	0.348527i	0.0128382	+	0.0128382i
$738$		0			0
$739$	−26.0793			−0.959341			−0.479670	−	0.877449i	$-0.659244\pi$
$739$	−26.0793			−0.959341			−0.479670	+	0.877449i	$0.659244\pi$
$740$		0			0
$741$	−16.9019			−0.620907
$742$		0			0
$743$	−7.17052	+	7.17052i	−0.263061	+	0.263061i	−0.826296	−	0.563235i	$-0.809556\pi$
$743$	−7.17052	+	7.17052i	−0.263061	+	0.263061i	0.563235	+	0.826296i	$0.309556\pi$
$744$		0			0
$745$	−5.83898	+	10.2800i	−0.213924	+	0.376630i
$746$		0			0
$747$	5.99917	+	5.99917i	0.219498	+	0.219498i
$748$		0			0
$749$		−	30.2194i		−	1.10419i
$750$		0			0
$751$	38.2209			1.39470			0.697351	−	0.716730i	$-0.254362\pi$
$751$	38.2209			1.39470			0.697351	+	0.716730i	$0.254362\pi$
$752$		0			0
$753$	11.0591	+	11.0591i	0.403017	+	0.403017i
$754$		0			0
$755$	−0.766157	+	1.34888i	−0.0278833	+	0.0490908i
$756$		0			0
$757$	23.9112	+	23.9112i	0.869068	+	0.869068i	0.992369	−	0.123301i	$-0.0393482\pi$
$757$	23.9112	+	23.9112i	0.869068	+	0.869068i	−0.123301	+	0.992369i	$0.539348\pi$
$758$		0			0
$759$	1.57361			0.0571183
$760$		0			0
$761$			0.244217i			0.00885287i	0.999990	+	0.00442643i	$0.00140898\pi$
$761$			0.244217i			0.00885287i	−0.999990	+	0.00442643i	$0.998591\pi$
$762$		0			0
$763$	8.05341	+	8.05341i	0.291553	+	0.291553i
$764$		0			0
$765$	2.64338	−	0.728290i	0.0955717	−	0.0263314i
$766$		0			0
$767$	13.0801	+	13.0801i	0.472294	+	0.472294i
$768$		0			0
$769$		−	25.9174i		−	0.934604i	−0.884098	−	0.467302i	$-0.845226\pi$
$769$		−	25.9174i		−	0.934604i	0.884098	−	0.467302i	$-0.154774\pi$
$770$		0			0
$771$			17.0611i			0.614440i
$772$		0			0
$773$	18.0433	−	18.0433i	0.648971	−	0.648971i	−0.303773	−	0.952744i	$-0.598247\pi$
$773$	18.0433	−	18.0433i	0.648971	−	0.648971i	0.952744	+	0.303773i	$0.0982466\pi$
$774$		0			0
$775$	27.2450	−	5.71909i	0.978671	−	0.205436i
$776$		0			0
$777$	4.15599	−	4.15599i	0.149095	−	0.149095i
$778$		0			0
$779$			25.5142i			0.914141i
$780$		0			0
$781$			2.56544i			0.0917988i
$782$		0			0
$783$	2.16139	+	2.16139i	0.0772417	+	0.0772417i
$784$		0			0
$785$	0.282230	−	0.0777585i	0.0100732	−	0.00277532i
$786$		0			0
$787$	−24.9163	−	24.9163i	−0.888171	−	0.888171i	0.106176	−	0.994347i	$-0.466139\pi$
$787$	−24.9163	−	24.9163i	−0.888171	−	0.888171i	−0.994347	+	0.106176i	$0.966139\pi$
$788$		0			0
$789$			10.9910i			0.391291i
$790$		0			0
$791$	8.34565			0.296737
$792$		0			0
$793$	2.91510	+	2.91510i	0.103518	+	0.103518i
$794$		0			0
$795$	−1.88425	+	3.31736i	−0.0668273	+	0.117655i
$796$		0			0
$797$	−0.254437	−	0.254437i	−0.00901263	−	0.00901263i	0.702586	−	0.711599i	$-0.252029\pi$
$797$	−0.254437	−	0.254437i	−0.00901263	−	0.00901263i	−0.711599	+	0.702586i	$0.752029\pi$
$798$		0			0
$799$	−6.14445			−0.217375
$800$		0			0
$801$			7.46314i			0.263697i
$802$		0			0
$803$	2.14787	+	2.14787i	0.0757966	+	0.0757966i
$804$		0			0
$805$	−9.17086	+	16.1460i	−0.323230	+	0.569072i
$806$		0			0
$807$	13.7869	−	13.7869i	0.485321	−	0.485321i
$808$		0			0
$809$	−0.546906			−0.0192282			−0.00961409	−	0.999954i	$-0.503060\pi$
$809$	−0.546906			−0.0192282			−0.00961409	+	0.999954i	$0.503060\pi$
$810$		0			0
$811$	−44.3086			−1.55588			−0.777942	−	0.628336i	$-0.783736\pi$
$811$	−44.3086			−1.55588			−0.777942	+	0.628336i	$0.783736\pi$
$812$		0			0
$813$	5.90924	+	5.90924i	0.207246	+	0.207246i
$814$		0			0
$815$	11.4444	+	41.5385i	0.400882	+	1.45503i
$816$		0			0
$817$	−5.58695	−	5.58695i	−0.195463	−	0.195463i
$818$		0			0
$819$	9.92214			0.346708
$820$		0			0
$821$		−	18.4461i		−	0.643772i	−0.946778	−	0.321886i	$-0.895683\pi$
$821$		−	18.4461i		−	0.643772i	0.946778	−	0.321886i	$-0.104317\pi$
$822$		0			0
$823$	14.3035	−	14.3035i	0.498588	−	0.498588i	−0.412410	−	0.910998i	$-0.635313\pi$
$823$	14.3035	−	14.3035i	0.498588	−	0.498588i	0.910998	+	0.412410i	$0.135313\pi$
$824$		0			0
$825$	−0.427684	+	1.69110i	−0.0148900	+	0.0588764i
$826$		0			0
$827$	−34.3298	−	34.3298i	−1.19376	−	1.19376i	−0.976002	−	0.217761i	$-0.930125\pi$
$827$	−34.3298	−	34.3298i	−1.19376	−	1.19376i	−0.217761	−	0.976002i	$-0.569875\pi$
$828$		0			0
$829$	13.3161			0.462487			0.231244	−	0.972896i	$-0.425721\pi$
$829$	13.3161			0.462487			0.231244	+	0.972896i	$0.425721\pi$
$830$		0			0
$831$	−13.2139			−0.458385
$832$		0			0
$833$	−3.13059	+	3.13059i	−0.108468	+	0.108468i
$834$		0			0
$835$	−2.54477	−	9.23644i	−0.0880655	−	0.319640i
$836$		0			0
$837$	5.00224	−	2.44491i	0.172903	−	0.0845086i
$838$		0			0
$839$			49.8915i			1.72245i	0.508228	+	0.861223i	$0.330301\pi$
$839$			49.8915i			1.72245i	−0.508228	+	0.861223i	$0.669699\pi$
$840$		0			0
$841$	−19.6568			−0.677821
$842$		0			0
$843$	4.01540	−	4.01540i	0.138298	−	0.138298i
$844$		0			0
$845$	17.7206	−	31.1986i	0.609609	−	1.07326i
$846$		0			0
$847$	−14.1615	+	14.1615i	−0.486593	+	0.486593i
$848$		0			0
$849$	33.4390			1.14762
$850$		0			0
$851$	14.4000			0.493626
$852$		0			0
$853$	7.59092	+	7.59092i	0.259908	+	0.259908i	0.825017	−	0.565109i	$-0.191166\pi$
$853$	7.59092	+	7.59092i	0.259908	+	0.259908i	−0.565109	+	0.825017i	$0.691166\pi$
$854$		0			0
$855$	6.09762	+	3.46342i	0.208534	+	0.118446i
$856$		0			0
$857$	−29.9631	+	29.9631i	−1.02352	+	1.02352i	−0.0238045	+	0.999717i	$0.507578\pi$
$857$	−29.9631	+	29.9631i	−1.02352	+	1.02352i	−0.999717	+	0.0238045i	$0.992422\pi$
$858$		0			0
$859$	3.51310			0.119865			0.0599327	−	0.998202i	$-0.480911\pi$
$859$	3.51310			0.119865			0.0599327	+	0.998202i	$0.480911\pi$
$860$		0			0
$861$		−	14.9779i		−	0.510446i
$862$		0			0
$863$	−3.63860	+	3.63860i	−0.123859	+	0.123859i	−0.766319	−	0.642460i	$-0.777914\pi$
$863$	−3.63860	+	3.63860i	−0.123859	+	0.123859i	0.642460	+	0.766319i	$0.277914\pi$
$864$		0			0
$865$	−6.73765	−	24.4548i	−0.229087	−	0.831489i
$866$		0			0
$867$	10.9576	+	10.9576i	0.372141	+	0.372141i
$868$		0			0
$869$		−	3.75342i		−	0.127326i
$870$		0			0
$871$			7.61437i			0.258003i
$872$		0			0
$873$	1.18994	+	1.18994i	0.0402734	+	0.0402734i
$874$		0			0
$875$	−14.8590	−	14.2438i	−0.502326	−	0.481529i
$876$		0			0
$877$	26.1815	−	26.1815i	0.884088	−	0.884088i	−0.109859	−	0.993947i	$-0.535040\pi$
$877$	26.1815	−	26.1815i	0.884088	−	0.884088i	0.993947	+	0.109859i	$0.0350400\pi$
$878$		0			0
$879$	14.4688			0.488019
$880$		0			0
$881$		−	23.0918i		−	0.777983i	−0.921241	−	0.388991i	$-0.872824\pi$
$881$		−	23.0918i		−	0.777983i	0.921241	−	0.388991i	$-0.127176\pi$
$882$		0			0
$883$	22.7075	−	22.7075i	0.764167	−	0.764167i	−0.212906	−	0.977073i	$-0.568293\pi$
$883$	22.7075	−	22.7075i	0.764167	−	0.764167i	0.977073	+	0.212906i	$0.0682928\pi$
$884$		0			0
$885$	−2.03856	−	7.39911i	−0.0685255	−	0.248718i
$886$		0			0
$887$	16.5220	−	16.5220i	0.554756	−	0.554756i	−0.373054	−	0.927810i	$-0.621689\pi$
$887$	16.5220	−	16.5220i	0.554756	−	0.554756i	0.927810	+	0.373054i	$0.121689\pi$
$888$		0			0
$889$	−14.2293			−0.477234
$890$		0			0
$891$			0.348868i			0.0116875i
$892$		0			0
$893$	−11.1121	−	11.1121i	−0.371853	−	0.371853i
$894$		0			0
$895$	−23.8675	−	13.5566i	−0.797801	−	0.453147i
$896$		0			0
$897$	17.1895	+	17.1895i	0.573942	+	0.573942i
$898$		0			0
$899$	5.52737	−	16.0962i	0.184348	−	0.536838i
$900$		0			0
$901$	2.09213			0.0696989
$902$		0			0
$903$	3.27978	+	3.27978i	0.109144	+	0.109144i
$904$		0			0
$905$	−5.66517	+	9.97398i	−0.188317	+	0.331546i
$906$		0			0
$907$	−22.0275	+	22.0275i	−0.731411	+	0.731411i	−0.970899	−	0.239488i	$-0.923020\pi$
$907$	−22.0275	+	22.0275i	−0.731411	+	0.731411i	0.239488	+	0.970899i	$0.423020\pi$
$908$		0			0
$909$		−	19.4720i		−	0.645844i
$910$		0			0
$911$		−	26.5767i		−	0.880526i	−0.897869	−	0.440263i	$-0.854885\pi$
$911$		−	26.5767i		−	0.880526i	0.897869	−	0.440263i	$-0.145115\pi$
$912$		0			0
$913$	2.09292	+	2.09292i	0.0692654	+	0.0692654i
$914$		0			0
$915$	−0.454325	−	1.64901i	−0.0150195	−	0.0545145i
$916$		0			0
$917$	−24.9009	+	24.9009i	−0.822300	+	0.822300i
$918$		0			0
$919$			12.1285i			0.400082i	0.979787	+	0.200041i	$0.0641076\pi$
$919$			12.1285i			0.400082i	−0.979787	+	0.200041i	$0.935892\pi$
$920$		0			0
$921$			8.88143i			0.292653i
$922$		0			0
$923$	−28.0240	+	28.0240i	−0.922422	+	0.922422i
$924$		0			0
$925$	−3.91371	+	15.4751i	−0.128682	+	0.508819i
$926$		0			0
$927$	−3.31073	+	3.31073i	−0.108739	+	0.108739i
$928$		0			0
$929$	38.1417			1.25139			0.625694	−	0.780069i	$-0.284816\pi$
$929$	38.1417			1.25139			0.625694	+	0.780069i	$0.284816\pi$
$930$		0			0
$931$	−11.3232			−0.371104
$932$		0			0
$933$	4.51136	−	4.51136i	0.147695	−	0.147695i
$934$		0			0
$935$	0.922191	−	0.254077i	0.0301589	−	0.00830920i
$936$		0			0
$937$	−24.0826	+	24.0826i	−0.786744	+	0.786744i	−0.980959	−	0.194215i	$-0.937784\pi$
$937$	−24.0826	+	24.0826i	−0.786744	+	0.786744i	0.194215	+	0.980959i	$0.437784\pi$
$938$		0			0
$939$			20.3316i			0.663496i
$940$		0			0
$941$			37.5428i			1.22386i	0.790912	+	0.611930i	$0.209607\pi$
$941$			37.5428i			1.22386i	−0.790912	+	0.611930i	$0.790393\pi$
$942$		0			0
$943$	25.9484	−	25.9484i	0.844995	−	0.844995i
$944$		0			0
$945$	−3.57956	−	2.03317i	−0.116443	−	0.0661391i
$946$		0			0
$947$	−8.46134	−	8.46134i	−0.274957	−	0.274957i	0.556135	−	0.831092i	$-0.312284\pi$
$947$	−8.46134	−	8.46134i	−0.274957	−	0.274957i	−0.831092	+	0.556135i	$0.812284\pi$
$948$		0			0
$949$			46.9251i			1.52325i
$950$		0			0
$951$		−	16.9924i		−	0.551016i
$952$		0			0
$953$	36.6226	−	36.6226i	1.18632	−	1.18632i	0.208245	−	0.978077i	$-0.433225\pi$
$953$	36.6226	−	36.6226i	1.18632	−	1.18632i	0.978077	−	0.208245i	$-0.0667750\pi$
$954$		0			0
$955$	−12.6490	−	7.18457i	−0.409312	−	0.232487i
$956$		0			0
$957$	0.754038	+	0.754038i	0.0243746	+	0.0243746i
$958$		0			0
$959$	30.1072			0.972213
$960$		0			0
$961$	−24.4601	−	19.0448i	−0.789035	−	0.614348i
$962$		0			0
$963$	11.6067	+	11.6067i	0.374021	+	0.374021i
$964$		0			0
$965$	12.9982	+	47.1781i	0.418428	+	1.51872i
$966$		0			0
$967$	−5.24076	−	5.24076i	−0.168532	−	0.168532i	0.617802	−	0.786334i	$-0.288023\pi$
$967$	−5.24076	−	5.24076i	−0.168532	−	0.168532i	−0.786334	+	0.617802i	$0.788023\pi$
$968$		0			0
$969$		−	3.84552i		−	0.123536i
$970$		0			0
$971$	37.9342			1.21737			0.608684	−	0.793413i	$-0.291698\pi$
$971$	37.9342			1.21737			0.608684	+	0.793413i	$0.291698\pi$
$972$		0			0
$973$	−16.7058	+	16.7058i	−0.535563	+	0.535563i
$974$		0			0
$975$	−23.1448	+	13.8011i	−0.741227	+	0.441988i
$976$		0			0
$977$	12.6104	−	12.6104i	0.403443	−	0.403443i	−0.476002	−	0.879444i	$-0.657914\pi$
$977$	12.6104	−	12.6104i	0.403443	−	0.403443i	0.879444	+	0.476002i	$0.157914\pi$
$978$		0			0
$979$			2.60365i			0.0832130i
$980$		0			0
$981$	−6.18632			−0.197514
$982$		0			0
$983$	24.5105	−	24.5105i	0.781763	−	0.781763i	−0.198365	−	0.980128i	$-0.563563\pi$
$983$	24.5105	−	24.5105i	0.781763	−	0.781763i	0.980128	+	0.198365i	$0.0635631\pi$
$984$		0			0
$985$	−3.85598	−	13.9956i	−0.122862	−	0.445936i
$986$		0			0
$987$	6.52330	+	6.52330i	0.207639	+	0.207639i
$988$		0			0
$989$			11.3641i			0.361356i
$990$		0			0
$991$		−	47.7251i		−	1.51604i	−0.652233	−	0.758019i	$-0.726167\pi$
$991$		−	47.7251i		−	1.51604i	0.652233	−	0.758019i	$-0.273833\pi$
$992$		0			0
$993$	6.62699	+	6.62699i	0.210301	+	0.210301i
$994$		0			0
$995$	42.3700	+	24.0660i	1.34322	+	0.762942i
$996$		0			0
$997$	−10.3135	+	10.3135i	−0.326632	+	0.326632i	−0.851304	−	0.524672i	$-0.824188\pi$
$997$	−10.3135	+	10.3135i	−0.326632	+	0.326632i	0.524672	+	0.851304i	$0.324188\pi$
$998$		0			0
$999$			3.19247i			0.101005i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1860.2.s.a.433.9	✓	64
5.2	odd	4	inner	1860.2.s.a.1177.25	yes	64
31.30	odd	2	inner	1860.2.s.a.433.25	yes	64
155.92	even	4	inner	1860.2.s.a.1177.9	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1860.2.s.a.433.9	✓	64	1.1	even	1	trivial
1860.2.s.a.433.25	yes	64	31.30	odd	2	inner
1860.2.s.a.1177.9	yes	64	155.92	even	4	inner
1860.2.s.a.1177.25	yes	64	5.2	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1860 = 2^{2} \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1860.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{3} +(1.94432 + 1.10436i) q^{5} +(-1.30181 + 1.30181i) q^{7} -1.00000i q^{9} -0.348868i q^{11} +(3.81091 - 3.81091i) q^{13} +(-2.15575 + 0.593939i) q^{15} +(0.867057 + 0.867057i) q^{17} +3.13612i q^{19} -1.84104i q^{21} +(3.18948 - 3.18948i) q^{23} +(2.56076 + 4.29447i) q^{25} +(0.707107 + 0.707107i) q^{27} +3.05666 q^{29} +(1.80830 - 5.26593i) q^{31} +(0.246687 + 0.246687i) q^{33} +(-3.96880 + 1.09346i) q^{35} +(2.25742 + 2.25742i) q^{37} +5.38944i q^{39} +8.13560 q^{41} +(-1.78149 + 1.78149i) q^{43} +(1.10436 - 1.94432i) q^{45} +(-3.54328 + 3.54328i) q^{47} +3.61059i q^{49} -1.22620 q^{51} +(1.20645 - 1.20645i) q^{53} +(0.385277 - 0.678310i) q^{55} +(-2.21757 - 2.21757i) q^{57} +3.43227i q^{59} +0.764936i q^{61} +(1.30181 + 1.30181i) q^{63} +(11.6183 - 3.20099i) q^{65} +(-0.999024 + 0.999024i) q^{67} +4.51061i q^{69} -7.35363 q^{71} +(-6.15668 + 6.15668i) q^{73} +(-4.84738 - 1.22592i) q^{75} +(0.454159 + 0.454159i) q^{77} +10.7589 q^{79} -1.00000 q^{81} +(-5.99917 + 5.99917i) q^{83} +(0.728290 + 2.64338i) q^{85} +(-2.16139 + 2.16139i) q^{87} -7.46314 q^{89} +9.92214i q^{91} +(2.44491 + 5.00224i) q^{93} +(-3.46342 + 6.09762i) q^{95} +(-1.18994 + 1.18994i) q^{97} -0.348868 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{7} + 16 q^{25} + 8 q^{31} - 8 q^{33} + 24 q^{35} + 16 q^{41} + 56 q^{47} + 8 q^{63} - 32 q^{67} - 16 q^{71} - 64 q^{81} - 32 q^{87} - 32 q^{95} + 64 q^{97}+O(q^{100}) \) 64 * q - 8 * q^7 + 16 * q^25 + 8 * q^31 - 8 * q^33 + 24 * q^35 + 16 * q^41 + 56 * q^47 + 8 * q^63 - 32 * q^67 - 16 * q^71 - 64 * q^81 - 32 * q^87 - 32 * q^95 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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