LMFDB - Embedded newform 1860.2.s.a.1177.25

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			1177.25
Character	$\chi$	$=$	1860.1177
Dual form			1860.2.s.a.433.25

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 0.707107i) q^{3} +(1.94432 - 1.10436i) q^{5} +(-1.30181 - 1.30181i) q^{7} +1.00000i q^{9} -0.348868i q^{11} +(-3.81091 - 3.81091i) q^{13} +(2.15575 + 0.593939i) q^{15} +(-0.867057 + 0.867057i) q^{17} -3.13612i q^{19} -1.84104i q^{21} +(-3.18948 - 3.18948i) q^{23} +(2.56076 - 4.29447i) q^{25} +(-0.707107 + 0.707107i) q^{27} -3.05666 q^{29} +(1.80830 - 5.26593i) q^{31} +(0.246687 - 0.246687i) q^{33} +(-3.96880 - 1.09346i) q^{35} +(-2.25742 + 2.25742i) q^{37} -5.38944i q^{39} +8.13560 q^{41} +(1.78149 + 1.78149i) q^{43} +(1.10436 + 1.94432i) q^{45} +(-3.54328 - 3.54328i) q^{47} -3.61059i q^{49} -1.22620 q^{51} +(-1.20645 - 1.20645i) q^{53} +(-0.385277 - 0.678310i) q^{55} +(2.21757 - 2.21757i) q^{57} -3.43227i q^{59} +0.764936i q^{61} +(1.30181 - 1.30181i) q^{63} +(-11.6183 - 3.20099i) q^{65} +(-0.999024 - 0.999024i) q^{67} -4.51061i q^{69} -7.35363 q^{71} +(6.15668 + 6.15668i) q^{73} +(4.84738 - 1.22592i) q^{75} +(-0.454159 + 0.454159i) q^{77} -10.7589 q^{79} -1.00000 q^{81} +(5.99917 + 5.99917i) q^{83} +(-0.728290 + 2.64338i) q^{85} +(-2.16139 - 2.16139i) q^{87} +7.46314 q^{89} +9.92214i q^{91} +(5.00224 - 2.44491i) q^{93} +(-3.46342 - 6.09762i) q^{95} +(-1.18994 - 1.18994i) q^{97} +0.348868 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1860\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	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	0.416910	−	0.908948i	$-0.363113\pi$
$7$	−1.30181	−	1.30181i	−0.492037	−	0.492037i	−0.908948	+	0.416910i	$0.863113\pi$
$8$		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	−0.998277	−	0.0586785i	$-0.981311\pi$
$13$	−3.81091	−	3.81091i	−1.05696	−	1.05696i	−0.0586785	−	0.998277i	$-0.518689\pi$
$14$		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	$-0.797509\pi$
$17$	−0.867057	+	0.867057i	−0.210292	+	0.210292i	0.594099	+	0.804392i	$0.297509\pi$
$18$		0			0
$19$		−	3.13612i		−	0.719475i	−0.933054	−	0.359737i	$-0.882866\pi$
$19$		−	3.13612i		−	0.719475i	0.933054	−	0.359737i	$-0.117134\pi$
$20$		0			0
$21$		−	1.84104i		−	0.401747i
$22$		0			0
$23$	−3.18948	−	3.18948i	−0.665054	−	0.665054i	0.291513	−	0.956567i	$-0.405841\pi$
$23$	−3.18948	−	3.18948i	−0.665054	−	0.665054i	−0.956567	+	0.291513i	$0.905841\pi$
$24$		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	$-0.591597\pi$
$29$	−3.05666			−0.567608			−0.283804	+	0.958882i	$0.591597\pi$
$30$		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	$-0.834520\pi$
$37$	−2.25742	+	2.25742i	−0.371117	+	0.371117i	0.496767	+	0.867884i	$0.334520\pi$
$38$		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	$-0.188469\pi$
$43$	1.78149	+	1.78149i	0.271674	+	0.271674i	−0.558100	+	0.829774i	$0.688469\pi$
$44$		0			0
$45$	1.10436	+	1.94432i	0.164629	+	0.289842i
$46$		0			0
$47$	−3.54328	−	3.54328i	−0.516840	−	0.516840i	0.399774	−	0.916614i	$-0.369089\pi$
$47$	−3.54328	−	3.54328i	−0.516840	−	0.516840i	−0.916614	+	0.399774i	$0.869089\pi$
$48$		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	$-0.287386\pi$
$53$	−1.20645	−	1.20645i	−0.165719	−	0.165719i	−0.785095	+	0.619376i	$0.787386\pi$
$54$		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	$-0.928277\pi$
$59$		−	3.43227i		−	0.446844i	0.974722	−	0.223422i	$-0.0717228\pi$
$60$		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	0.643443	−	0.765494i	$-0.277505\pi$
$67$	−0.999024	−	0.999024i	−0.122050	−	0.122050i	−0.765494	+	0.643443i	$0.777505\pi$
$68$		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	$-0.0798190\pi$
$73$	6.15668	+	6.15668i	0.720585	+	0.720585i	−0.248139	+	0.968724i	$0.579819\pi$
$74$		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	$-0.706920\pi$
$79$	−10.7589			−1.21047			−0.605234	+	0.796048i	$0.706920\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	5.99917	+	5.99917i	0.658494	+	0.658494i	0.955024	−	0.296530i	$-0.0958293\pi$
$83$	5.99917	+	5.99917i	0.658494	+	0.658494i	−0.296530	+	0.955024i	$0.595829\pi$
$84$		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	$-0.370555\pi$
$89$	7.46314			0.791091			0.395546	+	0.918446i	$0.370555\pi$
$90$		0			0
$91$			9.92214i			1.04012i
$92$		0			0
$93$	5.00224	−	2.44491i	0.518708	−	0.253526i
$94$		0			0
$95$	−3.46342	−	6.09762i	−0.355339	−	0.625602i
$96$		0			0
$97$	−1.18994	−	1.18994i	−0.120820	−	0.120820i	0.644111	−	0.764932i	$-0.277227\pi$
$97$	−1.18994	−	1.18994i	−0.120820	−	0.120820i	−0.764932	+	0.644111i	$0.777227\pi$
$98$		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	−0.851146	−	0.524930i	$-0.824092\pi$
$103$	−3.31073	+	3.31073i	−0.326216	+	0.326216i	0.524930	+	0.851146i	$0.324092\pi$
$104$		0			0
$105$	−2.03317	−	3.57956i	−0.198417	−	0.349330i
$106$		0			0
$107$	−11.6067	−	11.6067i	−1.12206	−	1.12206i	−0.991431	−	0.130631i	$-0.958300\pi$
$107$	−11.6067	−	11.6067i	−1.12206	−	1.12206i	−0.130631	−	0.991431i	$-0.541700\pi$
$108$		0			0
$109$			6.18632i			0.592542i	0.955104	+	0.296271i	$0.0957432\pi$
$109$			6.18632i			0.592542i	−0.955104	+	0.296271i	$0.904257\pi$
$110$		0			0
$111$	−3.19247			−0.303016
$112$		0			0
$113$	−3.20541	+	3.20541i	−0.301539	+	0.301539i	−0.841616	−	0.540077i	$-0.818395\pi$
$113$	−3.20541	+	3.20541i	−0.301539	+	0.301539i	0.540077	+	0.841616i	$0.318395\pi$
$114$		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	$-0.861415\pi$
$127$	−5.46519	+	5.46519i	−0.484957	+	0.484957i	0.421754	+	0.906711i	$0.361415\pi$
$128$		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	$-0.503814\pi$
$137$	11.5636	−	11.5636i	0.987946	−	0.987946i	0.999928	+	0.0119821i	$0.00381411\pi$
$138$		0			0
$139$	−12.8328			−1.08846			−0.544230	−	0.838936i	$-0.683178\pi$
$139$	−12.8328			−1.08846			−0.544230	+	0.838936i	$0.683178\pi$
$140$		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	$-0.930512\pi$
$149$		−	5.28719i		−	0.433144i	0.976267	−	0.216572i	$-0.0694876\pi$
$150$		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
$155$	−2.29959	−	12.2357i	−0.184707	−	0.982794i
$156$		0			0
$157$	0.0925744	+	0.0925744i	0.00738824	+	0.00738824i	0.710791	−	0.703403i	$-0.248337\pi$
$157$	0.0925744	+	0.0925744i	0.00738824	+	0.00738824i	−0.703403	+	0.710791i	$0.748337\pi$
$158$		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	0.0696232	−	0.997573i	$-0.477820\pi$
$163$	13.6251	−	13.6251i	1.06720	−	1.06720i	0.997573	−	0.0696232i	$-0.0221797\pi$
$164$		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	$-0.696987\pi$
$167$	3.02965	−	3.02965i	0.234441	−	0.234441i	0.814544	+	0.580102i	$0.196987\pi$
$168$		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	−0.942909	−	0.333051i	$-0.891922\pi$
$173$	−8.02143	+	8.02143i	−0.609858	+	0.609858i	0.333051	+	0.942909i	$0.391922\pi$
$174$		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	$-0.348295\pi$
$179$	12.2755			0.917512			0.458756	+	0.888562i	$0.348295\pi$
$180$		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	0.121291	−	0.992617i	$-0.461297\pi$
$193$	15.4749	−	15.4749i	1.11391	−	1.11391i	0.992617	−	0.121291i	$-0.0387034\pi$
$194$		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	$-0.675710\pi$
$197$	4.59069	−	4.59069i	0.327073	−	0.327073i	0.851473	+	0.524399i	$0.175710\pi$
$198$		0			0
$199$	−21.7917			−1.54477			−0.772386	−	0.635153i	$-0.780937\pi$
$199$	−21.7917			−1.54477			−0.772386	+	0.635153i	$0.780937\pi$
$200$		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
$217$	−9.20930	+	4.50117i	−0.625168	+	0.305560i
$218$		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	$-0.125237\pi$
$223$	8.06725	+	8.06725i	0.540223	+	0.540223i	−0.383371	+	0.923594i	$0.625237\pi$
$224$		0			0
$225$	4.29447	+	2.56076i	0.286298	+	0.170717i
$226$		0			0
$227$	−4.97666	−	4.97666i	−0.330312	−	0.330312i	0.522393	−	0.852705i	$-0.325040\pi$
$227$	−4.97666	−	4.97666i	−0.330312	−	0.330312i	−0.852705	+	0.522393i	$0.825040\pi$
$228$		0			0
$229$	−11.9227			−0.787876			−0.393938	−	0.919137i	$-0.628887\pi$
$229$	−11.9227			−0.787876			−0.393938	+	0.919137i	$0.628887\pi$
$230$		0			0
$231$	−0.642278			−0.0422588
$232$		0			0
$233$	−1.09023	+	1.09023i	−0.0714234	+	0.0714234i	−0.741916	−	0.670493i	$-0.766083\pi$
$233$	−1.09023	+	1.09023i	−0.0714234	+	0.0714234i	0.670493	+	0.741916i	$0.266083\pi$
$234$		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	$-0.102910\pi$
$239$	29.3174			1.89638			0.948192	+	0.317699i	$0.102910\pi$
$240$		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	0.974951	−	0.222419i	$-0.0713953\pi$
$257$	12.0640	+	12.0640i	0.752532	+	0.752532i	−0.222419	+	0.974951i	$0.571395\pi$
$258$		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	$-0.360044\pi$
$263$	−7.77183	−	7.77183i	−0.479232	−	0.479232i	−0.904886	+	0.425654i	$0.860044\pi$
$264$		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	$-0.297392\pi$
$269$	19.4976			1.18879			0.594394	+	0.804174i	$0.297392\pi$
$270$		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	$-0.879939\pi$
$277$	−9.34364	+	9.34364i	−0.561405	+	0.561405i	0.368302	+	0.929706i	$0.379939\pi$
$278$		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	−0.624614	+	0.780934i	$0.714744\pi$
$283$	−23.6450	+	23.6450i	−1.40555	+	1.40555i	−0.780934	+	0.624614i	$0.785256\pi$
$284$		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	−0.939700	−	0.342001i	$-0.888895\pi$
$293$	−10.2310	+	10.2310i	−0.597699	+	0.597699i	0.342001	+	0.939700i	$0.388895\pi$
$294$		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	0.863232	−	0.504807i	$-0.168436\pi$
$307$	6.28012	+	6.28012i	0.358425	+	0.358425i	−0.504807	+	0.863232i	$0.668436\pi$
$308$		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	$-0.444844\pi$
$313$	−14.3766	−	14.3766i	−0.812613	−	0.812613i	−0.985025	+	0.172412i	$0.944844\pi$
$314$		0			0
$315$	1.09346	−	3.96880i	0.0616096	−	0.223617i
$316$		0			0
$317$	−12.0154	−	12.0154i	−0.674854	−	0.674854i	0.283977	−	0.958831i	$-0.408346\pi$
$317$	−12.0154	−	12.0154i	−0.674854	−	0.674854i	−0.958831	+	0.283977i	$0.908346\pi$
$318$		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	$-0.601504\pi$
$337$	11.6769	−	11.6769i	0.636080	−	0.636080i	0.949586	+	0.313506i	$0.101504\pi$
$338$		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	$-0.638532\pi$
$347$	9.03788	−	9.03788i	0.485179	−	0.485179i	0.906781	+	0.421602i	$0.138532\pi$
$348$		0			0
$349$			30.2184i			1.61755i	0.588116	+	0.808776i	$0.299870\pi$
$349$			30.2184i			1.61755i	−0.588116	+	0.808776i	$0.700130\pi$
$350$		0			0
$351$	5.38944			0.287667
$352$		0			0
$353$	−16.9052	−	16.9052i	−0.899775	−	0.899775i	0.0956412	−	0.995416i	$-0.469510\pi$
$353$	−16.9052	−	16.9052i	−0.899775	−	0.899775i	−0.995416	+	0.0956412i	$0.969510\pi$
$354$		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	$0.0997902\pi$
$359$			11.6863i			0.616780i	−0.951260	+	0.308390i	$0.900210\pi$
$360$		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	$-0.803686\pi$
$367$	−4.54775	+	4.54775i	−0.237391	+	0.237391i	0.578378	+	0.815769i	$0.303686\pi$
$368$		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	−0.986241	−	0.165317i	$-0.947135\pi$
$373$	−15.8547	+	15.8547i	−0.820924	+	0.820924i	0.165317	+	0.986241i	$0.447135\pi$
$374$		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	$0.169599\pi$
$379$			19.7777i			1.01591i	−0.861383	+	0.507956i	$0.830401\pi$
$380$		0			0
$381$	−7.72894			−0.395966
$382$		0			0
$383$	1.91240	+	1.91240i	0.0977190	+	0.0977190i	0.754276	−	0.656557i	$-0.227988\pi$
$383$	1.91240	+	1.91240i	0.0977190	+	0.0977190i	−0.656557	+	0.754276i	$0.727988\pi$
$384$		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	$-0.360608\pi$
$389$	16.7272			0.848101			0.424051	+	0.905638i	$0.360608\pi$
$390$		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	0.990989	−	0.133947i	$-0.0427651\pi$
$397$	17.0764	+	17.0764i	0.857042	+	0.857042i	−0.133947	+	0.990989i	$0.542765\pi$
$398$		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
$403$	−26.9592	+	13.1767i	−1.34294	+	0.656378i
$404$		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	$-0.0926457\pi$
$409$	38.7463			1.91588			0.957942	+	0.286963i	$0.0926457\pi$
$410$		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	$-0.920818\pi$
$419$		−	10.0792i		−	0.492401i	0.969219	−	0.246201i	$-0.0791822\pi$
$420$		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	0.997901	+	0.0647524i	$0.0206258\pi$
$433$	22.1124	+	22.1124i	1.06265	+	1.06265i	0.0647524	+	0.997901i	$0.479374\pi$
$434$		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	$0.0177969\pi$
$439$			2.34169i			0.111763i	−0.998437	+	0.0558813i	$0.982203\pi$
$440$		0			0
$441$	3.61059			0.171933
$442$		0			0
$443$	−11.9067	+	11.9067i	−0.565705	+	0.565705i	−0.930922	−	0.365217i	$-0.880995\pi$
$443$	−11.9067	+	11.9067i	−0.565705	+	0.565705i	0.365217	+	0.930922i	$0.380995\pi$
$444$		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	$-0.544611\pi$
$449$	−5.92002			−0.279383			−0.139692	+	0.990195i	$0.544611\pi$
$450$		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	$-0.724742\pi$
$457$	2.39647	−	2.39647i	0.112102	−	0.112102i	0.760933	+	0.648831i	$0.224742\pi$
$458$		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	$-0.313363\pi$
$463$	−6.01752	−	6.01752i	−0.279658	−	0.279658i	−0.832972	+	0.553314i	$0.813363\pi$
$464$		0			0
$465$	7.02588	−	10.2780i	0.325817	−	0.476630i
$466$		0			0
$467$	10.1040	+	10.1040i	0.467556	+	0.467556i	0.901122	−	0.433566i	$-0.142745\pi$
$467$	10.1040	+	10.1040i	0.467556	+	0.467556i	−0.433566	+	0.901122i	$0.642745\pi$
$468$		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	$0.0665793\pi$
$479$			9.08899i			0.415286i	−0.978205	+	0.207643i	$0.933421\pi$
$480$		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	$-0.970324\pi$
$487$	−19.9178	+	19.9178i	−0.902563	+	0.902563i	0.0930941	+	0.995657i	$0.470324\pi$
$488$		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	$-0.916817\pi$
$499$	−43.1597			−1.93210			−0.966048	+	0.258364i	$0.916817\pi$
$500$		0			0
$501$	4.28457			0.191421
$502$		0			0
$503$	3.03688	−	3.03688i	0.135408	−	0.135408i	−0.636154	−	0.771562i	$-0.719476\pi$
$503$	3.03688	−	3.03688i	0.135408	−	0.135408i	0.771562	+	0.636154i	$0.219476\pi$
$504$		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	$-0.344703\pi$
$509$	21.1512			0.937511			0.468756	+	0.883328i	$0.344703\pi$
$510$		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	$-0.0906102\pi$
$523$	15.5265	+	15.5265i	0.678925	+	0.678925i	−0.280832	+	0.959757i	$0.590610\pi$
$524$		0			0
$525$	−7.90628	−	4.71445i	−0.345058	−	0.205756i
$526$		0			0
$527$	2.99796	+	6.13377i	0.130593	+	0.267191i
$528$		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	0.622111	−	0.782929i	$-0.286275\pi$
$547$	−3.76122	−	3.76122i	−0.160818	−	0.160818i	−0.782929	+	0.622111i	$0.786275\pi$
$548$		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	$-0.605592\pi$
$557$	14.6279	−	14.6279i	0.619804	−	0.619804i	0.945481	+	0.325677i	$0.105592\pi$
$558$		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	−0.999976	−	0.00691209i	$-0.997800\pi$
$563$	−23.5630	+	23.5630i	−0.993064	+	0.993064i	0.00691209	+	0.999976i	$0.497800\pi$
$564$		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	$-0.608587\pi$
$569$	−15.9609			−0.669114			−0.334557	+	0.942376i	$0.608587\pi$
$570$		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	−0.999711	−	0.0240404i	$-0.992347\pi$
$577$	−24.5914	−	24.5914i	−1.02375	−	1.02375i	−0.0240404	−	0.999711i	$-0.507653\pi$
$578$		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	$-0.729201\pi$
$587$	2.23731	−	2.23731i	0.0923437	−	0.0923437i	0.751770	+	0.659426i	$0.229201\pi$
$588$		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	−0.452108	−	0.891963i	$-0.649328\pi$
$593$	10.7112	−	10.7112i	0.439855	−	0.439855i	0.891963	+	0.452108i	$0.149328\pi$
$594$		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	$-0.756220\pi$
$599$		−	33.9293i		−	1.38631i	0.720788	−	0.693156i	$-0.243780\pi$
$600$		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	0.629836	−	0.776728i	$-0.283122\pi$
$607$	−3.61903	−	3.61903i	−0.146892	−	0.146892i	−0.776728	+	0.629836i	$0.783122\pi$
$608$		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	0.993280	+	0.115732i	$0.0369215\pi$
$613$	27.4579	+	27.4579i	1.10901	+	1.10901i	0.115732	+	0.993280i	$0.463078\pi$
$614$		0			0
$615$	17.5383	+	4.83205i	0.707212	+	0.194847i
$616$		0			0
$617$	−17.7030	−	17.7030i	−0.712697	−	0.712697i	0.254402	−	0.967099i	$-0.418121\pi$
$617$	−17.7030	−	17.7030i	−0.712697	−	0.712697i	−0.967099	+	0.254402i	$0.918121\pi$
$618$		0			0
$619$	13.2075			0.530853			0.265427	−	0.964131i	$-0.414487\pi$
$619$	13.2075			0.530853			0.265427	+	0.964131i	$0.414487\pi$
$620$		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	$-0.290393\pi$
$643$	−4.53851	−	4.53851i	−0.178981	−	0.178981i	−0.790912	+	0.611930i	$0.790393\pi$
$644$		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	$-0.741947\pi$
$647$	0.909934	−	0.909934i	0.0357732	−	0.0357732i	0.724767	+	0.688994i	$0.241947\pi$
$648$		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	−0.487037	−	0.873381i	$-0.661922\pi$
$653$	9.87258	−	9.87258i	0.386344	−	0.386344i	0.873381	+	0.487037i	$0.161922\pi$
$654$		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	$0.0897641\pi$
$659$			14.2874i			0.556559i	−0.960500	+	0.278279i	$0.910236\pi$
$660$		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	$-0.201312\pi$
$673$	5.58983	+	5.58983i	0.215472	+	0.215472i	−0.591115	+	0.806587i	$0.701312\pi$
$674$		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	$-0.665455\pi$
$677$	9.65893	−	9.65893i	0.371223	−	0.371223i	0.867922	+	0.496700i	$0.165455\pi$
$678$		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	−0.896112	−	0.443827i	$-0.853620\pi$
$683$	−11.8201	+	11.8201i	−0.452285	+	0.452285i	0.443827	+	0.896112i	$0.353620\pi$
$684$		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	$-0.349039\pi$
$709$	24.3199			0.913354			0.456677	+	0.889632i	$0.349039\pi$
$710$		0			0
$711$		−	10.7589i		−	0.403489i
$712$		0			0
$713$	−22.5632	+	11.0281i	−0.844997	+	0.413004i
$714$		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	$-0.477369\pi$
$719$	3.80962			0.142075			0.0710374	+	0.997474i	$0.477369\pi$
$720$		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	0.539547	−	0.841956i	$-0.318596\pi$
$727$	−8.15383	−	8.15383i	−0.302409	−	0.302409i	−0.841956	+	0.539547i	$0.818596\pi$
$728$		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	−0.802301	−	0.596920i	$-0.796391\pi$
$733$	−5.56049	+	5.56049i	−0.205381	+	0.205381i	0.596920	+	0.802301i	$0.296391\pi$
$734$		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	$-0.340756\pi$
$739$	26.0793			0.959341			0.479670	+	0.877449i	$0.340756\pi$
$740$		0			0
$741$	−16.9019			−0.620907
$742$		0			0
$743$	7.17052	+	7.17052i	0.263061	+	0.263061i	0.826296	−	0.563235i	$-0.190444\pi$
$743$	7.17052	+	7.17052i	0.263061	+	0.263061i	−0.563235	+	0.826296i	$0.690444\pi$
$744$		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	$-0.960652\pi$
$757$	−23.9112	+	23.9112i	−0.869068	+	0.869068i	0.123301	+	0.992369i	$0.460652\pi$
$758$		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	$0.154774\pi$
$769$			25.9174i			0.934604i	−0.884098	+	0.467302i	$0.845226\pi$
$770$		0			0
$771$			17.0611i			0.614440i
$772$		0			0
$773$	−18.0433	−	18.0433i	−0.648971	−	0.648971i	0.303773	−	0.952744i	$-0.401753\pi$
$773$	−18.0433	−	18.0433i	−0.648971	−	0.648971i	−0.952744	+	0.303773i	$0.901753\pi$
$774$		0			0
$775$	−17.9838	−	21.2505i	−0.645996	−	0.763341i
$776$		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	$-0.533861\pi$
$787$	24.9163	−	24.9163i	0.888171	−	0.888171i	0.994347	+	0.106176i	$0.0338607\pi$
$788$		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	$-0.747971\pi$
$797$	0.254437	−	0.254437i	0.00901263	−	0.00901263i	0.711599	+	0.702586i	$0.247971\pi$
$798$		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	$-0.496940\pi$
$809$	0.546906			0.0192282			0.00961409	+	0.999954i	$0.496940\pi$
$810$		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	$-0.364687\pi$
$823$	−14.3035	−	14.3035i	−0.498588	−	0.498588i	−0.910998	+	0.412410i	$0.864687\pi$
$824$		0			0
$825$	−0.427684	−	1.69110i	−0.0148900	−	0.0588764i
$826$		0			0
$827$	34.3298	−	34.3298i	1.19376	−	1.19376i	0.217761	−	0.976002i	$-0.430125\pi$
$827$	34.3298	−	34.3298i	1.19376	−	1.19376i	0.976002	−	0.217761i	$-0.0698754\pi$
$828$		0			0
$829$	−13.3161			−0.462487			−0.231244	−	0.972896i	$-0.574279\pi$
$829$	−13.3161			−0.462487			−0.231244	+	0.972896i	$0.574279\pi$
$830$		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
$837$	2.44491	+	5.00224i	0.0845086	+	0.172903i
$838$		0			0
$839$		−	49.8915i		−	1.72245i	−0.508228	−	0.861223i	$-0.669699\pi$
$839$		−	49.8915i		−	1.72245i	0.508228	−	0.861223i	$-0.330301\pi$
$840$		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	−0.565109	−	0.825017i	$-0.691166\pi$
$853$	7.59092	−	7.59092i	0.259908	−	0.259908i	0.825017	+	0.565109i	$0.191166\pi$
$854$		0			0
$855$	6.09762	−	3.46342i	0.208534	−	0.118446i
$856$		0			0
$857$	−29.9631	−	29.9631i	−1.02352	−	1.02352i	−0.999717	−	0.0238045i	$-0.992422\pi$
$857$	−29.9631	−	29.9631i	−1.02352	−	1.02352i	−0.0238045	−	0.999717i	$-0.507578\pi$
$858$		0			0
$859$	−3.51310			−0.119865			−0.0599327	−	0.998202i	$-0.519089\pi$
$859$	−3.51310			−0.119865			−0.0599327	+	0.998202i	$0.519089\pi$
$860$		0			0
$861$		−	14.9779i		−	0.510446i
$862$		0			0
$863$	3.63860	+	3.63860i	0.123859	+	0.123859i	0.766319	−	0.642460i	$-0.222086\pi$
$863$	3.63860	+	3.63860i	0.123859	+	0.123859i	−0.642460	+	0.766319i	$0.722086\pi$
$864$		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	0.993947	−	0.109859i	$-0.0350400\pi$
$877$	26.1815	+	26.1815i	0.884088	+	0.884088i	−0.109859	+	0.993947i	$0.535040\pi$
$878$		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	$-0.431707\pi$
$883$	−22.7075	−	22.7075i	−0.764167	−	0.764167i	−0.977073	+	0.212906i	$0.931707\pi$
$884$		0			0
$885$	2.03856	−	7.39911i	0.0685255	−	0.248718i
$886$		0			0
$887$	16.5220	+	16.5220i	0.554756	+	0.554756i	0.927810	−	0.373054i	$-0.121689\pi$
$887$	16.5220	+	16.5220i	0.554756	+	0.554756i	−0.373054	+	0.927810i	$0.621689\pi$
$888$		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	0.239488	−	0.970899i	$-0.423020\pi$
$907$	−22.0275	−	22.0275i	−0.731411	−	0.731411i	−0.970899	+	0.239488i	$0.923020\pi$
$908$		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	$-0.935892\pi$
$919$		−	12.1285i		−	0.400082i	0.979787	−	0.200041i	$-0.0641076\pi$
$920$		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	$-0.715184\pi$
$929$	−38.1417			−1.25139			−0.625694	+	0.780069i	$0.715184\pi$
$930$		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	0.194215	−	0.980959i	$-0.437784\pi$
$937$	−24.0826	−	24.0826i	−0.786744	−	0.786744i	−0.980959	+	0.194215i	$0.937784\pi$
$938$		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	$-0.687716\pi$
$947$	8.46134	−	8.46134i	0.274957	−	0.274957i	0.831092	+	0.556135i	$0.187716\pi$
$948$		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	−0.978077	−	0.208245i	$-0.933225\pi$
$953$	−36.6226	−	36.6226i	−1.18632	−	1.18632i	−0.208245	−	0.978077i	$-0.566775\pi$
$954$		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	$-0.711977\pi$
$967$	5.24076	−	5.24076i	0.168532	−	0.168532i	0.786334	+	0.617802i	$0.211977\pi$
$968$		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	0.879444	−	0.476002i	$-0.157914\pi$
$977$	12.6104	+	12.6104i	0.403443	+	0.403443i	−0.476002	+	0.879444i	$0.657914\pi$
$978$		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	$-0.436437\pi$
$983$	−24.5105	−	24.5105i	−0.781763	−	0.781763i	−0.980128	+	0.198365i	$0.936437\pi$
$984$		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	0.524672	−	0.851304i	$-0.324188\pi$
$997$	−10.3135	−	10.3135i	−0.326632	−	0.326632i	−0.851304	+	0.524672i	$0.824188\pi$
$998$		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.1177.25	yes	64
5.3	odd	4	inner	1860.2.s.a.433.9	✓	64
31.30	odd	2	inner	1860.2.s.a.1177.9	yes	64
155.123	even	4	inner	1860.2.s.a.433.25	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1860.2.s.a.433.9	✓	64	5.3	odd	4	inner
1860.2.s.a.433.25	yes	64	155.123	even	4	inner
1860.2.s.a.1177.9	yes	64	31.30	odd	2	inner
1860.2.s.a.1177.25	yes	64	1.1	even	1	trivial

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)

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