LMFDB - Embedded newform 936.2.j.a.755.36

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(755,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.755"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.j (of order $2$, degree $1$, 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:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			755.36
Character	$\chi$	$=$	936.755
Dual form			936.2.j.a.755.35

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.668898 + 1.24602i) q^{2} +(-1.10515 + 1.66693i) q^{4} +3.68104 q^{5} +5.03597i q^{7} +(-2.81626 - 0.262038i) q^{8} +(2.46224 + 4.58666i) q^{10} +3.64499i q^{11} -1.00000i q^{13} +(-6.27493 + 3.36855i) q^{14} +(-1.55729 - 3.68441i) q^{16} -5.67150i q^{17} -1.84246 q^{19} +(-4.06810 + 6.13602i) q^{20} +(-4.54174 + 2.43813i) q^{22} -2.33832 q^{23} +8.55005 q^{25} +(1.24602 - 0.668898i) q^{26} +(-8.39459 - 5.56550i) q^{28} +4.56030 q^{29} -10.2251i q^{31} +(3.54919 - 4.40491i) q^{32} +(7.06682 - 3.79366i) q^{34} +18.5376i q^{35} +1.61780i q^{37} +(-1.23242 - 2.29575i) q^{38} +(-10.3668 - 0.964574i) q^{40} +11.3322i q^{41} -1.54519 q^{43} +(-6.07592 - 4.02826i) q^{44} +(-1.56410 - 2.91360i) q^{46} +7.17063 q^{47} -18.3610 q^{49} +(5.71912 + 10.6536i) q^{50} +(1.66693 + 1.10515i) q^{52} -2.41759 q^{53} +13.4173i q^{55} +(1.31962 - 14.1826i) q^{56} +(3.05038 + 5.68225i) q^{58} +7.69002i q^{59} -10.7635i q^{61} +(12.7408 - 6.83958i) q^{62} +(7.86267 + 1.47594i) q^{64} -3.68104i q^{65} +1.62542 q^{67} +(9.45397 + 6.26786i) q^{68} +(-23.0983 + 12.3998i) q^{70} +6.50058 q^{71} +7.47814 q^{73} +(-2.01582 + 1.08214i) q^{74} +(2.03620 - 3.07125i) q^{76} -18.3560 q^{77} +5.87670i q^{79} +(-5.73244 - 13.5624i) q^{80} +(-14.1202 + 7.58009i) q^{82} -1.25689i q^{83} -20.8770i q^{85} +(-1.03357 - 1.92534i) q^{86} +(0.955127 - 10.2652i) q^{88} +1.11241i q^{89} +5.03597 q^{91} +(2.58419 - 3.89780i) q^{92} +(4.79642 + 8.93477i) q^{94} -6.78218 q^{95} +6.82755 q^{97} +(-12.2816 - 22.8782i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 8 q^{4} + 16 q^{10} + 8 q^{16} + 32 q^{19} + 48 q^{25} - 24 q^{28} + 32 q^{34} - 32 q^{40} - 32 q^{43} + 24 q^{46} - 48 q^{49} + 8 q^{52} - 40 q^{58} + 40 q^{64} + 32 q^{67} - 40 q^{70} + 40 q^{76}+ \cdots - 32 q^{97}+O(q^{100}) $ 48 * q - 8 * q^4 + 16 * q^10 + 8 * q^16 + 32 * q^19 + 48 * q^25 - 24 * q^28 + 32 * q^34 - 32 * q^40 - 32 * q^43 + 24 * q^46 - 48 * q^49 + 8 * q^52 - 40 * q^58 + 40 * q^64 + 32 * q^67 - 40 * q^70 + 40 * q^76 + 16 * q^82 + 48 * q^88 + 32 * q^94 - 32 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.668898	+	1.24602i	0.472983	+	0.881072i
$2$	0.668898	+	1.24602i	0.472983	+	0.881072i
$3$		0			0
$3$		0			0
$4$	−1.10515	+	1.66693i	−0.552575	+	0.833463i
$5$	3.68104			1.64621			0.823106	−	0.567888i	$-0.192240\pi$
$5$	3.68104			1.64621			0.823106	+	0.567888i	$0.192240\pi$
$6$		0			0
$7$			5.03597i			1.90342i	0.307004	+	0.951708i	$0.400674\pi$
$7$			5.03597i			1.90342i	−0.307004	+	0.951708i	$0.599326\pi$
$8$	−2.81626	−	0.262038i	−0.995699	−	0.0926446i
$9$		0			0
$10$	2.46224	+	4.58666i	0.778629	+	1.45043i
$11$			3.64499i			1.09900i	0.835492	+	0.549502i	$0.185183\pi$
$11$			3.64499i			1.09900i	−0.835492	+	0.549502i	$0.814817\pi$
$12$		0			0
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	−6.27493	+	3.36855i	−1.67705	+	0.900283i
$15$		0			0
$16$	−1.55729	−	3.68441i	−0.389322	−	0.921102i
$17$		−	5.67150i		−	1.37554i	−0.725928	−	0.687770i	$-0.758590\pi$
$17$		−	5.67150i		−	1.37554i	0.725928	−	0.687770i	$-0.241410\pi$
$18$		0			0
$19$	−1.84246			−0.422690			−0.211345	−	0.977412i	$-0.567784\pi$
$19$	−1.84246			−0.422690			−0.211345	+	0.977412i	$0.567784\pi$
$20$	−4.06810	+	6.13602i	−0.909655	+	1.37206i
$21$		0			0
$22$	−4.54174	+	2.43813i	−0.968302	+	0.519810i
$23$	−2.33832			−0.487573			−0.243786	−	0.969829i	$-0.578390\pi$
$23$	−2.33832			−0.487573			−0.243786	+	0.969829i	$0.578390\pi$
$24$		0			0
$25$	8.55005			1.71001
$26$	1.24602	−	0.668898i	0.244365	−	0.131182i
$27$		0			0
$28$	−8.39459	−	5.56550i	−1.58643	−	1.05178i
$29$	4.56030			0.846827			0.423414	−	0.905937i	$-0.360832\pi$
$29$	4.56030			0.846827			0.423414	+	0.905937i	$0.360832\pi$
$30$		0			0
$31$		−	10.2251i		−	1.83649i	−0.396013	−	0.918245i	$-0.629607\pi$
$31$		−	10.2251i		−	1.83649i	0.396013	−	0.918245i	$-0.370393\pi$
$32$	3.54919	−	4.40491i	0.627414	−	0.778686i
$33$		0			0
$34$	7.06682	−	3.79366i	1.21195	−	0.650607i
$35$			18.5376i			3.13343i
$36$		0			0
$37$			1.61780i			0.265965i	0.991118	+	0.132982i	$0.0424554\pi$
$37$			1.61780i			0.265965i	−0.991118	+	0.132982i	$0.957545\pi$
$38$	−1.23242	−	2.29575i	−0.199925	−	0.372420i
$39$		0			0
$40$	−10.3668	−	0.964574i	−1.63913	−	0.152513i
$41$			11.3322i			1.76979i	0.465788	+	0.884896i	$0.345771\pi$
$41$			11.3322i			1.76979i	−0.465788	+	0.884896i	$0.654229\pi$
$42$		0			0
$43$	−1.54519			−0.235639			−0.117820	−	0.993035i	$-0.537590\pi$
$43$	−1.54519			−0.235639			−0.117820	+	0.993035i	$0.537590\pi$
$44$	−6.07592	−	4.02826i	−0.915980	−	0.607283i
$45$		0			0
$46$	−1.56410	−	2.91360i	−0.230613	−	0.429587i
$47$	7.17063			1.04594			0.522972	−	0.852350i	$-0.324823\pi$
$47$	7.17063			1.04594			0.522972	+	0.852350i	$0.324823\pi$
$48$		0			0
$49$	−18.3610			−2.62299
$50$	5.71912	+	10.6536i	0.808805	+	1.50664i
$51$		0			0
$52$	1.66693	+	1.10515i	0.231161	+	0.153257i
$53$	−2.41759			−0.332081			−0.166041	−	0.986119i	$-0.553098\pi$
$53$	−2.41759			−0.332081			−0.166041	+	0.986119i	$0.553098\pi$
$54$		0			0
$55$			13.4173i			1.80919i
$56$	1.31962	−	14.1826i	0.176341	−	1.89523i
$57$		0			0
$58$	3.05038	+	5.68225i	0.400534	+	0.746115i
$59$			7.69002i			1.00116i	0.865692	+	0.500578i	$0.166879\pi$
$59$			7.69002i			1.00116i	−0.865692	+	0.500578i	$0.833121\pi$
$60$		0			0
$61$		−	10.7635i		−	1.37813i	−0.724699	−	0.689066i	$-0.758021\pi$
$61$		−	10.7635i		−	1.37813i	0.724699	−	0.689066i	$-0.241979\pi$
$62$	12.7408	−	6.83958i	1.61808	−	0.868628i
$63$		0			0
$64$	7.86267	+	1.47594i	0.982834	+	0.184492i
$65$		−	3.68104i		−	0.456577i
$66$		0			0
$67$	1.62542			0.198576			0.0992881	−	0.995059i	$-0.468343\pi$
$67$	1.62542			0.198576			0.0992881	+	0.995059i	$0.468343\pi$
$68$	9.45397	+	6.26786i	1.14646	+	0.760089i
$69$		0			0
$70$	−23.0983	+	12.3998i	−2.76077	+	1.48206i
$71$	6.50058			0.771477			0.385739	−	0.922608i	$-0.373947\pi$
$71$	6.50058			0.771477			0.385739	+	0.922608i	$0.373947\pi$
$72$		0			0
$73$	7.47814			0.875250			0.437625	−	0.899158i	$-0.355820\pi$
$73$	7.47814			0.875250			0.437625	+	0.899158i	$0.355820\pi$
$74$	−2.01582	+	1.08214i	−0.234334	+	0.125797i
$75$		0			0
$76$	2.03620	−	3.07125i	0.233568	−	0.352296i
$77$	−18.3560			−2.09186
$78$		0			0
$79$			5.87670i			0.661180i	0.943774	+	0.330590i	$0.107248\pi$
$79$			5.87670i			0.661180i	−0.943774	+	0.330590i	$0.892752\pi$
$80$	−5.73244	−	13.5624i	−0.640906	−	1.51633i
$81$		0			0
$82$	−14.1202	+	7.58009i	−1.55931	+	0.837081i
$83$		−	1.25689i		−	0.137962i	−0.997618	−	0.0689810i	$-0.978025\pi$
$83$		−	1.25689i		−	0.137962i	0.997618	−	0.0689810i	$-0.0219748\pi$
$84$		0			0
$85$		−	20.8770i		−	2.26443i
$86$	−1.03357	−	1.92534i	−0.111453	−	0.207615i
$87$		0			0
$88$	0.955127	−	10.2652i	0.101817	−	1.09428i
$89$			1.11241i			0.117915i	0.998260	+	0.0589577i	$0.0187777\pi$
$89$			1.11241i			0.117915i	−0.998260	+	0.0589577i	$0.981222\pi$
$90$		0			0
$91$	5.03597			0.527913
$92$	2.58419	−	3.89780i	0.269421	−	0.406374i
$93$		0			0
$94$	4.79642	+	8.93477i	0.494713	+	0.921551i
$95$	−6.78218			−0.695837
$96$		0			0
$97$	6.82755			0.693232			0.346616	−	0.938007i	$-0.387331\pi$
$97$	6.82755			0.693232			0.346616	+	0.938007i	$0.387331\pi$
$98$	−12.2816	−	22.8782i	−1.24063	−	2.31105i
$99$		0			0
$100$	−9.44909	+	14.2523i	−0.944909	+	1.42523i
$101$	−6.22342			−0.619253			−0.309626	−	0.950858i	$-0.600204\pi$
$101$	−6.22342			−0.619253			−0.309626	+	0.950858i	$0.600204\pi$
$102$		0			0
$103$		−	10.9213i		−	1.07611i	−0.842910	−	0.538055i	$-0.819159\pi$
$103$		−	10.9213i		−	1.07611i	0.842910	−	0.538055i	$-0.180841\pi$
$104$	−0.262038	+	2.81626i	−0.0256950	+	0.276157i
$105$		0			0
$106$	−1.61712	−	3.01237i	−0.157069	−	0.292587i
$107$		−	5.68490i		−	0.549580i	−0.961504	−	0.274790i	$-0.911392\pi$
$107$		−	5.68490i		−	0.549580i	0.961504	−	0.274790i	$-0.0886084\pi$
$108$		0			0
$109$			4.19341i			0.401656i	0.979627	+	0.200828i	$0.0643633\pi$
$109$			4.19341i			0.401656i	−0.979627	+	0.200828i	$0.935637\pi$
$110$	−16.7183	+	8.97484i	−1.59403	+	0.855717i
$111$		0			0
$112$	18.5546	−	7.84245i	1.75324	−	0.741042i
$113$			5.05332i			0.475376i	0.971342	+	0.237688i	$0.0763896\pi$
$113$			5.05332i			0.475376i	−0.971342	+	0.237688i	$0.923610\pi$
$114$		0			0
$115$	−8.60744			−0.802648
$116$	−5.03982	+	7.60169i	−0.467935	+	0.705799i
$117$		0			0
$118$	−9.58195	+	5.14384i	−0.882090	+	0.473529i
$119$	28.5615			2.61823
$120$		0			0
$121$	−2.28593			−0.207812
$122$	13.4116	−	7.19972i	1.21423	−	0.651832i
$123$		0			0
$124$	17.0446	+	11.3003i	1.53065	+	1.01480i
$125$	13.0679			1.16883
$126$		0			0
$127$			4.48123i			0.397645i	0.980036	+	0.198822i	$0.0637117\pi$
$127$			4.48123i			0.397645i	−0.980036	+	0.198822i	$0.936288\pi$
$128$	3.42027	+	10.7843i	0.302312	+	0.953209i
$129$		0			0
$130$	4.58666	−	2.46224i	0.402277	−	0.215953i
$131$		−	7.62358i		−	0.666075i	−0.942914	−	0.333037i	$-0.891926\pi$
$131$		−	7.62358i		−	0.666075i	0.942914	−	0.333037i	$-0.108074\pi$
$132$		0			0
$133$		−	9.27858i		−	0.804555i
$134$	1.08724	+	2.02531i	0.0939231	+	0.174960i
$135$		0			0
$136$	−1.48615	+	15.9724i	−0.127436	+	1.36963i
$137$			17.3289i			1.48051i	0.672329	+	0.740253i	$0.265294\pi$
$137$			17.3289i			1.48051i	−0.672329	+	0.740253i	$0.734706\pi$
$138$		0			0
$139$	7.88936			0.669167			0.334583	−	0.942366i	$-0.391404\pi$
$139$	7.88936			0.669167			0.334583	+	0.942366i	$0.391404\pi$
$140$	−30.9008	−	20.4868i	−2.61159	−	1.73145i
$141$		0			0
$142$	4.34823	+	8.09988i	0.364895	+	0.679727i
$143$	3.64499			0.304809
$144$		0			0
$145$	16.7867			1.39406
$146$	5.00212	+	9.31794i	0.413978	+	0.771158i
$147$		0			0
$148$	−2.69676	−	1.78791i	−0.221672	−	0.146966i
$149$	−5.49996			−0.450574			−0.225287	−	0.974292i	$-0.572332\pi$
$149$	−5.49996			−0.450574			−0.225287	+	0.974292i	$0.572332\pi$
$150$		0			0
$151$		−	1.85944i		−	0.151319i	−0.997134	−	0.0756596i	$-0.975894\pi$
$151$		−	1.85944i		−	0.151319i	0.997134	−	0.0756596i	$-0.0241062\pi$
$152$	5.18886	+	0.482796i	0.420872	+	0.0391599i
$153$		0			0
$154$	−12.2783	−	22.8721i	−0.989415	−	1.84308i
$155$		−	37.6392i		−	3.02325i
$156$		0			0
$157$		−	7.49398i		−	0.598084i	−0.954240	−	0.299042i	$-0.903333\pi$
$157$		−	7.49398i		−	0.598084i	0.954240	−	0.299042i	$-0.0966671\pi$
$158$	−7.32250	+	3.93091i	−0.582547	+	0.312727i
$159$		0			0
$160$	13.0647	−	16.2147i	1.03286	−	1.28188i
$161$		−	11.7757i		−	0.928054i
$162$		0			0
$163$	−21.4154			−1.67738			−0.838692	−	0.544606i	$-0.816679\pi$
$163$	−21.4154			−1.67738			−0.838692	+	0.544606i	$0.816679\pi$
$164$	−18.8900	−	12.5238i	−1.47506	−	0.977943i
$165$		0			0
$166$	1.56612	−	0.840734i	0.121554	−	0.0652536i
$167$	13.6647			1.05740			0.528701	−	0.848808i	$-0.322679\pi$
$167$	13.6647			1.05740			0.528701	+	0.848808i	$0.322679\pi$
$168$		0			0
$169$	−1.00000			−0.0769231
$170$	26.0133	−	13.9646i	1.99513	−	1.07104i
$171$		0			0
$172$	1.70767	−	2.57572i	0.130208	−	0.196397i
$173$	16.1562			1.22833			0.614166	−	0.789177i	$-0.289492\pi$
$173$	16.1562			1.22833			0.614166	+	0.789177i	$0.289492\pi$
$174$		0			0
$175$			43.0578i			3.25486i
$176$	13.4296	−	5.67629i	1.01230	−	0.427867i
$177$		0			0
$178$	−1.38609	+	0.744091i	−0.103892	+	0.0557720i
$179$			0.653655i			0.0488565i	0.999702	+	0.0244282i	$0.00777652\pi$
$179$			0.653655i			0.0488565i	−0.999702	+	0.0244282i	$0.992223\pi$
$180$		0			0
$181$		−	22.3117i		−	1.65842i	−0.558939	−	0.829209i	$-0.688791\pi$
$181$		−	22.3117i		−	1.65842i	0.558939	−	0.829209i	$-0.311209\pi$
$182$	3.36855	+	6.27493i	0.249694	+	0.465129i
$183$		0			0
$184$	6.58532	+	0.612729i	0.485476	+	0.0451710i
$185$			5.95519i			0.437834i
$186$		0			0
$187$	20.6725			1.51173
$188$	−7.92462	+	11.9529i	−0.577962	+	0.871755i
$189$		0			0
$190$	−4.53659	−	8.45075i	−0.329119	−	0.613082i
$191$	10.9536			0.792574			0.396287	−	0.918127i	$-0.370298\pi$
$191$	10.9536			0.792574			0.396287	+	0.918127i	$0.370298\pi$
$192$		0			0
$193$	3.55477			0.255878			0.127939	−	0.991782i	$-0.459164\pi$
$193$	3.55477			0.255878			0.127939	+	0.991782i	$0.459164\pi$
$194$	4.56693	+	8.50728i	0.327887	+	0.610787i
$195$		0			0
$196$	20.2916	−	30.6064i	1.44940	−	2.18617i
$197$	3.42987			0.244368			0.122184	−	0.992507i	$-0.461010\pi$
$197$	3.42987			0.244368			0.122184	+	0.992507i	$0.461010\pi$
$198$		0			0
$199$		−	8.30930i		−	0.589031i	−0.955647	−	0.294515i	$-0.904842\pi$
$199$		−	8.30930i		−	0.589031i	0.955647	−	0.294515i	$-0.0951582\pi$
$200$	−24.0792	−	2.24044i	−1.70266	−	0.158423i
$201$		0			0
$202$	−4.16283	−	7.75452i	−0.292896	−	0.545606i
$203$			22.9655i			1.61186i
$204$		0			0
$205$			41.7143i			2.91345i
$206$	13.6082	−	7.30526i	0.948131	−	0.508982i
$207$		0			0
$208$	−3.68441	+	1.55729i	−0.255468	+	0.107978i
$209$		−	6.71575i		−	0.464538i
$210$		0			0
$211$	−14.4537			−0.995035			−0.497518	−	0.867454i	$-0.665755\pi$
$211$	−14.4537			−0.995035			−0.497518	+	0.867454i	$0.665755\pi$
$212$	2.67180	−	4.02994i	0.183500	−	0.276777i
$213$		0			0
$214$	7.08352	−	3.80262i	0.484220	−	0.259942i
$215$	−5.68790			−0.387912
$216$		0			0
$217$	51.4935			3.49560
$218$	−5.22509	+	2.80497i	−0.353888	+	0.189976i
$219$		0			0
$220$	−22.3657	−	14.8282i	−1.50790	−	0.999715i
$221$	−5.67150			−0.381506
$222$		0			0
$223$		−	15.6375i		−	1.04716i	−0.851976	−	0.523581i	$-0.824596\pi$
$223$		−	15.6375i		−	1.04716i	0.851976	−	0.523581i	$-0.175404\pi$
$224$	22.1830	+	17.8736i	1.48216	+	1.19423i
$225$		0			0
$226$	−6.29655	+	3.38016i	−0.418840	+	0.224845i
$227$			21.4645i			1.42465i	0.701852	+	0.712323i	$0.252357\pi$
$227$			21.4645i			1.42465i	−0.701852	+	0.712323i	$0.747643\pi$
$228$		0			0
$229$		−	7.07271i		−	0.467378i	−0.972311	−	0.233689i	$-0.924920\pi$
$229$		−	7.07271i		−	0.467378i	0.972311	−	0.233689i	$-0.0750798\pi$
$230$	−5.75750	−	10.7251i	−0.379638	−	0.707190i
$231$		0			0
$232$	−12.8430	−	1.19497i	−0.843185	−	0.0784539i
$233$		−	11.3692i		−	0.744822i	−0.928068	−	0.372411i	$-0.878531\pi$
$233$		−	11.3692i		−	0.744822i	0.928068	−	0.372411i	$-0.121469\pi$
$234$		0			0
$235$	26.3954			1.72184
$236$	−12.8187	−	8.49863i	−0.834426	−	0.553214i
$237$		0			0
$238$	19.1047	+	35.5883i	1.23838	+	2.30685i
$239$	−1.08095			−0.0699210			−0.0349605	−	0.999389i	$-0.511131\pi$
$239$	−1.08095			−0.0699210			−0.0349605	+	0.999389i	$0.511131\pi$
$240$		0			0
$241$	19.1818			1.23561			0.617803	−	0.786333i	$-0.288023\pi$
$241$	19.1818			1.23561			0.617803	+	0.786333i	$0.288023\pi$
$242$	−1.52905	−	2.84832i	−0.0982913	−	0.183097i
$243$		0			0
$244$	17.9420	+	11.8953i	1.14862	+	0.761521i
$245$	−67.5874			−4.31800
$246$		0			0
$247$			1.84246i			0.117233i
$248$	−2.67938	+	28.7967i	−0.170141	+	1.82859i
$249$		0			0
$250$	8.74109	+	16.2829i	0.552835	+	1.02982i
$251$		−	24.2949i		−	1.53348i	−0.641956	−	0.766741i	$-0.721877\pi$
$251$		−	24.2949i		−	1.53348i	0.641956	−	0.766741i	$-0.278123\pi$
$252$		0			0
$253$		−	8.52314i		−	0.535845i
$254$	−5.58372	+	2.99749i	−0.350354	+	0.188079i
$255$		0			0
$256$	−11.1497	+	11.4754i	−0.696857	+	0.717210i
$257$		−	1.24472i		−	0.0776433i	−0.999246	−	0.0388217i	$-0.987640\pi$
$257$		−	1.24472i		−	0.0776433i	0.999246	−	0.0388217i	$-0.0123604\pi$
$258$		0			0
$259$	−8.14720			−0.506242
$260$	6.13602	+	4.06810i	0.380540	+	0.252293i
$261$		0			0
$262$	9.49916	−	5.09940i	0.586860	−	0.315042i
$263$	−0.293106			−0.0180737			−0.00903685	−	0.999959i	$-0.502877\pi$
$263$	−0.293106			−0.0180737			−0.00903685	+	0.999959i	$0.502877\pi$
$264$		0			0
$265$	−8.89924			−0.546676
$266$	11.5613	−	6.20643i	0.708871	−	0.380540i
$267$		0			0
$268$	−1.79633	+	2.70945i	−0.109728	+	0.165506i
$269$	−24.4807			−1.49261			−0.746307	−	0.665602i	$-0.768175\pi$
$269$	−24.4807			−1.49261			−0.746307	+	0.665602i	$0.768175\pi$
$270$		0			0
$271$			8.63161i			0.524333i	0.965023	+	0.262167i	$0.0844370\pi$
$271$			8.63161i			0.524333i	−0.965023	+	0.262167i	$0.915563\pi$
$272$	−20.8961	+	8.83216i	−1.26701	+	0.535528i
$273$		0			0
$274$	−21.5922	+	11.5913i	−1.30443	+	0.700253i
$275$			31.1648i			1.87931i
$276$		0			0
$277$			27.9090i			1.67689i	0.544985	+	0.838446i	$0.316535\pi$
$277$			27.9090i			1.67689i	−0.544985	+	0.838446i	$0.683465\pi$
$278$	5.27718	+	9.83033i	0.316504	+	0.589584i
$279$		0			0
$280$	4.85756	−	52.2067i	0.290295	−	3.11995i
$281$		−	17.0623i		−	1.01785i	−0.860811	−	0.508926i	$-0.830043\pi$
$281$		−	17.0623i		−	1.01785i	0.860811	−	0.508926i	$-0.169957\pi$
$282$		0			0
$283$	−20.4942			−1.21826			−0.609128	−	0.793072i	$-0.708481\pi$
$283$	−20.4942			−1.21826			−0.609128	+	0.793072i	$0.708481\pi$
$284$	−7.18412	+	10.8360i	−0.426299	+	0.642998i
$285$		0			0
$286$	2.43813	+	4.54174i	0.144169	+	0.268559i
$287$	−57.0686			−3.36865
$288$		0			0
$289$	−15.1659			−0.892113
$290$	11.2286	+	20.9166i	0.659364	+	1.22826i
$291$		0			0
$292$	−8.26446	+	12.4655i	−0.483641	+	0.729489i
$293$	22.6573			1.32366			0.661828	−	0.749656i	$-0.269781\pi$
$293$	22.6573			1.32366			0.661828	+	0.749656i	$0.269781\pi$
$294$		0			0
$295$			28.3073i			1.64811i
$296$	0.423926	−	4.55615i	0.0246402	−	0.264821i
$297$		0			0
$298$	−3.67892	−	6.85308i	−0.213114	−	0.396988i
$299$			2.33832i			0.135228i
$300$		0			0
$301$		−	7.78152i		−	0.448520i
$302$	2.31691	−	1.24378i	0.133323	−	0.0715714i
$303$		0			0
$304$	2.86924	+	6.78838i	0.164562	+	0.389340i
$305$		−	39.6210i		−	2.26869i
$306$		0			0
$307$	−19.7184			−1.12539			−0.562695	−	0.826664i	$-0.690236\pi$
$307$	−19.7184			−1.12539			−0.562695	+	0.826664i	$0.690236\pi$
$308$	20.2862	−	30.5982i	1.15591	−	1.74349i
$309$		0			0
$310$	46.8993	−	25.1768i	2.66370	−	1.42994i
$311$	−14.8987			−0.844826			−0.422413	−	0.906404i	$-0.638817\pi$
$311$	−14.8987			−0.844826			−0.422413	+	0.906404i	$0.638817\pi$
$312$		0			0
$313$	12.3374			0.697350			0.348675	−	0.937244i	$-0.386632\pi$
$313$	12.3374			0.697350			0.348675	+	0.937244i	$0.386632\pi$
$314$	9.33767	−	5.01271i	0.526955	−	0.282884i
$315$		0			0
$316$	−9.79602	−	6.49463i	−0.551069	−	0.365351i
$317$	5.04413			0.283307			0.141653	−	0.989916i	$-0.454758\pi$
$317$	5.04413			0.283307			0.141653	+	0.989916i	$0.454758\pi$
$318$		0			0
$319$			16.6222i			0.930667i
$320$	28.9428	+	5.43299i	1.61795	+	0.303713i
$321$		0			0
$322$	14.6728	−	7.87674i	0.817682	−	0.438953i
$323$			10.4495i			0.581427i
$324$		0			0
$325$		−	8.55005i		−	0.474272i
$326$	−14.3247	−	26.6841i	−0.793374	−	1.47790i
$327$		0			0
$328$	2.96947	−	31.9145i	0.163962	−	1.76218i
$329$			36.1110i			1.99087i
$330$		0			0
$331$	−13.2874			−0.730344			−0.365172	−	0.930940i	$-0.618990\pi$
$331$	−13.2874			−0.730344			−0.365172	+	0.930940i	$0.618990\pi$
$332$	2.09515	+	1.38906i	0.114986	+	0.0762344i
$333$		0			0
$334$	9.14027	+	17.0265i	0.500133	+	0.931648i
$335$	5.98322			0.326898
$336$		0			0
$337$	−13.9595			−0.760424			−0.380212	−	0.924899i	$-0.624149\pi$
$337$	−13.9595			−0.760424			−0.380212	+	0.924899i	$0.624149\pi$
$338$	−0.668898	−	1.24602i	−0.0363833	−	0.0677748i
$339$		0			0
$340$	34.8005	+	23.0722i	1.88732	+	1.25127i
$341$	37.2705			2.01831
$342$		0			0
$343$		−	57.2134i		−	3.08923i
$344$	4.35166	+	0.404899i	0.234626	+	0.0218307i
$345$		0			0
$346$	10.8069	+	20.1310i	0.580980	+	1.08225i
$347$		−	18.7966i		−	1.00905i	−0.863396	−	0.504526i	$-0.831667\pi$
$347$		−	18.7966i		−	1.00905i	0.863396	−	0.504526i	$-0.168333\pi$
$348$		0			0
$349$		−	29.1945i		−	1.56275i	−0.624065	−	0.781373i	$-0.714520\pi$
$349$		−	29.1945i		−	1.56275i	0.624065	−	0.781373i	$-0.285480\pi$
$350$	−53.6510	+	28.8013i	−2.86777	+	1.53949i
$351$		0			0
$352$	16.0558	+	12.9368i	0.855779	+	0.689531i
$353$		−	18.4044i		−	0.979566i	−0.871844	−	0.489783i	$-0.837076\pi$
$353$		−	18.4044i		−	0.979566i	0.871844	−	0.489783i	$-0.162924\pi$
$354$		0			0
$355$	23.9289			1.27001
$356$	−1.85431	−	1.22938i	−0.0982782	−	0.0651571i
$357$		0			0
$358$	−0.814470	+	0.437229i	−0.0430461	+	0.0231083i
$359$	20.7408			1.09466			0.547328	−	0.836918i	$-0.315645\pi$
$359$	20.7408			1.09466			0.547328	+	0.836918i	$0.315645\pi$
$360$		0			0
$361$	−15.6053			−0.821333
$362$	27.8009	−	14.9243i	1.46118	−	0.784403i
$363$		0			0
$364$	−5.56550	+	8.39459i	−0.291711	+	0.439996i
$365$	27.5273			1.44085
$366$		0			0
$367$			2.93048i			0.152970i	0.997071	+	0.0764848i	$0.0243697\pi$
$367$			2.93048i			0.152970i	−0.997071	+	0.0764848i	$0.975630\pi$
$368$	3.64143	+	8.61531i	0.189823	+	0.449104i
$369$		0			0
$370$	−7.42031	+	3.98342i	−0.385764	+	0.207088i
$371$		−	12.1749i		−	0.632089i
$372$		0			0
$373$			15.3057i			0.792497i	0.918143	+	0.396248i	$0.129688\pi$
$373$			15.3057i			0.792497i	−0.918143	+	0.396248i	$0.870312\pi$
$374$	13.8278	+	25.7585i	0.715020	+	1.33194i
$375$		0			0
$376$	−20.1944	−	1.87898i	−1.04145	−	0.0969010i
$377$		−	4.56030i		−	0.234868i
$378$		0			0
$379$	−26.5979			−1.36624			−0.683121	−	0.730305i	$-0.739378\pi$
$379$	−26.5979			−1.36624			−0.683121	+	0.730305i	$0.739378\pi$
$380$	7.49532	−	11.3054i	0.384502	−	0.579954i
$381$		0			0
$382$	7.32684	+	13.6484i	0.374874	+	0.698315i
$383$	20.1991			1.03213			0.516063	−	0.856551i	$-0.327397\pi$
$383$	20.1991			1.03213			0.516063	+	0.856551i	$0.327397\pi$
$384$		0			0
$385$	−67.5693			−3.44365
$386$	2.37778	+	4.42933i	0.121026	+	0.225447i
$387$		0			0
$388$	−7.54546	+	11.3810i	−0.383063	+	0.577784i
$389$	−6.68598			−0.338992			−0.169496	−	0.985531i	$-0.554214\pi$
$389$	−6.68598			−0.338992			−0.169496	+	0.985531i	$0.554214\pi$
$390$		0			0
$391$			13.2618i			0.670676i
$392$	51.7093	+	4.81128i	2.61171	+	0.243006i
$393$		0			0
$394$	2.29424	+	4.27370i	0.115582	+	0.215306i
$395$			21.6323i			1.08844i
$396$		0			0
$397$		−	21.4797i		−	1.07803i	−0.842295	−	0.539016i	$-0.818796\pi$
$397$		−	21.4797i		−	1.07803i	0.842295	−	0.539016i	$-0.181204\pi$
$398$	10.3536	−	5.55808i	0.518978	−	0.278601i
$399$		0			0
$400$	−13.3149	−	31.5019i	−0.665745	−	1.57509i
$401$		−	9.82187i		−	0.490481i	−0.969462	−	0.245240i	$-0.921133\pi$
$401$		−	9.82187i		−	0.490481i	0.969462	−	0.245240i	$-0.0788669\pi$
$402$		0			0
$403$	−10.2251			−0.509351
$404$	6.87781	−	10.3740i	0.342184	−	0.516125i
$405$		0			0
$406$	−28.6156	+	15.3616i	−1.42017	+	0.762384i
$407$	−5.89687			−0.292297
$408$		0			0
$409$	−36.5607			−1.80781			−0.903905	−	0.427734i	$-0.859312\pi$
$409$	−36.5607			−1.80781			−0.903905	+	0.427734i	$0.859312\pi$
$410$	−51.9770	+	27.9026i	−2.56696	+	1.37801i
$411$		0			0
$412$	18.2051	+	12.0697i	0.896898	+	0.594632i
$413$	−38.7267			−1.90562
$414$		0			0
$415$		−	4.62668i		−	0.227115i
$416$	−4.40491	−	3.54919i	−0.215969	−	0.174013i
$417$		0			0
$418$	8.36799	−	4.49216i	0.409292	−	0.219718i
$419$		−	35.9043i		−	1.75404i	−0.480453	−	0.877021i	$-0.659528\pi$
$419$		−	35.9043i		−	1.75404i	0.480453	−	0.877021i	$-0.340472\pi$
$420$		0			0
$421$			14.5773i			0.710453i	0.934780	+	0.355227i	$0.115596\pi$
$421$			14.5773i			0.710453i	−0.934780	+	0.355227i	$0.884404\pi$
$422$	−9.66807	−	18.0097i	−0.470634	−	0.876697i
$423$		0			0
$424$	6.80856	+	0.633501i	0.330653	+	0.0307655i
$425$		−	48.4916i		−	2.35219i
$426$		0			0
$427$	54.2049			2.62316
$428$	9.47631	+	6.28267i	0.458055	+	0.303684i
$429$		0			0
$430$	−3.80463	−	7.08726i	−0.183476	−	0.341778i
$431$	−10.4588			−0.503783			−0.251891	−	0.967756i	$-0.581053\pi$
$431$	−10.4588			−0.503783			−0.251891	+	0.967756i	$0.581053\pi$
$432$		0			0
$433$	10.4427			0.501844			0.250922	−	0.968007i	$-0.419266\pi$
$433$	10.4427			0.501844			0.250922	+	0.968007i	$0.419266\pi$
$434$	34.4439	+	64.1621i	1.65336	+	3.07988i
$435$		0			0
$436$	−6.99011	−	4.63435i	−0.334766	−	0.221945i
$437$	4.30826			0.206092
$438$		0			0
$439$			0.817762i			0.0390296i	0.999810	+	0.0195148i	$0.00621216\pi$
$439$			0.817762i			0.0390296i	−0.999810	+	0.0195148i	$0.993788\pi$
$440$	3.51586	−	37.7868i	0.167612	−	1.80141i
$441$		0			0
$442$	−3.79366	−	7.06682i	−0.180446	−	0.336135i
$443$			11.2120i			0.532700i	0.963876	+	0.266350i	$0.0858177\pi$
$443$			11.2120i			0.532700i	−0.963876	+	0.266350i	$0.914182\pi$
$444$		0			0
$445$			4.09483i			0.194114i
$446$	19.4847	−	10.4599i	0.922626	−	0.495290i
$447$		0			0
$448$	−7.43278	+	39.5962i	−0.351166	+	1.87074i
$449$		−	12.4892i		−	0.589404i	−0.955589	−	0.294702i	$-0.904780\pi$
$449$		−	12.4892i		−	0.589404i	0.955589	−	0.294702i	$-0.0952204\pi$
$450$		0			0
$451$	−41.3057			−1.94501
$452$	−8.42351	−	5.58467i	−0.396208	−	0.262681i
$453$		0			0
$454$	−26.7452	+	14.3575i	−1.25522	+	0.673833i
$455$	18.5376			0.869056
$456$		0			0
$457$	−7.14195			−0.334086			−0.167043	−	0.985950i	$-0.553422\pi$
$457$	−7.14195			−0.334086			−0.167043	+	0.985950i	$0.553422\pi$
$458$	8.81277	−	4.73093i	0.411794	−	0.221062i
$459$		0			0
$460$	9.51251	−	14.3480i	0.443523	−	0.668977i
$461$	−0.248079			−0.0115542			−0.00577710	−	0.999983i	$-0.501839\pi$
$461$	−0.248079			−0.0115542			−0.00577710	+	0.999983i	$0.501839\pi$
$462$		0			0
$463$			13.7435i			0.638716i	0.947634	+	0.319358i	$0.103467\pi$
$463$			13.7435i			0.638716i	−0.947634	+	0.319358i	$0.896533\pi$
$464$	−7.10170	−	16.8020i	−0.329688	−	0.780014i
$465$		0			0
$466$	14.1663	−	7.60485i	0.656242	−	0.352288i
$467$			27.3218i			1.26430i	0.774845	+	0.632151i	$0.217828\pi$
$467$			27.3218i			1.26430i	−0.774845	+	0.632151i	$0.782172\pi$
$468$		0			0
$469$			8.18554i			0.377973i
$470$	17.6558	+	32.8893i	0.814402	+	1.51707i
$471$		0			0
$472$	2.01508	−	21.6571i	0.0927516	−	0.996850i
$473$		−	5.63220i		−	0.258969i
$474$		0			0
$475$	−15.7532			−0.722804
$476$	−31.5647	+	47.6099i	−1.44677	+	2.18220i
$477$		0			0
$478$	−0.723047	−	1.34689i	−0.0330714	−	0.0616054i
$479$	1.34816			0.0615992			0.0307996	−	0.999526i	$-0.490195\pi$
$479$	1.34816			0.0615992			0.0307996	+	0.999526i	$0.490195\pi$
$480$		0			0
$481$	1.61780			0.0737654
$482$	12.8307	+	23.9009i	0.584420	+	1.08866i
$483$		0			0
$484$	2.52629	−	3.81048i	0.114832	−	0.173203i
$485$	25.1325			1.14121
$486$		0			0
$487$		−	4.50149i		−	0.203982i	−0.994785	−	0.101991i	$-0.967479\pi$
$487$		−	4.50149i		−	0.203982i	0.994785	−	0.101991i	$-0.0325213\pi$
$488$	−2.82046	+	30.3130i	−0.127676	+	1.37220i
$489$		0			0
$490$	−45.2091	−	84.2155i	−2.04234	−	3.80447i
$491$			10.2836i			0.464094i	0.972705	+	0.232047i	$0.0745424\pi$
$491$			10.2836i			0.464094i	−0.972705	+	0.232047i	$0.925458\pi$
$492$		0			0
$493$		−	25.8638i		−	1.16485i
$494$	−2.29575	+	1.23242i	−0.103291	+	0.0554492i
$495$		0			0
$496$	−37.6736	+	15.9235i	−1.69159	+	0.714986i
$497$			32.7367i			1.46844i
$498$		0			0
$499$	−4.23698			−0.189673			−0.0948367	−	0.995493i	$-0.530233\pi$
$499$	−4.23698			−0.189673			−0.0948367	+	0.995493i	$0.530233\pi$
$500$	−14.4420	+	21.7832i	−0.645865	+	0.974175i
$501$		0			0
$502$	30.2721	−	16.2508i	1.35111	−	0.725311i
$503$	−8.09287			−0.360843			−0.180422	−	0.983589i	$-0.557746\pi$
$503$	−8.09287			−0.360843			−0.180422	+	0.983589i	$0.557746\pi$
$504$		0			0
$505$	−22.9086			−1.01942
$506$	10.6200	−	5.70111i	0.472118	−	0.253445i
$507$		0			0
$508$	−7.46988	−	4.95243i	−0.331422	−	0.219729i
$509$	−23.8614			−1.05764			−0.528818	−	0.848735i	$-0.677365\pi$
$509$	−23.8614			−1.05764			−0.528818	+	0.848735i	$0.677365\pi$
$510$		0			0
$511$			37.6597i			1.66597i
$512$	−21.7566	−	6.21695i	−0.961515	−	0.274753i
$513$		0			0
$514$	1.55095	−	0.832589i	0.0684093	−	0.0367239i
$515$		−	40.2018i		−	1.77150i
$516$		0			0
$517$			26.1368i			1.14950i
$518$	−5.44965	−	10.1516i	−0.239444	−	0.446036i
$519$		0			0
$520$	−0.964574	+	10.3668i	−0.0422994	+	0.454613i
$521$			29.3962i			1.28787i	0.765080	+	0.643936i	$0.222700\pi$
$521$			29.3962i			1.28787i	−0.765080	+	0.643936i	$0.777300\pi$
$522$		0			0
$523$	33.2174			1.45250			0.726249	−	0.687432i	$-0.241262\pi$
$523$	33.2174			1.45250			0.726249	+	0.687432i	$0.241262\pi$
$524$	12.7079	+	8.42519i	0.555149	+	0.368056i
$525$		0			0
$526$	−0.196058	−	0.365217i	−0.00854854	−	0.0159242i
$527$	−57.9919			−2.52617
$528$		0			0
$529$	−17.5323			−0.762273
$530$	−5.95268	−	11.0887i	−0.258568	−	0.481661i
$531$		0			0
$532$	15.4667	+	10.2542i	0.670567	+	0.444577i
$533$	11.3322			0.490852
$534$		0			0
$535$		−	20.9263i		−	0.904725i
$536$	−4.57760	−	0.425922i	−0.197722	−	0.0183970i
$537$		0			0
$538$	−16.3751	−	30.5035i	−0.705981	−	1.31510i
$539$		−	66.9255i		−	2.88268i
$540$		0			0
$541$		−	17.4819i		−	0.751606i	−0.926700	−	0.375803i	$-0.877367\pi$
$541$		−	17.4819i		−	0.751606i	0.926700	−	0.375803i	$-0.122633\pi$
$542$	−10.7552	+	5.77367i	−0.461975	+	0.248000i
$543$		0			0
$544$	−24.9825	−	20.1292i	−1.07111	−	0.863034i
$545$			15.4361i			0.661211i
$546$		0			0
$547$	−24.8804			−1.06381			−0.531904	−	0.846805i	$-0.678523\pi$
$547$	−24.8804			−1.06381			−0.531904	+	0.846805i	$0.678523\pi$
$548$	−28.8860	−	19.1510i	−1.23395	−	0.818090i
$549$		0			0
$550$	−38.8321	+	20.8461i	−1.65581	+	0.888881i
$551$	−8.40219			−0.357945
$552$		0			0
$553$	−29.5948			−1.25850
$554$	−34.7753	+	18.6683i	−1.47746	+	0.793141i
$555$		0			0
$556$	−8.71893	+	13.1510i	−0.369765	+	0.557726i
$557$	−6.63815			−0.281268			−0.140634	−	0.990062i	$-0.544914\pi$
$557$	−6.63815			−0.281268			−0.140634	+	0.990062i	$0.544914\pi$
$558$		0			0
$559$			1.54519i			0.0653546i
$560$	68.3000	−	28.8684i	2.88620	−	1.21991i
$561$		0			0
$562$	21.2600	−	11.4129i	0.896800	−	0.481426i
$563$		−	5.50030i		−	0.231810i	−0.993260	−	0.115905i	$-0.963023\pi$
$563$		−	5.50030i		−	0.231810i	0.993260	−	0.115905i	$-0.0369768\pi$
$564$		0			0
$565$			18.6015i			0.782569i
$566$	−13.7086	−	25.5363i	−0.576214	−	1.07337i
$567$		0			0
$568$	−18.3074	−	1.70340i	−0.768160	−	0.0714732i
$569$			9.67742i			0.405699i	0.979210	+	0.202849i	$0.0650202\pi$
$569$			9.67742i			0.405699i	−0.979210	+	0.202849i	$0.934980\pi$
$570$		0			0
$571$	0.128939			0.00539593			0.00269796	−	0.999996i	$-0.499141\pi$
$571$	0.128939			0.00539593			0.00269796	+	0.999996i	$0.499141\pi$
$572$	−4.02826	+	6.07592i	−0.168430	+	0.254047i
$573$		0			0
$574$	−38.1731	−	71.1088i	−1.59331	−	2.96803i
$575$	−19.9927			−0.833755
$576$		0			0
$577$	12.6458			0.526450			0.263225	−	0.964734i	$-0.415214\pi$
$577$	12.6458			0.526450			0.263225	+	0.964734i	$0.415214\pi$
$578$	−10.1445	−	18.8971i	−0.421954	−	0.786015i
$579$		0			0
$580$	−18.5518	+	27.9821i	−0.770320	+	1.16189i
$581$	6.32968			0.262599
$582$		0			0
$583$		−	8.81207i		−	0.364959i
$584$	−21.0604	−	1.95956i	−0.871486	−	0.0810872i
$585$		0			0
$586$	15.1554	+	28.2316i	0.626066	+	1.16624i
$587$			3.64701i			0.150528i	0.997164	+	0.0752640i	$0.0239800\pi$
$587$			3.64701i			0.150528i	−0.997164	+	0.0752640i	$0.976020\pi$
$588$		0			0
$589$			18.8394i			0.776266i
$590$	−35.2715	+	18.9347i	−1.45211	+	0.779529i
$591$		0			0
$592$	5.96064	−	2.51938i	0.244981	−	0.103546i
$593$			43.0021i			1.76588i	0.469483	+	0.882941i	$0.344440\pi$
$593$			43.0021i			1.76588i	−0.469483	+	0.882941i	$0.655560\pi$
$594$		0			0
$595$	105.136			4.31015
$596$	6.07828	−	9.16803i	0.248976	−	0.375537i
$597$		0			0
$598$	−2.91360	+	1.56410i	−0.119146	+	0.0639607i
$599$	−10.2243			−0.417752			−0.208876	−	0.977942i	$-0.566981\pi$
$599$	−10.2243			−0.417752			−0.208876	+	0.977942i	$0.566981\pi$
$600$		0			0
$601$	35.2405			1.43749			0.718744	−	0.695275i	$-0.244717\pi$
$601$	35.2405			1.43749			0.718744	+	0.695275i	$0.244717\pi$
$602$	9.69596	−	5.20505i	0.395178	−	0.212142i
$603$		0			0
$604$	3.09955	+	2.05496i	0.126119	+	0.0836152i
$605$	−8.41460			−0.342102
$606$		0			0
$607$			25.5242i			1.03600i	0.855382	+	0.517998i	$0.173322\pi$
$607$			25.5242i			1.03600i	−0.855382	+	0.517998i	$0.826678\pi$
$608$	−6.53925	+	8.11588i	−0.265202	+	0.329143i
$609$		0			0
$610$	49.3688	−	26.5025i	1.99888	−	1.07305i
$611$		−	7.17063i		−	0.290093i
$612$		0			0
$613$			44.9278i			1.81462i	0.420467	+	0.907308i	$0.361866\pi$
$613$			44.9278i			1.81462i	−0.420467	+	0.907308i	$0.638134\pi$
$614$	−13.1896	−	24.5696i	−0.532290	−	0.991550i
$615$		0			0
$616$	51.6954	+	4.80999i	2.08287	+	0.193800i
$617$			33.7645i			1.35931i	0.733532	+	0.679655i	$0.237870\pi$
$617$			33.7645i			1.35931i	−0.733532	+	0.679655i	$0.762130\pi$
$618$		0			0
$619$	−3.68450			−0.148093			−0.0740463	−	0.997255i	$-0.523591\pi$
$619$	−3.68450			−0.148093			−0.0740463	+	0.997255i	$0.523591\pi$
$620$	62.7417	+	41.5969i	2.51977	+	1.67057i
$621$		0			0
$622$	−9.96569	−	18.5641i	−0.399588	−	0.744352i
$623$	−5.60207			−0.224442
$624$		0			0
$625$	5.35316			0.214126
$626$	8.25246	+	15.3727i	0.329835	+	0.614416i
$627$		0			0
$628$	12.4919	+	8.28197i	0.498481	+	0.330486i
$629$	9.17536			0.365846
$630$		0			0
$631$		−	10.1326i		−	0.403373i	−0.979450	−	0.201687i	$-0.935358\pi$
$631$		−	10.1326i		−	0.403373i	0.979450	−	0.201687i	$-0.0646423\pi$
$632$	1.53992	−	16.5503i	0.0612547	−	0.658336i
$633$		0			0
$634$	3.37401	+	6.28511i	0.133999	+	0.249614i
$635$			16.4956i			0.654608i
$636$		0			0
$637$			18.3610i			0.727488i
$638$	−20.7117	+	11.1186i	−0.819984	+	0.440189i
$639$		0			0
$640$	12.5902	+	39.6975i	0.497670	+	1.56918i
$641$			11.5800i			0.457383i	0.973499	+	0.228692i	$0.0734447\pi$
$641$			11.5800i			0.457383i	−0.973499	+	0.228692i	$0.926555\pi$
$642$		0			0
$643$	−37.5537			−1.48097			−0.740486	−	0.672072i	$-0.765405\pi$
$643$	−37.5537			−1.48097			−0.740486	+	0.672072i	$0.765405\pi$
$644$	19.6292	+	13.0139i	0.773499	+	0.512819i
$645$		0			0
$646$	−13.0204	+	6.98967i	−0.512279	+	0.275005i
$647$	34.7651			1.36676			0.683378	−	0.730065i	$-0.260510\pi$
$647$	34.7651			1.36676			0.683378	+	0.730065i	$0.260510\pi$
$648$		0			0
$649$	−28.0300			−1.10027
$650$	10.6536	−	5.71912i	0.417867	−	0.224322i
$651$		0			0
$652$	23.6672	−	35.6979i	0.926881	−	1.39804i
$653$	5.37682			0.210411			0.105206	−	0.994450i	$-0.466450\pi$
$653$	5.37682			0.210411			0.105206	+	0.994450i	$0.466450\pi$
$654$		0			0
$655$		−	28.0627i		−	1.09650i
$656$	41.7525	−	17.6475i	1.63016	−	0.689019i
$657$		0			0
$658$	−44.9952	+	24.1546i	−1.75410	+	0.941645i
$659$			36.1020i			1.40633i	0.711024	+	0.703167i	$0.248232\pi$
$659$			36.1020i			1.40633i	−0.711024	+	0.703167i	$0.751768\pi$
$660$		0			0
$661$			20.2346i			0.787033i	0.919317	+	0.393517i	$0.128742\pi$
$661$			20.2346i			0.787033i	−0.919317	+	0.393517i	$0.871258\pi$
$662$	−8.88795	−	16.5565i	−0.345440	−	0.643486i
$663$		0			0
$664$	−0.329355	+	3.53974i	−0.0127814	+	0.137369i
$665$		−	34.1548i		−	1.32447i
$666$		0			0
$667$	−10.6634			−0.412890
$668$	−15.1015	+	22.7780i	−0.584294	+	0.881306i
$669$		0			0
$670$	4.00217	+	7.45524i	0.154617	+	0.288021i
$671$	39.2330			1.51457
$672$		0			0
$673$	6.18244			0.238316			0.119158	−	0.992875i	$-0.461981\pi$
$673$	6.18244			0.238316			0.119158	+	0.992875i	$0.461981\pi$
$674$	−9.33750	−	17.3939i	−0.359667	−	0.669988i
$675$		0			0
$676$	1.10515	−	1.66693i	0.0425058	−	0.0641126i
$677$	−43.2294			−1.66144			−0.830720	−	0.556691i	$-0.812071\pi$
$677$	−43.2294			−1.66144			−0.830720	+	0.556691i	$0.812071\pi$
$678$		0			0
$679$			34.3833i			1.31951i
$680$	−5.47058	+	58.7952i	−0.209787	+	2.25469i
$681$		0			0
$682$	24.9302	+	46.4399i	0.954626	+	1.77828i
$683$			1.60920i			0.0615745i	0.999526	+	0.0307872i	$0.00980143\pi$
$683$			1.60920i			0.0615745i	−0.999526	+	0.0307872i	$0.990199\pi$
$684$		0			0
$685$			63.7883i			2.43722i
$686$	71.2893	−	38.2700i	2.72184	−	1.46115i
$687$		0			0
$688$	2.40630	+	5.69311i	0.0917395	+	0.217048i
$689$			2.41759i			0.0921028i
$690$		0			0
$691$	−30.7774			−1.17083			−0.585413	−	0.810735i	$-0.699068\pi$
$691$	−30.7774			−1.17083			−0.585413	+	0.810735i	$0.699068\pi$
$692$	−17.8550	+	26.9312i	−0.678746	+	1.02377i
$693$		0			0
$694$	23.4210	−	12.5730i	0.889048	−	0.477264i
$695$	29.0411			1.10159
$696$		0			0
$697$	64.2706			2.43442
$698$	36.3770	−	19.5282i	1.37689	−	0.739151i
$699$		0			0
$700$	−71.7742	−	47.5853i	−2.71281	−	1.79856i
$701$	34.1094			1.28829			0.644147	−	0.764902i	$-0.277213\pi$
$701$	34.1094			1.28829			0.644147	+	0.764902i	$0.277213\pi$
$702$		0			0
$703$		−	2.98074i		−	0.112421i
$704$	−5.37978	+	28.6593i	−0.202758	+	1.08014i
$705$		0			0
$706$	22.9323	−	12.3107i	0.863068	−	0.463318i
$707$		−	31.3409i		−	1.17870i
$708$		0			0
$709$		−	40.8849i		−	1.53546i	−0.640772	−	0.767731i	$-0.721386\pi$
$709$		−	40.8849i		−	1.53546i	0.640772	−	0.767731i	$-0.278614\pi$
$710$	16.0060	+	29.8160i	0.600695	+	1.11897i
$711$		0			0
$712$	0.291495	−	3.13284i	0.0109242	−	0.117408i
$713$			23.9096i			0.895422i
$714$		0			0
$715$	13.4173			0.501780
$716$	−1.08959	−	0.722387i	−0.0407201	−	0.0269969i
$717$		0			0
$718$	13.8735	+	25.8435i	0.517753	+	0.964471i
$719$	4.94266			0.184330			0.0921651	−	0.995744i	$-0.470621\pi$
$719$	4.94266			0.184330			0.0921651	+	0.995744i	$0.470621\pi$
$720$		0			0
$721$	54.9994			2.04829
$722$	−10.4384	−	19.4446i	−0.388476	−	0.723654i
$723$		0			0
$724$	37.1920	+	24.6578i	1.38223	+	0.916400i
$725$	38.9908			1.44808
$726$		0			0
$727$		−	38.8777i		−	1.44189i	−0.692991	−	0.720946i	$-0.743707\pi$
$727$		−	38.8777i		−	1.44189i	0.692991	−	0.720946i	$-0.256293\pi$
$728$	−14.1826	−	1.31962i	−0.525642	−	0.0489083i
$729$		0			0
$730$	18.4130	+	34.2997i	0.681495	+	1.26949i
$731$			8.76354i			0.324131i
$732$		0			0
$733$			26.9534i			0.995548i	0.867307	+	0.497774i	$0.165849\pi$
$733$			26.9534i			0.995548i	−0.867307	+	0.497774i	$0.834151\pi$
$734$	−3.65144	+	1.96019i	−0.134777	+	0.0723520i
$735$		0			0
$736$	−8.29913	+	10.3001i	−0.305910	+	0.379666i
$737$			5.92462i			0.218236i
$738$		0			0
$739$	31.3793			1.15431			0.577153	−	0.816636i	$-0.304163\pi$
$739$	31.3793			1.15431			0.577153	+	0.816636i	$0.304163\pi$
$740$	−9.92687	−	6.58138i	−0.364919	−	0.241936i
$741$		0			0
$742$	15.1702	−	8.14376i	0.556916	−	0.298967i
$743$	−11.9414			−0.438087			−0.219043	−	0.975715i	$-0.570294\pi$
$743$	−11.9414			−0.438087			−0.219043	+	0.975715i	$0.570294\pi$
$744$		0			0
$745$	−20.2456			−0.741741
$746$	−19.0712	+	10.2379i	−0.698247	+	0.374837i
$747$		0			0
$748$	−22.8463	+	34.4596i	−0.835342	+	1.25997i
$749$	28.6290			1.04608
$750$		0			0
$751$		−	54.1741i		−	1.97684i	−0.151742	−	0.988420i	$-0.548488\pi$
$751$		−	54.1741i		−	1.97684i	0.151742	−	0.988420i	$-0.451512\pi$
$752$	−11.1667	−	26.4195i	−0.407209	−	0.963420i
$753$		0			0
$754$	5.68225	−	3.05038i	0.206935	−	0.111088i
$755$		−	6.84468i		−	0.249103i
$756$		0			0
$757$		−	42.7529i		−	1.55388i	−0.629573	−	0.776941i	$-0.716770\pi$
$757$		−	42.7529i		−	1.55388i	0.629573	−	0.776941i	$-0.283230\pi$
$758$	−17.7913	−	33.1416i	−0.646209	−	1.20376i
$759$		0			0
$760$	19.1004	+	1.77719i	0.692844	+	0.0644655i
$761$		−	43.7611i		−	1.58634i	−0.609002	−	0.793169i	$-0.708430\pi$
$761$		−	43.7611i		−	1.58634i	0.609002	−	0.793169i	$-0.291570\pi$
$762$		0			0
$763$	−21.1179			−0.764519
$764$	−12.1054	+	18.2588i	−0.437957	+	0.660582i
$765$		0			0
$766$	13.5111	+	25.1685i	0.488177	+	0.909376i
$767$	7.69002			0.277671
$768$		0			0
$769$	15.5085			0.559251			0.279625	−	0.960109i	$-0.409790\pi$
$769$	15.5085			0.559251			0.279625	+	0.960109i	$0.409790\pi$
$770$	−45.1970	−	84.1929i	−1.62879	−	3.03410i
$771$		0			0
$772$	−3.92856	+	5.92554i	−0.141392	+	0.213265i
$773$	−27.7466			−0.997976			−0.498988	−	0.866609i	$-0.666295\pi$
$773$	−27.7466			−0.997976			−0.498988	+	0.866609i	$0.666295\pi$
$774$		0			0
$775$		−	87.4255i		−	3.14042i
$776$	−19.2282	−	1.78908i	−0.690251	−	0.0642242i
$777$		0			0
$778$	−4.47224	−	8.33088i	−0.160338	−	0.298677i
$779$		−	20.8792i		−	0.748074i
$780$		0			0
$781$			23.6945i			0.847858i
$782$	−16.5245	+	8.87078i	−0.590914	+	0.317218i
$783$		0			0
$784$	28.5933	+	67.6493i	1.02119	+	2.41604i
$785$		−	27.5856i		−	0.984573i
$786$		0			0
$787$	−15.5184			−0.553170			−0.276585	−	0.960989i	$-0.589203\pi$
$787$	−15.5184			−0.553170			−0.276585	+	0.960989i	$0.589203\pi$
$788$	−3.79053	+	5.71735i	−0.135032	+	0.203672i
$789$		0			0
$790$	−26.9544	+	14.4698i	−0.958995	+	0.514814i
$791$	−25.4483			−0.904839
$792$		0			0
$793$	−10.7635			−0.382225
$794$	26.7642	−	14.3677i	0.949824	−	0.509891i
$795$		0			0
$796$	13.8510	+	9.18302i	0.490935	+	0.325483i
$797$	25.0216			0.886312			0.443156	−	0.896445i	$-0.353859\pi$
$797$	25.0216			0.886312			0.443156	+	0.896445i	$0.353859\pi$
$798$		0			0
$799$		−	40.6682i		−	1.43874i
$800$	30.3458	−	37.6622i	1.07289	−	1.33156i
$801$		0			0
$802$	12.2383	−	6.56983i	0.432149	−	0.231989i
$803$			27.2577i			0.961904i
$804$		0			0
$805$		−	43.3468i		−	1.52777i
$806$	−6.83958	−	12.7408i	−0.240914	−	0.448774i
$807$		0			0
$808$	17.5268	+	1.63077i	0.616590	+	0.0573704i
$809$			31.6832i			1.11392i	0.830539	+	0.556960i	$0.188032\pi$
$809$			31.6832i			1.11392i	−0.830539	+	0.556960i	$0.811968\pi$
$810$		0			0
$811$	−47.7481			−1.67666			−0.838331	−	0.545161i	$-0.816468\pi$
$811$	−47.7481			−1.67666			−0.838331	+	0.545161i	$0.816468\pi$
$812$	−38.2819	−	25.3804i	−1.34343	−	0.890676i
$813$		0			0
$814$	−3.94440	−	7.34763i	−0.138251	−	0.257534i
$815$	−78.8310			−2.76133
$816$		0			0
$817$	2.84695			0.0996023
$818$	−24.4554	−	45.5555i	−0.855062	−	1.59281i
$819$		0			0
$820$	−69.5347	−	46.1005i	−2.42826	−	1.60990i
$821$	13.8464			0.483242			0.241621	−	0.970371i	$-0.422321\pi$
$821$	13.8464			0.483242			0.241621	+	0.970371i	$0.422321\pi$
$822$		0			0
$823$		−	30.2978i		−	1.05611i	−0.849209	−	0.528057i	$-0.822921\pi$
$823$		−	30.2978i		−	1.05611i	0.849209	−	0.528057i	$-0.177079\pi$
$824$	−2.86181	+	30.7573i	−0.0996958	+	1.07148i
$825$		0			0
$826$	−25.9042	−	48.2544i	−0.901323	−	1.67898i
$827$		−	15.4604i		−	0.537611i	−0.963195	−	0.268805i	$-0.913371\pi$
$827$		−	15.4604i		−	0.537611i	0.963195	−	0.268805i	$-0.0866288\pi$
$828$		0			0
$829$		−	17.3407i		−	0.602266i	−0.953582	−	0.301133i	$-0.902635\pi$
$829$		−	17.3407i		−	0.602266i	0.953582	−	0.301133i	$-0.0973649\pi$
$830$	5.76495	−	3.09478i	0.200104	−	0.107421i
$831$		0			0
$832$	1.47594	−	7.86267i	0.0511689	−	0.272589i
$833$			104.134i			3.60804i
$834$		0			0
$835$	50.3001			1.74071
$836$	11.1947	+	7.42191i	0.387176	+	0.256692i
$837$		0			0
$838$	44.7376	−	24.0164i	1.54544	−	0.829631i
$839$	−15.1899			−0.524414			−0.262207	−	0.965012i	$-0.584450\pi$
$839$	−15.1899			−0.524414			−0.262207	+	0.965012i	$0.584450\pi$
$840$		0			0
$841$	−8.20364			−0.282884
$842$	−18.1636	+	9.75072i	−0.625960	+	0.336032i
$843$		0			0
$844$	15.9735	−	24.0933i	0.549831	−	0.829325i
$845$	−3.68104			−0.126632
$846$		0			0
$847$		−	11.5119i		−	0.395552i
$848$	3.76488	+	8.90738i	0.129286	+	0.305881i
$849$		0			0
$850$	60.4217	−	32.4360i	2.07245	−	1.11254i
$851$		−	3.78293i		−	0.129677i
$852$		0			0
$853$			47.8191i			1.63730i	0.574295	+	0.818648i	$0.305276\pi$
$853$			47.8191i			1.63730i	−0.574295	+	0.818648i	$0.694724\pi$
$854$	36.2575	+	67.5405i	1.24071	+	2.31119i
$855$		0			0
$856$	−1.48966	+	16.0102i	−0.0509156	+	0.547217i
$857$		−	31.9686i		−	1.09203i	−0.837776	−	0.546013i	$-0.816145\pi$
$857$		−	31.9686i		−	1.09203i	0.837776	−	0.546013i	$-0.183855\pi$
$858$		0			0
$859$	−16.9344			−0.577794			−0.288897	−	0.957360i	$-0.593289\pi$
$859$	−16.9344			−0.577794			−0.288897	+	0.957360i	$0.593289\pi$
$860$	6.28599	−	9.48132i	0.214350	−	0.323310i
$861$		0			0
$862$	−6.99587	−	13.0319i	−0.238280	−	0.443869i
$863$	−6.87079			−0.233885			−0.116942	−	0.993139i	$-0.537309\pi$
$863$	−6.87079			−0.233885			−0.116942	+	0.993139i	$0.537309\pi$
$864$		0			0
$865$	59.4716			2.02209
$866$	6.98510	+	13.0118i	0.237363	+	0.442161i
$867$		0			0
$868$	−56.9080	+	85.8358i	−1.93158	+	2.91346i
$869$	−21.4205			−0.726640
$870$		0			0
$871$		−	1.62542i		−	0.0550751i
$872$	1.09884	−	11.8098i	0.0372113	−	0.399929i
$873$		0			0
$874$	2.88179	+	5.36820i	0.0974780	+	0.181582i
$875$			65.8095i			2.22477i
$876$		0			0
$877$		−	30.8633i		−	1.04218i	−0.853502	−	0.521090i	$-0.825525\pi$
$877$		−	30.8633i		−	1.04218i	0.853502	−	0.521090i	$-0.174475\pi$
$878$	−1.01895	+	0.547000i	−0.0343879	+	0.0184603i
$879$		0			0
$880$	49.4349	−	20.8947i	1.66645	−	0.704359i
$881$			34.4698i			1.16132i	0.814147	+	0.580659i	$0.197205\pi$
$881$			34.4698i			1.16132i	−0.814147	+	0.580659i	$0.802795\pi$
$882$		0			0
$883$	57.4034			1.93178			0.965889	−	0.258958i	$-0.0833790\pi$
$883$	57.4034			1.93178			0.965889	+	0.258958i	$0.0833790\pi$
$884$	6.26786	−	9.45397i	0.210811	−	0.317972i
$885$		0			0
$886$	−13.9705	+	7.49971i	−0.469347	+	0.251958i
$887$	53.5228			1.79712			0.898561	−	0.438849i	$-0.144614\pi$
$887$	53.5228			1.79712			0.898561	+	0.438849i	$0.144614\pi$
$888$		0			0
$889$	−22.5673			−0.756884
$890$	−5.10226	+	2.73903i	−0.171028	+	0.0918124i
$891$		0			0
$892$	26.0665	+	17.2818i	0.872772	+	0.578636i
$893$	−13.2116			−0.442110
$894$		0			0
$895$			2.40613i			0.0804281i
$896$	−54.3095	+	17.2244i	−1.81435	+	0.575426i
$897$		0			0
$898$	15.5619	−	8.35404i	0.519307	−	0.278778i
$899$		−	46.6297i		−	1.55519i
$900$		0			0
$901$			13.7113i			0.456791i
$902$	−27.6293	−	51.4679i	−0.919956	−	1.71369i
$903$		0			0
$904$	1.32416	−	14.2315i	0.0440410	−	0.473332i
$905$		−	82.1303i		−	2.73011i
$906$		0			0
$907$	−10.1576			−0.337279			−0.168639	−	0.985678i	$-0.553937\pi$
$907$	−10.1576			−0.337279			−0.168639	+	0.985678i	$0.553937\pi$
$908$	−35.7797	−	23.7214i	−1.18739	−	0.787224i
$909$		0			0
$910$	12.3998	+	23.0983i	0.411048	+	0.765701i
$911$	17.4313			0.577525			0.288762	−	0.957401i	$-0.406756\pi$
$911$	17.4313			0.577525			0.288762	+	0.957401i	$0.406756\pi$
$912$		0			0
$913$	4.58136			0.151621
$914$	−4.77724	−	8.89904i	−0.158017	−	0.294354i
$915$		0			0
$916$	11.7897	+	7.81641i	0.389542	+	0.258261i
$917$	38.3921			1.26782
$918$		0			0
$919$		−	36.5971i		−	1.20723i	−0.797277	−	0.603613i	$-0.793727\pi$
$919$		−	36.5971i		−	1.20723i	0.797277	−	0.603613i	$-0.206273\pi$
$920$	24.2408	+	2.25548i	0.799196	+	0.0743610i
$921$		0			0
$922$	−0.165940	−	0.309113i	−0.00546494	−	0.0101801i
$923$		−	6.50058i		−	0.213969i
$924$		0			0
$925$			13.8323i			0.454803i
$926$	−17.1248	+	9.19303i	−0.562755	+	0.302102i
$927$		0			0
$928$	16.1854	−	20.0877i	0.531311	−	0.659412i
$929$			3.06906i			0.100693i	0.998732	+	0.0503463i	$0.0160325\pi$
$929$			3.06906i			0.100693i	−0.998732	+	0.0503463i	$0.983968\pi$
$930$		0			0
$931$	33.8294			1.10871
$932$	18.9517	+	12.5647i	0.620782	+	0.411570i
$933$		0			0
$934$	−34.0436	+	18.2755i	−1.11394	+	0.597993i
$935$	76.0965			2.48862
$936$		0			0
$937$	−1.04578			−0.0341642			−0.0170821	−	0.999854i	$-0.505438\pi$
$937$	−1.04578			−0.0341642			−0.0170821	+	0.999854i	$0.505438\pi$
$938$	−10.1994	+	5.47530i	−0.333022	+	0.178775i
$939$		0			0
$940$	−29.1708	+	43.9991i	−0.951448	+	1.43509i
$941$	−6.33655			−0.206566			−0.103283	−	0.994652i	$-0.532935\pi$
$941$	−6.33655			−0.206566			−0.103283	+	0.994652i	$0.532935\pi$
$942$		0			0
$943$		−	26.4983i		−	0.862903i
$944$	28.3332	−	11.9756i	0.922166	−	0.389772i
$945$		0			0
$946$	7.01785	−	3.76737i	0.228170	−	0.122488i
$947$			38.8914i			1.26380i	0.775049	+	0.631901i	$0.217725\pi$
$947$			38.8914i			1.26380i	−0.775049	+	0.631901i	$0.782275\pi$
$948$		0			0
$949$		−	7.47814i		−	0.242751i
$950$	−10.5373	−	19.6288i	−0.341874	−	0.636842i
$951$		0			0
$952$	−80.4367	−	7.48421i	−2.60697	−	0.242565i
$953$		−	42.9963i		−	1.39279i	−0.717660	−	0.696394i	$-0.754787\pi$
$953$		−	42.9963i		−	1.39279i	0.717660	−	0.696394i	$-0.245213\pi$
$954$		0			0
$955$	40.3206			1.30474
$956$	1.19461	−	1.80187i	0.0386366	−	0.0582766i
$957$		0			0
$958$	0.901785	+	1.67984i	0.0291354	+	0.0542733i
$959$	−87.2676			−2.81802
$960$		0			0
$961$	−73.5535			−2.37269
$962$	1.08214	+	2.01582i	0.0348898	+	0.0649926i
$963$		0			0
$964$	−21.1987	+	31.9746i	−0.682765	+	1.02983i
$965$	13.0853			0.421229
$966$		0			0
$967$			13.6970i			0.440467i	0.975447	+	0.220234i	$0.0706819\pi$
$967$			13.6970i			0.440467i	−0.975447	+	0.220234i	$0.929318\pi$
$968$	6.43778	+	0.599001i	0.206918	+	0.0192526i
$969$		0			0
$970$	16.8111	+	31.3156i	0.539771	+	1.00548i
$971$			30.7654i			0.987309i	0.869658	+	0.493654i	$0.164339\pi$
$971$			30.7654i			0.987309i	−0.869658	+	0.493654i	$0.835661\pi$
$972$		0			0
$973$			39.7306i			1.27370i
$974$	5.60896	−	3.01104i	0.179723	−	0.0964799i
$975$		0			0
$976$	−39.6573	+	16.7619i	−1.26940	+	0.536537i
$977$		−	53.1078i		−	1.69907i	−0.527534	−	0.849534i	$-0.676883\pi$
$977$		−	53.1078i		−	1.69907i	0.527534	−	0.849534i	$-0.323117\pi$
$978$		0			0
$979$	−4.05473			−0.129590
$980$	74.6942	−	112.663i	2.38602	−	3.59890i
$981$		0			0
$982$	−12.8137	+	6.87871i	−0.408900	+	0.219509i
$983$	−34.7616			−1.10872			−0.554361	−	0.832276i	$-0.687037\pi$
$983$	−34.7616			−1.10872			−0.554361	+	0.832276i	$0.687037\pi$
$984$		0			0
$985$	12.6255			0.402282
$986$	32.2269	−	17.3002i	1.02631	−	0.550952i
$987$		0			0
$988$	−3.07125	−	2.03620i	−0.0977095	−	0.0647801i
$989$	3.61314			0.114891
$990$		0			0
$991$			30.6042i			0.972176i	0.873910	+	0.486088i	$0.161577\pi$
$991$			30.6042i			0.972176i	−0.873910	+	0.486088i	$0.838423\pi$
$992$	−45.0408	−	36.2910i	−1.43005	−	1.15224i
$993$		0			0
$994$	−40.7907	+	21.8975i	−1.29380	+	0.694548i
$995$		−	30.5869i		−	0.969669i
$996$		0			0
$997$			19.0359i			0.602872i	0.953486	+	0.301436i	$0.0974659\pi$
$997$			19.0359i			0.602872i	−0.953486	+	0.301436i	$0.902534\pi$
$998$	−2.83411	−	5.27938i	−0.0897123	−	0.167116i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.j.a.755.36	yes	48
3.2	odd	2	inner	936.2.j.a.755.13	✓	48
4.3	odd	2		3744.2.j.a.2159.46		48
8.3	odd	2	inner	936.2.j.a.755.14	yes	48
8.5	even	2		3744.2.j.a.2159.3		48
12.11	even	2		3744.2.j.a.2159.4		48
24.5	odd	2		3744.2.j.a.2159.45		48
24.11	even	2	inner	936.2.j.a.755.35	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.j.a.755.13	✓	48	3.2	odd	2	inner
936.2.j.a.755.14	yes	48	8.3	odd	2	inner
936.2.j.a.755.35	yes	48	24.11	even	2	inner
936.2.j.a.755.36	yes	48	1.1	even	1	trivial
3744.2.j.a.2159.3		48	8.5	even	2
3744.2.j.a.2159.4		48	12.11	even	2
3744.2.j.a.2159.45		48	24.5	odd	2
3744.2.j.a.2159.46		48	4.3	odd	2

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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.668898 + 1.24602i) q^{2} +(-1.10515 + 1.66693i) q^{4} +3.68104 q^{5} +5.03597i q^{7} +(-2.81626 - 0.262038i) q^{8} +(2.46224 + 4.58666i) q^{10} +3.64499i q^{11} -1.00000i q^{13} +(-6.27493 + 3.36855i) q^{14} +(-1.55729 - 3.68441i) q^{16} -5.67150i q^{17} -1.84246 q^{19} +(-4.06810 + 6.13602i) q^{20} +(-4.54174 + 2.43813i) q^{22} -2.33832 q^{23} +8.55005 q^{25} +(1.24602 - 0.668898i) q^{26} +(-8.39459 - 5.56550i) q^{28} +4.56030 q^{29} -10.2251i q^{31} +(3.54919 - 4.40491i) q^{32} +(7.06682 - 3.79366i) q^{34} +18.5376i q^{35} +1.61780i q^{37} +(-1.23242 - 2.29575i) q^{38} +(-10.3668 - 0.964574i) q^{40} +11.3322i q^{41} -1.54519 q^{43} +(-6.07592 - 4.02826i) q^{44} +(-1.56410 - 2.91360i) q^{46} +7.17063 q^{47} -18.3610 q^{49} +(5.71912 + 10.6536i) q^{50} +(1.66693 + 1.10515i) q^{52} -2.41759 q^{53} +13.4173i q^{55} +(1.31962 - 14.1826i) q^{56} +(3.05038 + 5.68225i) q^{58} +7.69002i q^{59} -10.7635i q^{61} +(12.7408 - 6.83958i) q^{62} +(7.86267 + 1.47594i) q^{64} -3.68104i q^{65} +1.62542 q^{67} +(9.45397 + 6.26786i) q^{68} +(-23.0983 + 12.3998i) q^{70} +6.50058 q^{71} +7.47814 q^{73} +(-2.01582 + 1.08214i) q^{74} +(2.03620 - 3.07125i) q^{76} -18.3560 q^{77} +5.87670i q^{79} +(-5.73244 - 13.5624i) q^{80} +(-14.1202 + 7.58009i) q^{82} -1.25689i q^{83} -20.8770i q^{85} +(-1.03357 - 1.92534i) q^{86} +(0.955127 - 10.2652i) q^{88} +1.11241i q^{89} +5.03597 q^{91} +(2.58419 - 3.89780i) q^{92} +(4.79642 + 8.93477i) q^{94} -6.78218 q^{95} +6.82755 q^{97} +(-12.2816 - 22.8782i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 8 q^{4} + 16 q^{10} + 8 q^{16} + 32 q^{19} + 48 q^{25} - 24 q^{28} + 32 q^{34} - 32 q^{40} - 32 q^{43} + 24 q^{46} - 48 q^{49} + 8 q^{52} - 40 q^{58} + 40 q^{64} + 32 q^{67} - 40 q^{70} + 40 q^{76}+ \cdots - 32 q^{97}+O(q^{100}) \) 48 * q - 8 * q^4 + 16 * q^10 + 8 * q^16 + 32 * q^19 + 48 * q^25 - 24 * q^28 + 32 * q^34 - 32 * q^40 - 32 * q^43 + 24 * q^46 - 48 * q^49 + 8 * q^52 - 40 * q^58 + 40 * q^64 + 32 * q^67 - 40 * q^70 + 40 * q^76 + 16 * q^82 + 48 * q^88 + 32 * q^94 - 32 * q^97

Introduction

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