LMFDB - Embedded newform 945.2.k.b.361.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [945,2,Mod(361,945)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(945, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("945.361"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.k (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.10
Character	$\chi$	$=$	945.361
Dual form			945.2.k.b.856.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.08176 - 1.87367i) q^{2} +(-1.34041 - 2.32167i) q^{4} +1.00000 q^{5} +(2.14928 - 1.54292i) q^{7} -1.47299 q^{8} +(1.08176 - 1.87367i) q^{10} -2.52066 q^{11} +(-0.542414 + 0.939489i) q^{13} +(-0.565917 - 5.69610i) q^{14} +(1.08741 - 1.88345i) q^{16} +(2.85163 - 4.93917i) q^{17} +(1.75436 + 3.03863i) q^{19} +(-1.34041 - 2.32167i) q^{20} +(-2.72676 + 4.72288i) q^{22} +0.273308 q^{23} +1.00000 q^{25} +(1.17352 + 2.03260i) q^{26} +(-6.46307 - 2.92175i) q^{28} +(-4.63947 - 8.03580i) q^{29} +(0.884081 + 1.53127i) q^{31} +(-3.82562 - 6.62617i) q^{32} +(-6.16956 - 10.6860i) q^{34} +(2.14928 - 1.54292i) q^{35} +(1.14456 + 1.98243i) q^{37} +7.59118 q^{38} -1.47299 q^{40} +(-2.65518 + 4.59891i) q^{41} +(3.14508 + 5.44743i) q^{43} +(3.37874 + 5.85214i) q^{44} +(0.295654 - 0.512088i) q^{46} +(2.34203 - 4.05652i) q^{47} +(2.23878 - 6.63234i) q^{49} +(1.08176 - 1.87367i) q^{50} +2.90824 q^{52} +(-4.86938 + 8.43401i) q^{53} -2.52066 q^{55} +(-3.16586 + 2.27271i) q^{56} -20.0752 q^{58} +(-1.68373 - 2.91631i) q^{59} +(-2.47366 + 4.28451i) q^{61} +3.82546 q^{62} -12.2040 q^{64} +(-0.542414 + 0.939489i) q^{65} +(6.42542 + 11.1292i) q^{67} -15.2895 q^{68} +(-0.565917 - 5.69610i) q^{70} -10.9734 q^{71} +(-0.107878 + 0.186850i) q^{73} +4.95255 q^{74} +(4.70313 - 8.14606i) q^{76} +(-5.41761 + 3.88919i) q^{77} +(1.95176 - 3.38055i) q^{79} +(1.08741 - 1.88345i) q^{80} +(5.74454 + 9.94984i) q^{82} +(-5.18081 - 8.97342i) q^{83} +(2.85163 - 4.93917i) q^{85} +13.6089 q^{86} +3.71291 q^{88} +(6.78158 + 11.7460i) q^{89} +(0.283761 + 2.85612i) q^{91} +(-0.366346 - 0.634530i) q^{92} +(-5.06704 - 8.77636i) q^{94} +(1.75436 + 3.03863i) q^{95} +(-6.91171 - 11.9714i) q^{97} +(-10.0050 - 11.3693i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{2} - 7 q^{4} + 24 q^{5} + 7 q^{7} - 12 q^{8} + q^{10} + 2 q^{11} - 4 q^{13} + 13 q^{14} - 5 q^{16} + 7 q^{17} - 2 q^{19} - 7 q^{20} + 19 q^{22} + 2 q^{23} + 24 q^{25} - 11 q^{26} - 28 q^{28}+ \cdots + 15 q^{98}+O(q^{100}) $ 24 * q + q^2 - 7 * q^4 + 24 * q^5 + 7 * q^7 - 12 * q^8 + q^10 + 2 * q^11 - 4 * q^13 + 13 * q^14 - 5 * q^16 + 7 * q^17 - 2 * q^19 - 7 * q^20 + 19 * q^22 + 2 * q^23 + 24 * q^25 - 11 * q^26 - 28 * q^28 + 8 * q^31 - 17 * q^32 + q^34 + 7 * q^35 + 17 * q^37 - 70 * q^38 - 12 * q^40 - 20 * q^41 + 31 * q^43 + 7 * q^44 - 10 * q^46 + 31 * q^47 - 11 * q^49 + q^50 + 8 * q^52 - 8 * q^53 + 2 * q^55 - 45 * q^56 - 90 * q^58 + 21 * q^59 + 5 * q^61 - 14 * q^62 - 56 * q^64 - 4 * q^65 + 43 * q^67 - 96 * q^68 + 13 * q^70 - 24 * q^71 - 18 * q^73 + 18 * q^74 - 13 * q^76 - 5 * q^77 + 40 * q^79 - 5 * q^80 + 5 * q^82 + 60 * q^83 + 7 * q^85 + 24 * q^86 - 100 * q^88 + 4 * q^89 - 33 * q^91 + 18 * q^92 - 11 * q^94 - 2 * q^95 + 6 * q^97 + 15 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	1.08176	−	1.87367i	0.764921	−	1.32488i	−0.175368	−	0.984503i	$-0.556111\pi$
$2$	1.08176	−	1.87367i	0.764921	−	1.32488i	0.940289	−	0.340378i	$-0.110555\pi$
$3$		0			0
$3$		0			0
$4$	−1.34041	−	2.32167i	−0.670207	−	1.16083i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	2.14928	−	1.54292i	0.812350	−	0.583170i
$7$	2.14928	−	1.54292i	0.812350	−	0.583170i
$8$	−1.47299			−0.520780
$9$		0			0
$10$	1.08176	−	1.87367i	0.342083	−	0.592505i
$11$	−2.52066			−0.760009			−0.380005	−	0.924985i	$-0.624078\pi$
$11$	−2.52066			−0.760009			−0.380005	+	0.924985i	$0.624078\pi$
$12$		0			0
$13$	−0.542414	+	0.939489i	−0.150439	+	0.260567i	−0.931389	−	0.364026i	$-0.881402\pi$
$13$	−0.542414	+	0.939489i	−0.150439	+	0.260567i	0.780950	+	0.624593i	$0.214735\pi$
$14$	−0.565917	−	5.69610i	−0.151248	−	1.52235i
$15$		0			0
$16$	1.08741	−	1.88345i	0.271852	−	0.470861i
$17$	2.85163	−	4.93917i	0.691622	−	1.19792i	−0.279684	−	0.960092i	$-0.590230\pi$
$17$	2.85163	−	4.93917i	0.691622	−	1.19792i	0.971306	−	0.237832i	$-0.0764368\pi$
$18$		0			0
$19$	1.75436	+	3.03863i	0.402477	+	0.697111i	0.994024	−	0.109160i	$-0.0348160\pi$
$19$	1.75436	+	3.03863i	0.402477	+	0.697111i	−0.591547	+	0.806270i	$0.701483\pi$
$20$	−1.34041	−	2.32167i	−0.299726	−	0.519140i
$21$		0			0
$22$	−2.72676	+	4.72288i	−0.581347	+	1.00692i
$23$	0.273308			0.0569887			0.0284943	−	0.999594i	$-0.490929\pi$
$23$	0.273308			0.0569887			0.0284943	+	0.999594i	$0.490929\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	1.17352	+	2.03260i	0.230147	+	0.398627i
$27$		0			0
$28$	−6.46307	−	2.92175i	−1.22141	−	0.552158i
$29$	−4.63947	−	8.03580i	−0.861528	−	1.49221i	−0.870454	−	0.492250i	$-0.836175\pi$
$29$	−4.63947	−	8.03580i	−0.861528	−	1.49221i	0.00892568	−	0.999960i	$-0.497159\pi$
$30$		0			0
$31$	0.884081	+	1.53127i	0.158786	+	0.275025i	0.934431	−	0.356144i	$-0.115909\pi$
$31$	0.884081	+	1.53127i	0.158786	+	0.275025i	−0.775645	+	0.631169i	$0.782575\pi$
$32$	−3.82562	−	6.62617i	−0.676280	−	1.17135i
$33$		0			0
$34$	−6.16956	−	10.6860i	−1.05807	−	1.83263i
$35$	2.14928	−	1.54292i	0.363294	−	0.260802i
$36$		0			0
$37$	1.14456	+	1.98243i	0.188164	+	0.325909i	0.944638	−	0.328114i	$-0.106413\pi$
$37$	1.14456	+	1.98243i	0.188164	+	0.325909i	−0.756474	+	0.654024i	$0.773080\pi$
$38$	7.59118			1.23145
$39$		0			0
$40$	−1.47299			−0.232900
$41$	−2.65518	+	4.59891i	−0.414670	+	0.718229i	−0.995394	−	0.0958717i	$-0.969436\pi$
$41$	−2.65518	+	4.59891i	−0.414670	+	0.718229i	0.580724	+	0.814100i	$0.302769\pi$
$42$		0			0
$43$	3.14508	+	5.44743i	0.479620	+	0.830726i	0.999727	−	0.0233755i	$-0.00744132\pi$
$43$	3.14508	+	5.44743i	0.479620	+	0.830726i	−0.520107	+	0.854101i	$0.674108\pi$
$44$	3.37874	+	5.85214i	0.509364	+	0.882243i
$45$		0			0
$46$	0.295654	−	0.512088i	0.0435918	−	0.0755032i
$47$	2.34203	−	4.05652i	0.341620	−	0.591704i	−0.643113	−	0.765771i	$-0.722358\pi$
$47$	2.34203	−	4.05652i	0.341620	−	0.591704i	0.984734	+	0.174067i	$0.0556910\pi$
$48$		0			0
$49$	2.23878	−	6.63234i	0.319826	−	0.947476i
$50$	1.08176	−	1.87367i	0.152984	−	0.264976i
$51$		0			0
$52$	2.90824			0.403300
$53$	−4.86938	+	8.43401i	−0.668861	+	1.15850i	0.309362	+	0.950944i	$0.399884\pi$
$53$	−4.86938	+	8.43401i	−0.668861	+	1.15850i	−0.978223	+	0.207557i	$0.933449\pi$
$54$		0			0
$55$	−2.52066			−0.339886
$56$	−3.16586	+	2.27271i	−0.423056	+	0.303703i
$57$		0			0
$58$	−20.0752			−2.63600
$59$	−1.68373	−	2.91631i	−0.219203	−	0.379671i	0.735361	−	0.677675i	$-0.237012\pi$
$59$	−1.68373	−	2.91631i	−0.219203	−	0.379671i	−0.954565	+	0.298004i	$0.903679\pi$
$60$		0			0
$61$	−2.47366	+	4.28451i	−0.316720	+	0.548575i	−0.979802	−	0.199972i	$-0.935915\pi$
$61$	−2.47366	+	4.28451i	−0.316720	+	0.548575i	0.663081	+	0.748547i	$0.269248\pi$
$62$	3.82546			0.485834
$63$		0			0
$64$	−12.2040			−1.52550
$65$	−0.542414	+	0.939489i	−0.0672782	+	0.116529i
$66$		0			0
$67$	6.42542	+	11.1292i	0.784990	+	1.35964i	0.929005	+	0.370068i	$0.120665\pi$
$67$	6.42542	+	11.1292i	0.784990	+	1.35964i	−0.144015	+	0.989576i	$0.546001\pi$
$68$	−15.2895			−1.85412
$69$		0			0
$70$	−0.565917	−	5.69610i	−0.0676400	−	0.680814i
$71$	−10.9734			−1.30230			−0.651149	−	0.758950i	$-0.725713\pi$
$71$	−10.9734			−1.30230			−0.651149	+	0.758950i	$0.725713\pi$
$72$		0			0
$73$	−0.107878	+	0.186850i	−0.0126262	+	0.0218692i	−0.872269	−	0.489026i	$-0.837352\pi$
$73$	−0.107878	+	0.186850i	−0.0126262	+	0.0218692i	0.859643	+	0.510895i	$0.170686\pi$
$74$	4.95255			0.575722
$75$		0			0
$76$	4.70313	−	8.14606i	0.539486	−	0.934417i
$77$	−5.41761	+	3.88919i	−0.617393	+	0.443214i
$78$		0			0
$79$	1.95176	−	3.38055i	0.219590	−	0.380342i	−0.735092	−	0.677967i	$-0.762861\pi$
$79$	1.95176	−	3.38055i	0.219590	−	0.380342i	0.954683	+	0.297625i	$0.0961946\pi$
$80$	1.08741	−	1.88345i	0.121576	−	0.210576i
$81$		0			0
$82$	5.74454	+	9.94984i	0.634379	+	1.09878i
$83$	−5.18081	−	8.97342i	−0.568667	−	0.984961i	−0.996698	−	0.0811964i	$-0.974126\pi$
$83$	−5.18081	−	8.97342i	−0.568667	−	0.984961i	0.428031	−	0.903764i	$-0.359207\pi$
$84$		0			0
$85$	2.85163	−	4.93917i	0.309303	−	0.535728i
$86$	13.6089			1.46748
$87$		0			0
$88$	3.71291			0.395797
$89$	6.78158	+	11.7460i	0.718846	+	1.24508i	0.961457	+	0.274954i	$0.0886625\pi$
$89$	6.78158	+	11.7460i	0.718846	+	1.24508i	−0.242612	+	0.970123i	$0.578004\pi$
$90$		0			0
$91$	0.283761	+	2.85612i	0.0297462	+	0.299403i
$92$	−0.366346	−	0.634530i	−0.0381942	−	0.0661543i
$93$		0			0
$94$	−5.06704	−	8.77636i	−0.522625	−	0.905213i
$95$	1.75436	+	3.03863i	0.179993	+	0.311757i
$96$		0			0
$97$	−6.91171	−	11.9714i	−0.701778	−	1.21552i	−0.967842	−	0.251560i	$-0.919056\pi$
$97$	−6.91171	−	11.9714i	−0.701778	−	1.21552i	0.266064	−	0.963955i	$-0.414277\pi$
$98$	−10.0050	−	11.3693i	−1.01065	−	1.14848i
$99$		0			0
$100$	−1.34041	−	2.32167i	−0.134041	−	0.232167i
$101$	10.2886			1.02376			0.511878	−	0.859058i	$-0.328950\pi$
$101$	10.2886			1.02376			0.511878	+	0.859058i	$0.328950\pi$
$102$		0			0
$103$	18.3697			1.81002			0.905008	−	0.425395i	$-0.139865\pi$
$103$	18.3697			1.81002			0.905008	+	0.425395i	$0.139865\pi$
$104$	0.798969	−	1.38386i	0.0783454	−	0.135698i
$105$		0			0
$106$	10.5350	+	18.2472i	1.02325	+	1.77232i
$107$	7.21802	+	12.5020i	0.697793	+	1.20861i	0.969230	+	0.246156i	$0.0791677\pi$
$107$	7.21802	+	12.5020i	0.697793	+	1.20861i	−0.271437	+	0.962456i	$0.587499\pi$
$108$		0			0
$109$	−10.0219	+	17.3584i	−0.959924	+	1.66264i	−0.237249	+	0.971449i	$0.576246\pi$
$109$	−10.0219	+	17.3584i	−0.959924	+	1.66264i	−0.722675	+	0.691188i	$0.757088\pi$
$110$	−2.72676	+	4.72288i	−0.259986	+	0.450309i
$111$		0			0
$112$	−0.568871	−	5.72583i	−0.0537533	−	0.541040i
$113$	−9.36733	+	16.2247i	−0.881204	+	1.52629i	−0.0312006	+	0.999513i	$0.509933\pi$
$113$	−9.36733	+	16.2247i	−0.881204	+	1.52629i	−0.850003	+	0.526777i	$0.823400\pi$
$114$		0			0
$115$	0.273308			0.0254861
$116$	−12.4376	+	21.5426i	−1.15480	+	2.00018i
$117$		0			0
$118$	−7.28559			−0.670693
$119$	−1.49181	−	15.0155i	−0.136754	−	1.37647i
$120$		0			0
$121$	−4.64625			−0.422386
$122$	5.35183	+	9.26963i	0.484532	+	0.839233i
$123$		0			0
$124$	2.37007	−	4.10508i	0.212839	−	0.368647i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−10.6444			−0.944539			−0.472269	−	0.881454i	$-0.656565\pi$
$127$	−10.6444			−0.944539			−0.472269	+	0.881454i	$0.656565\pi$
$128$	−5.55057	+	9.61386i	−0.490605	+	0.849753i
$129$		0			0
$130$	1.17352	+	2.03260i	0.102925	+	0.178271i
$131$	19.8935			1.73810			0.869052	−	0.494722i	$-0.164730\pi$
$131$	19.8935			1.73810			0.869052	+	0.494722i	$0.164730\pi$
$132$		0			0
$133$	8.45898	+	3.82403i	0.733486	+	0.331585i
$134$	27.8031			2.40182
$135$		0			0
$136$	−4.20042	+	7.27533i	−0.360183	+	0.623855i
$137$	13.5567			1.15823			0.579113	−	0.815247i	$-0.303399\pi$
$137$	13.5567			1.15823			0.579113	+	0.815247i	$0.303399\pi$
$138$		0			0
$139$	5.37133	−	9.30342i	0.455590	−	0.789105i	−0.543132	−	0.839648i	$-0.682762\pi$
$139$	5.37133	−	9.30342i	0.455590	−	0.789105i	0.998722	+	0.0505421i	$0.0160949\pi$
$140$	−6.46307	−	2.92175i	−0.546229	−	0.246933i
$141$		0			0
$142$	−11.8705	+	20.5604i	−0.996154	+	1.72539i
$143$	1.36724	−	2.36814i	0.114335	−	0.198033i
$144$		0			0
$145$	−4.63947	−	8.03580i	−0.385287	−	0.667337i
$146$	0.233397	+	0.404255i	0.0193161	+	0.0334564i
$147$		0			0
$148$	3.06836	−	5.31456i	0.252218	−	0.436854i
$149$	11.9813			0.981543			0.490772	−	0.871288i	$-0.336715\pi$
$149$	11.9813			0.981543			0.490772	+	0.871288i	$0.336715\pi$
$150$		0			0
$151$	5.76381			0.469052			0.234526	−	0.972110i	$-0.424646\pi$
$151$	5.76381			0.469052			0.234526	+	0.972110i	$0.424646\pi$
$152$	−2.58415	−	4.47587i	−0.209602	−	0.363041i
$153$		0			0
$154$	1.42649	+	14.3580i	0.114950	+	1.15700i
$155$	0.884081	+	1.53127i	0.0710111	+	0.122995i
$156$		0			0
$157$	5.56990	+	9.64735i	0.444527	+	0.769943i	0.998019	−	0.0629115i	$-0.0200386\pi$
$157$	5.56990	+	9.64735i	0.444527	+	0.769943i	−0.553493	+	0.832854i	$0.686705\pi$
$158$	−4.22268	−	7.31390i	−0.335939	−	0.581863i
$159$		0			0
$160$	−3.82562	−	6.62617i	−0.302442	−	0.523844i
$161$	0.587415	−	0.421693i	0.0462947	−	0.0332341i
$162$		0			0
$163$	−0.636575	−	1.10258i	−0.0498604	−	0.0863607i	0.840018	−	0.542558i	$-0.182544\pi$
$163$	−0.636575	−	1.10258i	−0.0498604	−	0.0863607i	−0.889878	+	0.456198i	$0.849211\pi$
$164$	14.2362			1.11166
$165$		0			0
$166$	−22.4176			−1.73994
$167$	0.472660	−	0.818671i	0.0365755	−	0.0633506i	−0.847158	−	0.531341i	$-0.821688\pi$
$167$	0.472660	−	0.818671i	0.0365755	−	0.0633506i	0.883734	+	0.467990i	$0.155022\pi$
$168$		0			0
$169$	5.91157	+	10.2391i	0.454736	+	0.787627i
$170$	−6.16956	−	10.6860i	−0.473184	−	0.819579i
$171$		0			0
$172$	8.43141	−	14.6036i	0.642889	−	1.11352i
$173$	−3.52039	+	6.09749i	−0.267650	+	0.463584i	−0.968255	−	0.249966i	$-0.919580\pi$
$173$	−3.52039	+	6.09749i	−0.267650	+	0.463584i	0.700604	+	0.713550i	$0.252914\pi$
$174$		0			0
$175$	2.14928	−	1.54292i	0.162470	−	0.116634i
$176$	−2.74099	+	4.74753i	−0.206610	+	0.357859i
$177$		0			0
$178$	29.3442			2.19944
$179$	3.95249	−	6.84590i	0.295423	−	0.511687i	−0.679661	−	0.733527i	$-0.737873\pi$
$179$	3.95249	−	6.84590i	0.295423	−	0.511687i	0.975083	+	0.221840i	$0.0712062\pi$
$180$		0			0
$181$	13.2016			0.981268			0.490634	−	0.871366i	$-0.336765\pi$
$181$	13.2016			0.981268			0.490634	+	0.871366i	$0.336765\pi$
$182$	5.65838	+	2.55797i	0.419427	+	0.189609i
$183$		0			0
$184$	−0.402579			−0.0296785
$185$	1.14456	+	1.98243i	0.0841495	+	0.145751i
$186$		0			0
$187$	−7.18800	+	12.4500i	−0.525639	+	0.910433i
$188$	−12.5572			−0.915826
$189$		0			0
$190$	7.59118			0.550722
$191$	−3.46679	+	6.00466i	−0.250848	+	0.434482i	−0.963760	−	0.266772i	$-0.914043\pi$
$191$	−3.46679	+	6.00466i	−0.250848	+	0.434482i	0.712911	+	0.701254i	$0.247376\pi$
$192$		0			0
$193$	−4.91963	−	8.52105i	−0.354123	−	0.613359i	0.632845	−	0.774279i	$-0.281887\pi$
$193$	−4.91963	−	8.52105i	−0.354123	−	0.613359i	−0.986967	+	0.160920i	$0.948554\pi$
$194$	−29.9073			−2.14722
$195$		0			0
$196$	−18.3990	+	3.69238i	−1.31421	+	0.263742i
$197$	−4.92577			−0.350947			−0.175473	−	0.984484i	$-0.556146\pi$
$197$	−4.92577			−0.350947			−0.175473	+	0.984484i	$0.556146\pi$
$198$		0			0
$199$	2.96416	−	5.13407i	0.210123	−	0.363945i	−0.741630	−	0.670810i	$-0.765947\pi$
$199$	2.96416	−	5.13407i	0.210123	−	0.363945i	0.951753	+	0.306865i	$0.0992801\pi$
$200$	−1.47299			−0.104156
$201$		0			0
$202$	11.1298	−	19.2774i	0.783092	−	1.35635i
$203$	−22.3701	−	10.1128i	−1.57007	−	0.709780i
$204$		0			0
$205$	−2.65518	+	4.59891i	−0.185446	+	0.321202i
$206$	19.8716	−	34.4186i	1.38452	−	2.39806i
$207$		0			0
$208$	1.17965	+	2.04321i	0.0817940	+	0.141671i
$209$	−4.42214	−	7.65938i	−0.305886	−	0.529810i
$210$		0			0
$211$	1.57045	−	2.72010i	0.108114	−	0.187260i	−0.806892	−	0.590699i	$-0.798852\pi$
$211$	1.57045	−	2.72010i	0.108114	−	0.187260i	0.915006	+	0.403439i	$0.132185\pi$
$212$	26.1079			1.79310
$213$		0			0
$214$	31.2327			2.13502
$215$	3.14508	+	5.44743i	0.214492	+	0.371512i
$216$		0			0
$217$	4.26277	+	1.92706i	0.289376	+	0.130817i
$218$	21.6826	+	37.5554i	1.46853	+	2.54357i
$219$		0			0
$220$	3.37874	+	5.85214i	0.227794	+	0.394551i
$221$	3.09353	+	5.35815i	0.208093	+	0.360428i
$222$		0			0
$223$	−1.24047	−	2.14855i	−0.0830679	−	0.143878i	0.821498	−	0.570211i	$-0.193138\pi$
$223$	−1.24047	−	2.14855i	−0.0830679	−	0.143878i	−0.904566	+	0.426333i	$0.859805\pi$
$224$	−18.4460	−	8.33883i	−1.23247	−	0.557161i
$225$		0			0
$226$	20.2664	+	35.1025i	1.34810	+	2.33498i
$227$	−26.5203			−1.76021			−0.880106	−	0.474778i	$-0.842528\pi$
$227$	−26.5203			−1.76021			−0.880106	+	0.474778i	$0.842528\pi$
$228$		0			0
$229$	−20.4619			−1.35216			−0.676079	−	0.736829i	$-0.736322\pi$
$229$	−20.4619			−1.35216			−0.676079	+	0.736829i	$0.736322\pi$
$230$	0.295654	−	0.512088i	0.0194948	−	0.0337661i
$231$		0			0
$232$	6.83388	+	11.8366i	0.448666	+	0.777113i
$233$	−10.3634	−	17.9499i	−0.678929	−	1.17594i	−0.975304	−	0.220868i	$-0.929111\pi$
$233$	−10.3634	−	17.9499i	−0.678929	−	1.17594i	0.296374	−	0.955072i	$-0.404222\pi$
$234$		0			0
$235$	2.34203	−	4.05652i	0.152777	−	0.264618i
$236$	−4.51380	+	7.81813i	−0.293823	+	0.508917i
$237$		0			0
$238$	−29.7478	−	13.4480i	−1.92826	−	0.871705i
$239$	1.88457	−	3.26418i	0.121903	−	0.211142i	−0.798615	−	0.601842i	$-0.794434\pi$
$239$	1.88457	−	3.26418i	0.121903	−	0.211142i	0.920518	+	0.390700i	$0.127767\pi$
$240$		0			0
$241$	7.18908			0.463089			0.231545	−	0.972824i	$-0.425622\pi$
$241$	7.18908			0.463089			0.231545	+	0.972824i	$0.425622\pi$
$242$	−5.02613	+	8.70551i	−0.323092	+	0.559612i
$243$		0			0
$244$	13.2629			0.849072
$245$	2.23878	−	6.63234i	0.143030	−	0.423724i
$246$		0			0
$247$	−3.80635			−0.242192
$248$	−1.30224	−	2.25555i	−0.0826924	−	0.143227i
$249$		0			0
$250$	1.08176	−	1.87367i	0.0684166	−	0.118501i
$251$	12.3897			0.782031			0.391016	−	0.920384i	$-0.372124\pi$
$251$	12.3897			0.782031			0.391016	+	0.920384i	$0.372124\pi$
$252$		0			0
$253$	−0.688918			−0.0433119
$254$	−11.5147	+	19.9441i	−0.722497	+	1.25140i
$255$		0			0
$256$	−0.195217	−	0.338126i	−0.0122011	−	0.0211329i
$257$	−24.4919			−1.52776			−0.763880	−	0.645358i	$-0.776708\pi$
$257$	−24.4919			−1.52776			−0.763880	+	0.645358i	$0.776708\pi$
$258$		0			0
$259$	5.51870	+	2.49483i	0.342916	+	0.155021i
$260$	2.90824			0.180361
$261$		0			0
$262$	21.5200	−	37.2738i	1.32951	−	2.30278i
$263$	−8.08761			−0.498703			−0.249352	−	0.968413i	$-0.580217\pi$
$263$	−8.08761			−0.498703			−0.249352	+	0.968413i	$0.580217\pi$
$264$		0			0
$265$	−4.86938	+	8.43401i	−0.299124	+	0.518097i
$266$	16.3155	−	11.7126i	1.00037	−	0.718146i
$267$		0			0
$268$	17.2255	−	29.8354i	1.05221	−	1.82249i
$269$	2.38892	−	4.13774i	0.145655	−	0.252282i	−0.783962	−	0.620809i	$-0.786804\pi$
$269$	2.38892	−	4.13774i	0.145655	−	0.252282i	0.929617	+	0.368527i	$0.120138\pi$
$270$		0			0
$271$	0.249128	+	0.431503i	0.0151335	+	0.0262119i	0.873493	−	0.486837i	$-0.161849\pi$
$271$	0.249128	+	0.431503i	0.0151335	+	0.0262119i	−0.858359	+	0.513049i	$0.828516\pi$
$272$	−6.20177	−	10.7418i	−0.376037	−	0.651316i
$273$		0			0
$274$	14.6651	−	25.4007i	0.885951	−	1.53451i
$275$	−2.52066			−0.152002
$276$		0			0
$277$	−27.8993			−1.67630			−0.838152	−	0.545437i	$-0.816364\pi$
$277$	−27.8993			−1.67630			−0.838152	+	0.545437i	$0.816364\pi$
$278$	−11.6210	−	20.1281i	−0.696981	−	1.20721i
$279$		0			0
$280$	−3.16586	+	2.27271i	−0.189196	+	0.135820i
$281$	2.67023	+	4.62498i	0.159293	+	0.275903i	0.934614	−	0.355664i	$-0.115745\pi$
$281$	2.67023	+	4.62498i	0.159293	+	0.275903i	−0.775321	+	0.631567i	$0.782412\pi$
$282$		0			0
$283$	15.8455	+	27.4453i	0.941920	+	1.63145i	0.761804	+	0.647808i	$0.224314\pi$
$283$	15.8455	+	27.4453i	0.941920	+	1.63145i	0.180116	+	0.983645i	$0.442353\pi$
$284$	14.7088	+	25.4765i	0.872809	+	1.51175i
$285$		0			0
$286$	−2.95806	−	5.12352i	−0.174914	−	0.302960i
$287$	1.38904	+	13.9811i	0.0819926	+	0.825276i
$288$		0			0
$289$	−7.76359	−	13.4469i	−0.456682	−	0.790996i
$290$	−20.0752			−1.17886
$291$		0			0
$292$	0.578406			0.0338486
$293$	2.45898	−	4.25908i	0.143655	−	0.248818i	−0.785215	−	0.619223i	$-0.787448\pi$
$293$	2.45898	−	4.25908i	0.143655	−	0.248818i	0.928870	+	0.370405i	$0.120781\pi$
$294$		0			0
$295$	−1.68373	−	2.91631i	−0.0980307	−	0.169794i
$296$	−1.68592	−	2.92010i	−0.0979920	−	0.169727i
$297$		0			0
$298$	12.9609	−	22.4489i	0.750803	−	1.30043i
$299$	−0.148246	+	0.256770i	−0.00857329	+	0.0148494i
$300$		0			0
$301$	15.1646	+	6.85543i	0.874073	+	0.395140i
$302$	6.23506	−	10.7994i	0.358788	−	0.621438i
$303$		0			0
$304$	7.63080			0.437657
$305$	−2.47366	+	4.28451i	−0.141642	+	0.245330i
$306$		0			0
$307$	−13.9386			−0.795519			−0.397760	−	0.917490i	$-0.630212\pi$
$307$	−13.9386			−0.795519			−0.397760	+	0.917490i	$0.630212\pi$
$308$	16.2912	+	7.36474i	0.928279	+	0.419645i
$309$		0			0
$310$	3.82546			0.217272
$311$	1.34331	+	2.32668i	0.0761722	+	0.131934i	0.901595	−	0.432580i	$-0.142397\pi$
$311$	1.34331	+	2.32668i	0.0761722	+	0.131934i	−0.825423	+	0.564514i	$0.809063\pi$
$312$		0			0
$313$	0.832722	−	1.44232i	0.0470682	−	0.0815245i	−0.841531	−	0.540208i	$-0.818346\pi$
$313$	0.832722	−	1.44232i	0.0470682	−	0.0815245i	0.888600	+	0.458684i	$0.151679\pi$
$314$	24.1012			1.36011
$315$		0			0
$316$	−10.4647			−0.588684
$317$	−14.4913	+	25.0996i	−0.813910	+	1.40973i	0.0961980	+	0.995362i	$0.469332\pi$
$317$	−14.4913	+	25.0996i	−0.813910	+	1.40973i	−0.910108	+	0.414371i	$0.864002\pi$
$318$		0			0
$319$	11.6946	+	20.2556i	0.654769	+	1.13409i
$320$	−12.2040			−0.682224
$321$		0			0
$322$	−0.154670	−	1.55679i	−0.00861940	−	0.0867565i
$323$	20.0111			1.11345
$324$		0			0
$325$	−0.542414	+	0.939489i	−0.0300877	+	0.0521135i
$326$	−2.75449			−0.152557
$327$		0			0
$328$	3.91105	−	6.77414i	0.215952	−	0.374039i
$329$	−1.22522	−	12.3321i	−0.0675486	−	0.679893i
$330$		0			0
$331$	12.5999	−	21.8237i	0.692555	−	1.19954i	−0.278443	−	0.960453i	$-0.589818\pi$
$331$	12.5999	−	21.8237i	0.692555	−	1.19954i	0.970998	−	0.239088i	$-0.0768485\pi$
$332$	−13.8889	+	24.0562i	−0.762250	+	1.32026i
$333$		0			0
$334$	−1.02261	−	1.77121i	−0.0559547	−	0.0969164i
$335$	6.42542	+	11.1292i	0.351058	+	0.608051i
$336$		0			0
$337$	−8.11842	+	14.0615i	−0.442238	+	0.765979i	−0.997855	−	0.0654591i	$-0.979149\pi$
$337$	−8.11842	+	14.0615i	−0.442238	+	0.765979i	0.555617	+	0.831438i	$0.312482\pi$
$338$	25.5796			1.39135
$339$		0			0
$340$	−15.2895			−0.829188
$341$	−2.22847	−	3.85983i	−0.120679	−	0.209021i
$342$		0			0
$343$	−5.42143	−	17.7090i	−0.292730	−	0.956195i
$344$	−4.63266	−	8.02400i	−0.249776	−	0.432625i
$345$		0			0
$346$	7.61644	+	13.1921i	0.409462	+	0.709209i
$347$	5.16058	+	8.93839i	0.277035	+	0.479838i	0.970646	−	0.240511i	$-0.0773150\pi$
$347$	5.16058	+	8.93839i	0.277035	+	0.479838i	−0.693612	+	0.720349i	$0.743982\pi$
$348$		0			0
$349$	1.88276	+	3.26103i	0.100782	+	0.174559i	0.912007	−	0.410175i	$-0.134532\pi$
$349$	1.88276	+	3.26103i	0.100782	+	0.174559i	−0.811225	+	0.584734i	$0.801199\pi$
$350$	−0.565917	−	5.69610i	−0.0302495	−	0.304469i
$351$		0			0
$352$	9.64310	+	16.7023i	0.513979	+	0.890238i
$353$	−14.9957			−0.798140			−0.399070	−	0.916921i	$-0.630667\pi$
$353$	−14.9957			−0.798140			−0.399070	+	0.916921i	$0.630667\pi$
$354$		0			0
$355$	−10.9734			−0.582405
$356$	18.1802	−	31.4891i	0.963551	−	1.66892i
$357$		0			0
$358$	−8.55129	−	14.8113i	−0.451950	−	0.782800i
$359$	3.80747	+	6.59474i	0.200951	+	0.348057i	0.948835	−	0.315772i	$-0.102264\pi$
$359$	3.80747	+	6.59474i	0.200951	+	0.348057i	−0.747884	+	0.663829i	$0.768930\pi$
$360$		0			0
$361$	3.34447	−	5.79279i	0.176025	−	0.304883i
$362$	14.2810	−	24.7354i	0.750592	−	1.30006i
$363$		0			0
$364$	6.25061	−	4.48719i	0.327621	−	0.235192i
$365$	−0.107878	+	0.186850i	−0.00564660	+	0.00978020i
$366$		0			0
$367$	−10.1947			−0.532160			−0.266080	−	0.963951i	$-0.585728\pi$
$367$	−10.1947			−0.532160			−0.266080	+	0.963951i	$0.585728\pi$
$368$	0.297197	−	0.514761i	0.0154925	−	0.0268338i
$369$		0			0
$370$	4.95255			0.257471
$371$	2.54739	+	25.6401i	0.132254	+	1.33117i
$372$		0			0
$373$	−20.1884			−1.04531			−0.522657	−	0.852543i	$-0.675059\pi$
$373$	−20.1884			−1.04531			−0.522657	+	0.852543i	$0.675059\pi$
$374$	15.5514	+	26.9358i	0.804144	+	1.39282i
$375$		0			0
$376$	−3.44978	+	5.97520i	−0.177909	+	0.308147i
$377$	10.0661			0.518428
$378$		0			0
$379$	−15.9413			−0.818852			−0.409426	−	0.912343i	$-0.634271\pi$
$379$	−15.9413			−0.818852			−0.409426	+	0.912343i	$0.634271\pi$
$380$	4.70313	−	8.14606i	0.241265	−	0.417884i
$381$		0			0
$382$	7.50048	+	12.9912i	0.383758	+	0.664688i
$383$	29.6997			1.51758			0.758792	−	0.651333i	$-0.225790\pi$
$383$	29.6997			1.51758			0.758792	+	0.651333i	$0.225790\pi$
$384$		0			0
$385$	−5.41761	+	3.88919i	−0.276107	+	0.198212i
$386$	−21.2875			−1.08350
$387$		0			0
$388$	−18.5291	+	32.0934i	−0.940673	+	1.62929i
$389$	−0.947100			−0.0480199			−0.0240099	−	0.999712i	$-0.507643\pi$
$389$	−0.947100			−0.0480199			−0.0240099	+	0.999712i	$0.507643\pi$
$390$		0			0
$391$	0.779373	−	1.34991i	0.0394146	−	0.0682681i
$392$	−3.29769	+	9.76935i	−0.166559	+	0.493427i
$393$		0			0
$394$	−5.32851	+	9.22925i	−0.268446	+	0.464963i
$395$	1.95176	−	3.38055i	0.0982038	−	0.170094i
$396$		0			0
$397$	5.41011	+	9.37059i	0.271526	+	0.470297i	0.969253	−	0.246067i	$-0.0791384\pi$
$397$	5.41011	+	9.37059i	0.271526	+	0.470297i	−0.697727	+	0.716364i	$0.745805\pi$
$398$	−6.41302	−	11.1077i	−0.321456	−	0.556777i
$399$		0			0
$400$	1.08741	−	1.88345i	0.0543704	−	0.0941723i
$401$	3.26387			0.162990			0.0814950	−	0.996674i	$-0.474031\pi$
$401$	3.26387			0.162990			0.0814950	+	0.996674i	$0.474031\pi$
$402$		0			0
$403$	−1.91815			−0.0955500
$404$	−13.7910	−	23.8867i	−0.686128	−	1.18841i
$405$		0			0
$406$	−43.1471	+	30.9745i	−2.14136	+	1.53724i
$407$	−2.88504	−	4.99704i	−0.143006	−	0.247694i
$408$		0			0
$409$	−16.4987	−	28.5765i	−0.815807	−	1.41302i	−0.908747	−	0.417348i	$-0.862960\pi$
$409$	−16.4987	−	28.5765i	−0.815807	−	1.41302i	0.0929397	−	0.995672i	$-0.470374\pi$
$410$	5.74454	+	9.94984i	0.283703	+	0.491388i
$411$		0			0
$412$	−24.6229	−	42.6482i	−1.21309	−	2.10113i
$413$	−8.11845	−	3.67009i	−0.399483	−	0.180593i
$414$		0			0
$415$	−5.18081	−	8.97342i	−0.254316	−	0.440488i
$416$	8.30028			0.406955
$417$		0			0
$418$	−19.1348			−0.935915
$419$	−17.0245	+	29.4874i	−0.831703	+	1.44055i	0.0649832	+	0.997886i	$0.479301\pi$
$419$	−17.0245	+	29.4874i	−0.831703	+	1.44055i	−0.896687	+	0.442666i	$0.854033\pi$
$420$		0			0
$421$	8.49807	+	14.7191i	0.414171	+	0.717364i	0.995341	−	0.0964175i	$-0.0307384\pi$
$421$	8.49807	+	14.7191i	0.414171	+	0.717364i	−0.581170	+	0.813782i	$0.697405\pi$
$422$	−3.39771	−	5.88500i	−0.165398	−	0.286478i
$423$		0			0
$424$	7.17254	−	12.4232i	0.348329	−	0.603324i
$425$	2.85163	−	4.93917i	0.138324	−	0.239585i
$426$		0			0
$427$	1.29408	+	13.0253i	0.0626251	+	0.630337i
$428$	19.3503	−	33.5157i	0.935331	−	1.62004i
$429$		0			0
$430$	13.6089			0.656279
$431$	1.15916	−	2.00773i	0.0558349	−	0.0967090i	−0.836757	−	0.547574i	$-0.815551\pi$
$431$	1.15916	−	2.00773i	0.0558349	−	0.0967090i	0.892592	+	0.450866i	$0.148885\pi$
$432$		0			0
$433$	−21.8516			−1.05012			−0.525062	−	0.851064i	$-0.675958\pi$
$433$	−21.8516			−1.05012			−0.525062	+	0.851064i	$0.675958\pi$
$434$	8.22197	−	5.90239i	0.394667	−	0.283324i
$435$		0			0
$436$	53.7340			2.57339
$437$	0.479480	+	0.830483i	0.0229366	+	0.0397274i
$438$		0			0
$439$	−8.39926	+	14.5479i	−0.400875	+	0.694335i	−0.993832	−	0.110899i	$-0.964627\pi$
$439$	−8.39926	+	14.5479i	−0.400875	+	0.694335i	0.592957	+	0.805234i	$0.297960\pi$
$440$	3.71291			0.177006
$441$		0			0
$442$	13.3858			0.636699
$443$	8.17378	−	14.1574i	0.388348	−	0.672639i	−0.603879	−	0.797076i	$-0.706379\pi$
$443$	8.17378	−	14.1574i	0.388348	−	0.672639i	0.992228	+	0.124437i	$0.0397125\pi$
$444$		0			0
$445$	6.78158	+	11.7460i	0.321478	+	0.556815i
$446$	−5.36756			−0.254161
$447$		0			0
$448$	−26.2298	+	18.8298i	−1.23924	+	0.889625i
$449$	−24.9939			−1.17953			−0.589767	−	0.807574i	$-0.700780\pi$
$449$	−24.9939			−1.17953			−0.589767	+	0.807574i	$0.700780\pi$
$450$		0			0
$451$	6.69282	−	11.5923i	0.315153	−	0.545860i
$452$	50.2244			2.36236
$453$		0			0
$454$	−28.6886	+	49.6901i	−1.34642	+	2.33207i
$455$	0.283761	+	2.85612i	0.0133029	+	0.133897i
$456$		0			0
$457$	2.47421	−	4.28546i	0.115739	−	0.200465i	−0.802336	−	0.596873i	$-0.796410\pi$
$457$	2.47421	−	4.28546i	0.115739	−	0.200465i	0.918075	+	0.396407i	$0.129743\pi$
$458$	−22.1349	+	38.3387i	−1.03429	+	1.79145i
$459$		0			0
$460$	−0.366346	−	0.634530i	−0.0170810	−	0.0295851i
$461$	−6.77101	−	11.7277i	−0.315358	−	0.546215i	0.664156	−	0.747594i	$-0.268791\pi$
$461$	−6.77101	−	11.7277i	−0.315358	−	0.546215i	−0.979513	+	0.201379i	$0.935458\pi$
$462$		0			0
$463$	14.7612	−	25.5672i	0.686012	−	1.18821i	−0.287106	−	0.957899i	$-0.592693\pi$
$463$	14.7612	−	25.5672i	0.686012	−	1.18821i	0.973118	−	0.230308i	$-0.0739734\pi$
$464$	−20.1800			−0.936832
$465$		0			0
$466$	−44.8429			−2.07731
$467$	−5.21574	−	9.03393i	−0.241356	−	0.418040i	0.719745	−	0.694239i	$-0.244259\pi$
$467$	−5.21574	−	9.03393i	−0.241356	−	0.418040i	−0.961101	+	0.276198i	$0.910925\pi$
$468$		0			0
$469$	30.9814	+	14.0057i	1.43059	+	0.646723i
$470$	−5.06704	−	8.77636i	−0.233725	−	0.404824i
$471$		0			0
$472$	2.48012	+	4.29569i	0.114157	+	0.197725i
$473$	−7.92768	−	13.7312i	−0.364515	−	0.631359i
$474$		0			0
$475$	1.75436	+	3.03863i	0.0804954	+	0.139422i
$476$	−32.8613	+	23.5905i	−1.50619	+	1.08127i
$477$		0			0
$478$	−4.07732	−	7.06212i	−0.186492	−	0.323014i
$479$	−30.2584			−1.38254			−0.691270	−	0.722597i	$-0.742948\pi$
$479$	−30.2584			−1.38254			−0.691270	+	0.722597i	$0.742948\pi$
$480$		0			0
$481$	−2.48329			−0.113228
$482$	7.77687	−	13.4699i	0.354227	−	0.613538i
$483$		0			0
$484$	6.22790	+	10.7870i	0.283086	+	0.490320i
$485$	−6.91171	−	11.9714i	−0.313845	−	0.543595i
$486$		0			0
$487$	6.50566	−	11.2681i	0.294799	−	0.510608i	−0.680139	−	0.733083i	$-0.738080\pi$
$487$	6.50566	−	11.2681i	0.294799	−	0.510608i	0.974938	+	0.222476i	$0.0714138\pi$
$488$	3.64368	−	6.31103i	0.164941	−	0.285687i
$489$		0			0
$490$	−10.0050	−	11.3693i	−0.451978	−	0.513614i
$491$	−4.60953	+	7.98393i	−0.208025	+	0.360310i	−0.951092	−	0.308907i	$-0.900037\pi$
$491$	−4.60953	+	7.98393i	−0.208025	+	0.360310i	0.743067	+	0.669217i	$0.233370\pi$
$492$		0			0
$493$	−52.9202			−2.38341
$494$	−4.11756	+	7.13183i	−0.185258	+	0.320876i
$495$		0			0
$496$	3.84543			0.172665
$497$	−23.5848	+	16.9310i	−1.05792	+	0.759461i
$498$		0			0
$499$	22.3488			1.00047			0.500235	−	0.865890i	$-0.333247\pi$
$499$	22.3488			1.00047			0.500235	+	0.865890i	$0.333247\pi$
$500$	−1.34041	−	2.32167i	−0.0599452	−	0.103828i
$501$		0			0
$502$	13.4027	−	23.2142i	0.598192	−	1.03610i
$503$	16.6128			0.740728			0.370364	−	0.928887i	$-0.379233\pi$
$503$	16.6128			0.740728			0.370364	+	0.928887i	$0.379233\pi$
$504$		0			0
$505$	10.2886			0.457837
$506$	−0.745245	+	1.29080i	−0.0331302	+	0.0573831i
$507$		0			0
$508$	14.2679	+	24.7128i	0.633037	+	1.09645i
$509$	16.2874			0.721928			0.360964	−	0.932580i	$-0.382448\pi$
$509$	16.2874			0.721928			0.360964	+	0.932580i	$0.382448\pi$
$510$		0			0
$511$	0.0564358	+	0.568041i	0.00249657	+	0.0251286i
$512$	−23.0470			−1.01854
$513$		0			0
$514$	−26.4943	+	45.8895i	−1.16862	+	2.02410i
$515$	18.3697			0.809464
$516$		0			0
$517$	−5.90348	+	10.2251i	−0.259635	+	0.449700i
$518$	10.6444	−	7.64140i	0.467688	−	0.335744i
$519$		0			0
$520$	0.798969	−	1.38386i	0.0350371	−	0.0606861i
$521$	8.40287	−	14.5542i	0.368136	−	0.637631i	−0.621138	−	0.783701i	$-0.713329\pi$
$521$	8.40287	−	14.5542i	0.368136	−	0.637631i	0.989274	+	0.146071i	$0.0466627\pi$
$522$		0			0
$523$	4.58284	+	7.93771i	0.200394	+	0.347092i	0.948655	−	0.316312i	$-0.102445\pi$
$523$	4.58284	+	7.93771i	0.200394	+	0.347092i	−0.748262	+	0.663404i	$0.769111\pi$
$524$	−26.6655	−	46.1861i	−1.16489	−	2.01765i
$525$		0			0
$526$	−8.74886	+	15.1535i	−0.381468	+	0.660723i
$527$	10.0843			0.439279
$528$		0			0
$529$	−22.9253			−0.996752
$530$	10.5350	+	18.2472i	0.457612	+	0.792607i
$531$		0			0
$532$	−2.46041	−	24.7647i	−0.106673	−	1.07369i
$533$	−2.88041	−	4.98902i	−0.124765	−	0.216099i
$534$		0			0
$535$	7.21802	+	12.5020i	0.312062	+	0.540508i
$536$	−9.46457	−	16.3931i	−0.408807	−	0.708075i
$537$		0			0
$538$	−5.16849	−	8.95209i	−0.222829	−	0.385952i
$539$	−5.64321	+	16.7179i	−0.243070	+	0.720091i
$540$		0			0
$541$	−11.0257	−	19.0970i	−0.474030	−	0.821044i	0.525528	−	0.850776i	$-0.323868\pi$
$541$	−11.0257	−	19.0970i	−0.474030	−	0.821044i	−0.999558	+	0.0297324i	$0.990534\pi$
$542$	1.07799			0.0463036
$543$		0			0
$544$	−43.6370			−1.87092
$545$	−10.0219	+	17.3584i	−0.429291	+	0.743554i
$546$		0			0
$547$	1.95281	+	3.38236i	0.0834960	+	0.144619i	0.904749	−	0.425944i	$-0.140058\pi$
$547$	1.95281	+	3.38236i	0.0834960	+	0.144619i	−0.821253	+	0.570564i	$0.806725\pi$
$548$	−18.1716	−	31.4741i	−0.776251	−	1.34451i
$549$		0			0
$550$	−2.72676	+	4.72288i	−0.116269	+	0.201384i
$551$	16.2786	−	28.1953i	0.693490	−	1.20116i
$552$		0			0
$553$	−1.02105	−	10.2772i	−0.0434196	−	0.437029i
$554$	−30.1803	+	52.2739i	−1.28224	+	2.22090i
$555$		0			0
$556$	−28.7992			−1.22136
$557$	−0.621333	+	1.07618i	−0.0263267	+	0.0455992i	−0.878889	−	0.477027i	$-0.841714\pi$
$557$	−0.621333	+	1.07618i	−0.0263267	+	0.0455992i	0.852562	+	0.522626i	$0.175048\pi$
$558$		0			0
$559$	−6.82373			−0.288613
$560$	−0.568871	−	5.72583i	−0.0240392	−	0.241960i
$561$		0			0
$562$	11.5542			0.487385
$563$	2.06788	+	3.58167i	0.0871506	+	0.150949i	0.906306	−	0.422623i	$-0.138891\pi$
$563$	2.06788	+	3.58167i	0.0871506	+	0.150949i	−0.819155	+	0.573572i	$0.805557\pi$
$564$		0			0
$565$	−9.36733	+	16.2247i	−0.394086	+	0.682578i
$566$	68.5644			2.88198
$567$		0			0
$568$	16.1636			0.678210
$569$	−5.64630	+	9.77967i	−0.236705	+	0.409985i	−0.959767	−	0.280798i	$-0.909401\pi$
$569$	−5.64630	+	9.77967i	−0.236705	+	0.409985i	0.723062	+	0.690783i	$0.242734\pi$
$570$		0			0
$571$	−20.6379	−	35.7459i	−0.863670	−	1.49592i	−0.868361	−	0.495932i	$-0.834827\pi$
$571$	−20.6379	−	35.7459i	−0.863670	−	1.49592i	0.00469093	−	0.999989i	$-0.498507\pi$
$572$	−7.33069			−0.306512
$573$		0			0
$574$	27.6984	+	12.5216i	1.15611	+	0.522640i
$575$	0.273308			0.0113977
$576$		0			0
$577$	4.01893	−	6.96099i	0.167310	−	0.289790i	−0.770163	−	0.637847i	$-0.779825\pi$
$577$	4.01893	−	6.96099i	0.167310	−	0.289790i	0.937473	+	0.348057i	$0.113159\pi$
$578$	−33.5934			−1.39730
$579$		0			0
$580$	−12.4376	+	21.5426i	−0.516444	+	0.894508i
$581$	−24.9803	−	11.2928i	−1.03636	−	0.468503i
$582$		0			0
$583$	12.2741	−	21.2593i	0.508340	−	0.880471i
$584$	0.158903	−	0.275228i	0.00657546	−	0.0113890i
$585$		0			0
$586$	−5.32006	−	9.21462i	−0.219770	−	0.380652i
$587$	9.64751	+	16.7100i	0.398195	+	0.689695i	0.993503	−	0.113803i	$-0.0363033\pi$
$587$	9.64751	+	16.7100i	0.398195	+	0.689695i	−0.595308	+	0.803498i	$0.702970\pi$
$588$		0			0
$589$	−3.10199	+	5.37280i	−0.127815	+	0.221382i
$590$	−7.28559			−0.299943
$591$		0			0
$592$	4.97840			0.204611
$593$	14.8846	+	25.7809i	0.611237	+	1.05869i	0.991032	+	0.133623i	$0.0426613\pi$
$593$	14.8846	+	25.7809i	0.611237	+	1.05869i	−0.379795	+	0.925071i	$0.624005\pi$
$594$		0			0
$595$	−1.49181	−	15.0155i	−0.0611584	−	0.615575i
$596$	−16.0599	−	27.8165i	−0.657837	−	1.13941i
$597$		0			0
$598$	0.320734	+	0.555527i	0.0131158	+	0.0227172i
$599$	5.02705	+	8.70711i	0.205400	+	0.355763i	0.950260	−	0.311458i	$-0.100817\pi$
$599$	5.02705	+	8.70711i	0.205400	+	0.355763i	−0.744860	+	0.667220i	$0.767484\pi$
$600$		0			0
$601$	4.59732	+	7.96278i	0.187528	+	0.324809i	0.944426	−	0.328725i	$-0.106619\pi$
$601$	4.59732	+	7.96278i	0.187528	+	0.324809i	−0.756897	+	0.653534i	$0.773286\pi$
$602$	29.2493	−	20.9975i	1.19211	−	0.855793i
$603$		0			0
$604$	−7.72589	−	13.3816i	−0.314362	−	0.544491i
$605$	−4.64625			−0.188897
$606$		0			0
$607$	−0.368646			−0.0149629			−0.00748145	−	0.999972i	$-0.502381\pi$
$607$	−0.368646			−0.0149629			−0.00748145	+	0.999972i	$0.502381\pi$
$608$	13.4230	−	23.2493i	0.544374	−	0.942884i
$609$		0			0
$610$	5.35183	+	9.26963i	0.216689	+	0.375317i
$611$	2.54070	+	4.40062i	0.102786	+	0.178030i
$612$		0			0
$613$	7.89766	−	13.6791i	0.318983	−	0.552496i	−0.661293	−	0.750128i	$-0.729992\pi$
$613$	7.89766	−	13.6791i	0.318983	−	0.552496i	0.980276	+	0.197632i	$0.0633252\pi$
$614$	−15.0783	+	26.1163i	−0.608509	+	1.05397i
$615$		0			0
$616$	7.98007	−	5.72873i	0.321526	−	0.230817i
$617$	6.94086	−	12.0219i	0.279428	−	0.483984i	−0.691814	−	0.722075i	$-0.743188\pi$
$617$	6.94086	−	12.0219i	0.279428	−	0.483984i	0.971243	+	0.238091i	$0.0765217\pi$
$618$		0			0
$619$	2.56086			0.102930			0.0514648	−	0.998675i	$-0.483611\pi$
$619$	2.56086			0.102930			0.0514648	+	0.998675i	$0.483611\pi$
$620$	2.37007	−	4.10508i	0.0951843	−	0.164864i
$621$		0			0
$622$	5.81257			0.233063
$623$	32.6987	+	14.7820i	1.31005	+	0.592229i
$624$		0			0
$625$	1.00000			0.0400000
$626$	−1.80161	−	3.12048i	−0.0720069	−	0.124720i
$627$		0			0
$628$	14.9320	−	25.8629i	0.595850	−	1.03204i
$629$	13.0554			0.520553
$630$		0			0
$631$	−42.1192			−1.67674			−0.838370	−	0.545102i	$-0.816491\pi$
$631$	−42.1192			−1.67674			−0.838370	+	0.545102i	$0.816491\pi$
$632$	−2.87492	+	4.97951i	−0.114358	+	0.198074i
$633$		0			0
$634$	31.3522	+	54.3035i	1.24515	+	2.15667i
$635$	−10.6444			−0.422411
$636$		0			0
$637$	5.01666	+	5.70078i	0.198767	+	0.225873i
$638$	50.6028			2.00339
$639$		0			0
$640$	−5.55057	+	9.61386i	−0.219405	+	0.380021i
$641$	26.7464			1.05642			0.528209	−	0.849114i	$-0.322864\pi$
$641$	26.7464			1.05642			0.528209	+	0.849114i	$0.322864\pi$
$642$		0			0
$643$	21.5988	−	37.4102i	0.851773	−	1.47531i	−0.0278342	−	0.999613i	$-0.508861\pi$
$643$	21.5988	−	37.4102i	0.851773	−	1.47531i	0.879607	−	0.475701i	$-0.157806\pi$
$644$	−1.76641	−	0.798537i	−0.0696063	−	0.0314667i
$645$		0			0
$646$	21.6472	−	37.4941i	0.851699	−	1.47519i
$647$	11.1554	−	19.3217i	0.438564	−	0.759616i	−0.559015	−	0.829158i	$-0.688820\pi$
$647$	11.1554	−	19.3217i	0.438564	−	0.759616i	0.997579	+	0.0695419i	$0.0221538\pi$
$648$		0			0
$649$	4.24413	+	7.35104i	0.166597	+	0.288554i
$650$	1.17352	+	2.03260i	0.0460294	+	0.0797253i
$651$		0			0
$652$	−1.70655	+	2.95583i	−0.0668336	+	0.115759i
$653$	−22.1446			−0.866584			−0.433292	−	0.901254i	$-0.642648\pi$
$653$	−22.1446			−0.866584			−0.433292	+	0.901254i	$0.642648\pi$
$654$		0			0
$655$	19.8935			0.777303
$656$	5.77453	+	10.0018i	0.225457	+	0.390504i
$657$		0			0
$658$	−24.4317	−	11.0448i	−0.952447	−	0.430571i
$659$	−19.3173	−	33.4585i	−0.752494	−	1.30336i	−0.946610	−	0.322380i	$-0.895517\pi$
$659$	−19.3173	−	33.4585i	−0.752494	−	1.30336i	0.194116	−	0.980979i	$-0.437816\pi$
$660$		0			0
$661$	−23.2242	−	40.2255i	−0.903318	−	1.56459i	−0.823159	−	0.567810i	$-0.807791\pi$
$661$	−23.2242	−	40.2255i	−0.903318	−	1.56459i	−0.0801584	−	0.996782i	$-0.525543\pi$
$662$	−27.2602	−	47.2161i	−1.05950	−	1.83511i
$663$		0			0
$664$	7.63126	+	13.2177i	0.296150	+	0.512948i
$665$	8.45898	+	3.82403i	0.328025	+	0.148289i
$666$		0			0
$667$	−1.26800	−	2.19625i	−0.0490973	−	0.0850391i
$668$	−2.53424			−0.0980527
$669$		0			0
$670$	27.8031			1.07413
$671$	6.23528	−	10.7998i	0.240710	−	0.416922i
$672$		0			0
$673$	−13.5441	−	23.4590i	−0.522086	−	0.904280i	−0.999670	−	0.0256936i	$-0.991821\pi$
$673$	−13.5441	−	23.4590i	−0.522086	−	0.904280i	0.477584	−	0.878586i	$-0.341513\pi$
$674$	17.5644	+	30.4224i	0.676555	+	1.17183i
$675$		0			0
$676$	15.8479	−	27.4494i	0.609535	−	1.05575i
$677$	11.8568	−	20.5365i	0.455693	−	0.789283i	−0.543035	−	0.839710i	$-0.682725\pi$
$677$	11.8568	−	20.5365i	0.455693	−	0.789283i	0.998728	+	0.0504268i	$0.0160582\pi$
$678$		0			0
$679$	−33.3262	−	15.0657i	−1.27894	−	0.578168i
$680$	−4.20042	+	7.27533i	−0.161079	+	0.278996i
$681$		0			0
$682$	−9.64270			−0.369238
$683$	−11.9778	+	20.7462i	−0.458319	+	0.793831i	−0.998872	−	0.0474784i	$-0.984881\pi$
$683$	−11.9778	+	20.7462i	−0.458319	+	0.793831i	0.540554	+	0.841310i	$0.318215\pi$
$684$		0			0
$685$	13.5567			0.517974
$686$	−39.0454	−	8.99895i	−1.49076	−	0.343582i
$687$		0			0
$688$	13.6799			0.521542
$689$	−5.28244	−	9.14945i	−0.201245	−	0.348566i
$690$		0			0
$691$	5.46854	−	9.47179i	0.208033	−	0.360324i	−0.743062	−	0.669223i	$-0.766627\pi$
$691$	5.46854	−	9.47179i	0.208033	−	0.360324i	0.951095	+	0.308899i	$0.0999605\pi$
$692$	18.8751			0.717524
$693$		0			0
$694$	22.3301			0.847638
$695$	5.37133	−	9.30342i	0.203746	−	0.352899i
$696$		0			0
$697$	15.1432	+	26.2288i	0.573589	+	0.993485i
$698$	8.14678			0.308360
$699$		0			0
$700$	−6.46307	−	2.92175i	−0.244281	−	0.110432i
$701$	−39.4789			−1.49110			−0.745550	−	0.666450i	$-0.767813\pi$
$701$	−39.4789			−1.49110			−0.745550	+	0.666450i	$0.767813\pi$
$702$		0			0
$703$	−4.01592	+	6.95578i	−0.151463	+	0.262342i
$704$	30.7622			1.15939
$705$		0			0
$706$	−16.2217	+	28.0969i	−0.610513	+	1.05744i
$707$	22.1131	−	15.8745i	0.831648	−	0.597024i
$708$		0			0
$709$	3.91439	−	6.77992i	0.147008	−	0.254625i	−0.783112	−	0.621880i	$-0.786369\pi$
$709$	3.91439	−	6.77992i	0.147008	−	0.254625i	0.930120	+	0.367255i	$0.119702\pi$
$710$	−11.8705	+	20.5604i	−0.445494	+	0.771618i
$711$		0			0
$712$	−9.98918	−	17.3018i	−0.374360	−	0.648411i
$713$	0.241627	+	0.418509i	0.00904899	+	0.0156733i
$714$		0			0
$715$	1.36724	−	2.36814i	0.0511320	−	0.0885633i
$716$	−21.1919			−0.791977
$717$		0			0
$718$	16.4751			0.614845
$719$	−10.3821	−	17.9824i	−0.387188	−	0.670629i	0.604882	−	0.796315i	$-0.293220\pi$
$719$	−10.3821	−	17.9824i	−0.387188	−	0.670629i	−0.992070	+	0.125686i	$0.959887\pi$
$720$		0			0
$721$	39.4815	−	28.3430i	1.47037	−	1.05555i
$722$	−7.23583	−	12.5328i	−0.269290	−	0.466423i
$723$		0			0
$724$	−17.6956	−	30.6497i	−0.657653	−	1.13909i
$725$	−4.63947	−	8.03580i	−0.172306	−	0.298442i
$726$		0			0
$727$	16.9614	+	29.3780i	0.629063	+	1.08957i	0.987740	+	0.156108i	$0.0498947\pi$
$727$	16.9614	+	29.3780i	0.629063	+	1.08957i	−0.358677	+	0.933462i	$0.616772\pi$
$728$	−0.417976	−	4.20704i	−0.0154912	−	0.155923i
$729$		0			0
$730$	0.233397	+	0.404255i	0.00863840	+	0.0149622i
$731$	35.8744			1.32686
$732$		0			0
$733$	48.3519			1.78592			0.892960	−	0.450136i	$-0.148625\pi$
$733$	48.3519			1.78592			0.892960	+	0.450136i	$0.148625\pi$
$734$	−11.0282	+	19.1015i	−0.407060	+	0.705048i
$735$		0			0
$736$	−1.04557	−	1.81098i	−0.0385403	−	0.0667538i
$737$	−16.1963	−	28.0529i	−0.596600	−	1.03334i
$738$		0			0
$739$	20.2749	−	35.1172i	0.745825	−	1.29181i	−0.203983	−	0.978974i	$-0.565389\pi$
$739$	20.2749	−	35.1172i	0.745825	−	1.29181i	0.949808	−	0.312832i	$-0.101278\pi$
$740$	3.06836	−	5.31456i	0.112795	−	0.195367i
$741$		0			0
$742$	50.7966	+	22.9635i	1.86480	+	0.843017i
$743$	10.6501	−	18.4465i	0.390714	−	0.676736i	−0.601830	−	0.798624i	$-0.705562\pi$
$743$	10.6501	−	18.4465i	0.390714	−	0.676736i	0.992544	+	0.121888i	$0.0388948\pi$
$744$		0			0
$745$	11.9813			0.438960
$746$	−21.8390	+	37.8262i	−0.799582	+	1.38492i
$747$		0			0
$748$	38.5396			1.40915
$749$	34.8031	+	15.7334i	1.27168	+	0.574885i
$750$		0			0
$751$	28.8893			1.05418			0.527092	−	0.849808i	$-0.323282\pi$
$751$	28.8893			1.05418			0.527092	+	0.849808i	$0.323282\pi$
$752$	−5.09348	−	8.82217i	−0.185740	−	0.321712i
$753$		0			0
$754$	10.8891	−	18.8604i	0.396556	−	0.686856i
$755$	5.76381			0.209766
$756$		0			0
$757$	−42.7548			−1.55395			−0.776975	−	0.629531i	$-0.783247\pi$
$757$	−42.7548			−1.55395			−0.776975	+	0.629531i	$0.783247\pi$
$758$	−17.2447	+	29.8687i	−0.626357	+	1.08488i
$759$		0			0
$760$	−2.58415	−	4.47587i	−0.0937368	−	0.162357i
$761$	−16.8231			−0.609837			−0.304918	−	0.952379i	$-0.598629\pi$
$761$	−16.8231			−0.609837			−0.304918	+	0.952379i	$0.598629\pi$
$762$		0			0
$763$	5.24290	+	52.7711i	0.189806	+	1.91044i
$764$	18.5878			0.672481
$765$		0			0
$766$	32.1280	−	55.6473i	1.16083	−	2.01062i
$767$	3.65312			0.131907
$768$		0			0
$769$	10.7497	−	18.6190i	0.387643	−	0.671417i	−0.604489	−	0.796613i	$-0.706623\pi$
$769$	10.7497	−	18.6190i	0.387643	−	0.671417i	0.992132	+	0.125197i	$0.0399561\pi$
$770$	1.42649	+	14.3580i	0.0514070	+	0.517425i
$771$		0			0
$772$	−13.1887	+	22.8435i	−0.474671	+	0.822155i
$773$	−2.71661	+	4.70531i	−0.0977098	+	0.169238i	−0.910736	−	0.412988i	$-0.864485\pi$
$773$	−2.71661	+	4.70531i	−0.0977098	+	0.169238i	0.813027	+	0.582227i	$0.197818\pi$
$774$		0			0
$775$	0.884081	+	1.53127i	0.0317571	+	0.0550050i
$776$	10.1809	+	17.6338i	0.365472	+	0.633016i
$777$		0			0
$778$	−1.02454	+	1.77455i	−0.0367314	+	0.0636207i
$779$	−18.6325			−0.667580
$780$		0			0
$781$	27.6601			0.989758
$782$	−1.68619	−	2.92057i	−0.0602981	−	0.104439i
$783$		0			0
$784$	−10.0572	−	11.4287i	−0.359185	−	0.408167i
$785$	5.56990	+	9.64735i	0.198798	+	0.344329i
$786$		0			0
$787$	−13.2465	−	22.9436i	−0.472187	−	0.817852i	0.527307	−	0.849675i	$-0.323202\pi$
$787$	−13.2465	−	22.9436i	−0.472187	−	0.817852i	−0.999494	+	0.0318233i	$0.989869\pi$
$788$	6.60257	+	11.4360i	0.235207	+	0.407390i
$789$		0			0
$790$	−4.22268	−	7.31390i	−0.150236	−	0.260217i
$791$	4.90046	+	49.3244i	0.174240	+	1.75377i
$792$		0			0
$793$	−2.68350	−	4.64796i	−0.0952939	−	0.165054i
$794$	23.4098			0.830783
$795$		0			0
$796$	−15.8928			−0.563305
$797$	−18.9194	+	32.7694i	−0.670160	+	1.16075i	0.307698	+	0.951484i	$0.400441\pi$
$797$	−18.9194	+	32.7694i	−0.670160	+	1.16075i	−0.977858	+	0.209268i	$0.932892\pi$
$798$		0			0
$799$	−13.3572	−	23.1354i	−0.472544	−	0.818471i
$800$	−3.82562	−	6.62617i	−0.135256	−	0.234270i
$801$		0			0
$802$	3.53073	−	6.11540i	0.124674	−	0.215942i
$803$	0.271925	−	0.470987i	0.00959601	−	0.0166208i
$804$		0			0
$805$	0.587415	−	0.421693i	0.0207036	−	0.0148627i
$806$	−2.07498	+	3.59398i	−0.0730882	+	0.126592i
$807$		0			0
$808$	−15.1550			−0.533151
$809$	17.1655	−	29.7315i	0.603506	−	1.04530i	−0.388780	−	0.921331i	$-0.627103\pi$
$809$	17.1655	−	29.7315i	0.603506	−	1.04530i	0.992286	−	0.123972i	$-0.0395633\pi$
$810$		0			0
$811$	25.0033			0.877983			0.438992	−	0.898491i	$-0.355336\pi$
$811$	25.0033			0.877983			0.438992	+	0.898491i	$0.355336\pi$
$812$	6.50667	+	65.4913i	0.228339	+	2.29829i
$813$		0			0
$814$	−12.4837			−0.437554
$815$	−0.636575	−	1.10258i	−0.0222982	−	0.0386217i
$816$		0			0
$817$	−11.0352	+	19.1135i	−0.386072	+	0.668696i
$818$	−71.3905			−2.49611
$819$		0			0
$820$	14.2362			0.497149
$821$	21.8766	−	37.8914i	0.763499	−	1.32242i	−0.177537	−	0.984114i	$-0.556813\pi$
$821$	21.8766	−	37.8914i	0.763499	−	1.32242i	0.941037	−	0.338305i	$-0.109854\pi$
$822$		0			0
$823$	1.09251	+	1.89229i	0.0380826	+	0.0659610i	0.884438	−	0.466657i	$-0.154542\pi$
$823$	1.09251	+	1.89229i	0.0380826	+	0.0659610i	−0.846356	+	0.532618i	$0.821208\pi$
$824$	−27.0583			−0.942620
$825$		0			0
$826$	−15.6587	+	11.2411i	−0.544837	+	0.391128i
$827$	−30.4431			−1.05861			−0.529305	−	0.848432i	$-0.677547\pi$
$827$	−30.4431			−1.05861			−0.529305	+	0.848432i	$0.677547\pi$
$828$		0			0
$829$	−15.0073	+	25.9934i	−0.521225	+	0.902789i	0.478470	+	0.878104i	$0.341192\pi$
$829$	−15.0073	+	25.9934i	−0.521225	+	0.902789i	−0.999695	+	0.0246849i	$0.992142\pi$
$830$	−22.4176			−0.778125
$831$		0			0
$832$	6.61962	−	11.4655i	0.229494	−	0.397495i
$833$	−26.3741	−	29.9707i	−0.913807	−	1.03842i
$834$		0			0
$835$	0.472660	−	0.818671i	0.0163571	−	0.0283313i
$836$	−11.8550	+	20.5335i	−0.410014	+	0.710165i
$837$		0			0
$838$	36.8330	+	63.7966i	1.27237	+	2.20382i
$839$	2.88789	+	5.00197i	0.0997009	+	0.172687i	0.911561	−	0.411165i	$-0.134878\pi$
$839$	2.88789	+	5.00197i	0.0997009	+	0.172687i	−0.811860	+	0.583852i	$0.801545\pi$
$840$		0			0
$841$	−28.5494	+	49.4490i	−0.984461	+	1.70514i
$842$	36.7715			1.26723
$843$		0			0
$844$	−8.42023			−0.289836
$845$	5.91157	+	10.2391i	0.203364	+	0.352237i
$846$		0			0
$847$	−9.98607	+	7.16880i	−0.343125	+	0.246323i
$848$	10.5900	+	18.3424i	0.363662	+	0.629881i
$849$		0			0
$850$	−6.16956	−	10.6860i	−0.211614	−	0.366527i
$851$	0.312816	+	0.541814i	0.0107232	+	0.0185731i
$852$		0			0
$853$	22.8381	+	39.5568i	0.781962	+	1.35440i	0.930797	+	0.365536i	$0.119114\pi$
$853$	22.8381	+	39.5568i	0.781962	+	1.35440i	−0.148835	+	0.988862i	$0.547552\pi$
$854$	25.8049	+	11.6656i	0.883025	+	0.399187i
$855$		0			0
$856$	−10.6321	−	18.4153i	−0.363396	−	0.629421i
$857$	−33.7447			−1.15270			−0.576348	−	0.817204i	$-0.695523\pi$
$857$	−33.7447			−1.15270			−0.576348	+	0.817204i	$0.695523\pi$
$858$		0			0
$859$	51.2677			1.74923			0.874615	−	0.484818i	$-0.161114\pi$
$859$	51.2677			1.74923			0.874615	+	0.484818i	$0.161114\pi$
$860$	8.43141	−	14.6036i	0.287509	−	0.497980i
$861$		0			0
$862$	−2.50788	−	4.34377i	−0.0854186	−	0.147949i
$863$	−8.50532	−	14.7316i	−0.289524	−	0.501471i	0.684172	−	0.729321i	$-0.260164\pi$
$863$	−8.50532	−	14.7316i	−0.289524	−	0.501471i	−0.973696	+	0.227850i	$0.926831\pi$
$864$		0			0
$865$	−3.52039	+	6.09749i	−0.119697	+	0.207321i
$866$	−23.6383	+	40.9427i	−0.803261	+	1.39129i
$867$		0			0
$868$	−1.23989	−	12.4798i	−0.0420846	−	0.423592i
$869$	−4.91974	+	8.52124i	−0.166891	+	0.289063i
$870$		0			0
$871$	−13.9410			−0.472371
$872$	14.7621	−	25.5688i	0.499909	−	0.865868i
$873$		0			0
$874$	2.07473			0.0701788
$875$	2.14928	−	1.54292i	0.0726588	−	0.0521603i
$876$		0			0
$877$	−35.0553			−1.18373			−0.591867	−	0.806036i	$-0.701609\pi$
$877$	−35.0553			−1.18373			−0.591867	+	0.806036i	$0.701609\pi$
$878$	18.1720	+	31.4748i	0.613275	+	1.06222i
$879$		0			0
$880$	−2.74099	+	4.74753i	−0.0923988	+	0.160039i
$881$	25.6988			0.865813			0.432907	−	0.901439i	$-0.357488\pi$
$881$	25.6988			0.865813			0.432907	+	0.901439i	$0.357488\pi$
$882$		0			0
$883$	28.5262			0.959985			0.479992	−	0.877273i	$-0.340639\pi$
$883$	28.5262			0.959985			0.479992	+	0.877273i	$0.340639\pi$
$884$	8.29322	−	14.3643i	0.278931	−	0.483123i
$885$		0			0
$886$	−17.6842	−	30.6299i	−0.594111	−	1.02903i
$887$	−17.8373			−0.598919			−0.299460	−	0.954109i	$-0.596806\pi$
$887$	−17.8373			−0.598919			−0.299460	+	0.954109i	$0.596806\pi$
$888$		0			0
$889$	−22.8778	+	16.4235i	−0.767296	+	0.550827i
$890$	29.3442			0.983619
$891$		0			0
$892$	−3.32548	+	5.75990i	−0.111345	+	0.192856i
$893$	16.4350			0.549977
$894$		0			0
$895$	3.95249	−	6.84590i	0.132117	−	0.228833i
$896$	2.90375	+	29.2269i	0.0970074	+	0.976404i
$897$		0			0
$898$	−27.0374	+	46.8301i	−0.902249	+	1.56274i
$899$	8.20334	−	14.2086i	0.273597	−	0.473883i
$900$		0			0
$901$	27.7713	+	48.1014i	0.925197	+	1.60249i
$902$	−14.4801	−	25.0802i	−0.482133	−	0.835080i
$903$		0			0
$904$	13.7980	−	23.8988i	0.458913	−	0.794861i
$905$	13.2016			0.438837
$906$		0			0
$907$	23.9137			0.794043			0.397021	−	0.917809i	$-0.370044\pi$
$907$	23.9137			0.794043			0.397021	+	0.917809i	$0.370044\pi$
$908$	35.5481	+	61.5712i	1.17971	+	2.04331i
$909$		0			0
$910$	5.65838	+	2.55797i	0.187574	+	0.0847959i
$911$	8.81756	+	15.2725i	0.292139	+	0.505999i	0.974315	−	0.225188i	$-0.0722997\pi$
$911$	8.81756	+	15.2725i	0.292139	+	0.505999i	−0.682176	+	0.731188i	$0.738966\pi$
$912$		0			0
$913$	13.0591	+	22.6190i	0.432192	+	0.748579i
$914$	−5.35301	−	9.27169i	−0.177062	−	0.306680i
$915$		0			0
$916$	27.4274	+	47.5056i	0.906226	+	1.56963i
$917$	42.7566	−	30.6941i	1.41195	−	1.01361i
$918$		0			0
$919$	−0.708010	−	1.22631i	−0.0233551	−	0.0404522i	0.854112	−	0.520090i	$-0.174101\pi$
$919$	−0.708010	−	1.22631i	−0.0233551	−	0.0404522i	−0.877467	+	0.479638i	$0.840768\pi$
$920$	−0.402579			−0.0132727
$921$		0			0
$922$	−29.2985			−0.964894
$923$	5.95210	−	10.3093i	0.195916	−	0.339336i
$924$		0			0
$925$	1.14456	+	1.98243i	0.0376328	+	0.0651819i
$926$	−31.9362	−	55.3151i	−1.04949	−	1.81777i
$927$		0			0
$928$	−35.4977	+	61.4838i	−1.16527	+	2.01830i
$929$	−9.67639	+	16.7600i	−0.317472	+	0.549878i	−0.979960	−	0.199195i	$-0.936167\pi$
$929$	−9.67639	+	16.7600i	−0.317472	+	0.549878i	0.662488	+	0.749073i	$0.269501\pi$
$930$		0			0
$931$	24.0809	−	4.83265i	0.789218	−	0.158384i
$932$	−27.7825	+	48.1207i	−0.910047	+	1.57625i
$933$		0			0
$934$	−22.5687			−0.738472
$935$	−7.18800	+	12.4500i	−0.235073	+	0.407158i
$936$		0			0
$937$	9.34357			0.305241			0.152621	−	0.988285i	$-0.451229\pi$
$937$	9.34357			0.305241			0.152621	+	0.988285i	$0.451229\pi$
$938$	59.7565	−	42.8980i	1.95112	−	1.40067i
$939$		0			0
$940$	−12.5572			−0.409570
$941$	−16.3696	−	28.3530i	−0.533634	−	0.924281i	−0.999228	−	0.0392827i	$-0.987493\pi$
$941$	−16.3696	−	28.3530i	−0.533634	−	0.924281i	0.465594	−	0.884998i	$-0.345841\pi$
$942$		0			0
$943$	−0.725682	+	1.25692i	−0.0236315	+	0.0409309i
$944$	−7.32362			−0.238363
$945$		0			0
$946$	−34.3034			−1.11530
$947$	9.85492	−	17.0692i	0.320242	−	0.554675i	−0.660296	−	0.751005i	$-0.729569\pi$
$947$	9.85492	−	17.0692i	0.320242	−	0.554675i	0.980538	+	0.196330i	$0.0629025\pi$
$948$		0			0
$949$	−0.117029	−	0.202701i	−0.00379893	−	0.00657994i
$950$	7.59118			0.246290
$951$		0			0
$952$	2.19742	+	22.1176i	0.0712189	+	0.716836i
$953$	−10.9242			−0.353870			−0.176935	−	0.984223i	$-0.556618\pi$
$953$	−10.9242			−0.353870			−0.176935	+	0.984223i	$0.556618\pi$
$954$		0			0
$955$	−3.46679	+	6.00466i	−0.112183	+	0.194306i
$956$	−10.1044			−0.326801
$957$		0			0
$958$	−32.7323	+	56.6940i	−1.05753	+	1.83170i
$959$	29.1371	−	20.9169i	0.940885	−	0.675443i
$960$		0			0
$961$	13.9368	−	24.1392i	0.449574	−	0.778685i
$962$	−2.68633	+	4.65286i	−0.0866108	+	0.150014i
$963$		0			0
$964$	−9.63634	−	16.6906i	−0.310366	−	0.537569i
$965$	−4.91963	−	8.52105i	−0.158369	−	0.274302i
$966$		0			0
$967$	3.26247	−	5.65076i	0.104914	−	0.181716i	−0.808789	−	0.588099i	$-0.799877\pi$
$967$	3.26247	−	5.65076i	0.104914	−	0.181716i	0.913703	+	0.406383i	$0.133210\pi$
$968$	6.84387			0.219970
$969$		0			0
$970$	−29.9073			−0.960265
$971$	−12.6674	−	21.9406i	−0.406516	−	0.704107i	0.587980	−	0.808875i	$-0.299923\pi$
$971$	−12.6674	−	21.9406i	−0.406516	−	0.704107i	−0.994497	+	0.104768i	$0.966590\pi$
$972$		0			0
$973$	−2.80998	−	28.2832i	−0.0900838	−	0.906716i
$974$	−14.0751	−	24.3788i	−0.450996	−	0.781149i
$975$		0			0
$976$	5.37976	+	9.31802i	0.172202	+	0.298263i
$977$	12.6098	+	21.8408i	0.403423	+	0.698749i	0.994137	−	0.108132i	$-0.0344870\pi$
$977$	12.6098	+	21.8408i	0.403423	+	0.698749i	−0.590713	+	0.806881i	$0.701154\pi$
$978$		0			0
$979$	−17.0941	−	29.6078i	−0.546329	−	0.946270i
$980$	−18.3990	+	3.69238i	−0.587733	+	0.117949i
$981$		0			0
$982$	9.97281	+	17.2734i	0.318245	+	0.551217i
$983$	−22.8298			−0.728159			−0.364079	−	0.931368i	$-0.618616\pi$
$983$	−22.8298			−0.728159			−0.364079	+	0.931368i	$0.618616\pi$
$984$		0			0
$985$	−4.92577			−0.156948
$986$	−57.2470	+	99.1548i	−1.82312	+	3.15773i
$987$		0			0
$988$	5.10209	+	8.83707i	0.162319	+	0.281145i
$989$	0.859575	+	1.48883i	0.0273329	+	0.0473419i
$990$		0			0
$991$	−9.84990	+	17.0605i	−0.312892	+	0.541946i	−0.978987	−	0.203921i	$-0.934631\pi$
$991$	−9.84990	+	17.0605i	−0.312892	+	0.541946i	0.666095	+	0.745867i	$0.267965\pi$
$992$	6.76432	−	11.7161i	0.214767	−	0.371988i
$993$		0			0
$994$	6.21001	+	62.5053i	0.196969	+	1.98255i
$995$	2.96416	−	5.13407i	0.0939701	−	0.162761i
$996$		0			0
$997$	−6.93585			−0.219660			−0.109830	−	0.993950i	$-0.535031\pi$
$997$	−6.93585			−0.219660			−0.109830	+	0.993950i	$0.535031\pi$
$998$	24.1760	−	41.8741i	0.765279	−	1.32550i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.k.b.361.10		24
3.2	odd	2		315.2.k.b.256.3	yes	24
7.2	even	3		945.2.l.b.226.3		24
9.2	odd	6		315.2.l.b.151.10	yes	24
9.7	even	3		945.2.l.b.46.3		24
21.2	odd	6		315.2.l.b.121.10	yes	24
63.2	odd	6		315.2.k.b.16.3	✓	24
63.16	even	3	inner	945.2.k.b.856.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.b.16.3	✓	24	63.2	odd	6
315.2.k.b.256.3	yes	24	3.2	odd	2
315.2.l.b.121.10	yes	24	21.2	odd	6
315.2.l.b.151.10	yes	24	9.2	odd	6
945.2.k.b.361.10		24	1.1	even	1	trivial
945.2.k.b.856.10		24	63.16	even	3	inner
945.2.l.b.46.3		24	9.7	even	3
945.2.l.b.226.3		24	7.2	even	3

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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.k (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.08176 - 1.87367i) q^{2} +(-1.34041 - 2.32167i) q^{4} +1.00000 q^{5} +(2.14928 - 1.54292i) q^{7} -1.47299 q^{8} +(1.08176 - 1.87367i) q^{10} -2.52066 q^{11} +(-0.542414 + 0.939489i) q^{13} +(-0.565917 - 5.69610i) q^{14} +(1.08741 - 1.88345i) q^{16} +(2.85163 - 4.93917i) q^{17} +(1.75436 + 3.03863i) q^{19} +(-1.34041 - 2.32167i) q^{20} +(-2.72676 + 4.72288i) q^{22} +0.273308 q^{23} +1.00000 q^{25} +(1.17352 + 2.03260i) q^{26} +(-6.46307 - 2.92175i) q^{28} +(-4.63947 - 8.03580i) q^{29} +(0.884081 + 1.53127i) q^{31} +(-3.82562 - 6.62617i) q^{32} +(-6.16956 - 10.6860i) q^{34} +(2.14928 - 1.54292i) q^{35} +(1.14456 + 1.98243i) q^{37} +7.59118 q^{38} -1.47299 q^{40} +(-2.65518 + 4.59891i) q^{41} +(3.14508 + 5.44743i) q^{43} +(3.37874 + 5.85214i) q^{44} +(0.295654 - 0.512088i) q^{46} +(2.34203 - 4.05652i) q^{47} +(2.23878 - 6.63234i) q^{49} +(1.08176 - 1.87367i) q^{50} +2.90824 q^{52} +(-4.86938 + 8.43401i) q^{53} -2.52066 q^{55} +(-3.16586 + 2.27271i) q^{56} -20.0752 q^{58} +(-1.68373 - 2.91631i) q^{59} +(-2.47366 + 4.28451i) q^{61} +3.82546 q^{62} -12.2040 q^{64} +(-0.542414 + 0.939489i) q^{65} +(6.42542 + 11.1292i) q^{67} -15.2895 q^{68} +(-0.565917 - 5.69610i) q^{70} -10.9734 q^{71} +(-0.107878 + 0.186850i) q^{73} +4.95255 q^{74} +(4.70313 - 8.14606i) q^{76} +(-5.41761 + 3.88919i) q^{77} +(1.95176 - 3.38055i) q^{79} +(1.08741 - 1.88345i) q^{80} +(5.74454 + 9.94984i) q^{82} +(-5.18081 - 8.97342i) q^{83} +(2.85163 - 4.93917i) q^{85} +13.6089 q^{86} +3.71291 q^{88} +(6.78158 + 11.7460i) q^{89} +(0.283761 + 2.85612i) q^{91} +(-0.366346 - 0.634530i) q^{92} +(-5.06704 - 8.77636i) q^{94} +(1.75436 + 3.03863i) q^{95} +(-6.91171 - 11.9714i) q^{97} +(-10.0050 - 11.3693i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} - 7 q^{4} + 24 q^{5} + 7 q^{7} - 12 q^{8} + q^{10} + 2 q^{11} - 4 q^{13} + 13 q^{14} - 5 q^{16} + 7 q^{17} - 2 q^{19} - 7 q^{20} + 19 q^{22} + 2 q^{23} + 24 q^{25} - 11 q^{26} - 28 q^{28}+ \cdots + 15 q^{98}+O(q^{100}) \) 24 * q + q^2 - 7 * q^4 + 24 * q^5 + 7 * q^7 - 12 * q^8 + q^10 + 2 * q^11 - 4 * q^13 + 13 * q^14 - 5 * q^16 + 7 * q^17 - 2 * q^19 - 7 * q^20 + 19 * q^22 + 2 * q^23 + 24 * q^25 - 11 * q^26 - 28 * q^28 + 8 * q^31 - 17 * q^32 + q^34 + 7 * q^35 + 17 * q^37 - 70 * q^38 - 12 * q^40 - 20 * q^41 + 31 * q^43 + 7 * q^44 - 10 * q^46 + 31 * q^47 - 11 * q^49 + q^50 + 8 * q^52 - 8 * q^53 + 2 * q^55 - 45 * q^56 - 90 * q^58 + 21 * q^59 + 5 * q^61 - 14 * q^62 - 56 * q^64 - 4 * q^65 + 43 * q^67 - 96 * q^68 + 13 * q^70 - 24 * q^71 - 18 * q^73 + 18 * q^74 - 13 * q^76 - 5 * q^77 + 40 * q^79 - 5 * q^80 + 5 * q^82 + 60 * q^83 + 7 * q^85 + 24 * q^86 - 100 * q^88 + 4 * q^89 - 33 * q^91 + 18 * q^92 - 11 * q^94 - 2 * q^95 + 6 * q^97 + 15 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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