LMFDB - Embedded newform 1232.2.bi.b.879.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1232,2,Mod(527,1232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1232, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 2, 3]))

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

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

chi := DirichletCharacter("1232.527");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1232 = 2^{4} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1232.bi (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.83756952902$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			879.2
Character	$\chi$	$=$	1232.879
Dual form			1232.2.bi.b.527.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.36660 - 1.36635i) q^{3} +(-0.921875 - 1.59674i) q^{5} +(-0.396390 - 2.61589i) q^{7} +(2.23385 + 3.86914i) q^{9} +O(q^{10})$	\(q+(-2.36660 - 1.36635i) q^{3} +(-0.921875 - 1.59674i) q^{5} +(-0.396390 - 2.61589i) q^{7} +(2.23385 + 3.86914i) q^{9} +(2.51312 + 2.16431i) q^{11} +6.17407i q^{13} +5.03843i q^{15} +(4.14248 + 2.39166i) q^{17} +(0.0381762 + 0.0661231i) q^{19} +(-2.63614 + 6.73236i) q^{21} +(2.14990 - 1.24124i) q^{23} +(0.800292 - 1.38615i) q^{25} -4.01079i q^{27} +7.13316i q^{29} +(-4.75299 - 2.74414i) q^{31} +(-2.99032 - 8.55586i) q^{33} +(-3.81146 + 3.04445i) q^{35} +(3.83285 + 6.63869i) q^{37} +(8.43596 - 14.6115i) q^{39} -9.30520i q^{41} +6.89962 q^{43} +(4.11866 - 7.13373i) q^{45} +(0.725870 - 0.419081i) q^{47} +(-6.68575 + 2.07383i) q^{49} +(-6.53571 - 11.3202i) q^{51} +(0.492147 - 0.852423i) q^{53} +(1.13905 - 6.00801i) q^{55} -0.208649i q^{57} +(-2.20732 - 1.27439i) q^{59} +(6.50177 - 3.75380i) q^{61} +(9.23577 - 7.37719i) q^{63} +(9.85835 - 5.69172i) q^{65} +(-6.06206 - 3.49993i) q^{67} -6.78392 q^{69} +12.3556i q^{71} +(8.99208 + 5.19158i) q^{73} +(-3.78793 + 2.18696i) q^{75} +(4.66542 - 7.43195i) q^{77} +(1.83066 + 3.17080i) q^{79} +(1.22138 - 2.11550i) q^{81} +4.42129 q^{83} -8.81925i q^{85} +(9.74642 - 16.8813i) q^{87} +(-0.870563 - 1.50786i) q^{89} +(16.1507 - 2.44734i) q^{91} +(7.49894 + 12.9885i) q^{93} +(0.0703873 - 0.121914i) q^{95} +4.56529 q^{97} +(-2.76010 + 14.5583i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{5} + 12 q^{9}+O(q^{10}) $ 32 * q - 2 * q^5 + 12 * q^9	$ 32 q - 2 q^{5} + 12 q^{9} + 9 q^{11} + 18 q^{23} - 6 q^{25} + 5 q^{33} - 6 q^{37} - 10 q^{45} + 36 q^{47} - 32 q^{49} + 42 q^{59} + 18 q^{67} - 24 q^{69} + 78 q^{75} - 19 q^{77} - 24 q^{81} - 8 q^{89} + 18 q^{91} + 2 q^{93} + 12 q^{97}+O(q^{100}) $ 32 * q - 2 * q^5 + 12 * q^9 + 9 * q^11 + 18 * q^23 - 6 * q^25 + 5 * q^33 - 6 * q^37 - 10 * q^45 + 36 * q^47 - 32 * q^49 + 42 * q^59 + 18 * q^67 - 24 * q^69 + 78 * q^75 - 19 * q^77 - 24 * q^81 - 8 * q^89 + 18 * q^91 + 2 * q^93 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times$.

$n$	$309$	$353$	$463$	$673$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.36660	−	1.36635i	−1.36635	−	0.788865i	−0.375894	−	0.926663i	$-0.622664\pi$
$3$	−2.36660	−	1.36635i	−1.36635	−	0.788865i	−0.990460	+	0.137797i	$0.955998\pi$
$4$		0			0
$5$	−0.921875	−	1.59674i	−0.412275	−	0.714082i	0.582863	−	0.812570i	$-0.301932\pi$
$5$	−0.921875	−	1.59674i	−0.412275	−	0.714082i	−0.995138	+	0.0984889i	$0.968599\pi$
$6$		0			0
$7$	−0.396390	−	2.61589i	−0.149821	−	0.988713i
$7$	−0.396390	−	2.61589i	−0.149821	−	0.988713i
$8$		0			0
$9$	2.23385	+	3.86914i	0.744616	+	1.28971i
$10$		0			0
$11$	2.51312	+	2.16431i	0.757733	+	0.652564i
$11$	2.51312	+	2.16431i	0.757733	+	0.652564i
$12$		0			0
$13$			6.17407i			1.71238i	0.516663	+	0.856189i	$0.327174\pi$
$13$			6.17407i			1.71238i	−0.516663	+	0.856189i	$0.672826\pi$
$14$		0			0
$15$			5.03843i			1.30092i
$16$		0			0
$17$	4.14248	+	2.39166i	1.00470	+	0.580063i	0.909635	−	0.415409i	$-0.136361\pi$
$17$	4.14248	+	2.39166i	1.00470	+	0.580063i	0.0950631	+	0.995471i	$0.469695\pi$
$18$		0			0
$19$	0.0381762	+	0.0661231i	0.00875821	+	0.0151697i	0.870371	−	0.492396i	$-0.163879\pi$
$19$	0.0381762	+	0.0661231i	0.00875821	+	0.0151697i	−0.861613	+	0.507566i	$0.830545\pi$
$20$		0			0
$21$	−2.63614	+	6.73236i	−0.575252	+	1.46912i
$22$		0			0
$23$	2.14990	−	1.24124i	0.448285	−	0.258817i	−0.258821	−	0.965925i	$-0.583334\pi$
$23$	2.14990	−	1.24124i	0.448285	−	0.258817i	0.707105	+	0.707108i	$0.250001\pi$
$24$		0			0
$25$	0.800292	−	1.38615i	0.160058	−	0.277229i
$26$		0			0
$27$		−	4.01079i		−	0.771877i
$28$		0			0
$29$			7.13316i			1.32459i	0.749241	+	0.662297i	$0.230418\pi$
$29$			7.13316i			1.32459i	−0.749241	+	0.662297i	$0.769582\pi$
$30$		0			0
$31$	−4.75299	−	2.74414i	−0.853662	−	0.492862i	0.00822254	−	0.999966i	$-0.497383\pi$
$31$	−4.75299	−	2.74414i	−0.853662	−	0.492862i	−0.861885	+	0.507104i	$0.830716\pi$
$32$		0			0
$33$	−2.99032	−	8.55586i	−0.520547	−	1.48938i
$34$		0			0
$35$	−3.81146	+	3.04445i	−0.644254	+	0.514607i
$36$		0			0
$37$	3.83285	+	6.63869i	0.630117	+	1.09139i	0.987527	+	0.157447i	$0.0503262\pi$
$37$	3.83285	+	6.63869i	0.630117	+	1.09139i	−0.357411	+	0.933947i	$0.616340\pi$
$38$		0			0
$39$	8.43596	−	14.6115i	1.35084	−	2.33972i
$40$		0			0
$41$		−	9.30520i		−	1.45323i	−0.687046	−	0.726614i	$-0.741093\pi$
$41$		−	9.30520i		−	1.45323i	0.687046	−	0.726614i	$-0.258907\pi$
$42$		0			0
$43$	6.89962			1.05218			0.526091	−	0.850428i	$-0.323657\pi$
$43$	6.89962			1.05218			0.526091	+	0.850428i	$0.323657\pi$
$44$		0			0
$45$	4.11866	−	7.13373i	0.613974	−	1.06343i
$46$		0			0
$47$	0.725870	−	0.419081i	0.105879	−	0.0611293i	−0.446125	−	0.894970i	$-0.647196\pi$
$47$	0.725870	−	0.419081i	0.105879	−	0.0611293i	0.552004	+	0.833841i	$0.313863\pi$
$48$		0			0
$49$	−6.68575	+	2.07383i	−0.955107	+	0.296261i
$50$		0			0
$51$	−6.53571	−	11.3202i	−0.915183	−	1.58514i
$52$		0			0
$53$	0.492147	−	0.852423i	0.0676016	−	0.117089i	−0.830244	−	0.557401i	$-0.811799\pi$
$53$	0.492147	−	0.852423i	0.0676016	−	0.117089i	0.897845	+	0.440312i	$0.145132\pi$
$54$		0			0
$55$	1.13905	−	6.00801i	0.153589	−	0.810120i
$56$		0			0
$57$		−	0.208649i		−	0.0276362i
$58$		0			0
$59$	−2.20732	−	1.27439i	−0.287368	−	0.165912i	0.349386	−	0.936979i	$-0.386390\pi$
$59$	−2.20732	−	1.27439i	−0.287368	−	0.165912i	−0.636754	+	0.771067i	$0.719723\pi$
$60$		0			0
$61$	6.50177	−	3.75380i	0.832466	−	0.480625i	−0.0222302	−	0.999753i	$-0.507077\pi$
$61$	6.50177	−	3.75380i	0.832466	−	0.480625i	0.854696	+	0.519128i	$0.173743\pi$
$62$		0			0
$63$	9.23577	−	7.37719i	1.16360	−	0.929439i
$64$		0			0
$65$	9.85835	−	5.69172i	1.22278	−	0.705971i
$66$		0			0
$67$	−6.06206	−	3.49993i	−0.740599	−	0.427585i	0.0816882	−	0.996658i	$-0.473969\pi$
$67$	−6.06206	−	3.49993i	−0.740599	−	0.427585i	−0.822287	+	0.569073i	$0.807302\pi$
$68$		0			0
$69$	−6.78392			−0.816688
$70$		0			0
$71$			12.3556i			1.46634i	0.680045	+	0.733171i	$0.261960\pi$
$71$			12.3556i			1.46634i	−0.680045	+	0.733171i	$0.738040\pi$
$72$		0			0
$73$	8.99208	+	5.19158i	1.05244	+	0.607628i	0.923332	−	0.384002i	$-0.125454\pi$
$73$	8.99208	+	5.19158i	1.05244	+	0.607628i	0.129111	+	0.991630i	$0.458788\pi$
$74$		0			0
$75$	−3.78793	+	2.18696i	−0.437393	+	0.252529i
$76$		0			0
$77$	4.66542	−	7.43195i	0.531674	−	0.846949i
$78$		0			0
$79$	1.83066	+	3.17080i	0.205966	+	0.356743i	0.950440	−	0.310908i	$-0.100633\pi$
$79$	1.83066	+	3.17080i	0.205966	+	0.356743i	−0.744474	+	0.667651i	$0.767300\pi$
$80$		0			0
$81$	1.22138	−	2.11550i	0.135709	−	0.235055i
$82$		0			0
$83$	4.42129			0.485300			0.242650	−	0.970114i	$-0.421983\pi$
$83$	4.42129			0.485300			0.242650	+	0.970114i	$0.421983\pi$
$84$		0			0
$85$		−	8.81925i		−	0.956582i
$86$		0			0
$87$	9.74642	−	16.8813i	1.04493	−	1.80987i
$88$		0			0
$89$	−0.870563	−	1.50786i	−0.0922795	−	0.159833i	0.816190	−	0.577783i	$-0.196082\pi$
$89$	−0.870563	−	1.50786i	−0.0922795	−	0.159833i	−0.908470	+	0.417950i	$0.862749\pi$
$90$		0			0
$91$	16.1507	−	2.44734i	1.69305	−	0.256551i
$92$		0			0
$93$	7.49894	+	12.9885i	0.777604	+	1.34685i
$94$		0			0
$95$	0.0703873	−	0.121914i	0.00722159	−	0.0125082i
$96$		0			0
$97$	4.56529			0.463535			0.231767	−	0.972771i	$-0.425549\pi$
$97$	4.56529			0.463535			0.231767	+	0.972771i	$0.425549\pi$
$98$		0			0
$99$	−2.76010	+	14.5583i	−0.277400	+	1.46317i
$100$		0			0
$101$	−12.1443	−	7.01151i	−1.20840	−	0.697671i	−0.245992	−	0.969272i	$-0.579114\pi$
$101$	−12.1443	−	7.01151i	−1.20840	−	0.697671i	−0.962410	+	0.271600i	$0.912447\pi$
$102$		0			0
$103$	−8.17208	+	4.71815i	−0.805219	+	0.464894i	−0.845293	−	0.534303i	$-0.820574\pi$
$103$	−8.17208	+	4.71815i	−0.805219	+	0.464894i	0.0400737	+	0.999197i	$0.487241\pi$
$104$		0			0
$105$	13.1800	−	1.99719i	1.28623	−	0.194905i
$106$		0			0
$107$	8.66222	+	15.0034i	0.837408	+	1.45043i	0.892055	+	0.451927i	$0.149263\pi$
$107$	8.66222	+	15.0034i	0.837408	+	1.45043i	−0.0546467	+	0.998506i	$0.517403\pi$
$108$		0			0
$109$	3.37584	+	1.94904i	0.323347	+	0.186684i	0.652883	−	0.757459i	$-0.273559\pi$
$109$	3.37584	+	1.94904i	0.323347	+	0.186684i	−0.329537	+	0.944143i	$0.606893\pi$
$110$		0			0
$111$		−	20.9481i		−	1.98831i
$112$		0			0
$113$	−3.54349			−0.333344			−0.166672	−	0.986012i	$-0.553302\pi$
$113$	−3.54349			−0.333344			−0.166672	+	0.986012i	$0.553302\pi$
$114$		0			0
$115$	−3.96388	−	2.28854i	−0.369633	−	0.213408i
$116$		0			0
$117$	−23.8883	+	13.7919i	−2.20848	+	1.27506i
$118$		0			0
$119$	4.61428	−	11.7843i	0.422990	−	1.08026i
$120$		0			0
$121$	1.63152	+	10.8783i	0.148320	+	0.988939i
$122$		0			0
$123$	−12.7142	+	22.0216i	−1.14640	+	1.98562i
$124$		0			0
$125$	−12.1698			−1.08850
$126$		0			0
$127$	21.4774			1.90581			0.952906	−	0.303265i	$-0.0980768\pi$
$127$	21.4774			1.90581			0.952906	+	0.303265i	$0.0980768\pi$
$128$		0			0
$129$	−16.3286	−	9.42732i	−1.43765	−	0.830029i
$130$		0			0
$131$	−4.87332	−	8.44084i	−0.425784	−	0.737480i	0.570709	−	0.821152i	$-0.306668\pi$
$131$	−4.87332	−	8.44084i	−0.425784	−	0.737480i	−0.996493	+	0.0836726i	$0.973335\pi$
$132$		0			0
$133$	0.157838	−	0.126075i	0.0136863	−	0.0109321i
$134$		0			0
$135$	−6.40417	+	3.69745i	−0.551184	+	0.318226i
$136$		0			0
$137$	9.25832	−	16.0359i	0.790992	−	1.37004i	−0.134362	−	0.990932i	$-0.542898\pi$
$137$	9.25832	−	16.0359i	0.790992	−	1.37004i	0.925353	−	0.379106i	$-0.123768\pi$
$138$		0			0
$139$	13.0874			1.11006			0.555031	−	0.831829i	$-0.312706\pi$
$139$	13.0874			1.11006			0.555031	+	0.831829i	$0.312706\pi$
$140$		0			0
$141$	−2.29045			−0.192891
$142$		0			0
$143$	−13.3626	+	15.5162i	−1.11744	+	1.29753i
$144$		0			0
$145$	11.3898	−	6.57588i	0.945868	−	0.546097i
$146$		0			0
$147$	18.6560	+	4.22720i	1.53872	+	0.348653i
$148$		0			0
$149$	6.99422	−	4.03811i	0.572989	−	0.330815i	−0.185354	−	0.982672i	$-0.559343\pi$
$149$	6.99422	−	4.03811i	0.572989	−	0.330815i	0.758342	+	0.651857i	$0.226010\pi$
$150$		0			0
$151$	1.34124	−	2.32309i	0.109148	−	0.189051i	−0.806277	−	0.591538i	$-0.798521\pi$
$151$	1.34124	−	2.32309i	0.109148	−	0.189051i	0.915425	+	0.402487i	$0.131854\pi$
$152$		0			0
$153$			21.3704i			1.72770i
$154$		0			0
$155$			10.1190i			0.812779i
$156$		0			0
$157$	11.5737	−	20.0463i	0.923685	−	1.59987i	0.130023	−	0.991511i	$-0.458495\pi$
$157$	11.5737	−	20.0463i	0.923685	−	1.59987i	0.793662	−	0.608358i	$-0.208172\pi$
$158$		0			0
$159$	−2.32942	+	1.34489i	−0.184735	+	0.106657i
$160$		0			0
$161$	−4.09915	−	5.13188i	−0.323059	−	0.404448i
$162$		0			0
$163$	0.328085	−	0.189420i	0.0256976	−	0.0148365i	−0.487096	−	0.873348i	$-0.661944\pi$
$163$	0.328085	−	0.189420i	0.0256976	−	0.0148365i	0.512794	+	0.858512i	$0.328611\pi$
$164$		0			0
$165$	−10.9047	+	12.6622i	−0.848933	+	0.985749i
$166$		0			0
$167$	−15.0298			−1.16304			−0.581519	−	0.813533i	$-0.697541\pi$
$167$	−15.0298			−1.16304			−0.581519	+	0.813533i	$0.697541\pi$
$168$		0			0
$169$	−25.1191			−1.93224
$170$		0			0
$171$	−0.170560	+	0.295418i	−0.0130430	+	0.0225912i
$172$		0			0
$173$	−1.78819	+	1.03241i	−0.135954	+	0.0784928i	−0.566434	−	0.824107i	$-0.691677\pi$
$173$	−1.78819	+	1.03241i	−0.135954	+	0.0784928i	0.430481	+	0.902600i	$0.358344\pi$
$174$		0			0
$175$	−3.94323	−	1.54402i	−0.298080	−	0.116717i
$176$		0			0
$177$	3.48255	+	6.03195i	0.261764	+	0.453389i
$178$		0			0
$179$	−22.8324	−	13.1823i	−1.70658	−	0.985292i	−0.938728	−	0.344659i	$-0.887995\pi$
$179$	−22.8324	−	13.1823i	−1.70658	−	0.985292i	−0.767847	−	0.640633i	$-0.778672\pi$
$180$		0			0
$181$	−12.7234			−0.945720			−0.472860	−	0.881137i	$-0.656778\pi$
$181$	−12.7234			−0.945720			−0.472860	+	0.881137i	$0.656778\pi$
$182$		0			0
$183$	−20.5161			−1.51659
$184$		0			0
$185$	7.06682	−	12.2401i	0.519563	−	0.899909i
$186$		0			0
$187$	5.23423	+	14.9761i	0.382765	+	1.09516i
$188$		0			0
$189$	−10.4918	+	1.58984i	−0.763165	+	0.115644i
$190$		0			0
$191$	4.77585	−	2.75734i	0.345569	−	0.199514i	−0.317163	−	0.948371i	$-0.602730\pi$
$191$	4.77585	−	2.75734i	0.345569	−	0.199514i	0.662732	+	0.748857i	$0.269397\pi$
$192$		0			0
$193$	21.9717	+	12.6854i	1.58156	+	0.913114i	0.994632	+	0.103475i	$0.0329963\pi$
$193$	21.9717	+	12.6854i	1.58156	+	0.913114i	0.586928	+	0.809639i	$0.300337\pi$
$194$		0			0
$195$	−31.1076			−2.22766
$196$		0			0
$197$			8.74130i			0.622792i	0.950280	+	0.311396i	$0.100796\pi$
$197$			8.74130i			0.622792i	−0.950280	+	0.311396i	$0.899204\pi$
$198$		0			0
$199$	14.1898	+	8.19246i	1.00589	+	0.580748i	0.909984	−	0.414643i	$-0.136093\pi$
$199$	14.1898	+	8.19246i	1.00589	+	0.580748i	0.0959009	+	0.995391i	$0.469427\pi$
$200$		0			0
$201$	9.56430	+	16.5659i	0.674614	+	1.16847i
$202$		0			0
$203$	18.6595	−	2.82752i	1.30964	−	0.198453i
$204$		0			0
$205$	−14.8579	+	8.57823i	−1.03772	+	0.599130i
$206$		0			0
$207$	9.60509	+	5.54550i	0.667600	+	0.385439i
$208$		0			0
$209$	−0.0471697	+	0.248800i	−0.00326279	+	0.0172099i
$210$		0			0
$211$	2.53570			0.174565			0.0872824	−	0.996184i	$-0.472182\pi$
$211$	2.53570			0.174565			0.0872824	+	0.996184i	$0.472182\pi$
$212$		0			0
$213$	16.8821	−	29.2407i	1.15675	−	2.00354i
$214$		0			0
$215$	−6.36059	−	11.0169i	−0.433788	−	0.751343i
$216$		0			0
$217$	−5.29433	+	13.5210i	−0.359402	+	0.917868i
$218$		0			0
$219$	−14.1871	−	24.5727i	−0.958673	−	1.66047i
$220$		0			0
$221$	−14.7663	+	25.5759i	−0.993287	+	1.72042i
$222$		0			0
$223$			18.7972i			1.25875i	0.777100	+	0.629377i	$0.216690\pi$
$223$			18.7972i			1.25875i	−0.777100	+	0.629377i	$0.783310\pi$
$224$		0			0
$225$	7.15092			0.476728
$226$		0			0
$227$	5.19061	−	8.99041i	0.344513	−	0.596714i	−0.640752	−	0.767748i	$-0.721377\pi$
$227$	5.19061	−	8.99041i	0.344513	−	0.596714i	0.985265	+	0.171034i	$0.0547106\pi$
$228$		0			0
$229$	4.00835	+	6.94267i	0.264879	+	0.458785i	0.967532	−	0.252749i	$-0.0813345\pi$
$229$	4.00835	+	6.94267i	0.264879	+	0.458785i	−0.702653	+	0.711533i	$0.748001\pi$
$230$		0			0
$231$	−21.1958	+	11.2138i	−1.39458	+	0.737813i
$232$		0			0
$233$	17.4124	−	10.0531i	1.14073	−	0.658599i	0.194117	−	0.980978i	$-0.437816\pi$
$233$	17.4124	−	10.0531i	1.14073	−	0.658599i	0.946611	+	0.322379i	$0.104483\pi$
$234$		0			0
$235$	−1.33832	−	0.772682i	−0.0873026	−	0.0504042i
$236$		0			0
$237$		−	10.0053i		−	0.649917i
$238$		0			0
$239$	−18.8253			−1.21771			−0.608855	−	0.793282i	$-0.708371\pi$
$239$	−18.8253			−1.21771			−0.608855	+	0.793282i	$0.708371\pi$
$240$		0			0
$241$	3.09551	+	1.78719i	0.199399	+	0.115123i	0.596375	−	0.802706i	$-0.296607\pi$
$241$	3.09551	+	1.78719i	0.199399	+	0.115123i	−0.396976	+	0.917829i	$0.629940\pi$
$242$		0			0
$243$	−16.2014	+	9.35387i	−1.03932	+	0.600051i
$244$		0			0
$245$	9.47478	+	8.76356i	0.605321	+	0.559883i
$246$		0			0
$247$	−0.408248	+	0.235702i	−0.0259762	+	0.0149974i
$248$		0			0
$249$	−10.4634	−	6.04105i	−0.663092	−	0.382836i
$250$		0			0
$251$			6.57261i			0.414860i	0.978250	+	0.207430i	$0.0665099\pi$
$251$			6.57261i			0.414860i	−0.978250	+	0.207430i	$0.933490\pi$
$252$		0			0
$253$	8.08938	+	1.53365i	0.508575	+	0.0964201i
$254$		0			0
$255$	−12.0502	+	20.8716i	−0.754614	+	1.30703i
$256$		0			0
$257$	14.4039	+	24.9483i	0.898493	+	1.55624i	0.829421	+	0.558624i	$0.188670\pi$
$257$	14.4039	+	24.9483i	0.898493	+	1.55624i	0.0690715	+	0.997612i	$0.477996\pi$
$258$		0			0
$259$	15.8468	−	12.6578i	0.984670	−	0.786519i
$260$		0			0
$261$	−27.5992	+	15.9344i	−1.70835	+	0.986315i
$262$		0			0
$263$	−10.0726	+	17.4462i	−0.621101	+	1.07578i	0.368180	+	0.929755i	$0.379981\pi$
$263$	−10.0726	+	17.4462i	−0.621101	+	1.07578i	−0.989281	+	0.146024i	$0.953352\pi$
$264$		0			0
$265$	−1.81479			−0.111482
$266$		0			0
$267$			4.75799i			0.291184i
$268$		0			0
$269$	5.33615	−	9.24248i	0.325351	−	0.563524i	−0.656233	−	0.754559i	$-0.727851\pi$
$269$	5.33615	−	9.24248i	0.325351	−	0.563524i	0.981583	+	0.191035i	$0.0611843\pi$
$270$		0			0
$271$	11.2056	+	19.4087i	0.680692	+	1.17899i	0.974770	+	0.223212i	$0.0716543\pi$
$271$	11.2056	+	19.4087i	0.680692	+	1.17899i	−0.294078	+	0.955782i	$0.595012\pi$
$272$		0			0
$273$	−41.5660	−	16.2757i	−2.51569	−	0.985049i
$274$		0			0
$275$	5.01128	−	1.75147i	0.302191	−	0.105617i
$276$		0			0
$277$	−17.1742	−	9.91555i	−1.03190	−	0.595767i	−0.114371	−	0.993438i	$-0.536485\pi$
$277$	−17.1742	−	9.91555i	−1.03190	−	0.595767i	−0.917528	+	0.397671i	$0.869819\pi$
$278$		0			0
$279$		−	24.5200i		−	1.46797i
$280$		0			0
$281$		−	9.20533i		−	0.549144i	−0.961567	−	0.274572i	$-0.911464\pi$
$281$		−	9.20533i		−	0.549144i	0.961567	−	0.274572i	$-0.0885362\pi$
$282$		0			0
$283$	−10.1600	+	17.5977i	−0.603950	+	1.04607i	0.388266	+	0.921547i	$0.373074\pi$
$283$	−10.1600	+	17.5977i	−0.603950	+	1.04607i	−0.992216	+	0.124525i	$0.960259\pi$
$284$		0			0
$285$	−0.333157	+	0.192348i	−0.0197345	+	0.0113937i
$286$		0			0
$287$	−24.3414	+	3.68849i	−1.43683	+	0.217725i
$288$		0			0
$289$	2.94007	+	5.09236i	0.172946	+	0.299550i
$290$		0			0
$291$	−10.8042	−	6.23780i	−0.633353	−	0.365666i
$292$		0			0
$293$			21.4719i			1.25440i	0.778858	+	0.627200i	$0.215799\pi$
$293$			21.4719i			1.25440i	−0.778858	+	0.627200i	$0.784201\pi$
$294$		0			0
$295$			4.69933i			0.273606i
$296$		0			0
$297$	8.68060	−	10.0796i	0.503700	−	0.584877i
$298$		0			0
$299$	7.66352	+	13.2736i	0.443193	+	0.767633i
$300$		0			0
$301$	−2.73494	−	18.0486i	−0.157639	−	1.04031i
$302$		0			0
$303$	19.1604	+	33.1868i	1.10074	+	1.90653i
$304$		0			0
$305$	−11.9876	−	6.92107i	−0.686410	−	0.396299i
$306$		0			0
$307$	13.1655			0.751393			0.375697	−	0.926743i	$-0.377403\pi$
$307$	13.1655			0.751393			0.375697	+	0.926743i	$0.377403\pi$
$308$		0			0
$309$	25.7867			1.46695
$310$		0			0
$311$	16.4361	+	9.48938i	0.932005	+	0.538093i	0.887445	−	0.460914i	$-0.152478\pi$
$311$	16.4361	+	9.48938i	0.932005	+	0.538093i	0.0445596	+	0.999007i	$0.485812\pi$
$312$		0			0
$313$	−2.44234	−	4.23026i	−0.138049	−	0.239108i	0.788709	−	0.614767i	$-0.210750\pi$
$313$	−2.44234	−	4.23026i	−0.138049	−	0.239108i	−0.926758	+	0.375658i	$0.877417\pi$
$314$		0			0
$315$	−20.2936	−	7.94622i	−1.14342	−	0.447719i
$316$		0			0
$317$	5.22681	+	9.05310i	0.293567	+	0.508473i	0.974651	−	0.223733i	$-0.0718243\pi$
$317$	5.22681	+	9.05310i	0.293567	+	0.508473i	−0.681084	+	0.732206i	$0.738491\pi$
$318$		0			0
$319$	−15.4384	+	17.9265i	−0.864383	+	1.00369i
$320$		0			0
$321$		−	47.3426i		−	2.64241i
$322$		0			0
$323$			0.365218i			0.0203213i
$324$		0			0
$325$	8.55816	+	4.94105i	0.474721	+	0.274080i
$326$		0			0
$327$	−5.32616	−	9.22518i	−0.294537	−	0.510154i
$328$		0			0
$329$	−1.38400	−	1.73268i	−0.0763023	−	0.0955255i
$330$		0			0
$331$	7.61073	−	4.39406i	0.418324	−	0.241519i	−0.276036	−	0.961147i	$-0.589021\pi$
$331$	7.61073	−	4.39406i	0.418324	−	0.241519i	0.694360	+	0.719628i	$0.255688\pi$
$332$		0			0
$333$	−17.1240	+	29.6597i	−0.938390	+	1.62534i
$334$		0			0
$335$			12.9060i			0.705131i
$336$		0			0
$337$		−	19.0714i		−	1.03889i	−0.854505	−	0.519443i	$-0.826140\pi$
$337$		−	19.0714i		−	1.03889i	0.854505	−	0.519443i	$-0.173860\pi$
$338$		0			0
$339$	8.38601	+	4.84166i	0.455466	+	0.262963i
$340$		0			0
$341$	−6.00565	−	17.1833i	−0.325224	−	0.930528i
$342$		0			0
$343$	8.07507	+	16.6671i	0.436013	+	0.899941i
$344$		0			0
$345$	6.25393	+	10.8321i	0.336700	+	0.583182i
$346$		0			0
$347$	3.79571	−	6.57437i	0.203765	−	0.352931i	−0.745974	−	0.665975i	$-0.768016\pi$
$347$	3.79571	−	6.57437i	0.203765	−	0.352931i	0.949738	+	0.313045i	$0.101349\pi$
$348$		0			0
$349$			5.40205i			0.289165i	0.989493	+	0.144583i	$0.0461840\pi$
$349$			5.40205i			0.289165i	−0.989493	+	0.144583i	$0.953816\pi$
$350$		0			0
$351$	24.7629			1.32175
$352$		0			0
$353$	2.61595	−	4.53096i	0.139233	−	0.241159i	−0.787974	−	0.615709i	$-0.788870\pi$
$353$	2.61595	−	4.53096i	0.139233	−	0.241159i	0.927207	+	0.374551i	$0.122203\pi$
$354$		0			0
$355$	19.7286	−	11.3903i	1.04709	−	0.604536i
$356$		0			0
$357$	−27.0216	+	21.5839i	−1.43014	+	1.14234i
$358$		0			0
$359$	−7.51573	−	13.0176i	−0.396665	−	0.687044i	0.596647	−	0.802504i	$-0.296499\pi$
$359$	−7.51573	−	13.0176i	−0.396665	−	0.687044i	−0.993312	+	0.115459i	$0.963166\pi$
$360$		0			0
$361$	9.49709	−	16.4494i	0.499847	−	0.865760i
$362$		0			0
$363$	11.0025	−	27.9738i	0.577483	−	1.46825i
$364$		0			0
$365$		−	19.1440i		−	1.00204i
$366$		0			0
$367$	7.13169	+	4.11748i	0.372271	+	0.214931i	0.674450	−	0.738320i	$-0.264381\pi$
$367$	7.13169	+	4.11748i	0.372271	+	0.214931i	−0.302179	+	0.953251i	$0.597714\pi$
$368$		0			0
$369$	36.0031	−	20.7864i	1.87425	−	1.08210i
$370$		0			0
$371$	−2.42493	−	0.949509i	−0.125896	−	0.0492960i
$372$		0			0
$373$	4.32971	−	2.49976i	0.224184	−	0.129433i	−0.383702	−	0.923457i	$-0.625351\pi$
$373$	4.32971	−	2.49976i	0.224184	−	0.129433i	0.607886	+	0.794024i	$0.292018\pi$
$374$		0			0
$375$	28.8011	+	16.6283i	1.48728	+	0.858682i
$376$		0			0
$377$	−44.0406			−2.26821
$378$		0			0
$379$		−	23.5047i		−	1.20736i	−0.797228	−	0.603679i	$-0.793701\pi$
$379$		−	23.5047i		−	1.20736i	0.797228	−	0.603679i	$-0.206299\pi$
$380$		0			0
$381$	−50.8284	−	29.3458i	−2.60402	−	1.50343i
$382$		0			0
$383$	24.7435	−	14.2856i	1.26433	−	0.729962i	0.290422	−	0.956899i	$-0.406204\pi$
$383$	24.7435	−	14.2856i	1.26433	−	0.729962i	0.973910	+	0.226937i	$0.0728711\pi$
$384$		0			0
$385$	−16.1678	−	0.598112i	−0.823987	−	0.0304826i
$386$		0			0
$387$	15.4127	+	26.6956i	0.783472	+	1.35701i
$388$		0			0
$389$	−5.43026	+	9.40548i	−0.275325	+	0.476877i	−0.970217	−	0.242237i	$-0.922119\pi$
$389$	−5.43026	+	9.40548i	−0.275325	+	0.476877i	0.694892	+	0.719114i	$0.255452\pi$
$390$		0			0
$391$	11.8745			0.600521
$392$		0			0
$393$			26.6347i			1.34354i
$394$		0			0
$395$	3.37529	−	5.84617i	0.169829	−	0.294153i
$396$		0			0
$397$	−12.1286	−	21.0074i	−0.608718	−	1.05433i	−0.991452	−	0.130472i	$-0.958351\pi$
$397$	−12.1286	−	21.0074i	−0.608718	−	1.05433i	0.382734	−	0.923859i	$-0.374983\pi$
$398$		0			0
$399$	−0.545802	+	0.0827063i	−0.0273243	+	0.00414050i
$400$		0			0
$401$	−1.78234	−	3.08710i	−0.0890056	−	0.154162i	0.818085	−	0.575097i	$-0.195036\pi$
$401$	−1.78234	−	3.08710i	−0.0890056	−	0.154162i	−0.907091	+	0.420934i	$0.861702\pi$
$402$		0			0
$403$	16.9425	−	29.3453i	0.843966	−	1.46179i
$404$		0			0
$405$	−4.50385			−0.223798
$406$		0			0
$407$	−4.73579	+	24.9793i	−0.234744	+	1.23818i
$408$		0			0
$409$	12.3017	+	7.10238i	0.608279	+	0.351190i	0.772292	−	0.635268i	$-0.219110\pi$
$409$	12.3017	+	7.10238i	0.608279	+	0.351190i	−0.164013	+	0.986458i	$0.552444\pi$
$410$		0			0
$411$	−43.8214	+	25.3003i	−2.16155	+	1.24797i
$412$		0			0
$413$	−2.45872	+	6.27925i	−0.120985	+	0.308982i
$414$		0			0
$415$	−4.07588	−	7.05963i	−0.200077	−	0.346544i
$416$		0			0
$417$	−30.9727	−	17.8821i	−1.51674	−	0.875690i
$418$		0			0
$419$			2.08642i			0.101928i	0.998700	+	0.0509641i	$0.0162294\pi$
$419$			2.08642i			0.101928i	−0.998700	+	0.0509641i	$0.983771\pi$
$420$		0			0
$421$	34.0540			1.65969			0.829845	−	0.557994i	$-0.188429\pi$
$421$	34.0540			1.65969			0.829845	+	0.557994i	$0.188429\pi$
$422$		0			0
$423$	3.24297	+	1.87233i	0.157679	+	0.0910358i
$424$		0			0
$425$	6.63038	−	3.82805i	0.321621	−	0.185688i
$426$		0			0
$427$	−12.3968	−	15.5199i	−0.599921	−	0.751062i
$428$		0			0
$429$	52.8244	−	18.4624i	2.55039	−	0.891374i
$430$		0			0
$431$	3.71344	−	6.43186i	0.178870	−	0.309812i	−0.762624	−	0.646842i	$-0.776089\pi$
$431$	3.71344	−	6.43186i	0.178870	−	0.309812i	0.941494	+	0.337030i	$0.109423\pi$
$432$		0			0
$433$	38.0888			1.83043			0.915214	−	0.402967i	$-0.132021\pi$
$433$	38.0888			1.83043			0.915214	+	0.402967i	$0.132021\pi$
$434$		0			0
$435$	−35.9399			−1.72319
$436$		0			0
$437$	0.164150	+	0.0947719i	0.00785235	+	0.00453355i
$438$		0			0
$439$	1.56882	+	2.71728i	0.0748758	+	0.129689i	0.901032	−	0.433752i	$-0.142811\pi$
$439$	1.56882	+	2.71728i	0.0748758	+	0.129689i	−0.826156	+	0.563441i	$0.809477\pi$
$440$		0			0
$441$	−22.9589	−	21.2355i	−1.09328	−	1.01121i
$442$		0			0
$443$	−16.6860	+	9.63366i	−0.792775	+	0.457709i	−0.840939	−	0.541130i	$-0.817997\pi$
$443$	−16.6860	+	9.63366i	−0.792775	+	0.457709i	0.0481634	+	0.998839i	$0.484663\pi$
$444$		0			0
$445$	−1.60510	+	2.78012i	−0.0760891	+	0.131790i
$446$		0			0
$447$	−22.0700			−1.04387
$448$		0			0
$449$	1.33723			0.0631077			0.0315539	−	0.999502i	$-0.489954\pi$
$449$	1.33723			0.0631077			0.0315539	+	0.999502i	$0.489954\pi$
$450$		0			0
$451$	20.1393	−	23.3851i	0.948325	−	1.10116i
$452$		0			0
$453$	−6.34833	+	3.66521i	−0.298271	+	0.172207i
$454$		0			0
$455$	−18.7967	−	23.5322i	−0.881201	−	1.10321i
$456$		0			0
$457$	17.4393	−	10.0686i	0.815777	−	0.470989i	−0.0331810	−	0.999449i	$-0.510564\pi$
$457$	17.4393	−	10.0686i	0.815777	−	0.470989i	0.848958	+	0.528460i	$0.177230\pi$
$458$		0			0
$459$	9.59245	−	16.6146i	0.447737	−	0.775504i
$460$		0			0
$461$		−	12.6639i		−	0.589818i	−0.955525	−	0.294909i	$-0.904711\pi$
$461$		−	12.6639i		−	0.589818i	0.955525	−	0.294909i	$-0.0952893\pi$
$462$		0			0
$463$		−	18.2055i		−	0.846081i	−0.906111	−	0.423040i	$-0.860963\pi$
$463$		−	18.2055i		−	0.846081i	0.906111	−	0.423040i	$-0.139037\pi$
$464$		0			0
$465$	13.8262	−	23.9476i	0.641173	−	1.11054i
$466$		0			0
$467$	2.60403	−	1.50344i	0.120500	−	0.0695709i	−0.438538	−	0.898712i	$-0.644504\pi$
$467$	2.60403	−	1.50344i	0.120500	−	0.0695709i	0.559039	+	0.829142i	$0.311170\pi$
$468$		0			0
$469$	−6.75249	+	17.2450i	−0.311801	+	0.796301i
$470$		0			0
$471$	−54.7807	+	31.6277i	−2.52416	+	1.45733i
$472$		0			0
$473$	17.3395	+	14.9329i	0.797273	+	0.686616i
$474$		0			0
$475$	0.122208			0.00560730
$476$		0			0
$477$	4.39753			0.201349
$478$		0			0
$479$	2.55143	−	4.41920i	0.116578	−	0.201919i	−0.801832	−	0.597550i	$-0.796141\pi$
$479$	2.55143	−	4.41920i	0.116578	−	0.201919i	0.918409	+	0.395631i	$0.129474\pi$
$480$		0			0
$481$	−40.9877	+	23.6643i	−1.86888	+	1.07900i
$482$		0			0
$483$	2.68908	+	17.7460i	0.122357	+	0.807470i
$484$		0			0
$485$	−4.20863	−	7.28955i	−0.191104	−	0.331002i
$486$		0			0
$487$	−36.7933	−	21.2426i	−1.66726	−	0.962595i	−0.969104	−	0.246653i	$-0.920669\pi$
$487$	−36.7933	−	21.2426i	−1.66726	−	0.962595i	−0.698160	−	0.715942i	$-0.745997\pi$
$488$		0			0
$489$	−1.03526			−0.0468161
$490$		0			0
$491$	24.9159			1.12444			0.562218	−	0.826989i	$-0.309948\pi$
$491$	24.9159			1.12444			0.562218	+	0.826989i	$0.309948\pi$
$492$		0			0
$493$	−17.0601	+	29.5489i	−0.768348	+	1.33082i
$494$		0			0
$495$	25.7903	−	9.01384i	1.15919	−	0.405142i
$496$		0			0
$497$	32.3209	−	4.89764i	1.44979	−	0.219689i
$498$		0			0
$499$	16.3033	−	9.41272i	0.729836	−	0.421371i	−0.0885260	−	0.996074i	$-0.528216\pi$
$499$	16.3033	−	9.41272i	0.729836	−	0.421371i	0.818362	+	0.574703i	$0.194882\pi$
$500$		0			0
$501$	35.5693	+	20.5360i	1.58912	+	0.917480i
$502$		0			0
$503$	−14.4104			−0.642528			−0.321264	−	0.946990i	$-0.604108\pi$
$503$	−14.4104			−0.642528			−0.321264	+	0.946990i	$0.604108\pi$
$504$		0			0
$505$			25.8550i			1.15053i
$506$		0			0
$507$	59.4468	+	34.3216i	2.64012	+	1.52428i
$508$		0			0
$509$	−15.7215	−	27.2305i	−0.696844	−	1.20697i	−0.969555	−	0.244873i	$-0.921254\pi$
$509$	−15.7215	−	27.2305i	−0.696844	−	1.20697i	0.272711	−	0.962096i	$-0.412080\pi$
$510$		0			0
$511$	10.0162	−	25.5802i	0.443091	−	1.13160i
$512$		0			0
$513$	0.265206	−	0.153117i	0.0117091	−	0.00676027i
$514$		0			0
$515$	15.0673	+	8.69910i	0.663944	+	0.383328i
$516$		0			0
$517$	2.73122	+	0.517808i	0.120119	+	0.0227732i
$518$		0			0
$519$	5.64256			0.247681
$520$		0			0
$521$	−7.09844	+	12.2949i	−0.310988	+	0.538648i	−0.978577	−	0.205883i	$-0.933993\pi$
$521$	−7.09844	+	12.2949i	−0.310988	+	0.538648i	0.667588	+	0.744531i	$0.267327\pi$
$522$		0			0
$523$	17.7141	+	30.6817i	0.774583	+	1.34162i	0.935029	+	0.354572i	$0.115373\pi$
$523$	17.7141	+	30.6817i	0.774583	+	1.34162i	−0.160446	+	0.987045i	$0.551293\pi$
$524$		0			0
$525$	7.22235	+	9.04192i	0.315209	+	0.394622i
$526$		0			0
$527$	−13.1261	−	22.7351i	−0.571782	−	0.990355i
$528$		0			0
$529$	−8.41863	+	14.5815i	−0.366027	+	0.633978i
$530$		0			0
$531$		−	11.3872i		−	0.494163i
$532$		0			0
$533$	57.4509			2.48848
$534$		0			0
$535$	15.9710	−	27.6625i	0.690485	−	1.19596i
$536$		0			0
$537$	36.0234	+	62.3944i	1.55452	+	2.69252i
$538$		0			0
$539$	−21.2905	−	9.25827i	−0.917046	−	0.398782i
$540$		0			0
$541$	−31.7599	+	18.3366i	−1.36546	+	0.788351i	−0.990345	−	0.138625i	$-0.955732\pi$
$541$	−31.7599	+	18.3366i	−1.36546	+	0.788351i	−0.375120	+	0.926976i	$0.622398\pi$
$542$		0			0
$543$	30.1111	+	17.3846i	1.29219	+	0.746046i
$544$		0			0
$545$		−	7.18709i		−	0.307861i
$546$		0			0
$547$	12.0112			0.513563			0.256781	−	0.966470i	$-0.417338\pi$
$547$	12.0112			0.513563			0.256781	+	0.966470i	$0.417338\pi$
$548$		0			0
$549$	29.0479	+	16.7708i	1.23974	+	0.715762i
$550$		0			0
$551$	−0.471666	+	0.272317i	−0.0200937	+	0.0116011i
$552$		0			0
$553$	7.56881	−	6.04569i	0.321859	−	0.257089i
$554$		0			0
$555$	−33.4486	+	19.3116i	−1.41981	+	0.819730i
$556$		0			0
$557$	−9.56466	−	5.52216i	−0.405268	−	0.233981i	0.283487	−	0.958976i	$-0.408509\pi$
$557$	−9.56466	−	5.52216i	−0.405268	−	0.233981i	−0.688754	+	0.724995i	$0.741842\pi$
$558$		0			0
$559$			42.5987i			1.80173i
$560$		0			0
$561$	8.07539	−	42.5943i	0.340943	−	1.79833i
$562$		0			0
$563$	1.44517	−	2.50310i	0.0609065	−	0.105493i	−0.833964	−	0.551818i	$-0.813934\pi$
$563$	1.44517	−	2.50310i	0.0609065	−	0.105493i	0.894871	+	0.446325i	$0.147268\pi$
$564$		0			0
$565$	3.26666	+	5.65802i	0.137429	+	0.238035i
$566$		0			0
$567$	−6.01805	−	2.35644i	−0.252734	−	0.0989611i
$568$		0			0
$569$	−26.4397	+	15.2650i	−1.10841	+	0.639942i	−0.938417	−	0.345503i	$-0.887708\pi$
$569$	−26.4397	+	15.2650i	−1.10841	+	0.639942i	−0.169994	+	0.985445i	$0.554375\pi$
$570$		0			0
$571$	−5.79230	+	10.0326i	−0.242400	+	0.419849i	−0.961397	−	0.275163i	$-0.911268\pi$
$571$	−5.79230	+	10.0326i	−0.242400	+	0.419849i	0.718997	+	0.695013i	$0.244601\pi$
$572$		0			0
$573$	−15.0700			−0.629559
$574$		0			0
$575$		−	3.97343i		−	0.165703i
$576$		0			0
$577$	−2.13486	+	3.69769i	−0.0888756	+	0.153937i	−0.907036	−	0.421053i	$-0.861661\pi$
$577$	−2.13486	+	3.69769i	−0.0888756	+	0.153937i	0.818161	+	0.574990i	$0.194994\pi$
$578$		0			0
$579$	−34.6655	−	60.0424i	−1.44065	−	2.49528i
$580$		0			0
$581$	−1.75256	−	11.5656i	−0.0727083	−	0.479822i
$582$		0			0
$583$	3.08173	−	1.07708i	0.127632	−	0.0446081i
$584$		0			0
$585$	44.0441	+	25.4289i	1.82100	+	1.05136i
$586$		0			0
$587$		−	26.9663i		−	1.11302i	−0.830841	−	0.556510i	$-0.812140\pi$
$587$		−	26.9663i		−	1.11302i	0.830841	−	0.556510i	$-0.187860\pi$
$588$		0			0
$589$		−	0.419043i		−	0.0172664i
$590$		0			0
$591$	11.9437	−	20.6871i	0.491299	−	0.850954i
$592$		0			0
$593$	1.11945	−	0.646317i	0.0459705	−	0.0265411i	−0.476839	−	0.878991i	$-0.658217\pi$
$593$	1.11945	−	0.646317i	0.0459705	−	0.0265411i	0.522809	+	0.852450i	$0.324884\pi$
$594$		0			0
$595$	−23.0702	+	3.49587i	−0.945785	+	0.143317i
$596$		0			0
$597$	−22.3876	−	38.7765i	−0.916264	−	1.58702i
$598$		0			0
$599$	−23.7684	−	13.7227i	−0.971151	−	0.560694i	−0.0715641	−	0.997436i	$-0.522799\pi$
$599$	−23.7684	−	13.7227i	−0.971151	−	0.560694i	−0.899587	+	0.436742i	$0.856132\pi$
$600$		0			0
$601$			46.4003i			1.89271i	0.323134	+	0.946353i	$0.395264\pi$
$601$			46.4003i			1.89271i	−0.323134	+	0.946353i	$0.604736\pi$
$602$		0			0
$603$		−	31.2733i		−	1.27355i
$604$		0			0
$605$	15.8658	−	12.6336i	0.645035	−	0.513628i
$606$		0			0
$607$	−20.4155	−	35.3606i	−0.828638	−	1.43524i	−0.899107	−	0.437729i	$-0.855783\pi$
$607$	−20.4155	−	35.3606i	−0.828638	−	1.43524i	0.0704687	−	0.997514i	$-0.477550\pi$
$608$		0			0
$609$	−48.0230	−	18.8040i	−1.94599	−	0.761976i
$610$		0			0
$611$	2.58744	+	4.48157i	0.104676	+	0.181305i
$612$		0			0
$613$	17.6736	+	10.2039i	0.713830	+	0.412130i	0.812477	−	0.582993i	$-0.198118\pi$
$613$	17.6736	+	10.2039i	0.713830	+	0.412130i	−0.0986478	+	0.995122i	$0.531452\pi$
$614$		0			0
$615$	46.8836			1.89053
$616$		0			0
$617$	20.2163			0.813878			0.406939	−	0.913455i	$-0.366596\pi$
$617$	20.2163			0.813878			0.406939	+	0.913455i	$0.366596\pi$
$618$		0			0
$619$	22.8202	+	13.1753i	0.917223	+	0.529559i	0.882748	−	0.469846i	$-0.155691\pi$
$619$	22.8202	+	13.1753i	0.917223	+	0.529559i	0.0344751	+	0.999406i	$0.489024\pi$
$620$		0			0
$621$	−4.97837	−	8.62279i	−0.199775	−	0.346021i
$622$		0			0
$623$	−3.59931	+	2.87500i	−0.144203	+	0.115184i
$624$		0			0
$625$	7.21761	+	12.5013i	0.288704	+	0.500051i
$626$		0			0
$627$	0.451581	−	0.524359i	0.0180344	−	0.0209409i
$628$		0			0
$629$			36.6675i			1.46203i
$630$		0			0
$631$		−	7.01354i		−	0.279205i	−0.990208	−	0.139602i	$-0.955418\pi$
$631$		−	7.01354i		−	0.279205i	0.990208	−	0.139602i	$-0.0445824\pi$
$632$		0			0
$633$	−6.00098	−	3.46467i	−0.238517	−	0.137708i
$634$		0			0
$635$	−19.7995	−	34.2937i	−0.785719	−	1.36091i
$636$		0			0
$637$	−12.8039	−	41.2783i	−0.507311	−	1.63550i
$638$		0			0
$639$	−47.8056	+	27.6006i	−1.89116	+	1.09186i
$640$		0			0
$641$	−12.1738	+	21.0856i	−0.480834	+	0.832830i	−0.999758	−	0.0219910i	$-0.992999\pi$
$641$	−12.1738	+	21.0856i	−0.480834	+	0.832830i	0.518924	+	0.854820i	$0.326333\pi$
$642$		0			0
$643$			35.7907i			1.41145i	0.708487	+	0.705724i	$0.249378\pi$
$643$			35.7907i			1.41145i	−0.708487	+	0.705724i	$0.750622\pi$
$644$		0			0
$645$			34.7633i			1.36880i
$646$		0			0
$647$	12.2099	+	7.04939i	0.480021	+	0.277140i	0.720425	−	0.693533i	$-0.243947\pi$
$647$	12.2099	+	7.04939i	0.480021	+	0.277140i	−0.240404	+	0.970673i	$0.577280\pi$
$648$		0			0
$649$	−2.78906	−	7.98002i	−0.109480	−	0.313243i
$650$		0			0
$651$	31.0041	−	24.7649i	1.21515	−	0.970614i
$652$		0			0
$653$	13.1384	+	22.7564i	0.514146	+	0.890526i	0.999865	+	0.0164118i	$0.00522428\pi$
$653$	13.1384	+	22.7564i	0.514146	+	0.890526i	−0.485720	+	0.874115i	$0.661442\pi$
$654$		0			0
$655$	−8.98519	+	15.5628i	−0.351080	+	0.608089i
$656$		0			0
$657$			46.3888i			1.80980i
$658$		0			0
$659$	−37.6304			−1.46587			−0.732937	−	0.680297i	$-0.761851\pi$
$659$	−37.6304			−1.46587			−0.732937	+	0.680297i	$0.761851\pi$
$660$		0			0
$661$	−9.95072	+	17.2352i	−0.387038	+	0.670370i	−0.992050	−	0.125847i	$-0.959835\pi$
$661$	−9.95072	+	17.2352i	−0.387038	+	0.670370i	0.605011	+	0.796217i	$0.293169\pi$
$662$		0			0
$663$	69.8916	−	40.3519i	2.71436	−	1.56714i
$664$		0			0
$665$	−0.346816	−	0.135800i	−0.0134489	−	0.00526609i
$666$		0			0
$667$	8.85399	+	15.3356i	0.342828	+	0.593795i
$668$		0			0
$669$	25.6837	−	44.4854i	0.992987	−	1.71990i
$670$		0			0
$671$	24.4641	+	4.63811i	0.944426	+	0.179052i
$672$		0			0
$673$			14.9594i			0.576642i	0.957534	+	0.288321i	$0.0930971\pi$
$673$			14.9594i			0.576642i	−0.957534	+	0.288321i	$0.906903\pi$
$674$		0			0
$675$	−5.55954	−	3.20980i	−0.213987	−	0.123545i
$676$		0			0
$677$	−11.2660	+	6.50443i	−0.432987	+	0.249985i	−0.700619	−	0.713536i	$-0.747092\pi$
$677$	−11.2660	+	6.50443i	−0.432987	+	0.249985i	0.267631	+	0.963521i	$0.413759\pi$
$678$		0			0
$679$	−1.80964	−	11.9423i	−0.0694474	−	0.458303i
$680$		0			0
$681$	−24.5682	+	14.1844i	−0.941454	+	0.543549i
$682$		0			0
$683$	−12.2862	−	7.09346i	−0.470120	−	0.271424i	0.246170	−	0.969227i	$-0.420828\pi$
$683$	−12.2862	−	7.09346i	−0.470120	−	0.271424i	−0.716290	+	0.697803i	$0.754161\pi$
$684$		0			0
$685$	−34.1401			−1.30443
$686$		0			0
$687$		−	21.9073i		−	0.835816i
$688$		0			0
$689$	5.26292	+	3.03855i	0.200501	+	0.115759i
$690$		0			0
$691$	−12.7549	+	7.36405i	−0.485220	+	0.280142i	−0.722589	−	0.691278i	$-0.757048\pi$
$691$	−12.7549	+	7.36405i	−0.485220	+	0.280142i	0.237369	+	0.971419i	$0.423715\pi$
$692$		0			0
$693$	39.1771	+	1.44932i	1.48821	+	0.0550551i
$694$		0			0
$695$	−12.0650	−	20.8972i	−0.457651	−	0.792676i
$696$		0			0
$697$	22.2549	−	38.5466i	0.842963	−	1.46006i
$698$		0			0
$699$	−54.9443			−2.07818
$700$		0			0
$701$		−	18.8287i		−	0.711150i	−0.934648	−	0.355575i	$-0.884285\pi$
$701$		−	18.8287i		−	0.711150i	0.934648	−	0.355575i	$-0.115715\pi$
$702$		0			0
$703$	−0.292647	+	0.506880i	−0.0110374	+	0.0191173i
$704$		0			0
$705$	2.11151	+	3.65725i	0.0795242	+	0.137740i
$706$		0			0
$707$	−13.5275	+	34.5474i	−0.508752	+	1.29929i
$708$		0			0
$709$	12.6591	+	21.9263i	0.475424	+	0.823459i	0.999604	−	0.0281488i	$-0.00896121\pi$
$709$	12.6591	+	21.9263i	0.475424	+	0.823459i	−0.524179	+	0.851608i	$0.675628\pi$
$710$		0			0
$711$	−8.17885	+	14.1662i	−0.306731	+	0.531274i
$712$		0			0
$713$	−13.6246			−0.510245
$714$		0			0
$715$	37.0938	+	7.03257i	1.38723	+	0.263003i
$716$		0			0
$717$	44.5519	+	25.7221i	1.66382	+	0.960608i
$718$		0			0
$719$	−4.42880	+	2.55697i	−0.165167	+	0.0953589i	−0.580305	−	0.814399i	$-0.697067\pi$
$719$	−4.42880	+	2.55697i	−0.165167	+	0.0953589i	0.415138	+	0.909758i	$0.363733\pi$
$720$		0			0
$721$	15.5815	+	19.5070i	0.580285	+	0.726480i
$722$		0			0
$723$	−4.88388	−	8.45912i	−0.181633	−	0.314598i
$724$		0			0
$725$	9.88760	+	5.70861i	0.367216	+	0.212012i
$726$		0			0
$727$		−	37.7325i		−	1.39942i	−0.714427	−	0.699710i	$-0.753312\pi$
$727$		−	37.7325i		−	1.39942i	0.714427	−	0.699710i	$-0.246688\pi$
$728$		0			0
$729$	43.7945			1.62202
$730$		0			0
$731$	28.5815	+	16.5015i	1.05712	+	0.610331i
$732$		0			0
$733$	−32.4929	+	18.7598i	−1.20015	+	0.692909i	−0.960589	−	0.277972i	$-0.910338\pi$
$733$	−32.4929	+	18.7598i	−1.20015	+	0.692909i	−0.239564	+	0.970881i	$0.577005\pi$
$734$		0			0
$735$	−10.4488	−	33.6857i	−0.385411	−	1.24252i
$736$		0			0
$737$	−7.65973	−	21.9159i	−0.282150	−	0.807284i
$738$		0			0
$739$	13.7372	−	23.7935i	0.505330	−	0.875257i	−0.494651	−	0.869092i	$-0.664704\pi$
$739$	13.7372	−	23.7935i	0.505330	−	0.875257i	0.999981	−	0.00616541i	$-0.00196252\pi$
$740$		0			0
$741$	1.28821			0.0473236
$742$		0			0
$743$	19.4883			0.714957			0.357479	−	0.933921i	$-0.383636\pi$
$743$	19.4883			0.714957			0.357479	+	0.933921i	$0.383636\pi$
$744$		0			0
$745$	−12.8956	−	7.44527i	−0.472458	−	0.272774i
$746$		0			0
$747$	9.87650	+	17.1066i	0.361362	+	0.625898i
$748$		0			0
$749$	35.8136	−	28.6066i	1.30860	−	1.04526i
$750$		0			0
$751$	−12.3565	+	7.13403i	−0.450895	+	0.260324i	−0.708208	−	0.706004i	$-0.750496\pi$
$751$	−12.3565	+	7.13403i	−0.450895	+	0.260324i	0.257313	+	0.966328i	$0.417163\pi$
$752$		0			0
$753$	8.98052	−	15.5547i	0.327268	−	0.566845i
$754$		0			0
$755$	−4.94582			−0.179997
$756$		0			0
$757$	−26.2019			−0.952322			−0.476161	−	0.879358i	$-0.657972\pi$
$757$	−26.2019			−0.952322			−0.476161	+	0.879358i	$0.657972\pi$
$758$		0			0
$759$	−17.0488	−	14.6825i	−0.618831	−	0.532941i
$760$		0			0
$761$	19.0866	−	11.0197i	0.691890	−	0.399463i	−0.112430	−	0.993660i	$-0.535863\pi$
$761$	19.0866	−	11.0197i	0.691890	−	0.399463i	0.804320	+	0.594197i	$0.202530\pi$
$762$		0			0
$763$	3.76032	−	9.60340i	0.136133	−	0.347666i
$764$		0			0
$765$	34.1229	−	19.7009i	1.23372	−	0.712287i
$766$		0			0
$767$	7.86820	−	13.6281i	0.284104	−	0.492083i
$768$		0			0
$769$		−	35.9809i		−	1.29750i	−0.761000	−	0.648751i	$-0.775292\pi$
$769$		−	35.9809i		−	1.29750i	0.761000	−	0.648751i	$-0.224708\pi$
$770$		0			0
$771$		−	78.7235i		−	2.83516i
$772$		0			0
$773$	8.54251	−	14.7961i	0.307253	−	0.532177i	−0.670508	−	0.741903i	$-0.733924\pi$
$773$	8.54251	−	14.7961i	0.307253	−	0.532177i	0.977760	+	0.209725i	$0.0672570\pi$
$774$		0			0
$775$	−7.60756	+	4.39222i	−0.273271	+	0.157773i
$776$		0			0
$777$	−54.7980	+	8.30363i	−1.96587	+	0.297891i
$778$		0			0
$779$	0.615288	−	0.355237i	0.0220450	−	0.0127277i
$780$		0			0
$781$	−26.7414	+	31.0511i	−0.956882	+	1.11110i
$782$		0			0
$783$	28.6096			1.02242
$784$		0			0
$785$	−42.6782			−1.52325
$786$		0			0
$787$	−15.4398	+	26.7425i	−0.550369	+	0.953268i	0.447878	+	0.894095i	$0.352180\pi$
$787$	−15.4398	+	26.7425i	−0.550369	+	0.953268i	−0.998248	+	0.0591733i	$0.981154\pi$
$788$		0			0
$789$	47.6754	−	27.5254i	1.69729	−	0.979930i
$790$		0			0
$791$	1.40461	+	9.26938i	0.0499420	+	0.329581i
$792$		0			0
$793$	23.1762	+	40.1424i	0.823011	+	1.42550i
$794$		0			0
$795$	4.29488	+	2.47965i	0.152324	+	0.0879441i
$796$		0			0
$797$	−41.1482			−1.45754			−0.728771	−	0.684757i	$-0.759908\pi$
$797$	−41.1482			−1.45754			−0.728771	+	0.684757i	$0.759908\pi$
$798$		0			0
$799$	4.00920			0.141835
$800$		0			0
$801$	3.88941	−	6.73666i	0.137426	−	0.238028i
$802$		0			0
$803$	11.3620	+	32.5087i	0.400955	+	1.14721i
$804$		0			0
$805$	−4.41534	+	11.2762i	−0.155620	+	0.397434i
$806$		0			0
$807$	−25.2570	+	14.5821i	−0.889089	+	0.513316i
$808$		0			0
$809$	−35.8087	−	20.6742i	−1.25897	−	0.726865i	−0.286093	−	0.958202i	$-0.592357\pi$
$809$	−35.8087	−	20.6742i	−1.25897	−	0.726865i	−0.972874	+	0.231337i	$0.925690\pi$
$810$		0			0
$811$	47.5022			1.66803			0.834013	−	0.551744i	$-0.186038\pi$
$811$	47.5022			1.66803			0.834013	+	0.551744i	$0.186038\pi$
$812$		0			0
$813$		−	61.2433i		−	2.14790i
$814$		0			0
$815$	−0.604907	−	0.349243i	−0.0211890	−	0.0122335i
$816$		0			0
$817$	0.263401	+	0.456224i	0.00921523	+	0.0159612i
$818$		0			0
$819$	45.5473	+	57.0222i	1.59155	+	1.99252i
$820$		0			0
$821$	−36.0917	+	20.8376i	−1.25961	+	0.727236i	−0.972998	−	0.230812i	$-0.925862\pi$
$821$	−36.0917	+	20.8376i	−1.25961	+	0.727236i	−0.286610	+	0.958047i	$0.592529\pi$
$822$		0			0
$823$	15.8686	+	9.16174i	0.553144	+	0.319358i	0.750389	−	0.660996i	$-0.229866\pi$
$823$	15.8686	+	9.16174i	0.553144	+	0.319358i	−0.197245	+	0.980354i	$0.563199\pi$
$824$		0			0
$825$	−14.2528	−	2.70217i	−0.496218	−	0.0940774i
$826$		0			0
$827$	−14.6116			−0.508095			−0.254047	−	0.967192i	$-0.581762\pi$
$827$	−14.6116			−0.508095			−0.254047	+	0.967192i	$0.581762\pi$
$828$		0			0
$829$	1.11203	−	1.92609i	0.0386223	−	0.0668958i	−0.846068	−	0.533075i	$-0.821036\pi$
$829$	1.11203	−	1.92609i	0.0386223	−	0.0668958i	0.884690	+	0.466179i	$0.154370\pi$
$830$		0			0
$831$	27.0963	+	46.9322i	0.939960	+	1.62806i
$832$		0			0
$833$	−32.6554	−	7.39926i	−1.13144	−	0.256369i
$834$		0			0
$835$	13.8556	+	23.9985i	0.479491	+	0.830504i
$836$		0			0
$837$	−11.0062	+	19.0633i	−0.380429	+	0.658923i
$838$		0			0
$839$			36.2097i			1.25010i	0.780585	+	0.625049i	$0.214921\pi$
$839$			36.2097i			1.25010i	−0.780585	+	0.625049i	$0.785079\pi$
$840$		0			0
$841$	−21.8819			−0.754550
$842$		0			0
$843$	−12.5778	+	21.7853i	−0.433201	+	0.750326i
$844$		0			0
$845$	23.1567	+	40.1086i	0.796614	+	1.37978i
$846$		0			0
$847$	27.8098	−	8.57993i	0.955556	−	0.294810i
$848$		0			0
$849$	48.0893	−	27.7644i	1.65042	−	0.952871i
$850$		0			0
$851$	16.4805	+	9.51500i	0.564943	+	0.326170i
$852$		0			0
$853$			1.78168i			0.0610036i	0.999535	+	0.0305018i	$0.00971053\pi$
$853$			1.78168i			0.0610036i	−0.999535	+	0.0305018i	$0.990289\pi$
$854$		0			0
$855$	0.628939			0.0215093
$856$		0			0
$857$	−45.6936	−	26.3812i	−1.56086	−	0.901165i	−0.997170	−	0.0751810i	$-0.976047\pi$
$857$	−45.6936	−	26.3812i	−1.56086	−	0.901165i	−0.563694	−	0.825984i	$-0.690620\pi$
$858$		0			0
$859$	−9.06495	+	5.23365i	−0.309292	+	0.178570i	−0.646610	−	0.762821i	$-0.723814\pi$
$859$	−9.06495	+	5.23365i	−0.309292	+	0.178570i	0.337317	+	0.941391i	$0.390480\pi$
$860$		0			0
$861$	62.6460	+	24.5298i	2.13497	+	0.835972i
$862$		0			0
$863$	31.8213	−	18.3721i	1.08321	−	0.625392i	0.151450	−	0.988465i	$-0.451606\pi$
$863$	31.8213	−	18.3721i	1.08321	−	0.625392i	0.931761	+	0.363073i	$0.118272\pi$
$864$		0			0
$865$	3.29698	+	1.90351i	0.112101	+	0.0647213i
$866$		0			0
$867$		−	16.0687i		−	0.545723i
$868$		0			0
$869$	−2.26193	+	11.9307i	−0.0767307	+	0.404722i
$870$		0			0
$871$	21.6088	−	37.4276i	0.732187	−	1.26819i
$872$		0			0
$873$	10.1982	+	17.6637i	0.345156	+	0.597827i
$874$		0			0
$875$	4.82400	+	31.8349i	0.163081	+	1.07622i
$876$		0			0
$877$	23.3289	−	13.4690i	0.787762	−	0.454814i	−0.0514124	−	0.998678i	$-0.516372\pi$
$877$	23.3289	−	13.4690i	0.787762	−	0.454814i	0.839174	+	0.543863i	$0.183039\pi$
$878$		0			0
$879$	29.3382	−	50.8152i	0.989552	−	1.71395i
$880$		0			0
$881$	−21.0892			−0.710515			−0.355257	−	0.934769i	$-0.615607\pi$
$881$	−21.0892			−0.710515			−0.355257	+	0.934769i	$0.615607\pi$
$882$		0			0
$883$			4.73889i			0.159476i	0.996816	+	0.0797381i	$0.0254084\pi$
$883$			4.73889i			0.159476i	−0.996816	+	0.0797381i	$0.974592\pi$
$884$		0			0
$885$	6.42095	−	11.1214i	0.215838	−	0.373842i
$886$		0			0
$887$	−8.45609	−	14.6464i	−0.283928	−	0.491777i	0.688421	−	0.725311i	$-0.258304\pi$
$887$	−8.45609	−	14.6464i	−0.283928	−	0.491777i	−0.972349	+	0.233534i	$0.924971\pi$
$888$		0			0
$889$	−8.51344	−	56.1825i	−0.285532	−	1.88430i
$890$		0			0
$891$	7.64807	−	2.67304i	0.256220	−	0.0895502i
$892$		0			0
$893$	0.0554219	+	0.0319978i	0.00185462	+	0.00107077i
$894$		0			0
$895$			48.6098i			1.62485i
$896$		0			0
$897$		−	41.8844i		−	1.39848i
$898$		0			0
$899$	19.5744	−	33.9038i	0.652842	−	1.13076i
$900$		0			0
$901$	4.07741	−	2.35410i	0.135838	−	0.0784263i
$902$		0			0
$903$	−18.1883	+	46.4507i	−0.605270	+	1.54578i
$904$		0			0
$905$	11.7294	+	20.3158i	0.389897	+	0.675321i
$906$		0			0
$907$	−37.6834	−	21.7565i	−1.25126	−	0.722413i	−0.279897	−	0.960030i	$-0.590300\pi$
$907$	−37.6834	−	21.7565i	−1.25126	−	0.722413i	−0.971359	+	0.237617i	$0.923634\pi$
$908$		0			0
$909$		−	62.6506i		−	2.07799i
$910$		0			0
$911$		−	38.7627i		−	1.28427i	−0.766593	−	0.642133i	$-0.778050\pi$
$911$		−	38.7627i		−	1.28427i	0.766593	−	0.642133i	$-0.221950\pi$
$912$		0			0
$913$	11.1112	+	9.56905i	0.367728	+	0.316689i
$914$		0			0
$915$	18.9133	+	32.7587i	0.625253	+	1.08297i
$916$		0			0
$917$	−20.1486	+	16.0939i	−0.665364	+	0.531469i
$918$		0			0
$919$	10.7000	+	18.5329i	0.352959	+	0.611343i	0.986766	−	0.162148i	$-0.0518422\pi$
$919$	10.7000	+	18.5329i	0.352959	+	0.611343i	−0.633807	+	0.773491i	$0.718509\pi$
$920$		0			0
$921$	−31.1573	−	17.9887i	−1.02667	−	0.592748i
$922$		0			0
$923$	−76.2844			−2.51093
$924$		0			0
$925$	12.2696			0.403422
$926$		0			0
$927$	−36.5104	−	21.0793i	−1.19916	−	0.692335i
$928$		0			0
$929$	1.74271	+	3.01847i	0.0571765	+	0.0990327i	0.893197	−	0.449666i	$-0.148457\pi$
$929$	1.74271	+	3.01847i	0.0571765	+	0.0990327i	−0.836020	+	0.548698i	$0.815124\pi$
$930$		0			0
$931$	−0.392364	−	0.362912i	−0.0128592	−	0.0118939i
$932$		0			0
$933$	−25.9317	−	44.9150i	−0.848966	−	1.47045i
$934$		0			0
$935$	19.0876	−	22.1638i	0.624231	−	0.724834i
$936$		0			0
$937$			19.1232i			0.624727i	0.949963	+	0.312363i	$0.101121\pi$
$937$			19.1232i			0.624727i	−0.949963	+	0.312363i	$0.898879\pi$
$938$		0			0
$939$			13.3484i			0.435609i
$940$		0			0
$941$	3.13877	+	1.81217i	0.102321	+	0.0590750i	0.550287	−	0.834975i	$-0.314518\pi$
$941$	3.13877	+	1.81217i	0.102321	+	0.0590750i	−0.447966	+	0.894050i	$0.647852\pi$
$942$		0			0
$943$	−11.5500	−	20.0052i	−0.376120	−	0.651460i
$944$		0			0
$945$	12.2107	+	15.2870i	0.397213	+	0.497285i
$946$		0			0
$947$	30.0146	−	17.3289i	0.975343	−	0.563114i	0.0744818	−	0.997222i	$-0.476270\pi$
$947$	30.0146	−	17.3289i	0.975343	−	0.563114i	0.900861	+	0.434108i	$0.142936\pi$
$948$		0			0
$949$	−32.0531	+	55.5177i	−1.04049	+	1.80218i
$950$		0			0
$951$		−	28.5667i		−	0.926339i
$952$		0			0
$953$			24.7336i			0.801199i	0.916253	+	0.400600i	$0.131198\pi$
$953$			24.7336i			0.801199i	−0.916253	+	0.400600i	$0.868802\pi$
$954$		0			0
$955$	−8.80548	−	5.08385i	−0.284939	−	0.164509i
$956$		0			0
$957$	61.0303	−	21.3304i	1.97283	−	0.689514i
$958$		0			0
$959$	−45.6180	−	17.8623i	−1.47308	−	0.576803i
$960$		0			0
$961$	−0.439387	−	0.761040i	−0.0141738	−	0.0245497i
$962$		0			0
$963$	−38.7002	+	67.0307i	−1.24710	+	2.16003i
$964$		0			0
$965$		−	46.7774i		−	1.50582i
$966$		0			0
$967$	−11.6024			−0.373108			−0.186554	−	0.982445i	$-0.559732\pi$
$967$	−11.6024			−0.373108			−0.186554	+	0.982445i	$0.559732\pi$
$968$		0			0
$969$	0.499017	−	0.864323i	0.0160307	−	0.0277660i
$970$		0			0
$971$	−16.5816	+	9.57341i	−0.532130	+	0.307225i	−0.741883	−	0.670529i	$-0.766067\pi$
$971$	−16.5816	+	9.57341i	−0.532130	+	0.307225i	0.209753	+	0.977754i	$0.432734\pi$
$972$		0			0
$973$	−5.18774	−	34.2353i	−0.166311	−	1.09753i
$974$		0			0
$975$	−13.5025	−	23.3870i	−0.432425	−	0.748982i
$976$		0			0
$977$	16.6964	−	28.9189i	0.534164	−	0.925199i	−0.465040	−	0.885290i	$-0.653960\pi$
$977$	16.6964	−	28.9189i	0.534164	−	0.925199i	0.999203	−	0.0399089i	$-0.0127068\pi$
$978$		0			0
$979$	1.07565	−	5.67360i	0.0343779	−	0.181329i
$980$		0			0
$981$			17.4155i			0.556033i
$982$		0			0
$983$	−2.09139	−	1.20746i	−0.0667050	−	0.0385121i	0.466277	−	0.884639i	$-0.345595\pi$
$983$	−2.09139	−	1.20746i	−0.0667050	−	0.0385121i	−0.532982	+	0.846127i	$0.678928\pi$
$984$		0			0
$985$	13.9575	−	8.05839i	0.444724	−	0.256762i
$986$		0			0
$987$	0.907914	+	5.99158i	0.0288992	+	0.190714i
$988$		0			0
$989$	14.8335	−	8.56410i	0.471677	−	0.272323i
$990$		0			0
$991$	6.21162	+	3.58628i	0.197318	+	0.113922i	0.595404	−	0.803426i	$-0.296992\pi$
$991$	6.21162	+	3.58628i	0.197318	+	0.113922i	−0.398086	+	0.917348i	$0.630325\pi$
$992$		0			0
$993$	−24.0154			−0.762105
$994$		0			0
$995$		−	30.2097i		−	0.957712i
$996$		0			0
$997$	−18.8211	−	10.8664i	−0.596070	−	0.344141i	0.171424	−	0.985197i	$-0.445163\pi$
$997$	−18.8211	−	10.8664i	−0.596070	−	0.344141i	−0.767494	+	0.641056i	$0.778496\pi$
$998$		0			0
$999$	26.6264	−	15.3728i	0.842422	−	0.486373i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1232.2.bi.b.879.2	yes	32
4.3	odd	2		1232.2.bi.a.879.15	yes	32
7.2	even	3		1232.2.bi.a.527.16	yes	32
11.10	odd	2	inner	1232.2.bi.b.879.1	yes	32
28.23	odd	6	inner	1232.2.bi.b.527.1	yes	32
44.43	even	2		1232.2.bi.a.879.16	yes	32
77.65	odd	6		1232.2.bi.a.527.15	✓	32
308.219	even	6	inner	1232.2.bi.b.527.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1232.2.bi.a.527.15	✓	32	77.65	odd	6
1232.2.bi.a.527.16	yes	32	7.2	even	3
1232.2.bi.a.879.15	yes	32	4.3	odd	2
1232.2.bi.a.879.16	yes	32	44.43	even	2
1232.2.bi.b.527.1	yes	32	28.23	odd	6	inner
1232.2.bi.b.527.2	yes	32	308.219	even	6	inner
1232.2.bi.b.879.1	yes	32	11.10	odd	2	inner
1232.2.bi.b.879.2	yes	32	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1232.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.36660 - 1.36635i) q^{3} +(-0.921875 - 1.59674i) q^{5} +(-0.396390 - 2.61589i) q^{7} +(2.23385 + 3.86914i) q^{9} +O(q^{10})\)	\(q+(-2.36660 - 1.36635i) q^{3} +(-0.921875 - 1.59674i) q^{5} +(-0.396390 - 2.61589i) q^{7} +(2.23385 + 3.86914i) q^{9} +(2.51312 + 2.16431i) q^{11} +6.17407i q^{13} +5.03843i q^{15} +(4.14248 + 2.39166i) q^{17} +(0.0381762 + 0.0661231i) q^{19} +(-2.63614 + 6.73236i) q^{21} +(2.14990 - 1.24124i) q^{23} +(0.800292 - 1.38615i) q^{25} -4.01079i q^{27} +7.13316i q^{29} +(-4.75299 - 2.74414i) q^{31} +(-2.99032 - 8.55586i) q^{33} +(-3.81146 + 3.04445i) q^{35} +(3.83285 + 6.63869i) q^{37} +(8.43596 - 14.6115i) q^{39} -9.30520i q^{41} +6.89962 q^{43} +(4.11866 - 7.13373i) q^{45} +(0.725870 - 0.419081i) q^{47} +(-6.68575 + 2.07383i) q^{49} +(-6.53571 - 11.3202i) q^{51} +(0.492147 - 0.852423i) q^{53} +(1.13905 - 6.00801i) q^{55} -0.208649i q^{57} +(-2.20732 - 1.27439i) q^{59} +(6.50177 - 3.75380i) q^{61} +(9.23577 - 7.37719i) q^{63} +(9.85835 - 5.69172i) q^{65} +(-6.06206 - 3.49993i) q^{67} -6.78392 q^{69} +12.3556i q^{71} +(8.99208 + 5.19158i) q^{73} +(-3.78793 + 2.18696i) q^{75} +(4.66542 - 7.43195i) q^{77} +(1.83066 + 3.17080i) q^{79} +(1.22138 - 2.11550i) q^{81} +4.42129 q^{83} -8.81925i q^{85} +(9.74642 - 16.8813i) q^{87} +(-0.870563 - 1.50786i) q^{89} +(16.1507 - 2.44734i) q^{91} +(7.49894 + 12.9885i) q^{93} +(0.0703873 - 0.121914i) q^{95} +4.56529 q^{97} +(-2.76010 + 14.5583i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{5} + 12 q^{9}+O(q^{10}) \) 32 * q - 2 * q^5 + 12 * q^9	\( 32 q - 2 q^{5} + 12 q^{9} + 9 q^{11} + 18 q^{23} - 6 q^{25} + 5 q^{33} - 6 q^{37} - 10 q^{45} + 36 q^{47} - 32 q^{49} + 42 q^{59} + 18 q^{67} - 24 q^{69} + 78 q^{75} - 19 q^{77} - 24 q^{81} - 8 q^{89} + 18 q^{91} + 2 q^{93} + 12 q^{97}+O(q^{100}) \) 32 * q - 2 * q^5 + 12 * q^9 + 9 * q^11 + 18 * q^23 - 6 * q^25 + 5 * q^33 - 6 * q^37 - 10 * q^45 + 36 * q^47 - 32 * q^49 + 42 * q^59 + 18 * q^67 - 24 * q^69 + 78 * q^75 - 19 * q^77 - 24 * q^81 - 8 * q^89 + 18 * q^91 + 2 * q^93 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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