LMFDB - Embedded newform 1764.2.b.l.1567.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1764,2,Mod(1567,1764)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1764, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1764.1567"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,-4,0,-4,0,0,0,-4,0,0,0,0,0,0,0,-4,0,0,0,-24,0,0,0,0,-12,24, 0,0,-32,0,-16,-4,0,-32,0,0,32,-24,0,32,0,0,0,24,0,24,0,0,0,28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(50)] == traces)

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

Self dual:	no
Analytic conductor:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.15911316233388032.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 10 x^{10} - 20 x^{9} + 35 x^{8} - 56 x^{7} + 84 x^{6} - 112 x^{5} + 140 x^{4} + \cdots + 64 $ x^12 - 4x^11 + 10x^10 - 20x^9 + 35x^8 - 56x^7 + 84x^6 - 112x^5 + 140x^4 - 160x^3 + 160x^2 - 128*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 588)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1567.1
Root			$1.34902 + 0.424442i$ of defining polynomial
Character	$\chi$	$=$	1764.1567
Dual form			1764.2.b.l.1567.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.34902 - 0.424442i) q^{2} +(1.63970 + 1.14516i) q^{4} +0.127929i q^{5} +(-1.72593 - 2.24080i) q^{8} +(0.0542984 - 0.172579i) q^{10} -3.99455i q^{11} -0.891655i q^{13} +(1.37722 + 3.75543i) q^{16} -5.82842i q^{17} +6.31490 q^{19} +(-0.146499 + 0.209765i) q^{20} +(-1.69545 + 5.38872i) q^{22} +6.60535i q^{23} +4.98363 q^{25} +(-0.378456 + 1.20286i) q^{26} -2.82968 q^{29} -8.45337 q^{31} +(-0.263934 - 5.65069i) q^{32} +(-2.47383 + 7.86264i) q^{34} -8.67912 q^{37} +(-8.51891 - 2.68031i) q^{38} +(0.286663 - 0.220796i) q^{40} -3.24650i q^{41} -0.881836i q^{43} +(4.57439 - 6.54985i) q^{44} +(2.80359 - 8.91074i) q^{46} -10.0136 q^{47} +(-6.72301 - 2.11526i) q^{50} +(1.02109 - 1.46204i) q^{52} +7.53454 q^{53} +0.511019 q^{55} +(3.81729 + 1.20104i) q^{58} -0.588819 q^{59} -1.68795i q^{61} +(11.4037 + 3.58796i) q^{62} +(-2.04234 + 7.73491i) q^{64} +0.114069 q^{65} -6.35238i q^{67} +(6.67447 - 9.55685i) q^{68} +11.3856i q^{71} -15.5139i q^{73} +(11.7083 + 3.68378i) q^{74} +(10.3545 + 7.23156i) q^{76} -9.82324i q^{79} +(-0.480429 + 0.176187i) q^{80} +(-1.37795 + 4.37958i) q^{82} -1.48021 q^{83} +0.745624 q^{85} +(-0.374288 + 1.18961i) q^{86} +(-8.95097 + 6.89430i) q^{88} -0.449983i q^{89} +(-7.56418 + 10.8308i) q^{92} +(13.5085 + 4.25018i) q^{94} +0.807859i q^{95} -16.2042i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - 4 q^{4} - 4 q^{8} - 4 q^{16} - 24 q^{20} - 12 q^{25} + 24 q^{26} - 32 q^{29} - 16 q^{31} - 4 q^{32} - 32 q^{34} + 32 q^{37} - 24 q^{38} + 32 q^{40} + 24 q^{44} + 24 q^{46} + 28 q^{50} - 32 q^{52}+ \cdots + 24 q^{88}+O(q^{100}) $ 12 * q - 4 * q^2 - 4 * q^4 - 4 * q^8 - 4 * q^16 - 24 * q^20 - 12 * q^25 + 24 * q^26 - 32 * q^29 - 16 * q^31 - 4 * q^32 - 32 * q^34 + 32 * q^37 - 24 * q^38 + 32 * q^40 + 24 * q^44 + 24 * q^46 + 28 * q^50 - 32 * q^52 + 32 * q^53 - 16 * q^55 + 16 * q^58 - 16 * q^59 + 8 * q^62 - 4 * q^64 - 8 * q^68 + 32 * q^74 + 32 * q^76 - 16 * q^80 - 32 * q^82 - 16 * q^83 + 16 * q^85 + 24 * q^86 + 24 * q^88

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.34902	−	0.424442i	−0.953900	−	0.300126i
$2$	−1.34902	−	0.424442i	−0.953900	−	0.300126i
$3$		0			0
$3$		0			0
$4$	1.63970	+	1.14516i	0.819849	+	0.572580i
$5$			0.127929i			0.0572116i	0.999591	+	0.0286058i	$0.00910675\pi$
$5$			0.127929i			0.0572116i	−0.999591	+	0.0286058i	$0.990893\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.72593	−	2.24080i	−0.610208	−	0.792241i
$9$		0			0
$10$	0.0542984	−	0.172579i	0.0171707	−	0.0545741i
$11$		−	3.99455i		−	1.20440i	−0.798345	−	0.602201i	$-0.794291\pi$
$11$		−	3.99455i		−	1.20440i	0.798345	−	0.602201i	$-0.205709\pi$
$12$		0			0
$13$		−	0.891655i		−	0.247301i	−0.992326	−	0.123650i	$-0.960540\pi$
$13$		−	0.891655i		−	0.247301i	0.992326	−	0.123650i	$-0.0394601\pi$
$14$		0			0
$15$		0			0
$16$	1.37722	+	3.75543i	0.344305	+	0.938858i
$17$		−	5.82842i		−	1.41360i	−0.707414	−	0.706800i	$-0.750138\pi$
$17$		−	5.82842i		−	1.41360i	0.707414	−	0.706800i	$-0.249862\pi$
$18$		0			0
$19$	6.31490			1.44874			0.724368	−	0.689413i	$-0.242132\pi$
$19$	6.31490			1.44874			0.724368	+	0.689413i	$0.242132\pi$
$20$	−0.146499	+	0.209765i	−0.0327582	+	0.0469049i
$21$		0			0
$22$	−1.69545	+	5.38872i	−0.361472	+	1.14888i
$23$			6.60535i			1.37731i	0.725089	+	0.688656i	$0.241799\pi$
$23$			6.60535i			1.37731i	−0.725089	+	0.688656i	$0.758201\pi$
$24$		0			0
$25$	4.98363			0.996727
$26$	−0.378456	+	1.20286i	−0.0742212	+	0.235900i
$27$		0			0
$28$		0			0
$29$	−2.82968			−0.525459			−0.262729	−	0.964870i	$-0.584623\pi$
$29$	−2.82968			−0.525459			−0.262729	+	0.964870i	$0.584623\pi$
$30$		0			0
$31$	−8.45337			−1.51827			−0.759135	−	0.650934i	$-0.774378\pi$
$31$	−8.45337			−1.51827			−0.759135	+	0.650934i	$0.774378\pi$
$32$	−0.263934	−	5.65069i	−0.0466573	−	0.998911i
$33$		0			0
$34$	−2.47383	+	7.86264i	−0.424258	+	1.34843i
$35$		0			0
$36$		0			0
$37$	−8.67912			−1.42684			−0.713419	−	0.700737i	$-0.752854\pi$
$37$	−8.67912			−1.42684			−0.713419	+	0.700737i	$0.752854\pi$
$38$	−8.51891	−	2.68031i	−1.38195	−	0.434803i
$39$		0			0
$40$	0.286663	−	0.220796i	0.0453254	−	0.0349110i
$41$		−	3.24650i		−	0.507018i	−0.967333	−	0.253509i	$-0.918415\pi$
$41$		−	3.24650i		−	0.507018i	0.967333	−	0.253509i	$-0.0815847\pi$
$42$		0			0
$43$		−	0.881836i		−	0.134479i	−0.997737	−	0.0672394i	$-0.978581\pi$
$43$		−	0.881836i		−	0.134479i	0.997737	−	0.0672394i	$-0.0214191\pi$
$44$	4.57439	−	6.54985i	0.689616	−	0.987427i
$45$		0			0
$46$	2.80359	−	8.91074i	0.413366	−	1.31382i
$47$	−10.0136			−1.46063			−0.730314	−	0.683111i	$-0.760626\pi$
$47$	−10.0136			−1.46063			−0.730314	+	0.683111i	$0.760626\pi$
$48$		0			0
$49$		0			0
$50$	−6.72301	−	2.11526i	−0.950777	−	0.299143i
$51$		0			0
$52$	1.02109	−	1.46204i	0.141599	−	0.202749i
$53$	7.53454			1.03495			0.517474	−	0.855699i	$-0.326872\pi$
$53$	7.53454			1.03495			0.517474	+	0.855699i	$0.326872\pi$
$54$		0			0
$55$	0.511019			0.0689057
$56$		0			0
$57$		0			0
$58$	3.81729	+	1.20104i	0.501235	+	0.157704i
$59$	−0.588819			−0.0766577			−0.0383288	−	0.999265i	$-0.512203\pi$
$59$	−0.588819			−0.0766577			−0.0383288	+	0.999265i	$0.512203\pi$
$60$		0			0
$61$		−	1.68795i		−	0.216120i	−0.994144	−	0.108060i	$-0.965536\pi$
$61$		−	1.68795i		−	0.216120i	0.994144	−	0.108060i	$-0.0344638\pi$
$62$	11.4037	+	3.58796i	1.44828	+	0.455672i
$63$		0			0
$64$	−2.04234	+	7.73491i	−0.255292	+	0.966864i
$65$	0.114069			0.0141485
$66$		0			0
$67$		−	6.35238i		−	0.776067i	−0.921645	−	0.388033i	$-0.873154\pi$
$67$		−	6.35238i		−	0.776067i	0.921645	−	0.388033i	$-0.126846\pi$
$68$	6.67447	−	9.55685i	0.809398	−	1.15894i
$69$		0			0
$70$		0			0
$71$			11.3856i			1.35122i	0.737259	+	0.675610i	$0.236120\pi$
$71$			11.3856i			1.35122i	−0.737259	+	0.675610i	$0.763880\pi$
$72$		0			0
$73$		−	15.5139i		−	1.81577i	−0.419223	−	0.907883i	$-0.637697\pi$
$73$		−	15.5139i		−	1.81577i	0.419223	−	0.907883i	$-0.362303\pi$
$74$	11.7083	+	3.68378i	1.36106	+	0.428231i
$75$		0			0
$76$	10.3545	+	7.23156i	1.18775	+	0.829517i
$77$		0			0
$78$		0			0
$79$		−	9.82324i		−	1.10520i	−0.833446	−	0.552601i	$-0.813636\pi$
$79$		−	9.82324i		−	1.10520i	0.833446	−	0.552601i	$-0.186364\pi$
$80$	−0.480429	+	0.176187i	−0.0537136	+	0.0196983i
$81$		0			0
$82$	−1.37795	+	4.37958i	−0.152169	+	0.483644i
$83$	−1.48021			−0.162474			−0.0812371	−	0.996695i	$-0.525887\pi$
$83$	−1.48021			−0.162474			−0.0812371	+	0.996695i	$0.525887\pi$
$84$		0			0
$85$	0.745624			0.0808743
$86$	−0.374288	+	1.18961i	−0.0403605	+	0.128279i
$87$		0			0
$88$	−8.95097	+	6.89430i	−0.954177	+	0.734935i
$89$		−	0.449983i		−	0.0476981i	−0.999716	−	0.0238490i	$-0.992408\pi$
$89$		−	0.449983i		−	0.0476981i	0.999716	−	0.0238490i	$-0.00759210\pi$
$90$		0			0
$91$		0			0
$92$	−7.56418	+	10.8308i	−0.788620	+	1.12919i
$93$		0			0
$94$	13.5085	+	4.25018i	1.39329	+	0.438372i
$95$			0.807859i			0.0828845i
$96$		0			0
$97$		−	16.2042i		−	1.64529i	−0.568555	−	0.822645i	$-0.692497\pi$
$97$		−	16.2042i		−	1.64529i	0.568555	−	0.822645i	$-0.307503\pi$
$98$		0			0
$99$		0			0
$100$	8.17166	+	5.70705i	0.817166	+	0.570705i
$101$		−	12.0661i		−	1.20062i	−0.799767	−	0.600310i	$-0.795044\pi$
$101$		−	12.0661i		−	1.20062i	0.799767	−	0.600310i	$-0.204956\pi$
$102$		0			0
$103$	−3.28431			−0.323612			−0.161806	−	0.986823i	$-0.551732\pi$
$103$	−3.28431			−0.323612			−0.161806	+	0.986823i	$0.551732\pi$
$104$	−1.99802	+	1.53893i	−0.195922	+	0.150905i
$105$		0			0
$106$	−10.1642	−	3.19797i	−0.987237	−	0.310615i
$107$		−	3.33543i		−	0.322449i	−0.986918	−	0.161224i	$-0.948456\pi$
$107$		−	3.33543i		−	0.322449i	0.986918	−	0.161224i	$-0.0515443\pi$
$108$		0			0
$109$	4.46096			0.427283			0.213641	−	0.976912i	$-0.431468\pi$
$109$	4.46096			0.427283			0.213641	+	0.976912i	$0.431468\pi$
$110$	−0.689373	−	0.216898i	−0.0657292	−	0.0206804i
$111$		0			0
$112$		0			0
$113$	9.16272			0.861956			0.430978	−	0.902362i	$-0.358169\pi$
$113$	9.16272			0.861956			0.430978	+	0.902362i	$0.358169\pi$
$114$		0			0
$115$	−0.845016			−0.0787982
$116$	−4.63983	−	3.24044i	−0.430797	−	0.300867i
$117$		0			0
$118$	0.794327	+	0.249919i	0.0731237	+	0.0230069i
$119$		0			0
$120$		0			0
$121$	−4.95641			−0.450583
$122$	−0.716436	+	2.27707i	−0.0648631	+	0.206157i
$123$		0			0
$124$	−13.8610	−	9.68045i	−1.24475	−	0.869330i
$125$			1.27720i			0.114236i
$126$		0			0
$127$		−	14.0775i		−	1.24917i	−0.780955	−	0.624587i	$-0.785267\pi$
$127$		−	14.0775i		−	1.24917i	0.780955	−	0.624587i	$-0.214733\pi$
$128$	6.03817	−	9.56768i	0.533704	−	0.845671i
$129$		0			0
$130$	−0.153880	−	0.0484155i	−0.0134962	−	0.00424632i
$131$	9.76967			0.853580			0.426790	−	0.904351i	$-0.359644\pi$
$131$	9.76967			0.853580			0.426790	+	0.904351i	$0.359644\pi$
$132$		0			0
$133$		0			0
$134$	−2.69622	+	8.56948i	−0.232918	+	0.740290i
$135$		0			0
$136$	−13.0603	+	10.0594i	−1.11991	+	0.862590i
$137$	3.96852			0.339054			0.169527	−	0.985526i	$-0.445776\pi$
$137$	3.96852			0.339054			0.169527	+	0.985526i	$0.445776\pi$
$138$		0			0
$139$	−0.262023			−0.0222245			−0.0111122	−	0.999938i	$-0.503537\pi$
$139$	−0.262023			−0.0222245			−0.0111122	+	0.999938i	$0.503537\pi$
$140$		0			0
$141$		0			0
$142$	4.83252	−	15.3594i	0.405536	−	1.28893i
$143$	−3.56176			−0.297849
$144$		0			0
$145$		−	0.361999i		−	0.0300623i
$146$	−6.58476	+	20.9286i	−0.544958	+	1.73206i
$147$		0			0
$148$	−14.2311	−	9.93897i	−1.16979	−	0.816979i
$149$	−2.69549			−0.220823			−0.110411	−	0.993886i	$-0.535217\pi$
$149$	−2.69549			−0.220823			−0.110411	+	0.993886i	$0.535217\pi$
$150$		0			0
$151$			4.31664i			0.351284i	0.984454	+	0.175642i	$0.0562000\pi$
$151$			4.31664i			0.351284i	−0.984454	+	0.175642i	$0.943800\pi$
$152$	−10.8991	−	14.1504i	−0.884031	−	1.14775i
$153$		0			0
$154$		0			0
$155$		−	1.08143i		−	0.0868626i
$156$		0			0
$157$		−	3.20616i		−	0.255879i	−0.991782	−	0.127940i	$-0.959164\pi$
$157$		−	3.20616i		−	0.255879i	0.991782	−	0.127940i	$-0.0408364\pi$
$158$	−4.16940	+	13.2517i	−0.331699	+	1.05425i
$159$		0			0
$160$	0.722888	−	0.0337648i	0.0571493	−	0.00266934i
$161$		0			0
$162$		0			0
$163$			23.2619i			1.82201i	0.412393	+	0.911006i	$0.364693\pi$
$163$			23.2619i			1.82201i	−0.412393	+	0.911006i	$0.635307\pi$
$164$	3.71776	−	5.32328i	0.290308	−	0.415678i
$165$		0			0
$166$	1.99683	+	0.628263i	0.154984	+	0.0487627i
$167$	−9.66864			−0.748182			−0.374091	−	0.927392i	$-0.622045\pi$
$167$	−9.66864			−0.748182			−0.374091	+	0.927392i	$0.622045\pi$
$168$		0			0
$169$	12.2050			0.938842
$170$	−1.00586	−	0.316474i	−0.0771460	−	0.0242725i
$171$		0			0
$172$	1.00984	−	1.44595i	0.0769998	−	0.110252i
$173$		−	20.7065i		−	1.57429i	−0.616768	−	0.787145i	$-0.711559\pi$
$173$		−	20.7065i		−	1.57429i	0.616768	−	0.787145i	$-0.288441\pi$
$174$		0			0
$175$		0			0
$176$	15.0012	−	5.50137i	1.13076	−	0.414682i
$177$		0			0
$178$	−0.190991	+	0.607035i	−0.0143154	+	0.0454992i
$179$		−	1.46793i		−	0.109718i	−0.998494	−	0.0548589i	$-0.982529\pi$
$179$		−	1.46793i		−	0.109718i	0.998494	−	0.0548589i	$-0.0174709\pi$
$180$		0			0
$181$		−	23.5472i		−	1.75025i	−0.483898	−	0.875124i	$-0.660779\pi$
$181$		−	23.5472i		−	1.75025i	0.483898	−	0.875124i	$-0.339221\pi$
$182$		0			0
$183$		0			0
$184$	14.8013	−	11.4004i	1.09116	−	0.840446i
$185$		−	1.11031i		−	0.0816317i
$186$		0			0
$187$	−23.2819			−1.70254
$188$	−16.4192	−	11.4671i	−1.19749	−	0.836326i
$189$		0			0
$190$	0.342889	−	1.08982i	0.0248758	−	0.0790635i
$191$		−	3.69128i		−	0.267092i	−0.991043	−	0.133546i	$-0.957364\pi$
$191$		−	3.69128i		−	0.267092i	0.991043	−	0.133546i	$-0.0426364\pi$
$192$		0			0
$193$	−2.71674			−0.195555			−0.0977777	−	0.995208i	$-0.531173\pi$
$193$	−2.71674			−0.195555			−0.0977777	+	0.995208i	$0.531173\pi$
$194$	−6.87775	+	21.8598i	−0.493794	+	1.56944i
$195$		0			0
$196$		0			0
$197$	−4.09843			−0.292001			−0.146001	−	0.989284i	$-0.546640\pi$
$197$	−4.09843			−0.292001			−0.146001	+	0.989284i	$0.546640\pi$
$198$		0			0
$199$	−0.208229			−0.0147610			−0.00738048	−	0.999973i	$-0.502349\pi$
$199$	−0.208229			−0.0147610			−0.00738048	+	0.999973i	$0.502349\pi$
$200$	−8.60140	−	11.1673i	−0.608211	−	0.789648i
$201$		0			0
$202$	−5.12135	+	16.2774i	−0.360337	+	1.14527i
$203$		0			0
$204$		0			0
$205$	0.415321			0.0290073
$206$	4.43059	+	1.39400i	0.308694	+	0.0971243i
$207$		0			0
$208$	3.34855	−	1.22801i	0.232180	−	0.0851469i
$209$		−	25.2252i		−	1.74486i
$210$		0			0
$211$			16.5850i			1.14176i	0.821034	+	0.570880i	$0.193398\pi$
$211$			16.5850i			1.14176i	−0.821034	+	0.570880i	$0.806602\pi$
$212$	12.3544	+	8.62825i	0.848502	+	0.592591i
$213$		0			0
$214$	−1.41570	+	4.49956i	−0.0967751	+	0.307584i
$215$	0.112812			0.00769375
$216$		0			0
$217$		0			0
$218$	−6.01792	−	1.89342i	−0.407585	−	0.128238i
$219$		0			0
$220$	0.837916	+	0.585198i	0.0564923	+	0.0394540i
$221$	−5.19694			−0.349584
$222$		0			0
$223$	−21.3432			−1.42925			−0.714624	−	0.699509i	$-0.753402\pi$
$223$	−21.3432			−1.42925			−0.714624	+	0.699509i	$0.753402\pi$
$224$		0			0
$225$		0			0
$226$	−12.3607	−	3.88904i	−0.822220	−	0.258695i
$227$	−26.9972			−1.79187			−0.895935	−	0.444185i	$-0.853493\pi$
$227$	−26.9972			−1.79187			−0.895935	+	0.444185i	$0.853493\pi$
$228$		0			0
$229$			2.91694i			0.192757i	0.995345	+	0.0963783i	$0.0307259\pi$
$229$			2.91694i			0.192757i	−0.995345	+	0.0963783i	$0.969274\pi$
$230$	1.13994	+	0.358660i	0.0751656	+	0.0236494i
$231$		0			0
$232$	4.88383	+	6.34074i	0.320639	+	0.416290i
$233$	−20.3989			−1.33638			−0.668189	−	0.743991i	$-0.732930\pi$
$233$	−20.3989			−1.33638			−0.668189	+	0.743991i	$0.732930\pi$
$234$		0			0
$235$		−	1.28103i		−	0.0835649i
$236$	−0.965485	−	0.674291i	−0.0628477	−	0.0438926i
$237$		0			0
$238$		0			0
$239$		−	25.2554i		−	1.63364i	−0.576895	−	0.816818i	$-0.695736\pi$
$239$		−	25.2554i		−	1.63364i	0.576895	−	0.816818i	$-0.304264\pi$
$240$		0			0
$241$		−	8.20938i		−	0.528813i	−0.964411	−	0.264406i	$-0.914824\pi$
$241$		−	8.20938i		−	0.528813i	0.964411	−	0.264406i	$-0.0851760\pi$
$242$	6.68629	+	2.10371i	0.429811	+	0.135231i
$243$		0			0
$244$	1.93297	−	2.76773i	0.123746	−	0.177186i
$245$		0			0
$246$		0			0
$247$		−	5.63071i		−	0.358273i
$248$	14.5899	+	18.9423i	0.926460	+	1.20284i
$249$		0			0
$250$	0.542096	−	1.72296i	0.0342851	−	0.108970i
$251$	6.55180			0.413546			0.206773	−	0.978389i	$-0.433704\pi$
$251$	6.55180			0.413546			0.206773	+	0.978389i	$0.433704\pi$
$252$		0			0
$253$	26.3854			1.65884
$254$	−5.97507	+	18.9908i	−0.374909	+	1.19159i
$255$		0			0
$256$	−12.2065	+	10.3441i	−0.762908	+	0.646507i
$257$			18.7522i			1.16973i	0.811130	+	0.584866i	$0.198853\pi$
$257$			18.7522i			1.16973i	−0.811130	+	0.584866i	$0.801147\pi$
$258$		0			0
$259$		0			0
$260$	0.187038	+	0.130627i	0.0115996	+	0.00810112i
$261$		0			0
$262$	−13.1795	−	4.14666i	−0.814229	−	0.256181i
$263$			2.10526i			0.129816i	0.997891	+	0.0649079i	$0.0206754\pi$
$263$			2.10526i			0.129816i	−0.997891	+	0.0649079i	$0.979325\pi$
$264$		0			0
$265$			0.963886i			0.0592111i
$266$		0			0
$267$		0			0
$268$	7.27449	−	10.4160i	0.444360	−	0.636258i
$269$			11.8021i			0.719586i	0.933032	+	0.359793i	$0.117153\pi$
$269$			11.8021i			0.719586i	−0.933032	+	0.359793i	$0.882847\pi$
$270$		0			0
$271$	11.3243			0.687900			0.343950	−	0.938988i	$-0.388235\pi$
$271$	11.3243			0.687900			0.343950	+	0.938988i	$0.388235\pi$
$272$	21.8882	−	8.02702i	1.32717	−	0.486710i
$273$		0			0
$274$	−5.35361	−	1.68441i	−0.323423	−	0.101759i
$275$		−	19.9074i		−	1.20046i
$276$		0			0
$277$	−11.7638			−0.706821			−0.353410	−	0.935468i	$-0.614978\pi$
$277$	−11.7638			−0.706821			−0.353410	+	0.935468i	$0.614978\pi$
$278$	0.353473	+	0.111213i	0.0211999	+	0.00667014i
$279$		0			0
$280$		0			0
$281$	9.80481			0.584906			0.292453	−	0.956280i	$-0.405529\pi$
$281$	9.80481			0.584906			0.292453	+	0.956280i	$0.405529\pi$
$282$		0			0
$283$	24.6465			1.46508			0.732542	−	0.680722i	$-0.238334\pi$
$283$	24.6465			1.46508			0.732542	+	0.680722i	$0.238334\pi$
$284$	−13.0383	+	18.6689i	−0.773681	+	1.10780i
$285$		0			0
$286$	4.80487	+	1.51176i	0.284118	+	0.0893922i
$287$		0			0
$288$		0			0
$289$	−16.9705			−0.998264
$290$	−0.153647	+	0.488343i	−0.00902248	+	0.0286765i
$291$		0			0
$292$	17.7659	−	25.4381i	1.03967	−	1.48865i
$293$			2.41042i			0.140818i	0.997518	+	0.0704091i	$0.0224305\pi$
$293$			2.41042i			0.140818i	−0.997518	+	0.0704091i	$0.977570\pi$
$294$		0			0
$295$		−	0.0753270i		−	0.00438571i
$296$	14.9795	+	19.4481i	0.870668	+	1.13040i
$297$		0			0
$298$	3.63626	+	1.14408i	0.210643	+	0.0662746i
$299$	5.88969			0.340610
$300$		0			0
$301$		0			0
$302$	1.83216	−	5.82323i	0.105429	−	0.335089i
$303$		0			0
$304$	8.69701	+	23.7152i	0.498808	+	1.36016i
$305$	0.215938			0.0123646
$306$		0			0
$307$	−24.4054			−1.39289			−0.696446	−	0.717609i	$-0.745236\pi$
$307$	−24.4054			−1.39289			−0.696446	+	0.717609i	$0.745236\pi$
$308$		0			0
$309$		0			0
$310$	−0.459004	+	1.45887i	−0.0260697	+	0.0828582i
$311$	31.1866			1.76843			0.884215	−	0.467079i	$-0.154694\pi$
$311$	31.1866			1.76843			0.884215	+	0.467079i	$0.154694\pi$
$312$		0			0
$313$		−	2.53807i		−	0.143460i	−0.997424	−	0.0717302i	$-0.977148\pi$
$313$		−	2.53807i		−	0.143460i	0.997424	−	0.0717302i	$-0.0228521\pi$
$314$	−1.36083	+	4.32516i	−0.0767959	+	0.244083i
$315$		0			0
$316$	11.2492	−	16.1072i	0.632816	−	0.906098i
$317$	18.2520			1.02514			0.512568	−	0.858646i	$-0.328694\pi$
$317$	18.2520			1.02514			0.512568	+	0.858646i	$0.328694\pi$
$318$		0			0
$319$			11.3033i			0.632864i
$320$	−0.989520	−	0.261274i	−0.0553158	−	0.0146057i
$321$		0			0
$322$		0			0
$323$		−	36.8059i		−	2.04793i
$324$		0			0
$325$		−	4.44368i		−	0.246491i
$326$	9.87332	−	31.3807i	0.546832	−	1.73802i
$327$		0			0
$328$	−7.27474	+	5.60322i	−0.401680	+	0.309386i
$329$		0			0
$330$		0			0
$331$			20.7274i			1.13928i	0.821895	+	0.569639i	$0.192917\pi$
$331$			20.7274i			1.13928i	−0.821895	+	0.569639i	$0.807083\pi$
$332$	−2.42710	−	1.69508i	−0.133204	−	0.0930294i
$333$		0			0
$334$	13.0432	+	4.10378i	0.713690	+	0.224549i
$335$	0.812654			0.0444000
$336$		0			0
$337$	−0.330532			−0.0180052			−0.00900261	−	0.999959i	$-0.502866\pi$
$337$	−0.330532			−0.0180052			−0.00900261	+	0.999959i	$0.502866\pi$
$338$	−16.4647	−	5.18029i	−0.895561	−	0.281771i
$339$		0			0
$340$	1.22260	+	0.853858i	0.0663047	+	0.0463070i
$341$			33.7674i			1.82861i
$342$		0			0
$343$		0			0
$344$	−1.97602	+	1.52199i	−0.106540	+	0.0820600i
$345$		0			0
$346$	−8.78872	+	27.9335i	−0.472485	+	1.50171i
$347$			21.9951i			1.18076i	0.807127	+	0.590378i	$0.201021\pi$
$347$			21.9951i			1.18076i	−0.807127	+	0.590378i	$0.798979\pi$
$348$		0			0
$349$			26.6709i			1.42766i	0.700318	+	0.713831i	$0.253041\pi$
$349$			26.6709i			1.42766i	−0.700318	+	0.713831i	$0.746959\pi$
$350$		0			0
$351$		0			0
$352$	−22.5720	+	1.05430i	−1.20309	+	0.0561941i
$353$			7.77165i			0.413643i	0.978379	+	0.206822i	$0.0663120\pi$
$353$			7.77165i			0.413643i	−0.978379	+	0.206822i	$0.933688\pi$
$354$		0			0
$355$	−1.45655			−0.0773055
$356$	0.515302	−	0.737836i	0.0273109	−	0.0391052i
$357$		0			0
$358$	−0.623049	+	1.98026i	−0.0329292	+	0.104660i
$359$			16.7870i			0.885984i	0.896526	+	0.442992i	$0.146083\pi$
$359$			16.7870i			0.885984i	−0.896526	+	0.442992i	$0.853917\pi$
$360$		0			0
$361$	20.8779			1.09884
$362$	−9.99441	+	31.7656i	−0.525295	+	1.66956i
$363$		0			0
$364$		0			0
$365$	1.98468			0.103883
$366$		0			0
$367$	−4.03640			−0.210698			−0.105349	−	0.994435i	$-0.533596\pi$
$367$	−4.03640			−0.210698			−0.105349	+	0.994435i	$0.533596\pi$
$368$	−24.8059	+	9.09703i	−1.29310	+	0.474215i
$369$		0			0
$370$	−0.471263	+	1.49783i	−0.0244998	+	0.0778685i
$371$		0			0
$372$		0			0
$373$	20.7790			1.07590			0.537948	−	0.842978i	$-0.319200\pi$
$373$	20.7790			1.07590			0.537948	+	0.842978i	$0.319200\pi$
$374$	31.4077	+	9.88181i	1.62405	+	0.510976i
$375$		0			0
$376$	17.2827	+	22.4384i	0.891287	+	1.15717i
$377$			2.52310i			0.129946i
$378$		0			0
$379$			10.7800i			0.553732i	0.960909	+	0.276866i	$0.0892958\pi$
$379$			10.7800i			0.553732i	−0.960909	+	0.276866i	$0.910704\pi$
$380$	−0.925127	+	1.32464i	−0.0474580	+	0.0679528i
$381$		0			0
$382$	−1.56673	+	4.97960i	−0.0801611	+	0.254779i
$383$	6.52981			0.333658			0.166829	−	0.985986i	$-0.446647\pi$
$383$	6.52981			0.333658			0.166829	+	0.985986i	$0.446647\pi$
$384$		0			0
$385$		0			0
$386$	3.66493	+	1.15310i	0.186540	+	0.0586912i
$387$		0			0
$388$	18.5564	−	26.5701i	0.942060	−	1.34889i
$389$	−31.8697			−1.61586			−0.807928	−	0.589281i	$-0.799411\pi$
$389$	−31.8697			−1.61586			−0.807928	+	0.589281i	$0.799411\pi$
$390$		0			0
$391$	38.4988			1.94697
$392$		0			0
$393$		0			0
$394$	5.52886	+	1.73955i	0.278540	+	0.0876371i
$395$	1.25668			0.0632303
$396$		0			0
$397$			15.4218i			0.773997i	0.922080	+	0.386999i	$0.126488\pi$
$397$			15.4218i			0.773997i	−0.922080	+	0.386999i	$0.873512\pi$
$398$	0.280905	+	0.0883811i	0.0140805	+	0.00443015i
$399$		0			0
$400$	6.86357	+	18.7157i	0.343178	+	0.935785i
$401$	−27.6959			−1.38307			−0.691533	−	0.722345i	$-0.743064\pi$
$401$	−27.6959			−1.38307			−0.691533	+	0.722345i	$0.743064\pi$
$402$		0			0
$403$			7.53748i			0.375469i
$404$	13.8176	−	19.7847i	0.687450	−	0.984327i
$405$		0			0
$406$		0			0
$407$			34.6692i			1.71849i
$408$		0			0
$409$			24.8476i			1.22864i	0.789058	+	0.614319i	$0.210569\pi$
$409$			24.8476i			1.22864i	−0.789058	+	0.614319i	$0.789431\pi$
$410$	−0.560276	−	0.176280i	−0.0276700	−	0.00870583i
$411$		0			0
$412$	−5.38527	−	3.76105i	−0.265313	−	0.185294i
$413$		0			0
$414$		0			0
$415$		−	0.189362i		−	0.00929541i
$416$	−5.03847	+	0.235338i	−0.247031	+	0.0115384i
$417$		0			0
$418$	−10.7066	+	34.0292i	−0.523677	+	1.66442i
$419$	21.9087			1.07031			0.535155	−	0.844754i	$-0.320253\pi$
$419$	21.9087			1.07031			0.535155	+	0.844754i	$0.320253\pi$
$420$		0			0
$421$	−18.8226			−0.917357			−0.458679	−	0.888602i	$-0.651677\pi$
$421$	−18.8226			−0.917357			−0.458679	+	0.888602i	$0.651677\pi$
$422$	7.03938	−	22.3735i	0.342671	−	1.08912i
$423$		0			0
$424$	−13.0041	−	16.8834i	−0.631534	−	0.819929i
$425$		−	29.0467i		−	1.40897i
$426$		0			0
$427$		0			0
$428$	3.81960	−	5.46911i	0.184628	−	0.264359i
$429$		0			0
$430$	−0.152186	−	0.0478823i	−0.00733906	−	0.00230909i
$431$		−	21.8458i		−	1.05227i	−0.850400	−	0.526137i	$-0.823640\pi$
$431$		−	21.8458i		−	1.05227i	0.850400	−	0.526137i	$-0.176360\pi$
$432$		0			0
$433$		−	23.7440i		−	1.14107i	−0.821275	−	0.570533i	$-0.806737\pi$
$433$		−	23.7440i		−	1.14107i	0.821275	−	0.570533i	$-0.193263\pi$
$434$		0			0
$435$		0			0
$436$	7.31463	+	5.10851i	0.350307	+	0.244653i
$437$			41.7121i			1.99536i
$438$		0			0
$439$	31.8858			1.52183			0.760914	−	0.648852i	$-0.224751\pi$
$439$	31.8858			1.52183			0.760914	+	0.648852i	$0.224751\pi$
$440$	−0.881982	−	1.14509i	−0.0420468	−	0.0545900i
$441$		0			0
$442$	7.01076	+	2.20580i	0.333468	+	0.104919i
$443$		−	15.6824i		−	0.745095i	−0.928013	−	0.372548i	$-0.878484\pi$
$443$		−	15.6824i		−	0.745095i	0.928013	−	0.372548i	$-0.121516\pi$
$444$		0			0
$445$	0.0575658			0.00272888
$446$	28.7924	+	9.05895i	1.36336	+	0.428954i
$447$		0			0
$448$		0			0
$449$	9.72484			0.458943			0.229472	−	0.973315i	$-0.426300\pi$
$449$	9.72484			0.458943			0.229472	+	0.973315i	$0.426300\pi$
$450$		0			0
$451$	−12.9683			−0.610653
$452$	15.0241	+	10.4928i	0.706674	+	0.493539i
$453$		0			0
$454$	36.4198	+	11.4588i	1.70926	+	0.537786i
$455$		0			0
$456$		0			0
$457$	−11.4077			−0.533628			−0.266814	−	0.963748i	$-0.585971\pi$
$457$	−11.4077			−0.533628			−0.266814	+	0.963748i	$0.585971\pi$
$458$	1.23807	−	3.93500i	0.0578512	−	0.183870i
$459$		0			0
$460$	−1.38557	−	0.967678i	−0.0646026	−	0.0451182i
$461$			19.6446i			0.914940i	0.889225	+	0.457470i	$0.151244\pi$
$461$			19.6446i			0.914940i	−0.889225	+	0.457470i	$0.848756\pi$
$462$		0			0
$463$		−	6.73057i		−	0.312796i	−0.987694	−	0.156398i	$-0.950012\pi$
$463$		−	6.73057i		−	0.312796i	0.987694	−	0.156398i	$-0.0499883\pi$
$464$	−3.89710	−	10.6267i	−0.180918	−	0.493331i
$465$		0			0
$466$	27.5185	+	8.65816i	1.27477	+	0.401082i
$467$	22.1216			1.02367			0.511833	−	0.859085i	$-0.328966\pi$
$467$	22.1216			1.02367			0.511833	+	0.859085i	$0.328966\pi$
$468$		0			0
$469$		0			0
$470$	−0.543721	+	1.72813i	−0.0250800	+	0.0797125i
$471$		0			0
$472$	1.01626	+	1.31942i	0.0467771	+	0.0607314i
$473$	−3.52254			−0.161966
$474$		0			0
$475$	31.4711			1.44399
$476$		0			0
$477$		0			0
$478$	−10.7194	+	34.0700i	−0.490296	+	1.55832i
$479$	21.2649			0.971618			0.485809	−	0.874065i	$-0.338525\pi$
$479$	21.2649			0.971618			0.485809	+	0.874065i	$0.338525\pi$
$480$		0			0
$481$			7.73878i			0.352858i
$482$	−3.48441	+	11.0746i	−0.158710	+	0.504434i
$483$		0			0
$484$	−8.12702	−	5.67588i	−0.369410	−	0.257995i
$485$	2.07299			0.0941297
$486$		0			0
$487$		−	35.4341i		−	1.60567i	−0.596200	−	0.802836i	$-0.703323\pi$
$487$		−	35.4341i		−	1.60567i	0.596200	−	0.802836i	$-0.296677\pi$
$488$	−3.78235	+	2.91328i	−0.171219	+	0.131878i
$489$		0			0
$490$		0			0
$491$			15.1925i			0.685628i	0.939403	+	0.342814i	$0.111380\pi$
$491$			15.1925i			0.685628i	−0.939403	+	0.342814i	$0.888620\pi$
$492$		0			0
$493$			16.4926i			0.742789i
$494$	−2.38991	+	7.59592i	−0.107527	+	0.341757i
$495$		0			0
$496$	−11.6422	−	31.7460i	−0.522748	−	1.42544i
$497$		0			0
$498$		0			0
$499$		−	11.0894i		−	0.496431i	−0.968705	−	0.248216i	$-0.920156\pi$
$499$		−	11.0894i		−	0.496431i	0.968705	−	0.248216i	$-0.0798442\pi$
$500$	−1.46259	+	2.09422i	−0.0654092	+	0.0936562i
$501$		0			0
$502$	−8.83849	−	2.78086i	−0.394481	−	0.124116i
$503$	−5.67396			−0.252989			−0.126495	−	0.991967i	$-0.540373\pi$
$503$	−5.67396			−0.252989			−0.126495	+	0.991967i	$0.540373\pi$
$504$		0			0
$505$	1.54360			0.0686894
$506$	−35.5944	−	11.1991i	−1.58236	−	0.497859i
$507$		0			0
$508$	16.1210	−	23.0828i	0.715252	−	1.02413i
$509$			12.7986i			0.567288i	0.958930	+	0.283644i	$0.0915435\pi$
$509$			12.7986i			0.567288i	−0.958930	+	0.283644i	$0.908457\pi$
$510$		0			0
$511$		0			0
$512$	20.8573	−	8.77344i	0.921771	−	0.387735i
$513$		0			0
$514$	7.95924	−	25.2971i	0.351067	−	1.11581i
$515$		−	0.420158i		−	0.0185144i
$516$		0			0
$517$			39.9997i			1.75918i
$518$		0			0
$519$		0			0
$520$	−0.196874	−	0.255604i	−0.00863350	−	0.0112090i
$521$		−	28.2632i		−	1.23823i	−0.785299	−	0.619117i	$-0.787491\pi$
$521$		−	28.2632i		−	1.23823i	0.785299	−	0.619117i	$-0.212509\pi$
$522$		0			0
$523$	−10.7622			−0.470599			−0.235300	−	0.971923i	$-0.575607\pi$
$523$	−10.7622			−0.470599			−0.235300	+	0.971923i	$0.575607\pi$
$524$	16.0193	+	11.1878i	0.699807	+	0.488742i
$525$		0			0
$526$	0.893560	−	2.84003i	0.0389611	−	0.123831i
$527$			49.2698i			2.14623i
$528$		0			0
$529$	−20.6307			−0.896986
$530$	0.409114	−	1.30030i	0.0177708	−	0.0564814i
$531$		0			0
$532$		0			0
$533$	−2.89475			−0.125386
$534$		0			0
$535$	0.426699			0.0184478
$536$	−14.2344	+	10.9638i	−0.614832	+	0.473562i
$537$		0			0
$538$	5.00930	−	15.9212i	0.215966	−	0.686413i
$539$		0			0
$540$		0			0
$541$	−5.32590			−0.228978			−0.114489	−	0.993424i	$-0.536523\pi$
$541$	−5.32590			−0.228978			−0.114489	+	0.993424i	$0.536523\pi$
$542$	−15.2766	−	4.80649i	−0.656187	−	0.206456i
$543$		0			0
$544$	−32.9346	+	1.53832i	−1.41206	+	0.0659548i
$545$			0.570686i			0.0244455i
$546$		0			0
$547$		−	18.5001i		−	0.791007i	−0.918465	−	0.395503i	$-0.870570\pi$
$547$		−	18.5001i		−	0.791007i	0.918465	−	0.395503i	$-0.129430\pi$
$548$	6.50718	+	4.54459i	0.277973	+	0.194135i
$549$		0			0
$550$	−8.44952	+	26.8554i	−0.360289	+	1.14512i
$551$	−17.8692			−0.761252
$552$		0			0
$553$		0			0
$554$	15.8696	+	4.99307i	0.674236	+	0.212135i
$555$		0			0
$556$	−0.429638	−	0.300058i	−0.0182207	−	0.0127253i
$557$	29.9362			1.26844			0.634219	−	0.773153i	$-0.281322\pi$
$557$	29.9362			1.26844			0.634219	+	0.773153i	$0.281322\pi$
$558$		0			0
$559$	−0.786294			−0.0332567
$560$		0			0
$561$		0			0
$562$	−13.2269	−	4.16157i	−0.557941	−	0.175545i
$563$	12.3772			0.521635			0.260818	−	0.965388i	$-0.416008\pi$
$563$	12.3772			0.521635			0.260818	+	0.965388i	$0.416008\pi$
$564$		0			0
$565$			1.17218i			0.0493139i
$566$	−33.2486	−	10.4610i	−1.39754	−	0.439709i
$567$		0			0
$568$	25.5128	−	19.6507i	1.07049	−	0.824525i
$569$	36.7233			1.53952			0.769761	−	0.638332i	$-0.220375\pi$
$569$	36.7233			1.53952			0.769761	+	0.638332i	$0.220375\pi$
$570$		0			0
$571$			6.32118i			0.264533i	0.991214	+	0.132267i	$0.0422255\pi$
$571$			6.32118i			0.264533i	−0.991214	+	0.132267i	$0.957775\pi$
$572$	−5.84021	−	4.07878i	−0.244191	−	0.170542i
$573$		0			0
$574$		0			0
$575$			32.9187i			1.37280i
$576$		0			0
$577$			5.08565i			0.211718i	0.994381	+	0.105859i	$0.0337593\pi$
$577$			5.08565i			0.211718i	−0.994381	+	0.105859i	$0.966241\pi$
$578$	22.8935	+	7.20299i	0.952244	+	0.299605i
$579$		0			0
$580$	0.414546	−	0.593569i	0.0172131	−	0.0246466i
$581$		0			0
$582$		0			0
$583$		−	30.0971i		−	1.24649i
$584$	−34.7635	+	26.7759i	−1.43853	+	1.10800i
$585$		0			0
$586$	1.02308	−	3.25170i	0.0422631	−	0.134326i
$587$	−30.0719			−1.24120			−0.620601	−	0.784127i	$-0.713111\pi$
$587$	−30.0719			−1.24120			−0.620601	+	0.784127i	$0.713111\pi$
$588$		0			0
$589$	−53.3821			−2.19957
$590$	−0.0319719	+	0.101617i	−0.00131626	+	0.00418353i
$591$		0			0
$592$	−11.9531	−	32.5938i	−0.491268	−	1.33960i
$593$			21.5543i			0.885130i	0.896736	+	0.442565i	$0.145931\pi$
$593$			21.5543i			0.885130i	−0.896736	+	0.442565i	$0.854069\pi$
$594$		0			0
$595$		0			0
$596$	−4.41978	−	3.08676i	−0.181041	−	0.126439i
$597$		0			0
$598$	−7.94530	−	2.49983i	−0.324908	−	0.102226i
$599$			18.3543i			0.749936i	0.927038	+	0.374968i	$0.122346\pi$
$599$			18.3543i			0.749936i	−0.927038	+	0.374968i	$0.877654\pi$
$600$		0			0
$601$			12.2204i			0.498482i	0.968441	+	0.249241i	$0.0801812\pi$
$601$			12.2204i			0.498482i	−0.968441	+	0.249241i	$0.919819\pi$
$602$		0			0
$603$		0			0
$604$	−4.94325	+	7.07799i	−0.201138	+	0.288000i
$605$		−	0.634069i		−	0.0257786i
$606$		0			0
$607$	26.5749			1.07864			0.539322	−	0.842100i	$-0.318681\pi$
$607$	26.5749			1.07864			0.539322	+	0.842100i	$0.318681\pi$
$608$	−1.66671	−	35.6835i	−0.0675942	−	1.44716i
$609$		0			0
$610$	−0.291304	−	0.0916530i	−0.0117945	−	0.00371092i
$611$			8.92864i			0.361214i
$612$		0			0
$613$	−19.1590			−0.773824			−0.386912	−	0.922117i	$-0.626458\pi$
$613$	−19.1590			−0.773824			−0.386912	+	0.922117i	$0.626458\pi$
$614$	32.9234	+	10.3587i	1.32868	+	0.418043i
$615$		0			0
$616$		0			0
$617$	14.7860			0.595263			0.297632	−	0.954681i	$-0.403803\pi$
$617$	14.7860			0.595263			0.297632	+	0.954681i	$0.403803\pi$
$618$		0			0
$619$	25.3494			1.01888			0.509439	−	0.860507i	$-0.329853\pi$
$619$	25.3494			1.01888			0.509439	+	0.860507i	$0.329853\pi$
$620$	1.23841	−	1.77322i	0.0497358	−	0.0712142i
$621$		0			0
$622$	−42.0713	−	13.2369i	−1.68691	−	0.530751i
$623$		0			0
$624$		0			0
$625$	24.7548			0.990191
$626$	−1.07726	+	3.42391i	−0.0430561	+	0.136847i
$627$		0			0
$628$	3.67156	−	5.25713i	0.146511	−	0.209782i
$629$			50.5856i			2.01698i
$630$		0			0
$631$		−	36.7075i		−	1.46130i	−0.682752	−	0.730650i	$-0.739217\pi$
$631$		−	36.7075i		−	1.46130i	0.682752	−	0.730650i	$-0.260783\pi$
$632$	−22.0119	+	16.9542i	−0.875586	+	0.674403i
$633$		0			0
$634$	−24.6223	−	7.74693i	−0.977878	−	0.307670i
$635$	1.80092			0.0714673
$636$		0			0
$637$		0			0
$638$	4.79760	−	15.2484i	0.189939	−	0.603688i
$639$		0			0
$640$	1.22398	+	0.772457i	0.0483822	+	0.0305341i
$641$	7.29371			0.288084			0.144042	−	0.989572i	$-0.453990\pi$
$641$	7.29371			0.288084			0.144042	+	0.989572i	$0.453990\pi$
$642$		0			0
$643$	−20.6956			−0.816155			−0.408077	−	0.912947i	$-0.633801\pi$
$643$	−20.6956			−0.816155			−0.408077	+	0.912947i	$0.633801\pi$
$644$		0			0
$645$		0			0
$646$	−15.6220	+	49.6518i	−0.614638	+	1.95352i
$647$	−15.8548			−0.623315			−0.311658	−	0.950194i	$-0.600884\pi$
$647$	−15.8548			−0.623315			−0.311658	+	0.950194i	$0.600884\pi$
$648$		0			0
$649$			2.35206i			0.0923266i
$650$	−1.88608	+	5.99461i	−0.0739783	+	0.235128i
$651$		0			0
$652$	−26.6386	+	38.1425i	−1.04325	+	1.49377i
$653$	28.8161			1.12766			0.563831	−	0.825890i	$-0.309327\pi$
$653$	28.8161			1.12766			0.563831	+	0.825890i	$0.309327\pi$
$654$		0			0
$655$			1.24982i			0.0488347i
$656$	12.1920	−	4.47114i	0.476017	−	0.174569i
$657$		0			0
$658$		0			0
$659$		−	20.6316i		−	0.803693i	−0.915707	−	0.401846i	$-0.868369\pi$
$659$		−	20.6316i		−	0.803693i	0.915707	−	0.401846i	$-0.131631\pi$
$660$		0			0
$661$			23.9517i			0.931611i	0.884887	+	0.465806i	$0.154235\pi$
$661$			23.9517i			0.931611i	−0.884887	+	0.465806i	$0.845765\pi$
$662$	8.79756	−	27.9616i	0.341927	−	1.08676i
$663$		0			0
$664$	2.55474	+	3.31685i	0.0991431	+	0.128719i
$665$		0			0
$666$		0			0
$667$		−	18.6911i		−	0.723721i
$668$	−15.8537	−	11.0721i	−0.613396	−	0.428394i
$669$		0			0
$670$	−1.09628	−	0.344924i	−0.0423532	−	0.0133256i
$671$	−6.74259			−0.260295
$672$		0			0
$673$	3.43936			0.132577			0.0662887	−	0.997800i	$-0.478884\pi$
$673$	3.43936			0.132577			0.0662887	+	0.997800i	$0.478884\pi$
$674$	0.445894	+	0.140292i	0.0171752	+	0.00540383i
$675$		0			0
$676$	20.0124	+	13.9766i	0.769709	+	0.537562i
$677$		−	33.1949i		−	1.27579i	−0.770125	−	0.637893i	$-0.779806\pi$
$677$		−	33.1949i		−	1.27579i	0.770125	−	0.637893i	$-0.220194\pi$
$678$		0			0
$679$		0			0
$680$	−1.28689	−	1.67079i	−0.0493501	−	0.0640720i
$681$		0			0
$682$	14.3323	−	45.5528i	0.548812	−	1.74431i
$683$			8.54104i			0.326814i	0.986559	+	0.163407i	$0.0522483\pi$
$683$			8.54104i			0.326814i	−0.986559	+	0.163407i	$0.947752\pi$
$684$		0			0
$685$			0.507689i			0.0193978i
$686$		0			0
$687$		0			0
$688$	3.31168	−	1.21448i	0.126256	−	0.0463017i
$689$		−	6.71821i		−	0.255943i
$690$		0			0
$691$	−2.45848			−0.0935249			−0.0467625	−	0.998906i	$-0.514890\pi$
$691$	−2.45848			−0.0935249			−0.0467625	+	0.998906i	$0.514890\pi$
$692$	23.7123	−	33.9525i	0.901406	−	1.29068i
$693$		0			0
$694$	9.33563	−	29.6717i	0.354375	−	1.12632i
$695$		−	0.0335203i		−	0.00127150i
$696$		0			0
$697$	−18.9220			−0.716720
$698$	11.3203	−	35.9795i	0.428478	−	1.36185i
$699$		0			0
$700$		0			0
$701$	−43.1693			−1.63048			−0.815241	−	0.579123i	$-0.803395\pi$
$701$	−43.1693			−1.63048			−0.815241	+	0.579123i	$0.803395\pi$
$702$		0			0
$703$	−54.8077			−2.06711
$704$	30.8975	+	8.15822i	1.16449	+	0.307475i
$705$		0			0
$706$	3.29861	−	10.4841i	0.124145	−	0.394574i
$707$		0			0
$708$		0			0
$709$	26.0798			0.979447			0.489723	−	0.871878i	$-0.337098\pi$
$709$	26.0798			0.979447			0.489723	+	0.871878i	$0.337098\pi$
$710$	1.96491	+	0.618219i	0.0737417	+	0.0232014i
$711$		0			0
$712$	−1.00832	+	0.776638i	−0.0377884	+	0.0291057i
$713$		−	55.8375i		−	2.09113i
$714$		0			0
$715$		−	0.455652i		−	0.0170404i
$716$	1.68101	−	2.40695i	0.0628222	−	0.0899521i
$717$		0			0
$718$	7.12511	−	22.6460i	0.265907	−	0.845140i
$719$	−38.1219			−1.42171			−0.710854	−	0.703340i	$-0.751691\pi$
$719$	−38.1219			−1.42171			−0.710854	+	0.703340i	$0.751691\pi$
$720$		0			0
$721$		0			0
$722$	−28.1647	−	8.86146i	−1.04818	−	0.329789i
$723$		0			0
$724$	26.9653	−	38.6103i	1.00216	−	1.43494i
$725$	−14.1021			−0.523739
$726$		0			0
$727$	30.8059			1.14253			0.571264	−	0.820766i	$-0.306453\pi$
$727$	30.8059			1.14253			0.571264	+	0.820766i	$0.306453\pi$
$728$		0			0
$729$		0			0
$730$	−2.67737	−	0.842381i	−0.0990939	−	0.0311779i
$731$	−5.13971			−0.190099
$732$		0			0
$733$		−	41.1095i		−	1.51841i	−0.650849	−	0.759207i	$-0.725587\pi$
$733$		−	41.1095i		−	1.51841i	0.650849	−	0.759207i	$-0.274413\pi$
$734$	5.44517	+	1.71322i	0.200985	+	0.0632360i
$735$		0			0
$736$	37.3248	−	1.74337i	1.37581	−	0.0642617i
$737$	−25.3749			−0.934696
$738$		0			0
$739$			28.8483i			1.06120i	0.847622	+	0.530600i	$0.178033\pi$
$739$			28.8483i			1.06120i	−0.847622	+	0.530600i	$0.821967\pi$
$740$	1.27148	−	1.82058i	0.0467407	−	0.0669257i
$741$		0			0
$742$		0			0
$743$		−	0.365822i		−	0.0134207i	−0.999977	−	0.00671036i	$-0.997864\pi$
$743$		−	0.365822i		−	0.0134207i	0.999977	−	0.00671036i	$-0.00213599\pi$
$744$		0			0
$745$		−	0.344831i		−	0.0126336i
$746$	−28.0312	−	8.81948i	−1.02630	−	0.322904i
$747$		0			0
$748$	−38.1753	−	26.6615i	−1.39583	−	0.974841i
$749$		0			0
$750$		0			0
$751$		−	19.9623i		−	0.728434i	−0.931314	−	0.364217i	$-0.881337\pi$
$751$		−	19.9623i		−	0.728434i	0.931314	−	0.364217i	$-0.118663\pi$
$752$	−13.7909	−	37.6052i	−0.502902	−	1.37132i
$753$		0			0
$754$	1.07091	−	3.40371i	0.0390002	−	0.123956i
$755$	−0.552224			−0.0200975
$756$		0			0
$757$	−3.04476			−0.110664			−0.0553319	−	0.998468i	$-0.517622\pi$
$757$	−3.04476			−0.110664			−0.0553319	+	0.998468i	$0.517622\pi$
$758$	4.57549	−	14.5424i	0.166189	−	0.528205i
$759$		0			0
$760$	1.81025	−	1.39431i	0.0656646	−	0.0505768i
$761$		−	7.52068i		−	0.272624i	−0.990666	−	0.136312i	$-0.956475\pi$
$761$		−	7.52068i		−	0.272624i	0.990666	−	0.136312i	$-0.0435250\pi$
$762$		0			0
$763$		0			0
$764$	4.22711	−	6.05259i	0.152931	−	0.218975i
$765$		0			0
$766$	−8.80884	−	2.77153i	−0.318276	−	0.100139i
$767$			0.525023i			0.0189575i
$768$		0			0
$769$			42.4363i			1.53029i	0.643857	+	0.765146i	$0.277333\pi$
$769$			42.4363i			1.53029i	−0.643857	+	0.765146i	$0.722667\pi$
$770$		0			0
$771$		0			0
$772$	−4.45464	−	3.11110i	−0.160326	−	0.111971i
$773$			23.7646i			0.854752i	0.904074	+	0.427376i	$0.140562\pi$
$773$			23.7646i			0.854752i	−0.904074	+	0.427376i	$0.859438\pi$
$774$		0			0
$775$	−42.1285			−1.51330
$776$	−36.3104	+	27.9673i	−1.30347	+	1.00397i
$777$		0			0
$778$	42.9928	+	13.5268i	1.54137	+	0.484960i
$779$		−	20.5013i		−	0.734535i
$780$		0			0
$781$	45.4803			1.62741
$782$	−51.9355	−	16.3405i	−1.85721	−	0.584335i
$783$		0			0
$784$		0			0
$785$	0.410160			0.0146393
$786$		0			0
$787$	19.9519			0.711210			0.355605	−	0.934636i	$-0.384275\pi$
$787$	19.9519			0.711210			0.355605	+	0.934636i	$0.384275\pi$
$788$	−6.72019	−	4.69336i	−0.239397	−	0.167194i
$789$		0			0
$790$	−1.69528	−	0.533387i	−0.0603154	−	0.0189770i
$791$		0			0
$792$		0			0
$793$	−1.50507			−0.0534465
$794$	6.54565	−	20.8043i	0.232296	−	0.738316i
$795$		0			0
$796$	−0.341433	−	0.238455i	−0.0121018	−	0.00845183i
$797$			27.9236i			0.989106i	0.869147	+	0.494553i	$0.164668\pi$
$797$			27.9236i			0.989106i	−0.869147	+	0.494553i	$0.835332\pi$
$798$		0			0
$799$			58.3633i			2.06474i
$800$	−1.31535	−	28.1610i	−0.0465046	−	0.995641i
$801$		0			0
$802$	37.3622	+	11.7553i	1.31931	+	0.415093i
$803$	−61.9711			−2.18691
$804$		0			0
$805$		0			0
$806$	3.19922	−	10.1682i	0.112688	−	0.358160i
$807$		0			0
$808$	−27.0376	+	20.8252i	−0.951181	+	0.732628i
$809$	21.7399			0.764333			0.382166	−	0.924094i	$-0.375178\pi$
$809$	21.7399			0.764333			0.382166	+	0.924094i	$0.375178\pi$
$810$		0			0
$811$	−21.4122			−0.751885			−0.375942	−	0.926643i	$-0.622681\pi$
$811$	−21.4122			−0.751885			−0.375942	+	0.926643i	$0.622681\pi$
$812$		0			0
$813$		0			0
$814$	14.7150	−	46.7693i	0.515762	−	1.63926i
$815$	−2.97587			−0.104240
$816$		0			0
$817$		−	5.56870i		−	0.194824i
$818$	10.5464	−	33.5199i	0.368746	−	1.17200i
$819$		0			0
$820$	0.681001	+	0.475609i	0.0237816	+	0.0166090i
$821$	26.7099			0.932183			0.466092	−	0.884736i	$-0.345662\pi$
$821$	26.7099			0.932183			0.466092	+	0.884736i	$0.345662\pi$
$822$		0			0
$823$			24.2476i			0.845217i	0.906312	+	0.422608i	$0.138885\pi$
$823$			24.2476i			0.845217i	−0.906312	+	0.422608i	$0.861115\pi$
$824$	5.66848	+	7.35946i	0.197471	+	0.256379i
$825$		0			0
$826$		0			0
$827$			34.2930i			1.19248i	0.802805	+	0.596242i	$0.203340\pi$
$827$			34.2930i			1.19248i	−0.802805	+	0.596242i	$0.796660\pi$
$828$		0			0
$829$		−	0.807148i		−	0.0280334i	−0.999902	−	0.0140167i	$-0.995538\pi$
$829$		−	0.807148i		−	0.0280334i	0.999902	−	0.0140167i	$-0.00446180\pi$
$830$	−0.0803731	+	0.255453i	−0.00278979	+	0.00886689i
$831$		0			0
$832$	6.89687	+	1.82106i	0.239106	+	0.0631340i
$833$		0			0
$834$		0			0
$835$		−	1.23690i		−	0.0428047i
$836$	28.8868	−	41.3616i	0.999071	−	1.43052i
$837$		0			0
$838$	−29.5552	−	9.29896i	−1.02097	−	0.321227i
$839$	27.7282			0.957284			0.478642	−	0.878010i	$-0.341129\pi$
$839$	27.7282			0.957284			0.478642	+	0.878010i	$0.341129\pi$
$840$		0			0
$841$	−20.9929			−0.723893
$842$	25.3920	+	7.98910i	0.875067	+	0.275322i
$843$		0			0
$844$	−18.9925	+	27.1944i	−0.653748	+	0.936071i
$845$			1.56137i			0.0537127i
$846$		0			0
$847$		0			0
$848$	10.3767	+	28.2954i	0.356338	+	0.971670i
$849$		0			0
$850$	−12.3286	+	39.1845i	−0.422869	+	1.34402i
$851$		−	57.3287i		−	1.96520i
$852$		0			0
$853$			16.3380i			0.559402i	0.960087	+	0.279701i	$0.0902354\pi$
$853$			16.3380i			0.559402i	−0.960087	+	0.279701i	$0.909765\pi$
$854$		0			0
$855$		0			0
$856$	−7.47403	+	5.75672i	−0.255457	+	0.196761i
$857$		−	29.5296i		−	1.00871i	−0.863496	−	0.504355i	$-0.831730\pi$
$857$		−	29.5296i		−	1.00871i	0.863496	−	0.504355i	$-0.168270\pi$
$858$		0			0
$859$	−15.1259			−0.516090			−0.258045	−	0.966133i	$-0.583078\pi$
$859$	−15.1259			−0.516090			−0.258045	+	0.966133i	$0.583078\pi$
$860$	0.184978	+	0.129188i	0.00630771	+	0.00440528i
$861$		0			0
$862$	−9.27225	+	29.4703i	−0.315814	+	1.00376i
$863$		−	16.1792i		−	0.550748i	−0.961337	−	0.275374i	$-0.911198\pi$
$863$		−	16.1792i		−	0.550748i	0.961337	−	0.275374i	$-0.0888016\pi$
$864$		0			0
$865$	2.64897			0.0900676
$866$	−10.0780	+	32.0311i	−0.342463	+	1.08846i
$867$		0			0
$868$		0			0
$869$	−39.2394			−1.33111
$870$		0			0
$871$	−5.66413			−0.191922
$872$	−7.69930	−	9.99611i	−0.260731	−	0.338511i
$873$		0			0
$874$	17.7044	−	56.2704i	0.598859	−	1.90337i
$875$		0			0
$876$		0			0
$877$	39.6822			1.33997			0.669987	−	0.742373i	$-0.266300\pi$
$877$	39.6822			1.33997			0.669987	+	0.742373i	$0.266300\pi$
$878$	−43.0146	−	13.5337i	−1.45167	−	0.456740i
$879$		0			0
$880$	0.703786	+	1.91910i	0.0237246	+	0.0646927i
$881$			27.4290i			0.924106i	0.886852	+	0.462053i	$0.152887\pi$
$881$			27.4290i			0.924106i	−0.886852	+	0.462053i	$0.847113\pi$
$882$		0			0
$883$			37.1425i			1.24994i	0.780647	+	0.624972i	$0.214890\pi$
$883$			37.1425i			1.24994i	−0.780647	+	0.624972i	$0.785110\pi$
$884$	−8.52141	−	5.95132i	−0.286606	−	0.200165i
$885$		0			0
$886$	−6.65628	+	21.1559i	−0.223622	+	0.710746i
$887$	27.7126			0.930497			0.465248	−	0.885180i	$-0.345965\pi$
$887$	27.7126			0.930497			0.465248	+	0.885180i	$0.345965\pi$
$888$		0			0
$889$		0			0
$890$	−0.0776574	−	0.0244334i	−0.00260308	−	0.000819008i
$891$		0			0
$892$	−34.9964	−	24.4414i	−1.17177	−	0.818358i
$893$	−63.2346			−2.11607
$894$		0			0
$895$	0.187790			0.00627714
$896$		0			0
$897$		0			0
$898$	−13.1190	−	4.12763i	−0.437786	−	0.137741i
$899$	23.9203			0.797788
$900$		0			0
$901$		−	43.9145i		−	1.46300i
$902$	17.4944	+	5.50428i	0.582501	+	0.183273i
$903$		0			0
$904$	−15.8142	−	20.5318i	−0.525973	−	0.682877i
$905$	3.01237			0.100135
$906$		0			0
$907$		−	39.9740i		−	1.32732i	−0.748036	−	0.663658i	$-0.769003\pi$
$907$		−	39.9740i		−	1.32732i	0.748036	−	0.663658i	$-0.230997\pi$
$908$	−44.2673	−	30.9161i	−1.46906	−	1.02599i
$909$		0			0
$910$		0			0
$911$		−	35.0711i		−	1.16196i	−0.813918	−	0.580979i	$-0.802670\pi$
$911$		−	35.0711i		−	1.16196i	0.813918	−	0.580979i	$-0.197330\pi$
$912$		0			0
$913$			5.91277i			0.195684i
$914$	15.3891	+	4.84189i	0.509028	+	0.160155i
$915$		0			0
$916$	−3.34036	+	4.78290i	−0.110369	+	0.158031i
$917$		0			0
$918$		0			0
$919$		−	0.330846i		−	0.0109136i	−0.999985	−	0.00545681i	$-0.998263\pi$
$919$		−	0.330846i		−	0.0109136i	0.999985	−	0.00545681i	$-0.00173696\pi$
$920$	1.45844	+	1.89351i	0.0480833	+	0.0624272i
$921$		0			0
$922$	8.33799	−	26.5009i	0.274597	−	0.872761i
$923$	10.1520			0.334157
$924$		0			0
$925$	−43.2536			−1.42217
$926$	−2.85674	+	9.07966i	−0.0938782	+	0.298376i
$927$		0			0
$928$	0.746849	+	15.9897i	0.0245165	+	0.524887i
$929$		−	28.4574i		−	0.933658i	−0.884348	−	0.466829i	$-0.845396\pi$
$929$		−	28.4574i		−	0.933658i	0.884348	−	0.466829i	$-0.154604\pi$
$930$		0			0
$931$		0			0
$932$	−33.4481	−	23.3600i	−1.09563	−	0.765183i
$933$		0			0
$934$	−29.8425	−	9.38934i	−0.976476	−	0.307229i
$935$		−	2.97843i		−	0.0974051i
$936$		0			0
$937$		−	11.8966i		−	0.388645i	−0.980938	−	0.194323i	$-0.937749\pi$
$937$		−	11.8966i		−	0.388645i	0.980938	−	0.194323i	$-0.0622509\pi$
$938$		0			0
$939$		0			0
$940$	1.46698	−	2.10050i	0.0478475	−	0.0685106i
$941$		−	16.7967i		−	0.547556i	−0.961793	−	0.273778i	$-0.911727\pi$
$941$		−	16.7967i		−	0.547556i	0.961793	−	0.273778i	$-0.0882733\pi$
$942$		0			0
$943$	21.4443			0.698321
$944$	−0.810934	−	2.21127i	−0.0263936	−	0.0719707i
$945$		0			0
$946$	4.75197	+	1.49511i	0.154500	+	0.0486103i
$947$		−	20.6321i		−	0.670455i	−0.942137	−	0.335227i	$-0.891187\pi$
$947$		−	20.6321i		−	0.670455i	0.942137	−	0.335227i	$-0.108813\pi$
$948$		0			0
$949$	−13.8331			−0.449040
$950$	−42.4551	−	13.3577i	−1.37743	−	0.433380i
$951$		0			0
$952$		0			0
$953$	−21.9025			−0.709492			−0.354746	−	0.934963i	$-0.615433\pi$
$953$	−21.9025			−0.709492			−0.354746	+	0.934963i	$0.615433\pi$
$954$		0			0
$955$	0.472222			0.0152807
$956$	28.9215	−	41.4112i	0.935387	−	1.33934i
$957$		0			0
$958$	−28.6867	−	9.02571i	−0.926826	−	0.291608i
$959$		0			0
$960$		0			0
$961$	40.4594			1.30514
$962$	3.28466	−	10.4398i	0.105902	−	0.336591i
$963$		0			0
$964$	9.40105	−	13.4609i	0.302787	−	0.433547i
$965$		−	0.347550i		−	0.0111880i
$966$		0			0
$967$		−	0.651178i		−	0.0209405i	−0.999945	−	0.0104702i	$-0.996667\pi$
$967$		−	0.651178i		−	0.0209405i	0.999945	−	0.0104702i	$-0.00333284\pi$
$968$	8.55441	+	11.1063i	0.274949	+	0.356970i
$969$		0			0
$970$	−2.79650	−	0.879864i	−0.0897903	−	0.0282507i
$971$	59.4641			1.90829			0.954147	−	0.299338i	$-0.0967659\pi$
$971$	59.4641			1.90829			0.954147	+	0.299338i	$0.0967659\pi$
$972$		0			0
$973$		0			0
$974$	−15.0397	+	47.8012i	−0.481904	+	1.53165i
$975$		0			0
$976$	6.33898	−	2.32468i	0.202906	−	0.0744111i
$977$	22.2437			0.711639			0.355819	−	0.934555i	$-0.384202\pi$
$977$	22.2437			0.711639			0.355819	+	0.934555i	$0.384202\pi$
$978$		0			0
$979$	−1.79748			−0.0574476
$980$		0			0
$981$		0			0
$982$	6.44834	−	20.4950i	0.205775	−	0.654021i
$983$	−19.0956			−0.609055			−0.304527	−	0.952504i	$-0.598498\pi$
$983$	−19.0956			−0.609055			−0.304527	+	0.952504i	$0.598498\pi$
$984$		0			0
$985$		−	0.524309i		−	0.0167059i
$986$	7.00014	−	22.2488i	0.222930	−	0.708546i
$987$		0			0
$988$	6.44806	−	9.23266i	0.205140	−	0.293730i
$989$	5.82484			0.185219
$990$		0			0
$991$			27.3523i			0.868876i	0.900702	+	0.434438i	$0.143053\pi$
$991$			27.3523i			0.868876i	−0.900702	+	0.434438i	$0.856947\pi$
$992$	2.23113	+	47.7674i	0.0708384	+	1.51662i
$993$		0			0
$994$		0			0
$995$		−	0.0266385i		−	0.000844499i
$996$		0			0
$997$			32.6936i			1.03542i	0.855557	+	0.517708i	$0.173215\pi$
$997$			32.6936i			1.03542i	−0.855557	+	0.517708i	$0.826785\pi$
$998$	−4.70682	+	14.9598i	−0.148992	+	0.473546i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.b.l.1567.1		12
3.2	odd	2		588.2.b.c.391.12	yes	12
4.3	odd	2		1764.2.b.m.1567.2		12
7.6	odd	2		1764.2.b.m.1567.1		12
12.11	even	2		588.2.b.d.391.11	yes	12
21.2	odd	6		588.2.o.f.31.7		24
21.5	even	6		588.2.o.e.31.7		24
21.11	odd	6		588.2.o.f.19.4		24
21.17	even	6		588.2.o.e.19.4		24
21.20	even	2		588.2.b.d.391.12	yes	12
28.27	even	2	inner	1764.2.b.l.1567.2		12
84.11	even	6		588.2.o.e.19.7		24
84.23	even	6		588.2.o.e.31.4		24
84.47	odd	6		588.2.o.f.31.4		24
84.59	odd	6		588.2.o.f.19.7		24
84.83	odd	2		588.2.b.c.391.11	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.b.c.391.11	✓	12	84.83	odd	2
588.2.b.c.391.12	yes	12	3.2	odd	2
588.2.b.d.391.11	yes	12	12.11	even	2
588.2.b.d.391.12	yes	12	21.20	even	2
588.2.o.e.19.4		24	21.17	even	6
588.2.o.e.19.7		24	84.11	even	6
588.2.o.e.31.4		24	84.23	even	6
588.2.o.e.31.7		24	21.5	even	6
588.2.o.f.19.4		24	21.11	odd	6
588.2.o.f.19.7		24	84.59	odd	6
588.2.o.f.31.4		24	84.47	odd	6
588.2.o.f.31.7		24	21.2	odd	6
1764.2.b.l.1567.1		12	1.1	even	1	trivial
1764.2.b.l.1567.2		12	28.27	even	2	inner
1764.2.b.m.1567.1		12	7.6	odd	2
1764.2.b.m.1567.2		12	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34902 - 0.424442i) q^{2} +(1.63970 + 1.14516i) q^{4} +0.127929i q^{5} +(-1.72593 - 2.24080i) q^{8} +(0.0542984 - 0.172579i) q^{10} -3.99455i q^{11} -0.891655i q^{13} +(1.37722 + 3.75543i) q^{16} -5.82842i q^{17} +6.31490 q^{19} +(-0.146499 + 0.209765i) q^{20} +(-1.69545 + 5.38872i) q^{22} +6.60535i q^{23} +4.98363 q^{25} +(-0.378456 + 1.20286i) q^{26} -2.82968 q^{29} -8.45337 q^{31} +(-0.263934 - 5.65069i) q^{32} +(-2.47383 + 7.86264i) q^{34} -8.67912 q^{37} +(-8.51891 - 2.68031i) q^{38} +(0.286663 - 0.220796i) q^{40} -3.24650i q^{41} -0.881836i q^{43} +(4.57439 - 6.54985i) q^{44} +(2.80359 - 8.91074i) q^{46} -10.0136 q^{47} +(-6.72301 - 2.11526i) q^{50} +(1.02109 - 1.46204i) q^{52} +7.53454 q^{53} +0.511019 q^{55} +(3.81729 + 1.20104i) q^{58} -0.588819 q^{59} -1.68795i q^{61} +(11.4037 + 3.58796i) q^{62} +(-2.04234 + 7.73491i) q^{64} +0.114069 q^{65} -6.35238i q^{67} +(6.67447 - 9.55685i) q^{68} +11.3856i q^{71} -15.5139i q^{73} +(11.7083 + 3.68378i) q^{74} +(10.3545 + 7.23156i) q^{76} -9.82324i q^{79} +(-0.480429 + 0.176187i) q^{80} +(-1.37795 + 4.37958i) q^{82} -1.48021 q^{83} +0.745624 q^{85} +(-0.374288 + 1.18961i) q^{86} +(-8.95097 + 6.89430i) q^{88} -0.449983i q^{89} +(-7.56418 + 10.8308i) q^{92} +(13.5085 + 4.25018i) q^{94} +0.807859i q^{95} -16.2042i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - 4 q^{4} - 4 q^{8} - 4 q^{16} - 24 q^{20} - 12 q^{25} + 24 q^{26} - 32 q^{29} - 16 q^{31} - 4 q^{32} - 32 q^{34} + 32 q^{37} - 24 q^{38} + 32 q^{40} + 24 q^{44} + 24 q^{46} + 28 q^{50} - 32 q^{52}+ \cdots + 24 q^{88}+O(q^{100}) \) 12 * q - 4 * q^2 - 4 * q^4 - 4 * q^8 - 4 * q^16 - 24 * q^20 - 12 * q^25 + 24 * q^26 - 32 * q^29 - 16 * q^31 - 4 * q^32 - 32 * q^34 + 32 * q^37 - 24 * q^38 + 32 * q^40 + 24 * q^44 + 24 * q^46 + 28 * q^50 - 32 * q^52 + 32 * q^53 - 16 * q^55 + 16 * q^58 - 16 * q^59 + 8 * q^62 - 4 * q^64 - 8 * q^68 + 32 * q^74 + 32 * q^76 - 16 * q^80 - 32 * q^82 - 16 * q^83 + 16 * q^85 + 24 * q^86 + 24 * q^88

Introduction

L-functions

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Database

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