LMFDB - Embedded newform 416.2.i.g.289.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [416,2,Mod(289,416)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("416.289"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(416, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.6927565824.3
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 23x^{4} + 10x^{2} + 4 $ x^8 + 5x^6 + 23x^4 + 10*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.3
Root			$1.06789 - 1.84964i$ of defining polynomial
Character	$\chi$	$=$	416.289
Dual form			416.2.i.g.321.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.599676 + 1.03867i) q^{3} +1.56155 q^{5} +(1.53610 - 2.66061i) q^{7} +(0.780776 - 1.35234i) q^{9} +(-2.73546 - 4.73795i) q^{11} +(3.34233 + 1.35234i) q^{13} +(0.936426 + 1.62194i) q^{15} +(1.06155 - 1.83866i) q^{17} +(-3.67188 + 6.35989i) q^{19} +3.68466 q^{21} +(1.79903 + 3.11601i) q^{23} -2.56155 q^{25} +5.47091 q^{27} +(2.50000 + 4.33013i) q^{29} -6.67026 q^{31} +(3.28078 - 5.68247i) q^{33} +(2.39871 - 4.15468i) q^{35} +(3.06155 + 5.30277i) q^{37} +(0.599676 + 4.28255i) q^{39} +(-2.06155 - 3.57071i) q^{41} +(0.336750 - 0.583268i) q^{43} +(1.21922 - 2.11176i) q^{45} +0.525853 q^{47} +(-1.21922 - 2.11176i) q^{49} +2.54635 q^{51} +1.56155 q^{53} +(-4.27156 - 7.39856i) q^{55} -8.80776 q^{57} +(-5.13416 + 8.89263i) q^{59} +(-2.62311 + 4.54335i) q^{61} +(-2.39871 - 4.15468i) q^{63} +(5.21922 + 2.11176i) q^{65} +(-2.47253 - 4.28255i) q^{67} +(-2.15767 + 3.73720i) q^{69} +(3.67188 - 6.35989i) q^{71} -16.6847 q^{73} +(-1.53610 - 2.66061i) q^{75} -16.8078 q^{77} +15.7392 q^{79} +(0.938447 + 1.62544i) q^{81} +8.54312 q^{83} +(1.65767 - 2.87117i) q^{85} +(-2.99838 + 5.19335i) q^{87} +(0.842329 + 1.45896i) q^{89} +(8.73222 - 6.81529i) q^{91} +(-4.00000 - 6.92820i) q^{93} +(-5.73384 + 9.93130i) q^{95} +(-5.40388 + 9.35980i) q^{97} -8.54312 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{5} - 2 q^{9} + 2 q^{13} - 8 q^{17} - 20 q^{21} - 4 q^{25} + 20 q^{29} + 18 q^{33} + 8 q^{37} + 18 q^{45} - 18 q^{49} - 4 q^{53} + 12 q^{57} + 12 q^{61} + 50 q^{65} - 42 q^{69} - 84 q^{73} - 52 q^{77}+ \cdots - 2 q^{97}+O(q^{100}) $ 8 * q - 4 * q^5 - 2 * q^9 + 2 * q^13 - 8 * q^17 - 20 * q^21 - 4 * q^25 + 20 * q^29 + 18 * q^33 + 8 * q^37 + 18 * q^45 - 18 * q^49 - 4 * q^53 + 12 * q^57 + 12 * q^61 + 50 * q^65 - 42 * q^69 - 84 * q^73 - 52 * q^77 + 24 * q^81 + 38 * q^85 - 18 * q^89 - 32 * q^93 - 2 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.599676	+	1.03867i	0.346223	+	0.599676i	0.985575	−	0.169238i	$-0.0541306\pi$
$3$	0.599676	+	1.03867i	0.346223	+	0.599676i	−0.639352	+	0.768914i	$0.720797\pi$
$4$		0			0
$5$	1.56155			0.698348			0.349174	−	0.937058i	$-0.386462\pi$
$5$	1.56155			0.698348			0.349174	+	0.937058i	$0.386462\pi$
$6$		0			0
$7$	1.53610	−	2.66061i	0.580592	−	1.00562i	−0.414817	−	0.909905i	$-0.636154\pi$
$7$	1.53610	−	2.66061i	0.580592	−	1.00562i	0.995409	−	0.0957104i	$-0.0305123\pi$
$8$		0			0
$9$	0.780776	−	1.35234i	0.260259	−	0.450781i
$10$		0			0
$11$	−2.73546	−	4.73795i	−0.824771	−	1.42855i	−0.902094	−	0.431539i	$-0.857971\pi$
$11$	−2.73546	−	4.73795i	−0.824771	−	1.42855i	0.0773234	−	0.997006i	$-0.475363\pi$
$12$		0			0
$13$	3.34233	+	1.35234i	0.926995	+	0.375073i
$13$	3.34233	+	1.35234i	0.926995	+	0.375073i
$14$		0			0
$15$	0.936426	+	1.62194i	0.241784	+	0.418783i
$16$		0			0
$17$	1.06155	−	1.83866i	0.257464	−	0.445941i	−0.708098	−	0.706115i	$-0.750446\pi$
$17$	1.06155	−	1.83866i	0.257464	−	0.445941i	0.965562	+	0.260173i	$0.0837797\pi$
$18$		0			0
$19$	−3.67188	+	6.35989i	−0.842388	+	1.45906i	0.0454833	+	0.998965i	$0.485517\pi$
$19$	−3.67188	+	6.35989i	−0.842388	+	1.45906i	−0.887871	+	0.460093i	$0.847816\pi$
$20$		0			0
$21$	3.68466			0.804058
$22$		0			0
$23$	1.79903	+	3.11601i	0.375124	+	0.649733i	0.990346	−	0.138621i	$-0.0442670\pi$
$23$	1.79903	+	3.11601i	0.375124	+	0.649733i	−0.615222	+	0.788354i	$0.710934\pi$
$24$		0			0
$25$	−2.56155			−0.512311
$26$		0			0
$27$	5.47091			1.05288
$28$		0			0
$29$	2.50000	+	4.33013i	0.464238	+	0.804084i	0.999167	−	0.0408130i	$-0.0129948\pi$
$29$	2.50000	+	4.33013i	0.464238	+	0.804084i	−0.534928	+	0.844897i	$0.679661\pi$
$30$		0			0
$31$	−6.67026			−1.19801			−0.599007	−	0.800743i	$-0.704438\pi$
$31$	−6.67026			−1.19801			−0.599007	+	0.800743i	$0.704438\pi$
$32$		0			0
$33$	3.28078	−	5.68247i	0.571110	−	0.989191i
$34$		0			0
$35$	2.39871	−	4.15468i	0.405455	−	0.702269i
$36$		0			0
$37$	3.06155	+	5.30277i	0.503316	+	0.871769i	0.999993	+	0.00383344i	$0.00122022\pi$
$37$	3.06155	+	5.30277i	0.503316	+	0.871769i	−0.496676	+	0.867936i	$0.665446\pi$
$38$		0			0
$39$	0.599676	+	4.28255i	0.0960251	+	0.685756i
$40$		0			0
$41$	−2.06155	−	3.57071i	−0.321960	−	0.557652i	0.658932	−	0.752202i	$-0.271008\pi$
$41$	−2.06155	−	3.57071i	−0.321960	−	0.557652i	−0.980892	+	0.194551i	$0.937675\pi$
$42$		0			0
$43$	0.336750	−	0.583268i	0.0513539	−	0.0889475i	−0.839206	−	0.543814i	$-0.816980\pi$
$43$	0.336750	−	0.583268i	0.0513539	−	0.0889475i	0.890560	+	0.454866i	$0.150313\pi$
$44$		0			0
$45$	1.21922	−	2.11176i	0.181751	−	0.314802i
$46$		0			0
$47$	0.525853			0.0767035			0.0383518	−	0.999264i	$-0.487789\pi$
$47$	0.525853			0.0767035			0.0383518	+	0.999264i	$0.487789\pi$
$48$		0			0
$49$	−1.21922	−	2.11176i	−0.174175	−	0.301680i
$50$		0			0
$51$	2.54635			0.356561
$52$		0			0
$53$	1.56155			0.214496			0.107248	−	0.994232i	$-0.465796\pi$
$53$	1.56155			0.214496			0.107248	+	0.994232i	$0.465796\pi$
$54$		0			0
$55$	−4.27156	−	7.39856i	−0.575977	−	0.997621i
$56$		0			0
$57$	−8.80776			−1.16662
$58$		0			0
$59$	−5.13416	+	8.89263i	−0.668411	+	1.15772i	0.309938	+	0.950757i	$0.399692\pi$
$59$	−5.13416	+	8.89263i	−0.668411	+	1.15772i	−0.978348	+	0.206965i	$0.933641\pi$
$60$		0			0
$61$	−2.62311	+	4.54335i	−0.335854	+	0.581717i	−0.983649	−	0.180099i	$-0.942358\pi$
$61$	−2.62311	+	4.54335i	−0.335854	+	0.581717i	0.647794	+	0.761815i	$0.275692\pi$
$62$		0			0
$63$	−2.39871	−	4.15468i	−0.302209	−	0.523440i
$64$		0			0
$65$	5.21922	+	2.11176i	0.647365	+	0.261931i
$66$		0			0
$67$	−2.47253	−	4.28255i	−0.302068	−	0.523196i	0.674537	−	0.738241i	$-0.264343\pi$
$67$	−2.47253	−	4.28255i	−0.302068	−	0.523196i	−0.976604	+	0.215045i	$0.931010\pi$
$68$		0			0
$69$	−2.15767	+	3.73720i	−0.259753	+	0.449905i
$70$		0			0
$71$	3.67188	−	6.35989i	0.435772	−	0.754780i	−0.561586	−	0.827418i	$-0.689809\pi$
$71$	3.67188	−	6.35989i	0.435772	−	0.754780i	0.997358	+	0.0726387i	$0.0231420\pi$
$72$		0			0
$73$	−16.6847			−1.95279			−0.976396	−	0.215989i	$-0.930702\pi$
$73$	−16.6847			−1.95279			−0.976396	+	0.215989i	$0.930702\pi$
$74$		0			0
$75$	−1.53610	−	2.66061i	−0.177374	−	0.307221i
$76$		0			0
$77$	−16.8078			−1.91542
$78$		0			0
$79$	15.7392			1.77080			0.885401	−	0.464828i	$-0.153884\pi$
$79$	15.7392			1.77080			0.885401	+	0.464828i	$0.153884\pi$
$80$		0			0
$81$	0.938447	+	1.62544i	0.104272	+	0.180604i
$82$		0			0
$83$	8.54312			0.937729			0.468864	−	0.883270i	$-0.344663\pi$
$83$	8.54312			0.937729			0.468864	+	0.883270i	$0.344663\pi$
$84$		0			0
$85$	1.65767	−	2.87117i	0.179800	−	0.311422i
$86$		0			0
$87$	−2.99838	+	5.19335i	−0.321460	+	0.556786i
$88$		0			0
$89$	0.842329	+	1.45896i	0.0892867	+	0.154649i	0.907210	−	0.420678i	$-0.138208\pi$
$89$	0.842329	+	1.45896i	0.0892867	+	0.154649i	−0.817923	+	0.575328i	$0.804875\pi$
$90$		0			0
$91$	8.73222	−	6.81529i	0.915385	−	0.714436i
$92$		0			0
$93$	−4.00000	−	6.92820i	−0.414781	−	0.718421i
$94$		0			0
$95$	−5.73384	+	9.93130i	−0.588279	+	1.01893i
$96$		0			0
$97$	−5.40388	+	9.35980i	−0.548681	+	0.950344i	0.449684	+	0.893188i	$0.351537\pi$
$97$	−5.40388	+	9.35980i	−0.548681	+	0.950344i	−0.998365	+	0.0571559i	$0.981797\pi$
$98$		0			0
$99$	−8.54312			−0.858616
$100$		0			0
$101$	−4.06155	−	7.03482i	−0.404140	−	0.699990i	0.590081	−	0.807344i	$-0.299096\pi$
$101$	−4.06155	−	7.03482i	−0.404140	−	0.699990i	−0.994221	+	0.107353i	$0.965762\pi$
$102$		0			0
$103$	−10.4160			−1.02632			−0.513158	−	0.858294i	$-0.671525\pi$
$103$	−10.4160			−1.02632			−0.513158	+	0.858294i	$0.671525\pi$
$104$		0			0
$105$	5.75379			0.561512
$106$		0			0
$107$	2.47253	+	4.28255i	0.239028	+	0.414009i	0.960436	−	0.278502i	$-0.0898378\pi$
$107$	2.47253	+	4.28255i	0.239028	+	0.414009i	−0.721407	+	0.692511i	$0.756504\pi$
$108$		0			0
$109$	−7.12311			−0.682270			−0.341135	−	0.940014i	$-0.610811\pi$
$109$	−7.12311			−0.682270			−0.341135	+	0.940014i	$0.610811\pi$
$110$		0			0
$111$	−3.67188	+	6.35989i	−0.348520	+	0.603654i
$112$		0			0
$113$	4.18466	−	7.24804i	0.393660	−	0.681838i	−0.599270	−	0.800547i	$-0.704542\pi$
$113$	4.18466	−	7.24804i	0.393660	−	0.681838i	0.992929	+	0.118709i	$0.0378756\pi$
$114$		0			0
$115$	2.80928	+	4.86581i	0.261967	+	0.453740i
$116$		0			0
$117$	4.43845	−	3.46410i	0.410335	−	0.320256i
$118$		0			0
$119$	−3.26131	−	5.64875i	−0.298964	−	0.517820i
$120$		0			0
$121$	−9.46543	+	16.3946i	−0.860494	+	1.49042i
$122$		0			0
$123$	2.47253	−	4.28255i	0.222940	−	0.386144i
$124$		0			0
$125$	−11.8078			−1.05612
$126$		0			0
$127$	4.87123	+	8.43723i	0.432252	+	0.748683i	0.997067	−	0.0765350i	$-0.0243857\pi$
$127$	4.87123	+	8.43723i	0.432252	+	0.748683i	−0.564815	+	0.825218i	$0.691052\pi$
$128$		0			0
$129$	0.807764			0.0711197
$130$		0			0
$131$	−18.9591			−1.65646			−0.828232	−	0.560386i	$-0.810653\pi$
$131$	−18.9591			−1.65646			−0.828232	+	0.560386i	$0.810653\pi$
$132$		0			0
$133$	11.2808	+	19.5389i	0.978167	+	1.69424i
$134$		0			0
$135$	8.54312			0.735274
$136$		0			0
$137$	8.50000	−	14.7224i	0.726204	−	1.25782i	−0.232273	−	0.972651i	$-0.574616\pi$
$137$	8.50000	−	14.7224i	0.726204	−	1.25782i	0.958477	−	0.285171i	$-0.0920506\pi$
$138$		0			0
$139$	−2.20960	+	3.82714i	−0.187416	+	0.324614i	−0.944388	−	0.328833i	$-0.893345\pi$
$139$	−2.20960	+	3.82714i	−0.187416	+	0.324614i	0.756972	+	0.653447i	$0.226678\pi$
$140$		0			0
$141$	0.315342	+	0.546188i	0.0265566	+	0.0459973i
$142$		0			0
$143$	−2.73546	−	19.5351i	−0.228750	−	1.63360i
$144$		0			0
$145$	3.90388	+	6.76172i	0.324200	+	0.561530i
$146$		0			0
$147$	1.46228	−	2.53274i	0.120607	−	0.208897i
$148$		0			0
$149$	11.6231	−	20.1318i	0.952202	−	1.64926i	0.211557	−	0.977366i	$-0.432147\pi$
$149$	11.6231	−	20.1318i	0.952202	−	1.64926i	0.740645	−	0.671896i	$-0.234520\pi$
$150$		0			0
$151$	14.1617			1.15246			0.576230	−	0.817287i	$-0.304523\pi$
$151$	14.1617			1.15246			0.576230	+	0.817287i	$0.304523\pi$
$152$		0			0
$153$	−1.65767	−	2.87117i	−0.134015	−	0.232120i
$154$		0			0
$155$	−10.4160			−0.836631
$156$		0			0
$157$	−12.6847			−1.01235			−0.506173	−	0.862432i	$-0.668940\pi$
$157$	−12.6847			−1.01235			−0.506173	+	0.862432i	$0.668940\pi$
$158$		0			0
$159$	0.936426	+	1.62194i	0.0742634	+	0.128628i
$160$		0			0
$161$	11.0540			0.871175
$162$		0			0
$163$	2.20960	−	3.82714i	0.173069	−	0.299765i	−0.766422	−	0.642337i	$-0.777965\pi$
$163$	2.20960	−	3.82714i	0.173069	−	0.299765i	0.939491	+	0.342572i	$0.111298\pi$
$164$		0			0
$165$	5.12311	−	8.87348i	0.398833	−	0.690799i
$166$		0			0
$167$	5.13416	+	8.89263i	0.397293	+	0.688132i	0.993391	−	0.114780i	$-0.0366162\pi$
$167$	5.13416	+	8.89263i	0.397293	+	0.688132i	−0.596098	+	0.802912i	$0.703283\pi$
$168$		0			0
$169$	9.34233	+	9.03996i	0.718641	+	0.695382i
$170$		0			0
$171$	5.73384	+	9.93130i	0.438478	+	0.759465i
$172$		0			0
$173$	−6.28078	+	10.8786i	−0.477519	+	0.827086i	−0.999668	−	0.0257676i	$-0.991797\pi$
$173$	−6.28078	+	10.8786i	−0.477519	+	0.827086i	0.522149	+	0.852854i	$0.325130\pi$
$174$		0			0
$175$	−3.93481	+	6.81529i	−0.297444	+	0.515187i
$176$		0			0
$177$	−12.3153			−0.925678
$178$		0			0
$179$	3.93481	+	6.81529i	0.294101	+	0.509399i	0.974775	−	0.223188i	$-0.0716463\pi$
$179$	3.93481	+	6.81529i	0.294101	+	0.509399i	−0.680674	+	0.732586i	$0.738313\pi$
$180$		0			0
$181$	−0.192236			−0.0142888			−0.00714439	−	0.999974i	$-0.502274\pi$
$181$	−0.192236			−0.0142888			−0.00714439	+	0.999974i	$0.502274\pi$
$182$		0			0
$183$	−6.29206			−0.465122
$184$		0			0
$185$	4.78078	+	8.28055i	0.351490	+	0.608798i
$186$		0			0
$187$	−11.6153			−0.849396
$188$		0			0
$189$	8.40388	−	14.5560i	0.611292	−	1.05879i
$190$		0			0
$191$	6.74409	−	11.6811i	0.487985	−	0.845215i	−0.511919	−	0.859033i	$-0.671065\pi$
$191$	6.74409	−	11.6811i	0.487985	−	0.845215i	0.999905	+	0.0138185i	$0.00439872\pi$
$192$		0			0
$193$	5.06155	+	8.76687i	0.364339	+	0.631053i	0.988670	−	0.150107i	$-0.0479618\pi$
$193$	5.06155	+	8.76687i	0.364339	+	0.631053i	−0.624331	+	0.781160i	$0.714628\pi$
$194$		0			0
$195$	0.936426	+	6.68742i	0.0670589	+	0.478896i
$196$		0			0
$197$	−7.40388	−	12.8239i	−0.527505	−	0.913665i	−0.999486	−	0.0320565i	$-0.989794\pi$
$197$	−7.40388	−	12.8239i	−0.527505	−	0.913665i	0.471981	−	0.881609i	$-0.343539\pi$
$198$		0			0
$199$	1.79903	−	3.11601i	0.127530	−	0.220888i	−0.795189	−	0.606361i	$-0.792628\pi$
$199$	1.79903	−	3.11601i	0.127530	−	0.220888i	0.922719	+	0.385473i	$0.125962\pi$
$200$		0			0
$201$	2.96543	−	5.13628i	0.209166	−	0.362286i
$202$		0			0
$203$	15.3610			1.07813
$204$		0			0
$205$	−3.21922	−	5.57586i	−0.224840	−	0.389435i
$206$		0			0
$207$	5.61856			0.390517
$208$		0			0
$209$	40.1771			2.77911
$210$		0			0
$211$	0.599676	+	1.03867i	0.0412834	+	0.0715050i	0.885929	−	0.463821i	$-0.153522\pi$
$211$	0.599676	+	1.03867i	0.0412834	+	0.0715050i	−0.844645	+	0.535326i	$0.820189\pi$
$212$		0			0
$213$	8.80776			0.603498
$214$		0			0
$215$	0.525853	−	0.910804i	0.0358629	−	0.0621163i
$216$		0			0
$217$	−10.2462	+	17.7470i	−0.695558	+	1.20474i
$218$		0			0
$219$	−10.0054	−	17.3299i	−0.676102	−	1.17104i
$220$		0			0
$221$	6.03457	−	4.70983i	0.405929	−	0.316818i
$222$		0			0
$223$	−6.74409	−	11.6811i	−0.451618	−	0.782224i	0.546869	−	0.837218i	$-0.315819\pi$
$223$	−6.74409	−	11.6811i	−0.451618	−	0.782224i	−0.998487	+	0.0549936i	$0.982486\pi$
$224$		0			0
$225$	−2.00000	+	3.46410i	−0.133333	+	0.230940i
$226$		0			0
$227$	11.5415	−	19.9905i	0.766036	−	1.32681i	−0.173661	−	0.984806i	$-0.555560\pi$
$227$	11.5415	−	19.9905i	0.766036	−	1.32681i	0.939697	−	0.342008i	$-0.111107\pi$
$228$		0			0
$229$	5.36932			0.354814			0.177407	−	0.984138i	$-0.443229\pi$
$229$	5.36932			0.354814			0.177407	+	0.984138i	$0.443229\pi$
$230$		0			0
$231$	−10.0792	−	17.4577i	−0.663164	−	1.14863i
$232$		0			0
$233$	9.36932			0.613804			0.306902	−	0.951741i	$-0.400708\pi$
$233$	9.36932			0.613804			0.306902	+	0.951741i	$0.400708\pi$
$234$		0			0
$235$	0.821147			0.0535657
$236$		0			0
$237$	9.43845	+	16.3479i	0.613093	+	1.06191i
$238$		0			0
$239$	−13.3405			−0.862927			−0.431464	−	0.902130i	$-0.642003\pi$
$239$	−13.3405			−0.862927			−0.431464	+	0.902130i	$0.642003\pi$
$240$		0			0
$241$	13.0616	−	22.6233i	0.841369	−	1.45729i	−0.0473693	−	0.998877i	$-0.515084\pi$
$241$	13.0616	−	22.6233i	0.841369	−	1.45729i	0.888738	−	0.458416i	$-0.151583\pi$
$242$		0			0
$243$	7.08084	−	12.2644i	0.454236	−	0.786760i
$244$		0			0
$245$	−1.90388	−	3.29762i	−0.121635	−	0.210677i
$246$		0			0
$247$	−20.8734	+	16.2912i	−1.32814	+	1.03658i
$248$		0			0
$249$	5.12311	+	8.87348i	0.324664	+	0.562334i
$250$		0			0
$251$	−4.87123	+	8.43723i	−0.307470	+	0.532553i	−0.977808	−	0.209502i	$-0.932816\pi$
$251$	−4.87123	+	8.43723i	−0.307470	+	0.532553i	0.670339	+	0.742055i	$0.266149\pi$
$252$		0			0
$253$	9.84233	−	17.0474i	0.618782	−	1.07176i
$254$		0			0
$255$	3.97626			0.249003
$256$		0			0
$257$	−2.06155	−	3.57071i	−0.128596	−	0.222735i	0.794537	−	0.607216i	$-0.207714\pi$
$257$	−2.06155	−	3.57071i	−0.128596	−	0.222735i	−0.923133	+	0.384481i	$0.874380\pi$
$258$		0			0
$259$	18.8114			1.16889
$260$		0			0
$261$	7.80776			0.483288
$262$		0			0
$263$	15.5501	+	26.9336i	0.958862	+	1.66080i	0.725272	+	0.688463i	$0.241714\pi$
$263$	15.5501	+	26.9336i	0.958862	+	1.66080i	0.233591	+	0.972335i	$0.424952\pi$
$264$		0			0
$265$	2.43845			0.149793
$266$		0			0
$267$	−1.01025	+	1.74980i	−0.0618263	+	0.107086i
$268$		0			0
$269$	3.15767	−	5.46925i	0.192527	−	0.333466i	−0.753560	−	0.657379i	$-0.771665\pi$
$269$	3.15767	−	5.46925i	0.192527	−	0.333466i	0.946087	+	0.323913i	$0.104999\pi$
$270$		0			0
$271$	5.13416	+	8.89263i	0.311878	+	0.540189i	0.978769	−	0.204967i	$-0.0657086\pi$
$271$	5.13416	+	8.89263i	0.311878	+	0.540189i	−0.666891	+	0.745155i	$0.732375\pi$
$272$		0			0
$273$	12.3153	+	4.98293i	0.745358	+	0.301580i
$274$		0			0
$275$	7.00701	+	12.1365i	0.422539	+	0.731859i
$276$		0			0
$277$	−13.1847	+	22.8365i	−0.792189	+	1.37211i	0.132419	+	0.991194i	$0.457725\pi$
$277$	−13.1847	+	22.8365i	−0.792189	+	1.37211i	−0.924609	+	0.380918i	$0.875608\pi$
$278$		0			0
$279$	−5.20798	+	9.02049i	−0.311794	+	0.540043i
$280$		0			0
$281$	−24.6847			−1.47256			−0.736282	−	0.676675i	$-0.763420\pi$
$281$	−24.6847			−1.47256			−0.736282	+	0.676675i	$0.763420\pi$
$282$		0			0
$283$	1.01025	+	1.74980i	0.0600531	+	0.104015i	0.894489	−	0.447090i	$-0.147540\pi$
$283$	1.01025	+	1.74980i	0.0600531	+	0.104015i	−0.834436	+	0.551105i	$0.814206\pi$
$284$		0			0
$285$	−13.7538			−0.814704
$286$		0			0
$287$	−12.6670			−0.747711
$288$		0			0
$289$	6.24621	+	10.8188i	0.367424	+	0.636397i
$290$		0			0
$291$	−12.9623			−0.759865
$292$		0			0
$293$	0.500000	−	0.866025i	0.0292103	−	0.0505937i	−0.851051	−	0.525084i	$-0.824034\pi$
$293$	0.500000	−	0.866025i	0.0292103	−	0.0505937i	0.880261	+	0.474490i	$0.157367\pi$
$294$		0			0
$295$	−8.01726	+	13.8863i	−0.466783	+	0.808492i
$296$		0			0
$297$	−14.9654	−	25.9209i	−0.868383	−	1.50408i
$298$		0			0
$299$	1.79903	+	12.8476i	0.104041	+	0.742998i
$300$		0			0
$301$	−1.03457	−	1.79192i	−0.0596313	−	0.103285i
$302$		0			0
$303$	4.87123	−	8.43723i	0.279845	−	0.484706i
$304$		0			0
$305$	−4.09612	+	7.09468i	−0.234543	+	0.406240i
$306$		0			0
$307$	−24.8082			−1.41588			−0.707939	−	0.706273i	$-0.750375\pi$
$307$	−24.8082			−1.41588			−0.707939	+	0.706273i	$0.750375\pi$
$308$		0			0
$309$	−6.24621	−	10.8188i	−0.355335	−	0.615457i
$310$		0			0
$311$	20.0108			1.13471			0.567354	−	0.823474i	$-0.307967\pi$
$311$	20.0108			1.13471			0.567354	+	0.823474i	$0.307967\pi$
$312$		0			0
$313$	4.87689			0.275658			0.137829	−	0.990456i	$-0.455988\pi$
$313$	4.87689			0.275658			0.137829	+	0.990456i	$0.455988\pi$
$314$		0			0
$315$	−3.74571	−	6.48775i	−0.211047	−	0.365543i
$316$		0			0
$317$	−17.8078			−1.00018			−0.500092	−	0.865972i	$-0.666700\pi$
$317$	−17.8078			−1.00018			−0.500092	+	0.865972i	$0.666700\pi$
$318$		0			0
$319$	13.6773	−	23.6897i	0.765781	−	1.32637i
$320$		0			0
$321$	−2.96543	+	5.13628i	−0.165514	+	0.286679i
$322$		0			0
$323$	7.79579	+	13.5027i	0.433770	+	0.751311i
$324$		0			0
$325$	−8.56155	−	3.46410i	−0.474910	−	0.192154i
$326$		0			0
$327$	−4.27156	−	7.39856i	−0.236218	−	0.409141i
$328$		0			0
$329$	0.807764	−	1.39909i	0.0445335	−	0.0771342i
$330$		0			0
$331$	−6.33351	+	10.9700i	−0.348121	+	0.602964i	−0.985916	−	0.167243i	$-0.946514\pi$
$331$	−6.33351	+	10.9700i	−0.348121	+	0.602964i	0.637794	+	0.770207i	$0.279847\pi$
$332$		0			0
$333$	9.56155			0.523970
$334$		0			0
$335$	−3.86098	−	6.68742i	−0.210948	−	0.365373i
$336$		0			0
$337$	−27.4233			−1.49384			−0.746921	−	0.664913i	$-0.768469\pi$
$337$	−27.4233			−1.49384			−0.746921	+	0.664913i	$0.768469\pi$
$338$		0			0
$339$	10.0378			0.545176
$340$		0			0
$341$	18.2462	+	31.6034i	0.988088	+	1.71142i
$342$		0			0
$343$	14.0140			0.756686
$344$		0			0
$345$	−3.36932	+	5.83583i	−0.181398	+	0.314190i
$346$		0			0
$347$	3.67188	−	6.35989i	0.197117	−	0.341417i	−0.750475	−	0.660898i	$-0.770175\pi$
$347$	3.67188	−	6.35989i	0.197117	−	0.341417i	0.947592	+	0.319482i	$0.103509\pi$
$348$		0			0
$349$	16.2808	+	28.1991i	0.871490	+	1.50946i	0.860455	+	0.509526i	$0.170179\pi$
$349$	16.2808	+	28.1991i	0.871490	+	1.50946i	0.0110346	+	0.999939i	$0.496488\pi$
$350$		0			0
$351$	18.2856	+	7.39856i	0.976012	+	0.394906i
$352$		0			0
$353$	−9.74621	−	16.8809i	−0.518738	−	0.898481i	−0.999763	−	0.0217742i	$-0.993069\pi$
$353$	−9.74621	−	16.8809i	−0.518738	−	0.898481i	0.481024	−	0.876707i	$-0.340265\pi$
$354$		0			0
$355$	5.73384	−	9.93130i	0.304321	−	0.527099i
$356$		0			0
$357$	3.91146	−	6.77485i	0.207016	−	0.358563i
$358$		0			0
$359$	−30.4268			−1.60586			−0.802932	−	0.596071i	$-0.796728\pi$
$359$	−30.4268			−1.60586			−0.802932	+	0.596071i	$0.796728\pi$
$360$		0			0
$361$	−17.4654	−	30.2510i	−0.919233	−	1.59216i
$362$		0			0
$363$	−22.7048			−1.19169
$364$		0			0
$365$	−26.0540			−1.36373
$366$		0			0
$367$	−11.5415	−	19.9905i	−0.602461	−	1.04349i	−0.992447	−	0.122673i	$-0.960853\pi$
$367$	−11.5415	−	19.9905i	−0.602461	−	1.04349i	0.389986	−	0.920821i	$-0.372480\pi$
$368$		0			0
$369$	−6.43845			−0.335172
$370$		0			0
$371$	2.39871	−	4.15468i	0.124535	−	0.215700i
$372$		0			0
$373$	0.184658	−	0.319838i	0.00956125	−	0.0165606i	−0.861205	−	0.508257i	$-0.830290\pi$
$373$	0.184658	−	0.319838i	0.00956125	−	0.0165606i	0.870766	+	0.491697i	$0.163623\pi$
$374$		0			0
$375$	−7.08084	−	12.2644i	−0.365653	−	0.633329i
$376$		0			0
$377$	2.50000	+	17.8536i	0.128757	+	0.919506i
$378$		0			0
$379$	0.599676	+	1.03867i	0.0308033	+	0.0533529i	0.881016	−	0.473086i	$-0.156860\pi$
$379$	0.599676	+	1.03867i	0.0308033	+	0.0533529i	−0.850213	+	0.526439i	$0.823527\pi$
$380$		0			0
$381$	−5.84233	+	10.1192i	−0.299312	+	0.518423i
$382$		0			0
$383$	−8.87987	+	15.3804i	−0.453740	+	0.785901i	−0.998615	−	0.0526167i	$-0.983244\pi$
$383$	−8.87987	+	15.3804i	−0.453740	+	0.785901i	0.544875	+	0.838517i	$0.316577\pi$
$384$		0			0
$385$	−26.2462			−1.33763
$386$		0			0
$387$	−0.525853	−	0.910804i	−0.0267306	−	0.0462988i
$388$		0			0
$389$	−13.8078			−0.700081			−0.350041	−	0.936734i	$-0.613832\pi$
$389$	−13.8078			−0.700081			−0.350041	+	0.936734i	$0.613832\pi$
$390$		0			0
$391$	7.63906			0.386324
$392$		0			0
$393$	−11.3693	−	19.6922i	−0.573506	−	0.993342i
$394$		0			0
$395$	24.5776			1.23664
$396$		0			0
$397$	3.15767	−	5.46925i	0.158479	−	0.274494i	−0.775841	−	0.630928i	$-0.782674\pi$
$397$	3.15767	−	5.46925i	0.158479	−	0.274494i	0.934320	+	0.356434i	$0.116008\pi$
$398$		0			0
$399$	−13.5296	+	23.4340i	−0.677329	+	1.17317i
$400$		0			0
$401$	−5.18466	−	8.98009i	−0.258909	−	0.448444i	0.707041	−	0.707173i	$-0.250030\pi$
$401$	−5.18466	−	8.98009i	−0.258909	−	0.448444i	−0.965950	+	0.258729i	$0.916696\pi$
$402$		0			0
$403$	−22.2942	−	9.02049i	−1.11055	−	0.449343i
$404$		0			0
$405$	1.46543	+	2.53821i	0.0728180	+	0.126125i
$406$		0			0
$407$	16.7495	−	29.0110i	0.830241	−	1.43802i
$408$		0			0
$409$	−2.06155	+	3.57071i	−0.101937	+	0.176560i	−0.912483	−	0.409115i	$-0.865837\pi$
$409$	−2.06155	+	3.57071i	−0.101937	+	0.176560i	0.810546	+	0.585676i	$0.199171\pi$
$410$		0			0
$411$	20.3890			1.00572
$412$		0			0
$413$	15.7732	+	27.3200i	0.776148	+	1.34433i
$414$		0			0
$415$	13.3405			0.654861
$416$		0			0
$417$	−5.30019			−0.259551
$418$		0			0
$419$	−12.8885	−	22.3235i	−0.629644	−	1.09058i	−0.987623	−	0.156846i	$-0.949867\pi$
$419$	−12.8885	−	22.3235i	−0.629644	−	1.09058i	0.357979	−	0.933730i	$-0.383466\pi$
$420$		0			0
$421$	3.31534			0.161580			0.0807899	−	0.996731i	$-0.474256\pi$
$421$	3.31534			0.161580			0.0807899	+	0.996731i	$0.474256\pi$
$422$		0			0
$423$	0.410574	−	0.711134i	0.0199628	−	0.0345765i
$424$		0			0
$425$	−2.71922	+	4.70983i	−0.131902	+	0.228460i
$426$		0			0
$427$	8.05872	+	13.9581i	0.389989	+	0.675480i
$428$		0			0
$429$	18.6501	−	14.5560i	0.900435	−	0.702768i
$430$		0			0
$431$	13.0038	+	22.5232i	0.626370	+	1.08490i	0.988274	+	0.152689i	$0.0487934\pi$
$431$	13.0038	+	22.5232i	0.626370	+	1.08490i	−0.361904	+	0.932215i	$0.617873\pi$
$432$		0			0
$433$	6.81534	−	11.8045i	0.327524	−	0.567289i	−0.654496	−	0.756066i	$-0.727119\pi$
$433$	6.81534	−	11.8045i	0.327524	−	0.567289i	0.982020	+	0.188777i	$0.0604523\pi$
$434$		0			0
$435$	−4.68213	+	8.10969i	−0.224491	+	0.388830i
$436$		0			0
$437$	−26.4233			−1.26400
$438$		0			0
$439$	6.33351	+	10.9700i	0.302282	+	0.523568i	0.976653	−	0.214825i	$-0.0689182\pi$
$439$	6.33351	+	10.9700i	0.302282	+	0.523568i	−0.674370	+	0.738393i	$0.735585\pi$
$440$		0			0
$441$	−3.80776			−0.181322
$442$		0			0
$443$	−8.54312			−0.405896			−0.202948	−	0.979190i	$-0.565052\pi$
$443$	−8.54312			−0.405896			−0.202948	+	0.979190i	$0.565052\pi$
$444$		0			0
$445$	1.31534	+	2.27824i	0.0623532	+	0.107999i
$446$		0			0
$447$	27.8804			1.31870
$448$		0			0
$449$	6.28078	−	10.8786i	0.296408	−	0.513394i	−0.678903	−	0.734228i	$-0.737544\pi$
$449$	6.28078	−	10.8786i	0.296408	−	0.513394i	0.975311	+	0.220834i	$0.0708778\pi$
$450$		0			0
$451$	−11.2786	+	19.5351i	−0.531087	+	0.919870i
$452$		0			0
$453$	8.49242	+	14.7093i	0.399009	+	0.691104i
$454$		0			0
$455$	13.6358	−	10.6424i	0.639257	−	0.498925i
$456$		0			0
$457$	2.25379	+	3.90368i	0.105428	+	0.182606i	0.913913	−	0.405910i	$-0.133045\pi$
$457$	2.25379	+	3.90368i	0.105428	+	0.182606i	−0.808485	+	0.588517i	$0.799712\pi$
$458$		0			0
$459$	5.80766	−	10.0592i	0.271078	−	0.469522i
$460$		0			0
$461$	1.06155	−	1.83866i	0.0494414	−	0.0856351i	−0.840246	−	0.542206i	$-0.817589\pi$
$461$	1.06155	−	1.83866i	0.0494414	−	0.0856351i	0.889687	+	0.456571i	$0.150923\pi$
$462$		0			0
$463$	−13.3405			−0.619987			−0.309993	−	0.950739i	$-0.600327\pi$
$463$	−13.3405			−0.619987			−0.309993	+	0.950739i	$0.600327\pi$
$464$		0			0
$465$	−6.24621	−	10.8188i	−0.289661	−	0.501708i
$466$		0			0
$467$	−15.7392			−0.728325			−0.364162	−	0.931335i	$-0.618645\pi$
$467$	−15.7392			−0.728325			−0.364162	+	0.931335i	$0.618645\pi$
$468$		0			0
$469$	−15.1922			−0.701512
$470$		0			0
$471$	−7.60669	−	13.1752i	−0.350498	−	0.607080i
$472$		0			0
$473$	−3.68466			−0.169421
$474$		0			0
$475$	9.40572	−	16.2912i	0.431564	−	0.747491i
$476$		0			0
$477$	1.21922	−	2.11176i	0.0558244	−	0.0966907i
$478$		0			0
$479$	2.99838	+	5.19335i	0.137000	+	0.237290i	0.926360	−	0.376640i	$-0.122921\pi$
$479$	2.99838	+	5.19335i	0.137000	+	0.237290i	−0.789360	+	0.613931i	$0.789587\pi$
$480$		0			0
$481$	3.06155	+	21.8639i	0.139595	+	0.996906i
$482$		0			0
$483$	6.62881	+	11.4814i	0.301621	+	0.522423i
$484$		0			0
$485$	−8.43845	+	14.6158i	−0.383170	+	0.663670i
$486$		0			0
$487$	16.6018	−	28.7552i	0.752301	−	1.30302i	−0.194404	−	0.980922i	$-0.562277\pi$
$487$	16.6018	−	28.7552i	0.752301	−	1.30302i	0.946705	−	0.322102i	$-0.104389\pi$
$488$		0			0
$489$	5.30019			0.239683
$490$		0			0
$491$	−21.0210	−	36.4095i	−0.948666	−	1.64314i	−0.748238	−	0.663430i	$-0.769100\pi$
$491$	−21.0210	−	36.4095i	−0.948666	−	1.64314i	−0.200428	−	0.979708i	$-0.564233\pi$
$492$		0			0
$493$	10.6155			0.478099
$494$		0			0
$495$	−13.3405			−0.599612
$496$		0			0
$497$	−11.2808	−	19.5389i	−0.506012	−	0.876438i
$498$		0			0
$499$	21.0625			0.942887			0.471443	−	0.881896i	$-0.343733\pi$
$499$	21.0625			0.942887			0.471443	+	0.881896i	$0.343733\pi$
$500$		0			0
$501$	−6.15767	+	10.6654i	−0.275104	+	0.476495i
$502$		0			0
$503$	−4.08246	+	7.07102i	−0.182028	+	0.315281i	−0.942571	−	0.334006i	$-0.891599\pi$
$503$	−4.08246	+	7.07102i	−0.182028	+	0.315281i	0.760543	+	0.649287i	$0.224933\pi$
$504$		0			0
$505$	−6.34233	−	10.9852i	−0.282230	−	0.488837i
$506$		0			0
$507$	−3.78716	+	15.1246i	−0.168194	+	0.671709i
$508$		0			0
$509$	−7.18466	−	12.4442i	−0.318454	−	0.551579i	0.661711	−	0.749759i	$-0.269830\pi$
$509$	−7.18466	−	12.4442i	−0.318454	−	0.551579i	−0.980166	+	0.198180i	$0.936497\pi$
$510$		0			0
$511$	−25.6294	+	44.3913i	−1.13378	+	1.96376i
$512$		0			0
$513$	−20.0885	+	34.7944i	−0.886931	+	1.53621i
$514$		0			0
$515$	−16.2651			−0.716725
$516$		0			0
$517$	−1.43845	−	2.49146i	−0.0632628	−	0.109574i
$518$		0			0
$519$	−15.0657			−0.661312
$520$		0			0
$521$	37.5616			1.64560			0.822801	−	0.568330i	$-0.192410\pi$
$521$	37.5616			1.64560			0.822801	+	0.568330i	$0.192410\pi$
$522$		0			0
$523$	−0.189103	−	0.327536i	−0.00826889	−	0.0143221i	0.861861	−	0.507144i	$-0.169299\pi$
$523$	−0.189103	−	0.327536i	−0.00826889	−	0.0143221i	−0.870130	+	0.492822i	$0.835965\pi$
$524$		0			0
$525$	−9.43845			−0.411928
$526$		0			0
$527$	−7.08084	+	12.2644i	−0.308446	+	0.534244i
$528$		0			0
$529$	5.02699	−	8.70700i	0.218565	−	0.378565i
$530$		0			0
$531$	8.01726	+	13.8863i	0.347920	+	0.602614i
$532$		0			0
$533$	−2.06155	−	14.7224i	−0.0892958	−	0.637699i
$534$		0			0
$535$	3.86098	+	6.68742i	0.166925	+	0.289122i
$536$		0			0
$537$	−4.71922	+	8.17394i	−0.203650	+	0.352731i
$538$		0			0
$539$	−6.67026	+	11.5532i	−0.287309	+	0.497633i
$540$		0			0
$541$	35.1771			1.51238			0.756190	−	0.654352i	$-0.227058\pi$
$541$	35.1771			1.51238			0.756190	+	0.654352i	$0.227058\pi$
$542$		0			0
$543$	−0.115279	−	0.199670i	−0.00494711	−	0.00856865i
$544$		0			0
$545$	−11.1231			−0.476461
$546$		0			0
$547$	24.8082			1.06072			0.530361	−	0.847772i	$-0.322056\pi$
$547$	24.8082			1.06072			0.530361	+	0.847772i	$0.322056\pi$
$548$		0			0
$549$	4.09612	+	7.09468i	0.174818	+	0.302794i
$550$		0			0
$551$	−36.7188			−1.56427
$552$		0			0
$553$	24.1771	−	41.8759i	1.02811	−	1.78075i
$554$		0			0
$555$	−5.73384	+	9.93130i	−0.243388	+	0.421560i
$556$		0			0
$557$	14.9924	+	25.9676i	0.635249	+	1.10028i	0.986462	+	0.163988i	$0.0524360\pi$
$557$	14.9924	+	25.9676i	0.635249	+	1.10028i	−0.351213	+	0.936296i	$0.614231\pi$
$558$		0			0
$559$	1.91431	−	1.49407i	0.0809666	−	0.0631925i
$560$		0			0
$561$	−6.96543	−	12.0645i	−0.294081	−	0.509363i
$562$		0			0
$563$	−2.20960	+	3.82714i	−0.0931237	+	0.161295i	−0.908824	−	0.417180i	$-0.863019\pi$
$563$	−2.20960	+	3.82714i	−0.0931237	+	0.161295i	0.815700	+	0.578475i	$0.196352\pi$
$564$		0			0
$565$	6.53457	−	11.3182i	0.274911	−	0.476160i
$566$		0			0
$567$	5.76621			0.242158
$568$		0			0
$569$	21.3348	+	36.9529i	0.894399	+	1.54915i	0.834546	+	0.550938i	$0.185730\pi$
$569$	21.3348	+	36.9529i	0.894399	+	1.54915i	0.0598531	+	0.998207i	$0.480937\pi$
$570$		0			0
$571$	42.7156			1.78759			0.893796	−	0.448474i	$-0.148032\pi$
$571$	42.7156			1.78759			0.893796	+	0.448474i	$0.148032\pi$
$572$		0			0
$573$	16.1771			0.675807
$574$		0			0
$575$	−4.60831	−	7.98182i	−0.192180	−	0.332865i
$576$		0			0
$577$	−14.9309			−0.621580			−0.310790	−	0.950479i	$-0.600594\pi$
$577$	−14.9309			−0.621580			−0.310790	+	0.950479i	$0.600594\pi$
$578$		0			0
$579$	−6.07059	+	10.5146i	−0.252285	+	0.436970i
$580$		0			0
$581$	13.1231	−	22.7299i	0.544438	−	0.942995i
$582$		0			0
$583$	−4.27156	−	7.39856i	−0.176910	−	0.306417i
$584$		0			0
$585$	6.93087	−	5.40938i	0.286556	−	0.223650i
$586$		0			0
$587$	−11.4262	−	19.7908i	−0.471611	−	0.816853i	0.527862	−	0.849330i	$-0.322994\pi$
$587$	−11.4262	−	19.7908i	−0.471611	−	0.816853i	−0.999472	+	0.0324768i	$0.989661\pi$
$588$		0			0
$589$	24.4924	−	42.4221i	1.00919	−	1.74797i
$590$		0			0
$591$	8.87987	−	15.3804i	0.365269	−	0.632664i
$592$		0			0
$593$	26.0540			1.06991			0.534954	−	0.844881i	$-0.320329\pi$
$593$	26.0540			1.06991			0.534954	+	0.844881i	$0.320329\pi$
$594$		0			0
$595$	−5.09271	−	8.82082i	−0.208781	−	0.361619i
$596$		0			0
$597$	4.31534			0.176615
$598$		0			0
$599$	4.27156			0.174531			0.0872656	−	0.996185i	$-0.472187\pi$
$599$	4.27156			0.174531			0.0872656	+	0.996185i	$0.472187\pi$
$600$		0			0
$601$	1.06155	+	1.83866i	0.0433016	+	0.0750006i	0.886864	−	0.462031i	$-0.152879\pi$
$601$	1.06155	+	1.83866i	0.0433016	+	0.0750006i	−0.843562	+	0.537031i	$0.819546\pi$
$602$		0			0
$603$	−7.72197			−0.314463
$604$		0			0
$605$	−14.7808	+	25.6011i	−0.600924	+	1.04083i
$606$		0			0
$607$	21.8098	−	37.7757i	0.885233	−	1.53327i	0.0397874	−	0.999208i	$-0.487332\pi$
$607$	21.8098	−	37.7757i	0.885233	−	1.53327i	0.845446	−	0.534061i	$-0.179335\pi$
$608$		0			0
$609$	9.21165	+	15.9550i	0.373275	+	0.646531i
$610$		0			0
$611$	1.75757	+	0.711134i	0.0711038	+	0.0287694i
$612$		0			0
$613$	0.815342	+	1.41221i	0.0329313	+	0.0570387i	0.882021	−	0.471209i	$-0.156182\pi$
$613$	0.815342	+	1.41221i	0.0329313	+	0.0570387i	−0.849090	+	0.528248i	$0.822849\pi$
$614$		0			0
$615$	3.86098	−	6.68742i	0.155690	−	0.269663i
$616$		0			0
$617$	3.62311	−	6.27540i	0.145861	−	0.252638i	−0.783833	−	0.620972i	$-0.786738\pi$
$617$	3.62311	−	6.27540i	0.145861	−	0.252638i	0.929694	+	0.368333i	$0.120072\pi$
$618$		0			0
$619$	8.54312			0.343377			0.171688	−	0.985151i	$-0.445078\pi$
$619$	8.54312			0.343377			0.171688	+	0.985151i	$0.445078\pi$
$620$		0			0
$621$	9.84233	+	17.0474i	0.394959	+	0.684089i
$622$		0			0
$623$	5.17562			0.207357
$624$		0			0
$625$	−5.63068			−0.225227
$626$		0			0
$627$	24.0932	+	41.7307i	0.962192	+	1.66656i
$628$		0			0
$629$	13.0000			0.518344
$630$		0			0
$631$	−11.9521	+	20.7016i	−0.475804	+	0.824118i	−0.999616	−	0.0277168i	$-0.991176\pi$
$631$	−11.9521	+	20.7016i	−0.475804	+	0.824118i	0.523811	+	0.851834i	$0.324510\pi$
$632$		0			0
$633$	−0.719224	+	1.24573i	−0.0285866	+	0.0495134i
$634$		0			0
$635$	7.60669	+	13.1752i	0.301862	+	0.522841i
$636$		0			0
$637$	−1.21922	−	8.70700i	−0.0483074	−	0.344984i
$638$		0			0
$639$	−5.73384	−	9.93130i	−0.226827	−	0.392876i
$640$		0			0
$641$	15.3078	−	26.5138i	0.604620	−	1.04723i	−0.387491	−	0.921873i	$-0.626658\pi$
$641$	15.3078	−	26.5138i	0.604620	−	1.04723i	0.992111	−	0.125360i	$-0.0400085\pi$
$642$		0			0
$643$	4.08246	−	7.07102i	0.160996	−	0.278854i	−0.774230	−	0.632904i	$-0.781863\pi$
$643$	4.08246	−	7.07102i	0.160996	−	0.278854i	0.935226	+	0.354051i	$0.115196\pi$
$644$		0			0
$645$	1.26137			0.0496662
$646$		0			0
$647$	12.5932	+	21.8121i	0.495090	+	0.857521i	0.999984	−	0.00566038i	$-0.00180176\pi$
$647$	12.5932	+	21.8121i	0.495090	+	0.857521i	−0.504894	+	0.863181i	$0.668468\pi$
$648$		0			0
$649$	56.1771			2.20514
$650$		0			0
$651$	−24.5776			−0.963274
$652$		0			0
$653$	0.280776	+	0.486319i	0.0109876	+	0.0190311i	0.871467	−	0.490454i	$-0.163169\pi$
$653$	0.280776	+	0.486319i	0.0109876	+	0.0190311i	−0.860479	+	0.509485i	$0.829836\pi$
$654$		0			0
$655$	−29.6056			−1.15679
$656$		0			0
$657$	−13.0270	+	22.5634i	−0.508231	+	0.880282i
$658$		0			0
$659$	12.6256	−	21.8681i	0.491822	−	0.851862i	−0.508133	−	0.861279i	$-0.669664\pi$
$659$	12.6256	−	21.8681i	0.491822	−	0.851862i	0.999956	+	0.00941700i	$0.00299757\pi$
$660$		0			0
$661$	7.93845	+	13.7498i	0.308770	+	0.534805i	0.978094	−	0.208166i	$-0.0667494\pi$
$661$	7.93845	+	13.7498i	0.308770	+	0.534805i	−0.669324	+	0.742971i	$0.733416\pi$
$662$		0			0
$663$	8.51075	+	3.44355i	0.330530	+	0.133736i
$664$		0			0
$665$	17.6155	+	30.5110i	0.683101	+	1.18317i
$666$		0			0
$667$	−8.99515	+	15.5801i	−0.348293	+	0.603262i
$668$		0			0
$669$	8.08854	−	14.0098i	0.312721	−	0.541649i
$670$		0			0
$671$	28.7016			1.10801
$672$		0			0
$673$	−12.8693	−	22.2903i	−0.496076	−	0.859228i	0.503914	−	0.863754i	$-0.331893\pi$
$673$	−12.8693	−	22.2903i	−0.496076	−	0.859228i	−0.999990	+	0.00452547i	$0.998559\pi$
$674$		0			0
$675$	−14.0140			−0.539400
$676$		0			0
$677$	−23.1231			−0.888693			−0.444347	−	0.895855i	$-0.646564\pi$
$677$	−23.1231			−0.888693			−0.444347	+	0.895855i	$0.646564\pi$
$678$		0			0
$679$	16.6018	+	28.7552i	0.637120	+	1.10352i
$680$		0			0
$681$	27.6847			1.06088
$682$		0			0
$683$	11.5415	−	19.9905i	0.441623	−	0.764914i	−0.556187	−	0.831057i	$-0.687736\pi$
$683$	11.5415	−	19.9905i	0.441623	−	0.764914i	0.997810	+	0.0661434i	$0.0210695\pi$
$684$		0			0
$685$	13.2732	−	22.9899i	0.507143	−	0.878397i
$686$		0			0
$687$	3.21985	+	5.57695i	0.122845	+	0.212774i
$688$		0			0
$689$	5.21922	+	2.11176i	0.198837	+	0.0804515i
$690$		0			0
$691$	−24.6191	−	42.6415i	−0.936555	−	1.62216i	−0.771838	−	0.635819i	$-0.780662\pi$
$691$	−24.6191	−	42.6415i	−0.936555	−	1.62216i	−0.164717	−	0.986341i	$-0.552671\pi$
$692$		0			0
$693$	−13.1231	+	22.7299i	−0.498506	+	0.863437i
$694$		0			0
$695$	−3.45041	+	5.97629i	−0.130882	+	0.226694i
$696$		0			0
$697$	−8.75379			−0.331573
$698$		0			0
$699$	5.61856	+	9.73163i	0.212513	+	0.368084i
$700$		0			0
$701$	−23.1231			−0.873348			−0.436674	−	0.899620i	$-0.643844\pi$
$701$	−23.1231			−0.873348			−0.436674	+	0.899620i	$0.643844\pi$
$702$		0			0
$703$	−44.9666			−1.69595
$704$		0			0
$705$	0.492423	+	0.852901i	0.0185457	+	0.0321221i
$706$		0			0
$707$	−24.9559			−0.938561
$708$		0			0
$709$	5.93845	−	10.2857i	0.223023	−	0.386287i	−0.732701	−	0.680550i	$-0.761741\pi$
$709$	5.93845	−	10.2857i	0.223023	−	0.386287i	0.955725	+	0.294263i	$0.0950741\pi$
$710$		0			0
$711$	12.2888	−	21.2849i	0.460867	−	0.798245i
$712$		0			0
$713$	−12.0000	−	20.7846i	−0.449404	−	0.778390i
$714$		0			0
$715$	−4.27156	−	30.5050i	−0.159747	−	1.14082i
$716$		0			0
$717$	−8.00000	−	13.8564i	−0.298765	−	0.517477i
$718$		0			0
$719$	18.6223	−	32.2548i	0.694496	−	1.20290i	−0.275854	−	0.961199i	$-0.588961\pi$
$719$	18.6223	−	32.2548i	0.694496	−	1.20290i	0.970350	−	0.241703i	$-0.0777059\pi$
$720$		0			0
$721$	−16.0000	+	27.7128i	−0.595871	+	1.03208i
$722$		0			0
$723$	31.3308			1.16521
$724$		0			0
$725$	−6.40388	−	11.0918i	−0.237834	−	0.411941i
$726$		0			0
$727$	−22.9354			−0.850625			−0.425313	−	0.905047i	$-0.639836\pi$
$727$	−22.9354			−0.850625			−0.425313	+	0.905047i	$0.639836\pi$
$728$		0			0
$729$	22.6155			0.837612
$730$		0			0
$731$	−0.714956	−	1.23834i	−0.0264436	−	0.0458016i
$732$		0			0
$733$	16.9309			0.625356			0.312678	−	0.949859i	$-0.398774\pi$
$733$	16.9309			0.625356			0.312678	+	0.949859i	$0.398774\pi$
$734$		0			0
$735$	2.28343	−	3.95501i	0.0842254	−	0.145883i
$736$		0			0
$737$	−13.5270	+	23.4294i	−0.498273	+	0.863034i
$738$		0			0
$739$	−19.1482	−	33.1656i	−0.704378	−	1.22002i	−0.966916	−	0.255096i	$-0.917893\pi$
$739$	−19.1482	−	33.1656i	−0.704378	−	1.22002i	0.262538	−	0.964922i	$-0.415440\pi$
$740$		0			0
$741$	−29.4384	−	11.9111i	−1.08145	−	0.437566i
$742$		0			0
$743$	5.28181	+	9.14836i	0.193771	+	0.335621i	0.946497	−	0.322713i	$-0.104595\pi$
$743$	5.28181	+	9.14836i	0.193771	+	0.335621i	−0.752726	+	0.658334i	$0.771262\pi$
$744$		0			0
$745$	18.1501	−	31.4369i	0.664968	−	1.15176i
$746$		0			0
$747$	6.67026	−	11.5532i	0.244052	−	0.422711i
$748$		0			0
$749$	15.1922			0.555112
$750$		0			0
$751$	−13.0038	−	22.5232i	−0.474515	−	0.821883i	0.525060	−	0.851066i	$-0.324043\pi$
$751$	−13.0038	−	22.5232i	−0.474515	−	0.821883i	−0.999574	+	0.0291821i	$0.990710\pi$
$752$		0			0
$753$	−11.6847			−0.425813
$754$		0			0
$755$	22.1142			0.804818
$756$		0			0
$757$	−24.2116	−	41.9358i	−0.879987	−	1.52418i	−0.851353	−	0.524593i	$-0.824218\pi$
$757$	−24.2116	−	41.9358i	−0.879987	−	1.52418i	−0.0286339	−	0.999590i	$-0.509116\pi$
$758$		0			0
$759$	23.6089			0.856947
$760$		0			0
$761$	−15.9654	+	27.6529i	−0.578747	+	1.00242i	0.416877	+	0.908963i	$0.363125\pi$
$761$	−15.9654	+	27.6529i	−0.578747	+	1.00242i	−0.995623	+	0.0934555i	$0.970209\pi$
$762$		0			0
$763$	−10.9418	+	18.9518i	−0.396121	+	0.686101i
$764$		0			0
$765$	−2.58854	−	4.48348i	−0.0935889	−	0.162101i
$766$		0			0
$767$	−29.1860	+	22.7789i	−1.05384	+	0.822500i
$768$		0			0
$769$	16.5270	+	28.6256i	0.595978	+	1.03226i	0.993408	+	0.114632i	$0.0365690\pi$
$769$	16.5270	+	28.6256i	0.595978	+	1.03226i	−0.397430	+	0.917633i	$0.630098\pi$
$770$		0			0
$771$	2.47253	−	4.28255i	0.0890460	−	0.154232i
$772$		0			0
$773$	3.15767	−	5.46925i	0.113574	−	0.196715i	−0.803635	−	0.595122i	$-0.797104\pi$
$773$	3.15767	−	5.46925i	0.113574	−	0.196715i	0.917209	+	0.398407i	$0.130437\pi$
$774$		0			0
$775$	17.0862			0.613756
$776$		0			0
$777$	11.2808	+	19.5389i	0.404696	+	0.700953i
$778$		0			0
$779$	30.2791			1.08486
$780$		0			0
$781$	−40.1771			−1.43765
$782$		0			0
$783$	13.6773	+	23.6897i	0.488786	+	0.846602i
$784$		0			0
$785$	−19.8078			−0.706969
$786$		0			0
$787$	−15.2872	+	26.4782i	−0.544930	+	0.943846i	0.453681	+	0.891164i	$0.350110\pi$
$787$	−15.2872	+	26.4782i	−0.544930	+	0.943846i	−0.998611	+	0.0526824i	$0.983223\pi$
$788$		0			0
$789$	−18.6501	+	32.3029i	−0.663961	+	1.15001i
$790$		0			0
$791$	−12.8561	−	22.2675i	−0.457111	−	0.791740i
$792$		0			0
$793$	−14.9115	+	11.6380i	−0.529521	+	0.413279i
$794$		0			0
$795$	1.46228	+	2.53274i	0.0518617	+	0.0898271i
$796$		0			0
$797$	7.47301	−	12.9436i	0.264708	−	0.458487i	−0.702779	−	0.711408i	$-0.748058\pi$
$797$	7.47301	−	12.9436i	0.264708	−	0.458487i	0.967487	+	0.252921i	$0.0813912\pi$
$798$		0			0
$799$	0.558221	−	0.966866i	0.0197484	−	0.0342053i
$800$		0			0
$801$	2.63068			0.0929506
$802$		0			0
$803$	45.6401	+	79.0510i	1.61061	+	2.78965i
$804$		0			0
$805$	17.2614			0.608383
$806$		0			0
$807$	7.57432			0.266629
$808$		0			0
$809$	−3.81534	−	6.60837i	−0.134140	−	0.232338i	0.791128	−	0.611650i	$-0.209494\pi$
$809$	−3.81534	−	6.60837i	−0.134140	−	0.232338i	−0.925269	+	0.379312i	$0.876161\pi$
$810$		0			0
$811$	−22.4095			−0.786904			−0.393452	−	0.919345i	$-0.628719\pi$
$811$	−22.4095			−0.786904			−0.393452	+	0.919345i	$0.628719\pi$
$812$		0			0
$813$	−6.15767	+	10.6654i	−0.215959	+	0.374052i
$814$		0			0
$815$	3.45041	−	5.97629i	0.120863	−	0.209340i
$816$		0			0
$817$	2.47301	+	4.28338i	0.0865197	+	0.149857i
$818$		0			0
$819$	−2.39871	−	17.1302i	−0.0838176	−	0.598577i
$820$		0			0
$821$	0.596118	+	1.03251i	0.0208047	+	0.0360347i	0.876240	−	0.481874i	$-0.160044\pi$
$821$	0.596118	+	1.03251i	0.0208047	+	0.0360347i	−0.855436	+	0.517909i	$0.826711\pi$
$822$		0			0
$823$	−8.20637	+	14.2138i	−0.286056	+	0.495463i	−0.972865	−	0.231375i	$-0.925678\pi$
$823$	−8.20637	+	14.2138i	−0.286056	+	0.495463i	0.686809	+	0.726838i	$0.259011\pi$
$824$		0			0
$825$	−8.40388	+	14.5560i	−0.292586	+	0.506773i
$826$		0			0
$827$	−19.7802			−0.687826			−0.343913	−	0.939001i	$-0.611753\pi$
$827$	−19.7802			−0.687826			−0.343913	+	0.939001i	$0.611753\pi$
$828$		0			0
$829$	−9.99242	−	17.3074i	−0.347051	−	0.601110i	0.638673	−	0.769478i	$-0.279484\pi$
$829$	−9.99242	−	17.3074i	−0.347051	−	0.601110i	−0.985724	+	0.168368i	$0.946150\pi$
$830$		0			0
$831$	−31.6261			−1.09710
$832$		0			0
$833$	−5.17708			−0.179375
$834$		0			0
$835$	8.01726	+	13.8863i	0.277449	+	0.480556i
$836$		0			0
$837$	−36.4924			−1.26136
$838$		0			0
$839$	−5.92294	+	10.2588i	−0.204483	+	0.354174i	−0.949968	−	0.312348i	$-0.898885\pi$
$839$	−5.92294	+	10.2588i	−0.204483	+	0.354174i	0.745485	+	0.666522i	$0.232218\pi$
$840$		0			0
$841$	2.00000	−	3.46410i	0.0689655	−	0.119452i
$842$		0			0
$843$	−14.8028	−	25.6392i	−0.509836	−	0.883061i
$844$		0			0
$845$	14.5885	+	14.1164i	0.501861	+	0.485618i
$846$		0			0
$847$	29.0798	+	50.3676i	0.999192	+	1.73065i
$848$		0			0
$849$	−1.21165	+	2.09863i	−0.0415836	+	0.0720249i
$850$		0			0
$851$	−11.0156	+	19.0797i	−0.377611	+	0.654042i
$852$		0			0
$853$	14.0540			0.481199			0.240599	−	0.970624i	$-0.422656\pi$
$853$	14.0540			0.481199			0.240599	+	0.970624i	$0.422656\pi$
$854$		0			0
$855$	8.95369	+	15.5082i	0.306210	+	0.530371i
$856$		0			0
$857$	21.5616			0.736529			0.368264	−	0.929721i	$-0.379952\pi$
$857$	21.5616			0.736529			0.368264	+	0.929721i	$0.379952\pi$
$858$		0			0
$859$	−22.7048			−0.774678			−0.387339	−	0.921937i	$-0.626606\pi$
$859$	−22.7048			−0.774678			−0.387339	+	0.921937i	$0.626606\pi$
$860$		0			0
$861$	−7.59612	−	13.1569i	−0.258875	−	0.448385i
$862$		0			0
$863$	34.1725			1.16324			0.581622	−	0.813459i	$-0.302418\pi$
$863$	34.1725			1.16324			0.581622	+	0.813459i	$0.302418\pi$
$864$		0			0
$865$	−9.80776	+	16.9875i	−0.333474	+	0.577594i
$866$		0			0
$867$	−7.49141	+	12.9755i	−0.254422	+	0.440671i
$868$		0			0
$869$	−43.0540	−	74.5717i	−1.46051	−	2.52967i
$870$		0			0
$871$	−2.47253	−	17.6574i	−0.0837785	−	0.598298i
$872$		0			0
$873$	8.43845	+	14.6158i	0.285598	+	0.494671i
$874$		0			0
$875$	−18.1379	+	31.4158i	−0.613174	+	1.06205i
$876$		0			0
$877$	3.62311	−	6.27540i	0.122344	−	0.211905i	−0.798348	−	0.602197i	$-0.794292\pi$
$877$	3.62311	−	6.27540i	0.122344	−	0.211905i	0.920691	+	0.390291i	$0.127626\pi$
$878$		0			0
$879$	1.19935			0.0404532
$880$		0			0
$881$	14.4309	+	24.9950i	0.486188	+	0.842103i	0.999874	−	0.0158756i	$-0.00505356\pi$
$881$	14.4309	+	24.9950i	0.486188	+	0.842103i	−0.513686	+	0.857978i	$0.671720\pi$
$882$		0			0
$883$	−36.0453			−1.21302			−0.606511	−	0.795075i	$-0.707431\pi$
$883$	−36.0453			−1.21302			−0.606511	+	0.795075i	$0.707431\pi$
$884$		0			0
$885$	−19.2311			−0.646445
$886$		0			0
$887$	−16.6018	−	28.7552i	−0.557435	−	0.965506i	−0.997710	−	0.0676427i	$-0.978452\pi$
$887$	−16.6018	−	28.7552i	−0.557435	−	0.965506i	0.440274	−	0.897863i	$-0.354881\pi$
$888$		0			0
$889$	29.9309			1.00385
$890$		0			0
$891$	5.13416	−	8.89263i	0.172001	−	0.297914i
$892$		0			0
$893$	−1.93087	+	3.34436i	−0.0646141	+	0.111915i
$894$		0			0
$895$	6.14441	+	10.6424i	0.205385	+	0.355737i
$896$		0			0
$897$	−12.2656	+	9.57302i	−0.409537	+	0.319634i
$898$		0			0
$899$	−16.6757	−	28.8831i	−0.556164	−	0.963305i
$900$		0			0
$901$	1.65767	−	2.87117i	0.0552250	−	0.0956525i
$902$		0			0
$903$	1.24081	−	2.14914i	0.0412915	−	0.0715190i
$904$		0			0
$905$	−0.300187			−0.00997854
$906$		0			0
$907$	8.73222	+	15.1246i	0.289949	+	0.502206i	0.973797	−	0.227418i	$-0.0730285\pi$
$907$	8.73222	+	15.1246i	0.289949	+	0.502206i	−0.683849	+	0.729624i	$0.739695\pi$
$908$		0			0
$909$	−12.6847			−0.420724
$910$		0			0
$911$	51.2587			1.69828			0.849138	−	0.528171i	$-0.177122\pi$
$911$	51.2587			1.69828			0.849138	+	0.528171i	$0.177122\pi$
$912$		0			0
$913$	−23.3693	−	40.4768i	−0.773412	−	1.33959i
$914$		0			0
$915$	−9.82538			−0.324817
$916$		0			0
$917$	−29.1231	+	50.4427i	−0.961730	+	1.66576i
$918$		0			0
$919$	26.7549	−	46.3408i	0.882562	−	1.52864i	0.0340794	−	0.999419i	$-0.489150\pi$
$919$	26.7549	−	46.3408i	0.882562	−	1.52864i	0.848483	−	0.529223i	$-0.177517\pi$
$920$		0			0
$921$	−14.8769	−	25.7675i	−0.490210	−	0.849069i
$922$		0			0
$923$	20.8734	−	16.2912i	0.687056	−	0.536231i
$924$		0			0
$925$	−7.84233	−	13.5833i	−0.257854	−	0.446617i
$926$		0			0
$927$	−8.13254	+	14.0860i	−0.267108	+	0.462644i
$928$		0			0
$929$	−10.9384	+	18.9459i	−0.358879	+	0.621596i	−0.987774	−	0.155894i	$-0.950174\pi$
$929$	−10.9384	+	18.9459i	−0.358879	+	0.621596i	0.628895	+	0.777490i	$0.283508\pi$
$930$		0			0
$931$	17.9074			0.586891
$932$		0			0
$933$	12.0000	+	20.7846i	0.392862	+	0.680458i
$934$		0			0
$935$	−18.1379			−0.593174
$936$		0			0
$937$	−28.1922			−0.921000			−0.460500	−	0.887660i	$-0.652330\pi$
$937$	−28.1922			−0.921000			−0.460500	+	0.887660i	$0.652330\pi$
$938$		0			0
$939$	2.92456	+	5.06548i	0.0954394	+	0.165306i
$940$		0			0
$941$	−2.00000			−0.0651981			−0.0325991	−	0.999469i	$-0.510378\pi$
$941$	−2.00000			−0.0651981			−0.0325991	+	0.999469i	$0.510378\pi$
$942$		0			0
$943$	7.41759	−	12.8476i	0.241550	−	0.418377i
$944$		0			0
$945$	13.1231	−	22.7299i	0.426895	−	0.739403i
$946$		0			0
$947$	−11.6891	−	20.2462i	−0.379846	−	0.657913i	0.611193	−	0.791481i	$-0.290690\pi$
$947$	−11.6891	−	20.2462i	−0.379846	−	0.657913i	−0.991040	+	0.133568i	$0.957356\pi$
$948$		0			0
$949$	−55.7656	−	22.5634i	−1.81023	−	0.732439i
$950$		0			0
$951$	−10.6789	−	18.4964i	−0.346287	−	0.599787i
$952$		0			0
$953$	−25.8963	+	44.8537i	−0.838864	+	1.45295i	0.0519819	+	0.998648i	$0.483446\pi$
$953$	−25.8963	+	44.8537i	−0.838864	+	1.45295i	−0.890846	+	0.454306i	$0.849887\pi$
$954$		0			0
$955$	10.5312	−	18.2407i	0.340783	−	0.590254i
$956$		0			0
$957$	32.8078			1.06052
$958$		0			0
$959$	−26.1137	−	45.2303i	−0.843257	−	1.46056i
$960$		0			0
$961$	13.4924			0.435239
$962$		0			0
$963$	7.72197			0.248837
$964$		0			0
$965$	7.90388	+	13.6899i	0.254435	+	0.440694i
$966$		0			0
$967$	10.4160			0.334955			0.167478	−	0.985876i	$-0.446438\pi$
$967$	10.4160			0.334955			0.167478	+	0.985876i	$0.446438\pi$
$968$		0			0
$969$	−9.34991	+	16.1945i	−0.300362	+	0.520243i
$970$		0			0
$971$	−9.66865	+	16.7466i	−0.310282	+	0.537424i	−0.978423	−	0.206611i	$-0.933757\pi$
$971$	−9.66865	+	16.7466i	−0.310282	+	0.537424i	0.668142	+	0.744034i	$0.267090\pi$
$972$		0			0
$973$	6.78835	+	11.7578i	0.217625	+	0.376937i
$974$		0			0
$975$	−1.53610	−	10.9700i	−0.0491947	−	0.351320i
$976$		0			0
$977$	−16.8693	−	29.2185i	−0.539697	−	0.934783i	−0.998920	−	0.0464620i	$-0.985205\pi$
$977$	−16.8693	−	29.2185i	−0.539697	−	0.934783i	0.459223	−	0.888321i	$-0.348128\pi$
$978$		0			0
$979$	4.60831	−	7.98182i	0.147282	−	0.255100i
$980$		0			0
$981$	−5.56155	+	9.63289i	−0.177567	+	0.307555i
$982$		0			0
$983$	−60.0324			−1.91474			−0.957368	−	0.288872i	$-0.906720\pi$
$983$	−60.0324			−1.91474			−0.957368	+	0.288872i	$0.906720\pi$
$984$		0			0
$985$	−11.5616	−	20.0252i	−0.368382	−	0.638056i
$986$		0			0
$987$	1.93759			0.0616741
$988$		0			0
$989$	2.42329			0.0770562
$990$		0			0
$991$	−5.54473	−	9.60376i	−0.176134	−	0.305074i	0.764419	−	0.644720i	$-0.223026\pi$
$991$	−5.54473	−	9.60376i	−0.176134	−	0.305074i	−0.940553	+	0.339646i	$0.889693\pi$
$992$		0			0
$993$	−15.1922			−0.482111
$994$		0			0
$995$	2.80928	−	4.86581i	0.0890601	−	0.154257i
$996$		0			0
$997$	−27.1155	+	46.9655i	−0.858757	+	1.48741i	0.0143575	+	0.999897i	$0.495430\pi$
$997$	−27.1155	+	46.9655i	−0.858757	+	1.48741i	−0.873115	+	0.487515i	$0.837904\pi$
$998$		0			0
$999$	16.7495	+	29.0110i	0.529930	+	0.917866i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.2.i.g.289.3	yes	8
4.3	odd	2	inner	416.2.i.g.289.2	✓	8
8.3	odd	2		832.2.i.q.705.3		8
8.5	even	2		832.2.i.q.705.2		8
13.3	even	3		5408.2.a.bh.1.2		4
13.9	even	3	inner	416.2.i.g.321.3	yes	8
13.10	even	6		5408.2.a.bi.1.2		4
52.3	odd	6		5408.2.a.bh.1.3		4
52.23	odd	6		5408.2.a.bi.1.3		4
52.35	odd	6	inner	416.2.i.g.321.2	yes	8
104.35	odd	6		832.2.i.q.321.3		8
104.61	even	6		832.2.i.q.321.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
416.2.i.g.289.2	✓	8	4.3	odd	2	inner
416.2.i.g.289.3	yes	8	1.1	even	1	trivial
416.2.i.g.321.2	yes	8	52.35	odd	6	inner
416.2.i.g.321.3	yes	8	13.9	even	3	inner
832.2.i.q.321.2		8	104.61	even	6
832.2.i.q.321.3		8	104.35	odd	6
832.2.i.q.705.2		8	8.5	even	2
832.2.i.q.705.3		8	8.3	odd	2
5408.2.a.bh.1.2		4	13.3	even	3
5408.2.a.bh.1.3		4	52.3	odd	6
5408.2.a.bi.1.2		4	13.10	even	6
5408.2.a.bi.1.3		4	52.23	odd	6

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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.599676 + 1.03867i) q^{3} +1.56155 q^{5} +(1.53610 - 2.66061i) q^{7} +(0.780776 - 1.35234i) q^{9} +(-2.73546 - 4.73795i) q^{11} +(3.34233 + 1.35234i) q^{13} +(0.936426 + 1.62194i) q^{15} +(1.06155 - 1.83866i) q^{17} +(-3.67188 + 6.35989i) q^{19} +3.68466 q^{21} +(1.79903 + 3.11601i) q^{23} -2.56155 q^{25} +5.47091 q^{27} +(2.50000 + 4.33013i) q^{29} -6.67026 q^{31} +(3.28078 - 5.68247i) q^{33} +(2.39871 - 4.15468i) q^{35} +(3.06155 + 5.30277i) q^{37} +(0.599676 + 4.28255i) q^{39} +(-2.06155 - 3.57071i) q^{41} +(0.336750 - 0.583268i) q^{43} +(1.21922 - 2.11176i) q^{45} +0.525853 q^{47} +(-1.21922 - 2.11176i) q^{49} +2.54635 q^{51} +1.56155 q^{53} +(-4.27156 - 7.39856i) q^{55} -8.80776 q^{57} +(-5.13416 + 8.89263i) q^{59} +(-2.62311 + 4.54335i) q^{61} +(-2.39871 - 4.15468i) q^{63} +(5.21922 + 2.11176i) q^{65} +(-2.47253 - 4.28255i) q^{67} +(-2.15767 + 3.73720i) q^{69} +(3.67188 - 6.35989i) q^{71} -16.6847 q^{73} +(-1.53610 - 2.66061i) q^{75} -16.8078 q^{77} +15.7392 q^{79} +(0.938447 + 1.62544i) q^{81} +8.54312 q^{83} +(1.65767 - 2.87117i) q^{85} +(-2.99838 + 5.19335i) q^{87} +(0.842329 + 1.45896i) q^{89} +(8.73222 - 6.81529i) q^{91} +(-4.00000 - 6.92820i) q^{93} +(-5.73384 + 9.93130i) q^{95} +(-5.40388 + 9.35980i) q^{97} -8.54312 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{5} - 2 q^{9} + 2 q^{13} - 8 q^{17} - 20 q^{21} - 4 q^{25} + 20 q^{29} + 18 q^{33} + 8 q^{37} + 18 q^{45} - 18 q^{49} - 4 q^{53} + 12 q^{57} + 12 q^{61} + 50 q^{65} - 42 q^{69} - 84 q^{73} - 52 q^{77}+ \cdots - 2 q^{97}+O(q^{100}) \) 8 * q - 4 * q^5 - 2 * q^9 + 2 * q^13 - 8 * q^17 - 20 * q^21 - 4 * q^25 + 20 * q^29 + 18 * q^33 + 8 * q^37 + 18 * q^45 - 18 * q^49 - 4 * q^53 + 12 * q^57 + 12 * q^61 + 50 * q^65 - 42 * q^69 - 84 * q^73 - 52 * q^77 + 24 * q^81 + 38 * q^85 - 18 * q^89 - 32 * q^93 - 2 * q^97

Introduction

L-functions

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