LMFDB - Embedded newform 256.2.i.a.49.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,2,Mod(17,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("256.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	256.i (of order $16$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.04417029174$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 64)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			49.5
Character	$\chi$	$=$	256.49
Dual form			256.2.i.a.209.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22190 - 0.243052i) q^{3} +(0.884671 + 1.32400i) q^{5} +(2.40727 + 0.997123i) q^{7} +(-1.33766 + 0.554078i) q^{9} +O(q^{10})$	\(q+(1.22190 - 0.243052i) q^{3} +(0.884671 + 1.32400i) q^{5} +(2.40727 + 0.997123i) q^{7} +(-1.33766 + 0.554078i) q^{9} +(0.432397 - 2.17381i) q^{11} +(-2.18211 + 3.26576i) q^{13} +(1.40279 + 1.40279i) q^{15} +(4.38547 - 4.38547i) q^{17} +(-2.64242 - 1.76561i) q^{19} +(3.18380 + 0.633298i) q^{21} +(2.12144 + 5.12160i) q^{23} +(0.943074 - 2.27678i) q^{25} +(-4.60747 + 3.07861i) q^{27} +(-0.836699 - 4.20637i) q^{29} -8.37185i q^{31} -2.76128i q^{33} +(0.809445 + 4.06936i) q^{35} +(-5.42017 + 3.62164i) q^{37} +(-1.87258 + 4.52081i) q^{39} +(3.00227 + 7.24812i) q^{41} +(-8.60595 - 1.71183i) q^{43} +(-1.91699 - 1.28089i) q^{45} +(-0.0771294 + 0.0771294i) q^{47} +(-0.149067 - 0.149067i) q^{49} +(4.29273 - 6.42453i) q^{51} +(0.846775 - 4.25703i) q^{53} +(3.26066 - 1.35061i) q^{55} +(-3.65792 - 1.51516i) q^{57} +(0.657977 + 0.984732i) q^{59} +(-9.90754 + 1.97073i) q^{61} -3.77259 q^{63} -6.25433 q^{65} +(9.06082 - 1.80231i) q^{67} +(3.83701 + 5.74249i) q^{69} +(-9.94840 - 4.12076i) q^{71} +(-10.8278 + 4.48502i) q^{73} +(0.598970 - 3.01123i) q^{75} +(3.20845 - 4.80178i) q^{77} +(0.842912 + 0.842912i) q^{79} +(-1.81022 + 1.81022i) q^{81} +(-0.766957 - 0.512464i) q^{83} +(9.68608 + 1.92668i) q^{85} +(-2.04473 - 4.93642i) q^{87} +(2.03287 - 4.90777i) q^{89} +(-8.50928 + 5.68572i) q^{91} +(-2.03480 - 10.2296i) q^{93} -5.06055i q^{95} -5.90730i q^{97} +(0.626056 + 3.14740i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9}+O(q^{10}) $ 56 * q + 8 * q^3 - 8 * q^5 + 8 * q^7 - 8 * q^9	$ 56 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9} + 8 q^{11} - 8 q^{13} + 8 q^{15} - 8 q^{17} + 8 q^{19} - 8 q^{21} + 8 q^{23} - 8 q^{25} + 8 q^{27} - 8 q^{29} + 8 q^{35} - 8 q^{37} + 8 q^{39} - 8 q^{41} + 8 q^{43} - 8 q^{45} + 8 q^{47} - 8 q^{49} - 24 q^{51} - 8 q^{53} - 56 q^{55} - 8 q^{57} - 56 q^{59} - 8 q^{61} - 64 q^{63} - 16 q^{65} - 72 q^{67} - 8 q^{69} - 56 q^{71} - 8 q^{73} - 56 q^{75} - 8 q^{77} - 24 q^{79} - 8 q^{81} + 8 q^{83} - 8 q^{85} + 8 q^{87} - 8 q^{89} + 8 q^{91} + 16 q^{93} - 16 q^{99}+O(q^{100}) $ 56 * q + 8 * q^3 - 8 * q^5 + 8 * q^7 - 8 * q^9 + 8 * q^11 - 8 * q^13 + 8 * q^15 - 8 * q^17 + 8 * q^19 - 8 * q^21 + 8 * q^23 - 8 * q^25 + 8 * q^27 - 8 * q^29 + 8 * q^35 - 8 * q^37 + 8 * q^39 - 8 * q^41 + 8 * q^43 - 8 * q^45 + 8 * q^47 - 8 * q^49 - 24 * q^51 - 8 * q^53 - 56 * q^55 - 8 * q^57 - 56 * q^59 - 8 * q^61 - 64 * q^63 - 16 * q^65 - 72 * q^67 - 8 * q^69 - 56 * q^71 - 8 * q^73 - 56 * q^75 - 8 * q^77 - 24 * q^79 - 8 * q^81 + 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^89 + 8 * q^91 + 16 * q^93 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{5}{16}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.22190	−	0.243052i	0.705467	−	0.140326i	0.170697	−	0.985324i	$-0.445398\pi$
$3$	1.22190	−	0.243052i	0.705467	−	0.140326i	0.534770	+	0.844997i	$0.320398\pi$
$4$		0			0
$5$	0.884671	+	1.32400i	0.395637	+	0.592113i	0.974795	−	0.223103i	$-0.0716186\pi$
$5$	0.884671	+	1.32400i	0.395637	+	0.592113i	−0.579158	+	0.815215i	$0.696619\pi$
$6$		0			0
$7$	2.40727	+	0.997123i	0.909861	+	0.376877i	0.788004	−	0.615671i	$-0.211115\pi$
$7$	2.40727	+	0.997123i	0.909861	+	0.376877i	0.121858	+	0.992548i	$0.461115\pi$
$8$		0			0
$9$	−1.33766	+	0.554078i	−0.445887	+	0.184693i
$10$		0			0
$11$	0.432397	−	2.17381i	0.130373	−	0.655427i	−0.859229	−	0.511591i	$-0.829056\pi$
$11$	0.432397	−	2.17381i	0.130373	−	0.655427i	0.989602	−	0.143836i	$-0.0459438\pi$
$12$		0			0
$13$	−2.18211	+	3.26576i	−0.605208	+	0.905758i	−0.999915	−	0.0130490i	$-0.995846\pi$
$13$	−2.18211	+	3.26576i	−0.605208	+	0.905758i	0.394707	+	0.918807i	$0.370846\pi$
$14$		0			0
$15$	1.40279	+	1.40279i	0.362198	+	0.362198i
$16$		0			0
$17$	4.38547	−	4.38547i	1.06363	−	1.06363i	0.0658001	−	0.997833i	$-0.479040\pi$
$17$	4.38547	−	4.38547i	1.06363	−	1.06363i	0.997833	−	0.0658001i	$-0.0209600\pi$
$18$		0			0
$19$	−2.64242	−	1.76561i	−0.606212	−	0.405058i	0.214234	−	0.976782i	$-0.431275\pi$
$19$	−2.64242	−	1.76561i	−0.606212	−	0.405058i	−0.820446	+	0.571724i	$0.806275\pi$
$20$		0			0
$21$	3.18380	+	0.633298i	0.694763	+	0.138197i
$22$		0			0
$23$	2.12144	+	5.12160i	0.442350	+	1.06793i	0.975122	+	0.221669i	$0.0711505\pi$
$23$	2.12144	+	5.12160i	0.442350	+	1.06793i	−0.532772	+	0.846259i	$0.678850\pi$
$24$		0			0
$25$	0.943074	−	2.27678i	0.188615	−	0.455356i
$26$		0			0
$27$	−4.60747	+	3.07861i	−0.886708	+	0.592479i
$28$		0			0
$29$	−0.836699	−	4.20637i	−0.155371	−	0.781104i	−0.977357	−	0.211596i	$-0.932134\pi$
$29$	−0.836699	−	4.20637i	−0.155371	−	0.781104i	0.821986	−	0.569508i	$-0.192866\pi$
$30$		0			0
$31$		−	8.37185i		−	1.50363i	−0.659375	−	0.751815i	$-0.729179\pi$
$31$		−	8.37185i		−	1.50363i	0.659375	−	0.751815i	$-0.270821\pi$
$32$		0			0
$33$		−	2.76128i		−	0.480677i
$34$		0			0
$35$	0.809445	+	4.06936i	0.136821	+	0.687847i
$36$		0			0
$37$	−5.42017	+	3.62164i	−0.891070	+	0.595394i	−0.914614	−	0.404329i	$-0.867505\pi$
$37$	−5.42017	+	3.62164i	−0.891070	+	0.595394i	0.0235436	+	0.999723i	$0.492505\pi$
$38$		0			0
$39$	−1.87258	+	4.52081i	−0.299853	+	0.723909i
$40$		0			0
$41$	3.00227	+	7.24812i	0.468876	+	1.13197i	0.964655	+	0.263517i	$0.0848825\pi$
$41$	3.00227	+	7.24812i	0.468876	+	1.13197i	−0.495779	+	0.868449i	$0.665117\pi$
$42$		0			0
$43$	−8.60595	−	1.71183i	−1.31239	−	0.261052i	−0.511203	−	0.859460i	$-0.670800\pi$
$43$	−8.60595	−	1.71183i	−1.31239	−	0.261052i	−0.801191	+	0.598408i	$0.795800\pi$
$44$		0			0
$45$	−1.91699	−	1.28089i	−0.285768	−	0.190944i
$46$		0			0
$47$	−0.0771294	+	0.0771294i	−0.0112505	+	0.0112505i	−0.712710	−	0.701459i	$-0.752532\pi$
$47$	−0.0771294	+	0.0771294i	−0.0112505	+	0.0112505i	0.701459	+	0.712710i	$0.252532\pi$
$48$		0			0
$49$	−0.149067	−	0.149067i	−0.0212953	−	0.0212953i
$50$		0			0
$51$	4.29273	−	6.42453i	0.601103	−	0.899614i
$52$		0			0
$53$	0.846775	−	4.25703i	0.116314	−	0.584748i	−0.878036	−	0.478594i	$-0.841147\pi$
$53$	0.846775	−	4.25703i	0.116314	−	0.584748i	0.994350	−	0.106153i	$-0.0338535\pi$
$54$		0			0
$55$	3.26066	−	1.35061i	0.439667	−	0.182116i
$56$		0			0
$57$	−3.65792	−	1.51516i	−0.484503	−	0.200688i
$58$		0			0
$59$	0.657977	+	0.984732i	0.0856613	+	0.128201i	0.871826	−	0.489816i	$-0.162936\pi$
$59$	0.657977	+	0.984732i	0.0856613	+	0.128201i	−0.786164	+	0.618017i	$0.787936\pi$
$60$		0			0
$61$	−9.90754	+	1.97073i	−1.26853	+	0.252327i	−0.783071	−	0.621932i	$-0.786348\pi$
$61$	−9.90754	+	1.97073i	−1.26853	+	0.252327i	−0.485460	+	0.874259i	$0.661348\pi$
$62$		0			0
$63$	−3.77259			−0.475302
$64$		0			0
$65$	−6.25433			−0.775754
$66$		0			0
$67$	9.06082	−	1.80231i	1.10696	−	0.220187i	0.392420	−	0.919786i	$-0.371638\pi$
$67$	9.06082	−	1.80231i	1.10696	−	0.220187i	0.714536	+	0.699599i	$0.246638\pi$
$68$		0			0
$69$	3.83701	+	5.74249i	0.461922	+	0.691315i
$70$		0			0
$71$	−9.94840	−	4.12076i	−1.18066	−	0.489044i	−0.295956	−	0.955202i	$-0.595638\pi$
$71$	−9.94840	−	4.12076i	−1.18066	−	0.489044i	−0.884702	+	0.466157i	$0.845638\pi$
$72$		0			0
$73$	−10.8278	+	4.48502i	−1.26730	+	0.524931i	−0.912141	−	0.409876i	$-0.865572\pi$
$73$	−10.8278	+	4.48502i	−1.26730	+	0.524931i	−0.355155	+	0.934807i	$0.615572\pi$
$74$		0			0
$75$	0.598970	−	3.01123i	0.0691631	−	0.347706i
$76$		0			0
$77$	3.20845	−	4.80178i	0.365636	−	0.547214i
$78$		0			0
$79$	0.842912	+	0.842912i	0.0948351	+	0.0948351i	0.752933	−	0.658098i	$-0.228639\pi$
$79$	0.842912	+	0.842912i	0.0948351	+	0.0948351i	−0.658098	+	0.752933i	$0.728639\pi$
$80$		0			0
$81$	−1.81022	+	1.81022i	−0.201136	+	0.201136i
$82$		0			0
$83$	−0.766957	−	0.512464i	−0.0841845	−	0.0562503i	0.512766	−	0.858529i	$-0.328621\pi$
$83$	−0.766957	−	0.512464i	−0.0841845	−	0.0562503i	−0.596950	+	0.802278i	$0.703621\pi$
$84$		0			0
$85$	9.68608	+	1.92668i	1.05060	+	0.208978i
$86$		0			0
$87$	−2.04473	−	4.93642i	−0.219218	−	0.529240i
$88$		0			0
$89$	2.03287	−	4.90777i	0.215483	−	0.520223i	−0.778766	−	0.627315i	$-0.784154\pi$
$89$	2.03287	−	4.90777i	0.215483	−	0.520223i	0.994249	+	0.107092i	$0.0341539\pi$
$90$		0			0
$91$	−8.50928	+	5.68572i	−0.892015	+	0.596025i
$92$		0			0
$93$	−2.03480	−	10.2296i	−0.210998	−	1.06076i
$94$		0			0
$95$		−	5.06055i		−	0.519202i
$96$		0			0
$97$		−	5.90730i		−	0.599796i	−0.953971	−	0.299898i	$-0.903047\pi$
$97$		−	5.90730i		−	0.599796i	0.953971	−	0.299898i	$-0.0969526\pi$
$98$		0			0
$99$	0.626056	+	3.14740i	0.0629210	+	0.316325i
$100$		0			0
$101$	−0.429855	+	0.287220i	−0.0427722	+	0.0285794i	−0.576773	−	0.816905i	$-0.695688\pi$
$101$	−0.429855	+	0.287220i	−0.0427722	+	0.0285794i	0.534000	+	0.845484i	$0.320688\pi$
$102$		0			0
$103$	−3.33979	+	8.06296i	−0.329079	+	0.794467i	0.669582	+	0.742738i	$0.266473\pi$
$103$	−3.33979	+	8.06296i	−0.329079	+	0.794467i	−0.998661	+	0.0517290i	$0.983527\pi$
$104$		0			0
$105$	1.97813	+	4.77563i	0.193046	+	0.466054i
$106$		0			0
$107$	18.7622	+	3.73203i	1.81381	+	0.360789i	0.981188	−	0.193054i	$-0.0618392\pi$
$107$	18.7622	+	3.73203i	1.81381	+	0.360789i	0.832621	+	0.553843i	$0.186839\pi$
$108$		0			0
$109$	10.6124	+	7.09099i	1.01648	+	0.679193i	0.947938	−	0.318455i	$-0.103164\pi$
$109$	10.6124	+	7.09099i	1.01648	+	0.679193i	0.0685465	+	0.997648i	$0.478164\pi$
$110$		0			0
$111$	−5.74268	+	5.74268i	−0.545071	+	0.545071i
$112$		0			0
$113$	11.6172	+	11.6172i	1.09285	+	1.09285i	0.995223	+	0.0976320i	$0.0311268\pi$
$113$	11.6172	+	11.6172i	1.09285	+	1.09285i	0.0976320	+	0.995223i	$0.468873\pi$
$114$		0			0
$115$	−4.90425	+	7.33973i	−0.457323	+	0.684433i
$116$		0			0
$117$	1.10944	−	5.57754i	0.102568	−	0.515643i
$118$		0			0
$119$	14.9299	−	6.18415i	1.36862	−	0.566900i
$120$		0			0
$121$	5.62421	+	2.32962i	0.511292	+	0.211784i
$122$		0			0
$123$	5.43016	+	8.12680i	0.489621	+	0.732769i
$124$		0			0
$125$	11.6576	−	2.31885i	1.04269	−	0.207404i
$126$		0			0
$127$	−2.24655			−0.199349			−0.0996747	−	0.995020i	$-0.531780\pi$
$127$	−2.24655			−0.199349			−0.0996747	+	0.995020i	$0.531780\pi$
$128$		0			0
$129$	−10.9317			−0.962484
$130$		0			0
$131$	5.29169	−	1.05258i	0.462338	−	0.0919646i	0.0415748	−	0.999135i	$-0.486763\pi$
$131$	5.29169	−	1.05258i	0.462338	−	0.0919646i	0.420763	+	0.907171i	$0.361763\pi$
$132$		0			0
$133$	−4.60048	−	6.88510i	−0.398912	−	0.597014i
$134$		0			0
$135$	−8.15219	−	3.37675i	−0.701629	−	0.290624i
$136$		0			0
$137$	6.00408	−	2.48697i	0.512963	−	0.212476i	−0.111160	−	0.993803i	$-0.535457\pi$
$137$	6.00408	−	2.48697i	0.512963	−	0.212476i	0.624123	+	0.781326i	$0.285457\pi$
$138$		0			0
$139$	0.350641	−	1.76279i	0.0297410	−	0.149518i	−0.963061	−	0.269282i	$-0.913214\pi$
$139$	0.350641	−	1.76279i	0.0297410	−	0.149518i	0.992802	+	0.119764i	$0.0382137\pi$
$140$		0			0
$141$	−0.0754983	+	0.112991i	−0.00635811	+	0.00951558i
$142$		0			0
$143$	6.15559	+	6.15559i	0.514756	+	0.514756i
$144$		0			0
$145$	4.82905	−	4.82905i	0.401031	−	0.401031i
$146$		0			0
$147$	−0.218377	−	0.145915i	−0.0180114	−	0.0120349i
$148$		0			0
$149$	−3.29611	−	0.655636i	−0.270028	−	0.0537118i	0.0582192	−	0.998304i	$-0.481458\pi$
$149$	−3.29611	−	0.655636i	−0.270028	−	0.0537118i	−0.328247	+	0.944592i	$0.606458\pi$
$150$		0			0
$151$	1.32342	+	3.19501i	0.107698	+	0.260007i	0.968536	−	0.248873i	$-0.0800600\pi$
$151$	1.32342	+	3.19501i	0.107698	+	0.260007i	−0.860838	+	0.508879i	$0.830060\pi$
$152$		0			0
$153$	−3.43638	+	8.29617i	−0.277815	+	0.670705i
$154$		0			0
$155$	11.0844	−	7.40634i	0.890318	−	0.594891i
$156$		0			0
$157$	−0.605421	−	3.04366i	−0.0483178	−	0.242910i	0.949077	−	0.315044i	$-0.102019\pi$
$157$	−0.605421	−	3.04366i	−0.0483178	−	0.242910i	−0.997395	+	0.0721336i	$0.977019\pi$
$158$		0			0
$159$		−	5.40749i		−	0.428842i
$160$		0			0
$161$			14.4444i			1.13838i
$162$		0			0
$163$	−0.0943209	−	0.474183i	−0.00738778	−	0.0371409i	0.976916	−	0.213626i	$-0.0685273\pi$
$163$	−0.0943209	−	0.474183i	−0.00738778	−	0.0371409i	−0.984303	+	0.176485i	$0.943527\pi$
$164$		0			0
$165$	3.65594	−	2.44282i	0.284615	−	0.190174i
$166$		0			0
$167$	3.40598	−	8.22277i	0.263563	−	0.636297i	−0.735591	−	0.677426i	$-0.763095\pi$
$167$	3.40598	−	8.22277i	0.263563	−	0.636297i	0.999154	+	0.0411288i	$0.0130954\pi$
$168$		0			0
$169$	−0.928687	−	2.24205i	−0.0714375	−	0.172465i
$170$		0			0
$171$	4.51294	+	0.897680i	0.345113	+	0.0686473i
$172$		0			0
$173$	10.7422	+	7.17768i	0.816711	+	0.545709i	0.892307	−	0.451430i	$-0.149086\pi$
$173$	10.7422	+	7.17768i	0.816711	+	0.545709i	−0.0755956	+	0.997139i	$0.524086\pi$
$174$		0			0
$175$	4.54046	−	4.54046i	0.343227	−	0.343227i
$176$		0			0
$177$	1.04333	+	1.04333i	0.0784212	+	0.0784212i
$178$		0			0
$179$	−8.89422	+	13.3111i	−0.664785	+	0.994921i	0.333847	+	0.942627i	$0.391653\pi$
$179$	−8.89422	+	13.3111i	−0.664785	+	0.994921i	−0.998632	+	0.0522939i	$0.983347\pi$
$180$		0			0
$181$	−0.271646	+	1.36566i	−0.0201913	+	0.101508i	−0.989567	−	0.144075i	$-0.953979\pi$
$181$	−0.271646	+	1.36566i	−0.0201913	+	0.101508i	0.969376	+	0.245583i	$0.0789794\pi$
$182$		0			0
$183$	−11.6271	+	4.81610i	−0.859499	+	0.356016i
$184$		0			0
$185$	−9.59013	−	3.97236i	−0.705081	−	0.292054i
$186$		0			0
$187$	−7.63690	−	11.4294i	−0.558465	−	0.835803i
$188$		0			0
$189$	−14.1612	+	2.81683i	−1.03007	+	0.204894i
$190$		0			0
$191$	3.56574			0.258008			0.129004	−	0.991644i	$-0.458822\pi$
$191$	3.56574			0.258008			0.129004	+	0.991644i	$0.458822\pi$
$192$		0			0
$193$	−3.86751			−0.278389			−0.139195	−	0.990265i	$-0.544451\pi$
$193$	−3.86751			−0.278389			−0.139195	+	0.990265i	$0.544451\pi$
$194$		0			0
$195$	−7.64219	+	1.52013i	−0.547269	+	0.108859i
$196$		0			0
$197$	−10.0325	−	15.0147i	−0.714788	−	1.06976i	−0.993984	−	0.109522i	$-0.965068\pi$
$197$	−10.0325	−	15.0147i	−0.714788	−	1.06976i	0.279196	−	0.960234i	$-0.409932\pi$
$198$		0			0
$199$	12.9440	+	5.36160i	0.917579	+	0.380074i	0.790953	−	0.611877i	$-0.209585\pi$
$199$	12.9440	+	5.36160i	0.917579	+	0.380074i	0.126626	+	0.991951i	$0.459585\pi$
$200$		0			0
$201$	10.6334	−	4.40450i	0.750022	−	0.310669i
$202$		0			0
$203$	2.18011	−	10.9602i	0.153014	−	0.769252i
$204$		0			0
$205$	−6.94051	+	10.3872i	−0.484747	+	0.725474i
$206$		0			0
$207$	−5.67553	−	5.67553i	−0.394477	−	0.394477i
$208$		0			0
$209$	−4.98066	+	4.98066i	−0.344519	+	0.344519i
$210$		0			0
$211$	−15.7003	−	10.4906i	−1.08085	−	0.722204i	−0.118215	−	0.992988i	$-0.537717\pi$
$211$	−15.7003	−	10.4906i	−1.08085	−	0.722204i	−0.962640	+	0.270784i	$0.912717\pi$
$212$		0			0
$213$	−13.1576	−	2.61720i	−0.901541	−	0.179328i
$214$		0			0
$215$	−5.34696	−	12.9087i	−0.364660	−	0.880367i
$216$		0			0
$217$	8.34776	−	20.1533i	0.566683	−	1.36809i
$218$		0			0
$219$	−12.1404	+	8.11198i	−0.820374	+	0.548157i
$220$		0			0
$221$	4.75231	+	23.8915i	0.319675	+	1.60711i
$222$		0			0
$223$			25.9711i			1.73915i	0.493797	+	0.869577i	$0.335609\pi$
$223$			25.9711i			1.73915i	−0.493797	+	0.869577i	$0.664391\pi$
$224$		0			0
$225$			3.56810i			0.237873i
$226$		0			0
$227$	0.214031	+	1.07600i	0.0142057	+	0.0714169i	0.987238	−	0.159253i	$-0.0509084\pi$
$227$	0.214031	+	1.07600i	0.0142057	+	0.0714169i	−0.973032	+	0.230669i	$0.925908\pi$
$228$		0			0
$229$	−13.0798	+	8.73965i	−0.864338	+	0.577532i	−0.906798	−	0.421566i	$-0.861481\pi$
$229$	−13.0798	+	8.73965i	−0.864338	+	0.577532i	0.0424596	+	0.999098i	$0.486481\pi$
$230$		0			0
$231$	2.75333	−	6.64714i	0.181156	−	0.437349i
$232$		0			0
$233$	−7.41658	−	17.9052i	−0.485876	−	1.17301i	−0.956777	−	0.290823i	$-0.906071\pi$
$233$	−7.41658	−	17.9052i	−0.485876	−	1.17301i	0.470900	−	0.882186i	$-0.343929\pi$
$234$		0			0
$235$	−0.170354	−	0.0338855i	−0.0111127	−	0.00221044i
$236$		0			0
$237$	1.23483	+	0.825087i	0.0802108	+	0.0535952i
$238$		0			0
$239$	−7.81165	+	7.81165i	−0.505293	+	0.505293i	−0.913078	−	0.407785i	$-0.866301\pi$
$239$	−7.81165	+	7.81165i	−0.505293	+	0.505293i	0.407785	+	0.913078i	$0.366301\pi$
$240$		0			0
$241$	−6.52981	−	6.52981i	−0.420622	−	0.420622i	0.464796	−	0.885418i	$-0.346128\pi$
$241$	−6.52981	−	6.52981i	−0.420622	−	0.420622i	−0.885418	+	0.464796i	$0.846128\pi$
$242$		0			0
$243$	7.46390	−	11.1705i	0.478809	−	0.716589i
$244$		0			0
$245$	0.0654901	−	0.329241i	0.00418401	−	0.0210344i
$246$		0			0
$247$	11.5321	−	4.77675i	0.733769	−	0.303937i
$248$		0			0
$249$	−1.06170	−	0.439772i	−0.0672828	−	0.0278694i
$250$		0			0
$251$	4.91732	+	7.35930i	0.310379	+	0.464515i	0.953562	−	0.301198i	$-0.0973865\pi$
$251$	4.91732	+	7.35930i	0.310379	+	0.464515i	−0.643183	+	0.765713i	$0.722386\pi$
$252$		0			0
$253$	12.0507	−	2.39703i	0.757619	−	0.150700i
$254$		0			0
$255$	12.3038			0.770491
$256$		0			0
$257$	4.85309			0.302727			0.151364	−	0.988478i	$-0.451634\pi$
$257$	4.85309			0.302727			0.151364	+	0.988478i	$0.451634\pi$
$258$		0			0
$259$	−16.6590	+	3.31368i	−1.03514	+	0.205902i
$260$		0			0
$261$	3.44988	+	5.16310i	0.213542	+	0.319588i
$262$		0			0
$263$	−15.7364	−	6.51821i	−0.970346	−	0.401930i	−0.159505	−	0.987197i	$-0.550990\pi$
$263$	−15.7364	−	6.51821i	−0.970346	−	0.401930i	−0.810841	+	0.585267i	$0.800990\pi$
$264$		0			0
$265$	6.38544	−	2.64493i	0.392254	−	0.162477i
$266$		0			0
$267$	1.29113	−	6.49093i	0.0790156	−	0.397238i
$268$		0			0
$269$	1.78214	−	2.66716i	0.108659	−	0.162620i	−0.773155	−	0.634217i	$-0.781322\pi$
$269$	1.78214	−	2.66716i	0.108659	−	0.162620i	0.881814	+	0.471598i	$0.156322\pi$
$270$		0			0
$271$	4.32788	+	4.32788i	0.262900	+	0.262900i	0.826231	−	0.563331i	$-0.190480\pi$
$271$	4.32788	+	4.32788i	0.262900	+	0.262900i	−0.563331	+	0.826231i	$0.690480\pi$
$272$		0			0
$273$	−9.01561	+	9.01561i	−0.545649	+	0.545649i
$274$		0			0
$275$	−4.54150	−	3.03453i	−0.273863	−	0.182989i
$276$		0			0
$277$	3.82789	+	0.761415i	0.229996	+	0.0457490i	0.308742	−	0.951146i	$-0.400092\pi$
$277$	3.82789	+	0.761415i	0.229996	+	0.0457490i	−0.0787468	+	0.996895i	$0.525092\pi$
$278$		0			0
$279$	4.63866	+	11.1987i	0.277709	+	0.670449i
$280$		0			0
$281$	2.18086	−	5.26507i	0.130099	−	0.314088i	−0.845385	−	0.534158i	$-0.820629\pi$
$281$	2.18086	−	5.26507i	0.130099	−	0.314088i	0.975484	+	0.220070i	$0.0706287\pi$
$282$		0			0
$283$	18.8263	−	12.5793i	1.11911	−	0.747764i	0.148615	−	0.988895i	$-0.452518\pi$
$283$	18.8263	−	12.5793i	1.11911	−	0.747764i	0.970492	+	0.241131i	$0.0775185\pi$
$284$		0			0
$285$	−1.22998	−	6.18351i	−0.0728576	−	0.366280i
$286$		0			0
$287$			20.4418i			1.20664i
$288$		0			0
$289$		−	21.4647i		−	1.26263i
$290$		0			0
$291$	−1.43578	−	7.21816i	−0.0841670	−	0.423136i
$292$		0			0
$293$	−5.52242	+	3.68996i	−0.322623	+	0.215570i	−0.706326	−	0.707887i	$-0.749649\pi$
$293$	−5.52242	+	3.68996i	−0.322623	+	0.215570i	0.383703	+	0.923457i	$0.374649\pi$
$294$		0			0
$295$	−0.721696	+	1.74233i	−0.0420187	+	0.101442i
$296$		0			0
$297$	4.70005	+	11.3469i	0.272725	+	0.658415i
$298$		0			0
$299$	−21.3551	−	4.24780i	−1.23500	−	0.245657i
$300$		0			0
$301$	−19.0099	−	12.7020i	−1.09571	−	0.732132i
$302$		0			0
$303$	−0.455432	+	0.455432i	−0.0261639	+	0.0261639i
$304$		0			0
$305$	−11.3742	−	11.3742i	−0.651283	−	0.651283i
$306$		0			0
$307$	−1.13328	+	1.69608i	−0.0646798	+	0.0968002i	−0.862400	−	0.506228i	$-0.831039\pi$
$307$	−1.13328	+	1.69608i	−0.0646798	+	0.0968002i	0.797720	+	0.603028i	$0.206039\pi$
$308$		0			0
$309$	−2.12118	+	10.6639i	−0.120670	+	0.606649i
$310$		0			0
$311$	−24.3362	+	10.0804i	−1.37998	+	0.571607i	−0.944476	−	0.328580i	$-0.893430\pi$
$311$	−24.3362	+	10.0804i	−1.37998	+	0.571607i	−0.435505	+	0.900186i	$0.643430\pi$
$312$		0			0
$313$	10.8933	+	4.51214i	0.615725	+	0.255041i	0.668674	−	0.743556i	$-0.266862\pi$
$313$	10.8933	+	4.51214i	0.615725	+	0.255041i	−0.0529494	+	0.998597i	$0.516862\pi$
$314$		0			0
$315$	−3.33750	−	4.99493i	−0.188047	−	0.281432i
$316$		0			0
$317$	13.7108	−	2.72726i	0.770078	−	0.153178i	0.205611	−	0.978634i	$-0.434082\pi$
$317$	13.7108	−	2.72726i	0.770078	−	0.153178i	0.564467	+	0.825456i	$0.309082\pi$
$318$		0			0
$319$	−9.50562			−0.532213
$320$		0			0
$321$	23.8327			1.33021
$322$		0			0
$323$	−19.3313	+	3.84523i	−1.07562	+	0.213954i
$324$		0			0
$325$	5.37753	+	8.04804i	0.298292	+	0.446425i
$326$		0			0
$327$	14.6908	+	6.08514i	0.812405	+	0.336509i
$328$		0			0
$329$	−0.262578	+	0.108764i	−0.0144764	+	0.00599633i
$330$		0			0
$331$	−6.48019	+	32.5781i	−0.356184	+	1.79066i	0.222318	+	0.974974i	$0.428638\pi$
$331$	−6.48019	+	32.5781i	−0.356184	+	1.79066i	−0.578501	+	0.815682i	$0.696362\pi$
$332$		0			0
$333$	5.24368	−	7.84772i	0.287352	−	0.430052i
$334$		0			0
$335$	10.4021	+	10.4021i	0.568328	+	0.568328i
$336$		0			0
$337$	4.67117	−	4.67117i	0.254455	−	0.254455i	−0.568339	−	0.822794i	$-0.692414\pi$
$337$	4.67117	−	4.67117i	0.254455	−	0.254455i	0.822794	+	0.568339i	$0.192414\pi$
$338$		0			0
$339$	17.0187	+	11.3715i	0.924329	+	0.617617i
$340$		0			0
$341$	−18.1988	−	3.61996i	−0.985520	−	0.196032i
$342$		0			0
$343$	−7.19006	−	17.3584i	−0.388227	−	0.937263i
$344$		0			0
$345$	−4.20859	+	10.1604i	−0.226583	+	0.547019i
$346$		0			0
$347$	11.6056	−	7.75460i	0.623020	−	0.416289i	−0.203596	−	0.979055i	$-0.565263\pi$
$347$	11.6056	−	7.75460i	0.623020	−	0.416289i	0.826616	+	0.562766i	$0.190263\pi$
$348$		0			0
$349$	3.22983	+	16.2374i	0.172889	+	0.869170i	0.965692	+	0.259692i	$0.0836210\pi$
$349$	3.22983	+	16.2374i	0.172889	+	0.869170i	−0.792803	+	0.609478i	$0.791379\pi$
$350$		0			0
$351$		−	21.7647i		−	1.16172i
$352$		0			0
$353$			29.4440i			1.56715i	0.621299	+	0.783573i	$0.286605\pi$
$353$			29.4440i			1.56715i	−0.621299	+	0.783573i	$0.713395\pi$
$354$		0			0
$355$	−3.34516	−	16.8172i	−0.177542	−	0.892566i
$356$		0			0
$357$	16.7398	−	11.1852i	0.885964	−	0.591982i
$358$		0			0
$359$	6.81567	−	16.4545i	0.359717	−	0.868435i	−0.635622	−	0.772001i	$-0.719256\pi$
$359$	6.81567	−	16.4545i	0.359717	−	0.868435i	0.995339	−	0.0964342i	$-0.0307437\pi$
$360$		0			0
$361$	−3.40598	−	8.22277i	−0.179262	−	0.432777i
$362$		0			0
$363$	7.43847	+	1.47960i	0.390418	+	0.0776590i
$364$		0			0
$365$	−15.5172	−	10.3683i	−0.812208	−	0.542700i
$366$		0			0
$367$	21.7396	−	21.7396i	1.13480	−	1.13480i	0.145427	−	0.989369i	$-0.453545\pi$
$367$	21.7396	−	21.7396i	1.13480	−	1.13480i	0.989369	−	0.145427i	$-0.0464555\pi$
$368$		0			0
$369$	−8.03204	−	8.03204i	−0.418131	−	0.418131i
$370$		0			0
$371$	6.28319	−	9.40346i	0.326207	−	0.488203i
$372$		0			0
$373$	−2.98424	+	15.0028i	−0.154518	+	0.776816i	0.823340	+	0.567548i	$0.192108\pi$
$373$	−2.98424	+	15.0028i	−0.154518	+	0.776816i	−0.977858	+	0.209268i	$0.932892\pi$
$374$		0			0
$375$	13.6809	−	5.66682i	0.706479	−	0.292633i
$376$		0			0
$377$	15.5628	+	6.44631i	0.801523	+	0.332002i
$378$		0			0
$379$	9.23758	+	13.8250i	0.474503	+	0.710143i	0.989093	−	0.147293i	$-0.0470560\pi$
$379$	9.23758	+	13.8250i	0.474503	+	0.710143i	−0.514590	+	0.857436i	$0.672056\pi$
$380$		0			0
$381$	−2.74508	+	0.546029i	−0.140634	+	0.0279739i
$382$		0			0
$383$	10.4632			0.534645			0.267322	−	0.963607i	$-0.413861\pi$
$383$	10.4632			0.534645			0.267322	+	0.963607i	$0.413861\pi$
$384$		0			0
$385$	9.19599			0.468671
$386$		0			0
$387$	12.4603	−	2.47851i	0.633394	−	0.125990i
$388$		0			0
$389$	5.64815	+	8.45306i	0.286373	+	0.428587i	0.946567	−	0.322508i	$-0.104526\pi$
$389$	5.64815	+	8.45306i	0.286373	+	0.428587i	−0.660194	+	0.751095i	$0.729526\pi$
$390$		0			0
$391$	31.7641	+	13.1571i	1.60638	+	0.665385i
$392$		0			0
$393$	6.21011	−	2.57231i	0.313259	−	0.129756i
$394$		0			0
$395$	−0.370319	+	1.86172i	−0.0186328	+	0.0936733i
$396$		0			0
$397$	−1.45561	+	2.17847i	−0.0730549	+	0.109334i	−0.866198	−	0.499701i	$-0.833443\pi$
$397$	−1.45561	+	2.17847i	−0.0730549	+	0.109334i	0.793143	+	0.609035i	$0.208443\pi$
$398$		0			0
$399$	−7.29478	−	7.29478i	−0.365196	−	0.365196i
$400$		0			0
$401$	−14.8490	+	14.8490i	−0.741524	+	0.741524i	−0.972871	−	0.231347i	$-0.925687\pi$
$401$	−14.8490	+	14.8490i	−0.741524	+	0.741524i	0.231347	+	0.972871i	$0.425687\pi$
$402$		0			0
$403$	27.3404	+	18.2683i	1.36192	+	0.910009i
$404$		0			0
$405$	−3.99819	−	0.795289i	−0.198671	−	0.0395182i
$406$		0			0
$407$	5.52908	+	13.3484i	0.274066	+	0.661655i
$408$		0			0
$409$	−8.95302	+	21.6145i	−0.442698	+	1.06877i	0.532300	+	0.846556i	$0.321328\pi$
$409$	−8.95302	+	21.6145i	−0.442698	+	1.06877i	−0.974998	+	0.222212i	$0.928672\pi$
$410$		0			0
$411$	6.73195	−	4.49814i	0.332062	−	0.221877i
$412$		0			0
$413$	0.602027	+	3.02660i	0.0296238	+	0.148929i
$414$		0			0
$415$		−	1.46882i		−	0.0721014i
$416$		0			0
$417$		−	2.23918i		−	0.109653i
$418$		0			0
$419$	2.28680	+	11.4965i	0.111718	+	0.561643i	0.995582	+	0.0938989i	$0.0299331\pi$
$419$	2.28680	+	11.4965i	0.111718	+	0.561643i	−0.883864	+	0.467744i	$0.845067\pi$
$420$		0			0
$421$	27.2435	−	18.2035i	1.32777	−	0.887185i	0.329392	−	0.944193i	$-0.393156\pi$
$421$	27.2435	−	18.2035i	1.32777	−	0.887185i	0.998374	+	0.0570087i	$0.0181563\pi$
$422$		0			0
$423$	0.0604374	−	0.145909i	0.00293856	−	0.00709432i
$424$		0			0
$425$	−5.84894	−	14.1206i	−0.283715	−	0.684949i
$426$		0			0
$427$	−25.8152	−	5.13496i	−1.24928	−	0.248498i
$428$		0			0
$429$	9.01767	+	6.02541i	0.435377	+	0.290910i
$430$		0			0
$431$	−11.1659	+	11.1659i	−0.537842	+	0.537842i	−0.922895	−	0.385053i	$-0.874183\pi$
$431$	−11.1659	+	11.1659i	−0.537842	+	0.537842i	0.385053	+	0.922895i	$0.374183\pi$
$432$		0			0
$433$	15.3110	+	15.3110i	0.735802	+	0.735802i	0.971763	−	0.235961i	$-0.0758237\pi$
$433$	15.3110	+	15.3110i	0.735802	+	0.735802i	−0.235961	+	0.971763i	$0.575824\pi$
$434$		0			0
$435$	4.72693	−	7.07435i	0.226639	−	0.339189i
$436$		0			0
$437$	3.43701	−	17.2790i	0.164415	−	0.826568i
$438$		0			0
$439$	−37.8088	+	15.6609i	−1.80452	+	0.747455i	−0.819951	+	0.572434i	$0.805999\pi$
$439$	−37.8088	+	15.6609i	−1.80452	+	0.747455i	−0.984565	+	0.175021i	$0.944001\pi$
$440$		0			0
$441$	0.281996	+	0.116807i	0.0134284	+	0.00556222i
$442$		0			0
$443$	−18.8638	−	28.2317i	−0.896247	−	1.34133i	−0.939602	−	0.342269i	$-0.888805\pi$
$443$	−18.8638	−	28.2317i	−0.896247	−	1.34133i	0.0433550	−	0.999060i	$-0.486195\pi$
$444$		0			0
$445$	8.29633	−	1.65024i	0.393284	−	0.0782290i
$446$		0			0
$447$	−4.18688			−0.198033
$448$		0			0
$449$	−2.12507			−0.100288			−0.0501442	−	0.998742i	$-0.515968\pi$
$449$	−2.12507			−0.100288			−0.0501442	+	0.998742i	$0.515968\pi$
$450$		0			0
$451$	17.0542	−	3.39229i	0.803050	−	0.159737i
$452$		0			0
$453$	2.39365	+	3.58234i	0.112463	+	0.168313i
$454$		0			0
$455$	−15.0558	−	6.23633i	−0.705828	−	0.292364i
$456$		0			0
$457$	−32.1519	+	13.3177i	−1.50400	+	0.622978i	−0.974310	−	0.225213i	$-0.927692\pi$
$457$	−32.1519	+	13.3177i	−1.50400	+	0.622978i	−0.529691	+	0.848190i	$0.677692\pi$
$458$		0			0
$459$	−6.70476	+	33.7071i	−0.312951	+	1.57331i
$460$		0			0
$461$	7.57489	−	11.3366i	0.352798	−	0.528000i	−0.612046	−	0.790822i	$-0.709653\pi$
$461$	7.57489	−	11.3366i	0.352798	−	0.528000i	0.964844	+	0.262822i	$0.0846534\pi$
$462$		0			0
$463$	−16.2876	−	16.2876i	−0.756949	−	0.756949i	0.218817	−	0.975766i	$-0.429780\pi$
$463$	−16.2876	−	16.2876i	−0.756949	−	0.756949i	−0.975766	+	0.218817i	$0.929780\pi$
$464$		0			0
$465$	11.7439	−	11.7439i	0.544611	−	0.544611i
$466$		0			0
$467$	13.6451	+	9.11734i	0.631418	+	0.421900i	0.829672	−	0.558250i	$-0.188527\pi$
$467$	13.6451	+	9.11734i	0.631418	+	0.421900i	−0.198254	+	0.980151i	$0.563527\pi$
$468$		0			0
$469$	23.6089	+	4.69611i	1.09016	+	0.216846i
$470$		0			0
$471$	−1.47953	−	3.57191i	−0.0681733	−	0.164585i
$472$		0			0
$473$	−7.44237	+	17.9675i	−0.342201	+	0.826145i
$474$		0			0
$475$	−6.51190	+	4.35111i	−0.298786	+	0.199643i
$476$		0			0
$477$	1.22602	+	6.16364i	0.0561358	+	0.282214i
$478$		0			0
$479$		−	4.14550i		−	0.189413i	−0.995505	−	0.0947064i	$-0.969809\pi$
$479$		−	4.14550i		−	0.189413i	0.995505	−	0.0947064i	$-0.0301912\pi$
$480$		0			0
$481$		−	25.6038i		−	1.16743i
$482$		0			0
$483$	3.51074	+	17.6497i	0.159744	+	0.803088i
$484$		0			0
$485$	7.82129	−	5.22602i	0.355146	−	0.237301i
$486$		0			0
$487$	−0.228313	+	0.551195i	−0.0103458	+	0.0249770i	−0.928968	−	0.370160i	$-0.879303\pi$
$487$	−0.228313	+	0.551195i	−0.0103458	+	0.0249770i	0.918622	+	0.395137i	$0.129303\pi$
$488$		0			0
$489$	−0.230502	−	0.556482i	−0.0104237	−	0.0251650i
$490$		0			0
$491$	31.2490	+	6.21581i	1.41025	+	0.280516i	0.840726	−	0.541461i	$-0.182129\pi$
$491$	31.2490	+	6.21581i	1.41025	+	0.280516i	0.569521	+	0.821977i	$0.307129\pi$
$492$		0			0
$493$	−22.1162	−	14.7776i	−0.996065	−	0.665550i
$494$		0			0
$495$	−3.61331	+	3.61331i	−0.162406	+	0.162406i
$496$		0			0
$497$	−19.8395	−	19.8395i	−0.889925	−	0.889925i
$498$		0			0
$499$	−4.65337	+	6.96426i	−0.208313	+	0.311763i	−0.920884	−	0.389838i	$-0.872531\pi$
$499$	−4.65337	+	6.96426i	−0.208313	+	0.311763i	0.712570	+	0.701601i	$0.247531\pi$
$500$		0			0
$501$	2.16323	−	10.8753i	0.0966459	−	0.485871i
$502$		0			0
$503$	−16.9351	+	7.01476i	−0.755100	+	0.312772i	−0.726820	−	0.686828i	$-0.759003\pi$
$503$	−16.9351	+	7.01476i	−0.755100	+	0.312772i	−0.0282792	+	0.999600i	$0.509003\pi$
$504$		0			0
$505$	−0.760560	−	0.315034i	−0.0338445	−	0.0140188i
$506$		0			0
$507$	−1.67970	−	2.51385i	−0.0745982	−	0.111644i
$508$		0			0
$509$	−13.8146	+	2.74790i	−0.612322	+	0.121798i	−0.491503	−	0.870876i	$-0.663552\pi$
$509$	−13.8146	+	2.74790i	−0.612322	+	0.121798i	−0.120819	+	0.992675i	$0.538552\pi$
$510$		0			0
$511$	−30.5375			−1.35090
$512$		0			0
$513$	17.6105			0.777521
$514$		0			0
$515$	−13.6300	+	2.71118i	−0.600610	+	0.119469i
$516$		0			0
$517$	0.134314	+	0.201015i	0.00590712	+	0.00884062i
$518$		0			0
$519$	14.8704	+	6.15954i	0.652740	+	0.270374i
$520$		0			0
$521$	1.55454	−	0.643912i	0.0681057	−	0.0282103i	−0.348371	−	0.937357i	$-0.613265\pi$
$521$	1.55454	−	0.643912i	0.0681057	−	0.0282103i	0.416476	+	0.909147i	$0.363265\pi$
$522$		0			0
$523$	5.90096	−	29.6661i	0.258031	−	1.29721i	−0.606683	−	0.794944i	$-0.707500\pi$
$523$	5.90096	−	29.6661i	0.258031	−	1.29721i	0.864714	−	0.502265i	$-0.167500\pi$
$524$		0			0
$525$	4.44444	−	6.65158i	0.193971	−	0.290299i
$526$		0			0
$527$	−36.7145	−	36.7145i	−1.59931	−	1.59931i
$528$		0			0
$529$	−5.46686	+	5.46686i	−0.237690	+	0.237690i
$530$		0			0
$531$	−1.42577	−	0.952668i	−0.0618731	−	0.0413423i
$532$		0			0
$533$	−30.2219	−	6.01150i	−1.30905	−	0.260387i
$534$		0			0
$535$	11.6571	+	28.1428i	0.503982	+	1.21672i
$536$		0			0
$537$	−7.63259	+	18.4267i	−0.329371	+	0.795171i
$538$		0			0
$539$	−0.388500	+	0.259587i	−0.0167339	+	0.0111812i
$540$		0			0
$541$	−5.86328	−	29.4767i	−0.252082	−	1.26730i	−0.874657	−	0.484742i	$-0.838913\pi$
$541$	−5.86328	−	29.4767i	−0.252082	−	1.26730i	0.622575	−	0.782560i	$-0.286087\pi$
$542$		0			0
$543$			1.73473i			0.0744442i
$544$		0			0
$545$			20.3241i			0.870587i
$546$		0			0
$547$	−8.35722	−	42.0146i	−0.357329	−	1.79641i	−0.572572	−	0.819854i	$-0.694054\pi$
$547$	−8.35722	−	42.0146i	−0.357329	−	1.79641i	0.215243	−	0.976560i	$-0.430946\pi$
$548$		0			0
$549$	12.1610	−	8.12572i	0.519019	−	0.346797i
$550$		0			0
$551$	−5.21589	+	12.5923i	−0.222204	+	0.536449i
$552$		0			0
$553$	1.18863	+	2.86960i	0.0505456	+	0.122028i
$554$		0			0
$555$	−12.6837	−	2.52295i	−0.538394	−	0.107093i
$556$		0			0
$557$	−6.44120	−	4.30387i	−0.272923	−	0.182361i	0.411576	−	0.911376i	$-0.364979\pi$
$557$	−6.44120	−	4.30387i	−0.272923	−	0.182361i	−0.684498	+	0.729015i	$0.739979\pi$
$558$		0			0
$559$	24.3695	−	24.3695i	1.03072	−	1.03072i
$560$		0			0
$561$	−12.1095	−	12.1095i	−0.511264	−	0.511264i
$562$		0			0
$563$	1.09582	−	1.64001i	0.0461832	−	0.0691181i	−0.807659	−	0.589649i	$-0.799266\pi$
$563$	1.09582	−	1.64001i	0.0461832	−	0.0691181i	0.853843	+	0.520531i	$0.174266\pi$
$564$		0			0
$565$	−5.10382	+	25.6586i	−0.214719	+	1.07947i
$566$		0			0
$567$	−6.16269	+	2.55267i	−0.258809	+	0.107202i
$568$		0			0
$569$	−35.9156	−	14.8767i	−1.50566	−	0.623664i	−0.531002	−	0.847370i	$-0.678184\pi$
$569$	−35.9156	−	14.8767i	−1.50566	−	0.623664i	−0.974657	+	0.223706i	$0.928184\pi$
$570$		0			0
$571$	7.30296	+	10.9297i	0.305619	+	0.457392i	0.952209	−	0.305446i	$-0.0988055\pi$
$571$	7.30296	+	10.9297i	0.305619	+	0.457392i	−0.646590	+	0.762838i	$0.723806\pi$
$572$		0			0
$573$	4.35700	−	0.866660i	0.182016	−	0.0362053i
$574$		0			0
$575$	13.6614			0.569722
$576$		0			0
$577$	3.92683			0.163476			0.0817381	−	0.996654i	$-0.473953\pi$
$577$	3.92683			0.163476			0.0817381	+	0.996654i	$0.473953\pi$
$578$		0			0
$579$	−4.72573	+	0.940005i	−0.196394	+	0.0390653i
$580$		0			0
$581$	−1.33528	−	1.99839i	−0.0553968	−	0.0829072i
$582$		0			0
$583$	−8.88781	−	3.68145i	−0.368095	−	0.152470i
$584$		0			0
$585$	8.36617	−	3.46538i	0.345899	−	0.143276i
$586$		0			0
$587$	−7.25567	+	36.4767i	−0.299473	+	1.50555i	0.478965	+	0.877834i	$0.341012\pi$
$587$	−7.25567	+	36.4767i	−0.299473	+	1.50555i	−0.778439	+	0.627721i	$0.783988\pi$
$588$		0			0
$589$	−14.7814	+	22.1219i	−0.609057	+	0.911518i
$590$		0			0
$591$	−15.9082	−	15.9082i	−0.654374	−	0.654374i
$592$		0			0
$593$	6.42206	−	6.42206i	0.263723	−	0.263723i	−0.562842	−	0.826565i	$-0.690292\pi$
$593$	6.42206	−	6.42206i	0.263723	−	0.263723i	0.826565	+	0.562842i	$0.190292\pi$
$594$		0			0
$595$	21.3958	+	14.2962i	0.877144	+	0.586089i
$596$		0			0
$597$	17.1195	+	3.40529i	0.700656	+	0.139369i
$598$		0			0
$599$	−12.0671	−	29.1324i	−0.493046	−	1.19032i	−0.953162	−	0.302460i	$-0.902192\pi$
$599$	−12.0671	−	29.1324i	−0.493046	−	1.19032i	0.460116	−	0.887859i	$-0.347808\pi$
$600$		0			0
$601$	−13.5123	+	32.6215i	−0.551177	+	1.33066i	0.365419	+	0.930843i	$0.380926\pi$
$601$	−13.5123	+	32.6215i	−0.551177	+	1.33066i	−0.916596	+	0.399815i	$0.869074\pi$
$602$		0			0
$603$	−11.1217	+	7.43128i	−0.452910	+	0.302625i
$604$		0			0
$605$	1.89114	+	9.50742i	0.0768859	+	0.386532i
$606$		0			0
$607$			12.7147i			0.516076i	0.966135	+	0.258038i	$0.0830759\pi$
$607$			12.7147i			0.516076i	−0.966135	+	0.258038i	$0.916924\pi$
$608$		0			0
$609$		−	13.9221i		−	0.564154i
$610$		0			0
$611$	−0.0835811	−	0.420191i	−0.00338133	−	0.0169991i
$612$		0			0
$613$	−0.425673	+	0.284426i	−0.0171928	+	0.0114878i	−0.564137	−	0.825681i	$-0.690791\pi$
$613$	−0.425673	+	0.284426i	−0.0171928	+	0.0114878i	0.546944	+	0.837169i	$0.315791\pi$
$614$		0			0
$615$	−5.95602	+	14.3791i	−0.240170	+	0.579821i
$616$		0			0
$617$	4.10135	+	9.90154i	0.165114	+	0.398621i	0.984682	−	0.174362i	$-0.0557862\pi$
$617$	4.10135	+	9.90154i	0.165114	+	0.398621i	−0.819567	+	0.572983i	$0.805786\pi$
$618$		0			0
$619$	−27.4882	−	5.46774i	−1.10484	−	0.219767i	−0.391220	−	0.920297i	$-0.627947\pi$
$619$	−27.4882	−	5.46774i	−1.10484	−	0.219767i	−0.713623	+	0.700530i	$0.752947\pi$
$620$		0			0
$621$	−25.5419	−	17.0665i	−1.02496	−	0.684857i
$622$		0			0
$623$	9.78730	−	9.78730i	0.392120	−	0.392120i
$624$		0			0
$625$	4.67046	+	4.67046i	0.186818	+	0.186818i
$626$		0			0
$627$	−4.87533	+	7.29645i	−0.194702	+	0.291392i
$628$		0			0
$629$	−7.88739	+	39.6526i	−0.314491	+	1.58105i
$630$		0			0
$631$	39.9593	−	16.5517i	1.59075	−	0.658911i	0.600683	−	0.799487i	$-0.294895\pi$
$631$	39.9593	−	16.5517i	1.59075	−	0.658911i	0.990070	+	0.140576i	$0.0448955\pi$
$632$		0			0
$633$	−21.7341	−	9.00254i	−0.863852	−	0.357819i
$634$		0			0
$635$	−1.98746	−	2.97445i	−0.0788700	−	0.118037i
$636$		0			0
$637$	0.812099	−	0.161536i	0.0321765	−	0.00640031i
$638$		0			0
$639$	15.5908			0.616763
$640$		0			0
$641$	5.29159			0.209005			0.104503	−	0.994525i	$-0.466675\pi$
$641$	5.29159			0.209005			0.104503	+	0.994525i	$0.466675\pi$
$642$		0			0
$643$	20.3921	−	4.05624i	0.804185	−	0.159962i	0.224151	−	0.974554i	$-0.428039\pi$
$643$	20.3921	−	4.05624i	0.804185	−	0.159962i	0.580034	+	0.814592i	$0.303039\pi$
$644$		0			0
$645$	−9.67097	−	14.4736i	−0.380794	−	0.569899i
$646$		0			0
$647$	10.8250	+	4.48386i	0.425575	+	0.176279i	0.585182	−	0.810902i	$-0.301023\pi$
$647$	10.8250	+	4.48386i	0.425575	+	0.176279i	−0.159608	+	0.987181i	$0.551023\pi$
$648$		0			0
$649$	2.42512	−	1.00452i	0.0951944	−	0.0394308i
$650$		0			0
$651$	5.30188	−	26.6543i	0.207797	−	1.04467i
$652$		0			0
$653$	20.9476	−	31.3503i	0.819744	−	1.22683i	−0.151431	−	0.988468i	$-0.548388\pi$
$653$	20.9476	−	31.3503i	0.819744	−	1.22683i	0.971175	−	0.238366i	$-0.0766117\pi$
$654$		0			0
$655$	6.07503	+	6.07503i	0.237371	+	0.237371i
$656$		0			0
$657$	11.9989	−	11.9989i	0.468120	−	0.468120i
$658$		0			0
$659$	−29.0678	−	19.4225i	−1.13232	−	0.756594i	−0.159283	−	0.987233i	$-0.550918\pi$
$659$	−29.0678	−	19.4225i	−1.13232	−	0.756594i	−0.973039	+	0.230639i	$0.925918\pi$
$660$		0			0
$661$	43.2043	+	8.59387i	1.68045	+	0.334263i	0.940861	−	0.338793i	$-0.110019\pi$
$661$	43.2043	+	8.59387i	1.68045	+	0.334263i	0.739592	+	0.673056i	$0.235019\pi$
$662$		0			0
$663$	11.6137	+	28.0380i	0.451040	+	1.08891i
$664$		0			0
$665$	5.04599	−	12.1821i	0.195675	−	0.472402i
$666$		0			0
$667$	19.7684	−	13.2088i	0.765434	−	0.511447i
$668$		0			0
$669$	6.31233	+	31.7342i	0.244049	+	1.22692i
$670$		0			0
$671$			22.3892i			0.864326i
$672$		0			0
$673$		−	6.94905i		−	0.267866i	−0.990990	−	0.133933i	$-0.957239\pi$
$673$		−	6.94905i		−	0.267866i	0.990990	−	0.133933i	$-0.0427607\pi$
$674$		0			0
$675$	2.66414	+	13.3936i	0.102543	+	0.515518i
$676$		0			0
$677$	−27.1193	+	18.1206i	−1.04228	+	0.696430i	−0.954043	−	0.299670i	$-0.903123\pi$
$677$	−27.1193	+	18.1206i	−1.04228	+	0.696430i	−0.0882375	+	0.996099i	$0.528123\pi$
$678$		0			0
$679$	5.89030	−	14.2204i	0.226049	−	0.545731i
$680$		0			0
$681$	0.523050	+	1.26275i	0.0200433	+	0.0483889i
$682$		0			0
$683$	11.0672	+	2.20141i	0.423476	+	0.0842347i	0.402228	−	0.915540i	$-0.368236\pi$
$683$	11.0672	+	2.20141i	0.423476	+	0.0842347i	0.0212483	+	0.999774i	$0.493236\pi$
$684$		0			0
$685$	8.60439	+	5.74927i	0.328757	+	0.219668i
$686$		0			0
$687$	−13.8581	+	13.8581i	−0.528719	+	0.528719i
$688$		0			0
$689$	12.0547	+	12.0547i	0.459246	+	0.459246i
$690$		0			0
$691$	7.02304	−	10.5107i	0.267169	−	0.399846i	−0.673492	−	0.739194i	$-0.735206\pi$
$691$	7.02304	−	10.5107i	0.267169	−	0.399846i	0.940661	+	0.339348i	$0.110206\pi$
$692$		0			0
$693$	−1.63126	+	8.20088i	−0.0619663	+	0.311526i
$694$		0			0
$695$	2.64414	−	1.09524i	0.100298	−	0.0415448i
$696$		0			0
$697$	44.9528	+	18.6200i	1.70271	+	0.705284i
$698$		0			0
$699$	−13.4143	−	20.0758i	−0.507374	−	0.759338i
$700$		0			0
$701$	−31.1018	+	6.18654i	−1.17470	+	0.233662i	−0.743589	−	0.668637i	$-0.766878\pi$
$701$	−31.1018	+	6.18654i	−1.17470	+	0.233662i	−0.431111	+	0.902299i	$0.641878\pi$
$702$		0			0
$703$	20.7167			0.781347
$704$		0			0
$705$	−0.216392			−0.00814980
$706$		0			0
$707$	−1.32117	+	0.262797i	−0.0496877	+	0.00988349i
$708$		0			0
$709$	−9.97024	−	14.9215i	−0.374440	−	0.560389i	0.595616	−	0.803269i	$-0.296908\pi$
$709$	−9.97024	−	14.9215i	−0.374440	−	0.560389i	−0.970056	+	0.242880i	$0.921908\pi$
$710$		0			0
$711$	−1.59457	−	0.660493i	−0.0598011	−	0.0247704i
$712$		0			0
$713$	42.8773	−	17.7604i	1.60577	−	0.665131i
$714$		0			0
$715$	−2.70435	+	13.5957i	−0.101137	+	0.508450i
$716$		0			0
$717$	−7.64645	+	11.4437i	−0.285562	+	0.427374i
$718$		0			0
$719$	30.0253	+	30.0253i	1.11975	+	1.11975i	0.991777	+	0.127978i	$0.0408485\pi$
$719$	30.0253	+	30.0253i	1.11975	+	1.11975i	0.127978	+	0.991777i	$0.459151\pi$
$720$		0			0
$721$	−16.0795	+	16.0795i	−0.598833	+	0.598833i
$722$		0			0
$723$	−9.56589	−	6.39172i	−0.355759	−	0.237711i
$724$		0			0
$725$	−10.3661	−	2.06194i	−0.384986	−	0.0765784i
$726$		0			0
$727$	−14.5339	−	35.0878i	−0.539031	−	1.30134i	−0.925400	−	0.378992i	$-0.876271\pi$
$727$	−14.5339	−	35.0878i	−0.539031	−	1.30134i	0.386369	−	0.922344i	$-0.373729\pi$
$728$		0			0
$729$	9.34421	−	22.5589i	0.346082	−	0.835515i
$730$		0			0
$731$	−45.2483	+	30.2340i	−1.67357	+	1.11824i
$732$		0			0
$733$	−7.98081	−	40.1222i	−0.294778	−	1.48195i	−0.789960	−	0.613159i	$-0.789899\pi$
$733$	−7.98081	−	40.1222i	−0.294778	−	1.48195i	0.495182	−	0.868789i	$-0.335101\pi$
$734$		0			0
$735$		−	0.418219i		−	0.0154262i
$736$		0			0
$737$		−	20.4758i		−	0.754235i
$738$		0			0
$739$	−2.49769	−	12.5568i	−0.0918791	−	0.461908i	−0.999145	−	0.0413495i	$-0.986834\pi$
$739$	−2.49769	−	12.5568i	−0.0918791	−	0.461908i	0.907266	−	0.420558i	$-0.138166\pi$
$740$		0			0
$741$	12.9301	−	8.63963i	0.475000	−	0.317385i
$742$		0			0
$743$	−0.0423479	+	0.102237i	−0.00155359	+	0.00375071i	−0.924654	−	0.380807i	$-0.875646\pi$
$743$	−0.0423479	+	0.102237i	−0.00155359	+	0.00375071i	0.923101	+	0.384558i	$0.125646\pi$
$744$		0			0
$745$	−2.04791	−	4.94408i	−0.0750294	−	0.181137i
$746$		0			0
$747$	1.30987	+	0.260550i	0.0479258	+	0.00953303i
$748$		0			0
$749$	41.4443	+	27.6922i	1.51434	+	1.01185i
$750$		0			0
$751$	−1.45742	+	1.45742i	−0.0531820	+	0.0531820i	−0.733198	−	0.680016i	$-0.761973\pi$
$751$	−1.45742	+	1.45742i	−0.0531820	+	0.0531820i	0.680016	+	0.733198i	$0.261973\pi$
$752$		0			0
$753$	7.79719	+	7.79719i	0.284146	+	0.284146i
$754$		0			0
$755$	−3.05942	+	4.57875i	−0.111344	+	0.166638i
$756$		0			0
$757$	6.72211	−	33.7943i	0.244319	−	1.22828i	−0.642546	−	0.766247i	$-0.722122\pi$
$757$	6.72211	−	33.7943i	0.244319	−	1.22828i	0.886865	−	0.462028i	$-0.152878\pi$
$758$		0			0
$759$	14.1422	−	5.85788i	0.513328	−	0.212628i
$760$		0			0
$761$	20.6469	+	8.55221i	0.748448	+	0.310018i	0.724108	−	0.689686i	$-0.242252\pi$
$761$	20.6469	+	8.55221i	0.748448	+	0.310018i	0.0243401	+	0.999704i	$0.492252\pi$
$762$		0			0
$763$	18.4763	+	27.6518i	0.668888	+	1.00106i
$764$		0			0
$765$	−14.0242	+	2.78959i	−0.507047	+	0.100858i
$766$		0			0
$767$	−4.65167			−0.167962
$768$		0			0
$769$	−23.8846			−0.861299			−0.430650	−	0.902519i	$-0.641716\pi$
$769$	−23.8846			−0.861299			−0.430650	+	0.902519i	$0.641716\pi$
$770$		0			0
$771$	5.93001	−	1.17955i	0.213564	−	0.0424805i
$772$		0			0
$773$	11.9528	+	17.8887i	0.429914	+	0.643412i	0.981669	−	0.190595i	$-0.0610416\pi$
$773$	11.9528	+	17.8887i	0.429914	+	0.643412i	−0.551755	+	0.834006i	$0.686042\pi$
$774$		0			0
$775$	−19.0609	−	7.89528i	−0.684687	−	0.283607i
$776$		0			0
$777$	−19.5503	+	8.09801i	−0.701364	+	0.290515i
$778$		0			0
$779$	4.86408	−	24.4534i	0.174274	−	0.876133i
$780$		0			0
$781$	−13.2594	+	19.8441i	−0.474459	+	0.710077i
$782$		0			0
$783$	16.8048	+	16.8048i	0.600556	+	0.600556i
$784$		0			0
$785$	3.49421	−	3.49421i	0.124714	−	0.124714i
$786$		0			0
$787$	16.2057	+	10.8283i	0.577672	+	0.385988i	0.809808	−	0.586695i	$-0.199571\pi$
$787$	16.2057	+	10.8283i	0.577672	+	0.385988i	−0.232136	+	0.972683i	$0.574571\pi$
$788$		0			0
$789$	−20.8126	−	4.13988i	−0.740948	−	0.147384i
$790$		0			0
$791$	16.3819	+	39.5495i	0.582474	+	1.40622i
$792$		0			0
$793$	15.1834	−	36.6560i	0.539179	−	1.30169i
$794$		0			0
$795$	7.15954	−	4.78385i	0.253923	−	0.169666i
$796$		0			0
$797$	0.0842043	+	0.423324i	0.00298267	+	0.0149949i	0.982248	−	0.187587i	$-0.0600667\pi$
$797$	0.0842043	+	0.423324i	0.00298267	+	0.0149949i	−0.979265	+	0.202582i	$0.935067\pi$
$798$		0			0
$799$			0.676497i			0.0239328i
$800$		0			0
$801$			7.69131i			0.271759i
$802$		0			0
$803$	5.06765	+	25.4768i	0.178834	+	0.899057i
$804$		0			0
$805$	−19.1244	+	12.7785i	−0.674048	+	0.450384i
$806$		0			0
$807$	1.52935	−	3.69217i	0.0538355	−	0.129971i
$808$		0			0
$809$	−8.87822	−	21.4339i	−0.312142	−	0.753576i	−0.999625	−	0.0273765i	$-0.991285\pi$
$809$	−8.87822	−	21.4339i	−0.312142	−	0.753576i	0.687484	−	0.726200i	$-0.258715\pi$
$810$		0			0
$811$	0.570557	+	0.113491i	0.0200350	+	0.00398520i	0.205098	−	0.978742i	$-0.434249\pi$
$811$	0.570557	+	0.113491i	0.0200350	+	0.00398520i	−0.185063	+	0.982727i	$0.559249\pi$
$812$		0			0
$813$	6.34016	+	4.23636i	0.222359	+	0.148576i
$814$		0			0
$815$	0.544377	−	0.544377i	0.0190687	−	0.0190687i
$816$		0			0
$817$	19.7181	+	19.7181i	0.689849	+	0.689849i
$818$		0			0
$819$	8.23221	−	12.3204i	0.287657	−	0.430509i
$820$		0			0
$821$	0.267849	−	1.34657i	0.00934799	−	0.0469955i	−0.975830	−	0.218532i	$-0.929873\pi$
$821$	0.267849	−	1.34657i	0.00934799	−	0.0469955i	0.985178	+	0.171537i	$0.0548732\pi$
$822$		0			0
$823$	−32.6695	+	13.5321i	−1.13879	+	0.471701i	−0.870759	−	0.491710i	$-0.836372\pi$
$823$	−32.6695	+	13.5321i	−1.13879	+	0.471701i	−0.268028	+	0.963411i	$0.586372\pi$
$824$		0			0
$825$	−6.28683	−	2.60409i	−0.218879	−	0.0906628i
$826$		0			0
$827$	−16.7811	−	25.1146i	−0.583534	−	0.873321i	0.415813	−	0.909450i	$-0.363497\pi$
$827$	−16.7811	−	25.1146i	−0.583534	−	0.873321i	−0.999347	+	0.0361292i	$0.988497\pi$
$828$		0			0
$829$	43.8051	−	8.71338i	1.52142	−	0.302628i	0.637564	−	0.770397i	$-0.279942\pi$
$829$	43.8051	−	8.71338i	1.52142	−	0.302628i	0.883851	+	0.467769i	$0.154942\pi$
$830$		0			0
$831$	4.86238			0.168674
$832$		0			0
$833$	−1.30746			−0.0453008
$834$		0			0
$835$	13.9002	−	2.76491i	0.481035	−	0.0956838i
$836$		0			0
$837$	25.7737	+	38.5730i	0.890869	+	1.33328i
$838$		0			0
$839$	22.5256	+	9.33043i	0.777672	+	0.322122i	0.735976	−	0.677008i	$-0.236724\pi$
$839$	22.5256	+	9.33043i	0.777672	+	0.322122i	0.0416962	+	0.999130i	$0.486724\pi$
$840$		0			0
$841$	9.79901	−	4.05888i	0.337897	−	0.139961i
$842$		0			0
$843$	1.38512	−	6.96348i	0.0477061	−	0.239835i
$844$		0			0
$845$	2.14690	−	3.21306i	0.0738556	−	0.110533i
$846$		0			0
$847$	11.2160	+	11.2160i	0.385388	+	0.385388i
$848$		0			0
$849$	19.9465	−	19.9465i	0.684563	−	0.684563i
$850$		0			0
$851$	−30.0472	−	20.0769i	−1.03000	−	0.688226i
$852$		0			0
$853$	−30.2500	−	6.01711i	−1.03574	−	0.206022i	−0.352193	−	0.935927i	$-0.614564\pi$
$853$	−30.2500	−	6.01711i	−1.03574	−	0.206022i	−0.683548	+	0.729905i	$0.739564\pi$
$854$		0			0
$855$	2.80394	+	6.76931i	0.0958927	+	0.231505i
$856$		0			0
$857$	9.31614	−	22.4912i	0.318233	−	0.768283i	−0.681115	−	0.732177i	$-0.738504\pi$
$857$	9.31614	−	22.4912i	0.318233	−	0.768283i	0.999348	−	0.0361064i	$-0.0114955\pi$
$858$		0			0
$859$	−0.219064	+	0.146374i	−0.00747437	+	0.00499421i	−0.559302	−	0.828964i	$-0.688931\pi$
$859$	−0.219064	+	0.146374i	−0.00747437	+	0.00499421i	0.551827	+	0.833958i	$0.313931\pi$
$860$		0			0
$861$	4.96842	+	24.9779i	0.169323	+	0.851245i
$862$		0			0
$863$		−	24.2153i		−	0.824299i	−0.911116	−	0.412150i	$-0.864778\pi$
$863$		−	24.2153i		−	0.824299i	0.911116	−	0.412150i	$-0.135222\pi$
$864$		0			0
$865$			20.5725i			0.699487i
$866$		0			0
$867$	−5.21704	−	26.2278i	−0.177180	−	0.890744i
$868$		0			0
$869$	2.19680	−	1.46786i	0.0745214	−	0.0497936i
$870$		0			0
$871$	−13.8858	+	33.5233i	−0.470502	+	1.13589i
$872$		0			0
$873$	3.27310	+	7.90197i	0.110778	+	0.267441i
$874$		0			0
$875$	30.3752	+	6.04200i	1.02687	+	0.204257i
$876$		0			0
$877$	17.9632	+	12.0027i	0.606576	+	0.405301i	0.820580	−	0.571532i	$-0.193651\pi$
$877$	17.9632	+	12.0027i	0.606576	+	0.405301i	−0.214004	+	0.976833i	$0.568651\pi$
$878$		0			0
$879$	−5.85102	+	5.85102i	−0.197350	+	0.197350i
$880$		0			0
$881$	−15.8713	−	15.8713i	−0.534718	−	0.534718i	0.387255	−	0.921973i	$-0.373423\pi$
$881$	−15.8713	−	15.8713i	−0.534718	−	0.534718i	−0.921973	+	0.387255i	$0.873423\pi$
$882$		0			0
$883$	−16.2902	+	24.3799i	−0.548207	+	0.820450i	−0.997330	−	0.0730197i	$-0.976736\pi$
$883$	−16.2902	+	24.3799i	−0.548207	+	0.820450i	0.449123	+	0.893470i	$0.351736\pi$
$884$		0			0
$885$	−0.458367	+	2.30437i	−0.0154078	+	0.0774605i
$886$		0			0
$887$	34.2563	−	14.1894i	1.15021	−	0.476435i	0.275609	−	0.961270i	$-0.411120\pi$
$887$	34.2563	−	14.1894i	1.15021	−	0.476435i	0.874606	+	0.484835i	$0.161120\pi$
$888$		0			0
$889$	−5.40805	−	2.24009i	−0.181380	−	0.0751302i
$890$		0			0
$891$	3.15233	+	4.71780i	0.105607	+	0.158052i
$892$		0			0
$893$	0.339988	−	0.0676279i	0.0113773	−	0.00226308i
$894$		0			0
$895$	−25.4925			−0.852119
$896$		0			0
$897$	−27.1264			−0.905723
$898$		0			0
$899$	−35.2151	+	7.00472i	−1.17449	+	0.233621i
$900$		0			0
$901$	−14.9556	−	22.3826i	−0.498242	−	0.745672i
$902$		0			0
$903$	−26.3155	−	10.9003i	−0.875727	−	0.362738i
$904$		0			0
$905$	−2.04845	+	0.848496i	−0.0680928	+	0.0282050i
$906$		0			0
$907$	0.117687	−	0.591654i	0.00390775	−	0.0196456i	−0.978782	−	0.204903i	$-0.934312\pi$
$907$	0.117687	−	0.591654i	0.00390775	−	0.0196456i	0.982690	+	0.185258i	$0.0593120\pi$
$908$		0			0
$909$	0.415858	−	0.622376i	0.0137931	−	0.0206429i
$910$		0			0
$911$	25.7854	+	25.7854i	0.854308	+	0.854308i	0.990660	−	0.136352i	$-0.0435379\pi$
$911$	25.7854	+	25.7854i	0.854308	+	0.854308i	−0.136352	+	0.990660i	$0.543538\pi$
$912$		0			0
$913$	−1.44563	+	1.44563i	−0.0478433	+	0.0478433i
$914$		0			0
$915$	−16.6627	−	11.1336i	−0.550851	−	0.368067i
$916$		0			0
$917$	13.7881	+	2.74262i	0.455322	+	0.0905693i
$918$		0			0
$919$	−13.0040	−	31.3945i	−0.428964	−	1.03561i	−0.979617	−	0.200876i	$-0.935621\pi$
$919$	−13.0040	−	31.3945i	−0.428964	−	1.03561i	0.550653	−	0.834734i	$-0.314379\pi$
$920$		0			0
$921$	−0.972528	+	2.34789i	−0.0320459	+	0.0773656i
$922$		0			0
$923$	35.1659	−	23.4971i	1.15750	−	0.773417i
$924$		0			0
$925$	3.13407	+	15.7560i	0.103047	+	0.518055i
$926$		0			0
$927$		−	12.6360i		−	0.415021i
$928$		0			0
$929$		−	9.78678i		−	0.321094i	−0.987028	−	0.160547i	$-0.948674\pi$
$929$		−	9.78678i		−	0.321094i	0.987028	−	0.160547i	$-0.0513258\pi$
$930$		0			0
$931$	0.130704	+	0.657092i	0.00428364	+	0.0215353i
$932$		0			0
$933$	−27.2865	+	18.2323i	−0.893320	+	0.596897i
$934$		0			0
$935$	8.37646	−	20.2226i	0.273940	−	0.661349i
$936$		0			0
$937$	9.02858	+	21.7969i	0.294951	+	0.712075i	0.999996	+	0.00291192i	$0.000926893\pi$
$937$	9.02858	+	21.7969i	0.294951	+	0.712075i	−0.705045	+	0.709163i	$0.749073\pi$
$938$		0			0
$939$	14.4072	+	2.86578i	0.470162	+	0.0935211i
$940$		0			0
$941$	6.14014	+	4.10271i	0.200163	+	0.133745i	0.651612	−	0.758552i	$-0.274093\pi$
$941$	6.14014	+	4.10271i	0.200163	+	0.133745i	−0.451450	+	0.892297i	$0.649093\pi$
$942$		0			0
$943$	−30.7529	+	30.7529i	−1.00145	+	1.00145i
$944$		0			0
$945$	−16.2575	−	16.2575i	−0.528855	−	0.528855i
$946$		0			0
$947$	−10.3655	+	15.5130i	−0.336832	+	0.504105i	−0.960762	−	0.277376i	$-0.910535\pi$
$947$	−10.3655	+	15.5130i	−0.336832	+	0.504105i	0.623929	+	0.781481i	$0.285535\pi$
$948$		0			0
$949$	8.98044	−	45.1477i	0.291517	−	1.46556i
$950$		0			0
$951$	16.0905	−	6.66490i	0.521770	−	0.216124i
$952$		0			0
$953$	−1.50663	−	0.624068i	−0.0488047	−	0.0202156i	0.358148	−	0.933665i	$-0.383408\pi$
$953$	−1.50663	−	0.624068i	−0.0488047	−	0.0202156i	−0.406952	+	0.913449i	$0.633408\pi$
$954$		0			0
$955$	3.15451	+	4.72105i	0.102077	+	0.152770i
$956$		0			0
$957$	−11.6150	+	2.31036i	−0.375459	+	0.0746833i
$958$		0			0
$959$	16.9332			0.546802
$960$		0			0
$961$	−39.0879			−1.26090
$962$		0			0
$963$	−27.1653	+	5.40351i	−0.875389	+	0.174126i
$964$		0			0
$965$	−3.42147	−	5.12059i	−0.110141	−	0.164838i
$966$		0			0
$967$	−6.20220	−	2.56904i	−0.199449	−	0.0826147i	0.280723	−	0.959789i	$-0.409426\pi$
$967$	−6.20220	−	2.56904i	−0.199449	−	0.0826147i	−0.480172	+	0.877174i	$0.659426\pi$
$968$		0			0
$969$	−22.6864	+	9.39700i	−0.728791	+	0.301875i
$970$		0			0
$971$	4.68288	−	23.5424i	0.150281	−	0.755512i	−0.829979	−	0.557795i	$-0.811647\pi$
$971$	4.68288	−	23.5424i	0.150281	−	0.755512i	0.980259	−	0.197716i	$-0.0633525\pi$
$972$		0			0
$973$	2.60180	−	3.89387i	0.0834100	−	0.124832i
$974$		0			0
$975$	8.52692	+	8.52692i	0.273080	+	0.273080i
$976$		0			0
$977$	−24.0769	+	24.0769i	−0.770289	+	0.770289i	−0.978157	−	0.207868i	$-0.933348\pi$
$977$	−24.0769	+	24.0769i	−0.770289	+	0.770289i	0.207868	+	0.978157i	$0.433348\pi$
$978$		0			0
$979$	−9.78954	−	6.54116i	−0.312875	−	0.209057i
$980$		0			0
$981$	−18.1248	−	3.60524i	−0.578679	−	0.115106i
$982$		0			0
$983$	−18.5278	−	44.7301i	−0.590946	−	1.42667i	−0.882590	−	0.470143i	$-0.844202\pi$
$983$	−18.5278	−	44.7301i	−0.590946	−	1.42667i	0.291644	−	0.956527i	$-0.405798\pi$
$984$		0			0
$985$	11.0041	−	26.5662i	0.350619	−	0.846470i
$986$		0			0
$987$	−0.294411	+	0.196719i	−0.00937120	+	0.00626163i
$988$		0			0
$989$	−9.48967	−	47.7078i	−0.301754	−	1.51702i
$990$		0			0
$991$		−	23.7163i		−	0.753372i	−0.926341	−	0.376686i	$-0.877064\pi$
$991$		−	23.7163i		−	0.753372i	0.926341	−	0.376686i	$-0.122936\pi$
$992$		0			0
$993$			41.3824i			1.31323i
$994$		0			0
$995$	4.35244	+	21.8812i	0.137982	+	0.693681i
$996$		0			0
$997$	−42.3286	+	28.2831i	−1.34056	+	0.895734i	−0.999026	−	0.0441354i	$-0.985947\pi$
$997$	−42.3286	+	28.2831i	−1.34056	+	0.895734i	−0.341535	+	0.939869i	$0.610947\pi$
$998$		0			0
$999$	13.8236	−	33.3732i	0.437360	−	1.05588i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.2.i.a.49.5		56
4.3	odd	2		64.2.i.a.53.7	yes	56
8.3	odd	2		512.2.i.b.353.5		56
8.5	even	2		512.2.i.a.353.3		56
12.11	even	2		576.2.bd.a.181.1		56
64.3	odd	16		512.2.i.b.161.5		56
64.29	even	16	inner	256.2.i.a.209.5		56
64.35	odd	16		64.2.i.a.29.7	✓	56
64.61	even	16		512.2.i.a.161.3		56
192.35	even	16		576.2.bd.a.541.1		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.29.7	✓	56	64.35	odd	16
64.2.i.a.53.7	yes	56	4.3	odd	2
256.2.i.a.49.5		56	1.1	even	1	trivial
256.2.i.a.209.5		56	64.29	even	16	inner
512.2.i.a.161.3		56	64.61	even	16
512.2.i.a.353.3		56	8.5	even	2
512.2.i.b.161.5		56	64.3	odd	16
512.2.i.b.353.5		56	8.3	odd	2
576.2.bd.a.181.1		56	12.11	even	2
576.2.bd.a.541.1		56	192.35	even	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	256.i (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22190 - 0.243052i) q^{3} +(0.884671 + 1.32400i) q^{5} +(2.40727 + 0.997123i) q^{7} +(-1.33766 + 0.554078i) q^{9} +O(q^{10})\)	\(q+(1.22190 - 0.243052i) q^{3} +(0.884671 + 1.32400i) q^{5} +(2.40727 + 0.997123i) q^{7} +(-1.33766 + 0.554078i) q^{9} +(0.432397 - 2.17381i) q^{11} +(-2.18211 + 3.26576i) q^{13} +(1.40279 + 1.40279i) q^{15} +(4.38547 - 4.38547i) q^{17} +(-2.64242 - 1.76561i) q^{19} +(3.18380 + 0.633298i) q^{21} +(2.12144 + 5.12160i) q^{23} +(0.943074 - 2.27678i) q^{25} +(-4.60747 + 3.07861i) q^{27} +(-0.836699 - 4.20637i) q^{29} -8.37185i q^{31} -2.76128i q^{33} +(0.809445 + 4.06936i) q^{35} +(-5.42017 + 3.62164i) q^{37} +(-1.87258 + 4.52081i) q^{39} +(3.00227 + 7.24812i) q^{41} +(-8.60595 - 1.71183i) q^{43} +(-1.91699 - 1.28089i) q^{45} +(-0.0771294 + 0.0771294i) q^{47} +(-0.149067 - 0.149067i) q^{49} +(4.29273 - 6.42453i) q^{51} +(0.846775 - 4.25703i) q^{53} +(3.26066 - 1.35061i) q^{55} +(-3.65792 - 1.51516i) q^{57} +(0.657977 + 0.984732i) q^{59} +(-9.90754 + 1.97073i) q^{61} -3.77259 q^{63} -6.25433 q^{65} +(9.06082 - 1.80231i) q^{67} +(3.83701 + 5.74249i) q^{69} +(-9.94840 - 4.12076i) q^{71} +(-10.8278 + 4.48502i) q^{73} +(0.598970 - 3.01123i) q^{75} +(3.20845 - 4.80178i) q^{77} +(0.842912 + 0.842912i) q^{79} +(-1.81022 + 1.81022i) q^{81} +(-0.766957 - 0.512464i) q^{83} +(9.68608 + 1.92668i) q^{85} +(-2.04473 - 4.93642i) q^{87} +(2.03287 - 4.90777i) q^{89} +(-8.50928 + 5.68572i) q^{91} +(-2.03480 - 10.2296i) q^{93} -5.06055i q^{95} -5.90730i q^{97} +(0.626056 + 3.14740i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9}+O(q^{10}) \) 56 * q + 8 * q^3 - 8 * q^5 + 8 * q^7 - 8 * q^9	\( 56 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9} + 8 q^{11} - 8 q^{13} + 8 q^{15} - 8 q^{17} + 8 q^{19} - 8 q^{21} + 8 q^{23} - 8 q^{25} + 8 q^{27} - 8 q^{29} + 8 q^{35} - 8 q^{37} + 8 q^{39} - 8 q^{41} + 8 q^{43} - 8 q^{45} + 8 q^{47} - 8 q^{49} - 24 q^{51} - 8 q^{53} - 56 q^{55} - 8 q^{57} - 56 q^{59} - 8 q^{61} - 64 q^{63} - 16 q^{65} - 72 q^{67} - 8 q^{69} - 56 q^{71} - 8 q^{73} - 56 q^{75} - 8 q^{77} - 24 q^{79} - 8 q^{81} + 8 q^{83} - 8 q^{85} + 8 q^{87} - 8 q^{89} + 8 q^{91} + 16 q^{93} - 16 q^{99}+O(q^{100}) \) 56 * q + 8 * q^3 - 8 * q^5 + 8 * q^7 - 8 * q^9 + 8 * q^11 - 8 * q^13 + 8 * q^15 - 8 * q^17 + 8 * q^19 - 8 * q^21 + 8 * q^23 - 8 * q^25 + 8 * q^27 - 8 * q^29 + 8 * q^35 - 8 * q^37 + 8 * q^39 - 8 * q^41 + 8 * q^43 - 8 * q^45 + 8 * q^47 - 8 * q^49 - 24 * q^51 - 8 * q^53 - 56 * q^55 - 8 * q^57 - 56 * q^59 - 8 * q^61 - 64 * q^63 - 16 * q^65 - 72 * q^67 - 8 * q^69 - 56 * q^71 - 8 * q^73 - 56 * q^75 - 8 * q^77 - 24 * q^79 - 8 * q^81 + 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^89 + 8 * q^91 + 16 * q^93 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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