LMFDB - Embedded newform 896.2.u.c.113.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(113,896)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("896.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.u (of order $8$, degree $4$, 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:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$13$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 224)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			113.12
Character	$\chi$	$=$	896.113
Dual form			896.2.u.c.785.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951433 + 2.29696i) q^{3} +(2.43243 + 1.00754i) q^{5} +(0.707107 + 0.707107i) q^{7} +(-2.24949 + 2.24949i) q^{9} +O(q^{10})$	\(q+(0.951433 + 2.29696i) q^{3} +(2.43243 + 1.00754i) q^{5} +(0.707107 + 0.707107i) q^{7} +(-2.24949 + 2.24949i) q^{9} +(-1.78280 + 4.30406i) q^{11} +(-3.07190 + 1.27242i) q^{13} +6.54580i q^{15} -5.68680i q^{17} +(-4.96193 + 2.05530i) q^{19} +(-0.951433 + 2.29696i) q^{21} +(1.95665 - 1.95665i) q^{23} +(1.36602 + 1.36602i) q^{25} +(-0.416353 - 0.172459i) q^{27} +(-0.351023 - 0.847445i) q^{29} +5.83199 q^{31} -11.5825 q^{33} +(1.00754 + 2.43243i) q^{35} +(10.3708 + 4.29574i) q^{37} +(-5.84542 - 5.84542i) q^{39} +(5.18689 - 5.18689i) q^{41} +(2.98343 - 7.20263i) q^{43} +(-7.73818 + 3.20526i) q^{45} +5.68010i q^{47} +1.00000i q^{49} +(13.0624 - 5.41061i) q^{51} +(-2.40269 + 5.80060i) q^{53} +(-8.67306 + 8.67306i) q^{55} +(-9.44189 - 9.44189i) q^{57} +(-2.82084 - 1.16843i) q^{59} +(1.52240 + 3.67539i) q^{61} -3.18126 q^{63} -8.75420 q^{65} +(-4.74280 - 11.4501i) q^{67} +(6.35599 + 2.63274i) q^{69} +(-6.92236 - 6.92236i) q^{71} +(0.588366 - 0.588366i) q^{73} +(-1.83802 + 4.43736i) q^{75} +(-4.30406 + 1.78280i) q^{77} +5.65657i q^{79} +8.42336i q^{81} +(-5.68616 + 2.35528i) q^{83} +(5.72970 - 13.8327i) q^{85} +(1.61257 - 1.61257i) q^{87} +(9.56223 + 9.56223i) q^{89} +(-3.07190 - 1.27242i) q^{91} +(5.54875 + 13.3959i) q^{93} -14.1403 q^{95} -7.57309 q^{97} +(-5.67156 - 13.6924i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q+O(q^{10}) $ 52 * q	$ 52 q + 20 q^{23} + 24 q^{27} - 48 q^{33} + 24 q^{39} + 44 q^{43} + 40 q^{45} - 16 q^{51} - 36 q^{53} - 32 q^{55} - 32 q^{61} - 68 q^{63} + 80 q^{65} - 28 q^{67} - 32 q^{69} - 32 q^{75} - 12 q^{77} + 64 q^{85} + 56 q^{87} + 64 q^{95} - 72 q^{97} + 64 q^{99}+O(q^{100}) $ 52 * q + 20 * q^23 + 24 * q^27 - 48 * q^33 + 24 * q^39 + 44 * q^43 + 40 * q^45 - 16 * q^51 - 36 * q^53 - 32 * q^55 - 32 * q^61 - 68 * q^63 + 80 * q^65 - 28 * q^67 - 32 * q^69 - 32 * q^75 - 12 * q^77 + 64 * q^85 + 56 * q^87 + 64 * q^95 - 72 * q^97 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{8}\right)$

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
$3$	0.951433	+	2.29696i	0.549310	+	1.32615i	0.917993	+	0.396597i	$0.129809\pi$
$3$	0.951433	+	2.29696i	0.549310	+	1.32615i	−0.368683	+	0.929555i	$0.620191\pi$
$4$		0			0
$5$	2.43243	+	1.00754i	1.08781	+	0.450587i	0.853244	−	0.521512i	$-0.174632\pi$
$5$	2.43243	+	1.00754i	1.08781	+	0.450587i	0.234570	+	0.972099i	$0.424632\pi$
$6$		0			0
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$		0			0
$9$	−2.24949	+	2.24949i	−0.749831	+	0.749831i
$10$		0			0
$11$	−1.78280	+	4.30406i	−0.537535	+	1.29772i	0.388904	+	0.921278i	$0.372854\pi$
$11$	−1.78280	+	4.30406i	−0.537535	+	1.29772i	−0.926439	+	0.376445i	$0.877146\pi$
$12$		0			0
$13$	−3.07190	+	1.27242i	−0.851993	+	0.352907i	−0.765571	−	0.643352i	$-0.777543\pi$
$13$	−3.07190	+	1.27242i	−0.851993	+	0.352907i	−0.0864220	+	0.996259i	$0.527543\pi$
$14$		0			0
$15$			6.54580i			1.69012i
$16$		0			0
$17$		−	5.68680i		−	1.37925i	−0.724166	−	0.689626i	$-0.757775\pi$
$17$		−	5.68680i		−	1.37925i	0.724166	−	0.689626i	$-0.242225\pi$
$18$		0			0
$19$	−4.96193	+	2.05530i	−1.13834	+	0.471518i	−0.870610	−	0.491975i	$-0.836275\pi$
$19$	−4.96193	+	2.05530i	−1.13834	+	0.471518i	−0.267735	+	0.963493i	$0.586275\pi$
$20$		0			0
$21$	−0.951433	+	2.29696i	−0.207620	+	0.501238i
$22$		0			0
$23$	1.95665	−	1.95665i	0.407991	−	0.407991i	−0.473047	−	0.881037i	$-0.656846\pi$
$23$	1.95665	−	1.95665i	0.407991	−	0.407991i	0.881037	+	0.473047i	$0.156846\pi$
$24$		0			0
$25$	1.36602	+	1.36602i	0.273203	+	0.273203i
$26$		0			0
$27$	−0.416353	−	0.172459i	−0.0801271	−	0.0331897i
$28$		0			0
$29$	−0.351023	−	0.847445i	−0.0651833	−	0.157367i	0.887931	−	0.459976i	$-0.152142\pi$
$29$	−0.351023	−	0.847445i	−0.0651833	−	0.157367i	−0.953115	+	0.302610i	$0.902142\pi$
$30$		0			0
$31$	5.83199			1.04746			0.523728	−	0.851886i	$-0.324541\pi$
$31$	5.83199			1.04746			0.523728	+	0.851886i	$0.324541\pi$
$32$		0			0
$33$	−11.5825			−2.01625
$34$		0			0
$35$	1.00754	+	2.43243i	0.170306	+	0.411155i
$36$		0			0
$37$	10.3708	+	4.29574i	1.70496	+	0.706216i	0.999995	−	0.00302981i	$-0.000964419\pi$
$37$	10.3708	+	4.29574i	1.70496	+	0.706216i	0.704961	+	0.709246i	$0.250964\pi$
$38$		0			0
$39$	−5.84542	−	5.84542i	−0.936017	−	0.936017i
$40$		0			0
$41$	5.18689	−	5.18689i	0.810056	−	0.810056i	−0.174586	−	0.984642i	$-0.555859\pi$
$41$	5.18689	−	5.18689i	0.810056	−	0.810056i	0.984642	+	0.174586i	$0.0558588\pi$
$42$		0			0
$43$	2.98343	−	7.20263i	0.454968	−	1.09839i	−0.515441	−	0.856925i	$-0.672372\pi$
$43$	2.98343	−	7.20263i	0.454968	−	1.09839i	0.970409	−	0.241466i	$-0.0776281\pi$
$44$		0			0
$45$	−7.73818	+	3.20526i	−1.15354	+	0.477812i
$46$		0			0
$47$			5.68010i			0.828528i	0.910157	+	0.414264i	$0.135961\pi$
$47$			5.68010i			0.828528i	−0.910157	+	0.414264i	$0.864039\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$	13.0624	−	5.41061i	1.82910	−	0.757637i
$52$		0			0
$53$	−2.40269	+	5.80060i	−0.330034	+	0.796774i	0.668554	+	0.743663i	$0.266913\pi$
$53$	−2.40269	+	5.80060i	−0.330034	+	0.796774i	−0.998589	+	0.0531103i	$0.983087\pi$
$54$		0			0
$55$	−8.67306	+	8.67306i	−1.16948	+	1.16948i
$56$		0			0
$57$	−9.44189	−	9.44189i	−1.25061	−	1.25061i
$58$		0			0
$59$	−2.82084	−	1.16843i	−0.367242	−	0.152117i	0.191428	−	0.981507i	$-0.438688\pi$
$59$	−2.82084	−	1.16843i	−0.367242	−	0.152117i	−0.558670	+	0.829390i	$0.688688\pi$
$60$		0			0
$61$	1.52240	+	3.67539i	0.194923	+	0.470586i	0.990877	−	0.134772i	$-0.0430301\pi$
$61$	1.52240	+	3.67539i	0.194923	+	0.470586i	−0.795954	+	0.605358i	$0.793030\pi$
$62$		0			0
$63$	−3.18126			−0.400801
$64$		0			0
$65$	−8.75420			−1.08582
$66$		0			0
$67$	−4.74280	−	11.4501i	−0.579425	−	1.39886i	−0.893330	−	0.449402i	$-0.851637\pi$
$67$	−4.74280	−	11.4501i	−0.579425	−	1.39886i	0.313905	−	0.949454i	$-0.398363\pi$
$68$		0			0
$69$	6.35599	+	2.63274i	0.765171	+	0.316944i
$70$		0			0
$71$	−6.92236	−	6.92236i	−0.821534	−	0.821534i	0.164794	−	0.986328i	$-0.447304\pi$
$71$	−6.92236	−	6.92236i	−0.821534	−	0.821534i	−0.986328	+	0.164794i	$0.947304\pi$
$72$		0			0
$73$	0.588366	−	0.588366i	0.0688631	−	0.0688631i	−0.671836	−	0.740700i	$-0.734494\pi$
$73$	0.588366	−	0.588366i	0.0688631	−	0.0688631i	0.740700	+	0.671836i	$0.234494\pi$
$74$		0			0
$75$	−1.83802	+	4.43736i	−0.212236	+	0.512383i
$76$		0			0
$77$	−4.30406	+	1.78280i	−0.490493	+	0.203169i
$78$		0			0
$79$			5.65657i			0.636414i	0.948021	+	0.318207i	$0.103081\pi$
$79$			5.65657i			0.636414i	−0.948021	+	0.318207i	$0.896919\pi$
$80$		0			0
$81$			8.42336i			0.935929i
$82$		0			0
$83$	−5.68616	+	2.35528i	−0.624137	+	0.258526i	−0.672260	−	0.740316i	$-0.734676\pi$
$83$	−5.68616	+	2.35528i	−0.624137	+	0.258526i	0.0481229	+	0.998841i	$0.484676\pi$
$84$		0			0
$85$	5.72970	−	13.8327i	0.621473	−	1.50037i
$86$		0			0
$87$	1.61257	−	1.61257i	0.172886	−	0.172886i
$88$		0			0
$89$	9.56223	+	9.56223i	1.01359	+	1.01359i	0.999906	+	0.0136885i	$0.00435733\pi$
$89$	9.56223	+	9.56223i	1.01359	+	1.01359i	0.0136885	+	0.999906i	$0.495643\pi$
$90$		0			0
$91$	−3.07190	−	1.27242i	−0.322023	−	0.133386i
$92$		0			0
$93$	5.54875	+	13.3959i	0.575378	+	1.38909i
$94$		0			0
$95$	−14.1403			−1.45077
$96$		0			0
$97$	−7.57309			−0.768930			−0.384465	−	0.923139i	$-0.625614\pi$
$97$	−7.57309			−0.768930			−0.384465	+	0.923139i	$0.625614\pi$
$98$		0			0
$99$	−5.67156	−	13.6924i	−0.570013	−	1.37613i
$100$		0			0
$101$	9.26603	+	3.83811i	0.922004	+	0.381907i	0.792640	−	0.609690i	$-0.208706\pi$
$101$	9.26603	+	3.83811i	0.922004	+	0.381907i	0.129365	+	0.991597i	$0.458706\pi$
$102$		0			0
$103$	−0.365215	−	0.365215i	−0.0359857	−	0.0359857i	0.688885	−	0.724871i	$-0.258101\pi$
$103$	−0.365215	−	0.365215i	−0.0359857	−	0.0359857i	−0.724871	+	0.688885i	$0.758101\pi$
$104$		0			0
$105$	−4.62858	+	4.62858i	−0.451703	+	0.451703i
$106$		0			0
$107$	1.57897	−	3.81196i	0.152645	−	0.368517i	−0.828997	−	0.559254i	$-0.811088\pi$
$107$	1.57897	−	3.81196i	0.152645	−	0.368517i	0.981641	+	0.190737i	$0.0610878\pi$
$108$		0			0
$109$	8.46350	−	3.50570i	0.810656	−	0.335785i	0.0614406	−	0.998111i	$-0.480431\pi$
$109$	8.46350	−	3.50570i	0.810656	−	0.335785i	0.749216	+	0.662326i	$0.230431\pi$
$110$		0			0
$111$			27.9086i			2.64896i
$112$		0			0
$113$		−	1.79894i		−	0.169230i	−0.996414	−	0.0846150i	$-0.973034\pi$
$113$		−	1.79894i		−	0.169230i	0.996414	−	0.0846150i	$-0.0269660\pi$
$114$		0			0
$115$	6.73083	−	2.78800i	0.627653	−	0.259983i
$116$		0			0
$117$	4.04791	−	9.77253i	0.374230	−	0.903471i
$118$		0			0
$119$	4.02117	−	4.02117i	0.368620	−	0.368620i
$120$		0			0
$121$	−7.56840	−	7.56840i	−0.688036	−	0.688036i
$122$		0			0
$123$	16.8491	+	6.97911i	1.51923	+	0.629285i
$124$		0			0
$125$	−3.09131	−	7.46307i	−0.276495	−	0.667517i
$126$		0			0
$127$	5.27769			0.468320			0.234160	−	0.972198i	$-0.424766\pi$
$127$	5.27769			0.468320			0.234160	+	0.972198i	$0.424766\pi$
$128$		0			0
$129$	19.3827			1.70655
$130$		0			0
$131$	7.81378	+	18.8641i	0.682693	+	1.64817i	0.759007	+	0.651082i	$0.225685\pi$
$131$	7.81378	+	18.8641i	0.682693	+	1.64817i	−0.0763142	+	0.997084i	$0.524315\pi$
$132$		0			0
$133$	−4.96193	−	2.05530i	−0.430254	−	0.178217i
$134$		0			0
$135$	−0.838987	−	0.838987i	−0.0722085	−	0.0722085i
$136$		0			0
$137$	0.975495	−	0.975495i	0.0833422	−	0.0833422i	−0.664207	−	0.747549i	$-0.731231\pi$
$137$	0.975495	−	0.975495i	0.0833422	−	0.0833422i	0.747549	+	0.664207i	$0.231231\pi$
$138$		0			0
$139$	7.40149	−	17.8688i	0.627786	−	1.51561i	−0.214581	−	0.976706i	$-0.568839\pi$
$139$	7.40149	−	17.8688i	0.627786	−	1.51561i	0.842367	−	0.538904i	$-0.181161\pi$
$140$		0			0
$141$	−13.0470	+	5.40424i	−1.09875	+	0.455119i
$142$		0			0
$143$		−	15.4901i		−	1.29535i
$144$		0			0
$145$		−	2.41502i		−	0.200556i
$146$		0			0
$147$	−2.29696	+	0.951433i	−0.189450	+	0.0784729i
$148$		0			0
$149$	3.56443	−	8.60530i	0.292010	−	0.704974i	−0.707989	−	0.706223i	$-0.750398\pi$
$149$	3.56443	−	8.60530i	0.292010	−	0.704974i	0.999999	+	0.00124907i	$0.000397593\pi$
$150$		0			0
$151$	12.6676	−	12.6676i	1.03087	−	1.03087i	0.0313657	−	0.999508i	$-0.490014\pi$
$151$	12.6676	−	12.6676i	1.03087	−	1.03087i	0.999508	−	0.0313657i	$-0.00998564\pi$
$152$		0			0
$153$	12.7924	+	12.7924i	1.03421	+	1.03421i
$154$		0			0
$155$	14.1859	+	5.87598i	1.13944	+	0.471970i
$156$		0			0
$157$	−1.75570	−	4.23863i	−0.140120	−	0.338279i	0.838205	−	0.545355i	$-0.183605\pi$
$157$	−1.75570	−	4.23863i	−0.140120	−	0.338279i	−0.978325	+	0.207076i	$0.933605\pi$
$158$		0			0
$159$	−15.6098			−1.23793
$160$		0			0
$161$	2.76713			0.218080
$162$		0			0
$163$	−1.39627	−	3.37089i	−0.109364	−	0.264029i	0.859717	−	0.510771i	$-0.170640\pi$
$163$	−1.39627	−	3.37089i	−0.109364	−	0.264029i	−0.969081	+	0.246742i	$0.920640\pi$
$164$		0			0
$165$	−28.1735	−	11.6699i	−2.19331	−	0.908497i
$166$		0			0
$167$	9.04980	+	9.04980i	0.700294	+	0.700294i	0.964474	−	0.264179i	$-0.0851011\pi$
$167$	9.04980	+	9.04980i	0.700294	+	0.700294i	−0.264179	+	0.964474i	$0.585101\pi$
$168$		0			0
$169$	−1.37486	+	1.37486i	−0.105758	+	0.105758i
$170$		0			0
$171$	6.53844	−	15.7852i	0.500007	−	1.20712i
$172$		0			0
$173$	7.34660	−	3.04306i	0.558552	−	0.231360i	−0.0855047	−	0.996338i	$-0.527250\pi$
$173$	7.34660	−	3.04306i	0.558552	−	0.231360i	0.644056	+	0.764978i	$0.277250\pi$
$174$		0			0
$175$			1.93184i			0.146033i
$176$		0			0
$177$		−	7.59104i		−	0.570578i
$178$		0			0
$179$	0.0747400	−	0.0309583i	0.00558633	−	0.00231393i	−0.379889	−	0.925032i	$-0.624038\pi$
$179$	0.0747400	−	0.0309583i	0.00558633	−	0.00231393i	0.385475	+	0.922718i	$0.374038\pi$
$180$		0			0
$181$	−7.59834	+	18.3440i	−0.564780	+	1.36350i	0.341125	+	0.940018i	$0.389192\pi$
$181$	−7.59834	+	18.3440i	−0.564780	+	1.36350i	−0.905905	+	0.423482i	$0.860808\pi$
$182$		0			0
$183$	−6.99378	+	6.99378i	−0.516995	+	0.516995i
$184$		0			0
$185$	20.8982	+	20.8982i	1.53646	+	1.53646i
$186$		0			0
$187$	24.4763	+	10.1384i	1.78989	+	0.741395i
$188$		0			0
$189$	−0.172459	−	0.416353i	−0.0125445	−	0.0302852i
$190$		0			0
$191$	−8.10976			−0.586801			−0.293401	−	0.955990i	$-0.594787\pi$
$191$	−8.10976			−0.586801			−0.293401	+	0.955990i	$0.594787\pi$
$192$		0			0
$193$	−19.1690			−1.37981			−0.689907	−	0.723898i	$-0.742348\pi$
$193$	−19.1690			−1.37981			−0.689907	+	0.723898i	$0.742348\pi$
$194$		0			0
$195$	−8.32904	−	20.1081i	−0.596455	−	1.43997i
$196$		0			0
$197$	12.9903	+	5.38074i	0.925518	+	0.383362i	0.793976	−	0.607949i	$-0.208007\pi$
$197$	12.9903	+	5.38074i	0.925518	+	0.383362i	0.131542	+	0.991311i	$0.458007\pi$
$198$		0			0
$199$	−0.762165	−	0.762165i	−0.0540285	−	0.0540285i	0.679576	−	0.733605i	$-0.262164\pi$
$199$	−0.762165	−	0.762165i	−0.0540285	−	0.0540285i	−0.733605	+	0.679576i	$0.762164\pi$
$200$		0			0
$201$	21.7881	−	21.7881i	1.53681	−	1.53681i
$202$		0			0
$203$	0.351023	−	0.847445i	0.0246370	−	0.0594789i
$204$		0			0
$205$	17.8427	−	7.39070i	1.24619	−	0.516189i
$206$		0			0
$207$			8.80296i			0.611848i
$208$		0			0
$209$		−	25.0206i		−	1.73071i
$210$		0			0
$211$	−23.0889	+	9.56374i	−1.58951	+	0.658395i	−0.989883	−	0.141887i	$-0.954683\pi$
$211$	−23.0889	+	9.56374i	−1.58951	+	0.658395i	−0.599623	+	0.800282i	$0.704683\pi$
$212$		0			0
$213$	9.31425	−	22.4866i	0.638202	−	1.54076i
$214$		0			0
$215$	14.5139	−	14.5139i	0.989842	−	0.989842i
$216$		0			0
$217$	4.12384	+	4.12384i	0.279944	+	0.279944i
$218$		0			0
$219$	1.91125	+	0.791664i	0.129150	+	0.0534957i
$220$		0			0
$221$	7.23602	+	17.4693i	0.486747	+	1.17511i
$222$		0			0
$223$	−0.575573			−0.0385432			−0.0192716	−	0.999814i	$-0.506135\pi$
$223$	−0.575573			−0.0385432			−0.0192716	+	0.999814i	$0.506135\pi$
$224$		0			0
$225$	−6.14569			−0.409713
$226$		0			0
$227$	−2.73500	−	6.60287i	−0.181528	−	0.438248i	0.806754	−	0.590888i	$-0.201222\pi$
$227$	−2.73500	−	6.60287i	−0.181528	−	0.438248i	−0.988282	+	0.152640i	$0.951222\pi$
$228$		0			0
$229$	−9.51574	−	3.94155i	−0.628818	−	0.260465i	0.0454330	−	0.998967i	$-0.485533\pi$
$229$	−9.51574	−	3.94155i	−0.628818	−	0.260465i	−0.674251	+	0.738503i	$0.735533\pi$
$230$		0			0
$231$	−8.19005	−	8.19005i	−0.538866	−	0.538866i
$232$		0			0
$233$	−14.9151	+	14.9151i	−0.977121	+	0.977121i	−0.999744	−	0.0226234i	$-0.992798\pi$
$233$	−14.9151	+	14.9151i	−0.977121	+	0.977121i	0.0226234	+	0.999744i	$0.492798\pi$
$234$		0			0
$235$	−5.72295	+	13.8164i	−0.373324	+	0.901285i
$236$		0			0
$237$	−12.9929	+	5.38185i	−0.843982	+	0.349589i
$238$		0			0
$239$		−	24.2799i		−	1.57054i	−0.619155	−	0.785269i	$-0.712525\pi$
$239$		−	24.2799i		−	1.57054i	0.619155	−	0.785269i	$-0.287475\pi$
$240$		0			0
$241$		−	22.1413i		−	1.42625i	−0.701039	−	0.713123i	$-0.747280\pi$
$241$		−	22.1413i		−	1.42625i	0.701039	−	0.713123i	$-0.252720\pi$
$242$		0			0
$243$	−20.5972	+	8.53164i	−1.32131	+	0.547305i
$244$		0			0
$245$	−1.00754	+	2.43243i	−0.0643696	+	0.155402i
$246$		0			0
$247$	12.6274	−	12.6274i	0.803460	−	0.803460i
$248$		0			0
$249$	−10.8200	−	10.8200i	−0.685689	−	0.685689i
$250$		0			0
$251$	−12.2356	−	5.06815i	−0.772304	−	0.319899i	−0.0384986	−	0.999259i	$-0.512258\pi$
$251$	−12.2356	−	5.06815i	−0.772304	−	0.319899i	−0.733805	+	0.679360i	$0.762258\pi$
$252$		0			0
$253$	4.93324	+	11.9099i	0.310150	+	0.748768i
$254$		0			0
$255$	37.2247			2.33110
$256$		0			0
$257$	13.6722			0.852848			0.426424	−	0.904523i	$-0.359773\pi$
$257$	13.6722			0.852848			0.426424	+	0.904523i	$0.359773\pi$
$258$		0			0
$259$	4.29574	+	10.3708i	0.266925	+	0.644413i
$260$		0			0
$261$	2.69594	+	1.11670i	0.166875	+	0.0691218i
$262$		0			0
$263$	9.03142	+	9.03142i	0.556901	+	0.556901i	0.928424	−	0.371523i	$-0.121164\pi$
$263$	9.03142	+	9.03142i	0.556901	+	0.556901i	−0.371523	+	0.928424i	$0.621164\pi$
$264$		0			0
$265$	−11.6887	+	11.6887i	−0.718032	+	0.718032i
$266$		0			0
$267$	−12.8663	+	31.0619i	−0.787403	+	1.90096i
$268$		0			0
$269$	−4.30799	+	1.78443i	−0.262663	+	0.108799i	−0.510129	−	0.860098i	$-0.670402\pi$
$269$	−4.30799	+	1.78443i	−0.262663	+	0.108799i	0.247466	+	0.968897i	$0.420402\pi$
$270$		0			0
$271$		−	25.2374i		−	1.53306i	−0.642208	−	0.766531i	$-0.721981\pi$
$271$		−	25.2374i		−	1.53306i	0.642208	−	0.766531i	$-0.278019\pi$
$272$		0			0
$273$		−	8.26667i		−	0.500322i
$274$		0			0
$275$	−8.31476	+	3.44409i	−0.501399	+	0.207686i
$276$		0			0
$277$	11.2951	−	27.2687i	0.678655	−	1.63842i	−0.0878144	−	0.996137i	$-0.527988\pi$
$277$	11.2951	−	27.2687i	0.678655	−	1.63842i	0.766469	−	0.642281i	$-0.222012\pi$
$278$		0			0
$279$	−13.1190	+	13.1190i	−0.785414	+	0.785414i
$280$		0			0
$281$	−5.07693	−	5.07693i	−0.302864	−	0.302864i	0.539269	−	0.842133i	$-0.318701\pi$
$281$	−5.07693	−	5.07693i	−0.302864	−	0.302864i	−0.842133	+	0.539269i	$0.818701\pi$
$282$		0			0
$283$	15.0500	+	6.23392i	0.894631	+	0.370568i	0.782153	−	0.623086i	$-0.214121\pi$
$283$	15.0500	+	6.23392i	0.894631	+	0.370568i	0.112478	+	0.993654i	$0.464121\pi$
$284$		0			0
$285$	−13.4536	−	32.4798i	−0.796921	−	1.92394i
$286$		0			0
$287$	7.33536			0.432993
$288$		0			0
$289$	−15.3397			−0.902334
$290$		0			0
$291$	−7.20528	−	17.3951i	−0.422381	−	1.01972i
$292$		0			0
$293$	−3.64388	−	1.50934i	−0.212878	−	0.0881768i	0.273696	−	0.961816i	$-0.411754\pi$
$293$	−3.64388	−	1.50934i	−0.212878	−	0.0881768i	−0.486574	+	0.873639i	$0.661754\pi$
$294$		0			0
$295$	−5.68424	−	5.68424i	−0.330949	−	0.330949i
$296$		0			0
$297$	1.48455	−	1.48455i	0.0861422	−	0.0861422i
$298$		0			0
$299$	−3.52096	+	8.50035i	−0.203622	+	0.491588i
$300$		0			0
$301$	7.20263	−	2.98343i	0.415153	−	0.171962i
$302$		0			0
$303$			24.9354i			1.43250i
$304$		0			0
$305$			10.4740i			0.599740i
$306$		0			0
$307$	−3.60399	+	1.49282i	−0.205691	+	0.0851998i	−0.483150	−	0.875537i	$-0.660508\pi$
$307$	−3.60399	+	1.49282i	−0.205691	+	0.0851998i	0.277460	+	0.960737i	$0.410508\pi$
$308$		0			0
$309$	0.491408	−	1.18636i	0.0279552	−	0.0674898i
$310$		0			0
$311$	1.98833	−	1.98833i	0.112748	−	0.112748i	−0.648482	−	0.761230i	$-0.724596\pi$
$311$	1.98833	−	1.98833i	0.112748	−	0.112748i	0.761230	+	0.648482i	$0.224596\pi$
$312$		0			0
$313$	−9.61665	−	9.61665i	−0.543565	−	0.543565i	0.381007	−	0.924572i	$-0.375577\pi$
$313$	−9.61665	−	9.61665i	−0.543565	−	0.543565i	−0.924572	+	0.381007i	$0.875577\pi$
$314$		0			0
$315$	−7.73818	−	3.20526i	−0.435997	−	0.180596i
$316$		0			0
$317$	8.93463	+	21.5701i	0.501819	+	1.21150i	0.948492	+	0.316801i	$0.102609\pi$
$317$	8.93463	+	21.5701i	0.501819	+	1.21150i	−0.446673	+	0.894697i	$0.647391\pi$
$318$		0			0
$319$	4.27326			0.239257
$320$		0			0
$321$	10.2582			0.572558
$322$		0			0
$323$	11.6881	+	28.2175i	0.650342	+	1.57006i
$324$		0			0
$325$	−5.93443	−	2.45812i	−0.329183	−	0.136352i
$326$		0			0
$327$	16.1049	+	16.1049i	0.890604	+	0.890604i
$328$		0			0
$329$	−4.01644	+	4.01644i	−0.221434	+	0.221434i
$330$		0			0
$331$	10.9089	−	26.3364i	0.599606	−	1.44758i	−0.274377	−	0.961622i	$-0.588472\pi$
$331$	10.9089	−	26.3364i	0.599606	−	1.44758i	0.873983	−	0.485956i	$-0.161528\pi$
$332$		0			0
$333$	−32.9924	+	13.6659i	−1.80797	+	0.748886i
$334$		0			0
$335$		−	32.6302i		−	1.78278i
$336$		0			0
$337$		−	16.2174i		−	0.883418i	−0.897158	−	0.441709i	$-0.854372\pi$
$337$		−	16.2174i		−	0.883418i	0.897158	−	0.441709i	$-0.145628\pi$
$338$		0			0
$339$	4.13210	−	1.71157i	0.224425	−	0.0929598i
$340$		0			0
$341$	−10.3973	+	25.1012i	−0.563044	+	1.35931i
$342$		0			0
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$		0			0
$345$	12.8079	+	12.8079i	0.689553	+	0.689553i
$346$		0			0
$347$	−20.5850	−	8.52660i	−1.10506	−	0.457732i	−0.245828	−	0.969313i	$-0.579060\pi$
$347$	−20.5850	−	8.52660i	−1.10506	−	0.457732i	−0.859235	+	0.511582i	$0.829060\pi$
$348$		0			0
$349$	−9.98948	−	24.1167i	−0.534724	−	1.29094i	−0.928363	−	0.371674i	$-0.878784\pi$
$349$	−9.98948	−	24.1167i	−0.534724	−	1.29094i	0.393639	−	0.919265i	$-0.371216\pi$
$350$		0			0
$351$	1.49844			0.0799806
$352$		0			0
$353$	27.4438			1.46069			0.730343	−	0.683080i	$-0.239360\pi$
$353$	27.4438			1.46069			0.730343	+	0.683080i	$0.239360\pi$
$354$		0			0
$355$	−9.86355	−	23.8127i	−0.523503	−	1.26385i
$356$		0			0
$357$	13.0624	+	5.41061i	0.691334	+	0.286360i
$358$		0			0
$359$	1.32818	+	1.32818i	0.0700988	+	0.0700988i	0.741287	−	0.671188i	$-0.234216\pi$
$359$	1.32818	+	1.32818i	0.0700988	+	0.0700988i	−0.671188	+	0.741287i	$0.734216\pi$
$360$		0			0
$361$	6.96147	−	6.96147i	0.366393	−	0.366393i
$362$		0			0
$363$	10.1835	−	24.5851i	0.534495	−	1.29039i
$364$		0			0
$365$	2.02396	−	0.838353i	0.105939	−	0.0438814i
$366$		0			0
$367$			20.9471i			1.09343i	0.837319	+	0.546715i	$0.184122\pi$
$367$			20.9471i			1.09343i	−0.837319	+	0.546715i	$0.815878\pi$
$368$		0			0
$369$			23.3357i			1.21481i
$370$		0			0
$371$	−5.80060	+	2.40269i	−0.301152	+	0.124741i
$372$		0			0
$373$	3.72616	−	8.99574i	0.192933	−	0.465782i	−0.797578	−	0.603216i	$-0.793886\pi$
$373$	3.72616	−	8.99574i	0.192933	−	0.465782i	0.990511	+	0.137434i	$0.0438857\pi$
$374$		0			0
$375$	14.2012	−	14.2012i	0.733348	−	0.733348i
$376$		0			0
$377$	2.15662	+	2.15662i	0.111071	+	0.111071i
$378$		0			0
$379$	−26.6919	−	11.0562i	−1.37107	−	0.567917i	−0.428993	−	0.903308i	$-0.641131\pi$
$379$	−26.6919	−	11.0562i	−1.37107	−	0.567917i	−0.942079	+	0.335391i	$0.891131\pi$
$380$		0			0
$381$	5.02137	+	12.1227i	0.257253	+	0.621063i
$382$		0			0
$383$	−0.165877			−0.00847592			−0.00423796	−	0.999991i	$-0.501349\pi$
$383$	−0.165877			−0.00847592			−0.00423796	+	0.999991i	$0.501349\pi$
$384$		0			0
$385$	−12.2656			−0.625111
$386$		0			0
$387$	9.49106	+	22.9135i	0.482458	+	1.16476i
$388$		0			0
$389$	−26.8852	−	11.1362i	−1.36313	−	0.564628i	−0.423215	−	0.906029i	$-0.639099\pi$
$389$	−26.8852	−	11.1362i	−1.36313	−	0.564628i	−0.939918	+	0.341401i	$0.889099\pi$
$390$		0			0
$391$	−11.1271	−	11.1271i	−0.562722	−	0.562722i
$392$		0			0
$393$	−35.8959	+	35.8959i	−1.81071	+	1.81071i
$394$		0			0
$395$	−5.69924	+	13.7592i	−0.286760	+	0.692300i
$396$		0			0
$397$	9.33927	−	3.86845i	0.468725	−	0.194152i	−0.135804	−	0.990736i	$-0.543362\pi$
$397$	9.33927	−	3.86845i	0.468725	−	0.194152i	0.604528	+	0.796584i	$0.293362\pi$
$398$		0			0
$399$		−	13.3528i		−	0.668478i
$400$		0			0
$401$			6.02526i			0.300887i	0.988619	+	0.150443i	$0.0480702\pi$
$401$			6.02526i			0.300887i	−0.988619	+	0.150443i	$0.951930\pi$
$402$		0			0
$403$	−17.9153	+	7.42076i	−0.892425	+	0.369654i
$404$		0			0
$405$	−8.48690	+	20.4892i	−0.421717	+	1.01812i
$406$		0			0
$407$	−36.9783	+	36.9783i	−1.83295	+	1.83295i
$408$		0			0
$409$	2.46836	+	2.46836i	0.122052	+	0.122052i	0.765495	−	0.643442i	$-0.222494\pi$
$409$	2.46836	+	2.46836i	0.122052	+	0.122052i	−0.643442	+	0.765495i	$0.722494\pi$
$410$		0			0
$411$	3.16879	+	1.31256i	0.156305	+	0.0647437i
$412$		0			0
$413$	−1.16843	−	2.82084i	−0.0574947	−	0.138804i
$414$		0			0
$415$	−16.2042			−0.795433
$416$		0			0
$417$	48.0859			2.35478
$418$		0			0
$419$	12.3376	+	29.7856i	0.602732	+	1.45512i	0.870758	+	0.491712i	$0.163629\pi$
$419$	12.3376	+	29.7856i	0.602732	+	1.45512i	−0.268025	+	0.963412i	$0.586371\pi$
$420$		0			0
$421$	11.4194	+	4.73007i	0.556548	+	0.230530i	0.643186	−	0.765710i	$-0.277612\pi$
$421$	11.4194	+	4.73007i	0.556548	+	0.230530i	−0.0866380	+	0.996240i	$0.527612\pi$
$422$		0			0
$423$	−12.7774	−	12.7774i	−0.621256	−	0.621256i
$424$		0			0
$425$	7.76826	−	7.76826i	0.376816	−	0.376816i
$426$		0			0
$427$	−1.52240	+	3.67539i	−0.0736740	+	0.177865i
$428$		0			0
$429$	35.5803	−	14.7378i	1.71783	−	0.711549i
$430$		0			0
$431$			31.6262i			1.52338i	0.647941	+	0.761691i	$0.275630\pi$
$431$			31.6262i			1.52338i	−0.647941	+	0.761691i	$0.724370\pi$
$432$		0			0
$433$			6.30953i			0.303217i	0.988441	+	0.151608i	$0.0484452\pi$
$433$			6.30953i			0.303217i	−0.988441	+	0.151608i	$0.951555\pi$
$434$		0			0
$435$	5.54720	−	2.29773i	0.265968	−	0.110168i
$436$		0			0
$437$	−5.68727	+	13.7303i	−0.272059	+	0.656809i
$438$		0			0
$439$	8.30311	−	8.30311i	0.396286	−	0.396286i	−0.480635	−	0.876921i	$-0.659594\pi$
$439$	8.30311	−	8.30311i	0.396286	−	0.396286i	0.876921	+	0.480635i	$0.159594\pi$
$440$		0			0
$441$	−2.24949	−	2.24949i	−0.107119	−	0.107119i
$442$		0			0
$443$	7.88157	+	3.26465i	0.374465	+	0.155108i	0.561975	−	0.827154i	$-0.310042\pi$
$443$	7.88157	+	3.26465i	0.374465	+	0.155108i	−0.187510	+	0.982263i	$0.560042\pi$
$444$		0			0
$445$	13.6251	+	32.8938i	0.645890	+	1.55932i
$446$		0			0
$447$	23.1574			1.09531
$448$		0			0
$449$	−17.4849			−0.825165			−0.412583	−	0.910920i	$-0.635373\pi$
$449$	−17.4849			−0.825165			−0.412583	+	0.910920i	$0.635373\pi$
$450$		0			0
$451$	13.0775	+	31.5719i	0.615795	+	1.48666i
$452$		0			0
$453$	41.1493	+	17.0446i	1.93336	+	0.800826i
$454$		0			0
$455$	−6.19015	−	6.19015i	−0.290199	−	0.290199i
$456$		0			0
$457$	14.9661	−	14.9661i	0.700086	−	0.700086i	−0.264343	−	0.964429i	$-0.585155\pi$
$457$	14.9661	−	14.9661i	0.700086	−	0.700086i	0.964429	+	0.264343i	$0.0851549\pi$
$458$		0			0
$459$	−0.980739	+	2.36771i	−0.0457770	+	0.110515i
$460$		0			0
$461$	−34.1636	+	14.1510i	−1.59116	+	0.659080i	−0.990131	−	0.140148i	$-0.955242\pi$
$461$	−34.1636	+	14.1510i	−1.59116	+	0.659080i	−0.601028	+	0.799228i	$0.705242\pi$
$462$		0			0
$463$		−	12.5394i		−	0.582755i	−0.956608	−	0.291377i	$-0.905886\pi$
$463$		−	12.5394i		−	0.582755i	0.956608	−	0.291377i	$-0.0941135\pi$
$464$		0			0
$465$			38.1750i			1.77032i
$466$		0			0
$467$	1.61466	−	0.668814i	0.0747176	−	0.0309490i	−0.345012	−	0.938598i	$-0.612125\pi$
$467$	1.61466	−	0.668814i	0.0747176	−	0.0309490i	0.419729	+	0.907649i	$0.362125\pi$
$468$		0			0
$469$	4.74280	−	11.4501i	0.219002	−	0.528718i
$470$		0			0
$471$	8.06554	−	8.06554i	0.371641	−	0.371641i
$472$		0			0
$473$	25.6817	+	25.6817i	1.18085	+	1.18085i
$474$		0			0
$475$	−9.58565	−	3.97051i	−0.439820	−	0.182179i
$476$		0			0
$477$	−7.64358	−	18.4532i	−0.349975	−	0.844915i
$478$		0			0
$479$	13.6711			0.624651			0.312325	−	0.949975i	$-0.398892\pi$
$479$	13.6711			0.624651			0.312325	+	0.949975i	$0.398892\pi$
$480$		0			0
$481$	−37.3242			−1.70184
$482$		0			0
$483$	2.63274	+	6.35599i	0.119794	+	0.289207i
$484$		0			0
$485$	−18.4210	−	7.63022i	−0.836453	−	0.346470i
$486$		0			0
$487$	5.04576	+	5.04576i	0.228645	+	0.228645i	0.812127	−	0.583481i	$-0.198310\pi$
$487$	5.04576	+	5.04576i	0.228645	+	0.228645i	−0.583481	+	0.812127i	$0.698310\pi$
$488$		0			0
$489$	6.41436	−	6.41436i	0.290067	−	0.290067i
$490$		0			0
$491$	−5.50800	+	13.2975i	−0.248573	+	0.600107i	−0.998083	−	0.0618849i	$-0.980289\pi$
$491$	−5.50800	+	13.2975i	−0.248573	+	0.600107i	0.749511	+	0.661992i	$0.230289\pi$
$492$		0			0
$493$	−4.81925	+	1.99620i	−0.217048	+	0.0899042i
$494$		0			0
$495$		−	39.0200i		−	1.75382i
$496$		0			0
$497$		−	9.78970i		−	0.439128i
$498$		0			0
$499$	−7.69740	+	3.18837i	−0.344583	+	0.142731i	−0.548262	−	0.836307i	$-0.684710\pi$
$499$	−7.69740	+	3.18837i	−0.344583	+	0.142731i	0.203679	+	0.979038i	$0.434710\pi$
$500$		0			0
$501$	−12.1768	+	29.3973i	−0.544018	+	1.31338i
$502$		0			0
$503$	−3.92716	+	3.92716i	−0.175103	+	0.175103i	−0.789217	−	0.614114i	$-0.789514\pi$
$503$	−3.92716	+	3.92716i	−0.175103	+	0.175103i	0.614114	+	0.789217i	$0.289514\pi$
$504$		0			0
$505$	18.6719	+	18.6719i	0.830887	+	0.830887i
$506$		0			0
$507$	−4.46609	−	1.84991i	−0.198346	−	0.0821576i
$508$		0			0
$509$	−2.49836	−	6.03158i	−0.110738	−	0.267345i	0.858789	−	0.512329i	$-0.171217\pi$
$509$	−2.49836	−	6.03158i	−0.110738	−	0.267345i	−0.969527	+	0.244984i	$0.921217\pi$
$510$		0			0
$511$	0.832076			0.0368089
$512$		0			0
$513$	2.42037			0.106862
$514$		0			0
$515$	−0.520388	−	1.25633i	−0.0229310	−	0.0553604i
$516$		0			0
$517$	−24.4475	−	10.1265i	−1.07520	−	0.445363i
$518$		0			0
$519$	13.9796	+	13.9796i	0.613636	+	0.613636i
$520$		0			0
$521$	−17.8501	+	17.8501i	−0.782029	+	0.782029i	−0.980173	−	0.198144i	$-0.936509\pi$
$521$	−17.8501	+	17.8501i	−0.782029	+	0.782029i	0.198144	+	0.980173i	$0.436509\pi$
$522$		0			0
$523$	2.00194	−	4.83311i	0.0875387	−	0.211337i	−0.874047	−	0.485841i	$-0.838514\pi$
$523$	2.00194	−	4.83311i	0.0875387	−	0.211337i	0.961586	+	0.274504i	$0.0885135\pi$
$524$		0			0
$525$	−4.43736	+	1.83802i	−0.193662	+	0.0802176i
$526$		0			0
$527$		−	33.1653i		−	1.44470i
$528$		0			0
$529$			15.3430i			0.667087i
$530$		0			0
$531$	8.97383	−	3.71708i	0.389431	−	0.161308i
$532$		0			0
$533$	−9.33369	+	22.5335i	−0.404287	+	0.976036i
$534$		0			0
$535$	7.68144	−	7.68144i	0.332098	−	0.332098i
$536$		0			0
$537$	0.142220	+	0.142220i	0.00613725	+	0.00613725i
$538$		0			0
$539$	−4.30406	−	1.78280i	−0.185389	−	0.0767907i
$540$		0			0
$541$	−15.0049	−	36.2251i	−0.645112	−	1.55744i	−0.819698	−	0.572797i	$-0.805859\pi$
$541$	−15.0049	−	36.2251i	−0.645112	−	1.55744i	0.174585	−	0.984642i	$-0.444141\pi$
$542$		0			0
$543$	−49.3648			−2.11845
$544$		0			0
$545$	24.1190			1.03314
$546$		0			0
$547$	−3.24372	−	7.83102i	−0.138691	−	0.334830i	0.839239	−	0.543763i	$-0.183001\pi$
$547$	−3.24372	−	7.83102i	−0.138691	−	0.334830i	−0.977930	+	0.208933i	$0.933001\pi$
$548$		0			0
$549$	−11.6924	−	4.84315i	−0.499019	−	0.206700i
$550$		0			0
$551$	3.48350	+	3.48350i	0.148402	+	0.148402i
$552$		0			0
$553$	−3.99980	+	3.99980i	−0.170089	+	0.170089i
$554$		0			0
$555$	−28.1191	+	67.8855i	−1.19359	+	2.88158i
$556$		0			0
$557$	1.09232	−	0.452455i	0.0462832	−	0.0191711i	−0.359422	−	0.933175i	$-0.617026\pi$
$557$	1.09232	−	0.452455i	0.0462832	−	0.0191711i	0.405705	+	0.914004i	$0.367026\pi$
$558$		0			0
$559$			25.9220i			1.09638i
$560$		0			0
$561$			65.8673i			2.78092i
$562$		0			0
$563$	23.2825	−	9.64391i	0.981239	−	0.406442i	0.166354	−	0.986066i	$-0.446800\pi$
$563$	23.2825	−	9.64391i	0.981239	−	0.406442i	0.814884	+	0.579624i	$0.196800\pi$
$564$		0			0
$565$	1.81251	−	4.37579i	0.0762529	−	0.184091i
$566$		0			0
$567$	−5.95621	+	5.95621i	−0.250137	+	0.250137i
$568$		0			0
$569$	−16.7301	−	16.7301i	−0.701364	−	0.701364i	0.263339	−	0.964703i	$-0.415176\pi$
$569$	−16.7301	−	16.7301i	−0.701364	−	0.701364i	−0.964703	+	0.263339i	$0.915176\pi$
$570$		0			0
$571$	−21.4095	−	8.86811i	−0.895960	−	0.371119i	−0.113294	−	0.993561i	$-0.536140\pi$
$571$	−21.4095	−	8.86811i	−0.895960	−	0.371119i	−0.782665	+	0.622443i	$0.786140\pi$
$572$		0			0
$573$	−7.71589	−	18.6278i	−0.322336	−	0.778188i
$574$		0			0
$575$	5.34565			0.222929
$576$		0			0
$577$	18.2366			0.759199			0.379599	−	0.925151i	$-0.376062\pi$
$577$	18.2366			0.759199			0.379599	+	0.925151i	$0.376062\pi$
$578$		0			0
$579$	−18.2380	−	44.0304i	−0.757945	−	1.82984i
$580$		0			0
$581$	−5.68616	−	2.35528i	−0.235901	−	0.0977136i
$582$		0			0
$583$	−20.6826	−	20.6826i	−0.856587	−	0.856587i
$584$		0			0
$585$	19.6925	−	19.6925i	0.814185	−	0.814185i
$586$		0			0
$587$	2.43633	−	5.88182i	0.100558	−	0.242769i	−0.865592	−	0.500750i	$-0.833057\pi$
$587$	2.43633	−	5.88182i	0.100558	−	0.242769i	0.966150	+	0.257982i	$0.0830574\pi$
$588$		0			0
$589$	−28.9379	+	11.9865i	−1.19237	+	0.493894i
$590$		0			0
$591$			34.9576i			1.43796i
$592$		0			0
$593$			36.9247i			1.51631i	0.652072	+	0.758157i	$0.273900\pi$
$593$			36.9247i			1.51631i	−0.652072	+	0.758157i	$0.726100\pi$
$594$		0			0
$595$	13.8327	−	5.72970i	0.567086	−	0.234895i
$596$		0			0
$597$	1.02552	−	2.47581i	0.0419716	−	0.101328i
$598$		0			0
$599$	−7.00201	+	7.00201i	−0.286094	+	0.286094i	−0.835534	−	0.549439i	$-0.814841\pi$
$599$	−7.00201	+	7.00201i	−0.286094	+	0.286094i	0.549439	+	0.835534i	$0.314841\pi$
$600$		0			0
$601$	11.4941	+	11.4941i	0.468853	+	0.468853i	0.901543	−	0.432690i	$-0.142435\pi$
$601$	11.4941	+	11.4941i	0.468853	+	0.468853i	−0.432690	+	0.901543i	$0.642435\pi$
$602$		0			0
$603$	36.4259	+	15.0881i	1.48338	+	0.614434i
$604$		0			0
$605$	−10.7841	−	26.0351i	−0.438435	−	1.05848i
$606$		0			0
$607$	−8.56097			−0.347479			−0.173739	−	0.984792i	$-0.555585\pi$
$607$	−8.56097			−0.347479			−0.173739	+	0.984792i	$0.555585\pi$
$608$		0			0
$609$	2.28052			0.0924115
$610$		0			0
$611$	−7.22750	−	17.4487i	−0.292393	−	0.705900i
$612$		0			0
$613$	−40.9006	−	16.9416i	−1.65196	−	0.684264i	−0.654539	−	0.756028i	$-0.727137\pi$
$613$	−40.9006	−	16.9416i	−1.65196	−	0.684264i	−0.997422	+	0.0717639i	$0.977137\pi$
$614$		0			0
$615$	33.9523	+	33.9523i	1.36909	+	1.36909i
$616$		0			0
$617$	16.1478	−	16.1478i	0.650087	−	0.650087i	−0.302927	−	0.953014i	$-0.597964\pi$
$617$	16.1478	−	16.1478i	0.650087	−	0.650087i	0.953014	+	0.302927i	$0.0979638\pi$
$618$		0			0
$619$	−0.202034	+	0.487753i	−0.00812042	+	0.0196044i	−0.927888	−	0.372860i	$-0.878377\pi$
$619$	−0.202034	+	0.487753i	−0.00812042	+	0.0196044i	0.919767	+	0.392464i	$0.128377\pi$
$620$		0			0
$621$	−1.15210	+	0.477216i	−0.0462322	+	0.0191500i
$622$		0			0
$623$			13.5230i			0.541789i
$624$		0			0
$625$		−	30.9272i		−	1.23709i
$626$		0			0
$627$	57.4715	−	23.8055i	2.29519	−	0.950699i
$628$		0			0
$629$	24.4290	−	58.9769i	0.974050	−	2.35156i
$630$		0			0
$631$	14.1655	−	14.1655i	0.563920	−	0.563920i	−0.366498	−	0.930419i	$-0.619443\pi$
$631$	14.1655	−	14.1655i	0.563920	−	0.563920i	0.930419	+	0.366498i	$0.119443\pi$
$632$		0			0
$633$	−43.9351	−	43.9351i	−1.74626	−	1.74626i
$634$		0			0
$635$	12.8376	+	5.31751i	0.509445	+	0.211019i
$636$		0			0
$637$	−1.27242	−	3.07190i	−0.0504153	−	0.121713i
$638$		0			0
$639$	31.1436			1.23202
$640$		0			0
$641$	−5.55171			−0.219280			−0.109640	−	0.993971i	$-0.534970\pi$
$641$	−5.55171			−0.219280			−0.109640	+	0.993971i	$0.534970\pi$
$642$		0			0
$643$	2.49243	+	6.01727i	0.0982920	+	0.237298i	0.965375	−	0.260866i	$-0.0840080\pi$
$643$	2.49243	+	6.01727i	0.0982920	+	0.237298i	−0.867083	+	0.498163i	$0.834008\pi$
$644$		0			0
$645$	47.1470	+	19.5289i	1.85641	+	0.768951i
$646$		0			0
$647$	−2.88804	−	2.88804i	−0.113541	−	0.113541i	0.648054	−	0.761594i	$-0.275583\pi$
$647$	−2.88804	−	2.88804i	−0.113541	−	0.113541i	−0.761594	+	0.648054i	$0.775583\pi$
$648$		0			0
$649$	10.0580	−	10.0580i	0.394811	−	0.394811i
$650$		0			0
$651$	−5.54875	+	13.3959i	−0.217472	+	0.525025i
$652$		0			0
$653$	5.93298	−	2.45752i	0.232176	−	0.0961703i	−0.263563	−	0.964642i	$-0.584898\pi$
$653$	5.93298	−	2.45752i	0.232176	−	0.0961703i	0.495738	+	0.868472i	$0.334898\pi$
$654$		0			0
$655$			53.7583i			2.10051i
$656$		0			0
$657$			2.64705i			0.103271i
$658$		0			0
$659$	−20.7803	+	8.60749i	−0.809487	+	0.335300i	−0.748749	−	0.662853i	$-0.769345\pi$
$659$	−20.7803	+	8.60749i	−0.809487	+	0.335300i	−0.0607375	+	0.998154i	$0.519345\pi$
$660$		0			0
$661$	−3.83333	+	9.25447i	−0.149099	+	0.359957i	−0.980729	−	0.195373i	$-0.937408\pi$
$661$	−3.83333	+	9.25447i	−0.149099	+	0.359957i	0.831630	+	0.555330i	$0.187408\pi$
$662$		0			0
$663$	−33.2417	+	33.2417i	−1.29100	+	1.29100i
$664$		0			0
$665$	−9.99872	−	9.99872i	−0.387734	−	0.387734i
$666$		0			0
$667$	−2.34499	−	0.971325i	−0.0907983	−	0.0376099i
$668$		0			0
$669$	−0.547619	−	1.32207i	−0.0211722	−	0.0511142i
$670$		0			0
$671$	−18.5333			−0.715468
$672$		0			0
$673$	−23.6457			−0.911473			−0.455737	−	0.890115i	$-0.650624\pi$
$673$	−23.6457			−0.911473			−0.455737	+	0.890115i	$0.650624\pi$
$674$		0			0
$675$	−0.333163	−	0.804327i	−0.0128235	−	0.0309586i
$676$		0			0
$677$	−5.08540	−	2.10644i	−0.195448	−	0.0809571i	0.282813	−	0.959175i	$-0.408732\pi$
$677$	−5.08540	−	2.10644i	−0.195448	−	0.0809571i	−0.478260	+	0.878218i	$0.658732\pi$
$678$		0			0
$679$	−5.35498	−	5.35498i	−0.205505	−	0.205505i
$680$		0			0
$681$	12.5644	−	12.5644i	0.481468	−	0.481468i
$682$		0			0
$683$	−8.84219	+	21.3469i	−0.338337	+	0.816818i	0.659539	+	0.751671i	$0.270752\pi$
$683$	−8.84219	+	21.3469i	−0.338337	+	0.816818i	−0.997876	+	0.0651472i	$0.979248\pi$
$684$		0			0
$685$	3.35567	−	1.38997i	0.128214	−	0.0531078i
$686$		0			0
$687$		−	25.6074i		−	0.976984i
$688$		0			0
$689$		−	20.8761i		−	0.795317i
$690$		0			0
$691$	11.8967	−	4.92779i	0.452573	−	0.187462i	−0.144740	−	0.989470i	$-0.546235\pi$
$691$	11.8967	−	4.92779i	0.452573	−	0.187462i	0.597314	+	0.802008i	$0.296235\pi$
$692$		0			0
$693$	5.67156	−	13.6924i	0.215445	−	0.520129i
$694$		0			0
$695$	36.0071	−	36.0071i	1.36583	−	1.36583i
$696$		0			0
$697$	−29.4968	−	29.4968i	−1.11727	−	1.11727i
$698$		0			0
$699$	−48.4501	−	20.0687i	−1.83255	−	0.759068i
$700$		0			0
$701$	−19.4313	−	46.9113i	−0.733910	−	1.77182i	−0.629102	−	0.777323i	$-0.716577\pi$
$701$	−19.4313	−	46.9113i	−0.733910	−	1.77182i	−0.104808	−	0.994493i	$-0.533423\pi$
$702$		0			0
$703$	−60.2885			−2.27382
$704$		0			0
$705$	−37.1808			−1.40031
$706$		0			0
$707$	3.83811	+	9.26603i	0.144347	+	0.348485i
$708$		0			0
$709$	−18.0916	−	7.49378i	−0.679444	−	0.281435i	0.0161506	−	0.999870i	$-0.494859\pi$
$709$	−18.0916	−	7.49378i	−0.679444	−	0.281435i	−0.695594	+	0.718435i	$0.744859\pi$
$710$		0			0
$711$	−12.7244	−	12.7244i	−0.477203	−	0.477203i
$712$		0			0
$713$	11.4112	−	11.4112i	0.427352	−	0.427352i
$714$		0			0
$715$	15.6070	−	37.6786i	0.583669	−	1.40910i
$716$		0			0
$717$	55.7701	−	23.1007i	2.08277	−	0.862712i
$718$		0			0
$719$		−	2.51172i		−	0.0936714i	−0.998903	−	0.0468357i	$-0.985086\pi$
$719$		−	2.51172i		−	0.0936714i	0.998903	−	0.0468357i	$-0.0149137\pi$
$720$		0			0
$721$		−	0.516492i		−	0.0192352i
$722$		0			0
$723$	50.8577	−	21.0659i	1.89142	−	0.783451i
$724$		0			0
$725$	0.678120	−	1.63713i	0.0251848	−	0.0608014i
$726$		0			0
$727$	5.80535	−	5.80535i	0.215309	−	0.215309i	−0.591209	−	0.806518i	$-0.701349\pi$
$727$	5.80535	−	5.80535i	0.215309	−	0.215309i	0.806518	+	0.591209i	$0.201349\pi$
$728$		0			0
$729$	−21.3251	−	21.3251i	−0.789817	−	0.789817i
$730$		0			0
$731$	−40.9599	−	16.9662i	−1.51496	−	0.627516i
$732$		0			0
$733$	8.32995	+	20.1103i	0.307674	+	0.742790i	0.999780	+	0.0209941i	$0.00668311\pi$
$733$	8.32995	+	20.1103i	0.307674	+	0.742790i	−0.692106	+	0.721796i	$0.743317\pi$
$734$		0			0
$735$	−6.54580			−0.241446
$736$		0			0
$737$	57.7375			2.12679
$738$		0			0
$739$	−10.4066	−	25.1238i	−0.382814	−	0.924194i	−0.991419	−	0.130721i	$-0.958271\pi$
$739$	−10.4066	−	25.1238i	−0.382814	−	0.924194i	0.608606	−	0.793473i	$-0.291729\pi$
$740$		0			0
$741$	41.0187	+	16.9905i	1.50686	+	0.624161i
$742$		0			0
$743$	−14.5846	−	14.5846i	−0.535057	−	0.535057i	0.387016	−	0.922073i	$-0.373506\pi$
$743$	−14.5846	−	14.5846i	−0.535057	−	0.535057i	−0.922073	+	0.387016i	$0.873506\pi$
$744$		0			0
$745$	17.3404	−	17.3404i	0.635305	−	0.635305i
$746$		0			0
$747$	7.49277	−	18.0892i	0.274146	−	0.661848i
$748$		0			0
$749$	3.81196	−	1.57897i	0.139286	−	0.0576942i
$750$		0			0
$751$		−	21.2866i		−	0.776759i	−0.921500	−	0.388379i	$-0.873035\pi$
$751$		−	21.2866i		−	0.776759i	0.921500	−	0.388379i	$-0.126965\pi$
$752$		0			0
$753$		−	32.9267i		−	1.19992i
$754$		0			0
$755$	43.5761	−	18.0498i	1.58590	−	0.656900i
$756$		0			0
$757$	−7.12091	+	17.1914i	−0.258814	+	0.624832i	−0.998861	−	0.0477233i	$-0.984803\pi$
$757$	−7.12091	+	17.1914i	−0.258814	+	0.624832i	0.740047	+	0.672556i	$0.234803\pi$
$758$		0			0
$759$	−22.6629	+	22.6629i	−0.822612	+	0.822612i
$760$		0			0
$761$	−24.5343	−	24.5343i	−0.889368	−	0.889368i	0.105095	−	0.994462i	$-0.466485\pi$
$761$	−24.5343	−	24.5343i	−0.889368	−	0.889368i	−0.994462	+	0.105095i	$0.966485\pi$
$762$		0			0
$763$	8.46350	+	3.50570i	0.306399	+	0.126915i
$764$		0			0
$765$	18.2277	+	44.0055i	0.659023	+	1.59102i
$766$		0			0
$767$	10.1521			0.366570
$768$		0			0
$769$	16.8823			0.608791			0.304395	−	0.952546i	$-0.401546\pi$
$769$	16.8823			0.608791			0.304395	+	0.952546i	$0.401546\pi$
$770$		0			0
$771$	13.0082	+	31.4045i	0.468478	+	1.13101i
$772$		0			0
$773$	22.6748	+	9.39219i	0.815554	+	0.337814i	0.751168	−	0.660111i	$-0.229491\pi$
$773$	22.6748	+	9.39219i	0.815554	+	0.337814i	0.0643866	+	0.997925i	$0.479491\pi$
$774$		0			0
$775$	7.96659	+	7.96659i	0.286168	+	0.286168i
$776$		0			0
$777$	−19.7343	+	19.7343i	−0.707965	+	0.707965i
$778$		0			0
$779$	−15.0764	+	36.3976i	−0.540167	+	1.30408i
$780$		0			0
$781$	42.1355	−	17.4531i	1.50773	−	0.624521i
$782$		0			0
$783$			0.413373i			0.0147727i
$784$		0			0
$785$		−	12.0791i		−	0.431121i
$786$		0			0
$787$	−29.0721	+	12.0420i	−1.03631	+	0.429252i	−0.834985	−	0.550273i	$-0.814524\pi$
$787$	−29.0721	+	12.0420i	−1.03631	+	0.429252i	−0.201322	+	0.979525i	$0.564524\pi$
$788$		0			0
$789$	−12.1520	+	29.3376i	−0.432624	+	1.04445i
$790$		0			0
$791$	1.27204	−	1.27204i	0.0452286	−	0.0452286i
$792$		0			0
$793$	−9.35332	−	9.35332i	−0.332146	−	0.332146i
$794$		0			0
$795$	−37.9696	−	15.7275i	−1.34664	−	0.557797i
$796$		0			0
$797$	9.37688	+	22.6378i	0.332146	+	0.801871i	0.998421	+	0.0561657i	$0.0178875\pi$
$797$	9.37688	+	22.6378i	0.332146	+	0.801871i	−0.666275	+	0.745706i	$0.732112\pi$
$798$		0			0
$799$	32.3016			1.14275
$800$		0			0
$801$	−43.0203			−1.52005
$802$		0			0
$803$	1.48343	+	3.58131i	0.0523489	+	0.126382i
$804$		0			0
$805$	6.73083	+	2.78800i	0.237231	+	0.0982642i
$806$		0			0
$807$	−8.19753	−	8.19753i	−0.288567	−	0.288567i
$808$		0			0
$809$	0.571651	−	0.571651i	0.0200982	−	0.0200982i	−0.696986	−	0.717084i	$-0.745476\pi$
$809$	0.571651	−	0.571651i	0.0200982	−	0.0200982i	0.717084	+	0.696986i	$0.245476\pi$
$810$		0			0
$811$	10.1470	−	24.4970i	0.356309	−	0.860207i	−0.639503	−	0.768788i	$-0.720860\pi$
$811$	10.1470	−	24.4970i	0.356309	−	0.860207i	0.995813	−	0.0914183i	$-0.0291400\pi$
$812$		0			0
$813$	57.9693	−	24.0117i	2.03307	−	0.842126i
$814$		0			0
$815$		−	9.60626i		−	0.336492i
$816$		0			0
$817$			41.8708i			1.46487i
$818$		0			0
$819$	9.77253	−	4.04791i	0.341480	−	0.141446i
$820$		0			0
$821$	−14.2385	+	34.3748i	−0.496927	+	1.19969i	0.454204	+	0.890898i	$0.349924\pi$
$821$	−14.2385	+	34.3748i	−0.496927	+	1.19969i	−0.951130	+	0.308790i	$0.900076\pi$
$822$		0			0
$823$	−39.0004	+	39.0004i	−1.35947	+	1.35947i	−0.484895	+	0.874572i	$0.661142\pi$
$823$	−39.0004	+	39.0004i	−1.35947	+	1.35947i	−0.874572	+	0.484895i	$0.838858\pi$
$824$		0			0
$825$	−15.8219	−	15.8219i	−0.550847	−	0.550847i
$826$		0			0
$827$	29.7323	+	12.3155i	1.03389	+	0.428253i	0.834116	−	0.551589i	$-0.185978\pi$
$827$	29.7323	+	12.3155i	1.03389	+	0.428253i	0.199777	+	0.979841i	$0.435978\pi$
$828$		0			0
$829$	19.2282	+	46.4211i	0.667825	+	1.61227i	0.785242	+	0.619189i	$0.212538\pi$
$829$	19.2282	+	46.4211i	0.667825	+	1.61227i	−0.117418	+	0.993083i	$0.537462\pi$
$830$		0			0
$831$	73.3817			2.54558
$832$		0			0
$833$	5.68680			0.197036
$834$		0			0
$835$	12.8949	+	31.1310i	0.446246	+	1.07733i
$836$		0			0
$837$	−2.42816	−	1.00578i	−0.0839296	−	0.0347648i
$838$		0			0
$839$	−4.15958	−	4.15958i	−0.143605	−	0.143605i	0.631650	−	0.775254i	$-0.282378\pi$
$839$	−4.15958	−	4.15958i	−0.143605	−	0.143605i	−0.775254	+	0.631650i	$0.782378\pi$
$840$		0			0
$841$	19.9112	−	19.9112i	0.686591	−	0.686591i
$842$		0			0
$843$	6.83116	−	16.4919i	0.235278	−	0.568010i
$844$		0			0
$845$	−4.72948	+	1.95901i	−0.162699	+	0.0673921i
$846$		0			0
$847$		−	10.7033i		−	0.367771i
$848$		0			0
$849$			40.5005i			1.38997i
$850$		0			0
$851$	28.6975	−	11.8869i	0.983736	−	0.407477i
$852$		0			0
$853$	−15.2995	+	36.9363i	−0.523845	+	1.26467i	0.411652	+	0.911341i	$0.364952\pi$
$853$	−15.2995	+	36.9363i	−0.523845	+	1.26467i	−0.935497	+	0.353333i	$0.885048\pi$
$854$		0			0
$855$	31.8086	−	31.8086i	1.08783	−	1.08783i
$856$		0			0
$857$	0.0829726	+	0.0829726i	0.00283429	+	0.00283429i	0.708523	−	0.705688i	$-0.249362\pi$
$857$	0.0829726	+	0.0829726i	0.00283429	+	0.00283429i	−0.705688	+	0.708523i	$0.749362\pi$
$858$		0			0
$859$	42.4264	+	17.5736i	1.44757	+	0.599604i	0.961621	−	0.274382i	$-0.0884734\pi$
$859$	42.4264	+	17.5736i	1.44757	+	0.599604i	0.485951	+	0.873986i	$0.338473\pi$
$860$		0			0
$861$	6.97911	+	16.8491i	0.237847	+	0.574214i
$862$		0			0
$863$	4.91048			0.167155			0.0835774	−	0.996501i	$-0.473365\pi$
$863$	4.91048			0.167155			0.0835774	+	0.996501i	$0.473365\pi$
$864$		0			0
$865$	20.9361			0.711848
$866$		0			0
$867$	−14.5947	−	35.2347i	−0.495661	−	1.19663i
$868$		0			0
$869$	−24.3462	−	10.0845i	−0.825889	−	0.342095i
$870$		0			0
$871$	29.1388	+	29.1388i	0.987332	+	0.987332i
$872$		0			0
$873$	17.0356	−	17.0356i	0.576568	−	0.576568i
$874$		0			0
$875$	3.09131	−	7.46307i	0.104505	−	0.252298i
$876$		0			0
$877$	−10.7461	+	4.45119i	−0.362870	+	0.150306i	−0.556667	−	0.830736i	$-0.687920\pi$
$877$	−10.7461	+	4.45119i	−0.362870	+	0.150306i	0.193796	+	0.981042i	$0.437920\pi$
$878$		0			0
$879$		−	9.80589i		−	0.330744i
$880$		0			0
$881$			11.3184i			0.381325i	0.981656	+	0.190663i	$0.0610637\pi$
$881$			11.3184i			0.381325i	−0.981656	+	0.190663i	$0.938936\pi$
$882$		0			0
$883$	17.1090	−	7.08676i	0.575762	−	0.238489i	−0.0757498	−	0.997127i	$-0.524135\pi$
$883$	17.1090	−	7.08676i	0.575762	−	0.238489i	0.651512	+	0.758638i	$0.274135\pi$
$884$		0			0
$885$	7.64831	−	18.4646i	0.257095	−	0.620682i
$886$		0			0
$887$	−15.6391	+	15.6391i	−0.525108	+	0.525108i	−0.919110	−	0.394002i	$-0.871090\pi$
$887$	−15.6391	+	15.6391i	−0.525108	+	0.525108i	0.394002	+	0.919110i	$0.371090\pi$
$888$		0			0
$889$	3.73189	+	3.73189i	0.125164	+	0.125164i
$890$		0			0
$891$	−36.2547	−	15.0172i	−1.21458	−	0.503094i
$892$		0			0
$893$	−11.6743	−	28.1843i	−0.390666	−	0.943151i
$894$		0			0
$895$	0.212991			0.00711951
$896$		0			0
$897$	−22.8749			−0.763772
$898$		0			0
$899$	−2.04716	−	4.94229i	−0.0682767	−	0.164834i
$900$		0			0
$901$	32.9868	+	13.6636i	1.09895	+	0.455201i
$902$		0			0
$903$	13.7056	+	13.7056i	0.456095	+	0.456095i
$904$		0			0
$905$	−36.9648	+	36.9648i	−1.22875	+	1.22875i
$906$		0			0
$907$	13.0375	−	31.4753i	0.432903	−	1.04512i	−0.545443	−	0.838148i	$-0.683639\pi$
$907$	13.0375	−	31.4753i	0.432903	−	1.04512i	0.978347	−	0.206973i	$-0.0663614\pi$
$908$		0			0
$909$	−29.4777	+	12.2100i	−0.977712	+	0.404982i
$910$		0			0
$911$		−	41.3901i		−	1.37131i	−0.727925	−	0.685657i	$-0.759515\pi$
$911$		−	41.3901i		−	1.37131i	0.727925	−	0.685657i	$-0.240485\pi$
$912$		0			0
$913$		−	28.6726i		−	0.948924i
$914$		0			0
$915$	−24.0584	+	9.96531i	−0.795346	+	0.329443i
$916$		0			0
$917$	−7.81378	+	18.8641i	−0.258034	+	0.622948i
$918$		0			0
$919$	−25.4321	+	25.4321i	−0.838928	+	0.838928i	−0.988718	−	0.149790i	$-0.952140\pi$
$919$	−25.4321	+	25.4321i	−0.838928	+	0.838928i	0.149790	+	0.988718i	$0.452140\pi$
$920$		0			0
$921$	−6.85791	−	6.85791i	−0.225976	−	0.225976i
$922$		0			0
$923$	30.0730	+	12.4567i	0.989866	+	0.410016i
$924$		0			0
$925$	8.29869	+	20.0348i	0.272859	+	0.658741i
$926$		0			0
$927$	1.64310			0.0539664
$928$		0			0
$929$	−55.5530			−1.82263			−0.911317	−	0.411706i	$-0.864933\pi$
$929$	−55.5530			−1.82263			−0.911317	+	0.411706i	$0.864933\pi$
$930$		0			0
$931$	−2.05530	−	4.96193i	−0.0673597	−	0.162621i
$932$		0			0
$933$	6.45889	+	2.67536i	0.211454	+	0.0875873i
$934$		0			0
$935$	49.3220	+	49.3220i	1.61300	+	1.61300i
$936$		0			0
$937$	19.1775	−	19.1775i	0.626503	−	0.626503i	−0.320683	−	0.947186i	$-0.603913\pi$
$937$	19.1775	−	19.1775i	0.626503	−	0.626503i	0.947186	+	0.320683i	$0.103913\pi$
$938$		0			0
$939$	12.9395	−	31.2387i	0.422264	−	1.01944i
$940$		0			0
$941$	−1.22607	+	0.507856i	−0.0399689	+	0.0165556i	−0.402578	−	0.915386i	$-0.631886\pi$
$941$	−1.22607	+	0.507856i	−0.0399689	+	0.0165556i	0.362609	+	0.931941i	$0.381886\pi$
$942$		0			0
$943$		−	20.2979i		−	0.660990i
$944$		0			0
$945$		−	1.18651i		−	0.0385971i
$946$		0			0
$947$	−31.6795	+	13.1221i	−1.02944	+	0.426410i	−0.832512	−	0.554007i	$-0.813098\pi$
$947$	−31.6795	+	13.1221i	−1.02944	+	0.426410i	−0.196932	+	0.980417i	$0.563098\pi$
$948$		0			0
$949$	−1.05875	+	2.55606i	−0.0343686	+	0.0829731i
$950$		0			0
$951$	−41.0450	+	41.0450i	−1.33098	+	1.33098i
$952$		0			0
$953$	9.78733	+	9.78733i	0.317043	+	0.317043i	0.847630	−	0.530587i	$-0.178029\pi$
$953$	9.78733	+	9.78733i	0.317043	+	0.317043i	−0.530587	+	0.847630i	$0.678029\pi$
$954$		0			0
$955$	−19.7264	−	8.17093i	−0.638331	−	0.264405i
$956$		0			0
$957$	4.06572	+	9.81551i	0.131426	+	0.317291i
$958$		0			0
$959$	1.37956			0.0445483
$960$		0			0
$961$	3.01207			0.0971636
$962$		0			0
$963$	5.02311	+	12.1269i	0.161867	+	0.390783i
$964$		0			0
$965$	−46.6271	−	19.3136i	−1.50098	−	0.621726i
$966$		0			0
$967$	1.95420	+	1.95420i	0.0628429	+	0.0628429i	0.737830	−	0.674987i	$-0.235851\pi$
$967$	1.95420	+	1.95420i	0.0628429	+	0.0628429i	−0.674987	+	0.737830i	$0.735851\pi$
$968$		0			0
$969$	−53.6941	+	53.6941i	−1.72490	+	1.72490i
$970$		0			0
$971$	3.42340	−	8.26482i	0.109862	−	0.265231i	−0.859381	−	0.511336i	$-0.829151\pi$
$971$	3.42340	−	8.26482i	0.109862	−	0.265231i	0.969243	+	0.246105i	$0.0791508\pi$
$972$		0			0
$973$	17.8688	−	7.40149i	0.572847	−	0.237281i
$974$		0			0
$975$		−	15.9699i		−	0.511446i
$976$		0			0
$977$		−	44.2735i		−	1.41644i	−0.705994	−	0.708218i	$-0.749499\pi$
$977$		−	44.2735i		−	1.41644i	0.705994	−	0.708218i	$-0.250501\pi$
$978$		0			0
$979$	−58.2040	+	24.1089i	−1.86021	+	0.770524i
$980$		0			0
$981$	−11.1525	+	26.9246i	−0.356073	+	0.859637i
$982$		0			0
$983$	12.3821	−	12.3821i	0.394928	−	0.394928i	−0.481512	−	0.876440i	$-0.659912\pi$
$983$	12.3821	−	12.3821i	0.394928	−	0.394928i	0.876440	+	0.481512i	$0.159912\pi$
$984$		0			0
$985$	26.1765	+	26.1765i	0.834053	+	0.834053i
$986$		0			0
$987$	−13.0470	−	5.40424i	−0.415290	−	0.172019i
$988$		0			0
$989$	−8.25552	−	19.9306i	−0.262510	−	0.633756i
$990$		0			0
$991$	47.7352			1.51636			0.758180	−	0.652045i	$-0.226089\pi$
$991$	47.7352			1.51636			0.758180	+	0.652045i	$0.226089\pi$
$992$		0			0
$993$	70.8727			2.24908
$994$		0			0
$995$	−1.08600	−	2.62183i	−0.0344284	−	0.0831175i
$996$		0			0
$997$	37.5919	+	15.5711i	1.19055	+	0.493140i	0.887933	−	0.459973i	$-0.152141\pi$
$997$	37.5919	+	15.5711i	1.19055	+	0.493140i	0.302613	+	0.953113i	$0.402141\pi$
$998$		0			0
$999$	−3.57709	−	3.57709i	−0.113174	−	0.113174i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.u.c.113.12		52
4.3	odd	2		224.2.u.c.197.4	yes	52
32.13	even	8	inner	896.2.u.c.785.12		52
32.19	odd	8		224.2.u.c.141.4	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.u.c.141.4	✓	52	32.19	odd	8
224.2.u.c.197.4	yes	52	4.3	odd	2
896.2.u.c.113.12		52	1.1	even	1	trivial
896.2.u.c.785.12		52	32.13	even	8	inner

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:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.u (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.951433 + 2.29696i) q^{3} +(2.43243 + 1.00754i) q^{5} +(0.707107 + 0.707107i) q^{7} +(-2.24949 + 2.24949i) q^{9} +O(q^{10})\)	\(q+(0.951433 + 2.29696i) q^{3} +(2.43243 + 1.00754i) q^{5} +(0.707107 + 0.707107i) q^{7} +(-2.24949 + 2.24949i) q^{9} +(-1.78280 + 4.30406i) q^{11} +(-3.07190 + 1.27242i) q^{13} +6.54580i q^{15} -5.68680i q^{17} +(-4.96193 + 2.05530i) q^{19} +(-0.951433 + 2.29696i) q^{21} +(1.95665 - 1.95665i) q^{23} +(1.36602 + 1.36602i) q^{25} +(-0.416353 - 0.172459i) q^{27} +(-0.351023 - 0.847445i) q^{29} +5.83199 q^{31} -11.5825 q^{33} +(1.00754 + 2.43243i) q^{35} +(10.3708 + 4.29574i) q^{37} +(-5.84542 - 5.84542i) q^{39} +(5.18689 - 5.18689i) q^{41} +(2.98343 - 7.20263i) q^{43} +(-7.73818 + 3.20526i) q^{45} +5.68010i q^{47} +1.00000i q^{49} +(13.0624 - 5.41061i) q^{51} +(-2.40269 + 5.80060i) q^{53} +(-8.67306 + 8.67306i) q^{55} +(-9.44189 - 9.44189i) q^{57} +(-2.82084 - 1.16843i) q^{59} +(1.52240 + 3.67539i) q^{61} -3.18126 q^{63} -8.75420 q^{65} +(-4.74280 - 11.4501i) q^{67} +(6.35599 + 2.63274i) q^{69} +(-6.92236 - 6.92236i) q^{71} +(0.588366 - 0.588366i) q^{73} +(-1.83802 + 4.43736i) q^{75} +(-4.30406 + 1.78280i) q^{77} +5.65657i q^{79} +8.42336i q^{81} +(-5.68616 + 2.35528i) q^{83} +(5.72970 - 13.8327i) q^{85} +(1.61257 - 1.61257i) q^{87} +(9.56223 + 9.56223i) q^{89} +(-3.07190 - 1.27242i) q^{91} +(5.54875 + 13.3959i) q^{93} -14.1403 q^{95} -7.57309 q^{97} +(-5.67156 - 13.6924i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q+O(q^{10}) \) 52 * q	\( 52 q + 20 q^{23} + 24 q^{27} - 48 q^{33} + 24 q^{39} + 44 q^{43} + 40 q^{45} - 16 q^{51} - 36 q^{53} - 32 q^{55} - 32 q^{61} - 68 q^{63} + 80 q^{65} - 28 q^{67} - 32 q^{69} - 32 q^{75} - 12 q^{77} + 64 q^{85} + 56 q^{87} + 64 q^{95} - 72 q^{97} + 64 q^{99}+O(q^{100}) \) 52 * q + 20 * q^23 + 24 * q^27 - 48 * q^33 + 24 * q^39 + 44 * q^43 + 40 * q^45 - 16 * q^51 - 36 * q^53 - 32 * q^55 - 32 * q^61 - 68 * q^63 + 80 * q^65 - 28 * q^67 - 32 * q^69 - 32 * q^75 - 12 * q^77 + 64 * q^85 + 56 * q^87 + 64 * q^95 - 72 * q^97 + 64 * q^99

Introduction

L-functions

Modular forms

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