LMFDB - Embedded newform 896.2.bh.a.529.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(81,896)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 9, 16]))

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

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

chi := DirichletCharacter("896.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.bh (of order $24$, 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:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 224)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			529.27
Character	$\chi$	$=$	896.529
Dual form			896.2.bh.a.625.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.44087 + 1.87778i) q^{3} +(-2.75892 - 2.11700i) q^{5} +(1.14468 - 2.38531i) q^{7} +(-0.673491 + 2.51350i) q^{9} +O(q^{10})$	\(q+(1.44087 + 1.87778i) q^{3} +(-2.75892 - 2.11700i) q^{5} +(1.14468 - 2.38531i) q^{7} +(-0.673491 + 2.51350i) q^{9} +(-2.68201 - 0.353093i) q^{11} +(1.84002 + 0.762162i) q^{13} -8.23097i q^{15} +(-6.86527 - 3.96366i) q^{17} +(-0.226114 - 1.71751i) q^{19} +(6.12843 - 1.28747i) q^{21} +(1.20290 - 4.48927i) q^{23} +(1.83589 + 6.85163i) q^{25} +(0.869948 - 0.360344i) q^{27} +(0.0946303 - 0.228458i) q^{29} +(4.72355 - 8.18143i) q^{31} +(-3.20140 - 5.54498i) q^{33} +(-8.20778 + 4.15761i) q^{35} +(-3.74651 - 2.87479i) q^{37} +(1.22006 + 4.55333i) q^{39} +(0.823484 + 0.823484i) q^{41} +(2.05302 + 4.95643i) q^{43} +(7.17918 - 5.50878i) q^{45} +(-0.844781 + 0.487734i) q^{47} +(-4.37942 - 5.46083i) q^{49} +(-2.44908 - 18.6026i) q^{51} +(-7.52554 - 0.990756i) q^{53} +(6.65195 + 6.65195i) q^{55} +(2.89930 - 2.89930i) q^{57} +(-0.187527 + 1.42441i) q^{59} +(-5.51757 + 0.726402i) q^{61} +(5.22455 + 4.48364i) q^{63} +(-3.46298 - 5.99807i) q^{65} +(7.06937 + 9.21298i) q^{67} +(10.1631 - 4.20969i) q^{69} +(0.823109 - 0.823109i) q^{71} +(13.8498 - 3.71104i) q^{73} +(-10.2206 + 13.3197i) q^{75} +(-3.91227 + 5.99324i) q^{77} +(0.377642 - 0.218032i) q^{79} +(8.69076 + 5.01761i) q^{81} +(8.69345 + 3.60095i) q^{83} +(10.5497 + 25.4692i) q^{85} +(0.565344 - 0.151483i) q^{87} +(6.94761 + 1.86161i) q^{89} +(3.92423 - 3.51659i) q^{91} +(22.1690 - 2.91860i) q^{93} +(-3.01212 + 5.21715i) q^{95} -9.00485 q^{97} +(2.69381 - 6.50342i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9}+O(q^{10}) $ 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9	$ 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9} + 4 q^{11} - 16 q^{13} + 4 q^{19} - 8 q^{21} + 12 q^{23} - 4 q^{25} + 16 q^{27} - 16 q^{29} + 56 q^{31} - 8 q^{33} + 32 q^{35} - 4 q^{37} + 4 q^{39} - 16 q^{41} + 8 q^{45} + 28 q^{51} - 20 q^{53} + 16 q^{55} - 16 q^{57} + 36 q^{59} - 4 q^{61} + 16 q^{63} - 8 q^{65} - 36 q^{67} - 16 q^{69} - 48 q^{71} - 4 q^{73} - 16 q^{75} - 8 q^{77} + 96 q^{83} - 56 q^{85} + 4 q^{87} - 4 q^{89} + 56 q^{91} + 20 q^{93} + 8 q^{95} - 32 q^{97} - 8 q^{99}+O(q^{100}) $ 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9 + 4 * q^11 - 16 * q^13 + 4 * q^19 - 8 * q^21 + 12 * q^23 - 4 * q^25 + 16 * q^27 - 16 * q^29 + 56 * q^31 - 8 * q^33 + 32 * q^35 - 4 * q^37 + 4 * q^39 - 16 * q^41 + 8 * q^45 + 28 * q^51 - 20 * q^53 + 16 * q^55 - 16 * q^57 + 36 * q^59 - 4 * q^61 + 16 * q^63 - 8 * q^65 - 36 * q^67 - 16 * q^69 - 48 * q^71 - 4 * q^73 - 16 * q^75 - 8 * q^77 + 96 * q^83 - 56 * q^85 + 4 * q^87 - 4 * q^89 + 56 * q^91 + 20 * q^93 + 8 * q^95 - 32 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$129$	$645$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{8}\right)$

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
$3$	1.44087	+	1.87778i	0.831887	+	1.08414i	0.995229	+	0.0975672i	$0.0311061\pi$
$3$	1.44087	+	1.87778i	0.831887	+	1.08414i	−0.163341	+	0.986570i	$0.552227\pi$
$4$		0			0
$5$	−2.75892	−	2.11700i	−1.23383	−	0.946749i	−0.234152	−	0.972200i	$-0.575231\pi$
$5$	−2.75892	−	2.11700i	−1.23383	−	0.946749i	−0.999676	+	0.0254506i	$0.991898\pi$
$6$		0			0
$7$	1.14468	−	2.38531i	0.432648	−	0.901563i
$7$	1.14468	−	2.38531i	0.432648	−	0.901563i
$8$		0			0
$9$	−0.673491	+	2.51350i	−0.224497	+	0.837834i
$10$		0			0
$11$	−2.68201	−	0.353093i	−0.808655	−	0.106461i	−0.285149	−	0.958483i	$-0.592043\pi$
$11$	−2.68201	−	0.353093i	−0.808655	−	0.106461i	−0.523506	+	0.852022i	$0.675376\pi$
$12$		0			0
$13$	1.84002	+	0.762162i	0.510330	+	0.211386i	0.622963	−	0.782251i	$-0.285929\pi$
$13$	1.84002	+	0.762162i	0.510330	+	0.211386i	−0.112633	+	0.993637i	$0.535929\pi$
$14$		0			0
$15$		−	8.23097i		−	2.12523i
$16$		0			0
$17$	−6.86527	−	3.96366i	−1.66507	−	0.961330i	−0.970236	−	0.242161i	$-0.922144\pi$
$17$	−6.86527	−	3.96366i	−1.66507	−	0.961330i	−0.694836	−	0.719168i	$-0.744523\pi$
$18$		0			0
$19$	−0.226114	−	1.71751i	−0.0518741	−	0.394023i	−0.997611	−	0.0690882i	$-0.977991\pi$
$19$	−0.226114	−	1.71751i	−0.0518741	−	0.394023i	0.945736	−	0.324935i	$-0.105342\pi$
$20$		0			0
$21$	6.12843	−	1.28747i	1.33733	−	0.280949i
$22$		0			0
$23$	1.20290	−	4.48927i	0.250821	−	0.936077i	−0.719546	−	0.694444i	$-0.755650\pi$
$23$	1.20290	−	4.48927i	0.250821	−	0.936077i	0.970368	−	0.241633i	$-0.0776831\pi$
$24$		0			0
$25$	1.83589	+	6.85163i	0.367178	+	1.37033i
$26$		0			0
$27$	0.869948	−	0.360344i	0.167421	−	0.0693483i
$28$		0			0
$29$	0.0946303	−	0.228458i	0.0175724	−	0.0424235i	−0.914850	−	0.403794i	$-0.867691\pi$
$29$	0.0946303	−	0.228458i	0.0175724	−	0.0424235i	0.932422	+	0.361371i	$0.117691\pi$
$30$		0			0
$31$	4.72355	−	8.18143i	0.848375	−	1.46943i	−0.0342833	−	0.999412i	$-0.510915\pi$
$31$	4.72355	−	8.18143i	0.848375	−	1.46943i	0.882658	−	0.470016i	$-0.155752\pi$
$32$		0			0
$33$	−3.20140	−	5.54498i	−0.557291	−	0.965257i
$34$		0			0
$35$	−8.20778	+	4.15761i	−1.38737	+	0.702764i
$36$		0			0
$37$	−3.74651	−	2.87479i	−0.615922	−	0.472613i	0.253065	−	0.967449i	$-0.418561\pi$
$37$	−3.74651	−	2.87479i	−0.615922	−	0.472613i	−0.868986	+	0.494836i	$0.835228\pi$
$38$		0			0
$39$	1.22006	+	4.55333i	0.195366	+	0.729117i
$40$		0			0
$41$	0.823484	+	0.823484i	0.128607	+	0.128607i	0.768480	−	0.639874i	$-0.221013\pi$
$41$	0.823484	+	0.823484i	0.128607	+	0.128607i	−0.639874	+	0.768480i	$0.721013\pi$
$42$		0			0
$43$	2.05302	+	4.95643i	0.313082	+	0.755848i	0.999587	+	0.0287228i	$0.00914402\pi$
$43$	2.05302	+	4.95643i	0.313082	+	0.755848i	−0.686505	+	0.727125i	$0.740856\pi$
$44$		0			0
$45$	7.17918	−	5.50878i	1.07021	−	0.821200i
$46$		0			0
$47$	−0.844781	+	0.487734i	−0.123224	+	0.0711434i	−0.560345	−	0.828259i	$-0.689331\pi$
$47$	−0.844781	+	0.487734i	−0.123224	+	0.0711434i	0.437121	+	0.899403i	$0.355998\pi$
$48$		0			0
$49$	−4.37942	−	5.46083i	−0.625631	−	0.780119i
$50$		0			0
$51$	−2.44908	−	18.6026i	−0.342939	−	2.60488i
$52$		0			0
$53$	−7.52554	−	0.990756i	−1.03371	−	0.136091i	−0.405470	−	0.914108i	$-0.632892\pi$
$53$	−7.52554	−	0.990756i	−1.03371	−	0.136091i	−0.628242	+	0.778018i	$0.716225\pi$
$54$		0			0
$55$	6.65195	+	6.65195i	0.896949	+	0.896949i
$56$		0			0
$57$	2.89930	−	2.89930i	0.384021	−	0.384021i
$58$		0			0
$59$	−0.187527	+	1.42441i	−0.0244139	+	0.185442i	−0.999307	−	0.0372330i	$-0.988146\pi$
$59$	−0.187527	+	1.42441i	−0.0244139	+	0.185442i	0.974893	+	0.222675i	$0.0714790\pi$
$60$		0			0
$61$	−5.51757	+	0.726402i	−0.706452	+	0.0930062i	−0.475187	−	0.879885i	$-0.657620\pi$
$61$	−5.51757	+	0.726402i	−0.706452	+	0.0930062i	−0.231265	+	0.972891i	$0.574286\pi$
$62$		0			0
$63$	5.22455	+	4.48364i	0.658232	+	0.564885i
$64$		0			0
$65$	−3.46298	−	5.99807i	−0.429530	−	0.743968i
$66$		0			0
$67$	7.06937	+	9.21298i	0.863661	+	1.12554i	0.991023	+	0.133688i	$0.0426821\pi$
$67$	7.06937	+	9.21298i	0.863661	+	1.12554i	−0.127363	+	0.991856i	$0.540651\pi$
$68$		0			0
$69$	10.1631	−	4.20969i	1.22349	−	0.506787i
$70$		0			0
$71$	0.823109	−	0.823109i	0.0976851	−	0.0976851i	−0.656575	−	0.754260i	$-0.727996\pi$
$71$	0.823109	−	0.823109i	0.0976851	−	0.0976851i	0.754260	+	0.656575i	$0.227996\pi$
$72$		0			0
$73$	13.8498	−	3.71104i	1.62100	−	0.434345i	0.669702	−	0.742630i	$-0.266422\pi$
$73$	13.8498	−	3.71104i	1.62100	−	0.434345i	0.951294	+	0.308285i	$0.0997552\pi$
$74$		0			0
$75$	−10.2206	+	13.3197i	−1.18017	+	1.53803i
$76$		0			0
$77$	−3.91227	+	5.99324i	−0.445845	+	0.682993i
$78$		0			0
$79$	0.377642	−	0.218032i	0.0424880	−	0.0245305i	−0.478606	−	0.878030i	$-0.658858\pi$
$79$	0.377642	−	0.218032i	0.0424880	−	0.0245305i	0.521094	+	0.853500i	$0.325524\pi$
$80$		0			0
$81$	8.69076	+	5.01761i	0.965640	+	0.557513i
$82$		0			0
$83$	8.69345	+	3.60095i	0.954230	+	0.395255i	0.804819	−	0.593520i	$-0.202262\pi$
$83$	8.69345	+	3.60095i	0.954230	+	0.395255i	0.149411	+	0.988775i	$0.452262\pi$
$84$		0			0
$85$	10.5497	+	25.4692i	1.14427	+	2.76252i
$86$		0			0
$87$	0.565344	−	0.151483i	0.0606112	−	0.0162407i
$88$		0			0
$89$	6.94761	+	1.86161i	0.736445	+	0.197330i	0.607498	−	0.794322i	$-0.292173\pi$
$89$	6.94761	+	1.86161i	0.736445	+	0.197330i	0.128948	+	0.991651i	$0.458840\pi$
$90$		0			0
$91$	3.92423	−	3.51659i	0.411371	−	0.368639i
$92$		0			0
$93$	22.1690	−	2.91860i	2.29881	−	0.302644i
$94$		0			0
$95$	−3.01212	+	5.21715i	−0.309037	+	0.535268i
$96$		0			0
$97$	−9.00485			−0.914304			−0.457152	−	0.889389i	$-0.651131\pi$
$97$	−9.00485			−0.914304			−0.457152	+	0.889389i	$0.651131\pi$
$98$		0			0
$99$	2.69381	−	6.50342i	0.270738	−	0.653618i
$100$		0			0
$101$	1.14590	−	8.70397i	0.114021	−	0.866077i	−0.834864	−	0.550456i	$-0.814454\pi$
$101$	1.14590	−	8.70397i	0.114021	−	0.866077i	0.948885	−	0.315621i	$-0.102213\pi$
$102$		0			0
$103$	−16.7898	−	4.49881i	−1.65435	−	0.443281i	−0.693521	−	0.720437i	$-0.743941\pi$
$103$	−16.7898	−	4.49881i	−1.65435	−	0.443281i	−0.960825	+	0.277156i	$0.910608\pi$
$104$		0			0
$105$	−19.6334	−	9.42183i	−1.91603	−	0.919476i
$106$		0			0
$107$	1.12333	−	1.46395i	0.108596	−	0.141526i	−0.735893	−	0.677098i	$-0.763237\pi$
$107$	1.12333	−	1.46395i	0.108596	−	0.141526i	0.844489	+	0.535572i	$0.179904\pi$
$108$		0			0
$109$	−6.62330	+	5.08224i	−0.634398	+	0.486790i	−0.875186	−	0.483787i	$-0.839261\pi$
$109$	−6.62330	+	5.08224i	−0.634398	+	0.486790i	0.240788	+	0.970578i	$0.422594\pi$
$110$		0			0
$111$		−	11.1773i		−	1.06090i
$112$		0			0
$113$			0.411718i			0.0387312i	0.999812	+	0.0193656i	$0.00616464\pi$
$113$			0.411718i			0.0387312i	−0.999812	+	0.0193656i	$0.993835\pi$
$114$		0			0
$115$	−12.8225	+	9.83902i	−1.19570	+	0.917494i
$116$		0			0
$117$	−3.15493	+	4.11159i	−0.291674	+	0.380116i
$118$		0			0
$119$	−17.3131	+	11.8387i	−1.58709	+	1.08525i
$120$		0			0
$121$	−3.55670	−	0.953015i	−0.323336	−	0.0866377i
$122$		0			0
$123$	−0.359787	+	2.73286i	−0.0324409	+	0.246413i
$124$		0			0
$125$	2.78580	−	6.72552i	0.249170	−	0.601549i
$126$		0			0
$127$	11.2634			0.999464			0.499732	−	0.866180i	$-0.333432\pi$
$127$	11.2634			0.999464			0.499732	+	0.866180i	$0.333432\pi$
$128$		0			0
$129$	−6.34894	+	10.9967i	−0.558993	+	0.968205i
$130$		0			0
$131$	14.7315	−	1.93944i	1.28710	−	0.169450i	0.544257	−	0.838919i	$-0.316812\pi$
$131$	14.7315	−	1.93944i	1.28710	−	0.169450i	0.742840	+	0.669469i	$0.233478\pi$
$132$		0			0
$133$	−4.35561	−	1.42664i	−0.377680	−	0.123706i
$134$		0			0
$135$	−3.16297	−	0.847514i	−0.272225	−	0.0729424i
$136$		0			0
$137$	−6.28819	+	1.68492i	−0.537236	+	0.143952i	−0.517228	−	0.855848i	$-0.673036\pi$
$137$	−6.28819	+	1.68492i	−0.537236	+	0.143952i	−0.0200085	+	0.999800i	$0.506369\pi$
$138$		0			0
$139$	−0.00331720	−	0.00800842i	−0.000281361	−	0.000679266i	0.923739	−	0.383023i	$-0.125117\pi$
$139$	−0.00331720	−	0.00800842i	−0.000281361	−	0.000679266i	−0.924020	+	0.382344i	$0.875117\pi$
$140$		0			0
$141$	−2.13308	−	0.883550i	−0.179638	−	0.0744083i
$142$		0			0
$143$	−4.66584	−	2.69382i	−0.390177	−	0.225269i
$144$		0			0
$145$	−0.744722	+	0.429965i	−0.0618458	+	0.0357067i
$146$		0			0
$147$	3.94407	−	16.0919i	0.325302	−	1.32724i
$148$		0			0
$149$	−8.39232	+	10.9371i	−0.687525	+	0.896001i	−0.998519	−	0.0544116i	$-0.982672\pi$
$149$	−8.39232	+	10.9371i	−0.687525	+	0.896001i	0.310993	+	0.950412i	$0.399338\pi$
$150$		0			0
$151$	−4.06949	+	1.09042i	−0.331170	+	0.0887368i	−0.420573	−	0.907259i	$-0.638171\pi$
$151$	−4.06949	+	1.09042i	−0.331170	+	0.0887368i	0.0894026	+	0.995996i	$0.471504\pi$
$152$		0			0
$153$	14.5864	−	14.5864i	1.17924	−	1.17924i
$154$		0			0
$155$	−30.3520	+	12.5722i	−2.43793	+	1.00982i
$156$		0			0
$157$	9.39972	+	12.2500i	0.750180	+	0.977653i	0.999956	+	0.00934970i	$0.00297615\pi$
$157$	9.39972	+	12.2500i	0.750180	+	0.977653i	−0.249777	+	0.968303i	$0.580357\pi$
$158$		0			0
$159$	−8.98291	−	15.5589i	−0.712391	−	1.23390i
$160$		0			0
$161$	−9.33137	−	8.00806i	−0.735415	−	0.631123i
$162$		0			0
$163$	−5.81892	+	0.766076i	−0.455773	+	0.0600037i	−0.354918	−	0.934897i	$-0.615491\pi$
$163$	−5.81892	+	0.766076i	−0.455773	+	0.0600037i	−0.100855	+	0.994901i	$0.532158\pi$
$164$		0			0
$165$	−2.90630	+	22.0755i	−0.226255	+	1.71858i
$166$		0			0
$167$	3.20407	−	3.20407i	0.247938	−	0.247938i	−0.572186	−	0.820124i	$-0.693904\pi$
$167$	3.20407	−	3.20407i	0.247938	−	0.247938i	0.820124	+	0.572186i	$0.193904\pi$
$168$		0			0
$169$	−6.38760	−	6.38760i	−0.491354	−	0.491354i
$170$		0			0
$171$	4.46924	+	0.588386i	0.341771	+	0.0449950i
$172$		0			0
$173$	−2.02443	−	15.3771i	−0.153915	−	1.16910i	−0.877747	−	0.479124i	$-0.840954\pi$
$173$	−2.02443	−	15.3771i	−0.153915	−	1.16910i	0.723832	−	0.689976i	$-0.242379\pi$
$174$		0			0
$175$	18.4448	+	3.46376i	1.39429	+	0.261835i
$176$		0			0
$177$	−2.94493	+	1.70026i	−0.221354	+	0.127799i
$178$		0			0
$179$	−6.63005	+	5.08741i	−0.495553	+	0.380251i	−0.826087	−	0.563543i	$-0.809438\pi$
$179$	−6.63005	+	5.08741i	−0.495553	+	0.380251i	0.330534	+	0.943794i	$0.392771\pi$
$180$		0			0
$181$	−6.21583	−	15.0064i	−0.462019	−	1.11541i	−0.967567	−	0.252615i	$-0.918710\pi$
$181$	−6.21583	−	15.0064i	−0.462019	−	1.11541i	0.505548	−	0.862799i	$-0.331290\pi$
$182$		0			0
$183$	−9.31413	−	9.31413i	−0.688520	−	0.688520i
$184$		0			0
$185$	4.25039	+	15.8627i	0.312495	+	1.16625i
$186$		0			0
$187$	17.0131	+	13.0546i	1.24412	+	0.954650i
$188$		0			0
$189$	0.136279	−	2.48757i	0.00991282	−	0.180944i
$190$		0			0
$191$	7.87208	+	13.6348i	0.569604	+	0.986583i	0.996605	+	0.0823317i	$0.0262367\pi$
$191$	7.87208	+	13.6348i	0.569604	+	0.986583i	−0.427001	+	0.904251i	$0.640430\pi$
$192$		0			0
$193$	7.16214	−	12.4052i	0.515542	−	0.892945i	−0.484295	−	0.874905i	$-0.660924\pi$
$193$	7.16214	−	12.4052i	0.515542	−	0.892945i	0.999837	−	0.0180405i	$-0.00574277\pi$
$194$		0			0
$195$	6.27333	−	15.1452i	0.449243	−	1.08457i
$196$		0			0
$197$	8.63148	−	3.57528i	0.614967	−	0.254728i	−0.0533834	−	0.998574i	$-0.517001\pi$
$197$	8.63148	−	3.57528i	0.614967	−	0.254728i	0.668351	+	0.743846i	$0.267001\pi$
$198$		0			0
$199$	−2.44416	−	9.12172i	−0.173262	−	0.646622i	−0.996841	−	0.0794207i	$-0.974693\pi$
$199$	−2.44416	−	9.12172i	−0.173262	−	0.646622i	0.823579	−	0.567201i	$-0.191974\pi$
$200$		0			0
$201$	−7.11390	+	26.5494i	−0.501776	+	1.87265i
$202$		0			0
$203$	−0.436621	−	0.487234i	−0.0306448	−	0.0341971i
$204$		0			0
$205$	−0.528616	−	4.01524i	−0.0369202	−	0.280437i
$206$		0			0
$207$	10.4736	+	6.04696i	0.727969	+	0.420293i
$208$		0			0
$209$			4.68620i			0.324151i
$210$		0			0
$211$	−10.7623	−	4.45790i	−0.740908	−	0.306894i	−0.0198823	−	0.999802i	$-0.506329\pi$
$211$	−10.7623	−	4.45790i	−0.740908	−	0.306894i	−0.721026	+	0.692908i	$0.756329\pi$
$212$		0			0
$213$	2.73161	+	0.359624i	0.187167	+	0.0246410i
$214$		0			0
$215$	4.82861	−	18.0206i	0.329309	−	1.22900i
$216$		0			0
$217$	−14.1083	−	20.6323i	−0.957734	−	1.40061i
$218$		0			0
$219$	26.9243	+	20.6597i	1.81937	+	1.39606i
$220$		0			0
$221$	−9.61129	−	12.5257i	−0.646525	−	0.842568i
$222$		0			0
$223$	20.9534			1.40315			0.701573	−	0.712597i	$-0.252481\pi$
$223$	20.9534			1.40315			0.701573	+	0.712597i	$0.252481\pi$
$224$		0			0
$225$	−18.4580			−1.23054
$226$		0			0
$227$	−0.300327	−	0.391394i	−0.0199334	−	0.0259777i	0.783280	−	0.621669i	$-0.213545\pi$
$227$	−0.300327	−	0.391394i	−0.0199334	−	0.0259777i	−0.803214	+	0.595691i	$0.796878\pi$
$228$		0			0
$229$	13.0467	+	10.0111i	0.862152	+	0.661552i	0.942131	−	0.335244i	$-0.108819\pi$
$229$	13.0467	+	10.0111i	0.862152	+	0.661552i	−0.0799794	+	0.996797i	$0.525485\pi$
$230$		0			0
$231$	−16.8911	+	1.28910i	−1.11135	+	0.0848163i
$232$		0			0
$233$	−3.09783	+	11.5613i	−0.202946	+	0.757404i	0.787120	+	0.616800i	$0.211571\pi$
$233$	−3.09783	+	11.5613i	−0.202946	+	0.757404i	−0.990066	+	0.140604i	$0.955095\pi$
$234$		0			0
$235$	3.36322	+	0.442776i	0.219392	+	0.0288835i
$236$		0			0
$237$	0.953548	+	0.394973i	0.0619396	+	0.0256562i
$238$		0			0
$239$			21.1899i			1.37066i	0.728234	+	0.685329i	$0.240342\pi$
$239$			21.1899i			1.37066i	−0.728234	+	0.685329i	$0.759658\pi$
$240$		0			0
$241$	−2.64873	−	1.52924i	−0.170620	−	0.0985073i	0.412258	−	0.911067i	$-0.364740\pi$
$241$	−2.64873	−	1.52924i	−0.170620	−	0.0985073i	−0.582878	+	0.812560i	$0.698073\pi$
$242$		0			0
$243$	2.73157	+	20.7484i	0.175231	+	1.33101i
$244$		0			0
$245$	0.521906	+	24.3372i	0.0333433	+	1.55485i
$246$		0			0
$247$	0.892963	−	3.33258i	0.0568179	−	0.212047i
$248$		0			0
$249$	5.76436	+	21.5129i	0.365302	+	1.36332i
$250$		0			0
$251$	1.84890	−	0.765839i	0.116701	−	0.0483393i	−0.323569	−	0.946205i	$-0.604883\pi$
$251$	1.84890	−	0.765839i	0.116701	−	0.0483393i	0.440270	+	0.897865i	$0.354883\pi$
$252$		0			0
$253$	−4.81130	+	11.6155i	−0.302484	+	0.730261i
$254$		0			0
$255$	−32.6248	+	56.5078i	−2.04304	+	3.53866i
$256$		0			0
$257$	−4.12526	−	7.14516i	−0.257327	−	0.445703i	0.708198	−	0.706014i	$-0.249508\pi$
$257$	−4.12526	−	7.14516i	−0.257327	−	0.445703i	−0.965525	+	0.260311i	$0.916175\pi$
$258$		0			0
$259$	−11.1458	+	5.64586i	−0.692568	+	0.350817i
$260$		0			0
$261$	0.510496	+	0.391718i	0.0315989	+	0.0242467i
$262$		0			0
$263$	2.34212	+	8.74090i	0.144421	+	0.538987i	0.999780	+	0.0209518i	$0.00666964\pi$
$263$	2.34212	+	8.74090i	0.144421	+	0.538987i	−0.855359	+	0.518035i	$0.826664\pi$
$264$		0			0
$265$	18.6650	+	18.6650i	1.14658	+	1.14658i
$266$		0			0
$267$	6.51492	+	15.7284i	0.398707	+	0.962563i
$268$		0			0
$269$	4.43119	−	3.40017i	0.270174	−	0.207312i	−0.464784	−	0.885424i	$-0.653868\pi$
$269$	4.43119	−	3.40017i	0.270174	−	0.207312i	0.734959	+	0.678112i	$0.237201\pi$
$270$		0			0
$271$	−5.37806	+	3.10502i	−0.326694	+	0.188617i	−0.654372	−	0.756173i	$-0.727067\pi$
$271$	−5.37806	+	3.10502i	−0.326694	+	0.188617i	0.327678	+	0.944789i	$0.393734\pi$
$272$		0			0
$273$	12.2577	+	2.30188i	0.741870	+	0.139316i
$274$		0			0
$275$	−2.50460	−	19.0244i	−0.151033	−	1.14721i
$276$		0			0
$277$	−4.95715	−	0.652622i	−0.297846	−	0.0392122i	−0.0198780	−	0.999802i	$-0.506328\pi$
$277$	−4.95715	−	0.652622i	−0.297846	−	0.0392122i	−0.277969	+	0.960590i	$0.589661\pi$
$278$		0			0
$279$	17.3828	+	17.3828i	1.04068	+	1.04068i
$280$		0			0
$281$	12.7750	−	12.7750i	0.762093	−	0.762093i	−0.214607	−	0.976700i	$-0.568847\pi$
$281$	12.7750	−	12.7750i	0.762093	−	0.762093i	0.976700	+	0.214607i	$0.0688472\pi$
$282$		0			0
$283$	2.65472	−	20.1646i	0.157806	−	1.19866i	−0.710886	−	0.703307i	$-0.751706\pi$
$283$	2.65472	−	20.1646i	0.157806	−	1.19866i	0.868693	−	0.495352i	$-0.164961\pi$
$284$		0			0
$285$	−14.1367	+	1.86114i	−0.837388	+	0.110244i
$286$		0			0
$287$	2.90689	−	1.02164i	0.171588	−	0.0603055i
$288$		0			0
$289$	22.9213	+	39.7008i	1.34831	+	2.33534i
$290$		0			0
$291$	−12.9748	−	16.9091i	−0.760598	−	0.991231i
$292$		0			0
$293$	−23.9894	+	9.93674i	−1.40148	+	0.580510i	−0.950134	−	0.311841i	$-0.899054\pi$
$293$	−23.9894	+	9.93674i	−1.40148	+	0.580510i	−0.451341	+	0.892351i	$0.649054\pi$
$294$		0			0
$295$	3.53284	−	3.53284i	0.205690	−	0.205690i
$296$		0			0
$297$	−2.46044	+	0.659273i	−0.142769	+	0.0382549i
$298$		0			0
$299$	5.63491	−	7.34355i	0.325875	−	0.424689i
$300$		0			0
$301$	14.1727	+	0.776433i	0.816899	+	0.0447528i
$302$		0			0
$303$	17.9952	−	10.3895i	1.03380	−	0.596864i
$304$		0			0
$305$	16.7603	+	9.67659i	0.959694	+	0.554080i
$306$		0			0
$307$	1.52272	+	0.630732i	0.0869063	+	0.0359978i	0.425713	−	0.904858i	$-0.360023\pi$
$307$	1.52272	+	0.630732i	0.0869063	+	0.0359978i	−0.338807	+	0.940856i	$0.610023\pi$
$308$		0			0
$309$	−15.7441	−	38.0097i	−0.895653	−	2.16230i
$310$		0			0
$311$	22.4323	−	6.01071i	1.27202	−	0.340836i	0.441214	−	0.897402i	$-0.354548\pi$
$311$	22.4323	−	6.01071i	1.27202	−	0.340836i	0.830804	+	0.556566i	$0.187881\pi$
$312$		0			0
$313$	15.0729	+	4.03878i	0.851971	+	0.228285i	0.658276	−	0.752777i	$-0.271286\pi$
$313$	15.0729	+	4.03878i	0.851971	+	0.228285i	0.193695	+	0.981062i	$0.437953\pi$
$314$		0			0
$315$	−4.92229	−	23.4304i	−0.277339	−	1.32015i
$316$		0			0
$317$	7.27433	−	0.957684i	0.408567	−	0.0537889i	0.0765581	−	0.997065i	$-0.475607\pi$
$317$	7.27433	−	0.957684i	0.408567	−	0.0537889i	0.332009	+	0.943276i	$0.392274\pi$
$318$		0			0
$319$	−0.334466	+	0.579312i	−0.0187265	+	0.0324352i
$320$		0			0
$321$	4.36755			0.243773
$322$		0			0
$323$	−5.25528	+	12.6874i	−0.292412	+	0.705944i
$324$		0			0
$325$	−1.84398	+	14.0064i	−0.102285	+	0.776935i
$326$		0			0
$327$	−19.0867	−	5.11426i	−1.05549	−	0.282819i
$328$		0			0
$329$	0.196395	+	2.57336i	0.0108276	+	0.141874i
$330$		0			0
$331$	0.486928	−	0.634576i	0.0267640	−	0.0348795i	−0.779780	−	0.626054i	$-0.784669\pi$
$331$	0.486928	−	0.634576i	0.0267640	−	0.0348795i	0.806544	+	0.591175i	$0.201336\pi$
$332$		0			0
$333$	9.74904	−	7.48070i	0.534244	−	0.409940i
$334$		0			0
$335$		−	40.3837i		−	2.20640i
$336$		0			0
$337$			31.5554i			1.71893i	0.511193	+	0.859466i	$0.329204\pi$
$337$			31.5554i			1.71893i	−0.511193	+	0.859466i	$0.670796\pi$
$338$		0			0
$339$	−0.773116	+	0.593232i	−0.0419899	+	0.0322200i
$340$		0			0
$341$	−15.5574	+	20.2748i	−0.842480	+	1.09794i
$342$		0			0
$343$	−18.0388	+	4.19536i	−0.974005	+	0.226528i
$344$		0			0
$345$	−36.9510	−	9.90100i	−1.98938	−	0.533052i
$346$		0			0
$347$	4.20229	−	31.9196i	0.225591	−	1.71353i	−0.386117	−	0.922450i	$-0.626184\pi$
$347$	4.20229	−	31.9196i	0.225591	−	1.71353i	0.611708	−	0.791084i	$-0.290483\pi$
$348$		0			0
$349$	12.9498	−	31.2635i	0.693185	−	1.67350i	−0.0450790	−	0.998983i	$-0.514354\pi$
$349$	12.9498	−	31.2635i	0.693185	−	1.67350i	0.738264	−	0.674512i	$-0.235646\pi$
$350$		0			0
$351$	1.87536			0.100099
$352$		0			0
$353$	16.4146	−	28.4310i	0.873664	−	1.51323i	0.0154841	−	0.999880i	$-0.495071\pi$
$353$	16.4146	−	28.4310i	0.873664	−	1.51323i	0.858180	−	0.513350i	$-0.171596\pi$
$354$		0			0
$355$	−4.01341	+	0.528376i	−0.213010	+	0.0280433i
$356$		0			0
$357$	−47.1764	−	15.4522i	−2.49684	−	0.817817i
$358$		0			0
$359$	29.7349	+	7.96745i	1.56935	+	0.420506i	0.935608	−	0.353040i	$-0.114852\pi$
$359$	29.7349	+	7.96745i	1.56935	+	0.420506i	0.633741	+	0.773546i	$0.281519\pi$
$360$		0			0
$361$	15.4539	−	4.14086i	0.813363	−	0.217940i
$362$		0			0
$363$	−3.33520	−	8.05187i	−0.175052	−	0.422614i
$364$		0			0
$365$	−46.0668	−	19.0815i	−2.41125	−	0.998770i
$366$		0			0
$367$	−4.58516	−	2.64724i	−0.239343	−	0.138185i	0.375532	−	0.926810i	$-0.377460\pi$
$367$	−4.58516	−	2.64724i	−0.239343	−	0.138185i	−0.614875	+	0.788625i	$0.710793\pi$
$368$		0			0
$369$	−2.62444	+	1.51522i	−0.136623	+	0.0788791i
$370$		0			0
$371$	−10.9776	+	16.8167i	−0.569928	+	0.873077i
$372$		0			0
$373$	7.79880	−	10.1636i	0.403807	−	0.526251i	−0.546545	−	0.837430i	$-0.684057\pi$
$373$	7.79880	−	10.1636i	0.403807	−	0.526251i	0.950351	+	0.311179i	$0.100724\pi$
$374$		0			0
$375$	16.6430	−	4.45948i	0.859442	−	0.230287i
$376$		0			0
$377$	0.348244	−	0.348244i	0.0179355	−	0.0179355i
$378$		0			0
$379$	5.09850	−	2.11187i	0.261892	−	0.108479i	−0.247874	−	0.968792i	$-0.579732\pi$
$379$	5.09850	−	2.11187i	0.261892	−	0.108479i	0.509766	+	0.860313i	$0.329732\pi$
$380$		0			0
$381$	16.2291	+	21.1502i	0.831442	+	1.08356i
$382$		0			0
$383$	−3.57816	−	6.19756i	−0.182836	−	0.316681i	0.760009	−	0.649912i	$-0.225194\pi$
$383$	−3.57816	−	6.19756i	−0.182836	−	0.316681i	−0.942845	+	0.333231i	$0.891861\pi$
$384$		0			0
$385$	23.4813	−	8.25262i	1.19672	−	0.420592i
$386$		0			0
$387$	−13.8407	+	1.82216i	−0.703561	+	0.0926256i
$388$		0			0
$389$	0.357906	−	2.71857i	0.0181466	−	0.137837i	−0.979973	−	0.199129i	$-0.936189\pi$
$389$	0.357906	−	2.71857i	0.0181466	−	0.137837i	0.998120	+	0.0612920i	$0.0195221\pi$
$390$		0			0
$391$	−26.0522	+	26.0522i	−1.31751	+	1.31751i
$392$		0			0
$393$	24.8680	+	24.8680i	1.25443	+	1.25443i
$394$		0			0
$395$	−1.50346	−	0.197934i	−0.0756471	−	0.00995913i
$396$		0			0
$397$	0.537590	+	4.08340i	0.0269809	+	0.204940i	0.999626	−	0.0273571i	$-0.00870912\pi$
$397$	0.537590	+	4.08340i	0.0269809	+	0.204940i	−0.972645	+	0.232297i	$0.925376\pi$
$398$		0			0
$399$	−3.59696	−	10.2345i	−0.180073	−	0.512365i
$400$		0			0
$401$	30.4012	−	17.5522i	1.51817	−	0.876513i	0.518394	−	0.855142i	$-0.326530\pi$
$401$	30.4012	−	17.5522i	1.51817	−	0.876513i	0.999772	−	0.0213718i	$-0.00680336\pi$
$402$		0			0
$403$	14.9270	−	11.4539i	0.743567	−	0.570559i
$404$		0			0
$405$	−13.3549	−	32.2415i	−0.663609	−	1.60209i
$406$		0			0
$407$	9.03308	+	9.03308i	0.447753	+	0.447753i
$408$		0			0
$409$	2.50492	+	9.34849i	0.123860	+	0.462253i	0.999796	−	0.0201740i	$-0.00642203\pi$
$409$	2.50492	+	9.34849i	0.123860	+	0.462253i	−0.875936	+	0.482427i	$0.839755\pi$
$410$		0			0
$411$	−12.2244	−	9.38009i	−0.602984	−	0.462686i
$412$		0			0
$413$	3.18300	+	2.07780i	0.156625	+	0.102242i
$414$		0			0
$415$	−16.3614	−	28.3387i	−0.803148	−	1.39109i
$416$		0			0
$417$	0.0102584	−	0.0177681i	0.000502356	−	0.000870107i
$418$		0			0
$419$	3.83604	−	9.26102i	0.187403	−	0.452430i	−0.802055	−	0.597250i	$-0.796260\pi$
$419$	3.83604	−	9.26102i	0.187403	−	0.452430i	0.989458	+	0.144819i	$0.0462601\pi$
$420$		0			0
$421$	21.6933	−	8.98568i	1.05727	−	0.437935i	0.214788	−	0.976661i	$-0.431094\pi$
$421$	21.6933	−	8.98568i	1.05727	−	0.437935i	0.842481	+	0.538726i	$0.181094\pi$
$422$		0			0
$423$	−0.656969	−	2.45184i	−0.0319429	−	0.119213i
$424$		0			0
$425$	14.5537	−	54.3151i	0.705958	−	2.63467i
$426$		0			0
$427$	−4.58316	+	13.9926i	−0.221794	+	0.677150i
$428$		0			0
$429$	−1.66446	−	12.6429i	−0.0803611	−	0.610403i
$430$		0			0
$431$	21.6047	+	12.4735i	1.04066	+	0.600827i	0.920021	−	0.391869i	$-0.128171\pi$
$431$	21.6047	+	12.4735i	1.04066	+	0.600827i	0.120642	+	0.992696i	$0.461505\pi$
$432$		0			0
$433$		−	27.3257i		−	1.31319i	−0.754243	−	0.656596i	$-0.771996\pi$
$433$		−	27.3257i		−	1.31319i	0.754243	−	0.656596i	$-0.228004\pi$
$434$		0			0
$435$	−1.88043	−	0.778899i	−0.0901597	−	0.0373454i
$436$		0			0
$437$	−7.98234	−	1.05089i	−0.381847	−	0.0502711i
$438$		0			0
$439$	−0.645658	+	2.40963i	−0.0308156	+	0.115005i	−0.979621	−	0.200857i	$-0.935627\pi$
$439$	−0.645658	+	2.40963i	−0.0308156	+	0.115005i	0.948805	+	0.315863i	$0.102294\pi$
$440$		0			0
$441$	16.6753	−	7.32985i	0.794062	−	0.349040i
$442$		0			0
$443$	16.3557	+	12.5501i	0.777081	+	0.596275i	0.919299	−	0.393560i	$-0.128757\pi$
$443$	16.3557	+	12.5501i	0.777081	+	0.596275i	−0.142218	+	0.989835i	$0.545423\pi$
$444$		0			0
$445$	−15.2269	−	19.8441i	−0.721825	−	0.940700i
$446$		0			0
$447$	−32.6297			−1.54333
$448$		0			0
$449$	−16.6657			−0.786502			−0.393251	−	0.919431i	$-0.628650\pi$
$449$	−16.6657			−0.786502			−0.393251	+	0.919431i	$0.628650\pi$
$450$		0			0
$451$	−1.91782	−	2.49935i	−0.0903067	−	0.117690i
$452$		0			0
$453$	−7.91117	−	6.07045i	−0.371699	−	0.285215i
$454$		0			0
$455$	−18.2713	+	1.39443i	−0.856570	+	0.0653719i
$456$		0			0
$457$	−1.00153	+	3.73775i	−0.0468494	+	0.174844i	−0.985386	−	0.170335i	$-0.945515\pi$
$457$	−1.00153	+	3.73775i	−0.0468494	+	0.174844i	0.938537	+	0.345179i	$0.112182\pi$
$458$		0			0
$459$	−7.40071	−	0.974321i	−0.345435	−	0.0454774i
$460$		0			0
$461$	14.0710	+	5.82839i	0.655351	+	0.271455i	0.685481	−	0.728091i	$-0.259592\pi$
$461$	14.0710	+	5.82839i	0.655351	+	0.271455i	−0.0301296	+	0.999546i	$0.509592\pi$
$462$		0			0
$463$			25.2657i			1.17420i	0.809515	+	0.587099i	$0.199730\pi$
$463$			25.2657i			1.17420i	−0.809515	+	0.587099i	$0.800270\pi$
$464$		0			0
$465$	−67.3411	−	38.8794i	−3.12287	−	1.80299i
$466$		0			0
$467$	−1.49931	−	11.3884i	−0.0693797	−	0.526991i	−0.990479	−	0.137663i	$-0.956041\pi$
$467$	−1.49931	−	11.3884i	−0.0693797	−	0.526991i	0.921099	−	0.389327i	$-0.127293\pi$
$468$		0			0
$469$	30.0680	−	6.31673i	1.38841	−	0.291679i
$470$		0			0
$471$	−9.45894	+	35.3012i	−0.435845	+	1.62659i
$472$		0			0
$473$	−3.75613	−	14.0181i	−0.172707	−	0.644552i
$474$		0			0
$475$	11.3526	−	4.70240i	0.520893	−	0.215761i
$476$		0			0
$477$	7.55865	−	18.2482i	0.346087	−	0.835527i
$478$		0			0
$479$	−1.40022	+	2.42526i	−0.0639778	+	0.110813i	−0.896240	−	0.443569i	$-0.853712\pi$
$479$	−1.40022	+	2.42526i	−0.0639778	+	0.110813i	0.832262	+	0.554382i	$0.187045\pi$
$480$		0			0
$481$	−4.70259	−	8.14513i	−0.214420	−	0.371386i
$482$		0			0
$483$	1.59206	−	29.0608i	0.0724414	−	1.32231i
$484$		0			0
$485$	24.8437	+	19.0632i	1.12809	+	0.865617i
$486$		0			0
$487$	3.28151	+	12.2468i	0.148699	+	0.554953i	0.999563	+	0.0295666i	$0.00941272\pi$
$487$	3.28151	+	12.2468i	0.148699	+	0.554953i	−0.850863	+	0.525387i	$0.823921\pi$
$488$		0			0
$489$	−9.82284	−	9.82284i	−0.444204	−	0.444204i
$490$		0			0
$491$	−15.7884	−	38.1167i	−0.712523	−	1.72018i	−0.693599	−	0.720361i	$-0.743976\pi$
$491$	−15.7884	−	38.1167i	−0.712523	−	1.72018i	−0.0189236	−	0.999821i	$-0.506024\pi$
$492$		0			0
$493$	−1.55519	+	1.19334i	−0.0700423	+	0.0537454i
$494$		0			0
$495$	−21.1997	+	12.2397i	−0.952857	+	0.550132i
$496$		0			0
$497$	−1.02118	−	2.90557i	−0.0458060	−	0.130333i
$498$		0			0
$499$	1.58992	+	12.0767i	0.0711748	+	0.540626i	0.989471	+	0.144732i	$0.0462319\pi$
$499$	1.58992	+	12.0767i	0.0711748	+	0.540626i	−0.918296	+	0.395894i	$0.870435\pi$
$500$		0			0
$501$	10.6332	+	1.39989i	0.475056	+	0.0625423i
$502$		0			0
$503$	−18.3719	−	18.3719i	−0.819162	−	0.819162i	0.166824	−	0.985987i	$-0.446649\pi$
$503$	−18.3719	−	18.3719i	−0.819162	−	0.819162i	−0.985987	+	0.166824i	$0.946649\pi$
$504$		0			0
$505$	−21.5877	+	21.5877i	−0.960641	+	0.960641i
$506$		0			0
$507$	2.79080	−	21.1982i	0.123944	−	0.941446i
$508$		0			0
$509$	−20.5602	+	2.70680i	−0.911314	+	0.119977i	−0.571582	−	0.820545i	$-0.693670\pi$
$509$	−20.5602	+	2.70680i	−0.911314	+	0.119977i	−0.339733	+	0.940522i	$0.610337\pi$
$510$		0			0
$511$	7.00159	−	37.2840i	0.309732	−	1.64935i
$512$		0			0
$513$	−0.815600	−	1.41266i	−0.0360096	−	0.0623705i
$514$		0			0
$515$	36.7977	+	47.9558i	1.62150	+	2.11318i
$516$		0			0
$517$	2.43792	−	1.00982i	0.107220	−	0.0444119i
$518$		0			0
$519$	25.9579	−	25.9579i	1.13942	−	1.13942i
$520$		0			0
$521$	−11.2859	+	3.02404i	−0.494444	+	0.132486i	−0.497420	−	0.867510i	$-0.665719\pi$
$521$	−11.2859	+	3.02404i	−0.494444	+	0.132486i	0.00297645	+	0.999996i	$0.499053\pi$
$522$		0			0
$523$	7.43424	−	9.68849i	0.325077	−	0.423648i	−0.602014	−	0.798486i	$-0.705635\pi$
$523$	7.43424	−	9.68849i	0.325077	−	0.423648i	0.927091	+	0.374838i	$0.122302\pi$
$524$		0			0
$525$	20.0724	+	39.6261i	0.876030	+	1.72942i
$526$		0			0
$527$	−64.8569	+	37.4451i	−2.82521	+	1.63114i
$528$		0			0
$529$	1.21200	+	0.699749i	0.0526957	+	0.0304239i
$530$		0			0
$531$	−3.45396	−	1.43068i	−0.149889	−	0.0620860i
$532$		0			0
$533$	0.887600	+	2.14286i	0.0384462	+	0.0928174i
$534$		0			0
$535$	−6.19836	+	1.66085i	−0.267978	+	0.0718046i
$536$		0			0
$537$	−19.1061	−	5.11946i	−0.824489	−	0.220921i
$538$		0			0
$539$	9.81744	+	16.1923i	0.422867	+	0.697453i
$540$		0			0
$541$	−13.8708	+	1.82612i	−0.596351	+	0.0785111i	−0.422659	−	0.906289i	$-0.638903\pi$
$541$	−13.8708	+	1.82612i	−0.596351	+	0.0785111i	−0.173692	+	0.984800i	$0.555570\pi$
$542$		0			0
$543$	19.2224	−	33.2942i	0.824913	−	1.42879i
$544$		0			0
$545$	29.0323			1.24361
$546$		0			0
$547$	9.20321	−	22.2185i	0.393501	−	0.949995i	−0.595670	−	0.803229i	$-0.703114\pi$
$547$	9.20321	−	22.2185i	0.393501	−	0.949995i	0.989171	−	0.146766i	$-0.0468865\pi$
$548$		0			0
$549$	1.89022	−	14.3576i	0.0806726	−	0.612769i
$550$		0			0
$551$	−0.413775	−	0.110871i	−0.0176274	−	0.00472325i
$552$		0			0
$553$	−0.0877941	−	1.15037i	−0.00373339	−	0.0489187i
$554$		0			0
$555$	−23.6623	+	30.8374i	−1.00441	+	1.30897i
$556$		0			0
$557$	−12.4764	+	9.57349i	−0.528643	+	0.405642i	−0.838302	−	0.545206i	$-0.816452\pi$
$557$	−12.4764	+	9.57349i	−0.528643	+	0.405642i	0.309659	+	0.950848i	$0.399785\pi$
$558$		0			0
$559$			10.6847i			0.451913i
$560$		0			0
$561$			50.7570i			2.14296i
$562$		0			0
$563$	14.0673	−	10.7942i	0.592866	−	0.454922i	−0.268237	−	0.963353i	$-0.586441\pi$
$563$	14.0673	−	10.7942i	0.592866	−	0.454922i	0.861103	+	0.508431i	$0.169774\pi$
$564$		0			0
$565$	0.871605	−	1.13590i	0.0366687	−	0.0477876i
$566$		0			0
$567$	21.9167	−	14.9866i	0.920415	−	0.629378i
$568$		0			0
$569$	18.4201	+	4.93565i	0.772211	+	0.206913i	0.623348	−	0.781944i	$-0.285772\pi$
$569$	18.4201	+	4.93565i	0.772211	+	0.206913i	0.148863	+	0.988858i	$0.452439\pi$
$570$		0			0
$571$	−5.35143	+	40.6481i	−0.223950	+	1.70107i	0.397488	+	0.917607i	$0.369882\pi$
$571$	−5.35143	+	40.6481i	−0.223950	+	1.70107i	−0.621438	+	0.783463i	$0.713451\pi$
$572$		0			0
$573$	−14.2606	+	34.4281i	−0.595744	+	1.43825i
$574$		0			0
$575$	32.9672			1.37483
$576$		0			0
$577$	−15.8000	+	27.3664i	−0.657764	+	1.13928i	0.323430	+	0.946252i	$0.395164\pi$
$577$	−15.8000	+	27.3664i	−0.657764	+	1.13928i	−0.981193	+	0.193028i	$0.938169\pi$
$578$		0			0
$579$	33.6139	−	4.42536i	1.39695	−	0.183912i
$580$		0			0
$581$	18.5406	−	16.6147i	0.769194	−	0.689292i
$582$		0			0
$583$	19.8337	+	5.31443i	0.821428	+	0.220101i
$584$		0			0
$585$	17.4084	−	4.66458i	0.719750	−	0.192856i
$586$		0			0
$587$	−8.61161	−	20.7903i	−0.355439	−	0.858106i	−0.995929	−	0.0901398i	$-0.971269\pi$
$587$	−8.61161	−	20.7903i	−0.355439	−	0.858106i	0.640490	−	0.767967i	$-0.278731\pi$
$588$		0			0
$589$	−15.1197	−	6.26279i	−0.622997	−	0.258054i
$590$		0			0
$591$	19.1504	+	11.0565i	0.787743	+	0.454804i
$592$		0			0
$593$	10.5063	−	6.06579i	0.431440	−	0.249092i	−0.268520	−	0.963274i	$-0.586534\pi$
$593$	10.5063	−	6.06579i	0.431440	−	0.249092i	0.699960	+	0.714182i	$0.253201\pi$
$594$		0			0
$595$	72.8279	+	3.98979i	2.98565	+	0.163566i
$596$		0			0
$597$	13.6069	−	17.7328i	0.556892	−	0.725756i
$598$		0			0
$599$	−19.3969	+	5.19739i	−0.792537	+	0.212360i	−0.632305	−	0.774720i	$-0.717891\pi$
$599$	−19.3969	+	5.19739i	−0.792537	+	0.212360i	−0.160232	+	0.987079i	$0.551224\pi$
$600$		0			0
$601$	−26.4614	+	26.4614i	−1.07938	+	1.07938i	−0.0828178	+	0.996565i	$0.526392\pi$
$601$	−26.4614	+	26.4614i	−1.07938	+	1.07938i	−0.996565	+	0.0828178i	$0.973608\pi$
$602$		0			0
$603$	−27.9180	+	11.5640i	−1.13691	+	0.470923i
$604$		0			0
$605$	7.79514	+	10.1588i	0.316917	+	0.413015i
$606$		0			0
$607$	−8.97752	−	15.5495i	−0.364386	−	0.631136i	0.624291	−	0.781192i	$-0.285388\pi$
$607$	−8.97752	−	15.5495i	−0.364386	−	0.631136i	−0.988677	+	0.150056i	$0.952055\pi$
$608$		0			0
$609$	0.285803	−	1.52192i	0.0115813	−	0.0616713i
$610$		0			0
$611$	−1.92615	+	0.253582i	−0.0779236	+	0.0102588i
$612$		0			0
$613$	−0.963901	+	7.32155i	−0.0389316	+	0.295715i	0.960892	+	0.276924i	$0.0893150\pi$
$613$	−0.963901	+	7.32155i	−0.0389316	+	0.295715i	−0.999823	+	0.0187908i	$0.994018\pi$
$614$		0			0
$615$	6.77807	−	6.77807i	0.273318	−	0.273318i
$616$		0			0
$617$	−8.61926	−	8.61926i	−0.346999	−	0.346999i	0.511992	−	0.858990i	$-0.328908\pi$
$617$	−8.61926	−	8.61926i	−0.346999	−	0.346999i	−0.858990	+	0.511992i	$0.828908\pi$
$618$		0			0
$619$	39.9239	+	5.25608i	1.60468	+	0.211260i	0.879016	−	0.476793i	$-0.158201\pi$
$619$	39.9239	+	5.25608i	1.60468	+	0.211260i	0.725661	+	0.688053i	$0.241534\pi$
$620$		0			0
$621$	−0.571225	−	4.33889i	−0.0229225	−	0.174113i
$622$		0			0
$623$	12.3933	−	14.4413i	0.496527	−	0.578577i
$624$		0			0
$625$	8.79131	−	5.07567i	0.351652	−	0.203027i
$626$		0			0
$627$	−8.79965	+	6.75221i	−0.351424	+	0.269657i
$628$		0			0
$629$	14.3260	+	34.5861i	0.571217	+	1.37904i
$630$		0			0
$631$	−2.16966	−	2.16966i	−0.0863726	−	0.0863726i	0.662600	−	0.748973i	$-0.269453\pi$
$631$	−2.16966	−	2.16966i	−0.0863726	−	0.0863726i	−0.748973	+	0.662600i	$0.769453\pi$
$632$		0			0
$633$	−7.13616	−	26.6325i	−0.283637	−	1.05855i
$634$		0			0
$635$	−31.0748	−	23.8446i	−1.23317	−	0.946242i
$636$		0			0
$637$	−3.89618	−	13.3859i	−0.154372	−	0.530368i
$638$		0			0
$639$	1.51453	+	2.62324i	0.0599139	+	0.103774i
$640$		0			0
$641$	−1.28091	+	2.21860i	−0.0505930	+	0.0876296i	−0.890213	−	0.455545i	$-0.849444\pi$
$641$	−1.28091	+	2.21860i	−0.0505930	+	0.0876296i	0.839620	+	0.543174i	$0.182778\pi$
$642$		0			0
$643$	−1.92686	+	4.65185i	−0.0759880	+	0.183451i	−0.957309	−	0.289067i	$-0.906655\pi$
$643$	−1.92686	+	4.65185i	−0.0759880	+	0.183451i	0.881321	+	0.472518i	$0.156655\pi$
$644$		0			0
$645$	40.7962	−	16.8983i	1.60635	−	0.665371i
$646$		0			0
$647$	5.66762	+	21.1519i	0.222817	+	0.831565i	0.983267	+	0.182169i	$0.0583117\pi$
$647$	5.66762	+	21.1519i	0.222817	+	0.831565i	−0.760450	+	0.649396i	$0.775022\pi$
$648$		0			0
$649$	1.00590	−	3.75406i	0.0394849	−	0.147360i
$650$		0			0
$651$	18.4146	−	56.2207i	0.721725	−	2.20346i
$652$		0			0
$653$	4.72054	+	35.8560i	0.184729	+	1.40316i	0.792901	+	0.609350i	$0.208570\pi$
$653$	4.72054	+	35.8560i	0.184729	+	1.40316i	−0.608172	+	0.793805i	$0.708097\pi$
$654$		0			0
$655$	−44.7488	−	25.8358i	−1.74848	−	1.00949i
$656$		0			0
$657$			37.3108i			1.45563i
$658$		0			0
$659$	−15.1726	−	6.28471i	−0.591041	−	0.244817i	0.0670571	−	0.997749i	$-0.478639\pi$
$659$	−15.1726	−	6.28471i	−0.591041	−	0.244817i	−0.658099	+	0.752932i	$0.728639\pi$
$660$		0			0
$661$	31.5018	+	4.14729i	1.22528	+	0.161311i	0.715263	−	0.698855i	$-0.246307\pi$
$661$	31.5018	+	4.14729i	1.22528	+	0.161311i	0.510014	+	0.860166i	$0.329640\pi$
$662$		0			0
$663$	9.67183	−	36.0958i	0.375623	−	1.40184i
$664$		0			0
$665$	8.99661	+	13.1568i	0.348873	+	0.510199i
$666$		0			0
$667$	−0.911778	−	0.699632i	−0.0353042	−	0.0270899i
$668$		0			0
$669$	30.1912	+	39.3460i	1.16726	+	1.52120i
$670$		0			0
$671$	15.0546			0.581178
$672$		0			0
$673$	33.1865			1.27924			0.639622	−	0.768689i	$-0.279091\pi$
$673$	33.1865			1.27924			0.639622	+	0.768689i	$0.279091\pi$
$674$		0			0
$675$	4.06607	+	5.29901i	0.156503	+	0.203959i
$676$		0			0
$677$	−34.1214	−	26.1823i	−1.31139	−	1.00627i	−0.998402	−	0.0565108i	$-0.982002\pi$
$677$	−34.1214	−	26.1823i	−1.31139	−	1.00627i	−0.312991	−	0.949756i	$-0.601331\pi$
$678$		0			0
$679$	−10.3077	+	21.4794i	−0.395572	+	0.824303i
$680$		0			0
$681$	0.302219	−	1.12790i	0.0115811	−	0.0432211i
$682$		0			0
$683$	−19.5305	−	2.57124i	−0.747314	−	0.0983857i	−0.252755	−	0.967530i	$-0.581337\pi$
$683$	−19.5305	−	2.57124i	−0.747314	−	0.0983857i	−0.494558	+	0.869144i	$0.664670\pi$
$684$		0			0
$685$	20.9156	+	8.66352i	0.799144	+	0.331016i
$686$		0			0
$687$			38.9236i			1.48503i
$688$		0			0
$689$	−13.0920	−	7.55869i	−0.498767	−	0.287963i
$690$		0			0
$691$	4.88106	+	37.0753i	0.185684	+	1.41041i	0.789727	+	0.613459i	$0.210222\pi$
$691$	4.88106	+	37.0753i	0.185684	+	1.41041i	−0.604043	+	0.796952i	$0.706444\pi$
$692$		0			0
$693$	−12.4291	−	13.8699i	−0.472144	−	0.526874i
$694$		0			0
$695$	−0.00780191	+	0.0291171i	−0.000295943	+	0.00110448i
$696$		0			0
$697$	−2.38942	−	8.91745i	−0.0905059	−	0.337772i
$698$		0			0
$699$	−26.1731	+	10.8413i	−0.989958	+	0.410054i
$700$		0			0
$701$	−2.62484	+	6.33692i	−0.0991388	+	0.239342i	−0.965666	−	0.259788i	$-0.916347\pi$
$701$	−2.62484	+	6.33692i	−0.0991388	+	0.239342i	0.866527	+	0.499131i	$0.166347\pi$
$702$		0			0
$703$	−4.09034	+	7.08468i	−0.154270	+	0.267204i
$704$		0			0
$705$	4.01453	+	6.95336i	0.151196	+	0.261879i
$706$		0			0
$707$	−19.4500	−	12.6966i	−0.731492	−	0.477504i
$708$		0			0
$709$	−23.9384	−	18.3686i	−0.899027	−	0.689848i	0.0521017	−	0.998642i	$-0.483408\pi$
$709$	−23.9384	−	18.3686i	−0.899027	−	0.689848i	−0.951129	+	0.308794i	$0.900075\pi$
$710$		0			0
$711$	0.293684	+	1.09604i	0.0110140	+	0.0411049i
$712$		0			0
$713$	−31.0467	−	31.0467i	−1.16271	−	1.16271i
$714$		0			0
$715$	7.16987	+	17.3096i	0.268138	+	0.647342i
$716$		0			0
$717$	−39.7899	+	30.5319i	−1.48598	+	1.14023i
$718$		0			0
$719$	−3.28187	+	1.89479i	−0.122393	+	0.0706637i	−0.559947	−	0.828529i	$-0.689178\pi$
$719$	−3.28187	+	1.89479i	−0.122393	+	0.0706637i	0.437554	+	0.899192i	$0.355845\pi$
$720$		0			0
$721$	−29.9500	+	34.8991i	−1.11540	+	1.29971i
$722$		0			0
$723$	−0.944893	−	7.17717i	−0.0351409	−	0.266922i
$724$		0			0
$725$	1.73904	+	0.228949i	0.0645863	+	0.00850294i
$726$		0			0
$727$	−10.0645	−	10.0645i	−0.373272	−	0.373272i	0.495395	−	0.868668i	$-0.335023\pi$
$727$	−10.0645	−	10.0645i	−0.373272	−	0.373272i	−0.868668	+	0.495395i	$0.835023\pi$
$728$		0			0
$729$	−13.7371	+	13.7371i	−0.508781	+	0.508781i
$730$		0			0
$731$	5.55108	−	42.1647i	0.205314	−	1.55952i
$732$		0			0
$733$	−3.00160	+	0.395168i	−0.110866	+	0.0145958i	−0.185755	−	0.982596i	$-0.559473\pi$
$733$	−3.00160	+	0.395168i	−0.110866	+	0.0145958i	0.0748888	+	0.997192i	$0.476140\pi$
$734$		0			0
$735$	−44.9480	+	36.0468i	−1.65793	+	1.32961i
$736$		0			0
$737$	−15.7071	−	27.2054i	−0.578577	−	1.00212i
$738$		0			0
$739$	−5.27338	−	6.87241i	−0.193985	−	0.252806i	0.686227	−	0.727388i	$-0.259266\pi$
$739$	−5.27338	−	6.87241i	−0.193985	−	0.252806i	−0.880211	+	0.474582i	$0.842599\pi$
$740$		0			0
$741$	7.54450	−	3.12504i	0.277154	−	0.114801i
$742$		0			0
$743$	30.6105	−	30.6105i	1.12299	−	1.12299i	0.131699	−	0.991290i	$-0.457957\pi$
$743$	30.6105	−	30.6105i	1.12299	−	1.12299i	0.991290	−	0.131699i	$-0.0420433\pi$
$744$		0			0
$745$	46.3075	−	12.4081i	1.69658	−	0.454596i
$746$		0			0
$747$	−14.9059	+	19.4258i	−0.545380	+	0.710753i
$748$		0			0
$749$	−2.20613	−	4.35525i	−0.0806101	−	0.159137i
$750$		0			0
$751$	43.0634	−	24.8627i	1.57141	−	0.907252i	0.575410	−	0.817865i	$-0.304843\pi$
$751$	43.0634	−	24.8627i	1.57141	−	0.907252i	0.995997	−	0.0893869i	$-0.0284908\pi$
$752$		0			0
$753$	4.10210	+	2.36835i	0.149489	+	0.0863074i
$754$		0			0
$755$	13.5358	+	5.60672i	0.492619	+	0.204049i
$756$		0			0
$757$	−2.17686	−	5.25541i	−0.0791193	−	0.191011i	0.879370	−	0.476139i	$-0.157964\pi$
$757$	−2.17686	−	5.25541i	−0.0791193	−	0.191011i	−0.958490	+	0.285128i	$0.907964\pi$
$758$		0			0
$759$	−28.7439	+	7.70189i	−1.04334	+	0.279561i
$760$		0			0
$761$	15.1537	+	4.06042i	0.549321	+	0.147190i	0.522796	−	0.852458i	$-0.324889\pi$
$761$	15.1537	+	4.06042i	0.549321	+	0.147190i	0.0265254	+	0.999648i	$0.491556\pi$
$762$		0			0
$763$	4.54116	+	21.6162i	0.164401	+	0.782558i
$764$		0			0
$765$	−71.1219	+	9.36338i	−2.57142	+	0.338534i
$766$		0			0
$767$	−1.43068	+	2.47802i	−0.0516590	+	0.0894760i
$768$		0			0
$769$	−5.19904			−0.187482			−0.0937411	−	0.995597i	$-0.529883\pi$
$769$	−5.19904			−0.187482			−0.0937411	+	0.995597i	$0.529883\pi$
$770$		0			0
$771$	7.47307	−	18.0416i	0.269136	−	0.649752i
$772$		0			0
$773$	−2.37738	+	18.0580i	−0.0855084	+	0.649500i	0.893996	+	0.448076i	$0.147890\pi$
$773$	−2.37738	+	18.0580i	−0.0855084	+	0.649500i	−0.979504	+	0.201425i	$0.935443\pi$
$774$		0			0
$775$	64.7280	+	17.3438i	2.32510	+	0.623009i
$776$		0			0
$777$	−26.6614	−	12.7945i	−0.956472	−	0.458999i
$778$		0			0
$779$	1.22814	−	1.60054i	0.0440026	−	0.0573453i
$780$		0			0
$781$	−2.49822	+	1.91695i	−0.0893933	+	0.0685939i
$782$		0			0
$783$		−	0.232846i		−	0.00832123i
$784$		0			0
$785$		−	53.6959i		−	1.91649i
$786$		0			0
$787$	−7.32521	+	5.62083i	−0.261116	+	0.200361i	−0.731020	−	0.682356i	$-0.760955\pi$
$787$	−7.32521	+	5.62083i	−0.261116	+	0.200361i	0.469904	+	0.882718i	$0.344289\pi$
$788$		0			0
$789$	−13.0388	+	16.9925i	−0.464193	+	0.604949i
$790$		0			0
$791$	0.982075	+	0.471285i	0.0349186	+	0.0167570i
$792$		0			0
$793$	−10.7061	−	2.86869i	−0.380184	−	0.101870i
$794$		0			0
$795$	−8.15488	+	61.9425i	−0.289224	+	2.19687i
$796$		0			0
$797$	−3.28952	+	7.94160i	−0.116521	+	0.281306i	−0.971371	−	0.237570i	$-0.923649\pi$
$797$	−3.28952	+	7.94160i	−0.116521	+	0.281306i	0.854850	+	0.518876i	$0.173649\pi$
$798$		0			0
$799$	7.73286			0.273569
$800$		0			0
$801$	−9.35830	+	16.2091i	−0.330659	+	0.572719i
$802$		0			0
$803$	−38.4556	+	5.06277i	−1.35707	+	0.178661i
$804$		0			0
$805$	8.79151	+	41.8481i	0.309860	+	1.47495i
$806$		0			0
$807$	12.7695	+	3.42159i	0.449509	+	0.120446i
$808$		0			0
$809$	−26.2561	+	7.03530i	−0.923115	+	0.247348i	−0.688917	−	0.724841i	$-0.741913\pi$
$809$	−26.2561	+	7.03530i	−0.923115	+	0.247348i	−0.234199	+	0.972189i	$0.575247\pi$
$810$		0			0
$811$	−8.45170	−	20.4042i	−0.296779	−	0.716489i	−0.999985	−	0.00550212i	$-0.998249\pi$
$811$	−8.45170	−	20.4042i	−0.296779	−	0.716489i	0.703205	−	0.710987i	$-0.251751\pi$
$812$		0			0
$813$	−13.5796	−	5.62487i	−0.476259	−	0.197273i
$814$		0			0
$815$	17.6757	+	10.2051i	0.619154	+	0.357469i
$816$		0			0
$817$	8.04848	−	4.64679i	0.281580	−	0.162571i
$818$		0			0
$819$	6.19603	+	12.2319i	0.216507	+	0.427419i
$820$		0			0
$821$	8.21023	−	10.6998i	0.286539	−	0.373425i	−0.627800	−	0.778375i	$-0.716044\pi$
$821$	8.21023	−	10.6998i	0.286539	−	0.373425i	0.914339	+	0.404950i	$0.132711\pi$
$822$		0			0
$823$	−2.05346	+	0.550223i	−0.0715791	+	0.0191796i	−0.294431	−	0.955673i	$-0.595130\pi$
$823$	−2.05346	+	0.550223i	−0.0715791	+	0.0191796i	0.222852	+	0.974852i	$0.428463\pi$
$824$		0			0
$825$	32.1147	−	32.1147i	1.11809	−	1.11809i
$826$		0			0
$827$	−24.8151	+	10.2787i	−0.862905	+	0.357427i	−0.769843	−	0.638233i	$-0.779666\pi$
$827$	−24.8151	+	10.2787i	−0.862905	+	0.357427i	−0.0930623	+	0.995660i	$0.529666\pi$
$828$		0			0
$829$	−25.8651	−	33.7080i	−0.898331	−	1.17073i	−0.984664	−	0.174461i	$-0.944182\pi$
$829$	−25.8651	−	33.7080i	−0.898331	−	1.17073i	0.0863332	−	0.996266i	$-0.472485\pi$
$830$		0			0
$831$	−5.91714	−	10.2488i	−0.205263	−	0.355527i
$832$		0			0
$833$	8.42095	+	54.8486i	0.291769	+	1.90039i
$834$		0			0
$835$	−15.6228	+	2.05678i	−0.540649	+	0.0711778i
$836$		0			0
$837$	1.16111	−	8.81952i	0.0401339	−	0.304847i
$838$		0			0
$839$	21.6483	−	21.6483i	0.747383	−	0.747383i	−0.226604	−	0.973987i	$-0.572762\pi$
$839$	21.6483	−	21.6483i	0.747383	−	0.747383i	0.973987	+	0.226604i	$0.0727623\pi$
$840$		0			0
$841$	20.4629	+	20.4629i	0.705616	+	0.705616i
$842$		0			0
$843$	42.3958	+	5.58151i	1.46019	+	0.192238i
$844$		0			0
$845$	4.10037	+	31.1454i	0.141057	+	1.07143i
$846$		0			0
$847$	−6.34452	+	7.39294i	−0.218000	+	0.254024i
$848$		0			0
$849$	41.6897	−	24.0696i	1.43079	−	0.826065i
$850$		0			0
$851$	−17.4124	+	13.3610i	−0.596889	+	0.458009i
$852$		0			0
$853$	−12.9262	−	31.2066i	−0.442585	−	1.06849i	−0.975039	−	0.222036i	$-0.928730\pi$
$853$	−12.9262	−	31.2066i	−0.442585	−	1.06849i	0.532454	−	0.846459i	$-0.321270\pi$
$854$		0			0
$855$	−11.0847	−	11.0847i	−0.379088	−	0.379088i
$856$		0			0
$857$	11.9622	+	44.6435i	0.408621	+	1.52499i	0.797279	+	0.603611i	$0.206272\pi$
$857$	11.9622	+	44.6435i	0.408621	+	1.52499i	−0.388659	+	0.921382i	$0.627061\pi$
$858$		0			0
$859$	22.2045	+	17.0381i	0.757606	+	0.581332i	0.913690	−	0.406412i	$-0.133220\pi$
$859$	22.2045	+	17.0381i	0.757606	+	0.581332i	−0.156084	+	0.987744i	$0.549887\pi$
$860$		0			0
$861$	6.10687	+	3.98645i	0.208122	+	0.135858i
$862$		0			0
$863$	7.85966	+	13.6133i	0.267546	+	0.463403i	0.968228	−	0.250071i	$-0.0804539\pi$
$863$	7.85966	+	13.6133i	0.267546	+	0.463403i	−0.700681	+	0.713474i	$0.747121\pi$
$864$		0			0
$865$	−26.9680	+	46.7100i	−0.916940	+	1.58819i
$866$		0			0
$867$	−41.5228	+	100.245i	−1.41019	+	3.40449i
$868$		0			0
$869$	−1.08982	+	0.451419i	−0.0369697	+	0.0153134i
$870$		0			0
$871$	5.98601	+	22.3401i	0.202828	+	0.756965i
$872$		0			0
$873$	6.06468	−	22.6337i	0.205258	−	0.766035i
$874$		0			0
$875$	−12.8536	−	14.3436i	−0.434531	−	0.484901i
$876$		0			0
$877$	−5.25920	−	39.9476i	−0.177590	−	1.34893i	−0.815471	−	0.578798i	$-0.803522\pi$
$877$	−5.25920	−	39.9476i	−0.177590	−	1.34893i	0.637880	−	0.770136i	$-0.279811\pi$
$878$		0			0
$879$	−53.2246	−	30.7293i	−1.79522	−	1.03647i
$880$		0			0
$881$			2.08556i			0.0702642i	0.999383	+	0.0351321i	$0.0111852\pi$
$881$			2.08556i			0.0702642i	−0.999383	+	0.0351321i	$0.988815\pi$
$882$		0			0
$883$	−10.3216	−	4.27536i	−0.347351	−	0.143877i	0.202186	−	0.979347i	$-0.435196\pi$
$883$	−10.3216	−	4.27536i	−0.347351	−	0.143877i	−0.549536	+	0.835470i	$0.685196\pi$
$884$		0			0
$885$	11.7243	+	1.54353i	0.394107	+	0.0518852i
$886$		0			0
$887$	−10.5997	+	39.5585i	−0.355902	+	1.32824i	0.523444	+	0.852060i	$0.324647\pi$
$887$	−10.5997	+	39.5585i	−0.355902	+	1.32824i	−0.879346	+	0.476184i	$0.842020\pi$
$888$		0			0
$889$	12.8930	−	26.8667i	0.432417	−	0.901080i
$890$		0			0
$891$	−21.5370	−	16.5259i	−0.721516	−	0.553639i
$892$		0			0
$893$	1.02870	+	1.34063i	0.0344242	+	0.0448625i
$894$		0			0
$895$	29.0618			0.971430
$896$		0			0
$897$	21.9088			0.731512
$898$		0			0
$899$	−1.42212	−	1.85334i	−0.0474304	−	0.0618124i
$900$		0			0
$901$	47.7378	+	36.6305i	1.59038	+	1.22034i
$902$		0			0
$903$	18.9630	+	27.7319i	0.631050	+	0.922860i
$904$		0			0
$905$	−14.6194	+	54.5603i	−0.485965	+	1.81364i
$906$		0			0
$907$	0.556878	+	0.0733143i	0.0184908	+	0.00243436i	0.139766	−	0.990185i	$-0.455365\pi$
$907$	0.556878	+	0.0733143i	0.0184908	+	0.00243436i	−0.121275	+	0.992619i	$0.538698\pi$
$908$		0			0
$909$	21.1057	+	8.74226i	0.700031	+	0.289962i
$910$		0			0
$911$		−	30.4575i		−	1.00910i	−0.863382	−	0.504551i	$-0.831658\pi$
$911$		−	30.4575i		−	1.00910i	0.863382	−	0.504551i	$-0.168342\pi$
$912$		0			0
$913$	−22.0444	−	12.7274i	−0.729564	−	0.421214i
$914$		0			0
$915$	5.97899	+	45.4149i	0.197659	+	1.50137i
$916$		0			0
$917$	12.2367	−	37.3592i	0.404091	−	1.23371i
$918$		0			0
$919$	8.69186	−	32.4385i	0.286718	−	1.07005i	−0.660857	−	0.750512i	$-0.729807\pi$
$919$	8.69186	−	32.4385i	0.286718	−	1.07005i	0.947575	−	0.319534i	$-0.103526\pi$
$920$		0			0
$921$	1.00967	+	3.76814i	0.0332698	+	0.124164i
$922$		0			0
$923$	2.14188	−	0.887197i	0.0705009	−	0.0292024i
$924$		0			0
$925$	12.8189	−	30.9475i	0.421482	−	1.01755i
$926$		0			0
$927$	22.6155	−	39.1712i	0.742791	−	1.28655i
$928$		0			0
$929$	22.1332	+	38.3359i	0.726168	+	1.25776i	0.958492	+	0.285121i	$0.0920338\pi$
$929$	22.1332	+	38.3359i	0.726168	+	1.25776i	−0.232324	+	0.972639i	$0.574633\pi$
$930$		0			0
$931$	−8.38877	+	8.75644i	−0.274931	+	0.286981i
$932$		0			0
$933$	43.6088	+	33.4622i	1.42769	+	1.09550i
$934$		0			0
$935$	−19.3013	−	72.0335i	−0.631221	−	2.35575i
$936$		0			0
$937$	−30.0129	−	30.0129i	−0.980480	−	0.980480i	0.0193331	−	0.999813i	$-0.493846\pi$
$937$	−30.0129	−	30.0129i	−0.980480	−	0.980480i	−0.999813	+	0.0193331i	$0.993846\pi$
$938$		0			0
$939$	14.1342	+	34.1230i	0.461252	+	1.11356i
$940$		0			0
$941$	−9.67554	+	7.42430i	−0.315414	+	0.242025i	−0.754319	−	0.656508i	$-0.772033\pi$
$941$	−9.67554	+	7.42430i	−0.315414	+	0.242025i	0.438906	+	0.898533i	$0.355366\pi$
$942$		0			0
$943$	4.68741	−	2.70628i	0.152643	−	0.0881284i
$944$		0			0
$945$	−5.64217	+	6.57452i	−0.183540	+	0.213869i
$946$		0			0
$947$	−5.79803	−	44.0404i	−0.188411	−	1.43112i	−0.780453	−	0.625214i	$-0.785012\pi$
$947$	−5.79803	−	44.0404i	−0.188411	−	1.43112i	0.592042	−	0.805907i	$-0.298322\pi$
$948$		0			0
$949$	28.3123	+	3.72739i	0.919057	+	0.120996i
$950$		0			0
$951$	12.2797	+	12.2797i	0.398196	+	0.398196i
$952$		0			0
$953$	−18.1908	+	18.1908i	−0.589258	+	0.589258i	−0.937430	−	0.348173i	$-0.886802\pi$
$953$	−18.1908	+	18.1908i	−0.589258	+	0.589258i	0.348173	+	0.937430i	$0.386802\pi$
$954$		0			0
$955$	7.14645	−	54.2827i	0.231254	−	1.75655i
$956$		0			0
$957$	−1.56974	+	0.206661i	−0.0507426	+	0.00668039i
$958$		0			0
$959$	−3.17892	+	16.9280i	−0.102653	+	0.546633i
$960$		0			0
$961$	−29.1239	−	50.4440i	−0.939479	−	1.62723i
$962$		0			0
$963$	2.92309	+	3.80945i	0.0941953	+	0.122758i
$964$		0			0
$965$	−46.0215	+	19.0627i	−1.48149	+	0.613651i
$966$		0			0
$967$	−6.72772	+	6.72772i	−0.216349	+	0.216349i	−0.806958	−	0.590609i	$-0.798888\pi$
$967$	−6.72772	+	6.72772i	−0.216349	+	0.216349i	0.590609	+	0.806958i	$0.298888\pi$
$968$		0			0
$969$	−31.3963	+	8.41261i	−1.00859	+	0.270252i
$970$		0			0
$971$	−29.2178	+	38.0774i	−0.937645	+	1.22196i	0.0372522	+	0.999306i	$0.488140\pi$
$971$	−29.2178	+	38.0774i	−0.937645	+	1.22196i	−0.974897	+	0.222657i	$0.928527\pi$
$972$		0			0
$973$	−0.0228997	−	0.00125453i	−0.000734131	−	4.02185e-5i
$974$		0			0
$975$	−28.9579	+	16.7188i	−0.927394	+	0.535431i
$976$		0			0
$977$	−10.7981	−	6.23428i	−0.345462	−	0.199452i	0.317223	−	0.948351i	$-0.397250\pi$
$977$	−10.7981	−	6.23428i	−0.345462	−	0.199452i	−0.662685	+	0.748899i	$0.730583\pi$
$978$		0			0
$979$	−17.9762	−	7.44599i	−0.574522	−	0.237975i
$980$		0			0
$981$	−8.31348	−	20.0705i	−0.265429	−	0.640803i
$982$		0			0
$983$	−6.79271	+	1.82010i	−0.216654	+	0.0580522i	−0.365513	−	0.930806i	$-0.619106\pi$
$983$	−6.79271	+	1.82010i	−0.216654	+	0.0580522i	0.148859	+	0.988858i	$0.452440\pi$
$984$		0			0
$985$	−31.3824	−	8.40890i	−0.999927	−	0.267930i
$986$		0			0
$987$	−4.54923	+	4.07667i	−0.144804	+	0.129762i
$988$		0			0
$989$	24.7203	−	3.25449i	0.786060	−	0.103487i
$990$		0			0
$991$	−14.3047	+	24.7765i	−0.454404	+	0.787050i	−0.998654	−	0.0518729i	$-0.983481\pi$
$991$	−14.3047	+	24.7765i	−0.454404	+	0.787050i	0.544250	+	0.838923i	$0.316814\pi$
$992$		0			0
$993$	1.89320			0.0600787
$994$		0			0
$995$	−12.5674	+	30.3404i	−0.398414	+	0.961855i
$996$		0			0
$997$	5.68821	−	43.2063i	0.180148	−	1.36836i	−0.627466	−	0.778644i	$-0.715908\pi$
$997$	5.68821	−	43.2063i	0.180148	−	1.36836i	0.807613	−	0.589712i	$-0.200759\pi$
$998$		0			0
$999$	−4.29518	−	1.15089i	−0.135893	−	0.0364125i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.bh.a.529.27		240
4.3	odd	2		224.2.bd.a.109.9	yes	240
7.2	even	3	inner	896.2.bh.a.401.4		240
28.23	odd	6		224.2.bd.a.205.11	yes	240
32.5	even	8	inner	896.2.bh.a.753.4		240
32.27	odd	8		224.2.bd.a.165.11	yes	240
224.37	even	24	inner	896.2.bh.a.625.27		240
224.219	odd	24		224.2.bd.a.37.9	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.37.9	✓	240	224.219	odd	24
224.2.bd.a.109.9	yes	240	4.3	odd	2
224.2.bd.a.165.11	yes	240	32.27	odd	8
224.2.bd.a.205.11	yes	240	28.23	odd	6
896.2.bh.a.401.4		240	7.2	even	3	inner
896.2.bh.a.529.27		240	1.1	even	1	trivial
896.2.bh.a.625.27		240	224.37	even	24	inner
896.2.bh.a.753.4		240	32.5	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.bh (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.44087 + 1.87778i) q^{3} +(-2.75892 - 2.11700i) q^{5} +(1.14468 - 2.38531i) q^{7} +(-0.673491 + 2.51350i) q^{9} +O(q^{10})\)	\(q+(1.44087 + 1.87778i) q^{3} +(-2.75892 - 2.11700i) q^{5} +(1.14468 - 2.38531i) q^{7} +(-0.673491 + 2.51350i) q^{9} +(-2.68201 - 0.353093i) q^{11} +(1.84002 + 0.762162i) q^{13} -8.23097i q^{15} +(-6.86527 - 3.96366i) q^{17} +(-0.226114 - 1.71751i) q^{19} +(6.12843 - 1.28747i) q^{21} +(1.20290 - 4.48927i) q^{23} +(1.83589 + 6.85163i) q^{25} +(0.869948 - 0.360344i) q^{27} +(0.0946303 - 0.228458i) q^{29} +(4.72355 - 8.18143i) q^{31} +(-3.20140 - 5.54498i) q^{33} +(-8.20778 + 4.15761i) q^{35} +(-3.74651 - 2.87479i) q^{37} +(1.22006 + 4.55333i) q^{39} +(0.823484 + 0.823484i) q^{41} +(2.05302 + 4.95643i) q^{43} +(7.17918 - 5.50878i) q^{45} +(-0.844781 + 0.487734i) q^{47} +(-4.37942 - 5.46083i) q^{49} +(-2.44908 - 18.6026i) q^{51} +(-7.52554 - 0.990756i) q^{53} +(6.65195 + 6.65195i) q^{55} +(2.89930 - 2.89930i) q^{57} +(-0.187527 + 1.42441i) q^{59} +(-5.51757 + 0.726402i) q^{61} +(5.22455 + 4.48364i) q^{63} +(-3.46298 - 5.99807i) q^{65} +(7.06937 + 9.21298i) q^{67} +(10.1631 - 4.20969i) q^{69} +(0.823109 - 0.823109i) q^{71} +(13.8498 - 3.71104i) q^{73} +(-10.2206 + 13.3197i) q^{75} +(-3.91227 + 5.99324i) q^{77} +(0.377642 - 0.218032i) q^{79} +(8.69076 + 5.01761i) q^{81} +(8.69345 + 3.60095i) q^{83} +(10.5497 + 25.4692i) q^{85} +(0.565344 - 0.151483i) q^{87} +(6.94761 + 1.86161i) q^{89} +(3.92423 - 3.51659i) q^{91} +(22.1690 - 2.91860i) q^{93} +(-3.01212 + 5.21715i) q^{95} -9.00485 q^{97} +(2.69381 - 6.50342i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9}+O(q^{10}) \) 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9	\( 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9} + 4 q^{11} - 16 q^{13} + 4 q^{19} - 8 q^{21} + 12 q^{23} - 4 q^{25} + 16 q^{27} - 16 q^{29} + 56 q^{31} - 8 q^{33} + 32 q^{35} - 4 q^{37} + 4 q^{39} - 16 q^{41} + 8 q^{45} + 28 q^{51} - 20 q^{53} + 16 q^{55} - 16 q^{57} + 36 q^{59} - 4 q^{61} + 16 q^{63} - 8 q^{65} - 36 q^{67} - 16 q^{69} - 48 q^{71} - 4 q^{73} - 16 q^{75} - 8 q^{77} + 96 q^{83} - 56 q^{85} + 4 q^{87} - 4 q^{89} + 56 q^{91} + 20 q^{93} + 8 q^{95} - 32 q^{97} - 8 q^{99}+O(q^{100}) \) 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9 + 4 * q^11 - 16 * q^13 + 4 * q^19 - 8 * q^21 + 12 * q^23 - 4 * q^25 + 16 * q^27 - 16 * q^29 + 56 * q^31 - 8 * q^33 + 32 * q^35 - 4 * q^37 + 4 * q^39 - 16 * q^41 + 8 * q^45 + 28 * q^51 - 20 * q^53 + 16 * q^55 - 16 * q^57 + 36 * q^59 - 4 * q^61 + 16 * q^63 - 8 * q^65 - 36 * q^67 - 16 * q^69 - 48 * q^71 - 4 * q^73 - 16 * q^75 - 8 * q^77 + 96 * q^83 - 56 * q^85 + 4 * q^87 - 4 * q^89 + 56 * q^91 + 20 * q^93 + 8 * q^95 - 32 * q^97 - 8 * q^99

Introduction

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Database

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