LMFDB - Embedded newform 896.2.bh.a.81.10

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			81.10
Character	$\chi$	$=$	896.81
Dual form			896.2.bh.a.177.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.867605 + 0.665736i) q^{3} +(-0.00636490 + 0.00829490i) q^{5} +(0.529064 + 2.59231i) q^{7} +(-0.466924 + 1.74259i) q^{9} +O(q^{10})$	\(q+(-0.867605 + 0.665736i) q^{3} +(-0.00636490 + 0.00829490i) q^{5} +(0.529064 + 2.59231i) q^{7} +(-0.466924 + 1.74259i) q^{9} +(-0.0658296 + 0.500025i) q^{11} +(0.148833 - 0.359315i) q^{13} -0.0114340i q^{15} +(-3.83439 - 2.21379i) q^{17} +(2.30771 - 0.303816i) q^{19} +(-2.18482 - 1.89689i) q^{21} +(-0.117964 + 0.440249i) q^{23} +(1.29407 + 4.82952i) q^{25} +(-2.01050 - 4.85376i) q^{27} +(-8.23722 - 3.41197i) q^{29} +(-3.54295 + 6.13657i) q^{31} +(-0.275771 - 0.477649i) q^{33} +(-0.0248704 - 0.0121113i) q^{35} +(0.810667 - 1.05648i) q^{37} +(0.110081 + 0.410827i) q^{39} +(0.726254 + 0.726254i) q^{41} +(1.00055 - 0.414442i) q^{43} +(-0.0114826 - 0.0149645i) q^{45} +(-6.68936 + 3.86210i) q^{47} +(-6.44018 + 2.74300i) q^{49} +(4.80054 - 0.632003i) q^{51} +(-1.43102 + 10.8696i) q^{53} +(-0.00372866 - 0.00372866i) q^{55} +(-1.79992 + 1.79992i) q^{57} +(5.07149 + 0.667674i) q^{59} +(-0.787418 - 5.98103i) q^{61} +(-4.76436 - 0.288476i) q^{63} +(0.00203318 + 0.00352156i) q^{65} +(-7.37282 + 5.65736i) q^{67} +(-0.190743 - 0.460495i) q^{69} +(-3.01032 + 3.01032i) q^{71} +(-0.568628 + 0.152363i) q^{73} +(-4.33793 - 3.32861i) q^{75} +(-1.33105 + 0.0938943i) q^{77} +(-9.83347 + 5.67736i) q^{79} +(0.288563 + 0.166602i) q^{81} +(4.51148 - 10.8917i) q^{83} +(0.0427687 - 0.0177154i) q^{85} +(9.41812 - 2.52358i) q^{87} +(14.1112 + 3.78107i) q^{89} +(1.01020 + 0.195722i) q^{91} +(-1.01146 - 7.68279i) q^{93} +(-0.0121682 + 0.0210760i) q^{95} +11.9213 q^{97} +(-0.840599 - 0.348188i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

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

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
$3$	−0.867605	+	0.665736i	−0.500912	+	0.384363i	−0.828086	−	0.560601i	$-0.810570\pi$
$3$	−0.867605	+	0.665736i	−0.500912	+	0.384363i	0.327174	+	0.944964i	$0.393904\pi$
$4$		0			0
$5$	−0.00636490	+	0.00829490i	−0.00284647	+	0.00370959i	−0.794774	−	0.606905i	$-0.792411\pi$
$5$	−0.00636490	+	0.00829490i	−0.00284647	+	0.00370959i	0.791928	+	0.610615i	$0.209078\pi$
$6$		0			0
$7$	0.529064	+	2.59231i	0.199967	+	0.979803i
$7$	0.529064	+	2.59231i	0.199967	+	0.979803i
$8$		0			0
$9$	−0.466924	+	1.74259i	−0.155641	+	0.580862i
$10$		0			0
$11$	−0.0658296	+	0.500025i	−0.0198484	+	0.150763i	−0.998499	−	0.0547667i	$-0.982558\pi$
$11$	−0.0658296	+	0.500025i	−0.0198484	+	0.150763i	0.978651	+	0.205530i	$0.0658918\pi$
$12$		0			0
$13$	0.148833	−	0.359315i	0.0412789	−	0.0996562i	−0.901895	−	0.431955i	$-0.857824\pi$
$13$	0.148833	−	0.359315i	0.0412789	−	0.0996562i	0.943174	+	0.332298i	$0.107824\pi$
$14$		0			0
$15$		−	0.0114340i		−	0.00295226i
$16$		0			0
$17$	−3.83439	−	2.21379i	−0.929977	−	0.536923i	−0.0431727	−	0.999068i	$-0.513747\pi$
$17$	−3.83439	−	2.21379i	−0.929977	−	0.536923i	−0.886804	+	0.462145i	$0.847080\pi$
$18$		0			0
$19$	2.30771	−	0.303816i	0.529425	−	0.0697001i	0.138925	−	0.990303i	$-0.455635\pi$
$19$	2.30771	−	0.303816i	0.529425	−	0.0697001i	0.390500	+	0.920603i	$0.372302\pi$
$20$		0			0
$21$	−2.18482	−	1.89689i	−0.476766	−	0.413935i
$22$		0			0
$23$	−0.117964	+	0.440249i	−0.0245973	+	0.0917983i	−0.977133	−	0.212628i	$-0.931798\pi$
$23$	−0.117964	+	0.440249i	−0.0245973	+	0.0917983i	0.952536	+	0.304426i	$0.0984646\pi$
$24$		0			0
$25$	1.29407	+	4.82952i	0.258813	+	0.965905i
$26$		0			0
$27$	−2.01050	−	4.85376i	−0.386920	−	0.934107i
$28$		0			0
$29$	−8.23722	−	3.41197i	−1.52961	−	0.633587i	−0.550124	−	0.835083i	$-0.685420\pi$
$29$	−8.23722	−	3.41197i	−1.52961	−	0.633587i	−0.979489	+	0.201496i	$0.935420\pi$
$30$		0			0
$31$	−3.54295	+	6.13657i	−0.636333	+	1.10216i	0.349898	+	0.936788i	$0.386216\pi$
$31$	−3.54295	+	6.13657i	−0.636333	+	1.10216i	−0.986231	+	0.165373i	$0.947117\pi$
$32$		0			0
$33$	−0.275771	−	0.477649i	−0.0480056	−	0.0831481i
$34$		0			0
$35$	−0.0248704	−	0.0121113i	−0.00420387	−	0.00204718i
$36$		0			0
$37$	0.810667	−	1.05648i	0.133273	−	0.173685i	−0.721950	−	0.691946i	$-0.756754\pi$
$37$	0.810667	−	1.05648i	0.133273	−	0.173685i	0.855222	+	0.518261i	$0.173420\pi$
$38$		0			0
$39$	0.110081	+	0.410827i	0.0176270	+	0.0657850i
$40$		0			0
$41$	0.726254	+	0.726254i	0.113422	+	0.113422i	0.761540	−	0.648118i	$-0.224444\pi$
$41$	0.726254	+	0.726254i	0.113422	+	0.113422i	−0.648118	+	0.761540i	$0.724444\pi$
$42$		0			0
$43$	1.00055	−	0.414442i	0.152583	−	0.0632019i	−0.305085	−	0.952325i	$-0.598685\pi$
$43$	1.00055	−	0.414442i	0.152583	−	0.0632019i	0.457668	+	0.889123i	$0.348685\pi$
$44$		0			0
$45$	−0.0114826	−	0.0149645i	−0.00171173	−	0.00223077i
$46$		0			0
$47$	−6.68936	+	3.86210i	−0.975743	+	0.563345i	−0.900982	−	0.433856i	$-0.857153\pi$
$47$	−6.68936	+	3.86210i	−0.975743	+	0.563345i	−0.0747608	+	0.997201i	$0.523819\pi$
$48$		0			0
$49$	−6.44018	+	2.74300i	−0.920026	+	0.391857i
$50$		0			0
$51$	4.80054	−	0.632003i	0.672210	−	0.0884981i
$52$		0			0
$53$	−1.43102	+	10.8696i	−0.196565	+	1.49306i	0.554141	+	0.832423i	$0.313047\pi$
$53$	−1.43102	+	10.8696i	−0.196565	+	1.49306i	−0.750706	+	0.660637i	$0.770286\pi$
$54$		0			0
$55$	−0.00372866	−	0.00372866i	−0.000502773	−	0.000502773i
$56$		0			0
$57$	−1.79992	+	1.79992i	−0.238405	+	0.238405i
$58$		0			0
$59$	5.07149	+	0.667674i	0.660251	+	0.0869237i	0.453203	−	0.891407i	$-0.350281\pi$
$59$	5.07149	+	0.667674i	0.660251	+	0.0869237i	0.207048	+	0.978331i	$0.433614\pi$
$60$		0			0
$61$	−0.787418	−	5.98103i	−0.100819	−	0.765793i	−0.964933	−	0.262497i	$-0.915454\pi$
$61$	−0.787418	−	5.98103i	−0.100819	−	0.765793i	0.864114	−	0.503296i	$-0.167879\pi$
$62$		0			0
$63$	−4.76436	−	0.288476i	−0.600253	−	0.0363445i
$64$		0			0
$65$	0.00203318	+	0.00352156i	0.000252184	+	0.000436796i
$66$		0			0
$67$	−7.37282	+	5.65736i	−0.900733	+	0.691157i	−0.951531	−	0.307552i	$-0.900490\pi$
$67$	−7.37282	+	5.65736i	−0.900733	+	0.691157i	0.0507983	+	0.998709i	$0.483823\pi$
$68$		0			0
$69$	−0.190743	−	0.460495i	−0.0229628	−	0.0554371i
$70$		0			0
$71$	−3.01032	+	3.01032i	−0.357259	+	0.357259i	−0.862802	−	0.505542i	$-0.831292\pi$
$71$	−3.01032	+	3.01032i	−0.357259	+	0.357259i	0.505542	+	0.862802i	$0.331292\pi$
$72$		0			0
$73$	−0.568628	+	0.152363i	−0.0665529	+	0.0178328i	−0.291942	−	0.956436i	$-0.594301\pi$
$73$	−0.568628	+	0.152363i	−0.0665529	+	0.0178328i	0.225389	+	0.974269i	$0.427635\pi$
$74$		0			0
$75$	−4.33793	−	3.32861i	−0.500901	−	0.384355i
$76$		0			0
$77$	−1.33105	+	0.0938943i	−0.151687	+	0.0107002i
$78$		0			0
$79$	−9.83347	+	5.67736i	−1.10635	+	0.638752i	−0.937882	−	0.346954i	$-0.887216\pi$
$79$	−9.83347	+	5.67736i	−1.10635	+	0.638752i	−0.168470	+	0.985707i	$0.553883\pi$
$80$		0			0
$81$	0.288563	+	0.166602i	0.0320626	+	0.0185113i
$82$		0			0
$83$	4.51148	−	10.8917i	0.495200	−	1.19552i	−0.456842	−	0.889548i	$-0.651019\pi$
$83$	4.51148	−	10.8917i	0.495200	−	1.19552i	0.952041	−	0.305969i	$-0.0989805\pi$
$84$		0			0
$85$	0.0427687	−	0.0177154i	0.00463892	−	0.00192150i
$86$		0			0
$87$	9.41812	−	2.52358i	1.00973	−	0.270556i
$88$		0			0
$89$	14.1112	+	3.78107i	1.49578	+	0.400793i	0.911684	−	0.410892i	$-0.134783\pi$
$89$	14.1112	+	3.78107i	1.49578	+	0.400793i	0.584095	+	0.811685i	$0.301449\pi$
$90$		0			0
$91$	1.01020	+	0.195722i	0.105898	+	0.0205172i
$92$		0			0
$93$	−1.01146	−	7.68279i	−0.104883	−	0.796668i
$94$		0			0
$95$	−0.0121682	+	0.0210760i	−0.00124843	+	0.00216235i
$96$		0			0
$97$	11.9213			1.21042			0.605211	−	0.796065i	$-0.293089\pi$
$97$	11.9213			1.21042			0.605211	+	0.796065i	$0.293089\pi$
$98$		0			0
$99$	−0.840599	−	0.348188i	−0.0844834	−	0.0349942i
$100$		0			0
$101$	−14.5149	−	1.91092i	−1.44428	−	0.190144i	−0.632708	−	0.774390i	$-0.718057\pi$
$101$	−14.5149	−	1.91092i	−1.44428	−	0.190144i	−0.811576	+	0.584247i	$0.801390\pi$
$102$		0			0
$103$	−10.4395	−	2.79725i	−1.02863	−	0.275621i	−0.295238	−	0.955424i	$-0.595399\pi$
$103$	−10.4395	−	2.79725i	−1.02863	−	0.275621i	−0.733395	+	0.679802i	$0.762066\pi$
$104$		0			0
$105$	0.0296406	−	0.00604934i	0.00289263	−	0.000590355i
$106$		0			0
$107$	−8.98433	−	6.89392i	−0.868548	−	0.666460i	0.0751850	−	0.997170i	$-0.476045\pi$
$107$	−8.98433	−	6.89392i	−0.868548	−	0.666460i	−0.943733	+	0.330710i	$0.892712\pi$
$108$		0			0
$109$	4.27270	+	5.56829i	0.409250	+	0.533345i	0.951817	−	0.306668i	$-0.0992140\pi$
$109$	4.27270	+	5.56829i	0.409250	+	0.533345i	−0.542567	+	0.840013i	$0.682547\pi$
$110$		0			0
$111$			1.45630i			0.138226i
$112$		0			0
$113$			5.73929i			0.539907i	0.962873	+	0.269954i	$0.0870083\pi$
$113$			5.73929i			0.539907i	−0.962873	+	0.269954i	$0.912992\pi$
$114$		0			0
$115$	−0.00290099	−	0.00378065i	−0.000270519	−	0.000352547i
$116$		0			0
$117$	0.556644	+	0.427128i	0.0514618	+	0.0394880i
$118$		0			0
$119$	3.71020	−	11.1112i	0.340113	−	1.01856i
$120$		0			0
$121$	10.3795	+	2.78118i	0.943590	+	0.252834i
$122$		0			0
$123$	−1.11360	−	0.146608i	−0.100410	−	0.0132192i
$124$		0			0
$125$	−0.0965951	−	0.0400110i	−0.00863973	−	0.00357869i
$126$		0			0
$127$	4.26570			0.378519			0.189260	−	0.981927i	$-0.439391\pi$
$127$	4.26570			0.378519			0.189260	+	0.981927i	$0.439391\pi$
$128$		0			0
$129$	−0.592174	+	1.02568i	−0.0521380	+	0.0903057i
$130$		0			0
$131$	0.523674	+	3.97770i	0.0457536	+	0.347533i	0.998975	+	0.0452607i	$0.0144119\pi$
$131$	0.523674	+	3.97770i	0.0457536	+	0.347533i	−0.953222	+	0.302272i	$0.902255\pi$
$132$		0			0
$133$	2.00851	+	5.82157i	0.174160	+	0.504794i
$134$		0			0
$135$	0.0530581	+	0.0142169i	0.00456651	+	0.00122359i
$136$		0			0
$137$	6.44018	−	1.72564i	0.550222	−	0.147431i	0.0270114	−	0.999635i	$-0.491401\pi$
$137$	6.44018	−	1.72564i	0.550222	−	0.147431i	0.523210	+	0.852204i	$0.324734\pi$
$138$		0			0
$139$	14.1258	−	5.85112i	1.19814	−	0.496285i	0.307742	−	0.951470i	$-0.400427\pi$
$139$	14.1258	−	5.85112i	1.19814	−	0.496285i	0.890397	+	0.455185i	$0.150427\pi$
$140$		0			0
$141$	3.23257	−	7.80413i	0.272232	−	0.657226i
$142$		0			0
$143$	0.169869	+	0.0980740i	0.0142052	+	0.00820136i
$144$		0			0
$145$	0.0807311	−	0.0466101i	0.00670435	−	0.00387076i
$146$		0			0
$147$	3.76142	−	6.66730i	0.310237	−	0.549910i
$148$		0			0
$149$	3.97302	+	3.04860i	0.325482	+	0.249751i	0.758557	−	0.651607i	$-0.225905\pi$
$149$	3.97302	+	3.04860i	0.325482	+	0.249751i	−0.433075	+	0.901358i	$0.642571\pi$
$150$		0			0
$151$	6.18175	−	1.65640i	0.503064	−	0.134796i	0.00164238	−	0.999999i	$-0.499477\pi$
$151$	6.18175	−	1.65640i	0.503064	−	0.134796i	0.501422	+	0.865203i	$0.332811\pi$
$152$		0			0
$153$	5.64809	−	5.64809i	0.456621	−	0.456621i
$154$		0			0
$155$	−0.0283517	−	0.0684471i	−0.00227726	−	0.00549780i
$156$		0			0
$157$	14.3418	−	11.0049i	1.14460	−	0.878283i	0.150702	−	0.988579i	$-0.451847\pi$
$157$	14.3418	−	11.0049i	1.14460	−	0.878283i	0.993899	+	0.110296i	$0.0351799\pi$
$158$		0			0
$159$	−5.99476	−	10.3832i	−0.475415	−	0.823443i
$160$		0			0
$161$	−1.20367	−	0.0728809i	−0.0948629	−	0.00574382i
$162$		0			0
$163$	2.25530	+	17.1307i	0.176649	+	1.34178i	0.818302	+	0.574788i	$0.194915\pi$
$163$	2.25530	+	17.1307i	0.176649	+	1.34178i	−0.641653	+	0.766995i	$0.721751\pi$
$164$		0			0
$165$	0.00571731		0.000752698i	0.000445092		5.85975e-5i
$166$		0			0
$167$	15.4656	−	15.4656i	1.19676	−	1.19676i	0.221630	−	0.975131i	$-0.428862\pi$
$167$	15.4656	−	15.4656i	1.19676	−	1.19676i	0.975131	−	0.221630i	$-0.0711378\pi$
$168$		0			0
$169$	9.08543	+	9.08543i	0.698879	+	0.698879i
$170$		0			0
$171$	−0.548101	+	4.16324i	−0.0419143	+	0.318371i
$172$		0			0
$173$	−15.1655	+	1.99658i	−1.15301	+	0.151797i	−0.682697	−	0.730702i	$-0.739193\pi$
$173$	−15.1655	+	1.99658i	−1.15301	+	0.151797i	−0.470315	+	0.882499i	$0.655860\pi$
$174$		0			0
$175$	−11.8350	+	5.90975i	−0.894642	+	0.446735i
$176$		0			0
$177$	−4.84454	+	2.79700i	−0.364138	+	0.210235i
$178$		0			0
$179$	11.0619	+	14.4162i	0.826808	+	1.07752i	0.995769	+	0.0918946i	$0.0292923\pi$
$179$	11.0619	+	14.4162i	0.826808	+	1.07752i	−0.168961	+	0.985623i	$0.554041\pi$
$180$		0			0
$181$	1.82296	−	0.755095i	0.135500	−	0.0561258i	−0.313903	−	0.949455i	$-0.601637\pi$
$181$	1.82296	−	0.755095i	0.135500	−	0.0561258i	0.449403	+	0.893329i	$0.351637\pi$
$182$		0			0
$183$	4.66496	+	4.66496i	0.344844	+	0.344844i
$184$		0			0
$185$	0.00360360	+	0.0134488i	0.000264942	+	0.000988776i
$186$		0			0
$187$	1.35937	−	1.77156i	0.0994067	−	0.129549i
$188$		0			0
$189$	11.5188	−	7.77979i	0.837869	−	0.565896i
$190$		0			0
$191$	4.79102	+	8.29829i	0.346666	+	0.600443i	0.985655	−	0.168773i	$-0.0539804\pi$
$191$	4.79102	+	8.29829i	0.346666	+	0.600443i	−0.638989	+	0.769216i	$0.720647\pi$
$192$		0			0
$193$	5.51517	−	9.55256i	0.396991	−	0.687608i	−0.596362	−	0.802715i	$-0.703388\pi$
$193$	5.51517	−	9.55256i	0.396991	−	0.687608i	0.993353	+	0.115107i	$0.0367211\pi$
$194$		0			0
$195$	−0.00410843	−	0.00170177i	−0.000294211	−	0.000121866i
$196$		0			0
$197$	−1.63754	−	3.95337i	−0.116670	−	0.281666i	0.854747	−	0.519044i	$-0.173712\pi$
$197$	−1.63754	−	3.95337i	−0.116670	−	0.281666i	−0.971417	+	0.237378i	$0.923712\pi$
$198$		0			0
$199$	5.99880	+	22.3878i	0.425244	+	1.58703i	0.763390	+	0.645938i	$0.223533\pi$
$199$	5.99880	+	22.3878i	0.425244	+	1.58703i	−0.338146	+	0.941093i	$0.609800\pi$
$200$		0			0
$201$	2.63038	−	9.81670i	0.185533	−	0.692417i
$202$		0			0
$203$	4.48688	−	23.1586i	0.314917	−	1.62542i
$204$		0			0
$205$	−0.0106467	+	0.00140167i	−0.000743601	+	9.78969e-5i
$206$		0			0
$207$	−0.712091	−	0.411126i	−0.0494938	−	0.0285752i
$208$		0			0
$209$			1.17391i			0.0812012i
$210$		0			0
$211$	−6.39410	+	15.4367i	−0.440188	+	1.06271i	0.535694	+	0.844412i	$0.320050\pi$
$211$	−6.39410	+	15.4367i	−0.440188	+	1.06271i	−0.975882	+	0.218296i	$0.929950\pi$
$212$		0			0
$213$	0.607688	−	4.61585i	0.0416381	−	0.316273i
$214$		0			0
$215$	−0.00293066	+	0.0109374i	−0.000199869	+	0.000745922i
$216$		0			0
$217$	−17.7824	−	5.93780i	−1.20715	−	0.403084i
$218$		0			0
$219$	0.391910	−	0.510747i	0.0264828	−	0.0345131i
$220$		0			0
$221$	−1.36613	+	1.04827i	−0.0918961	+	0.0705144i
$222$		0			0
$223$	23.6506			1.58376			0.791880	−	0.610677i	$-0.209103\pi$
$223$	23.6506			1.58376			0.791880	+	0.610677i	$0.209103\pi$
$224$		0			0
$225$	−9.02009			−0.601339
$226$		0			0
$227$	20.7791	−	15.9443i	1.37915	−	1.05826i	0.388561	−	0.921423i	$-0.372972\pi$
$227$	20.7791	−	15.9443i	1.37915	−	1.05826i	0.990593	−	0.136839i	$-0.0436944\pi$
$228$		0			0
$229$	−15.9348	+	20.7667i	−1.05300	+	1.37230i	−0.128247	+	0.991742i	$0.540935\pi$
$229$	−15.9348	+	20.7667i	−1.05300	+	1.37230i	−0.924757	+	0.380559i	$0.875732\pi$
$230$		0			0
$231$	1.09232	−	0.967592i	0.0718691	−	0.0636629i
$232$		0			0
$233$	0.774736	−	2.89136i	0.0507547	−	0.189419i	−0.935894	−	0.352281i	$-0.885406\pi$
$233$	0.774736	−	2.89136i	0.0507547	−	0.189419i	0.986649	+	0.162862i	$0.0520727\pi$
$234$		0			0
$235$	0.0105413	−	0.0800695i	0.000687641	−	0.00522316i
$236$		0			0
$237$	4.75194	−	11.4722i	0.308672	−	0.745199i
$238$		0			0
$239$		−	13.3435i		−	0.863119i	−0.902085	−	0.431559i	$-0.857964\pi$
$239$		−	13.3435i		−	0.863119i	0.902085	−	0.431559i	$-0.142036\pi$
$240$		0			0
$241$	−21.9939	−	12.6982i	−1.41675	−	0.817960i	−0.420737	−	0.907183i	$-0.638228\pi$
$241$	−21.9939	−	12.6982i	−1.41675	−	0.817960i	−0.996012	+	0.0892225i	$0.971562\pi$
$242$		0			0
$243$	15.2649	−	2.00966i	0.979245	−	0.128920i
$244$		0			0
$245$	0.0182382	−	0.0708796i	0.00116520	−	0.00452833i
$246$		0			0
$247$	0.234298	−	0.874413i	0.0149080	−	0.0556376i
$248$		0			0
$249$	3.33681	+	12.4531i	0.211461	+	0.789185i
$250$		0			0
$251$	−0.987986	−	2.38521i	−0.0623611	−	0.150553i	0.889627	−	0.456688i	$-0.150964\pi$
$251$	−0.987986	−	2.38521i	−0.0623611	−	0.150553i	−0.951988	+	0.306134i	$0.900964\pi$
$252$		0			0
$253$	−0.212370	−	0.0879666i	−0.0133516	−	0.00553041i
$254$		0			0
$255$	−0.0253125	+	0.0438426i	−0.00158513	+	0.00274553i
$256$		0			0
$257$	−14.7969	−	25.6290i	−0.923005	−	1.59869i	−0.794739	−	0.606951i	$-0.792392\pi$
$257$	−14.7969	−	25.6290i	−0.923005	−	1.59869i	−0.128266	−	0.991740i	$-0.540941\pi$
$258$		0			0
$259$	3.16763	+	1.54256i	0.196827	+	0.0958499i
$260$		0			0
$261$	9.79181	−	12.7609i	0.606098	−	0.789882i
$262$		0			0
$263$	2.58399	+	9.64359i	0.159336	+	0.594649i	0.998695	+	0.0510720i	$0.0162638\pi$
$263$	2.58399	+	9.64359i	0.159336	+	0.594649i	−0.839359	+	0.543577i	$0.817070\pi$
$264$		0			0
$265$	−0.0810543	−	0.0810543i	−0.00497913	−	0.00497913i
$266$		0			0
$267$	−14.7601	+	6.11383i	−0.903303	+	0.374160i
$268$		0			0
$269$	11.0921	+	14.4555i	0.676298	+	0.881369i	0.997851	−	0.0655227i	$-0.0208715\pi$
$269$	11.0921	+	14.4555i	0.676298	+	0.881369i	−0.321553	+	0.946892i	$0.604205\pi$
$270$		0			0
$271$	−3.45951	+	1.99735i	−0.210150	+	0.121330i	−0.601381	−	0.798962i	$-0.705383\pi$
$271$	−3.45951	+	1.99735i	−0.210150	+	0.121330i	0.391231	+	0.920292i	$0.372049\pi$
$272$		0			0
$273$	−1.00675	+	0.502718i	−0.0609315	+	0.0304259i
$274$		0			0
$275$	−2.50007	+	0.329141i	−0.150760	+	0.0198479i
$276$		0			0
$277$	−0.618521	+	4.69813i	−0.0371633	+	0.282283i	0.962765	+	0.270339i	$0.0871356\pi$
$277$	−0.618521	+	4.69813i	−0.0371633	+	0.282283i	−0.999929	+	0.0119449i	$0.996198\pi$
$278$		0			0
$279$	−9.03921	−	9.03921i	−0.541163	−	0.541163i
$280$		0			0
$281$	7.03491	−	7.03491i	0.419667	−	0.419667i	−0.465422	−	0.885089i	$-0.654097\pi$
$281$	7.03491	−	7.03491i	0.419667	−	0.419667i	0.885089	+	0.465422i	$0.154097\pi$
$282$		0			0
$283$	−5.14854	−	0.677819i	−0.306049	−	0.0402921i	−0.0240625	−	0.999710i	$-0.507660\pi$
$283$	−5.14854	−	0.677819i	−0.306049	−	0.0402921i	−0.281987	+	0.959418i	$0.590993\pi$
$284$		0			0
$285$	−0.00347384	−	0.0263864i	−0.000205773	−	0.00156300i
$286$		0			0
$287$	−1.49844	+	2.26691i	−0.0884504	+	0.133812i
$288$		0			0
$289$	1.30172	+	2.25464i	0.0765716	+	0.132626i
$290$		0			0
$291$	−10.3430	+	7.93643i	−0.606315	+	0.465242i
$292$		0			0
$293$	1.86694	+	4.50719i	0.109068	+	0.263313i	0.968985	−	0.247121i	$-0.0794847\pi$
$293$	1.86694	+	4.50719i	0.109068	+	0.263313i	−0.859917	+	0.510434i	$0.829485\pi$
$294$		0			0
$295$	−0.0378178	+	0.0378178i	−0.00220184	+	0.00220184i
$296$		0			0
$297$	2.55935	−	0.685777i	0.148509	−	0.0397928i
$298$		0			0
$299$	0.140631	+	0.107910i	0.00813292	+	0.00624061i
$300$		0			0
$301$	1.60372	+	2.37448i	0.0924369	+	0.136863i
$302$		0			0
$303$	13.8653	−	8.00516i	0.796543	−	0.459884i
$304$		0			0
$305$	0.0546239	+	0.0315371i	0.00312776	+	0.00180581i
$306$		0			0
$307$	−6.41434	+	15.4856i	−0.366086	+	0.883809i	0.628298	+	0.777973i	$0.283752\pi$
$307$	−6.41434	+	15.4856i	−0.366086	+	0.883809i	−0.994384	+	0.105836i	$0.966248\pi$
$308$		0			0
$309$	10.9196	−	4.52304i	0.621193	−	0.257307i
$310$		0			0
$311$	−2.47066	+	0.662011i	−0.140098	+	0.0375392i	−0.328187	−	0.944613i	$-0.606437\pi$
$311$	−2.47066	+	0.662011i	−0.140098	+	0.0375392i	0.188089	+	0.982152i	$0.439771\pi$
$312$		0			0
$313$	−4.97674	−	1.33351i	−0.281302	−	0.0753747i	0.115409	−	0.993318i	$-0.463182\pi$
$313$	−4.97674	−	1.33351i	−0.281302	−	0.0753747i	−0.396712	+	0.917943i	$0.629849\pi$
$314$		0			0
$315$	0.0327176	−	0.0376838i	0.00184343	−	0.00212324i
$316$		0			0
$317$	0.0159808	+	0.121386i	0.000897570	+	0.00681772i	0.991888	−	0.127117i	$-0.0405722\pi$
$317$	0.0159808	+	0.121386i	0.000897570	+	0.00681772i	−0.990990	+	0.133934i	$0.957239\pi$
$318$		0			0
$319$	2.24832	−	3.89421i	0.125882	−	0.218034i
$320$		0			0
$321$	12.3844			0.691228
$322$		0			0
$323$	−9.52125	−	3.94383i	−0.529776	−	0.219441i
$324$		0			0
$325$	1.92792	+	0.253816i	0.106942	+	0.0140792i
$326$		0			0
$327$	−7.41402	−	1.98658i	−0.409996	−	0.109858i
$328$		0			0
$329$	−13.5509	−	15.2976i	−0.747084	−	0.843385i
$330$		0			0
$331$	−17.7930	−	13.6530i	−0.977990	−	0.750438i	−0.00961889	−	0.999954i	$-0.503062\pi$
$331$	−17.7930	−	13.6530i	−0.977990	−	0.750438i	−0.968371	+	0.249516i	$0.919729\pi$
$332$		0			0
$333$	1.46249	+	1.90596i	0.0801440	+	0.104446i
$334$		0			0
$335$		−	0.0971653i		−	0.00530871i
$336$		0			0
$337$			20.3116i			1.10645i	0.833033	+	0.553223i	$0.186602\pi$
$337$			20.3116i			1.10645i	−0.833033	+	0.553223i	$0.813398\pi$
$338$		0			0
$339$	−3.82085	−	4.97943i	−0.207520	−	0.270446i
$340$		0			0
$341$	−2.83521	−	2.17553i	−0.153535	−	0.117812i
$342$		0			0
$343$	−10.5180	−	15.2438i	−0.567918	−	0.823085i
$344$		0			0
$345$	0.00503383	+	0.00134881i	0.000271012	+	7.26175e-5i
$346$		0			0
$347$	−15.4472	−	2.03366i	−0.829248	−	0.109173i	−0.296060	−	0.955169i	$-0.595673\pi$
$347$	−15.4472	−	2.03366i	−0.829248	−	0.109173i	−0.533188	+	0.845997i	$0.679006\pi$
$348$		0			0
$349$	16.8470	+	6.97826i	0.901800	+	0.373538i	0.784912	−	0.619607i	$-0.212708\pi$
$349$	16.8470	+	6.97826i	0.901800	+	0.373538i	0.116888	+	0.993145i	$0.462708\pi$
$350$		0			0
$351$	−2.04326			−0.109061
$352$		0			0
$353$	−13.0112	+	22.5360i	−0.692514	+	1.19947i	0.278497	+	0.960437i	$0.410164\pi$
$353$	−13.0112	+	22.5360i	−0.692514	+	1.19947i	−0.971011	+	0.239033i	$0.923170\pi$
$354$		0			0
$355$	−0.00580992	−	0.0441307i	−0.000308358	−	0.00234221i
$356$		0			0
$357$	4.17814	+	12.1101i	0.221131	+	0.640936i
$358$		0			0
$359$	24.4780	+	6.55887i	1.29190	+	0.346164i	0.838382	−	0.545083i	$-0.183502\pi$
$359$	24.4780	+	6.55887i	1.29190	+	0.346164i	0.453519	+	0.891247i	$0.350168\pi$
$360$		0			0
$361$	−13.1194	+	3.51533i	−0.690493	+	0.185017i
$362$		0			0
$363$	−10.8568	+	4.49704i	−0.569836	+	0.236034i
$364$		0			0
$365$	0.00235542	−	0.00568649i	0.000123288	−	0.000297644i
$366$		0			0
$367$	−10.4795	−	6.05033i	−0.547024	−	0.315825i	0.200897	−	0.979612i	$-0.435614\pi$
$367$	−10.4795	−	6.05033i	−0.547024	−	0.315825i	−0.747921	+	0.663788i	$0.768948\pi$
$368$		0			0
$369$	−1.60467	+	0.926455i	−0.0835356	+	0.0482293i
$370$		0			0
$371$	−28.9346	+	2.04109i	−1.50221	+	0.105968i
$372$		0			0
$373$	28.1953	+	21.6350i	1.45990	+	1.12022i	0.968419	+	0.249328i	$0.0802098\pi$
$373$	28.1953	+	21.6350i	1.45990	+	1.12022i	0.491478	+	0.870890i	$0.336457\pi$
$374$		0			0
$375$	0.110443	−	0.0295931i	0.00570326	−	0.00152818i
$376$		0			0
$377$	−2.45195	+	2.45195i	−0.126282	+	0.126282i
$378$		0			0
$379$	11.3445	+	27.3882i	0.582730	+	1.40684i	0.890328	+	0.455319i	$0.150475\pi$
$379$	11.3445	+	27.3882i	0.582730	+	1.40684i	−0.307598	+	0.951516i	$0.599525\pi$
$380$		0			0
$381$	−3.70094	+	2.83983i	−0.189605	+	0.145489i
$382$		0			0
$383$	−0.0605146	−	0.104814i	−0.00309215	−	0.00535576i	0.864475	−	0.502675i	$-0.167651\pi$
$383$	−0.0605146	−	0.104814i	−0.00309215	−	0.00535576i	−0.867567	+	0.497320i	$0.834318\pi$
$384$		0			0
$385$	0.00769316	−	0.0116386i	0.000392080	−	0.000593156i
$386$		0			0
$387$	0.255019	+	1.93706i	0.0129633	+	0.0984664i
$388$		0			0
$389$	−6.89891	−	0.908259i	−0.349789	−	0.0460506i	−0.0464151	−	0.998922i	$-0.514780\pi$
$389$	−6.89891	−	0.908259i	−0.349789	−	0.0460506i	−0.303374	+	0.952872i	$0.598113\pi$
$390$		0			0
$391$	1.42694	−	1.42694i	0.0721635	−	0.0721635i
$392$		0			0
$393$	−3.10244	−	3.10244i	−0.156497	−	0.156497i
$394$		0			0
$395$	0.0154960	−	0.117703i	0.000779686	−	0.00592230i
$396$		0			0
$397$	−16.9158	+	2.22700i	−0.848978	+	0.111770i	−0.542446	−	0.840090i	$-0.682502\pi$
$397$	−16.9158	+	2.22700i	−0.848978	+	0.111770i	−0.306532	+	0.951860i	$0.599169\pi$
$398$		0			0
$399$	−5.61822	−	3.71368i	−0.281263	−	0.185917i
$400$		0			0
$401$	30.3311	−	17.5117i	1.51467	−	0.874492i	0.514813	−	0.857303i	$-0.327861\pi$
$401$	30.3311	−	17.5117i	1.51467	−	0.874492i	0.999852	−	0.0171899i	$-0.00547197\pi$
$402$		0			0
$403$	1.67765	+	2.18636i	0.0835699	+	0.108910i
$404$		0			0
$405$	−0.00321862	+	0.00133320i	−0.000159935	+	6.62471e-5i
$406$		0			0
$407$	0.474902	+	0.474902i	0.0235400	+	0.0235400i
$408$		0			0
$409$	6.04090	+	22.5450i	0.298703	+	1.11478i	0.938231	+	0.346008i	$0.112463\pi$
$409$	6.04090	+	22.5450i	0.298703	+	1.11478i	−0.639528	+	0.768768i	$0.720870\pi$
$410$		0			0
$411$	−4.43871	+	5.78463i	−0.218945	+	0.285335i
$412$		0			0
$413$	0.952319	+	13.5001i	0.0468606	+	0.664298i
$414$		0			0
$415$	0.0616303	+	0.106747i	0.00302531	+	0.00523999i
$416$		0			0
$417$	−8.36035	+	14.4805i	−0.409408	+	0.709115i
$418$		0			0
$419$	−2.52990	−	1.04792i	−0.123594	−	0.0511942i	0.320029	−	0.947408i	$-0.396307\pi$
$419$	−2.52990	−	1.04792i	−0.123594	−	0.0511942i	−0.443623	+	0.896213i	$0.646307\pi$
$420$		0			0
$421$	−5.46512	−	13.1940i	−0.266354	−	0.643035i	0.732952	−	0.680280i	$-0.238142\pi$
$421$	−5.46512	−	13.1940i	−0.266354	−	0.643035i	−0.999306	+	0.0372451i	$0.988142\pi$
$422$		0			0
$423$	−3.60662	−	13.4601i	−0.175360	−	0.654452i
$424$		0			0
$425$	5.72958	−	21.3831i	0.277925	−	1.03723i
$426$		0			0
$427$	15.0881	−	5.20558i	0.730165	−	0.251916i
$428$		0			0
$429$	−0.212671	+	0.0279986i	−0.0102678	+	0.00135179i
$430$		0			0
$431$	17.3306	+	10.0059i	0.834788	+	0.481965i	0.855489	−	0.517821i	$-0.173257\pi$
$431$	17.3306	+	10.0059i	0.834788	+	0.481965i	−0.0207012	+	0.999786i	$0.506590\pi$
$432$		0			0
$433$		−	7.27777i		−	0.349747i	−0.984591	−	0.174874i	$-0.944048\pi$
$433$		−	7.27777i		−	0.349747i	0.984591	−	0.174874i	$-0.0559517\pi$
$434$		0			0
$435$	−0.0390126	+	0.0941847i	−0.00187051	+	0.00451581i
$436$		0			0
$437$	−0.138473	+	1.05181i	−0.00662406	+	0.0503147i
$438$		0			0
$439$	1.37044	−	5.11457i	0.0654077	−	0.244105i	−0.925480	−	0.378797i	$-0.876338\pi$
$439$	1.37044	−	5.11457i	0.0654077	−	0.244105i	0.990888	+	0.134692i	$0.0430045\pi$
$440$		0			0
$441$	−1.77283	−	12.5033i	−0.0844205	−	0.595397i
$442$		0			0
$443$	3.60281	−	4.69527i	0.171175	−	0.223079i	−0.699886	−	0.714254i	$-0.746766\pi$
$443$	3.60281	−	4.69527i	0.171175	−	0.223079i	0.871061	+	0.491175i	$0.163433\pi$
$444$		0			0
$445$	−0.121180	+	0.0929845i	−0.00574447	+	0.00440789i
$446$		0			0
$447$	−5.47657			−0.259033
$448$		0			0
$449$	−28.7167			−1.35522			−0.677612	−	0.735420i	$-0.736985\pi$
$449$	−28.7167			−1.35522			−0.677612	+	0.735420i	$0.736985\pi$
$450$		0			0
$451$	−0.410955	+	0.315336i	−0.0193511	+	0.0148486i
$452$		0			0
$453$	−4.26059	+	5.55252i	−0.200180	+	0.260880i
$454$		0			0
$455$	−0.00805332	+	0.00713376i	−0.000377546	+	0.000334436i
$456$		0			0
$457$	−8.64296	+	32.2560i	−0.404301	+	1.50887i	0.401042	+	0.916060i	$0.368648\pi$
$457$	−8.64296	+	32.2560i	−0.404301	+	1.50887i	−0.805342	+	0.592810i	$0.798018\pi$
$458$		0			0
$459$	−3.03618	+	23.0621i	−0.141717	+	1.07644i
$460$		0			0
$461$	8.16892	−	19.7215i	0.380464	−	0.918522i	−0.611411	−	0.791313i	$-0.709398\pi$
$461$	8.16892	−	19.7215i	0.380464	−	0.918522i	0.991876	−	0.127210i	$-0.0406021\pi$
$462$		0			0
$463$		−	18.0618i		−	0.839401i	−0.907663	−	0.419701i	$-0.862135\pi$
$463$		−	18.0618i		−	0.839401i	0.907663	−	0.419701i	$-0.137865\pi$
$464$		0			0
$465$	0.0701658	+	0.0405102i	0.00325386	+	0.00187862i
$466$		0			0
$467$	−6.31804	+	0.831786i	−0.292364	+	0.0384905i	−0.275282	−	0.961364i	$-0.588771\pi$
$467$	−6.31804	+	0.831786i	−0.292364	+	0.0384905i	−0.0170824	+	0.999854i	$0.505438\pi$
$468$		0			0
$469$	−18.5663	−	16.1196i	−0.857314	−	0.744332i
$470$		0			0
$471$	−5.11669	+	19.0957i	−0.235764	+	0.879885i
$472$		0			0
$473$	0.141366	+	0.527584i	0.00650000	+	0.0242583i
$474$		0			0
$475$	4.45361	+	10.7520i	0.204346	+	0.493335i
$476$		0			0
$477$	−18.2731	−	7.56897i	−0.836668	−	0.346559i
$478$		0			0
$479$	−16.7851	+	29.0727i	−0.766931	+	1.32836i	0.172288	+	0.985047i	$0.444884\pi$
$479$	−16.7851	+	29.0727i	−0.766931	+	1.32836i	−0.939220	+	0.343317i	$0.888449\pi$
$480$		0			0
$481$	−0.258956	−	0.448525i	−0.0118074	−	0.0204510i
$482$		0			0
$483$	1.09283	−	0.738098i	0.0497256	−	0.0335846i
$484$		0			0
$485$	−0.0758778	+	0.0988859i	−0.00344543	+	0.00449018i
$486$		0			0
$487$	−5.62751	−	21.0022i	−0.255007	−	0.951699i	−0.968087	−	0.250616i	$-0.919367\pi$
$487$	−5.62751	−	21.0022i	−0.255007	−	0.951699i	0.713080	−	0.701083i	$-0.247300\pi$
$488$		0			0
$489$	−13.3613	−	13.3613i	−0.604217	−	0.604217i
$490$		0			0
$491$	−22.6071	+	9.36415i	−1.02024	+	0.422598i	−0.829181	−	0.558980i	$-0.811193\pi$
$491$	−22.6071	+	9.36415i	−1.02024	+	0.422598i	−0.191061	+	0.981578i	$0.561193\pi$
$492$		0			0
$493$	24.0314	+	31.3183i	1.08232	+	1.41051i
$494$		0			0
$495$	0.00823851	−	0.00475651i	0.000370294	−	0.000213789i
$496$		0			0
$497$	−9.39635	−	6.21104i	−0.421484	−	0.278603i
$498$		0			0
$499$	14.1903	−	1.86819i	0.635246	−	0.0836318i	0.193976	−	0.981006i	$-0.437861\pi$
$499$	14.1903	−	1.86819i	0.635246	−	0.0836318i	0.441270	+	0.897374i	$0.354528\pi$
$500$		0			0
$501$	−3.12200	+	23.7140i	−0.139481	+	1.05946i
$502$		0			0
$503$	−2.74437	−	2.74437i	−0.122365	−	0.122365i	0.643272	−	0.765638i	$-0.277576\pi$
$503$	−2.74437	−	2.74437i	−0.122365	−	0.122365i	−0.765638	+	0.643272i	$0.777576\pi$
$504$		0			0
$505$	0.108237	−	0.108237i	0.00481647	−	0.00481647i
$506$		0			0
$507$	−13.9311	−	1.83406i	−0.618700	−	0.0814534i
$508$		0			0
$509$	3.95223	+	30.0202i	0.175180	+	1.33062i	0.822657	+	0.568538i	$0.192491\pi$
$509$	3.95223	+	30.0202i	0.175180	+	1.33062i	−0.647478	+	0.762084i	$0.724176\pi$
$510$		0			0
$511$	−0.695814	−	1.39345i	−0.0307810	−	0.0616427i
$512$		0			0
$513$	−6.11429	−	10.5903i	−0.269952	−	0.467571i
$514$		0			0
$515$	0.0896492	−	0.0687903i	0.00395042	−	0.00303126i
$516$		0			0
$517$	−1.49079	−	3.59909i	−0.0655649	−	0.158288i
$518$		0			0
$519$	11.8285	−	11.8285i	0.519212	−	0.519212i
$520$		0			0
$521$	14.1991	−	3.80463i	0.622073	−	0.166684i	0.0660028	−	0.997819i	$-0.478975\pi$
$521$	14.1991	−	3.80463i	0.622073	−	0.166684i	0.556070	+	0.831136i	$0.312309\pi$
$522$		0			0
$523$	23.4627	+	18.0036i	1.02595	+	0.787241i	0.977361	−	0.211578i	$-0.0678602\pi$
$523$	23.4627	+	18.0036i	1.02595	+	0.787241i	0.0485911	+	0.998819i	$0.484527\pi$
$524$		0			0
$525$	6.33376	−	13.0063i	0.276428	−	0.567642i
$526$		0			0
$527$	27.1701	−	15.6867i	1.18355	−	0.683323i
$528$		0			0
$529$	19.7387	+	11.3961i	0.858204	+	0.495484i
$530$		0			0
$531$	−3.53148	+	8.52574i	−0.153253	+	0.369986i
$532$		0			0
$533$	0.369045	−	0.152864i	0.0159851	−	0.00662126i
$534$		0			0
$535$	0.114369	−	0.0306450i	0.00494459	−	0.00132490i
$536$		0			0
$537$	−19.1948	−	5.14323i	−0.828316	−	0.221947i
$538$		0			0
$539$	−0.947614	−	3.40082i	−0.0408166	−	0.146484i
$540$		0			0
$541$	3.42109	+	25.9857i	0.147084	+	1.11721i	0.892640	+	0.450771i	$0.148851\pi$
$541$	3.42109	+	25.9857i	0.147084	+	1.11721i	−0.745556	+	0.666443i	$0.767816\pi$
$542$		0			0
$543$	−1.07891	+	1.86874i	−0.0463007	+	0.0801951i
$544$		0			0
$545$	−0.0733837			−0.00314341
$546$		0			0
$547$	−25.6722	−	10.6338i	−1.09766	−	0.454667i	−0.240991	−	0.970527i	$-0.577472\pi$
$547$	−25.6722	−	10.6338i	−1.09766	−	0.454667i	−0.856673	+	0.515860i	$0.827472\pi$
$548$		0			0
$549$	10.7901	+	1.42055i	0.460511	+	0.0606275i
$550$		0			0
$551$	−20.0457	−	5.37123i	−0.853976	−	0.228822i
$552$		0			0
$553$	−19.9200	−	22.4878i	−0.847085	−	0.956277i
$554$		0			0
$555$	−0.0120799	−	0.00926920i	−0.000512762	−	0.000393456i
$556$		0			0
$557$	−21.3227	−	27.7882i	−0.903471	−	1.17743i	−0.983550	−	0.180637i	$-0.942184\pi$
$557$	−21.3227	−	27.7882i	−0.903471	−	1.17743i	0.0800792	−	0.996789i	$-0.474483\pi$
$558$		0			0
$559$		−	0.421197i		−	0.0178147i
$560$		0			0
$561$			2.44199i			0.103101i
$562$		0			0
$563$	−26.9090	−	35.0685i	−1.13408	−	1.47796i	−0.855688	−	0.517492i	$-0.826866\pi$
$563$	−26.9090	−	35.0685i	−1.13408	−	1.47796i	−0.278390	−	0.960468i	$-0.589801\pi$
$564$		0			0
$565$	−0.0476069	−	0.0365300i	−0.00200284	−	0.00153683i
$566$		0			0
$567$	−0.279216	+	0.836189i	−0.0117260	+	0.0351166i
$568$		0			0
$569$	−16.9469	−	4.54092i	−0.710452	−	0.190365i	−0.114545	−	0.993418i	$-0.536541\pi$
$569$	−16.9469	−	4.54092i	−0.710452	−	0.190365i	−0.595908	+	0.803053i	$0.703208\pi$
$570$		0			0
$571$	36.3266	+	4.78249i	1.52022	+	0.200141i	0.843913	−	0.536479i	$-0.180246\pi$
$571$	36.3266	+	4.78249i	1.52022	+	0.200141i	0.676307	+	0.736620i	$0.263579\pi$
$572$		0			0
$573$	−9.68118	−	4.01008i	−0.404437	−	0.167523i
$574$		0			0
$575$	−2.27885			−0.0950345
$576$		0			0
$577$	0.637232	−	1.10372i	0.0265283	−	0.0459484i	−0.852456	−	0.522798i	$-0.824888\pi$
$577$	0.637232	−	1.10372i	0.0265283	−	0.0459484i	0.878985	+	0.476850i	$0.158221\pi$
$578$		0			0
$579$	1.57450	+	11.9595i	0.0654339	+	0.497020i
$580$		0			0
$581$	30.6215	+	5.93278i	1.27039	+	0.246133i
$582$		0			0
$583$	−5.34089	−	1.43109i	−0.221197	−	0.0592696i
$584$		0			0
$585$	−0.00708597	+	0.00189868i	−0.000292969	+	7.85007e-5i
$586$		0			0
$587$	7.20554	−	2.98463i	0.297404	−	0.123189i	−0.228992	−	0.973428i	$-0.573543\pi$
$587$	7.20554	−	2.98463i	0.297404	−	0.123189i	0.526396	+	0.850239i	$0.323543\pi$
$588$		0			0
$589$	−6.31171	+	15.2378i	−0.260070	+	0.627863i
$590$		0			0
$591$	4.05264	+	2.33979i	0.166703	+	0.0962462i
$592$		0			0
$593$	36.3322	−	20.9764i	1.49198	−	0.861397i	0.492026	−	0.870580i	$-0.336256\pi$
$593$	36.3322	−	20.9764i	1.49198	−	0.861397i	0.999958	+	0.00918306i	$0.00292310\pi$
$594$		0			0
$595$	0.0685512	+	0.101497i	0.00281032	+	0.00416098i
$596$		0			0
$597$	−20.1090	−	15.4302i	−0.823006	−	0.631514i
$598$		0			0
$599$	−32.4372	+	8.69153i	−1.32535	+	0.355126i	−0.850979	−	0.525199i	$-0.823991\pi$
$599$	−32.4372	+	8.69153i	−1.32535	+	0.355126i	−0.474370	+	0.880325i	$0.657324\pi$
$600$		0			0
$601$	−10.4156	+	10.4156i	−0.424863	+	0.424863i	−0.886874	−	0.462011i	$-0.847128\pi$
$601$	−10.4156	+	10.4156i	−0.424863	+	0.424863i	0.462011	+	0.886874i	$0.347128\pi$
$602$		0			0
$603$	−6.41589	−	15.4893i	−0.261275	−	0.630774i
$604$		0			0
$605$	−0.0891340	+	0.0683949i	−0.00362381	+	0.00278065i
$606$		0			0
$607$	−17.2810	−	29.9315i	−0.701413	−	1.21488i	−0.967971	−	0.251064i	$-0.919220\pi$
$607$	−17.2810	−	29.9315i	−0.701413	−	1.21488i	0.266558	−	0.963819i	$-0.414114\pi$
$608$		0			0
$609$	11.5247	+	23.0796i	0.467004	+	0.935232i
$610$		0			0
$611$	0.392114	+	2.97840i	0.0158632	+	0.120493i
$612$		0			0
$613$	−12.1286	−	1.59676i	−0.489870	−	0.0644926i	−0.118455	−	0.992959i	$-0.537794\pi$
$613$	−12.1286	−	1.59676i	−0.489870	−	0.0644926i	−0.371415	+	0.928467i	$0.621127\pi$
$614$		0			0
$615$	0.00830402	−	0.00830402i	0.000334850	−	0.000334850i
$616$		0			0
$617$	21.6358	+	21.6358i	0.871026	+	0.871026i	0.992584	−	0.121558i	$-0.0387890\pi$
$617$	21.6358	+	21.6358i	0.871026	+	0.871026i	−0.121558	+	0.992584i	$0.538789\pi$
$618$		0			0
$619$	−5.11447	+	38.8483i	−0.205568	+	1.56144i	0.508311	+	0.861174i	$0.330270\pi$
$619$	−5.11447	+	38.8483i	−0.205568	+	1.56144i	−0.713879	+	0.700270i	$0.753063\pi$
$620$		0			0
$621$	2.37403	−	0.312547i	0.0952666	−	0.0125421i
$622$		0			0
$623$	−2.33603	+	38.5810i	−0.0935909	+	1.54571i
$624$		0			0
$625$	−21.6492	+	12.4992i	−0.865969	+	0.499967i
$626$		0			0
$627$	−0.781516	−	1.01849i	−0.0312108	−	0.0406746i
$628$		0			0
$629$	−5.44725	+	2.25632i	−0.217196	+	0.0899655i
$630$		0			0
$631$	31.4063	+	31.4063i	1.25027	+	1.25027i	0.955600	+	0.294666i	$0.0952084\pi$
$631$	31.4063	+	31.4063i	1.25027	+	1.25027i	0.294666	+	0.955600i	$0.404792\pi$
$632$		0			0
$633$	−4.72924	−	17.6498i	−0.187970	−	0.701515i
$634$		0			0
$635$	−0.0271507	+	0.0353835i	−0.00107744	+	0.00140415i
$636$		0			0
$637$	0.0270878	+	2.72231i	0.00107326	+	0.107862i
$638$		0			0
$639$	−3.84015	−	6.65133i	−0.151914	−	0.263123i
$640$		0			0
$641$	14.7676	−	25.5783i	0.583286	−	1.01028i	−0.411800	−	0.911274i	$-0.635100\pi$
$641$	14.7676	−	25.5783i	0.583286	−	1.01028i	0.995087	−	0.0990074i	$-0.0315668\pi$
$642$		0			0
$643$	−7.31913	−	3.03168i	−0.288638	−	0.119558i	0.233666	−	0.972317i	$-0.424928\pi$
$643$	−7.31913	−	3.03168i	−0.288638	−	0.119558i	−0.522305	+	0.852759i	$0.674928\pi$
$644$		0			0
$645$	−0.00473875	−	0.0114404i	−0.000186588	−	0.000450463i
$646$		0			0
$647$	5.17547	+	19.3151i	0.203469	+	0.759355i	0.989911	+	0.141692i	$0.0452541\pi$
$647$	5.17547	+	19.3151i	0.203469	+	0.759355i	−0.786442	+	0.617664i	$0.788079\pi$
$648$		0			0
$649$	−0.667707	+	2.49192i	−0.0262098	+	0.0978163i
$650$		0			0
$651$	19.3811	−	6.68670i	0.759604	−	0.262072i
$652$		0			0
$653$	−37.3274	+	4.91425i	−1.46073	+	0.192309i	−0.818636	−	0.574313i	$-0.805269\pi$
$653$	−37.3274	+	4.91425i	−1.46073	+	0.192309i	−0.642098	+	0.766622i	$0.721936\pi$
$654$		0			0
$655$	−0.0363277	−	0.0209738i	−0.00141944	−	0.000819515i
$656$		0			0
$657$		−	1.06202i		−	0.0414335i
$658$		0			0
$659$	−5.38612	+	13.0032i	−0.209813	+	0.506534i	−0.993394	−	0.114756i	$-0.963391\pi$
$659$	−5.38612	+	13.0032i	−0.209813	+	0.506534i	0.783580	+	0.621290i	$0.213391\pi$
$660$		0			0
$661$	4.28061	−	32.5145i	0.166496	−	1.26467i	−0.680374	−	0.732865i	$-0.738182\pi$
$661$	4.28061	−	32.5145i	0.166496	−	1.26467i	0.846870	−	0.531800i	$-0.178484\pi$
$662$		0			0
$663$	0.487391	−	1.81897i	0.0189287	−	0.0706429i
$664$		0			0
$665$	−0.0610733	−	0.0203933i	−0.00236832	−	0.000790819i
$666$		0			0
$667$	2.47382	−	3.22394i	0.0957865	−	0.124831i
$668$		0			0
$669$	−20.5193	+	15.7450i	−0.793324	+	0.608739i
$670$		0			0
$671$	3.04250			0.117454
$672$		0			0
$673$	26.3926			1.01736			0.508680	−	0.860956i	$-0.330134\pi$
$673$	26.3926			1.01736			0.508680	+	0.860956i	$0.330134\pi$
$674$		0			0
$675$	20.8397	−	15.9908i	0.802119	−	0.615487i
$676$		0			0
$677$	−12.7929	+	16.6721i	−0.491672	+	0.640759i	−0.971623	−	0.236536i	$-0.923988\pi$
$677$	−12.7929	+	16.6721i	−0.491672	+	0.640759i	0.479951	+	0.877295i	$0.340654\pi$
$678$		0			0
$679$	6.30712	+	30.9037i	0.242045	+	1.18598i
$680$		0			0
$681$	−7.41328	+	27.6667i	−0.284078	+	1.06019i
$682$		0			0
$683$	−1.65133	+	12.5431i	−0.0631864	+	0.479949i	0.930371	+	0.366619i	$0.119485\pi$
$683$	−1.65133	+	12.5431i	−0.0631864	+	0.479949i	−0.993557	+	0.113329i	$0.963848\pi$
$684$		0			0
$685$	−0.0266771	+	0.0644042i	−0.00101928	+	0.00246076i
$686$		0			0
$687$		−	28.6257i		−	1.09214i
$688$		0			0
$689$	3.69265	+	2.13195i	0.140679	+	0.0812208i
$690$		0			0
$691$	−9.29360	+	1.22353i	−0.353545	+	0.0465451i	−0.305207	−	0.952286i	$-0.598726\pi$
$691$	−9.29360	+	1.22353i	−0.353545	+	0.0465451i	−0.0483379	+	0.998831i	$0.515392\pi$
$692$		0			0
$693$	0.457881	−	2.36331i	0.0173935	−	0.0897748i
$694$		0			0
$695$	−0.0413752	+	0.154414i	−0.00156945	+	0.00585727i
$696$		0			0
$697$	−1.17697	−	4.39252i	−0.0445810	−	0.166379i
$698$		0			0
$699$	1.25272	+	3.02432i	0.0473821	+	0.114390i
$700$		0			0
$701$	−13.6747	−	5.66427i	−0.516488	−	0.213936i	0.109185	−	0.994021i	$-0.465176\pi$
$701$	−13.6747	−	5.66427i	−0.516488	−	0.213936i	−0.625674	+	0.780085i	$0.715176\pi$
$702$		0			0
$703$	1.54981	−	2.68435i	0.0584521	−	0.101242i
$704$		0			0
$705$	0.0441594	+	0.0764864i	0.00166314	+	0.00288064i
$706$		0			0
$707$	−2.72559	−	38.6381i	−0.102506	−	1.45314i
$708$		0			0
$709$	30.6243	−	39.9103i	1.15012	−	1.49886i	0.314750	−	0.949175i	$-0.398079\pi$
$709$	30.6243	−	39.9103i	1.15012	−	1.49886i	0.835369	−	0.549689i	$-0.185254\pi$
$710$		0			0
$711$	−5.30179	−	19.7866i	−0.198833	−	0.742054i
$712$		0			0
$713$	−2.28368	−	2.28368i	−0.0855244	−	0.0855244i
$714$		0			0
$715$	−0.00189471		0.000784816i	−7.08583e−5		2.93505e-5i
$716$		0			0
$717$	8.88325	+	11.5769i	0.331751	+	0.432346i
$718$		0			0
$719$	22.5745	−	13.0334i	0.841885	−	0.486063i	−0.0160195	−	0.999872i	$-0.505099\pi$
$719$	22.5745	−	13.0334i	0.841885	−	0.486063i	0.857905	+	0.513809i	$0.171766\pi$
$720$		0			0
$721$	1.72820	−	28.5424i	0.0643616	−	1.06297i
$722$		0			0
$723$	27.5356	−	3.62513i	1.02406	−	0.134820i
$724$		0			0
$725$	5.81867	−	44.1972i	0.216100	−	1.64144i
$726$		0			0
$727$	1.78370	+	1.78370i	0.0661537	+	0.0661537i	0.739410	−	0.673256i	$-0.235105\pi$
$727$	1.78370	+	1.78370i	0.0661537	+	0.0661537i	−0.673256	+	0.739410i	$0.735105\pi$
$728$		0			0
$729$	−12.6128	+	12.6128i	−0.467142	+	0.467142i
$730$		0			0
$731$	−4.75400	−	0.625876i	−0.175833	−	0.0231489i
$732$		0			0
$733$	−0.142345	−	1.08122i	−0.00525762	−	0.0399356i	0.988615	−	0.150468i	$-0.0480779\pi$
$733$	−0.142345	−	1.08122i	−0.00525762	−	0.0399356i	−0.993873	+	0.110532i	$0.964745\pi$
$734$		0			0
$735$	0.0313636	+	0.0736373i	0.00115686	+	0.00271615i
$736$		0			0
$737$	−2.34347	−	4.05902i	−0.0863230	−	0.149516i
$738$		0			0
$739$	6.00863	−	4.61058i	0.221031	−	0.169603i	−0.492311	−	0.870420i	$-0.663848\pi$
$739$	6.00863	−	4.61058i	0.221031	−	0.169603i	0.713341	+	0.700817i	$0.247181\pi$
$740$		0			0
$741$	0.378850	+	0.914626i	0.0139174	+	0.0335996i
$742$		0			0
$743$	−2.26102	+	2.26102i	−0.0829487	+	0.0829487i	−0.747364	−	0.664415i	$-0.768681\pi$
$743$	−2.26102	+	2.26102i	−0.0829487	+	0.0829487i	0.664415	+	0.747364i	$0.268681\pi$
$744$		0			0
$745$	−0.0505757	+	0.0135517i	−0.00185295	+	0.000496497i
$746$		0			0
$747$	16.8732	+	12.9472i	0.617357	+	0.473715i
$748$		0			0
$749$	13.1179	−	26.9375i	0.479318	−	0.984275i
$750$		0			0
$751$	28.9562	−	16.7179i	1.05663	−	0.610045i	0.132131	−	0.991232i	$-0.457818\pi$
$751$	28.9562	−	16.7179i	1.05663	−	0.610045i	0.924498	+	0.381188i	$0.124485\pi$
$752$		0			0
$753$	2.44510	+	1.41168i	0.0891045	+	0.0514445i
$754$		0			0
$755$	−0.0256066	+	0.0618198i	−0.000931920	+	0.00224985i
$756$		0			0
$757$	−0.849473	+	0.351863i	−0.0308746	+	0.0127887i	−0.398067	−	0.917356i	$-0.630319\pi$
$757$	−0.849473	+	0.351863i	−0.0308746	+	0.0127887i	0.367193	+	0.930145i	$0.380319\pi$
$758$		0			0
$759$	0.242816	−	0.0650623i	0.00881366	−	0.00236161i
$760$		0			0
$761$	12.9202	+	3.46197i	0.468359	+	0.125496i	0.485277	−	0.874361i	$-0.338719\pi$
$761$	12.9202	+	3.46197i	0.468359	+	0.125496i	−0.0169183	+	0.999857i	$0.505386\pi$
$762$		0			0
$763$	−12.1742	+	14.0221i	−0.440736	+	0.507636i
$764$		0			0
$765$	0.0109008	+	0.0827999i	0.000394120	+	0.00299364i
$766$		0			0
$767$	0.994711	−	1.72289i	0.0359169	−	0.0622100i
$768$		0			0
$769$	18.4371			0.664858			0.332429	−	0.943128i	$-0.392132\pi$
$769$	18.4371			0.664858			0.332429	+	0.943128i	$0.392132\pi$
$770$		0			0
$771$	29.9000	+	12.3850i	1.07682	+	0.446034i
$772$		0			0
$773$	25.3477	+	3.33709i	0.911694	+	0.120027i	0.571759	−	0.820422i	$-0.306261\pi$
$773$	25.3477	+	3.33709i	0.911694	+	0.120027i	0.339936	+	0.940449i	$0.389595\pi$
$774$		0			0
$775$	−34.2215	−	9.16963i	−1.22927	−	0.329383i
$776$		0			0
$777$	−3.77519	+	0.770475i	−0.135434	+	0.0276407i
$778$		0			0
$779$	1.89663	+	1.45534i	0.0679539	+	0.0521428i
$780$		0			0
$781$	−1.30707	−	1.70340i	−0.0467706	−	0.0609526i
$782$		0			0
$783$			46.8413i			1.67397i
$784$		0			0
$785$			0.189009i			0.00674601i
$786$		0			0
$787$	−15.4011	−	20.0712i	−0.548992	−	0.715460i	0.433628	−	0.901092i	$-0.357233\pi$
$787$	−15.4011	−	20.0712i	−0.548992	−	0.715460i	−0.982619	+	0.185632i	$0.940567\pi$
$788$		0			0
$789$	−8.66197	−	6.64656i	−0.308374	−	0.236624i
$790$		0			0
$791$	−14.8780	+	3.03645i	−0.529002	+	0.107964i
$792$		0			0
$793$	−2.26627	−	0.607245i	−0.0804776	−	0.0215639i
$794$		0			0
$795$	0.124284	+	0.0163623i	0.00440790	+	0.000580310i
$796$		0			0
$797$	−9.04304	−	3.74575i	−0.320321	−	0.132681i	0.216729	−	0.976232i	$-0.430461\pi$
$797$	−9.04304	−	3.74575i	−0.320321	−	0.132681i	−0.537050	+	0.843551i	$0.680461\pi$
$798$		0			0
$799$	34.1995			1.20989
$800$		0			0
$801$	−13.1777	+	22.8244i	−0.465611	+	0.806461i
$802$		0			0
$803$	−0.0387530	−	0.294358i	−0.00136756	−	0.0103877i
$804$		0			0
$805$	0.00826581	−	0.00952048i	0.000291332	−	0.000335553i
$806$		0			0
$807$	−19.2471	−	5.15725i	−0.677531	−	0.181544i
$808$		0			0
$809$	16.0911	−	4.31159i	0.565731	−	0.151587i	0.0353933	−	0.999373i	$-0.488732\pi$
$809$	16.0911	−	4.31159i	0.565731	−	0.151587i	0.530338	+	0.847786i	$0.322065\pi$
$810$		0			0
$811$	35.3358	−	14.6366i	1.24081	−	0.513960i	0.336842	−	0.941561i	$-0.390641\pi$
$811$	35.3358	−	14.6366i	1.24081	−	0.513960i	0.903967	+	0.427601i	$0.140641\pi$
$812$		0			0
$813$	1.67178	−	4.03603i	0.0586318	−	0.141550i
$814$		0			0
$815$	−0.156453	−	0.0903279i	−0.00548029	−	0.00316405i
$816$		0			0
$817$	2.18307	−	1.26040i	0.0763759	−	0.0440957i
$818$		0			0
$819$	−0.812750	+	1.66897i	−0.0283998	+	0.0583187i
$820$		0			0
$821$	−11.0736	−	8.49704i	−0.386470	−	0.296549i	0.397193	−	0.917735i	$-0.369984\pi$
$821$	−11.0736	−	8.49704i	−0.386470	−	0.296549i	−0.783663	+	0.621186i	$0.786651\pi$
$822$		0			0
$823$	7.99525	−	2.14232i	0.278697	−	0.0746766i	−0.116763	−	0.993160i	$-0.537252\pi$
$823$	7.99525	−	2.14232i	0.278697	−	0.0746766i	0.395460	+	0.918483i	$0.370585\pi$
$824$		0			0
$825$	1.94995	−	1.94995i	0.0678886	−	0.0678886i
$826$		0			0
$827$	−11.3603	−	27.4263i	−0.395038	−	0.953706i	−0.988825	−	0.149083i	$-0.952368\pi$
$827$	−11.3603	−	27.4263i	−0.395038	−	0.953706i	0.593787	−	0.804622i	$-0.297632\pi$
$828$		0			0
$829$	8.29638	−	6.36603i	0.288145	−	0.221102i	−0.454567	−	0.890713i	$-0.650206\pi$
$829$	8.29638	−	6.36603i	0.288145	−	0.221102i	0.742712	+	0.669611i	$0.233539\pi$
$830$		0			0
$831$	−2.59109	−	4.48789i	−0.0898838	−	0.155683i
$832$		0			0
$833$	30.7666	+	3.73947i	1.06600	+	0.129565i
$834$		0			0
$835$	0.0298485	+	0.226722i	0.00103295	+	0.00784604i
$836$		0			0
$837$	36.9085	+	4.85910i	1.27575	+	0.167955i
$838$		0			0
$839$	18.6175	−	18.6175i	0.642748	−	0.642748i	−0.308482	−	0.951230i	$-0.599821\pi$
$839$	18.6175	−	18.6175i	0.642748	−	0.642748i	0.951230	+	0.308482i	$0.0998210\pi$
$840$		0			0
$841$	35.7042	+	35.7042i	1.23118	+	1.23118i
$842$		0			0
$843$	−1.42012	+	10.7869i	−0.0489117	+	0.371521i
$844$		0			0
$845$	−0.133191	+	0.0175349i	−0.00458190	+	0.000603218i
$846$		0			0
$847$	−1.71827	+	28.3783i	−0.0590405	+	0.975091i
$848$		0			0
$849$	4.91815	−	2.83949i	0.168790	−	0.0974512i
$850$		0			0
$851$	0.369486	+	0.481523i	0.0126658	+	0.0165064i
$852$		0			0
$853$	−9.86904	+	4.08789i	−0.337909	+	0.139967i	−0.545185	−	0.838316i	$-0.683540\pi$
$853$	−9.86904	+	4.08789i	−0.337909	+	0.139967i	0.207275	+	0.978283i	$0.433540\pi$
$854$		0			0
$855$	−0.0310451	−	0.0310451i	−0.00106172	−	0.00106172i
$856$		0			0
$857$	−14.4932	−	54.0893i	−0.495078	−	1.84765i	−0.529595	−	0.848251i	$-0.677656\pi$
$857$	−14.4932	−	54.0893i	−0.495078	−	1.84765i	0.0345174	−	0.999404i	$-0.489011\pi$
$858$		0			0
$859$	9.22273	−	12.0193i	0.314676	−	0.410093i	−0.609060	−	0.793124i	$-0.708453\pi$
$859$	9.22273	−	12.0193i	0.314676	−	0.410093i	0.923735	+	0.383031i	$0.125120\pi$
$860$		0			0
$861$	−0.209110	−	2.96435i	−0.00712645	−	0.101025i
$862$		0			0
$863$	0.157887	+	0.273468i	0.00537453	+	0.00930896i	0.868700	−	0.495338i	$-0.164956\pi$
$863$	0.157887	+	0.273468i	0.00537453	+	0.00930896i	−0.863326	+	0.504647i	$0.831623\pi$
$864$		0			0
$865$	0.0799655	−	0.138504i	0.00271891	−	0.00470929i
$866$		0			0
$867$	−2.63037	−	1.08953i	−0.0893321	−	0.0370025i
$868$		0			0
$869$	−2.19149	−	5.29072i	−0.0743411	−	0.179475i
$870$		0			0
$871$	0.935456	+	3.49117i	0.0316967	+	0.118294i
$872$		0			0
$873$	−5.56634	+	20.7739i	−0.188392	+	0.703089i
$874$		0			0
$875$	0.0526161	−	0.271573i	0.00177875	−	0.00918085i
$876$		0			0
$877$	−21.3945	+	2.81664i	−0.722442	+	0.0951112i	−0.482776	−	0.875744i	$-0.660371\pi$
$877$	−21.3945	+	2.81664i	−0.722442	+	0.0951112i	−0.239666	+	0.970855i	$0.577038\pi$
$878$		0			0
$879$	−4.62036	−	2.66757i	−0.155841	−	0.0899749i
$880$		0			0
$881$			38.9692i			1.31291i	0.754367	+	0.656453i	$0.227944\pi$
$881$			38.9692i			1.31291i	−0.754367	+	0.656453i	$0.772056\pi$
$882$		0			0
$883$	19.0782	−	46.0588i	0.642032	−	1.55000i	−0.181901	−	0.983317i	$-0.558225\pi$
$883$	19.0782	−	46.0588i	0.642032	−	1.55000i	0.823934	−	0.566686i	$-0.191775\pi$
$884$		0			0
$885$	0.00763421	−	0.0579876i	0.000256621	−	0.00194923i
$886$		0			0
$887$	−6.48715	+	24.2104i	−0.217817	+	0.812905i	0.767339	+	0.641242i	$0.221581\pi$
$887$	−6.48715	+	24.2104i	−0.217817	+	0.812905i	−0.985156	+	0.171663i	$0.945086\pi$
$888$		0			0
$889$	2.25682	+	11.0580i	0.0756915	+	0.370874i
$890$		0			0
$891$	−0.102301	+	0.133321i	−0.00342722	+	0.00446644i
$892$		0			0
$893$	−14.2637	+	10.9449i	−0.477317	+	0.366258i
$894$		0			0
$895$	−0.189989			−0.00635064
$896$		0			0
$897$	−0.193852			−0.00647253
$898$		0			0
$899$	50.1219	−	38.4599i	1.67166	−	1.28271i
$900$		0			0
$901$	29.5502	−	38.5105i	0.984458	−	1.28297i
$902$		0			0
$903$	−2.97217	−	0.992454i	−0.0989077	−	0.0330268i
$904$		0			0
$905$	−0.00533953	+	0.0199274i	−0.000177492	+	0.000662409i
$906$		0			0
$907$	5.25225	−	39.8948i	0.174398	−	1.32468i	−0.650545	−	0.759468i	$-0.725459\pi$
$907$	5.25225	−	39.8948i	0.174398	−	1.32468i	0.824943	−	0.565216i	$-0.191207\pi$
$908$		0			0
$909$	10.1073	−	24.4012i	0.335238	−	0.809336i
$910$		0			0
$911$			0.734154i			0.0243236i	0.999926	+	0.0121618i	$0.00387132\pi$
$911$			0.734154i			0.0243236i	−0.999926	+	0.0121618i	$0.996129\pi$
$912$		0			0
$913$	5.14913	+	2.97285i	0.170411	+	0.0983870i
$914$		0			0
$915$	−0.0683874	+	0.00900337i	−0.00226082	+	0.000297642i
$916$		0			0
$917$	−10.0344	+	3.46198i	−0.331365	+	0.114325i
$918$		0			0
$919$	−14.4840	+	54.0552i	−0.477785	+	1.78312i	0.132775	+	0.991146i	$0.457611\pi$
$919$	−14.4840	+	54.0552i	−0.477785	+	1.78312i	−0.610559	+	0.791970i	$0.709055\pi$
$920$		0			0
$921$	−4.74421	−	17.7056i	−0.156327	−	0.583420i
$922$		0			0
$923$	0.633619	+	1.52969i	0.0208558	+	0.0503504i
$924$		0			0
$925$	6.15136	+	2.54798i	0.202256	+	0.0837770i
$926$		0			0
$927$	9.74890	−	16.8856i	0.320196	−	0.554596i
$928$		0			0
$929$	23.3147	+	40.3823i	0.764932	+	1.32490i	0.940282	+	0.340395i	$0.110561\pi$
$929$	23.3147	+	40.3823i	0.764932	+	1.32490i	−0.175350	+	0.984506i	$0.556106\pi$
$930$		0			0
$931$	−14.0287	+	8.28667i	−0.459772	+	0.271585i
$932$		0			0
$933$	1.70283	−	2.21917i	0.0557481	−	0.0726523i
$934$		0			0
$935$	0.00604269	+	0.0225516i	0.000197617	+	0.000737517i
$936$		0			0
$937$	−9.25935	−	9.25935i	−0.302490	−	0.302490i	0.539497	−	0.841987i	$-0.318614\pi$
$937$	−9.25935	−	9.25935i	−0.302490	−	0.302490i	−0.841987	+	0.539497i	$0.818614\pi$
$938$		0			0
$939$	5.20561	−	2.15624i	0.169879	−	0.0703661i
$940$		0			0
$941$	15.6620	+	20.4111i	0.510566	+	0.665383i	0.975509	−	0.219958i	$-0.0705920\pi$
$941$	15.6620	+	20.4111i	0.510566	+	0.665383i	−0.464943	+	0.885340i	$0.653925\pi$
$942$		0			0
$943$	−0.405405	+	0.234061i	−0.0132018	+	0.00762207i
$944$		0			0
$945$	−0.00878349	+	0.145065i	−0.000285727	+	0.00471896i
$946$		0			0
$947$	−10.1116	+	1.33121i	−0.328582	+	0.0432586i	−0.293013	−	0.956109i	$-0.594658\pi$
$947$	−10.1116	+	1.33121i	−0.328582	+	0.0432586i	−0.0355693	+	0.999367i	$0.511324\pi$
$948$		0			0
$949$	−0.0298843	+	0.226993i	−0.000970084	+	0.00736852i
$950$		0			0
$951$	−0.0946761	−	0.0946761i	−0.00307008	−	0.00307008i
$952$		0			0
$953$	19.2898	−	19.2898i	0.624856	−	0.624856i	−0.321913	−	0.946769i	$-0.604326\pi$
$953$	19.2898	−	19.2898i	0.624856	−	0.624856i	0.946769	+	0.321913i	$0.104326\pi$
$954$		0			0
$955$	−0.0993278	−	0.0130768i	−0.00321417	−	0.000423154i
$956$		0			0
$957$	0.641862	+	4.87542i	0.0207484	+	0.157600i
$958$		0			0
$959$	7.88067	+	15.7820i	0.254480	+	0.509627i
$960$		0			0
$961$	−9.60499	−	16.6363i	−0.309838	−	0.536656i
$962$		0			0
$963$	16.2082	−	12.4370i	0.522303	−	0.400777i
$964$		0			0
$965$	0.0441340	+	0.106549i	0.00142072	+	0.00342993i
$966$		0			0
$967$	−5.46434	+	5.46434i	−0.175721	+	0.175721i	−0.789488	−	0.613766i	$-0.789654\pi$
$967$	−5.46434	+	5.46434i	−0.175721	+	0.175721i	0.613766	+	0.789488i	$0.289654\pi$
$968$		0			0
$969$	10.8862	−	2.91696i	0.349716	−	0.0937061i
$970$		0			0
$971$	17.8660	+	13.7091i	0.573349	+	0.439946i	0.854303	−	0.519775i	$-0.173984\pi$
$971$	17.8660	+	13.7091i	0.573349	+	0.439946i	−0.280954	+	0.959721i	$0.590651\pi$
$972$		0			0
$973$	22.6414	+	33.5230i	0.725850	+	1.07470i
$974$		0			0
$975$	−1.84165	+	1.06328i	−0.0589800	+	0.0340521i
$976$		0			0
$977$	33.0032	+	19.0544i	1.05587	+	0.609605i	0.924286	−	0.381700i	$-0.124661\pi$
$977$	33.0032	+	19.0544i	1.05587	+	0.609605i	0.131581	+	0.991305i	$0.457995\pi$
$978$		0			0
$979$	−2.81956	+	6.80703i	−0.0901136	+	0.217553i
$980$		0			0
$981$	−11.6982	+	4.84557i	−0.373496	+	0.154707i
$982$		0			0
$983$	21.0422	−	5.63823i	0.671141	−	0.179832i	0.0928721	−	0.995678i	$-0.470395\pi$
$983$	21.0422	−	5.63823i	0.671141	−	0.179832i	0.578269	+	0.815846i	$0.303729\pi$
$984$		0			0
$985$	0.0432156	+	0.0115796i	0.00137696	+	0.000368956i
$986$		0			0
$987$	21.9410	+	4.25097i	0.698389	+	0.135310i
$988$		0			0
$989$	0.0644283	+	0.489382i	0.00204870	+	0.0155614i
$990$		0			0
$991$	17.9837	−	31.1487i	0.571271	−	0.989470i	−0.425165	−	0.905116i	$-0.639784\pi$
$991$	17.9837	−	31.1487i	0.571271	−	0.989470i	0.996436	−	0.0843544i	$-0.0268828\pi$
$992$		0			0
$993$	24.5266			0.778327
$994$		0			0
$995$	−0.223887	−	0.0927369i	−0.00709768	−	0.00293996i
$996$		0			0
$997$	−50.4453	−	6.64125i	−1.59762	−	0.210330i	−0.721496	−	0.692419i	$-0.756545\pi$
$997$	−50.4453	−	6.64125i	−1.59762	−	0.210330i	−0.876122	+	0.482089i	$0.839878\pi$
$998$		0			0
$999$	−6.75776	−	1.81074i	−0.213806	−	0.0572892i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.bh.a.81.10		240
4.3	odd	2		224.2.bd.a.221.27	yes	240
7.2	even	3	inner	896.2.bh.a.849.10		240
28.23	odd	6		224.2.bd.a.93.14	yes	240
32.11	odd	8		224.2.bd.a.53.14	✓	240
32.21	even	8	inner	896.2.bh.a.305.10		240
224.107	odd	24		224.2.bd.a.149.27	yes	240
224.149	even	24	inner	896.2.bh.a.177.10		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.53.14	✓	240	32.11	odd	8
224.2.bd.a.93.14	yes	240	28.23	odd	6
224.2.bd.a.149.27	yes	240	224.107	odd	24
224.2.bd.a.221.27	yes	240	4.3	odd	2
896.2.bh.a.81.10		240	1.1	even	1	trivial
896.2.bh.a.177.10		240	224.149	even	24	inner
896.2.bh.a.305.10		240	32.21	even	8	inner
896.2.bh.a.849.10		240	7.2	even	3	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)

\(f(q)\)	\(=\)	\(q+(-0.867605 + 0.665736i) q^{3} +(-0.00636490 + 0.00829490i) q^{5} +(0.529064 + 2.59231i) q^{7} +(-0.466924 + 1.74259i) q^{9} +O(q^{10})\)	\(q+(-0.867605 + 0.665736i) q^{3} +(-0.00636490 + 0.00829490i) q^{5} +(0.529064 + 2.59231i) q^{7} +(-0.466924 + 1.74259i) q^{9} +(-0.0658296 + 0.500025i) q^{11} +(0.148833 - 0.359315i) q^{13} -0.0114340i q^{15} +(-3.83439 - 2.21379i) q^{17} +(2.30771 - 0.303816i) q^{19} +(-2.18482 - 1.89689i) q^{21} +(-0.117964 + 0.440249i) q^{23} +(1.29407 + 4.82952i) q^{25} +(-2.01050 - 4.85376i) q^{27} +(-8.23722 - 3.41197i) q^{29} +(-3.54295 + 6.13657i) q^{31} +(-0.275771 - 0.477649i) q^{33} +(-0.0248704 - 0.0121113i) q^{35} +(0.810667 - 1.05648i) q^{37} +(0.110081 + 0.410827i) q^{39} +(0.726254 + 0.726254i) q^{41} +(1.00055 - 0.414442i) q^{43} +(-0.0114826 - 0.0149645i) q^{45} +(-6.68936 + 3.86210i) q^{47} +(-6.44018 + 2.74300i) q^{49} +(4.80054 - 0.632003i) q^{51} +(-1.43102 + 10.8696i) q^{53} +(-0.00372866 - 0.00372866i) q^{55} +(-1.79992 + 1.79992i) q^{57} +(5.07149 + 0.667674i) q^{59} +(-0.787418 - 5.98103i) q^{61} +(-4.76436 - 0.288476i) q^{63} +(0.00203318 + 0.00352156i) q^{65} +(-7.37282 + 5.65736i) q^{67} +(-0.190743 - 0.460495i) q^{69} +(-3.01032 + 3.01032i) q^{71} +(-0.568628 + 0.152363i) q^{73} +(-4.33793 - 3.32861i) q^{75} +(-1.33105 + 0.0938943i) q^{77} +(-9.83347 + 5.67736i) q^{79} +(0.288563 + 0.166602i) q^{81} +(4.51148 - 10.8917i) q^{83} +(0.0427687 - 0.0177154i) q^{85} +(9.41812 - 2.52358i) q^{87} +(14.1112 + 3.78107i) q^{89} +(1.01020 + 0.195722i) q^{91} +(-1.01146 - 7.68279i) q^{93} +(-0.0121682 + 0.0210760i) q^{95} +11.9213 q^{97} +(-0.840599 - 0.348188i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9}+O(q^{10}) \) 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

L-functions

Modular forms

Varieties

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