LMFDB - Embedded newform 825.2.bx.f.724.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(49,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 4]))

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

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

chi := DirichletCharacter("825.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.bx (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{14} + 15x^{12} - 59x^{10} + 104x^{8} - 59x^{6} + 15x^{4} - x^{2} + 1 $ x^16 - x^14 + 15x^12 - 59x^10 + 104x^8 - 59x^6 + 15*x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			724.1
Root			$-0.280526 - 0.386111i$ of defining polynomial
Character	$\chi$	$=$	825.724
Dual form			825.2.bx.f.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40496 - 0.456498i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.147481 + 0.107152i) q^{4} +(-0.456498 - 1.40496i) q^{6} +(-1.34895 + 1.85666i) q^{7} +(1.57833 + 2.17239i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-1.40496 - 0.456498i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.147481 + 0.107152i) q^{4} +(-0.456498 - 1.40496i) q^{6} +(-1.34895 + 1.85666i) q^{7} +(1.57833 + 2.17239i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-3.12020 - 1.12443i) q^{11} +0.182297i q^{12} +(2.03600 + 0.661536i) q^{13} +(2.74278 - 1.99274i) q^{14} +(-1.33846 - 4.11937i) q^{16} +(-0.517799 + 0.168243i) q^{17} +(0.868312 - 1.19513i) q^{18} +(-1.76552 + 1.28272i) q^{19} -2.29496 q^{21} +(3.87045 + 3.00415i) q^{22} -2.03908i q^{23} +(-0.829779 + 2.55380i) q^{24} +(-2.55850 - 1.85886i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(-0.397889 + 0.129282i) q^{28} +(-8.04603 - 5.84578i) q^{29} +(2.09249 - 6.44002i) q^{31} +1.02811i q^{32} +(-0.924324 - 3.18522i) q^{33} +0.804288 q^{34} +(-0.147481 + 0.107152i) q^{36} +(-5.18403 + 7.13520i) q^{37} +(3.06604 - 0.996215i) q^{38} +(0.661536 + 2.03600i) q^{39} +(1.47470 - 1.07143i) q^{41} +(3.22433 + 1.04765i) q^{42} +0.620713i q^{43} +(-0.339687 - 0.500167i) q^{44} +(-0.930836 + 2.86482i) q^{46} +(0.222188 + 0.305816i) q^{47} +(2.54591 - 3.50415i) q^{48} +(0.535571 + 1.64832i) q^{49} +(-0.440466 - 0.320017i) q^{51} +(0.229387 + 0.315724i) q^{52} +(-11.0257 - 3.58246i) q^{53} +1.47726 q^{54} -6.16248 q^{56} +(-2.07549 - 0.674367i) q^{57} +(8.63574 + 11.8861i) q^{58} +(-6.53518 - 4.74808i) q^{59} +(2.69647 + 8.29887i) q^{61} +(-5.87971 + 8.09273i) q^{62} +(-1.34895 - 1.85666i) q^{63} +(-2.20760 + 6.79429i) q^{64} +(-0.155412 + 4.89705i) q^{66} -9.75802i q^{67} +(-0.0943932 - 0.0306702i) q^{68} +(1.64965 - 1.19854i) q^{69} +(-4.63426 - 14.2628i) q^{71} +(-2.55380 + 0.829779i) q^{72} +(-4.61907 + 6.35761i) q^{73} +(10.5405 - 7.65815i) q^{74} -0.397826 q^{76} +(6.29667 - 4.27637i) q^{77} -3.16248i q^{78} +(2.85054 - 8.77306i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-2.56099 + 0.832118i) q^{82} +(-8.98969 + 2.92093i) q^{83} +(-0.338464 - 0.245909i) q^{84} +(0.283354 - 0.872075i) q^{86} -9.94544i q^{87} +(-2.48201 - 8.55302i) q^{88} -0.583290 q^{89} +(-3.97470 + 2.88779i) q^{91} +(0.218490 - 0.300726i) q^{92} +(6.44002 - 2.09249i) q^{93} +(-0.172561 - 0.531087i) q^{94} +(-0.831757 + 0.604307i) q^{96} +(-5.11479 - 1.66190i) q^{97} -2.56031i q^{98} +(2.03359 - 2.62002i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} + 8 q^{6} + 4 q^{9}+O(q^{10}) $ 16 * q - 4 * q^4 + 8 * q^6 + 4 * q^9	$ 16 q - 4 q^{4} + 8 q^{6} + 4 q^{9} + 6 q^{11} + 8 q^{14} - 24 q^{16} - 4 q^{19} - 24 q^{21} - 8 q^{24} + 4 q^{26} - 20 q^{29} + 38 q^{31} + 12 q^{34} + 4 q^{36} + 8 q^{39} - 18 q^{41} - 34 q^{44} - 44 q^{46} - 2 q^{49} + 20 q^{51} + 12 q^{54} - 32 q^{56} - 26 q^{59} + 26 q^{61} - 78 q^{64} - 22 q^{66} - 18 q^{69} - 22 q^{71} + 86 q^{74} - 76 q^{76} + 44 q^{79} - 4 q^{81} - 8 q^{84} + 40 q^{86} + 40 q^{89} - 22 q^{91} + 70 q^{94} - 16 q^{96} + 14 q^{99}+O(q^{100}) $ 16 * q - 4 * q^4 + 8 * q^6 + 4 * q^9 + 6 * q^11 + 8 * q^14 - 24 * q^16 - 4 * q^19 - 24 * q^21 - 8 * q^24 + 4 * q^26 - 20 * q^29 + 38 * q^31 + 12 * q^34 + 4 * q^36 + 8 * q^39 - 18 * q^41 - 34 * q^44 - 44 * q^46 - 2 * q^49 + 20 * q^51 + 12 * q^54 - 32 * q^56 - 26 * q^59 + 26 * q^61 - 78 * q^64 - 22 * q^66 - 18 * q^69 - 22 * q^71 + 86 * q^74 - 76 * q^76 + 44 * q^79 - 4 * q^81 - 8 * q^84 + 40 * q^86 + 40 * q^89 - 22 * q^91 + 70 * q^94 - 16 * q^96 + 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.40496	−	0.456498i	−0.993455	−	0.322793i	−0.233208	−	0.972427i	$-0.574922\pi$
$2$	−1.40496	−	0.456498i	−0.993455	−	0.322793i	−0.760247	+	0.649634i	$0.774922\pi$
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$4$	0.147481	+	0.107152i	0.0737407	+	0.0535758i
$5$		0			0
$5$		0			0
$6$	−0.456498	−	1.40496i	−0.186365	−	0.573572i
$7$	−1.34895	+	1.85666i	−0.509853	+	0.701753i	−0.983895	−	0.178750i	$-0.942795\pi$
$7$	−1.34895	+	1.85666i	−0.509853	+	0.701753i	0.474041	+	0.880503i	$0.342795\pi$
$8$	1.57833	+	2.17239i	0.558025	+	0.768055i
$9$	−0.309017	+	0.951057i	−0.103006	+	0.317019i
$10$		0			0
$11$	−3.12020	−	1.12443i	−0.940776	−	0.339029i
$11$	−3.12020	−	1.12443i	−0.940776	−	0.339029i
$12$			0.182297i			0.0526246i
$13$	2.03600	+	0.661536i	0.564684	+	0.183477i	0.577428	−	0.816442i	$-0.304057\pi$
$13$	2.03600	+	0.661536i	0.564684	+	0.183477i	−0.0127437	+	0.999919i	$0.504057\pi$
$14$	2.74278	−	1.99274i	0.733038	−	0.532583i
$15$		0			0
$16$	−1.33846	−	4.11937i	−0.334616	−	1.02984i
$17$	−0.517799	+	0.168243i	−0.125585	+	0.0408049i	−0.371135	−	0.928579i	$-0.621031\pi$
$17$	−0.517799	+	0.168243i	−0.125585	+	0.0408049i	0.245550	+	0.969384i	$0.421031\pi$
$18$	0.868312	−	1.19513i	0.204663	−	0.281694i
$19$	−1.76552	+	1.28272i	−0.405037	+	0.294277i	−0.771590	−	0.636121i	$-0.780538\pi$
$19$	−1.76552	+	1.28272i	−0.405037	+	0.294277i	0.366553	+	0.930397i	$0.380538\pi$
$20$		0			0
$21$	−2.29496			−0.500802
$22$	3.87045	+	3.00415i	0.825183	+	0.640486i
$23$		−	2.03908i		−	0.425177i	−0.977142	−	0.212589i	$-0.931811\pi$
$23$		−	2.03908i		−	0.425177i	0.977142	−	0.212589i	$-0.0681894\pi$
$24$	−0.829779	+	2.55380i	−0.169378	+	0.521291i
$25$		0			0
$26$	−2.55850	−	1.85886i	−0.501763	−	0.364552i
$27$	−0.951057	+	0.309017i	−0.183031	+	0.0594703i
$28$	−0.397889	+	0.129282i	−0.0751939	+	0.0244320i
$29$	−8.04603	−	5.84578i	−1.49411	−	1.08553i	−0.972655	−	0.232256i	$-0.925389\pi$
$29$	−8.04603	−	5.84578i	−1.49411	−	1.08553i	−0.521455	−	0.853279i	$-0.674611\pi$
$30$		0			0
$31$	2.09249	−	6.44002i	0.375822	−	1.15666i	−0.567101	−	0.823649i	$-0.691935\pi$
$31$	2.09249	−	6.44002i	0.375822	−	1.15666i	0.942922	−	0.333012i	$-0.108065\pi$
$32$			1.02811i			0.181746i
$33$	−0.924324	−	3.18522i	−0.160904	−	0.554476i
$34$	0.804288			0.137934
$35$		0			0
$36$	−0.147481	+	0.107152i	−0.0245802	+	0.0178586i
$37$	−5.18403	+	7.13520i	−0.852249	+	1.17302i	0.131114	+	0.991367i	$0.458145\pi$
$37$	−5.18403	+	7.13520i	−0.852249	+	1.17302i	−0.983363	+	0.181652i	$0.941855\pi$
$38$	3.06604	−	0.996215i	0.497377	−	0.161607i
$39$	0.661536	+	2.03600i	0.105930	+	0.326020i
$40$		0			0
$41$	1.47470	−	1.07143i	0.230309	−	0.167329i	−0.466646	−	0.884444i	$-0.654538\pi$
$41$	1.47470	−	1.07143i	0.230309	−	0.167329i	0.696955	+	0.717115i	$0.254538\pi$
$42$	3.22433	+	1.04765i	0.497524	+	0.161655i
$43$			0.620713i			0.0946578i	0.998879	+	0.0473289i	$0.0150709\pi$
$43$			0.620713i			0.0946578i	−0.998879	+	0.0473289i	$0.984929\pi$
$44$	−0.339687	−	0.500167i	−0.0512098	−	0.0754030i
$45$		0			0
$46$	−0.930836	+	2.86482i	−0.137244	+	0.422394i
$47$	0.222188	+	0.305816i	0.0324095	+	0.0446078i	0.824914	−	0.565258i	$-0.191223\pi$
$47$	0.222188	+	0.305816i	0.0324095	+	0.0446078i	−0.792505	+	0.609866i	$0.791223\pi$
$48$	2.54591	−	3.50415i	0.367471	−	0.505780i
$49$	0.535571	+	1.64832i	0.0765102	+	0.235474i
$50$		0			0
$51$	−0.440466	−	0.320017i	−0.0616776	−	0.0448114i
$52$	0.229387	+	0.315724i	0.0318103	+	0.0437831i
$53$	−11.0257	−	3.58246i	−1.51449	−	0.492089i	−0.570288	−	0.821445i	$-0.693169\pi$
$53$	−11.0257	−	3.58246i	−1.51449	−	0.492089i	−0.944206	+	0.329355i	$0.893169\pi$
$54$	1.47726			0.201030
$55$		0			0
$56$	−6.16248			−0.823496
$57$	−2.07549	−	0.674367i	−0.274905	−	0.0893221i
$58$	8.63574	+	11.8861i	1.13393	+	1.56072i
$59$	−6.53518	−	4.74808i	−0.850807	−	0.618148i	0.0745611	−	0.997216i	$-0.476244\pi$
$59$	−6.53518	−	4.74808i	−0.850807	−	0.618148i	−0.925369	+	0.379069i	$0.876244\pi$
$60$		0			0
$61$	2.69647	+	8.29887i	0.345247	+	1.06256i	0.961451	+	0.274975i	$0.0886697\pi$
$61$	2.69647	+	8.29887i	0.345247	+	1.06256i	−0.616204	+	0.787587i	$0.711330\pi$
$62$	−5.87971	+	8.09273i	−0.746724	+	1.02778i
$63$	−1.34895	−	1.85666i	−0.169951	−	0.233918i
$64$	−2.20760	+	6.79429i	−0.275950	+	0.849286i
$65$		0			0
$66$	−0.155412	+	4.89705i	−0.0191299	+	0.602785i
$67$		−	9.75802i		−	1.19213i	−0.802936	−	0.596066i	$-0.796730\pi$
$67$		−	9.75802i		−	1.19213i	0.802936	−	0.596066i	$-0.203270\pi$
$68$	−0.0943932	−	0.0306702i	−0.0114469	−	0.00371931i
$69$	1.64965	−	1.19854i	0.198594	−	0.144287i
$70$		0			0
$71$	−4.63426	−	14.2628i	−0.549985	−	1.69268i	−0.708833	−	0.705376i	$-0.750778\pi$
$71$	−4.63426	−	14.2628i	−0.549985	−	1.69268i	0.158848	−	0.987303i	$-0.449222\pi$
$72$	−2.55380	+	0.829779i	−0.300968	+	0.0977903i
$73$	−4.61907	+	6.35761i	−0.540622	+	0.744102i	−0.988702	−	0.149891i	$-0.952108\pi$
$73$	−4.61907	+	6.35761i	−0.540622	+	0.744102i	0.448081	+	0.893993i	$0.352108\pi$
$74$	10.5405	−	7.65815i	1.22531	−	0.890242i
$75$		0			0
$76$	−0.397826			−0.0456338
$77$	6.29667	−	4.27637i	0.717572	−	0.487337i
$78$		−	3.16248i		−	0.358080i
$79$	2.85054	−	8.77306i	0.320711	−	0.987046i	−0.652629	−	0.757678i	$-0.726334\pi$
$79$	2.85054	−	8.77306i	0.320711	−	0.987046i	0.973340	−	0.229369i	$-0.0736661\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−2.56099	+	0.832118i	−0.282815	+	0.0918920i
$83$	−8.98969	+	2.92093i	−0.986747	+	0.320613i	−0.757557	−	0.652769i	$-0.773607\pi$
$83$	−8.98969	+	2.92093i	−0.986747	+	0.320613i	−0.229189	+	0.973382i	$0.573607\pi$
$84$	−0.338464	−	0.245909i	−0.0369295	−	0.0268309i
$85$		0			0
$86$	0.283354	−	0.872075i	0.0305549	−	0.0940383i
$87$		−	9.94544i		−	1.06626i
$88$	−2.48201	−	8.55302i	−0.264583	−	0.911754i
$89$	−0.583290			−0.0618287			−0.0309143	−	0.999522i	$-0.509842\pi$
$89$	−0.583290			−0.0618287			−0.0309143	+	0.999522i	$0.509842\pi$
$90$		0			0
$91$	−3.97470	+	2.88779i	−0.416662	+	0.302722i
$92$	0.218490	−	0.300726i	0.0227792	−	0.0313529i
$93$	6.44002	−	2.09249i	0.667798	−	0.216981i
$94$	−0.172561	−	0.531087i	−0.0177983	−	0.0547774i
$95$		0			0
$96$	−0.831757	+	0.604307i	−0.0848908	+	0.0616768i
$97$	−5.11479	−	1.66190i	−0.519328	−	0.168740i	0.0376122	−	0.999292i	$-0.488025\pi$
$97$	−5.11479	−	1.66190i	−0.519328	−	0.168740i	−0.556940	+	0.830552i	$0.688025\pi$
$98$		−	2.56031i		−	0.258630i
$99$	2.03359	−	2.62002i	0.204384	−	0.263322i
$100$		0			0
$101$	−6.03482	+	18.5733i	−0.600487	+	1.84811i	−0.0752256	+	0.997167i	$0.523968\pi$
$101$	−6.03482	+	18.5733i	−0.600487	+	1.84811i	−0.525261	+	0.850941i	$0.676032\pi$
$102$	0.472749	+	0.650683i	0.0468091	+	0.0644272i
$103$	−7.64487	+	10.5223i	−0.753271	+	1.03679i	0.244473	+	0.969656i	$0.421385\pi$
$103$	−7.64487	+	10.5223i	−0.753271	+	1.03679i	−0.997744	+	0.0671325i	$0.978615\pi$
$104$	1.77637	+	5.46710i	0.174187	+	0.536093i
$105$		0			0
$106$	13.8552	+	10.0664i	1.34574	+	0.977737i
$107$	−1.16002	−	1.59663i	−0.112144	−	0.154352i	0.749256	−	0.662281i	$-0.230411\pi$
$107$	−1.16002	−	1.59663i	−0.112144	−	0.154352i	−0.861399	+	0.507928i	$0.830411\pi$
$108$	−0.173375	−	0.0563329i	−0.0166830	−	0.00542064i
$109$	−10.6212			−1.01733			−0.508663	−	0.860966i	$-0.669860\pi$
$109$	−10.6212			−1.01733			−0.508663	+	0.860966i	$0.669860\pi$
$110$		0			0
$111$	−8.81959			−0.837119
$112$	9.45380	+	3.07173i	0.893300	+	0.290251i
$113$	−9.93096	−	13.6688i	−0.934226	−	1.28585i	−0.958188	−	0.286139i	$-0.907628\pi$
$113$	−9.93096	−	13.6688i	−0.934226	−	1.28585i	0.0239621	−	0.999713i	$-0.492372\pi$
$114$	2.60813	+	1.89491i	0.244273	+	0.177475i
$115$		0			0
$116$	−0.560255	−	1.72429i	−0.0520184	−	0.160096i
$117$	−1.25832	+	1.73192i	−0.116331	+	0.160116i
$118$	7.01415	+	9.65415i	0.645705	+	0.888737i
$119$	0.386111	−	1.18833i	0.0353948	−	0.108934i
$120$		0			0
$121$	8.47131	+	7.01690i	0.770119	+	0.637900i
$122$		−	12.8905i		−	1.16705i
$123$	1.73361	+	0.563285i	0.156314	+	0.0507897i
$124$	0.998661	−	0.725569i	0.0896824	−	0.0651581i
$125$		0			0
$126$	1.04765	+	3.22433i	0.0933318	+	0.287246i
$127$	−3.93022	+	1.27701i	−0.348751	+	0.113316i	−0.478154	−	0.878276i	$-0.658694\pi$
$127$	−3.93022	+	1.27701i	−0.348751	+	0.113316i	0.129403	+	0.991592i	$0.458694\pi$
$128$	7.41178	−	10.2014i	0.655115	−	0.901689i
$129$	−0.502167	+	0.364846i	−0.0442133	+	0.0321229i
$130$		0			0
$131$	−0.436527			−0.0381395			−0.0190698	−	0.999818i	$-0.506070\pi$
$131$	−0.436527			−0.0381395			−0.0190698	+	0.999818i	$0.506070\pi$
$132$	0.204981	−	0.568804i	0.0178413	−	0.0495080i
$133$		−	5.00829i		−	0.434274i
$134$	−4.45452	+	13.7096i	−0.384812	+	1.18433i
$135$		0			0
$136$	−1.18275	−	0.859317i	−0.101420	−	0.0736858i
$137$	7.48281	−	2.43131i	0.639300	−	0.207721i	0.0286095	−	0.999591i	$-0.490892\pi$
$137$	7.48281	−	2.43131i	0.639300	−	0.207721i	0.610690	+	0.791870i	$0.290892\pi$
$138$	−2.86482	+	0.930836i	−0.243869	+	0.0792380i
$139$	14.2736	+	10.3704i	1.21067	+	0.879604i	0.995292	−	0.0969265i	$-0.0309012\pi$
$139$	14.2736	+	10.3704i	1.21067	+	0.879604i	0.215379	+	0.976530i	$0.430901\pi$
$140$		0			0
$141$	−0.116811	+	0.359508i	−0.00983728	+	0.0302760i
$142$			22.1541i			1.85913i
$143$	−5.60887	−	4.35346i	−0.469037	−	0.364055i
$144$	4.33136			0.360947
$145$		0			0
$146$	9.39184	−	6.82357i	0.777274	−	0.564723i
$147$	−1.01872	+	1.40214i	−0.0840224	+	0.115647i
$148$	−1.52910	+	0.496833i	−0.125691	+	0.0408394i
$149$	3.38687	+	10.4237i	0.277463	+	0.853943i	0.988557	+	0.150846i	$0.0481999\pi$
$149$	3.38687	+	10.4237i	0.277463	+	0.853943i	−0.711094	+	0.703097i	$0.751800\pi$
$150$		0			0
$151$	16.2065	−	11.7747i	1.31887	−	0.958214i	0.318923	−	0.947781i	$-0.396679\pi$
$151$	16.2065	−	11.7747i	1.31887	−	0.958214i	0.999946	−	0.0104337i	$-0.00332120\pi$
$152$	−5.57314	−	1.81082i	−0.452041	−	0.146877i
$153$		−	0.544446i		−	0.0440158i
$154$	−10.7987	+	3.13370i	−0.870185	+	0.252520i
$155$		0			0
$156$	−0.120596	+	0.371156i	−0.00965541	+	0.0297163i
$157$	−5.38098	−	7.40629i	−0.429449	−	0.591086i	0.538377	−	0.842704i	$-0.319037\pi$
$157$	−5.38098	−	7.40629i	−0.429449	−	0.591086i	−0.967827	+	0.251618i	$0.919037\pi$
$158$	−8.00978	+	11.0245i	−0.637224	+	0.877063i
$159$	−3.58246	−	11.0257i	−0.284108	−	0.874394i
$160$		0			0
$161$	3.78588	+	2.75060i	0.298369	+	0.216778i
$162$	0.868312	+	1.19513i	0.0682210	+	0.0938982i
$163$	10.7775	+	3.50181i	0.844155	+	0.274283i	0.698996	−	0.715126i	$-0.253631\pi$
$163$	10.7775	+	3.50181i	0.844155	+	0.274283i	0.145159	+	0.989408i	$0.453631\pi$
$164$	0.332296			0.0259480
$165$		0			0
$166$	13.9635			1.08378
$167$	14.3611	+	4.66619i	1.11129	+	0.361081i	0.806438	−	0.591318i	$-0.201392\pi$
$167$	14.3611	+	4.66619i	1.11129	+	0.361081i	0.304854	+	0.952399i	$0.401392\pi$
$168$	−3.62221	−	4.98555i	−0.279460	−	0.384644i
$169$	−6.80957	−	4.94744i	−0.523813	−	0.380572i
$170$		0			0
$171$	−0.674367	−	2.07549i	−0.0515701	−	0.158717i
$172$	−0.0665103	+	0.0915436i	−0.00507136	+	0.00698013i
$173$	10.7354	+	14.7760i	0.816195	+	1.12340i	0.990338	+	0.138676i	$0.0442847\pi$
$173$	10.7354	+	14.7760i	0.816195	+	1.12340i	−0.174143	+	0.984720i	$0.555715\pi$
$174$	−4.54008	+	13.9729i	−0.344182	+	1.05928i
$175$		0			0
$176$	−0.455671	+	14.3583i	−0.0343475	+	1.08230i
$177$		−	8.07792i		−	0.607174i
$178$	0.819498	+	0.266271i	0.0614240	+	0.0199579i
$179$	−0.425073	+	0.308833i	−0.0317714	+	0.0230833i	−0.603558	−	0.797319i	$-0.706251\pi$
$179$	−0.425073	+	0.308833i	−0.0317714	+	0.0230833i	0.571786	+	0.820403i	$0.306251\pi$
$180$		0			0
$181$	−5.47289	−	16.8438i	−0.406797	−	1.25199i	−0.919386	−	0.393358i	$-0.871313\pi$
$181$	−5.47289	−	16.8438i	−0.406797	−	1.25199i	0.512589	−	0.858634i	$-0.328687\pi$
$182$	6.90255	−	2.24278i	0.511651	−	0.166246i
$183$	−5.12899	+	7.05944i	−0.379146	+	0.521849i
$184$	4.42967	−	3.21834i	0.326560	−	0.237259i
$185$		0			0
$186$	−10.0032			−0.733468
$187$	1.80481	+	0.0572771i	0.131981	+	0.00418852i
$188$			0.0689100i			0.00502578i
$189$	0.709183	−	2.18264i	0.0515854	−	0.158764i
$190$		0			0
$191$	13.3908	+	9.72899i	0.968925	+	0.703965i	0.955206	−	0.295941i	$-0.0956331\pi$
$191$	13.3908	+	9.72899i	0.968925	+	0.703965i	0.0137185	+	0.999906i	$0.495633\pi$
$192$	−6.79429	+	2.20760i	−0.490336	+	0.159320i
$193$	−23.3040	+	7.57191i	−1.67746	+	0.545038i	−0.984415	−	0.175860i	$-0.943729\pi$
$193$	−23.3040	+	7.57191i	−1.67746	+	0.545038i	−0.693040	+	0.720899i	$0.743729\pi$
$194$	6.42741	+	4.66979i	0.461461	+	0.335271i
$195$		0			0
$196$	−0.0976331	+	0.300484i	−0.00697379	+	0.0214631i
$197$		−	7.50877i		−	0.534978i	−0.963561	−	0.267489i	$-0.913806\pi$
$197$		−	7.50877i		−	0.534978i	0.963561	−	0.267489i	$-0.0861938\pi$
$198$	−4.05315	+	2.75268i	−0.288045	+	0.195625i
$199$	20.0956			1.42454			0.712270	−	0.701906i	$-0.247667\pi$
$199$	20.0956			1.42454			0.712270	+	0.701906i	$0.247667\pi$
$200$		0			0
$201$	7.89440	−	5.73562i	0.556828	−	0.404559i
$202$	16.9573	−	23.3398i	1.19311	−	1.64218i
$203$	21.7073	−	7.05313i	1.52355	−	0.495033i
$204$	−0.0306702	−	0.0943932i	−0.00214734	−	0.00660885i
$205$		0			0
$206$	15.5441	−	11.2935i	1.08301	−	0.786852i
$207$	1.93928	+	0.630110i	0.134789	+	0.0437956i
$208$		−	9.27247i		−	0.642930i
$209$	6.95110	−	2.01715i	0.480817	−	0.139529i
$210$		0			0
$211$	1.67444	−	5.15339i	0.115273	−	0.354774i	−0.876731	−	0.480981i	$-0.840280\pi$
$211$	1.67444	−	5.15339i	0.115273	−	0.354774i	0.992004	+	0.126207i	$0.0402804\pi$
$212$	−1.24222	−	1.70977i	−0.0853159	−	0.117427i
$213$	8.81488	−	12.1326i	0.603985	−	0.831315i
$214$	0.900921	+	2.77275i	0.0615857	+	0.189541i
$215$		0			0
$216$	−2.17239	−	1.57833i	−0.147812	−	0.107392i
$217$	9.13429	+	12.5723i	0.620076	+	0.853462i
$218$	14.9223	+	4.84856i	1.01067	+	0.328386i
$219$	−7.85844			−0.531024
$220$		0			0
$221$	−1.16554			−0.0784024
$222$	12.3912	+	4.02613i	0.831640	+	0.270216i
$223$	9.23259	+	12.7076i	0.618260	+	0.850961i	0.997225	−	0.0744495i	$-0.0237200\pi$
$223$	9.23259	+	12.7076i	0.618260	+	0.850961i	−0.378965	+	0.925411i	$0.623720\pi$
$224$	−1.90885	−	1.38686i	−0.127541	−	0.0926636i
$225$		0			0
$226$	7.71280	+	23.7375i	0.513048	+	1.57900i
$227$	−0.864876	+	1.19040i	−0.0574038	+	0.0790096i	−0.836754	−	0.547579i	$-0.815549\pi$
$227$	−0.864876	+	1.19040i	−0.0574038	+	0.0790096i	0.779350	+	0.626589i	$0.215549\pi$
$228$	−0.233837	−	0.321848i	−0.0154862	−	0.0213149i
$229$	4.93656	−	15.1932i	0.326217	−	1.00399i	−0.644671	−	0.764460i	$-0.723006\pi$
$229$	4.93656	−	15.1932i	0.326217	−	1.00399i	0.970888	−	0.239533i	$-0.0769945\pi$
$230$		0			0
$231$	7.16075	+	2.58053i	0.471142	+	0.169786i
$232$		−	26.7057i		−	1.75331i
$233$	24.3833	+	7.92263i	1.59741	+	0.519029i	0.966464	−	0.256802i	$-0.0826688\pi$
$233$	24.3833	+	7.92263i	1.59741	+	0.519029i	0.630942	+	0.775830i	$0.282669\pi$
$234$	2.55850	−	1.85886i	0.167254	−	0.121517i
$235$		0			0
$236$	−0.455053	−	1.40051i	−0.0296214	−	0.0911653i
$237$	8.77306	−	2.85054i	0.569872	−	0.185162i
$238$	−1.08494	+	1.49329i	−0.0703262	+	0.0967958i
$239$	−3.38336	+	2.45816i	−0.218851	+	0.159005i	−0.691809	−	0.722080i	$-0.743186\pi$
$239$	−3.38336	+	2.45816i	−0.218851	+	0.159005i	0.472958	+	0.881085i	$0.343186\pi$
$240$		0			0
$241$	−3.29180			−0.212043			−0.106022	−	0.994364i	$-0.533811\pi$
$241$	−3.29180			−0.212043			−0.106022	+	0.994364i	$0.533811\pi$
$242$	−8.69862	−	13.7256i	−0.559169	−	0.882314i
$243$		−	1.00000i		−	0.0641500i
$244$	−0.491558	+	1.51286i	−0.0314688	+	0.0968510i
$245$		0			0
$246$	−2.17851	−	1.58278i	−0.138897	−	0.100914i
$247$	−4.44315	+	1.44367i	−0.282711	+	0.0918583i
$248$	17.2929	−	5.61879i	1.09810	−	0.356794i
$249$	−7.64709	−	5.55593i	−0.484614	−	0.352093i
$250$		0			0
$251$	−2.89382	+	8.90626i	−0.182656	+	0.562158i	−0.999900	−	0.0141339i	$-0.995501\pi$
$251$	−2.89382	+	8.90626i	−0.182656	+	0.562158i	0.817244	+	0.576292i	$0.195501\pi$
$252$		−	0.418365i		−	0.0263545i
$253$	−2.29280	+	6.36233i	−0.144147	+	0.399996i
$254$	6.10475			0.383046
$255$		0			0
$256$	−3.51104	+	2.55092i	−0.219440	+	0.159433i
$257$	−7.38928	+	10.1705i	−0.460930	+	0.634416i	−0.974701	−	0.223511i	$-0.928248\pi$
$257$	−7.38928	+	10.1705i	−0.460930	+	0.634416i	0.513771	+	0.857927i	$0.328248\pi$
$258$	0.872075	−	0.283354i	0.0542930	−	0.0176409i
$259$	−6.25470	−	19.2500i	−0.388648	−	1.19614i
$260$		0			0
$261$	8.04603	−	5.84578i	0.498037	−	0.361845i
$262$	0.613302	+	0.199274i	0.0378899	+	0.0123112i
$263$		−	4.82946i		−	0.297797i	−0.988852	−	0.148899i	$-0.952427\pi$
$263$		−	4.82946i		−	0.297797i	0.988852	−	0.148899i	$-0.0475728\pi$
$264$	5.46064	−	7.03533i	0.336079	−	0.432994i
$265$		0			0
$266$	−2.28628	+	7.03644i	−0.140181	+	0.431432i
$267$	−0.342849	−	0.471892i	−0.0209820	−	0.0288793i
$268$	1.04559	−	1.43913i	0.0638694	−	0.0879087i
$269$	1.61594	+	4.97335i	0.0985255	+	0.303230i	0.988156	−	0.153450i	$-0.0490383\pi$
$269$	1.61594	+	4.97335i	0.0985255	+	0.303230i	−0.889631	+	0.456680i	$0.849038\pi$
$270$		0			0
$271$	−24.5383	−	17.8281i	−1.49060	−	1.08298i	−0.973944	−	0.226789i	$-0.927177\pi$
$271$	−24.5383	−	17.8281i	−1.49060	−	1.08298i	−0.516654	−	0.856194i	$-0.672823\pi$
$272$	1.38611	+	1.90782i	0.0840453	+	0.115678i
$273$	−4.67254	−	1.51820i	−0.282795	−	0.0918856i
$274$	−11.6229			−0.702167
$275$		0			0
$276$	0.371718			0.0223748
$277$	15.1878	+	4.93483i	0.912549	+	0.296505i	0.727407	−	0.686206i	$-0.240725\pi$
$277$	15.1878	+	4.93483i	0.912549	+	0.296505i	0.185142	+	0.982712i	$0.440725\pi$
$278$	−15.3197	−	21.0858i	−0.918817	−	1.26464i
$279$	5.47820	+	3.98015i	0.327972	+	0.238285i
$280$		0			0
$281$	−0.429741	−	1.32261i	−0.0256362	−	0.0789000i	0.937420	−	0.348201i	$-0.113207\pi$
$281$	−0.429741	−	1.32261i	−0.0256362	−	0.0789000i	−0.963056	+	0.269301i	$0.913207\pi$
$282$	0.328230	−	0.451769i	0.0195458	−	0.0269025i
$283$	3.45296	+	4.75259i	0.205257	+	0.282512i	0.899218	−	0.437500i	$-0.144136\pi$
$283$	3.45296	+	4.75259i	0.205257	+	0.282512i	−0.693961	+	0.720013i	$0.744136\pi$
$284$	0.844811	−	2.60006i	0.0501303	−	0.154285i
$285$		0			0
$286$	5.89287	+	8.67687i	0.348453	+	0.513074i
$287$			4.18332i			0.246934i
$288$	−0.977789	−	0.317703i	−0.0576168	−	0.0187208i
$289$	−13.5135	+	9.81812i	−0.794911	+	0.577536i
$290$		0			0
$291$	−1.66190	−	5.11479i	−0.0974221	−	0.299834i
$292$	−1.36246	+	0.442688i	−0.0797317	+	0.0259064i
$293$	−11.7407	+	16.1597i	−0.685900	+	0.944060i	−0.999986	−	0.00533421i	$-0.998302\pi$
$293$	−11.7407	+	16.1597i	−0.685900	+	0.944060i	0.314086	+	0.949395i	$0.398302\pi$
$294$	2.07133	−	1.50491i	0.120802	−	0.0877681i
$295$		0			0
$296$	−23.6825			−1.37652
$297$	3.31496	+	0.105203i	0.192353	+	0.00610448i
$298$		−	16.1910i		−	0.937917i
$299$	1.34892	−	4.15156i	0.0780102	−	0.240091i
$300$		0			0
$301$	−1.15245	−	0.837307i	−0.0664264	−	0.0482616i
$302$	−28.1446	+	9.14475i	−1.61954	+	0.526221i
$303$	−18.5733	+	6.03482i	−1.06701	+	0.346691i
$304$	7.64709	+	5.55593i	0.438590	+	0.318655i
$305$		0			0
$306$	−0.248539	+	0.764923i	−0.0142080	+	0.0437278i
$307$			19.4372i			1.10934i	0.832070	+	0.554671i	$0.187156\pi$
$307$			19.4372i			1.10934i	−0.832070	+	0.554671i	$0.812844\pi$
$308$	1.38686	+	0.0440131i	0.0790238	+	0.00250788i
$309$	−13.0062			−0.739898
$310$		0			0
$311$	−4.87175	+	3.53954i	−0.276252	+	0.200709i	−0.717281	−	0.696784i	$-0.754614\pi$
$311$	−4.87175	+	3.53954i	−0.276252	+	0.200709i	0.441029	+	0.897493i	$0.354614\pi$
$312$	−3.37885	+	4.65059i	−0.191290	+	0.263288i
$313$	−4.85831	+	1.57856i	−0.274608	+	0.0892256i	−0.443084	−	0.896480i	$-0.646116\pi$
$313$	−4.85831	+	1.57856i	−0.274608	+	0.0892256i	0.168476	+	0.985706i	$0.446116\pi$
$314$	4.17910	+	12.8619i	0.235840	+	0.725841i
$315$		0			0
$316$	1.36045	−	0.988424i	0.0765312	−	0.0556032i
$317$	13.0093	+	4.22699i	0.730677	+	0.237411i	0.650646	−	0.759381i	$-0.274498\pi$
$317$	13.0093	+	4.22699i	0.730677	+	0.237411i	0.0800306	+	0.996792i	$0.474498\pi$
$318$			17.1260i			0.960379i
$319$	18.5320	+	27.2872i	1.03760	+	1.52779i
$320$		0			0
$321$	0.609860	−	1.87695i	0.0340390	−	0.104761i
$322$	−4.06336	−	5.59273i	−0.226442	−	0.311671i
$323$	0.698373	−	0.961227i	0.0388585	−	0.0534841i
$324$	−0.0563329	−	0.173375i	−0.00312961	−	0.00963194i
$325$		0			0
$326$	−13.5433	−	9.83978i	−0.750094	−	0.544975i
$327$	−6.24299	−	8.59273i	−0.345238	−	0.475179i
$328$	4.65513	+	1.51254i	0.257036	+	0.0835162i
$329$	−0.867517			−0.0478278
$330$		0			0
$331$	11.4695			0.630418			0.315209	−	0.949022i	$-0.397925\pi$
$331$	11.4695			0.630418			0.315209	+	0.949022i	$0.397925\pi$
$332$	−1.63879	−	0.532477i	−0.0899405	−	0.0292234i
$333$	−5.18403	−	7.13520i	−0.284083	−	0.391007i
$334$	−18.0466	−	13.1116i	−0.987465	−	0.717435i
$335$		0			0
$336$	3.07173	+	9.45380i	0.167576	+	0.515747i
$337$	2.21245	−	3.04517i	0.120520	−	0.165881i	−0.744494	−	0.667629i	$-0.767309\pi$
$337$	2.21245	−	3.04517i	0.120520	−	0.165881i	0.865014	+	0.501748i	$0.167309\pi$
$338$	7.30865	+	10.0595i	0.397538	+	0.547165i
$339$	5.22101	−	16.0686i	0.283567	−	0.872728i
$340$		0			0
$341$	−13.7703	+	17.7413i	−0.745706	+	0.960744i
$342$			3.22382i			0.174324i
$343$	−19.0613	−	6.19339i	−1.02921	−	0.334412i
$344$	−1.34843	+	0.979691i	−0.0727024	+	0.0528214i
$345$		0			0
$346$	−8.33754	−	25.6603i	−0.448229	−	1.37951i
$347$	0.376600	−	0.122365i	0.0202169	−	0.00656888i	−0.298891	−	0.954287i	$-0.596617\pi$
$347$	0.376600	−	0.122365i	0.0202169	−	0.00656888i	0.319108	+	0.947718i	$0.396617\pi$
$348$	1.06567	−	1.46677i	0.0571259	−	0.0786270i
$349$	−10.6554	+	7.74158i	−0.570369	+	0.414398i	−0.835239	−	0.549887i	$-0.814671\pi$
$349$	−10.6554	+	7.74158i	−0.570369	+	0.414398i	0.264870	+	0.964284i	$0.414671\pi$
$350$		0			0
$351$	−2.14077			−0.114266
$352$	1.15604	−	3.20790i	0.0616170	−	0.170982i
$353$		−	11.3853i		−	0.605977i	−0.952994	−	0.302989i	$-0.902016\pi$
$353$		−	11.3853i		−	0.605977i	0.952994	−	0.302989i	$-0.0979844\pi$
$354$	−3.68756	+	11.3491i	−0.195992	+	0.603200i
$355$		0			0
$356$	−0.0860245	−	0.0625005i	−0.00455929	−	0.00331252i
$357$	1.18833	−	0.386111i	0.0628930	−	0.0204352i
$358$	0.738191	−	0.239853i	0.0390146	−	0.0126766i
$359$	−11.6241	−	8.44543i	−0.613499	−	0.445733i	0.237146	−	0.971474i	$-0.423788\pi$
$359$	−11.6241	−	8.44543i	−0.613499	−	0.445733i	−0.850645	+	0.525741i	$0.823788\pi$
$360$		0			0
$361$	−4.39965	+	13.5407i	−0.231561	+	0.712671i
$362$			26.1632i			1.37511i
$363$	−0.697484	+	10.9779i	−0.0366084	+	0.576188i
$364$	−0.895625			−0.0469435
$365$		0			0
$366$	10.4286	−	7.57685i	0.545113	−	0.396048i
$367$	−15.4376	+	21.2480i	−0.805836	+	1.10914i	0.186117	+	0.982528i	$0.440410\pi$
$367$	−15.4376	+	21.2480i	−0.805836	+	1.10914i	−0.991953	+	0.126610i	$0.959590\pi$
$368$	−8.39972	+	2.72923i	−0.437865	+	0.142271i
$369$	0.563285	+	1.73361i	0.0293234	+	0.0902482i
$370$		0			0
$371$	21.5245	−	15.6384i	1.11750	−	0.811908i
$372$	1.17400	+	0.381454i	0.0608689	+	0.0197775i
$373$		−	21.8951i		−	1.13368i	−0.823827	−	0.566842i	$-0.808165\pi$
$373$		−	21.8951i		−	1.13368i	0.823827	−	0.566842i	$-0.191835\pi$
$374$	−2.50954	−	0.904367i	−0.129765	−	0.0467637i
$375$		0			0
$376$	−0.313664	+	0.965358i	−0.0161760	+	0.0497845i
$377$	−12.5145	−	17.2247i	−0.644529	−	0.887119i
$378$	−1.99274	+	2.74278i	−0.102496	+	0.141073i
$379$	−7.89836	−	24.3087i	−0.405711	−	1.24865i	−0.920300	−	0.391214i	$-0.872055\pi$
$379$	−7.89836	−	24.3087i	−0.405711	−	1.24865i	0.514588	−	0.857437i	$-0.327945\pi$
$380$		0			0
$381$	−3.34325	−	2.42901i	−0.171280	−	0.124442i
$382$	−14.3722	−	19.7817i	−0.735348	−	1.01212i
$383$	−18.1195	−	5.88737i	−0.925862	−	0.300831i	−0.192992	−	0.981200i	$-0.561819\pi$
$383$	−18.1195	−	5.88737i	−0.925862	−	0.300831i	−0.732869	+	0.680370i	$0.761819\pi$
$384$	12.6097			0.643485
$385$		0			0
$386$	36.1976			1.84241
$387$	−0.590333	−	0.191811i	−0.0300083	−	0.00975029i
$388$	−0.576262	−	0.793157i	−0.0292553	−	0.0402664i
$389$	13.2618	+	9.63528i	0.672401	+	0.488528i	0.870828	−	0.491587i	$-0.163583\pi$
$389$	13.2618	+	9.63528i	0.672401	+	0.488528i	−0.198427	+	0.980116i	$0.563583\pi$
$390$		0			0
$391$	0.343061	+	1.05583i	0.0173493	+	0.0533957i
$392$	−2.73548	+	3.76506i	−0.138163	+	0.190164i
$393$	−0.256584	−	0.353158i	−0.0129430	−	0.0178145i
$394$	−3.42774	+	10.5495i	−0.172687	+	0.531476i
$395$		0			0
$396$	0.580656	−	0.168502i	0.0291791	−	0.00846752i
$397$			30.9826i			1.55497i	0.628901	+	0.777485i	$0.283505\pi$
$397$			30.9826i			1.55497i	−0.628901	+	0.777485i	$0.716495\pi$
$398$	−28.2335	−	9.17361i	−1.41522	−	0.459832i
$399$	4.05179	−	2.94380i	0.202843	−	0.147374i
$400$		0			0
$401$	−1.96723	−	6.05453i	−0.0982390	−	0.302349i	0.889845	−	0.456262i	$-0.150812\pi$
$401$	−1.96723	−	6.05453i	−0.0982390	−	0.302349i	−0.988084	+	0.153914i	$0.950812\pi$
$402$	−13.7096	+	4.45452i	−0.683773	+	0.222171i
$403$	8.52060	−	11.7276i	0.424441	−	0.584193i
$404$	−2.88018	+	2.09257i	−0.143294	+	0.104109i
$405$		0			0
$406$	−33.7176			−1.67338
$407$	24.1982	−	16.4342i	1.19946	−	0.814612i
$408$		−	1.46196i		−	0.0723776i
$409$	1.93715	−	5.96193i	0.0957858	−	0.294798i	−0.891672	−	0.452682i	$-0.850467\pi$
$409$	1.93715	−	5.96193i	0.0957858	−	0.294798i	0.987458	+	0.157884i	$0.0504672\pi$
$410$		0			0
$411$	6.36526	+	4.62463i	0.313975	+	0.228116i
$412$	−2.25495	+	0.732678i	−0.111093	+	0.0360965i
$413$	17.6312	−	5.72872i	0.867574	−	0.281892i
$414$	−2.43696	−	1.77055i	−0.119770	−	0.0870180i
$415$		0			0
$416$	−0.680130	+	2.09323i	−0.0333461	+	0.102629i
$417$			17.6431i			0.863988i
$418$	−10.6868	−	0.339154i	−0.522710	−	0.0165886i
$419$	−3.90332			−0.190689			−0.0953447	−	0.995444i	$-0.530395\pi$
$419$	−3.90332			−0.190689			−0.0953447	+	0.995444i	$0.530395\pi$
$420$		0			0
$421$	−14.0539	+	10.2107i	−0.684944	+	0.497641i	−0.874994	−	0.484134i	$-0.839135\pi$
$421$	−14.0539	+	10.2107i	−0.684944	+	0.497641i	0.190050	+	0.981774i	$0.439135\pi$
$422$	−4.70503	+	6.47592i	−0.229037	+	0.315243i
$423$	−0.359508	+	0.116811i	−0.0174799	+	0.00567956i
$424$	−9.61970	−	29.6064i	−0.467174	−	1.43781i
$425$		0			0
$426$	−17.9231	+	13.0219i	−0.868375	+	0.630911i
$427$	−19.0456	−	6.18829i	−0.921682	−	0.299473i
$428$		−	0.359772i		−	0.0173902i
$429$	0.225215	−	7.09657i	0.0108735	−	0.342626i
$430$		0			0
$431$	−2.17440	+	6.69212i	−0.104737	+	0.322348i	−0.989669	−	0.143373i	$-0.954205\pi$
$431$	−2.17440	+	6.69212i	−0.104737	+	0.322348i	0.884931	+	0.465721i	$0.154205\pi$
$432$	2.54591	+	3.50415i	0.122490	+	0.168593i
$433$	−1.61776	+	2.22665i	−0.0777445	+	0.107006i	−0.846118	−	0.532995i	$-0.821066\pi$
$433$	−1.61776	+	2.22665i	−0.0777445	+	0.107006i	0.768374	+	0.640002i	$0.221066\pi$
$434$	−7.09407	−	21.8333i	−0.340526	−	1.04803i
$435$		0			0
$436$	−1.56643	−	1.13808i	−0.0750184	−	0.0545041i
$437$	2.61557	+	3.60002i	0.125120	+	0.172212i
$438$	11.0408	+	3.58736i	0.527548	+	0.171411i
$439$	2.73703			0.130631			0.0653157	−	0.997865i	$-0.479195\pi$
$439$	2.73703			0.130631			0.0653157	+	0.997865i	$0.479195\pi$
$440$		0			0
$441$	−1.73315			−0.0825307
$442$	1.63753	+	0.532065i	0.0778893	+	0.0253078i
$443$	6.52688	+	8.98348i	0.310102	+	0.426818i	0.935413	−	0.353557i	$-0.115028\pi$
$443$	6.52688	+	8.98348i	0.310102	+	0.426818i	−0.625311	+	0.780375i	$0.715028\pi$
$444$	−1.30073	−	0.945033i	−0.0617297	−	0.0448493i
$445$		0			0
$446$	−7.17041	−	22.0683i	−0.339529	−	1.04496i
$447$	−6.44220	+	8.86693i	−0.304706	+	0.419392i
$448$	−9.63679	−	13.2639i	−0.455295	−	0.626660i
$449$	−4.58174	+	14.1012i	−0.216226	+	0.665475i	0.782838	+	0.622225i	$0.213771\pi$
$449$	−4.58174	+	14.1012i	−0.216226	+	0.665475i	−0.999064	+	0.0432498i	$0.986229\pi$
$450$		0			0
$451$	−5.80610	+	1.68488i	−0.273399	+	0.0793380i
$452$		−	3.08001i		−	0.144872i
$453$	19.0519	+	6.19034i	0.895137	+	0.290848i
$454$	1.75853	−	1.27765i	0.0825319	−	0.0599629i
$455$		0			0
$456$	−1.81082	−	5.57314i	−0.0847996	−	0.260986i
$457$	−27.7542	+	9.01788i	−1.29829	+	0.421838i	−0.874985	−	0.484151i	$-0.839129\pi$
$457$	−27.7542	+	9.01788i	−1.29829	+	0.421838i	−0.423301	+	0.905989i	$0.639129\pi$
$458$	−13.8713	+	19.0922i	−0.648165	+	0.892122i
$459$	0.440466	−	0.320017i	0.0205592	−	0.0149371i
$460$		0			0
$461$	−31.1798			−1.45219			−0.726094	−	0.687595i	$-0.758666\pi$
$461$	−31.1798			−1.45219			−0.726094	+	0.687595i	$0.758666\pi$
$462$	−8.88254	−	6.89440i	−0.413253	−	0.320757i
$463$		−	41.1642i		−	1.91306i	−0.291631	−	0.956531i	$-0.594198\pi$
$463$		−	41.1642i		−	1.91306i	0.291631	−	0.956531i	$-0.405802\pi$
$464$	−13.3116	+	40.9689i	−0.617976	+	1.90194i
$465$		0			0
$466$	−30.6409	−	22.2619i	−1.41941	−	1.03126i
$467$	−36.8788	+	11.9826i	−1.70655	+	0.554490i	−0.989752	−	0.142795i	$-0.954391\pi$
$467$	−36.8788	+	11.9826i	−1.70655	+	0.554490i	−0.716794	+	0.697285i	$0.754391\pi$
$468$	−0.371156	+	0.120596i	−0.0171567	+	0.00557455i
$469$	18.1174	+	13.1630i	0.836582	+	0.607812i
$470$		0			0
$471$	2.82895	−	8.70662i	0.130351	−	0.401180i
$472$		−	21.6910i		−	0.998409i
$473$	0.697949	−	1.93675i	0.0320917	−	0.0890518i
$474$	−13.6270			−0.625911
$475$		0			0
$476$	0.184276	−	0.133884i	0.00844626	−	0.00613656i
$477$	6.81425	−	9.37901i	0.312003	−	0.429435i
$478$	5.87562	−	1.90911i	0.268745	−	0.0873205i
$479$	−5.15675	−	15.8708i	−0.235618	−	0.725158i	−0.997039	−	0.0768997i	$-0.975498\pi$
$479$	−5.15675	−	15.8708i	−0.235618	−	0.725158i	0.761421	−	0.648258i	$-0.224502\pi$
$480$		0			0
$481$	−15.2748	+	11.0978i	−0.696473	+	0.506017i
$482$	4.62483	+	1.50270i	0.210655	+	0.0684461i
$483$			4.67961i			0.212930i
$484$	0.497489	+	1.94258i	0.0226131	+	0.0882989i
$485$		0			0
$486$	−0.456498	+	1.40496i	−0.0207072	+	0.0637302i
$487$	−1.47648	−	2.03220i	−0.0669056	−	0.0920877i	0.774253	−	0.632876i	$-0.218126\pi$
$487$	−1.47648	−	2.03220i	−0.0669056	−	0.0920877i	−0.841158	+	0.540789i	$0.818126\pi$
$488$	−13.7725	+	18.9562i	−0.623450	+	0.858105i
$489$	3.50181	+	10.7775i	0.158357	+	0.487373i
$490$		0			0
$491$	6.11508	+	4.44286i	0.275970	+	0.200504i	0.717158	−	0.696911i	$-0.245443\pi$
$491$	6.11508	+	4.44286i	0.275970	+	0.200504i	−0.441188	+	0.897415i	$0.645443\pi$
$492$	0.195319	+	0.268833i	0.00880565	+	0.0121199i
$493$	5.14974	+	1.67325i	0.231932	+	0.0753594i
$494$	6.90147			0.310512
$495$		0			0
$496$	−29.3295			−1.31693
$497$	32.7325	+	10.6354i	1.46825	+	0.477065i
$498$	8.20756	+	11.2967i	0.367789	+	0.506219i
$499$	13.5886	+	9.87269i	0.608309	+	0.441962i	0.848818	−	0.528685i	$-0.177315\pi$
$499$	13.5886	+	9.87269i	0.608309	+	0.441962i	−0.240510	+	0.970647i	$0.577315\pi$
$500$		0			0
$501$	4.66619	+	14.3611i	0.208470	+	0.641605i
$502$	8.13139	−	11.1919i	0.362922	−	0.499519i
$503$	4.48632	+	6.17489i	0.200035	+	0.275325i	0.897236	−	0.441551i	$-0.145572\pi$
$503$	4.48632	+	6.17489i	0.200035	+	0.275325i	−0.697201	+	0.716876i	$0.745572\pi$
$504$	1.90431	−	5.86087i	0.0848248	−	0.261064i
$505$		0			0
$506$	6.12569	−	7.89215i	0.272320	−	0.350849i
$507$		−	8.41709i		−	0.373816i
$508$	−0.716469	−	0.232795i	−0.0317882	−	0.0103286i
$509$	26.6198	−	19.3404i	1.17990	−	0.857249i	0.187741	−	0.982219i	$-0.439883\pi$
$509$	26.6198	−	19.3404i	1.17990	−	0.857249i	0.992161	+	0.124970i	$0.0398834\pi$
$510$		0			0
$511$	−5.57307	−	17.1521i	−0.246538	−	0.758766i
$512$	−17.8877	+	5.81206i	−0.790531	+	0.256859i
$513$	1.28272	−	1.76552i	0.0566336	−	0.0779494i
$514$	15.0244	−	10.9159i	0.662699	−	0.481479i
$515$		0			0
$516$	−0.113154			−0.00498133
$517$	−0.349403	−	1.20404i	−0.0153667	−	0.0529537i
$518$			29.9007i			1.31376i
$519$	−5.64392	+	17.3702i	−0.247741	+	0.762467i
$520$		0			0
$521$	−0.645559	−	0.469026i	−0.0282824	−	0.0205484i	0.573554	−	0.819168i	$-0.305564\pi$
$521$	−0.645559	−	0.469026i	−0.0282824	−	0.0205484i	−0.601837	+	0.798619i	$0.705564\pi$
$522$	−13.9729	+	4.54008i	−0.611578	+	0.198714i
$523$	4.09443	−	1.33036i	0.179037	−	0.0581727i	−0.218127	−	0.975920i	$-0.569995\pi$
$523$	4.09443	−	1.33036i	0.179037	−	0.0581727i	0.397164	+	0.917748i	$0.369995\pi$
$524$	−0.0643796	−	0.0467745i	−0.00281244	−	0.00204336i
$525$		0			0
$526$	−2.20464	+	6.78519i	−0.0961270	+	0.295848i
$527$			3.68668i			0.160594i
$528$	−11.8839	+	8.07094i	−0.517181	+	0.351242i
$529$	18.8422			0.819224
$530$		0			0
$531$	6.53518	−	4.74808i	0.283602	−	0.206049i
$532$	0.536646	−	0.738630i	0.0232666	−	0.0320237i
$533$	3.71127	−	1.20586i	0.160753	−	0.0522318i
$534$	0.266271	+	0.819498i	0.0115227	+	0.0354632i
$535$		0			0
$536$	21.1982	−	15.4014i	0.915623	−	0.665239i
$537$	−0.499703	−	0.162363i	−0.0215638	−	0.00700649i
$538$		−	7.72502i		−	0.333049i
$539$	0.182331	−	5.74530i	0.00785357	−	0.247468i
$540$		0			0
$541$	−7.01720	+	21.5967i	−0.301693	+	0.928516i	0.679198	+	0.733955i	$0.262328\pi$
$541$	−7.01720	+	21.5967i	−0.301693	+	0.928516i	−0.980891	+	0.194560i	$0.937672\pi$
$542$	26.3368	+	36.2495i	1.13126	+	1.55705i
$543$	10.4101	−	14.3282i	0.446738	−	0.614883i
$544$	−0.172972	−	0.532353i	−0.00741611	−	0.0228245i
$545$		0			0
$546$	5.87166	+	4.26601i	0.251284	+	0.182568i
$547$	−18.9003	−	26.0140i	−0.808117	−	1.11228i	−0.991611	−	0.129257i	$-0.958741\pi$
$547$	−18.9003	−	26.0140i	−0.808117	−	1.11228i	0.183494	−	0.983021i	$-0.441259\pi$
$548$	1.36409	+	0.443221i	0.0582712	+	0.0189335i
$549$	−8.72595			−0.372415
$550$		0			0
$551$	21.7039			0.924617
$552$	5.20739	+	1.69198i	0.221641	+	0.0720156i
$553$	12.4434	+	17.1269i	0.529147	+	0.728309i
$554$	−19.0855	−	13.8665i	−0.810867	−	0.589129i
$555$		0			0
$556$	0.993889	+	3.05888i	0.0421503	+	0.129725i
$557$	22.1684	−	30.5122i	0.939306	−	1.29284i	−0.0168116	−	0.999859i	$-0.505352\pi$
$557$	22.1684	−	30.5122i	0.939306	−	1.29284i	0.956117	−	0.292985i	$-0.0946484\pi$
$558$	−5.87971	−	8.09273i	−0.248908	−	0.342593i
$559$	−0.410623	+	1.26377i	−0.0173675	+	0.0534517i
$560$		0			0
$561$	1.01450	+	1.49379i	0.0428324	+	0.0630679i
$562$			2.05438i			0.0866588i
$563$	−20.9109	−	6.79438i	−0.881291	−	0.286349i	−0.166798	−	0.985991i	$-0.553343\pi$
$563$	−20.9109	−	6.79438i	−0.881291	−	0.286349i	−0.714493	+	0.699642i	$0.753343\pi$
$564$	−0.0557493	+	0.0405043i	−0.00234747	+	0.00170554i
$565$		0			0
$566$	−2.68171	−	8.25347i	−0.112721	−	0.346919i
$567$	2.18264	−	0.709183i	0.0916622	−	0.0297829i
$568$	23.6699	−	32.5788i	0.993166	−	1.36698i
$569$	−16.5690	+	12.0381i	−0.694609	+	0.504663i	−0.878172	−	0.478345i	$-0.841237\pi$
$569$	−16.5690	+	12.0381i	−0.694609	+	0.504663i	0.183563	+	0.983008i	$0.441237\pi$
$570$		0			0
$571$	17.4373			0.729728			0.364864	−	0.931061i	$-0.381116\pi$
$571$	17.4373			0.729728			0.364864	+	0.931061i	$0.381116\pi$
$572$	−0.360724	−	1.24305i	−0.0150826	−	0.0519747i
$573$			16.5519i			0.691467i
$574$	1.90968	−	5.87739i	0.0797085	−	0.245317i
$575$		0			0
$576$	−5.77957	−	4.19910i	−0.240815	−	0.174963i
$577$	31.6082	−	10.2701i	1.31587	−	0.427551i	0.434794	−	0.900530i	$-0.356821\pi$
$577$	31.6082	−	10.2701i	1.31587	−	0.427551i	0.881074	+	0.472978i	$0.156821\pi$
$578$	23.4678	−	7.62516i	0.976133	−	0.317165i
$579$	−19.8235	−	14.4026i	−0.823838	−	0.598553i
$580$		0			0
$581$	6.70342	−	20.6310i	0.278105	−	0.855918i
$582$			7.94472i			0.329319i
$583$	30.3741	+	23.5756i	1.25797	+	0.976403i
$584$	−21.1016			−0.873192
$585$		0			0
$586$	23.8721	−	17.3441i	0.986147	−	0.716478i
$587$	−25.1545	+	34.6222i	−1.03824	+	1.42901i	−0.139657	+	0.990200i	$0.544600\pi$
$587$	−25.1545	+	34.6222i	−1.03824	+	1.42901i	−0.898580	+	0.438811i	$0.855400\pi$
$588$	−0.300484	+	0.0976331i	−0.0123917	+	0.00402632i
$589$	4.56643	+	14.0540i	0.188156	+	0.579086i
$590$		0			0
$591$	6.07472	−	4.41354i	0.249881	−	0.181549i
$592$	36.3312	+	11.8047i	1.49320	+	0.485171i
$593$			42.6570i			1.75171i	0.482570	+	0.875857i	$0.339703\pi$
$593$			42.6570i			1.75171i	−0.482570	+	0.875857i	$0.660297\pi$
$594$	−4.60935	−	1.66108i	−0.189124	−	0.0681548i
$595$		0			0
$596$	−0.617416	+	1.90021i	−0.0252903	+	0.0778357i
$597$	11.8119	+	16.2577i	0.483429	+	0.665383i
$598$	−3.79036	+	5.21698i	−0.154999	+	0.213338i
$599$	−8.75148	−	26.9343i	−0.357576	−	1.10051i	−0.954501	−	0.298208i	$-0.903611\pi$
$599$	−8.75148	−	26.9343i	−0.357576	−	1.10051i	0.596925	−	0.802297i	$-0.296389\pi$
$600$		0			0
$601$	6.19268	+	4.49925i	0.252605	+	0.183528i	0.706880	−	0.707333i	$-0.250102\pi$
$601$	6.19268	+	4.49925i	0.252605	+	0.183528i	−0.454276	+	0.890861i	$0.650102\pi$
$602$	1.23692	+	1.70248i	0.0504131	+	0.0693877i
$603$	9.28043	+	3.01539i	0.377928	+	0.122796i
$604$	3.65184			0.148591
$605$		0			0
$606$	28.8495			1.17193
$607$	11.0309	+	3.58415i	0.447730	+	0.145476i	0.524199	−	0.851596i	$-0.324365\pi$
$607$	11.0309	+	3.58415i	0.447730	+	0.145476i	−0.0764693	+	0.997072i	$0.524365\pi$
$608$	−1.31878	−	1.81514i	−0.0534835	−	0.0736137i
$609$	18.4653	+	13.4159i	0.748253	+	0.543638i
$610$		0			0
$611$	0.250066	+	0.769625i	0.0101166	+	0.0311357i
$612$	0.0583382	−	0.0802957i	0.00235818	−	0.00324576i
$613$	−18.8725	−	25.9757i	−0.762251	−	1.04915i	−0.997023	−	0.0770985i	$-0.975434\pi$
$613$	−18.8725	−	25.9757i	−0.762251	−	1.04915i	0.234772	−	0.972050i	$-0.424566\pi$
$614$	8.87307	−	27.3085i	0.358088	−	1.10208i
$615$		0			0
$616$	19.2282	+	6.92929i	0.774725	+	0.279189i
$617$		−	18.7392i		−	0.754414i	−0.926129	−	0.377207i	$-0.876885\pi$
$617$		−	18.7392i		−	0.754414i	0.926129	−	0.377207i	$-0.123115\pi$
$618$	18.2732	+	5.93732i	0.735056	+	0.238834i
$619$	−31.6002	+	22.9589i	−1.27012	+	0.922796i	−0.999207	−	0.0398085i	$-0.987325\pi$
$619$	−31.6002	+	22.9589i	−1.27012	+	0.922796i	−0.270912	+	0.962604i	$0.587325\pi$
$620$		0			0
$621$	0.630110	+	1.93928i	0.0252854	+	0.0778205i
$622$	8.46040	−	2.74895i	0.339231	−	0.110223i
$623$	0.786827	−	1.08297i	0.0315236	−	0.0433884i
$624$	7.50158	−	5.45022i	0.300304	−	0.218183i
$625$		0			0
$626$	7.54633			0.301612
$627$	5.71766	+	4.43790i	0.228341	+	0.177233i
$628$		−	1.66887i		−	0.0665952i
$629$	1.48383	−	4.56677i	0.0591644	−	0.182089i
$630$		0			0
$631$	−36.4512	−	26.4833i	−1.45110	−	1.05428i	−0.985573	−	0.169249i	$-0.945866\pi$
$631$	−36.4512	−	26.4833i	−1.45110	−	1.05428i	−0.465524	−	0.885035i	$-0.654134\pi$
$632$	23.5576	−	7.65433i	0.937071	−	0.304473i
$633$	5.15339	−	1.67444i	0.204829	−	0.0665530i
$634$	−16.3479	−	11.8775i	−0.649260	−	0.471715i
$635$		0			0
$636$	0.653073	−	2.00995i	0.0258960	−	0.0796997i
$637$			3.71027i			0.147006i
$638$	−13.5802	−	46.7972i	−0.537644	−	1.85272i
$639$	14.9968			0.593263
$640$		0			0
$641$	−20.9477	+	15.2194i	−0.827384	+	0.601130i	−0.918818	−	0.394682i	$-0.870855\pi$
$641$	−20.9477	+	15.2194i	−0.827384	+	0.601130i	0.0914341	+	0.995811i	$0.470855\pi$
$642$	−1.71365	+	2.35864i	−0.0676325	+	0.0930882i
$643$	29.1386	−	9.46770i	1.14911	−	0.373370i	0.328304	−	0.944572i	$-0.393523\pi$
$643$	29.1386	−	9.46770i	1.14911	−	0.373370i	0.820809	+	0.571202i	$0.193523\pi$
$644$	0.263616	+	0.811326i	0.0103879	+	0.0319707i
$645$		0			0
$646$	−1.41998	+	1.03168i	−0.0558685	+	0.0405908i
$647$	−14.3689	−	4.66875i	−0.564901	−	0.183547i	0.0126243	−	0.999920i	$-0.495981\pi$
$647$	−14.3689	−	4.66875i	−0.564901	−	0.183547i	−0.577525	+	0.816373i	$0.695981\pi$
$648$		−	2.68522i		−	0.105485i
$649$	15.0522	+	22.1633i	0.590849	+	0.869987i
$650$		0			0
$651$	−4.80218	+	14.7796i	−0.188212	+	0.579258i
$652$	1.21425	+	1.67127i	0.0475537	+	0.0654521i
$653$	3.07722	−	4.23543i	0.120421	−	0.165745i	−0.744551	−	0.667566i	$-0.767336\pi$
$653$	3.07722	−	4.23543i	0.120421	−	0.165745i	0.864972	+	0.501821i	$0.167336\pi$
$654$	4.84856	+	14.9223i	0.189594	+	0.583510i
$655$		0			0
$656$	−6.38745	−	4.64075i	−0.249388	−	0.181191i
$657$	−4.61907	−	6.35761i	−0.180207	−	0.248034i
$658$	1.21882	+	0.396020i	0.0475147	+	0.0154385i
$659$	−14.9207			−0.581229			−0.290615	−	0.956840i	$-0.593860\pi$
$659$	−14.9207			−0.581229			−0.290615	+	0.956840i	$0.593860\pi$
$660$		0			0
$661$	45.7403			1.77909			0.889545	−	0.456847i	$-0.151021\pi$
$661$	45.7403			1.77909			0.889545	+	0.456847i	$0.151021\pi$
$662$	−16.1141	−	5.23579i	−0.626292	−	0.203495i
$663$	−0.685085	−	0.942938i	−0.0266065	−	0.0366207i
$664$	−20.5341	−	14.9189i	−0.796878	−	0.578966i
$665$		0			0
$666$	4.02613	+	12.3912i	0.156009	+	0.480147i
$667$	−11.9200	+	16.4065i	−0.461544	+	0.635261i
$668$	1.61800	+	2.22699i	0.0626023	+	0.0861647i
$669$	−4.85386	+	14.9386i	−0.187661	+	0.577561i
$670$		0			0
$671$	0.917993	−	28.9261i	0.0354387	−	1.11668i
$672$		−	2.35947i		−	0.0910185i
$673$	−20.0755	−	6.52294i	−0.773855	−	0.251441i	−0.104641	−	0.994510i	$-0.533369\pi$
$673$	−20.0755	−	6.52294i	−0.773855	−	0.251441i	−0.669214	+	0.743069i	$0.733369\pi$
$674$	−4.49852	+	3.26836i	−0.173276	+	0.125893i
$675$		0			0
$676$	−0.474159	−	1.45931i	−0.0182369	−	0.0561273i
$677$	41.9125	−	13.6182i	1.61083	−	0.523390i	0.641077	−	0.767477i	$-0.278488\pi$
$677$	41.9125	−	13.6182i	1.61083	−	0.523390i	0.969753	+	0.244087i	$0.0784881\pi$
$678$	−14.6706	+	20.1924i	−0.563421	+	0.775483i
$679$	9.98516	−	7.25464i	0.383195	−	0.278408i
$680$		0			0
$681$	−1.47141			−0.0563847
$682$	27.4456	−	18.6396i	1.05095	−	0.713748i
$683$			42.5318i			1.62743i	0.581261	+	0.813717i	$0.302560\pi$
$683$			42.5318i			1.62743i	−0.581261	+	0.813717i	$0.697440\pi$
$684$	0.122935	−	0.378355i	0.00470054	−	0.0144668i
$685$		0			0
$686$	23.9531	+	17.4029i	0.914532	+	0.664446i
$687$	15.1932	−	4.93656i	0.579656	−	0.188342i
$688$	2.55694	−	0.830802i	0.0974826	−	0.0316740i
$689$	−20.0783	−	14.5878i	−0.764924	−	0.555750i
$690$		0			0
$691$	−1.77552	+	5.46449i	−0.0675439	+	0.207879i	−0.979132	−	0.203227i	$-0.934857\pi$
$691$	−1.77552	+	5.46449i	−0.0675439	+	0.207879i	0.911588	+	0.411105i	$0.134857\pi$
$692$			3.32949i			0.126568i
$693$	2.12129	+	7.30996i	0.0805811	+	0.277682i
$694$	−0.584966			−0.0222050
$695$		0			0
$696$	21.6054	−	15.6972i	0.818949	−	0.595001i
$697$	−0.583336	+	0.802893i	−0.0220954	+	0.0304117i
$698$	18.5044	−	6.01244i	0.700401	−	0.227574i
$699$	7.92263	+	24.3833i	0.299661	+	0.922263i
$700$		0			0
$701$	0.983718	−	0.714713i	0.0371545	−	0.0269943i	−0.569053	−	0.822301i	$-0.692690\pi$
$701$	0.983718	−	0.714713i	0.0371545	−	0.0269943i	0.606208	+	0.795307i	$0.292690\pi$
$702$	3.00770	+	0.977260i	0.113518	+	0.0368843i
$703$		−	19.2470i		−	0.725913i
$704$	14.5279	−	18.7173i	0.547540	−	0.705433i
$705$		0			0
$706$	−5.19736	+	15.9958i	−0.195605	+	0.602011i
$707$	−26.3437	−	36.2589i	−0.990755	−	1.36366i
$708$	0.865562	−	1.19134i	0.0325298	−	0.0447734i
$709$	8.16115	+	25.1174i	0.306498	+	0.943305i	0.979114	+	0.203313i	$0.0651709\pi$
$709$	8.16115	+	25.1174i	0.306498	+	0.943305i	−0.672615	+	0.739992i	$0.734829\pi$
$710$		0			0
$711$	7.46281	+	5.42205i	0.279877	+	0.203343i
$712$	−0.920626	−	1.26713i	−0.0345019	−	0.0474878i
$713$	−13.1317	−	4.26675i	−0.491786	−	0.159791i
$714$	−1.84581			−0.0690777
$715$		0			0
$716$	−0.0957823			−0.00357955
$717$	−3.97738	−	1.29233i	−0.148538	−	0.0482629i
$718$	12.4761	+	17.1719i	0.465604	+	0.640849i
$719$	40.0007	+	29.0622i	1.49177	+	1.08384i	0.973518	+	0.228611i	$0.0734183\pi$
$719$	40.0007	+	29.0622i	1.49177	+	1.08384i	0.518255	+	0.855226i	$0.326582\pi$
$720$		0			0
$721$	−9.22379	−	28.3879i	−0.343512	−	1.05722i
$722$	12.3627	−	17.0157i	0.460090	−	0.633260i
$723$	−1.93487	−	2.66312i	−0.0719586	−	0.0990425i
$724$	0.997692	−	3.07058i	0.0370789	−	0.114117i
$725$		0			0
$726$	5.99131	−	15.1050i	0.222359	−	0.560600i
$727$		−	39.2447i		−	1.45551i	−0.685839	−	0.727753i	$-0.740565\pi$
$727$		−	39.2447i		−	1.45551i	0.685839	−	0.727753i	$-0.259435\pi$
$728$	−12.5468	−	4.07670i	−0.465015	−	0.151093i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$		0			0
$731$	−0.104431	−	0.321404i	−0.00386250	−	0.0118876i
$732$	−1.51286	+	0.491558i	−0.0559169	+	0.0181685i
$733$	−3.05601	+	4.20624i	−0.112876	+	0.155361i	−0.861717	−	0.507389i	$-0.830611\pi$
$733$	−3.05601	+	4.20624i	−0.112876	+	0.155361i	0.748841	+	0.662750i	$0.230611\pi$
$734$	31.3888	−	22.8053i	1.15858	−	0.841760i
$735$		0			0
$736$	2.09639			0.0772740
$737$	−10.9722	+	30.4470i	−0.404167	+	1.12153i
$738$		−	2.69279i		−	0.0991229i
$739$	−8.96428	+	27.5892i	−0.329757	+	1.01489i	0.639491	+	0.768799i	$0.279145\pi$
$739$	−8.96428	+	27.5892i	−0.329757	+	1.01489i	−0.969248	+	0.246088i	$0.920855\pi$
$740$		0			0
$741$	−3.77957	−	2.74602i	−0.138846	−	0.100877i
$742$	−37.3799	+	12.1455i	−1.37226	+	0.445874i
$743$	8.09042	−	2.62874i	0.296809	−	0.0964390i	−0.156827	−	0.987626i	$-0.550127\pi$
$743$	8.09042	−	2.62874i	0.296809	−	0.0964390i	0.453636	+	0.891187i	$0.350127\pi$
$744$	14.7102	+	10.6876i	0.539301	+	0.391825i
$745$		0			0
$746$	−9.99506	+	30.7616i	−0.365945	+	1.12626i
$747$		−	9.45232i		−	0.345842i
$748$	0.260039	+	0.201836i	0.00950798	+	0.00737985i
$749$	4.52922			0.165494
$750$		0			0
$751$	28.4006	−	20.6343i	1.03635	−	0.752955i	0.0667831	−	0.997768i	$-0.478726\pi$
$751$	28.4006	−	20.6343i	1.03635	−	0.752955i	0.969570	+	0.244813i	$0.0787264\pi$
$752$	0.962377	−	1.32460i	0.0350943	−	0.0483032i
$753$	−8.90626	+	2.89382i	−0.324562	+	0.105457i
$754$	9.71928	+	29.9129i	0.353955	+	1.08936i
$755$		0			0
$756$	0.338464	−	0.245909i	0.0123098	−	0.00894362i
$757$	−6.83159	−	2.21972i	−0.248298	−	0.0806771i	0.182224	−	0.983257i	$-0.441671\pi$
$757$	−6.83159	−	2.21972i	−0.248298	−	0.0806771i	−0.430522	+	0.902580i	$0.641671\pi$
$758$			37.7582i			1.37144i
$759$	−6.49491	+	1.88477i	−0.235750	+	0.0684128i
$760$		0			0
$761$	−13.4072	+	41.2631i	−0.486011	+	1.49579i	0.344501	+	0.938786i	$0.388048\pi$
$761$	−13.4072	+	41.2631i	−0.486011	+	1.49579i	−0.830512	+	0.557001i	$0.811952\pi$
$762$	3.58828	+	4.93885i	0.129990	+	0.178916i
$763$	14.3274	−	19.7200i	0.518687	−	0.713912i
$764$	0.932419	+	2.86969i	0.0337337	+	0.103822i
$765$		0			0
$766$	22.7695	+	16.5430i	0.822696	+	0.597724i
$767$	−10.1646	−	13.9903i	−0.367021	−	0.505162i
$768$	−4.12748	−	1.34110i	−0.148937	−	0.0483927i
$769$	19.6548			0.708771			0.354385	−	0.935099i	$-0.384690\pi$
$769$	19.6548			0.708771			0.354385	+	0.935099i	$0.384690\pi$
$770$		0			0
$771$	−12.5714			−0.452747
$772$	−4.24824	−	1.38034i	−0.152898	−	0.0496795i
$773$	−14.3631	−	19.7691i	−0.516604	−	0.711044i	0.468412	−	0.883510i	$-0.344826\pi$
$773$	−14.3631	−	19.7691i	−0.516604	−	0.711044i	−0.985015	+	0.172466i	$0.944826\pi$
$774$	0.741831	+	0.538972i	0.0266646	+	0.0193729i
$775$		0			0
$776$	−4.46256	−	13.7343i	−0.160196	−	0.493034i
$777$	11.8971	−	16.3750i	0.426808	−	0.587450i
$778$	−14.2338	−	19.5912i	−0.510307	−	0.702377i
$779$	−1.22925	+	3.78326i	−0.0440426	+	0.135549i
$780$		0			0
$781$	−1.57770	+	49.7136i	−0.0564545	+	1.77889i
$782$		−	1.64001i		−	0.0586465i
$783$	9.45867	+	3.07331i	0.338025	+	0.109831i
$784$	6.07319	−	4.41243i	0.216900	−	0.157587i
$785$		0			0
$786$	0.199274	+	0.613302i	0.00710786	+	0.0218758i
$787$	32.4721	−	10.5508i	1.15750	−	0.376096i	0.333539	−	0.942736i	$-0.391757\pi$
$787$	32.4721	−	10.5508i	1.15750	−	0.376096i	0.823965	+	0.566640i	$0.191757\pi$
$788$	0.804576	−	1.10740i	0.0286618	−	0.0394496i
$789$	3.90712	−	2.83869i	0.139097	−	0.101060i
$790$		0			0
$791$	38.7747			1.37867
$792$	8.90139	+	0.282492i	0.316297	+	0.0100379i
$793$			18.6803i			0.663357i
$794$	14.1435	−	43.5292i	0.501934	−	1.54479i
$795$		0			0
$796$	2.96373	+	2.15327i	0.105047	+	0.0763208i
$797$	2.89410	−	0.940349i	0.102514	−	0.0333089i	−0.257311	−	0.966329i	$-0.582836\pi$
$797$	2.89410	−	0.940349i	0.102514	−	0.0333089i	0.359825	+	0.933020i	$0.382836\pi$
$798$	−7.03644	+	2.28628i	−0.249087	+	0.0809333i
$799$	−0.166500	−	0.120969i	−0.00589035	−	0.00427959i
$800$		0			0
$801$	0.180247	−	0.554742i	0.00636870	−	0.0196008i
$802$			9.40439i			0.332081i
$803$	21.5611	−	14.6432i	0.760876	−	0.516747i
$804$	1.77886			0.0627355
$805$		0			0
$806$	−17.3247	+	12.5871i	−0.610237	+	0.443363i
$807$	−3.07370	+	4.23058i	−0.108199	+	0.148924i
$808$	−49.8733	+	16.2048i	−1.75454	+	0.570083i
$809$	3.43043	+	10.5578i	0.120607	+	0.371191i	0.993075	−	0.117480i	$-0.0374816\pi$
$809$	3.43043	+	10.5578i	0.120607	+	0.371191i	−0.872468	+	0.488672i	$0.837482\pi$
$810$		0			0
$811$	−33.4336	+	24.2909i	−1.17401	+	0.852969i	−0.991484	−	0.130231i	$-0.958428\pi$
$811$	−33.4336	+	24.2909i	−1.17401	+	0.852969i	−0.182528	+	0.983201i	$0.558428\pi$
$812$	3.95718	+	1.28577i	0.138870	+	0.0451215i
$813$		−	30.3311i		−	1.06376i
$814$	−41.4997	+	12.0429i	−1.45456	+	0.422102i
$815$		0			0
$816$	−0.728721	+	2.24277i	−0.0255103	+	0.0785128i
$817$	−0.796202	−	1.09588i	−0.0278556	−	0.0383399i
$818$	−5.44322	+	7.49195i	−0.190318	+	0.261950i
$819$	−1.51820	−	4.67254i	−0.0530502	−	0.163272i
$820$		0			0
$821$	−6.61681	−	4.80739i	−0.230928	−	0.167779i	0.466304	−	0.884625i	$-0.345585\pi$
$821$	−6.61681	−	4.80739i	−0.230928	−	0.167779i	−0.697232	+	0.716845i	$0.745585\pi$
$822$	−6.83178	−	9.40314i	−0.238286	−	0.327972i
$823$	−12.5514	−	4.07819i	−0.437513	−	0.142157i	0.0819748	−	0.996634i	$-0.473877\pi$
$823$	−12.5514	−	4.07819i	−0.437513	−	0.142157i	−0.519488	+	0.854478i	$0.673877\pi$
$824$	−34.9246			−1.21665
$825$		0			0
$826$	−27.3862			−0.952889
$827$	−29.2326	−	9.49825i	−1.01652	−	0.330287i	−0.247071	−	0.968997i	$-0.579468\pi$
$827$	−29.2326	−	9.49825i	−1.01652	−	0.330287i	−0.769447	+	0.638711i	$0.779468\pi$
$828$	0.218490	+	0.300726i	0.00759306	+	0.0104510i
$829$	2.98357	+	2.16769i	0.103624	+	0.0752871i	0.638390	−	0.769713i	$-0.279601\pi$
$829$	2.98357	+	2.16769i	0.103624	+	0.0752871i	−0.534767	+	0.845000i	$0.679601\pi$
$830$		0			0
$831$	4.93483	+	15.1878i	0.171187	+	0.526861i
$832$	−8.98933	+	12.3728i	−0.311649	+	0.428948i
$833$	−0.554636	−	0.763391i	−0.0192170	−	0.0264499i
$834$	8.05407	−	24.7879i	0.278889	−	0.858334i
$835$		0			0
$836$	1.24130	+	0.447329i	0.0429312	+	0.0154712i
$837$			6.77143i			0.234055i
$838$	5.48399	+	1.78186i	0.189441	+	0.0615533i
$839$	35.2341	−	25.5991i	1.21642	−	0.883778i	0.220618	−	0.975360i	$-0.429192\pi$
$839$	35.2341	−	25.5991i	1.21642	−	0.883778i	0.995798	+	0.0915823i	$0.0291924\pi$
$840$		0			0
$841$	21.6039	+	66.4900i	0.744963	+	2.29276i
$842$	24.4063	−	7.93008i	0.841096	−	0.273289i
$843$	0.817415	−	1.12508i	0.0281533	−	0.0387497i
$844$	0.799143	−	0.580611i	0.0275076	−	0.0199855i
$845$		0			0
$846$	0.558418			0.0191988
$847$	−24.4554	+	6.26295i	−0.840296	+	0.215198i
$848$			50.2139i			1.72435i
$849$	−1.81533	+	5.58701i	−0.0623019	+	0.191746i
$850$		0			0
$851$	14.5492	+	10.5706i	0.498741	+	0.362357i
$852$	2.60006	−	0.844811i	0.0890766	−	0.0289428i
$853$	−28.8583	+	9.37662i	−0.988088	+	0.321049i	−0.758096	−	0.652143i	$-0.773870\pi$
$853$	−28.8583	+	9.37662i	−0.988088	+	0.321049i	−0.229992	+	0.973192i	$0.573870\pi$
$854$	23.9333	+	17.3886i	0.818982	+	0.595025i
$855$		0			0
$856$	1.63761	−	5.04004i	0.0559723	−	0.172265i
$857$			12.5402i			0.428365i	0.976794	+	0.214182i	$0.0687087\pi$
$857$			12.5402i			0.428365i	−0.976794	+	0.214182i	$0.931291\pi$
$858$	−3.55599	+	9.86757i	−0.121400	+	0.336873i
$859$	8.67783			0.296084			0.148042	−	0.988981i	$-0.452703\pi$
$859$	8.67783			0.296084			0.148042	+	0.988981i	$0.452703\pi$
$860$		0			0
$861$	−3.38438	+	2.45889i	−0.115339	+	0.0837989i
$862$	6.10988	−	8.40953i	0.208103	−	0.286430i
$863$	−36.5128	+	11.8637i	−1.24291	+	0.403846i	−0.855375	−	0.518009i	$-0.826673\pi$
$863$	−36.5128	+	11.8637i	−1.24291	+	0.403846i	−0.387535	+	0.921855i	$0.626673\pi$
$864$	−0.317703	−	0.977789i	−0.0108085	−	0.0332651i
$865$		0			0
$866$	3.28935	−	2.38985i	0.111777	−	0.0812104i
$867$	−15.8860	−	5.16169i	−0.539518	−	0.175300i
$868$			2.83293i			0.0961559i
$869$	−18.7590	+	24.1685i	−0.636354	+	0.819859i
$870$		0			0
$871$	6.45528	−	19.8673i	0.218729	−	0.673178i
$872$	−16.7638	−	23.0734i	−0.567693	−	0.781363i
$873$	3.16111	−	4.35090i	0.106988	−	0.147256i
$874$	−2.03136	−	6.25188i	−0.0687118	−	0.211473i
$875$		0			0
$876$	−1.15897	−	0.842044i	−0.0391581	−	0.0284500i
$877$	−18.3917	−	25.3140i	−0.621043	−	0.854792i	0.376385	−	0.926463i	$-0.377167\pi$
$877$	−18.3917	−	25.3140i	−0.621043	−	0.854792i	−0.997428	+	0.0716708i	$0.977167\pi$
$878$	−3.84542	−	1.24945i	−0.129777	−	0.0421669i
$879$	−19.9745			−0.673723
$880$		0			0
$881$	49.2703			1.65996			0.829979	−	0.557795i	$-0.188353\pi$
$881$	49.2703			1.65996			0.829979	+	0.557795i	$0.188353\pi$
$882$	2.43500	+	0.791178i	0.0819906	+	0.0266404i
$883$	16.5674	+	22.8031i	0.557537	+	0.767385i	0.991011	−	0.133782i	$-0.0427122\pi$
$883$	16.5674	+	22.8031i	0.557537	+	0.767385i	−0.433473	+	0.901166i	$0.642712\pi$
$884$	−0.171895	−	0.124889i	−0.00578145	−	0.00420047i
$885$		0			0
$886$	−5.06905	−	15.6009i	−0.170298	−	0.524123i
$887$	−14.9852	+	20.6253i	−0.503153	+	0.692531i	−0.982746	−	0.184960i	$-0.940784\pi$
$887$	−14.9852	+	20.6253i	−0.503153	+	0.692531i	0.479593	+	0.877491i	$0.340784\pi$
$888$	−13.9202	−	19.1596i	−0.467133	−	0.642953i
$889$	2.93068	−	9.01972i	0.0982920	−	0.302512i
$890$		0			0
$891$	1.86337	+	2.74369i	0.0624253	+	0.0919171i
$892$			2.86342i			0.0958743i
$893$	−0.784553	−	0.254917i	−0.0262541	−	0.00853047i
$894$	13.0988	−	9.51681i	0.438088	−	0.318290i
$895$		0			0
$896$	8.94256	+	27.5224i	0.298750	+	0.919458i
$897$	4.15156	−	1.34892i	0.138616	−	0.0450392i
$898$	12.8743	−	17.7200i	0.429621	−	0.591323i
$899$	−54.4831	+	39.5843i	−1.81711	+	1.32021i
$900$		0			0
$901$	6.31181			0.210277
$902$	8.92648	+	0.283289i	0.297219	+	0.00943248i
$903$		−	1.42451i		−	0.0474048i
$904$	14.0196	−	43.1478i	0.466284	−	1.43507i
$905$		0			0
$906$	−23.9413	−	17.3943i	−0.795395	−	0.577888i
$907$	−2.35913	+	0.766528i	−0.0783337	+	0.0254522i	−0.347922	−	0.937524i	$-0.613112\pi$
$907$	−2.35913	+	0.766528i	−0.0783337	+	0.0254522i	0.269588	+	0.962976i	$0.413112\pi$
$908$	−0.255106	+	0.0828891i	−0.00846600	+	0.00275077i
$909$	−15.7994	−	11.4789i	−0.524031	−	0.380731i
$910$		0			0
$911$	0.839165	−	2.58268i	0.0278028	−	0.0855681i	−0.936192	−	0.351488i	$-0.885676\pi$
$911$	0.839165	−	2.58268i	0.0278028	−	0.0855681i	0.963995	+	0.265920i	$0.0856757\pi$
$912$			9.45232i			0.312998i
$913$	31.3340	+	0.994409i	1.03700	+	0.0329101i
$914$	43.1101			1.42595
$915$		0			0
$916$	2.35602	−	1.71175i	0.0778453	−	0.0565579i
$917$	0.588851	−	0.810484i	0.0194456	−	0.0267645i
$918$	−0.764923	+	0.248539i	−0.0252462	+	0.00820300i
$919$	−1.00091	−	3.08047i	−0.0330169	−	0.101615i	0.933190	−	0.359383i	$-0.117013\pi$
$919$	−1.00091	−	3.08047i	−0.0330169	−	0.101615i	−0.966207	+	0.257768i	$0.917013\pi$
$920$		0			0
$921$	−15.7251	+	11.4249i	−0.518158	+	0.376464i
$922$	43.8063	+	14.2335i	1.44268	+	0.468757i
$923$		−	32.1047i		−	1.05674i
$924$	0.779570	+	1.14786i	0.0256460	+	0.0377620i
$925$		0			0
$926$	−18.7914	+	57.8339i	−0.617523	+	1.90054i
$927$	−7.64487	−	10.5223i	−0.251090	−	0.345596i
$928$	6.01010	−	8.27219i	0.197291	−	0.271548i
$929$	−2.21938	−	6.83056i	−0.0728156	−	0.224103i	0.908025	−	0.418916i	$-0.137590\pi$
$929$	−2.21938	−	6.83056i	−0.0728156	−	0.224103i	−0.980840	+	0.194813i	$0.937590\pi$
$930$		0			0
$931$	−3.05989	−	2.22314i	−0.100284	−	0.0728606i
$932$	2.74717	+	3.78115i	0.0899865	+	0.123856i
$933$	−5.72709	−	1.86084i	−0.187496	−	0.0609213i
$934$	57.2832			1.87436
$935$		0			0
$936$	−5.74845			−0.187894
$937$	19.3185	+	6.27696i	0.631108	+	0.205059i	0.607066	−	0.794652i	$-0.292346\pi$
$937$	19.3185	+	6.27696i	0.631108	+	0.205059i	0.0240421	+	0.999711i	$0.492346\pi$
$938$	−19.4452	−	26.7641i	−0.634909	−	0.873877i
$939$	−4.13273	−	3.00260i	−0.134866	−	0.0979862i
$940$		0			0
$941$	−7.85663	−	24.1802i	−0.256119	−	0.788253i	−0.993607	−	0.112893i	$-0.963988\pi$
$941$	−7.85663	−	24.1802i	−0.256119	−	0.788253i	0.737488	−	0.675360i	$-0.236012\pi$
$942$	−7.94911	+	10.9410i	−0.258996	+	0.356478i
$943$	−2.18473	−	3.00702i	−0.0711446	−	0.0979222i
$944$	−10.8120	+	33.2760i	−0.351901	+	1.08304i
$945$		0			0
$946$	−1.86471	+	2.40244i	−0.0606270	+	0.0781099i
$947$		−	4.55536i		−	0.148029i	−0.997257	−	0.0740147i	$-0.976419\pi$
$947$		−	4.55536i		−	0.148029i	0.997257	−	0.0740147i	$-0.0235812\pi$
$948$	1.59930	+	0.519645i	0.0519430	+	0.0168773i
$949$	−13.6102	+	9.88839i	−0.441806	+	0.320991i
$950$		0			0
$951$	4.22699	+	13.0093i	0.137069	+	0.421856i
$952$	3.19092	−	1.03679i	0.103418	−	0.0336027i
$953$	24.4433	−	33.6433i	0.791797	−	1.08981i	−0.202085	−	0.979368i	$-0.564772\pi$
$953$	24.4433	−	33.6433i	0.791797	−	1.08981i	0.993882	−	0.110447i	$-0.0352282\pi$
$954$	−13.8552	+	10.0664i	−0.448580	+	0.325912i
$955$		0			0
$956$	−0.762378			−0.0246571
$957$	−11.1830	+	31.0318i	−0.361494	+	1.00311i
$958$			24.6519i			0.796467i
$959$	−5.57977	+	17.1728i	−0.180180	+	0.554538i
$960$		0			0
$961$	−12.0158	−	8.72996i	−0.387605	−	0.281612i
$962$	26.5267	−	8.61903i	0.855254	−	0.277889i
$963$	1.87695	−	0.609860i	0.0604840	−	0.0196525i
$964$	−0.485479	−	0.352721i	−0.0156362	−	0.0113604i
$965$		0			0
$966$	2.13623	−	6.57465i	0.0687322	−	0.211536i
$967$		−	16.2161i		−	0.521476i	−0.965410	−	0.260738i	$-0.916034\pi$
$967$		−	16.2161i		−	0.521476i	0.965410	−	0.260738i	$-0.0839658\pi$
$968$	−1.87290	+	29.4780i	−0.0601972	+	0.947458i
$969$	1.18814			0.0381686
$970$		0			0
$971$	10.8979	−	7.91778i	0.349730	−	0.254094i	−0.399026	−	0.916940i	$-0.630652\pi$
$971$	10.8979	−	7.91778i	0.349730	−	0.254094i	0.748756	+	0.662846i	$0.230652\pi$
$972$	0.107152	−	0.147481i	0.00343689	−	0.00473047i
$973$	−38.5086	+	12.5122i	−1.23453	+	0.401123i
$974$	1.14669	+	3.52916i	0.0367425	+	0.113082i
$975$		0			0
$976$	30.5770	−	22.2155i	0.978746	−	0.711101i
$977$	−13.8284	−	4.49311i	−0.442409	−	0.143747i	0.0793377	−	0.996848i	$-0.474719\pi$
$977$	−13.8284	−	4.49311i	−0.442409	−	0.143747i	−0.521747	+	0.853100i	$0.674719\pi$
$978$		−	16.7404i		−	0.535300i
$979$	1.81998	+	0.655870i	0.0581669	+	0.0209617i
$980$		0			0
$981$	3.28213	−	10.1014i	0.104790	−	0.322512i
$982$	−6.56326	−	9.03356i	−0.209442	−	0.288272i
$983$	14.4559	−	19.8968i	0.461072	−	0.634611i	−0.513659	−	0.857994i	$-0.671710\pi$
$983$	14.4559	−	19.8968i	0.461072	−	0.634611i	0.974731	+	0.223384i	$0.0717103\pi$
$984$	1.51254	+	4.65513i	0.0482181	+	0.148400i
$985$		0			0
$986$	−6.47132	−	4.70169i	−0.206089	−	0.149732i
$987$	−0.509914	−	0.701836i	−0.0162307	−	0.0223397i
$988$	−0.809973	−	0.263176i	−0.0257687	−	0.00837275i
$989$	1.26568			0.0402463
$990$		0			0
$991$	4.43775			0.140970			0.0704848	−	0.997513i	$-0.477545\pi$
$991$	4.43775			0.140970			0.0704848	+	0.997513i	$0.477545\pi$
$992$	6.62103	+	2.15130i	0.210218	+	0.0683040i
$993$	6.74158	+	9.27899i	0.213938	+	0.294460i
$994$	−41.1328	−	29.8847i	−1.30465	−	0.947885i
$995$		0			0
$996$	−0.532477	−	1.63879i	−0.0168722	−	0.0519272i
$997$	0.00615442	−	0.00847083i	0.000194912	−	0.000268274i	−0.808920	−	0.587919i	$-0.799947\pi$
$997$	0.00615442	−	0.00847083i	0.000194912	−	0.000268274i	0.809114	+	0.587651i	$0.199947\pi$
$998$	−14.5845	−	20.0739i	−0.461665	−	0.635427i
$999$	2.72540	−	8.38793i	0.0862280	−	0.265382i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.bx.f.724.1		16
5.2	odd	4		825.2.n.g.526.2		8
5.3	odd	4		165.2.m.d.31.1	yes	8
5.4	even	2	inner	825.2.bx.f.724.4		16
11.5	even	5	inner	825.2.bx.f.49.4		16
15.8	even	4		495.2.n.a.361.2		8
55.7	even	20		9075.2.a.cm.1.2		4
55.18	even	20		1815.2.a.w.1.3		4
55.27	odd	20		825.2.n.g.676.2		8
55.37	odd	20		9075.2.a.di.1.3		4
55.38	odd	20		165.2.m.d.16.1	✓	8
55.48	odd	20		1815.2.a.p.1.2		4
55.49	even	10	inner	825.2.bx.f.49.1		16
165.38	even	20		495.2.n.a.181.2		8
165.128	odd	20		5445.2.a.bf.1.2		4
165.158	even	20		5445.2.a.bt.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.d.16.1	✓	8	55.38	odd	20
165.2.m.d.31.1	yes	8	5.3	odd	4
495.2.n.a.181.2		8	165.38	even	20
495.2.n.a.361.2		8	15.8	even	4
825.2.n.g.526.2		8	5.2	odd	4
825.2.n.g.676.2		8	55.27	odd	20
825.2.bx.f.49.1		16	55.49	even	10	inner
825.2.bx.f.49.4		16	11.5	even	5	inner
825.2.bx.f.724.1		16	1.1	even	1	trivial
825.2.bx.f.724.4		16	5.4	even	2	inner
1815.2.a.p.1.2		4	55.48	odd	20
1815.2.a.w.1.3		4	55.18	even	20
5445.2.a.bf.1.2		4	165.128	odd	20
5445.2.a.bt.1.3		4	165.158	even	20
9075.2.a.cm.1.2		4	55.7	even	20
9075.2.a.di.1.3		4	55.37	odd	20

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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.bx (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.40496 - 0.456498i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.147481 + 0.107152i) q^{4} +(-0.456498 - 1.40496i) q^{6} +(-1.34895 + 1.85666i) q^{7} +(1.57833 + 2.17239i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-1.40496 - 0.456498i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.147481 + 0.107152i) q^{4} +(-0.456498 - 1.40496i) q^{6} +(-1.34895 + 1.85666i) q^{7} +(1.57833 + 2.17239i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-3.12020 - 1.12443i) q^{11} +0.182297i q^{12} +(2.03600 + 0.661536i) q^{13} +(2.74278 - 1.99274i) q^{14} +(-1.33846 - 4.11937i) q^{16} +(-0.517799 + 0.168243i) q^{17} +(0.868312 - 1.19513i) q^{18} +(-1.76552 + 1.28272i) q^{19} -2.29496 q^{21} +(3.87045 + 3.00415i) q^{22} -2.03908i q^{23} +(-0.829779 + 2.55380i) q^{24} +(-2.55850 - 1.85886i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(-0.397889 + 0.129282i) q^{28} +(-8.04603 - 5.84578i) q^{29} +(2.09249 - 6.44002i) q^{31} +1.02811i q^{32} +(-0.924324 - 3.18522i) q^{33} +0.804288 q^{34} +(-0.147481 + 0.107152i) q^{36} +(-5.18403 + 7.13520i) q^{37} +(3.06604 - 0.996215i) q^{38} +(0.661536 + 2.03600i) q^{39} +(1.47470 - 1.07143i) q^{41} +(3.22433 + 1.04765i) q^{42} +0.620713i q^{43} +(-0.339687 - 0.500167i) q^{44} +(-0.930836 + 2.86482i) q^{46} +(0.222188 + 0.305816i) q^{47} +(2.54591 - 3.50415i) q^{48} +(0.535571 + 1.64832i) q^{49} +(-0.440466 - 0.320017i) q^{51} +(0.229387 + 0.315724i) q^{52} +(-11.0257 - 3.58246i) q^{53} +1.47726 q^{54} -6.16248 q^{56} +(-2.07549 - 0.674367i) q^{57} +(8.63574 + 11.8861i) q^{58} +(-6.53518 - 4.74808i) q^{59} +(2.69647 + 8.29887i) q^{61} +(-5.87971 + 8.09273i) q^{62} +(-1.34895 - 1.85666i) q^{63} +(-2.20760 + 6.79429i) q^{64} +(-0.155412 + 4.89705i) q^{66} -9.75802i q^{67} +(-0.0943932 - 0.0306702i) q^{68} +(1.64965 - 1.19854i) q^{69} +(-4.63426 - 14.2628i) q^{71} +(-2.55380 + 0.829779i) q^{72} +(-4.61907 + 6.35761i) q^{73} +(10.5405 - 7.65815i) q^{74} -0.397826 q^{76} +(6.29667 - 4.27637i) q^{77} -3.16248i q^{78} +(2.85054 - 8.77306i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-2.56099 + 0.832118i) q^{82} +(-8.98969 + 2.92093i) q^{83} +(-0.338464 - 0.245909i) q^{84} +(0.283354 - 0.872075i) q^{86} -9.94544i q^{87} +(-2.48201 - 8.55302i) q^{88} -0.583290 q^{89} +(-3.97470 + 2.88779i) q^{91} +(0.218490 - 0.300726i) q^{92} +(6.44002 - 2.09249i) q^{93} +(-0.172561 - 0.531087i) q^{94} +(-0.831757 + 0.604307i) q^{96} +(-5.11479 - 1.66190i) q^{97} -2.56031i q^{98} +(2.03359 - 2.62002i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} + 8 q^{6} + 4 q^{9}+O(q^{10}) \) 16 * q - 4 * q^4 + 8 * q^6 + 4 * q^9	\( 16 q - 4 q^{4} + 8 q^{6} + 4 q^{9} + 6 q^{11} + 8 q^{14} - 24 q^{16} - 4 q^{19} - 24 q^{21} - 8 q^{24} + 4 q^{26} - 20 q^{29} + 38 q^{31} + 12 q^{34} + 4 q^{36} + 8 q^{39} - 18 q^{41} - 34 q^{44} - 44 q^{46} - 2 q^{49} + 20 q^{51} + 12 q^{54} - 32 q^{56} - 26 q^{59} + 26 q^{61} - 78 q^{64} - 22 q^{66} - 18 q^{69} - 22 q^{71} + 86 q^{74} - 76 q^{76} + 44 q^{79} - 4 q^{81} - 8 q^{84} + 40 q^{86} + 40 q^{89} - 22 q^{91} + 70 q^{94} - 16 q^{96} + 14 q^{99}+O(q^{100}) \) 16 * q - 4 * q^4 + 8 * q^6 + 4 * q^9 + 6 * q^11 + 8 * q^14 - 24 * q^16 - 4 * q^19 - 24 * q^21 - 8 * q^24 + 4 * q^26 - 20 * q^29 + 38 * q^31 + 12 * q^34 + 4 * q^36 + 8 * q^39 - 18 * q^41 - 34 * q^44 - 44 * q^46 - 2 * q^49 + 20 * q^51 + 12 * q^54 - 32 * q^56 - 26 * q^59 + 26 * q^61 - 78 * q^64 - 22 * q^66 - 18 * q^69 - 22 * q^71 + 86 * q^74 - 76 * q^76 + 44 * q^79 - 4 * q^81 - 8 * q^84 + 40 * q^86 + 40 * q^89 - 22 * q^91 + 70 * q^94 - 16 * q^96 + 14 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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