LMFDB - Embedded newform 775.2.k.c.326.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [775,2,Mod(101,775)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("775.101"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(775, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.k (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			326.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	775.326
Dual form			775.2.k.c.126.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.30902 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(0.190983 - 0.587785i) q^{4} -1.61803 q^{6} +(-0.927051 + 2.85317i) q^{7} +(0.690983 + 2.12663i) q^{8} +(-0.618034 - 1.90211i) q^{9} +(-1.61803 + 4.97980i) q^{11} +(-0.500000 + 0.363271i) q^{12} +(-1.50000 - 1.08981i) q^{13} +(1.50000 + 4.61653i) q^{14} +(3.92705 + 2.85317i) q^{16} +(1.30902 + 4.02874i) q^{17} +(-2.61803 - 1.90211i) q^{18} +(-4.04508 + 2.93893i) q^{19} +(2.42705 - 1.76336i) q^{21} +(2.61803 + 8.05748i) q^{22} +(-1.07295 - 3.30220i) q^{23} +(0.690983 - 2.12663i) q^{24} -3.00000 q^{26} +(-1.54508 + 4.75528i) q^{27} +(1.50000 + 1.08981i) q^{28} +(5.16312 - 3.75123i) q^{29} +(0.0450850 + 5.56758i) q^{31} +3.38197 q^{32} +(4.23607 - 3.07768i) q^{33} +(5.54508 + 4.02874i) q^{34} -1.23607 q^{36} +4.23607 q^{37} +(-2.50000 + 7.69421i) q^{38} +(0.572949 + 1.76336i) q^{39} +(2.00000 - 1.45309i) q^{41} +(1.50000 - 4.61653i) q^{42} +(-1.92705 + 1.40008i) q^{43} +(2.61803 + 1.90211i) q^{44} +(-4.54508 - 3.30220i) q^{46} +(-4.54508 - 3.30220i) q^{47} +(-1.50000 - 4.61653i) q^{48} +(-1.61803 - 1.17557i) q^{49} +(1.30902 - 4.02874i) q^{51} +(-0.927051 + 0.673542i) q^{52} +(-0.218847 - 0.673542i) q^{53} +(2.50000 + 7.69421i) q^{54} -6.70820 q^{56} +5.00000 q^{57} +(3.19098 - 9.82084i) q^{58} +(-0.427051 - 0.310271i) q^{59} +10.9443 q^{61} +(5.35410 + 7.24518i) q^{62} +6.00000 q^{63} +(-3.42705 + 2.48990i) q^{64} +(2.61803 - 8.05748i) q^{66} -0.236068 q^{67} +2.61803 q^{68} +(-1.07295 + 3.30220i) q^{69} +(-3.42705 - 10.5474i) q^{71} +(3.61803 - 2.62866i) q^{72} +(-3.57295 + 10.9964i) q^{73} +(5.54508 - 4.02874i) q^{74} +(0.954915 + 2.93893i) q^{76} +(-12.7082 - 9.23305i) q^{77} +(2.42705 + 1.76336i) q^{78} +(-0.809017 + 0.587785i) q^{81} +(1.23607 - 3.80423i) q^{82} +(5.73607 - 4.16750i) q^{83} +(-0.572949 - 1.76336i) q^{84} +(-1.19098 + 3.66547i) q^{86} -6.38197 q^{87} -11.7082 q^{88} +(-2.66312 + 8.19624i) q^{89} +(4.50000 - 3.26944i) q^{91} -2.14590 q^{92} +(3.23607 - 4.53077i) q^{93} -9.09017 q^{94} +(-2.73607 - 1.98787i) q^{96} +(5.78115 - 17.7926i) q^{97} -3.23607 q^{98} +10.4721 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} - q^{3} + 3 q^{4} - 2 q^{6} + 3 q^{7} + 5 q^{8} + 2 q^{9} - 2 q^{11} - 2 q^{12} - 6 q^{13} + 6 q^{14} + 9 q^{16} + 3 q^{17} - 6 q^{18} - 5 q^{19} + 3 q^{21} + 6 q^{22} - 11 q^{23} + 5 q^{24}+ \cdots + 24 q^{99}+O(q^{100}) $ 4 * q + 3 * q^2 - q^3 + 3 * q^4 - 2 * q^6 + 3 * q^7 + 5 * q^8 + 2 * q^9 - 2 * q^11 - 2 * q^12 - 6 * q^13 + 6 * q^14 + 9 * q^16 + 3 * q^17 - 6 * q^18 - 5 * q^19 + 3 * q^21 + 6 * q^22 - 11 * q^23 + 5 * q^24 - 12 * q^26 + 5 * q^27 + 6 * q^28 + 5 * q^29 - 11 * q^31 + 18 * q^32 + 8 * q^33 + 11 * q^34 + 4 * q^36 + 8 * q^37 - 10 * q^38 + 9 * q^39 + 8 * q^41 + 6 * q^42 - q^43 + 6 * q^44 - 7 * q^46 - 7 * q^47 - 6 * q^48 - 2 * q^49 + 3 * q^51 + 3 * q^52 - 21 * q^53 + 10 * q^54 + 20 * q^57 + 15 * q^58 + 5 * q^59 + 8 * q^61 + 8 * q^62 + 24 * q^63 - 7 * q^64 + 6 * q^66 + 8 * q^67 + 6 * q^68 - 11 * q^69 - 7 * q^71 + 10 * q^72 - 21 * q^73 + 11 * q^74 + 15 * q^76 - 24 * q^77 + 3 * q^78 - q^81 - 4 * q^82 + 14 * q^83 - 9 * q^84 - 7 * q^86 - 30 * q^87 - 20 * q^88 + 5 * q^89 + 18 * q^91 - 22 * q^92 + 4 * q^93 - 14 * q^94 - 2 * q^96 + 3 * q^97 - 4 * q^98 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/775\mathbb{Z}\right)^\times$.

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	1.30902	−	0.951057i	0.925615	−	0.672499i	−0.0193004	−	0.999814i	$-0.506144\pi$
$2$	1.30902	−	0.951057i	0.925615	−	0.672499i	0.944915	+	0.327315i	$0.106144\pi$
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i	0.329218	−	0.944254i	$-0.393215\pi$
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i	−0.796305	+	0.604896i	$0.793215\pi$
$4$	0.190983	−	0.587785i	0.0954915	−	0.293893i
$5$		0			0
$5$		0			0
$6$	−1.61803			−0.660560
$7$	−0.927051	+	2.85317i	−0.350392	+	1.07840i	0.608241	+	0.793752i	$0.291875\pi$
$7$	−0.927051	+	2.85317i	−0.350392	+	1.07840i	−0.958633	+	0.284644i	$0.908125\pi$
$8$	0.690983	+	2.12663i	0.244299	+	0.751876i
$9$	−0.618034	−	1.90211i	−0.206011	−	0.634038i
$10$		0			0
$11$	−1.61803	+	4.97980i	−0.487856	+	1.50147i	0.339946	+	0.940445i	$0.389591\pi$
$11$	−1.61803	+	4.97980i	−0.487856	+	1.50147i	−0.827802	+	0.561020i	$0.810409\pi$
$12$	−0.500000	+	0.363271i	−0.144338	+	0.104867i
$13$	−1.50000	−	1.08981i	−0.416025	−	0.302260i	0.360011	−	0.932948i	$-0.382773\pi$
$13$	−1.50000	−	1.08981i	−0.416025	−	0.302260i	−0.776037	+	0.630688i	$0.782773\pi$
$14$	1.50000	+	4.61653i	0.400892	+	1.23382i
$15$		0			0
$16$	3.92705	+	2.85317i	0.981763	+	0.713292i
$17$	1.30902	+	4.02874i	0.317483	+	0.977113i	0.974720	+	0.223429i	$0.0717251\pi$
$17$	1.30902	+	4.02874i	0.317483	+	0.977113i	−0.657237	+	0.753684i	$0.728275\pi$
$18$	−2.61803	−	1.90211i	−0.617077	−	0.448332i
$19$	−4.04508	+	2.93893i	−0.928006	+	0.674236i	−0.945504	−	0.325611i	$-0.894430\pi$
$19$	−4.04508	+	2.93893i	−0.928006	+	0.674236i	0.0174977	+	0.999847i	$0.494430\pi$
$20$		0			0
$21$	2.42705	−	1.76336i	0.529626	−	0.384796i
$22$	2.61803	+	8.05748i	0.558167	+	1.71786i
$23$	−1.07295	−	3.30220i	−0.223725	−	0.688556i	−0.998418	−	0.0562184i	$-0.982096\pi$
$23$	−1.07295	−	3.30220i	−0.223725	−	0.688556i	0.774693	−	0.632337i	$-0.217904\pi$
$24$	0.690983	−	2.12663i	0.141046	−	0.434096i
$25$		0			0
$26$	−3.00000			−0.588348
$27$	−1.54508	+	4.75528i	−0.297352	+	0.915155i
$28$	1.50000	+	1.08981i	0.283473	+	0.205955i
$29$	5.16312	−	3.75123i	0.958767	−	0.696585i	0.00590304	−	0.999983i	$-0.498121\pi$
$29$	5.16312	−	3.75123i	0.958767	−	0.696585i	0.952864	+	0.303397i	$0.0981210\pi$
$30$		0			0
$31$	0.0450850	+	5.56758i	0.00809750	+	0.999967i
$31$	0.0450850	+	5.56758i	0.00809750	+	0.999967i
$32$	3.38197			0.597853
$33$	4.23607	−	3.07768i	0.737405	−	0.535756i
$34$	5.54508	+	4.02874i	0.950974	+	0.690923i
$35$		0			0
$36$	−1.23607			−0.206011
$37$	4.23607			0.696405			0.348203	−	0.937419i	$-0.386792\pi$
$37$	4.23607			0.696405			0.348203	+	0.937419i	$0.386792\pi$
$38$	−2.50000	+	7.69421i	−0.405554	+	1.24817i
$39$	0.572949	+	1.76336i	0.0917453	+	0.282363i
$40$		0			0
$41$	2.00000	−	1.45309i	0.312348	−	0.226934i	−0.420556	−	0.907267i	$-0.638165\pi$
$41$	2.00000	−	1.45309i	0.312348	−	0.226934i	0.732903	+	0.680333i	$0.238165\pi$
$42$	1.50000	−	4.61653i	0.231455	−	0.712345i
$43$	−1.92705	+	1.40008i	−0.293873	+	0.213511i	−0.724946	−	0.688806i	$-0.758135\pi$
$43$	−1.92705	+	1.40008i	−0.293873	+	0.213511i	0.431073	+	0.902317i	$0.358135\pi$
$44$	2.61803	+	1.90211i	0.394683	+	0.286754i
$45$		0			0
$46$	−4.54508	−	3.30220i	−0.670136	−	0.486882i
$47$	−4.54508	−	3.30220i	−0.662969	−	0.481675i	0.204695	−	0.978826i	$-0.434380\pi$
$47$	−4.54508	−	3.30220i	−0.662969	−	0.481675i	−0.867664	+	0.497151i	$0.834380\pi$
$48$	−1.50000	−	4.61653i	−0.216506	−	0.666338i
$49$	−1.61803	−	1.17557i	−0.231148	−	0.167939i
$50$		0			0
$51$	1.30902	−	4.02874i	0.183299	−	0.564136i
$52$	−0.927051	+	0.673542i	−0.128559	+	0.0934035i
$53$	−0.218847	−	0.673542i	−0.0300610	−	0.0925181i	0.934900	−	0.354910i	$-0.115489\pi$
$53$	−0.218847	−	0.673542i	−0.0300610	−	0.0925181i	−0.964961	+	0.262392i	$0.915489\pi$
$54$	2.50000	+	7.69421i	0.340207	+	1.04705i
$55$		0			0
$56$	−6.70820			−0.896421
$57$	5.00000			0.662266
$58$	3.19098	−	9.82084i	0.418997	−	1.28954i
$59$	−0.427051	−	0.310271i	−0.0555973	−	0.0403938i	0.559640	−	0.828736i	$-0.310940\pi$
$59$	−0.427051	−	0.310271i	−0.0555973	−	0.0403938i	−0.615237	+	0.788342i	$0.710940\pi$
$60$		0			0
$61$	10.9443			1.40127			0.700635	−	0.713520i	$-0.252900\pi$
$61$	10.9443			1.40127			0.700635	+	0.713520i	$0.252900\pi$
$62$	5.35410	+	7.24518i	0.679972	+	0.920139i
$63$	6.00000			0.755929
$64$	−3.42705	+	2.48990i	−0.428381	+	0.311237i
$65$		0			0
$66$	2.61803	−	8.05748i	0.322258	−	0.991807i
$67$	−0.236068			−0.0288403			−0.0144201	−	0.999896i	$-0.504590\pi$
$67$	−0.236068			−0.0288403			−0.0144201	+	0.999896i	$0.504590\pi$
$68$	2.61803			0.317483
$69$	−1.07295	+	3.30220i	−0.129168	+	0.397538i
$70$		0			0
$71$	−3.42705	−	10.5474i	−0.406716	−	1.25174i	−0.919454	−	0.393198i	$-0.871369\pi$
$71$	−3.42705	−	10.5474i	−0.406716	−	1.25174i	0.512738	−	0.858545i	$-0.328631\pi$
$72$	3.61803	−	2.62866i	0.426389	−	0.309790i
$73$	−3.57295	+	10.9964i	−0.418182	+	1.28703i	0.491192	+	0.871052i	$0.336562\pi$
$73$	−3.57295	+	10.9964i	−0.418182	+	1.28703i	−0.909374	+	0.415980i	$0.863438\pi$
$74$	5.54508	−	4.02874i	0.644603	−	0.468332i
$75$		0			0
$76$	0.954915	+	2.93893i	0.109536	+	0.337118i
$77$	−12.7082	−	9.23305i	−1.44823	−	1.05220i
$78$	2.42705	+	1.76336i	0.274809	+	0.199661i
$79$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$79$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	1.23607	−	3.80423i	0.136501	−	0.420106i
$83$	5.73607	−	4.16750i	0.629615	−	0.457442i	−0.226652	−	0.973976i	$-0.572778\pi$
$83$	5.73607	−	4.16750i	0.629615	−	0.457442i	0.856267	+	0.516534i	$0.172778\pi$
$84$	−0.572949	−	1.76336i	−0.0625139	−	0.192398i
$85$		0			0
$86$	−1.19098	+	3.66547i	−0.128427	+	0.395258i
$87$	−6.38197			−0.684219
$88$	−11.7082			−1.24810
$89$	−2.66312	+	8.19624i	−0.282290	+	0.868799i	0.704908	+	0.709299i	$0.250988\pi$
$89$	−2.66312	+	8.19624i	−0.282290	+	0.868799i	−0.987198	+	0.159500i	$0.949012\pi$
$90$		0			0
$91$	4.50000	−	3.26944i	0.471728	−	0.342731i
$92$	−2.14590			−0.223725
$93$	3.23607	−	4.53077i	0.335565	−	0.469819i
$94$	−9.09017			−0.937579
$95$		0			0
$96$	−2.73607	−	1.98787i	−0.279249	−	0.202886i
$97$	5.78115	−	17.7926i	0.586987	−	1.80656i	−0.00415240	−	0.999991i	$-0.501322\pi$
$97$	5.78115	−	17.7926i	0.586987	−	1.80656i	0.591140	−	0.806569i	$-0.298678\pi$
$98$	−3.23607			−0.326892
$99$	10.4721			1.05249
$100$		0			0
$101$	2.85410	+	8.78402i	0.283994	+	0.874043i	0.986698	+	0.162561i	$0.0519755\pi$
$101$	2.85410	+	8.78402i	0.283994	+	0.874043i	−0.702705	+	0.711482i	$0.748024\pi$
$102$	−2.11803	−	6.51864i	−0.209717	−	0.645441i
$103$	−5.54508	+	4.02874i	−0.546373	+	0.396964i	−0.826447	−	0.563015i	$-0.809641\pi$
$103$	−5.54508	+	4.02874i	−0.546373	+	0.396964i	0.280073	+	0.959979i	$0.409641\pi$
$104$	1.28115	−	3.94298i	0.125627	−	0.386641i
$105$		0			0
$106$	−0.927051	−	0.673542i	−0.0900432	−	0.0654202i
$107$	3.11803	+	9.59632i	0.301432	+	0.927711i	0.980985	+	0.194085i	$0.0621738\pi$
$107$	3.11803	+	9.59632i	0.301432	+	0.927711i	−0.679553	+	0.733626i	$0.737826\pi$
$108$	2.50000	+	1.81636i	0.240563	+	0.174779i
$109$	−14.8992	−	10.8249i	−1.42708	−	1.03684i	−0.990551	−	0.137148i	$-0.956206\pi$
$109$	−14.8992	−	10.8249i	−1.42708	−	1.03684i	−0.436533	−	0.899688i	$-0.643794\pi$
$110$		0			0
$111$	−3.42705	−	2.48990i	−0.325281	−	0.236331i
$112$	−11.7812	+	8.55951i	−1.11321	+	0.808798i
$113$	−1.50000	+	4.61653i	−0.141108	+	0.434286i	−0.996490	−	0.0837117i	$-0.973323\pi$
$113$	−1.50000	+	4.61653i	−0.141108	+	0.434286i	0.855382	+	0.517998i	$0.173323\pi$
$114$	6.54508	−	4.75528i	0.613003	−	0.445373i
$115$		0			0
$116$	−1.21885	−	3.75123i	−0.113167	−	0.348293i
$117$	−1.14590	+	3.52671i	−0.105938	+	0.326045i
$118$	−0.854102			−0.0786265
$119$	−12.7082			−1.16496
$120$		0			0
$121$	−13.2812	−	9.64932i	−1.20738	−	0.877211i
$122$	14.3262	−	10.4086i	1.29704	−	0.942352i
$123$	−2.47214			−0.222905
$124$	3.28115	+	1.03681i	0.294656	+	0.0931086i
$125$		0			0
$126$	7.85410	−	5.70634i	0.699699	−	0.508361i
$127$	4.66312	+	3.38795i	0.413785	+	0.300632i	0.775132	−	0.631799i	$-0.217683\pi$
$127$	4.66312	+	3.38795i	0.413785	+	0.300632i	−0.361347	+	0.932431i	$0.617683\pi$
$128$	−4.20820	+	12.9515i	−0.371956	+	1.14476i
$129$	2.38197			0.209720
$130$		0			0
$131$	−3.42705	+	10.5474i	−0.299423	+	0.921529i	0.682277	+	0.731094i	$0.260990\pi$
$131$	−3.42705	+	10.5474i	−0.299423	+	0.921529i	−0.981700	+	0.190435i	$0.939010\pi$
$132$	−1.00000	−	3.07768i	−0.0870388	−	0.267878i
$133$	−4.63525	−	14.2658i	−0.401928	−	1.23701i
$134$	−0.309017	+	0.224514i	−0.0266950	+	0.0193951i
$135$		0			0
$136$	−7.66312	+	5.56758i	−0.657107	+	0.477416i
$137$	2.00000	+	1.45309i	0.170872	+	0.124145i	0.669934	−	0.742420i	$-0.266322\pi$
$137$	2.00000	+	1.45309i	0.170872	+	0.124145i	−0.499063	+	0.866566i	$0.666322\pi$
$138$	1.73607	+	5.34307i	0.147784	+	0.454832i
$139$	0.690983	+	0.502029i	0.0586084	+	0.0425815i	0.616704	−	0.787195i	$-0.288468\pi$
$139$	0.690983	+	0.502029i	0.0586084	+	0.0425815i	−0.558095	+	0.829777i	$0.688468\pi$
$140$		0			0
$141$	1.73607	+	5.34307i	0.146203	+	0.449967i
$142$	−14.5172	−	10.5474i	−1.21826	−	0.885116i
$143$	7.85410	−	5.70634i	0.656793	−	0.477188i
$144$	3.00000	−	9.23305i	0.250000	−	0.769421i
$145$		0			0
$146$	5.78115	+	17.7926i	0.478452	+	1.47252i
$147$	0.618034	+	1.90211i	0.0509746	+	0.156884i
$148$	0.809017	−	2.48990i	0.0665008	−	0.204668i
$149$	12.0344			0.985900			0.492950	−	0.870058i	$-0.335919\pi$
$149$	12.0344			0.985900			0.492950	+	0.870058i	$0.335919\pi$
$150$		0			0
$151$	5.71885	−	17.6008i	0.465393	−	1.43233i	−0.393094	−	0.919498i	$-0.628595\pi$
$151$	5.71885	−	17.6008i	0.465393	−	1.43233i	0.858487	−	0.512835i	$-0.171405\pi$
$152$	−9.04508	−	6.57164i	−0.733653	−	0.533030i
$153$	6.85410	−	4.97980i	0.554121	−	0.402593i
$154$	−25.4164			−2.04811
$155$		0			0
$156$	1.14590			0.0917453
$157$	−3.00000	+	2.17963i	−0.239426	+	0.173953i	−0.701028	−	0.713134i	$-0.747275\pi$
$157$	−3.00000	+	2.17963i	−0.239426	+	0.173953i	0.461601	+	0.887087i	$0.347275\pi$
$158$		0			0
$159$	−0.218847	+	0.673542i	−0.0173557	+	0.0534154i
$160$		0			0
$161$	10.4164			0.820928
$162$	−0.500000	+	1.53884i	−0.0392837	+	0.120903i
$163$	−0.218847	−	0.673542i	−0.0171414	−	0.0527559i	0.942120	−	0.335276i	$-0.108830\pi$
$163$	−0.218847	−	0.673542i	−0.0171414	−	0.0527559i	−0.959261	+	0.282520i	$0.908830\pi$
$164$	−0.472136	−	1.45309i	−0.0368676	−	0.113467i
$165$		0			0
$166$	3.54508	−	10.9106i	0.275152	−	0.846831i
$167$	−3.85410	+	2.80017i	−0.298239	+	0.216684i	−0.726834	−	0.686813i	$-0.759009\pi$
$167$	−3.85410	+	2.80017i	−0.298239	+	0.216684i	0.428594	+	0.903497i	$0.359009\pi$
$168$	5.42705	+	3.94298i	0.418706	+	0.304208i
$169$	−2.95492	−	9.09429i	−0.227301	−	0.699561i
$170$		0			0
$171$	8.09017	+	5.87785i	0.618671	+	0.449491i
$172$	0.454915	+	1.40008i	0.0346869	+	0.106755i
$173$	9.78115	+	7.10642i	0.743647	+	0.540291i	0.893851	−	0.448364i	$-0.147993\pi$
$173$	9.78115	+	7.10642i	0.743647	+	0.540291i	−0.150204	+	0.988655i	$0.547993\pi$
$174$	−8.35410	+	6.06961i	−0.633323	+	0.460136i
$175$		0			0
$176$	−20.5623	+	14.9394i	−1.54994	+	1.12610i
$177$	0.163119	+	0.502029i	0.0122608	+	0.0377348i
$178$	4.30902	+	13.2618i	0.322974	+	0.994013i
$179$	−1.48278	+	4.56352i	−0.110828	+	0.341094i	−0.991054	−	0.133461i	$-0.957391\pi$
$179$	−1.48278	+	4.56352i	−0.110828	+	0.341094i	0.880226	+	0.474555i	$0.157391\pi$
$180$		0			0
$181$	17.0000			1.26360			0.631800	−	0.775131i	$-0.282316\pi$
$181$	17.0000			1.26360			0.631800	+	0.775131i	$0.282316\pi$
$182$	2.78115	−	8.55951i	0.206153	−	0.634473i
$183$	−8.85410	−	6.43288i	−0.654514	−	0.475532i
$184$	6.28115	−	4.56352i	0.463053	−	0.336428i
$185$		0			0
$186$	−0.0729490	−	9.00854i	−0.00534888	−	0.660538i
$187$	−22.1803			−1.62199
$188$	−2.80902	+	2.04087i	−0.204869	+	0.148846i
$189$	−12.1353	−	8.81678i	−0.882710	−	0.641326i
$190$		0			0
$191$	−4.90983			−0.355263			−0.177631	−	0.984097i	$-0.556843\pi$
$191$	−4.90983			−0.355263			−0.177631	+	0.984097i	$0.556843\pi$
$192$	4.23607			0.305712
$193$	1.42705	−	4.39201i	0.102721	−	0.316144i	−0.886468	−	0.462791i	$-0.846848\pi$
$193$	1.42705	−	4.39201i	0.102721	−	0.316144i	0.989189	+	0.146647i	$0.0468481\pi$
$194$	−9.35410	−	28.7890i	−0.671585	−	2.06693i
$195$		0			0
$196$	−1.00000	+	0.726543i	−0.0714286	+	0.0518959i
$197$	3.21885	−	9.90659i	0.229333	−	0.705815i	−0.768489	−	0.639863i	$-0.778991\pi$
$197$	3.21885	−	9.90659i	0.229333	−	0.705815i	0.997823	−	0.0659530i	$-0.0210087\pi$
$198$	13.7082	−	9.95959i	0.974200	−	0.707797i
$199$	10.7533	+	7.81272i	0.762280	+	0.553829i	0.899609	−	0.436696i	$-0.143852\pi$
$199$	10.7533	+	7.81272i	0.762280	+	0.553829i	−0.137329	+	0.990526i	$0.543852\pi$
$200$		0			0
$201$	0.190983	+	0.138757i	0.0134709	+	0.00978718i
$202$	12.0902	+	8.78402i	0.850661	+	0.618042i
$203$	5.91641	+	18.2088i	0.415250	+	1.27801i
$204$	−2.11803	−	1.53884i	−0.148292	−	0.107740i
$205$		0			0
$206$	−3.42705	+	10.5474i	−0.238774	+	0.734871i
$207$	−5.61803	+	4.08174i	−0.390480	+	0.283701i
$208$	−2.78115	−	8.55951i	−0.192838	−	0.593495i
$209$	−8.09017	−	24.8990i	−0.559609	−	1.72230i
$210$		0			0
$211$	−8.00000			−0.550743			−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000			−0.550743			−0.275371	+	0.961338i	$0.588801\pi$
$212$	−0.437694			−0.0300610
$213$	−3.42705	+	10.5474i	−0.234818	+	0.722694i
$214$	13.2082	+	9.59632i	0.902894	+	0.655991i
$215$		0			0
$216$	−11.1803			−0.760726
$217$	−15.9271	−	5.03280i	−1.08120	−	0.341649i
$218$	−29.7984			−2.01820
$219$	9.35410	−	6.79615i	0.632092	−	0.459241i
$220$		0			0
$221$	2.42705	−	7.46969i	0.163261	−	0.502466i
$222$	−6.85410			−0.460017
$223$	12.7082			0.851004			0.425502	−	0.904957i	$-0.360097\pi$
$223$	12.7082			0.851004			0.425502	+	0.904957i	$0.360097\pi$
$224$	−3.13525	+	9.64932i	−0.209483	+	0.644722i
$225$		0			0
$226$	2.42705	+	7.46969i	0.161445	+	0.496877i
$227$	17.5902	−	12.7800i	1.16750	−	0.848239i	0.176793	−	0.984248i	$-0.443428\pi$
$227$	17.5902	−	12.7800i	1.16750	−	0.848239i	0.990708	+	0.136009i	$0.0434277\pi$
$228$	0.954915	−	2.93893i	0.0632408	−	0.194635i
$229$	2.23607	−	1.62460i	0.147764	−	0.107356i	−0.511447	−	0.859315i	$-0.670890\pi$
$229$	2.23607	−	1.62460i	0.147764	−	0.107356i	0.659211	+	0.751958i	$0.270890\pi$
$230$		0			0
$231$	4.85410	+	14.9394i	0.319376	+	0.982940i
$232$	11.5451	+	8.38800i	0.757972	+	0.550699i
$233$	−4.69098	−	3.40820i	−0.307317	−	0.223279i	0.423428	−	0.905930i	$-0.360827\pi$
$233$	−4.69098	−	3.40820i	−0.307317	−	0.223279i	−0.730744	+	0.682651i	$0.760827\pi$
$234$	1.85410	+	5.70634i	0.121206	+	0.373035i
$235$		0			0
$236$	−0.263932	+	0.191758i	−0.0171805	+	0.0124824i
$237$		0			0
$238$	−16.6353	+	12.0862i	−1.07830	+	0.783433i
$239$	4.14590	+	12.7598i	0.268176	+	0.825360i	0.990945	+	0.134271i	$0.0428691\pi$
$239$	4.14590	+	12.7598i	0.268176	+	0.825360i	−0.722769	+	0.691090i	$0.757131\pi$
$240$		0			0
$241$	−5.39919	+	16.6170i	−0.347792	+	1.07039i	0.612280	+	0.790641i	$0.290253\pi$
$241$	−5.39919	+	16.6170i	−0.347792	+	1.07039i	−0.960072	+	0.279753i	$0.909747\pi$
$242$	−26.5623			−1.70749
$243$	16.0000			1.02640
$244$	2.09017	−	6.43288i	0.133809	−	0.411823i
$245$		0			0
$246$	−3.23607	+	2.35114i	−0.206324	+	0.149903i
$247$	9.27051			0.589868
$248$	−11.8090	+	3.94298i	−0.749873	+	0.250380i
$249$	−7.09017			−0.449321
$250$		0			0
$251$	13.7082	+	9.95959i	0.865254	+	0.628644i	0.929309	−	0.369302i	$-0.120403\pi$
$251$	13.7082	+	9.95959i	0.865254	+	0.628644i	−0.0640551	+	0.997946i	$0.520403\pi$
$252$	1.14590	−	3.52671i	0.0721848	−	0.222162i
$253$	18.1803			1.14299
$254$	9.32624			0.585180
$255$		0			0
$256$	4.19098	+	12.8985i	0.261936	+	0.806157i
$257$	7.85410	+	24.1724i	0.489925	+	1.50784i	0.824718	+	0.565544i	$0.191334\pi$
$257$	7.85410	+	24.1724i	0.489925	+	1.50784i	−0.334793	+	0.942292i	$0.608666\pi$
$258$	3.11803	−	2.26538i	0.194120	−	0.141037i
$259$	−3.92705	+	12.0862i	−0.244015	+	0.751001i
$260$		0			0
$261$	−10.3262	−	7.50245i	−0.639178	−	0.464390i
$262$	5.54508	+	17.0660i	0.342576	+	1.05434i
$263$	11.1631	+	8.11048i	0.688347	+	0.500114i	0.876116	−	0.482100i	$-0.160126\pi$
$263$	11.1631	+	8.11048i	0.688347	+	0.500114i	−0.187769	+	0.982213i	$0.560126\pi$
$264$	9.47214	+	6.88191i	0.582970	+	0.423552i
$265$		0			0
$266$	−19.6353	−	14.2658i	−1.20391	−	0.874695i
$267$	6.97214	−	5.06555i	0.426688	−	0.310007i
$268$	−0.0450850	+	0.138757i	−0.00275400	+	0.00847595i
$269$	2.92705	−	2.12663i	0.178465	−	0.129663i	−0.494966	−	0.868912i	$-0.664820\pi$
$269$	2.92705	−	2.12663i	0.178465	−	0.129663i	0.673432	+	0.739249i	$0.264820\pi$
$270$		0			0
$271$	−3.26393	−	10.0453i	−0.198270	−	0.610212i	−0.999923	−	0.0124220i	$-0.996046\pi$
$271$	−3.26393	−	10.0453i	−0.198270	−	0.610212i	0.801653	−	0.597790i	$-0.203954\pi$
$272$	−6.35410	+	19.5559i	−0.385274	+	1.18575i
$273$	−5.56231			−0.336646
$274$	4.00000			0.241649
$275$		0			0
$276$	1.73607	+	1.26133i	0.104499	+	0.0759230i
$277$	−1.88197	+	1.36733i	−0.113076	+	0.0821548i	−0.642886	−	0.765962i	$-0.722263\pi$
$277$	−1.88197	+	1.36733i	−0.113076	+	0.0821548i	0.529810	+	0.848116i	$0.322263\pi$
$278$	1.38197			0.0828848
$279$	10.5623	−	3.52671i	0.632349	−	0.211139i
$280$		0			0
$281$	8.11803	−	5.89810i	0.484281	−	0.351851i	−0.318700	−	0.947856i	$-0.603246\pi$
$281$	8.11803	−	5.89810i	0.484281	−	0.351851i	0.802981	+	0.596005i	$0.203246\pi$
$282$	7.35410	+	5.34307i	0.437930	+	0.318175i
$283$	4.19098	−	12.8985i	0.249128	−	0.766737i	−0.745802	−	0.666168i	$-0.767933\pi$
$283$	4.19098	−	12.8985i	0.249128	−	0.766737i	0.994930	−	0.100570i	$-0.0320665\pi$
$284$	−6.85410			−0.406716
$285$		0			0
$286$	4.85410	−	14.9394i	0.287029	−	0.883385i
$287$	2.29180	+	7.05342i	0.135280	+	0.416350i
$288$	−2.09017	−	6.43288i	−0.123164	−	0.379061i
$289$	−0.763932	+	0.555029i	−0.0449372	+	0.0326488i
$290$		0			0
$291$	−15.1353	+	10.9964i	−0.887244	+	0.644621i
$292$	5.78115	+	4.20025i	0.338316	+	0.245801i
$293$	1.16312	+	3.57971i	0.0679501	+	0.209129i	0.979266	−	0.202579i	$-0.0649323\pi$
$293$	1.16312	+	3.57971i	0.0679501	+	0.209129i	−0.911316	+	0.411708i	$0.864932\pi$
$294$	2.61803	+	1.90211i	0.152687	+	0.110933i
$295$		0			0
$296$	2.92705	+	9.00854i	0.170131	+	0.523611i
$297$	−21.1803	−	15.3884i	−1.22901	−	0.892927i
$298$	15.7533	−	11.4454i	0.912564	−	0.663016i
$299$	−1.98936	+	6.12261i	−0.115047	+	0.354080i
$300$		0			0
$301$	−2.20820	−	6.79615i	−0.127279	−	0.391724i
$302$	−9.25329	−	28.4787i	−0.532467	−	1.63876i
$303$	2.85410	−	8.78402i	0.163964	−	0.504629i
$304$	−24.2705			−1.39201
$305$		0			0
$306$	4.23607	−	13.0373i	0.242160	−	0.745292i
$307$	−4.11803	−	2.99193i	−0.235029	−	0.170758i	0.464037	−	0.885816i	$-0.346400\pi$
$307$	−4.11803	−	2.99193i	−0.235029	−	0.170758i	−0.699066	+	0.715058i	$0.746400\pi$
$308$	−7.85410	+	5.70634i	−0.447529	+	0.325149i
$309$	6.85410			0.389916
$310$		0			0
$311$	7.52786			0.426866			0.213433	−	0.976958i	$-0.431535\pi$
$311$	7.52786			0.426866			0.213433	+	0.976958i	$0.431535\pi$
$312$	−3.35410	+	2.43690i	−0.189889	+	0.137962i
$313$	−2.61803	−	1.90211i	−0.147980	−	0.107514i	0.511332	−	0.859383i	$-0.329152\pi$
$313$	−2.61803	−	1.90211i	−0.147980	−	0.107514i	−0.659312	+	0.751870i	$0.729152\pi$
$314$	−1.85410	+	5.70634i	−0.104633	+	0.322027i
$315$		0			0
$316$		0			0
$317$	3.05573	−	9.40456i	0.171627	−	0.528213i	−0.827837	−	0.560969i	$-0.810429\pi$
$317$	3.05573	−	9.40456i	0.171627	−	0.528213i	0.999463	+	0.0327564i	$0.0104286\pi$
$318$	0.354102	+	1.08981i	0.0198571	+	0.0611137i
$319$	10.3262	+	31.7809i	0.578158	+	1.77939i
$320$		0			0
$321$	3.11803	−	9.59632i	0.174032	−	0.535614i
$322$	13.6353	−	9.90659i	0.759863	−	0.552073i
$323$	−17.1353	−	12.4495i	−0.953431	−	0.692708i
$324$	0.190983	+	0.587785i	0.0106102	+	0.0326547i
$325$		0			0
$326$	−0.927051	−	0.673542i	−0.0513446	−	0.0373040i
$327$	5.69098	+	17.5150i	0.314712	+	0.968584i
$328$	4.47214	+	3.24920i	0.246932	+	0.179407i
$329$	13.6353	−	9.90659i	0.751736	−	0.546168i
$330$		0			0
$331$	18.0172	−	13.0903i	0.990316	−	0.719507i	0.0303258	−	0.999540i	$-0.490346\pi$
$331$	18.0172	−	13.0903i	0.990316	−	0.719507i	0.959990	+	0.280033i	$0.0903455\pi$
$332$	−1.35410	−	4.16750i	−0.0743160	−	0.228721i
$333$	−2.61803	−	8.05748i	−0.143467	−	0.441547i
$334$	−2.38197	+	7.33094i	−0.130335	+	0.401131i
$335$		0			0
$336$	14.5623			0.794439
$337$	8.64590	−	26.6093i	0.470972	−	1.44950i	−0.380342	−	0.924846i	$-0.624194\pi$
$337$	8.64590	−	26.6093i	0.470972	−	1.44950i	0.851314	−	0.524657i	$-0.175806\pi$
$338$	−12.5172	−	9.09429i	−0.680847	−	0.494664i
$339$	3.92705	−	2.85317i	0.213288	−	0.154963i
$340$		0			0
$341$	−27.7984	−	8.78402i	−1.50537	−	0.475681i
$342$	16.1803			0.874933
$343$	−12.1353	+	8.81678i	−0.655242	+	0.476061i
$344$	−4.30902	−	3.13068i	−0.232327	−	0.168795i
$345$		0			0
$346$	19.5623			1.05168
$347$	32.1246			1.72454			0.862270	−	0.506449i	$-0.169042\pi$
$347$	32.1246			1.72454			0.862270	+	0.506449i	$0.169042\pi$
$348$	−1.21885	+	3.75123i	−0.0653371	+	0.201087i
$349$	−1.01722	−	3.13068i	−0.0544506	−	0.167582i	0.920133	−	0.391606i	$-0.128080\pi$
$349$	−1.01722	−	3.13068i	−0.0544506	−	0.167582i	−0.974584	+	0.224025i	$0.928080\pi$
$350$		0			0
$351$	7.50000	−	5.44907i	0.400320	−	0.290850i
$352$	−5.47214	+	16.8415i	−0.291666	+	0.897655i
$353$	−28.0066	+	20.3480i	−1.49064	+	1.08301i	−0.516711	+	0.856160i	$0.672844\pi$
$353$	−28.0066	+	20.3480i	−1.49064	+	1.08301i	−0.973929	+	0.226853i	$0.927156\pi$
$354$	0.690983	+	0.502029i	0.0367253	+	0.0266825i
$355$		0			0
$356$	4.30902	+	3.13068i	0.228377	+	0.165926i
$357$	10.2812	+	7.46969i	0.544136	+	0.395338i
$358$	2.39919	+	7.38394i	0.126801	+	0.390253i
$359$	7.82624	+	5.68609i	0.413053	+	0.300101i	0.774837	−	0.632161i	$-0.217832\pi$
$359$	7.82624	+	5.68609i	0.413053	+	0.300101i	−0.361784	+	0.932262i	$0.617832\pi$
$360$		0			0
$361$	1.85410	−	5.70634i	0.0975843	−	0.300334i
$362$	22.2533	−	16.1680i	1.16961	−	0.849769i
$363$	5.07295	+	15.6129i	0.266261	+	0.819466i
$364$	−1.06231	−	3.26944i	−0.0556800	−	0.171365i
$365$		0			0
$366$	−17.7082			−0.925623
$367$	2.72949			0.142478			0.0712391	−	0.997459i	$-0.477305\pi$
$367$	2.72949			0.142478			0.0712391	+	0.997459i	$0.477305\pi$
$368$	5.20820	−	16.0292i	0.271496	−	0.835580i
$369$	−4.00000	−	2.90617i	−0.208232	−	0.151289i
$370$		0			0
$371$	2.12461			0.110304
$372$	−2.04508	−	2.76741i	−0.106033	−	0.143484i
$373$	31.6525			1.63890			0.819452	−	0.573148i	$-0.194278\pi$
$373$	31.6525			1.63890			0.819452	+	0.573148i	$0.194278\pi$
$374$	−29.0344	+	21.0948i	−1.50134	+	1.09078i
$375$		0			0
$376$	3.88197	−	11.9475i	0.200197	−	0.616143i
$377$	−11.8328			−0.609421
$378$	−24.2705			−1.24834
$379$	2.60081	−	8.00448i	0.133595	−	0.411162i	−0.861774	−	0.507292i	$-0.830646\pi$
$379$	2.60081	−	8.00448i	0.133595	−	0.411162i	0.995369	+	0.0961299i	$0.0306464\pi$
$380$		0			0
$381$	−1.78115	−	5.48183i	−0.0912512	−	0.280842i
$382$	−6.42705	+	4.66953i	−0.328837	+	0.238914i
$383$	3.13525	−	9.64932i	0.160204	−	0.493057i	−0.838447	−	0.544983i	$-0.816536\pi$
$383$	3.13525	−	9.64932i	0.160204	−	0.493057i	0.998651	+	0.0519260i	$0.0165360\pi$
$384$	11.0172	−	8.00448i	0.562220	−	0.408477i
$385$		0			0
$386$	−2.30902	−	7.10642i	−0.117526	−	0.361707i
$387$	3.85410	+	2.80017i	0.195915	+	0.142341i
$388$	−9.35410	−	6.79615i	−0.474883	−	0.345022i
$389$	8.98278	+	27.6462i	0.455445	+	1.40172i	0.870612	+	0.491970i	$0.163723\pi$
$389$	8.98278	+	27.6462i	0.455445	+	1.40172i	−0.415167	+	0.909745i	$0.636277\pi$
$390$		0			0
$391$	11.8992	−	8.64527i	0.601768	−	0.437210i
$392$	1.38197	−	4.25325i	0.0697998	−	0.214822i
$393$	8.97214	−	6.51864i	0.452584	−	0.328822i
$394$	−5.20820	−	16.0292i	−0.262386	−	0.807540i
$395$		0			0
$396$	2.00000	−	6.15537i	0.100504	−	0.309319i
$397$	−29.7082			−1.49101			−0.745506	−	0.666499i	$-0.767792\pi$
$397$	−29.7082			−1.49101			−0.745506	+	0.666499i	$0.767792\pi$
$398$	21.5066			1.07803
$399$	−4.63525	+	14.2658i	−0.232053	+	0.714186i
$400$		0			0
$401$	−19.2812	+	14.0086i	−0.962855	+	0.699555i	−0.953812	−	0.300404i	$-0.902878\pi$
$401$	−19.2812	+	14.0086i	−0.962855	+	0.699555i	−0.00904282	+	0.999959i	$0.502878\pi$
$402$	0.381966			0.0190507
$403$	6.00000	−	8.40051i	0.298881	−	0.418459i
$404$	5.70820			0.283994
$405$		0			0
$406$	25.0623	+	18.2088i	1.24382	+	0.903689i
$407$	−6.85410	+	21.0948i	−0.339745	+	1.04563i
$408$	9.47214			0.468941
$409$	16.1803			0.800066			0.400033	−	0.916501i	$-0.368999\pi$
$409$	16.1803			0.800066			0.400033	+	0.916501i	$0.368999\pi$
$410$		0			0
$411$	−0.763932	−	2.35114i	−0.0376820	−	0.115973i
$412$	1.30902	+	4.02874i	0.0644906	+	0.198482i
$413$	1.28115	−	0.930812i	0.0630414	−	0.0458023i
$414$	−3.47214	+	10.6861i	−0.170646	+	0.525195i
$415$		0			0
$416$	−5.07295	−	3.68571i	−0.248722	−	0.180707i
$417$	−0.263932	−	0.812299i	−0.0129248	−	0.0397785i
$418$	−34.2705	−	24.8990i	−1.67623	−	1.21785i
$419$	3.61803	+	2.62866i	0.176753	+	0.128418i	0.672644	−	0.739966i	$-0.265159\pi$
$419$	3.61803	+	2.62866i	0.176753	+	0.128418i	−0.495891	+	0.868385i	$0.665159\pi$
$420$		0			0
$421$	−15.5623	−	11.3067i	−0.758460	−	0.551054i	0.139977	−	0.990155i	$-0.455297\pi$
$421$	−15.5623	−	11.3067i	−0.758460	−	0.551054i	−0.898438	+	0.439101i	$0.855297\pi$
$422$	−10.4721	+	7.60845i	−0.509776	+	0.370374i
$423$	−3.47214	+	10.6861i	−0.168821	+	0.519578i
$424$	1.28115	−	0.930812i	0.0622183	−	0.0452042i
$425$		0			0
$426$	5.54508	+	17.0660i	0.268660	+	0.826851i
$427$	−10.1459	+	31.2259i	−0.490994	+	1.51113i
$428$	6.23607			0.301432
$429$	−9.70820			−0.468717
$430$		0			0
$431$	−20.0344	−	14.5559i	−0.965025	−	0.701132i	−0.0107127	−	0.999943i	$-0.503410\pi$
$431$	−20.0344	−	14.5559i	−0.965025	−	0.701132i	−0.954312	+	0.298811i	$0.903410\pi$
$432$	−19.6353	+	14.2658i	−0.944702	+	0.686366i
$433$	−27.4164			−1.31755			−0.658774	−	0.752341i	$-0.728925\pi$
$433$	−27.4164			−1.31755			−0.658774	+	0.752341i	$0.728925\pi$
$434$	−25.6353	+	8.55951i	−1.23053	+	0.410870i
$435$		0			0
$436$	−9.20820	+	6.69015i	−0.440993	+	0.320400i
$437$	14.0451	+	10.2044i	0.671868	+	0.488140i
$438$	5.78115	−	17.7926i	0.276234	−	0.850161i
$439$	−11.8328			−0.564749			−0.282375	−	0.959304i	$-0.591122\pi$
$439$	−11.8328			−0.564749			−0.282375	+	0.959304i	$0.591122\pi$
$440$		0			0
$441$	−1.23607	+	3.80423i	−0.0588604	+	0.181154i
$442$	−3.92705	−	12.0862i	−0.186791	−	0.574883i
$443$	0.270510	+	0.832544i	0.0128523	+	0.0395553i	0.957277	−	0.289172i	$-0.0933801\pi$
$443$	0.270510	+	0.832544i	0.0128523	+	0.0395553i	−0.944425	+	0.328728i	$0.893380\pi$
$444$	−2.11803	+	1.53884i	−0.100517	+	0.0730302i
$445$		0			0
$446$	16.6353	−	12.0862i	0.787702	−	0.572299i
$447$	−9.73607	−	7.07367i	−0.460500	−	0.334573i
$448$	−3.92705	−	12.0862i	−0.185536	−	0.571020i
$449$	27.5623	+	20.0252i	1.30075	+	0.945047i	0.999963	−	0.00864558i	$-0.00275201\pi$
$449$	27.5623	+	20.0252i	1.30075	+	0.945047i	0.300783	+	0.953693i	$0.402752\pi$
$450$		0			0
$451$	4.00000	+	12.3107i	0.188353	+	0.579690i
$452$	2.42705	+	1.76336i	0.114159	+	0.0829413i
$453$	−14.9721	+	10.8779i	−0.703452	+	0.511088i
$454$	10.8713	−	33.4585i	0.510216	−	1.57028i
$455$		0			0
$456$	3.45492	+	10.6331i	0.161791	+	0.497942i
$457$	−8.26393	−	25.4338i	−0.386570	−	1.18974i	−0.935335	−	0.353764i	$-0.884902\pi$
$457$	−8.26393	−	25.4338i	−0.386570	−	1.18974i	0.548764	−	0.835977i	$-0.315098\pi$
$458$	1.38197	−	4.25325i	0.0645750	−	0.198742i
$459$	−21.1803			−0.988614
$460$		0			0
$461$	−9.80902	+	30.1891i	−0.456851	+	1.40604i	0.412096	+	0.911140i	$0.364797\pi$
$461$	−9.80902	+	30.1891i	−0.456851	+	1.40604i	−0.868948	+	0.494904i	$0.835203\pi$
$462$	20.5623	+	14.9394i	0.956645	+	0.695043i
$463$	7.38197	−	5.36331i	0.343069	−	0.249254i	−0.402887	−	0.915250i	$-0.631993\pi$
$463$	7.38197	−	5.36331i	0.343069	−	0.249254i	0.745956	+	0.665996i	$0.231993\pi$
$464$	30.9787			1.43815
$465$		0			0
$466$	−9.38197			−0.434611
$467$	31.3713	−	22.7926i	1.45169	−	1.05472i	0.466259	−	0.884648i	$-0.345601\pi$
$467$	31.3713	−	22.7926i	1.45169	−	1.05472i	0.985432	−	0.170068i	$-0.0543986\pi$
$468$	1.85410	+	1.34708i	0.0857059	+	0.0622690i
$469$	0.218847	−	0.673542i	0.0101054	−	0.0311013i
$470$		0			0
$471$	3.70820			0.170865
$472$	0.364745	−	1.12257i	0.0167888	−	0.0516705i
$473$	−3.85410	−	11.8617i	−0.177212	−	0.545402i
$474$		0			0
$475$		0			0
$476$	−2.42705	+	7.46969i	−0.111244	+	0.342373i
$477$	−1.14590	+	0.832544i	−0.0524671	+	0.0381196i
$478$	17.5623	+	12.7598i	0.803281	+	0.583618i
$479$	2.76393	+	8.50651i	0.126287	+	0.388672i	0.994133	−	0.108161i	$-0.0344961\pi$
$479$	2.76393	+	8.50651i	0.126287	+	0.388672i	−0.867846	+	0.496833i	$0.834496\pi$
$480$		0			0
$481$	−6.35410	−	4.61653i	−0.289722	−	0.210495i
$482$	8.73607	+	26.8869i	0.397917	+	1.22466i
$483$	−8.42705	−	6.12261i	−0.383444	−	0.278588i
$484$	−8.20820	+	5.96361i	−0.373100	+	0.271073i
$485$		0			0
$486$	20.9443	−	15.2169i	0.950051	−	0.690253i
$487$	12.9549	+	39.8711i	0.587043	+	1.80673i	0.590906	+	0.806741i	$0.298771\pi$
$487$	12.9549	+	39.8711i	0.587043	+	1.80673i	−0.00386229	+	0.999993i	$0.501229\pi$
$488$	7.56231	+	23.2744i	0.342330	+	1.05358i
$489$	−0.218847	+	0.673542i	−0.00989661	+	0.0304586i
$490$		0			0
$491$	21.5967			0.974648			0.487324	−	0.873221i	$-0.337973\pi$
$491$	21.5967			0.974648			0.487324	+	0.873221i	$0.337973\pi$
$492$	−0.472136	+	1.45309i	−0.0212855	+	0.0655101i
$493$	21.8713	+	15.8904i	0.985035	+	0.715670i
$494$	12.1353	−	8.81678i	0.545991	−	0.396686i
$495$		0			0
$496$	−15.7082	+	21.9928i	−0.705319	+	0.987506i
$497$	33.2705			1.49239
$498$	−9.28115	+	6.74315i	−0.415898	+	0.302168i
$499$	−8.78115	−	6.37988i	−0.393098	−	0.285603i	0.373626	−	0.927580i	$-0.378114\pi$
$499$	−8.78115	−	6.37988i	−0.393098	−	0.285603i	−0.766724	+	0.641977i	$0.778114\pi$
$500$		0			0
$501$	4.76393			0.212837
$502$	27.4164			1.22365
$503$	−6.13525	+	18.8824i	−0.273557	+	0.841923i	0.716040	+	0.698059i	$0.245953\pi$
$503$	−6.13525	+	18.8824i	−0.273557	+	0.841923i	−0.989597	+	0.143864i	$0.954047\pi$
$504$	4.14590	+	12.7598i	0.184673	+	0.568365i
$505$		0			0
$506$	23.7984	−	17.2905i	1.05797	−	0.768658i
$507$	−2.95492	+	9.09429i	−0.131232	+	0.403892i
$508$	2.88197	−	2.09387i	0.127867	−	0.0929005i
$509$	10.5902	+	7.69421i	0.469401	+	0.341040i	0.797208	−	0.603705i	$-0.206310\pi$
$509$	10.5902	+	7.69421i	0.469401	+	0.341040i	−0.327807	+	0.944745i	$0.606310\pi$
$510$		0			0
$511$	−28.0623	−	20.3885i	−1.24140	−	0.901932i
$512$	−4.28115	−	3.11044i	−0.189202	−	0.137463i
$513$	−7.72542	−	23.7764i	−0.341086	−	1.04975i
$514$	33.2705	+	24.1724i	1.46750	+	1.06620i
$515$		0			0
$516$	0.454915	−	1.40008i	0.0200265	−	0.0616353i
$517$	23.7984	−	17.2905i	1.04665	−	0.760437i
$518$	6.35410	+	19.5559i	0.279183	+	0.859238i
$519$	−3.73607	−	11.4984i	−0.163995	−	0.504725i
$520$		0			0
$521$	−27.0689			−1.18591			−0.592955	−	0.805236i	$-0.702039\pi$
$521$	−27.0689			−1.18591			−0.592955	+	0.805236i	$0.702039\pi$
$522$	−20.6525			−0.903934
$523$	1.89261	−	5.82485i	0.0827580	−	0.254703i	−0.901112	−	0.433586i	$-0.857248\pi$
$523$	1.89261	−	5.82485i	0.0827580	−	0.254703i	0.983870	+	0.178883i	$0.0572482\pi$
$524$	5.54508	+	4.02874i	0.242238	+	0.175996i
$525$		0			0
$526$	22.3262			0.973470
$527$	−22.3713	+	7.46969i	−0.974510	+	0.325385i
$528$	25.4164			1.10611
$529$	8.85410	−	6.43288i	0.384961	−	0.279691i
$530$		0			0
$531$	−0.326238	+	1.00406i	−0.0141575	+	0.0435724i
$532$	−9.27051			−0.401928
$533$	−4.58359			−0.198537
$534$	4.30902	−	13.2618i	0.186469	−	0.573894i
$535$		0			0
$536$	−0.163119	−	0.502029i	−0.00704567	−	0.0216843i
$537$	3.88197	−	2.82041i	0.167519	−	0.121710i
$538$	1.80902	−	5.56758i	0.0779923	−	0.240035i
$539$	8.47214	−	6.15537i	0.364921	−	0.265130i
$540$		0			0
$541$	6.79837	+	20.9232i	0.292285	+	0.899560i	0.984120	+	0.177505i	$0.0568025\pi$
$541$	6.79837	+	20.9232i	0.292285	+	0.899560i	−0.691835	+	0.722056i	$0.743197\pi$
$542$	−13.8262	−	10.0453i	−0.593888	−	0.431485i
$543$	−13.7533	−	9.99235i	−0.590210	−	0.428813i
$544$	4.42705	+	13.6251i	0.189808	+	0.584170i
$545$		0			0
$546$	−7.28115	+	5.29007i	−0.311605	+	0.226394i
$547$	3.18034	−	9.78808i	0.135982	−	0.418508i	−0.859760	−	0.510698i	$-0.829387\pi$
$547$	3.18034	−	9.78808i	0.135982	−	0.418508i	0.995741	+	0.0921904i	$0.0293869\pi$
$548$	1.23607	−	0.898056i	0.0528022	−	0.0383630i
$549$	−6.76393	−	20.8172i	−0.288678	−	0.888458i
$550$		0			0
$551$	−9.86068	+	30.3481i	−0.420079	+	1.29287i
$552$	−7.76393			−0.330455
$553$		0			0
$554$	−1.16312	+	3.57971i	−0.0494162	+	0.152087i
$555$		0			0
$556$	0.427051	−	0.310271i	0.0181110	−	0.0131584i
$557$	−0.111456			−0.00472255			−0.00236127	−	0.999997i	$-0.500752\pi$
$557$	−0.111456			−0.00472255			−0.00236127	+	0.999997i	$0.500752\pi$
$558$	10.4721	−	14.6619i	0.443321	−	0.620687i
$559$	4.41641			0.186794
$560$		0			0
$561$	17.9443	+	13.0373i	0.757608	+	0.550434i
$562$	5.01722	−	15.4414i	0.211639	−	0.651357i
$563$	−11.5623			−0.487293			−0.243647	−	0.969864i	$-0.578344\pi$
$563$	−11.5623			−0.487293			−0.243647	+	0.969864i	$0.578344\pi$
$564$	3.47214			0.146203
$565$		0			0
$566$	−6.78115	−	20.8702i	−0.285033	−	0.877242i
$567$	−0.927051	−	2.85317i	−0.0389325	−	0.119822i
$568$	20.0623	−	14.5761i	0.841796	−	0.611600i
$569$	7.56231	−	23.2744i	0.317028	−	0.975713i	−0.657883	−	0.753120i	$-0.728548\pi$
$569$	7.56231	−	23.2744i	0.317028	−	0.975713i	0.974911	−	0.222593i	$-0.0714521\pi$
$570$		0			0
$571$	−5.66312	−	4.11450i	−0.236994	−	0.172186i	0.462949	−	0.886385i	$-0.346791\pi$
$571$	−5.66312	−	4.11450i	−0.236994	−	0.172186i	−0.699943	+	0.714199i	$0.746791\pi$
$572$	−1.85410	−	5.70634i	−0.0775239	−	0.238594i
$573$	3.97214	+	2.88593i	0.165938	+	0.120561i
$574$	9.70820	+	7.05342i	0.405213	+	0.294404i
$575$		0			0
$576$	6.85410	+	4.97980i	0.285588	+	0.207492i
$577$	−6.45492	+	4.68977i	−0.268722	+	0.195238i	−0.713983	−	0.700163i	$-0.753111\pi$
$577$	−6.45492	+	4.68977i	−0.268722	+	0.195238i	0.445262	+	0.895401i	$0.353111\pi$
$578$	−0.472136	+	1.45309i	−0.0196383	+	0.0604404i
$579$	−3.73607	+	2.71441i	−0.155266	+	0.112807i
$580$		0			0
$581$	6.57295	+	20.2295i	0.272692	+	0.839259i
$582$	−9.35410	+	28.7890i	−0.387740	+	1.19334i
$583$	3.70820			0.153578
$584$	−25.8541			−1.06985
$585$		0			0
$586$	4.92705	+	3.57971i	0.203535	+	0.147877i
$587$	−32.3713	+	23.5191i	−1.33611	+	0.970739i	−0.336530	+	0.941673i	$0.609253\pi$
$587$	−32.3713	+	23.5191i	−1.33611	+	0.970739i	−0.999577	+	0.0290662i	$0.990747\pi$
$588$	1.23607			0.0509746
$589$	−16.5451	−	22.3888i	−0.681728	−	0.922516i
$590$		0			0
$591$	−8.42705	+	6.12261i	−0.346643	+	0.251851i
$592$	16.6353	+	12.0862i	0.683705	+	0.496741i
$593$	−12.9443	+	39.8384i	−0.531558	+	1.63597i	0.219414	+	0.975632i	$0.429585\pi$
$593$	−12.9443	+	39.8384i	−0.531558	+	1.63597i	−0.750972	+	0.660334i	$0.770415\pi$
$594$	−42.3607			−1.73808
$595$		0			0
$596$	2.29837	−	7.07367i	0.0941451	−	0.289749i
$597$	−4.10739	−	12.6412i	−0.168104	−	0.517372i
$598$	3.21885	+	9.90659i	0.131628	+	0.405111i
$599$	−4.20820	+	3.05744i	−0.171943	+	0.124924i	−0.670428	−	0.741974i	$-0.733890\pi$
$599$	−4.20820	+	3.05744i	−0.171943	+	0.124924i	0.498486	+	0.866898i	$0.333890\pi$
$600$		0			0
$601$	−17.7984	+	12.9313i	−0.726011	+	0.527478i	−0.888299	−	0.459266i	$-0.848113\pi$
$601$	−17.7984	+	12.9313i	−0.726011	+	0.527478i	0.162288	+	0.986743i	$0.448113\pi$
$602$	−9.35410	−	6.79615i	−0.381245	−	0.276991i
$603$	0.145898	+	0.449028i	0.00594143	+	0.0182858i
$604$	−9.25329	−	6.72291i	−0.376511	−	0.273551i
$605$		0			0
$606$	−4.61803	−	14.2128i	−0.187595	−	0.577357i
$607$	1.14590	+	0.832544i	0.0465106	+	0.0337919i	0.610798	−	0.791787i	$-0.290849\pi$
$607$	1.14590	+	0.832544i	0.0465106	+	0.0337919i	−0.564287	+	0.825579i	$0.690849\pi$
$608$	−13.6803	+	9.93935i	−0.554811	+	0.403094i
$609$	5.91641	−	18.2088i	0.239745	−	0.737859i
$610$		0			0
$611$	3.21885	+	9.90659i	0.130221	+	0.400778i
$612$	−1.61803	−	4.97980i	−0.0654051	−	0.201296i
$613$	−13.2705	+	40.8424i	−0.535991	+	1.64961i	0.205508	+	0.978656i	$0.434115\pi$
$613$	−13.2705	+	40.8424i	−0.535991	+	1.64961i	−0.741498	+	0.670955i	$0.765885\pi$
$614$	−8.23607			−0.332381
$615$		0			0
$616$	10.8541	−	33.4055i	0.437324	−	1.34595i
$617$	−7.89919	−	5.73910i	−0.318009	−	0.231047i	0.417316	−	0.908761i	$-0.362971\pi$
$617$	−7.89919	−	5.73910i	−0.318009	−	0.231047i	−0.735326	+	0.677714i	$0.762971\pi$
$618$	8.97214	−	6.51864i	0.360912	−	0.262218i
$619$	−40.0000			−1.60774			−0.803868	−	0.594808i	$-0.797228\pi$
$619$	−40.0000			−1.60774			−0.803868	+	0.594808i	$0.797228\pi$
$620$		0			0
$621$	17.3607			0.696660
$622$	9.85410	−	7.15942i	0.395113	−	0.287067i
$623$	−20.9164	−	15.1967i	−0.837998	−	0.608841i
$624$	−2.78115	+	8.55951i	−0.111335	+	0.342655i
$625$		0			0
$626$	−5.23607			−0.209275
$627$	−8.09017	+	24.8990i	−0.323090	+	0.994370i
$628$	0.708204	+	2.17963i	0.0282604	+	0.0869766i
$629$	5.54508	+	17.0660i	0.221097	+	0.680467i
$630$		0			0
$631$	−13.0623	+	40.2016i	−0.520002	+	1.60040i	0.253990	+	0.967207i	$0.418257\pi$
$631$	−13.0623	+	40.2016i	−0.520002	+	1.60040i	−0.773992	+	0.633195i	$0.781743\pi$
$632$		0			0
$633$	6.47214	+	4.70228i	0.257244	+	0.186899i
$634$	−4.94427	−	15.2169i	−0.196362	−	0.604340i
$635$		0			0
$636$	0.354102	+	0.257270i	0.0140411	+	0.0102014i
$637$	1.14590	+	3.52671i	0.0454021	+	0.139733i
$638$	43.7426	+	31.7809i	1.73179	+	1.25822i
$639$	−17.9443	+	13.0373i	−0.709864	+	0.515747i
$640$		0			0
$641$	24.1976	−	17.5806i	0.955746	−	0.694390i	0.00358727	−	0.999994i	$-0.498858\pi$
$641$	24.1976	−	17.5806i	0.955746	−	0.694390i	0.952159	+	0.305603i	$0.0988581\pi$
$642$	−5.04508	−	15.5272i	−0.199114	−	0.612809i
$643$	−4.59017	−	14.1271i	−0.181019	−	0.557118i	0.818838	−	0.574024i	$-0.194618\pi$
$643$	−4.59017	−	14.1271i	−0.181019	−	0.557118i	−0.999857	+	0.0169060i	$0.994618\pi$
$644$	1.98936	−	6.12261i	0.0783916	−	0.241265i
$645$		0			0
$646$	−34.2705			−1.34836
$647$	−1.81966	+	5.60034i	−0.0715382	+	0.220172i	−0.980433	−	0.196854i	$-0.936928\pi$
$647$	−1.81966	+	5.60034i	−0.0715382	+	0.220172i	0.908895	+	0.417026i	$0.136928\pi$
$648$	−1.80902	−	1.31433i	−0.0710649	−	0.0516317i
$649$	2.23607	−	1.62460i	0.0877733	−	0.0637711i
$650$		0			0
$651$	9.92705	+	13.4333i	0.389072	+	0.526493i
$652$	−0.437694			−0.0171414
$653$	6.75329	−	4.90655i	0.264277	−	0.192008i	−0.447754	−	0.894157i	$-0.647776\pi$
$653$	6.75329	−	4.90655i	0.264277	−	0.192008i	0.712030	+	0.702149i	$0.247776\pi$
$654$	24.1074	+	17.5150i	0.942674	+	0.684892i
$655$		0			0
$656$	12.0000			0.468521
$657$	23.1246			0.902177
$658$	8.42705	−	25.9358i	0.328521	−	1.01108i
$659$	−11.6459	−	35.8424i	−0.453660	−	1.39622i	−0.872701	−	0.488254i	$-0.837634\pi$
$659$	−11.6459	−	35.8424i	−0.453660	−	1.39622i	0.419042	−	0.907967i	$-0.362366\pi$
$660$		0			0
$661$	11.6353	−	8.45351i	0.452559	−	0.328803i	−0.338046	−	0.941129i	$-0.609766\pi$
$661$	11.6353	−	8.45351i	0.452559	−	0.328803i	0.790605	+	0.612326i	$0.209766\pi$
$662$	11.1353	−	34.2708i	0.432784	−	1.33197i
$663$	−6.35410	+	4.61653i	−0.246773	+	0.179291i
$664$	12.8262	+	9.31881i	0.497755	+	0.361640i
$665$		0			0
$666$	−11.0902	−	8.05748i	−0.429735	−	0.312221i
$667$	−17.9271	−	13.0248i	−0.694138	−	0.504321i
$668$	0.909830	+	2.80017i	0.0352024	+	0.108342i
$669$	−10.2812	−	7.46969i	−0.397492	−	0.288795i
$670$		0			0
$671$	−17.7082	+	54.5002i	−0.683618	+	2.10396i
$672$	8.20820	−	5.96361i	0.316638	−	0.230051i
$673$	−6.92705	−	21.3193i	−0.267018	−	0.821797i	−0.991222	−	0.132211i	$-0.957792\pi$
$673$	−6.92705	−	21.3193i	−0.267018	−	0.821797i	0.724203	−	0.689586i	$-0.242208\pi$
$674$	−13.9894	−	43.0548i	−0.538850	−	1.65841i
$675$		0			0
$676$	−5.90983			−0.227301
$677$	2.65248			0.101943			0.0509715	−	0.998700i	$-0.483768\pi$
$677$	2.65248			0.101943			0.0509715	+	0.998700i	$0.483768\pi$
$678$	2.42705	−	7.46969i	0.0932103	−	0.286872i
$679$	45.4058	+	32.9892i	1.74251	+	1.26601i
$680$		0			0
$681$	−21.7426			−0.833180
$682$	−44.7426	+	14.9394i	−1.71328	+	0.572059i
$683$	−27.9443			−1.06926			−0.534629	−	0.845087i	$-0.679549\pi$
$683$	−27.9443			−1.06926			−0.534629	+	0.845087i	$0.679549\pi$
$684$	5.00000	−	3.63271i	0.191180	−	0.138900i
$685$		0			0
$686$	−7.50000	+	23.0826i	−0.286351	+	0.881299i
$687$	−2.76393			−0.105451
$688$	−11.5623			−0.440809
$689$	−0.405765	+	1.24882i	−0.0154584	+	0.0475761i
$690$		0			0
$691$	−15.3992	−	47.3938i	−0.585813	−	1.80295i	−0.595982	−	0.802998i	$-0.703237\pi$
$691$	−15.3992	−	47.3938i	−0.585813	−	1.80295i	0.0101694	−	0.999948i	$-0.496763\pi$
$692$	6.04508	−	4.39201i	0.229800	−	0.166959i
$693$	−9.70820	+	29.8788i	−0.368784	+	1.13500i
$694$	42.0517	−	30.5523i	1.59626	−	1.15975i
$695$		0			0
$696$	−4.40983	−	13.5721i	−0.167154	−	0.514448i
$697$	8.47214	+	6.15537i	0.320905	+	0.233151i
$698$	−4.30902	−	3.13068i	−0.163099	−	0.118498i
$699$	1.79180	+	5.51458i	0.0677720	+	0.208581i
$700$		0			0
$701$	0.781153	−	0.567541i	0.0295037	−	0.0214357i	−0.572936	−	0.819600i	$-0.694196\pi$
$701$	0.781153	−	0.567541i	0.0295037	−	0.0214357i	0.602439	+	0.798165i	$0.294196\pi$
$702$	4.63525	−	14.2658i	0.174946	−	0.538430i
$703$	−17.1353	+	12.4495i	−0.646268	+	0.469541i
$704$	−6.85410	−	21.0948i	−0.258324	−	0.795039i
$705$		0			0
$706$	−17.3090	+	53.2717i	−0.651433	+	2.00491i
$707$	−27.7082			−1.04207
$708$	0.326238			0.0122608
$709$	3.35410	−	10.3229i	0.125966	−	0.387683i	−0.868110	−	0.496372i	$-0.834665\pi$
$709$	3.35410	−	10.3229i	0.125966	−	0.387683i	0.994076	+	0.108689i	$0.0346652\pi$
$710$		0			0
$711$		0			0
$712$	−19.2705			−0.722193
$713$	18.3369	−	6.12261i	0.686722	−	0.229294i
$714$	20.5623			0.769525
$715$		0			0
$716$	2.39919	+	1.74311i	0.0896618	+	0.0651431i
$717$	4.14590	−	12.7598i	0.154831	−	0.476522i
$718$	15.6525			0.584145
$719$	−43.6180			−1.62668			−0.813339	−	0.581790i	$-0.802353\pi$
$719$	−43.6180			−1.62668			−0.813339	+	0.581790i	$0.802353\pi$
$720$		0			0
$721$	−6.35410	−	19.5559i	−0.236639	−	0.728300i
$722$	−3.00000	−	9.23305i	−0.111648	−	0.343619i
$723$	14.1353	−	10.2699i	0.525696	−	0.381940i
$724$	3.24671	−	9.99235i	0.120663	−	0.371363i
$725$		0			0
$726$	21.4894	+	15.6129i	0.797545	+	0.579450i
$727$	−9.21885	−	28.3727i	−0.341908	−	1.05228i	−0.963218	−	0.268720i	$-0.913399\pi$
$727$	−9.21885	−	28.3727i	−0.341908	−	1.05228i	0.621310	−	0.783565i	$-0.286601\pi$
$728$	10.0623	+	7.31069i	0.372934	+	0.270952i
$729$	−10.5172	−	7.64121i	−0.389527	−	0.283008i
$730$		0			0
$731$	−8.16312	−	5.93085i	−0.301924	−	0.219361i
$732$	−5.47214	+	3.97574i	−0.202256	+	0.146948i
$733$	−3.10739	+	9.56357i	−0.114774	+	0.353238i	−0.991900	−	0.127022i	$-0.959458\pi$
$733$	−3.10739	+	9.56357i	−0.114774	+	0.353238i	0.877126	+	0.480261i	$0.159458\pi$
$734$	3.57295	−	2.59590i	0.131880	−	0.0958164i
$735$		0			0
$736$	−3.62868	−	11.1679i	−0.133755	−	0.411655i
$737$	0.381966	−	1.17557i	0.0140699	−	0.0433027i
$738$	−8.00000			−0.294484
$739$	8.29180			0.305019			0.152509	−	0.988302i	$-0.451265\pi$
$739$	8.29180			0.305019			0.152509	+	0.988302i	$0.451265\pi$
$740$		0			0
$741$	−7.50000	−	5.44907i	−0.275519	−	0.200177i
$742$	2.78115	−	2.02063i	0.102099	−	0.0741795i
$743$	23.5623			0.864417			0.432209	−	0.901774i	$-0.357734\pi$
$743$	23.5623			0.864417			0.432209	+	0.901774i	$0.357734\pi$
$744$	11.8713	+	3.75123i	0.435224	+	0.137527i
$745$		0			0
$746$	41.4336	−	30.1033i	1.51699	−	1.10216i
$747$	−11.4721	−	8.33499i	−0.419744	−	0.304962i
$748$	−4.23607	+	13.0373i	−0.154886	+	0.476690i
$749$	−30.2705			−1.10606
$750$		0			0
$751$	4.27458	−	13.1558i	0.155981	−	0.480062i	−0.842278	−	0.539044i	$-0.818786\pi$
$751$	4.27458	−	13.1558i	0.155981	−	0.480062i	0.998259	+	0.0589825i	$0.0187856\pi$
$752$	−8.42705	−	25.9358i	−0.307303	−	0.945781i
$753$	−5.23607	−	16.1150i	−0.190813	−	0.587262i
$754$	−15.4894	+	11.2537i	−0.564089	+	0.409835i
$755$		0			0
$756$	−7.50000	+	5.44907i	−0.272772	+	0.198181i
$757$	2.32624	+	1.69011i	0.0845486	+	0.0614281i	0.629257	−	0.777198i	$-0.283359\pi$
$757$	2.32624	+	1.69011i	0.0845486	+	0.0614281i	−0.544708	+	0.838626i	$0.683359\pi$
$758$	−4.20820	−	12.9515i	−0.152849	−	0.470420i
$759$	−14.7082	−	10.6861i	−0.533874	−	0.387882i
$760$		0			0
$761$	−10.6631	−	32.8177i	−0.386538	−	1.18964i	−0.935359	−	0.353701i	$-0.884923\pi$
$761$	−10.6631	−	32.8177i	−0.386538	−	1.18964i	0.548821	−	0.835940i	$-0.315077\pi$
$762$	−7.54508	−	5.48183i	−0.273330	−	0.198586i
$763$	44.6976	−	32.4747i	1.61816	−	1.17566i
$764$	−0.937694	+	2.88593i	−0.0339246	+	0.104409i
$765$		0			0
$766$	−5.07295	−	15.6129i	−0.183293	−	0.564118i
$767$	0.302439	+	0.930812i	0.0109204	+	0.0336097i
$768$	4.19098	−	12.8985i	0.151229	−	0.465435i
$769$	−11.2574			−0.405951			−0.202975	−	0.979184i	$-0.565061\pi$
$769$	−11.2574			−0.405951			−0.202975	+	0.979184i	$0.565061\pi$
$770$		0			0
$771$	7.85410	−	24.1724i	0.282859	−	0.870549i
$772$	−2.30902	−	1.67760i	−0.0831033	−	0.0603781i
$773$	−6.39919	+	4.64928i	−0.230163	+	0.167223i	−0.696889	−	0.717179i	$-0.745433\pi$
$773$	−6.39919	+	4.64928i	−0.230163	+	0.167223i	0.466727	+	0.884402i	$0.345433\pi$
$774$	7.70820			0.277066
$775$		0			0
$776$	41.8328			1.50171
$777$	10.2812	−	7.46969i	0.368834	−	0.267974i
$778$	38.0517	+	27.6462i	1.36422	+	0.991163i
$779$	−3.81966	+	11.7557i	−0.136854	+	0.421192i
$780$		0			0
$781$	58.0689			2.07787
$782$	7.35410	−	22.6336i	0.262982	−	0.809376i
$783$	9.86068	+	30.3481i	0.352392	+	1.08455i
$784$	−3.00000	−	9.23305i	−0.107143	−	0.329752i
$785$		0			0
$786$	5.54508	−	17.0660i	0.197787	−	0.608725i
$787$	36.1697	−	26.2788i	1.28931	−	0.936739i	0.289519	−	0.957172i	$-0.406505\pi$
$787$	36.1697	−	26.2788i	1.28931	−	0.936739i	0.999791	+	0.0204333i	$0.00650458\pi$
$788$	−5.20820	−	3.78398i	−0.185535	−	0.134799i
$789$	−4.26393	−	13.1230i	−0.151800	−	0.467192i
$790$		0			0
$791$	−11.7812	−	8.55951i	−0.418890	−	0.304341i
$792$	7.23607	+	22.2703i	0.257122	+	0.791342i
$793$	−16.4164	−	11.9272i	−0.582964	−	0.423548i
$794$	−38.8885	+	28.2542i	−1.38010	+	1.00270i
$795$		0			0
$796$	6.64590	−	4.82853i	0.235558	−	0.171143i
$797$	−8.32624	−	25.6255i	−0.294930	−	0.907703i	−0.983245	−	0.182290i	$-0.941649\pi$
$797$	−8.32624	−	25.6255i	−0.294930	−	0.907703i	0.688314	−	0.725413i	$-0.258351\pi$
$798$	7.50000	+	23.0826i	0.265497	+	0.817116i
$799$	7.35410	−	22.6336i	0.260169	−	0.800719i
$800$		0			0
$801$	17.2361			0.609007
$802$	−11.9164	+	36.6749i	−0.420783	+	1.29504i
$803$	−48.9787	−	35.5851i	−1.72842	−	1.25577i
$804$	0.118034	−	0.0857567i	0.00416274	−	0.00302441i
$805$		0			0
$806$	−0.135255	−	16.7027i	−0.00476415	−	0.588329i
$807$	−3.61803			−0.127361
$808$	−16.7082	+	12.1392i	−0.587793	+	0.427056i
$809$	−24.4336	−	17.7521i	−0.859041	−	0.624130i	0.0685832	−	0.997645i	$-0.478152\pi$
$809$	−24.4336	−	17.7521i	−0.859041	−	0.624130i	−0.927624	+	0.373516i	$0.878152\pi$
$810$		0			0
$811$	−28.7771			−1.01050			−0.505250	−	0.862973i	$-0.668600\pi$
$811$	−28.7771			−1.01050			−0.505250	+	0.862973i	$0.668600\pi$
$812$	11.8328			0.415250
$813$	−3.26393	+	10.0453i	−0.114471	+	0.352306i
$814$	11.0902	+	34.1320i	0.388710	+	1.19633i
$815$		0			0
$816$	16.6353	−	12.0862i	0.582350	−	0.423102i
$817$	3.68034	−	11.3269i	0.128759	−	0.396279i
$818$	21.1803	−	15.3884i	0.740553	−	0.538043i
$819$	−9.00000	−	6.53888i	−0.314485	−	0.228487i
$820$		0			0
$821$	19.0344	+	13.8293i	0.664307	+	0.482647i	0.868115	−	0.496364i	$-0.165332\pi$
$821$	19.0344	+	13.8293i	0.664307	+	0.482647i	−0.203808	+	0.979011i	$0.565332\pi$
$822$	−3.23607	−	2.35114i	−0.112871	−	0.0820055i
$823$	−10.5451	−	32.4544i	−0.367579	−	1.13129i	−0.948351	−	0.317224i	$-0.897249\pi$
$823$	−10.5451	−	32.4544i	−0.367579	−	1.13129i	0.580772	−	0.814066i	$-0.302751\pi$
$824$	−12.3992	−	9.00854i	−0.431946	−	0.313827i
$825$		0			0
$826$	0.791796	−	2.43690i	0.0275501	−	0.0847905i
$827$	14.8262	−	10.7719i	0.515559	−	0.374575i	−0.299369	−	0.954137i	$-0.596776\pi$
$827$	14.8262	−	10.7719i	0.515559	−	0.374575i	0.814928	+	0.579562i	$0.196776\pi$
$828$	1.32624	+	4.08174i	0.0460900	+	0.141850i
$829$	−2.56231	−	7.88597i	−0.0889926	−	0.273891i	0.896649	−	0.442742i	$-0.145994\pi$
$829$	−2.56231	−	7.88597i	−0.0889926	−	0.273891i	−0.985642	+	0.168851i	$0.945994\pi$
$830$		0			0
$831$	2.32624			0.0806963
$832$	7.85410			0.272292
$833$	2.61803	−	8.05748i	0.0907095	−	0.279175i
$834$	−1.11803	−	0.812299i	−0.0387144	−	0.0281276i
$835$		0			0
$836$	−16.1803			−0.559609
$837$	−26.5451	−	8.38800i	−0.917532	−	0.289932i
$838$	7.23607			0.249966
$839$	9.04508	−	6.57164i	0.312271	−	0.226878i	−0.420599	−	0.907246i	$-0.638180\pi$
$839$	9.04508	−	6.57164i	0.312271	−	0.226878i	0.732870	+	0.680368i	$0.238180\pi$
$840$		0			0
$841$	3.62461	−	11.1554i	0.124987	−	0.384669i
$842$	−31.1246			−1.07262
$843$	−10.0344			−0.345605
$844$	−1.52786	+	4.70228i	−0.0525912	+	0.161859i
$845$		0			0
$846$	5.61803	+	17.2905i	0.193152	+	0.594461i
$847$	39.8435	−	28.9480i	1.36904	−	0.994664i
$848$	1.06231	−	3.26944i	0.0364797	−	0.112273i
$849$	−10.9721	+	7.97172i	−0.376563	+	0.273589i
$850$		0			0
$851$	−4.54508	−	13.9883i	−0.155804	−	0.479514i
$852$	5.54508	+	4.02874i	0.189971	+	0.138022i
$853$	3.23607	+	2.35114i	0.110801	+	0.0805015i	0.641806	−	0.766867i	$-0.278185\pi$
$853$	3.23607	+	2.35114i	0.110801	+	0.0805015i	−0.531005	+	0.847369i	$0.678185\pi$
$854$	16.4164	+	50.5245i	0.561758	+	1.72891i
$855$		0			0
$856$	−18.2533	+	13.2618i	−0.623885	+	0.453279i
$857$	−4.38197	+	13.4863i	−0.149685	+	0.460683i	−0.997584	−	0.0694751i	$-0.977868\pi$
$857$	−4.38197	+	13.4863i	−0.149685	+	0.460683i	0.847899	+	0.530158i	$0.177868\pi$
$858$	−12.7082	+	9.23305i	−0.433851	+	0.315211i
$859$	17.5238	+	53.9327i	0.597904	+	1.84016i	0.539703	+	0.841855i	$0.318536\pi$
$859$	17.5238	+	53.9327i	0.597904	+	1.84016i	0.0582010	+	0.998305i	$0.481464\pi$
$860$		0			0
$861$	2.29180	−	7.05342i	0.0781042	−	0.240380i
$862$	−40.0689			−1.36475
$863$	−40.5066			−1.37886			−0.689430	−	0.724352i	$-0.742139\pi$
$863$	−40.5066			−1.37886			−0.689430	+	0.724352i	$0.742139\pi$
$864$	−5.22542	+	16.0822i	−0.177773	+	0.547128i
$865$		0			0
$866$	−35.8885	+	26.0746i	−1.21954	+	0.886049i
$867$	0.944272			0.0320692
$868$	−6.00000	+	8.40051i	−0.203653	+	0.285132i
$869$		0			0
$870$		0			0
$871$	0.354102	+	0.257270i	0.0119983	+	0.00871727i
$872$	12.7254	−	39.1648i	0.430937	−	1.32629i
$873$	−37.4164			−1.26635
$874$	28.0902			0.950164
$875$		0			0
$876$	−2.20820	−	6.79615i	−0.0746083	−	0.229621i
$877$	−9.18034	−	28.2542i	−0.309998	−	0.954076i	−0.977765	−	0.209705i	$-0.932750\pi$
$877$	−9.18034	−	28.2542i	−0.309998	−	0.954076i	0.667767	−	0.744371i	$-0.267250\pi$
$878$	−15.4894	+	11.2537i	−0.522740	+	0.379793i
$879$	1.16312	−	3.57971i	0.0392310	−	0.120741i
$880$		0			0
$881$	−23.7533	−	17.2578i	−0.800269	−	0.581429i	0.110724	−	0.993851i	$-0.464683\pi$
$881$	−23.7533	−	17.2578i	−0.800269	−	0.581429i	−0.910993	+	0.412422i	$0.864683\pi$
$882$	2.00000	+	6.15537i	0.0673435	+	0.207262i
$883$	−0.809017	−	0.587785i	−0.0272256	−	0.0197805i	0.574089	−	0.818793i	$-0.305356\pi$
$883$	−0.809017	−	0.587785i	−0.0272256	−	0.0197805i	−0.601315	+	0.799012i	$0.705356\pi$
$884$	−3.92705	−	2.85317i	−0.132081	−	0.0959625i
$885$		0			0
$886$	1.14590	+	0.832544i	0.0384972	+	0.0279699i
$887$	−38.9164	+	28.2744i	−1.30669	+	0.949362i	−0.999997	−	0.00244778i	$-0.999221\pi$
$887$	−38.9164	+	28.2744i	−1.30669	+	0.949362i	−0.306688	+	0.951810i	$0.599221\pi$
$888$	2.92705	−	9.00854i	0.0982254	−	0.302307i
$889$	−13.9894	+	10.1639i	−0.469188	+	0.340885i
$890$		0			0
$891$	−1.61803	−	4.97980i	−0.0542062	−	0.166829i
$892$	2.42705	−	7.46969i	0.0812637	−	0.250104i
$893$	28.0902			0.940002
$894$	−19.4721			−0.651246
$895$		0			0
$896$	−33.0517	−	24.0134i	−1.10418	−	0.802233i
$897$	5.20820	−	3.78398i	0.173897	−	0.126343i
$898$	55.1246			1.83953
$899$	21.1180	+	28.5770i	0.704326	+	0.953095i
$900$		0			0
$901$	2.42705	−	1.76336i	0.0808568	−	0.0587459i
$902$	16.9443	+	12.3107i	0.564183	+	0.409903i
$903$	−2.20820	+	6.79615i	−0.0734844	+	0.226162i
$904$	−10.8541			−0.361002
$905$		0			0
$906$	−9.25329	+	28.4787i	−0.307420	+	0.946141i
$907$	3.68441	+	11.3394i	0.122339	+	0.376520i	0.993407	−	0.114642i	$-0.0365722\pi$
$907$	3.68441	+	11.3394i	0.122339	+	0.376520i	−0.871068	+	0.491162i	$0.836572\pi$
$908$	−4.15248	−	12.7800i	−0.137805	−	0.424119i
$909$	14.9443	−	10.8576i	0.495670	−	0.360125i
$910$		0			0
$911$	11.4721	−	8.33499i	0.380089	−	0.276151i	−0.381293	−	0.924454i	$-0.624521\pi$
$911$	11.4721	−	8.33499i	0.380089	−	0.276151i	0.761382	+	0.648303i	$0.224521\pi$
$912$	19.6353	+	14.2658i	0.650188	+	0.472389i
$913$	11.4721	+	35.3076i	0.379672	+	1.16851i
$914$	−35.0066	−	25.4338i	−1.15791	−	0.841274i
$915$		0			0
$916$	−0.527864	−	1.62460i	−0.0174411	−	0.0536782i
$917$	−26.9164	−	19.5559i	−0.888858	−	0.645793i
$918$	−27.7254	+	20.1437i	−0.915075	+	0.664841i
$919$	15.4894	−	47.6713i	0.510947	−	1.57253i	−0.279591	−	0.960119i	$-0.590199\pi$
$919$	15.4894	−	47.6713i	0.510947	−	1.57253i	0.790538	−	0.612413i	$-0.209801\pi$
$920$		0			0
$921$	1.57295	+	4.84104i	0.0518304	+	0.159518i
$922$	15.8713	+	48.8469i	0.522694	+	1.60869i
$923$	−6.35410	+	19.5559i	−0.209148	+	0.643691i
$924$	9.70820			0.319376
$925$		0			0
$926$	4.56231	−	14.0413i	0.149927	−	0.461427i
$927$	11.0902	+	8.05748i	0.364249	+	0.264642i
$928$	17.4615	−	12.6865i	0.573202	−	0.416455i
$929$	−33.5410			−1.10045			−0.550223	−	0.835018i	$-0.685457\pi$
$929$	−33.5410			−1.10045			−0.550223	+	0.835018i	$0.685457\pi$
$930$		0			0
$931$	10.0000			0.327737
$932$	−2.89919	+	2.10638i	−0.0949660	+	0.0689969i
$933$	−6.09017	−	4.42477i	−0.199383	−	0.144860i
$934$	19.3885	−	59.6718i	0.634413	−	1.95252i
$935$		0			0
$936$	−8.29180			−0.271026
$937$	13.7467	−	42.3080i	0.449085	−	1.38214i	−0.428855	−	0.903373i	$-0.641083\pi$
$937$	13.7467	−	42.3080i	0.449085	−	1.38214i	0.877941	−	0.478770i	$-0.158917\pi$
$938$	−0.354102	−	1.08981i	−0.0115618	−	0.0355837i
$939$	1.00000	+	3.07768i	0.0326338	+	0.100436i
$940$		0			0
$941$	17.1246	−	52.7041i	0.558246	−	1.71811i	−0.128966	−	0.991649i	$-0.541166\pi$
$941$	17.1246	−	52.7041i	0.558246	−	1.71811i	0.687212	−	0.726457i	$-0.258834\pi$
$942$	4.85410	−	3.52671i	0.158155	−	0.114906i
$943$	−6.94427	−	5.04531i	−0.226137	−	0.164298i
$944$	−0.791796	−	2.43690i	−0.0257708	−	0.0793143i
$945$		0			0
$946$	−16.3262	−	11.8617i	−0.530812	−	0.385657i
$947$	11.1459	+	34.3035i	0.362193	+	1.11472i	0.951720	+	0.306967i	$0.0993141\pi$
$947$	11.1459	+	34.3035i	0.362193	+	1.11472i	−0.589527	+	0.807749i	$0.700686\pi$
$948$		0			0
$949$	17.3435	−	12.6008i	0.562992	−	0.409038i
$950$		0			0
$951$	−8.00000	+	5.81234i	−0.259418	+	0.188478i
$952$	−8.78115	−	27.0256i	−0.284599	−	0.875905i
$953$	2.84752	+	8.76378i	0.0922404	+	0.283887i	0.986525	−	0.163613i	$-0.0523147\pi$
$953$	2.84752	+	8.76378i	0.0922404	+	0.283887i	−0.894284	+	0.447499i	$0.852315\pi$
$954$	−0.708204	+	2.17963i	−0.0229289	+	0.0705680i
$955$		0			0
$956$	8.29180			0.268176
$957$	10.3262	−	31.7809i	0.333800	−	1.02733i
$958$	11.7082	+	8.50651i	0.378275	+	0.274833i
$959$	−6.00000	+	4.35926i	−0.193750	+	0.140768i
$960$		0			0
$961$	−30.9959	+	0.502029i	−0.999869	+	0.0161945i
$962$	−12.7082			−0.409729
$963$	16.3262	−	11.8617i	0.526106	−	0.382238i
$964$	8.73607	+	6.34712i	0.281370	+	0.204427i
$965$		0			0
$966$	−16.8541			−0.542272
$967$	−12.3475			−0.397070			−0.198535	−	0.980094i	$-0.563618\pi$
$967$	−12.3475			−0.397070			−0.198535	+	0.980094i	$0.563618\pi$
$968$	11.3435	−	34.9116i	0.364593	−	1.12210i
$969$	6.54508	+	20.1437i	0.210258	+	0.647109i
$970$		0			0
$971$	0.354102	−	0.257270i	0.0113637	−	0.00825619i	−0.582089	−	0.813125i	$-0.697764\pi$
$971$	0.354102	−	0.257270i	0.0113637	−	0.00825619i	0.593453	+	0.804869i	$0.297764\pi$
$972$	3.05573	−	9.40456i	0.0980125	−	0.301652i
$973$	−2.07295	+	1.50609i	−0.0664557	+	0.0482829i
$974$	54.8779	+	39.8711i	1.75840	+	1.27755i
$975$		0			0
$976$	42.9787	+	31.2259i	1.37572	+	0.999516i
$977$	42.1246	+	30.6053i	1.34769	+	0.979151i	0.999123	+	0.0418654i	$0.0133301\pi$
$977$	42.1246	+	30.6053i	1.34769	+	0.979151i	0.348562	+	0.937286i	$0.386670\pi$
$978$	0.354102	+	1.08981i	0.0113229	+	0.0348484i
$979$	−36.5066	−	26.5236i	−1.16676	−	0.847697i
$980$		0			0
$981$	−11.3820	+	35.0301i	−0.363398	+	1.11842i
$982$	28.2705	−	20.5397i	0.902148	−	0.655449i
$983$	2.48278	+	7.64121i	0.0791884	+	0.243717i	0.982812	−	0.184612i	$-0.0591027\pi$
$983$	2.48278	+	7.64121i	0.0791884	+	0.243717i	−0.903623	+	0.428328i	$0.859103\pi$
$984$	−1.70820	−	5.25731i	−0.0544556	−	0.167597i
$985$		0			0
$986$	43.7426			1.39305
$987$	−16.8541			−0.536472
$988$	1.77051	−	5.44907i	0.0563274	−	0.173358i
$989$	6.69098	+	4.86128i	0.212761	+	0.154580i
$990$		0			0
$991$	16.2705			0.516850			0.258425	−	0.966031i	$-0.416797\pi$
$991$	16.2705			0.516850			0.258425	+	0.966031i	$0.416797\pi$
$992$	0.152476	+	18.8294i	0.00484111	+	0.597833i
$993$	−22.2705			−0.706733
$994$	43.5517	−	31.6421i	1.38137	−	1.00363i
$995$		0			0
$996$	−1.35410	+	4.16750i	−0.0429064	+	0.132052i
$997$	−53.2492			−1.68642			−0.843210	−	0.537584i	$-0.819337\pi$
$997$	−53.2492			−1.68642			−0.843210	+	0.537584i	$0.819337\pi$
$998$	−17.5623			−0.555925
$999$	−6.54508	+	20.1437i	−0.207077	+	0.637318i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.k.c.326.1		4
5.2	odd	4		775.2.bf.a.574.2		8
5.3	odd	4		775.2.bf.a.574.1		8
5.4	even	2		31.2.d.a.16.1	yes	4
15.14	odd	2		279.2.i.a.109.1		4
20.19	odd	2		496.2.n.b.481.1		4
31.2	even	5	inner	775.2.k.c.126.1		4
155.2	odd	20		775.2.bf.a.374.1		8
155.4	even	10		961.2.d.f.628.1		4
155.9	even	30		961.2.c.f.521.2		4
155.14	even	30		961.2.c.f.439.2		4
155.19	even	30		961.2.g.b.816.1		8
155.24	odd	30		961.2.g.g.846.1		8
155.29	odd	10		961.2.d.b.374.1		4
155.33	odd	20		775.2.bf.a.374.2		8
155.34	odd	30		961.2.g.g.547.1		8
155.39	even	10		961.2.a.d.1.2		2
155.44	odd	30		961.2.g.g.844.1		8
155.49	even	30		961.2.g.f.844.1		8
155.54	odd	10		961.2.a.e.1.2		2
155.59	even	30		961.2.g.f.547.1		8
155.64	even	10		31.2.d.a.2.1	✓	4
155.69	even	30		961.2.g.f.846.1		8
155.74	odd	30		961.2.g.c.816.1		8
155.79	odd	30		961.2.c.d.439.2		4
155.84	odd	30		961.2.c.d.521.2		4
155.89	odd	10		961.2.d.e.628.1		4
155.99	odd	6		961.2.g.c.235.1		8
155.104	odd	30		961.2.g.g.448.1		8
155.109	even	10		961.2.d.f.531.1		4
155.114	odd	30		961.2.g.c.732.1		8
155.119	odd	6		961.2.g.c.338.1		8
155.129	even	6		961.2.g.b.338.1		8
155.134	even	30		961.2.g.b.732.1		8
155.139	odd	10		961.2.d.e.531.1		4
155.144	even	30		961.2.g.f.448.1		8
155.149	even	6		961.2.g.b.235.1		8
155.154	odd	2		961.2.d.b.388.1		4
465.194	odd	10		8649.2.a.g.1.1		2
465.209	even	10		8649.2.a.f.1.1		2
465.374	odd	10		279.2.i.a.64.1		4
620.219	odd	10		496.2.n.b.33.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.d.a.2.1	✓	4	155.64	even	10
31.2.d.a.16.1	yes	4	5.4	even	2
279.2.i.a.64.1		4	465.374	odd	10
279.2.i.a.109.1		4	15.14	odd	2
496.2.n.b.33.1		4	620.219	odd	10
496.2.n.b.481.1		4	20.19	odd	2
775.2.k.c.126.1		4	31.2	even	5	inner
775.2.k.c.326.1		4	1.1	even	1	trivial
775.2.bf.a.374.1		8	155.2	odd	20
775.2.bf.a.374.2		8	155.33	odd	20
775.2.bf.a.574.1		8	5.3	odd	4
775.2.bf.a.574.2		8	5.2	odd	4
961.2.a.d.1.2		2	155.39	even	10
961.2.a.e.1.2		2	155.54	odd	10
961.2.c.d.439.2		4	155.79	odd	30
961.2.c.d.521.2		4	155.84	odd	30
961.2.c.f.439.2		4	155.14	even	30
961.2.c.f.521.2		4	155.9	even	30
961.2.d.b.374.1		4	155.29	odd	10
961.2.d.b.388.1		4	155.154	odd	2
961.2.d.e.531.1		4	155.139	odd	10
961.2.d.e.628.1		4	155.89	odd	10
961.2.d.f.531.1		4	155.109	even	10
961.2.d.f.628.1		4	155.4	even	10
961.2.g.b.235.1		8	155.149	even	6
961.2.g.b.338.1		8	155.129	even	6
961.2.g.b.732.1		8	155.134	even	30
961.2.g.b.816.1		8	155.19	even	30
961.2.g.c.235.1		8	155.99	odd	6
961.2.g.c.338.1		8	155.119	odd	6
961.2.g.c.732.1		8	155.114	odd	30
961.2.g.c.816.1		8	155.74	odd	30
961.2.g.f.448.1		8	155.144	even	30
961.2.g.f.547.1		8	155.59	even	30
961.2.g.f.844.1		8	155.49	even	30
961.2.g.f.846.1		8	155.69	even	30
961.2.g.g.448.1		8	155.104	odd	30
961.2.g.g.547.1		8	155.34	odd	30
961.2.g.g.844.1		8	155.44	odd	30
961.2.g.g.846.1		8	155.24	odd	30
8649.2.a.f.1.1		2	465.209	even	10
8649.2.a.g.1.1		2	465.194	odd	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30902 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(0.190983 - 0.587785i) q^{4} -1.61803 q^{6} +(-0.927051 + 2.85317i) q^{7} +(0.690983 + 2.12663i) q^{8} +(-0.618034 - 1.90211i) q^{9} +(-1.61803 + 4.97980i) q^{11} +(-0.500000 + 0.363271i) q^{12} +(-1.50000 - 1.08981i) q^{13} +(1.50000 + 4.61653i) q^{14} +(3.92705 + 2.85317i) q^{16} +(1.30902 + 4.02874i) q^{17} +(-2.61803 - 1.90211i) q^{18} +(-4.04508 + 2.93893i) q^{19} +(2.42705 - 1.76336i) q^{21} +(2.61803 + 8.05748i) q^{22} +(-1.07295 - 3.30220i) q^{23} +(0.690983 - 2.12663i) q^{24} -3.00000 q^{26} +(-1.54508 + 4.75528i) q^{27} +(1.50000 + 1.08981i) q^{28} +(5.16312 - 3.75123i) q^{29} +(0.0450850 + 5.56758i) q^{31} +3.38197 q^{32} +(4.23607 - 3.07768i) q^{33} +(5.54508 + 4.02874i) q^{34} -1.23607 q^{36} +4.23607 q^{37} +(-2.50000 + 7.69421i) q^{38} +(0.572949 + 1.76336i) q^{39} +(2.00000 - 1.45309i) q^{41} +(1.50000 - 4.61653i) q^{42} +(-1.92705 + 1.40008i) q^{43} +(2.61803 + 1.90211i) q^{44} +(-4.54508 - 3.30220i) q^{46} +(-4.54508 - 3.30220i) q^{47} +(-1.50000 - 4.61653i) q^{48} +(-1.61803 - 1.17557i) q^{49} +(1.30902 - 4.02874i) q^{51} +(-0.927051 + 0.673542i) q^{52} +(-0.218847 - 0.673542i) q^{53} +(2.50000 + 7.69421i) q^{54} -6.70820 q^{56} +5.00000 q^{57} +(3.19098 - 9.82084i) q^{58} +(-0.427051 - 0.310271i) q^{59} +10.9443 q^{61} +(5.35410 + 7.24518i) q^{62} +6.00000 q^{63} +(-3.42705 + 2.48990i) q^{64} +(2.61803 - 8.05748i) q^{66} -0.236068 q^{67} +2.61803 q^{68} +(-1.07295 + 3.30220i) q^{69} +(-3.42705 - 10.5474i) q^{71} +(3.61803 - 2.62866i) q^{72} +(-3.57295 + 10.9964i) q^{73} +(5.54508 - 4.02874i) q^{74} +(0.954915 + 2.93893i) q^{76} +(-12.7082 - 9.23305i) q^{77} +(2.42705 + 1.76336i) q^{78} +(-0.809017 + 0.587785i) q^{81} +(1.23607 - 3.80423i) q^{82} +(5.73607 - 4.16750i) q^{83} +(-0.572949 - 1.76336i) q^{84} +(-1.19098 + 3.66547i) q^{86} -6.38197 q^{87} -11.7082 q^{88} +(-2.66312 + 8.19624i) q^{89} +(4.50000 - 3.26944i) q^{91} -2.14590 q^{92} +(3.23607 - 4.53077i) q^{93} -9.09017 q^{94} +(-2.73607 - 1.98787i) q^{96} +(5.78115 - 17.7926i) q^{97} -3.23607 q^{98} +10.4721 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} - q^{3} + 3 q^{4} - 2 q^{6} + 3 q^{7} + 5 q^{8} + 2 q^{9} - 2 q^{11} - 2 q^{12} - 6 q^{13} + 6 q^{14} + 9 q^{16} + 3 q^{17} - 6 q^{18} - 5 q^{19} + 3 q^{21} + 6 q^{22} - 11 q^{23} + 5 q^{24}+ \cdots + 24 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 - q^3 + 3 * q^4 - 2 * q^6 + 3 * q^7 + 5 * q^8 + 2 * q^9 - 2 * q^11 - 2 * q^12 - 6 * q^13 + 6 * q^14 + 9 * q^16 + 3 * q^17 - 6 * q^18 - 5 * q^19 + 3 * q^21 + 6 * q^22 - 11 * q^23 + 5 * q^24 - 12 * q^26 + 5 * q^27 + 6 * q^28 + 5 * q^29 - 11 * q^31 + 18 * q^32 + 8 * q^33 + 11 * q^34 + 4 * q^36 + 8 * q^37 - 10 * q^38 + 9 * q^39 + 8 * q^41 + 6 * q^42 - q^43 + 6 * q^44 - 7 * q^46 - 7 * q^47 - 6 * q^48 - 2 * q^49 + 3 * q^51 + 3 * q^52 - 21 * q^53 + 10 * q^54 + 20 * q^57 + 15 * q^58 + 5 * q^59 + 8 * q^61 + 8 * q^62 + 24 * q^63 - 7 * q^64 + 6 * q^66 + 8 * q^67 + 6 * q^68 - 11 * q^69 - 7 * q^71 + 10 * q^72 - 21 * q^73 + 11 * q^74 + 15 * q^76 - 24 * q^77 + 3 * q^78 - q^81 - 4 * q^82 + 14 * q^83 - 9 * q^84 - 7 * q^86 - 30 * q^87 - 20 * q^88 + 5 * q^89 + 18 * q^91 - 22 * q^92 + 4 * q^93 - 14 * q^94 - 2 * q^96 + 3 * q^97 - 4 * q^98 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

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