LMFDB - Embedded newform 825.2.n.f.676.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(301,825)]

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, 0, 2]))

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

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

chi := DirichletCharacter("825.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.n (of order $5$, degree $4$, 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:	$4$
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 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			676.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	825.676
Dual form			825.2.n.f.526.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.190983 + 0.587785i) q^{2} +(0.809017 + 0.587785i) q^{3} +(1.30902 - 0.951057i) q^{4} +(-0.190983 + 0.587785i) q^{6} +(2.42705 - 1.76336i) q^{7} +(1.80902 + 1.31433i) q^{8} +(0.309017 + 0.951057i) q^{9} +(1.69098 - 2.85317i) q^{11} +1.61803 q^{12} +(-0.545085 - 1.67760i) q^{13} +(1.50000 + 1.08981i) q^{14} +(0.572949 - 1.76336i) q^{16} +(-0.500000 + 1.53884i) q^{17} +(-0.500000 + 0.363271i) q^{18} +(-4.73607 - 3.44095i) q^{19} +3.00000 q^{21} +(2.00000 + 0.449028i) q^{22} -3.47214 q^{23} +(0.690983 + 2.12663i) q^{24} +(0.881966 - 0.640786i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(1.50000 - 4.61653i) q^{28} +(-3.61803 + 2.62866i) q^{29} +(0.881966 + 2.71441i) q^{31} +5.61803 q^{32} +(3.04508 - 1.31433i) q^{33} -1.00000 q^{34} +(1.30902 + 0.951057i) q^{36} +(0.190983 - 0.138757i) q^{37} +(1.11803 - 3.44095i) q^{38} +(0.545085 - 1.67760i) q^{39} +(9.66312 + 7.02067i) q^{41} +(0.572949 + 1.76336i) q^{42} -6.23607 q^{43} +(-0.500000 - 5.34307i) q^{44} +(-0.663119 - 2.04087i) q^{46} +(1.30902 + 0.951057i) q^{47} +(1.50000 - 1.08981i) q^{48} +(0.618034 - 1.90211i) q^{49} +(-1.30902 + 0.951057i) q^{51} +(-2.30902 - 1.67760i) q^{52} +(2.97214 + 9.14729i) q^{53} -0.618034 q^{54} +6.70820 q^{56} +(-1.80902 - 5.56758i) q^{57} +(-2.23607 - 1.62460i) q^{58} +(-8.35410 + 6.06961i) q^{59} +(2.42705 - 7.46969i) q^{61} +(-1.42705 + 1.03681i) q^{62} +(2.42705 + 1.76336i) q^{63} +(-0.0729490 - 0.224514i) q^{64} +(1.35410 + 1.53884i) q^{66} +9.56231 q^{67} +(0.809017 + 2.48990i) q^{68} +(-2.80902 - 2.04087i) q^{69} +(-1.71885 + 5.29007i) q^{71} +(-0.690983 + 2.12663i) q^{72} +(-2.61803 + 1.90211i) q^{73} +(0.118034 + 0.0857567i) q^{74} -9.47214 q^{76} +(-0.927051 - 9.90659i) q^{77} +1.09017 q^{78} +(2.92705 + 9.00854i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-2.28115 + 7.02067i) q^{82} +(-0.218847 + 0.673542i) q^{83} +(3.92705 - 2.85317i) q^{84} +(-1.19098 - 3.66547i) q^{86} -4.47214 q^{87} +(6.80902 - 2.93893i) q^{88} +0.527864 q^{89} +(-4.28115 - 3.11044i) q^{91} +(-4.54508 + 3.30220i) q^{92} +(-0.881966 + 2.71441i) q^{93} +(-0.309017 + 0.951057i) q^{94} +(4.54508 + 3.30220i) q^{96} +(4.33688 + 13.3475i) q^{97} +1.23607 q^{98} +(3.23607 + 0.726543i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} + q^{3} + 3 q^{4} - 3 q^{6} + 3 q^{7} + 5 q^{8} - q^{9} + 9 q^{11} + 2 q^{12} + 9 q^{13} + 6 q^{14} + 9 q^{16} - 2 q^{17} - 2 q^{18} - 10 q^{19} + 12 q^{21} + 8 q^{22} + 4 q^{23} + 5 q^{24}+ \cdots + 4 q^{99}+O(q^{100}) $ 4 * q + 3 * q^2 + q^3 + 3 * q^4 - 3 * q^6 + 3 * q^7 + 5 * q^8 - q^9 + 9 * q^11 + 2 * q^12 + 9 * q^13 + 6 * q^14 + 9 * q^16 - 2 * q^17 - 2 * q^18 - 10 * q^19 + 12 * q^21 + 8 * q^22 + 4 * q^23 + 5 * q^24 + 8 * q^26 + q^27 + 6 * q^28 - 10 * q^29 + 8 * q^31 + 18 * q^32 + q^33 - 4 * q^34 + 3 * q^36 + 3 * q^37 - 9 * q^39 + 23 * q^41 + 9 * q^42 - 16 * q^43 - 2 * q^44 + 13 * q^46 + 3 * q^47 + 6 * q^48 - 2 * q^49 - 3 * q^51 - 7 * q^52 - 6 * q^53 + 2 * q^54 - 5 * q^57 - 20 * q^59 + 3 * q^61 + q^62 + 3 * q^63 - 7 * q^64 - 8 * q^66 - 2 * q^67 + q^68 - 9 * q^69 - 27 * q^71 - 5 * q^72 - 6 * q^73 - 4 * q^74 - 20 * q^76 + 3 * q^77 - 18 * q^78 + 5 * q^79 - q^81 + 11 * q^82 - 21 * q^83 + 9 * q^84 - 7 * q^86 + 25 * q^88 + 20 * q^89 + 3 * q^91 - 7 * q^92 - 8 * q^93 + q^94 + 7 * q^96 + 33 * q^97 - 4 * q^98 + 4 * q^99

Character values

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

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

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 $

$2$	0.190983	+	0.587785i	0.135045	+	0.415627i	0.995597	−	0.0937362i	$-0.0298810\pi$
$2$	0.190983	+	0.587785i	0.135045	+	0.415627i	−0.860552	+	0.509363i	$0.829881\pi$
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$	1.30902	−	0.951057i	0.654508	−	0.475528i
$5$		0			0
$5$		0			0
$6$	−0.190983	+	0.587785i	−0.0779685	+	0.239962i
$7$	2.42705	−	1.76336i	0.917339	−	0.666486i	−0.0255212	−	0.999674i	$-0.508125\pi$
$7$	2.42705	−	1.76336i	0.917339	−	0.666486i	0.942860	+	0.333188i	$0.108125\pi$
$8$	1.80902	+	1.31433i	0.639584	+	0.464685i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$		0			0
$11$	1.69098	−	2.85317i	0.509851	−	0.860263i
$11$	1.69098	−	2.85317i	0.509851	−	0.860263i
$12$	1.61803			0.467086
$13$	−0.545085	−	1.67760i	−0.151179	−	0.465282i	0.846574	−	0.532270i	$-0.178661\pi$
$13$	−0.545085	−	1.67760i	−0.151179	−	0.465282i	−0.997754	+	0.0669881i	$0.978661\pi$
$14$	1.50000	+	1.08981i	0.400892	+	0.291265i
$15$		0			0
$16$	0.572949	−	1.76336i	0.143237	−	0.440839i
$17$	−0.500000	+	1.53884i	−0.121268	+	0.373224i	−0.993203	−	0.116398i	$-0.962865\pi$
$17$	−0.500000	+	1.53884i	−0.121268	+	0.373224i	0.871935	+	0.489622i	$0.162865\pi$
$18$	−0.500000	+	0.363271i	−0.117851	+	0.0856239i
$19$	−4.73607	−	3.44095i	−1.08653	−	0.789409i	−0.107719	−	0.994181i	$-0.534355\pi$
$19$	−4.73607	−	3.44095i	−1.08653	−	0.789409i	−0.978810	+	0.204772i	$0.934355\pi$
$20$		0			0
$21$	3.00000			0.654654
$22$	2.00000	+	0.449028i	0.426401	+	0.0957331i
$23$	−3.47214			−0.723990			−0.361995	−	0.932180i	$-0.617904\pi$
$23$	−3.47214			−0.723990			−0.361995	+	0.932180i	$0.617904\pi$
$24$	0.690983	+	2.12663i	0.141046	+	0.434096i
$25$		0			0
$26$	0.881966	−	0.640786i	0.172968	−	0.125668i
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	1.50000	−	4.61653i	0.283473	−	0.872441i
$29$	−3.61803	+	2.62866i	−0.671852	+	0.488129i	−0.870645	−	0.491912i	$-0.836298\pi$
$29$	−3.61803	+	2.62866i	−0.671852	+	0.488129i	0.198793	+	0.980042i	$0.436298\pi$
$30$		0			0
$31$	0.881966	+	2.71441i	0.158406	+	0.487523i	0.998490	−	0.0549331i	$-0.0174946\pi$
$31$	0.881966	+	2.71441i	0.158406	+	0.487523i	−0.840084	+	0.542456i	$0.817495\pi$
$32$	5.61803			0.993137
$33$	3.04508	−	1.31433i	0.530081	−	0.228795i
$34$	−1.00000			−0.171499
$35$		0			0
$36$	1.30902	+	0.951057i	0.218169	+	0.158509i
$37$	0.190983	−	0.138757i	0.0313974	−	0.0228116i	−0.571976	−	0.820270i	$-0.693823\pi$
$37$	0.190983	−	0.138757i	0.0313974	−	0.0228116i	0.603373	+	0.797459i	$0.293823\pi$
$38$	1.11803	−	3.44095i	0.181369	−	0.558197i
$39$	0.545085	−	1.67760i	0.0872835	−	0.268631i
$40$		0			0
$41$	9.66312	+	7.02067i	1.50913	+	1.09644i	0.966563	+	0.256428i	$0.0825458\pi$
$41$	9.66312	+	7.02067i	1.50913	+	1.09644i	0.542562	+	0.840015i	$0.317454\pi$
$42$	0.572949	+	1.76336i	0.0884080	+	0.272092i
$43$	−6.23607			−0.950991			−0.475496	−	0.879718i	$-0.657731\pi$
$43$	−6.23607			−0.950991			−0.475496	+	0.879718i	$0.657731\pi$
$44$	−0.500000	−	5.34307i	−0.0753778	−	0.805498i
$45$		0			0
$46$	−0.663119	−	2.04087i	−0.0977716	−	0.300910i
$47$	1.30902	+	0.951057i	0.190940	+	0.138726i	0.679148	−	0.734001i	$-0.262349\pi$
$47$	1.30902	+	0.951057i	0.190940	+	0.138726i	−0.488208	+	0.872727i	$0.662349\pi$
$48$	1.50000	−	1.08981i	0.216506	−	0.157301i
$49$	0.618034	−	1.90211i	0.0882906	−	0.271730i
$50$		0			0
$51$	−1.30902	+	0.951057i	−0.183299	+	0.133175i
$52$	−2.30902	−	1.67760i	−0.320203	−	0.232641i
$53$	2.97214	+	9.14729i	0.408254	+	1.25648i	0.918147	+	0.396240i	$0.129685\pi$
$53$	2.97214	+	9.14729i	0.408254	+	1.25648i	−0.509893	+	0.860238i	$0.670315\pi$
$54$	−0.618034			−0.0841038
$55$		0			0
$56$	6.70820			0.896421
$57$	−1.80902	−	5.56758i	−0.239610	−	0.737444i
$58$	−2.23607	−	1.62460i	−0.293610	−	0.213320i
$59$	−8.35410	+	6.06961i	−1.08761	+	0.790196i	−0.978994	−	0.203888i	$-0.934642\pi$
$59$	−8.35410	+	6.06961i	−1.08761	+	0.790196i	−0.108617	+	0.994084i	$0.534642\pi$
$60$		0			0
$61$	2.42705	−	7.46969i	0.310752	−	0.956396i	−0.666716	−	0.745312i	$-0.732301\pi$
$61$	2.42705	−	7.46969i	0.310752	−	0.956396i	0.977468	−	0.211084i	$-0.0676995\pi$
$62$	−1.42705	+	1.03681i	−0.181236	+	0.131675i
$63$	2.42705	+	1.76336i	0.305780	+	0.222162i
$64$	−0.0729490	−	0.224514i	−0.00911863	−	0.0280642i
$65$		0			0
$66$	1.35410	+	1.53884i	0.166678	+	0.189418i
$67$	9.56231			1.16822			0.584111	−	0.811674i	$-0.301443\pi$
$67$	9.56231			1.16822			0.584111	+	0.811674i	$0.301443\pi$
$68$	0.809017	+	2.48990i	0.0981077	+	0.301945i
$69$	−2.80902	−	2.04087i	−0.338166	−	0.245692i
$70$		0			0
$71$	−1.71885	+	5.29007i	−0.203990	+	0.627815i	0.795764	+	0.605607i	$0.207070\pi$
$71$	−1.71885	+	5.29007i	−0.203990	+	0.627815i	−0.999753	+	0.0222083i	$0.992930\pi$
$72$	−0.690983	+	2.12663i	−0.0814331	+	0.250625i
$73$	−2.61803	+	1.90211i	−0.306418	+	0.222625i	−0.730358	−	0.683065i	$-0.760647\pi$
$73$	−2.61803	+	1.90211i	−0.306418	+	0.222625i	0.423940	+	0.905690i	$0.360647\pi$
$74$	0.118034	+	0.0857567i	0.0137212	+	0.00996902i
$75$		0			0
$76$	−9.47214			−1.08653
$77$	−0.927051	−	9.90659i	−0.105647	−	1.12896i
$78$	1.09017			0.123437
$79$	2.92705	+	9.00854i	0.329319	+	1.01354i	0.969453	+	0.245276i	$0.0788787\pi$
$79$	2.92705	+	9.00854i	0.329319	+	1.01354i	−0.640134	+	0.768263i	$0.721121\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−2.28115	+	7.02067i	−0.251911	+	0.775303i
$83$	−0.218847	+	0.673542i	−0.0240216	+	0.0739308i	−0.962349	−	0.271818i	$-0.912375\pi$
$83$	−0.218847	+	0.673542i	−0.0240216	+	0.0739308i	0.938327	+	0.345749i	$0.112375\pi$
$84$	3.92705	−	2.85317i	0.428476	−	0.311306i
$85$		0			0
$86$	−1.19098	−	3.66547i	−0.128427	−	0.395258i
$87$	−4.47214			−0.479463
$88$	6.80902	−	2.93893i	0.725844	−	0.313291i
$89$	0.527864			0.0559535			0.0279767	−	0.999609i	$-0.491094\pi$
$89$	0.527864			0.0559535			0.0279767	+	0.999609i	$0.491094\pi$
$90$		0			0
$91$	−4.28115	−	3.11044i	−0.448787	−	0.326063i
$92$	−4.54508	+	3.30220i	−0.473858	+	0.344278i
$93$	−0.881966	+	2.71441i	−0.0914556	+	0.281471i
$94$	−0.309017	+	0.951057i	−0.0318727	+	0.0980940i
$95$		0			0
$96$	4.54508	+	3.30220i	0.463881	+	0.337029i
$97$	4.33688	+	13.3475i	0.440344	+	1.35524i	0.887510	+	0.460788i	$0.152433\pi$
$97$	4.33688	+	13.3475i	0.440344	+	1.35524i	−0.447167	+	0.894451i	$0.647567\pi$
$98$	1.23607			0.124862
$99$	3.23607	+	0.726543i	0.325237	+	0.0730203i
$100$		0			0
$101$	−0.927051	−	2.85317i	−0.0922450	−	0.283901i	0.894281	−	0.447506i	$-0.147688\pi$
$101$	−0.927051	−	2.85317i	−0.0922450	−	0.283901i	−0.986526	+	0.163605i	$0.947688\pi$
$102$	−0.809017	−	0.587785i	−0.0801046	−	0.0581994i
$103$	−4.85410	+	3.52671i	−0.478289	+	0.347497i	−0.800663	−	0.599115i	$-0.795519\pi$
$103$	−4.85410	+	3.52671i	−0.478289	+	0.347497i	0.322374	+	0.946612i	$0.395519\pi$
$104$	1.21885	−	3.75123i	0.119518	−	0.367838i
$105$		0			0
$106$	−4.80902	+	3.49396i	−0.467093	+	0.339363i
$107$	−3.42705	−	2.48990i	−0.331306	−	0.240708i	0.409679	−	0.912230i	$-0.365641\pi$
$107$	−3.42705	−	2.48990i	−0.331306	−	0.240708i	−0.740984	+	0.671522i	$0.765641\pi$
$108$	0.500000	+	1.53884i	0.0481125	+	0.148075i
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$		0			0
$111$	0.236068			0.0224066
$112$	−1.71885	−	5.29007i	−0.162416	−	0.499864i
$113$	0.572949	+	0.416272i	0.0538985	+	0.0391596i	0.614408	−	0.788988i	$-0.289395\pi$
$113$	0.572949	+	0.416272i	0.0538985	+	0.0391596i	−0.560510	+	0.828148i	$0.689395\pi$
$114$	2.92705	−	2.12663i	0.274143	−	0.199177i
$115$		0			0
$116$	−2.23607	+	6.88191i	−0.207614	+	0.638969i
$117$	1.42705	−	1.03681i	0.131931	−	0.0958534i
$118$	−5.16312	−	3.75123i	−0.475304	−	0.345328i
$119$	1.50000	+	4.61653i	0.137505	+	0.423196i
$120$		0			0
$121$	−5.28115	−	9.64932i	−0.480105	−	0.877211i
$122$	4.85410			0.439470
$123$	3.69098	+	11.3597i	0.332805	+	1.02427i
$124$	3.73607	+	2.71441i	0.335509	+	0.243761i
$125$		0			0
$126$	−0.572949	+	1.76336i	−0.0510424	+	0.157092i
$127$	1.14590	−	3.52671i	0.101682	−	0.312945i	−0.887255	−	0.461279i	$-0.847391\pi$
$127$	1.14590	−	3.52671i	0.101682	−	0.312945i	0.988937	+	0.148333i	$0.0473909\pi$
$128$	9.20820	−	6.69015i	0.813898	−	0.591331i
$129$	−5.04508	−	3.66547i	−0.444195	−	0.322727i
$130$		0			0
$131$	−7.14590			−0.624340			−0.312170	−	0.950026i	$-0.601056\pi$
$131$	−7.14590			−0.624340			−0.312170	+	0.950026i	$0.601056\pi$
$132$	2.73607	−	4.61653i	0.238144	−	0.401817i
$133$	−17.5623			−1.52285
$134$	1.82624	+	5.62058i	0.157763	+	0.485544i
$135$		0			0
$136$	−2.92705	+	2.12663i	−0.250993	+	0.182357i
$137$	−2.30902	+	7.10642i	−0.197273	+	0.607143i	0.802670	+	0.596424i	$0.203412\pi$
$137$	−2.30902	+	7.10642i	−0.197273	+	0.607143i	−0.999943	+	0.0107192i	$0.996588\pi$
$138$	0.663119	−	2.04087i	0.0564484	−	0.173730i
$139$	0.690983	−	0.502029i	0.0586084	−	0.0425815i	−0.558095	−	0.829777i	$-0.688468\pi$
$139$	0.690983	−	0.502029i	0.0586084	−	0.0425815i	0.616704	+	0.787195i	$0.288468\pi$
$140$		0			0
$141$	0.500000	+	1.53884i	0.0421076	+	0.129594i
$142$	−3.43769			−0.288485
$143$	−5.70820	−	1.28157i	−0.477344	−	0.107170i
$144$	1.85410			0.154508
$145$		0			0
$146$	−1.61803	−	1.17557i	−0.133909	−	0.0972909i
$147$	1.61803	−	1.17557i	0.133453	−	0.0969594i
$148$	0.118034	−	0.363271i	0.00970233	−	0.0298607i
$149$	4.63525	−	14.2658i	0.379735	−	1.16870i	−0.560493	−	0.828159i	$-0.689388\pi$
$149$	4.63525	−	14.2658i	0.379735	−	1.16870i	0.940228	−	0.340545i	$-0.110612\pi$
$150$		0			0
$151$	−1.61803	−	1.17557i	−0.131674	−	0.0956666i	0.519999	−	0.854167i	$-0.325932\pi$
$151$	−1.61803	−	1.17557i	−0.131674	−	0.0956666i	−0.651673	+	0.758500i	$0.725932\pi$
$152$	−4.04508	−	12.4495i	−0.328100	−	1.00979i
$153$	−1.61803			−0.130810
$154$	5.64590	−	2.43690i	0.454959	−	0.196371i
$155$		0			0
$156$	−0.881966	−	2.71441i	−0.0706138	−	0.217327i
$157$	−3.00000	−	2.17963i	−0.239426	−	0.173953i	0.461601	−	0.887087i	$-0.347275\pi$
$157$	−3.00000	−	2.17963i	−0.239426	−	0.173953i	−0.701028	+	0.713134i	$0.747275\pi$
$158$	−4.73607	+	3.44095i	−0.376781	+	0.273748i
$159$	−2.97214	+	9.14729i	−0.235706	+	0.725428i
$160$		0			0
$161$	−8.42705	+	6.12261i	−0.664145	+	0.482529i
$162$	−0.500000	−	0.363271i	−0.0392837	−	0.0285413i
$163$	−5.64590	−	17.3763i	−0.442221	−	1.36102i	−0.885503	−	0.464634i	$-0.846186\pi$
$163$	−5.64590	−	17.3763i	−0.442221	−	1.36102i	0.443282	−	0.896382i	$-0.353814\pi$
$164$	19.3262			1.50913
$165$		0			0
$166$	−0.437694			−0.0339717
$167$	−3.10081	−	9.54332i	−0.239948	−	0.738484i	−0.996426	−	0.0844656i	$-0.973082\pi$
$167$	−3.10081	−	9.54332i	−0.239948	−	0.738484i	0.756478	−	0.654019i	$-0.226918\pi$
$168$	5.42705	+	3.94298i	0.418706	+	0.304208i
$169$	8.00000	−	5.81234i	0.615385	−	0.447103i
$170$		0			0
$171$	1.80902	−	5.56758i	0.138339	−	0.425764i
$172$	−8.16312	+	5.93085i	−0.622432	+	0.452223i
$173$	12.4443	+	9.04129i	0.946120	+	0.687397i	0.949886	−	0.312596i	$-0.101199\pi$
$173$	12.4443	+	9.04129i	0.946120	+	0.687397i	−0.00376565	+	0.999993i	$0.501199\pi$
$174$	−0.854102	−	2.62866i	−0.0647493	−	0.199278i
$175$		0			0
$176$	−4.06231	−	4.61653i	−0.306208	−	0.347984i
$177$	−10.3262			−0.776168
$178$	0.100813	+	0.310271i	0.00755626	+	0.0232558i
$179$	1.80902	+	1.31433i	0.135212	+	0.0982375i	0.653335	−	0.757069i	$-0.273369\pi$
$179$	1.80902	+	1.31433i	0.135212	+	0.0982375i	−0.518123	+	0.855306i	$0.673369\pi$
$180$		0			0
$181$	−5.39919	+	16.6170i	−0.401318	+	1.23513i	0.522612	+	0.852571i	$0.324958\pi$
$181$	−5.39919	+	16.6170i	−0.401318	+	1.23513i	−0.923930	+	0.382560i	$0.875042\pi$
$182$	1.01064	−	3.11044i	0.0749139	−	0.230561i
$183$	6.35410	−	4.61653i	0.469709	−	0.341263i
$184$	−6.28115	−	4.56352i	−0.463053	−	0.336428i
$185$		0			0
$186$	−1.76393			−0.129338
$187$	3.54508	+	4.02874i	0.259242	+	0.294611i
$188$	2.61803			0.190940
$189$	0.927051	+	2.85317i	0.0674330	+	0.207538i
$190$		0			0
$191$	6.04508	−	4.39201i	0.437407	−	0.317795i	−0.347197	−	0.937792i	$-0.612866\pi$
$191$	6.04508	−	4.39201i	0.437407	−	0.317795i	0.784604	+	0.619998i	$0.212866\pi$
$192$	0.0729490	−	0.224514i	0.00526464	−	0.0162029i
$193$	5.73607	−	17.6538i	0.412891	−	1.27075i	−0.501232	−	0.865313i	$-0.667120\pi$
$193$	5.73607	−	17.6538i	0.412891	−	1.27075i	0.914124	−	0.405436i	$-0.132880\pi$
$194$	−7.01722	+	5.09831i	−0.503807	+	0.366037i
$195$		0			0
$196$	−1.00000	−	3.07768i	−0.0714286	−	0.219835i
$197$	−24.3820			−1.73714			−0.868572	−	0.495564i	$-0.834961\pi$
$197$	−24.3820			−1.73714			−0.868572	+	0.495564i	$0.834961\pi$
$198$	0.190983	+	2.04087i	0.0135726	+	0.145038i
$199$	−16.7082			−1.18441			−0.592207	−	0.805786i	$-0.701743\pi$
$199$	−16.7082			−1.18441			−0.592207	+	0.805786i	$0.701743\pi$
$200$		0			0
$201$	7.73607	+	5.62058i	0.545660	+	0.396445i
$202$	1.50000	−	1.08981i	0.105540	−	0.0766790i
$203$	−4.14590	+	12.7598i	−0.290985	+	0.895560i
$204$	−0.809017	+	2.48990i	−0.0566425	+	0.174328i
$205$		0			0
$206$	−3.00000	−	2.17963i	−0.209020	−	0.151862i
$207$	−1.07295	−	3.30220i	−0.0745751	−	0.229519i
$208$	−3.27051			−0.226769
$209$	−17.8262	+	7.69421i	−1.23307	+	0.532220i
$210$		0			0
$211$	−6.88197	−	21.1805i	−0.473774	−	1.45813i	−0.847604	−	0.530629i	$-0.821956\pi$
$211$	−6.88197	−	21.1805i	−0.473774	−	1.45813i	0.373830	−	0.927497i	$-0.378044\pi$
$212$	12.5902	+	9.14729i	0.864696	+	0.628239i
$213$	−4.50000	+	3.26944i	−0.308335	+	0.224018i
$214$	0.809017	−	2.48990i	0.0553033	−	0.170206i
$215$		0			0
$216$	−1.80902	+	1.31433i	−0.123088	+	0.0894287i
$217$	6.92705	+	5.03280i	0.470239	+	0.341649i
$218$		0			0
$219$	−3.23607			−0.218673
$220$		0			0
$221$	2.85410			0.191988
$222$	0.0450850	+	0.138757i	0.00302591	+	0.00931278i
$223$	0.572949	+	0.416272i	0.0383675	+	0.0278756i	0.606804	−	0.794852i	$-0.292451\pi$
$223$	0.572949	+	0.416272i	0.0383675	+	0.0278756i	−0.568436	+	0.822727i	$0.692451\pi$
$224$	13.6353	−	9.90659i	0.911044	−	0.661912i
$225$		0			0
$226$	−0.135255	+	0.416272i	−0.00899702	+	0.0276900i
$227$	−20.1353	+	14.6291i	−1.33642	+	0.970969i	−0.336856	+	0.941556i	$0.609364\pi$
$227$	−20.1353	+	14.6291i	−1.33642	+	0.970969i	−0.999567	+	0.0294127i	$0.990636\pi$
$228$	−7.66312	−	5.56758i	−0.507502	−	0.368722i
$229$	3.09017	+	9.51057i	0.204204	+	0.628476i	0.999745	+	0.0225760i	$0.00718678\pi$
$229$	3.09017	+	9.51057i	0.204204	+	0.628476i	−0.795541	+	0.605900i	$0.792813\pi$
$230$		0			0
$231$	5.07295	−	8.55951i	0.333776	−	0.563174i
$232$	−10.0000			−0.656532
$233$	−7.51722	−	23.1356i	−0.492470	−	1.51567i	−0.820863	−	0.571124i	$-0.806507\pi$
$233$	−7.51722	−	23.1356i	−0.492470	−	1.51567i	0.328394	−	0.944541i	$-0.393493\pi$
$234$	0.881966	+	0.640786i	0.0576559	+	0.0418895i
$235$		0			0
$236$	−5.16312	+	15.8904i	−0.336090	+	1.03438i
$237$	−2.92705	+	9.00854i	−0.190132	+	0.585167i
$238$	−2.42705	+	1.76336i	−0.157322	+	0.114301i
$239$	−2.07295	−	1.50609i	−0.134088	−	0.0974206i	0.518719	−	0.854945i	$-0.326409\pi$
$239$	−2.07295	−	1.50609i	−0.134088	−	0.0974206i	−0.652807	+	0.757524i	$0.726409\pi$
$240$		0			0
$241$	−23.1246			−1.48959			−0.744794	−	0.667295i	$-0.767452\pi$
$241$	−23.1246			−1.48959			−0.744794	+	0.667295i	$0.767452\pi$
$242$	4.66312	−	4.94704i	0.299757	−	0.318008i
$243$	−1.00000			−0.0641500
$244$	−3.92705	−	12.0862i	−0.251404	−	0.773741i
$245$		0			0
$246$	−5.97214	+	4.33901i	−0.380769	+	0.276645i
$247$	−3.19098	+	9.82084i	−0.203037	+	0.624885i
$248$	−1.97214	+	6.06961i	−0.125231	+	0.385421i
$249$	−0.572949	+	0.416272i	−0.0363092	+	0.0263802i
$250$		0			0
$251$	−2.40983	−	7.41669i	−0.152107	−	0.468138i	0.845749	−	0.533581i	$-0.179154\pi$
$251$	−2.40983	−	7.41669i	−0.152107	−	0.468138i	−0.997856	+	0.0654431i	$0.979154\pi$
$252$	4.85410			0.305780
$253$	−5.87132	+	9.90659i	−0.369127	+	0.622822i
$254$	2.29180			0.143800
$255$		0			0
$256$	5.30902	+	3.85723i	0.331814	+	0.241077i
$257$	−9.44427	+	6.86167i	−0.589117	+	0.428019i	−0.842000	−	0.539478i	$-0.818622\pi$
$257$	−9.44427	+	6.86167i	−0.589117	+	0.428019i	0.252882	+	0.967497i	$0.418622\pi$
$258$	1.19098	−	3.66547i	0.0741474	−	0.228202i
$259$	0.218847	−	0.673542i	0.0135985	−	0.0418519i
$260$		0			0
$261$	−3.61803	−	2.62866i	−0.223951	−	0.162710i
$262$	−1.36475	−	4.20025i	−0.0843142	−	0.259493i
$263$	16.3262			1.00672			0.503359	−	0.864077i	$-0.332097\pi$
$263$	16.3262			1.00672			0.503359	+	0.864077i	$0.332097\pi$
$264$	7.23607	+	1.62460i	0.445349	+	0.0999871i
$265$		0			0
$266$	−3.35410	−	10.3229i	−0.205653	−	0.632935i
$267$	0.427051	+	0.310271i	0.0261351	+	0.0189883i
$268$	12.5172	−	9.09429i	0.764611	−	0.555522i
$269$	4.79837	−	14.7679i	0.292562	−	0.900413i	−0.691467	−	0.722408i	$-0.743035\pi$
$269$	4.79837	−	14.7679i	0.292562	−	0.900413i	0.984029	−	0.178006i	$-0.0569645\pi$
$270$		0			0
$271$	22.0623	−	16.0292i	1.34019	−	0.973705i	0.340753	−	0.940153i	$-0.389318\pi$
$271$	22.0623	−	16.0292i	1.34019	−	0.973705i	0.999437	−	0.0335518i	$-0.0106819\pi$
$272$	2.42705	+	1.76336i	0.147162	+	0.106919i
$273$	−1.63525	−	5.03280i	−0.0989701	−	0.304599i
$274$	−4.61803			−0.278986
$275$		0			0
$276$	−5.61803			−0.338166
$277$	−9.44427	−	29.0665i	−0.567451	−	1.74644i	−0.660554	−	0.750779i	$-0.729678\pi$
$277$	−9.44427	−	29.0665i	−0.567451	−	1.74644i	0.0931022	−	0.995657i	$-0.470322\pi$
$278$	0.427051	+	0.310271i	0.0256128	+	0.0186088i
$279$	−2.30902	+	1.67760i	−0.138237	+	0.100435i
$280$		0			0
$281$	−0.236068	+	0.726543i	−0.0140826	+	0.0433419i	−0.957851	−	0.287266i	$-0.907254\pi$
$281$	−0.236068	+	0.726543i	−0.0140826	+	0.0433419i	0.943768	+	0.330608i	$0.107254\pi$
$282$	−0.809017	+	0.587785i	−0.0481763	+	0.0350021i
$283$	0.145898	+	0.106001i	0.00867274	+	0.00630111i	0.592113	−	0.805855i	$-0.298294\pi$
$283$	0.145898	+	0.106001i	0.00867274	+	0.00630111i	−0.583440	+	0.812156i	$0.698294\pi$
$284$	2.78115	+	8.55951i	0.165031	+	0.507913i
$285$		0			0
$286$	−0.336881	−	3.59996i	−0.0199202	−	0.212870i
$287$	35.8328			2.11514
$288$	1.73607	+	5.34307i	0.102299	+	0.314843i
$289$	11.6353	+	8.45351i	0.684427	+	0.497265i
$290$		0			0
$291$	−4.33688	+	13.3475i	−0.254232	+	0.782447i
$292$	−1.61803	+	4.97980i	−0.0946883	+	0.291421i
$293$	0.0450850	−	0.0327561i	0.00263389	−	0.00191363i	−0.586468	−	0.809973i	$-0.699482\pi$
$293$	0.0450850	−	0.0327561i	0.00263389	−	0.00191363i	0.589101	+	0.808059i	$0.299482\pi$
$294$	1.00000	+	0.726543i	0.0583212	+	0.0423728i
$295$		0			0
$296$	0.527864			0.0306815
$297$	2.19098	+	2.48990i	0.127134	+	0.144479i
$298$	9.27051			0.537026
$299$	1.89261	+	5.82485i	0.109452	+	0.336860i
$300$		0			0
$301$	−15.1353	+	10.9964i	−0.872382	+	0.633822i
$302$	0.381966	−	1.17557i	0.0219797	−	0.0676465i
$303$	0.927051	−	2.85317i	0.0532577	−	0.163910i
$304$	−8.78115	+	6.37988i	−0.503634	+	0.365911i
$305$		0			0
$306$	−0.309017	−	0.951057i	−0.0176653	−	0.0543683i
$307$	−0.562306			−0.0320925			−0.0160462	−	0.999871i	$-0.505108\pi$
$307$	−0.562306			−0.0320925			−0.0160462	+	0.999871i	$0.505108\pi$
$308$	−10.6353	−	12.0862i	−0.606000	−	0.688676i
$309$	−6.00000			−0.341328
$310$		0			0
$311$	−2.04508	−	1.48584i	−0.115966	−	0.0842543i	0.528291	−	0.849064i	$-0.322833\pi$
$311$	−2.04508	−	1.48584i	−0.115966	−	0.0842543i	−0.644257	+	0.764809i	$0.722833\pi$
$312$	3.19098	−	2.31838i	0.180654	−	0.131253i
$313$	−7.98278	+	24.5685i	−0.451213	+	1.38869i	0.424310	+	0.905517i	$0.360517\pi$
$313$	−7.98278	+	24.5685i	−0.451213	+	1.38869i	−0.875524	+	0.483175i	$0.839483\pi$
$314$	0.708204	−	2.17963i	0.0399663	−	0.123004i
$315$		0			0
$316$	12.3992	+	9.00854i	0.697509	+	0.506770i
$317$	5.98278	+	18.4131i	0.336026	+	1.03418i	0.966214	+	0.257740i	$0.0829778\pi$
$317$	5.98278	+	18.4131i	0.336026	+	1.03418i	−0.630188	+	0.776443i	$0.717022\pi$
$318$	−5.94427			−0.333338
$319$	1.38197	+	14.7679i	0.0773752	+	0.826842i
$320$		0			0
$321$	−1.30902	−	4.02874i	−0.0730622	−	0.224862i
$322$	−5.20820	−	3.78398i	−0.290242	−	0.210873i
$323$	7.66312	−	5.56758i	0.426387	−	0.309789i
$324$	−0.500000	+	1.53884i	−0.0277778	+	0.0854912i
$325$		0			0
$326$	9.13525	−	6.63715i	0.505955	−	0.367598i
$327$		0			0
$328$	8.25329	+	25.4010i	0.455712	+	1.40254i
$329$	4.85410			0.267615
$330$		0			0
$331$	26.5967			1.46189			0.730945	−	0.682437i	$-0.239080\pi$
$331$	26.5967			1.46189			0.730945	+	0.682437i	$0.239080\pi$
$332$	0.354102	+	1.08981i	0.0194339	+	0.0598113i
$333$	0.190983	+	0.138757i	0.0104658	+	0.00760385i
$334$	5.01722	−	3.64522i	0.274530	−	0.199458i
$335$		0			0
$336$	1.71885	−	5.29007i	0.0937708	−	0.288597i
$337$	−0.236068	+	0.171513i	−0.0128594	+	0.00934293i	−0.594196	−	0.804320i	$-0.702530\pi$
$337$	−0.236068	+	0.171513i	−0.0128594	+	0.00934293i	0.581337	+	0.813663i	$0.302530\pi$
$338$	4.94427	+	3.59222i	0.268933	+	0.195391i
$339$	0.218847	+	0.673542i	0.0118861	+	0.0365818i
$340$		0			0
$341$	9.23607	+	2.07363i	0.500161	+	0.112293i
$342$	3.61803			0.195641
$343$	4.63525	+	14.2658i	0.250280	+	0.770283i
$344$	−11.2812	−	8.19624i	−0.608239	−	0.441912i
$345$		0			0
$346$	−2.93769	+	9.04129i	−0.157931	+	0.486063i
$347$	6.47214	−	19.9192i	0.347442	−	1.06932i	−0.612821	−	0.790222i	$-0.709965\pi$
$347$	6.47214	−	19.9192i	0.347442	−	1.06932i	0.960263	−	0.279096i	$-0.0900348\pi$
$348$	−5.85410	+	4.25325i	−0.313813	+	0.227998i
$349$	8.19098	+	5.95110i	0.438453	+	0.318555i	0.785020	−	0.619470i	$-0.212653\pi$
$349$	8.19098	+	5.95110i	0.438453	+	0.318555i	−0.346567	+	0.938025i	$0.612653\pi$
$350$		0			0
$351$	1.76393			0.0941517
$352$	9.50000	−	16.0292i	0.506352	−	0.854359i
$353$	10.4721			0.557376			0.278688	−	0.960382i	$-0.410101\pi$
$353$	10.4721			0.557376			0.278688	+	0.960382i	$0.410101\pi$
$354$	−1.97214	−	6.06961i	−0.104818	−	0.322596i
$355$		0			0
$356$	0.690983	−	0.502029i	0.0366220	−	0.0266075i
$357$	−1.50000	+	4.61653i	−0.0793884	+	0.244332i
$358$	−0.427051	+	1.31433i	−0.0225703	+	0.0694644i
$359$	10.3262	−	7.50245i	0.544998	−	0.395964i	−0.280940	−	0.959725i	$-0.590646\pi$
$359$	10.3262	−	7.50245i	0.544998	−	0.395964i	0.825938	+	0.563761i	$0.190646\pi$
$360$		0			0
$361$	4.71885	+	14.5231i	0.248360	+	0.764375i
$362$	−10.7984			−0.567550
$363$	1.39919	−	10.9106i	0.0734383	−	0.572661i
$364$	−8.56231			−0.448787
$365$		0			0
$366$	3.92705	+	2.85317i	0.205270	+	0.149138i
$367$	4.50000	−	3.26944i	0.234898	−	0.170663i	−0.464109	−	0.885778i	$-0.653625\pi$
$367$	4.50000	−	3.26944i	0.234898	−	0.170663i	0.699007	+	0.715115i	$0.253625\pi$
$368$	−1.98936	+	6.12261i	−0.103702	+	0.319163i
$369$	−3.69098	+	11.3597i	−0.192145	+	0.591361i
$370$		0			0
$371$	23.3435	+	16.9600i	1.21193	+	0.880520i
$372$	1.42705	+	4.39201i	0.0739891	+	0.227715i
$373$	4.41641			0.228673			0.114336	−	0.993442i	$-0.463526\pi$
$373$	4.41641			0.228673			0.114336	+	0.993442i	$0.463526\pi$
$374$	−1.69098	+	2.85317i	−0.0874386	+	0.147534i
$375$		0			0
$376$	1.11803	+	3.44095i	0.0576582	+	0.177454i
$377$	6.38197	+	4.63677i	0.328688	+	0.238806i
$378$	−1.50000	+	1.08981i	−0.0771517	+	0.0560540i
$379$	0.489357	−	1.50609i	0.0251366	−	0.0773624i	−0.937701	−	0.347443i	$-0.887050\pi$
$379$	0.489357	−	1.50609i	0.0251366	−	0.0773624i	0.962838	+	0.270080i	$0.0870502\pi$
$380$		0			0
$381$	3.00000	−	2.17963i	0.153695	−	0.111666i
$382$	3.73607	+	2.71441i	0.191154	+	0.138881i
$383$	−8.30902	−	25.5725i	−0.424571	−	1.30669i	−0.903405	−	0.428789i	$-0.858940\pi$
$383$	−8.30902	−	25.5725i	−0.424571	−	1.30669i	0.478834	−	0.877906i	$-0.341060\pi$
$384$	11.3820			0.580834
$385$		0			0
$386$	11.4721			0.583916
$387$	−1.92705	−	5.93085i	−0.0979575	−	0.301482i
$388$	18.3713	+	13.3475i	0.932663	+	0.677619i
$389$	−19.6353	+	14.2658i	−0.995547	+	0.723307i	−0.961129	−	0.276100i	$-0.910958\pi$
$389$	−19.6353	+	14.2658i	−0.995547	+	0.723307i	−0.0344181	+	0.999408i	$0.510958\pi$
$390$		0			0
$391$	1.73607	−	5.34307i	0.0877967	−	0.270211i
$392$	3.61803	−	2.62866i	0.182738	−	0.132767i
$393$	−5.78115	−	4.20025i	−0.291621	−	0.211875i
$394$	−4.65654	−	14.3314i	−0.234593	−	0.722003i
$395$		0			0
$396$	4.92705	−	2.12663i	0.247594	−	0.106867i
$397$	38.7082			1.94271			0.971355	−	0.237635i	$-0.0763722\pi$
$397$	38.7082			1.94271			0.971355	+	0.237635i	$0.0763722\pi$
$398$	−3.19098	−	9.82084i	−0.159950	−	0.492274i
$399$	−14.2082	−	10.3229i	−0.711300	−	0.516790i
$400$		0			0
$401$	−8.06231	+	24.8132i	−0.402612	+	1.23911i	0.520260	+	0.854008i	$0.325835\pi$
$401$	−8.06231	+	24.8132i	−0.402612	+	1.23911i	−0.922873	+	0.385106i	$0.874165\pi$
$402$	−1.82624	+	5.62058i	−0.0910845	+	0.280329i
$403$	4.07295	−	2.95917i	0.202888	−	0.147407i
$404$	−3.92705	−	2.85317i	−0.195378	−	0.141950i
$405$		0			0
$406$	−8.29180			−0.411515
$407$	−0.0729490	−	0.779543i	−0.00361595	−	0.0386405i
$408$	−3.61803			−0.179119
$409$	−3.41641	−	10.5146i	−0.168930	−	0.519915i	0.830374	−	0.557207i	$-0.188127\pi$
$409$	−3.41641	−	10.5146i	−0.168930	−	0.519915i	−0.999304	+	0.0372920i	$0.988127\pi$
$410$		0			0
$411$	−6.04508	+	4.39201i	−0.298182	+	0.216642i
$412$	−3.00000	+	9.23305i	−0.147799	+	0.454880i
$413$	−9.57295	+	29.4625i	−0.471054	+	1.44976i
$414$	1.73607	−	1.26133i	0.0853231	−	0.0619909i
$415$		0			0
$416$	−3.06231	−	9.42481i	−0.150142	−	0.462089i
$417$	0.854102			0.0418256
$418$	−7.92705	−	9.00854i	−0.387725	−	0.440622i
$419$	16.5066			0.806399			0.403200	−	0.915112i	$-0.367898\pi$
$419$	16.5066			0.806399			0.403200	+	0.915112i	$0.367898\pi$
$420$		0			0
$421$	30.1525	+	21.9071i	1.46954	+	1.06768i	0.980746	+	0.195286i	$0.0625636\pi$
$421$	30.1525	+	21.9071i	1.46954	+	1.06768i	0.488795	+	0.872398i	$0.337436\pi$
$422$	11.1353	−	8.09024i	0.542056	−	0.393827i
$423$	−0.500000	+	1.53884i	−0.0243108	+	0.0748210i
$424$	−6.64590	+	20.4540i	−0.322753	+	0.993333i
$425$		0			0
$426$	−2.78115	−	2.02063i	−0.134747	−	0.0978996i
$427$	−7.28115	−	22.4091i	−0.352360	−	1.08445i
$428$	−6.85410			−0.331306
$429$	−3.86475	−	4.39201i	−0.186592	−	0.212048i
$430$		0			0
$431$	−12.2082	−	37.5730i	−0.588048	−	1.80983i	−0.586667	−	0.809828i	$-0.699560\pi$
$431$	−12.2082	−	37.5730i	−0.588048	−	1.80983i	−0.00138127	−	0.999999i	$-0.500440\pi$
$432$	1.50000	+	1.08981i	0.0721688	+	0.0524337i
$433$	−4.85410	+	3.52671i	−0.233273	+	0.169483i	−0.698281	−	0.715824i	$-0.746051\pi$
$433$	−4.85410	+	3.52671i	−0.233273	+	0.169483i	0.465008	+	0.885307i	$0.346051\pi$
$434$	−1.63525	+	5.03280i	−0.0784947	+	0.241582i
$435$		0			0
$436$		0			0
$437$	16.4443	+	11.9475i	0.786636	+	0.571525i
$438$	−0.618034	−	1.90211i	−0.0295308	−	0.0908865i
$439$	3.29180			0.157109			0.0785544	−	0.996910i	$-0.474970\pi$
$439$	3.29180			0.157109			0.0785544	+	0.996910i	$0.474970\pi$
$440$		0			0
$441$	2.00000			0.0952381
$442$	0.545085	+	1.67760i	0.0259270	+	0.0797952i
$443$	−33.2705	−	24.1724i	−1.58073	−	1.14847i	−0.915853	−	0.401514i	$-0.868484\pi$
$443$	−33.2705	−	24.1724i	−1.58073	−	1.14847i	−0.664877	−	0.746953i	$-0.731516\pi$
$444$	0.309017	−	0.224514i	0.0146653	−	0.0106550i
$445$		0			0
$446$	−0.135255	+	0.416272i	−0.00640451	+	0.0197110i
$447$	12.1353	−	8.81678i	0.573978	−	0.417019i
$448$	−0.572949	−	0.416272i	−0.0270693	−	0.0196670i
$449$	−7.56231	−	23.2744i	−0.356887	−	1.09839i	−0.954907	−	0.296905i	$-0.904046\pi$
$449$	−7.56231	−	23.2744i	−0.356887	−	1.09839i	0.598020	−	0.801481i	$-0.295954\pi$
$450$		0			0
$451$	36.3713	−	15.6987i	1.71266	−	0.739222i
$452$	1.14590			0.0538985
$453$	−0.618034	−	1.90211i	−0.0290378	−	0.0893691i
$454$	−12.4443	−	9.04129i	−0.584039	−	0.424329i
$455$		0			0
$456$	4.04508	−	12.4495i	0.189428	−	0.583001i
$457$	−2.53444	+	7.80021i	−0.118556	+	0.364878i	−0.992672	−	0.120839i	$-0.961442\pi$
$457$	−2.53444	+	7.80021i	−0.118556	+	0.364878i	0.874116	+	0.485717i	$0.161442\pi$
$458$	−5.00000	+	3.63271i	−0.233635	+	0.169746i
$459$	−1.30902	−	0.951057i	−0.0610997	−	0.0443915i
$460$		0			0
$461$	−21.0902			−0.982267			−0.491134	−	0.871084i	$-0.663417\pi$
$461$	−21.0902			−0.982267			−0.491134	+	0.871084i	$0.663417\pi$
$462$	6.00000	+	1.34708i	0.279145	+	0.0626720i
$463$	15.7984			0.734213			0.367106	−	0.930179i	$-0.380349\pi$
$463$	15.7984			0.734213			0.367106	+	0.930179i	$0.380349\pi$
$464$	2.56231	+	7.88597i	0.118952	+	0.366097i
$465$		0			0
$466$	12.1631	−	8.83702i	0.563446	−	0.409367i
$467$	3.01722	−	9.28605i	0.139620	−	0.429707i	−0.856660	−	0.515882i	$-0.827464\pi$
$467$	3.01722	−	9.28605i	0.139620	−	0.429707i	0.996280	+	0.0861747i	$0.0274643\pi$
$468$	0.881966	−	2.71441i	0.0407689	−	0.125474i
$469$	23.2082	−	16.8617i	1.07166	−	0.778603i
$470$		0			0
$471$	−1.14590	−	3.52671i	−0.0528002	−	0.162502i
$472$	−23.0902			−1.06281
$473$	−10.5451	+	17.7926i	−0.484864	+	0.818103i
$474$	−5.85410			−0.268888
$475$		0			0
$476$	6.35410	+	4.61653i	0.291240	+	0.211598i
$477$	−7.78115	+	5.65334i	−0.356275	+	0.258849i
$478$	0.489357	−	1.50609i	0.0223827	−	0.0688868i
$479$	−8.68034	+	26.7153i	−0.396615	+	1.22066i	0.531082	+	0.847320i	$0.321786\pi$
$479$	−8.68034	+	26.7153i	−0.396615	+	1.22066i	−0.927697	+	0.373335i	$0.878214\pi$
$480$		0			0
$481$	−0.336881	−	0.244758i	−0.0153605	−	0.0111600i
$482$	−4.41641	−	13.5923i	−0.201162	−	0.619113i
$483$	−10.4164			−0.473963
$484$	−16.0902	−	7.60845i	−0.731371	−	0.345839i
$485$		0			0
$486$	−0.190983	−	0.587785i	−0.00866317	−	0.0266625i
$487$	13.6074	+	9.88635i	0.616610	+	0.447993i	0.851736	−	0.523972i	$-0.175550\pi$
$487$	13.6074	+	9.88635i	0.616610	+	0.447993i	−0.235126	+	0.971965i	$0.575550\pi$
$488$	14.2082	−	10.3229i	0.643175	−	0.467294i
$489$	5.64590	−	17.3763i	0.255316	−	0.785783i
$490$		0			0
$491$	−20.3992	+	14.8209i	−0.920602	+	0.668857i	−0.943674	−	0.330877i	$-0.892655\pi$
$491$	−20.3992	+	14.8209i	−0.920602	+	0.668857i	0.0230715	+	0.999734i	$0.492655\pi$
$492$	15.6353	+	11.3597i	0.704892	+	0.512134i
$493$	−2.23607	−	6.88191i	−0.100707	−	0.309946i
$494$	−6.38197			−0.287138
$495$		0			0
$496$	5.29180			0.237609
$497$	5.15654	+	15.8702i	0.231302	+	0.711876i
$498$	−0.354102	−	0.257270i	−0.0158677	−	0.0115286i
$499$	14.2082	−	10.3229i	0.636047	−	0.462115i	−0.222443	−	0.974946i	$-0.571403\pi$
$499$	14.2082	−	10.3229i	0.636047	−	0.462115i	0.858490	+	0.512831i	$0.171403\pi$
$500$		0			0
$501$	3.10081	−	9.54332i	0.138534	−	0.426364i
$502$	3.89919	−	2.83293i	0.174029	−	0.126440i
$503$	22.7082	+	16.4985i	1.01251	+	0.735631i	0.964734	−	0.263227i	$-0.0847870\pi$
$503$	22.7082	+	16.4985i	1.01251	+	0.735631i	0.0477750	+	0.998858i	$0.484787\pi$
$504$	2.07295	+	6.37988i	0.0923365	+	0.284182i
$505$		0			0
$506$	−6.94427	−	1.55909i	−0.308711	−	0.0693098i
$507$	9.88854			0.439166
$508$	−1.85410	−	5.70634i	−0.0822625	−	0.253178i
$509$	−19.1074	−	13.8823i	−0.846920	−	0.615324i	0.0773749	−	0.997002i	$-0.475346\pi$
$509$	−19.1074	−	13.8823i	−0.846920	−	0.615324i	−0.924295	+	0.381679i	$0.875346\pi$
$510$		0			0
$511$	−3.00000	+	9.23305i	−0.132712	+	0.408446i
$512$	5.78115	−	17.7926i	0.255493	−	0.786327i
$513$	4.73607	−	3.44095i	0.209103	−	0.151922i
$514$	−5.83688	−	4.24074i	−0.257454	−	0.187051i
$515$		0			0
$516$	−10.0902			−0.444195
$517$	4.92705	−	2.12663i	0.216691	−	0.0935289i
$518$	0.437694			0.0192312
$519$	4.75329	+	14.6291i	0.208646	+	0.642147i
$520$		0			0
$521$	12.0000	−	8.71851i	0.525730	−	0.381965i	−0.293028	−	0.956104i	$-0.594663\pi$
$521$	12.0000	−	8.71851i	0.525730	−	0.381965i	0.818758	+	0.574139i	$0.194663\pi$
$522$	0.854102	−	2.62866i	0.0373830	−	0.115053i
$523$	3.70163	−	11.3924i	0.161861	−	0.498156i	−0.836930	−	0.547309i	$-0.815652\pi$
$523$	3.70163	−	11.3924i	0.161861	−	0.498156i	0.998791	+	0.0491529i	$0.0156522\pi$
$524$	−9.35410	+	6.79615i	−0.408636	+	0.296891i
$525$		0			0
$526$	3.11803	+	9.59632i	0.135953	+	0.418420i
$527$	−4.61803			−0.201165
$528$	−0.572949	−	6.12261i	−0.0249344	−	0.266452i
$529$	−10.9443			−0.475838
$530$		0			0
$531$	−8.35410	−	6.06961i	−0.362537	−	0.263399i
$532$	−22.9894	+	16.7027i	−0.996715	+	0.724156i
$533$	6.51064	−	20.0377i	0.282007	−	0.867929i
$534$	−0.100813	+	0.310271i	−0.00436261	+	0.0134267i
$535$		0			0
$536$	17.2984	+	12.5680i	0.747176	+	0.542855i
$537$	0.690983	+	2.12663i	0.0298181	+	0.0917707i
$538$	9.59675			0.413745
$539$	−4.38197	−	4.97980i	−0.188745	−	0.214495i
$540$		0			0
$541$	6.04508	+	18.6049i	0.259899	+	0.799885i	0.992825	+	0.119577i	$0.0381540\pi$
$541$	6.04508	+	18.6049i	0.259899	+	0.799885i	−0.732926	+	0.680308i	$0.761846\pi$
$542$	13.6353	+	9.90659i	0.585684	+	0.425525i
$543$	−14.1353	+	10.2699i	−0.606602	+	0.440722i
$544$	−2.80902	+	8.64527i	−0.120436	+	0.370663i
$545$		0			0
$546$	2.64590	−	1.92236i	0.113234	−	0.0822693i
$547$	17.4894	+	12.7068i	0.747791	+	0.543302i	0.895141	−	0.445782i	$-0.147075\pi$
$547$	17.4894	+	12.7068i	0.747791	+	0.543302i	−0.147350	+	0.989084i	$0.547075\pi$
$548$	3.73607	+	11.4984i	0.159597	+	0.491189i
$549$	7.85410			0.335205
$550$		0			0
$551$	26.1803			1.11532
$552$	−2.39919	−	7.38394i	−0.102116	−	0.314281i
$553$	22.9894	+	16.7027i	0.977607	+	0.710273i
$554$	15.2812	−	11.1024i	0.649234	−	0.471696i
$555$		0			0
$556$	0.427051	−	1.31433i	0.0181110	−	0.0557399i
$557$	12.0623	−	8.76378i	0.511096	−	0.371333i	−0.302143	−	0.953263i	$-0.597702\pi$
$557$	12.0623	−	8.76378i	0.511096	−	0.371333i	0.813239	+	0.581929i	$0.197702\pi$
$558$	−1.42705	−	1.03681i	−0.0604119	−	0.0438918i
$559$	3.39919	+	10.4616i	0.143770	+	0.442479i
$560$		0			0
$561$	0.500000	+	5.34307i	0.0211100	+	0.225585i
$562$	−0.472136			−0.0199159
$563$	2.74671	+	8.45351i	0.115760	+	0.356273i	0.992105	−	0.125412i	$-0.0400251\pi$
$563$	2.74671	+	8.45351i	0.115760	+	0.356273i	−0.876345	+	0.481684i	$0.840025\pi$
$564$	2.11803	+	1.53884i	0.0891853	+	0.0647969i
$565$		0			0
$566$	−0.0344419	+	0.106001i	−0.00144770	+	0.00445556i
$567$	−0.927051	+	2.85317i	−0.0389325	+	0.119822i
$568$	−10.0623	+	7.31069i	−0.422205	+	0.306750i
$569$	19.4721	+	14.1473i	0.816314	+	0.593087i	0.915654	−	0.401966i	$-0.131673\pi$
$569$	19.4721	+	14.1473i	0.816314	+	0.593087i	−0.0993400	+	0.995054i	$0.531673\pi$
$570$		0			0
$571$	34.6869			1.45160			0.725801	−	0.687905i	$-0.241469\pi$
$571$	34.6869			1.45160			0.725801	+	0.687905i	$0.241469\pi$
$572$	−8.69098	+	3.75123i	−0.363388	+	0.156847i
$573$	7.47214			0.312153
$574$	6.84346	+	21.0620i	0.285640	+	0.879111i
$575$		0			0
$576$	0.190983	−	0.138757i	0.00795763	−	0.00578155i
$577$	−3.32624	+	10.2371i	−0.138473	+	0.426176i	−0.996114	−	0.0880726i	$-0.971929\pi$
$577$	−3.32624	+	10.2371i	−0.138473	+	0.426176i	0.857641	+	0.514249i	$0.171929\pi$
$578$	−2.74671	+	8.45351i	−0.114248	+	0.351620i
$579$	15.0172	−	10.9106i	0.624094	−	0.453431i
$580$		0			0
$581$	0.656541	+	2.02063i	0.0272379	+	0.0838297i
$582$	−8.67376			−0.359539
$583$	31.1246	+	6.98791i	1.28905	+	0.289410i
$584$	−7.23607			−0.299431
$585$		0			0
$586$	0.0278640	+	0.0202444i	0.00115105	+	0.000836289i
$587$	−30.9894	+	22.5151i	−1.27907	+	0.929297i	−0.999524	−	0.0308361i	$-0.990183\pi$
$587$	−30.9894	+	22.5151i	−1.27907	+	0.929297i	−0.279543	+	0.960133i	$0.590183\pi$
$588$	1.00000	−	3.07768i	0.0412393	−	0.126922i
$589$	5.16312	−	15.8904i	0.212743	−	0.654754i
$590$		0			0
$591$	−19.7254	−	14.3314i	−0.811396	−	0.589513i
$592$	−0.135255	−	0.416272i	−0.00555894	−	0.0171087i
$593$	−22.2148			−0.912252			−0.456126	−	0.889915i	$-0.650763\pi$
$593$	−22.2148			−0.912252			−0.456126	+	0.889915i	$0.650763\pi$
$594$	−1.04508	+	1.76336i	−0.0428804	+	0.0723514i
$595$		0			0
$596$	−7.50000	−	23.0826i	−0.307212	−	0.945501i
$597$	−13.5172	−	9.82084i	−0.553223	−	0.401940i
$598$	−3.06231	+	2.22490i	−0.125227	+	0.0909827i
$599$	−2.56231	+	7.88597i	−0.104693	+	0.322212i	−0.989658	−	0.143445i	$-0.954182\pi$
$599$	−2.56231	+	7.88597i	−0.104693	+	0.322212i	0.884965	+	0.465657i	$0.154182\pi$
$600$		0			0
$601$	−27.3713	+	19.8864i	−1.11650	+	0.811184i	−0.983675	−	0.179955i	$-0.942405\pi$
$601$	−27.3713	+	19.8864i	−1.11650	+	0.811184i	−0.132825	+	0.991140i	$0.542405\pi$
$602$	−9.35410	−	6.79615i	−0.381245	−	0.276991i
$603$	2.95492	+	9.09429i	0.120333	+	0.370348i
$604$	−3.23607			−0.131674
$605$		0			0
$606$	1.85410			0.0753177
$607$	−4.11803	−	12.6740i	−0.167146	−	0.514422i	0.832042	−	0.554712i	$-0.187172\pi$
$607$	−4.11803	−	12.6740i	−0.167146	−	0.514422i	−0.999188	+	0.0402904i	$0.987172\pi$
$608$	−26.6074	−	19.3314i	−1.07907	−	0.783992i
$609$	−10.8541	+	7.88597i	−0.439830	+	0.319555i
$610$		0			0
$611$	0.881966	−	2.71441i	0.0356805	−	0.109813i
$612$	−2.11803	+	1.53884i	−0.0856164	+	0.0622040i
$613$	28.0344	+	20.3682i	1.13230	+	0.822664i	0.986028	−	0.166580i	$-0.0532724\pi$
$613$	28.0344	+	20.3682i	1.13230	+	0.822664i	0.146272	+	0.989244i	$0.453272\pi$
$614$	−0.107391	−	0.330515i	−0.00433394	−	0.0133385i
$615$		0			0
$616$	11.3435	−	19.1396i	0.457041	−	0.771158i
$617$	−19.5836			−0.788406			−0.394203	−	0.919023i	$-0.628979\pi$
$617$	−19.5836			−0.788406			−0.394203	+	0.919023i	$0.628979\pi$
$618$	−1.14590	−	3.52671i	−0.0460948	−	0.141865i
$619$	7.13525	+	5.18407i	0.286790	+	0.208365i	0.721874	−	0.692025i	$-0.243281\pi$
$619$	7.13525	+	5.18407i	0.286790	+	0.208365i	−0.435084	+	0.900390i	$0.643281\pi$
$620$		0			0
$621$	1.07295	−	3.30220i	0.0430560	−	0.132513i
$622$	0.482779	−	1.48584i	0.0193577	−	0.0595768i
$623$	1.28115	−	0.930812i	0.0513283	−	0.0372922i
$624$	−2.64590	−	1.92236i	−0.105921	−	0.0769559i
$625$		0			0
$626$	−15.9656			−0.638112
$627$	−18.9443	−	4.25325i	−0.756561	−	0.169859i
$628$	−6.00000			−0.239426
$629$	0.118034	+	0.363271i	0.00470632	+	0.0144846i
$630$		0			0
$631$	−37.4336	+	27.1971i	−1.49021	+	1.08270i	−0.516125	+	0.856513i	$0.672626\pi$
$631$	−37.4336	+	27.1971i	−1.49021	+	1.08270i	−0.974084	+	0.226187i	$0.927374\pi$
$632$	−6.54508	+	20.1437i	−0.260350	+	0.801273i
$633$	6.88197	−	21.1805i	0.273534	−	0.841850i
$634$	−9.68034	+	7.03318i	−0.384455	+	0.279323i
$635$		0			0
$636$	4.80902	+	14.8006i	0.190690	+	0.586883i
$637$	−3.52786			−0.139779
$638$	−8.41641	+	3.63271i	−0.333209	+	0.143820i
$639$	−5.56231			−0.220041
$640$		0			0
$641$	−28.9164	−	21.0090i	−1.14213	−	0.829806i	−0.154715	−	0.987959i	$-0.549446\pi$
$641$	−28.9164	−	21.0090i	−1.14213	−	0.829806i	−0.987415	+	0.158154i	$0.949446\pi$
$642$	2.11803	−	1.53884i	0.0835921	−	0.0607332i
$643$	11.9164	−	36.6749i	0.469937	−	1.44632i	−0.382728	−	0.923861i	$-0.625015\pi$
$643$	11.9164	−	36.6749i	0.469937	−	1.44632i	0.852666	−	0.522457i	$-0.174985\pi$
$644$	−5.20820	+	16.0292i	−0.205232	+	0.631639i
$645$		0			0
$646$	4.73607	+	3.44095i	0.186338	+	0.135383i
$647$	−8.59017	−	26.4378i	−0.337714	−	1.03938i	−0.965369	−	0.260887i	$-0.915985\pi$
$647$	−8.59017	−	26.4378i	−0.337714	−	1.03938i	0.627655	−	0.778492i	$-0.284015\pi$
$648$	−2.23607			−0.0878410
$649$	3.19098	+	34.0993i	0.125257	+	1.33851i
$650$		0			0
$651$	2.64590	+	8.14324i	0.103701	+	0.319159i
$652$	−23.9164	−	17.3763i	−0.936639	−	0.680508i
$653$	41.2877	−	29.9973i	1.61571	−	1.17388i	0.776390	−	0.630252i	$-0.217049\pi$
$653$	41.2877	−	29.9973i	1.61571	−	1.17388i	0.839323	−	0.543632i	$-0.182951\pi$
$654$		0			0
$655$		0			0
$656$	17.9164	−	13.0170i	0.699518	−	0.508230i
$657$	−2.61803	−	1.90211i	−0.102139	−	0.0742085i
$658$	0.927051	+	2.85317i	0.0361402	+	0.111228i
$659$	−10.6525			−0.414962			−0.207481	−	0.978239i	$-0.566526\pi$
$659$	−10.6525			−0.414962			−0.207481	+	0.978239i	$0.566526\pi$
$660$		0			0
$661$	−9.90983			−0.385448			−0.192724	−	0.981253i	$-0.561732\pi$
$661$	−9.90983			−0.385448			−0.192724	+	0.981253i	$0.561732\pi$
$662$	5.07953	+	15.6332i	0.197421	+	0.607601i
$663$	2.30902	+	1.67760i	0.0896748	+	0.0651525i
$664$	−1.28115	+	0.930812i	−0.0497184	+	0.0361225i
$665$		0			0
$666$	−0.0450850	+	0.138757i	−0.00174701	+	0.00537674i
$667$	12.5623	−	9.12705i	0.486414	−	0.353401i
$668$	−13.1353	−	9.54332i	−0.508218	−	0.369242i
$669$	0.218847	+	0.673542i	0.00846112	+	0.0260406i
$670$		0			0
$671$	−17.2082	−	19.5559i	−0.664315	−	0.754948i
$672$	16.8541			0.650161
$673$	−3.83688	−	11.8087i	−0.147901	−	0.455192i	0.849472	−	0.527634i	$-0.176921\pi$
$673$	−3.83688	−	11.8087i	−0.147901	−	0.455192i	−0.997373	+	0.0724420i	$0.976921\pi$
$674$	−0.145898	−	0.106001i	−0.00561978	−	0.00408301i
$675$		0			0
$676$	4.94427	−	15.2169i	0.190164	−	0.585266i
$677$	−4.18034	+	12.8658i	−0.160664	+	0.494471i	−0.998691	−	0.0511572i	$-0.983709\pi$
$677$	−4.18034	+	12.8658i	−0.160664	+	0.494471i	0.838027	+	0.545629i	$0.183709\pi$
$678$	−0.354102	+	0.257270i	−0.0135992	+	0.00988040i
$679$	34.0623	+	24.7477i	1.30719	+	0.949730i
$680$		0			0
$681$	−24.8885			−0.953731
$682$	0.545085	+	5.82485i	0.0208724	+	0.223045i
$683$	3.11146			0.119057			0.0595283	−	0.998227i	$-0.481040\pi$
$683$	3.11146			0.119057			0.0595283	+	0.998227i	$0.481040\pi$
$684$	−2.92705	−	9.00854i	−0.111919	−	0.344450i
$685$		0			0
$686$	−7.50000	+	5.44907i	−0.286351	+	0.208046i
$687$	−3.09017	+	9.51057i	−0.117897	+	0.362851i
$688$	−3.57295	+	10.9964i	−0.136217	+	0.419234i
$689$	13.7254	−	9.97210i	0.522897	−	0.379907i
$690$		0			0
$691$	−8.12461	−	25.0050i	−0.309075	−	0.951234i	−0.978125	−	0.208017i	$-0.933299\pi$
$691$	−8.12461	−	25.0050i	−0.309075	−	0.951234i	0.669050	−	0.743217i	$-0.266701\pi$
$692$	24.8885			0.946120
$693$	9.13525	−	3.94298i	0.347020	−	0.149782i
$694$	12.9443			0.491358
$695$		0			0
$696$	−8.09017	−	5.87785i	−0.306657	−	0.222799i
$697$	−15.6353	+	11.3597i	−0.592228	+	0.430278i
$698$	−1.93363	+	5.95110i	−0.0731889	+	0.225252i
$699$	7.51722	−	23.1356i	0.284327	−	0.875070i
$700$		0			0
$701$	8.64590	+	6.28161i	0.326551	+	0.237253i	0.738966	−	0.673743i	$-0.235315\pi$
$701$	8.64590	+	6.28161i	0.326551	+	0.237253i	−0.412415	+	0.910996i	$0.635315\pi$
$702$	0.336881	+	1.03681i	0.0127148	+	0.0391320i
$703$	−1.38197			−0.0521218
$704$	−0.763932	−	0.171513i	−0.0287918	−	0.00646416i
$705$		0			0
$706$	2.00000	+	6.15537i	0.0752710	+	0.231660i
$707$	−7.28115	−	5.29007i	−0.273836	−	0.198953i
$708$	−13.5172	+	9.82084i	−0.508008	+	0.369090i
$709$	15.0623	−	46.3570i	0.565677	−	1.74097i	−0.100255	−	0.994962i	$-0.531966\pi$
$709$	15.0623	−	46.3570i	0.565677	−	1.74097i	0.665932	−	0.746012i	$-0.268034\pi$
$710$		0			0
$711$	−7.66312	+	5.56758i	−0.287389	+	0.208801i
$712$	0.954915	+	0.693786i	0.0357870	+	0.0260007i
$713$	−3.06231	−	9.42481i	−0.114684	−	0.352962i
$714$	−3.00000			−0.112272
$715$		0			0
$716$	3.61803			0.135212
$717$	−0.791796	−	2.43690i	−0.0295702	−	0.0910076i
$718$	6.38197	+	4.63677i	0.238173	+	0.173043i
$719$	1.28115	−	0.930812i	0.0477789	−	0.0347134i	−0.563639	−	0.826021i	$-0.690599\pi$
$719$	1.28115	−	0.930812i	0.0477789	−	0.0347134i	0.611418	+	0.791307i	$0.290599\pi$
$720$		0			0
$721$	−5.56231	+	17.1190i	−0.207151	+	0.637546i
$722$	−7.63525	+	5.54734i	−0.284155	+	0.206451i
$723$	−18.7082	−	13.5923i	−0.695766	−	0.505503i
$724$	8.73607	+	26.8869i	0.324673	+	0.999242i
$725$		0			0
$726$	6.68034	−	1.26133i	0.247931	−	0.0468122i
$727$	−38.8541			−1.44102			−0.720509	−	0.693445i	$-0.756092\pi$
$727$	−38.8541			−1.44102			−0.720509	+	0.693445i	$0.756092\pi$
$728$	−3.65654	−	11.2537i	−0.135520	−	0.417089i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$		0			0
$731$	3.11803	−	9.59632i	0.115325	−	0.354933i
$732$	3.92705	−	12.0862i	0.145148	−	0.446720i
$733$	−30.5066	+	22.1643i	−1.12679	+	0.818658i	−0.985224	−	0.171271i	$-0.945213\pi$
$733$	−30.5066	+	22.1643i	−1.12679	+	0.818658i	−0.141562	+	0.989929i	$0.545213\pi$
$734$	2.78115	+	2.02063i	0.102654	+	0.0745827i
$735$		0			0
$736$	−19.5066			−0.719022
$737$	16.1697	−	27.2829i	0.595618	−	1.00498i
$738$	−7.38197			−0.271734
$739$	−7.72542	−	23.7764i	−0.284184	−	0.874629i	−0.986642	−	0.162904i	$-0.947914\pi$
$739$	−7.72542	−	23.7764i	−0.284184	−	0.874629i	0.702458	−	0.711726i	$-0.252086\pi$
$740$		0			0
$741$	−8.35410	+	6.06961i	−0.306896	+	0.222973i
$742$	−5.51064	+	16.9600i	−0.202302	+	0.622622i
$743$	−10.8713	+	33.4585i	−0.398830	+	1.22747i	0.527108	+	0.849798i	$0.323276\pi$
$743$	−10.8713	+	33.4585i	−0.398830	+	1.22747i	−0.925938	+	0.377675i	$0.876724\pi$
$744$	−5.16312	+	3.75123i	−0.189289	+	0.137527i
$745$		0			0
$746$	0.843459	+	2.59590i	0.0308812	+	0.0950426i
$747$	−0.708204			−0.0259118
$748$	8.47214	+	1.90211i	0.309772	+	0.0695481i
$749$	−12.7082			−0.464348
$750$		0			0
$751$	−9.64590	−	7.00816i	−0.351984	−	0.255731i	0.397717	−	0.917508i	$-0.369803\pi$
$751$	−9.64590	−	7.00816i	−0.351984	−	0.255731i	−0.749701	+	0.661777i	$0.769803\pi$
$752$	2.42705	−	1.76336i	0.0885054	−	0.0643030i
$753$	2.40983	−	7.41669i	0.0878191	−	0.270279i
$754$	−1.50658	+	4.63677i	−0.0548663	+	0.168861i
$755$		0			0
$756$	3.92705	+	2.85317i	0.142825	+	0.103769i
$757$	−0.600813	−	1.84911i	−0.0218369	−	0.0672071i	0.939544	−	0.342428i	$-0.111249\pi$
$757$	−0.600813	−	1.84911i	−0.0218369	−	0.0672071i	−0.961381	+	0.275220i	$0.911249\pi$
$758$	0.978714			0.0355485
$759$	−10.5729	+	4.56352i	−0.383774	+	0.165645i
$760$		0			0
$761$	−9.54508	−	29.3768i	−0.346009	−	1.06491i	−0.961041	−	0.276404i	$-0.910857\pi$
$761$	−9.54508	−	29.3768i	−0.346009	−	1.06491i	0.615032	−	0.788502i	$-0.289143\pi$
$762$	1.85410	+	1.34708i	0.0671670	+	0.0487997i
$763$		0			0
$764$	3.73607	−	11.4984i	0.135166	−	0.415999i
$765$		0			0
$766$	13.4443	−	9.76784i	0.485761	−	0.352926i
$767$	14.7361	+	10.7064i	0.532089	+	0.386585i
$768$	2.02786	+	6.24112i	0.0731742	+	0.225207i
$769$	12.6869			0.457502			0.228751	−	0.973485i	$-0.426536\pi$
$769$	12.6869			0.457502			0.228751	+	0.973485i	$0.426536\pi$
$770$		0			0
$771$	−11.6738			−0.420420
$772$	−9.28115	−	28.5645i	−0.334036	−	1.02806i
$773$	−25.2812	−	18.3678i	−0.909300	−	0.660645i	0.0315378	−	0.999503i	$-0.489960\pi$
$773$	−25.2812	−	18.3678i	−0.909300	−	0.660645i	−0.940838	+	0.338858i	$0.889960\pi$
$774$	3.11803	−	2.26538i	0.112075	−	0.0814276i
$775$		0			0
$776$	−9.69756	+	29.8460i	−0.348122	+	1.07141i
$777$	0.572949	−	0.416272i	0.0205544	−	0.0149337i
$778$	−12.1353	−	8.81678i	−0.435070	−	0.316097i
$779$	−21.6074	−	66.5007i	−0.774165	−	2.38264i
$780$		0			0
$781$	12.1869	+	13.8496i	0.436082	+	0.495577i
$782$	3.47214			0.124163
$783$	−1.38197	−	4.25325i	−0.0493874	−	0.151999i
$784$	−3.00000	−	2.17963i	−0.107143	−	0.0778438i
$785$		0			0
$786$	1.36475	−	4.20025i	0.0486788	−	0.149818i
$787$	3.18034	−	9.78808i	0.113367	−	0.348907i	−0.878236	−	0.478227i	$-0.841279\pi$
$787$	3.18034	−	9.78808i	0.113367	−	0.348907i	0.991603	+	0.129320i	$0.0412795\pi$
$788$	−31.9164	+	23.1886i	−1.13697	+	0.826061i
$789$	13.2082	+	9.59632i	0.470225	+	0.341638i
$790$		0			0
$791$	2.12461			0.0755425
$792$	4.89919	+	5.56758i	0.174085	+	0.197835i
$793$	−13.8541			−0.491974
$794$	7.39261	+	22.7521i	0.262354	+	0.807442i
$795$		0			0
$796$	−21.8713	+	15.8904i	−0.775208	+	0.563222i
$797$	−3.32624	+	10.2371i	−0.117821	+	0.362617i	−0.992525	−	0.122041i	$-0.961056\pi$
$797$	−3.32624	+	10.2371i	−0.117821	+	0.362617i	0.874704	+	0.484658i	$0.161056\pi$
$798$	3.35410	−	10.3229i	0.118734	−	0.365425i
$799$	−2.11803	+	1.53884i	−0.0749307	+	0.0544403i
$800$		0			0
$801$	0.163119	+	0.502029i	0.00576353	+	0.0177383i
$802$	−16.1246			−0.569380
$803$	1.00000	+	10.6861i	0.0352892	+	0.377106i
$804$	15.4721			0.545660
$805$		0			0
$806$	2.51722	+	1.82887i	0.0886653	+	0.0644191i
$807$	12.5623	−	9.12705i	0.442214	−	0.321287i
$808$	2.07295	−	6.37988i	0.0729261	−	0.224443i
$809$	2.98936	−	9.20029i	0.105100	−	0.323465i	−0.884654	−	0.466249i	$-0.845605\pi$
$809$	2.98936	−	9.20029i	0.105100	−	0.323465i	0.989754	+	0.142783i	$0.0456052\pi$
$810$		0			0
$811$	−2.63525	−	1.91462i	−0.0925363	−	0.0672316i	0.540555	−	0.841309i	$-0.318214\pi$
$811$	−2.63525	−	1.91462i	−0.0925363	−	0.0672316i	−0.633091	+	0.774077i	$0.718214\pi$
$812$	6.70820	+	20.6457i	0.235412	+	0.724523i
$813$	27.2705			0.956419
$814$	0.444272	−	0.191758i	0.0155717	−	0.00672111i
$815$		0			0
$816$	0.927051	+	2.85317i	0.0324533	+	0.0998809i
$817$	29.5344	+	21.4580i	1.03328	+	0.750721i
$818$	5.52786	−	4.01623i	0.193277	−	0.140424i
$819$	1.63525	−	5.03280i	0.0571404	−	0.175860i
$820$		0			0
$821$	−32.6976	+	23.7562i	−1.14115	+	0.829096i	−0.987279	−	0.158995i	$-0.949175\pi$
$821$	−32.6976	+	23.7562i	−1.14115	+	0.829096i	−0.153873	+	0.988091i	$0.549175\pi$
$822$	−3.73607	−	2.71441i	−0.130310	−	0.0946760i
$823$	10.9615	+	33.7360i	0.382094	+	1.17596i	0.938567	+	0.345098i	$0.112154\pi$
$823$	10.9615	+	33.7360i	0.382094	+	1.17596i	−0.556473	+	0.830866i	$0.687846\pi$
$824$	−13.4164			−0.467383
$825$		0			0
$826$	−19.1459			−0.666171
$827$	−16.4164	−	50.5245i	−0.570854	−	1.75691i	−0.649880	−	0.760037i	$-0.725181\pi$
$827$	−16.4164	−	50.5245i	−0.570854	−	1.75691i	0.0790257	−	0.996873i	$-0.474819\pi$
$828$	−4.54508	−	3.30220i	−0.157953	−	0.114759i
$829$	−14.3090	+	10.3961i	−0.496973	+	0.361072i	−0.807859	−	0.589375i	$-0.799374\pi$
$829$	−14.3090	+	10.3961i	−0.496973	+	0.361072i	0.310887	+	0.950447i	$0.399374\pi$
$830$		0			0
$831$	9.44427	−	29.0665i	0.327618	−	1.00831i
$832$	−0.336881	+	0.244758i	−0.0116792	+	0.00848547i
$833$	2.61803	+	1.90211i	0.0907095	+	0.0659043i
$834$	0.163119	+	0.502029i	0.00564835	+	0.0173838i
$835$		0			0
$836$	−16.0172	+	27.0256i	−0.553967	+	0.934700i
$837$	−2.85410			−0.0986522
$838$	3.15248	+	9.70232i	0.108900	+	0.335161i
$839$	29.6976	+	21.5765i	1.02527	+	0.744905i	0.967357	−	0.253417i	$-0.0815543\pi$
$839$	29.6976	+	21.5765i	1.02527	+	0.744905i	0.0579164	+	0.998321i	$0.481554\pi$
$840$		0			0
$841$	−2.78115	+	8.55951i	−0.0959018	+	0.295155i
$842$	−7.11803	+	21.9071i	−0.245304	+	0.754967i
$843$	−0.618034	+	0.449028i	−0.0212862	+	0.0154653i
$844$	−29.1525	−	21.1805i	−1.00347	−	0.729063i
$845$		0			0
$846$	−1.00000			−0.0343807
$847$	−29.8328	−	14.1068i	−1.02507	−	0.484717i
$848$	17.8328			0.612381
$849$	0.0557281	+	0.171513i	0.00191258	+	0.00588633i
$850$		0			0
$851$	−0.663119	+	0.481784i	−0.0227314	+	0.0165153i
$852$	−2.78115	+	8.55951i	−0.0952807	+	0.293244i
$853$	3.07295	−	9.45756i	0.105216	−	0.323821i	−0.884565	−	0.466416i	$-0.845545\pi$
$853$	3.07295	−	9.45756i	0.105216	−	0.323821i	0.989781	+	0.142596i	$0.0455448\pi$
$854$	11.7812	−	8.55951i	0.403143	−	0.292900i
$855$		0			0
$856$	−2.92705	−	9.00854i	−0.100045	−	0.307905i
$857$	−47.7214			−1.63013			−0.815065	−	0.579369i	$-0.803299\pi$
$857$	−47.7214			−1.63013			−0.815065	+	0.579369i	$0.803299\pi$
$858$	1.84346	−	3.11044i	0.0629346	−	0.106189i
$859$	7.11146			0.242640			0.121320	−	0.992613i	$-0.461287\pi$
$859$	7.11146			0.242640			0.121320	+	0.992613i	$0.461287\pi$
$860$		0			0
$861$	28.9894	+	21.0620i	0.987955	+	0.717791i
$862$	19.7533	−	14.3516i	0.672800	−	0.488818i
$863$	−3.67376	+	11.3067i	−0.125056	+	0.384884i	−0.993911	−	0.110183i	$-0.964856\pi$
$863$	−3.67376	+	11.3067i	−0.125056	+	0.384884i	0.868855	+	0.495067i	$0.164856\pi$
$864$	−1.73607	+	5.34307i	−0.0590622	+	0.181775i
$865$		0			0
$866$	−3.00000	−	2.17963i	−0.101944	−	0.0740668i
$867$	4.44427	+	13.6781i	0.150935	+	0.464531i
$868$	13.8541			0.470239
$869$	30.6525	+	6.88191i	1.03981	+	0.233453i
$870$		0			0
$871$	−5.21227	−	16.0417i	−0.176611	−	0.543553i
$872$		0			0
$873$	−11.3541	+	8.24924i	−0.384278	+	0.279194i
$874$	−3.88197	+	11.9475i	−0.131309	+	0.404129i
$875$		0			0
$876$	−4.23607	+	3.07768i	−0.143123	+	0.103985i
$877$	5.19098	+	3.77147i	0.175287	+	0.127353i	0.671969	−	0.740579i	$-0.265449\pi$
$877$	5.19098	+	3.77147i	0.175287	+	0.127353i	−0.496682	+	0.867932i	$0.665449\pi$
$878$	0.628677	+	1.93487i	0.0212168	+	0.0652987i
$879$	0.0557281			0.00187966
$880$		0			0
$881$	13.9098			0.468634			0.234317	−	0.972160i	$-0.424715\pi$
$881$	13.9098			0.468634			0.234317	+	0.972160i	$0.424715\pi$
$882$	0.381966	+	1.17557i	0.0128615	+	0.0395835i
$883$	8.56231	+	6.22088i	0.288145	+	0.209349i	0.722462	−	0.691411i	$-0.243010\pi$
$883$	8.56231	+	6.22088i	0.288145	+	0.209349i	−0.434318	+	0.900760i	$0.643010\pi$
$884$	3.73607	−	2.71441i	0.125658	−	0.0912956i
$885$		0			0
$886$	7.85410	−	24.1724i	0.263864	−	0.812089i
$887$	2.42705	−	1.76336i	0.0814924	−	0.0592077i	−0.546293	−	0.837594i	$-0.683962\pi$
$887$	2.42705	−	1.76336i	0.0814924	−	0.0592077i	0.627785	+	0.778386i	$0.283962\pi$
$888$	0.427051	+	0.310271i	0.0143309	+	0.0104120i
$889$	−3.43769	−	10.5801i	−0.115297	−	0.354846i
$890$		0			0
$891$	0.309017	+	3.30220i	0.0103525	+	0.110628i
$892$	1.14590			0.0383675
$893$	−2.92705	−	9.00854i	−0.0979500	−	0.301459i
$894$	7.50000	+	5.44907i	0.250838	+	0.182244i
$895$		0			0
$896$	10.5517	−	32.4747i	0.352506	−	1.08490i
$897$	−1.89261	+	5.82485i	−0.0631924	+	0.194486i
$898$	12.2361	−	8.89002i	0.408323	−	0.296664i
$899$	−10.3262	−	7.50245i	−0.344399	−	0.250221i
$900$		0			0
$901$	−15.5623			−0.518456
$902$	16.1738	+	18.3803i	0.538527	+	0.611999i
$903$	−18.7082			−0.622570
$904$	0.489357	+	1.50609i	0.0162758	+	0.0500917i
$905$		0			0
$906$	1.00000	−	0.726543i	0.0332228	−	0.0241378i
$907$	13.2812	−	40.8752i	0.440993	−	1.35724i	−0.445825	−	0.895120i	$-0.647090\pi$
$907$	13.2812	−	40.8752i	0.440993	−	1.35724i	0.886818	−	0.462118i	$-0.152910\pi$
$908$	−12.4443	+	38.2995i	−0.412978	+	1.27101i
$909$	2.42705	−	1.76336i	0.0805002	−	0.0584868i
$910$		0			0
$911$	5.57953	+	17.1720i	0.184858	+	0.568934i	0.999946	−	0.0104029i	$-0.00331142\pi$
$911$	5.57953	+	17.1720i	0.184858	+	0.568934i	−0.815088	+	0.579337i	$0.803311\pi$
$912$	−10.8541			−0.359415
$913$	1.55166	+	1.76336i	0.0513525	+	0.0583586i
$914$	−5.06888			−0.167664
$915$		0			0
$916$	13.0902	+	9.51057i	0.432511	+	0.314238i
$917$	−17.3435	+	12.6008i	−0.572731	+	0.416114i
$918$	0.309017	−	0.951057i	0.0101991	−	0.0313895i
$919$	14.5106	−	44.6592i	0.478662	−	1.47317i	−0.362293	−	0.932064i	$-0.618006\pi$
$919$	14.5106	−	44.6592i	0.478662	−	1.47317i	0.840955	−	0.541106i	$-0.181994\pi$
$920$		0			0
$921$	−0.454915	−	0.330515i	−0.0149900	−	0.0108908i
$922$	−4.02786	−	12.3965i	−0.132651	−	0.408257i
$923$	9.81153			0.322950
$924$	−1.50000	−	16.0292i	−0.0493464	−	0.527322i
$925$		0			0
$926$	3.01722	+	9.28605i	0.0991520	+	0.305159i
$927$	−4.85410	−	3.52671i	−0.159430	−	0.115832i
$928$	−20.3262	+	14.7679i	−0.667241	+	0.484779i
$929$	−10.1631	+	31.2789i	−0.333441	+	1.02623i	0.634044	+	0.773297i	$0.281394\pi$
$929$	−10.1631	+	31.2789i	−0.333441	+	1.02623i	−0.967485	+	0.252929i	$0.918606\pi$
$930$		0			0
$931$	−9.47214	+	6.88191i	−0.310437	+	0.225545i
$932$	−31.8435	−	23.1356i	−1.04307	−	0.757833i
$933$	−0.781153	−	2.40414i	−0.0255738	−	0.0787081i
$934$	6.03444			0.197453
$935$		0			0
$936$	3.94427			0.128923
$937$	5.12868	+	15.7844i	0.167547	+	0.515655i	0.999215	−	0.0396173i	$-0.0126139\pi$
$937$	5.12868	+	15.7844i	0.167547	+	0.515655i	−0.831668	+	0.555273i	$0.812614\pi$
$938$	14.3435	+	10.4211i	0.468331	+	0.340262i
$939$	−20.8992	+	15.1841i	−0.682019	+	0.495516i
$940$		0			0
$941$	−13.7918	+	42.4468i	−0.449600	+	1.38373i	0.427760	+	0.903892i	$0.359303\pi$
$941$	−13.7918	+	42.4468i	−0.449600	+	1.38373i	−0.877360	+	0.479833i	$0.840697\pi$
$942$	1.85410	−	1.34708i	0.0604099	−	0.0438904i
$943$	−33.5517	−	24.3767i	−1.09259	−	0.793815i
$944$	5.91641	+	18.2088i	0.192563	+	0.592647i
$945$		0			0
$946$	−12.4721	−	2.80017i	−0.405504	−	0.0910413i
$947$	−18.3262			−0.595523			−0.297761	−	0.954640i	$-0.596240\pi$
$947$	−18.3262			−0.595523			−0.297761	+	0.954640i	$0.596240\pi$
$948$	4.73607	+	14.5761i	0.153820	+	0.473410i
$949$	4.61803	+	3.35520i	0.149908	+	0.108914i
$950$		0			0
$951$	−5.98278	+	18.4131i	−0.194005	+	0.597086i
$952$	−3.35410	+	10.3229i	−0.108707	+	0.334566i
$953$	30.5967	−	22.2298i	0.991126	−	0.720095i	0.0309585	−	0.999521i	$-0.490144\pi$
$953$	30.5967	−	22.2298i	0.991126	−	0.720095i	0.960167	+	0.279426i	$0.0901440\pi$
$954$	−4.80902	−	3.49396i	−0.155698	−	0.113121i
$955$		0			0
$956$	−4.14590			−0.134088
$957$	−7.56231	+	12.7598i	−0.244455	+	0.412465i
$958$	−17.3607			−0.560898
$959$	6.92705	+	21.3193i	0.223686	+	0.688435i
$960$		0			0
$961$	18.4894	−	13.4333i	0.596431	−	0.433332i
$962$	0.0795268	−	0.244758i	0.00256405	−	0.00789133i
$963$	1.30902	−	4.02874i	0.0421825	−	0.129824i
$964$	−30.2705	+	21.9928i	−0.974947	+	0.708341i
$965$		0			0
$966$	−1.98936	−	6.12261i	−0.0640065	−	0.196992i
$967$	34.6869			1.11546			0.557728	−	0.830024i	$-0.311673\pi$
$967$	34.6869			1.11546			0.557728	+	0.830024i	$0.311673\pi$
$968$	3.12868	−	24.3970i	0.100559	−	0.784148i
$969$	9.47214			0.304289
$970$		0			0
$971$	−30.5623	−	22.2048i	−0.980791	−	0.712586i	−0.0229058	−	0.999738i	$-0.507292\pi$
$971$	−30.5623	−	22.2048i	−0.980791	−	0.712586i	−0.957885	+	0.287151i	$0.907292\pi$
$972$	−1.30902	+	0.951057i	−0.0419867	+	0.0305052i
$973$	0.791796	−	2.43690i	0.0253838	−	0.0781234i
$974$	−3.21227	+	9.88635i	−0.102928	+	0.316779i
$975$		0			0
$976$	−11.7812	−	8.55951i	−0.377106	−	0.273983i
$977$	1.43363	+	4.41226i	0.0458658	+	0.141161i	0.971367	−	0.237585i	$-0.0763557\pi$
$977$	1.43363	+	4.41226i	0.0458658	+	0.141161i	−0.925501	+	0.378745i	$0.876356\pi$
$978$	11.2918			0.361072
$979$	0.892609	−	1.50609i	0.0285279	−	0.0481347i
$980$		0			0
$981$		0			0
$982$	−12.6074	−	9.15981i	−0.402318	−	0.292301i
$983$	−22.0902	+	16.0494i	−0.704567	+	0.511898i	−0.881416	−	0.472340i	$-0.843409\pi$
$983$	−22.0902	+	16.0494i	−0.704567	+	0.511898i	0.176849	+	0.984238i	$0.443409\pi$
$984$	−8.25329	+	25.4010i	−0.263105	+	0.809755i
$985$		0			0
$986$	3.61803	−	2.62866i	0.115222	−	0.0837134i
$987$	3.92705	+	2.85317i	0.124999	+	0.0908174i
$988$	5.16312	+	15.8904i	0.164261	+	0.505542i
$989$	21.6525			0.688509
$990$		0			0
$991$	21.2705			0.675680			0.337840	−	0.941204i	$-0.390304\pi$
$991$	21.2705			0.675680			0.337840	+	0.941204i	$0.390304\pi$
$992$	4.95492	+	15.2497i	0.157319	+	0.484177i
$993$	21.5172	+	15.6332i	0.682828	+	0.496104i
$994$	−8.34346	+	6.06188i	−0.264638	+	0.192271i
$995$		0			0
$996$	−0.354102	+	1.08981i	−0.0112202	+	0.0345321i
$997$	−10.5000	+	7.62870i	−0.332538	+	0.241603i	−0.741507	−	0.670945i	$-0.765889\pi$
$997$	−10.5000	+	7.62870i	−0.332538	+	0.241603i	0.408969	+	0.912548i	$0.365889\pi$
$998$	8.78115	+	6.37988i	0.277963	+	0.201952i
$999$	0.0729490	+	0.224514i	0.00230800	+	0.00710331i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.n.f.676.1		4
5.2	odd	4		825.2.bx.b.49.1		8
5.3	odd	4		825.2.bx.b.49.2		8
5.4	even	2		33.2.e.a.16.1	✓	4
11.3	even	5		9075.2.a.x.1.2		2
11.8	odd	10		9075.2.a.bv.1.1		2
11.9	even	5	inner	825.2.n.f.526.1		4
15.14	odd	2		99.2.f.b.82.1		4
20.19	odd	2		528.2.y.f.49.1		4
45.4	even	6		891.2.n.d.379.1		8
45.14	odd	6		891.2.n.a.379.1		8
45.29	odd	6		891.2.n.a.676.1		8
45.34	even	6		891.2.n.d.676.1		8
55.4	even	10		363.2.e.h.124.1		4
55.9	even	10		33.2.e.a.31.1	yes	4
55.14	even	10		363.2.a.h.1.1		2
55.19	odd	10		363.2.a.e.1.2		2
55.24	odd	10		363.2.e.j.130.1		4
55.29	odd	10		363.2.e.c.124.1		4
55.39	odd	10		363.2.e.c.202.1		4
55.42	odd	20		825.2.bx.b.724.2		8
55.49	even	10		363.2.e.h.202.1		4
55.53	odd	20		825.2.bx.b.724.1		8
55.54	odd	2		363.2.e.j.148.1		4
165.14	odd	10		1089.2.a.m.1.2		2
165.74	even	10		1089.2.a.s.1.1		2
165.119	odd	10		99.2.f.b.64.1		4
220.19	even	10		5808.2.a.bm.1.1		2
220.119	odd	10		528.2.y.f.97.1		4
220.179	odd	10		5808.2.a.bl.1.1		2
495.119	odd	30		891.2.n.a.757.1		8
495.229	even	30		891.2.n.d.460.1		8
495.284	odd	30		891.2.n.a.460.1		8
495.394	even	30		891.2.n.d.757.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.e.a.16.1	✓	4	5.4	even	2
33.2.e.a.31.1	yes	4	55.9	even	10
99.2.f.b.64.1		4	165.119	odd	10
99.2.f.b.82.1		4	15.14	odd	2
363.2.a.e.1.2		2	55.19	odd	10
363.2.a.h.1.1		2	55.14	even	10
363.2.e.c.124.1		4	55.29	odd	10
363.2.e.c.202.1		4	55.39	odd	10
363.2.e.h.124.1		4	55.4	even	10
363.2.e.h.202.1		4	55.49	even	10
363.2.e.j.130.1		4	55.24	odd	10
363.2.e.j.148.1		4	55.54	odd	2
528.2.y.f.49.1		4	20.19	odd	2
528.2.y.f.97.1		4	220.119	odd	10
825.2.n.f.526.1		4	11.9	even	5	inner
825.2.n.f.676.1		4	1.1	even	1	trivial
825.2.bx.b.49.1		8	5.2	odd	4
825.2.bx.b.49.2		8	5.3	odd	4
825.2.bx.b.724.1		8	55.53	odd	20
825.2.bx.b.724.2		8	55.42	odd	20
891.2.n.a.379.1		8	45.14	odd	6
891.2.n.a.460.1		8	495.284	odd	30
891.2.n.a.676.1		8	45.29	odd	6
891.2.n.a.757.1		8	495.119	odd	30
891.2.n.d.379.1		8	45.4	even	6
891.2.n.d.460.1		8	495.229	even	30
891.2.n.d.676.1		8	45.34	even	6
891.2.n.d.757.1		8	495.394	even	30
1089.2.a.m.1.2		2	165.14	odd	10
1089.2.a.s.1.1		2	165.74	even	10
5808.2.a.bl.1.1		2	220.179	odd	10
5808.2.a.bm.1.1		2	220.19	even	10
9075.2.a.x.1.2		2	11.3	even	5
9075.2.a.bv.1.1		2	11.8	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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.190983 + 0.587785i) q^{2} +(0.809017 + 0.587785i) q^{3} +(1.30902 - 0.951057i) q^{4} +(-0.190983 + 0.587785i) q^{6} +(2.42705 - 1.76336i) q^{7} +(1.80902 + 1.31433i) q^{8} +(0.309017 + 0.951057i) q^{9} +(1.69098 - 2.85317i) q^{11} +1.61803 q^{12} +(-0.545085 - 1.67760i) q^{13} +(1.50000 + 1.08981i) q^{14} +(0.572949 - 1.76336i) q^{16} +(-0.500000 + 1.53884i) q^{17} +(-0.500000 + 0.363271i) q^{18} +(-4.73607 - 3.44095i) q^{19} +3.00000 q^{21} +(2.00000 + 0.449028i) q^{22} -3.47214 q^{23} +(0.690983 + 2.12663i) q^{24} +(0.881966 - 0.640786i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(1.50000 - 4.61653i) q^{28} +(-3.61803 + 2.62866i) q^{29} +(0.881966 + 2.71441i) q^{31} +5.61803 q^{32} +(3.04508 - 1.31433i) q^{33} -1.00000 q^{34} +(1.30902 + 0.951057i) q^{36} +(0.190983 - 0.138757i) q^{37} +(1.11803 - 3.44095i) q^{38} +(0.545085 - 1.67760i) q^{39} +(9.66312 + 7.02067i) q^{41} +(0.572949 + 1.76336i) q^{42} -6.23607 q^{43} +(-0.500000 - 5.34307i) q^{44} +(-0.663119 - 2.04087i) q^{46} +(1.30902 + 0.951057i) q^{47} +(1.50000 - 1.08981i) q^{48} +(0.618034 - 1.90211i) q^{49} +(-1.30902 + 0.951057i) q^{51} +(-2.30902 - 1.67760i) q^{52} +(2.97214 + 9.14729i) q^{53} -0.618034 q^{54} +6.70820 q^{56} +(-1.80902 - 5.56758i) q^{57} +(-2.23607 - 1.62460i) q^{58} +(-8.35410 + 6.06961i) q^{59} +(2.42705 - 7.46969i) q^{61} +(-1.42705 + 1.03681i) q^{62} +(2.42705 + 1.76336i) q^{63} +(-0.0729490 - 0.224514i) q^{64} +(1.35410 + 1.53884i) q^{66} +9.56231 q^{67} +(0.809017 + 2.48990i) q^{68} +(-2.80902 - 2.04087i) q^{69} +(-1.71885 + 5.29007i) q^{71} +(-0.690983 + 2.12663i) q^{72} +(-2.61803 + 1.90211i) q^{73} +(0.118034 + 0.0857567i) q^{74} -9.47214 q^{76} +(-0.927051 - 9.90659i) q^{77} +1.09017 q^{78} +(2.92705 + 9.00854i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-2.28115 + 7.02067i) q^{82} +(-0.218847 + 0.673542i) q^{83} +(3.92705 - 2.85317i) q^{84} +(-1.19098 - 3.66547i) q^{86} -4.47214 q^{87} +(6.80902 - 2.93893i) q^{88} +0.527864 q^{89} +(-4.28115 - 3.11044i) q^{91} +(-4.54508 + 3.30220i) q^{92} +(-0.881966 + 2.71441i) q^{93} +(-0.309017 + 0.951057i) q^{94} +(4.54508 + 3.30220i) q^{96} +(4.33688 + 13.3475i) q^{97} +1.23607 q^{98} +(3.23607 + 0.726543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} + q^{3} + 3 q^{4} - 3 q^{6} + 3 q^{7} + 5 q^{8} - q^{9} + 9 q^{11} + 2 q^{12} + 9 q^{13} + 6 q^{14} + 9 q^{16} - 2 q^{17} - 2 q^{18} - 10 q^{19} + 12 q^{21} + 8 q^{22} + 4 q^{23} + 5 q^{24}+ \cdots + 4 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 + q^3 + 3 * q^4 - 3 * q^6 + 3 * q^7 + 5 * q^8 - q^9 + 9 * q^11 + 2 * q^12 + 9 * q^13 + 6 * q^14 + 9 * q^16 - 2 * q^17 - 2 * q^18 - 10 * q^19 + 12 * q^21 + 8 * q^22 + 4 * q^23 + 5 * q^24 + 8 * q^26 + q^27 + 6 * q^28 - 10 * q^29 + 8 * q^31 + 18 * q^32 + q^33 - 4 * q^34 + 3 * q^36 + 3 * q^37 - 9 * q^39 + 23 * q^41 + 9 * q^42 - 16 * q^43 - 2 * q^44 + 13 * q^46 + 3 * q^47 + 6 * q^48 - 2 * q^49 - 3 * q^51 - 7 * q^52 - 6 * q^53 + 2 * q^54 - 5 * q^57 - 20 * q^59 + 3 * q^61 + q^62 + 3 * q^63 - 7 * q^64 - 8 * q^66 - 2 * q^67 + q^68 - 9 * q^69 - 27 * q^71 - 5 * q^72 - 6 * q^73 - 4 * q^74 - 20 * q^76 + 3 * q^77 - 18 * q^78 + 5 * q^79 - q^81 + 11 * q^82 - 21 * q^83 + 9 * q^84 - 7 * q^86 + 25 * q^88 + 20 * q^89 + 3 * q^91 - 7 * q^92 - 8 * q^93 + q^94 + 7 * q^96 + 33 * q^97 - 4 * q^98 + 4 * q^99

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