LMFDB - Embedded newform 825.2.bx.b.724.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("825.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			724.2
Root			$0.587785 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	825.724
Dual form			825.2.bx.b.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.587785 + 0.190983i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(-1.30902 - 0.951057i) q^{4} +(-0.190983 - 0.587785i) q^{6} +(-1.76336 + 2.42705i) q^{7} +(-1.31433 - 1.80902i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(1.69098 + 2.85317i) q^{11} +1.61803i q^{12} +(1.67760 + 0.545085i) q^{13} +(-1.50000 + 1.08981i) q^{14} +(0.572949 + 1.76336i) q^{16} +(1.53884 - 0.500000i) q^{17} +(-0.363271 + 0.500000i) q^{18} +(4.73607 - 3.44095i) q^{19} +3.00000 q^{21} +(0.449028 + 2.00000i) q^{22} +3.47214i q^{23} +(-0.690983 + 2.12663i) q^{24} +(0.881966 + 0.640786i) q^{26} +(0.951057 - 0.309017i) q^{27} +(4.61653 - 1.50000i) q^{28} +(3.61803 + 2.62866i) q^{29} +(0.881966 - 2.71441i) q^{31} +5.61803i q^{32} +(1.31433 - 3.04508i) q^{33} +1.00000 q^{34} +(1.30902 - 0.951057i) q^{36} +(-0.138757 + 0.190983i) q^{37} +(3.44095 - 1.11803i) q^{38} +(-0.545085 - 1.67760i) q^{39} +(9.66312 - 7.02067i) q^{41} +(1.76336 + 0.572949i) q^{42} +6.23607i q^{43} +(0.500000 - 5.34307i) q^{44} +(-0.663119 + 2.04087i) q^{46} +(0.951057 + 1.30902i) q^{47} +(1.08981 - 1.50000i) q^{48} +(-0.618034 - 1.90211i) q^{49} +(-1.30902 - 0.951057i) q^{51} +(-1.67760 - 2.30902i) q^{52} +(-9.14729 - 2.97214i) q^{53} +0.618034 q^{54} +6.70820 q^{56} +(-5.56758 - 1.80902i) q^{57} +(1.62460 + 2.23607i) q^{58} +(8.35410 + 6.06961i) q^{59} +(2.42705 + 7.46969i) q^{61} +(1.03681 - 1.42705i) q^{62} +(-1.76336 - 2.42705i) q^{63} +(0.0729490 - 0.224514i) q^{64} +(1.35410 - 1.53884i) q^{66} +9.56231i q^{67} +(-2.48990 - 0.809017i) q^{68} +(2.80902 - 2.04087i) q^{69} +(-1.71885 - 5.29007i) q^{71} +(2.12663 - 0.690983i) q^{72} +(-1.90211 + 2.61803i) q^{73} +(-0.118034 + 0.0857567i) q^{74} -9.47214 q^{76} +(-9.90659 - 0.927051i) q^{77} -1.09017i q^{78} +(-2.92705 + 9.00854i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(7.02067 - 2.28115i) q^{82} +(-0.673542 + 0.218847i) q^{83} +(-3.92705 - 2.85317i) q^{84} +(-1.19098 + 3.66547i) q^{86} -4.47214i q^{87} +(2.93893 - 6.80902i) q^{88} -0.527864 q^{89} +(-4.28115 + 3.11044i) q^{91} +(3.30220 - 4.54508i) q^{92} +(-2.71441 + 0.881966i) q^{93} +(0.309017 + 0.951057i) q^{94} +(4.54508 - 3.30220i) q^{96} +(13.3475 + 4.33688i) q^{97} -1.23607i q^{98} +(-3.23607 + 0.726543i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{4} - 6 q^{6} + 2 q^{9} + 18 q^{11} - 12 q^{14} + 18 q^{16} + 20 q^{19} + 24 q^{21} - 10 q^{24} + 16 q^{26} + 20 q^{29} + 16 q^{31} + 8 q^{34} + 6 q^{36} + 18 q^{39} + 46 q^{41} + 4 q^{44} + 26 q^{46}+ \cdots - 8 q^{99}+O(q^{100}) $ 8 * q - 6 * q^4 - 6 * q^6 + 2 * q^9 + 18 * q^11 - 12 * q^14 + 18 * q^16 + 20 * q^19 + 24 * q^21 - 10 * q^24 + 16 * q^26 + 20 * q^29 + 16 * q^31 + 8 * q^34 + 6 * q^36 + 18 * q^39 + 46 * q^41 + 4 * q^44 + 26 * q^46 + 4 * q^49 - 6 * q^51 - 4 * q^54 + 40 * q^59 + 6 * q^61 + 14 * q^64 - 16 * q^66 + 18 * q^69 - 54 * q^71 + 8 * q^74 - 40 * q^76 - 10 * q^79 - 2 * q^81 - 18 * q^84 - 14 * q^86 - 40 * q^89 + 6 * q^91 - 2 * q^94 + 14 * q^96 - 8 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$	0.587785	+	0.190983i	0.415627	+	0.135045i	0.509363	−	0.860552i	$-0.329881\pi$
$2$	0.587785	+	0.190983i	0.415627	+	0.135045i	−0.0937362	+	0.995597i	$0.529881\pi$
$3$	−0.587785	−	0.809017i	−0.339358	−	0.467086i
$3$	−0.587785	−	0.809017i	−0.339358	−	0.467086i
$4$	−1.30902	−	0.951057i	−0.654508	−	0.475528i
$5$		0			0
$5$		0			0
$6$	−0.190983	−	0.587785i	−0.0779685	−	0.239962i
$7$	−1.76336	+	2.42705i	−0.666486	+	0.917339i	−0.999674	−	0.0255212i	$-0.991875\pi$
$7$	−1.76336	+	2.42705i	−0.666486	+	0.917339i	0.333188	+	0.942860i	$0.391875\pi$
$8$	−1.31433	−	1.80902i	−0.464685	−	0.639584i
$9$	−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
$12$			1.61803i			0.467086i
$13$	1.67760	+	0.545085i	0.465282	+	0.151179i	0.532270	−	0.846574i	$-0.321339\pi$
$13$	1.67760	+	0.545085i	0.465282	+	0.151179i	−0.0669881	+	0.997754i	$0.521339\pi$
$14$	−1.50000	+	1.08981i	−0.400892	+	0.291265i
$15$		0			0
$16$	0.572949	+	1.76336i	0.143237	+	0.440839i
$17$	1.53884	−	0.500000i	0.373224	−	0.121268i	−0.116398	−	0.993203i	$-0.537135\pi$
$17$	1.53884	−	0.500000i	0.373224	−	0.121268i	0.489622	+	0.871935i	$0.337135\pi$
$18$	−0.363271	+	0.500000i	−0.0856239	+	0.117851i
$19$	4.73607	−	3.44095i	1.08653	−	0.789409i	0.107719	−	0.994181i	$-0.465645\pi$
$19$	4.73607	−	3.44095i	1.08653	−	0.789409i	0.978810	+	0.204772i	$0.0656454\pi$
$20$		0			0
$21$	3.00000			0.654654
$22$	0.449028	+	2.00000i	0.0957331	+	0.426401i
$23$			3.47214i			0.723990i	0.932180	+	0.361995i	$0.117904\pi$
$23$			3.47214i			0.723990i	−0.932180	+	0.361995i	$0.882096\pi$
$24$	−0.690983	+	2.12663i	−0.141046	+	0.434096i
$25$		0			0
$26$	0.881966	+	0.640786i	0.172968	+	0.125668i
$27$	0.951057	−	0.309017i	0.183031	−	0.0594703i
$28$	4.61653	−	1.50000i	0.872441	−	0.283473i
$29$	3.61803	+	2.62866i	0.671852	+	0.488129i	0.870645	−	0.491912i	$-0.163702\pi$
$29$	3.61803	+	2.62866i	0.671852	+	0.488129i	−0.198793	+	0.980042i	$0.563702\pi$
$30$		0			0
$31$	0.881966	−	2.71441i	0.158406	−	0.487523i	−0.840084	−	0.542456i	$-0.817495\pi$
$31$	0.881966	−	2.71441i	0.158406	−	0.487523i	0.998490	+	0.0549331i	$0.0174946\pi$
$32$			5.61803i			0.993137i
$33$	1.31433	−	3.04508i	0.228795	−	0.530081i
$34$	1.00000			0.171499
$35$		0			0
$36$	1.30902	−	0.951057i	0.218169	−	0.158509i
$37$	−0.138757	+	0.190983i	−0.0228116	+	0.0313974i	−0.820270	−	0.571976i	$-0.806177\pi$
$37$	−0.138757	+	0.190983i	−0.0228116	+	0.0313974i	0.797459	+	0.603373i	$0.206177\pi$
$38$	3.44095	−	1.11803i	0.558197	−	0.181369i
$39$	−0.545085	−	1.67760i	−0.0872835	−	0.268631i
$40$		0			0
$41$	9.66312	−	7.02067i	1.50913	−	1.09644i	0.542562	−	0.840015i	$-0.317454\pi$
$41$	9.66312	−	7.02067i	1.50913	−	1.09644i	0.966563	−	0.256428i	$-0.0825458\pi$
$42$	1.76336	+	0.572949i	0.272092	+	0.0884080i
$43$			6.23607i			0.950991i	0.879718	+	0.475496i	$0.157731\pi$
$43$			6.23607i			0.950991i	−0.879718	+	0.475496i	$0.842269\pi$
$44$	0.500000	−	5.34307i	0.0753778	−	0.805498i
$45$		0			0
$46$	−0.663119	+	2.04087i	−0.0977716	+	0.300910i
$47$	0.951057	+	1.30902i	0.138726	+	0.190940i	0.872727	−	0.488208i	$-0.162349\pi$
$47$	0.951057	+	1.30902i	0.138726	+	0.190940i	−0.734001	+	0.679148i	$0.762349\pi$
$48$	1.08981	−	1.50000i	0.157301	−	0.216506i
$49$	−0.618034	−	1.90211i	−0.0882906	−	0.271730i
$50$		0			0
$51$	−1.30902	−	0.951057i	−0.183299	−	0.133175i
$52$	−1.67760	−	2.30902i	−0.232641	−	0.320203i
$53$	−9.14729	−	2.97214i	−1.25648	−	0.408254i	−0.396240	−	0.918147i	$-0.629685\pi$
$53$	−9.14729	−	2.97214i	−1.25648	−	0.408254i	−0.860238	+	0.509893i	$0.829685\pi$
$54$	0.618034			0.0841038
$55$		0			0
$56$	6.70820			0.896421
$57$	−5.56758	−	1.80902i	−0.737444	−	0.239610i
$58$	1.62460	+	2.23607i	0.213320	+	0.293610i
$59$	8.35410	+	6.06961i	1.08761	+	0.790196i	0.978994	−	0.203888i	$-0.0653577\pi$
$59$	8.35410	+	6.06961i	1.08761	+	0.790196i	0.108617	+	0.994084i	$0.465358\pi$
$60$		0			0
$61$	2.42705	+	7.46969i	0.310752	+	0.956396i	0.977468	+	0.211084i	$0.0676995\pi$
$61$	2.42705	+	7.46969i	0.310752	+	0.956396i	−0.666716	+	0.745312i	$0.732301\pi$
$62$	1.03681	−	1.42705i	0.131675	−	0.181236i
$63$	−1.76336	−	2.42705i	−0.222162	−	0.305780i
$64$	0.0729490	−	0.224514i	0.00911863	−	0.0280642i
$65$		0			0
$66$	1.35410	−	1.53884i	0.166678	−	0.189418i
$67$			9.56231i			1.16822i	0.811674	+	0.584111i	$0.198557\pi$
$67$			9.56231i			1.16822i	−0.811674	+	0.584111i	$0.801443\pi$
$68$	−2.48990	−	0.809017i	−0.301945	−	0.0981077i
$69$	2.80902	−	2.04087i	0.338166	−	0.245692i
$70$		0			0
$71$	−1.71885	−	5.29007i	−0.203990	−	0.627815i	−0.999753	−	0.0222083i	$-0.992930\pi$
$71$	−1.71885	−	5.29007i	−0.203990	−	0.627815i	0.795764	−	0.605607i	$-0.207070\pi$
$72$	2.12663	−	0.690983i	0.250625	−	0.0814331i
$73$	−1.90211	+	2.61803i	−0.222625	+	0.306418i	−0.905690	−	0.423940i	$-0.860647\pi$
$73$	−1.90211	+	2.61803i	−0.222625	+	0.306418i	0.683065	+	0.730358i	$0.260647\pi$
$74$	−0.118034	+	0.0857567i	−0.0137212	+	0.00996902i
$75$		0			0
$76$	−9.47214			−1.08653
$77$	−9.90659	−	0.927051i	−1.12896	−	0.105647i
$78$		−	1.09017i		−	0.123437i
$79$	−2.92705	+	9.00854i	−0.329319	+	1.01354i	0.640134	+	0.768263i	$0.278879\pi$
$79$	−2.92705	+	9.00854i	−0.329319	+	1.01354i	−0.969453	+	0.245276i	$0.921121\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	7.02067	−	2.28115i	0.775303	−	0.251911i
$83$	−0.673542	+	0.218847i	−0.0739308	+	0.0240216i	−0.345749	−	0.938327i	$-0.612375\pi$
$83$	−0.673542	+	0.218847i	−0.0739308	+	0.0240216i	0.271818	+	0.962349i	$0.412375\pi$
$84$	−3.92705	−	2.85317i	−0.428476	−	0.311306i
$85$		0			0
$86$	−1.19098	+	3.66547i	−0.128427	+	0.395258i
$87$		−	4.47214i		−	0.479463i
$88$	2.93893	−	6.80902i	0.313291	−	0.725844i
$89$	−0.527864			−0.0559535			−0.0279767	−	0.999609i	$-0.508906\pi$
$89$	−0.527864			−0.0559535			−0.0279767	+	0.999609i	$0.508906\pi$
$90$		0			0
$91$	−4.28115	+	3.11044i	−0.448787	+	0.326063i
$92$	3.30220	−	4.54508i	0.344278	−	0.473858i
$93$	−2.71441	+	0.881966i	−0.281471	+	0.0914556i
$94$	0.309017	+	0.951057i	0.0318727	+	0.0980940i
$95$		0			0
$96$	4.54508	−	3.30220i	0.463881	−	0.337029i
$97$	13.3475	+	4.33688i	1.35524	+	0.440344i	0.894451	−	0.447167i	$-0.147567\pi$
$97$	13.3475	+	4.33688i	1.35524	+	0.440344i	0.460788	+	0.887510i	$0.347567\pi$
$98$		−	1.23607i		−	0.124862i
$99$	−3.23607	+	0.726543i	−0.325237	+	0.0730203i
$100$		0			0
$101$	−0.927051	+	2.85317i	−0.0922450	+	0.283901i	−0.986526	−	0.163605i	$-0.947688\pi$
$101$	−0.927051	+	2.85317i	−0.0922450	+	0.283901i	0.894281	+	0.447506i	$0.147688\pi$
$102$	−0.587785	−	0.809017i	−0.0581994	−	0.0801046i
$103$	−3.52671	+	4.85410i	−0.347497	+	0.478289i	−0.946612	−	0.322374i	$-0.895519\pi$
$103$	−3.52671	+	4.85410i	−0.347497	+	0.478289i	0.599115	+	0.800663i	$0.295519\pi$
$104$	−1.21885	−	3.75123i	−0.119518	−	0.367838i
$105$		0			0
$106$	−4.80902	−	3.49396i	−0.467093	−	0.339363i
$107$	−2.48990	−	3.42705i	−0.240708	−	0.331306i	0.671522	−	0.740984i	$-0.265641\pi$
$107$	−2.48990	−	3.42705i	−0.240708	−	0.331306i	−0.912230	+	0.409679i	$0.865641\pi$
$108$	−1.53884	−	0.500000i	−0.148075	−	0.0481125i
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$		0			0
$111$	0.236068			0.0224066
$112$	−5.29007	−	1.71885i	−0.499864	−	0.162416i
$113$	−0.416272	−	0.572949i	−0.0391596	−	0.0538985i	0.788988	−	0.614408i	$-0.210605\pi$
$113$	−0.416272	−	0.572949i	−0.0391596	−	0.0538985i	−0.828148	+	0.560510i	$0.810605\pi$
$114$	−2.92705	−	2.12663i	−0.274143	−	0.199177i
$115$		0			0
$116$	−2.23607	−	6.88191i	−0.207614	−	0.638969i
$117$	−1.03681	+	1.42705i	−0.0958534	+	0.131931i
$118$	3.75123	+	5.16312i	0.345328	+	0.475304i
$119$	−1.50000	+	4.61653i	−0.137505	+	0.423196i
$120$		0			0
$121$	−5.28115	+	9.64932i	−0.480105	+	0.877211i
$122$			4.85410i			0.439470i
$123$	−11.3597	−	3.69098i	−1.02427	−	0.332805i
$124$	−3.73607	+	2.71441i	−0.335509	+	0.243761i
$125$		0			0
$126$	−0.572949	−	1.76336i	−0.0510424	−	0.157092i
$127$	−3.52671	+	1.14590i	−0.312945	+	0.101682i	−0.461279	−	0.887255i	$-0.652609\pi$
$127$	−3.52671	+	1.14590i	−0.312945	+	0.101682i	0.148333	+	0.988937i	$0.452609\pi$
$128$	6.69015	−	9.20820i	0.591331	−	0.813898i
$129$	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	$0.601056\pi$
$132$	−4.61653	+	2.73607i	−0.401817	+	0.238144i
$133$			17.5623i			1.52285i
$134$	−1.82624	+	5.62058i	−0.157763	+	0.485544i
$135$		0			0
$136$	−2.92705	−	2.12663i	−0.250993	−	0.182357i
$137$	7.10642	−	2.30902i	0.607143	−	0.197273i	0.0107192	−	0.999943i	$-0.496588\pi$
$137$	7.10642	−	2.30902i	0.607143	−	0.197273i	0.596424	+	0.802670i	$0.296588\pi$
$138$	2.04087	−	0.663119i	0.173730	−	0.0564484i
$139$	−0.690983	−	0.502029i	−0.0586084	−	0.0425815i	0.558095	−	0.829777i	$-0.311532\pi$
$139$	−0.690983	−	0.502029i	−0.0586084	−	0.0425815i	−0.616704	+	0.787195i	$0.711532\pi$
$140$		0			0
$141$	0.500000	−	1.53884i	0.0421076	−	0.129594i
$142$		−	3.43769i		−	0.288485i
$143$	1.28157	+	5.70820i	0.107170	+	0.477344i
$144$	−1.85410			−0.154508
$145$		0			0
$146$	−1.61803	+	1.17557i	−0.133909	+	0.0972909i
$147$	−1.17557	+	1.61803i	−0.0969594	+	0.133453i
$148$	0.363271	−	0.118034i	0.0298607	−	0.00970233i
$149$	−4.63525	−	14.2658i	−0.379735	−	1.16870i	−0.940228	−	0.340545i	$-0.889388\pi$
$149$	−4.63525	−	14.2658i	−0.379735	−	1.16870i	0.560493	−	0.828159i	$-0.310612\pi$
$150$		0			0
$151$	−1.61803	+	1.17557i	−0.131674	+	0.0956666i	−0.651673	−	0.758500i	$-0.725932\pi$
$151$	−1.61803	+	1.17557i	−0.131674	+	0.0956666i	0.519999	+	0.854167i	$0.325932\pi$
$152$	−12.4495	−	4.04508i	−1.00979	−	0.328100i
$153$			1.61803i			0.130810i
$154$	−5.64590	−	2.43690i	−0.454959	−	0.196371i
$155$		0			0
$156$	−0.881966	+	2.71441i	−0.0706138	+	0.217327i
$157$	−2.17963	−	3.00000i	−0.173953	−	0.239426i	0.713134	−	0.701028i	$-0.247275\pi$
$157$	−2.17963	−	3.00000i	−0.173953	−	0.239426i	−0.887087	+	0.461601i	$0.847275\pi$
$158$	−3.44095	+	4.73607i	−0.273748	+	0.376781i
$159$	2.97214	+	9.14729i	0.235706	+	0.725428i
$160$		0			0
$161$	−8.42705	−	6.12261i	−0.664145	−	0.482529i
$162$	−0.363271	−	0.500000i	−0.0285413	−	0.0392837i
$163$	17.3763	+	5.64590i	1.36102	+	0.442221i	0.896382	−	0.443282i	$-0.146186\pi$
$163$	17.3763	+	5.64590i	1.36102	+	0.442221i	0.464634	+	0.885503i	$0.346186\pi$
$164$	−19.3262			−1.50913
$165$		0			0
$166$	−0.437694			−0.0339717
$167$	−9.54332	−	3.10081i	−0.738484	−	0.239948i	−0.0844656	−	0.996426i	$-0.526918\pi$
$167$	−9.54332	−	3.10081i	−0.738484	−	0.239948i	−0.654019	+	0.756478i	$0.726918\pi$
$168$	−3.94298	−	5.42705i	−0.304208	−	0.418706i
$169$	−8.00000	−	5.81234i	−0.615385	−	0.447103i
$170$		0			0
$171$	1.80902	+	5.56758i	0.138339	+	0.425764i
$172$	5.93085	−	8.16312i	0.452223	−	0.622432i
$173$	−9.04129	−	12.4443i	−0.687397	−	0.946120i	0.312596	−	0.949886i	$-0.398801\pi$
$173$	−9.04129	−	12.4443i	−0.687397	−	0.946120i	−0.999993	+	0.00376565i	$0.998801\pi$
$174$	0.854102	−	2.62866i	0.0647493	−	0.199278i
$175$		0			0
$176$	−4.06231	+	4.61653i	−0.306208	+	0.347984i
$177$		−	10.3262i		−	0.776168i
$178$	−0.310271	−	0.100813i	−0.0232558	−	0.00755626i
$179$	−1.80902	+	1.31433i	−0.135212	+	0.0982375i	−0.653335	−	0.757069i	$-0.726631\pi$
$179$	−1.80902	+	1.31433i	−0.135212	+	0.0982375i	0.518123	+	0.855306i	$0.326631\pi$
$180$		0			0
$181$	−5.39919	−	16.6170i	−0.401318	−	1.23513i	−0.923930	−	0.382560i	$-0.875042\pi$
$181$	−5.39919	−	16.6170i	−0.401318	−	1.23513i	0.522612	−	0.852571i	$-0.324958\pi$
$182$	−3.11044	+	1.01064i	−0.230561	+	0.0749139i
$183$	4.61653	−	6.35410i	0.341263	−	0.469709i
$184$	6.28115	−	4.56352i	0.463053	−	0.336428i
$185$		0			0
$186$	−1.76393			−0.129338
$187$	4.02874	+	3.54508i	0.294611	+	0.259242i
$188$		−	2.61803i		−	0.190940i
$189$	−0.927051	+	2.85317i	−0.0674330	+	0.207538i
$190$		0			0
$191$	6.04508	+	4.39201i	0.437407	+	0.317795i	0.784604	−	0.619998i	$-0.212866\pi$
$191$	6.04508	+	4.39201i	0.437407	+	0.317795i	−0.347197	+	0.937792i	$0.612866\pi$
$192$	−0.224514	+	0.0729490i	−0.0162029	+	0.00526464i
$193$	17.6538	−	5.73607i	1.27075	−	0.412891i	0.405436	−	0.914124i	$-0.367120\pi$
$193$	17.6538	−	5.73607i	1.27075	−	0.412891i	0.865313	+	0.501232i	$0.167120\pi$
$194$	7.01722	+	5.09831i	0.503807	+	0.366037i
$195$		0			0
$196$	−1.00000	+	3.07768i	−0.0714286	+	0.219835i
$197$		−	24.3820i		−	1.73714i	−0.495564	−	0.868572i	$-0.665039\pi$
$197$		−	24.3820i		−	1.73714i	0.495564	−	0.868572i	$-0.334961\pi$
$198$	−2.04087	−	0.190983i	−0.145038	−	0.0135726i
$199$	16.7082			1.18441			0.592207	−	0.805786i	$-0.298257\pi$
$199$	16.7082			1.18441			0.592207	+	0.805786i	$0.298257\pi$
$200$		0			0
$201$	7.73607	−	5.62058i	0.545660	−	0.396445i
$202$	−1.08981	+	1.50000i	−0.0766790	+	0.105540i
$203$	−12.7598	+	4.14590i	−0.895560	+	0.290985i
$204$	0.809017	+	2.48990i	0.0566425	+	0.174328i
$205$		0			0
$206$	−3.00000	+	2.17963i	−0.209020	+	0.151862i
$207$	−3.30220	−	1.07295i	−0.229519	−	0.0745751i
$208$			3.27051i			0.226769i
$209$	17.8262	+	7.69421i	1.23307	+	0.532220i
$210$		0			0
$211$	−6.88197	+	21.1805i	−0.473774	+	1.45813i	0.373830	+	0.927497i	$0.378044\pi$
$211$	−6.88197	+	21.1805i	−0.473774	+	1.45813i	−0.847604	+	0.530629i	$0.821956\pi$
$212$	9.14729	+	12.5902i	0.628239	+	0.864696i
$213$	−3.26944	+	4.50000i	−0.224018	+	0.308335i
$214$	−0.809017	−	2.48990i	−0.0553033	−	0.170206i
$215$		0			0
$216$	−1.80902	−	1.31433i	−0.123088	−	0.0894287i
$217$	5.03280	+	6.92705i	0.341649	+	0.470239i
$218$		0			0
$219$	3.23607			0.218673
$220$		0			0
$221$	2.85410			0.191988
$222$	0.138757	+	0.0450850i	0.00931278	+	0.00302591i
$223$	−0.416272	−	0.572949i	−0.0278756	−	0.0383675i	0.794852	−	0.606804i	$-0.207549\pi$
$223$	−0.416272	−	0.572949i	−0.0278756	−	0.0383675i	−0.822727	+	0.568436i	$0.807549\pi$
$224$	−13.6353	−	9.90659i	−0.911044	−	0.661912i
$225$		0			0
$226$	−0.135255	−	0.416272i	−0.00899702	−	0.0276900i
$227$	14.6291	−	20.1353i	0.970969	−	1.33642i	0.0294127	−	0.999567i	$-0.490636\pi$
$227$	14.6291	−	20.1353i	0.970969	−	1.33642i	0.941556	−	0.336856i	$-0.109364\pi$
$228$	5.56758	+	7.66312i	0.368722	+	0.507502i
$229$	−3.09017	+	9.51057i	−0.204204	+	0.628476i	0.795541	+	0.605900i	$0.207187\pi$
$229$	−3.09017	+	9.51057i	−0.204204	+	0.628476i	−0.999745	+	0.0225760i	$0.992813\pi$
$230$		0			0
$231$	5.07295	+	8.55951i	0.333776	+	0.563174i
$232$		−	10.0000i		−	0.656532i
$233$	23.1356	+	7.51722i	1.51567	+	0.492470i	0.944541	−	0.328394i	$-0.106507\pi$
$233$	23.1356	+	7.51722i	1.51567	+	0.492470i	0.571124	+	0.820863i	$0.306507\pi$
$234$	−0.881966	+	0.640786i	−0.0576559	+	0.0418895i
$235$		0			0
$236$	−5.16312	−	15.8904i	−0.336090	−	1.03438i
$237$	9.00854	−	2.92705i	0.585167	−	0.190132i
$238$	−1.76336	+	2.42705i	−0.114301	+	0.157322i
$239$	2.07295	−	1.50609i	0.134088	−	0.0974206i	−0.518719	−	0.854945i	$-0.673591\pi$
$239$	2.07295	−	1.50609i	0.134088	−	0.0974206i	0.652807	+	0.757524i	$0.273591\pi$
$240$		0			0
$241$	−23.1246			−1.48959			−0.744794	−	0.667295i	$-0.767452\pi$
$241$	−23.1246			−1.48959			−0.744794	+	0.667295i	$0.767452\pi$
$242$	−4.94704	+	4.66312i	−0.318008	+	0.299757i
$243$			1.00000i			0.0641500i
$244$	3.92705	−	12.0862i	0.251404	−	0.773741i
$245$		0			0
$246$	−5.97214	−	4.33901i	−0.380769	−	0.276645i
$247$	9.82084	−	3.19098i	0.624885	−	0.203037i
$248$	−6.06961	+	1.97214i	−0.385421	+	0.125231i
$249$	0.572949	+	0.416272i	0.0363092	+	0.0263802i
$250$		0			0
$251$	−2.40983	+	7.41669i	−0.152107	+	0.468138i	−0.997856	−	0.0654431i	$-0.979154\pi$
$251$	−2.40983	+	7.41669i	−0.152107	+	0.468138i	0.845749	+	0.533581i	$0.179154\pi$
$252$			4.85410i			0.305780i
$253$	−9.90659	+	5.87132i	−0.622822	+	0.369127i
$254$	−2.29180			−0.143800
$255$		0			0
$256$	5.30902	−	3.85723i	0.331814	−	0.241077i
$257$	6.86167	−	9.44427i	0.428019	−	0.589117i	−0.539478	−	0.842000i	$-0.681378\pi$
$257$	6.86167	−	9.44427i	0.428019	−	0.589117i	0.967497	+	0.252882i	$0.0813785\pi$
$258$	3.66547	−	1.19098i	0.228202	−	0.0741474i
$259$	−0.218847	−	0.673542i	−0.0135985	−	0.0418519i
$260$		0			0
$261$	−3.61803	+	2.62866i	−0.223951	+	0.162710i
$262$	−4.20025	−	1.36475i	−0.259493	−	0.0843142i
$263$		−	16.3262i		−	1.00672i	−0.864077	−	0.503359i	$-0.832097\pi$
$263$		−	16.3262i		−	1.00672i	0.864077	−	0.503359i	$-0.167903\pi$
$264$	−7.23607	+	1.62460i	−0.445349	+	0.0999871i
$265$		0			0
$266$	−3.35410	+	10.3229i	−0.205653	+	0.632935i
$267$	0.310271	+	0.427051i	0.0189883	+	0.0261351i
$268$	9.09429	−	12.5172i	0.555522	−	0.764611i
$269$	−4.79837	−	14.7679i	−0.292562	−	0.900413i	−0.984029	−	0.178006i	$-0.943035\pi$
$269$	−4.79837	−	14.7679i	−0.292562	−	0.900413i	0.691467	−	0.722408i	$-0.256965\pi$
$270$		0			0
$271$	22.0623	+	16.0292i	1.34019	+	0.973705i	0.999437	+	0.0335518i	$0.0106819\pi$
$271$	22.0623	+	16.0292i	1.34019	+	0.973705i	0.340753	+	0.940153i	$0.389318\pi$
$272$	1.76336	+	2.42705i	0.106919	+	0.147162i
$273$	5.03280	+	1.63525i	0.304599	+	0.0989701i
$274$	4.61803			0.278986
$275$		0			0
$276$	−5.61803			−0.338166
$277$	−29.0665	−	9.44427i	−1.74644	−	0.567451i	−0.750779	−	0.660554i	$-0.770322\pi$
$277$	−29.0665	−	9.44427i	−1.74644	−	0.567451i	−0.995657	+	0.0931022i	$0.970322\pi$
$278$	−0.310271	−	0.427051i	−0.0186088	−	0.0256128i
$279$	2.30902	+	1.67760i	0.138237	+	0.100435i
$280$		0			0
$281$	−0.236068	−	0.726543i	−0.0140826	−	0.0433419i	0.943768	−	0.330608i	$-0.107254\pi$
$281$	−0.236068	−	0.726543i	−0.0140826	−	0.0433419i	−0.957851	+	0.287266i	$0.907254\pi$
$282$	0.587785	−	0.809017i	0.0350021	−	0.0481763i
$283$	−0.106001	−	0.145898i	−0.00630111	−	0.00867274i	0.805855	−	0.592113i	$-0.201706\pi$
$283$	−0.106001	−	0.145898i	−0.00630111	−	0.00867274i	−0.812156	+	0.583440i	$0.801706\pi$
$284$	−2.78115	+	8.55951i	−0.165031	+	0.507913i
$285$		0			0
$286$	−0.336881	+	3.59996i	−0.0199202	+	0.212870i
$287$			35.8328i			2.11514i
$288$	−5.34307	−	1.73607i	−0.314843	−	0.102299i
$289$	−11.6353	+	8.45351i	−0.684427	+	0.497265i
$290$		0			0
$291$	−4.33688	−	13.3475i	−0.254232	−	0.782447i
$292$	4.97980	−	1.61803i	0.291421	−	0.0946883i
$293$	0.0327561	−	0.0450850i	0.00191363	−	0.00263389i	−0.808059	−	0.589101i	$-0.799482\pi$
$293$	0.0327561	−	0.0450850i	0.00191363	−	0.00263389i	0.809973	+	0.586468i	$0.199482\pi$
$294$	−1.00000	+	0.726543i	−0.0583212	+	0.0423728i
$295$		0			0
$296$	0.527864			0.0306815
$297$	2.48990	+	2.19098i	0.144479	+	0.127134i
$298$		−	9.27051i		−	0.537026i
$299$	−1.89261	+	5.82485i	−0.109452	+	0.336860i
$300$		0			0
$301$	−15.1353	−	10.9964i	−0.872382	−	0.633822i
$302$	−1.17557	+	0.381966i	−0.0676465	+	0.0219797i
$303$	2.85317	−	0.927051i	0.163910	−	0.0532577i
$304$	8.78115	+	6.37988i	0.503634	+	0.365911i
$305$		0			0
$306$	−0.309017	+	0.951057i	−0.0176653	+	0.0543683i
$307$		−	0.562306i		−	0.0320925i	−0.999871	−	0.0160462i	$-0.994892\pi$
$307$		−	0.562306i		−	0.0320925i	0.999871	−	0.0160462i	$-0.00510790\pi$
$308$	12.0862	+	10.6353i	0.688676	+	0.606000i
$309$	6.00000			0.341328
$310$		0			0
$311$	−2.04508	+	1.48584i	−0.115966	+	0.0842543i	−0.644257	−	0.764809i	$-0.722833\pi$
$311$	−2.04508	+	1.48584i	−0.115966	+	0.0842543i	0.528291	+	0.849064i	$0.322833\pi$
$312$	−2.31838	+	3.19098i	−0.131253	+	0.180654i
$313$	−24.5685	+	7.98278i	−1.38869	+	0.451213i	−0.905517	−	0.424310i	$-0.860517\pi$
$313$	−24.5685	+	7.98278i	−1.38869	+	0.451213i	−0.483175	+	0.875524i	$0.660517\pi$
$314$	−0.708204	−	2.17963i	−0.0399663	−	0.123004i
$315$		0			0
$316$	12.3992	−	9.00854i	0.697509	−	0.506770i
$317$	18.4131	+	5.98278i	1.03418	+	0.336026i	0.776443	−	0.630188i	$-0.217022\pi$
$317$	18.4131	+	5.98278i	1.03418	+	0.336026i	0.257740	+	0.966214i	$0.417022\pi$
$318$			5.94427i			0.333338i
$319$	−1.38197	+	14.7679i	−0.0773752	+	0.826842i
$320$		0			0
$321$	−1.30902	+	4.02874i	−0.0730622	+	0.224862i
$322$	−3.78398	−	5.20820i	−0.210873	−	0.290242i
$323$	5.56758	−	7.66312i	0.309789	−	0.426387i
$324$	0.500000	+	1.53884i	0.0277778	+	0.0854912i
$325$		0			0
$326$	9.13525	+	6.63715i	0.505955	+	0.367598i
$327$		0			0
$328$	−25.4010	−	8.25329i	−1.40254	−	0.455712i
$329$	−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	$0.239080\pi$
$332$	1.08981	+	0.354102i	0.0598113	+	0.0194339i
$333$	−0.138757	−	0.190983i	−0.00760385	−	0.0104658i
$334$	−5.01722	−	3.64522i	−0.274530	−	0.199458i
$335$		0			0
$336$	1.71885	+	5.29007i	0.0937708	+	0.288597i
$337$	0.171513	−	0.236068i	0.00934293	−	0.0128594i	−0.804320	−	0.594196i	$-0.797470\pi$
$337$	0.171513	−	0.236068i	0.00934293	−	0.0128594i	0.813663	+	0.581337i	$0.197470\pi$
$338$	−3.59222	−	4.94427i	−0.195391	−	0.268933i
$339$	−0.218847	+	0.673542i	−0.0118861	+	0.0365818i
$340$		0			0
$341$	9.23607	−	2.07363i	0.500161	−	0.112293i
$342$			3.61803i			0.195641i
$343$	−14.2658	−	4.63525i	−0.770283	−	0.250280i
$344$	11.2812	−	8.19624i	0.608239	−	0.441912i
$345$		0			0
$346$	−2.93769	−	9.04129i	−0.157931	−	0.486063i
$347$	−19.9192	+	6.47214i	−1.06932	+	0.347442i	−0.790222	−	0.612821i	$-0.790035\pi$
$347$	−19.9192	+	6.47214i	−1.06932	+	0.347442i	−0.279096	+	0.960263i	$0.590035\pi$
$348$	−4.25325	+	5.85410i	−0.227998	+	0.313813i
$349$	−8.19098	+	5.95110i	−0.438453	+	0.318555i	−0.785020	−	0.619470i	$-0.787347\pi$
$349$	−8.19098	+	5.95110i	−0.438453	+	0.318555i	0.346567	+	0.938025i	$0.387347\pi$
$350$		0			0
$351$	1.76393			0.0941517
$352$	−16.0292	+	9.50000i	−0.854359	+	0.506352i
$353$		−	10.4721i		−	0.557376i	−0.960382	−	0.278688i	$-0.910101\pi$
$353$		−	10.4721i		−	0.557376i	0.960382	−	0.278688i	$-0.0898995\pi$
$354$	1.97214	−	6.06961i	0.104818	−	0.322596i
$355$		0			0
$356$	0.690983	+	0.502029i	0.0366220	+	0.0266075i
$357$	4.61653	−	1.50000i	0.244332	−	0.0793884i
$358$	−1.31433	+	0.427051i	−0.0694644	+	0.0225703i
$359$	−10.3262	−	7.50245i	−0.544998	−	0.395964i	0.280940	−	0.959725i	$-0.409354\pi$
$359$	−10.3262	−	7.50245i	−0.544998	−	0.395964i	−0.825938	+	0.563761i	$0.809354\pi$
$360$		0			0
$361$	4.71885	−	14.5231i	0.248360	−	0.764375i
$362$		−	10.7984i		−	0.567550i
$363$	10.9106	−	1.39919i	0.572661	−	0.0734383i
$364$	8.56231			0.448787
$365$		0			0
$366$	3.92705	−	2.85317i	0.205270	−	0.149138i
$367$	−3.26944	+	4.50000i	−0.170663	+	0.234898i	−0.885778	−	0.464109i	$-0.846375\pi$
$367$	−3.26944	+	4.50000i	−0.170663	+	0.234898i	0.715115	+	0.699007i	$0.246375\pi$
$368$	−6.12261	+	1.98936i	−0.319163	+	0.103702i
$369$	3.69098	+	11.3597i	0.192145	+	0.591361i
$370$		0			0
$371$	23.3435	−	16.9600i	1.21193	−	0.880520i
$372$	4.39201	+	1.42705i	0.227715	+	0.0739891i
$373$		−	4.41641i		−	0.228673i	−0.993442	−	0.114336i	$-0.963526\pi$
$373$		−	4.41641i		−	0.228673i	0.993442	−	0.114336i	$-0.0364742\pi$
$374$	1.69098	+	2.85317i	0.0874386	+	0.147534i
$375$		0			0
$376$	1.11803	−	3.44095i	0.0576582	−	0.177454i
$377$	4.63677	+	6.38197i	0.238806	+	0.328688i
$378$	−1.08981	+	1.50000i	−0.0560540	+	0.0771517i
$379$	−0.489357	−	1.50609i	−0.0251366	−	0.0773624i	0.937701	−	0.347443i	$-0.112950\pi$
$379$	−0.489357	−	1.50609i	−0.0251366	−	0.0773624i	−0.962838	+	0.270080i	$0.912950\pi$
$380$		0			0
$381$	3.00000	+	2.17963i	0.153695	+	0.111666i
$382$	2.71441	+	3.73607i	0.138881	+	0.191154i
$383$	25.5725	+	8.30902i	1.30669	+	0.424571i	0.877906	−	0.478834i	$-0.158940\pi$
$383$	25.5725	+	8.30902i	1.30669	+	0.424571i	0.428789	+	0.903405i	$0.358940\pi$
$384$	−11.3820			−0.580834
$385$		0			0
$386$	11.4721			0.583916
$387$	−5.93085	−	1.92705i	−0.301482	−	0.0979575i
$388$	−13.3475	−	18.3713i	−0.677619	−	0.932663i
$389$	19.6353	+	14.2658i	0.995547	+	0.723307i	0.961129	−	0.276100i	$-0.0890422\pi$
$389$	19.6353	+	14.2658i	0.995547	+	0.723307i	0.0344181	+	0.999408i	$0.489042\pi$
$390$		0			0
$391$	1.73607	+	5.34307i	0.0877967	+	0.270211i
$392$	−2.62866	+	3.61803i	−0.132767	+	0.182738i
$393$	4.20025	+	5.78115i	0.211875	+	0.291621i
$394$	4.65654	−	14.3314i	0.234593	−	0.722003i
$395$		0			0
$396$	4.92705	+	2.12663i	0.247594	+	0.106867i
$397$			38.7082i			1.94271i	0.237635	+	0.971355i	$0.423628\pi$
$397$			38.7082i			1.94271i	−0.237635	+	0.971355i	$0.576372\pi$
$398$	9.82084	+	3.19098i	0.492274	+	0.159950i
$399$	14.2082	−	10.3229i	0.711300	−	0.516790i
$400$		0			0
$401$	−8.06231	−	24.8132i	−0.402612	−	1.23911i	−0.922873	−	0.385106i	$-0.874165\pi$
$401$	−8.06231	−	24.8132i	−0.402612	−	1.23911i	0.520260	−	0.854008i	$-0.325835\pi$
$402$	5.62058	−	1.82624i	0.280329	−	0.0910845i
$403$	2.95917	−	4.07295i	0.147407	−	0.202888i
$404$	3.92705	−	2.85317i	0.195378	−	0.141950i
$405$		0			0
$406$	−8.29180			−0.411515
$407$	−0.779543	−	0.0729490i	−0.0386405	−	0.00361595i
$408$			3.61803i			0.179119i
$409$	3.41641	−	10.5146i	0.168930	−	0.519915i	−0.830374	−	0.557207i	$-0.811873\pi$
$409$	3.41641	−	10.5146i	0.168930	−	0.519915i	0.999304	+	0.0372920i	$0.0118732\pi$
$410$		0			0
$411$	−6.04508	−	4.39201i	−0.298182	−	0.216642i
$412$	9.23305	−	3.00000i	0.454880	−	0.147799i
$413$	−29.4625	+	9.57295i	−1.44976	+	0.471054i
$414$	−1.73607	−	1.26133i	−0.0853231	−	0.0619909i
$415$		0			0
$416$	−3.06231	+	9.42481i	−0.150142	+	0.462089i
$417$			0.854102i			0.0418256i
$418$	9.00854	+	7.92705i	0.440622	+	0.387725i
$419$	−16.5066			−0.806399			−0.403200	−	0.915112i	$-0.632102\pi$
$419$	−16.5066			−0.806399			−0.403200	+	0.915112i	$0.632102\pi$
$420$		0			0
$421$	30.1525	−	21.9071i	1.46954	−	1.06768i	0.488795	−	0.872398i	$-0.337436\pi$
$421$	30.1525	−	21.9071i	1.46954	−	1.06768i	0.980746	−	0.195286i	$-0.0625636\pi$
$422$	−8.09024	+	11.1353i	−0.393827	+	0.542056i
$423$	−1.53884	+	0.500000i	−0.0748210	+	0.0243108i
$424$	6.64590	+	20.4540i	0.322753	+	0.993333i
$425$		0			0
$426$	−2.78115	+	2.02063i	−0.134747	+	0.0978996i
$427$	−22.4091	−	7.28115i	−1.08445	−	0.352360i
$428$			6.85410i			0.331306i
$429$	3.86475	−	4.39201i	0.186592	−	0.212048i
$430$		0			0
$431$	−12.2082	+	37.5730i	−0.588048	+	1.80983i	−0.00138127	+	0.999999i	$0.500440\pi$
$431$	−12.2082	+	37.5730i	−0.588048	+	1.80983i	−0.586667	+	0.809828i	$0.699560\pi$
$432$	1.08981	+	1.50000i	0.0524337	+	0.0721688i
$433$	−3.52671	+	4.85410i	−0.169483	+	0.233273i	−0.885307	−	0.465008i	$-0.846051\pi$
$433$	−3.52671	+	4.85410i	−0.169483	+	0.233273i	0.715824	+	0.698281i	$0.246051\pi$
$434$	1.63525	+	5.03280i	0.0784947	+	0.241582i
$435$		0			0
$436$		0			0
$437$	11.9475	+	16.4443i	0.571525	+	0.786636i
$438$	1.90211	+	0.618034i	0.0908865	+	0.0295308i
$439$	−3.29180			−0.157109			−0.0785544	−	0.996910i	$-0.525030\pi$
$439$	−3.29180			−0.157109			−0.0785544	+	0.996910i	$0.525030\pi$
$440$		0			0
$441$	2.00000			0.0952381
$442$	1.67760	+	0.545085i	0.0797952	+	0.0259270i
$443$	24.1724	+	33.2705i	1.14847	+	1.58073i	0.746953	+	0.664877i	$0.231516\pi$
$443$	24.1724	+	33.2705i	1.14847	+	1.58073i	0.401514	+	0.915853i	$0.368484\pi$
$444$	−0.309017	−	0.224514i	−0.0146653	−	0.0106550i
$445$		0			0
$446$	−0.135255	−	0.416272i	−0.00640451	−	0.0197110i
$447$	−8.81678	+	12.1353i	−0.417019	+	0.573978i
$448$	0.416272	+	0.572949i	0.0196670	+	0.0270693i
$449$	7.56231	−	23.2744i	0.356887	−	1.09839i	−0.598020	−	0.801481i	$-0.704046\pi$
$449$	7.56231	−	23.2744i	0.356887	−	1.09839i	0.954907	−	0.296905i	$-0.0959544\pi$
$450$		0			0
$451$	36.3713	+	15.6987i	1.71266	+	0.739222i
$452$			1.14590i			0.0538985i
$453$	1.90211	+	0.618034i	0.0893691	+	0.0290378i
$454$	12.4443	−	9.04129i	0.584039	−	0.424329i
$455$		0			0
$456$	4.04508	+	12.4495i	0.189428	+	0.583001i
$457$	7.80021	−	2.53444i	0.364878	−	0.118556i	−0.120839	−	0.992672i	$-0.538558\pi$
$457$	7.80021	−	2.53444i	0.364878	−	0.118556i	0.485717	+	0.874116i	$0.338558\pi$
$458$	−3.63271	+	5.00000i	−0.169746	+	0.233635i
$459$	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	$0.663417\pi$
$462$	1.34708	+	6.00000i	0.0626720	+	0.279145i
$463$		−	15.7984i		−	0.734213i	−0.930179	−	0.367106i	$-0.880349\pi$
$463$		−	15.7984i		−	0.734213i	0.930179	−	0.367106i	$-0.119651\pi$
$464$	−2.56231	+	7.88597i	−0.118952	+	0.366097i
$465$		0			0
$466$	12.1631	+	8.83702i	0.563446	+	0.409367i
$467$	−9.28605	+	3.01722i	−0.429707	+	0.139620i	−0.515882	−	0.856660i	$-0.672536\pi$
$467$	−9.28605	+	3.01722i	−0.429707	+	0.139620i	0.0861747	+	0.996280i	$0.472536\pi$
$468$	2.71441	−	0.881966i	0.125474	−	0.0407689i
$469$	−23.2082	−	16.8617i	−1.07166	−	0.778603i
$470$		0			0
$471$	−1.14590	+	3.52671i	−0.0528002	+	0.162502i
$472$		−	23.0902i		−	1.06281i
$473$	−17.7926	+	10.5451i	−0.818103	+	0.484864i
$474$	5.85410			0.268888
$475$		0			0
$476$	6.35410	−	4.61653i	0.291240	−	0.211598i
$477$	5.65334	−	7.78115i	0.258849	−	0.356275i
$478$	1.50609	−	0.489357i	0.0688868	−	0.0223827i
$479$	8.68034	+	26.7153i	0.396615	+	1.22066i	0.927697	+	0.373335i	$0.121786\pi$
$479$	8.68034	+	26.7153i	0.396615	+	1.22066i	−0.531082	+	0.847320i	$0.678214\pi$
$480$		0			0
$481$	−0.336881	+	0.244758i	−0.0153605	+	0.0111600i
$482$	−13.5923	−	4.41641i	−0.619113	−	0.201162i
$483$			10.4164i			0.473963i
$484$	16.0902	−	7.60845i	0.731371	−	0.345839i
$485$		0			0
$486$	−0.190983	+	0.587785i	−0.00866317	+	0.0266625i
$487$	9.88635	+	13.6074i	0.447993	+	0.616610i	0.971965	−	0.235126i	$-0.0755503\pi$
$487$	9.88635	+	13.6074i	0.447993	+	0.616610i	−0.523972	+	0.851736i	$0.675550\pi$
$488$	10.3229	−	14.2082i	0.467294	−	0.643175i
$489$	−5.64590	−	17.3763i	−0.255316	−	0.785783i
$490$		0			0
$491$	−20.3992	−	14.8209i	−0.920602	−	0.668857i	0.0230715	−	0.999734i	$-0.492655\pi$
$491$	−20.3992	−	14.8209i	−0.920602	−	0.668857i	−0.943674	+	0.330877i	$0.892655\pi$
$492$	11.3597	+	15.6353i	0.512134	+	0.704892i
$493$	6.88191	+	2.23607i	0.309946	+	0.100707i
$494$	6.38197			0.287138
$495$		0			0
$496$	5.29180			0.237609
$497$	15.8702	+	5.15654i	0.711876	+	0.231302i
$498$	0.257270	+	0.354102i	0.0115286	+	0.0158677i
$499$	−14.2082	−	10.3229i	−0.636047	−	0.462115i	0.222443	−	0.974946i	$-0.428597\pi$
$499$	−14.2082	−	10.3229i	−0.636047	−	0.462115i	−0.858490	+	0.512831i	$0.828597\pi$
$500$		0			0
$501$	3.10081	+	9.54332i	0.138534	+	0.426364i
$502$	−2.83293	+	3.89919i	−0.126440	+	0.174029i
$503$	−16.4985	−	22.7082i	−0.735631	−	1.01251i	−0.998858	−	0.0477750i	$-0.984787\pi$
$503$	−16.4985	−	22.7082i	−0.735631	−	1.01251i	0.263227	−	0.964734i	$-0.415213\pi$
$504$	−2.07295	+	6.37988i	−0.0923365	+	0.284182i
$505$		0			0
$506$	−6.94427	+	1.55909i	−0.308711	+	0.0693098i
$507$			9.88854i			0.439166i
$508$	5.70634	+	1.85410i	0.253178	+	0.0822625i
$509$	19.1074	−	13.8823i	0.846920	−	0.615324i	−0.0773749	−	0.997002i	$-0.524654\pi$
$509$	19.1074	−	13.8823i	0.846920	−	0.615324i	0.924295	+	0.381679i	$0.124654\pi$
$510$		0			0
$511$	−3.00000	−	9.23305i	−0.132712	−	0.408446i
$512$	−17.7926	+	5.78115i	−0.786327	+	0.255493i
$513$	3.44095	−	4.73607i	0.151922	−	0.209103i
$514$	5.83688	−	4.24074i	0.257454	−	0.187051i
$515$		0			0
$516$	−10.0902			−0.444195
$517$	−2.12663	+	4.92705i	−0.0935289	+	0.216691i
$518$		−	0.437694i		−	0.0192312i
$519$	−4.75329	+	14.6291i	−0.208646	+	0.642147i
$520$		0			0
$521$	12.0000	+	8.71851i	0.525730	+	0.381965i	0.818758	−	0.574139i	$-0.194663\pi$
$521$	12.0000	+	8.71851i	0.525730	+	0.381965i	−0.293028	+	0.956104i	$0.594663\pi$
$522$	−2.62866	+	0.854102i	−0.115053	+	0.0373830i
$523$	11.3924	−	3.70163i	0.498156	−	0.161861i	−0.0491529	−	0.998791i	$-0.515652\pi$
$523$	11.3924	−	3.70163i	0.498156	−	0.161861i	0.547309	+	0.836930i	$0.315652\pi$
$524$	9.35410	+	6.79615i	0.408636	+	0.296891i
$525$		0			0
$526$	3.11803	−	9.59632i	0.135953	−	0.418420i
$527$		−	4.61803i		−	0.201165i
$528$	6.12261	+	0.572949i	0.266452	+	0.0249344i
$529$	10.9443			0.475838
$530$		0			0
$531$	−8.35410	+	6.06961i	−0.362537	+	0.263399i
$532$	16.7027	−	22.9894i	0.724156	−	0.996715i
$533$	20.0377	−	6.51064i	0.867929	−	0.282007i
$534$	0.100813	+	0.310271i	0.00436261	+	0.0134267i
$535$		0			0
$536$	17.2984	−	12.5680i	0.747176	−	0.542855i
$537$	2.12663	+	0.690983i	0.0917707	+	0.0298181i
$538$		−	9.59675i		−	0.413745i
$539$	4.38197	−	4.97980i	0.188745	−	0.214495i
$540$		0			0
$541$	6.04508	−	18.6049i	0.259899	−	0.799885i	−0.732926	−	0.680308i	$-0.761846\pi$
$541$	6.04508	−	18.6049i	0.259899	−	0.799885i	0.992825	−	0.119577i	$-0.0381540\pi$
$542$	9.90659	+	13.6353i	0.425525	+	0.585684i
$543$	−10.2699	+	14.1353i	−0.440722	+	0.606602i
$544$	2.80902	+	8.64527i	0.120436	+	0.370663i
$545$		0			0
$546$	2.64590	+	1.92236i	0.113234	+	0.0822693i
$547$	12.7068	+	17.4894i	0.543302	+	0.747791i	0.989084	−	0.147350i	$-0.0470745\pi$
$547$	12.7068	+	17.4894i	0.543302	+	0.747791i	−0.445782	+	0.895141i	$0.647075\pi$
$548$	−11.4984	−	3.73607i	−0.491189	−	0.159597i
$549$	−7.85410			−0.335205
$550$		0			0
$551$	26.1803			1.11532
$552$	−7.38394	−	2.39919i	−0.314281	−	0.102116i
$553$	−16.7027	−	22.9894i	−0.710273	−	0.977607i
$554$	−15.2812	−	11.1024i	−0.649234	−	0.471696i
$555$		0			0
$556$	0.427051	+	1.31433i	0.0181110	+	0.0557399i
$557$	−8.76378	+	12.0623i	−0.371333	+	0.511096i	−0.953263	−	0.302143i	$-0.902298\pi$
$557$	−8.76378	+	12.0623i	−0.371333	+	0.511096i	0.581929	+	0.813239i	$0.302298\pi$
$558$	1.03681	+	1.42705i	0.0438918	+	0.0604119i
$559$	−3.39919	+	10.4616i	−0.143770	+	0.442479i
$560$		0			0
$561$	0.500000	−	5.34307i	0.0211100	−	0.225585i
$562$		−	0.472136i		−	0.0199159i
$563$	−8.45351	−	2.74671i	−0.356273	−	0.115760i	0.125412	−	0.992105i	$-0.459975\pi$
$563$	−8.45351	−	2.74671i	−0.356273	−	0.115760i	−0.481684	+	0.876345i	$0.659975\pi$
$564$	−2.11803	+	1.53884i	−0.0891853	+	0.0647969i
$565$		0			0
$566$	−0.0344419	−	0.106001i	−0.00144770	−	0.00445556i
$567$	2.85317	−	0.927051i	0.119822	−	0.0389325i
$568$	−7.31069	+	10.0623i	−0.306750	+	0.422205i
$569$	−19.4721	+	14.1473i	−0.816314	+	0.593087i	−0.915654	−	0.401966i	$-0.868327\pi$
$569$	−19.4721	+	14.1473i	−0.816314	+	0.593087i	0.0993400	+	0.995054i	$0.468327\pi$
$570$		0			0
$571$	34.6869			1.45160			0.725801	−	0.687905i	$-0.241469\pi$
$571$	34.6869			1.45160			0.725801	+	0.687905i	$0.241469\pi$
$572$	3.75123	−	8.69098i	0.156847	−	0.363388i
$573$		−	7.47214i		−	0.312153i
$574$	−6.84346	+	21.0620i	−0.285640	+	0.879111i
$575$		0			0
$576$	0.190983	+	0.138757i	0.00795763	+	0.00578155i
$577$	10.2371	−	3.32624i	0.426176	−	0.138473i	−0.0880726	−	0.996114i	$-0.528071\pi$
$577$	10.2371	−	3.32624i	0.426176	−	0.138473i	0.514249	+	0.857641i	$0.328071\pi$
$578$	−8.45351	+	2.74671i	−0.351620	+	0.114248i
$579$	−15.0172	−	10.9106i	−0.624094	−	0.453431i
$580$		0			0
$581$	0.656541	−	2.02063i	0.0272379	−	0.0838297i
$582$		−	8.67376i		−	0.359539i
$583$	−6.98791	−	31.1246i	−0.289410	−	1.28905i
$584$	7.23607			0.299431
$585$		0			0
$586$	0.0278640	−	0.0202444i	0.00115105	−	0.000836289i
$587$	22.5151	−	30.9894i	0.929297	−	1.27907i	−0.0308361	−	0.999524i	$-0.509817\pi$
$587$	22.5151	−	30.9894i	0.929297	−	1.27907i	0.960133	−	0.279543i	$-0.0901830\pi$
$588$	3.07768	−	1.00000i	0.126922	−	0.0412393i
$589$	−5.16312	−	15.8904i	−0.212743	−	0.654754i
$590$		0			0
$591$	−19.7254	+	14.3314i	−0.811396	+	0.589513i
$592$	−0.416272	−	0.135255i	−0.0171087	−	0.00555894i
$593$			22.2148i			0.912252i	0.889915	+	0.456126i	$0.150763\pi$
$593$			22.2148i			0.912252i	−0.889915	+	0.456126i	$0.849237\pi$
$594$	1.04508	+	1.76336i	0.0428804	+	0.0723514i
$595$		0			0
$596$	−7.50000	+	23.0826i	−0.307212	+	0.945501i
$597$	−9.82084	−	13.5172i	−0.401940	−	0.553223i
$598$	−2.22490	+	3.06231i	−0.0909827	+	0.125227i
$599$	2.56231	+	7.88597i	0.104693	+	0.322212i	0.989658	−	0.143445i	$-0.0458181\pi$
$599$	2.56231	+	7.88597i	0.104693	+	0.322212i	−0.884965	+	0.465657i	$0.845818\pi$
$600$		0			0
$601$	−27.3713	−	19.8864i	−1.11650	−	0.811184i	−0.132825	−	0.991140i	$-0.542405\pi$
$601$	−27.3713	−	19.8864i	−1.11650	−	0.811184i	−0.983675	+	0.179955i	$0.942405\pi$
$602$	−6.79615	−	9.35410i	−0.276991	−	0.381245i
$603$	−9.09429	−	2.95492i	−0.370348	−	0.120333i
$604$	3.23607			0.131674
$605$		0			0
$606$	1.85410			0.0753177
$607$	−12.6740	−	4.11803i	−0.514422	−	0.167146i	0.0402904	−	0.999188i	$-0.487172\pi$
$607$	−12.6740	−	4.11803i	−0.514422	−	0.167146i	−0.554712	+	0.832042i	$0.687172\pi$
$608$	19.3314	+	26.6074i	0.783992	+	1.07907i
$609$	10.8541	+	7.88597i	0.439830	+	0.319555i
$610$		0			0
$611$	0.881966	+	2.71441i	0.0356805	+	0.109813i
$612$	1.53884	−	2.11803i	0.0622040	−	0.0856164i
$613$	−20.3682	−	28.0344i	−0.822664	−	1.13230i	−0.989244	−	0.146272i	$-0.953272\pi$
$613$	−20.3682	−	28.0344i	−0.822664	−	1.13230i	0.166580	−	0.986028i	$-0.446728\pi$
$614$	0.107391	−	0.330515i	0.00433394	−	0.0133385i
$615$		0			0
$616$	11.3435	+	19.1396i	0.457041	+	0.771158i
$617$		−	19.5836i		−	0.788406i	−0.919023	−	0.394203i	$-0.871021\pi$
$617$		−	19.5836i		−	0.788406i	0.919023	−	0.394203i	$-0.128979\pi$
$618$	3.52671	+	1.14590i	0.141865	+	0.0460948i
$619$	−7.13525	+	5.18407i	−0.286790	+	0.208365i	−0.721874	−	0.692025i	$-0.756719\pi$
$619$	−7.13525	+	5.18407i	−0.286790	+	0.208365i	0.435084	+	0.900390i	$0.356719\pi$
$620$		0			0
$621$	1.07295	+	3.30220i	0.0430560	+	0.132513i
$622$	−1.48584	+	0.482779i	−0.0595768	+	0.0193577i
$623$	0.930812	−	1.28115i	0.0372922	−	0.0513283i
$624$	2.64590	−	1.92236i	0.105921	−	0.0769559i
$625$		0			0
$626$	−15.9656			−0.638112
$627$	−4.25325	−	18.9443i	−0.169859	−	0.756561i
$628$			6.00000i			0.239426i
$629$	−0.118034	+	0.363271i	−0.00470632	+	0.0144846i
$630$		0			0
$631$	−37.4336	−	27.1971i	−1.49021	−	1.08270i	−0.974084	−	0.226187i	$-0.927374\pi$
$631$	−37.4336	−	27.1971i	−1.49021	−	1.08270i	−0.516125	−	0.856513i	$-0.672626\pi$
$632$	20.1437	−	6.54508i	0.801273	−	0.260350i
$633$	21.1805	−	6.88197i	0.841850	−	0.273534i
$634$	9.68034	+	7.03318i	0.384455	+	0.279323i
$635$		0			0
$636$	4.80902	−	14.8006i	0.190690	−	0.586883i
$637$		−	3.52786i		−	0.139779i
$638$	−3.63271	+	8.41641i	−0.143820	+	0.333209i
$639$	5.56231			0.220041
$640$		0			0
$641$	−28.9164	+	21.0090i	−1.14213	+	0.829806i	−0.987415	−	0.158154i	$-0.949446\pi$
$641$	−28.9164	+	21.0090i	−1.14213	+	0.829806i	−0.154715	+	0.987959i	$0.549446\pi$
$642$	−1.53884	+	2.11803i	−0.0607332	+	0.0835921i
$643$	36.6749	−	11.9164i	1.44632	−	0.469937i	0.522457	−	0.852666i	$-0.325015\pi$
$643$	36.6749	−	11.9164i	1.44632	−	0.469937i	0.923861	+	0.382728i	$0.125015\pi$
$644$	5.20820	+	16.0292i	0.205232	+	0.631639i
$645$		0			0
$646$	4.73607	−	3.44095i	0.186338	−	0.135383i
$647$	−26.4378	−	8.59017i	−1.03938	−	0.337714i	−0.260887	−	0.965369i	$-0.584015\pi$
$647$	−26.4378	−	8.59017i	−1.03938	−	0.337714i	−0.778492	+	0.627655i	$0.784015\pi$
$648$			2.23607i			0.0878410i
$649$	−3.19098	+	34.0993i	−0.125257	+	1.33851i
$650$		0			0
$651$	2.64590	−	8.14324i	0.103701	−	0.319159i
$652$	−17.3763	−	23.9164i	−0.680508	−	0.936639i
$653$	29.9973	−	41.2877i	1.17388	−	1.61571i	0.543632	−	0.839323i	$-0.317049\pi$
$653$	29.9973	−	41.2877i	1.17388	−	1.61571i	0.630252	−	0.776390i	$-0.282951\pi$
$654$		0			0
$655$		0			0
$656$	17.9164	+	13.0170i	0.699518	+	0.508230i
$657$	−1.90211	−	2.61803i	−0.0742085	−	0.102139i
$658$	−2.85317	−	0.927051i	−0.111228	−	0.0361402i
$659$	10.6525			0.414962			0.207481	−	0.978239i	$-0.433474\pi$
$659$	10.6525			0.414962			0.207481	+	0.978239i	$0.433474\pi$
$660$		0			0
$661$	−9.90983			−0.385448			−0.192724	−	0.981253i	$-0.561732\pi$
$661$	−9.90983			−0.385448			−0.192724	+	0.981253i	$0.561732\pi$
$662$	15.6332	+	5.07953i	0.607601	+	0.197421i
$663$	−1.67760	−	2.30902i	−0.0651525	−	0.0896748i
$664$	1.28115	+	0.930812i	0.0497184	+	0.0361225i
$665$		0			0
$666$	−0.0450850	−	0.138757i	−0.00174701	−	0.00537674i
$667$	−9.12705	+	12.5623i	−0.353401	+	0.486414i
$668$	9.54332	+	13.1353i	0.369242	+	0.508218i
$669$	−0.218847	+	0.673542i	−0.00846112	+	0.0260406i
$670$		0			0
$671$	−17.2082	+	19.5559i	−0.664315	+	0.754948i
$672$			16.8541i			0.650161i
$673$	11.8087	+	3.83688i	0.455192	+	0.147901i	0.527634	−	0.849472i	$-0.323079\pi$
$673$	11.8087	+	3.83688i	0.455192	+	0.147901i	−0.0724420	+	0.997373i	$0.523079\pi$
$674$	0.145898	−	0.106001i	0.00561978	−	0.00408301i
$675$		0			0
$676$	4.94427	+	15.2169i	0.190164	+	0.585266i
$677$	12.8658	−	4.18034i	0.494471	−	0.160664i	−0.0511572	−	0.998691i	$-0.516291\pi$
$677$	12.8658	−	4.18034i	0.494471	−	0.160664i	0.545629	+	0.838027i	$0.316291\pi$
$678$	−0.257270	+	0.354102i	−0.00988040	+	0.0135992i
$679$	−34.0623	+	24.7477i	−1.30719	+	0.949730i
$680$		0			0
$681$	−24.8885			−0.953731
$682$	5.82485	+	0.545085i	0.223045	+	0.0208724i
$683$		−	3.11146i		−	0.119057i	−0.998227	−	0.0595283i	$-0.981040\pi$
$683$		−	3.11146i		−	0.119057i	0.998227	−	0.0595283i	$-0.0189596\pi$
$684$	2.92705	−	9.00854i	0.111919	−	0.344450i
$685$		0			0
$686$	−7.50000	−	5.44907i	−0.286351	−	0.208046i
$687$	9.51057	−	3.09017i	0.362851	−	0.117897i
$688$	−10.9964	+	3.57295i	−0.419234	+	0.136217i
$689$	−13.7254	−	9.97210i	−0.522897	−	0.379907i
$690$		0			0
$691$	−8.12461	+	25.0050i	−0.309075	+	0.951234i	0.669050	+	0.743217i	$0.266701\pi$
$691$	−8.12461	+	25.0050i	−0.309075	+	0.951234i	−0.978125	+	0.208017i	$0.933299\pi$
$692$			24.8885i			0.946120i
$693$	3.94298	−	9.13525i	0.149782	−	0.347020i
$694$	−12.9443			−0.491358
$695$		0			0
$696$	−8.09017	+	5.87785i	−0.306657	+	0.222799i
$697$	11.3597	−	15.6353i	0.430278	−	0.592228i
$698$	−5.95110	+	1.93363i	−0.225252	+	0.0731889i
$699$	−7.51722	−	23.1356i	−0.284327	−	0.875070i
$700$		0			0
$701$	8.64590	−	6.28161i	0.326551	−	0.237253i	−0.412415	−	0.910996i	$-0.635315\pi$
$701$	8.64590	−	6.28161i	0.326551	−	0.237253i	0.738966	+	0.673743i	$0.235315\pi$
$702$	1.03681	+	0.336881i	0.0391320	+	0.0127148i
$703$			1.38197i			0.0521218i
$704$	0.763932	−	0.171513i	0.0287918	−	0.00646416i
$705$		0			0
$706$	2.00000	−	6.15537i	0.0752710	−	0.231660i
$707$	−5.29007	−	7.28115i	−0.198953	−	0.273836i
$708$	−9.82084	+	13.5172i	−0.369090	+	0.508008i
$709$	−15.0623	−	46.3570i	−0.565677	−	1.74097i	−0.665932	−	0.746012i	$-0.731966\pi$
$709$	−15.0623	−	46.3570i	−0.565677	−	1.74097i	0.100255	−	0.994962i	$-0.468034\pi$
$710$		0			0
$711$	−7.66312	−	5.56758i	−0.287389	−	0.208801i
$712$	0.693786	+	0.954915i	0.0260007	+	0.0357870i
$713$	9.42481	+	3.06231i	0.352962	+	0.114684i
$714$	3.00000			0.112272
$715$		0			0
$716$	3.61803			0.135212
$717$	−2.43690	−	0.791796i	−0.0910076	−	0.0295702i
$718$	−4.63677	−	6.38197i	−0.173043	−	0.238173i
$719$	−1.28115	−	0.930812i	−0.0477789	−	0.0347134i	0.563639	−	0.826021i	$-0.309401\pi$
$719$	−1.28115	−	0.930812i	−0.0477789	−	0.0347134i	−0.611418	+	0.791307i	$0.709401\pi$
$720$		0			0
$721$	−5.56231	−	17.1190i	−0.207151	−	0.637546i
$722$	5.54734	−	7.63525i	0.206451	−	0.284155i
$723$	13.5923	+	18.7082i	0.505503	+	0.695766i
$724$	−8.73607	+	26.8869i	−0.324673	+	0.999242i
$725$		0			0
$726$	6.68034	+	1.26133i	0.247931	+	0.0468122i
$727$		−	38.8541i		−	1.44102i	−0.693445	−	0.720509i	$-0.743908\pi$
$727$		−	38.8541i		−	1.44102i	0.693445	−	0.720509i	$-0.256092\pi$
$728$	11.2537	+	3.65654i	0.417089	+	0.135520i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$		0			0
$731$	3.11803	+	9.59632i	0.115325	+	0.354933i
$732$	−12.0862	+	3.92705i	−0.446720	+	0.145148i
$733$	−22.1643	+	30.5066i	−0.818658	+	1.12679i	0.171271	+	0.985224i	$0.445213\pi$
$733$	−22.1643	+	30.5066i	−0.818658	+	1.12679i	−0.989929	+	0.141562i	$0.954787\pi$
$734$	−2.78115	+	2.02063i	−0.102654	+	0.0745827i
$735$		0			0
$736$	−19.5066			−0.719022
$737$	−27.2829	+	16.1697i	−1.00498	+	0.595618i
$738$			7.38197i			0.271734i
$739$	7.72542	−	23.7764i	0.284184	−	0.874629i	−0.702458	−	0.711726i	$-0.747914\pi$
$739$	7.72542	−	23.7764i	0.284184	−	0.874629i	0.986642	−	0.162904i	$-0.0520860\pi$
$740$		0			0
$741$	−8.35410	−	6.06961i	−0.306896	−	0.222973i
$742$	16.9600	−	5.51064i	0.622622	−	0.202302i
$743$	−33.4585	+	10.8713i	−1.22747	+	0.398830i	−0.849798	−	0.527108i	$-0.823276\pi$
$743$	−33.4585	+	10.8713i	−1.22747	+	0.398830i	−0.377675	+	0.925938i	$0.623276\pi$
$744$	5.16312	+	3.75123i	0.189289	+	0.137527i
$745$		0			0
$746$	0.843459	−	2.59590i	0.0308812	−	0.0950426i
$747$		−	0.708204i		−	0.0259118i
$748$	−1.90211	−	8.47214i	−0.0695481	−	0.309772i
$749$	12.7082			0.464348
$750$		0			0
$751$	−9.64590	+	7.00816i	−0.351984	+	0.255731i	−0.749701	−	0.661777i	$-0.769803\pi$
$751$	−9.64590	+	7.00816i	−0.351984	+	0.255731i	0.397717	+	0.917508i	$0.369803\pi$
$752$	−1.76336	+	2.42705i	−0.0643030	+	0.0885054i
$753$	7.41669	−	2.40983i	0.270279	−	0.0878191i
$754$	1.50658	+	4.63677i	0.0548663	+	0.168861i
$755$		0			0
$756$	3.92705	−	2.85317i	0.142825	−	0.103769i
$757$	−1.84911	−	0.600813i	−0.0672071	−	0.0218369i	0.275220	−	0.961381i	$-0.411249\pi$
$757$	−1.84911	−	0.600813i	−0.0672071	−	0.0218369i	−0.342428	+	0.939544i	$0.611249\pi$
$758$		−	0.978714i		−	0.0355485i
$759$	10.5729	+	4.56352i	0.383774	+	0.165645i
$760$		0			0
$761$	−9.54508	+	29.3768i	−0.346009	+	1.06491i	0.615032	+	0.788502i	$0.289143\pi$
$761$	−9.54508	+	29.3768i	−0.346009	+	1.06491i	−0.961041	+	0.276404i	$0.910857\pi$
$762$	1.34708	+	1.85410i	0.0487997	+	0.0671670i
$763$		0			0
$764$	−3.73607	−	11.4984i	−0.135166	−	0.415999i
$765$		0			0
$766$	13.4443	+	9.76784i	0.485761	+	0.352926i
$767$	10.7064	+	14.7361i	0.386585	+	0.532089i
$768$	−6.24112	−	2.02786i	−0.225207	−	0.0731742i
$769$	−12.6869			−0.457502			−0.228751	−	0.973485i	$-0.573464\pi$
$769$	−12.6869			−0.457502			−0.228751	+	0.973485i	$0.573464\pi$
$770$		0			0
$771$	−11.6738			−0.420420
$772$	−28.5645	−	9.28115i	−1.02806	−	0.334036i
$773$	18.3678	+	25.2812i	0.660645	+	0.909300i	0.999503	−	0.0315378i	$-0.0100405\pi$
$773$	18.3678	+	25.2812i	0.660645	+	0.909300i	−0.338858	+	0.940838i	$0.610040\pi$
$774$	−3.11803	−	2.26538i	−0.112075	−	0.0814276i
$775$		0			0
$776$	−9.69756	−	29.8460i	−0.348122	−	1.07141i
$777$	−0.416272	+	0.572949i	−0.0149337	+	0.0205544i
$778$	8.81678	+	12.1353i	0.316097	+	0.435070i
$779$	21.6074	−	66.5007i	0.774165	−	2.38264i
$780$		0			0
$781$	12.1869	−	13.8496i	0.436082	−	0.495577i
$782$			3.47214i			0.124163i
$783$	4.25325	+	1.38197i	0.151999	+	0.0493874i
$784$	3.00000	−	2.17963i	0.107143	−	0.0778438i
$785$		0			0
$786$	1.36475	+	4.20025i	0.0486788	+	0.149818i
$787$	−9.78808	+	3.18034i	−0.348907	+	0.113367i	−0.478227	−	0.878236i	$-0.658721\pi$
$787$	−9.78808	+	3.18034i	−0.348907	+	0.113367i	0.129320	+	0.991603i	$0.458721\pi$
$788$	−23.1886	+	31.9164i	−0.826061	+	1.13697i
$789$	−13.2082	+	9.59632i	−0.470225	+	0.341638i
$790$		0			0
$791$	2.12461			0.0755425
$792$	5.56758	+	4.89919i	0.197835	+	0.174085i
$793$			13.8541i			0.491974i
$794$	−7.39261	+	22.7521i	−0.262354	+	0.807442i
$795$		0			0
$796$	−21.8713	−	15.8904i	−0.775208	−	0.563222i
$797$	10.2371	−	3.32624i	0.362617	−	0.117821i	−0.122041	−	0.992525i	$-0.538944\pi$
$797$	10.2371	−	3.32624i	0.362617	−	0.117821i	0.484658	+	0.874704i	$0.338944\pi$
$798$	10.3229	−	3.35410i	0.365425	−	0.118734i
$799$	2.11803	+	1.53884i	0.0749307	+	0.0544403i
$800$		0			0
$801$	0.163119	−	0.502029i	0.00576353	−	0.0177383i
$802$		−	16.1246i		−	0.569380i
$803$	−10.6861	−	1.00000i	−0.377106	−	0.0352892i
$804$	−15.4721			−0.545660
$805$		0			0
$806$	2.51722	−	1.82887i	0.0886653	−	0.0644191i
$807$	−9.12705	+	12.5623i	−0.321287	+	0.442214i
$808$	6.37988	−	2.07295i	0.224443	−	0.0729261i
$809$	−2.98936	−	9.20029i	−0.105100	−	0.323465i	0.884654	−	0.466249i	$-0.154395\pi$
$809$	−2.98936	−	9.20029i	−0.105100	−	0.323465i	−0.989754	+	0.142783i	$0.954395\pi$
$810$		0			0
$811$	−2.63525	+	1.91462i	−0.0925363	+	0.0672316i	−0.633091	−	0.774077i	$-0.718214\pi$
$811$	−2.63525	+	1.91462i	−0.0925363	+	0.0672316i	0.540555	+	0.841309i	$0.318214\pi$
$812$	20.6457	+	6.70820i	0.724523	+	0.235412i
$813$		−	27.2705i		−	0.956419i
$814$	−0.444272	−	0.191758i	−0.0155717	−	0.00672111i
$815$		0			0
$816$	0.927051	−	2.85317i	0.0324533	−	0.0998809i
$817$	21.4580	+	29.5344i	0.750721	+	1.03328i
$818$	4.01623	−	5.52786i	0.140424	−	0.193277i
$819$	−1.63525	−	5.03280i	−0.0571404	−	0.175860i
$820$		0			0
$821$	−32.6976	−	23.7562i	−1.14115	−	0.829096i	−0.153873	−	0.988091i	$-0.549175\pi$
$821$	−32.6976	−	23.7562i	−1.14115	−	0.829096i	−0.987279	+	0.158995i	$0.949175\pi$
$822$	−2.71441	−	3.73607i	−0.0946760	−	0.130310i
$823$	−33.7360	−	10.9615i	−1.17596	−	0.382094i	−0.345098	−	0.938567i	$-0.612154\pi$
$823$	−33.7360	−	10.9615i	−1.17596	−	0.382094i	−0.830866	+	0.556473i	$0.812154\pi$
$824$	13.4164			0.467383
$825$		0			0
$826$	−19.1459			−0.666171
$827$	−50.5245	−	16.4164i	−1.75691	−	0.570854i	−0.760037	−	0.649880i	$-0.774819\pi$
$827$	−50.5245	−	16.4164i	−1.75691	−	0.570854i	−0.996873	+	0.0790257i	$0.974819\pi$
$828$	3.30220	+	4.54508i	0.114759	+	0.157953i
$829$	14.3090	+	10.3961i	0.496973	+	0.361072i	0.807859	−	0.589375i	$-0.200626\pi$
$829$	14.3090	+	10.3961i	0.496973	+	0.361072i	−0.310887	+	0.950447i	$0.600626\pi$
$830$		0			0
$831$	9.44427	+	29.0665i	0.327618	+	1.00831i
$832$	0.244758	−	0.336881i	0.00848547	−	0.0116792i
$833$	−1.90211	−	2.61803i	−0.0659043	−	0.0907095i
$834$	−0.163119	+	0.502029i	−0.00564835	+	0.0173838i
$835$		0			0
$836$	−16.0172	−	27.0256i	−0.553967	−	0.934700i
$837$		−	2.85410i		−	0.0986522i
$838$	−9.70232	−	3.15248i	−0.335161	−	0.108900i
$839$	−29.6976	+	21.5765i	−1.02527	+	0.744905i	−0.967357	−	0.253417i	$-0.918446\pi$
$839$	−29.6976	+	21.5765i	−1.02527	+	0.744905i	−0.0579164	+	0.998321i	$0.518446\pi$
$840$		0			0
$841$	−2.78115	−	8.55951i	−0.0959018	−	0.295155i
$842$	21.9071	−	7.11803i	0.754967	−	0.245304i
$843$	−0.449028	+	0.618034i	−0.0154653	+	0.0212862i
$844$	29.1525	−	21.1805i	1.00347	−	0.729063i
$845$		0			0
$846$	−1.00000			−0.0343807
$847$	−14.1068	−	29.8328i	−0.484717	−	1.02507i
$848$		−	17.8328i		−	0.612381i
$849$	−0.0557281	+	0.171513i	−0.00191258	+	0.00588633i
$850$		0			0
$851$	−0.663119	−	0.481784i	−0.0227314	−	0.0165153i
$852$	8.55951	−	2.78115i	0.293244	−	0.0952807i
$853$	9.45756	−	3.07295i	0.323821	−	0.105216i	−0.142596	−	0.989781i	$-0.545545\pi$
$853$	9.45756	−	3.07295i	0.323821	−	0.105216i	0.466416	+	0.884565i	$0.345545\pi$
$854$	−11.7812	−	8.55951i	−0.403143	−	0.292900i
$855$		0			0
$856$	−2.92705	+	9.00854i	−0.100045	+	0.307905i
$857$		−	47.7214i		−	1.63013i	−0.579369	−	0.815065i	$-0.696701\pi$
$857$		−	47.7214i		−	1.63013i	0.579369	−	0.815065i	$-0.303299\pi$
$858$	3.11044	−	1.84346i	0.106189	−	0.0629346i
$859$	−7.11146			−0.242640			−0.121320	−	0.992613i	$-0.538713\pi$
$859$	−7.11146			−0.242640			−0.121320	+	0.992613i	$0.538713\pi$
$860$		0			0
$861$	28.9894	−	21.0620i	0.987955	−	0.717791i
$862$	−14.3516	+	19.7533i	−0.488818	+	0.672800i
$863$	−11.3067	+	3.67376i	−0.384884	+	0.125056i	−0.495067	−	0.868855i	$-0.664856\pi$
$863$	−11.3067	+	3.67376i	−0.384884	+	0.125056i	0.110183	+	0.993911i	$0.464856\pi$
$864$	1.73607	+	5.34307i	0.0590622	+	0.181775i
$865$		0			0
$866$	−3.00000	+	2.17963i	−0.101944	+	0.0740668i
$867$	13.6781	+	4.44427i	0.464531	+	0.150935i
$868$		−	13.8541i		−	0.470239i
$869$	−30.6525	+	6.88191i	−1.03981	+	0.233453i
$870$		0			0
$871$	−5.21227	+	16.0417i	−0.176611	+	0.543553i
$872$		0			0
$873$	−8.24924	+	11.3541i	−0.279194	+	0.384278i
$874$	3.88197	+	11.9475i	0.131309	+	0.404129i
$875$		0			0
$876$	−4.23607	−	3.07768i	−0.143123	−	0.103985i
$877$	3.77147	+	5.19098i	0.127353	+	0.175287i	0.867932	−	0.496682i	$-0.165449\pi$
$877$	3.77147	+	5.19098i	0.127353	+	0.175287i	−0.740579	+	0.671969i	$0.765449\pi$
$878$	−1.93487	−	0.628677i	−0.0652987	−	0.0212168i
$879$	−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	$0.424715\pi$
$882$	1.17557	+	0.381966i	0.0395835	+	0.0128615i
$883$	−6.22088	−	8.56231i	−0.209349	−	0.288145i	0.691411	−	0.722462i	$-0.256990\pi$
$883$	−6.22088	−	8.56231i	−0.209349	−	0.288145i	−0.900760	+	0.434318i	$0.856990\pi$
$884$	−3.73607	−	2.71441i	−0.125658	−	0.0912956i
$885$		0			0
$886$	7.85410	+	24.1724i	0.263864	+	0.812089i
$887$	−1.76336	+	2.42705i	−0.0592077	+	0.0814924i	−0.837594	−	0.546293i	$-0.816038\pi$
$887$	−1.76336	+	2.42705i	−0.0592077	+	0.0814924i	0.778386	+	0.627785i	$0.216038\pi$
$888$	−0.310271	−	0.427051i	−0.0104120	−	0.0143309i
$889$	3.43769	−	10.5801i	0.115297	−	0.354846i
$890$		0			0
$891$	0.309017	−	3.30220i	0.0103525	−	0.110628i
$892$			1.14590i			0.0383675i
$893$	9.00854	+	2.92705i	0.301459	+	0.0979500i
$894$	−7.50000	+	5.44907i	−0.250838	+	0.182244i
$895$		0			0
$896$	10.5517	+	32.4747i	0.352506	+	1.08490i
$897$	5.82485	−	1.89261i	0.194486	−	0.0631924i
$898$	8.89002	−	12.2361i	0.296664	−	0.408323i
$899$	10.3262	−	7.50245i	0.344399	−	0.250221i
$900$		0			0
$901$	−15.5623			−0.518456
$902$	18.3803	+	16.1738i	0.611999	+	0.538527i
$903$			18.7082i			0.622570i
$904$	−0.489357	+	1.50609i	−0.0162758	+	0.0500917i
$905$		0			0
$906$	1.00000	+	0.726543i	0.0332228	+	0.0241378i
$907$	−40.8752	+	13.2812i	−1.35724	+	0.440993i	−0.895120	−	0.445825i	$-0.852910\pi$
$907$	−40.8752	+	13.2812i	−1.35724	+	0.440993i	−0.462118	+	0.886818i	$0.652910\pi$
$908$	−38.2995	+	12.4443i	−1.27101	+	0.412978i
$909$	−2.42705	−	1.76336i	−0.0805002	−	0.0584868i
$910$		0			0
$911$	5.57953	−	17.1720i	0.184858	−	0.568934i	−0.815088	−	0.579337i	$-0.803311\pi$
$911$	5.57953	−	17.1720i	0.184858	−	0.568934i	0.999946	+	0.0104029i	$0.00331142\pi$
$912$		−	10.8541i		−	0.359415i
$913$	−1.76336	−	1.55166i	−0.0583586	−	0.0513525i
$914$	5.06888			0.167664
$915$		0			0
$916$	13.0902	−	9.51057i	0.432511	−	0.314238i
$917$	12.6008	−	17.3435i	0.416114	−	0.572731i
$918$	0.951057	−	0.309017i	0.0313895	−	0.0101991i
$919$	−14.5106	−	44.6592i	−0.478662	−	1.47317i	−0.840955	−	0.541106i	$-0.818006\pi$
$919$	−14.5106	−	44.6592i	−0.478662	−	1.47317i	0.362293	−	0.932064i	$-0.381994\pi$
$920$		0			0
$921$	−0.454915	+	0.330515i	−0.0149900	+	0.0108908i
$922$	−12.3965	−	4.02786i	−0.408257	−	0.132651i
$923$		−	9.81153i		−	0.322950i
$924$	1.50000	−	16.0292i	0.0493464	−	0.527322i
$925$		0			0
$926$	3.01722	−	9.28605i	0.0991520	−	0.305159i
$927$	−3.52671	−	4.85410i	−0.115832	−	0.159430i
$928$	−14.7679	+	20.3262i	−0.484779	+	0.667241i
$929$	10.1631	+	31.2789i	0.333441	+	1.02623i	0.967485	+	0.252929i	$0.0813939\pi$
$929$	10.1631	+	31.2789i	0.333441	+	1.02623i	−0.634044	+	0.773297i	$0.718606\pi$
$930$		0			0
$931$	−9.47214	−	6.88191i	−0.310437	−	0.225545i
$932$	−23.1356	−	31.8435i	−0.757833	−	1.04307i
$933$	2.40414	+	0.781153i	0.0787081	+	0.0255738i
$934$	−6.03444			−0.197453
$935$		0			0
$936$	3.94427			0.128923
$937$	15.7844	+	5.12868i	0.515655	+	0.167547i	0.555273	−	0.831668i	$-0.312614\pi$
$937$	15.7844	+	5.12868i	0.515655	+	0.167547i	−0.0396173	+	0.999215i	$0.512614\pi$
$938$	−10.4211	−	14.3435i	−0.340262	−	0.468331i
$939$	20.8992	+	15.1841i	0.682019	+	0.495516i
$940$		0			0
$941$	−13.7918	−	42.4468i	−0.449600	−	1.38373i	−0.877360	−	0.479833i	$-0.840697\pi$
$941$	−13.7918	−	42.4468i	−0.449600	−	1.38373i	0.427760	−	0.903892i	$-0.359303\pi$
$942$	−1.34708	+	1.85410i	−0.0438904	+	0.0604099i
$943$	24.3767	+	33.5517i	0.793815	+	1.09259i
$944$	−5.91641	+	18.2088i	−0.192563	+	0.592647i
$945$		0			0
$946$	−12.4721	+	2.80017i	−0.405504	+	0.0910413i
$947$		−	18.3262i		−	0.595523i	−0.954640	−	0.297761i	$-0.903760\pi$
$947$		−	18.3262i		−	0.595523i	0.954640	−	0.297761i	$-0.0962400\pi$
$948$	−14.5761	−	4.73607i	−0.473410	−	0.153820i
$949$	−4.61803	+	3.35520i	−0.149908	+	0.108914i
$950$		0			0
$951$	−5.98278	−	18.4131i	−0.194005	−	0.597086i
$952$	10.3229	−	3.35410i	0.334566	−	0.108707i
$953$	22.2298	−	30.5967i	0.720095	−	0.991126i	−0.279426	−	0.960167i	$-0.590144\pi$
$953$	22.2298	−	30.5967i	0.720095	−	0.991126i	0.999521	−	0.0309585i	$-0.00985598\pi$
$954$	4.80902	−	3.49396i	0.155698	−	0.113121i
$955$		0			0
$956$	−4.14590			−0.134088
$957$	12.7598	−	7.56231i	0.412465	−	0.244455i
$958$			17.3607i			0.560898i
$959$	−6.92705	+	21.3193i	−0.223686	+	0.688435i
$960$		0			0
$961$	18.4894	+	13.4333i	0.596431	+	0.433332i
$962$	−0.244758	+	0.0795268i	−0.00789133	+	0.00256405i
$963$	4.02874	−	1.30902i	0.129824	−	0.0421825i
$964$	30.2705	+	21.9928i	0.974947	+	0.708341i
$965$		0			0
$966$	−1.98936	+	6.12261i	−0.0640065	+	0.196992i
$967$			34.6869i			1.11546i	0.830024	+	0.557728i	$0.188327\pi$
$967$			34.6869i			1.11546i	−0.830024	+	0.557728i	$0.811673\pi$
$968$	24.3970	−	3.12868i	0.784148	−	0.100559i
$969$	−9.47214			−0.304289
$970$		0			0
$971$	−30.5623	+	22.2048i	−0.980791	+	0.712586i	−0.957885	−	0.287151i	$-0.907292\pi$
$971$	−30.5623	+	22.2048i	−0.980791	+	0.712586i	−0.0229058	+	0.999738i	$0.507292\pi$
$972$	0.951057	−	1.30902i	0.0305052	−	0.0419867i
$973$	2.43690	−	0.791796i	0.0781234	−	0.0253838i
$974$	3.21227	+	9.88635i	0.102928	+	0.316779i
$975$		0			0
$976$	−11.7812	+	8.55951i	−0.377106	+	0.273983i
$977$	4.41226	+	1.43363i	0.141161	+	0.0458658i	0.378745	−	0.925501i	$-0.376356\pi$
$977$	4.41226	+	1.43363i	0.141161	+	0.0458658i	−0.237585	+	0.971367i	$0.576356\pi$
$978$		−	11.2918i		−	0.361072i
$979$	−0.892609	−	1.50609i	−0.0285279	−	0.0481347i
$980$		0			0
$981$		0			0
$982$	−9.15981	−	12.6074i	−0.292301	−	0.402318i
$983$	−16.0494	+	22.0902i	−0.511898	+	0.704567i	−0.984238	−	0.176849i	$-0.943409\pi$
$983$	−16.0494	+	22.0902i	−0.511898	+	0.704567i	0.472340	+	0.881416i	$0.343409\pi$
$984$	8.25329	+	25.4010i	0.263105	+	0.809755i
$985$		0			0
$986$	3.61803	+	2.62866i	0.115222	+	0.0837134i
$987$	2.85317	+	3.92705i	0.0908174	+	0.124999i
$988$	−15.8904	−	5.16312i	−0.505542	−	0.164261i
$989$	−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	$0.390304\pi$
$992$	15.2497	+	4.95492i	0.484177	+	0.157319i
$993$	−15.6332	−	21.5172i	−0.496104	−	0.682828i
$994$	8.34346	+	6.06188i	0.264638	+	0.192271i
$995$		0			0
$996$	−0.354102	−	1.08981i	−0.0112202	−	0.0345321i
$997$	7.62870	−	10.5000i	0.241603	−	0.332538i	−0.670945	−	0.741507i	$-0.734111\pi$
$997$	7.62870	−	10.5000i	0.241603	−	0.332538i	0.912548	+	0.408969i	$0.134111\pi$
$998$	−6.37988	−	8.78115i	−0.201952	−	0.277963i
$999$	−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.bx.b.724.2		8
5.2	odd	4		33.2.e.a.31.1	yes	4
5.3	odd	4		825.2.n.f.526.1		4
5.4	even	2	inner	825.2.bx.b.724.1		8
11.5	even	5	inner	825.2.bx.b.49.1		8
15.2	even	4		99.2.f.b.64.1		4
20.7	even	4		528.2.y.f.97.1		4
45.2	even	12		891.2.n.a.757.1		8
45.7	odd	12		891.2.n.d.757.1		8
45.22	odd	12		891.2.n.d.460.1		8
45.32	even	12		891.2.n.a.460.1		8
55.2	even	20		363.2.e.c.124.1		4
55.7	even	20		363.2.a.e.1.2		2
55.17	even	20		363.2.e.j.148.1		4
55.18	even	20		9075.2.a.bv.1.1		2
55.27	odd	20		33.2.e.a.16.1	✓	4
55.32	even	4		363.2.e.j.130.1		4
55.37	odd	20		363.2.a.h.1.1		2
55.38	odd	20		825.2.n.f.676.1		4
55.42	odd	20		363.2.e.h.124.1		4
55.47	odd	20		363.2.e.h.202.1		4
55.48	odd	20		9075.2.a.x.1.2		2
55.49	even	10	inner	825.2.bx.b.49.2		8
55.52	even	20		363.2.e.c.202.1		4
165.62	odd	20		1089.2.a.s.1.1		2
165.92	even	20		1089.2.a.m.1.2		2
165.137	even	20		99.2.f.b.82.1		4
220.7	odd	20		5808.2.a.bm.1.1		2
220.27	even	20		528.2.y.f.49.1		4
220.147	even	20		5808.2.a.bl.1.1		2
495.137	even	60		891.2.n.a.676.1		8
495.247	odd	60		891.2.n.d.379.1		8
495.302	even	60		891.2.n.a.379.1		8
495.412	odd	60		891.2.n.d.676.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.e.a.16.1	✓	4	55.27	odd	20
33.2.e.a.31.1	yes	4	5.2	odd	4
99.2.f.b.64.1		4	15.2	even	4
99.2.f.b.82.1		4	165.137	even	20
363.2.a.e.1.2		2	55.7	even	20
363.2.a.h.1.1		2	55.37	odd	20
363.2.e.c.124.1		4	55.2	even	20
363.2.e.c.202.1		4	55.52	even	20
363.2.e.h.124.1		4	55.42	odd	20
363.2.e.h.202.1		4	55.47	odd	20
363.2.e.j.130.1		4	55.32	even	4
363.2.e.j.148.1		4	55.17	even	20
528.2.y.f.49.1		4	220.27	even	20
528.2.y.f.97.1		4	20.7	even	4
825.2.n.f.526.1		4	5.3	odd	4
825.2.n.f.676.1		4	55.38	odd	20
825.2.bx.b.49.1		8	11.5	even	5	inner
825.2.bx.b.49.2		8	55.49	even	10	inner
825.2.bx.b.724.1		8	5.4	even	2	inner
825.2.bx.b.724.2		8	1.1	even	1	trivial
891.2.n.a.379.1		8	495.302	even	60
891.2.n.a.460.1		8	45.32	even	12
891.2.n.a.676.1		8	495.137	even	60
891.2.n.a.757.1		8	45.2	even	12
891.2.n.d.379.1		8	495.247	odd	60
891.2.n.d.460.1		8	45.22	odd	12
891.2.n.d.676.1		8	495.412	odd	60
891.2.n.d.757.1		8	45.7	odd	12
1089.2.a.m.1.2		2	165.92	even	20
1089.2.a.s.1.1		2	165.62	odd	20
5808.2.a.bl.1.1		2	220.147	even	20
5808.2.a.bm.1.1		2	220.7	odd	20
9075.2.a.x.1.2		2	55.48	odd	20
9075.2.a.bv.1.1		2	55.18	even	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.587785 + 0.190983i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(-1.30902 - 0.951057i) q^{4} +(-0.190983 - 0.587785i) q^{6} +(-1.76336 + 2.42705i) q^{7} +(-1.31433 - 1.80902i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(1.69098 + 2.85317i) q^{11} +1.61803i q^{12} +(1.67760 + 0.545085i) q^{13} +(-1.50000 + 1.08981i) q^{14} +(0.572949 + 1.76336i) q^{16} +(1.53884 - 0.500000i) q^{17} +(-0.363271 + 0.500000i) q^{18} +(4.73607 - 3.44095i) q^{19} +3.00000 q^{21} +(0.449028 + 2.00000i) q^{22} +3.47214i q^{23} +(-0.690983 + 2.12663i) q^{24} +(0.881966 + 0.640786i) q^{26} +(0.951057 - 0.309017i) q^{27} +(4.61653 - 1.50000i) q^{28} +(3.61803 + 2.62866i) q^{29} +(0.881966 - 2.71441i) q^{31} +5.61803i q^{32} +(1.31433 - 3.04508i) q^{33} +1.00000 q^{34} +(1.30902 - 0.951057i) q^{36} +(-0.138757 + 0.190983i) q^{37} +(3.44095 - 1.11803i) q^{38} +(-0.545085 - 1.67760i) q^{39} +(9.66312 - 7.02067i) q^{41} +(1.76336 + 0.572949i) q^{42} +6.23607i q^{43} +(0.500000 - 5.34307i) q^{44} +(-0.663119 + 2.04087i) q^{46} +(0.951057 + 1.30902i) q^{47} +(1.08981 - 1.50000i) q^{48} +(-0.618034 - 1.90211i) q^{49} +(-1.30902 - 0.951057i) q^{51} +(-1.67760 - 2.30902i) q^{52} +(-9.14729 - 2.97214i) q^{53} +0.618034 q^{54} +6.70820 q^{56} +(-5.56758 - 1.80902i) q^{57} +(1.62460 + 2.23607i) q^{58} +(8.35410 + 6.06961i) q^{59} +(2.42705 + 7.46969i) q^{61} +(1.03681 - 1.42705i) q^{62} +(-1.76336 - 2.42705i) q^{63} +(0.0729490 - 0.224514i) q^{64} +(1.35410 - 1.53884i) q^{66} +9.56231i q^{67} +(-2.48990 - 0.809017i) q^{68} +(2.80902 - 2.04087i) q^{69} +(-1.71885 - 5.29007i) q^{71} +(2.12663 - 0.690983i) q^{72} +(-1.90211 + 2.61803i) q^{73} +(-0.118034 + 0.0857567i) q^{74} -9.47214 q^{76} +(-9.90659 - 0.927051i) q^{77} -1.09017i q^{78} +(-2.92705 + 9.00854i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(7.02067 - 2.28115i) q^{82} +(-0.673542 + 0.218847i) q^{83} +(-3.92705 - 2.85317i) q^{84} +(-1.19098 + 3.66547i) q^{86} -4.47214i q^{87} +(2.93893 - 6.80902i) q^{88} -0.527864 q^{89} +(-4.28115 + 3.11044i) q^{91} +(3.30220 - 4.54508i) q^{92} +(-2.71441 + 0.881966i) q^{93} +(0.309017 + 0.951057i) q^{94} +(4.54508 - 3.30220i) q^{96} +(13.3475 + 4.33688i) q^{97} -1.23607i q^{98} +(-3.23607 + 0.726543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{4} - 6 q^{6} + 2 q^{9} + 18 q^{11} - 12 q^{14} + 18 q^{16} + 20 q^{19} + 24 q^{21} - 10 q^{24} + 16 q^{26} + 20 q^{29} + 16 q^{31} + 8 q^{34} + 6 q^{36} + 18 q^{39} + 46 q^{41} + 4 q^{44} + 26 q^{46}+ \cdots - 8 q^{99}+O(q^{100}) \) 8 * q - 6 * q^4 - 6 * q^6 + 2 * q^9 + 18 * q^11 - 12 * q^14 + 18 * q^16 + 20 * q^19 + 24 * q^21 - 10 * q^24 + 16 * q^26 + 20 * q^29 + 16 * q^31 + 8 * q^34 + 6 * q^36 + 18 * q^39 + 46 * q^41 + 4 * q^44 + 26 * q^46 + 4 * q^49 - 6 * q^51 - 4 * q^54 + 40 * q^59 + 6 * q^61 + 14 * q^64 - 16 * q^66 + 18 * q^69 - 54 * q^71 + 8 * q^74 - 40 * q^76 - 10 * q^79 - 2 * q^81 - 18 * q^84 - 14 * q^86 - 40 * q^89 + 6 * q^91 - 2 * q^94 + 14 * q^96 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more