LMFDB - Embedded newform 825.2.bx.c.499.2

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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			499.2
Root			$-0.951057 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	825.499
Dual form			825.2.bx.c.124.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.363271 - 0.500000i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.500000 + 1.53884i) q^{4} +(0.500000 - 0.363271i) q^{6} +(0.726543 - 0.236068i) q^{7} +(2.12663 + 0.690983i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.363271 - 0.500000i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.500000 + 1.53884i) q^{4} +(0.500000 - 0.363271i) q^{6} +(0.726543 - 0.236068i) q^{7} +(2.12663 + 0.690983i) q^{8} +(0.809017 + 0.587785i) q^{9} +(3.23607 - 0.726543i) q^{11} +1.61803i q^{12} +(0.726543 - 1.00000i) q^{13} +(0.145898 - 0.449028i) q^{14} +(-1.50000 + 1.08981i) q^{16} +(-1.17557 - 1.61803i) q^{17} +(0.587785 - 0.190983i) q^{18} +(-1.54508 + 4.75528i) q^{19} +0.763932 q^{21} +(0.812299 - 1.88197i) q^{22} -2.38197i q^{23} +(1.80902 + 1.31433i) q^{24} +(-0.236068 - 0.726543i) q^{26} +(0.587785 + 0.809017i) q^{27} +(0.726543 + 1.00000i) q^{28} +(1.80902 + 5.56758i) q^{29} +(-5.66312 - 4.11450i) q^{31} +5.61803i q^{32} +(3.30220 + 0.309017i) q^{33} -1.23607 q^{34} +(-0.500000 + 1.53884i) q^{36} +(7.10642 - 2.30902i) q^{37} +(1.81636 + 2.50000i) q^{38} +(1.00000 - 0.726543i) q^{39} +(0.781153 - 2.40414i) q^{41} +(0.277515 - 0.381966i) q^{42} +2.09017i q^{43} +(2.73607 + 4.61653i) q^{44} +(-1.19098 - 0.865300i) q^{46} +(4.84104 + 1.57295i) q^{47} +(-1.76336 + 0.572949i) q^{48} +(-5.19098 + 3.77147i) q^{49} +(-0.618034 - 1.90211i) q^{51} +(1.90211 + 0.618034i) q^{52} +(4.47777 - 6.16312i) q^{53} +0.618034 q^{54} +1.70820 q^{56} +(-2.93893 + 4.04508i) q^{57} +(3.44095 + 1.11803i) q^{58} +(2.07295 + 6.37988i) q^{59} +(-5.66312 + 4.11450i) q^{61} +(-4.11450 + 1.33688i) q^{62} +(0.726543 + 0.236068i) q^{63} +(-0.190983 - 0.138757i) q^{64} +(1.35410 - 1.53884i) q^{66} -9.38197i q^{67} +(1.90211 - 2.61803i) q^{68} +(0.736068 - 2.26538i) q^{69} +(6.47214 - 4.70228i) q^{71} +(1.31433 + 1.80902i) q^{72} +(-12.8128 + 4.16312i) q^{73} +(1.42705 - 4.39201i) q^{74} -8.09017 q^{76} +(2.17963 - 1.29180i) q^{77} -0.763932i q^{78} +(-6.54508 - 4.75528i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-0.918300 - 1.26393i) q^{82} +(-3.35520 - 4.61803i) q^{83} +(0.381966 + 1.17557i) q^{84} +(1.04508 + 0.759299i) q^{86} +5.85410i q^{87} +(7.38394 + 0.690983i) q^{88} -10.8541 q^{89} +(0.291796 - 0.898056i) q^{91} +(3.66547 - 1.19098i) q^{92} +(-4.11450 - 5.66312i) q^{93} +(2.54508 - 1.84911i) q^{94} +(-1.73607 + 5.34307i) q^{96} +(6.74315 - 9.28115i) q^{97} +3.96556i q^{98} +(3.04508 + 1.31433i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} + 4 q^{6} + 2 q^{9}+O(q^{10}) $ 8 * q + 4 * q^4 + 4 * q^6 + 2 * q^9	$ 8 q + 4 q^{4} + 4 q^{6} + 2 q^{9} + 8 q^{11} + 28 q^{14} - 12 q^{16} + 10 q^{19} + 24 q^{21} + 10 q^{24} + 16 q^{26} + 10 q^{29} - 14 q^{31} + 8 q^{34} - 4 q^{36} + 8 q^{39} - 34 q^{41} + 4 q^{44} - 14 q^{46} - 46 q^{49} + 4 q^{51} - 4 q^{54} - 40 q^{56} + 30 q^{59} - 14 q^{61} - 6 q^{64} - 16 q^{66} - 12 q^{69} + 16 q^{71} - 2 q^{74} - 20 q^{76} - 30 q^{79} - 2 q^{81} + 12 q^{84} - 14 q^{86} - 60 q^{89} + 56 q^{91} - 2 q^{94} + 4 q^{96} + 2 q^{99}+O(q^{100}) $ 8 * q + 4 * q^4 + 4 * q^6 + 2 * q^9 + 8 * q^11 + 28 * q^14 - 12 * q^16 + 10 * q^19 + 24 * q^21 + 10 * q^24 + 16 * q^26 + 10 * q^29 - 14 * q^31 + 8 * q^34 - 4 * q^36 + 8 * q^39 - 34 * q^41 + 4 * q^44 - 14 * q^46 - 46 * q^49 + 4 * q^51 - 4 * q^54 - 40 * q^56 + 30 * q^59 - 14 * q^61 - 6 * q^64 - 16 * q^66 - 12 * q^69 + 16 * q^71 - 2 * q^74 - 20 * q^76 - 30 * q^79 - 2 * q^81 + 12 * q^84 - 14 * q^86 - 60 * q^89 + 56 * q^91 - 2 * q^94 + 4 * q^96 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.363271	−	0.500000i	0.256872	−	0.353553i	−0.661031	−	0.750358i	$-0.729881\pi$
$2$	0.363271	−	0.500000i	0.256872	−	0.353553i	0.917903	+	0.396805i	$0.129881\pi$
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$4$	0.500000	+	1.53884i	0.250000	+	0.769421i
$5$		0			0
$5$		0			0
$6$	0.500000	−	0.363271i	0.204124	−	0.148305i
$7$	0.726543	−	0.236068i	0.274607	−	0.0892253i	−0.168476	−	0.985706i	$-0.553885\pi$
$7$	0.726543	−	0.236068i	0.274607	−	0.0892253i	0.443083	+	0.896480i	$0.353885\pi$
$8$	2.12663	+	0.690983i	0.751876	+	0.244299i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$		0			0
$11$	3.23607	−	0.726543i	0.975711	−	0.219061i
$11$	3.23607	−	0.726543i	0.975711	−	0.219061i
$12$			1.61803i			0.467086i
$13$	0.726543	−	1.00000i	0.201507	−	0.277350i	−0.696290	−	0.717761i	$-0.745167\pi$
$13$	0.726543	−	1.00000i	0.201507	−	0.277350i	0.897796	+	0.440411i	$0.145167\pi$
$14$	0.145898	−	0.449028i	0.0389929	−	0.120008i
$15$		0			0
$16$	−1.50000	+	1.08981i	−0.375000	+	0.272453i
$17$	−1.17557	−	1.61803i	−0.285118	−	0.392431i	0.642303	−	0.766451i	$-0.277979\pi$
$17$	−1.17557	−	1.61803i	−0.285118	−	0.392431i	−0.927421	+	0.374020i	$0.877979\pi$
$18$	0.587785	−	0.190983i	0.138542	−	0.0450151i
$19$	−1.54508	+	4.75528i	−0.354467	+	1.09094i	0.601851	+	0.798608i	$0.294430\pi$
$19$	−1.54508	+	4.75528i	−0.354467	+	1.09094i	−0.956318	+	0.292328i	$0.905570\pi$
$20$		0			0
$21$	0.763932			0.166704
$22$	0.812299	−	1.88197i	0.173183	−	0.401237i
$23$		−	2.38197i		−	0.496674i	−0.968674	−	0.248337i	$-0.920116\pi$
$23$		−	2.38197i		−	0.496674i	0.968674	−	0.248337i	$-0.0798841\pi$
$24$	1.80902	+	1.31433i	0.369264	+	0.268286i
$25$		0			0
$26$	−0.236068	−	0.726543i	−0.0462967	−	0.142487i
$27$	0.587785	+	0.809017i	0.113119	+	0.155695i
$28$	0.726543	+	1.00000i	0.137304	+	0.188982i
$29$	1.80902	+	5.56758i	0.335926	+	1.03387i	0.966264	+	0.257553i	$0.0829163\pi$
$29$	1.80902	+	5.56758i	0.335926	+	1.03387i	−0.630338	+	0.776321i	$0.717084\pi$
$30$		0			0
$31$	−5.66312	−	4.11450i	−1.01713	−	0.738985i	−0.0514344	−	0.998676i	$-0.516379\pi$
$31$	−5.66312	−	4.11450i	−1.01713	−	0.738985i	−0.965692	+	0.259691i	$0.916379\pi$
$32$			5.61803i			0.993137i
$33$	3.30220	+	0.309017i	0.574839	+	0.0537930i
$34$	−1.23607			−0.211984
$35$		0			0
$36$	−0.500000	+	1.53884i	−0.0833333	+	0.256474i
$37$	7.10642	−	2.30902i	1.16829	−	0.379600i	0.340285	−	0.940322i	$-0.389476\pi$
$37$	7.10642	−	2.30902i	1.16829	−	0.379600i	0.828004	+	0.560722i	$0.189476\pi$
$38$	1.81636	+	2.50000i	0.294652	+	0.405554i
$39$	1.00000	−	0.726543i	0.160128	−	0.116340i
$40$		0			0
$41$	0.781153	−	2.40414i	0.121996	−	0.375464i	−0.871346	−	0.490669i	$-0.836752\pi$
$41$	0.781153	−	2.40414i	0.121996	−	0.375464i	0.993342	+	0.115205i	$0.0367525\pi$
$42$	0.277515	−	0.381966i	0.0428214	−	0.0589386i
$43$			2.09017i			0.318748i	0.987218	+	0.159374i	$0.0509476\pi$
$43$			2.09017i			0.318748i	−0.987218	+	0.159374i	$0.949052\pi$
$44$	2.73607	+	4.61653i	0.412478	+	0.695967i
$45$		0			0
$46$	−1.19098	−	0.865300i	−0.175601	−	0.127581i
$47$	4.84104	+	1.57295i	0.706138	+	0.229438i	0.640003	−	0.768372i	$-0.278933\pi$
$47$	4.84104	+	1.57295i	0.706138	+	0.229438i	0.0661352	+	0.997811i	$0.478933\pi$
$48$	−1.76336	+	0.572949i	−0.254518	+	0.0826981i
$49$	−5.19098	+	3.77147i	−0.741569	+	0.538781i
$50$		0			0
$51$	−0.618034	−	1.90211i	−0.0865421	−	0.266349i
$52$	1.90211	+	0.618034i	0.263776	+	0.0857059i
$53$	4.47777	−	6.16312i	0.615069	−	0.846569i	−0.381914	−	0.924198i	$-0.624735\pi$
$53$	4.47777	−	6.16312i	0.615069	−	0.846569i	0.996982	+	0.0776285i	$0.0247348\pi$
$54$	0.618034			0.0841038
$55$		0			0
$56$	1.70820			0.228268
$57$	−2.93893	+	4.04508i	−0.389270	+	0.535785i
$58$	3.44095	+	1.11803i	0.451820	+	0.146805i
$59$	2.07295	+	6.37988i	0.269875	+	0.830590i	0.990530	+	0.137296i	$0.0438412\pi$
$59$	2.07295	+	6.37988i	0.269875	+	0.830590i	−0.720655	+	0.693294i	$0.756159\pi$
$60$		0			0
$61$	−5.66312	+	4.11450i	−0.725088	+	0.526807i	−0.888006	−	0.459832i	$-0.847910\pi$
$61$	−5.66312	+	4.11450i	−0.725088	+	0.526807i	0.162918	+	0.986640i	$0.447910\pi$
$62$	−4.11450	+	1.33688i	−0.522542	+	0.169784i
$63$	0.726543	+	0.236068i	0.0915358	+	0.0297418i
$64$	−0.190983	−	0.138757i	−0.0238729	−	0.0173447i
$65$		0			0
$66$	1.35410	−	1.53884i	0.166678	−	0.189418i
$67$		−	9.38197i		−	1.14619i	−0.819489	−	0.573095i	$-0.805743\pi$
$67$		−	9.38197i		−	1.14619i	0.819489	−	0.573095i	$-0.194257\pi$
$68$	1.90211	−	2.61803i	0.230665	−	0.317483i
$69$	0.736068	−	2.26538i	0.0886122	−	0.272720i
$70$		0			0
$71$	6.47214	−	4.70228i	0.768101	−	0.558058i	−0.133283	−	0.991078i	$-0.542552\pi$
$71$	6.47214	−	4.70228i	0.768101	−	0.558058i	0.901384	+	0.433020i	$0.142552\pi$
$72$	1.31433	+	1.80902i	0.154895	+	0.213195i
$73$	−12.8128	+	4.16312i	−1.49962	+	0.487256i	−0.939907	−	0.341430i	$-0.889089\pi$
$73$	−12.8128	+	4.16312i	−1.49962	+	0.487256i	−0.559713	+	0.828686i	$0.689089\pi$
$74$	1.42705	−	4.39201i	0.165891	−	0.510561i
$75$		0			0
$76$	−8.09017			−0.928006
$77$	2.17963	−	1.29180i	0.248392	−	0.147214i
$78$		−	0.763932i		−	0.0864983i
$79$	−6.54508	−	4.75528i	−0.736380	−	0.535011i	0.155196	−	0.987884i	$-0.450399\pi$
$79$	−6.54508	−	4.75528i	−0.736380	−	0.535011i	−0.891575	+	0.452873i	$0.850399\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	−0.918300	−	1.26393i	−0.101409	−	0.139578i
$83$	−3.35520	−	4.61803i	−0.368281	−	0.506895i	0.584152	−	0.811644i	$-0.301427\pi$
$83$	−3.35520	−	4.61803i	−0.368281	−	0.506895i	−0.952433	+	0.304749i	$0.901427\pi$
$84$	0.381966	+	1.17557i	0.0416759	+	0.128265i
$85$		0			0
$86$	1.04508	+	0.759299i	0.112694	+	0.0818773i
$87$			5.85410i			0.627626i
$88$	7.38394	+	0.690983i	0.787130	+	0.0736590i
$89$	−10.8541			−1.15053			−0.575266	−	0.817966i	$-0.695102\pi$
$89$	−10.8541			−1.15053			−0.575266	+	0.817966i	$0.695102\pi$
$90$		0			0
$91$	0.291796	−	0.898056i	0.0305885	−	0.0941418i
$92$	3.66547	−	1.19098i	0.382152	−	0.124169i
$93$	−4.11450	−	5.66312i	−0.426653	−	0.587238i
$94$	2.54508	−	1.84911i	0.262505	−	0.190721i
$95$		0			0
$96$	−1.73607	+	5.34307i	−0.177187	+	0.545325i
$97$	6.74315	−	9.28115i	0.684663	−	0.942358i	−0.315315	−	0.948987i	$-0.602110\pi$
$97$	6.74315	−	9.28115i	0.684663	−	0.942358i	0.999978	+	0.00662888i	$0.00211005\pi$
$98$			3.96556i			0.400582i
$99$	3.04508	+	1.31433i	0.306043	+	0.132095i
$100$		0			0
$101$	0.454915	+	0.330515i	0.0452657	+	0.0328875i	0.610188	−	0.792257i	$-0.291094\pi$
$101$	0.454915	+	0.330515i	0.0452657	+	0.0328875i	−0.564922	+	0.825144i	$0.691094\pi$
$102$	−1.17557	−	0.381966i	−0.116399	−	0.0378203i
$103$	2.26538	−	0.736068i	0.223215	−	0.0725269i	−0.195274	−	0.980749i	$-0.562560\pi$
$103$	2.26538	−	0.736068i	0.223215	−	0.0725269i	0.418489	+	0.908222i	$0.362560\pi$
$104$	2.23607	−	1.62460i	0.219265	−	0.159305i
$105$		0			0
$106$	−1.45492	−	4.47777i	−0.141314	−	0.434919i
$107$	2.71441	+	0.881966i	0.262412	+	0.0852629i	0.437268	−	0.899331i	$-0.355946\pi$
$107$	2.71441	+	0.881966i	0.262412	+	0.0852629i	−0.174856	+	0.984594i	$0.555946\pi$
$108$	−0.951057	+	1.30902i	−0.0915155	+	0.125960i
$109$	−4.14590			−0.397105			−0.198553	−	0.980090i	$-0.563624\pi$
$109$	−4.14590			−0.397105			−0.198553	+	0.980090i	$0.563624\pi$
$110$		0			0
$111$	7.47214			0.709224
$112$	−0.832544	+	1.14590i	−0.0786680	+	0.108277i
$113$	−5.20431	−	1.69098i	−0.489580	−	0.159074i	0.0538155	−	0.998551i	$-0.482862\pi$
$113$	−5.20431	−	1.69098i	−0.489580	−	0.159074i	−0.543396	+	0.839477i	$0.682862\pi$
$114$	0.954915	+	2.93893i	0.0894360	+	0.275256i
$115$		0			0
$116$	−7.66312	+	5.56758i	−0.711503	+	0.516937i
$117$	1.17557	−	0.381966i	0.108682	−	0.0353128i
$118$	3.94298	+	1.28115i	0.362981	+	0.117940i
$119$	−1.23607	−	0.898056i	−0.113310	−	0.0823247i
$120$		0			0
$121$	9.94427	−	4.70228i	0.904025	−	0.427480i
$122$			4.32624i			0.391679i
$123$	1.48584	−	2.04508i	0.133974	−	0.184399i
$124$	3.50000	−	10.7719i	0.314309	−	0.967344i
$125$		0			0
$126$	0.381966	−	0.277515i	0.0340282	−	0.0247230i
$127$	−9.37181	−	12.8992i	−0.831613	−	1.14462i	−0.987621	−	0.156862i	$-0.949862\pi$
$127$	−9.37181	−	12.8992i	−0.831613	−	1.14462i	0.156007	−	0.987756i	$-0.450138\pi$
$128$	−10.8249	+	3.51722i	−0.956794	+	0.310881i
$129$	−0.645898	+	1.98787i	−0.0568682	+	0.175022i
$130$		0			0
$131$	13.1803			1.15157			0.575786	−	0.817601i	$-0.304696\pi$
$131$	13.1803			1.15157			0.575786	+	0.817601i	$0.304696\pi$
$132$	1.17557	+	5.23607i	0.102320	+	0.455741i
$133$			3.81966i			0.331207i
$134$	−4.69098	−	3.40820i	−0.405239	−	0.294424i
$135$		0			0
$136$	−1.38197	−	4.25325i	−0.118503	−	0.364714i
$137$	−10.9964	−	15.1353i	−0.939486	−	1.29309i	−0.956042	−	0.293229i	$-0.905270\pi$
$137$	−10.9964	−	15.1353i	−0.939486	−	1.29309i	0.0165558	−	0.999863i	$-0.494730\pi$
$138$	−0.865300	−	1.19098i	−0.0736592	−	0.101383i
$139$	−6.54508	−	20.1437i	−0.555147	−	1.70857i	−0.695555	−	0.718473i	$-0.744842\pi$
$139$	−6.54508	−	20.1437i	−0.555147	−	1.70857i	0.140408	−	0.990094i	$-0.455158\pi$
$140$		0			0
$141$	4.11803	+	2.99193i	0.346801	+	0.251966i
$142$		−	4.94427i		−	0.414914i
$143$	1.62460	−	3.76393i	0.135856	−	0.314756i
$144$	−1.85410			−0.154508
$145$		0			0
$146$	−2.57295	+	7.91872i	−0.212939	+	0.655358i
$147$	−6.10237	+	1.98278i	−0.503315	+	0.163537i
$148$	7.10642	+	9.78115i	0.584144	+	0.804006i
$149$	16.2812	−	11.8290i	1.33380	−	0.969065i	0.334156	−	0.942518i	$-0.391549\pi$
$149$	16.2812	−	11.8290i	1.33380	−	0.969065i	0.999648	−	0.0265477i	$-0.00845140\pi$
$150$		0			0
$151$	−3.32624	+	10.2371i	−0.270685	+	0.833084i	0.719643	+	0.694344i	$0.244305\pi$
$151$	−3.32624	+	10.2371i	−0.270685	+	0.833084i	−0.990329	+	0.138740i	$0.955695\pi$
$152$	−6.57164	+	9.04508i	−0.533030	+	0.733653i
$153$		−	2.00000i		−	0.161690i
$154$	0.145898	−	1.55909i	0.0117568	−	0.125635i
$155$		0			0
$156$	1.61803	+	1.17557i	0.129546	+	0.0941210i
$157$	−3.16344	−	1.02786i	−0.252470	−	0.0820325i	0.180048	−	0.983658i	$-0.442375\pi$
$157$	−3.16344	−	1.02786i	−0.252470	−	0.0820325i	−0.432518	+	0.901625i	$0.642375\pi$
$158$	−4.75528	+	1.54508i	−0.378310	+	0.122920i
$159$	6.16312	−	4.47777i	0.488767	−	0.355110i
$160$		0			0
$161$	−0.562306	−	1.73060i	−0.0443159	−	0.136390i
$162$	0.587785	+	0.190983i	0.0461808	+	0.0150050i
$163$	−7.97172	+	10.9721i	−0.624394	+	0.859404i	−0.997664	−	0.0683187i	$-0.978237\pi$
$163$	−7.97172	+	10.9721i	−0.624394	+	0.859404i	0.373270	+	0.927723i	$0.378237\pi$
$164$	4.09017			0.319389
$165$		0			0
$166$	−3.52786			−0.273815
$167$	−11.7759	+	16.2082i	−0.911250	+	1.25423i	0.0554876	+	0.998459i	$0.482329\pi$
$167$	−11.7759	+	16.2082i	−0.911250	+	1.25423i	−0.966738	+	0.255769i	$0.917671\pi$
$168$	1.62460	+	0.527864i	0.125340	+	0.0407256i
$169$	3.54508	+	10.9106i	0.272699	+	0.839281i
$170$		0			0
$171$	−4.04508	+	2.93893i	−0.309335	+	0.224745i
$172$	−3.21644	+	1.04508i	−0.245251	+	0.0796870i
$173$	−3.38795	−	1.10081i	−0.257581	−	0.0836933i	0.177380	−	0.984142i	$-0.443238\pi$
$173$	−3.38795	−	1.10081i	−0.257581	−	0.0836933i	−0.434961	+	0.900449i	$0.643238\pi$
$174$	2.92705	+	2.12663i	0.221899	+	0.161219i
$175$		0			0
$176$	−4.06231	+	4.61653i	−0.306208	+	0.347984i
$177$			6.70820i			0.504219i
$178$	−3.94298	+	5.42705i	−0.295539	+	0.406775i
$179$	6.01722	−	18.5191i	0.449748	−	1.38418i	−0.427443	−	0.904042i	$-0.640586\pi$
$179$	6.01722	−	18.5191i	0.449748	−	1.38418i	0.877192	−	0.480141i	$-0.159414\pi$
$180$		0			0
$181$	4.23607	−	3.07768i	0.314864	−	0.228762i	−0.419117	−	0.907932i	$-0.637660\pi$
$181$	4.23607	−	3.07768i	0.314864	−	0.228762i	0.733981	+	0.679170i	$0.237660\pi$
$182$	−0.343027	−	0.472136i	−0.0254268	−	0.0349970i
$183$	−6.65740	+	2.16312i	−0.492129	+	0.159902i
$184$	1.64590	−	5.06555i	0.121337	−	0.373438i
$185$		0			0
$186$	−4.32624			−0.317215
$187$	−4.97980	−	4.38197i	−0.364159	−	0.320441i
$188$			8.23607i			0.600677i
$189$	0.618034	+	0.449028i	0.0449554	+	0.0326620i
$190$		0			0
$191$	3.21885	+	9.90659i	0.232908	+	0.716816i	0.997392	+	0.0721737i	$0.0229936\pi$
$191$	3.21885	+	9.90659i	0.232908	+	0.716816i	−0.764484	+	0.644642i	$0.777006\pi$
$192$	−0.138757	−	0.190983i	−0.0100139	−	0.0137830i
$193$	−12.3637	−	17.0172i	−0.889961	−	1.22493i	−0.973561	−	0.228427i	$-0.926642\pi$
$193$	−12.3637	−	17.0172i	−0.889961	−	1.22493i	0.0836000	−	0.996499i	$-0.473358\pi$
$194$	−2.19098	−	6.74315i	−0.157303	−	0.484130i
$195$		0			0
$196$	−8.39919	−	6.10237i	−0.599942	−	0.435883i
$197$			14.2361i			1.01428i	0.861864	+	0.507139i	$0.169297\pi$
$197$			14.2361i			1.01428i	−0.861864	+	0.507139i	$0.830703\pi$
$198$	1.76336	−	1.04508i	0.125316	−	0.0742710i
$199$	−19.7984			−1.40347			−0.701735	−	0.712438i	$-0.747591\pi$
$199$	−19.7984			−1.40347			−0.701735	+	0.712438i	$0.747591\pi$
$200$		0			0
$201$	2.89919	−	8.92278i	0.204493	−	0.629364i
$202$	0.330515	−	0.107391i	0.0232550	−	0.00755600i
$203$	2.62866	+	3.61803i	0.184495	+	0.253936i
$204$	2.61803	−	1.90211i	0.183299	−	0.133175i
$205$		0			0
$206$	0.454915	−	1.40008i	0.0316954	−	0.0975485i
$207$	1.40008	−	1.92705i	0.0973126	−	0.133939i
$208$			2.29180i			0.158907i
$209$	−1.54508	+	16.5110i	−0.106876	+	1.14209i
$210$		0			0
$211$	3.11803	+	2.26538i	0.214654	+	0.155955i	0.689917	−	0.723888i	$-0.257647\pi$
$211$	3.11803	+	2.26538i	0.214654	+	0.155955i	−0.475263	+	0.879844i	$0.657647\pi$
$212$	11.7229	+	3.80902i	0.805135	+	0.261604i
$213$	7.60845	−	2.47214i	0.521323	−	0.169388i
$214$	1.42705	−	1.03681i	0.0975512	−	0.0708751i
$215$		0			0
$216$	0.690983	+	2.12663i	0.0470154	+	0.144699i
$217$	−5.08580	−	1.65248i	−0.345246	−	0.112177i
$218$	−1.50609	+	2.07295i	−0.102005	+	0.140398i
$219$	−13.4721			−0.910363
$220$		0			0
$221$	−2.47214			−0.166294
$222$	2.71441	−	3.73607i	0.182179	−	0.250748i
$223$	−7.64121	−	2.48278i	−0.511693	−	0.166259i	0.0417790	−	0.999127i	$-0.486697\pi$
$223$	−7.64121	−	2.48278i	−0.511693	−	0.166259i	−0.553472	+	0.832868i	$0.686697\pi$
$224$	1.32624	+	4.08174i	0.0886130	+	0.272723i
$225$		0			0
$226$	−2.73607	+	1.98787i	−0.182001	+	0.132231i
$227$	−24.6745	+	8.01722i	−1.63770	+	0.532122i	−0.976023	−	0.217666i	$-0.930156\pi$
$227$	−24.6745	+	8.01722i	−1.63770	+	0.532122i	−0.661679	+	0.749788i	$0.730156\pi$
$228$	−7.69421	−	2.50000i	−0.509561	−	0.165567i
$229$	14.6353	+	10.6331i	0.967125	+	0.702657i	0.954795	−	0.297267i	$-0.0960750\pi$
$229$	14.6353	+	10.6331i	0.967125	+	0.702657i	0.0123304	+	0.999924i	$0.496075\pi$
$230$		0			0
$231$	2.47214	−	0.555029i	0.162655	−	0.0365182i
$232$			13.0902i			0.859412i
$233$	13.6781	−	18.8262i	0.896080	−	1.23335i	−0.0756220	−	0.997137i	$-0.524094\pi$
$233$	13.6781	−	18.8262i	0.896080	−	1.23335i	0.971702	−	0.236211i	$-0.0759058\pi$
$234$	0.236068	−	0.726543i	0.0154322	−	0.0474956i
$235$		0			0
$236$	−8.78115	+	6.37988i	−0.571604	+	0.415295i
$237$	−4.75528	−	6.54508i	−0.308889	−	0.425149i
$238$	−0.898056	+	0.291796i	−0.0582123	+	0.0189143i
$239$	2.17376	−	6.69015i	0.140609	−	0.432750i	−0.855811	−	0.517288i	$-0.826942\pi$
$239$	2.17376	−	6.69015i	0.140609	−	0.432750i	0.996420	+	0.0845383i	$0.0269415\pi$
$240$		0			0
$241$	−1.61803			−0.104227			−0.0521134	−	0.998641i	$-0.516596\pi$
$241$	−1.61803			−0.104227			−0.0521134	+	0.998641i	$0.516596\pi$
$242$	1.26133	−	6.68034i	0.0810812	−	0.429429i
$243$			1.00000i			0.0641500i
$244$	−9.16312	−	6.65740i	−0.586609	−	0.426196i
$245$		0			0
$246$	−0.482779	−	1.48584i	−0.0307809	−	0.0947338i
$247$	3.63271	+	5.00000i	0.231144	+	0.318142i
$248$	−9.20029	−	12.6631i	−0.584219	−	0.804109i
$249$	−1.76393	−	5.42882i	−0.111785	−	0.344038i
$250$		0			0
$251$	−6.09017	−	4.42477i	−0.384408	−	0.279289i	0.378752	−	0.925498i	$-0.376353\pi$
$251$	−6.09017	−	4.42477i	−0.384408	−	0.279289i	−0.763160	+	0.646209i	$0.776353\pi$
$252$			1.23607i			0.0778650i
$253$	−1.73060	−	7.70820i	−0.108802	−	0.484611i
$254$	−9.85410			−0.618301
$255$		0			0
$256$	−2.02786	+	6.24112i	−0.126742	+	0.390070i
$257$	10.0453	−	3.26393i	0.626612	−	0.203598i	0.0215381	−	0.999768i	$-0.493144\pi$
$257$	10.0453	−	3.26393i	0.626612	−	0.203598i	0.605074	+	0.796170i	$0.293144\pi$
$258$	0.759299	+	1.04508i	0.0472719	+	0.0650641i
$259$	4.61803	−	3.35520i	0.286951	−	0.208482i
$260$		0			0
$261$	−1.80902	+	5.56758i	−0.111975	+	0.344625i
$262$	4.78804	−	6.59017i	0.295806	−	0.407142i
$263$			27.2148i			1.67814i	0.544027	+	0.839068i	$0.316899\pi$
$263$			27.2148i			1.67814i	−0.544027	+	0.839068i	$0.683101\pi$
$264$	6.80902	+	2.93893i	0.419066	+	0.180878i
$265$		0			0
$266$	1.90983	+	1.38757i	0.117099	+	0.0850775i
$267$	−10.3229	−	3.35410i	−0.631749	−	0.205268i
$268$	14.4374	−	4.69098i	0.881902	−	0.286547i
$269$	−4.73607	+	3.44095i	−0.288763	+	0.209799i	−0.722731	−	0.691130i	$-0.757113\pi$
$269$	−4.73607	+	3.44095i	−0.288763	+	0.209799i	0.433967	+	0.900929i	$0.357113\pi$
$270$		0			0
$271$	6.37132	+	19.6089i	0.387030	+	1.19116i	0.934997	+	0.354656i	$0.115402\pi$
$271$	6.37132	+	19.6089i	0.387030	+	1.19116i	−0.547966	+	0.836500i	$0.684598\pi$
$272$	3.52671	+	1.14590i	0.213838	+	0.0694803i
$273$	0.555029	−	0.763932i	0.0335919	−	0.0462353i
$274$	−11.5623			−0.698504
$275$		0			0
$276$	3.85410			0.231990
$277$	−5.08580	+	7.00000i	−0.305576	+	0.420589i	−0.933995	−	0.357286i	$-0.883702\pi$
$277$	−5.08580	+	7.00000i	−0.305576	+	0.420589i	0.628419	+	0.777875i	$0.283702\pi$
$278$	−12.4495	−	4.04508i	−0.746671	−	0.242608i
$279$	−2.16312	−	6.65740i	−0.129503	−	0.398568i
$280$		0			0
$281$	−8.16312	+	5.93085i	−0.486971	+	0.353805i	−0.804018	−	0.594605i	$-0.797309\pi$
$281$	−8.16312	+	5.93085i	−0.486971	+	0.353805i	0.317047	+	0.948410i	$0.397309\pi$
$282$	2.99193	−	0.972136i	0.178167	−	0.0578899i
$283$	−12.3965	−	4.02786i	−0.736895	−	0.239432i	−0.0835622	−	0.996503i	$-0.526630\pi$
$283$	−12.3965	−	4.02786i	−0.736895	−	0.239432i	−0.653333	+	0.757071i	$0.726630\pi$
$284$	10.4721	+	7.60845i	0.621407	+	0.451479i
$285$		0			0
$286$	−1.29180	−	2.17963i	−0.0763855	−	0.128884i
$287$		−	1.93112i		−	0.113990i
$288$	−3.30220	+	4.54508i	−0.194584	+	0.267822i
$289$	4.01722	−	12.3637i	0.236307	−	0.727279i
$290$		0			0
$291$	9.28115	−	6.74315i	0.544071	−	0.395291i
$292$	−12.8128	−	17.6353i	−0.749810	−	1.03203i
$293$	15.7189	−	5.10739i	0.918310	−	0.298377i	0.188537	−	0.982066i	$-0.439626\pi$
$293$	15.7189	−	5.10739i	0.918310	−	0.298377i	0.729773	+	0.683689i	$0.239626\pi$
$294$	−1.22542	+	3.77147i	−0.0714682	+	0.219957i
$295$		0			0
$296$	16.7082			0.971145
$297$	2.48990	+	2.19098i	0.144479	+	0.127134i
$298$		−	12.4377i		−	0.720496i
$299$	−2.38197	−	1.73060i	−0.137753	−	0.100083i
$300$		0			0
$301$	0.493422	+	1.51860i	0.0284404	+	0.0875305i
$302$	3.91023	+	5.38197i	0.225008	+	0.309697i
$303$	0.330515	+	0.454915i	0.0189876	+	0.0261342i
$304$	−2.86475	−	8.81678i	−0.164304	−	0.505677i
$305$		0			0
$306$	−1.00000	−	0.726543i	−0.0571662	−	0.0415337i
$307$			12.1246i			0.691988i	0.938237	+	0.345994i	$0.112458\pi$
$307$			12.1246i			0.691988i	−0.938237	+	0.345994i	$0.887542\pi$
$308$	3.07768	+	2.70820i	0.175367	+	0.154314i
$309$	2.38197			0.135505
$310$		0			0
$311$	6.63525	−	20.4212i	0.376251	−	1.15798i	−0.566380	−	0.824144i	$-0.691657\pi$
$311$	6.63525	−	20.4212i	0.376251	−	1.15798i	0.942631	−	0.333837i	$-0.108343\pi$
$312$	2.62866	−	0.854102i	0.148818	−	0.0483540i
$313$	0.277515	+	0.381966i	0.0156860	+	0.0215900i	0.816788	−	0.576938i	$-0.195753\pi$
$313$	0.277515	+	0.381966i	0.0156860	+	0.0215900i	−0.801102	+	0.598528i	$0.795753\pi$
$314$	−1.66312	+	1.20833i	−0.0938552	+	0.0681898i
$315$		0			0
$316$	4.04508	−	12.4495i	0.227554	−	0.700339i
$317$	17.8783	−	24.6074i	1.00415	−	1.38209i	0.0813997	−	0.996682i	$-0.474061\pi$
$317$	17.8783	−	24.6074i	1.00415	−	1.38209i	0.922747	−	0.385407i	$-0.125939\pi$
$318$		−	4.70820i		−	0.264023i
$319$	9.89919	+	16.7027i	0.554248	+	0.935174i
$320$		0			0
$321$	2.30902	+	1.67760i	0.128877	+	0.0936344i
$322$	−1.06957	−	0.347524i	−0.0596048	−	0.0193668i
$323$	9.51057	−	3.09017i	0.529182	−	0.171942i
$324$	−1.30902	+	0.951057i	−0.0727232	+	0.0528365i
$325$		0			0
$326$	2.59017	+	7.97172i	0.143456	+	0.441513i
$327$	−3.94298	−	1.28115i	−0.218047	−	0.0708479i
$328$	3.32244	−	4.57295i	0.183451	−	0.252499i
$329$	3.88854			0.214382
$330$		0			0
$331$	21.5967			1.18706			0.593532	−	0.804810i	$-0.297733\pi$
$331$	21.5967			1.18706			0.593532	+	0.804810i	$0.297733\pi$
$332$	5.42882	−	7.47214i	0.297945	−	0.410087i
$333$	7.10642	+	2.30902i	0.389430	+	0.126533i
$334$	3.82624	+	11.7759i	0.209362	+	0.644351i
$335$		0			0
$336$	−1.14590	+	0.832544i	−0.0625139	+	0.0454190i
$337$	21.0620	−	6.84346i	1.14732	−	0.372787i	0.327187	−	0.944960i	$-0.393899\pi$
$337$	21.0620	−	6.84346i	1.14732	−	0.372787i	0.820133	+	0.572173i	$0.193899\pi$
$338$	6.74315	+	2.19098i	0.366779	+	0.119174i
$339$	−4.42705	−	3.21644i	−0.240444	−	0.174693i
$340$		0			0
$341$	−21.3156	−	9.20029i	−1.15430	−	0.498224i
$342$			3.09017i			0.167097i
$343$	−6.02434	+	8.29180i	−0.325284	+	0.447715i
$344$	−1.44427	+	4.44501i	−0.0778699	+	0.239659i
$345$		0			0
$346$	−1.78115	+	1.29408i	−0.0957554	+	0.0695704i
$347$	−3.42071	−	4.70820i	−0.183633	−	0.252750i	0.707269	−	0.706945i	$-0.249927\pi$
$347$	−3.42071	−	4.70820i	−0.183633	−	0.252750i	−0.890902	+	0.454195i	$0.849927\pi$
$348$	−9.00854	+	2.92705i	−0.482908	+	0.156906i
$349$	−8.57953	+	26.4051i	−0.459252	+	1.41343i	0.406819	+	0.913509i	$0.366638\pi$
$349$	−8.57953	+	26.4051i	−0.459252	+	1.41343i	−0.866070	+	0.499922i	$0.833362\pi$
$350$		0			0
$351$	1.23607			0.0659764
$352$	4.08174	+	18.1803i	0.217558	+	0.969015i
$353$			35.8328i			1.90719i	0.301095	+	0.953594i	$0.402648\pi$
$353$			35.8328i			1.90719i	−0.301095	+	0.953594i	$0.597352\pi$
$354$	3.35410	+	2.43690i	0.178269	+	0.129520i
$355$		0			0
$356$	−5.42705	−	16.7027i	−0.287633	−	0.885244i
$357$	−0.898056	−	1.23607i	−0.0475302	−	0.0654197i
$358$	−7.07367	−	9.73607i	−0.373855	−	0.514567i
$359$	−5.16312	−	15.8904i	−0.272499	−	0.838666i	−0.989870	−	0.141975i	$-0.954655\pi$
$359$	−5.16312	−	15.8904i	−0.272499	−	0.838666i	0.717371	−	0.696691i	$-0.245345\pi$
$360$		0			0
$361$	−4.85410	−	3.52671i	−0.255479	−	0.185616i
$362$		−	3.23607i		−	0.170084i
$363$	10.9106	−	1.39919i	0.572661	−	0.0734383i
$364$	1.52786			0.0800818
$365$		0			0
$366$	−1.33688	+	4.11450i	−0.0698799	+	0.215068i
$367$	17.2375	−	5.60081i	0.899792	−	0.292360i	0.177641	−	0.984095i	$-0.443154\pi$
$367$	17.2375	−	5.60081i	0.899792	−	0.292360i	0.722151	+	0.691735i	$0.243154\pi$
$368$	2.59590	+	3.57295i	0.135321	+	0.186253i
$369$	2.04508	−	1.48584i	0.106463	−	0.0773498i
$370$		0			0
$371$	1.79837	−	5.53483i	0.0933669	−	0.287354i
$372$	6.65740	−	9.16312i	0.345170	−	0.475086i
$373$		−	9.74265i		−	0.504455i	−0.967668	−	0.252228i	$-0.918837\pi$
$373$		−	9.74265i		−	0.504455i	0.967668	−	0.252228i	$-0.0811631\pi$
$374$	−4.00000	+	0.898056i	−0.206835	+	0.0464374i
$375$		0			0
$376$	9.20820	+	6.69015i	0.474877	+	0.345018i
$377$	6.88191	+	2.23607i	0.354436	+	0.115163i
$378$	0.449028	−	0.145898i	0.0230955	−	0.00750419i
$379$	−4.04508	+	2.93893i	−0.207782	+	0.150963i	−0.686810	−	0.726837i	$-0.740989\pi$
$379$	−4.04508	+	2.93893i	−0.207782	+	0.150963i	0.479028	+	0.877800i	$0.340989\pi$
$380$		0			0
$381$	−4.92705	−	15.1639i	−0.252420	−	0.776870i
$382$	6.12261	+	1.98936i	0.313260	+	0.101784i
$383$	18.4333	−	25.3713i	0.941900	−	1.29641i	−0.0131328	−	0.999914i	$-0.504180\pi$
$383$	18.4333	−	25.3713i	0.941900	−	1.29641i	0.955033	−	0.296500i	$-0.0958196\pi$
$384$	−11.3820			−0.580834
$385$		0			0
$386$	−13.0000			−0.661683
$387$	−1.22857	+	1.69098i	−0.0624518	+	0.0859575i
$388$	17.6538	+	5.73607i	0.896236	+	0.291205i
$389$	12.0344	+	37.0382i	0.610170	+	1.87791i	0.456316	+	0.889818i	$0.349169\pi$
$389$	12.0344	+	37.0382i	0.610170	+	1.87791i	0.153855	+	0.988093i	$0.450831\pi$
$390$		0			0
$391$	−3.85410	+	2.80017i	−0.194910	+	0.141611i
$392$	−13.6453	+	4.43363i	−0.689192	+	0.223932i
$393$	12.5352	+	4.07295i	0.632320	+	0.205453i
$394$	7.11803	+	5.17155i	0.358601	+	0.260539i
$395$		0			0
$396$	−0.500000	+	5.34307i	−0.0251259	+	0.268499i
$397$			36.2705i			1.82036i	0.414208	+	0.910182i	$0.364059\pi$
$397$			36.2705i			1.82036i	−0.414208	+	0.910182i	$0.635941\pi$
$398$	−7.19218	+	9.89919i	−0.360511	+	0.496201i
$399$	−1.18034	+	3.63271i	−0.0590909	+	0.181863i
$400$		0			0
$401$	−3.95492	+	2.87341i	−0.197499	+	0.143491i	−0.682140	−	0.731222i	$-0.738950\pi$
$401$	−3.95492	+	2.87341i	−0.197499	+	0.143491i	0.484641	+	0.874713i	$0.338950\pi$
$402$	−3.40820	−	4.69098i	−0.169985	−	0.233965i
$403$	−8.22899	+	2.67376i	−0.409915	+	0.133190i
$404$	−0.281153	+	0.865300i	−0.0139879	+	0.0430503i
$405$		0			0
$406$	2.76393			0.137172
$407$	21.3193	−	12.6353i	1.05676	−	0.626306i
$408$		−	4.47214i		−	0.221404i
$409$	29.3713	+	21.3395i	1.45232	+	1.05517i	0.985283	+	0.170933i	$0.0546781\pi$
$409$	29.3713	+	21.3395i	1.45232	+	1.05517i	0.467036	+	0.884238i	$0.345322\pi$
$410$		0			0
$411$	−5.78115	−	17.7926i	−0.285163	−	0.877642i
$412$	2.26538	+	3.11803i	0.111607	+	0.153615i
$413$	3.01217	+	4.14590i	0.148219	+	0.204006i
$414$	−0.454915	−	1.40008i	−0.0223579	−	0.0688104i
$415$		0			0
$416$	5.61803	+	4.08174i	0.275447	+	0.200124i
$417$		−	21.1803i		−	1.03721i
$418$	7.69421	+	6.77051i	0.376336	+	0.331156i
$419$	−24.5967			−1.20163			−0.600815	−	0.799388i	$-0.705157\pi$
$419$	−24.5967			−1.20163			−0.600815	+	0.799388i	$0.705157\pi$
$420$		0			0
$421$	0.881966	−	2.71441i	0.0429844	−	0.132292i	−0.927261	−	0.374415i	$-0.877844\pi$
$421$	0.881966	−	2.71441i	0.0429844	−	0.132292i	0.970246	+	0.242123i	$0.0778436\pi$
$422$	2.26538	−	0.736068i	0.110277	−	0.0358312i
$423$	2.99193	+	4.11803i	0.145472	+	0.200226i
$424$	13.7812	−	10.0126i	0.669272	−	0.486255i
$425$		0			0
$426$	1.52786	−	4.70228i	0.0740253	−	0.227826i
$427$	−3.14320	+	4.32624i	−0.152110	+	0.209361i
$428$			4.61803i			0.223221i
$429$	2.70820	−	3.07768i	0.130753	−	0.148592i
$430$		0			0
$431$	−16.0902	−	11.6902i	−0.775036	−	0.563097i	0.128449	−	0.991716i	$-0.459000\pi$
$431$	−16.0902	−	11.6902i	−0.775036	−	0.563097i	−0.903485	+	0.428619i	$0.859000\pi$
$432$	−1.76336	−	0.572949i	−0.0848395	−	0.0275660i
$433$	26.6623	−	8.66312i	1.28131	−	0.416323i	0.412269	−	0.911062i	$-0.364736\pi$
$433$	26.6623	−	8.66312i	1.28131	−	0.416323i	0.869041	+	0.494739i	$0.164736\pi$
$434$	−2.67376	+	1.94260i	−0.128345	+	0.0932479i
$435$		0			0
$436$	−2.07295	−	6.37988i	−0.0992763	−	0.305541i
$437$	11.3269	+	3.68034i	0.541840	+	0.176055i
$438$	−4.89404	+	6.73607i	−0.233846	+	0.321862i
$439$	−9.67376			−0.461703			−0.230852	−	0.972989i	$-0.574151\pi$
$439$	−9.67376			−0.461703			−0.230852	+	0.972989i	$0.574151\pi$
$440$		0			0
$441$	−6.41641			−0.305543
$442$	−0.898056	+	1.23607i	−0.0427162	+	0.0587938i
$443$	−24.0337	−	7.80902i	−1.14187	−	0.371018i	−0.323798	−	0.946126i	$-0.604960\pi$
$443$	−24.0337	−	7.80902i	−1.14187	−	0.371018i	−0.818077	+	0.575109i	$0.804960\pi$
$444$	3.73607	+	11.4984i	0.177306	+	0.545692i
$445$		0			0
$446$	−4.01722	+	2.91868i	−0.190221	+	0.138204i
$447$	19.1396	−	6.21885i	0.905274	−	0.294141i
$448$	−0.171513	−	0.0557281i	−0.00810325	−	0.00263290i
$449$	−0.590170	−	0.428784i	−0.0278518	−	0.0202355i	0.573772	−	0.819015i	$-0.305479\pi$
$449$	−0.590170	−	0.428784i	−0.0278518	−	0.0202355i	−0.601624	+	0.798779i	$0.705479\pi$
$450$		0			0
$451$	0.781153	−	8.34751i	0.0367831	−	0.393069i
$452$		−	8.85410i		−	0.416462i
$453$	−6.32688	+	8.70820i	−0.297263	+	0.409147i
$454$	−4.95492	+	15.2497i	−0.232546	+	0.715702i
$455$		0			0
$456$	−9.04508	+	6.57164i	−0.423575	+	0.307745i
$457$	−0.865300	−	1.19098i	−0.0404770	−	0.0557118i	0.788299	−	0.615293i	$-0.210962\pi$
$457$	−0.865300	−	1.19098i	−0.0404770	−	0.0557118i	−0.828776	+	0.559581i	$0.810962\pi$
$458$	10.6331	−	3.45492i	0.496854	−	0.161438i
$459$	0.618034	−	1.90211i	0.0288474	−	0.0887830i
$460$		0			0
$461$	25.9443			1.20835			0.604173	−	0.796853i	$-0.293504\pi$
$461$	25.9443			1.20835			0.604173	+	0.796853i	$0.293504\pi$
$462$	0.620541	−	1.43769i	0.0288702	−	0.0668876i
$463$			33.2705i			1.54621i	0.634277	+	0.773106i	$0.281298\pi$
$463$			33.2705i			1.54621i	−0.634277	+	0.773106i	$0.718702\pi$
$464$	−8.78115	−	6.37988i	−0.407655	−	0.296179i
$465$		0			0
$466$	−4.44427	−	13.6781i	−0.205877	−	0.633624i
$467$	−2.87341	−	3.95492i	−0.132966	−	0.183012i	0.737342	−	0.675519i	$-0.236080\pi$
$467$	−2.87341	−	3.95492i	−0.132966	−	0.183012i	−0.870308	+	0.492507i	$0.836080\pi$
$468$	1.17557	+	1.61803i	0.0543408	+	0.0747936i
$469$	−2.21478	−	6.81640i	−0.102269	−	0.314752i
$470$		0			0
$471$	−2.69098	−	1.95511i	−0.123994	−	0.0900869i
$472$			15.0000i			0.690431i
$473$	1.51860	+	6.76393i	0.0698252	+	0.311006i
$474$	−5.00000			−0.229658
$475$		0			0
$476$	0.763932	−	2.35114i	0.0350148	−	0.107764i
$477$	7.24518	−	2.35410i	0.331734	−	0.107787i
$478$	−2.55541	−	3.51722i	−0.116882	−	0.160874i
$479$	27.0344	−	19.6417i	1.23524	−	0.897451i	0.237964	−	0.971274i	$-0.423520\pi$
$479$	27.0344	−	19.6417i	1.23524	−	0.897451i	0.997271	+	0.0738231i	$0.0235200\pi$
$480$		0			0
$481$	2.85410	−	8.78402i	0.130136	−	0.400517i
$482$	−0.587785	+	0.809017i	−0.0267729	+	0.0368497i
$483$		−	1.81966i		−	0.0827974i
$484$	12.2082	+	12.9515i	0.554918	+	0.588705i
$485$		0			0
$486$	0.500000	+	0.363271i	0.0226805	+	0.0164783i
$487$	−13.4863	−	4.38197i	−0.611123	−	0.198566i	−0.0129278	−	0.999916i	$-0.504115\pi$
$487$	−13.4863	−	4.38197i	−0.611123	−	0.198566i	−0.598195	+	0.801351i	$0.704115\pi$
$488$	−14.8864	+	4.83688i	−0.673875	+	0.218955i
$489$	−10.9721	+	7.97172i	−0.496177	+	0.360494i
$490$		0			0
$491$	9.82624	+	30.2421i	0.443452	+	1.36480i	0.884173	+	0.467160i	$0.154723\pi$
$491$	9.82624	+	30.2421i	0.443452	+	1.36480i	−0.440721	+	0.897644i	$0.645277\pi$
$492$	3.88998	+	1.26393i	0.175374	+	0.0569825i
$493$	6.88191	−	9.47214i	0.309946	−	0.426604i
$494$	3.81966			0.171855
$495$		0			0
$496$	12.9787			0.582761
$497$	3.59222	−	4.94427i	0.161133	−	0.221781i
$498$	−3.35520	−	1.09017i	−0.150350	−	0.0488517i
$499$	3.45492	+	10.6331i	0.154663	+	0.476005i	0.998127	−	0.0611822i	$-0.0194871\pi$
$499$	3.45492	+	10.6331i	0.154663	+	0.476005i	−0.843463	+	0.537187i	$0.819487\pi$
$500$		0			0
$501$	−16.2082	+	11.7759i	−0.724129	+	0.526111i
$502$	−4.42477	+	1.43769i	−0.197487	+	0.0641674i
$503$	20.8172	+	6.76393i	0.928195	+	0.301589i	0.733824	−	0.679339i	$-0.237734\pi$
$503$	20.8172	+	6.76393i	0.928195	+	0.301589i	0.194371	+	0.980928i	$0.437734\pi$
$504$	1.38197	+	1.00406i	0.0615577	+	0.0447243i
$505$		0			0
$506$	−4.48278	−	1.93487i	−0.199284	−	0.0860154i
$507$			11.4721i			0.509495i
$508$	15.1639	−	20.8713i	0.672789	−	0.926015i
$509$	−0.163119	+	0.502029i	−0.00723012	+	0.0222520i	−0.954606	−	0.297870i	$-0.903724\pi$
$509$	−0.163119	+	0.502029i	−0.00723012	+	0.0222520i	0.947376	+	0.320122i	$0.103724\pi$
$510$		0			0
$511$	−8.32624	+	6.04937i	−0.368331	+	0.267608i
$512$	−10.9964	−	15.1353i	−0.485977	−	0.668890i
$513$	−4.75528	+	1.54508i	−0.209951	+	0.0682172i
$514$	2.01722	−	6.20837i	0.0889758	−	0.273839i
$515$		0			0
$516$	−3.38197			−0.148883
$517$	16.8087	+	1.57295i	0.739248	+	0.0691782i
$518$		−	3.52786i		−	0.155005i
$519$	−2.88197	−	2.09387i	−0.126504	−	0.0919107i
$520$		0			0
$521$	−4.74671	−	14.6089i	−0.207957	−	0.640026i	−0.999579	−	0.0290150i	$-0.990763\pi$
$521$	−4.74671	−	14.6089i	−0.207957	−	0.640026i	0.791622	−	0.611011i	$-0.209237\pi$
$522$	2.12663	+	2.92705i	0.0930799	+	0.128114i
$523$	4.84104	+	6.66312i	0.211684	+	0.291358i	0.901635	−	0.432498i	$-0.142368\pi$
$523$	4.84104	+	6.66312i	0.211684	+	0.291358i	−0.689951	+	0.723856i	$0.742368\pi$
$524$	6.59017	+	20.2825i	0.287893	+	0.886043i
$525$		0			0
$526$	13.6074	+	9.88635i	0.593310	+	0.431065i
$527$			14.0000i			0.609850i
$528$	−5.29007	+	3.13525i	−0.230221	+	0.136444i
$529$	17.3262			0.753315
$530$		0			0
$531$	−2.07295	+	6.37988i	−0.0899583	+	0.276863i
$532$	−5.87785	+	1.90983i	−0.254837	+	0.0828016i
$533$	−1.83660	−	2.52786i	−0.0795520	−	0.109494i
$534$	−5.42705	+	3.94298i	−0.234851	+	0.170630i
$535$		0			0
$536$	6.48278	−	19.9519i	0.280013	−	0.861793i
$537$	11.4454	−	15.7533i	0.493907	−	0.679805i
$538$			3.61803i			0.155985i
$539$	−14.0582	+	15.9762i	−0.605531	+	0.688144i
$540$		0			0
$541$	−0.500000	−	0.363271i	−0.0214967	−	0.0156183i	0.576985	−	0.816755i	$-0.304229\pi$
$541$	−0.500000	−	0.363271i	−0.0214967	−	0.0156183i	−0.598482	+	0.801136i	$0.704229\pi$
$542$	12.1190	+	3.93769i	0.520555	+	0.169138i
$543$	4.97980	−	1.61803i	0.213704	−	0.0694365i
$544$	9.09017	−	6.60440i	0.389738	−	0.283161i
$545$		0			0
$546$	−0.180340	−	0.555029i	−0.00771783	−	0.0237531i
$547$	−24.1194	−	7.83688i	−1.03127	−	0.335081i	−0.255979	−	0.966682i	$-0.582398\pi$
$547$	−24.1194	−	7.83688i	−1.03127	−	0.335081i	−0.775293	+	0.631601i	$0.782398\pi$
$548$	17.7926	−	24.4894i	0.760060	−	1.04613i
$549$	−7.00000			−0.298753
$550$		0			0
$551$	−29.2705			−1.24697
$552$	3.13068	−	4.30902i	0.133251	−	0.183404i
$553$	−5.87785	−	1.90983i	−0.249952	−	0.0812142i
$554$	1.65248	+	5.08580i	0.0702070	+	0.216075i
$555$		0			0
$556$	27.7254	−	20.1437i	1.17582	−	0.854283i
$557$	−29.8585	+	9.70163i	−1.26515	+	0.411071i	−0.863326	−	0.504647i	$-0.831623\pi$
$557$	−29.8585	+	9.70163i	−1.26515	+	0.411071i	−0.401821	+	0.915718i	$0.631623\pi$
$558$	−4.11450	−	1.33688i	−0.174181	−	0.0565947i
$559$	2.09017	+	1.51860i	0.0884048	+	0.0642298i
$560$		0			0
$561$	−3.38197	−	5.70634i	−0.142787	−	0.240922i
$562$			6.23607i			0.263053i
$563$	−21.3520	+	29.3885i	−0.899881	+	1.23858i	0.0706255	+	0.997503i	$0.477500\pi$
$563$	−21.3520	+	29.3885i	−0.899881	+	1.23858i	−0.970506	+	0.241077i	$0.922500\pi$
$564$	−2.54508	+	7.83297i	−0.107167	+	0.329827i
$565$		0			0
$566$	−6.51722	+	4.73504i	−0.273939	+	0.199028i
$567$	0.449028	+	0.618034i	0.0188574	+	0.0259550i
$568$	17.0130	−	5.52786i	0.713850	−	0.231944i
$569$	0.753289	−	2.31838i	0.0315795	−	0.0971917i	−0.934024	−	0.357209i	$-0.883728\pi$
$569$	0.753289	−	2.31838i	0.0315795	−	0.0971917i	0.965604	+	0.260017i	$0.0837283\pi$
$570$		0			0
$571$	0.0901699			0.00377349			0.00188675	−	0.999998i	$-0.499399\pi$
$571$	0.0901699			0.00377349			0.00188675	+	0.999998i	$0.499399\pi$
$572$	6.60440	+	0.618034i	0.276144	+	0.0258413i
$573$			10.4164i			0.435152i
$574$	−0.965558	−	0.701519i	−0.0403016	−	0.0292808i
$575$		0			0
$576$	−0.0729490	−	0.224514i	−0.00303954	−	0.00935475i
$577$	27.0459	+	37.2254i	1.12593	+	1.54971i	0.795571	+	0.605861i	$0.207171\pi$
$577$	27.0459	+	37.2254i	1.12593	+	1.54971i	0.330363	+	0.943854i	$0.392829\pi$
$578$	−4.72253	−	6.50000i	−0.196431	−	0.270364i
$579$	−6.50000	−	20.0049i	−0.270131	−	0.831377i
$580$		0			0
$581$	−3.52786	−	2.56314i	−0.146360	−	0.106337i
$582$		−	7.09017i		−	0.293897i
$583$	10.0126	−	23.1976i	0.414679	−	0.960745i
$584$	−30.1246			−1.24657
$585$		0			0
$586$	3.15654	−	9.71483i	0.130396	−	0.401316i
$587$	18.4333	−	5.98936i	0.760826	−	0.247207i	0.0971926	−	0.995266i	$-0.469014\pi$
$587$	18.4333	−	5.98936i	0.760826	−	0.247207i	0.663633	+	0.748058i	$0.269014\pi$
$588$	−6.10237	−	8.39919i	−0.251657	−	0.346377i
$589$	28.3156	−	20.5725i	1.16672	−	0.847674i
$590$		0			0
$591$	−4.39919	+	13.5393i	−0.180958	+	0.556933i
$592$	−8.14324	+	11.2082i	−0.334685	+	0.460654i
$593$		−	38.8885i		−	1.59696i	−0.602021	−	0.798481i	$-0.705638\pi$
$593$		−	38.8885i		−	1.59696i	0.602021	−	0.798481i	$-0.294362\pi$
$594$	2.00000	−	0.449028i	0.0820610	−	0.0184238i
$595$		0			0
$596$	26.3435	+	19.1396i	1.07907	+	0.783990i
$597$	−18.8294	−	6.11803i	−0.770635	−	0.250394i
$598$	−1.73060	+	0.562306i	−0.0707695	+	0.0229944i
$599$	−17.9894	+	13.0700i	−0.735025	+	0.534027i	−0.891149	−	0.453710i	$-0.850100\pi$
$599$	−17.9894	+	13.0700i	−0.735025	+	0.534027i	0.156124	+	0.987737i	$0.450100\pi$
$600$		0			0
$601$	10.6180	+	32.6789i	0.433119	+	1.33300i	0.895002	+	0.446062i	$0.147174\pi$
$601$	10.6180	+	32.6789i	0.433119	+	1.33300i	−0.461884	+	0.886941i	$0.652826\pi$
$602$	0.938545	+	0.304952i	0.0382522	+	0.0124289i
$603$	5.51458	−	7.59017i	0.224571	−	0.309096i
$604$	−17.4164			−0.708664
$605$		0			0
$606$	0.347524			0.0141172
$607$	−19.3969	+	26.6976i	−0.787296	+	1.08362i	0.207143	+	0.978311i	$0.433583\pi$
$607$	−19.3969	+	26.6976i	−0.787296	+	1.08362i	−0.994439	+	0.105310i	$0.966417\pi$
$608$	−26.7153	−	8.68034i	−1.08345	−	0.352034i
$609$	1.38197	+	4.25325i	0.0560001	+	0.172351i
$610$		0			0
$611$	5.09017	−	3.69822i	0.205926	−	0.149614i
$612$	3.07768	−	1.00000i	0.124408	−	0.0404226i
$613$	−7.83297	−	2.54508i	−0.316371	−	0.102795i	0.146527	−	0.989207i	$-0.453190\pi$
$613$	−7.83297	−	2.54508i	−0.316371	−	0.102795i	−0.462898	+	0.886412i	$0.653190\pi$
$614$	6.06231	+	4.40452i	0.244655	+	0.177752i
$615$		0			0
$616$	5.52786	−	1.24108i	0.222724	−	0.0500047i
$617$		−	38.2492i		−	1.53986i	−0.638131	−	0.769928i	$-0.720292\pi$
$617$		−	38.2492i		−	1.53986i	0.638131	−	0.769928i	$-0.279708\pi$
$618$	0.865300	−	1.19098i	0.0348075	−	0.0479084i
$619$	−2.19756	+	6.76340i	−0.0883274	+	0.271844i	−0.985457	−	0.169923i	$-0.945648\pi$
$619$	−2.19756	+	6.76340i	−0.0883274	+	0.271844i	0.897130	+	0.441767i	$0.145648\pi$
$620$		0			0
$621$	1.92705	−	1.40008i	0.0773299	−	0.0561835i
$622$	−7.80021	−	10.7361i	−0.312760	−	0.430477i
$623$	−7.88597	+	2.56231i	−0.315945	+	0.102657i
$624$	−0.708204	+	2.17963i	−0.0283508	+	0.0872549i
$625$		0			0
$626$	0.291796			0.0116625
$627$	−6.57164	+	15.2254i	−0.262446	+	0.608045i
$628$		−	5.38197i		−	0.214764i
$629$	−12.0902	−	8.78402i	−0.482067	−	0.350242i
$630$		0			0
$631$	11.9377	+	36.7404i	0.475232	+	1.46261i	0.845644	+	0.533747i	$0.179216\pi$
$631$	11.9377	+	36.7404i	0.475232	+	1.46261i	−0.370412	+	0.928867i	$0.620784\pi$
$632$	−10.6331	−	14.6353i	−0.422963	−	0.582159i
$633$	2.26538	+	3.11803i	0.0900409	+	0.123931i
$634$	−5.80902	−	17.8783i	−0.230706	−	0.710039i
$635$		0			0
$636$	9.97214	+	7.24518i	0.395421	+	0.287290i
$637$			7.93112i			0.314242i
$638$	11.9475	+	1.11803i	0.473005	+	0.0442634i
$639$	8.00000			0.316475
$640$		0			0
$641$	−0.0729490	+	0.224514i	−0.00288131	+	0.00886777i	−0.952487	−	0.304580i	$-0.901484\pi$
$641$	−0.0729490	+	0.224514i	−0.00288131	+	0.00886777i	0.949606	+	0.313448i	$0.101484\pi$
$642$	1.67760	−	0.545085i	0.0662096	−	0.0215128i
$643$	−17.2375	−	23.7254i	−0.679782	−	0.935639i	0.320149	−	0.947367i	$-0.396267\pi$
$643$	−17.2375	−	23.7254i	−0.679782	−	0.935639i	−0.999931	+	0.0117276i	$0.996267\pi$
$644$	2.38197	−	1.73060i	0.0938626	−	0.0681952i
$645$		0			0
$646$	1.90983	−	5.87785i	0.0751413	−	0.231261i
$647$	−10.3431	+	14.2361i	−0.406630	+	0.559678i	−0.962392	−	0.271663i	$-0.912426\pi$
$647$	−10.3431	+	14.2361i	−0.406630	+	0.559678i	0.555763	+	0.831341i	$0.312426\pi$
$648$			2.23607i			0.0878410i
$649$	11.3435	+	19.1396i	0.445270	+	0.751297i
$650$		0			0
$651$	−4.32624	−	3.14320i	−0.169559	−	0.123192i
$652$	−20.8702	−	6.78115i	−0.817342	−	0.265570i
$653$	22.2906	−	7.24265i	0.872297	−	0.283427i	0.161542	−	0.986866i	$-0.448353\pi$
$653$	22.2906	−	7.24265i	0.872297	−	0.283427i	0.710755	+	0.703439i	$0.248353\pi$
$654$	−2.07295	+	1.50609i	−0.0810587	+	0.0588926i
$655$		0			0
$656$	1.44834	+	4.45752i	0.0565481	+	0.174037i
$657$	−12.8128	−	4.16312i	−0.499873	−	0.162419i
$658$	1.41260	−	1.94427i	0.0550687	−	0.0757956i
$659$	−12.9656			−0.505066			−0.252533	−	0.967588i	$-0.581264\pi$
$659$	−12.9656			−0.505066			−0.252533	+	0.967588i	$0.581264\pi$
$660$		0			0
$661$	3.90983			0.152075			0.0760374	−	0.997105i	$-0.475773\pi$
$661$	3.90983			0.152075			0.0760374	+	0.997105i	$0.475773\pi$
$662$	7.84548	−	10.7984i	0.304923	−	0.419691i
$663$	−2.35114	−	0.763932i	−0.0913108	−	0.0296687i
$664$	−3.94427	−	12.1392i	−0.153067	−	0.471093i
$665$		0			0
$666$	3.73607	−	2.71441i	0.144770	−	0.105181i
$667$	13.2618	−	4.30902i	0.513499	−	0.166846i
$668$	−30.8298	−	10.0172i	−1.19284	−	0.387578i
$669$	−6.50000	−	4.72253i	−0.251305	−	0.182583i
$670$		0			0
$671$	−15.3369	+	17.4293i	−0.592074	+	0.672850i
$672$			4.29180i			0.165560i
$673$	−16.0494	+	22.0902i	−0.618661	+	0.851513i	−0.997255	−	0.0740494i	$-0.976408\pi$
$673$	−16.0494	+	22.0902i	−0.618661	+	0.851513i	0.378594	+	0.925563i	$0.376408\pi$
$674$	4.22949	−	13.0170i	0.162914	−	0.501397i
$675$		0			0
$676$	−15.0172	+	10.9106i	−0.577585	+	0.419640i
$677$	7.02067	+	9.66312i	0.269826	+	0.371384i	0.922331	−	0.386401i	$-0.126282\pi$
$677$	7.02067	+	9.66312i	0.269826	+	0.371384i	−0.652505	+	0.757785i	$0.726282\pi$
$678$	−3.21644	+	1.04508i	−0.123527	+	0.0401362i
$679$	2.70820	−	8.33499i	0.103931	−	0.319868i
$680$		0			0
$681$	−25.9443			−0.994187
$682$	−12.3435	+	7.31559i	−0.472657	+	0.280129i
$683$			2.29180i			0.0876931i	0.999038	+	0.0438466i	$0.0139613\pi$
$683$			2.29180i			0.0876931i	−0.999038	+	0.0438466i	$0.986039\pi$
$684$	−6.54508	−	4.75528i	−0.250258	−	0.181823i
$685$		0			0
$686$	1.95743	+	6.02434i	0.0747349	+	0.230010i
$687$	10.6331	+	14.6353i	0.405679	+	0.558370i
$688$	−2.27790	−	3.13525i	−0.0868440	−	0.119530i
$689$	−2.90983	−	8.95554i	−0.110856	−	0.341179i
$690$		0			0
$691$	−26.9443	−	19.5762i	−1.02501	−	0.744712i	−0.0577049	−	0.998334i	$-0.518378\pi$
$691$	−26.9443	−	19.5762i	−1.02501	−	0.744712i	−0.967304	+	0.253621i	$0.918378\pi$
$692$		−	5.76393i		−	0.219112i
$693$	2.52265	+	0.236068i	0.0958277	+	0.00896748i
$694$	−3.59675			−0.136531
$695$		0			0
$696$	−4.04508	+	12.4495i	−0.153329	+	0.471897i
$697$	−4.80828	+	1.56231i	−0.182127	+	0.0591766i
$698$	10.0858	+	13.8820i	0.381755	+	0.525440i
$699$	18.8262	−	13.6781i	0.712074	−	0.517352i
$700$		0			0
$701$	4.19756	−	12.9188i	0.158540	−	0.487935i	−0.839963	−	0.542644i	$-0.817423\pi$
$701$	4.19756	−	12.9188i	0.158540	−	0.487935i	0.998502	+	0.0547093i	$0.0174232\pi$
$702$	0.449028	−	0.618034i	0.0169475	−	0.0233262i
$703$			37.3607i			1.40908i
$704$	−0.718847	−	0.310271i	−0.0270926	−	0.0116938i
$705$		0			0
$706$	17.9164	+	13.0170i	0.674293	+	0.489902i
$707$	0.408539	+	0.132742i	0.0153647	+	0.00499229i
$708$	−10.3229	+	3.35410i	−0.387957	+	0.126055i
$709$	33.3156	−	24.2052i	1.25119	−	0.909045i	0.252903	−	0.967492i	$-0.418615\pi$
$709$	33.3156	−	24.2052i	1.25119	−	0.909045i	0.998291	+	0.0584464i	$0.0186147\pi$
$710$		0			0
$711$	−2.50000	−	7.69421i	−0.0937573	−	0.288555i
$712$	−23.0826	−	7.50000i	−0.865058	−	0.281074i
$713$	−9.80059	+	13.4894i	−0.367035	+	0.505180i
$714$	−0.944272			−0.0353385
$715$		0			0
$716$	31.5066			1.17746
$717$	4.13474	−	5.69098i	0.154415	−	0.212534i
$718$	−9.82084	−	3.19098i	−0.366510	−	0.119086i
$719$	−11.7705	−	36.2259i	−0.438966	−	1.35100i	−0.888967	−	0.457970i	$-0.848577\pi$
$719$	−11.7705	−	36.2259i	−0.438966	−	1.35100i	0.450001	−	0.893028i	$-0.351423\pi$
$720$		0			0
$721$	1.47214	−	1.06957i	0.0548252	−	0.0398328i
$722$	−3.52671	+	1.14590i	−0.131251	+	0.0426459i
$723$	−1.53884	−	0.500000i	−0.0572301	−	0.0185952i
$724$	6.85410	+	4.97980i	0.254731	+	0.185073i
$725$		0			0
$726$	3.26393	−	5.96361i	0.121136	−	0.221330i
$727$			37.3262i			1.38435i	0.721728	+	0.692177i	$0.243348\pi$
$727$			37.3262i			1.38435i	−0.721728	+	0.692177i	$0.756652\pi$
$728$	1.24108	−	1.70820i	0.0459976	−	0.0633102i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$		0			0
$731$	3.38197	−	2.45714i	0.125087	−	0.0908807i
$732$	−6.65740	−	9.16312i	−0.246064	−	0.338679i
$733$	1.76336	−	0.572949i	0.0651310	−	0.0211624i	−0.276270	−	0.961080i	$-0.589098\pi$
$733$	1.76336	−	0.572949i	0.0651310	−	0.0211624i	0.341401	+	0.939918i	$0.389098\pi$
$734$	3.46149	−	10.6534i	0.127766	−	0.393223i
$735$		0			0
$736$	13.3820			0.493266
$737$	−6.81640	−	30.3607i	−0.251085	−	1.11835i
$738$		−	1.56231i		−	0.0575093i
$739$	−16.1803	−	11.7557i	−0.595203	−	0.432441i	0.248970	−	0.968511i	$-0.419908\pi$
$739$	−16.1803	−	11.7557i	−0.595203	−	0.432441i	−0.844173	+	0.536071i	$0.819908\pi$
$740$		0			0
$741$	1.90983	+	5.87785i	0.0701594	+	0.215928i
$742$	−2.11412	−	2.90983i	−0.0776116	−	0.106823i
$743$	0.204270	+	0.281153i	0.00749392	+	0.0103145i	0.812748	−	0.582616i	$-0.197971\pi$
$743$	0.204270	+	0.281153i	0.00749392	+	0.0103145i	−0.805254	+	0.592931i	$0.797971\pi$
$744$	−4.83688	−	14.8864i	−0.177329	−	0.545762i
$745$		0			0
$746$	−4.87132	−	3.53922i	−0.178352	−	0.129580i
$747$		−	5.70820i		−	0.208852i
$748$	4.25325	−	9.85410i	0.155514	−	0.360302i
$749$	2.18034			0.0796679
$750$		0			0
$751$	−14.1803	+	43.6426i	−0.517448	+	1.59254i	0.261335	+	0.965248i	$0.415837\pi$
$751$	−14.1803	+	43.6426i	−0.517448	+	1.59254i	−0.778783	+	0.627293i	$0.784163\pi$
$752$	−8.97578	+	2.91641i	−0.327313	+	0.106350i
$753$	−4.42477	−	6.09017i	−0.161247	−	0.221938i
$754$	3.61803	−	2.62866i	0.131761	−	0.0957300i
$755$		0			0
$756$	−0.381966	+	1.17557i	−0.0138920	+	0.0427551i
$757$	−14.2128	+	19.5623i	−0.516575	+	0.711004i	−0.985011	−	0.172493i	$-0.944818\pi$
$757$	−14.2128	+	19.5623i	−0.516575	+	0.711004i	0.468436	+	0.883497i	$0.344818\pi$
$758$			3.09017i			0.112240i
$759$	0.736068	−	7.86572i	0.0267176	−	0.285508i
$760$		0			0
$761$	−31.5795	−	22.9439i	−1.14476	−	0.831715i	−0.156982	−	0.987601i	$-0.550176\pi$
$761$	−31.5795	−	22.9439i	−1.14476	−	0.831715i	−0.987775	+	0.155887i	$0.950176\pi$
$762$	−9.37181	−	3.04508i	−0.339505	−	0.110312i
$763$	−3.01217	+	0.978714i	−0.109048	+	0.0354318i
$764$	−13.6353	+	9.90659i	−0.493306	+	0.358408i
$765$		0			0
$766$	−5.98936	−	18.4333i	−0.216404	−	0.666024i
$767$	7.88597	+	2.56231i	0.284746	+	0.0925195i
$768$	−3.85723	+	5.30902i	−0.139186	+	0.191573i
$769$	−12.7639			−0.460279			−0.230140	−	0.973158i	$-0.573918\pi$
$769$	−12.7639			−0.460279			−0.230140	+	0.973158i	$0.573918\pi$
$770$		0			0
$771$	10.5623			0.380392
$772$	20.0049	−	27.5344i	0.719994	−	0.990986i
$773$	9.99235	+	3.24671i	0.359400	+	0.116776i	0.483151	−	0.875537i	$-0.339492\pi$
$773$	9.99235	+	3.24671i	0.359400	+	0.116776i	−0.123751	+	0.992313i	$0.539492\pi$
$774$	0.399187	+	1.22857i	0.0143485	+	0.0441601i
$775$		0			0
$776$	20.7533	−	15.0781i	0.745000	−	0.541274i
$777$	5.42882	−	1.76393i	0.194758	−	0.0632807i
$778$	22.8909	+	7.43769i	0.820677	+	0.266654i
$779$	10.2254	+	7.42921i	0.366364	+	0.266179i
$780$		0			0
$781$	17.5279	−	19.9192i	0.627196	−	0.712765i
$782$			2.94427i			0.105287i
$783$	−3.44095	+	4.73607i	−0.122970	+	0.169253i
$784$	3.67627	−	11.3144i	0.131296	−	0.404086i
$785$		0			0
$786$	6.59017	−	4.78804i	0.235064	−	0.170784i
$787$	4.82079	+	6.63525i	0.171843	+	0.236521i	0.886248	−	0.463211i	$-0.153303\pi$
$787$	4.82079	+	6.63525i	0.171843	+	0.236521i	−0.714405	+	0.699732i	$0.753303\pi$
$788$	−21.9071	+	7.11803i	−0.780407	+	0.253569i
$789$	−8.40983	+	25.8828i	−0.299398	+	0.921452i
$790$		0			0
$791$	−4.18034			−0.148636
$792$	5.56758	+	4.89919i	0.197835	+	0.174085i
$793$			8.65248i			0.307258i
$794$	18.1353	+	13.1760i	0.643596	+	0.467600i
$795$		0			0
$796$	−9.89919	−	30.4666i	−0.350867	−	1.07986i
$797$	−16.8743	−	23.2254i	−0.597717	−	0.822687i	0.397780	−	0.917481i	$-0.369781\pi$
$797$	−16.8743	−	23.2254i	−0.597717	−	0.822687i	−0.995497	+	0.0947941i	$0.969781\pi$
$798$	1.38757	+	1.90983i	0.0491195	+	0.0676073i
$799$	−3.14590	−	9.68208i	−0.111294	−	0.342527i
$800$		0			0
$801$	−8.78115	−	6.37988i	−0.310267	−	0.225422i
$802$			3.02129i			0.106685i
$803$	−38.4383	+	22.7812i	−1.35646	+	0.803929i
$804$	15.1803			0.535369
$805$		0			0
$806$	−1.65248	+	5.08580i	−0.0582060	+	0.179140i
$807$	−5.56758	+	1.80902i	−0.195988	+	0.0636804i
$808$	0.739054	+	1.01722i	0.0259998	+	0.0357857i
$809$	36.6697	−	26.6421i	1.28924	−	0.936686i	0.289448	−	0.957194i	$-0.406528\pi$
$809$	36.6697	−	26.6421i	1.28924	−	0.936686i	0.999790	+	0.0205075i	$0.00652821\pi$
$810$		0			0
$811$	−10.7016	+	32.9362i	−0.375785	+	1.15655i	0.567163	+	0.823606i	$0.308041\pi$
$811$	−10.7016	+	32.9362i	−0.375785	+	1.15655i	−0.942948	+	0.332941i	$0.891959\pi$
$812$	−4.25325	+	5.85410i	−0.149260	+	0.205439i
$813$			20.6180i			0.723106i
$814$	1.42705	−	15.2497i	0.0500181	−	0.534500i
$815$		0			0
$816$	3.00000	+	2.17963i	0.105021	+	0.0763022i
$817$	−9.93935	−	3.22949i	−0.347734	−	0.112986i
$818$	21.3395	−	6.93363i	0.746119	−	0.242429i
$819$	0.763932	−	0.555029i	0.0266939	−	0.0193943i
$820$		0			0
$821$	13.3435	+	41.0669i	0.465690	+	1.43325i	0.858113	+	0.513461i	$0.171637\pi$
$821$	13.3435	+	41.0669i	0.465690	+	1.43325i	−0.392423	+	0.919785i	$0.628363\pi$
$822$	−10.9964	−	3.57295i	−0.383544	−	0.124621i
$823$	−14.9721	+	20.6074i	−0.521896	+	0.718328i	−0.985868	−	0.167521i	$-0.946424\pi$
$823$	−14.9721	+	20.6074i	−0.521896	+	0.718328i	0.463972	+	0.885850i	$0.346424\pi$
$824$	5.32624			0.185548
$825$		0			0
$826$	3.16718			0.110200
$827$	−14.4499	+	19.8885i	−0.502471	+	0.691592i	−0.982627	−	0.185591i	$-0.940580\pi$
$827$	−14.4499	+	19.8885i	−0.502471	+	0.691592i	0.480156	+	0.877183i	$0.340580\pi$
$828$	3.66547	+	1.19098i	0.127384	+	0.0413895i
$829$	−0.892609	−	2.74717i	−0.0310016	−	0.0954131i	0.934358	−	0.356335i	$-0.115974\pi$
$829$	−0.892609	−	2.74717i	−0.0310016	−	0.0954131i	−0.965360	+	0.260921i	$0.915974\pi$
$830$		0			0
$831$	−7.00000	+	5.08580i	−0.242827	+	0.176424i
$832$	−0.277515	+	0.0901699i	−0.00962109	+	0.00312608i
$833$	12.2047	+	3.96556i	0.422869	+	0.137398i
$834$	−10.5902	−	7.69421i	−0.366708	−	0.266429i
$835$		0			0
$836$	−26.1803	+	5.87785i	−0.905466	+	0.203290i
$837$		−	7.00000i		−	0.241955i
$838$	−8.93529	+	12.2984i	−0.308665	+	0.424840i
$839$	8.12868	−	25.0175i	0.280633	−	0.863700i	−0.707041	−	0.707173i	$-0.749970\pi$
$839$	8.12868	−	25.0175i	0.280633	−	0.863700i	0.987674	−	0.156527i	$-0.0500298\pi$
$840$		0			0
$841$	−4.26393	+	3.09793i	−0.147032	+	0.106825i
$842$	−1.03681	−	1.42705i	−0.0357309	−	0.0491794i
$843$	−9.59632	+	3.11803i	−0.330515	+	0.107391i
$844$	−1.92705	+	5.93085i	−0.0663318	+	0.204148i
$845$		0			0
$846$	3.14590			0.108158
$847$	6.11488	−	5.76393i	0.210110	−	0.198051i
$848$			14.1246i			0.485041i
$849$	−10.5451	−	7.66145i	−0.361906	−	0.262940i
$850$		0			0
$851$	−5.50000	−	16.9273i	−0.188538	−	0.580259i
$852$	7.60845	+	10.4721i	0.260661	+	0.358769i
$853$	−12.5555	−	17.2812i	−0.429892	−	0.591695i	0.538037	−	0.842922i	$-0.319166\pi$
$853$	−12.5555	−	17.2812i	−0.429892	−	0.591695i	−0.967928	+	0.251226i	$0.919166\pi$
$854$	1.02129	+	3.14320i	0.0349477	+	0.107558i
$855$		0			0
$856$	5.16312	+	3.75123i	0.176472	+	0.128214i
$857$			35.0132i			1.19603i	0.801486	+	0.598013i	$0.204043\pi$
$857$			35.0132i			1.19603i	−0.801486	+	0.598013i	$0.795957\pi$
$858$	−0.555029	−	2.47214i	−0.0189484	−	0.0843973i
$859$	5.72949			0.195488			0.0977438	−	0.995212i	$-0.468837\pi$
$859$	5.72949			0.195488			0.0977438	+	0.995212i	$0.468837\pi$
$860$		0			0
$861$	0.596748	−	1.83660i	0.0203371	−	0.0625912i
$862$	−11.6902	+	3.79837i	−0.398170	+	0.129373i
$863$	−3.54696	−	4.88197i	−0.120740	−	0.166184i	0.744369	−	0.667769i	$-0.232751\pi$
$863$	−3.54696	−	4.88197i	−0.120740	−	0.166184i	−0.865108	+	0.501585i	$0.832751\pi$
$864$	−4.54508	+	3.30220i	−0.154627	+	0.112343i
$865$		0			0
$866$	5.35410	−	16.4782i	0.181940	−	0.559953i
$867$	7.64121	−	10.5172i	0.259509	−	0.357184i
$868$		−	8.65248i		−	0.293684i
$869$	−24.6353	−	10.6331i	−0.835694	−	0.360704i
$870$		0			0
$871$	−9.38197	−	6.81640i	−0.317896	−	0.230965i
$872$	−8.81678	−	2.86475i	−0.298574	−	0.0970125i
$873$	10.9106	−	3.54508i	0.369270	−	0.119983i
$874$	5.95492	−	4.32650i	0.201428	−	0.146346i
$875$		0			0
$876$	−6.73607	−	20.7315i	−0.227591	−	0.700452i
$877$	15.6659	+	5.09017i	0.529001	+	0.171883i	0.561326	−	0.827595i	$-0.310291\pi$
$877$	15.6659	+	5.09017i	0.529001	+	0.171883i	−0.0323254	+	0.999477i	$0.510291\pi$
$878$	−3.51420	+	4.83688i	−0.118598	+	0.163237i
$879$	16.5279			0.557471
$880$		0			0
$881$	−23.8541			−0.803665			−0.401833	−	0.915713i	$-0.631627\pi$
$881$	−23.8541			−0.803665			−0.401833	+	0.915713i	$0.631627\pi$
$882$	−2.33090	+	3.20820i	−0.0784854	+	0.108026i
$883$	−17.8456	−	5.79837i	−0.600551	−	0.195131i	−0.00706479	−	0.999975i	$-0.502249\pi$
$883$	−17.8456	−	5.79837i	−0.600551	−	0.195131i	−0.593486	+	0.804844i	$0.702249\pi$
$884$	−1.23607	−	3.80423i	−0.0415735	−	0.127950i
$885$		0			0
$886$	−12.6353	+	9.18005i	−0.424490	+	0.308410i
$887$	−51.1981	+	16.6353i	−1.71906	+	0.558557i	−0.991800	−	0.127802i	$-0.959208\pi$
$887$	−51.1981	+	16.6353i	−1.71906	+	0.558557i	−0.727263	+	0.686359i	$0.759208\pi$
$888$	15.8904	+	5.16312i	0.533248	+	0.173263i
$889$	−9.85410	−	7.15942i	−0.330496	−	0.240119i
$890$		0			0
$891$	1.69098	+	2.85317i	0.0566501	+	0.0955848i
$892$		−	13.0000i		−	0.435272i
$893$	−14.9596	+	20.5902i	−0.500605	+	0.689024i
$894$	3.84346	−	11.8290i	0.128544	−	0.395619i
$895$		0			0
$896$	−7.03444	+	5.11082i	−0.235004	+	0.170741i
$897$	−1.73060	−	2.38197i	−0.0577830	−	0.0795315i
$898$	−0.428784	+	0.139320i	−0.0143087	+	0.00464918i
$899$	12.6631	−	38.9731i	0.422339	−	1.29982i
$900$		0			0
$901$	−15.2361			−0.507587
$902$	−3.88998	−	3.42299i	−0.129522	−	0.113973i
$903$			1.59675i			0.0531364i
$904$	−9.89919	−	7.19218i	−0.329242	−	0.239208i
$905$		0			0
$906$	2.05573	+	6.32688i	0.0682970	+	0.210197i
$907$	−5.35558	−	7.37132i	−0.177829	−	0.244761i	0.710793	−	0.703402i	$-0.248336\pi$
$907$	−5.35558	−	7.37132i	−0.177829	−	0.244761i	−0.888622	+	0.458641i	$0.848336\pi$
$908$	−24.6745	−	33.9615i	−0.818851	−	1.12705i
$909$	0.173762	+	0.534785i	0.00576332	+	0.0177377i
$910$		0			0
$911$	47.6525	+	34.6216i	1.57880	+	1.14706i	0.918057	+	0.396448i	$0.129757\pi$
$911$	47.6525	+	34.6216i	1.57880	+	1.14706i	0.660740	+	0.750615i	$0.270243\pi$
$912$		−	9.27051i		−	0.306977i
$913$	−14.2128	−	12.5066i	−0.470377	−	0.413907i
$914$	−0.909830			−0.0300945
$915$		0			0
$916$	−9.04508	+	27.8379i	−0.298858	+	0.919790i
$917$	9.57608	−	3.11146i	0.316230	−	0.102749i
$918$	−0.726543	−	1.00000i	−0.0239795	−	0.0330049i
$919$	−14.3713	+	10.4414i	−0.474066	+	0.344429i	−0.799024	−	0.601299i	$-0.794650\pi$
$919$	−14.3713	+	10.4414i	−0.474066	+	0.344429i	0.324958	+	0.945729i	$0.394650\pi$
$920$		0			0
$921$	−3.74671	+	11.5312i	−0.123458	+	0.379966i
$922$	9.42481	−	12.9721i	0.310390	−	0.427215i
$923$		−	9.88854i		−	0.325485i
$924$	2.09017	+	3.52671i	0.0687615	+	0.116020i
$925$		0			0
$926$	16.6353	+	12.0862i	0.546668	+	0.397178i
$927$	2.26538	+	0.736068i	0.0744050	+	0.0241756i
$928$	−31.2789	+	10.1631i	−1.02678	+	0.333621i
$929$	−3.35410	+	2.43690i	−0.110045	+	0.0799520i	−0.641447	−	0.767168i	$-0.721665\pi$
$929$	−3.35410	+	2.43690i	−0.110045	+	0.0799520i	0.531402	+	0.847120i	$0.321665\pi$
$930$		0			0
$931$	−9.91390	−	30.5118i	−0.324915	−	0.999985i
$932$	35.8096	+	11.6353i	1.17298	+	0.381125i
$933$	12.6210	−	17.3713i	0.413193	−	0.568712i
$934$	−3.02129			−0.0988595
$935$		0			0
$936$	2.76393			0.0903419
$937$	24.5685	−	33.8156i	0.802617	−	1.10471i	−0.189804	−	0.981822i	$-0.560785\pi$
$937$	24.5685	−	33.8156i	0.802617	−	1.10471i	0.992421	−	0.122885i	$-0.0392147\pi$
$938$	−4.21277	−	1.36881i	−0.137552	−	0.0446932i
$939$	0.145898	+	0.449028i	0.00476120	+	0.0146535i
$940$		0			0
$941$	−3.00000	+	2.17963i	−0.0977972	+	0.0710538i	−0.635609	−	0.772011i	$-0.719251\pi$
$941$	−3.00000	+	2.17963i	−0.0977972	+	0.0710538i	0.537812	+	0.843065i	$0.319251\pi$
$942$	−1.95511	+	0.635255i	−0.0637010	+	0.0206977i
$943$	−5.72658	−	1.86068i	−0.186483	−	0.0605921i
$944$	−10.0623	−	7.31069i	−0.327500	−	0.237943i
$945$		0			0
$946$	3.93363	+	1.69784i	0.127893	+	0.0552017i
$947$		−	15.5623i		−	0.505707i	−0.967505	−	0.252853i	$-0.918631\pi$
$947$		−	15.5623i		−	0.505707i	0.967505	−	0.252853i	$-0.0813691\pi$
$948$	7.69421	−	10.5902i	0.249896	−	0.343953i
$949$	−5.14590	+	15.8374i	−0.167043	+	0.514105i
$950$		0			0
$951$	24.6074	−	17.8783i	0.797949	−	0.579744i
$952$	−2.00811	−	2.76393i	−0.0650834	−	0.0895796i
$953$	36.0544	−	11.7148i	1.16792	−	0.379479i	0.340052	−	0.940407i	$-0.389555\pi$
$953$	36.0544	−	11.7148i	1.16792	−	0.379479i	0.827865	+	0.560928i	$0.189555\pi$
$954$	1.45492	−	4.47777i	0.0471046	−	0.144973i
$955$		0			0
$956$	11.3820			0.368119
$957$	4.25325	+	18.9443i	0.137488	+	0.612381i
$958$		−	20.6525i		−	0.667251i
$959$	−11.5623	−	8.40051i	−0.373366	−	0.271267i
$960$		0			0
$961$	5.56231	+	17.1190i	0.179429	+	0.552226i
$962$	−3.35520	−	4.61803i	−0.108176	−	0.148891i
$963$	1.67760	+	2.30902i	0.0540599	+	0.0744070i
$964$	−0.809017	−	2.48990i	−0.0260567	−	0.0801942i
$965$		0			0
$966$	−0.909830	−	0.661030i	−0.0292733	−	0.0212683i
$967$		−	48.3262i		−	1.55407i	−0.629459	−	0.777034i	$-0.716724\pi$
$967$		−	48.3262i		−	1.55407i	0.629459	−	0.777034i	$-0.283276\pi$
$968$	24.3970	−	3.12868i	0.784148	−	0.100559i
$969$	10.0000			0.321246
$970$		0			0
$971$	10.9828	−	33.8015i	0.352454	−	1.08474i	−0.605017	−	0.796213i	$-0.706834\pi$
$971$	10.9828	−	33.8015i	0.352454	−	1.08474i	0.957471	−	0.288530i	$-0.0931664\pi$
$972$	−1.53884	+	0.500000i	−0.0493584	+	0.0160375i
$973$	−9.51057	−	13.0902i	−0.304895	−	0.419652i
$974$	−7.09017	+	5.15131i	−0.227184	+	0.165059i
$975$		0			0
$976$	4.01064	−	12.3435i	0.128378	−	0.395105i
$977$	−20.5195	+	28.2426i	−0.656476	+	0.903562i	−0.999358	−	0.0358162i	$-0.988597\pi$
$977$	−20.5195	+	28.2426i	−0.656476	+	0.903562i	0.342882	+	0.939378i	$0.388597\pi$
$978$			8.38197i			0.268026i
$979$	−35.1246	+	7.88597i	−1.12259	+	0.252037i
$980$		0			0
$981$	−3.35410	−	2.43690i	−0.107088	−	0.0778042i
$982$	18.6906	+	6.07295i	0.596441	+	0.193796i
$983$	−18.0701	+	5.87132i	−0.576346	+	0.187266i	−0.582663	−	0.812714i	$-0.697989\pi$
$983$	−18.0701	+	5.87132i	−0.576346	+	0.187266i	0.00631707	+	0.999980i	$0.497989\pi$
$984$	4.57295	−	3.32244i	0.145780	−	0.105916i
$985$		0			0
$986$	−2.23607	−	6.88191i	−0.0712109	−	0.219165i
$987$	3.69822	+	1.20163i	0.117716	+	0.0382482i
$988$	−5.87785	+	8.09017i	−0.186999	+	0.257383i
$989$	4.97871			0.158314
$990$		0			0
$991$	−8.00000			−0.254128			−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000			−0.254128			−0.127064	+	0.991894i	$0.540555\pi$
$992$	23.1154	−	31.8156i	0.733914	−	1.01015i
$993$	20.5397	+	6.67376i	0.651809	+	0.211785i
$994$	−1.16718	−	3.59222i	−0.0370208	−	0.113938i
$995$		0			0
$996$	7.47214	−	5.42882i	0.236764	−	0.172019i
$997$	23.4989	−	7.63525i	0.744218	−	0.241811i	0.0877264	−	0.996145i	$-0.472040\pi$
$997$	23.4989	−	7.63525i	0.744218	−	0.241811i	0.656491	+	0.754334i	$0.272040\pi$
$998$	6.57164	+	2.13525i	0.208022	+	0.0675903i
$999$	6.04508	+	4.39201i	0.191258	+	0.138957i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.bx.c.499.2		8
5.2	odd	4		825.2.n.d.301.1	yes	4
5.3	odd	4		825.2.n.b.301.1	✓	4
5.4	even	2	inner	825.2.bx.c.499.1		8
11.3	even	5	inner	825.2.bx.c.124.1		8
55.3	odd	20		825.2.n.b.751.1	yes	4
55.14	even	10	inner	825.2.bx.c.124.2		8
55.17	even	20		9075.2.a.bc.1.2		2
55.27	odd	20		9075.2.a.by.1.1		2
55.28	even	20		9075.2.a.bt.1.1		2
55.38	odd	20		9075.2.a.z.1.2		2
55.47	odd	20		825.2.n.d.751.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.n.b.301.1	✓	4	5.3	odd	4
825.2.n.b.751.1	yes	4	55.3	odd	20
825.2.n.d.301.1	yes	4	5.2	odd	4
825.2.n.d.751.1	yes	4	55.47	odd	20
825.2.bx.c.124.1		8	11.3	even	5	inner
825.2.bx.c.124.2		8	55.14	even	10	inner
825.2.bx.c.499.1		8	5.4	even	2	inner
825.2.bx.c.499.2		8	1.1	even	1	trivial
9075.2.a.z.1.2		2	55.38	odd	20
9075.2.a.bc.1.2		2	55.17	even	20
9075.2.a.bt.1.1		2	55.28	even	20
9075.2.a.by.1.1		2	55.27	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.363271 - 0.500000i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.500000 + 1.53884i) q^{4} +(0.500000 - 0.363271i) q^{6} +(0.726543 - 0.236068i) q^{7} +(2.12663 + 0.690983i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.363271 - 0.500000i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.500000 + 1.53884i) q^{4} +(0.500000 - 0.363271i) q^{6} +(0.726543 - 0.236068i) q^{7} +(2.12663 + 0.690983i) q^{8} +(0.809017 + 0.587785i) q^{9} +(3.23607 - 0.726543i) q^{11} +1.61803i q^{12} +(0.726543 - 1.00000i) q^{13} +(0.145898 - 0.449028i) q^{14} +(-1.50000 + 1.08981i) q^{16} +(-1.17557 - 1.61803i) q^{17} +(0.587785 - 0.190983i) q^{18} +(-1.54508 + 4.75528i) q^{19} +0.763932 q^{21} +(0.812299 - 1.88197i) q^{22} -2.38197i q^{23} +(1.80902 + 1.31433i) q^{24} +(-0.236068 - 0.726543i) q^{26} +(0.587785 + 0.809017i) q^{27} +(0.726543 + 1.00000i) q^{28} +(1.80902 + 5.56758i) q^{29} +(-5.66312 - 4.11450i) q^{31} +5.61803i q^{32} +(3.30220 + 0.309017i) q^{33} -1.23607 q^{34} +(-0.500000 + 1.53884i) q^{36} +(7.10642 - 2.30902i) q^{37} +(1.81636 + 2.50000i) q^{38} +(1.00000 - 0.726543i) q^{39} +(0.781153 - 2.40414i) q^{41} +(0.277515 - 0.381966i) q^{42} +2.09017i q^{43} +(2.73607 + 4.61653i) q^{44} +(-1.19098 - 0.865300i) q^{46} +(4.84104 + 1.57295i) q^{47} +(-1.76336 + 0.572949i) q^{48} +(-5.19098 + 3.77147i) q^{49} +(-0.618034 - 1.90211i) q^{51} +(1.90211 + 0.618034i) q^{52} +(4.47777 - 6.16312i) q^{53} +0.618034 q^{54} +1.70820 q^{56} +(-2.93893 + 4.04508i) q^{57} +(3.44095 + 1.11803i) q^{58} +(2.07295 + 6.37988i) q^{59} +(-5.66312 + 4.11450i) q^{61} +(-4.11450 + 1.33688i) q^{62} +(0.726543 + 0.236068i) q^{63} +(-0.190983 - 0.138757i) q^{64} +(1.35410 - 1.53884i) q^{66} -9.38197i q^{67} +(1.90211 - 2.61803i) q^{68} +(0.736068 - 2.26538i) q^{69} +(6.47214 - 4.70228i) q^{71} +(1.31433 + 1.80902i) q^{72} +(-12.8128 + 4.16312i) q^{73} +(1.42705 - 4.39201i) q^{74} -8.09017 q^{76} +(2.17963 - 1.29180i) q^{77} -0.763932i q^{78} +(-6.54508 - 4.75528i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-0.918300 - 1.26393i) q^{82} +(-3.35520 - 4.61803i) q^{83} +(0.381966 + 1.17557i) q^{84} +(1.04508 + 0.759299i) q^{86} +5.85410i q^{87} +(7.38394 + 0.690983i) q^{88} -10.8541 q^{89} +(0.291796 - 0.898056i) q^{91} +(3.66547 - 1.19098i) q^{92} +(-4.11450 - 5.66312i) q^{93} +(2.54508 - 1.84911i) q^{94} +(-1.73607 + 5.34307i) q^{96} +(6.74315 - 9.28115i) q^{97} +3.96556i q^{98} +(3.04508 + 1.31433i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} + 4 q^{6} + 2 q^{9}+O(q^{10}) \) 8 * q + 4 * q^4 + 4 * q^6 + 2 * q^9	\( 8 q + 4 q^{4} + 4 q^{6} + 2 q^{9} + 8 q^{11} + 28 q^{14} - 12 q^{16} + 10 q^{19} + 24 q^{21} + 10 q^{24} + 16 q^{26} + 10 q^{29} - 14 q^{31} + 8 q^{34} - 4 q^{36} + 8 q^{39} - 34 q^{41} + 4 q^{44} - 14 q^{46} - 46 q^{49} + 4 q^{51} - 4 q^{54} - 40 q^{56} + 30 q^{59} - 14 q^{61} - 6 q^{64} - 16 q^{66} - 12 q^{69} + 16 q^{71} - 2 q^{74} - 20 q^{76} - 30 q^{79} - 2 q^{81} + 12 q^{84} - 14 q^{86} - 60 q^{89} + 56 q^{91} - 2 q^{94} + 4 q^{96} + 2 q^{99}+O(q^{100}) \) 8 * q + 4 * q^4 + 4 * q^6 + 2 * q^9 + 8 * q^11 + 28 * q^14 - 12 * q^16 + 10 * q^19 + 24 * q^21 + 10 * q^24 + 16 * q^26 + 10 * q^29 - 14 * q^31 + 8 * q^34 - 4 * q^36 + 8 * q^39 - 34 * q^41 + 4 * q^44 - 14 * q^46 - 46 * q^49 + 4 * q^51 - 4 * q^54 - 40 * q^56 + 30 * q^59 - 14 * q^61 - 6 * q^64 - 16 * q^66 - 12 * q^69 + 16 * q^71 - 2 * q^74 - 20 * q^76 - 30 * q^79 - 2 * q^81 + 12 * q^84 - 14 * q^86 - 60 * q^89 + 56 * q^91 - 2 * q^94 + 4 * q^96 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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