LMFDB - Embedded newform 603.2.g.c.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(37,603)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(603, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("603.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.g (of order $3$, degree $2$, 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:	$4.81497924188$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.2
Root			$-0.309017 - 0.535233i$ of defining polynomial
Character	$\chi$	$=$	603.37
Dual form			603.2.g.c.163.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.535233i) q^{2} +(0.809017 - 1.40126i) q^{4} +3.23607 q^{5} +(-2.11803 + 3.66854i) q^{7} +2.23607 q^{8} +O(q^{10})$	\(q+(0.309017 + 0.535233i) q^{2} +(0.809017 - 1.40126i) q^{4} +3.23607 q^{5} +(-2.11803 + 3.66854i) q^{7} +2.23607 q^{8} +(1.00000 + 1.73205i) q^{10} +(-2.50000 + 4.33013i) q^{11} +(2.11803 + 3.66854i) q^{13} -2.61803 q^{14} +(-0.927051 - 1.60570i) q^{16} +(-1.11803 - 1.93649i) q^{17} +(3.11803 + 5.40059i) q^{19} +(2.61803 - 4.53457i) q^{20} -3.09017 q^{22} +(-3.11803 - 5.40059i) q^{23} +5.47214 q^{25} +(-1.30902 + 2.26728i) q^{26} +(3.42705 + 5.93583i) q^{28} +(4.73607 - 8.20311i) q^{29} +(3.35410 - 5.80948i) q^{31} +(2.80902 - 4.86536i) q^{32} +(0.690983 - 1.19682i) q^{34} +(-6.85410 + 11.8717i) q^{35} +(-0.736068 - 1.27491i) q^{37} +(-1.92705 + 3.33775i) q^{38} +7.23607 q^{40} +(0.118034 - 0.204441i) q^{41} -5.23607 q^{43} +(4.04508 + 7.00629i) q^{44} +(1.92705 - 3.33775i) q^{46} +(3.11803 - 5.40059i) q^{47} +(-5.47214 - 9.47802i) q^{49} +(1.69098 + 2.92887i) q^{50} +6.85410 q^{52} -3.70820 q^{53} +(-8.09017 + 14.0126i) q^{55} +(-4.73607 + 8.20311i) q^{56} +5.85410 q^{58} -6.00000 q^{59} +(0.354102 + 0.613323i) q^{61} +4.14590 q^{62} -0.236068 q^{64} +(6.85410 + 11.8717i) q^{65} +(-8.00000 + 1.73205i) q^{67} -3.61803 q^{68} -8.47214 q^{70} +(6.73607 - 11.6672i) q^{71} +(5.35410 + 9.27358i) q^{73} +(0.454915 - 0.787936i) q^{74} +10.0902 q^{76} +(-10.5902 - 18.3427i) q^{77} +(-0.263932 + 0.457144i) q^{79} +(-3.00000 - 5.19615i) q^{80} +0.145898 q^{82} +(5.50000 + 9.52628i) q^{83} +(-3.61803 - 6.26662i) q^{85} +(-1.61803 - 2.80252i) q^{86} +(-5.59017 + 9.68246i) q^{88} +2.00000 q^{89} -17.9443 q^{91} -10.0902 q^{92} +3.85410 q^{94} +(10.0902 + 17.4767i) q^{95} +(-4.50000 - 7.79423i) q^{97} +(3.38197 - 5.85774i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + q^{4} + 4 q^{5} - 4 q^{7}+O(q^{10}) $ 4 * q - q^2 + q^4 + 4 * q^5 - 4 * q^7	$ 4 q - q^{2} + q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{10} - 10 q^{11} + 4 q^{13} - 6 q^{14} + 3 q^{16} + 8 q^{19} + 6 q^{20} + 10 q^{22} - 8 q^{23} + 4 q^{25} - 3 q^{26} + 7 q^{28} + 10 q^{29} + 9 q^{32} + 5 q^{34} - 14 q^{35} + 6 q^{37} - q^{38} + 20 q^{40} - 4 q^{41} - 12 q^{43} + 5 q^{44} + q^{46} + 8 q^{47} - 4 q^{49} + 9 q^{50} + 14 q^{52} + 12 q^{53} - 10 q^{55} - 10 q^{56} + 10 q^{58} - 24 q^{59} - 12 q^{61} + 30 q^{62} + 8 q^{64} + 14 q^{65} - 32 q^{67} - 10 q^{68} - 16 q^{70} + 18 q^{71} + 8 q^{73} + 13 q^{74} + 18 q^{76} - 20 q^{77} - 10 q^{79} - 12 q^{80} + 14 q^{82} + 22 q^{83} - 10 q^{85} - 2 q^{86} + 8 q^{89} - 36 q^{91} - 18 q^{92} + 2 q^{94} + 18 q^{95} - 18 q^{97} + 18 q^{98}+O(q^{100}) $ 4 * q - q^2 + q^4 + 4 * q^5 - 4 * q^7 + 4 * q^10 - 10 * q^11 + 4 * q^13 - 6 * q^14 + 3 * q^16 + 8 * q^19 + 6 * q^20 + 10 * q^22 - 8 * q^23 + 4 * q^25 - 3 * q^26 + 7 * q^28 + 10 * q^29 + 9 * q^32 + 5 * q^34 - 14 * q^35 + 6 * q^37 - q^38 + 20 * q^40 - 4 * q^41 - 12 * q^43 + 5 * q^44 + q^46 + 8 * q^47 - 4 * q^49 + 9 * q^50 + 14 * q^52 + 12 * q^53 - 10 * q^55 - 10 * q^56 + 10 * q^58 - 24 * q^59 - 12 * q^61 + 30 * q^62 + 8 * q^64 + 14 * q^65 - 32 * q^67 - 10 * q^68 - 16 * q^70 + 18 * q^71 + 8 * q^73 + 13 * q^74 + 18 * q^76 - 20 * q^77 - 10 * q^79 - 12 * q^80 + 14 * q^82 + 22 * q^83 - 10 * q^85 - 2 * q^86 + 8 * q^89 - 36 * q^91 - 18 * q^92 + 2 * q^94 + 18 * q^95 - 18 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/603\mathbb{Z}\right)^\times$.

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.309017	+	0.535233i	0.218508	+	0.378467i	0.954352	−	0.298684i	$-0.0965477\pi$
$2$	0.309017	+	0.535233i	0.218508	+	0.378467i	−0.735844	+	0.677151i	$0.763214\pi$
$3$		0			0
$3$		0			0
$4$	0.809017	−	1.40126i	0.404508	−	0.700629i
$5$	3.23607			1.44721			0.723607	−	0.690212i	$-0.242483\pi$
$5$	3.23607			1.44721			0.723607	+	0.690212i	$0.242483\pi$
$6$		0			0
$7$	−2.11803	+	3.66854i	−0.800542	+	1.38658i	0.118718	+	0.992928i	$0.462121\pi$
$7$	−2.11803	+	3.66854i	−0.800542	+	1.38658i	−0.919260	+	0.393651i	$0.871212\pi$
$8$	2.23607			0.790569
$9$		0			0
$10$	1.00000	+	1.73205i	0.316228	+	0.547723i
$11$	−2.50000	+	4.33013i	−0.753778	+	1.30558i	0.192201	+	0.981356i	$0.438437\pi$
$11$	−2.50000	+	4.33013i	−0.753778	+	1.30558i	−0.945979	+	0.324227i	$0.894896\pi$
$12$		0			0
$13$	2.11803	+	3.66854i	0.587437	+	1.01747i	0.994567	+	0.104100i	$0.0331963\pi$
$13$	2.11803	+	3.66854i	0.587437	+	1.01747i	−0.407130	+	0.913370i	$0.633470\pi$
$14$	−2.61803			−0.699699
$15$		0			0
$16$	−0.927051	−	1.60570i	−0.231763	−	0.401425i
$17$	−1.11803	−	1.93649i	−0.271163	−	0.469668i	0.697997	−	0.716101i	$-0.254075\pi$
$17$	−1.11803	−	1.93649i	−0.271163	−	0.469668i	−0.969160	+	0.246433i	$0.920742\pi$
$18$		0			0
$19$	3.11803	+	5.40059i	0.715326	+	1.23898i	0.962834	+	0.270095i	$0.0870551\pi$
$19$	3.11803	+	5.40059i	0.715326	+	1.23898i	−0.247508	+	0.968886i	$0.579612\pi$
$20$	2.61803	−	4.53457i	0.585410	−	1.01396i
$21$		0			0
$22$	−3.09017			−0.658826
$23$	−3.11803	−	5.40059i	−0.650155	−	1.12610i	−0.983085	−	0.183150i	$-0.941371\pi$
$23$	−3.11803	−	5.40059i	−0.650155	−	1.12610i	0.332930	−	0.942952i	$-0.391963\pi$
$24$		0			0
$25$	5.47214			1.09443
$26$	−1.30902	+	2.26728i	−0.256719	+	0.444651i
$27$		0			0
$28$	3.42705	+	5.93583i	0.647652	+	1.12177i
$29$	4.73607	−	8.20311i	0.879466	−	1.52328i	0.0275375	−	0.999621i	$-0.491233\pi$
$29$	4.73607	−	8.20311i	0.879466	−	1.52328i	0.851928	−	0.523659i	$-0.175433\pi$
$30$		0			0
$31$	3.35410	−	5.80948i	0.602414	−	1.04341i	−0.390040	−	0.920798i	$-0.627539\pi$
$31$	3.35410	−	5.80948i	0.602414	−	1.04341i	0.992454	−	0.122615i	$-0.0391279\pi$
$32$	2.80902	−	4.86536i	0.496569	−	0.860082i
$33$		0			0
$34$	0.690983	−	1.19682i	0.118503	−	0.205253i
$35$	−6.85410	+	11.8717i	−1.15855	+	2.00668i
$36$		0			0
$37$	−0.736068	−	1.27491i	−0.121009	−	0.209593i	0.799157	−	0.601122i	$-0.205280\pi$
$37$	−0.736068	−	1.27491i	−0.121009	−	0.209593i	−0.920166	+	0.391529i	$0.871946\pi$
$38$	−1.92705	+	3.33775i	−0.312609	+	0.541455i
$39$		0			0
$40$	7.23607			1.14412
$41$	0.118034	−	0.204441i	0.0184338	−	0.0319283i	−0.856661	−	0.515879i	$-0.827465\pi$
$41$	0.118034	−	0.204441i	0.0184338	−	0.0319283i	0.875095	+	0.483951i	$0.160799\pi$
$42$		0			0
$43$	−5.23607			−0.798493			−0.399246	−	0.916844i	$-0.630728\pi$
$43$	−5.23607			−0.798493			−0.399246	+	0.916844i	$0.630728\pi$
$44$	4.04508	+	7.00629i	0.609820	+	1.05624i
$45$		0			0
$46$	1.92705	−	3.33775i	0.284128	−	0.492124i
$47$	3.11803	−	5.40059i	0.454812	−	0.787757i	−0.543865	−	0.839172i	$-0.683040\pi$
$47$	3.11803	−	5.40059i	0.454812	−	0.787757i	0.998677	+	0.0514150i	$0.0163731\pi$
$48$		0			0
$49$	−5.47214	−	9.47802i	−0.781734	−	1.35400i
$50$	1.69098	+	2.92887i	0.239141	+	0.414205i
$51$		0			0
$52$	6.85410			0.950493
$53$	−3.70820			−0.509361			−0.254680	−	0.967025i	$-0.581970\pi$
$53$	−3.70820			−0.509361			−0.254680	+	0.967025i	$0.581970\pi$
$54$		0			0
$55$	−8.09017	+	14.0126i	−1.09088	+	1.88946i
$56$	−4.73607	+	8.20311i	−0.632884	+	1.09619i
$57$		0			0
$58$	5.85410			0.768681
$59$	−6.00000			−0.781133			−0.390567	−	0.920575i	$-0.627721\pi$
$59$	−6.00000			−0.781133			−0.390567	+	0.920575i	$0.627721\pi$
$60$		0			0
$61$	0.354102	+	0.613323i	0.0453381	+	0.0785279i	0.887804	−	0.460222i	$-0.152230\pi$
$61$	0.354102	+	0.613323i	0.0453381	+	0.0785279i	−0.842466	+	0.538750i	$0.818897\pi$
$62$	4.14590			0.526530
$63$		0			0
$64$	−0.236068			−0.0295085
$65$	6.85410	+	11.8717i	0.850147	+	1.47250i
$66$		0			0
$67$	−8.00000	+	1.73205i	−0.977356	+	0.211604i
$67$	−8.00000	+	1.73205i	−0.977356	+	0.211604i
$68$	−3.61803			−0.438751
$69$		0			0
$70$	−8.47214			−1.01261
$71$	6.73607	−	11.6672i	0.799424	−	1.38464i	−0.120567	−	0.992705i	$-0.538471\pi$
$71$	6.73607	−	11.6672i	0.799424	−	1.38464i	0.919992	−	0.391938i	$-0.128195\pi$
$72$		0			0
$73$	5.35410	+	9.27358i	0.626650	+	1.08539i	0.988219	+	0.153045i	$0.0489079\pi$
$73$	5.35410	+	9.27358i	0.626650	+	1.08539i	−0.361569	+	0.932345i	$0.617759\pi$
$74$	0.454915	−	0.787936i	0.0528828	−	0.0915957i
$75$		0			0
$76$	10.0902			1.15742
$77$	−10.5902	−	18.3427i	−1.20686	−	2.09035i
$78$		0			0
$79$	−0.263932	+	0.457144i	−0.0296947	+	0.0514327i	−0.880491	−	0.474063i	$-0.842787\pi$
$79$	−0.263932	+	0.457144i	−0.0296947	+	0.0514327i	0.850796	+	0.525496i	$0.176120\pi$
$80$	−3.00000	−	5.19615i	−0.335410	−	0.580948i
$81$		0			0
$82$	0.145898			0.0161117
$83$	5.50000	+	9.52628i	0.603703	+	1.04565i	0.992255	+	0.124218i	$0.0396422\pi$
$83$	5.50000	+	9.52628i	0.603703	+	1.04565i	−0.388552	+	0.921427i	$0.627024\pi$
$84$		0			0
$85$	−3.61803	−	6.26662i	−0.392431	−	0.679710i
$86$	−1.61803	−	2.80252i	−0.174477	−	0.302203i
$87$		0			0
$88$	−5.59017	+	9.68246i	−0.595914	+	1.03215i
$89$	2.00000			0.212000			0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000			0.212000			0.106000	+	0.994366i	$0.466196\pi$
$90$		0			0
$91$	−17.9443			−1.88107
$92$	−10.0902			−1.05197
$93$		0			0
$94$	3.85410			0.397520
$95$	10.0902	+	17.4767i	1.03523	+	1.79307i
$96$		0			0
$97$	−4.50000	−	7.79423i	−0.456906	−	0.791384i	0.541890	−	0.840450i	$-0.317709\pi$
$97$	−4.50000	−	7.79423i	−0.456906	−	0.791384i	−0.998796	+	0.0490655i	$0.984376\pi$
$98$	3.38197	−	5.85774i	0.341630	−	0.591721i
$99$		0			0
$100$	4.42705	−	7.66788i	0.442705	−	0.766788i
$101$	−1.26393	+	2.18919i	−0.125766	+	0.217833i	−0.922032	−	0.387113i	$-0.873472\pi$
$101$	−1.26393	+	2.18919i	−0.125766	+	0.217833i	0.796266	+	0.604946i	$0.206805\pi$
$102$		0			0
$103$	−3.73607	+	6.47106i	−0.368126	+	0.637612i	−0.989273	−	0.146082i	$-0.953334\pi$
$103$	−3.73607	+	6.47106i	−0.368126	+	0.637612i	0.621147	+	0.783694i	$0.286667\pi$
$104$	4.73607	+	8.20311i	0.464410	+	0.804381i
$105$		0			0
$106$	−1.14590	−	1.98475i	−0.111299	−	0.192776i
$107$	−11.7082			−1.13187			−0.565937	−	0.824448i	$-0.691486\pi$
$107$	−11.7082			−1.13187			−0.565937	+	0.824448i	$0.691486\pi$
$108$		0			0
$109$	8.94427			0.856706			0.428353	−	0.903612i	$-0.359094\pi$
$109$	8.94427			0.856706			0.428353	+	0.903612i	$0.359094\pi$
$110$	−10.0000			−0.953463
$111$		0			0
$112$	7.85410			0.742143
$113$	5.35410	−	9.27358i	0.503672	−	0.872385i	−0.496319	−	0.868140i	$-0.665316\pi$
$113$	5.35410	−	9.27358i	0.503672	−	0.872385i	0.999991	−	0.00424474i	$-0.00135115\pi$
$114$		0			0
$115$	−10.0902	−	17.4767i	−0.940913	−	1.62971i
$116$	−7.66312	−	13.2729i	−0.711503	−	1.23236i
$117$		0			0
$118$	−1.85410	−	3.21140i	−0.170684	−	0.295633i
$119$	9.47214			0.868309
$120$		0			0
$121$	−7.00000	−	12.1244i	−0.636364	−	1.10221i
$122$	−0.218847	+	0.379054i	−0.0198135	+	0.0343180i
$123$		0			0
$124$	−5.42705	−	9.39993i	−0.487364	−	0.844138i
$125$	1.52786			0.136656
$126$		0			0
$127$	5.59017	−	9.68246i	0.496047	−	0.859179i	−0.503942	−	0.863737i	$-0.668118\pi$
$127$	5.59017	−	9.68246i	0.496047	−	0.859179i	0.999990	+	0.00455811i	$0.00145090\pi$
$128$	−5.69098	−	9.85707i	−0.503017	−	0.871250i
$129$		0			0
$130$	−4.23607	+	7.33708i	−0.371528	+	0.643505i
$131$	−1.52786			−0.133490			−0.0667451	−	0.997770i	$-0.521261\pi$
$131$	−1.52786			−0.133490			−0.0667451	+	0.997770i	$0.521261\pi$
$132$		0			0
$133$	−26.4164			−2.29059
$134$	−3.39919	−	3.74663i	−0.293645	−	0.323660i
$135$		0			0
$136$	−2.50000	−	4.33013i	−0.214373	−	0.371305i
$137$	15.8885			1.35745			0.678725	−	0.734393i	$-0.262533\pi$
$137$	15.8885			1.35745			0.678725	+	0.734393i	$0.262533\pi$
$138$		0			0
$139$	8.94427			0.758643			0.379322	−	0.925265i	$-0.376157\pi$
$139$	8.94427			0.758643			0.379322	+	0.925265i	$0.376157\pi$
$140$	11.0902	+	19.2087i	0.937290	+	1.62343i
$141$		0			0
$142$	8.32624			0.698722
$143$	−21.1803			−1.77119
$144$		0			0
$145$	15.3262	−	26.5458i	1.27277	−	2.20451i
$146$	−3.30902	+	5.73139i	−0.273856	+	0.474333i
$147$		0			0
$148$	−2.38197			−0.195796
$149$	−7.52786			−0.616707			−0.308353	−	0.951272i	$-0.599778\pi$
$149$	−7.52786			−0.616707			−0.308353	+	0.951272i	$0.599778\pi$
$150$		0			0
$151$	−4.11803	−	7.13264i	−0.335121	−	0.580446i	0.648387	−	0.761311i	$-0.275444\pi$
$151$	−4.11803	−	7.13264i	−0.335121	−	0.580446i	−0.983508	+	0.180864i	$0.942110\pi$
$152$	6.97214	+	12.0761i	0.565515	+	0.979501i
$153$		0			0
$154$	6.54508	−	11.3364i	0.527418	−	0.913515i
$155$	10.8541	−	18.7999i	0.871822	−	1.51004i
$156$		0			0
$157$	5.35410	+	9.27358i	0.427304	+	0.740112i	0.996632	−	0.0819980i	$-0.0261301\pi$
$157$	5.35410	+	9.27358i	0.427304	+	0.740112i	−0.569329	+	0.822110i	$0.692797\pi$
$158$	−0.326238			−0.0259541
$159$		0			0
$160$	9.09017	−	15.7446i	0.718641	−	1.24472i
$161$	26.4164			2.08190
$162$		0			0
$163$	−7.73607	+	13.3993i	−0.605936	+	1.04951i	0.385967	+	0.922512i	$0.373868\pi$
$163$	−7.73607	+	13.3993i	−0.605936	+	1.04951i	−0.991903	+	0.126999i	$0.959466\pi$
$164$	−0.190983	−	0.330792i	−0.0149133	−	0.0258305i
$165$		0			0
$166$	−3.39919	+	5.88756i	−0.263828	+	0.456964i
$167$	0.645898	−	1.11873i	0.0499811	−	0.0865698i	−0.839952	−	0.542660i	$-0.817417\pi$
$167$	0.645898	−	1.11873i	0.0499811	−	0.0865698i	0.889934	+	0.456090i	$0.150751\pi$
$168$		0			0
$169$	−2.47214	+	4.28187i	−0.190164	+	0.329374i
$170$	2.23607	−	3.87298i	0.171499	−	0.297044i
$171$		0			0
$172$	−4.23607	+	7.33708i	−0.322997	+	0.559447i
$173$	−1.35410	−	2.34537i	−0.102950	−	0.178315i	0.809949	−	0.586501i	$-0.199495\pi$
$173$	−1.35410	−	2.34537i	−0.102950	−	0.178315i	−0.912899	+	0.408186i	$0.866162\pi$
$174$		0			0
$175$	−11.5902	+	20.0748i	−0.876134	+	1.51751i
$176$	9.27051			0.698791
$177$		0			0
$178$	0.618034	+	1.07047i	0.0463236	+	0.0802348i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$		0			0
$181$	0.500000	−	0.866025i	0.0371647	−	0.0643712i	−0.846845	−	0.531840i	$-0.821501\pi$
$181$	0.500000	−	0.866025i	0.0371647	−	0.0643712i	0.884009	+	0.467469i	$0.154834\pi$
$182$	−5.54508	−	9.60437i	−0.411029	−	0.711923i
$183$		0			0
$184$	−6.97214	−	12.0761i	−0.513993	−	0.890261i
$185$	−2.38197	−	4.12569i	−0.175126	−	0.303326i
$186$		0			0
$187$	11.1803			0.817587
$188$	−5.04508	−	8.73834i	−0.367951	−	0.637309i
$189$		0			0
$190$	−6.23607	+	10.8012i	−0.452412	+	0.783600i
$191$	9.20820	+	15.9491i	0.666282	+	1.15403i	0.978936	+	0.204168i	$0.0654487\pi$
$191$	9.20820	+	15.9491i	0.666282	+	1.15403i	−0.312654	+	0.949867i	$0.601218\pi$
$192$		0			0
$193$	−25.8885			−1.86350			−0.931749	−	0.363103i	$-0.881717\pi$
$193$	−25.8885			−1.86350			−0.931749	+	0.363103i	$0.881717\pi$
$194$	2.78115	−	4.81710i	0.199675	−	0.345847i
$195$		0			0
$196$	−17.7082			−1.26487
$197$	−8.97214	+	15.5402i	−0.639238	+	1.10719i	0.346362	+	0.938101i	$0.387417\pi$
$197$	−8.97214	+	15.5402i	−0.639238	+	1.10719i	−0.985600	+	0.169092i	$0.945916\pi$
$198$		0			0
$199$	11.9721	+	20.7363i	0.848682	+	1.46996i	0.882385	+	0.470529i	$0.155937\pi$
$199$	11.9721	+	20.7363i	0.848682	+	1.46996i	−0.0337024	+	0.999432i	$0.510730\pi$
$200$	12.2361			0.865221
$201$		0			0
$202$	−1.56231			−0.109923
$203$	20.0623	+	34.7489i	1.40810	+	2.43890i
$204$		0			0
$205$	0.381966	−	0.661585i	0.0266777	−	0.0462071i
$206$	−4.61803			−0.321754
$207$		0			0
$208$	3.92705	−	6.80185i	0.272292	−	0.471624i
$209$	−31.1803			−2.15679
$210$		0			0
$211$	−1.73607	−	3.00696i	−0.119516	−	0.207008i	0.800060	−	0.599920i	$-0.204801\pi$
$211$	−1.73607	−	3.00696i	−0.119516	−	0.207008i	−0.919576	+	0.392912i	$0.871468\pi$
$212$	−3.00000	+	5.19615i	−0.206041	+	0.356873i
$213$		0			0
$214$	−3.61803	−	6.26662i	−0.247324	−	0.428377i
$215$	−16.9443			−1.15559
$216$		0			0
$217$	14.2082	+	24.6093i	0.964516	+	1.67059i
$218$	2.76393	+	4.78727i	0.187197	+	0.324235i
$219$		0			0
$220$	13.0902	+	22.6728i	0.882539	+	1.52860i
$221$	4.73607	−	8.20311i	0.318582	−	0.551801i
$222$		0			0
$223$	5.41641			0.362709			0.181355	−	0.983418i	$-0.441952\pi$
$223$	5.41641			0.362709			0.181355	+	0.983418i	$0.441952\pi$
$224$	11.8992	+	20.6100i	0.795048	+	1.37706i
$225$		0			0
$226$	6.61803			0.440225
$227$	3.35410	−	5.80948i	0.222620	−	0.385588i	−0.732983	−	0.680247i	$-0.761873\pi$
$227$	3.35410	−	5.80948i	0.222620	−	0.385588i	0.955603	+	0.294658i	$0.0952059\pi$
$228$		0			0
$229$	−7.20820	−	12.4850i	−0.476332	−	0.825030i	0.523301	−	0.852148i	$-0.324700\pi$
$229$	−7.20820	−	12.4850i	−0.476332	−	0.825030i	−0.999632	+	0.0271177i	$0.991367\pi$
$230$	6.23607	−	10.8012i	0.411194	−	0.712209i
$231$		0			0
$232$	10.5902	−	18.3427i	0.695279	−	1.20426i
$233$	−9.06231	+	15.6964i	−0.593691	+	1.02830i	0.400039	+	0.916498i	$0.368997\pi$
$233$	−9.06231	+	15.6964i	−0.593691	+	1.02830i	−0.993730	+	0.111805i	$0.964337\pi$
$234$		0			0
$235$	10.0902	−	17.4767i	0.658210	−	1.14005i
$236$	−4.85410	+	8.40755i	−0.315975	+	0.547285i
$237$		0			0
$238$	2.92705	+	5.06980i	0.189733	+	0.328626i
$239$	14.5902	−	25.2709i	0.943760	−	1.63464i	0.185544	−	0.982636i	$-0.440595\pi$
$239$	14.5902	−	25.2709i	0.943760	−	1.63464i	0.758216	−	0.652004i	$-0.226071\pi$
$240$		0			0
$241$	6.18034			0.398111			0.199055	−	0.979988i	$-0.436213\pi$
$241$	6.18034			0.398111			0.199055	+	0.979988i	$0.436213\pi$
$242$	4.32624	−	7.49326i	0.278101	−	0.481685i
$243$		0			0
$244$	1.14590			0.0733586
$245$	−17.7082	−	30.6715i	−1.13134	−	1.95953i
$246$		0			0
$247$	−13.2082	+	22.8773i	−0.840418	+	1.45565i
$248$	7.50000	−	12.9904i	0.476250	−	0.824890i
$249$		0			0
$250$	0.472136	+	0.817763i	0.0298605	+	0.0517199i
$251$	−11.6803	−	20.2309i	−0.737257	−	1.27697i	−0.953726	−	0.300676i	$-0.902788\pi$
$251$	−11.6803	−	20.2309i	−0.737257	−	1.27697i	0.216470	−	0.976289i	$-0.430546\pi$
$252$		0			0
$253$	31.1803			1.96029
$254$	6.90983			0.433561
$255$		0			0
$256$	3.28115	−	5.68312i	0.205072	−	0.355195i
$257$	−14.2984	+	24.7655i	−0.891908	+	1.54483i	−0.0543228	+	0.998523i	$0.517300\pi$
$257$	−14.2984	+	24.7655i	−0.891908	+	1.54483i	−0.837585	+	0.546307i	$0.816033\pi$
$258$		0			0
$259$	6.23607			0.387490
$260$	22.1803			1.37557
$261$		0			0
$262$	−0.472136	−	0.817763i	−0.0291687	−	0.0505216i
$263$	−13.1246			−0.809298			−0.404649	−	0.914472i	$-0.632606\pi$
$263$	−13.1246			−0.809298			−0.404649	+	0.914472i	$0.632606\pi$
$264$		0			0
$265$	−12.0000			−0.737154
$266$	−8.16312	−	14.1389i	−0.500513	−	0.866914i
$267$		0			0
$268$	−4.04508	+	12.6113i	−0.247093	+	0.770359i
$269$	−27.8885			−1.70039			−0.850197	−	0.526464i	$-0.823517\pi$
$269$	−27.8885			−1.70039			−0.850197	+	0.526464i	$0.823517\pi$
$270$		0			0
$271$	−24.3607			−1.47981			−0.739903	−	0.672714i	$-0.765129\pi$
$271$	−24.3607			−1.47981			−0.739903	+	0.672714i	$0.765129\pi$
$272$	−2.07295	+	3.59045i	−0.125691	+	0.217703i
$273$		0			0
$274$	4.90983	+	8.50408i	0.296614	+	0.513750i
$275$	−13.6803	+	23.6950i	−0.824956	+	1.42886i
$276$		0			0
$277$	−2.65248			−0.159372			−0.0796859	−	0.996820i	$-0.525392\pi$
$277$	−2.65248			−0.159372			−0.0796859	+	0.996820i	$0.525392\pi$
$278$	2.76393	+	4.78727i	0.165770	+	0.287121i
$279$		0			0
$280$	−15.3262	+	26.5458i	−0.915918	+	1.58642i
$281$	−6.50000	−	11.2583i	−0.387757	−	0.671616i	0.604390	−	0.796689i	$-0.293417\pi$
$281$	−6.50000	−	11.2583i	−0.387757	−	0.671616i	−0.992148	+	0.125073i	$0.960084\pi$
$282$		0			0
$283$	19.7082			1.17153			0.585766	−	0.810481i	$-0.300794\pi$
$283$	19.7082			1.17153			0.585766	+	0.810481i	$0.300794\pi$
$284$	−10.8992	−	18.8779i	−0.646748	−	1.12020i
$285$		0			0
$286$	−6.54508	−	11.3364i	−0.387019	−	0.670337i
$287$	0.500000	+	0.866025i	0.0295141	+	0.0511199i
$288$		0			0
$289$	6.00000	−	10.3923i	0.352941	−	0.611312i
$290$	18.9443			1.11245
$291$		0			0
$292$	17.3262			1.01394
$293$	−10.6525			−0.622324			−0.311162	−	0.950357i	$-0.600718\pi$
$293$	−10.6525			−0.622324			−0.311162	+	0.950357i	$0.600718\pi$
$294$		0			0
$295$	−19.4164			−1.13047
$296$	−1.64590	−	2.85078i	−0.0956659	−	0.165698i
$297$		0			0
$298$	−2.32624	−	4.02916i	−0.134755	−	0.233403i
$299$	13.2082	−	22.8773i	0.763850	−	1.32303i
$300$		0			0
$301$	11.0902	−	19.2087i	0.639227	−	1.10717i
$302$	2.54508	−	4.40822i	0.146453	−	0.253664i
$303$		0			0
$304$	5.78115	−	10.0133i	0.331572	−	0.574299i
$305$	1.14590	+	1.98475i	0.0656139	+	0.113647i
$306$		0			0
$307$	−0.444272	−	0.769502i	−0.0253559	−	0.0439178i	0.853069	−	0.521798i	$-0.174739\pi$
$307$	−0.444272	−	0.769502i	−0.0253559	−	0.0439178i	−0.878425	+	0.477880i	$0.841405\pi$
$308$	−34.2705			−1.95274
$309$		0			0
$310$	13.4164			0.762001
$311$	26.9443			1.52787			0.763935	−	0.645294i	$-0.223265\pi$
$311$	26.9443			1.52787			0.763935	+	0.645294i	$0.223265\pi$
$312$		0			0
$313$	16.6525			0.941254			0.470627	−	0.882332i	$-0.344028\pi$
$313$	16.6525			0.941254			0.470627	+	0.882332i	$0.344028\pi$
$314$	−3.30902	+	5.73139i	−0.186739	+	0.323441i
$315$		0			0
$316$	0.427051	+	0.739674i	0.0240235	+	0.0416099i
$317$	14.3541	+	24.8620i	0.806207	+	1.39639i	0.915473	+	0.402378i	$0.131816\pi$
$317$	14.3541	+	24.8620i	0.806207	+	1.39639i	−0.109267	+	0.994012i	$0.534850\pi$
$318$		0			0
$319$	23.6803	+	41.0156i	1.32584	+	2.29643i
$320$	−0.763932			−0.0427051
$321$		0			0
$322$	8.16312	+	14.1389i	0.454913	+	0.787932i
$323$	6.97214	−	12.0761i	0.387940	−	0.671932i
$324$		0			0
$325$	11.5902	+	20.0748i	0.642907	+	1.11355i
$326$	−9.56231			−0.529607
$327$		0			0
$328$	0.263932	−	0.457144i	0.0145732	−	0.0252415i
$329$	13.2082	+	22.8773i	0.728192	+	1.26127i
$330$		0			0
$331$	−5.26393	+	9.11740i	−0.289332	+	0.501138i	−0.973650	−	0.228046i	$-0.926766\pi$
$331$	−5.26393	+	9.11740i	−0.289332	+	0.501138i	0.684319	+	0.729183i	$0.260100\pi$
$332$	17.7984			0.976813
$333$		0			0
$334$	0.798374			0.0436851
$335$	−25.8885	+	5.60503i	−1.41444	+	0.306236i
$336$		0			0
$337$	4.20820	+	7.28882i	0.229235	+	0.397047i	0.957582	−	0.288162i	$-0.0930441\pi$
$337$	4.20820	+	7.28882i	0.229235	+	0.397047i	−0.728346	+	0.685209i	$0.759711\pi$
$338$	−3.05573			−0.166210
$339$		0			0
$340$	−11.7082			−0.634967
$341$	16.7705	+	29.0474i	0.908174	+	1.57300i
$342$		0			0
$343$	16.7082			0.902158
$344$	−11.7082			−0.631264
$345$		0			0
$346$	0.836881	−	1.44952i	0.0449910	−	0.0779267i
$347$	−5.11803	+	8.86469i	−0.274750	+	0.475882i	−0.970072	−	0.242817i	$-0.921929\pi$
$347$	−5.11803	+	8.86469i	−0.274750	+	0.475882i	0.695322	+	0.718699i	$0.255262\pi$
$348$		0			0
$349$	−28.0689			−1.50249			−0.751246	−	0.660022i	$-0.770547\pi$
$349$	−28.0689			−1.50249			−0.751246	+	0.660022i	$0.770547\pi$
$350$	−14.3262			−0.765770
$351$		0			0
$352$	14.0451	+	24.3268i	0.748606	+	1.29662i
$353$	3.26393	+	5.65330i	0.173722	+	0.300895i	0.939718	−	0.341950i	$-0.111087\pi$
$353$	3.26393	+	5.65330i	0.173722	+	0.300895i	−0.765997	+	0.642845i	$0.777754\pi$
$354$		0			0
$355$	21.7984	−	37.7559i	1.15694	−	2.00387i
$356$	1.61803	−	2.80252i	0.0857556	−	0.148533i
$357$		0			0
$358$		0			0
$359$	−1.34752			−0.0711196			−0.0355598	−	0.999368i	$-0.511321\pi$
$359$	−1.34752			−0.0711196			−0.0355598	+	0.999368i	$0.511321\pi$
$360$		0			0
$361$	−9.94427	+	17.2240i	−0.523383	+	0.906525i
$362$	0.618034			0.0324831
$363$		0			0
$364$	−14.5172	+	25.1446i	−0.760909	+	1.31793i
$365$	17.3262	+	30.0099i	0.906897	+	1.57079i
$366$		0			0
$367$	9.68034	−	16.7668i	0.505310	−	0.875222i	−0.494672	−	0.869080i	$-0.664712\pi$
$367$	9.68034	−	16.7668i	0.505310	−	0.875222i	0.999981	−	0.00614192i	$-0.00195505\pi$
$368$	−5.78115	+	10.0133i	−0.301363	+	0.521977i
$369$		0			0
$370$	1.47214	−	2.54981i	0.0765327	−	0.132559i
$371$	7.85410	−	13.6037i	0.407765	−	0.706269i
$372$		0			0
$373$	−1.73607	+	3.00696i	−0.0898902	+	0.155694i	−0.907465	−	0.420129i	$-0.861985\pi$
$373$	−1.73607	+	3.00696i	−0.0898902	+	0.155694i	0.817574	+	0.575823i	$0.195318\pi$
$374$	3.45492	+	5.98409i	0.178649	+	0.309430i
$375$		0			0
$376$	6.97214	−	12.0761i	0.359560	−	0.622777i
$377$	40.1246			2.06652
$378$		0			0
$379$	8.26393	+	14.3136i	0.424490	+	0.735238i	0.996373	−	0.0850975i	$-0.0271202\pi$
$379$	8.26393	+	14.3136i	0.424490	+	0.735238i	−0.571883	+	0.820335i	$0.693787\pi$
$380$	32.6525			1.67504
$381$		0			0
$382$	−5.69098	+	9.85707i	−0.291176	+	0.504332i
$383$	−4.26393	−	7.38535i	−0.217877	−	0.377374i	0.736282	−	0.676675i	$-0.236580\pi$
$383$	−4.26393	−	7.38535i	−0.217877	−	0.377374i	−0.954159	+	0.299301i	$0.903246\pi$
$384$		0			0
$385$	−34.2705	−	59.3583i	−1.74659	−	3.02518i
$386$	−8.00000	−	13.8564i	−0.407189	−	0.705273i
$387$		0			0
$388$	−14.5623			−0.739289
$389$	−2.50000	−	4.33013i	−0.126755	−	0.219546i	0.795663	−	0.605740i	$-0.207123\pi$
$389$	−2.50000	−	4.33013i	−0.126755	−	0.219546i	−0.922418	+	0.386194i	$0.873790\pi$
$390$		0			0
$391$	−6.97214	+	12.0761i	−0.352596	+	0.610714i
$392$	−12.2361	−	21.1935i	−0.618015	−	1.07043i
$393$		0			0
$394$	−11.0902			−0.558715
$395$	−0.854102	+	1.47935i	−0.0429745	+	0.0744341i
$396$		0			0
$397$	−7.88854			−0.395915			−0.197957	−	0.980211i	$-0.563431\pi$
$397$	−7.88854			−0.395915			−0.197957	+	0.980211i	$0.563431\pi$
$398$	−7.39919	+	12.8158i	−0.370888	+	0.642396i
$399$		0			0
$400$	−5.07295	−	8.78661i	−0.253647	−	0.439330i
$401$	−8.94427			−0.446656			−0.223328	−	0.974743i	$-0.571692\pi$
$401$	−8.94427			−0.446656			−0.223328	+	0.974743i	$0.571692\pi$
$402$		0			0
$403$	28.4164			1.41552
$404$	2.04508	+	3.54219i	0.101747	+	0.176231i
$405$		0			0
$406$	−12.3992	+	21.4760i	−0.615361	+	1.06584i
$407$	7.36068			0.364855
$408$		0			0
$409$	8.97214	−	15.5402i	0.443644	−	0.768413i	−0.554313	−	0.832308i	$-0.687019\pi$
$409$	8.97214	−	15.5402i	0.443644	−	0.768413i	0.997957	+	0.0638951i	$0.0203523\pi$
$410$	0.472136			0.0233171
$411$		0			0
$412$	6.04508	+	10.4704i	0.297820	+	0.515839i
$413$	12.7082	−	22.0113i	0.625330	−	1.08310i
$414$		0			0
$415$	17.7984	+	30.8277i	0.873688	+	1.51327i
$416$	23.7984			1.16681
$417$		0			0
$418$	−9.63525	−	16.6888i	−0.471276	−	0.816273i
$419$	−2.82624	−	4.89519i	−0.138071	−	0.239146i	0.788696	−	0.614784i	$-0.210757\pi$
$419$	−2.82624	−	4.89519i	−0.138071	−	0.239146i	−0.926766	+	0.375638i	$0.877423\pi$
$420$		0			0
$421$	1.59017	+	2.75426i	0.0775001	+	0.134234i	0.902171	−	0.431379i	$-0.141973\pi$
$421$	1.59017	+	2.75426i	0.0775001	+	0.134234i	−0.824671	+	0.565613i	$0.808640\pi$
$422$	1.07295	−	1.85840i	0.0522303	−	0.0904656i
$423$		0			0
$424$	−8.29180			−0.402685
$425$	−6.11803	−	10.5967i	−0.296768	−	0.514018i
$426$		0			0
$427$	−3.00000			−0.145180
$428$	−9.47214	+	16.4062i	−0.457853	+	0.793025i
$429$		0			0
$430$	−5.23607	−	9.06914i	−0.252506	−	0.437353i
$431$	12.5344	−	21.7103i	0.603763	−	1.04575i	−0.388483	−	0.921456i	$-0.627001\pi$
$431$	12.5344	−	21.7103i	0.603763	−	1.04575i	0.992246	−	0.124292i	$-0.0396659\pi$
$432$		0			0
$433$	13.8820	−	24.0443i	0.667125	−	1.15549i	−0.311580	−	0.950220i	$-0.600858\pi$
$433$	13.8820	−	24.0443i	0.667125	−	1.15549i	0.978705	−	0.205274i	$-0.0658085\pi$
$434$	−8.78115	+	15.2094i	−0.421509	+	0.730075i
$435$		0			0
$436$	7.23607	−	12.5332i	0.346545	−	0.600233i
$437$	19.4443	−	33.6785i	0.930146	−	1.61106i
$438$		0			0
$439$	17.2984	+	29.9617i	0.825606	+	1.42999i	0.901455	+	0.432873i	$0.142500\pi$
$439$	17.2984	+	29.9617i	0.825606	+	1.42999i	−0.0758487	+	0.997119i	$0.524167\pi$
$440$	−18.0902	+	31.3331i	−0.862415	+	1.49375i
$441$		0			0
$442$	5.85410			0.278451
$443$	6.20820	−	10.7529i	0.294961	−	0.510887i	−0.680015	−	0.733198i	$-0.738027\pi$
$443$	6.20820	−	10.7529i	0.294961	−	0.510887i	0.974976	+	0.222311i	$0.0713601\pi$
$444$		0			0
$445$	6.47214			0.306809
$446$	1.67376	+	2.89904i	0.0792549	+	0.137274i
$447$		0			0
$448$	0.500000	−	0.866025i	0.0236228	−	0.0409159i
$449$	2.59017	−	4.48631i	0.122238	−	0.211722i	−0.798412	−	0.602111i	$-0.794326\pi$
$449$	2.59017	−	4.48631i	0.122238	−	0.211722i	0.920650	+	0.390389i	$0.127660\pi$
$450$		0			0
$451$	0.590170	+	1.02220i	0.0277900	+	0.0481337i
$452$	−8.66312	−	15.0050i	−0.407479	−	0.705774i
$453$		0			0
$454$	4.14590			0.194577
$455$	−58.0689			−2.72231
$456$		0			0
$457$	6.35410	−	11.0056i	0.297232	−	0.514822i	−0.678269	−	0.734813i	$-0.737270\pi$
$457$	6.35410	−	11.0056i	0.297232	−	0.514822i	0.975502	+	0.219992i	$0.0706031\pi$
$458$	4.45492	−	7.71614i	0.208165	−	0.360552i
$459$		0			0
$460$	−32.6525			−1.52243
$461$	−25.5279			−1.18895			−0.594476	−	0.804114i	$-0.702640\pi$
$461$	−25.5279			−1.18895			−0.594476	+	0.804114i	$0.702640\pi$
$462$		0			0
$463$	−8.59017	−	14.8786i	−0.399219	−	0.691468i	0.594411	−	0.804162i	$-0.297385\pi$
$463$	−8.59017	−	14.8786i	−0.399219	−	0.691468i	−0.993630	+	0.112694i	$0.964052\pi$
$464$	−17.5623			−0.815310
$465$		0			0
$466$	−11.2016			−0.518905
$467$	1.06231	+	1.83997i	0.0491577	+	0.0851436i	0.889557	−	0.456824i	$-0.151013\pi$
$467$	1.06231	+	1.83997i	0.0491577	+	0.0851436i	−0.840400	+	0.541967i	$0.817680\pi$
$468$		0			0
$469$	10.5902	−	33.0169i	0.489009	−	1.52458i
$470$	12.4721			0.575297
$471$		0			0
$472$	−13.4164			−0.617540
$473$	13.0902	−	22.6728i	0.601887	−	1.04250i
$474$		0			0
$475$	17.0623	+	29.5528i	0.782872	+	1.35597i
$476$	7.66312	−	13.2729i	0.351238	−	0.608363i
$477$		0			0
$478$	18.0344			0.824876
$479$	2.02786	+	3.51236i	0.0926555	+	0.160484i	0.908628	−	0.417607i	$-0.137131\pi$
$479$	2.02786	+	3.51236i	0.0926555	+	0.160484i	−0.815972	+	0.578091i	$0.803798\pi$
$480$		0			0
$481$	3.11803	−	5.40059i	0.142170	−	0.246246i
$482$	1.90983	+	3.30792i	0.0869904	+	0.150672i
$483$		0			0
$484$	−22.6525			−1.02966
$485$	−14.5623	−	25.2227i	−0.661240	−	1.14530i
$486$		0			0
$487$	4.79180	+	8.29963i	0.217137	+	0.376092i	0.953932	−	0.300024i	$-0.0969948\pi$
$487$	4.79180	+	8.29963i	0.217137	+	0.376092i	−0.736795	+	0.676117i	$0.763661\pi$
$488$	0.791796	+	1.37143i	0.0358429	+	0.0620818i
$489$		0			0
$490$	10.9443	−	18.9560i	0.494412	−	0.856346i
$491$	−18.2918			−0.825497			−0.412749	−	0.910845i	$-0.635431\pi$
$491$	−18.2918			−0.825497			−0.412749	+	0.910845i	$0.635431\pi$
$492$		0			0
$493$	−21.1803			−0.953915
$494$	−16.3262			−0.734552
$495$		0			0
$496$	−12.4377			−0.558469
$497$	28.5344	+	49.4231i	1.27994	+	2.21693i
$498$		0			0
$499$	−0.590170	−	1.02220i	−0.0264196	−	0.0457602i	0.852513	−	0.522706i	$-0.175077\pi$
$499$	−0.590170	−	1.02220i	−0.0264196	−	0.0457602i	−0.878933	+	0.476945i	$0.841744\pi$
$500$	1.23607	−	2.14093i	0.0552786	−	0.0957454i
$501$		0			0
$502$	7.21885	−	12.5034i	0.322193	−	0.558054i
$503$	6.20820	−	10.7529i	0.276810	−	0.479449i	−0.693780	−	0.720187i	$-0.744056\pi$
$503$	6.20820	−	10.7529i	0.276810	−	0.479449i	0.970590	+	0.240738i	$0.0773894\pi$
$504$		0			0
$505$	−4.09017	+	7.08438i	−0.182010	+	0.315251i
$506$	9.63525	+	16.6888i	0.428339	+	0.741905i
$507$		0			0
$508$	−9.04508	−	15.6665i	−0.401311	−	0.695091i
$509$	16.2918			0.722121			0.361061	−	0.932542i	$-0.382415\pi$
$509$	16.2918			0.722121			0.361061	+	0.932542i	$0.382415\pi$
$510$		0			0
$511$	−45.3607			−2.00664
$512$	−18.7082			−0.826794
$513$		0			0
$514$	−17.6738			−0.779556
$515$	−12.0902	+	20.9408i	−0.532757	+	0.922761i
$516$		0			0
$517$	15.5902	+	27.0030i	0.685655	+	1.18759i
$518$	1.92705	+	3.33775i	0.0846698	+	0.146652i
$519$		0			0
$520$	15.3262	+	26.5458i	0.672100	+	1.16411i
$521$	4.47214			0.195928			0.0979639	−	0.995190i	$-0.468767\pi$
$521$	4.47214			0.195928			0.0979639	+	0.995190i	$0.468767\pi$
$522$		0			0
$523$	−10.8820	−	18.8481i	−0.475835	−	0.824171i	0.523782	−	0.851853i	$-0.324521\pi$
$523$	−10.8820	−	18.8481i	−0.475835	−	0.824171i	−0.999617	+	0.0276819i	$0.991187\pi$
$524$	−1.23607	+	2.14093i	−0.0539979	+	0.0935271i
$525$		0			0
$526$	−4.05573	−	7.02473i	−0.176838	−	0.306293i
$527$	−15.0000			−0.653410
$528$		0			0
$529$	−7.94427	+	13.7599i	−0.345403	+	0.598256i
$530$	−3.70820	−	6.42280i	−0.161074	−	0.278989i
$531$		0			0
$532$	−21.3713	+	37.0162i	−0.926564	+	1.60486i
$533$	1.00000			0.0433148
$534$		0			0
$535$	−37.8885			−1.63806
$536$	−17.8885	+	3.87298i	−0.772667	+	0.167287i
$537$		0			0
$538$	−8.61803	−	14.9269i	−0.371550	−	0.643543i
$539$	54.7214			2.35702
$540$		0			0
$541$	29.1246			1.25216			0.626082	−	0.779757i	$-0.284657\pi$
$541$	29.1246			1.25216			0.626082	+	0.779757i	$0.284657\pi$
$542$	−7.52786	−	13.0386i	−0.323349	−	0.560058i
$543$		0			0
$544$	−12.5623			−0.538604
$545$	28.9443			1.23984
$546$		0			0
$547$	−3.91641	+	6.78342i	−0.167454	+	0.290038i	−0.937524	−	0.347921i	$-0.886888\pi$
$547$	−3.91641	+	6.78342i	−0.167454	+	0.290038i	0.770070	+	0.637959i	$0.220221\pi$
$548$	12.8541	−	22.2640i	0.549100	−	0.951069i
$549$		0			0
$550$	−16.9098			−0.721038
$551$	59.0689			2.51642
$552$		0			0
$553$	−1.11803	−	1.93649i	−0.0475436	−	0.0823480i
$554$	−0.819660	−	1.41969i	−0.0348240	−	0.0603170i
$555$		0			0
$556$	7.23607	−	12.5332i	0.306878	−	0.531528i
$557$	−14.6803	+	25.4271i	−0.622026	+	1.07738i	0.367082	+	0.930189i	$0.380357\pi$
$557$	−14.6803	+	25.4271i	−0.622026	+	1.07738i	−0.989108	+	0.147192i	$0.952976\pi$
$558$		0			0
$559$	−11.0902	−	19.2087i	−0.469064	−	0.812443i
$560$	25.4164			1.07404
$561$		0			0
$562$	4.01722	−	6.95803i	0.169456	−	0.293507i
$563$	−22.5410			−0.949991			−0.474995	−	0.879988i	$-0.657550\pi$
$563$	−22.5410			−0.949991			−0.474995	+	0.879988i	$0.657550\pi$
$564$		0			0
$565$	17.3262	−	30.0099i	0.728920	−	1.26253i
$566$	6.09017	+	10.5485i	0.255989	+	0.443386i
$567$		0			0
$568$	15.0623	−	26.0887i	0.632000	−	1.09466i
$569$	−1.20820	+	2.09267i	−0.0506505	+	0.0877293i	−0.890239	−	0.455494i	$-0.849463\pi$
$569$	−1.20820	+	2.09267i	−0.0506505	+	0.0877293i	0.839589	+	0.543223i	$0.182796\pi$
$570$		0			0
$571$	−12.1180	+	20.9891i	−0.507124	+	0.878364i	0.492842	+	0.870119i	$0.335958\pi$
$571$	−12.1180	+	20.9891i	−0.507124	+	0.878364i	−0.999966	+	0.00824564i	$0.997375\pi$
$572$	−17.1353	+	29.6791i	−0.716461	+	1.24095i
$573$		0			0
$574$	−0.309017	+	0.535233i	−0.0128981	+	0.0223402i
$575$	−17.0623	−	29.5528i	−0.711547	−	1.23244i
$576$		0			0
$577$	0.263932	−	0.457144i	0.0109876	−	0.0190311i	−0.860479	−	0.509485i	$-0.829836\pi$
$577$	0.263932	−	0.457144i	0.0109876	−	0.0190311i	0.871467	+	0.490454i	$0.163169\pi$
$578$	7.41641			0.308482
$579$		0			0
$580$	−24.7984	−	42.9520i	−1.02970	−	1.78349i
$581$	−46.5967			−1.93316
$582$		0			0
$583$	9.27051	−	16.0570i	0.383945	−	0.665013i
$584$	11.9721	+	20.7363i	0.495411	+	0.858076i
$585$		0			0
$586$	−3.29180	−	5.70156i	−0.135983	−	0.235529i
$587$	−9.82624	−	17.0195i	−0.405572	−	0.702472i	0.588816	−	0.808267i	$-0.299594\pi$
$587$	−9.82624	−	17.0195i	−0.405572	−	0.702472i	−0.994388	+	0.105796i	$0.966261\pi$
$588$		0			0
$589$	41.8328			1.72369
$590$	−6.00000	−	10.3923i	−0.247016	−	0.427844i
$591$		0			0
$592$	−1.36475	+	2.36381i	−0.0560907	+	0.0971519i
$593$	15.6803	+	27.1591i	0.643914	+	1.11529i	0.984551	+	0.175097i	$0.0560240\pi$
$593$	15.6803	+	27.1591i	0.643914	+	1.11529i	−0.340637	+	0.940195i	$0.610643\pi$
$594$		0			0
$595$	30.6525			1.25663
$596$	−6.09017	+	10.5485i	−0.249463	+	0.432083i
$597$		0			0
$598$	16.3262			0.667630
$599$	−15.3541	+	26.5941i	−0.627352	+	1.08660i	0.360729	+	0.932670i	$0.382528\pi$
$599$	−15.3541	+	26.5941i	−0.627352	+	1.08660i	−0.988081	+	0.153934i	$0.950806\pi$
$600$		0			0
$601$	−19.3541	−	33.5223i	−0.789470	−	1.36740i	−0.926292	−	0.376807i	$-0.877022\pi$
$601$	−19.3541	−	33.5223i	−0.789470	−	1.36740i	0.136822	−	0.990596i	$-0.456311\pi$
$602$	13.7082			0.558705
$603$		0			0
$604$	−13.3262			−0.542237
$605$	−22.6525	−	39.2352i	−0.920954	−	1.59514i
$606$		0			0
$607$	−1.20820	+	2.09267i	−0.0490395	+	0.0849389i	−0.889503	−	0.456929i	$-0.848949\pi$
$607$	−1.20820	+	2.09267i	−0.0490395	+	0.0849389i	0.840464	+	0.541868i	$0.182283\pi$
$608$	35.0344			1.42083
$609$		0			0
$610$	−0.708204	+	1.22665i	−0.0286743	+	0.0496654i
$611$	26.4164			1.06869
$612$		0			0
$613$	−6.68034	−	11.5707i	−0.269816	−	0.467336i	0.698998	−	0.715124i	$-0.253630\pi$
$613$	−6.68034	−	11.5707i	−0.269816	−	0.467336i	−0.968814	+	0.247788i	$0.920296\pi$
$614$	0.274575	−	0.475578i	0.0110810	−	0.0191928i
$615$		0			0
$616$	−23.6803	−	41.0156i	−0.954108	−	1.65256i
$617$	2.29180			0.0922642			0.0461321	−	0.998935i	$-0.485310\pi$
$617$	2.29180			0.0922642			0.0461321	+	0.998935i	$0.485310\pi$
$618$		0			0
$619$	18.3541	+	31.7902i	0.737714	+	1.27776i	0.953522	+	0.301322i	$0.0974279\pi$
$619$	18.3541	+	31.7902i	0.737714	+	1.27776i	−0.215809	+	0.976436i	$0.569239\pi$
$620$	−17.5623	−	30.4188i	−0.705319	−	1.22165i
$621$		0			0
$622$	8.32624	+	14.4215i	0.333852	+	0.578248i
$623$	−4.23607	+	7.33708i	−0.169714	+	0.293954i
$624$		0			0
$625$	−22.4164			−0.896656
$626$	5.14590	+	8.91296i	0.205671	+	0.356233i
$627$		0			0
$628$	17.3262			0.691392
$629$	−1.64590	+	2.85078i	−0.0656263	+	0.113668i
$630$		0			0
$631$	−22.4443	−	38.8746i	−0.893492	−	1.54757i	−0.835659	−	0.549248i	$-0.814914\pi$
$631$	−22.4443	−	38.8746i	−0.893492	−	1.54757i	−0.0578329	−	0.998326i	$-0.518419\pi$
$632$	−0.590170	+	1.02220i	−0.0234757	+	0.0406611i
$633$		0			0
$634$	−8.87132	+	15.3656i	−0.352325	+	0.610245i
$635$	18.0902	−	31.3331i	0.717886	−	1.24342i
$636$		0			0
$637$	23.1803	−	40.1495i	0.918439	−	1.59078i
$638$	−14.6353	+	25.3490i	−0.579415	+	1.00358i
$639$		0			0
$640$	−18.4164	−	31.8982i	−0.727972	−	1.26089i
$641$	−13.4098	+	23.2265i	−0.529656	+	0.917392i	0.469745	+	0.882802i	$0.344346\pi$
$641$	−13.4098	+	23.2265i	−0.529656	+	0.917392i	−0.999402	+	0.0345898i	$0.988988\pi$
$642$		0			0
$643$	−21.7082			−0.856088			−0.428044	−	0.903758i	$-0.640797\pi$
$643$	−21.7082			−0.856088			−0.428044	+	0.903758i	$0.640797\pi$
$644$	21.3713	−	37.0162i	0.842148	−	1.45864i
$645$		0			0
$646$	8.61803			0.339072
$647$	17.1180	+	29.6493i	0.672979	+	1.16563i	0.977055	+	0.212987i	$0.0683191\pi$
$647$	17.1180	+	29.6493i	0.672979	+	1.16563i	−0.304076	+	0.952648i	$0.598348\pi$
$648$		0			0
$649$	15.0000	−	25.9808i	0.588802	−	1.01983i
$650$	−7.16312	+	12.4069i	−0.280961	+	0.486638i
$651$		0			0
$652$	12.5172	+	21.6805i	0.490212	+	0.849072i
$653$	9.88197	+	17.1161i	0.386711	+	0.669803i	0.992005	−	0.126199i	$-0.0402777\pi$
$653$	9.88197	+	17.1161i	0.386711	+	0.669803i	−0.605294	+	0.796002i	$0.706944\pi$
$654$		0			0
$655$	−4.94427			−0.193189
$656$	−0.437694			−0.0170891
$657$		0			0
$658$	−8.16312	+	14.1389i	−0.318232	+	0.551193i
$659$	−13.3885	+	23.1896i	−0.521544	+	0.903340i	0.478142	+	0.878282i	$0.341310\pi$
$659$	−13.3885	+	23.1896i	−0.521544	+	0.903340i	−0.999686	+	0.0250577i	$0.992023\pi$
$660$		0			0
$661$	8.36068			0.325193			0.162596	−	0.986693i	$-0.448013\pi$
$661$	8.36068			0.325193			0.162596	+	0.986693i	$0.448013\pi$
$662$	−6.50658			−0.252885
$663$		0			0
$664$	12.2984	+	21.3014i	0.477269	+	0.826655i
$665$	−85.4853			−3.31498
$666$		0			0
$667$	−59.0689			−2.28716
$668$	−1.04508	−	1.81014i	−0.0404356	−	0.0700364i
$669$		0			0
$670$	−11.0000	−	12.1244i	−0.424967	−	0.468405i
$671$	−3.54102			−0.136700
$672$		0			0
$673$	26.3607			1.01613			0.508065	−	0.861319i	$-0.330361\pi$
$673$	26.3607			1.01613			0.508065	+	0.861319i	$0.330361\pi$
$674$	−2.60081	+	4.50474i	−0.100180	+	0.173516i
$675$		0			0
$676$	4.00000	+	6.92820i	0.153846	+	0.266469i
$677$	1.73607	−	3.00696i	0.0667225	−	0.115567i	−0.830734	−	0.556669i	$-0.812079\pi$
$677$	1.73607	−	3.00696i	0.0667225	−	0.115567i	0.897457	+	0.441102i	$0.145412\pi$
$678$		0			0
$679$	38.1246			1.46309
$680$	−8.09017	−	14.0126i	−0.310244	−	0.537358i
$681$		0			0
$682$	−10.3647	+	17.9523i	−0.396887	+	0.687428i
$683$	3.11803	+	5.40059i	0.119308	+	0.206648i	0.919494	−	0.393105i	$-0.128599\pi$
$683$	3.11803	+	5.40059i	0.119308	+	0.206648i	−0.800185	+	0.599753i	$0.795266\pi$
$684$		0			0
$685$	51.4164			1.96452
$686$	5.16312	+	8.94278i	0.197129	+	0.341437i
$687$		0			0
$688$	4.85410	+	8.40755i	0.185061	+	0.320535i
$689$	−7.85410	−	13.6037i	−0.299217	−	0.518260i
$690$		0			0
$691$	0.555728	−	0.962549i	0.0211409	−	0.0366171i	−0.855261	−	0.518197i	$-0.826603\pi$
$691$	0.555728	−	0.962549i	0.0211409	−	0.0366171i	0.876402	+	0.481580i	$0.159937\pi$
$692$	−4.38197			−0.166577
$693$		0			0
$694$	−6.32624			−0.240141
$695$	28.9443			1.09792
$696$		0			0
$697$	−0.527864			−0.0199943
$698$	−8.67376	−	15.0234i	−0.328307	−	0.568644i
$699$		0			0
$700$	18.7533	+	32.4816i	0.708808	+	1.22769i
$701$	−12.2639	+	21.2418i	−0.463202	+	0.802290i	−0.999118	−	0.0419813i	$-0.986633\pi$
$701$	−12.2639	+	21.2418i	−0.463202	+	0.802290i	0.535916	+	0.844271i	$0.319966\pi$
$702$		0			0
$703$	4.59017	−	7.95041i	0.173122	−	0.299855i
$704$	0.590170	−	1.02220i	0.0222429	−	0.0385258i
$705$		0			0
$706$	−2.01722	+	3.49393i	−0.0759191	+	0.131496i
$707$	−5.35410	−	9.27358i	−0.201362	−	0.348769i
$708$		0			0
$709$	13.0623	+	22.6246i	0.490565	+	0.849684i	0.999941	−	0.0108603i	$-0.00345702\pi$
$709$	13.0623	+	22.6246i	0.490565	+	0.849684i	−0.509376	+	0.860544i	$0.670124\pi$
$710$	26.9443			1.01120
$711$		0			0
$712$	4.47214			0.167600
$713$	−41.8328			−1.56665
$714$		0			0
$715$	−68.5410			−2.56329
$716$		0			0
$717$		0			0
$718$	−0.416408	−	0.721240i	−0.0155402	−	0.0269164i
$719$	10.6459	+	18.4392i	0.397025	+	0.687667i	0.993357	−	0.115070i	$-0.0367093\pi$
$719$	10.6459	+	18.4392i	0.397025	+	0.687667i	−0.596332	+	0.802738i	$0.703376\pi$
$720$		0			0
$721$	−15.8262	−	27.4118i	−0.589400	−	1.02087i
$722$	−12.2918			−0.457453
$723$		0			0
$724$	−0.809017	−	1.40126i	−0.0300669	−	0.0520774i
$725$	25.9164	−	44.8885i	0.962511	−	1.66712i
$726$		0			0
$727$	−2.68034	−	4.64248i	−0.0994083	−	0.172180i	0.812032	−	0.583613i	$-0.198362\pi$
$727$	−2.68034	−	4.64248i	−0.0994083	−	0.172180i	−0.911440	+	0.411433i	$0.865028\pi$
$728$	−40.1246			−1.48712
$729$		0			0
$730$	−10.7082	+	18.5472i	−0.396328	+	0.686461i
$731$	5.85410	+	10.1396i	0.216522	+	0.375027i
$732$		0			0
$733$	−16.6803	+	28.8912i	−0.616102	+	1.06712i	0.374088	+	0.927393i	$0.377956\pi$
$733$	−16.6803	+	28.8912i	−0.616102	+	1.06712i	−0.990190	+	0.139727i	$0.955377\pi$
$734$	11.9656			0.441657
$735$		0			0
$736$	−35.0344			−1.29139
$737$	12.5000	−	38.9711i	0.460443	−	1.43552i
$738$		0			0
$739$	−4.35410	−	7.54153i	−0.160168	−	0.277420i	0.774761	−	0.632255i	$-0.217870\pi$
$739$	−4.35410	−	7.54153i	−0.160168	−	0.277420i	−0.934929	+	0.354835i	$0.884537\pi$
$740$	−7.70820			−0.283359
$741$		0			0
$742$	9.70820			0.356399
$743$	−6.40983	−	11.1022i	−0.235154	−	0.407298i	0.724164	−	0.689628i	$-0.242226\pi$
$743$	−6.40983	−	11.1022i	−0.235154	−	0.407298i	−0.959317	+	0.282330i	$0.908893\pi$
$744$		0			0
$745$	−24.3607			−0.892506
$746$	−2.14590			−0.0785669
$747$		0			0
$748$	9.04508	−	15.6665i	0.330721	−	0.572826i
$749$	24.7984	−	42.9520i	0.906113	−	1.56943i
$750$		0			0
$751$	−7.34752			−0.268115			−0.134057	−	0.990974i	$-0.542801\pi$
$751$	−7.34752			−0.268115			−0.134057	+	0.990974i	$0.542801\pi$
$752$	−11.5623			−0.421634
$753$		0			0
$754$	12.3992	+	21.4760i	0.451552	+	0.782111i
$755$	−13.3262	−	23.0817i	−0.484991	−	0.840030i
$756$		0			0
$757$	−6.68034	+	11.5707i	−0.242801	+	0.420544i	−0.961511	−	0.274766i	$-0.911400\pi$
$757$	−6.68034	+	11.5707i	−0.242801	+	0.420544i	0.718710	+	0.695310i	$0.244733\pi$
$758$	−5.10739	+	8.84626i	−0.185509	+	0.321311i
$759$		0			0
$760$	22.5623	+	39.0791i	0.818421	+	1.41755i
$761$	−41.2361			−1.49481			−0.747403	−	0.664371i	$-0.768700\pi$
$761$	−41.2361			−1.49481			−0.747403	+	0.664371i	$0.768700\pi$
$762$		0			0
$763$	−18.9443	+	32.8124i	−0.685829	+	1.18789i
$764$	29.7984			1.07807
$765$		0			0
$766$	2.63525	−	4.56440i	0.0952156	−	0.164918i
$767$	−12.7082	−	22.0113i	−0.458867	−	0.794780i
$768$		0			0
$769$	−17.2984	+	29.9617i	−0.623795	+	1.08045i	0.364977	+	0.931016i	$0.381077\pi$
$769$	−17.2984	+	29.9617i	−0.623795	+	1.08045i	−0.988773	+	0.149429i	$0.952257\pi$
$770$	21.1803	−	36.6854i	0.763286	−	1.32205i
$771$		0			0
$772$	−20.9443	+	36.2765i	−0.753801	+	1.30562i
$773$	5.11803	−	8.86469i	0.184083	−	0.318841i	−0.759184	−	0.650876i	$-0.774402\pi$
$773$	5.11803	−	8.86469i	0.184083	−	0.318841i	0.943267	+	0.332035i	$0.107735\pi$
$774$		0			0
$775$	18.3541	−	31.7902i	0.659299	−	1.14194i
$776$	−10.0623	−	17.4284i	−0.361216	−	0.625644i
$777$		0			0
$778$	1.54508	−	2.67617i	0.0553940	−	0.0959452i
$779$	1.47214			0.0527447
$780$		0			0
$781$	33.6803	+	58.3361i	1.20518	+	2.08743i
$782$	−8.61803			−0.308180
$783$		0			0
$784$	−10.1459	+	17.5732i	−0.362354	+	0.627615i
$785$	17.3262	+	30.0099i	0.618400	+	1.07110i
$786$		0			0
$787$	10.7361	+	18.5954i	0.382699	+	0.662855i	0.991447	−	0.130509i	$-0.0416611\pi$
$787$	10.7361	+	18.5954i	0.382699	+	0.662855i	−0.608748	+	0.793364i	$0.708328\pi$
$788$	14.5172	+	25.1446i	0.517155	+	0.895738i
$789$		0			0
$790$	−1.05573			−0.0375611
$791$	22.6803	+	39.2835i	0.806420	+	1.39676i
$792$		0			0
$793$	−1.50000	+	2.59808i	−0.0532666	+	0.0922604i
$794$	−2.43769	−	4.22221i	−0.0865105	−	0.149841i
$795$		0			0
$796$	38.7426			1.37320
$797$	17.5902	−	30.4671i	0.623076	−	1.07920i	−0.365834	−	0.930680i	$-0.619216\pi$
$797$	17.5902	−	30.4671i	0.623076	−	1.07920i	0.988910	−	0.148519i	$-0.0474505\pi$
$798$		0			0
$799$	−13.9443			−0.493313
$800$	15.3713	−	26.6239i	0.543458	−	0.941297i
$801$		0			0
$802$	−2.76393	−	4.78727i	−0.0975978	−	0.169044i
$803$	−53.5410			−1.88942
$804$		0			0
$805$	85.4853			3.01296
$806$	8.78115	+	15.2094i	0.309303	+	0.535728i
$807$		0			0
$808$	−2.82624	+	4.89519i	−0.0994267	+	0.172212i
$809$	3.59675			0.126455			0.0632275	−	0.997999i	$-0.479861\pi$
$809$	3.59675			0.126455			0.0632275	+	0.997999i	$0.479861\pi$
$810$		0			0
$811$	−10.9164	+	18.9078i	−0.383327	+	0.663942i	−0.991536	−	0.129836i	$-0.958555\pi$
$811$	−10.9164	+	18.9078i	−0.383327	+	0.663942i	0.608209	+	0.793777i	$0.291888\pi$
$812$	64.9230			2.27835
$813$		0			0
$814$	2.27458	+	3.93968i	0.0797238	+	0.138086i
$815$	−25.0344	+	43.3609i	−0.876918	+	1.51887i
$816$		0			0
$817$	−16.3262	−	28.2779i	−0.571183	−	0.989318i
$818$	11.0902			0.387759
$819$		0			0
$820$	−0.618034	−	1.07047i	−0.0215827	−	0.0373823i
$821$	19.6803	+	34.0873i	0.686849	+	1.18966i	0.972852	+	0.231428i	$0.0743398\pi$
$821$	19.6803	+	34.0873i	0.686849	+	1.18966i	−0.286003	+	0.958229i	$0.592327\pi$
$822$		0			0
$823$	−3.20820	−	5.55677i	−0.111831	−	0.193697i	0.804678	−	0.593712i	$-0.202338\pi$
$823$	−3.20820	−	5.55677i	−0.111831	−	0.193697i	−0.916509	+	0.400015i	$0.869005\pi$
$824$	−8.35410	+	14.4697i	−0.291029	+	0.504077i
$825$		0			0
$826$	15.7082			0.546558
$827$	−14.5902	−	25.2709i	−0.507350	−	0.878756i	−0.999964	−	0.00850785i	$-0.997292\pi$
$827$	−14.5902	−	25.2709i	−0.507350	−	0.878756i	0.492614	−	0.870248i	$-0.336041\pi$
$828$		0			0
$829$	41.4164			1.43845			0.719226	−	0.694777i	$-0.244497\pi$
$829$	41.4164			1.43845			0.719226	+	0.694777i	$0.244497\pi$
$830$	−11.0000	+	19.0526i	−0.381816	+	0.661324i
$831$		0			0
$832$	−0.500000	−	0.866025i	−0.0173344	−	0.0300240i
$833$	−12.2361	+	21.1935i	−0.423955	+	0.734311i
$834$		0			0
$835$	2.09017	−	3.62028i	0.0723333	−	0.125285i
$836$	−25.2254	+	43.6917i	−0.872440	+	1.51111i
$837$		0			0
$838$	1.74671	−	3.02539i	0.0603391	−	0.104510i
$839$	6.53444	−	11.3180i	0.225594	−	0.390740i	−0.730903	−	0.682481i	$-0.760901\pi$
$839$	6.53444	−	11.3180i	0.225594	−	0.390740i	0.956497	+	0.291741i	$0.0942344\pi$
$840$		0			0
$841$	−30.3607	−	52.5862i	−1.04692	−	1.81332i
$842$	−0.982779	+	1.70222i	−0.0338688	+	0.0586625i
$843$		0			0
$844$	−5.61803			−0.193381
$845$	−8.00000	+	13.8564i	−0.275208	+	0.476675i
$846$		0			0
$847$	59.3050			2.03774
$848$	3.43769	+	5.95426i	0.118051	+	0.204470i
$849$		0			0
$850$	3.78115	−	6.54915i	0.129692	−	0.224634i
$851$	−4.59017	+	7.95041i	−0.157349	+	0.272536i
$852$		0			0
$853$	−4.06231	−	7.03612i	−0.139091	−	0.240912i	0.788062	−	0.615596i	$-0.211085\pi$
$853$	−4.06231	−	7.03612i	−0.139091	−	0.240912i	−0.927153	+	0.374684i	$0.877751\pi$
$854$	−0.927051	−	1.60570i	−0.0317230	−	0.0549459i
$855$		0			0
$856$	−26.1803			−0.894826
$857$	15.7082			0.536582			0.268291	−	0.963338i	$-0.413541\pi$
$857$	15.7082			0.536582			0.268291	+	0.963338i	$0.413541\pi$
$858$		0			0
$859$	15.9721	−	27.6646i	0.544962	−	0.943902i	−0.453647	−	0.891181i	$-0.649877\pi$
$859$	15.9721	−	27.6646i	0.544962	−	0.943902i	0.998609	−	0.0527209i	$-0.0167894\pi$
$860$	−13.7082	+	23.7433i	−0.467446	+	0.809640i
$861$		0			0
$862$	15.4934			0.527708
$863$	43.1935			1.47032			0.735162	−	0.677892i	$-0.237106\pi$
$863$	43.1935			1.47032			0.735162	+	0.677892i	$0.237106\pi$
$864$		0			0
$865$	−4.38197	−	7.58979i	−0.148991	−	0.258061i
$866$	17.1591			0.583088
$867$		0			0
$868$	45.9787			1.56062
$869$	−1.31966	−	2.28572i	−0.0447664	−	0.0775377i
$870$		0			0
$871$	−23.2984	−	25.6798i	−0.789435	−	0.870127i
$872$	20.0000			0.677285
$873$		0			0
$874$	24.0344			0.812977
$875$	−3.23607	+	5.60503i	−0.109399	+	0.189485i
$876$		0			0
$877$	24.5902	+	42.5914i	0.830351	+	1.43821i	0.897760	+	0.440485i	$0.145193\pi$
$877$	24.5902	+	42.5914i	0.830351	+	1.43821i	−0.0674090	+	0.997725i	$0.521473\pi$
$878$	−10.6910	+	18.5173i	−0.360803	+	0.624929i
$879$		0			0
$880$	30.0000			1.01130
$881$	1.40983	+	2.44190i	0.0474984	+	0.0822696i	0.888797	−	0.458301i	$-0.151542\pi$
$881$	1.40983	+	2.44190i	0.0474984	+	0.0822696i	−0.841299	+	0.540570i	$0.818208\pi$
$882$		0			0
$883$	−16.7361	+	28.9877i	−0.563214	+	0.975514i	0.434000	+	0.900913i	$0.357102\pi$
$883$	−16.7361	+	28.9877i	−0.563214	+	0.975514i	−0.997213	+	0.0746015i	$0.976232\pi$
$884$	−7.66312	−	13.2729i	−0.257739	−	0.446416i
$885$		0			0
$886$	7.67376			0.257805
$887$	−3.31966	−	5.74982i	−0.111463	−	0.193060i	0.804897	−	0.593414i	$-0.202220\pi$
$887$	−3.31966	−	5.74982i	−0.111463	−	0.193060i	−0.916360	+	0.400354i	$0.868887\pi$
$888$		0			0
$889$	23.6803	+	41.0156i	0.794213	+	1.37562i
$890$	2.00000	+	3.46410i	0.0670402	+	0.116117i
$891$		0			0
$892$	4.38197	−	7.58979i	0.146719	−	0.254125i
$893$	38.8885			1.30136
$894$		0			0
$895$		0			0
$896$	48.2148			1.61074
$897$		0			0
$898$	3.20163			0.106840
$899$	−31.7705	−	55.0281i	−1.05961	−	1.83529i
$900$		0			0
$901$	4.14590	+	7.18091i	0.138120	+	0.239231i
$902$	−0.364745	+	0.631757i	−0.0121447	+	0.0210352i
$903$		0			0
$904$	11.9721	−	20.7363i	0.398187	−	0.689681i
$905$	1.61803	−	2.80252i	0.0537853	−	0.0931588i
$906$		0			0
$907$	−21.2639	+	36.8302i	−0.706057	+	1.22293i	0.260251	+	0.965541i	$0.416195\pi$
$907$	−21.2639	+	36.8302i	−0.706057	+	1.22293i	−0.966309	+	0.257386i	$0.917139\pi$
$908$	−5.42705	−	9.39993i	−0.180103	−	0.311948i
$909$		0			0
$910$	−17.9443	−	31.0804i	−0.594847	−	1.03030i
$911$	−50.2492			−1.66483			−0.832416	−	0.554152i	$-0.813043\pi$
$911$	−50.2492			−1.66483			−0.832416	+	0.554152i	$0.813043\pi$
$912$		0			0
$913$	−55.0000			−1.82023
$914$	7.85410			0.259791
$915$		0			0
$916$	−23.3262			−0.770721
$917$	3.23607	−	5.60503i	0.106864	−	0.185095i
$918$		0			0
$919$	14.7361	+	25.5236i	0.486098	+	0.841946i	0.999872	−	0.0159789i	$-0.00508646\pi$
$919$	14.7361	+	25.5236i	0.486098	+	0.841946i	−0.513774	+	0.857925i	$0.671753\pi$
$920$	−22.5623	−	39.0791i	−0.743857	−	1.28840i
$921$		0			0
$922$	−7.88854	−	13.6634i	−0.259795	−	0.449979i
$923$	57.0689			1.87845
$924$		0			0
$925$	−4.02786	−	6.97647i	−0.132435	−	0.229385i
$926$	5.30902	−	9.19549i	0.174465	−	0.302182i
$927$		0			0
$928$	−26.6074	−	46.0854i	−0.873430	−	1.51283i
$929$	38.9443			1.27772			0.638860	−	0.769323i	$-0.279406\pi$
$929$	38.9443			1.27772			0.638860	+	0.769323i	$0.279406\pi$
$930$		0			0
$931$	34.1246	−	59.1056i	1.11839	−	1.93711i
$932$	14.6631	+	25.3973i	0.480306	+	0.831915i
$933$		0			0
$934$	−0.656541	+	1.13716i	−0.0214827	+	0.0372091i
$935$	36.1803			1.18322
$936$		0			0
$937$	34.7214			1.13430			0.567149	−	0.823615i	$-0.308046\pi$
$937$	34.7214			1.13430			0.567149	+	0.823615i	$0.308046\pi$
$938$	20.9443	−	4.53457i	0.683855	−	0.148059i
$939$		0			0
$940$	−16.3262	−	28.2779i	−0.532503	−	0.922323i
$941$	33.3050			1.08571			0.542855	−	0.839826i	$-0.317343\pi$
$941$	33.3050			1.08571			0.542855	+	0.839826i	$0.317343\pi$
$942$		0			0
$943$	−1.47214			−0.0479393
$944$	5.56231	+	9.63420i	0.181038	+	0.313566i
$945$		0			0
$946$	16.1803			0.526068
$947$	−35.2361			−1.14502			−0.572509	−	0.819898i	$-0.694030\pi$
$947$	−35.2361			−1.14502			−0.572509	+	0.819898i	$0.694030\pi$
$948$		0			0
$949$	−22.6803	+	39.2835i	−0.736235	+	1.27520i
$950$	−10.5451	+	18.2646i	−0.342128	+	0.592583i
$951$		0			0
$952$	21.1803			0.686459
$953$	36.2492			1.17423			0.587114	−	0.809504i	$-0.300264\pi$
$953$	36.2492			1.17423			0.587114	+	0.809504i	$0.300264\pi$
$954$		0			0
$955$	29.7984	+	51.6123i	0.964253	+	1.67013i
$956$	−23.6074	−	40.8892i	−0.763518	−	1.32245i
$957$		0			0
$958$	−1.25329	+	2.17076i	−0.0404919	+	0.0701341i
$959$	−33.6525	+	58.2878i	−1.08670	+	1.88221i
$960$		0			0
$961$	−7.00000	−	12.1244i	−0.225806	−	0.391108i
$962$	3.85410			0.124261
$963$		0			0
$964$	5.00000	−	8.66025i	0.161039	−	0.278928i
$965$	−83.7771			−2.69688
$966$		0			0
$967$	4.97214	−	8.61199i	0.159893	−	0.276943i	−0.774937	−	0.632039i	$-0.782218\pi$
$967$	4.97214	−	8.61199i	0.159893	−	0.276943i	0.934830	+	0.355096i	$0.115552\pi$
$968$	−15.6525	−	27.1109i	−0.503090	−	0.871377i
$969$		0			0
$970$	9.00000	−	15.5885i	0.288973	−	0.500515i
$971$	−14.2426	+	24.6690i	−0.457068	+	0.791665i	−0.998805	−	0.0488831i	$-0.984434\pi$
$971$	−14.2426	+	24.6690i	−0.457068	+	0.791665i	0.541736	+	0.840549i	$0.317767\pi$
$972$		0			0
$973$	−18.9443	+	32.8124i	−0.607325	+	1.05192i
$974$	−2.96149	+	5.12946i	−0.0948924	+	0.164358i
$975$		0			0
$976$	0.656541	−	1.13716i	0.0210154	−	0.0363997i
$977$	6.02786	+	10.4406i	0.192848	+	0.334023i	0.946193	−	0.323603i	$-0.104894\pi$
$977$	6.02786	+	10.4406i	0.192848	+	0.334023i	−0.753345	+	0.657626i	$0.771561\pi$
$978$		0			0
$979$	−5.00000	+	8.66025i	−0.159801	+	0.276783i
$980$	−57.3050			−1.83054
$981$		0			0
$982$	−5.65248	−	9.79038i	−0.180378	−	0.312423i
$983$	18.9443			0.604228			0.302114	−	0.953272i	$-0.402308\pi$
$983$	18.9443			0.604228			0.302114	+	0.953272i	$0.402308\pi$
$984$		0			0
$985$	−29.0344	+	50.2891i	−0.925114	+	1.60234i
$986$	−6.54508	−	11.3364i	−0.208438	−	0.361025i
$987$		0			0
$988$	21.3713	+	37.0162i	0.679912	+	1.17764i
$989$	16.3262	+	28.2779i	0.519144	+	0.899184i
$990$		0			0
$991$	−38.0000			−1.20711			−0.603555	−	0.797321i	$-0.706250\pi$
$991$	−38.0000			−1.20711			−0.603555	+	0.797321i	$0.706250\pi$
$992$	−18.8435	−	32.6378i	−0.598280	−	1.03625i
$993$		0			0
$994$	−17.6353	+	30.5452i	−0.559356	+	0.968834i
$995$	38.7426	+	67.1042i	1.22822	+	2.12735i
$996$		0			0
$997$	24.5836			0.778570			0.389285	−	0.921117i	$-0.372722\pi$
$997$	24.5836			0.778570			0.389285	+	0.921117i	$0.372722\pi$
$998$	0.364745	−	0.631757i	0.0115458	−	0.0199979i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.g.c.37.2	✓	4
3.2	odd	2		603.2.g.d.37.1	yes	4
67.29	even	3	inner	603.2.g.c.163.2	yes	4
201.29	odd	6		603.2.g.d.163.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
603.2.g.c.37.2	✓	4	1.1	even	1	trivial
603.2.g.c.163.2	yes	4	67.29	even	3	inner
603.2.g.d.37.1	yes	4	3.2	odd	2
603.2.g.d.163.1	yes	4	201.29	odd	6

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:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.535233i) q^{2} +(0.809017 - 1.40126i) q^{4} +3.23607 q^{5} +(-2.11803 + 3.66854i) q^{7} +2.23607 q^{8} +O(q^{10})\)	\(q+(0.309017 + 0.535233i) q^{2} +(0.809017 - 1.40126i) q^{4} +3.23607 q^{5} +(-2.11803 + 3.66854i) q^{7} +2.23607 q^{8} +(1.00000 + 1.73205i) q^{10} +(-2.50000 + 4.33013i) q^{11} +(2.11803 + 3.66854i) q^{13} -2.61803 q^{14} +(-0.927051 - 1.60570i) q^{16} +(-1.11803 - 1.93649i) q^{17} +(3.11803 + 5.40059i) q^{19} +(2.61803 - 4.53457i) q^{20} -3.09017 q^{22} +(-3.11803 - 5.40059i) q^{23} +5.47214 q^{25} +(-1.30902 + 2.26728i) q^{26} +(3.42705 + 5.93583i) q^{28} +(4.73607 - 8.20311i) q^{29} +(3.35410 - 5.80948i) q^{31} +(2.80902 - 4.86536i) q^{32} +(0.690983 - 1.19682i) q^{34} +(-6.85410 + 11.8717i) q^{35} +(-0.736068 - 1.27491i) q^{37} +(-1.92705 + 3.33775i) q^{38} +7.23607 q^{40} +(0.118034 - 0.204441i) q^{41} -5.23607 q^{43} +(4.04508 + 7.00629i) q^{44} +(1.92705 - 3.33775i) q^{46} +(3.11803 - 5.40059i) q^{47} +(-5.47214 - 9.47802i) q^{49} +(1.69098 + 2.92887i) q^{50} +6.85410 q^{52} -3.70820 q^{53} +(-8.09017 + 14.0126i) q^{55} +(-4.73607 + 8.20311i) q^{56} +5.85410 q^{58} -6.00000 q^{59} +(0.354102 + 0.613323i) q^{61} +4.14590 q^{62} -0.236068 q^{64} +(6.85410 + 11.8717i) q^{65} +(-8.00000 + 1.73205i) q^{67} -3.61803 q^{68} -8.47214 q^{70} +(6.73607 - 11.6672i) q^{71} +(5.35410 + 9.27358i) q^{73} +(0.454915 - 0.787936i) q^{74} +10.0902 q^{76} +(-10.5902 - 18.3427i) q^{77} +(-0.263932 + 0.457144i) q^{79} +(-3.00000 - 5.19615i) q^{80} +0.145898 q^{82} +(5.50000 + 9.52628i) q^{83} +(-3.61803 - 6.26662i) q^{85} +(-1.61803 - 2.80252i) q^{86} +(-5.59017 + 9.68246i) q^{88} +2.00000 q^{89} -17.9443 q^{91} -10.0902 q^{92} +3.85410 q^{94} +(10.0902 + 17.4767i) q^{95} +(-4.50000 - 7.79423i) q^{97} +(3.38197 - 5.85774i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + q^{4} + 4 q^{5} - 4 q^{7}+O(q^{10}) \) 4 * q - q^2 + q^4 + 4 * q^5 - 4 * q^7	\( 4 q - q^{2} + q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{10} - 10 q^{11} + 4 q^{13} - 6 q^{14} + 3 q^{16} + 8 q^{19} + 6 q^{20} + 10 q^{22} - 8 q^{23} + 4 q^{25} - 3 q^{26} + 7 q^{28} + 10 q^{29} + 9 q^{32} + 5 q^{34} - 14 q^{35} + 6 q^{37} - q^{38} + 20 q^{40} - 4 q^{41} - 12 q^{43} + 5 q^{44} + q^{46} + 8 q^{47} - 4 q^{49} + 9 q^{50} + 14 q^{52} + 12 q^{53} - 10 q^{55} - 10 q^{56} + 10 q^{58} - 24 q^{59} - 12 q^{61} + 30 q^{62} + 8 q^{64} + 14 q^{65} - 32 q^{67} - 10 q^{68} - 16 q^{70} + 18 q^{71} + 8 q^{73} + 13 q^{74} + 18 q^{76} - 20 q^{77} - 10 q^{79} - 12 q^{80} + 14 q^{82} + 22 q^{83} - 10 q^{85} - 2 q^{86} + 8 q^{89} - 36 q^{91} - 18 q^{92} + 2 q^{94} + 18 q^{95} - 18 q^{97} + 18 q^{98}+O(q^{100}) \) 4 * q - q^2 + q^4 + 4 * q^5 - 4 * q^7 + 4 * q^10 - 10 * q^11 + 4 * q^13 - 6 * q^14 + 3 * q^16 + 8 * q^19 + 6 * q^20 + 10 * q^22 - 8 * q^23 + 4 * q^25 - 3 * q^26 + 7 * q^28 + 10 * q^29 + 9 * q^32 + 5 * q^34 - 14 * q^35 + 6 * q^37 - q^38 + 20 * q^40 - 4 * q^41 - 12 * q^43 + 5 * q^44 + q^46 + 8 * q^47 - 4 * q^49 + 9 * q^50 + 14 * q^52 + 12 * q^53 - 10 * q^55 - 10 * q^56 + 10 * q^58 - 24 * q^59 - 12 * q^61 + 30 * q^62 + 8 * q^64 + 14 * q^65 - 32 * q^67 - 10 * q^68 - 16 * q^70 + 18 * q^71 + 8 * q^73 + 13 * q^74 + 18 * q^76 - 20 * q^77 - 10 * q^79 - 12 * q^80 + 14 * q^82 + 22 * q^83 - 10 * q^85 - 2 * q^86 + 8 * q^89 - 36 * q^91 - 18 * q^92 + 2 * q^94 + 18 * q^95 - 18 * q^97 + 18 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more