LMFDB - Embedded newform 1134.2.e.o.865.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(865,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1134.865");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.e (of order $3$, degree $2$, 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:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 378)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			865.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1134.865
Dual form			1134.2.e.o.919.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{4} +(1.00000 - 1.73205i) q^{5} +(2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{4} +(1.00000 - 1.73205i) q^{5} +(2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(1.00000 - 1.73205i) q^{10} +(-2.50000 - 4.33013i) q^{11} +(-3.00000 - 5.19615i) q^{13} +(2.00000 + 1.73205i) q^{14} +1.00000 q^{16} +(2.00000 - 3.46410i) q^{17} +(2.00000 + 3.46410i) q^{19} +(1.00000 - 1.73205i) q^{20} +(-2.50000 - 4.33013i) q^{22} +(2.00000 - 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{25} +(-3.00000 - 5.19615i) q^{26} +(2.00000 + 1.73205i) q^{28} +(-3.50000 + 6.06218i) q^{29} +3.00000 q^{31} +1.00000 q^{32} +(2.00000 - 3.46410i) q^{34} +(5.00000 - 1.73205i) q^{35} +(-4.00000 - 6.92820i) q^{37} +(2.00000 + 3.46410i) q^{38} +(1.00000 - 1.73205i) q^{40} +(3.00000 + 5.19615i) q^{41} +(-4.00000 + 6.92820i) q^{43} +(-2.50000 - 4.33013i) q^{44} +(2.00000 - 3.46410i) q^{46} +6.00000 q^{47} +(1.00000 + 6.92820i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-3.00000 - 5.19615i) q^{52} +(3.00000 - 5.19615i) q^{53} -10.0000 q^{55} +(2.00000 + 1.73205i) q^{56} +(-3.50000 + 6.06218i) q^{58} +7.00000 q^{59} +3.00000 q^{62} +1.00000 q^{64} -12.0000 q^{65} +10.0000 q^{67} +(2.00000 - 3.46410i) q^{68} +(5.00000 - 1.73205i) q^{70} -4.00000 q^{71} +(-6.50000 + 11.2583i) q^{73} +(-4.00000 - 6.92820i) q^{74} +(2.00000 + 3.46410i) q^{76} +(2.50000 - 12.9904i) q^{77} -3.00000 q^{79} +(1.00000 - 1.73205i) q^{80} +(3.00000 + 5.19615i) q^{82} +(3.50000 - 6.06218i) q^{83} +(-4.00000 - 6.92820i) q^{85} +(-4.00000 + 6.92820i) q^{86} +(-2.50000 - 4.33013i) q^{88} +(-3.00000 - 5.19615i) q^{89} +(3.00000 - 15.5885i) q^{91} +(2.00000 - 3.46410i) q^{92} +6.00000 q^{94} +8.00000 q^{95} +(2.50000 - 4.33013i) q^{97} +(1.00000 + 6.92820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{4} + 2 q^{5} + 4 q^{7} + 2 q^{8}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^5 + 4 * q^7 + 2 * q^8	$ 2 q + 2 q^{2} + 2 q^{4} + 2 q^{5} + 4 q^{7} + 2 q^{8} + 2 q^{10} - 5 q^{11} - 6 q^{13} + 4 q^{14} + 2 q^{16} + 4 q^{17} + 4 q^{19} + 2 q^{20} - 5 q^{22} + 4 q^{23} + q^{25} - 6 q^{26} + 4 q^{28} - 7 q^{29} + 6 q^{31} + 2 q^{32} + 4 q^{34} + 10 q^{35} - 8 q^{37} + 4 q^{38} + 2 q^{40} + 6 q^{41} - 8 q^{43} - 5 q^{44} + 4 q^{46} + 12 q^{47} + 2 q^{49} + q^{50} - 6 q^{52} + 6 q^{53} - 20 q^{55} + 4 q^{56} - 7 q^{58} + 14 q^{59} + 6 q^{62} + 2 q^{64} - 24 q^{65} + 20 q^{67} + 4 q^{68} + 10 q^{70} - 8 q^{71} - 13 q^{73} - 8 q^{74} + 4 q^{76} + 5 q^{77} - 6 q^{79} + 2 q^{80} + 6 q^{82} + 7 q^{83} - 8 q^{85} - 8 q^{86} - 5 q^{88} - 6 q^{89} + 6 q^{91} + 4 q^{92} + 12 q^{94} + 16 q^{95} + 5 q^{97} + 2 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^5 + 4 * q^7 + 2 * q^8 + 2 * q^10 - 5 * q^11 - 6 * q^13 + 4 * q^14 + 2 * q^16 + 4 * q^17 + 4 * q^19 + 2 * q^20 - 5 * q^22 + 4 * q^23 + q^25 - 6 * q^26 + 4 * q^28 - 7 * q^29 + 6 * q^31 + 2 * q^32 + 4 * q^34 + 10 * q^35 - 8 * q^37 + 4 * q^38 + 2 * q^40 + 6 * q^41 - 8 * q^43 - 5 * q^44 + 4 * q^46 + 12 * q^47 + 2 * q^49 + q^50 - 6 * q^52 + 6 * q^53 - 20 * q^55 + 4 * q^56 - 7 * q^58 + 14 * q^59 + 6 * q^62 + 2 * q^64 - 24 * q^65 + 20 * q^67 + 4 * q^68 + 10 * q^70 - 8 * q^71 - 13 * q^73 - 8 * q^74 + 4 * q^76 + 5 * q^77 - 6 * q^79 + 2 * q^80 + 6 * q^82 + 7 * q^83 - 8 * q^85 - 8 * q^86 - 5 * q^88 - 6 * q^89 + 6 * q^91 + 4 * q^92 + 12 * q^94 + 16 * q^95 + 5 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	1.00000	−	1.73205i	0.447214	−	0.774597i	−0.550990	−	0.834512i	$-0.685750\pi$
$5$	1.00000	−	1.73205i	0.447214	−	0.774597i	0.998203	+	0.0599153i	$0.0190830\pi$
$6$		0			0
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$8$	1.00000			0.353553
$9$		0			0
$10$	1.00000	−	1.73205i	0.316228	−	0.547723i
$11$	−2.50000	−	4.33013i	−0.753778	−	1.30558i	−0.945979	−	0.324227i	$-0.894896\pi$
$11$	−2.50000	−	4.33013i	−0.753778	−	1.30558i	0.192201	−	0.981356i	$-0.438437\pi$
$12$		0			0
$13$	−3.00000	−	5.19615i	−0.832050	−	1.44115i	−0.896410	−	0.443227i	$-0.853834\pi$
$13$	−3.00000	−	5.19615i	−0.832050	−	1.44115i	0.0643593	−	0.997927i	$-0.479500\pi$
$14$	2.00000	+	1.73205i	0.534522	+	0.462910i
$15$		0			0
$16$	1.00000			0.250000
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	−0.514782	−	0.857321i	$-0.672127\pi$
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	0.999853	+	0.0171533i	$0.00546033\pi$
$18$		0			0
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	0.998899	−	0.0469020i	$-0.0149348\pi$
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	−0.540068	+	0.841621i	$0.681602\pi$
$20$	1.00000	−	1.73205i	0.223607	−	0.387298i
$21$		0			0
$22$	−2.50000	−	4.33013i	−0.533002	−	0.923186i
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	−0.578610	−	0.815604i	$-0.696405\pi$
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	0.995639	+	0.0932891i	$0.0297381\pi$
$24$		0			0
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−3.00000	−	5.19615i	−0.588348	−	1.01905i
$27$		0			0
$28$	2.00000	+	1.73205i	0.377964	+	0.327327i
$29$	−3.50000	+	6.06218i	−0.649934	+	1.12572i	0.333205	+	0.942855i	$0.391870\pi$
$29$	−3.50000	+	6.06218i	−0.649934	+	1.12572i	−0.983138	+	0.182864i	$0.941463\pi$
$30$		0			0
$31$	3.00000			0.538816			0.269408	−	0.963026i	$-0.413172\pi$
$31$	3.00000			0.538816			0.269408	+	0.963026i	$0.413172\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	2.00000	−	3.46410i	0.342997	−	0.594089i
$35$	5.00000	−	1.73205i	0.845154	−	0.292770i
$36$		0			0
$37$	−4.00000	−	6.92820i	−0.657596	−	1.13899i	−0.981236	−	0.192809i	$-0.938240\pi$
$37$	−4.00000	−	6.92820i	−0.657596	−	1.13899i	0.323640	−	0.946180i	$-0.395093\pi$
$38$	2.00000	+	3.46410i	0.324443	+	0.561951i
$39$		0			0
$40$	1.00000	−	1.73205i	0.158114	−	0.273861i
$41$	3.00000	+	5.19615i	0.468521	+	0.811503i	0.999353	−	0.0359748i	$-0.0114536\pi$
$41$	3.00000	+	5.19615i	0.468521	+	0.811503i	−0.530831	+	0.847477i	$0.678120\pi$
$42$		0			0
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	0.381246	+	0.924473i	$0.375495\pi$
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	−0.991241	+	0.132068i	$0.957838\pi$
$44$	−2.50000	−	4.33013i	−0.376889	−	0.652791i
$45$		0			0
$46$	2.00000	−	3.46410i	0.294884	−	0.510754i
$47$	6.00000			0.875190			0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000			0.875190			0.437595	+	0.899172i	$0.355830\pi$
$48$		0			0
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$		0			0
$52$	−3.00000	−	5.19615i	−0.416025	−	0.720577i
$53$	3.00000	−	5.19615i	0.412082	−	0.713746i	−0.583036	−	0.812447i	$-0.698135\pi$
$53$	3.00000	−	5.19615i	0.412082	−	0.713746i	0.995117	+	0.0987002i	$0.0314685\pi$
$54$		0			0
$55$	−10.0000			−1.34840
$56$	2.00000	+	1.73205i	0.267261	+	0.231455i
$57$		0			0
$58$	−3.50000	+	6.06218i	−0.459573	+	0.796003i
$59$	7.00000			0.911322			0.455661	−	0.890153i	$-0.349403\pi$
$59$	7.00000			0.911322			0.455661	+	0.890153i	$0.349403\pi$
$60$		0			0
$61$		0			0			−	1.00000i	$-0.5\pi$
$61$		0			0				1.00000i	$0.5\pi$
$62$	3.00000			0.381000
$63$		0			0
$64$	1.00000			0.125000
$65$	−12.0000			−1.48842
$66$		0			0
$67$	10.0000			1.22169			0.610847	−	0.791748i	$-0.290829\pi$
$67$	10.0000			1.22169			0.610847	+	0.791748i	$0.290829\pi$
$68$	2.00000	−	3.46410i	0.242536	−	0.420084i
$69$		0			0
$70$	5.00000	−	1.73205i	0.597614	−	0.207020i
$71$	−4.00000			−0.474713			−0.237356	−	0.971423i	$-0.576281\pi$
$71$	−4.00000			−0.474713			−0.237356	+	0.971423i	$0.576281\pi$
$72$		0			0
$73$	−6.50000	+	11.2583i	−0.760767	+	1.31769i	0.181688	+	0.983356i	$0.441844\pi$
$73$	−6.50000	+	11.2583i	−0.760767	+	1.31769i	−0.942455	+	0.334332i	$0.891489\pi$
$74$	−4.00000	−	6.92820i	−0.464991	−	0.805387i
$75$		0			0
$76$	2.00000	+	3.46410i	0.229416	+	0.397360i
$77$	2.50000	−	12.9904i	0.284901	−	1.48039i
$78$		0			0
$79$	−3.00000			−0.337526			−0.168763	−	0.985657i	$-0.553977\pi$
$79$	−3.00000			−0.337526			−0.168763	+	0.985657i	$0.553977\pi$
$80$	1.00000	−	1.73205i	0.111803	−	0.193649i
$81$		0			0
$82$	3.00000	+	5.19615i	0.331295	+	0.573819i
$83$	3.50000	−	6.06218i	0.384175	−	0.665410i	−0.607479	−	0.794335i	$-0.707819\pi$
$83$	3.50000	−	6.06218i	0.384175	−	0.665410i	0.991654	+	0.128925i	$0.0411526\pi$
$84$		0			0
$85$	−4.00000	−	6.92820i	−0.433861	−	0.751469i
$86$	−4.00000	+	6.92820i	−0.431331	+	0.747087i
$87$		0			0
$88$	−2.50000	−	4.33013i	−0.266501	−	0.461593i
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	0.662071	−	0.749441i	$-0.269678\pi$
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	−0.980071	+	0.198650i	$0.936344\pi$
$90$		0			0
$91$	3.00000	−	15.5885i	0.314485	−	1.63411i
$92$	2.00000	−	3.46410i	0.208514	−	0.361158i
$93$		0			0
$94$	6.00000			0.618853
$95$	8.00000			0.820783
$96$		0			0
$97$	2.50000	−	4.33013i	0.253837	−	0.439658i	−0.710742	−	0.703452i	$-0.751641\pi$
$97$	2.50000	−	4.33013i	0.253837	−	0.439658i	0.964579	+	0.263795i	$0.0849741\pi$
$98$	1.00000	+	6.92820i	0.101015	+	0.699854i
$99$		0			0
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	2.50000	+	4.33013i	0.248759	+	0.430864i	0.963182	−	0.268851i	$-0.0866439\pi$
$101$	2.50000	+	4.33013i	0.248759	+	0.430864i	−0.714423	+	0.699715i	$0.753311\pi$
$102$		0			0
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	−0.992990	−	0.118199i	$-0.962288\pi$
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	0.598858	+	0.800855i	$0.295621\pi$
$104$	−3.00000	−	5.19615i	−0.294174	−	0.509525i
$105$		0			0
$106$	3.00000	−	5.19615i	0.291386	−	0.504695i
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	−0.995474	−	0.0950377i	$-0.969703\pi$
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	0.415432	−	0.909624i	$-0.363630\pi$
$108$		0			0
$109$	−8.00000	+	13.8564i	−0.766261	+	1.32720i	0.173316	+	0.984866i	$0.444552\pi$
$109$	−8.00000	+	13.8564i	−0.766261	+	1.32720i	−0.939577	+	0.342337i	$0.888782\pi$
$110$	−10.0000			−0.953463
$111$		0			0
$112$	2.00000	+	1.73205i	0.188982	+	0.163663i
$113$	−2.00000	−	3.46410i	−0.188144	−	0.325875i	0.756487	−	0.654008i	$-0.226914\pi$
$113$	−2.00000	−	3.46410i	−0.188144	−	0.325875i	−0.944632	+	0.328133i	$0.893581\pi$
$114$		0			0
$115$	−4.00000	−	6.92820i	−0.373002	−	0.646058i
$116$	−3.50000	+	6.06218i	−0.324967	+	0.562859i
$117$		0			0
$118$	7.00000			0.644402
$119$	10.0000	−	3.46410i	0.916698	−	0.317554i
$120$		0			0
$121$	−7.00000	+	12.1244i	−0.636364	+	1.10221i
$122$		0			0
$123$		0			0
$124$	3.00000			0.269408
$125$	12.0000			1.07331
$126$		0			0
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	−12.0000			−1.05247
$131$	−6.50000	+	11.2583i	−0.567908	+	0.983645i	0.428865	+	0.903369i	$0.358914\pi$
$131$	−6.50000	+	11.2583i	−0.567908	+	0.983645i	−0.996773	+	0.0802763i	$0.974420\pi$
$132$		0			0
$133$	−2.00000	+	10.3923i	−0.173422	+	0.901127i
$134$	10.0000			0.863868
$135$		0			0
$136$	2.00000	−	3.46410i	0.171499	−	0.297044i
$137$	4.00000	+	6.92820i	0.341743	+	0.591916i	0.984757	−	0.173939i	$-0.0556494\pi$
$137$	4.00000	+	6.92820i	0.341743	+	0.591916i	−0.643013	+	0.765855i	$0.722316\pi$
$138$		0			0
$139$	4.00000	+	6.92820i	0.339276	+	0.587643i	0.984297	−	0.176522i	$-0.0564848\pi$
$139$	4.00000	+	6.92820i	0.339276	+	0.587643i	−0.645021	+	0.764165i	$0.723151\pi$
$140$	5.00000	−	1.73205i	0.422577	−	0.146385i
$141$		0			0
$142$	−4.00000			−0.335673
$143$	−15.0000	+	25.9808i	−1.25436	+	2.17262i
$144$		0			0
$145$	7.00000	+	12.1244i	0.581318	+	1.00687i
$146$	−6.50000	+	11.2583i	−0.537944	+	0.931746i
$147$		0			0
$148$	−4.00000	−	6.92820i	−0.328798	−	0.569495i
$149$	−4.50000	+	7.79423i	−0.368654	+	0.638528i	−0.989355	−	0.145519i	$-0.953515\pi$
$149$	−4.50000	+	7.79423i	−0.368654	+	0.638528i	0.620701	+	0.784047i	$0.286848\pi$
$150$		0			0
$151$	8.50000	+	14.7224i	0.691720	+	1.19809i	0.971274	+	0.237964i	$0.0764802\pi$
$151$	8.50000	+	14.7224i	0.691720	+	1.19809i	−0.279554	+	0.960130i	$0.590186\pi$
$152$	2.00000	+	3.46410i	0.162221	+	0.280976i
$153$		0			0
$154$	2.50000	−	12.9904i	0.201456	−	1.04679i
$155$	3.00000	−	5.19615i	0.240966	−	0.417365i
$156$		0			0
$157$	14.0000			1.11732			0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000			1.11732			0.558661	+	0.829396i	$0.311315\pi$
$158$	−3.00000			−0.238667
$159$		0			0
$160$	1.00000	−	1.73205i	0.0790569	−	0.136931i
$161$	10.0000	−	3.46410i	0.788110	−	0.273009i
$162$		0			0
$163$	−1.00000	−	1.73205i	−0.0783260	−	0.135665i	0.824202	−	0.566296i	$-0.191624\pi$
$163$	−1.00000	−	1.73205i	−0.0783260	−	0.135665i	−0.902528	+	0.430632i	$0.858291\pi$
$164$	3.00000	+	5.19615i	0.234261	+	0.405751i
$165$		0			0
$166$	3.50000	−	6.06218i	0.271653	−	0.470516i
$167$	7.00000	+	12.1244i	0.541676	+	0.938211i	0.998808	+	0.0488118i	$0.0155435\pi$
$167$	7.00000	+	12.1244i	0.541676	+	0.938211i	−0.457132	+	0.889399i	$0.651123\pi$
$168$		0			0
$169$	−11.5000	+	19.9186i	−0.884615	+	1.53220i
$170$	−4.00000	−	6.92820i	−0.306786	−	0.531369i
$171$		0			0
$172$	−4.00000	+	6.92820i	−0.304997	+	0.528271i
$173$	1.00000			0.0760286			0.0380143	−	0.999277i	$-0.487897\pi$
$173$	1.00000			0.0760286			0.0380143	+	0.999277i	$0.487897\pi$
$174$		0			0
$175$	−0.500000	+	2.59808i	−0.0377964	+	0.196396i
$176$	−2.50000	−	4.33013i	−0.188445	−	0.326396i
$177$		0			0
$178$	−3.00000	−	5.19615i	−0.224860	−	0.389468i
$179$	7.50000	−	12.9904i	0.560576	−	0.970947i	−0.436870	−	0.899525i	$-0.643913\pi$
$179$	7.50000	−	12.9904i	0.560576	−	0.970947i	0.997446	−	0.0714220i	$-0.0227537\pi$
$180$		0			0
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$	3.00000	−	15.5885i	0.222375	−	1.15549i
$183$		0			0
$184$	2.00000	−	3.46410i	0.147442	−	0.255377i
$185$	−16.0000			−1.17634
$186$		0			0
$187$	−20.0000			−1.46254
$188$	6.00000			0.437595
$189$		0			0
$190$	8.00000			0.580381
$191$	−18.0000			−1.30243			−0.651217	−	0.758891i	$-0.725741\pi$
$191$	−18.0000			−1.30243			−0.651217	+	0.758891i	$0.725741\pi$
$192$		0			0
$193$	−19.0000			−1.36765			−0.683825	−	0.729646i	$-0.739685\pi$
$193$	−19.0000			−1.36765			−0.683825	+	0.729646i	$0.739685\pi$
$194$	2.50000	−	4.33013i	0.179490	−	0.310885i
$195$		0			0
$196$	1.00000	+	6.92820i	0.0714286	+	0.494872i
$197$	−25.0000			−1.78118			−0.890588	−	0.454811i	$-0.849707\pi$
$197$	−25.0000			−1.78118			−0.890588	+	0.454811i	$0.849707\pi$
$198$		0			0
$199$	9.50000	−	16.4545i	0.673437	−	1.16643i	−0.303486	−	0.952836i	$-0.598151\pi$
$199$	9.50000	−	16.4545i	0.673437	−	1.16643i	0.976923	−	0.213591i	$-0.0685161\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$		0			0
$202$	2.50000	+	4.33013i	0.175899	+	0.304667i
$203$	−17.5000	+	6.06218i	−1.22826	+	0.425481i
$204$		0			0
$205$	12.0000			0.838116
$206$	−4.00000	+	6.92820i	−0.278693	+	0.482711i
$207$		0			0
$208$	−3.00000	−	5.19615i	−0.208013	−	0.360288i
$209$	10.0000	−	17.3205i	0.691714	−	1.19808i
$210$		0			0
$211$	−13.0000	−	22.5167i	−0.894957	−	1.55011i	−0.833858	−	0.551979i	$-0.813873\pi$
$211$	−13.0000	−	22.5167i	−0.894957	−	1.55011i	−0.0610990	−	0.998132i	$-0.519461\pi$
$212$	3.00000	−	5.19615i	0.206041	−	0.356873i
$213$		0			0
$214$	−6.00000	−	10.3923i	−0.410152	−	0.710403i
$215$	8.00000	+	13.8564i	0.545595	+	0.944999i
$216$		0			0
$217$	6.00000	+	5.19615i	0.407307	+	0.352738i
$218$	−8.00000	+	13.8564i	−0.541828	+	0.938474i
$219$		0			0
$220$	−10.0000			−0.674200
$221$	−24.0000			−1.61441
$222$		0			0
$223$	0.500000	−	0.866025i	0.0334825	−	0.0579934i	−0.848799	−	0.528716i	$-0.822674\pi$
$223$	0.500000	−	0.866025i	0.0334825	−	0.0579934i	0.882281	+	0.470723i	$0.156007\pi$
$224$	2.00000	+	1.73205i	0.133631	+	0.115728i
$225$		0			0
$226$	−2.00000	−	3.46410i	−0.133038	−	0.230429i
$227$	13.5000	+	23.3827i	0.896026	+	1.55196i	0.832529	+	0.553981i	$0.186892\pi$
$227$	13.5000	+	23.3827i	0.896026	+	1.55196i	0.0634974	+	0.997982i	$0.479775\pi$
$228$		0			0
$229$	−2.00000	+	3.46410i	−0.132164	+	0.228914i	−0.924510	−	0.381157i	$-0.875526\pi$
$229$	−2.00000	+	3.46410i	−0.132164	+	0.228914i	0.792347	+	0.610071i	$0.208859\pi$
$230$	−4.00000	−	6.92820i	−0.263752	−	0.456832i
$231$		0			0
$232$	−3.50000	+	6.06218i	−0.229786	+	0.398001i
$233$	11.0000	+	19.0526i	0.720634	+	1.24817i	0.960746	+	0.277429i	$0.0894825\pi$
$233$	11.0000	+	19.0526i	0.720634	+	1.24817i	−0.240112	+	0.970745i	$0.577184\pi$
$234$		0			0
$235$	6.00000	−	10.3923i	0.391397	−	0.677919i
$236$	7.00000			0.455661
$237$		0			0
$238$	10.0000	−	3.46410i	0.648204	−	0.224544i
$239$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$239$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$240$		0			0
$241$	0.500000	+	0.866025i	0.0322078	+	0.0557856i	0.881680	−	0.471848i	$-0.156413\pi$
$241$	0.500000	+	0.866025i	0.0322078	+	0.0557856i	−0.849472	+	0.527633i	$0.823079\pi$
$242$	−7.00000	+	12.1244i	−0.449977	+	0.779383i
$243$		0			0
$244$		0			0
$245$	13.0000	+	5.19615i	0.830540	+	0.331970i
$246$		0			0
$247$	12.0000	−	20.7846i	0.763542	−	1.32249i
$248$	3.00000			0.190500
$249$		0			0
$250$	12.0000			0.758947
$251$	−21.0000			−1.32551			−0.662754	−	0.748837i	$-0.730613\pi$
$251$	−21.0000			−1.32551			−0.662754	+	0.748837i	$0.730613\pi$
$252$		0			0
$253$	−20.0000			−1.25739
$254$		0			0
$255$		0			0
$256$	1.00000			0.0625000
$257$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$257$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$258$		0			0
$259$	4.00000	−	20.7846i	0.248548	−	1.29149i
$260$	−12.0000			−0.744208
$261$		0			0
$262$	−6.50000	+	11.2583i	−0.401571	+	0.695542i
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	0.619586	−	0.784929i	$-0.287301\pi$
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	−0.989561	+	0.144112i	$0.953967\pi$
$264$		0			0
$265$	−6.00000	−	10.3923i	−0.368577	−	0.638394i
$266$	−2.00000	+	10.3923i	−0.122628	+	0.637193i
$267$		0			0
$268$	10.0000			0.610847
$269$	−15.5000	+	26.8468i	−0.945052	+	1.63688i	−0.189404	+	0.981899i	$0.560656\pi$
$269$	−15.5000	+	26.8468i	−0.945052	+	1.63688i	−0.755648	+	0.654978i	$0.772678\pi$
$270$		0			0
$271$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$271$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$272$	2.00000	−	3.46410i	0.121268	−	0.210042i
$273$		0			0
$274$	4.00000	+	6.92820i	0.241649	+	0.418548i
$275$	2.50000	−	4.33013i	0.150756	−	0.261116i
$276$		0			0
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	0.834419	−	0.551131i	$-0.185804\pi$
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	−0.894503	+	0.447062i	$0.852470\pi$
$278$	4.00000	+	6.92820i	0.239904	+	0.415526i
$279$		0			0
$280$	5.00000	−	1.73205i	0.298807	−	0.103510i
$281$	−1.00000	+	1.73205i	−0.0596550	+	0.103325i	−0.894311	−	0.447447i	$-0.852333\pi$
$281$	−1.00000	+	1.73205i	−0.0596550	+	0.103325i	0.834656	+	0.550772i	$0.185667\pi$
$282$		0			0
$283$	16.0000			0.951101			0.475551	−	0.879688i	$-0.342249\pi$
$283$	16.0000			0.951101			0.475551	+	0.879688i	$0.342249\pi$
$284$	−4.00000			−0.237356
$285$		0			0
$286$	−15.0000	+	25.9808i	−0.886969	+	1.53627i
$287$	−3.00000	+	15.5885i	−0.177084	+	0.920158i
$288$		0			0
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$	7.00000	+	12.1244i	0.411054	+	0.711967i
$291$		0			0
$292$	−6.50000	+	11.2583i	−0.380384	+	0.658844i
$293$	−13.5000	−	23.3827i	−0.788678	−	1.36603i	−0.926777	−	0.375613i	$-0.877432\pi$
$293$	−13.5000	−	23.3827i	−0.788678	−	1.36603i	0.138098	−	0.990419i	$-0.455901\pi$
$294$		0			0
$295$	7.00000	−	12.1244i	0.407556	−	0.705907i
$296$	−4.00000	−	6.92820i	−0.232495	−	0.402694i
$297$		0			0
$298$	−4.50000	+	7.79423i	−0.260678	+	0.451508i
$299$	−24.0000			−1.38796
$300$		0			0
$301$	−20.0000	+	6.92820i	−1.15278	+	0.399335i
$302$	8.50000	+	14.7224i	0.489120	+	0.847181i
$303$		0			0
$304$	2.00000	+	3.46410i	0.114708	+	0.198680i
$305$		0			0
$306$		0			0
$307$	−2.00000			−0.114146			−0.0570730	−	0.998370i	$-0.518177\pi$
$307$	−2.00000			−0.114146			−0.0570730	+	0.998370i	$0.518177\pi$
$308$	2.50000	−	12.9904i	0.142451	−	0.740196i
$309$		0			0
$310$	3.00000	−	5.19615i	0.170389	−	0.295122i
$311$	22.0000			1.24751			0.623753	−	0.781622i	$-0.285607\pi$
$311$	22.0000			1.24751			0.623753	+	0.781622i	$0.285607\pi$
$312$		0			0
$313$	10.0000			0.565233			0.282617	−	0.959233i	$-0.408798\pi$
$313$	10.0000			0.565233			0.282617	+	0.959233i	$0.408798\pi$
$314$	14.0000			0.790066
$315$		0			0
$316$	−3.00000			−0.168763
$317$	−33.0000			−1.85346			−0.926732	−	0.375722i	$-0.877395\pi$
$317$	−33.0000			−1.85346			−0.926732	+	0.375722i	$0.877395\pi$
$318$		0			0
$319$	35.0000			1.95962
$320$	1.00000	−	1.73205i	0.0559017	−	0.0968246i
$321$		0			0
$322$	10.0000	−	3.46410i	0.557278	−	0.193047i
$323$	16.0000			0.890264
$324$		0			0
$325$	3.00000	−	5.19615i	0.166410	−	0.288231i
$326$	−1.00000	−	1.73205i	−0.0553849	−	0.0959294i
$327$		0			0
$328$	3.00000	+	5.19615i	0.165647	+	0.286910i
$329$	12.0000	+	10.3923i	0.661581	+	0.572946i
$330$		0			0
$331$	32.0000			1.75888			0.879440	−	0.476011i	$-0.157918\pi$
$331$	32.0000			1.75888			0.879440	+	0.476011i	$0.157918\pi$
$332$	3.50000	−	6.06218i	0.192087	−	0.332705i
$333$		0			0
$334$	7.00000	+	12.1244i	0.383023	+	0.663415i
$335$	10.0000	−	17.3205i	0.546358	−	0.946320i
$336$		0			0
$337$	13.5000	+	23.3827i	0.735392	+	1.27374i	0.954551	+	0.298047i	$0.0963352\pi$
$337$	13.5000	+	23.3827i	0.735392	+	1.27374i	−0.219159	+	0.975689i	$0.570331\pi$
$338$	−11.5000	+	19.9186i	−0.625518	+	1.08343i
$339$		0			0
$340$	−4.00000	−	6.92820i	−0.216930	−	0.375735i
$341$	−7.50000	−	12.9904i	−0.406148	−	0.703469i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	−4.00000	+	6.92820i	−0.215666	+	0.373544i
$345$		0			0
$346$	1.00000			0.0537603
$347$	−27.0000			−1.44944			−0.724718	−	0.689046i	$-0.758030\pi$
$347$	−27.0000			−1.44944			−0.724718	+	0.689046i	$0.758030\pi$
$348$		0			0
$349$	10.0000	−	17.3205i	0.535288	−	0.927146i	−0.463862	−	0.885908i	$-0.653537\pi$
$349$	10.0000	−	17.3205i	0.535288	−	0.927146i	0.999149	−	0.0412379i	$-0.0131301\pi$
$350$	−0.500000	+	2.59808i	−0.0267261	+	0.138873i
$351$		0			0
$352$	−2.50000	−	4.33013i	−0.133250	−	0.230797i
$353$	15.0000	+	25.9808i	0.798369	+	1.38282i	0.920677	+	0.390324i	$0.127637\pi$
$353$	15.0000	+	25.9808i	0.798369	+	1.38282i	−0.122308	+	0.992492i	$0.539030\pi$
$354$		0			0
$355$	−4.00000	+	6.92820i	−0.212298	+	0.367711i
$356$	−3.00000	−	5.19615i	−0.159000	−	0.275396i
$357$		0			0
$358$	7.50000	−	12.9904i	0.396387	−	0.686563i
$359$	−8.00000	−	13.8564i	−0.422224	−	0.731313i	0.573933	−	0.818902i	$-0.305417\pi$
$359$	−8.00000	−	13.8564i	−0.422224	−	0.731313i	−0.996157	+	0.0875892i	$0.972084\pi$
$360$		0			0
$361$	1.50000	−	2.59808i	0.0789474	−	0.136741i
$362$		0			0
$363$		0			0
$364$	3.00000	−	15.5885i	0.157243	−	0.817057i
$365$	13.0000	+	22.5167i	0.680451	+	1.17858i
$366$		0			0
$367$	2.00000	+	3.46410i	0.104399	+	0.180825i	0.913493	−	0.406855i	$-0.133375\pi$
$367$	2.00000	+	3.46410i	0.104399	+	0.180825i	−0.809093	+	0.587680i	$0.800041\pi$
$368$	2.00000	−	3.46410i	0.104257	−	0.180579i
$369$		0			0
$370$	−16.0000			−0.831800
$371$	15.0000	−	5.19615i	0.778761	−	0.269771i
$372$		0			0
$373$	10.0000	−	17.3205i	0.517780	−	0.896822i	−0.482006	−	0.876168i	$-0.660092\pi$
$373$	10.0000	−	17.3205i	0.517780	−	0.896822i	0.999787	−	0.0206542i	$-0.00657489\pi$
$374$	−20.0000			−1.03418
$375$		0			0
$376$	6.00000			0.309426
$377$	42.0000			2.16311
$378$		0			0
$379$	10.0000			0.513665			0.256833	−	0.966456i	$-0.417321\pi$
$379$	10.0000			0.513665			0.256833	+	0.966456i	$0.417321\pi$
$380$	8.00000			0.410391
$381$		0			0
$382$	−18.0000			−0.920960
$383$	2.00000	−	3.46410i	0.102195	−	0.177007i	−0.810394	−	0.585886i	$-0.800747\pi$
$383$	2.00000	−	3.46410i	0.102195	−	0.177007i	0.912589	+	0.408879i	$0.134080\pi$
$384$		0			0
$385$	−20.0000	−	17.3205i	−1.01929	−	0.882735i
$386$	−19.0000			−0.967075
$387$		0			0
$388$	2.50000	−	4.33013i	0.126918	−	0.219829i
$389$	−0.500000	−	0.866025i	−0.0253510	−	0.0439092i	0.853072	−	0.521794i	$-0.174737\pi$
$389$	−0.500000	−	0.866025i	−0.0253510	−	0.0439092i	−0.878423	+	0.477885i	$0.841404\pi$
$390$		0			0
$391$	−8.00000	−	13.8564i	−0.404577	−	0.700749i
$392$	1.00000	+	6.92820i	0.0505076	+	0.349927i
$393$		0			0
$394$	−25.0000			−1.25948
$395$	−3.00000	+	5.19615i	−0.150946	+	0.261447i
$396$		0			0
$397$	9.00000	+	15.5885i	0.451697	+	0.782362i	0.998492	−	0.0549046i	$-0.0174855\pi$
$397$	9.00000	+	15.5885i	0.451697	+	0.782362i	−0.546795	+	0.837267i	$0.684152\pi$
$398$	9.50000	−	16.4545i	0.476192	−	0.824789i
$399$		0			0
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	9.00000	−	15.5885i	0.449439	−	0.778450i	−0.548911	−	0.835881i	$-0.684957\pi$
$401$	9.00000	−	15.5885i	0.449439	−	0.778450i	0.998350	+	0.0574304i	$0.0182907\pi$
$402$		0			0
$403$	−9.00000	−	15.5885i	−0.448322	−	0.776516i
$404$	2.50000	+	4.33013i	0.124380	+	0.215432i
$405$		0			0
$406$	−17.5000	+	6.06218i	−0.868510	+	0.300861i
$407$	−20.0000	+	34.6410i	−0.991363	+	1.71709i
$408$		0			0
$409$	−10.0000			−0.494468			−0.247234	−	0.968956i	$-0.579522\pi$
$409$	−10.0000			−0.494468			−0.247234	+	0.968956i	$0.579522\pi$
$410$	12.0000			0.592638
$411$		0			0
$412$	−4.00000	+	6.92820i	−0.197066	+	0.341328i
$413$	14.0000	+	12.1244i	0.688895	+	0.596601i
$414$		0			0
$415$	−7.00000	−	12.1244i	−0.343616	−	0.595161i
$416$	−3.00000	−	5.19615i	−0.147087	−	0.254762i
$417$		0			0
$418$	10.0000	−	17.3205i	0.489116	−	0.847174i
$419$	−6.00000	−	10.3923i	−0.293119	−	0.507697i	0.681426	−	0.731887i	$-0.261360\pi$
$419$	−6.00000	−	10.3923i	−0.293119	−	0.507697i	−0.974546	+	0.224189i	$0.928027\pi$
$420$		0			0
$421$	9.00000	−	15.5885i	0.438633	−	0.759735i	−0.558951	−	0.829201i	$-0.688796\pi$
$421$	9.00000	−	15.5885i	0.438633	−	0.759735i	0.997584	+	0.0694656i	$0.0221294\pi$
$422$	−13.0000	−	22.5167i	−0.632830	−	1.09609i
$423$		0			0
$424$	3.00000	−	5.19615i	0.145693	−	0.252347i
$425$	4.00000			0.194029
$426$		0			0
$427$		0			0
$428$	−6.00000	−	10.3923i	−0.290021	−	0.502331i
$429$		0			0
$430$	8.00000	+	13.8564i	0.385794	+	0.668215i
$431$	9.00000	−	15.5885i	0.433515	−	0.750870i	−0.563658	−	0.826008i	$-0.690607\pi$
$431$	9.00000	−	15.5885i	0.433515	−	0.750870i	0.997173	+	0.0751385i	$0.0239399\pi$
$432$		0			0
$433$	−7.00000			−0.336399			−0.168199	−	0.985753i	$-0.553795\pi$
$433$	−7.00000			−0.336399			−0.168199	+	0.985753i	$0.553795\pi$
$434$	6.00000	+	5.19615i	0.288009	+	0.249423i
$435$		0			0
$436$	−8.00000	+	13.8564i	−0.383131	+	0.663602i
$437$	16.0000			0.765384
$438$		0			0
$439$	3.00000			0.143182			0.0715911	−	0.997434i	$-0.477192\pi$
$439$	3.00000			0.143182			0.0715911	+	0.997434i	$0.477192\pi$
$440$	−10.0000			−0.476731
$441$		0			0
$442$	−24.0000			−1.14156
$443$	11.0000			0.522626			0.261313	−	0.965254i	$-0.415845\pi$
$443$	11.0000			0.522626			0.261313	+	0.965254i	$0.415845\pi$
$444$		0			0
$445$	−12.0000			−0.568855
$446$	0.500000	−	0.866025i	0.0236757	−	0.0410075i
$447$		0			0
$448$	2.00000	+	1.73205i	0.0944911	+	0.0818317i
$449$	−14.0000			−0.660701			−0.330350	−	0.943858i	$-0.607167\pi$
$449$	−14.0000			−0.660701			−0.330350	+	0.943858i	$0.607167\pi$
$450$		0			0
$451$	15.0000	−	25.9808i	0.706322	−	1.22339i
$452$	−2.00000	−	3.46410i	−0.0940721	−	0.162938i
$453$		0			0
$454$	13.5000	+	23.3827i	0.633586	+	1.09740i
$455$	−24.0000	−	20.7846i	−1.12514	−	0.974398i
$456$		0			0
$457$	−26.0000			−1.21623			−0.608114	−	0.793849i	$-0.708074\pi$
$457$	−26.0000			−1.21623			−0.608114	+	0.793849i	$0.708074\pi$
$458$	−2.00000	+	3.46410i	−0.0934539	+	0.161867i
$459$		0			0
$460$	−4.00000	−	6.92820i	−0.186501	−	0.323029i
$461$	11.5000	−	19.9186i	0.535608	−	0.927701i	−0.463525	−	0.886084i	$-0.653416\pi$
$461$	11.5000	−	19.9186i	0.535608	−	0.927701i	0.999134	−	0.0416172i	$-0.0132510\pi$
$462$		0			0
$463$	14.5000	+	25.1147i	0.673872	+	1.16718i	0.976797	+	0.214166i	$0.0687035\pi$
$463$	14.5000	+	25.1147i	0.673872	+	1.16718i	−0.302925	+	0.953014i	$0.597963\pi$
$464$	−3.50000	+	6.06218i	−0.162483	+	0.281430i
$465$		0			0
$466$	11.0000	+	19.0526i	0.509565	+	0.882593i
$467$	−3.50000	−	6.06218i	−0.161961	−	0.280524i	0.773611	−	0.633661i	$-0.218448\pi$
$467$	−3.50000	−	6.06218i	−0.161961	−	0.280524i	−0.935572	+	0.353137i	$0.885115\pi$
$468$		0			0
$469$	20.0000	+	17.3205i	0.923514	+	0.799787i
$470$	6.00000	−	10.3923i	0.276759	−	0.479361i
$471$		0			0
$472$	7.00000			0.322201
$473$	40.0000			1.83920
$474$		0			0
$475$	−2.00000	+	3.46410i	−0.0917663	+	0.158944i
$476$	10.0000	−	3.46410i	0.458349	−	0.158777i
$477$		0			0
$478$		0			0
$479$	−13.0000	−	22.5167i	−0.593985	−	1.02881i	−0.993689	−	0.112168i	$-0.964220\pi$
$479$	−13.0000	−	22.5167i	−0.593985	−	1.02881i	0.399704	−	0.916644i	$-0.369113\pi$
$480$		0			0
$481$	−24.0000	+	41.5692i	−1.09431	+	1.89539i
$482$	0.500000	+	0.866025i	0.0227744	+	0.0394464i
$483$		0			0
$484$	−7.00000	+	12.1244i	−0.318182	+	0.551107i
$485$	−5.00000	−	8.66025i	−0.227038	−	0.393242i
$486$		0			0
$487$	6.50000	−	11.2583i	0.294543	−	0.510164i	−0.680335	−	0.732901i	$-0.738166\pi$
$487$	6.50000	−	11.2583i	0.294543	−	0.510164i	0.974879	+	0.222737i	$0.0714992\pi$
$488$		0			0
$489$		0			0
$490$	13.0000	+	5.19615i	0.587280	+	0.234738i
$491$	−6.00000	−	10.3923i	−0.270776	−	0.468998i	0.698285	−	0.715820i	$-0.253947\pi$
$491$	−6.00000	−	10.3923i	−0.270776	−	0.468998i	−0.969061	+	0.246822i	$0.920614\pi$
$492$		0			0
$493$	14.0000	+	24.2487i	0.630528	+	1.09211i
$494$	12.0000	−	20.7846i	0.539906	−	0.935144i
$495$		0			0
$496$	3.00000			0.134704
$497$	−8.00000	−	6.92820i	−0.358849	−	0.310772i
$498$		0			0
$499$	4.00000	−	6.92820i	0.179065	−	0.310149i	−0.762496	−	0.646993i	$-0.776026\pi$
$499$	4.00000	−	6.92820i	0.179065	−	0.310149i	0.941560	+	0.336844i	$0.109360\pi$
$500$	12.0000			0.536656
$501$		0			0
$502$	−21.0000			−0.937276
$503$	6.00000			0.267527			0.133763	−	0.991013i	$-0.457294\pi$
$503$	6.00000			0.267527			0.133763	+	0.991013i	$0.457294\pi$
$504$		0			0
$505$	10.0000			0.444994
$506$	−20.0000			−0.889108
$507$		0			0
$508$		0			0
$509$	−1.50000	+	2.59808i	−0.0664863	+	0.115158i	−0.897352	−	0.441315i	$-0.854512\pi$
$509$	−1.50000	+	2.59808i	−0.0664863	+	0.115158i	0.830866	+	0.556473i	$0.187846\pi$
$510$		0			0
$511$	−32.5000	+	11.2583i	−1.43772	+	0.498039i
$512$	1.00000			0.0441942
$513$		0			0
$514$		0			0
$515$	8.00000	+	13.8564i	0.352522	+	0.610586i
$516$		0			0
$517$	−15.0000	−	25.9808i	−0.659699	−	1.14263i
$518$	4.00000	−	20.7846i	0.175750	−	0.913223i
$519$		0			0
$520$	−12.0000			−0.526235
$521$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$521$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$522$		0			0
$523$	−13.0000	−	22.5167i	−0.568450	−	0.984585i	−0.996719	−	0.0809336i	$-0.974210\pi$
$523$	−13.0000	−	22.5167i	−0.568450	−	0.984585i	0.428269	−	0.903651i	$-0.359124\pi$
$524$	−6.50000	+	11.2583i	−0.283954	+	0.491822i
$525$		0			0
$526$	−6.00000	−	10.3923i	−0.261612	−	0.453126i
$527$	6.00000	−	10.3923i	0.261364	−	0.452696i
$528$		0			0
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$	−6.00000	−	10.3923i	−0.260623	−	0.451413i
$531$		0			0
$532$	−2.00000	+	10.3923i	−0.0867110	+	0.450564i
$533$	18.0000	−	31.1769i	0.779667	−	1.35042i
$534$		0			0
$535$	−24.0000			−1.03761
$536$	10.0000			0.431934
$537$		0			0
$538$	−15.5000	+	26.8468i	−0.668252	+	1.15745i
$539$	27.5000	−	21.6506i	1.18451	−	0.932559i
$540$		0			0
$541$	15.0000	+	25.9808i	0.644900	+	1.11700i	0.984325	+	0.176367i	$0.0564345\pi$
$541$	15.0000	+	25.9808i	0.644900	+	1.11700i	−0.339424	+	0.940633i	$0.610232\pi$
$542$		0			0
$543$		0			0
$544$	2.00000	−	3.46410i	0.0857493	−	0.148522i
$545$	16.0000	+	27.7128i	0.685365	+	1.18709i
$546$		0			0
$547$	9.00000	−	15.5885i	0.384812	−	0.666514i	−0.606931	−	0.794755i	$-0.707600\pi$
$547$	9.00000	−	15.5885i	0.384812	−	0.666514i	0.991743	+	0.128240i	$0.0409329\pi$
$548$	4.00000	+	6.92820i	0.170872	+	0.295958i
$549$		0			0
$550$	2.50000	−	4.33013i	0.106600	−	0.184637i
$551$	−28.0000			−1.19284
$552$		0			0
$553$	−6.00000	−	5.19615i	−0.255146	−	0.220963i
$554$	−1.00000	−	1.73205i	−0.0424859	−	0.0735878i
$555$		0			0
$556$	4.00000	+	6.92820i	0.169638	+	0.293821i
$557$	5.50000	−	9.52628i	0.233042	−	0.403641i	−0.725660	−	0.688054i	$-0.758465\pi$
$557$	5.50000	−	9.52628i	0.233042	−	0.403641i	0.958702	+	0.284413i	$0.0917985\pi$
$558$		0			0
$559$	48.0000			2.03018
$560$	5.00000	−	1.73205i	0.211289	−	0.0731925i
$561$		0			0
$562$	−1.00000	+	1.73205i	−0.0421825	+	0.0730622i
$563$	20.0000			0.842900			0.421450	−	0.906852i	$-0.361521\pi$
$563$	20.0000			0.842900			0.421450	+	0.906852i	$0.361521\pi$
$564$		0			0
$565$	−8.00000			−0.336563
$566$	16.0000			0.672530
$567$		0			0
$568$	−4.00000			−0.167836
$569$	−12.0000			−0.503066			−0.251533	−	0.967849i	$-0.580935\pi$
$569$	−12.0000			−0.503066			−0.251533	+	0.967849i	$0.580935\pi$
$570$		0			0
$571$		0			0			−	1.00000i	$-0.5\pi$
$571$		0			0				1.00000i	$0.5\pi$
$572$	−15.0000	+	25.9808i	−0.627182	+	1.08631i
$573$		0			0
$574$	−3.00000	+	15.5885i	−0.125218	+	0.650650i
$575$	4.00000			0.166812
$576$		0			0
$577$	−21.5000	+	37.2391i	−0.895057	+	1.55028i	−0.0613223	+	0.998118i	$0.519532\pi$
$577$	−21.5000	+	37.2391i	−0.895057	+	1.55028i	−0.833734	+	0.552166i	$0.813802\pi$
$578$	0.500000	+	0.866025i	0.0207973	+	0.0360219i
$579$		0			0
$580$	7.00000	+	12.1244i	0.290659	+	0.503436i
$581$	17.5000	−	6.06218i	0.726022	−	0.251502i
$582$		0			0
$583$	−30.0000			−1.24247
$584$	−6.50000	+	11.2583i	−0.268972	+	0.465873i
$585$		0			0
$586$	−13.5000	−	23.3827i	−0.557680	−	0.965930i
$587$	−10.0000	+	17.3205i	−0.412744	+	0.714894i	−0.995189	−	0.0979766i	$-0.968763\pi$
$587$	−10.0000	+	17.3205i	−0.412744	+	0.714894i	0.582445	+	0.812870i	$0.302096\pi$
$588$		0			0
$589$	6.00000	+	10.3923i	0.247226	+	0.428207i
$590$	7.00000	−	12.1244i	0.288185	−	0.499152i
$591$		0			0
$592$	−4.00000	−	6.92820i	−0.164399	−	0.284747i
$593$	−18.0000	−	31.1769i	−0.739171	−	1.28028i	−0.952869	−	0.303383i	$-0.901884\pi$
$593$	−18.0000	−	31.1769i	−0.739171	−	1.28028i	0.213697	−	0.976900i	$-0.431449\pi$
$594$		0			0
$595$	4.00000	−	20.7846i	0.163984	−	0.852086i
$596$	−4.50000	+	7.79423i	−0.184327	+	0.319264i
$597$		0			0
$598$	−24.0000			−0.981433
$599$	30.0000			1.22577			0.612883	−	0.790173i	$-0.290010\pi$
$599$	30.0000			1.22577			0.612883	+	0.790173i	$0.290010\pi$
$600$		0			0
$601$	5.00000	−	8.66025i	0.203954	−	0.353259i	−0.745845	−	0.666120i	$-0.767954\pi$
$601$	5.00000	−	8.66025i	0.203954	−	0.353259i	0.949799	+	0.312861i	$0.101287\pi$
$602$	−20.0000	+	6.92820i	−0.815139	+	0.282372i
$603$		0			0
$604$	8.50000	+	14.7224i	0.345860	+	0.599047i
$605$	14.0000	+	24.2487i	0.569181	+	0.985850i
$606$		0			0
$607$	4.50000	−	7.79423i	0.182649	−	0.316358i	−0.760133	−	0.649768i	$-0.774866\pi$
$607$	4.50000	−	7.79423i	0.182649	−	0.316358i	0.942782	+	0.333410i	$0.108199\pi$
$608$	2.00000	+	3.46410i	0.0811107	+	0.140488i
$609$		0			0
$610$		0			0
$611$	−18.0000	−	31.1769i	−0.728202	−	1.26128i
$612$		0			0
$613$	3.00000	−	5.19615i	0.121169	−	0.209871i	−0.799060	−	0.601251i	$-0.794669\pi$
$613$	3.00000	−	5.19615i	0.121169	−	0.209871i	0.920229	+	0.391381i	$0.128002\pi$
$614$	−2.00000			−0.0807134
$615$		0			0
$616$	2.50000	−	12.9904i	0.100728	−	0.523397i
$617$	−1.00000	−	1.73205i	−0.0402585	−	0.0697297i	0.845194	−	0.534460i	$-0.179485\pi$
$617$	−1.00000	−	1.73205i	−0.0402585	−	0.0697297i	−0.885453	+	0.464730i	$0.846151\pi$
$618$		0			0
$619$	−2.00000	−	3.46410i	−0.0803868	−	0.139234i	0.823029	−	0.567999i	$-0.192282\pi$
$619$	−2.00000	−	3.46410i	−0.0803868	−	0.139234i	−0.903416	+	0.428765i	$0.858949\pi$
$620$	3.00000	−	5.19615i	0.120483	−	0.208683i
$621$		0			0
$622$	22.0000			0.882120
$623$	3.00000	−	15.5885i	0.120192	−	0.624538i
$624$		0			0
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$	10.0000			0.399680
$627$		0			0
$628$	14.0000			0.558661
$629$	−32.0000			−1.27592
$630$		0			0
$631$	5.00000			0.199047			0.0995234	−	0.995035i	$-0.468268\pi$
$631$	5.00000			0.199047			0.0995234	+	0.995035i	$0.468268\pi$
$632$	−3.00000			−0.119334
$633$		0			0
$634$	−33.0000			−1.31060
$635$		0			0
$636$		0			0
$637$	33.0000	−	25.9808i	1.30751	−	1.02940i
$638$	35.0000			1.38566
$639$		0			0
$640$	1.00000	−	1.73205i	0.0395285	−	0.0684653i
$641$	−7.00000	−	12.1244i	−0.276483	−	0.478883i	0.694025	−	0.719951i	$-0.255836\pi$
$641$	−7.00000	−	12.1244i	−0.276483	−	0.478883i	−0.970508	+	0.241068i	$0.922502\pi$
$642$		0			0
$643$	−7.00000	−	12.1244i	−0.276053	−	0.478138i	0.694347	−	0.719640i	$-0.255693\pi$
$643$	−7.00000	−	12.1244i	−0.276053	−	0.478138i	−0.970400	+	0.241502i	$0.922360\pi$
$644$	10.0000	−	3.46410i	0.394055	−	0.136505i
$645$		0			0
$646$	16.0000			0.629512
$647$	9.00000	−	15.5885i	0.353827	−	0.612845i	−0.633090	−	0.774078i	$-0.718214\pi$
$647$	9.00000	−	15.5885i	0.353827	−	0.612845i	0.986916	+	0.161233i	$0.0515470\pi$
$648$		0			0
$649$	−17.5000	−	30.3109i	−0.686935	−	1.18981i
$650$	3.00000	−	5.19615i	0.117670	−	0.203810i
$651$		0			0
$652$	−1.00000	−	1.73205i	−0.0391630	−	0.0678323i
$653$	−9.00000	+	15.5885i	−0.352197	+	0.610023i	−0.986634	−	0.162951i	$-0.947899\pi$
$653$	−9.00000	+	15.5885i	−0.352197	+	0.610023i	0.634437	+	0.772975i	$0.281232\pi$
$654$		0			0
$655$	13.0000	+	22.5167i	0.507952	+	0.879799i
$656$	3.00000	+	5.19615i	0.117130	+	0.202876i
$657$		0			0
$658$	12.0000	+	10.3923i	0.467809	+	0.405134i
$659$	−20.5000	+	35.5070i	−0.798567	+	1.38316i	0.121983	+	0.992532i	$0.461075\pi$
$659$	−20.5000	+	35.5070i	−0.798567	+	1.38316i	−0.920550	+	0.390626i	$0.872259\pi$
$660$		0			0
$661$	−38.0000			−1.47803			−0.739014	−	0.673690i	$-0.764708\pi$
$661$	−38.0000			−1.47803			−0.739014	+	0.673690i	$0.764708\pi$
$662$	32.0000			1.24372
$663$		0			0
$664$	3.50000	−	6.06218i	0.135826	−	0.235258i
$665$	16.0000	+	13.8564i	0.620453	+	0.537328i
$666$		0			0
$667$	14.0000	+	24.2487i	0.542082	+	0.938914i
$668$	7.00000	+	12.1244i	0.270838	+	0.469105i
$669$		0			0
$670$	10.0000	−	17.3205i	0.386334	−	0.669150i
$671$		0			0
$672$		0			0
$673$	−1.00000	+	1.73205i	−0.0385472	+	0.0667657i	−0.884655	−	0.466246i	$-0.845606\pi$
$673$	−1.00000	+	1.73205i	−0.0385472	+	0.0667657i	0.846108	+	0.533011i	$0.178940\pi$
$674$	13.5000	+	23.3827i	0.520001	+	0.900667i
$675$		0			0
$676$	−11.5000	+	19.9186i	−0.442308	+	0.766099i
$677$	9.00000			0.345898			0.172949	−	0.984931i	$-0.444670\pi$
$677$	9.00000			0.345898			0.172949	+	0.984931i	$0.444670\pi$
$678$		0			0
$679$	12.5000	−	4.33013i	0.479706	−	0.166175i
$680$	−4.00000	−	6.92820i	−0.153393	−	0.265684i
$681$		0			0
$682$	−7.50000	−	12.9904i	−0.287190	−	0.497427i
$683$	−10.5000	+	18.1865i	−0.401771	+	0.695888i	−0.993940	−	0.109926i	$-0.964939\pi$
$683$	−10.5000	+	18.1865i	−0.401771	+	0.695888i	0.592168	+	0.805814i	$0.298272\pi$
$684$		0			0
$685$	16.0000			0.611329
$686$	−10.0000	+	15.5885i	−0.381802	+	0.595170i
$687$		0			0
$688$	−4.00000	+	6.92820i	−0.152499	+	0.264135i
$689$	−36.0000			−1.37149
$690$		0			0
$691$	8.00000			0.304334			0.152167	−	0.988355i	$-0.451375\pi$
$691$	8.00000			0.304334			0.152167	+	0.988355i	$0.451375\pi$
$692$	1.00000			0.0380143
$693$		0			0
$694$	−27.0000			−1.02491
$695$	16.0000			0.606915
$696$		0			0
$697$	24.0000			0.909065
$698$	10.0000	−	17.3205i	0.378506	−	0.655591i
$699$		0			0
$700$	−0.500000	+	2.59808i	−0.0188982	+	0.0981981i
$701$	−14.0000			−0.528773			−0.264386	−	0.964417i	$-0.585169\pi$
$701$	−14.0000			−0.528773			−0.264386	+	0.964417i	$0.585169\pi$
$702$		0			0
$703$	16.0000	−	27.7128i	0.603451	−	1.04521i
$704$	−2.50000	−	4.33013i	−0.0942223	−	0.163198i
$705$		0			0
$706$	15.0000	+	25.9808i	0.564532	+	0.977799i
$707$	−2.50000	+	12.9904i	−0.0940222	+	0.488554i
$708$		0			0
$709$	8.00000			0.300446			0.150223	−	0.988652i	$-0.452001\pi$
$709$	8.00000			0.300446			0.150223	+	0.988652i	$0.452001\pi$
$710$	−4.00000	+	6.92820i	−0.150117	+	0.260011i
$711$		0			0
$712$	−3.00000	−	5.19615i	−0.112430	−	0.194734i
$713$	6.00000	−	10.3923i	0.224702	−	0.389195i
$714$		0			0
$715$	30.0000	+	51.9615i	1.12194	+	1.94325i
$716$	7.50000	−	12.9904i	0.280288	−	0.485473i
$717$		0			0
$718$	−8.00000	−	13.8564i	−0.298557	−	0.517116i
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	0.804648	−	0.593753i	$-0.202354\pi$
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	−0.916529	+	0.399969i	$0.869021\pi$
$720$		0			0
$721$	−20.0000	+	6.92820i	−0.744839	+	0.258020i
$722$	1.50000	−	2.59808i	0.0558242	−	0.0966904i
$723$		0			0
$724$		0			0
$725$	−7.00000			−0.259973
$726$		0			0
$727$	16.0000	−	27.7128i	0.593407	−	1.02781i	−0.400362	−	0.916357i	$-0.631116\pi$
$727$	16.0000	−	27.7128i	0.593407	−	1.02781i	0.993770	−	0.111454i	$-0.0355509\pi$
$728$	3.00000	−	15.5885i	0.111187	−	0.577747i
$729$		0			0
$730$	13.0000	+	22.5167i	0.481152	+	0.833379i
$731$	16.0000	+	27.7128i	0.591781	+	1.02500i
$732$		0			0
$733$	18.0000	−	31.1769i	0.664845	−	1.15155i	−0.314482	−	0.949263i	$-0.601831\pi$
$733$	18.0000	−	31.1769i	0.664845	−	1.15155i	0.979327	−	0.202282i	$-0.0648358\pi$
$734$	2.00000	+	3.46410i	0.0738213	+	0.127862i
$735$		0			0
$736$	2.00000	−	3.46410i	0.0737210	−	0.127688i
$737$	−25.0000	−	43.3013i	−0.920887	−	1.59502i
$738$		0			0
$739$	3.00000	−	5.19615i	0.110357	−	0.191144i	−0.805557	−	0.592518i	$-0.798134\pi$
$739$	3.00000	−	5.19615i	0.110357	−	0.191144i	0.915914	+	0.401374i	$0.131467\pi$
$740$	−16.0000			−0.588172
$741$		0			0
$742$	15.0000	−	5.19615i	0.550667	−	0.190757i
$743$	3.00000	+	5.19615i	0.110059	+	0.190628i	0.915794	−	0.401648i	$-0.131563\pi$
$743$	3.00000	+	5.19615i	0.110059	+	0.190628i	−0.805735	+	0.592277i	$0.798229\pi$
$744$		0			0
$745$	9.00000	+	15.5885i	0.329734	+	0.571117i
$746$	10.0000	−	17.3205i	0.366126	−	0.634149i
$747$		0			0
$748$	−20.0000			−0.731272
$749$	6.00000	−	31.1769i	0.219235	−	1.13918i
$750$		0			0
$751$	−6.00000	+	10.3923i	−0.218943	+	0.379221i	−0.954485	−	0.298259i	$-0.903594\pi$
$751$	−6.00000	+	10.3923i	−0.218943	+	0.379221i	0.735542	+	0.677479i	$0.236928\pi$
$752$	6.00000			0.218797
$753$		0			0
$754$	42.0000			1.52955
$755$	34.0000			1.23739
$756$		0			0
$757$	−18.0000			−0.654221			−0.327111	−	0.944986i	$-0.606075\pi$
$757$	−18.0000			−0.654221			−0.327111	+	0.944986i	$0.606075\pi$
$758$	10.0000			0.363216
$759$		0			0
$760$	8.00000			0.290191
$761$	−4.00000	+	6.92820i	−0.145000	+	0.251147i	−0.929373	−	0.369142i	$-0.879652\pi$
$761$	−4.00000	+	6.92820i	−0.145000	+	0.251147i	0.784373	+	0.620289i	$0.212985\pi$
$762$		0			0
$763$	−40.0000	+	13.8564i	−1.44810	+	0.501636i
$764$	−18.0000			−0.651217
$765$		0			0
$766$	2.00000	−	3.46410i	0.0722629	−	0.125163i
$767$	−21.0000	−	36.3731i	−0.758266	−	1.31336i
$768$		0			0
$769$	−0.500000	−	0.866025i	−0.0180305	−	0.0312297i	0.856869	−	0.515534i	$-0.172406\pi$
$769$	−0.500000	−	0.866025i	−0.0180305	−	0.0312297i	−0.874900	+	0.484304i	$0.839073\pi$
$770$	−20.0000	−	17.3205i	−0.720750	−	0.624188i
$771$		0			0
$772$	−19.0000			−0.683825
$773$	19.0000	−	32.9090i	0.683383	−	1.18365i	−0.290560	−	0.956857i	$-0.593841\pi$
$773$	19.0000	−	32.9090i	0.683383	−	1.18365i	0.973942	−	0.226796i	$-0.0728252\pi$
$774$		0			0
$775$	1.50000	+	2.59808i	0.0538816	+	0.0933257i
$776$	2.50000	−	4.33013i	0.0897448	−	0.155443i
$777$		0			0
$778$	−0.500000	−	0.866025i	−0.0179259	−	0.0310485i
$779$	−12.0000	+	20.7846i	−0.429945	+	0.744686i
$780$		0			0
$781$	10.0000	+	17.3205i	0.357828	+	0.619777i
$782$	−8.00000	−	13.8564i	−0.286079	−	0.495504i
$783$		0			0
$784$	1.00000	+	6.92820i	0.0357143	+	0.247436i
$785$	14.0000	−	24.2487i	0.499681	−	0.865474i
$786$		0			0
$787$	18.0000			0.641631			0.320815	−	0.947142i	$-0.396043\pi$
$787$	18.0000			0.641631			0.320815	+	0.947142i	$0.396043\pi$
$788$	−25.0000			−0.890588
$789$		0			0
$790$	−3.00000	+	5.19615i	−0.106735	+	0.184871i
$791$	2.00000	−	10.3923i	0.0711118	−	0.369508i
$792$		0			0
$793$		0			0
$794$	9.00000	+	15.5885i	0.319398	+	0.553214i
$795$		0			0
$796$	9.50000	−	16.4545i	0.336719	−	0.583214i
$797$	−16.5000	−	28.5788i	−0.584460	−	1.01231i	−0.994943	−	0.100446i	$-0.967973\pi$
$797$	−16.5000	−	28.5788i	−0.584460	−	1.01231i	0.410483	−	0.911868i	$-0.365360\pi$
$798$		0			0
$799$	12.0000	−	20.7846i	0.424529	−	0.735307i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$		0			0
$802$	9.00000	−	15.5885i	0.317801	−	0.550448i
$803$	65.0000			2.29380
$804$		0			0
$805$	4.00000	−	20.7846i	0.140981	−	0.732561i
$806$	−9.00000	−	15.5885i	−0.317011	−	0.549080i
$807$		0			0
$808$	2.50000	+	4.33013i	0.0879497	+	0.152333i
$809$	−17.0000	+	29.4449i	−0.597688	+	1.03523i	0.395473	+	0.918477i	$0.370581\pi$
$809$	−17.0000	+	29.4449i	−0.597688	+	1.03523i	−0.993161	+	0.116749i	$0.962753\pi$
$810$		0			0
$811$	−50.0000			−1.75574			−0.877869	−	0.478901i	$-0.841035\pi$
$811$	−50.0000			−1.75574			−0.877869	+	0.478901i	$0.841035\pi$
$812$	−17.5000	+	6.06218i	−0.614130	+	0.212741i
$813$		0			0
$814$	−20.0000	+	34.6410i	−0.701000	+	1.21417i
$815$	−4.00000			−0.140114
$816$		0			0
$817$	−32.0000			−1.11954
$818$	−10.0000			−0.349642
$819$		0			0
$820$	12.0000			0.419058
$821$	−49.0000			−1.71011			−0.855056	−	0.518536i	$-0.826477\pi$
$821$	−49.0000			−1.71011			−0.855056	+	0.518536i	$0.826477\pi$
$822$		0			0
$823$	13.0000			0.453152			0.226576	−	0.973994i	$-0.427247\pi$
$823$	13.0000			0.453152			0.226576	+	0.973994i	$0.427247\pi$
$824$	−4.00000	+	6.92820i	−0.139347	+	0.241355i
$825$		0			0
$826$	14.0000	+	12.1244i	0.487122	+	0.421860i
$827$	51.0000			1.77344			0.886722	−	0.462303i	$-0.152977\pi$
$827$	51.0000			1.77344			0.886722	+	0.462303i	$0.152977\pi$
$828$		0			0
$829$	−11.0000	+	19.0526i	−0.382046	+	0.661723i	−0.991355	−	0.131210i	$-0.958114\pi$
$829$	−11.0000	+	19.0526i	−0.382046	+	0.661723i	0.609309	+	0.792933i	$0.291447\pi$
$830$	−7.00000	−	12.1244i	−0.242974	−	0.420843i
$831$		0			0
$832$	−3.00000	−	5.19615i	−0.104006	−	0.180144i
$833$	26.0000	+	10.3923i	0.900847	+	0.360072i
$834$		0			0
$835$	28.0000			0.968980
$836$	10.0000	−	17.3205i	0.345857	−	0.599042i
$837$		0			0
$838$	−6.00000	−	10.3923i	−0.207267	−	0.358996i
$839$	2.00000	−	3.46410i	0.0690477	−	0.119594i	−0.829435	−	0.558604i	$-0.811337\pi$
$839$	2.00000	−	3.46410i	0.0690477	−	0.119594i	0.898482	+	0.439010i	$0.144671\pi$
$840$		0			0
$841$	−10.0000	−	17.3205i	−0.344828	−	0.597259i
$842$	9.00000	−	15.5885i	0.310160	−	0.537214i
$843$		0			0
$844$	−13.0000	−	22.5167i	−0.447478	−	0.775055i
$845$	23.0000	+	39.8372i	0.791224	+	1.37044i
$846$		0			0
$847$	−35.0000	+	12.1244i	−1.20261	+	0.416598i
$848$	3.00000	−	5.19615i	0.103020	−	0.178437i
$849$		0			0
$850$	4.00000			0.137199
$851$	−32.0000			−1.09695
$852$		0			0
$853$	23.0000	−	39.8372i	0.787505	−	1.36400i	−0.139986	−	0.990153i	$-0.544706\pi$
$853$	23.0000	−	39.8372i	0.787505	−	1.36400i	0.927491	−	0.373845i	$-0.121961\pi$
$854$		0			0
$855$		0			0
$856$	−6.00000	−	10.3923i	−0.205076	−	0.355202i
$857$	−15.0000	−	25.9808i	−0.512390	−	0.887486i	−0.999897	−	0.0143666i	$-0.995427\pi$
$857$	−15.0000	−	25.9808i	−0.512390	−	0.887486i	0.487507	−	0.873119i	$-0.337907\pi$
$858$		0			0
$859$	8.00000	−	13.8564i	0.272956	−	0.472774i	−0.696661	−	0.717400i	$-0.745332\pi$
$859$	8.00000	−	13.8564i	0.272956	−	0.472774i	0.969618	+	0.244626i	$0.0786652\pi$
$860$	8.00000	+	13.8564i	0.272798	+	0.472500i
$861$		0			0
$862$	9.00000	−	15.5885i	0.306541	−	0.530945i
$863$	19.0000	+	32.9090i	0.646768	+	1.12023i	0.983890	+	0.178774i	$0.0572129\pi$
$863$	19.0000	+	32.9090i	0.646768	+	1.12023i	−0.337123	+	0.941461i	$0.609454\pi$
$864$		0			0
$865$	1.00000	−	1.73205i	0.0340010	−	0.0588915i
$866$	−7.00000			−0.237870
$867$		0			0
$868$	6.00000	+	5.19615i	0.203653	+	0.176369i
$869$	7.50000	+	12.9904i	0.254420	+	0.440668i
$870$		0			0
$871$	−30.0000	−	51.9615i	−1.01651	−	1.76065i
$872$	−8.00000	+	13.8564i	−0.270914	+	0.469237i
$873$		0			0
$874$	16.0000			0.541208
$875$	24.0000	+	20.7846i	0.811348	+	0.702648i
$876$		0			0
$877$	−17.0000	+	29.4449i	−0.574049	+	0.994282i	0.422095	+	0.906552i	$0.361295\pi$
$877$	−17.0000	+	29.4449i	−0.574049	+	0.994282i	−0.996144	+	0.0877308i	$0.972038\pi$
$878$	3.00000			0.101245
$879$		0			0
$880$	−10.0000			−0.337100
$881$	−54.0000			−1.81931			−0.909653	−	0.415369i	$-0.863653\pi$
$881$	−54.0000			−1.81931			−0.909653	+	0.415369i	$0.863653\pi$
$882$		0			0
$883$	2.00000			0.0673054			0.0336527	−	0.999434i	$-0.489286\pi$
$883$	2.00000			0.0673054			0.0336527	+	0.999434i	$0.489286\pi$
$884$	−24.0000			−0.807207
$885$		0			0
$886$	11.0000			0.369552
$887$	21.0000	−	36.3731i	0.705111	−	1.22129i	−0.261540	−	0.965193i	$-0.584230\pi$
$887$	21.0000	−	36.3731i	0.705111	−	1.22129i	0.966651	−	0.256096i	$-0.0824362\pi$
$888$		0			0
$889$		0			0
$890$	−12.0000			−0.402241
$891$		0			0
$892$	0.500000	−	0.866025i	0.0167412	−	0.0289967i
$893$	12.0000	+	20.7846i	0.401565	+	0.695530i
$894$		0			0
$895$	−15.0000	−	25.9808i	−0.501395	−	0.868441i
$896$	2.00000	+	1.73205i	0.0668153	+	0.0578638i
$897$		0			0
$898$	−14.0000			−0.467186
$899$	−10.5000	+	18.1865i	−0.350195	+	0.606555i
$900$		0			0
$901$	−12.0000	−	20.7846i	−0.399778	−	0.692436i
$902$	15.0000	−	25.9808i	0.499445	−	0.865065i
$903$		0			0
$904$	−2.00000	−	3.46410i	−0.0665190	−	0.115214i
$905$		0			0
$906$		0			0
$907$	21.0000	+	36.3731i	0.697294	+	1.20775i	0.969401	+	0.245481i	$0.0789459\pi$
$907$	21.0000	+	36.3731i	0.697294	+	1.20775i	−0.272108	+	0.962267i	$0.587721\pi$
$908$	13.5000	+	23.3827i	0.448013	+	0.775982i
$909$		0			0
$910$	−24.0000	−	20.7846i	−0.795592	−	0.689003i
$911$	−18.0000	+	31.1769i	−0.596367	+	1.03294i	0.396986	+	0.917825i	$0.370056\pi$
$911$	−18.0000	+	31.1769i	−0.596367	+	1.03294i	−0.993352	+	0.115113i	$0.963277\pi$
$912$		0			0
$913$	−35.0000			−1.15833
$914$	−26.0000			−0.860004
$915$		0			0
$916$	−2.00000	+	3.46410i	−0.0660819	+	0.114457i
$917$	−32.5000	+	11.2583i	−1.07324	+	0.371783i
$918$		0			0
$919$	−6.50000	−	11.2583i	−0.214415	−	0.371378i	0.738676	−	0.674060i	$-0.235451\pi$
$919$	−6.50000	−	11.2583i	−0.214415	−	0.371378i	−0.953092	+	0.302682i	$0.902118\pi$
$920$	−4.00000	−	6.92820i	−0.131876	−	0.228416i
$921$		0			0
$922$	11.5000	−	19.9186i	0.378732	−	0.655984i
$923$	12.0000	+	20.7846i	0.394985	+	0.684134i
$924$		0			0
$925$	4.00000	−	6.92820i	0.131519	−	0.227798i
$926$	14.5000	+	25.1147i	0.476500	+	0.825321i
$927$		0			0
$928$	−3.50000	+	6.06218i	−0.114893	+	0.199001i
$929$	36.0000			1.18112			0.590561	−	0.806993i	$-0.298907\pi$
$929$	36.0000			1.18112			0.590561	+	0.806993i	$0.298907\pi$
$930$		0			0
$931$	−22.0000	+	17.3205i	−0.721021	+	0.567657i
$932$	11.0000	+	19.0526i	0.360317	+	0.624087i
$933$		0			0
$934$	−3.50000	−	6.06218i	−0.114523	−	0.198361i
$935$	−20.0000	+	34.6410i	−0.654070	+	1.13288i
$936$		0			0
$937$	14.0000			0.457360			0.228680	−	0.973502i	$-0.426559\pi$
$937$	14.0000			0.457360			0.228680	+	0.973502i	$0.426559\pi$
$938$	20.0000	+	17.3205i	0.653023	+	0.565535i
$939$		0			0
$940$	6.00000	−	10.3923i	0.195698	−	0.338960i
$941$	13.0000			0.423788			0.211894	−	0.977293i	$-0.432037\pi$
$941$	13.0000			0.423788			0.211894	+	0.977293i	$0.432037\pi$
$942$		0			0
$943$	24.0000			0.781548
$944$	7.00000			0.227831
$945$		0			0
$946$	40.0000			1.30051
$947$	25.0000			0.812391			0.406195	−	0.913786i	$-0.366855\pi$
$947$	25.0000			0.812391			0.406195	+	0.913786i	$0.366855\pi$
$948$		0			0
$949$	78.0000			2.53199
$950$	−2.00000	+	3.46410i	−0.0648886	+	0.112390i
$951$		0			0
$952$	10.0000	−	3.46410i	0.324102	−	0.112272i
$953$	2.00000			0.0647864			0.0323932	−	0.999475i	$-0.489687\pi$
$953$	2.00000			0.0647864			0.0323932	+	0.999475i	$0.489687\pi$
$954$		0			0
$955$	−18.0000	+	31.1769i	−0.582466	+	1.00886i
$956$		0			0
$957$		0			0
$958$	−13.0000	−	22.5167i	−0.420011	−	0.727480i
$959$	−4.00000	+	20.7846i	−0.129167	+	0.671170i
$960$		0			0
$961$	−22.0000			−0.709677
$962$	−24.0000	+	41.5692i	−0.773791	+	1.34025i
$963$		0			0
$964$	0.500000	+	0.866025i	0.0161039	+	0.0278928i
$965$	−19.0000	+	32.9090i	−0.611632	+	1.05938i
$966$		0			0
$967$	−4.00000	−	6.92820i	−0.128631	−	0.222796i	0.794515	−	0.607244i	$-0.207725\pi$
$967$	−4.00000	−	6.92820i	−0.128631	−	0.222796i	−0.923147	+	0.384448i	$0.874392\pi$
$968$	−7.00000	+	12.1244i	−0.224989	+	0.389692i
$969$		0			0
$970$	−5.00000	−	8.66025i	−0.160540	−	0.278064i
$971$	−6.00000	−	10.3923i	−0.192549	−	0.333505i	0.753545	−	0.657396i	$-0.228342\pi$
$971$	−6.00000	−	10.3923i	−0.192549	−	0.333505i	−0.946094	+	0.323891i	$0.895009\pi$
$972$		0			0
$973$	−4.00000	+	20.7846i	−0.128234	+	0.666324i
$974$	6.50000	−	11.2583i	0.208273	−	0.360740i
$975$		0			0
$976$		0			0
$977$	−18.0000			−0.575871			−0.287936	−	0.957650i	$-0.592969\pi$
$977$	−18.0000			−0.575871			−0.287936	+	0.957650i	$0.592969\pi$
$978$		0			0
$979$	−15.0000	+	25.9808i	−0.479402	+	0.830349i
$980$	13.0000	+	5.19615i	0.415270	+	0.165985i
$981$		0			0
$982$	−6.00000	−	10.3923i	−0.191468	−	0.331632i
$983$	−18.0000	−	31.1769i	−0.574111	−	0.994389i	−0.996138	−	0.0878058i	$-0.972015\pi$
$983$	−18.0000	−	31.1769i	−0.574111	−	0.994389i	0.422027	−	0.906583i	$-0.361319\pi$
$984$		0			0
$985$	−25.0000	+	43.3013i	−0.796566	+	1.37969i
$986$	14.0000	+	24.2487i	0.445851	+	0.772236i
$987$		0			0
$988$	12.0000	−	20.7846i	0.381771	−	0.661247i
$989$	16.0000	+	27.7128i	0.508770	+	0.881216i
$990$		0			0
$991$	−4.00000	+	6.92820i	−0.127064	+	0.220082i	−0.922538	−	0.385906i	$-0.873889\pi$
$991$	−4.00000	+	6.92820i	−0.127064	+	0.220082i	0.795474	+	0.605988i	$0.207222\pi$
$992$	3.00000			0.0952501
$993$		0			0
$994$	−8.00000	−	6.92820i	−0.253745	−	0.219749i
$995$	−19.0000	−	32.9090i	−0.602340	−	1.04328i
$996$		0			0
$997$	29.0000	+	50.2295i	0.918439	+	1.59078i	0.801786	+	0.597611i	$0.203883\pi$
$997$	29.0000	+	50.2295i	0.918439	+	1.59078i	0.116653	+	0.993173i	$0.462784\pi$
$998$	4.00000	−	6.92820i	0.126618	−	0.219308i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.e.o.865.1		2
3.2	odd	2		1134.2.e.b.865.1		2
7.2	even	3		1134.2.h.b.541.1		2
9.2	odd	6		378.2.g.d.109.1	yes	2
9.4	even	3		1134.2.h.b.109.1		2
9.5	odd	6		1134.2.h.o.109.1		2
9.7	even	3		378.2.g.c.109.1	✓	2
21.2	odd	6		1134.2.h.o.541.1		2
63.2	odd	6		378.2.g.d.163.1	yes	2
63.11	odd	6		2646.2.a.k.1.1		1
63.16	even	3		378.2.g.c.163.1	yes	2
63.23	odd	6		1134.2.e.b.919.1		2
63.25	even	3		2646.2.a.t.1.1		1
63.38	even	6		2646.2.a.c.1.1		1
63.52	odd	6		2646.2.a.bb.1.1		1
63.58	even	3	inner	1134.2.e.o.919.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.g.c.109.1	✓	2	9.7	even	3
378.2.g.c.163.1	yes	2	63.16	even	3
378.2.g.d.109.1	yes	2	9.2	odd	6
378.2.g.d.163.1	yes	2	63.2	odd	6
1134.2.e.b.865.1		2	3.2	odd	2
1134.2.e.b.919.1		2	63.23	odd	6
1134.2.e.o.865.1		2	1.1	even	1	trivial
1134.2.e.o.919.1		2	63.58	even	3	inner
1134.2.h.b.109.1		2	9.4	even	3
1134.2.h.b.541.1		2	7.2	even	3
1134.2.h.o.109.1		2	9.5	odd	6
1134.2.h.o.541.1		2	21.2	odd	6
2646.2.a.c.1.1		1	63.38	even	6
2646.2.a.k.1.1		1	63.11	odd	6
2646.2.a.t.1.1		1	63.25	even	3
2646.2.a.bb.1.1		1	63.52	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:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(1.00000 - 1.73205i) q^{5} +(2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(1.00000 - 1.73205i) q^{5} +(2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(1.00000 - 1.73205i) q^{10} +(-2.50000 - 4.33013i) q^{11} +(-3.00000 - 5.19615i) q^{13} +(2.00000 + 1.73205i) q^{14} +1.00000 q^{16} +(2.00000 - 3.46410i) q^{17} +(2.00000 + 3.46410i) q^{19} +(1.00000 - 1.73205i) q^{20} +(-2.50000 - 4.33013i) q^{22} +(2.00000 - 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{25} +(-3.00000 - 5.19615i) q^{26} +(2.00000 + 1.73205i) q^{28} +(-3.50000 + 6.06218i) q^{29} +3.00000 q^{31} +1.00000 q^{32} +(2.00000 - 3.46410i) q^{34} +(5.00000 - 1.73205i) q^{35} +(-4.00000 - 6.92820i) q^{37} +(2.00000 + 3.46410i) q^{38} +(1.00000 - 1.73205i) q^{40} +(3.00000 + 5.19615i) q^{41} +(-4.00000 + 6.92820i) q^{43} +(-2.50000 - 4.33013i) q^{44} +(2.00000 - 3.46410i) q^{46} +6.00000 q^{47} +(1.00000 + 6.92820i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-3.00000 - 5.19615i) q^{52} +(3.00000 - 5.19615i) q^{53} -10.0000 q^{55} +(2.00000 + 1.73205i) q^{56} +(-3.50000 + 6.06218i) q^{58} +7.00000 q^{59} +3.00000 q^{62} +1.00000 q^{64} -12.0000 q^{65} +10.0000 q^{67} +(2.00000 - 3.46410i) q^{68} +(5.00000 - 1.73205i) q^{70} -4.00000 q^{71} +(-6.50000 + 11.2583i) q^{73} +(-4.00000 - 6.92820i) q^{74} +(2.00000 + 3.46410i) q^{76} +(2.50000 - 12.9904i) q^{77} -3.00000 q^{79} +(1.00000 - 1.73205i) q^{80} +(3.00000 + 5.19615i) q^{82} +(3.50000 - 6.06218i) q^{83} +(-4.00000 - 6.92820i) q^{85} +(-4.00000 + 6.92820i) q^{86} +(-2.50000 - 4.33013i) q^{88} +(-3.00000 - 5.19615i) q^{89} +(3.00000 - 15.5885i) q^{91} +(2.00000 - 3.46410i) q^{92} +6.00000 q^{94} +8.00000 q^{95} +(2.50000 - 4.33013i) q^{97} +(1.00000 + 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{4} + 2 q^{5} + 4 q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^5 + 4 * q^7 + 2 * q^8	\( 2 q + 2 q^{2} + 2 q^{4} + 2 q^{5} + 4 q^{7} + 2 q^{8} + 2 q^{10} - 5 q^{11} - 6 q^{13} + 4 q^{14} + 2 q^{16} + 4 q^{17} + 4 q^{19} + 2 q^{20} - 5 q^{22} + 4 q^{23} + q^{25} - 6 q^{26} + 4 q^{28} - 7 q^{29} + 6 q^{31} + 2 q^{32} + 4 q^{34} + 10 q^{35} - 8 q^{37} + 4 q^{38} + 2 q^{40} + 6 q^{41} - 8 q^{43} - 5 q^{44} + 4 q^{46} + 12 q^{47} + 2 q^{49} + q^{50} - 6 q^{52} + 6 q^{53} - 20 q^{55} + 4 q^{56} - 7 q^{58} + 14 q^{59} + 6 q^{62} + 2 q^{64} - 24 q^{65} + 20 q^{67} + 4 q^{68} + 10 q^{70} - 8 q^{71} - 13 q^{73} - 8 q^{74} + 4 q^{76} + 5 q^{77} - 6 q^{79} + 2 q^{80} + 6 q^{82} + 7 q^{83} - 8 q^{85} - 8 q^{86} - 5 q^{88} - 6 q^{89} + 6 q^{91} + 4 q^{92} + 12 q^{94} + 16 q^{95} + 5 q^{97} + 2 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^5 + 4 * q^7 + 2 * q^8 + 2 * q^10 - 5 * q^11 - 6 * q^13 + 4 * q^14 + 2 * q^16 + 4 * q^17 + 4 * q^19 + 2 * q^20 - 5 * q^22 + 4 * q^23 + q^25 - 6 * q^26 + 4 * q^28 - 7 * q^29 + 6 * q^31 + 2 * q^32 + 4 * q^34 + 10 * q^35 - 8 * q^37 + 4 * q^38 + 2 * q^40 + 6 * q^41 - 8 * q^43 - 5 * q^44 + 4 * q^46 + 12 * q^47 + 2 * q^49 + q^50 - 6 * q^52 + 6 * q^53 - 20 * q^55 + 4 * q^56 - 7 * q^58 + 14 * q^59 + 6 * q^62 + 2 * q^64 - 24 * q^65 + 20 * q^67 + 4 * q^68 + 10 * q^70 - 8 * q^71 - 13 * q^73 - 8 * q^74 + 4 * q^76 + 5 * q^77 - 6 * q^79 + 2 * q^80 + 6 * q^82 + 7 * q^83 - 8 * q^85 - 8 * q^86 - 5 * q^88 - 6 * q^89 + 6 * q^91 + 4 * q^92 + 12 * q^94 + 16 * q^95 + 5 * q^97 + 2 * q^98

Introduction

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