LMFDB - Embedded newform 315.2.p.b.118.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(118,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("315.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.p (of order $4$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 25 $ x^4 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			118.2
Root			$1.58114 - 1.58114i$ of defining polynomial
Character	$\chi$	$=$	315.118
Dual form			315.2.p.b.307.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.58114 - 1.58114i) q^{2} -3.00000i q^{4} +(2.00000 + 1.00000i) q^{5} +(2.58114 + 0.581139i) q^{7} +(-1.58114 - 1.58114i) q^{8} +O(q^{10})$	\(q+(1.58114 - 1.58114i) q^{2} -3.00000i q^{4} +(2.00000 + 1.00000i) q^{5} +(2.58114 + 0.581139i) q^{7} +(-1.58114 - 1.58114i) q^{8} +(4.74342 - 1.58114i) q^{10} -3.16228 q^{11} +(-3.16228 + 3.16228i) q^{13} +(5.00000 - 3.16228i) q^{14} +1.00000 q^{16} +(-5.00000 - 5.00000i) q^{17} -3.16228 q^{19} +(3.00000 - 6.00000i) q^{20} +(-5.00000 + 5.00000i) q^{22} +(-3.16228 - 3.16228i) q^{23} +(3.00000 + 4.00000i) q^{25} +10.0000i q^{26} +(1.74342 - 7.74342i) q^{28} -3.16228i q^{31} +(4.74342 - 4.74342i) q^{32} -15.8114 q^{34} +(4.58114 + 3.74342i) q^{35} +(-3.00000 + 3.00000i) q^{37} +(-5.00000 + 5.00000i) q^{38} +(-1.58114 - 4.74342i) q^{40} +(6.00000 + 6.00000i) q^{43} +9.48683i q^{44} -10.0000 q^{46} +(6.32456 + 3.00000i) q^{49} +(11.0680 + 1.58114i) q^{50} +(9.48683 + 9.48683i) q^{52} +(3.16228 + 3.16228i) q^{53} +(-6.32456 - 3.16228i) q^{55} +(-3.16228 - 5.00000i) q^{56} +12.6491i q^{61} +(-5.00000 - 5.00000i) q^{62} -13.0000i q^{64} +(-9.48683 + 3.16228i) q^{65} +(8.00000 - 8.00000i) q^{67} +(-15.0000 + 15.0000i) q^{68} +(13.1623 - 1.32456i) q^{70} -9.48683 q^{71} +(9.48683 - 9.48683i) q^{73} +9.48683i q^{74} +9.48683i q^{76} +(-8.16228 - 1.83772i) q^{77} -4.00000i q^{79} +(2.00000 + 1.00000i) q^{80} +(10.0000 - 10.0000i) q^{83} +(-5.00000 - 15.0000i) q^{85} +18.9737 q^{86} +(5.00000 + 5.00000i) q^{88} -10.0000 q^{89} +(-10.0000 + 6.32456i) q^{91} +(-9.48683 + 9.48683i) q^{92} +(-6.32456 - 3.16228i) q^{95} +(-3.16228 - 3.16228i) q^{97} +(14.7434 - 5.25658i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{5} + 4 q^{7}+O(q^{10}) $ 4 * q + 8 * q^5 + 4 * q^7	$ 4 q + 8 q^{5} + 4 q^{7} + 20 q^{14} + 4 q^{16} - 20 q^{17} + 12 q^{20} - 20 q^{22} + 12 q^{25} - 12 q^{28} + 12 q^{35} - 12 q^{37} - 20 q^{38} + 24 q^{43} - 40 q^{46} - 20 q^{62} + 32 q^{67} - 60 q^{68} + 40 q^{70} - 20 q^{77} + 8 q^{80} + 40 q^{83} - 20 q^{85} + 20 q^{88} - 40 q^{89} - 40 q^{91} + 40 q^{98}+O(q^{100}) $ 4 * q + 8 * q^5 + 4 * q^7 + 20 * q^14 + 4 * q^16 - 20 * q^17 + 12 * q^20 - 20 * q^22 + 12 * q^25 - 12 * q^28 + 12 * q^35 - 12 * q^37 - 20 * q^38 + 24 * q^43 - 40 * q^46 - 20 * q^62 + 32 * q^67 - 60 * q^68 + 40 * q^70 - 20 * q^77 + 8 * q^80 + 40 * q^83 - 20 * q^85 + 20 * q^88 - 40 * q^89 - 40 * q^91 + 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.58114	−	1.58114i	1.11803	−	1.11803i	0.126004	−	0.992030i	$-0.459785\pi$
$2$	1.58114	−	1.58114i	1.11803	−	1.11803i	0.992030	−	0.126004i	$-0.0402153\pi$
$3$		0			0
$3$		0			0
$4$		−	3.00000i		−	1.50000i
$5$	2.00000	+	1.00000i	0.894427	+	0.447214i
$5$	2.00000	+	1.00000i	0.894427	+	0.447214i
$6$		0			0
$7$	2.58114	+	0.581139i	0.975579	+	0.219650i
$7$	2.58114	+	0.581139i	0.975579	+	0.219650i
$8$	−1.58114	−	1.58114i	−0.559017	−	0.559017i
$9$		0			0
$10$	4.74342	−	1.58114i	1.50000	−	0.500000i
$11$	−3.16228			−0.953463			−0.476731	−	0.879049i	$-0.658179\pi$
$11$	−3.16228			−0.953463			−0.476731	+	0.879049i	$0.658179\pi$
$12$		0			0
$13$	−3.16228	+	3.16228i	−0.877058	+	0.877058i	−0.993229	−	0.116171i	$-0.962938\pi$
$13$	−3.16228	+	3.16228i	−0.877058	+	0.877058i	0.116171	+	0.993229i	$0.462938\pi$
$14$	5.00000	−	3.16228i	1.33631	−	0.845154i
$15$		0			0
$16$	1.00000			0.250000
$17$	−5.00000	−	5.00000i	−1.21268	−	1.21268i	−0.970143	−	0.242536i	$-0.922021\pi$
$17$	−5.00000	−	5.00000i	−1.21268	−	1.21268i	−0.242536	−	0.970143i	$-0.577979\pi$
$18$		0			0
$19$	−3.16228			−0.725476			−0.362738	−	0.931891i	$-0.618158\pi$
$19$	−3.16228			−0.725476			−0.362738	+	0.931891i	$0.618158\pi$
$20$	3.00000	−	6.00000i	0.670820	−	1.34164i
$21$		0			0
$22$	−5.00000	+	5.00000i	−1.06600	+	1.06600i
$23$	−3.16228	−	3.16228i	−0.659380	−	0.659380i	0.295853	−	0.955233i	$-0.404396\pi$
$23$	−3.16228	−	3.16228i	−0.659380	−	0.659380i	−0.955233	+	0.295853i	$0.904396\pi$
$24$		0			0
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$			10.0000i			1.96116i
$27$		0			0
$28$	1.74342	−	7.74342i	0.329475	−	1.46337i
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$		0			0
$31$		−	3.16228i		−	0.567962i	−0.958830	−	0.283981i	$-0.908345\pi$
$31$		−	3.16228i		−	0.567962i	0.958830	−	0.283981i	$-0.0916552\pi$
$32$	4.74342	−	4.74342i	0.838525	−	0.838525i
$33$		0			0
$34$	−15.8114			−2.71163
$35$	4.58114	+	3.74342i	0.774354	+	0.632753i
$36$		0			0
$37$	−3.00000	+	3.00000i	−0.493197	+	0.493197i	−0.909312	−	0.416115i	$-0.863391\pi$
$37$	−3.00000	+	3.00000i	−0.493197	+	0.493197i	0.416115	+	0.909312i	$0.363391\pi$
$38$	−5.00000	+	5.00000i	−0.811107	+	0.811107i
$39$		0			0
$40$	−1.58114	−	4.74342i	−0.250000	−	0.750000i
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$		0			0
$43$	6.00000	+	6.00000i	0.914991	+	0.914991i	0.996660	−	0.0816682i	$-0.0260248\pi$
$43$	6.00000	+	6.00000i	0.914991	+	0.914991i	−0.0816682	+	0.996660i	$0.526025\pi$
$44$			9.48683i			1.43019i
$45$		0			0
$46$	−10.0000			−1.47442
$47$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$47$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$48$		0			0
$49$	6.32456	+	3.00000i	0.903508	+	0.428571i
$50$	11.0680	+	1.58114i	1.56525	+	0.223607i
$51$		0			0
$52$	9.48683	+	9.48683i	1.31559	+	1.31559i
$53$	3.16228	+	3.16228i	0.434372	+	0.434372i	0.890113	−	0.455740i	$-0.150625\pi$
$53$	3.16228	+	3.16228i	0.434372	+	0.434372i	−0.455740	+	0.890113i	$0.650625\pi$
$54$		0			0
$55$	−6.32456	−	3.16228i	−0.852803	−	0.426401i
$56$	−3.16228	−	5.00000i	−0.422577	−	0.668153i
$57$		0			0
$58$		0			0
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$		0			0
$61$			12.6491i			1.61955i	0.586739	+	0.809776i	$0.300412\pi$
$61$			12.6491i			1.61955i	−0.586739	+	0.809776i	$0.699588\pi$
$62$	−5.00000	−	5.00000i	−0.635001	−	0.635001i
$63$		0			0
$64$		−	13.0000i		−	1.62500i
$65$	−9.48683	+	3.16228i	−1.17670	+	0.392232i
$66$		0			0
$67$	8.00000	−	8.00000i	0.977356	−	0.977356i	−0.0223937	−	0.999749i	$-0.507129\pi$
$67$	8.00000	−	8.00000i	0.977356	−	0.977356i	0.999749	+	0.0223937i	$0.00712872\pi$
$68$	−15.0000	+	15.0000i	−1.81902	+	1.81902i
$69$		0			0
$70$	13.1623	−	1.32456i	1.57319	−	0.158315i
$71$	−9.48683			−1.12588			−0.562940	−	0.826498i	$-0.690330\pi$
$71$	−9.48683			−1.12588			−0.562940	+	0.826498i	$0.690330\pi$
$72$		0			0
$73$	9.48683	−	9.48683i	1.11035	−	1.11035i	0.117247	−	0.993103i	$-0.462593\pi$
$73$	9.48683	−	9.48683i	1.11035	−	1.11035i	0.993103	−	0.117247i	$-0.0374069\pi$
$74$			9.48683i			1.10282i
$75$		0			0
$76$			9.48683i			1.08821i
$77$	−8.16228	−	1.83772i	−0.930178	−	0.209428i
$78$		0			0
$79$		−	4.00000i		−	0.450035i	−0.974355	−	0.225018i	$-0.927756\pi$
$79$		−	4.00000i		−	0.450035i	0.974355	−	0.225018i	$-0.0722440\pi$
$80$	2.00000	+	1.00000i	0.223607	+	0.111803i
$81$		0			0
$82$		0			0
$83$	10.0000	−	10.0000i	1.09764	−	1.09764i	0.102957	−	0.994686i	$-0.467170\pi$
$83$	10.0000	−	10.0000i	1.09764	−	1.09764i	0.994686	−	0.102957i	$-0.0328303\pi$
$84$		0			0
$85$	−5.00000	−	15.0000i	−0.542326	−	1.62698i
$86$	18.9737			2.04598
$87$		0			0
$88$	5.00000	+	5.00000i	0.533002	+	0.533002i
$89$	−10.0000			−1.06000			−0.529999	−	0.847998i	$-0.677808\pi$
$89$	−10.0000			−1.06000			−0.529999	+	0.847998i	$0.677808\pi$
$90$		0			0
$91$	−10.0000	+	6.32456i	−1.04828	+	0.662994i
$92$	−9.48683	+	9.48683i	−0.989071	+	0.989071i
$93$		0			0
$94$		0			0
$95$	−6.32456	−	3.16228i	−0.648886	−	0.324443i
$96$		0			0
$97$	−3.16228	−	3.16228i	−0.321081	−	0.321081i	0.528101	−	0.849182i	$-0.322904\pi$
$97$	−3.16228	−	3.16228i	−0.321081	−	0.321081i	−0.849182	+	0.528101i	$0.822904\pi$
$98$	14.7434	−	5.25658i	1.48931	−	0.530995i
$99$		0			0
$100$	12.0000	−	9.00000i	1.20000	−	0.900000i
$101$			10.0000i			0.995037i	0.867453	+	0.497519i	$0.165755\pi$
$101$			10.0000i			0.995037i	−0.867453	+	0.497519i	$0.834245\pi$
$102$		0			0
$103$	3.16228	−	3.16228i	0.311588	−	0.311588i	−0.533936	−	0.845525i	$-0.679288\pi$
$103$	3.16228	−	3.16228i	0.311588	−	0.311588i	0.845525	+	0.533936i	$0.179288\pi$
$104$	10.0000			0.980581
$105$		0			0
$106$	10.0000			0.971286
$107$	9.48683	−	9.48683i	0.917127	−	0.917127i	−0.0796927	−	0.996819i	$-0.525394\pi$
$107$	9.48683	−	9.48683i	0.917127	−	0.917127i	0.996819	+	0.0796927i	$0.0253939\pi$
$108$		0			0
$109$			4.00000i			0.383131i	0.981480	+	0.191565i	$0.0613564\pi$
$109$			4.00000i			0.383131i	−0.981480	+	0.191565i	$0.938644\pi$
$110$	−15.0000	+	5.00000i	−1.43019	+	0.476731i
$111$		0			0
$112$	2.58114	+	0.581139i	0.243895	+	0.0549125i
$113$	9.48683	+	9.48683i	0.892446	+	0.892446i	0.994753	−	0.102307i	$-0.0326223\pi$
$113$	9.48683	+	9.48683i	0.892446	+	0.892446i	−0.102307	+	0.994753i	$0.532622\pi$
$114$		0			0
$115$	−3.16228	−	9.48683i	−0.294884	−	0.884652i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−10.0000	−	15.8114i	−0.916698	−	1.44943i
$120$		0			0
$121$	−1.00000			−0.0909091
$122$	20.0000	+	20.0000i	1.81071	+	1.81071i
$123$		0			0
$124$	−9.48683			−0.851943
$125$	2.00000	+	11.0000i	0.178885	+	0.983870i
$126$		0			0
$127$	−12.0000	+	12.0000i	−1.06483	+	1.06483i	−0.0670802	+	0.997748i	$0.521368\pi$
$127$	−12.0000	+	12.0000i	−1.06483	+	1.06483i	−0.997748	+	0.0670802i	$0.978632\pi$
$128$	−11.0680	−	11.0680i	−0.978280	−	0.978280i
$129$		0			0
$130$	−10.0000	+	20.0000i	−0.877058	+	1.75412i
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$		0			0
$133$	−8.16228	−	1.83772i	−0.707759	−	0.159351i
$134$		−	25.2982i		−	2.18543i
$135$		0			0
$136$			15.8114i			1.35582i
$137$	−3.16228	+	3.16228i	−0.270172	+	0.270172i	−0.829169	−	0.558998i	$-0.811186\pi$
$137$	−3.16228	+	3.16228i	−0.270172	+	0.270172i	0.558998	+	0.829169i	$0.311186\pi$
$138$		0			0
$139$	9.48683			0.804663			0.402331	−	0.915494i	$-0.368200\pi$
$139$	9.48683			0.804663			0.402331	+	0.915494i	$0.368200\pi$
$140$	11.2302	−	13.7434i	0.949129	−	1.16153i
$141$		0			0
$142$	−15.0000	+	15.0000i	−1.25877	+	1.25877i
$143$	10.0000	−	10.0000i	0.836242	−	0.836242i
$144$		0			0
$145$		0			0
$146$		−	30.0000i		−	2.48282i
$147$		0			0
$148$	9.00000	+	9.00000i	0.739795	+	0.739795i
$149$			18.9737i			1.55438i	0.629264	+	0.777192i	$0.283356\pi$
$149$			18.9737i			1.55438i	−0.629264	+	0.777192i	$0.716644\pi$
$150$		0			0
$151$	−12.0000			−0.976546			−0.488273	−	0.872691i	$-0.662373\pi$
$151$	−12.0000			−0.976546			−0.488273	+	0.872691i	$0.662373\pi$
$152$	5.00000	+	5.00000i	0.405554	+	0.405554i
$153$		0			0
$154$	−15.8114	+	10.0000i	−1.27412	+	0.805823i
$155$	3.16228	−	6.32456i	0.254000	−	0.508001i
$156$		0			0
$157$	−15.8114	−	15.8114i	−1.26189	−	1.26189i	−0.950178	−	0.311708i	$-0.899099\pi$
$157$	−15.8114	−	15.8114i	−1.26189	−	1.26189i	−0.311708	−	0.950178i	$-0.600901\pi$
$158$	−6.32456	−	6.32456i	−0.503155	−	0.503155i
$159$		0			0
$160$	14.2302	−	4.74342i	1.12500	−	0.375000i
$161$	−6.32456	−	10.0000i	−0.498445	−	0.788110i
$162$		0			0
$163$	−6.00000	−	6.00000i	−0.469956	−	0.469956i	0.431944	−	0.901900i	$-0.357828\pi$
$163$	−6.00000	−	6.00000i	−0.469956	−	0.469956i	−0.901900	+	0.431944i	$0.857828\pi$
$164$		0			0
$165$		0			0
$166$		−	31.6228i		−	2.45440i
$167$	10.0000	+	10.0000i	0.773823	+	0.773823i	0.978773	−	0.204949i	$-0.0657030\pi$
$167$	10.0000	+	10.0000i	0.773823	+	0.773823i	−0.204949	+	0.978773i	$0.565703\pi$
$168$		0			0
$169$		−	7.00000i		−	0.538462i
$170$	−31.6228	−	15.8114i	−2.42536	−	1.21268i
$171$		0			0
$172$	18.0000	−	18.0000i	1.37249	−	1.37249i
$173$	5.00000	−	5.00000i	0.380143	−	0.380143i	−0.491011	−	0.871154i	$-0.663372\pi$
$173$	5.00000	−	5.00000i	0.380143	−	0.380143i	0.871154	+	0.491011i	$0.163372\pi$
$174$		0			0
$175$	5.41886	+	12.0680i	0.409627	+	0.912253i
$176$	−3.16228			−0.238366
$177$		0			0
$178$	−15.8114	+	15.8114i	−1.18511	+	1.18511i
$179$		−	9.48683i		−	0.709079i	−0.935041	−	0.354540i	$-0.884638\pi$
$179$		−	9.48683i		−	0.709079i	0.935041	−	0.354540i	$-0.115362\pi$
$180$		0			0
$181$		−	6.32456i		−	0.470100i	−0.971983	−	0.235050i	$-0.924475\pi$
$181$		−	6.32456i		−	0.470100i	0.971983	−	0.235050i	$-0.0755255\pi$
$182$	−5.81139	+	25.8114i	−0.430769	+	1.91327i
$183$		0			0
$184$			10.0000i			0.737210i
$185$	−9.00000	+	3.00000i	−0.661693	+	0.220564i
$186$		0			0
$187$	15.8114	+	15.8114i	1.15624	+	1.15624i
$188$		0			0
$189$		0			0
$190$	−15.0000	+	5.00000i	−1.08821	+	0.362738i
$191$	9.48683			0.686443			0.343222	−	0.939254i	$-0.388482\pi$
$191$	9.48683			0.686443			0.343222	+	0.939254i	$0.388482\pi$
$192$		0			0
$193$	1.00000	+	1.00000i	0.0719816	+	0.0719816i	0.742181	−	0.670199i	$-0.233791\pi$
$193$	1.00000	+	1.00000i	0.0719816	+	0.0719816i	−0.670199	+	0.742181i	$0.733791\pi$
$194$	−10.0000			−0.717958
$195$		0			0
$196$	9.00000	−	18.9737i	0.642857	−	1.35526i
$197$	−3.16228	+	3.16228i	−0.225303	+	0.225303i	−0.810727	−	0.585424i	$-0.800928\pi$
$197$	−3.16228	+	3.16228i	−0.225303	+	0.225303i	0.585424	+	0.810727i	$0.300928\pi$
$198$		0			0
$199$	−9.48683			−0.672504			−0.336252	−	0.941772i	$-0.609159\pi$
$199$	−9.48683			−0.672504			−0.336252	+	0.941772i	$0.609159\pi$
$200$	1.58114	−	11.0680i	0.111803	−	0.782624i
$201$		0			0
$202$	15.8114	+	15.8114i	1.11249	+	1.11249i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		−	10.0000i		−	0.696733i
$207$		0			0
$208$	−3.16228	+	3.16228i	−0.219265	+	0.219265i
$209$	10.0000			0.691714
$210$		0			0
$211$	8.00000			0.550743			0.275371	−	0.961338i	$-0.411199\pi$
$211$	8.00000			0.550743			0.275371	+	0.961338i	$0.411199\pi$
$212$	9.48683	−	9.48683i	0.651558	−	0.651558i
$213$		0			0
$214$		−	30.0000i		−	2.05076i
$215$	6.00000	+	18.0000i	0.409197	+	1.22759i
$216$		0			0
$217$	1.83772	−	8.16228i	0.124753	−	0.554092i
$218$	6.32456	+	6.32456i	0.428353	+	0.428353i
$219$		0			0
$220$	−9.48683	+	18.9737i	−0.639602	+	1.27920i
$221$	31.6228			2.12718
$222$		0			0
$223$	18.9737	−	18.9737i	1.27057	−	1.27057i	0.324782	−	0.945789i	$-0.394709\pi$
$223$	18.9737	−	18.9737i	1.27057	−	1.27057i	0.945789	−	0.324782i	$-0.105291\pi$
$224$	15.0000	−	9.48683i	1.00223	−	0.633866i
$225$		0			0
$226$	30.0000			1.99557
$227$	−10.0000	−	10.0000i	−0.663723	−	0.663723i	0.292532	−	0.956256i	$-0.405502\pi$
$227$	−10.0000	−	10.0000i	−0.663723	−	0.663723i	−0.956256	+	0.292532i	$0.905502\pi$
$228$		0			0
$229$	12.6491			0.835877			0.417938	−	0.908475i	$-0.362753\pi$
$229$	12.6491			0.835877			0.417938	+	0.908475i	$0.362753\pi$
$230$	−20.0000	−	10.0000i	−1.31876	−	0.659380i
$231$		0			0
$232$		0			0
$233$	9.48683	+	9.48683i	0.621503	+	0.621503i	0.945916	−	0.324413i	$-0.105167\pi$
$233$	9.48683	+	9.48683i	0.621503	+	0.621503i	−0.324413	+	0.945916i	$0.605167\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$	−40.8114	−	9.18861i	−2.64541	−	0.595609i
$239$		−	22.1359i		−	1.43186i	−0.698175	−	0.715928i	$-0.746004\pi$
$239$		−	22.1359i		−	1.43186i	0.698175	−	0.715928i	$-0.253996\pi$
$240$		0			0
$241$		−	6.32456i		−	0.407400i	−0.979033	−	0.203700i	$-0.934703\pi$
$241$		−	6.32456i		−	0.407400i	0.979033	−	0.203700i	$-0.0652968\pi$
$242$	−1.58114	+	1.58114i	−0.101639	+	0.101639i
$243$		0			0
$244$	37.9473			2.42933
$245$	9.64911	+	12.3246i	0.616459	+	0.787387i
$246$		0			0
$247$	10.0000	−	10.0000i	0.636285	−	0.636285i
$248$	−5.00000	+	5.00000i	−0.317500	+	0.317500i
$249$		0			0
$250$	20.5548	+	14.2302i	1.30000	+	0.900000i
$251$			20.0000i			1.26239i	0.775625	+	0.631194i	$0.217435\pi$
$251$			20.0000i			1.26239i	−0.775625	+	0.631194i	$0.782565\pi$
$252$		0			0
$253$	10.0000	+	10.0000i	0.628695	+	0.628695i
$254$			37.9473i			2.38103i
$255$		0			0
$256$	−9.00000			−0.562500
$257$	5.00000	+	5.00000i	0.311891	+	0.311891i	0.845642	−	0.533751i	$-0.179218\pi$
$257$	5.00000	+	5.00000i	0.311891	+	0.311891i	−0.533751	+	0.845642i	$0.679218\pi$
$258$		0			0
$259$	−9.48683	+	6.00000i	−0.589483	+	0.372822i
$260$	9.48683	+	28.4605i	0.588348	+	1.76505i
$261$		0			0
$262$		0			0
$263$	−6.32456	−	6.32456i	−0.389989	−	0.389989i	0.484695	−	0.874683i	$-0.338931\pi$
$263$	−6.32456	−	6.32456i	−0.389989	−	0.389989i	−0.874683	+	0.484695i	$0.838931\pi$
$264$		0			0
$265$	3.16228	+	9.48683i	0.194257	+	0.582772i
$266$	−15.8114	+	10.0000i	−0.969458	+	0.613139i
$267$		0			0
$268$	−24.0000	−	24.0000i	−1.46603	−	1.46603i
$269$	−30.0000			−1.82913			−0.914566	−	0.404436i	$-0.867468\pi$
$269$	−30.0000			−1.82913			−0.914566	+	0.404436i	$0.867468\pi$
$270$		0			0
$271$			22.1359i			1.34466i	0.740250	+	0.672331i	$0.234707\pi$
$271$			22.1359i			1.34466i	−0.740250	+	0.672331i	$0.765293\pi$
$272$	−5.00000	−	5.00000i	−0.303170	−	0.303170i
$273$		0			0
$274$			10.0000i			0.604122i
$275$	−9.48683	−	12.6491i	−0.572078	−	0.762770i
$276$		0			0
$277$	3.00000	−	3.00000i	0.180253	−	0.180253i	−0.611213	−	0.791466i	$-0.709318\pi$
$277$	3.00000	−	3.00000i	0.180253	−	0.180253i	0.791466	+	0.611213i	$0.209318\pi$
$278$	15.0000	−	15.0000i	0.899640	−	0.899640i
$279$		0			0
$280$	−1.32456	−	13.1623i	−0.0791573	−	0.786597i
$281$	−18.9737			−1.13187			−0.565937	−	0.824448i	$-0.691485\pi$
$281$	−18.9737			−1.13187			−0.565937	+	0.824448i	$0.691485\pi$
$282$		0			0
$283$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$283$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$284$			28.4605i			1.68882i
$285$		0			0
$286$		−	31.6228i		−	1.86989i
$287$		0			0
$288$		0			0
$289$			33.0000i			1.94118i
$290$		0			0
$291$		0			0
$292$	−28.4605	−	28.4605i	−1.66552	−	1.66552i
$293$	−5.00000	+	5.00000i	−0.292103	+	0.292103i	−0.837911	−	0.545807i	$-0.816223\pi$
$293$	−5.00000	+	5.00000i	−0.292103	+	0.292103i	0.545807	+	0.837911i	$0.316223\pi$
$294$		0			0
$295$		0			0
$296$	9.48683			0.551411
$297$		0			0
$298$	30.0000	+	30.0000i	1.73785	+	1.73785i
$299$	20.0000			1.15663
$300$		0			0
$301$	12.0000	+	18.9737i	0.691669	+	1.09362i
$302$	−18.9737	+	18.9737i	−1.09181	+	1.09181i
$303$		0			0
$304$	−3.16228			−0.181369
$305$	−12.6491	+	25.2982i	−0.724286	+	1.44857i
$306$		0			0
$307$	−9.48683	−	9.48683i	−0.541442	−	0.541442i	0.382509	−	0.923952i	$-0.375060\pi$
$307$	−9.48683	−	9.48683i	−0.541442	−	0.541442i	−0.923952	+	0.382509i	$0.875060\pi$
$308$	−5.51317	+	24.4868i	−0.314142	+	1.39527i
$309$		0			0
$310$	−5.00000	−	15.0000i	−0.283981	−	0.851943i
$311$		−	20.0000i		−	1.13410i	−0.823685	−	0.567048i	$-0.808085\pi$
$311$		−	20.0000i		−	1.13410i	0.823685	−	0.567048i	$-0.191915\pi$
$312$		0			0
$313$	−9.48683	+	9.48683i	−0.536228	+	0.536228i	−0.922419	−	0.386191i	$-0.873790\pi$
$313$	−9.48683	+	9.48683i	−0.536228	+	0.536228i	0.386191	+	0.922419i	$0.373790\pi$
$314$	−50.0000			−2.82166
$315$		0			0
$316$	−12.0000			−0.675053
$317$	22.1359	−	22.1359i	1.24328	−	1.24328i	0.284646	−	0.958633i	$-0.408124\pi$
$317$	22.1359	−	22.1359i	1.24328	−	1.24328i	0.958633	−	0.284646i	$-0.0918759\pi$
$318$		0			0
$319$		0			0
$320$	13.0000	−	26.0000i	0.726722	−	1.45344i
$321$		0			0
$322$	−25.8114	−	5.81139i	−1.43841	−	0.323856i
$323$	15.8114	+	15.8114i	0.879769	+	0.879769i
$324$		0			0
$325$	−22.1359	−	3.16228i	−1.22788	−	0.175412i
$326$	−18.9737			−1.05085
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−12.0000			−0.659580			−0.329790	−	0.944054i	$-0.606978\pi$
$331$	−12.0000			−0.659580			−0.329790	+	0.944054i	$0.606978\pi$
$332$	−30.0000	−	30.0000i	−1.64646	−	1.64646i
$333$		0			0
$334$	31.6228			1.73032
$335$	24.0000	−	8.00000i	1.31126	−	0.437087i
$336$		0			0
$337$	7.00000	−	7.00000i	0.381314	−	0.381314i	−0.490261	−	0.871576i	$-0.663099\pi$
$337$	7.00000	−	7.00000i	0.381314	−	0.381314i	0.871576	+	0.490261i	$0.163099\pi$
$338$	−11.0680	−	11.0680i	−0.602018	−	0.602018i
$339$		0			0
$340$	−45.0000	+	15.0000i	−2.44047	+	0.813489i
$341$			10.0000i			0.541530i
$342$		0			0
$343$	14.5811	+	11.4189i	0.787307	+	0.616561i
$344$		−	18.9737i		−	1.02299i
$345$		0			0
$346$		−	15.8114i		−	0.850026i
$347$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$347$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$348$		0			0
$349$	12.6491			0.677091			0.338546	−	0.940950i	$-0.390065\pi$
$349$	12.6491			0.677091			0.338546	+	0.940950i	$0.390065\pi$
$350$	27.6491	+	10.5132i	1.47791	+	0.561952i
$351$		0			0
$352$	−15.0000	+	15.0000i	−0.799503	+	0.799503i
$353$	−15.0000	+	15.0000i	−0.798369	+	0.798369i	−0.982838	−	0.184469i	$-0.940943\pi$
$353$	−15.0000	+	15.0000i	−0.798369	+	0.798369i	0.184469	+	0.982838i	$0.440943\pi$
$354$		0			0
$355$	−18.9737	−	9.48683i	−1.00702	−	0.503509i
$356$			30.0000i			1.59000i
$357$		0			0
$358$	−15.0000	−	15.0000i	−0.792775	−	0.792775i
$359$			22.1359i			1.16829i	0.811649	+	0.584145i	$0.198570\pi$
$359$			22.1359i			1.16829i	−0.811649	+	0.584145i	$0.801430\pi$
$360$		0			0
$361$	−9.00000			−0.473684
$362$	−10.0000	−	10.0000i	−0.525588	−	0.525588i
$363$		0			0
$364$	18.9737	+	30.0000i	0.994490	+	1.57243i
$365$	28.4605	−	9.48683i	1.48969	−	0.496564i
$366$		0			0
$367$	−6.32456	−	6.32456i	−0.330139	−	0.330139i	0.522500	−	0.852639i	$-0.324999\pi$
$367$	−6.32456	−	6.32456i	−0.330139	−	0.330139i	−0.852639	+	0.522500i	$0.824999\pi$
$368$	−3.16228	−	3.16228i	−0.164845	−	0.164845i
$369$		0			0
$370$	−9.48683	+	18.9737i	−0.493197	+	0.986394i
$371$	6.32456	+	10.0000i	0.328355	+	0.519174i
$372$		0			0
$373$	9.00000	+	9.00000i	0.466002	+	0.466002i	0.900617	−	0.434614i	$-0.143115\pi$
$373$	9.00000	+	9.00000i	0.466002	+	0.466002i	−0.434614	+	0.900617i	$0.643115\pi$
$374$	50.0000			2.58544
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$			4.00000i			0.205466i	0.994709	+	0.102733i	$0.0327588\pi$
$379$			4.00000i			0.205466i	−0.994709	+	0.102733i	$0.967241\pi$
$380$	−9.48683	+	18.9737i	−0.486664	+	0.973329i
$381$		0			0
$382$	15.0000	−	15.0000i	0.767467	−	0.767467i
$383$	−10.0000	+	10.0000i	−0.510976	+	0.510976i	−0.914825	−	0.403849i	$-0.867672\pi$
$383$	−10.0000	+	10.0000i	−0.510976	+	0.510976i	0.403849	+	0.914825i	$0.367672\pi$
$384$		0			0
$385$	−14.4868	−	11.8377i	−0.738317	−	0.603306i
$386$	3.16228			0.160956
$387$		0			0
$388$	−9.48683	+	9.48683i	−0.481621	+	0.481621i
$389$		−	6.32456i		−	0.320668i	−0.987063	−	0.160334i	$-0.948743\pi$
$389$		−	6.32456i		−	0.320668i	0.987063	−	0.160334i	$-0.0512571\pi$
$390$		0			0
$391$			31.6228i			1.59923i
$392$	−5.25658	−	14.7434i	−0.265498	−	0.744655i
$393$		0			0
$394$			10.0000i			0.503793i
$395$	4.00000	−	8.00000i	0.201262	−	0.402524i
$396$		0			0
$397$	−9.48683	−	9.48683i	−0.476130	−	0.476130i	0.427761	−	0.903892i	$-0.359302\pi$
$397$	−9.48683	−	9.48683i	−0.476130	−	0.476130i	−0.903892	+	0.427761i	$0.859302\pi$
$398$	−15.0000	+	15.0000i	−0.751882	+	0.751882i
$399$		0			0
$400$	3.00000	+	4.00000i	0.150000	+	0.200000i
$401$	−12.6491			−0.631666			−0.315833	−	0.948815i	$-0.602284\pi$
$401$	−12.6491			−0.631666			−0.315833	+	0.948815i	$0.602284\pi$
$402$		0			0
$403$	10.0000	+	10.0000i	0.498135	+	0.498135i
$404$	30.0000			1.49256
$405$		0			0
$406$		0			0
$407$	9.48683	−	9.48683i	0.470245	−	0.470245i
$408$		0			0
$409$	25.2982			1.25092			0.625458	−	0.780258i	$-0.284912\pi$
$409$	25.2982			1.25092			0.625458	+	0.780258i	$0.284912\pi$
$410$		0			0
$411$		0			0
$412$	−9.48683	−	9.48683i	−0.467383	−	0.467383i
$413$		0			0
$414$		0			0
$415$	30.0000	−	10.0000i	1.47264	−	0.490881i
$416$			30.0000i			1.47087i
$417$		0			0
$418$	15.8114	−	15.8114i	0.773360	−	0.773360i
$419$	20.0000			0.977064			0.488532	−	0.872546i	$-0.337533\pi$
$419$	20.0000			0.977064			0.488532	+	0.872546i	$0.337533\pi$
$420$		0			0
$421$	−8.00000			−0.389896			−0.194948	−	0.980814i	$-0.562454\pi$
$421$	−8.00000			−0.389896			−0.194948	+	0.980814i	$0.562454\pi$
$422$	12.6491	−	12.6491i	0.615749	−	0.615749i
$423$		0			0
$424$		−	10.0000i		−	0.485643i
$425$	5.00000	−	35.0000i	0.242536	−	1.69775i
$426$		0			0
$427$	−7.35089	+	32.6491i	−0.355734	+	1.58000i
$428$	−28.4605	−	28.4605i	−1.37569	−	1.37569i
$429$		0			0
$430$	37.9473	+	18.9737i	1.82998	+	0.914991i
$431$	22.1359			1.06625			0.533125	−	0.846036i	$-0.321017\pi$
$431$	22.1359			1.06625			0.533125	+	0.846036i	$0.321017\pi$
$432$		0			0
$433$	−9.48683	+	9.48683i	−0.455908	+	0.455908i	−0.897310	−	0.441402i	$-0.854481\pi$
$433$	−9.48683	+	9.48683i	−0.455908	+	0.455908i	0.441402	+	0.897310i	$0.354481\pi$
$434$	−10.0000	−	15.8114i	−0.480015	−	0.758971i
$435$		0			0
$436$	12.0000			0.574696
$437$	10.0000	+	10.0000i	0.478365	+	0.478365i
$438$		0			0
$439$	3.16228			0.150927			0.0754636	−	0.997149i	$-0.475956\pi$
$439$	3.16228			0.150927			0.0754636	+	0.997149i	$0.475956\pi$
$440$	5.00000	+	15.0000i	0.238366	+	0.715097i
$441$		0			0
$442$	50.0000	−	50.0000i	2.37826	−	2.37826i
$443$	−25.2982	−	25.2982i	−1.20195	−	1.20195i	−0.973571	−	0.228384i	$-0.926656\pi$
$443$	−25.2982	−	25.2982i	−1.20195	−	1.20195i	−0.228384	−	0.973571i	$-0.573344\pi$
$444$		0			0
$445$	−20.0000	−	10.0000i	−0.948091	−	0.474045i
$446$		−	60.0000i		−	2.84108i
$447$		0			0
$448$	7.55480	−	33.5548i	0.356931	−	1.58532i
$449$			25.2982i			1.19390i	0.802280	+	0.596948i	$0.203620\pi$
$449$			25.2982i			1.19390i	−0.802280	+	0.596948i	$0.796380\pi$
$450$		0			0
$451$		0			0
$452$	28.4605	−	28.4605i	1.33867	−	1.33867i
$453$		0			0
$454$	−31.6228			−1.48413
$455$	−26.3246	+	2.64911i	−1.23411	+	0.124192i
$456$		0			0
$457$	17.0000	−	17.0000i	0.795226	−	0.795226i	−0.187112	−	0.982339i	$-0.559913\pi$
$457$	17.0000	−	17.0000i	0.795226	−	0.795226i	0.982339	+	0.187112i	$0.0599128\pi$
$458$	20.0000	−	20.0000i	0.934539	−	0.934539i
$459$		0			0
$460$	−28.4605	+	9.48683i	−1.32698	+	0.442326i
$461$			20.0000i			0.931493i	0.884918	+	0.465746i	$0.154214\pi$
$461$			20.0000i			0.931493i	−0.884918	+	0.465746i	$0.845786\pi$
$462$		0			0
$463$	−16.0000	−	16.0000i	−0.743583	−	0.743583i	0.229683	−	0.973266i	$-0.426231\pi$
$463$	−16.0000	−	16.0000i	−0.743583	−	0.743583i	−0.973266	+	0.229683i	$0.926231\pi$
$464$		0			0
$465$		0			0
$466$	30.0000			1.38972
$467$	−10.0000	−	10.0000i	−0.462745	−	0.462745i	0.436809	−	0.899554i	$-0.356108\pi$
$467$	−10.0000	−	10.0000i	−0.462745	−	0.462745i	−0.899554	+	0.436809i	$0.856108\pi$
$468$		0			0
$469$	25.2982	−	16.0000i	1.16816	−	0.738811i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−18.9737	−	18.9737i	−0.872410	−	0.872410i
$474$		0			0
$475$	−9.48683	−	12.6491i	−0.435286	−	0.580381i
$476$	−47.4342	+	30.0000i	−2.17414	+	1.37505i
$477$		0			0
$478$	−35.0000	−	35.0000i	−1.60086	−	1.60086i
$479$	20.0000			0.913823			0.456912	−	0.889512i	$-0.348956\pi$
$479$	20.0000			0.913823			0.456912	+	0.889512i	$0.348956\pi$
$480$		0			0
$481$		−	18.9737i		−	0.865125i
$482$	−10.0000	−	10.0000i	−0.455488	−	0.455488i
$483$		0			0
$484$			3.00000i			0.136364i
$485$	−3.16228	−	9.48683i	−0.143592	−	0.430775i
$486$		0			0
$487$	−8.00000	+	8.00000i	−0.362515	+	0.362515i	−0.864738	−	0.502223i	$-0.832516\pi$
$487$	−8.00000	+	8.00000i	−0.362515	+	0.362515i	0.502223	+	0.864738i	$0.332516\pi$
$488$	20.0000	−	20.0000i	0.905357	−	0.905357i
$489$		0			0
$490$	34.7434	+	4.23025i	1.56955	+	0.191103i
$491$	−34.7851			−1.56983			−0.784914	−	0.619605i	$-0.787293\pi$
$491$	−34.7851			−1.56983			−0.784914	+	0.619605i	$0.787293\pi$
$492$		0			0
$493$		0			0
$494$		−	31.6228i		−	1.42278i
$495$		0			0
$496$		−	3.16228i		−	0.141990i
$497$	−24.4868	−	5.51317i	−1.09838	−	0.247299i
$498$		0			0
$499$		−	16.0000i		−	0.716258i	−0.933672	−	0.358129i	$-0.883415\pi$
$499$		−	16.0000i		−	0.716258i	0.933672	−	0.358129i	$-0.116585\pi$
$500$	33.0000	−	6.00000i	1.47580	−	0.268328i
$501$		0			0
$502$	31.6228	+	31.6228i	1.41139	+	1.41139i
$503$	−10.0000	+	10.0000i	−0.445878	+	0.445878i	−0.893982	−	0.448104i	$-0.852100\pi$
$503$	−10.0000	+	10.0000i	−0.445878	+	0.445878i	0.448104	+	0.893982i	$0.352100\pi$
$504$		0			0
$505$	−10.0000	+	20.0000i	−0.444994	+	0.889988i
$506$	31.6228			1.40580
$507$		0			0
$508$	36.0000	+	36.0000i	1.59724	+	1.59724i
$509$		0			0			−	1.00000i	$-0.5\pi$
$509$		0			0				1.00000i	$0.5\pi$
$510$		0			0
$511$	30.0000	−	18.9737i	1.32712	−	0.839346i
$512$	7.90569	−	7.90569i	0.349386	−	0.349386i
$513$		0			0
$514$	15.8114			0.697410
$515$	9.48683	−	3.16228i	0.418040	−	0.139347i
$516$		0			0
$517$		0			0
$518$	−5.51317	+	24.4868i	−0.242235	+	1.07589i
$519$		0			0
$520$	20.0000	+	10.0000i	0.877058	+	0.438529i
$521$		−	10.0000i		−	0.438108i	−0.975713	−	0.219054i	$-0.929703\pi$
$521$		−	10.0000i		−	0.438108i	0.975713	−	0.219054i	$-0.0702971\pi$
$522$		0			0
$523$	9.48683	−	9.48683i	0.414830	−	0.414830i	−0.468587	−	0.883417i	$-0.655237\pi$
$523$	9.48683	−	9.48683i	0.414830	−	0.414830i	0.883417	+	0.468587i	$0.155237\pi$
$524$		0			0
$525$		0			0
$526$	−20.0000			−0.872041
$527$	−15.8114	+	15.8114i	−0.688755	+	0.688755i
$528$		0			0
$529$		−	3.00000i		−	0.130435i
$530$	20.0000	+	10.0000i	0.868744	+	0.434372i
$531$		0			0
$532$	−5.51317	+	24.4868i	−0.239026	+	1.06164i
$533$		0			0
$534$		0			0
$535$	28.4605	−	9.48683i	1.23045	−	0.410152i
$536$	−25.2982			−1.09272
$537$		0			0
$538$	−47.4342	+	47.4342i	−2.04503	+	2.04503i
$539$	−20.0000	−	9.48683i	−0.861461	−	0.408627i
$540$		0			0
$541$	−18.0000			−0.773880			−0.386940	−	0.922105i	$-0.626468\pi$
$541$	−18.0000			−0.773880			−0.386940	+	0.922105i	$0.626468\pi$
$542$	35.0000	+	35.0000i	1.50338	+	1.50338i
$543$		0			0
$544$	−47.4342			−2.03372
$545$	−4.00000	+	8.00000i	−0.171341	+	0.342682i
$546$		0			0
$547$	8.00000	−	8.00000i	0.342055	−	0.342055i	−0.515084	−	0.857140i	$-0.672239\pi$
$547$	8.00000	−	8.00000i	0.342055	−	0.342055i	0.857140	+	0.515084i	$0.172239\pi$
$548$	9.48683	+	9.48683i	0.405257	+	0.405257i
$549$		0			0
$550$	−35.0000	−	5.00000i	−1.49241	−	0.213201i
$551$		0			0
$552$		0			0
$553$	2.32456	−	10.3246i	0.0988501	−	0.439045i
$554$		−	9.48683i		−	0.403057i
$555$		0			0
$556$		−	28.4605i		−	1.20699i
$557$	−9.48683	+	9.48683i	−0.401970	+	0.401970i	−0.878927	−	0.476957i	$-0.841740\pi$
$557$	−9.48683	+	9.48683i	−0.401970	+	0.401970i	0.476957	+	0.878927i	$0.341740\pi$
$558$		0			0
$559$	−37.9473			−1.60500
$560$	4.58114	+	3.74342i	0.193588	+	0.158188i
$561$		0			0
$562$	−30.0000	+	30.0000i	−1.26547	+	1.26547i
$563$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$563$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$564$		0			0
$565$	9.48683	+	28.4605i	0.399114	+	1.19734i
$566$		0			0
$567$		0			0
$568$	15.0000	+	15.0000i	0.629386	+	0.629386i
$569$		−	12.6491i		−	0.530278i	−0.964210	−	0.265139i	$-0.914582\pi$
$569$		−	12.6491i		−	0.530278i	0.964210	−	0.265139i	$-0.0854179\pi$
$570$		0			0
$571$	−8.00000			−0.334790			−0.167395	−	0.985890i	$-0.553535\pi$
$571$	−8.00000			−0.334790			−0.167395	+	0.985890i	$0.553535\pi$
$572$	−30.0000	−	30.0000i	−1.25436	−	1.25436i
$573$		0			0
$574$		0			0
$575$	3.16228	−	22.1359i	0.131876	−	0.923133i
$576$		0			0
$577$	22.1359	+	22.1359i	0.921531	+	0.921531i	0.997138	−	0.0756064i	$-0.0240892\pi$
$577$	22.1359	+	22.1359i	0.921531	+	0.921531i	−0.0756064	+	0.997138i	$0.524089\pi$
$578$	52.1776	+	52.1776i	2.17030	+	2.17030i
$579$		0			0
$580$		0			0
$581$	31.6228	−	20.0000i	1.31193	−	0.829740i
$582$		0			0
$583$	−10.0000	−	10.0000i	−0.414158	−	0.414158i
$584$	−30.0000			−1.24141
$585$		0			0
$586$			15.8114i			0.653162i
$587$	20.0000	+	20.0000i	0.825488	+	0.825488i	0.986889	−	0.161401i	$-0.0516011\pi$
$587$	20.0000	+	20.0000i	0.825488	+	0.825488i	−0.161401	+	0.986889i	$0.551601\pi$
$588$		0			0
$589$			10.0000i			0.412043i
$590$		0			0
$591$		0			0
$592$	−3.00000	+	3.00000i	−0.123299	+	0.123299i
$593$	25.0000	−	25.0000i	1.02663	−	1.02663i	0.0269913	−	0.999636i	$-0.491407\pi$
$593$	25.0000	−	25.0000i	1.02663	−	1.02663i	0.999636	−	0.0269913i	$-0.00859264\pi$
$594$		0			0
$595$	−4.18861	−	41.6228i	−0.171716	−	1.70637i
$596$	56.9210			2.33157
$597$		0			0
$598$	31.6228	−	31.6228i	1.29315	−	1.29315i
$599$			15.8114i			0.646036i	0.946393	+	0.323018i	$0.104697\pi$
$599$			15.8114i			0.646036i	−0.946393	+	0.323018i	$0.895303\pi$
$600$		0			0
$601$		−	31.6228i		−	1.28992i	−0.764216	−	0.644960i	$-0.776874\pi$
$601$		−	31.6228i		−	1.28992i	0.764216	−	0.644960i	$-0.223126\pi$
$602$	48.9737	+	11.0263i	1.99602	+	0.449400i
$603$		0			0
$604$			36.0000i			1.46482i
$605$	−2.00000	−	1.00000i	−0.0813116	−	0.0406558i
$606$		0			0
$607$	−18.9737	−	18.9737i	−0.770117	−	0.770117i	0.208009	−	0.978127i	$-0.433302\pi$
$607$	−18.9737	−	18.9737i	−0.770117	−	0.770117i	−0.978127	+	0.208009i	$0.933302\pi$
$608$	−15.0000	+	15.0000i	−0.608330	+	0.608330i
$609$		0			0
$610$	20.0000	+	60.0000i	0.809776	+	2.42933i
$611$		0			0
$612$		0			0
$613$	−1.00000	−	1.00000i	−0.0403896	−	0.0403896i	0.686624	−	0.727013i	$-0.259092\pi$
$613$	−1.00000	−	1.00000i	−0.0403896	−	0.0403896i	−0.727013	+	0.686624i	$0.759092\pi$
$614$	−30.0000			−1.21070
$615$		0			0
$616$	10.0000	+	15.8114i	0.402911	+	0.637059i
$617$	−15.8114	+	15.8114i	−0.636543	+	0.636543i	−0.949701	−	0.313158i	$-0.898613\pi$
$617$	−15.8114	+	15.8114i	−0.636543	+	0.636543i	0.313158	+	0.949701i	$0.398613\pi$
$618$		0			0
$619$	−3.16228			−0.127103			−0.0635513	−	0.997979i	$-0.520243\pi$
$619$	−3.16228			−0.127103			−0.0635513	+	0.997979i	$0.520243\pi$
$620$	−18.9737	−	9.48683i	−0.762001	−	0.381000i
$621$		0			0
$622$	−31.6228	−	31.6228i	−1.26796	−	1.26796i
$623$	−25.8114	−	5.81139i	−1.03411	−	0.232828i
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$			30.0000i			1.19904i
$627$		0			0
$628$	−47.4342	+	47.4342i	−1.89283	+	1.89283i
$629$	30.0000			1.19618
$630$		0			0
$631$	−28.0000			−1.11466			−0.557331	−	0.830290i	$-0.688175\pi$
$631$	−28.0000			−1.11466			−0.557331	+	0.830290i	$0.688175\pi$
$632$	−6.32456	+	6.32456i	−0.251577	+	0.251577i
$633$		0			0
$634$		−	70.0000i		−	2.78006i
$635$	−36.0000	+	12.0000i	−1.42862	+	0.476205i
$636$		0			0
$637$	−29.4868	+	10.5132i	−1.16831	+	0.416547i
$638$		0			0
$639$		0			0
$640$	−11.0680	−	33.2039i	−0.437500	−	1.31250i
$641$	−31.6228			−1.24902			−0.624512	−	0.781015i	$-0.714702\pi$
$641$	−31.6228			−1.24902			−0.624512	+	0.781015i	$0.714702\pi$
$642$		0			0
$643$	−9.48683	+	9.48683i	−0.374124	+	0.374124i	−0.868977	−	0.494853i	$-0.835222\pi$
$643$	−9.48683	+	9.48683i	−0.374124	+	0.374124i	0.494853	+	0.868977i	$0.335222\pi$
$644$	−30.0000	+	18.9737i	−1.18217	+	0.747667i
$645$		0			0
$646$	50.0000			1.96722
$647$	−10.0000	−	10.0000i	−0.393141	−	0.393141i	0.482665	−	0.875805i	$-0.339669\pi$
$647$	−10.0000	−	10.0000i	−0.393141	−	0.393141i	−0.875805	+	0.482665i	$0.839669\pi$
$648$		0			0
$649$		0			0
$650$	−40.0000	+	30.0000i	−1.56893	+	1.17670i
$651$		0			0
$652$	−18.0000	+	18.0000i	−0.704934	+	0.704934i
$653$	15.8114	+	15.8114i	0.618747	+	0.618747i	0.945210	−	0.326463i	$-0.105857\pi$
$653$	15.8114	+	15.8114i	0.618747	+	0.618747i	−0.326463	+	0.945210i	$0.605857\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$			41.1096i			1.60140i	0.599064	+	0.800702i	$0.295540\pi$
$659$			41.1096i			1.60140i	−0.599064	+	0.800702i	$0.704460\pi$
$660$		0			0
$661$			12.6491i			0.491993i	0.969271	+	0.245997i	$0.0791152\pi$
$661$			12.6491i			0.491993i	−0.969271	+	0.245997i	$0.920885\pi$
$662$	−18.9737	+	18.9737i	−0.737432	+	0.737432i
$663$		0			0
$664$	−31.6228			−1.22720
$665$	−14.4868	−	11.8377i	−0.561775	−	0.459047i
$666$		0			0
$667$		0			0
$668$	30.0000	−	30.0000i	1.16073	−	1.16073i
$669$		0			0
$670$	25.2982	−	50.5964i	0.977356	−	1.95471i
$671$		−	40.0000i		−	1.54418i
$672$		0			0
$673$	−9.00000	−	9.00000i	−0.346925	−	0.346925i	0.512038	−	0.858963i	$-0.328891\pi$
$673$	−9.00000	−	9.00000i	−0.346925	−	0.346925i	−0.858963	+	0.512038i	$0.828891\pi$
$674$		−	22.1359i		−	0.852645i
$675$		0			0
$676$	−21.0000			−0.807692
$677$	15.0000	+	15.0000i	0.576497	+	0.576497i	0.933936	−	0.357439i	$-0.116350\pi$
$677$	15.0000	+	15.0000i	0.576497	+	0.576497i	−0.357439	+	0.933936i	$0.616350\pi$
$678$		0			0
$679$	−6.32456	−	10.0000i	−0.242714	−	0.383765i
$680$	−15.8114	+	31.6228i	−0.606339	+	1.21268i
$681$		0			0
$682$	15.8114	+	15.8114i	0.605449	+	0.605449i
$683$	−12.6491	−	12.6491i	−0.484005	−	0.484005i	0.422403	−	0.906408i	$-0.361187\pi$
$683$	−12.6491	−	12.6491i	−0.484005	−	0.484005i	−0.906408	+	0.422403i	$0.861187\pi$
$684$		0			0
$685$	−9.48683	+	3.16228i	−0.362473	+	0.120824i
$686$	41.1096	−	5.00000i	1.56957	−	0.190901i
$687$		0			0
$688$	6.00000	+	6.00000i	0.228748	+	0.228748i
$689$	−20.0000			−0.761939
$690$		0			0
$691$		−	3.16228i		−	0.120299i	−0.998189	−	0.0601494i	$-0.980842\pi$
$691$		−	3.16228i		−	0.120299i	0.998189	−	0.0601494i	$-0.0191577\pi$
$692$	−15.0000	−	15.0000i	−0.570214	−	0.570214i
$693$		0			0
$694$		0			0
$695$	18.9737	+	9.48683i	0.719712	+	0.359856i
$696$		0			0
$697$		0			0
$698$	20.0000	−	20.0000i	0.757011	−	0.757011i
$699$		0			0
$700$	36.2039	−	16.2566i	1.36838	−	0.614441i
$701$	−12.6491			−0.477750			−0.238875	−	0.971050i	$-0.576779\pi$
$701$	−12.6491			−0.477750			−0.238875	+	0.971050i	$0.576779\pi$
$702$		0			0
$703$	9.48683	−	9.48683i	0.357803	−	0.357803i
$704$			41.1096i			1.54938i
$705$		0			0
$706$			47.4342i			1.78521i
$707$	−5.81139	+	25.8114i	−0.218560	+	0.970737i
$708$		0			0
$709$			24.0000i			0.901339i	0.892691	+	0.450669i	$0.148815\pi$
$709$			24.0000i			0.901339i	−0.892691	+	0.450669i	$0.851185\pi$
$710$	−45.0000	+	15.0000i	−1.68882	+	0.562940i
$711$		0			0
$712$	15.8114	+	15.8114i	0.592557	+	0.592557i
$713$	−10.0000	+	10.0000i	−0.374503	+	0.374503i
$714$		0			0
$715$	30.0000	−	10.0000i	1.12194	−	0.373979i
$716$	−28.4605			−1.06362
$717$		0			0
$718$	35.0000	+	35.0000i	1.30619	+	1.30619i
$719$	20.0000			0.745874			0.372937	−	0.927857i	$-0.378351\pi$
$719$	20.0000			0.745874			0.372937	+	0.927857i	$0.378351\pi$
$720$		0			0
$721$	10.0000	−	6.32456i	0.372419	−	0.235539i
$722$	−14.2302	+	14.2302i	−0.529595	+	0.529595i
$723$		0			0
$724$	−18.9737			−0.705151
$725$		0			0
$726$		0			0
$727$	18.9737	+	18.9737i	0.703694	+	0.703694i	0.965202	−	0.261507i	$-0.0842195\pi$
$727$	18.9737	+	18.9737i	0.703694	+	0.703694i	−0.261507	+	0.965202i	$0.584220\pi$
$728$	25.8114	+	5.81139i	0.956634	+	0.215384i
$729$		0			0
$730$	30.0000	−	60.0000i	1.11035	−	2.22070i
$731$		−	60.0000i		−	2.21918i
$732$		0			0
$733$	15.8114	−	15.8114i	0.584007	−	0.584007i	−0.351995	−	0.936002i	$-0.614497\pi$
$733$	15.8114	−	15.8114i	0.584007	−	0.584007i	0.936002	+	0.351995i	$0.114497\pi$
$734$	−20.0000			−0.738213
$735$		0			0
$736$	−30.0000			−1.10581
$737$	−25.2982	+	25.2982i	−0.931872	+	0.931872i
$738$		0			0
$739$		−	44.0000i		−	1.61857i	−0.587419	−	0.809283i	$-0.699856\pi$
$739$		−	44.0000i		−	1.61857i	0.587419	−	0.809283i	$-0.300144\pi$
$740$	9.00000	+	27.0000i	0.330847	+	0.992540i
$741$		0			0
$742$	25.8114	+	5.81139i	0.947566	+	0.213343i
$743$	18.9737	+	18.9737i	0.696076	+	0.696076i	0.963562	−	0.267486i	$-0.0861928\pi$
$743$	18.9737	+	18.9737i	0.696076	+	0.696076i	−0.267486	+	0.963562i	$0.586193\pi$
$744$		0			0
$745$	−18.9737	+	37.9473i	−0.695141	+	1.39028i
$746$	28.4605			1.04201
$747$		0			0
$748$	47.4342	−	47.4342i	1.73436	−	1.73436i
$749$	30.0000	−	18.9737i	1.09618	−	0.693283i
$750$		0			0
$751$	−32.0000			−1.16770			−0.583848	−	0.811863i	$-0.698454\pi$
$751$	−32.0000			−1.16770			−0.583848	+	0.811863i	$0.698454\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−24.0000	−	12.0000i	−0.873449	−	0.436725i
$756$		0			0
$757$	17.0000	−	17.0000i	0.617876	−	0.617876i	−0.327111	−	0.944986i	$-0.606075\pi$
$757$	17.0000	−	17.0000i	0.617876	−	0.617876i	0.944986	+	0.327111i	$0.106075\pi$
$758$	6.32456	+	6.32456i	0.229718	+	0.229718i
$759$		0			0
$760$	5.00000	+	15.0000i	0.181369	+	0.544107i
$761$		−	20.0000i		−	0.724999i	−0.931984	−	0.362500i	$-0.881923\pi$
$761$		−	20.0000i		−	0.724999i	0.931984	−	0.362500i	$-0.118077\pi$
$762$		0			0
$763$	−2.32456	+	10.3246i	−0.0841546	+	0.373774i
$764$		−	28.4605i		−	1.02966i
$765$		0			0
$766$			31.6228i			1.14258i
$767$		0			0
$768$		0			0
$769$	−6.32456			−0.228069			−0.114035	−	0.993477i	$-0.536377\pi$
$769$	−6.32456			−0.228069			−0.114035	+	0.993477i	$0.536377\pi$
$770$	−41.6228	+	4.18861i	−1.49998	+	0.150947i
$771$		0			0
$772$	3.00000	−	3.00000i	0.107972	−	0.107972i
$773$	−35.0000	+	35.0000i	−1.25886	+	1.25886i	−0.307226	+	0.951637i	$0.599401\pi$
$773$	−35.0000	+	35.0000i	−1.25886	+	1.25886i	−0.951637	+	0.307226i	$0.900599\pi$
$774$		0			0
$775$	12.6491	−	9.48683i	0.454369	−	0.340777i
$776$			10.0000i			0.358979i
$777$		0			0
$778$	−10.0000	−	10.0000i	−0.358517	−	0.358517i
$779$		0			0
$780$		0			0
$781$	30.0000			1.07348
$782$	50.0000	+	50.0000i	1.78800	+	1.78800i
$783$		0			0
$784$	6.32456	+	3.00000i	0.225877	+	0.107143i
$785$	−15.8114	−	47.4342i	−0.564333	−	1.69300i
$786$		0			0
$787$	15.8114	+	15.8114i	0.563615	+	0.563615i	0.930332	−	0.366717i	$-0.119518\pi$
$787$	15.8114	+	15.8114i	0.563615	+	0.563615i	−0.366717	+	0.930332i	$0.619518\pi$
$788$	9.48683	+	9.48683i	0.337954	+	0.337954i
$789$		0			0
$790$	−6.32456	−	18.9737i	−0.225018	−	0.675053i
$791$	18.9737	+	30.0000i	0.674626	+	1.06668i
$792$		0			0
$793$	−40.0000	−	40.0000i	−1.42044	−	1.42044i
$794$	−30.0000			−1.06466
$795$		0			0
$796$			28.4605i			1.00876i
$797$	25.0000	+	25.0000i	0.885545	+	0.885545i	0.994091	−	0.108546i	$-0.0346195\pi$
$797$	25.0000	+	25.0000i	0.885545	+	0.885545i	−0.108546	+	0.994091i	$0.534619\pi$
$798$		0			0
$799$		0			0
$800$	33.2039	+	4.74342i	1.17394	+	0.167705i
$801$		0			0
$802$	−20.0000	+	20.0000i	−0.706225	+	0.706225i
$803$	−30.0000	+	30.0000i	−1.05868	+	1.05868i
$804$		0			0
$805$	−2.64911	−	26.3246i	−0.0933689	−	0.927819i
$806$	31.6228			1.11386
$807$		0			0
$808$	15.8114	−	15.8114i	0.556243	−	0.556243i
$809$		−	18.9737i		−	0.667079i	−0.942736	−	0.333539i	$-0.891757\pi$
$809$		−	18.9737i		−	0.667079i	0.942736	−	0.333539i	$-0.108243\pi$
$810$		0			0
$811$			47.4342i			1.66564i	0.553545	+	0.832819i	$0.313275\pi$
$811$			47.4342i			1.66564i	−0.553545	+	0.832819i	$0.686725\pi$
$812$		0			0
$813$		0			0
$814$		−	30.0000i		−	1.05150i
$815$	−6.00000	−	18.0000i	−0.210171	−	0.630512i
$816$		0			0
$817$	−18.9737	−	18.9737i	−0.663805	−	0.663805i
$818$	40.0000	−	40.0000i	1.39857	−	1.39857i
$819$		0			0
$820$		0			0
$821$	12.6491			0.441457			0.220729	−	0.975335i	$-0.429157\pi$
$821$	12.6491			0.441457			0.220729	+	0.975335i	$0.429157\pi$
$822$		0			0
$823$	24.0000	+	24.0000i	0.836587	+	0.836587i	0.988408	−	0.151821i	$-0.0485136\pi$
$823$	24.0000	+	24.0000i	0.836587	+	0.836587i	−0.151821	+	0.988408i	$0.548514\pi$
$824$	−10.0000			−0.348367
$825$		0			0
$826$		0			0
$827$	22.1359	−	22.1359i	0.769742	−	0.769742i	−0.208319	−	0.978061i	$-0.566799\pi$
$827$	22.1359	−	22.1359i	0.769742	−	0.769742i	0.978061	+	0.208319i	$0.0667992\pi$
$828$		0			0
$829$	18.9737			0.658983			0.329491	−	0.944159i	$-0.393123\pi$
$829$	18.9737			0.658983			0.329491	+	0.944159i	$0.393123\pi$
$830$	31.6228	−	63.2456i	1.09764	−	2.19529i
$831$		0			0
$832$	41.1096	+	41.1096i	1.42522	+	1.42522i
$833$	−16.6228	−	46.6228i	−0.575945	−	1.61538i
$834$		0			0
$835$	10.0000	+	30.0000i	0.346064	+	1.03819i
$836$		−	30.0000i		−	1.03757i
$837$		0			0
$838$	31.6228	−	31.6228i	1.09239	−	1.09239i
$839$	−40.0000			−1.38095			−0.690477	−	0.723355i	$-0.742599\pi$
$839$	−40.0000			−1.38095			−0.690477	+	0.723355i	$0.742599\pi$
$840$		0			0
$841$	29.0000			1.00000
$842$	−12.6491	+	12.6491i	−0.435917	+	0.435917i
$843$		0			0
$844$		−	24.0000i		−	0.826114i
$845$	7.00000	−	14.0000i	0.240807	−	0.481615i
$846$		0			0
$847$	−2.58114	−	0.581139i	−0.0886890	−	0.0199682i
$848$	3.16228	+	3.16228i	0.108593	+	0.108593i
$849$		0			0
$850$	−47.4342	−	63.2456i	−1.62698	−	2.16930i
$851$	18.9737			0.650409
$852$		0			0
$853$	9.48683	−	9.48683i	0.324823	−	0.324823i	−0.525791	−	0.850614i	$-0.676231\pi$
$853$	9.48683	−	9.48683i	0.324823	−	0.324823i	0.850614	+	0.525791i	$0.176231\pi$
$854$	40.0000	+	63.2456i	1.36877	+	2.16422i
$855$		0			0
$856$	−30.0000			−1.02538
$857$	−5.00000	−	5.00000i	−0.170797	−	0.170797i	0.616533	−	0.787329i	$-0.288537\pi$
$857$	−5.00000	−	5.00000i	−0.170797	−	0.170797i	−0.787329	+	0.616533i	$0.788537\pi$
$858$		0			0
$859$	−22.1359			−0.755269			−0.377634	−	0.925955i	$-0.623262\pi$
$859$	−22.1359			−0.755269			−0.377634	+	0.925955i	$0.623262\pi$
$860$	54.0000	−	18.0000i	1.84138	−	0.613795i
$861$		0			0
$862$	35.0000	−	35.0000i	1.19210	−	1.19210i
$863$	15.8114	+	15.8114i	0.538226	+	0.538226i	0.923008	−	0.384782i	$-0.125723\pi$
$863$	15.8114	+	15.8114i	0.538226	+	0.538226i	−0.384782	+	0.923008i	$0.625723\pi$
$864$		0			0
$865$	15.0000	−	5.00000i	0.510015	−	0.170005i
$866$			30.0000i			1.01944i
$867$		0			0
$868$	−24.4868	−	5.51317i	−0.831137	−	0.187129i
$869$			12.6491i			0.429092i
$870$		0			0
$871$			50.5964i			1.71440i
$872$	6.32456	−	6.32456i	0.214176	−	0.214176i
$873$		0			0
$874$	31.6228			1.06966
$875$	−1.23025	+	29.5548i	−0.0415900	+	0.999135i
$876$		0			0
$877$	23.0000	−	23.0000i	0.776655	−	0.776655i	−0.202606	−	0.979260i	$-0.564941\pi$
$877$	23.0000	−	23.0000i	0.776655	−	0.776655i	0.979260	+	0.202606i	$0.0649409\pi$
$878$	5.00000	−	5.00000i	0.168742	−	0.168742i
$879$		0			0
$880$	−6.32456	−	3.16228i	−0.213201	−	0.106600i
$881$		−	30.0000i		−	1.01073i	−0.862907	−	0.505363i	$-0.831359\pi$
$881$		−	30.0000i		−	1.01073i	0.862907	−	0.505363i	$-0.168641\pi$
$882$		0			0
$883$	36.0000	+	36.0000i	1.21150	+	1.21150i	0.970535	+	0.240962i	$0.0774629\pi$
$883$	36.0000	+	36.0000i	1.21150	+	1.21150i	0.240962	+	0.970535i	$0.422537\pi$
$884$		−	94.8683i		−	3.19077i
$885$		0			0
$886$	−80.0000			−2.68765
$887$	20.0000	+	20.0000i	0.671534	+	0.671534i	0.958070	−	0.286535i	$-0.0925036\pi$
$887$	20.0000	+	20.0000i	0.671534	+	0.671534i	−0.286535	+	0.958070i	$0.592504\pi$
$888$		0			0
$889$	−37.9473	+	24.0000i	−1.27271	+	0.804934i
$890$	−47.4342	+	15.8114i	−1.59000	+	0.529999i
$891$		0			0
$892$	−56.9210	−	56.9210i	−1.90586	−	1.90586i
$893$		0			0
$894$		0			0
$895$	9.48683	−	18.9737i	0.317110	−	0.634220i
$896$	−22.1359	−	35.0000i	−0.739510	−	1.16927i
$897$		0			0
$898$	40.0000	+	40.0000i	1.33482	+	1.33482i
$899$		0			0
$900$		0			0
$901$		−	31.6228i		−	1.05351i
$902$		0			0
$903$		0			0
$904$		−	30.0000i		−	0.997785i
$905$	6.32456	−	12.6491i	0.210235	−	0.420471i
$906$		0			0
$907$	−8.00000	+	8.00000i	−0.265636	+	0.265636i	−0.827339	−	0.561703i	$-0.810146\pi$
$907$	−8.00000	+	8.00000i	−0.265636	+	0.265636i	0.561703	+	0.827339i	$0.310146\pi$
$908$	−30.0000	+	30.0000i	−0.995585	+	0.995585i
$909$		0			0
$910$	−37.4342	+	45.8114i	−1.24093	+	1.51863i
$911$	−28.4605			−0.942938			−0.471469	−	0.881883i	$-0.656276\pi$
$911$	−28.4605			−0.942938			−0.471469	+	0.881883i	$0.656276\pi$
$912$		0			0
$913$	−31.6228	+	31.6228i	−1.04656	+	1.04656i
$914$		−	53.7587i		−	1.77818i
$915$		0			0
$916$		−	37.9473i		−	1.25382i
$917$		0			0
$918$		0			0
$919$			24.0000i			0.791687i	0.918318	+	0.395843i	$0.129548\pi$
$919$			24.0000i			0.791687i	−0.918318	+	0.395843i	$0.870452\pi$
$920$	−10.0000	+	20.0000i	−0.329690	+	0.659380i
$921$		0			0
$922$	31.6228	+	31.6228i	1.04144	+	1.04144i
$923$	30.0000	−	30.0000i	0.987462	−	0.987462i
$924$		0			0
$925$	−21.0000	−	3.00000i	−0.690476	−	0.0986394i
$926$	−50.5964			−1.66270
$927$		0			0
$928$		0			0
$929$	20.0000			0.656179			0.328089	−	0.944647i	$-0.393595\pi$
$929$	20.0000			0.656179			0.328089	+	0.944647i	$0.393595\pi$
$930$		0			0
$931$	−20.0000	−	9.48683i	−0.655474	−	0.310918i
$932$	28.4605	−	28.4605i	0.932255	−	0.932255i
$933$		0			0
$934$	−31.6228			−1.03473
$935$	15.8114	+	47.4342i	0.517088	+	1.55126i
$936$		0			0
$937$	9.48683	+	9.48683i	0.309921	+	0.309921i	0.844879	−	0.534958i	$-0.179672\pi$
$937$	9.48683	+	9.48683i	0.309921	+	0.309921i	−0.534958	+	0.844879i	$0.679672\pi$
$938$	14.7018	−	65.2982i	0.480030	−	2.13206i
$939$		0			0
$940$		0			0
$941$			60.0000i			1.95594i	0.208736	+	0.977972i	$0.433065\pi$
$941$			60.0000i			1.95594i	−0.208736	+	0.977972i	$0.566935\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	−60.0000			−1.95077
$947$	−25.2982	+	25.2982i	−0.822082	+	0.822082i	−0.986406	−	0.164325i	$-0.947456\pi$
$947$	−25.2982	+	25.2982i	−0.822082	+	0.822082i	0.164325	+	0.986406i	$0.447456\pi$
$948$		0			0
$949$			60.0000i			1.94768i
$950$	−35.0000	−	5.00000i	−1.13555	−	0.162221i
$951$		0			0
$952$	−9.18861	+	40.8114i	−0.297805	+	1.32270i
$953$	−28.4605	−	28.4605i	−0.921926	−	0.921926i	0.0752395	−	0.997165i	$-0.476028\pi$
$953$	−28.4605	−	28.4605i	−0.921926	−	0.921926i	−0.997165	+	0.0752395i	$0.976028\pi$
$954$		0			0
$955$	18.9737	+	9.48683i	0.613973	+	0.306987i
$956$	−66.4078			−2.14778
$957$		0			0
$958$	31.6228	−	31.6228i	1.02169	−	1.02169i
$959$	−10.0000	+	6.32456i	−0.322917	+	0.204231i
$960$		0			0
$961$	21.0000			0.677419
$962$	−30.0000	−	30.0000i	−0.967239	−	0.967239i
$963$		0			0
$964$	−18.9737			−0.611101
$965$	1.00000	+	3.00000i	0.0321911	+	0.0965734i
$966$		0			0
$967$	−42.0000	+	42.0000i	−1.35063	+	1.35063i	−0.465671	+	0.884958i	$0.654187\pi$
$967$	−42.0000	+	42.0000i	−1.35063	+	1.35063i	−0.884958	+	0.465671i	$0.845813\pi$
$968$	1.58114	+	1.58114i	0.0508197	+	0.0508197i
$969$		0			0
$970$	−20.0000	−	10.0000i	−0.642161	−	0.321081i
$971$			20.0000i			0.641831i	0.947108	+	0.320915i	$0.103990\pi$
$971$			20.0000i			0.641831i	−0.947108	+	0.320915i	$0.896010\pi$
$972$		0			0
$973$	24.4868	+	5.51317i	0.785012	+	0.176744i
$974$			25.2982i			0.810607i
$975$		0			0
$976$			12.6491i			0.404888i
$977$	−3.16228	+	3.16228i	−0.101170	+	0.101170i	−0.755880	−	0.654710i	$-0.772791\pi$
$977$	−3.16228	+	3.16228i	−0.101170	+	0.101170i	0.654710	+	0.755880i	$0.272791\pi$
$978$		0			0
$979$	31.6228			1.01067
$980$	36.9737	−	28.9473i	1.18108	−	0.924689i
$981$		0			0
$982$	−55.0000	+	55.0000i	−1.75512	+	1.75512i
$983$	20.0000	−	20.0000i	0.637901	−	0.637901i	−0.312136	−	0.950037i	$-0.601045\pi$
$983$	20.0000	−	20.0000i	0.637901	−	0.637901i	0.950037	+	0.312136i	$0.101045\pi$
$984$		0			0
$985$	−9.48683	+	3.16228i	−0.302276	+	0.100759i
$986$		0			0
$987$		0			0
$988$	−30.0000	−	30.0000i	−0.954427	−	0.954427i
$989$		−	37.9473i		−	1.20665i
$990$		0			0
$991$	28.0000			0.889449			0.444725	−	0.895667i	$-0.353302\pi$
$991$	28.0000			0.889449			0.444725	+	0.895667i	$0.353302\pi$
$992$	−15.0000	−	15.0000i	−0.476250	−	0.476250i
$993$		0			0
$994$	−47.4342	+	30.0000i	−1.50452	+	0.951542i
$995$	−18.9737	−	9.48683i	−0.601506	−	0.300753i
$996$		0			0
$997$	−9.48683	−	9.48683i	−0.300451	−	0.300451i	0.540739	−	0.841190i	$-0.318145\pi$
$997$	−9.48683	−	9.48683i	−0.300451	−	0.300451i	−0.841190	+	0.540739i	$0.818145\pi$
$998$	−25.2982	−	25.2982i	−0.800801	−	0.800801i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.p.b.118.2	yes	4
3.2	odd	2		315.2.p.a.118.1	✓	4
5.2	odd	4		315.2.p.a.307.2	yes	4
7.6	odd	2		315.2.p.a.118.2	yes	4
15.2	even	4	inner	315.2.p.b.307.1	yes	4
21.20	even	2	inner	315.2.p.b.118.1	yes	4
35.27	even	4	inner	315.2.p.b.307.2	yes	4
105.62	odd	4		315.2.p.a.307.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.p.a.118.1	✓	4	3.2	odd	2
315.2.p.a.118.2	yes	4	7.6	odd	2
315.2.p.a.307.1	yes	4	105.62	odd	4
315.2.p.a.307.2	yes	4	5.2	odd	4
315.2.p.b.118.1	yes	4	21.20	even	2	inner
315.2.p.b.118.2	yes	4	1.1	even	1	trivial
315.2.p.b.307.1	yes	4	15.2	even	4	inner
315.2.p.b.307.2	yes	4	35.27	even	4	inner

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.58114 - 1.58114i) q^{2} -3.00000i q^{4} +(2.00000 + 1.00000i) q^{5} +(2.58114 + 0.581139i) q^{7} +(-1.58114 - 1.58114i) q^{8} +O(q^{10})\)	\(q+(1.58114 - 1.58114i) q^{2} -3.00000i q^{4} +(2.00000 + 1.00000i) q^{5} +(2.58114 + 0.581139i) q^{7} +(-1.58114 - 1.58114i) q^{8} +(4.74342 - 1.58114i) q^{10} -3.16228 q^{11} +(-3.16228 + 3.16228i) q^{13} +(5.00000 - 3.16228i) q^{14} +1.00000 q^{16} +(-5.00000 - 5.00000i) q^{17} -3.16228 q^{19} +(3.00000 - 6.00000i) q^{20} +(-5.00000 + 5.00000i) q^{22} +(-3.16228 - 3.16228i) q^{23} +(3.00000 + 4.00000i) q^{25} +10.0000i q^{26} +(1.74342 - 7.74342i) q^{28} -3.16228i q^{31} +(4.74342 - 4.74342i) q^{32} -15.8114 q^{34} +(4.58114 + 3.74342i) q^{35} +(-3.00000 + 3.00000i) q^{37} +(-5.00000 + 5.00000i) q^{38} +(-1.58114 - 4.74342i) q^{40} +(6.00000 + 6.00000i) q^{43} +9.48683i q^{44} -10.0000 q^{46} +(6.32456 + 3.00000i) q^{49} +(11.0680 + 1.58114i) q^{50} +(9.48683 + 9.48683i) q^{52} +(3.16228 + 3.16228i) q^{53} +(-6.32456 - 3.16228i) q^{55} +(-3.16228 - 5.00000i) q^{56} +12.6491i q^{61} +(-5.00000 - 5.00000i) q^{62} -13.0000i q^{64} +(-9.48683 + 3.16228i) q^{65} +(8.00000 - 8.00000i) q^{67} +(-15.0000 + 15.0000i) q^{68} +(13.1623 - 1.32456i) q^{70} -9.48683 q^{71} +(9.48683 - 9.48683i) q^{73} +9.48683i q^{74} +9.48683i q^{76} +(-8.16228 - 1.83772i) q^{77} -4.00000i q^{79} +(2.00000 + 1.00000i) q^{80} +(10.0000 - 10.0000i) q^{83} +(-5.00000 - 15.0000i) q^{85} +18.9737 q^{86} +(5.00000 + 5.00000i) q^{88} -10.0000 q^{89} +(-10.0000 + 6.32456i) q^{91} +(-9.48683 + 9.48683i) q^{92} +(-6.32456 - 3.16228i) q^{95} +(-3.16228 - 3.16228i) q^{97} +(14.7434 - 5.25658i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{5} + 4 q^{7}+O(q^{10}) \) 4 * q + 8 * q^5 + 4 * q^7	\( 4 q + 8 q^{5} + 4 q^{7} + 20 q^{14} + 4 q^{16} - 20 q^{17} + 12 q^{20} - 20 q^{22} + 12 q^{25} - 12 q^{28} + 12 q^{35} - 12 q^{37} - 20 q^{38} + 24 q^{43} - 40 q^{46} - 20 q^{62} + 32 q^{67} - 60 q^{68} + 40 q^{70} - 20 q^{77} + 8 q^{80} + 40 q^{83} - 20 q^{85} + 20 q^{88} - 40 q^{89} - 40 q^{91} + 40 q^{98}+O(q^{100}) \) 4 * q + 8 * q^5 + 4 * q^7 + 20 * q^14 + 4 * q^16 - 20 * q^17 + 12 * q^20 - 20 * q^22 + 12 * q^25 - 12 * q^28 + 12 * q^35 - 12 * q^37 - 20 * q^38 + 24 * q^43 - 40 * q^46 - 20 * q^62 + 32 * q^67 - 60 * q^68 + 40 * q^70 - 20 * q^77 + 8 * q^80 + 40 * q^83 - 20 * q^85 + 20 * q^88 - 40 * q^89 - 40 * q^91 + 40 * q^98

Introduction

L-functions

Modular forms

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