LMFDB - Embedded newform 350.2.e.c.51.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(51,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("350.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.79476407074$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			51.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	350.51
Dual form			350.2.e.c.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.00000 - 1.73205i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.00000 - 1.73205i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(-1.50000 - 2.59808i) q^{11} -5.00000 q^{13} +(2.50000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(1.50000 + 2.59808i) q^{18} +(2.50000 - 4.33013i) q^{19} +3.00000 q^{22} +(3.50000 - 6.06218i) q^{23} +(2.50000 - 4.33013i) q^{26} +(-0.500000 + 2.59808i) q^{28} -4.00000 q^{29} +(1.00000 + 1.73205i) q^{31} +(-0.500000 - 0.866025i) q^{32} -2.00000 q^{34} -3.00000 q^{36} +(-0.500000 + 0.866025i) q^{37} +(2.50000 + 4.33013i) q^{38} +3.00000 q^{41} +2.00000 q^{43} +(-1.50000 + 2.59808i) q^{44} +(3.50000 + 6.06218i) q^{46} +(3.50000 - 6.06218i) q^{47} +(1.00000 + 6.92820i) q^{49} +(2.50000 + 4.33013i) q^{52} +(-4.50000 - 7.79423i) q^{53} +(-2.00000 - 1.73205i) q^{56} +(2.00000 - 3.46410i) q^{58} +(2.00000 + 3.46410i) q^{59} +(-3.00000 + 5.19615i) q^{61} -2.00000 q^{62} +(-7.50000 + 2.59808i) q^{63} +1.00000 q^{64} +(-1.00000 - 1.73205i) q^{67} +(1.00000 - 1.73205i) q^{68} -6.00000 q^{71} +(1.50000 - 2.59808i) q^{72} +(8.00000 + 13.8564i) q^{73} +(-0.500000 - 0.866025i) q^{74} -5.00000 q^{76} +(-1.50000 + 7.79423i) q^{77} +(-7.00000 + 12.1244i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-1.50000 + 2.59808i) q^{82} -6.00000 q^{83} +(-1.00000 + 1.73205i) q^{86} +(-1.50000 - 2.59808i) q^{88} +(-1.00000 + 1.73205i) q^{89} +(10.0000 + 8.66025i) q^{91} -7.00000 q^{92} +(3.50000 + 6.06218i) q^{94} -12.0000 q^{97} +(-6.50000 - 2.59808i) q^{98} -9.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} - 4 q^{7} + 2 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q - q^2 - q^4 - 4 * q^7 + 2 * q^8 + 3 * q^9	$ 2 q - q^{2} - q^{4} - 4 q^{7} + 2 q^{8} + 3 q^{9} - 3 q^{11} - 10 q^{13} + 5 q^{14} - q^{16} + 2 q^{17} + 3 q^{18} + 5 q^{19} + 6 q^{22} + 7 q^{23} + 5 q^{26} - q^{28} - 8 q^{29} + 2 q^{31} - q^{32} - 4 q^{34} - 6 q^{36} - q^{37} + 5 q^{38} + 6 q^{41} + 4 q^{43} - 3 q^{44} + 7 q^{46} + 7 q^{47} + 2 q^{49} + 5 q^{52} - 9 q^{53} - 4 q^{56} + 4 q^{58} + 4 q^{59} - 6 q^{61} - 4 q^{62} - 15 q^{63} + 2 q^{64} - 2 q^{67} + 2 q^{68} - 12 q^{71} + 3 q^{72} + 16 q^{73} - q^{74} - 10 q^{76} - 3 q^{77} - 14 q^{79} - 9 q^{81} - 3 q^{82} - 12 q^{83} - 2 q^{86} - 3 q^{88} - 2 q^{89} + 20 q^{91} - 14 q^{92} + 7 q^{94} - 24 q^{97} - 13 q^{98} - 18 q^{99}+O(q^{100}) $ 2 * q - q^2 - q^4 - 4 * q^7 + 2 * q^8 + 3 * q^9 - 3 * q^11 - 10 * q^13 + 5 * q^14 - q^16 + 2 * q^17 + 3 * q^18 + 5 * q^19 + 6 * q^22 + 7 * q^23 + 5 * q^26 - q^28 - 8 * q^29 + 2 * q^31 - q^32 - 4 * q^34 - 6 * q^36 - q^37 + 5 * q^38 + 6 * q^41 + 4 * q^43 - 3 * q^44 + 7 * q^46 + 7 * q^47 + 2 * q^49 + 5 * q^52 - 9 * q^53 - 4 * q^56 + 4 * q^58 + 4 * q^59 - 6 * q^61 - 4 * q^62 - 15 * q^63 + 2 * q^64 - 2 * q^67 + 2 * q^68 - 12 * q^71 + 3 * q^72 + 16 * q^73 - q^74 - 10 * q^76 - 3 * q^77 - 14 * q^79 - 9 * q^81 - 3 * q^82 - 12 * q^83 - 2 * q^86 - 3 * q^88 - 2 * q^89 + 20 * q^91 - 14 * q^92 + 7 * q^94 - 24 * q^97 - 13 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$3$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$		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
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$		0			0
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$		0			0
$13$	−5.00000			−1.38675			−0.693375	−	0.720577i	$-0.743877\pi$
$13$	−5.00000			−1.38675			−0.693375	+	0.720577i	$0.743877\pi$
$14$	2.50000	−	0.866025i	0.668153	−	0.231455i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	0.961436	−	0.275029i	$-0.0886875\pi$
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	−0.718900	+	0.695113i	$0.755354\pi$
$18$	1.50000	+	2.59808i	0.353553	+	0.612372i
$19$	2.50000	−	4.33013i	0.573539	−	0.993399i	−0.422659	−	0.906289i	$-0.638903\pi$
$19$	2.50000	−	4.33013i	0.573539	−	0.993399i	0.996199	−	0.0871106i	$-0.0277634\pi$
$20$		0			0
$21$		0			0
$22$	3.00000			0.639602
$23$	3.50000	−	6.06218i	0.729800	−	1.26405i	−0.227167	−	0.973856i	$-0.572946\pi$
$23$	3.50000	−	6.06218i	0.729800	−	1.26405i	0.956967	−	0.290196i	$-0.0937204\pi$
$24$		0			0
$25$		0			0
$26$	2.50000	−	4.33013i	0.490290	−	0.849208i
$27$		0			0
$28$	−0.500000	+	2.59808i	−0.0944911	+	0.490990i
$29$	−4.00000			−0.742781			−0.371391	−	0.928477i	$-0.621119\pi$
$29$	−4.00000			−0.742781			−0.371391	+	0.928477i	$0.621119\pi$
$30$		0			0
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	0.941745	−	0.336327i	$-0.109185\pi$
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	−0.762140	+	0.647412i	$0.775851\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−2.00000			−0.342997
$35$		0			0
$36$	−3.00000			−0.500000
$37$	−0.500000	+	0.866025i	−0.0821995	+	0.142374i	−0.904194	−	0.427121i	$-0.859528\pi$
$37$	−0.500000	+	0.866025i	−0.0821995	+	0.142374i	0.821995	+	0.569495i	$0.192861\pi$
$38$	2.50000	+	4.33013i	0.405554	+	0.702439i
$39$		0			0
$40$		0			0
$41$	3.00000			0.468521			0.234261	−	0.972174i	$-0.424733\pi$
$41$	3.00000			0.468521			0.234261	+	0.972174i	$0.424733\pi$
$42$		0			0
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$	−1.50000	+	2.59808i	−0.226134	+	0.391675i
$45$		0			0
$46$	3.50000	+	6.06218i	0.516047	+	0.893819i
$47$	3.50000	−	6.06218i	0.510527	−	0.884260i	−0.489398	−	0.872060i	$-0.662783\pi$
$47$	3.50000	−	6.06218i	0.510527	−	0.884260i	0.999926	−	0.0121990i	$-0.00388317\pi$
$48$		0			0
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$		0			0
$51$		0			0
$52$	2.50000	+	4.33013i	0.346688	+	0.600481i
$53$	−4.50000	−	7.79423i	−0.618123	−	1.07062i	−0.989828	−	0.142269i	$-0.954560\pi$
$53$	−4.50000	−	7.79423i	−0.618123	−	1.07062i	0.371706	−	0.928351i	$-0.378773\pi$
$54$		0			0
$55$		0			0
$56$	−2.00000	−	1.73205i	−0.267261	−	0.231455i
$57$		0			0
$58$	2.00000	−	3.46410i	0.262613	−	0.454859i
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	0.966342	−	0.257260i	$-0.0828195\pi$
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	−0.705965	+	0.708247i	$0.749486\pi$
$60$		0			0
$61$	−3.00000	+	5.19615i	−0.384111	+	0.665299i	−0.991645	−	0.128994i	$-0.958825\pi$
$61$	−3.00000	+	5.19615i	−0.384111	+	0.665299i	0.607535	+	0.794293i	$0.292159\pi$
$62$	−2.00000			−0.254000
$63$	−7.50000	+	2.59808i	−0.944911	+	0.327327i
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	0.798454	−	0.602056i	$-0.205652\pi$
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	−0.920623	+	0.390453i	$0.872318\pi$
$68$	1.00000	−	1.73205i	0.121268	−	0.210042i
$69$		0			0
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$	1.50000	−	2.59808i	0.176777	−	0.306186i
$73$	8.00000	+	13.8564i	0.936329	+	1.62177i	0.772246	+	0.635323i	$0.219133\pi$
$73$	8.00000	+	13.8564i	0.936329	+	1.62177i	0.164083	+	0.986447i	$0.447534\pi$
$74$	−0.500000	−	0.866025i	−0.0581238	−	0.100673i
$75$		0			0
$76$	−5.00000			−0.573539
$77$	−1.50000	+	7.79423i	−0.170941	+	0.888235i
$78$		0			0
$79$	−7.00000	+	12.1244i	−0.787562	+	1.36410i	0.139895	+	0.990166i	$0.455323\pi$
$79$	−7.00000	+	12.1244i	−0.787562	+	1.36410i	−0.927457	+	0.373930i	$0.878010\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−1.50000	+	2.59808i	−0.165647	+	0.286910i
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$		0			0
$85$		0			0
$86$	−1.00000	+	1.73205i	−0.107833	+	0.186772i
$87$		0			0
$88$	−1.50000	−	2.59808i	−0.159901	−	0.276956i
$89$	−1.00000	+	1.73205i	−0.106000	+	0.183597i	−0.914146	−	0.405385i	$-0.867138\pi$
$89$	−1.00000	+	1.73205i	−0.106000	+	0.183597i	0.808146	+	0.588982i	$0.200471\pi$
$90$		0			0
$91$	10.0000	+	8.66025i	1.04828	+	0.907841i
$92$	−7.00000			−0.729800
$93$		0			0
$94$	3.50000	+	6.06218i	0.360997	+	0.625266i
$95$		0			0
$96$		0			0
$97$	−12.0000			−1.21842			−0.609208	−	0.793011i	$-0.708512\pi$
$97$	−12.0000			−1.21842			−0.609208	+	0.793011i	$0.708512\pi$
$98$	−6.50000	−	2.59808i	−0.656599	−	0.262445i
$99$	−9.00000			−0.904534
$100$		0			0
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$		0			0
$103$	4.00000	−	6.92820i	0.394132	−	0.682656i	−0.598858	−	0.800855i	$-0.704379\pi$
$103$	4.00000	−	6.92820i	0.394132	−	0.682656i	0.992990	+	0.118199i	$0.0377120\pi$
$104$	−5.00000			−0.490290
$105$		0			0
$106$	9.00000			0.874157
$107$	8.00000	−	13.8564i	0.773389	−	1.33955i	−0.162306	−	0.986740i	$-0.551893\pi$
$107$	8.00000	−	13.8564i	0.773389	−	1.33955i	0.935695	−	0.352809i	$-0.114773\pi$
$108$		0			0
$109$	−1.00000	−	1.73205i	−0.0957826	−	0.165900i	0.814152	−	0.580651i	$-0.197202\pi$
$109$	−1.00000	−	1.73205i	−0.0957826	−	0.165900i	−0.909935	+	0.414751i	$0.863869\pi$
$110$		0			0
$111$		0			0
$112$	2.50000	−	0.866025i	0.236228	−	0.0818317i
$113$	14.0000			1.31701			0.658505	−	0.752577i	$-0.271189\pi$
$113$	14.0000			1.31701			0.658505	+	0.752577i	$0.271189\pi$
$114$		0			0
$115$		0			0
$116$	2.00000	+	3.46410i	0.185695	+	0.321634i
$117$	−7.50000	+	12.9904i	−0.693375	+	1.20096i
$118$	−4.00000			−0.368230
$119$	1.00000	−	5.19615i	0.0916698	−	0.476331i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	−3.00000	−	5.19615i	−0.271607	−	0.470438i
$123$		0			0
$124$	1.00000	−	1.73205i	0.0898027	−	0.155543i
$125$		0			0
$126$	1.50000	−	7.79423i	0.133631	−	0.694365i
$127$	7.00000			0.621150			0.310575	−	0.950549i	$-0.399478\pi$
$127$	7.00000			0.621150			0.310575	+	0.950549i	$0.399478\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$		0			0
$131$	0.500000	−	0.866025i	0.0436852	−	0.0756650i	−0.843356	−	0.537355i	$-0.819423\pi$
$131$	0.500000	−	0.866025i	0.0436852	−	0.0756650i	0.887041	+	0.461690i	$0.152757\pi$
$132$		0			0
$133$	−12.5000	+	4.33013i	−1.08389	+	0.375470i
$134$	2.00000			0.172774
$135$		0			0
$136$	1.00000	+	1.73205i	0.0857493	+	0.148522i
$137$	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
$139$	16.0000			1.35710			0.678551	−	0.734553i	$-0.262608\pi$
$139$	16.0000			1.35710			0.678551	+	0.734553i	$0.262608\pi$
$140$		0			0
$141$		0			0
$142$	3.00000	−	5.19615i	0.251754	−	0.436051i
$143$	7.50000	+	12.9904i	0.627182	+	1.08631i
$144$	1.50000	+	2.59808i	0.125000	+	0.216506i
$145$		0			0
$146$	−16.0000			−1.32417
$147$		0			0
$148$	1.00000			0.0821995
$149$	9.00000	−	15.5885i	0.737309	−	1.27706i	−0.216394	−	0.976306i	$-0.569430\pi$
$149$	9.00000	−	15.5885i	0.737309	−	1.27706i	0.953703	−	0.300750i	$-0.0972370\pi$
$150$		0			0
$151$	3.00000	+	5.19615i	0.244137	+	0.422857i	0.961888	−	0.273442i	$-0.0881622\pi$
$151$	3.00000	+	5.19615i	0.244137	+	0.422857i	−0.717752	+	0.696299i	$0.754829\pi$
$152$	2.50000	−	4.33013i	0.202777	−	0.351220i
$153$	6.00000			0.485071
$154$	−6.00000	−	5.19615i	−0.483494	−	0.418718i
$155$		0			0
$156$		0			0
$157$	4.50000	+	7.79423i	0.359139	+	0.622047i	0.987817	−	0.155618i	$-0.0497370\pi$
$157$	4.50000	+	7.79423i	0.359139	+	0.622047i	−0.628678	+	0.777666i	$0.716404\pi$
$158$	−7.00000	−	12.1244i	−0.556890	−	0.964562i
$159$		0			0
$160$		0			0
$161$	−17.5000	+	6.06218i	−1.37919	+	0.477767i
$162$	9.00000			0.707107
$163$	6.00000	−	10.3923i	0.469956	−	0.813988i	−0.529454	−	0.848339i	$-0.677603\pi$
$163$	6.00000	−	10.3923i	0.469956	−	0.813988i	0.999410	+	0.0343508i	$0.0109363\pi$
$164$	−1.50000	−	2.59808i	−0.117130	−	0.202876i
$165$		0			0
$166$	3.00000	−	5.19615i	0.232845	−	0.403300i
$167$	15.0000			1.16073			0.580367	−	0.814355i	$-0.302909\pi$
$167$	15.0000			1.16073			0.580367	+	0.814355i	$0.302909\pi$
$168$		0			0
$169$	12.0000			0.923077
$170$		0			0
$171$	−7.50000	−	12.9904i	−0.573539	−	0.993399i
$172$	−1.00000	−	1.73205i	−0.0762493	−	0.132068i
$173$	−4.50000	+	7.79423i	−0.342129	+	0.592584i	−0.984828	−	0.173534i	$-0.944481\pi$
$173$	−4.50000	+	7.79423i	−0.342129	+	0.592584i	0.642699	+	0.766119i	$0.277815\pi$
$174$		0			0
$175$		0			0
$176$	3.00000			0.226134
$177$		0			0
$178$	−1.00000	−	1.73205i	−0.0749532	−	0.129823i
$179$	−6.50000	−	11.2583i	−0.485833	−	0.841487i	0.514035	−	0.857769i	$-0.328150\pi$
$179$	−6.50000	−	11.2583i	−0.485833	−	0.841487i	−0.999867	+	0.0162823i	$0.994817\pi$
$180$		0			0
$181$	26.0000			1.93256			0.966282	−	0.257485i	$-0.0828937\pi$
$181$	26.0000			1.93256			0.966282	+	0.257485i	$0.0828937\pi$
$182$	−12.5000	+	4.33013i	−0.926562	+	0.320970i
$183$		0			0
$184$	3.50000	−	6.06218i	0.258023	−	0.446910i
$185$		0			0
$186$		0			0
$187$	3.00000	−	5.19615i	0.219382	−	0.379980i
$188$	−7.00000			−0.510527
$189$		0			0
$190$		0			0
$191$	10.0000	−	17.3205i	0.723575	−	1.25327i	−0.235983	−	0.971757i	$-0.575831\pi$
$191$	10.0000	−	17.3205i	0.723575	−	1.25327i	0.959558	−	0.281511i	$-0.0908356\pi$
$192$		0			0
$193$	5.00000	+	8.66025i	0.359908	+	0.623379i	0.987945	−	0.154805i	$-0.0494748\pi$
$193$	5.00000	+	8.66025i	0.359908	+	0.623379i	−0.628037	+	0.778183i	$0.716141\pi$
$194$	6.00000	−	10.3923i	0.430775	−	0.746124i
$195$		0			0
$196$	5.50000	−	4.33013i	0.392857	−	0.309295i
$197$	−5.00000			−0.356235			−0.178118	−	0.984009i	$-0.557001\pi$
$197$	−5.00000			−0.356235			−0.178118	+	0.984009i	$0.557001\pi$
$198$	4.50000	−	7.79423i	0.319801	−	0.553912i
$199$	−9.00000	−	15.5885i	−0.637993	−	1.10504i	−0.985873	−	0.167497i	$-0.946431\pi$
$199$	−9.00000	−	15.5885i	−0.637993	−	1.10504i	0.347879	−	0.937539i	$-0.386902\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	8.00000	+	6.92820i	0.561490	+	0.486265i
$204$		0			0
$205$		0			0
$206$	4.00000	+	6.92820i	0.278693	+	0.482711i
$207$	−10.5000	−	18.1865i	−0.729800	−	1.26405i
$208$	2.50000	−	4.33013i	0.173344	−	0.300240i
$209$	−15.0000			−1.03757
$210$		0			0
$211$	−9.00000			−0.619586			−0.309793	−	0.950804i	$-0.600260\pi$
$211$	−9.00000			−0.619586			−0.309793	+	0.950804i	$0.600260\pi$
$212$	−4.50000	+	7.79423i	−0.309061	+	0.535310i
$213$		0			0
$214$	8.00000	+	13.8564i	0.546869	+	0.947204i
$215$		0			0
$216$		0			0
$217$	1.00000	−	5.19615i	0.0678844	−	0.352738i
$218$	2.00000			0.135457
$219$		0			0
$220$		0			0
$221$	−5.00000	−	8.66025i	−0.336336	−	0.582552i
$222$		0			0
$223$	−8.00000			−0.535720			−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000			−0.535720			−0.267860	+	0.963458i	$0.586316\pi$
$224$	−0.500000	+	2.59808i	−0.0334077	+	0.173591i
$225$		0			0
$226$	−7.00000	+	12.1244i	−0.465633	+	0.806500i
$227$	3.00000	+	5.19615i	0.199117	+	0.344881i	0.948242	−	0.317547i	$-0.102859\pi$
$227$	3.00000	+	5.19615i	0.199117	+	0.344881i	−0.749125	+	0.662428i	$0.769526\pi$
$228$		0			0
$229$	−8.00000	+	13.8564i	−0.528655	+	0.915657i	0.470787	+	0.882247i	$0.343970\pi$
$229$	−8.00000	+	13.8564i	−0.528655	+	0.915657i	−0.999442	+	0.0334101i	$0.989363\pi$
$230$		0			0
$231$		0			0
$232$	−4.00000			−0.262613
$233$	4.00000	−	6.92820i	0.262049	−	0.453882i	−0.704737	−	0.709468i	$-0.748935\pi$
$233$	4.00000	−	6.92820i	0.262049	−	0.453882i	0.966786	+	0.255586i	$0.0822686\pi$
$234$	−7.50000	−	12.9904i	−0.490290	−	0.849208i
$235$		0			0
$236$	2.00000	−	3.46410i	0.130189	−	0.225494i
$237$		0			0
$238$	4.00000	+	3.46410i	0.259281	+	0.224544i
$239$	20.0000			1.29369			0.646846	−	0.762620i	$-0.276088\pi$
$239$	20.0000			1.29369			0.646846	+	0.762620i	$0.276088\pi$
$240$		0			0
$241$	4.50000	+	7.79423i	0.289870	+	0.502070i	0.973779	−	0.227498i	$-0.0730544\pi$
$241$	4.50000	+	7.79423i	0.289870	+	0.502070i	−0.683908	+	0.729568i	$0.739721\pi$
$242$	1.00000	+	1.73205i	0.0642824	+	0.111340i
$243$		0			0
$244$	6.00000			0.384111
$245$		0			0
$246$		0			0
$247$	−12.5000	+	21.6506i	−0.795356	+	1.37760i
$248$	1.00000	+	1.73205i	0.0635001	+	0.109985i
$249$		0			0
$250$		0			0
$251$	5.00000			0.315597			0.157799	−	0.987471i	$-0.449560\pi$
$251$	5.00000			0.315597			0.157799	+	0.987471i	$0.449560\pi$
$252$	6.00000	+	5.19615i	0.377964	+	0.327327i
$253$	−21.0000			−1.32026
$254$	−3.50000	+	6.06218i	−0.219610	+	0.380375i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	−0.757159	−	0.653231i	$-0.773413\pi$
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	0.944294	+	0.329104i	$0.106747\pi$
$258$		0			0
$259$	2.50000	−	0.866025i	0.155342	−	0.0538122i
$260$		0			0
$261$	−6.00000	+	10.3923i	−0.371391	+	0.643268i
$262$	0.500000	+	0.866025i	0.0308901	+	0.0535032i
$263$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$263$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$264$		0			0
$265$		0			0
$266$	2.50000	−	12.9904i	0.153285	−	0.796491i
$267$		0			0
$268$	−1.00000	+	1.73205i	−0.0610847	+	0.105802i
$269$	5.00000	+	8.66025i	0.304855	+	0.528025i	0.977229	−	0.212187i	$-0.0680585\pi$
$269$	5.00000	+	8.66025i	0.304855	+	0.528025i	−0.672374	+	0.740212i	$0.734725\pi$
$270$		0			0
$271$	−12.0000	+	20.7846i	−0.728948	+	1.26258i	0.228380	+	0.973572i	$0.426657\pi$
$271$	−12.0000	+	20.7846i	−0.728948	+	1.26258i	−0.957328	+	0.289003i	$0.906676\pi$
$272$	−2.00000			−0.121268
$273$		0			0
$274$	−8.00000			−0.483298
$275$		0			0
$276$		0			0
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	0.894503	−	0.447062i	$-0.147530\pi$
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	−0.834419	+	0.551131i	$0.814196\pi$
$278$	−8.00000	+	13.8564i	−0.479808	+	0.831052i
$279$	6.00000			0.359211
$280$		0			0
$281$	9.00000			0.536895			0.268447	−	0.963294i	$-0.413489\pi$
$281$	9.00000			0.536895			0.268447	+	0.963294i	$0.413489\pi$
$282$		0			0
$283$	−7.00000	−	12.1244i	−0.416107	−	0.720718i	0.579437	−	0.815017i	$-0.303272\pi$
$283$	−7.00000	−	12.1244i	−0.416107	−	0.720718i	−0.995544	+	0.0942988i	$0.969939\pi$
$284$	3.00000	+	5.19615i	0.178017	+	0.308335i
$285$		0			0
$286$	−15.0000			−0.886969
$287$	−6.00000	−	5.19615i	−0.354169	−	0.306719i
$288$	−3.00000			−0.176777
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$		0			0
$291$		0			0
$292$	8.00000	−	13.8564i	0.468165	−	0.810885i
$293$	−9.00000			−0.525786			−0.262893	−	0.964825i	$-0.584677\pi$
$293$	−9.00000			−0.525786			−0.262893	+	0.964825i	$0.584677\pi$
$294$		0			0
$295$		0			0
$296$	−0.500000	+	0.866025i	−0.0290619	+	0.0503367i
$297$		0			0
$298$	9.00000	+	15.5885i	0.521356	+	0.903015i
$299$	−17.5000	+	30.3109i	−1.01205	+	1.75292i
$300$		0			0
$301$	−4.00000	−	3.46410i	−0.230556	−	0.199667i
$302$	−6.00000			−0.345261
$303$		0			0
$304$	2.50000	+	4.33013i	0.143385	+	0.248350i
$305$		0			0
$306$	−3.00000	+	5.19615i	−0.171499	+	0.297044i
$307$	−22.0000			−1.25561			−0.627803	−	0.778372i	$-0.716046\pi$
$307$	−22.0000			−1.25561			−0.627803	+	0.778372i	$0.716046\pi$
$308$	7.50000	−	2.59808i	0.427352	−	0.148039i
$309$		0			0
$310$		0			0
$311$	−3.00000	−	5.19615i	−0.170114	−	0.294647i	0.768345	−	0.640036i	$-0.221080\pi$
$311$	−3.00000	−	5.19615i	−0.170114	−	0.294647i	−0.938460	+	0.345389i	$0.887747\pi$
$312$		0			0
$313$	11.0000	−	19.0526i	0.621757	−	1.07691i	−0.367402	−	0.930062i	$-0.619753\pi$
$313$	11.0000	−	19.0526i	0.621757	−	1.07691i	0.989158	−	0.146852i	$-0.0469141\pi$
$314$	−9.00000			−0.507899
$315$		0			0
$316$	14.0000			0.787562
$317$	1.00000	−	1.73205i	0.0561656	−	0.0972817i	−0.836576	−	0.547852i	$-0.815446\pi$
$317$	1.00000	−	1.73205i	0.0561656	−	0.0972817i	0.892741	+	0.450570i	$0.148779\pi$
$318$		0			0
$319$	6.00000	+	10.3923i	0.335936	+	0.581857i
$320$		0			0
$321$		0			0
$322$	3.50000	−	18.1865i	0.195047	−	1.01350i
$323$	10.0000			0.556415
$324$	−4.50000	+	7.79423i	−0.250000	+	0.433013i
$325$		0			0
$326$	6.00000	+	10.3923i	0.332309	+	0.575577i
$327$		0			0
$328$	3.00000			0.165647
$329$	−17.5000	+	6.06218i	−0.964806	+	0.334219i
$330$		0			0
$331$	−2.50000	+	4.33013i	−0.137412	+	0.238005i	−0.926516	−	0.376254i	$-0.877212\pi$
$331$	−2.50000	+	4.33013i	−0.137412	+	0.238005i	0.789104	+	0.614260i	$0.210545\pi$
$332$	3.00000	+	5.19615i	0.164646	+	0.285176i
$333$	1.50000	+	2.59808i	0.0821995	+	0.142374i
$334$	−7.50000	+	12.9904i	−0.410382	+	0.710802i
$335$		0			0
$336$		0			0
$337$	10.0000			0.544735			0.272367	−	0.962193i	$-0.412193\pi$
$337$	10.0000			0.544735			0.272367	+	0.962193i	$0.412193\pi$
$338$	−6.00000	+	10.3923i	−0.326357	+	0.565267i
$339$		0			0
$340$		0			0
$341$	3.00000	−	5.19615i	0.162459	−	0.281387i
$342$	15.0000			0.811107
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	2.00000			0.107833
$345$		0			0
$346$	−4.50000	−	7.79423i	−0.241921	−	0.419020i
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	0.980921	−	0.194409i	$-0.0622790\pi$
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	−0.658824	+	0.752297i	$0.728946\pi$
$348$		0			0
$349$	−12.0000			−0.642345			−0.321173	−	0.947021i	$-0.604077\pi$
$349$	−12.0000			−0.642345			−0.321173	+	0.947021i	$0.604077\pi$
$350$		0			0
$351$		0			0
$352$	−1.50000	+	2.59808i	−0.0799503	+	0.138478i
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	−0.985719	−	0.168397i	$-0.946141\pi$
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	0.347024	−	0.937856i	$-0.387192\pi$
$354$		0			0
$355$		0			0
$356$	2.00000			0.106000
$357$		0			0
$358$	13.0000			0.687071
$359$	−8.00000	+	13.8564i	−0.422224	+	0.731313i	−0.996157	−	0.0875892i	$-0.972084\pi$
$359$	−8.00000	+	13.8564i	−0.422224	+	0.731313i	0.573933	+	0.818902i	$0.305417\pi$
$360$		0			0
$361$	−3.00000	−	5.19615i	−0.157895	−	0.273482i
$362$	−13.0000	+	22.5167i	−0.683265	+	1.18345i
$363$		0			0
$364$	2.50000	−	12.9904i	0.131036	−	0.680881i
$365$		0			0
$366$		0			0
$367$	−6.50000	−	11.2583i	−0.339297	−	0.587680i	0.645003	−	0.764180i	$-0.276856\pi$
$367$	−6.50000	−	11.2583i	−0.339297	−	0.587680i	−0.984301	+	0.176500i	$0.943523\pi$
$368$	3.50000	+	6.06218i	0.182450	+	0.316013i
$369$	4.50000	−	7.79423i	0.234261	−	0.405751i
$370$		0			0
$371$	−4.50000	+	23.3827i	−0.233628	+	1.21397i
$372$		0			0
$373$	−13.0000	+	22.5167i	−0.673114	+	1.16587i	0.303902	+	0.952703i	$0.401711\pi$
$373$	−13.0000	+	22.5167i	−0.673114	+	1.16587i	−0.977016	+	0.213165i	$0.931623\pi$
$374$	3.00000	+	5.19615i	0.155126	+	0.268687i
$375$		0			0
$376$	3.50000	−	6.06218i	0.180499	−	0.312633i
$377$	20.0000			1.03005
$378$		0			0
$379$	−29.0000			−1.48963			−0.744815	−	0.667271i	$-0.767462\pi$
$379$	−29.0000			−1.48963			−0.744815	+	0.667271i	$0.767462\pi$
$380$		0			0
$381$		0			0
$382$	10.0000	+	17.3205i	0.511645	+	0.886194i
$383$	−10.5000	+	18.1865i	−0.536525	+	0.929288i	0.462563	+	0.886586i	$0.346930\pi$
$383$	−10.5000	+	18.1865i	−0.536525	+	0.929288i	−0.999088	+	0.0427020i	$0.986403\pi$
$384$		0			0
$385$		0			0
$386$	−10.0000			−0.508987
$387$	3.00000	−	5.19615i	0.152499	−	0.264135i
$388$	6.00000	+	10.3923i	0.304604	+	0.527589i
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	0.932002	−	0.362454i	$-0.118061\pi$
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	−0.779895	+	0.625910i	$0.784728\pi$
$390$		0			0
$391$	14.0000			0.708010
$392$	1.00000	+	6.92820i	0.0505076	+	0.349927i
$393$		0			0
$394$	2.50000	−	4.33013i	0.125948	−	0.218149i
$395$		0			0
$396$	4.50000	+	7.79423i	0.226134	+	0.391675i
$397$	7.00000	−	12.1244i	0.351320	−	0.608504i	−0.635161	−	0.772380i	$-0.719066\pi$
$397$	7.00000	−	12.1244i	0.351320	−	0.608504i	0.986481	+	0.163876i	$0.0523996\pi$
$398$	18.0000			0.902258
$399$		0			0
$400$		0			0
$401$	7.50000	−	12.9904i	0.374532	−	0.648709i	−0.615725	−	0.787961i	$-0.711137\pi$
$401$	7.50000	−	12.9904i	0.374532	−	0.648709i	0.990257	+	0.139253i	$0.0444700\pi$
$402$		0			0
$403$	−5.00000	−	8.66025i	−0.249068	−	0.431398i
$404$		0			0
$405$		0			0
$406$	−10.0000	+	3.46410i	−0.496292	+	0.171920i
$407$	3.00000			0.148704
$408$		0			0
$409$	7.00000	+	12.1244i	0.346128	+	0.599511i	0.985558	−	0.169338i	$-0.0541630\pi$
$409$	7.00000	+	12.1244i	0.346128	+	0.599511i	−0.639430	+	0.768849i	$0.720830\pi$
$410$		0			0
$411$		0			0
$412$	−8.00000			−0.394132
$413$	2.00000	−	10.3923i	0.0984136	−	0.511372i
$414$	21.0000			1.03209
$415$		0			0
$416$	2.50000	+	4.33013i	0.122573	+	0.212302i
$417$		0			0
$418$	7.50000	−	12.9904i	0.366837	−	0.635380i
$419$	35.0000			1.70986			0.854931	−	0.518742i	$-0.173599\pi$
$419$	35.0000			1.70986			0.854931	+	0.518742i	$0.173599\pi$
$420$		0			0
$421$	−20.0000			−0.974740			−0.487370	−	0.873195i	$-0.662044\pi$
$421$	−20.0000			−0.974740			−0.487370	+	0.873195i	$0.662044\pi$
$422$	4.50000	−	7.79423i	0.219057	−	0.379417i
$423$	−10.5000	−	18.1865i	−0.510527	−	0.884260i
$424$	−4.50000	−	7.79423i	−0.218539	−	0.378521i
$425$		0			0
$426$		0			0
$427$	15.0000	−	5.19615i	0.725901	−	0.251459i
$428$	−16.0000			−0.773389
$429$		0			0
$430$		0			0
$431$	−1.00000	−	1.73205i	−0.0481683	−	0.0834300i	0.840936	−	0.541135i	$-0.182005\pi$
$431$	−1.00000	−	1.73205i	−0.0481683	−	0.0834300i	−0.889104	+	0.457705i	$0.848672\pi$
$432$		0			0
$433$	28.0000			1.34559			0.672797	−	0.739827i	$-0.265093\pi$
$433$	28.0000			1.34559			0.672797	+	0.739827i	$0.265093\pi$
$434$	4.00000	+	3.46410i	0.192006	+	0.166282i
$435$		0			0
$436$	−1.00000	+	1.73205i	−0.0478913	+	0.0829502i
$437$	−17.5000	−	30.3109i	−0.837139	−	1.44997i
$438$		0			0
$439$	14.0000	−	24.2487i	0.668184	−	1.15733i	−0.310228	−	0.950662i	$-0.600405\pi$
$439$	14.0000	−	24.2487i	0.668184	−	1.15733i	0.978412	−	0.206666i	$-0.0662612\pi$
$440$		0			0
$441$	19.5000	+	7.79423i	0.928571	+	0.371154i
$442$	10.0000			0.475651
$443$	−15.0000	+	25.9808i	−0.712672	+	1.23438i	0.251179	+	0.967941i	$0.419182\pi$
$443$	−15.0000	+	25.9808i	−0.712672	+	1.23438i	−0.963851	+	0.266443i	$0.914152\pi$
$444$		0			0
$445$		0			0
$446$	4.00000	−	6.92820i	0.189405	−	0.328060i
$447$		0			0
$448$	−2.00000	−	1.73205i	−0.0944911	−	0.0818317i
$449$	5.00000			0.235965			0.117982	−	0.993016i	$-0.462357\pi$
$449$	5.00000			0.235965			0.117982	+	0.993016i	$0.462357\pi$
$450$		0			0
$451$	−4.50000	−	7.79423i	−0.211897	−	0.367016i
$452$	−7.00000	−	12.1244i	−0.329252	−	0.570282i
$453$		0			0
$454$	−6.00000			−0.281594
$455$		0			0
$456$		0			0
$457$	5.00000	−	8.66025i	0.233890	−	0.405110i	−0.725059	−	0.688686i	$-0.758188\pi$
$457$	5.00000	−	8.66025i	0.233890	−	0.405110i	0.958950	+	0.283577i	$0.0915211\pi$
$458$	−8.00000	−	13.8564i	−0.373815	−	0.647467i
$459$		0			0
$460$		0			0
$461$	−32.0000			−1.49039			−0.745194	−	0.666847i	$-0.767643\pi$
$461$	−32.0000			−1.49039			−0.745194	+	0.666847i	$0.767643\pi$
$462$		0			0
$463$	−17.0000			−0.790057			−0.395029	−	0.918669i	$-0.629265\pi$
$463$	−17.0000			−0.790057			−0.395029	+	0.918669i	$0.629265\pi$
$464$	2.00000	−	3.46410i	0.0928477	−	0.160817i
$465$		0			0
$466$	4.00000	+	6.92820i	0.185296	+	0.320943i
$467$	−17.0000	+	29.4449i	−0.786666	+	1.36255i	0.141332	+	0.989962i	$0.454861\pi$
$467$	−17.0000	+	29.4449i	−0.786666	+	1.36255i	−0.927999	+	0.372584i	$0.878472\pi$
$468$	15.0000			0.693375
$469$	−1.00000	+	5.19615i	−0.0461757	+	0.239936i
$470$		0			0
$471$		0			0
$472$	2.00000	+	3.46410i	0.0920575	+	0.159448i
$473$	−3.00000	−	5.19615i	−0.137940	−	0.238919i
$474$		0			0
$475$		0			0
$476$	−5.00000	+	1.73205i	−0.229175	+	0.0793884i
$477$	−27.0000			−1.23625
$478$	−10.0000	+	17.3205i	−0.457389	+	0.792222i
$479$	−18.0000	−	31.1769i	−0.822441	−	1.42451i	−0.903859	−	0.427830i	$-0.859278\pi$
$479$	−18.0000	−	31.1769i	−0.822441	−	1.42451i	0.0814184	−	0.996680i	$-0.474055\pi$
$480$		0			0
$481$	2.50000	−	4.33013i	0.113990	−	0.197437i
$482$	−9.00000			−0.409939
$483$		0			0
$484$	−2.00000			−0.0909091
$485$		0			0
$486$		0			0
$487$	16.0000	+	27.7128i	0.725029	+	1.25579i	0.958962	+	0.283535i	$0.0915071\pi$
$487$	16.0000	+	27.7128i	0.725029	+	1.25579i	−0.233933	+	0.972253i	$0.575160\pi$
$488$	−3.00000	+	5.19615i	−0.135804	+	0.235219i
$489$		0			0
$490$		0			0
$491$	24.0000			1.08310			0.541552	−	0.840667i	$-0.317837\pi$
$491$	24.0000			1.08310			0.541552	+	0.840667i	$0.317837\pi$
$492$		0			0
$493$	−4.00000	−	6.92820i	−0.180151	−	0.312031i
$494$	−12.5000	−	21.6506i	−0.562402	−	0.974108i
$495$		0			0
$496$	−2.00000			−0.0898027
$497$	12.0000	+	10.3923i	0.538274	+	0.466159i
$498$		0			0
$499$	−2.00000	+	3.46410i	−0.0895323	+	0.155074i	−0.907314	−	0.420455i	$-0.861871\pi$
$499$	−2.00000	+	3.46410i	−0.0895323	+	0.155074i	0.817781	+	0.575529i	$0.195204\pi$
$500$		0			0
$501$		0			0
$502$	−2.50000	+	4.33013i	−0.111580	+	0.193263i
$503$	40.0000			1.78351			0.891756	−	0.452517i	$-0.149474\pi$
$503$	40.0000			1.78351			0.891756	+	0.452517i	$0.149474\pi$
$504$	−7.50000	+	2.59808i	−0.334077	+	0.115728i
$505$		0			0
$506$	10.5000	−	18.1865i	0.466782	−	0.808490i
$507$		0			0
$508$	−3.50000	−	6.06218i	−0.155287	−	0.268966i
$509$	17.0000	−	29.4449i	0.753512	−	1.30512i	−0.192599	−	0.981278i	$-0.561692\pi$
$509$	17.0000	−	29.4449i	0.753512	−	1.30512i	0.946111	−	0.323843i	$-0.104975\pi$
$510$		0			0
$511$	8.00000	−	41.5692i	0.353899	−	1.83891i
$512$	1.00000			0.0441942
$513$		0			0
$514$	3.00000	+	5.19615i	0.132324	+	0.229192i
$515$		0			0
$516$		0			0
$517$	−21.0000			−0.923579
$518$	−0.500000	+	2.59808i	−0.0219687	+	0.114153i
$519$		0			0
$520$		0			0
$521$	13.5000	+	23.3827i	0.591446	+	1.02441i	0.994038	+	0.109035i	$0.0347759\pi$
$521$	13.5000	+	23.3827i	0.591446	+	1.02441i	−0.402592	+	0.915379i	$0.631891\pi$
$522$	−6.00000	−	10.3923i	−0.262613	−	0.454859i
$523$	−8.00000	+	13.8564i	−0.349816	+	0.605898i	−0.986216	−	0.165460i	$-0.947089\pi$
$523$	−8.00000	+	13.8564i	−0.349816	+	0.605898i	0.636401	+	0.771358i	$0.280422\pi$
$524$	−1.00000			−0.0436852
$525$		0			0
$526$		0			0
$527$	−2.00000	+	3.46410i	−0.0871214	+	0.150899i
$528$		0			0
$529$	−13.0000	−	22.5167i	−0.565217	−	0.978985i
$530$		0			0
$531$	12.0000			0.520756
$532$	10.0000	+	8.66025i	0.433555	+	0.375470i
$533$	−15.0000			−0.649722
$534$		0			0
$535$		0			0
$536$	−1.00000	−	1.73205i	−0.0431934	−	0.0748132i
$537$		0			0
$538$	−10.0000			−0.431131
$539$	16.5000	−	12.9904i	0.710705	−	0.559535i
$540$		0			0
$541$	8.00000	−	13.8564i	0.343947	−	0.595733i	−0.641215	−	0.767361i	$-0.721569\pi$
$541$	8.00000	−	13.8564i	0.343947	−	0.595733i	0.985162	+	0.171628i	$0.0549027\pi$
$542$	−12.0000	−	20.7846i	−0.515444	−	0.892775i
$543$		0			0
$544$	1.00000	−	1.73205i	0.0428746	−	0.0742611i
$545$		0			0
$546$		0			0
$547$	−26.0000			−1.11168			−0.555840	−	0.831289i	$-0.687603\pi$
$547$	−26.0000			−1.11168			−0.555840	+	0.831289i	$0.687603\pi$
$548$	4.00000	−	6.92820i	0.170872	−	0.295958i
$549$	9.00000	+	15.5885i	0.384111	+	0.665299i
$550$		0			0
$551$	−10.0000	+	17.3205i	−0.426014	+	0.737878i
$552$		0			0
$553$	35.0000	−	12.1244i	1.48835	−	0.515580i
$554$	−2.00000			−0.0849719
$555$		0			0
$556$	−8.00000	−	13.8564i	−0.339276	−	0.587643i
$557$	−11.5000	−	19.9186i	−0.487271	−	0.843978i	0.512622	−	0.858614i	$-0.328674\pi$
$557$	−11.5000	−	19.9186i	−0.487271	−	0.843978i	−0.999893	+	0.0146368i	$0.995341\pi$
$558$	−3.00000	+	5.19615i	−0.127000	+	0.219971i
$559$	−10.0000			−0.422955
$560$		0			0
$561$		0			0
$562$	−4.50000	+	7.79423i	−0.189821	+	0.328780i
$563$	−1.00000	−	1.73205i	−0.0421450	−	0.0729972i	0.844183	−	0.536054i	$-0.180086\pi$
$563$	−1.00000	−	1.73205i	−0.0421450	−	0.0729972i	−0.886328	+	0.463057i	$0.846752\pi$
$564$		0			0
$565$		0			0
$566$	14.0000			0.588464
$567$	−4.50000	+	23.3827i	−0.188982	+	0.981981i
$568$	−6.00000			−0.251754
$569$	7.50000	−	12.9904i	0.314416	−	0.544585i	−0.664897	−	0.746935i	$-0.731525\pi$
$569$	7.50000	−	12.9904i	0.314416	−	0.544585i	0.979313	+	0.202350i	$0.0648579\pi$
$570$		0			0
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	−0.978022	−	0.208502i	$-0.933141\pi$
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	0.308443	−	0.951243i	$-0.400192\pi$
$572$	7.50000	−	12.9904i	0.313591	−	0.543155i
$573$		0			0
$574$	7.50000	−	2.59808i	0.313044	−	0.108442i
$575$		0			0
$576$	1.50000	−	2.59808i	0.0625000	−	0.108253i
$577$	2.00000	+	3.46410i	0.0832611	+	0.144212i	0.904649	−	0.426158i	$-0.140133\pi$
$577$	2.00000	+	3.46410i	0.0832611	+	0.144212i	−0.821388	+	0.570370i	$0.806800\pi$
$578$	6.50000	+	11.2583i	0.270364	+	0.468285i
$579$		0			0
$580$		0			0
$581$	12.0000	+	10.3923i	0.497844	+	0.431145i
$582$		0			0
$583$	−13.5000	+	23.3827i	−0.559113	+	0.968412i
$584$	8.00000	+	13.8564i	0.331042	+	0.573382i
$585$		0			0
$586$	4.50000	−	7.79423i	0.185893	−	0.321977i
$587$	34.0000			1.40333			0.701665	−	0.712507i	$-0.252440\pi$
$587$	34.0000			1.40333			0.701665	+	0.712507i	$0.252440\pi$
$588$		0			0
$589$	10.0000			0.412043
$590$		0			0
$591$		0			0
$592$	−0.500000	−	0.866025i	−0.0205499	−	0.0355934i
$593$	3.00000	−	5.19615i	0.123195	−	0.213380i	−0.797831	−	0.602881i	$-0.794019\pi$
$593$	3.00000	−	5.19615i	0.123195	−	0.213380i	0.921026	+	0.389501i	$0.127353\pi$
$594$		0			0
$595$		0			0
$596$	−18.0000			−0.737309
$597$		0			0
$598$	−17.5000	−	30.3109i	−0.715628	−	1.23950i
$599$	6.00000	+	10.3923i	0.245153	+	0.424618i	0.962175	−	0.272433i	$-0.0878284\pi$
$599$	6.00000	+	10.3923i	0.245153	+	0.424618i	−0.717021	+	0.697051i	$0.754495\pi$
$600$		0			0
$601$	−22.0000			−0.897399			−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000			−0.897399			−0.448699	+	0.893683i	$0.648113\pi$
$602$	5.00000	−	1.73205i	0.203785	−	0.0705931i
$603$	−6.00000			−0.244339
$604$	3.00000	−	5.19615i	0.122068	−	0.211428i
$605$		0			0
$606$		0			0
$607$	6.50000	−	11.2583i	0.263827	−	0.456962i	−0.703429	−	0.710766i	$-0.748349\pi$
$607$	6.50000	−	11.2583i	0.263827	−	0.456962i	0.967256	+	0.253804i	$0.0816819\pi$
$608$	−5.00000			−0.202777
$609$		0			0
$610$		0			0
$611$	−17.5000	+	30.3109i	−0.707974	+	1.22625i
$612$	−3.00000	−	5.19615i	−0.121268	−	0.210042i
$613$	7.50000	+	12.9904i	0.302922	+	0.524677i	0.976797	−	0.214169i	$-0.0687045\pi$
$613$	7.50000	+	12.9904i	0.302922	+	0.524677i	−0.673874	+	0.738846i	$0.735371\pi$
$614$	11.0000	−	19.0526i	0.443924	−	0.768899i
$615$		0			0
$616$	−1.50000	+	7.79423i	−0.0604367	+	0.314038i
$617$	14.0000			0.563619			0.281809	−	0.959470i	$-0.409065\pi$
$617$	14.0000			0.563619			0.281809	+	0.959470i	$0.409065\pi$
$618$		0			0
$619$	−9.50000	−	16.4545i	−0.381837	−	0.661361i	0.609488	−	0.792796i	$-0.291375\pi$
$619$	−9.50000	−	16.4545i	−0.381837	−	0.661361i	−0.991325	+	0.131434i	$0.958042\pi$
$620$		0			0
$621$		0			0
$622$	6.00000			0.240578
$623$	5.00000	−	1.73205i	0.200321	−	0.0693932i
$624$		0			0
$625$		0			0
$626$	11.0000	+	19.0526i	0.439648	+	0.761493i
$627$		0			0
$628$	4.50000	−	7.79423i	0.179570	−	0.311024i
$629$	−2.00000			−0.0797452
$630$		0			0
$631$	−18.0000			−0.716569			−0.358284	−	0.933613i	$-0.616638\pi$
$631$	−18.0000			−0.716569			−0.358284	+	0.933613i	$0.616638\pi$
$632$	−7.00000	+	12.1244i	−0.278445	+	0.482281i
$633$		0			0
$634$	1.00000	+	1.73205i	0.0397151	+	0.0687885i
$635$		0			0
$636$		0			0
$637$	−5.00000	−	34.6410i	−0.198107	−	1.37253i
$638$	−12.0000			−0.475085
$639$	−9.00000	+	15.5885i	−0.356034	+	0.616670i
$640$		0			0
$641$	2.50000	+	4.33013i	0.0987441	+	0.171030i	0.911165	−	0.412042i	$-0.135184\pi$
$641$	2.50000	+	4.33013i	0.0987441	+	0.171030i	−0.812421	+	0.583071i	$0.801851\pi$
$642$		0			0
$643$	−14.0000			−0.552106			−0.276053	−	0.961142i	$-0.589027\pi$
$643$	−14.0000			−0.552106			−0.276053	+	0.961142i	$0.589027\pi$
$644$	14.0000	+	12.1244i	0.551677	+	0.477767i
$645$		0			0
$646$	−5.00000	+	8.66025i	−0.196722	+	0.340733i
$647$	13.5000	+	23.3827i	0.530740	+	0.919268i	0.999357	+	0.0358667i	$0.0114192\pi$
$647$	13.5000	+	23.3827i	0.530740	+	0.919268i	−0.468617	+	0.883402i	$0.655247\pi$
$648$	−4.50000	−	7.79423i	−0.176777	−	0.306186i
$649$	6.00000	−	10.3923i	0.235521	−	0.407934i
$650$		0			0
$651$		0			0
$652$	−12.0000			−0.469956
$653$	−1.50000	+	2.59808i	−0.0586995	+	0.101671i	−0.893882	−	0.448303i	$-0.852029\pi$
$653$	−1.50000	+	2.59808i	−0.0586995	+	0.101671i	0.835182	+	0.549973i	$0.185362\pi$
$654$		0			0
$655$		0			0
$656$	−1.50000	+	2.59808i	−0.0585652	+	0.101438i
$657$	48.0000			1.87266
$658$	3.50000	−	18.1865i	0.136444	−	0.708985i
$659$	−36.0000			−1.40236			−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000			−1.40236			−0.701180	+	0.712984i	$0.747343\pi$
$660$		0			0
$661$	−8.00000	−	13.8564i	−0.311164	−	0.538952i	0.667451	−	0.744654i	$-0.267385\pi$
$661$	−8.00000	−	13.8564i	−0.311164	−	0.538952i	−0.978615	+	0.205702i	$0.934052\pi$
$662$	−2.50000	−	4.33013i	−0.0971653	−	0.168295i
$663$		0			0
$664$	−6.00000			−0.232845
$665$		0			0
$666$	−3.00000			−0.116248
$667$	−14.0000	+	24.2487i	−0.542082	+	0.938914i
$668$	−7.50000	−	12.9904i	−0.290184	−	0.502613i
$669$		0			0
$670$		0			0
$671$	18.0000			0.694882
$672$		0			0
$673$	32.0000			1.23351			0.616755	−	0.787155i	$-0.288447\pi$
$673$	32.0000			1.23351			0.616755	+	0.787155i	$0.288447\pi$
$674$	−5.00000	+	8.66025i	−0.192593	+	0.333581i
$675$		0			0
$676$	−6.00000	−	10.3923i	−0.230769	−	0.399704i
$677$	8.50000	−	14.7224i	0.326682	−	0.565829i	−0.655170	−	0.755482i	$-0.727403\pi$
$677$	8.50000	−	14.7224i	0.326682	−	0.565829i	0.981851	+	0.189653i	$0.0607362\pi$
$678$		0			0
$679$	24.0000	+	20.7846i	0.921035	+	0.797640i
$680$		0			0
$681$		0			0
$682$	3.00000	+	5.19615i	0.114876	+	0.198971i
$683$	22.0000	+	38.1051i	0.841807	+	1.45805i	0.888366	+	0.459136i	$0.151841\pi$
$683$	22.0000	+	38.1051i	0.841807	+	1.45805i	−0.0465592	+	0.998916i	$0.514826\pi$
$684$	−7.50000	+	12.9904i	−0.286770	+	0.496700i
$685$		0			0
$686$	8.50000	+	16.4545i	0.324532	+	0.628235i
$687$		0			0
$688$	−1.00000	+	1.73205i	−0.0381246	+	0.0660338i
$689$	22.5000	+	38.9711i	0.857182	+	1.48468i
$690$		0			0
$691$	22.0000	−	38.1051i	0.836919	−	1.44959i	−0.0555386	−	0.998457i	$-0.517688\pi$
$691$	22.0000	−	38.1051i	0.836919	−	1.44959i	0.892458	−	0.451130i	$-0.148979\pi$
$692$	9.00000			0.342129
$693$	18.0000	+	15.5885i	0.683763	+	0.592157i
$694$	−12.0000			−0.455514
$695$		0			0
$696$		0			0
$697$	3.00000	+	5.19615i	0.113633	+	0.196818i
$698$	6.00000	−	10.3923i	0.227103	−	0.393355i
$699$		0			0
$700$		0			0
$701$	26.0000			0.982006			0.491003	−	0.871158i	$-0.336630\pi$
$701$	26.0000			0.982006			0.491003	+	0.871158i	$0.336630\pi$
$702$		0			0
$703$	2.50000	+	4.33013i	0.0942893	+	0.163314i
$704$	−1.50000	−	2.59808i	−0.0565334	−	0.0979187i
$705$		0			0
$706$	24.0000			0.903252
$707$		0			0
$708$		0			0
$709$	−6.00000	+	10.3923i	−0.225335	+	0.390291i	−0.956420	−	0.291995i	$-0.905681\pi$
$709$	−6.00000	+	10.3923i	−0.225335	+	0.390291i	0.731085	+	0.682286i	$0.239014\pi$
$710$		0			0
$711$	21.0000	+	36.3731i	0.787562	+	1.36410i
$712$	−1.00000	+	1.73205i	−0.0374766	+	0.0649113i
$713$	14.0000			0.524304
$714$		0			0
$715$		0			0
$716$	−6.50000	+	11.2583i	−0.242916	+	0.420744i
$717$		0			0
$718$	−8.00000	−	13.8564i	−0.298557	−	0.517116i
$719$	−13.0000	+	22.5167i	−0.484818	+	0.839730i	−0.999848	−	0.0174426i	$-0.994448\pi$
$719$	−13.0000	+	22.5167i	−0.484818	+	0.839730i	0.515030	+	0.857172i	$0.327781\pi$
$720$		0			0
$721$	−20.0000	+	6.92820i	−0.744839	+	0.258020i
$722$	6.00000			0.223297
$723$		0			0
$724$	−13.0000	−	22.5167i	−0.483141	−	0.836825i
$725$		0			0
$726$		0			0
$727$	−29.0000			−1.07555			−0.537775	−	0.843088i	$-0.680735\pi$
$727$	−29.0000			−1.07555			−0.537775	+	0.843088i	$0.680735\pi$
$728$	10.0000	+	8.66025i	0.370625	+	0.320970i
$729$	−27.0000			−1.00000
$730$		0			0
$731$	2.00000	+	3.46410i	0.0739727	+	0.128124i
$732$		0			0
$733$	−20.5000	+	35.5070i	−0.757185	+	1.31148i	0.187096	+	0.982342i	$0.440092\pi$
$733$	−20.5000	+	35.5070i	−0.757185	+	1.31148i	−0.944281	+	0.329141i	$0.893241\pi$
$734$	13.0000			0.479839
$735$		0			0
$736$	−7.00000			−0.258023
$737$	−3.00000	+	5.19615i	−0.110506	+	0.191403i
$738$	4.50000	+	7.79423i	0.165647	+	0.286910i
$739$	14.5000	+	25.1147i	0.533391	+	0.923861i	0.999239	+	0.0389959i	$0.0124159\pi$
$739$	14.5000	+	25.1147i	0.533391	+	0.923861i	−0.465848	+	0.884865i	$0.654251\pi$
$740$		0			0
$741$		0			0
$742$	−18.0000	−	15.5885i	−0.660801	−	0.572270i
$743$	−21.0000			−0.770415			−0.385208	−	0.922830i	$-0.625870\pi$
$743$	−21.0000			−0.770415			−0.385208	+	0.922830i	$0.625870\pi$
$744$		0			0
$745$		0			0
$746$	−13.0000	−	22.5167i	−0.475964	−	0.824394i
$747$	−9.00000	+	15.5885i	−0.329293	+	0.570352i
$748$	−6.00000			−0.219382
$749$	−40.0000	+	13.8564i	−1.46157	+	0.506302i
$750$		0			0
$751$	−14.0000	+	24.2487i	−0.510867	+	0.884848i	0.489053	+	0.872254i	$0.337342\pi$
$751$	−14.0000	+	24.2487i	−0.510867	+	0.884848i	−0.999921	+	0.0125942i	$0.995991\pi$
$752$	3.50000	+	6.06218i	0.127632	+	0.221065i
$753$		0			0
$754$	−10.0000	+	17.3205i	−0.364179	+	0.630776i
$755$		0			0
$756$		0			0
$757$	42.0000			1.52652			0.763258	−	0.646094i	$-0.223599\pi$
$757$	42.0000			1.52652			0.763258	+	0.646094i	$0.223599\pi$
$758$	14.5000	−	25.1147i	0.526664	−	0.912208i
$759$		0			0
$760$		0			0
$761$	−0.500000	+	0.866025i	−0.0181250	+	0.0313934i	−0.874946	−	0.484221i	$-0.839103\pi$
$761$	−0.500000	+	0.866025i	−0.0181250	+	0.0313934i	0.856821	+	0.515615i	$0.172436\pi$
$762$		0			0
$763$	−1.00000	+	5.19615i	−0.0362024	+	0.188113i
$764$	−20.0000			−0.723575
$765$		0			0
$766$	−10.5000	−	18.1865i	−0.379380	−	0.657106i
$767$	−10.0000	−	17.3205i	−0.361079	−	0.625407i
$768$		0			0
$769$	−29.0000			−1.04577			−0.522883	−	0.852404i	$-0.675144\pi$
$769$	−29.0000			−1.04577			−0.522883	+	0.852404i	$0.675144\pi$
$770$		0			0
$771$		0			0
$772$	5.00000	−	8.66025i	0.179954	−	0.311689i
$773$	−22.5000	−	38.9711i	−0.809269	−	1.40169i	−0.913371	−	0.407128i	$-0.866530\pi$
$773$	−22.5000	−	38.9711i	−0.809269	−	1.40169i	0.104102	−	0.994567i	$-0.466803\pi$
$774$	3.00000	+	5.19615i	0.107833	+	0.186772i
$775$		0			0
$776$	−12.0000			−0.430775
$777$		0			0
$778$	−6.00000			−0.215110
$779$	7.50000	−	12.9904i	0.268715	−	0.465429i
$780$		0			0
$781$	9.00000	+	15.5885i	0.322045	+	0.557799i
$782$	−7.00000	+	12.1244i	−0.250319	+	0.433566i
$783$		0			0
$784$	−6.50000	−	2.59808i	−0.232143	−	0.0927884i
$785$		0			0
$786$		0			0
$787$	−9.00000	−	15.5885i	−0.320815	−	0.555668i	0.659841	−	0.751405i	$-0.270624\pi$
$787$	−9.00000	−	15.5885i	−0.320815	−	0.555668i	−0.980656	+	0.195737i	$0.937290\pi$
$788$	2.50000	+	4.33013i	0.0890588	+	0.154254i
$789$		0			0
$790$		0			0
$791$	−28.0000	−	24.2487i	−0.995565	−	0.862185i
$792$	−9.00000			−0.319801
$793$	15.0000	−	25.9808i	0.532666	−	0.922604i
$794$	7.00000	+	12.1244i	0.248421	+	0.430277i
$795$		0			0
$796$	−9.00000	+	15.5885i	−0.318997	+	0.552518i
$797$	−2.00000			−0.0708436			−0.0354218	−	0.999372i	$-0.511277\pi$
$797$	−2.00000			−0.0708436			−0.0354218	+	0.999372i	$0.511277\pi$
$798$		0			0
$799$	14.0000			0.495284
$800$		0			0
$801$	3.00000	+	5.19615i	0.106000	+	0.183597i
$802$	7.50000	+	12.9904i	0.264834	+	0.458706i
$803$	24.0000	−	41.5692i	0.846942	−	1.46695i
$804$		0			0
$805$		0			0
$806$	10.0000			0.352235
$807$		0			0
$808$		0			0
$809$	2.50000	+	4.33013i	0.0878953	+	0.152239i	0.906621	−	0.421945i	$-0.138653\pi$
$809$	2.50000	+	4.33013i	0.0878953	+	0.152239i	−0.818726	+	0.574184i	$0.805319\pi$
$810$		0			0
$811$	−33.0000			−1.15879			−0.579393	−	0.815048i	$-0.696710\pi$
$811$	−33.0000			−1.15879			−0.579393	+	0.815048i	$0.696710\pi$
$812$	2.00000	−	10.3923i	0.0701862	−	0.364698i
$813$		0			0
$814$	−1.50000	+	2.59808i	−0.0525750	+	0.0910625i
$815$		0			0
$816$		0			0
$817$	5.00000	−	8.66025i	0.174928	−	0.302984i
$818$	−14.0000			−0.489499
$819$	37.5000	−	12.9904i	1.31036	−	0.453921i
$820$		0			0
$821$	9.00000	−	15.5885i	0.314102	−	0.544041i	−0.665144	−	0.746715i	$-0.731630\pi$
$821$	9.00000	−	15.5885i	0.314102	−	0.544041i	0.979246	+	0.202674i	$0.0649632\pi$
$822$		0			0
$823$	12.0000	+	20.7846i	0.418294	+	0.724506i	0.995768	−	0.0919029i	$-0.0292950\pi$
$823$	12.0000	+	20.7846i	0.418294	+	0.724506i	−0.577474	+	0.816409i	$0.695962\pi$
$824$	4.00000	−	6.92820i	0.139347	−	0.241355i
$825$		0			0
$826$	8.00000	+	6.92820i	0.278356	+	0.241063i
$827$	−22.0000			−0.765015			−0.382507	−	0.923952i	$-0.624939\pi$
$827$	−22.0000			−0.765015			−0.382507	+	0.923952i	$0.624939\pi$
$828$	−10.5000	+	18.1865i	−0.364900	+	0.632026i
$829$	13.0000	+	22.5167i	0.451509	+	0.782036i	0.998480	−	0.0551154i	$-0.0175527\pi$
$829$	13.0000	+	22.5167i	0.451509	+	0.782036i	−0.546971	+	0.837151i	$0.684219\pi$
$830$		0			0
$831$		0			0
$832$	−5.00000			−0.173344
$833$	−11.0000	+	8.66025i	−0.381127	+	0.300060i
$834$		0			0
$835$		0			0
$836$	7.50000	+	12.9904i	0.259393	+	0.449282i
$837$		0			0
$838$	−17.5000	+	30.3109i	−0.604527	+	1.04707i
$839$	−34.0000			−1.17381			−0.586905	−	0.809656i	$-0.699654\pi$
$839$	−34.0000			−1.17381			−0.586905	+	0.809656i	$0.699654\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$	10.0000	−	17.3205i	0.344623	−	0.596904i
$843$		0			0
$844$	4.50000	+	7.79423i	0.154896	+	0.268288i
$845$		0			0
$846$	21.0000			0.721995
$847$	−5.00000	+	1.73205i	−0.171802	+	0.0595140i
$848$	9.00000			0.309061
$849$		0			0
$850$		0			0
$851$	3.50000	+	6.06218i	0.119978	+	0.207809i
$852$		0			0
$853$	−43.0000			−1.47229			−0.736146	−	0.676823i	$-0.763356\pi$
$853$	−43.0000			−1.47229			−0.736146	+	0.676823i	$0.763356\pi$
$854$	−3.00000	+	15.5885i	−0.102658	+	0.533426i
$855$		0			0
$856$	8.00000	−	13.8564i	0.273434	−	0.473602i
$857$	−4.00000	−	6.92820i	−0.136637	−	0.236663i	0.789584	−	0.613642i	$-0.210296\pi$
$857$	−4.00000	−	6.92820i	−0.136637	−	0.236663i	−0.926222	+	0.376979i	$0.876963\pi$
$858$		0			0
$859$	6.00000	−	10.3923i	0.204717	−	0.354581i	−0.745325	−	0.666701i	$-0.767706\pi$
$859$	6.00000	−	10.3923i	0.204717	−	0.354581i	0.950043	+	0.312120i	$0.101039\pi$
$860$		0			0
$861$		0			0
$862$	2.00000			0.0681203
$863$	5.50000	−	9.52628i	0.187222	−	0.324278i	−0.757101	−	0.653298i	$-0.773385\pi$
$863$	5.50000	−	9.52628i	0.187222	−	0.324278i	0.944323	+	0.329020i	$0.106718\pi$
$864$		0			0
$865$		0			0
$866$	−14.0000	+	24.2487i	−0.475739	+	0.824005i
$867$		0			0
$868$	−5.00000	+	1.73205i	−0.169711	+	0.0587896i
$869$	42.0000			1.42475
$870$		0			0
$871$	5.00000	+	8.66025i	0.169419	+	0.293442i
$872$	−1.00000	−	1.73205i	−0.0338643	−	0.0586546i
$873$	−18.0000	+	31.1769i	−0.609208	+	1.05518i
$874$	35.0000			1.18389
$875$		0			0
$876$		0			0
$877$	−15.5000	+	26.8468i	−0.523398	+	0.906552i	0.476231	+	0.879320i	$0.342002\pi$
$877$	−15.5000	+	26.8468i	−0.523398	+	0.906552i	−0.999629	+	0.0272316i	$0.991331\pi$
$878$	14.0000	+	24.2487i	0.472477	+	0.818354i
$879$		0			0
$880$		0			0
$881$	−15.0000			−0.505363			−0.252681	−	0.967550i	$-0.581312\pi$
$881$	−15.0000			−0.505363			−0.252681	+	0.967550i	$0.581312\pi$
$882$	−16.5000	+	12.9904i	−0.555584	+	0.437409i
$883$	16.0000			0.538443			0.269221	−	0.963078i	$-0.413234\pi$
$883$	16.0000			0.538443			0.269221	+	0.963078i	$0.413234\pi$
$884$	−5.00000	+	8.66025i	−0.168168	+	0.291276i
$885$		0			0
$886$	−15.0000	−	25.9808i	−0.503935	−	0.872841i
$887$	−18.0000	+	31.1769i	−0.604381	+	1.04682i	0.387768	+	0.921757i	$0.373246\pi$
$887$	−18.0000	+	31.1769i	−0.604381	+	1.04682i	−0.992149	+	0.125061i	$0.960087\pi$
$888$		0			0
$889$	−14.0000	−	12.1244i	−0.469545	−	0.406638i
$890$		0			0
$891$	−13.5000	+	23.3827i	−0.452267	+	0.783349i
$892$	4.00000	+	6.92820i	0.133930	+	0.231973i
$893$	−17.5000	−	30.3109i	−0.585615	−	1.01432i
$894$		0			0
$895$		0			0
$896$	2.50000	−	0.866025i	0.0835191	−	0.0289319i
$897$		0			0
$898$	−2.50000	+	4.33013i	−0.0834261	+	0.144498i
$899$	−4.00000	−	6.92820i	−0.133407	−	0.231069i
$900$		0			0
$901$	9.00000	−	15.5885i	0.299833	−	0.519327i
$902$	9.00000			0.299667
$903$		0			0
$904$	14.0000			0.465633
$905$		0			0
$906$		0			0
$907$	20.0000	+	34.6410i	0.664089	+	1.15024i	0.979531	+	0.201291i	$0.0645138\pi$
$907$	20.0000	+	34.6410i	0.664089	+	1.15024i	−0.315442	+	0.948945i	$0.602153\pi$
$908$	3.00000	−	5.19615i	0.0995585	−	0.172440i
$909$		0			0
$910$		0			0
$911$	2.00000			0.0662630			0.0331315	−	0.999451i	$-0.489452\pi$
$911$	2.00000			0.0662630			0.0331315	+	0.999451i	$0.489452\pi$
$912$		0			0
$913$	9.00000	+	15.5885i	0.297857	+	0.515903i
$914$	5.00000	+	8.66025i	0.165385	+	0.286456i
$915$		0			0
$916$	16.0000			0.528655
$917$	−2.50000	+	0.866025i	−0.0825573	+	0.0285987i
$918$		0			0
$919$	−10.0000	+	17.3205i	−0.329870	+	0.571351i	−0.982486	−	0.186338i	$-0.940338\pi$
$919$	−10.0000	+	17.3205i	−0.329870	+	0.571351i	0.652616	+	0.757689i	$0.273671\pi$
$920$		0			0
$921$		0			0
$922$	16.0000	−	27.7128i	0.526932	−	0.912673i
$923$	30.0000			0.987462
$924$		0			0
$925$		0			0
$926$	8.50000	−	14.7224i	0.279327	−	0.483809i
$927$	−12.0000	−	20.7846i	−0.394132	−	0.682656i
$928$	2.00000	+	3.46410i	0.0656532	+	0.113715i
$929$	−10.5000	+	18.1865i	−0.344494	+	0.596681i	−0.985262	−	0.171054i	$-0.945283\pi$
$929$	−10.5000	+	18.1865i	−0.344494	+	0.596681i	0.640768	+	0.767735i	$0.278616\pi$
$930$		0			0
$931$	32.5000	+	12.9904i	1.06514	+	0.425743i
$932$	−8.00000			−0.262049
$933$		0			0
$934$	−17.0000	−	29.4449i	−0.556257	−	0.963465i
$935$		0			0
$936$	−7.50000	+	12.9904i	−0.245145	+	0.424604i
$937$	−26.0000			−0.849383			−0.424691	−	0.905338i	$-0.639617\pi$
$937$	−26.0000			−0.849383			−0.424691	+	0.905338i	$0.639617\pi$
$938$	−4.00000	−	3.46410i	−0.130605	−	0.113107i
$939$		0			0
$940$		0			0
$941$	14.0000	+	24.2487i	0.456387	+	0.790485i	0.998767	−	0.0496480i	$-0.0158099\pi$
$941$	14.0000	+	24.2487i	0.456387	+	0.790485i	−0.542380	+	0.840133i	$0.682477\pi$
$942$		0			0
$943$	10.5000	−	18.1865i	0.341927	−	0.592235i
$944$	−4.00000			−0.130189
$945$		0			0
$946$	6.00000			0.195077
$947$	6.00000	−	10.3923i	0.194974	−	0.337705i	−0.751918	−	0.659256i	$-0.770871\pi$
$947$	6.00000	−	10.3923i	0.194974	−	0.337705i	0.946892	+	0.321552i	$0.104204\pi$
$948$		0			0
$949$	−40.0000	−	69.2820i	−1.29845	−	2.24899i
$950$		0			0
$951$		0			0
$952$	1.00000	−	5.19615i	0.0324102	−	0.168408i
$953$	−24.0000			−0.777436			−0.388718	−	0.921357i	$-0.627082\pi$
$953$	−24.0000			−0.777436			−0.388718	+	0.921357i	$0.627082\pi$
$954$	13.5000	−	23.3827i	0.437079	−	0.757042i
$955$		0			0
$956$	−10.0000	−	17.3205i	−0.323423	−	0.560185i
$957$		0			0
$958$	36.0000			1.16311
$959$	4.00000	−	20.7846i	0.129167	−	0.671170i
$960$		0			0
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$	2.50000	+	4.33013i	0.0806032	+	0.139609i
$963$	−24.0000	−	41.5692i	−0.773389	−	1.33955i
$964$	4.50000	−	7.79423i	0.144935	−	0.251035i
$965$		0			0
$966$		0			0
$967$	32.0000			1.02905			0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000			1.02905			0.514525	+	0.857475i	$0.327968\pi$
$968$	1.00000	−	1.73205i	0.0321412	−	0.0556702i
$969$		0			0
$970$		0			0
$971$	16.5000	−	28.5788i	0.529510	−	0.917139i	−0.469897	−	0.882721i	$-0.655709\pi$
$971$	16.5000	−	28.5788i	0.529510	−	0.917139i	0.999408	−	0.0344175i	$-0.0109576\pi$
$972$		0			0
$973$	−32.0000	−	27.7128i	−1.02587	−	0.888432i
$974$	−32.0000			−1.02535
$975$		0			0
$976$	−3.00000	−	5.19615i	−0.0960277	−	0.166325i
$977$	−27.0000	−	46.7654i	−0.863807	−	1.49616i	−0.868227	−	0.496167i	$-0.834741\pi$
$977$	−27.0000	−	46.7654i	−0.863807	−	1.49616i	0.00442082	−	0.999990i	$-0.498593\pi$
$978$		0			0
$979$	6.00000			0.191761
$980$		0			0
$981$	−6.00000			−0.191565
$982$	−12.0000	+	20.7846i	−0.382935	+	0.663264i
$983$	14.5000	+	25.1147i	0.462478	+	0.801036i	0.999084	−	0.0427975i	$-0.0136270\pi$
$983$	14.5000	+	25.1147i	0.462478	+	0.801036i	−0.536606	+	0.843833i	$0.680294\pi$
$984$		0			0
$985$		0			0
$986$	8.00000			0.254772
$987$		0			0
$988$	25.0000			0.795356
$989$	7.00000	−	12.1244i	0.222587	−	0.385532i
$990$		0			0
$991$	4.00000	+	6.92820i	0.127064	+	0.220082i	0.922538	−	0.385906i	$-0.126111\pi$
$991$	4.00000	+	6.92820i	0.127064	+	0.220082i	−0.795474	+	0.605988i	$0.792778\pi$
$992$	1.00000	−	1.73205i	0.0317500	−	0.0549927i
$993$		0			0
$994$	−15.0000	+	5.19615i	−0.475771	+	0.164812i
$995$		0			0
$996$		0			0
$997$	19.0000	+	32.9090i	0.601736	+	1.04224i	0.992558	+	0.121771i	$0.0388574\pi$
$997$	19.0000	+	32.9090i	0.601736	+	1.04224i	−0.390822	+	0.920466i	$0.627809\pi$
$998$	−2.00000	−	3.46410i	−0.0633089	−	0.109654i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.e.c.51.1		2
5.2	odd	4		70.2.i.b.9.1	✓	4
5.3	odd	4		70.2.i.b.9.2	yes	4
5.4	even	2		350.2.e.j.51.1		2
7.2	even	3		2450.2.a.ba.1.1		1
7.4	even	3	inner	350.2.e.c.151.1		2
7.5	odd	6		2450.2.a.bb.1.1		1
15.2	even	4		630.2.u.a.289.2		4
15.8	even	4		630.2.u.a.289.1		4
20.3	even	4		560.2.bw.d.289.1		4
20.7	even	4		560.2.bw.d.289.2		4
35.2	odd	12		490.2.c.a.99.2		2
35.3	even	12		490.2.i.a.459.1		4
35.4	even	6		350.2.e.j.151.1		2
35.9	even	6		2450.2.a.k.1.1		1
35.12	even	12		490.2.c.d.99.2		2
35.13	even	4		490.2.i.a.79.2		4
35.17	even	12		490.2.i.a.459.2		4
35.18	odd	12		70.2.i.b.39.1	yes	4
35.19	odd	6		2450.2.a.j.1.1		1
35.23	odd	12		490.2.c.a.99.1		2
35.27	even	4		490.2.i.a.79.1		4
35.32	odd	12		70.2.i.b.39.2	yes	4
35.33	even	12		490.2.c.d.99.1		2
105.32	even	12		630.2.u.a.109.1		4
105.53	even	12		630.2.u.a.109.2		4
140.67	even	12		560.2.bw.d.529.1		4
140.123	even	12		560.2.bw.d.529.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.i.b.9.1	✓	4	5.2	odd	4
70.2.i.b.9.2	yes	4	5.3	odd	4
70.2.i.b.39.1	yes	4	35.18	odd	12
70.2.i.b.39.2	yes	4	35.32	odd	12
350.2.e.c.51.1		2	1.1	even	1	trivial
350.2.e.c.151.1		2	7.4	even	3	inner
350.2.e.j.51.1		2	5.4	even	2
350.2.e.j.151.1		2	35.4	even	6
490.2.c.a.99.1		2	35.23	odd	12
490.2.c.a.99.2		2	35.2	odd	12
490.2.c.d.99.1		2	35.33	even	12
490.2.c.d.99.2		2	35.12	even	12
490.2.i.a.79.1		4	35.27	even	4
490.2.i.a.79.2		4	35.13	even	4
490.2.i.a.459.1		4	35.3	even	12
490.2.i.a.459.2		4	35.17	even	12
560.2.bw.d.289.1		4	20.3	even	4
560.2.bw.d.289.2		4	20.7	even	4
560.2.bw.d.529.1		4	140.67	even	12
560.2.bw.d.529.2		4	140.123	even	12
630.2.u.a.109.1		4	105.32	even	12
630.2.u.a.109.2		4	105.53	even	12
630.2.u.a.289.1		4	15.8	even	4
630.2.u.a.289.2		4	15.2	even	4
2450.2.a.j.1.1		1	35.19	odd	6
2450.2.a.k.1.1		1	35.9	even	6
2450.2.a.ba.1.1		1	7.2	even	3
2450.2.a.bb.1.1		1	7.5	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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.00000 - 1.73205i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.00000 - 1.73205i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(-1.50000 - 2.59808i) q^{11} -5.00000 q^{13} +(2.50000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(1.50000 + 2.59808i) q^{18} +(2.50000 - 4.33013i) q^{19} +3.00000 q^{22} +(3.50000 - 6.06218i) q^{23} +(2.50000 - 4.33013i) q^{26} +(-0.500000 + 2.59808i) q^{28} -4.00000 q^{29} +(1.00000 + 1.73205i) q^{31} +(-0.500000 - 0.866025i) q^{32} -2.00000 q^{34} -3.00000 q^{36} +(-0.500000 + 0.866025i) q^{37} +(2.50000 + 4.33013i) q^{38} +3.00000 q^{41} +2.00000 q^{43} +(-1.50000 + 2.59808i) q^{44} +(3.50000 + 6.06218i) q^{46} +(3.50000 - 6.06218i) q^{47} +(1.00000 + 6.92820i) q^{49} +(2.50000 + 4.33013i) q^{52} +(-4.50000 - 7.79423i) q^{53} +(-2.00000 - 1.73205i) q^{56} +(2.00000 - 3.46410i) q^{58} +(2.00000 + 3.46410i) q^{59} +(-3.00000 + 5.19615i) q^{61} -2.00000 q^{62} +(-7.50000 + 2.59808i) q^{63} +1.00000 q^{64} +(-1.00000 - 1.73205i) q^{67} +(1.00000 - 1.73205i) q^{68} -6.00000 q^{71} +(1.50000 - 2.59808i) q^{72} +(8.00000 + 13.8564i) q^{73} +(-0.500000 - 0.866025i) q^{74} -5.00000 q^{76} +(-1.50000 + 7.79423i) q^{77} +(-7.00000 + 12.1244i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-1.50000 + 2.59808i) q^{82} -6.00000 q^{83} +(-1.00000 + 1.73205i) q^{86} +(-1.50000 - 2.59808i) q^{88} +(-1.00000 + 1.73205i) q^{89} +(10.0000 + 8.66025i) q^{91} -7.00000 q^{92} +(3.50000 + 6.06218i) q^{94} -12.0000 q^{97} +(-6.50000 - 2.59808i) q^{98} -9.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} - 4 q^{7} + 2 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q - q^2 - q^4 - 4 * q^7 + 2 * q^8 + 3 * q^9	\( 2 q - q^{2} - q^{4} - 4 q^{7} + 2 q^{8} + 3 q^{9} - 3 q^{11} - 10 q^{13} + 5 q^{14} - q^{16} + 2 q^{17} + 3 q^{18} + 5 q^{19} + 6 q^{22} + 7 q^{23} + 5 q^{26} - q^{28} - 8 q^{29} + 2 q^{31} - q^{32} - 4 q^{34} - 6 q^{36} - q^{37} + 5 q^{38} + 6 q^{41} + 4 q^{43} - 3 q^{44} + 7 q^{46} + 7 q^{47} + 2 q^{49} + 5 q^{52} - 9 q^{53} - 4 q^{56} + 4 q^{58} + 4 q^{59} - 6 q^{61} - 4 q^{62} - 15 q^{63} + 2 q^{64} - 2 q^{67} + 2 q^{68} - 12 q^{71} + 3 q^{72} + 16 q^{73} - q^{74} - 10 q^{76} - 3 q^{77} - 14 q^{79} - 9 q^{81} - 3 q^{82} - 12 q^{83} - 2 q^{86} - 3 q^{88} - 2 q^{89} + 20 q^{91} - 14 q^{92} + 7 q^{94} - 24 q^{97} - 13 q^{98} - 18 q^{99}+O(q^{100}) \) 2 * q - q^2 - q^4 - 4 * q^7 + 2 * q^8 + 3 * q^9 - 3 * q^11 - 10 * q^13 + 5 * q^14 - q^16 + 2 * q^17 + 3 * q^18 + 5 * q^19 + 6 * q^22 + 7 * q^23 + 5 * q^26 - q^28 - 8 * q^29 + 2 * q^31 - q^32 - 4 * q^34 - 6 * q^36 - q^37 + 5 * q^38 + 6 * q^41 + 4 * q^43 - 3 * q^44 + 7 * q^46 + 7 * q^47 + 2 * q^49 + 5 * q^52 - 9 * q^53 - 4 * q^56 + 4 * q^58 + 4 * q^59 - 6 * q^61 - 4 * q^62 - 15 * q^63 + 2 * q^64 - 2 * q^67 + 2 * q^68 - 12 * q^71 + 3 * q^72 + 16 * q^73 - q^74 - 10 * q^76 - 3 * q^77 - 14 * q^79 - 9 * q^81 - 3 * q^82 - 12 * q^83 - 2 * q^86 - 3 * q^88 - 2 * q^89 + 20 * q^91 - 14 * q^92 + 7 * q^94 - 24 * q^97 - 13 * q^98 - 18 * q^99

Introduction

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