LMFDB - Embedded newform 350.2.e.c.151.1

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			151.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	350.151
Dual form			350.2.e.c.51.1

$q$-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 $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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	$-0.833333\pi$
$3$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$4$	−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	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	0.546259	+	0.837616i	$0.316051\pi$
$12$		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	−0.718900	−	0.695113i	$-0.755354\pi$
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	0.961436	+	0.275029i	$0.0886875\pi$
$18$	1.50000	−	2.59808i	0.353553	−	0.612372i
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	0.996199	+	0.0871106i	$0.0277634\pi$
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	−0.422659	+	0.906289i	$0.638903\pi$
$20$		0			0
$21$		0			0
$22$	3.00000			0.639602
$23$	3.50000	+	6.06218i	0.729800	+	1.26405i	0.956967	+	0.290196i	$0.0937204\pi$
$23$	3.50000	+	6.06218i	0.729800	+	1.26405i	−0.227167	+	0.973856i	$0.572946\pi$
$24$		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	−0.762140	−	0.647412i	$-0.775851\pi$
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	0.941745	+	0.336327i	$0.109185\pi$
$32$	−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	0.821995	−	0.569495i	$-0.192861\pi$
$37$	−0.500000	−	0.866025i	−0.0821995	−	0.142374i	−0.904194	+	0.427121i	$0.859528\pi$
$38$	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	0.999926	+	0.0121990i	$0.00388317\pi$
$47$	3.50000	+	6.06218i	0.510527	+	0.884260i	−0.489398	+	0.872060i	$0.662783\pi$
$48$		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	0.371706	+	0.928351i	$0.378773\pi$
$53$	−4.50000	+	7.79423i	−0.618123	+	1.07062i	−0.989828	+	0.142269i	$0.954560\pi$
$54$		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	−0.705965	−	0.708247i	$-0.749486\pi$
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	0.966342	+	0.257260i	$0.0828195\pi$
$60$		0			0
$61$	−3.00000	−	5.19615i	−0.384111	−	0.665299i	0.607535	−	0.794293i	$-0.292159\pi$
$61$	−3.00000	−	5.19615i	−0.384111	−	0.665299i	−0.991645	+	0.128994i	$0.958825\pi$
$62$	−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	−0.920623	−	0.390453i	$-0.872318\pi$
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	0.798454	+	0.602056i	$0.205652\pi$
$68$	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	0.164083	−	0.986447i	$-0.447534\pi$
$73$	8.00000	−	13.8564i	0.936329	−	1.62177i	0.772246	−	0.635323i	$-0.219133\pi$
$74$	−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	−0.927457	−	0.373930i	$-0.878010\pi$
$79$	−7.00000	−	12.1244i	−0.787562	−	1.36410i	0.139895	−	0.990166i	$-0.455323\pi$
$80$		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	0.808146	−	0.588982i	$-0.200471\pi$
$89$	−1.00000	−	1.73205i	−0.106000	−	0.183597i	−0.914146	+	0.405385i	$0.867138\pi$
$90$		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	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$		0			0
$103$	4.00000	+	6.92820i	0.394132	+	0.682656i	0.992990	−	0.118199i	$-0.0377120\pi$
$103$	4.00000	+	6.92820i	0.394132	+	0.682656i	−0.598858	+	0.800855i	$0.704379\pi$
$104$	−5.00000			−0.490290
$105$		0			0
$106$	9.00000			0.874157
$107$	8.00000	+	13.8564i	0.773389	+	1.33955i	0.935695	+	0.352809i	$0.114773\pi$
$107$	8.00000	+	13.8564i	0.773389	+	1.33955i	−0.162306	+	0.986740i	$0.551893\pi$
$108$		0			0
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	−0.909935	−	0.414751i	$-0.863869\pi$
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	0.814152	+	0.580651i	$0.197202\pi$
$110$		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	0.887041	−	0.461690i	$-0.152757\pi$
$131$	0.500000	+	0.866025i	0.0436852	+	0.0756650i	−0.843356	+	0.537355i	$0.819423\pi$
$132$		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	−0.643013	−	0.765855i	$-0.722316\pi$
$137$	4.00000	−	6.92820i	0.341743	−	0.591916i	0.984757	+	0.173939i	$0.0556494\pi$
$138$		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	0.953703	+	0.300750i	$0.0972370\pi$
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	−0.216394	+	0.976306i	$0.569430\pi$
$150$		0			0
$151$	3.00000	−	5.19615i	0.244137	−	0.422857i	−0.717752	−	0.696299i	$-0.754829\pi$
$151$	3.00000	−	5.19615i	0.244137	−	0.422857i	0.961888	+	0.273442i	$0.0881622\pi$
$152$	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	−0.628678	−	0.777666i	$-0.716404\pi$
$157$	4.50000	−	7.79423i	0.359139	−	0.622047i	0.987817	+	0.155618i	$0.0497370\pi$
$158$	−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	0.999410	−	0.0343508i	$-0.0109363\pi$
$163$	6.00000	+	10.3923i	0.469956	+	0.813988i	−0.529454	+	0.848339i	$0.677603\pi$
$164$	−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	0.642699	−	0.766119i	$-0.277815\pi$
$173$	−4.50000	−	7.79423i	−0.342129	−	0.592584i	−0.984828	+	0.173534i	$0.944481\pi$
$174$		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	−0.999867	−	0.0162823i	$-0.994817\pi$
$179$	−6.50000	+	11.2583i	−0.485833	+	0.841487i	0.514035	+	0.857769i	$0.328150\pi$
$180$		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	0.959558	+	0.281511i	$0.0908356\pi$
$191$	10.0000	+	17.3205i	0.723575	+	1.25327i	−0.235983	+	0.971757i	$0.575831\pi$
$192$		0			0
$193$	5.00000	−	8.66025i	0.359908	−	0.623379i	−0.628037	−	0.778183i	$-0.716141\pi$
$193$	5.00000	−	8.66025i	0.359908	−	0.623379i	0.987945	+	0.154805i	$0.0494748\pi$
$194$	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	0.347879	+	0.937539i	$0.386902\pi$
$199$	−9.00000	+	15.5885i	−0.637993	+	1.10504i	−0.985873	+	0.167497i	$0.946431\pi$
$200$		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	−0.749125	−	0.662428i	$-0.769526\pi$
$227$	3.00000	−	5.19615i	0.199117	−	0.344881i	0.948242	+	0.317547i	$0.102859\pi$
$228$		0			0
$229$	−8.00000	−	13.8564i	−0.528655	−	0.915657i	−0.999442	−	0.0334101i	$-0.989363\pi$
$229$	−8.00000	−	13.8564i	−0.528655	−	0.915657i	0.470787	−	0.882247i	$-0.343970\pi$
$230$		0			0
$231$		0			0
$232$	−4.00000			−0.262613
$233$	4.00000	+	6.92820i	0.262049	+	0.453882i	0.966786	−	0.255586i	$-0.0822686\pi$
$233$	4.00000	+	6.92820i	0.262049	+	0.453882i	−0.704737	+	0.709468i	$0.748935\pi$
$234$	−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	−0.683908	−	0.729568i	$-0.739721\pi$
$241$	4.50000	−	7.79423i	0.289870	−	0.502070i	0.973779	+	0.227498i	$0.0730544\pi$
$242$	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	0.944294	−	0.329104i	$-0.106747\pi$
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	−0.757159	+	0.653231i	$0.773413\pi$
$258$		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	$-0.833333\pi$
$263$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$264$		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	−0.672374	−	0.740212i	$-0.734725\pi$
$269$	5.00000	−	8.66025i	0.304855	−	0.528025i	0.977229	+	0.212187i	$0.0680585\pi$
$270$		0			0
$271$	−12.0000	−	20.7846i	−0.728948	−	1.26258i	−0.957328	−	0.289003i	$-0.906676\pi$
$271$	−12.0000	−	20.7846i	−0.728948	−	1.26258i	0.228380	−	0.973572i	$-0.426657\pi$
$272$	−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	−0.834419	−	0.551131i	$-0.814196\pi$
$277$	1.00000	−	1.73205i	0.0600842	−	0.104069i	0.894503	+	0.447062i	$0.147530\pi$
$278$	−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	−0.995544	−	0.0942988i	$-0.969939\pi$
$283$	−7.00000	+	12.1244i	−0.416107	+	0.720718i	0.579437	+	0.815017i	$0.303272\pi$
$284$	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	−0.938460	−	0.345389i	$-0.887747\pi$
$311$	−3.00000	+	5.19615i	−0.170114	+	0.294647i	0.768345	+	0.640036i	$0.221080\pi$
$312$		0			0
$313$	11.0000	+	19.0526i	0.621757	+	1.07691i	0.989158	+	0.146852i	$0.0469141\pi$
$313$	11.0000	+	19.0526i	0.621757	+	1.07691i	−0.367402	+	0.930062i	$0.619753\pi$
$314$	−9.00000			−0.507899
$315$		0			0
$316$	14.0000			0.787562
$317$	1.00000	+	1.73205i	0.0561656	+	0.0972817i	0.892741	−	0.450570i	$-0.148779\pi$
$317$	1.00000	+	1.73205i	0.0561656	+	0.0972817i	−0.836576	+	0.547852i	$0.815446\pi$
$318$		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	0.789104	−	0.614260i	$-0.210545\pi$
$331$	−2.50000	−	4.33013i	−0.137412	−	0.238005i	−0.926516	+	0.376254i	$0.877212\pi$
$332$	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	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$		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	0.347024	+	0.937856i	$0.387192\pi$
$353$	−12.0000	+	20.7846i	−0.638696	+	1.10625i	−0.985719	+	0.168397i	$0.946141\pi$
$354$		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	0.573933	−	0.818902i	$-0.305417\pi$
$359$	−8.00000	−	13.8564i	−0.422224	−	0.731313i	−0.996157	+	0.0875892i	$0.972084\pi$
$360$		0			0
$361$	−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	−0.984301	−	0.176500i	$-0.943523\pi$
$367$	−6.50000	+	11.2583i	−0.339297	+	0.587680i	0.645003	+	0.764180i	$0.276856\pi$
$368$	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	−0.977016	−	0.213165i	$-0.931623\pi$
$373$	−13.0000	−	22.5167i	−0.673114	−	1.16587i	0.303902	−	0.952703i	$-0.401711\pi$
$374$	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	−0.999088	−	0.0427020i	$-0.986403\pi$
$383$	−10.5000	−	18.1865i	−0.536525	−	0.929288i	0.462563	−	0.886586i	$-0.346930\pi$
$384$		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	−0.779895	−	0.625910i	$-0.784728\pi$
$389$	3.00000	−	5.19615i	0.152106	−	0.263455i	0.932002	+	0.362454i	$0.118061\pi$
$390$		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	0.986481	−	0.163876i	$-0.0523996\pi$
$397$	7.00000	+	12.1244i	0.351320	+	0.608504i	−0.635161	+	0.772380i	$0.719066\pi$
$398$	18.0000			0.902258
$399$		0			0
$400$		0			0
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	0.990257	−	0.139253i	$-0.0444700\pi$
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	−0.615725	+	0.787961i	$0.711137\pi$
$402$		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	−0.639430	−	0.768849i	$-0.720830\pi$
$409$	7.00000	−	12.1244i	0.346128	−	0.599511i	0.985558	+	0.169338i	$0.0541630\pi$
$410$		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	−0.889104	−	0.457705i	$-0.848672\pi$
$431$	−1.00000	+	1.73205i	−0.0481683	+	0.0834300i	0.840936	+	0.541135i	$0.182005\pi$
$432$		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	0.978412	+	0.206666i	$0.0662612\pi$
$439$	14.0000	+	24.2487i	0.668184	+	1.15733i	−0.310228	+	0.950662i	$0.600405\pi$
$440$		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	−0.963851	−	0.266443i	$-0.914152\pi$
$443$	−15.0000	−	25.9808i	−0.712672	−	1.23438i	0.251179	−	0.967941i	$-0.419182\pi$
$444$		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	0.958950	−	0.283577i	$-0.0915211\pi$
$457$	5.00000	+	8.66025i	0.233890	+	0.405110i	−0.725059	+	0.688686i	$0.758188\pi$
$458$	−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	−0.927999	−	0.372584i	$-0.878472\pi$
$467$	−17.0000	−	29.4449i	−0.786666	−	1.36255i	0.141332	−	0.989962i	$-0.454861\pi$
$468$	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	0.0814184	+	0.996680i	$0.474055\pi$
$479$	−18.0000	+	31.1769i	−0.822441	+	1.42451i	−0.903859	+	0.427830i	$0.859278\pi$
$480$		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	−0.233933	−	0.972253i	$-0.575160\pi$
$487$	16.0000	−	27.7128i	0.725029	−	1.25579i	0.958962	−	0.283535i	$-0.0915071\pi$
$488$	−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	0.817781	−	0.575529i	$-0.195204\pi$
$499$	−2.00000	−	3.46410i	−0.0895323	−	0.155074i	−0.907314	+	0.420455i	$0.861871\pi$
$500$		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	0.946111	+	0.323843i	$0.104975\pi$
$509$	17.0000	+	29.4449i	0.753512	+	1.30512i	−0.192599	+	0.981278i	$0.561692\pi$
$510$		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	−0.402592	−	0.915379i	$-0.631891\pi$
$521$	13.5000	−	23.3827i	0.591446	−	1.02441i	0.994038	−	0.109035i	$-0.0347759\pi$
$522$	−6.00000	+	10.3923i	−0.262613	+	0.454859i
$523$	−8.00000	−	13.8564i	−0.349816	−	0.605898i	0.636401	−	0.771358i	$-0.280422\pi$
$523$	−8.00000	−	13.8564i	−0.349816	−	0.605898i	−0.986216	+	0.165460i	$0.947089\pi$
$524$	−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	0.985162	−	0.171628i	$-0.0549027\pi$
$541$	8.00000	+	13.8564i	0.343947	+	0.595733i	−0.641215	+	0.767361i	$0.721569\pi$
$542$	−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	−0.999893	−	0.0146368i	$-0.995341\pi$
$557$	−11.5000	+	19.9186i	−0.487271	+	0.843978i	0.512622	+	0.858614i	$0.328674\pi$
$558$	−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	−0.886328	−	0.463057i	$-0.846752\pi$
$563$	−1.00000	+	1.73205i	−0.0421450	+	0.0729972i	0.844183	+	0.536054i	$0.180086\pi$
$564$		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	0.979313	−	0.202350i	$-0.0648579\pi$
$569$	7.50000	+	12.9904i	0.314416	+	0.544585i	−0.664897	+	0.746935i	$0.731525\pi$
$570$		0			0
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	0.308443	+	0.951243i	$0.400192\pi$
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	−0.978022	+	0.208502i	$0.933141\pi$
$572$	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	−0.821388	−	0.570370i	$-0.806800\pi$
$577$	2.00000	−	3.46410i	0.0832611	−	0.144212i	0.904649	+	0.426158i	$0.140133\pi$
$578$	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	0.921026	−	0.389501i	$-0.127353\pi$
$593$	3.00000	+	5.19615i	0.123195	+	0.213380i	−0.797831	+	0.602881i	$0.794019\pi$
$594$		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	−0.717021	−	0.697051i	$-0.754495\pi$
$599$	6.00000	−	10.3923i	0.245153	−	0.424618i	0.962175	+	0.272433i	$0.0878284\pi$
$600$		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	0.967256	−	0.253804i	$-0.0816819\pi$
$607$	6.50000	+	11.2583i	0.263827	+	0.456962i	−0.703429	+	0.710766i	$0.748349\pi$
$608$	−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	−0.673874	−	0.738846i	$-0.735371\pi$
$613$	7.50000	−	12.9904i	0.302922	−	0.524677i	0.976797	+	0.214169i	$0.0687045\pi$
$614$	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	−0.991325	−	0.131434i	$-0.958042\pi$
$619$	−9.50000	+	16.4545i	−0.381837	+	0.661361i	0.609488	+	0.792796i	$0.291375\pi$
$620$		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	−0.812421	−	0.583071i	$-0.801851\pi$
$641$	2.50000	−	4.33013i	0.0987441	−	0.171030i	0.911165	+	0.412042i	$0.135184\pi$
$642$		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	−0.468617	−	0.883402i	$-0.655247\pi$
$647$	13.5000	−	23.3827i	0.530740	−	0.919268i	0.999357	−	0.0358667i	$-0.0114192\pi$
$648$	−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	0.835182	−	0.549973i	$-0.185362\pi$
$653$	−1.50000	−	2.59808i	−0.0586995	−	0.101671i	−0.893882	+	0.448303i	$0.852029\pi$
$654$		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	−0.978615	−	0.205702i	$-0.934052\pi$
$661$	−8.00000	+	13.8564i	−0.311164	+	0.538952i	0.667451	+	0.744654i	$0.267385\pi$
$662$	−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	0.981851	−	0.189653i	$-0.0607362\pi$
$677$	8.50000	+	14.7224i	0.326682	+	0.565829i	−0.655170	+	0.755482i	$0.727403\pi$
$678$		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	−0.0465592	−	0.998916i	$-0.514826\pi$
$683$	22.0000	−	38.1051i	0.841807	−	1.45805i	0.888366	−	0.459136i	$-0.151841\pi$
$684$	−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	0.892458	+	0.451130i	$0.148979\pi$
$691$	22.0000	+	38.1051i	0.836919	+	1.44959i	−0.0555386	+	0.998457i	$0.517688\pi$
$692$	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	0.731085	−	0.682286i	$-0.239014\pi$
$709$	−6.00000	−	10.3923i	−0.225335	−	0.390291i	−0.956420	+	0.291995i	$0.905681\pi$
$710$		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	0.515030	−	0.857172i	$-0.327781\pi$
$719$	−13.0000	−	22.5167i	−0.484818	−	0.839730i	−0.999848	+	0.0174426i	$0.994448\pi$
$720$		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	−0.944281	−	0.329141i	$-0.893241\pi$
$733$	−20.5000	−	35.5070i	−0.757185	−	1.31148i	0.187096	−	0.982342i	$-0.440092\pi$
$734$	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	−0.465848	−	0.884865i	$-0.654251\pi$
$739$	14.5000	−	25.1147i	0.533391	−	0.923861i	0.999239	−	0.0389959i	$-0.0124159\pi$
$740$		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	−0.999921	−	0.0125942i	$-0.995991\pi$
$751$	−14.0000	−	24.2487i	−0.510867	−	0.884848i	0.489053	−	0.872254i	$-0.337342\pi$
$752$	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	0.856821	−	0.515615i	$-0.172436\pi$
$761$	−0.500000	−	0.866025i	−0.0181250	−	0.0313934i	−0.874946	+	0.484221i	$0.839103\pi$
$762$		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	0.104102	+	0.994567i	$0.466803\pi$
$773$	−22.5000	+	38.9711i	−0.809269	+	1.40169i	−0.913371	+	0.407128i	$0.866530\pi$
$774$	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	−0.980656	−	0.195737i	$-0.937290\pi$
$787$	−9.00000	+	15.5885i	−0.320815	+	0.555668i	0.659841	+	0.751405i	$0.270624\pi$
$788$	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	−0.818726	−	0.574184i	$-0.805319\pi$
$809$	2.50000	−	4.33013i	0.0878953	−	0.152239i	0.906621	+	0.421945i	$0.138653\pi$
$810$		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	0.979246	−	0.202674i	$-0.0649632\pi$
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	−0.665144	+	0.746715i	$0.731630\pi$
$822$		0			0
$823$	12.0000	−	20.7846i	0.418294	−	0.724506i	−0.577474	−	0.816409i	$-0.695962\pi$
$823$	12.0000	−	20.7846i	0.418294	−	0.724506i	0.995768	+	0.0919029i	$0.0292950\pi$
$824$	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	−0.546971	−	0.837151i	$-0.684219\pi$
$829$	13.0000	−	22.5167i	0.451509	−	0.782036i	0.998480	+	0.0551154i	$0.0175527\pi$
$830$		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	−0.926222	−	0.376979i	$-0.876963\pi$
$857$	−4.00000	+	6.92820i	−0.136637	+	0.236663i	0.789584	+	0.613642i	$0.210296\pi$
$858$		0			0
$859$	6.00000	+	10.3923i	0.204717	+	0.354581i	0.950043	−	0.312120i	$-0.101039\pi$
$859$	6.00000	+	10.3923i	0.204717	+	0.354581i	−0.745325	+	0.666701i	$0.767706\pi$
$860$		0			0
$861$		0			0
$862$	2.00000			0.0681203
$863$	5.50000	+	9.52628i	0.187222	+	0.324278i	0.944323	−	0.329020i	$-0.106718\pi$
$863$	5.50000	+	9.52628i	0.187222	+	0.324278i	−0.757101	+	0.653298i	$0.773385\pi$
$864$		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	−0.999629	−	0.0272316i	$-0.991331\pi$
$877$	−15.5000	−	26.8468i	−0.523398	−	0.906552i	0.476231	−	0.879320i	$-0.342002\pi$
$878$	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	−0.992149	−	0.125061i	$-0.960087\pi$
$887$	−18.0000	−	31.1769i	−0.604381	−	1.04682i	0.387768	−	0.921757i	$-0.373246\pi$
$888$		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	−0.315442	−	0.948945i	$-0.602153\pi$
$907$	20.0000	−	34.6410i	0.664089	−	1.15024i	0.979531	−	0.201291i	$-0.0645138\pi$
$908$	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	0.652616	−	0.757689i	$-0.273671\pi$
$919$	−10.0000	−	17.3205i	−0.329870	−	0.571351i	−0.982486	+	0.186338i	$0.940338\pi$
$920$		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	0.640768	−	0.767735i	$-0.278616\pi$
$929$	−10.5000	−	18.1865i	−0.344494	−	0.596681i	−0.985262	+	0.171054i	$0.945283\pi$
$930$		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	−0.542380	−	0.840133i	$-0.682477\pi$
$941$	14.0000	−	24.2487i	0.456387	−	0.790485i	0.998767	+	0.0496480i	$0.0158099\pi$
$942$		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	0.946892	−	0.321552i	$-0.104204\pi$
$947$	6.00000	+	10.3923i	0.194974	+	0.337705i	−0.751918	+	0.659256i	$0.770871\pi$
$948$		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	0.999408	+	0.0344175i	$0.0109576\pi$
$971$	16.5000	+	28.5788i	0.529510	+	0.917139i	−0.469897	+	0.882721i	$0.655709\pi$
$972$		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	0.00442082	+	0.999990i	$0.498593\pi$
$977$	−27.0000	+	46.7654i	−0.863807	+	1.49616i	−0.868227	+	0.496167i	$0.834741\pi$
$978$		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	−0.536606	−	0.843833i	$-0.680294\pi$
$983$	14.5000	−	25.1147i	0.462478	−	0.801036i	0.999084	+	0.0427975i	$0.0136270\pi$
$984$		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	−0.795474	−	0.605988i	$-0.792778\pi$
$991$	4.00000	−	6.92820i	0.127064	−	0.220082i	0.922538	+	0.385906i	$0.126111\pi$
$992$	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	−0.390822	−	0.920466i	$-0.627809\pi$
$997$	19.0000	−	32.9090i	0.601736	−	1.04224i	0.992558	−	0.121771i	$-0.0388574\pi$
$998$	−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.151.1		2
5.2	odd	4		70.2.i.b.39.2	yes	4
5.3	odd	4		70.2.i.b.39.1	yes	4
5.4	even	2		350.2.e.j.151.1		2
7.2	even	3	inner	350.2.e.c.51.1		2
7.3	odd	6		2450.2.a.bb.1.1		1
7.4	even	3		2450.2.a.ba.1.1		1
15.2	even	4		630.2.u.a.109.1		4
15.8	even	4		630.2.u.a.109.2		4
20.3	even	4		560.2.bw.d.529.2		4
20.7	even	4		560.2.bw.d.529.1		4
35.2	odd	12		70.2.i.b.9.1	✓	4
35.3	even	12		490.2.c.d.99.1		2
35.4	even	6		2450.2.a.k.1.1		1
35.9	even	6		350.2.e.j.51.1		2
35.12	even	12		490.2.i.a.79.1		4
35.13	even	4		490.2.i.a.459.1		4
35.17	even	12		490.2.c.d.99.2		2
35.18	odd	12		490.2.c.a.99.1		2
35.23	odd	12		70.2.i.b.9.2	yes	4
35.24	odd	6		2450.2.a.j.1.1		1
35.27	even	4		490.2.i.a.459.2		4
35.32	odd	12		490.2.c.a.99.2		2
35.33	even	12		490.2.i.a.79.2		4
105.2	even	12		630.2.u.a.289.2		4
105.23	even	12		630.2.u.a.289.1		4
140.23	even	12		560.2.bw.d.289.1		4
140.107	even	12		560.2.bw.d.289.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.i.b.9.1	✓	4	35.2	odd	12
70.2.i.b.9.2	yes	4	35.23	odd	12
70.2.i.b.39.1	yes	4	5.3	odd	4
70.2.i.b.39.2	yes	4	5.2	odd	4
350.2.e.c.51.1		2	7.2	even	3	inner
350.2.e.c.151.1		2	1.1	even	1	trivial
350.2.e.j.51.1		2	35.9	even	6
350.2.e.j.151.1		2	5.4	even	2
490.2.c.a.99.1		2	35.18	odd	12
490.2.c.a.99.2		2	35.32	odd	12
490.2.c.d.99.1		2	35.3	even	12
490.2.c.d.99.2		2	35.17	even	12
490.2.i.a.79.1		4	35.12	even	12
490.2.i.a.79.2		4	35.33	even	12
490.2.i.a.459.1		4	35.13	even	4
490.2.i.a.459.2		4	35.27	even	4
560.2.bw.d.289.1		4	140.23	even	12
560.2.bw.d.289.2		4	140.107	even	12
560.2.bw.d.529.1		4	20.7	even	4
560.2.bw.d.529.2		4	20.3	even	4
630.2.u.a.109.1		4	15.2	even	4
630.2.u.a.109.2		4	15.8	even	4
630.2.u.a.289.1		4	105.23	even	12
630.2.u.a.289.2		4	105.2	even	12
2450.2.a.j.1.1		1	35.24	odd	6
2450.2.a.k.1.1		1	35.4	even	6
2450.2.a.ba.1.1		1	7.4	even	3
2450.2.a.bb.1.1		1	7.3	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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