LMFDB - Embedded newform 350.4.e.b.151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,4,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, 4, names="a")

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

chi := DirichletCharacter("350.51");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
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:	$20.6506685020$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 14)
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			350.4.e.b.51.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-2.00000 + 3.46410i) q^{4} +2.00000 q^{6} +(10.0000 + 15.5885i) q^{7} +8.00000 q^{8} +(13.0000 + 22.5167i) q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.73205i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-2.00000 + 3.46410i) q^{4} +2.00000 q^{6} +(10.0000 + 15.5885i) q^{7} +8.00000 q^{8} +(13.0000 + 22.5167i) q^{9} +(-17.5000 + 30.3109i) q^{11} +(-2.00000 - 3.46410i) q^{12} -66.0000 q^{13} +(17.0000 - 32.9090i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(29.5000 - 51.0955i) q^{17} +(26.0000 - 45.0333i) q^{18} +(-68.5000 - 118.645i) q^{19} +(-18.5000 + 0.866025i) q^{21} +70.0000 q^{22} +(-3.50000 - 6.06218i) q^{23} +(-4.00000 + 6.92820i) q^{24} +(66.0000 + 114.315i) q^{26} -53.0000 q^{27} +(-74.0000 + 3.46410i) q^{28} +106.000 q^{29} +(-37.5000 + 64.9519i) q^{31} +(-16.0000 + 27.7128i) q^{32} +(-17.5000 - 30.3109i) q^{33} -118.000 q^{34} -104.000 q^{36} +(5.50000 + 9.52628i) q^{37} +(-137.000 + 237.291i) q^{38} +(33.0000 - 57.1577i) q^{39} -498.000 q^{41} +(20.0000 + 31.1769i) q^{42} -260.000 q^{43} +(-70.0000 - 121.244i) q^{44} +(-7.00000 + 12.1244i) q^{46} +(-85.5000 - 148.090i) q^{47} +16.0000 q^{48} +(-143.000 + 311.769i) q^{49} +(29.5000 + 51.0955i) q^{51} +(132.000 - 228.631i) q^{52} +(-208.500 + 361.133i) q^{53} +(53.0000 + 91.7987i) q^{54} +(80.0000 + 124.708i) q^{56} +137.000 q^{57} +(-106.000 - 183.597i) q^{58} +(8.50000 - 14.7224i) q^{59} +(-25.5000 - 44.1673i) q^{61} +150.000 q^{62} +(-221.000 + 427.817i) q^{63} +64.0000 q^{64} +(-35.0000 + 60.6218i) q^{66} +(219.500 - 380.185i) q^{67} +(118.000 + 204.382i) q^{68} +7.00000 q^{69} -784.000 q^{71} +(104.000 + 180.133i) q^{72} +(147.500 - 255.477i) q^{73} +(11.0000 - 19.0526i) q^{74} +548.000 q^{76} +(-647.500 + 30.3109i) q^{77} -132.000 q^{78} +(247.500 + 428.683i) q^{79} +(-324.500 + 562.050i) q^{81} +(498.000 + 862.561i) q^{82} -932.000 q^{83} +(34.0000 - 65.8179i) q^{84} +(260.000 + 450.333i) q^{86} +(-53.0000 + 91.7987i) q^{87} +(-140.000 + 242.487i) q^{88} +(436.500 + 756.040i) q^{89} +(-660.000 - 1028.84i) q^{91} +28.0000 q^{92} +(-37.5000 - 64.9519i) q^{93} +(-171.000 + 296.181i) q^{94} +(-16.0000 - 27.7128i) q^{96} +290.000 q^{97} +(683.000 - 64.0859i) q^{98} -910.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - q^{3} - 4 q^{4} + 4 q^{6} + 20 q^{7} + 16 q^{8} + 26 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - q^3 - 4 * q^4 + 4 * q^6 + 20 * q^7 + 16 * q^8 + 26 * q^9	$ 2 q - 2 q^{2} - q^{3} - 4 q^{4} + 4 q^{6} + 20 q^{7} + 16 q^{8} + 26 q^{9} - 35 q^{11} - 4 q^{12} - 132 q^{13} + 34 q^{14} - 16 q^{16} + 59 q^{17} + 52 q^{18} - 137 q^{19} - 37 q^{21} + 140 q^{22} - 7 q^{23} - 8 q^{24} + 132 q^{26} - 106 q^{27} - 148 q^{28} + 212 q^{29} - 75 q^{31} - 32 q^{32} - 35 q^{33} - 236 q^{34} - 208 q^{36} + 11 q^{37} - 274 q^{38} + 66 q^{39} - 996 q^{41} + 40 q^{42} - 520 q^{43} - 140 q^{44} - 14 q^{46} - 171 q^{47} + 32 q^{48} - 286 q^{49} + 59 q^{51} + 264 q^{52} - 417 q^{53} + 106 q^{54} + 160 q^{56} + 274 q^{57} - 212 q^{58} + 17 q^{59} - 51 q^{61} + 300 q^{62} - 442 q^{63} + 128 q^{64} - 70 q^{66} + 439 q^{67} + 236 q^{68} + 14 q^{69} - 1568 q^{71} + 208 q^{72} + 295 q^{73} + 22 q^{74} + 1096 q^{76} - 1295 q^{77} - 264 q^{78} + 495 q^{79} - 649 q^{81} + 996 q^{82} - 1864 q^{83} + 68 q^{84} + 520 q^{86} - 106 q^{87} - 280 q^{88} + 873 q^{89} - 1320 q^{91} + 56 q^{92} - 75 q^{93} - 342 q^{94} - 32 q^{96} + 580 q^{97} + 1366 q^{98} - 1820 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - q^3 - 4 * q^4 + 4 * q^6 + 20 * q^7 + 16 * q^8 + 26 * q^9 - 35 * q^11 - 4 * q^12 - 132 * q^13 + 34 * q^14 - 16 * q^16 + 59 * q^17 + 52 * q^18 - 137 * q^19 - 37 * q^21 + 140 * q^22 - 7 * q^23 - 8 * q^24 + 132 * q^26 - 106 * q^27 - 148 * q^28 + 212 * q^29 - 75 * q^31 - 32 * q^32 - 35 * q^33 - 236 * q^34 - 208 * q^36 + 11 * q^37 - 274 * q^38 + 66 * q^39 - 996 * q^41 + 40 * q^42 - 520 * q^43 - 140 * q^44 - 14 * q^46 - 171 * q^47 + 32 * q^48 - 286 * q^49 + 59 * q^51 + 264 * q^52 - 417 * q^53 + 106 * q^54 + 160 * q^56 + 274 * q^57 - 212 * q^58 + 17 * q^59 - 51 * q^61 + 300 * q^62 - 442 * q^63 + 128 * q^64 - 70 * q^66 + 439 * q^67 + 236 * q^68 + 14 * q^69 - 1568 * q^71 + 208 * q^72 + 295 * q^73 + 22 * q^74 + 1096 * q^76 - 1295 * q^77 - 264 * q^78 + 495 * q^79 - 649 * q^81 + 996 * q^82 - 1864 * q^83 + 68 * q^84 + 520 * q^86 - 106 * q^87 - 280 * q^88 + 873 * q^89 - 1320 * q^91 + 56 * q^92 - 75 * q^93 - 342 * q^94 - 32 * q^96 + 580 * q^97 + 1366 * q^98 - 1820 * 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 $

$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$3$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i	−0.910119	−	0.414346i	$-0.864010\pi$
$3$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i	0.813894	+	0.581013i	$0.197344\pi$
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	2.00000			0.136083
$7$	10.0000	+	15.5885i	0.539949	+	0.841698i
$7$	10.0000	+	15.5885i	0.539949	+	0.841698i
$8$	8.00000			0.353553
$9$	13.0000	+	22.5167i	0.481481	+	0.833950i
$10$		0			0
$11$	−17.5000	+	30.3109i	−0.479677	+	0.830825i	−0.999728	−	0.0233099i	$-0.992580\pi$
$11$	−17.5000	+	30.3109i	−0.479677	+	0.830825i	0.520051	+	0.854135i	$0.325913\pi$
$12$	−2.00000	−	3.46410i	−0.0481125	−	0.0833333i
$13$	−66.0000			−1.40809			−0.704043	−	0.710158i	$-0.748624\pi$
$13$	−66.0000			−1.40809			−0.704043	+	0.710158i	$0.748624\pi$
$14$	17.0000	−	32.9090i	0.324532	−	0.628235i
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	29.5000	−	51.0955i	0.420871	−	0.728969i	−0.575154	−	0.818045i	$-0.695058\pi$
$17$	29.5000	−	51.0955i	0.420871	−	0.728969i	0.996025	+	0.0890757i	$0.0283913\pi$
$18$	26.0000	−	45.0333i	0.340459	−	0.589692i
$19$	−68.5000	−	118.645i	−0.827104	−	1.43259i	−0.900301	−	0.435269i	$-0.856653\pi$
$19$	−68.5000	−	118.645i	−0.827104	−	1.43259i	0.0731965	−	0.997318i	$-0.476680\pi$
$20$		0			0
$21$	−18.5000	+	0.866025i	−0.192240	+	0.00899915i
$22$	70.0000			0.678366
$23$	−3.50000	−	6.06218i	−0.0317305	−	0.0549588i	0.849724	−	0.527228i	$-0.176768\pi$
$23$	−3.50000	−	6.06218i	−0.0317305	−	0.0549588i	−0.881455	+	0.472269i	$0.843435\pi$
$24$	−4.00000	+	6.92820i	−0.0340207	+	0.0589256i
$25$		0			0
$26$	66.0000	+	114.315i	0.497833	+	0.862273i
$27$	−53.0000			−0.377772
$28$	−74.0000	+	3.46410i	−0.499453	+	0.0233805i
$29$	106.000			0.678748			0.339374	−	0.940651i	$-0.389785\pi$
$29$	106.000			0.678748			0.339374	+	0.940651i	$0.389785\pi$
$30$		0			0
$31$	−37.5000	+	64.9519i	−0.217264	+	0.376313i	−0.953971	−	0.299900i	$-0.903047\pi$
$31$	−37.5000	+	64.9519i	−0.217264	+	0.376313i	0.736706	+	0.676213i	$0.236380\pi$
$32$	−16.0000	+	27.7128i	−0.0883883	+	0.153093i
$33$	−17.5000	−	30.3109i	−0.0923139	−	0.159892i
$34$	−118.000			−0.595201
$35$		0			0
$36$	−104.000			−0.481481
$37$	5.50000	+	9.52628i	0.0244377	+	0.0423273i	0.877986	−	0.478687i	$-0.158887\pi$
$37$	5.50000	+	9.52628i	0.0244377	+	0.0423273i	−0.853548	+	0.521014i	$0.825554\pi$
$38$	−137.000	+	237.291i	−0.584851	+	1.01299i
$39$	33.0000	−	57.1577i	0.135493	−	0.234681i
$40$		0			0
$41$	−498.000			−1.89694			−0.948470	−	0.316867i	$-0.897369\pi$
$41$	−498.000			−1.89694			−0.948470	+	0.316867i	$0.897369\pi$
$42$	20.0000	+	31.1769i	0.0734778	+	0.114541i
$43$	−260.000			−0.922084			−0.461042	−	0.887378i	$-0.652524\pi$
$43$	−260.000			−0.922084			−0.461042	+	0.887378i	$0.652524\pi$
$44$	−70.0000	−	121.244i	−0.239839	−	0.415413i
$45$		0			0
$46$	−7.00000	+	12.1244i	−0.0224368	+	0.0388617i
$47$	−85.5000	−	148.090i	−0.265350	−	0.459600i	0.702305	−	0.711876i	$-0.252154\pi$
$47$	−85.5000	−	148.090i	−0.265350	−	0.459600i	−0.967655	+	0.252276i	$0.918821\pi$
$48$	16.0000			0.0481125
$49$	−143.000	+	311.769i	−0.416910	+	0.908948i
$50$		0			0
$51$	29.5000	+	51.0955i	0.0809966	+	0.140290i
$52$	132.000	−	228.631i	0.352021	−	0.609719i
$53$	−208.500	+	361.133i	−0.540371	+	0.935951i	0.458511	+	0.888689i	$0.348383\pi$
$53$	−208.500	+	361.133i	−0.540371	+	0.935951i	−0.998883	+	0.0472619i	$0.984950\pi$
$54$	53.0000	+	91.7987i	0.133563	+	0.231337i
$55$		0			0
$56$	80.0000	+	124.708i	0.190901	+	0.297585i
$57$	137.000			0.318353
$58$	−106.000	−	183.597i	−0.239974	−	0.415647i
$59$	8.50000	−	14.7224i	0.0187560	−	0.0324864i	−0.856495	−	0.516155i	$-0.827363\pi$
$59$	8.50000	−	14.7224i	0.0187560	−	0.0324864i	0.875251	+	0.483669i	$0.160696\pi$
$60$		0			0
$61$	−25.5000	−	44.1673i	−0.0535236	−	0.0927056i	0.838022	−	0.545636i	$-0.183712\pi$
$61$	−25.5000	−	44.1673i	−0.0535236	−	0.0927056i	−0.891546	+	0.452930i	$0.850379\pi$
$62$	150.000			0.307258
$63$	−221.000	+	427.817i	−0.441958	+	0.855553i
$64$	64.0000			0.125000
$65$		0			0
$66$	−35.0000	+	60.6218i	−0.0652758	+	0.113061i
$67$	219.500	−	380.185i	0.400242	−	0.693239i	−0.593513	−	0.804824i	$-0.702260\pi$
$67$	219.500	−	380.185i	0.400242	−	0.693239i	0.993755	+	0.111585i	$0.0355928\pi$
$68$	118.000	+	204.382i	0.210435	+	0.364485i
$69$	7.00000			0.0122131
$70$		0			0
$71$	−784.000			−1.31047			−0.655237	−	0.755423i	$-0.727431\pi$
$71$	−784.000			−1.31047			−0.655237	+	0.755423i	$0.727431\pi$
$72$	104.000	+	180.133i	0.170229	+	0.294846i
$73$	147.500	−	255.477i	0.236487	−	0.409608i	−0.723217	−	0.690621i	$-0.757337\pi$
$73$	147.500	−	255.477i	0.236487	−	0.409608i	0.959704	+	0.281013i	$0.0906705\pi$
$74$	11.0000	−	19.0526i	0.0172801	−	0.0299299i
$75$		0			0
$76$	548.000			0.827104
$77$	−647.500	+	30.3109i	−0.958305	+	0.0448603i
$78$	−132.000			−0.191616
$79$	247.500	+	428.683i	0.352480	+	0.610513i	0.986683	−	0.162653i	$-0.0520051\pi$
$79$	247.500	+	428.683i	0.352480	+	0.610513i	−0.634203	+	0.773166i	$0.718672\pi$
$80$		0			0
$81$	−324.500	+	562.050i	−0.445130	+	0.770988i
$82$	498.000	+	862.561i	0.670670	+	1.16163i
$83$	−932.000			−1.23253			−0.616267	−	0.787537i	$-0.711356\pi$
$83$	−932.000			−1.23253			−0.616267	+	0.787537i	$0.711356\pi$
$84$	34.0000	−	65.8179i	0.0441631	−	0.0854920i
$85$		0			0
$86$	260.000	+	450.333i	0.326006	+	0.564659i
$87$	−53.0000	+	91.7987i	−0.0653126	+	0.113125i
$88$	−140.000	+	242.487i	−0.169591	+	0.293741i
$89$	436.500	+	756.040i	0.519875	+	0.900451i	0.999733	+	0.0231042i	$0.00735495\pi$
$89$	436.500	+	756.040i	0.519875	+	0.900451i	−0.479858	+	0.877346i	$0.659312\pi$
$90$		0			0
$91$	−660.000	−	1028.84i	−0.760294	−	1.18518i
$92$	28.0000			0.0317305
$93$	−37.5000	−	64.9519i	−0.0418126	−	0.0724215i
$94$	−171.000	+	296.181i	−0.187631	+	0.324986i
$95$		0			0
$96$	−16.0000	−	27.7128i	−0.0170103	−	0.0294628i
$97$	290.000			0.303557			0.151779	−	0.988415i	$-0.451500\pi$
$97$	290.000			0.303557			0.151779	+	0.988415i	$0.451500\pi$
$98$	683.000	−	64.0859i	0.704014	−	0.0660577i
$99$	−910.000			−0.923823
$100$		0			0
$101$	542.500	−	939.638i	0.534463	−	0.925717i	−0.464726	−	0.885454i	$-0.653847\pi$
$101$	542.500	−	939.638i	0.534463	−	0.925717i	0.999189	−	0.0402627i	$-0.0128195\pi$
$102$	59.0000	−	102.191i	0.0572732	−	0.0992002i
$103$	776.500	+	1344.94i	0.742823	+	1.28661i	0.951205	+	0.308560i	$0.0998472\pi$
$103$	776.500	+	1344.94i	0.742823	+	1.28661i	−0.208381	+	0.978048i	$0.566819\pi$
$104$	−528.000			−0.497833
$105$		0			0
$106$	834.000			0.764200
$107$	64.5000	+	111.717i	0.0582752	+	0.100936i	0.893691	−	0.448682i	$-0.148107\pi$
$107$	64.5000	+	111.717i	0.0582752	+	0.100936i	−0.835416	+	0.549618i	$0.814773\pi$
$108$	106.000	−	183.597i	0.0944431	−	0.163580i
$109$	482.500	−	835.715i	0.423992	−	0.734376i	−0.572334	−	0.820021i	$-0.693962\pi$
$109$	482.500	−	835.715i	0.423992	−	0.734376i	0.996326	+	0.0856452i	$0.0272952\pi$
$110$		0			0
$111$	−11.0000			−0.00940607
$112$	136.000	−	263.272i	0.114739	−	0.222115i
$113$	50.0000			0.0416248			0.0208124	−	0.999783i	$-0.493375\pi$
$113$	50.0000			0.0416248			0.0208124	+	0.999783i	$0.493375\pi$
$114$	−137.000	−	237.291i	−0.112555	−	0.194950i
$115$		0			0
$116$	−212.000	+	367.195i	−0.169687	+	0.293907i
$117$	−858.000	−	1486.10i	−0.677967	−	1.17427i
$118$	−34.0000			−0.0265250
$119$	1091.50	−	51.0955i	0.840821	−	0.0393606i
$120$		0			0
$121$	53.0000	+	91.7987i	0.0398197	+	0.0689697i
$122$	−51.0000	+	88.3346i	−0.0378469	+	0.0655528i
$123$	249.000	−	431.281i	0.182533	−	0.316157i
$124$	−150.000	−	259.808i	−0.108632	−	0.188157i
$125$		0			0
$126$	962.000	−	45.0333i	0.680173	−	0.0318404i
$127$	−936.000			−0.653989			−0.326994	−	0.945026i	$-0.606036\pi$
$127$	−936.000			−0.653989			−0.326994	+	0.945026i	$0.606036\pi$
$128$	−64.0000	−	110.851i	−0.0441942	−	0.0765466i
$129$	130.000	−	225.167i	0.0887276	−	0.153681i
$130$		0			0
$131$	377.500	+	653.849i	0.251773	+	0.436084i	0.964014	−	0.265851i	$-0.0856529\pi$
$131$	377.500	+	653.849i	0.251773	+	0.436084i	−0.712241	+	0.701935i	$0.752320\pi$
$132$	140.000			0.0923139
$133$	1164.50	−	2254.26i	0.759210	−	1.46970i
$134$	−878.000			−0.566027
$135$		0			0
$136$	236.000	−	408.764i	0.148800	−	0.257730i
$137$	−1178.50	+	2041.22i	−0.734935	+	1.27294i	0.219817	+	0.975541i	$0.429454\pi$
$137$	−1178.50	+	2041.22i	−0.734935	+	1.27294i	−0.954752	+	0.297403i	$0.903879\pi$
$138$	−7.00000	−	12.1244i	−0.00431797	−	0.00747894i
$139$	28.0000			0.0170858			0.00854291	−	0.999964i	$-0.497281\pi$
$139$	28.0000			0.0170858			0.00854291	+	0.999964i	$0.497281\pi$
$140$		0			0
$141$	171.000			0.102133
$142$	784.000	+	1357.93i	0.463323	+	0.802498i
$143$	1155.00	−	2000.52i	0.675426	−	1.16987i
$144$	208.000	−	360.267i	0.120370	−	0.208488i
$145$		0			0
$146$	−590.000			−0.334443
$147$	−198.500	−	279.726i	−0.111374	−	0.156948i
$148$	−44.0000			−0.0244377
$149$	−1147.50	−	1987.53i	−0.630919	−	1.09278i	−0.987364	−	0.158467i	$-0.949345\pi$
$149$	−1147.50	−	1987.53i	−0.630919	−	1.09278i	0.356446	−	0.934316i	$-0.383988\pi$
$150$		0			0
$151$	554.500	−	960.422i	0.298838	−	0.517603i	−0.677032	−	0.735953i	$-0.736734\pi$
$151$	554.500	−	960.422i	0.298838	−	0.517603i	0.975870	+	0.218350i	$0.0700676\pi$
$152$	−548.000	−	949.164i	−0.292425	−	0.506496i
$153$	1534.00			0.810566
$154$	700.000	+	1091.19i	0.366283	+	0.570979i
$155$		0			0
$156$	132.000	+	228.631i	0.0677465	+	0.117340i
$157$	779.500	−	1350.13i	0.396248	−	0.686321i	−0.597012	−	0.802232i	$-0.703646\pi$
$157$	779.500	−	1350.13i	0.396248	−	0.686321i	0.993260	+	0.115911i	$0.0369789\pi$
$158$	495.000	−	857.365i	0.249241	−	0.431698i
$159$	−208.500	−	361.133i	−0.103995	−	0.180124i
$160$		0			0
$161$	59.5000	−	115.181i	0.0291258	−	0.0563824i
$162$	1298.00			0.629509
$163$	−1125.50	−	1949.42i	−0.540834	−	0.936752i	−0.998856	−	0.0478115i	$-0.984775\pi$
$163$	−1125.50	−	1949.42i	−0.540834	−	0.936752i	0.458022	−	0.888941i	$-0.348558\pi$
$164$	996.000	−	1725.12i	0.474235	−	0.821399i
$165$		0			0
$166$	932.000	+	1614.27i	0.435766	+	0.754770i
$167$	−2788.00			−1.29187			−0.645934	−	0.763393i	$-0.723532\pi$
$167$	−2788.00			−1.29187			−0.645934	+	0.763393i	$0.723532\pi$
$168$	−148.000	+	6.92820i	−0.0679670	+	0.00318168i
$169$	2159.00			0.982704
$170$		0			0
$171$	1781.00	−	3084.78i	0.796471	−	1.37953i
$172$	520.000	−	900.666i	0.230521	−	0.399274i
$173$	789.500	+	1367.45i	0.346963	+	0.600957i	0.985708	−	0.168461i	$-0.0538797\pi$
$173$	789.500	+	1367.45i	0.346963	+	0.600957i	−0.638746	+	0.769418i	$0.720546\pi$
$174$	212.000			0.0923660
$175$		0			0
$176$	560.000			0.239839
$177$	8.50000	+	14.7224i	0.00360960	+	0.00625201i
$178$	873.000	−	1512.08i	0.367607	−	0.636715i
$179$	−1225.50	+	2122.63i	−0.511722	+	0.886328i	0.488186	+	0.872740i	$0.337659\pi$
$179$	−1225.50	+	2122.63i	−0.511722	+	0.886328i	−0.999908	+	0.0135883i	$0.995675\pi$
$180$		0			0
$181$	−1170.00			−0.480472			−0.240236	−	0.970715i	$-0.577225\pi$
$181$	−1170.00			−0.480472			−0.240236	+	0.970715i	$0.577225\pi$
$182$	−1122.00	+	2171.99i	−0.456968	+	0.884608i
$183$	51.0000			0.0206012
$184$	−28.0000	−	48.4974i	−0.0112184	−	0.0194309i
$185$		0			0
$186$	−75.0000	+	129.904i	−0.0295660	+	0.0512097i
$187$	1032.50	+	1788.34i	0.403764	+	0.699340i
$188$	684.000			0.265350
$189$	−530.000	−	826.188i	−0.203978	−	0.317970i
$190$		0			0
$191$	637.500	+	1104.18i	0.241507	+	0.418303i	0.961144	−	0.276048i	$-0.0890249\pi$
$191$	637.500	+	1104.18i	0.241507	+	0.418303i	−0.719637	+	0.694351i	$0.755692\pi$
$192$	−32.0000	+	55.4256i	−0.0120281	+	0.0208333i
$193$	17.5000	−	30.3109i	0.00652683	−	0.0113048i	−0.862744	−	0.505642i	$-0.831256\pi$
$193$	17.5000	−	30.3109i	0.00652683	−	0.0113048i	0.869270	+	0.494337i	$0.164589\pi$
$194$	−290.000	−	502.295i	−0.107324	−	0.185890i
$195$		0			0
$196$	−794.000	−	1118.90i	−0.289359	−	0.407764i
$197$	2734.00			0.988779			0.494389	−	0.869241i	$-0.335392\pi$
$197$	2734.00			0.988779			0.494389	+	0.869241i	$0.335392\pi$
$198$	910.000	+	1576.17i	0.326621	+	0.565724i
$199$	−1121.50	+	1942.49i	−0.399503	+	0.691959i	−0.993665	−	0.112387i	$-0.964151\pi$
$199$	−1121.50	+	1942.49i	−0.399503	+	0.691959i	0.594162	+	0.804345i	$0.297484\pi$
$200$		0			0
$201$	219.500	+	380.185i	0.0770265	+	0.133414i
$202$	−2170.00			−0.755845
$203$	1060.00	+	1652.38i	0.366490	+	0.571301i
$204$	−236.000			−0.0809966
$205$		0			0
$206$	1553.00	−	2689.87i	0.525256	−	0.909769i
$207$	91.0000	−	157.617i	0.0305553	−	0.0529232i
$208$	528.000	+	914.523i	0.176011	+	0.304859i
$209$	4795.00			1.58697
$210$		0			0
$211$	1172.00			0.382388			0.191194	−	0.981552i	$-0.438764\pi$
$211$	1172.00			0.382388			0.191194	+	0.981552i	$0.438764\pi$
$212$	−834.000	−	1444.53i	−0.270186	−	0.467975i
$213$	392.000	−	678.964i	0.126100	−	0.218412i
$214$	129.000	−	223.435i	0.0412068	−	0.0713723i
$215$		0			0
$216$	−424.000			−0.133563
$217$	−1387.50	+	64.9519i	−0.434054	+	0.0203190i
$218$	−1930.00			−0.599615
$219$	147.500	+	255.477i	0.0455120	+	0.0788291i
$220$		0			0
$221$	−1947.00	+	3372.30i	−0.592622	+	1.02645i
$222$	11.0000	+	19.0526i	0.00332555	+	0.00576002i
$223$	−2024.00			−0.607790			−0.303895	−	0.952706i	$-0.598287\pi$
$223$	−2024.00			−0.607790			−0.303895	+	0.952706i	$0.598287\pi$
$224$	−592.000	+	27.7128i	−0.176583	+	0.00826625i
$225$		0			0
$226$	−50.0000	−	86.6025i	−0.0147166	−	0.0254899i
$227$	1285.50	−	2226.55i	0.375866	−	0.651019i	−0.614590	−	0.788847i	$-0.710679\pi$
$227$	1285.50	−	2226.55i	0.375866	−	0.651019i	0.990456	+	0.137827i	$0.0440119\pi$
$228$	−274.000	+	474.582i	−0.0795881	+	0.137851i
$229$	−447.500	−	775.093i	−0.129134	−	0.223666i	0.794207	−	0.607647i	$-0.207886\pi$
$229$	−447.500	−	775.093i	−0.129134	−	0.223666i	−0.923341	+	0.383980i	$0.874553\pi$
$230$		0			0
$231$	297.500	−	575.907i	0.0847362	−	0.164034i
$232$	848.000			0.239974
$233$	893.500	+	1547.59i	0.251224	+	0.435132i	0.963863	−	0.266398i	$-0.0858337\pi$
$233$	893.500	+	1547.59i	0.251224	+	0.435132i	−0.712639	+	0.701531i	$0.752500\pi$
$234$	−1716.00	+	2972.20i	−0.479395	+	0.830336i
$235$		0			0
$236$	34.0000	+	58.8897i	0.00937801	+	0.0162432i
$237$	−495.000			−0.135670
$238$	−1180.00	−	1839.44i	−0.321378	−	0.500979i
$239$	−5100.00			−1.38030			−0.690150	−	0.723667i	$-0.742455\pi$
$239$	−5100.00			−1.38030			−0.690150	+	0.723667i	$0.742455\pi$
$240$		0			0
$241$	2088.50	−	3617.39i	0.558225	−	0.966873i	−0.439420	−	0.898282i	$-0.644816\pi$
$241$	2088.50	−	3617.39i	0.558225	−	0.966873i	0.997645	−	0.0685917i	$-0.0218506\pi$
$242$	106.000	−	183.597i	0.0281568	−	0.0487690i
$243$	−1040.00	−	1801.33i	−0.274552	−	0.475537i
$244$	204.000			0.0535236
$245$		0			0
$246$	−996.000			−0.258141
$247$	4521.00	+	7830.60i	1.16463	+	2.01720i
$248$	−300.000	+	519.615i	−0.0768146	+	0.133047i
$249$	466.000	−	807.136i	0.118601	−	0.205422i
$250$		0			0
$251$	−4680.00			−1.17689			−0.588444	−	0.808538i	$-0.700259\pi$
$251$	−4680.00			−1.17689			−0.588444	+	0.808538i	$0.700259\pi$
$252$	−1040.00	−	1621.20i	−0.259976	−	0.405262i
$253$	245.000			0.0608815
$254$	936.000	+	1621.20i	0.231220	+	0.400485i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−874.500	−	1514.68i	−0.212256	−	0.367638i	0.740164	−	0.672426i	$-0.234748\pi$
$257$	−874.500	−	1514.68i	−0.212256	−	0.367638i	−0.952420	+	0.304788i	$0.901414\pi$
$258$	−520.000			−0.125480
$259$	−93.5000	+	180.999i	−0.0224317	+	0.0434237i
$260$		0			0
$261$	1378.00	+	2386.77i	0.326805	+	0.566043i
$262$	755.000	−	1307.70i	0.178031	−	0.308358i
$263$	−2236.50	+	3873.73i	−0.524367	+	0.908230i	0.475231	+	0.879861i	$0.342365\pi$
$263$	−2236.50	+	3873.73i	−0.524367	+	0.908230i	−0.999598	+	0.0283689i	$0.990969\pi$
$264$	−140.000	−	242.487i	−0.0326379	−	0.0565305i
$265$		0			0
$266$	−5069.00	+	237.291i	−1.16842	+	0.0546964i
$267$	−873.000			−0.200100
$268$	878.000	+	1520.74i	0.200121	+	0.346619i
$269$	−987.500	+	1710.40i	−0.223825	+	0.387676i	−0.955966	−	0.293476i	$-0.905188\pi$
$269$	−987.500	+	1710.40i	−0.223825	+	0.387676i	0.732141	+	0.681153i	$0.238521\pi$
$270$		0			0
$271$	4219.50	+	7308.39i	0.945817	+	1.63820i	0.754107	+	0.656751i	$0.228070\pi$
$271$	4219.50	+	7308.39i	0.945817	+	1.63820i	0.191710	+	0.981452i	$0.438597\pi$
$272$	−944.000			−0.210435
$273$	1221.00	−	57.1577i	0.270690	−	0.0126716i
$274$	4714.00			1.03935
$275$		0			0
$276$	−14.0000	+	24.2487i	−0.00305326	+	0.00528841i
$277$	263.500	−	456.395i	0.0571559	−	0.0989969i	−0.836032	−	0.548681i	$-0.815130\pi$
$277$	263.500	−	456.395i	0.0571559	−	0.0989969i	0.893188	+	0.449684i	$0.148463\pi$
$278$	−28.0000	−	48.4974i	−0.00604075	−	0.0104629i
$279$	−1950.00			−0.418435
$280$		0			0
$281$	−202.000			−0.0428837			−0.0214418	−	0.999770i	$-0.506826\pi$
$281$	−202.000			−0.0428837			−0.0214418	+	0.999770i	$0.506826\pi$
$282$	−171.000	−	296.181i	−0.0361096	−	0.0625436i
$283$	−3974.50	+	6884.04i	−0.834839	+	1.44598i	0.0593220	+	0.998239i	$0.481106\pi$
$283$	−3974.50	+	6884.04i	−0.834839	+	1.44598i	−0.894161	+	0.447745i	$0.852227\pi$
$284$	1568.00	−	2715.86i	0.327619	−	0.567452i
$285$		0			0
$286$	−4620.00			−0.955197
$287$	−4980.00	−	7763.05i	−1.02425	−	1.59665i
$288$	−832.000			−0.170229
$289$	716.000	+	1240.15i	0.145736	+	0.252422i
$290$		0			0
$291$	−145.000	+	251.147i	−0.0292098	+	0.0505929i
$292$	590.000	+	1021.91i	0.118244	+	0.204804i
$293$	−318.000			−0.0634053			−0.0317027	−	0.999497i	$-0.510093\pi$
$293$	−318.000			−0.0634053			−0.0317027	+	0.999497i	$0.510093\pi$
$294$	−286.000	+	623.538i	−0.0567342	+	0.123692i
$295$		0			0
$296$	44.0000	+	76.2102i	0.00864003	+	0.0149650i
$297$	927.500	−	1606.48i	0.181209	−	0.313863i
$298$	−2295.00	+	3975.06i	−0.446127	+	0.772714i
$299$	231.000	+	400.104i	0.0446792	+	0.0773866i
$300$		0			0
$301$	−2600.00	−	4053.00i	−0.497879	−	0.776116i
$302$	−2218.00			−0.422621
$303$	542.500	+	939.638i	0.102857	+	0.178154i
$304$	−1096.00	+	1898.33i	−0.206776	+	0.358147i
$305$		0			0
$306$	−1534.00	−	2656.97i	−0.286578	−	0.496368i
$307$	8132.00			1.51178			0.755892	−	0.654696i	$-0.227203\pi$
$307$	8132.00			1.51178			0.755892	+	0.654696i	$0.227203\pi$
$308$	1190.00	−	2303.63i	0.220151	−	0.426173i
$309$	−1553.00			−0.285913
$310$		0			0
$311$	464.500	−	804.538i	0.0846925	−	0.146692i	−0.820568	−	0.571549i	$-0.806343\pi$
$311$	464.500	−	804.538i	0.0846925	−	0.146692i	0.905260	+	0.424858i	$0.139676\pi$
$312$	264.000	−	457.261i	0.0479040	−	0.0829722i
$313$	−104.500	−	180.999i	−0.0188712	−	0.0326859i	0.856436	−	0.516254i	$-0.172674\pi$
$313$	−104.500	−	180.999i	−0.0188712	−	0.0326859i	−0.875307	+	0.483568i	$0.839341\pi$
$314$	−3118.00			−0.560379
$315$		0			0
$316$	−1980.00			−0.352480
$317$	3565.50	+	6175.63i	0.631730	+	1.09419i	0.987198	+	0.159500i	$0.0509882\pi$
$317$	3565.50	+	6175.63i	0.631730	+	1.09419i	−0.355468	+	0.934689i	$0.615678\pi$
$318$	−417.000	+	722.265i	−0.0735352	+	0.127367i
$319$	−1855.00	+	3212.95i	−0.325580	+	0.563921i
$320$		0			0
$321$	−129.000			−0.0224301
$322$	−259.000	+	12.1244i	−0.0448246	+	0.00209834i
$323$	−8083.00			−1.39242
$324$	−1298.00	−	2248.20i	−0.222565	−	0.385494i
$325$		0			0
$326$	−2251.00	+	3898.85i	−0.382427	+	0.662384i
$327$	482.500	+	835.715i	0.0815973	+	0.141331i
$328$	−3984.00			−0.670670
$329$	1453.50	−	2813.72i	0.243569	−	0.471505i
$330$		0			0
$331$	3285.50	+	5690.65i	0.545581	+	0.944975i	0.998570	+	0.0534583i	$0.0170244\pi$
$331$	3285.50	+	5690.65i	0.545581	+	0.944975i	−0.452989	+	0.891516i	$0.649642\pi$
$332$	1864.00	−	3228.54i	0.308133	−	0.533703i
$333$	−143.000	+	247.683i	−0.0235326	+	0.0407596i
$334$	2788.00	+	4828.96i	0.456744	+	0.791104i
$335$		0			0
$336$	160.000	+	249.415i	0.0259783	+	0.0404962i
$337$	11466.0			1.85339			0.926696	−	0.375813i	$-0.122636\pi$
$337$	11466.0			1.85339			0.926696	+	0.375813i	$0.122636\pi$
$338$	−2159.00	−	3739.50i	−0.347438	−	0.601781i
$339$	−25.0000	+	43.3013i	−0.00400535	+	0.00693747i
$340$		0			0
$341$	−1312.50	−	2273.32i	−0.208434	−	0.361018i
$342$	−7124.00			−1.12638
$343$	−6290.00	+	888.542i	−0.990169	+	0.139874i
$344$	−2080.00			−0.326006
$345$		0			0
$346$	1579.00	−	2734.91i	0.245340	−	0.424941i
$347$	−4888.50	+	8467.13i	−0.756278	+	1.30991i	0.188459	+	0.982081i	$0.439651\pi$
$347$	−4888.50	+	8467.13i	−0.756278	+	1.30991i	−0.944737	+	0.327831i	$0.893682\pi$
$348$	−212.000	−	367.195i	−0.0326563	−	0.0565624i
$349$	11914.0			1.82734			0.913670	−	0.406456i	$-0.133236\pi$
$349$	11914.0			1.82734			0.913670	+	0.406456i	$0.133236\pi$
$350$		0			0
$351$	3498.00			0.531936
$352$	−560.000	−	969.948i	−0.0847957	−	0.146871i
$353$	4561.50	−	7900.75i	0.687774	−	1.19126i	−0.284783	−	0.958592i	$-0.591921\pi$
$353$	4561.50	−	7900.75i	0.687774	−	1.19126i	0.972556	−	0.232667i	$-0.0747452\pi$
$354$	17.0000	−	29.4449i	0.00255237	−	0.00442084i
$355$		0			0
$356$	−3492.00			−0.519875
$357$	−501.500	+	970.814i	−0.0743479	+	0.143924i
$358$	4902.00			0.723684
$359$	−4074.50	−	7057.24i	−0.599008	−	1.03751i	−0.992968	−	0.118385i	$-0.962228\pi$
$359$	−4074.50	−	7057.24i	−0.599008	−	1.03751i	0.393960	−	0.919128i	$-0.371105\pi$
$360$		0			0
$361$	−5955.00	+	10314.4i	−0.868202	+	1.50377i
$362$	1170.00	+	2026.50i	0.169872	+	0.294228i
$363$	−106.000			−0.0153266
$364$	4884.00	−	228.631i	0.703272	−	0.0329217i
$365$		0			0
$366$	−51.0000	−	88.3346i	−0.00728364	−	0.0126156i
$367$	4835.50	−	8375.33i	0.687769	−	1.19125i	−0.284790	−	0.958590i	$-0.591924\pi$
$367$	4835.50	−	8375.33i	0.687769	−	1.19125i	0.972558	−	0.232660i	$-0.0747429\pi$
$368$	−56.0000	+	96.9948i	−0.00793261	+	0.0137397i
$369$	−6474.00	−	11213.3i	−0.913341	−	1.58195i
$370$		0			0
$371$	−7714.50	+	361.133i	−1.07956	+	0.0505366i
$372$	300.000			0.0418126
$373$	−2054.50	−	3558.50i	−0.285196	−	0.493973i	0.687461	−	0.726221i	$-0.258725\pi$
$373$	−2054.50	−	3558.50i	−0.285196	−	0.493973i	−0.972657	+	0.232248i	$0.925392\pi$
$374$	2065.00	−	3576.68i	0.285504	−	0.494508i
$375$		0			0
$376$	−684.000	−	1184.72i	−0.0938154	−	0.162493i
$377$	−6996.00			−0.955736
$378$	−901.000	+	1744.18i	−0.122599	+	0.237330i
$379$	−3488.00			−0.472735			−0.236367	−	0.971664i	$-0.575957\pi$
$379$	−3488.00			−0.472735			−0.236367	+	0.971664i	$0.575957\pi$
$380$		0			0
$381$	468.000	−	810.600i	0.0629301	−	0.108998i
$382$	1275.00	−	2208.36i	0.170771	−	0.295785i
$383$	4358.50	+	7549.14i	0.581485	+	1.00716i	0.995304	+	0.0968028i	$0.0308616\pi$
$383$	4358.50	+	7549.14i	0.581485	+	1.00716i	−0.413818	+	0.910360i	$0.635805\pi$
$384$	128.000			0.0170103
$385$		0			0
$386$	−70.0000			−0.00923033
$387$	−3380.00	−	5854.33i	−0.443967	−	0.768973i
$388$	−580.000	+	1004.59i	−0.0758893	+	0.131444i
$389$	−81.5000	+	141.162i	−0.0106227	+	0.0183990i	−0.871288	−	0.490772i	$-0.836715\pi$
$389$	−81.5000	+	141.162i	−0.0106227	+	0.0183990i	0.860665	+	0.509171i	$0.170048\pi$
$390$		0			0
$391$	−413.000			−0.0534177
$392$	−1144.00	+	2494.15i	−0.147400	+	0.321362i
$393$	−755.000			−0.0969077
$394$	−2734.00	−	4735.43i	−0.349586	−	0.605501i
$395$		0			0
$396$	1820.00	−	3152.33i	0.230956	−	0.400027i
$397$	499.500	+	865.159i	0.0631466	+	0.109373i	0.895870	−	0.444316i	$-0.146553\pi$
$397$	499.500	+	865.159i	0.0631466	+	0.109373i	−0.832724	+	0.553689i	$0.813220\pi$
$398$	4486.00			0.564982
$399$	1370.00	+	2135.62i	0.171894	+	0.267957i
$400$		0			0
$401$	7378.50	+	12779.9i	0.918865	+	1.59152i	0.801143	+	0.598474i	$0.204226\pi$
$401$	7378.50	+	12779.9i	0.918865	+	1.59152i	0.117722	+	0.993047i	$0.462441\pi$
$402$	439.000	−	760.370i	0.0544660	−	0.0943379i
$403$	2475.00	−	4286.83i	0.305927	−	0.529881i
$404$	2170.00	+	3758.55i	0.267232	+	0.462859i
$405$		0			0
$406$	1802.00	−	3488.35i	0.220275	−	0.426414i
$407$	−385.000			−0.0468888
$408$	236.000	+	408.764i	0.0286366	+	0.0496001i
$409$	66.5000	−	115.181i	0.00803964	−	0.0139251i	−0.861978	−	0.506946i	$-0.830774\pi$
$409$	66.5000	−	115.181i	0.00803964	−	0.0139251i	0.870017	+	0.493021i	$0.164108\pi$
$410$		0			0
$411$	−1178.50	−	2041.22i	−0.141438	−	0.244978i
$412$	−6212.00			−0.742823
$413$	314.500	−	14.7224i	0.0374710	−	0.00175410i
$414$	−364.000			−0.0432117
$415$		0			0
$416$	1056.00	−	1829.05i	0.124458	−	0.215568i
$417$	−14.0000	+	24.2487i	−0.00164408	+	0.00284764i
$418$	−4795.00	−	8305.18i	−0.561079	−	0.971818i
$419$	−6420.00			−0.748538			−0.374269	−	0.927320i	$-0.622106\pi$
$419$	−6420.00			−0.748538			−0.374269	+	0.927320i	$0.622106\pi$
$420$		0			0
$421$	10266.0			1.18844			0.594221	−	0.804302i	$-0.297460\pi$
$421$	10266.0			1.18844			0.594221	+	0.804302i	$0.297460\pi$
$422$	−1172.00	−	2029.96i	−0.135194	−	0.234164i
$423$	2223.00	−	3850.35i	0.255522	−	0.442578i
$424$	−1668.00	+	2889.06i	−0.191050	+	0.330908i
$425$		0			0
$426$	−1568.00			−0.178333
$427$	433.500	−	839.179i	0.0491301	−	0.0951070i
$428$	−516.000			−0.0582752
$429$	1155.00	+	2000.52i	0.129986	+	0.225142i
$430$		0			0
$431$	7606.50	−	13174.8i	0.850098	−	1.47241i	−0.0310213	−	0.999519i	$-0.509876\pi$
$431$	7606.50	−	13174.8i	0.850098	−	1.47241i	0.881119	−	0.472894i	$-0.156791\pi$
$432$	424.000	+	734.390i	0.0472215	+	0.0817901i
$433$	1378.00			0.152939			0.0764693	−	0.997072i	$-0.475635\pi$
$433$	1378.00			0.152939			0.0764693	+	0.997072i	$0.475635\pi$
$434$	1500.00	+	2338.27i	0.165904	+	0.258619i
$435$		0			0
$436$	1930.00	+	3342.86i	0.211996	+	0.367188i
$437$	−479.500	+	830.518i	−0.0524888	+	0.0909132i
$438$	295.000	−	510.955i	0.0321818	−	0.0557406i
$439$	1381.50	+	2392.83i	0.150195	+	0.260145i	0.931299	−	0.364256i	$-0.118677\pi$
$439$	1381.50	+	2392.83i	0.150195	+	0.260145i	−0.781104	+	0.624401i	$0.785343\pi$
$440$		0			0
$441$	−8879.00	+	833.116i	−0.958752	+	0.0899597i
$442$	7788.00			0.838094
$443$	2924.50	+	5065.38i	0.313651	+	0.543259i	0.979150	−	0.203140i	$-0.0651146\pi$
$443$	2924.50	+	5065.38i	0.313651	+	0.543259i	−0.665499	+	0.746399i	$0.731781\pi$
$444$	22.0000	−	38.1051i	0.00235152	−	0.00407295i
$445$		0			0
$446$	2024.00	+	3505.67i	0.214886	+	0.372194i
$447$	2295.00			0.242841
$448$	640.000	+	997.661i	0.0674937	+	0.105212i
$449$	4582.00			0.481599			0.240799	−	0.970575i	$-0.422590\pi$
$449$	4582.00			0.481599			0.240799	+	0.970575i	$0.422590\pi$
$450$		0			0
$451$	8715.00	−	15094.8i	0.909919	−	1.57603i
$452$	−100.000	+	173.205i	−0.0104062	+	0.0180241i
$453$	554.500	+	960.422i	0.0575114	+	0.0996127i
$454$	−5142.00			−0.531555
$455$		0			0
$456$	1096.00			0.112555
$457$	5775.50	+	10003.5i	0.591174	+	1.02394i	0.994075	+	0.108700i	$0.0346687\pi$
$457$	5775.50	+	10003.5i	0.591174	+	1.02394i	−0.402901	+	0.915244i	$0.631998\pi$
$458$	−895.000	+	1550.19i	−0.0913114	+	0.158156i
$459$	−1563.50	+	2708.06i	−0.158993	+	0.275384i
$460$		0			0
$461$	−9494.00			−0.959175			−0.479587	−	0.877494i	$-0.659214\pi$
$461$	−9494.00			−0.959175			−0.479587	+	0.877494i	$0.659214\pi$
$462$	−1295.00	+	60.6218i	−0.130409	+	0.00610472i
$463$	10160.0			1.01982			0.509908	−	0.860229i	$-0.329679\pi$
$463$	10160.0			1.01982			0.509908	+	0.860229i	$0.329679\pi$
$464$	−848.000	−	1468.78i	−0.0848436	−	0.146953i
$465$		0			0
$466$	1787.00	−	3095.17i	0.177642	−	0.307685i
$467$	−653.500	−	1131.90i	−0.0647545	−	0.112158i	0.831831	−	0.555030i	$-0.187293\pi$
$467$	−653.500	−	1131.90i	−0.0647545	−	0.112158i	−0.896585	+	0.442872i	$0.853960\pi$
$468$	6864.00			0.677967
$469$	8121.50	−	380.185i	0.799608	−	0.0374314i
$470$		0			0
$471$	779.500	+	1350.13i	0.0762579	+	0.132083i
$472$	68.0000	−	117.779i	0.00663126	−	0.0114857i
$473$	4550.00	−	7880.83i	0.442303	−	0.766091i
$474$	495.000	+	857.365i	0.0479665	+	0.0830803i
$475$		0			0
$476$	−2006.00	+	3883.26i	−0.193161	+	0.373926i
$477$	−10842.0			−1.04072
$478$	5100.00	+	8833.46i	0.488010	+	0.845257i
$479$	−9143.50	+	15837.0i	−0.872186	+	1.51067i	−0.0124559	+	0.999922i	$0.503965\pi$
$479$	−9143.50	+	15837.0i	−0.872186	+	1.51067i	−0.859730	+	0.510748i	$0.829368\pi$
$480$		0			0
$481$	−363.000	−	628.734i	−0.0344103	−	0.0596005i
$482$	−8354.00			−0.789449
$483$	70.0000	+	109.119i	0.00659443	+	0.0102797i
$484$	−424.000			−0.0398197
$485$		0			0
$486$	−2080.00	+	3602.67i	−0.194137	+	0.336256i
$487$	−7476.50	+	12949.7i	−0.695673	+	1.20494i	0.274281	+	0.961650i	$0.411560\pi$
$487$	−7476.50	+	12949.7i	−0.695673	+	1.20494i	−0.969953	+	0.243291i	$0.921773\pi$
$488$	−204.000	−	353.338i	−0.0189235	−	0.0327764i
$489$	2251.00			0.208167
$490$		0			0
$491$	14352.0			1.31914			0.659569	−	0.751644i	$-0.270739\pi$
$491$	14352.0			1.31914			0.659569	+	0.751644i	$0.270739\pi$
$492$	996.000	+	1725.12i	0.0912666	+	0.158078i
$493$	3127.00	−	5416.12i	0.285665	−	0.494787i
$494$	9042.00	−	15661.2i	0.823520	−	1.42638i
$495$		0			0
$496$	1200.00			0.108632
$497$	−7840.00	−	12221.4i	−0.707590	−	1.10302i
$498$	−1864.00			−0.167727
$499$	2765.50	+	4789.99i	0.248098	+	0.429718i	0.962998	−	0.269509i	$-0.0868612\pi$
$499$	2765.50	+	4789.99i	0.248098	+	0.429718i	−0.714900	+	0.699226i	$0.753528\pi$
$500$		0			0
$501$	1394.00	−	2414.48i	0.124310	−	0.215311i
$502$	4680.00	+	8106.00i	0.416093	+	0.720694i
$503$	−8400.00			−0.744607			−0.372304	−	0.928111i	$-0.621432\pi$
$503$	−8400.00			−0.744607			−0.372304	+	0.928111i	$0.621432\pi$
$504$	−1768.00	+	3422.53i	−0.156256	+	0.302484i
$505$		0			0
$506$	−245.000	−	424.352i	−0.0215249	−	0.0372821i
$507$	−1079.50	+	1869.75i	−0.0945607	+	0.163784i
$508$	1872.00	−	3242.40i	0.163497	−	0.283185i
$509$	1192.50	+	2065.47i	0.103844	+	0.179863i	0.913265	−	0.407365i	$-0.133552\pi$
$509$	1192.50	+	2065.47i	0.103844	+	0.179863i	−0.809421	+	0.587228i	$0.800219\pi$
$510$		0			0
$511$	5457.50	−	255.477i	0.472457	−	0.0221167i
$512$	512.000			0.0441942
$513$	3630.50	+	6288.21i	0.312457	+	0.541192i
$514$	−1749.00	+	3029.36i	−0.150088	+	0.259960i
$515$		0			0
$516$	520.000	+	900.666i	0.0443638	+	0.0768404i
$517$	5985.00			0.509130
$518$	407.000	−	19.0526i	0.0345223	−	0.00161606i
$519$	−1579.00			−0.133546
$520$		0			0
$521$	4576.50	−	7926.73i	0.384837	−	0.666557i	−0.606910	−	0.794771i	$-0.707591\pi$
$521$	4576.50	−	7926.73i	0.384837	−	0.666557i	0.991747	+	0.128214i	$0.0409243\pi$
$522$	2756.00	−	4773.53i	0.231086	−	0.400253i
$523$	−6903.50	−	11957.2i	−0.577187	−	0.999718i	−0.995800	−	0.0915530i	$-0.970817\pi$
$523$	−6903.50	−	11957.2i	−0.577187	−	0.999718i	0.418613	−	0.908165i	$-0.362516\pi$
$524$	−3020.00			−0.251773
$525$		0			0
$526$	8946.00			0.741567
$527$	2212.50	+	3832.16i	0.182880	+	0.316758i
$528$	−280.000	+	484.974i	−0.0230785	+	0.0399731i
$529$	6059.00	−	10494.5i	0.497986	−	0.862538i
$530$		0			0
$531$	442.000			0.0361227
$532$	5480.00	+	8542.47i	0.446594	+	0.696172i
$533$	32868.0			2.67105
$534$	873.000	+	1512.08i	0.0707461	+	0.122536i
$535$		0			0
$536$	1756.00	−	3041.48i	0.141507	−	0.245097i
$537$	−1225.50	−	2122.63i	−0.0984809	−	0.170574i
$538$	3950.00			0.316536
$539$	−6947.50	−	9790.42i	−0.555195	−	0.782381i
$540$		0			0
$541$	−4087.50	−	7079.76i	−0.324834	−	0.562629i	0.656645	−	0.754200i	$-0.271975\pi$
$541$	−4087.50	−	7079.76i	−0.324834	−	0.562629i	−0.981479	+	0.191571i	$0.938642\pi$
$542$	8439.00	−	14616.8i	0.668794	−	1.15838i
$543$	585.000	−	1013.25i	0.0462334	−	0.0800787i
$544$	944.000	+	1635.06i	0.0744001	+	0.128865i
$545$		0			0
$546$	−1320.00	−	2057.68i	−0.103463	−	0.161283i
$547$	−4656.00			−0.363942			−0.181971	−	0.983304i	$-0.558248\pi$
$547$	−4656.00			−0.363942			−0.181971	+	0.983304i	$0.558248\pi$
$548$	−4714.00	−	8164.89i	−0.367467	−	0.636472i
$549$	663.000	−	1148.35i	0.0515413	−	0.0892721i
$550$		0			0
$551$	−7261.00	−	12576.4i	−0.561396	−	0.972366i
$552$	56.0000			0.00431797
$553$	−4207.50	+	8144.97i	−0.323546	+	0.626328i
$554$	−1054.00			−0.0808306
$555$		0			0
$556$	−56.0000	+	96.9948i	−0.00427146	+	0.00739838i
$557$	3501.50	−	6064.78i	0.266361	−	0.461352i	−0.701558	−	0.712612i	$-0.747512\pi$
$557$	3501.50	−	6064.78i	0.266361	−	0.461352i	0.967919	+	0.251261i	$0.0808452\pi$
$558$	1950.00	+	3377.50i	0.147939	+	0.256238i
$559$	17160.0			1.29837
$560$		0			0
$561$	−2065.00			−0.155409
$562$	202.000	+	349.874i	0.0151617	+	0.0262608i
$563$	−9876.50	+	17106.6i	−0.739334	+	1.28056i	0.213462	+	0.976951i	$0.431526\pi$
$563$	−9876.50	+	17106.6i	−0.739334	+	1.28056i	−0.952796	+	0.303612i	$0.901807\pi$
$564$	−342.000	+	592.361i	−0.0255333	+	0.0442250i
$565$		0			0
$566$	15898.0			1.18064
$567$	−12006.5	+	562.050i	−0.889287	+	0.0416295i
$568$	−6272.00			−0.463323
$569$	3448.50	+	5972.98i	0.254075	+	0.440071i	0.964644	−	0.263557i	$-0.0848957\pi$
$569$	3448.50	+	5972.98i	0.254075	+	0.440071i	−0.710569	+	0.703628i	$0.751562\pi$
$570$		0			0
$571$	−12457.5	+	21577.0i	−0.913013	+	1.58138i	−0.103227	+	0.994658i	$0.532917\pi$
$571$	−12457.5	+	21577.0i	−0.913013	+	1.58138i	−0.809785	+	0.586726i	$0.800416\pi$
$572$	4620.00	+	8002.07i	0.337713	+	0.584936i
$573$	−1275.00			−0.0929562
$574$	−8466.00	+	16388.7i	−0.615617	+	1.19172i
$575$		0			0
$576$	832.000	+	1441.07i	0.0601852	+	0.104244i
$577$	63.5000	−	109.985i	0.00458152	−	0.00793543i	−0.863726	−	0.503962i	$-0.831875\pi$
$577$	63.5000	−	109.985i	0.00458152	−	0.00793543i	0.868307	+	0.496027i	$0.165208\pi$
$578$	1432.00	−	2480.30i	0.103051	−	0.178489i
$579$	17.5000	+	30.3109i	0.00125609	+	0.00217561i
$580$		0			0
$581$	−9320.00	−	14528.4i	−0.665506	−	1.03742i
$582$	580.000			0.0413089
$583$	−7297.50	−	12639.6i	−0.518407	−	0.897908i
$584$	1180.00	−	2043.82i	0.0836109	−	0.144818i
$585$		0			0
$586$	318.000	+	550.792i	0.0224172	+	0.0388277i
$587$	−9044.00			−0.635921			−0.317961	−	0.948104i	$-0.602998\pi$
$587$	−9044.00			−0.635921			−0.317961	+	0.948104i	$0.602998\pi$
$588$	1366.00	−	128.172i	0.0958042	−	0.00898931i
$589$	10275.0			0.718801
$590$		0			0
$591$	−1367.00	+	2367.71i	−0.0951453	+	0.164796i
$592$	88.0000	−	152.420i	0.00610942	−	0.0105818i
$593$	−5350.50	−	9267.34i	−0.370521	−	0.641760i	0.619125	−	0.785292i	$-0.287487\pi$
$593$	−5350.50	−	9267.34i	−0.370521	−	0.641760i	−0.989646	+	0.143532i	$0.954154\pi$
$594$	−3710.00			−0.256268
$595$		0			0
$596$	9180.00			0.630919
$597$	−1121.50	−	1942.49i	−0.0768843	−	0.133168i
$598$	462.000	−	800.207i	0.0315930	−	0.0547206i
$599$	−10399.5	+	18012.5i	−0.709369	+	1.22866i	0.255722	+	0.966750i	$0.417687\pi$
$599$	−10399.5	+	18012.5i	−0.709369	+	1.22866i	−0.965091	+	0.261913i	$0.915647\pi$
$600$		0			0
$601$	−1402.00			−0.0951560			−0.0475780	−	0.998868i	$-0.515150\pi$
$601$	−1402.00			−0.0951560			−0.0475780	+	0.998868i	$0.515150\pi$
$602$	−4420.00	+	8556.33i	−0.299245	+	0.579286i
$603$	11414.0			0.770836
$604$	2218.00	+	3841.69i	0.149419	+	0.258801i
$605$		0			0
$606$	1085.00	−	1879.28i	0.0727312	−	0.125974i
$607$	3262.50	+	5650.82i	0.218156	+	0.377858i	0.954244	−	0.299028i	$-0.0966625\pi$
$607$	3262.50	+	5650.82i	0.218156	+	0.377858i	−0.736088	+	0.676886i	$0.763329\pi$
$608$	4384.00			0.292425
$609$	−1961.00	+	91.7987i	−0.130482	+	0.00610816i
$610$		0			0
$611$	5643.00	+	9773.96i	0.373636	+	0.647156i
$612$	−3068.00	+	5313.93i	−0.202641	+	0.350985i
$613$	7525.50	−	13034.5i	0.495844	−	0.858826i	−0.504145	−	0.863619i	$-0.668192\pi$
$613$	7525.50	−	13034.5i	0.495844	−	0.858826i	0.999989	+	0.00479285i	$0.00152562\pi$
$614$	−8132.00	−	14085.0i	−0.534496	−	0.925775i
$615$		0			0
$616$	−5180.00	+	242.487i	−0.338812	+	0.0158605i
$617$	−11150.0			−0.727524			−0.363762	−	0.931492i	$-0.618508\pi$
$617$	−11150.0			−0.727524			−0.363762	+	0.931492i	$0.618508\pi$
$618$	1553.00	+	2689.87i	0.101085	+	0.175085i
$619$	−1707.50	+	2957.48i	−0.110873	+	0.192037i	−0.916122	−	0.400899i	$-0.868698\pi$
$619$	−1707.50	+	2957.48i	−0.110873	+	0.192037i	0.805250	+	0.592936i	$0.202031\pi$
$620$		0			0
$621$	185.500	+	321.295i	0.0119869	+	0.0207619i
$622$	−1858.00			−0.119773
$623$	−7420.50	+	14364.8i	−0.477201	+	0.923775i
$624$	−1056.00			−0.0677465
$625$		0			0
$626$	−209.000	+	361.999i	−0.0133440	+	0.0231124i
$627$	−2397.50	+	4152.59i	−0.152706	+	0.264495i
$628$	3118.00	+	5400.53i	0.198124	+	0.343160i
$629$	649.000			0.0411404
$630$		0			0
$631$	−21184.0			−1.33648			−0.668242	−	0.743944i	$-0.732953\pi$
$631$	−21184.0			−1.33648			−0.668242	+	0.743944i	$0.732953\pi$
$632$	1980.00	+	3429.46i	0.124621	+	0.215849i
$633$	−586.000	+	1014.98i	−0.0367953	+	0.0637313i
$634$	7131.00	−	12351.3i	0.446701	−	0.773708i
$635$		0			0
$636$	1668.00			0.103995
$637$	9438.00	−	20576.8i	0.587044	−	1.27988i
$638$	7420.00			0.460440
$639$	−10192.0	−	17653.1i	−0.630969	−	1.09287i
$640$		0			0
$641$	5352.50	−	9270.80i	0.329814	−	0.571255i	−0.652660	−	0.757651i	$-0.726347\pi$
$641$	5352.50	−	9270.80i	0.329814	−	0.571255i	0.982475	+	0.186395i	$0.0596805\pi$
$642$	129.000	+	223.435i	0.00793026	+	0.0137356i
$643$	−6860.00			−0.420734			−0.210367	−	0.977622i	$-0.567466\pi$
$643$	−6860.00			−0.420734			−0.210367	+	0.977622i	$0.567466\pi$
$644$	280.000	+	436.477i	0.0171328	+	0.0267074i
$645$		0			0
$646$	8083.00	+	14000.2i	0.492293	+	0.852677i
$647$	7231.50	−	12525.3i	0.439412	−	0.761084i	−0.558232	−	0.829685i	$-0.688520\pi$
$647$	7231.50	−	12525.3i	0.439412	−	0.761084i	0.997644	+	0.0686008i	$0.0218535\pi$
$648$	−2596.00	+	4496.40i	−0.157377	+	0.272586i
$649$	297.500	+	515.285i	0.0179937	+	0.0311660i
$650$		0			0
$651$	637.500	−	1234.09i	0.0383803	−	0.0742975i
$652$	9004.00			0.540834
$653$	2989.50	+	5177.97i	0.179155	+	0.310305i	0.941591	−	0.336758i	$-0.109330\pi$
$653$	2989.50	+	5177.97i	0.179155	+	0.310305i	−0.762436	+	0.647063i	$0.775997\pi$
$654$	965.000	−	1671.43i	0.0576980	−	0.0999359i
$655$		0			0
$656$	3984.00	+	6900.49i	0.237117	+	0.410700i
$657$	7670.00			0.455457
$658$	−6327.00	+	296.181i	−0.374851	+	0.0175476i
$659$	−6940.00			−0.410234			−0.205117	−	0.978737i	$-0.565757\pi$
$659$	−6940.00			−0.410234			−0.205117	+	0.978737i	$0.565757\pi$
$660$		0			0
$661$	−6699.50	+	11603.9i	−0.394221	+	0.682812i	−0.993001	−	0.118102i	$-0.962319\pi$
$661$	−6699.50	+	11603.9i	−0.394221	+	0.682812i	0.598780	+	0.800914i	$0.295652\pi$
$662$	6571.00	−	11381.3i	0.385784	−	0.668198i
$663$	−1947.00	−	3372.30i	−0.114050	−	0.197541i
$664$	−7456.00			−0.435766
$665$		0			0
$666$	572.000			0.0332801
$667$	−371.000	−	642.591i	−0.0215370	−	0.0373032i
$668$	5576.00	−	9657.92i	0.322967	−	0.559395i
$669$	1012.00	−	1752.84i	0.0584846	−	0.101298i
$670$		0			0
$671$	1785.00			0.102696
$672$	272.000	−	526.543i	0.0156140	−	0.0302260i
$673$	−29510.0			−1.69023			−0.845117	−	0.534582i	$-0.820469\pi$
$673$	−29510.0			−1.69023			−0.845117	+	0.534582i	$0.820469\pi$
$674$	−11466.0	−	19859.7i	−0.655273	−	1.13497i
$675$		0			0
$676$	−4318.00	+	7479.00i	−0.245676	+	0.425523i
$677$	−13000.5	−	22517.5i	−0.738035	−	1.27831i	−0.953379	−	0.301776i	$-0.902421\pi$
$677$	−13000.5	−	22517.5i	−0.738035	−	1.27831i	0.215344	−	0.976538i	$-0.430913\pi$
$678$	100.000			0.00566442
$679$	2900.00	+	4520.65i	0.163905	+	0.255503i
$680$		0			0
$681$	1285.50	+	2226.55i	0.0723355	+	0.125289i
$682$	−2625.00	+	4546.63i	−0.147385	+	0.255278i
$683$	−4402.50	+	7625.35i	−0.246643	+	0.427198i	−0.962592	−	0.270954i	$-0.912661\pi$
$683$	−4402.50	+	7625.35i	−0.246643	+	0.427198i	0.715949	+	0.698152i	$0.245994\pi$
$684$	7124.00	+	12339.1i	0.398235	+	0.689764i
$685$		0			0
$686$	7829.00	+	10006.1i	0.435733	+	0.556899i
$687$	895.000			0.0497036
$688$	2080.00	+	3602.67i	0.115261	+	0.199637i
$689$	13761.0	−	23834.8i	0.760889	−	1.31790i
$690$		0			0
$691$	−14342.5	−	24841.9i	−0.789601	−	1.36763i	−0.926211	−	0.377004i	$-0.876954\pi$
$691$	−14342.5	−	24841.9i	−0.789601	−	1.36763i	0.136610	−	0.990625i	$-0.456379\pi$
$692$	−6316.00			−0.346963
$693$	−9100.00	−	14185.5i	−0.498817	−	0.777579i
$694$	19554.0			1.06954
$695$		0			0
$696$	−424.000	+	734.390i	−0.0230915	+	0.0399956i
$697$	−14691.0	+	25445.6i	−0.798366	+	1.38281i
$698$	−11914.0	−	20635.7i	−0.646062	−	1.11901i
$699$	−1787.00			−0.0966961
$700$		0			0
$701$	−3146.00			−0.169505			−0.0847523	−	0.996402i	$-0.527010\pi$
$701$	−3146.00			−0.169505			−0.0847523	+	0.996402i	$0.527010\pi$
$702$	−3498.00	−	6058.71i	−0.188068	−	0.325743i
$703$	753.500	−	1305.10i	0.0404250	−	0.0700182i
$704$	−1120.00	+	1939.90i	−0.0599596	+	0.103853i
$705$		0			0
$706$	−18246.0			−0.972659
$707$	20072.5	−	939.638i	1.06776	−	0.0499840i
$708$	−68.0000			−0.00360960
$709$	−629.500	−	1090.33i	−0.0333447	−	0.0577547i	0.848871	−	0.528599i	$-0.177283\pi$
$709$	−629.500	−	1090.33i	−0.0333447	−	0.0577547i	−0.882216	+	0.470845i	$0.843949\pi$
$710$		0			0
$711$	−6435.00	+	11145.7i	−0.339425	+	0.587902i
$712$	3492.00	+	6048.32i	0.183804	+	0.318357i
$713$	525.000			0.0275756
$714$	2183.00	−	102.191i	0.114421	−	0.00535631i
$715$		0			0
$716$	−4902.00	−	8490.51i	−0.255861	−	0.443164i
$717$	2550.00	−	4416.73i	0.132819	−	0.230050i
$718$	−8149.00	+	14114.5i	−0.423563	+	0.733632i
$719$	−8212.50	−	14224.5i	−0.425973	−	0.737807i	0.570538	−	0.821271i	$-0.306735\pi$
$719$	−8212.50	−	14224.5i	−0.425973	−	0.737807i	−0.996511	+	0.0834645i	$0.973401\pi$
$720$		0			0
$721$	−13200.5	+	25553.8i	−0.681848	+	1.31994i
$722$	23820.0			1.22782
$723$	2088.50	+	3617.39i	0.107430	+	0.186075i
$724$	2340.00	−	4053.00i	0.120118	−	0.208050i
$725$		0			0
$726$	106.000	+	183.597i	0.00541877	+	0.00938559i
$727$	6032.00			0.307723			0.153861	−	0.988092i	$-0.450829\pi$
$727$	6032.00			0.307723			0.153861	+	0.988092i	$0.450829\pi$
$728$	−5280.00	−	8230.71i	−0.268805	−	0.419025i
$729$	−15443.0			−0.784586
$730$		0			0
$731$	−7670.00	+	13284.8i	−0.388078	+	0.672171i
$732$	−102.000	+	176.669i	−0.00515031	+	0.00892060i
$733$	7621.50	+	13200.8i	0.384047	+	0.665189i	0.991636	−	0.129062i	$-0.0411967\pi$
$733$	7621.50	+	13200.8i	0.384047	+	0.665189i	−0.607589	+	0.794251i	$0.707863\pi$
$734$	−19342.0			−0.972652
$735$		0			0
$736$	224.000			0.0112184
$737$	7682.50	+	13306.5i	0.383974	+	0.665062i
$738$	−12948.0	+	22426.6i	−0.645830	+	1.11861i
$739$	5026.50	−	8706.15i	0.250207	−	0.433371i	−0.713376	−	0.700782i	$-0.752835\pi$
$739$	5026.50	−	8706.15i	0.250207	−	0.433371i	0.963583	+	0.267411i	$0.0861681\pi$
$740$		0			0
$741$	−9042.00			−0.448267
$742$	8340.00	+	13000.8i	0.412629	+	0.643226i
$743$	−24384.0			−1.20399			−0.601993	−	0.798501i	$-0.705627\pi$
$743$	−24384.0			−1.20399			−0.601993	+	0.798501i	$0.705627\pi$
$744$	−300.000	−	519.615i	−0.0147830	−	0.0256049i
$745$		0			0
$746$	−4109.00	+	7117.00i	−0.201664	+	0.349292i
$747$	−12116.0	−	20985.5i	−0.593442	−	1.02787i
$748$	−8260.00			−0.403764
$749$	−1096.50	+	2122.63i	−0.0534916	+	0.103550i
$750$		0			0
$751$	−5794.50	−	10036.4i	−0.281550	−	0.487660i	0.690216	−	0.723603i	$-0.257515\pi$
$751$	−5794.50	−	10036.4i	−0.281550	−	0.487660i	−0.971767	+	0.235943i	$0.924182\pi$
$752$	−1368.00	+	2369.45i	−0.0663375	+	0.114900i
$753$	2340.00	−	4053.00i	0.113246	−	0.196148i
$754$	6996.00	+	12117.4i	0.337904	+	0.585266i
$755$		0			0
$756$	3922.00	−	183.597i	0.188680	−	0.00883250i
$757$	−14562.0			−0.699161			−0.349581	−	0.936906i	$-0.613676\pi$
$757$	−14562.0			−0.699161			−0.349581	+	0.936906i	$0.613676\pi$
$758$	3488.00	+	6041.39i	0.167137	+	0.289490i
$759$	−122.500	+	212.176i	−0.00585832	+	0.0101469i
$760$		0			0
$761$	11382.5	+	19715.1i	0.542201	+	0.939120i	0.998777	+	0.0494360i	$0.0157424\pi$
$761$	11382.5	+	19715.1i	0.542201	+	0.939120i	−0.456576	+	0.889684i	$0.650924\pi$
$762$	−1872.00			−0.0889966
$763$	17852.5	−	835.715i	0.847056	−	0.0396526i
$764$	−5100.00			−0.241507
$765$		0			0
$766$	8717.00	−	15098.3i	0.411172	−	0.712171i
$767$	−561.000	+	971.681i	−0.0264101	+	0.0457436i
$768$	−128.000	−	221.703i	−0.00601407	−	0.0104167i
$769$	3766.00			0.176600			0.0883000	−	0.996094i	$-0.471857\pi$
$769$	3766.00			0.176600			0.0883000	+	0.996094i	$0.471857\pi$
$770$		0			0
$771$	1749.00			0.0816974
$772$	70.0000	+	121.244i	0.00326341	+	0.00565240i
$773$	−13430.5	+	23262.3i	−0.624918	+	1.08239i	0.363639	+	0.931540i	$0.381534\pi$
$773$	−13430.5	+	23262.3i	−0.624918	+	1.08239i	−0.988557	+	0.150849i	$0.951799\pi$
$774$	−6760.00	+	11708.7i	−0.313932	+	0.543746i
$775$		0			0
$776$	2320.00			0.107324
$777$	−110.000	−	171.473i	−0.00507880	−	0.00791707i
$778$	326.000			0.0150227
$779$	34113.0	+	59085.4i	1.56897	+	2.71753i
$780$		0			0
$781$	13720.0	−	23763.7i	0.628605	−	1.08878i
$782$	413.000	+	715.337i	0.0188860	+	0.0327115i
$783$	−5618.00			−0.256412
$784$	5464.00	−	512.687i	0.248907	−	0.0233549i
$785$		0			0
$786$	755.000	+	1307.70i	0.0342620	+	0.0593436i
$787$	−1048.50	+	1816.06i	−0.0474905	+	0.0822559i	−0.888793	−	0.458308i	$-0.848456\pi$
$787$	−1048.50	+	1816.06i	−0.0474905	+	0.0822559i	0.841303	+	0.540564i	$0.181789\pi$
$788$	−5468.00	+	9470.85i	−0.247195	+	0.428154i
$789$	−2236.50	−	3873.73i	−0.100914	−	0.174789i
$790$		0			0
$791$	500.000	+	779.423i	0.0224753	+	0.0350355i
$792$	−7280.00			−0.326621
$793$	1683.00	+	2915.04i	0.0753658	+	0.130537i
$794$	999.000	−	1730.32i	0.0446514	−	0.0773384i
$795$		0			0
$796$	−4486.00	−	7769.98i	−0.199751	−	0.345979i
$797$	35334.0			1.57038			0.785191	−	0.619254i	$-0.212565\pi$
$797$	35334.0			1.57038			0.785191	+	0.619254i	$0.212565\pi$
$798$	2329.00	−	4508.53i	0.103315	−	0.200000i
$799$	−10089.0			−0.446712
$800$		0			0
$801$	−11349.0	+	19657.0i	−0.500621	+	0.867101i
$802$	14757.0	−	25559.9i	0.649735	−	1.12537i
$803$	5162.50	+	8941.71i	0.226875	+	0.392959i
$804$	−1756.00			−0.0770265
$805$		0			0
$806$	−9900.00			−0.432646
$807$	−987.500	−	1710.40i	−0.0430752	−	0.0746083i
$808$	4340.00	−	7517.10i	0.188961	−	0.327290i
$809$	−21267.5	+	36836.4i	−0.924259	+	1.60086i	−0.131510	+	0.991315i	$0.541983\pi$
$809$	−21267.5	+	36836.4i	−0.924259	+	1.60086i	−0.792749	+	0.609549i	$0.791351\pi$
$810$		0			0
$811$	30676.0			1.32821			0.664106	−	0.747638i	$-0.268812\pi$
$811$	30676.0			1.32821			0.664106	+	0.747638i	$0.268812\pi$
$812$	−7844.00	+	367.195i	−0.339003	+	0.0158695i
$813$	−8439.00			−0.364045
$814$	385.000	+	666.840i	0.0165777	+	0.0287134i
$815$		0			0
$816$	472.000	−	817.528i	0.0202491	−	0.0350726i
$817$	17810.0	+	30847.8i	0.762660	+	1.32097i
$818$	−266.000			−0.0113698
$819$	14586.0	−	28235.9i	0.622315	−	1.20469i
$820$		0			0
$821$	−18671.5	−	32340.0i	−0.793715	−	1.37475i	−0.923652	−	0.383232i	$-0.874811\pi$
$821$	−18671.5	−	32340.0i	−0.793715	−	1.37475i	0.129937	−	0.991522i	$-0.458522\pi$
$822$	−2357.00	+	4082.44i	−0.100012	+	0.173226i
$823$	1407.50	−	2437.86i	0.0596141	−	0.103255i	−0.834678	−	0.550738i	$-0.814346\pi$
$823$	1407.50	−	2437.86i	0.0596141	−	0.103255i	0.894292	+	0.447483i	$0.147680\pi$
$824$	6212.00	+	10759.5i	0.262628	+	0.454885i
$825$		0			0
$826$	−340.000	−	530.008i	−0.0143222	−	0.0223261i
$827$	9276.00			0.390034			0.195017	−	0.980800i	$-0.437524\pi$
$827$	9276.00			0.390034			0.195017	+	0.980800i	$0.437524\pi$
$828$	364.000	+	630.466i	0.0152776	+	0.0264616i
$829$	−9285.50	+	16083.0i	−0.389021	+	0.673805i	−0.992318	−	0.123712i	$-0.960520\pi$
$829$	−9285.50	+	16083.0i	−0.389021	+	0.673805i	0.603297	+	0.797517i	$0.293853\pi$
$830$		0			0
$831$	263.500	+	456.395i	0.0109997	+	0.0190520i
$832$	−4224.00			−0.176011
$833$	11711.5	+	16503.8i	0.487130	+	0.686464i
$834$	56.0000			0.00232509
$835$		0			0
$836$	−9590.00	+	16610.4i	−0.396743	+	0.687179i
$837$	1987.50	−	3442.45i	0.0820765	−	0.142161i
$838$	6420.00	+	11119.8i	0.264648	+	0.458384i
$839$	29048.0			1.19529			0.597645	−	0.801761i	$-0.296103\pi$
$839$	29048.0			1.19529			0.597645	+	0.801761i	$0.296103\pi$
$840$		0			0
$841$	−13153.0			−0.539301
$842$	−10266.0	−	17781.2i	−0.420178	−	0.727769i
$843$	101.000	−	174.937i	0.00412648	−	0.00714728i
$844$	−2344.00	+	4059.93i	−0.0955969	+	0.165579i
$845$		0			0
$846$	−8892.00			−0.361363
$847$	−901.000	+	1744.18i	−0.0365510	+	0.0707563i
$848$	6672.00			0.270186
$849$	−3974.50	−	6884.04i	−0.160665	−	0.278280i
$850$		0			0
$851$	38.5000	−	66.6840i	0.00155084	−	0.00268613i
$852$	1568.00	+	2715.86i	0.0630502	+	0.109206i
$853$	−32090.0			−1.28809			−0.644045	−	0.764988i	$-0.722745\pi$
$853$	−32090.0			−1.28809			−0.644045	+	0.764988i	$0.722745\pi$
$854$	−1887.00	+	88.3346i	−0.0756110	+	0.00353952i
$855$		0			0
$856$	516.000	+	893.738i	0.0206034	+	0.0356861i
$857$	−12268.5	+	21249.7i	−0.489013	+	0.846995i	−0.999920	−	0.0126408i	$-0.995976\pi$
$857$	−12268.5	+	21249.7i	−0.489013	+	0.846995i	0.510907	+	0.859636i	$0.329310\pi$
$858$	2310.00	−	4001.04i	0.0919139	−	0.159199i
$859$	−10412.5	−	18035.0i	−0.413585	−	0.716351i	0.581693	−	0.813408i	$-0.302390\pi$
$859$	−10412.5	−	18035.0i	−0.413585	−	0.716351i	−0.995279	+	0.0970571i	$0.969057\pi$
$860$		0			0
$861$	9213.00	−	431.281i	0.364667	−	0.0170709i
$862$	−30426.0			−1.20222
$863$	−11423.5	−	19786.1i	−0.450591	−	0.780447i	0.547831	−	0.836589i	$-0.315454\pi$
$863$	−11423.5	−	19786.1i	−0.450591	−	0.780447i	−0.998423	+	0.0561414i	$0.982120\pi$
$864$	848.000	−	1468.78i	0.0333907	−	0.0578344i
$865$		0			0
$866$	−1378.00	−	2386.77i	−0.0540720	−	0.0936554i
$867$	−1432.00			−0.0560937
$868$	2550.00	−	4936.34i	0.0997150	−	0.193030i
$869$	−17325.0			−0.676307
$870$		0			0
$871$	−14487.0	+	25092.2i	−0.563574	+	0.976139i
$872$	3860.00	−	6685.72i	0.149904	−	0.259641i
$873$	3770.00	+	6529.83i	0.146157	+	0.253152i
$874$	1918.00			0.0742303
$875$		0			0
$876$	−1180.00			−0.0455120
$877$	−21368.5	−	37011.3i	−0.822763	−	1.42507i	−0.903617	−	0.428341i	$-0.859098\pi$
$877$	−21368.5	−	37011.3i	−0.822763	−	1.42507i	0.0808543	−	0.996726i	$-0.474235\pi$
$878$	2763.00	−	4785.66i	0.106204	−	0.183950i
$879$	159.000	−	275.396i	0.00610118	−	0.0105676i
$880$		0			0
$881$	6162.00			0.235645			0.117822	−	0.993035i	$-0.462409\pi$
$881$	6162.00			0.235645			0.117822	+	0.993035i	$0.462409\pi$
$882$	10322.0	+	14545.8i	0.394059	+	0.555308i
$883$	−7748.00			−0.295290			−0.147645	−	0.989040i	$-0.547169\pi$
$883$	−7748.00			−0.295290			−0.147645	+	0.989040i	$0.547169\pi$
$884$	−7788.00	−	13489.2i	−0.296311	−	0.513225i
$885$		0			0
$886$	5849.00	−	10130.8i	0.221784	−	0.384142i
$887$	−12961.5	−	22450.0i	−0.490648	−	0.849827i	0.509294	−	0.860592i	$-0.329906\pi$
$887$	−12961.5	−	22450.0i	−0.490648	−	0.849827i	−0.999942	+	0.0107656i	$0.996573\pi$
$888$	−88.0000			−0.00332555
$889$	−9360.00	−	14590.8i	−0.353121	−	0.550461i
$890$		0			0
$891$	−11357.5	−	19671.8i	−0.427038	−	0.739651i
$892$	4048.00	−	7011.34i	0.151947	−	0.263181i
$893$	−11713.5	+	20288.4i	−0.438944	+	0.760274i
$894$	−2295.00	−	3975.06i	−0.0858571	−	0.148709i
$895$		0			0
$896$	1088.00	−	2106.17i	0.0405664	−	0.0785294i
$897$	−462.000			−0.0171970
$898$	−4582.00	−	7936.26i	−0.170271	−	0.294918i
$899$	−3975.00	+	6884.90i	−0.147468	+	0.255422i
$900$		0			0
$901$	12301.5	+	21306.8i	0.454853	+	0.787828i
$902$	−34860.0			−1.28682
$903$	4810.00	−	225.167i	0.177261	−	0.00829798i
$904$	400.000			0.0147166
$905$		0			0
$906$	1109.00	−	1920.84i	0.0406667	−	0.0704368i
$907$	15967.5	−	27656.5i	0.584556	−	1.01248i	−0.410375	−	0.911917i	$-0.634602\pi$
$907$	15967.5	−	27656.5i	0.584556	−	1.01248i	0.994931	−	0.100563i	$-0.0320645\pi$
$908$	5142.00	+	8906.21i	0.187933	+	0.325510i
$909$	28210.0			1.02934
$910$		0			0
$911$	3408.00			0.123943			0.0619715	−	0.998078i	$-0.480261\pi$
$911$	3408.00			0.123943			0.0619715	+	0.998078i	$0.480261\pi$
$912$	−1096.00	−	1898.33i	−0.0397941	−	0.0689253i
$913$	16310.0	−	28249.7i	0.591218	−	1.02402i
$914$	11551.0	−	20006.9i	0.418023	−	0.724037i
$915$		0			0
$916$	3580.00			0.129134
$917$	−6417.50	+	12423.1i	−0.231106	+	0.447381i
$918$	6254.00			0.224850
$919$	−6954.50	−	12045.5i	−0.249628	−	0.432368i	0.713795	−	0.700355i	$-0.246975\pi$
$919$	−6954.50	−	12045.5i	−0.249628	−	0.432368i	−0.963423	+	0.267987i	$0.913642\pi$
$920$		0			0
$921$	−4066.00	+	7042.52i	−0.145472	+	0.251964i
$922$	9494.00	+	16444.1i	0.339120	+	0.587372i
$923$	51744.0			1.84526
$924$	1400.00	+	2182.38i	0.0498448	+	0.0777004i
$925$		0			0
$926$	−10160.0	−	17597.6i	−0.360560	−	0.624508i
$927$	−20189.0	+	34968.4i	−0.715311	+	1.23896i
$928$	−1696.00	+	2937.56i	−0.0599935	+	0.103912i
$929$	12268.5	+	21249.7i	0.433279	+	0.750462i	0.997153	−	0.0753990i	$-0.0240231\pi$
$929$	12268.5	+	21249.7i	0.433279	+	0.750462i	−0.563874	+	0.825861i	$0.690690\pi$
$930$		0			0
$931$	46785.5	−	4389.88i	1.64697	−	0.154536i
$932$	−7148.00			−0.251224
$933$	464.500	+	804.538i	0.0162991	+	0.0282308i
$934$	−1307.00	+	2263.79i	−0.0457884	+	0.0793078i
$935$		0			0
$936$	−6864.00	−	11888.8i	−0.239697	−	0.415168i
$937$	32758.0			1.14211			0.571055	−	0.820912i	$-0.306534\pi$
$937$	32758.0			1.14211			0.571055	+	0.820912i	$0.306534\pi$
$938$	−8780.00	−	13686.7i	−0.305626	−	0.476424i
$939$	209.000			0.00726353
$940$		0			0
$941$	19280.5	−	33394.8i	0.667934	−	1.15690i	−0.310546	−	0.950558i	$-0.600512\pi$
$941$	19280.5	−	33394.8i	0.667934	−	1.15690i	0.978481	−	0.206338i	$-0.0661547\pi$
$942$	1559.00	−	2700.27i	0.0539225	−	0.0933965i
$943$	1743.00	+	3018.96i	0.0601908	+	0.104253i
$944$	−272.000			−0.00937801
$945$		0			0
$946$	−18200.0			−0.625511
$947$	19830.5	+	34347.4i	0.680470	+	1.17861i	0.974838	+	0.222916i	$0.0715575\pi$
$947$	19830.5	+	34347.4i	0.680470	+	1.17861i	−0.294368	+	0.955692i	$0.595109\pi$
$948$	990.000	−	1714.73i	0.0339174	−	0.0587467i
$949$	−9735.00	+	16861.5i	−0.332994	+	0.576763i
$950$		0			0
$951$	−7131.00			−0.243153
$952$	8732.00	−	408.764i	0.297275	−	0.0139161i
$953$	46618.0			1.58458			0.792290	−	0.610144i	$-0.208889\pi$
$953$	46618.0			1.58458			0.792290	+	0.610144i	$0.208889\pi$
$954$	10842.0	+	18778.9i	0.367948	+	0.637305i
$955$		0			0
$956$	10200.0	−	17666.9i	0.345075	−	0.597687i
$957$	−1855.00	−	3212.95i	−0.0626579	−	0.108527i
$958$	36574.0			1.23346
$959$	−43604.5	+	2041.22i	−1.46826	+	0.0687325i
$960$		0			0
$961$	12083.0	+	20928.4i	0.405592	+	0.702506i
$962$	−726.000	+	1257.47i	−0.0243318	+	0.0421439i
$963$	−1677.00	+	2904.65i	−0.0561169	+	0.0971973i
$964$	8354.00	+	14469.6i	0.279112	+	0.483437i
$965$		0			0
$966$	119.000	−	230.363i	0.00396352	−	0.00767267i
$967$	−14816.0			−0.492710			−0.246355	−	0.969180i	$-0.579233\pi$
$967$	−14816.0			−0.492710			−0.246355	+	0.969180i	$0.579233\pi$
$968$	424.000	+	734.390i	0.0140784	+	0.0243845i
$969$	4041.50	−	7000.08i	0.133985	−	0.232069i
$970$		0			0
$971$	8437.50	+	14614.2i	0.278859	+	0.482998i	0.971102	−	0.238667i	$-0.0767104\pi$
$971$	8437.50	+	14614.2i	0.278859	+	0.482998i	−0.692242	+	0.721665i	$0.743377\pi$
$972$	8320.00			0.274552
$973$	280.000	+	436.477i	0.00922548	+	0.0143811i
$974$	29906.0			0.983830
$975$		0			0
$976$	−408.000	+	706.677i	−0.0133809	+	0.0231764i
$977$	−7918.50	+	13715.2i	−0.259299	+	0.449119i	−0.966054	−	0.258339i	$-0.916825\pi$
$977$	−7918.50	+	13715.2i	−0.259299	+	0.449119i	0.706755	+	0.707458i	$0.250158\pi$
$978$	−2251.00	−	3898.85i	−0.0735982	−	0.127476i
$979$	−30555.0			−0.997489
$980$		0			0
$981$	25090.0			0.816577
$982$	−14352.0	−	24858.4i	−0.466386	−	0.807804i
$983$	4957.50	−	8586.64i	0.160854	−	0.278608i	−0.774321	−	0.632793i	$-0.781908\pi$
$983$	4957.50	−	8586.64i	0.160854	−	0.278608i	0.935175	+	0.354185i	$0.115242\pi$
$984$	1992.00	−	3450.25i	0.0645352	−	0.111778i
$985$		0			0
$986$	−12508.0			−0.403992
$987$	1710.00	+	2665.63i	0.0551468	+	0.0859654i
$988$	−36168.0			−1.16463
$989$	910.000	+	1576.17i	0.0292582	+	0.0506766i
$990$		0			0
$991$	21840.5	−	37828.9i	0.700087	−	1.21259i	−0.268348	−	0.963322i	$-0.586478\pi$
$991$	21840.5	−	37828.9i	0.700087	−	1.21259i	0.968435	−	0.249265i	$-0.0801889\pi$
$992$	−1200.00	−	2078.46i	−0.0384073	−	0.0665234i
$993$	−6571.00			−0.209994
$994$	−13328.0	+	25800.6i	−0.425290	+	0.823286i
$995$		0			0
$996$	1864.00	+	3228.54i	0.0593003	+	0.102711i
$997$	−23556.5	+	40801.1i	−0.748287	+	1.29607i	0.200357	+	0.979723i	$0.435790\pi$
$997$	−23556.5	+	40801.1i	−0.748287	+	1.29607i	−0.948643	+	0.316348i	$0.897543\pi$
$998$	5531.00	−	9579.97i	0.175432	−	0.303856i
$999$	−291.500	−	504.893i	−0.00923188	−	0.0159901i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.4.e.b.151.1		2
5.2	odd	4		350.4.j.d.249.2		4
5.3	odd	4		350.4.j.d.249.1		4
5.4	even	2		14.4.c.b.11.1	yes	2
7.2	even	3	inner	350.4.e.b.51.1		2
7.3	odd	6		2450.4.a.bf.1.1		1
7.4	even	3		2450.4.a.bh.1.1		1
15.14	odd	2		126.4.g.c.109.1		2
20.19	odd	2		112.4.i.b.81.1		2
35.2	odd	12		350.4.j.d.149.1		4
35.4	even	6		98.4.a.b.1.1		1
35.9	even	6		14.4.c.b.9.1	✓	2
35.19	odd	6		98.4.c.e.79.1		2
35.23	odd	12		350.4.j.d.149.2		4
35.24	odd	6		98.4.a.c.1.1		1
35.34	odd	2		98.4.c.e.67.1		2
40.19	odd	2		448.4.i.d.193.1		2
40.29	even	2		448.4.i.c.193.1		2
105.44	odd	6		126.4.g.c.37.1		2
105.59	even	6		882.4.a.p.1.1		1
105.74	odd	6		882.4.a.k.1.1		1
105.89	even	6		882.4.g.d.667.1		2
105.104	even	2		882.4.g.d.361.1		2
140.39	odd	6		784.4.a.l.1.1		1
140.59	even	6		784.4.a.j.1.1		1
140.79	odd	6		112.4.i.b.65.1		2
280.149	even	6		448.4.i.c.65.1		2
280.219	odd	6		448.4.i.d.65.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.4.c.b.9.1	✓	2	35.9	even	6
14.4.c.b.11.1	yes	2	5.4	even	2
98.4.a.b.1.1		1	35.4	even	6
98.4.a.c.1.1		1	35.24	odd	6
98.4.c.e.67.1		2	35.34	odd	2
98.4.c.e.79.1		2	35.19	odd	6
112.4.i.b.65.1		2	140.79	odd	6
112.4.i.b.81.1		2	20.19	odd	2
126.4.g.c.37.1		2	105.44	odd	6
126.4.g.c.109.1		2	15.14	odd	2
350.4.e.b.51.1		2	7.2	even	3	inner
350.4.e.b.151.1		2	1.1	even	1	trivial
350.4.j.d.149.1		4	35.2	odd	12
350.4.j.d.149.2		4	35.23	odd	12
350.4.j.d.249.1		4	5.3	odd	4
350.4.j.d.249.2		4	5.2	odd	4
448.4.i.c.65.1		2	280.149	even	6
448.4.i.c.193.1		2	40.29	even	2
448.4.i.d.65.1		2	280.219	odd	6
448.4.i.d.193.1		2	40.19	odd	2
784.4.a.j.1.1		1	140.59	even	6
784.4.a.l.1.1		1	140.39	odd	6
882.4.a.k.1.1		1	105.74	odd	6
882.4.a.p.1.1		1	105.59	even	6
882.4.g.d.361.1		2	105.104	even	2
882.4.g.d.667.1		2	105.89	even	6
2450.4.a.bf.1.1		1	7.3	odd	6
2450.4.a.bh.1.1		1	7.4	even	3

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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	350.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-2.00000 + 3.46410i) q^{4} +2.00000 q^{6} +(10.0000 + 15.5885i) q^{7} +8.00000 q^{8} +(13.0000 + 22.5167i) q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-2.00000 + 3.46410i) q^{4} +2.00000 q^{6} +(10.0000 + 15.5885i) q^{7} +8.00000 q^{8} +(13.0000 + 22.5167i) q^{9} +(-17.5000 + 30.3109i) q^{11} +(-2.00000 - 3.46410i) q^{12} -66.0000 q^{13} +(17.0000 - 32.9090i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(29.5000 - 51.0955i) q^{17} +(26.0000 - 45.0333i) q^{18} +(-68.5000 - 118.645i) q^{19} +(-18.5000 + 0.866025i) q^{21} +70.0000 q^{22} +(-3.50000 - 6.06218i) q^{23} +(-4.00000 + 6.92820i) q^{24} +(66.0000 + 114.315i) q^{26} -53.0000 q^{27} +(-74.0000 + 3.46410i) q^{28} +106.000 q^{29} +(-37.5000 + 64.9519i) q^{31} +(-16.0000 + 27.7128i) q^{32} +(-17.5000 - 30.3109i) q^{33} -118.000 q^{34} -104.000 q^{36} +(5.50000 + 9.52628i) q^{37} +(-137.000 + 237.291i) q^{38} +(33.0000 - 57.1577i) q^{39} -498.000 q^{41} +(20.0000 + 31.1769i) q^{42} -260.000 q^{43} +(-70.0000 - 121.244i) q^{44} +(-7.00000 + 12.1244i) q^{46} +(-85.5000 - 148.090i) q^{47} +16.0000 q^{48} +(-143.000 + 311.769i) q^{49} +(29.5000 + 51.0955i) q^{51} +(132.000 - 228.631i) q^{52} +(-208.500 + 361.133i) q^{53} +(53.0000 + 91.7987i) q^{54} +(80.0000 + 124.708i) q^{56} +137.000 q^{57} +(-106.000 - 183.597i) q^{58} +(8.50000 - 14.7224i) q^{59} +(-25.5000 - 44.1673i) q^{61} +150.000 q^{62} +(-221.000 + 427.817i) q^{63} +64.0000 q^{64} +(-35.0000 + 60.6218i) q^{66} +(219.500 - 380.185i) q^{67} +(118.000 + 204.382i) q^{68} +7.00000 q^{69} -784.000 q^{71} +(104.000 + 180.133i) q^{72} +(147.500 - 255.477i) q^{73} +(11.0000 - 19.0526i) q^{74} +548.000 q^{76} +(-647.500 + 30.3109i) q^{77} -132.000 q^{78} +(247.500 + 428.683i) q^{79} +(-324.500 + 562.050i) q^{81} +(498.000 + 862.561i) q^{82} -932.000 q^{83} +(34.0000 - 65.8179i) q^{84} +(260.000 + 450.333i) q^{86} +(-53.0000 + 91.7987i) q^{87} +(-140.000 + 242.487i) q^{88} +(436.500 + 756.040i) q^{89} +(-660.000 - 1028.84i) q^{91} +28.0000 q^{92} +(-37.5000 - 64.9519i) q^{93} +(-171.000 + 296.181i) q^{94} +(-16.0000 - 27.7128i) q^{96} +290.000 q^{97} +(683.000 - 64.0859i) q^{98} -910.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - q^{3} - 4 q^{4} + 4 q^{6} + 20 q^{7} + 16 q^{8} + 26 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - q^3 - 4 * q^4 + 4 * q^6 + 20 * q^7 + 16 * q^8 + 26 * q^9	\( 2 q - 2 q^{2} - q^{3} - 4 q^{4} + 4 q^{6} + 20 q^{7} + 16 q^{8} + 26 q^{9} - 35 q^{11} - 4 q^{12} - 132 q^{13} + 34 q^{14} - 16 q^{16} + 59 q^{17} + 52 q^{18} - 137 q^{19} - 37 q^{21} + 140 q^{22} - 7 q^{23} - 8 q^{24} + 132 q^{26} - 106 q^{27} - 148 q^{28} + 212 q^{29} - 75 q^{31} - 32 q^{32} - 35 q^{33} - 236 q^{34} - 208 q^{36} + 11 q^{37} - 274 q^{38} + 66 q^{39} - 996 q^{41} + 40 q^{42} - 520 q^{43} - 140 q^{44} - 14 q^{46} - 171 q^{47} + 32 q^{48} - 286 q^{49} + 59 q^{51} + 264 q^{52} - 417 q^{53} + 106 q^{54} + 160 q^{56} + 274 q^{57} - 212 q^{58} + 17 q^{59} - 51 q^{61} + 300 q^{62} - 442 q^{63} + 128 q^{64} - 70 q^{66} + 439 q^{67} + 236 q^{68} + 14 q^{69} - 1568 q^{71} + 208 q^{72} + 295 q^{73} + 22 q^{74} + 1096 q^{76} - 1295 q^{77} - 264 q^{78} + 495 q^{79} - 649 q^{81} + 996 q^{82} - 1864 q^{83} + 68 q^{84} + 520 q^{86} - 106 q^{87} - 280 q^{88} + 873 q^{89} - 1320 q^{91} + 56 q^{92} - 75 q^{93} - 342 q^{94} - 32 q^{96} + 580 q^{97} + 1366 q^{98} - 1820 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - q^3 - 4 * q^4 + 4 * q^6 + 20 * q^7 + 16 * q^8 + 26 * q^9 - 35 * q^11 - 4 * q^12 - 132 * q^13 + 34 * q^14 - 16 * q^16 + 59 * q^17 + 52 * q^18 - 137 * q^19 - 37 * q^21 + 140 * q^22 - 7 * q^23 - 8 * q^24 + 132 * q^26 - 106 * q^27 - 148 * q^28 + 212 * q^29 - 75 * q^31 - 32 * q^32 - 35 * q^33 - 236 * q^34 - 208 * q^36 + 11 * q^37 - 274 * q^38 + 66 * q^39 - 996 * q^41 + 40 * q^42 - 520 * q^43 - 140 * q^44 - 14 * q^46 - 171 * q^47 + 32 * q^48 - 286 * q^49 + 59 * q^51 + 264 * q^52 - 417 * q^53 + 106 * q^54 + 160 * q^56 + 274 * q^57 - 212 * q^58 + 17 * q^59 - 51 * q^61 + 300 * q^62 - 442 * q^63 + 128 * q^64 - 70 * q^66 + 439 * q^67 + 236 * q^68 + 14 * q^69 - 1568 * q^71 + 208 * q^72 + 295 * q^73 + 22 * q^74 + 1096 * q^76 - 1295 * q^77 - 264 * q^78 + 495 * q^79 - 649 * q^81 + 996 * q^82 - 1864 * q^83 + 68 * q^84 + 520 * q^86 - 106 * q^87 - 280 * q^88 + 873 * q^89 - 1320 * q^91 + 56 * q^92 - 75 * q^93 - 342 * q^94 - 32 * q^96 + 580 * q^97 + 1366 * q^98 - 1820 * q^99

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