LMFDB - Embedded newform 98.4.c.e.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,4,Mod(67,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("98.67");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	98.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.78218718056$
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			67.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	98.67
Dual form			98.4.c.e.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(3.50000 + 6.06218i) q^{5} -2.00000 q^{6} -8.00000 q^{8} +(13.0000 + 22.5167i) q^{9} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(3.50000 + 6.06218i) q^{5} -2.00000 q^{6} -8.00000 q^{8} +(13.0000 + 22.5167i) q^{9} +(-7.00000 + 12.1244i) q^{10} +(-17.5000 + 30.3109i) q^{11} +(-2.00000 - 3.46410i) q^{12} -66.0000 q^{13} -7.00000 q^{15} +(-8.00000 - 13.8564i) q^{16} +(29.5000 - 51.0955i) q^{17} +(-26.0000 + 45.0333i) q^{18} +(68.5000 + 118.645i) q^{19} -28.0000 q^{20} -70.0000 q^{22} +(3.50000 + 6.06218i) q^{23} +(4.00000 - 6.92820i) q^{24} +(38.0000 - 65.8179i) q^{25} +(-66.0000 - 114.315i) q^{26} -53.0000 q^{27} +106.000 q^{29} +(-7.00000 - 12.1244i) q^{30} +(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} +(-28.0000 - 48.4974i) q^{40} +498.000 q^{41} +260.000 q^{43} +(-70.0000 - 121.244i) q^{44} +(-91.0000 + 157.617i) q^{45} +(-7.00000 + 12.1244i) q^{46} +(-85.5000 - 148.090i) q^{47} +16.0000 q^{48} +152.000 q^{50} +(29.5000 + 51.0955i) q^{51} +(132.000 - 228.631i) q^{52} +(208.500 - 361.133i) q^{53} +(-53.0000 - 91.7987i) q^{54} -245.000 q^{55} -137.000 q^{57} +(106.000 + 183.597i) q^{58} +(-8.50000 + 14.7224i) q^{59} +(14.0000 - 24.2487i) q^{60} +(25.5000 + 44.1673i) q^{61} +150.000 q^{62} +64.0000 q^{64} +(-231.000 - 400.104i) q^{65} +(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} +(38.0000 + 65.8179i) q^{75} -548.000 q^{76} +132.000 q^{78} +(247.500 + 428.683i) q^{79} +(56.0000 - 96.9948i) q^{80} +(-324.500 + 562.050i) q^{81} +(498.000 + 862.561i) q^{82} -932.000 q^{83} +413.000 q^{85} +(260.000 + 450.333i) q^{86} +(-53.0000 + 91.7987i) q^{87} +(140.000 - 242.487i) q^{88} +(-436.500 - 756.040i) q^{89} -364.000 q^{90} -28.0000 q^{92} +(37.5000 + 64.9519i) q^{93} +(171.000 - 296.181i) q^{94} +(-479.500 + 830.518i) q^{95} +(16.0000 + 27.7128i) q^{96} +290.000 q^{97} -910.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - q^{3} - 4 q^{4} + 7 q^{5} - 4 q^{6} - 16 q^{8} + 26 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - q^3 - 4 * q^4 + 7 * q^5 - 4 * q^6 - 16 * q^8 + 26 * q^9	\( 2 q + 2 q^{2} - q^{3} - 4 q^{4} + 7 q^{5} - 4 q^{6} - 16 q^{8} + 26 q^{9} - 14 q^{10} - 35 q^{11} - 4 q^{12} - 132 q^{13} - 14 q^{15} - 16 q^{16} + 59 q^{17} - 52 q^{18} + 137 q^{19} - 56 q^{20} - 140 q^{22} + 7 q^{23} + 8 q^{24} + 76 q^{25} - 132 q^{26} - 106 q^{27} + 212 q^{29} - 14 q^{30} + 75 q^{31} + 32 q^{32} - 35 q^{33} + 236 q^{34} - 208 q^{36} - 11 q^{37} - 274 q^{38} + 66 q^{39} - 56 q^{40} + 996 q^{41} + 520 q^{43} - 140 q^{44} - 182 q^{45} - 14 q^{46} - 171 q^{47} + 32 q^{48} + 304 q^{50} + 59 q^{51} + 264 q^{52} + 417 q^{53} - 106 q^{54} - 490 q^{55} - 274 q^{57} + 212 q^{58} - 17 q^{59} + 28 q^{60} + 51 q^{61} + 300 q^{62} + 128 q^{64} - 462 q^{65} + 70 q^{66} - 439 q^{67} + 236 q^{68} - 14 q^{69} - 1568 q^{71} - 208 q^{72} + 295 q^{73} + 22 q^{74} + 76 q^{75} - 1096 q^{76} + 264 q^{78} + 495 q^{79} + 112 q^{80} - 649 q^{81} + 996 q^{82} - 1864 q^{83} + 826 q^{85} + 520 q^{86} - 106 q^{87} + 280 q^{88} - 873 q^{89} - 728 q^{90} - 56 q^{92} + 75 q^{93} + 342 q^{94} - 959 q^{95} + 32 q^{96} + 580 q^{97} - 1820 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - q^3 - 4 * q^4 + 7 * q^5 - 4 * q^6 - 16 * q^8 + 26 * q^9 - 14 * q^10 - 35 * q^11 - 4 * q^12 - 132 * q^13 - 14 * q^15 - 16 * q^16 + 59 * q^17 - 52 * q^18 + 137 * q^19 - 56 * q^20 - 140 * q^22 + 7 * q^23 + 8 * q^24 + 76 * q^25 - 132 * q^26 - 106 * q^27 + 212 * q^29 - 14 * q^30 + 75 * q^31 + 32 * q^32 - 35 * q^33 + 236 * q^34 - 208 * q^36 - 11 * q^37 - 274 * q^38 + 66 * q^39 - 56 * q^40 + 996 * q^41 + 520 * q^43 - 140 * q^44 - 182 * q^45 - 14 * q^46 - 171 * q^47 + 32 * q^48 + 304 * q^50 + 59 * q^51 + 264 * q^52 + 417 * q^53 - 106 * q^54 - 490 * q^55 - 274 * q^57 + 212 * q^58 - 17 * q^59 + 28 * q^60 + 51 * q^61 + 300 * q^62 + 128 * q^64 - 462 * q^65 + 70 * q^66 - 439 * q^67 + 236 * q^68 - 14 * q^69 - 1568 * q^71 - 208 * q^72 + 295 * q^73 + 22 * q^74 + 76 * q^75 - 1096 * q^76 + 264 * q^78 + 495 * q^79 + 112 * q^80 - 649 * q^81 + 996 * q^82 - 1864 * q^83 + 826 * q^85 + 520 * q^86 - 106 * q^87 + 280 * q^88 - 873 * q^89 - 728 * q^90 - 56 * q^92 + 75 * q^93 + 342 * q^94 - 959 * q^95 + 32 * q^96 + 580 * q^97 - 1820 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	1.00000	+	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
$5$	3.50000	+	6.06218i	0.313050	+	0.542218i	0.979021	−	0.203760i	$-0.0653161\pi$
$5$	3.50000	+	6.06218i	0.313050	+	0.542218i	−0.665971	+	0.745977i	$0.731983\pi$
$6$	−2.00000			−0.136083
$7$		0			0
$7$		0			0
$8$	−8.00000			−0.353553
$9$	13.0000	+	22.5167i	0.481481	+	0.833950i
$10$	−7.00000	+	12.1244i	−0.221359	+	0.383406i
$11$	−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	$0.748624\pi$
$14$		0			0
$15$	−7.00000			−0.120493
$16$	−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	$0.143347\pi$
$19$	68.5000	+	118.645i	0.827104	+	1.43259i	−0.0731965	+	0.997318i	$0.523320\pi$
$20$	−28.0000			−0.313050
$21$		0			0
$22$	−70.0000			−0.678366
$23$	3.50000	+	6.06218i	0.0317305	+	0.0549588i	0.881455	−	0.472269i	$-0.156565\pi$
$23$	3.50000	+	6.06218i	0.0317305	+	0.0549588i	−0.849724	+	0.527228i	$0.823232\pi$
$24$	4.00000	−	6.92820i	0.0340207	−	0.0589256i
$25$	38.0000	−	65.8179i	0.304000	−	0.526543i
$26$	−66.0000	−	114.315i	−0.497833	−	0.862273i
$27$	−53.0000			−0.377772
$28$		0			0
$29$	106.000			0.678748			0.339374	−	0.940651i	$-0.389785\pi$
$29$	106.000			0.678748			0.339374	+	0.940651i	$0.389785\pi$
$30$	−7.00000	−	12.1244i	−0.0426006	−	0.0737865i
$31$	37.5000	−	64.9519i	0.217264	−	0.376313i	−0.736706	−	0.676213i	$-0.763620\pi$
$31$	37.5000	−	64.9519i	0.217264	−	0.376313i	0.953971	+	0.299900i	$0.0969533\pi$
$32$	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	0.853548	−	0.521014i	$-0.174446\pi$
$37$	−5.50000	−	9.52628i	−0.0244377	−	0.0423273i	−0.877986	+	0.478687i	$0.841113\pi$
$38$	−137.000	+	237.291i	−0.584851	+	1.01299i
$39$	33.0000	−	57.1577i	0.135493	−	0.234681i
$40$	−28.0000	−	48.4974i	−0.110680	−	0.191703i
$41$	498.000			1.89694			0.948470	−	0.316867i	$-0.102631\pi$
$41$	498.000			1.89694			0.948470	+	0.316867i	$0.102631\pi$
$42$		0			0
$43$	260.000			0.922084			0.461042	−	0.887378i	$-0.347476\pi$
$43$	260.000			0.922084			0.461042	+	0.887378i	$0.347476\pi$
$44$	−70.0000	−	121.244i	−0.239839	−	0.415413i
$45$	−91.0000	+	157.617i	−0.301455	+	0.522136i
$46$	−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
$49$		0			0
$50$	152.000			0.429921
$51$	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	$-0.651617\pi$
$53$	208.500	−	361.133i	0.540371	−	0.935951i	0.998883	−	0.0472619i	$-0.0150495\pi$
$54$	−53.0000	−	91.7987i	−0.133563	−	0.231337i
$55$	−245.000			−0.600651
$56$		0			0
$57$	−137.000			−0.318353
$58$	106.000	+	183.597i	0.239974	+	0.415647i
$59$	−8.50000	+	14.7224i	−0.0187560	+	0.0324864i	−0.875251	−	0.483669i	$-0.839304\pi$
$59$	−8.50000	+	14.7224i	−0.0187560	+	0.0324864i	0.856495	+	0.516155i	$0.172637\pi$
$60$	14.0000	−	24.2487i	0.0301232	−	0.0521749i
$61$	25.5000	+	44.1673i	0.0535236	+	0.0927056i	0.891546	−	0.452930i	$-0.149621\pi$
$61$	25.5000	+	44.1673i	0.0535236	+	0.0927056i	−0.838022	+	0.545636i	$0.816288\pi$
$62$	150.000			0.307258
$63$		0			0
$64$	64.0000			0.125000
$65$	−231.000	−	400.104i	−0.440800	−	0.763489i
$66$	35.0000	−	60.6218i	0.0652758	−	0.113061i
$67$	−219.500	+	380.185i	−0.400242	+	0.693239i	−0.993755	−	0.111585i	$-0.964407\pi$
$67$	−219.500	+	380.185i	−0.400242	+	0.693239i	0.593513	+	0.804824i	$0.297740\pi$
$68$	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
$75$	38.0000	+	65.8179i	0.0585048	+	0.101333i
$76$	−548.000			−0.827104
$77$		0			0
$78$	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	$0.718672\pi$
$80$	56.0000	−	96.9948i	0.0782624	−	0.135554i
$81$	−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	$0.711356\pi$
$84$		0			0
$85$	413.000			0.527013
$86$	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	$-0.992645\pi$
$89$	−436.500	−	756.040i	−0.519875	−	0.900451i	0.479858	−	0.877346i	$-0.340688\pi$
$90$	−364.000			−0.426322
$91$		0			0
$92$	−28.0000			−0.0317305
$93$	37.5000	+	64.9519i	0.0418126	+	0.0724215i
$94$	171.000	−	296.181i	0.187631	−	0.324986i
$95$	−479.500	+	830.518i	−0.517849	+	0.896941i
$96$	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	$0.451500\pi$
$98$		0			0
$99$	−910.000			−0.923823
$100$	152.000	+	263.272i	0.152000	+	0.263272i
$101$	−542.500	+	939.638i	−0.534463	+	0.925717i	0.464726	+	0.885454i	$0.346153\pi$
$101$	−542.500	+	939.638i	−0.534463	+	0.925717i	−0.999189	+	0.0402627i	$0.987181\pi$
$102$	−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	0.835416	−	0.549618i	$-0.185227\pi$
$107$	−64.5000	−	111.717i	−0.0582752	−	0.100936i	−0.893691	+	0.448682i	$0.851893\pi$
$108$	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	$0.0272952\pi$
$110$	−245.000	−	424.352i	−0.212362	−	0.367822i
$111$	11.0000			0.00940607
$112$		0			0
$113$	−50.0000			−0.0416248			−0.0208124	−	0.999783i	$-0.506625\pi$
$113$	−50.0000			−0.0416248			−0.0208124	+	0.999783i	$0.506625\pi$
$114$	−137.000	−	237.291i	−0.112555	−	0.194950i
$115$	−24.5000	+	42.4352i	−0.0198664	+	0.0344096i
$116$	−212.000	+	367.195i	−0.169687	+	0.293907i
$117$	−858.000	−	1486.10i	−0.677967	−	1.17427i
$118$	−34.0000			−0.0265250
$119$		0			0
$120$	56.0000			0.0426006
$121$	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
$125$	1407.00			1.00677
$126$		0			0
$127$	936.000			0.653989			0.326994	−	0.945026i	$-0.393964\pi$
$127$	936.000			0.653989			0.326994	+	0.945026i	$0.393964\pi$
$128$	64.0000	+	110.851i	0.0441942	+	0.0765466i
$129$	−130.000	+	225.167i	−0.0887276	+	0.153681i
$130$	462.000	−	800.207i	0.311693	−	0.539868i
$131$	−377.500	−	653.849i	−0.251773	−	0.436084i	0.712241	−	0.701935i	$-0.247680\pi$
$131$	−377.500	−	653.849i	−0.251773	−	0.436084i	−0.964014	+	0.265851i	$0.914347\pi$
$132$	140.000			0.0923139
$133$		0			0
$134$	−878.000			−0.566027
$135$	−185.500	−	321.295i	−0.118261	−	0.204835i
$136$	−236.000	+	408.764i	−0.148800	+	0.257730i
$137$	1178.50	−	2041.22i	0.734935	−	1.27294i	−0.219817	−	0.975541i	$-0.570546\pi$
$137$	1178.50	−	2041.22i	0.734935	−	1.27294i	0.954752	−	0.297403i	$-0.0961205\pi$
$138$	−7.00000	−	12.1244i	−0.00431797	−	0.00747894i
$139$	−28.0000			−0.0170858			−0.00854291	−	0.999964i	$-0.502719\pi$
$139$	−28.0000			−0.0170858			−0.00854291	+	0.999964i	$0.502719\pi$
$140$		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
$145$	371.000	+	642.591i	0.212482	+	0.368029i
$146$	590.000			0.334443
$147$		0			0
$148$	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	$-0.383988\pi$
$150$	−76.0000	+	131.636i	−0.0413692	+	0.0716535i
$151$	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
$154$		0			0
$155$	525.000			0.272058
$156$	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
$160$	224.000			0.110680
$161$		0			0
$162$	−1298.00			−0.629509
$163$	1125.50	+	1949.42i	0.540834	+	0.936752i	0.998856	+	0.0478115i	$0.0152247\pi$
$163$	1125.50	+	1949.42i	0.540834	+	0.936752i	−0.458022	+	0.888941i	$0.651442\pi$
$164$	−996.000	+	1725.12i	−0.474235	+	0.821399i
$165$	122.500	−	212.176i	0.0577976	−	0.100108i
$166$	−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	$0.723532\pi$
$168$		0			0
$169$	2159.00			0.982704
$170$	413.000	+	715.337i	0.186327	+	0.322728i
$171$	−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	$0.995675\pi$
$180$	−364.000	−	630.466i	−0.150728	−	0.261068i
$181$	1170.00			0.480472			0.240236	−	0.970715i	$-0.422775\pi$
$181$	1170.00			0.480472			0.240236	+	0.970715i	$0.422775\pi$
$182$		0			0
$183$	−51.0000			−0.0206012
$184$	−28.0000	−	48.4974i	−0.0112184	−	0.0194309i
$185$	38.5000	−	66.6840i	0.0153004	−	0.0265011i
$186$	−75.0000	+	129.904i	−0.0295660	+	0.0512097i
$187$	1032.50	+	1788.34i	0.403764	+	0.699340i
$188$	684.000			0.265350
$189$		0			0
$190$	−1918.00			−0.732349
$191$	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	−0.869270	−	0.494337i	$-0.835411\pi$
$193$	−17.5000	+	30.3109i	−0.00652683	+	0.0113048i	0.862744	+	0.505642i	$0.168744\pi$
$194$	290.000	+	502.295i	0.107324	+	0.185890i
$195$	462.000			0.169664
$196$		0			0
$197$	−2734.00			−0.988779			−0.494389	−	0.869241i	$-0.664608\pi$
$197$	−2734.00			−0.988779			−0.494389	+	0.869241i	$0.664608\pi$
$198$	−910.000	−	1576.17i	−0.326621	−	0.565724i
$199$	1121.50	−	1942.49i	0.399503	−	0.691959i	−0.594162	−	0.804345i	$-0.702516\pi$
$199$	1121.50	−	1942.49i	0.399503	−	0.691959i	0.993665	+	0.112387i	$0.0358495\pi$
$200$	−304.000	+	526.543i	−0.107480	+	0.186161i
$201$	−219.500	−	380.185i	−0.0770265	−	0.133414i
$202$	−2170.00			−0.755845
$203$		0			0
$204$	−236.000			−0.0809966
$205$	1743.00	+	3018.96i	0.593836	+	1.02855i
$206$	−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
$215$	910.000	+	1576.17i	0.288658	+	0.499970i
$216$	424.000			0.133563
$217$		0			0
$218$	1930.00			0.599615
$219$	147.500	+	255.477i	0.0455120	+	0.0788291i
$220$	490.000	−	848.705i	0.150163	−	0.260089i
$221$	−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	$0.598287\pi$
$224$		0			0
$225$	1976.00			0.585481
$226$	−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	0.923341	−	0.383980i	$-0.125447\pi$
$229$	447.500	+	775.093i	0.129134	+	0.223666i	−0.794207	+	0.607647i	$0.792114\pi$
$230$	−98.0000			−0.0280953
$231$		0			0
$232$	−848.000			−0.239974
$233$	−893.500	−	1547.59i	−0.251224	−	0.435132i	0.712639	−	0.701531i	$-0.247500\pi$
$233$	−893.500	−	1547.59i	−0.251224	−	0.435132i	−0.963863	+	0.266398i	$0.914166\pi$
$234$	1716.00	−	2972.20i	0.479395	−	0.830336i
$235$	598.500	−	1036.63i	0.166135	−	0.287755i
$236$	−34.0000	−	58.8897i	−0.00937801	−	0.0162432i
$237$	−495.000			−0.135670
$238$		0			0
$239$	−5100.00			−1.38030			−0.690150	−	0.723667i	$-0.742455\pi$
$239$	−5100.00			−1.38030			−0.690150	+	0.723667i	$0.742455\pi$
$240$	56.0000	+	96.9948i	0.0150616	+	0.0260875i
$241$	−2088.50	+	3617.39i	−0.558225	+	0.966873i	0.439420	+	0.898282i	$0.355184\pi$
$241$	−2088.50	+	3617.39i	−0.558225	+	0.966873i	−0.997645	+	0.0685917i	$0.978149\pi$
$242$	−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
$250$	1407.00	+	2437.00i	0.355946	+	0.616517i
$251$	4680.00			1.17689			0.588444	−	0.808538i	$-0.299741\pi$
$251$	4680.00			1.17689			0.588444	+	0.808538i	$0.299741\pi$
$252$		0			0
$253$	−245.000			−0.0608815
$254$	936.000	+	1621.20i	0.231220	+	0.400485i
$255$	−206.500	+	357.668i	−0.0507119	+	0.0878356i
$256$	−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
$259$		0			0
$260$	1848.00			0.440800
$261$	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	$-0.657635\pi$
$263$	2236.50	−	3873.73i	0.524367	−	0.908230i	0.999598	−	0.0283689i	$-0.00903130\pi$
$264$	140.000	+	242.487i	0.0326379	+	0.0565305i
$265$	2919.00			0.676652
$266$		0			0
$267$	873.000			0.200100
$268$	−878.000	−	1520.74i	−0.200121	−	0.346619i
$269$	987.500	−	1710.40i	0.223825	−	0.387676i	−0.732141	−	0.681153i	$-0.761479\pi$
$269$	987.500	−	1710.40i	0.223825	−	0.387676i	0.955966	+	0.293476i	$0.0948122\pi$
$270$	371.000	−	642.591i	0.0836235	−	0.144840i
$271$	−4219.50	−	7308.39i	−0.945817	−	1.63820i	−0.754107	−	0.656751i	$-0.771930\pi$
$271$	−4219.50	−	7308.39i	−0.945817	−	1.63820i	−0.191710	−	0.981452i	$-0.561403\pi$
$272$	−944.000			−0.210435
$273$		0			0
$274$	4714.00			1.03935
$275$	1330.00	+	2303.63i	0.291644	+	0.505142i
$276$	14.0000	−	24.2487i	0.00305326	−	0.00528841i
$277$	−263.500	+	456.395i	−0.0571559	+	0.0989969i	−0.893188	−	0.449684i	$-0.851537\pi$
$277$	−263.500	+	456.395i	−0.0571559	+	0.0989969i	0.836032	+	0.548681i	$0.184870\pi$
$278$	−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
$285$	−479.500	−	830.518i	−0.0996601	−	0.172616i
$286$	4620.00			0.955197
$287$		0			0
$288$	832.000			0.170229
$289$	716.000	+	1240.15i	0.145736	+	0.252422i
$290$	−742.000	+	1285.18i	−0.150247	+	0.260236i
$291$	−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	$0.510093\pi$
$294$		0			0
$295$	−119.000			−0.0234863
$296$	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
$300$	−304.000			−0.0585048
$301$		0			0
$302$	2218.00			0.422621
$303$	−542.500	−	939.638i	−0.102857	−	0.178154i
$304$	1096.00	−	1898.33i	0.206776	−	0.358147i
$305$	−178.500	+	309.171i	−0.0335111	+	0.0580429i
$306$	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	$0.227203\pi$
$308$		0			0
$309$	−1553.00			−0.285913
$310$	525.000	+	909.327i	0.0961871	+	0.166601i
$311$	−464.500	+	804.538i	−0.0846925	+	0.146692i	−0.905260	−	0.424858i	$-0.860324\pi$
$311$	−464.500	+	804.538i	−0.0846925	+	0.146692i	0.820568	+	0.571549i	$0.193657\pi$
$312$	−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	$-0.949012\pi$
$317$	−3565.50	−	6175.63i	−0.631730	−	1.09419i	0.355468	−	0.934689i	$-0.384322\pi$
$318$	−417.000	+	722.265i	−0.0735352	+	0.127367i
$319$	−1855.00	+	3212.95i	−0.325580	+	0.563921i
$320$	224.000	+	387.979i	0.0391312	+	0.0677772i
$321$	129.000			0.0224301
$322$		0			0
$323$	8083.00			1.39242
$324$	−1298.00	−	2248.20i	−0.222565	−	0.385494i
$325$	−2508.00	+	4343.98i	−0.428058	+	0.741418i
$326$	−2251.00	+	3898.85i	−0.382427	+	0.662384i
$327$	482.500	+	835.715i	0.0815973	+	0.141331i
$328$	−3984.00			−0.670670
$329$		0			0
$330$	490.000			0.0817382
$331$	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
$335$	−3073.00			−0.501182
$336$		0			0
$337$	−11466.0			−1.85339			−0.926696	−	0.375813i	$-0.877364\pi$
$337$	−11466.0			−1.85339			−0.926696	+	0.375813i	$0.877364\pi$
$338$	2159.00	+	3739.50i	0.347438	+	0.601781i
$339$	25.0000	−	43.3013i	0.00400535	−	0.00693747i
$340$	−826.000	+	1430.67i	−0.131753	+	0.228203i
$341$	1312.50	+	2273.32i	0.208434	+	0.361018i
$342$	−7124.00			−1.12638
$343$		0			0
$344$	−2080.00			−0.326006
$345$	−24.5000	−	42.4352i	−0.00382329	−	0.00662214i
$346$	−1579.00	+	2734.91i	−0.245340	+	0.424941i
$347$	4888.50	−	8467.13i	0.756278	−	1.30991i	−0.188459	−	0.982081i	$-0.560349\pi$
$347$	4888.50	−	8467.13i	0.756278	−	1.30991i	0.944737	−	0.327831i	$-0.106318\pi$
$348$	−212.000	−	367.195i	−0.0326563	−	0.0565624i
$349$	−11914.0			−1.82734			−0.913670	−	0.406456i	$-0.866764\pi$
$349$	−11914.0			−1.82734			−0.913670	+	0.406456i	$0.866764\pi$
$350$		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
$355$	−2744.00	−	4752.75i	−0.410243	−	0.710562i
$356$	3492.00			0.519875
$357$		0			0
$358$	−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	$-0.371105\pi$
$360$	728.000	−	1260.93i	0.106580	−	0.184603i
$361$	−5955.00	+	10314.4i	−0.868202	+	1.50377i
$362$	1170.00	+	2026.50i	0.169872	+	0.294228i
$363$	−106.000			−0.0153266
$364$		0			0
$365$	2065.00			0.296129
$366$	−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
$370$	154.000			0.0216381
$371$		0			0
$372$	−300.000			−0.0418126
$373$	2054.50	+	3558.50i	0.285196	+	0.493973i	0.972657	−	0.232248i	$-0.0746081\pi$
$373$	2054.50	+	3558.50i	0.285196	+	0.493973i	−0.687461	+	0.726221i	$0.741275\pi$
$374$	−2065.00	+	3576.68i	−0.285504	+	0.494508i
$375$	−703.500	+	1218.50i	−0.0968762	+	0.167795i
$376$	684.000	+	1184.72i	0.0938154	+	0.162493i
$377$	−6996.00			−0.955736
$378$		0			0
$379$	−3488.00			−0.472735			−0.236367	−	0.971664i	$-0.575957\pi$
$379$	−3488.00			−0.472735			−0.236367	+	0.971664i	$0.575957\pi$
$380$	−1918.00	−	3322.07i	−0.258925	−	0.448470i
$381$	−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	$0.170048\pi$
$390$	462.000	+	800.207i	0.0599853	+	0.103898i
$391$	413.000			0.0534177
$392$		0			0
$393$	755.000			0.0969077
$394$	−2734.00	−	4735.43i	−0.349586	−	0.605501i
$395$	−1732.50	+	3000.78i	−0.220687	+	0.382242i
$396$	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
$399$		0			0
$400$	−1216.00			−0.152000
$401$	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
$405$	−4543.00			−0.557391
$406$		0			0
$407$	385.000			0.0468888
$408$	−236.000	−	408.764i	−0.0286366	−	0.0496001i
$409$	−66.5000	+	115.181i	−0.00803964	+	0.0139251i	−0.870017	−	0.493021i	$-0.835892\pi$
$409$	−66.5000	+	115.181i	−0.00803964	+	0.0139251i	0.861978	+	0.506946i	$0.169226\pi$
$410$	−3486.00	+	6037.93i	−0.419906	+	0.727298i
$411$	1178.50	+	2041.22i	0.141438	+	0.244978i
$412$	−6212.00			−0.742823
$413$		0			0
$414$	−364.000			−0.0432117
$415$	−3262.00	−	5649.95i	−0.385844	−	0.668302i
$416$	−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	$-0.377894\pi$
$419$	6420.00			0.748538			0.374269	+	0.927320i	$0.377894\pi$
$420$		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
$425$	−2242.00	−	3883.26i	−0.255889	−	0.443213i
$426$	1568.00			0.178333
$427$		0			0
$428$	516.000			0.0582752
$429$	1155.00	+	2000.52i	0.129986	+	0.225142i
$430$	−1820.00	+	3152.33i	−0.204112	+	0.353532i
$431$	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	$0.475635\pi$
$434$		0			0
$435$	−742.000			−0.0817843
$436$	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	0.781104	−	0.624401i	$-0.214657\pi$
$439$	−1381.50	−	2392.83i	−0.150195	−	0.260145i	−0.931299	+	0.364256i	$0.881323\pi$
$440$	1960.00			0.212362
$441$		0			0
$442$	−7788.00			−0.838094
$443$	−2924.50	−	5065.38i	−0.313651	−	0.543259i	0.665499	−	0.746399i	$-0.268219\pi$
$443$	−2924.50	−	5065.38i	−0.313651	−	0.543259i	−0.979150	+	0.203140i	$0.934885\pi$
$444$	−22.0000	+	38.1051i	−0.00235152	+	0.00407295i
$445$	3055.50	−	5292.28i	0.325493	−	0.563771i
$446$	−2024.00	−	3505.67i	−0.214886	−	0.372194i
$447$	2295.00			0.242841
$448$		0			0
$449$	4582.00			0.481599			0.240799	−	0.970575i	$-0.422590\pi$
$449$	4582.00			0.481599			0.240799	+	0.970575i	$0.422590\pi$
$450$	1976.00	+	3422.53i	0.206999	+	0.358533i
$451$	−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	$-0.965331\pi$
$457$	−5775.50	−	10003.5i	−0.591174	−	1.02394i	0.402901	−	0.915244i	$-0.368002\pi$
$458$	−895.000	+	1550.19i	−0.0913114	+	0.158156i
$459$	−1563.50	+	2708.06i	−0.158993	+	0.275384i
$460$	−98.0000	−	169.741i	−0.00993320	−	0.0172048i
$461$	9494.00			0.959175			0.479587	−	0.877494i	$-0.340786\pi$
$461$	9494.00			0.959175			0.479587	+	0.877494i	$0.340786\pi$
$462$		0			0
$463$	−10160.0			−1.01982			−0.509908	−	0.860229i	$-0.670321\pi$
$463$	−10160.0			−1.01982			−0.509908	+	0.860229i	$0.670321\pi$
$464$	−848.000	−	1468.78i	−0.0848436	−	0.146953i
$465$	−262.500	+	454.663i	−0.0261788	+	0.0453430i
$466$	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
$469$		0			0
$470$	2394.00			0.234951
$471$	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
$475$	10412.0			1.00576
$476$		0			0
$477$	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	$-0.496035\pi$
$479$	9143.50	−	15837.0i	0.872186	−	1.51067i	0.859730	−	0.510748i	$-0.170632\pi$
$480$	−112.000	+	193.990i	−0.0106502	+	0.0184466i
$481$	363.000	+	628.734i	0.0344103	+	0.0596005i
$482$	−8354.00			−0.789449
$483$		0			0
$484$	−424.000			−0.0398197
$485$	1015.00	+	1758.03i	0.0950284	+	0.164594i
$486$	2080.00	−	3602.67i	0.194137	−	0.336256i
$487$	7476.50	−	12949.7i	0.695673	−	1.20494i	−0.274281	−	0.961650i	$-0.588440\pi$
$487$	7476.50	−	12949.7i	0.695673	−	1.20494i	0.969953	−	0.243291i	$-0.0782269\pi$
$488$	−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
$495$	−3185.00	−	5516.58i	−0.289202	−	0.500913i
$496$	−1200.00			−0.108632
$497$		0			0
$498$	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	$0.753528\pi$
$500$	−2814.00	+	4873.99i	−0.251692	+	0.435943i
$501$	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	$0.621432\pi$
$504$		0			0
$505$	−7595.00			−0.669254
$506$	−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	0.809421	−	0.587228i	$-0.199781\pi$
$509$	−1192.50	−	2065.47i	−0.103844	−	0.179863i	−0.913265	+	0.407365i	$0.866448\pi$
$510$	−826.000			−0.0717174
$511$		0			0
$512$	−512.000			−0.0441942
$513$	−3630.50	−	6288.21i	−0.312457	−	0.541192i
$514$	1749.00	−	3029.36i	0.150088	−	0.259960i
$515$	−5435.50	+	9414.56i	−0.465081	+	0.805544i
$516$	−520.000	−	900.666i	−0.0443638	−	0.0768404i
$517$	5985.00			0.509130
$518$		0			0
$519$	−1579.00			−0.133546
$520$	1848.00	+	3200.83i	0.155846	+	0.269934i
$521$	−4576.50	+	7926.73i	−0.384837	+	0.666557i	−0.991747	−	0.128214i	$-0.959076\pi$
$521$	−4576.50	+	7926.73i	−0.384837	+	0.666557i	0.606910	+	0.794771i	$0.292409\pi$
$522$	−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
$530$	2919.00	+	5055.86i	0.239233	+	0.414363i
$531$	−442.000			−0.0361227
$532$		0			0
$533$	−32868.0			−2.67105
$534$	873.000	+	1512.08i	0.0707461	+	0.122536i
$535$	451.500	−	782.021i	0.0364861	−	0.0631957i
$536$	1756.00	−	3041.48i	0.141507	−	0.245097i
$537$	−1225.50	−	2122.63i	−0.0984809	−	0.170574i
$538$	3950.00			0.316536
$539$		0			0
$540$	1484.00			0.118261
$541$	−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
$545$	6755.00			0.530922
$546$		0			0
$547$	4656.00			0.363942			0.181971	−	0.983304i	$-0.441752\pi$
$547$	4656.00			0.363942			0.181971	+	0.983304i	$0.441752\pi$
$548$	4714.00	+	8164.89i	0.367467	+	0.636472i
$549$	−663.000	+	1148.35i	−0.0515413	+	0.0892721i
$550$	−2660.00	+	4607.26i	−0.206223	+	0.357189i
$551$	7261.00	+	12576.4i	0.561396	+	0.972366i
$552$	56.0000			0.00431797
$553$		0			0
$554$	−1054.00			−0.0808306
$555$	38.5000	+	66.6840i	0.00294457	+	0.00510014i
$556$	56.0000	−	96.9948i	0.00427146	−	0.00739838i
$557$	−3501.50	+	6064.78i	−0.266361	+	0.461352i	−0.967919	−	0.251261i	$-0.919155\pi$
$557$	−3501.50	+	6064.78i	−0.266361	+	0.461352i	0.701558	+	0.712612i	$0.252488\pi$
$558$	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
$565$	−175.000	−	303.109i	−0.0130306	−	0.0225697i
$566$	−15898.0			−1.18064
$567$		0			0
$568$	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	$0.751562\pi$
$570$	959.000	−	1661.04i	0.0704703	−	0.122058i
$571$	−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
$574$		0			0
$575$	532.000			0.0385842
$576$	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
$580$	−2968.00			−0.212482
$581$		0			0
$582$	−580.000			−0.0413089
$583$	7297.50	+	12639.6i	0.518407	+	0.897908i
$584$	−1180.00	+	2043.82i	−0.0836109	+	0.144818i
$585$	6006.00	−	10402.7i	0.424474	−	0.735211i
$586$	−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	$0.602998\pi$
$588$		0			0
$589$	10275.0			0.718801
$590$	−119.000	−	206.114i	−0.00830365	−	0.0143823i
$591$	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	$0.915647\pi$
$600$	−304.000	−	526.543i	−0.0206846	−	0.0358267i
$601$	1402.00			0.0951560			0.0475780	−	0.998868i	$-0.484850\pi$
$601$	1402.00			0.0951560			0.0475780	+	0.998868i	$0.484850\pi$
$602$		0			0
$603$	−11414.0			−0.770836
$604$	2218.00	+	3841.69i	0.149419	+	0.258801i
$605$	−371.000	+	642.591i	−0.0249311	+	0.0431819i
$606$	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
$609$		0			0
$610$	−714.000			−0.0473918
$611$	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	−0.999989	−	0.00479285i	$-0.998474\pi$
$613$	−7525.50	+	13034.5i	−0.495844	+	0.858826i	0.504145	+	0.863619i	$0.331808\pi$
$614$	8132.00	+	14085.0i	0.534496	+	0.925775i
$615$	−3486.00			−0.228568
$616$		0			0
$617$	11150.0			0.727524			0.363762	−	0.931492i	$-0.381492\pi$
$617$	11150.0			0.727524			0.363762	+	0.931492i	$0.381492\pi$
$618$	−1553.00	−	2689.87i	−0.101085	−	0.175085i
$619$	1707.50	−	2957.48i	0.110873	−	0.192037i	−0.805250	−	0.592936i	$-0.797969\pi$
$619$	1707.50	−	2957.48i	0.110873	−	0.192037i	0.916122	+	0.400899i	$0.131302\pi$
$620$	−1050.00	+	1818.65i	−0.0680145	+	0.117805i
$621$	−185.500	−	321.295i	−0.0119869	−	0.0207619i
$622$	−1858.00			−0.119773
$623$		0			0
$624$	−1056.00			−0.0677465
$625$	174.500	+	302.243i	0.0111680	+	0.0193435i
$626$	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
$635$	3276.00	+	5674.20i	0.204731	+	0.354604i
$636$	−1668.00			−0.103995
$637$		0			0
$638$	−7420.00			−0.460440
$639$	−10192.0	−	17653.1i	−0.630969	−	1.09287i
$640$	−448.000	+	775.959i	−0.0276699	+	0.0479257i
$641$	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	$0.567466\pi$
$644$		0			0
$645$	−1820.00			−0.111105
$646$	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
$650$	−10032.0			−0.605365
$651$		0			0
$652$	−9004.00			−0.540834
$653$	−2989.50	−	5177.97i	−0.179155	−	0.310305i	0.762436	−	0.647063i	$-0.224003\pi$
$653$	−2989.50	−	5177.97i	−0.179155	−	0.310305i	−0.941591	+	0.336758i	$0.890670\pi$
$654$	−965.000	+	1671.43i	−0.0576980	+	0.0999359i
$655$	2642.50	−	4576.94i	0.157635	−	0.273032i
$656$	−3984.00	−	6900.49i	−0.237117	−	0.410700i
$657$	7670.00			0.455457
$658$		0			0
$659$	−6940.00			−0.410234			−0.205117	−	0.978737i	$-0.565757\pi$
$659$	−6940.00			−0.410234			−0.205117	+	0.978737i	$0.565757\pi$
$660$	490.000	+	848.705i	0.0288988	+	0.0500542i
$661$	6699.50	−	11603.9i	0.394221	−	0.682812i	−0.598780	−	0.800914i	$-0.704348\pi$
$661$	6699.50	−	11603.9i	0.394221	−	0.682812i	0.993001	+	0.118102i	$0.0376810\pi$
$662$	−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
$670$	−3073.00	−	5322.59i	−0.177195	−	0.306910i
$671$	−1785.00			−0.102696
$672$		0			0
$673$	29510.0			1.69023			0.845117	−	0.534582i	$-0.179531\pi$
$673$	29510.0			1.69023			0.845117	+	0.534582i	$0.179531\pi$
$674$	−11466.0	−	19859.7i	−0.655273	−	1.13497i
$675$	−2014.00	+	3488.35i	−0.114843	+	0.198914i
$676$	−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
$679$		0			0
$680$	−3304.00			−0.186327
$681$	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	−0.715949	−	0.698152i	$-0.754006\pi$
$683$	4402.50	−	7625.35i	0.246643	−	0.427198i	0.962592	+	0.270954i	$0.0873393\pi$
$684$	−7124.00	−	12339.1i	−0.398235	−	0.689764i
$685$	16499.0			0.920284
$686$		0			0
$687$	−895.000			−0.0497036
$688$	−2080.00	−	3602.67i	−0.115261	−	0.199637i
$689$	−13761.0	+	23834.8i	−0.760889	+	1.31790i
$690$	49.0000	−	84.8705i	0.00270348	−	0.00468256i
$691$	14342.5	+	24841.9i	0.789601	+	1.36763i	0.926211	+	0.377004i	$0.123046\pi$
$691$	14342.5	+	24841.9i	0.789601	+	1.36763i	−0.136610	+	0.990625i	$0.543621\pi$
$692$	−6316.00			−0.346963
$693$		0			0
$694$	19554.0			1.06954
$695$	−98.0000	−	169.741i	−0.00534871	−	0.00926423i
$696$	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
$705$	598.500	+	1036.63i	0.0319728	+	0.0553785i
$706$	18246.0			0.972659
$707$		0			0
$708$	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	$0.843949\pi$
$710$	5488.00	−	9505.49i	0.290086	−	0.502443i
$711$	−6435.00	+	11145.7i	−0.339425	+	0.587902i
$712$	3492.00	+	6048.32i	0.183804	+	0.318357i
$713$	525.000			0.0275756
$714$		0			0
$715$	16170.0			0.845767
$716$	−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	0.996511	−	0.0834645i	$-0.0265985\pi$
$719$	8212.50	+	14224.5i	0.425973	+	0.737807i	−0.570538	+	0.821271i	$0.693265\pi$
$720$	2912.00			0.150728
$721$		0			0
$722$	−23820.0			−1.22782
$723$	−2088.50	−	3617.39i	−0.107430	−	0.186075i
$724$	−2340.00	+	4053.00i	−0.120118	+	0.208050i
$725$	4028.00	−	6976.70i	0.206340	−	0.357391i
$726$	−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	$0.450829\pi$
$728$		0			0
$729$	−15443.0			−0.784586
$730$	2065.00	+	3576.68i	0.104697	+	0.181341i
$731$	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	$0.0861681\pi$
$740$	154.000	+	266.736i	0.00765021	+	0.0132505i
$741$	9042.00			0.448267
$742$		0			0
$743$	24384.0			1.20399			0.601993	−	0.798501i	$-0.294373\pi$
$743$	24384.0			1.20399			0.601993	+	0.798501i	$0.294373\pi$
$744$	−300.000	−	519.615i	−0.0147830	−	0.0256049i
$745$	8032.50	−	13912.7i	0.395017	−	0.684190i
$746$	−4109.00	+	7117.00i	−0.201664	+	0.349292i
$747$	−12116.0	−	20985.5i	−0.593442	−	1.02787i
$748$	−8260.00			−0.403764
$749$		0			0
$750$	−2814.00			−0.137004
$751$	−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
$755$	7763.00			0.374205
$756$		0			0
$757$	14562.0			0.699161			0.349581	−	0.936906i	$-0.386324\pi$
$757$	14562.0			0.699161			0.349581	+	0.936906i	$0.386324\pi$
$758$	−3488.00	−	6041.39i	−0.167137	−	0.289490i
$759$	122.500	−	212.176i	0.00585832	−	0.0101469i
$760$	3836.00	−	6644.15i	0.183087	−	0.317116i
$761$	−11382.5	−	19715.1i	−0.542201	−	0.939120i	−0.998777	−	0.0494360i	$-0.984258\pi$
$761$	−11382.5	−	19715.1i	−0.542201	−	0.939120i	0.456576	−	0.889684i	$-0.349076\pi$
$762$	−1872.00			−0.0889966
$763$		0			0
$764$	−5100.00			−0.241507
$765$	5369.00	+	9299.38i	0.253747	+	0.439503i
$766$	−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	$-0.528143\pi$
$769$	−3766.00			−0.176600			−0.0883000	+	0.996094i	$0.528143\pi$
$770$		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
$775$	−2850.00	−	4936.34i	−0.132097	−	0.228798i
$776$	−2320.00			−0.107324
$777$		0			0
$778$	−326.000			−0.0150227
$779$	34113.0	+	59085.4i	1.56897	+	2.71753i
$780$	−924.000	+	1600.41i	−0.0424160	+	0.0734667i
$781$	13720.0	−	23763.7i	0.628605	−	1.08878i
$782$	413.000	+	715.337i	0.0188860	+	0.0327115i
$783$	−5618.00			−0.256412
$784$		0			0
$785$	10913.0			0.496180
$786$	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
$790$	−6930.00			−0.312099
$791$		0			0
$792$	7280.00			0.326621
$793$	−1683.00	−	2915.04i	−0.0753658	−	0.130537i
$794$	−999.000	+	1730.32i	−0.0446514	+	0.0773384i
$795$	−1459.50	+	2527.93i	−0.0651109	+	0.112775i
$796$	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	$0.212565\pi$
$798$		0			0
$799$	−10089.0			−0.446712
$800$	−1216.00	−	2106.17i	−0.0537401	−	0.0930806i
$801$	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	$0.791351\pi$
$810$	−4543.00	−	7868.71i	−0.197068	−	0.341331i
$811$	−30676.0			−1.32821			−0.664106	−	0.747638i	$-0.731188\pi$
$811$	−30676.0			−1.32821			−0.664106	+	0.747638i	$0.731188\pi$
$812$		0			0
$813$	8439.00			0.364045
$814$	385.000	+	666.840i	0.0165777	+	0.0287134i
$815$	−7878.50	+	13646.0i	−0.338616	+	0.586500i
$816$	472.000	−	817.528i	0.0202491	−	0.0350726i
$817$	17810.0	+	30847.8i	0.762660	+	1.32097i
$818$	−266.000			−0.0113698
$819$		0			0
$820$	−13944.0			−0.593836
$821$	−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	−0.894292	−	0.447483i	$-0.852320\pi$
$823$	−1407.50	+	2437.86i	−0.0596141	+	0.103255i	0.834678	+	0.550738i	$0.185654\pi$
$824$	−6212.00	−	10759.5i	−0.262628	−	0.454885i
$825$	−2660.00			−0.112254
$826$		0			0
$827$	−9276.00			−0.390034			−0.195017	−	0.980800i	$-0.562476\pi$
$827$	−9276.00			−0.390034			−0.195017	+	0.980800i	$0.562476\pi$
$828$	−364.000	−	630.466i	−0.0152776	−	0.0264616i
$829$	9285.50	−	16083.0i	0.389021	−	0.673805i	−0.603297	−	0.797517i	$-0.706147\pi$
$829$	9285.50	−	16083.0i	0.389021	−	0.673805i	0.992318	+	0.123712i	$0.0394799\pi$
$830$	6524.00	−	11299.9i	0.272833	−	0.472561i
$831$	−263.500	−	456.395i	−0.0109997	−	0.0190520i
$832$	−4224.00			−0.176011
$833$		0			0
$834$	56.0000			0.00232509
$835$	−9758.00	−	16901.4i	−0.404419	−	0.700474i
$836$	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	$-0.703897\pi$
$839$	−29048.0			−1.19529			−0.597645	+	0.801761i	$0.703897\pi$
$840$		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
$845$	7556.50	+	13088.2i	0.307635	+	0.532839i
$846$	8892.00			0.361363
$847$		0			0
$848$	−6672.00			−0.270186
$849$	−3974.50	−	6884.04i	−0.160665	−	0.278280i
$850$	4484.00	−	7766.52i	0.180941	−	0.313399i
$851$	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	$0.722745\pi$
$854$		0			0
$855$	−24934.0			−0.997339
$856$	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	0.995279	−	0.0970571i	$-0.0309430\pi$
$859$	10412.5	+	18035.0i	0.413585	+	0.716351i	−0.581693	+	0.813408i	$0.697610\pi$
$860$	−7280.00			−0.288658
$861$		0			0
$862$	30426.0			1.20222
$863$	11423.5	+	19786.1i	0.450591	+	0.780447i	0.998423	−	0.0561414i	$-0.0178798\pi$
$863$	11423.5	+	19786.1i	0.450591	+	0.780447i	−0.547831	+	0.836589i	$0.684546\pi$
$864$	−848.000	+	1468.78i	−0.0333907	+	0.0578344i
$865$	−5526.50	+	9572.18i	−0.217233	+	0.376259i
$866$	1378.00	+	2386.77i	0.0540720	+	0.0936554i
$867$	−1432.00			−0.0560937
$868$		0			0
$869$	−17325.0			−0.676307
$870$	−742.000	−	1285.18i	−0.0289151	−	0.0500825i
$871$	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	$0.140902\pi$
$877$	21368.5	+	37011.3i	0.822763	+	1.42507i	−0.0808543	+	0.996726i	$0.525765\pi$
$878$	2763.00	−	4785.66i	0.106204	−	0.183950i
$879$	159.000	−	275.396i	0.00610118	−	0.0105676i
$880$	1960.00	+	3394.82i	0.0750813	+	0.130045i
$881$	−6162.00			−0.235645			−0.117822	−	0.993035i	$-0.537591\pi$
$881$	−6162.00			−0.235645			−0.117822	+	0.993035i	$0.537591\pi$
$882$		0			0
$883$	7748.00			0.295290			0.147645	−	0.989040i	$-0.452831\pi$
$883$	7748.00			0.295290			0.147645	+	0.989040i	$0.452831\pi$
$884$	−7788.00	−	13489.2i	−0.296311	−	0.513225i
$885$	59.5000	−	103.057i	0.00225997	−	0.00391438i
$886$	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
$889$		0			0
$890$	12222.0			0.460317
$891$	−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
$895$	−17157.0			−0.640777
$896$		0			0
$897$	462.000			0.0171970
$898$	4582.00	+	7936.26i	0.170271	+	0.294918i
$899$	3975.00	−	6884.90i	0.147468	−	0.255422i
$900$	−3952.00	+	6845.06i	−0.146370	+	0.253521i
$901$	−12301.5	−	21306.8i	−0.454853	−	0.787828i
$902$	−34860.0			−1.28682
$903$		0			0
$904$	400.000			0.0147166
$905$	4095.00	+	7092.75i	0.150411	+	0.260520i
$906$	−1109.00	+	1920.84i	−0.0406667	+	0.0704368i
$907$	−15967.5	+	27656.5i	−0.584556	+	1.01248i	0.410375	+	0.911917i	$0.365398\pi$
$907$	−15967.5	+	27656.5i	−0.584556	+	1.01248i	−0.994931	+	0.100563i	$0.967935\pi$
$908$	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
$915$	−178.500	−	309.171i	−0.00644921	−	0.0111704i
$916$	−3580.00			−0.129134
$917$		0			0
$918$	−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	$0.913642\pi$
$920$	196.000	−	339.482i	0.00702384	−	0.0121656i
$921$	−4066.00	+	7042.52i	−0.145472	+	0.251964i
$922$	9494.00	+	16444.1i	0.339120	+	0.587372i
$923$	51744.0			1.84526
$924$		0			0
$925$	−836.000			−0.0297162
$926$	−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	0.563874	−	0.825861i	$-0.309310\pi$
$929$	−12268.5	−	21249.7i	−0.433279	−	0.750462i	−0.997153	+	0.0753990i	$0.975977\pi$
$930$	−1050.00			−0.0370224
$931$		0			0
$932$	7148.00			0.251224
$933$	−464.500	−	804.538i	−0.0162991	−	0.0282308i
$934$	1307.00	−	2263.79i	0.0457884	−	0.0793078i
$935$	−7227.50	+	12518.4i	−0.252796	+	0.437856i
$936$	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	$0.306534\pi$
$938$		0			0
$939$	209.000			0.00726353
$940$	2394.00	+	4146.53i	0.0830677	+	0.143878i
$941$	−19280.5	+	33394.8i	−0.667934	+	1.15690i	0.310546	+	0.950558i	$0.399488\pi$
$941$	−19280.5	+	33394.8i	−0.667934	+	1.15690i	−0.978481	+	0.206338i	$0.933845\pi$
$942$	−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	$-0.928443\pi$
$947$	−19830.5	−	34347.4i	−0.680470	−	1.17861i	0.294368	−	0.955692i	$-0.404891\pi$
$948$	990.000	−	1714.73i	0.0339174	−	0.0587467i
$949$	−9735.00	+	16861.5i	−0.332994	+	0.576763i
$950$	10412.0	+	18034.1i	0.355589	+	0.615899i
$951$	7131.00			0.243153
$952$		0			0
$953$	−46618.0			−1.58458			−0.792290	−	0.610144i	$-0.791111\pi$
$953$	−46618.0			−1.58458			−0.792290	+	0.610144i	$0.791111\pi$
$954$	10842.0	+	18778.9i	0.367948	+	0.637305i
$955$	−4462.50	+	7729.28i	−0.151207	+	0.261899i
$956$	10200.0	−	17666.9i	0.345075	−	0.597687i
$957$	−1855.00	−	3212.95i	−0.0626579	−	0.108527i
$958$	36574.0			1.23346
$959$		0			0
$960$	−448.000			−0.0150616
$961$	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
$965$	−245.000			−0.00817288
$966$		0			0
$967$	14816.0			0.492710			0.246355	−	0.969180i	$-0.420767\pi$
$967$	14816.0			0.492710			0.246355	+	0.969180i	$0.420767\pi$
$968$	−424.000	−	734.390i	−0.0140784	−	0.0243845i
$969$	−4041.50	+	7000.08i	−0.133985	+	0.232069i
$970$	−2030.00	+	3516.06i	−0.0671952	+	0.116386i
$971$	−8437.50	−	14614.2i	−0.278859	−	0.482998i	0.692242	−	0.721665i	$-0.256623\pi$
$971$	−8437.50	−	14614.2i	−0.278859	−	0.482998i	−0.971102	+	0.238667i	$0.923290\pi$
$972$	8320.00			0.274552
$973$		0			0
$974$	29906.0			0.983830
$975$	−2508.00	−	4343.98i	−0.0823798	−	0.142686i
$976$	408.000	−	706.677i	0.0133809	−	0.0231764i
$977$	7918.50	−	13715.2i	0.259299	−	0.449119i	−0.706755	−	0.707458i	$-0.749842\pi$
$977$	7918.50	−	13715.2i	0.259299	−	0.449119i	0.966054	+	0.258339i	$0.0831751\pi$
$978$	−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
$985$	−9569.00	−	16574.0i	−0.309537	−	0.536133i
$986$	12508.0			0.403992
$987$		0			0
$988$	36168.0			1.16463
$989$	910.000	+	1576.17i	0.0292582	+	0.0506766i
$990$	6370.00	−	11033.2i	0.204497	−	0.354199i
$991$	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
$994$		0			0
$995$	15701.0			0.500256
$996$	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	98.4.c.e.67.1		2
3.2	odd	2		882.4.g.d.361.1		2
7.2	even	3	inner	98.4.c.e.79.1		2
7.3	odd	6		98.4.a.b.1.1		1
7.4	even	3		98.4.a.c.1.1		1
7.5	odd	6		14.4.c.b.9.1	✓	2
7.6	odd	2		14.4.c.b.11.1	yes	2
21.2	odd	6		882.4.g.d.667.1		2
21.5	even	6		126.4.g.c.37.1		2
21.11	odd	6		882.4.a.p.1.1		1
21.17	even	6		882.4.a.k.1.1		1
21.20	even	2		126.4.g.c.109.1		2
28.3	even	6		784.4.a.l.1.1		1
28.11	odd	6		784.4.a.j.1.1		1
28.19	even	6		112.4.i.b.65.1		2
28.27	even	2		112.4.i.b.81.1		2
35.4	even	6		2450.4.a.bf.1.1		1
35.12	even	12		350.4.j.d.149.2		4
35.13	even	4		350.4.j.d.249.2		4
35.19	odd	6		350.4.e.b.51.1		2
35.24	odd	6		2450.4.a.bh.1.1		1
35.27	even	4		350.4.j.d.249.1		4
35.33	even	12		350.4.j.d.149.1		4
35.34	odd	2		350.4.e.b.151.1		2
56.5	odd	6		448.4.i.c.65.1		2
56.13	odd	2		448.4.i.c.193.1		2
56.19	even	6		448.4.i.d.65.1		2
56.27	even	2		448.4.i.d.193.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.4.c.b.9.1	✓	2	7.5	odd	6
14.4.c.b.11.1	yes	2	7.6	odd	2
98.4.a.b.1.1		1	7.3	odd	6
98.4.a.c.1.1		1	7.4	even	3
98.4.c.e.67.1		2	1.1	even	1	trivial
98.4.c.e.79.1		2	7.2	even	3	inner
112.4.i.b.65.1		2	28.19	even	6
112.4.i.b.81.1		2	28.27	even	2
126.4.g.c.37.1		2	21.5	even	6
126.4.g.c.109.1		2	21.20	even	2
350.4.e.b.51.1		2	35.19	odd	6
350.4.e.b.151.1		2	35.34	odd	2
350.4.j.d.149.1		4	35.33	even	12
350.4.j.d.149.2		4	35.12	even	12
350.4.j.d.249.1		4	35.27	even	4
350.4.j.d.249.2		4	35.13	even	4
448.4.i.c.65.1		2	56.5	odd	6
448.4.i.c.193.1		2	56.13	odd	2
448.4.i.d.65.1		2	56.19	even	6
448.4.i.d.193.1		2	56.27	even	2
784.4.a.j.1.1		1	28.11	odd	6
784.4.a.l.1.1		1	28.3	even	6
882.4.a.k.1.1		1	21.17	even	6
882.4.a.p.1.1		1	21.11	odd	6
882.4.g.d.361.1		2	3.2	odd	2
882.4.g.d.667.1		2	21.2	odd	6
2450.4.a.bf.1.1		1	35.4	even	6
2450.4.a.bh.1.1		1	35.24	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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	98.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(3.50000 + 6.06218i) q^{5} -2.00000 q^{6} -8.00000 q^{8} +(13.0000 + 22.5167i) q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(3.50000 + 6.06218i) q^{5} -2.00000 q^{6} -8.00000 q^{8} +(13.0000 + 22.5167i) q^{9} +(-7.00000 + 12.1244i) q^{10} +(-17.5000 + 30.3109i) q^{11} +(-2.00000 - 3.46410i) q^{12} -66.0000 q^{13} -7.00000 q^{15} +(-8.00000 - 13.8564i) q^{16} +(29.5000 - 51.0955i) q^{17} +(-26.0000 + 45.0333i) q^{18} +(68.5000 + 118.645i) q^{19} -28.0000 q^{20} -70.0000 q^{22} +(3.50000 + 6.06218i) q^{23} +(4.00000 - 6.92820i) q^{24} +(38.0000 - 65.8179i) q^{25} +(-66.0000 - 114.315i) q^{26} -53.0000 q^{27} +106.000 q^{29} +(-7.00000 - 12.1244i) q^{30} +(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} +(-28.0000 - 48.4974i) q^{40} +498.000 q^{41} +260.000 q^{43} +(-70.0000 - 121.244i) q^{44} +(-91.0000 + 157.617i) q^{45} +(-7.00000 + 12.1244i) q^{46} +(-85.5000 - 148.090i) q^{47} +16.0000 q^{48} +152.000 q^{50} +(29.5000 + 51.0955i) q^{51} +(132.000 - 228.631i) q^{52} +(208.500 - 361.133i) q^{53} +(-53.0000 - 91.7987i) q^{54} -245.000 q^{55} -137.000 q^{57} +(106.000 + 183.597i) q^{58} +(-8.50000 + 14.7224i) q^{59} +(14.0000 - 24.2487i) q^{60} +(25.5000 + 44.1673i) q^{61} +150.000 q^{62} +64.0000 q^{64} +(-231.000 - 400.104i) q^{65} +(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} +(38.0000 + 65.8179i) q^{75} -548.000 q^{76} +132.000 q^{78} +(247.500 + 428.683i) q^{79} +(56.0000 - 96.9948i) q^{80} +(-324.500 + 562.050i) q^{81} +(498.000 + 862.561i) q^{82} -932.000 q^{83} +413.000 q^{85} +(260.000 + 450.333i) q^{86} +(-53.0000 + 91.7987i) q^{87} +(140.000 - 242.487i) q^{88} +(-436.500 - 756.040i) q^{89} -364.000 q^{90} -28.0000 q^{92} +(37.5000 + 64.9519i) q^{93} +(171.000 - 296.181i) q^{94} +(-479.500 + 830.518i) q^{95} +(16.0000 + 27.7128i) q^{96} +290.000 q^{97} -910.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - q^{3} - 4 q^{4} + 7 q^{5} - 4 q^{6} - 16 q^{8} + 26 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - q^3 - 4 * q^4 + 7 * q^5 - 4 * q^6 - 16 * q^8 + 26 * q^9	\( 2 q + 2 q^{2} - q^{3} - 4 q^{4} + 7 q^{5} - 4 q^{6} - 16 q^{8} + 26 q^{9} - 14 q^{10} - 35 q^{11} - 4 q^{12} - 132 q^{13} - 14 q^{15} - 16 q^{16} + 59 q^{17} - 52 q^{18} + 137 q^{19} - 56 q^{20} - 140 q^{22} + 7 q^{23} + 8 q^{24} + 76 q^{25} - 132 q^{26} - 106 q^{27} + 212 q^{29} - 14 q^{30} + 75 q^{31} + 32 q^{32} - 35 q^{33} + 236 q^{34} - 208 q^{36} - 11 q^{37} - 274 q^{38} + 66 q^{39} - 56 q^{40} + 996 q^{41} + 520 q^{43} - 140 q^{44} - 182 q^{45} - 14 q^{46} - 171 q^{47} + 32 q^{48} + 304 q^{50} + 59 q^{51} + 264 q^{52} + 417 q^{53} - 106 q^{54} - 490 q^{55} - 274 q^{57} + 212 q^{58} - 17 q^{59} + 28 q^{60} + 51 q^{61} + 300 q^{62} + 128 q^{64} - 462 q^{65} + 70 q^{66} - 439 q^{67} + 236 q^{68} - 14 q^{69} - 1568 q^{71} - 208 q^{72} + 295 q^{73} + 22 q^{74} + 76 q^{75} - 1096 q^{76} + 264 q^{78} + 495 q^{79} + 112 q^{80} - 649 q^{81} + 996 q^{82} - 1864 q^{83} + 826 q^{85} + 520 q^{86} - 106 q^{87} + 280 q^{88} - 873 q^{89} - 728 q^{90} - 56 q^{92} + 75 q^{93} + 342 q^{94} - 959 q^{95} + 32 q^{96} + 580 q^{97} - 1820 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - q^3 - 4 * q^4 + 7 * q^5 - 4 * q^6 - 16 * q^8 + 26 * q^9 - 14 * q^10 - 35 * q^11 - 4 * q^12 - 132 * q^13 - 14 * q^15 - 16 * q^16 + 59 * q^17 - 52 * q^18 + 137 * q^19 - 56 * q^20 - 140 * q^22 + 7 * q^23 + 8 * q^24 + 76 * q^25 - 132 * q^26 - 106 * q^27 + 212 * q^29 - 14 * q^30 + 75 * q^31 + 32 * q^32 - 35 * q^33 + 236 * q^34 - 208 * q^36 - 11 * q^37 - 274 * q^38 + 66 * q^39 - 56 * q^40 + 996 * q^41 + 520 * q^43 - 140 * q^44 - 182 * q^45 - 14 * q^46 - 171 * q^47 + 32 * q^48 + 304 * q^50 + 59 * q^51 + 264 * q^52 + 417 * q^53 - 106 * q^54 - 490 * q^55 - 274 * q^57 + 212 * q^58 - 17 * q^59 + 28 * q^60 + 51 * q^61 + 300 * q^62 + 128 * q^64 - 462 * q^65 + 70 * q^66 - 439 * q^67 + 236 * q^68 - 14 * q^69 - 1568 * q^71 - 208 * q^72 + 295 * q^73 + 22 * q^74 + 76 * q^75 - 1096 * q^76 + 264 * q^78 + 495 * q^79 + 112 * q^80 - 649 * q^81 + 996 * q^82 - 1864 * q^83 + 826 * q^85 + 520 * q^86 - 106 * q^87 + 280 * q^88 - 873 * q^89 - 728 * q^90 - 56 * q^92 + 75 * q^93 + 342 * q^94 - 959 * q^95 + 32 * q^96 + 580 * q^97 - 1820 * q^99

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