LMFDB - Embedded newform 603.2.z.c.10.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(10,603)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(603, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 16]))

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

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

chi := DirichletCharacter("603.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.z (of order $33$, degree $20$, 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:	$4.81497924188$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$5$ over $\Q(\zeta_{33})$
Twist minimal:	no (minimal twist has level 67)
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			10.4
Character	$\chi$	$=$	603.10
Dual form			603.2.z.c.181.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.70724 + 1.62785i) q^{2} +(0.169609 + 3.56053i) q^{4} +(1.68411 - 3.68769i) q^{5} +(0.549774 - 2.26620i) q^{7} +(-2.41691 + 2.78926i) q^{8} +O(q^{10})$	\(q+(1.70724 + 1.62785i) q^{2} +(0.169609 + 3.56053i) q^{4} +(1.68411 - 3.68769i) q^{5} +(0.549774 - 2.26620i) q^{7} +(-2.41691 + 2.78926i) q^{8} +(8.87819 - 3.55429i) q^{10} +(-0.983759 - 1.38150i) q^{11} +(0.422812 - 1.22164i) q^{13} +(4.62763 - 2.97400i) q^{14} +(-1.56988 + 0.149905i) q^{16} +(-0.0468218 + 0.982912i) q^{17} +(1.13372 + 4.67325i) q^{19} +(13.4158 + 5.37086i) q^{20} +(0.569356 - 3.95996i) q^{22} +(-3.76952 + 2.96439i) q^{23} +(-7.48850 - 8.64219i) q^{25} +(2.71048 - 1.39735i) q^{26} +(8.16212 + 1.57312i) q^{28} +(-4.13926 + 7.16942i) q^{29} +(2.45685 + 7.09859i) q^{31} +(2.87802 + 2.26330i) q^{32} +(-1.67997 + 1.60185i) q^{34} +(-7.43115 - 5.84392i) q^{35} +(-2.41638 - 4.18530i) q^{37} +(-5.67182 + 9.82389i) q^{38} +(6.21557 + 13.6102i) q^{40} +(0.731937 - 0.377340i) q^{41} +(-1.94182 - 1.24793i) q^{43} +(4.75201 - 3.73702i) q^{44} +(-11.2611 - 1.07530i) q^{46} +(3.06971 + 1.22892i) q^{47} +(1.38844 + 0.715791i) q^{49} +(1.28352 - 26.9445i) q^{50} +(4.42139 + 1.29824i) q^{52} +(-2.16276 + 1.38992i) q^{53} +(-6.75128 + 1.30120i) q^{55} +(4.99226 + 7.01065i) q^{56} +(-18.7375 + 5.50182i) q^{58} +(0.544959 - 0.628917i) q^{59} +(-0.733033 + 1.02940i) q^{61} +(-7.36102 + 16.1184i) q^{62} +(1.67802 + 11.6709i) q^{64} +(-3.79295 - 3.61657i) q^{65} +(6.95871 + 4.31002i) q^{67} -3.50763 q^{68} +(-3.17373 - 22.0738i) q^{70} +(0.205892 + 4.32220i) q^{71} +(-1.93341 + 2.71510i) q^{73} +(2.68769 - 11.0788i) q^{74} +(-16.4470 + 4.82927i) q^{76} +(-3.67159 + 1.46988i) q^{77} +(6.60307 - 1.27264i) q^{79} +(-2.09104 + 6.04168i) q^{80} +(1.86385 + 0.547274i) q^{82} +(5.75628 - 0.549658i) q^{83} +(3.54582 + 1.82800i) q^{85} +(-1.28371 - 5.29151i) q^{86} +(6.23100 + 0.594989i) q^{88} +(-1.19689 + 8.32458i) q^{89} +(-2.53602 - 1.62980i) q^{91} +(-11.1941 - 12.9187i) q^{92} +(3.24022 + 7.09509i) q^{94} +(19.1428 + 3.68947i) q^{95} +(-6.23553 - 10.8003i) q^{97} +(1.20520 + 3.48220i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 24 q^{2} - 18 q^{4} + 16 q^{5} - 24 q^{7} - 23 q^{8}+O(q^{10}) $ 100 * q + 24 * q^2 - 18 * q^4 + 16 * q^5 - 24 * q^7 - 23 * q^8	$ 100 q + 24 q^{2} - 18 q^{4} + 16 q^{5} - 24 q^{7} - 23 q^{8} + 8 q^{10} + 24 q^{11} - 22 q^{13} + 32 q^{14} - 28 q^{16} - 17 q^{17} + 15 q^{20} + 49 q^{22} + 13 q^{23} - 34 q^{25} + 27 q^{26} + 22 q^{28} - 8 q^{29} + 10 q^{31} - 34 q^{32} - 50 q^{34} + q^{35} + 7 q^{37} - 50 q^{38} + 43 q^{40} + 5 q^{41} + 2 q^{43} + 19 q^{44} + 52 q^{46} + 6 q^{47} - 27 q^{49} - 134 q^{50} + 120 q^{52} + 52 q^{53} - 64 q^{55} + 124 q^{56} - 56 q^{58} - 27 q^{59} - 16 q^{61} + 74 q^{62} - 197 q^{64} + 92 q^{65} - 56 q^{67} - 16 q^{68} - 22 q^{70} + 113 q^{71} + q^{73} + 24 q^{74} - 144 q^{76} - 85 q^{77} + 36 q^{79} + 13 q^{80} - 20 q^{82} + 61 q^{83} - 6 q^{85} - 189 q^{86} + 129 q^{88} - 95 q^{89} + 42 q^{91} - 4 q^{92} + 70 q^{94} + 20 q^{95} + 53 q^{97} - q^{98}+O(q^{100}) $ 100 * q + 24 * q^2 - 18 * q^4 + 16 * q^5 - 24 * q^7 - 23 * q^8 + 8 * q^10 + 24 * q^11 - 22 * q^13 + 32 * q^14 - 28 * q^16 - 17 * q^17 + 15 * q^20 + 49 * q^22 + 13 * q^23 - 34 * q^25 + 27 * q^26 + 22 * q^28 - 8 * q^29 + 10 * q^31 - 34 * q^32 - 50 * q^34 + q^35 + 7 * q^37 - 50 * q^38 + 43 * q^40 + 5 * q^41 + 2 * q^43 + 19 * q^44 + 52 * q^46 + 6 * q^47 - 27 * q^49 - 134 * q^50 + 120 * q^52 + 52 * q^53 - 64 * q^55 + 124 * q^56 - 56 * q^58 - 27 * q^59 - 16 * q^61 + 74 * q^62 - 197 * q^64 + 92 * q^65 - 56 * q^67 - 16 * q^68 - 22 * q^70 + 113 * q^71 + q^73 + 24 * q^74 - 144 * q^76 - 85 * q^77 + 36 * q^79 + 13 * q^80 - 20 * q^82 + 61 * q^83 - 6 * q^85 - 189 * q^86 + 129 * q^88 - 95 * q^89 + 42 * q^91 - 4 * q^92 + 70 * q^94 + 20 * q^95 + 53 * q^97 - q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/603\mathbb{Z}\right)^\times$.

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{8}{33}\right)$	$1$

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 $

$2$	1.70724	+	1.62785i	1.20720	+	1.15106i	0.984352	+	0.176211i	$0.0563843\pi$
$2$	1.70724	+	1.62785i	1.20720	+	1.15106i	0.222849	+	0.974853i	$0.428464\pi$
$3$		0			0
$3$		0			0
$4$	0.169609	+	3.56053i	0.0848045	+	1.78027i
$5$	1.68411	−	3.68769i	0.753157	−	1.64918i	−0.00745126	−	0.999972i	$-0.502372\pi$
$5$	1.68411	−	3.68769i	0.753157	−	1.64918i	0.760608	−	0.649211i	$-0.224901\pi$
$6$		0			0
$7$	0.549774	−	2.26620i	0.207795	−	0.856543i	−0.768456	−	0.639902i	$-0.778975\pi$
$7$	0.549774	−	2.26620i	0.207795	−	0.856543i	0.976251	−	0.216641i	$-0.0695100\pi$
$8$	−2.41691	+	2.78926i	−0.854505	+	0.986152i
$9$		0			0
$10$	8.87819	−	3.55429i	2.80753	−	1.12396i
$11$	−0.983759	−	1.38150i	−0.296615	−	0.416537i	0.639194	−	0.769046i	$-0.279268\pi$
$11$	−0.983759	−	1.38150i	−0.296615	−	0.416537i	−0.935809	+	0.352509i	$0.885329\pi$
$12$		0			0
$13$	0.422812	−	1.22164i	0.117267	−	0.338821i	−0.871058	−	0.491180i	$-0.836566\pi$
$13$	0.422812	−	1.22164i	0.117267	−	0.338821i	0.988325	+	0.152359i	$0.0486870\pi$
$14$	4.62763	−	2.97400i	1.23679	−	0.794834i
$15$		0			0
$16$	−1.56988	+	0.149905i	−0.392470	+	0.0374763i
$17$	−0.0468218	+	0.982912i	−0.0113560	+	0.238391i	0.986052	+	0.166437i	$0.0532264\pi$
$17$	−0.0468218	+	0.982912i	−0.0113560	+	0.238391i	−0.997408	+	0.0719536i	$0.977077\pi$
$18$		0			0
$19$	1.13372	+	4.67325i	0.260093	+	1.07212i	0.940638	+	0.339411i	$0.110228\pi$
$19$	1.13372	+	4.67325i	0.260093	+	1.07212i	−0.680545	+	0.732706i	$0.738257\pi$
$20$	13.4158	+	5.37086i	2.99986	+	1.20096i
$21$		0			0
$22$	0.569356	−	3.95996i	0.121387	−	0.844266i
$23$	−3.76952	+	2.96439i	−0.786000	+	0.618117i	−0.928354	−	0.371698i	$-0.878776\pi$
$23$	−3.76952	+	2.96439i	−0.786000	+	0.618117i	0.142353	+	0.989816i	$0.454533\pi$
$24$		0			0
$25$	−7.48850	−	8.64219i	−1.49770	−	1.72844i
$26$	2.71048	−	1.39735i	0.531570	−	0.274043i
$27$		0			0
$28$	8.16212	+	1.57312i	1.54250	+	0.297292i
$29$	−4.13926	+	7.16942i	−0.768642	+	1.33133i	0.169657	+	0.985503i	$0.445734\pi$
$29$	−4.13926	+	7.16942i	−0.768642	+	1.33133i	−0.938299	+	0.345824i	$0.887599\pi$
$30$		0			0
$31$	2.45685	+	7.09859i	0.441263	+	1.27494i	0.918238	+	0.396028i	$0.129612\pi$
$31$	2.45685	+	7.09859i	0.441263	+	1.27494i	−0.476976	+	0.878916i	$0.658267\pi$
$32$	2.87802	+	2.26330i	0.508766	+	0.400098i
$33$		0			0
$34$	−1.67997	+	1.60185i	−0.288112	+	0.274715i
$35$	−7.43115	−	5.84392i	−1.25609	−	0.987803i
$36$		0			0
$37$	−2.41638	−	4.18530i	−0.397251	−	0.688059i	0.596135	−	0.802884i	$-0.296702\pi$
$37$	−2.41638	−	4.18530i	−0.397251	−	0.688059i	−0.993386	+	0.114826i	$0.963369\pi$
$38$	−5.67182	+	9.82389i	−0.920091	+	1.59365i
$39$		0			0
$40$	6.21557	+	13.6102i	0.982769	+	2.15196i
$41$	0.731937	−	0.377340i	0.114309	−	0.0589306i	−0.400124	−	0.916461i	$-0.631033\pi$
$41$	0.731937	−	0.377340i	0.114309	−	0.0589306i	0.514433	+	0.857531i	$0.328002\pi$
$42$		0			0
$43$	−1.94182	−	1.24793i	−0.296125	−	0.190308i	0.384139	−	0.923275i	$-0.374498\pi$
$43$	−1.94182	−	1.24793i	−0.296125	−	0.190308i	−0.680264	+	0.732968i	$0.738135\pi$
$44$	4.75201	−	3.73702i	0.716392	−	0.563377i
$45$		0			0
$46$	−11.2611	−	1.07530i	−1.66035	−	0.158545i
$47$	3.06971	+	1.22892i	0.447763	+	0.179257i	0.584575	−	0.811340i	$-0.301261\pi$
$47$	3.06971	+	1.22892i	0.447763	+	0.179257i	−0.136812	+	0.990597i	$0.543686\pi$
$48$		0			0
$49$	1.38844	+	0.715791i	0.198349	+	0.102256i
$50$	1.28352	−	26.9445i	0.181518	−	3.81052i
$51$		0			0
$52$	4.42139	+	1.29824i	0.613136	+	0.180033i
$53$	−2.16276	+	1.38992i	−0.297077	+	0.190920i	−0.680685	−	0.732576i	$-0.738318\pi$
$53$	−2.16276	+	1.38992i	−0.297077	+	0.190920i	0.383608	+	0.923496i	$0.374681\pi$
$54$		0			0
$55$	−6.75128	+	1.30120i	−0.910343	+	0.175454i
$56$	4.99226	+	7.01065i	0.667119	+	0.936838i
$57$		0			0
$58$	−18.7375	+	5.50182i	−2.46035	+	0.722424i
$59$	0.544959	−	0.628917i	0.0709477	−	0.0818780i	−0.719166	−	0.694838i	$-0.755476\pi$
$59$	0.544959	−	0.628917i	0.0709477	−	0.0818780i	0.790114	+	0.612960i	$0.210021\pi$
$60$		0			0
$61$	−0.733033	+	1.02940i	−0.0938552	+	0.131801i	−0.858833	−	0.512255i	$-0.828810\pi$
$61$	−0.733033	+	1.02940i	−0.0938552	+	0.131801i	0.764978	+	0.644056i	$0.222750\pi$
$62$	−7.36102	+	16.1184i	−0.934851	+	2.04704i
$63$		0			0
$64$	1.67802	+	11.6709i	0.209753	+	1.45886i
$65$	−3.79295	−	3.61657i	−0.470457	−	0.448580i
$66$		0			0
$67$	6.95871	+	4.31002i	0.850142	+	0.526553i
$67$	6.95871	+	4.31002i	0.850142	+	0.526553i
$68$	−3.50763			−0.425363
$69$		0			0
$70$	−3.17373	−	22.0738i	−0.379334	−	2.63832i
$71$	0.205892	+	4.32220i	0.0244348	+	0.512950i	0.977596	+	0.210488i	$0.0675054\pi$
$71$	0.205892	+	4.32220i	0.0244348	+	0.512950i	−0.953162	+	0.302462i	$0.902192\pi$
$72$		0			0
$73$	−1.93341	+	2.71510i	−0.226289	+	0.317778i	−0.912074	−	0.410026i	$-0.865520\pi$
$73$	−1.93341	+	2.71510i	−0.226289	+	0.317778i	0.685785	+	0.727804i	$0.259459\pi$
$74$	2.68769	−	11.0788i	0.312438	−	1.28789i
$75$		0			0
$76$	−16.4470	+	4.82927i	−1.88660	+	0.553955i
$77$	−3.67159	+	1.46988i	−0.418417	+	0.167509i
$78$		0			0
$79$	6.60307	−	1.27264i	0.742903	−	0.143183i	0.196264	−	0.980551i	$-0.437119\pi$
$79$	6.60307	−	1.27264i	0.742903	−	0.143183i	0.546639	+	0.837368i	$0.315907\pi$
$80$	−2.09104	+	6.04168i	−0.233786	+	0.675480i
$81$		0			0
$82$	1.86385	+	0.547274i	0.205827	+	0.0604363i
$83$	5.75628	−	0.549658i	0.631834	−	0.0603328i	0.225775	−	0.974180i	$-0.427509\pi$
$83$	5.75628	−	0.549658i	0.631834	−	0.0603328i	0.406059	+	0.913847i	$0.366903\pi$
$84$		0			0
$85$	3.54582	+	1.82800i	0.384598	+	0.198274i
$86$	−1.28371	−	5.29151i	−0.138426	−	0.570598i
$87$		0			0
$88$	6.23100	+	0.594989i	0.664227	+	0.0634260i
$89$	−1.19689	+	8.32458i	−0.126870	+	0.882403i	0.822616	+	0.568597i	$0.192513\pi$
$89$	−1.19689	+	8.32458i	−0.126870	+	0.882403i	−0.949487	+	0.313807i	$0.898396\pi$
$90$		0			0
$91$	−2.53602	−	1.62980i	−0.265847	−	0.170850i
$92$	−11.1941	−	12.9187i	−1.16707	−	1.34687i
$93$		0			0
$94$	3.24022	+	7.09509i	0.334203	+	0.731803i
$95$	19.1428	+	3.68947i	1.96401	+	0.378532i
$96$		0			0
$97$	−6.23553	−	10.8003i	−0.633123	−	1.09660i	−0.986910	−	0.161274i	$-0.948440\pi$
$97$	−6.23553	−	10.8003i	−0.633123	−	1.09660i	0.353787	−	0.935326i	$-0.384894\pi$
$98$	1.20520	+	3.48220i	0.121744	+	0.351756i
$99$		0			0
$100$	29.5007	−	28.1288i	2.95007	−	2.81288i
$101$	5.13535	−	4.89655i	0.510986	−	0.487225i	−0.390155	−	0.920749i	$-0.627579\pi$
$101$	5.13535	−	4.89655i	0.510986	−	0.487225i	0.901142	+	0.433524i	$0.142730\pi$
$102$		0			0
$103$	−4.02911	−	11.6413i	−0.397000	−	1.14706i	−0.949561	−	0.313583i	$-0.898470\pi$
$103$	−4.02911	−	11.6413i	−0.397000	−	1.14706i	0.552561	−	0.833473i	$-0.313651\pi$
$104$	2.38556	+	4.13191i	0.233923	+	0.405167i
$105$		0			0
$106$	−5.95493	−	1.14772i	−0.578394	−	0.111476i
$107$	−3.97698	−	8.70837i	−0.384469	−	0.841870i	−0.998612	−	0.0526746i	$-0.983225\pi$
$107$	−3.97698	−	8.70837i	−0.384469	−	0.841870i	0.614143	−	0.789195i	$-0.289502\pi$
$108$		0			0
$109$	−11.4007	−	13.1571i	−1.09199	−	1.26023i	−0.963267	−	0.268545i	$-0.913457\pi$
$109$	−11.4007	−	13.1571i	−1.09199	−	1.26023i	−0.128725	−	0.991680i	$-0.541088\pi$
$110$	−13.6442	−	8.76862i	−1.30093	−	0.836055i
$111$		0			0
$112$	−0.523363	+	3.64007i	−0.0494532	+	0.343954i
$113$	4.71405	+	0.450138i	0.443461	+	0.0423454i	0.314399	−	0.949291i	$-0.398197\pi$
$113$	4.71405	+	0.450138i	0.443461	+	0.0423454i	0.129062	+	0.991636i	$0.458803\pi$
$114$		0			0
$115$	4.58344	+	18.8932i	0.427408	+	1.76180i
$116$	−26.2290	−	13.5220i	−2.43530	−	1.25548i
$117$		0			0
$118$	1.95416	−	0.186600i	0.179895	−	0.0171779i
$119$	2.20173	+	0.646487i	0.201832	+	0.0592633i
$120$		0			0
$121$	2.65700	−	7.67689i	0.241545	−	0.697899i
$122$	−2.92717	+	0.564167i	−0.265014	+	0.0510772i
$123$		0			0
$124$	−24.8581	+	9.95167i	−2.23232	+	0.893686i
$125$	−25.0320	+	7.35007i	−2.23893	+	0.657410i
$126$		0			0
$127$	1.63151	−	6.72520i	0.144774	−	0.596765i	−0.852484	−	0.522754i	$-0.824905\pi$
$127$	1.63151	−	6.72520i	0.144774	−	0.596765i	0.997257	−	0.0740111i	$-0.0235800\pi$
$128$	−11.8861	+	16.6917i	−1.05059	+	1.47535i
$129$		0			0
$130$	−0.588241	−	12.3487i	−0.0515922	−	1.08305i
$131$	1.34939	+	9.38522i	0.117897	+	0.819991i	0.959865	+	0.280463i	$0.0904880\pi$
$131$	1.34939	+	9.38522i	0.117897	+	0.819991i	−0.841968	+	0.539528i	$0.818603\pi$
$132$		0			0
$133$	11.2138			0.972360
$134$	4.86413	+	18.6860i	0.420197	+	1.61422i
$135$		0			0
$136$	−2.62843	−	2.50620i	−0.225386	−	0.214905i
$137$	−3.07537	−	21.3897i	−0.262746	−	1.82744i	−0.511979	−	0.858998i	$-0.671087\pi$
$137$	−3.07537	−	21.3897i	−0.262746	−	1.82744i	0.249232	−	0.968444i	$-0.419822\pi$
$138$		0			0
$139$	1.44167	−	3.15681i	0.122281	−	0.267757i	−0.838586	−	0.544770i	$-0.816617\pi$
$139$	1.44167	−	3.15681i	0.122281	−	0.267757i	0.960866	+	0.277012i	$0.0893443\pi$
$140$	19.5471	−	27.4500i	1.65203	−	2.31995i
$141$		0			0
$142$	−6.68438	+	7.71419i	−0.560941	+	0.647360i
$143$	−2.10363	+	0.617682i	−0.175915	+	0.0516532i
$144$		0			0
$145$	19.4676	+	27.3384i	1.61669	+	2.27033i
$146$	−7.72057	+	1.48802i	−0.638959	+	0.123149i
$147$		0			0
$148$	14.4921	−	9.31348i	1.19124	−	0.765563i
$149$	13.5572	+	3.98074i	1.11065	+	0.326115i	0.785074	−	0.619402i	$-0.212625\pi$
$149$	13.5572	+	3.98074i	1.11065	+	0.326115i	0.325572	+	0.945517i	$0.394443\pi$
$150$		0			0
$151$	−0.148228	+	3.11168i	−0.0120626	+	0.253225i	0.984779	+	0.173811i	$0.0556080\pi$
$151$	−0.148228	+	3.11168i	−0.0120626	+	0.253225i	−0.996842	+	0.0794143i	$0.974695\pi$
$152$	−15.7750	−	8.13257i	−1.27952	−	0.659639i
$153$		0			0
$154$	−8.66104	−	3.46736i	−0.697927	−	0.279408i
$155$	30.3150	+	2.89473i	2.43496	+	0.232510i
$156$		0			0
$157$	4.24408	−	3.33758i	0.338714	−	0.266368i	−0.434284	−	0.900776i	$-0.642999\pi$
$157$	4.24408	−	3.33758i	0.338714	−	0.266368i	0.772998	+	0.634408i	$0.218756\pi$
$158$	13.3447	+	8.57611i	1.06165	+	0.682279i
$159$		0			0
$160$	13.1932	−	6.80158i	1.04302	−	0.537712i
$161$	4.64550	+	10.1722i	0.366117	+	0.801685i
$162$		0			0
$163$	−11.4768	+	19.8784i	−0.898931	+	1.55699i	−0.0700689	+	0.997542i	$0.522322\pi$
$163$	−11.4768	+	19.8784i	−0.898931	+	1.55699i	−0.828862	+	0.559453i	$0.811011\pi$
$164$	1.46767	+	2.54208i	0.114606	+	0.198503i
$165$		0			0
$166$	10.7221	+	8.43197i	0.832198	+	0.654448i
$167$	−3.61942	+	3.45111i	−0.280079	+	0.267055i	−0.817077	−	0.576529i	$-0.804407\pi$
$167$	−3.61942	+	3.45111i	−0.280079	+	0.267055i	0.536998	+	0.843584i	$0.319558\pi$
$168$		0			0
$169$	8.90507	+	7.00302i	0.685005	+	0.538694i
$170$	3.07786	+	8.89289i	0.236061	+	0.682053i
$171$		0			0
$172$	4.11395	−	7.12557i	0.313686	−	0.543320i
$173$	−17.3466	−	3.34327i	−1.31883	−	0.254184i	−0.519190	−	0.854659i	$-0.673766\pi$
$173$	−17.3466	−	3.34327i	−1.31883	−	0.254184i	−0.799644	+	0.600474i	$0.794978\pi$
$174$		0			0
$175$	−23.7019	+	12.2192i	−1.79170	+	0.923683i
$176$	1.75148	+	2.02131i	0.132022	+	0.152362i
$177$		0			0
$178$	−15.5946	+	12.2637i	−1.16886	+	0.919203i
$179$	2.19716	−	15.2816i	0.164223	−	1.14220i	−0.726339	−	0.687337i	$-0.758780\pi$
$179$	2.19716	−	15.2816i	0.164223	−	1.14220i	0.890562	−	0.454862i	$-0.150311\pi$
$180$		0			0
$181$	−22.3722	−	8.95649i	−1.66291	−	0.665731i	−0.666128	−	0.745837i	$-0.732050\pi$
$181$	−22.3722	−	8.95649i	−1.66291	−	0.665731i	−0.996786	+	0.0801067i	$0.974474\pi$
$182$	−1.67652	−	6.91072i	−0.124272	−	0.512257i
$183$		0			0
$184$	0.842146	−	17.6788i	0.0620838	−	1.30330i
$185$	−19.5035	+	1.86236i	−1.43393	+	0.136923i
$186$		0			0
$187$	1.40395	−	0.902264i	0.102667	−	0.0659801i
$188$	−3.85498	+	11.1382i	−0.281153	+	0.812338i
$189$		0			0
$190$	26.6754	+	37.4604i	1.93524	+	2.71766i
$191$	−20.0967	+	8.04550i	−1.45414	+	0.582152i	−0.958174	−	0.286187i	$-0.907612\pi$
$191$	−20.0967	+	8.04550i	−1.45414	+	0.582152i	−0.495971	+	0.868339i	$0.665188\pi$
$192$		0			0
$193$	3.67885	−	4.24562i	0.264810	−	0.305607i	−0.607736	−	0.794139i	$-0.707922\pi$
$193$	3.67885	−	4.24562i	0.264810	−	0.305607i	0.872546	+	0.488532i	$0.162468\pi$
$194$	6.93566	−	28.5892i	0.497951	−	2.05258i
$195$		0			0
$196$	−2.31311	+	5.06500i	−0.165222	+	0.361785i
$197$	0.524912	+	11.0193i	0.0373984	+	0.785089i	0.937200	+	0.348791i	$0.113408\pi$
$197$	0.524912	+	11.0193i	0.0373984	+	0.785089i	−0.899802	+	0.436298i	$0.856289\pi$
$198$		0			0
$199$	−2.46824	−	2.35346i	−0.174969	−	0.166832i	0.597534	−	0.801843i	$-0.296147\pi$
$199$	−2.46824	−	2.35346i	−0.174969	−	0.166832i	−0.772503	+	0.635011i	$0.780996\pi$
$200$	42.2043			2.98430
$201$		0			0
$202$	16.7381			1.17769
$203$	13.9717	+	13.3220i	0.980619	+	0.935018i
$204$		0			0
$205$	−0.158848	−	3.33463i	−0.0110944	−	0.232901i
$206$	12.0717	−	26.4334i	0.841076	−	1.84170i
$207$		0			0
$208$	−0.480634	+	1.98120i	−0.0333260	+	0.137372i
$209$	5.34077	−	6.16358i	0.369429	−	0.426344i
$210$		0			0
$211$	8.03985	−	3.21867i	0.553486	−	0.221582i	−0.0780221	−	0.996952i	$-0.524860\pi$
$211$	8.03985	−	3.21867i	0.553486	−	0.221582i	0.631508	+	0.775369i	$0.282436\pi$
$212$	−5.31567	−	7.46482i	−0.365082	−	0.512686i
$213$		0			0
$214$	7.38626	−	21.3412i	0.504915	−	1.45885i
$215$	−7.87222	+	5.05917i	−0.536881	+	0.345032i
$216$		0			0
$217$	17.4375	−	1.66508i	1.18374	−	0.113033i
$218$	1.95408	−	41.0211i	0.132347	−	2.77830i
$219$		0			0
$220$	−5.77806	−	23.8175i	−0.389556	−	1.60577i
$221$	1.18096	+	0.472786i	0.0794402	+	0.0318031i
$222$		0			0
$223$	−2.79342	+	19.4287i	−0.187061	+	1.30104i	0.652506	+	0.757783i	$0.273718\pi$
$223$	−2.79342	+	19.4287i	−0.187061	+	1.30104i	−0.839567	+	0.543256i	$0.817191\pi$
$224$	6.71134	−	5.27786i	0.448420	−	0.352642i
$225$		0			0
$226$	7.31527	+	8.44227i	0.486605	+	0.561572i
$227$	−13.4704	+	6.94445i	−0.894059	+	0.460920i	−0.843085	−	0.537780i	$-0.819263\pi$
$227$	−13.4704	+	6.94445i	−0.894059	+	0.460920i	−0.0509743	+	0.998700i	$0.516233\pi$
$228$		0			0
$229$	−6.79834	−	1.31027i	−0.449247	−	0.0865853i	−0.0403907	−	0.999184i	$-0.512860\pi$
$229$	−6.79834	−	1.31027i	−0.449247	−	0.0865853i	−0.408857	+	0.912599i	$0.634072\pi$
$230$	−22.9303	+	39.7164i	−1.51198	+	2.61882i
$231$		0			0
$232$	−9.99314	−	28.8733i	−0.656082	−	1.89562i
$233$	8.61240	+	6.77287i	0.564217	+	0.443705i	0.859085	−	0.511833i	$-0.171033\pi$
$233$	8.61240	+	6.77287i	0.564217	+	0.443705i	−0.294868	+	0.955538i	$0.595276\pi$
$234$		0			0
$235$	9.70161	−	9.25047i	0.632863	−	0.603434i
$236$	2.33171	+	1.83368i	0.151781	+	0.119362i
$237$		0			0
$238$	2.70650	+	4.68780i	0.175437	+	0.303865i
$239$	−3.46894	+	6.00839i	−0.224387	+	0.388650i	−0.956135	−	0.292925i	$-0.905371\pi$
$239$	−3.46894	+	6.00839i	−0.224387	+	0.388650i	0.731748	+	0.681575i	$0.238705\pi$
$240$		0			0
$241$	−9.10034	−	19.9270i	−0.586205	−	1.28361i	−0.937709	−	0.347423i	$-0.887057\pi$
$241$	−9.10034	−	19.9270i	−0.586205	−	1.28361i	0.351504	−	0.936186i	$-0.385670\pi$
$242$	17.0330	−	8.78110i	1.09492	−	0.564471i
$243$		0			0
$244$	−3.78954	−	2.43539i	−0.242601	−	0.155910i
$245$	4.97790	−	3.91467i	0.318026	−	0.250099i
$246$		0			0
$247$	6.18836	+	0.590917i	0.393756	+	0.0375991i
$248$	−25.7378	−	10.3038i	−1.63435	−	0.654295i
$249$		0			0
$250$	−54.7005	−	28.2001i	−3.45956	−	1.78353i
$251$	−0.704986	+	14.7995i	−0.0444983	+	0.934134i	0.860692	+	0.509127i	$0.170032\pi$
$251$	−0.704986	+	14.7995i	−0.0444983	+	0.934134i	−0.905190	+	0.425008i	$0.860271\pi$
$252$		0			0
$253$	7.80360	+	2.29134i	0.490608	+	0.144055i
$254$	13.7330	−	8.82567i	0.861685	−	0.553772i
$255$		0			0
$256$	−24.3084	+	4.68507i	−1.51928	+	0.292817i
$257$	−3.78201	−	5.31110i	−0.235916	−	0.331297i	0.679598	−	0.733585i	$-0.262154\pi$
$257$	−3.78201	−	5.31110i	−0.235916	−	0.331297i	−0.915513	+	0.402288i	$0.868215\pi$
$258$		0			0
$259$	−10.8132	+	3.17504i	−0.671899	+	0.197287i
$260$	12.2336	−	14.1183i	0.758695	−	0.875581i
$261$		0			0
$262$	−12.9740	+	18.2194i	−0.801537	+	1.12560i
$263$	8.05180	−	17.6310i	0.496495	−	1.08717i	−0.481097	−	0.876667i	$-0.659762\pi$
$263$	8.05180	−	17.6310i	0.496495	−	1.08717i	0.977593	−	0.210506i	$-0.0675110\pi$
$264$		0			0
$265$	1.48327	+	10.3163i	0.0911163	+	0.633728i
$266$	19.1447	+	18.2544i	1.17383	+	1.11925i
$267$		0			0
$268$	−14.1657	+	25.5077i	−0.865309	+	1.55813i
$269$	−18.9281			−1.15407			−0.577034	−	0.816720i	$-0.695790\pi$
$269$	−18.9281			−1.15407			−0.577034	+	0.816720i	$0.695790\pi$
$270$		0			0
$271$	0.0964425	+	0.670772i	0.00585846	+	0.0407465i	0.992541	−	0.121911i	$-0.0389024\pi$
$271$	0.0964425	+	0.670772i	0.00585846	+	0.0407465i	−0.986683	+	0.162658i	$0.947993\pi$
$272$	−0.0738390	−	1.55007i	−0.00447714	−	0.0939868i
$273$		0			0
$274$	29.5688	−	41.5235i	1.78632	−	2.50853i
$275$	−4.57227	+	18.8472i	−0.275719	+	1.13653i
$276$		0			0
$277$	−27.5272	+	8.08272i	−1.65395	+	0.485644i	−0.969842	−	0.243736i	$-0.921627\pi$
$277$	−27.5272	+	8.08272i	−1.65395	+	0.485644i	−0.684109	+	0.729380i	$0.739809\pi$
$278$	7.60009	−	3.04262i	0.455823	−	0.182484i
$279$		0			0
$280$	34.2606	−	6.60319i	2.04746	−	0.394616i
$281$	−2.37894	+	6.87349i	−0.141916	+	0.410038i	−0.993451	−	0.114259i	$-0.963551\pi$
$281$	−2.37894	+	6.87349i	−0.141916	+	0.410038i	0.851535	+	0.524297i	$0.175672\pi$
$282$		0			0
$283$	−5.37726	−	1.57891i	−0.319645	−	0.0938562i	0.117974	−	0.993017i	$-0.462360\pi$
$283$	−5.37726	−	1.57891i	−0.319645	−	0.0938562i	−0.437619	+	0.899160i	$0.644178\pi$
$284$	−15.3544	+	1.46617i	−0.911116	+	0.0870010i
$285$		0			0
$286$	−4.59690	−	2.36987i	−0.271820	−	0.140133i
$287$	−0.452727	−	1.86617i	−0.0267236	−	0.110156i
$288$		0			0
$289$	15.9591	+	1.52391i	0.938771	+	0.0896417i
$290$	−11.2670	+	78.3635i	−0.661620	+	4.60167i
$291$		0			0
$292$	−9.99511	−	6.42347i	−0.584920	−	0.375905i
$293$	−19.3517	−	22.3331i	−1.13054	−	1.30471i	−0.946831	−	0.321731i	$-0.895735\pi$
$293$	−19.3517	−	22.3331i	−1.13054	−	1.30471i	−0.183708	−	0.982981i	$-0.558810\pi$
$294$		0			0
$295$	−1.40148	−	3.06880i	−0.0815971	−	0.178673i
$296$	17.5141	+	3.37556i	1.01798	+	0.196200i
$297$		0			0
$298$	16.6653	+	28.8651i	0.965394	+	1.67211i
$299$	2.02760	+	5.85837i	0.117259	+	0.338798i
$300$		0			0
$301$	−3.89562	+	3.71447i	−0.224540	+	0.214098i
$302$	−5.31841	+	5.07109i	−0.306040	+	0.291809i
$303$		0			0
$304$	−2.48034	−	7.16648i	−0.142258	−	0.411026i
$305$	2.56160	+	4.43682i	0.146677	+	0.254051i
$306$		0			0
$307$	4.17398	+	0.804469i	0.238222	+	0.0459135i	0.306965	−	0.951721i	$-0.400687\pi$
$307$	4.17398	+	0.804469i	0.238222	+	0.0459135i	−0.0687428	+	0.997634i	$0.521899\pi$
$308$	−5.85630	−	12.8235i	−0.333694	−	0.730688i
$309$		0			0
$310$	47.0428	+	54.2903i	2.67185	+	3.08348i
$311$	14.6651	+	9.42466i	0.831579	+	0.534423i	0.885779	−	0.464107i	$-0.153625\pi$
$311$	14.6651	+	9.42466i	0.831579	+	0.534423i	−0.0542003	+	0.998530i	$0.517261\pi$
$312$		0			0
$313$	−4.33802	+	30.1716i	−0.245199	+	1.70540i	0.380043	+	0.924969i	$0.375909\pi$
$313$	−4.33802	+	30.1716i	−0.245199	+	1.70540i	−0.625242	+	0.780431i	$0.715000\pi$
$314$	12.6787	+	1.21067i	0.715503	+	0.0683222i
$315$		0			0
$316$	5.65121	+	23.2946i	0.317905	+	1.31042i
$317$	−15.0865	−	7.77761i	−0.847340	−	0.436834i	−0.0208478	−	0.999783i	$-0.506637\pi$
$317$	−15.0865	−	7.77761i	−0.847340	−	0.436834i	−0.826492	+	0.562949i	$0.809667\pi$
$318$		0			0
$319$	13.9766	−	1.33460i	0.782537	−	0.0747232i
$320$	45.8646	+	13.4671i	2.56391	+	0.752832i
$321$		0			0
$322$	−8.62789	+	24.9286i	−0.480813	+	1.38922i
$323$	−4.64647	+	0.895535i	−0.258537	+	0.0498289i
$324$		0			0
$325$	−13.7238	+	5.49420i	−0.761262	+	0.304763i
$326$	−51.9527	+	15.2547i	−2.87739	+	0.844879i
$327$		0			0
$328$	−0.716525	+	2.95356i	−0.0395635	+	0.163083i
$329$	4.47263	−	6.28093i	0.246584	−	0.346279i
$330$		0			0
$331$	0.0817484	+	1.71611i	0.00449330	+	0.0943260i	1.00000		0.000365861i	$-0.000116457\pi$
$331$	0.0817484	+	1.71611i	0.00449330	+	0.0943260i	−0.995507	+	0.0946918i	$0.969813\pi$
$332$	2.93339	+	20.4022i	0.160991	+	1.11972i
$333$		0			0
$334$	−11.7971			−0.645509
$335$	27.6133	−	18.4030i	1.50867	−	1.00546i
$336$		0			0
$337$	−9.23040	−	8.80117i	−0.502812	−	0.479430i	0.395699	−	0.918380i	$-0.370502\pi$
$337$	−9.23040	−	8.80117i	−0.502812	−	0.479430i	−0.898512	+	0.438950i	$0.855351\pi$
$338$	3.80322	+	26.4520i	0.206868	+	1.43880i
$339$		0			0
$340$	−5.90723	+	12.9350i	−0.320365	+	0.701501i
$341$	7.38973	−	10.3774i	0.400177	−	0.561969i
$342$		0			0
$343$	13.0751	−	15.0895i	0.705989	−	0.814754i
$344$	8.17400	−	2.40010i	0.440712	−	0.129405i
$345$		0			0
$346$	−24.1724	−	33.9454i	−1.29952	−	1.82492i
$347$	25.0366	−	4.82541i	1.34404	−	0.259042i	0.534031	−	0.845465i	$-0.320677\pi$
$347$	25.0366	−	4.82541i	1.34404	−	0.259042i	0.810005	+	0.586423i	$0.199464\pi$
$348$		0			0
$349$	−7.26168	+	4.66680i	−0.388709	+	0.249808i	−0.720369	−	0.693591i	$-0.756028\pi$
$349$	−7.26168	+	4.66680i	−0.388709	+	0.249808i	0.331660	+	0.943399i	$0.392391\pi$
$350$	−60.3559	−	17.7221i	−3.22616	−	0.947285i
$351$		0			0
$352$	0.295462	−	6.20251i	0.0157482	−	0.330595i
$353$	21.1012	+	10.8784i	1.12310	+	0.578999i	0.916743	−	0.399478i	$-0.130808\pi$
$353$	21.1012	+	10.8784i	1.12310	+	0.578999i	0.206358	+	0.978477i	$0.433839\pi$
$354$		0			0
$355$	16.2856	+	6.51979i	0.864352	+	0.346034i
$356$	−29.8429	−	2.84965i	−1.58167	−	0.151031i
$357$		0			0
$358$	28.6272	−	22.5127i	1.51299	−	1.18983i
$359$	−19.9466	−	12.8189i	−1.05274	−	0.676555i	−0.104635	−	0.994511i	$-0.533367\pi$
$359$	−19.9466	−	12.8189i	−1.05274	−	0.676555i	−0.948106	+	0.317956i	$0.897004\pi$
$360$		0			0
$361$	−3.66608	+	1.88999i	−0.192951	+	0.0994734i
$362$	−23.6150	−	51.7095i	−1.24117	−	2.71779i
$363$		0			0
$364$	5.37283	−	9.30601i	0.281613	−	0.487767i
$365$	6.75635	+	11.7023i	0.353643	+	0.612528i
$366$		0			0
$367$	−9.77911	−	7.69038i	−0.510466	−	0.401435i	0.329432	−	0.944179i	$-0.393143\pi$
$367$	−9.77911	−	7.69038i	−0.510466	−	0.401435i	−0.839898	+	0.542745i	$0.817385\pi$
$368$	5.47332	−	5.21880i	0.285316	−	0.272049i
$369$		0			0
$370$	−36.3289	−	28.5693i	−1.88865	−	1.48525i
$371$	1.96081	+	5.66538i	0.101800	+	0.294132i
$372$		0			0
$373$	−8.25888	+	14.3048i	−0.427629	+	0.740675i	−0.996662	−	0.0816398i	$-0.973984\pi$
$373$	−8.25888	+	14.3048i	−0.427629	+	0.740675i	0.569033	+	0.822315i	$0.307318\pi$
$374$	3.86563	+	0.745040i	0.199887	+	0.0385251i
$375$		0			0
$376$	−10.8470	+	5.59201i	−0.559390	+	0.288386i
$377$	7.00828	+	8.08799i	0.360945	+	0.416553i
$378$		0			0
$379$	15.4660	−	12.1626i	0.794434	−	0.624750i	−0.136208	−	0.990680i	$-0.543492\pi$
$379$	15.4660	−	12.1626i	0.794434	−	0.624750i	0.930642	+	0.365931i	$0.119249\pi$
$380$	−9.88969	+	68.7843i	−0.507330	+	3.52856i
$381$		0			0
$382$	−47.4067	−	18.9788i	−2.42554	−	0.971040i
$383$	7.02640	+	28.9632i	0.359032	+	1.47995i	0.809480	+	0.587148i	$0.199749\pi$
$383$	7.02640	+	28.9632i	0.359032	+	1.47995i	−0.450447	+	0.892803i	$0.648735\pi$
$384$		0			0
$385$	−0.762894	+	16.0151i	−0.0388807	+	0.816206i
$386$	13.1919	−	1.25968i	0.671451	−	0.0641158i
$387$		0			0
$388$	37.3971	−	24.0336i	1.89855	−	1.22012i
$389$	9.73451	−	28.1260i	0.493559	−	1.42605i	−0.373401	−	0.927670i	$-0.621809\pi$
$389$	9.73451	−	28.1260i	0.493559	−	1.42605i	0.866961	−	0.498376i	$-0.166070\pi$
$390$		0			0
$391$	−2.73723	−	3.84391i	−0.138428	−	0.194395i
$392$	−5.35226	+	2.14272i	−0.270330	+	0.108224i
$393$		0			0
$394$	−17.0416	+	19.6670i	−0.858541	+	0.990809i
$395$	6.42721	−	26.4933i	0.323388	−	1.33302i
$396$		0			0
$397$	10.0570	−	22.0218i	0.504748	−	1.10524i	−0.470148	−	0.882587i	$-0.655800\pi$
$397$	10.0570	−	22.0218i	0.504748	−	1.10524i	0.974897	−	0.222657i	$-0.0714731\pi$
$398$	−0.382794	−	8.03584i	−0.0191878	−	0.402800i
$399$		0			0
$400$	13.0515	+	12.4446i	0.652577	+	0.622231i
$401$	12.0916			0.603827			0.301914	−	0.953335i	$-0.402375\pi$
$401$	12.0916			0.603827			0.301914	+	0.953335i	$0.402375\pi$
$402$		0			0
$403$	9.71068			0.483723
$404$	18.3053	+	17.4541i	0.910723	+	0.868373i
$405$		0			0
$406$	2.16684	+	45.4876i	0.107538	+	2.25751i
$407$	−3.40484	+	7.45555i	−0.168771	+	0.369558i
$408$		0			0
$409$	−6.92973	+	28.5647i	−0.342653	+	1.41243i	0.496262	+	0.868173i	$0.334705\pi$
$409$	−6.92973	+	28.5647i	−0.342653	+	1.41243i	−0.838915	+	0.544262i	$0.816810\pi$
$410$	5.15710	−	5.95161i	0.254691	−	0.293929i
$411$		0			0
$412$	40.7660	−	16.3203i	2.00840	−	0.804041i
$413$	−1.12565	−	1.58075i	−0.0553894	−	0.0777835i
$414$		0			0
$415$	7.66725	−	22.1531i	0.376370	−	1.08745i
$416$	3.98179	−	2.55894i	0.195223	−	0.125462i
$417$		0			0
$418$	19.1514	−	1.82873i	0.936724	−	0.0894463i
$419$	0.559066	−	11.7362i	0.0273121	−	0.573352i	−0.943189	−	0.332256i	$-0.892190\pi$
$419$	0.559066	−	11.7362i	0.0273121	−	0.573352i	0.970501	−	0.241096i	$-0.0775069\pi$
$420$		0			0
$421$	−4.94431	−	20.3807i	−0.240971	−	0.993296i	−0.955805	−	0.294001i	$-0.905013\pi$
$421$	−4.94431	−	20.3807i	−0.240971	−	0.993296i	0.714834	−	0.699294i	$-0.246502\pi$
$422$	18.9655	+	7.59263i	0.923225	+	0.369604i
$423$		0			0
$424$	1.35034	−	9.39179i	0.0655781	−	0.456106i
$425$	8.84514	−	6.95589i	0.429052	−	0.337410i
$426$		0			0
$427$	1.92982	+	2.22714i	0.0933907	+	0.107779i
$428$	30.3319	−	15.6372i	1.46615	−	0.755851i
$429$		0			0
$430$	−21.6753	−	4.17758i	−1.04528	−	0.201461i
$431$	13.2004	−	22.8638i	0.635842	−	1.10131i	−0.350494	−	0.936565i	$-0.613986\pi$
$431$	13.2004	−	22.8638i	0.635842	−	1.10131i	0.986336	−	0.164746i	$-0.0526804\pi$
$432$		0			0
$433$	2.97280	+	8.58935i	0.142864	+	0.412778i	0.993620	−	0.112783i	$-0.0359766\pi$
$433$	2.97280	+	8.58935i	0.142864	+	0.412778i	−0.850756	+	0.525561i	$0.823855\pi$
$434$	32.4806	+	25.5430i	1.55912	+	1.22610i
$435$		0			0
$436$	44.9128	−	42.8242i	2.15093	−	2.05091i
$437$	−18.1269	−	14.2552i	−0.867127	−	0.681916i
$438$		0			0
$439$	18.3008	+	31.6978i	0.873447	+	1.51286i	0.858407	+	0.512968i	$0.171454\pi$
$439$	18.3008	+	31.6978i	0.873447	+	1.51286i	0.0150400	+	0.999887i	$0.495212\pi$
$440$	12.6878	−	21.9760i	0.604868	−	1.04766i
$441$		0			0
$442$	1.24656	+	2.72959i	0.0592930	+	0.129833i
$443$	11.7512	−	6.05816i	0.558316	−	0.287832i	−0.155882	−	0.987776i	$-0.549822\pi$
$443$	11.7512	−	6.05816i	0.558316	−	0.287832i	0.714198	+	0.699944i	$0.246792\pi$
$444$		0			0
$445$	28.6827	+	18.4333i	1.35969	+	0.873821i
$446$	−36.3960	+	28.6221i	−1.72340	+	1.35530i
$447$		0			0
$448$	27.3711	+	2.61363i	1.29316	+	0.123482i
$449$	−13.1639	−	5.27005i	−0.621245	−	0.248709i	0.0396188	−	0.999215i	$-0.487386\pi$
$449$	−13.1639	−	5.27005i	−0.621245	−	0.248709i	−0.660864	+	0.750506i	$0.729810\pi$
$450$		0			0
$451$	−1.24134	−	0.639957i	−0.0584526	−	0.0301344i
$452$	−0.803183	+	16.8609i	−0.0377786	+	0.793070i
$453$		0			0
$454$	−34.3017	−	10.0719i	−1.60986	−	0.472697i
$455$	−10.2811	+	6.60728i	−0.481987	+	0.309754i
$456$		0			0
$457$	7.61250	−	1.46719i	0.356098	−	0.0686322i	−0.00806523	−	0.999967i	$-0.502567\pi$
$457$	7.61250	−	1.46719i	0.356098	−	0.0686322i	0.364163	+	0.931335i	$0.381355\pi$
$458$	−9.47348	−	13.3036i	−0.442667	−	0.621638i
$459$		0			0
$460$	−66.4924	+	19.5239i	−3.10022	+	0.910308i
$461$	7.81140	−	9.01483i	0.363813	−	0.419863i	−0.544101	−	0.839020i	$-0.683129\pi$
$461$	7.81140	−	9.01483i	0.363813	−	0.419863i	0.907914	+	0.419157i	$0.137674\pi$
$462$		0			0
$463$	−2.05728	+	2.88904i	−0.0956097	+	0.134265i	−0.859610	−	0.510951i	$-0.829293\pi$
$463$	−2.05728	+	2.88904i	−0.0956097	+	0.134265i	0.764000	+	0.645216i	$0.223233\pi$
$464$	5.42341	−	11.8756i	0.251775	−	0.551311i
$465$		0			0
$466$	3.67823	+	25.5826i	0.170390	+	1.18509i
$467$	8.03883	+	7.66501i	0.371993	+	0.354694i	0.852897	−	0.522078i	$-0.174843\pi$
$467$	8.03883	+	7.66501i	0.371993	+	0.354694i	−0.480905	+	0.876773i	$0.659692\pi$
$468$		0			0
$469$	13.5931	−	13.4003i	0.627671	−	0.618768i
$470$	31.6214			1.45859
$471$		0			0
$472$	0.437095	+	3.04006i	0.0201189	+	0.139930i
$473$	0.186270	+	3.91028i	0.00856469	+	0.179795i
$474$		0			0
$475$	31.8973	−	44.7934i	1.46355	−	2.05526i
$476$	−1.92840	+	7.94899i	−0.0883882	+	0.364341i
$477$		0			0
$478$	−15.7031	+	4.61084i	−0.718242	+	0.210895i
$479$	13.3259	−	5.33489i	0.608876	−	0.243757i	−0.0466725	−	0.998910i	$-0.514862\pi$
$479$	13.3259	−	5.33489i	0.608876	−	0.243757i	0.655549	+	0.755153i	$0.272437\pi$
$480$		0			0
$481$	−6.13459	+	1.18235i	−0.279713	+	0.0539103i
$482$	16.9017	−	48.8341i	0.769850	−	2.22433i
$483$		0			0
$484$	27.7845	+	8.15825i	1.26293	+	0.370830i
$485$	−50.3293	+	4.80587i	−2.28534	+	0.218223i
$486$		0			0
$487$	−2.60481	−	1.34287i	−0.118035	−	0.0608513i	0.398198	−	0.917300i	$-0.369636\pi$
$487$	−2.60481	−	1.34287i	−0.118035	−	0.0608513i	−0.516233	+	0.856448i	$0.672666\pi$
$488$	−1.09959	−	4.53258i	−0.0497762	−	0.205180i
$489$		0			0
$490$	14.8710	+	1.42001i	0.671802	+	0.0641493i
$491$	3.57046	−	24.8331i	0.161132	−	1.12070i	−0.735371	−	0.677665i	$-0.762992\pi$
$491$	3.57046	−	24.8331i	0.161132	−	1.12070i	0.896504	−	0.443036i	$-0.146099\pi$
$492$		0			0
$493$	−6.85309	−	4.40422i	−0.308648	−	0.198356i
$494$	9.60310	+	11.0826i	0.432064	+	0.498628i
$495$		0			0
$496$	−4.92107	−	10.7756i	−0.220962	−	0.483840i
$497$	9.90815	+	1.90964i	0.444441	+	0.0856590i
$498$		0			0
$499$	−0.0190544	−	0.0330032i	−0.000852993	−	0.00147743i	0.865599	−	0.500739i	$-0.166938\pi$
$499$	−0.0190544	−	0.0330032i	−0.000852993	−	0.00147743i	−0.866452	+	0.499261i	$0.833605\pi$
$500$	−30.4158	−	87.8807i	−1.36024	−	3.93014i
$501$		0			0
$502$	−25.2949	+	24.1187i	−1.12897	+	1.07647i
$503$	28.8426	−	27.5013i	1.28603	−	1.22622i	0.326306	−	0.945264i	$-0.394196\pi$
$503$	28.8426	−	27.5013i	1.28603	−	1.22622i	0.959720	−	0.280959i	$-0.0906525\pi$
$504$		0			0
$505$	−9.40843	−	27.1839i	−0.418670	−	1.20967i
$506$	9.59265	+	16.6150i	0.426445	+	0.738625i
$507$		0			0
$508$	24.2220	+	4.66841i	1.07468	+	0.207127i
$509$	8.62498	+	18.8861i	0.382296	+	0.837111i	0.998763	+	0.0497300i	$0.0158361\pi$
$509$	8.62498	+	18.8861i	0.382296	+	0.837111i	−0.616467	+	0.787381i	$0.711437\pi$
$510$		0			0
$511$	5.09001	+	5.87418i	0.225169	+	0.259859i
$512$	−14.6502	−	9.41509i	−0.647452	−	0.416092i
$513$		0			0
$514$	2.18886	−	15.2239i	0.0965466	−	0.671496i
$515$	−49.7151	−	4.74722i	−2.19071	−	0.209187i
$516$		0			0
$517$	−1.32210	−	5.44975i	−0.0581457	−	0.239680i
$518$	−23.6292	−	12.1817i	−1.03821	−	0.535233i
$519$		0			0
$520$	19.2547	−	1.83861i	0.844376	−	0.0806282i
$521$	9.46928	+	2.78043i	0.414857	+	0.121813i	0.482499	−	0.875897i	$-0.339729\pi$
$521$	9.46928	+	2.78043i	0.414857	+	0.121813i	−0.0676419	+	0.997710i	$0.521548\pi$
$522$		0			0
$523$	9.01310	−	26.0416i	0.394115	−	1.13872i	−0.557167	−	0.830400i	$-0.688112\pi$
$523$	9.01310	−	26.0416i	0.394115	−	1.13872i	0.951282	−	0.308321i	$-0.0997671\pi$
$524$	−33.1875	+	6.39637i	−1.44980	+	0.279427i
$525$		0			0
$526$	42.4470	−	16.9932i	1.85078	−	0.740939i
$527$	−7.09232	+	2.08249i	−0.308946	+	0.0907149i
$528$		0			0
$529$	−0.000728675		0.00300364i	−3.16815e−5		0.000130593i
$530$	−14.2612	+	20.0270i	−0.619466	+	0.869918i
$531$		0			0
$532$	1.90196	+	39.9271i	0.0824605	+	1.73106i
$533$	−0.151500	−	1.05370i	−0.00656218	−	0.0456410i
$534$		0			0
$535$	−38.8114			−1.67796
$536$	−28.8403	+	8.99273i	−1.24571	+	0.388427i
$537$		0			0
$538$	−32.3148	−	30.8121i	−1.39319	−	1.32841i
$539$	−0.377029	−	2.62229i	−0.0162398	−	0.112950i
$540$		0			0
$541$	−1.18932	+	2.60424i	−0.0511328	+	0.111965i	−0.933474	−	0.358645i	$-0.883239\pi$
$541$	−1.18932	+	2.60424i	−0.0511328	+	0.111965i	0.882341	+	0.470610i	$0.155966\pi$
$542$	−0.927267	+	1.30216i	−0.0398295	+	0.0559327i
$543$		0			0
$544$	−2.35937	+	2.72286i	−0.101157	+	0.116742i
$545$	−67.7195	+	19.8842i	−2.90078	+	0.851747i
$546$		0			0
$547$	−11.3597	−	15.9525i	−0.485707	−	0.682079i	0.496894	−	0.867811i	$-0.334474\pi$
$547$	−11.3597	−	15.9525i	−0.485707	−	0.682079i	−0.982600	+	0.185732i	$0.940534\pi$
$548$	75.6370	−	14.5778i	3.23105	−	0.622734i
$549$		0			0
$550$	−38.4864	+	24.7337i	−1.64106	+	1.05465i
$551$	−38.1972	−	11.2157i	−1.62726	−	0.477806i
$552$		0			0
$553$	0.746146	−	15.6635i	0.0317294	−	0.666081i
$554$	−60.1531	−	31.0111i	−2.55566	−	1.31753i
$555$		0			0
$556$	11.4845	+	4.59768i	0.487049	+	0.194985i
$557$	42.7005	+	4.07741i	1.80928	+	0.172765i	0.944309	−	0.329059i	$-0.106731\pi$
$557$	42.7005	+	4.07741i	1.80928	+	0.172765i	0.864970	+	0.501824i	$0.167337\pi$
$558$		0			0
$559$	−2.34554	+	1.84456i	−0.0992059	+	0.0780164i
$560$	12.5420	+	8.06028i	0.529998	+	0.340609i
$561$		0			0
$562$	−15.2504	+	7.86215i	−0.643301	+	0.331645i
$563$	10.6216	+	23.2580i	0.447647	+	0.980210i	0.990131	+	0.140144i	$0.0447565\pi$
$563$	10.6216	+	23.2580i	0.447647	+	0.980210i	−0.542484	+	0.840066i	$0.682516\pi$
$564$		0			0
$565$	9.59895	−	16.6259i	0.403831	−	0.699456i
$566$	−6.61005	−	11.4489i	−0.277841	−	0.481235i
$567$		0			0
$568$	−12.5533	−	9.87205i	−0.526726	−	0.414222i
$569$	−25.8665	+	24.6636i	−1.08438	+	1.03395i	−0.0850848	+	0.996374i	$0.527116\pi$
$569$	−25.8665	+	24.6636i	−1.08438	+	1.03395i	−0.999294	+	0.0375791i	$0.988035\pi$
$570$		0			0
$571$	−3.06374	−	2.40935i	−0.128213	−	0.100828i	0.551993	−	0.833849i	$-0.313867\pi$
$571$	−3.06374	−	2.40935i	−0.128213	−	0.100828i	−0.680206	+	0.733021i	$0.738110\pi$
$572$	−2.55607	−	7.38528i	−0.106875	−	0.308794i
$573$		0			0
$574$	2.26493	−	3.92297i	0.0945362	−	0.163741i
$575$	53.8469	+	10.3781i	2.24557	+	0.432798i
$576$		0			0
$577$	21.6117	−	11.1416i	0.899709	−	0.463832i	0.0546500	−	0.998506i	$-0.482596\pi$
$577$	21.6117	−	11.1416i	0.899709	−	0.463832i	0.845059	+	0.534673i	$0.179565\pi$
$578$	24.7653	+	28.5807i	1.03010	+	1.18880i
$579$		0			0
$580$	−94.0374	+	73.9518i	−3.90469	+	3.07068i
$581$	1.91902	−	13.3471i	0.0796143	−	0.553730i
$582$		0			0
$583$	4.04780	+	1.62049i	0.167643	+	0.0671140i
$584$	−2.90023	−	11.9549i	−0.120012	−	0.494698i
$585$		0			0
$586$	3.31687	−	69.6296i	0.137019	−	2.87637i
$587$	−26.1731	+	2.49923i	−1.08028	+	0.103154i	−0.619986	−	0.784613i	$-0.712862\pi$
$587$	−26.1731	+	2.49923i	−1.08028	+	0.103154i	−0.460294	+	0.887767i	$0.652256\pi$
$588$		0			0
$589$	−30.3881	+	19.5293i	−1.25212	+	0.804689i
$590$	2.60290	−	7.52058i	0.107160	−	0.309617i
$591$		0			0
$592$	4.42083	+	6.20818i	0.181695	+	0.255155i
$593$	4.32623	−	1.73196i	0.177657	−	0.0711231i	−0.281129	−	0.959670i	$-0.590709\pi$
$593$	4.32623	−	1.73196i	0.177657	−	0.0711231i	0.458786	+	0.888547i	$0.348285\pi$
$594$		0			0
$595$	6.09200	−	7.03054i	0.249748	−	0.288224i
$596$	−11.8741	+	48.9459i	−0.486384	+	2.00490i
$597$		0			0
$598$	−6.07495	+	13.3023i	−0.248423	+	0.543970i
$599$	1.91051	+	40.1065i	0.0780612	+	1.63871i	0.610342	+	0.792138i	$0.291032\pi$
$599$	1.91051	+	40.1065i	0.0780612	+	1.63871i	−0.532280	+	0.846568i	$0.678665\pi$
$600$		0			0
$601$	4.83991	+	4.61484i	0.197424	+	0.188243i	0.782342	−	0.622849i	$-0.214025\pi$
$601$	4.83991	+	4.61484i	0.197424	+	0.188243i	−0.584918	+	0.811092i	$0.698873\pi$
$602$	−12.6974			−0.517506
$603$		0			0
$604$	−11.1044			−0.451831
$605$	−23.8353	−	22.7269i	−0.969042	−	0.923980i
$606$		0			0
$607$	0.178730	+	3.75201i	0.00725443	+	0.152289i	0.999588	+	0.0287012i	$0.00913712\pi$
$607$	0.178730	+	3.75201i	0.00725443	+	0.152289i	−0.992334	+	0.123588i	$0.960560\pi$
$608$	−7.31409	+	16.0156i	−0.296626	+	0.649520i
$609$		0			0
$610$	−2.84921	+	11.7446i	−0.115361	+	0.475526i
$611$	2.79921	−	3.23046i	0.113244	−	0.130690i
$612$		0			0
$613$	7.93797	−	3.17788i	0.320612	−	0.128354i	−0.205774	−	0.978600i	$-0.565971\pi$
$613$	7.93797	−	3.17788i	0.320612	−	0.128354i	0.526386	+	0.850246i	$0.323547\pi$
$614$	5.81644	+	8.16804i	0.234732	+	0.329635i
$615$		0			0
$616$	4.77401	−	13.7936i	0.192350	−	0.555759i
$617$	6.62685	−	4.25882i	0.266787	−	0.171454i	−0.400407	−	0.916337i	$-0.631131\pi$
$617$	6.62685	−	4.25882i	0.266787	−	0.171454i	0.667194	+	0.744884i	$0.267495\pi$
$618$		0			0
$619$	−22.2777	+	2.12726i	−0.895416	+	0.0855018i	−0.532608	−	0.846362i	$-0.678788\pi$
$619$	−22.2777	+	2.12726i	−0.895416	+	0.0855018i	−0.362808	+	0.931864i	$0.618182\pi$
$620$	−5.16508	+	108.428i	−0.207435	+	4.35459i
$621$		0			0
$622$	9.69484	+	39.9627i	0.388728	+	1.60236i
$623$	18.2071	+	7.28903i	0.729453	+	0.292029i
$624$		0			0
$625$	−6.91491	+	48.0943i	−0.276596	+	1.92377i
$626$	−56.5209	+	44.4485i	−2.25903	+	1.77652i
$627$		0			0
$628$	12.6034	+	14.5451i	0.502930	+	0.580412i
$629$	4.22692	−	2.17913i	0.168538	−	0.0868875i
$630$		0			0
$631$	−25.3647	−	4.88864i	−1.00975	−	0.194614i	−0.342557	−	0.939497i	$-0.611293\pi$
$631$	−25.3647	−	4.88864i	−1.00975	−	0.194614i	−0.667195	+	0.744883i	$0.732505\pi$
$632$	−12.4093	+	21.4935i	−0.493615	+	0.854966i
$633$		0			0
$634$	−13.0954	−	37.8367i	−0.520086	−	1.50269i
$635$	−22.0528	−	17.3425i	−0.875137	−	0.688216i
$636$		0			0
$637$	1.46149	−	1.39352i	0.0579062	−	0.0552135i
$638$	26.0339	+	20.4733i	1.03069	+	0.810545i
$639$		0			0
$640$	41.5363	+	71.9430i	1.64187	+	2.84380i
$641$	−3.38149	+	5.85691i	−0.133561	+	0.231334i	−0.925047	−	0.379853i	$-0.875974\pi$
$641$	−3.38149	+	5.85691i	−0.133561	+	0.231334i	0.791486	+	0.611187i	$0.209308\pi$
$642$		0			0
$643$	9.75608	+	21.3628i	0.384742	+	0.842468i	0.998592	+	0.0530450i	$0.0168927\pi$
$643$	9.75608	+	21.3628i	0.384742	+	0.842468i	−0.613850	+	0.789423i	$0.710380\pi$
$644$	−35.4307	+	18.2658i	−1.39616	+	0.719772i
$645$		0			0
$646$	−9.39045	−	6.03487i	−0.369462	−	0.237439i
$647$	−0.447389	+	0.351830i	−0.0175887	+	0.0138319i	−0.626915	−	0.779088i	$-0.715683\pi$
$647$	−0.447389	+	0.351830i	−0.0175887	+	0.0138319i	0.609326	+	0.792920i	$0.291440\pi$
$648$		0			0
$649$	−1.40495	−	0.134157i	−0.0551493	−	0.00526612i
$650$	−32.3736	−	12.9605i	−1.26980	−	0.508351i
$651$		0			0
$652$	−72.7242	−	37.4919i	−2.84810	−	1.46830i
$653$	−0.0312763	+	0.656571i	−0.00122394	+	0.0256936i	−0.999397	−	0.0347312i	$-0.988942\pi$
$653$	−0.0312763	+	0.656571i	−0.00122394	+	0.0256936i	0.998173	+	0.0604248i	$0.0192455\pi$
$654$		0			0
$655$	36.8823	+	10.8296i	1.44111	+	0.423148i
$656$	−1.09249	+	0.702098i	−0.0426544	+	0.0274123i
$657$		0			0
$658$	17.8603	−	3.44229i	0.696266	−	0.134194i
$659$	−13.5038	−	18.9634i	−0.526032	−	0.738708i	0.463008	−	0.886354i	$-0.346770\pi$
$659$	−13.5038	−	18.9634i	−0.526032	−	0.738708i	−0.989040	+	0.147645i	$0.952831\pi$
$660$		0			0
$661$	18.8915	−	5.54704i	0.734793	−	0.215755i	0.107136	−	0.994244i	$-0.465832\pi$
$661$	18.8915	−	5.54704i	0.734793	−	0.215755i	0.627657	+	0.778490i	$0.284014\pi$
$662$	−2.65401	+	3.06289i	−0.103151	+	0.119043i
$663$		0			0
$664$	−12.3793	+	17.3842i	−0.480408	+	0.674639i
$665$	18.8853	−	41.3530i	0.732340	−	1.60360i
$666$		0			0
$667$	−5.64986	−	39.2957i	−0.218764	−	1.52153i
$668$	−12.9017	−	12.3017i	−0.499180	−	0.475968i
$669$		0			0
$670$	77.0998	+	13.5319i	2.97863	+	0.522783i
$671$	2.14324			0.0827389
$672$		0			0
$673$	−4.36576	−	30.3645i	−0.168288	−	1.17047i	−0.882422	−	0.470458i	$-0.844089\pi$
$673$	−4.36576	−	30.3645i	−0.168288	−	1.17047i	0.714134	−	0.700009i	$-0.246821\pi$
$674$	−1.43153	−	30.0514i	−0.0551404	−	1.15754i
$675$		0			0
$676$	−23.4241	+	32.8946i	−0.900927	+	1.26518i
$677$	4.34076	−	17.8929i	0.166829	−	0.687678i	−0.825537	−	0.564348i	$-0.809128\pi$
$677$	4.34076	−	17.8929i	0.166829	−	0.687678i	0.992366	−	0.123330i	$-0.0393573\pi$
$678$		0			0
$679$	−27.9037	+	8.19326i	−1.07084	+	0.314428i
$680$	−13.6687	+	5.47210i	−0.524169	+	0.209846i
$681$		0			0
$682$	29.5090	−	5.68739i	1.12996	−	0.217781i
$683$	−1.29135	+	3.73112i	−0.0494123	+	0.142767i	−0.967007	−	0.254750i	$-0.918007\pi$
$683$	−1.29135	+	3.73112i	−0.0494123	+	0.142767i	0.917595	+	0.397517i	$0.130128\pi$
$684$		0			0
$685$	−84.0576	−	24.6815i	−3.21168	−	0.943033i
$686$	46.8857	−	4.47704i	1.79011	−	0.170934i
$687$		0			0
$688$	3.23549	+	1.66801i	0.123352	+	0.0635924i
$689$	0.783535	+	3.22978i	0.0298503	+	0.123045i
$690$		0			0
$691$	25.3906	+	2.42451i	0.965906	+	0.0922328i	0.566073	−	0.824355i	$-0.308462\pi$
$691$	25.3906	+	2.42451i	0.965906	+	0.0922328i	0.399833	+	0.916588i	$0.369068\pi$
$692$	8.96170	−	62.3300i	0.340673	−	2.36943i
$693$		0			0
$694$	50.5986	+	32.5177i	1.92070	+	1.23436i
$695$	−9.21341	−	10.6328i	−0.349484	−	0.403326i
$696$		0			0
$697$	0.336621	+	0.737097i	0.0127504	+	0.0279195i
$698$	−19.9943	−	3.85358i	−0.756795	−	0.145860i
$699$		0			0
$700$	−47.5269	−	82.3189i	−1.79635	−	3.11136i
$701$	−0.767509	−	2.21757i	−0.0289884	−	0.0837566i	0.929578	−	0.368625i	$-0.120171\pi$
$701$	−0.767509	−	2.21757i	−0.0289884	−	0.0837566i	−0.958567	+	0.284868i	$0.908050\pi$
$702$		0			0
$703$	16.8195	−	16.0373i	0.634358	−	0.604859i
$704$	14.4725	−	13.7995i	0.545455	−	0.520090i
$705$		0			0
$706$	18.3163	+	52.9216i	0.689345	+	1.99173i
$707$	−8.27327	−	14.3297i	−0.311148	−	0.538925i
$708$		0			0
$709$	−43.8832	−	8.45780i	−1.64807	−	0.317639i	−0.721115	−	0.692815i	$-0.756370\pi$
$709$	−43.8832	−	8.45780i	−1.64807	−	0.317639i	−0.926954	+	0.375176i	$0.877582\pi$
$710$	17.1903	+	37.6415i	0.645140	+	1.41266i
$711$		0			0
$712$	−20.3266	−	23.4582i	−0.761772	−	0.879132i
$713$	−30.3041	−	19.4753i	−1.13490	−	0.729355i
$714$		0			0
$715$	−1.26493	+	8.79778i	−0.0473057	+	0.329018i
$716$	54.7832	+	5.23116i	2.04734	+	0.195498i
$717$		0			0
$718$	−13.1864	−	54.3550i	−0.492111	−	2.02851i
$719$	−16.0815	−	8.29058i	−0.599738	−	0.309186i	0.131492	−	0.991317i	$-0.458023\pi$
$719$	−16.0815	−	8.29058i	−0.599738	−	0.309186i	−0.731230	+	0.682131i	$0.761053\pi$
$720$		0			0
$721$	−28.5967	+	2.73065i	−1.06500	+	0.101695i
$722$	−9.33551	−	2.74115i	−0.347432	−	0.102015i
$723$		0			0
$724$	28.0953	−	81.1761i	1.04415	−	3.01689i
$725$	92.9563	−	17.9159i	3.45231	−	0.665379i
$726$		0			0
$727$	−12.0841	+	4.83774i	−0.448174	+	0.179422i	−0.584760	−	0.811206i	$-0.698811\pi$
$727$	−12.0841	+	4.83774i	−0.448174	+	0.179422i	0.136586	+	0.990628i	$0.456387\pi$
$728$	10.6753	−	3.13454i	0.395651	−	0.116174i
$729$		0			0
$730$	−7.51495	+	30.9770i	−0.278141	+	1.14651i
$731$	1.31753	−	1.85021i	0.0487305	−	0.0684323i
$732$		0			0
$733$	0.853046	+	17.9076i	0.0315080	+	0.661433i	0.958284	+	0.285819i	$0.0922654\pi$
$733$	0.853046	+	17.9076i	0.0315080	+	0.661433i	−0.926776	+	0.375615i	$0.877432\pi$
$734$	−4.17651	−	29.0483i	−0.154158	−	1.07219i
$735$		0			0
$736$	−17.5580			−0.647198
$737$	−0.891419	−	13.8535i	−0.0328358	−	0.510299i
$738$		0			0
$739$	11.3107	+	10.7848i	0.416073	+	0.396724i	0.868991	−	0.494827i	$-0.164769\pi$
$739$	11.3107	+	10.7848i	0.416073	+	0.396724i	−0.452919	+	0.891552i	$0.649617\pi$
$740$	−9.93897	−	69.1271i	−0.365364	−	2.54116i
$741$		0			0
$742$	−5.87482	+	12.8641i	−0.215671	+	0.472255i
$743$	13.9042	−	19.5257i	0.510094	−	0.716327i	−0.476563	−	0.879140i	$-0.658118\pi$
$743$	13.9042	−	19.5257i	0.510094	−	0.716327i	0.986657	+	0.162814i	$0.0520569\pi$
$744$		0			0
$745$	37.5115	−	43.2906i	1.37431	−	1.58604i
$746$	−37.3860	+	10.9775i	−1.36880	+	0.401916i
$747$		0			0
$748$	3.45066	+	4.84578i	0.126169	+	0.177179i
$749$	−21.9213	+	4.22499i	−0.800988	+	0.154378i
$750$		0			0
$751$	3.60023	−	2.31372i	0.131374	−	0.0844290i	−0.473303	−	0.880900i	$-0.656938\pi$
$751$	3.60023	−	2.31372i	0.131374	−	0.0844290i	0.604677	+	0.796471i	$0.293302\pi$
$752$	−5.00329	−	1.46910i	−0.182451	−	0.0535725i
$753$		0			0
$754$	−1.20121	+	25.2166i	−0.0437456	+	0.918334i
$755$	11.2253	+	5.78703i	0.408529	+	0.210611i
$756$		0			0
$757$	6.84690	+	2.74108i	0.248855	+	0.0996264i	0.492737	−	0.870179i	$-0.335997\pi$
$757$	6.84690	+	2.74108i	0.248855	+	0.0996264i	−0.243882	+	0.969805i	$0.578421\pi$
$758$	46.2030	+	4.41185i	1.67817	+	0.160246i
$759$		0			0
$760$	−56.5572	+	44.4771i	−2.05155	+	1.61335i
$761$	7.76090	+	4.98763i	0.281332	+	0.180801i	0.673695	−	0.739009i	$-0.264706\pi$
$761$	7.76090	+	4.98763i	0.281332	+	0.180801i	−0.392363	+	0.919810i	$0.628342\pi$
$762$		0			0
$763$	−36.0845	+	18.6029i	−1.30635	+	0.673469i
$764$	−32.0548	−	70.1903i	−1.15970	−	2.53940i
$765$		0			0
$766$	−35.1520	+	60.8851i	−1.27009	+	2.19987i
$767$	−0.537892	−	0.931656i	−0.0194221	−	0.0336401i
$768$		0			0
$769$	−33.4411	−	26.2983i	−1.20592	−	0.948342i	−0.206369	−	0.978474i	$-0.566165\pi$
$769$	−33.4411	−	26.2983i	−1.20592	−	0.948342i	−0.999546	+	0.0301320i	$0.990407\pi$
$770$	−27.3727	+	26.0998i	−0.986443	+	0.940571i
$771$		0			0
$772$	15.7406	+	12.3786i	0.566518	+	0.445515i
$773$	3.53748	+	10.2209i	0.127234	+	0.367620i	0.990569	−	0.137011i	$-0.0437497\pi$
$773$	3.53748	+	10.2209i	0.127234	+	0.367620i	−0.863335	+	0.504631i	$0.831629\pi$
$774$		0			0
$775$	42.9493	−	74.3904i	1.54278	−	2.67218i
$776$	45.1954	+	8.71070i	1.62242	+	0.312696i
$777$		0			0
$778$	62.4041	−	32.1716i	2.23730	−	1.15341i
$779$	2.59321	+	2.99273i	0.0929115	+	0.107226i
$780$		0			0
$781$	5.76855	−	4.53644i	0.206415	−	0.162327i
$782$	1.58419	−	11.0183i	0.0566505	−	0.394013i
$783$		0			0
$784$	−2.28698	−	0.915571i	−0.0816780	−	0.0326990i
$785$	−5.16045	−	21.2717i	−0.184184	−	0.759219i
$786$		0			0
$787$	−0.967419	+	20.3086i	−0.0344848	+	0.723924i	0.913735	+	0.406310i	$0.133185\pi$
$787$	−0.967419	+	20.3086i	−0.0344848	+	0.723924i	−0.948220	+	0.317614i	$0.897118\pi$
$788$	−39.1454	+	3.73793i	−1.39450	+	0.133158i
$789$		0			0
$790$	54.0999	−	34.7679i	1.92479	−	1.23699i
$791$	3.61177	−	10.4355i	0.128420	−	0.371044i
$792$		0			0
$793$	0.947617	+	1.33074i	0.0336509	+	0.0472560i
$794$	53.0181	−	21.2252i	1.88154	−	0.753255i
$795$		0			0
$796$	7.96093	−	9.18741i	0.282168	−	0.325639i
$797$	7.32893	−	30.2103i	0.259604	−	1.07010i	−0.681455	−	0.731860i	$-0.738652\pi$
$797$	7.32893	−	30.2103i	0.259604	−	1.07010i	0.941059	−	0.338243i	$-0.109832\pi$
$798$		0			0
$799$	−1.35165	+	2.95971i	−0.0478181	+	0.104707i
$800$	−1.99218	−	41.8211i	−0.0704343	−	1.47860i
$801$		0			0
$802$	20.6433	+	19.6834i	0.728941	+	0.695044i
$803$	5.65291			0.199487
$804$		0			0
$805$	45.3356			1.59787
$806$	16.5785	+	15.8075i	0.583952	+	0.556797i
$807$		0			0
$808$	1.24607	+	26.1583i	0.0438367	+	0.920246i
$809$	−21.2092	+	46.4417i	−0.745676	+	1.63280i	0.0283100	+	0.999599i	$0.490987\pi$
$809$	−21.2092	+	46.4417i	−0.745676	+	1.63280i	−0.773986	+	0.633203i	$0.781740\pi$
$810$		0			0
$811$	−1.46874	+	6.05423i	−0.0515744	+	0.212593i	−0.991768	−	0.128048i	$-0.959129\pi$
$811$	−1.46874	+	6.05423i	−0.0515744	+	0.212593i	0.940194	+	0.340641i	$0.110644\pi$
$812$	−45.0635	+	52.0061i	−1.58142	+	1.82506i
$813$		0			0
$814$	−17.9494	+	7.18586i	−0.629126	+	0.251864i
$815$	53.9771	+	75.8002i	1.89073	+	2.65516i
$816$		0			0
$817$	3.63042	−	10.4894i	0.127012	−	0.366978i
$818$	−58.3298	+	37.4863i	−2.03945	+	1.31068i
$819$		0			0
$820$	11.8461	−	1.13117i	0.413685	−	0.0395021i
$821$	−1.39519	+	29.2887i	−0.0486926	+	1.02218i	0.833862	+	0.551973i	$0.186125\pi$
$821$	−1.39519	+	29.2887i	−0.0486926	+	1.02218i	−0.882555	+	0.470210i	$0.844178\pi$
$822$		0			0
$823$	−2.11294	−	8.70967i	−0.0736526	−	0.303600i	0.923056	−	0.384665i	$-0.125683\pi$
$823$	−2.11294	−	8.70967i	−0.0736526	−	0.303600i	−0.996709	+	0.0810650i	$0.974168\pi$
$824$	42.2087	+	16.8978i	1.47041	+	0.588663i
$825$		0			0
$826$	0.651474	−	4.53110i	0.0226677	−	0.157657i
$827$	21.6793	−	17.0488i	0.753862	−	0.592844i	−0.165521	−	0.986206i	$-0.552931\pi$
$827$	21.6793	−	17.0488i	0.753862	−	0.592844i	0.919383	+	0.393362i	$0.128688\pi$
$828$		0			0
$829$	30.5090	+	35.2092i	1.05962	+	1.22287i	0.974002	+	0.226540i	$0.0727413\pi$
$829$	30.5090	+	35.2092i	1.05962	+	1.22287i	0.0856188	+	0.996328i	$0.472713\pi$
$830$	49.1517	−	25.3395i	1.70608	−	0.879546i
$831$		0			0
$832$	14.9671	+	2.88467i	0.518891	+	0.100008i
$833$	−0.768569	+	1.33120i	−0.0266293	+	0.0461234i
$834$		0			0
$835$	6.63111	+	19.1593i	0.229479	+	0.663036i
$836$	22.8515	+	17.9706i	0.790335	+	0.621526i
$837$		0			0
$838$	20.0593	−	19.1265i	0.692937	−	0.660714i
$839$	4.22821	+	3.32510i	0.145974	+	0.114795i	0.688475	−	0.725260i	$-0.258280\pi$
$839$	4.22821	+	3.32510i	0.145974	+	0.114795i	−0.542501	+	0.840055i	$0.682523\pi$
$840$		0			0
$841$	−19.7670	−	34.2375i	−0.681621	−	1.18060i
$842$	24.7356	−	42.8434i	0.852447	−	1.47648i
$843$		0			0
$844$	12.8238	+	28.0802i	0.441414	+	0.966561i
$845$	40.8221	−	21.0452i	1.40432	−	0.723978i
$846$		0			0
$847$	−15.9366	−	10.2418i	−0.547588	−	0.351914i
$848$	3.18691	−	2.50621i	0.109439	−	0.0860637i
$849$		0			0
$850$	26.4239	+	2.52318i	0.906333	+	0.0865443i
$851$	21.5155	+	8.61349i	0.737541	+	0.295267i
$852$		0			0
$853$	1.91673	+	0.988141i	0.0656275	+	0.0338333i	0.490728	−	0.871313i	$-0.336731\pi$
$853$	1.91673	+	0.988141i	0.0656275	+	0.0338333i	−0.425100	+	0.905146i	$0.639761\pi$
$854$	−0.330770	+	6.94372i	−0.0113187	+	0.237609i
$855$		0			0
$856$	33.9019	+	9.95449i	1.15874	+	0.340237i
$857$	−0.343394	+	0.220686i	−0.0117301	+	0.00753848i	−0.546493	−	0.837464i	$-0.684037\pi$
$857$	−0.343394	+	0.220686i	−0.0117301	+	0.00753848i	0.534763	+	0.845002i	$0.320401\pi$
$858$		0			0
$859$	−5.76802	+	1.11169i	−0.196802	+	0.0379305i	−0.286700	−	0.958020i	$-0.592558\pi$
$859$	−5.76802	+	1.11169i	−0.196802	+	0.0379305i	0.0898974	+	0.995951i	$0.471346\pi$
$860$	−19.3485	−	27.1712i	−0.659779	−	0.926530i
$861$		0			0
$862$	59.7552	−	17.5457i	2.03527	−	0.597609i
$863$	−16.7009	+	19.2738i	−0.568505	+	0.656089i	−0.965093	−	0.261907i	$-0.915649\pi$
$863$	−16.7009	+	19.2738i	−0.568505	+	0.656089i	0.396588	+	0.917997i	$0.370194\pi$
$864$		0			0
$865$	−41.5425	+	58.3382i	−1.41249	+	1.98356i
$866$	−8.90689	+	19.5034i	−0.302669	+	0.662752i
$867$		0			0
$868$	8.88614	+	61.8045i	0.301615	+	2.09778i
$869$	−8.25397	−	7.87015i	−0.279997	−	0.266977i
$870$		0			0
$871$	8.20751	−	6.67869i	0.278101	−	0.226299i
$872$	64.2532			2.17589
$873$		0			0
$874$	−7.74172	−	53.8449i	−0.261868	−	1.82133i
$875$	2.89476	+	60.7684i	0.0978606	+	2.05435i
$876$		0			0
$877$	−8.12769	+	11.4137i	−0.274453	+	0.385415i	−0.928679	−	0.370884i	$-0.879055\pi$
$877$	−8.12769	+	11.4137i	−0.274453	+	0.385415i	0.654227	+	0.756299i	$0.272994\pi$
$878$	−20.3556	+	83.9068i	−0.686967	+	2.83172i
$879$		0			0
$880$	10.4036	−	3.05478i	0.350707	−	0.102977i
$881$	30.4095	−	12.1741i	1.02452	−	0.410157i	0.202301	−	0.979323i	$-0.435158\pi$
$881$	30.4095	−	12.1741i	1.02452	−	0.410157i	0.822222	+	0.569166i	$0.192734\pi$
$882$		0			0
$883$	37.8627	−	7.29744i	1.27418	−	0.245578i	0.493081	−	0.869984i	$-0.335871\pi$
$883$	37.8627	−	7.29744i	1.27418	−	0.245578i	0.781100	+	0.624405i	$0.214659\pi$
$884$	−1.48307	+	4.28505i	−0.0498810	+	0.144122i
$885$		0			0
$886$	29.9239	+	8.78645i	1.00531	+	0.295186i
$887$	39.1380	−	3.73722i	1.31412	−	0.125484i	0.585654	−	0.810561i	$-0.300838\pi$
$887$	39.1380	−	3.73722i	1.31412	−	0.125484i	0.728470	+	0.685078i	$0.240232\pi$
$888$		0			0
$889$	−14.3437	−	7.39468i	−0.481071	−	0.248009i
$890$	18.9617	+	78.1612i	0.635598	+	2.61997i
$891$		0			0
$892$	−69.6502	−	6.65078i	−2.33206	−	0.222685i
$893$	−2.26289	+	15.7388i	−0.0757248	+	0.526677i
$894$		0			0
$895$	−52.6534	−	33.8383i	−1.76001	−	1.13109i
$896$	31.2921	+	36.1130i	1.04540	+	1.20645i
$897$		0			0
$898$	−13.8952	−	30.4262i	−0.463688	−	1.01533i
$899$	−61.0623	−	11.7688i	−2.03654	−	0.392511i
$900$		0			0
$901$	−1.26490	−	2.19088i	−0.0421400	−	0.0729887i
$902$	−1.07752	−	3.11328i	−0.0358774	−	0.103661i
$903$		0			0
$904$	−12.6490	+	12.0608i	−0.420699	+	0.401135i
$905$	−70.7060	+	67.4180i	−2.35035	+	2.24105i
$906$		0			0
$907$	12.2150	+	35.2928i	0.405591	+	1.17188i	0.944214	+	0.329332i	$0.106824\pi$
$907$	12.2150	+	35.2928i	0.405591	+	1.17188i	−0.538623	+	0.842547i	$0.681055\pi$
$908$	−27.0106	−	46.7838i	−0.896380	−	1.55258i
$909$		0			0
$910$	−28.3080	−	5.45593i	−0.938402	−	0.180862i
$911$	7.82033	+	17.1241i	0.259099	+	0.567348i	0.993818	−	0.111024i	$-0.0354131\pi$
$911$	7.82033	+	17.1241i	0.259099	+	0.567348i	−0.734719	+	0.678372i	$0.762686\pi$
$912$		0			0
$913$	−6.42215	−	7.41155i	−0.212542	−	0.245287i
$914$	15.3847	+	9.88717i	0.508882	+	0.327038i
$915$		0			0
$916$	3.51221	−	24.4280i	0.116047	−	0.807123i
$917$	22.0106	+	2.10176i	0.726855	+	0.0694063i
$918$		0			0
$919$	5.03659	+	20.7611i	0.166142	+	0.684845i	0.992557	+	0.121784i	$0.0388614\pi$
$919$	5.03659	+	20.7611i	0.166142	+	0.684845i	−0.826415	+	0.563061i	$0.809623\pi$
$920$	−63.7757	−	32.8787i	−2.10262	−	1.08398i
$921$		0			0
$922$	28.0107	−	2.67470i	0.922485	−	0.0880866i
$923$	5.36720	+	1.57595i	0.176664	+	0.0518731i
$924$		0			0
$925$	−18.0751	+	52.2245i	−0.594304	+	1.71713i
$926$	−8.21519	+	1.58335i	−0.269968	+	0.0520320i
$927$		0			0
$928$	−28.1394	+	11.2653i	−0.923721	+	0.369802i
$929$	−13.7103	+	4.02571i	−0.449820	+	0.132079i	−0.498793	−	0.866721i	$-0.666223\pi$
$929$	−13.7103	+	4.02571i	−0.449820	+	0.132079i	0.0489730	+	0.998800i	$0.484405\pi$
$930$		0			0
$931$	−1.77097	+	7.30004i	−0.0580412	+	0.239249i
$932$	−22.6543	+	31.8135i	−0.742065	+	1.04208i
$933$		0			0
$934$	1.24673	+	26.1720i	0.0407942	+	0.856376i
$935$	−0.962860	−	6.69684i	−0.0314889	−	0.219010i
$936$		0			0
$937$	56.9154			1.85935			0.929673	−	0.368386i	$-0.120089\pi$
$937$	56.9154			1.85935			0.929673	+	0.368386i	$0.120089\pi$
$938$	45.0204	−	0.750009i	1.46997	−	0.0244887i
$939$		0			0
$940$	34.5821	+	32.9739i	1.12794	+	1.07549i
$941$	−3.24809	−	22.5910i	−0.105885	−	0.736445i	−0.971724	−	0.236122i	$-0.924124\pi$
$941$	−3.24809	−	22.5910i	−0.105885	−	0.736445i	0.865839	−	0.500323i	$-0.166785\pi$
$942$		0			0
$943$	−1.64047	+	3.59214i	−0.0534212	+	0.116976i
$944$	−0.761242	+	1.06901i	−0.0247763	+	0.0347935i
$945$		0			0
$946$	−6.04735	+	6.97901i	−0.196616	+	0.226907i
$947$	13.8389	−	4.06347i	0.449704	−	0.132045i	−0.0490355	−	0.998797i	$-0.515615\pi$
$947$	13.8389	−	4.06347i	0.449704	−	0.132045i	0.498739	+	0.866752i	$0.333797\pi$
$948$		0			0
$949$	2.49939	+	3.50990i	0.0811336	+	0.113936i
$950$	127.373	−	24.5492i	4.13254	−	0.796481i
$951$		0			0
$952$	−7.12460	+	4.57870i	−0.230910	+	0.148397i
$953$	−17.3071	−	5.08182i	−0.560632	−	0.164616i	−0.0108746	−	0.999941i	$-0.503462\pi$
$953$	−17.3071	−	5.08182i	−0.560632	−	0.164616i	−0.549757	+	0.835325i	$0.685280\pi$
$954$		0			0
$955$	−4.17575	+	87.6598i	−0.135124	+	2.83660i
$956$	−21.9814	−	11.3322i	−0.710930	−	0.366510i
$957$		0			0
$958$	31.4349	+	12.5846i	1.01562	+	0.406591i
$959$	−50.1640	−	4.79008i	−1.61988	−	0.154680i
$960$		0			0
$961$	−19.9863	+	15.7174i	−0.644718	+	0.507012i
$962$	−12.3979	−	7.96765i	−0.399724	−	0.256887i
$963$		0			0
$964$	69.4071	−	35.7819i	2.23545	−	1.15246i
$965$	−9.46093	−	20.7166i	−0.304558	−	0.666889i
$966$		0			0
$967$	5.39334	−	9.34155i	0.173438	−	0.300404i	−0.766181	−	0.642624i	$-0.777846\pi$
$967$	5.39334	−	9.34155i	0.173438	−	0.300404i	0.939620	+	0.342220i	$0.111179\pi$
$968$	14.9911	+	25.9654i	0.481833	+	0.834559i
$969$		0			0
$970$	−93.7475	−	73.7238i	−3.01005	−	2.36713i
$971$	−21.7943	+	20.7808i	−0.699413	+	0.666889i	−0.953878	−	0.300193i	$-0.902949\pi$
$971$	−21.7943	+	20.7808i	−0.699413	+	0.666889i	0.254466	+	0.967082i	$0.418100\pi$
$972$		0			0
$973$	−6.36137	−	5.00264i	−0.203936	−	0.160377i
$974$	−2.26104	−	6.53284i	−0.0724484	−	0.209326i
$975$		0			0
$976$	0.996460	−	1.72592i	0.0318959	−	0.0552453i
$977$	−39.8068	−	7.67213i	−1.27353	−	0.245453i	−0.492702	−	0.870198i	$-0.663991\pi$
$977$	−39.8068	−	7.67213i	−1.27353	−	0.245453i	−0.780829	+	0.624745i	$0.785203\pi$
$978$		0			0
$979$	12.6778	−	6.53588i	0.405185	−	0.208887i
$980$	14.7826	+	17.0600i	0.472213	+	0.544962i
$981$		0			0
$982$	46.5202	−	36.5839i	1.48452	−	1.16744i
$983$	4.12945	−	28.7210i	0.131709	−	0.916057i	−0.811617	−	0.584190i	$-0.801412\pi$
$983$	4.12945	−	28.7210i	0.131709	−	0.916057i	0.943326	−	0.331867i	$-0.107679\pi$
$984$		0			0
$985$	41.5196	+	16.6219i	1.32292	+	0.529619i
$986$	−4.53048	−	18.6749i	−0.144280	−	0.594729i
$987$		0			0
$988$	−1.05438	+	22.1341i	−0.0335442	+	0.704179i
$989$	11.0191	−	1.05220i	0.350387	−	0.0334579i
$990$		0			0
$991$	−9.79888	+	6.29736i	−0.311272	+	0.200042i	−0.686944	−	0.726710i	$-0.741048\pi$
$991$	−9.79888	+	6.29736i	−0.311272	+	0.200042i	0.375672	+	0.926753i	$0.377412\pi$
$992$	−8.99538	+	25.9904i	−0.285603	+	0.825197i
$993$		0			0
$994$	13.8070	+	19.3892i	0.437931	+	0.614988i
$995$	−12.8356	+	5.13860i	−0.406916	+	0.162905i
$996$		0			0
$997$	37.1416	−	42.8637i	1.17629	−	1.35751i	0.255801	−	0.966729i	$-0.417661\pi$
$997$	37.1416	−	42.8637i	1.17629	−	1.35751i	0.920485	−	0.390778i	$-0.127794\pi$
$998$	0.0211938	−	0.0873622i	0.000670879	−	0.00276540i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.z.c.10.4		100
3.2	odd	2		67.2.g.a.10.2	✓	100
67.47	even	33	inner	603.2.z.c.181.4		100
201.47	odd	66		67.2.g.a.47.2	yes	100
201.95	even	66		4489.2.a.q.1.44		50
201.173	odd	66		4489.2.a.p.1.7		50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
67.2.g.a.10.2	✓	100	3.2	odd	2
67.2.g.a.47.2	yes	100	201.47	odd	66
603.2.z.c.10.4		100	1.1	even	1	trivial
603.2.z.c.181.4		100	67.47	even	33	inner
4489.2.a.p.1.7		50	201.173	odd	66
4489.2.a.q.1.44		50	201.95	even	66

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:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.z (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(1.70724 + 1.62785i) q^{2} +(0.169609 + 3.56053i) q^{4} +(1.68411 - 3.68769i) q^{5} +(0.549774 - 2.26620i) q^{7} +(-2.41691 + 2.78926i) q^{8} +O(q^{10})\)	\(q+(1.70724 + 1.62785i) q^{2} +(0.169609 + 3.56053i) q^{4} +(1.68411 - 3.68769i) q^{5} +(0.549774 - 2.26620i) q^{7} +(-2.41691 + 2.78926i) q^{8} +(8.87819 - 3.55429i) q^{10} +(-0.983759 - 1.38150i) q^{11} +(0.422812 - 1.22164i) q^{13} +(4.62763 - 2.97400i) q^{14} +(-1.56988 + 0.149905i) q^{16} +(-0.0468218 + 0.982912i) q^{17} +(1.13372 + 4.67325i) q^{19} +(13.4158 + 5.37086i) q^{20} +(0.569356 - 3.95996i) q^{22} +(-3.76952 + 2.96439i) q^{23} +(-7.48850 - 8.64219i) q^{25} +(2.71048 - 1.39735i) q^{26} +(8.16212 + 1.57312i) q^{28} +(-4.13926 + 7.16942i) q^{29} +(2.45685 + 7.09859i) q^{31} +(2.87802 + 2.26330i) q^{32} +(-1.67997 + 1.60185i) q^{34} +(-7.43115 - 5.84392i) q^{35} +(-2.41638 - 4.18530i) q^{37} +(-5.67182 + 9.82389i) q^{38} +(6.21557 + 13.6102i) q^{40} +(0.731937 - 0.377340i) q^{41} +(-1.94182 - 1.24793i) q^{43} +(4.75201 - 3.73702i) q^{44} +(-11.2611 - 1.07530i) q^{46} +(3.06971 + 1.22892i) q^{47} +(1.38844 + 0.715791i) q^{49} +(1.28352 - 26.9445i) q^{50} +(4.42139 + 1.29824i) q^{52} +(-2.16276 + 1.38992i) q^{53} +(-6.75128 + 1.30120i) q^{55} +(4.99226 + 7.01065i) q^{56} +(-18.7375 + 5.50182i) q^{58} +(0.544959 - 0.628917i) q^{59} +(-0.733033 + 1.02940i) q^{61} +(-7.36102 + 16.1184i) q^{62} +(1.67802 + 11.6709i) q^{64} +(-3.79295 - 3.61657i) q^{65} +(6.95871 + 4.31002i) q^{67} -3.50763 q^{68} +(-3.17373 - 22.0738i) q^{70} +(0.205892 + 4.32220i) q^{71} +(-1.93341 + 2.71510i) q^{73} +(2.68769 - 11.0788i) q^{74} +(-16.4470 + 4.82927i) q^{76} +(-3.67159 + 1.46988i) q^{77} +(6.60307 - 1.27264i) q^{79} +(-2.09104 + 6.04168i) q^{80} +(1.86385 + 0.547274i) q^{82} +(5.75628 - 0.549658i) q^{83} +(3.54582 + 1.82800i) q^{85} +(-1.28371 - 5.29151i) q^{86} +(6.23100 + 0.594989i) q^{88} +(-1.19689 + 8.32458i) q^{89} +(-2.53602 - 1.62980i) q^{91} +(-11.1941 - 12.9187i) q^{92} +(3.24022 + 7.09509i) q^{94} +(19.1428 + 3.68947i) q^{95} +(-6.23553 - 10.8003i) q^{97} +(1.20520 + 3.48220i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 24 q^{2} - 18 q^{4} + 16 q^{5} - 24 q^{7} - 23 q^{8}+O(q^{10}) \) 100 * q + 24 * q^2 - 18 * q^4 + 16 * q^5 - 24 * q^7 - 23 * q^8	\( 100 q + 24 q^{2} - 18 q^{4} + 16 q^{5} - 24 q^{7} - 23 q^{8} + 8 q^{10} + 24 q^{11} - 22 q^{13} + 32 q^{14} - 28 q^{16} - 17 q^{17} + 15 q^{20} + 49 q^{22} + 13 q^{23} - 34 q^{25} + 27 q^{26} + 22 q^{28} - 8 q^{29} + 10 q^{31} - 34 q^{32} - 50 q^{34} + q^{35} + 7 q^{37} - 50 q^{38} + 43 q^{40} + 5 q^{41} + 2 q^{43} + 19 q^{44} + 52 q^{46} + 6 q^{47} - 27 q^{49} - 134 q^{50} + 120 q^{52} + 52 q^{53} - 64 q^{55} + 124 q^{56} - 56 q^{58} - 27 q^{59} - 16 q^{61} + 74 q^{62} - 197 q^{64} + 92 q^{65} - 56 q^{67} - 16 q^{68} - 22 q^{70} + 113 q^{71} + q^{73} + 24 q^{74} - 144 q^{76} - 85 q^{77} + 36 q^{79} + 13 q^{80} - 20 q^{82} + 61 q^{83} - 6 q^{85} - 189 q^{86} + 129 q^{88} - 95 q^{89} + 42 q^{91} - 4 q^{92} + 70 q^{94} + 20 q^{95} + 53 q^{97} - q^{98}+O(q^{100}) \) 100 * q + 24 * q^2 - 18 * q^4 + 16 * q^5 - 24 * q^7 - 23 * q^8 + 8 * q^10 + 24 * q^11 - 22 * q^13 + 32 * q^14 - 28 * q^16 - 17 * q^17 + 15 * q^20 + 49 * q^22 + 13 * q^23 - 34 * q^25 + 27 * q^26 + 22 * q^28 - 8 * q^29 + 10 * q^31 - 34 * q^32 - 50 * q^34 + q^35 + 7 * q^37 - 50 * q^38 + 43 * q^40 + 5 * q^41 + 2 * q^43 + 19 * q^44 + 52 * q^46 + 6 * q^47 - 27 * q^49 - 134 * q^50 + 120 * q^52 + 52 * q^53 - 64 * q^55 + 124 * q^56 - 56 * q^58 - 27 * q^59 - 16 * q^61 + 74 * q^62 - 197 * q^64 + 92 * q^65 - 56 * q^67 - 16 * q^68 - 22 * q^70 + 113 * q^71 + q^73 + 24 * q^74 - 144 * q^76 - 85 * q^77 + 36 * q^79 + 13 * q^80 - 20 * q^82 + 61 * q^83 - 6 * q^85 - 189 * q^86 + 129 * q^88 - 95 * q^89 + 42 * q^91 - 4 * q^92 + 70 * q^94 + 20 * q^95 + 53 * q^97 - q^98

Introduction

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