LMFDB - Embedded newform 603.2.z.c.19.4

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			19.4
Character	$\chi$	$=$	603.19
Dual form			603.2.z.c.127.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.32946 + 0.685383i) q^{2} +(0.137594 + 0.193224i) q^{4} +(1.91440 + 2.20934i) q^{5} +(-0.175175 - 3.67738i) q^{7} +(-0.375236 - 2.60982i) q^{8} +O(q^{10})$	\(q+(1.32946 + 0.685383i) q^{2} +(0.137594 + 0.193224i) q^{4} +(1.91440 + 2.20934i) q^{5} +(-0.175175 - 3.67738i) q^{7} +(-0.375236 - 2.60982i) q^{8} +(1.03087 + 4.24932i) q^{10} +(0.823666 - 0.158749i) q^{11} +(5.84030 - 2.33810i) q^{13} +(2.28752 - 5.00898i) q^{14} +(1.44504 - 4.17515i) q^{16} +(-1.42274 + 1.99796i) q^{17} +(-0.252413 + 5.29880i) q^{19} +(-0.163487 + 0.673901i) q^{20} +(1.20383 + 0.353477i) q^{22} +(2.81340 + 2.68257i) q^{23} +(-0.504663 + 3.51001i) q^{25} +(9.36693 + 0.894434i) q^{26} +(0.686455 - 0.539835i) q^{28} +(-2.49264 + 4.31737i) q^{29} +(-6.54848 - 2.62162i) q^{31} +(0.966212 - 0.921282i) q^{32} +(-3.26084 + 1.68108i) q^{34} +(7.78921 - 7.42700i) q^{35} +(1.03264 + 1.78858i) q^{37} +(-3.96728 + 6.87154i) q^{38} +(5.04763 - 5.82527i) q^{40} +(-5.54544 - 0.529525i) q^{41} +(-1.29060 - 2.82603i) q^{43} +(0.144006 + 0.137309i) q^{44} +(1.90171 + 5.49463i) q^{46} +(0.256241 - 1.05624i) q^{47} +(-6.52411 + 0.622977i) q^{49} +(-3.07663 + 4.32052i) q^{50} +(1.25537 + 0.806778i) q^{52} +(-2.21500 + 4.85017i) q^{53} +(1.92756 + 1.51585i) q^{55} +(-9.53157 + 1.83706i) q^{56} +(-6.27291 + 4.03136i) q^{58} +(-1.04245 - 7.25040i) q^{59} +(12.1612 + 2.34388i) q^{61} +(-6.90912 - 7.97354i) q^{62} +(-6.56240 + 1.92689i) q^{64} +(16.3463 + 8.42713i) q^{65} +(7.68628 + 2.81445i) q^{67} -0.581815 q^{68} +(15.4458 - 4.53529i) q^{70} +(-1.62144 - 2.27699i) q^{71} +(-11.6242 - 2.24039i) q^{73} +(0.146985 + 3.08559i) q^{74} +(-1.05859 + 0.680313i) q^{76} +(-0.728064 - 3.00112i) q^{77} +(-4.51271 - 3.54884i) q^{79} +(11.9907 - 4.80035i) q^{80} +(-7.00950 - 4.50473i) q^{82} +(3.47174 - 10.0309i) q^{83} +(-7.13786 + 0.681583i) q^{85} +(0.221109 - 4.64165i) q^{86} +(-0.723375 - 2.09005i) q^{88} +(-4.93543 - 1.44917i) q^{89} +(-9.62117 - 21.0674i) q^{91} +(-0.131230 + 0.912725i) q^{92} +(1.06459 - 1.22860i) q^{94} +(-12.1901 + 9.58637i) q^{95} +(4.97137 + 8.61067i) q^{97} +(-9.10051 - 3.64329i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/603\mathbb{Z}\right)^\times$.

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{5}{33}\right)$	$1$

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 $

$2$	1.32946	+	0.685383i	0.940069	+	0.484639i	0.858947	−	0.512065i	$-0.171119\pi$
$2$	1.32946	+	0.685383i	0.940069	+	0.484639i	0.0811220	+	0.996704i	$0.474150\pi$
$3$		0			0
$3$		0			0
$4$	0.137594	+	0.193224i	0.0687972	+	0.0966122i
$5$	1.91440	+	2.20934i	0.856146	+	0.988046i	0.999999	−	0.00155356i	$-0.000494515\pi$
$5$	1.91440	+	2.20934i	0.856146	+	0.988046i	−0.143852	+	0.989599i	$0.545949\pi$
$6$		0			0
$7$	−0.175175	−	3.67738i	−0.0662099	−	1.38992i	−0.750578	−	0.660781i	$-0.770225\pi$
$7$	−0.175175	−	3.67738i	−0.0662099	−	1.38992i	0.684368	−	0.729136i	$-0.260078\pi$
$8$	−0.375236	−	2.60982i	−0.132666	−	0.922712i
$9$		0			0
$10$	1.03087	+	4.24932i	0.325991	+	1.34375i
$11$	0.823666	−	0.158749i	0.248345	−	0.0478645i	−0.0635596	−	0.997978i	$-0.520245\pi$
$11$	0.823666	−	0.158749i	0.248345	−	0.0478645i	0.311904	+	0.950114i	$0.399033\pi$
$12$		0			0
$13$	5.84030	−	2.33810i	1.61981	−	0.648474i	0.628236	−	0.778023i	$-0.283777\pi$
$13$	5.84030	−	2.33810i	1.61981	−	0.648474i	0.991573	+	0.129550i	$0.0413532\pi$
$14$	2.28752	−	5.00898i	0.611367	−	1.33871i
$15$		0			0
$16$	1.44504	−	4.17515i	0.361259	−	1.04379i
$17$	−1.42274	+	1.99796i	−0.345065	+	0.484576i	−0.950241	−	0.311516i	$-0.899163\pi$
$17$	−1.42274	+	1.99796i	−0.345065	+	0.484576i	0.605176	+	0.796092i	$0.293103\pi$
$18$		0			0
$19$	−0.252413	+	5.29880i	−0.0579075	+	1.21563i	0.763698	+	0.645573i	$0.223381\pi$
$19$	−0.252413	+	5.29880i	−0.0579075	+	1.21563i	−0.821606	+	0.570056i	$0.806922\pi$
$20$	−0.163487	+	0.673901i	−0.0365567	+	0.150689i
$21$		0			0
$22$	1.20383	+	0.353477i	0.256658	+	0.0753616i
$23$	2.81340	+	2.68257i	0.586635	+	0.559355i	0.924182	−	0.381953i	$-0.124749\pi$
$23$	2.81340	+	2.68257i	0.586635	+	0.559355i	−0.337547	+	0.941309i	$0.609597\pi$
$24$		0			0
$25$	−0.504663	+	3.51001i	−0.100933	+	0.702002i
$26$	9.36693	+	0.894434i	1.83701	+	0.175413i
$27$		0			0
$28$	0.686455	−	0.539835i	0.129728	−	0.102019i
$29$	−2.49264	+	4.31737i	−0.462871	+	0.801716i	−0.999103	−	0.0423547i	$-0.986514\pi$
$29$	−2.49264	+	4.31737i	−0.462871	+	0.801716i	0.536232	+	0.844071i	$0.319847\pi$
$30$		0			0
$31$	−6.54848	−	2.62162i	−1.17614	−	0.470856i	−0.300483	−	0.953787i	$-0.597148\pi$
$31$	−6.54848	−	2.62162i	−1.17614	−	0.470856i	−0.875658	+	0.482931i	$0.839572\pi$
$32$	0.966212	−	0.921282i	0.170804	−	0.162861i
$33$		0			0
$34$	−3.26084	+	1.68108i	−0.559229	+	0.288303i
$35$	7.78921	−	7.42700i	1.31662	−	1.25539i
$36$		0			0
$37$	1.03264	+	1.78858i	0.169765	+	0.294041i	0.938337	−	0.345722i	$-0.112366\pi$
$37$	1.03264	+	1.78858i	0.169765	+	0.294041i	−0.768572	+	0.639763i	$0.779033\pi$
$38$	−3.96728	+	6.87154i	−0.643578	+	1.11471i
$39$		0			0
$40$	5.04763	−	5.82527i	0.798100	−	0.921056i
$41$	−5.54544	−	0.529525i	−0.866052	−	0.0826980i	−0.347435	−	0.937704i	$-0.612947\pi$
$41$	−5.54544	−	0.529525i	−0.866052	−	0.0826980i	−0.518618	+	0.855006i	$0.673553\pi$
$42$		0			0
$43$	−1.29060	−	2.82603i	−0.196815	−	0.430966i	0.785333	−	0.619074i	$-0.212492\pi$
$43$	−1.29060	−	2.82603i	−0.196815	−	0.430966i	−0.982148	+	0.188108i	$0.939764\pi$
$44$	0.144006	+	0.137309i	0.0217097	+	0.0207002i
$45$		0			0
$46$	1.90171	+	5.49463i	0.280392	+	0.810139i
$47$	0.256241	−	1.05624i	0.0373766	−	0.154068i	−0.950065	−	0.312051i	$-0.898984\pi$
$47$	0.256241	−	1.05624i	0.0373766	−	0.154068i	0.987442	+	0.157983i	$0.0504991\pi$
$48$		0			0
$49$	−6.52411	+	0.622977i	−0.932016	+	0.0889967i
$50$	−3.07663	+	4.32052i	−0.435101	+	0.611014i
$51$		0			0
$52$	1.25537	+	0.806778i	0.174089	+	0.111880i
$53$	−2.21500	+	4.85017i	−0.304254	+	0.666223i	−0.998571	−	0.0534466i	$-0.982979\pi$
$53$	−2.21500	+	4.85017i	−0.304254	+	0.666223i	0.694317	+	0.719669i	$0.255707\pi$
$54$		0			0
$55$	1.92756	+	1.51585i	0.259912	+	0.204397i
$56$	−9.53157	+	1.83706i	−1.27371	+	0.245487i
$57$		0			0
$58$	−6.27291	+	4.03136i	−0.823674	+	0.529343i
$59$	−1.04245	−	7.25040i	−0.135715	−	0.943921i	−0.937915	−	0.346865i	$-0.887246\pi$
$59$	−1.04245	−	7.25040i	−0.135715	−	0.943921i	0.802200	−	0.597056i	$-0.203663\pi$
$60$		0			0
$61$	12.1612	+	2.34388i	1.55709	+	0.300104i	0.893871	−	0.448325i	$-0.147979\pi$
$61$	12.1612	+	2.34388i	1.55709	+	0.300104i	0.663215	+	0.748429i	$0.269191\pi$
$62$	−6.90912	−	7.97354i	−0.877459	−	1.01264i
$63$		0			0
$64$	−6.56240	+	1.92689i	−0.820300	+	0.240862i
$65$	16.3463	+	8.42713i	2.02751	+	1.04526i
$66$		0			0
$67$	7.68628	+	2.81445i	0.939028	+	0.343840i
$67$	7.68628	+	2.81445i	0.939028	+	0.343840i
$68$	−0.581815			−0.0705554
$69$		0			0
$70$	15.4458	−	4.53529i	1.84612	−	0.542070i
$71$	−1.62144	−	2.27699i	−0.192429	−	0.270229i	0.707077	−	0.707136i	$-0.250013\pi$
$71$	−1.62144	−	2.27699i	−0.192429	−	0.270229i	−0.899507	+	0.436907i	$0.856074\pi$
$72$		0			0
$73$	−11.6242	−	2.24039i	−1.36051	−	0.262218i	−0.543778	−	0.839229i	$-0.683007\pi$
$73$	−11.6242	−	2.24039i	−1.36051	−	0.262218i	−0.816736	+	0.577011i	$0.804219\pi$
$74$	0.146985	+	3.08559i	0.0170867	+	0.358693i
$75$		0			0
$76$	−1.05859	+	0.680313i	−0.121428	+	0.0780373i
$77$	−0.728064	−	3.00112i	−0.0829706	−	0.342010i
$78$		0			0
$79$	−4.51271	−	3.54884i	−0.507720	−	0.399275i	0.331175	−	0.943569i	$-0.392555\pi$
$79$	−4.51271	−	3.54884i	−0.507720	−	0.399275i	−0.838894	+	0.544294i	$0.816798\pi$
$80$	11.9907	−	4.80035i	1.34060	−	0.536696i
$81$		0			0
$82$	−7.00950	−	4.50473i	−0.774070	−	0.497465i
$83$	3.47174	−	10.0309i	0.381073	−	1.10104i	−0.577550	−	0.816356i	$-0.695991\pi$
$83$	3.47174	−	10.0309i	0.381073	−	1.10104i	0.958622	−	0.284681i	$-0.0918878\pi$
$84$		0			0
$85$	−7.13786	+	0.681583i	−0.774209	+	0.0739280i
$86$	0.221109	−	4.64165i	0.0238428	−	0.500522i
$87$		0			0
$88$	−0.723375	−	2.09005i	−0.0771120	−	0.222801i
$89$	−4.93543	−	1.44917i	−0.523155	−	0.153612i	0.00948356	−	0.999955i	$-0.496981\pi$
$89$	−4.93543	−	1.44917i	−0.523155	−	0.153612i	−0.532638	+	0.846343i	$0.678799\pi$
$90$		0			0
$91$	−9.62117	−	21.0674i	−1.00857	−	2.20847i
$92$	−0.131230	+	0.912725i	−0.0136817	+	0.0951582i
$93$		0			0
$94$	1.06459	−	1.22860i	0.109804	−	0.126721i
$95$	−12.1901	+	9.58637i	−1.25067	+	0.983541i
$96$		0			0
$97$	4.97137	+	8.61067i	0.504767	+	0.874281i	0.999985	+	0.00551273i	$0.00175476\pi$
$97$	4.97137	+	8.61067i	0.504767	+	0.874281i	−0.495218	+	0.868769i	$0.664912\pi$
$98$	−9.10051	−	3.64329i	−0.919290	−	0.368028i
$99$		0			0
$100$	−0.747658	+	0.385444i	−0.0747658	+	0.0385444i
$101$	−1.21264	+	0.625161i	−0.120662	+	0.0622058i	−0.517501	−	0.855683i	$-0.673138\pi$
$101$	−1.21264	+	0.625161i	−0.120662	+	0.0622058i	0.396838	+	0.917888i	$0.370107\pi$
$102$		0			0
$103$	−2.66109	−	1.06534i	−0.262205	−	0.104971i	0.236835	−	0.971550i	$-0.423890\pi$
$103$	−2.66109	−	1.06534i	−0.262205	−	0.104971i	−0.499040	+	0.866579i	$0.666314\pi$
$104$	−8.29353	−	14.3648i	−0.813248	−	1.40859i
$105$		0			0
$106$	−6.26898	+	4.92998i	−0.608897	+	0.478842i
$107$	−7.11109	+	8.20663i	−0.687455	+	0.793365i	−0.987001	−	0.160717i	$-0.948619\pi$
$107$	−7.11109	+	8.20663i	−0.687455	+	0.793365i	0.299546	+	0.954082i	$0.403165\pi$
$108$		0			0
$109$	−1.37468	+	9.56108i	−0.131670	+	0.915785i	0.811707	+	0.584064i	$0.198538\pi$
$109$	−1.37468	+	9.56108i	−0.131670	+	0.915785i	−0.943378	+	0.331721i	$0.892371\pi$
$110$	1.52367	+	3.33637i	0.145276	+	0.318111i
$111$		0			0
$112$	−15.6068	−	4.58256i	−1.47470	−	0.433011i
$113$	4.59406	+	13.2737i	0.432172	+	1.24868i	0.925470	+	0.378820i	$0.123670\pi$
$113$	4.59406	+	13.2737i	0.432172	+	1.24868i	−0.493298	+	0.869860i	$0.664209\pi$
$114$		0			0
$115$	−0.540728	+	11.3513i	−0.0504231	+	1.05851i
$116$	−1.17719	+	0.112408i	−0.109300	+	0.0104369i
$117$		0			0
$118$	3.58341	−	10.3536i	0.329879	−	0.953124i
$119$	7.59647	+	4.88196i	0.696367	+	0.447528i
$120$		0			0
$121$	−9.55882	+	3.82678i	−0.868984	+	0.347889i
$122$	14.5614	+	11.4512i	1.31833	+	1.03674i
$123$		0			0
$124$	−0.394474	−	1.62604i	−0.0354248	−	0.146023i
$125$	3.57556	−	2.29787i	0.319808	−	0.205528i
$126$		0			0
$127$	0.325027	+	6.82316i	0.0288415	+	0.605458i	0.966309	+	0.257385i	$0.0828608\pi$
$127$	0.325027	+	6.82316i	0.0288415	+	0.605458i	−0.937467	+	0.348073i	$0.886836\pi$
$128$	−12.6669	−	2.44135i	−1.11961	−	0.215787i
$129$		0			0
$130$	15.9560	+	22.4070i	1.39943	+	1.96523i
$131$	−20.7608	+	6.09593i	−1.81388	+	0.532604i	−0.998900	−	0.0468838i	$-0.985071\pi$
$131$	−20.7608	+	6.09593i	−1.81388	+	0.532604i	−0.814981	+	0.579487i	$0.803253\pi$
$132$		0			0
$133$	19.5299			1.69346
$134$	8.28961	+	9.00974i	0.716113	+	0.778323i
$135$		0			0
$136$	5.74818	+	2.96339i	0.492902	+	0.254109i
$137$	−15.8636	+	4.65798i	−1.35532	+	0.397958i	−0.877111	−	0.480287i	$-0.840533\pi$
$137$	−15.8636	+	4.65798i	−1.35532	+	0.397958i	−0.478210	+	0.878245i	$0.658714\pi$
$138$		0			0
$139$	−7.81242	−	9.01602i	−0.662641	−	0.764728i	0.320565	−	0.947226i	$-0.396127\pi$
$139$	−7.81242	−	9.01602i	−0.662641	−	0.764728i	−0.983206	+	0.182498i	$0.941582\pi$
$140$	2.50683	+	0.483151i	0.211866	+	0.0408338i
$141$		0			0
$142$	−0.595022	−	4.13847i	−0.0499331	−	0.347292i
$143$	4.43929	−	2.85296i	0.371232	−	0.238576i
$144$		0			0
$145$	−14.3104	+	2.75811i	−1.18842	+	0.229049i
$146$	−13.9184	−	10.9456i	−1.15190	−	0.905861i
$147$		0			0
$148$	−0.203512	+	0.445629i	−0.0167286	+	0.0366305i
$149$	−0.462040	−	0.296935i	−0.0378518	−	0.0243259i	0.521578	−	0.853204i	$-0.325344\pi$
$149$	−0.462040	−	0.296935i	−0.0378518	−	0.0243259i	−0.559430	+	0.828878i	$0.688980\pi$
$150$		0			0
$151$	2.47931	−	3.48171i	0.201764	−	0.283337i	−0.701280	−	0.712886i	$-0.747388\pi$
$151$	2.47931	−	3.48171i	0.201764	−	0.283337i	0.903044	+	0.429548i	$0.141327\pi$
$152$	13.9237	−	1.32955i	1.12936	−	0.107841i
$153$		0			0
$154$	1.08899	−	4.48887i	0.0877531	−	0.361723i
$155$	−6.74438	−	19.4866i	−0.541722	−	1.56520i
$156$		0			0
$157$	5.14300	+	4.90384i	0.410456	+	0.391369i	0.866981	−	0.498342i	$-0.166057\pi$
$157$	5.14300	+	4.90384i	0.410456	+	0.391369i	−0.456524	+	0.889711i	$0.650906\pi$
$158$	−3.56715	−	7.81097i	−0.283787	−	0.621407i
$159$		0			0
$160$	3.88514	+	0.370986i	0.307147	+	0.0293290i
$161$	9.37200	−	10.8159i	0.738617	−	0.852409i
$162$		0			0
$163$	9.56622	−	16.5692i	0.749285	−	1.29780i	−0.198881	−	0.980024i	$-0.563731\pi$
$163$	9.56622	−	16.5692i	0.749285	−	1.29780i	0.948166	−	0.317775i	$-0.102936\pi$
$164$	−0.660704	−	1.14437i	−0.0515924	−	0.0893606i
$165$		0			0
$166$	11.4906	−	10.9562i	0.891840	−	0.850368i
$167$	−6.31880	+	3.25757i	−0.488964	+	0.252078i	−0.685033	−	0.728512i	$-0.740212\pi$
$167$	−6.31880	+	3.25757i	−0.488964	+	0.252078i	0.196070	+	0.980590i	$0.437182\pi$
$168$		0			0
$169$	19.2339	−	18.3394i	1.47953	−	1.41073i
$170$	−9.95662	−	3.98603i	−0.763638	−	0.305715i
$171$		0			0
$172$	0.368478	−	0.638222i	0.0280962	−	0.0486640i
$173$	7.72424	−	6.07441i	0.587263	−	0.461829i	−0.279779	−	0.960065i	$-0.590261\pi$
$173$	7.72424	−	6.07441i	0.587263	−	0.461829i	0.867042	+	0.498236i	$0.166019\pi$
$174$		0			0
$175$	12.9960	+	1.24097i	0.982408	+	0.0938086i
$176$	0.527426	−	3.66833i	0.0397563	−	0.276511i
$177$		0			0
$178$	−5.56821	−	5.30928i	−0.417355	−	0.397947i
$179$	2.14326	+	0.629318i	0.160195	+	0.0470375i	0.360847	−	0.932625i	$-0.382488\pi$
$179$	2.14326	+	0.629318i	0.160195	+	0.0470375i	−0.200652	+	0.979663i	$0.564306\pi$
$180$		0			0
$181$	−3.22214	+	13.2818i	−0.239500	+	0.987231i	0.717365	+	0.696698i	$0.245348\pi$
$181$	−3.22214	+	13.2818i	−0.239500	+	0.987231i	−0.956865	+	0.290534i	$0.906167\pi$
$182$	1.64832	−	34.6024i	0.122181	−	2.56490i
$183$		0			0
$184$	5.94535	−	8.34908i	0.438297	−	0.615502i
$185$	−1.97469	+	5.70551i	−0.145182	+	0.419477i
$186$		0			0
$187$	−0.854689	+	1.87151i	−0.0625011	+	0.136858i
$188$	0.239348	−	0.0958206i	0.0174563	−	0.00698844i
$189$		0			0
$190$	−22.7765	+	4.38981i	−1.65238	+	0.318471i
$191$	2.70828	+	11.1637i	0.195964	+	0.807775i	0.981890	+	0.189454i	$0.0606717\pi$
$191$	2.70828	+	11.1637i	0.195964	+	0.807775i	−0.785926	+	0.618321i	$0.787813\pi$
$192$		0			0
$193$	−0.592330	−	4.11975i	−0.0426369	−	0.296546i	−0.999971	−	0.00756391i	$-0.997592\pi$
$193$	−0.592330	−	4.11975i	−0.0426369	−	0.296546i	0.957335	−	0.288982i	$-0.0933168\pi$
$194$	0.707622	+	14.8548i	0.0508043	+	1.06651i
$195$		0			0
$196$	−1.01806	−	1.17490i	−0.0727182	−	0.0839213i
$197$	9.06743	+	12.7334i	0.646028	+	0.907219i	0.999603	−	0.0281871i	$-0.00897343\pi$
$197$	9.06743	+	12.7334i	0.646028	+	0.907219i	−0.353575	+	0.935406i	$0.615034\pi$
$198$		0			0
$199$	6.93715	+	3.57635i	0.491761	+	0.253521i	0.686225	−	0.727389i	$-0.259266\pi$
$199$	6.93715	+	3.57635i	0.491761	+	0.253521i	−0.194464	+	0.980910i	$0.562297\pi$
$200$	9.34987			0.661136
$201$		0			0
$202$	−2.04063			−0.143578
$203$	16.3133	+	8.41007i	1.14497	+	0.590271i
$204$		0			0
$205$	−9.44630	−	13.2655i	−0.659758	−	0.926501i
$206$	−2.80764	−	3.24019i	−0.195618	−	0.225755i
$207$		0			0
$208$	−1.32251	−	27.7628i	−0.0916993	−	1.92500i
$209$	0.633274	+	4.40452i	0.0438045	+	0.304667i
$210$		0			0
$211$	1.26377	+	5.20933i	0.0870014	+	0.358625i	0.998626	−	0.0523986i	$-0.0166866\pi$
$211$	1.26377	+	5.20933i	0.0870014	+	0.358625i	−0.911625	+	0.411023i	$0.865171\pi$
$212$	−1.24194	+	0.239365i	−0.0852970	+	0.0164397i
$213$		0			0
$214$	−15.0786	+	6.03655i	−1.03075	+	0.412650i
$215$	3.77292	−	8.26154i	0.257311	−	0.563432i
$216$		0			0
$217$	−8.49354	+	24.5405i	−0.576579	+	1.66592i
$218$	−8.38058	+	11.7689i	−0.567604	+	0.797089i
$219$		0			0
$220$	−0.0276775	+	0.581023i	−0.00186602	+	0.0391726i
$221$	−3.63779	+	14.9952i	−0.244704	+	1.00869i
$222$		0			0
$223$	0.757473	+	0.222414i	0.0507242	+	0.0148940i	0.306996	−	0.951711i	$-0.400676\pi$
$223$	0.757473	+	0.222414i	0.0507242	+	0.0148940i	−0.256272	+	0.966605i	$0.582494\pi$
$224$	−3.55716	−	3.39174i	−0.237672	−	0.226620i
$225$		0			0
$226$	−2.98993	+	20.7955i	−0.198888	+	1.38329i
$227$	14.0330	+	1.33999i	0.931403	+	0.0889382i	0.549714	−	0.835353i	$-0.314737\pi$
$227$	14.0330	+	1.33999i	0.931403	+	0.0889382i	0.381689	+	0.924291i	$0.375343\pi$
$228$		0			0
$229$	−0.533754	+	0.419749i	−0.0352715	+	0.0277378i	−0.635639	−	0.771986i	$-0.719263\pi$
$229$	−0.533754	+	0.419749i	−0.0352715	+	0.0277378i	0.600368	+	0.799724i	$0.295021\pi$
$230$	−8.49885	+	14.7204i	−0.560398	+	0.970637i
$231$		0			0
$232$	12.2029	+	4.88531i	0.801160	+	0.320736i
$233$	16.2709	−	15.5142i	1.06594	−	1.01637i	0.0661125	−	0.997812i	$-0.478940\pi$
$233$	16.2709	−	15.5142i	1.06594	−	1.01637i	0.999828	−	0.0185598i	$-0.00590812\pi$
$234$		0			0
$235$	2.82414	−	1.45594i	0.184226	−	0.0949752i
$236$	1.25752	−	1.19904i	0.0818574	−	0.0780509i
$237$		0			0
$238$	6.75318	+	11.6968i	0.437743	+	0.758194i
$239$	2.61156	−	4.52336i	0.168928	−	0.292592i	−0.769115	−	0.639110i	$-0.779303\pi$
$239$	2.61156	−	4.52336i	0.168928	−	0.292592i	0.938043	+	0.346518i	$0.112636\pi$
$240$		0			0
$241$	2.61340	−	3.01602i	0.168344	−	0.194279i	−0.665309	−	0.746568i	$-0.731700\pi$
$241$	2.61340	−	3.01602i	0.168344	−	0.194279i	0.833653	+	0.552289i	$0.186246\pi$
$242$	−15.3309	−	1.46392i	−0.985505	−	0.0941043i
$243$		0			0
$244$	1.22042	+	2.67235i	0.0781295	+	0.171080i
$245$	−13.8661	−	13.2213i	−0.885875	−	0.844680i
$246$		0			0
$247$	10.9150	+	31.5368i	0.694504	+	2.00664i
$248$	−4.38473	+	18.0741i	−0.278430	+	1.14771i
$249$		0			0
$250$	6.32849	−	0.604297i	0.400249	−	0.0382191i
$251$	9.33192	−	13.1049i	0.589026	−	0.827171i	−0.407257	−	0.913314i	$-0.633515\pi$
$251$	9.33192	−	13.1049i	0.589026	−	0.827171i	0.996283	+	0.0861427i	$0.0274541\pi$
$252$		0			0
$253$	2.74316	+	1.76292i	0.172461	+	0.110834i
$254$	−4.24437	+	9.29388i	−0.266315	+	0.583150i
$255$		0			0
$256$	−4.41454	−	3.47163i	−0.275909	−	0.216977i
$257$	−22.3693	+	4.31133i	−1.39536	+	0.268933i	−0.830851	−	0.556495i	$-0.812146\pi$
$257$	−22.3693	+	4.31133i	−1.39536	+	0.268933i	−0.564507	+	0.825428i	$0.690934\pi$
$258$		0			0
$259$	6.39639	−	4.11071i	0.397452	−	0.255427i
$260$	0.620840	+	4.31804i	0.0385029	+	0.267793i
$261$		0			0
$262$	−31.7787	−	6.12484i	−1.96329	−	0.378394i
$263$	−1.01010	−	1.16572i	−0.0622855	−	0.0718813i	0.723752	−	0.690060i	$-0.242416\pi$
$263$	−1.01010	−	1.16572i	−0.0622855	−	0.0718813i	−0.786037	+	0.618179i	$0.787871\pi$
$264$		0			0
$265$	−14.9561	+	4.39150i	−0.918744	+	0.269768i
$266$	25.9642	+	13.3855i	1.59197	+	0.820716i
$267$		0			0
$268$	0.513769	+	1.87243i	0.0313834	+	0.114377i
$269$	−28.6883			−1.74916			−0.874580	−	0.484882i	$-0.838863\pi$
$269$	−28.6883			−1.74916			−0.874580	+	0.484882i	$0.838863\pi$
$270$		0			0
$271$	11.0379	−	3.24102i	0.670504	−	0.196878i	0.0712765	−	0.997457i	$-0.477293\pi$
$271$	11.0379	−	3.24102i	0.670504	−	0.196878i	0.599227	+	0.800579i	$0.295475\pi$
$272$	6.28587	+	8.82727i	0.381137	+	0.535232i
$273$		0			0
$274$	−24.2825	−	4.68008i	−1.46696	−	0.282734i
$275$	0.141535	+	2.97119i	0.00853490	+	0.179170i
$276$		0			0
$277$	−7.59899	+	4.88357i	−0.456579	+	0.293426i	−0.748643	−	0.662973i	$-0.769294\pi$
$277$	−7.59899	+	4.88357i	−0.456579	+	0.293426i	0.292064	+	0.956399i	$0.405658\pi$
$278$	−4.20686	−	17.3409i	−0.252311	−	1.04004i
$279$		0			0
$280$	−22.3059	−	17.5416i	−1.33303	−	1.04831i
$281$	20.4670	−	8.19376i	1.22096	−	0.488799i	0.330477	−	0.943814i	$-0.392790\pi$
$281$	20.4670	−	8.19376i	1.22096	−	0.488799i	0.890484	+	0.455015i	$0.150366\pi$
$282$		0			0
$283$	9.42623	+	6.05787i	0.560331	+	0.360103i	0.789944	−	0.613179i	$-0.210110\pi$
$283$	9.42623	+	6.05787i	0.560331	+	0.360103i	−0.229613	+	0.973282i	$0.573746\pi$
$284$	0.216869	−	0.626602i	0.0128688	−	0.0371820i
$285$		0			0
$286$	7.85722	−	0.750273i	0.464607	−	0.0443646i
$287$	−0.975842	+	20.4854i	−0.0576021	+	1.20922i
$288$		0			0
$289$	3.59251	+	10.3799i	0.211324	+	0.610581i
$290$	−20.9155	−	6.14134i	−1.22820	−	0.360632i
$291$		0			0
$292$	−1.16653	−	2.55435i	−0.0682662	−	0.149482i
$293$	3.73184	−	25.9555i	0.218016	−	1.51634i	−0.527330	−	0.849660i	$-0.676807\pi$
$293$	3.73184	−	25.9555i	0.218016	−	1.51634i	0.745347	−	0.666677i	$-0.232284\pi$
$294$		0			0
$295$	14.0229	−	16.1833i	0.816445	−	0.942228i
$296$	4.28040	−	3.36614i	0.248793	−	0.195653i
$297$		0			0
$298$	−0.410748	−	0.711437i	−0.0237940	−	0.0412124i
$299$	22.7033	+	9.08901i	1.31296	+	0.525631i
$300$		0			0
$301$	−10.1663	+	5.24109i	−0.585976	+	0.302091i
$302$	5.68245	−	2.92951i	0.326988	−	0.168574i
$303$		0			0
$304$	21.7586	+	8.71082i	1.24794	+	0.499600i
$305$	18.1030	+	31.3554i	1.03658	+	1.79540i
$306$		0			0
$307$	−4.80391	+	3.77784i	−0.274174	+	0.215613i	−0.745773	−	0.666201i	$-0.767919\pi$
$307$	−4.80391	+	3.77784i	−0.274174	+	0.215613i	0.471599	+	0.881813i	$0.343677\pi$
$308$	0.479712	−	0.553617i	0.0273341	−	0.0315453i
$309$		0			0
$310$	4.38943	−	30.5291i	0.249303	−	1.73394i
$311$	−3.46600	−	7.58949i	−0.196539	−	0.430360i	0.785545	−	0.618805i	$-0.212383\pi$
$311$	−3.46600	−	7.58949i	−0.196539	−	0.430360i	−0.982084	+	0.188444i	$0.939656\pi$
$312$		0			0
$313$	−10.9123	−	3.20413i	−0.616797	−	0.181108i	−0.0416154	−	0.999134i	$-0.513250\pi$
$313$	−10.9123	−	3.20413i	−0.616797	−	0.181108i	−0.575182	+	0.818026i	$0.695069\pi$
$314$	3.47639	+	10.0444i	0.196184	+	0.566837i
$315$		0			0
$316$	0.0647974	−	1.36027i	0.00364514	−	0.0765209i
$317$	20.1835	−	1.92730i	1.13362	−	0.108248i	0.488668	−	0.872470i	$-0.337483\pi$
$317$	20.1835	−	1.92730i	1.13362	−	0.108248i	0.644953	+	0.764222i	$0.276877\pi$
$318$		0			0
$319$	−1.36772	+	3.95178i	−0.0765778	+	0.221257i
$320$	−16.8202	−	10.8097i	−0.940279	−	0.604281i
$321$		0			0
$322$	19.8727	−	7.95582i	1.10746	−	0.443361i
$323$	−10.2277	−	8.04313i	−0.569083	−	0.447531i
$324$		0			0
$325$	5.25938	+	21.6795i	0.291738	+	1.20256i
$326$	24.0741	−	15.4715i	1.33334	−	0.856888i
$327$		0			0
$328$	0.698881	+	14.6713i	0.0385892	+	0.810088i
$329$	−3.92907	−	0.757267i	−0.216617	−	0.0417495i
$330$		0			0
$331$	2.39736	+	3.36662i	0.131771	+	0.185046i	0.875190	−	0.483780i	$-0.160737\pi$
$331$	2.39736	+	3.36662i	0.131771	+	0.185046i	−0.743419	+	0.668826i	$0.766797\pi$
$332$	2.41591	−	0.709375i	0.132590	−	0.0389320i
$333$		0			0
$334$	−10.6333			−0.581826
$335$	8.49656	+	22.3696i	0.464216	+	1.22218i
$336$		0			0
$337$	−21.4776	−	11.0725i	−1.16996	−	0.603156i	−0.239983	−	0.970777i	$-0.577142\pi$
$337$	−21.4776	−	11.0725i	−1.16996	−	0.603156i	−0.929976	+	0.367621i	$0.880172\pi$
$338$	38.1402	−	11.1990i	2.07455	−	0.609143i
$339$		0			0
$340$	−1.11383	−	1.28543i	−0.0604058	−	0.0697120i
$341$	−5.80994	−	1.11977i	−0.314626	−	0.0606392i
$342$		0			0
$343$	−0.233789	−	1.62604i	−0.0126234	−	0.0877977i
$344$	−6.89116	+	4.42868i	−0.371546	+	0.238778i
$345$		0			0
$346$	14.4323	−	2.78161i	0.775888	−	0.149540i
$347$	1.75724	+	1.38191i	0.0943334	+	0.0741846i	0.664212	−	0.747544i	$-0.268767\pi$
$347$	1.75724	+	1.38191i	0.0943334	+	0.0741846i	−0.569878	+	0.821729i	$0.693010\pi$
$348$		0			0
$349$	11.8148	−	25.8707i	0.632430	−	1.38483i	−0.273695	−	0.961817i	$-0.588246\pi$
$349$	11.8148	−	25.8707i	0.632430	−	1.38483i	0.906125	−	0.423011i	$-0.139027\pi$
$350$	16.4271	+	10.5571i	0.878067	+	0.564300i
$351$		0			0
$352$	0.649584	−	0.912213i	0.0346230	−	0.0486211i
$353$	−5.42887	+	0.518394i	−0.288949	+	0.0275913i	−0.238524	−	0.971137i	$-0.576664\pi$
$353$	−5.42887	+	0.518394i	−0.288949	+	0.0275913i	−0.0504251	+	0.998728i	$0.516058\pi$
$354$		0			0
$355$	1.92656	−	7.94137i	0.102251	−	0.421484i
$356$	−0.399072	−	1.15304i	−0.0211508	−	0.0611112i
$357$		0			0
$358$	2.41805	+	2.30561i	0.127798	+	0.121855i
$359$	−5.33620	−	11.6847i	−0.281634	−	0.616693i	0.714959	−	0.699166i	$-0.246445\pi$
$359$	−5.33620	−	11.6847i	−0.281634	−	0.616693i	−0.996593	+	0.0824736i	$0.973718\pi$
$360$		0			0
$361$	−9.09964	−	0.868911i	−0.478929	−	0.0457321i
$362$	−13.3869	+	15.4492i	−0.703597	+	0.811994i
$363$		0			0
$364$	2.74692	−	4.75780i	0.143978	−	0.249377i
$365$	−17.3037	−	29.9709i	−0.905716	−	1.56875i
$366$		0			0
$367$	10.3433	−	9.86231i	0.539916	−	0.514809i	−0.370317	−	0.928905i	$-0.620751\pi$
$367$	10.3433	−	9.86231i	0.539916	−	0.514809i	0.910233	+	0.414097i	$0.135903\pi$
$368$	15.2656	−	7.86998i	0.795776	−	0.410251i
$369$		0			0
$370$	−6.53573	+	6.23181i	−0.339776	+	0.323976i
$371$	18.2239	+	7.29576i	0.946139	+	0.378777i
$372$		0			0
$373$	8.60170	−	14.8986i	0.445379	−	0.771419i	−0.552700	−	0.833381i	$-0.686402\pi$
$373$	8.60170	−	14.8986i	0.445379	−	0.771419i	0.998079	+	0.0619616i	$0.0197356\pi$
$374$	−2.41897	+	1.90230i	−0.125082	+	0.0983657i
$375$		0			0
$376$	−2.85275	−	0.272404i	−0.147119	−	0.0140482i
$377$	−4.46328	+	31.0428i	−0.229871	+	1.59879i
$378$		0			0
$379$	24.9812	+	23.8195i	1.28320	+	1.22353i	0.960902	+	0.276889i	$0.0893033\pi$
$379$	24.9812	+	23.8195i	1.28320	+	1.22353i	0.322296	+	0.946639i	$0.395545\pi$
$380$	−3.52960	−	1.03639i	−0.181065	−	0.0531655i
$381$		0			0
$382$	−4.05085	+	16.6978i	−0.207260	+	0.854335i
$383$	−0.704870	+	14.7970i	−0.0360172	+	0.756093i	0.906554	+	0.422089i	$0.138703\pi$
$383$	−0.704870	+	14.7970i	−0.0360172	+	0.756093i	−0.942572	+	0.334004i	$0.891600\pi$
$384$		0			0
$385$	5.23668	−	7.35389i	0.266886	−	0.374789i
$386$	2.03613	−	5.88300i	0.103636	−	0.299437i
$387$		0			0
$388$	−0.979758	+	2.14537i	−0.0497397	+	0.108915i
$389$	−0.410677	+	0.164410i	−0.0208221	+	0.00833592i	−0.382050	−	0.924142i	$-0.624782\pi$
$389$	−0.410677	+	0.164410i	−0.0208221	+	0.00833592i	0.361228	+	0.932478i	$0.382358\pi$
$390$		0			0
$391$	−9.36241	+	1.80446i	−0.473477	+	0.0912553i
$392$	4.07394	+	16.7930i	0.205765	+	0.848175i
$393$		0			0
$394$	3.32749	+	23.1432i	0.167637	+	1.16594i
$395$	−0.798568	−	16.7640i	−0.0401803	−	0.843488i
$396$		0			0
$397$	6.06585	+	7.00037i	0.304436	+	0.351338i	0.887268	−	0.461255i	$-0.152601\pi$
$397$	6.06585	+	7.00037i	0.304436	+	0.351338i	−0.582831	+	0.812593i	$0.698055\pi$
$398$	6.77147	+	9.50921i	0.339423	+	0.476653i
$399$		0			0
$400$	13.9256	+	7.17913i	0.696279	+	0.358957i
$401$	−3.56201			−0.177878			−0.0889390	−	0.996037i	$-0.528348\pi$
$401$	−3.56201			−0.177878			−0.0889390	+	0.996037i	$0.528348\pi$
$402$		0			0
$403$	−44.3747			−2.21046
$404$	−0.287649	−	0.148293i	−0.0143111	−	0.00737788i
$405$		0			0
$406$	15.9237	+	22.3617i	0.790279	+	1.10979i
$407$	1.13448	+	1.30926i	0.0562343	+	0.0648978i
$408$		0			0
$409$	0.211006	+	4.42956i	0.0104336	+	0.219027i	0.998063	+	0.0622187i	$0.0198176\pi$
$409$	0.211006	+	4.42956i	0.0104336	+	0.219027i	−0.987629	+	0.156809i	$0.949879\pi$
$410$	−3.46653	−	24.1102i	−0.171200	−	1.19072i
$411$		0			0
$412$	−0.160302	−	0.660772i	−0.00789749	−	0.0325539i
$413$	−26.4798	+	5.10357i	−1.30299	+	0.251130i
$414$		0			0
$415$	28.8080	−	11.5330i	1.41413	−	0.566132i
$416$	3.48892	−	7.63967i	0.171058	−	0.374566i
$417$		0			0
$418$	−2.17687	+	6.28965i	−0.106474	+	0.307637i
$419$	7.64396	−	10.7344i	0.373432	−	0.524412i	−0.584505	−	0.811390i	$-0.698711\pi$
$419$	7.64396	−	10.7344i	0.373432	−	0.524412i	0.957937	+	0.286978i	$0.0926508\pi$
$420$		0			0
$421$	1.04984	−	22.0388i	0.0511660	−	1.07411i	−0.816622	−	0.577172i	$-0.804156\pi$
$421$	1.04984	−	22.0388i	0.0511660	−	1.07411i	0.867788	−	0.496934i	$-0.165541\pi$
$422$	−1.89026	+	7.79174i	−0.0920163	+	0.379296i
$423$		0			0
$424$	13.4892	+	3.96080i	0.655096	+	0.192353i
$425$	−6.29485	−	6.00212i	−0.305345	−	0.291146i
$426$		0			0
$427$	6.48900	−	45.1320i	0.314025	−	2.18409i
$428$	−2.56417	−	0.244848i	−0.123944	−	0.0118352i
$429$		0			0
$430$	10.6783	−	8.39747i	0.514951	−	0.404962i
$431$	18.9490	−	32.8207i	0.912743	−	1.58092i	0.102571	−	0.994726i	$-0.467293\pi$
$431$	18.9490	−	32.8207i	0.912743	−	1.58092i	0.810172	−	0.586192i	$-0.199374\pi$
$432$		0			0
$433$	−12.8785	−	5.15579i	−0.618903	−	0.247772i	0.0409557	−	0.999161i	$-0.486960\pi$
$433$	−12.8785	−	5.15579i	−0.618903	−	0.247772i	−0.659859	+	0.751389i	$0.729384\pi$
$434$	−28.1114	+	26.8042i	−1.34939	+	1.28664i
$435$		0			0
$436$	−2.03658	+	1.04993i	−0.0975345	+	0.0502825i
$437$	−14.9246	+	14.2306i	−0.713939	+	0.680740i
$438$		0			0
$439$	12.0835	+	20.9293i	0.576716	+	0.998902i	0.995853	+	0.0909787i	$0.0289995\pi$
$439$	12.0835	+	20.9293i	0.576716	+	0.998902i	−0.419137	+	0.907923i	$0.637667\pi$
$440$	3.23281	−	5.59938i	0.154118	−	0.266940i
$441$		0			0
$442$	−15.1137	+	17.4422i	−0.718887	+	0.829640i
$443$	−4.31584	−	0.412113i	−0.205052	−	0.0195801i	−0.00797543	−	0.999968i	$-0.502539\pi$
$443$	−4.31584	−	0.412113i	−0.205052	−	0.0195801i	−0.197077	+	0.980388i	$0.563145\pi$
$444$		0			0
$445$	−6.24669	−	13.6783i	−0.296121	−	0.648415i
$446$	0.854590	+	0.814850i	0.0404660	+	0.0385843i
$447$		0			0
$448$	8.23548	+	23.7949i	0.389090	+	1.12420i
$449$	−0.0399651	+	0.164738i	−0.00188607	+	0.00777449i	−0.972747	−	0.231870i	$-0.925516\pi$
$449$	−0.0399651	+	0.164738i	−0.00188607	+	0.00777449i	0.970861	+	0.239644i	$0.0770308\pi$
$450$		0			0
$451$	−4.65165	+	0.444179i	−0.219038	+	0.0209156i
$452$	−1.93268	+	2.71406i	−0.0909054	+	0.127659i
$453$		0			0
$454$	17.7379	+	11.3994i	0.832480	+	0.535002i
$455$	28.1262	−	61.5879i	1.31858	−	2.88728i
$456$		0			0
$457$	21.0945	+	16.5889i	0.986760	+	0.775996i	0.974605	−	0.223930i	$-0.0718886\pi$
$457$	21.0945	+	16.5889i	0.986760	+	0.775996i	0.0121545	+	0.999926i	$0.496131\pi$
$458$	−0.997293	+	0.192212i	−0.0466004	+	0.00898150i
$459$		0			0
$460$	−2.26774	+	1.45739i	−0.105734	+	0.0679512i
$461$	4.40732	+	30.6536i	0.205269	+	1.42768i	0.788331	+	0.615252i	$0.210946\pi$
$461$	4.40732	+	30.6536i	0.205269	+	1.42768i	−0.583061	+	0.812428i	$0.698145\pi$
$462$		0			0
$463$	−41.4815	−	7.99491i	−1.92781	−	0.371555i	−0.927811	−	0.373051i	$-0.878311\pi$
$463$	−41.4815	−	7.99491i	−1.92781	−	0.371555i	−0.999999	+	0.00149662i	$0.999524\pi$
$464$	14.4238	+	16.6459i	0.669606	+	0.772767i
$465$		0			0
$466$	32.2646	−	9.47375i	1.49463	−	0.438863i
$467$	−32.8560	−	16.9384i	−1.52039	−	0.783818i	−0.522755	−	0.852483i	$-0.675096\pi$
$467$	−32.8560	−	16.9384i	−1.52039	−	0.783818i	−0.997640	+	0.0686652i	$0.978126\pi$
$468$		0			0
$469$	9.00335	−	28.7584i	0.415736	−	1.32794i
$470$	4.75245			0.219214
$471$		0			0
$472$	−18.5311	+	5.44122i	−0.852963	+	0.250452i
$473$	−1.51166	−	2.12282i	−0.0695060	−	0.0976075i
$474$		0			0
$475$	−18.4715	−	3.56008i	−0.847529	−	0.163348i
$476$	0.101919	+	2.13955i	0.00467147	+	0.0980662i
$477$		0			0
$478$	6.57220	−	4.22370i	0.300605	−	0.193187i
$479$	−4.30064	−	17.7275i	−0.196501	−	0.809989i	−0.981652	−	0.190684i	$-0.938930\pi$
$479$	−4.30064	−	17.7275i	−0.196501	−	0.809989i	0.785150	−	0.619305i	$-0.212586\pi$
$480$		0			0
$481$	10.2128	+	8.03144i	0.465664	+	0.366202i
$482$	5.54153	−	2.21850i	0.252410	−	0.101050i
$483$		0			0
$484$	−2.05467	−	1.32045i	−0.0933939	−	0.0600206i
$485$	−9.50667	+	27.4677i	−0.431676	+	1.24725i
$486$		0			0
$487$	−2.92097	+	0.278919i	−0.132362	+	0.0126390i	−0.161027	−	0.986950i	$-0.551481\pi$
$487$	−2.92097	+	0.278919i	−0.132362	+	0.0126390i	0.0286648	+	0.999589i	$0.490874\pi$
$488$	1.55379	−	32.6182i	0.0703370	−	1.47655i
$489$		0			0
$490$	−9.37276	−	27.0808i	−0.423418	−	1.22339i
$491$	23.6180	+	6.93486i	1.06586	+	0.312966i	0.767210	−	0.641396i	$-0.221644\pi$
$491$	23.6180	+	6.93486i	1.06586	+	0.312966i	0.298653	+	0.954362i	$0.403463\pi$
$492$		0			0
$493$	−5.07956	−	11.1227i	−0.228772	−	0.500940i
$494$	−7.10377	+	49.4078i	−0.319614	+	2.22296i
$495$		0			0
$496$	−20.4084	+	23.5526i	−0.916366	+	1.05754i
$497$	−8.08931	+	6.36151i	−0.362855	+	0.285353i
$498$		0			0
$499$	1.93618	+	3.35355i	0.0866751	+	0.150126i	0.906104	−	0.423055i	$-0.139042\pi$
$499$	1.93618	+	3.35355i	0.0866751	+	0.150126i	−0.819429	+	0.573181i	$0.805709\pi$
$500$	0.935983	+	0.374711i	0.0418584	+	0.0167576i
$501$		0			0
$502$	21.3882	−	11.0264i	0.954604	−	0.492133i
$503$	−23.0466	+	11.8814i	−1.02760	+	0.529764i	−0.887710	−	0.460404i	$-0.847705\pi$
$503$	−23.0466	+	11.8814i	−1.02760	+	0.529764i	−0.139889	+	0.990167i	$0.544674\pi$
$504$		0			0
$505$	−3.70268	−	1.48233i	−0.164767	−	0.0659627i
$506$	2.43864	+	4.22385i	0.108411	+	0.187773i
$507$		0			0
$508$	−1.27368	+	1.00163i	−0.0565104	+	0.0444402i
$509$	12.7095	−	14.6675i	0.563339	−	0.650128i	−0.400600	−	0.916253i	$-0.631198\pi$
$509$	12.7095	−	14.6675i	0.563339	−	0.650128i	0.963938	+	0.266126i	$0.0857436\pi$
$510$		0			0
$511$	−6.20248	+	43.1392i	−0.274381	+	1.90836i
$512$	7.22819	+	15.8275i	0.319444	+	0.699484i
$513$		0			0
$514$	−32.6940	−	9.59981i	−1.44207	−	0.423429i
$515$	−2.74070	−	7.91874i	−0.120770	−	0.348941i
$516$		0			0
$517$	0.0433804	−	0.910666i	0.00190787	−	0.0400510i
$518$	11.3211	−	1.08104i	0.497423	−	0.0474981i
$519$		0			0
$520$	15.8596	−	45.8232i	0.695488	−	2.00948i
$521$	13.7279	+	8.82238i	0.601430	+	0.386515i	0.805635	−	0.592413i	$-0.201825\pi$
$521$	13.7279	+	8.82238i	0.601430	+	0.386515i	−0.204205	+	0.978928i	$0.565461\pi$
$522$		0			0
$523$	31.1671	−	12.4774i	1.36284	−	0.545600i	0.429007	−	0.903301i	$-0.358863\pi$
$523$	31.1671	−	12.4774i	1.36284	−	0.545600i	0.933836	+	0.357701i	$0.116439\pi$
$524$	−4.03445	−	3.17273i	−0.176246	−	0.138601i
$525$		0			0
$526$	−0.543923	−	2.24208i	−0.0237162	−	0.0977593i
$527$	14.5547	−	9.35371i	0.634011	−	0.407454i
$528$		0			0
$529$	−0.375353	−	7.87963i	−0.0163197	−	0.342592i
$530$	−22.8933	−	4.41233i	−0.994422	−	0.191659i
$531$		0			0
$532$	2.68721	+	3.77365i	0.116505	+	0.163609i
$533$	−33.6251	+	9.87323i	−1.45647	+	0.427657i
$534$		0			0
$535$	−31.7447			−1.37244
$536$	4.46105	−	21.1159i	0.192688	−	0.912068i
$537$		0			0
$538$	−38.1400	−	19.6625i	−1.64433	−	0.847711i
$539$	−5.27479	+	1.54882i	−0.227201	+	0.0667123i
$540$		0			0
$541$	5.89166	+	6.79934i	0.253302	+	0.292326i	0.868132	−	0.496334i	$-0.165321\pi$
$541$	5.89166	+	6.79934i	0.253302	+	0.292326i	−0.614830	+	0.788660i	$0.710775\pi$
$542$	16.8957	+	3.25639i	0.725734	+	0.139874i
$543$		0			0
$544$	0.466013	+	3.24119i	0.0199802	+	0.138965i
$545$	−23.7553	+	15.2666i	−1.01757	+	0.653950i
$546$		0			0
$547$	−11.4459	+	2.20602i	−0.489393	+	0.0943227i	−0.427977	−	0.903790i	$-0.640774\pi$
$547$	−11.4459	+	2.20602i	−0.489393	+	0.0943227i	−0.0614156	+	0.998112i	$0.519562\pi$
$548$	−3.08278	−	2.42433i	−0.131690	−	0.103562i
$549$		0			0
$550$	−1.84824	+	4.04708i	−0.0788092	+	0.172568i
$551$	−22.2477	−	14.2978i	−0.947786	−	0.609105i
$552$		0			0
$553$	−12.2599	+	17.2166i	−0.521344	+	0.732125i
$554$	−13.4497	+	1.28429i	−0.571421	+	0.0545641i
$555$		0			0
$556$	0.667168	−	2.75010i	0.0282942	−	0.116630i
$557$	−6.70977	−	19.3866i	−0.284302	−	0.821437i	−0.993231	−	0.116157i	$-0.962942\pi$
$557$	−6.70977	−	19.3866i	−0.284302	−	0.821437i	0.708929	−	0.705280i	$-0.249179\pi$
$558$		0			0
$559$	−14.1451	−	13.4873i	−0.598273	−	0.570452i
$560$	−19.7532	−	43.2534i	−0.834724	−	1.82779i
$561$		0			0
$562$	32.8259	+	3.13449i	1.38468	+	0.132221i
$563$	−0.135261	+	0.156099i	−0.00570055	+	0.00657879i	−0.758593	−	0.651565i	$-0.774113\pi$
$563$	−0.135261	+	0.156099i	−0.00570055	+	0.00657879i	0.752892	+	0.658144i	$0.228658\pi$
$564$		0			0
$565$	−20.5311	+	35.5609i	−0.863750	+	1.49606i
$566$	8.37981	+	14.5143i	0.352230	+	0.610080i
$567$		0			0
$568$	−5.33412	+	5.08607i	−0.223815	+	0.213407i
$569$	24.3960	−	12.5770i	1.02273	−	0.527256i	0.136572	−	0.990630i	$-0.456392\pi$
$569$	24.3960	−	12.5770i	1.02273	−	0.527256i	0.886163	+	0.463374i	$0.153361\pi$
$570$		0			0
$571$	4.64403	−	4.42808i	0.194347	−	0.185309i	−0.586657	−	0.809835i	$-0.699556\pi$
$571$	4.64403	−	4.42808i	0.194347	−	0.185309i	0.781004	+	0.624526i	$0.214708\pi$
$572$	1.16208	+	0.465228i	0.0485891	+	0.0194521i
$573$		0			0
$574$	−15.3377	+	26.5657i	−0.640184	+	1.10883i
$575$	−10.8357	+	8.52127i	−0.451879	+	0.355362i
$576$		0			0
$577$	1.44772	+	0.138241i	0.0602695	+	0.00575504i	0.125147	−	0.992138i	$-0.460060\pi$
$577$	1.44772	+	0.138241i	0.0602695	+	0.00575504i	−0.0648777	+	0.997893i	$0.520666\pi$
$578$	−2.33810	+	16.2618i	−0.0972522	+	0.676404i
$579$		0			0
$580$	−2.50197	−	2.38562i	−0.103889	−	0.0990577i
$581$	−37.4956	−	11.0097i	−1.55558	−	0.456760i
$582$		0			0
$583$	−1.05446	+	4.34655i	−0.0436714	+	0.180016i
$584$	−1.48519	+	31.1779i	−0.0614574	+	1.29015i
$585$		0			0
$586$	22.7508	−	31.9490i	0.939827	−	1.31980i
$587$	−0.807337	+	2.33265i	−0.0333224	+	0.0962786i	−0.960435	−	0.278504i	$-0.910161\pi$
$587$	−0.807337	+	2.33265i	−0.0333224	+	0.0962786i	0.927113	+	0.374783i	$0.122283\pi$
$588$		0			0
$589$	15.5443	−	34.0374i	0.640494	−	1.40249i
$590$	29.7346	−	11.9039i	1.22415	−	0.490078i
$591$		0			0
$592$	8.95980	−	1.72686i	0.368245	−	0.0709735i
$593$	−7.61418	−	31.3861i	−0.312677	−	1.28887i	−0.883745	−	0.467969i	$-0.844986\pi$
$593$	−7.61418	−	31.3861i	−0.312677	−	1.28887i	0.571068	−	0.820903i	$-0.306529\pi$
$594$		0			0
$595$	3.75681	+	26.1292i	0.154014	+	1.07119i
$596$	−0.00619904	−	0.130134i	−0.000253923	−	0.00533049i
$597$		0			0
$598$	23.9536	+	27.6439i	0.979534	+	1.13044i
$599$	−0.986822	−	1.38580i	−0.0403205	−	0.0566222i	0.793924	−	0.608018i	$-0.208035\pi$
$599$	−0.986822	−	1.38580i	−0.0403205	−	0.0566222i	−0.834244	+	0.551395i	$0.814096\pi$
$600$		0			0
$601$	20.8728	+	10.7607i	0.851419	+	0.438937i	0.827960	−	0.560788i	$-0.189502\pi$
$601$	20.8728	+	10.7607i	0.851419	+	0.438937i	0.0234593	+	0.999725i	$0.492532\pi$
$602$	−17.1078			−0.697263
$603$		0			0
$604$	1.01389			0.0412546
$605$	−26.7541	−	13.7927i	−1.08771	−	0.560752i
$606$		0			0
$607$	−17.4005	−	24.4356i	−0.706265	−	0.991810i	−0.999362	−	0.0357272i	$-0.988625\pi$
$607$	−17.4005	−	24.4356i	−0.706265	−	0.991810i	0.293097	−	0.956083i	$-0.405314\pi$
$608$	4.63781	+	5.35231i	0.188088	+	0.217065i
$609$		0			0
$610$	2.57678	+	54.0932i	0.104331	+	2.19017i
$611$	−0.973073	−	6.76787i	−0.0393663	−	0.273799i
$612$		0			0
$613$	−9.84670	−	40.5887i	−0.397704	−	1.63936i	−0.720908	−	0.693031i	$-0.756275\pi$
$613$	−9.84670	−	40.5887i	−0.397704	−	1.63936i	0.323204	−	0.946329i	$-0.395240\pi$
$614$	−8.97587	+	1.72996i	−0.362237	+	0.0698154i
$615$		0			0
$616$	−7.55920	+	3.02625i	−0.304569	+	0.121931i
$617$	7.00109	−	15.3302i	0.281853	−	0.617172i	−0.714763	−	0.699367i	$-0.753466\pi$
$617$	7.00109	−	15.3302i	0.281853	−	0.617172i	0.996616	+	0.0821943i	$0.0261928\pi$
$618$		0			0
$619$	−1.95304	+	5.64295i	−0.0784994	+	0.226809i	−0.977421	−	0.211300i	$-0.932230\pi$
$619$	−1.95304	+	5.64295i	−0.0784994	+	0.226809i	0.898922	+	0.438109i	$0.144352\pi$
$620$	2.83730	−	3.98443i	0.113949	−	0.160019i
$621$		0			0
$622$	0.593802	−	12.4654i	0.0238093	−	0.499819i
$623$	−4.46459	+	18.4033i	−0.178870	+	0.737313i
$624$		0			0
$625$	28.9342	+	8.49583i	1.15737	+	0.339833i
$626$	−12.3113	−	11.7388i	−0.492060	−	0.469178i
$627$		0			0
$628$	−0.239893	+	1.66849i	−0.00957279	+	0.0665802i
$629$	−5.04268	−	0.481518i	−0.201065	−	0.0191994i
$630$		0			0
$631$	−4.95458	+	3.89633i	−0.197239	+	0.155110i	−0.711894	−	0.702287i	$-0.752162\pi$
$631$	−4.95458	+	3.89633i	−0.197239	+	0.155110i	0.514655	+	0.857397i	$0.327920\pi$
$632$	−7.56850	+	13.1090i	−0.301059	+	0.521449i
$633$		0			0
$634$	28.1541	+	11.2712i	1.11814	+	0.447637i
$635$	−14.4524	+	13.7804i	−0.573527	+	0.546857i
$636$		0			0
$637$	−36.6462	+	18.8924i	−1.45197	+	0.748545i
$638$	−4.52681	+	4.31631i	−0.179218	+	0.170884i
$639$		0			0
$640$	−18.8558	−	32.6592i	−0.745341	−	1.29097i
$641$	11.1521	−	19.3160i	0.440481	−	0.762935i	−0.557244	−	0.830349i	$-0.688141\pi$
$641$	11.1521	−	19.3160i	0.440481	−	0.762935i	0.997725	+	0.0674134i	$0.0214746\pi$
$642$		0			0
$643$	−18.4987	+	21.3487i	−0.729518	+	0.841909i	−0.992417	−	0.122914i	$-0.960776\pi$
$643$	−18.4987	+	21.3487i	−0.729518	+	0.841909i	0.262899	+	0.964823i	$0.415321\pi$
$644$	3.37942	+	0.322696i	0.133168	+	0.0127160i
$645$		0			0
$646$	−8.08463	−	17.7029i	−0.318085	−	0.696510i
$647$	28.3178	+	27.0009i	1.11329	+	1.06152i	0.997670	+	0.0682226i	$0.0217328\pi$
$647$	28.3178	+	27.0009i	1.11329	+	1.06152i	0.115616	+	0.993294i	$0.463116\pi$
$648$		0			0
$649$	−2.00962	−	5.80642i	−0.0788846	−	0.227922i
$650$	−7.86662	+	32.4266i	−0.308554	+	1.27188i
$651$		0			0
$652$	4.51783	−	0.431400i	0.176932	−	0.0168949i
$653$	20.9326	−	29.3957i	0.819157	−	1.15034i	−0.167233	−	0.985917i	$-0.553483\pi$
$653$	20.9326	−	29.3957i	0.819157	−	1.15034i	0.986389	−	0.164427i	$-0.0525775\pi$
$654$		0			0
$655$	−53.2125	−	34.1976i	−2.07918	−	1.33621i
$656$	−10.2242	+	22.3879i	−0.399188	+	0.874100i
$657$		0			0
$658$	−4.70452	−	3.69968i	−0.183401	−	0.144228i
$659$	35.3793	−	6.81880i	1.37818	−	0.265623i	0.554268	−	0.832338i	$-0.312998\pi$
$659$	35.3793	−	6.81880i	1.37818	−	0.265623i	0.823914	+	0.566715i	$0.191786\pi$
$660$		0			0
$661$	−10.6430	+	6.83985i	−0.413965	+	0.266039i	−0.731004	−	0.682373i	$-0.760948\pi$
$661$	−10.6430	+	6.83985i	−0.413965	+	0.266039i	0.317039	+	0.948413i	$0.397312\pi$
$662$	0.879763	+	6.11888i	0.0341929	+	0.237817i
$663$		0			0
$664$	−27.4817	−	5.29666i	−1.06650	−	0.205550i
$665$	37.3881	+	43.1482i	1.44985	+	1.67321i
$666$		0			0
$667$	−18.5945	+	5.45983i	−0.719981	+	0.211405i
$668$	−1.49887	−	0.772723i	−0.0579932	−	0.0298976i
$669$		0			0
$670$	−4.03591	+	35.5628i	−0.155921	+	1.37391i
$671$	10.3889			0.401058
$672$		0			0
$673$	26.2600	−	7.71064i	1.01225	−	0.297223i	0.266776	−	0.963759i	$-0.414042\pi$
$673$	26.2600	−	7.71064i	1.01225	−	0.297223i	0.745473	+	0.666535i	$0.232223\pi$
$674$	−20.9647	−	29.4408i	−0.807529	−	1.13402i
$675$		0			0
$676$	6.19010	+	1.19304i	0.238081	+	0.0458863i
$677$	0.851648	+	17.8783i	0.0327315	+	0.687118i	0.954291	+	0.298880i	$0.0966132\pi$
$677$	0.851648	+	17.8783i	0.0327315	+	0.687118i	−0.921559	+	0.388238i	$0.873084\pi$
$678$		0			0
$679$	30.7938	−	19.7900i	1.18176	−	0.759470i
$680$	4.45719	+	18.3728i	0.170925	+	0.704564i
$681$		0			0
$682$	−6.95659	−	5.47073i	−0.266382	−	0.209485i
$683$	−31.0814	+	12.4431i	−1.18930	+	0.476123i	−0.880061	−	0.474861i	$-0.842498\pi$
$683$	−31.0814	+	12.4431i	−1.18930	+	0.476123i	−0.309238	+	0.950985i	$0.600074\pi$
$684$		0			0
$685$	−40.6604	−	26.1309i	−1.55355	−	0.998409i
$686$	0.803646	−	2.32198i	0.0306833	−	0.0886537i
$687$		0			0
$688$	−13.6641	+	1.30476i	−0.520938	+	0.0497436i
$689$	−1.59606	+	33.5054i	−0.0608050	+	1.27645i
$690$		0			0
$691$	−7.02760	−	20.3049i	−0.267342	−	0.772435i	−0.996146	−	0.0877123i	$-0.972044\pi$
$691$	−7.02760	−	20.3049i	−0.267342	−	0.772435i	0.728803	−	0.684723i	$-0.240077\pi$
$692$	2.23653	+	0.656706i	0.0850203	+	0.0249642i
$693$		0			0
$694$	1.38904	+	3.04157i	0.0527271	+	0.115456i
$695$	4.96331	−	34.5205i	0.188269	−	1.30944i
$696$		0			0
$697$	8.94768	−	10.3262i	0.338918	−	0.391132i
$698$	33.4386	−	26.2964i	1.26567	−	0.995333i
$699$		0			0
$700$	1.54840	+	2.68190i	0.0585239	+	0.101366i
$701$	−19.5594	−	7.83040i	−0.738748	−	0.295750i	−0.0283959	−	0.999597i	$-0.509040\pi$
$701$	−19.5594	−	7.83040i	−0.738748	−	0.295750i	−0.710352	+	0.703847i	$0.751464\pi$
$702$		0			0
$703$	−9.73799	+	5.02028i	−0.367275	+	0.189344i
$704$	−5.09933	+	2.62889i	−0.192188	+	0.0990800i
$705$		0			0
$706$	−7.57275	−	3.03167i	−0.285004	−	0.114098i
$707$	2.51138	+	4.34983i	0.0944501	+	0.163592i
$708$		0			0
$709$	−25.1925	+	19.8116i	−0.946124	+	0.744040i	−0.966744	−	0.255748i	$-0.917678\pi$
$709$	−25.1925	+	19.8116i	−0.946124	+	0.744040i	0.0206200	+	0.999787i	$0.493436\pi$
$710$	8.00416	−	9.23729i	0.300391	−	0.346669i
$711$		0			0
$712$	−1.93014	+	13.4244i	−0.0723349	+	0.503100i
$713$	−11.3908	−	24.9424i	−0.426590	−	0.934102i
$714$		0			0
$715$	14.8017	+	4.34618i	0.553553	+	0.162538i
$716$	0.173301	+	0.500721i	0.00647657	+	0.0187128i
$717$		0			0
$718$	0.914209	−	19.1916i	0.0341180	−	0.716224i
$719$	−48.9875	+	4.67774i	−1.82693	+	0.174450i	−0.951245	−	0.308437i	$-0.900194\pi$
$719$	−48.9875	+	4.67774i	−1.82693	+	0.174450i	−0.875682	+	0.482888i	$0.839588\pi$
$720$		0			0
$721$	−3.45150	+	9.97246i	−0.128541	+	0.371394i
$722$	−11.5021	−	7.39192i	−0.428062	−	0.275099i
$723$		0			0
$724$	−3.00972	+	1.20491i	−0.111855	+	0.0447802i
$725$	−13.8961	−	10.9280i	−0.516088	−	0.405856i
$726$		0			0
$727$	4.52472	+	18.6511i	0.167812	+	0.691732i	0.992088	+	0.125544i	$0.0400675\pi$
$727$	4.52472	+	18.6511i	0.167812	+	0.691732i	−0.824276	+	0.566189i	$0.808417\pi$
$728$	−51.3720	+	33.0148i	−1.90397	+	1.22361i
$729$		0			0
$730$	−2.46300	−	51.7047i	−0.0911596	−	1.91368i
$731$	7.48248	+	1.44213i	0.276750	+	0.0533391i
$732$		0			0
$733$	−3.16970	−	4.45122i	−0.117075	−	0.164409i	0.751880	−	0.659300i	$-0.229147\pi$
$733$	−3.16970	−	4.45122i	−0.117075	−	0.164409i	−0.868955	+	0.494891i	$0.835208\pi$
$734$	20.5104	−	6.02241i	0.757054	−	0.222291i
$735$		0			0
$736$	5.18975			0.191297
$737$	6.77772	+	1.09798i	0.249660	+	0.0404446i
$738$		0			0
$739$	30.6305	+	15.7911i	1.12676	+	0.580886i	0.917802	−	0.397038i	$-0.129962\pi$
$739$	30.6305	+	15.7911i	1.12676	+	0.580886i	0.208960	+	0.977924i	$0.432992\pi$
$740$	−1.37415	+	0.403487i	−0.0505147	+	0.0148325i
$741$		0			0
$742$	19.2276	+	22.1898i	0.705866	+	0.814613i
$743$	−52.8023	−	10.1768i	−1.93713	−	0.373351i	−0.999682	−	0.0252237i	$-0.991970\pi$
$743$	−52.8023	−	10.1768i	−1.93713	−	0.373351i	−0.937447	−	0.348127i	$-0.886818\pi$
$744$		0			0
$745$	−0.228500	−	1.58925i	−0.00837161	−	0.0582258i
$746$	21.6468	−	13.9116i	0.792547	−	0.509339i
$747$		0			0
$748$	−0.479221	+	0.0923623i	−0.0175221	+	0.00337710i
$749$	31.4246	+	24.7125i	1.14823	+	0.902977i
$750$		0			0
$751$	8.99795	−	19.7028i	0.328340	−	0.718964i	−0.671416	−	0.741081i	$-0.734313\pi$
$751$	8.99795	−	19.7028i	0.328340	−	0.718964i	0.999755	+	0.0221172i	$0.00704070\pi$
$752$	−4.03968	−	2.59615i	−0.147312	−	0.0946717i
$753$		0			0
$754$	−27.2100	+	38.2111i	−0.990929	+	1.39156i
$755$	12.4387	−	1.18775i	0.452690	−	0.0432266i
$756$		0			0
$757$	−8.10276	+	33.4000i	−0.294500	+	1.21394i	0.611698	+	0.791091i	$0.290487\pi$
$757$	−8.10276	+	33.4000i	−0.294500	+	1.21394i	−0.906198	+	0.422853i	$0.861029\pi$
$758$	16.8860	+	48.7888i	0.613326	+	1.77209i
$759$		0			0
$760$	29.5929	+	28.2168i	1.07345	+	1.02353i
$761$	−2.44685	−	5.35786i	−0.0886983	−	0.194222i	0.860084	−	0.510152i	$-0.170411\pi$
$761$	−2.44685	−	5.35786i	−0.0886983	−	0.194222i	−0.948783	+	0.315930i	$0.897684\pi$
$762$		0			0
$763$	35.4005	+	3.38034i	1.28158	+	0.122376i
$764$	−1.78445	+	2.05936i	−0.0645591	+	0.0745051i
$765$		0			0
$766$	−11.0787	+	19.1889i	−0.400291	+	0.693324i
$767$	−23.0404	−	39.9072i	−0.831941	−	1.44096i
$768$		0			0
$769$	−31.5272	+	30.0612i	−1.13690	+	1.08403i	−0.141336	+	0.989962i	$0.545140\pi$
$769$	−31.5272	+	30.0612i	−1.13690	+	1.08403i	−0.995565	+	0.0940714i	$0.970012\pi$
$770$	12.0022	−	6.18756i	0.432529	−	0.222984i
$771$		0			0
$772$	0.714534	−	0.681307i	0.0257166	−	0.0245208i
$773$	1.64195	+	0.657338i	0.0590569	+	0.0236428i	0.401003	−	0.916077i	$-0.368662\pi$
$773$	1.64195	+	0.657338i	0.0590569	+	0.0236428i	−0.341946	+	0.939720i	$0.611086\pi$
$774$		0			0
$775$	12.5067	−	21.6622i	0.449253	−	0.778129i
$776$	20.6069	−	16.2054i	0.739744	−	0.581741i
$777$		0			0
$778$	−0.658661	−	0.0628945i	−0.0236142	−	0.00225488i
$779$	4.20559	−	29.2505i	0.150681	−	1.04801i
$780$		0			0
$781$	−1.69699	−	1.61808i	−0.0607231	−	0.0578994i
$782$	−13.6837	−	4.01789i	−0.489327	−	0.143679i
$783$		0			0
$784$	−6.82654	+	28.1394i	−0.243805	+	1.00498i
$785$	−0.988471	+	20.7506i	−0.0352800	+	0.740619i
$786$		0			0
$787$	−9.12228	+	12.8104i	−0.325174	+	0.456643i	−0.944510	−	0.328483i	$-0.893463\pi$
$787$	−9.12228	+	12.8104i	−0.325174	+	0.456643i	0.619336	+	0.785126i	$0.287402\pi$
$788$	−1.21278	+	3.50410i	−0.0432035	+	0.124828i
$789$		0			0
$790$	10.4281	−	22.8344i	0.371015	−	0.812410i
$791$	48.0075	−	19.2193i	1.70695	−	0.683359i
$792$		0			0
$793$	76.5055	−	14.7452i	2.71679	−	0.523618i
$794$	3.26636	+	13.4641i	0.115919	+	0.477824i
$795$		0			0
$796$	0.263475	+	1.83251i	0.00933863	+	0.0649516i
$797$	1.06094	+	22.2718i	0.0375803	+	0.788907i	0.936473	+	0.350739i	$0.114070\pi$
$797$	1.06094	+	22.2718i	0.0375803	+	0.788907i	−0.898893	+	0.438168i	$0.855627\pi$
$798$		0			0
$799$	1.74576	+	2.01471i	0.0617604	+	0.0712753i
$800$	2.74610	+	3.85635i	0.0970891	+	0.136343i
$801$		0			0
$802$	−4.73554	−	2.44134i	−0.167218	−	0.0862067i
$803$	−9.93015			−0.350427
$804$		0			0
$805$	41.8376			1.47458
$806$	−58.9943	−	30.4137i	−2.07799	−	1.07128i
$807$		0			0
$808$	2.08659	+	2.93020i	0.0734059	+	0.103084i
$809$	7.00019	+	8.07865i	0.246114	+	0.284030i	0.865343	−	0.501180i	$-0.167100\pi$
$809$	7.00019	+	8.07865i	0.246114	+	0.284030i	−0.619230	+	0.785210i	$0.712555\pi$
$810$		0			0
$811$	−1.28416	−	26.9579i	−0.0450931	−	0.946621i	−0.902156	−	0.431409i	$-0.858016\pi$
$811$	−1.28416	−	26.9579i	−0.0450931	−	0.946621i	0.857063	−	0.515211i	$-0.172287\pi$
$812$	0.619583	+	4.30930i	0.0217431	+	0.151227i
$813$		0			0
$814$	0.610901	+	2.51817i	0.0214121	+	0.0882617i
$815$	54.9205	−	10.5851i	1.92378	−	0.370779i
$816$		0			0
$817$	15.3003	−	6.12533i	0.535291	−	0.214298i
$818$	−2.75542	+	6.03353i	−0.0963410	+	0.210957i
$819$		0			0
$820$	1.26345	−	3.65051i	0.0441217	−	0.127481i
$821$	−14.3148	+	20.1023i	−0.499590	+	0.701576i	−0.984970	−	0.172727i	$-0.944742\pi$
$821$	−14.3148	+	20.1023i	−0.499590	+	0.701576i	0.485379	+	0.874304i	$0.338681\pi$
$822$		0			0
$823$	1.00636	−	21.1261i	0.0350795	−	0.736410i	−0.910987	−	0.412436i	$-0.864678\pi$
$823$	1.00636	−	21.1261i	0.0350795	−	0.736410i	0.946066	−	0.323974i	$-0.105019\pi$
$824$	−1.78181	+	7.34473i	−0.0620724	+	0.255866i
$825$		0			0
$826$	−38.7017	−	11.3639i	−1.34661	−	0.395399i
$827$	−11.2865	−	10.7616i	−0.392469	−	0.374218i	0.467994	−	0.883732i	$-0.344977\pi$
$827$	−11.2865	−	10.7616i	−0.392469	−	0.374218i	−0.860463	+	0.509513i	$0.829825\pi$
$828$		0			0
$829$	2.29021	−	15.9287i	0.0795422	−	0.553228i	−0.910614	−	0.413259i	$-0.864391\pi$
$829$	2.29021	−	15.9287i	0.0795422	−	0.553228i	0.990156	−	0.139969i	$-0.0447004\pi$
$830$	46.2035	+	4.41190i	1.60375	+	0.153139i
$831$		0			0
$832$	−33.8211	+	26.5972i	−1.17254	+	0.922092i
$833$	8.03742	−	13.9212i	0.278480	−	0.482342i
$834$		0			0
$835$	−19.2938	−	7.72407i	−0.667689	−	0.267302i
$836$	−0.763925	+	0.728401i	−0.0264209	+	0.0251923i
$837$		0			0
$838$	17.5195	−	9.03194i	0.605202	−	0.312003i
$839$	−14.5760	+	13.8982i	−0.503220	+	0.479819i	−0.898644	−	0.438680i	$-0.855446\pi$
$839$	−14.5760	+	13.8982i	−0.503220	+	0.479819i	0.395423	+	0.918499i	$0.370598\pi$
$840$		0			0
$841$	2.07352	+	3.59144i	0.0715007	+	0.123843i
$842$	16.5007	−	28.5801i	0.568653	−	0.984936i
$843$		0			0
$844$	−0.832681	+	0.960965i	−0.0286621	+	0.0330778i
$845$	77.3394	+	7.38501i	2.66055	+	0.254052i
$846$		0			0
$847$	15.7470	+	34.4810i	0.541072	+	1.18478i
$848$	17.0495	+	16.2566i	0.585481	+	0.558255i
$849$		0			0
$850$	−4.25498	−	12.2940i	−0.145945	−	0.421679i
$851$	−1.89277	+	7.80212i	−0.0648835	+	0.267453i
$852$		0			0
$853$	1.90609	−	0.182009i	0.0652632	−	0.00623188i	−0.0623734	−	0.998053i	$-0.519867\pi$
$853$	1.90609	−	0.182009i	0.0652632	−	0.00623188i	0.127637	+	0.991821i	$0.459261\pi$
$854$	39.5596	−	55.5537i	1.35370	−	1.90101i
$855$		0			0
$856$	24.0862	+	15.4793i	0.823249	+	0.529070i
$857$	7.88548	−	17.2668i	0.269363	−	0.589822i	−0.725817	−	0.687888i	$-0.758538\pi$
$857$	7.88548	−	17.2668i	0.269363	−	0.589822i	0.995180	+	0.0980653i	$0.0312654\pi$
$858$		0			0
$859$	−30.1155	−	23.6831i	−1.02753	−	0.808057i	−0.0459164	−	0.998945i	$-0.514621\pi$
$859$	−30.1155	−	23.6831i	−1.02753	−	0.808057i	−0.981612	+	0.190888i	$0.938863\pi$
$860$	2.11546	−	0.407722i	0.0721367	−	0.0139032i
$861$		0			0
$862$	47.6867	−	30.6464i	1.62422	−	1.04382i
$863$	5.02199	+	34.9287i	0.170951	+	1.18899i	0.876881	+	0.480707i	$0.159620\pi$
$863$	5.02199	+	34.9287i	0.170951	+	1.18899i	−0.705931	+	0.708281i	$0.749471\pi$
$864$		0			0
$865$	28.2077	+	5.43659i	0.959091	+	0.184850i
$866$	−13.5878	−	15.6811i	−0.461732	−	0.532867i
$867$		0			0
$868$	−5.91048	+	1.73547i	−0.200615	+	0.0589058i
$869$	−4.28034	−	2.20667i	−0.145201	−	0.0748561i
$870$		0			0
$871$	51.4707	−	1.53409i	1.74402	−	0.0519805i
$872$	25.4686			0.862474
$873$		0			0
$874$	−29.5950	+	8.68987i	−1.00106	+	0.293939i
$875$	−9.07650	−	12.7462i	−0.306842	−	0.430899i
$876$		0			0
$877$	11.8493	+	2.28376i	0.400121	+	0.0771170i	0.385342	−	0.922774i	$-0.374083\pi$
$877$	11.8493	+	2.28376i	0.400121	+	0.0771170i	0.0147789	+	0.999891i	$0.495296\pi$
$878$	1.71996	+	36.1065i	0.0580460	+	1.21854i
$879$		0			0
$880$	9.11429	−	5.85740i	0.307243	−	0.197453i
$881$	−5.90814	−	24.3537i	−0.199050	−	0.820497i	−0.980498	−	0.196527i	$-0.937034\pi$
$881$	−5.90814	−	24.3537i	−0.199050	−	0.820497i	0.781448	−	0.623970i	$-0.214481\pi$
$882$		0			0
$883$	30.2475	+	23.7869i	1.01791	+	0.800493i	0.980042	−	0.198790i	$-0.0637012\pi$
$883$	30.2475	+	23.7869i	1.01791	+	0.800493i	0.0378673	+	0.999283i	$0.487944\pi$
$884$	−3.39797	+	1.36034i	−0.114286	+	0.0457533i
$885$		0			0
$886$	−5.45528	−	3.50589i	−0.183274	−	0.117783i
$887$	−4.05293	+	11.7102i	−0.136084	+	0.393189i	−0.992367	−	0.123317i	$-0.960647\pi$
$887$	−4.05293	+	11.7102i	−0.136084	+	0.393189i	0.856283	+	0.516507i	$0.172768\pi$
$888$		0			0
$889$	25.0344	−	2.39050i	0.839627	−	0.0801746i
$890$	1.07019	−	22.4661i	0.0358730	−	0.753067i
$891$		0			0
$892$	0.0612483	+	0.176965i	0.00205074	+	0.00592523i
$893$	5.53212	+	1.62438i	0.185125	+	0.0543577i
$894$		0			0
$895$	2.71269	+	5.93996i	0.0906751	+	0.198551i
$896$	−6.75883	+	47.0087i	−0.225797	+	1.57045i
$897$		0			0
$898$	−0.166041	+	0.191621i	−0.00554086	+	0.00639449i
$899$	27.6415	−	21.7375i	0.921895	−	0.724986i
$900$		0			0
$901$	−6.53907	−	11.3260i	−0.217848	−	0.377324i
$902$	−6.48861	−	2.59765i	−0.216047	−	0.0864922i
$903$		0			0
$904$	32.9180	−	16.9704i	1.09484	−	0.564428i
$905$	−35.5125	+	18.3080i	−1.18048	+	0.608578i
$906$		0			0
$907$	−27.2081	−	10.8925i	−0.903431	−	0.361679i	−0.127016	−	0.991901i	$-0.540540\pi$
$907$	−27.2081	−	10.8925i	−0.903431	−	0.361679i	−0.776415	+	0.630221i	$0.782964\pi$
$908$	1.67194	+	2.89589i	0.0554854	+	0.0961036i
$909$		0			0
$910$	79.6040	−	62.6013i	2.63885	−	2.07521i
$911$	−10.6554	+	12.2970i	−0.353031	+	0.407419i	−0.904293	−	0.426913i	$-0.859601\pi$
$911$	−10.6554	+	12.2970i	−0.353031	+	0.407419i	0.551262	+	0.834332i	$0.314146\pi$
$912$		0			0
$913$	1.26716	−	8.81327i	0.0419368	−	0.291677i
$914$	16.6745	+	36.5121i	0.551544	+	1.20771i
$915$		0			0
$916$	−0.154547	−	0.0453792i	−0.00510639	−	0.00149937i
$917$	26.0538	+	75.2775i	0.860372	+	2.48588i
$918$		0			0
$919$	−1.38442	+	29.0626i	−0.0456678	+	0.958685i	0.853503	+	0.521088i	$0.174474\pi$
$919$	−1.38442	+	29.0626i	−0.0456678	+	0.958685i	−0.899171	+	0.437598i	$0.855829\pi$
$920$	29.8277	−	2.84820i	0.983391	−	0.0939025i
$921$		0			0
$922$	−15.1501	+	43.7734i	−0.498942	+	1.44160i
$923$	−14.7935	−	9.50722i	−0.486935	−	0.312934i
$924$		0			0
$925$	−6.79907	+	2.72194i	−0.223552	+	0.0894967i
$926$	−49.6684	−	39.0596i	−1.63220	−	1.28358i
$927$		0			0
$928$	1.56910	+	6.46792i	0.0515083	+	0.212320i
$929$	11.7669	−	7.56210i	0.386058	−	0.248104i	−0.333187	−	0.942861i	$-0.608124\pi$
$929$	11.7669	−	7.56210i	0.386058	−	0.248104i	0.719245	+	0.694756i	$0.244488\pi$
$930$		0			0
$931$	−1.65426	−	34.7272i	−0.0542162	−	1.13814i
$932$	5.23651	+	1.00925i	0.171528	+	0.0330592i
$933$		0			0
$934$	−32.0713	−	45.0379i	−1.04941	−	1.47369i
$935$	−5.77101	+	1.69452i	−0.188732	+	0.0554168i
$936$		0			0
$937$	21.0445			0.687495			0.343748	−	0.939062i	$-0.388304\pi$
$937$	21.0445			0.687495			0.343748	+	0.939062i	$0.388304\pi$
$938$	31.6801	−	32.0623i	1.03439	−	1.04687i
$939$		0			0
$940$	0.669909	+	0.345362i	0.0218500	+	0.0112645i
$941$	28.3913	−	8.33645i	0.925531	−	0.271760i	0.215966	−	0.976401i	$-0.430710\pi$
$941$	28.3913	−	8.33645i	0.925531	−	0.271760i	0.709565	+	0.704640i	$0.248892\pi$
$942$		0			0
$943$	−14.1811	−	16.3658i	−0.461799	−	0.532945i
$944$	−31.7779	−	6.12469i	−1.03428	−	0.199342i
$945$		0			0
$946$	−0.554735	−	3.85827i	−0.0180360	−	0.125443i
$947$	18.2503	−	11.7287i	0.593054	−	0.381133i	−0.209415	−	0.977827i	$-0.567156\pi$
$947$	18.2503	−	11.7287i	0.593054	−	0.381133i	0.802469	+	0.596694i	$0.203519\pi$
$948$		0			0
$949$	−73.1273	+	14.0941i	−2.37381	+	0.457515i
$950$	−22.1170	−	17.3930i	−0.717571	−	0.564304i
$951$		0			0
$952$	9.89057	−	21.6573i	0.320555	−	0.701918i
$953$	26.5710	+	17.0762i	0.860720	+	0.553151i	0.894901	−	0.446264i	$-0.147246\pi$
$953$	26.5710	+	17.0762i	0.860720	+	0.553151i	−0.0341811	+	0.999416i	$0.510882\pi$
$954$		0			0
$955$	−19.4796	+	27.3552i	−0.630344	+	0.885195i
$956$	1.23336	−	0.117772i	0.0398897	−	0.00380901i
$957$		0			0
$958$	6.43259	−	26.5155i	0.207828	−	0.856677i
$959$	19.9081	+	57.5206i	0.642865	+	1.85744i
$960$		0			0
$961$	13.5739	+	12.9427i	0.437869	+	0.417507i
$962$	8.07288	+	17.6771i	0.260280	+	0.569934i
$963$		0			0
$964$	0.942358	+	0.0899843i	0.0303513	+	0.00289820i
$965$	7.96795	−	9.19551i	0.256498	−	0.296014i
$966$		0			0
$967$	22.1824	−	38.4211i	0.713339	−	1.23554i	−0.250257	−	0.968179i	$-0.580515\pi$
$967$	22.1824	−	38.4211i	0.713339	−	1.23554i	0.963597	−	0.267361i	$-0.0861515\pi$
$968$	13.5740	+	23.5109i	0.436285	+	0.755669i
$969$		0			0
$970$	−31.4646	+	30.0015i	−1.01027	+	0.963289i
$971$	−20.9088	+	10.7792i	−0.670995	+	0.345922i	−0.759828	−	0.650124i	$-0.774717\pi$
$971$	−20.9088	+	10.7792i	−0.670995	+	0.345922i	0.0888324	+	0.996047i	$0.471686\pi$
$972$		0			0
$973$	−31.7867	+	30.3086i	−1.01904	+	0.971649i
$974$	−4.07448	−	1.63117i	−0.130555	−	0.0522662i
$975$		0			0
$976$	27.3595	−	47.3880i	0.875756	−	1.51685i
$977$	9.96503	−	7.83658i	0.318809	−	0.250715i	−0.445910	−	0.895078i	$-0.647120\pi$
$977$	9.96503	−	7.83658i	0.318809	−	0.250715i	0.764720	+	0.644363i	$0.222877\pi$
$978$		0			0
$979$	−4.29520	−	0.410142i	−0.137275	−	0.0131082i
$980$	0.646780	−	4.49845i	0.0206606	−	0.143698i
$981$		0			0
$982$	26.6460	+	25.4069i	0.850309	+	0.810768i
$983$	37.5508	+	11.0259i	1.19768	+	0.351671i	0.818967	−	0.573841i	$-0.194547\pi$
$983$	37.5508	+	11.0259i	1.19768	+	0.351671i	0.378717	+	0.925513i	$0.376366\pi$
$984$		0			0
$985$	−10.7737	+	44.4099i	−0.343279	+	1.41502i
$986$	0.870240	−	18.2686i	0.0277141	−	0.581790i
$987$		0			0
$988$	−4.59183	+	6.44833i	−0.146086	+	0.205149i
$989$	3.95004	−	11.4129i	0.125604	−	0.362909i
$990$		0			0
$991$	18.7004	−	40.9483i	0.594039	−	1.30076i	−0.338931	−	0.940811i	$-0.610065\pi$
$991$	18.7004	−	40.9483i	0.594039	−	1.30076i	0.932970	−	0.359953i	$-0.117207\pi$
$992$	−8.74247	+	3.49996i	−0.277574	+	0.111124i
$993$		0			0
$994$	−15.1145	+	2.91308i	−0.479402	+	0.0923971i
$995$	5.37913	+	22.1731i	0.170530	+	0.702933i
$996$		0			0
$997$	7.54252	+	52.4593i	0.238874	+	1.66140i	0.657657	+	0.753318i	$0.271548\pi$
$997$	7.54252	+	52.4593i	0.238874	+	1.66140i	−0.418783	+	0.908086i	$0.637543\pi$
$998$	0.275594	+	5.78543i	0.00872378	+	0.183135i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.z.c.19.4		100
3.2	odd	2		67.2.g.a.19.2	✓	100
67.60	even	33	inner	603.2.z.c.127.4		100
201.23	odd	66		4489.2.a.p.1.39		50
201.44	even	66		4489.2.a.q.1.12		50
201.194	odd	66		67.2.g.a.60.2	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
67.2.g.a.19.2	✓	100	3.2	odd	2
67.2.g.a.60.2	yes	100	201.194	odd	66
603.2.z.c.19.4		100	1.1	even	1	trivial
603.2.z.c.127.4		100	67.60	even	33	inner
4489.2.a.p.1.39		50	201.23	odd	66
4489.2.a.q.1.12		50	201.44	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)

\(f(q)\)	\(=\)	\(q+(1.32946 + 0.685383i) q^{2} +(0.137594 + 0.193224i) q^{4} +(1.91440 + 2.20934i) q^{5} +(-0.175175 - 3.67738i) q^{7} +(-0.375236 - 2.60982i) q^{8} +O(q^{10})\)	\(q+(1.32946 + 0.685383i) q^{2} +(0.137594 + 0.193224i) q^{4} +(1.91440 + 2.20934i) q^{5} +(-0.175175 - 3.67738i) q^{7} +(-0.375236 - 2.60982i) q^{8} +(1.03087 + 4.24932i) q^{10} +(0.823666 - 0.158749i) q^{11} +(5.84030 - 2.33810i) q^{13} +(2.28752 - 5.00898i) q^{14} +(1.44504 - 4.17515i) q^{16} +(-1.42274 + 1.99796i) q^{17} +(-0.252413 + 5.29880i) q^{19} +(-0.163487 + 0.673901i) q^{20} +(1.20383 + 0.353477i) q^{22} +(2.81340 + 2.68257i) q^{23} +(-0.504663 + 3.51001i) q^{25} +(9.36693 + 0.894434i) q^{26} +(0.686455 - 0.539835i) q^{28} +(-2.49264 + 4.31737i) q^{29} +(-6.54848 - 2.62162i) q^{31} +(0.966212 - 0.921282i) q^{32} +(-3.26084 + 1.68108i) q^{34} +(7.78921 - 7.42700i) q^{35} +(1.03264 + 1.78858i) q^{37} +(-3.96728 + 6.87154i) q^{38} +(5.04763 - 5.82527i) q^{40} +(-5.54544 - 0.529525i) q^{41} +(-1.29060 - 2.82603i) q^{43} +(0.144006 + 0.137309i) q^{44} +(1.90171 + 5.49463i) q^{46} +(0.256241 - 1.05624i) q^{47} +(-6.52411 + 0.622977i) q^{49} +(-3.07663 + 4.32052i) q^{50} +(1.25537 + 0.806778i) q^{52} +(-2.21500 + 4.85017i) q^{53} +(1.92756 + 1.51585i) q^{55} +(-9.53157 + 1.83706i) q^{56} +(-6.27291 + 4.03136i) q^{58} +(-1.04245 - 7.25040i) q^{59} +(12.1612 + 2.34388i) q^{61} +(-6.90912 - 7.97354i) q^{62} +(-6.56240 + 1.92689i) q^{64} +(16.3463 + 8.42713i) q^{65} +(7.68628 + 2.81445i) q^{67} -0.581815 q^{68} +(15.4458 - 4.53529i) q^{70} +(-1.62144 - 2.27699i) q^{71} +(-11.6242 - 2.24039i) q^{73} +(0.146985 + 3.08559i) q^{74} +(-1.05859 + 0.680313i) q^{76} +(-0.728064 - 3.00112i) q^{77} +(-4.51271 - 3.54884i) q^{79} +(11.9907 - 4.80035i) q^{80} +(-7.00950 - 4.50473i) q^{82} +(3.47174 - 10.0309i) q^{83} +(-7.13786 + 0.681583i) q^{85} +(0.221109 - 4.64165i) q^{86} +(-0.723375 - 2.09005i) q^{88} +(-4.93543 - 1.44917i) q^{89} +(-9.62117 - 21.0674i) q^{91} +(-0.131230 + 0.912725i) q^{92} +(1.06459 - 1.22860i) q^{94} +(-12.1901 + 9.58637i) q^{95} +(4.97137 + 8.61067i) q^{97} +(-9.10051 - 3.64329i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 24 q^{2} - 18 q^{4} + 16 q^{5} - 24 q^{7} - 23 q^{8}+O(q^{10}) \) 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

L-functions

Modular forms

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