LMFDB - Embedded newform 575.2.k.g.101.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [575,2,Mod(26,575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(575, base_ring=CyclotomicField(22))

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("575.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 575 = 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	575.k (of order $11$, degree $10$, 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:	$4.59139811622$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$10$ over $\Q(\zeta_{11})$
Twist minimal:	no (minimal twist has level 115)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			101.1
Character	$\chi$	$=$	575.101
Dual form			575.2.k.g.501.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.53313 + 0.743795i) q^{2} +(-1.16633 - 1.34601i) q^{3} +(4.18102 - 2.68698i) q^{4} +(3.95561 + 2.54212i) q^{6} +(0.855264 - 1.87277i) q^{7} +(-5.13475 + 5.92582i) q^{8} +(-0.0244873 + 0.170313i) q^{9} +O(q^{10})$	\(q+(-2.53313 + 0.743795i) q^{2} +(-1.16633 - 1.34601i) q^{3} +(4.18102 - 2.68698i) q^{4} +(3.95561 + 2.54212i) q^{6} +(0.855264 - 1.87277i) q^{7} +(-5.13475 + 5.92582i) q^{8} +(-0.0244873 + 0.170313i) q^{9} +(-5.55748 - 1.63182i) q^{11} +(-8.49314 - 2.49381i) q^{12} +(-1.31185 - 2.87256i) q^{13} +(-0.773542 + 5.38010i) q^{14} +(4.47020 - 9.78837i) q^{16} +(1.71958 + 1.10511i) q^{17} +(-0.0646484 - 0.449639i) q^{18} +(1.77165 - 1.13857i) q^{19} +(-3.51828 + 1.03306i) q^{21} +15.2916 q^{22} +(4.63949 - 1.21456i) q^{23} +13.9650 q^{24} +(5.45969 + 6.30081i) q^{26} +(-4.23709 + 2.72301i) q^{27} +(-1.45621 - 10.1281i) q^{28} +(-1.74171 - 1.11933i) q^{29} +(-1.04153 + 1.20200i) q^{31} +(-1.81129 + 12.5978i) q^{32} +(4.28538 + 9.38367i) q^{33} +(-5.17791 - 1.52037i) q^{34} +(0.355246 + 0.777880i) q^{36} +(0.0892232 - 0.620561i) q^{37} +(-3.64095 + 4.20189i) q^{38} +(-2.33645 + 5.11610i) q^{39} +(0.289709 + 2.01497i) q^{41} +(8.14389 - 5.23376i) q^{42} +(-2.72250 - 3.14193i) q^{43} +(-27.6206 + 8.11014i) q^{44} +(-10.8491 + 6.52746i) q^{46} +0.403164 q^{47} +(-18.3890 + 5.39949i) q^{48} +(1.80825 + 2.08683i) q^{49} +(-0.518105 - 3.60350i) q^{51} +(-13.2034 - 8.48529i) q^{52} +(-3.42609 + 7.50209i) q^{53} +(8.70774 - 10.0493i) q^{54} +(6.70611 + 14.6843i) q^{56} +(-3.59885 - 1.05672i) q^{57} +(5.24454 + 1.53994i) q^{58} +(-3.73431 - 8.17700i) q^{59} +(0.892000 - 1.02942i) q^{61} +(1.74431 - 3.81950i) q^{62} +(0.298014 + 0.191522i) q^{63} +(-1.71909 - 11.9565i) q^{64} +(-17.8350 - 20.5826i) q^{66} +(-6.45923 + 1.89660i) q^{67} +10.1590 q^{68} +(-7.04596 - 4.82824i) q^{69} +(-13.3319 + 3.91459i) q^{71} +(-0.883509 - 1.01962i) q^{72} +(-8.68396 + 5.58084i) q^{73} +(0.235556 + 1.63833i) q^{74} +(4.34798 - 9.52075i) q^{76} +(-7.80913 + 9.01222i) q^{77} +(2.11320 - 14.6976i) q^{78} +(3.54206 + 7.75603i) q^{79} +(9.10231 + 2.67268i) q^{81} +(-2.23259 - 4.88870i) q^{82} +(1.17187 - 8.15053i) q^{83} +(-11.9342 + 13.7728i) q^{84} +(9.23341 + 5.93395i) q^{86} +(0.524772 + 3.64987i) q^{87} +(38.2062 - 24.5536i) q^{88} +(-2.09382 - 2.41639i) q^{89} -6.50160 q^{91} +(16.1343 - 17.5443i) q^{92} +2.83267 q^{93} +(-1.02127 + 0.299871i) q^{94} +(19.0693 - 12.2551i) q^{96} +(1.42525 + 9.91281i) q^{97} +(-6.13270 - 3.94125i) q^{98} +(0.414009 - 0.906553i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 14 q^{4} - 18 q^{6} + 12 q^{9}+O(q^{10}) $ 100 * q + 14 * q^4 - 18 * q^6 + 12 * q^9	$ 100 q + 14 q^{4} - 18 q^{6} + 12 q^{9} - 26 q^{11} + 26 q^{14} - 18 q^{16} + 14 q^{19} - 22 q^{21} + 68 q^{24} - 42 q^{26} + 24 q^{29} - 12 q^{31} - 8 q^{34} - 10 q^{36} - 14 q^{39} + 8 q^{41} - 166 q^{44} - 18 q^{46} - 32 q^{49} - 22 q^{51} - 116 q^{54} - 116 q^{56} - 50 q^{59} - 38 q^{61} - 10 q^{64} - 28 q^{66} - 80 q^{69} - 110 q^{71} - 22 q^{74} + 4 q^{76} - 42 q^{79} + 204 q^{81} - 56 q^{84} + 132 q^{86} + 66 q^{89} + 76 q^{91} + 70 q^{94} + 236 q^{96} + 60 q^{99}+O(q^{100}) $ 100 * q + 14 * q^4 - 18 * q^6 + 12 * q^9 - 26 * q^11 + 26 * q^14 - 18 * q^16 + 14 * q^19 - 22 * q^21 + 68 * q^24 - 42 * q^26 + 24 * q^29 - 12 * q^31 - 8 * q^34 - 10 * q^36 - 14 * q^39 + 8 * q^41 - 166 * q^44 - 18 * q^46 - 32 * q^49 - 22 * q^51 - 116 * q^54 - 116 * q^56 - 50 * q^59 - 38 * q^61 - 10 * q^64 - 28 * q^66 - 80 * q^69 - 110 * q^71 - 22 * q^74 + 4 * q^76 - 42 * q^79 + 204 * q^81 - 56 * q^84 + 132 * q^86 + 66 * q^89 + 76 * q^91 + 70 * q^94 + 236 * q^96 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/575\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$

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 $

$2$	−2.53313	+	0.743795i	−1.79119	+	0.525942i	−0.996689	−	0.0813139i	$-0.974088\pi$
$2$	−2.53313	+	0.743795i	−1.79119	+	0.525942i	−0.794506	+	0.607256i	$0.792270\pi$
$3$	−1.16633	−	1.34601i	−0.673379	−	0.777120i	0.311522	−	0.950239i	$-0.399161\pi$
$3$	−1.16633	−	1.34601i	−0.673379	−	0.777120i	−0.984901	+	0.173118i	$0.944616\pi$
$4$	4.18102	−	2.68698i	2.09051	−	1.34349i
$5$		0			0
$5$		0			0
$6$	3.95561	+	2.54212i	1.61487	+	1.03782i
$7$	0.855264	−	1.87277i	0.323259	−	0.707839i	−0.676327	−	0.736601i	$-0.736429\pi$
$7$	0.855264	−	1.87277i	0.323259	−	0.707839i	0.999586	+	0.0287625i	$0.00915665\pi$
$8$	−5.13475	+	5.92582i	−1.81541	+	2.09509i
$9$	−0.0244873	+	0.170313i	−0.00816245	+	0.0567711i
$10$		0			0
$11$	−5.55748	−	1.63182i	−1.67564	−	0.492013i	−0.700511	−	0.713641i	$-0.747045\pi$
$11$	−5.55748	−	1.63182i	−1.67564	−	0.492013i	−0.975131	+	0.221628i	$0.928863\pi$
$12$	−8.49314	−	2.49381i	−2.45176	−	0.719901i
$13$	−1.31185	−	2.87256i	−0.363842	−	0.796703i	−0.999690	−	0.0248891i	$-0.992077\pi$
$13$	−1.31185	−	2.87256i	−0.363842	−	0.796703i	0.635848	−	0.771814i	$-0.280651\pi$
$14$	−0.773542	+	5.38010i	−0.206738	+	1.43789i
$15$		0			0
$16$	4.47020	−	9.78837i	1.11755	−	2.44709i
$17$	1.71958	+	1.10511i	0.417060	+	0.268029i	0.732298	−	0.680984i	$-0.238448\pi$
$17$	1.71958	+	1.10511i	0.417060	+	0.268029i	−0.315238	+	0.949013i	$0.602084\pi$
$18$	−0.0646484	−	0.449639i	−0.0152378	−	0.105981i
$19$	1.77165	−	1.13857i	0.406444	−	0.261206i	−0.321407	−	0.946941i	$-0.604156\pi$
$19$	1.77165	−	1.13857i	0.406444	−	0.261206i	0.727851	+	0.685736i	$0.240519\pi$
$20$		0			0
$21$	−3.51828	+	1.03306i	−0.767752	+	0.225432i
$22$	15.2916			3.26017
$23$	4.63949	−	1.21456i	0.967400	−	0.253253i
$23$	4.63949	−	1.21456i	0.967400	−	0.253253i
$24$	13.9650			2.85060
$25$		0			0
$26$	5.45969	+	6.30081i	1.07073	+	1.23569i
$27$	−4.23709	+	2.72301i	−0.815428	+	0.524044i
$28$	−1.45621	−	10.1281i	−0.275197	−	1.91404i
$29$	−1.74171	−	1.11933i	−0.323428	−	0.207855i	0.368844	−	0.929491i	$-0.379754\pi$
$29$	−1.74171	−	1.11933i	−0.323428	−	0.207855i	−0.692272	+	0.721637i	$0.743390\pi$
$30$		0			0
$31$	−1.04153	+	1.20200i	−0.187065	+	0.215885i	−0.841534	−	0.540204i	$-0.818347\pi$
$31$	−1.04153	+	1.20200i	−0.187065	+	0.215885i	0.654469	+	0.756089i	$0.272892\pi$
$32$	−1.81129	+	12.5978i	−0.320193	+	2.22699i
$33$	4.28538	+	9.38367i	0.745989	+	1.63349i
$34$	−5.17791	−	1.52037i	−0.888004	−	0.260742i
$35$		0			0
$36$	0.355246	+	0.777880i	0.0592076	+	0.129647i
$37$	0.0892232	−	0.620561i	0.0146682	−	0.102020i	−0.981172	−	0.193136i	$-0.938134\pi$
$37$	0.0892232	−	0.620561i	0.0146682	−	0.102020i	0.995840	+	0.0911159i	$0.0290434\pi$
$38$	−3.64095	+	4.20189i	−0.590641	+	0.681636i
$39$	−2.33645	+	5.11610i	−0.374131	+	0.819232i
$40$		0			0
$41$	0.289709	+	2.01497i	0.0452449	+	0.314685i	0.999858	+	0.0168374i	$0.00535976\pi$
$41$	0.289709	+	2.01497i	0.0452449	+	0.314685i	−0.954613	+	0.297848i	$0.903731\pi$
$42$	8.14389	−	5.23376i	1.25663	−	0.807586i
$43$	−2.72250	−	3.14193i	−0.415178	−	0.479141i	0.509184	−	0.860658i	$-0.329947\pi$
$43$	−2.72250	−	3.14193i	−0.415178	−	0.479141i	−0.924362	+	0.381517i	$0.875402\pi$
$44$	−27.6206	+	8.11014i	−4.16396	+	1.22265i
$45$		0			0
$46$	−10.8491	+	6.52746i	−1.59961	+	0.962421i
$47$	0.403164			0.0588075			0.0294037	−	0.999568i	$-0.490639\pi$
$47$	0.403164			0.0588075			0.0294037	+	0.999568i	$0.490639\pi$
$48$	−18.3890	+	5.39949i	−2.65422	+	0.779349i
$49$	1.80825	+	2.08683i	0.258321	+	0.298119i
$50$		0			0
$51$	−0.518105	−	3.60350i	−0.0725492	−	0.504591i
$52$	−13.2034	−	8.48529i	−1.83098	−	1.17670i
$53$	−3.42609	+	7.50209i	−0.470610	+	1.03049i	0.514330	+	0.857593i	$0.328041\pi$
$53$	−3.42609	+	7.50209i	−0.470610	+	1.03049i	−0.984940	+	0.172899i	$0.944687\pi$
$54$	8.70774	−	10.0493i	1.18497	−	1.36753i
$55$		0			0
$56$	6.70611	+	14.6843i	0.896141	+	1.96228i
$57$	−3.59885	−	1.05672i	−0.476679	−	0.139965i
$58$	5.24454	+	1.53994i	0.688642	+	0.202203i
$59$	−3.73431	−	8.17700i	−0.486166	−	1.06455i	−0.980722	−	0.195409i	$-0.937397\pi$
$59$	−3.73431	−	8.17700i	−0.486166	−	1.06455i	0.494556	−	0.869146i	$-0.335331\pi$
$60$		0			0
$61$	0.892000	−	1.02942i	0.114209	−	0.131804i	−0.695766	−	0.718268i	$-0.744935\pi$
$61$	0.892000	−	1.02942i	0.114209	−	0.131804i	0.809975	+	0.586464i	$0.199481\pi$
$62$	1.74431	−	3.81950i	0.221527	−	0.485077i
$63$	0.298014	+	0.191522i	0.0375462	+	0.0241295i
$64$	−1.71909	−	11.9565i	−0.214886	−	1.49457i
$65$		0			0
$66$	−17.8350	−	20.5826i	−2.19533	−	2.53355i
$67$	−6.45923	+	1.89660i	−0.789121	+	0.231707i	−0.651370	−	0.758760i	$-0.725805\pi$
$67$	−6.45923	+	1.89660i	−0.789121	+	0.231707i	−0.137751	+	0.990467i	$0.543987\pi$
$68$	10.1590			1.23196
$69$	−7.04596	−	4.82824i	−0.848234	−	0.581251i
$70$		0			0
$71$	−13.3319	+	3.91459i	−1.58220	+	0.464577i	−0.950524	−	0.310653i	$-0.899452\pi$
$71$	−13.3319	+	3.91459i	−1.58220	+	0.464577i	−0.631680	+	0.775229i	$0.717634\pi$
$72$	−0.883509	−	1.01962i	−0.104123	−	0.120164i
$73$	−8.68396	+	5.58084i	−1.01638	+	0.653188i	−0.939037	−	0.343817i	$-0.888280\pi$
$73$	−8.68396	+	5.58084i	−1.01638	+	0.653188i	−0.0773434	+	0.997005i	$0.524644\pi$
$74$	0.235556	+	1.63833i	0.0273828	+	0.190452i
$75$		0			0
$76$	4.34798	−	9.52075i	0.498748	−	1.09211i
$77$	−7.80913	+	9.01222i	−0.889933	+	1.02704i
$78$	2.11320	−	14.6976i	0.239272	−	1.66418i
$79$	3.54206	+	7.75603i	0.398513	+	0.872621i	0.997419	+	0.0718020i	$0.0228750\pi$
$79$	3.54206	+	7.75603i	0.398513	+	0.872621i	−0.598906	+	0.800819i	$0.704398\pi$
$80$		0			0
$81$	9.10231	+	2.67268i	1.01137	+	0.296965i
$82$	−2.23259	−	4.88870i	−0.246549	−	0.539867i
$83$	1.17187	−	8.15053i	0.128629	−	0.894637i	−0.818665	−	0.574272i	$-0.805285\pi$
$83$	1.17187	−	8.15053i	0.128629	−	0.894637i	0.947294	−	0.320365i	$-0.103806\pi$
$84$	−11.9342	+	13.7728i	−1.30213	+	1.50273i
$85$		0			0
$86$	9.23341	+	5.93395i	0.995664	+	0.639875i
$87$	0.524772	+	3.64987i	0.0562615	+	0.391307i
$88$	38.2062	−	24.5536i	4.07279	−	2.61742i
$89$	−2.09382	−	2.41639i	−0.221944	−	0.256137i	0.633847	−	0.773458i	$-0.281475\pi$
$89$	−2.09382	−	2.41639i	−0.221944	−	0.256137i	−0.855791	+	0.517321i	$0.826929\pi$
$90$		0			0
$91$	−6.50160			−0.681553
$92$	16.1343	−	17.5443i	1.68212	−	1.82912i
$93$	2.83267			0.293734
$94$	−1.02127	+	0.299871i	−0.105336	+	0.0309293i
$95$		0			0
$96$	19.0693	−	12.2551i	1.94625	−	1.25078i
$97$	1.42525	+	9.91281i	0.144712	+	1.00649i	0.924699	+	0.380698i	$0.124316\pi$
$97$	1.42525	+	9.91281i	0.144712	+	1.00649i	−0.779987	+	0.625795i	$0.784775\pi$
$98$	−6.13270	−	3.94125i	−0.619497	−	0.398126i
$99$	0.414009	−	0.906553i	0.0416095	−	0.0911120i
$100$		0			0
$101$	−2.66635	+	18.5449i	−0.265312	+	1.84529i	0.225780	+	0.974178i	$0.427507\pi$
$101$	−2.66635	+	18.5449i	−0.265312	+	1.84529i	−0.491092	+	0.871108i	$0.663402\pi$
$102$	3.99269	+	8.74278i	0.395335	+	0.865664i
$103$	−12.5496	−	3.68489i	−1.23655	−	0.363083i	−0.402830	−	0.915275i	$-0.631973\pi$
$103$	−12.5496	−	3.68489i	−1.23655	−	0.363083i	−0.833717	+	0.552192i	$0.813792\pi$
$104$	23.7583	+	6.97606i	2.32969	+	0.684059i
$105$		0			0
$106$	3.09872	−	21.5521i	0.300975	−	2.09332i
$107$	1.47495	−	1.70218i	0.142588	−	0.164556i	−0.679963	−	0.733246i	$-0.738004\pi$
$107$	1.47495	−	1.70218i	0.142588	−	0.164556i	0.822552	+	0.568690i	$0.192550\pi$
$108$	−10.3987	+	22.7699i	−1.00061	+	2.19104i
$109$	−5.07750	−	3.26311i	−0.486336	−	0.312549i	0.274394	−	0.961617i	$-0.411523\pi$
$109$	−5.07750	−	3.26311i	−0.486336	−	0.312549i	−0.760730	+	0.649068i	$0.775159\pi$
$110$		0			0
$111$	−0.939346	+	0.603681i	−0.0891588	+	0.0572989i
$112$	−14.5081	−	16.7433i	−1.37089	−	1.58209i
$113$	5.10615	−	1.49930i	0.480346	−	0.141042i	−0.0325904	−	0.999469i	$-0.510376\pi$
$113$	5.10615	−	1.49930i	0.480346	−	0.141042i	0.512937	+	0.858426i	$0.328557\pi$
$114$	9.90233			0.927438
$115$		0			0
$116$	−10.2898			−0.955379
$117$	0.521358	−	0.153084i	0.0481996	−	0.0141527i
$118$	15.5415	+	17.9358i	1.43071	+	1.65113i
$119$	3.54031	−	2.27522i	0.324540	−	0.208569i
$120$		0			0
$121$	18.9689	+	12.1906i	1.72445	+	1.10824i
$122$	−1.49387	+	3.27113i	−0.135249	+	0.296154i
$123$	2.37428	−	2.74006i	0.214081	−	0.247063i
$124$	−1.12494	+	7.82415i	−0.101023	+	0.702629i
$125$		0			0
$126$	−0.897361	−	0.263489i	−0.0799433	−	0.0234735i
$127$	8.32204	+	2.44357i	0.738461	+	0.216832i	0.629268	−	0.777189i	$-0.283355\pi$
$127$	8.32204	+	2.44357i	0.738461	+	0.216832i	0.109194	+	0.994020i	$0.465173\pi$
$128$	2.67364	+	5.85445i	0.236318	+	0.517465i
$129$	−1.05376	+	7.32904i	−0.0927781	+	0.645286i
$130$		0			0
$131$	6.45185	−	14.1276i	0.563701	−	1.23433i	−0.386383	−	0.922338i	$-0.626276\pi$
$131$	6.45185	−	14.1276i	0.563701	−	1.23433i	0.950084	−	0.311994i	$-0.100997\pi$
$132$	43.1310	+	27.7186i	3.75407	+	2.41259i
$133$	−0.617047	−	4.29166i	−0.0535048	−	0.372134i
$134$	14.9514	−	9.60869i	1.29160	−	0.830064i
$135$		0			0
$136$	−15.3783	+	4.51548i	−1.31868	+	0.387199i
$137$	−10.4860			−0.895881			−0.447940	−	0.894063i	$-0.647842\pi$
$137$	−10.4860			−0.895881			−0.447940	+	0.894063i	$0.647842\pi$
$138$	21.4396	+	6.98981i	1.82506	+	0.595012i
$139$	−13.5504			−1.14933			−0.574664	−	0.818389i	$-0.694867\pi$
$139$	−13.5504			−1.14933			−0.574664	+	0.818389i	$0.694867\pi$
$140$		0			0
$141$	−0.470220	−	0.542663i	−0.0395997	−	0.0457005i
$142$	30.8598	−	19.8324i	2.58969	−	1.66430i
$143$	2.60309	+	18.1049i	0.217681	+	1.51401i
$144$	1.55762	+	1.00102i	0.129802	+	0.0834187i
$145$		0			0
$146$	17.8466	−	20.5961i	1.47700	−	1.70454i
$147$	0.699891	−	4.86785i	0.0577260	−	0.401493i
$148$	−1.29439	−	2.83432i	−0.106398	−	0.232980i
$149$	17.5725	+	5.15974i	1.43959	+	0.422702i	0.906086	−	0.423094i	$-0.139056\pi$
$149$	17.5725	+	5.15974i	1.43959	+	0.422702i	0.533506	+	0.845796i	$0.320874\pi$
$150$		0			0
$151$	−7.26401	−	15.9060i	−0.591137	−	1.29441i	−0.934753	−	0.355299i	$-0.884379\pi$
$151$	−7.26401	−	15.9060i	−0.591137	−	1.29441i	0.343615	−	0.939110i	$-0.388348\pi$
$152$	−2.35002	+	16.3447i	−0.190612	+	1.32573i
$153$	−0.230323	+	0.265807i	−0.0186205	+	0.0214892i
$154$	13.0783	−	28.6375i	1.05388	−	2.30768i
$155$		0			0
$156$	3.97813	+	27.6685i	0.318505	+	2.21525i
$157$	0.953842	−	0.612997i	0.0761249	−	0.0489225i	−0.502025	−	0.864853i	$-0.667411\pi$
$157$	0.953842	−	0.612997i	0.0761249	−	0.0489225i	0.578150	+	0.815931i	$0.303775\pi$
$158$	−14.7414	−	17.0125i	−1.17276	−	1.35344i
$159$	14.0938	−	4.13833i	1.11771	−	0.328191i
$160$		0			0
$161$	1.69340	−	9.72744i	0.133459	−	0.766630i
$162$	−25.0453			−1.96774
$163$	7.43577	−	2.18334i	0.582415	−	0.171012i	0.0227638	−	0.999741i	$-0.492753\pi$
$163$	7.43577	−	2.18334i	0.582415	−	0.171012i	0.559651	+	0.828728i	$0.310935\pi$
$164$	6.62546	+	7.64619i	0.517361	+	0.597067i
$165$		0			0
$166$	3.09382	+	21.5180i	0.240127	+	1.67012i
$167$	8.01781	+	5.15274i	0.620437	+	0.398731i	0.812758	−	0.582601i	$-0.197965\pi$
$167$	8.01781	+	5.15274i	0.620437	+	0.398731i	−0.192321	+	0.981332i	$0.561601\pi$
$168$	11.9438	−	26.1532i	0.921482	−	2.01776i
$169$	1.98257	−	2.28801i	0.152506	−	0.176001i
$170$		0			0
$171$	0.150530	+	0.329615i	0.0115113	+	0.0252063i
$172$	−19.8251	−	5.82119i	−1.51165	−	0.443861i
$173$	−10.7715	−	3.16279i	−0.818941	−	0.240463i	−0.154681	−	0.987964i	$-0.549435\pi$
$173$	−10.7715	−	3.16279i	−0.818941	−	0.240463i	−0.664260	+	0.747502i	$0.731253\pi$
$174$	−4.04407	−	8.85528i	−0.306580	−	0.671317i
$175$		0			0
$176$	−40.8159	+	47.1041i	−3.07661	+	3.55060i
$177$	−6.65091	+	14.5635i	−0.499913	+	1.09466i
$178$	7.10121	+	4.56367i	0.532259	+	0.342062i
$179$	0.703686	+	4.89425i	0.0525960	+	0.365813i	0.999073	+	0.0430426i	$0.0137051\pi$
$179$	0.703686	+	4.89425i	0.0525960	+	0.365813i	−0.946477	+	0.322771i	$0.895386\pi$
$180$		0			0
$181$	−5.18515	−	5.98398i	−0.385409	−	0.444786i	0.529583	−	0.848258i	$-0.322349\pi$
$181$	−5.18515	−	5.98398i	−0.385409	−	0.444786i	−0.914992	+	0.403472i	$0.867803\pi$
$182$	16.4694	−	4.83586i	1.22079	−	0.358458i
$183$	−2.42598			−0.179333
$184$	−16.6254	+	33.7292i	−1.22564	+	2.48655i
$185$		0			0
$186$	−7.17552	+	2.10692i	−0.526135	+	0.154487i
$187$	−7.75321	−	8.94768i	−0.566971	−	0.654319i
$188$	1.68563	−	1.08329i	0.122938	−	0.0790072i
$189$	1.47574	+	10.2640i	0.107344	+	0.746594i
$190$		0			0
$191$	−5.60445	+	12.2720i	−0.405524	+	0.887973i	0.591157	+	0.806557i	$0.298672\pi$
$191$	−5.60445	+	12.2720i	−0.405524	+	0.887973i	−0.996680	+	0.0814161i	$0.974056\pi$
$192$	−14.0886	+	16.2591i	−1.01676	+	1.17340i
$193$	0.786454	−	5.46991i	0.0566102	−	0.393733i	−0.941741	−	0.336338i	$-0.890812\pi$
$193$	0.786454	−	5.46991i	0.0566102	−	0.393733i	0.998352	−	0.0573948i	$-0.0182794\pi$
$194$	−10.9834	−	24.0504i	−0.788565	−	1.72672i
$195$		0			0
$196$	13.1676	+	3.86635i	0.940542	+	0.276168i
$197$	−8.07729	−	17.6868i	−0.575483	−	1.26013i	−0.943826	−	0.330442i	$-0.892802\pi$
$197$	−8.07729	−	17.6868i	−0.575483	−	1.26013i	0.368344	−	0.929690i	$-0.379925\pi$
$198$	−0.374450	+	2.60436i	−0.0266110	+	0.185084i
$199$	−7.00184	+	8.08056i	−0.496347	+	0.572815i	−0.947551	−	0.319606i	$-0.896450\pi$
$199$	−7.00184	+	8.08056i	−0.496347	+	0.572815i	0.451203	+	0.892421i	$0.350995\pi$
$200$		0			0
$201$	10.0864	+	6.48215i	0.711441	+	0.457216i
$202$	−7.03937	−	48.9599i	−0.495288	−	3.44481i
$203$	−3.58587	+	2.30450i	−0.251679	+	0.161744i
$204$	−11.8487	−	13.6742i	−0.829577	−	0.957383i
$205$		0			0
$206$	34.5306			2.40586
$207$	0.0932464	+	0.819907i	0.00648107	+	0.0569875i
$208$	−33.9819			−2.35622
$209$	−11.7038	+	3.43656i	−0.809571	+	0.237712i
$210$		0			0
$211$	10.5813	−	6.80021i	0.728449	−	0.468146i	−0.123118	−	0.992392i	$-0.539289\pi$
$211$	10.5813	−	6.80021i	0.728449	−	0.468146i	0.851567	+	0.524246i	$0.175653\pi$
$212$	5.83341	+	40.5722i	0.400640	+	2.78651i
$213$	20.8184	+	13.3792i	1.42645	+	0.916726i
$214$	−2.47016	+	5.40890i	−0.168857	+	0.369745i
$215$		0			0
$216$	5.62032	−	39.0902i	0.382414	−	2.65975i
$217$	1.36027	+	2.97857i	0.0923411	+	0.202199i
$218$	15.2891	+	4.48927i	1.03551	+	0.304052i
$219$	17.6402	+	5.17963i	1.19201	+	0.350007i
$220$		0			0
$221$	0.918649	−	6.38934i	0.0617950	−	0.429794i
$222$	1.93047	−	2.22788i	0.129565	−	0.149526i
$223$	−2.08200	+	4.55894i	−0.139421	+	0.305289i	−0.966443	−	0.256880i	$-0.917306\pi$
$223$	−2.08200	+	4.55894i	−0.139421	+	0.305289i	0.827022	+	0.562169i	$0.190033\pi$
$224$	22.0436	+	14.1665i	1.47285	+	0.946542i
$225$		0			0
$226$	−11.8194	+	7.59586i	−0.786214	+	0.505269i
$227$	−9.15555	−	10.5661i	−0.607675	−	0.701294i	0.365643	−	0.930755i	$-0.380849\pi$
$227$	−9.15555	−	10.5661i	−0.607675	−	0.701294i	−0.973318	+	0.229461i	$0.926304\pi$
$228$	−17.8862	+	5.25187i	−1.18454	+	0.347813i
$229$	11.7736			0.778020			0.389010	−	0.921234i	$-0.372817\pi$
$229$	11.7736			0.778020			0.389010	+	0.921234i	$0.372817\pi$
$230$		0			0
$231$	21.2385			1.39739
$232$	15.5762	−	4.57359i	1.02263	−	0.300271i
$233$	−3.25100	−	3.75185i	−0.212980	−	0.245792i	0.639200	−	0.769040i	$-0.279265\pi$
$233$	−3.25100	−	3.75185i	−0.212980	−	0.245792i	−0.852180	+	0.523248i	$0.824720\pi$
$234$	−1.20680	+	0.775566i	−0.0788913	+	0.0507004i
$235$		0			0
$236$	−37.5846	−	24.1542i	−2.44655	−	1.57230i
$237$	6.30851	−	13.8137i	0.409782	−	0.897297i
$238$	−7.27578	+	8.39669i	−0.471619	+	0.544277i
$239$	2.02431	−	14.0794i	0.130942	−	0.910719i	−0.813389	−	0.581721i	$-0.802380\pi$
$239$	2.02431	−	14.0794i	0.130942	−	0.910719i	0.944330	−	0.328999i	$-0.106711\pi$
$240$		0			0
$241$	3.60661	+	1.05900i	0.232322	+	0.0682160i	0.395822	−	0.918327i	$-0.370460\pi$
$241$	3.60661	+	1.05900i	0.232322	+	0.0682160i	−0.163499	+	0.986543i	$0.552278\pi$
$242$	−57.1181	−	16.7714i	−3.67169	−	1.07811i
$243$	−0.741924	−	1.62459i	−0.0475945	−	0.104217i
$244$	0.963432	−	6.70082i	0.0616774	−	0.428976i
$245$		0			0
$246$	−3.97632	+	8.70692i	−0.253521	+	0.555133i
$247$	−5.59474	−	3.59552i	−0.355985	−	0.228778i
$248$	−1.77478	−	12.3439i	−0.112699	−	0.783838i
$249$	−12.3375	+	7.92883i	−0.781857	+	0.502469i
$250$		0			0
$251$	−16.9265	+	4.97006i	−1.06839	+	0.313708i	−0.768225	−	0.640180i	$-0.778860\pi$
$251$	−16.9265	+	4.97006i	−1.06839	+	0.313708i	−0.300165	+	0.953887i	$0.597042\pi$
$252$	1.76062			0.110908
$253$	−27.7658	−	0.820947i	−1.74562	−	0.0516125i
$254$	−22.8983			−1.43677
$255$		0			0
$256$	4.69358	+	5.41668i	0.293349	+	0.338542i
$257$	5.18281	−	3.33079i	0.323295	−	0.207769i	−0.368919	−	0.929462i	$-0.620272\pi$
$257$	5.18281	−	3.33079i	0.323295	−	0.207769i	0.692214	+	0.721693i	$0.256636\pi$
$258$	−2.78200	−	19.3492i	−0.173199	−	1.20463i
$259$	−1.08586	−	0.697838i	−0.0674718	−	0.0433615i
$260$		0			0
$261$	0.233287	−	0.269227i	0.0144401	−	0.0166647i
$262$	−5.83537	+	40.5859i	−0.360510	+	2.50740i
$263$	−8.53638	−	18.6921i	−0.526376	−	1.15260i	−0.966969	−	0.254895i	$-0.917959\pi$
$263$	−8.53638	−	18.6921i	−0.526376	−	1.15260i	0.440593	−	0.897707i	$-0.354768\pi$
$264$	−77.6103	−	22.7884i	−4.77658	−	1.40253i
$265$		0			0
$266$	4.75517	+	10.4124i	0.291558	+	0.638424i
$267$	−0.810422	+	5.63661i	−0.0495970	+	0.344955i
$268$	−21.9100	+	25.2855i	−1.33837	+	1.54456i
$269$	6.21519	−	13.6094i	0.378947	−	0.829777i	−0.620031	−	0.784577i	$-0.712880\pi$
$269$	6.21519	−	13.6094i	0.378947	−	0.829777i	0.998978	−	0.0452002i	$-0.0143926\pi$
$270$		0			0
$271$	−2.11531	−	14.7123i	−0.128496	−	0.893710i	−0.947462	−	0.319868i	$-0.896361\pi$
$271$	−2.11531	−	14.7123i	−0.128496	−	0.893710i	0.818966	−	0.573842i	$-0.194548\pi$
$272$	18.5041	−	11.8919i	1.12198	−	0.721050i
$273$	7.58299	+	8.75124i	0.458943	+	0.529649i
$274$	26.5625	−	7.79944i	1.60470	−	0.471181i
$275$		0			0
$276$	−42.4327	−	1.25460i	−2.55415	−	0.0755181i
$277$	9.98105			0.599703			0.299852	−	0.953986i	$-0.403063\pi$
$277$	9.98105			0.599703			0.299852	+	0.953986i	$0.403063\pi$
$278$	34.3249	−	10.0787i	2.05867	−	0.604481i
$279$	−0.179211	−	0.206821i	−0.0107291	−	0.0123820i
$280$		0			0
$281$	−3.63986	−	25.3158i	−0.217136	−	1.51021i	−0.748538	−	0.663092i	$-0.769244\pi$
$281$	−3.63986	−	25.3158i	−0.217136	−	1.51021i	0.531402	−	0.847120i	$-0.321665\pi$
$282$	1.59476	+	1.02489i	0.0949666	+	0.0610313i
$283$	2.90734	−	6.36619i	0.172824	−	0.378431i	−0.803323	−	0.595544i	$-0.796937\pi$
$283$	2.90734	−	6.36619i	0.172824	−	0.378431i	0.976147	+	0.217113i	$0.0696639\pi$
$284$	−45.2224	+	52.1895i	−2.68346	+	3.09688i
$285$		0			0
$286$	−20.0603	−	43.9259i	−1.18619	−	2.59739i
$287$	4.02134	+	1.18077i	0.237372	+	0.0696988i
$288$	−2.10121	−	0.616972i	−0.123815	−	0.0363554i
$289$	−5.32635	−	11.6631i	−0.313315	−	0.686064i
$290$		0			0
$291$	11.6805	−	13.4800i	0.684721	−	0.790210i
$292$	−21.3122	+	46.6672i	−1.24720	+	2.73099i
$293$	8.74634	+	5.62093i	0.510966	+	0.328378i	0.770589	−	0.637332i	$-0.219962\pi$
$293$	8.74634	+	5.62093i	0.510966	+	0.328378i	−0.259623	+	0.965710i	$0.583598\pi$
$294$	1.84776	+	12.8515i	0.107764	+	0.749513i
$295$		0			0
$296$	3.21919	+	3.71515i	0.187112	+	0.215939i
$297$	27.9910	−	8.21890i	1.62420	−	0.476909i
$298$	−48.3512			−2.80091
$299$	−9.57520	−	11.7339i	−0.553748	−	0.678587i
$300$		0			0
$301$	−8.21257	+	2.41143i	−0.473364	+	0.138992i
$302$	30.2315	+	34.8890i	1.73963	+	2.00764i
$303$	28.0715	−	18.0405i	1.61267	−	1.03640i
$304$	−3.22511	−	22.4312i	−0.184973	−	1.28652i
$305$		0			0
$306$	0.385733	−	0.844637i	0.0220509	−	0.0482847i
$307$	−1.71250	+	1.97633i	−0.0977376	+	0.112795i	−0.802511	−	0.596637i	$-0.796503\pi$
$307$	−1.71250	+	1.97633i	−0.0977376	+	0.112795i	0.704773	+	0.709432i	$0.251049\pi$
$308$	−8.43450	+	58.6632i	−0.480600	+	3.34265i
$309$	9.67700	+	21.1897i	0.550505	+	1.20544i
$310$		0			0
$311$	25.6899	+	7.54323i	1.45674	+	0.427737i	0.911764	−	0.410715i	$-0.134721\pi$
$311$	25.6899	+	7.54323i	1.45674	+	0.427737i	0.544975	+	0.838452i	$0.316539\pi$
$312$	−18.3200	−	40.1153i	−1.03717	−	2.27108i
$313$	−2.36838	+	16.4725i	−0.133869	+	0.931079i	0.806575	+	0.591131i	$0.201318\pi$
$313$	−2.36838	+	16.4725i	−0.133869	+	0.931079i	−0.940444	+	0.339948i	$0.889591\pi$
$314$	−1.96026	+	2.26227i	−0.110624	+	0.127667i
$315$		0			0
$316$	35.6497	+	22.9107i	2.00545	+	1.28883i
$317$	3.73091	+	25.9491i	0.209549	+	1.45744i	0.774633	+	0.632411i	$0.217935\pi$
$317$	3.73091	+	25.9491i	0.209549	+	1.45744i	−0.565084	+	0.825033i	$0.691156\pi$
$318$	−32.6235	+	20.9659i	−1.82944	+	1.17571i
$319$	7.85298	+	9.06282i	0.439682	+	0.507421i
$320$		0			0
$321$	−4.01142			−0.223896
$322$	2.94560	+	25.9004i	0.164152	+	1.44337i
$323$	4.30474			0.239522
$324$	45.2384	−	13.2832i	2.51324	−	0.737955i
$325$		0			0
$326$	−17.2118	+	11.0614i	−0.953275	+	0.612633i
$327$	1.52983	+	10.6402i	0.0846000	+	0.588406i
$328$	−13.4279	−	8.62961i	−0.741433	−	0.476490i
$329$	0.344811	−	0.755031i	0.0190101	−	0.0416262i
$330$		0			0
$331$	−1.00431	+	6.98511i	−0.0552017	+	0.383936i	0.943427	+	0.331581i	$0.107582\pi$
$331$	−1.00431	+	6.98511i	−0.0552017	+	0.383936i	−0.998629	+	0.0523554i	$0.983327\pi$
$332$	−17.0007	−	37.2263i	−0.933034	−	2.04306i
$333$	0.103505	+	0.0303918i	0.00567204	+	0.00166546i
$334$	−24.1428	−	7.08895i	−1.32103	−	0.387890i
$335$		0			0
$336$	−5.61544	+	39.0562i	−0.306347	+	2.13069i
$337$	−10.7031	+	12.3520i	−0.583034	+	0.672857i	−0.968254	−	0.249967i	$-0.919580\pi$
$337$	−10.7031	+	12.3520i	−0.583034	+	0.672857i	0.385220	+	0.922825i	$0.374126\pi$
$338$	−3.32031	+	7.27046i	−0.180601	+	0.395461i
$339$	−7.97352	−	5.12427i	−0.433062	−	0.278312i
$340$		0			0
$341$	7.74975	−	4.98046i	0.419672	−	0.269707i
$342$	−0.626479	−	0.722996i	−0.0338761	−	0.0390951i
$343$	19.2826	−	5.66189i	1.04116	−	0.305713i
$344$	32.5979			1.75756
$345$		0			0
$346$	29.6381			1.59335
$347$	20.0659	−	5.89187i	1.07719	−	0.316292i	0.305437	−	0.952212i	$-0.401197\pi$
$347$	20.0659	−	5.89187i	1.07719	−	0.316292i	0.771755	+	0.635920i	$0.219379\pi$
$348$	12.0012	+	13.8501i	0.643332	+	0.742445i
$349$	20.8831	−	13.4207i	1.11785	−	0.718396i	0.154857	−	0.987937i	$-0.450508\pi$
$349$	20.8831	−	13.4207i	1.11785	−	0.718396i	0.962989	+	0.269541i	$0.0868720\pi$
$350$		0			0
$351$	13.3804	+	8.59908i	0.714194	+	0.458985i
$352$	30.6235	−	67.0562i	1.63224	−	3.57411i
$353$	−8.08999	+	9.33634i	−0.430587	+	0.496923i	−0.929033	−	0.369997i	$-0.879359\pi$
$353$	−8.08999	+	9.33634i	−0.430587	+	0.496923i	0.498446	+	0.866921i	$0.333904\pi$
$354$	6.01541	−	41.8381i	0.319715	−	2.22367i
$355$		0			0
$356$	−15.2471	−	4.47695i	−0.808094	−	0.237278i
$357$	−7.19163	−	2.11165i	−0.380621	−	0.111760i
$358$	−5.42284	−	11.8744i	−0.286606	−	0.627580i
$359$	1.64830	−	11.4642i	0.0869940	−	0.605057i	−0.898959	−	0.438033i	$-0.855675\pi$
$359$	1.64830	−	11.4642i	0.0869940	−	0.605057i	0.985953	−	0.167024i	$-0.0534157\pi$
$360$		0			0
$361$	−6.05049	+	13.2487i	−0.318447	+	0.697301i
$362$	17.5855	+	11.3015i	0.924275	+	0.593995i
$363$	−5.71527	−	39.7506i	−0.299974	−	2.08637i
$364$	−27.1833	+	17.4697i	−1.42479	+	0.915659i
$365$		0			0
$366$	6.14532	−	1.80443i	0.321221	−	0.0943190i
$367$	−8.34483			−0.435596			−0.217798	−	0.975994i	$-0.569887\pi$
$367$	−8.34483			−0.435596			−0.217798	+	0.975994i	$0.569887\pi$
$368$	8.85089	−	50.8423i	0.461385	−	2.65034i
$369$	−0.350270			−0.0182343
$370$		0			0
$371$	11.1195	+	12.8325i	0.577293	+	0.666232i
$372$	11.8434	−	7.61132i	0.614054	−	0.394629i
$373$	3.91020	+	27.1960i	0.202462	+	1.40816i	0.796947	+	0.604049i	$0.206447\pi$
$373$	3.91020	+	27.1960i	0.202462	+	1.40816i	−0.594485	+	0.804107i	$0.702644\pi$
$374$	26.2951	+	16.8989i	1.35969	+	0.873819i
$375$		0			0
$376$	−2.07015	+	2.38908i	−0.106760	+	0.123207i
$377$	−0.930470	+	6.47156i	−0.0479217	+	0.333302i
$378$	−11.3725	−	24.9023i	−0.584939	−	1.28084i
$379$	−9.48787	−	2.78589i	−0.487359	−	0.143102i	0.0288157	−	0.999585i	$-0.490826\pi$
$379$	−9.48787	−	2.78589i	−0.487359	−	0.143102i	−0.516175	+	0.856483i	$0.672645\pi$
$380$		0			0
$381$	−6.41713	−	14.0516i	−0.328760	−	0.719883i
$382$	5.06894	−	35.2552i	0.259349	−	1.80381i
$383$	7.36591	−	8.50071i	0.376380	−	0.434366i	−0.535681	−	0.844421i	$-0.679945\pi$
$383$	7.36591	−	8.50071i	0.376380	−	0.434366i	0.912061	+	0.410055i	$0.134490\pi$
$384$	4.76182	−	10.4269i	0.243001	−	0.532097i
$385$		0			0
$386$	2.07630	+	14.4410i	0.105681	+	0.735026i
$387$	0.601780	−	0.386740i	0.0305902	−	0.0196591i
$388$	32.5945	+	37.6161i	1.65473	+	1.90967i
$389$	−7.81767	+	2.29548i	−0.396372	+	0.116385i	−0.473843	−	0.880609i	$-0.657134\pi$
$389$	−7.81767	+	2.29548i	−0.396372	+	0.116385i	0.0774712	+	0.996995i	$0.475315\pi$
$390$		0			0
$391$	9.32021	+	3.03861i	0.471343	+	0.153669i
$392$	−21.6511			−1.09355
$393$	−26.5409	+	7.79310i	−1.33881	+	0.393110i
$394$	33.6162	+	38.7951i	1.69356	+	1.95447i
$395$		0			0
$396$	−0.704909	−	4.90275i	−0.0354230	−	0.246372i
$397$	−11.2972	−	7.26030i	−0.566992	−	0.364384i	0.225521	−	0.974238i	$-0.427592\pi$
$397$	−11.2972	−	7.26030i	−0.566992	−	0.364384i	−0.792514	+	0.609854i	$0.791228\pi$
$398$	11.7263	−	25.6770i	0.587787	−	1.28707i
$399$	−5.05694	+	5.83602i	−0.253164	+	0.292167i
$400$		0			0
$401$	−5.88901	−	12.8951i	−0.294083	−	0.643952i	0.703701	−	0.710497i	$-0.251530\pi$
$401$	−5.88901	−	12.8951i	−0.294083	−	0.643952i	−0.997783	+	0.0665450i	$0.978802\pi$
$402$	−30.3716	−	8.91791i	−1.51480	−	0.444785i
$403$	4.81914	+	1.41503i	0.240058	+	0.0704875i
$404$	38.6817	+	84.7010i	1.92448	+	4.21403i
$405$		0			0
$406$	7.36940	−	8.50474i	0.365737	−	0.422083i
$407$	−1.50850	+	3.30316i	−0.0747737	+	0.163731i
$408$	24.0140	+	15.4329i	1.18887	+	0.764041i
$409$	2.61692	+	18.2011i	0.129398	+	0.899985i	0.946319	+	0.323235i	$0.104770\pi$
$409$	2.61692	+	18.2011i	0.129398	+	0.899985i	−0.816921	+	0.576750i	$0.804321\pi$
$410$		0			0
$411$	12.2301	+	14.1143i	0.603267	+	0.696207i
$412$	−62.3713	+	18.3139i	−3.07281	+	0.902259i
$413$	−18.5074			−0.910690
$414$	−0.846048	−	2.00758i	−0.0415810	−	0.0986671i
$415$		0			0
$416$	38.5640	−	11.3234i	1.89075	−	0.555175i
$417$	15.8042	+	18.2390i	0.773933	+	0.893167i
$418$	27.0913	−	17.4105i	1.32508	−	0.851575i
$419$	−4.24524	−	29.5263i	−0.207394	−	1.44245i	−0.781619	−	0.623757i	$-0.785606\pi$
$419$	−4.24524	−	29.5263i	−0.207394	−	1.44245i	0.574225	−	0.818698i	$-0.305303\pi$
$420$		0			0
$421$	−14.0057	+	30.6682i	−0.682595	+	1.49468i	0.177274	+	0.984162i	$0.443272\pi$
$421$	−14.0057	+	30.6682i	−0.682595	+	1.49468i	−0.859869	+	0.510514i	$0.829455\pi$
$422$	−21.7460	+	25.0962i	−1.05858	+	1.22166i
$423$	−0.00987241	+	0.0686641i	−0.000480013	+	0.00333856i
$424$	−26.8639	−	58.8238i	−1.30463	−	2.85674i
$425$		0			0
$426$	−62.6871	−	18.4066i	−3.03720	−	0.891803i
$427$	−1.16497	−	2.55093i	−0.0563770	−	0.123448i
$428$	1.59306	−	11.0800i	0.0770036	−	0.535572i
$429$	21.3333	−	24.6200i	1.02998	−	1.18866i
$430$		0			0
$431$	−17.0992	−	10.9890i	−0.823639	−	0.529321i	0.0596115	−	0.998222i	$-0.481014\pi$
$431$	−17.0992	−	10.9890i	−0.823639	−	0.529321i	−0.883251	+	0.468901i	$0.844650\pi$
$432$	7.71321	+	53.6465i	0.371102	+	2.58107i
$433$	30.4798	−	19.5882i	1.46476	−	0.941346i	0.466376	−	0.884587i	$-0.345559\pi$
$433$	30.4798	−	19.5882i	1.46476	−	0.941346i	0.998388	−	0.0567597i	$-0.0180769\pi$
$434$	−5.66119	−	6.53336i	−0.271746	−	0.313611i
$435$		0			0
$436$	−29.9970			−1.43660
$437$	6.83668	−	7.43414i	0.327043	−	0.355623i
$438$	−48.5375			−2.31921
$439$	−2.29415	+	0.673622i	−0.109494	+	0.0321502i	−0.336020	−	0.941855i	$-0.609081\pi$
$439$	−2.29415	+	0.673622i	−0.109494	+	0.0321502i	0.226527	+	0.974005i	$0.427263\pi$
$440$		0			0
$441$	−0.399694	+	0.256868i	−0.0190330	+	0.0122318i
$442$	2.42530	+	16.8683i	0.115360	+	0.802345i
$443$	8.66351	+	5.56770i	0.411616	+	0.264529i	0.730020	−	0.683426i	$-0.239511\pi$
$443$	8.66351	+	5.56770i	0.411616	+	0.264529i	−0.318405	+	0.947955i	$0.603147\pi$
$444$	−2.30535	+	5.04800i	−0.109407	+	0.239568i
$445$		0			0
$446$	1.88306	−	13.0970i	0.0891656	−	0.620160i
$447$	−13.5501	−	29.6707i	−0.640900	−	1.40338i
$448$	−23.8621	−	7.00653i	−1.12738	−	0.331027i
$449$	−30.8344	−	9.05378i	−1.45516	−	0.427275i	−0.543918	−	0.839138i	$-0.683060\pi$
$449$	−30.8344	−	9.05378i	−1.45516	−	0.427275i	−0.911245	+	0.411864i	$0.864878\pi$
$450$		0			0
$451$	1.67802	−	11.6709i	0.0790150	−	0.549561i
$452$	17.3203	−	19.9887i	0.814680	−	0.940191i
$453$	−12.9374	+	28.3290i	−0.607853	+	1.33101i
$454$	31.0512	+	19.9554i	1.45730	+	0.936553i
$455$		0			0
$456$	24.7411	−	15.9001i	1.15861	−	0.744592i
$457$	−8.76749	−	10.1182i	−0.410126	−	0.473310i	0.512678	−	0.858581i	$-0.328654\pi$
$457$	−8.76749	−	10.1182i	−0.410126	−	0.473310i	−0.922804	+	0.385271i	$0.874108\pi$
$458$	−29.8240	+	8.75712i	−1.39359	+	0.409194i
$459$	−10.2953			−0.480541
$460$		0			0
$461$	−30.5197			−1.42144			−0.710721	−	0.703474i	$-0.751631\pi$
$461$	−30.5197			−1.42144			−0.710721	+	0.703474i	$0.751631\pi$
$462$	−53.8000	+	15.7971i	−2.50300	+	0.734948i
$463$	−13.7024	−	15.8135i	−0.636807	−	0.734914i	0.342000	−	0.939700i	$-0.388896\pi$
$463$	−13.7024	−	15.8135i	−0.636807	−	0.734914i	−0.978807	+	0.204786i	$0.934350\pi$
$464$	−18.7422	+	12.0449i	−0.870086	+	0.559170i
$465$		0			0
$466$	11.0258	+	7.08586i	0.510761	+	0.328246i
$467$	13.6210	−	29.8259i	0.630307	−	1.38018i	−0.277474	−	0.960733i	$-0.589497\pi$
$467$	13.6210	−	29.8259i	0.630307	−	1.38018i	0.907780	−	0.419446i	$-0.137776\pi$
$468$	1.76847	−	2.04093i	0.0817477	−	0.0943419i
$469$	−1.97246	+	13.7187i	−0.0910795	+	0.633472i
$470$		0			0
$471$	−1.93759	−	0.568929i	−0.0892796	−	0.0262148i
$472$	67.6302	+	19.8580i	3.11293	+	0.914039i
$473$	10.0032	+	21.9039i	0.459946	+	1.00714i
$474$	−5.70572	+	39.6842i	−0.262073	+	1.82275i
$475$		0			0
$476$	8.68864	−	19.0255i	0.398243	−	0.872031i
$477$	−1.19381	−	0.767215i	−0.0546608	−	0.0351284i
$478$	5.34433	+	37.1706i	0.244444	+	1.70014i
$479$	27.9627	−	17.9705i	1.27765	−	0.821093i	0.287051	−	0.957915i	$-0.407325\pi$
$479$	27.9627	−	17.9705i	1.27765	−	0.821093i	0.990596	+	0.136822i	$0.0436889\pi$
$480$		0			0
$481$	−1.89964	+	0.557786i	−0.0866163	+	0.0254328i
$482$	−9.92371			−0.452012
$483$	−15.0683	+	9.06603i	−0.685632	+	0.412519i
$484$	112.065			5.09388
$485$		0			0
$486$	3.08775	+	3.56345i	0.140063	+	0.161642i
$487$	17.8279	−	11.4573i	0.807860	−	0.519180i	−0.0703122	−	0.997525i	$-0.522400\pi$
$487$	17.8279	−	11.4573i	0.807860	−	0.519180i	0.878172	+	0.478345i	$0.158763\pi$
$488$	1.51998	+	10.5717i	0.0688060	+	0.478557i
$489$	−11.6113	−	7.46215i	−0.525083	−	0.337450i
$490$		0			0
$491$	−10.2856	+	11.8702i	−0.464182	+	0.535695i	−0.938784	−	0.344506i	$-0.888047\pi$
$491$	−10.2856	+	11.8702i	−0.464182	+	0.535695i	0.474602	+	0.880200i	$0.342592\pi$
$492$	2.56441	−	17.8359i	0.115613	−	0.804104i
$493$	−1.75804	−	3.84957i	−0.0791781	−	0.173376i
$494$	16.8465	+	4.94659i	0.757962	+	0.222558i
$495$		0			0
$496$	7.10970	+	15.5681i	0.319235	+	0.699027i
$497$	−4.07116	+	28.3155i	−0.182616	+	1.27012i
$498$	25.3551	−	29.2613i	1.13619	−	1.31123i
$499$	−17.0012	+	37.2275i	−0.761080	+	1.66653i	−0.0157140	+	0.999877i	$0.505002\pi$
$499$	−17.0012	+	37.2275i	−0.761080	+	1.66653i	−0.745366	+	0.666656i	$0.767725\pi$
$500$		0			0
$501$	−2.41574	−	16.8018i	−0.107927	−	0.750651i
$502$	39.1803	−	25.1797i	1.74870	−	1.12382i
$503$	−17.2403	−	19.8964i	−0.768707	−	0.887135i	0.227533	−	0.973770i	$-0.426934\pi$
$503$	−17.2403	−	19.8964i	−0.768707	−	0.887135i	−0.996240	+	0.0866353i	$0.972389\pi$
$504$	−2.66515	+	0.782559i	−0.118715	+	0.0348579i
$505$		0			0
$506$	70.9450	−	18.5725i	3.15389	−	0.825648i
$507$	−5.39201			−0.239468
$508$	41.3604	−	12.1445i	1.83507	−	0.538826i
$509$	−4.83472	−	5.57956i	−0.214295	−	0.247310i	0.638417	−	0.769690i	$-0.279589\pi$
$509$	−4.83472	−	5.57956i	−0.214295	−	0.247310i	−0.852712	+	0.522381i	$0.825044\pi$
$510$		0			0
$511$	3.02454	+	21.0361i	0.133798	+	0.930583i
$512$	−26.7471	−	17.1893i	−1.18206	−	0.759667i
$513$	−4.40629	+	9.64843i	−0.194542	+	0.425989i
$514$	−10.6513	+	12.2923i	−0.469809	+	0.542189i
$515$		0			0
$516$	15.2872	+	33.4743i	0.672981	+	1.47362i
$517$	−2.24057	−	0.657892i	−0.0985403	−	0.0289340i
$518$	3.26967	+	0.960060i	0.143661	+	0.0421826i
$519$	8.30590	+	18.1874i	0.364589	+	0.798338i
$520$		0			0
$521$	19.9029	−	22.9691i	0.871960	−	1.00630i	−0.127935	−	0.991783i	$-0.540835\pi$
$521$	19.9029	−	22.9691i	0.871960	−	1.00630i	0.999895	−	0.0145129i	$-0.00461977\pi$
$522$	−0.390696	+	0.855506i	−0.0171003	+	0.0374445i
$523$	−4.93004	−	3.16834i	−0.215576	−	0.138542i	0.428397	−	0.903591i	$-0.359079\pi$
$523$	−4.93004	−	3.16834i	−0.215576	−	0.138542i	−0.643972	+	0.765049i	$0.722715\pi$
$524$	−10.9852	−	76.4037i	−0.479890	−	3.33771i
$525$		0			0
$526$	35.5268	+	41.0001i	1.54904	+	1.78769i
$527$	−3.11934	+	0.915922i	−0.135881	+	0.0398982i
$528$	111.007			4.83097
$529$	20.0497	−	11.2698i	0.871726	−	0.489993i
$530$		0			0
$531$	1.48409	−	0.435769i	0.0644042	−	0.0189108i
$532$	−14.1115	−	16.2855i	−0.611810	−	0.706066i
$533$	5.40806	−	3.47555i	0.234249	−	0.150543i
$534$	−2.13957	−	14.8811i	−0.0925883	−	0.643966i
$535$		0			0
$536$	21.9276	−	48.0148i	0.947130	−	2.07392i
$537$	5.76699	−	6.65546i	0.248864	−	0.287204i
$538$	−5.62132	+	39.0971i	−0.242352	+	1.68560i
$539$	−6.64396	−	14.5483i	−0.286176	−	0.626638i
$540$		0			0
$541$	−4.01909	−	1.18011i	−0.172794	−	0.0507369i	0.194191	−	0.980964i	$-0.437792\pi$
$541$	−4.01909	−	1.18011i	−0.172794	−	0.0507369i	−0.366985	+	0.930227i	$0.619610\pi$
$542$	16.3013	+	35.6949i	0.700201	+	1.53323i
$543$	−2.00694	+	13.9586i	−0.0861259	+	0.599019i
$544$	−17.0366	+	19.6613i	−0.730438	+	0.842970i
$545$		0			0
$546$	−25.7178	−	16.5278i	−1.10062	−	0.707327i
$547$	−2.83470	−	19.7158i	−0.121203	−	0.842986i	−0.956196	−	0.292726i	$-0.905438\pi$
$547$	−2.83470	−	19.7158i	−0.121203	−	0.842986i	0.834993	−	0.550260i	$-0.185471\pi$
$548$	−43.8422	+	28.1757i	−1.87285	+	1.20361i
$549$	0.153482	+	0.177127i	0.00655043	+	0.00755960i
$550$		0			0
$551$	−4.36014			−0.185748
$552$	64.7905	−	16.9613i	2.75767	−	0.721922i
$553$	17.5546			0.746498
$554$	−25.2833	+	7.42385i	−1.07419	+	0.315409i
$555$		0			0
$556$	−56.6544	+	36.4096i	−2.40268	+	1.54411i
$557$	−6.41476	−	44.6156i	−0.271802	−	1.89042i	−0.429705	−	0.902969i	$-0.641383\pi$
$557$	−6.41476	−	44.6156i	−0.271802	−	1.89042i	0.157903	−	0.987455i	$-0.449527\pi$
$558$	0.607798	+	0.390608i	0.0257301	+	0.0165358i
$559$	−5.45386	+	11.9423i	−0.230674	+	0.505105i
$560$		0			0
$561$	−3.00092	+	20.8718i	−0.126699	+	0.881209i
$562$	28.0500	+	61.4209i	1.18322	+	2.59088i
$563$	18.0518	+	5.30049i	0.760794	+	0.223389i	0.639042	−	0.769172i	$-0.279331\pi$
$563$	18.0518	+	5.30049i	0.760794	+	0.223389i	0.121751	+	0.992561i	$0.461149\pi$
$564$	−3.42412	−	1.00541i	−0.144182	−	0.0423355i
$565$		0			0
$566$	−2.62954	+	18.2889i	−0.110528	+	0.768739i
$567$	12.7902	−	14.7607i	0.537137	−	0.619889i
$568$	45.2587	−	99.1028i	1.89901	−	4.15826i
$569$	−9.05830	−	5.82142i	−0.379744	−	0.244047i	0.336818	−	0.941570i	$-0.390649\pi$
$569$	−9.05830	−	5.82142i	−0.379744	−	0.244047i	−0.716562	+	0.697523i	$0.754285\pi$
$570$		0			0
$571$	−12.9103	+	8.29697i	−0.540281	+	0.347217i	−0.782149	−	0.623092i	$-0.785876\pi$
$571$	−12.9103	+	8.29697i	−0.540281	+	0.347217i	0.241868	+	0.970309i	$0.422240\pi$
$572$	59.5310	+	68.7024i	2.48911	+	2.87259i
$573$	23.0549	−	6.76953i	0.963133	−	0.282801i
$574$	−11.0648			−0.461838
$575$		0			0
$576$	2.07845			0.0866021
$577$	14.8855	−	4.37078i	0.619692	−	0.181958i	0.0432076	−	0.999066i	$-0.486242\pi$
$577$	14.8855	−	4.37078i	0.619692	−	0.181958i	0.576484	+	0.817108i	$0.304424\pi$
$578$	22.1673	+	25.5824i	0.922038	+	1.06409i
$579$	−8.27983	+	5.32112i	−0.344098	+	0.221138i
$580$		0			0
$581$	−14.2618	−	9.16549i	−0.591678	−	0.380249i
$582$	−19.5618	+	42.8344i	−0.810864	+	1.77554i
$583$	31.2825	−	36.1019i	1.29559	−	1.49519i
$584$	11.5189	−	80.1158i	0.476656	−	3.31522i
$585$		0			0
$586$	−26.3364	−	7.73308i	−1.08795	−	0.319450i
$587$	42.8243	+	12.5744i	1.76755	+	0.518999i	0.993470	−	0.114091i	$-0.0363957\pi$
$587$	42.8243	+	12.5744i	1.76755	+	0.518999i	0.774078	+	0.633090i	$0.218214\pi$
$588$	−10.1535	−	22.2332i	−0.418725	−	0.916880i
$589$	−0.476678	+	3.31537i	−0.0196412	+	0.136607i
$590$		0			0
$591$	−14.3859	+	31.5007i	−0.591756	+	1.29576i
$592$	−5.67543	−	3.64738i	−0.233259	−	0.149906i
$593$	1.24649	+	8.66953i	0.0511872	+	0.356015i	0.999277	+	0.0380129i	$0.0121028\pi$
$593$	1.24649	+	8.66953i	0.0511872	+	0.356015i	−0.948090	+	0.318002i	$0.896988\pi$
$594$	−64.7917	+	41.6391i	−2.65844	+	1.70847i
$595$		0			0
$596$	87.3349	−	25.6438i	3.57738	−	1.05041i
$597$	19.0430			0.779376
$598$	32.9828	+	22.6014i	1.34877	+	0.924242i
$599$	−26.2217			−1.07139			−0.535694	−	0.844412i	$-0.679950\pi$
$599$	−26.2217			−1.07139			−0.535694	+	0.844412i	$0.679950\pi$
$600$		0			0
$601$	−12.2537	−	14.1415i	−0.499838	−	0.576843i	0.448630	−	0.893718i	$-0.351912\pi$
$601$	−12.2537	−	14.1415i	−0.499838	−	0.576843i	−0.948468	+	0.316874i	$0.897367\pi$
$602$	19.0099	−	12.2169i	0.774786	−	0.497925i
$603$	−0.164847	−	1.14654i	−0.00671309	−	0.0466905i
$604$	−73.1100	−	46.9849i	−2.97480	−	1.91179i
$605$		0			0
$606$	−57.6904	+	66.5783i	−2.34351	+	2.70456i
$607$	−0.495843	+	3.44867i	−0.0201257	+	0.139977i	−0.997407	−	0.0719701i	$-0.977071\pi$
$607$	−0.495843	+	3.44867i	−0.0201257	+	0.139977i	0.977281	+	0.211947i	$0.0679805\pi$
$608$	11.1345	+	24.3811i	0.451563	+	0.988784i
$609$	7.28417	+	2.13883i	0.295170	+	0.0866696i
$610$		0			0
$611$	−0.528891	−	1.15811i	−0.0213966	−	0.0468521i
$612$	−0.248767	+	1.73022i	−0.0100558	+	0.0699398i
$613$	10.5961	−	12.2285i	0.427971	−	0.493905i	−0.500278	−	0.865865i	$-0.666769\pi$
$613$	10.5961	−	12.2285i	0.427971	−	0.493905i	0.928249	+	0.371960i	$0.121314\pi$
$614$	2.86801	−	6.28006i	0.115743	−	0.253443i
$615$		0			0
$616$	−13.3068	−	92.5510i	−0.536147	−	3.72899i
$617$	−28.2285	+	18.1414i	−1.13644	+	0.730344i	−0.966894	−	0.255178i	$-0.917866\pi$
$617$	−28.2285	+	18.1414i	−1.13644	+	0.730344i	−0.169544	+	0.985523i	$0.554229\pi$
$618$	−40.2739	−	46.4785i	−1.62005	−	1.86964i
$619$	−7.07680	+	2.07794i	−0.284441	+	0.0835193i	−0.420841	−	0.907135i	$-0.638265\pi$
$619$	−7.07680	+	2.07794i	−0.284441	+	0.0835193i	0.136400	+	0.990654i	$0.456447\pi$
$620$		0			0
$621$	−16.3507	+	17.7796i	−0.656130	+	0.713469i
$622$	−70.6865			−2.83427
$623$	−6.31611	+	1.85458i	−0.253049	+	0.0743020i
$624$	39.6339	+	45.7400i	1.58663	+	1.83106i
$625$		0			0
$626$	−6.25270	−	43.4885i	−0.249908	−	1.73815i
$627$	18.2761	+	11.7454i	0.729878	+	0.469064i
$628$	2.34092	−	5.12591i	0.0934130	−	0.204546i
$629$	0.839215	−	0.968506i	0.0334617	−	0.0386169i
$630$		0			0
$631$	7.29135	+	15.9658i	0.290264	+	0.635590i	0.997445	−	0.0714433i	$-0.0227605\pi$
$631$	7.29135	+	15.9658i	0.290264	+	0.635590i	−0.707181	+	0.707033i	$0.750033\pi$
$632$	−64.1484	−	18.8357i	−2.55169	−	0.749243i
$633$	−21.4944	−	6.31134i	−0.854328	−	0.250853i
$634$	−28.7517	−	62.9574i	−1.14187	−	2.50036i
$635$		0			0
$636$	47.8070	−	55.1723i	1.89567	−	2.18772i
$637$	3.62238	−	7.93191i	0.143524	−	0.314274i
$638$	−26.6335	−	17.1163i	−1.05443	−	0.677642i
$639$	−0.340245	−	2.36645i	−0.0134599	−	0.0936155i
$640$		0			0
$641$	−21.4742	−	24.7826i	−0.848181	−	0.978853i	0.151773	−	0.988415i	$-0.451502\pi$
$641$	−21.4742	−	24.7826i	−0.848181	−	0.978853i	−0.999954	+	0.00956193i	$0.996956\pi$
$642$	10.1615	−	2.98367i	0.401041	−	0.117756i
$643$	−17.2988			−0.682198			−0.341099	−	0.940027i	$-0.610799\pi$
$643$	−17.2988			−0.682198			−0.341099	+	0.940027i	$0.610799\pi$
$644$	−19.0573	−	45.2208i	−0.750962	−	1.78195i
$645$		0			0
$646$	−10.9045	+	3.20184i	−0.429031	+	0.125975i
$647$	−24.0270	−	27.7286i	−0.944599	−	1.09012i	−0.995811	−	0.0914371i	$-0.970854\pi$
$647$	−24.0270	−	27.7286i	−0.944599	−	1.09012i	0.0512122	−	0.998688i	$-0.483692\pi$
$648$	−62.5760	+	40.2151i	−2.45822	+	1.57980i
$649$	7.40993	+	51.5372i	0.290865	+	2.02301i
$650$		0			0
$651$	2.42268	−	5.30493i	0.0949523	−	0.207916i
$652$	25.2225	−	29.1083i	0.987790	−	1.13997i
$653$	4.53054	−	31.5106i	0.177294	−	1.23311i	−0.685697	−	0.727887i	$-0.740503\pi$
$653$	4.53054	−	31.5106i	0.177294	−	1.23311i	0.862991	−	0.505219i	$-0.168588\pi$
$654$	−11.7894	−	25.8152i	−0.461003	−	1.00945i
$655$		0			0
$656$	21.0183	+	6.17153i	0.820627	+	0.240958i
$657$	−0.737844	−	1.61565i	−0.0287860	−	0.0630326i
$658$	−0.311864	+	2.16906i	−0.0121577	+	0.0845588i
$659$	−20.1626	+	23.2689i	−0.785424	+	0.906428i	−0.997489	−	0.0708277i	$-0.977436\pi$
$659$	−20.1626	+	23.2689i	−0.785424	+	0.906428i	0.212064	+	0.977256i	$0.431981\pi$
$660$		0			0
$661$	−28.3663	−	18.2299i	−1.10332	−	0.709061i	−0.143493	−	0.989651i	$-0.545834\pi$
$661$	−28.3663	−	18.2299i	−1.10332	−	0.709061i	−0.959828	+	0.280590i	$0.909470\pi$
$662$	−2.65144	−	18.4412i	−0.103051	−	0.716737i
$663$	−9.67157	+	6.21554i	−0.375613	+	0.241392i
$664$	42.2813	+	48.7952i	1.64083	+	1.89362i
$665$		0			0
$666$	−0.284797			−0.0110357
$667$	−9.44015	−	3.07771i	−0.365524	−	0.119169i
$668$	47.3679			1.83272
$669$	8.56468	−	2.51482i	0.331130	−	0.0972285i
$670$		0			0
$671$	−6.63710	+	4.26541i	−0.256223	+	0.164664i
$672$	−6.64165	−	46.1937i	−0.256207	−	1.78196i
$673$	−2.37968	−	1.52933i	−0.0917298	−	0.0589511i	0.493972	−	0.869478i	$-0.335545\pi$
$673$	−2.37968	−	1.52933i	−0.0917298	−	0.0589511i	−0.585702	+	0.810527i	$0.699181\pi$
$674$	17.9250	−	39.2502i	0.690444	−	1.51186i
$675$		0			0
$676$	2.14134	−	14.8933i	0.0823592	−	0.572821i
$677$	0.731565	+	1.60190i	0.0281163	+	0.0615662i	0.923169	−	0.384394i	$-0.125590\pi$
$677$	0.731565	+	1.60190i	0.0281163	+	0.0615662i	−0.895053	+	0.445960i	$0.852862\pi$
$678$	24.0094	+	7.04979i	0.922074	+	0.270745i
$679$	19.7833	+	5.80891i	0.759215	+	0.222926i
$680$		0			0
$681$	−3.54370	+	24.6470i	−0.135795	+	0.944473i
$682$	−15.9267	+	18.3804i	−0.609865	+	0.703821i
$683$	−5.38662	+	11.7951i	−0.206113	+	0.451326i	−0.984253	−	0.176766i	$-0.943436\pi$
$683$	−5.38662	+	11.7951i	−0.206113	+	0.451326i	0.778139	+	0.628092i	$0.216164\pi$
$684$	1.51504	+	0.973657i	0.0579290	+	0.0372287i
$685$		0			0
$686$	−44.6341	+	28.6846i	−1.70414	+	1.09518i
$687$	−13.7318	−	15.8474i	−0.523902	−	0.604615i
$688$	−42.9245	+	12.6038i	−1.63648	+	0.480515i
$689$	26.0447			0.992224
$690$		0			0
$691$	−9.31109			−0.354210			−0.177105	−	0.984192i	$-0.556673\pi$
$691$	−9.31109			−0.354210			−0.177105	+	0.984192i	$0.556673\pi$
$692$	−53.5341	+	15.7190i	−2.03506	+	0.597548i
$693$	−1.34367	−	1.55068i	−0.0510420	−	0.0589056i
$694$	−46.4471	+	29.8498i	−1.76311	+	1.13308i
$695$		0			0
$696$	−24.3231	−	15.6315i	−0.921963	−	0.592510i
$697$	−1.72858	+	3.78507i	−0.0654748	+	0.143370i
$698$	−42.9173	+	49.5292i	−1.62444	+	1.87471i
$699$	−1.25831	+	8.75176i	−0.0475938	+	0.331022i
$700$		0			0
$701$	24.1132	+	7.08026i	0.910742	+	0.267418i	0.703353	−	0.710841i	$-0.251685\pi$
$701$	24.1132	+	7.08026i	0.910742	+	0.267418i	0.207389	+	0.978259i	$0.433504\pi$
$702$	−40.2903	−	11.8303i	−1.52066	−	0.446506i
$703$	−0.548479	−	1.20100i	−0.0206863	−	0.0452967i
$704$	−9.95713	+	69.2534i	−0.375274	+	2.61009i
$705$		0			0
$706$	13.5487	−	29.6675i	0.509911	−	1.11655i
$707$	32.4498	+	20.8542i	1.22040	+	0.784304i
$708$	11.3241	+	78.7610i	0.425586	+	2.96002i
$709$	−24.3663	+	15.6593i	−0.915095	+	0.588096i	−0.911230	−	0.411897i	$-0.864866\pi$
$709$	−24.3663	+	15.6593i	−0.915095	+	0.588096i	−0.00386426	+	0.999993i	$0.501230\pi$
$710$		0			0
$711$	−1.40769	+	0.413335i	−0.0527925	+	0.0155013i
$712$	25.0703			0.939551
$713$	−3.37230	+	6.84165i	−0.126293	+	0.256222i
$714$	19.7880			0.740546
$715$		0			0
$716$	16.0929	+	18.5721i	0.601418	+	0.694074i
$717$	−21.3120	+	13.6964i	−0.795912	+	0.511502i
$718$	4.35164	+	30.2663i	0.162402	+	1.12953i
$719$	24.1127	+	15.4963i	0.899253	+	0.577915i	0.906569	−	0.422059i	$-0.138692\pi$
$719$	24.1127	+	15.4963i	0.899253	+	0.577915i	−0.00731583	+	0.999973i	$0.502329\pi$
$720$		0			0
$721$	−17.6341	+	20.3509i	−0.656730	+	0.757907i
$722$	5.47236	−	38.0611i	0.203660	−	1.41649i
$723$	−2.78107	−	6.08968i	−0.103429	−	0.226478i
$724$	−37.7580	−	11.0868i	−1.40327	−	0.412036i
$725$		0			0
$726$	44.0438	+	96.4425i	1.63462	+	3.57932i
$727$	−3.75859	+	26.1416i	−0.139398	+	0.969538i	0.793287	+	0.608848i	$0.208368\pi$
$727$	−3.75859	+	26.1416i	−0.139398	+	0.969538i	−0.932686	+	0.360690i	$0.882541\pi$
$728$	33.3841	−	38.5273i	1.23730	−	1.42792i
$729$	10.5012	−	22.9945i	0.388934	−	0.851647i
$730$		0			0
$731$	−1.20939	−	8.41149i	−0.0447309	−	0.311110i
$732$	−10.1431	+	6.51855i	−0.374898	+	0.240932i
$733$	−34.8517	−	40.2210i	−1.28728	−	1.48560i	−0.782954	−	0.622080i	$-0.786288\pi$
$733$	−34.8517	−	40.2210i	−1.28728	−	1.48560i	−0.504322	−	0.863516i	$-0.668257\pi$
$734$	21.1385	−	6.20684i	0.780238	−	0.229099i
$735$		0			0
$736$	6.89728	+	60.6472i	0.254237	+	2.23548i
$737$	38.9920			1.43629
$738$	0.887281	−	0.260529i	0.0326612	−	0.00959021i
$739$	−16.3546	−	18.8742i	−0.601614	−	0.694300i	0.370493	−	0.928835i	$-0.379189\pi$
$739$	−16.3546	−	18.8742i	−0.601614	−	0.694300i	−0.972108	+	0.234535i	$0.924643\pi$
$740$		0			0
$741$	1.68568	+	11.7241i	0.0619249	+	0.430697i
$742$	−37.7118	−	24.2359i	−1.38444	−	0.889728i
$743$	−13.1040	+	28.6938i	−0.480741	+	1.05267i	0.501519	+	0.865147i	$0.332775\pi$
$743$	−13.1040	+	28.6938i	−0.480741	+	1.05267i	−0.982259	+	0.187528i	$0.939952\pi$
$744$	−14.5451	+	16.7859i	−0.533248	+	0.615400i
$745$		0			0
$746$	−30.1333	−	65.9827i	−1.10326	−	2.41580i
$747$	1.35945	+	0.399170i	0.0497396	+	0.0146049i
$748$	−56.4585	−	16.5777i	−2.06433	−	0.606142i
$749$	−1.92631	−	4.21804i	−0.0703860	−	0.154124i
$750$		0			0
$751$	−0.178172	+	0.205622i	−0.00650159	+	0.00750324i	−0.758991	−	0.651101i	$-0.774307\pi$
$751$	−0.178172	+	0.205622i	−0.00650159	+	0.00750324i	0.752489	+	0.658604i	$0.228853\pi$
$752$	1.80222	−	3.94631i	0.0657202	−	0.143907i
$753$	26.4316	+	16.9865i	0.963220	+	0.619024i
$754$	−2.45651	−	17.0854i	−0.0894608	−	0.622213i
$755$		0			0
$756$	33.7491	+	38.9486i	1.22744	+	1.41655i
$757$	−1.98009	+	0.581408i	−0.0719678	+	0.0211316i	−0.317518	−	0.948252i	$-0.602849\pi$
$757$	−1.98009	+	0.581408i	−0.0719678	+	0.0211316i	0.245550	+	0.969384i	$0.421031\pi$
$758$	26.1062			0.948219
$759$	31.2790	+	38.3306i	1.13535	+	1.39131i
$760$		0			0
$761$	39.8954	−	11.7143i	1.44621	−	0.424644i	0.537921	−	0.842996i	$-0.319210\pi$
$761$	39.8954	−	11.7143i	1.44621	−	0.424644i	0.908285	+	0.418351i	$0.137392\pi$
$762$	26.7069	+	30.8214i	0.967489	+	1.11654i
$763$	−10.4536	+	6.71815i	−0.378447	+	0.243213i
$764$	9.54237	+	66.3686i	0.345231	+	2.40113i
$765$		0			0
$766$	−12.3360	+	27.0122i	−0.445719	+	0.975989i
$767$	−18.5900	+	21.4540i	−0.671246	+	0.774660i
$768$	1.81667	−	12.6352i	0.0655535	−	0.455934i
$769$	−18.8182	−	41.2062i	−0.678602	−	1.48593i	−0.864117	−	0.503290i	$-0.832123\pi$
$769$	−18.8182	−	41.2062i	−0.678602	−	1.48593i	0.185515	−	0.982641i	$-0.440605\pi$
$770$		0			0
$771$	−10.5281	−	3.09134i	−0.379161	−	0.111332i
$772$	−11.4093	−	24.9830i	−0.410631	−	0.899157i
$773$	−1.67397	+	11.6427i	−0.0602085	+	0.418759i	0.937318	+	0.348474i	$0.113300\pi$
$773$	−1.67397	+	11.6427i	−0.0602085	+	0.418759i	−0.997527	+	0.0702852i	$0.977609\pi$
$774$	−1.23673	+	1.42727i	−0.0444534	+	0.0513020i
$775$		0			0
$776$	−66.0598	−	42.4541i	−2.37141	−	1.52401i
$777$	0.327165	+	2.27548i	0.0117370	+	0.0816325i
$778$	18.0958	−	11.6295i	0.648767	−	0.416937i
$779$	2.80744	+	3.23996i	0.100587	+	0.116084i
$780$		0			0
$781$	80.4796			2.87979
$782$	−25.8694	−	0.764877i	−0.925089	−	0.0273520i
$783$	10.4277			0.372657
$784$	28.5099	−	8.37126i	1.01821	−	0.298973i
$785$		0			0
$786$	61.4350	−	39.4819i	2.19132	−	1.40827i
$787$	5.05835	+	35.1816i	0.180311	+	1.25409i	0.856029	+	0.516928i	$0.172925\pi$
$787$	5.05835	+	35.1816i	0.180311	+	1.25409i	−0.675718	+	0.737160i	$0.736166\pi$
$788$	−81.2953	−	52.2453i	−2.89602	−	1.86116i
$789$	−15.2035	+	33.2911i	−0.541260	+	1.18519i
$790$		0			0
$791$	1.55927	−	10.8449i	0.0554411	−	0.385601i
$792$	3.24624	+	7.10827i	0.115350	+	0.252581i
$793$	−4.12724	−	1.21187i	−0.146563	−	0.0430347i
$794$	34.0176	+	9.98846i	1.20724	+	0.354477i
$795$		0			0
$796$	−7.56256	+	52.5988i	−0.268048	+	1.86431i
$797$	−3.83750	+	4.42871i	−0.135931	+	0.156873i	−0.819634	−	0.572888i	$-0.805823\pi$
$797$	−3.83750	+	4.42871i	−0.135931	+	0.156873i	0.683703	+	0.729761i	$0.260369\pi$
$798$	8.46910	−	18.5447i	0.299803	−	0.656477i
$799$	0.693274	+	0.445540i	0.0245263	+	0.0157621i
$800$		0			0
$801$	0.462816	−	0.297434i	0.0163528	−	0.0105093i
$802$	24.5090	+	28.2848i	0.865441	+	0.998772i
$803$	57.3678	−	16.8447i	2.02447	−	0.594437i
$804$	59.5889			2.10154
$805$		0			0
$806$	−13.2600			−0.467064
$807$	−25.5673	+	7.50723i	−0.900011	+	0.264267i
$808$	−96.2027	−	111.024i	−3.38440	−	3.90580i
$809$	−31.2095	+	20.0571i	−1.09727	+	0.705171i	−0.958482	−	0.285152i	$-0.907956\pi$
$809$	−31.2095	+	20.0571i	−1.09727	+	0.705171i	−0.138785	+	0.990323i	$0.544320\pi$
$810$		0			0
$811$	−8.22031	−	5.28287i	−0.288654	−	0.185507i	0.388298	−	0.921534i	$-0.373063\pi$
$811$	−8.22031	−	5.28287i	−0.288654	−	0.185507i	−0.676952	+	0.736027i	$0.736700\pi$
$812$	−8.80045	+	19.2703i	−0.308835	+	0.676255i
$813$	−17.3358	+	20.0066i	−0.607994	+	0.701662i
$814$	1.36436	−	9.48935i	0.0478209	−	0.332602i
$815$		0			0
$816$	−37.5884	−	11.0370i	−1.31586	−	0.386371i
$817$	−8.40062	−	2.46665i	−0.293901	−	0.0862970i
$818$	−20.1669	−	44.1593i	−0.705118	−	1.54399i
$819$	0.159207	−	1.10731i	0.00556314	−	0.0386925i
$820$		0			0
$821$	1.01096	−	2.21369i	0.0352827	−	0.0772583i	−0.891170	−	0.453669i	$-0.850115\pi$
$821$	1.01096	−	2.21369i	0.0352827	−	0.0772583i	0.926453	+	0.376411i	$0.122842\pi$
$822$	−41.4786	−	26.6567i	−1.44673	−	0.929759i
$823$	−6.02292	−	41.8903i	−0.209946	−	1.46020i	−0.773327	−	0.634007i	$-0.781409\pi$
$823$	−6.02292	−	41.8903i	−0.209946	−	1.46020i	0.563381	−	0.826197i	$-0.309500\pi$
$824$	86.2750	−	55.4456i	3.00553	−	1.93154i
$825$		0			0
$826$	46.8817	−	13.7657i	1.63122	−	0.478971i
$827$	−31.4841			−1.09481			−0.547406	−	0.836867i	$-0.684384\pi$
$827$	−31.4841			−1.09481			−0.547406	+	0.836867i	$0.684384\pi$
$828$	2.59294	+	3.17750i	0.0901108	+	0.110426i
$829$	39.5914			1.37507			0.687534	−	0.726152i	$-0.258693\pi$
$829$	39.5914			1.37507			0.687534	+	0.726152i	$0.258693\pi$
$830$		0			0
$831$	−11.6412	−	13.4346i	−0.403827	−	0.466042i
$832$	−32.0906	+	20.6234i	−1.11254	+	0.714987i
$833$	0.803260	+	5.58679i	0.0278313	+	0.193571i
$834$	−53.6001	−	34.4467i	−1.85602	−	1.19279i
$835$		0			0
$836$	−39.7000	+	45.8162i	−1.37305	+	1.58459i
$837$	1.14003	−	7.92907i	0.0394051	−	0.274069i
$838$	32.7153	+	71.6364i	1.13013	+	2.47464i
$839$	7.51083	+	2.20538i	0.259303	+	0.0761382i	0.408800	−	0.912624i	$-0.365947\pi$
$839$	7.51083	+	2.20538i	0.259303	+	0.0761382i	−0.149497	+	0.988762i	$0.547766\pi$
$840$		0			0
$841$	−10.2664	−	22.4802i	−0.354013	−	0.775180i
$842$	12.6674	−	88.1039i	0.436548	−	3.03626i
$843$	−29.8301	+	34.4257i	−1.02740	+	1.18569i
$844$	25.9687	−	56.8636i	0.893881	−	1.95733i
$845$		0			0
$846$	−0.0260639	−	0.181278i	−0.000896095	−	0.00623248i
$847$	39.0536	−	25.0982i	1.34190	−	0.862384i
$848$	58.1179	+	67.0717i	1.99578	+	2.30325i
$849$	−11.9599	+	3.51174i	−0.410462	+	0.120523i
$850$		0			0
$851$	−0.339757	−	2.98745i	−0.0116467	−	0.102409i
$852$	122.992			4.21363
$853$	16.0602	−	4.71569i	0.549890	−	0.161462i	0.00502706	−	0.999987i	$-0.498400\pi$
$853$	16.0602	−	4.71569i	0.549890	−	0.161462i	0.544863	+	0.838525i	$0.316582\pi$
$854$	4.84840	+	5.59535i	0.165909	+	0.191469i
$855$		0			0
$856$	2.51332	+	17.4805i	0.0859036	+	0.597472i
$857$	34.0126	+	21.8585i	1.16185	+	0.746673i	0.971963	−	0.235133i	$-0.0755526\pi$
$857$	34.0126	+	21.8585i	1.16185	+	0.746673i	0.189883	+	0.981807i	$0.439189\pi$
$858$	−35.7279	+	78.2332i	−1.21973	+	2.67084i
$859$	23.0015	−	26.5451i	0.784800	−	0.905708i	−0.212646	−	0.977129i	$-0.568208\pi$
$859$	23.0015	−	26.5451i	0.784800	−	0.905708i	0.997446	+	0.0714213i	$0.0227535\pi$
$860$		0			0
$861$	−3.10086	−	6.78994i	−0.105677	−	0.231401i
$862$	51.4881	+	15.1183i	1.75369	+	0.514930i
$863$	24.3424	+	7.14758i	0.828626	+	0.243307i	0.668427	−	0.743778i	$-0.266968\pi$
$863$	24.3424	+	7.14758i	0.828626	+	0.243307i	0.160199	+	0.987085i	$0.448786\pi$
$864$	−26.6293	−	58.3100i	−0.905947	−	1.98375i
$865$		0			0
$866$	−62.6397	+	72.2900i	−2.12858	+	2.45652i
$867$	−9.48639	+	20.7723i	−0.322175	+	0.705464i
$868$	13.6907	+	8.79846i	0.464692	+	0.298639i
$869$	−7.02845	−	48.8840i	−0.238424	−	1.65827i
$870$		0			0
$871$	13.9217	+	16.0664i	0.471717	+	0.544391i
$872$	45.4083	−	13.3331i	1.53772	−	0.451515i
$873$	−1.72318			−0.0583209
$874$	−11.7887	+	23.9167i	−0.398760	+	0.808996i
$875$		0			0
$876$	87.6716	−	25.7427i	2.96215	−	0.869765i
$877$	−16.9189	−	19.5255i	−0.571312	−	0.659329i	0.394402	−	0.918938i	$-0.370952\pi$
$877$	−16.9189	−	19.5255i	−0.571312	−	0.659329i	−0.965714	+	0.259609i	$0.916406\pi$
$878$	5.31034	−	3.41275i	0.179215	−	0.115175i
$879$	−2.63524	−	18.3285i	−0.0888845	−	0.618205i
$880$		0			0
$881$	1.31705	−	2.88393i	0.0443725	−	0.0971622i	−0.886148	−	0.463403i	$-0.846628\pi$
$881$	1.31705	−	2.88393i	0.0443725	−	0.0971622i	0.930520	+	0.366241i	$0.119355\pi$
$882$	0.821421	−	0.947970i	0.0276587	−	0.0319198i
$883$	−0.460370	+	3.20194i	−0.0154927	+	0.107754i	−0.996100	−	0.0882269i	$-0.971880\pi$
$883$	−0.460370	+	3.20194i	−0.0154927	+	0.107754i	0.980608	+	0.195981i	$0.0627890\pi$
$884$	−13.3271	−	29.1823i	−0.448240	−	0.981509i
$885$		0			0
$886$	−26.0870	−	7.65984i	−0.876411	−	0.257337i
$887$	−10.6605	−	23.3433i	−0.357946	−	0.783792i	−0.999855	−	0.0170118i	$-0.994585\pi$
$887$	−10.6605	−	23.3433i	−0.357946	−	0.783792i	0.641909	−	0.766781i	$-0.278143\pi$
$888$	1.24600	−	8.66615i	0.0418132	−	0.290817i
$889$	11.6938	−	13.4953i	0.392196	−	0.452619i
$890$		0			0
$891$	−46.2246	−	29.7067i	−1.54858	−	0.995213i
$892$	3.54490	+	24.6553i	0.118692	+	0.825521i
$893$	0.714264	−	0.459029i	0.0239019	−	0.0153608i
$894$	56.3932	+	65.0812i	1.88607	+	2.17664i
$895$		0			0
$896$	13.2507			0.442674
$897$	−4.62611	+	26.5739i	−0.154461	+	0.887275i
$898$	84.8416			2.83120
$899$	3.15948	−	0.927708i	0.105375	−	0.0309408i
$900$		0			0
$901$	−14.1821	+	9.11428i	−0.472474	+	0.303641i
$902$	4.43010	+	30.8120i	0.147506	+	1.02593i
$903$	12.8243	+	8.24170i	0.426767	+	0.274267i
$904$	−17.3342	+	37.9567i	−0.576528	+	1.26242i
$905$		0			0
$906$	11.7012	−	81.3839i	0.388748	−	2.70380i
$907$	6.05013	+	13.2479i	0.200891	+	0.439890i	0.983086	−	0.183143i	$-0.0586272\pi$
$907$	6.05013	+	13.2479i	0.200891	+	0.439890i	−0.782195	+	0.623034i	$0.785900\pi$
$908$	−66.6703	−	19.5762i	−2.21253	−	0.649658i
$909$	−3.09315	−	0.908231i	−0.102593	−	0.0301241i
$910$		0			0
$911$	−5.66346	+	39.3902i	−0.187639	+	1.30506i	0.650461	+	0.759539i	$0.274576\pi$
$911$	−5.66346	+	39.3902i	−0.187639	+	1.30506i	−0.838100	+	0.545516i	$0.816334\pi$
$912$	−26.4311	+	30.5031i	−0.875220	+	1.01006i
$913$	−19.8129	+	43.3841i	−0.655710	+	1.43580i
$914$	29.7351	+	19.1096i	0.983549	+	0.632089i
$915$		0			0
$916$	49.2256	−	31.6353i	1.62646	−	1.04526i
$917$	−20.9396	−	24.1656i	−0.691487	−	0.798019i
$918$	26.0792	−	7.65756i	0.860743	−	0.252737i
$919$	−14.0233			−0.462587			−0.231293	−	0.972884i	$-0.574296\pi$
$919$	−14.0233			−0.462587			−0.231293	+	0.972884i	$0.574296\pi$
$920$		0			0
$921$	4.65750			0.153470
$922$	77.3103	−	22.7004i	2.54608	−	0.747596i
$923$	28.7343	+	33.1612i	0.945802	+	1.09151i
$924$	88.7988	−	57.0675i	2.92126	−	1.87738i
$925$		0			0
$926$	46.4721	+	29.8658i	1.52717	+	0.981450i
$927$	0.934892	−	2.04713i	0.0307059	−	0.0672365i
$928$	17.2558	−	19.9143i	0.566450	−	0.653718i
$929$	−6.86381	+	47.7389i	−0.225194	+	1.56626i	0.492756	+	0.870167i	$0.335989\pi$
$929$	−6.86381	+	47.7389i	−0.225194	+	1.56626i	−0.717951	+	0.696094i	$0.754920\pi$
$930$		0			0
$931$	5.57958	+	1.63831i	0.182863	+	0.0536935i
$932$	−23.6736	−	6.95120i	−0.775455	−	0.227694i
$933$	−19.8095	−	43.3767i	−0.648534	−	1.42009i
$934$	−12.3195	+	85.6842i	−0.403107	+	2.80367i
$935$		0			0
$936$	−1.76989	+	3.87552i	−0.0578507	+	0.126675i
$937$	−24.9268	−	16.0195i	−0.814325	−	0.523335i	0.0659368	−	0.997824i	$-0.478996\pi$
$937$	−24.9268	−	16.0195i	−0.814325	−	0.523335i	−0.880261	+	0.474489i	$0.842633\pi$
$938$	−5.20743	−	36.2184i	−0.170028	−	1.18257i
$939$	24.9344	−	16.0244i	0.813705	−	0.522936i
$940$		0			0
$941$	15.2867	−	4.48857i	0.498331	−	0.146323i	−0.0229019	−	0.999738i	$-0.507291\pi$
$941$	15.2867	−	4.48857i	0.498331	−	0.146323i	0.521233	+	0.853415i	$0.325472\pi$
$942$	5.33134			0.173705
$943$	3.79140	+	8.99656i	0.123465	+	0.292968i
$944$	−96.7325			−3.14838
$945$		0			0
$946$	−41.6313	−	48.0451i	−1.35355	−	1.56208i
$947$	−46.9537	+	30.1753i	−1.52579	+	0.980565i	−0.535045	+	0.844823i	$0.679706\pi$
$947$	−46.9537	+	30.1753i	−1.52579	+	0.980565i	−0.990744	+	0.135742i	$0.956658\pi$
$948$	−10.7411	−	74.7062i	−0.348856	−	2.42635i
$949$	27.4233	+	17.6239i	0.890199	+	0.572096i
$950$		0			0
$951$	30.5763	−	35.2869i	0.991504	−	1.14426i
$952$	−4.69608	+	32.6619i	−0.152201	+	1.05858i
$953$	18.1999	+	39.8521i	0.589551	+	1.29094i	0.935713	+	0.352763i	$0.114758\pi$
$953$	18.1999	+	39.8521i	0.589551	+	1.29094i	−0.346162	+	0.938175i	$0.612515\pi$
$954$	3.59473	+	1.05551i	0.116384	+	0.0341733i
$955$		0			0
$956$	−29.3673	−	64.3054i	−0.949807	−	2.07979i
$957$	3.03953	−	21.1404i	0.0982541	−	0.683372i
$958$	−57.4667	+	66.3201i	−1.85667	+	2.14271i
$959$	−8.96831	+	19.6379i	−0.289602	+	0.634139i
$960$		0			0
$961$	4.05176	+	28.1806i	0.130702	+	0.909052i
$962$	4.39717	−	2.82589i	0.141770	−	0.0911103i
$963$	0.253786	+	0.292885i	0.00817814	+	0.00943808i
$964$	17.9248	−	5.26320i	0.577320	−	0.169516i
$965$		0			0
$966$	31.4268	−	34.1732i	1.01114	−	1.09950i
$967$	13.4070			0.431139			0.215570	−	0.976488i	$-0.430839\pi$
$967$	13.4070			0.431139			0.215570	+	0.976488i	$0.430839\pi$
$968$	−169.640	+	49.8108i	−5.45244	+	1.60098i
$969$	−5.02073	−	5.79423i	−0.161289	−	0.186138i
$970$		0			0
$971$	5.71226	+	39.7296i	0.183315	+	1.27498i	0.848856	+	0.528623i	$0.177292\pi$
$971$	5.71226	+	39.7296i	0.183315	+	1.27498i	−0.665541	+	0.746361i	$0.731799\pi$
$972$	−7.46723	−	4.79890i	−0.239511	−	0.153925i
$973$	−11.5892	+	25.3767i	−0.371531	+	0.813540i
$974$	−36.6386	+	42.2832i	−1.17398	+	1.35484i
$975$		0			0
$976$	−6.08895	−	13.3329i	−0.194903	−	0.426777i
$977$	35.6061	+	10.4549i	1.13914	+	0.334482i	0.796294	−	0.604910i	$-0.206791\pi$
$977$	35.6061	+	10.4549i	1.13914	+	0.334482i	0.342846	+	0.939392i	$0.388609\pi$
$978$	34.9634	+	10.2662i	1.11800	+	0.328276i
$979$	7.69322	+	16.8458i	0.245876	+	0.538394i
$980$		0			0
$981$	0.680086	−	0.784861i	0.0217135	−	0.0250587i
$982$	17.2258	−	37.7192i	0.549696	−	1.20367i
$983$	−27.0372	−	17.3757i	−0.862352	−	0.554200i	0.0330527	−	0.999454i	$-0.489477\pi$
$983$	−27.0372	−	17.3757i	−0.862352	−	0.554200i	−0.895404	+	0.445254i	$0.853113\pi$
$984$	4.04579	+	28.1391i	0.128975	+	0.897041i
$985$		0			0
$986$	7.31663	+	8.44384i	0.233009	+	0.268907i
$987$	−1.41844	+	0.416493i	−0.0451495	+	0.0132571i
$988$	−33.0528			−1.05155
$989$	−16.4471	−	11.2703i	−0.522987	−	0.358376i
$990$		0			0
$991$	3.91774	−	1.15035i	0.124451	−	0.0365421i	−0.218914	−	0.975744i	$-0.570251\pi$
$991$	3.91774	−	1.15035i	0.124451	−	0.0365421i	0.343365	+	0.939202i	$0.388433\pi$
$992$	−13.2560	−	15.2982i	−0.420877	−	0.485718i
$993$	10.5734	−	6.79510i	0.335536	−	0.215636i
$994$	−10.7481	−	74.7550i	−0.340911	−	2.37108i
$995$		0			0
$996$	−30.2787	+	66.3011i	−0.959418	+	2.10083i
$997$	12.0826	−	13.9441i	0.382660	−	0.441613i	−0.531444	−	0.847094i	$-0.678350\pi$
$997$	12.0826	−	13.9441i	0.382660	−	0.441613i	0.914104	+	0.405480i	$0.132896\pi$
$998$	15.3767	−	106.948i	0.486742	−	3.38537i
$999$	1.31175	+	2.87233i	0.0415019	+	0.0908764i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	575.2.k.g.101.1		100
5.2	odd	4		115.2.j.a.9.1	✓	100
5.3	odd	4		115.2.j.a.9.10	yes	100
5.4	even	2	inner	575.2.k.g.101.10		100
23.18	even	11	inner	575.2.k.g.501.1		100
115.18	odd	44		115.2.j.a.64.1	yes	100
115.64	even	22	inner	575.2.k.g.501.10		100
115.87	odd	44		115.2.j.a.64.10	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.j.a.9.1	✓	100	5.2	odd	4
115.2.j.a.9.10	yes	100	5.3	odd	4
115.2.j.a.64.1	yes	100	115.18	odd	44
115.2.j.a.64.10	yes	100	115.87	odd	44
575.2.k.g.101.1		100	1.1	even	1	trivial
575.2.k.g.101.10		100	5.4	even	2	inner
575.2.k.g.501.1		100	23.18	even	11	inner
575.2.k.g.501.10		100	115.64	even	22	inner

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:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.k (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.53313 + 0.743795i) q^{2} +(-1.16633 - 1.34601i) q^{3} +(4.18102 - 2.68698i) q^{4} +(3.95561 + 2.54212i) q^{6} +(0.855264 - 1.87277i) q^{7} +(-5.13475 + 5.92582i) q^{8} +(-0.0244873 + 0.170313i) q^{9} +O(q^{10})\)	\(q+(-2.53313 + 0.743795i) q^{2} +(-1.16633 - 1.34601i) q^{3} +(4.18102 - 2.68698i) q^{4} +(3.95561 + 2.54212i) q^{6} +(0.855264 - 1.87277i) q^{7} +(-5.13475 + 5.92582i) q^{8} +(-0.0244873 + 0.170313i) q^{9} +(-5.55748 - 1.63182i) q^{11} +(-8.49314 - 2.49381i) q^{12} +(-1.31185 - 2.87256i) q^{13} +(-0.773542 + 5.38010i) q^{14} +(4.47020 - 9.78837i) q^{16} +(1.71958 + 1.10511i) q^{17} +(-0.0646484 - 0.449639i) q^{18} +(1.77165 - 1.13857i) q^{19} +(-3.51828 + 1.03306i) q^{21} +15.2916 q^{22} +(4.63949 - 1.21456i) q^{23} +13.9650 q^{24} +(5.45969 + 6.30081i) q^{26} +(-4.23709 + 2.72301i) q^{27} +(-1.45621 - 10.1281i) q^{28} +(-1.74171 - 1.11933i) q^{29} +(-1.04153 + 1.20200i) q^{31} +(-1.81129 + 12.5978i) q^{32} +(4.28538 + 9.38367i) q^{33} +(-5.17791 - 1.52037i) q^{34} +(0.355246 + 0.777880i) q^{36} +(0.0892232 - 0.620561i) q^{37} +(-3.64095 + 4.20189i) q^{38} +(-2.33645 + 5.11610i) q^{39} +(0.289709 + 2.01497i) q^{41} +(8.14389 - 5.23376i) q^{42} +(-2.72250 - 3.14193i) q^{43} +(-27.6206 + 8.11014i) q^{44} +(-10.8491 + 6.52746i) q^{46} +0.403164 q^{47} +(-18.3890 + 5.39949i) q^{48} +(1.80825 + 2.08683i) q^{49} +(-0.518105 - 3.60350i) q^{51} +(-13.2034 - 8.48529i) q^{52} +(-3.42609 + 7.50209i) q^{53} +(8.70774 - 10.0493i) q^{54} +(6.70611 + 14.6843i) q^{56} +(-3.59885 - 1.05672i) q^{57} +(5.24454 + 1.53994i) q^{58} +(-3.73431 - 8.17700i) q^{59} +(0.892000 - 1.02942i) q^{61} +(1.74431 - 3.81950i) q^{62} +(0.298014 + 0.191522i) q^{63} +(-1.71909 - 11.9565i) q^{64} +(-17.8350 - 20.5826i) q^{66} +(-6.45923 + 1.89660i) q^{67} +10.1590 q^{68} +(-7.04596 - 4.82824i) q^{69} +(-13.3319 + 3.91459i) q^{71} +(-0.883509 - 1.01962i) q^{72} +(-8.68396 + 5.58084i) q^{73} +(0.235556 + 1.63833i) q^{74} +(4.34798 - 9.52075i) q^{76} +(-7.80913 + 9.01222i) q^{77} +(2.11320 - 14.6976i) q^{78} +(3.54206 + 7.75603i) q^{79} +(9.10231 + 2.67268i) q^{81} +(-2.23259 - 4.88870i) q^{82} +(1.17187 - 8.15053i) q^{83} +(-11.9342 + 13.7728i) q^{84} +(9.23341 + 5.93395i) q^{86} +(0.524772 + 3.64987i) q^{87} +(38.2062 - 24.5536i) q^{88} +(-2.09382 - 2.41639i) q^{89} -6.50160 q^{91} +(16.1343 - 17.5443i) q^{92} +2.83267 q^{93} +(-1.02127 + 0.299871i) q^{94} +(19.0693 - 12.2551i) q^{96} +(1.42525 + 9.91281i) q^{97} +(-6.13270 - 3.94125i) q^{98} +(0.414009 - 0.906553i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 14 q^{4} - 18 q^{6} + 12 q^{9}+O(q^{10}) \) 100 * q + 14 * q^4 - 18 * q^6 + 12 * q^9	\( 100 q + 14 q^{4} - 18 q^{6} + 12 q^{9} - 26 q^{11} + 26 q^{14} - 18 q^{16} + 14 q^{19} - 22 q^{21} + 68 q^{24} - 42 q^{26} + 24 q^{29} - 12 q^{31} - 8 q^{34} - 10 q^{36} - 14 q^{39} + 8 q^{41} - 166 q^{44} - 18 q^{46} - 32 q^{49} - 22 q^{51} - 116 q^{54} - 116 q^{56} - 50 q^{59} - 38 q^{61} - 10 q^{64} - 28 q^{66} - 80 q^{69} - 110 q^{71} - 22 q^{74} + 4 q^{76} - 42 q^{79} + 204 q^{81} - 56 q^{84} + 132 q^{86} + 66 q^{89} + 76 q^{91} + 70 q^{94} + 236 q^{96} + 60 q^{99}+O(q^{100}) \) 100 * q + 14 * q^4 - 18 * q^6 + 12 * q^9 - 26 * q^11 + 26 * q^14 - 18 * q^16 + 14 * q^19 - 22 * q^21 + 68 * q^24 - 42 * q^26 + 24 * q^29 - 12 * q^31 - 8 * q^34 - 10 * q^36 - 14 * q^39 + 8 * q^41 - 166 * q^44 - 18 * q^46 - 32 * q^49 - 22 * q^51 - 116 * q^54 - 116 * q^56 - 50 * q^59 - 38 * q^61 - 10 * q^64 - 28 * q^66 - 80 * q^69 - 110 * q^71 - 22 * q^74 + 4 * q^76 - 42 * q^79 + 204 * q^81 - 56 * q^84 + 132 * q^86 + 66 * q^89 + 76 * q^91 + 70 * q^94 + 236 * q^96 + 60 * q^99

Introduction

L-functions

Modular forms

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Database

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