LMFDB - Embedded newform 575.2.k.g.101.10

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			101.10
Character	$\chi$	$=$	575.101
Dual form			575.2.k.g.501.10

$q$-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	0.794506	−	0.607256i	$-0.207730\pi$
$2$	2.53313	−	0.743795i	1.79119	−	0.525942i	0.996689	+	0.0813139i	$0.0259116\pi$
$3$	1.16633	+	1.34601i	0.673379	+	0.777120i	0.984901	−	0.173118i	$-0.0553843\pi$
$3$	1.16633	+	1.34601i	0.673379	+	0.777120i	−0.311522	+	0.950239i	$0.600839\pi$
$4$	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	−0.999586	−	0.0287625i	$-0.990843\pi$
$7$	−0.855264	+	1.87277i	−0.323259	+	0.707839i	0.676327	+	0.736601i	$0.263571\pi$
$8$	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	$0.00792327\pi$
$13$	1.31185	+	2.87256i	0.363842	+	0.796703i	−0.635848	+	0.771814i	$0.719349\pi$
$14$	−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	0.315238	−	0.949013i	$-0.397916\pi$
$17$	−1.71958	−	1.10511i	−0.417060	−	0.268029i	−0.732298	+	0.680984i	$0.761552\pi$
$18$	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	−0.995840	−	0.0911159i	$-0.970957\pi$
$37$	−0.0892232	+	0.620561i	−0.0146682	+	0.102020i	0.981172	+	0.193136i	$0.0618657\pi$
$38$	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	0.924362	−	0.381517i	$-0.124598\pi$
$43$	2.72250	+	3.14193i	0.415178	+	0.479141i	−0.509184	+	0.860658i	$0.670053\pi$
$44$	−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	$-0.509361\pi$
$47$	−0.403164			−0.0588075			−0.0294037	+	0.999568i	$0.509361\pi$
$48$	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	$-0.671959\pi$
$53$	3.42609	−	7.50209i	0.470610	−	1.03049i	0.984940	−	0.172899i	$-0.0553135\pi$
$54$	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	0.137751	−	0.990467i	$-0.456013\pi$
$67$	6.45923	−	1.89660i	0.789121	−	0.231707i	0.651370	+	0.758760i	$0.274195\pi$
$68$	−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	0.0773434	−	0.997005i	$-0.475356\pi$
$73$	8.68396	−	5.58084i	1.01638	−	0.653188i	0.939037	+	0.343817i	$0.111720\pi$
$74$	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	$0.194715\pi$
$83$	−1.17187	+	8.15053i	−0.128629	+	0.894637i	−0.947294	+	0.320365i	$0.896194\pi$
$84$	−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	$-0.875684\pi$
$97$	−1.42525	−	9.91281i	−0.144712	−	1.00649i	0.779987	−	0.625795i	$-0.215225\pi$
$98$	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	0.833717	−	0.552192i	$-0.186208\pi$
$103$	12.5496	+	3.68489i	1.23655	+	0.363083i	0.402830	+	0.915275i	$0.368027\pi$
$104$	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	−0.822552	−	0.568690i	$-0.807450\pi$
$107$	−1.47495	+	1.70218i	−0.142588	+	0.164556i	0.679963	+	0.733246i	$0.261996\pi$
$108$	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	−0.512937	−	0.858426i	$-0.671443\pi$
$113$	−5.10615	+	1.49930i	−0.480346	+	0.141042i	0.0325904	+	0.999469i	$0.489624\pi$
$114$	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	−0.109194	−	0.994020i	$-0.534827\pi$
$127$	−8.32204	−	2.44357i	−0.738461	−	0.216832i	−0.629268	+	0.777189i	$0.716645\pi$
$128$	−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	$-0.352158\pi$
$137$	10.4860			0.895881			0.447940	+	0.894063i	$0.352158\pi$
$138$	−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	−0.578150	−	0.815931i	$-0.696225\pi$
$157$	−0.953842	+	0.612997i	−0.0761249	+	0.0489225i	0.502025	+	0.864853i	$0.332589\pi$
$158$	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	−0.559651	−	0.828728i	$-0.689065\pi$
$163$	−7.43577	+	2.18334i	−0.582415	+	0.171012i	−0.0227638	+	0.999741i	$0.507247\pi$
$164$	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	0.192321	−	0.981332i	$-0.438399\pi$
$167$	−8.01781	−	5.15274i	−0.620437	−	0.398731i	−0.812758	+	0.582601i	$0.802035\pi$
$168$	−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	0.664260	−	0.747502i	$-0.268747\pi$
$173$	10.7715	+	3.16279i	0.818941	+	0.240463i	0.154681	+	0.987964i	$0.450565\pi$
$174$	−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	$0.109188\pi$
$193$	−0.786454	+	5.46991i	−0.0566102	+	0.393733i	−0.998352	+	0.0573948i	$0.981721\pi$
$194$	−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	$0.107198\pi$
$197$	8.07729	+	17.6868i	0.575483	+	1.26013i	−0.368344	+	0.929690i	$0.620075\pi$
$198$	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	−0.827022	−	0.562169i	$-0.809967\pi$
$223$	2.08200	−	4.55894i	0.139421	−	0.305289i	0.966443	+	0.256880i	$0.0826944\pi$
$224$	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	0.973318	−	0.229461i	$-0.0736963\pi$
$227$	9.15555	+	10.5661i	0.607675	+	0.701294i	−0.365643	+	0.930755i	$0.619151\pi$
$228$	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	0.852180	−	0.523248i	$-0.175280\pi$
$233$	3.25100	+	3.75185i	0.212980	+	0.245792i	−0.639200	+	0.769040i	$0.720735\pi$
$234$	−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	−0.692214	−	0.721693i	$-0.743364\pi$
$257$	−5.18281	+	3.33079i	−0.323295	+	0.207769i	0.368919	+	0.929462i	$0.379728\pi$
$258$	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	$0.0820409\pi$
$263$	8.53638	+	18.6921i	0.526376	+	1.15260i	−0.440593	+	0.897707i	$0.645232\pi$
$264$	−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	$-0.596937\pi$
$277$	−9.98105			−0.599703			−0.299852	+	0.953986i	$0.596937\pi$
$278$	−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	−0.976147	−	0.217113i	$-0.930336\pi$
$283$	−2.90734	+	6.36619i	−0.172824	+	0.378431i	0.803323	+	0.595544i	$0.203063\pi$
$284$	−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	0.259623	−	0.965710i	$-0.416402\pi$
$293$	−8.74634	−	5.62093i	−0.510966	−	0.328378i	−0.770589	+	0.637332i	$0.780038\pi$
$294$	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	−0.704773	−	0.709432i	$-0.748951\pi$
$307$	1.71250	−	1.97633i	0.0977376	−	0.112795i	0.802511	+	0.596637i	$0.203497\pi$
$308$	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	$-0.798682\pi$
$313$	2.36838	−	16.4725i	0.133869	−	0.931079i	0.940444	−	0.339948i	$-0.110409\pi$
$314$	−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	$-0.782065\pi$
$317$	−3.73091	−	25.9491i	−0.209549	−	1.45744i	0.565084	−	0.825033i	$-0.308844\pi$
$318$	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	−0.385220	−	0.922825i	$-0.625874\pi$
$337$	10.7031	−	12.3520i	0.583034	−	0.672857i	0.968254	+	0.249967i	$0.0804199\pi$
$338$	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	−0.771755	−	0.635920i	$-0.780621\pi$
$347$	−20.0659	+	5.89187i	−1.07719	+	0.316292i	−0.305437	+	0.952212i	$0.598803\pi$
$348$	−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	−0.498446	−	0.866921i	$-0.666096\pi$
$353$	8.08999	−	9.33634i	0.430587	−	0.496923i	0.929033	+	0.369997i	$0.120641\pi$
$354$	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	$-0.430113\pi$
$367$	8.34483			0.435596			0.217798	+	0.975994i	$0.430113\pi$
$368$	−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	$-0.793553\pi$
$373$	−3.91020	−	27.1960i	−0.202462	−	1.40816i	0.594485	−	0.804107i	$-0.297356\pi$
$374$	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	−0.912061	−	0.410055i	$-0.865510\pi$
$383$	−7.36591	+	8.50071i	−0.376380	+	0.434366i	0.535681	+	0.844421i	$0.320055\pi$
$384$	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	0.792514	−	0.609854i	$-0.208772\pi$
$397$	11.2972	+	7.26030i	0.566992	+	0.364384i	−0.225521	+	0.974238i	$0.572408\pi$
$398$	−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	$0.654441\pi$
$433$	−30.4798	+	19.5882i	−1.46476	+	0.941346i	−0.998388	+	0.0567597i	$0.981923\pi$
$434$	−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	0.318405	−	0.947955i	$-0.396853\pi$
$443$	−8.66351	−	5.56770i	−0.411616	−	0.264529i	−0.730020	+	0.683426i	$0.760489\pi$
$444$	−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	0.922804	−	0.385271i	$-0.125892\pi$
$457$	8.76749	+	10.1182i	0.410126	+	0.473310i	−0.512678	+	0.858581i	$0.671346\pi$
$458$	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	0.978807	−	0.204786i	$-0.0656498\pi$
$463$	13.7024	+	15.8135i	0.636807	+	0.734914i	−0.342000	+	0.939700i	$0.611104\pi$
$464$	−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	$0.410503\pi$
$467$	−13.6210	+	29.8259i	−0.630307	+	1.38018i	−0.907780	+	0.419446i	$0.862224\pi$
$468$	−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	−0.878172	−	0.478345i	$-0.841237\pi$
$487$	−17.8279	+	11.4573i	−0.807860	+	0.519180i	0.0703122	+	0.997525i	$0.477600\pi$
$488$	−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	0.996240	−	0.0866353i	$-0.0276115\pi$
$503$	17.2403	+	19.8964i	0.768707	+	0.887135i	−0.227533	+	0.973770i	$0.573066\pi$
$504$	−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	0.643972	−	0.765049i	$-0.277285\pi$
$523$	4.93004	+	3.16834i	0.215576	+	0.138542i	−0.428397	+	0.903591i	$0.640921\pi$
$524$	−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	$0.0945624\pi$
$547$	2.83470	+	19.7158i	0.121203	+	0.842986i	−0.834993	+	0.550260i	$0.814529\pi$
$548$	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	$0.358617\pi$
$557$	6.41476	+	44.6156i	0.271802	+	1.89042i	−0.157903	+	0.987455i	$0.550473\pi$
$558$	−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	−0.121751	−	0.992561i	$-0.538851\pi$
$563$	−18.0518	−	5.30049i	−0.760794	−	0.223389i	−0.639042	+	0.769172i	$0.720669\pi$
$564$	−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	−0.576484	−	0.817108i	$-0.695576\pi$
$577$	−14.8855	+	4.37078i	−0.619692	+	0.181958i	−0.0432076	+	0.999066i	$0.513758\pi$
$578$	−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	−0.774078	−	0.633090i	$-0.781786\pi$
$587$	−42.8243	−	12.5744i	−1.76755	−	0.518999i	−0.993470	+	0.114091i	$0.963604\pi$
$588$	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	$-0.987897\pi$
$593$	−1.24649	−	8.66953i	−0.0511872	−	0.356015i	0.948090	−	0.318002i	$-0.103012\pi$
$594$	−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	−0.977281	−	0.211947i	$-0.932020\pi$
$607$	0.495843	−	3.44867i	0.0201257	−	0.139977i	0.997407	+	0.0719701i	$0.0229286\pi$
$608$	−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	−0.928249	−	0.371960i	$-0.878686\pi$
$613$	−10.5961	+	12.2285i	−0.427971	+	0.493905i	0.500278	+	0.865865i	$0.333231\pi$
$614$	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	0.169544	−	0.985523i	$-0.445771\pi$
$617$	28.2285	−	18.1414i	1.13644	−	0.730344i	0.966894	+	0.255178i	$0.0821342\pi$
$618$	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	$-0.389201\pi$
$643$	17.2988			0.682198			0.341099	+	0.940027i	$0.389201\pi$
$644$	−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	$0.0291461\pi$
$647$	24.0270	+	27.7286i	0.944599	+	1.09012i	−0.0512122	+	0.998688i	$0.516308\pi$
$648$	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	$0.259497\pi$
$653$	−4.53054	+	31.5106i	−0.177294	+	1.23311i	−0.862991	+	0.505219i	$0.831412\pi$
$654$	−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	0.585702	−	0.810527i	$-0.300819\pi$
$673$	2.37968	+	1.52933i	0.0917298	+	0.0589511i	−0.493972	+	0.869478i	$0.664455\pi$
$674$	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	0.895053	−	0.445960i	$-0.147138\pi$
$677$	−0.731565	−	1.60190i	−0.0281163	−	0.0615662i	−0.923169	+	0.384394i	$0.874410\pi$
$678$	−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	−0.778139	−	0.628092i	$-0.783836\pi$
$683$	5.38662	−	11.7951i	0.206113	−	0.451326i	0.984253	+	0.176766i	$0.0565636\pi$
$684$	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	$-0.791632\pi$
$727$	3.75859	−	26.1416i	0.139398	−	0.969538i	0.932686	−	0.360690i	$-0.117459\pi$
$728$	−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	$0.213712\pi$
$733$	34.8517	+	40.2210i	1.28728	+	1.48560i	0.504322	+	0.863516i	$0.331743\pi$
$734$	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	$-0.667225\pi$
$743$	13.1040	−	28.6938i	0.480741	−	1.05267i	0.982259	−	0.187528i	$-0.0600476\pi$
$744$	−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	−0.245550	−	0.969384i	$-0.578969\pi$
$757$	1.98009	−	0.581408i	0.0719678	−	0.0211316i	0.317518	+	0.948252i	$0.397151\pi$
$758$	−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	$-0.886700\pi$
$773$	1.67397	−	11.6427i	0.0602085	−	0.418759i	0.997527	−	0.0702852i	$-0.0223909\pi$
$774$	−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	$-0.827075\pi$
$787$	−5.05835	−	35.1816i	−0.180311	−	1.25409i	0.675718	−	0.737160i	$-0.263834\pi$
$788$	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	−0.683703	−	0.729761i	$-0.739631\pi$
$797$	3.83750	−	4.42871i	0.135931	−	0.156873i	0.819634	+	0.572888i	$0.194177\pi$
$798$	−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	$0.218591\pi$
$823$	6.02292	+	41.8903i	0.209946	+	1.46020i	−0.563381	+	0.826197i	$0.690500\pi$
$824$	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	$-0.315616\pi$
$827$	31.4841			1.09481			0.547406	+	0.836867i	$0.315616\pi$
$828$	−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	−0.544863	−	0.838525i	$-0.683418\pi$
$853$	−16.0602	+	4.71569i	−0.549890	+	0.161462i	−0.00502706	+	0.999987i	$0.501600\pi$
$854$	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	−0.189883	−	0.981807i	$-0.560811\pi$
$857$	−34.0126	−	21.8585i	−1.16185	−	0.746673i	−0.971963	+	0.235133i	$0.924447\pi$
$858$	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	−0.160199	−	0.987085i	$-0.551214\pi$
$863$	−24.3424	−	7.14758i	−0.828626	−	0.243307i	−0.668427	+	0.743778i	$0.733032\pi$
$864$	−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	0.965714	−	0.259609i	$-0.0835937\pi$
$877$	16.9189	+	19.5255i	0.571312	+	0.659329i	−0.394402	+	0.918938i	$0.629048\pi$
$878$	−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	−0.980608	−	0.195981i	$-0.937211\pi$
$883$	0.460370	−	3.20194i	0.0154927	−	0.107754i	0.996100	+	0.0882269i	$0.0281201\pi$
$884$	−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	$0.00541528\pi$
$887$	10.6605	+	23.3433i	0.357946	+	0.783792i	−0.641909	+	0.766781i	$0.721857\pi$
$888$	−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	0.782195	−	0.623034i	$-0.214100\pi$
$907$	−6.05013	−	13.2479i	−0.200891	−	0.439890i	−0.983086	+	0.183143i	$0.941373\pi$
$908$	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	0.880261	−	0.474489i	$-0.157367\pi$
$937$	24.9268	+	16.0195i	0.814325	+	0.523335i	−0.0659368	+	0.997824i	$0.521004\pi$
$938$	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	$-0.320294\pi$
$947$	46.9537	−	30.1753i	1.52579	−	0.980565i	0.990744	−	0.135742i	$-0.0433419\pi$
$948$	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	$-0.885242\pi$
$953$	−18.1999	−	39.8521i	−0.589551	−	1.29094i	0.346162	−	0.938175i	$-0.387485\pi$
$954$	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	$-0.569161\pi$
$967$	−13.4070			−0.431139			−0.215570	+	0.976488i	$0.569161\pi$
$968$	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	−0.342846	−	0.939392i	$-0.611391\pi$
$977$	−35.6061	−	10.4549i	−1.13914	−	0.334482i	−0.796294	+	0.604910i	$0.793209\pi$
$978$	−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	0.895404	−	0.445254i	$-0.146887\pi$
$983$	27.0372	+	17.3757i	0.862352	+	0.554200i	−0.0330527	+	0.999454i	$0.510523\pi$
$984$	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	−0.914104	−	0.405480i	$-0.867104\pi$
$997$	−12.0826	+	13.9441i	−0.382660	+	0.441613i	0.531444	+	0.847094i	$0.321650\pi$
$998$	−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.101.10		100
5.2	odd	4		115.2.j.a.9.10	yes	100
5.3	odd	4		115.2.j.a.9.1	✓	100
5.4	even	2	inner	575.2.k.g.101.1		100
23.18	even	11	inner	575.2.k.g.501.10		100
115.18	odd	44		115.2.j.a.64.10	yes	100
115.64	even	22	inner	575.2.k.g.501.1		100
115.87	odd	44		115.2.j.a.64.1	yes	100

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