LMFDB - Embedded newform 875.2.bb.c.768.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [875,2,Mod(82,875)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("875.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(875, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([27, 50])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.bb (of order $60$, degree $16$, not minimal)

Newform invariants

comment:select newform

sage:traces = [288,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			768.17
Character	$\chi$	$=$	875.768
Dual form			875.2.bb.c.507.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.17136 - 1.41010i) q^{2} +(-2.28251 + 0.876172i) q^{3} +(1.91296 - 4.29657i) q^{4} +(-3.72066 + 5.12104i) q^{6} +(0.791332 + 2.52464i) q^{7} +(-1.09484 - 6.91252i) q^{8} +(2.21272 - 1.99235i) q^{9} +(3.62858 - 4.02995i) q^{11} +(-0.601800 + 11.4830i) q^{12} +(-0.126124 - 0.247532i) q^{13} +(5.27825 + 4.36604i) q^{14} +(-5.83052 - 6.47545i) q^{16} +(3.51929 - 2.84986i) q^{17} +(1.99522 - 7.44626i) q^{18} +(0.0187763 - 0.00835976i) q^{19} +(-4.01824 - 5.06916i) q^{21} +(2.19634 - 13.8671i) q^{22} +(-2.97345 - 4.57872i) q^{23} +(8.55552 + 14.8186i) q^{24} +(-0.622904 - 0.359634i) q^{26} +(0.0249589 - 0.0489845i) q^{27} +(12.3611 + 1.42951i) q^{28} +(-0.413497 - 0.569129i) q^{29} +(4.01573 + 0.422070i) q^{31} +(-8.27077 - 2.21615i) q^{32} +(-4.75134 + 12.3777i) q^{33} +(3.62306 - 11.1506i) q^{34} +(-4.32741 - 13.3184i) q^{36} +(-0.0237221 - 0.00124322i) q^{37} +(0.0289821 - 0.0446285i) q^{38} +(0.504758 + 0.454487i) q^{39} +(-5.37154 - 1.74532i) q^{41} +(-15.8731 - 5.34086i) q^{42} +(4.35752 + 4.35752i) q^{43} +(-10.3736 - 23.2996i) q^{44} +(-12.9129 - 5.74918i) q^{46} +(2.16788 - 2.67711i) q^{47} +(18.9818 + 9.67172i) q^{48} +(-5.74759 + 3.99565i) q^{49} +(-5.53583 + 9.58833i) q^{51} +(-1.30481 + 0.0683820i) q^{52} +(-1.33455 - 3.47662i) q^{53} +(-0.0148783 - 0.141557i) q^{54} +(16.5852 - 8.23416i) q^{56} +(-0.0355325 + 0.0355325i) q^{57} +(-1.70038 - 0.652714i) q^{58} +(-5.48952 + 1.16683i) q^{59} +(-0.400242 + 1.88299i) q^{61} +(9.31476 - 4.74610i) q^{62} +(6.78095 + 4.00972i) q^{63} +(-4.50960 + 1.46526i) q^{64} +(7.13684 + 33.5762i) q^{66} +(9.56525 + 11.8121i) q^{67} +(-5.51240 - 20.5725i) q^{68} +(10.7987 + 7.84569i) q^{69} +(1.09682 - 0.796887i) q^{71} +(-16.1947 - 13.1142i) q^{72} +(0.429591 + 8.19708i) q^{73} +(-0.0532622 + 0.0307510i) q^{74} -0.0966658i q^{76} +(13.0456 + 5.97183i) q^{77} +(1.73688 + 0.275095i) q^{78} +(2.52418 - 0.265302i) q^{79} +(-0.947755 + 9.01728i) q^{81} +(-14.1246 + 3.78468i) q^{82} +(6.74923 - 1.06897i) q^{83} +(-29.4667 + 7.56756i) q^{84} +(15.6063 + 3.31721i) q^{86} +(1.44246 + 0.936747i) q^{87} +(-31.8298 - 20.6705i) q^{88} +(-8.02339 - 1.70542i) q^{89} +(0.525122 - 0.514296i) q^{91} +(-25.3609 + 4.01677i) q^{92} +(-9.53573 + 2.55509i) q^{93} +(0.932265 - 8.86991i) q^{94} +(20.8198 - 2.18825i) q^{96} +(-13.8647 - 2.19595i) q^{97} +(-6.84583 + 16.7807i) q^{98} -16.1466i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 8 q^{2} + 24 q^{3} - 10 q^{4} + 10 q^{7} + 36 q^{8} - 10 q^{9} - 6 q^{11} + 36 q^{12} - 20 q^{14} - 30 q^{16} + 42 q^{17} + 14 q^{18} - 30 q^{19} - 12 q^{21} - 32 q^{22} + 40 q^{23} - 48 q^{26}+ \cdots - 222 q^{98}+O(q^{100}) $ 288 * q + 8 * q^2 + 24 * q^3 - 10 * q^4 + 10 * q^7 + 36 * q^8 - 10 * q^9 - 6 * q^11 + 36 * q^12 - 20 * q^14 - 30 * q^16 + 42 * q^17 + 14 * q^18 - 30 * q^19 - 12 * q^21 - 32 * q^22 + 40 * q^23 - 48 * q^26 - 22 * q^28 - 18 * q^31 - 8 * q^32 + 30 * q^33 + 40 * q^36 + 10 * q^37 - 72 * q^38 + 30 * q^39 - 6 * q^42 + 108 * q^43 - 10 * q^44 - 6 * q^46 + 54 * q^47 - 16 * q^51 - 216 * q^52 - 50 * q^53 - 30 * q^54 + 4 * q^56 + 216 * q^57 + 4 * q^58 + 90 * q^59 - 18 * q^61 + 66 * q^63 - 100 * q^64 - 90 * q^66 - 4 * q^67 - 342 * q^68 - 24 * q^71 - 58 * q^72 + 6 * q^73 + 80 * q^77 + 132 * q^78 - 10 * q^79 - 10 * q^81 - 216 * q^82 + 20 * q^84 - 6 * q^86 + 48 * q^87 + 122 * q^88 + 120 * q^89 - 12 * q^91 + 4 * q^92 - 106 * q^93 - 30 * q^94 - 90 * q^96 - 222 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	2.17136	−	1.41010i	1.53538	−	0.997090i	0.548410	−	0.836210i	$-0.315233\pi$
$2$	2.17136	−	1.41010i	1.53538	−	0.997090i	0.986974	−	0.160880i	$-0.0514334\pi$
$3$	−2.28251	+	0.876172i	−1.31781	+	0.505858i	−0.912782	−	0.408448i	$-0.866070\pi$
$3$	−2.28251	+	0.876172i	−1.31781	+	0.505858i	−0.405024	+	0.914306i	$0.632737\pi$
$4$	1.91296	−	4.29657i	0.956479	−	2.14829i
$5$		0			0
$5$		0			0
$6$	−3.72066	+	5.12104i	−1.51895	+	2.09066i
$7$	0.791332	+	2.52464i	0.299095	+	0.954223i
$7$	0.791332	+	2.52464i	0.299095	+	0.954223i
$8$	−1.09484	−	6.91252i	−0.387083	−	2.44394i
$9$	2.21272	−	1.99235i	0.737575	−	0.664115i
$10$		0			0
$11$	3.62858	−	4.02995i	1.09406	−	1.21508i	0.119055	−	0.992888i	$-0.462013\pi$
$11$	3.62858	−	4.02995i	1.09406	−	1.21508i	0.975004	−	0.222188i	$-0.0713199\pi$
$12$	−0.601800	+	11.4830i	−0.173725	+	3.31487i
$13$	−0.126124	−	0.247532i	−0.0349804	−	0.0686529i	0.872855	−	0.487980i	$-0.162266\pi$
$13$	−0.126124	−	0.247532i	−0.0349804	−	0.0686529i	−0.907835	+	0.419327i	$0.862266\pi$
$14$	5.27825	+	4.36604i	1.41067	+	1.16687i
$15$		0			0
$16$	−5.83052	−	6.47545i	−1.45763	−	1.61886i
$17$	3.51929	−	2.84986i	0.853553	−	0.691193i	−0.0991581	−	0.995072i	$-0.531615\pi$
$17$	3.51929	−	2.84986i	0.853553	−	0.691193i	0.952711	+	0.303878i	$0.0982816\pi$
$18$	1.99522	−	7.44626i	0.470278	−	1.75510i
$19$	0.0187763	−	0.00835976i	0.00430759	−	0.00191786i	−0.404582	−	0.914502i	$-0.632583\pi$
$19$	0.0187763	−	0.00835976i	0.00430759	−	0.00191786i	0.408889	+	0.912584i	$0.365916\pi$
$20$		0			0
$21$	−4.01824	−	5.06916i	−0.876851	−	1.10618i
$22$	2.19634	−	13.8671i	0.468261	−	2.95648i
$23$	−2.97345	−	4.57872i	−0.620008	−	0.954728i	−0.999563	−	0.0295591i	$-0.990590\pi$
$23$	−2.97345	−	4.57872i	−0.620008	−	0.954728i	0.379555	−	0.925169i	$-0.376077\pi$
$24$	8.55552	+	14.8186i	1.74639	+	3.02483i
$25$		0			0
$26$	−0.622904	−	0.359634i	−0.122162	−	0.0705300i
$27$	0.0249589	−	0.0489845i	0.00480333	−	0.00942707i
$28$	12.3611	+	1.42951i	2.33602	+	0.270152i
$29$	−0.413497	−	0.569129i	−0.0767844	−	0.105685i	0.768897	−	0.639372i	$-0.220806\pi$
$29$	−0.413497	−	0.569129i	−0.0767844	−	0.105685i	−0.845682	+	0.533688i	$0.820806\pi$
$30$		0			0
$31$	4.01573	+	0.422070i	0.721246	+	0.0758060i	0.458037	−	0.888933i	$-0.348553\pi$
$31$	4.01573	+	0.422070i	0.721246	+	0.0758060i	0.263209	+	0.964739i	$0.415219\pi$
$32$	−8.27077	−	2.21615i	−1.46208	−	0.391763i
$33$	−4.75134	+	12.3777i	−0.827101	+	2.15467i
$34$	3.62306	−	11.1506i	0.621349	−	1.91232i
$35$		0			0
$36$	−4.32741	−	13.3184i	−0.721235	−	2.21973i
$37$	−0.0237221	−	0.00124322i	−0.00389988	−	0.000204384i	0.0503859	−	0.998730i	$-0.483955\pi$
$37$	−0.0237221	−	0.00124322i	−0.00389988	−	0.000204384i	−0.0542858	+	0.998525i	$0.517288\pi$
$38$	0.0289821	−	0.0446285i	0.00470152	−	0.00723970i
$39$	0.504758	+	0.454487i	0.0808260	+	0.0727761i
$40$		0			0
$41$	−5.37154	−	1.74532i	−0.838894	−	0.272573i	−0.142107	−	0.989851i	$-0.545388\pi$
$41$	−5.37154	−	1.74532i	−0.838894	−	0.272573i	−0.696787	+	0.717278i	$0.745388\pi$
$42$	−15.8731	−	5.34086i	−2.44927	−	0.824113i
$43$	4.35752	+	4.35752i	0.664515	+	0.664515i	0.956441	−	0.291926i	$-0.0942961\pi$
$43$	4.35752	+	4.35752i	0.664515	+	0.664515i	−0.291926	+	0.956441i	$0.594296\pi$
$44$	−10.3736	−	23.2996i	−1.56389	−	3.51255i
$45$		0			0
$46$	−12.9129	−	5.74918i	−1.90390	−	0.847671i
$47$	2.16788	−	2.67711i	0.316218	−	0.390497i	−0.594110	−	0.804384i	$-0.702496\pi$
$47$	2.16788	−	2.67711i	0.316218	−	0.390497i	0.910328	+	0.413887i	$0.135829\pi$
$48$	18.9818	+	9.67172i	2.73979	+	1.39599i
$49$	−5.74759	+	3.99565i	−0.821084	+	0.570807i
$50$		0			0
$51$	−5.53583	+	9.58833i	−0.775171	+	1.34264i
$52$	−1.30481	+	0.0683820i	−0.180944	+	0.00948288i
$53$	−1.33455	−	3.47662i	−0.183315	−	0.477551i	0.810872	−	0.585224i	$-0.198993\pi$
$53$	−1.33455	−	3.47662i	−0.183315	−	0.477551i	−0.994186	+	0.107673i	$0.965660\pi$
$54$	−0.0148783	−	0.141557i	−0.00202468	−	0.0192635i
$55$		0			0
$56$	16.5852	−	8.23416i	2.21629	−	1.10034i
$57$	−0.0355325	+	0.0355325i	−0.00470640	+	0.00470640i
$58$	−1.70038	−	0.652714i	−0.223271	−	0.0857056i
$59$	−5.48952	+	1.16683i	−0.714674	+	0.151909i	−0.550878	−	0.834586i	$-0.685707\pi$
$59$	−5.48952	+	1.16683i	−0.714674	+	0.151909i	−0.163796	+	0.986494i	$0.552374\pi$
$60$		0			0
$61$	−0.400242	+	1.88299i	−0.0512457	+	0.241092i	−0.996314	−	0.0857806i	$-0.972662\pi$
$61$	−0.400242	+	1.88299i	−0.0512457	+	0.241092i	0.945068	+	0.326873i	$0.105995\pi$
$62$	9.31476	−	4.74610i	1.18298	−	0.602756i
$63$	6.78095	+	4.00972i	0.854319	+	0.505177i
$64$	−4.50960	+	1.46526i	−0.563700	+	0.183157i
$65$		0			0
$66$	7.13684	+	33.5762i	0.878484	+	4.13294i
$67$	9.56525	+	11.8121i	1.16858	+	1.44308i	0.872973	+	0.487768i	$0.162189\pi$
$67$	9.56525	+	11.8121i	1.16858	+	1.44308i	0.295608	+	0.955309i	$0.404478\pi$
$68$	−5.51240	−	20.5725i	−0.668476	−	2.49479i
$69$	10.7987	+	7.84569i	1.30001	+	0.944510i
$70$		0			0
$71$	1.09682	−	0.796887i	0.130169	−	0.0945731i	−0.520796	−	0.853681i	$-0.674365\pi$
$71$	1.09682	−	0.796887i	0.130169	−	0.0945731i	0.650964	+	0.759108i	$0.274365\pi$
$72$	−16.1947	−	13.1142i	−1.90856	−	1.54552i
$73$	0.429591	+	8.19708i	0.0502798	+	0.959396i	0.901011	+	0.433796i	$0.142826\pi$
$73$	0.429591	+	8.19708i	0.0502798	+	0.959396i	−0.850731	+	0.525601i	$0.823841\pi$
$74$	−0.0532622	+	0.0307510i	−0.00619161	+	0.00357473i
$75$		0			0
$76$		−	0.0966658i		−	0.0110883i
$77$	13.0456	+	5.97183i	1.48668	+	0.680553i
$78$	1.73688	+	0.275095i	0.196663	+	0.0311484i
$79$	2.52418	−	0.265302i	0.283992	−	0.0298488i	0.0385386	−	0.999257i	$-0.487730\pi$
$79$	2.52418	−	0.265302i	0.283992	−	0.0298488i	0.245454	+	0.969408i	$0.421063\pi$
$80$		0			0
$81$	−0.947755	+	9.01728i	−0.105306	+	1.00192i
$82$	−14.1246	+	3.78468i	−1.55980	+	0.417948i
$83$	6.74923	−	1.06897i	0.740825	−	0.117335i	0.225396	−	0.974267i	$-0.427633\pi$
$83$	6.74923	−	1.06897i	0.740825	−	0.117335i	0.515429	+	0.856932i	$0.327633\pi$
$84$	−29.4667	+	7.56756i	−3.21508	+	0.825689i
$85$		0			0
$86$	15.6063	+	3.31721i	1.68287	+	0.357704i
$87$	1.44246	+	0.936747i	0.154648	+	0.100430i
$88$	−31.8298	−	20.6705i	−3.39307	−	2.20348i
$89$	−8.02339	−	1.70542i	−0.850478	−	0.180775i	−0.238003	−	0.971265i	$-0.576493\pi$
$89$	−8.02339	−	1.70542i	−0.850478	−	0.180775i	−0.612475	+	0.790490i	$0.709826\pi$
$90$		0			0
$91$	0.525122	−	0.514296i	0.0550477	−	0.0539129i
$92$	−25.3609	+	4.01677i	−2.64405	+	0.418777i
$93$	−9.53573	+	2.55509i	−0.988809	+	0.264951i
$94$	0.932265	−	8.86991i	0.0961558	−	0.914861i
$95$		0			0
$96$	20.8198	−	2.18825i	2.12491	−	0.223337i
$97$	−13.8647	−	2.19595i	−1.40775	−	0.222965i	−0.594130	−	0.804369i	$-0.702504\pi$
$97$	−13.8647	−	2.19595i	−1.40775	−	0.222965i	−0.813615	+	0.581404i	$0.802504\pi$
$98$	−6.84583	+	16.7807i	−0.691533	+	1.69510i
$99$		−	16.1466i		−	1.62279i
$100$		0			0
$101$	−1.86039	+	1.07409i	−0.185115	+	0.106876i	−0.589694	−	0.807627i	$-0.700752\pi$
$101$	−1.86039	+	1.07409i	−0.185115	+	0.106876i	0.404579	+	0.914503i	$0.367418\pi$
$102$	1.50021	+	28.6258i	0.148543	+	2.83438i
$103$	7.91574	+	6.41004i	0.779961	+	0.631600i	0.934328	−	0.356414i	$-0.116001\pi$
$103$	7.91574	+	6.41004i	0.779961	+	0.631600i	−0.154368	+	0.988013i	$0.549334\pi$
$104$	−1.57298	+	1.14284i	−0.154244	+	0.112065i
$105$		0			0
$106$	−7.80017	−	5.66716i	−0.757620	−	0.550443i
$107$	−1.63621	−	6.10643i	−0.158179	−	0.590331i	−0.998812	−	0.0487267i	$-0.984484\pi$
$107$	−1.63621	−	6.10643i	−0.158179	−	0.590331i	0.840633	−	0.541605i	$-0.182183\pi$
$108$	−0.162720	−	0.200943i	−0.0156578	−	0.0193357i
$109$	3.50177	+	16.4745i	0.335408	+	1.57797i	0.745868	+	0.666094i	$0.232035\pi$
$109$	3.50177	+	16.4745i	0.335408	+	1.57797i	−0.410460	+	0.911879i	$0.634632\pi$
$110$		0			0
$111$	0.0552351	−	0.0179470i	0.00524268	−	0.00170345i
$112$	11.7343	−	19.8442i	1.10879	−	1.87510i
$113$	−1.89387	+	0.964975i	−0.178160	+	0.0907772i	−0.540796	−	0.841154i	$-0.681877\pi$
$113$	−1.89387	+	0.964975i	−0.178160	+	0.0907772i	0.362636	+	0.931931i	$0.381877\pi$
$114$	−0.0270496	+	0.127258i	−0.00253342	+	0.0119188i
$115$		0			0
$116$	−3.23631	+	0.687899i	−0.300484	+	0.0638698i
$117$	−0.772245	−	0.296437i	−0.0713941	−	0.0274056i
$118$	−10.2744	+	10.2744i	−0.945833	+	0.945833i
$119$	9.97980	+	6.62974i	0.914846	+	0.607747i
$120$		0			0
$121$	−1.92407	−	18.3063i	−0.174915	−	1.66421i
$122$	1.78613	+	4.65303i	0.161709	+	0.421266i
$123$	13.7898	−	0.722692i	1.24338	−	0.0651629i
$124$	9.49537	−	16.4465i	0.852710	−	1.47694i
$125$		0			0
$126$	20.3780	−	0.855257i	1.81542	−	0.0761923i
$127$	−9.31183	−	4.74461i	−0.826291	−	0.421016i	−0.0109096	−	0.999940i	$-0.503473\pi$
$127$	−9.31183	−	4.74461i	−0.826291	−	0.421016i	−0.815381	+	0.578924i	$0.803473\pi$
$128$	3.05134	−	3.76809i	0.269703	−	0.333055i
$129$	−13.7640	−	6.12812i	−1.21185	−	0.539551i
$130$		0			0
$131$	7.54242	+	16.9405i	0.658984	+	1.48010i	0.865113	+	0.501577i	$0.167247\pi$
$131$	7.54242	+	16.9405i	0.658984	+	1.48010i	−0.206129	+	0.978525i	$0.566087\pi$
$132$	44.0924	+	44.0924i	3.83775	+	3.83775i
$133$	0.0359637	+	0.0407881i	0.00311845	+	0.00353678i
$134$	37.4258	+	12.1604i	3.23310	+	1.05050i
$135$		0			0
$136$	−23.5528	−	21.2070i	−2.01963	−	1.81849i
$137$	−6.00254	+	9.24309i	−0.512831	+	0.789691i	−0.996325	−	0.0856572i	$-0.972701\pi$
$137$	−6.00254	+	9.24309i	−0.512831	+	0.789691i	0.483493	+	0.875348i	$0.339368\pi$
$138$	34.5110	+	1.80864i	2.93777	+	0.153962i
$139$	−1.73378	−	5.33603i	−0.147058	−	0.452597i	0.850212	−	0.526440i	$-0.176474\pi$
$139$	−1.73378	−	5.33603i	−0.147058	−	0.452597i	−0.997270	+	0.0738434i	$0.976474\pi$
$140$		0			0
$141$	−2.60260	+	8.00997i	−0.219178	+	0.674561i
$142$	1.25790	−	3.27695i	0.105561	−	0.274996i
$143$	−1.45519	−	0.389917i	−0.121689	−	0.0326065i
$144$	−25.8027	−	2.71197i	−2.15022	−	0.225998i
$145$		0			0
$146$	12.4915	+	17.1931i	1.03380	+	1.42291i
$147$	9.61803	−	14.1560i	0.793282	−	1.16757i
$148$	−0.0507209	+	0.0995454i	−0.00416923	+	0.00818258i
$149$	−2.27766	−	1.31501i	−0.186593	−	0.107730i	0.403794	−	0.914850i	$-0.367691\pi$
$149$	−2.27766	−	1.31501i	−0.186593	−	0.107730i	−0.590387	+	0.807121i	$0.701025\pi$
$150$		0			0
$151$	2.52619	+	4.37549i	0.205579	+	0.356073i	0.950317	−	0.311284i	$-0.100759\pi$
$151$	2.52619	+	4.37549i	0.205579	+	0.356073i	−0.744738	+	0.667357i	$0.767426\pi$
$152$	−0.0783440	−	0.120639i	−0.00635454	−	0.00978513i
$153$	2.10930	−	13.3176i	0.170527	−	1.07666i
$154$	36.7475	−	5.42855i	2.96120	−	0.437445i
$155$		0			0
$156$	2.91832	−	1.29932i	0.233652	−	0.104029i
$157$	1.62461	−	6.06312i	0.129658	−	0.483890i	−0.870305	−	0.492513i	$-0.836078\pi$
$157$	1.62461	−	6.06312i	0.129658	−	0.483890i	0.999963	+	0.00862335i	$0.00274493\pi$
$158$	5.10680	−	4.13540i	0.406275	−	0.328995i
$159$	6.09224	+	6.76612i	0.483146	+	0.536588i
$160$		0			0
$161$	9.20661	−	11.1302i	0.725582	−	0.877180i
$162$	10.6573	+	20.9162i	0.837320	+	1.64333i
$163$	−1.02197	+	19.5004i	−0.0800471	+	1.52739i	0.603429	+	0.797417i	$0.293801\pi$
$163$	−1.02197	+	19.5004i	−0.0800471	+	1.52739i	−0.683476	+	0.729973i	$0.739532\pi$
$164$	−17.7744	+	19.7405i	−1.38795	+	1.54147i
$165$		0			0
$166$	13.1477	−	11.8382i	1.02046	−	0.918823i
$167$	−2.80249	−	17.6942i	−0.216863	−	1.36922i	−0.820357	−	0.571852i	$-0.806225\pi$
$167$	−2.80249	−	17.6942i	−0.216863	−	1.36922i	0.603494	−	0.797367i	$-0.293775\pi$
$168$	−30.6413	+	33.3260i	−2.36403	+	2.57116i
$169$	7.59584	−	10.4548i	0.584296	−	0.804214i
$170$		0			0
$171$	0.0248913	−	0.0559068i	0.00190349	−	0.00427530i
$172$	27.0581	−	10.3866i	2.06316	−	0.791974i
$173$	−12.9168	+	8.38829i	−0.982049	+	0.637750i	−0.932556	−	0.361024i	$-0.882427\pi$
$173$	−12.9168	+	8.38829i	−0.982049	+	0.637750i	−0.0494928	+	0.998774i	$0.515760\pi$
$174$	4.45302			0.337582
$175$		0			0
$176$	−47.2523			−3.56177
$177$	11.5075	−	7.47307i	0.864958	−	0.561710i
$178$	−19.8265	+	7.61068i	−1.48606	+	0.570444i
$179$	0.204955	−	0.460337i	0.0153191	−	0.0344072i	−0.905724	−	0.423868i	$-0.860672\pi$
$179$	0.204955	−	0.460337i	0.0153191	−	0.0344072i	0.921043	+	0.389461i	$0.127339\pi$
$180$		0			0
$181$	−7.22957	+	9.95064i	−0.537369	+	0.739625i	−0.988231	−	0.152968i	$-0.951117\pi$
$181$	−7.22957	+	9.95064i	−0.537369	+	0.739625i	0.450862	+	0.892594i	$0.351117\pi$
$182$	0.415021	−	1.85720i	0.0307634	−	0.137665i
$183$	−0.736269	−	4.64862i	−0.0544266	−	0.343636i
$184$	−28.3950	+	25.5670i	−2.09331	+	1.88482i
$185$		0			0
$186$	−17.1026	+	18.9943i	−1.25402	+	1.39273i
$187$	1.28522	−	24.5235i	0.0939848	−	1.79334i
$188$	−7.35535	−	14.4357i	−0.536444	−	1.05283i
$189$	0.143419	+	0.0242491i	0.0104322	+	0.00176386i
$190$		0			0
$191$	−8.94987	−	9.93984i	−0.647590	−	0.719222i	0.326547	−	0.945181i	$-0.394115\pi$
$191$	−8.94987	−	9.93984i	−0.647590	−	0.719222i	−0.974137	+	0.225960i	$0.927448\pi$
$192$	9.00938	−	7.29565i	0.650196	−	0.526518i
$193$	0.646732	−	2.41364i	0.0465528	−	0.173737i	−0.938735	−	0.344639i	$-0.888001\pi$
$193$	0.646732	−	2.41364i	0.0465528	−	0.173737i	0.985288	+	0.170902i	$0.0546680\pi$
$194$	−33.2017	+	14.7824i	−2.38375	+	1.06131i
$195$		0			0
$196$	6.17272	+	32.3384i	0.440908	+	2.30989i
$197$	−4.03436	+	25.4720i	−0.287436	+	1.81480i	0.246348	+	0.969181i	$0.420769\pi$
$197$	−4.03436	+	25.4720i	−0.287436	+	1.81480i	−0.533784	+	0.845621i	$0.679231\pi$
$198$	−22.7682	−	35.0600i	−1.61807	−	2.49161i
$199$	9.50790	+	16.4682i	0.673997	+	1.16740i	0.976761	+	0.214332i	$0.0687573\pi$
$199$	9.50790	+	16.4682i	0.673997	+	1.16740i	−0.302764	+	0.953066i	$0.597909\pi$
$200$		0			0
$201$	−32.1822	−	18.5804i	−2.26996	−	1.31056i
$202$	−2.52499	+	4.95557i	−0.177658	+	0.348673i
$203$	1.10963	−	1.49430i	0.0778809	−	0.104879i
$204$	30.6072	+	42.1272i	2.14293	+	2.94949i
$205$		0			0
$206$	26.2267	+	2.75654i	1.82730	+	0.192057i
$207$	−15.7018	−	4.20729i	−1.09135	−	0.292427i
$208$	−0.867512	+	2.25995i	−0.0601511	+	0.156699i
$209$	0.0344421	−	0.106002i	0.00238241	−	0.00733230i
$210$		0			0
$211$	1.55379	+	4.78206i	0.106967	+	0.329211i	0.990187	−	0.139748i	$-0.0446293\pi$
$211$	1.55379	+	4.78206i	0.106967	+	0.329211i	−0.883220	+	0.468959i	$0.844629\pi$
$212$	−17.4905	−	0.916639i	−1.20125	−	0.0629550i
$213$	−1.80529	+	2.77990i	−0.123696	+	0.190476i
$214$	−12.1635	−	10.9521i	−0.831479	−	0.748667i
$215$		0			0
$216$	−0.365932	−	0.118899i	−0.0248985	−	0.00809002i
$217$	2.11220	+	10.4723i	0.143385	+	0.710903i
$218$	30.8343	+	30.8343i	2.08836	+	2.08836i
$219$	−8.16260	−	18.3335i	−0.551577	−	1.23886i
$220$		0			0
$221$	−1.14930	−	0.511700i	−0.0773101	−	0.0344207i
$222$	0.0946283	−	0.116856i	0.00635103	−	0.00784287i
$223$	−24.4072	−	12.4361i	−1.63443	−	0.832782i	−0.998116	−	0.0613496i	$-0.980460\pi$
$223$	−24.4072	−	12.4361i	−1.63443	−	0.832782i	−0.636311	−	0.771433i	$-0.719540\pi$
$224$	−0.949958	−	22.6344i	−0.0634717	−	1.51232i
$225$		0			0
$226$	−2.75157	+	4.76585i	−0.183031	+	0.317020i
$227$	−11.4176	+	0.598369i	−0.757810	+	0.0397151i	−0.427327	−	0.904097i	$-0.640545\pi$
$227$	−11.4176	+	0.598369i	−0.757810	+	0.0397151i	−0.330482	+	0.943812i	$0.607211\pi$
$228$	0.0846959	+	0.220640i	0.00560912	+	0.0146123i
$229$	−1.12550	−	10.7085i	−0.0743754	−	0.707634i	−0.966643	−	0.256128i	$-0.917553\pi$
$229$	−1.12550	−	10.7085i	−0.0743754	−	0.707634i	0.892268	−	0.451507i	$-0.149113\pi$
$230$		0			0
$231$	−35.0090	−	2.20057i	−2.30342	−	0.144787i
$232$	−3.48141	+	3.48141i	−0.228566	+	0.228566i
$233$	−6.47619	−	2.48598i	−0.424269	−	0.162862i	0.136859	−	0.990591i	$-0.456299\pi$
$233$	−6.47619	−	2.48598i	−0.424269	−	0.162862i	−0.561128	+	0.827729i	$0.689633\pi$
$234$	−2.09483	+	0.445270i	−0.136943	+	0.0291082i
$235$		0			0
$236$	−5.48783	+	25.8182i	−0.357227	+	1.68062i
$237$	−5.52900	+	2.81717i	−0.359147	+	0.182995i
$238$	31.0183	+	0.323063i	2.01062	+	0.0209411i
$239$	−16.7344	+	5.43732i	−1.08246	+	0.351711i	−0.795327	−	0.606181i	$-0.792701\pi$
$239$	−16.7344	+	5.43732i	−1.08246	+	0.351711i	−0.287129	+	0.957892i	$0.592701\pi$
$240$		0			0
$241$	0.222094	+	1.04487i	0.0143064	+	0.0673061i	0.984722	−	0.174136i	$-0.0557131\pi$
$241$	0.222094	+	1.04487i	0.0143064	+	0.0673061i	−0.970415	+	0.241442i	$0.922380\pi$
$242$	−29.9915	−	37.0364i	−1.92793	−	2.38079i
$243$	−5.69475	−	21.2531i	−0.365318	−	1.36339i
$244$	7.32476	+	5.32175i	0.468920	+	0.340690i
$245$		0			0
$246$	28.9235	−	21.0142i	1.84410	−	1.33981i
$247$	−0.00443745	−	0.00359337i	−0.000282348	−	0.000228641i
$248$	−1.47899	−	28.2209i	−0.0939162	−	1.79203i
$249$	−14.4686	+	8.35343i	−0.916908	+	0.529377i
$250$		0			0
$251$		−	20.3040i		−	1.28158i	−0.767716	−	0.640790i	$-0.778607\pi$
$251$		−	20.3040i		−	1.28158i	0.767716	−	0.640790i	$-0.221393\pi$
$252$	30.1997	−	21.4644i	1.90240	−	1.35213i
$253$	−29.2414	−	4.63139i	−1.83839	−	0.291173i
$254$	−26.9097	+	2.82832i	−1.68846	+	0.177465i
$255$		0			0
$256$	2.30346	−	21.9160i	0.143966	−	1.36975i
$257$	22.1448	−	5.93369i	1.38136	−	0.370133i	0.509742	−	0.860327i	$-0.329741\pi$
$257$	22.1448	−	5.93369i	1.38136	−	0.370133i	0.871613	+	0.490194i	$0.163074\pi$
$258$	−38.5278	+	6.10221i	−2.39864	+	0.379907i
$259$	−0.0156333	−	0.0608734i	−0.000971409	−	0.00378249i
$260$		0			0
$261$	−2.04886	−	0.435498i	−0.126821	−	0.0269566i
$262$	40.2651	+	26.1485i	2.48759	+	1.61546i
$263$	19.9431	+	12.9512i	1.22974	+	0.798604i	0.985262	−	0.171051i	$-0.0547163\pi$
$263$	19.9431	+	12.9512i	1.22974	+	0.798604i	0.244479	+	0.969654i	$0.421383\pi$
$264$	90.7627	+	19.2922i	5.58606	+	1.18735i
$265$		0			0
$266$	0.135605	+	0.0378533i	0.00831450	+	0.00232094i
$267$	19.8077	−	3.13723i	1.21221	−	0.191995i
$268$	69.0495	−	18.5017i	4.21787	−	1.13017i
$269$	−0.607763	+	5.78248i	−0.0370559	+	0.352564i	0.960246	+	0.279155i	$0.0900544\pi$
$269$	−0.607763	+	5.78248i	−0.0370559	+	0.352564i	−0.997302	+	0.0734086i	$0.976612\pi$
$270$		0			0
$271$	16.7703	−	1.76263i	1.01872	−	0.107072i	0.419584	−	0.907717i	$-0.362176\pi$
$271$	16.7703	−	1.76263i	1.01872	−	0.107072i	0.599140	+	0.800644i	$0.295509\pi$
$272$	−38.9734	−	6.17279i	−2.36311	−	0.374280i
$273$	−0.747982	+	1.63398i	−0.0452700	+	0.0988931i
$274$			28.5343i			1.72382i
$275$		0			0
$276$	54.3670	−	31.3888i	3.27251	−	1.88938i
$277$	1.09198	+	20.8362i	0.0656105	+	1.25192i	0.810901	+	0.585183i	$0.198977\pi$
$277$	1.09198	+	20.8362i	0.0656105	+	1.25192i	−0.745291	+	0.666740i	$0.767689\pi$
$278$	−11.2890	−	9.14165i	−0.677069	−	0.548280i
$279$	9.72661	−	7.06679i	0.582317	−	0.423078i
$280$		0			0
$281$	−10.0464	−	7.29912i	−0.599316	−	0.435429i	0.246320	−	0.969189i	$-0.420779\pi$
$281$	−10.0464	−	7.29912i	−0.599316	−	0.435429i	−0.845636	+	0.533760i	$0.820779\pi$
$282$	5.64367	+	21.0625i	0.336076	+	1.25425i
$283$	3.12173	+	3.85501i	0.185567	+	0.229157i	0.861437	−	0.507865i	$-0.169565\pi$
$283$	3.12173	+	3.85501i	0.185567	+	0.229157i	−0.675869	+	0.737021i	$0.736232\pi$
$284$	−1.32571	−	6.23698i	−0.0786665	−	0.370097i
$285$		0			0
$286$	−3.70957	+	1.20531i	−0.219351	+	0.0712715i
$287$	0.155628	−	14.9423i	0.00918642	−	0.882017i
$288$	−22.7163	+	11.5745i	−1.33857	+	0.682035i
$289$	0.729170	−	3.43047i	0.0428923	−	0.201793i
$290$		0			0
$291$	33.5703	−	7.13558i	1.96792	−	0.418295i
$292$	36.0412	+	13.8349i	2.10915	+	0.809627i
$293$	7.51221	−	7.51221i	0.438868	−	0.438868i	−0.452763	−	0.891631i	$-0.649562\pi$
$293$	7.51221	−	7.51221i	0.438868	−	0.438868i	0.891631	+	0.452763i	$0.149562\pi$
$294$	0.922892	−	44.3001i	0.0538242	−	2.58363i
$295$		0			0
$296$	0.0173780	+	0.165340i	0.00101007	+	0.00961021i
$297$	−0.106840	−	0.278327i	−0.00619948	−	0.0161502i
$298$	−6.79991	+	0.356368i	−0.393908	+	0.0206438i
$299$	−0.758354	+	1.31351i	−0.0438568	+	0.0759621i
$300$		0			0
$301$	−7.55291	+	14.4494i	−0.435342	+	0.832849i
$302$	11.6552	+	5.93860i	0.670679	+	0.341728i
$303$	3.30525	−	4.08165i	0.189882	−	0.234484i
$304$	−0.163609	−	0.0728435i	−0.00938362	−	0.00417786i
$305$		0			0
$306$	−14.1991	−	31.8916i	−0.811707	−	1.82312i
$307$	−2.99332	−	2.99332i	−0.170838	−	0.170838i	0.616510	−	0.787347i	$-0.288546\pi$
$307$	−2.99332	−	2.99332i	−0.170838	−	0.170838i	−0.787347	+	0.616510i	$0.788546\pi$
$308$	50.6140	−	44.6274i	2.88400	−	2.54288i
$309$	−23.6840	−	7.69540i	−1.34734	−	0.437776i
$310$		0			0
$311$	3.00568	+	2.70633i	0.170436	+	0.153462i	0.749935	−	0.661512i	$-0.230085\pi$
$311$	3.00568	+	2.70633i	0.170436	+	0.153462i	−0.579498	+	0.814973i	$0.696752\pi$
$312$	2.58902	−	3.98674i	0.146574	−	0.225705i
$313$	−14.3275	−	0.750874i	−0.809840	−	0.0424419i	−0.357079	−	0.934074i	$-0.616227\pi$
$313$	−14.3275	−	0.750874i	−0.809840	−	0.0424419i	−0.452760	+	0.891632i	$0.649561\pi$
$314$	−5.02199	−	15.4561i	−0.283407	−	0.872238i
$315$		0			0
$316$	3.68876	−	11.3528i	0.207509	−	0.638646i
$317$	−8.19543	+	21.3498i	−0.460301	+	1.19913i	0.485459	+	0.874259i	$0.338652\pi$
$317$	−8.19543	+	21.3498i	−0.460301	+	1.19913i	−0.945760	+	0.324866i	$0.894681\pi$
$318$	22.7693	+	6.10103i	1.27684	+	0.342129i
$319$	−3.79397	−	0.398762i	−0.212422	−	0.0223264i
$320$		0			0
$321$	9.08496	+	12.5044i	0.507073	+	0.697926i
$322$	4.29623	−	37.1498i	0.239420	−	2.07028i
$323$	0.0422552	−	0.0829304i	0.00235114	−	0.00461437i
$324$	36.9304	+	21.3218i	2.05169	+	1.18454i
$325$		0			0
$326$	25.2784	+	43.7835i	1.40004	+	2.42494i
$327$	−22.4273	−	34.5350i	−1.24023	−	1.90979i
$328$	−6.18360	+	39.0417i	−0.341432	+	2.15572i
$329$	8.47426	+	3.35464i	0.467201	+	0.184947i
$330$		0			0
$331$	30.8373	−	13.7297i	1.69497	−	0.754651i	0.695631	−	0.718400i	$-0.255125\pi$
$331$	30.8373	−	13.7297i	1.69497	−	0.754651i	0.999343	−	0.0362512i	$-0.0115417\pi$
$332$	8.31808	−	31.0435i	0.456514	−	1.70373i
$333$	−0.0549673	+	0.0445117i	−0.00301219	+	0.00243922i
$334$	−31.0358	−	34.4687i	−1.69820	−	1.88605i
$335$		0			0
$336$	−9.39667	+	55.5757i	−0.512630	+	3.03191i
$337$	−11.5586	−	22.6851i	−0.629640	−	1.23574i	−0.956794	−	0.290766i	$-0.906090\pi$
$337$	−11.5586	−	22.6851i	−0.629640	−	1.23574i	0.327155	−	0.944971i	$-0.393910\pi$
$338$	1.75105	−	33.4120i	0.0952445	−	1.81737i
$339$	3.47729	−	3.86192i	0.188860	−	0.209751i
$340$		0			0
$341$	16.2723	−	14.6517i	0.881196	−	0.793432i
$342$	−0.0247861	−	0.156493i	−0.00134028	−	0.00846217i
$343$	−14.6358	−	11.3487i	−0.790260	−	0.612772i
$344$	25.3506	−	34.8922i	1.36682	−	1.88126i
$345$		0			0
$346$	−16.2188	+	36.4280i	−0.871928	+	1.95838i
$347$	−0.206693	+	0.0793419i	−0.0110959	+	0.00425930i	−0.363910	−	0.931434i	$-0.618558\pi$
$347$	−0.206693	+	0.0793419i	−0.0110959	+	0.00425930i	0.352814	+	0.935694i	$0.385225\pi$
$348$	6.78418	−	4.40570i	0.363670	−	0.236170i
$349$	−9.15927			−0.490285			−0.245142	−	0.969487i	$-0.578835\pi$
$349$	−9.15927			−0.490285			−0.245142	+	0.969487i	$0.578835\pi$
$350$		0			0
$351$	−0.0152731			−0.000815219
$352$	−38.9421	+	25.2893i	−2.07562	+	1.34793i
$353$	18.4768	−	7.09257i	0.983419	−	0.377499i	0.187077	−	0.982345i	$-0.440099\pi$
$353$	18.4768	−	7.09257i	0.983419	−	0.377499i	0.796343	+	0.604846i	$0.206765\pi$
$354$	14.4492	−	32.4535i	0.767967	−	1.72488i
$355$		0			0
$356$	−22.6759	+	31.2107i	−1.20182	+	1.65416i
$357$	−28.5877	−	6.38840i	−1.51302	−	0.338110i
$358$	−0.204089	−	1.28856i	−0.0107864	−	0.0681027i
$359$	7.13913	−	6.42810i	0.376789	−	0.339262i	−0.458877	−	0.888500i	$-0.651748\pi$
$359$	7.13913	−	6.42810i	0.376789	−	0.339262i	0.835666	+	0.549237i	$0.185082\pi$
$360$		0			0
$361$	−12.7132	+	14.1194i	−0.669116	+	0.743128i
$362$	−1.66661	+	31.8008i	−0.0875951	+	1.67141i
$363$	20.4311	+	40.0984i	1.07236	+	2.10462i
$364$	−1.20518	−	3.24005i	−0.0631683	−	0.169825i
$365$		0			0
$366$	−8.15372	−	9.05562i	−0.426202	−	0.473345i
$367$	12.5688	−	10.1780i	0.656085	−	0.531287i	−0.242464	−	0.970160i	$-0.577956\pi$
$367$	12.5688	−	10.1780i	0.656085	−	0.531287i	0.898549	+	0.438873i	$0.144622\pi$
$368$	−12.3125	+	45.9507i	−0.641832	+	2.39535i
$369$	−15.3630	+	6.84006i	−0.799767	+	0.356079i
$370$		0			0
$371$	7.72114	−	6.12042i	0.400862	−	0.317756i
$372$	−7.26331	+	45.8588i	−0.376585	+	2.37767i
$373$	−7.93327	−	12.2162i	−0.410769	−	0.632529i	0.571368	−	0.820694i	$-0.306413\pi$
$373$	−7.93327	−	12.2162i	−0.410769	−	0.632529i	−0.982137	+	0.188165i	$0.939746\pi$
$374$	−31.7899	−	55.0617i	−1.64382	−	2.84717i
$375$		0			0
$376$	−20.8791	−	12.0545i	−1.07676	−	0.621665i
$377$	−0.0887258	+	0.174134i	−0.00456961	+	0.00896837i
$378$	0.345608	−	0.149581i	0.0177761	−	0.00769363i
$379$	−12.1419	−	16.7119i	−0.623687	−	0.858432i	0.373928	−	0.927458i	$-0.378011\pi$
$379$	−12.1419	−	16.7119i	−0.623687	−	0.858432i	−0.997615	+	0.0690260i	$0.978011\pi$
$380$		0			0
$381$	25.4114	+	2.67085i	1.30187	+	0.136832i
$382$	−33.4496	−	8.96278i	−1.71143	−	0.458576i
$383$	−12.2744	+	31.9758i	−0.627190	+	1.63389i	0.138264	+	0.990395i	$0.455848\pi$
$383$	−12.2744	+	31.9758i	−0.627190	+	1.63389i	−0.765454	+	0.643491i	$0.777486\pi$
$384$	−3.66321	+	11.2742i	−0.186937	+	0.575333i
$385$		0			0
$386$	−1.99918	−	6.15283i	−0.101755	−	0.313171i
$387$	18.3237	+	0.960302i	0.931444	+	0.0488149i
$388$	−35.9576	+	55.3699i	−1.82547	+	2.81098i
$389$	−2.20850	−	1.98855i	−0.111976	−	0.100823i	0.611241	−	0.791444i	$-0.290671\pi$
$389$	−2.20850	−	1.98855i	−0.111976	−	0.100823i	−0.723217	+	0.690621i	$0.757337\pi$
$390$		0			0
$391$	−23.5131	−	7.63989i	−1.18911	−	0.386366i
$392$	33.9127	+	35.3557i	1.71285	+	1.78573i
$393$	−32.0585	−	32.0585i	−1.61713	−	1.61713i
$394$	27.1579	+	60.9977i	1.36820	+	3.07302i
$395$		0			0
$396$	−69.3749	−	30.8877i	−3.48622	−	1.55216i
$397$	−11.4107	+	14.0910i	−0.572684	+	0.707206i	−0.978383	−	0.206801i	$-0.933695\pi$
$397$	−11.4107	+	14.0910i	−0.572684	+	0.707206i	0.405699	+	0.914007i	$0.367028\pi$
$398$	43.8668	+	22.3513i	2.19884	+	1.12037i
$399$	−0.117825	−	0.0615887i	−0.00589861	−	0.00308329i
$400$		0			0
$401$	14.8272	−	25.6815i	0.740436	−	1.28247i	−0.211862	−	0.977300i	$-0.567953\pi$
$401$	14.8272	−	25.6815i	0.740436	−	1.28247i	0.952297	−	0.305172i	$-0.0987141\pi$
$402$	−96.0793	+	5.03530i	−4.79200	+	0.251138i
$403$	−0.402003	−	1.04725i	−0.0200252	−	0.0521674i
$404$	1.05609	+	10.0480i	0.0525422	+	0.499906i
$405$		0			0
$406$	0.302303	−	4.80935i	0.0150031	−	0.238684i
$407$	−0.0910876	+	0.0910876i	−0.00451505	+	0.00451505i
$408$	72.3404	+	27.7689i	3.58138	+	1.37476i
$409$	−8.77033	+	1.86419i	−0.433665	+	0.0921783i	−0.419571	−	0.907722i	$-0.637820\pi$
$409$	−8.77033	+	1.86419i	−0.433665	+	0.0921783i	−0.0140936	+	0.999901i	$0.504486\pi$
$410$		0			0
$411$	5.60228	−	26.3567i	0.276340	−	1.30008i
$412$	42.6837	−	21.7484i	2.10287	−	1.07147i
$413$	−7.28986	−	12.9357i	−0.358711	−	0.636524i
$414$	−40.0270	+	13.0056i	−1.96722	+	0.639188i
$415$		0			0
$416$	0.494574	+	2.32679i	0.0242485	+	0.114080i
$417$	8.63266	+	10.6604i	0.422743	+	0.522044i
$418$	−0.0746868	−	0.278735i	−0.00365305	−	0.0136334i
$419$	13.9434	+	10.1305i	0.681179	+	0.494905i	0.873748	−	0.486378i	$-0.161682\pi$
$419$	13.9434	+	10.1305i	0.681179	+	0.494905i	−0.192570	+	0.981283i	$0.561682\pi$
$420$		0			0
$421$	−9.71469	+	7.05813i	−0.473465	+	0.343992i	−0.798790	−	0.601610i	$-0.794526\pi$
$421$	−9.71469	+	7.05813i	−0.473465	+	0.343992i	0.325325	+	0.945602i	$0.394526\pi$
$422$	10.1170	+	8.19259i	0.492488	+	0.398809i
$423$	−0.536807	−	10.2429i	−0.0261005	−	0.498026i
$424$	−22.5711	+	13.0314i	−1.09615	+	0.632863i
$425$		0			0
$426$			8.58181i			0.415790i
$427$	−5.07059	+	0.479604i	−0.245383	+	0.0232097i
$428$	−29.3668	−	4.65124i	−1.41950	−	0.224826i
$429$	3.66312	−	0.385009i	0.176857	−	0.0185884i
$430$		0			0
$431$	2.37991	−	22.6434i	0.114636	−	1.09069i	−0.774349	−	0.632758i	$-0.781923\pi$
$431$	2.37991	−	22.6434i	0.114636	−	1.09069i	0.888986	−	0.457935i	$-0.151411\pi$
$432$	−0.462720	+	0.123985i	−0.0222626	+	0.00596525i
$433$	4.17371	−	0.661050i	0.200576	−	0.0317680i	−0.0553382	−	0.998468i	$-0.517624\pi$
$433$	4.17371	−	0.661050i	0.200576	−	0.0317680i	0.255914	+	0.966700i	$0.417624\pi$
$434$	19.3533	+	19.7606i	0.928986	+	0.948541i
$435$		0			0
$436$	77.4827	+	16.4695i	3.71075	+	0.788744i
$437$	−0.0941075	−	0.0611141i	−0.00450177	−	0.00292349i
$438$	−43.5760	−	28.2986i	−2.08214	−	1.35216i
$439$	12.2431	+	2.60236i	0.584333	+	0.124204i	0.490587	−	0.871392i	$-0.336782\pi$
$439$	12.2431	+	2.60236i	0.584333	+	0.124204i	0.0937461	+	0.995596i	$0.470116\pi$
$440$		0			0
$441$	−4.75711	+	20.2925i	−0.226529	+	0.966307i
$442$	−3.21709	+	0.509536i	−0.153021	+	0.0242362i
$443$	16.0567	−	4.30238i	0.762877	−	0.204412i	0.143655	−	0.989628i	$-0.454115\pi$
$443$	16.0567	−	4.30238i	0.762877	−	0.204412i	0.619223	+	0.785216i	$0.287448\pi$
$444$	0.0285519	−	0.271653i	0.00135501	−	0.0128921i
$445$		0			0
$446$	−70.5330	+	7.41331i	−3.33983	+	0.351031i
$447$	6.35094	+	1.00589i	0.300389	+	0.0475770i
$448$	−7.26784	−	10.2256i	−0.343373	−	0.483114i
$449$			30.5962i			1.44392i	0.691934	+	0.721961i	$0.256759\pi$
$449$			30.5962i			1.44392i	−0.691934	+	0.721961i	$0.743241\pi$
$450$		0			0
$451$	−26.5246	+	15.3140i	−1.24900	+	0.721108i
$452$	0.523193	+	9.98311i	0.0246089	+	0.469566i
$453$	−9.59974	−	7.77371i	−0.451035	−	0.365241i
$454$	−23.9479	+	17.3991i	−1.12393	+	0.816582i
$455$		0			0
$456$	0.284521	+	0.206717i	0.0133239	+	0.00968041i
$457$	7.33215	+	27.3640i	0.342984	+	1.28003i	0.894950	+	0.446166i	$0.147211\pi$
$457$	7.33215	+	27.3640i	0.342984	+	1.28003i	−0.551967	+	0.833866i	$0.686122\pi$
$458$	−17.5438	−	21.6648i	−0.819770	−	1.01233i
$459$	−0.0517618	−	0.243520i	−0.00241603	−	0.0113665i
$460$		0			0
$461$	5.27336	−	1.71342i	0.245605	−	0.0798018i	−0.183628	−	0.982996i	$-0.558784\pi$
$461$	5.27336	−	1.71342i	0.245605	−	0.0798018i	0.429233	+	0.903194i	$0.358784\pi$
$462$	−79.1201	+	44.5878i	−3.68100	+	2.07441i
$463$	34.5741	−	17.6164i	1.60680	−	0.818703i	0.607085	−	0.794637i	$-0.292339\pi$
$463$	34.5741	−	17.6164i	1.60680	−	0.818703i	0.999710	−	0.0240660i	$-0.00766117\pi$
$464$	−1.27447	+	5.99590i	−0.0591657	+	0.278353i
$465$		0			0
$466$	−17.5676	+	3.73411i	−0.813804	+	0.172979i
$467$	−17.5988	−	6.75555i	−0.814376	−	0.312610i	−0.0847034	−	0.996406i	$-0.526994\pi$
$467$	−17.5988	−	6.75555i	−0.814376	−	0.312610i	−0.729673	+	0.683796i	$0.760328\pi$
$468$	−2.75094	+	2.75094i	−0.127162	+	0.127162i
$469$	−22.2520	+	33.4961i	−1.02750	+	1.54671i
$470$		0			0
$471$	1.60416	+	15.2626i	0.0739158	+	0.703262i
$472$	14.0759	+	36.6689i	0.647895	+	1.68782i
$473$	33.3722	−	1.74896i	1.53445	−	0.0804174i
$474$	−8.03298	+	13.9135i	−0.368967	+	0.639069i
$475$		0			0
$476$	47.5761	−	30.1965i	2.18065	−	1.38406i
$477$	−9.87963	−	5.03392i	−0.452357	−	0.230487i
$478$	−28.6692	+	35.4035i	−1.31130	+	1.61932i
$479$	17.7397	+	7.89824i	0.810549	+	0.360880i	0.769796	−	0.638289i	$-0.220358\pi$
$479$	17.7397	+	7.89824i	0.810549	+	0.360880i	0.0407529	+	0.999169i	$0.487024\pi$
$480$		0			0
$481$	0.00268418	+	0.00602876i	0.000122388	+	0.000274888i
$482$	1.95562	+	1.95562i	0.0890760	+	0.0890760i
$483$	−11.2622	+	33.4713i	−0.512448	+	1.52300i
$484$	−82.3349	−	26.7522i	−3.74250	−	1.21601i
$485$		0			0
$486$	−42.3343	−	38.1180i	−1.92032	−	1.72907i
$487$	−0.640008	+	0.985526i	−0.0290015	+	0.0446585i	−0.852874	−	0.522117i	$-0.825143\pi$
$487$	−0.640008	+	0.985526i	−0.0290015	+	0.0446585i	0.823872	+	0.566775i	$0.191809\pi$
$488$	13.4544	+	0.705116i	0.609052	+	0.0319191i
$489$	−14.7531	−	45.4052i	−0.667156	−	2.05330i
$490$		0			0
$491$	4.11148	−	12.6538i	0.185548	−	0.571059i	−0.814409	−	0.580291i	$-0.802939\pi$
$491$	4.11148	−	12.6538i	0.185548	−	0.571059i	0.999957	+	0.00923217i	$0.00293873\pi$
$492$	23.2742	−	60.6313i	1.04928	−	2.73347i
$493$	−3.07716	−	0.824521i	−0.138588	−	0.0371346i
$494$	−0.0147023	−	0.00154527i	−0.000661488	−	6.95252e-5i
$495$		0			0
$496$	−20.6807	−	28.4645i	−0.928591	−	1.27810i
$497$	2.87980	+	2.13847i	0.129177	+	0.0959236i
$498$	−19.6373	+	38.5404i	−0.879969	+	1.72704i
$499$	−31.8592	−	18.3939i	−1.42621	−	0.823426i	−0.429395	−	0.903117i	$-0.641273\pi$
$499$	−31.8592	−	18.3939i	−1.42621	−	0.823426i	−0.996820	+	0.0796912i	$0.974607\pi$
$500$		0			0
$501$	21.8999	+	37.9317i	0.978414	+	1.69466i
$502$	−28.6307	−	44.0874i	−1.27785	−	1.96772i
$503$	−2.14933	+	13.5703i	−0.0958339	+	0.605072i	0.892296	+	0.451451i	$0.149093\pi$
$503$	−2.14933	+	13.5703i	−0.0958339	+	0.605072i	−0.988130	+	0.153621i	$0.950907\pi$
$504$	20.2932	−	51.2634i	0.903933	−	2.28345i
$505$		0			0
$506$	−70.0244	+	31.1769i	−3.11296	+	1.38598i
$507$	−8.17737	+	30.5184i	−0.363170	+	1.35537i
$508$	−38.1987	+	30.9327i	−1.69479	+	1.37242i
$509$	17.4013	+	19.3261i	0.771300	+	0.856615i	0.992953	−	0.118511i	$-0.0378119\pi$
$509$	17.4013	+	19.3261i	0.771300	+	0.856615i	−0.221653	+	0.975126i	$0.571145\pi$
$510$		0			0
$511$	−20.3547	+	7.57117i	−0.900440	+	0.334929i
$512$	−21.4996	−	42.1953i	−0.950156	−	1.86479i
$513$	5.91369e−5	−	0.00112840i	2.61096e−6	−	4.98201e-5i
$514$	39.7173	−	44.1105i	1.75186	−	1.94563i
$515$		0			0
$516$	−52.6599	+	47.4152i	−2.31822	+	2.08734i
$517$	−2.92229	−	18.4506i	−0.128522	−	0.811456i
$518$	−0.119783	−	0.110134i	−0.00526297	−	0.00483899i
$519$	22.1332	−	30.4637i	0.971539	−	1.33721i
$520$		0			0
$521$	15.4098	−	34.6110i	0.675115	−	1.51633i	−0.172097	−	0.985080i	$-0.555054\pi$
$521$	15.4098	−	34.6110i	0.675115	−	1.51633i	0.847213	−	0.531254i	$-0.178279\pi$
$522$	−5.06290	+	1.94347i	−0.221597	+	0.0850632i
$523$	−5.76773	+	3.74561i	−0.252205	+	0.163784i	−0.664550	−	0.747244i	$-0.731377\pi$
$523$	−5.76773	+	3.74561i	−0.252205	+	0.163784i	0.412345	+	0.911028i	$0.364710\pi$
$524$	87.2146			3.80999
$525$		0			0
$526$	61.5660			2.68441
$527$	15.3353	−	9.95889i	0.668018	−	0.433816i
$528$	107.854	−	41.4011i	4.69373	−	1.80175i
$529$	−2.76827	+	6.21764i	−0.120360	+	0.270332i
$530$		0			0
$531$	−9.82205	+	13.5189i	−0.426241	+	0.586670i
$532$	0.244046	−	0.0764947i	0.0105807	−	0.00331647i
$533$	0.245457	+	1.54975i	0.0106319	+	0.0671272i
$534$	38.5858	−	34.7428i	1.66977	−	1.50347i
$535$		0			0
$536$	71.1790	−	79.0523i	3.07446	−	3.41454i
$537$	−0.0644772	+	1.23030i	−0.00278240	+	0.0530913i
$538$	6.83419	+	13.4128i	0.294643	+	0.578269i
$539$	−4.75333	+	37.6610i	−0.204740	+	1.62218i
$540$		0			0
$541$	20.9559	+	23.2739i	0.900966	+	1.00062i	0.999985	+	0.00553845i	$0.00176295\pi$
$541$	20.9559	+	23.2739i	0.900966	+	1.00062i	−0.0990188	+	0.995086i	$0.531570\pi$
$542$	33.9289	−	27.4751i	1.45737	−	1.18016i
$543$	7.78305	−	29.0468i	0.334003	−	1.24652i
$544$	−35.4229	+	15.7713i	−1.51875	+	0.676189i
$545$		0			0
$546$	0.679935	+	4.60269i	0.0290985	+	0.196977i
$547$	−5.53710	+	34.9599i	−0.236749	+	1.49478i	0.527333	+	0.849659i	$0.323192\pi$
$547$	−5.53710	+	34.9599i	−0.236749	+	1.49478i	−0.764082	+	0.645119i	$0.776808\pi$
$548$	28.2310	+	43.4720i	1.20597	+	1.85703i
$549$	2.86594	+	4.96396i	0.122315	+	0.211857i
$550$		0			0
$551$	−0.0125217	−	0.00722943i	−0.000533444	−	0.000307984i
$552$	42.4107	−	83.2357i	1.80512	−	3.54275i
$553$	2.66725	+	6.16269i	0.113423	+	0.262064i
$554$	31.7521	+	43.7030i	1.34902	+	1.85676i
$555$		0			0
$556$	−26.2433	−	2.75828i	−1.11296	−	0.116977i
$557$	1.98966	+	0.533128i	0.0843046	+	0.0225893i	0.300725	−	0.953711i	$-0.402771\pi$
$557$	1.98966	+	0.533128i	0.0843046	+	0.0225893i	−0.216420	+	0.976300i	$0.569438\pi$
$558$	11.1551	−	29.0600i	0.472233	−	1.23021i
$559$	0.529037	−	1.62821i	0.0223759	−	0.0688659i
$560$		0			0
$561$	18.5533	+	57.1012i	0.783321	+	2.41081i
$562$	−32.1068	−	1.68264i	−1.35434	−	0.0709781i
$563$	17.9354	−	27.6180i	0.755885	−	1.16396i	−0.225934	−	0.974143i	$-0.572543\pi$
$563$	17.9354	−	27.6180i	0.755885	−	1.16396i	0.981819	−	0.189818i	$-0.0607899\pi$
$564$	29.4368	+	26.5050i	1.23951	+	1.11606i
$565$		0			0
$566$	12.2143	+	3.96868i	0.513407	+	0.166816i
$567$	−23.5154	+	4.74293i	−0.987552	+	0.199184i
$568$	−6.70933	−	6.70933i	−0.281517	−	0.281517i
$569$	3.69598	+	8.30131i	0.154944	+	0.348009i	0.974293	−	0.225286i	$-0.0723316\pi$
$569$	3.69598	+	8.30131i	0.154944	+	0.348009i	−0.819349	+	0.573295i	$0.805665\pi$
$570$		0			0
$571$	34.5801	+	15.3961i	1.44713	+	0.644306i	0.971866	−	0.235535i	$-0.0756843\pi$
$571$	34.5801	+	15.3961i	1.44713	+	0.644306i	0.475268	+	0.879841i	$0.342351\pi$
$572$	−4.45903	+	5.50644i	−0.186441	+	0.230236i
$573$	29.1372	+	14.8461i	1.21722	+	0.620206i
$574$	−20.7322	−	32.6646i	−0.865346	−	1.36339i
$575$		0			0
$576$	−7.05920	+	12.2269i	−0.294133	+	0.509454i
$577$	17.7752	−	0.931561i	0.739993	−	0.0387814i	0.321385	−	0.946949i	$-0.395852\pi$
$577$	17.7752	−	0.931561i	0.739993	−	0.0387814i	0.418608	+	0.908167i	$0.362518\pi$
$578$	−3.25401	−	8.47700i	−0.135349	−	0.352597i
$579$	0.638591	+	6.07579i	0.0265390	+	0.252501i
$580$		0			0
$581$	8.03965	+	16.1935i	0.333541	+	0.671818i
$582$	62.8313	−	62.8313i	2.60444	−	2.60444i
$583$	−18.8531	−	7.23705i	−0.780818	−	0.299728i
$584$	56.1922	−	11.9440i	2.32525	−	0.494247i
$585$		0			0
$586$	5.71877	−	26.9047i	0.236240	−	1.11142i
$587$	−36.5596	+	18.6280i	−1.50898	+	0.768861i	−0.995984	−	0.0895323i	$-0.971463\pi$
$587$	−36.5596	+	18.6280i	−1.50898	+	0.768861i	−0.512991	+	0.858394i	$0.671463\pi$
$588$	−42.4233	−	68.4044i	−1.74951	−	2.82095i
$589$	0.0789291	−	0.0256456i	0.00325222	−	0.00105671i
$590$		0			0
$591$	−13.1094	−	61.6747i	−0.539247	−	2.53696i
$592$	0.130262	+	0.160860i	0.00535372	+	0.00661129i
$593$	0.682938	+	2.54876i	0.0280449	+	0.104665i	0.978530	−	0.206106i	$-0.0660793\pi$
$593$	0.682938	+	2.54876i	0.0280449	+	0.104665i	−0.950485	+	0.310771i	$0.899413\pi$
$594$	−0.624457	−	0.453694i	−0.0256218	−	0.0186153i
$595$		0			0
$596$	−10.0071	+	7.27057i	−0.409906	+	0.297814i
$597$	−36.1308	−	29.2581i	−1.47873	−	1.19746i
$598$	0.205515	+	3.92145i	0.00840412	+	0.160360i
$599$	15.2314	−	8.79385i	0.622338	−	0.359307i	−0.155441	−	0.987845i	$-0.549680\pi$
$599$	15.2314	−	8.79385i	0.622338	−	0.359307i	0.777779	+	0.628538i	$0.216346\pi$
$600$		0			0
$601$		−	4.58675i		−	0.187097i	−0.995615	−	0.0935487i	$-0.970179\pi$
$601$		−	4.58675i		−	0.187097i	0.995615	−	0.0935487i	$-0.0298211\pi$
$602$	3.97497	+	42.0252i	0.162008	+	1.71282i
$603$	44.6990	+	7.07963i	1.82029	+	0.288305i
$604$	23.6321	−	2.48384i	0.961578	−	0.101066i
$605$		0			0
$606$	1.42137	−	13.5235i	0.0577393	−	0.549353i
$607$	0.509336	−	0.136476i	0.0206733	−	0.00553939i	−0.248468	−	0.968640i	$-0.579927\pi$
$607$	0.509336	−	0.136476i	0.0206733	−	0.00553939i	0.269141	+	0.963101i	$0.413260\pi$
$608$	−0.173821	+	0.0275306i	−0.00704938	+	0.00111651i
$609$	−1.22348	+	4.38298i	−0.0495779	+	0.177607i
$610$		0			0
$611$	−0.936092	−	0.198973i	−0.0378702	−	0.00804957i
$612$	−53.1850	−	34.5388i	−2.14988	−	1.39615i
$613$	1.37000	+	0.889687i	0.0553337	+	0.0359341i	0.572009	−	0.820247i	$-0.306164\pi$
$613$	1.37000	+	0.889687i	0.0553337	+	0.0359341i	−0.516676	+	0.856181i	$0.672831\pi$
$614$	−10.7204	−	2.27870i	−0.432642	−	0.0919609i
$615$		0			0
$616$	26.9976	−	96.7160i	1.08777	−	3.89680i
$617$	3.65372	−	0.578692i	0.147093	−	0.0232973i	−0.0824536	−	0.996595i	$-0.526276\pi$
$617$	3.65372	−	0.578692i	0.147093	−	0.0232973i	0.229547	+	0.973298i	$0.426276\pi$
$618$	−62.2778	+	16.6873i	−2.50518	+	0.671261i
$619$	1.40210	−	13.3401i	0.0563552	−	0.536184i	−0.929528	−	0.368751i	$-0.879786\pi$
$619$	1.40210	−	13.3401i	0.0563552	−	0.536184i	0.985883	−	0.167433i	$-0.0535478\pi$
$620$		0			0
$621$	−0.298500	+	0.0313736i	−0.0119784	+	0.00125898i
$622$	10.3426	+	1.63811i	0.414700	+	0.0656821i
$623$	−2.04359	−	21.6057i	−0.0818745	−	0.865615i
$624$		−	5.91843i		−	0.236927i
$625$		0			0
$626$	−32.1690	+	18.5728i	−1.28573	+	0.742318i
$627$	0.0142616	+	0.272127i	0.000569552	+	0.0108677i
$628$	−22.9428	−	18.5788i	−0.915519	−	0.741373i
$629$	−0.0870278	+	0.0632294i	−0.00347003	+	0.00252112i
$630$		0			0
$631$	−2.90402	−	2.10989i	−0.115607	−	0.0839935i	0.528479	−	0.848946i	$-0.322762\pi$
$631$	−2.90402	−	2.10989i	−0.115607	−	0.0839935i	−0.644087	+	0.764953i	$0.722762\pi$
$632$	−4.59746	−	17.1580i	−0.182877	−	0.682507i
$633$	−7.73643	−	9.55370i	−0.307496	−	0.379726i
$634$	12.3101	+	57.9145i	0.488897	+	2.30008i
$635$		0			0
$636$	40.7253	−	13.2325i	1.61486	−	0.524701i
$637$	1.71396	+	0.918764i	0.0679095	+	0.0364027i
$638$	−8.80037	+	4.48401i	−0.348410	+	0.177524i
$639$	0.839287	−	3.94854i	0.0332017	−	0.156202i
$640$		0			0
$641$	−29.1690	+	6.20007i	−1.15211	+	0.244888i	−0.744086	−	0.668084i	$-0.767115\pi$
$641$	−29.1690	+	6.20007i	−1.15211	+	0.244888i	−0.408022	+	0.912972i	$0.633781\pi$
$642$	37.3591	+	14.3408i	1.47445	+	0.565987i
$643$	30.4036	−	30.4036i	1.19900	−	1.19900i	0.224535	−	0.974466i	$-0.427914\pi$
$643$	30.4036	−	30.4036i	1.19900	−	1.19900i	0.974466	−	0.224535i	$-0.0720863\pi$
$644$	−30.2097	−	60.8484i	−1.19043	−	2.39776i
$645$		0			0
$646$	−0.0251888	−	0.239656i	−0.000991041	−	0.00942913i
$647$	12.6184	+	32.8721i	0.496081	+	1.29234i	0.921865	+	0.387511i	$0.126665\pi$
$647$	12.6184	+	32.8721i	0.496081	+	1.29234i	−0.425784	+	0.904825i	$0.640002\pi$
$648$	63.3698	−	3.32107i	2.48940	−	0.130464i
$649$	−15.2169	+	26.3564i	−0.597315	+	1.03458i
$650$		0			0
$651$	−13.9966	−	22.0523i	−0.548570	−	0.864299i
$652$	81.8300	+	41.6945i	3.20471	+	1.63288i
$653$	−4.71025	+	5.81668i	−0.184327	+	0.227624i	−0.860930	−	0.508723i	$-0.830118\pi$
$653$	−4.71025	+	5.81668i	−0.184327	+	0.227624i	0.676604	+	0.736347i	$0.263451\pi$
$654$	−97.3956	−	43.3633i	−3.80847	−	1.69564i
$655$		0			0
$656$	20.0172	+	44.9593i	0.781539	+	1.75536i
$657$	17.2820	+	17.2820i	0.674235	+	0.674235i
$658$	23.1310	−	4.66541i	0.901742	−	0.181877i
$659$	18.3227	+	5.95342i	0.713753	+	0.231912i	0.643313	−	0.765604i	$-0.277560\pi$
$659$	18.3227	+	5.95342i	0.713753	+	0.231912i	0.0704403	+	0.997516i	$0.477560\pi$
$660$		0			0
$661$	−15.3915	−	13.8586i	−0.598662	−	0.539037i	0.313120	−	0.949714i	$-0.398626\pi$
$661$	−15.3915	−	13.8586i	−0.598662	−	0.539037i	−0.911781	+	0.410676i	$0.865293\pi$
$662$	47.5988	−	73.2957i	1.84998	−	2.84872i
$663$	3.07162	+	0.160977i	0.119292	+	0.00625181i
$664$	−14.7786	−	45.4839i	−0.573521	−	1.76512i
$665$		0			0
$666$	−0.0565881	+	0.174160i	−0.00219274	+	0.00674857i
$667$	−1.37637	+	3.58556i	−0.0532932	+	0.138834i
$668$	−81.3855	−	21.8072i	−3.14890	−	0.843745i
$669$	66.6058	+	7.00055i	2.57513	+	0.270657i
$670$		0			0
$671$	6.13605	+	8.44555i	0.236880	+	0.326037i
$672$	21.9999	+	50.8309i	0.848665	+	1.96084i
$673$	14.0858	−	27.6449i	0.542968	−	1.06563i	−0.442658	−	0.896691i	$-0.645964\pi$
$673$	14.0858	−	27.6449i	0.542968	−	1.06563i	0.985626	−	0.168944i	$-0.0540356\pi$
$674$	−57.0862	−	32.9588i	−2.19888	−	1.26952i
$675$		0			0
$676$	−30.3892	−	52.6357i	−1.16882	−	2.02445i
$677$	14.6977	+	22.6325i	0.564880	+	0.869838i	0.999527	−	0.0307626i	$-0.00979358\pi$
$677$	14.6977	+	22.6325i	0.564880	+	0.869838i	−0.434647	+	0.900601i	$0.643127\pi$
$678$	2.10476	−	13.2889i	0.0808329	−	0.510359i
$679$	−5.42759	−	36.7410i	−0.208292	−	1.40999i
$680$		0			0
$681$	25.5364	−	11.3695i	0.978556	−	0.435681i
$682$	14.6728	−	54.7596i	0.561851	−	2.09685i
$683$	−25.1653	+	20.3784i	−0.962922	+	0.779759i	−0.975463	−	0.220162i	$-0.929341\pi$
$683$	−25.1653	+	20.3784i	−0.962922	+	0.779759i	0.0125408	+	0.999921i	$0.496008\pi$
$684$	−0.192592	−	0.213895i	−0.00736392	−	0.00817847i
$685$		0			0
$686$	−47.7824	−	4.00416i	−1.82434	−	0.152879i
$687$	11.9514	+	23.4560i	0.455975	+	0.894901i
$688$	2.81029	−	53.6235i	0.107141	−	2.04438i
$689$	−0.692256	+	0.768828i	−0.0263729	+	0.0292900i
$690$		0			0
$691$	−13.4532	+	12.1133i	−0.511783	+	0.460811i	−0.884102	−	0.467293i	$-0.845229\pi$
$691$	−13.4532	+	12.1133i	−0.511783	+	0.460811i	0.372320	+	0.928105i	$0.378562\pi$
$692$	11.3316	+	71.5446i	0.430761	+	2.71972i
$693$	40.7642	−	12.7773i	1.54850	−	0.485369i
$694$	−0.336925	+	0.463737i	−0.0127895	+	0.0176032i
$695$		0			0
$696$	4.89602	−	10.9966i	0.185583	−	0.416827i
$697$	−23.8779	+	9.16588i	−0.904441	+	0.347182i
$698$	−19.8881	+	12.9155i	−0.752775	+	0.488858i
$699$	16.9601			0.641489
$700$		0			0
$701$	−8.89063			−0.335794			−0.167897	−	0.985805i	$-0.553698\pi$
$701$	−8.89063			−0.335794			−0.167897	+	0.985805i	$0.553698\pi$
$702$	−0.0331634	+	0.0215366i	−0.00125167	+	0.000812846i
$703$	−0.000455807	0	0.000174968i	−1.71911e−5	0	6.59903e-6i
$704$	−10.4585	+	23.4903i	−0.394171	+	0.885323i
$705$		0			0
$706$	30.1185	−	41.4546i	1.13353	−	1.56016i
$707$	−4.18388	−	3.84683i	−0.157351	−	0.144675i
$708$	−10.0952	−	63.7385i	−0.379401	−	2.39544i
$709$	−6.80098	+	6.12363i	−0.255416	+	0.229978i	−0.786884	−	0.617101i	$-0.788307\pi$
$709$	−6.80098	+	6.12363i	−0.255416	+	0.229978i	0.531468	+	0.847078i	$0.321641\pi$
$710$		0			0
$711$	5.05674	−	5.61607i	0.189642	−	0.210619i
$712$	−3.00449	+	57.3290i	−0.112598	+	2.14850i
$713$	−10.0080	−	19.6419i	−0.374804	−	0.735594i
$714$	−71.0826	+	26.4400i	−2.66020	+	0.989492i
$715$		0			0
$716$	−1.58580	−	1.76121i	−0.0592641	−	0.0658195i
$717$	33.4323	−	27.0729i	1.24855	−	1.01106i
$718$	6.43738	−	24.0246i	0.240241	−	0.896591i
$719$	−43.2253	+	19.2451i	−1.61203	+	0.717722i	−0.997466	−	0.0711450i	$-0.977335\pi$
$719$	−43.2253	+	19.2451i	−1.61203	+	0.717722i	−0.614564	+	0.788867i	$0.710668\pi$
$720$		0			0
$721$	−9.91904	+	25.0568i	−0.369405	+	0.933165i
$722$	−7.69515	+	48.5853i	−0.286384	+	1.80816i
$723$	−1.42242	−	2.19034i	−0.0529004	−	0.0814594i
$724$	28.9238	+	50.0975i	1.07495	+	1.86186i
$725$		0			0
$726$	100.906	+	58.2581i	3.74498	+	2.16216i
$727$	−17.8237	+	34.9809i	−0.661043	+	1.29737i	0.280298	+	0.959913i	$0.409567\pi$
$727$	−17.8237	+	34.9809i	−0.661043	+	1.29737i	−0.941341	+	0.337457i	$0.890433\pi$
$728$	−4.13000	−	3.06685i	−0.153068	−	0.113665i
$729$	15.6314	+	21.5148i	0.578941	+	0.796844i
$730$		0			0
$731$	27.7537	+	2.91703i	1.02651	+	0.107890i
$732$	−21.3816	−	5.72918i	−0.790286	−	0.211757i
$733$	−3.94744	+	10.2834i	−0.145802	+	0.379827i	−0.986961	−	0.160961i	$-0.948541\pi$
$733$	−3.94744	+	10.2834i	−0.145802	+	0.379827i	0.841159	+	0.540788i	$0.181874\pi$
$734$	12.9394	−	39.8233i	0.477601	−	1.46991i
$735$		0			0
$736$	14.4456	+	44.4591i	0.532473	+	1.63878i
$737$	82.3105	+	4.31371i	3.03195	+	0.158898i
$738$	−23.7135	+	36.5156i	−0.872906	+	1.34416i
$739$	24.5232	+	22.0807i	0.902099	+	0.812253i	0.982836	−	0.184482i	$-0.0590607\pi$
$739$	24.5232	+	22.0807i	0.902099	+	0.812253i	−0.0807371	+	0.996735i	$0.525727\pi$
$740$		0			0
$741$	0.0132769	+	0.00431393i	0.000487740	+	0.000158476i
$742$	8.13499	−	24.1772i	0.298645	−	0.887573i
$743$	2.10074	+	2.10074i	0.0770687	+	0.0770687i	0.744590	−	0.667522i	$-0.232645\pi$
$743$	2.10074	+	2.10074i	0.0770687	+	0.0770687i	−0.667522	+	0.744590i	$0.732645\pi$
$744$	28.1022	+	63.1185i	1.03028	+	2.31404i
$745$		0			0
$746$	−34.4520	−	15.3390i	−1.26138	−	0.561601i
$747$	12.8044	−	15.8122i	0.468489	−	0.578536i
$748$	−102.909	−	52.4345i	−3.76271	−	1.91720i
$749$	14.1217	−	8.96306i	0.515997	−	0.327503i
$750$		0			0
$751$	−9.49836	+	16.4516i	−0.346600	+	0.600329i	−0.985643	−	0.168842i	$-0.945997\pi$
$751$	−9.49836	+	16.4516i	−0.346600	+	0.600329i	0.639043	+	0.769171i	$0.279331\pi$
$752$	−29.9754	+	1.57095i	−1.09309	+	0.0572865i
$753$	17.7898	+	46.3441i	0.648298	+	1.68887i
$754$	0.0528906	+	0.503220i	0.00192616	+	0.0183262i
$755$		0			0
$756$	0.378542	−	0.569822i	0.0137674	−	0.0207242i
$757$	17.4136	−	17.4136i	0.632909	−	0.632909i	−0.315887	−	0.948797i	$-0.602302\pi$
$757$	17.4136	−	17.4136i	0.632909	−	0.632909i	0.948797	+	0.315887i	$0.102302\pi$
$758$	−49.9298	−	19.1663i	−1.81353	−	0.696150i
$759$	70.8016	−	15.0493i	2.56994	−	0.546257i
$760$		0			0
$761$	−6.85919	+	32.2700i	−0.248646	+	1.16979i	0.659688	+	0.751539i	$0.270688\pi$
$761$	−6.85919	+	32.2700i	−0.248646	+	1.16979i	−0.908334	+	0.418246i	$0.862645\pi$
$762$	58.9435	−	30.0332i	2.13530	−	1.08799i
$763$	−38.8211	+	21.8775i	−1.40542	+	0.792019i
$764$	−59.8280	+	19.4393i	−2.16450	+	0.703289i
$765$		0			0
$766$	18.4369	+	86.7390i	0.666154	+	3.13401i
$767$	0.981186	+	1.21166i	0.0354286	+	0.0437507i
$768$	13.9445	+	52.0416i	0.503179	+	1.87789i
$769$	−11.2664	−	8.18549i	−0.406275	−	0.295176i	0.365817	−	0.930687i	$-0.380790\pi$
$769$	−11.2664	−	8.18549i	−0.406275	−	0.295176i	−0.772092	+	0.635511i	$0.780790\pi$
$770$		0			0
$771$	−45.3468	+	32.9464i	−1.63312	+	1.18653i
$772$	−9.13320	−	7.39592i	−0.328711	−	0.266185i
$773$	0.313203	+	5.97627i	0.0112651	+	0.214952i	0.998462	+	0.0554438i	$0.0176574\pi$
$773$	0.313203	+	5.97627i	0.0112651	+	0.214952i	−0.987197	+	0.159508i	$0.949009\pi$
$774$	41.1414	−	23.7530i	1.47880	−	0.853784i
$775$		0			0
$776$			98.2441i			3.52676i
$777$	0.0890188	+	0.125246i	0.00319353	+	0.00449319i
$778$	−7.59951	−	1.20364i	−0.272456	−	0.0431527i
$779$	−0.115448	+	0.0121341i	−0.00413637	+	0.000434750i
$780$		0			0
$781$	0.768491	−	7.31170i	0.0274988	−	0.261633i
$782$	−61.8285	+	16.5669i	−2.21098	+	0.592431i
$783$	−0.0381989	+	0.00605012i	−0.00136512	+	0.000216214i
$784$	59.3851	+	13.9215i	2.12090	+	0.497196i
$785$		0			0
$786$	−114.816	−	24.4049i	−4.09535	−	0.870494i
$787$	−4.15789	−	2.70016i	−0.148213	−	0.0962505i	0.468402	−	0.883515i	$-0.344830\pi$
$787$	−4.15789	−	2.70016i	−0.148213	−	0.0962505i	−0.616615	+	0.787265i	$0.711496\pi$
$788$	101.725	+	66.0607i	3.62379	+	2.35332i
$789$	−56.8676	−	12.0876i	−2.02454	−	0.430329i
$790$		0			0
$791$	−3.93489	−	4.01772i	−0.139909	−	0.142854i
$792$	−111.613	+	17.6778i	−3.96601	+	0.628154i
$793$	0.516580	−	0.138417i	0.0183443	−	0.00491534i
$794$	−4.90698	+	46.6868i	−0.174142	+	1.65685i
$795$		0			0
$796$	88.9449	−	9.34848i	3.15257	−	0.331348i
$797$	38.0787	+	6.03107i	1.34882	+	0.213632i	0.788698	−	0.614781i	$-0.210756\pi$
$797$	38.0787	+	6.03107i	1.34882	+	0.213632i	0.560119	+	0.828412i	$0.310756\pi$
$798$	−0.342686	+	0.0324131i	−0.0121310	+	0.00114741i
$799$		−	15.5997i		−	0.551878i
$800$		0			0
$801$	−21.1513	+	12.2117i	−0.747346	+	0.431480i
$802$	−4.01819	−	76.6716i	−0.141887	−	2.70737i
$803$	34.5926	+	28.0126i	1.22075	+	0.988542i
$804$	−141.395	+	102.730i	−4.98662	+	3.62299i
$805$		0			0
$806$	−2.34962	−	1.70710i	−0.0827619	−	0.0601301i
$807$	−3.67922	−	13.7310i	−0.129515	−	0.483356i
$808$	9.46151	+	11.6840i	0.332855	+	0.411041i
$809$	−6.54501	−	30.7919i	−0.230110	−	1.08258i	−0.929779	−	0.368117i	$-0.880003\pi$
$809$	−6.54501	−	30.7919i	−0.230110	−	1.08258i	0.699669	−	0.714467i	$-0.253331\pi$
$810$		0			0
$811$	20.5598	−	6.68028i	0.721952	−	0.234576i	0.0750826	−	0.997177i	$-0.476078\pi$
$811$	20.5598	−	6.68028i	0.721952	−	0.234576i	0.646869	+	0.762601i	$0.276078\pi$
$812$	−4.29769	−	7.62615i	−0.150819	−	0.267625i
$813$	−36.7340	+	18.7169i	−1.28832	+	0.656430i
$814$	−0.0693416	+	0.326227i	−0.00243042	+	0.0114342i
$815$		0			0
$816$	94.3656	−	20.0580i	3.30346	−	0.702171i
$817$	0.118246	+	0.0453904i	0.00413690	+	0.00158801i
$818$	−16.4149	+	16.4149i	−0.573932	+	0.573932i
$819$	0.137294	−	2.18422i	0.00479745	−	0.0763228i
$820$		0			0
$821$	−0.622668	−	5.92429i	−0.0217313	−	0.206759i	0.978269	−	0.207342i	$-0.0664812\pi$
$821$	−0.622668	−	5.92429i	−0.0217313	−	0.206759i	−1.00000		0.000582675i	$0.999815\pi$
$822$	−25.0009	−	65.1296i	−0.872007	−	2.27166i
$823$	−35.8441	+	1.87851i	−1.24945	+	0.0654807i	−0.665553	−	0.746350i	$-0.731804\pi$
$823$	−35.8441	+	1.87851i	−1.24945	+	0.0654807i	−0.583892	+	0.811831i	$0.698471\pi$
$824$	35.6431	−	61.7356i	1.24169	−	2.15066i
$825$		0			0
$826$	−34.0695	−	17.8086i	−1.18543	−	0.619642i
$827$	−19.0825	−	9.72304i	−0.663565	−	0.338103i	0.0895595	−	0.995981i	$-0.471454\pi$
$827$	−19.0825	−	9.72304i	−0.663565	−	0.338103i	−0.753124	+	0.657878i	$0.771454\pi$
$828$	−48.1138	+	59.4156i	−1.67207	+	2.06484i
$829$	19.4671	+	8.66732i	0.676121	+	0.301028i	0.715923	−	0.698179i	$-0.246006\pi$
$829$	19.4671	+	8.66732i	0.676121	+	0.301028i	−0.0398022	+	0.999208i	$0.512673\pi$
$830$		0			0
$831$	−20.7485	−	46.6019i	−0.719758	−	1.61660i
$832$	0.931465	+	0.931465i	0.0322928	+	0.0322928i
$833$	−8.84036	+	30.4417i	−0.306300	+	1.05474i
$834$	33.7769	+	10.9748i	1.16960	+	0.380025i
$835$		0			0
$836$	−0.389558	−	0.350760i	−0.0134732	−	0.0121313i
$837$	0.120903	−	0.186174i	0.00417901	−	0.00643512i
$838$	44.5610	+	2.33535i	1.53934	+	0.0806732i
$839$	12.8534	+	39.5588i	0.443750	+	1.36572i	0.883849	+	0.467773i	$0.154943\pi$
$839$	12.8534	+	39.5588i	0.443750	+	1.36572i	−0.440099	+	0.897949i	$0.645057\pi$
$840$		0			0
$841$	8.80856	−	27.1100i	0.303744	−	0.934827i
$842$	−11.1414	+	29.0244i	−0.383959	+	1.00025i
$843$	29.3262	+	7.85793i	1.01005	+	0.270641i
$844$	23.5188	+	2.47193i	0.809551	+	0.0850872i
$845$		0			0
$846$	−15.6091	−	21.4841i	−0.536651	−	0.738637i
$847$	44.6941	−	19.3439i	1.53571	−	0.664665i
$848$	−14.7316	+	28.9124i	−0.505884	+	0.992854i
$849$	−10.5030	−	6.06392i	−0.360462	−	0.208113i
$850$		0			0
$851$	0.0648441	+	0.112313i	0.00222283	+	0.00385005i
$852$	8.49061	+	13.0744i	0.290884	+	0.447922i
$853$	5.74952	−	36.3011i	0.196860	−	1.24292i	−0.669237	−	0.743049i	$-0.733379\pi$
$853$	5.74952	−	36.3011i	0.196860	−	1.24292i	0.866097	−	0.499876i	$-0.166621\pi$
$854$	−10.3338	+	8.19143i	−0.353615	+	0.280305i
$855$		0			0
$856$	−40.4195	+	17.9959i	−1.38151	+	0.615087i
$857$	1.40103	−	5.22871i	0.0478582	−	0.178609i	−0.937860	−	0.347015i	$-0.887195\pi$
$857$	1.40103	−	5.22871i	0.0478582	−	0.178609i	0.985718	+	0.168406i	$0.0538619\pi$
$858$	7.41105	−	6.00135i	0.253009	−	0.204883i
$859$	13.7283	+	15.2469i	0.468405	+	0.520217i	0.930340	−	0.366697i	$-0.119511\pi$
$859$	13.7283	+	15.2469i	0.468405	+	0.520217i	−0.461935	+	0.886914i	$0.652845\pi$
$860$		0			0
$861$	12.7368	+	34.2423i	0.434070	+	1.16697i
$862$	−26.7617	−	52.5228i	−0.911508	−	1.78894i
$863$	0.107195	−	2.04541i	0.00364897	−	0.0696265i	−0.996198	−	0.0871174i	$-0.972234\pi$
$863$	0.107195	−	2.04541i	0.00364897	−	0.0696265i	0.999847	+	0.0174909i	$0.00556781\pi$
$864$	−0.314986	+	0.349827i	−0.0107160	+	0.0119014i
$865$		0			0
$866$	8.13048	−	7.32071i	0.276285	−	0.248768i
$867$	1.34135	+	8.46896i	0.0455547	+	0.287621i
$868$	49.0354	+	10.9578i	1.66437	+	0.371931i
$869$	8.09004	−	11.1350i	0.274436	−	0.377728i
$870$		0			0
$871$	1.71746	−	3.85749i	0.0581941	−	0.130706i
$872$	110.047	−	42.2429i	3.72665	−	1.43053i
$873$	−35.0538	+	22.7642i	−1.18639	+	0.770452i
$874$	−0.290518			−0.00982693
$875$		0			0
$876$	−94.3860			−3.18901
$877$	−22.4837	+	14.6011i	−0.759220	+	0.493043i	−0.865263	−	0.501319i	$-0.832848\pi$
$877$	−22.4837	+	14.6011i	−0.759220	+	0.493043i	0.106043	+	0.994362i	$0.466182\pi$
$878$	30.2538	−	11.6134i	1.02102	−	0.391932i
$879$	−10.5647	+	23.7287i	−0.356338	+	0.800348i
$880$		0			0
$881$	1.86581	−	2.56806i	0.0628607	−	0.0865203i	−0.776429	−	0.630204i	$-0.782971\pi$
$881$	1.86581	−	2.56806i	0.0628607	−	0.0865203i	0.839290	+	0.543684i	$0.182971\pi$
$882$	18.2850	+	50.7702i	0.615687	+	1.70952i
$883$	0.379650	+	2.39702i	0.0127763	+	0.0806661i	0.993253	−	0.115971i	$-0.0369979\pi$
$883$	0.379650	+	2.39702i	0.0127763	+	0.0806661i	−0.980476	+	0.196637i	$0.936998\pi$
$884$	−4.39711	+	3.95918i	−0.147891	+	0.133162i
$885$		0			0
$886$	28.7981	−	31.9836i	0.967492	−	1.07451i
$887$	0.276001	−	5.26642i	0.00926721	−	0.176829i	−0.990074	−	0.140545i	$-0.955115\pi$
$887$	0.276001	−	5.26642i	0.00926721	−	0.176829i	0.999342	−	0.0362841i	$-0.0115521\pi$
$888$	−0.184532	−	0.362164i	−0.00619249	−	0.0121534i
$889$	4.60968	−	27.2635i	0.154604	−	0.914390i
$890$		0			0
$891$	32.9002	+	36.5394i	1.10220	+	1.22411i
$892$	−100.123	+	81.0776i	−3.35235	+	2.71468i
$893$	0.0183249	−	0.0683894i	0.000613219	−	0.00228856i
$894$	15.2086	−	6.77130i	0.508651	−	0.226466i
$895$		0			0
$896$	11.9277	+	4.72171i	0.398476	+	0.157741i
$897$	0.580089	−	3.66254i	0.0193686	−	0.122289i
$898$	43.1436	+	66.4353i	1.43972	+	2.21698i
$899$	−1.42028	−	2.45999i	−0.0473689	−	0.0820454i
$900$		0			0
$901$	−14.6046	−	8.43195i	−0.486549	−	0.280909i
$902$	−36.0003	+	70.6546i	−1.19868	+	2.35254i
$903$	4.57941	−	39.5985i	0.152393	−	1.31775i
$904$	8.74389	+	12.0349i	0.290817	+	0.400276i
$905$		0			0
$906$	−31.8062	−	3.34297i	−1.05669	−	0.111063i
$907$	14.3895	+	3.85565i	0.477795	+	0.128025i	0.489676	−	0.871905i	$-0.337115\pi$
$907$	14.3895	+	3.85565i	0.477795	+	0.128025i	−0.0118806	+	0.999929i	$0.503782\pi$
$908$	−19.2704	+	50.2010i	−0.639509	+	1.66598i
$909$	−1.97655	+	6.08321i	−0.0655581	+	0.201767i
$910$		0			0
$911$	9.35146	+	28.7808i	0.309828	+	0.953551i	0.977831	+	0.209394i	$0.0671490\pi$
$911$	9.35146	+	28.7808i	0.309828	+	0.953551i	−0.668004	+	0.744158i	$0.732851\pi$
$912$	0.437262	+	0.0229159i	0.0144792	+	0.000758823i
$913$	20.1822	−	31.0779i	0.667935	−	1.02853i
$914$	54.5066	+	49.0780i	1.80292	+	1.62336i
$915$		0			0
$916$	−48.1627	−	15.6490i	−1.59134	−	0.517058i
$917$	−36.8002	+	32.4475i	−1.21525	+	1.07151i
$918$	−0.455780	−	0.455780i	−0.0150430	−	0.0150430i
$919$	−22.2819	−	50.0460i	−0.735013	−	1.65087i	−0.758947	−	0.651152i	$-0.774286\pi$
$919$	−22.2819	−	50.0460i	−0.735013	−	1.65087i	0.0239340	−	0.999714i	$-0.492381\pi$
$920$		0			0
$921$	9.45493	+	4.20961i	0.311551	+	0.138711i
$922$	9.03428	−	11.1564i	0.297528	−	0.367417i
$923$	−0.335590	−	0.170992i	−0.0110461	−	0.00562825i
$924$	−76.4256	+	146.209i	−2.51422	+	4.80992i
$925$		0			0
$926$	50.2320	−	87.0044i	1.65073	−	2.85914i
$927$	30.2863	−	1.58724i	0.994734	−	0.0521318i
$928$	2.15866	+	5.62351i	0.0708616	+	0.184601i
$929$	−5.88915	−	56.0316i	−0.193217	−	1.83834i	−0.476350	−	0.879256i	$-0.658041\pi$
$929$	−5.88915	−	56.0316i	−0.193217	−	1.83834i	0.283134	−	0.959081i	$-0.408626\pi$
$930$		0			0
$931$	−0.0745159	+	0.123072i	−0.00244216	+	0.00403353i
$932$	−23.0698	+	23.0698i	−0.755678	+	0.755678i
$933$	−9.23169	−	3.54371i	−0.302232	−	0.116016i
$934$	−47.7394	+	10.1473i	−1.56208	+	0.332030i
$935$		0			0
$936$	−1.20365	+	5.66271i	−0.0393424	+	0.185091i
$937$	−17.3680	+	8.84942i	−0.567387	+	0.289098i	−0.714057	−	0.700087i	$-0.753144\pi$
$937$	−17.3680	+	8.84942i	−0.567387	+	0.289098i	0.146670	+	0.989185i	$0.453144\pi$
$938$	−1.08433	+	104.110i	−0.0354045	+	3.39930i
$939$	33.3606	−	10.8395i	1.08868	−	0.353734i
$940$		0			0
$941$	−7.39757	−	34.8029i	−0.241154	−	1.13454i	−0.917432	−	0.397894i	$-0.869741\pi$
$941$	−7.39757	−	34.8029i	−0.241154	−	1.13454i	0.676278	−	0.736647i	$-0.263592\pi$
$942$	25.0049	+	30.8785i	0.814704	+	1.00608i
$943$	7.98070	+	29.7844i	0.259887	+	0.969913i
$944$	39.5625	+	28.7439i	1.28765	+	0.935533i
$945$		0			0
$946$	69.9968	−	50.8557i	2.27579	−	1.65346i
$947$	−19.2550	−	15.5924i	−0.625703	−	0.506684i	0.263223	−	0.964735i	$-0.415215\pi$
$947$	−19.2550	−	15.5924i	−0.625703	−	0.506684i	−0.888926	+	0.458051i	$0.848548\pi$
$948$	1.52742	+	29.1449i	0.0496083	+	0.946582i
$949$	1.97486	−	1.14018i	0.0641065	−	0.0370119i
$950$		0			0
$951$		−	55.9117i		−	1.81306i
$952$	34.9020	−	76.2440i	1.13118	−	2.47108i
$953$	−8.28414	−	1.31208i	−0.268350	−	0.0425024i	0.0208095	−	0.999783i	$-0.493376\pi$
$953$	−8.28414	−	1.31208i	−0.268350	−	0.0425024i	−0.289159	+	0.957281i	$0.593376\pi$
$954$	−28.5506	+	3.00079i	−0.924359	+	0.0971540i
$955$		0			0
$956$	−8.65027	+	82.3018i	−0.279770	+	2.66183i
$957$	9.00915	−	2.41399i	0.291224	−	0.0780333i
$958$	49.6567	−	7.86484i	1.60433	−	0.254102i
$959$	−28.0855	−	7.83987i	−0.906927	−	0.253163i
$960$		0			0
$961$	−14.3746	−	3.05543i	−0.463698	−	0.0985621i
$962$	0.0143295	+	0.00930566i	0.000462001	+	0.000300027i
$963$	−15.7866	−	10.2520i	−0.508717	−	0.330364i
$964$	4.91423	+	1.04455i	0.158277	+	0.0336427i
$965$		0			0
$966$	22.7435	+	88.5590i	0.731759	+	2.84934i
$967$	32.6157	−	5.16582i	1.04885	−	0.166121i	0.391863	−	0.920024i	$-0.371831\pi$
$967$	32.6157	−	5.16582i	1.04885	−	0.166121i	0.656987	+	0.753902i	$0.271831\pi$
$968$	−124.436	+	33.3425i	−3.99952	+	1.07167i
$969$	−0.0237863	+	0.226312i	−0.000764128	+	0.00727019i
$970$		0			0
$971$	−17.3276	+	1.82121i	−0.556070	+	0.0584453i	−0.378395	−	0.925644i	$-0.623524\pi$
$971$	−17.3276	+	1.82121i	−0.556070	+	0.0584453i	−0.177674	+	0.984089i	$0.556857\pi$
$972$	−102.209	−	16.1884i	−3.27836	−	0.519242i
$973$	12.0996	−	8.59975i	0.387894	−	0.275695i
$974$			3.04241i			0.0974850i
$975$		0			0
$976$	14.5268	−	8.38707i	0.464993	−	0.268464i
$977$	−1.20592	−	23.0102i	−0.0385806	−	0.736163i	−0.947610	−	0.319430i	$-0.896509\pi$
$977$	−1.20592	−	23.0102i	−0.0385806	−	0.736163i	0.909029	−	0.416732i	$-0.136825\pi$
$978$	−96.0601	−	77.7879i	−3.07166	−	2.48738i
$979$	−35.9863	+	26.1456i	−1.15013	+	0.835617i
$980$		0			0
$981$	40.5714	+	29.4768i	1.29534	+	0.941123i
$982$	−8.91563	−	33.2736i	−0.284509	−	1.06180i
$983$	−14.7447	−	18.2082i	−0.470284	−	0.580753i	0.485717	−	0.874116i	$-0.338559\pi$
$983$	−14.7447	−	18.2082i	−0.470284	−	0.580753i	−0.956001	+	0.293364i	$0.905225\pi$
$984$	−20.0932	−	94.5309i	−0.640546	−	3.01353i
$985$		0			0
$986$	−7.84427	+	2.54876i	−0.249812	+	0.0811690i
$987$	−22.2818	−	0.232070i	−0.709237	−	0.00738687i
$988$	−0.0239278	+	0.0121918i	−0.000761246	+	0.000387874i
$989$	6.99496	−	32.9087i	0.222427	−	1.04644i
$990$		0			0
$991$	−36.4122	+	7.73965i	−1.15667	+	0.245858i	−0.746013	−	0.665931i	$-0.768035\pi$
$991$	−36.4122	+	7.73965i	−1.15667	+	0.245858i	−0.410659	+	0.911789i	$0.634701\pi$
$992$	−32.2778	−	12.3903i	−1.02482	−	0.393392i
$993$	−58.3569	+	58.3569i	−1.85190	+	1.85190i
$994$	9.26854	+	0.582596i	0.293980	+	0.0184788i
$995$		0			0
$996$	8.21337	+	78.1450i	0.260251	+	2.47612i
$997$	−9.60493	−	25.0217i	−0.304191	−	0.792445i	−0.997424	−	0.0717313i	$-0.977148\pi$
$997$	−9.60493	−	25.0217i	−0.304191	−	0.792445i	0.693233	−	0.720714i	$-0.256186\pi$
$998$	−95.1151	+	4.98477i	−3.01082	+	0.157790i
$999$	−0.000652974		0.00113098i	−2.06592e−5		3.57828e-5i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.c.768.17		288
5.2	odd	4		875.2.bb.a.607.17		288
5.3	odd	4		875.2.bb.b.607.2		288
5.4	even	2		175.2.x.a.33.2	✓	288
7.3	odd	6	inner	875.2.bb.c.143.17		288
25.3	odd	20		175.2.x.a.47.2	yes	288
25.4	even	10		875.2.bb.b.243.17		288
25.21	even	5		875.2.bb.a.243.2		288
25.22	odd	20	inner	875.2.bb.c.257.17		288
35.3	even	12		875.2.bb.b.857.17		288
35.17	even	12		875.2.bb.a.857.2		288
35.24	odd	6		175.2.x.a.108.2	yes	288
175.3	even	60		175.2.x.a.122.2	yes	288
175.122	even	60	inner	875.2.bb.c.507.17		288
175.129	odd	30		875.2.bb.b.493.2		288
175.171	odd	30		875.2.bb.a.493.17		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.2	✓	288	5.4	even	2
175.2.x.a.47.2	yes	288	25.3	odd	20
175.2.x.a.108.2	yes	288	35.24	odd	6
175.2.x.a.122.2	yes	288	175.3	even	60
875.2.bb.a.243.2		288	25.21	even	5
875.2.bb.a.493.17		288	175.171	odd	30
875.2.bb.a.607.17		288	5.2	odd	4
875.2.bb.a.857.2		288	35.17	even	12
875.2.bb.b.243.17		288	25.4	even	10
875.2.bb.b.493.2		288	175.129	odd	30
875.2.bb.b.607.2		288	5.3	odd	4
875.2.bb.b.857.17		288	35.3	even	12
875.2.bb.c.143.17		288	7.3	odd	6	inner
875.2.bb.c.257.17		288	25.22	odd	20	inner
875.2.bb.c.507.17		288	175.122	even	60	inner
875.2.bb.c.768.17		288	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.bb (of order \(60\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.17136 - 1.41010i) q^{2} +(-2.28251 + 0.876172i) q^{3} +(1.91296 - 4.29657i) q^{4} +(-3.72066 + 5.12104i) q^{6} +(0.791332 + 2.52464i) q^{7} +(-1.09484 - 6.91252i) q^{8} +(2.21272 - 1.99235i) q^{9} +(3.62858 - 4.02995i) q^{11} +(-0.601800 + 11.4830i) q^{12} +(-0.126124 - 0.247532i) q^{13} +(5.27825 + 4.36604i) q^{14} +(-5.83052 - 6.47545i) q^{16} +(3.51929 - 2.84986i) q^{17} +(1.99522 - 7.44626i) q^{18} +(0.0187763 - 0.00835976i) q^{19} +(-4.01824 - 5.06916i) q^{21} +(2.19634 - 13.8671i) q^{22} +(-2.97345 - 4.57872i) q^{23} +(8.55552 + 14.8186i) q^{24} +(-0.622904 - 0.359634i) q^{26} +(0.0249589 - 0.0489845i) q^{27} +(12.3611 + 1.42951i) q^{28} +(-0.413497 - 0.569129i) q^{29} +(4.01573 + 0.422070i) q^{31} +(-8.27077 - 2.21615i) q^{32} +(-4.75134 + 12.3777i) q^{33} +(3.62306 - 11.1506i) q^{34} +(-4.32741 - 13.3184i) q^{36} +(-0.0237221 - 0.00124322i) q^{37} +(0.0289821 - 0.0446285i) q^{38} +(0.504758 + 0.454487i) q^{39} +(-5.37154 - 1.74532i) q^{41} +(-15.8731 - 5.34086i) q^{42} +(4.35752 + 4.35752i) q^{43} +(-10.3736 - 23.2996i) q^{44} +(-12.9129 - 5.74918i) q^{46} +(2.16788 - 2.67711i) q^{47} +(18.9818 + 9.67172i) q^{48} +(-5.74759 + 3.99565i) q^{49} +(-5.53583 + 9.58833i) q^{51} +(-1.30481 + 0.0683820i) q^{52} +(-1.33455 - 3.47662i) q^{53} +(-0.0148783 - 0.141557i) q^{54} +(16.5852 - 8.23416i) q^{56} +(-0.0355325 + 0.0355325i) q^{57} +(-1.70038 - 0.652714i) q^{58} +(-5.48952 + 1.16683i) q^{59} +(-0.400242 + 1.88299i) q^{61} +(9.31476 - 4.74610i) q^{62} +(6.78095 + 4.00972i) q^{63} +(-4.50960 + 1.46526i) q^{64} +(7.13684 + 33.5762i) q^{66} +(9.56525 + 11.8121i) q^{67} +(-5.51240 - 20.5725i) q^{68} +(10.7987 + 7.84569i) q^{69} +(1.09682 - 0.796887i) q^{71} +(-16.1947 - 13.1142i) q^{72} +(0.429591 + 8.19708i) q^{73} +(-0.0532622 + 0.0307510i) q^{74} -0.0966658i q^{76} +(13.0456 + 5.97183i) q^{77} +(1.73688 + 0.275095i) q^{78} +(2.52418 - 0.265302i) q^{79} +(-0.947755 + 9.01728i) q^{81} +(-14.1246 + 3.78468i) q^{82} +(6.74923 - 1.06897i) q^{83} +(-29.4667 + 7.56756i) q^{84} +(15.6063 + 3.31721i) q^{86} +(1.44246 + 0.936747i) q^{87} +(-31.8298 - 20.6705i) q^{88} +(-8.02339 - 1.70542i) q^{89} +(0.525122 - 0.514296i) q^{91} +(-25.3609 + 4.01677i) q^{92} +(-9.53573 + 2.55509i) q^{93} +(0.932265 - 8.86991i) q^{94} +(20.8198 - 2.18825i) q^{96} +(-13.8647 - 2.19595i) q^{97} +(-6.84583 + 16.7807i) q^{98} -16.1466i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 8 q^{2} + 24 q^{3} - 10 q^{4} + 10 q^{7} + 36 q^{8} - 10 q^{9} - 6 q^{11} + 36 q^{12} - 20 q^{14} - 30 q^{16} + 42 q^{17} + 14 q^{18} - 30 q^{19} - 12 q^{21} - 32 q^{22} + 40 q^{23} - 48 q^{26}+ \cdots - 222 q^{98}+O(q^{100}) \) 288 * q + 8 * q^2 + 24 * q^3 - 10 * q^4 + 10 * q^7 + 36 * q^8 - 10 * q^9 - 6 * q^11 + 36 * q^12 - 20 * q^14 - 30 * q^16 + 42 * q^17 + 14 * q^18 - 30 * q^19 - 12 * q^21 - 32 * q^22 + 40 * q^23 - 48 * q^26 - 22 * q^28 - 18 * q^31 - 8 * q^32 + 30 * q^33 + 40 * q^36 + 10 * q^37 - 72 * q^38 + 30 * q^39 - 6 * q^42 + 108 * q^43 - 10 * q^44 - 6 * q^46 + 54 * q^47 - 16 * q^51 - 216 * q^52 - 50 * q^53 - 30 * q^54 + 4 * q^56 + 216 * q^57 + 4 * q^58 + 90 * q^59 - 18 * q^61 + 66 * q^63 - 100 * q^64 - 90 * q^66 - 4 * q^67 - 342 * q^68 - 24 * q^71 - 58 * q^72 + 6 * q^73 + 80 * q^77 + 132 * q^78 - 10 * q^79 - 10 * q^81 - 216 * q^82 + 20 * q^84 - 6 * q^86 + 48 * q^87 + 122 * q^88 + 120 * q^89 - 12 * q^91 + 4 * q^92 - 106 * q^93 - 30 * q^94 - 90 * q^96 - 222 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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