LMFDB - Embedded newform 875.2.bb.c.507.17

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			507.17
Character	$\chi$	$=$	875.507
Dual form			875.2.bb.c.768.17

$q$-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 $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{6}\right)$

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	0.986974	+	0.160880i	$0.0514334\pi$
$2$	2.17136	+	1.41010i	1.53538	+	0.997090i	0.548410	+	0.836210i	$0.315233\pi$
$3$	−2.28251	−	0.876172i	−1.31781	−	0.505858i	−0.405024	−	0.914306i	$-0.632737\pi$
$3$	−2.28251	−	0.876172i	−1.31781	−	0.505858i	−0.912782	+	0.408448i	$0.866070\pi$
$4$	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	0.975004	+	0.222188i	$0.0713199\pi$
$11$	3.62858	+	4.02995i	1.09406	+	1.21508i	0.119055	+	0.992888i	$0.462013\pi$
$12$	−0.601800	−	11.4830i	−0.173725	−	3.31487i
$13$	−0.126124	+	0.247532i	−0.0349804	+	0.0686529i	−0.907835	−	0.419327i	$-0.862266\pi$
$13$	−0.126124	+	0.247532i	−0.0349804	+	0.0686529i	0.872855	+	0.487980i	$0.162266\pi$
$14$	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	0.952711	−	0.303878i	$-0.0982816\pi$
$17$	3.51929	+	2.84986i	0.853553	+	0.691193i	−0.0991581	+	0.995072i	$0.531615\pi$
$18$	1.99522	+	7.44626i	0.470278	+	1.75510i
$19$	0.0187763	+	0.00835976i	0.00430759	+	0.00191786i	0.408889	−	0.912584i	$-0.365916\pi$
$19$	0.0187763	+	0.00835976i	0.00430759	+	0.00191786i	−0.404582	+	0.914502i	$0.632583\pi$
$20$		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	0.379555	+	0.925169i	$0.376077\pi$
$23$	−2.97345	+	4.57872i	−0.620008	+	0.954728i	−0.999563	+	0.0295591i	$0.990590\pi$
$24$	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	−0.845682	−	0.533688i	$-0.820806\pi$
$29$	−0.413497	+	0.569129i	−0.0767844	+	0.105685i	0.768897	+	0.639372i	$0.220806\pi$
$30$		0			0
$31$	4.01573	−	0.422070i	0.721246	−	0.0758060i	0.263209	−	0.964739i	$-0.415219\pi$
$31$	4.01573	−	0.422070i	0.721246	−	0.0758060i	0.458037	+	0.888933i	$0.348553\pi$
$32$	−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	−0.0542858	−	0.998525i	$-0.517288\pi$
$37$	−0.0237221	+	0.00124322i	−0.00389988	+	0.000204384i	0.0503859	+	0.998730i	$0.483955\pi$
$38$	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	−0.696787	−	0.717278i	$-0.745388\pi$
$41$	−5.37154	+	1.74532i	−0.838894	+	0.272573i	−0.142107	+	0.989851i	$0.545388\pi$
$42$	−15.8731	+	5.34086i	−2.44927	+	0.824113i
$43$	4.35752	−	4.35752i	0.664515	−	0.664515i	−0.291926	−	0.956441i	$-0.594296\pi$
$43$	4.35752	−	4.35752i	0.664515	−	0.664515i	0.956441	+	0.291926i	$0.0942961\pi$
$44$	−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	0.910328	−	0.413887i	$-0.135829\pi$
$47$	2.16788	+	2.67711i	0.316218	+	0.390497i	−0.594110	+	0.804384i	$0.702496\pi$
$48$	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	−0.994186	−	0.107673i	$-0.965660\pi$
$53$	−1.33455	+	3.47662i	−0.183315	+	0.477551i	0.810872	+	0.585224i	$0.198993\pi$
$54$	−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	−0.163796	−	0.986494i	$-0.552374\pi$
$59$	−5.48952	−	1.16683i	−0.714674	−	0.151909i	−0.550878	+	0.834586i	$0.685707\pi$
$60$		0			0
$61$	−0.400242	−	1.88299i	−0.0512457	−	0.241092i	0.945068	−	0.326873i	$-0.105995\pi$
$61$	−0.400242	−	1.88299i	−0.0512457	−	0.241092i	−0.996314	+	0.0857806i	$0.972662\pi$
$62$	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	0.295608	−	0.955309i	$-0.404478\pi$
$67$	9.56525	−	11.8121i	1.16858	−	1.44308i	0.872973	−	0.487768i	$-0.162189\pi$
$68$	−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	0.650964	−	0.759108i	$-0.274365\pi$
$71$	1.09682	+	0.796887i	0.130169	+	0.0945731i	−0.520796	+	0.853681i	$0.674365\pi$
$72$	−16.1947	+	13.1142i	−1.90856	+	1.54552i
$73$	0.429591	−	8.19708i	0.0502798	−	0.959396i	−0.850731	−	0.525601i	$-0.823841\pi$
$73$	0.429591	−	8.19708i	0.0502798	−	0.959396i	0.901011	−	0.433796i	$-0.142826\pi$
$74$	−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	0.245454	−	0.969408i	$-0.421063\pi$
$79$	2.52418	+	0.265302i	0.283992	+	0.0298488i	0.0385386	+	0.999257i	$0.487730\pi$
$80$		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	0.515429	−	0.856932i	$-0.327633\pi$
$83$	6.74923	+	1.06897i	0.740825	+	0.117335i	0.225396	+	0.974267i	$0.427633\pi$
$84$	−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	−0.612475	−	0.790490i	$-0.709826\pi$
$89$	−8.02339	+	1.70542i	−0.850478	+	0.180775i	−0.238003	+	0.971265i	$0.576493\pi$
$90$		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	−0.813615	−	0.581404i	$-0.802504\pi$
$97$	−13.8647	+	2.19595i	−1.40775	+	0.222965i	−0.594130	+	0.804369i	$0.702504\pi$
$98$	−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	0.404579	−	0.914503i	$-0.367418\pi$
$101$	−1.86039	−	1.07409i	−0.185115	−	0.106876i	−0.589694	+	0.807627i	$0.700752\pi$
$102$	1.50021	−	28.6258i	0.148543	−	2.83438i
$103$	7.91574	−	6.41004i	0.779961	−	0.631600i	−0.154368	−	0.988013i	$-0.549334\pi$
$103$	7.91574	−	6.41004i	0.779961	−	0.631600i	0.934328	+	0.356414i	$0.116001\pi$
$104$	−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	0.840633	+	0.541605i	$0.182183\pi$
$107$	−1.63621	+	6.10643i	−0.158179	+	0.590331i	−0.998812	+	0.0487267i	$0.984484\pi$
$108$	−0.162720	+	0.200943i	−0.0156578	+	0.0193357i
$109$	3.50177	−	16.4745i	0.335408	−	1.57797i	−0.410460	−	0.911879i	$-0.634632\pi$
$109$	3.50177	−	16.4745i	0.335408	−	1.57797i	0.745868	−	0.666094i	$-0.232035\pi$
$110$		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	0.362636	−	0.931931i	$-0.381877\pi$
$113$	−1.89387	−	0.964975i	−0.178160	−	0.0907772i	−0.540796	+	0.841154i	$0.681877\pi$
$114$	−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	−0.815381	−	0.578924i	$-0.803473\pi$
$127$	−9.31183	+	4.74461i	−0.826291	+	0.421016i	−0.0109096	+	0.999940i	$0.503473\pi$
$128$	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	−0.206129	−	0.978525i	$-0.566087\pi$
$131$	7.54242	−	16.9405i	0.658984	−	1.48010i	0.865113	−	0.501577i	$-0.167247\pi$
$132$	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	0.483493	−	0.875348i	$-0.339368\pi$
$137$	−6.00254	−	9.24309i	−0.512831	−	0.789691i	−0.996325	+	0.0856572i	$0.972701\pi$
$138$	34.5110	−	1.80864i	2.93777	−	0.153962i
$139$	−1.73378	+	5.33603i	−0.147058	+	0.452597i	−0.997270	−	0.0738434i	$-0.976474\pi$
$139$	−1.73378	+	5.33603i	−0.147058	+	0.452597i	0.850212	+	0.526440i	$0.176474\pi$
$140$		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	−0.590387	−	0.807121i	$-0.701025\pi$
$149$	−2.27766	+	1.31501i	−0.186593	+	0.107730i	0.403794	+	0.914850i	$0.367691\pi$
$150$		0			0
$151$	2.52619	−	4.37549i	0.205579	−	0.356073i	−0.744738	−	0.667357i	$-0.767426\pi$
$151$	2.52619	−	4.37549i	0.205579	−	0.356073i	0.950317	+	0.311284i	$0.100759\pi$
$152$	−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	0.999963	−	0.00862335i	$-0.00274493\pi$
$157$	1.62461	+	6.06312i	0.129658	+	0.483890i	−0.870305	+	0.492513i	$0.836078\pi$
$158$	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	−0.683476	−	0.729973i	$-0.739532\pi$
$163$	−1.02197	−	19.5004i	−0.0800471	−	1.52739i	0.603429	−	0.797417i	$-0.293801\pi$
$164$	−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	0.603494	+	0.797367i	$0.293775\pi$
$167$	−2.80249	+	17.6942i	−0.216863	+	1.36922i	−0.820357	+	0.571852i	$0.806225\pi$
$168$	−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	−0.0494928	−	0.998774i	$-0.515760\pi$
$173$	−12.9168	−	8.38829i	−0.982049	−	0.637750i	−0.932556	+	0.361024i	$0.882427\pi$
$174$	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	0.921043	−	0.389461i	$-0.127339\pi$
$179$	0.204955	+	0.460337i	0.0153191	+	0.0344072i	−0.905724	+	0.423868i	$0.860672\pi$
$180$		0			0
$181$	−7.22957	−	9.95064i	−0.537369	−	0.739625i	0.450862	−	0.892594i	$-0.351117\pi$
$181$	−7.22957	−	9.95064i	−0.537369	−	0.739625i	−0.988231	+	0.152968i	$0.951117\pi$
$182$	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	−0.974137	−	0.225960i	$-0.927448\pi$
$191$	−8.94987	+	9.93984i	−0.647590	+	0.719222i	0.326547	+	0.945181i	$0.394115\pi$
$192$	9.00938	+	7.29565i	0.650196	+	0.526518i
$193$	0.646732	+	2.41364i	0.0465528	+	0.173737i	0.985288	−	0.170902i	$-0.0546680\pi$
$193$	0.646732	+	2.41364i	0.0465528	+	0.173737i	−0.938735	+	0.344639i	$0.888001\pi$
$194$	−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	−0.533784	−	0.845621i	$-0.679231\pi$
$197$	−4.03436	−	25.4720i	−0.287436	−	1.81480i	0.246348	−	0.969181i	$-0.420769\pi$
$198$	−22.7682	+	35.0600i	−1.61807	+	2.49161i
$199$	9.50790	−	16.4682i	0.673997	−	1.16740i	−0.302764	−	0.953066i	$-0.597909\pi$
$199$	9.50790	−	16.4682i	0.673997	−	1.16740i	0.976761	−	0.214332i	$-0.0687573\pi$
$200$		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	−0.883220	−	0.468959i	$-0.844629\pi$
$211$	1.55379	−	4.78206i	0.106967	−	0.329211i	0.990187	+	0.139748i	$0.0446293\pi$
$212$	−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	−0.636311	+	0.771433i	$0.719540\pi$
$223$	−24.4072	+	12.4361i	−1.63443	+	0.832782i	−0.998116	+	0.0613496i	$0.980460\pi$
$224$	−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	−0.330482	−	0.943812i	$-0.607211\pi$
$227$	−11.4176	−	0.598369i	−0.757810	−	0.0397151i	−0.427327	+	0.904097i	$0.640545\pi$
$228$	0.0846959	−	0.220640i	0.00560912	−	0.0146123i
$229$	−1.12550	+	10.7085i	−0.0743754	+	0.707634i	0.892268	+	0.451507i	$0.149113\pi$
$229$	−1.12550	+	10.7085i	−0.0743754	+	0.707634i	−0.966643	+	0.256128i	$0.917553\pi$
$230$		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	−0.561128	−	0.827729i	$-0.689633\pi$
$233$	−6.47619	+	2.48598i	−0.424269	+	0.162862i	0.136859	+	0.990591i	$0.456299\pi$
$234$	−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	−0.287129	−	0.957892i	$-0.592701\pi$
$239$	−16.7344	−	5.43732i	−1.08246	−	0.351711i	−0.795327	+	0.606181i	$0.792701\pi$
$240$		0			0
$241$	0.222094	−	1.04487i	0.0143064	−	0.0673061i	−0.970415	−	0.241442i	$-0.922380\pi$
$241$	0.222094	−	1.04487i	0.0143064	−	0.0673061i	0.984722	+	0.174136i	$0.0557131\pi$
$242$	−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	$0.221393\pi$
$251$			20.3040i			1.28158i	−0.767716	+	0.640790i	$0.778607\pi$
$252$	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	0.871613	−	0.490194i	$-0.163074\pi$
$257$	22.1448	+	5.93369i	1.38136	+	0.370133i	0.509742	+	0.860327i	$0.329741\pi$
$258$	−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	0.244479	−	0.969654i	$-0.421383\pi$
$263$	19.9431	−	12.9512i	1.22974	−	0.798604i	0.985262	+	0.171051i	$0.0547163\pi$
$264$	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	−0.997302	−	0.0734086i	$-0.976612\pi$
$269$	−0.607763	−	5.78248i	−0.0370559	−	0.352564i	0.960246	−	0.279155i	$-0.0900544\pi$
$270$		0			0
$271$	16.7703	+	1.76263i	1.01872	+	0.107072i	0.599140	−	0.800644i	$-0.295509\pi$
$271$	16.7703	+	1.76263i	1.01872	+	0.107072i	0.419584	+	0.907717i	$0.362176\pi$
$272$	−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	−0.745291	−	0.666740i	$-0.767689\pi$
$277$	1.09198	−	20.8362i	0.0656105	−	1.25192i	0.810901	−	0.585183i	$-0.198977\pi$
$278$	−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	−0.845636	−	0.533760i	$-0.820779\pi$
$281$	−10.0464	+	7.29912i	−0.599316	+	0.435429i	0.246320	+	0.969189i	$0.420779\pi$
$282$	5.64367	−	21.0625i	0.336076	−	1.25425i
$283$	3.12173	−	3.85501i	0.185567	−	0.229157i	−0.675869	−	0.737021i	$-0.736232\pi$
$283$	3.12173	−	3.85501i	0.185567	−	0.229157i	0.861437	+	0.507865i	$0.169565\pi$
$284$	−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	0.891631	−	0.452763i	$-0.149562\pi$
$293$	7.51221	+	7.51221i	0.438868	+	0.438868i	−0.452763	+	0.891631i	$0.649562\pi$
$294$	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	−0.787347	−	0.616510i	$-0.788546\pi$
$307$	−2.99332	+	2.99332i	−0.170838	+	0.170838i	0.616510	+	0.787347i	$0.288546\pi$
$308$	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	−0.579498	−	0.814973i	$-0.696752\pi$
$311$	3.00568	−	2.70633i	0.170436	−	0.153462i	0.749935	+	0.661512i	$0.230085\pi$
$312$	2.58902	+	3.98674i	0.146574	+	0.225705i
$313$	−14.3275	+	0.750874i	−0.809840	+	0.0424419i	−0.452760	−	0.891632i	$-0.649561\pi$
$313$	−14.3275	+	0.750874i	−0.809840	+	0.0424419i	−0.357079	+	0.934074i	$0.616227\pi$
$314$	−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	−0.945760	−	0.324866i	$-0.894681\pi$
$317$	−8.19543	−	21.3498i	−0.460301	−	1.19913i	0.485459	−	0.874259i	$-0.338652\pi$
$318$	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	0.999343	+	0.0362512i	$0.0115417\pi$
$331$	30.8373	+	13.7297i	1.69497	+	0.754651i	0.695631	+	0.718400i	$0.255125\pi$
$332$	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	0.327155	+	0.944971i	$0.393910\pi$
$337$	−11.5586	+	22.6851i	−0.629640	+	1.23574i	−0.956794	+	0.290766i	$0.906090\pi$
$338$	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	0.352814	−	0.935694i	$-0.385225\pi$
$347$	−0.206693	−	0.0793419i	−0.0110959	−	0.00425930i	−0.363910	+	0.931434i	$0.618558\pi$
$348$	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	0.796343	−	0.604846i	$-0.206765\pi$
$353$	18.4768	+	7.09257i	0.983419	+	0.377499i	0.187077	+	0.982345i	$0.440099\pi$
$354$	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	0.835666	−	0.549237i	$-0.185082\pi$
$359$	7.13913	+	6.42810i	0.376789	+	0.339262i	−0.458877	+	0.888500i	$0.651748\pi$
$360$		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	0.898549	−	0.438873i	$-0.144622\pi$
$367$	12.5688	+	10.1780i	0.656085	+	0.531287i	−0.242464	+	0.970160i	$0.577956\pi$
$368$	−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	−0.982137	−	0.188165i	$-0.939746\pi$
$373$	−7.93327	+	12.2162i	−0.410769	+	0.632529i	0.571368	+	0.820694i	$0.306413\pi$
$374$	−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	−0.997615	−	0.0690260i	$-0.978011\pi$
$379$	−12.1419	+	16.7119i	−0.623687	+	0.858432i	0.373928	+	0.927458i	$0.378011\pi$
$380$		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	−0.765454	−	0.643491i	$-0.777486\pi$
$383$	−12.2744	−	31.9758i	−0.627190	−	1.63389i	0.138264	−	0.990395i	$-0.455848\pi$
$384$	−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	−0.723217	−	0.690621i	$-0.757337\pi$
$389$	−2.20850	+	1.98855i	−0.111976	+	0.100823i	0.611241	+	0.791444i	$0.290671\pi$
$390$		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	0.405699	−	0.914007i	$-0.367028\pi$
$397$	−11.4107	−	14.0910i	−0.572684	−	0.707206i	−0.978383	+	0.206801i	$0.933695\pi$
$398$	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	0.952297	+	0.305172i	$0.0987141\pi$
$401$	14.8272	+	25.6815i	0.740436	+	1.28247i	−0.211862	+	0.977300i	$0.567953\pi$
$402$	−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	−0.0140936	−	0.999901i	$-0.504486\pi$
$409$	−8.77033	−	1.86419i	−0.433665	−	0.0921783i	−0.419571	+	0.907722i	$0.637820\pi$
$410$		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	−0.192570	−	0.981283i	$-0.561682\pi$
$419$	13.9434	−	10.1305i	0.681179	−	0.494905i	0.873748	+	0.486378i	$0.161682\pi$
$420$		0			0
$421$	−9.71469	−	7.05813i	−0.473465	−	0.343992i	0.325325	−	0.945602i	$-0.394526\pi$
$421$	−9.71469	−	7.05813i	−0.473465	−	0.343992i	−0.798790	+	0.601610i	$0.794526\pi$
$422$	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	0.888986	+	0.457935i	$0.151411\pi$
$431$	2.37991	+	22.6434i	0.114636	+	1.09069i	−0.774349	+	0.632758i	$0.781923\pi$
$432$	−0.462720	−	0.123985i	−0.0222626	−	0.00596525i
$433$	4.17371	+	0.661050i	0.200576	+	0.0317680i	0.255914	−	0.966700i	$-0.417624\pi$
$433$	4.17371	+	0.661050i	0.200576	+	0.0317680i	−0.0553382	+	0.998468i	$0.517624\pi$
$434$	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	0.0937461	−	0.995596i	$-0.470116\pi$
$439$	12.2431	−	2.60236i	0.584333	−	0.124204i	0.490587	+	0.871392i	$0.336782\pi$
$440$		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	0.619223	−	0.785216i	$-0.287448\pi$
$443$	16.0567	+	4.30238i	0.762877	+	0.204412i	0.143655	+	0.989628i	$0.454115\pi$
$444$	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	$-0.743241\pi$
$449$		−	30.5962i		−	1.44392i	0.691934	−	0.721961i	$-0.256759\pi$
$450$		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	−0.551967	−	0.833866i	$-0.686122\pi$
$457$	7.33215	−	27.3640i	0.342984	−	1.28003i	0.894950	−	0.446166i	$-0.147211\pi$
$458$	−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	0.429233	−	0.903194i	$-0.358784\pi$
$461$	5.27336	+	1.71342i	0.245605	+	0.0798018i	−0.183628	+	0.982996i	$0.558784\pi$
$462$	−79.1201	−	44.5878i	−3.68100	−	2.07441i
$463$	34.5741	+	17.6164i	1.60680	+	0.818703i	0.999710	+	0.0240660i	$0.00766117\pi$
$463$	34.5741	+	17.6164i	1.60680	+	0.818703i	0.607085	+	0.794637i	$0.292339\pi$
$464$	−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	−0.729673	−	0.683796i	$-0.760328\pi$
$467$	−17.5988	+	6.75555i	−0.814376	+	0.312610i	−0.0847034	+	0.996406i	$0.526994\pi$
$468$	−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	0.0407529	−	0.999169i	$-0.487024\pi$
$479$	17.7397	−	7.89824i	0.810549	−	0.360880i	0.769796	+	0.638289i	$0.220358\pi$
$480$		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	0.823872	−	0.566775i	$-0.191809\pi$
$487$	−0.640008	−	0.985526i	−0.0290015	−	0.0446585i	−0.852874	+	0.522117i	$0.825143\pi$
$488$	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	0.999957	−	0.00923217i	$-0.00293873\pi$
$491$	4.11148	+	12.6538i	0.185548	+	0.571059i	−0.814409	+	0.580291i	$0.802939\pi$
$492$	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	−0.996820	−	0.0796912i	$-0.974607\pi$
$499$	−31.8592	+	18.3939i	−1.42621	+	0.823426i	−0.429395	+	0.903117i	$0.641273\pi$
$500$		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	−0.988130	−	0.153621i	$-0.950907\pi$
$503$	−2.14933	−	13.5703i	−0.0958339	−	0.605072i	0.892296	−	0.451451i	$-0.149093\pi$
$504$	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	−0.221653	−	0.975126i	$-0.571145\pi$
$509$	17.4013	−	19.3261i	0.771300	−	0.856615i	0.992953	+	0.118511i	$0.0378119\pi$
$510$		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	0.847213	+	0.531254i	$0.178279\pi$
$521$	15.4098	+	34.6110i	0.675115	+	1.51633i	−0.172097	+	0.985080i	$0.555054\pi$
$522$	−5.06290	−	1.94347i	−0.221597	−	0.0850632i
$523$	−5.76773	−	3.74561i	−0.252205	−	0.163784i	0.412345	−	0.911028i	$-0.364710\pi$
$523$	−5.76773	−	3.74561i	−0.252205	−	0.163784i	−0.664550	+	0.747244i	$0.731377\pi$
$524$	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	−0.0990188	−	0.995086i	$-0.531570\pi$
$541$	20.9559	−	23.2739i	0.900966	−	1.00062i	0.999985	−	0.00553845i	$-0.00176295\pi$
$542$	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	−0.764082	−	0.645119i	$-0.776808\pi$
$547$	−5.53710	−	34.9599i	−0.236749	−	1.49478i	0.527333	−	0.849659i	$-0.323192\pi$
$548$	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	−0.216420	−	0.976300i	$-0.569438\pi$
$557$	1.98966	−	0.533128i	0.0843046	−	0.0225893i	0.300725	+	0.953711i	$0.402771\pi$
$558$	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	0.981819	+	0.189818i	$0.0607899\pi$
$563$	17.9354	+	27.6180i	0.755885	+	1.16396i	−0.225934	+	0.974143i	$0.572543\pi$
$564$	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	−0.819349	−	0.573295i	$-0.805665\pi$
$569$	3.69598	−	8.30131i	0.154944	−	0.348009i	0.974293	+	0.225286i	$0.0723316\pi$
$570$		0			0
$571$	34.5801	−	15.3961i	1.44713	−	0.644306i	0.475268	−	0.879841i	$-0.342351\pi$
$571$	34.5801	−	15.3961i	1.44713	−	0.644306i	0.971866	+	0.235535i	$0.0756843\pi$
$572$	−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	0.418608	−	0.908167i	$-0.362518\pi$
$577$	17.7752	+	0.931561i	0.739993	+	0.0387814i	0.321385	+	0.946949i	$0.395852\pi$
$578$	−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	−0.512991	−	0.858394i	$-0.671463\pi$
$587$	−36.5596	−	18.6280i	−1.50898	−	0.768861i	−0.995984	+	0.0895323i	$0.971463\pi$
$588$	−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	−0.950485	−	0.310771i	$-0.899413\pi$
$593$	0.682938	−	2.54876i	0.0280449	−	0.104665i	0.978530	+	0.206106i	$0.0660793\pi$
$594$	−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	0.777779	−	0.628538i	$-0.216346\pi$
$599$	15.2314	+	8.79385i	0.622338	+	0.359307i	−0.155441	+	0.987845i	$0.549680\pi$
$600$		0			0
$601$			4.58675i			0.187097i	0.995615	+	0.0935487i	$0.0298211\pi$
$601$			4.58675i			0.187097i	−0.995615	+	0.0935487i	$0.970179\pi$
$602$	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	0.269141	−	0.963101i	$-0.413260\pi$
$607$	0.509336	+	0.136476i	0.0206733	+	0.00553939i	−0.248468	+	0.968640i	$0.579927\pi$
$608$	−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	−0.516676	−	0.856181i	$-0.672831\pi$
$613$	1.37000	−	0.889687i	0.0553337	−	0.0359341i	0.572009	+	0.820247i	$0.306164\pi$
$614$	−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	0.229547	−	0.973298i	$-0.426276\pi$
$617$	3.65372	+	0.578692i	0.147093	+	0.0232973i	−0.0824536	+	0.996595i	$0.526276\pi$
$618$	−62.2778	−	16.6873i	−2.50518	−	0.671261i
$619$	1.40210	+	13.3401i	0.0563552	+	0.536184i	0.985883	+	0.167433i	$0.0535478\pi$
$619$	1.40210	+	13.3401i	0.0563552	+	0.536184i	−0.929528	+	0.368751i	$0.879786\pi$
$620$		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	−0.644087	−	0.764953i	$-0.722762\pi$
$631$	−2.90402	+	2.10989i	−0.115607	+	0.0839935i	0.528479	+	0.848946i	$0.322762\pi$
$632$	−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	−0.408022	−	0.912972i	$-0.633781\pi$
$641$	−29.1690	−	6.20007i	−1.15211	−	0.244888i	−0.744086	+	0.668084i	$0.767115\pi$
$642$	37.3591	−	14.3408i	1.47445	−	0.565987i
$643$	30.4036	+	30.4036i	1.19900	+	1.19900i	0.974466	+	0.224535i	$0.0720863\pi$
$643$	30.4036	+	30.4036i	1.19900	+	1.19900i	0.224535	+	0.974466i	$0.427914\pi$
$644$	−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	−0.425784	−	0.904825i	$-0.640002\pi$
$647$	12.6184	−	32.8721i	0.496081	−	1.29234i	0.921865	−	0.387511i	$-0.126665\pi$
$648$	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	0.676604	−	0.736347i	$-0.263451\pi$
$653$	−4.71025	−	5.81668i	−0.184327	−	0.227624i	−0.860930	+	0.508723i	$0.830118\pi$
$654$	−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	0.0704403	−	0.997516i	$-0.477560\pi$
$659$	18.3227	−	5.95342i	0.713753	−	0.231912i	0.643313	+	0.765604i	$0.277560\pi$
$660$		0			0
$661$	−15.3915	+	13.8586i	−0.598662	+	0.539037i	−0.911781	−	0.410676i	$-0.865293\pi$
$661$	−15.3915	+	13.8586i	−0.598662	+	0.539037i	0.313120	+	0.949714i	$0.398626\pi$
$662$	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	0.985626	+	0.168944i	$0.0540356\pi$
$673$	14.0858	+	27.6449i	0.542968	+	1.06563i	−0.442658	+	0.896691i	$0.645964\pi$
$674$	−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	−0.434647	−	0.900601i	$-0.643127\pi$
$677$	14.6977	−	22.6325i	0.564880	−	0.869838i	0.999527	+	0.0307626i	$0.00979358\pi$
$678$	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	0.0125408	−	0.999921i	$-0.496008\pi$
$683$	−25.1653	−	20.3784i	−0.962922	−	0.779759i	−0.975463	+	0.220162i	$0.929341\pi$
$684$	−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	0.372320	−	0.928105i	$-0.378562\pi$
$691$	−13.4532	−	12.1133i	−0.511783	−	0.460811i	−0.884102	+	0.467293i	$0.845229\pi$
$692$	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	0.531468	−	0.847078i	$-0.321641\pi$
$709$	−6.80098	−	6.12363i	−0.255416	−	0.229978i	−0.786884	+	0.617101i	$0.788307\pi$
$710$		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	−0.614564	−	0.788867i	$-0.710668\pi$
$719$	−43.2253	−	19.2451i	−1.61203	−	0.717722i	−0.997466	+	0.0711450i	$0.977335\pi$
$720$		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	−0.941341	−	0.337457i	$-0.890433\pi$
$727$	−17.8237	−	34.9809i	−0.661043	−	1.29737i	0.280298	−	0.959913i	$-0.409567\pi$
$728$	−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	0.841159	−	0.540788i	$-0.181874\pi$
$733$	−3.94744	−	10.2834i	−0.145802	−	0.379827i	−0.986961	+	0.160961i	$0.948541\pi$
$734$	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	−0.0807371	−	0.996735i	$-0.525727\pi$
$739$	24.5232	−	22.0807i	0.902099	−	0.812253i	0.982836	+	0.184482i	$0.0590607\pi$
$740$		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	−0.667522	−	0.744590i	$-0.732645\pi$
$743$	2.10074	−	2.10074i	0.0770687	−	0.0770687i	0.744590	+	0.667522i	$0.232645\pi$
$744$	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	0.639043	−	0.769171i	$-0.279331\pi$
$751$	−9.49836	−	16.4516i	−0.346600	−	0.600329i	−0.985643	+	0.168842i	$0.945997\pi$
$752$	−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	0.948797	−	0.315887i	$-0.102302\pi$
$757$	17.4136	+	17.4136i	0.632909	+	0.632909i	−0.315887	+	0.948797i	$0.602302\pi$
$758$	−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	−0.908334	−	0.418246i	$-0.862645\pi$
$761$	−6.85919	−	32.2700i	−0.248646	−	1.16979i	0.659688	−	0.751539i	$-0.270688\pi$
$762$	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	−0.772092	−	0.635511i	$-0.780790\pi$
$769$	−11.2664	+	8.18549i	−0.406275	+	0.295176i	0.365817	+	0.930687i	$0.380790\pi$
$770$		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	−0.987197	−	0.159508i	$-0.949009\pi$
$773$	0.313203	−	5.97627i	0.0112651	−	0.214952i	0.998462	−	0.0554438i	$-0.0176574\pi$
$774$	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	−0.616615	−	0.787265i	$-0.711496\pi$
$787$	−4.15789	+	2.70016i	−0.148213	+	0.0962505i	0.468402	+	0.883515i	$0.344830\pi$
$788$	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	0.560119	−	0.828412i	$-0.310756\pi$
$797$	38.0787	−	6.03107i	1.34882	−	0.213632i	0.788698	+	0.614781i	$0.210756\pi$
$798$	−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	0.699669	+	0.714467i	$0.253331\pi$
$809$	−6.54501	+	30.7919i	−0.230110	+	1.08258i	−0.929779	+	0.368117i	$0.880003\pi$
$810$		0			0
$811$	20.5598	+	6.68028i	0.721952	+	0.234576i	0.646869	−	0.762601i	$-0.276078\pi$
$811$	20.5598	+	6.68028i	0.721952	+	0.234576i	0.0750826	+	0.997177i	$0.476078\pi$
$812$	−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	−1.00000		0.000582675i	$-0.999815\pi$
$821$	−0.622668	+	5.92429i	−0.0217313	+	0.206759i	0.978269	+	0.207342i	$0.0664812\pi$
$822$	−25.0009	+	65.1296i	−0.872007	+	2.27166i
$823$	−35.8441	−	1.87851i	−1.24945	−	0.0654807i	−0.583892	−	0.811831i	$-0.698471\pi$
$823$	−35.8441	−	1.87851i	−1.24945	−	0.0654807i	−0.665553	+	0.746350i	$0.731804\pi$
$824$	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	−0.753124	−	0.657878i	$-0.771454\pi$
$827$	−19.0825	+	9.72304i	−0.663565	+	0.338103i	0.0895595	+	0.995981i	$0.471454\pi$
$828$	−48.1138	−	59.4156i	−1.67207	−	2.06484i
$829$	19.4671	−	8.66732i	0.676121	−	0.301028i	−0.0398022	−	0.999208i	$-0.512673\pi$
$829$	19.4671	−	8.66732i	0.676121	−	0.301028i	0.715923	+	0.698179i	$0.246006\pi$
$830$		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	−0.440099	−	0.897949i	$-0.645057\pi$
$839$	12.8534	−	39.5588i	0.443750	−	1.36572i	0.883849	−	0.467773i	$-0.154943\pi$
$840$		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	0.866097	+	0.499876i	$0.166621\pi$
$853$	5.74952	+	36.3011i	0.196860	+	1.24292i	−0.669237	+	0.743049i	$0.733379\pi$
$854$	−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	0.985718	−	0.168406i	$-0.0538619\pi$
$857$	1.40103	+	5.22871i	0.0478582	+	0.178609i	−0.937860	+	0.347015i	$0.887195\pi$
$858$	7.41105	+	6.00135i	0.253009	+	0.204883i
$859$	13.7283	−	15.2469i	0.468405	−	0.520217i	−0.461935	−	0.886914i	$-0.652845\pi$
$859$	13.7283	−	15.2469i	0.468405	−	0.520217i	0.930340	+	0.366697i	$0.119511\pi$
$860$		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	0.999847	−	0.0174909i	$-0.00556781\pi$
$863$	0.107195	+	2.04541i	0.00364897	+	0.0696265i	−0.996198	+	0.0871174i	$0.972234\pi$
$864$	−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	0.106043	−	0.994362i	$-0.466182\pi$
$877$	−22.4837	−	14.6011i	−0.759220	−	0.493043i	−0.865263	+	0.501319i	$0.832848\pi$
$878$	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	0.839290	−	0.543684i	$-0.182971\pi$
$881$	1.86581	+	2.56806i	0.0628607	+	0.0865203i	−0.776429	+	0.630204i	$0.782971\pi$
$882$	18.2850	−	50.7702i	0.615687	−	1.70952i
$883$	0.379650	−	2.39702i	0.0127763	−	0.0806661i	−0.980476	−	0.196637i	$-0.936998\pi$
$883$	0.379650	−	2.39702i	0.0127763	−	0.0806661i	0.993253	+	0.115971i	$0.0369979\pi$
$884$	−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	0.999342	+	0.0362841i	$0.0115521\pi$
$887$	0.276001	+	5.26642i	0.00926721	+	0.176829i	−0.990074	+	0.140545i	$0.955115\pi$
$888$	−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	−0.0118806	−	0.999929i	$-0.503782\pi$
$907$	14.3895	−	3.85565i	0.477795	−	0.128025i	0.489676	+	0.871905i	$0.337115\pi$
$908$	−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	−0.668004	−	0.744158i	$-0.732851\pi$
$911$	9.35146	−	28.7808i	0.309828	−	0.953551i	0.977831	−	0.209394i	$-0.0671490\pi$
$912$	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	0.0239340	+	0.999714i	$0.492381\pi$
$919$	−22.2819	+	50.0460i	−0.735013	+	1.65087i	−0.758947	+	0.651152i	$0.774286\pi$
$920$		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	0.283134	+	0.959081i	$0.408626\pi$
$929$	−5.88915	+	56.0316i	−0.193217	+	1.83834i	−0.476350	+	0.879256i	$0.658041\pi$
$930$		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	0.146670	−	0.989185i	$-0.453144\pi$
$937$	−17.3680	−	8.84942i	−0.567387	−	0.289098i	−0.714057	+	0.700087i	$0.753144\pi$
$938$	−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	0.676278	+	0.736647i	$0.263592\pi$
$941$	−7.39757	+	34.8029i	−0.241154	+	1.13454i	−0.917432	+	0.397894i	$0.869741\pi$
$942$	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	−0.888926	−	0.458051i	$-0.848548\pi$
$947$	−19.2550	+	15.5924i	−0.625703	+	0.506684i	0.263223	+	0.964735i	$0.415215\pi$
$948$	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	−0.289159	−	0.957281i	$-0.593376\pi$
$953$	−8.28414	+	1.31208i	−0.268350	+	0.0425024i	0.0208095	+	0.999783i	$0.493376\pi$
$954$	−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	0.656987	−	0.753902i	$-0.271831\pi$
$967$	32.6157	+	5.16582i	1.04885	+	0.166121i	0.391863	+	0.920024i	$0.371831\pi$
$968$	−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	−0.177674	−	0.984089i	$-0.556857\pi$
$971$	−17.3276	−	1.82121i	−0.556070	−	0.0584453i	−0.378395	+	0.925644i	$0.623524\pi$
$972$	−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	0.909029	+	0.416732i	$0.136825\pi$
$977$	−1.20592	+	23.0102i	−0.0385806	+	0.736163i	−0.947610	+	0.319430i	$0.896509\pi$
$978$	−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	−0.956001	−	0.293364i	$-0.905225\pi$
$983$	−14.7447	+	18.2082i	−0.470284	+	0.580753i	0.485717	+	0.874116i	$0.338559\pi$
$984$	−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	−0.410659	−	0.911789i	$-0.634701\pi$
$991$	−36.4122	−	7.73965i	−1.15667	−	0.245858i	−0.746013	+	0.665931i	$0.768035\pi$
$992$	−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	0.693233	+	0.720714i	$0.256186\pi$
$997$	−9.60493	+	25.0217i	−0.304191	+	0.792445i	−0.997424	+	0.0717313i	$0.977148\pi$
$998$	−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.507.17		288
5.2	odd	4		875.2.bb.b.493.2		288
5.3	odd	4		875.2.bb.a.493.17		288
5.4	even	2		175.2.x.a.122.2	yes	288
7.5	odd	6	inner	875.2.bb.c.257.17		288
25.6	even	5		875.2.bb.a.857.2		288
25.8	odd	20	inner	875.2.bb.c.143.17		288
25.17	odd	20		175.2.x.a.108.2	yes	288
25.19	even	10		875.2.bb.b.857.17		288
35.12	even	12		875.2.bb.b.243.17		288
35.19	odd	6		175.2.x.a.47.2	yes	288
35.33	even	12		875.2.bb.a.243.2		288
175.19	odd	30		875.2.bb.b.607.2		288
175.33	even	60	inner	875.2.bb.c.768.17		288
175.117	even	60		175.2.x.a.33.2	✓	288
175.131	odd	30		875.2.bb.a.607.17		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.2	✓	288	175.117	even	60
175.2.x.a.47.2	yes	288	35.19	odd	6
175.2.x.a.108.2	yes	288	25.17	odd	20
175.2.x.a.122.2	yes	288	5.4	even	2
875.2.bb.a.243.2		288	35.33	even	12
875.2.bb.a.493.17		288	5.3	odd	4
875.2.bb.a.607.17		288	175.131	odd	30
875.2.bb.a.857.2		288	25.6	even	5
875.2.bb.b.243.17		288	35.12	even	12
875.2.bb.b.493.2		288	5.2	odd	4
875.2.bb.b.607.2		288	175.19	odd	30
875.2.bb.b.857.17		288	25.19	even	10
875.2.bb.c.143.17		288	25.8	odd	20	inner
875.2.bb.c.257.17		288	7.5	odd	6	inner
875.2.bb.c.507.17		288	1.1	even	1	trivial
875.2.bb.c.768.17		288	175.33	even	60	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 $\F_{q}$
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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