LMFDB - Embedded newform 825.2.bx.h.124.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(49,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("825.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.bx (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{14} + 15x^{12} - 59x^{10} + 104x^{8} - 59x^{6} + 15x^{4} - x^{2} + 1 $ x^16 - x^14 + 15x^12 - 59x^10 + 104x^8 - 59x^6 + 15*x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			124.1
Root			$0.280526 + 0.386111i$ of defining polynomial
Character	$\chi$	$=$	825.124
Dual form			825.2.bx.h.499.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.62947 - 2.24278i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-1.75683 + 5.40697i) q^{4} +(-2.24278 - 1.62947i) q^{6} +(-2.16612 - 0.703814i) q^{7} +(9.71623 - 3.15700i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-1.62947 - 2.24278i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-1.75683 + 5.40697i) q^{4} +(-2.24278 - 1.62947i) q^{6} +(-2.16612 - 0.703814i) q^{7} +(9.71623 - 3.15700i) q^{8} +(0.809017 - 0.587785i) q^{9} +(-0.105203 + 3.31496i) q^{11} +5.68522i q^{12} +(-0.256120 - 0.352519i) q^{13} +(1.95113 + 6.00496i) q^{14} +(-13.7139 - 9.96371i) q^{16} +(2.93893 - 4.04508i) q^{17} +(-2.63654 - 0.856664i) q^{18} +(-1.45113 - 4.46612i) q^{19} -2.27759 q^{21} +(7.60613 - 5.16568i) q^{22} +0.845811i q^{23} +(8.26512 - 6.00496i) q^{24} +(-0.373280 + 1.14884i) q^{26} +(0.587785 - 0.809017i) q^{27} +(7.61100 - 10.4756i) q^{28} +(0.821093 - 2.52706i) q^{29} +(3.77637 - 2.74369i) q^{31} +26.5602i q^{32} +(0.924324 + 3.18522i) q^{33} -13.8611 q^{34} +(1.75683 + 5.40697i) q^{36} +(-8.42864 - 2.73863i) q^{37} +(-7.65193 + 10.5320i) q^{38} +(-0.352519 - 0.256120i) q^{39} +(-1.32697 - 4.08400i) q^{41} +(3.71127 + 5.10813i) q^{42} -7.00317i q^{43} +(-17.7390 - 6.39264i) q^{44} +(1.89696 - 1.37823i) q^{46} +(-0.445265 + 0.144675i) q^{47} +(-16.1216 - 5.23823i) q^{48} +(-1.46641 - 1.06541i) q^{49} +(1.54508 - 4.75528i) q^{51} +(2.35601 - 0.765515i) q^{52} +(-6.37078 - 8.76863i) q^{53} -2.77222 q^{54} -23.2684 q^{56} +(-2.76021 - 3.79911i) q^{57} +(-7.00558 + 2.27625i) q^{58} +(-1.21629 + 3.74334i) q^{59} +(-2.39913 - 1.74307i) q^{61} +(-12.3070 - 3.99878i) q^{62} +(-2.16612 + 0.703814i) q^{63} +(32.1409 - 23.3517i) q^{64} +(5.63757 - 7.26328i) q^{66} -2.47048i q^{67} +(16.7084 + 22.9972i) q^{68} +(0.261370 + 0.804414i) q^{69} +(9.15321 + 6.65020i) q^{71} +(6.00496 - 8.26512i) q^{72} +(-8.01655 - 2.60474i) q^{73} +(7.59209 + 23.3661i) q^{74} +26.6975 q^{76} +(2.56099 - 7.10654i) q^{77} +1.20796i q^{78} +(-8.79457 + 6.38963i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-6.99723 + 9.63087i) q^{82} +(3.47998 - 4.78978i) q^{83} +(4.00134 - 12.3149i) q^{84} +(-15.7065 + 11.4115i) q^{86} -2.65711i q^{87} +(9.44313 + 32.5410i) q^{88} -5.89958 q^{89} +(0.306678 + 0.943857i) q^{91} +(-4.57327 - 1.48595i) q^{92} +(2.74369 - 3.77637i) q^{93} +(1.05002 + 0.762885i) q^{94} +(8.20756 + 25.2603i) q^{96} +(5.08318 + 6.99640i) q^{97} +5.02487i q^{98} +(1.86337 + 2.74369i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} + 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^4 + 4 * q^9	$ 16 q + 4 q^{4} + 4 q^{9} - 6 q^{11} + 20 q^{14} - 40 q^{16} - 12 q^{19} - 8 q^{21} + 40 q^{24} - 16 q^{26} + 6 q^{31} - 100 q^{34} - 4 q^{36} - 12 q^{39} - 50 q^{41} - 14 q^{44} - 12 q^{46} - 42 q^{49} - 20 q^{51} - 20 q^{54} + 40 q^{56} - 70 q^{59} + 42 q^{61} + 154 q^{64} + 50 q^{66} + 10 q^{69} + 50 q^{71} + 58 q^{74} - 28 q^{76} - 60 q^{79} - 4 q^{81} + 68 q^{84} - 68 q^{86} - 64 q^{89} + 74 q^{91} + 78 q^{94} + 20 q^{96} + 6 q^{99}+O(q^{100}) $ 16 * q + 4 * q^4 + 4 * q^9 - 6 * q^11 + 20 * q^14 - 40 * q^16 - 12 * q^19 - 8 * q^21 + 40 * q^24 - 16 * q^26 + 6 * q^31 - 100 * q^34 - 4 * q^36 - 12 * q^39 - 50 * q^41 - 14 * q^44 - 12 * q^46 - 42 * q^49 - 20 * q^51 - 20 * q^54 + 40 * q^56 - 70 * q^59 + 42 * q^61 + 154 * q^64 + 50 * q^66 + 10 * q^69 + 50 * q^71 + 58 * q^74 - 28 * q^76 - 60 * q^79 - 4 * q^81 + 68 * q^84 - 68 * q^86 - 64 * q^89 + 74 * q^91 + 78 * q^94 + 20 * q^96 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.62947	−	2.24278i	−1.15221	−	1.58588i	−0.736584	−	0.676347i	$-0.763562\pi$
$2$	−1.62947	−	2.24278i	−1.15221	−	1.58588i	−0.415627	−	0.909535i	$-0.636438\pi$
$3$	0.951057	−	0.309017i	0.549093	−	0.178411i
$3$	0.951057	−	0.309017i	0.549093	−	0.178411i
$4$	−1.75683	+	5.40697i	−0.878415	+	2.70348i
$5$		0			0
$5$		0			0
$6$	−2.24278	−	1.62947i	−0.915609	−	0.665229i
$7$	−2.16612	−	0.703814i	−0.818716	−	0.266017i	−0.130431	−	0.991457i	$-0.541636\pi$
$7$	−2.16612	−	0.703814i	−0.818716	−	0.266017i	−0.688285	+	0.725441i	$0.741636\pi$
$8$	9.71623	−	3.15700i	3.43521	−	1.11617i
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$		0			0
$11$	−0.105203	+	3.31496i	−0.0317198	+	0.999497i
$11$	−0.105203	+	3.31496i	−0.0317198	+	0.999497i
$12$			5.68522i			1.64118i
$13$	−0.256120	−	0.352519i	−0.0710348	−	0.0977711i	0.772021	−	0.635597i	$-0.219246\pi$
$13$	−0.256120	−	0.352519i	−0.0710348	−	0.0977711i	−0.843056	+	0.537826i	$0.819246\pi$
$14$	1.95113	+	6.00496i	0.521461	+	1.60489i
$15$		0			0
$16$	−13.7139	−	9.96371i	−3.42847	−	2.49093i
$17$	2.93893	−	4.04508i	0.712794	−	0.981077i	−0.286938	−	0.957949i	$-0.592637\pi$
$17$	2.93893	−	4.04508i	0.712794	−	0.981077i	0.999733	−	0.0231281i	$-0.00736256\pi$
$18$	−2.63654	−	0.856664i	−0.621439	−	0.201918i
$19$	−1.45113	−	4.46612i	−0.332912	−	1.02460i	−0.967741	−	0.251946i	$-0.918930\pi$
$19$	−1.45113	−	4.46612i	−0.332912	−	1.02460i	0.634829	−	0.772652i	$-0.281070\pi$
$20$		0			0
$21$	−2.27759			−0.497011
$22$	7.60613	−	5.16568i	1.62163	−	1.10133i
$23$			0.845811i			0.176364i	0.996104	+	0.0881819i	$0.0281057\pi$
$23$			0.845811i			0.176364i	−0.996104	+	0.0881819i	$0.971894\pi$
$24$	8.26512	−	6.00496i	1.68711	−	1.22576i
$25$		0			0
$26$	−0.373280	+	1.14884i	−0.0732063	+	0.225306i
$27$	0.587785	−	0.809017i	0.113119	−	0.155695i
$28$	7.61100	−	10.4756i	1.43834	−	1.97971i
$29$	0.821093	−	2.52706i	0.152473	−	0.469264i	−0.845423	−	0.534097i	$-0.820652\pi$
$29$	0.821093	−	2.52706i	0.152473	−	0.469264i	0.997896	+	0.0648334i	$0.0206516\pi$
$30$		0			0
$31$	3.77637	−	2.74369i	0.678256	−	0.492782i	−0.194523	−	0.980898i	$-0.562316\pi$
$31$	3.77637	−	2.74369i	0.678256	−	0.492782i	0.872779	+	0.488116i	$0.162316\pi$
$32$			26.5602i			4.69523i
$33$	0.924324	+	3.18522i	0.160904	+	0.554476i
$34$	−13.8611			−2.37716
$35$		0			0
$36$	1.75683	+	5.40697i	0.292805	+	0.901161i
$37$	−8.42864	−	2.73863i	−1.38566	−	0.450228i	−0.481134	−	0.876647i	$-0.659775\pi$
$37$	−8.42864	−	2.73863i	−1.38566	−	0.450228i	−0.904526	+	0.426419i	$0.859775\pi$
$38$	−7.65193	+	10.5320i	−1.24131	+	1.70851i
$39$	−0.352519	−	0.256120i	−0.0564481	−	0.0410120i
$40$		0			0
$41$	−1.32697	−	4.08400i	−0.207238	−	0.637814i	−0.999614	−	0.0277805i	$-0.991156\pi$
$41$	−1.32697	−	4.08400i	−0.207238	−	0.637814i	0.792376	−	0.610033i	$-0.208844\pi$
$42$	3.71127	+	5.10813i	0.572661	+	0.788201i
$43$		−	7.00317i		−	1.06797i	−0.845493	−	0.533986i	$-0.820693\pi$
$43$		−	7.00317i		−	1.06797i	0.845493	−	0.533986i	$-0.179307\pi$
$44$	−17.7390	−	6.39264i	−2.67426	−	0.963727i
$45$		0			0
$46$	1.89696	−	1.37823i	0.279692	−	0.203208i
$47$	−0.445265	+	0.144675i	−0.0649485	+	0.0211031i	−0.341311	−	0.939950i	$-0.610871\pi$
$47$	−0.445265	+	0.144675i	−0.0649485	+	0.0211031i	0.276363	+	0.961053i	$0.410871\pi$
$48$	−16.1216	−	5.23823i	−2.32696	−	0.756074i
$49$	−1.46641	−	1.06541i	−0.209487	−	0.152201i
$50$		0			0
$51$	1.54508	−	4.75528i	0.216355	−	0.665873i
$52$	2.35601	−	0.765515i	0.326720	−	0.106158i
$53$	−6.37078	−	8.76863i	−0.875094	−	1.20446i	−0.977756	−	0.209747i	$-0.932736\pi$
$53$	−6.37078	−	8.76863i	−0.875094	−	1.20446i	0.102662	−	0.994716i	$-0.467264\pi$
$54$	−2.77222			−0.377252
$55$		0			0
$56$	−23.2684			−3.10938
$57$	−2.76021	−	3.79911i	−0.365599	−	0.503204i
$58$	−7.00558	+	2.27625i	−0.919878	+	0.298887i
$59$	−1.21629	+	3.74334i	−0.158347	+	0.487341i	−0.998485	−	0.0550316i	$-0.982474\pi$
$59$	−1.21629	+	3.74334i	−0.158347	+	0.487341i	0.840138	+	0.542373i	$0.182474\pi$
$60$		0			0
$61$	−2.39913	−	1.74307i	−0.307177	−	0.223177i	0.423507	−	0.905893i	$-0.360799\pi$
$61$	−2.39913	−	1.74307i	−0.307177	−	0.223177i	−0.730684	+	0.682715i	$0.760799\pi$
$62$	−12.3070	−	3.99878i	−1.56299	−	0.507845i
$63$	−2.16612	+	0.703814i	−0.272905	+	0.0886723i
$64$	32.1409	−	23.3517i	4.01761	−	2.91897i
$65$		0			0
$66$	5.63757	−	7.26328i	0.693937	−	0.894048i
$67$		−	2.47048i		−	0.301817i	−0.988548	−	0.150909i	$-0.951780\pi$
$67$		−	2.47048i		−	0.301817i	0.988548	−	0.150909i	$-0.0482199\pi$
$68$	16.7084	+	22.9972i	2.02620	+	2.78882i
$69$	0.261370	+	0.804414i	0.0314653	+	0.0968401i
$70$		0			0
$71$	9.15321	+	6.65020i	1.08629	+	0.789233i	0.978768	−	0.204970i	$-0.0657097\pi$
$71$	9.15321	+	6.65020i	1.08629	+	0.789233i	0.107518	+	0.994203i	$0.465710\pi$
$72$	6.00496	−	8.26512i	0.707691	−	0.974054i
$73$	−8.01655	−	2.60474i	−0.938266	−	0.304861i	−0.200328	−	0.979729i	$-0.564201\pi$
$73$	−8.01655	−	2.60474i	−0.938266	−	0.304861i	−0.737939	+	0.674868i	$0.764201\pi$
$74$	7.59209	+	23.3661i	0.882563	+	2.71625i
$75$		0			0
$76$	26.6975			3.06242
$77$	2.56099	−	7.10654i	0.291852	−	0.809866i
$78$			1.20796i			0.136775i
$79$	−8.79457	+	6.38963i	−0.989466	+	0.718889i	−0.959804	−	0.280671i	$-0.909443\pi$
$79$	−8.79457	+	6.38963i	−0.989466	+	0.718889i	−0.0296621	+	0.999560i	$0.509443\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−6.99723	+	9.63087i	−0.772715	+	1.06355i
$83$	3.47998	−	4.78978i	0.381978	−	0.525747i	−0.574130	−	0.818764i	$-0.694659\pi$
$83$	3.47998	−	4.78978i	0.381978	−	0.525747i	0.956107	+	0.293017i	$0.0946594\pi$
$84$	4.00134	−	12.3149i	0.436582	−	1.34366i
$85$		0			0
$86$	−15.7065	+	11.4115i	−1.69368	+	1.23053i
$87$		−	2.65711i		−	0.284872i
$88$	9.44313	+	32.5410i	1.00664	+	3.46888i
$89$	−5.89958			−0.625354			−0.312677	−	0.949859i	$-0.601226\pi$
$89$	−5.89958			−0.625354			−0.312677	+	0.949859i	$0.601226\pi$
$90$		0			0
$91$	0.306678	+	0.943857i	0.0321486	+	0.0989431i
$92$	−4.57327	−	1.48595i	−0.476796	−	0.154921i
$93$	2.74369	−	3.77637i	0.284508	−	0.391591i
$94$	1.05002	+	0.762885i	0.108301	+	0.0786855i
$95$		0			0
$96$	8.20756	+	25.2603i	0.837681	+	2.57812i
$97$	5.08318	+	6.99640i	0.516119	+	0.710377i	0.984936	−	0.172918i	$-0.0553196\pi$
$97$	5.08318	+	6.99640i	0.516119	+	0.710377i	−0.468817	+	0.883295i	$0.655320\pi$
$98$			5.02487i			0.507589i
$99$	1.86337	+	2.74369i	0.187276	+	0.275751i
$100$		0			0
$101$	4.59624	−	3.33936i	0.457343	−	0.332279i	−0.335145	−	0.942166i	$-0.608785\pi$
$101$	4.59624	−	3.33936i	0.457343	−	0.332279i	0.792488	+	0.609887i	$0.208785\pi$
$102$	−13.1827	+	4.28332i	−1.30528	+	0.424112i
$103$	1.23269	+	0.400526i	0.121461	+	0.0394650i	0.369117	−	0.929383i	$-0.379660\pi$
$103$	1.23269	+	0.400526i	0.121461	+	0.0394650i	−0.247656	+	0.968848i	$0.579660\pi$
$104$	−3.60142	−	2.61658i	−0.353148	−	0.256577i
$105$		0			0
$106$	−9.28505	+	28.5765i	−0.901844	+	2.77559i
$107$	11.6036	−	3.77024i	1.12176	−	0.364483i	0.311324	−	0.950304i	$-0.399228\pi$
$107$	11.6036	−	3.77024i	1.12176	−	0.364483i	0.810441	+	0.585821i	$0.199228\pi$
$108$	3.34169	+	4.59944i	0.321554	+	0.442581i
$109$	12.1644			1.16514			0.582568	−	0.812782i	$-0.302048\pi$
$109$	12.1644			1.16514			0.582568	+	0.812782i	$0.302048\pi$
$110$		0			0
$111$	−8.86239			−0.841181
$112$	22.6933	+	31.2346i	2.14431	+	2.95139i
$113$	0.135100	−	0.0438966i	0.0127091	−	0.00412944i	−0.302656	−	0.953100i	$-0.597873\pi$
$113$	0.135100	−	0.0438966i	0.0127091	−	0.00412944i	0.315365	+	0.948971i	$0.397873\pi$
$114$	−4.02286	+	12.3811i	−0.376775	+	1.15959i
$115$		0			0
$116$	12.2212	+	8.87924i	1.13471	+	0.824417i
$117$	−0.414410	−	0.134650i	−0.0383123	−	0.0124484i
$118$	10.3774	−	3.37181i	0.955315	−	0.310401i
$119$	−9.21305	+	6.69367i	−0.844559	+	0.613608i
$120$		0			0
$121$	−10.9779	−	0.697484i	−0.997988	−	0.0634077i
$122$			8.22100i			0.744294i
$123$	−2.52405	−	3.47406i	−0.227586	−	0.313245i
$124$	8.20061	+	25.2389i	0.736437	+	2.26652i
$125$		0			0
$126$	5.10813	+	3.71127i	0.455068	+	0.330626i
$127$	−0.296075	+	0.407512i	−0.0262724	+	0.0361609i	−0.821951	−	0.569558i	$-0.807114\pi$
$127$	−0.296075	+	0.407512i	−0.0262724	+	0.0361609i	0.795679	+	0.605719i	$0.207114\pi$
$128$	−54.2248	−	17.6187i	−4.79284	−	1.55729i
$129$	−2.16410	−	6.66041i	−0.190538	−	0.586416i
$130$		0			0
$131$	19.1098			1.66963			0.834816	−	0.550529i	$-0.185574\pi$
$131$	19.1098			1.66963			0.834816	+	0.550529i	$0.185574\pi$
$132$	−18.8463	−	0.598100i	−1.64036	−	0.0520579i
$133$			10.6955i			0.927415i
$134$	−5.54073	+	4.02558i	−0.478646	+	0.347757i
$135$		0			0
$136$	15.7850	−	48.5812i	1.35355	−	4.16580i
$137$	7.25608	−	9.98713i	0.619929	−	0.853258i	−0.377419	−	0.926043i	$-0.623188\pi$
$137$	7.25608	−	9.98713i	0.619929	−	0.853258i	0.997348	+	0.0727841i	$0.0231884\pi$
$138$	1.37823	−	1.89696i	0.117322	−	0.161480i
$139$	2.38943	−	7.35391i	0.202669	−	0.623750i	−0.797132	−	0.603805i	$-0.793651\pi$
$139$	2.38943	−	7.35391i	0.202669	−	0.623750i	0.999801	−	0.0199456i	$-0.00634930\pi$
$140$		0			0
$141$	−0.378765	+	0.275189i	−0.0318978	+	0.0231751i
$142$		−	31.3649i		−	2.63208i
$143$	1.19553	−	0.811940i	0.0999751	−	0.0678978i
$144$	−16.9513			−1.41261
$145$		0			0
$146$	7.22091	+	22.2237i	0.597607	+	1.83924i
$147$	−1.72386	−	0.560118i	−0.142182	−	0.0461977i
$148$	29.6154	−	40.7620i	2.43437	−	3.35062i
$149$	6.15577	+	4.47243i	0.504301	+	0.366396i	0.810657	−	0.585521i	$-0.199110\pi$
$149$	6.15577	+	4.47243i	0.504301	+	0.366396i	−0.306357	+	0.951917i	$0.599110\pi$
$150$		0			0
$151$	−0.826389	−	2.54336i	−0.0672506	−	0.206976i	0.911784	−	0.410670i	$-0.134705\pi$
$151$	−0.826389	−	2.54336i	−0.0672506	−	0.206976i	−0.979035	+	0.203694i	$0.934705\pi$
$152$	−28.1990	−	38.8126i	−2.28724	−	3.14812i
$153$		−	5.00000i		−	0.404226i
$154$	−20.1114	+	5.83617i	−1.62063	+	0.470292i
$155$		0			0
$156$	2.00415	−	1.45610i	0.160460	−	0.116581i
$157$	−19.2113	+	6.24214i	−1.53323	+	0.498177i	−0.949499	−	0.313770i	$-0.898408\pi$
$157$	−19.2113	+	6.24214i	−1.53323	+	0.498177i	−0.583731	+	0.811947i	$0.698408\pi$
$158$	28.6610	+	9.31252i	2.28015	+	0.740865i
$159$	−8.76863	−	6.37078i	−0.695397	−	0.505236i
$160$		0			0
$161$	0.595294	−	1.83213i	0.0469157	−	0.144392i
$162$	−2.63654	+	0.856664i	−0.207146	+	0.0673059i
$163$	−5.75784	−	7.92498i	−0.450989	−	0.620733i	0.521621	−	0.853177i	$-0.325328\pi$
$163$	−5.75784	−	7.92498i	−0.450989	−	0.620733i	−0.972610	+	0.232445i	$0.925328\pi$
$164$	24.4133			1.90636
$165$		0			0
$166$	−16.4129			−1.27389
$167$	−15.0341	−	20.6927i	−1.16338	−	1.60125i	−0.697910	−	0.716185i	$-0.745886\pi$
$167$	−15.0341	−	20.6927i	−1.16338	−	1.60125i	−0.465467	−	0.885065i	$-0.654114\pi$
$168$	−22.1296	+	7.19034i	−1.70734	+	0.554747i
$169$	3.95855	−	12.1832i	0.304504	−	0.937166i
$170$		0			0
$171$	−3.79911	−	2.76021i	−0.290525	−	0.211079i
$172$	37.8659	+	12.3034i	2.88725	+	0.938123i
$173$	−6.42349	+	2.08712i	−0.488369	+	0.158681i	−0.542843	−	0.839834i	$-0.682652\pi$
$173$	−6.42349	+	2.08712i	−0.488369	+	0.158681i	0.0544734	+	0.998515i	$0.482652\pi$
$174$	−5.95930	+	4.32969i	−0.451774	+	0.328233i
$175$		0			0
$176$	34.4720	−	44.4127i	2.59843	−	3.34773i
$177$			3.93598i			0.295846i
$178$	9.61320	+	13.2314i	0.720540	+	0.991738i
$179$	−2.01539	−	6.20274i	−0.150638	−	0.463615i	0.847055	−	0.531505i	$-0.178373\pi$
$179$	−2.01539	−	6.20274i	−0.150638	−	0.463615i	−0.997693	+	0.0678901i	$0.978373\pi$
$180$		0			0
$181$	−11.1257	−	8.08332i	−0.826970	−	0.600829i	0.0917306	−	0.995784i	$-0.470760\pi$
$181$	−11.1257	−	8.08332i	−0.826970	−	0.600829i	−0.918700	+	0.394955i	$0.870760\pi$
$182$	1.61714	−	2.22580i	0.119870	−	0.164987i
$183$	−2.82035	−	0.916387i	−0.208486	−	0.0677412i
$184$	2.67022	+	8.21810i	0.196851	+	0.605846i
$185$		0			0
$186$	−12.9403			−0.948830
$187$	13.1001	+	10.1680i	0.957974	+	0.743555i
$188$		−	2.66170i		−	0.194124i
$189$	−1.84261	+	1.33873i	−0.134030	+	0.0973786i
$190$		0			0
$191$	−6.00607	+	18.4848i	−0.434584	+	1.33751i	0.458929	+	0.888473i	$0.348233\pi$
$191$	−6.00607	+	18.4848i	−0.434584	+	1.33751i	−0.893512	+	0.449038i	$0.851767\pi$
$192$	23.3517	−	32.1409i	1.68527	−	2.31957i
$193$	−13.2912	+	18.2938i	−0.956722	+	1.31681i	−0.00824604	+	0.999966i	$0.502625\pi$
$193$	−13.2912	+	18.2938i	−0.956722	+	1.31681i	−0.948476	+	0.316849i	$0.897375\pi$
$194$	7.40846	−	22.8009i	0.531896	−	1.63701i
$195$		0			0
$196$	8.33685	−	6.05707i	0.595489	−	0.432648i
$197$			23.0300i			1.64082i	0.571776	+	0.820410i	$0.306255\pi$
$197$			23.0300i			1.64082i	−0.571776	+	0.820410i	$0.693745\pi$
$198$	3.11717	−	8.64989i	0.221528	−	0.614721i
$199$	19.6216			1.39094			0.695468	−	0.718557i	$-0.255197\pi$
$199$	19.6216			1.39094			0.695468	+	0.718557i	$0.255197\pi$
$200$		0			0
$201$	−0.763420	−	2.34957i	−0.0538475	−	0.165726i
$202$	−14.9789	−	4.86693i	−1.05391	−	0.342436i
$203$	−3.55717	+	4.89602i	−0.249664	+	0.343633i
$204$	22.9972	+	16.7084i	1.61013	+	1.16982i
$205$		0			0
$206$	−1.11035	−	3.41730i	−0.0773616	−	0.238095i
$207$	0.497155	+	0.684276i	0.0345547	+	0.0475604i
$208$			7.38630i			0.512148i
$209$	14.9577	−	4.34059i	1.03464	−	0.300245i
$210$		0			0
$211$	−0.0403903	+	0.0293453i	−0.00278059	+	0.00202021i	−0.589175	−	0.808006i	$-0.700547\pi$
$211$	−0.0403903	+	0.0293453i	−0.00278059	+	0.00202021i	0.586394	+	0.810026i	$0.300547\pi$
$212$	58.6040	−	19.0416i	4.02494	−	1.30778i
$213$	10.7602	+	3.49622i	0.737280	+	0.239557i
$214$	−27.3636	−	19.8808i	−1.87054	−	1.35902i
$215$		0			0
$216$	3.15700	−	9.71623i	0.214806	−	0.661106i
$217$	−10.1111	+	3.28530i	−0.686387	+	0.223021i
$218$	−19.8215	−	27.2819i	−1.34248	−	1.84777i
$219$	−8.42910			−0.569586
$220$		0			0
$221$	−2.17868			−0.146554
$222$	14.4410	+	19.8764i	0.969218	+	1.33401i
$223$	0.718012	−	0.233296i	0.0480816	−	0.0156227i	−0.284877	−	0.958564i	$-0.591953\pi$
$223$	0.718012	−	0.233296i	0.0480816	−	0.0156227i	0.332959	+	0.942941i	$0.391953\pi$
$224$	18.6935	−	57.5326i	1.24901	−	3.84406i
$225$		0			0
$226$	−0.318592	−	0.231470i	−0.0211924	−	0.0153972i
$227$	7.87855	+	2.55989i	0.522917	+	0.169906i	0.558569	−	0.829458i	$-0.311351\pi$
$227$	7.87855	+	2.55989i	0.522917	+	0.169906i	−0.0356515	+	0.999364i	$0.511351\pi$
$228$	25.3909	−	8.24999i	1.68155	−	0.546369i
$229$	−2.32691	+	1.69060i	−0.153767	+	0.111718i	−0.662008	−	0.749496i	$-0.730296\pi$
$229$	−2.32691	+	1.69060i	−0.153767	+	0.111718i	0.508242	+	0.861214i	$0.330296\pi$
$230$		0			0
$231$	0.239609	−	7.55011i	0.0157651	−	0.496761i
$232$		−	27.1457i		−	1.78220i
$233$	−3.04395	−	4.18964i	−0.199416	−	0.274473i	0.697584	−	0.716503i	$-0.254258\pi$
$233$	−3.04395	−	4.18964i	−0.199416	−	0.274473i	−0.897000	+	0.442030i	$0.854258\pi$
$234$	0.373280	+	1.14884i	0.0244021	+	0.0751019i
$235$		0			0
$236$	−18.1033	−	13.1528i	−1.17842	−	0.856176i
$237$	−6.38963	+	8.79457i	−0.415051	+	0.571269i
$238$	30.0248	+	9.75565i	1.94622	+	0.632365i
$239$	−3.34751	−	10.3026i	−0.216532	−	0.666418i	−0.999041	−	0.0437789i	$-0.986060\pi$
$239$	−3.34751	−	10.3026i	−0.216532	−	0.666418i	0.782509	−	0.622640i	$-0.213940\pi$
$240$		0			0
$241$	−2.96526			−0.191009			−0.0955045	−	0.995429i	$-0.530446\pi$
$241$	−2.96526			−0.191009			−0.0955045	+	0.995429i	$0.530446\pi$
$242$	16.3238	+	25.7574i	1.04933	+	1.65575i
$243$		−	1.00000i		−	0.0641500i
$244$	13.6396	−	9.90974i	0.873185	−	0.634406i
$245$		0			0
$246$	−3.67866	+	11.3218i	−0.234543	+	0.721849i
$247$	−1.20273	+	1.65541i	−0.0765277	+	0.105331i
$248$	28.0302	−	38.5803i	1.77992	−	2.44985i
$249$	1.82953	−	5.63073i	0.115942	−	0.356833i
$250$		0			0
$251$	14.2504	−	10.3535i	0.899475	−	0.653507i	−0.0388560	−	0.999245i	$-0.512371\pi$
$251$	14.2504	−	10.3535i	0.899475	−	0.653507i	0.938331	+	0.345738i	$0.112371\pi$
$252$		−	12.9486i		−	0.815685i
$253$	−2.80383	−	0.0889816i	−0.176275	−	0.00559422i
$254$	1.39640			0.0876182
$255$		0			0
$256$	24.2895	+	74.7554i	1.51809	+	4.67221i
$257$	19.9386	+	6.47845i	1.24374	+	0.404115i	0.855672	−	0.517518i	$-0.173144\pi$
$257$	19.9386	+	6.47845i	1.24374	+	0.404115i	0.388064	+	0.921632i	$0.373144\pi$
$258$	−11.4115	+	15.7065i	−0.710447	+	0.977846i
$259$	16.3299	+	11.8644i	1.01469	+	0.737217i
$260$		0			0
$261$	−0.821093	−	2.52706i	−0.0508244	−	0.156421i
$262$	−31.1389	−	42.8590i	−1.92377	−	2.64784i
$263$		−	8.43471i		−	0.520107i	−0.965594	−	0.260053i	$-0.916260\pi$
$263$		−	8.43471i		−	0.520107i	0.965594	−	0.260053i	$-0.0837402\pi$
$264$	19.0367	+	28.0302i	1.17163	+	1.72514i
$265$		0			0
$266$	23.9875	−	17.4280i	1.47077	−	1.06858i
$267$	−5.61084	+	1.82307i	−0.343378	+	0.111570i
$268$	13.3578	+	4.34021i	0.815958	+	0.265121i
$269$	7.80173	+	5.66829i	0.475680	+	0.345601i	0.799651	−	0.600466i	$-0.205018\pi$
$269$	7.80173	+	5.66829i	0.475680	+	0.345601i	−0.323971	+	0.946067i	$0.605018\pi$
$270$		0			0
$271$	3.16056	−	9.72719i	0.191990	−	0.590885i	−0.808008	−	0.589171i	$-0.799454\pi$
$271$	3.16056	−	9.72719i	0.191990	−	0.590885i	0.999999	−	0.00171395i	$-0.000545568\pi$
$272$	−80.6081	+	26.1912i	−4.88759	+	1.58807i
$273$	0.583336	+	0.802893i	0.0353051	+	0.0485933i
$274$	−34.2225			−2.06746
$275$		0			0
$276$	−4.80862			−0.289445
$277$	3.43210	+	4.72388i	0.206215	+	0.283830i	0.899580	−	0.436756i	$-0.143873\pi$
$277$	3.43210	+	4.72388i	0.206215	+	0.283830i	−0.693365	+	0.720586i	$0.743873\pi$
$278$	−20.3867	+	6.62403i	−1.22271	+	0.397283i
$279$	1.44244	−	4.43939i	0.0863569	−	0.265779i
$280$		0			0
$281$	−11.6611	−	8.47225i	−0.695640	−	0.505412i	0.182869	−	0.983137i	$-0.441461\pi$
$281$	−11.6611	−	8.47225i	−0.695640	−	0.505412i	−0.878509	+	0.477725i	$0.841461\pi$
$282$	1.23437	+	0.401072i	0.0735058	+	0.0238835i
$283$	−10.1130	+	3.28592i	−0.601156	+	0.195327i	−0.593756	−	0.804645i	$-0.702356\pi$
$283$	−10.1130	+	3.28592i	−0.601156	+	0.195327i	−0.00740011	+	0.999973i	$0.502356\pi$
$284$	−52.0380	+	37.8078i	−3.08789	+	2.24348i
$285$		0			0
$286$	−3.76908	−	1.35827i	−0.222870	−	0.0803161i
$287$			9.78037i			0.577317i
$288$	15.6117	+	21.4877i	0.919929	+	1.26617i
$289$	−2.47214	−	7.60845i	−0.145420	−	0.447556i
$290$		0			0
$291$	6.99640	+	5.08318i	0.410136	+	0.297982i
$292$	28.1674	−	38.7691i	1.64837	−	2.26879i
$293$	7.98484	+	2.59443i	0.466479	+	0.151568i	0.532820	−	0.846229i	$-0.321132\pi$
$293$	7.98484	+	2.59443i	0.466479	+	0.151568i	−0.0663405	+	0.997797i	$0.521132\pi$
$294$	1.55277	+	4.77894i	0.0905594	+	0.278713i
$295$		0			0
$296$	−90.5404			−5.26256
$297$	2.62002	+	2.03359i	0.152029	+	0.118001i
$298$		−	21.0937i		−	1.22193i
$299$	0.298164	−	0.216629i	0.0172433	−	0.0125280i
$300$		0			0
$301$	−4.92893	+	15.1697i	−0.284099	+	0.874366i
$302$	−4.35762	+	5.99774i	−0.250753	+	0.345131i
$303$	3.33936	−	4.59624i	0.191841	−	0.264047i
$304$	−24.5985	+	75.7065i	−1.41082	+	4.34206i
$305$		0			0
$306$	−11.2139	+	8.14736i	−0.641055	+	0.465753i
$307$			4.51902i			0.257914i	0.991650	+	0.128957i	$0.0411629\pi$
$307$			4.51902i			0.257914i	−0.991650	+	0.128957i	$0.958837\pi$
$308$	33.9256	+	26.3322i	1.93309	+	1.50042i
$309$	1.29613			0.0737343
$310$		0			0
$311$	7.41548	+	22.8225i	0.420493	+	1.29415i	0.907244	+	0.420604i	$0.138182\pi$
$311$	7.41548	+	22.8225i	0.420493	+	1.29415i	−0.486751	+	0.873541i	$0.661818\pi$
$312$	−4.23372	−	1.37562i	−0.239687	−	0.0778791i
$313$	15.2052	−	20.9281i	0.859448	−	1.18293i	−0.122253	−	0.992499i	$-0.539012\pi$
$313$	15.2052	−	20.9281i	0.859448	−	1.18293i	0.981701	−	0.190430i	$-0.0609882\pi$
$314$	45.3040	+	32.9153i	2.55665	+	1.85752i
$315$		0			0
$316$	−19.0979	−	58.7774i	−1.07434	−	3.30649i
$317$	−1.70645	−	2.34873i	−0.0958441	−	0.131918i	0.758402	−	0.651787i	$-0.225981\pi$
$317$	−1.70645	−	2.34873i	−0.0958441	−	0.131918i	−0.854246	+	0.519869i	$0.825981\pi$
$318$			30.0471i			1.68496i
$319$	8.29072	+	2.98774i	0.464191	+	0.167281i
$320$		0			0
$321$	9.87063	−	7.17143i	0.550925	−	0.400270i
$322$	−5.07906	+	1.65029i	−0.283045	+	0.0919669i
$323$	−22.3306	−	7.25565i	−1.24251	−	0.403715i
$324$	4.59944	+	3.34169i	0.255524	+	0.185649i
$325$		0			0
$326$	−8.39172	+	25.8271i	−0.464775	+	1.43043i
$327$	11.5690	−	3.75900i	0.639767	−	0.207873i
$328$	−25.7863	−	35.4919i	−1.42381	−	1.95971i
$329$	1.06632			0.0587881
$330$		0			0
$331$	10.9837			0.603720			0.301860	−	0.953352i	$-0.402392\pi$
$331$	10.9837			0.603720			0.301860	+	0.953352i	$0.402392\pi$
$332$	19.7845	+	27.2310i	1.08581	+	1.49449i
$333$	−8.42864	+	2.73863i	−0.461886	+	0.150076i
$334$	−21.9114	+	67.4364i	−1.19894	+	3.68996i
$335$		0			0
$336$	31.2346	+	22.6933i	1.70399	+	1.23802i
$337$	12.2174	+	3.96968i	0.665525	+	0.216242i	0.622247	−	0.782821i	$-0.286220\pi$
$337$	12.2174	+	3.96968i	0.665525	+	0.216242i	0.0432780	+	0.999063i	$0.486220\pi$
$338$	−33.7744	+	10.9740i	−1.83709	+	0.596906i
$339$	0.114923	−	0.0834963i	0.00624175	−	0.00453490i
$340$		0			0
$341$	8.69793	+	12.8071i	0.471020	+	0.693545i
$342$			13.0182i			0.703946i
$343$	11.7977	+	16.2381i	0.637016	+	0.876777i
$344$	−22.1090	−	68.0444i	−1.19204	−	3.66871i
$345$		0			0
$346$	15.1478	+	11.0056i	0.814353	+	0.591662i
$347$	−1.11074	+	1.52881i	−0.0596279	+	0.0820707i	−0.837790	−	0.545993i	$-0.816152\pi$
$347$	−1.11074	+	1.52881i	−0.0596279	+	0.0820707i	0.778162	+	0.628064i	$0.216152\pi$
$348$	14.3669	+	4.66809i	0.770147	+	0.250236i
$349$	−7.34802	−	22.6149i	−0.393330	−	1.21055i	−0.930254	−	0.366915i	$-0.880414\pi$
$349$	−7.34802	−	22.6149i	−0.393330	−	1.21055i	0.536924	−	0.843631i	$-0.319586\pi$
$350$		0			0
$351$	−0.435737			−0.0232579
$352$	−88.0460	−	2.79421i	−4.69287	−	0.148932i
$353$			20.2294i			1.07670i	0.842720	+	0.538352i	$0.180953\pi$
$353$			20.2294i			1.07670i	−0.842720	+	0.538352i	$0.819047\pi$
$354$	8.82752	−	6.41357i	0.469177	−	0.340877i
$355$		0			0
$356$	10.3646	−	31.8988i	0.549321	−	1.69063i
$357$	−6.69367	+	9.21305i	−0.354267	+	0.487606i
$358$	−10.6273	+	14.6273i	−0.561672	+	0.773075i
$359$	5.74455	−	17.6799i	0.303186	−	0.933109i	−0.677162	−	0.735834i	$-0.736791\pi$
$359$	5.74455	−	17.6799i	0.303186	−	0.933109i	0.980348	−	0.197276i	$-0.0632094\pi$
$360$		0			0
$361$	−2.46912	+	1.79392i	−0.129954	+	0.0944170i
$362$			38.1241i			2.00376i
$363$	−10.6561	+	2.72900i	−0.559300	+	0.143235i
$364$	−5.64219			−0.295731
$365$		0			0
$366$	2.54043	+	7.81863i	0.132790	+	0.408687i
$367$	5.61894	+	1.82571i	0.293306	+	0.0953010i	0.451974	−	0.892031i	$-0.350720\pi$
$367$	5.61894	+	1.82571i	0.293306	+	0.0953010i	−0.158668	+	0.987332i	$0.550720\pi$
$368$	8.42742	−	11.5993i	0.439310	−	0.604658i
$369$	−3.47406	−	2.52405i	−0.180852	−	0.131397i
$370$		0			0
$371$	7.62838	+	23.4777i	0.396046	+	1.21890i
$372$	15.5985	+	21.4695i	0.808744	+	1.11314i
$373$			1.66992i			0.0864650i	0.999065	+	0.0432325i	$0.0137656\pi$
$373$			1.66992i			0.0864650i	−0.999065	+	0.0432325i	$0.986234\pi$
$374$	1.45823	−	45.9490i	0.0754031	−	2.37597i
$375$		0			0
$376$	−3.86956	+	2.81140i	−0.199557	+	0.144987i
$377$	−1.10113	+	0.357780i	−0.0567113	+	0.0184266i
$378$	6.00496	+	1.95113i	0.308862	+	0.100355i
$379$	6.82420	+	4.95807i	0.350536	+	0.254679i	0.749094	−	0.662464i	$-0.230489\pi$
$379$	6.82420	+	4.95807i	0.350536	+	0.254679i	−0.398558	+	0.917143i	$0.630489\pi$
$380$		0			0
$381$	−0.155656	+	0.479059i	−0.00797449	+	0.0245430i
$382$	51.2439	−	16.6502i	2.62187	−	0.851896i
$383$	12.8616	+	17.7025i	0.657199	+	0.904558i	0.999385	−	0.0350750i	$-0.0111670\pi$
$383$	12.8616	+	17.7025i	0.657199	+	0.904558i	−0.342185	+	0.939633i	$0.611167\pi$
$384$	−57.0153			−2.90955
$385$		0			0
$386$	62.6865			3.19066
$387$	−4.11636	−	5.66568i	−0.209246	−	0.288003i
$388$	−46.7596	+	15.1931i	−2.37386	+	0.771314i
$389$	0.121163	−	0.372902i	0.00614322	−	0.0189069i	−0.947938	−	0.318455i	$-0.896836\pi$
$389$	0.121163	−	0.372902i	0.00614322	−	0.0189069i	0.954081	+	0.299548i	$0.0968360\pi$
$390$		0			0
$391$	3.42138	+	2.48578i	0.173027	+	0.125711i
$392$	−17.6114	−	5.72230i	−0.889512	−	0.289020i
$393$	18.1745	−	5.90526i	0.916783	−	0.297881i
$394$	51.6511	−	37.5267i	2.60215	−	1.89057i
$395$		0			0
$396$	−18.1087	+	5.25499i	−0.909995	+	0.264073i
$397$			35.7823i			1.79586i	0.440134	+	0.897932i	$0.354931\pi$
$397$			35.7823i			1.79586i	−0.440134	+	0.897932i	$0.645069\pi$
$398$	−31.9728	−	44.0068i	−1.60265	−	2.20586i
$399$	3.30508	+	10.1720i	0.165461	+	0.509237i
$400$		0			0
$401$	−24.6074	−	17.8783i	−1.22884	−	0.892802i	−0.232034	−	0.972708i	$-0.574538\pi$
$401$	−24.6074	−	17.8783i	−1.22884	−	0.892802i	−0.996802	+	0.0799056i	$0.974538\pi$
$402$	−4.02558	+	5.54073i	−0.200778	+	0.276347i
$403$	−1.93440	−	0.628526i	−0.0963596	−	0.0313091i
$404$	9.98101	+	30.7184i	0.496574	+	1.52830i
$405$		0			0
$406$	16.7770			0.832627
$407$	9.96515	−	27.6524i	0.493954	−	1.37068i
$408$		−	51.0813i		−	2.52890i
$409$	−13.1625	+	9.56310i	−0.650843	+	0.472865i	−0.863558	−	0.504249i	$-0.831769\pi$
$409$	−13.1625	+	9.56310i	−0.650843	+	0.472865i	0.212715	+	0.977114i	$0.431769\pi$
$410$		0			0
$411$	3.81475	−	11.7406i	0.188168	−	0.579120i
$412$	−4.33126	+	5.96147i	−0.213386	+	0.293701i
$413$	5.26923	−	7.25248i	0.259282	−	0.356871i
$414$	0.724576	−	2.23002i	0.0356110	−	0.109599i
$415$		0			0
$416$	9.36298	−	6.80260i	0.459058	−	0.333525i
$417$		−	7.73236i		−	0.378655i
$418$	−34.1080	−	26.4738i	−1.66828	−	1.29488i
$419$	40.0703			1.95756			0.978781	−	0.204910i	$-0.0656903\pi$
$419$	40.0703			1.95756			0.978781	+	0.204910i	$0.0656903\pi$
$420$		0			0
$421$	−5.99316	−	18.4450i	−0.292089	−	0.898956i	−0.984184	−	0.177150i	$-0.943312\pi$
$421$	−5.99316	−	18.4450i	−0.292089	−	0.898956i	0.692095	−	0.721806i	$-0.256688\pi$
$422$	0.131630	+	0.0427691i	0.00640764	+	0.00208197i
$423$	−0.275189	+	0.378765i	−0.0133801	+	0.0184162i
$424$	−89.5825	−	65.0855i	−4.35051	−	3.16083i
$425$		0			0
$426$	−9.69229	−	29.8298i	−0.469593	−	1.44526i
$427$	3.97000	+	5.46424i	0.192122	+	0.264433i
$428$			69.3640i			3.35284i
$429$	0.886111	−	1.14164i	0.0427819	−	0.0551188i
$430$		0			0
$431$	−27.4616	+	19.9520i	−1.32278	+	0.961056i	−0.322887	+	0.946438i	$0.604653\pi$
$431$	−27.4616	+	19.9520i	−1.32278	+	0.961056i	−0.999893	+	0.0146183i	$0.995347\pi$
$432$	−16.1216	+	5.23823i	−0.775652	+	0.252025i
$433$	12.4736	+	4.05291i	0.599442	+	0.194770i	0.592991	−	0.805209i	$-0.297947\pi$
$433$	12.4736	+	4.05291i	0.599442	+	0.194770i	0.00645020	+	0.999979i	$0.497947\pi$
$434$	23.8440	+	17.3236i	1.14455	+	0.831562i
$435$		0			0
$436$	−21.3707	+	65.7723i	−1.02347	+	3.14992i
$437$	3.77749	−	1.22738i	0.180702	−	0.0587136i
$438$	13.7350	+	18.9046i	0.656283	+	0.903296i
$439$	9.64731			0.460441			0.230220	−	0.973138i	$-0.426055\pi$
$439$	9.64731			0.460441			0.230220	+	0.973138i	$0.426055\pi$
$440$		0			0
$441$	−1.81258			−0.0863133
$442$	3.55010	+	4.88630i	0.168861	+	0.232418i
$443$	−8.47781	+	2.75461i	−0.402793	+	0.130875i	−0.503405	−	0.864050i	$-0.667920\pi$
$443$	−8.47781	+	2.75461i	−0.402793	+	0.130875i	0.100613	+	0.994926i	$0.467920\pi$
$444$	15.5697	−	47.9187i	0.738906	−	2.27412i
$445$		0			0
$446$	−1.69321	−	1.23019i	−0.0801759	−	0.0582512i
$447$	7.23654	+	2.35130i	0.342277	+	0.111212i
$448$	−86.0562	+	27.9614i	−4.06578	+	1.32105i
$449$	−10.0616	+	7.31019i	−0.474837	+	0.344989i	−0.799323	−	0.600901i	$-0.794809\pi$
$449$	−10.0616	+	7.31019i	−0.474837	+	0.344989i	0.324487	+	0.945890i	$0.394809\pi$
$450$		0			0
$451$	13.6779	−	3.96921i	0.644066	−	0.186903i
$452$			0.807599i			0.0379863i
$453$	−1.57188	−	2.16351i	−0.0738536	−	0.101651i
$454$	−7.09660	−	21.8411i	−0.333060	−	1.02505i
$455$		0			0
$456$	−38.8126	−	28.1990i	−1.81757	−	1.32054i
$457$	−22.4289	+	30.8707i	−1.04918	+	1.44407i	−0.159659	+	0.987172i	$0.551040\pi$
$457$	−22.4289	+	30.8707i	−1.04918	+	1.44407i	−0.889519	+	0.456898i	$0.848960\pi$
$458$	7.58327	+	2.46395i	0.354343	+	0.115133i
$459$	−1.54508	−	4.75528i	−0.0721184	−	0.221958i
$460$		0			0
$461$	34.3847			1.60145			0.800726	−	0.599030i	$-0.204447\pi$
$461$	34.3847			1.60145			0.800726	+	0.599030i	$0.204447\pi$
$462$	−17.3236	+	11.7653i	−0.805969	+	0.547372i
$463$			40.2561i			1.87086i	0.353511	+	0.935430i	$0.384988\pi$
$463$			40.2561i			1.87086i	−0.353511	+	0.935430i	$0.615012\pi$
$464$	−36.4393	+	26.4747i	−1.69165	+	1.22906i
$465$		0			0
$466$	−4.43639	+	13.6538i	−0.205512	+	0.632501i
$467$	8.88502	−	12.2292i	0.411150	−	0.565899i	−0.552349	−	0.833613i	$-0.686268\pi$
$467$	8.88502	−	12.2292i	0.411150	−	0.565899i	0.963498	+	0.267714i	$0.0862683\pi$
$468$	1.45610	−	2.00415i	0.0673081	−	0.0926417i
$469$	−1.73876	+	5.35135i	−0.0802885	+	0.247102i
$470$		0			0
$471$	−16.3421	+	11.8732i	−0.753005	+	0.547090i
$472$			40.2110i			1.85086i
$473$	23.2152	+	0.736752i	1.06744	+	0.0338759i
$474$	30.1360			1.38419
$475$		0			0
$476$	−20.0067	−	61.5743i	−0.917005	−	2.82225i
$477$	−10.3081	−	3.34932i	−0.471977	−	0.153355i
$478$	−17.6517	+	24.2955i	−0.807370	+	1.11125i
$479$	−23.3033	−	16.9308i	−1.06476	−	0.773590i	−0.0897931	−	0.995960i	$-0.528621\pi$
$479$	−23.3033	−	16.9308i	−1.06476	−	0.773590i	−0.974962	+	0.222370i	$0.928621\pi$
$480$		0			0
$481$	1.19332	+	3.67267i	0.0544108	+	0.167459i
$482$	4.83180	+	6.65040i	0.220083	+	0.302918i
$483$		−	1.92641i		−	0.0876548i
$484$	23.0575	−	58.1316i	1.04807	−	2.64234i
$485$		0			0
$486$	−2.24278	+	1.62947i	−0.101734	+	0.0739143i
$487$	−27.4404	+	8.91592i	−1.24344	+	0.404019i	−0.855567	−	0.517693i	$-0.826791\pi$
$487$	−27.4404	+	8.91592i	−1.24344	+	0.404019i	−0.387876	+	0.921712i	$0.626791\pi$
$488$	−28.8134	−	9.36204i	−1.30432	−	0.423799i
$489$	−7.92498	−	5.75784i	−0.358380	−	0.260378i
$490$		0			0
$491$	−4.61569	+	14.2056i	−0.208303	+	0.641092i	0.791258	+	0.611482i	$0.209426\pi$
$491$	−4.61569	+	14.2056i	−0.208303	+	0.641092i	−0.999562	+	0.0296097i	$0.990574\pi$
$492$	23.2184	−	7.54413i	1.04677	−	0.340116i
$493$	−7.80906	−	10.7482i	−0.351702	−	0.484076i
$494$	5.67253			0.255219
$495$		0			0
$496$	−79.1260			−3.55286
$497$	−15.1464	−	20.8473i	−0.679410	−	0.935128i
$498$	−15.6096	+	5.07188i	−0.699484	+	0.227276i
$499$	−6.85987	+	21.1125i	−0.307090	+	0.945125i	0.671799	+	0.740733i	$0.265522\pi$
$499$	−6.85987	+	21.1125i	−0.307090	+	0.945125i	−0.978889	+	0.204392i	$0.934478\pi$
$500$		0			0
$501$	−20.6927	−	15.0341i	−0.924483	−	0.671676i
$502$	−46.4411	−	15.0896i	−2.07277	−	0.673484i
$503$	0.147752	−	0.0480077i	0.00658795	−	0.00214056i	−0.305721	−	0.952121i	$-0.598898\pi$
$503$	0.147752	−	0.0480077i	0.00658795	−	0.00214056i	0.312309	+	0.949981i	$0.398898\pi$
$504$	−18.8246	+	13.6768i	−0.838513	+	0.609215i
$505$		0			0
$506$	4.36919	+	6.43335i	0.194234	+	0.285997i
$507$		−	12.8101i		−	0.568918i
$508$	−1.68325	−	2.31680i	−0.0746822	−	0.102791i
$509$	5.75932	+	17.7254i	0.255277	+	0.785663i	0.993775	+	0.111407i	$0.0355356\pi$
$509$	5.75932	+	17.7254i	0.255277	+	0.785663i	−0.738498	+	0.674256i	$0.764464\pi$
$510$		0			0
$511$	15.5315	+	11.2843i	0.687075	+	0.499189i
$512$	61.0550	−	84.0350i	2.69828	−	3.71386i
$513$	−4.46612	−	1.45113i	−0.197184	−	0.0640690i
$514$	−17.9597	−	55.2743i	−0.792169	−	2.43804i
$515$		0			0
$516$	39.8145			1.75274
$517$	−0.432749	−	1.49125i	−0.0190323	−	0.0655852i
$518$		−	55.9571i		−	2.45861i
$519$	−5.46415	+	3.96994i	−0.239850	+	0.174261i
$520$		0			0
$521$	9.69969	−	29.8526i	0.424951	−	1.30786i	−0.478090	−	0.878311i	$-0.658671\pi$
$521$	9.69969	−	29.8526i	0.424951	−	1.30786i	0.903041	−	0.429554i	$-0.141329\pi$
$522$	−4.32969	+	5.95930i	−0.189505	+	0.260832i
$523$	14.0975	−	19.4036i	0.616442	−	0.848459i	−0.380646	−	0.924721i	$-0.624298\pi$
$523$	14.0975	−	19.4036i	0.616442	−	0.848459i	0.997088	+	0.0762616i	$0.0242984\pi$
$524$	−33.5727	+	103.326i	−1.46663	+	4.51382i
$525$		0			0
$526$	−18.9172	+	13.7441i	−0.824828	+	0.599272i
$527$		−	23.3392i		−	1.01667i
$528$	19.0606	−	52.8914i	0.829504	−	2.30180i
$529$	22.2846			0.968896
$530$		0			0
$531$	1.21629	+	3.74334i	0.0527823	+	0.162447i
$532$	−57.8300	−	18.7901i	−2.50725	−	0.814655i
$533$	−1.09982	+	1.51378i	−0.0476386	+	0.0655689i
$534$	13.2314	+	9.61320i	0.572580	+	0.416004i
$535$		0			0
$536$	−7.79929	−	24.0038i	−0.336878	−	1.03680i
$537$	−3.83351	−	5.27637i	−0.165428	−	0.227692i
$538$		−	26.7338i		−	1.15258i
$539$	3.68605	−	4.74899i	0.158769	−	0.204554i
$540$		0			0
$541$	−8.06851	+	5.86211i	−0.346892	+	0.252032i	−0.747564	−	0.664190i	$-0.768777\pi$
$541$	−8.06851	+	5.86211i	−0.346892	+	0.252032i	0.400672	+	0.916222i	$0.368777\pi$
$542$	−26.9660	+	8.76177i	−1.15829	+	0.376350i
$543$	−13.0791	−	4.24966i	−0.561278	−	0.182370i
$544$	107.438	+	78.0586i	4.60638	+	3.34673i
$545$		0			0
$546$	0.850179	−	2.61658i	0.0363843	−	0.111979i
$547$	38.0582	−	12.3659i	1.62725	−	0.528726i	0.653614	−	0.756829i	$-0.273252\pi$
$547$	38.0582	−	12.3659i	1.62725	−	0.528726i	0.973637	+	0.228103i	$0.0732522\pi$
$548$	41.2524	+	56.7791i	1.76222	+	2.42548i
$549$	−2.96549			−0.126564
$550$		0			0
$551$	−12.4777			−0.531567
$552$	5.07906	+	6.99073i	0.216179	+	0.297545i
$553$	23.5472	−	7.65094i	1.00133	−	0.325351i
$554$	5.00209	−	15.3948i	0.212518	−	0.654064i
$555$		0			0
$556$	35.5645	+	25.8391i	1.50827	+	1.09582i
$557$	−7.38064	−	2.39812i	−0.312728	−	0.101611i	0.148448	−	0.988920i	$-0.452572\pi$
$557$	−7.38064	−	2.39812i	−0.312728	−	0.101611i	−0.461176	+	0.887309i	$0.652572\pi$
$558$	−12.3070	+	3.99878i	−0.520996	+	0.169282i
$559$	−2.46875	+	1.79365i	−0.104417	+	0.0758633i
$560$		0			0
$561$	15.6010	+	5.62216i	0.658675	+	0.237368i
$562$			39.9584i			1.68554i
$563$	10.8361	+	14.9146i	0.456688	+	0.628577i	0.973818	−	0.227330i	$-0.0729996\pi$
$563$	10.8361	+	14.9146i	0.456688	+	0.628577i	−0.517130	+	0.855907i	$0.673000\pi$
$564$	−0.822511	−	2.53143i	−0.0346340	−	0.106592i
$565$		0			0
$566$	23.8484	+	17.3269i	1.00242	+	0.728304i
$567$	−1.33873	+	1.84261i	−0.0562216	+	0.0773823i
$568$	109.929	+	35.7182i	4.61253	+	1.49870i
$569$	−3.40658	−	10.4844i	−0.142811	−	0.439528i	0.853912	−	0.520418i	$-0.174224\pi$
$569$	−3.40658	−	10.4844i	−0.142811	−	0.439528i	−0.996723	+	0.0808896i	$0.974224\pi$
$570$		0			0
$571$	−38.1338			−1.59585			−0.797926	−	0.602756i	$-0.794069\pi$
$571$	−38.1338			−1.59585			−0.797926	+	0.602756i	$0.794069\pi$
$572$	2.28979	+	7.89062i	0.0957410	+	0.329923i
$573$			19.4360i			0.811952i
$574$	21.9352	−	15.9368i	0.915556	−	0.665191i
$575$		0			0
$576$	12.2767	−	37.7839i	0.511530	−	1.57433i
$577$	6.47284	−	8.90910i	0.269468	−	0.370891i	−0.652742	−	0.757580i	$-0.726382\pi$
$577$	6.47284	−	8.90910i	0.269468	−	0.370891i	0.922210	+	0.386690i	$0.126382\pi$
$578$	−13.0358	+	17.9422i	−0.542217	+	0.746297i
$579$	−6.98760	+	21.5056i	−0.290395	+	0.893743i
$580$		0			0
$581$	−10.9092	+	7.92597i	−0.452589	+	0.328825i
$582$		−	23.9743i		−	0.993765i
$583$	29.7378	−	20.1964i	1.23162	−	0.836448i
$584$	−86.1138			−3.56341
$585$		0			0
$586$	−7.19234	−	22.1358i	−0.297113	−	0.914420i
$587$	11.2643	+	3.65999i	0.464927	+	0.151064i	0.532107	−	0.846677i	$-0.321400\pi$
$587$	11.2643	+	3.65999i	0.464927	+	0.151064i	−0.0671803	+	0.997741i	$0.521400\pi$
$588$	6.05707	−	8.33685i	0.249790	−	0.343806i
$589$	−17.7337	−	12.8843i	−0.730703	−	0.530887i
$590$		0			0
$591$	7.11666	+	21.9028i	0.292740	+	0.900962i
$592$	88.3024	+	121.538i	3.62920	+	4.99517i
$593$		−	9.25062i		−	0.379877i	−0.981796	−	0.189939i	$-0.939171\pi$
$593$		−	9.25062i		−	0.379877i	0.981796	−	0.189939i	$-0.0608289\pi$
$594$	0.291645	−	9.18980i	0.0119663	−	0.377062i
$595$		0			0
$596$	−34.9969	+	25.4267i	−1.43353	+	1.04152i
$597$	18.6612	−	6.06340i	0.763753	−	0.248158i
$598$	−0.971700	−	0.315724i	−0.0397358	−	0.0129109i
$599$	19.1603	+	13.9208i	0.782868	+	0.568787i	0.905838	−	0.423624i	$-0.139242\pi$
$599$	19.1603	+	13.9208i	0.782868	+	0.568787i	−0.122971	+	0.992410i	$0.539242\pi$
$600$		0			0
$601$	11.2090	−	34.4978i	0.457225	−	1.40719i	−0.411278	−	0.911510i	$-0.634917\pi$
$601$	11.2090	−	34.4978i	0.457225	−	1.40719i	0.868503	−	0.495684i	$-0.165083\pi$
$602$	42.0537	−	13.6641i	1.71398	−	0.556907i
$603$	−1.45211	−	1.99866i	−0.0591346	−	0.0813918i
$604$	15.2037			0.618630
$605$		0			0
$606$	−15.7497			−0.639789
$607$	14.4047	+	19.8264i	0.584669	+	0.804728i	0.994198	−	0.107569i	$-0.0343067\pi$
$607$	14.4047	+	19.8264i	0.584669	+	0.804728i	−0.409528	+	0.912297i	$0.634307\pi$
$608$	118.621	−	38.5424i	4.81072	−	1.56310i
$609$	−1.87011	+	5.75562i	−0.0757808	+	0.233229i
$610$		0			0
$611$	0.165042	+	0.119910i	0.00667688	+	0.00485103i
$612$	27.0348	+	8.78415i	1.09282	+	0.355078i
$613$	4.41763	−	1.43538i	0.178427	−	0.0579743i	−0.218441	−	0.975850i	$-0.570097\pi$
$613$	4.41763	−	1.43538i	0.178427	−	0.0579743i	0.396868	+	0.917876i	$0.370097\pi$
$614$	10.1351	−	7.36361i	0.409021	−	0.297171i
$615$		0			0
$616$	2.44790	−	77.1339i	0.0986288	−	3.10781i
$617$			41.7419i			1.68047i	0.542226	+	0.840233i	$0.317582\pi$
$617$			41.7419i			1.68047i	−0.542226	+	0.840233i	$0.682418\pi$
$618$	−2.11201	−	2.90693i	−0.0849574	−	0.116934i
$619$	13.6592	+	42.0385i	0.549008	+	1.68967i	0.711266	+	0.702923i	$0.248122\pi$
$619$	13.6592	+	42.0385i	0.549008	+	1.68967i	−0.162258	+	0.986748i	$0.551878\pi$
$620$		0			0
$621$	0.684276	+	0.497155i	0.0274590	+	0.0199502i
$622$	39.1024	−	53.8199i	1.56786	−	2.15798i
$623$	12.7792	+	4.15221i	0.511987	+	0.166355i
$624$	2.28249	+	7.02479i	0.0913728	+	0.281217i
$625$		0			0
$626$	−71.7136			−2.86625
$627$	12.8843	−	8.75031i	0.514548	−	0.349454i
$628$		−	114.841i		−	4.58267i
$629$	−35.8491	+	26.0459i	−1.42940	+	1.03852i
$630$		0			0
$631$	−4.98015	+	15.3273i	−0.198257	+	0.610171i	0.801667	+	0.597771i	$0.203947\pi$
$631$	−4.98015	+	15.3273i	−0.198257	+	0.610171i	−0.999923	+	0.0123995i	$0.996053\pi$
$632$	−65.2780	+	89.8475i	−2.59662	+	3.57394i
$633$	−0.0293453	+	0.0403903i	−0.00116637	+	0.00160537i
$634$	−2.48706	+	7.65439i	−0.0987739	+	0.303995i
$635$		0			0
$636$	49.8516	−	36.2193i	1.97674	−	1.43619i
$637$			0.789807i			0.0312933i
$638$	−6.80867	−	23.4627i	−0.269558	−	0.928896i
$639$	11.3140			0.447575
$640$		0			0
$641$	−2.84600	−	8.75909i	−0.112410	−	0.345963i	0.878988	−	0.476844i	$-0.158219\pi$
$641$	−2.84600	−	8.75909i	−0.112410	−	0.345963i	−0.991398	+	0.130881i	$0.958219\pi$
$642$	−32.1678	−	10.4520i	−1.26956	−	0.412506i
$643$	−2.36014	+	3.24845i	−0.0930747	+	0.128106i	−0.853015	−	0.521887i	$-0.825228\pi$
$643$	−2.36014	+	3.24845i	−0.0930747	+	0.128106i	0.759940	+	0.649993i	$0.225228\pi$
$644$	8.86041	+	6.43747i	0.349149	+	0.253672i
$645$		0			0
$646$	20.1143	+	61.9054i	0.791386	+	2.43564i
$647$	−8.38728	−	11.5441i	−0.329738	−	0.453846i	0.611671	−	0.791112i	$-0.290498\pi$
$647$	−8.38728	−	11.5441i	−0.329738	−	0.453846i	−0.941409	+	0.337267i	$0.890498\pi$
$648$		−	10.2163i		−	0.401332i
$649$	−12.2811	−	4.42574i	−0.482073	−	0.173726i
$650$		0			0
$651$	−8.60102	+	6.24901i	−0.337101	+	0.244918i
$652$	52.9656	−	17.2096i	2.07429	−	0.673979i
$653$	6.20252	+	2.01532i	0.242723	+	0.0788656i	0.427852	−	0.903849i	$-0.359270\pi$
$653$	6.20252	+	2.01532i	0.242723	+	0.0788656i	−0.185129	+	0.982714i	$0.559270\pi$
$654$	−27.2819	−	19.8215i	−1.06681	−	0.775082i
$655$		0			0
$656$	−22.4939	+	69.2291i	−0.878239	+	2.70294i
$657$	−8.01655	+	2.60474i	−0.312755	+	0.101620i
$658$	−1.73754	−	2.39152i	−0.0677363	−	0.0932311i
$659$	−6.74928			−0.262915			−0.131457	−	0.991322i	$-0.541966\pi$
$659$	−6.74928			−0.262915			−0.131457	+	0.991322i	$0.541966\pi$
$660$		0			0
$661$	9.65248			0.375438			0.187719	−	0.982223i	$-0.439891\pi$
$661$	9.65248			0.375438			0.187719	+	0.982223i	$0.439891\pi$
$662$	−17.8977	−	24.6340i	−0.695613	−	0.957429i
$663$	−2.07205	+	0.673251i	−0.0804718	+	0.0261469i
$664$	18.6910	−	57.5249i	0.725351	−	2.23240i
$665$		0			0
$666$	19.8764	+	14.4410i	0.770193	+	0.559578i
$667$	2.13742	+	0.694489i	0.0827612	+	0.0268907i
$668$	138.297	−	44.9355i	5.35088	−	1.73861i
$669$	0.610777	−	0.443756i	0.0236140	−	0.0171566i
$670$		0			0
$671$	6.03060	−	7.76964i	0.232809	−	0.299944i
$672$		−	60.4934i		−	2.33358i
$673$	−16.6693	−	22.9433i	−0.642553	−	0.884398i	0.356196	−	0.934411i	$-0.384074\pi$
$673$	−16.6693	−	22.9433i	−0.642553	−	0.884398i	−0.998749	+	0.0500135i	$0.984074\pi$
$674$	−11.0048	−	33.8694i	−0.423891	−	1.30460i
$675$		0			0
$676$	58.9194	+	42.8075i	2.26613	+	1.64644i
$677$	−2.99004	+	4.11544i	−0.114917	+	0.158169i	−0.862601	−	0.505885i	$-0.831166\pi$
$677$	−2.99004	+	4.11544i	−0.114917	+	0.158169i	0.747684	+	0.664055i	$0.231166\pi$
$678$	−0.374527	−	0.121691i	−0.0143836	−	0.00467352i
$679$	−6.08661	−	18.7327i	−0.233583	−	0.718893i
$680$		0			0
$681$	8.28399			0.317443
$682$	14.5505	−	40.3764i	0.557167	−	1.54609i
$683$		−	17.3612i		−	0.664310i	−0.943225	−	0.332155i	$-0.892224\pi$
$683$		−	17.3612i		−	0.664310i	0.943225	−	0.332155i	$-0.107776\pi$
$684$	21.5988	−	15.6924i	0.825849	−	0.600015i
$685$		0			0
$686$	17.1945	−	52.9192i	0.656489	−	2.02046i
$687$	−1.69060	+	2.32691i	−0.0645004	+	0.0887772i
$688$	−69.7776	+	96.0406i	−2.66024	+	3.66151i
$689$	−1.45942	+	4.49164i	−0.0555995	+	0.171118i
$690$		0			0
$691$	34.7708	−	25.2625i	1.32274	−	0.961029i	0.322850	−	0.946450i	$-0.395359\pi$
$691$	34.7708	−	25.2625i	1.32274	−	0.961029i	0.999894	−	0.0145791i	$-0.00464085\pi$
$692$		−	38.3983i		−	1.45969i
$693$	−2.10523	−	7.25463i	−0.0799712	−	0.275581i
$694$	5.23870			0.198858
$695$		0			0
$696$	−8.38849	−	25.8171i	−0.317965	−	0.978595i
$697$	−20.4200	−	6.63486i	−0.773463	−	0.251313i
$698$	−38.7467	+	53.3302i	−1.46658	+	2.01858i
$699$	−4.18964	−	3.04395i	−0.158467	−	0.115133i
$700$		0			0
$701$	−4.44621	−	13.6840i	−0.167931	−	0.516838i	0.831309	−	0.555810i	$-0.187592\pi$
$701$	−4.44621	−	13.6840i	−0.167931	−	0.516838i	−0.999240	+	0.0389718i	$0.987592\pi$
$702$	0.710021	+	0.977260i	0.0267980	+	0.0368843i
$703$			41.6174i			1.56963i
$704$	74.0286	+	109.002i	2.79006	+	4.10818i
$705$		0			0
$706$	45.3701	−	32.9633i	1.70753	−	1.24059i
$707$	−12.3063	+	3.99855i	−0.462825	+	0.150381i
$708$	−21.2817	−	6.91485i	−0.799816	−	0.259876i
$709$	41.4016	+	30.0800i	1.55487	+	1.12968i	0.940064	+	0.340998i	$0.110765\pi$
$709$	41.4016	+	30.0800i	1.55487	+	1.12968i	0.614805	+	0.788680i	$0.289235\pi$
$710$		0			0
$711$	−3.35923	+	10.3386i	−0.125981	+	0.387729i
$712$	−57.3217	+	18.6250i	−2.14822	+	0.698000i
$713$	2.32065	+	3.19409i	0.0869088	+	0.119620i
$714$	31.5700			1.18148
$715$		0			0
$716$	37.0787			1.38570
$717$	−6.36734	−	8.76390i	−0.237793	−	0.327294i
$718$	−49.0126	+	15.9252i	−1.82913	+	0.594322i
$719$	−16.0803	+	49.4902i	−0.599696	+	1.84567i	−0.0698891	+	0.997555i	$0.522265\pi$
$719$	−16.0803	+	49.4902i	−0.599696	+	1.84567i	−0.529806	+	0.848119i	$0.677735\pi$
$720$		0			0
$721$	−2.38826	−	1.73517i	−0.0889435	−	0.0646213i
$722$	8.04673	+	2.61454i	0.299468	+	0.0973032i
$723$	−2.82013	+	0.916315i	−0.104882	+	0.0340781i
$724$	63.2523	−	45.9555i	2.35075	−	1.70792i
$725$		0			0
$726$	23.4844	+	19.4524i	0.871586	+	0.721947i
$727$		−	18.2951i		−	0.678528i	−0.940691	−	0.339264i	$-0.889822\pi$
$727$		−	18.2951i		−	0.678528i	0.940691	−	0.339264i	$-0.110178\pi$
$728$	5.95951	+	8.20256i	0.220874	+	0.304007i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$		0			0
$731$	−28.3284	−	20.5818i	−1.04776	−	0.761245i
$732$	9.90974	−	13.6396i	0.366275	−	0.504134i
$733$	−35.6792	−	11.5929i	−1.31784	−	0.428192i	−0.436088	−	0.899904i	$-0.643636\pi$
$733$	−35.6792	−	11.5929i	−1.31784	−	0.428192i	−0.881753	+	0.471712i	$0.843636\pi$
$734$	−5.06126	−	15.5770i	−0.186815	−	0.574956i
$735$		0			0
$736$	−22.4649			−0.828069
$737$	8.18953	+	0.259901i	0.301665	+	0.00957358i
$738$			11.9044i			0.438207i
$739$	−22.0973	+	16.0546i	−0.812863	+	0.590579i	−0.914659	−	0.404226i	$-0.867541\pi$
$739$	−22.0973	+	16.0546i	−0.812863	+	0.590579i	0.101796	+	0.994805i	$0.467541\pi$
$740$		0			0
$741$	−0.632311	+	1.94605i	−0.0232285	+	0.0714900i
$742$	40.2250	−	55.3650i	1.47671	−	2.03251i
$743$	−11.0641	+	15.2284i	−0.405902	+	0.558677i	−0.962213	−	0.272298i	$-0.912216\pi$
$743$	−11.0641	+	15.2284i	−0.405902	+	0.558677i	0.556311	+	0.830974i	$0.312216\pi$
$744$	14.7364	−	45.3539i	0.540262	−	1.66275i
$745$		0			0
$746$	3.74525	−	2.72108i	0.137123	−	0.0996259i
$747$		−	5.92050i		−	0.216620i
$748$	−77.9925	+	52.9684i	−2.85169	+	1.93672i
$749$	−27.7884			−1.01536
$750$		0			0
$751$	−7.78395	−	23.9565i	−0.284040	−	0.874186i	−0.986685	−	0.162645i	$-0.947997\pi$
$751$	−7.78395	−	23.9565i	−0.284040	−	0.874186i	0.702644	−	0.711541i	$-0.252003\pi$
$752$	7.54781	+	2.45243i	0.275240	+	0.0894310i
$753$	10.3535	−	14.2504i	0.377302	−	0.519312i
$754$	2.59669	+	1.88660i	0.0945658	+	0.0687061i
$755$		0			0
$756$	−4.00134	−	12.3149i	−0.145527	−	0.447887i
$757$	−26.9170	−	37.0481i	−0.978315	−	1.34653i	−0.937733	−	0.347358i	$-0.887079\pi$
$757$	−26.9170	−	37.0481i	−0.978315	−	1.34653i	−0.0405820	−	0.999176i	$-0.512921\pi$
$758$		−	23.3842i		−	0.849352i
$759$	−2.69409	+	0.781804i	−0.0977894	+	0.0283777i
$760$		0			0
$761$	−6.48664	+	4.71282i	−0.235141	+	0.170840i	−0.699116	−	0.715009i	$-0.746423\pi$
$761$	−6.48664	+	4.71282i	−0.235141	+	0.170840i	0.463975	+	0.885848i	$0.346423\pi$
$762$	1.32806	−	0.431513i	0.0481105	−	0.0156321i
$763$	−26.3495	−	8.56146i	−0.953914	−	0.309946i
$764$	−89.3949	−	64.9492i	−3.23419	−	2.34978i
$765$		0			0
$766$	18.7451	−	57.6916i	0.677289	−	2.08448i
$767$	1.63111	−	0.529980i	0.0588960	−	0.0191365i
$768$	46.2014	+	63.5907i	1.66715	+	2.29463i
$769$	−40.0439			−1.44402			−0.722010	−	0.691883i	$-0.756782\pi$
$769$	−40.0439			−1.44402			−0.722010	+	0.691883i	$0.756782\pi$
$770$		0			0
$771$	20.9647			0.755025
$772$	−75.5634	−	104.004i	−2.71959	−	3.74319i
$773$	−22.6589	+	7.36232i	−0.814984	+	0.264804i	−0.686707	−	0.726934i	$-0.740945\pi$
$773$	−22.6589	+	7.36232i	−0.814984	+	0.264804i	−0.128277	+	0.991738i	$0.540945\pi$
$774$	−5.99936	+	18.4641i	−0.215643	+	0.663680i
$775$		0			0
$776$	71.4770	+	51.9311i	2.56588	+	1.86422i
$777$	19.1970	+	6.23748i	0.688688	+	0.223768i
$778$	−1.03377	+	0.335891i	−0.0370624	+	0.0120423i
$779$	−16.3140	+	11.8528i	−0.584511	+	0.424672i
$780$		0			0
$781$	−23.0081	+	29.6429i	−0.823293	+	1.06071i
$782$		−	11.7239i		−	0.419245i
$783$	−1.56181	−	2.14965i	−0.0558146	−	0.0768222i
$784$	9.49471	+	29.2217i	0.339097	+	1.04363i
$785$		0			0
$786$	−42.8590	−	31.1389i	−1.52873	−	1.11069i
$787$	−5.57737	+	7.67659i	−0.198812	+	0.273641i	−0.896769	−	0.442498i	$-0.854092\pi$
$787$	−5.57737	+	7.67659i	−0.198812	+	0.273641i	0.697958	+	0.716139i	$0.254092\pi$
$788$	−124.522	−	40.4598i	−4.43593	−	1.44132i
$789$	−2.60647	−	8.02189i	−0.0927928	−	0.285587i
$790$		0			0
$791$	−0.323537			−0.0115037
$792$	26.7668	+	20.7757i	0.951116	+	0.738232i
$793$			1.29217i			0.0458864i
$794$	80.2517	−	58.3063i	2.84803	−	2.06921i
$795$		0			0
$796$	−34.4718	+	106.093i	−1.22182	+	3.76037i
$797$	−13.9680	+	19.2254i	−0.494774	+	0.680998i	−0.981259	−	0.192691i	$-0.938279\pi$
$797$	−13.9680	+	19.2254i	−0.494774	+	0.680998i	0.486486	+	0.873688i	$0.338279\pi$
$798$	17.4280	−	23.9875i	0.616943	−	0.849149i
$799$	−0.723376	+	2.22632i	−0.0255912	+	0.0787617i
$800$		0			0
$801$	−4.77286	+	3.46769i	−0.168641	+	0.122525i
$802$			84.3212i			2.97749i
$803$	9.47795	−	26.3005i	0.334469	−	0.928124i
$804$	14.0452			0.495337
$805$		0			0
$806$	1.74241	+	5.36260i	0.0613739	+	0.188890i
$807$	9.17148	+	2.97999i	0.322851	+	0.104901i
$808$	34.1158	−	46.9563i	1.20019	−	1.65192i
$809$	−14.8963	−	10.8228i	−0.523726	−	0.380509i	0.294280	−	0.955719i	$-0.404920\pi$
$809$	−14.8963	−	10.8228i	−0.523726	−	0.380509i	−0.818006	+	0.575210i	$0.804920\pi$
$810$		0			0
$811$	7.30675	+	22.4879i	0.256575	+	0.789656i	0.993515	+	0.113698i	$0.0362697\pi$
$811$	7.30675	+	22.4879i	0.256575	+	0.789656i	−0.736941	+	0.675957i	$0.763730\pi$
$812$	−20.2233	−	27.8350i	−0.709698	−	0.976815i
$813$		−	10.2278i		−	0.358704i
$814$	−78.2562	+	22.7093i	−2.74288	+	0.795960i
$815$		0			0
$816$	−68.5694	+	49.8186i	−2.40041	+	1.74400i
$817$	−31.2770	+	10.1625i	−1.09424	+	0.355541i
$818$	42.8958	+	13.9377i	1.49982	+	0.487320i
$819$	0.802893	+	0.583336i	0.0280554	+	0.0203834i
$820$		0			0
$821$	8.13186	−	25.0273i	0.283804	−	0.873459i	−0.702951	−	0.711239i	$-0.748135\pi$
$821$	8.13186	−	25.0273i	0.283804	−	0.873459i	0.986755	−	0.162220i	$-0.0518654\pi$
$822$	−32.5475	+	10.5753i	−1.13522	+	0.368857i
$823$	23.7652	+	32.7100i	0.828403	+	1.14020i	0.988218	+	0.153051i	$0.0489100\pi$
$823$	23.7652	+	32.7100i	0.828403	+	1.14020i	−0.159816	+	0.987147i	$0.551090\pi$
$824$	13.2416			0.461293
$825$		0			0
$826$	−24.8517			−0.864703
$827$	−9.75293	−	13.4238i	−0.339143	−	0.466790i	0.605048	−	0.796189i	$-0.293154\pi$
$827$	−9.75293	−	13.4238i	−0.339143	−	0.466790i	−0.944191	+	0.329399i	$0.893154\pi$
$828$	−4.57327	+	1.48595i	−0.158932	+	0.0516402i
$829$	10.6015	−	32.6281i	0.368206	−	1.13322i	−0.579743	−	0.814800i	$-0.696847\pi$
$829$	10.6015	−	32.6281i	0.368206	−	1.13322i	0.947949	−	0.318422i	$-0.103153\pi$
$830$		0			0
$831$	4.72388	+	3.43210i	0.163869	+	0.119058i
$832$	−16.4638	−	5.34942i	−0.570781	−	0.185458i
$833$	−8.61932	+	2.80059i	−0.298642	+	0.0970346i
$834$	−17.3419	+	12.5997i	−0.600502	+	0.436290i
$835$		0			0
$836$	−2.80865	+	88.5012i	−0.0971393	+	3.06088i
$837$		−	4.66785i		−	0.161344i
$838$	−65.2934	−	89.8686i	−2.25552	−	3.10446i
$839$	1.04698	+	3.22229i	0.0361459	+	0.111246i	0.967502	−	0.252865i	$-0.0813729\pi$
$839$	1.04698	+	3.22229i	0.0361459	+	0.111246i	−0.931356	+	0.364111i	$0.881373\pi$
$840$		0			0
$841$	17.7496	+	12.8959i	0.612056	+	0.444685i
$842$	−31.6024	+	43.4970i	−1.08909	+	1.49901i
$843$	−13.7084	−	4.45412i	−0.472142	−	0.153408i
$844$	−0.0877101	−	0.269944i	−0.00301910	−	0.00929185i
$845$		0			0
$846$	1.29790			0.0446226
$847$	23.2884	+	9.23721i	0.800201	+	0.317394i
$848$			183.729i			6.30926i
$849$	−8.60264	+	6.25018i	−0.295242	+	0.214506i
$850$		0			0
$851$	2.31636	−	7.12903i	0.0794039	−	0.244380i
$852$	−37.8078	+	52.0380i	−1.29527	+	1.78279i
$853$	−9.64323	+	13.2728i	−0.330178	+	0.454451i	−0.941541	−	0.336900i	$-0.890622\pi$
$853$	−9.64323	+	13.2728i	−0.330178	+	0.454451i	0.611363	+	0.791351i	$0.290622\pi$
$854$	5.78606	−	17.8076i	0.197995	−	0.609365i
$855$		0			0
$856$	100.841	−	73.2651i	3.44667	−	2.50415i
$857$		−	3.37817i		−	0.115396i	−0.998334	−	0.0576981i	$-0.981624\pi$
$857$		−	3.37817i		−	0.115396i	0.998334	−	0.0576981i	$-0.0183761\pi$
$858$	−4.00433	−	0.127081i	−0.136706	−	0.00433846i
$859$	2.32376			0.0792855			0.0396428	−	0.999214i	$-0.487378\pi$
$859$	2.32376			0.0792855			0.0396428	+	0.999214i	$0.487378\pi$
$860$		0			0
$861$	3.02230	+	9.30168i	0.103000	+	0.317001i
$862$	89.4959	+	29.0790i	3.04824	+	0.990434i
$863$	11.9116	−	16.3949i	0.405476	−	0.558090i	−0.556632	−	0.830759i	$-0.687907\pi$
$863$	11.9116	−	16.3949i	0.405476	−	0.558090i	0.962108	+	0.272670i	$0.0879066\pi$
$864$	21.4877	+	15.6117i	0.731026	+	0.531121i
$865$		0			0
$866$	−11.2356	−	34.5795i	−0.381800	−	1.17506i
$867$	−4.70228	−	6.47214i	−0.159698	−	0.219805i
$868$		−	60.4421i		−	2.05154i
$869$	−20.2561	−	29.8258i	−0.687142	−	1.01177i
$870$		0			0
$871$	−0.870890	+	0.632739i	−0.0295090	+	0.0214395i
$872$	118.192	−	38.4029i	4.00248	−	1.30048i
$873$	8.22477	+	2.67239i	0.278366	+	0.0904466i
$874$	−8.90806	−	6.47209i	−0.301320	−	0.218922i
$875$		0			0
$876$	14.8085	−	45.5759i	0.500333	−	1.53987i
$877$	15.8073	−	5.13611i	0.533775	−	0.173434i	−0.0297127	−	0.999558i	$-0.509459\pi$
$877$	15.8073	−	5.13611i	0.533775	−	0.173434i	0.563488	+	0.826125i	$0.309459\pi$
$878$	−15.7200	−	21.6367i	−0.530525	−	0.730205i
$879$	8.39576			0.283182
$880$		0			0
$881$	−29.8895			−1.00700			−0.503502	−	0.863994i	$-0.667955\pi$
$881$	−29.8895			−1.00700			−0.503502	+	0.863994i	$0.667955\pi$
$882$	2.95355	+	4.06521i	0.0994511	+	0.136883i
$883$	13.3277	−	4.33042i	0.448511	−	0.145730i	−0.0760479	−	0.997104i	$-0.524230\pi$
$883$	13.3277	−	4.33042i	0.448511	−	0.145730i	0.524559	+	0.851374i	$0.324230\pi$
$884$	3.82758	−	11.7801i	0.128735	−	0.396207i
$885$		0			0
$886$	19.9923	+	14.5253i	0.671655	+	0.487986i
$887$	27.2079	+	8.84040i	0.913553	+	0.296831i	0.727820	−	0.685769i	$-0.240534\pi$
$887$	27.2079	+	8.84040i	0.913553	+	0.296831i	0.185734	+	0.982600i	$0.440534\pi$
$888$	−86.1091	+	27.9785i	−2.88963	+	0.938898i
$889$	0.928146	−	0.674338i	0.0311290	−	0.0226166i
$890$		0			0
$891$	3.12020	+	1.12443i	0.104531	+	0.0376699i
$892$			4.29213i			0.143711i
$893$	1.29227	+	1.77866i	0.0432443	+	0.0595207i
$894$	−6.51832	−	20.0613i	−0.218005	−	0.670951i
$895$		0			0
$896$	105.057	+	76.3284i	3.50971	+	2.54995i
$897$	0.216629	−	0.298164i	0.00723303	−	0.00995541i
$898$	32.7902	+	10.6542i	1.09422	+	0.355535i
$899$	−3.83274	−	11.7959i	−0.127829	−	0.393417i
$900$		0			0
$901$	−54.1931			−1.80543
$902$	−31.1898	−	24.2087i	−1.03851	−	0.806062i
$903$			15.9504i			0.530794i
$904$	1.17408	−	0.853019i	0.0390493	−	0.0283710i
$905$		0			0
$906$	−2.29093	+	7.05077i	−0.0761112	+	0.234246i
$907$	15.8521	−	21.8186i	0.526361	−	0.724474i	−0.460209	−	0.887811i	$-0.652226\pi$
$907$	15.8521	−	21.8186i	0.526361	−	0.724474i	0.986570	+	0.163336i	$0.0522256\pi$
$908$	−27.6825	+	38.1017i	−0.918677	+	1.26445i
$909$	1.75561	−	5.40320i	0.0582298	−	0.179213i
$910$		0			0
$911$	−5.77363	+	4.19479i	−0.191289	+	0.138980i	−0.679308	−	0.733854i	$-0.737720\pi$
$911$	−5.77363	+	4.19479i	−0.191289	+	0.138980i	0.488019	+	0.872833i	$0.337720\pi$
$912$			79.6025i			2.63590i
$913$	15.5118	+	12.0399i	0.513366	+	0.398462i
$914$	105.783			3.49900
$915$		0			0
$916$	−5.05303	−	15.5516i	−0.166957	−	0.513840i
$917$	−41.3941	−	13.4498i	−1.36695	−	0.444150i
$918$	−8.14736	+	11.2139i	−0.268903	+	0.370113i
$919$	−5.57755	−	4.05233i	−0.183987	−	0.133674i	0.491980	−	0.870607i	$-0.336273\pi$
$919$	−5.57755	−	4.05233i	−0.183987	−	0.133674i	−0.675966	+	0.736933i	$0.736273\pi$
$920$		0			0
$921$	1.39645	+	4.29784i	0.0460147	+	0.141619i
$922$	−56.0288	−	77.1171i	−1.84521	−	2.53971i
$923$		−	4.92992i		−	0.162270i
$924$	40.4023	+	14.5598i	1.32914	+	0.478983i
$925$		0			0
$926$	90.2854	−	65.5962i	2.96696	−	2.15563i
$927$	1.23269	−	0.400526i	0.0404869	−	0.0131550i
$928$	67.1194	+	21.8084i	2.20330	+	0.715896i
$929$	−29.4333	−	21.3846i	−0.965676	−	0.701605i	−0.0112141	−	0.999937i	$-0.503570\pi$
$929$	−29.4333	−	21.3846i	−0.965676	−	0.701605i	−0.954462	+	0.298332i	$0.903570\pi$
$930$		0			0
$931$	−2.63029	+	8.09519i	−0.0862042	+	0.265309i
$932$	28.0010	−	9.09807i	0.917202	−	0.298017i
$933$	14.1051	+	19.4140i	0.461780	+	0.635585i
$934$	−41.9052			−1.37118
$935$		0			0
$936$	−4.45160			−0.145505
$937$	−30.9724	−	42.6299i	−1.01183	−	1.39266i	−0.917780	−	0.397090i	$-0.870020\pi$
$937$	−30.9724	−	42.6299i	−1.01183	−	1.39266i	−0.0940454	−	0.995568i	$-0.529980\pi$
$938$	14.8351	−	4.82023i	0.484385	−	0.157386i
$939$	7.99384	−	24.6025i	0.260869	−	0.802873i
$940$		0			0
$941$	16.4217	+	11.9311i	0.535334	+	0.388943i	0.822349	−	0.568983i	$-0.192663\pi$
$941$	16.4217	+	11.9311i	0.535334	+	0.388943i	−0.287015	+	0.957926i	$0.592663\pi$
$942$	53.2581	+	17.3046i	1.73524	+	0.563814i
$943$	3.45429	−	1.12237i	0.112487	−	0.0365493i
$944$	53.9776	−	39.2170i	1.75682	−	1.27640i
$945$		0			0
$946$	−36.1761	−	53.2670i	−1.17619	−	1.73186i
$947$			14.5680i			0.473395i	0.971583	+	0.236698i	$0.0760651\pi$
$947$			14.5680i			0.473395i	−0.971583	+	0.236698i	$0.923935\pi$
$948$	−36.3264	−	49.9991i	−1.17983	−	1.62389i
$949$	1.13498	+	3.49311i	0.0368430	+	0.113391i
$950$		0			0
$951$	−2.34873	−	1.70645i	−0.0761629	−	0.0553356i
$952$	−68.3842	+	94.1228i	−2.21635	+	3.05054i
$953$	37.5718	+	12.2078i	1.21707	+	0.395450i	0.846014	−	0.533160i	$-0.178996\pi$
$953$	37.5718	+	12.2078i	1.21707	+	0.395450i	0.371056	+	0.928610i	$0.378996\pi$
$954$	9.28505	+	28.5765i	0.300615	+	0.925197i
$955$		0			0
$956$	61.5867			1.99186
$957$	8.80821	+	0.279535i	0.284729	+	0.00903609i
$958$			79.8524i			2.57991i
$959$	−22.7466	+	16.5264i	−0.734526	+	0.533665i
$960$		0			0
$961$	−2.84642	+	8.76037i	−0.0918199	+	0.282592i
$962$	6.29248	−	8.66086i	0.202878	−	0.279237i
$963$	7.17143	−	9.87063i	0.231096	−	0.318077i
$964$	5.20945	−	16.0330i	0.167785	−	0.516389i
$965$		0			0
$966$	−4.32051	+	3.13903i	−0.139010	+	0.100997i
$967$		−	44.8051i		−	1.44083i	−0.693541	−	0.720417i	$-0.743950\pi$
$967$		−	44.8051i		−	1.44083i	0.693541	−	0.720417i	$-0.256050\pi$
$968$	−108.865	+	27.8801i	−3.49907	+	0.896102i
$969$	−23.4798			−0.754279
$970$		0			0
$971$	5.60723	+	17.2573i	0.179945	+	0.553812i	0.999825	−	0.0187228i	$-0.00596000\pi$
$971$	5.60723	+	17.2573i	0.179945	+	0.553812i	−0.819880	+	0.572535i	$0.805960\pi$
$972$	5.40697	+	1.75683i	0.173428	+	0.0563503i
$973$	−10.3516	+	14.2477i	−0.331856	+	0.456761i
$974$	64.7097	+	47.0144i	2.07343	+	1.50644i
$975$		0			0
$976$	15.5339	+	47.8085i	0.497229	+	1.53031i
$977$	−30.5629	−	42.0662i	−0.977794	−	1.34582i	−0.938010	−	0.346609i	$-0.887333\pi$
$977$	−30.5629	−	42.0662i	−0.977794	−	1.34582i	−0.0397838	−	0.999208i	$-0.512667\pi$
$978$			27.1562i			0.868359i
$979$	0.620652	−	19.5569i	0.0198361	−	0.625040i
$980$		0			0
$981$	9.84118	−	7.15004i	0.314205	−	0.228283i
$982$	39.3812	−	12.7957i	1.25671	−	0.408328i
$983$	−42.1625	−	13.6994i	−1.34477	−	0.436943i	−0.453842	−	0.891082i	$-0.649947\pi$
$983$	−42.1625	−	13.6994i	−1.34477	−	0.436943i	−0.890931	+	0.454139i	$0.849947\pi$
$984$	−35.4919	−	25.7863i	−1.13144	−	0.822039i
$985$		0			0
$986$	−11.3813	+	35.0279i	−0.362453	+	1.11552i
$987$	1.01413	−	0.329511i	0.0322801	−	0.0104885i
$988$	−6.83777	−	9.41138i	−0.217538	−	0.299416i
$989$	5.92336			0.188352
$990$		0			0
$991$	10.4084			0.330635			0.165317	−	0.986240i	$-0.447135\pi$
$991$	10.4084			0.330635			0.165317	+	0.986240i	$0.447135\pi$
$992$	72.8731	+	100.301i	2.31372	+	3.18457i
$993$	10.4461	−	3.39416i	0.331498	−	0.107710i
$994$	−22.0751	+	67.9401i	−0.700179	+	2.15493i
$995$		0			0
$996$	27.2310	+	19.7845i	0.862846	+	0.626895i
$997$	6.20281	+	2.01541i	0.196445	+	0.0638288i	0.405587	−	0.914056i	$-0.367067\pi$
$997$	6.20281	+	2.01541i	0.196445	+	0.0638288i	−0.209142	+	0.977885i	$0.567067\pi$
$998$	58.5286	−	19.0171i	1.85269	−	0.601975i
$999$	−7.16983	+	5.20918i	−0.226843	+	0.164811i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.bx.h.124.1		16
5.2	odd	4		825.2.n.k.751.2		8
5.3	odd	4		165.2.m.a.91.1	✓	8
5.4	even	2	inner	825.2.bx.h.124.4		16
11.4	even	5	inner	825.2.bx.h.499.4		16
15.8	even	4		495.2.n.d.91.2		8
55.2	even	20		9075.2.a.dj.1.4		4
55.4	even	10	inner	825.2.bx.h.499.1		16
55.13	even	20		1815.2.a.o.1.1		4
55.37	odd	20		825.2.n.k.301.2		8
55.42	odd	20		9075.2.a.cl.1.1		4
55.48	odd	20		165.2.m.a.136.1	yes	8
55.53	odd	20		1815.2.a.x.1.4		4
165.53	even	20		5445.2.a.be.1.1		4
165.68	odd	20		5445.2.a.bv.1.4		4
165.158	even	20		495.2.n.d.136.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.a.91.1	✓	8	5.3	odd	4
165.2.m.a.136.1	yes	8	55.48	odd	20
495.2.n.d.91.2		8	15.8	even	4
495.2.n.d.136.2		8	165.158	even	20
825.2.n.k.301.2		8	55.37	odd	20
825.2.n.k.751.2		8	5.2	odd	4
825.2.bx.h.124.1		16	1.1	even	1	trivial
825.2.bx.h.124.4		16	5.4	even	2	inner
825.2.bx.h.499.1		16	55.4	even	10	inner
825.2.bx.h.499.4		16	11.4	even	5	inner
1815.2.a.o.1.1		4	55.13	even	20
1815.2.a.x.1.4		4	55.53	odd	20
5445.2.a.be.1.1		4	165.53	even	20
5445.2.a.bv.1.4		4	165.68	odd	20
9075.2.a.cl.1.1		4	55.42	odd	20
9075.2.a.dj.1.4		4	55.2	even	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.bx (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.62947 - 2.24278i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-1.75683 + 5.40697i) q^{4} +(-2.24278 - 1.62947i) q^{6} +(-2.16612 - 0.703814i) q^{7} +(9.71623 - 3.15700i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-1.62947 - 2.24278i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-1.75683 + 5.40697i) q^{4} +(-2.24278 - 1.62947i) q^{6} +(-2.16612 - 0.703814i) q^{7} +(9.71623 - 3.15700i) q^{8} +(0.809017 - 0.587785i) q^{9} +(-0.105203 + 3.31496i) q^{11} +5.68522i q^{12} +(-0.256120 - 0.352519i) q^{13} +(1.95113 + 6.00496i) q^{14} +(-13.7139 - 9.96371i) q^{16} +(2.93893 - 4.04508i) q^{17} +(-2.63654 - 0.856664i) q^{18} +(-1.45113 - 4.46612i) q^{19} -2.27759 q^{21} +(7.60613 - 5.16568i) q^{22} +0.845811i q^{23} +(8.26512 - 6.00496i) q^{24} +(-0.373280 + 1.14884i) q^{26} +(0.587785 - 0.809017i) q^{27} +(7.61100 - 10.4756i) q^{28} +(0.821093 - 2.52706i) q^{29} +(3.77637 - 2.74369i) q^{31} +26.5602i q^{32} +(0.924324 + 3.18522i) q^{33} -13.8611 q^{34} +(1.75683 + 5.40697i) q^{36} +(-8.42864 - 2.73863i) q^{37} +(-7.65193 + 10.5320i) q^{38} +(-0.352519 - 0.256120i) q^{39} +(-1.32697 - 4.08400i) q^{41} +(3.71127 + 5.10813i) q^{42} -7.00317i q^{43} +(-17.7390 - 6.39264i) q^{44} +(1.89696 - 1.37823i) q^{46} +(-0.445265 + 0.144675i) q^{47} +(-16.1216 - 5.23823i) q^{48} +(-1.46641 - 1.06541i) q^{49} +(1.54508 - 4.75528i) q^{51} +(2.35601 - 0.765515i) q^{52} +(-6.37078 - 8.76863i) q^{53} -2.77222 q^{54} -23.2684 q^{56} +(-2.76021 - 3.79911i) q^{57} +(-7.00558 + 2.27625i) q^{58} +(-1.21629 + 3.74334i) q^{59} +(-2.39913 - 1.74307i) q^{61} +(-12.3070 - 3.99878i) q^{62} +(-2.16612 + 0.703814i) q^{63} +(32.1409 - 23.3517i) q^{64} +(5.63757 - 7.26328i) q^{66} -2.47048i q^{67} +(16.7084 + 22.9972i) q^{68} +(0.261370 + 0.804414i) q^{69} +(9.15321 + 6.65020i) q^{71} +(6.00496 - 8.26512i) q^{72} +(-8.01655 - 2.60474i) q^{73} +(7.59209 + 23.3661i) q^{74} +26.6975 q^{76} +(2.56099 - 7.10654i) q^{77} +1.20796i q^{78} +(-8.79457 + 6.38963i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-6.99723 + 9.63087i) q^{82} +(3.47998 - 4.78978i) q^{83} +(4.00134 - 12.3149i) q^{84} +(-15.7065 + 11.4115i) q^{86} -2.65711i q^{87} +(9.44313 + 32.5410i) q^{88} -5.89958 q^{89} +(0.306678 + 0.943857i) q^{91} +(-4.57327 - 1.48595i) q^{92} +(2.74369 - 3.77637i) q^{93} +(1.05002 + 0.762885i) q^{94} +(8.20756 + 25.2603i) q^{96} +(5.08318 + 6.99640i) q^{97} +5.02487i q^{98} +(1.86337 + 2.74369i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} + 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^4 + 4 * q^9	\( 16 q + 4 q^{4} + 4 q^{9} - 6 q^{11} + 20 q^{14} - 40 q^{16} - 12 q^{19} - 8 q^{21} + 40 q^{24} - 16 q^{26} + 6 q^{31} - 100 q^{34} - 4 q^{36} - 12 q^{39} - 50 q^{41} - 14 q^{44} - 12 q^{46} - 42 q^{49} - 20 q^{51} - 20 q^{54} + 40 q^{56} - 70 q^{59} + 42 q^{61} + 154 q^{64} + 50 q^{66} + 10 q^{69} + 50 q^{71} + 58 q^{74} - 28 q^{76} - 60 q^{79} - 4 q^{81} + 68 q^{84} - 68 q^{86} - 64 q^{89} + 74 q^{91} + 78 q^{94} + 20 q^{96} + 6 q^{99}+O(q^{100}) \) 16 * q + 4 * q^4 + 4 * q^9 - 6 * q^11 + 20 * q^14 - 40 * q^16 - 12 * q^19 - 8 * q^21 + 40 * q^24 - 16 * q^26 + 6 * q^31 - 100 * q^34 - 4 * q^36 - 12 * q^39 - 50 * q^41 - 14 * q^44 - 12 * q^46 - 42 * q^49 - 20 * q^51 - 20 * q^54 + 40 * q^56 - 70 * q^59 + 42 * q^61 + 154 * q^64 + 50 * q^66 + 10 * q^69 + 50 * q^71 + 58 * q^74 - 28 * q^76 - 60 * q^79 - 4 * q^81 + 68 * q^84 - 68 * q^86 - 64 * q^89 + 74 * q^91 + 78 * q^94 + 20 * q^96 + 6 * q^99

Introduction

L-functions

Modular forms

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