LMFDB - Embedded newform 825.2.bx.h.124.4

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			124.4
Root			$-0.280526 - 0.386111i$ of defining polynomial
Character	$\chi$	$=$	825.124
Dual form			825.2.bx.h.499.4

$q$-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	$0.236438\pi$
$2$	1.62947	+	2.24278i	1.15221	+	1.58588i	0.415627	+	0.909535i	$0.363562\pi$
$3$	−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	0.688285	−	0.725441i	$-0.258364\pi$
$7$	2.16612	+	0.703814i	0.818716	+	0.266017i	0.130431	+	0.991457i	$0.458364\pi$
$8$	−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	0.843056	−	0.537826i	$-0.180754\pi$
$13$	0.256120	+	0.352519i	0.0710348	+	0.0977711i	−0.772021	+	0.635597i	$0.780754\pi$
$14$	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	$0.407363\pi$
$17$	−2.93893	+	4.04508i	−0.712794	+	0.981077i	−0.999733	+	0.0231281i	$0.992637\pi$
$18$	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	$-0.971894\pi$
$23$		−	0.845811i		−	0.176364i	0.996104	−	0.0881819i	$-0.0281057\pi$
$24$	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	0.904526	−	0.426419i	$-0.140225\pi$
$37$	8.42864	+	2.73863i	1.38566	+	0.450228i	0.481134	+	0.876647i	$0.340225\pi$
$38$	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	$0.179307\pi$
$43$			7.00317i			1.06797i	−0.845493	+	0.533986i	$0.820693\pi$
$44$	−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	−0.276363	−	0.961053i	$-0.589129\pi$
$47$	0.445265	−	0.144675i	0.0649485	−	0.0211031i	0.341311	+	0.939950i	$0.389129\pi$
$48$	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	$0.0672641\pi$
$53$	6.37078	+	8.76863i	0.875094	+	1.20446i	−0.102662	+	0.994716i	$0.532736\pi$
$54$	−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	$0.0482199\pi$
$67$			2.47048i			0.301817i	−0.988548	+	0.150909i	$0.951780\pi$
$68$	−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	0.737939	−	0.674868i	$-0.235799\pi$
$73$	8.01655	+	2.60474i	0.938266	+	0.304861i	0.200328	+	0.979729i	$0.435799\pi$
$74$	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	−0.956107	−	0.293017i	$-0.905341\pi$
$83$	−3.47998	+	4.78978i	−0.381978	+	0.525747i	0.574130	+	0.818764i	$0.305341\pi$
$84$	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	0.468817	−	0.883295i	$-0.344680\pi$
$97$	−5.08318	−	6.99640i	−0.516119	−	0.710377i	−0.984936	+	0.172918i	$0.944680\pi$
$98$		−	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	0.247656	−	0.968848i	$-0.420340\pi$
$103$	−1.23269	−	0.400526i	−0.121461	−	0.0394650i	−0.369117	+	0.929383i	$0.620340\pi$
$104$	−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	−0.810441	−	0.585821i	$-0.800772\pi$
$107$	−11.6036	+	3.77024i	−1.12176	+	0.364483i	−0.311324	+	0.950304i	$0.600772\pi$
$108$	−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	−0.315365	−	0.948971i	$-0.602127\pi$
$113$	−0.135100	+	0.0438966i	−0.0127091	+	0.00412944i	0.302656	+	0.953100i	$0.402127\pi$
$114$	−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	−0.795679	−	0.605719i	$-0.792886\pi$
$127$	0.296075	−	0.407512i	0.0262724	−	0.0361609i	0.821951	+	0.569558i	$0.192886\pi$
$128$	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	−0.997348	−	0.0727841i	$-0.976812\pi$
$137$	−7.25608	+	9.98713i	−0.619929	+	0.853258i	0.377419	+	0.926043i	$0.376812\pi$
$138$	−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	0.583731	−	0.811947i	$-0.301592\pi$
$157$	19.2113	−	6.24214i	1.53323	−	0.498177i	0.949499	+	0.313770i	$0.101592\pi$
$158$	−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	0.972610	−	0.232445i	$-0.0746725\pi$
$163$	5.75784	+	7.92498i	0.450989	+	0.620733i	−0.521621	+	0.853177i	$0.674672\pi$
$164$	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	$0.254114\pi$
$167$	15.0341	+	20.6927i	1.16338	+	1.60125i	0.465467	+	0.885065i	$0.345886\pi$
$168$	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	−0.0544734	−	0.998515i	$-0.517348\pi$
$173$	6.42349	−	2.08712i	0.488369	−	0.158681i	0.542843	+	0.839834i	$0.317348\pi$
$174$	−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	$-0.497375\pi$
$193$	13.2912	−	18.2938i	0.956722	−	1.31681i	0.948476	−	0.316849i	$-0.102625\pi$
$194$	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	$-0.693745\pi$
$197$		−	23.0300i		−	1.64082i	0.571776	−	0.820410i	$-0.306255\pi$
$198$	−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	−0.332959	−	0.942941i	$-0.608047\pi$
$223$	−0.718012	+	0.233296i	−0.0480816	+	0.0156227i	0.284877	+	0.958564i	$0.408047\pi$
$224$	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	0.0356515	−	0.999364i	$-0.488649\pi$
$227$	−7.87855	−	2.55989i	−0.522917	−	0.169906i	−0.558569	+	0.829458i	$0.688649\pi$
$228$	−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	0.897000	−	0.442030i	$-0.145742\pi$
$233$	3.04395	+	4.18964i	0.199416	+	0.274473i	−0.697584	+	0.716503i	$0.745742\pi$
$234$	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	−0.388064	−	0.921632i	$-0.626856\pi$
$257$	−19.9386	−	6.47845i	−1.24374	−	0.404115i	−0.855672	+	0.517518i	$0.826856\pi$
$258$	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	$0.0837402\pi$
$263$			8.43471i			0.520107i	−0.965594	+	0.260053i	$0.916260\pi$
$264$	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	0.693365	−	0.720586i	$-0.256127\pi$
$277$	−3.43210	−	4.72388i	−0.206215	−	0.283830i	−0.899580	+	0.436756i	$0.856127\pi$
$278$	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	0.00740011	−	0.999973i	$-0.497644\pi$
$283$	10.1130	−	3.28592i	0.601156	−	0.195327i	0.593756	+	0.804645i	$0.297644\pi$
$284$	−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	0.0663405	−	0.997797i	$-0.478868\pi$
$293$	−7.98484	−	2.59443i	−0.466479	−	0.151568i	−0.532820	+	0.846229i	$0.678868\pi$
$294$	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	$-0.958837\pi$
$307$		−	4.51902i		−	0.257914i	0.991650	−	0.128957i	$-0.0411629\pi$
$308$	−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	$0.460988\pi$
$313$	−15.2052	+	20.9281i	−0.859448	+	1.18293i	−0.981701	+	0.190430i	$0.939012\pi$
$314$	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	0.854246	−	0.519869i	$-0.174019\pi$
$317$	1.70645	+	2.34873i	0.0958441	+	0.131918i	−0.758402	+	0.651787i	$0.774019\pi$
$318$		−	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	−0.0432780	−	0.999063i	$-0.513780\pi$
$337$	−12.2174	−	3.96968i	−0.665525	−	0.216242i	−0.622247	+	0.782821i	$0.713780\pi$
$338$	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	−0.778162	−	0.628064i	$-0.783848\pi$
$347$	1.11074	−	1.52881i	0.0596279	−	0.0820707i	0.837790	+	0.545993i	$0.183848\pi$
$348$	−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	$-0.819047\pi$
$353$		−	20.2294i		−	1.07670i	0.842720	−	0.538352i	$-0.180953\pi$
$354$	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	0.158668	−	0.987332i	$-0.449280\pi$
$367$	−5.61894	−	1.82571i	−0.293306	−	0.0953010i	−0.451974	+	0.892031i	$0.649280\pi$
$368$	−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	$-0.986234\pi$
$373$		−	1.66992i		−	0.0864650i	0.999065	−	0.0432325i	$-0.0137656\pi$
$374$	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	0.342185	−	0.939633i	$-0.388833\pi$
$383$	−12.8616	−	17.7025i	−0.657199	−	0.904558i	−0.999385	+	0.0350750i	$0.988833\pi$
$384$	−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	$-0.645069\pi$
$397$		−	35.7823i		−	1.79586i	0.440134	−	0.897932i	$-0.354931\pi$
$398$	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	−0.00645020	−	0.999979i	$-0.502053\pi$
$433$	−12.4736	−	4.05291i	−0.599442	−	0.194770i	−0.592991	+	0.805209i	$0.702053\pi$
$434$	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	−0.100613	−	0.994926i	$-0.532080\pi$
$443$	8.47781	−	2.75461i	0.402793	−	0.130875i	0.503405	+	0.864050i	$0.332080\pi$
$444$	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	$-0.448960\pi$
$457$	22.4289	−	30.8707i	1.04918	−	1.44407i	0.889519	−	0.456898i	$-0.151040\pi$
$458$	−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	$-0.615012\pi$
$463$		−	40.2561i		−	1.87086i	0.353511	−	0.935430i	$-0.384988\pi$
$464$	−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	−0.963498	−	0.267714i	$-0.913732\pi$
$467$	−8.88502	+	12.2292i	−0.411150	+	0.565899i	0.552349	+	0.833613i	$0.313732\pi$
$468$	−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	0.387876	−	0.921712i	$-0.373209\pi$
$487$	27.4404	−	8.91592i	1.24344	−	0.404019i	0.855567	+	0.517693i	$0.173209\pi$
$488$	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	−0.312309	−	0.949981i	$-0.601102\pi$
$503$	−0.147752	+	0.0480077i	−0.00658795	+	0.00214056i	0.305721	+	0.952121i	$0.401102\pi$
$504$	−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	−0.997088	−	0.0762616i	$-0.975702\pi$
$523$	−14.0975	+	19.4036i	−0.616442	+	0.848459i	0.380646	+	0.924721i	$0.375702\pi$
$524$	−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	−0.973637	−	0.228103i	$-0.926748\pi$
$547$	−38.0582	+	12.3659i	−1.62725	+	0.528726i	−0.653614	+	0.756829i	$0.726748\pi$
$548$	−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	0.461176	−	0.887309i	$-0.347428\pi$
$557$	7.38064	+	2.39812i	0.312728	+	0.101611i	−0.148448	+	0.988920i	$0.547428\pi$
$558$	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	0.517130	−	0.855907i	$-0.327000\pi$
$563$	−10.8361	−	14.9146i	−0.456688	−	0.628577i	−0.973818	+	0.227330i	$0.927000\pi$
$564$	−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	−0.922210	−	0.386690i	$-0.873618\pi$
$577$	−6.47284	+	8.90910i	−0.269468	+	0.370891i	0.652742	+	0.757580i	$0.273618\pi$
$578$	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	0.0671803	−	0.997741i	$-0.478600\pi$
$587$	−11.2643	−	3.65999i	−0.464927	−	0.151064i	−0.532107	+	0.846677i	$0.678600\pi$
$588$	−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	$0.0608289\pi$
$593$			9.25062i			0.379877i	−0.981796	+	0.189939i	$0.939171\pi$
$594$	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	0.409528	−	0.912297i	$-0.365693\pi$
$607$	−14.4047	−	19.8264i	−0.584669	−	0.804728i	−0.994198	+	0.107569i	$0.965693\pi$
$608$	−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	−0.396868	−	0.917876i	$-0.629903\pi$
$613$	−4.41763	+	1.43538i	−0.178427	+	0.0579743i	0.218441	+	0.975850i	$0.429903\pi$
$614$	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	$-0.682418\pi$
$617$		−	41.7419i		−	1.68047i	0.542226	−	0.840233i	$-0.317582\pi$
$618$	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	−0.759940	−	0.649993i	$-0.774772\pi$
$643$	2.36014	−	3.24845i	0.0930747	−	0.128106i	0.853015	+	0.521887i	$0.174772\pi$
$644$	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	0.941409	−	0.337267i	$-0.109502\pi$
$647$	8.38728	+	11.5441i	0.329738	+	0.453846i	−0.611671	+	0.791112i	$0.709502\pi$
$648$			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	0.185129	−	0.982714i	$-0.440730\pi$
$653$	−6.20252	−	2.01532i	−0.242723	−	0.0788656i	−0.427852	+	0.903849i	$0.640730\pi$
$654$	−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	0.998749	−	0.0500135i	$-0.0159264\pi$
$673$	16.6693	+	22.9433i	0.642553	+	0.884398i	−0.356196	+	0.934411i	$0.615926\pi$
$674$	−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	−0.747684	−	0.664055i	$-0.768834\pi$
$677$	2.99004	−	4.11544i	0.114917	−	0.158169i	0.862601	+	0.505885i	$0.168834\pi$
$678$	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	$0.107776\pi$
$683$			17.3612i			0.664310i	−0.943225	+	0.332155i	$0.892224\pi$
$684$	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	$0.110178\pi$
$727$			18.2951i			0.678528i	−0.940691	+	0.339264i	$0.889822\pi$
$728$	−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	0.881753	−	0.471712i	$-0.156364\pi$
$733$	35.6792	+	11.5929i	1.31784	+	0.428192i	0.436088	+	0.899904i	$0.356364\pi$
$734$	−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	−0.556311	−	0.830974i	$-0.687784\pi$
$743$	11.0641	−	15.2284i	0.405902	−	0.558677i	0.962213	+	0.272298i	$0.0877835\pi$
$744$	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	$0.112921\pi$
$757$	26.9170	+	37.0481i	0.978315	+	1.34653i	0.0405820	+	0.999176i	$0.487079\pi$
$758$			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	0.128277	−	0.991738i	$-0.459055\pi$
$773$	22.6589	−	7.36232i	0.814984	−	0.264804i	0.686707	+	0.726934i	$0.259055\pi$
$774$	−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	−0.697958	−	0.716139i	$-0.745908\pi$
$787$	5.57737	−	7.67659i	0.198812	−	0.273641i	0.896769	+	0.442498i	$0.145908\pi$
$788$	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	−0.486486	−	0.873688i	$-0.661721\pi$
$797$	13.9680	−	19.2254i	0.494774	−	0.680998i	0.981259	+	0.192691i	$0.0617215\pi$
$798$	−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	$-0.951090\pi$
$823$	−23.7652	−	32.7100i	−0.828403	−	1.14020i	0.159816	−	0.987147i	$-0.448910\pi$
$824$	13.2416			0.461293
$825$		0			0
$826$	−24.8517			−0.864703
$827$	9.75293	+	13.4238i	0.339143	+	0.466790i	0.944191	−	0.329399i	$-0.106846\pi$
$827$	9.75293	+	13.4238i	0.339143	+	0.466790i	−0.605048	+	0.796189i	$0.706846\pi$
$828$	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	−0.611363	−	0.791351i	$-0.709378\pi$
$853$	9.64323	−	13.2728i	0.330178	−	0.454451i	0.941541	+	0.336900i	$0.109378\pi$
$854$	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	$0.0183761\pi$
$857$			3.37817i			0.115396i	−0.998334	+	0.0576981i	$0.981624\pi$
$858$	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	−0.962108	−	0.272670i	$-0.912093\pi$
$863$	−11.9116	+	16.3949i	−0.405476	+	0.558090i	0.556632	+	0.830759i	$0.312093\pi$
$864$	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	−0.563488	−	0.826125i	$-0.690541\pi$
$877$	−15.8073	+	5.13611i	−0.533775	+	0.173434i	0.0297127	+	0.999558i	$0.490541\pi$
$878$	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	−0.524559	−	0.851374i	$-0.675770\pi$
$883$	−13.3277	+	4.33042i	−0.448511	+	0.145730i	0.0760479	+	0.997104i	$0.475770\pi$
$884$	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	−0.185734	−	0.982600i	$-0.559466\pi$
$887$	−27.2079	−	8.84040i	−0.913553	−	0.296831i	−0.727820	+	0.685769i	$0.759466\pi$
$888$	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	−0.986570	−	0.163336i	$-0.947774\pi$
$907$	−15.8521	+	21.8186i	−0.526361	+	0.724474i	0.460209	+	0.887811i	$0.347774\pi$
$908$	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	$0.129980\pi$
$937$	30.9724	+	42.6299i	1.01183	+	1.39266i	0.0940454	+	0.995568i	$0.470020\pi$
$938$	−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	$-0.923935\pi$
$947$		−	14.5680i		−	0.473395i	0.971583	−	0.236698i	$-0.0760651\pi$
$948$	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	−0.371056	−	0.928610i	$-0.621004\pi$
$953$	−37.5718	−	12.2078i	−1.21707	−	0.395450i	−0.846014	+	0.533160i	$0.821004\pi$
$954$	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	$0.256050\pi$
$967$			44.8051i			1.44083i	−0.693541	+	0.720417i	$0.743950\pi$
$968$	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	$0.112667\pi$
$977$	30.5629	+	42.0662i	0.977794	+	1.34582i	0.0397838	+	0.999208i	$0.487333\pi$
$978$		−	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	0.890931	−	0.454139i	$-0.150053\pi$
$983$	42.1625	+	13.6994i	1.34477	+	0.436943i	0.453842	+	0.891082i	$0.350053\pi$
$984$	−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	0.209142	−	0.977885i	$-0.432933\pi$
$997$	−6.20281	−	2.01541i	−0.196445	−	0.0638288i	−0.405587	+	0.914056i	$0.632933\pi$
$998$	−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.124.4		16
5.2	odd	4		165.2.m.a.91.1	✓	8
5.3	odd	4		825.2.n.k.751.2		8
5.4	even	2	inner	825.2.bx.h.124.1		16
11.4	even	5	inner	825.2.bx.h.499.1		16
15.2	even	4		495.2.n.d.91.2		8
55.2	even	20		1815.2.a.o.1.1		4
55.4	even	10	inner	825.2.bx.h.499.4		16
55.13	even	20		9075.2.a.dj.1.4		4
55.37	odd	20		165.2.m.a.136.1	yes	8
55.42	odd	20		1815.2.a.x.1.4		4
55.48	odd	20		825.2.n.k.301.2		8
55.53	odd	20		9075.2.a.cl.1.1		4
165.2	odd	20		5445.2.a.bv.1.4		4
165.92	even	20		495.2.n.d.136.2		8
165.152	even	20		5445.2.a.be.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.a.91.1	✓	8	5.2	odd	4
165.2.m.a.136.1	yes	8	55.37	odd	20
495.2.n.d.91.2		8	15.2	even	4
495.2.n.d.136.2		8	165.92	even	20
825.2.n.k.301.2		8	55.48	odd	20
825.2.n.k.751.2		8	5.3	odd	4
825.2.bx.h.124.1		16	5.4	even	2	inner
825.2.bx.h.124.4		16	1.1	even	1	trivial
825.2.bx.h.499.1		16	11.4	even	5	inner
825.2.bx.h.499.4		16	55.4	even	10	inner
1815.2.a.o.1.1		4	55.2	even	20
1815.2.a.x.1.4		4	55.42	odd	20
5445.2.a.be.1.1		4	165.152	even	20
5445.2.a.bv.1.4		4	165.2	odd	20
9075.2.a.cl.1.1		4	55.53	odd	20
9075.2.a.dj.1.4		4	55.13	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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