LMFDB - Embedded newform 625.2.d.q.501.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(126,625)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(625, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("625.126");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.d (of order $5$, 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:	$4.99065012633$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
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} + 25x^{14} + 239x^{12} + 1165x^{10} + 3166x^{8} + 4820x^{6} + 3809x^{4} + 1205x^{2} + 1 $ x^16 + 25x^14 + 239x^12 + 1165x^10 + 3166x^8 + 4820x^6 + 3809x^4 + 1205*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			501.1
Root			$2.04679i$ of defining polynomial
Character	$\chi$	$=$	625.501
Dual form			625.2.d.q.126.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.823534 + 2.53458i) q^{2} +(0.614111 + 0.446178i) q^{3} +(-4.12784 - 2.99905i) q^{4} +(-1.63661 + 1.18907i) q^{6} +2.04213 q^{7} +(6.68866 - 4.85960i) q^{8} +(-0.748993 - 2.30516i) q^{9} +O(q^{10})$	\(q+(-0.823534 + 2.53458i) q^{2} +(0.614111 + 0.446178i) q^{3} +(-4.12784 - 2.99905i) q^{4} +(-1.63661 + 1.18907i) q^{6} +2.04213 q^{7} +(6.68866 - 4.85960i) q^{8} +(-0.748993 - 2.30516i) q^{9} +(0.416762 - 1.28266i) q^{11} +(-1.19684 - 3.68350i) q^{12} +(-0.407790 - 1.25505i) q^{13} +(-1.68176 + 5.17593i) q^{14} +(3.65530 + 11.2498i) q^{16} +(3.30659 - 2.40238i) q^{17} +6.45944 q^{18} +(3.95350 - 2.87239i) q^{19} +(1.25409 + 0.911152i) q^{21} +(2.90779 + 2.11263i) q^{22} +(0.845525 - 2.60226i) q^{23} +6.27582 q^{24} +3.51685 q^{26} +(1.27226 - 3.91560i) q^{27} +(-8.42958 - 6.12445i) q^{28} +(3.73696 + 2.71506i) q^{29} +(-5.79035 + 4.20694i) q^{31} -14.9886 q^{32} +(0.828234 - 0.601747i) q^{33} +(3.36593 + 10.3593i) q^{34} +(-3.82158 + 11.7616i) q^{36} +(2.67188 + 8.22321i) q^{37} +(4.02445 + 12.3860i) q^{38} +(0.309547 - 0.952686i) q^{39} +(-3.12094 - 9.60527i) q^{41} +(-3.34217 + 2.42823i) q^{42} -2.43460 q^{43} +(-5.56710 + 4.04474i) q^{44} +(5.89930 + 4.28610i) q^{46} +(6.12581 + 4.45066i) q^{47} +(-2.77467 + 8.53956i) q^{48} -2.82971 q^{49} +3.10250 q^{51} +(-2.08067 + 6.40363i) q^{52} +(-0.502597 - 0.365158i) q^{53} +(8.87665 + 6.44926i) q^{54} +(13.6591 - 9.92393i) q^{56} +3.70948 q^{57} +(-9.95905 + 7.23568i) q^{58} +(-3.50462 - 10.7861i) q^{59} +(0.200093 - 0.615822i) q^{61} +(-5.89425 - 18.1407i) q^{62} +(-1.52954 - 4.70744i) q^{63} +(5.03301 - 15.4900i) q^{64} +(0.843096 + 2.59478i) q^{66} +(8.84972 - 6.42970i) q^{67} -20.8539 q^{68} +(1.68031 - 1.22082i) q^{69} +(2.38846 + 1.73532i) q^{71} +(-16.2119 - 11.7787i) q^{72} +(-4.18378 + 12.8763i) q^{73} -23.0428 q^{74} -24.9339 q^{76} +(0.851083 - 2.61936i) q^{77} +(2.15974 + 1.56914i) q^{78} +(-1.52847 - 1.11050i) q^{79} +(-3.35431 + 2.43705i) q^{81} +26.9155 q^{82} +(1.92126 - 1.39588i) q^{83} +(-2.44410 - 7.52218i) q^{84} +(2.00497 - 6.17067i) q^{86} +(1.08351 + 3.33470i) q^{87} +(-3.44564 - 10.6046i) q^{88} +(2.26782 - 6.97963i) q^{89} +(-0.832761 - 2.56297i) q^{91} +(-11.2945 + 8.20593i) q^{92} -5.43296 q^{93} +(-16.3254 + 11.8611i) q^{94} +(-9.20465 - 6.68757i) q^{96} +(4.69161 + 3.40865i) q^{97} +(2.33036 - 7.17212i) q^{98} -3.26890 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 5 q^{2} - 3 q^{4} + 7 q^{6} - 20 q^{7} + 5 q^{8} - 12 q^{9}+O(q^{10}) $ 16 * q + 5 * q^2 - 3 * q^4 + 7 * q^6 - 20 * q^7 + 5 * q^8 - 12 * q^9	$ 16 q + 5 q^{2} - 3 q^{4} + 7 q^{6} - 20 q^{7} + 5 q^{8} - 12 q^{9} - 3 q^{11} - 15 q^{12} + 5 q^{13} - q^{14} + q^{16} + 25 q^{17} + 10 q^{18} + 10 q^{19} + 7 q^{21} + 35 q^{22} + 15 q^{23} + 10 q^{24} + 22 q^{26} - 35 q^{28} - 8 q^{31} - 60 q^{32} - 6 q^{34} + q^{36} + 5 q^{37} + 35 q^{38} + q^{39} - 8 q^{41} + 10 q^{42} - 31 q^{44} + 42 q^{46} + 5 q^{47} + 25 q^{48} - 8 q^{49} - 28 q^{51} - 15 q^{52} + 10 q^{53} + 50 q^{54} + 35 q^{56} + 20 q^{57} - 35 q^{58} - 15 q^{59} + 17 q^{61} - 5 q^{62} - 10 q^{63} + 37 q^{64} + 44 q^{66} + 10 q^{67} - 80 q^{68} - 9 q^{69} - 13 q^{71} - 20 q^{72} - 40 q^{73} - 36 q^{74} - 20 q^{76} + 45 q^{77} - 5 q^{78} - 55 q^{79} - 19 q^{81} + 90 q^{82} + 15 q^{83} + 59 q^{84} + 7 q^{86} + 60 q^{87} - 40 q^{88} - 28 q^{91} - 45 q^{92} + 80 q^{93} + 4 q^{94} - 43 q^{96} - 40 q^{97} - 45 q^{98} - 44 q^{99}+O(q^{100}) $ 16 * q + 5 * q^2 - 3 * q^4 + 7 * q^6 - 20 * q^7 + 5 * q^8 - 12 * q^9 - 3 * q^11 - 15 * q^12 + 5 * q^13 - q^14 + q^16 + 25 * q^17 + 10 * q^18 + 10 * q^19 + 7 * q^21 + 35 * q^22 + 15 * q^23 + 10 * q^24 + 22 * q^26 - 35 * q^28 - 8 * q^31 - 60 * q^32 - 6 * q^34 + q^36 + 5 * q^37 + 35 * q^38 + q^39 - 8 * q^41 + 10 * q^42 - 31 * q^44 + 42 * q^46 + 5 * q^47 + 25 * q^48 - 8 * q^49 - 28 * q^51 - 15 * q^52 + 10 * q^53 + 50 * q^54 + 35 * q^56 + 20 * q^57 - 35 * q^58 - 15 * q^59 + 17 * q^61 - 5 * q^62 - 10 * q^63 + 37 * q^64 + 44 * q^66 + 10 * q^67 - 80 * q^68 - 9 * q^69 - 13 * q^71 - 20 * q^72 - 40 * q^73 - 36 * q^74 - 20 * q^76 + 45 * q^77 - 5 * q^78 - 55 * q^79 - 19 * q^81 + 90 * q^82 + 15 * q^83 + 59 * q^84 + 7 * q^86 + 60 * q^87 - 40 * q^88 - 28 * q^91 - 45 * q^92 + 80 * q^93 + 4 * q^94 - 43 * q^96 - 40 * q^97 - 45 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	−0.823534	+	2.53458i	−0.582327	+	1.79222i	0.0274246	+	0.999624i	$0.491269\pi$
$2$	−0.823534	+	2.53458i	−0.582327	+	1.79222i	−0.609751	+	0.792593i	$0.708731\pi$
$3$	0.614111	+	0.446178i	0.354557	+	0.257601i	0.750778	−	0.660554i	$-0.229679\pi$
$3$	0.614111	+	0.446178i	0.354557	+	0.257601i	−0.396221	+	0.918155i	$0.629679\pi$
$4$	−4.12784	−	2.99905i	−2.06392	−	1.49953i
$5$		0			0
$5$		0			0
$6$	−1.63661	+	1.18907i	−0.668144	+	0.485435i
$7$	2.04213			0.771852			0.385926	−	0.922530i	$-0.373882\pi$
$7$	2.04213			0.771852			0.385926	+	0.922530i	$0.373882\pi$
$8$	6.68866	−	4.85960i	2.36480	−	1.71813i
$9$	−0.748993	−	2.30516i	−0.249664	−	0.768388i
$10$		0			0
$11$	0.416762	−	1.28266i	0.125659	−	0.386737i	−0.868362	−	0.495931i	$-0.834827\pi$
$11$	0.416762	−	1.28266i	0.125659	−	0.386737i	0.994020	+	0.109194i	$0.0348269\pi$
$12$	−1.19684	−	3.68350i	−0.345498	−	1.06333i
$13$	−0.407790	−	1.25505i	−0.113101	−	0.348088i	0.878445	−	0.477843i	$-0.158581\pi$
$13$	−0.407790	−	1.25505i	−0.113101	−	0.348088i	−0.991546	+	0.129754i	$0.958581\pi$
$14$	−1.68176	+	5.17593i	−0.449470	+	1.38333i
$15$		0			0
$16$	3.65530	+	11.2498i	0.913824	+	2.81246i
$17$	3.30659	−	2.40238i	0.801966	−	0.582663i	−0.109524	−	0.993984i	$-0.534933\pi$
$17$	3.30659	−	2.40238i	0.801966	−	0.582663i	0.911490	+	0.411321i	$0.134933\pi$
$18$	6.45944			1.52250
$19$	3.95350	−	2.87239i	0.906996	−	0.658971i	−0.0332573	−	0.999447i	$-0.510588\pi$
$19$	3.95350	−	2.87239i	0.906996	−	0.658971i	0.940253	+	0.340476i	$0.110588\pi$
$20$		0			0
$21$	1.25409	+	0.911152i	0.273666	+	0.198830i
$22$	2.90779	+	2.11263i	0.619943	+	0.450415i
$23$	0.845525	−	2.60226i	0.176304	−	0.542608i	−0.823387	−	0.567481i	$-0.807918\pi$
$23$	0.845525	−	2.60226i	0.176304	−	0.542608i	0.999691	+	0.0248727i	$0.00791806\pi$
$24$	6.27582			1.28105
$25$		0			0
$26$	3.51685			0.689711
$27$	1.27226	−	3.91560i	0.244846	−	0.753558i
$28$	−8.42958	−	6.12445i	−1.59304	−	1.15741i
$29$	3.73696	+	2.71506i	0.693937	+	0.504175i	0.877952	−	0.478749i	$-0.158910\pi$
$29$	3.73696	+	2.71506i	0.693937	+	0.504175i	−0.184015	+	0.982923i	$0.558910\pi$
$30$		0			0
$31$	−5.79035	+	4.20694i	−1.03998	+	0.755588i	−0.970281	−	0.241980i	$-0.922203\pi$
$31$	−5.79035	+	4.20694i	−1.03998	+	0.755588i	−0.0696967	+	0.997568i	$0.522203\pi$
$32$	−14.9886			−2.64963
$33$	0.828234	−	0.601747i	0.144177	−	0.104751i
$34$	3.36593	+	10.3593i	0.577252	+	1.77660i
$35$		0			0
$36$	−3.82158	+	11.7616i	−0.636930	+	1.96027i
$37$	2.67188	+	8.22321i	0.439255	+	1.35189i	0.888663	+	0.458561i	$0.151635\pi$
$37$	2.67188	+	8.22321i	0.439255	+	1.35189i	−0.449408	+	0.893327i	$0.648365\pi$
$38$	4.02445	+	12.3860i	0.652851	+	2.00927i
$39$	0.309547	−	0.952686i	0.0495671	−	0.152552i
$40$		0			0
$41$	−3.12094	−	9.60527i	−0.487409	−	1.50009i	−0.828461	−	0.560047i	$-0.810783\pi$
$41$	−3.12094	−	9.60527i	−0.487409	−	1.50009i	0.341051	−	0.940045i	$-0.389217\pi$
$42$	−3.34217	+	2.42823i	−0.515709	+	0.374684i
$43$	−2.43460			−0.371272			−0.185636	−	0.982619i	$-0.559435\pi$
$43$	−2.43460			−0.371272			−0.185636	+	0.982619i	$0.559435\pi$
$44$	−5.56710	+	4.04474i	−0.839272	+	0.609767i
$45$		0			0
$46$	5.89930	+	4.28610i	0.869805	+	0.631950i
$47$	6.12581	+	4.45066i	0.893542	+	0.649196i	0.936799	−	0.349868i	$-0.113774\pi$
$47$	6.12581	+	4.45066i	0.893542	+	0.649196i	−0.0432572	+	0.999064i	$0.513774\pi$
$48$	−2.77467	+	8.53956i	−0.400489	+	1.23258i
$49$	−2.82971			−0.404244
$50$		0			0
$51$	3.10250			0.434437
$52$	−2.08067	+	6.40363i	−0.288536	+	0.888024i
$53$	−0.502597	−	0.365158i	−0.0690371	−	0.0501584i	0.552731	−	0.833359i	$-0.313586\pi$
$53$	−0.502597	−	0.365158i	−0.0690371	−	0.0501584i	−0.621769	+	0.783201i	$0.713586\pi$
$54$	8.87665	+	6.44926i	1.20796	+	0.877634i
$55$		0			0
$56$	13.6591	−	9.92393i	1.82528	−	1.32614i
$57$	3.70948			0.491333
$58$	−9.95905	+	7.23568i	−1.30769	+	0.950091i
$59$	−3.50462	−	10.7861i	−0.456262	−	1.40423i	−0.869647	−	0.493674i	$-0.835653\pi$
$59$	−3.50462	−	10.7861i	−0.456262	−	1.40423i	0.413385	−	0.910557i	$-0.364347\pi$
$60$		0			0
$61$	0.200093	−	0.615822i	0.0256192	−	0.0788479i	−0.937429	−	0.348175i	$-0.886801\pi$
$61$	0.200093	−	0.615822i	0.0256192	−	0.0788479i	0.963049	+	0.269327i	$0.0868014\pi$
$62$	−5.89425	−	18.1407i	−0.748571	−	2.30387i
$63$	−1.52954	−	4.70744i	−0.192704	−	0.593082i
$64$	5.03301	−	15.4900i	0.629127	−	1.93625i
$65$		0			0
$66$	0.843096	+	2.59478i	0.103778	+	0.319396i
$67$	8.84972	−	6.42970i	1.08117	−	0.785513i	0.103280	−	0.994652i	$-0.467066\pi$
$67$	8.84972	−	6.42970i	1.08117	−	0.785513i	0.977886	+	0.209139i	$0.0670662\pi$
$68$	−20.8539			−2.52891
$69$	1.68031	−	1.22082i	0.202286	−	0.146969i
$70$		0			0
$71$	2.38846	+	1.73532i	0.283458	+	0.205945i	0.720424	−	0.693533i	$-0.243947\pi$
$71$	2.38846	+	1.73532i	0.283458	+	0.205945i	−0.436966	+	0.899478i	$0.643947\pi$
$72$	−16.2119	−	11.7787i	−1.91060	−	1.38813i
$73$	−4.18378	+	12.8763i	−0.489674	+	1.50706i	0.335421	+	0.942068i	$0.391121\pi$
$73$	−4.18378	+	12.8763i	−0.489674	+	1.50706i	−0.825095	+	0.564993i	$0.808879\pi$
$74$	−23.0428			−2.67867
$75$		0			0
$76$	−24.9339			−2.86011
$77$	0.851083	−	2.61936i	0.0969899	−	0.298504i
$78$	2.15974	+	1.56914i	0.244542	+	0.177670i
$79$	−1.52847	−	1.11050i	−0.171966	−	0.124941i	0.498473	−	0.866905i	$-0.333894\pi$
$79$	−1.52847	−	1.11050i	−0.171966	−	0.124941i	−0.670439	+	0.741964i	$0.733894\pi$
$80$		0			0
$81$	−3.35431	+	2.43705i	−0.372701	+	0.270783i
$82$	26.9155			2.97232
$83$	1.92126	−	1.39588i	0.210886	−	0.153218i	−0.477328	−	0.878725i	$-0.658395\pi$
$83$	1.92126	−	1.39588i	0.210886	−	0.153218i	0.688214	+	0.725507i	$0.258395\pi$
$84$	−2.44410	−	7.52218i	−0.266674	−	0.820737i
$85$		0			0
$86$	2.00497	−	6.17067i	0.216202	−	0.665401i
$87$	1.08351	+	3.33470i	0.116164	+	0.357517i
$88$	−3.44564	−	10.6046i	−0.367307	−	1.13045i
$89$	2.26782	−	6.97963i	0.240388	−	0.739840i	−0.755972	−	0.654604i	$-0.772836\pi$
$89$	2.26782	−	6.97963i	0.240388	−	0.739840i	0.996361	−	0.0852361i	$-0.0271644\pi$
$90$		0			0
$91$	−0.832761	−	2.56297i	−0.0872970	−	0.268673i
$92$	−11.2945	+	8.20593i	−1.17753	+	0.855527i
$93$	−5.43296			−0.563371
$94$	−16.3254	+	11.8611i	−1.68383	+	1.22338i
$95$		0			0
$96$	−9.20465	−	6.68757i	−0.939445	−	0.682547i
$97$	4.69161	+	3.40865i	0.476361	+	0.346096i	0.799915	−	0.600113i	$-0.204878\pi$
$97$	4.69161	+	3.40865i	0.476361	+	0.346096i	−0.323554	+	0.946210i	$0.604878\pi$
$98$	2.33036	−	7.17212i	0.235402	−	0.724493i
$99$	−3.26890			−0.328537
$100$		0			0
$101$	11.5536			1.14962			0.574812	−	0.818285i	$-0.305075\pi$
$101$	11.5536			1.14962			0.574812	+	0.818285i	$0.305075\pi$
$102$	−2.55502	+	7.86353i	−0.252984	+	0.778606i
$103$	9.39037	+	6.82250i	0.925260	+	0.672241i	0.944828	−	0.327568i	$-0.106229\pi$
$103$	9.39037	+	6.82250i	0.925260	+	0.672241i	−0.0195675	+	0.999809i	$0.506229\pi$
$104$	−8.82661	−	6.41291i	−0.865520	−	0.628837i
$105$		0			0
$106$	1.33943	−	0.973152i	0.130097	−	0.0945208i
$107$	−10.1703			−0.983204			−0.491602	−	0.870820i	$-0.663588\pi$
$107$	−10.1703			−0.983204			−0.491602	+	0.870820i	$0.663588\pi$
$108$	−16.9948	+	12.3474i	−1.63532	+	1.18813i
$109$	0.369198	+	1.13628i	0.0353628	+	0.108835i	0.967180	−	0.254093i	$-0.0817769\pi$
$109$	0.369198	+	1.13628i	0.0353628	+	0.108835i	−0.931817	+	0.362928i	$0.881777\pi$
$110$		0			0
$111$	−2.02818	+	6.24210i	−0.192506	+	0.592474i
$112$	7.46459	+	22.9736i	0.705337	+	2.17080i
$113$	−1.38519	−	4.26318i	−0.130308	−	0.401046i	0.864523	−	0.502593i	$-0.167621\pi$
$113$	−1.38519	−	4.26318i	−0.130308	−	0.401046i	−0.994831	+	0.101547i	$0.967621\pi$
$114$	−3.05489	+	9.40198i	−0.286116	+	0.880576i
$115$		0			0
$116$	−7.28297	−	22.4147i	−0.676207	−	2.08115i
$117$	−2.58766	+	1.88005i	−0.239230	+	0.173811i
$118$	30.2244			2.78238
$119$	6.75249	−	4.90597i	0.619000	−	0.449729i
$120$		0			0
$121$	7.42765	+	5.39651i	0.675241	+	0.490591i
$122$	1.39606	+	1.01430i	0.126394	+	0.0918304i
$123$	2.36905	−	7.29120i	0.213610	−	0.657425i
$124$	36.5185			3.27946
$125$		0			0
$126$	13.1910			1.17515
$127$	1.29072	−	3.97242i	0.114533	−	0.352495i	−0.877317	−	0.479912i	$-0.840669\pi$
$127$	1.29072	−	3.97242i	0.114533	−	0.352495i	0.991849	+	0.127417i	$0.0406686\pi$
$128$	10.8638	+	7.89300i	0.960231	+	0.697649i
$129$	−1.49511	−	1.08626i	−0.131637	−	0.0956400i
$130$		0			0
$131$	−2.74187	+	1.99209i	−0.239559	+	0.174049i	−0.701087	−	0.713076i	$-0.747301\pi$
$131$	−2.74187	+	1.99209i	−0.239559	+	0.174049i	0.461528	+	0.887126i	$0.347301\pi$
$132$	−5.22349			−0.454646
$133$	8.07356	−	5.86579i	0.700067	−	0.508628i
$134$	9.00853	+	27.7254i	0.778218	+	2.39511i
$135$		0			0
$136$	10.4421	−	32.1374i	0.895401	−	2.75576i
$137$	2.57596	+	7.92798i	0.220079	+	0.677333i	0.998754	+	0.0499056i	$0.0158920\pi$
$137$	2.57596	+	7.92798i	0.220079	+	0.677333i	−0.778675	+	0.627427i	$0.784108\pi$
$138$	1.71047	+	5.26427i	0.145605	+	0.448125i
$139$	−1.06102	+	3.26550i	−0.0899949	+	0.276976i	−0.985917	−	0.167235i	$-0.946516\pi$
$139$	−1.06102	+	3.26550i	−0.0899949	+	0.276976i	0.895922	+	0.444211i	$0.146516\pi$
$140$		0			0
$141$	1.77614	+	5.46640i	0.149578	+	0.460354i
$142$	−6.36528	+	4.62465i	−0.534163	+	0.388092i
$143$	−1.77976			−0.148831
$144$	23.1950	−	16.8521i	1.93291	−	1.40434i
$145$		0			0
$146$	−29.1906	−	21.2082i	−2.41583	−	1.75520i
$147$	−1.73775	−	1.26255i	−0.143328	−	0.104134i
$148$	13.6327	−	41.9572i	1.12060	−	3.44886i
$149$	9.96023			0.815974			0.407987	−	0.912988i	$-0.366231\pi$
$149$	9.96023			0.815974			0.407987	+	0.912988i	$0.366231\pi$
$150$		0			0
$151$	−21.0404			−1.71225			−0.856123	−	0.516772i	$-0.827134\pi$
$151$	−21.0404			−1.71225			−0.856123	+	0.516772i	$0.827134\pi$
$152$	12.4850	−	38.4249i	1.01267	−	3.11667i
$153$	−8.01450	−	5.82287i	−0.647934	−	0.470751i
$154$	5.93808	+	4.31427i	0.478504	+	0.347654i
$155$		0			0
$156$	−4.13491	+	3.00419i	−0.331058	+	0.240528i
$157$	−7.80843			−0.623181			−0.311590	−	0.950217i	$-0.600862\pi$
$157$	−7.80843			−0.623181			−0.311590	+	0.950217i	$0.600862\pi$
$158$	4.07339	−	2.95949i	0.324062	−	0.235445i
$159$	−0.145725	−	0.448495i	−0.0115567	−	0.0355680i
$160$		0			0
$161$	1.72667	−	5.31415i	0.136081	−	0.418813i
$162$	−3.41450	−	10.5088i	−0.268269	−	0.825646i
$163$	3.60887	+	11.1070i	0.282668	+	0.869963i	0.987088	+	0.160180i	$0.0512074\pi$
$163$	3.60887	+	11.1070i	0.282668	+	0.869963i	−0.704420	+	0.709784i	$0.748793\pi$
$164$	−15.9240	+	49.0089i	−1.24345	+	3.82695i
$165$		0			0
$166$	1.95574	+	6.01914i	0.151795	+	0.467176i
$167$	6.07732	−	4.41543i	0.470277	−	0.341676i	−0.327272	−	0.944930i	$-0.606129\pi$
$167$	6.07732	−	4.41543i	0.470277	−	0.341676i	0.797549	+	0.603254i	$0.206129\pi$
$168$	12.8160			0.988779
$169$	9.10836	−	6.61761i	0.700643	−	0.509047i
$170$		0			0
$171$	−9.58248	−	6.96208i	−0.732790	−	0.532403i
$172$	10.0496	+	7.30148i	0.766276	+	0.556732i
$173$	−1.64206	+	5.05374i	−0.124843	+	0.384229i	−0.993873	−	0.110532i	$-0.964744\pi$
$173$	−1.64206	+	5.05374i	−0.124843	+	0.384229i	0.869029	+	0.494761i	$0.164744\pi$
$174$	−9.34436			−0.708394
$175$		0			0
$176$	15.9532			1.20251
$177$	2.66029	−	8.18754i	0.199960	−	0.615413i
$178$	15.8228	+	11.4959i	1.18597	+	0.861657i
$179$	−1.05718	−	0.768083i	−0.0790171	−	0.0574093i	0.547575	−	0.836756i	$-0.315551\pi$
$179$	−1.05718	−	0.768083i	−0.0790171	−	0.0574093i	−0.626592	+	0.779347i	$0.715551\pi$
$180$		0			0
$181$	16.3120	−	11.8513i	1.21246	−	0.880904i	0.217008	−	0.976170i	$-0.430370\pi$
$181$	16.3120	−	11.8513i	1.21246	−	0.880904i	0.995452	+	0.0952662i	$0.0303702\pi$
$182$	7.18186			0.532355
$183$	0.397645	−	0.288906i	0.0293947	−	0.0213565i
$184$	−6.99050	−	21.5145i	−0.515346	−	1.58607i
$185$		0			0
$186$	4.47423	−	13.7703i	0.328066	−	1.00968i
$187$	−1.70338	−	5.24247i	−0.124563	−	0.383367i
$188$	−11.9386	−	36.7433i	−0.870713	−	2.67978i
$189$	2.59811	−	7.99616i	0.188985	−	0.581635i
$190$		0			0
$191$	6.58074	+	20.2534i	0.476166	+	1.46549i	0.844379	+	0.535746i	$0.179970\pi$
$191$	6.58074	+	20.2534i	0.476166	+	1.46549i	−0.368213	+	0.929741i	$0.620030\pi$
$192$	10.0021	−	7.26697i	0.721842	−	0.524449i
$193$	7.99352			0.575386			0.287693	−	0.957723i	$-0.407112\pi$
$193$	7.99352			0.575386			0.287693	+	0.957723i	$0.407112\pi$
$194$	−12.5032	+	9.08411i	−0.897677	+	0.652201i
$195$		0			0
$196$	11.6806	+	8.48644i	0.834328	+	0.606175i
$197$	−17.5568	−	12.7558i	−1.25087	−	0.908811i	−0.252599	−	0.967571i	$-0.581285\pi$
$197$	−17.5568	−	12.7558i	−1.25087	−	0.908811i	−0.998272	+	0.0587600i	$0.981285\pi$
$198$	2.69205	−	8.28528i	0.191316	−	0.588810i
$199$	9.34240			0.662265			0.331133	−	0.943584i	$-0.392569\pi$
$199$	9.34240			0.662265			0.331133	+	0.943584i	$0.392569\pi$
$200$		0			0
$201$	8.30350			0.585684
$202$	−9.51477	+	29.2834i	−0.669457	+	2.06038i
$203$	7.63136	+	5.54451i	0.535617	+	0.389148i
$204$	−12.8066	−	9.30456i	−0.896643	−	0.651450i
$205$		0			0
$206$	−25.0254	+	18.1820i	−1.74361	+	1.26680i
$207$	−6.63192			−0.460951
$208$	12.6285	−	9.17516i	0.875631	−	0.636183i
$209$	−2.03663	−	6.26812i	−0.140877	−	0.433575i
$210$		0			0
$211$	−2.12649	+	6.54467i	−0.146394	+	0.450554i	−0.997188	−	0.0749460i	$-0.976122\pi$
$211$	−2.12649	+	6.54467i	−0.146394	+	0.450554i	0.850794	+	0.525500i	$0.176122\pi$
$212$	0.979513	+	3.01463i	0.0672732	+	0.207046i
$213$	0.692520	+	2.13136i	0.0474507	+	0.146038i
$214$	8.37562	−	25.7775i	0.572546	−	1.76211i
$215$		0			0
$216$	−10.5186	−	32.3728i	−0.715697	−	2.20269i
$217$	−11.8246	+	8.59111i	−0.802709	+	0.583202i
$218$	−3.18402			−0.215649
$219$	−8.31444	+	6.04079i	−0.561838	+	0.408199i
$220$		0			0
$221$	−4.36350	−	3.17027i	−0.293521	−	0.213255i
$222$	−14.1508	−	10.2812i	−0.949740	−	0.690026i
$223$	−2.63127	+	8.09821i	−0.176203	+	0.542296i	−0.999686	−	0.0250437i	$-0.992028\pi$
$223$	−2.63127	+	8.09821i	−0.176203	+	0.542296i	0.823484	+	0.567340i	$0.192028\pi$
$224$	−30.6086			−2.04512
$225$		0			0
$226$	11.9461			0.794643
$227$	−6.48428	+	19.9566i	−0.430377	+	1.32456i	0.467374	+	0.884060i	$0.345200\pi$
$227$	−6.48428	+	19.9566i	−0.430377	+	1.32456i	−0.897751	+	0.440504i	$0.854800\pi$
$228$	−15.3122	−	11.1249i	−1.01407	−	0.736767i
$229$	−24.0787	−	17.4942i	−1.59116	−	1.15605i	−0.902256	−	0.431200i	$-0.858090\pi$
$229$	−24.0787	−	17.4942i	−1.59116	−	1.15605i	−0.688908	−	0.724849i	$-0.741910\pi$
$230$		0			0
$231$	1.69136	−	1.22884i	0.111283	−	0.0808521i
$232$	38.1894			2.50726
$233$	−1.83771	+	1.33518i	−0.120392	+	0.0874703i	−0.646352	−	0.763039i	$-0.723706\pi$
$233$	−1.83771	+	1.33518i	−0.120392	+	0.0874703i	0.525960	+	0.850510i	$0.323706\pi$
$234$	−2.63410	−	8.10692i	−0.172196	−	0.529966i
$235$		0			0
$236$	−17.8816	+	55.0338i	−1.16399	+	3.58240i
$237$	−0.443171	−	1.36394i	−0.0287870	−	0.0885973i
$238$	6.87366	+	21.1549i	0.445553	+	1.37127i
$239$	4.76838	−	14.6756i	0.308441	−	0.949283i	−0.669930	−	0.742424i	$-0.733676\pi$
$239$	4.76838	−	14.6756i	0.308441	−	0.949283i	0.978371	−	0.206859i	$-0.0663240\pi$
$240$		0			0
$241$	−1.49621	−	4.60486i	−0.0963793	−	0.296625i	0.891231	−	0.453549i	$-0.149842\pi$
$241$	−1.49621	−	4.60486i	−0.0963793	−	0.296625i	−0.987611	+	0.156924i	$0.949842\pi$
$242$	−19.7948	+	14.3818i	−1.27246	+	0.924494i
$243$	−15.4986			−0.994235
$244$	−2.67283	+	1.94192i	−0.171110	+	0.124319i
$245$		0			0
$246$	16.5291	+	12.0091i	1.05386	+	0.765672i
$247$	−5.21719	−	3.79051i	−0.331962	−	0.241184i
$248$	−18.2857	+	56.2776i	−1.16114	+	3.57363i
$249$	1.80268			0.114240
$250$		0			0
$251$	−17.8293			−1.12537			−0.562687	−	0.826670i	$-0.690232\pi$
$251$	−17.8293			−1.12537			−0.562687	+	0.826670i	$0.690232\pi$
$252$	−7.80416	+	24.0187i	−0.491616	+	1.51304i
$253$	−2.98544	−	2.16905i	−0.187693	−	0.136367i
$254$	9.00545	+	6.54284i	0.565052	+	0.410534i
$255$		0			0
$256$	−2.59889	+	1.88820i	−0.162431	+	0.118013i
$257$	−5.88929			−0.367364			−0.183682	−	0.982986i	$-0.558802\pi$
$257$	−5.88929			−0.367364			−0.183682	+	0.982986i	$0.558802\pi$
$258$	3.98449	−	2.89490i	0.248064	−	0.180229i
$259$	5.45633	+	16.7929i	0.339040	+	1.04346i
$260$		0			0
$261$	3.45971	−	10.6479i	0.214150	−	0.659087i
$262$	−2.79107	−	8.59004i	−0.172433	−	0.530695i
$263$	−7.31668	−	22.5184i	−0.451166	−	1.38855i	−0.875578	−	0.483077i	$-0.839519\pi$
$263$	−7.31668	−	22.5184i	−0.451166	−	1.38855i	0.424412	−	0.905469i	$-0.360481\pi$
$264$	2.61553	−	8.04977i	0.160975	−	0.495429i
$265$		0			0
$266$	8.21844	+	25.2938i	0.503905	+	1.55086i
$267$	4.50685	−	3.27442i	0.275815	−	0.200391i
$268$	−55.8132			−3.40934
$269$	−11.1208	+	8.07972i	−0.678046	+	0.492629i	−0.872709	−	0.488241i	$-0.837639\pi$
$269$	−11.1208	+	8.07972i	−0.678046	+	0.492629i	0.194663	+	0.980870i	$0.437639\pi$
$270$		0			0
$271$	−6.06667	−	4.40769i	−0.368524	−	0.267748i	0.388075	−	0.921628i	$-0.373140\pi$
$271$	−6.06667	−	4.40769i	−0.368524	−	0.267748i	−0.756599	+	0.653880i	$0.773140\pi$
$272$	39.1130	+	28.4172i	2.37157	+	1.72305i
$273$	0.632134	−	1.94551i	0.0382585	−	0.117748i
$274$	−22.2155			−1.34209
$275$		0			0
$276$	−10.5974			−0.637887
$277$	−0.876983	+	2.69908i	−0.0526928	+	0.162172i	−0.973940	−	0.226806i	$-0.927172\pi$
$277$	−0.876983	+	2.69908i	−0.0526928	+	0.162172i	0.921247	+	0.388978i	$0.127172\pi$
$278$	−7.40287	−	5.37850i	−0.443994	−	0.322581i
$279$	14.0346	+	10.1967i	0.840231	+	0.610463i
$280$		0			0
$281$	18.5758	−	13.4961i	1.10814	−	0.805110i	0.125770	−	0.992059i	$-0.459860\pi$
$281$	18.5758	−	13.4961i	1.10814	−	0.805110i	0.982370	+	0.186949i	$0.0598600\pi$
$282$	−15.3177			−0.912158
$283$	−20.3263	+	14.7679i	−1.20827	+	0.877861i	−0.995073	−	0.0991475i	$-0.968388\pi$
$283$	−20.3263	+	14.7679i	−1.20827	+	0.877861i	−0.213200	+	0.977009i	$0.568388\pi$
$284$	−4.65488	−	14.3262i	−0.276216	−	0.850106i
$285$		0			0
$286$	1.46569	−	4.51093i	0.0866681	−	0.266737i
$287$	−6.37337	−	19.6152i	−0.376208	−	1.15785i
$288$	11.2263	+	34.5511i	0.661519	+	2.03595i
$289$	−0.0911657	+	0.280579i	−0.00536269	+	0.0165047i
$290$		0			0
$291$	1.36030	+	4.18658i	0.0797424	+	0.245422i
$292$	55.8868	−	40.6041i	3.27053	−	2.37618i
$293$	28.8755			1.68692			0.843461	−	0.537190i	$-0.180514\pi$
$293$	28.8755			1.68692			0.843461	+	0.537190i	$0.180514\pi$
$294$	4.63114	−	3.36472i	0.270093	−	0.196234i
$295$		0			0
$296$	57.8329	+	42.0180i	3.36147	+	2.44225i
$297$	−4.49217	−	3.26375i	−0.260662	−	0.189382i
$298$	−8.20259	+	25.2450i	−0.475163	+	1.46240i
$299$	−3.61076			−0.208816
$300$		0			0
$301$	−4.97176			−0.286567
$302$	17.3275	−	53.3286i	0.997087	−	3.06872i
$303$	7.09518	+	5.15495i	0.407607	+	0.296144i
$304$	46.7652	+	33.9769i	2.68217	+	1.94871i
$305$		0			0
$306$	21.3587	−	15.5180i	1.22100	−	0.887107i
$307$	−23.9526			−1.36704			−0.683522	−	0.729930i	$-0.739553\pi$
$307$	−23.9526			−1.36704			−0.683522	+	0.729930i	$0.739553\pi$
$308$	−11.3687	+	8.25987i	−0.647794	+	0.470650i
$309$	2.72268	+	8.37954i	0.154888	+	0.476695i
$310$		0			0
$311$	−3.05567	+	9.40438i	−0.173271	+	0.533273i	−0.999550	−	0.0299874i	$-0.990453\pi$
$311$	−3.05567	+	9.40438i	−0.173271	+	0.533273i	0.826279	+	0.563261i	$0.190453\pi$
$312$	−2.55922	−	7.87647i	−0.144887	−	0.445917i
$313$	5.80289	+	17.8595i	0.327999	+	1.00948i	0.970069	+	0.242831i	$0.0780759\pi$
$313$	5.80289	+	17.8595i	0.327999	+	1.00948i	−0.642070	+	0.766646i	$0.721924\pi$
$314$	6.43051	−	19.7911i	0.362895	−	1.11687i
$315$		0			0
$316$	2.97884	+	9.16792i	0.167573	+	0.515736i
$317$	−20.9388	+	15.2130i	−1.17604	+	0.854445i	−0.991720	−	0.128421i	$-0.959009\pi$
$317$	−20.9388	+	15.2130i	−1.17604	+	0.854445i	−0.184323	+	0.982866i	$0.559009\pi$
$318$	1.25676			0.0704754
$319$	5.03994	−	3.66173i	0.282182	−	0.205017i
$320$		0			0
$321$	−6.24571	−	4.53778i	−0.348602	−	0.253274i
$322$	12.0471	+	8.75276i	0.671361	+	0.487772i
$323$	6.17206	−	18.9956i	0.343422	−	1.05695i
$324$	21.1549			1.17527
$325$		0			0
$326$	−31.1234			−1.72377
$327$	−0.280252	+	0.862527i	−0.0154980	+	0.0476978i
$328$	−67.5527	−	49.0799i	−3.72997	−	2.70998i
$329$	12.5097	+	9.08883i	0.689682	+	0.501083i
$330$		0			0
$331$	−1.04965	+	0.762612i	−0.0576938	+	0.0419170i	−0.616258	−	0.787544i	$-0.711352\pi$
$331$	−1.04965	+	0.762612i	−0.0576938	+	0.0419170i	0.558565	+	0.829461i	$0.311352\pi$
$332$	−12.1170			−0.665006
$333$	16.9546	−	12.3183i	0.929109	−	0.675037i
$334$	6.18637	+	19.0397i	0.338503	+	1.04181i
$335$		0			0
$336$	−5.66624	+	17.4389i	−0.309119	+	0.951369i
$337$	3.48476	+	10.7250i	0.189827	+	0.584228i	0.999998	−	0.00196599i	$-0.000625795\pi$
$337$	3.48476	+	10.7250i	0.189827	+	0.584228i	−0.810171	+	0.586194i	$0.800626\pi$
$338$	9.27181	+	28.5357i	0.504320	+	1.55214i
$339$	1.05147	−	3.23610i	0.0571082	−	0.175761i
$340$		0			0
$341$	2.98288	+	9.18036i	0.161532	+	0.497145i
$342$	25.5374	−	18.5540i	1.38091	−	1.00329i
$343$	−20.0735			−1.08387
$344$	−16.2842	+	11.8312i	−0.877985	+	0.637893i
$345$		0			0
$346$	−11.4568	−	8.32385i	−0.615921	−	0.447493i
$347$	1.74344	+	1.26668i	0.0935926	+	0.0679990i	0.633597	−	0.773663i	$-0.281578\pi$
$347$	1.74344	+	1.26668i	0.0935926	+	0.0679990i	−0.540005	+	0.841662i	$0.681578\pi$
$348$	5.52838	−	17.0146i	0.296352	−	0.912078i
$349$	5.60904			0.300245			0.150122	−	0.988667i	$-0.452033\pi$
$349$	5.60904			0.300245			0.150122	+	0.988667i	$0.452033\pi$
$350$		0			0
$351$	−5.43309			−0.289997
$352$	−6.24668	+	19.2253i	−0.332949	+	1.02471i
$353$	−14.9643	−	10.8722i	−0.796471	−	0.578670i	0.113406	−	0.993549i	$-0.463824\pi$
$353$	−14.9643	−	10.8722i	−0.796471	−	0.578670i	−0.909877	+	0.414879i	$0.863824\pi$
$354$	18.5611	+	13.4854i	0.986512	+	0.716743i
$355$		0			0
$356$	−30.2935	+	22.0095i	−1.60555	+	1.16650i
$357$	6.33571			0.335321
$358$	2.81739	−	2.04695i	0.148904	−	0.108185i
$359$	3.47489	+	10.6946i	0.183398	+	0.564440i	0.999917	−	0.0128782i	$-0.00409938\pi$
$359$	3.47489	+	10.6946i	0.183398	+	0.564440i	−0.816520	+	0.577318i	$0.804099\pi$
$360$		0			0
$361$	1.50825	−	4.64193i	0.0793818	−	0.244312i
$362$	16.6047	+	51.1040i	0.872723	+	2.68596i
$363$	2.15360	+	6.62810i	0.113035	+	0.347885i
$364$	−4.24899	+	13.0770i	−0.222707	+	0.685423i
$365$		0			0
$366$	0.404780	+	1.24578i	0.0211582	+	0.0651182i
$367$	−23.1117	+	16.7916i	−1.20642	+	0.876517i	−0.994901	−	0.100857i	$-0.967842\pi$
$367$	−23.1117	+	16.7916i	−1.20642	+	0.876517i	−0.211521	+	0.977374i	$0.567842\pi$
$368$	32.3656			1.68718
$369$	−19.8042	+	14.3886i	−1.03096	+	0.749039i
$370$		0			0
$371$	−1.02637	−	0.745700i	−0.0532864	−	0.0387148i
$372$	22.4264	+	16.2937i	1.16275	+	0.844790i
$373$	−4.35244	+	13.3954i	−0.225361	+	0.693590i	0.772894	+	0.634535i	$0.218809\pi$
$373$	−4.35244	+	13.3954i	−0.225361	+	0.693590i	−0.998255	+	0.0590544i	$0.981191\pi$
$374$	14.6902			0.759613
$375$		0			0
$376$	62.6020			3.22845
$377$	1.88364	−	5.79725i	0.0970125	−	0.298574i
$378$	18.1273	+	13.1702i	0.932366	+	0.677403i
$379$	−17.7905	−	12.9256i	−0.913839	−	0.663943i	0.0281442	−	0.999604i	$-0.491040\pi$
$379$	−17.7905	−	12.9256i	−0.913839	−	0.663943i	−0.941983	+	0.335661i	$0.891040\pi$
$380$		0			0
$381$	2.56505	−	1.86361i	0.131411	−	0.0954759i
$382$	−56.7534			−2.90376
$383$	−11.9278	+	8.66607i	−0.609484	+	0.442816i	−0.849232	−	0.528019i	$-0.822935\pi$
$383$	−11.9278	+	8.66607i	−0.609484	+	0.442816i	0.239749	+	0.970835i	$0.422935\pi$
$384$	3.14988	+	9.69435i	0.160742	+	0.494712i
$385$		0			0
$386$	−6.58294	+	20.2602i	−0.335063	+	1.03122i
$387$	1.82350	+	5.61214i	0.0926935	+	0.285281i
$388$	−9.14349	−	28.1408i	−0.464190	−	1.42863i
$389$	−4.40558	+	13.5590i	−0.223372	+	0.687468i	0.775081	+	0.631862i	$0.217709\pi$
$389$	−4.40558	+	13.5590i	−0.223372	+	0.687468i	−0.998453	+	0.0556059i	$0.982291\pi$
$390$		0			0
$391$	−3.45581	−	10.6359i	−0.174768	−	0.537879i
$392$	−18.9270	+	13.7513i	−0.955957	+	0.694543i
$393$	−2.57264			−0.129772
$394$	46.7891	−	33.9943i	2.35720	−	1.71261i
$395$		0			0
$396$	13.4935	+	9.80360i	0.678074	+	0.492650i
$397$	−4.44203	−	3.22732i	−0.222939	−	0.161975i	0.470710	−	0.882288i	$-0.343998\pi$
$397$	−4.44203	−	3.22732i	−0.222939	−	0.161975i	−0.693649	+	0.720314i	$0.743998\pi$
$398$	−7.69378	+	23.6790i	−0.385655	+	1.18692i
$399$	7.57525			0.379237
$400$		0			0
$401$	26.7528			1.33597			0.667985	−	0.744175i	$-0.267157\pi$
$401$	26.7528			1.33597			0.667985	+	0.744175i	$0.267157\pi$
$402$	−6.83821	+	21.0459i	−0.341059	+	1.04967i
$403$	7.64117	+	5.55163i	0.380634	+	0.276546i
$404$	−47.6913	−	34.6498i	−2.37273	−	1.72389i
$405$		0			0
$406$	−20.3377	+	14.7762i	−1.00934	+	0.733330i
$407$	11.6612			0.578022
$408$	20.7516	−	15.0769i	1.02736	−	0.746418i
$409$	1.58646	+	4.88262i	0.0784453	+	0.241430i	0.982587	−	0.185803i	$-0.0594886\pi$
$409$	1.58646	+	4.88262i	0.0784453	+	0.241430i	−0.904142	+	0.427233i	$0.859489\pi$
$410$		0			0
$411$	−1.95536	+	6.01799i	−0.0964510	+	0.296846i
$412$	−18.3009	−	56.3244i	−0.901621	−	2.77490i
$413$	−7.15688	−	22.0266i	−0.352167	−	1.08386i
$414$	5.46162	−	16.8091i	0.268424	−	0.826123i
$415$		0			0
$416$	6.11220	+	18.8114i	0.299675	+	0.922306i
$417$	−2.10858	+	1.53197i	−0.103258	+	0.0750210i
$418$	17.5643			0.859096
$419$	−25.7685	+	18.7219i	−1.25887	+	0.914625i	−0.998702	−	0.0509374i	$-0.983779\pi$
$419$	−25.7685	+	18.7219i	−1.25887	+	0.914625i	−0.260171	+	0.965562i	$0.583779\pi$
$420$		0			0
$421$	−2.49213	−	1.81064i	−0.121459	−	0.0882451i	0.525397	−	0.850857i	$-0.323917\pi$
$421$	−2.49213	−	1.81064i	−0.121459	−	0.0882451i	−0.646856	+	0.762612i	$0.723917\pi$
$422$	−14.8367	−	10.7795i	−0.722241	−	0.524739i
$423$	5.67132	−	17.4545i	0.275749	−	0.848668i
$424$	−5.13623			−0.249437
$425$		0			0
$426$	−5.97240			−0.289364
$427$	0.408615	−	1.25759i	0.0197743	−	0.0608589i
$428$	41.9815	+	30.5014i	2.02925	+	1.47434i
$429$	−1.09297	−	0.794088i	−0.0527690	−	0.0383389i
$430$		0			0
$431$	−18.8882	+	13.7231i	−0.909813	+	0.661018i	−0.940967	−	0.338497i	$-0.890081\pi$
$431$	−18.8882	+	13.7231i	−0.909813	+	0.661018i	0.0311549	+	0.999515i	$0.490081\pi$
$432$	48.7004			2.34310
$433$	6.64539	−	4.82816i	0.319357	−	0.232026i	−0.416544	−	0.909116i	$-0.636759\pi$
$433$	6.64539	−	4.82816i	0.319357	−	0.232026i	0.735901	+	0.677089i	$0.236759\pi$
$434$	−12.0368	−	37.0455i	−0.577786	−	1.77824i
$435$		0			0
$436$	1.88376	−	5.79761i	0.0902156	−	0.277655i
$437$	−4.13191	−	12.7167i	−0.197656	−	0.608323i
$438$	−8.46363	−	26.0484i	−0.404408	−	1.24464i
$439$	−7.51274	+	23.1218i	−0.358564	+	1.10355i	0.595351	+	0.803466i	$0.297013\pi$
$439$	−7.51274	+	23.1218i	−0.358564	+	1.10355i	−0.953914	+	0.300079i	$0.902987\pi$
$440$		0			0
$441$	2.11943	+	6.52295i	0.100925	+	0.310617i
$442$	11.6288	−	8.44881i	0.553125	−	0.401869i
$443$	−0.0631363			−0.00299970			−0.00149985	−	0.999999i	$-0.500477\pi$
$443$	−0.0631363			−0.00299970			−0.00149985	+	0.999999i	$0.500477\pi$
$444$	27.0924	−	19.6838i	1.28575	−	0.934150i
$445$		0			0
$446$	−18.3586	−	13.3383i	−0.869305	−	0.631587i
$447$	6.11668	+	4.44403i	0.289309	+	0.210195i
$448$	10.2781	−	31.6326i	0.485593	−	1.49450i
$449$	−11.5711			−0.546074			−0.273037	−	0.962004i	$-0.588028\pi$
$449$	−11.5711			−0.546074			−0.273037	+	0.962004i	$0.588028\pi$
$450$		0			0
$451$	−13.6210			−0.641389
$452$	−7.06764	+	21.7520i	−0.332434	+	1.02313i
$453$	−12.9212	−	9.38777i	−0.607089	−	0.441076i
$454$	−45.2414	−	32.8698i	−2.12328	−	1.54266i
$455$		0			0
$456$	24.8115	−	18.0266i	1.16190	−	0.844173i
$457$	41.3967			1.93646			0.968228	−	0.250071i	$-0.0804539\pi$
$457$	41.3967			1.93646			0.968228	+	0.250071i	$0.0804539\pi$
$458$	64.1700	−	46.6222i	2.99847	−	2.17851i
$459$	−5.19993	−	16.0037i	−0.242712	−	0.746991i
$460$		0			0
$461$	9.07604	−	27.9332i	0.422713	−	1.30098i	−0.482453	−	0.875922i	$-0.660254\pi$
$461$	9.07604	−	27.9332i	0.422713	−	1.30098i	0.905167	−	0.425056i	$-0.139746\pi$
$462$	1.72171	+	5.29888i	0.0801012	+	0.246526i
$463$	9.44049	+	29.0548i	0.438737	+	1.35029i	0.889208	+	0.457502i	$0.151256\pi$
$463$	9.44049	+	29.0548i	0.438737	+	1.35029i	−0.450472	+	0.892791i	$0.648744\pi$
$464$	−16.8843	+	51.9646i	−0.783835	+	2.41240i
$465$		0			0
$466$	−1.87069	−	5.75738i	−0.0866579	−	0.266706i
$467$	26.4669	−	19.2293i	1.22474	−	0.889827i	0.228257	−	0.973601i	$-0.426697\pi$
$467$	26.4669	−	19.2293i	1.22474	−	0.889827i	0.996485	+	0.0837742i	$0.0266974\pi$
$468$	16.3198			0.754384
$469$	18.0723	−	13.1303i	0.834500	−	0.606300i
$470$		0			0
$471$	−4.79524	−	3.48395i	−0.220953	−	0.160532i
$472$	−75.8573	−	55.1136i	−3.49162	−	2.53681i
$473$	−1.01465	+	3.12277i	−0.0466536	+	0.143585i
$474$	3.82197			0.175549
$475$		0			0
$476$	−42.5864			−1.95195
$477$	−0.465308	+	1.43207i	−0.0213050	+	0.0655700i
$478$	33.2694	+	24.1716i	1.52171	+	1.10559i
$479$	9.97945	+	7.25050i	0.455973	+	0.331284i	0.791949	−	0.610587i	$-0.209066\pi$
$479$	9.97945	+	7.25050i	0.455973	+	0.331284i	−0.335977	+	0.941870i	$0.609066\pi$
$480$		0			0
$481$	9.23098	−	6.70670i	0.420896	−	0.305799i
$482$	12.9036			0.587741
$483$	3.43142	−	2.49307i	0.156135	−	0.113439i
$484$	−14.4758	−	44.5518i	−0.657989	−	2.02508i
$485$		0			0
$486$	12.7636	−	39.2824i	0.578970	−	1.78189i
$487$	−10.9071	−	33.5687i	−0.494249	−	1.52114i	−0.818124	−	0.575042i	$-0.804986\pi$
$487$	−10.9071	−	33.5687i	−0.494249	−	1.52114i	0.323875	−	0.946100i	$-0.395014\pi$
$488$	−1.65429	−	5.09139i	−0.0748864	−	0.230476i
$489$	−2.73943	+	8.43109i	−0.123881	+	0.381267i
$490$		0			0
$491$	4.73278	+	14.5660i	0.213587	+	0.657354i	0.999251	+	0.0386999i	$0.0123216\pi$
$491$	4.73278	+	14.5660i	0.213587	+	0.657354i	−0.785664	+	0.618654i	$0.787678\pi$
$492$	−31.6457	+	22.9920i	−1.42670	+	1.03656i
$493$	18.8792			0.850278
$494$	13.9039	−	10.1018i	0.625565	−	0.454500i
$495$		0			0
$496$	−68.4929	−	49.7630i	−3.07542	−	2.23442i
$497$	4.87755	+	3.54375i	0.218788	+	0.158959i
$498$	−1.48457	+	4.56903i	−0.0665250	+	0.204743i
$499$	−35.1777			−1.57477			−0.787386	−	0.616461i	$-0.788566\pi$
$499$	−35.1777			−1.57477			−0.787386	+	0.616461i	$0.788566\pi$
$500$		0			0
$501$	5.70221			0.254756
$502$	14.6830	−	45.1897i	0.655335	−	2.01691i
$503$	5.93409	+	4.31137i	0.264588	+	0.192235i	0.712167	−	0.702010i	$-0.247714\pi$
$503$	5.93409	+	4.31137i	0.264588	+	0.192235i	−0.447579	+	0.894244i	$0.647714\pi$
$504$	−33.1069	−	24.0535i	−1.47470	−	1.07143i
$505$		0			0
$506$	7.95622	−	5.78054i	0.353697	−	0.256976i
$507$	8.54617			0.379549
$508$	−17.2413	+	12.5266i	−0.764961	+	0.555777i
$509$	1.76355	+	5.42765i	0.0781681	+	0.240577i	0.982503	−	0.186247i	$-0.0596325\pi$
$509$	1.76355	+	5.42765i	0.0781681	+	0.240577i	−0.904335	+	0.426824i	$0.859633\pi$
$510$		0			0
$511$	−8.54381	+	26.2951i	−0.377956	+	1.16323i
$512$	5.65366	+	17.4002i	0.249859	+	0.768987i
$513$	−6.21726	−	19.1348i	−0.274499	−	0.844820i
$514$	4.85003	−	14.9269i	0.213926	−	0.658395i
$515$		0			0
$516$	2.91382	+	8.96783i	0.128274	+	0.394787i
$517$	8.26171	−	6.00249i	0.363350	−	0.263989i
$518$	−47.0563			−2.06753
$519$	−3.26327	+	2.37090i	−0.143242	+	0.104071i
$520$		0			0
$521$	26.7705	+	19.4499i	1.17283	+	0.852114i	0.991346	−	0.131279i	$-0.0419082\pi$
$521$	26.7705	+	19.4499i	1.17283	+	0.852114i	0.181489	+	0.983393i	$0.441908\pi$
$522$	24.1387	+	17.5378i	1.05652	+	0.767608i
$523$	9.72536	−	29.9316i	0.425260	−	1.30882i	−0.477484	−	0.878640i	$-0.658451\pi$
$523$	9.72536	−	29.9316i	0.425260	−	1.30882i	0.902745	−	0.430177i	$-0.141549\pi$
$524$	17.2924			0.755421
$525$		0			0
$526$	63.1002			2.75130
$527$	−9.03967	+	27.8213i	−0.393774	+	1.21191i
$528$	9.79700	+	7.11794i	0.426360	+	0.309768i
$529$	12.5506	+	9.11851i	0.545676	+	0.396457i
$530$		0			0
$531$	−22.2388	+	16.1574i	−0.965082	+	0.701173i
$532$	−50.9182			−2.20758
$533$	−10.7824	+	7.83388i	−0.467038	+	0.339323i
$534$	4.58772	+	14.1196i	0.198530	+	0.611013i
$535$		0			0
$536$	27.9471	−	86.0122i	1.20713	−	3.71516i
$537$	−0.306522	−	0.943377i	−0.0132274	−	0.0407097i
$538$	−11.3203	−	34.8404i	−0.488054	−	1.50208i
$539$	−1.17932	+	3.62956i	−0.0507968	+	0.156336i
$540$		0			0
$541$	−7.06905	−	21.7563i	−0.303922	−	0.935376i	−0.980077	−	0.198617i	$-0.936355\pi$
$541$	−7.06905	−	21.7563i	−0.303922	−	0.935376i	0.676155	−	0.736759i	$-0.263645\pi$
$542$	16.1678	−	11.7466i	0.694464	−	0.504558i
$543$	15.3052			0.656808
$544$	−49.5611	+	36.0083i	−2.12492	+	1.54384i
$545$		0			0
$546$	4.41046	+	3.20439i	0.188750	+	0.137135i
$547$	14.3639	+	10.4360i	0.614157	+	0.446211i	0.850876	−	0.525367i	$-0.176072\pi$
$547$	14.3639	+	10.4360i	0.614157	+	0.446211i	−0.236719	+	0.971578i	$0.576072\pi$
$548$	13.1433	−	40.4508i	0.561453	−	1.72797i
$549$	−1.56944			−0.0669820
$550$		0			0
$551$	22.5728			0.961634
$552$	5.30636	−	16.3313i	0.225854	−	0.695107i
$553$	−3.12133	−	2.26778i	−0.132733	−	0.0964359i
$554$	−6.11879	−	4.44556i	−0.259962	−	0.188874i
$555$		0			0
$556$	14.1731	−	10.2974i	0.601075	−	0.436706i
$557$	2.27448			0.0963727			0.0481864	−	0.998838i	$-0.484656\pi$
$557$	2.27448			0.0963727			0.0481864	+	0.998838i	$0.484656\pi$
$558$	−37.4024	+	27.1745i	−1.58337	+	1.15039i
$559$	0.992805	+	3.05554i	0.0419912	+	0.129236i
$560$		0			0
$561$	1.29301	−	3.97946i	0.0545908	−	0.168013i
$562$	18.9091	+	58.1963i	0.797633	+	2.45486i
$563$	0.122896	+	0.378234i	0.00517943	+	0.0159407i	0.953613	−	0.301036i	$-0.0973324\pi$
$563$	0.122896	+	0.378234i	0.00517943	+	0.0159407i	−0.948433	+	0.316976i	$0.897332\pi$
$564$	9.06239	−	27.8912i	0.381595	−	1.17443i
$565$		0			0
$566$	−20.6910	−	63.6804i	−0.869709	−	2.67669i
$567$	−6.84994	+	4.97677i	−0.287670	+	0.209005i
$568$	24.4086			1.02416
$569$	9.05098	−	6.57592i	0.379437	−	0.275677i	−0.381676	−	0.924296i	$-0.624653\pi$
$569$	9.05098	−	6.57592i	0.379437	−	0.275677i	0.761113	+	0.648619i	$0.224653\pi$
$570$		0			0
$571$	15.3004	+	11.1164i	0.640303	+	0.465207i	0.859954	−	0.510371i	$-0.170492\pi$
$571$	15.3004	+	11.1164i	0.640303	+	0.465207i	−0.219651	+	0.975578i	$0.570492\pi$
$572$	7.34655	+	5.33758i	0.307175	+	0.223176i
$573$	−4.99533	+	15.3740i	−0.208683	+	0.642259i
$574$	54.9649			2.29419
$575$		0			0
$576$	−39.4768			−1.64486
$577$	1.85969	−	5.72355i	0.0774201	−	0.238274i	−0.904855	−	0.425720i	$-0.860021\pi$
$577$	1.85969	−	5.72355i	0.0774201	−	0.238274i	0.982275	+	0.187446i	$0.0600208\pi$
$578$	−0.636071	−	0.462133i	−0.0264571	−	0.0192222i
$579$	4.90891	+	3.56653i	0.204007	+	0.148220i
$580$		0			0
$581$	3.92347	−	2.85057i	0.162773	−	0.118261i
$582$	−11.7315			−0.486285
$583$	−0.677839	+	0.492479i	−0.0280732	+	0.0203964i
$584$	34.5900	+	106.457i	1.43134	+	4.40522i
$585$		0			0
$586$	−23.7799	+	73.1871i	−0.982340	+	3.02333i
$587$	5.04705	+	15.5332i	0.208314	+	0.641125i	0.999561	+	0.0296279i	$0.00943225\pi$
$587$	5.04705	+	15.5332i	0.208314	+	0.641125i	−0.791247	+	0.611497i	$0.790568\pi$
$588$	3.38671	+	10.4232i	0.139666	+	0.429847i
$589$	−10.8082	+	33.2643i	−0.445345	+	1.37063i
$590$		0			0
$591$	−5.09049	−	15.6669i	−0.209395	−	0.644451i
$592$	−82.7434	+	60.1166i	−3.40073	+	2.47078i
$593$	−8.40604			−0.345195			−0.172597	−	0.984992i	$-0.555216\pi$
$593$	−8.40604			−0.345195			−0.172597	+	0.984992i	$0.555216\pi$
$594$	11.9717	−	8.69794i	0.491204	−	0.356881i
$595$		0			0
$596$	−41.1142	−	29.8712i	−1.68410	−	1.22357i
$597$	5.73727	+	4.16837i	0.234811	+	0.170600i
$598$	2.97358	−	9.15175i	0.121599	−	0.374243i
$599$	13.1918			0.539001			0.269501	−	0.963000i	$-0.413141\pi$
$599$	13.1918			0.539001			0.269501	+	0.963000i	$0.413141\pi$
$600$		0			0
$601$	−6.06690			−0.247474			−0.123737	−	0.992315i	$-0.539488\pi$
$601$	−6.06690			−0.247474			−0.123737	+	0.992315i	$0.539488\pi$
$602$	4.09441	−	12.6013i	0.166876	−	0.513591i
$603$	−21.4499	−	15.5843i	−0.873508	−	0.634641i
$604$	86.8516	+	63.1014i	3.53394	+	2.56756i
$605$		0			0
$606$	−18.9087	+	13.7380i	−0.768115	+	0.558068i
$607$	14.9141			0.605345			0.302672	−	0.953095i	$-0.402121\pi$
$607$	14.9141			0.605345			0.302672	+	0.953095i	$0.402121\pi$
$608$	−59.2574	+	43.0530i	−2.40321	+	1.74603i
$609$	2.21267	+	6.80988i	0.0896617	+	0.275950i
$610$		0			0
$611$	3.08776	−	9.50314i	0.124917	−	0.384456i
$612$	15.6195	+	48.0718i	0.631380	+	1.94319i
$613$	11.2721	+	34.6919i	0.455275	+	1.40119i	0.870812	+	0.491617i	$0.163594\pi$
$613$	11.2721	+	34.6919i	0.455275	+	1.40119i	−0.415536	+	0.909577i	$0.636406\pi$
$614$	19.7257	−	60.7096i	0.796066	−	2.45004i
$615$		0			0
$616$	−7.03645	−	21.6560i	−0.283507	−	0.872543i
$617$	13.1336	−	9.54215i	0.528741	−	0.384153i	−0.291146	−	0.956679i	$-0.594036\pi$
$617$	13.1336	−	9.54215i	0.528741	−	0.384153i	0.819886	+	0.572526i	$0.194036\pi$
$618$	−23.4808			−0.944537
$619$	8.11932	−	5.89903i	0.326343	−	0.237102i	−0.412534	−	0.910942i	$-0.635356\pi$
$619$	8.11932	−	5.89903i	0.326343	−	0.237102i	0.738877	+	0.673840i	$0.235356\pi$
$620$		0			0
$621$	−9.11368	−	6.62148i	−0.365719	−	0.265711i
$622$	−21.3197	−	15.4896i	−0.854841	−	0.621078i
$623$	4.63118	−	14.2533i	0.185544	−	0.571047i
$624$	11.8491			0.474342
$625$		0			0
$626$	−50.0451			−2.00020
$627$	1.54597	−	4.75802i	0.0617403	−	0.190017i
$628$	32.2320	+	23.4179i	1.28619	+	0.934475i
$629$	28.5901	+	20.7719i	1.13996	+	0.828231i
$630$		0			0
$631$	−23.2657	+	16.9035i	−0.926194	+	0.672920i	−0.945058	−	0.326902i	$-0.893995\pi$
$631$	−23.2657	+	16.9035i	−0.926194	+	0.672920i	0.0188637	+	0.999822i	$0.493995\pi$
$632$	−15.6200			−0.621330
$633$	−4.22599	+	3.07036i	−0.167968	+	0.122036i
$634$	−21.3146	−	65.5995i	−0.846510	−	2.60529i
$635$		0			0
$636$	−0.743531	+	2.28835i	−0.0294829	+	0.0907391i
$637$	1.15393	+	3.55143i	0.0457203	+	0.140713i
$638$	5.13037	+	15.7897i	0.203113	+	0.625119i
$639$	2.21125	−	6.80554i	0.0874759	−	0.269223i
$640$		0			0
$641$	−5.63761	−	17.3508i	−0.222672	−	0.685315i	−0.998520	−	0.0543939i	$-0.982677\pi$
$641$	−5.63761	−	17.3508i	−0.222672	−	0.685315i	0.775847	−	0.630921i	$-0.217323\pi$
$642$	16.6449	−	12.0932i	0.656922	−	0.477282i
$643$	33.9734			1.33978			0.669890	−	0.742461i	$-0.266341\pi$
$643$	33.9734			1.33978			0.669890	+	0.742461i	$0.266341\pi$
$644$	−23.0648	+	16.7576i	−0.908881	+	0.660341i
$645$		0			0
$646$	43.0630	+	31.2871i	1.69429	+	1.23097i
$647$	38.3254	+	27.8450i	1.50673	+	1.09470i	0.967604	+	0.252473i	$0.0812440\pi$
$647$	38.3254	+	27.8450i	1.50673	+	1.09470i	0.539123	+	0.842227i	$0.318756\pi$
$648$	−10.5928	+	32.6012i	−0.416124	+	1.28070i
$649$	−15.2955			−0.600402
$650$		0			0
$651$	−11.0948			−0.434840
$652$	18.4135	−	56.6709i	0.721128	−	2.21940i
$653$	−30.2540	−	21.9808i	−1.18393	−	0.860175i	−0.191319	−	0.981528i	$-0.561277\pi$
$653$	−30.2540	−	21.9808i	−1.18393	−	0.860175i	−0.992609	+	0.121353i	$0.961277\pi$
$654$	−1.95534	−	1.42064i	−0.0764600	−	0.0555514i
$655$		0			0
$656$	96.6499	−	70.2202i	3.77354	−	2.74164i
$657$	32.8157			1.28026
$658$	−33.3385	+	24.2218i	−1.29967	+	0.944266i
$659$	−2.92996	−	9.01748i	−0.114135	−	0.351271i	0.877631	−	0.479337i	$-0.159123\pi$
$659$	−2.92996	−	9.01748i	−0.114135	−	0.351271i	−0.991766	+	0.128066i	$0.959123\pi$
$660$		0			0
$661$	−2.71344	+	8.35112i	−0.105541	+	0.324821i	−0.989857	−	0.142067i	$-0.954625\pi$
$661$	−2.71344	+	8.35112i	−0.105541	+	0.324821i	0.884316	+	0.466888i	$0.154625\pi$
$662$	−1.06848	−	3.28845i	−0.0415277	−	0.127809i
$663$	−1.26517	−	3.89379i	−0.0491351	−	0.151222i
$664$	6.06727	−	18.6731i	0.235456	−	0.724658i
$665$		0			0
$666$	17.2589	+	53.1174i	0.668768	+	2.05826i
$667$	10.2250	−	7.42889i	0.395913	−	0.287648i
$668$	−38.3283			−1.48297
$669$	−5.22913	+	3.79919i	−0.202170	+	0.146885i
$670$		0			0
$671$	−0.706500	−	0.513303i	−0.0272741	−	0.0198158i
$672$	−18.7971	−	13.6569i	−0.725113	−	0.526825i
$673$	−14.8408	+	45.6753i	−0.572072	+	1.76066i	0.0738696	+	0.997268i	$0.476465\pi$
$673$	−14.8408	+	45.6753i	−0.572072	+	1.76066i	−0.645941	+	0.763387i	$0.723535\pi$
$674$	−30.0531			−1.15760
$675$		0			0
$676$	−57.4444			−2.20940
$677$	4.76354	−	14.6607i	0.183078	−	0.563455i	−0.816832	−	0.576875i	$-0.804272\pi$
$677$	4.76354	−	14.6607i	0.183078	−	0.563455i	0.999910	+	0.0134203i	$0.00427195\pi$
$678$	7.33623	+	5.33008i	0.281746	+	0.204701i
$679$	9.58087	+	6.96091i	0.367680	+	0.267135i
$680$		0			0
$681$	−12.8862	+	9.36240i	−0.493802	+	0.358768i
$682$	−25.7248			−0.985055
$683$	−22.5086	+	16.3534i	−0.861267	+	0.625747i	−0.928229	−	0.372009i	$-0.878669\pi$
$683$	−22.5086	+	16.3534i	−0.861267	+	0.625747i	0.0669626	+	0.997755i	$0.478669\pi$
$684$	18.6753	+	57.4767i	0.714068	+	2.19768i
$685$		0			0
$686$	16.5312	−	50.8779i	0.631166	−	1.94253i
$687$	−6.98146	−	21.4867i	−0.266359	−	0.819770i
$688$	−8.89917	−	27.3888i	−0.339278	−	1.04419i
$689$	−0.253338	+	0.779693i	−0.00965139	+	0.0297039i
$690$		0			0
$691$	−6.21931	−	19.1411i	−0.236594	−	0.728161i	−0.996906	−	0.0786030i	$-0.974954\pi$
$691$	−6.21931	−	19.1411i	−0.236594	−	0.728161i	0.760312	−	0.649558i	$-0.225046\pi$
$692$	21.9346	−	15.9364i	0.833827	−	0.605811i
$693$	−6.67552			−0.253582
$694$	−4.64628	+	3.37572i	−0.176370	+	0.128141i
$695$		0			0
$696$	23.4525	+	17.0393i	0.888966	+	0.645871i
$697$	−33.3952	−	24.2630i	−1.26493	−	0.919028i
$698$	−4.61923	+	14.2165i	−0.174841	+	0.538104i
$699$	−1.72428			−0.0652184
$700$		0			0
$701$	31.6216			1.19433			0.597166	−	0.802118i	$-0.296293\pi$
$701$	31.6216			1.19433			0.597166	+	0.802118i	$0.296293\pi$
$702$	4.47433	−	13.7706i	0.168873	−	0.519737i
$703$	34.1836	+	24.8358i	1.28926	+	0.936701i
$704$	−17.7709	−	12.9113i	−0.669766	−	0.486614i
$705$		0			0
$706$	39.8801	−	28.9746i	1.50091	−	1.09047i
$707$	23.5939			0.887340
$708$	−35.5361	+	25.8185i	−1.33553	+	0.970319i
$709$	−1.47094	−	4.52710i	−0.0552425	−	0.170019i	0.919628	−	0.392790i	$-0.128490\pi$
$709$	−1.47094	−	4.52710i	−0.0552425	−	0.170019i	−0.974871	+	0.222771i	$0.928490\pi$
$710$		0			0
$711$	−1.41507	+	4.35513i	−0.0530692	+	0.163330i
$712$	−18.7495	−	57.7051i	−0.702668	−	2.16259i
$713$	6.05165	+	18.6251i	0.226636	+	0.697514i
$714$	−5.21767	+	16.0583i	−0.195266	+	0.600968i
$715$		0			0
$716$	2.06033	+	6.34105i	0.0769982	+	0.236976i
$717$	9.47621	−	6.88487i	0.353896	−	0.257120i
$718$	−29.9680			−1.11840
$719$	18.6662	−	13.5618i	0.696133	−	0.505770i	−0.182538	−	0.983199i	$-0.558431\pi$
$719$	18.6662	−	13.5618i	0.696133	−	0.505770i	0.878670	+	0.477429i	$0.158431\pi$
$720$		0			0
$721$	19.1763	+	13.9324i	0.714164	+	0.518871i
$722$	10.5232	+	7.64557i	0.391634	+	0.284539i
$723$	1.13575	−	3.49547i	0.0422389	−	0.129998i
$724$	−102.876			−3.82336
$725$		0			0
$726$	−18.5730			−0.689309
$727$	−4.81470	+	14.8181i	−0.178567	+	0.549574i	−0.999778	−	0.0210509i	$-0.993299\pi$
$727$	−4.81470	+	14.8181i	−0.178567	+	0.549574i	0.821211	+	0.570624i	$0.193299\pi$
$728$	−18.0251	−	13.0960i	−0.668054	−	0.485369i
$729$	0.545079	+	0.396023i	0.0201881	+	0.0146675i
$730$		0			0
$731$	−8.05022	+	5.84882i	−0.297748	+	0.216327i
$732$	−2.50786			−0.0926931
$733$	13.9325	−	10.1226i	0.514609	−	0.373886i	−0.299960	−	0.953952i	$-0.596973\pi$
$733$	13.9325	−	10.1226i	0.514609	−	0.373886i	0.814569	+	0.580066i	$0.196973\pi$
$734$	−23.5264	−	72.4069i	−0.868377	−	2.67259i
$735$		0			0
$736$	−12.6732	+	39.0041i	−0.467141	+	1.43771i
$737$	−4.55891	−	14.0309i	−0.167929	−	0.516834i
$738$	−20.1595	−	62.0447i	−0.742083	−	2.28390i
$739$	−8.49421	+	26.1425i	−0.312464	+	0.961667i	0.664321	+	0.747447i	$0.268721\pi$
$739$	−8.49421	+	26.1425i	−0.312464	+	0.961667i	−0.976786	+	0.214219i	$0.931279\pi$
$740$		0			0
$741$	−1.51269	−	4.65559i	−0.0555701	−	0.171027i
$742$	2.73529	−	1.98730i	0.100415	−	0.0729561i
$743$	−48.4801			−1.77856			−0.889280	−	0.457362i	$-0.848794\pi$
$743$	−48.4801			−1.77856			−0.889280	+	0.457362i	$0.848794\pi$
$744$	−36.3392	+	26.4020i	−1.33226	+	0.967944i
$745$		0			0
$746$	−30.3674	−	22.0632i	−1.11183	−	0.807792i
$747$	−4.65675	−	3.38332i	−0.170381	−	0.123789i
$748$	−8.69114	+	26.7486i	−0.317780	+	0.978025i
$749$	−20.7691			−0.758888
$750$		0			0
$751$	3.29720			0.120316			0.0601582	−	0.998189i	$-0.480839\pi$
$751$	3.29720			0.120316			0.0601582	+	0.998189i	$0.480839\pi$
$752$	−27.6776	+	85.1830i	−1.00930	+	3.10630i
$753$	−10.9491	−	7.95502i	−0.399009	−	0.289897i
$754$	13.1423	+	9.54847i	0.478616	+	0.347735i
$755$		0			0
$756$	−34.7055	+	25.2150i	−1.26223	+	0.917061i
$757$	35.7934			1.30093			0.650466	−	0.759535i	$-0.274574\pi$
$757$	35.7934			1.30093			0.650466	+	0.759535i	$0.274574\pi$
$758$	47.4120	−	34.4468i	1.72208	−	1.25117i
$759$	−0.865609	−	2.66407i	−0.0314196	−	0.0966996i
$760$		0			0
$761$	−0.205221	+	0.631606i	−0.00743927	+	0.0228957i	−0.954707	−	0.297547i	$-0.903832\pi$
$761$	−0.205221	+	0.631606i	−0.00743927	+	0.0228957i	0.947268	+	0.320442i	$0.103832\pi$
$762$	2.61107	+	8.03606i	0.0945892	+	0.291116i
$763$	0.753950	+	2.32042i	0.0272948	+	0.0840049i
$764$	33.5769	−	103.339i	1.21477	−	3.73867i
$765$		0			0
$766$	−12.1419	−	37.3688i	−0.438703	−	1.35019i
$767$	−12.1079	+	8.79694i	−0.437193	+	0.317639i
$768$	−2.43848			−0.0879911
$769$	−20.7990	+	15.1114i	−0.750032	+	0.544930i	−0.895837	−	0.444383i	$-0.853423\pi$
$769$	−20.7990	+	15.1114i	−0.750032	+	0.544930i	0.145805	+	0.989313i	$0.453423\pi$
$770$		0			0
$771$	−3.61667	−	2.62767i	−0.130251	−	0.0946331i
$772$	−32.9960	−	23.9730i	−1.18755	−	0.862806i
$773$	11.9113	−	36.6593i	0.428420	−	1.31854i	−0.471260	−	0.881994i	$-0.656201\pi$
$773$	11.9113	−	36.6593i	0.428420	−	1.31854i	0.899681	−	0.436548i	$-0.143799\pi$
$774$	−15.7261			−0.565264
$775$		0			0
$776$	47.9453			1.72114
$777$	−4.14181	+	12.7472i	−0.148586	+	0.457302i
$778$	−30.7382	−	22.3326i	−1.10202	−	0.800662i
$779$	−39.9287	−	29.0099i	−1.43060	−	1.03939i
$780$		0			0
$781$	3.22125	−	2.34038i	0.115265	−	0.0837452i
$782$	29.8034			1.06577
$783$	15.3855	−	11.1782i	0.549832	−	0.399476i
$784$	−10.3434	−	31.8338i	−0.369408	−	1.13692i
$785$		0			0
$786$	2.11866	−	6.52055i	0.0755699	−	0.232580i
$787$	11.1961	+	34.4579i	0.399096	+	1.22829i	0.925725	+	0.378197i	$0.123456\pi$
$787$	11.1961	+	34.4579i	0.399096	+	1.22829i	−0.526629	+	0.850095i	$0.676544\pi$
$788$	34.2165	+	105.308i	1.21891	+	3.75143i
$789$	5.55396	−	17.0933i	0.197726	−	0.608539i
$790$		0			0
$791$	−2.82874	−	8.70596i	−0.100578	−	0.309548i
$792$	−21.8646	+	15.8856i	−0.776924	+	0.564468i
$793$	−0.854482			−0.0303436
$794$	11.8381	−	8.60085i	0.420117	−	0.305233i
$795$		0			0
$796$	−38.5639	−	28.0183i	−1.36686	−	0.993084i
$797$	27.3671	+	19.8833i	0.969392	+	0.704304i	0.955313	−	0.295597i	$-0.0955184\pi$
$797$	27.3671	+	19.8833i	0.969392	+	0.704304i	0.0140788	+	0.999901i	$0.495518\pi$
$798$	−6.23847	+	19.2000i	−0.220840	+	0.679674i
$799$	30.9478			1.09485
$800$		0			0
$801$	−17.7878			−0.628501
$802$	−22.0318	+	67.8070i	−0.777971	+	2.39435i
$803$	14.7724	+	10.7328i	0.521305	+	0.378751i
$804$	−34.2755	−	24.9026i	−1.20880	−	0.878248i
$805$		0			0
$806$	−20.3638	+	14.7952i	−0.717284	+	0.521138i
$807$	−10.4344			−0.367308
$808$	77.2780	−	56.1458i	2.71863	−	1.97520i
$809$	−0.452429	−	1.39243i	−0.0159066	−	0.0489554i	0.942788	−	0.333392i	$-0.108193\pi$
$809$	−0.452429	−	1.39243i	−0.0159066	−	0.0489554i	−0.958695	+	0.284437i	$0.908193\pi$
$810$		0			0
$811$	−12.5734	+	38.6971i	−0.441513	+	1.35884i	0.444750	+	0.895655i	$0.353293\pi$
$811$	−12.5734	+	38.6971i	−0.441513	+	1.35884i	−0.886263	+	0.463182i	$0.846707\pi$
$812$	−14.8728	−	45.7737i	−0.521932	−	1.60634i
$813$	−1.75899	−	5.41362i	−0.0616906	−	0.189864i
$814$	−9.60336	+	29.5561i	−0.336598	+	1.03594i
$815$		0			0
$816$	11.3406	+	34.9027i	0.396999	+	1.22184i
$817$	−9.62518	+	6.99311i	−0.336743	+	0.244658i
$818$	−13.6819			−0.478375
$819$	−5.28434	+	3.83930i	−0.184650	+	0.134156i
$820$		0			0
$821$	24.2327	+	17.6061i	0.845729	+	0.614458i	0.923965	−	0.382477i	$-0.124929\pi$
$821$	24.2327	+	17.6061i	0.845729	+	0.614458i	−0.0782364	+	0.996935i	$0.524929\pi$
$822$	−13.6428	−	9.91204i	−0.475846	−	0.345722i
$823$	−5.85182	+	18.0100i	−0.203981	+	0.627790i	0.795772	+	0.605596i	$0.207065\pi$
$823$	−5.85182	+	18.0100i	−0.203981	+	0.627790i	−0.999754	+	0.0221943i	$0.992935\pi$
$824$	95.9636			3.34305
$825$		0			0
$826$	61.7221			2.14759
$827$	−6.26188	+	19.2721i	−0.217747	+	0.670156i	0.781200	+	0.624281i	$0.214608\pi$
$827$	−6.26188	+	19.2721i	−0.217747	+	0.670156i	−0.998947	+	0.0458757i	$0.985392\pi$
$828$	27.3755	+	19.8895i	0.951365	+	0.691207i
$829$	−13.4621	−	9.78077i	−0.467557	−	0.339700i	0.328931	−	0.944354i	$-0.393311\pi$
$829$	−13.4621	−	9.78077i	−0.467557	−	0.339700i	−0.796488	+	0.604654i	$0.793311\pi$
$830$		0			0
$831$	−1.74283	+	1.26624i	−0.0604582	+	0.0439254i
$832$	−21.4932			−0.745142
$833$	−9.35670	+	6.79804i	−0.324190	+	0.235538i
$834$	−2.14641	−	6.60599i	−0.0743243	−	0.228747i
$835$		0			0
$836$	−10.3915	+	31.9818i	−0.359398	+	1.10611i
$837$	9.10588	+	28.0250i	0.314745	+	0.968686i
$838$	−26.2309	−	80.7304i	−0.906131	−	2.78878i
$839$	−2.20535	+	6.78737i	−0.0761371	+	0.234326i	−0.981881	−	0.189500i	$-0.939313\pi$
$839$	−2.20535	+	6.78737i	−0.0761371	+	0.234326i	0.905744	+	0.423826i	$0.139313\pi$
$840$		0			0
$841$	−2.36816	−	7.28846i	−0.0816608	−	0.251326i
$842$	6.64156	−	4.82537i	0.228883	−	0.166293i
$843$	17.4293			0.600295
$844$	28.4056	−	20.6379i	0.977762	−	0.710385i
$845$		0			0
$846$	39.5693	+	28.7488i	1.36042	+	0.988404i
$847$	15.1682	+	11.0204i	0.521186	+	0.378664i
$848$	2.27083	−	6.98891i	0.0779807	−	0.240000i
$849$	−19.0717			−0.654539
$850$		0			0
$851$	23.6581			0.810988
$852$	3.53344	−	10.8748i	0.121054	−	0.372565i
$853$	25.7472	+	18.7064i	0.881566	+	0.640495i	0.933665	−	0.358147i	$-0.116591\pi$
$853$	25.7472	+	18.7064i	0.881566	+	0.640495i	−0.0520993	+	0.998642i	$0.516591\pi$
$854$	2.85094	+	2.07133i	0.0975573	+	0.0708795i
$855$		0			0
$856$	−68.0260	+	49.4238i	−2.32508	+	1.68927i
$857$	−43.1535			−1.47409			−0.737047	−	0.675842i	$-0.763780\pi$
$857$	−43.1535			−1.47409			−0.737047	+	0.675842i	$0.763780\pi$
$858$	2.91277	−	2.11625i	0.0994405	−	0.0722477i
$859$	9.54599	+	29.3795i	0.325705	+	1.00242i	0.971121	+	0.238586i	$0.0766839\pi$
$859$	9.54599	+	29.3795i	0.325705	+	1.00242i	−0.645416	+	0.763831i	$0.723316\pi$
$860$		0			0
$861$	4.83791	−	14.8896i	0.164876	−	0.507435i
$862$	−19.2271	−	59.1750i	−0.654879	−	2.01551i
$863$	−11.8017	−	36.3218i	−0.401734	−	1.23641i	−0.923592	−	0.383377i	$-0.874761\pi$
$863$	−11.8017	−	36.3218i	−0.401734	−	1.23641i	0.521858	−	0.853032i	$-0.325239\pi$
$864$	−19.0693	+	58.6893i	−0.648751	+	1.99665i
$865$		0			0
$866$	6.76464	+	20.8194i	0.229872	+	0.707472i
$867$	−0.181174	+	0.131631i	−0.00615299	+	0.00447041i
$868$	74.5754			2.53125
$869$	−2.06141	+	1.49770i	−0.0699284	+	0.0508059i
$870$		0			0
$871$	−11.6784	−	8.48487i	−0.395708	−	0.287499i
$872$	7.99128	+	5.80601i	0.270619	+	0.196616i
$873$	4.34352	−	13.3680i	0.147006	−	0.452438i
$874$	35.6343			1.20535
$875$		0			0
$876$	52.4373			1.77169
$877$	9.80348	−	30.1720i	0.331040	−	1.01884i	−0.637600	−	0.770368i	$-0.720073\pi$
$877$	9.80348	−	30.1720i	0.331040	−	1.01884i	0.968640	−	0.248469i	$-0.0799273\pi$
$878$	−52.4171	−	38.0832i	−1.76899	−	1.28525i
$879$	17.7327	+	12.8836i	0.598110	+	0.434553i
$880$		0			0
$881$	31.0994	−	22.5950i	1.04776	−	0.761245i	0.0759780	−	0.997109i	$-0.475792\pi$
$881$	31.0994	−	22.5950i	1.04776	−	0.761245i	0.971786	+	0.235864i	$0.0757921\pi$
$882$	−18.2783			−0.615464
$883$	−9.82933	+	7.14142i	−0.330783	+	0.240328i	−0.740763	−	0.671767i	$-0.765536\pi$
$883$	−9.82933	+	7.14142i	−0.330783	+	0.240328i	0.409980	+	0.912095i	$0.365536\pi$
$884$	8.50404	+	26.1727i	0.286022	+	0.880284i
$885$		0			0
$886$	0.0519949	−	0.160024i	0.00174680	−	0.00537611i
$887$	−7.49154	−	23.0566i	−0.251541	−	0.774165i	−0.994491	−	0.104818i	$-0.966574\pi$
$887$	−7.49154	−	23.0566i	−0.251541	−	0.774165i	0.742950	−	0.669347i	$-0.233426\pi$
$888$	16.7683	+	51.6074i	0.562706	+	1.73183i
$889$	2.63581	−	8.11219i	0.0884022	−	0.272074i
$890$		0			0
$891$	1.72796	+	5.31812i	0.0578889	+	0.178164i
$892$	35.1484	−	25.5368i	1.17686	−	0.855036i
$893$	37.0025			1.23824
$894$	−16.3010	+	11.8434i	−0.545188	+	0.396102i
$895$		0			0
$896$	22.1852	+	16.1185i	0.741157	+	0.538482i
$897$	−2.21741	−	1.61104i	−0.0740370	−	0.0537911i
$898$	9.52919	−	29.3278i	0.317993	−	0.978683i
$899$	−33.0604			−1.10263
$900$		0			0
$901$	−2.53913			−0.0845908
$902$	11.2174	−	34.5235i	0.373498	−	1.14951i
$903$	−3.05321	−	2.21829i	−0.101604	−	0.0738200i
$904$	−29.9824	−	21.7835i	−0.997200	−	0.724508i
$905$		0			0
$906$	34.4350	−	25.0185i	1.14403	−	0.831185i
$907$	−32.5046			−1.07930			−0.539649	−	0.841890i	$-0.681443\pi$
$907$	−32.5046			−1.07930			−0.539649	+	0.841890i	$0.681443\pi$
$908$	86.6168	−	62.9308i	2.87448	−	2.08843i
$909$	−8.65356	−	26.6329i	−0.287020	−	0.883358i
$910$		0			0
$911$	13.6665	−	42.0612i	0.452792	−	1.39355i	−0.420916	−	0.907100i	$-0.638291\pi$
$911$	13.6665	−	42.0612i	0.452792	−	1.39355i	0.873708	−	0.486451i	$-0.161709\pi$
$912$	13.5593	+	41.7311i	0.448992	+	1.38186i
$913$	−0.989732	−	3.04608i	−0.0327554	−	0.100811i
$914$	−34.0916	+	104.923i	−1.12765	+	3.47055i
$915$		0			0
$916$	46.9270	+	144.426i	1.55051	+	4.77198i
$917$	−5.59926	+	4.06810i	−0.184904	+	0.134340i
$918$	44.8450			1.48011
$919$	32.1937	−	23.3901i	1.06197	−	0.771568i	0.0875203	−	0.996163i	$-0.472106\pi$
$919$	32.1937	−	23.3901i	1.06197	−	0.771568i	0.974452	+	0.224594i	$0.0721057\pi$
$920$		0			0
$921$	−14.7095	−	10.6871i	−0.484695	−	0.352152i
$922$	63.3244	+	46.0079i	2.08548	+	1.51519i
$923$	1.20392	−	3.70529i	0.0396275	−	0.121961i
$924$	−10.6670			−0.350920
$925$		0			0
$926$	−81.4163			−2.67551
$927$	8.69366	−	26.7563i	0.285537	−	0.878794i
$928$	−56.0118	−	40.6949i	−1.83868	−	1.33588i
$929$	5.37690	+	3.90655i	0.176410	+	0.128170i	0.672487	−	0.740109i	$-0.265226\pi$
$929$	5.37690	+	3.90655i	0.176410	+	0.128170i	−0.496076	+	0.868279i	$0.665226\pi$
$930$		0			0
$931$	−11.1873	+	8.12803i	−0.366648	+	0.266385i
$932$	11.5900			0.379644
$933$	−6.07254	+	4.41196i	−0.198806	+	0.144441i
$934$	26.9418	+	82.9184i	0.881563	+	2.71317i
$935$		0			0
$936$	−8.17174	+	25.1500i	−0.267102	+	0.822054i
$937$	0.0709458	+	0.218349i	0.00231770	+	0.00713314i	0.952209	−	0.305448i	$-0.0988063\pi$
$937$	0.0709458	+	0.218349i	0.00231770	+	0.00713314i	−0.949891	+	0.312581i	$0.898806\pi$
$938$	18.3966	+	56.6188i	0.600669	+	1.84867i
$939$	−4.40487	+	13.5568i	−0.143748	+	0.442410i
$940$		0			0
$941$	8.75990	+	26.9602i	0.285565	+	0.878877i	0.986229	+	0.165386i	$0.0528871\pi$
$941$	8.75990	+	26.9602i	0.285565	+	0.878877i	−0.700664	+	0.713491i	$0.747113\pi$
$942$	12.7794	−	9.28476i	0.416375	−	0.302514i
$943$	−27.6342			−0.899894
$944$	108.532	−	78.8528i	3.53240	−	2.56644i
$945$		0			0
$946$	−7.07929	−	5.14341i	−0.230168	−	0.167227i
$947$	−38.8357	−	28.2158i	−1.26199	−	0.916891i	−0.263138	−	0.964758i	$-0.584758\pi$
$947$	−38.8357	−	28.2158i	−1.26199	−	0.916891i	−0.998854	+	0.0478673i	$0.984758\pi$
$948$	−2.26118	+	6.95921i	−0.0734399	+	0.226025i
$949$	17.8666			0.579973
$950$		0			0
$951$	−19.6464			−0.637080
$952$	21.3241	−	65.6288i	0.691117	−	2.12704i
$953$	21.7533	+	15.8047i	0.704657	+	0.511963i	0.881446	−	0.472286i	$-0.156571\pi$
$953$	21.7533	+	15.8047i	0.704657	+	0.511963i	−0.176789	+	0.984249i	$0.556571\pi$
$954$	−3.24650	−	2.35872i	−0.105109	−	0.0763663i
$955$		0			0
$956$	−63.6958	+	46.2777i	−2.06007	+	1.49673i
$957$	4.72886			0.152862
$958$	−26.5954	+	19.3227i	−0.859257	+	0.624287i
$959$	5.26043	+	16.1900i	0.169868	+	0.522801i
$960$		0			0
$961$	6.25033	−	19.2365i	0.201624	−	0.620534i
$962$	9.39662	+	28.9198i	0.302959	+	0.932412i
$963$	7.61752	+	23.4443i	0.245471	+	0.755482i
$964$	−7.63410	+	23.4953i	−0.245878	+	0.756734i
$965$		0			0
$966$	3.49299	+	10.7503i	0.112385	+	0.345886i
$967$	3.05821	−	2.22192i	0.0983456	−	0.0714522i	−0.537526	−	0.843247i	$-0.680641\pi$
$967$	3.05821	−	2.22192i	0.0983456	−	0.0714522i	0.635871	+	0.771795i	$0.280641\pi$
$968$	75.9059			2.43971
$969$	12.2658	−	8.91159i	0.394033	−	0.286282i
$970$		0			0
$971$	−9.13176	−	6.63461i	−0.293052	−	0.212915i	0.431538	−	0.902095i	$-0.357971\pi$
$971$	−9.13176	−	6.63461i	−0.293052	−	0.212915i	−0.724590	+	0.689180i	$0.757971\pi$
$972$	63.9757	+	46.4811i	2.05202	+	1.49088i
$973$	−2.16675	+	6.66857i	−0.0694628	+	0.213784i
$974$	94.0648			3.01403
$975$		0			0
$976$	7.65930			0.245168
$977$	6.26679	−	19.2872i	0.200492	−	0.617052i	−0.799376	−	0.600831i	$-0.794836\pi$
$977$	6.26679	−	19.2872i	0.200492	−	0.617052i	0.999868	−	0.0162210i	$-0.00516354\pi$
$978$	−19.1132	−	13.8866i	−0.611174	−	0.444044i
$979$	−8.00738	−	5.81770i	−0.255917	−	0.185934i
$980$		0			0
$981$	2.34277	−	1.70213i	0.0747990	−	0.0543447i
$982$	−40.8162			−1.30250
$983$	22.9055	−	16.6418i	0.730570	−	0.530790i	−0.159173	−	0.987251i	$-0.550883\pi$
$983$	22.9055	−	16.6418i	0.730570	−	0.530790i	0.889744	+	0.456460i	$0.150883\pi$
$984$	−19.5865	−	60.2810i	−0.624394	−	1.92169i
$985$		0			0
$986$	−15.5477	+	47.8509i	−0.495139	+	1.52388i
$987$	3.62711	+	11.1631i	0.115452	+	0.355325i
$988$	10.1678	+	31.2933i	0.323481	+	0.995571i
$989$	−2.05851	+	6.33544i	−0.0654568	+	0.201455i
$990$		0			0
$991$	7.37346	+	22.6932i	0.234226	+	0.720873i	0.997223	+	0.0744712i	$0.0237269\pi$
$991$	7.37346	+	22.6932i	0.234226	+	0.720873i	−0.762997	+	0.646402i	$0.776273\pi$
$992$	86.7892	−	63.0560i	2.75556	−	2.00203i
$993$	−0.984859			−0.0312536
$994$	−12.9987	+	9.44413i	−0.412295	+	0.299550i
$995$		0			0
$996$	−7.44117	−	5.40632i	−0.235782	−	0.171306i
$997$	−11.0609	−	8.03620i	−0.350301	−	0.254509i	0.398694	−	0.917084i	$-0.369464\pi$
$997$	−11.0609	−	8.03620i	−0.350301	−	0.254509i	−0.748996	+	0.662575i	$0.769464\pi$
$998$	28.9701	−	89.1607i	0.917031	−	2.82233i
$999$	35.5982			1.12628

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.d.q.501.1		16
5.2	odd	4		625.2.e.j.124.1		32
5.3	odd	4		625.2.e.j.124.8		32
5.4	even	2		625.2.d.m.501.4		16
25.2	odd	20		625.2.e.k.249.1		32
25.3	odd	20		625.2.e.k.374.1		32
25.4	even	10		625.2.d.n.251.1		16
25.6	even	5	inner	625.2.d.q.126.1		16
25.8	odd	20		625.2.e.j.499.1		32
25.9	even	10		625.2.a.g.1.8	yes	8
25.11	even	5		625.2.d.p.376.4		16
25.12	odd	20		625.2.b.d.624.1		16
25.13	odd	20		625.2.b.d.624.16		16
25.14	even	10		625.2.d.n.376.1		16
25.16	even	5		625.2.a.e.1.1	✓	8
25.17	odd	20		625.2.e.j.499.8		32
25.19	even	10		625.2.d.m.126.4		16
25.21	even	5		625.2.d.p.251.4		16
25.22	odd	20		625.2.e.k.374.8		32
25.23	odd	20		625.2.e.k.249.8		32
75.41	odd	10		5625.2.a.be.1.8		8
75.59	odd	10		5625.2.a.s.1.1		8
100.59	odd	10		10000.2.a.be.1.4		8
100.91	odd	10		10000.2.a.bn.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
625.2.a.e.1.1	✓	8	25.16	even	5
625.2.a.g.1.8	yes	8	25.9	even	10
625.2.b.d.624.1		16	25.12	odd	20
625.2.b.d.624.16		16	25.13	odd	20
625.2.d.m.126.4		16	25.19	even	10
625.2.d.m.501.4		16	5.4	even	2
625.2.d.n.251.1		16	25.4	even	10
625.2.d.n.376.1		16	25.14	even	10
625.2.d.p.251.4		16	25.21	even	5
625.2.d.p.376.4		16	25.11	even	5
625.2.d.q.126.1		16	25.6	even	5	inner
625.2.d.q.501.1		16	1.1	even	1	trivial
625.2.e.j.124.1		32	5.2	odd	4
625.2.e.j.124.8		32	5.3	odd	4
625.2.e.j.499.1		32	25.8	odd	20
625.2.e.j.499.8		32	25.17	odd	20
625.2.e.k.249.1		32	25.2	odd	20
625.2.e.k.249.8		32	25.23	odd	20
625.2.e.k.374.1		32	25.3	odd	20
625.2.e.k.374.8		32	25.22	odd	20
5625.2.a.s.1.1		8	75.59	odd	10
5625.2.a.be.1.8		8	75.41	odd	10
10000.2.a.be.1.4		8	100.59	odd	10
10000.2.a.bn.1.5		8	100.91	odd	10

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:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	625.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.823534 + 2.53458i) q^{2} +(0.614111 + 0.446178i) q^{3} +(-4.12784 - 2.99905i) q^{4} +(-1.63661 + 1.18907i) q^{6} +2.04213 q^{7} +(6.68866 - 4.85960i) q^{8} +(-0.748993 - 2.30516i) q^{9} +O(q^{10})\)	\(q+(-0.823534 + 2.53458i) q^{2} +(0.614111 + 0.446178i) q^{3} +(-4.12784 - 2.99905i) q^{4} +(-1.63661 + 1.18907i) q^{6} +2.04213 q^{7} +(6.68866 - 4.85960i) q^{8} +(-0.748993 - 2.30516i) q^{9} +(0.416762 - 1.28266i) q^{11} +(-1.19684 - 3.68350i) q^{12} +(-0.407790 - 1.25505i) q^{13} +(-1.68176 + 5.17593i) q^{14} +(3.65530 + 11.2498i) q^{16} +(3.30659 - 2.40238i) q^{17} +6.45944 q^{18} +(3.95350 - 2.87239i) q^{19} +(1.25409 + 0.911152i) q^{21} +(2.90779 + 2.11263i) q^{22} +(0.845525 - 2.60226i) q^{23} +6.27582 q^{24} +3.51685 q^{26} +(1.27226 - 3.91560i) q^{27} +(-8.42958 - 6.12445i) q^{28} +(3.73696 + 2.71506i) q^{29} +(-5.79035 + 4.20694i) q^{31} -14.9886 q^{32} +(0.828234 - 0.601747i) q^{33} +(3.36593 + 10.3593i) q^{34} +(-3.82158 + 11.7616i) q^{36} +(2.67188 + 8.22321i) q^{37} +(4.02445 + 12.3860i) q^{38} +(0.309547 - 0.952686i) q^{39} +(-3.12094 - 9.60527i) q^{41} +(-3.34217 + 2.42823i) q^{42} -2.43460 q^{43} +(-5.56710 + 4.04474i) q^{44} +(5.89930 + 4.28610i) q^{46} +(6.12581 + 4.45066i) q^{47} +(-2.77467 + 8.53956i) q^{48} -2.82971 q^{49} +3.10250 q^{51} +(-2.08067 + 6.40363i) q^{52} +(-0.502597 - 0.365158i) q^{53} +(8.87665 + 6.44926i) q^{54} +(13.6591 - 9.92393i) q^{56} +3.70948 q^{57} +(-9.95905 + 7.23568i) q^{58} +(-3.50462 - 10.7861i) q^{59} +(0.200093 - 0.615822i) q^{61} +(-5.89425 - 18.1407i) q^{62} +(-1.52954 - 4.70744i) q^{63} +(5.03301 - 15.4900i) q^{64} +(0.843096 + 2.59478i) q^{66} +(8.84972 - 6.42970i) q^{67} -20.8539 q^{68} +(1.68031 - 1.22082i) q^{69} +(2.38846 + 1.73532i) q^{71} +(-16.2119 - 11.7787i) q^{72} +(-4.18378 + 12.8763i) q^{73} -23.0428 q^{74} -24.9339 q^{76} +(0.851083 - 2.61936i) q^{77} +(2.15974 + 1.56914i) q^{78} +(-1.52847 - 1.11050i) q^{79} +(-3.35431 + 2.43705i) q^{81} +26.9155 q^{82} +(1.92126 - 1.39588i) q^{83} +(-2.44410 - 7.52218i) q^{84} +(2.00497 - 6.17067i) q^{86} +(1.08351 + 3.33470i) q^{87} +(-3.44564 - 10.6046i) q^{88} +(2.26782 - 6.97963i) q^{89} +(-0.832761 - 2.56297i) q^{91} +(-11.2945 + 8.20593i) q^{92} -5.43296 q^{93} +(-16.3254 + 11.8611i) q^{94} +(-9.20465 - 6.68757i) q^{96} +(4.69161 + 3.40865i) q^{97} +(2.33036 - 7.17212i) q^{98} -3.26890 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 5 q^{2} - 3 q^{4} + 7 q^{6} - 20 q^{7} + 5 q^{8} - 12 q^{9}+O(q^{10}) \) 16 * q + 5 * q^2 - 3 * q^4 + 7 * q^6 - 20 * q^7 + 5 * q^8 - 12 * q^9	\( 16 q + 5 q^{2} - 3 q^{4} + 7 q^{6} - 20 q^{7} + 5 q^{8} - 12 q^{9} - 3 q^{11} - 15 q^{12} + 5 q^{13} - q^{14} + q^{16} + 25 q^{17} + 10 q^{18} + 10 q^{19} + 7 q^{21} + 35 q^{22} + 15 q^{23} + 10 q^{24} + 22 q^{26} - 35 q^{28} - 8 q^{31} - 60 q^{32} - 6 q^{34} + q^{36} + 5 q^{37} + 35 q^{38} + q^{39} - 8 q^{41} + 10 q^{42} - 31 q^{44} + 42 q^{46} + 5 q^{47} + 25 q^{48} - 8 q^{49} - 28 q^{51} - 15 q^{52} + 10 q^{53} + 50 q^{54} + 35 q^{56} + 20 q^{57} - 35 q^{58} - 15 q^{59} + 17 q^{61} - 5 q^{62} - 10 q^{63} + 37 q^{64} + 44 q^{66} + 10 q^{67} - 80 q^{68} - 9 q^{69} - 13 q^{71} - 20 q^{72} - 40 q^{73} - 36 q^{74} - 20 q^{76} + 45 q^{77} - 5 q^{78} - 55 q^{79} - 19 q^{81} + 90 q^{82} + 15 q^{83} + 59 q^{84} + 7 q^{86} + 60 q^{87} - 40 q^{88} - 28 q^{91} - 45 q^{92} + 80 q^{93} + 4 q^{94} - 43 q^{96} - 40 q^{97} - 45 q^{98} - 44 q^{99}+O(q^{100}) \) 16 * q + 5 * q^2 - 3 * q^4 + 7 * q^6 - 20 * q^7 + 5 * q^8 - 12 * q^9 - 3 * q^11 - 15 * q^12 + 5 * q^13 - q^14 + q^16 + 25 * q^17 + 10 * q^18 + 10 * q^19 + 7 * q^21 + 35 * q^22 + 15 * q^23 + 10 * q^24 + 22 * q^26 - 35 * q^28 - 8 * q^31 - 60 * q^32 - 6 * q^34 + q^36 + 5 * q^37 + 35 * q^38 + q^39 - 8 * q^41 + 10 * q^42 - 31 * q^44 + 42 * q^46 + 5 * q^47 + 25 * q^48 - 8 * q^49 - 28 * q^51 - 15 * q^52 + 10 * q^53 + 50 * q^54 + 35 * q^56 + 20 * q^57 - 35 * q^58 - 15 * q^59 + 17 * q^61 - 5 * q^62 - 10 * q^63 + 37 * q^64 + 44 * q^66 + 10 * q^67 - 80 * q^68 - 9 * q^69 - 13 * q^71 - 20 * q^72 - 40 * q^73 - 36 * q^74 - 20 * q^76 + 45 * q^77 - 5 * q^78 - 55 * q^79 - 19 * q^81 + 90 * q^82 + 15 * q^83 + 59 * q^84 + 7 * q^86 + 60 * q^87 - 40 * q^88 - 28 * q^91 - 45 * q^92 + 80 * q^93 + 4 * q^94 - 43 * q^96 - 40 * q^97 - 45 * q^98 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more