LMFDB - Embedded newform 825.2.m.a.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(16,825)]

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, 2, 4]))

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

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

chi := DirichletCharacter("825.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.m (of order $5$, degree $4$, 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:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			361.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	825.361
Dual form			825.2.m.a.16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 1.53884i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.500000 + 0.363271i) q^{4} +(-1.80902 - 1.31433i) q^{5} +(-1.30902 + 0.951057i) q^{6} +(2.42705 + 1.76336i) q^{7} +(-1.80902 - 1.31433i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 1.53884i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.500000 + 0.363271i) q^{4} +(-1.80902 - 1.31433i) q^{5} +(-1.30902 + 0.951057i) q^{6} +(2.42705 + 1.76336i) q^{7} +(-1.80902 - 1.31433i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-1.11803 + 3.44095i) q^{10} +(-3.30902 - 0.224514i) q^{11} +(0.500000 + 0.363271i) q^{12} +(-2.61803 + 1.90211i) q^{13} +(1.50000 - 4.61653i) q^{14} +(-0.690983 + 2.12663i) q^{15} +(-1.50000 + 4.61653i) q^{16} +(0.618034 - 0.449028i) q^{17} +(1.30902 + 0.951057i) q^{18} +(1.11803 + 0.812299i) q^{19} +1.38197 q^{20} +(0.927051 - 2.85317i) q^{21} +(1.30902 + 5.20431i) q^{22} +(-1.50000 + 1.08981i) q^{23} +(-0.690983 + 2.12663i) q^{24} +(1.54508 + 4.75528i) q^{25} +(4.23607 + 3.07768i) q^{26} +(0.809017 + 0.587785i) q^{27} -1.85410 q^{28} +(-4.30902 + 3.13068i) q^{29} +3.61803 q^{30} -10.2361 q^{31} +3.38197 q^{32} +(0.809017 + 3.21644i) q^{33} +(-1.00000 - 0.726543i) q^{34} +(-2.07295 - 6.37988i) q^{35} +(0.190983 - 0.587785i) q^{36} +(-2.73607 - 8.42075i) q^{37} +(0.690983 - 2.12663i) q^{38} +(2.61803 + 1.90211i) q^{39} +(1.54508 + 4.75528i) q^{40} +0.0901699 q^{41} -4.85410 q^{42} +6.00000 q^{43} +(1.73607 - 1.08981i) q^{44} +2.23607 q^{45} +(2.42705 + 1.76336i) q^{46} +(3.11803 + 9.59632i) q^{47} +4.85410 q^{48} +(0.618034 + 1.90211i) q^{49} +(6.54508 - 4.75528i) q^{50} +(-0.618034 - 0.449028i) q^{51} +(0.618034 - 1.90211i) q^{52} +(5.47214 + 3.97574i) q^{53} +(0.500000 - 1.53884i) q^{54} +(5.69098 + 4.75528i) q^{55} +(-2.07295 - 6.37988i) q^{56} +(0.427051 - 1.31433i) q^{57} +(6.97214 + 5.06555i) q^{58} +(-1.70820 - 5.25731i) q^{59} +(-0.427051 - 1.31433i) q^{60} +(-7.04508 - 5.11855i) q^{61} +(5.11803 + 15.7517i) q^{62} -3.00000 q^{63} +(1.30902 + 4.02874i) q^{64} +7.23607 q^{65} +(4.54508 - 2.85317i) q^{66} +(-0.927051 - 2.85317i) q^{67} +(-0.145898 + 0.449028i) q^{68} +(1.50000 + 1.08981i) q^{69} +(-8.78115 + 6.37988i) q^{70} -9.38197 q^{71} +2.23607 q^{72} +8.56231 q^{73} +(-11.5902 + 8.42075i) q^{74} +(4.04508 - 2.93893i) q^{75} -0.854102 q^{76} +(-7.63525 - 6.37988i) q^{77} +(1.61803 - 4.97980i) q^{78} +(4.04508 + 2.93893i) q^{79} +(8.78115 - 6.37988i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-0.0450850 - 0.138757i) q^{82} +(4.35410 - 3.16344i) q^{83} +(0.572949 + 1.76336i) q^{84} -1.70820 q^{85} +(-3.00000 - 9.23305i) q^{86} +(4.30902 + 3.13068i) q^{87} +(5.69098 + 4.75528i) q^{88} +(1.80902 - 1.31433i) q^{89} +(-1.11803 - 3.44095i) q^{90} -9.70820 q^{91} +(0.354102 - 1.08981i) q^{92} +(3.16312 + 9.73508i) q^{93} +(13.2082 - 9.59632i) q^{94} +(-0.954915 - 2.93893i) q^{95} +(-1.04508 - 3.21644i) q^{96} +(-2.04508 - 1.48584i) q^{97} +(2.61803 - 1.90211i) q^{98} +(2.80902 - 1.76336i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + q^{3} - 2 q^{4} - 5 q^{5} - 3 q^{6} + 3 q^{7} - 5 q^{8} - q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + q^3 - 2 * q^4 - 5 * q^5 - 3 * q^6 + 3 * q^7 - 5 * q^8 - q^9	\( 4 q - 2 q^{2} + q^{3} - 2 q^{4} - 5 q^{5} - 3 q^{6} + 3 q^{7} - 5 q^{8} - q^{9} - 11 q^{11} + 2 q^{12} - 6 q^{13} + 6 q^{14} - 5 q^{15} - 6 q^{16} - 2 q^{17} + 3 q^{18} + 10 q^{20} - 3 q^{21} + 3 q^{22} - 6 q^{23} - 5 q^{24} - 5 q^{25} + 8 q^{26} + q^{27} + 6 q^{28} - 15 q^{29} + 10 q^{30} - 32 q^{31} + 18 q^{32} + q^{33} - 4 q^{34} - 15 q^{35} + 3 q^{36} - 2 q^{37} + 5 q^{38} + 6 q^{39} - 5 q^{40} - 22 q^{41} - 6 q^{42} + 24 q^{43} - 2 q^{44} + 3 q^{46} + 8 q^{47} + 6 q^{48} - 2 q^{49} + 15 q^{50} + 2 q^{51} - 2 q^{52} + 4 q^{53} + 2 q^{54} + 25 q^{55} - 15 q^{56} - 5 q^{57} + 10 q^{58} + 20 q^{59} + 5 q^{60} - 17 q^{61} + 16 q^{62} - 12 q^{63} + 3 q^{64} + 20 q^{65} + 7 q^{66} + 3 q^{67} - 14 q^{68} + 6 q^{69} - 15 q^{70} - 42 q^{71} - 6 q^{73} - 24 q^{74} + 5 q^{75} + 10 q^{76} + 3 q^{77} + 2 q^{78} + 5 q^{79} + 15 q^{80} - q^{81} + 11 q^{82} + 4 q^{83} + 9 q^{84} + 20 q^{85} - 12 q^{86} + 15 q^{87} + 25 q^{88} + 5 q^{89} - 12 q^{91} - 12 q^{92} - 3 q^{93} + 26 q^{94} - 15 q^{95} + 7 q^{96} + 3 q^{97} + 6 q^{98} + 9 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + q^3 - 2 * q^4 - 5 * q^5 - 3 * q^6 + 3 * q^7 - 5 * q^8 - q^9 - 11 * q^11 + 2 * q^12 - 6 * q^13 + 6 * q^14 - 5 * q^15 - 6 * q^16 - 2 * q^17 + 3 * q^18 + 10 * q^20 - 3 * q^21 + 3 * q^22 - 6 * q^23 - 5 * q^24 - 5 * q^25 + 8 * q^26 + q^27 + 6 * q^28 - 15 * q^29 + 10 * q^30 - 32 * q^31 + 18 * q^32 + q^33 - 4 * q^34 - 15 * q^35 + 3 * q^36 - 2 * q^37 + 5 * q^38 + 6 * q^39 - 5 * q^40 - 22 * q^41 - 6 * q^42 + 24 * q^43 - 2 * q^44 + 3 * q^46 + 8 * q^47 + 6 * q^48 - 2 * q^49 + 15 * q^50 + 2 * q^51 - 2 * q^52 + 4 * q^53 + 2 * q^54 + 25 * q^55 - 15 * q^56 - 5 * q^57 + 10 * q^58 + 20 * q^59 + 5 * q^60 - 17 * q^61 + 16 * q^62 - 12 * q^63 + 3 * q^64 + 20 * q^65 + 7 * q^66 + 3 * q^67 - 14 * q^68 + 6 * q^69 - 15 * q^70 - 42 * q^71 - 6 * q^73 - 24 * q^74 + 5 * q^75 + 10 * q^76 + 3 * q^77 + 2 * q^78 + 5 * q^79 + 15 * q^80 - q^81 + 11 * q^82 + 4 * q^83 + 9 * q^84 + 20 * q^85 - 12 * q^86 + 15 * q^87 + 25 * q^88 + 5 * q^89 - 12 * q^91 - 12 * q^92 - 3 * q^93 + 26 * q^94 - 15 * q^95 + 7 * q^96 + 3 * q^97 + 6 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.500000	−	1.53884i	−0.353553	−	1.08813i	−0.956844	−	0.290604i	$-0.906144\pi$
$2$	−0.500000	−	1.53884i	−0.353553	−	1.08813i	0.603290	−	0.797522i	$-0.293856\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	−0.500000	+	0.363271i	−0.250000	+	0.181636i
$5$	−1.80902	−	1.31433i	−0.809017	−	0.587785i
$5$	−1.80902	−	1.31433i	−0.809017	−	0.587785i
$6$	−1.30902	+	0.951057i	−0.534404	+	0.388267i
$7$	2.42705	+	1.76336i	0.917339	+	0.666486i	0.942860	−	0.333188i	$-0.108125\pi$
$7$	2.42705	+	1.76336i	0.917339	+	0.666486i	−0.0255212	+	0.999674i	$0.508125\pi$
$8$	−1.80902	−	1.31433i	−0.639584	−	0.464685i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−1.11803	+	3.44095i	−0.353553	+	1.08813i
$11$	−3.30902	−	0.224514i	−0.997706	−	0.0676935i
$11$	−3.30902	−	0.224514i	−0.997706	−	0.0676935i
$12$	0.500000	+	0.363271i	0.144338	+	0.104867i
$13$	−2.61803	+	1.90211i	−0.726112	+	0.527551i	−0.888331	−	0.459204i	$-0.848135\pi$
$13$	−2.61803	+	1.90211i	−0.726112	+	0.527551i	0.162219	+	0.986755i	$0.448135\pi$
$14$	1.50000	−	4.61653i	0.400892	−	1.23382i
$15$	−0.690983	+	2.12663i	−0.178411	+	0.549093i
$16$	−1.50000	+	4.61653i	−0.375000	+	1.15413i
$17$	0.618034	−	0.449028i	0.149895	−	0.108905i	−0.510310	−	0.859991i	$-0.670469\pi$
$17$	0.618034	−	0.449028i	0.149895	−	0.108905i	0.660205	+	0.751085i	$0.270469\pi$
$18$	1.30902	+	0.951057i	0.308538	+	0.224166i
$19$	1.11803	+	0.812299i	0.256495	+	0.186354i	0.708600	−	0.705610i	$-0.249327\pi$
$19$	1.11803	+	0.812299i	0.256495	+	0.186354i	−0.452106	+	0.891964i	$0.649327\pi$
$20$	1.38197			0.309017
$21$	0.927051	−	2.85317i	0.202299	−	0.622613i
$22$	1.30902	+	5.20431i	0.279083	+	1.10956i
$23$	−1.50000	+	1.08981i	−0.312772	+	0.227242i	−0.733085	−	0.680137i	$-0.761920\pi$
$23$	−1.50000	+	1.08981i	−0.312772	+	0.227242i	0.420313	+	0.907379i	$0.361920\pi$
$24$	−0.690983	+	2.12663i	−0.141046	+	0.434096i
$25$	1.54508	+	4.75528i	0.309017	+	0.951057i
$26$	4.23607	+	3.07768i	0.830761	+	0.603583i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	−1.85410			−0.350392
$29$	−4.30902	+	3.13068i	−0.800164	+	0.581353i	−0.910962	−	0.412490i	$-0.864659\pi$
$29$	−4.30902	+	3.13068i	−0.800164	+	0.581353i	0.110798	+	0.993843i	$0.464659\pi$
$30$	3.61803			0.660560
$31$	−10.2361			−1.83845			−0.919226	−	0.393730i	$-0.871184\pi$
$31$	−10.2361			−1.83845			−0.919226	+	0.393730i	$0.871184\pi$
$32$	3.38197			0.597853
$33$	0.809017	+	3.21644i	0.140832	+	0.559910i
$34$	−1.00000	−	0.726543i	−0.171499	−	0.124601i
$35$	−2.07295	−	6.37988i	−0.350392	−	1.07840i
$36$	0.190983	−	0.587785i	0.0318305	−	0.0979642i
$37$	−2.73607	−	8.42075i	−0.449807	−	1.38436i	−0.877125	−	0.480262i	$-0.840542\pi$
$37$	−2.73607	−	8.42075i	−0.449807	−	1.38436i	0.427318	−	0.904101i	$-0.359458\pi$
$38$	0.690983	−	2.12663i	0.112092	−	0.344984i
$39$	2.61803	+	1.90211i	0.419221	+	0.304582i
$40$	1.54508	+	4.75528i	0.244299	+	0.751876i
$41$	0.0901699			0.0140822			0.00704109	−	0.999975i	$-0.497759\pi$
$41$	0.0901699			0.0140822			0.00704109	+	0.999975i	$0.497759\pi$
$42$	−4.85410			−0.749004
$43$	6.00000			0.914991			0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000			0.914991			0.457496	+	0.889212i	$0.348747\pi$
$44$	1.73607	−	1.08981i	0.261722	−	0.164296i
$45$	2.23607			0.333333
$46$	2.42705	+	1.76336i	0.357849	+	0.259993i
$47$	3.11803	+	9.59632i	0.454812	+	1.39977i	0.871356	+	0.490652i	$0.163241\pi$
$47$	3.11803	+	9.59632i	0.454812	+	1.39977i	−0.416544	+	0.909116i	$0.636759\pi$
$48$	4.85410			0.700629
$49$	0.618034	+	1.90211i	0.0882906	+	0.271730i
$50$	6.54508	−	4.75528i	0.925615	−	0.672499i
$51$	−0.618034	−	0.449028i	−0.0865421	−	0.0628765i
$52$	0.618034	−	1.90211i	0.0857059	−	0.263776i
$53$	5.47214	+	3.97574i	0.751656	+	0.546110i	0.896340	−	0.443368i	$-0.146217\pi$
$53$	5.47214	+	3.97574i	0.751656	+	0.546110i	−0.144684	+	0.989478i	$0.546217\pi$
$54$	0.500000	−	1.53884i	0.0680414	−	0.209410i
$55$	5.69098	+	4.75528i	0.767372	+	0.641202i
$56$	−2.07295	−	6.37988i	−0.277009	−	0.852547i
$57$	0.427051	−	1.31433i	0.0565643	−	0.174087i
$58$	6.97214	+	5.06555i	0.915486	+	0.665140i
$59$	−1.70820	−	5.25731i	−0.222389	−	0.684444i	−0.998546	−	0.0539038i	$-0.982834\pi$
$59$	−1.70820	−	5.25731i	−0.222389	−	0.684444i	0.776157	−	0.630540i	$-0.217166\pi$
$60$	−0.427051	−	1.31433i	−0.0551320	−	0.169679i
$61$	−7.04508	−	5.11855i	−0.902031	−	0.655364i	0.0369561	−	0.999317i	$-0.488234\pi$
$61$	−7.04508	−	5.11855i	−0.902031	−	0.655364i	−0.938987	+	0.343953i	$0.888234\pi$
$62$	5.11803	+	15.7517i	0.649991	+	2.00047i
$63$	−3.00000			−0.377964
$64$	1.30902	+	4.02874i	0.163627	+	0.503593i
$65$	7.23607			0.897524
$66$	4.54508	−	2.85317i	0.559461	−	0.351201i
$67$	−0.927051	−	2.85317i	−0.113257	−	0.348570i	0.878322	−	0.478069i	$-0.158663\pi$
$67$	−0.927051	−	2.85317i	−0.113257	−	0.348570i	−0.991580	+	0.129499i	$0.958663\pi$
$68$	−0.145898	+	0.449028i	−0.0176927	+	0.0544526i
$69$	1.50000	+	1.08981i	0.180579	+	0.131198i
$70$	−8.78115	+	6.37988i	−1.04955	+	0.762542i
$71$	−9.38197			−1.11343			−0.556717	−	0.830702i	$-0.687939\pi$
$71$	−9.38197			−1.11343			−0.556717	+	0.830702i	$0.687939\pi$
$72$	2.23607			0.263523
$73$	8.56231			1.00214			0.501071	−	0.865406i	$-0.332940\pi$
$73$	8.56231			1.00214			0.501071	+	0.865406i	$0.332940\pi$
$74$	−11.5902	+	8.42075i	−1.34733	+	0.978892i
$75$	4.04508	−	2.93893i	0.467086	−	0.339358i
$76$	−0.854102			−0.0979722
$77$	−7.63525	−	6.37988i	−0.870118	−	0.727055i
$78$	1.61803	−	4.97980i	0.183206	−	0.563851i
$79$	4.04508	+	2.93893i	0.455108	+	0.330655i	0.791609	−	0.611028i	$-0.209244\pi$
$79$	4.04508	+	2.93893i	0.455108	+	0.330655i	−0.336501	+	0.941683i	$0.609244\pi$
$80$	8.78115	−	6.37988i	0.981763	−	0.713292i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−0.0450850	−	0.138757i	−0.00497880	−	0.0153232i
$83$	4.35410	−	3.16344i	0.477925	−	0.347233i	−0.322597	−	0.946536i	$-0.604556\pi$
$83$	4.35410	−	3.16344i	0.477925	−	0.347233i	0.800522	+	0.599304i	$0.204556\pi$
$84$	0.572949	+	1.76336i	0.0625139	+	0.192398i
$85$	−1.70820			−0.185281
$86$	−3.00000	−	9.23305i	−0.323498	−	0.995625i
$87$	4.30902	+	3.13068i	0.461975	+	0.335645i
$88$	5.69098	+	4.75528i	0.606661	+	0.506915i
$89$	1.80902	−	1.31433i	0.191755	−	0.139318i	−0.487765	−	0.872975i	$-0.662188\pi$
$89$	1.80902	−	1.31433i	0.191755	−	0.139318i	0.679521	+	0.733656i	$0.262188\pi$
$90$	−1.11803	−	3.44095i	−0.117851	−	0.362708i
$91$	−9.70820			−1.01770
$92$	0.354102	−	1.08981i	0.0369177	−	0.113621i
$93$	3.16312	+	9.73508i	0.328000	+	1.00948i
$94$	13.2082	−	9.59632i	1.36232	−	0.989785i
$95$	−0.954915	−	2.93893i	−0.0979722	−	0.301527i
$96$	−1.04508	−	3.21644i	−0.106664	−	0.328277i
$97$	−2.04508	−	1.48584i	−0.207647	−	0.150864i	0.479101	−	0.877760i	$-0.340963\pi$
$97$	−2.04508	−	1.48584i	−0.207647	−	0.150864i	−0.686748	+	0.726895i	$0.740963\pi$
$98$	2.61803	−	1.90211i	0.264461	−	0.192142i
$99$	2.80902	−	1.76336i	0.282317	−	0.177224i
$100$	−2.50000	−	1.81636i	−0.250000	−	0.181636i
$101$	0.781153	−	2.40414i	0.0777276	−	0.239221i	−0.904641	−	0.426174i	$-0.859861\pi$
$101$	0.781153	−	2.40414i	0.0777276	−	0.239221i	0.982369	+	0.186953i	$0.0598612\pi$
$102$	−0.381966	+	1.17557i	−0.0378203	+	0.116399i
$103$	1.42705	−	1.03681i	0.140612	−	0.102160i	−0.515256	−	0.857036i	$-0.672303\pi$
$103$	1.42705	−	1.03681i	0.140612	−	0.102160i	0.655867	+	0.754876i	$0.272303\pi$
$104$	7.23607			0.709555
$105$	−5.42705	+	3.94298i	−0.529626	+	0.384796i
$106$	3.38197	−	10.4086i	0.328486	−	1.01097i
$107$	−13.5902	+	9.87384i	−1.31381	+	0.954540i	−0.313824	+	0.949481i	$0.601610\pi$
$107$	−13.5902	+	9.87384i	−1.31381	+	0.954540i	−0.999987	+	0.00505866i	$0.998390\pi$
$108$	−0.618034			−0.0594703
$109$	−9.47214	−	6.88191i	−0.907266	−	0.659167i	0.0330559	−	0.999454i	$-0.489476\pi$
$109$	−9.47214	−	6.88191i	−0.907266	−	0.659167i	−0.940322	+	0.340286i	$0.889476\pi$
$110$	4.47214	−	11.1352i	0.426401	−	1.06170i
$111$	−7.16312	+	5.20431i	−0.679893	+	0.493971i
$112$	−11.7812	+	8.55951i	−1.11321	+	0.808798i
$113$	−10.1803			−0.957686			−0.478843	−	0.877901i	$-0.658944\pi$
$113$	−10.1803			−0.957686			−0.478843	+	0.877901i	$0.658944\pi$
$114$	−2.23607			−0.209427
$115$	4.14590			0.386607
$116$	1.01722	−	3.13068i	0.0944466	−	0.290677i
$117$	1.00000	−	3.07768i	0.0924500	−	0.284532i
$118$	−7.23607	+	5.25731i	−0.666134	+	0.483975i
$119$	2.29180			0.210089
$120$	4.04508	−	2.93893i	0.369264	−	0.268286i
$121$	10.8992	+	1.48584i	0.990835	+	0.135076i
$122$	−4.35410	+	13.4005i	−0.394202	+	1.21323i
$123$	−0.0278640	−	0.0857567i	−0.00251242	−	0.00773242i
$124$	5.11803	−	3.71847i	0.459613	−	0.333928i
$125$	3.45492	−	10.6331i	0.309017	−	0.951057i
$126$	1.50000	+	4.61653i	0.133631	+	0.411273i
$127$	−8.42705	−	6.12261i	−0.747780	−	0.543294i	0.147358	−	0.989083i	$-0.452923\pi$
$127$	−8.42705	−	6.12261i	−0.747780	−	0.543294i	−0.895138	+	0.445789i	$0.852923\pi$
$128$	11.0172	−	8.00448i	0.973794	−	0.707503i
$129$	−1.85410	−	5.70634i	−0.163245	−	0.502415i
$130$	−3.61803	−	11.1352i	−0.317323	−	0.976618i
$131$	−0.600813	−	1.84911i	−0.0524933	−	0.161558i	0.921373	−	0.388679i	$-0.127069\pi$
$131$	−0.600813	−	1.84911i	−0.0524933	−	0.161558i	−0.973866	+	0.227121i	$0.927069\pi$
$132$	−1.57295	−	1.31433i	−0.136908	−	0.114398i
$133$	1.28115	+	3.94298i	0.111090	+	0.341900i
$134$	−3.92705	+	2.85317i	−0.339246	+	0.246476i
$135$	−0.690983	−	2.12663i	−0.0594703	−	0.183031i
$136$	−1.70820			−0.146477
$137$	−4.64590	+	14.2986i	−0.396926	+	1.22161i	0.530526	+	0.847669i	$0.321995\pi$
$137$	−4.64590	+	14.2986i	−0.396926	+	1.22161i	−0.927452	+	0.373943i	$0.878005\pi$
$138$	0.927051	−	2.85317i	0.0789158	−	0.242878i
$139$	−13.9443			−1.18274			−0.591369	−	0.806401i	$-0.701412\pi$
$139$	−13.9443			−1.18274			−0.591369	+	0.806401i	$0.701412\pi$
$140$	3.35410	+	2.43690i	0.283473	+	0.205955i
$141$	8.16312	−	5.93085i	0.687459	−	0.499468i
$142$	4.69098	+	14.4374i	0.393659	+	1.21156i
$143$	9.09017	−	5.70634i	0.760158	−	0.477188i
$144$	−1.50000	−	4.61653i	−0.125000	−	0.384710i
$145$	11.9098			0.989058
$146$	−4.28115	−	13.1760i	−0.354311	−	1.09046i
$147$	1.61803	−	1.17557i	0.133453	−	0.0969594i
$148$	4.42705	+	3.21644i	0.363901	+	0.264390i
$149$	−2.66312	−	8.19624i	−0.218171	−	0.671462i	−0.998913	−	0.0466084i	$-0.985159\pi$
$149$	−2.66312	−	8.19624i	−0.218171	−	0.671462i	0.780742	−	0.624853i	$-0.214841\pi$
$150$	−6.54508	−	4.75528i	−0.534404	−	0.388267i
$151$	−12.2082	+	8.86978i	−0.993490	+	0.721812i	−0.960683	−	0.277649i	$-0.910445\pi$
$151$	−12.2082	+	8.86978i	−0.993490	+	0.721812i	−0.0328070	+	0.999462i	$0.510445\pi$
$152$	−0.954915	−	2.93893i	−0.0774538	−	0.238378i
$153$	−0.236068	+	0.726543i	−0.0190850	+	0.0587375i
$154$	−6.00000	+	14.9394i	−0.483494	+	1.20385i
$155$	18.5172	+	13.4535i	1.48734	+	1.08062i
$156$	−2.00000			−0.160128
$157$	−11.7812	+	8.55951i	−0.940238	+	0.683123i	−0.948478	−	0.316843i	$-0.897377\pi$
$157$	−11.7812	+	8.55951i	−0.940238	+	0.683123i	0.00823967	+	0.999966i	$0.497377\pi$
$158$	2.50000	−	7.69421i	0.198889	−	0.612118i
$159$	2.09017	−	6.43288i	0.165761	−	0.510161i
$160$	−6.11803	−	4.44501i	−0.483673	−	0.351409i
$161$	−5.56231			−0.438371
$162$	−1.61803			−0.127125
$163$	5.30902	−	3.85723i	0.415834	−	0.302121i	−0.360125	−	0.932904i	$-0.617266\pi$
$163$	5.30902	−	3.85723i	0.415834	−	0.302121i	0.775960	+	0.630783i	$0.217266\pi$
$164$	−0.0450850	+	0.0327561i	−0.00352054	+	0.00255783i
$165$	2.76393	−	6.88191i	0.215172	−	0.535756i
$166$	−7.04508	−	5.11855i	−0.546805	−	0.397277i
$167$	6.67376			0.516431			0.258216	−	0.966087i	$-0.416866\pi$
$167$	6.67376			0.516431			0.258216	+	0.966087i	$0.416866\pi$
$168$	−5.42705	+	3.94298i	−0.418706	+	0.304208i
$169$	−0.781153	+	2.40414i	−0.0600887	+	0.184934i
$170$	0.854102	+	2.62866i	0.0655066	+	0.201609i
$171$	−1.38197			−0.105682
$172$	−3.00000	+	2.17963i	−0.228748	+	0.166195i
$173$	−1.07295	+	3.30220i	−0.0815748	+	0.251061i	−0.983523	−	0.180783i	$-0.942137\pi$
$173$	−1.07295	+	3.30220i	−0.0815748	+	0.251061i	0.901948	+	0.431844i	$0.142137\pi$
$174$	2.66312	−	8.19624i	0.201891	−	0.621355i
$175$	−4.63525	+	14.2658i	−0.350392	+	1.07840i
$176$	6.00000	−	14.9394i	0.452267	−	1.12610i
$177$	−4.47214	+	3.24920i	−0.336146	+	0.244225i
$178$	−2.92705	−	2.12663i	−0.219392	−	0.159397i
$179$	−2.17376	−	6.69015i	−0.162475	−	0.500045i	0.836367	−	0.548170i	$-0.184675\pi$
$179$	−2.17376	−	6.69015i	−0.162475	−	0.500045i	−0.998841	+	0.0481249i	$0.984675\pi$
$180$	−1.11803	+	0.812299i	−0.0833333	+	0.0605452i
$181$	−17.3713	+	12.6210i	−1.29120	+	0.938112i	−0.999829	−	0.0184981i	$-0.994112\pi$
$181$	−17.3713	+	12.6210i	−1.29120	+	0.938112i	−0.291371	+	0.956610i	$0.594112\pi$
$182$	4.85410	+	14.9394i	0.359810	+	1.10738i
$183$	−2.69098	+	8.28199i	−0.198923	+	0.612223i
$184$	4.14590			0.305640
$185$	−6.11803	+	18.8294i	−0.449807	+	1.38436i
$186$	13.3992	−	9.73508i	0.982476	−	0.713811i
$187$	−2.14590	+	1.34708i	−0.156924	+	0.0985085i
$188$	−5.04508	−	3.66547i	−0.367951	−	0.267332i
$189$	0.927051	+	2.85317i	0.0674330	+	0.207538i
$190$	−4.04508	+	2.93893i	−0.293461	+	0.213212i
$191$	−0.500000	−	1.53884i	−0.0361787	−	0.111347i	0.931336	−	0.364160i	$-0.118644\pi$
$191$	−0.500000	−	1.53884i	−0.0361787	−	0.111347i	−0.967515	+	0.252814i	$0.918644\pi$
$192$	3.42705	−	2.48990i	0.247326	−	0.179693i
$193$	−5.38197	−	16.5640i	−0.387402	−	1.19230i	−0.934722	−	0.355379i	$-0.884352\pi$
$193$	−5.38197	−	16.5640i	−0.387402	−	1.19230i	0.547320	−	0.836923i	$-0.315648\pi$
$194$	−1.26393	+	3.88998i	−0.0907450	+	0.279284i
$195$	−2.23607	−	6.88191i	−0.160128	−	0.492824i
$196$	−1.00000	−	0.726543i	−0.0714286	−	0.0518959i
$197$	4.39919	−	13.5393i	0.313429	−	0.964636i	−0.662967	−	0.748649i	$-0.730703\pi$
$197$	4.39919	−	13.5393i	0.313429	−	0.964636i	0.976396	−	0.215987i	$-0.0692969\pi$
$198$	−4.11803	−	3.44095i	−0.292656	−	0.244538i
$199$	−9.79837			−0.694588			−0.347294	−	0.937756i	$-0.612899\pi$
$199$	−9.79837			−0.694588			−0.347294	+	0.937756i	$0.612899\pi$
$200$	3.45492	−	10.6331i	0.244299	−	0.751876i
$201$	−2.42705	+	1.76336i	−0.171191	+	0.124378i
$202$	−4.09017			−0.287783
$203$	−15.9787			−1.12149
$204$	0.472136			0.0330561
$205$	−0.163119	−	0.118513i	−0.0113927	−	0.00827730i
$206$	−2.30902	−	1.67760i	−0.160877	−	0.116884i
$207$	0.572949	−	1.76336i	0.0398227	−	0.122562i
$208$	−4.85410	−	14.9394i	−0.336571	−	1.03586i
$209$	−3.51722	−	2.93893i	−0.243291	−	0.203290i
$210$	8.78115	+	6.37988i	0.605957	+	0.440254i
$211$	−3.36475	−	10.3556i	−0.231639	−	0.712910i	−0.997550	−	0.0699636i	$-0.977712\pi$
$211$	−3.36475	−	10.3556i	−0.231639	−	0.712910i	0.765911	−	0.642947i	$-0.222288\pi$
$212$	−4.18034			−0.287107
$213$	2.89919	+	8.92278i	0.198649	+	0.611379i
$214$	21.9894	+	15.9762i	1.50316	+	1.09211i
$215$	−10.8541	−	7.88597i	−0.740244	−	0.537818i
$216$	−0.690983	−	2.12663i	−0.0470154	−	0.144699i
$217$	−24.8435	−	18.0498i	−1.68648	−	1.22530i
$218$	−5.85410	+	18.0171i	−0.396490	+	1.22027i
$219$	−2.64590	−	8.14324i	−0.178793	−	0.550269i
$220$	−4.57295	−	0.310271i	−0.308308	−	0.0209184i
$221$	−0.763932	+	2.35114i	−0.0513876	+	0.158155i
$222$	11.5902	+	8.42075i	0.777881	+	0.565164i
$223$	1.36475	−	4.20025i	0.0913901	−	0.281270i	−0.894906	−	0.446255i	$-0.852758\pi$
$223$	1.36475	−	4.20025i	0.0913901	−	0.281270i	0.986296	+	0.164985i	$0.0527575\pi$
$224$	8.20820	+	5.96361i	0.548434	+	0.398460i
$225$	−4.04508	−	2.93893i	−0.269672	−	0.195928i
$226$	5.09017	+	15.6659i	0.338593	+	1.04208i
$227$	−9.18034			−0.609321			−0.304660	−	0.952461i	$-0.598543\pi$
$227$	−9.18034			−0.609321			−0.304660	+	0.952461i	$0.598543\pi$
$228$	0.263932	+	0.812299i	0.0174793	+	0.0537958i
$229$	20.2254	+	14.6946i	1.33653	+	0.971049i	0.999564	+	0.0295331i	$0.00940206\pi$
$229$	20.2254	+	14.6946i	1.33653	+	0.971049i	0.336970	+	0.941515i	$0.390598\pi$
$230$	−2.07295	−	6.37988i	−0.136686	−	0.420677i
$231$	−3.70820	+	9.23305i	−0.243982	+	0.607490i
$232$	11.9098			0.781919
$233$	−15.7082			−1.02908			−0.514539	−	0.857467i	$-0.672037\pi$
$233$	−15.7082			−1.02908			−0.514539	+	0.857467i	$0.672037\pi$
$234$	−5.23607			−0.342292
$235$	6.97214	−	21.4580i	0.454812	−	1.39977i
$236$	2.76393	+	2.00811i	0.179917	+	0.130717i
$237$	1.54508	−	4.75528i	0.100364	−	0.308889i
$238$	−1.14590	−	3.52671i	−0.0742775	−	0.228603i
$239$	6.01722	−	18.5191i	0.389222	−	1.19790i	−0.544149	−	0.838988i	$-0.683148\pi$
$239$	6.01722	−	18.5191i	0.389222	−	1.19790i	0.933371	−	0.358913i	$-0.116852\pi$
$240$	−8.78115	−	6.37988i	−0.566821	−	0.411820i
$241$	−15.8262	−	11.4984i	−1.01946	−	0.740679i	−0.0532860	−	0.998579i	$-0.516969\pi$
$241$	−15.8262	−	11.4984i	−1.01946	−	0.740679i	−0.966172	+	0.257900i	$0.916969\pi$
$242$	−3.16312	−	17.5150i	−0.203333	−	1.12591i
$243$	−1.00000			−0.0641500
$244$	5.38197			0.344545
$245$	1.38197	−	4.25325i	0.0882906	−	0.271730i
$246$	−0.118034	+	0.0857567i	−0.00752557	+	0.00546765i
$247$	−4.47214			−0.284555
$248$	18.5172	+	13.4535i	1.17584	+	0.854301i
$249$	−4.35410	−	3.16344i	−0.275930	−	0.200475i
$250$	−18.0902			−1.14412
$251$	2.36475	−	7.27794i	0.149261	−	0.459379i	−0.848273	−	0.529559i	$-0.822357\pi$
$251$	2.36475	−	7.27794i	0.149261	−	0.459379i	0.997534	+	0.0701799i	$0.0223573\pi$
$252$	1.50000	−	1.08981i	0.0944911	−	0.0686518i
$253$	5.20820	−	3.26944i	0.327437	−	0.205548i
$254$	−5.20820	+	16.0292i	−0.326792	+	1.00576i
$255$	0.527864	+	1.62460i	0.0330561	+	0.101736i
$256$	−10.9721	−	7.97172i	−0.685758	−	0.498233i
$257$	14.5623	+	10.5801i	0.908372	+	0.659971i	0.940603	−	0.339510i	$-0.110261\pi$
$257$	14.5623	+	10.5801i	0.908372	+	0.659971i	−0.0322308	+	0.999480i	$0.510261\pi$
$258$	−7.85410	+	5.70634i	−0.488975	+	0.355261i
$259$	8.20820	−	25.2623i	0.510033	−	1.56972i
$260$	−3.61803	+	2.62866i	−0.224381	+	0.163022i
$261$	1.64590	−	5.06555i	0.101879	−	0.313550i
$262$	−2.54508	+	1.84911i	−0.157236	+	0.114239i
$263$	10.4721	+	7.60845i	0.645740	+	0.469157i	0.861817	−	0.507219i	$-0.169326\pi$
$263$	10.4721	+	7.60845i	0.645740	+	0.469157i	−0.216078	+	0.976376i	$0.569326\pi$
$264$	2.76393	−	6.88191i	0.170108	−	0.423552i
$265$	−4.67376	−	14.3844i	−0.287107	−	0.883624i
$266$	5.42705	−	3.94298i	0.332754	−	0.241760i
$267$	−1.80902	−	1.31433i	−0.110710	−	0.0804356i
$268$	1.50000	+	1.08981i	0.0916271	+	0.0665710i
$269$	−15.7533	+	11.4454i	−0.960495	+	0.697840i	−0.953266	−	0.302133i	$-0.902301\pi$
$269$	−15.7533	+	11.4454i	−0.960495	+	0.697840i	−0.00722933	+	0.999974i	$0.502301\pi$
$270$	−2.92705	+	2.12663i	−0.178135	+	0.129422i
$271$	3.38197	−	2.45714i	0.205440	−	0.149261i	−0.480308	−	0.877100i	$-0.659475\pi$
$271$	3.38197	−	2.45714i	0.205440	−	0.149261i	0.685748	+	0.727839i	$0.259475\pi$
$272$	1.14590	+	3.52671i	0.0694803	+	0.213838i
$273$	3.00000	+	9.23305i	0.181568	+	0.558810i
$274$	24.3262			1.46960
$275$	−4.04508	−	16.0822i	−0.243928	−	0.969793i
$276$	−1.14590			−0.0689750
$277$	−9.64590	−	29.6870i	−0.579566	−	1.78372i	−0.620077	−	0.784541i	$-0.712899\pi$
$277$	−9.64590	−	29.6870i	−0.579566	−	1.78372i	0.0405109	−	0.999179i	$-0.487101\pi$
$278$	6.97214	+	21.4580i	0.418161	+	1.28697i
$279$	8.28115	−	6.01661i	0.495780	−	0.360205i
$280$	−4.63525	+	14.2658i	−0.277009	+	0.852547i
$281$	−15.6631	+	11.3799i	−0.934383	+	0.678869i	−0.947062	−	0.321050i	$-0.895964\pi$
$281$	−15.6631	+	11.3799i	−0.934383	+	0.678869i	0.0126788	+	0.999920i	$0.495964\pi$
$282$	−13.2082	−	9.59632i	−0.786537	−	0.571453i
$283$	22.1803	+	16.1150i	1.31848	+	0.957935i	0.999950	+	0.0100237i	$0.00319070\pi$
$283$	22.1803	+	16.1150i	1.31848	+	0.957935i	0.318535	+	0.947911i	$0.396809\pi$
$284$	4.69098	−	3.40820i	0.278359	−	0.202239i
$285$	−2.50000	+	1.81636i	−0.148087	+	0.107592i
$286$	−13.3262	−	11.1352i	−0.787997	−	0.658436i
$287$	0.218847	+	0.159002i	0.0129181	+	0.00938557i
$288$	−2.73607	+	1.98787i	−0.161224	+	0.117136i
$289$	−5.07295	+	15.6129i	−0.298409	+	0.918408i
$290$	−5.95492	−	18.3273i	−0.349685	−	1.07622i
$291$	−0.781153	+	2.40414i	−0.0457920	+	0.140933i
$292$	−4.28115	+	3.11044i	−0.250536	+	0.182025i
$293$	−18.6353	−	13.5393i	−1.08868	−	0.790975i	−0.109507	−	0.993986i	$-0.534927\pi$
$293$	−18.6353	−	13.5393i	−1.08868	−	0.790975i	−0.979176	+	0.203011i	$0.934927\pi$
$294$	−2.61803	−	1.90211i	−0.152687	−	0.110933i
$295$	−3.81966	+	11.7557i	−0.222389	+	0.684444i
$296$	−6.11803	+	18.8294i	−0.355604	+	1.09444i
$297$	−2.54508	−	2.12663i	−0.147681	−	0.123399i
$298$	−11.2812	+	8.19624i	−0.653500	+	0.474795i
$299$	1.85410	−	5.70634i	0.107225	−	0.330006i
$300$	−0.954915	+	2.93893i	−0.0551320	+	0.169679i
$301$	14.5623	+	10.5801i	0.839357	+	0.609829i
$302$	19.7533	+	14.3516i	1.13667	+	0.825842i
$303$	−2.52786			−0.145222
$304$	−5.42705	+	3.94298i	−0.311263	+	0.226146i
$305$	6.01722	+	18.5191i	0.344545	+	1.06040i
$306$	1.23607			0.0706613
$307$	17.3262			0.988861			0.494430	−	0.869217i	$-0.335377\pi$
$307$	17.3262			0.988861			0.494430	+	0.869217i	$0.335377\pi$
$308$	6.13525	+	0.416272i	0.349589	+	0.0237193i
$309$	−1.42705	−	1.03681i	−0.0811821	−	0.0589822i
$310$	11.4443	−	35.2218i	0.649991	−	2.00047i
$311$	3.28115	−	10.0984i	0.186057	−	0.572625i	−0.813908	−	0.580994i	$-0.802664\pi$
$311$	3.28115	−	10.0984i	0.186057	−	0.572625i	0.999965	+	0.00836905i	$0.00266398\pi$
$312$	−2.23607	−	6.88191i	−0.126592	−	0.389611i
$313$	−9.00000	+	27.6992i	−0.508710	+	1.56565i	0.285733	+	0.958309i	$0.407763\pi$
$313$	−9.00000	+	27.6992i	−0.508710	+	1.56565i	−0.794443	+	0.607339i	$0.792237\pi$
$314$	19.0623	+	13.8496i	1.07575	+	0.781577i
$315$	5.42705	+	3.94298i	0.305780	+	0.222162i
$316$	−3.09017			−0.173836
$317$	−23.1246			−1.29881			−0.649404	−	0.760444i	$-0.724981\pi$
$317$	−23.1246			−1.29881			−0.649404	+	0.760444i	$0.724981\pi$
$318$	−10.9443			−0.613724
$319$	14.9615	−	9.39205i	0.837683	−	0.525854i
$320$	2.92705	−	9.00854i	0.163627	−	0.503593i
$321$	13.5902	+	9.87384i	0.758529	+	0.551104i
$322$	2.78115	+	8.55951i	0.154988	+	0.477003i
$323$	1.05573			0.0587423
$324$	0.190983	+	0.587785i	0.0106102	+	0.0326547i
$325$	−13.0902	−	9.51057i	−0.726112	−	0.527551i
$326$	−8.59017	−	6.24112i	−0.475766	−	0.345664i
$327$	−3.61803	+	11.1352i	−0.200078	+	0.615776i
$328$	−0.163119	−	0.118513i	−0.00900674	−	0.00654378i
$329$	−9.35410	+	28.7890i	−0.515708	+	1.58719i
$330$	−11.9721	−	0.812299i	−0.659044	−	0.0447156i
$331$	11.0451	+	33.9933i	0.607093	+	1.86844i	0.481709	+	0.876331i	$0.340016\pi$
$331$	11.0451	+	33.9933i	0.607093	+	1.86844i	0.125384	+	0.992108i	$0.459984\pi$
$332$	−1.02786	+	3.16344i	−0.0564114	+	0.173616i
$333$	7.16312	+	5.20431i	0.392537	+	0.285194i
$334$	−3.33688	−	10.2699i	−0.182586	−	0.561942i
$335$	−2.07295	+	6.37988i	−0.113257	+	0.348570i
$336$	11.7812	+	8.55951i	0.642715	+	0.466959i
$337$	6.20820	+	19.1069i	0.338182	+	1.04082i	0.965133	+	0.261760i	$0.0843027\pi$
$337$	6.20820	+	19.1069i	0.338182	+	1.04082i	−0.626951	+	0.779059i	$0.715697\pi$
$338$	4.09017			0.222476
$339$	3.14590	+	9.68208i	0.170862	+	0.525858i
$340$	0.854102	−	0.620541i	0.0463202	−	0.0336536i
$341$	33.8713	+	2.29814i	1.83423	+	0.124451i
$342$	0.690983	+	2.12663i	0.0373641	+	0.114995i
$343$	4.63525	−	14.2658i	0.250280	−	0.770283i
$344$	−10.8541	−	7.88597i	−0.585214	−	0.425183i
$345$	−1.28115	−	3.94298i	−0.0689750	−	0.212283i
$346$	5.61803			0.302027
$347$	25.7426			1.38194			0.690969	−	0.722885i	$-0.257184\pi$
$347$	25.7426			1.38194			0.690969	+	0.722885i	$0.257184\pi$
$348$	−3.29180			−0.176459
$349$	16.4443	−	11.9475i	0.880242	−	0.639533i	−0.0530737	−	0.998591i	$-0.516902\pi$
$349$	16.4443	−	11.9475i	0.880242	−	0.639533i	0.933315	+	0.359058i	$0.116902\pi$
$350$	24.2705			1.29731
$351$	−3.23607			−0.172729
$352$	−11.1910	−	0.759299i	−0.596481	−	0.0404708i
$353$	6.36475	−	19.5887i	0.338761	−	1.04260i	−0.626078	−	0.779760i	$-0.715341\pi$
$353$	6.36475	−	19.5887i	0.338761	−	1.04260i	0.964840	−	0.262840i	$-0.0846590\pi$
$354$	7.23607	+	5.25731i	0.384593	+	0.279423i
$355$	16.9721	+	12.3310i	0.900787	+	0.654460i
$356$	−0.427051	+	1.31433i	−0.0226337	+	0.0696592i
$357$	−0.708204	−	2.17963i	−0.0374821	−	0.115358i
$358$	−9.20820	+	6.69015i	−0.486669	+	0.353586i
$359$	4.14590	+	12.7598i	0.218812	+	0.673434i	0.998861	+	0.0477158i	$0.0151942\pi$
$359$	4.14590	+	12.7598i	0.218812	+	0.673434i	−0.780049	+	0.625719i	$0.784806\pi$
$360$	−4.04508	−	2.93893i	−0.213195	−	0.154895i
$361$	−5.28115	−	16.2537i	−0.277955	−	0.855459i
$362$	28.1074	+	20.4212i	1.47729	+	1.07332i
$363$	−1.95492	−	10.8249i	−0.102606	−	0.568160i
$364$	4.85410	−	3.52671i	0.254424	−	0.184850i
$365$	−15.4894	−	11.2537i	−0.810750	−	0.589044i
$366$	14.0902			0.736505
$367$	10.4549	−	32.1769i	0.545742	−	1.67962i	−0.173477	−	0.984838i	$-0.555500\pi$
$367$	10.4549	−	32.1769i	0.545742	−	1.67962i	0.719219	−	0.694784i	$-0.244500\pi$
$368$	−2.78115	−	8.55951i	−0.144978	−	0.446195i
$369$	−0.0729490	+	0.0530006i	−0.00379757	+	0.00275910i
$370$	32.0344			1.66539
$371$	6.27051	+	19.2986i	0.325549	+	1.00194i
$372$	−5.11803	−	3.71847i	−0.265358	−	0.192794i
$373$	15.3713	−	11.1679i	0.795897	−	0.578253i	−0.113811	−	0.993502i	$-0.536306\pi$
$373$	15.3713	−	11.1679i	0.795897	−	0.578253i	0.909708	+	0.415249i	$0.136306\pi$
$374$	3.14590	+	2.62866i	0.162671	+	0.135925i
$375$	−11.1803			−0.577350
$376$	6.97214	−	21.4580i	0.359560	−	1.10661i
$377$	5.32624	−	16.3925i	0.274315	−	0.844255i
$378$	3.92705	−	2.85317i	0.201986	−	0.146751i
$379$	21.8328			1.12148			0.560738	−	0.827993i	$-0.310517\pi$
$379$	21.8328			1.12148			0.560738	+	0.827993i	$0.310517\pi$
$380$	1.54508	+	1.12257i	0.0792612	+	0.0575866i
$381$	−3.21885	+	9.90659i	−0.164907	+	0.507530i
$382$	−2.11803	+	1.53884i	−0.108368	+	0.0787340i
$383$	−4.85410			−0.248033			−0.124017	−	0.992280i	$-0.539578\pi$
$383$	−4.85410			−0.248033			−0.124017	+	0.992280i	$0.539578\pi$
$384$	−11.0172	−	8.00448i	−0.562220	−	0.408477i
$385$	5.42705	+	21.5765i	0.276588	+	1.09964i
$386$	−22.7984	+	16.5640i	−1.16041	+	0.843085i
$387$	−4.85410	+	3.52671i	−0.246748	+	0.179273i
$388$	1.56231			0.0793141
$389$	14.7984			0.750307			0.375154	−	0.926963i	$-0.377590\pi$
$389$	14.7984			0.750307			0.375154	+	0.926963i	$0.377590\pi$
$390$	−9.47214	+	6.88191i	−0.479640	+	0.348479i
$391$	−0.437694	+	1.34708i	−0.0221351	+	0.0681250i
$392$	1.38197	−	4.25325i	0.0697998	−	0.214822i
$393$	−1.57295	+	1.14281i	−0.0793448	+	0.0576474i
$394$	−23.0344			−1.16046
$395$	−3.45492	−	10.6331i	−0.173836	−	0.535011i
$396$	−0.763932	+	1.90211i	−0.0383890	+	0.0955848i
$397$	6.57295	−	20.2295i	0.329887	−	1.01529i	−0.639299	−	0.768958i	$-0.720776\pi$
$397$	6.57295	−	20.2295i	0.329887	−	1.01529i	0.969186	−	0.246329i	$-0.0792245\pi$
$398$	4.89919	+	15.0781i	0.245574	+	0.755799i
$399$	3.35410	−	2.43690i	0.167915	−	0.121997i
$400$	−24.2705			−1.21353
$401$	5.88197	+	18.1028i	0.293731	+	0.904012i	0.983645	+	0.180120i	$0.0576487\pi$
$401$	5.88197	+	18.1028i	0.293731	+	0.904012i	−0.689913	+	0.723892i	$0.742351\pi$
$402$	3.92705	+	2.85317i	0.195864	+	0.142303i
$403$	26.7984	−	19.4702i	1.33492	−	0.969878i
$404$	0.482779	+	1.48584i	0.0240192	+	0.0739234i
$405$	−1.80902	+	1.31433i	−0.0898908	+	0.0653095i
$406$	7.98936	+	24.5887i	0.396505	+	1.22032i
$407$	7.16312	+	28.4787i	0.355063	+	1.41164i
$408$	0.527864	+	1.62460i	0.0261332	+	0.0804296i
$409$	24.1074	−	17.5150i	1.19203	−	0.866063i	0.198556	−	0.980090i	$-0.436375\pi$
$409$	24.1074	−	17.5150i	1.19203	−	0.866063i	0.993478	+	0.114026i	$0.0363748\pi$
$410$	−0.100813	+	0.310271i	−0.00497880	+	0.0153232i
$411$	15.0344			0.741594
$412$	−0.336881	+	1.03681i	−0.0165969	+	0.0510801i
$413$	5.12461	−	15.7719i	0.252166	−	0.776086i
$414$	−3.00000			−0.147442
$415$	−12.0344			−0.590748
$416$	−8.85410	+	6.43288i	−0.434108	+	0.315398i
$417$	4.30902	+	13.2618i	0.211013	+	0.649433i
$418$	−2.76393	+	6.88191i	−0.135188	+	0.336605i
$419$	7.29837	+	22.4621i	0.356549	+	1.09734i	0.955106	+	0.296264i	$0.0957410\pi$
$419$	7.29837	+	22.4621i	0.356549	+	1.09734i	−0.598557	+	0.801080i	$0.704259\pi$
$420$	1.28115	−	3.94298i	0.0625139	−	0.192398i
$421$	1.20820	+	3.71847i	0.0588843	+	0.181227i	0.976172	−	0.216998i	$-0.0696264\pi$
$421$	1.20820	+	3.71847i	0.0588843	+	0.181227i	−0.917288	+	0.398225i	$0.869626\pi$
$422$	−14.2533	+	10.3556i	−0.693839	+	0.504104i
$423$	−8.16312	−	5.93085i	−0.396904	−	0.288368i
$424$	−4.67376	−	14.3844i	−0.226978	−	0.698566i
$425$	3.09017	+	2.24514i	0.149895	+	0.108905i
$426$	12.2812	−	8.92278i	0.595024	−	0.432310i
$427$	−8.07295	−	24.8460i	−0.390677	−	1.20238i
$428$	3.20820	−	9.87384i	0.155074	−	0.477270i
$429$	−8.23607	−	6.88191i	−0.397641	−	0.332262i
$430$	−6.70820	+	20.6457i	−0.323498	+	0.995625i
$431$	7.65248			0.368607			0.184303	−	0.982869i	$-0.440997\pi$
$431$	7.65248			0.368607			0.184303	+	0.982869i	$0.440997\pi$
$432$	−3.92705	+	2.85317i	−0.188940	+	0.137273i
$433$	−10.9098	+	33.5770i	−0.524293	+	1.61361i	0.241417	+	0.970422i	$0.422388\pi$
$433$	−10.9098	+	33.5770i	−0.524293	+	1.61361i	−0.765710	+	0.643186i	$0.777612\pi$
$434$	−15.3541	+	47.2551i	−0.737020	+	2.26832i
$435$	−3.68034	−	11.3269i	−0.176459	−	0.543084i
$436$	7.23607			0.346545
$437$	−2.56231			−0.122572
$438$	−11.2082	+	8.14324i	−0.535549	+	0.389099i
$439$	21.3435	−	15.5069i	1.01867	−	0.740105i	0.0526584	−	0.998613i	$-0.483231\pi$
$439$	21.3435	−	15.5069i	1.01867	−	0.740105i	0.966009	+	0.258507i	$0.0832306\pi$
$440$	−4.04508	−	16.0822i	−0.192842	−	0.766689i
$441$	−1.61803	−	1.17557i	−0.0770492	−	0.0559795i
$442$	4.00000			0.190261
$443$	−4.59017	+	3.33495i	−0.218086	+	0.158448i	−0.691464	−	0.722410i	$-0.743034\pi$
$443$	−4.59017	+	3.33495i	−0.218086	+	0.158448i	0.473379	+	0.880859i	$0.343034\pi$
$444$	1.69098	−	5.20431i	0.0802505	−	0.246986i
$445$	−5.00000			−0.237023
$446$	−7.14590			−0.338368
$447$	−6.97214	+	5.06555i	−0.329771	+	0.239592i
$448$	−3.92705	+	12.0862i	−0.185536	+	0.571020i
$449$	9.10739	−	28.0297i	0.429804	−	1.32280i	−0.468514	−	0.883456i	$-0.655210\pi$
$449$	9.10739	−	28.0297i	0.429804	−	1.32280i	0.898318	−	0.439346i	$-0.144790\pi$
$450$	−2.50000	+	7.69421i	−0.117851	+	0.362708i
$451$	−0.298374	−	0.0202444i	−0.0140499	−	0.000953272i
$452$	5.09017	−	3.69822i	0.239421	−	0.173950i
$453$	12.2082	+	8.86978i	0.573591	+	0.416739i
$454$	4.59017	+	14.1271i	0.215427	+	0.663017i
$455$	17.5623	+	12.7598i	0.823334	+	0.598187i
$456$	−2.50000	+	1.81636i	−0.117073	+	0.0850587i
$457$	3.28115	+	10.0984i	0.153486	+	0.472381i	0.998004	−	0.0631455i	$-0.0201132\pi$
$457$	3.28115	+	10.0984i	0.153486	+	0.472381i	−0.844518	+	0.535526i	$0.820113\pi$
$458$	12.5000	−	38.4710i	0.584087	−	1.79763i
$459$	0.763932			0.0356573
$460$	−2.07295	+	1.50609i	−0.0966517	+	0.0702216i
$461$	−31.5795	+	22.9439i	−1.47081	+	1.06860i	−0.490426	+	0.871483i	$0.663159\pi$
$461$	−31.5795	+	22.9439i	−1.47081	+	1.06860i	−0.980379	+	0.197120i	$0.936841\pi$
$462$	16.0623	+	1.08981i	0.747286	+	0.0507027i
$463$	0.472136	+	0.343027i	0.0219420	+	0.0159418i	0.598702	−	0.800972i	$-0.295683\pi$
$463$	0.472136	+	0.343027i	0.0219420	+	0.0159418i	−0.576760	+	0.816914i	$0.695683\pi$
$464$	−7.98936	−	24.5887i	−0.370897	−	1.14150i
$465$	7.07295	−	21.7683i	0.328000	−	1.00948i
$466$	7.85410	+	24.1724i	0.363834	+	1.11977i
$467$	29.8885	−	21.7153i	1.38308	−	1.00486i	0.386492	−	0.922293i	$-0.373687\pi$
$467$	29.8885	−	21.7153i	1.38308	−	1.00486i	0.996585	−	0.0825713i	$-0.0263132\pi$
$468$	0.618034	+	1.90211i	0.0285686	+	0.0879252i
$469$	2.78115	−	8.55951i	0.128422	−	0.395241i
$470$	−36.5066			−1.68392
$471$	11.7812	+	8.55951i	0.542847	+	0.394401i
$472$	−3.81966	+	11.7557i	−0.175814	+	0.541100i
$473$	−19.8541	−	1.34708i	−0.912893	−	0.0619390i
$474$	−8.09017			−0.371594
$475$	−2.13525	+	6.57164i	−0.0979722	+	0.301527i
$476$	−1.14590	+	0.832544i	−0.0525222	+	0.0381596i
$477$	−6.76393			−0.309699
$478$	−31.5066			−1.44108
$479$	1.90983			0.0872624			0.0436312	−	0.999048i	$-0.486107\pi$
$479$	1.90983			0.0872624			0.0436312	+	0.999048i	$0.486107\pi$
$480$	−2.33688	+	7.19218i	−0.106664	+	0.328277i
$481$	23.1803	+	16.8415i	1.05693	+	0.767906i
$482$	−9.78115	+	30.1033i	−0.445519	+	1.37117i
$483$	1.71885	+	5.29007i	0.0782102	+	0.240706i
$484$	−5.98936	+	3.21644i	−0.272243	+	0.146202i
$485$	1.74671	+	5.37582i	0.0793141	+	0.244104i
$486$	0.500000	+	1.53884i	0.0226805	+	0.0698033i
$487$	−12.4721			−0.565166			−0.282583	−	0.959243i	$-0.591191\pi$
$487$	−12.4721			−0.565166			−0.282583	+	0.959243i	$0.591191\pi$
$488$	6.01722	+	18.5191i	0.272387	+	0.838320i
$489$	−5.30902	−	3.85723i	−0.240082	−	0.174430i
$490$	−7.23607			−0.326892
$491$	−11.8820	−	36.5689i	−0.536226	−	1.65033i	−0.740986	−	0.671521i	$-0.765641\pi$
$491$	−11.8820	−	36.5689i	−0.536226	−	1.65033i	0.204760	−	0.978812i	$-0.434359\pi$
$492$	0.0450850	+	0.0327561i	0.00203259	+	0.00147676i
$493$	−1.25735	+	3.86974i	−0.0566284	+	0.174284i
$494$	2.23607	+	6.88191i	0.100605	+	0.309632i
$495$	−7.39919	−	0.502029i	−0.332569	−	0.0225645i
$496$	15.3541	−	47.2551i	0.689420	−	2.12182i
$497$	−22.7705	−	16.5437i	−1.02140	−	0.742088i
$498$	−2.69098	+	8.28199i	−0.120586	+	0.371125i
$499$	12.2361	+	8.89002i	0.547762	+	0.397972i	0.826960	−	0.562261i	$-0.190069\pi$
$499$	12.2361	+	8.89002i	0.547762	+	0.397972i	−0.279198	+	0.960234i	$0.590069\pi$
$500$	2.13525	+	6.57164i	0.0954915	+	0.293893i
$501$	−2.06231	−	6.34712i	−0.0921370	−	0.283569i
$502$	−12.3820			−0.552634
$503$	5.40983	+	16.6497i	0.241212	+	0.742375i	0.996236	+	0.0866782i	$0.0276252\pi$
$503$	5.40983	+	16.6497i	0.241212	+	0.742375i	−0.755024	+	0.655697i	$0.772375\pi$
$504$	5.42705	+	3.94298i	0.241740	+	0.175634i
$505$	−4.57295	+	3.32244i	−0.203494	+	0.147847i
$506$	−7.63525	−	6.37988i	−0.339428	−	0.283620i
$507$	2.52786			0.112266
$508$	6.43769			0.285626
$509$	7.03444			0.311796			0.155898	−	0.987773i	$-0.450173\pi$
$509$	7.03444			0.311796			0.155898	+	0.987773i	$0.450173\pi$
$510$	2.23607	−	1.62460i	0.0990148	−	0.0719384i
$511$	20.7812	+	15.0984i	0.919304	+	0.667914i
$512$	1.63525	−	5.03280i	0.0722687	−	0.222420i
$513$	0.427051	+	1.31433i	0.0188548	+	0.0580290i
$514$	9.00000	−	27.6992i	0.396973	−	1.22176i
$515$	−3.94427			−0.173805
$516$	3.00000	+	2.17963i	0.132068	+	0.0959528i
$517$	−8.16312	−	32.4544i	−0.359014	−	1.42734i
$518$	−42.9787			−1.88838
$519$	3.47214			0.152410
$520$	−13.0902	−	9.51057i	−0.574042	−	0.417066i
$521$	−18.2254	+	13.2415i	−0.798470	+	0.580123i	−0.910465	−	0.413586i	$-0.864276\pi$
$521$	−18.2254	+	13.2415i	−0.798470	+	0.580123i	0.111995	+	0.993709i	$0.464276\pi$
$522$	−8.61803			−0.377201
$523$	−16.9894	−	12.3435i	−0.742893	−	0.539743i	0.150723	−	0.988576i	$-0.451840\pi$
$523$	−16.9894	−	12.3435i	−0.742893	−	0.539743i	−0.893616	+	0.448833i	$0.851840\pi$
$524$	0.972136	+	0.706298i	0.0424680	+	0.0308548i
$525$	15.0000			0.654654
$526$	6.47214	−	19.9192i	0.282199	−	0.868518i
$527$	−6.32624	+	4.59628i	−0.275575	+	0.200217i
$528$	−16.0623	−	1.08981i	−0.699022	−	0.0474281i
$529$	−6.04508	+	18.6049i	−0.262830	+	0.808907i
$530$	−19.7984	+	14.3844i	−0.859986	+	0.624817i
$531$	4.47214	+	3.24920i	0.194074	+	0.141003i
$532$	−2.07295	−	1.50609i	−0.0898737	−	0.0652971i
$533$	−0.236068	+	0.171513i	−0.0102252	+	0.00742907i
$534$	−1.11803	+	3.44095i	−0.0483821	+	0.148905i
$535$	37.5623			1.62396
$536$	−2.07295	+	6.37988i	−0.0895378	+	0.275569i
$537$	−5.69098	+	4.13474i	−0.245584	+	0.178427i
$538$	25.4894	+	18.5191i	1.09892	+	0.798415i
$539$	−1.61803	−	6.43288i	−0.0696937	−	0.277084i
$540$	1.11803	+	0.812299i	0.0481125	+	0.0349558i
$541$	−24.8713	+	18.0701i	−1.06930	+	0.776893i	−0.975787	−	0.218725i	$-0.929810\pi$
$541$	−24.8713	+	18.0701i	−1.06930	+	0.776893i	−0.0935151	+	0.995618i	$0.529810\pi$
$542$	−5.47214	−	3.97574i	−0.235048	−	0.170773i
$543$	17.3713	+	12.6210i	0.745475	+	0.541619i
$544$	2.09017	−	1.51860i	0.0896153	−	0.0651093i
$545$	8.09017	+	24.8990i	0.346545	+	1.06656i
$546$	12.7082	−	9.23305i	0.543861	−	0.395138i
$547$	−7.10739	−	21.8743i	−0.303890	−	0.935278i	−0.980089	−	0.198558i	$-0.936374\pi$
$547$	−7.10739	−	21.8743i	−0.303890	−	0.935278i	0.676199	−	0.736719i	$-0.263626\pi$
$548$	−2.87132	−	8.83702i	−0.122657	−	0.377499i
$549$	8.70820			0.371657
$550$	−22.7254	+	14.2658i	−0.969015	+	0.608298i
$551$	−7.36068			−0.313576
$552$	−1.28115	−	3.94298i	−0.0545295	−	0.167825i
$553$	4.63525	+	14.2658i	0.197111	+	0.606646i
$554$	−40.8607	+	29.6870i	−1.73600	+	1.26128i
$555$	19.7984			0.840394
$556$	6.97214	−	5.06555i	0.295684	−	0.214827i
$557$	−20.8262	−	15.1311i	−0.882436	−	0.641127i	0.0514588	−	0.998675i	$-0.483613\pi$
$557$	−20.8262	−	15.1311i	−0.882436	−	0.641127i	−0.933895	+	0.357548i	$0.883613\pi$
$558$	−13.3992	−	9.73508i	−0.567233	−	0.412119i
$559$	−15.7082	+	11.4127i	−0.664386	+	0.482705i
$560$	32.5623			1.37601
$561$	1.94427	+	1.62460i	0.0820872	+	0.0685906i
$562$	25.3435	+	18.4131i	1.06905	+	0.776710i
$563$	35.1697	−	25.5523i	1.48223	−	1.07690i	0.505395	−	0.862888i	$-0.331347\pi$
$563$	35.1697	−	25.5523i	1.48223	−	1.07690i	0.976831	−	0.214012i	$-0.0686532\pi$
$564$	−1.92705	+	5.93085i	−0.0811435	+	0.249734i
$565$	18.4164	+	13.3803i	0.774784	+	0.562914i
$566$	13.7082	−	42.1895i	0.576199	−	1.77336i
$567$	2.42705	−	1.76336i	0.101927	−	0.0740540i
$568$	16.9721	+	12.3310i	0.712135	+	0.517396i
$569$	9.63525	+	7.00042i	0.403931	+	0.293473i	0.771140	−	0.636665i	$-0.219687\pi$
$569$	9.63525	+	7.00042i	0.403931	+	0.293473i	−0.367209	+	0.930138i	$0.619687\pi$
$570$	4.04508	+	2.93893i	0.169430	+	0.123098i
$571$	9.60081	−	29.5483i	0.401782	−	1.23656i	−0.521771	−	0.853085i	$-0.674729\pi$
$571$	9.60081	−	29.5483i	0.401782	−	1.23656i	0.923553	−	0.383471i	$-0.125271\pi$
$572$	−2.47214	+	6.15537i	−0.103365	+	0.257369i
$573$	−1.30902	+	0.951057i	−0.0546850	+	0.0397310i
$574$	0.135255	−	0.416272i	0.00564543	−	0.0173749i
$575$	−7.50000	−	5.44907i	−0.312772	−	0.227242i
$576$	−3.42705	−	2.48990i	−0.142794	−	0.103746i
$577$	−7.04508	−	5.11855i	−0.293291	−	0.213088i	0.431403	−	0.902159i	$-0.358019\pi$
$577$	−7.04508	−	5.11855i	−0.293291	−	0.213088i	−0.724694	+	0.689071i	$0.758019\pi$
$578$	26.5623			1.10485
$579$	−14.0902	+	10.2371i	−0.585567	+	0.425440i
$580$	−5.95492	+	4.32650i	−0.247264	+	0.179648i
$581$	16.1459			0.669845
$582$	4.09017			0.169543
$583$	−17.2148	−	14.3844i	−0.712963	−	0.595739i
$584$	−15.4894	−	11.2537i	−0.640954	−	0.465680i
$585$	−5.85410	+	4.25325i	−0.242037	+	0.175850i
$586$	−11.5172	+	35.4464i	−0.475772	+	1.46428i
$587$	11.2082	+	34.4953i	0.462612	+	1.42377i	0.861961	+	0.506975i	$0.169236\pi$
$587$	11.2082	+	34.4953i	0.462612	+	1.42377i	−0.399349	+	0.916799i	$0.630764\pi$
$588$	−0.381966	+	1.17557i	−0.0157520	+	0.0484797i
$589$	−11.4443	−	8.31475i	−0.471553	−	0.342603i
$590$	20.0000			0.823387
$591$	−14.2361			−0.585594
$592$	42.9787			1.76641
$593$	6.00000			0.246390			0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000			0.246390			0.123195	+	0.992382i	$0.460686\pi$
$594$	−2.00000	+	4.97980i	−0.0820610	+	0.204324i
$595$	−4.14590	−	3.01217i	−0.169965	−	0.123487i
$596$	4.30902	+	3.13068i	0.176504	+	0.128238i
$597$	3.02786	+	9.31881i	0.123922	+	0.381393i
$598$	−9.70820			−0.396998
$599$	10.1631	+	31.2789i	0.415254	+	1.27802i	0.912024	+	0.410137i	$0.134519\pi$
$599$	10.1631	+	31.2789i	0.415254	+	1.27802i	−0.496770	+	0.867882i	$0.665481\pi$
$600$	−11.1803			−0.456435
$601$	18.0172	+	13.0903i	0.734938	+	0.533964i	0.891122	−	0.453764i	$-0.149919\pi$
$601$	18.0172	+	13.0903i	0.734938	+	0.533964i	−0.156184	+	0.987728i	$0.549919\pi$
$602$	9.00000	−	27.6992i	0.366813	−	1.12893i
$603$	2.42705	+	1.76336i	0.0988372	+	0.0718094i
$604$	2.88197	−	8.86978i	0.117266	−	0.360906i
$605$	−17.7639	−	17.0130i	−0.722207	−	0.691677i
$606$	1.26393	+	3.88998i	0.0513437	+	0.158020i
$607$	6.24671	−	19.2254i	0.253546	−	0.780335i	−0.740566	−	0.671983i	$-0.765443\pi$
$607$	6.24671	−	19.2254i	0.253546	−	0.780335i	0.994113	−	0.108352i	$-0.0345573\pi$
$608$	3.78115	+	2.74717i	0.153346	+	0.111412i
$609$	4.93769	+	15.1967i	0.200085	+	0.615800i
$610$	25.4894	−	18.5191i	1.03203	−	0.749817i
$611$	−26.4164	−	19.1926i	−1.06869	−	0.776451i
$612$	−0.145898	−	0.449028i	−0.00589758	−	0.0181509i
$613$	−45.7082			−1.84614			−0.923068	−	0.384636i	$-0.874327\pi$
$613$	−45.7082			−1.84614			−0.923068	+	0.384636i	$0.874327\pi$
$614$	−8.66312	−	26.6623i	−0.349615	−	1.07600i
$615$	−0.0623059	+	0.191758i	−0.00251242	+	0.00773242i
$616$	5.42705	+	21.5765i	0.218662	+	0.869344i
$617$	−8.79180	−	27.0584i	−0.353944	−	1.08933i	−0.956619	−	0.291342i	$-0.905898\pi$
$617$	−8.79180	−	27.0584i	−0.353944	−	1.08933i	0.602675	−	0.797987i	$-0.294102\pi$
$618$	−0.881966	+	2.71441i	−0.0354779	+	0.109190i
$619$	0.100813	+	0.0732450i	0.00405202	+	0.00294396i	0.589809	−	0.807542i	$-0.299203\pi$
$619$	0.100813	+	0.0732450i	0.00405202	+	0.00294396i	−0.585757	+	0.810486i	$0.699203\pi$
$620$	−14.1459			−0.568113
$621$	−1.85410			−0.0744025
$622$	−17.1803			−0.688869
$623$	6.70820			0.268759
$624$	−12.7082	+	9.23305i	−0.508735	+	0.369618i
$625$	−20.2254	+	14.6946i	−0.809017	+	0.587785i
$626$	47.1246			1.88348
$627$	−1.70820	+	4.25325i	−0.0682191	+	0.169859i
$628$	2.78115	−	8.55951i	0.110980	−	0.341562i
$629$	−5.47214	−	3.97574i	−0.218188	−	0.158523i
$630$	3.35410	−	10.3229i	0.133631	−	0.411273i
$631$	10.7812	−	33.1810i	0.429191	−	1.32091i	−0.469733	−	0.882809i	$-0.655650\pi$
$631$	10.7812	−	33.1810i	0.429191	−	1.32091i	0.898924	−	0.438105i	$-0.144350\pi$
$632$	−3.45492	−	10.6331i	−0.137429	−	0.422963i
$633$	−8.80902	+	6.40013i	−0.350127	+	0.254382i
$634$	11.5623	+	35.5851i	0.459198	+	1.41327i
$635$	7.19756	+	22.1518i	0.285626	+	0.879068i
$636$	1.29180	+	3.97574i	0.0512230	+	0.157648i
$637$	−5.23607	−	3.80423i	−0.207461	−	0.150729i
$638$	−21.9336	−	18.3273i	−0.868361	−	0.725586i
$639$	7.59017	−	5.51458i	0.300262	−	0.218153i
$640$	−30.4508			−1.20368
$641$	−34.9098			−1.37886			−0.689428	−	0.724355i	$-0.742138\pi$
$641$	−34.9098			−1.37886			−0.689428	+	0.724355i	$0.742138\pi$
$642$	8.39919	−	25.8500i	0.331489	−	1.02022i
$643$	−10.2426	−	31.5236i	−0.403931	−	1.24317i	−0.921785	−	0.387702i	$-0.873269\pi$
$643$	−10.2426	−	31.5236i	−0.403931	−	1.24317i	0.517854	−	0.855469i	$-0.326731\pi$
$644$	2.78115	−	2.02063i	0.109593	−	0.0796238i
$645$	−4.14590	+	12.7598i	−0.163245	+	0.502415i
$646$	−0.527864	−	1.62460i	−0.0207685	−	0.0639190i
$647$	−15.3992	−	11.1882i	−0.605405	−	0.439852i	0.242389	−	0.970179i	$-0.422069\pi$
$647$	−15.3992	−	11.1882i	−0.605405	−	0.439852i	−0.847793	+	0.530327i	$0.822069\pi$
$648$	−1.80902	+	1.31433i	−0.0710649	+	0.0516317i
$649$	4.47214	+	17.7800i	0.175547	+	0.697928i
$650$	−8.09017	+	24.8990i	−0.317323	+	0.976618i
$651$	−9.48936	+	29.2052i	−0.371917	+	1.14464i
$652$	−1.25329	+	3.85723i	−0.0490826	+	0.151061i
$653$	−33.2705	+	24.1724i	−1.30198	+	0.945941i	−0.999973	−	0.00736635i	$-0.997655\pi$
$653$	−33.2705	+	24.1724i	−1.30198	+	0.945941i	−0.302003	+	0.953307i	$0.597655\pi$
$654$	18.9443			0.740780
$655$	−1.34346	+	4.13474i	−0.0524933	+	0.161558i
$656$	−0.135255	+	0.416272i	−0.00528082	+	0.0162527i
$657$	−6.92705	+	5.03280i	−0.270250	+	0.196348i
$658$	48.9787			1.90939
$659$	−22.4615	−	16.3192i	−0.874976	−	0.635707i	0.0569419	−	0.998377i	$-0.481865\pi$
$659$	−22.4615	−	16.3192i	−0.874976	−	0.635707i	−0.931917	+	0.362671i	$0.881865\pi$
$660$	1.11803	+	4.44501i	0.0435194	+	0.173022i
$661$	11.7984	−	8.57202i	0.458904	−	0.333413i	−0.334197	−	0.942503i	$-0.608465\pi$
$661$	11.7984	−	8.57202i	0.458904	−	0.333413i	0.793101	+	0.609090i	$0.208465\pi$
$662$	46.7877	−	33.9933i	1.81846	−	1.32119i
$663$	2.47214			0.0960098
$664$	−12.0344			−0.467027
$665$	2.86475	−	8.81678i	0.111090	−	0.341900i
$666$	4.42705	−	13.6251i	0.171545	−	0.527960i
$667$	3.05166	−	9.39205i	0.118161	−	0.363662i
$668$	−3.33688	+	2.42439i	−0.129108	+	0.0938023i
$669$	−4.41641			−0.170748
$670$	10.8541			0.419331
$671$	22.1631	+	18.5191i	0.855598	+	0.714922i
$672$	3.13525	−	9.64932i	0.120945	−	0.372231i
$673$	1.72949	+	5.32282i	0.0666669	+	0.205180i	0.978841	−	0.204624i	$-0.0655972\pi$
$673$	1.72949	+	5.32282i	0.0666669	+	0.205180i	−0.912174	+	0.409804i	$0.865597\pi$
$674$	26.2984	−	19.1069i	1.01298	−	0.735970i
$675$	−1.54508	+	4.75528i	−0.0594703	+	0.183031i
$676$	−0.482779	−	1.48584i	−0.0185684	−	0.0571477i
$677$	36.2705	+	26.3521i	1.39399	+	1.01279i	0.995414	+	0.0956563i	$0.0304950\pi$
$677$	36.2705	+	26.3521i	1.39399	+	1.01279i	0.398575	+	0.917136i	$0.369505\pi$
$678$	13.3262	−	9.68208i	0.511791	−	0.371838i
$679$	−2.34346	−	7.21242i	−0.0899337	−	0.276787i
$680$	3.09017	+	2.24514i	0.118503	+	0.0860972i
$681$	2.83688	+	8.73102i	0.108710	+	0.334573i
$682$	−13.3992	−	53.2717i	−0.513081	−	2.03988i
$683$	5.67376	+	17.4620i	0.217100	+	0.668167i	0.998998	+	0.0447593i	$0.0142521\pi$
$683$	5.67376	+	17.4620i	0.217100	+	0.668167i	−0.781897	+	0.623407i	$0.785748\pi$
$684$	0.690983	−	0.502029i	0.0264204	−	0.0191955i
$685$	27.1976	−	19.7602i	1.03917	−	0.754998i
$686$	−24.2705			−0.926652
$687$	7.72542	−	23.7764i	0.294743	−	0.907127i
$688$	−9.00000	+	27.6992i	−0.343122	+	1.05602i
$689$	−21.8885			−0.833887
$690$	−5.42705	+	3.94298i	−0.206604	+	0.150107i
$691$	13.9721	−	10.1514i	0.531525	−	0.386176i	−0.289403	−	0.957207i	$-0.593457\pi$
$691$	13.9721	−	10.1514i	0.531525	−	0.386176i	0.820928	+	0.571032i	$0.193457\pi$
$692$	−0.663119	−	2.04087i	−0.0252080	−	0.0775822i
$693$	9.92705	+	0.673542i	0.377097	+	0.0255857i
$694$	−12.8713	−	39.6139i	−0.488589	−	1.50372i
$695$	25.2254	+	18.3273i	0.956855	+	0.695196i
$696$	−3.68034	−	11.3269i	−0.139503	−	0.429346i
$697$	0.0557281	−	0.0404888i	0.00211085	−	0.00153362i
$698$	−26.6074	−	19.3314i	−1.00710	−	0.731704i
$699$	4.85410	+	14.9394i	0.183599	+	0.565060i
$700$	−2.86475	−	8.81678i	−0.108277	−	0.333243i
$701$	−14.0172	+	10.1841i	−0.529423	+	0.384648i	−0.820142	−	0.572160i	$-0.806106\pi$
$701$	−14.0172	+	10.1841i	−0.529423	+	0.384648i	0.290719	+	0.956809i	$0.406106\pi$
$702$	1.61803	+	4.97980i	0.0610688	+	0.187950i
$703$	3.78115	−	11.6372i	0.142609	−	0.438905i
$704$	−3.42705	−	13.6251i	−0.129162	−	0.513514i
$705$	−22.5623			−0.849746
$706$	−33.3262			−1.25425
$707$	6.13525	−	4.45752i	0.230740	−	0.167642i
$708$	1.05573	−	3.24920i	0.0396767	−	0.122112i
$709$	−11.2188	+	34.5281i	−0.421333	+	1.29673i	0.485130	+	0.874442i	$0.338772\pi$
$709$	−11.2188	+	34.5281i	−0.421333	+	1.29673i	−0.906462	+	0.422286i	$0.861228\pi$
$710$	10.4894	−	32.2829i	0.393659	−	1.21156i
$711$	−5.00000			−0.187515
$712$	−5.00000			−0.187383
$713$	15.3541	−	11.1554i	0.575016	−	0.417773i
$714$	−3.00000	+	2.17963i	−0.112272	+	0.0815705i
$715$	−23.9443	−	1.62460i	−0.895465	−	0.0607565i
$716$	3.51722	+	2.55541i	0.131445	+	0.0955002i
$717$	−19.4721			−0.727200
$718$	17.5623	−	12.7598i	0.655419	−	0.476190i
$719$	5.52786	−	17.0130i	0.206155	−	0.634478i	−0.793509	−	0.608558i	$-0.791748\pi$
$719$	5.52786	−	17.0130i	0.206155	−	0.634478i	0.999664	−	0.0259205i	$-0.00825169\pi$
$720$	−3.35410	+	10.3229i	−0.125000	+	0.384710i
$721$	5.29180			0.197077
$722$	−22.3713	+	16.2537i	−0.832574	+	0.604901i
$723$	−6.04508	+	18.6049i	−0.224819	+	0.691922i
$724$	4.10081	−	12.6210i	0.152406	−	0.469056i
$725$	−21.5451	−	15.6534i	−0.800164	−	0.581353i
$726$	−15.6803	+	8.42075i	−0.581952	+	0.312523i
$727$	10.2533	−	7.44945i	0.380273	−	0.276285i	−0.381185	−	0.924499i	$-0.624484\pi$
$727$	10.2533	−	7.44945i	0.380273	−	0.276285i	0.761458	+	0.648214i	$0.224484\pi$
$728$	17.5623	+	12.7598i	0.650902	+	0.472908i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−9.57295	+	29.4625i	−0.354311	+	1.09046i
$731$	3.70820	−	2.69417i	0.137153	−	0.0996474i
$732$	−1.66312	−	5.11855i	−0.0614706	−	0.189187i
$733$	−4.10081	+	12.6210i	−0.151467	+	0.466167i	−0.997786	−	0.0665092i	$-0.978814\pi$
$733$	−4.10081	+	12.6210i	−0.151467	+	0.466167i	0.846319	+	0.532677i	$0.178814\pi$
$734$	−54.7426			−2.02059
$735$	−4.47214			−0.164957
$736$	−5.07295	+	3.68571i	−0.186991	+	0.135857i
$737$	2.42705	+	9.64932i	0.0894016	+	0.355437i
$738$	0.118034	+	0.0857567i	0.00434489	+	0.00315675i
$739$	−8.78115	−	27.0256i	−0.323020	−	0.994153i	−0.972326	−	0.233626i	$-0.924941\pi$
$739$	−8.78115	−	27.0256i	−0.323020	−	0.994153i	0.649307	−	0.760527i	$-0.275059\pi$
$740$	−3.78115	−	11.6372i	−0.138998	−	0.427792i
$741$	1.38197	+	4.25325i	0.0507678	+	0.156247i
$742$	26.5623	−	19.2986i	0.975133	−	0.708476i
$743$	4.12868	+	12.7068i	0.151466	+	0.466166i	0.997786	−	0.0665101i	$-0.0211865\pi$
$743$	4.12868	+	12.7068i	0.151466	+	0.466166i	−0.846319	+	0.532676i	$0.821186\pi$
$744$	7.07295	−	21.7683i	0.259307	−	0.798065i
$745$	−5.95492	+	18.3273i	−0.218171	+	0.671462i
$746$	−24.8713	−	18.0701i	−0.910604	−	0.661592i
$747$	−1.66312	+	5.11855i	−0.0608503	+	0.187278i
$748$	0.583592	−	1.45309i	0.0213382	−	0.0531301i
$749$	−50.3951			−1.84140
$750$	5.59017	+	17.2048i	0.204124	+	0.628230i
$751$	−29.9336	+	21.7481i	−1.09229	+	0.793598i	−0.979785	−	0.200053i	$-0.935889\pi$
$751$	−29.9336	+	21.7481i	−1.09229	+	0.793598i	−0.112509	+	0.993651i	$0.535889\pi$
$752$	−48.9787			−1.78607
$753$	−7.65248			−0.278872
$754$	−27.8885			−1.01564
$755$	33.7426			1.22802
$756$	−1.50000	−	1.08981i	−0.0545545	−	0.0396361i
$757$	−12.4098	+	38.1935i	−0.451043	+	1.38817i	0.424676	+	0.905346i	$0.360388\pi$
$757$	−12.4098	+	38.1935i	−0.451043	+	1.38817i	−0.875719	+	0.482822i	$0.839612\pi$
$758$	−10.9164	−	33.5972i	−0.396502	−	1.22031i
$759$	−4.71885	−	3.94298i	−0.171283	−	0.143121i
$760$	−2.13525	+	6.57164i	−0.0774538	+	0.238378i
$761$	−9.21885	−	28.3727i	−0.334183	−	1.02851i	−0.967123	−	0.254309i	$-0.918152\pi$
$761$	−9.21885	−	28.3727i	−0.334183	−	1.02851i	0.632940	−	0.774201i	$-0.281848\pi$
$762$	16.8541			0.610560
$763$	−10.8541	−	33.4055i	−0.392945	−	1.20936i
$764$	0.809017	+	0.587785i	0.0292692	+	0.0212653i
$765$	1.38197	−	1.00406i	0.0499651	−	0.0363018i
$766$	2.42705	+	7.46969i	0.0876929	+	0.269891i
$767$	14.4721	+	10.5146i	0.522559	+	0.379661i
$768$	−4.19098	+	12.8985i	−0.151229	+	0.465435i
$769$	5.00000	+	15.3884i	0.180305	+	0.554921i	0.999836	−	0.0181139i	$-0.00576614\pi$
$769$	5.00000	+	15.3884i	0.180305	+	0.554921i	−0.819531	+	0.573034i	$0.805766\pi$
$770$	30.4894	−	19.1396i	1.09876	−	0.689745i
$771$	5.56231	−	17.1190i	0.200322	−	0.616526i
$772$	8.70820	+	6.32688i	0.313415	+	0.227709i
$773$	15.4098	−	47.4266i	0.554253	−	1.70582i	−0.143655	−	0.989628i	$-0.545885\pi$
$773$	15.4098	−	47.4266i	0.554253	−	1.70582i	0.697908	−	0.716188i	$-0.254115\pi$
$774$	7.85410	+	5.70634i	0.282310	+	0.205110i
$775$	−15.8156	−	48.6754i	−0.568113	−	1.74847i
$776$	1.74671	+	5.37582i	0.0627033	+	0.192981i
$777$	−26.5623			−0.952917
$778$	−7.39919	−	22.7724i	−0.265274	−	0.816429i
$779$	0.100813	+	0.0732450i	0.00361200	+	0.00262427i
$780$	3.61803	+	2.62866i	0.129546	+	0.0941210i
$781$	31.0451	+	2.10638i	1.11088	+	0.0753723i
$782$	2.29180			0.0819545
$783$	−5.32624			−0.190344
$784$	−9.70820			−0.346722
$785$	32.5623			1.16220
$786$	2.54508	+	1.84911i	0.0907802	+	0.0659557i
$787$	−9.70820	+	29.8788i	−0.346060	+	1.06506i	0.614954	+	0.788563i	$0.289175\pi$
$787$	−9.70820	+	29.8788i	−0.346060	+	1.06506i	−0.961014	+	0.276500i	$0.910825\pi$
$788$	2.71885	+	8.36775i	0.0968549	+	0.298089i
$789$	4.00000	−	12.3107i	0.142404	−	0.438274i
$790$	−14.6353	+	10.6331i	−0.520699	+	0.378310i
$791$	−24.7082	−	17.9516i	−0.878523	−	0.638284i
$792$	−7.39919	−	0.502029i	−0.262919	−	0.0178388i
$793$	28.1803			1.00071
$794$	−34.4164			−1.22139
$795$	−12.2361	+	8.89002i	−0.433969	+	0.315297i
$796$	4.89919	−	3.55947i	0.173647	−	0.126162i
$797$	21.4721			0.760582			0.380291	−	0.924867i	$-0.375824\pi$
$797$	21.4721			0.760582			0.380291	+	0.924867i	$0.375824\pi$
$798$	−5.42705	−	3.94298i	−0.192116	−	0.139580i
$799$	6.23607	+	4.53077i	0.220616	+	0.160287i
$800$	5.22542	+	16.0822i	0.184747	+	0.568592i
$801$	−0.690983	+	2.12663i	−0.0244147	+	0.0751407i
$802$	24.9164	−	18.1028i	0.879829	−	0.639233i
$803$	−28.3328	−	1.92236i	−0.999843	−	0.0678385i
$804$	0.572949	−	1.76336i	0.0202064	−	0.0621888i
$805$	10.0623	+	7.31069i	0.354650	+	0.257668i
$806$	−43.3607	−	31.5034i	−1.52731	−	1.10966i
$807$	15.7533	+	11.4454i	0.554542	+	0.402898i
$808$	−4.57295	+	3.32244i	−0.160876	+	0.116883i
$809$	6.50658	−	20.0252i	0.228759	−	0.704048i	−0.769129	−	0.639093i	$-0.779310\pi$
$809$	6.50658	−	20.0252i	0.228759	−	0.704048i	0.997888	−	0.0649547i	$-0.0206903\pi$
$810$	2.92705	+	2.12663i	0.102846	+	0.0747221i
$811$	−10.3369	+	31.8136i	−0.362977	+	1.11713i	0.588261	+	0.808671i	$0.299813\pi$
$811$	−10.3369	+	31.8136i	−0.362977	+	1.11713i	−0.951238	+	0.308457i	$0.900187\pi$
$812$	7.98936	−	5.80461i	0.280371	−	0.203702i
$813$	−3.38197	−	2.45714i	−0.118611	−	0.0861757i
$814$	40.2426	−	25.2623i	1.41050	−	0.885442i
$815$	−14.6738			−0.513999
$816$	3.00000	−	2.17963i	0.105021	−	0.0763022i
$817$	6.70820	+	4.87380i	0.234690	+	0.170513i
$818$	−39.0066	−	28.3399i	−1.36383	−	0.990883i
$819$	7.85410	−	5.70634i	0.274445	−	0.199396i
$820$	0.124612			0.00435163
$821$	−7.14590	+	5.19180i	−0.249394	+	0.181195i	−0.705458	−	0.708752i	$-0.749259\pi$
$821$	−7.14590	+	5.19180i	−0.249394	+	0.181195i	0.456064	+	0.889947i	$0.349259\pi$
$822$	−7.51722	−	23.1356i	−0.262193	−	0.806948i
$823$	9.35410	+	28.7890i	0.326063	+	1.00352i	0.970958	+	0.239249i	$0.0769012\pi$
$823$	9.35410	+	28.7890i	0.326063	+	1.00352i	−0.644895	+	0.764271i	$0.723099\pi$
$824$	−3.94427			−0.137405
$825$	−14.0451	+	8.81678i	−0.488987	+	0.306961i
$826$	−26.8328			−0.933633
$827$	15.2918	+	47.0633i	0.531748	+	1.63655i	0.750573	+	0.660788i	$0.229778\pi$
$827$	15.2918	+	47.0633i	0.531748	+	1.63655i	−0.218825	+	0.975764i	$0.570222\pi$
$828$	0.354102	+	1.08981i	0.0123059	+	0.0378736i
$829$	−3.51722	+	2.55541i	−0.122158	+	0.0887531i	−0.647187	−	0.762331i	$-0.724055\pi$
$829$	−3.51722	+	2.55541i	−0.122158	+	0.0887531i	0.525029	+	0.851085i	$0.324055\pi$
$830$	6.01722	+	18.5191i	0.208861	+	0.642807i
$831$	−25.2533	+	18.3476i	−0.876027	+	0.636471i
$832$	−11.0902	−	8.05748i	−0.384482	−	0.279343i
$833$	1.23607	+	0.898056i	0.0428272	+	0.0311158i
$834$	18.2533	−	13.2618i	0.632060	−	0.459218i
$835$	−12.0729	−	8.77151i	−0.417802	−	0.303551i
$836$	2.82624	+	0.191758i	0.0977475	+	0.00663208i
$837$	−8.28115	−	6.01661i	−0.286239	−	0.207964i
$838$	30.9164	−	22.4621i	1.06799	−	0.775940i
$839$	−8.92047	+	27.4544i	−0.307969	+	0.947831i	0.670584	+	0.741834i	$0.266044\pi$
$839$	−8.92047	+	27.4544i	−0.307969	+	0.947831i	−0.978553	+	0.205997i	$0.933956\pi$
$840$	15.0000			0.517549
$841$	−0.195048	+	0.600297i	−0.00672580	+	0.0206999i
$842$	5.11803	−	3.71847i	0.176379	−	0.128147i
$843$	15.6631	+	11.3799i	0.539466	+	0.391945i
$844$	5.44427	+	3.95550i	0.187400	+	0.136154i
$845$	4.57295	−	3.32244i	0.157314	−	0.114295i
$846$	−5.04508	+	15.5272i	−0.173454	+	0.533835i
$847$	23.8328	+	22.8254i	0.818905	+	0.784289i
$848$	−26.5623	+	19.2986i	−0.912153	+	0.662718i
$849$	8.47214	−	26.0746i	0.290763	−	0.894876i
$850$	1.90983	−	5.87785i	0.0655066	−	0.201609i
$851$	13.2812	+	9.64932i	0.455272	+	0.330775i
$852$	−4.69098	−	3.40820i	−0.160710	−	0.116763i
$853$	13.2361			0.453194			0.226597	−	0.973989i	$-0.427240\pi$
$853$	13.2361			0.453194			0.226597	+	0.973989i	$0.427240\pi$
$854$	−34.1976	+	24.8460i	−1.17022	+	0.850212i
$855$	2.50000	+	1.81636i	0.0854982	+	0.0621181i
$856$	37.5623			1.28385
$857$	−16.4164			−0.560774			−0.280387	−	0.959887i	$-0.590463\pi$
$857$	−16.4164			−0.560774			−0.280387	+	0.959887i	$0.590463\pi$
$858$	−6.47214	+	16.1150i	−0.220955	+	0.550156i
$859$	−16.1803	−	11.7557i	−0.552066	−	0.401099i	0.276481	−	0.961020i	$-0.410832\pi$
$859$	−16.1803	−	11.7557i	−0.552066	−	0.401099i	−0.828547	+	0.559920i	$0.810832\pi$
$860$	8.29180			0.282748
$861$	0.0835921	−	0.257270i	0.00284881	−	0.00876774i
$862$	−3.82624	−	11.7759i	−0.130322	−	0.401090i
$863$	−6.72542	+	20.6987i	−0.228936	+	0.704593i	0.768932	+	0.639331i	$0.220788\pi$
$863$	−6.72542	+	20.6987i	−0.228936	+	0.704593i	−0.997868	+	0.0652624i	$0.979212\pi$
$864$	2.73607	+	1.98787i	0.0930829	+	0.0676287i
$865$	6.28115	−	4.56352i	0.213566	−	0.155164i
$866$	57.1246			1.94117
$867$	16.4164			0.557530
$868$	18.9787			0.644180
$869$	−12.7254	−	10.6331i	−0.431680	−	0.360704i
$870$	−15.5902	+	11.3269i	−0.528556	+	0.384019i
$871$	7.85410	+	5.70634i	0.266126	+	0.193352i
$872$	8.09017	+	24.8990i	0.273968	+	0.843186i
$873$	2.52786			0.0855552
$874$	1.28115	+	3.94298i	0.0433356	+	0.133373i
$875$	27.1353	−	19.7149i	0.917339	−	0.666486i
$876$	4.28115	+	3.11044i	0.144647	+	0.105092i
$877$	10.1910	−	31.3646i	0.344125	−	1.05911i	−0.617925	−	0.786237i	$-0.712027\pi$
$877$	10.1910	−	31.3646i	0.344125	−	1.05911i	0.962051	−	0.272871i	$-0.0879733\pi$
$878$	−34.5344	−	25.0907i	−1.16548	−	0.846771i
$879$	−7.11803	+	21.9071i	−0.240085	+	0.738907i
$880$	−30.4894	+	19.1396i	−1.02780	+	0.645197i
$881$	−15.3369	−	47.2021i	−0.516713	−	1.59028i	−0.780144	−	0.625600i	$-0.784854\pi$
$881$	−15.3369	−	47.2021i	−0.516713	−	1.59028i	0.263431	−	0.964678i	$-0.415146\pi$
$882$	−1.00000	+	3.07768i	−0.0336718	+	0.103631i
$883$	−30.6074	−	22.2376i	−1.03002	−	0.748354i	−0.0617079	−	0.998094i	$-0.519655\pi$
$883$	−30.6074	−	22.2376i	−1.03002	−	0.748354i	−0.968313	+	0.249740i	$0.919655\pi$
$884$	−0.472136	−	1.45309i	−0.0158797	−	0.0488725i
$885$	12.3607			0.415500
$886$	7.42705	+	5.39607i	0.249517	+	0.181284i
$887$	8.15654	+	25.1033i	0.273870	+	0.842885i	0.989516	+	0.144422i	$0.0461322\pi$
$887$	8.15654	+	25.1033i	0.273870	+	0.842885i	−0.715646	+	0.698463i	$0.753868\pi$
$888$	19.7984			0.664390
$889$	−9.65654	−	29.7198i	−0.323870	−	0.996769i
$890$	2.50000	+	7.69421i	0.0838002	+	0.257910i
$891$	−1.23607	+	3.07768i	−0.0414098	+	0.103106i
$892$	0.843459	+	2.59590i	0.0282411	+	0.0869171i
$893$	−4.30902	+	13.2618i	−0.144196	+	0.443789i
$894$	11.2812	+	8.19624i	0.377298	+	0.274123i
$895$	−4.86068	+	14.9596i	−0.162475	+	0.500045i
$896$	40.8541			1.36484
$897$	−6.00000			−0.200334
$898$	−47.6869			−1.59133
$899$	44.1074	−	32.0459i	1.47106	−	1.06879i
$900$	3.09017			0.103006
$901$	5.16718			0.172144
$902$	0.118034	+	0.469272i	0.00393010	+	0.0156251i
$903$	5.56231	−	17.1190i	0.185102	−	0.569685i
$904$	18.4164	+	13.3803i	0.612521	+	0.445022i
$905$	48.0132			1.59601
$906$	7.54508	−	23.2214i	0.250669	−	0.771479i
$907$	−13.8926	−	42.7571i	−0.461297	−	1.41972i	−0.863581	−	0.504210i	$-0.831784\pi$
$907$	−13.8926	−	42.7571i	−0.461297	−	1.41972i	0.402285	−	0.915515i	$-0.368216\pi$
$908$	4.59017	−	3.33495i	0.152330	−	0.110674i
$909$	0.781153	+	2.40414i	0.0259092	+	0.0797403i
$910$	10.8541	−	33.4055i	0.359810	−	1.10738i
$911$	13.2812	+	40.8752i	0.440024	+	1.35426i	0.887849	+	0.460134i	$0.152199\pi$
$911$	13.2812	+	40.8752i	0.440024	+	1.35426i	−0.447825	+	0.894121i	$0.647801\pi$
$912$	5.42705	+	3.94298i	0.179708	+	0.130565i
$913$	−15.1180	+	9.49032i	−0.500334	+	0.314084i
$914$	13.8992	−	10.0984i	0.459744	−	0.334024i
$915$	15.7533	−	11.4454i	0.520788	−	0.378374i
$916$	−15.4508			−0.510510
$917$	1.80244	−	5.54734i	0.0595218	−	0.183189i
$918$	−0.381966	−	1.17557i	−0.0126068	−	0.0387996i
$919$	5.42705	−	3.94298i	0.179022	−	0.130067i	−0.494666	−	0.869083i	$-0.664709\pi$
$919$	5.42705	−	3.94298i	0.179022	−	0.130067i	0.673687	+	0.739016i	$0.264709\pi$
$920$	−7.50000	−	5.44907i	−0.247268	−	0.179650i
$921$	−5.35410	−	16.4782i	−0.176424	−	0.542976i
$922$	51.0967	+	37.1240i	1.68278	+	1.22261i
$923$	24.5623	−	17.8456i	0.808478	−	0.587394i
$924$	−1.50000	−	5.96361i	−0.0493464	−	0.196188i
$925$	35.8156	−	26.0216i	1.17761	−	0.855583i
$926$	0.291796	−	0.898056i	0.00958901	−	0.0295119i
$927$	−0.545085	+	1.67760i	−0.0179029	+	0.0550996i
$928$	−14.5729	+	10.5879i	−0.478380	+	0.347564i
$929$	52.0344			1.70719			0.853597	−	0.520933i	$-0.174416\pi$
$929$	52.0344			1.70719			0.853597	+	0.520933i	$0.174416\pi$
$930$	−37.0344			−1.21441
$931$	−0.854102	+	2.62866i	−0.0279921	+	0.0861507i
$932$	7.85410	−	5.70634i	0.257270	−	0.186917i
$933$	−10.6180			−0.347619
$934$	−48.3607	−	35.1361i	−1.58241	−	1.14969i
$935$	5.65248	+	0.383516i	0.184856	+	0.0125423i
$936$	−5.85410	+	4.25325i	−0.191347	+	0.139022i
$937$	41.6976	−	30.2951i	1.36220	−	0.989696i	0.363898	−	0.931439i	$-0.381446\pi$
$937$	41.6976	−	30.2951i	1.36220	−	0.989696i	0.998302	−	0.0582575i	$-0.0185544\pi$
$938$	−14.5623			−0.475476
$939$	29.1246			0.950446
$940$	4.30902	+	13.2618i	0.140545	+	0.432552i
$941$	−5.56231	+	17.1190i	−0.181326	+	0.558064i	−0.999866	−	0.0163859i	$-0.994784\pi$
$941$	−5.56231	+	17.1190i	−0.181326	+	0.558064i	0.818540	+	0.574450i	$0.194784\pi$
$942$	7.28115	−	22.4091i	0.237233	−	0.730127i
$943$	−0.135255	+	0.0982684i	−0.00440451	+	0.00320006i
$944$	26.8328			0.873334
$945$	2.07295	−	6.37988i	0.0674330	−	0.207538i
$946$	7.85410	+	31.2259i	0.255359	+	1.01524i
$947$	3.70820	−	11.4127i	0.120500	−	0.370862i	−0.872554	−	0.488518i	$-0.837538\pi$
$947$	3.70820	−	11.4127i	0.120500	−	0.370862i	0.993054	+	0.117655i	$0.0375378\pi$
$948$	0.954915	+	2.93893i	0.0310142	+	0.0954519i
$949$	−22.4164	+	16.2865i	−0.727667	+	0.528681i
$950$	11.1803			0.362738
$951$	7.14590	+	21.9928i	0.231722	+	0.713166i
$952$	−4.14590	−	3.01217i	−0.134369	−	0.0976250i
$953$	−4.32624	+	3.14320i	−0.140141	+	0.101818i	−0.655647	−	0.755068i	$-0.727604\pi$
$953$	−4.32624	+	3.14320i	−0.140141	+	0.101818i	0.515506	+	0.856886i	$0.327604\pi$
$954$	3.38197	+	10.4086i	0.109495	+	0.336992i
$955$	−1.11803	+	3.44095i	−0.0361787	+	0.111347i
$956$	3.71885	+	11.4454i	0.120276	+	0.370172i
$957$	−13.5557	−	11.3269i	−0.438194	−	0.366147i
$958$	−0.954915	−	2.93893i	−0.0308519	−	0.0949524i
$959$	−36.4894	+	26.5111i	−1.17830	+	0.856087i
$960$	−9.47214			−0.305712
$961$	73.7771			2.37991
$962$	14.3262	−	44.0916i	0.461896	−	1.42157i
$963$	5.19098	−	15.9762i	0.167277	−	0.514826i
$964$	12.0902			0.389398
$965$	−12.0344	+	37.0382i	−0.387402	+	1.19230i
$966$	7.28115	−	5.29007i	0.234267	−	0.170205i
$967$	13.0172	+	40.0629i	0.418606	+	1.28834i	0.908986	+	0.416827i	$0.136858\pi$
$967$	13.0172	+	40.0629i	0.418606	+	1.28834i	−0.490380	+	0.871509i	$0.663142\pi$
$968$	−17.7639	−	17.0130i	−0.570954	−	0.546819i
$969$	−0.326238	−	1.00406i	−0.0104803	−	0.0322550i
$970$	7.39919	−	5.37582i	0.237574	−	0.172607i
$971$	−3.36475	−	10.3556i	−0.107980	−	0.332328i	0.882438	−	0.470428i	$-0.155900\pi$
$971$	−3.36475	−	10.3556i	−0.107980	−	0.332328i	−0.990418	+	0.138100i	$0.955900\pi$
$972$	0.500000	−	0.363271i	0.0160375	−	0.0116519i
$973$	−33.8435	−	24.5887i	−1.08497	−	0.788278i
$974$	6.23607	+	19.1926i	0.199817	+	0.614972i
$975$	−5.00000	+	15.3884i	−0.160128	+	0.492824i
$976$	34.1976	−	24.8460i	1.09464	−	0.795301i
$977$	−7.77458	−	23.9277i	−0.248731	−	0.765514i	−0.995000	−	0.0998707i	$-0.968157\pi$
$977$	−7.77458	−	23.9277i	−0.248731	−	0.765514i	0.746270	−	0.665644i	$-0.231843\pi$
$978$	−3.28115	+	10.0984i	−0.104920	+	0.322910i
$979$	−6.28115	+	3.94298i	−0.200747	+	0.126018i
$980$	0.854102	+	2.62866i	0.0272833	+	0.0839693i
$981$	11.7082			0.373814
$982$	−50.3328	+	36.5689i	−1.60618	+	1.16696i
$983$	3.80244	−	11.7027i	0.121279	−	0.373258i	−0.871926	−	0.489638i	$-0.837129\pi$
$983$	3.80244	−	11.7027i	0.121279	−	0.373258i	0.993205	+	0.116380i	$0.0371289\pi$
$984$	−0.0623059	+	0.191758i	−0.00198624	+	0.00611302i
$985$	−25.7533	+	18.7109i	−0.820568	+	0.596178i
$986$	6.58359			0.209664
$987$	30.2705			0.963521
$988$	2.23607	−	1.62460i	0.0711388	−	0.0516854i
$989$	−9.00000	+	6.53888i	−0.286183	+	0.207924i
$990$	2.92705	+	11.6372i	0.0930278	+	0.369854i
$991$	−17.7984	−	12.9313i	−0.565384	−	0.410776i	0.268041	−	0.963407i	$-0.413624\pi$
$991$	−17.7984	−	12.9313i	−0.565384	−	0.410776i	−0.833425	+	0.552632i	$0.813624\pi$
$992$	−34.6180			−1.09912
$993$	28.9164	−	21.0090i	0.917634	−	0.666700i
$994$	−14.0729	+	43.3121i	−0.446367	+	1.37378i
$995$	17.7254	+	12.8783i	0.561934	+	0.408269i
$996$	3.32624			0.105396
$997$	4.13525	−	3.00444i	0.130965	−	0.0951515i	−0.520374	−	0.853938i	$-0.674208\pi$
$997$	4.13525	−	3.00444i	0.130965	−	0.0951515i	0.651339	+	0.758787i	$0.274208\pi$
$998$	7.56231	−	23.2744i	0.239381	−	0.736738i
$999$	2.73607	−	8.42075i	0.0865654	−	0.266421i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.m.a.361.1	yes	4
11.5	even	5		825.2.o.b.511.1	yes	4
25.16	even	5		825.2.o.b.691.1	yes	4
275.16	even	5	inner	825.2.m.a.16.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.m.a.16.1	✓	4	275.16	even	5	inner
825.2.m.a.361.1	yes	4	1.1	even	1	trivial
825.2.o.b.511.1	yes	4	11.5	even	5
825.2.o.b.691.1	yes	4	25.16	even	5

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.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 1.53884i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.500000 + 0.363271i) q^{4} +(-1.80902 - 1.31433i) q^{5} +(-1.30902 + 0.951057i) q^{6} +(2.42705 + 1.76336i) q^{7} +(-1.80902 - 1.31433i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 1.53884i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.500000 + 0.363271i) q^{4} +(-1.80902 - 1.31433i) q^{5} +(-1.30902 + 0.951057i) q^{6} +(2.42705 + 1.76336i) q^{7} +(-1.80902 - 1.31433i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-1.11803 + 3.44095i) q^{10} +(-3.30902 - 0.224514i) q^{11} +(0.500000 + 0.363271i) q^{12} +(-2.61803 + 1.90211i) q^{13} +(1.50000 - 4.61653i) q^{14} +(-0.690983 + 2.12663i) q^{15} +(-1.50000 + 4.61653i) q^{16} +(0.618034 - 0.449028i) q^{17} +(1.30902 + 0.951057i) q^{18} +(1.11803 + 0.812299i) q^{19} +1.38197 q^{20} +(0.927051 - 2.85317i) q^{21} +(1.30902 + 5.20431i) q^{22} +(-1.50000 + 1.08981i) q^{23} +(-0.690983 + 2.12663i) q^{24} +(1.54508 + 4.75528i) q^{25} +(4.23607 + 3.07768i) q^{26} +(0.809017 + 0.587785i) q^{27} -1.85410 q^{28} +(-4.30902 + 3.13068i) q^{29} +3.61803 q^{30} -10.2361 q^{31} +3.38197 q^{32} +(0.809017 + 3.21644i) q^{33} +(-1.00000 - 0.726543i) q^{34} +(-2.07295 - 6.37988i) q^{35} +(0.190983 - 0.587785i) q^{36} +(-2.73607 - 8.42075i) q^{37} +(0.690983 - 2.12663i) q^{38} +(2.61803 + 1.90211i) q^{39} +(1.54508 + 4.75528i) q^{40} +0.0901699 q^{41} -4.85410 q^{42} +6.00000 q^{43} +(1.73607 - 1.08981i) q^{44} +2.23607 q^{45} +(2.42705 + 1.76336i) q^{46} +(3.11803 + 9.59632i) q^{47} +4.85410 q^{48} +(0.618034 + 1.90211i) q^{49} +(6.54508 - 4.75528i) q^{50} +(-0.618034 - 0.449028i) q^{51} +(0.618034 - 1.90211i) q^{52} +(5.47214 + 3.97574i) q^{53} +(0.500000 - 1.53884i) q^{54} +(5.69098 + 4.75528i) q^{55} +(-2.07295 - 6.37988i) q^{56} +(0.427051 - 1.31433i) q^{57} +(6.97214 + 5.06555i) q^{58} +(-1.70820 - 5.25731i) q^{59} +(-0.427051 - 1.31433i) q^{60} +(-7.04508 - 5.11855i) q^{61} +(5.11803 + 15.7517i) q^{62} -3.00000 q^{63} +(1.30902 + 4.02874i) q^{64} +7.23607 q^{65} +(4.54508 - 2.85317i) q^{66} +(-0.927051 - 2.85317i) q^{67} +(-0.145898 + 0.449028i) q^{68} +(1.50000 + 1.08981i) q^{69} +(-8.78115 + 6.37988i) q^{70} -9.38197 q^{71} +2.23607 q^{72} +8.56231 q^{73} +(-11.5902 + 8.42075i) q^{74} +(4.04508 - 2.93893i) q^{75} -0.854102 q^{76} +(-7.63525 - 6.37988i) q^{77} +(1.61803 - 4.97980i) q^{78} +(4.04508 + 2.93893i) q^{79} +(8.78115 - 6.37988i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-0.0450850 - 0.138757i) q^{82} +(4.35410 - 3.16344i) q^{83} +(0.572949 + 1.76336i) q^{84} -1.70820 q^{85} +(-3.00000 - 9.23305i) q^{86} +(4.30902 + 3.13068i) q^{87} +(5.69098 + 4.75528i) q^{88} +(1.80902 - 1.31433i) q^{89} +(-1.11803 - 3.44095i) q^{90} -9.70820 q^{91} +(0.354102 - 1.08981i) q^{92} +(3.16312 + 9.73508i) q^{93} +(13.2082 - 9.59632i) q^{94} +(-0.954915 - 2.93893i) q^{95} +(-1.04508 - 3.21644i) q^{96} +(-2.04508 - 1.48584i) q^{97} +(2.61803 - 1.90211i) q^{98} +(2.80902 - 1.76336i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + q^{3} - 2 q^{4} - 5 q^{5} - 3 q^{6} + 3 q^{7} - 5 q^{8} - q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + q^3 - 2 * q^4 - 5 * q^5 - 3 * q^6 + 3 * q^7 - 5 * q^8 - q^9	\( 4 q - 2 q^{2} + q^{3} - 2 q^{4} - 5 q^{5} - 3 q^{6} + 3 q^{7} - 5 q^{8} - q^{9} - 11 q^{11} + 2 q^{12} - 6 q^{13} + 6 q^{14} - 5 q^{15} - 6 q^{16} - 2 q^{17} + 3 q^{18} + 10 q^{20} - 3 q^{21} + 3 q^{22} - 6 q^{23} - 5 q^{24} - 5 q^{25} + 8 q^{26} + q^{27} + 6 q^{28} - 15 q^{29} + 10 q^{30} - 32 q^{31} + 18 q^{32} + q^{33} - 4 q^{34} - 15 q^{35} + 3 q^{36} - 2 q^{37} + 5 q^{38} + 6 q^{39} - 5 q^{40} - 22 q^{41} - 6 q^{42} + 24 q^{43} - 2 q^{44} + 3 q^{46} + 8 q^{47} + 6 q^{48} - 2 q^{49} + 15 q^{50} + 2 q^{51} - 2 q^{52} + 4 q^{53} + 2 q^{54} + 25 q^{55} - 15 q^{56} - 5 q^{57} + 10 q^{58} + 20 q^{59} + 5 q^{60} - 17 q^{61} + 16 q^{62} - 12 q^{63} + 3 q^{64} + 20 q^{65} + 7 q^{66} + 3 q^{67} - 14 q^{68} + 6 q^{69} - 15 q^{70} - 42 q^{71} - 6 q^{73} - 24 q^{74} + 5 q^{75} + 10 q^{76} + 3 q^{77} + 2 q^{78} + 5 q^{79} + 15 q^{80} - q^{81} + 11 q^{82} + 4 q^{83} + 9 q^{84} + 20 q^{85} - 12 q^{86} + 15 q^{87} + 25 q^{88} + 5 q^{89} - 12 q^{91} - 12 q^{92} - 3 q^{93} + 26 q^{94} - 15 q^{95} + 7 q^{96} + 3 q^{97} + 6 q^{98} + 9 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + q^3 - 2 * q^4 - 5 * q^5 - 3 * q^6 + 3 * q^7 - 5 * q^8 - q^9 - 11 * q^11 + 2 * q^12 - 6 * q^13 + 6 * q^14 - 5 * q^15 - 6 * q^16 - 2 * q^17 + 3 * q^18 + 10 * q^20 - 3 * q^21 + 3 * q^22 - 6 * q^23 - 5 * q^24 - 5 * q^25 + 8 * q^26 + q^27 + 6 * q^28 - 15 * q^29 + 10 * q^30 - 32 * q^31 + 18 * q^32 + q^33 - 4 * q^34 - 15 * q^35 + 3 * q^36 - 2 * q^37 + 5 * q^38 + 6 * q^39 - 5 * q^40 - 22 * q^41 - 6 * q^42 + 24 * q^43 - 2 * q^44 + 3 * q^46 + 8 * q^47 + 6 * q^48 - 2 * q^49 + 15 * q^50 + 2 * q^51 - 2 * q^52 + 4 * q^53 + 2 * q^54 + 25 * q^55 - 15 * q^56 - 5 * q^57 + 10 * q^58 + 20 * q^59 + 5 * q^60 - 17 * q^61 + 16 * q^62 - 12 * q^63 + 3 * q^64 + 20 * q^65 + 7 * q^66 + 3 * q^67 - 14 * q^68 + 6 * q^69 - 15 * q^70 - 42 * q^71 - 6 * q^73 - 24 * q^74 + 5 * q^75 + 10 * q^76 + 3 * q^77 + 2 * q^78 + 5 * q^79 + 15 * q^80 - q^81 + 11 * q^82 + 4 * q^83 + 9 * q^84 + 20 * q^85 - 12 * q^86 + 15 * q^87 + 25 * q^88 + 5 * q^89 - 12 * q^91 - 12 * q^92 - 3 * q^93 + 26 * q^94 - 15 * q^95 + 7 * q^96 + 3 * q^97 + 6 * q^98 + 9 * q^99

Introduction

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