LMFDB - Embedded newform 825.2.o.b.691.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(421,825)]

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, 6, 8]))

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

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

chi := DirichletCharacter("825.421");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.o (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:	$0$
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			691.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	825.691
Dual form			825.2.o.b.511.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30902 - 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.190983 - 0.587785i) q^{4} +(0.690983 - 2.12663i) q^{5} +1.61803 q^{6} +(2.42705 + 1.76336i) q^{7} +(0.690983 + 2.12663i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(1.30902 - 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.190983 - 0.587785i) q^{4} +(0.690983 - 2.12663i) q^{5} +1.61803 q^{6} +(2.42705 + 1.76336i) q^{7} +(0.690983 + 2.12663i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-1.11803 - 3.44095i) q^{10} +(-0.809017 - 3.21644i) q^{11} +(0.500000 - 0.363271i) q^{12} +(1.00000 + 3.07768i) q^{13} +4.85410 q^{14} +(1.80902 - 1.31433i) q^{15} +(3.92705 + 2.85317i) q^{16} -0.763932 q^{17} +(1.30902 + 0.951057i) q^{18} +(-0.427051 - 1.31433i) q^{19} +(-1.11803 - 0.812299i) q^{20} +(0.927051 + 2.85317i) q^{21} +(-4.11803 - 3.44095i) q^{22} +(-1.50000 - 1.08981i) q^{23} +(-0.690983 + 2.12663i) q^{24} +(-4.04508 - 2.93893i) q^{25} +(4.23607 + 3.07768i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(1.50000 - 1.08981i) q^{28} +(1.64590 - 5.06555i) q^{29} +(1.11803 - 3.44095i) q^{30} +(8.28115 + 6.01661i) q^{31} +3.38197 q^{32} +(1.23607 - 3.07768i) q^{33} +(-1.00000 + 0.726543i) q^{34} +(5.42705 - 3.94298i) q^{35} +0.618034 q^{36} -8.85410 q^{37} +(-1.80902 - 1.31433i) q^{38} +(-1.00000 + 3.07768i) q^{39} +5.00000 q^{40} +(0.0278640 - 0.0857567i) q^{41} +(3.92705 + 2.85317i) q^{42} +6.00000 q^{43} +(-2.04508 - 0.138757i) q^{44} +2.23607 q^{45} -3.00000 q^{46} +(-8.16312 - 5.93085i) q^{47} +(1.50000 + 4.61653i) q^{48} +(0.618034 + 1.90211i) q^{49} -8.09017 q^{50} +(-0.618034 - 0.449028i) q^{51} +2.00000 q^{52} -6.76393 q^{53} +(0.500000 + 1.53884i) q^{54} +(-7.39919 - 0.502029i) q^{55} +(-2.07295 + 6.37988i) q^{56} +(0.427051 - 1.31433i) q^{57} +(-2.66312 - 8.19624i) q^{58} -5.52786 q^{59} +(-0.427051 - 1.31433i) q^{60} +(2.69098 - 8.28199i) q^{61} +16.5623 q^{62} +(-0.927051 + 2.85317i) q^{63} +(-3.42705 + 2.48990i) q^{64} +7.23607 q^{65} +(-1.30902 - 5.20431i) q^{66} +(-0.927051 + 2.85317i) q^{67} +(-0.145898 + 0.449028i) q^{68} +(-0.572949 - 1.76336i) q^{69} +(3.35410 - 10.3229i) q^{70} +(7.59017 - 5.51458i) q^{71} +(-1.80902 + 1.31433i) q^{72} +(2.64590 + 8.14324i) q^{73} +(-11.5902 + 8.42075i) q^{74} +(-1.54508 - 4.75528i) q^{75} -0.854102 q^{76} +(3.70820 - 9.23305i) q^{77} +(1.61803 + 4.97980i) q^{78} -5.00000 q^{79} +(8.78115 - 6.37988i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-0.0450850 - 0.138757i) q^{82} -5.38197 q^{83} +1.85410 q^{84} +(-0.527864 + 1.62460i) q^{85} +(7.85410 - 5.70634i) q^{86} +(4.30902 - 3.13068i) q^{87} +(6.28115 - 3.94298i) q^{88} +(1.80902 + 1.31433i) q^{89} +(2.92705 - 2.12663i) q^{90} +(-3.00000 + 9.23305i) q^{91} +(-0.927051 + 0.673542i) q^{92} +(3.16312 + 9.73508i) q^{93} -16.3262 q^{94} -3.09017 q^{95} +(2.73607 + 1.98787i) q^{96} +2.52786 q^{97} +(2.61803 + 1.90211i) q^{98} +(2.80902 - 1.76336i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} + q^{3} + 3 q^{4} + 5 q^{5} + 2 q^{6} + 3 q^{7} + 5 q^{8} - q^{9}+O(q^{10}) $ 4 * q + 3 * q^2 + q^3 + 3 * q^4 + 5 * q^5 + 2 * q^6 + 3 * q^7 + 5 * q^8 - q^9	\( 4 q + 3 q^{2} + q^{3} + 3 q^{4} + 5 q^{5} + 2 q^{6} + 3 q^{7} + 5 q^{8} - q^{9} - q^{11} + 2 q^{12} + 4 q^{13} + 6 q^{14} + 5 q^{15} + 9 q^{16} - 12 q^{17} + 3 q^{18} + 5 q^{19} - 3 q^{21} - 12 q^{22} - 6 q^{23} - 5 q^{24} - 5 q^{25} + 8 q^{26} + q^{27} + 6 q^{28} + 20 q^{29} + 13 q^{31} + 18 q^{32} - 4 q^{33} - 4 q^{34} + 15 q^{35} - 2 q^{36} - 22 q^{37} - 5 q^{38} - 4 q^{39} + 20 q^{40} + 18 q^{41} + 9 q^{42} + 24 q^{43} + 3 q^{44} - 12 q^{46} - 17 q^{47} + 6 q^{48} - 2 q^{49} - 10 q^{50} + 2 q^{51} + 8 q^{52} - 36 q^{53} + 2 q^{54} - 5 q^{55} - 15 q^{56} - 5 q^{57} + 5 q^{58} - 40 q^{59} + 5 q^{60} + 13 q^{61} + 26 q^{62} + 3 q^{63} - 7 q^{64} + 20 q^{65} - 3 q^{66} + 3 q^{67} - 14 q^{68} - 9 q^{69} + 8 q^{71} - 5 q^{72} + 24 q^{73} - 24 q^{74} + 5 q^{75} + 10 q^{76} - 12 q^{77} + 2 q^{78} - 20 q^{79} + 15 q^{80} - q^{81} + 11 q^{82} - 26 q^{83} - 6 q^{84} - 20 q^{85} + 18 q^{86} + 15 q^{87} + 5 q^{88} + 5 q^{89} + 5 q^{90} - 12 q^{91} + 3 q^{92} - 3 q^{93} - 34 q^{94} + 10 q^{95} + 2 q^{96} + 28 q^{97} + 6 q^{98} + 9 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 + q^3 + 3 * q^4 + 5 * q^5 + 2 * q^6 + 3 * q^7 + 5 * q^8 - q^9 - q^11 + 2 * q^12 + 4 * q^13 + 6 * q^14 + 5 * q^15 + 9 * q^16 - 12 * q^17 + 3 * q^18 + 5 * q^19 - 3 * q^21 - 12 * q^22 - 6 * q^23 - 5 * q^24 - 5 * q^25 + 8 * q^26 + q^27 + 6 * q^28 + 20 * q^29 + 13 * q^31 + 18 * q^32 - 4 * q^33 - 4 * q^34 + 15 * q^35 - 2 * q^36 - 22 * q^37 - 5 * q^38 - 4 * q^39 + 20 * q^40 + 18 * q^41 + 9 * q^42 + 24 * q^43 + 3 * q^44 - 12 * q^46 - 17 * q^47 + 6 * q^48 - 2 * q^49 - 10 * q^50 + 2 * q^51 + 8 * q^52 - 36 * q^53 + 2 * q^54 - 5 * q^55 - 15 * q^56 - 5 * q^57 + 5 * q^58 - 40 * q^59 + 5 * q^60 + 13 * q^61 + 26 * q^62 + 3 * q^63 - 7 * q^64 + 20 * q^65 - 3 * q^66 + 3 * q^67 - 14 * q^68 - 9 * q^69 + 8 * q^71 - 5 * q^72 + 24 * q^73 - 24 * q^74 + 5 * q^75 + 10 * q^76 - 12 * q^77 + 2 * q^78 - 20 * q^79 + 15 * q^80 - q^81 + 11 * q^82 - 26 * q^83 - 6 * q^84 - 20 * q^85 + 18 * q^86 + 15 * q^87 + 5 * q^88 + 5 * q^89 + 5 * q^90 - 12 * q^91 + 3 * q^92 - 3 * q^93 - 34 * q^94 + 10 * q^95 + 2 * q^96 + 28 * q^97 + 6 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.30902	−	0.951057i	0.925615	−	0.672499i	−0.0193004	−	0.999814i	$-0.506144\pi$
$2$	1.30902	−	0.951057i	0.925615	−	0.672499i	0.944915	+	0.327315i	$0.106144\pi$
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$	0.190983	−	0.587785i	0.0954915	−	0.293893i
$5$	0.690983	−	2.12663i	0.309017	−	0.951057i
$5$	0.690983	−	2.12663i	0.309017	−	0.951057i
$6$	1.61803			0.660560
$7$	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	$0.508125\pi$
$8$	0.690983	+	2.12663i	0.244299	+	0.751876i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	−1.11803	−	3.44095i	−0.353553	−	1.08813i
$11$	−0.809017	−	3.21644i	−0.243928	−	0.969793i
$11$	−0.809017	−	3.21644i	−0.243928	−	0.969793i
$12$	0.500000	−	0.363271i	0.144338	−	0.104867i
$13$	1.00000	+	3.07768i	0.277350	+	0.853596i	0.988588	+	0.150644i	$0.0481349\pi$
$13$	1.00000	+	3.07768i	0.277350	+	0.853596i	−0.711238	+	0.702951i	$0.751865\pi$
$14$	4.85410			1.29731
$15$	1.80902	−	1.31433i	0.467086	−	0.339358i
$16$	3.92705	+	2.85317i	0.981763	+	0.713292i
$17$	−0.763932			−0.185281			−0.0926404	−	0.995700i	$-0.529531\pi$
$17$	−0.763932			−0.185281			−0.0926404	+	0.995700i	$0.529531\pi$
$18$	1.30902	+	0.951057i	0.308538	+	0.224166i
$19$	−0.427051	−	1.31433i	−0.0979722	−	0.301527i	0.890045	−	0.455873i	$-0.150673\pi$
$19$	−0.427051	−	1.31433i	−0.0979722	−	0.301527i	−0.988017	+	0.154346i	$0.950673\pi$
$20$	−1.11803	−	0.812299i	−0.250000	−	0.181636i
$21$	0.927051	+	2.85317i	0.202299	+	0.622613i
$22$	−4.11803	−	3.44095i	−0.877968	−	0.733614i
$23$	−1.50000	−	1.08981i	−0.312772	−	0.227242i	0.420313	−	0.907379i	$-0.361920\pi$
$23$	−1.50000	−	1.08981i	−0.312772	−	0.227242i	−0.733085	+	0.680137i	$0.761920\pi$
$24$	−0.690983	+	2.12663i	−0.141046	+	0.434096i
$25$	−4.04508	−	2.93893i	−0.809017	−	0.587785i
$26$	4.23607	+	3.07768i	0.830761	+	0.603583i
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	1.50000	−	1.08981i	0.283473	−	0.205955i
$29$	1.64590	−	5.06555i	0.305636	−	0.940650i	−0.673804	−	0.738910i	$-0.735341\pi$
$29$	1.64590	−	5.06555i	0.305636	−	0.940650i	0.979439	−	0.201739i	$-0.0646593\pi$
$30$	1.11803	−	3.44095i	0.204124	−	0.628230i
$31$	8.28115	+	6.01661i	1.48734	+	1.08062i	0.975098	+	0.221773i	$0.0711844\pi$
$31$	8.28115	+	6.01661i	1.48734	+	1.08062i	0.512241	+	0.858842i	$0.328816\pi$
$32$	3.38197			0.597853
$33$	1.23607	−	3.07768i	0.215172	−	0.535756i
$34$	−1.00000	+	0.726543i	−0.171499	+	0.124601i
$35$	5.42705	−	3.94298i	0.917339	−	0.666486i
$36$	0.618034			0.103006
$37$	−8.85410			−1.45561			−0.727803	−	0.685787i	$-0.759458\pi$
$37$	−8.85410			−1.45561			−0.727803	+	0.685787i	$0.759458\pi$
$38$	−1.80902	−	1.31433i	−0.293461	−	0.213212i
$39$	−1.00000	+	3.07768i	−0.160128	+	0.492824i
$40$	5.00000			0.790569
$41$	0.0278640	−	0.0857567i	0.00435163	−	0.0133929i	−0.948857	−	0.315706i	$-0.897759\pi$
$41$	0.0278640	−	0.0857567i	0.00435163	−	0.0133929i	0.953209	+	0.302313i	$0.0977587\pi$
$42$	3.92705	+	2.85317i	0.605957	+	0.440254i
$43$	6.00000			0.914991			0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000			0.914991			0.457496	+	0.889212i	$0.348747\pi$
$44$	−2.04508	−	0.138757i	−0.308308	−	0.0209184i
$45$	2.23607			0.333333
$46$	−3.00000			−0.442326
$47$	−8.16312	−	5.93085i	−1.19071	−	0.865104i	−0.197374	−	0.980328i	$-0.563241\pi$
$47$	−8.16312	−	5.93085i	−1.19071	−	0.865104i	−0.993339	+	0.115224i	$0.963241\pi$
$48$	1.50000	+	4.61653i	0.216506	+	0.666338i
$49$	0.618034	+	1.90211i	0.0882906	+	0.271730i
$50$	−8.09017			−1.14412
$51$	−0.618034	−	0.449028i	−0.0865421	−	0.0628765i
$52$	2.00000			0.277350
$53$	−6.76393			−0.929098			−0.464549	−	0.885548i	$-0.653783\pi$
$53$	−6.76393			−0.929098			−0.464549	+	0.885548i	$0.653783\pi$
$54$	0.500000	+	1.53884i	0.0680414	+	0.209410i
$55$	−7.39919	−	0.502029i	−0.997706	−	0.0676935i
$56$	−2.07295	+	6.37988i	−0.277009	+	0.852547i
$57$	0.427051	−	1.31433i	0.0565643	−	0.174087i
$58$	−2.66312	−	8.19624i	−0.349685	−	1.07622i
$59$	−5.52786			−0.719667			−0.359833	−	0.933017i	$-0.617166\pi$
$59$	−5.52786			−0.719667			−0.359833	+	0.933017i	$0.617166\pi$
$60$	−0.427051	−	1.31433i	−0.0551320	−	0.169679i
$61$	2.69098	−	8.28199i	0.344545	−	1.06040i	−0.617282	−	0.786742i	$-0.711766\pi$
$61$	2.69098	−	8.28199i	0.344545	−	1.06040i	0.961827	−	0.273659i	$-0.0882338\pi$
$62$	16.5623			2.10341
$63$	−0.927051	+	2.85317i	−0.116797	+	0.359466i
$64$	−3.42705	+	2.48990i	−0.428381	+	0.311237i
$65$	7.23607			0.897524
$66$	−1.30902	−	5.20431i	−0.161129	−	0.640606i
$67$	−0.927051	+	2.85317i	−0.113257	+	0.348570i	−0.991580	−	0.129499i	$-0.958663\pi$
$67$	−0.927051	+	2.85317i	−0.113257	+	0.348570i	0.878322	+	0.478069i	$0.158663\pi$
$68$	−0.145898	+	0.449028i	−0.0176927	+	0.0544526i
$69$	−0.572949	−	1.76336i	−0.0689750	−	0.212283i
$70$	3.35410	−	10.3229i	0.400892	−	1.23382i
$71$	7.59017	−	5.51458i	0.900787	−	0.654460i	−0.0378807	−	0.999282i	$-0.512061\pi$
$71$	7.59017	−	5.51458i	0.900787	−	0.654460i	0.938668	+	0.344822i	$0.112061\pi$
$72$	−1.80902	+	1.31433i	−0.213195	+	0.154895i
$73$	2.64590	+	8.14324i	0.309679	+	0.953094i	0.977890	+	0.209122i	$0.0670605\pi$
$73$	2.64590	+	8.14324i	0.309679	+	0.953094i	−0.668211	+	0.743972i	$0.732940\pi$
$74$	−11.5902	+	8.42075i	−1.34733	+	0.978892i
$75$	−1.54508	−	4.75528i	−0.178411	−	0.549093i
$76$	−0.854102			−0.0979722
$77$	3.70820	−	9.23305i	0.422589	−	1.05220i
$78$	1.61803	+	4.97980i	0.183206	+	0.563851i
$79$	−5.00000			−0.562544			−0.281272	−	0.959628i	$-0.590756\pi$
$79$	−5.00000			−0.562544			−0.281272	+	0.959628i	$0.590756\pi$
$80$	8.78115	−	6.37988i	0.981763	−	0.713292i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−0.0450850	−	0.138757i	−0.00497880	−	0.0153232i
$83$	−5.38197			−0.590748			−0.295374	−	0.955382i	$-0.595444\pi$
$83$	−5.38197			−0.590748			−0.295374	+	0.955382i	$0.595444\pi$
$84$	1.85410			0.202299
$85$	−0.527864	+	1.62460i	−0.0572549	+	0.176212i
$86$	7.85410	−	5.70634i	0.846930	−	0.615330i
$87$	4.30902	−	3.13068i	0.461975	−	0.335645i
$88$	6.28115	−	3.94298i	0.669573	−	0.420323i
$89$	1.80902	+	1.31433i	0.191755	+	0.139318i	0.679521	−	0.733656i	$-0.262188\pi$
$89$	1.80902	+	1.31433i	0.191755	+	0.139318i	−0.487765	+	0.872975i	$0.662188\pi$
$90$	2.92705	−	2.12663i	0.308538	−	0.224166i
$91$	−3.00000	+	9.23305i	−0.314485	+	0.967887i
$92$	−0.927051	+	0.673542i	−0.0966517	+	0.0702216i
$93$	3.16312	+	9.73508i	0.328000	+	1.00948i
$94$	−16.3262			−1.68392
$95$	−3.09017			−0.317045
$96$	2.73607	+	1.98787i	0.279249	+	0.202886i
$97$	2.52786			0.256666			0.128333	−	0.991731i	$-0.459037\pi$
$97$	2.52786			0.256666			0.128333	+	0.991731i	$0.459037\pi$
$98$	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	$0.0598612\pi$
$102$	−1.23607			−0.122389
$103$	−0.545085	+	1.67760i	−0.0537088	+	0.165299i	−0.974313	−	0.225199i	$-0.927697\pi$
$103$	−0.545085	+	1.67760i	−0.0537088	+	0.165299i	0.920604	+	0.390497i	$0.127697\pi$
$104$	−5.85410	+	4.25325i	−0.574042	+	0.417066i
$105$	6.70820			0.654654
$106$	−8.85410	+	6.43288i	−0.859986	+	0.624817i
$107$	−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	$0.998390\pi$
$108$	0.500000	+	0.363271i	0.0481125	+	0.0349558i
$109$	−9.47214	+	6.88191i	−0.907266	+	0.659167i	−0.940322	−	0.340286i	$-0.889476\pi$
$109$	−9.47214	+	6.88191i	−0.907266	+	0.659167i	0.0330559	+	0.999454i	$0.489476\pi$
$110$	−10.1631	+	6.37988i	−0.969015	+	0.608298i
$111$	−7.16312	−	5.20431i	−0.679893	−	0.493971i
$112$	4.50000	+	13.8496i	0.425210	+	1.30866i
$113$	−3.14590	+	9.68208i	−0.295941	+	0.910813i	0.686962	+	0.726693i	$0.258944\pi$
$113$	−3.14590	+	9.68208i	−0.295941	+	0.910813i	−0.982904	+	0.184120i	$0.941056\pi$
$114$	−0.690983	−	2.12663i	−0.0647165	−	0.199177i
$115$	−3.35410	+	2.43690i	−0.312772	+	0.227242i
$116$	−2.66312	−	1.93487i	−0.247264	−	0.179648i
$117$	−2.61803	+	1.90211i	−0.242037	+	0.175850i
$118$	−7.23607	+	5.25731i	−0.666134	+	0.483975i
$119$	−1.85410	−	1.34708i	−0.169965	−	0.123487i
$120$	4.04508	+	2.93893i	0.369264	+	0.268286i
$121$	−9.69098	+	5.20431i	−0.880998	+	0.473119i
$122$	−4.35410	−	13.4005i	−0.394202	−	1.21323i
$123$	0.0729490	−	0.0530006i	0.00657759	−	0.00477890i
$124$	5.11803	−	3.71847i	0.459613	−	0.333928i
$125$	−9.04508	+	6.57164i	−0.809017	+	0.587785i
$126$	1.50000	+	4.61653i	0.133631	+	0.411273i
$127$	3.21885	−	9.90659i	0.285626	−	0.879068i	−0.700584	−	0.713570i	$-0.747077\pi$
$127$	3.21885	−	9.90659i	0.285626	−	0.879068i	0.986210	−	0.165498i	$-0.0529230\pi$
$128$	−4.20820	+	12.9515i	−0.371956	+	1.14476i
$129$	4.85410	+	3.52671i	0.427380	+	0.310510i
$130$	9.47214	−	6.88191i	0.830761	−	0.603583i
$131$	−0.600813	+	1.84911i	−0.0524933	+	0.161558i	−0.973866	−	0.227121i	$-0.927069\pi$
$131$	−0.600813	+	1.84911i	−0.0524933	+	0.161558i	0.921373	+	0.388679i	$0.127069\pi$
$132$	−1.57295	−	1.31433i	−0.136908	−	0.114398i
$133$	1.28115	−	3.94298i	0.111090	−	0.341900i
$134$	1.50000	+	4.61653i	0.129580	+	0.398807i
$135$	1.80902	+	1.31433i	0.155695	+	0.113119i
$136$	−0.527864	−	1.62460i	−0.0452640	−	0.139308i
$137$	12.1631	+	8.83702i	1.03917	+	0.754998i	0.970122	−	0.242616i	$-0.0780055\pi$
$137$	12.1631	+	8.83702i	1.03917	+	0.754998i	0.0690429	+	0.997614i	$0.478005\pi$
$138$	−2.42705	−	1.76336i	−0.206604	−	0.150107i
$139$	−4.30902	−	13.2618i	−0.365486	−	1.12485i	−0.949676	−	0.313234i	$-0.898588\pi$
$139$	−4.30902	−	13.2618i	−0.365486	−	1.12485i	0.584190	−	0.811617i	$-0.301412\pi$
$140$	−1.28115	−	3.94298i	−0.108277	−	0.333243i
$141$	−3.11803	−	9.59632i	−0.262586	−	0.808156i
$142$	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
$145$	−9.63525	−	7.00042i	−0.800164	−	0.581353i
$146$	11.2082	+	8.14324i	0.927598	+	0.673939i
$147$	−0.618034	+	1.90211i	−0.0509746	+	0.156884i
$148$	−1.69098	+	5.20431i	−0.138998	+	0.427792i
$149$	−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	$0.510445\pi$
$152$	2.50000	−	1.81636i	0.202777	−	0.147326i
$153$	−0.236068	−	0.726543i	−0.0190850	−	0.0587375i
$154$	−3.92705	−	15.6129i	−0.316451	−	1.25813i
$155$	18.5172	−	13.4535i	1.48734	−	1.08062i
$156$	1.61803	+	1.17557i	0.129546	+	0.0941210i
$157$	−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	$0.497377\pi$
$158$	−6.54508	+	4.75528i	−0.520699	+	0.378310i
$159$	−5.47214	−	3.97574i	−0.433969	−	0.315297i
$160$	2.33688	−	7.19218i	0.184747	−	0.568592i
$161$	−1.71885	−	5.29007i	−0.135464	−	0.416916i
$162$	−0.500000	+	1.53884i	−0.0392837	+	0.120903i
$163$	−2.02786	−	6.24112i	−0.158835	−	0.488843i	0.839695	−	0.543059i	$-0.182734\pi$
$163$	−2.02786	−	6.24112i	−0.158835	−	0.488843i	−0.998529	+	0.0542163i	$0.982734\pi$
$164$	−0.0450850	−	0.0327561i	−0.00352054	−	0.00255783i
$165$	−5.69098	−	4.75528i	−0.443042	−	0.370198i
$166$	−7.04508	+	5.11855i	−0.546805	+	0.397277i
$167$	−5.39919	−	3.92274i	−0.417802	−	0.303551i	0.358951	−	0.933356i	$-0.383134\pi$
$167$	−5.39919	−	3.92274i	−0.417802	−	0.303551i	−0.776753	+	0.629806i	$0.783134\pi$
$168$	−5.42705	+	3.94298i	−0.418706	+	0.304208i
$169$	2.04508	−	1.48584i	0.157314	−	0.114295i
$170$	0.854102	+	2.62866i	0.0655066	+	0.201609i
$171$	1.11803	−	0.812299i	0.0854982	−	0.0621181i
$172$	1.14590	−	3.52671i	0.0873739	−	0.268909i
$173$	−3.47214			−0.263982			−0.131991	−	0.991251i	$-0.542137\pi$
$173$	−3.47214			−0.263982			−0.131991	+	0.991251i	$0.542137\pi$
$174$	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
$178$	3.61803			0.271183
$179$	5.69098	+	4.13474i	0.425364	+	0.309045i	0.779792	−	0.626038i	$-0.215325\pi$
$179$	5.69098	+	4.13474i	0.425364	+	0.309045i	−0.354428	+	0.935083i	$0.615325\pi$
$180$	0.427051	−	1.31433i	0.0318305	−	0.0979642i
$181$	21.4721			1.59601			0.798006	−	0.602650i	$-0.205888\pi$
$181$	21.4721			1.59601			0.798006	+	0.602650i	$0.205888\pi$
$182$	4.85410	+	14.9394i	0.359810	+	1.10738i
$183$	7.04508	−	5.11855i	0.520788	−	0.378374i
$184$	1.28115	−	3.94298i	0.0944478	−	0.290681i
$185$	−6.11803	+	18.8294i	−0.449807	+	1.38436i
$186$	13.3992	+	9.73508i	0.982476	+	0.713811i
$187$	0.618034	+	2.45714i	0.0451951	+	0.179684i
$188$	−5.04508	+	3.66547i	−0.367951	+	0.267332i
$189$	−2.42705	+	1.76336i	−0.176542	+	0.128265i
$190$	−4.04508	+	2.93893i	−0.293461	+	0.213212i
$191$	−1.61803			−0.117077			−0.0585384	−	0.998285i	$-0.518644\pi$
$191$	−1.61803			−0.117077			−0.0585384	+	0.998285i	$0.518644\pi$
$192$	−4.23607			−0.305712
$193$	−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	$-0.315648\pi$
$194$	3.30902	−	2.40414i	0.237574	−	0.172607i
$195$	5.85410	+	4.25325i	0.419221	+	0.304582i
$196$	1.23607			0.0882906
$197$	4.39919	+	13.5393i	0.313429	+	0.964636i	0.976396	+	0.215987i	$0.0692969\pi$
$197$	4.39919	+	13.5393i	0.313429	+	0.964636i	−0.662967	+	0.748649i	$0.730703\pi$
$198$	2.00000	−	4.97980i	0.142134	−	0.353899i
$199$	−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
$202$	−1.26393	−	3.88998i	−0.0889299	−	0.273698i
$203$	12.9271	−	9.39205i	0.907301	−	0.659193i
$204$	−0.381966	+	0.277515i	−0.0267430	+	0.0194299i
$205$	−0.163119	−	0.118513i	−0.0113927	−	0.00827730i
$206$	0.881966	+	2.71441i	0.0614495	+	0.189122i
$207$	0.572949	−	1.76336i	0.0398227	−	0.122562i
$208$	−4.85410	+	14.9394i	−0.336571	+	1.03586i
$209$	−3.88197	+	2.43690i	−0.268521	+	0.168564i
$210$	8.78115	−	6.37988i	0.605957	−	0.440254i
$211$	8.80902	−	6.40013i	0.606438	−	0.440603i	−0.241720	−	0.970346i	$-0.577712\pi$
$211$	8.80902	−	6.40013i	0.606438	−	0.440603i	0.848158	+	0.529743i	$0.177712\pi$
$212$	−1.29180	+	3.97574i	−0.0887209	+	0.273055i
$213$	9.38197			0.642842
$214$	−8.39919	+	25.8500i	−0.574157	+	1.76707i
$215$	4.14590	−	12.7598i	0.282748	−	0.870209i
$216$	−2.23607			−0.152145
$217$	9.48936	+	29.2052i	0.644180	+	1.98258i
$218$	−5.85410	+	18.0171i	−0.396490	+	1.22027i
$219$	−2.64590	+	8.14324i	−0.178793	+	0.550269i
$220$	−1.70820	+	4.25325i	−0.115167	+	0.286754i
$221$	−0.763932	−	2.35114i	−0.0513876	−	0.158155i
$222$	−14.3262			−0.961514
$223$	4.41641			0.295745			0.147872	−	0.989006i	$-0.452758\pi$
$223$	4.41641			0.295745			0.147872	+	0.989006i	$0.452758\pi$
$224$	8.20820	+	5.96361i	0.548434	+	0.398460i
$225$	1.54508	−	4.75528i	0.103006	−	0.317019i
$226$	5.09017	+	15.6659i	0.338593	+	1.04208i
$227$	−2.83688	−	8.73102i	−0.188290	−	0.579498i	0.811699	−	0.584076i	$-0.198543\pi$
$227$	−2.83688	−	8.73102i	−0.188290	−	0.579498i	−0.999990	+	0.00457752i	$0.998543\pi$
$228$	−0.690983	−	0.502029i	−0.0457615	−	0.0332477i
$229$	−25.0000			−1.65205			−0.826023	−	0.563636i	$-0.809402\pi$
$229$	−25.0000			−1.65205			−0.826023	+	0.563636i	$0.809402\pi$
$230$	−2.07295	+	6.37988i	−0.136686	+	0.420677i
$231$	8.42705	−	5.29007i	0.554459	−	0.348061i
$232$	11.9098			0.781919
$233$	12.7082	+	9.23305i	0.832542	+	0.604877i	0.920277	−	0.391267i	$-0.127963\pi$
$233$	12.7082	+	9.23305i	0.832542	+	0.604877i	−0.0877353	+	0.996144i	$0.527963\pi$
$234$	−1.61803	+	4.97980i	−0.105774	+	0.325539i
$235$	−18.2533	+	13.2618i	−1.19071	+	0.865104i
$236$	−1.05573	+	3.24920i	−0.0687220	+	0.211505i
$237$	−4.04508	−	2.93893i	−0.262757	−	0.190904i
$238$	−3.70820			−0.240367
$239$	19.4721			1.25955			0.629774	−	0.776779i	$-0.283148\pi$
$239$	19.4721			1.25955			0.629774	+	0.776779i	$0.283148\pi$
$240$	10.8541			0.700629
$241$	−15.8262	+	11.4984i	−1.01946	+	0.740679i	−0.966172	−	0.257900i	$-0.916969\pi$
$241$	−15.8262	+	11.4984i	−1.01946	+	0.740679i	−0.0532860	+	0.998579i	$0.516969\pi$
$242$	−7.73607	+	16.0292i	−0.497293	+	1.03040i
$243$	−1.00000			−0.0641500
$244$	−4.35410	−	3.16344i	−0.278743	−	0.202519i
$245$	4.47214			0.285714
$246$	0.0450850	−	0.138757i	0.00287451	−	0.00884684i
$247$	3.61803	−	2.62866i	0.230210	−	0.167257i
$248$	−7.07295	+	21.7683i	−0.449133	+	1.38229i
$249$	−4.35410	−	3.16344i	−0.275930	−	0.200475i
$250$	−5.59017	+	17.2048i	−0.353553	+	1.08813i
$251$	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
$253$	−2.29180	+	5.70634i	−0.144084	+	0.358754i
$254$	−5.20820	−	16.0292i	−0.326792	−	1.00576i
$255$	−1.38197	+	1.00406i	−0.0865421	+	0.0628765i
$256$	4.19098	+	12.8985i	0.261936	+	0.806157i
$257$	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	$0.510261\pi$
$258$	9.70820			0.604406
$259$	−21.4894	−	15.6129i	−1.33528	−	0.970140i
$260$	1.38197	−	4.25325i	0.0857059	−	0.263776i
$261$	5.32624			0.329686
$262$	0.972136	+	2.99193i	0.0600588	+	0.184842i
$263$	10.4721	−	7.60845i	0.645740	−	0.469157i	−0.216078	−	0.976376i	$-0.569326\pi$
$263$	10.4721	−	7.60845i	0.645740	−	0.469157i	0.861817	+	0.507219i	$0.169326\pi$
$264$	7.39919	+	0.502029i	0.455388	+	0.0308977i
$265$	−4.67376	+	14.3844i	−0.287107	+	0.883624i
$266$	−2.07295	−	6.37988i	−0.127101	−	0.391176i
$267$	0.690983	+	2.12663i	0.0422875	+	0.130147i
$268$	1.50000	+	1.08981i	0.0916271	+	0.0665710i
$269$	19.4721			1.18724			0.593619	−	0.804747i	$-0.297699\pi$
$269$	19.4721			1.18724			0.593619	+	0.804747i	$0.297699\pi$
$270$	3.61803			0.220187
$271$	−1.29180	+	3.97574i	−0.0784710	+	0.241509i	−0.982595	−	0.185762i	$-0.940525\pi$
$271$	−1.29180	+	3.97574i	−0.0784710	+	0.241509i	0.904124	+	0.427271i	$0.140525\pi$
$272$	−3.00000	−	2.17963i	−0.181902	−	0.132159i
$273$	−7.85410	+	5.70634i	−0.475352	+	0.345363i
$274$	24.3262			1.46960
$275$	−6.18034	+	15.3884i	−0.372689	+	0.927957i
$276$	−1.14590			−0.0689750
$277$	25.2533	−	18.3476i	1.51732	−	1.10240i	0.554529	−	0.832165i	$-0.312899\pi$
$277$	25.2533	−	18.3476i	1.51732	−	1.10240i	0.962794	−	0.270235i	$-0.0871014\pi$
$278$	−18.2533	−	13.2618i	−1.09476	−	0.795389i
$279$	−3.16312	+	9.73508i	−0.189371	+	0.582824i
$280$	12.1353	+	8.81678i	0.725220	+	0.526903i
$281$	19.3607			1.15496			0.577481	−	0.816404i	$-0.304036\pi$
$281$	19.3607			1.15496			0.577481	+	0.816404i	$0.304036\pi$
$282$	−13.2082	−	9.59632i	−0.786537	−	0.571453i
$283$	−8.47214	−	26.0746i	−0.503616	−	1.54997i	−0.803085	−	0.595865i	$-0.796809\pi$
$283$	−8.47214	−	26.0746i	−0.503616	−	1.54997i	0.299468	−	0.954106i	$-0.403191\pi$
$284$	−1.79180	−	5.51458i	−0.106324	−	0.327230i
$285$	−2.50000	−	1.81636i	−0.148087	−	0.107592i
$286$	6.47214	−	16.1150i	0.382705	−	0.952898i
$287$	0.218847	−	0.159002i	0.0129181	−	0.00938557i
$288$	1.04508	+	3.21644i	0.0615822	+	0.189531i
$289$	−16.4164			−0.965671
$290$	−19.2705			−1.13160
$291$	2.04508	+	1.48584i	0.119885	+	0.0871016i
$292$	5.29180			0.309679
$293$	−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	$0.934927\pi$
$294$	1.00000	+	3.07768i	0.0583212	+	0.179494i
$295$	−3.81966	+	11.7557i	−0.222389	+	0.684444i
$296$	−6.11803	−	18.8294i	−0.355604	−	1.09444i
$297$	3.30902	+	0.224514i	0.192009	+	0.0130276i
$298$	−11.2812	−	8.19624i	−0.653500	−	0.474795i
$299$	1.85410	−	5.70634i	0.107225	−	0.330006i
$300$	−3.09017			−0.178411
$301$	14.5623	+	10.5801i	0.839357	+	0.609829i
$302$	−7.54508	+	23.2214i	−0.434171	+	1.33624i
$303$	2.04508	−	1.48584i	0.117487	−	0.0853593i
$304$	2.07295	−	6.37988i	0.118892	−	0.365911i
$305$	−15.7533	−	11.4454i	−0.902031	−	0.655364i
$306$	−1.00000	−	0.726543i	−0.0571662	−	0.0415337i
$307$	17.3262			0.988861			0.494430	−	0.869217i	$-0.335377\pi$
$307$	17.3262			0.988861			0.494430	+	0.869217i	$0.335377\pi$
$308$	−4.71885	−	3.94298i	−0.268881	−	0.224672i
$309$	−1.42705	+	1.03681i	−0.0811821	+	0.0589822i
$310$	11.4443	−	35.2218i	0.649991	−	2.00047i
$311$	10.6180			0.602093			0.301047	−	0.953609i	$-0.402664\pi$
$311$	10.6180			0.602093			0.301047	+	0.953609i	$0.402664\pi$
$312$	−7.23607			−0.409662
$313$	23.5623	+	17.1190i	1.33182	+	0.967624i	0.999703	+	0.0243861i	$0.00776311\pi$
$313$	23.5623	+	17.1190i	1.33182	+	0.967624i	0.332118	+	0.943238i	$0.392237\pi$
$314$	−7.28115	+	22.4091i	−0.410899	+	1.26462i
$315$	5.42705	+	3.94298i	0.305780	+	0.222162i
$316$	−0.954915	+	2.93893i	−0.0537182	+	0.165328i
$317$	18.7082	+	13.5923i	1.05076	+	0.763420i	0.972356	−	0.233502i	$-0.0750185\pi$
$317$	18.7082	+	13.5923i	1.05076	+	0.763420i	0.0784011	+	0.996922i	$0.475019\pi$
$318$	−10.9443			−0.613724
$319$	−17.6246	−	1.19581i	−0.986789	−	0.0669528i
$320$	2.92705	+	9.00854i	0.163627	+	0.503593i
$321$	−16.7984			−0.937594
$322$	−7.28115	−	5.29007i	−0.405763	−	0.294804i
$323$	0.326238	+	1.00406i	0.0181524	+	0.0558672i
$324$	0.190983	+	0.587785i	0.0106102	+	0.0326547i
$325$	5.00000	−	15.3884i	0.277350	−	0.853596i
$326$	−8.59017	−	6.24112i	−0.475766	−	0.345664i
$327$	−11.7082			−0.647465
$328$	0.201626			0.0111329
$329$	−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	0.125384	−	0.992108i	$-0.459984\pi$
$331$	11.0451	−	33.9933i	0.607093	−	1.86844i	0.481709	−	0.876331i	$-0.340016\pi$
$332$	−1.02786	+	3.16344i	−0.0564114	+	0.173616i
$333$	−2.73607	−	8.42075i	−0.149936	−	0.461454i
$334$	−10.7984			−0.590861
$335$	5.42705	+	3.94298i	0.296511	+	0.215428i
$336$	−4.50000	+	13.8496i	−0.245495	+	0.755556i
$337$	20.0902			1.09438			0.547191	−	0.837008i	$-0.315697\pi$
$337$	20.0902			1.09438			0.547191	+	0.837008i	$0.315697\pi$
$338$	1.26393	−	3.88998i	0.0687488	−	0.211587i
$339$	−8.23607	+	5.98385i	−0.447322	+	0.324998i
$340$	0.854102	+	0.620541i	0.0463202	+	0.0336536i
$341$	12.6525	−	31.5034i	0.685170	−	1.70600i
$342$	0.690983	−	2.12663i	0.0373641	−	0.114995i
$343$	4.63525	−	14.2658i	0.250280	−	0.770283i
$344$	4.14590	+	12.7598i	0.223532	+	0.687960i
$345$	−4.14590			−0.223208
$346$	−4.54508	+	3.30220i	−0.244345	+	0.177527i
$347$	−20.8262	+	15.1311i	−1.11801	+	0.812283i	−0.983906	−	0.178685i	$-0.942816\pi$
$347$	−20.8262	+	15.1311i	−1.11801	+	0.812283i	−0.134105	+	0.990967i	$0.542816\pi$
$348$	−1.01722	−	3.13068i	−0.0545288	−	0.167822i
$349$	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	$0.116902\pi$
$350$	−19.6353	−	14.2658i	−1.04955	−	0.762542i
$351$	−3.23607			−0.172729
$352$	−2.73607	−	10.8779i	−0.145833	−	0.579794i
$353$	6.36475	+	19.5887i	0.338761	+	1.04260i	0.964840	+	0.262840i	$0.0846590\pi$
$353$	6.36475	+	19.5887i	0.338761	+	1.04260i	−0.626078	+	0.779760i	$0.715341\pi$
$354$	−8.94427			−0.475383
$355$	−6.48278	−	19.9519i	−0.344070	−	1.05894i
$356$	1.11803	−	0.812299i	0.0592557	−	0.0430518i
$357$	−0.708204	−	2.17963i	−0.0374821	−	0.115358i
$358$	11.3820			0.601556
$359$	13.4164			0.708091			0.354045	−	0.935228i	$-0.384806\pi$
$359$	13.4164			0.708091			0.354045	+	0.935228i	$0.384806\pi$
$360$	1.54508	+	4.75528i	0.0814331	+	0.250625i
$361$	13.8262	−	10.0453i	0.727697	−	0.528703i
$362$	28.1074	−	20.4212i	1.47729	−	1.07332i
$363$	−10.8992	−	1.48584i	−0.572059	−	0.0779864i
$364$	4.85410	+	3.52671i	0.254424	+	0.184850i
$365$	19.1459			1.00214
$366$	4.35410	−	13.4005i	0.227593	−	0.700458i
$367$	−27.3713	+	19.8864i	−1.42877	+	1.03806i	−0.438528	+	0.898718i	$0.644500\pi$
$367$	−27.3713	+	19.8864i	−1.42877	+	1.03806i	−0.990244	+	0.139345i	$0.955500\pi$
$368$	−2.78115	−	8.55951i	−0.144978	−	0.446195i
$369$	0.0901699			0.00469406
$370$	9.89919	+	30.4666i	0.514634	+	1.58388i
$371$	−16.4164	−	11.9272i	−0.852297	−	0.619230i
$372$	6.32624			0.328000
$373$	15.3713	+	11.1679i	0.795897	+	0.578253i	0.909708	−	0.415249i	$-0.136306\pi$
$373$	15.3713	+	11.1679i	0.795897	+	0.578253i	−0.113811	+	0.993502i	$0.536306\pi$
$374$	3.14590	+	2.62866i	0.162671	+	0.135925i
$375$	−11.1803			−0.577350
$376$	6.97214	−	21.4580i	0.359560	−	1.10661i
$377$	17.2361			0.887703
$378$	−1.50000	+	4.61653i	−0.0771517	+	0.237448i
$379$	−17.6631	+	12.8330i	−0.907293	+	0.659187i	−0.940329	−	0.340267i	$-0.889483\pi$
$379$	−17.6631	+	12.8330i	−0.907293	+	0.659187i	0.0330354	+	0.999454i	$0.489483\pi$
$380$	−0.590170	+	1.81636i	−0.0302751	+	0.0931771i
$381$	8.42705	−	6.12261i	0.431731	−	0.313671i
$382$	−2.11803	+	1.53884i	−0.108368	+	0.0787340i
$383$	3.92705	+	2.85317i	0.200663	+	0.145790i	0.683579	−	0.729876i	$-0.260422\pi$
$383$	3.92705	+	2.85317i	0.200663	+	0.145790i	−0.482916	+	0.875667i	$0.660422\pi$
$384$	−11.0172	+	8.00448i	−0.562220	+	0.408477i
$385$	−17.0729	−	14.2658i	−0.870118	−	0.727055i
$386$	−22.7984	−	16.5640i	−1.16041	−	0.843085i
$387$	1.85410	+	5.70634i	0.0942493	+	0.290070i
$388$	0.482779	−	1.48584i	0.0245094	−	0.0754322i
$389$	4.57295	+	14.0741i	0.231858	+	0.713585i	0.997523	+	0.0703451i	$0.0224101\pi$
$389$	4.57295	+	14.0741i	0.231858	+	0.713585i	−0.765665	+	0.643240i	$0.777590\pi$
$390$	11.7082			0.592868
$391$	1.14590	+	0.832544i	0.0579506	+	0.0421035i
$392$	−3.61803	+	2.62866i	−0.182738	+	0.132767i
$393$	−1.57295	+	1.14281i	−0.0793448	+	0.0576474i
$394$	18.6353	+	13.5393i	0.938831	+	0.682100i
$395$	−3.45492	+	10.6331i	−0.173836	+	0.535011i
$396$	−0.500000	−	1.98787i	−0.0251259	−	0.0998942i
$397$	6.57295	+	20.2295i	0.329887	+	1.01529i	0.969186	+	0.246329i	$0.0792245\pi$
$397$	6.57295	+	20.2295i	0.329887	+	1.01529i	−0.639299	+	0.768958i	$0.720776\pi$
$398$	−12.8262	+	9.31881i	−0.642921	+	0.467110i
$399$	3.35410	−	2.43690i	0.167915	−	0.121997i
$400$	−7.50000	−	23.0826i	−0.375000	−	1.15413i
$401$	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	$0.742351\pi$
$402$	−1.50000	+	4.61653i	−0.0748132	+	0.230251i
$403$	−10.2361	+	31.5034i	−0.509895	+	1.56930i
$404$	−1.26393	−	0.918300i	−0.0628830	−	0.0456872i
$405$	0.690983	+	2.12663i	0.0343352	+	0.105673i
$406$	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
$409$	−9.20820	−	28.3399i	−0.455316	−	1.40132i	−0.870763	−	0.491702i	$-0.836375\pi$
$409$	−9.20820	−	28.3399i	−0.455316	−	1.40132i	0.415447	−	0.909617i	$-0.363625\pi$
$410$	−0.326238			−0.0161117
$411$	4.64590	+	14.2986i	0.229165	+	0.705298i
$412$	0.881966	+	0.640786i	0.0434513	+	0.0315693i
$413$	−13.4164	−	9.74759i	−0.660178	−	0.479648i
$414$	−0.927051	−	2.85317i	−0.0455621	−	0.140226i
$415$	−3.71885	+	11.4454i	−0.182551	+	0.561834i
$416$	3.38197	+	10.4086i	0.165815	+	0.510325i
$417$	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	−0.598557	−	0.801080i	$-0.704259\pi$
$419$	7.29837	−	22.4621i	0.356549	−	1.09734i	0.955106	−	0.296264i	$-0.0957410\pi$
$420$	1.28115	−	3.94298i	0.0625139	−	0.192398i
$421$	−3.16312	−	2.29814i	−0.154161	−	0.112005i	0.508031	−	0.861339i	$-0.330374\pi$
$421$	−3.16312	−	2.29814i	−0.154161	−	0.112005i	−0.662192	+	0.749334i	$0.730374\pi$
$422$	5.44427	−	16.7557i	0.265023	−	0.815657i
$423$	3.11803	−	9.59632i	0.151604	−	0.466589i
$424$	−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
$427$	21.1353	−	15.3557i	1.02281	−	0.743113i
$428$	3.20820	+	9.87384i	0.155074	+	0.477270i
$429$	10.7082	+	0.726543i	0.516997	+	0.0350778i
$430$	−6.70820	−	20.6457i	−0.323498	−	0.995625i
$431$	−6.19098	−	4.49801i	−0.298209	−	0.216662i	0.428612	−	0.903489i	$-0.359003\pi$
$431$	−6.19098	−	4.49801i	−0.298209	−	0.216662i	−0.726821	+	0.686827i	$0.759003\pi$
$432$	−3.92705	+	2.85317i	−0.188940	+	0.137273i
$433$	28.5623	−	20.7517i	1.37262	−	0.997264i	0.375089	−	0.926989i	$-0.377612\pi$
$433$	28.5623	−	20.7517i	1.37262	−	0.997264i	0.997528	−	0.0702758i	$-0.0223879\pi$
$434$	40.1976	+	29.2052i	1.92954	+	1.40190i
$435$	−3.68034	−	11.3269i	−0.176459	−	0.543084i
$436$	2.23607	+	6.88191i	0.107088	+	0.329584i
$437$	−0.791796	+	2.43690i	−0.0378767	+	0.116573i
$438$	4.28115	+	13.1760i	0.204561	+	0.629575i
$439$	21.3435	+	15.5069i	1.01867	+	0.740105i	0.966009	−	0.258507i	$-0.0832306\pi$
$439$	21.3435	+	15.5069i	1.01867	+	0.740105i	0.0526584	+	0.998613i	$0.483231\pi$
$440$	−4.04508	−	16.0822i	−0.192842	−	0.766689i
$441$	−1.61803	+	1.17557i	−0.0770492	+	0.0559795i
$442$	−3.23607	−	2.35114i	−0.153924	−	0.111832i
$443$	−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	$0.343034\pi$
$444$	−4.42705	+	3.21644i	−0.210099	+	0.152646i
$445$	4.04508	−	2.93893i	0.191755	−	0.139318i
$446$	5.78115	−	4.20025i	0.273746	−	0.198888i
$447$	2.66312	−	8.19624i	0.125961	−	0.387669i
$448$	−12.7082			−0.600406
$449$	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
$453$	−15.0902			−0.708998
$454$	−12.0172	−	8.73102i	−0.563996	−	0.409767i
$455$	17.5623	+	12.7598i	0.823334	+	0.598187i
$456$	3.09017			0.144710
$457$	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	$0.820113\pi$
$458$	−32.7254	+	23.7764i	−1.52916	+	1.11100i
$459$	0.236068	−	0.726543i	0.0110187	−	0.0339121i
$460$	0.791796	+	2.43690i	0.0369177	+	0.113621i
$461$	−31.5795	−	22.9439i	−1.47081	−	1.06860i	−0.980379	−	0.197120i	$-0.936841\pi$
$461$	−31.5795	−	22.9439i	−1.47081	−	1.06860i	−0.490426	−	0.871483i	$-0.663159\pi$
$462$	6.00000	−	14.9394i	0.279145	−	0.695043i
$463$	0.472136	−	0.343027i	0.0219420	−	0.0159418i	−0.576760	−	0.816914i	$-0.695683\pi$
$463$	0.472136	−	0.343027i	0.0219420	−	0.0159418i	0.598702	+	0.800972i	$0.295683\pi$
$464$	20.9164	−	15.1967i	0.971020	−	0.705487i
$465$	22.8885			1.06143
$466$	25.4164			1.17739
$467$	−36.9443			−1.70958			−0.854789	−	0.518976i	$-0.826313\pi$
$467$	−36.9443			−1.70958			−0.854789	+	0.518976i	$0.826313\pi$
$468$	0.618034	+	1.90211i	0.0285686	+	0.0879252i
$469$	−7.28115	+	5.29007i	−0.336212	+	0.244273i
$470$	−11.2812	+	34.7198i	−0.520361	+	1.60151i
$471$	−14.5623			−0.670996
$472$	−3.81966	−	11.7557i	−0.175814	−	0.541100i
$473$	−4.85410	−	19.2986i	−0.223192	−	0.887353i
$474$	−8.09017			−0.371594
$475$	−2.13525	+	6.57164i	−0.0979722	+	0.301527i
$476$	−1.14590	+	0.832544i	−0.0525222	+	0.0381596i
$477$	−2.09017	−	6.43288i	−0.0957023	−	0.294541i
$478$	25.4894	−	18.5191i	1.16586	−	0.847044i
$479$	−1.54508	+	1.12257i	−0.0705967	+	0.0512915i	−0.622524	−	0.782601i	$-0.713893\pi$
$479$	−1.54508	+	1.12257i	−0.0705967	+	0.0512915i	0.551927	+	0.833892i	$0.313893\pi$
$480$	6.11803	−	4.44501i	0.279249	−	0.202886i
$481$	−8.85410	−	27.2501i	−0.403712	−	1.24250i
$482$	−9.78115	+	30.1033i	−0.445519	+	1.37117i
$483$	1.71885	−	5.29007i	0.0782102	−	0.240706i
$484$	1.20820	+	6.69015i	0.0549184	+	0.304098i
$485$	1.74671	−	5.37582i	0.0793141	−	0.244104i
$486$	−1.30902	+	0.951057i	−0.0593782	+	0.0431408i
$487$	−3.85410	+	11.8617i	−0.174646	+	0.537505i	−0.999617	−	0.0276697i	$-0.991191\pi$
$487$	−3.85410	+	11.8617i	−0.174646	+	0.537505i	0.824971	+	0.565175i	$0.191191\pi$
$488$	19.4721			0.881462
$489$	2.02786	−	6.24112i	0.0917032	−	0.282233i
$490$	5.85410	−	4.25325i	0.264461	−	0.192142i
$491$	−38.4508			−1.73526			−0.867631	−	0.497208i	$-0.834359\pi$
$491$	−38.4508			−1.73526			−0.867631	+	0.497208i	$0.834359\pi$
$492$	−0.0172209	−	0.0530006i	−0.000776379	−	0.00238945i
$493$	−1.25735	+	3.86974i	−0.0566284	+	0.174284i
$494$	2.23607	−	6.88191i	0.100605	−	0.309632i
$495$	−1.80902	−	7.19218i	−0.0813093	−	0.323264i
$496$	15.3541	+	47.2551i	0.689420	+	2.12182i
$497$	28.1459			1.26252
$498$	−8.70820			−0.390224
$499$	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
$502$	−3.82624	−	11.7759i	−0.170773	−	0.525586i
$503$	−14.1631	−	10.2901i	−0.631502	−	0.458813i	0.225418	−	0.974262i	$-0.427625\pi$
$503$	−14.1631	−	10.2901i	−0.631502	−	0.458813i	−0.856920	+	0.515449i	$0.827625\pi$
$504$	−6.70820			−0.298807
$505$	−4.57295	−	3.32244i	−0.203494	−	0.147847i
$506$	2.42705	+	9.64932i	0.107896	+	0.428965i
$507$	2.52786			0.112266
$508$	−5.20820	−	3.78398i	−0.231077	−	0.167887i
$509$	2.17376	−	6.69015i	0.0963503	−	0.296536i	−0.891253	−	0.453507i	$-0.850173\pi$
$509$	2.17376	−	6.69015i	0.0963503	−	0.296536i	0.987603	+	0.156971i	$0.0501729\pi$
$510$	−0.854102	+	2.62866i	−0.0378203	+	0.116399i
$511$	−7.93769	+	24.4297i	−0.351143	+	1.08071i
$512$	−4.28115	−	3.11044i	−0.189202	−	0.137463i
$513$	1.38197			0.0610153
$514$	29.1246			1.28463
$515$	3.19098	+	2.31838i	0.140612	+	0.102160i
$516$	3.00000	−	2.17963i	0.132068	−	0.0959528i
$517$	−12.4721	+	31.0543i	−0.548524	+	1.36577i
$518$	−42.9787			−1.88838
$519$	−2.80902	−	2.04087i	−0.123302	−	0.0895843i
$520$	5.00000	+	15.3884i	0.219265	+	0.674827i
$521$	6.96149	−	21.4253i	0.304989	−	0.938658i	−0.674693	−	0.738099i	$-0.735724\pi$
$521$	6.96149	−	21.4253i	0.304989	−	0.938658i	0.979681	−	0.200560i	$-0.0642761\pi$
$522$	6.97214	−	5.06555i	0.305162	−	0.221713i
$523$	6.48936	−	19.9722i	0.283760	−	0.873323i	−0.703008	−	0.711182i	$-0.748160\pi$
$523$	6.48936	−	19.9722i	0.283760	−	0.873323i	0.986768	−	0.162141i	$-0.0518398\pi$
$524$	0.972136	+	0.706298i	0.0424680	+	0.0308548i
$525$	4.63525	−	14.2658i	0.202299	−	0.622613i
$526$	6.47214	−	19.9192i	0.282199	−	0.868518i
$527$	−6.32624	−	4.59628i	−0.275575	−	0.200217i
$528$	13.6353	−	8.55951i	0.593398	−	0.372505i
$529$	−6.04508	−	18.6049i	−0.262830	−	0.808907i
$530$	7.56231	+	23.2744i	0.328486	+	1.01097i
$531$	−1.70820	−	5.25731i	−0.0741297	−	0.228148i
$532$	−2.07295	−	1.50609i	−0.0898737	−	0.0652971i
$533$	0.291796			0.0126391
$534$	2.92705	+	2.12663i	0.126666	+	0.0920282i
$535$	11.6074	+	35.7239i	0.501831	+	1.54448i
$536$	−6.70820			−0.289750
$537$	2.17376	+	6.69015i	0.0938048	+	0.288701i
$538$	25.4894	−	18.5191i	1.09892	−	0.798415i
$539$	5.61803	−	3.52671i	0.241986	−	0.151906i
$540$	1.11803	−	0.812299i	0.0481125	−	0.0349558i
$541$	9.50000	+	29.2380i	0.408437	+	1.25704i	0.917991	+	0.396601i	$0.129810\pi$
$541$	9.50000	+	29.2380i	0.408437	+	1.25704i	−0.509554	+	0.860439i	$0.670190\pi$
$542$	2.09017	+	6.43288i	0.0897805	+	0.276316i
$543$	17.3713	+	12.6210i	0.745475	+	0.541619i
$544$	−2.58359			−0.110771
$545$	8.09017	+	24.8990i	0.346545	+	1.06656i
$546$	−4.85410	+	14.9394i	−0.207736	+	0.639347i
$547$	18.6074	+	13.5191i	0.795595	+	0.578033i	0.909618	−	0.415445i	$-0.136374\pi$
$547$	18.6074	+	13.5191i	0.795595	+	0.578033i	−0.114024	+	0.993478i	$0.536374\pi$
$548$	7.51722	−	5.46158i	0.321120	−	0.233307i
$549$	8.70820			0.371657
$550$	6.54508	+	26.0216i	0.279083	+	1.10956i
$551$	−7.36068			−0.313576
$552$	3.35410	−	2.43690i	0.142760	−	0.103721i
$553$	−12.1353	−	8.81678i	−0.516044	−	0.374928i
$554$	15.6074	−	48.0346i	0.663094	−	2.04080i
$555$	−16.0172	+	11.6372i	−0.679893	+	0.493971i
$556$	−8.61803			−0.365486
$557$	−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	$0.883613\pi$
$558$	5.11803	+	15.7517i	0.216664	+	0.666822i
$559$	6.00000	+	18.4661i	0.253773	+	0.781033i
$560$	32.5623			1.37601
$561$	−0.944272	+	2.35114i	−0.0398672	+	0.0992653i
$562$	25.3435	−	18.4131i	1.06905	−	0.776710i
$563$	−13.4336	−	41.3445i	−0.566160	−	1.74246i	−0.664480	−	0.747306i	$-0.731347\pi$
$563$	−13.4336	−	41.3445i	−0.566160	−	1.74246i	0.0983198	−	0.995155i	$-0.468653\pi$
$564$	−6.23607			−0.262586
$565$	18.4164	+	13.3803i	0.774784	+	0.562914i
$566$	−35.8885	−	26.0746i	−1.50851	−	1.09600i
$567$	−3.00000			−0.125988
$568$	16.9721	+	12.3310i	0.712135	+	0.517396i
$569$	−3.68034	−	11.3269i	−0.154288	−	0.474849i	0.843800	−	0.536658i	$-0.180313\pi$
$569$	−3.68034	−	11.3269i	−0.154288	−	0.474849i	−0.998088	+	0.0618083i	$0.980313\pi$
$570$	−5.00000			−0.209427
$571$	9.60081	+	29.5483i	0.401782	+	1.23656i	0.923553	+	0.383471i	$0.125271\pi$
$571$	9.60081	+	29.5483i	0.401782	+	1.23656i	−0.521771	+	0.853085i	$0.674729\pi$
$572$	−1.61803	−	6.43288i	−0.0676534	−	0.268972i
$573$	−1.30902	−	0.951057i	−0.0546850	−	0.0397310i
$574$	0.135255	−	0.416272i	0.00564543	−	0.0173749i
$575$	2.86475	+	8.81678i	0.119468	+	0.367685i
$576$	−3.42705	−	2.48990i	−0.142794	−	0.103746i
$577$	2.69098	−	8.28199i	0.112027	−	0.344784i	−0.879288	−	0.476290i	$-0.841981\pi$
$577$	2.69098	−	8.28199i	0.112027	−	0.344784i	0.991315	+	0.131506i	$0.0419813\pi$
$578$	−21.4894	+	15.6129i	−0.893839	+	0.649412i
$579$	5.38197	−	16.5640i	0.223667	−	0.688376i
$580$	−5.95492	+	4.32650i	−0.247264	+	0.179648i
$581$	−13.0623	−	9.49032i	−0.541916	−	0.393725i
$582$	4.09017			0.169543
$583$	5.47214	+	21.7558i	0.226633	+	0.901033i
$584$	−15.4894	+	11.2537i	−0.640954	+	0.465680i
$585$	2.23607	+	6.88191i	0.0924500	+	0.284532i
$586$	−37.2705			−1.53963
$587$	36.2705			1.49704			0.748522	−	0.663110i	$-0.230764\pi$
$587$	36.2705			1.49704			0.748522	+	0.663110i	$0.230764\pi$
$588$	1.00000	+	0.726543i	0.0412393	+	0.0299621i
$589$	4.37132	−	13.4535i	0.180117	−	0.554344i
$590$	6.18034	+	19.0211i	0.254441	+	0.783088i
$591$	−4.39919	+	13.5393i	−0.180958	+	0.556933i
$592$	−34.7705	−	25.2623i	−1.42906	−	1.03827i
$593$	6.00000			0.246390			0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000			0.246390			0.123195	+	0.992382i	$0.460686\pi$
$594$	4.54508	−	2.85317i	0.186487	−	0.117067i
$595$	−4.14590	+	3.01217i	−0.169965	+	0.123487i
$596$	−5.32624			−0.218171
$597$	−7.92705	−	5.75934i	−0.324433	−	0.235714i
$598$	−3.00000	−	9.23305i	−0.122679	−	0.377568i
$599$	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	$0.665481\pi$
$600$	9.04508	−	6.57164i	0.369264	−	0.268286i
$601$	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	$0.549919\pi$
$602$	29.1246			1.18703
$603$	−3.00000			−0.122169
$604$	2.88197	+	8.86978i	0.117266	+	0.360906i
$605$	4.37132	+	24.2052i	0.177720	+	0.984081i
$606$	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	$-0.0345573\pi$
$608$	−1.44427	−	4.44501i	−0.0585730	−	0.180269i
$609$	15.9787			0.647490
$610$	−31.5066			−1.27566
$611$	10.0902	−	31.0543i	0.408205	−	1.25632i
$612$	−0.472136			−0.0190850
$613$	−14.1246	+	43.4711i	−0.570488	+	1.75578i	0.0805664	+	0.996749i	$0.474327\pi$
$613$	−14.1246	+	43.4711i	−0.570488	+	1.75578i	−0.651054	+	0.759031i	$0.725673\pi$
$614$	22.6803	−	16.4782i	0.915304	−	0.665007i
$615$	−0.0623059	−	0.191758i	−0.00251242	−	0.00773242i
$616$	22.1976	+	1.50609i	0.894365	+	0.0606819i
$617$	−8.79180	+	27.0584i	−0.353944	+	1.08933i	0.602675	+	0.797987i	$0.294102\pi$
$617$	−8.79180	+	27.0584i	−0.353944	+	1.08933i	−0.956619	+	0.291342i	$0.905898\pi$
$618$	−0.881966	+	2.71441i	−0.0354779	+	0.109190i
$619$	−0.0385072	−	0.118513i	−0.00154773	−	0.00476343i	0.950280	−	0.311398i	$-0.100797\pi$
$619$	−0.0385072	−	0.118513i	−0.00154773	−	0.00476343i	−0.951827	+	0.306634i	$0.900797\pi$
$620$	−4.37132	−	13.4535i	−0.175557	−	0.540308i
$621$	1.50000	−	1.08981i	0.0601929	−	0.0437327i
$622$	13.8992	−	10.0984i	0.557307	−	0.404907i
$623$	2.07295	+	6.37988i	0.0830509	+	0.255605i
$624$	−12.7082	+	9.23305i	−0.508735	+	0.369618i
$625$	7.72542	+	23.7764i	0.309017	+	0.951057i
$626$	47.1246			1.88348
$627$	−4.57295	−	0.310271i	−0.182626	−	0.0123910i
$628$	2.78115	+	8.55951i	0.110980	+	0.341562i
$629$	6.76393			0.269696
$630$	10.8541			0.432438
$631$	−28.2254	+	20.5070i	−1.12364	+	0.816370i	−0.984756	−	0.173940i	$-0.944350\pi$
$631$	−28.2254	+	20.5070i	−1.12364	+	0.816370i	−0.138880	+	0.990309i	$0.544350\pi$
$632$	−3.45492	−	10.6331i	−0.137429	−	0.422963i
$633$	10.8885			0.432781
$634$	37.4164			1.48600
$635$	−18.8435	−	13.6906i	−0.747780	−	0.543294i
$636$	−3.38197	+	2.45714i	−0.134104	+	0.0974320i
$637$	−5.23607	+	3.80423i	−0.207461	+	0.150729i
$638$	−24.2082	+	15.1967i	−0.958412	+	0.601642i
$639$	7.59017	+	5.51458i	0.300262	+	0.218153i
$640$	24.6353	+	17.8986i	0.973794	+	0.707503i
$641$	−10.7877	+	33.2012i	−0.426090	+	1.31137i	0.475857	+	0.879523i	$0.342138\pi$
$641$	−10.7877	+	33.2012i	−0.426090	+	1.31137i	−0.901947	+	0.431847i	$0.857862\pi$
$642$	−21.9894	+	15.9762i	−0.867851	+	0.630530i
$643$	−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	$-0.326731\pi$
$644$	−3.43769			−0.135464
$645$	10.8541	−	7.88597i	0.427380	−	0.310510i
$646$	1.38197	+	1.00406i	0.0543727	+	0.0395041i
$647$	19.0344			0.748321			0.374161	−	0.927364i	$-0.377931\pi$
$647$	19.0344			0.748321			0.374161	+	0.927364i	$0.377931\pi$
$648$	−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
$652$	−4.05573			−0.158835
$653$	12.7082	−	39.1118i	0.497310	−	1.53056i	−0.316014	−	0.948754i	$-0.602345\pi$
$653$	12.7082	−	39.1118i	0.497310	−	1.53056i	0.813325	−	0.581810i	$-0.197655\pi$
$654$	−15.3262	+	11.1352i	−0.599303	+	0.435419i
$655$	3.51722	+	2.55541i	0.137429	+	0.0998482i
$656$	0.354102	−	0.257270i	0.0138254	−	0.0100447i
$657$	−6.92705	+	5.03280i	−0.270250	+	0.196348i
$658$	−39.6246	−	28.7890i	−1.54473	−	1.12231i
$659$	−22.4615	+	16.3192i	−0.874976	+	0.635707i	−0.931917	−	0.362671i	$-0.881865\pi$
$659$	−22.4615	+	16.3192i	−0.874976	+	0.635707i	0.0569419	+	0.998377i	$0.481865\pi$
$660$	−3.88197	+	2.43690i	−0.151105	+	0.0948561i
$661$	11.7984	+	8.57202i	0.458904	+	0.333413i	0.793101	−	0.609090i	$-0.208465\pi$
$661$	11.7984	+	8.57202i	0.458904	+	0.333413i	−0.334197	+	0.942503i	$0.608465\pi$
$662$	−17.8713	−	55.0023i	−0.694589	−	2.13772i
$663$	0.763932	−	2.35114i	0.0296687	−	0.0913108i
$664$	−3.71885	−	11.4454i	−0.144319	−	0.444169i
$665$	−7.50000	−	5.44907i	−0.290838	−	0.211306i
$666$	−11.5902	−	8.42075i	−0.449110	−	0.326297i
$667$	−7.98936	+	5.80461i	−0.309349	+	0.224755i
$668$	−3.33688	+	2.42439i	−0.129108	+	0.0938023i
$669$	3.57295	+	2.59590i	0.138138	+	0.100363i
$670$	10.8541			0.419331
$671$	−28.8156	−	1.95511i	−1.11241	−	0.0754763i
$672$	3.13525	+	9.64932i	0.120945	+	0.372231i
$673$	−4.52786	+	3.28969i	−0.174536	+	0.126808i	−0.671624	−	0.740892i	$-0.734403\pi$
$673$	−4.52786	+	3.28969i	−0.174536	+	0.126808i	0.497087	+	0.867700i	$0.334403\pi$
$674$	26.2984	−	19.1069i	1.01298	−	0.735970i
$675$	4.04508	−	2.93893i	0.155695	−	0.113119i
$676$	−0.482779	−	1.48584i	−0.0185684	−	0.0571477i
$677$	−13.8541	+	42.6385i	−0.532456	+	1.63873i	0.216625	+	0.976255i	$0.430495\pi$
$677$	−13.8541	+	42.6385i	−0.532456	+	1.63873i	−0.749082	+	0.662477i	$0.769505\pi$
$678$	−5.09017	+	15.6659i	−0.195487	+	0.601647i
$679$	6.13525	+	4.45752i	0.235449	+	0.171064i
$680$	−3.81966			−0.146477
$681$	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	−0.781897	−	0.623407i	$-0.785748\pi$
$683$	5.67376	−	17.4620i	0.217100	−	0.668167i	0.998998	−	0.0447593i	$-0.0142521\pi$
$684$	−0.263932	−	0.812299i	−0.0100917	−	0.0310590i
$685$	27.1976	−	19.7602i	1.03917	−	0.754998i
$686$	−7.50000	−	23.0826i	−0.286351	−	0.881299i
$687$	−20.2254	−	14.6946i	−0.771648	−	0.560635i
$688$	23.5623	+	17.1190i	0.898304	+	0.652656i
$689$	−6.76393	−	20.8172i	−0.257685	−	0.793074i
$690$	−5.42705	+	3.94298i	−0.206604	+	0.150107i
$691$	−5.33688	−	16.4252i	−0.203025	−	0.624845i	−0.999789	−	0.0205549i	$-0.993457\pi$
$691$	−5.33688	−	16.4252i	−0.203025	−	0.624845i	0.796764	−	0.604290i	$-0.206543\pi$
$692$	−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
$695$	−31.1803			−1.18274
$696$	9.63525	+	7.00042i	0.365223	+	0.265350i
$697$	−0.0212862	+	0.0655123i	−0.000806274	+	0.00248146i
$698$	10.1631	−	31.2789i	0.384680	−	1.18392i
$699$	4.85410	+	14.9394i	0.183599	+	0.565060i
$700$	−9.27051			−0.350392
$701$	−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	$0.406106\pi$
$702$	−4.23607	+	3.07768i	−0.159880	+	0.116160i
$703$	3.78115	+	11.6372i	0.142609	+	0.438905i
$704$	10.7812	+	9.00854i	0.406330	+	0.339522i
$705$	−22.5623			−0.849746
$706$	26.9615	+	19.5887i	1.01471	+	0.737229i
$707$	6.13525	−	4.45752i	0.230740	−	0.167642i
$708$	−2.76393	+	2.00811i	−0.103875	+	0.0754696i
$709$	29.3713	+	21.3395i	1.10306	+	0.801422i	0.981557	−	0.191168i	$-0.0612277\pi$
$709$	29.3713	+	21.3395i	1.10306	+	0.801422i	0.121506	+	0.992591i	$0.461228\pi$
$710$	−27.4615	−	19.9519i	−1.03061	−	0.748783i
$711$	−1.54508	−	4.75528i	−0.0579452	−	0.178337i
$712$	−1.54508	+	4.75528i	−0.0579045	+	0.178212i
$713$	−5.86475	−	18.0498i	−0.219636	−	0.675971i
$714$	−3.00000	−	2.17963i	−0.112272	−	0.0815705i
$715$	−5.85410	−	23.2744i	−0.218931	−	0.870413i
$716$	3.51722	−	2.55541i	0.131445	−	0.0955002i
$717$	15.7533	+	11.4454i	0.588317	+	0.427438i
$718$	17.5623	−	12.7598i	0.655419	−	0.476190i
$719$	−14.4721	+	10.5146i	−0.539720	+	0.392129i	−0.823981	−	0.566618i	$-0.808252\pi$
$719$	−14.4721	+	10.5146i	−0.539720	+	0.392129i	0.284261	+	0.958747i	$0.408252\pi$
$720$	8.78115	+	6.37988i	0.327254	+	0.237764i
$721$	−4.28115	+	3.11044i	−0.159438	+	0.115839i
$722$	8.54508	−	26.2991i	0.318015	−	0.978750i
$723$	−19.5623			−0.727530
$724$	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	0.761458	−	0.648214i	$-0.224484\pi$
$727$	10.2533	+	7.44945i	0.380273	+	0.276285i	−0.381185	+	0.924499i	$0.624484\pi$
$728$	−21.7082			−0.804560
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	25.0623	−	18.2088i	0.927598	−	0.673939i
$731$	−4.58359			−0.169530
$732$	−1.66312	−	5.11855i	−0.0614706	−	0.189187i
$733$	10.7361	−	7.80021i	0.396546	−	0.288107i	−0.371587	−	0.928398i	$-0.621186\pi$
$733$	10.7361	−	7.80021i	0.396546	−	0.288107i	0.768133	+	0.640291i	$0.221186\pi$
$734$	−16.9164	+	52.0633i	−0.624396	+	1.92169i
$735$	3.61803	+	2.62866i	0.133453	+	0.0969594i
$736$	−5.07295	−	3.68571i	−0.186991	−	0.135857i
$737$	9.92705	+	0.673542i	0.365668	+	0.0248102i
$738$	0.118034	−	0.0857567i	0.00434489	−	0.00315675i
$739$	22.9894	−	16.7027i	0.845677	−	0.614420i	−0.0782736	−	0.996932i	$-0.524941\pi$
$739$	22.9894	−	16.7027i	0.845677	−	0.614420i	0.923951	+	0.382511i	$0.124941\pi$
$740$	9.89919	+	7.19218i	0.363901	+	0.264390i
$741$	4.47214			0.164288
$742$	−32.8328			−1.20533
$743$	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	$0.821186\pi$
$744$	−18.5172	+	13.4535i	−0.678874	+	0.493231i
$745$	−19.2705			−0.706017
$746$	30.7426			1.12557
$747$	−1.66312	−	5.11855i	−0.0608503	−	0.187278i
$748$	1.56231	+	0.106001i	0.0571236	+	0.00387579i
$749$	−50.3951			−1.84140
$750$	−14.6353	+	10.6331i	−0.534404	+	0.388267i
$751$	−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	$0.535889\pi$
$752$	−15.1353	−	46.5815i	−0.551926	−	1.69865i
$753$	6.19098	−	4.49801i	0.225612	−	0.163917i
$754$	22.5623	−	16.3925i	0.821671	−	0.596979i
$755$	10.4271	+	32.0912i	0.379479	+	1.16792i
$756$	0.572949	+	1.76336i	0.0208380	+	0.0641326i
$757$	−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
$759$	−5.20820	+	3.26944i	−0.189046	+	0.118673i
$760$	−2.13525	−	6.57164i	−0.0774538	−	0.238378i
$761$	24.1353	−	17.5353i	0.874902	−	0.635654i	−0.0569956	−	0.998374i	$-0.518152\pi$
$761$	24.1353	−	17.5353i	0.874902	−	0.635654i	0.931898	+	0.362721i	$0.118152\pi$
$762$	5.20820	−	16.0292i	0.188673	−	0.580677i
$763$	−35.1246			−1.27160
$764$	−0.309017	+	0.951057i	−0.0111798	+	0.0344080i
$765$	−1.70820			−0.0617602
$766$	7.85410			0.283780
$767$	−5.52786	−	17.0130i	−0.199600	−	0.614304i
$768$	−4.19098	+	12.8985i	−0.151229	+	0.465435i
$769$	5.00000	−	15.3884i	0.180305	−	0.554921i	−0.819531	−	0.573034i	$-0.805766\pi$
$769$	5.00000	−	15.3884i	0.180305	−	0.554921i	0.999836	+	0.0181139i	$0.00576614\pi$
$770$	−35.9164	−	2.43690i	−1.29434	−	0.0878197i
$771$	5.56231	+	17.1190i	0.200322	+	0.616526i
$772$	−10.7639			−0.387402
$773$	49.8673			1.79360			0.896800	−	0.442436i	$-0.145885\pi$
$773$	49.8673			1.79360			0.896800	+	0.442436i	$0.145885\pi$
$774$	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
$777$	−8.20820	−	25.2623i	−0.294468	−	0.906278i
$778$	19.3713	+	14.0741i	0.694496	+	0.504581i
$779$	−0.124612			−0.00446468
$780$	3.61803	−	2.62866i	0.129546	−	0.0941210i
$781$	−23.8779	−	19.9519i	−0.854418	−	0.713937i
$782$	2.29180			0.0819545
$783$	4.30902	+	3.13068i	0.153992	+	0.111882i
$784$	−3.00000	+	9.23305i	−0.107143	+	0.329752i
$785$	10.0623	+	30.9686i	0.359139	+	1.10532i
$786$	−0.972136	+	2.99193i	−0.0346749	+	0.106718i
$787$	25.4164	+	18.4661i	0.905997	+	0.658245i	0.939999	−	0.341176i	$-0.110825\pi$
$787$	25.4164	+	18.4661i	0.905997	+	0.658245i	−0.0340022	+	0.999422i	$0.510825\pi$
$788$	8.79837			0.313429
$789$	12.9443			0.460828
$790$	5.59017	+	17.2048i	0.198889	+	0.612118i
$791$	−24.7082	+	17.9516i	−0.878523	+	0.638284i
$792$	5.69098	+	4.75528i	0.202220	+	0.168972i
$793$	28.1803			1.00071
$794$	27.8435	+	20.2295i	0.988127	+	0.717917i
$795$	−12.2361	+	8.89002i	−0.433969	+	0.315297i
$796$	−1.87132	+	5.75934i	−0.0663273	+	0.204134i
$797$	−17.3713	+	12.6210i	−0.615324	+	0.447059i	−0.851285	−	0.524704i	$-0.824176\pi$
$797$	−17.3713	+	12.6210i	−0.615324	+	0.447059i	0.235961	+	0.971762i	$0.424176\pi$
$798$	2.07295	−	6.37988i	0.0733816	−	0.225845i
$799$	6.23607	+	4.53077i	0.220616	+	0.160287i
$800$	−13.6803	−	9.93935i	−0.483673	−	0.351409i
$801$	−0.690983	+	2.12663i	−0.0244147	+	0.0751407i
$802$	24.9164	+	18.1028i	0.879829	+	0.639233i
$803$	24.0517	−	15.0984i	0.848765	−	0.532811i
$804$	0.572949	+	1.76336i	0.0202064	+	0.0621888i
$805$	−12.4377			−0.438371
$806$	16.5623	+	50.9735i	0.583382	+	1.79547i
$807$	15.7533	+	11.4454i	0.554542	+	0.402898i
$808$	5.65248			0.198853
$809$	−17.0344	−	12.3762i	−0.598899	−	0.435126i	0.246589	−	0.969120i	$-0.420690\pi$
$809$	−17.0344	−	12.3762i	−0.598899	−	0.435126i	−0.845488	+	0.533995i	$0.820690\pi$
$810$	2.92705	+	2.12663i	0.102846	+	0.0747221i
$811$	−33.4508			−1.17462			−0.587309	−	0.809363i	$-0.699813\pi$
$811$	−33.4508			−1.17462			−0.587309	+	0.809363i	$0.699813\pi$
$812$	−3.05166	−	9.39205i	−0.107092	−	0.329596i
$813$	−3.38197	+	2.45714i	−0.118611	+	0.0861757i
$814$	36.4615	+	30.4666i	1.27797	+	1.06785i
$815$	−14.6738			−0.513999
$816$	−1.14590	−	3.52671i	−0.0401145	−	0.123460i
$817$	−2.56231	−	7.88597i	−0.0896437	−	0.275895i
$818$	−39.0066	−	28.3399i	−1.36383	−	0.990883i
$819$	−9.70820			−0.339232
$820$	−0.100813	+	0.0732450i	−0.00352054	+	0.00255783i
$821$	2.72949	−	8.40051i	0.0952599	−	0.293180i	−0.892061	−	0.451914i	$-0.850741\pi$
$821$	2.72949	−	8.40051i	0.0952599	−	0.293180i	0.987321	+	0.158734i	$0.0507413\pi$
$822$	19.6803	+	14.2986i	0.686431	+	0.498721i
$823$	−24.4894	+	17.7926i	−0.853645	+	0.620210i	−0.926149	−	0.377159i	$-0.876901\pi$
$823$	−24.4894	+	17.7926i	−0.853645	+	0.620210i	0.0725034	+	0.997368i	$0.476901\pi$
$824$	−3.94427			−0.137405
$825$	−14.0451	+	8.81678i	−0.488987	+	0.306961i
$826$	−26.8328			−0.933633
$827$	−40.0344	+	29.0867i	−1.39213	+	1.01144i	−0.396506	+	0.918032i	$0.629778\pi$
$827$	−40.0344	+	29.0867i	−1.39213	+	1.01144i	−0.995627	+	0.0934126i	$0.970222\pi$
$828$	−0.927051	−	0.673542i	−0.0322172	−	0.0234072i
$829$	1.34346	−	4.13474i	0.0466603	−	0.143605i	−0.925012	−	0.379938i	$-0.875945\pi$
$829$	1.34346	−	4.13474i	0.0466603	−	0.143605i	0.971672	+	0.236332i	$0.0759454\pi$
$830$	6.01722	+	18.5191i	0.208861	+	0.642807i
$831$	31.2148			1.08283
$832$	−11.0902	−	8.05748i	−0.384482	−	0.279343i
$833$	−0.472136	−	1.45309i	−0.0163585	−	0.0503464i
$834$	−6.97214	−	21.4580i	−0.241425	−	0.743031i
$835$	−12.0729	+	8.77151i	−0.417802	+	0.303551i
$836$	0.690983	+	2.74717i	0.0238981	+	0.0950128i
$837$	−8.28115	+	6.01661i	−0.286239	+	0.207964i
$838$	−11.8090	−	36.3444i	−0.407936	−	1.25550i
$839$	−28.8673			−0.996608			−0.498304	−	0.867002i	$-0.666044\pi$
$839$	−28.8673			−0.996608			−0.498304	+	0.867002i	$0.666044\pi$
$840$	4.63525	+	14.2658i	0.159931	+	0.492219i
$841$	0.510643	+	0.371004i	0.0176084	+	0.0127932i
$842$	−6.32624			−0.218017
$843$	15.6631	+	11.3799i	0.539466	+	0.391945i
$844$	−2.07953	−	6.40013i	−0.0715803	−	0.220301i
$845$	−1.74671	−	5.37582i	−0.0600887	−	0.184934i
$846$	−5.04508	−	15.5272i	−0.173454	−	0.533835i
$847$	−32.6976	−	4.45752i	−1.12350	−	0.153162i
$848$	−26.5623	−	19.2986i	−0.912153	−	0.662718i
$849$	8.47214	−	26.0746i	0.290763	−	0.894876i
$850$	6.18034			0.211984
$851$	13.2812	+	9.64932i	0.455272	+	0.330775i
$852$	1.79180	−	5.51458i	0.0613859	−	0.188926i
$853$	−10.7082	+	7.77997i	−0.366642	+	0.266381i	−0.755817	−	0.654783i	$-0.772760\pi$
$853$	−10.7082	+	7.77997i	−0.366642	+	0.266381i	0.389175	+	0.921164i	$0.372760\pi$
$854$	13.0623	−	40.2016i	0.446983	−	1.37567i
$855$	−0.954915	−	2.93893i	−0.0326574	−	0.100509i
$856$	−30.3885	−	22.0786i	−1.03866	−	0.754630i
$857$	−16.4164			−0.560774			−0.280387	−	0.959887i	$-0.590463\pi$
$857$	−16.4164			−0.560774			−0.280387	+	0.959887i	$0.590463\pi$
$858$	14.7082	−	9.23305i	0.502130	−	0.315211i
$859$	−16.1803	+	11.7557i	−0.552066	+	0.401099i	−0.828547	−	0.559920i	$-0.810832\pi$
$859$	−16.1803	+	11.7557i	−0.552066	+	0.401099i	0.276481	+	0.961020i	$0.410832\pi$
$860$	−6.70820	−	4.87380i	−0.228748	−	0.166195i
$861$	0.270510			0.00921895
$862$	−12.3820			−0.421731
$863$	17.6074	+	12.7925i	0.599363	+	0.435462i	0.845653	−	0.533734i	$-0.179212\pi$
$863$	17.6074	+	12.7925i	0.599363	+	0.435462i	−0.246290	+	0.969196i	$0.579212\pi$
$864$	−1.04508	+	3.21644i	−0.0355545	+	0.109426i
$865$	−2.39919	+	7.38394i	−0.0815748	+	0.251061i
$866$	17.6525	−	54.3287i	0.599856	−	1.84617i
$867$	−13.2812	−	9.64932i	−0.451052	−	0.327708i
$868$	18.9787			0.644180
$869$	4.04508	+	16.0822i	0.137220	+	0.545551i
$870$	−15.5902	−	11.3269i	−0.528556	−	0.384019i
$871$	−9.70820			−0.328950
$872$	−21.1803	−	15.3884i	−0.717257	−	0.521118i
$873$	0.781153	+	2.40414i	0.0264380	+	0.0813679i
$874$	1.28115	+	3.94298i	0.0433356	+	0.133373i
$875$	−33.5410			−1.13389
$876$	4.28115	+	3.11044i	0.144647	+	0.105092i
$877$	32.9787			1.11361			0.556806	−	0.830643i	$-0.312027\pi$
$877$	32.9787			1.11361			0.556806	+	0.830643i	$0.312027\pi$
$878$	42.6869			1.44061
$879$	−7.11803	−	21.9071i	−0.240085	−	0.738907i
$880$	−27.6246	−	23.0826i	−0.931225	−	0.778115i
$881$	−15.3369	+	47.2021i	−0.516713	+	1.59028i	0.263431	+	0.964678i	$0.415146\pi$
$881$	−15.3369	+	47.2021i	−0.516713	+	1.59028i	−0.780144	+	0.625600i	$0.784854\pi$
$882$	−1.00000	+	3.07768i	−0.0336718	+	0.103631i
$883$	11.6910	+	35.9811i	0.393433	+	1.21086i	0.930175	+	0.367116i	$0.119655\pi$
$883$	11.6910	+	35.9811i	0.393433	+	1.21086i	−0.536742	+	0.843746i	$0.680345\pi$
$884$	−1.52786			−0.0513876
$885$	−10.0000	+	7.26543i	−0.336146	+	0.244225i
$886$	−2.83688	+	8.73102i	−0.0953069	+	0.293324i
$887$	26.3951			0.886261			0.443131	−	0.896457i	$-0.353868\pi$
$887$	26.3951			0.886261			0.443131	+	0.896457i	$0.353868\pi$
$888$	6.11803	−	18.8294i	0.205308	−	0.631872i
$889$	25.2812	−	18.3678i	0.847903	−	0.616037i
$890$	2.50000	−	7.69421i	0.0838002	−	0.257910i
$891$	2.54508	+	2.12663i	0.0852636	+	0.0712447i
$892$	0.843459	−	2.59590i	0.0282411	−	0.0869171i
$893$	−4.30902	+	13.2618i	−0.144196	+	0.443789i
$894$	−4.30902	−	13.2618i	−0.144115	−	0.443541i
$895$	12.7254	−	9.24556i	0.425364	−	0.309045i
$896$	−33.0517	+	24.0134i	−1.10418	+	0.802233i
$897$	4.85410	−	3.52671i	0.162074	−	0.117753i
$898$	−14.7361	−	45.3530i	−0.491749	−	1.51345i
$899$	44.1074	−	32.0459i	1.47106	−	1.06879i
$900$	−2.50000	−	1.81636i	−0.0833333	−	0.0605452i
$901$	5.16718			0.172144
$902$	−0.409830	+	0.257270i	−0.0136458	+	0.00856616i
$903$	5.56231	+	17.1190i	0.185102	+	0.569685i
$904$	−22.7639			−0.757117
$905$	14.8369	−	45.6632i	0.493195	−	1.51790i
$906$	−19.7533	+	14.3516i	−0.656259	+	0.476800i
$907$	−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	$-0.368216\pi$
$908$	−5.67376			−0.188290
$909$	2.52786			0.0838440
$910$	35.1246			1.16437
$911$	−34.7705	+	25.2623i	−1.15200	+	0.836976i	−0.988745	−	0.149608i	$-0.952199\pi$
$911$	−34.7705	+	25.2623i	−1.15200	+	0.836976i	−0.163253	+	0.986584i	$0.552199\pi$
$912$	5.42705	−	3.94298i	0.179708	−	0.130565i
$913$	4.35410	+	17.3108i	0.144100	+	0.572903i
$914$	13.8992	+	10.0984i	0.459744	+	0.334024i
$915$	−6.01722	−	18.5191i	−0.198923	−	0.612223i
$916$	−4.77458	+	14.6946i	−0.157756	+	0.485524i
$917$	−4.71885	+	3.42844i	−0.155830	+	0.113217i
$918$	−0.381966	−	1.17557i	−0.0126068	−	0.0387996i
$919$	−6.70820			−0.221283			−0.110642	−	0.993860i	$-0.535291\pi$
$919$	−6.70820			−0.221283			−0.110642	+	0.993860i	$0.535291\pi$
$920$	−7.50000	−	5.44907i	−0.247268	−	0.179650i
$921$	14.0172	+	10.1841i	0.461883	+	0.335578i
$922$	−63.1591			−2.08003
$923$	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
$927$	−1.76393			−0.0579351
$928$	5.56637	−	17.1315i	0.182725	−	0.562370i
$929$	−42.0967	+	30.5851i	−1.38115	+	1.00346i	−0.384378	+	0.923176i	$0.625584\pi$
$929$	−42.0967	+	30.5851i	−1.38115	+	1.00346i	−0.996772	+	0.0802880i	$0.974416\pi$
$930$	29.9615	−	21.7683i	0.982476	−	0.713811i
$931$	2.23607	−	1.62460i	0.0732842	−	0.0532441i
$932$	7.85410	−	5.70634i	0.257270	−	0.186917i
$933$	8.59017	+	6.24112i	0.281230	+	0.204325i
$934$	−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
$937$	−15.9271	−	49.0184i	−0.520314	−	1.60136i	−0.773400	−	0.633918i	$-0.781446\pi$
$937$	−15.9271	−	49.0184i	−0.520314	−	1.60136i	0.253086	−	0.967444i	$-0.418554\pi$
$938$	−4.50000	+	13.8496i	−0.146930	+	0.452205i
$939$	9.00000	+	27.6992i	0.293704	+	0.903928i
$940$	4.30902	+	13.2618i	0.140545	+	0.432552i
$941$	14.5623	+	10.5801i	0.474718	+	0.344903i	0.799277	−	0.600963i	$-0.205216\pi$
$941$	14.5623	+	10.5801i	0.474718	+	0.344903i	−0.324559	+	0.945865i	$0.605216\pi$
$942$	−19.0623	+	13.8496i	−0.621083	+	0.451244i
$943$	−0.135255	+	0.0982684i	−0.00440451	+	0.00320006i
$944$	−21.7082	−	15.7719i	−0.706542	−	0.513333i
$945$	2.07295	+	6.37988i	0.0674330	+	0.207538i
$946$	−24.7082	−	20.6457i	−0.803333	−	0.671251i
$947$	3.70820	+	11.4127i	0.120500	+	0.370862i	0.993054	−	0.117655i	$-0.0375378\pi$
$947$	3.70820	+	11.4127i	0.120500	+	0.370862i	−0.872554	+	0.488518i	$0.837538\pi$
$948$	−2.50000	+	1.81636i	−0.0811962	+	0.0589925i
$949$	−22.4164	+	16.2865i	−0.727667	+	0.528681i
$950$	3.45492	+	10.6331i	0.112092	+	0.344984i
$951$	7.14590	+	21.9928i	0.231722	+	0.713166i
$952$	1.58359	−	4.87380i	0.0513245	−	0.157961i
$953$	1.65248	−	5.08580i	0.0535289	−	0.164745i	−0.920718	−	0.390228i	$-0.872396\pi$
$953$	1.65248	−	5.08580i	0.0535289	−	0.164745i	0.974247	+	0.225483i	$0.0723961\pi$
$954$	−8.85410	−	6.43288i	−0.286662	−	0.208272i
$955$	−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
$959$	13.9377	+	42.8958i	0.450072	+	1.38518i
$960$	−2.92705	+	9.00854i	−0.0944702	+	0.290749i
$961$	22.7984	+	70.1662i	0.735431	+	2.26343i
$962$	−37.5066	−	27.2501i	−1.20926	−	0.878579i
$963$	−13.5902	−	9.87384i	−0.437937	−	0.318180i
$964$	3.73607	+	11.4984i	0.120331	+	0.370340i
$965$	−38.9443			−1.25366
$966$	−2.78115	−	8.55951i	−0.0894821	−	0.275398i
$967$	13.0172	−	40.0629i	0.418606	−	1.28834i	−0.490380	−	0.871509i	$-0.663142\pi$
$967$	13.0172	−	40.0629i	0.418606	−	1.28834i	0.908986	−	0.416827i	$-0.136858\pi$
$968$	−17.7639	−	17.0130i	−0.570954	−	0.546819i
$969$	−0.326238	+	1.00406i	−0.0104803	+	0.0322550i
$970$	−2.82624	−	8.69827i	−0.0907450	−	0.279284i
$971$	8.80902	+	6.40013i	0.282695	+	0.205390i	0.720092	−	0.693879i	$-0.244100\pi$
$971$	8.80902	+	6.40013i	0.282695	+	0.205390i	−0.437397	+	0.899268i	$0.644100\pi$
$972$	−0.190983	+	0.587785i	−0.00612578	+	0.0188532i
$973$	12.9271	−	39.7854i	0.414422	−	1.27546i
$974$	6.23607	+	19.1926i	0.199817	+	0.614972i
$975$	13.0902	−	9.51057i	0.419221	−	0.304582i
$976$	34.1976	−	24.8460i	1.09464	−	0.795301i
$977$	20.3541	−	14.7881i	0.651185	−	0.473114i	−0.212489	−	0.977163i	$-0.568157\pi$
$977$	20.3541	−	14.7881i	0.651185	−	0.473114i	0.863675	+	0.504049i	$0.168157\pi$
$978$	−3.28115	−	10.0984i	−0.104920	−	0.322910i
$979$	2.76393	−	6.88191i	0.0883357	−	0.219947i
$980$	0.854102	−	2.62866i	0.0272833	−	0.0839693i
$981$	−9.47214	−	6.88191i	−0.302422	−	0.219722i
$982$	−50.3328	+	36.5689i	−1.60618	+	1.16696i
$983$	−9.95492	+	7.23267i	−0.317512	+	0.230686i	−0.735113	−	0.677944i	$-0.762871\pi$
$983$	−9.95492	+	7.23267i	−0.317512	+	0.230686i	0.417601	+	0.908631i	$0.362871\pi$
$984$	0.163119	+	0.118513i	0.00520004	+	0.00377805i
$985$	31.8328			1.01428
$986$	2.03444	+	6.26137i	0.0647898	+	0.199403i
$987$	9.35410	−	28.7890i	0.297744	−	0.916363i
$988$	−0.854102	−	2.62866i	−0.0271726	−	0.0836287i
$989$	−9.00000	−	6.53888i	−0.286183	−	0.207924i
$990$	−9.20820	−	7.69421i	−0.292656	−	0.244538i
$991$	−17.7984	+	12.9313i	−0.565384	+	0.410776i	−0.833425	−	0.552632i	$-0.813624\pi$
$991$	−17.7984	+	12.9313i	−0.565384	+	0.410776i	0.268041	+	0.963407i	$0.413624\pi$
$992$	28.0066	+	20.3480i	0.889210	+	0.646049i
$993$	28.9164	−	21.0090i	0.917634	−	0.666700i
$994$	36.8435	−	26.7683i	1.16860	−	0.849040i
$995$	−6.77051	+	20.8375i	−0.214640	+	0.660593i
$996$	−2.69098	+	1.95511i	−0.0852671	+	0.0619501i
$997$	−1.57953	+	4.86128i	−0.0500241	+	0.153958i	−0.972948	−	0.231024i	$-0.925792\pi$
$997$	−1.57953	+	4.86128i	−0.0500241	+	0.153958i	0.922924	+	0.384982i	$0.125792\pi$
$998$	24.4721			0.774652
$999$	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.o.b.691.1	yes	4
11.5	even	5		825.2.m.a.16.1	✓	4
25.11	even	5		825.2.m.a.361.1	yes	4
275.236	even	5	inner	825.2.o.b.511.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.m.a.16.1	✓	4	11.5	even	5
825.2.m.a.361.1	yes	4	25.11	even	5
825.2.o.b.511.1	yes	4	275.236	even	5	inner
825.2.o.b.691.1	yes	4	1.1	even	1	trivial

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

\(f(q)\)	\(=\)	\(q+(1.30902 - 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.190983 - 0.587785i) q^{4} +(0.690983 - 2.12663i) q^{5} +1.61803 q^{6} +(2.42705 + 1.76336i) q^{7} +(0.690983 + 2.12663i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(1.30902 - 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.190983 - 0.587785i) q^{4} +(0.690983 - 2.12663i) q^{5} +1.61803 q^{6} +(2.42705 + 1.76336i) q^{7} +(0.690983 + 2.12663i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-1.11803 - 3.44095i) q^{10} +(-0.809017 - 3.21644i) q^{11} +(0.500000 - 0.363271i) q^{12} +(1.00000 + 3.07768i) q^{13} +4.85410 q^{14} +(1.80902 - 1.31433i) q^{15} +(3.92705 + 2.85317i) q^{16} -0.763932 q^{17} +(1.30902 + 0.951057i) q^{18} +(-0.427051 - 1.31433i) q^{19} +(-1.11803 - 0.812299i) q^{20} +(0.927051 + 2.85317i) q^{21} +(-4.11803 - 3.44095i) q^{22} +(-1.50000 - 1.08981i) q^{23} +(-0.690983 + 2.12663i) q^{24} +(-4.04508 - 2.93893i) q^{25} +(4.23607 + 3.07768i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(1.50000 - 1.08981i) q^{28} +(1.64590 - 5.06555i) q^{29} +(1.11803 - 3.44095i) q^{30} +(8.28115 + 6.01661i) q^{31} +3.38197 q^{32} +(1.23607 - 3.07768i) q^{33} +(-1.00000 + 0.726543i) q^{34} +(5.42705 - 3.94298i) q^{35} +0.618034 q^{36} -8.85410 q^{37} +(-1.80902 - 1.31433i) q^{38} +(-1.00000 + 3.07768i) q^{39} +5.00000 q^{40} +(0.0278640 - 0.0857567i) q^{41} +(3.92705 + 2.85317i) q^{42} +6.00000 q^{43} +(-2.04508 - 0.138757i) q^{44} +2.23607 q^{45} -3.00000 q^{46} +(-8.16312 - 5.93085i) q^{47} +(1.50000 + 4.61653i) q^{48} +(0.618034 + 1.90211i) q^{49} -8.09017 q^{50} +(-0.618034 - 0.449028i) q^{51} +2.00000 q^{52} -6.76393 q^{53} +(0.500000 + 1.53884i) q^{54} +(-7.39919 - 0.502029i) q^{55} +(-2.07295 + 6.37988i) q^{56} +(0.427051 - 1.31433i) q^{57} +(-2.66312 - 8.19624i) q^{58} -5.52786 q^{59} +(-0.427051 - 1.31433i) q^{60} +(2.69098 - 8.28199i) q^{61} +16.5623 q^{62} +(-0.927051 + 2.85317i) q^{63} +(-3.42705 + 2.48990i) q^{64} +7.23607 q^{65} +(-1.30902 - 5.20431i) q^{66} +(-0.927051 + 2.85317i) q^{67} +(-0.145898 + 0.449028i) q^{68} +(-0.572949 - 1.76336i) q^{69} +(3.35410 - 10.3229i) q^{70} +(7.59017 - 5.51458i) q^{71} +(-1.80902 + 1.31433i) q^{72} +(2.64590 + 8.14324i) q^{73} +(-11.5902 + 8.42075i) q^{74} +(-1.54508 - 4.75528i) q^{75} -0.854102 q^{76} +(3.70820 - 9.23305i) q^{77} +(1.61803 + 4.97980i) q^{78} -5.00000 q^{79} +(8.78115 - 6.37988i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-0.0450850 - 0.138757i) q^{82} -5.38197 q^{83} +1.85410 q^{84} +(-0.527864 + 1.62460i) q^{85} +(7.85410 - 5.70634i) q^{86} +(4.30902 - 3.13068i) q^{87} +(6.28115 - 3.94298i) q^{88} +(1.80902 + 1.31433i) q^{89} +(2.92705 - 2.12663i) q^{90} +(-3.00000 + 9.23305i) q^{91} +(-0.927051 + 0.673542i) q^{92} +(3.16312 + 9.73508i) q^{93} -16.3262 q^{94} -3.09017 q^{95} +(2.73607 + 1.98787i) q^{96} +2.52786 q^{97} +(2.61803 + 1.90211i) q^{98} +(2.80902 - 1.76336i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} + q^{3} + 3 q^{4} + 5 q^{5} + 2 q^{6} + 3 q^{7} + 5 q^{8} - q^{9}+O(q^{10}) \) 4 * q + 3 * q^2 + q^3 + 3 * q^4 + 5 * q^5 + 2 * q^6 + 3 * q^7 + 5 * q^8 - q^9	\( 4 q + 3 q^{2} + q^{3} + 3 q^{4} + 5 q^{5} + 2 q^{6} + 3 q^{7} + 5 q^{8} - q^{9} - q^{11} + 2 q^{12} + 4 q^{13} + 6 q^{14} + 5 q^{15} + 9 q^{16} - 12 q^{17} + 3 q^{18} + 5 q^{19} - 3 q^{21} - 12 q^{22} - 6 q^{23} - 5 q^{24} - 5 q^{25} + 8 q^{26} + q^{27} + 6 q^{28} + 20 q^{29} + 13 q^{31} + 18 q^{32} - 4 q^{33} - 4 q^{34} + 15 q^{35} - 2 q^{36} - 22 q^{37} - 5 q^{38} - 4 q^{39} + 20 q^{40} + 18 q^{41} + 9 q^{42} + 24 q^{43} + 3 q^{44} - 12 q^{46} - 17 q^{47} + 6 q^{48} - 2 q^{49} - 10 q^{50} + 2 q^{51} + 8 q^{52} - 36 q^{53} + 2 q^{54} - 5 q^{55} - 15 q^{56} - 5 q^{57} + 5 q^{58} - 40 q^{59} + 5 q^{60} + 13 q^{61} + 26 q^{62} + 3 q^{63} - 7 q^{64} + 20 q^{65} - 3 q^{66} + 3 q^{67} - 14 q^{68} - 9 q^{69} + 8 q^{71} - 5 q^{72} + 24 q^{73} - 24 q^{74} + 5 q^{75} + 10 q^{76} - 12 q^{77} + 2 q^{78} - 20 q^{79} + 15 q^{80} - q^{81} + 11 q^{82} - 26 q^{83} - 6 q^{84} - 20 q^{85} + 18 q^{86} + 15 q^{87} + 5 q^{88} + 5 q^{89} + 5 q^{90} - 12 q^{91} + 3 q^{92} - 3 q^{93} - 34 q^{94} + 10 q^{95} + 2 q^{96} + 28 q^{97} + 6 q^{98} + 9 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 + q^3 + 3 * q^4 + 5 * q^5 + 2 * q^6 + 3 * q^7 + 5 * q^8 - q^9 - q^11 + 2 * q^12 + 4 * q^13 + 6 * q^14 + 5 * q^15 + 9 * q^16 - 12 * q^17 + 3 * q^18 + 5 * q^19 - 3 * q^21 - 12 * q^22 - 6 * q^23 - 5 * q^24 - 5 * q^25 + 8 * q^26 + q^27 + 6 * q^28 + 20 * q^29 + 13 * q^31 + 18 * q^32 - 4 * q^33 - 4 * q^34 + 15 * q^35 - 2 * q^36 - 22 * q^37 - 5 * q^38 - 4 * q^39 + 20 * q^40 + 18 * q^41 + 9 * q^42 + 24 * q^43 + 3 * q^44 - 12 * q^46 - 17 * q^47 + 6 * q^48 - 2 * q^49 - 10 * q^50 + 2 * q^51 + 8 * q^52 - 36 * q^53 + 2 * q^54 - 5 * q^55 - 15 * q^56 - 5 * q^57 + 5 * q^58 - 40 * q^59 + 5 * q^60 + 13 * q^61 + 26 * q^62 + 3 * q^63 - 7 * q^64 + 20 * q^65 - 3 * q^66 + 3 * q^67 - 14 * q^68 - 9 * q^69 + 8 * q^71 - 5 * q^72 + 24 * q^73 - 24 * q^74 + 5 * q^75 + 10 * q^76 - 12 * q^77 + 2 * q^78 - 20 * q^79 + 15 * q^80 - q^81 + 11 * q^82 - 26 * q^83 - 6 * q^84 - 20 * q^85 + 18 * q^86 + 15 * q^87 + 5 * q^88 + 5 * q^89 + 5 * q^90 - 12 * q^91 + 3 * q^92 - 3 * q^93 - 34 * q^94 + 10 * q^95 + 2 * q^96 + 28 * q^97 + 6 * q^98 + 9 * q^99

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