LMFDB - Embedded newform 172.2.f.a.123.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [172,2,Mod(7,172)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(172, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("172.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 172 = 2^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	172.f (of order $6$, degree $2$, 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:	$1.37342691477$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.157044178944.7
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 14x^{6} + 153x^{4} + 602x^{2} + 1849 $ x^8 + 14x^6 + 153x^4 + 602*x^2 + 1849
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			123.1
Root			$-1.06660 + 1.84740i$ of defining polynomial
Character	$\chi$	$=$	172.123
Dual form			172.2.f.a.7.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +(-1.06660 + 1.84740i) q^{3} -2.00000 q^{4} +(0.275255 + 0.158919i) q^{5} +(2.61262 + 1.50839i) q^{6} +(1.06660 + 1.84740i) q^{7} +2.82843i q^{8} +(-0.775255 - 1.34278i) q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +(-1.06660 + 1.84740i) q^{3} -2.00000 q^{4} +(0.275255 + 0.158919i) q^{5} +(2.61262 + 1.50839i) q^{6} +(1.06660 + 1.84740i) q^{7} +2.82843i q^{8} +(-0.775255 - 1.34278i) q^{9} +(0.224745 - 0.389270i) q^{10} +3.01679i q^{11} +(2.13319 - 3.69480i) q^{12} +(1.72474 + 2.98735i) q^{13} +(2.61262 - 1.50839i) q^{14} +(-0.587172 + 0.339004i) q^{15} +4.00000 q^{16} +(0.275255 + 0.476756i) q^{17} +(-1.89898 + 1.09638i) q^{18} +(1.06660 - 1.84740i) q^{19} +(-0.550510 - 0.317837i) q^{20} -4.55051 q^{21} +4.26639 q^{22} +(-5.81241 - 3.35579i) q^{23} +(-5.22523 - 3.01679i) q^{24} +(-2.44949 - 4.24264i) q^{25} +(4.22474 - 2.43916i) q^{26} -3.09204 q^{27} +(-2.13319 - 3.69480i) q^{28} +(-0.275255 + 0.158919i) q^{29} +(0.479424 + 0.830387i) q^{30} +(3.19979 + 1.84740i) q^{31} -5.65685i q^{32} +(-5.57321 - 3.21770i) q^{33} +(0.674235 - 0.389270i) q^{34} +0.678008i q^{35} +(1.55051 + 2.68556i) q^{36} +(5.17423 + 2.98735i) q^{37} +(-2.61262 - 1.50839i) q^{38} -7.35843 q^{39} +(-0.449490 + 0.778539i) q^{40} +7.34847 q^{41} +6.43539i q^{42} +(4.74581 + 4.52518i) q^{43} -6.03358i q^{44} -0.492810i q^{45} +(-4.74581 + 8.21998i) q^{46} -6.03358i q^{47} +(-4.26639 + 7.38960i) q^{48} +(1.22474 - 2.12132i) q^{49} +(-6.00000 + 3.46410i) q^{50} -1.17434 q^{51} +(-3.44949 - 5.97469i) q^{52} +(-3.94949 + 6.84072i) q^{53} +4.37281i q^{54} +(-0.479424 + 0.830387i) q^{55} +(-5.22523 + 3.01679i) q^{56} +(2.27526 + 3.94086i) q^{57} +(0.224745 + 0.389270i) q^{58} -13.4232i q^{59} +(1.17434 - 0.678008i) q^{60} +(-2.17423 + 1.25529i) q^{61} +(2.61262 - 4.52518i) q^{62} +(1.65377 - 2.86441i) q^{63} -8.00000 q^{64} +1.09638i q^{65} +(-4.55051 + 7.88171i) q^{66} +(11.0376 + 6.37258i) q^{67} +(-0.550510 - 0.953512i) q^{68} +(12.3990 - 7.15855i) q^{69} +0.958848 q^{70} +(-5.81241 - 10.0674i) q^{71} +(3.79796 - 2.19275i) q^{72} +(-2.17423 + 1.25529i) q^{73} +(4.22474 - 7.31747i) q^{74} +10.4505 q^{75} +(-2.13319 + 3.69480i) q^{76} +(-5.57321 + 3.21770i) q^{77} +10.4064i q^{78} +(3.19979 - 1.84740i) q^{79} +(1.10102 + 0.635674i) q^{80} +(5.62372 - 9.74058i) q^{81} -10.3923i q^{82} +(14.8246 + 8.55899i) q^{83} +9.10102 q^{84} +0.174973i q^{85} +(6.39958 - 6.71159i) q^{86} -0.678008i q^{87} -8.53277 q^{88} +(6.94949 + 4.01229i) q^{89} -0.696938 q^{90} +(-3.67921 + 6.37258i) q^{91} +(11.6248 + 6.71159i) q^{92} +(-6.82577 + 3.94086i) q^{93} -8.53277 q^{94} +(0.587172 - 0.339004i) q^{95} +(10.4505 + 6.03358i) q^{96} -6.44949 q^{97} +(-3.00000 - 1.73205i) q^{98} +(4.05089 - 2.33878i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 16 q^{4} + 12 q^{5} - 16 q^{9}+O(q^{10}) $ 8 * q - 16 * q^4 + 12 * q^5 - 16 * q^9	$ 8 q - 16 q^{4} + 12 q^{5} - 16 q^{9} - 8 q^{10} + 4 q^{13} + 32 q^{16} + 12 q^{17} + 24 q^{18} - 24 q^{20} - 56 q^{21} + 24 q^{26} - 12 q^{29} + 24 q^{33} - 24 q^{34} + 32 q^{36} + 12 q^{37} + 16 q^{40} - 48 q^{50} - 8 q^{52} - 12 q^{53} + 28 q^{57} - 8 q^{58} + 12 q^{61} - 64 q^{64} - 56 q^{66} - 24 q^{68} + 60 q^{69} - 48 q^{72} + 12 q^{73} + 24 q^{74} + 24 q^{77} + 48 q^{80} - 4 q^{81} + 112 q^{84} + 36 q^{89} + 112 q^{90} - 84 q^{93} - 32 q^{97} - 24 q^{98}+O(q^{100}) $ 8 * q - 16 * q^4 + 12 * q^5 - 16 * q^9 - 8 * q^10 + 4 * q^13 + 32 * q^16 + 12 * q^17 + 24 * q^18 - 24 * q^20 - 56 * q^21 + 24 * q^26 - 12 * q^29 + 24 * q^33 - 24 * q^34 + 32 * q^36 + 12 * q^37 + 16 * q^40 - 48 * q^50 - 8 * q^52 - 12 * q^53 + 28 * q^57 - 8 * q^58 + 12 * q^61 - 64 * q^64 - 56 * q^66 - 24 * q^68 + 60 * q^69 - 48 * q^72 + 12 * q^73 + 24 * q^74 + 24 * q^77 + 48 * q^80 - 4 * q^81 + 112 * q^84 + 36 * q^89 + 112 * q^90 - 84 * q^93 - 32 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/172\mathbb{Z}\right)^\times$.

$n$	$87$	$89$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	1.41421i		−	1.00000i
$2$		−	1.41421i		−	1.00000i
$3$	−1.06660	+	1.84740i	−0.615800	+	1.06660i	0.374444	+	0.927250i	$0.377834\pi$
$3$	−1.06660	+	1.84740i	−0.615800	+	1.06660i	−0.990244	+	0.139347i	$0.955500\pi$
$4$	−2.00000			−1.00000
$5$	0.275255	+	0.158919i	0.123098	+	0.0710706i	0.560285	−	0.828300i	$-0.310692\pi$
$5$	0.275255	+	0.158919i	0.123098	+	0.0710706i	−0.437187	+	0.899371i	$0.644025\pi$
$6$	2.61262	+	1.50839i	1.06660	+	0.615800i
$7$	1.06660	+	1.84740i	0.403135	+	0.698251i	0.994102	−	0.108445i	$-0.0345870\pi$
$7$	1.06660	+	1.84740i	0.403135	+	0.698251i	−0.590967	+	0.806696i	$0.701254\pi$
$8$			2.82843i			1.00000i
$9$	−0.775255	−	1.34278i	−0.258418	−	0.447594i
$10$	0.224745	−	0.389270i	0.0710706	−	0.123098i
$11$			3.01679i			0.909596i	0.890595	+	0.454798i	$0.150289\pi$
$11$			3.01679i			0.909596i	−0.890595	+	0.454798i	$0.849711\pi$
$12$	2.13319	−	3.69480i	0.615800	−	1.06660i
$13$	1.72474	+	2.98735i	0.478358	+	0.828541i	0.999692	−	0.0248121i	$-0.00789875\pi$
$13$	1.72474	+	2.98735i	0.478358	+	0.828541i	−0.521334	+	0.853353i	$0.674565\pi$
$14$	2.61262	−	1.50839i	0.698251	−	0.403135i
$15$	−0.587172	+	0.339004i	−0.151607	+	0.0875305i
$16$	4.00000			1.00000
$17$	0.275255	+	0.476756i	0.0667592	+	0.115630i	0.897473	−	0.441069i	$-0.145401\pi$
$17$	0.275255	+	0.476756i	0.0667592	+	0.115630i	−0.830714	+	0.556700i	$0.812067\pi$
$18$	−1.89898	+	1.09638i	−0.447594	+	0.258418i
$19$	1.06660	−	1.84740i	0.244694	−	0.423822i	−0.717352	−	0.696711i	$-0.754646\pi$
$19$	1.06660	−	1.84740i	0.244694	−	0.423822i	0.962046	+	0.272889i	$0.0879792\pi$
$20$	−0.550510	−	0.317837i	−0.123098	−	0.0710706i
$21$	−4.55051			−0.993003
$22$	4.26639			0.909596
$23$	−5.81241	−	3.35579i	−1.21197	−	0.699731i	−0.248782	−	0.968559i	$-0.580030\pi$
$23$	−5.81241	−	3.35579i	−1.21197	−	0.699731i	−0.963188	+	0.268828i	$0.913364\pi$
$24$	−5.22523	−	3.01679i	−1.06660	−	0.615800i
$25$	−2.44949	−	4.24264i	−0.489898	−	0.848528i
$26$	4.22474	−	2.43916i	0.828541	−	0.478358i
$27$	−3.09204			−0.595064
$28$	−2.13319	−	3.69480i	−0.403135	−	0.698251i
$29$	−0.275255	+	0.158919i	−0.0511136	+	0.0295104i	−0.525339	−	0.850893i	$-0.676061\pi$
$29$	−0.275255	+	0.158919i	−0.0511136	+	0.0295104i	0.474225	+	0.880403i	$0.342728\pi$
$30$	0.479424	+	0.830387i	0.0875305	+	0.151607i
$31$	3.19979	+	1.84740i	0.574699	+	0.331803i	0.759024	−	0.651063i	$-0.225677\pi$
$31$	3.19979	+	1.84740i	0.574699	+	0.331803i	−0.184325	+	0.982865i	$0.559010\pi$
$32$		−	5.65685i		−	1.00000i
$33$	−5.57321	−	3.21770i	−0.970172	−	0.560129i
$34$	0.674235	−	0.389270i	0.115630	−	0.0667592i
$35$			0.678008i			0.114604i
$36$	1.55051	+	2.68556i	0.258418	+	0.447594i
$37$	5.17423	+	2.98735i	0.850639	+	0.491117i	0.860866	−	0.508831i	$-0.169922\pi$
$37$	5.17423	+	2.98735i	0.850639	+	0.491117i	−0.0102275	+	0.999948i	$0.503256\pi$
$38$	−2.61262	−	1.50839i	−0.423822	−	0.244694i
$39$	−7.35843			−1.17829
$40$	−0.449490	+	0.778539i	−0.0710706	+	0.123098i
$41$	7.34847			1.14764			0.573819	−	0.818982i	$-0.305461\pi$
$41$	7.34847			1.14764			0.573819	+	0.818982i	$0.305461\pi$
$42$			6.43539i			0.993003i
$43$	4.74581	+	4.52518i	0.723729	+	0.690084i
$43$	4.74581	+	4.52518i	0.723729	+	0.690084i
$44$		−	6.03358i		−	0.909596i
$45$		−	0.492810i		−	0.0734638i
$46$	−4.74581	+	8.21998i	−0.699731	+	1.21197i
$47$		−	6.03358i		−	0.880088i	−0.897976	−	0.440044i	$-0.854963\pi$
$47$		−	6.03358i		−	0.880088i	0.897976	−	0.440044i	$-0.145037\pi$
$48$	−4.26639	+	7.38960i	−0.615800	+	1.06660i
$49$	1.22474	−	2.12132i	0.174964	−	0.303046i
$50$	−6.00000	+	3.46410i	−0.848528	+	0.489898i
$51$	−1.17434			−0.164441
$52$	−3.44949	−	5.97469i	−0.478358	−	0.828541i
$53$	−3.94949	+	6.84072i	−0.542504	+	0.939645i	0.456255	+	0.889849i	$0.349190\pi$
$53$	−3.94949	+	6.84072i	−0.542504	+	0.939645i	−0.998759	+	0.0497958i	$0.984143\pi$
$54$			4.37281i			0.595064i
$55$	−0.479424	+	0.830387i	−0.0646455	+	0.111969i
$56$	−5.22523	+	3.01679i	−0.698251	+	0.403135i
$57$	2.27526	+	3.94086i	0.301365	+	0.521979i
$58$	0.224745	+	0.389270i	0.0295104	+	0.0511136i
$59$		−	13.4232i		−	1.74755i	−0.486332	−	0.873774i	$-0.661665\pi$
$59$		−	13.4232i		−	1.74755i	0.486332	−	0.873774i	$-0.338335\pi$
$60$	1.17434	−	0.678008i	0.151607	−	0.0875305i
$61$	−2.17423	+	1.25529i	−0.278382	+	0.160724i	−0.632691	−	0.774405i	$-0.718050\pi$
$61$	−2.17423	+	1.25529i	−0.278382	+	0.160724i	0.354309	+	0.935129i	$0.384716\pi$
$62$	2.61262	−	4.52518i	0.331803	−	0.574699i
$63$	1.65377	−	2.86441i	0.208355	−	0.360882i
$64$	−8.00000			−1.00000
$65$			1.09638i			0.135989i
$66$	−4.55051	+	7.88171i	−0.560129	+	0.970172i
$67$	11.0376	+	6.37258i	1.34846	+	0.778535i	0.988032	−	0.154251i	$-0.0492965\pi$
$67$	11.0376	+	6.37258i	1.34846	+	0.778535i	0.360430	+	0.932786i	$0.382630\pi$
$68$	−0.550510	−	0.953512i	−0.0667592	−	0.115630i
$69$	12.3990	−	7.15855i	1.49266	−	0.861789i
$70$	0.958848			0.114604
$71$	−5.81241	−	10.0674i	−0.689806	−	1.19478i	−0.971901	−	0.235392i	$-0.924363\pi$
$71$	−5.81241	−	10.0674i	−0.689806	−	1.19478i	0.282095	−	0.959386i	$-0.408971\pi$
$72$	3.79796	−	2.19275i	0.447594	−	0.258418i
$73$	−2.17423	+	1.25529i	−0.254475	+	0.146921i	−0.621812	−	0.783167i	$-0.713603\pi$
$73$	−2.17423	+	1.25529i	−0.254475	+	0.146921i	0.367337	+	0.930088i	$0.380270\pi$
$74$	4.22474	−	7.31747i	0.491117	−	0.850639i
$75$	10.4505			1.20672
$76$	−2.13319	+	3.69480i	−0.244694	+	0.423822i
$77$	−5.57321	+	3.21770i	−0.635127	+	0.366691i
$78$			10.4064i			1.17829i
$79$	3.19979	−	1.84740i	0.360004	−	0.207849i	−0.309078	−	0.951037i	$-0.600021\pi$
$79$	3.19979	−	1.84740i	0.360004	−	0.207849i	0.669083	+	0.743188i	$0.266687\pi$
$80$	1.10102	+	0.635674i	0.123098	+	0.0710706i
$81$	5.62372	−	9.74058i	0.624858	−	1.08229i
$82$		−	10.3923i		−	1.14764i
$83$	14.8246	+	8.55899i	1.62721	+	0.939471i	0.984920	+	0.173010i	$0.0553493\pi$
$83$	14.8246	+	8.55899i	1.62721	+	0.939471i	0.642291	+	0.766461i	$0.277984\pi$
$84$	9.10102			0.993003
$85$			0.174973i			0.0189785i
$86$	6.39958	−	6.71159i	0.690084	−	0.723729i
$87$		−	0.678008i		−	0.0726901i
$88$	−8.53277			−0.909596
$89$	6.94949	+	4.01229i	0.736644	+	0.425302i	0.820848	−	0.571147i	$-0.193501\pi$
$89$	6.94949	+	4.01229i	0.736644	+	0.425302i	−0.0842036	+	0.996449i	$0.526835\pi$
$90$	−0.696938			−0.0734638
$91$	−3.67921	+	6.37258i	−0.385686	+	0.668028i
$92$	11.6248	+	6.71159i	1.21197	+	0.699731i
$93$	−6.82577	+	3.94086i	−0.707799	+	0.408648i
$94$	−8.53277			−0.880088
$95$	0.587172	−	0.339004i	0.0602426	−	0.0347811i
$96$	10.4505	+	6.03358i	1.06660	+	0.615800i
$97$	−6.44949			−0.654846			−0.327423	−	0.944878i	$-0.606180\pi$
$97$	−6.44949			−0.654846			−0.327423	+	0.944878i	$0.606180\pi$
$98$	−3.00000	−	1.73205i	−0.303046	−	0.174964i
$99$	4.05089	−	2.33878i	0.407130	−	0.235056i
$100$	4.89898	+	8.48528i	0.489898	+	0.848528i
$101$	−9.39898	−	16.2795i	−0.935233	−	1.61987i	−0.774217	−	0.632920i	$-0.781856\pi$
$101$	−9.39898	−	16.2795i	−0.935233	−	1.61987i	−0.161016	−	0.986952i	$-0.551477\pi$
$102$			1.66077i			0.164441i
$103$	11.0376	−	6.37258i	1.08757	−	0.627909i	0.154642	−	0.987971i	$-0.450578\pi$
$103$	11.0376	−	6.37258i	1.08757	−	0.627909i	0.932929	+	0.360061i	$0.117244\pi$
$104$	−8.44949	+	4.87832i	−0.828541	+	0.478358i
$105$	−1.25255	−	0.723161i	−0.122236	−	0.0705733i
$106$	9.67423	+	5.58542i	0.939645	+	0.542504i
$107$		−	6.03358i		−	0.583288i	−0.956527	−	0.291644i	$-0.905798\pi$
$107$		−	6.03358i		−	0.583288i	0.956527	−	0.291644i	$-0.0942023\pi$
$108$	6.18408			0.595064
$109$	−8.62372	+	14.9367i	−0.826003	+	1.43068i	0.0751474	+	0.997172i	$0.476057\pi$
$109$	−8.62372	+	14.9367i	−0.826003	+	1.43068i	−0.901150	+	0.433507i	$0.857276\pi$
$110$	1.17434	+	0.678008i	0.111969	+	0.0646455i
$111$	−11.0376	+	6.37258i	−1.04765	+	0.604859i
$112$	4.26639	+	7.38960i	0.403135	+	0.698251i
$113$		−	5.51399i		−	0.518713i	−0.965782	−	0.259356i	$-0.916490\pi$
$113$		−	5.51399i		−	0.518713i	0.965782	−	0.259356i	$-0.0835104\pi$
$114$	5.57321	−	3.21770i	0.521979	−	0.301365i
$115$	−1.06660	−	1.84740i	−0.0994606	−	0.172271i
$116$	0.550510	−	0.317837i	0.0511136	−	0.0295104i
$117$	2.67423	−	4.63191i	0.247233	−	0.428220i
$118$	−18.9832			−1.74755
$119$	−0.587172	+	1.01701i	−0.0538260	+	0.0932293i
$120$	−0.958848	−	1.66077i	−0.0875305	−	0.151607i
$121$	1.89898			0.172634
$122$	1.77526	+	3.07483i	0.160724	+	0.278382i
$123$	−7.83785	+	13.5756i	−0.706715	+	1.22407i
$124$	−6.39958	−	3.69480i	−0.574699	−	0.331803i
$125$		−	3.14626i		−	0.281410i
$126$	−4.05089	−	2.33878i	−0.360882	−	0.208355i
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$			11.3137i			1.00000i
$129$	−13.4217	+	3.94086i	−1.18171	+	0.346973i
$130$	1.55051			0.135989
$131$	−12.7992			−1.11827			−0.559134	−	0.829078i	$-0.688866\pi$
$131$	−12.7992			−1.11827			−0.559134	+	0.829078i	$0.688866\pi$
$132$	11.1464	+	6.43539i	0.970172	+	0.560129i
$133$	4.55051			0.394579
$134$	9.01219	−	15.6096i	0.778535	−	1.34846i
$135$	−0.851100	−	0.491383i	−0.0732510	−	0.0422915i
$136$	−1.34847	+	0.778539i	−0.115630	+	0.0667592i
$137$			15.2706i			1.30466i	0.757936	+	0.652329i	$0.226208\pi$
$137$			15.2706i			1.30466i	−0.757936	+	0.652329i	$0.773792\pi$
$138$	−10.1237	−	17.5348i	−0.861789	−	1.49266i
$139$	−4.63806	−	2.67779i	−0.393395	−	0.227127i	0.290235	−	0.956955i	$-0.406267\pi$
$139$	−4.63806	−	2.67779i	−0.393395	−	0.227127i	−0.683630	+	0.729829i	$0.739600\pi$
$140$		−	1.35602i		−	0.114604i
$141$	11.1464	+	6.43539i	0.938699	+	0.541958i
$142$	−14.2374	+	8.21998i	−1.19478	+	0.689806i
$143$	−9.01219	+	5.20319i	−0.753638	+	0.435113i
$144$	−3.10102	−	5.37113i	−0.258418	−	0.447594i
$145$	−0.101021			−0.00838930
$146$	1.77526	+	3.07483i	0.146921	+	0.254475i
$147$	2.61262	+	4.52518i	0.215485	+	0.373231i
$148$	−10.3485	−	5.97469i	−0.850639	−	0.491117i
$149$	8.60102	+	4.96580i	0.704623	+	0.406814i	0.809067	−	0.587716i	$-0.199973\pi$
$149$	8.60102	+	4.96580i	0.704623	+	0.406814i	−0.104444	+	0.994531i	$0.533306\pi$
$150$		−	14.7792i		−	1.20672i
$151$	−6.18408			−0.503253			−0.251627	−	0.967824i	$-0.580966\pi$
$151$	−6.18408			−0.503253			−0.251627	+	0.967824i	$0.580966\pi$
$152$	5.22523	+	3.01679i	0.423822	+	0.244694i
$153$	0.426786	−	0.739215i	0.0345036	−	0.0597620i
$154$	4.55051	+	7.88171i	0.366691	+	0.635127i
$155$	0.587172	+	1.01701i	0.0471628	+	0.0816884i
$156$	14.7169			1.17829
$157$	10.5000	−	6.06218i	0.837991	−	0.483814i	−0.0185897	−	0.999827i	$-0.505918\pi$
$157$	10.5000	−	6.06218i	0.837991	−	0.483814i	0.856581	+	0.516013i	$0.172584\pi$
$158$	−2.61262	−	4.52518i	−0.207849	−	0.360004i
$159$	−8.42502	−	14.5926i	−0.668148	−	1.15727i
$160$	0.898979	−	1.55708i	0.0710706	−	0.123098i
$161$		−	14.3171i		−	1.12835i
$162$	−13.7753	−	7.95315i	−1.08229	−	0.624858i
$163$	8.90445	+	15.4230i	0.697450	+	1.20802i	0.969348	+	0.245693i	$0.0790154\pi$
$163$	8.90445	+	15.4230i	0.697450	+	1.20802i	−0.271898	+	0.962326i	$0.587651\pi$
$164$	−14.6969			−1.14764
$165$	−1.02270	−	1.77138i	−0.0796174	−	0.137901i
$166$	12.1042	−	20.9651i	0.939471	−	1.62721i
$167$	−4.37413	−	2.52541i	−0.338481	−	0.195422i	0.321119	−	0.947039i	$-0.395941\pi$
$167$	−4.37413	−	2.52541i	−0.338481	−	0.195422i	−0.659600	+	0.751617i	$0.729274\pi$
$168$		−	12.8708i		−	0.993003i
$169$	0.550510	−	0.953512i	0.0423469	−	0.0733471i
$170$	0.247449			0.0189785
$171$	−3.30754			−0.252934
$172$	−9.49162	−	9.05037i	−0.723729	−	0.690084i
$173$	−4.65153			−0.353649			−0.176825	−	0.984242i	$-0.556583\pi$
$173$	−4.65153			−0.353649			−0.176825	+	0.984242i	$0.556583\pi$
$174$	−0.958848			−0.0726901
$175$	5.22523	−	9.05037i	0.394990	−	0.684144i
$176$			12.0672i			0.909596i
$177$	24.7980	+	14.3171i	1.86393	+	1.07614i
$178$	5.67423	−	9.82806i	0.425302	−	0.736644i
$179$	0.587172	+	1.01701i	0.0438873	+	0.0760150i	0.887135	−	0.461511i	$-0.152692\pi$
$179$	0.587172	+	1.01701i	0.0438873	+	0.0760150i	−0.843247	+	0.537526i	$0.819359\pi$
$180$			0.985620i			0.0734638i
$181$	−10.9495	−	18.9651i	−0.813869	−	1.40966i	−0.910137	−	0.414307i	$-0.864024\pi$
$181$	−10.9495	−	18.9651i	−0.813869	−	1.40966i	0.0962679	−	0.995355i	$-0.469309\pi$
$182$	9.01219	+	5.20319i	0.668028	+	0.385686i
$183$		−	5.35557i		−	0.395895i
$184$	9.49162	−	16.4400i	0.699731	−	1.21197i
$185$	0.949490	+	1.64456i	0.0698079	+	0.120911i
$186$	5.57321	+	9.65309i	0.408648	+	0.707799i
$187$	−1.43827	+	0.830387i	−0.105177	+	0.0607239i
$188$			12.0672i			0.880088i
$189$	−3.29796	−	5.71223i	−0.239891	−	0.415504i
$190$	−0.479424	−	0.830387i	−0.0347811	−	0.0602426i
$191$	−8.42502	+	14.5926i	−0.609613	+	1.05588i	0.381691	+	0.924290i	$0.375342\pi$
$191$	−8.42502	+	14.5926i	−0.609613	+	1.05588i	−0.991304	+	0.131591i	$0.957991\pi$
$192$	8.53277	−	14.7792i	0.615800	−	1.06660i
$193$	3.34847			0.241028			0.120514	−	0.992712i	$-0.461546\pi$
$193$	3.34847			0.241028			0.120514	+	0.992712i	$0.461546\pi$
$194$			9.12096i			0.654846i
$195$	−2.02544	−	1.16939i	−0.145045	−	0.0837418i
$196$	−2.44949	+	4.24264i	−0.174964	+	0.303046i
$197$	−5.72474	−	9.91555i	−0.407871	−	0.706454i	0.586780	−	0.809747i	$-0.300395\pi$
$197$	−5.72474	−	9.91555i	−0.407871	−	0.706454i	−0.994651	+	0.103293i	$0.967062\pi$
$198$	−3.30754	−	5.72882i	−0.235056	−	0.407130i
$199$	−18.9832			−1.34569			−0.672843	−	0.739785i	$-0.734927\pi$
$199$	−18.9832			−1.34569			−0.672843	+	0.739785i	$0.734927\pi$
$200$	12.0000	−	6.92820i	0.848528	−	0.489898i
$201$	−23.5454	+	13.5939i	−1.66077	+	0.958843i
$202$	−23.0227	+	13.2922i	−1.61987	+	0.935233i
$203$	−0.587172	−	0.339004i	−0.0412114	−	0.0237934i
$204$	2.34869			0.164441
$205$	2.02270	+	1.16781i	0.141272	+	0.0815633i
$206$	−9.01219	−	15.6096i	−0.627909	−	1.08757i
$207$			10.4064i			0.723294i
$208$	6.89898	+	11.9494i	0.478358	+	0.828541i
$209$	5.57321	+	3.21770i	0.385507	+	0.222573i
$210$	−1.02270	+	1.77138i	−0.0705733	+	0.122236i
$211$	19.9421			1.37287			0.686435	−	0.727191i	$-0.259175\pi$
$211$	19.9421			1.37287			0.686435	+	0.727191i	$0.259175\pi$
$212$	7.89898	−	13.6814i	0.542504	−	0.939645i
$213$	24.7980			1.69913
$214$	−8.53277			−0.583288
$215$	0.587172	+	1.99978i	0.0400448	+	0.136384i
$216$		−	8.74561i		−	0.595064i
$217$			7.88171i			0.535046i
$218$	21.1237	+	12.1958i	1.43068	+	0.826003i
$219$		−	5.35557i		−	0.361896i
$220$	0.958848	−	1.66077i	0.0646455	−	0.111969i
$221$	−0.949490	+	1.64456i	−0.0638696	+	0.110625i
$222$	9.01219	+	15.6096i	0.604859	+	1.04765i
$223$	−11.4093			−0.764024			−0.382012	−	0.924157i	$-0.624769\pi$
$223$	−11.4093			−0.764024			−0.382012	+	0.924157i	$0.624769\pi$
$224$	10.4505	−	6.03358i	0.698251	−	0.403135i
$225$	−3.79796	+	6.57826i	−0.253197	+	0.438551i
$226$	−7.79796			−0.518713
$227$	−2.02544	+	3.50817i	−0.134433	+	0.232846i	−0.925381	−	0.379039i	$-0.876255\pi$
$227$	−2.02544	+	3.50817i	−0.134433	+	0.232846i	0.790947	+	0.611884i	$0.209588\pi$
$228$	−4.55051	−	7.88171i	−0.301365	−	0.521979i
$229$	−5.50000	−	9.52628i	−0.363450	−	0.629514i	0.625076	−	0.780564i	$-0.285068\pi$
$229$	−5.50000	−	9.52628i	−0.363450	−	0.629514i	−0.988526	+	0.151050i	$0.951735\pi$
$230$	−2.61262	+	1.50839i	−0.172271	+	0.0994606i
$231$		−	13.7279i		−	0.903232i
$232$	−0.449490	−	0.778539i	−0.0295104	−	0.0511136i
$233$	−14.6010	+	8.42990i	−0.956545	+	0.552261i	−0.895108	−	0.445850i	$-0.852902\pi$
$233$	−14.6010	+	8.42990i	−0.956545	+	0.552261i	−0.0614368	+	0.998111i	$0.519568\pi$
$234$	−6.55051	−	3.78194i	−0.428220	−	0.247233i
$235$	0.958848	−	1.66077i	0.0625484	−	0.108337i
$236$			26.8464i			1.74755i
$237$			7.88171i			0.511972i
$238$	1.43827	+	0.830387i	0.0932293	+	0.0538260i
$239$	22.6624	+	13.0842i	1.46591	+	0.846345i	0.999274	−	0.0381036i	$-0.0121317\pi$
$239$	22.6624	+	13.0842i	1.46591	+	0.846345i	0.466638	+	0.884448i	$0.345465\pi$
$240$	−2.34869	+	1.35602i	−0.151607	+	0.0875305i
$241$	−0.151531	+	0.0874863i	−0.00976096	+	0.00563549i	−0.504873	−	0.863194i	$-0.668461\pi$
$241$	−0.151531	+	0.0874863i	−0.00976096	+	0.00563549i	0.495112	+	0.868829i	$0.335127\pi$
$242$		−	2.68556i		−	0.172634i
$243$	7.35843	+	12.7452i	0.472043	+	0.817603i
$244$	4.34847	−	2.51059i	0.278382	−	0.160724i
$245$	0.674235	−	0.389270i	0.0430753	−	0.0248695i
$246$	19.1987	+	11.0844i	1.22407	+	0.706715i
$247$	7.35843			0.468205
$248$	−5.22523	+	9.05037i	−0.331803	+	0.574699i
$249$	−31.6237	+	18.2580i	−2.00407	+	1.15705i
$250$	−4.44949			−0.281410
$251$	−6.98675	+	4.03380i	−0.441000	+	0.254611i	−0.704022	−	0.710179i	$-0.748614\pi$
$251$	−6.98675	+	4.03380i	−0.441000	+	0.254611i	0.263022	+	0.964790i	$0.415281\pi$
$252$	−3.30754	+	5.72882i	−0.208355	+	0.360882i
$253$	10.1237	−	17.5348i	0.636473	−	1.10240i
$254$		0			0
$255$	−0.323244	−	0.186625i	−0.0202423	−	0.0116869i
$256$	16.0000			1.00000
$257$		−	5.51399i		−	0.343953i	−0.985101	−	0.171977i	$-0.944985\pi$
$257$		−	5.51399i		−	0.343953i	0.985101	−	0.171977i	$-0.0550154\pi$
$258$	5.57321	+	18.9811i	0.346973	+	1.18171i
$259$			12.7452i			0.791946i
$260$		−	2.19275i		−	0.135989i
$261$	0.426786	+	0.246405i	0.0264174	+	0.0152521i
$262$			18.1007i			1.11827i
$263$	−8.42502	+	14.5926i	−0.519509	+	0.899816i	0.480234	+	0.877141i	$0.340552\pi$
$263$	−8.42502	+	14.5926i	−0.519509	+	0.899816i	−0.999743	+	0.0226756i	$0.992782\pi$
$264$	9.10102	−	15.7634i	0.560129	−	0.970172i
$265$	−2.17423	+	1.25529i	−0.133562	+	0.0771122i
$266$		−	6.43539i		−	0.394579i
$267$	−14.8246	+	8.55899i	−0.907251	+	0.523801i
$268$	−22.0753	−	12.7452i	−1.34846	−	0.778535i
$269$	8.69694			0.530262			0.265131	−	0.964212i	$-0.414585\pi$
$269$	8.69694			0.530262			0.265131	+	0.964212i	$0.414585\pi$
$270$	−0.694920	+	1.20364i	−0.0422915	+	0.0732510i
$271$	11.0376	−	6.37258i	0.670489	−	0.387107i	−0.125773	−	0.992059i	$-0.540141\pi$
$271$	11.0376	−	6.37258i	0.670489	−	0.387107i	0.796262	+	0.604952i	$0.206808\pi$
$272$	1.10102	+	1.90702i	0.0667592	+	0.115630i
$273$	−7.84847	−	13.5939i	−0.475011	−	0.822743i
$274$	21.5959			1.30466
$275$	12.7992	−	7.38960i	0.771818	−	0.445609i
$276$	−24.7980	+	14.3171i	−1.49266	+	0.861789i
$277$	−16.8712	−	9.74058i	−1.01369	−	0.585255i	−0.101420	−	0.994844i	$-0.532339\pi$
$277$	−16.8712	−	9.74058i	−1.01369	−	0.585255i	−0.912270	+	0.409589i	$0.865672\pi$
$278$	−3.78696	+	6.55921i	−0.227127	+	0.393395i
$279$		−	5.72882i		−	0.342976i
$280$	−1.91770			−0.114604
$281$	9.39898	−	16.2795i	0.560696	−	0.971154i	−0.436740	−	0.899588i	$-0.643867\pi$
$281$	9.39898	−	16.2795i	0.560696	−	0.971154i	0.997436	−	0.0715662i	$-0.0227997\pi$
$282$	9.10102	−	15.7634i	0.541958	−	0.938699i
$283$	18.8755	−	10.8978i	1.12203	−	0.647805i	0.180113	−	0.983646i	$-0.442354\pi$
$283$	18.8755	−	10.8978i	1.12203	−	0.647805i	0.941919	+	0.335841i	$0.109020\pi$
$284$	11.6248	+	20.1348i	0.689806	+	1.19478i
$285$			1.44632i			0.0856727i
$286$	7.35843	+	12.7452i	0.435113	+	0.753638i
$287$	7.83785	+	13.5756i	0.462654	+	0.801340i
$288$	−7.59592	+	4.38551i	−0.447594	+	0.258418i
$289$	8.34847	−	14.4600i	0.491086	−	0.850587i
$290$			0.142865i			0.00838930i
$291$	6.87900	−	11.9148i	0.403254	−	0.698457i
$292$	4.34847	−	2.51059i	0.254475	−	0.146921i
$293$	13.3485			0.779826			0.389913	−	0.920852i	$-0.372505\pi$
$293$	13.3485			0.779826			0.389913	+	0.920852i	$0.372505\pi$
$294$	6.39958	−	3.69480i	0.373231	−	0.215485i
$295$	2.13319	−	3.69480i	0.124199	−	0.215119i
$296$	−8.44949	+	14.6349i	−0.491117	+	0.850639i
$297$		−	9.32804i		−	0.541268i
$298$	7.02270	−	12.1637i	0.406814	−	0.704623i
$299$		−	23.1516i		−	1.33889i
$300$	−20.9009			−1.20672
$301$	−3.29796	+	13.5939i	−0.190091	+	0.783542i
$302$			8.74561i			0.503253i
$303$	40.0997			2.30367
$304$	4.26639	−	7.38960i	0.244694	−	0.423822i
$305$	−0.797959			−0.0456910
$306$	−1.04541	−	0.603566i	−0.0597620	−	0.0345036i
$307$	−23.8368	−	13.7622i	−1.36044	−	0.785449i	−0.370756	−	0.928730i	$-0.620901\pi$
$307$	−23.8368	−	13.7622i	−1.36044	−	0.785449i	−0.989682	+	0.143281i	$0.954235\pi$
$308$	11.1464	−	6.43539i	0.635127	−	0.366691i
$309$			27.1879i			1.54667i
$310$	1.43827	−	0.830387i	0.0816884	−	0.0471628i
$311$	−20.0498	−	11.5758i	−1.13692	−	0.656402i	−0.191255	−	0.981540i	$-0.561256\pi$
$311$	−20.0498	−	11.5758i	−1.13692	−	0.656402i	−0.945666	+	0.325138i	$0.894589\pi$
$312$		−	20.8128i		−	1.17829i
$313$	25.1969	+	14.5475i	1.42422	+	0.822271i	0.996656	−	0.0817162i	$-0.0260401\pi$
$313$	25.1969	+	14.5475i	1.42422	+	0.822271i	0.427560	+	0.903987i	$0.359373\pi$
$314$	−8.57321	−	14.8492i	−0.483814	−	0.837991i
$315$	0.910416	−	0.525629i	0.0512962	−	0.0296159i
$316$	−6.39958	+	3.69480i	−0.360004	+	0.207849i
$317$	−29.3939			−1.65092			−0.825462	−	0.564457i	$-0.809085\pi$
$317$	−29.3939			−1.65092			−0.825462	+	0.564457i	$0.809085\pi$
$318$	−20.6370	+	11.9148i	−1.15727	+	0.668148i
$319$	−0.479424	−	0.830387i	−0.0268426	−	0.0464927i
$320$	−2.20204	−	1.27135i	−0.123098	−	0.0710706i
$321$	11.1464	+	6.43539i	0.622133	+	0.359189i
$322$	−20.2474			−1.12835
$323$	1.17434			0.0653423
$324$	−11.2474	+	19.4812i	−0.624858	+	1.08229i
$325$	8.44949	−	14.6349i	0.468693	−	0.811801i
$326$	21.8113	−	12.5928i	1.20802	−	0.697450i
$327$	−18.3961	−	31.8629i	−1.01730	−	1.76202i
$328$			20.7846i			1.14764i
$329$	11.1464	−	6.43539i	0.614522	−	0.354795i
$330$	−2.50510	+	1.44632i	−0.137901	+	0.0796174i
$331$	1.06660	+	1.84740i	0.0586254	+	0.101542i	0.893849	−	0.448369i	$-0.147995\pi$
$331$	1.06660	+	1.84740i	0.0586254	+	0.101542i	−0.835223	+	0.549911i	$0.814662\pi$
$332$	−29.6492	−	17.1180i	−1.62721	−	0.939471i
$333$		−	9.26382i		−	0.507654i
$334$	−3.57146	+	6.18596i	−0.195422	+	0.338481i
$335$	2.02544	+	3.50817i	0.110662	+	0.191672i
$336$	−18.2020			−0.993003
$337$	−1.27526	−	2.20881i	−0.0694676	−	0.120321i	0.829199	−	0.558953i	$-0.188797\pi$
$337$	−1.27526	−	2.20881i	−0.0694676	−	0.120321i	−0.898667	+	0.438631i	$0.855463\pi$
$338$	−1.34847	−	0.778539i	−0.0733471	−	0.0423469i
$339$	10.1865	+	5.88120i	0.553257	+	0.319423i
$340$		−	0.349945i		−	0.0189785i
$341$	−5.57321	+	9.65309i	−0.301806	+	0.522744i
$342$			4.67756i			0.252934i
$343$	20.1576			1.08841
$344$	−12.7992	+	13.4232i	−0.690084	+	0.723729i
$345$	4.55051			0.244991
$346$			6.57826i			0.353649i
$347$	−0.587172	+	1.01701i	−0.0315211	+	0.0545961i	−0.881356	−	0.472454i	$-0.843368\pi$
$347$	−0.587172	+	1.01701i	−0.0315211	+	0.0545961i	0.849835	+	0.527050i	$0.176702\pi$
$348$			1.35602i			0.0726901i
$349$	19.8712	+	11.4726i	1.06368	+	0.614116i	0.926448	−	0.376423i	$-0.122846\pi$
$349$	19.8712	+	11.4726i	1.06368	+	0.614116i	0.137232	+	0.990539i	$0.456180\pi$
$350$	−12.7992	−	7.38960i	−0.684144	−	0.394990i
$351$	−5.33298	−	9.23699i	−0.284653	−	0.493034i
$352$	17.0655			0.909596
$353$	8.60102	+	14.8974i	0.457786	+	0.792909i	0.998844	−	0.0480768i	$-0.0153092\pi$
$353$	8.60102	+	14.8974i	0.457786	+	0.792909i	−0.541058	+	0.840986i	$0.681976\pi$
$354$	20.2474	−	35.0696i	1.07614	−	1.86393i
$355$		−	3.69480i		−	0.196100i
$356$	−13.8990	−	8.02458i	−0.736644	−	0.425302i
$357$	−1.25255	−	2.16948i	−0.0662920	−	0.114821i
$358$	1.43827	−	0.830387i	0.0760150	−	0.0438873i
$359$	13.6503	−	7.88098i	0.720433	−	0.415942i	−0.0944791	−	0.995527i	$-0.530119\pi$
$359$	13.6503	−	7.88098i	0.720433	−	0.415942i	0.814912	+	0.579585i	$0.196785\pi$
$360$	1.39388			0.0734638
$361$	7.22474	+	12.5136i	0.380250	+	0.658612i
$362$	−26.8207	+	15.4849i	−1.40966	+	0.813869i
$363$	−2.02544	+	3.50817i	−0.106308	+	0.184131i
$364$	7.35843	−	12.7452i	0.385686	−	0.668028i
$365$	−0.797959			−0.0417671
$366$	−7.57392			−0.395895
$367$	3.19979	+	1.84740i	0.167028	+	0.0964334i	0.581184	−	0.813773i	$-0.302590\pi$
$367$	3.19979	+	1.84740i	0.167028	+	0.0964334i	−0.414156	+	0.910206i	$0.635923\pi$
$368$	−23.2496	−	13.4232i	−1.21197	−	0.699731i
$369$	−5.69694	−	9.86739i	−0.296571	−	0.513676i
$370$	2.32577	−	1.34278i	0.120911	−	0.0698079i
$371$	−16.8500			−0.874811
$372$	13.6515	−	7.88171i	0.707799	−	0.408648i
$373$	−29.1742	+	16.8438i	−1.51058	+	0.872136i	−0.510661	+	0.859782i	$0.670599\pi$
$373$	−29.1742	+	16.8438i	−1.51058	+	0.872136i	−0.999924	+	0.0123542i	$0.996067\pi$
$374$	1.17434	+	2.03402i	0.0607239	+	0.105177i
$375$	5.81241	+	3.35579i	0.300151	+	0.173292i
$376$	17.0655			0.880088
$377$	−0.949490	−	0.548188i	−0.0489012	−	0.0282331i
$378$	−8.07832	+	4.66402i	−0.415504	+	0.239891i
$379$		−	22.1688i		−	1.13873i	−0.822083	−	0.569367i	$-0.807188\pi$
$379$		−	22.1688i		−	1.13873i	0.822083	−	0.569367i	$-0.192812\pi$
$380$	−1.17434	+	0.678008i	−0.0602426	+	0.0347811i
$381$		0			0
$382$	20.6370	+	11.9148i	1.05588	+	0.609613i
$383$		0			0			−	1.00000i	$-0.5\pi$
$383$		0			0				1.00000i	$0.5\pi$
$384$	−20.9009	−	12.0672i	−1.06660	−	0.615800i
$385$	−2.04541			−0.104244
$386$		−	4.73545i		−	0.241028i
$387$	2.39712	−	9.88076i	0.121852	−	0.502267i
$388$	12.8990			0.654846
$389$			1.06427i			0.0539605i	0.999636	+	0.0269803i	$0.00858913\pi$
$389$			1.06427i			0.0539605i	−0.999636	+	0.0269803i	$0.991411\pi$
$390$	−1.65377	+	2.86441i	−0.0837418	+	0.145045i
$391$		−	3.69480i		−	0.186854i
$392$	6.00000	+	3.46410i	0.303046	+	0.174964i
$393$	13.6515	−	23.6451i	0.688629	−	1.19274i
$394$	−14.0227	+	8.09601i	−0.706454	+	0.407871i
$395$	1.17434			0.0590877
$396$	−8.10178	+	4.67756i	−0.407130	+	0.235056i
$397$	−15.2980	+	26.4968i	−0.767783	+	1.32984i	0.170980	+	0.985274i	$0.445307\pi$
$397$	−15.2980	+	26.4968i	−0.767783	+	1.32984i	−0.938763	+	0.344564i	$0.888027\pi$
$398$			26.8464i			1.34569i
$399$	−4.85356	+	8.40661i	−0.242982	+	0.420857i
$400$	−9.79796	−	16.9706i	−0.489898	−	0.848528i
$401$	0.275255	+	0.476756i	0.0137456	+	0.0238081i	0.872816	−	0.488049i	$-0.162291\pi$
$401$	0.275255	+	0.476756i	0.0137456	+	0.0238081i	−0.859071	+	0.511857i	$0.828958\pi$
$402$	19.2247	+	33.2982i	0.958843	+	1.66077i
$403$			12.7452i			0.634882i
$404$	18.7980	+	32.5590i	0.935233	+	1.61987i
$405$	3.09592	−	1.78743i	0.153837	−	0.0888181i
$406$	−0.479424	+	0.830387i	−0.0237934	+	0.0412114i
$407$	−9.01219	+	15.6096i	−0.446718	+	0.773738i
$408$		−	3.32155i		−	0.164441i
$409$		−	31.6055i		−	1.56279i	−0.624036	−	0.781396i	$-0.714508\pi$
$409$		−	31.6055i		−	1.56279i	0.624036	−	0.781396i	$-0.285492\pi$
$410$	1.65153	−	2.86054i	0.0815633	−	0.141272i
$411$	−28.2109	−	16.2876i	−1.39154	−	0.803407i
$412$	−22.0753	+	12.7452i	−1.08757	+	0.627909i
$413$	24.7980	−	14.3171i	1.22023	−	0.704499i
$414$	14.7169			0.723294
$415$	2.72036	+	4.71181i	0.133537	+	0.231294i
$416$	16.8990	−	9.75663i	0.828541	−	0.478358i
$417$	9.89388	−	5.71223i	0.484505	−	0.279729i
$418$	4.55051	−	7.88171i	0.222573	−	0.385507i
$419$	−12.7992			−0.625280			−0.312640	−	0.949872i	$-0.601213\pi$
$419$	−12.7992			−0.625280			−0.312640	+	0.949872i	$0.601213\pi$
$420$	2.50510	+	1.44632i	0.122236	+	0.0705733i
$421$	−21.8258	+	12.6011i	−1.06372	+	0.614141i	−0.926460	−	0.376394i	$-0.877164\pi$
$421$	−21.8258	+	12.6011i	−1.06372	+	0.614141i	−0.137263	+	0.990535i	$0.543831\pi$
$422$		−	28.2024i		−	1.37287i
$423$	−8.10178	+	4.67756i	−0.393922	+	0.227431i
$424$	−19.3485	−	11.1708i	−0.939645	−	0.542504i
$425$	1.34847	−	2.33562i	0.0654104	−	0.113294i
$426$		−	35.0696i		−	1.69913i
$427$	−4.63806	−	2.67779i	−0.224452	−	0.129587i
$428$			12.0672i			0.583288i
$429$		−	22.1988i		−	1.07177i
$430$	2.82811	−	0.830387i	0.136384	−	0.0400448i
$431$			12.0672i			0.581255i	0.956836	+	0.290627i	$0.0938640\pi$
$431$			12.0672i			0.581255i	−0.956836	+	0.290627i	$0.906136\pi$
$432$	−12.3682			−0.595064
$433$	−16.8712	−	9.74058i	−0.810777	−	0.468102i	0.0364487	−	0.999336i	$-0.488395\pi$
$433$	−16.8712	−	9.74058i	−0.810777	−	0.468102i	−0.847226	+	0.531233i	$0.821729\pi$
$434$	11.1464			0.535046
$435$	0.107748	−	0.186625i	0.00516613	−	0.00894799i
$436$	17.2474	−	29.8735i	0.826003	−	1.43068i
$437$	−12.3990	+	7.15855i	−0.593124	+	0.342440i
$438$	−7.57392			−0.361896
$439$	3.19979	−	1.84740i	0.152718	−	0.0881715i	−0.421694	−	0.906738i	$-0.638564\pi$
$439$	3.19979	−	1.84740i	0.152718	−	0.0881715i	0.574411	+	0.818567i	$0.305231\pi$
$440$	−2.34869	−	1.35602i	−0.111969	−	0.0646455i
$441$	−3.79796			−0.180855
$442$	2.32577	+	1.34278i	0.110625	+	0.0638696i
$443$	4.37413	−	2.52541i	0.207821	−	0.119986i	−0.392477	−	0.919762i	$-0.628382\pi$
$443$	4.37413	−	2.52541i	0.207821	−	0.119986i	0.600298	+	0.799776i	$0.295048\pi$
$444$	22.0753	−	12.7452i	1.04765	−	0.604859i
$445$	1.27526	+	2.20881i	0.0604529	+	0.104707i
$446$			16.1352i			0.764024i
$447$	−18.3476	+	10.5930i	−0.867813	+	0.501032i
$448$	−8.53277	−	14.7792i	−0.403135	−	0.698251i
$449$	−17.7247	−	10.2334i	−0.836482	−	0.482943i	0.0195846	−	0.999808i	$-0.493766\pi$
$449$	−17.7247	−	10.2334i	−0.836482	−	0.482943i	−0.856067	+	0.516865i	$0.827099\pi$
$450$	9.30306	+	5.37113i	0.438551	+	0.253197i
$451$			22.1688i			1.04389i
$452$			11.0280i			0.518713i
$453$	6.59592	−	11.4245i	0.309903	−	0.536768i
$454$	4.96131	+	2.86441i	0.232846	+	0.134433i
$455$	−2.02544	+	1.16939i	−0.0949543	+	0.0548219i
$456$	−11.1464	+	6.43539i	−0.521979	+	0.301365i
$457$		−	12.7279i		−	0.595387i	−0.954661	−	0.297694i	$-0.903783\pi$
$457$		−	12.7279i		−	0.595387i	0.954661	−	0.297694i	$-0.0962174\pi$
$458$	−13.4722	+	7.77817i	−0.629514	+	0.363450i
$459$	−0.851100	−	1.47415i	−0.0397259	−	0.0688074i
$460$	2.13319	+	3.69480i	0.0994606	+	0.172271i
$461$	−8.29796	+	14.3725i	−0.386474	+	0.669393i	−0.991973	−	0.126453i	$-0.959641\pi$
$461$	−8.29796	+	14.3725i	−0.386474	+	0.669393i	0.605498	+	0.795847i	$0.292974\pi$
$462$	−19.4142			−0.903232
$463$	8.90445	−	15.4230i	0.413825	−	0.716765i	−0.581480	−	0.813561i	$-0.697526\pi$
$463$	8.90445	−	15.4230i	0.413825	−	0.716765i	0.995304	+	0.0967956i	$0.0308593\pi$
$464$	−1.10102	+	0.635674i	−0.0511136	+	0.0295104i
$465$	−2.50510			−0.116171
$466$	11.9217	+	20.6490i	0.552261	+	0.956545i
$467$	−0.587172	+	1.01701i	−0.0271711	+	0.0470617i	−0.879291	−	0.476285i	$-0.841983\pi$
$467$	−0.587172	+	1.01701i	−0.0271711	+	0.0470617i	0.852120	+	0.523346i	$0.175317\pi$
$468$	−5.34847	+	9.26382i	−0.247233	+	0.428220i
$469$			27.1879i			1.25542i
$470$	−2.34869	−	1.35602i	−0.108337	−	0.0625484i
$471$			25.8636i			1.19173i
$472$	37.9665			1.74755
$473$	−13.6515	+	14.3171i	−0.627698	+	0.658301i
$474$	11.1464			0.511972
$475$	−10.4505			−0.479500
$476$	1.17434	−	2.03402i	0.0538260	−	0.0932293i
$477$	12.2474			0.560772
$478$	18.5038	−	32.0495i	0.846345	−	1.46591i
$479$	22.6624	+	13.0842i	1.03547	+	0.597831i	0.918548	−	0.395310i	$-0.129363\pi$
$479$	22.6624	+	13.0842i	1.03547	+	0.597831i	0.116926	+	0.993141i	$0.462696\pi$
$480$	1.91770	+	3.32155i	0.0875305	+	0.151607i
$481$			20.6096i			0.939719i
$482$	0.123724	+	0.214297i	0.00563549	+	0.00976096i
$483$	26.4494	+	15.2706i	1.20349	+	0.694835i
$484$	−3.79796			−0.172634
$485$	−1.77526	−	1.02494i	−0.0806102	−	0.0465403i
$486$	18.0244	−	10.4064i	0.817603	−	0.472043i
$487$	−23.8368	+	13.7622i	−1.08015	+	0.623624i	−0.930936	−	0.365181i	$-0.881007\pi$
$487$	−23.8368	+	13.7622i	−1.08015	+	0.623624i	−0.149212	+	0.988805i	$0.547674\pi$
$488$	−3.55051	−	6.14966i	−0.160724	−	0.278382i
$489$	−37.9898			−1.71796
$490$	−0.550510	−	0.953512i	−0.0248695	−	0.0430753i
$491$	−5.81241	−	10.0674i	−0.262310	−	0.454335i	0.704545	−	0.709659i	$-0.251151\pi$
$491$	−5.81241	−	10.0674i	−0.262310	−	0.454335i	−0.966855	+	0.255325i	$0.917818\pi$
$492$	15.6757	−	27.1511i	0.706715	−	1.22407i
$493$	−0.151531	−	0.0874863i	−0.00682460	−	0.00394019i
$494$		−	10.4064i		−	0.468205i
$495$	1.48670			0.0668224
$496$	12.7992	+	7.38960i	0.574699	+	0.331803i
$497$	12.3990	−	21.4757i	0.556170	−	0.963315i
$498$	25.8207	+	44.7227i	1.15705	+	2.00407i
$499$	8.90445	+	15.4230i	0.398618	+	0.690426i	0.993556	−	0.113345i	$-0.0361567\pi$
$499$	8.90445	+	15.4230i	0.398618	+	0.690426i	−0.594938	+	0.803772i	$0.702823\pi$
$500$			6.29253i			0.281410i
$501$	9.33087	−	5.38718i	0.416872	−	0.240681i
$502$	5.70466	+	9.88076i	0.254611	+	0.441000i
$503$	16.2629	+	28.1681i	0.725126	+	1.25595i	0.958922	+	0.283669i	$0.0915517\pi$
$503$	16.2629	+	28.1681i	0.725126	+	1.25595i	−0.233797	+	0.972286i	$0.575115\pi$
$504$	8.10178	+	4.67756i	0.360882	+	0.208355i
$505$		−	5.97469i		−	0.265870i
$506$	−24.7980	−	14.3171i	−1.10240	−	0.636473i
$507$	1.17434	+	2.03402i	0.0521545	+	0.0903342i
$508$		0			0
$509$	−7.07321	−	12.2512i	−0.313515	−	0.543023i	0.665606	−	0.746303i	$-0.268173\pi$
$509$	−7.07321	−	12.2512i	−0.313515	−	0.543023i	−0.979121	+	0.203280i	$0.934840\pi$
$510$	−0.263928	+	0.457136i	−0.0116869	+	0.0202423i
$511$	−4.63806	−	2.67779i	−0.205176	−	0.118458i
$512$		−	22.6274i		−	1.00000i
$513$	−3.29796	+	5.71223i	−0.145608	+	0.252201i
$514$	−7.79796			−0.343953
$515$	4.05089			0.178503
$516$	26.8434	−	7.88171i	1.18171	−	0.346973i
$517$	18.2020			0.800525
$518$	18.0244			0.791946
$519$	4.96131	−	8.59323i	0.217777	−	0.377201i
$520$	−3.10102			−0.135989
$521$	34.6237	+	19.9900i	1.51689	+	0.875779i	0.999803	+	0.0198474i	$0.00631805\pi$
$521$	34.6237	+	19.9900i	1.51689	+	0.875779i	0.517090	+	0.855931i	$0.327015\pi$
$522$	0.348469	−	0.603566i	0.0152521	−	0.0264174i
$523$	−11.7326	−	20.3214i	−0.513029	−	0.888592i	−0.999886	−	0.0151105i	$-0.995190\pi$
$523$	−11.7326	−	20.3214i	−0.513029	−	0.888592i	0.486857	−	0.873482i	$-0.338143\pi$
$524$	25.5983			1.11827
$525$	11.1464	+	19.3062i	0.486470	+	0.842591i
$526$	20.6370	+	11.9148i	0.899816	+	0.519509i
$527$			2.03402i			0.0886035i
$528$	−22.2929	−	12.8708i	−0.970172	−	0.560129i
$529$	11.0227	+	19.0919i	0.479248	+	0.830082i
$530$	1.77526	+	3.07483i	0.0771122	+	0.133562i
$531$	−18.0244	+	10.4064i	−0.782192	+	0.451599i
$532$	−9.10102			−0.394579
$533$	12.6742	+	21.9524i	0.548982	+	0.950865i
$534$	12.1042	+	20.9651i	0.523801	+	0.907251i
$535$	0.958848	−	1.66077i	0.0414546	−	0.0718015i
$536$	−18.0244	+	31.2192i	−0.778535	+	1.34846i
$537$	−2.50510			−0.108103
$538$		−	12.2993i		−	0.530262i
$539$	6.39958	+	3.69480i	0.275649	+	0.159146i
$540$	1.70220	+	0.982766i	0.0732510	+	0.0422915i
$541$	−6.84847	−	11.8619i	−0.294439	−	0.509983i	0.680415	−	0.732827i	$-0.261799\pi$
$541$	−6.84847	−	11.8619i	−0.294439	−	0.509983i	−0.974854	+	0.222844i	$0.928466\pi$
$542$	−9.01219	−	15.6096i	−0.387107	−	0.670489i
$543$	46.7147			2.00472
$544$	2.69694	−	1.55708i	0.115630	−	0.0667592i
$545$	−4.74745	+	2.74094i	−0.203358	+	0.117409i
$546$	−19.2247	+	11.0994i	−0.822743	+	0.475011i
$547$	−31.6746	−	18.2874i	−1.35431	−	0.781911i	−0.365460	−	0.930827i	$-0.619088\pi$
$547$	−31.6746	−	18.2874i	−1.35431	−	0.781911i	−0.988850	+	0.148916i	$0.952422\pi$
$548$		−	30.5412i		−	1.30466i
$549$	3.37117	+	1.94635i	0.143878	+	0.0830681i
$550$	−10.4505	−	18.1007i	−0.445609	−	0.771818i
$551$			0.678008i			0.0288841i
$552$	20.2474	+	35.0696i	0.861789	+	1.49266i
$553$	6.82577	+	3.94086i	0.290261	+	0.167582i
$554$	−13.7753	+	23.8594i	−0.585255	+	1.01369i
$555$	−4.05089			−0.171951
$556$	9.27612	+	5.35557i	0.393395	+	0.227127i
$557$	−4.65153			−0.197092			−0.0985458	−	0.995133i	$-0.531419\pi$
$557$	−4.65153			−0.197092			−0.0985458	+	0.995133i	$0.531419\pi$
$558$	−8.10178			−0.342976
$559$	−5.33298	+	21.9822i	−0.225561	+	0.929746i
$560$			2.71203i			0.114604i
$561$		−	3.54275i		−	0.149575i
$562$	−23.0227	−	13.2922i	−0.971154	−	0.560696i
$563$		−	13.4232i		−	0.565719i	−0.959161	−	0.282860i	$-0.908717\pi$
$563$		−	13.4232i		−	0.565719i	0.959161	−	0.282860i	$-0.0912831\pi$
$564$	−22.2929	−	12.8708i	−0.938699	−	0.541958i
$565$	0.876276	−	1.51775i	0.0368652	−	0.0638524i
$566$	−15.4118	−	26.6940i	−0.647805	−	1.12203i
$567$	23.9930			1.00761
$568$	28.4749	−	16.4400i	1.19478	−	0.689806i
$569$	9.39898	−	16.2795i	0.394026	−	0.682473i	−0.598951	−	0.800786i	$-0.704415\pi$
$569$	9.39898	−	16.2795i	0.394026	−	0.682473i	0.992976	+	0.118313i	$0.0377488\pi$
$570$	2.04541			0.0856727
$571$	−19.5704	+	33.8969i	−0.818996	+	1.41854i	0.0874265	+	0.996171i	$0.472136\pi$
$571$	−19.5704	+	33.8969i	−0.818996	+	1.41854i	−0.906423	+	0.422372i	$0.861198\pi$
$572$	18.0244	−	10.4064i	0.753638	−	0.435113i
$573$	−17.9722	−	31.1288i	−0.750799	−	1.30042i
$574$	19.1987	−	11.0844i	0.801340	−	0.462654i
$575$			32.8799i			1.37119i
$576$	6.20204	+	10.7423i	0.258418	+	0.447594i
$577$	21.5227	−	12.4261i	0.896002	−	0.517307i	0.0201010	−	0.999798i	$-0.493601\pi$
$577$	21.5227	−	12.4261i	0.896002	−	0.517307i	0.875901	+	0.482491i	$0.160268\pi$
$578$	−20.4495	−	11.8065i	−0.850587	−	0.491086i
$579$	−3.57146	+	6.18596i	−0.148425	+	0.257080i
$580$	0.202041			0.00838930
$581$			36.5159i			1.51494i
$582$	−16.8500	−	9.72838i	−0.698457	−	0.403254i
$583$	−20.6370	−	11.9148i	−0.854697	−	0.493460i
$584$	−3.55051	−	6.14966i	−0.146921	−	0.254475i
$585$	1.47219	−	0.849971i	0.0608677	−	0.0351420i
$586$		−	18.8776i		−	0.779826i
$587$	−13.6503	−	23.6429i	−0.563406	−	0.975848i	−0.997196	−	0.0748342i	$-0.976157\pi$
$587$	−13.6503	−	23.6429i	−0.563406	−	0.975848i	0.433790	−	0.901014i	$-0.357176\pi$
$588$	−5.22523	−	9.05037i	−0.215485	−	0.373231i
$589$	6.82577	−	3.94086i	0.281251	−	0.162380i
$590$	−5.22523	−	3.01679i	−0.215119	−	0.124199i
$591$	24.4240			1.00467
$592$	20.6969	+	11.9494i	0.850639	+	0.491117i
$593$	−10.9949	+	6.34791i	−0.451506	+	0.260677i	−0.708466	−	0.705745i	$-0.750613\pi$
$593$	−10.9949	+	6.34791i	−0.451506	+	0.260677i	0.256960	+	0.966422i	$0.417279\pi$
$594$	−13.1918			−0.541268
$595$	−0.323244	+	0.186625i	−0.0132517	+	0.00765089i
$596$	−17.2020	−	9.93160i	−0.704623	−	0.406814i
$597$	20.2474	−	35.0696i	0.828673	−	1.43530i
$598$	−32.7412			−1.33889
$599$	−12.2120	−	7.05059i	−0.498968	−	0.288079i	0.229319	−	0.973351i	$-0.426350\pi$
$599$	−12.2120	−	7.05059i	−0.498968	−	0.288079i	−0.728287	+	0.685272i	$0.759683\pi$
$600$			29.5584i			1.20672i
$601$		−	46.2405i		−	1.88619i	−0.332527	−	0.943094i	$-0.607901\pi$
$601$		−	46.2405i		−	1.88619i	0.332527	−	0.943094i	$-0.392099\pi$
$602$	19.2247	+	4.66402i	0.783542	+	0.190091i
$603$		−	19.7615i		−	0.804751i
$604$	12.3682			0.503253
$605$	0.522704	+	0.301783i	0.0212509	+	0.0122692i
$606$		−	56.7095i		−	2.30367i
$607$	7.46617	−	12.9318i	0.303043	−	0.524885i	−0.673781	−	0.738931i	$-0.735331\pi$
$607$	7.46617	−	12.9318i	0.303043	−	0.524885i	0.976824	+	0.214046i	$0.0686642\pi$
$608$	−10.4505	−	6.03358i	−0.423822	−	0.244694i
$609$	1.25255	−	0.723161i	0.0507559	−	0.0293040i
$610$			1.12848i			0.0456910i
$611$	18.0244	−	10.4064i	0.729189	−	0.420997i
$612$	−0.853572	+	1.47843i	−0.0345036	+	0.0597620i
$613$	−20.0454			−0.809626			−0.404813	−	0.914399i	$-0.632663\pi$
$613$	−20.0454			−0.809626			−0.404813	+	0.914399i	$0.632663\pi$
$614$	−19.4627	+	33.7103i	−0.785449	+	1.36044i
$615$	−4.31482	+	2.49116i	−0.173990	+	0.100453i
$616$	−9.10102	−	15.7634i	−0.366691	−	0.635127i
$617$	−16.0732	−	27.8396i	−0.647083	−	1.12078i	−0.983816	−	0.179181i	$-0.942655\pi$
$617$	−16.0732	−	27.8396i	−0.647083	−	1.12078i	0.336733	−	0.941600i	$-0.390678\pi$
$618$	38.4495			1.54667
$619$	−31.6746	+	18.2874i	−1.27311	+	0.735031i	−0.975572	−	0.219678i	$-0.929499\pi$
$619$	−31.6746	+	18.2874i	−1.27311	+	0.735031i	−0.297539	+	0.954710i	$0.596166\pi$
$620$	−1.17434	−	2.03402i	−0.0471628	−	0.0816884i
$621$	17.9722	+	10.3763i	0.721199	+	0.416385i
$622$	−16.3706	+	28.3547i	−0.656402	+	1.13692i
$623$			17.1180i			0.685817i
$624$	−29.4337			−1.17829
$625$	−11.7474	+	20.3472i	−0.469898	+	0.813887i
$626$	20.5732	−	35.6339i	0.822271	−	1.42422i
$627$	−11.8887	+	6.86397i	−0.474790	+	0.274120i
$628$	−21.0000	+	12.1244i	−0.837991	+	0.483814i
$629$			3.28913i			0.131146i
$630$	−0.743352	−	1.28752i	−0.0296159	−	0.0512962i
$631$	−14.3452	−	24.8466i	−0.571072	−	0.989126i	−0.996456	−	0.0841134i	$-0.973194\pi$
$631$	−14.3452	−	24.8466i	−0.571072	−	0.989126i	0.425384	−	0.905013i	$-0.360139\pi$
$632$	5.22523	+	9.05037i	0.207849	+	0.360004i
$633$	−21.2702	+	36.8410i	−0.845413	+	1.46430i
$634$			41.5692i			1.65092i
$635$		0			0
$636$	16.8500	+	29.1851i	0.668148	+	1.15727i
$637$	8.44949			0.334781
$638$	−1.17434	+	0.678008i	−0.0464927	+	0.0268426i
$639$	−9.01219	+	15.6096i	−0.356517	+	0.617505i
$640$	−1.79796	+	3.11416i	−0.0710706	+	0.123098i
$641$			20.2918i			0.801478i	0.916192	+	0.400739i	$0.131247\pi$
$641$			20.2918i			0.801478i	−0.916192	+	0.400739i	$0.868753\pi$
$642$	9.10102	−	15.7634i	0.359189	−	0.622133i
$643$		−	18.1007i		−	0.713823i	−0.934138	−	0.356912i	$-0.883830\pi$
$643$		−	18.1007i		−	0.713823i	0.934138	−	0.356912i	$-0.116170\pi$
$644$			28.6342i			1.12835i
$645$	−4.32066	−	1.04821i	−0.170126	−	0.0412734i
$646$		−	1.66077i		−	0.0653423i
$647$	−2.87654			−0.113089			−0.0565443	−	0.998400i	$-0.518008\pi$
$647$	−2.87654			−0.113089			−0.0565443	+	0.998400i	$0.518008\pi$
$648$	27.5505	+	15.9063i	1.08229	+	0.624858i
$649$	40.4949			1.58956
$650$	−20.6969	−	11.9494i	−0.811801	−	0.468693i
$651$	−14.5607	−	8.40661i	−0.570678	−	0.329481i
$652$	−17.8089	−	30.8459i	−0.697450	−	1.20802i
$653$		−	3.17837i		−	0.124379i	−0.998064	−	0.0621897i	$-0.980192\pi$
$653$		−	3.17837i		−	0.124379i	0.998064	−	0.0621897i	$-0.0198084\pi$
$654$	−45.0610	+	26.0160i	−1.76202	+	1.01730i
$655$	−3.52303	−	2.03402i	−0.137656	−	0.0794759i
$656$	29.3939			1.14764
$657$	3.37117	+	1.94635i	0.131522	+	0.0759343i
$658$	−9.10102	−	15.7634i	−0.354795	−	0.614522i
$659$	21.4881	−	12.4062i	0.837058	−	0.483276i	−0.0192053	−	0.999816i	$-0.506114\pi$
$659$	21.4881	−	12.4062i	0.837058	−	0.483276i	0.856263	+	0.516540i	$0.172780\pi$
$660$	2.04541	+	3.54275i	0.0796174	+	0.137901i
$661$	−9.75255			−0.379330			−0.189665	−	0.981849i	$-0.560740\pi$
$661$	−9.75255			−0.379330			−0.189665	+	0.981849i	$0.560740\pi$
$662$	2.61262	−	1.50839i	0.101542	−	0.0586254i
$663$	−2.02544	−	3.50817i	−0.0786617	−	0.136246i
$664$	−24.2085	+	41.9303i	−0.939471	+	1.62721i
$665$	1.25255	+	0.723161i	0.0485719	+	0.0280430i
$666$	−13.1010			−0.507654
$667$	2.13319			0.0825975
$668$	8.74827	+	5.05081i	0.338481	+	0.195422i
$669$	12.1691	−	21.0776i	0.470486	−	0.814905i
$670$	4.96131	−	2.86441i	0.191672	−	0.110662i
$671$	−3.78696	−	6.55921i	−0.146194	−	0.253215i
$672$			25.7416i			0.993003i
$673$	−34.5000	+	19.9186i	−1.32988	+	0.767805i	−0.985280	−	0.170946i	$-0.945318\pi$
$673$	−34.5000	+	19.9186i	−1.32988	+	0.767805i	−0.344597	+	0.938751i	$0.611984\pi$
$674$	−3.12372	+	1.80348i	−0.120321	+	0.0694676i
$675$	7.57392	+	13.1184i	0.291520	+	0.504928i
$676$	−1.10102	+	1.90702i	−0.0423469	+	0.0733471i
$677$			9.89949i			0.380468i	0.981739	+	0.190234i	$0.0609248\pi$
$677$			9.89949i			0.380468i	−0.981739	+	0.190234i	$0.939075\pi$
$678$	8.31727	−	14.4059i	0.319423	−	0.553257i
$679$	−6.87900	−	11.9148i	−0.263992	−	0.457247i
$680$	−0.494897			−0.0189785
$681$	−4.32066	−	7.48361i	−0.165568	−	0.286772i
$682$	13.6515	+	7.88171i	0.522744	+	0.301806i
$683$	5.54848	+	3.20341i	0.212307	+	0.122575i	0.602383	−	0.798207i	$-0.294218\pi$
$683$	5.54848	+	3.20341i	0.212307	+	0.122575i	−0.390076	+	0.920783i	$0.627551\pi$
$684$	6.61507			0.252934
$685$	−2.42679	+	4.20332i	−0.0927227	+	0.160600i
$686$		−	28.5071i		−	1.08841i
$687$	23.4651			0.895250
$688$	18.9832	+	18.1007i	0.723729	+	0.690084i
$689$	−27.2474			−1.03805
$690$		−	6.43539i		−	0.244991i
$691$	−1.54602	+	2.67779i	−0.0588134	+	0.101868i	−0.893933	−	0.448201i	$-0.852065\pi$
$691$	−1.54602	+	2.67779i	−0.0588134	+	0.101868i	0.835120	+	0.550068i	$0.185398\pi$
$692$	9.30306			0.353649
$693$	8.64133	+	4.98907i	0.328257	+	0.189519i
$694$	1.43827	+	0.830387i	0.0545961	+	0.0315211i
$695$	−0.851100	−	1.47415i	−0.0322841	−	0.0559176i
$696$	1.91770			0.0726901
$697$	2.02270	+	3.50343i	0.0766154	+	0.132702i
$698$	16.2247	−	28.1021i	0.614116	−	1.06368i
$699$		−	35.9652i		−	1.36033i
$700$	−10.4505	+	18.1007i	−0.394990	+	0.684144i
$701$	−1.74745	−	3.02667i	−0.0660002	−	0.114316i	0.831137	−	0.556068i	$-0.187690\pi$
$701$	−1.74745	−	3.02667i	−0.0660002	−	0.114316i	−0.897137	+	0.441752i	$0.854357\pi$
$702$	−13.0631	+	7.54197i	−0.493034	+	0.284653i
$703$	11.0376	−	6.37258i	0.416292	−	0.240347i
$704$		−	24.1343i		−	0.909596i
$705$	2.04541	+	3.54275i	0.0770345	+	0.133428i
$706$	21.0681	−	12.1637i	0.792909	−	0.457786i
$707$	20.0498	−	34.7273i	0.754052	−	1.30606i
$708$	−49.5959	−	28.6342i	−1.86393	−	1.07614i
$709$	−15.1464			−0.568836			−0.284418	−	0.958700i	$-0.591800\pi$
$709$	−15.1464			−0.568836			−0.284418	+	0.958700i	$0.591800\pi$
$710$	−5.22523			−0.196100
$711$	−4.96131	−	2.86441i	−0.186063	−	0.107424i
$712$	−11.3485	+	19.6561i	−0.425302	+	0.736644i
$713$	−12.3990	−	21.4757i	−0.464345	−	0.804270i
$714$	−3.06811	+	1.77138i	−0.114821	+	0.0662920i
$715$	−3.30754			−0.123695
$716$	−1.17434	−	2.03402i	−0.0438873	−	0.0760150i
$717$	−48.3434	+	27.9111i	−1.80542	+	1.04236i
$718$	−11.1454	−	19.3044i	−0.415942	−	0.720433i
$719$	9.86329	+	5.69458i	0.367839	+	0.212372i	0.672514	−	0.740085i	$-0.265215\pi$
$719$	9.86329	+	5.69458i	0.367839	+	0.212372i	−0.304675	+	0.952456i	$0.598548\pi$
$720$		−	1.97124i		−	0.0734638i
$721$	23.5454	+	13.5939i	0.876877	+	0.506265i
$722$	17.6969	−	10.2173i	0.658612	−	0.380250i
$723$		−	0.373250i		−	0.0138813i
$724$	21.8990	+	37.9301i	0.813869	+	1.40966i
$725$	1.34847	+	0.778539i	0.0500809	+	0.0289142i
$726$	4.96131	+	2.86441i	0.184131	+	0.106308i
$727$	−21.3319			−0.791157			−0.395579	−	0.918432i	$-0.629456\pi$
$727$	−21.3319			−0.791157			−0.395579	+	0.918432i	$0.629456\pi$
$728$	−18.0244	−	10.4064i	−0.668028	−	0.385686i
$729$	2.34847			0.0869803
$730$			1.12848i			0.0417671i
$731$	−0.851100	+	3.50817i	−0.0314791	+	0.129754i
$732$			10.7111i			0.395895i
$733$		−	31.6055i		−	1.16738i	−0.811978	−	0.583688i	$-0.801609\pi$
$733$		−	31.6055i		−	1.16738i	0.811978	−	0.583688i	$-0.198391\pi$
$734$	2.61262	−	4.52518i	0.0964334	−	0.167028i
$735$			1.66077i			0.0612586i
$736$	−18.9832	+	32.8799i	−0.699731	+	1.21197i
$737$	−19.2247	+	33.2982i	−0.708153	+	1.22656i
$738$	−13.9546	+	8.05669i	−0.513676	+	0.296571i
$739$	29.8647			1.09859			0.549295	−	0.835628i	$-0.314896\pi$
$739$	29.8647			1.09859			0.549295	+	0.835628i	$0.314896\pi$
$740$	−1.89898	−	3.28913i	−0.0698079	−	0.120911i
$741$	−7.84847	+	13.5939i	−0.288321	+	0.499386i
$742$			23.8296i			0.874811i
$743$	20.0498	−	34.7273i	0.735557	−	1.27402i	−0.218922	−	0.975742i	$-0.570254\pi$
$743$	20.0498	−	34.7273i	0.735557	−	1.27402i	0.954479	−	0.298280i	$-0.0964128\pi$
$744$	−11.1464	−	19.3062i	−0.408648	−	0.707799i
$745$	1.57832	+	2.73372i	0.0578250	+	0.100156i
$746$	23.8207	+	41.2586i	0.872136	+	1.51058i
$747$		−	26.5416i		−	0.971106i
$748$	2.87654	−	1.66077i	0.105177	−	0.0607239i
$749$	11.1464	−	6.43539i	0.407282	−	0.235144i
$750$	4.74581	−	8.21998i	0.173292	−	0.300151i
$751$	−5.33298	+	9.23699i	−0.194603	+	0.337063i	−0.946770	−	0.321910i	$-0.895675\pi$
$751$	−5.33298	+	9.23699i	−0.194603	+	0.337063i	0.752167	+	0.658972i	$0.229009\pi$
$752$		−	24.1343i		−	0.880088i
$753$		−	17.2098i		−	0.627158i
$754$	−0.775255	+	1.34278i	−0.0282331	+	0.0489012i
$755$	−1.70220	−	0.982766i	−0.0619494	−	0.0357665i
$756$	6.59592	+	11.4245i	0.239891	+	0.415504i
$757$	−2.17423	+	1.25529i	−0.0790239	+	0.0456245i	−0.538991	−	0.842311i	$-0.681194\pi$
$757$	−2.17423	+	1.25529i	−0.0790239	+	0.0456245i	0.459967	+	0.887936i	$0.347861\pi$
$758$	−31.3514			−1.13873
$759$	21.5959	+	37.4051i	0.783880	+	1.35772i
$760$	0.958848	+	1.66077i	0.0347811	+	0.0602426i
$761$	20.4217	−	11.7905i	0.740285	−	0.427404i	−0.0818876	−	0.996642i	$-0.526095\pi$
$761$	20.4217	−	11.7905i	0.740285	−	0.427404i	0.822173	+	0.569238i	$0.192762\pi$
$762$		0			0
$763$	−36.7921			−1.33196
$764$	16.8500	−	29.1851i	0.609613	−	1.05588i
$765$	0.234950	−	0.135648i	0.00849464	−	0.00490438i
$766$		0			0
$767$	40.0997	−	23.1516i	1.44791	−	0.835954i
$768$	−17.0655	+	29.5584i	−0.615800	+	1.06660i
$769$	7.05051	−	12.2118i	0.254248	−	0.440370i	−0.710443	−	0.703755i	$-0.751505\pi$
$769$	7.05051	−	12.2118i	0.254248	−	0.440370i	0.964691	+	0.263384i	$0.0848388\pi$
$770$			2.89264i			0.104244i
$771$	10.1865	+	5.88120i	0.366859	+	0.211806i
$772$	−6.69694			−0.241028
$773$			0.207081i			0.00744818i	0.999993	+	0.00372409i	$0.00118542\pi$
$773$			0.207081i			0.00744818i	−0.999993	+	0.00372409i	$0.998815\pi$
$774$	−13.9735	−	3.39004i	−0.502267	−	0.121852i
$775$		−	18.1007i		−	0.650198i
$776$		−	18.2419i		−	0.654846i
$777$	−23.5454	−	13.5939i	−0.844687	−	0.487680i
$778$	1.50510			0.0539605
$779$	7.83785	−	13.5756i	0.280820	−	0.486395i
$780$	4.05089	+	2.33878i	0.145045	+	0.0837418i
$781$	30.3712	−	17.5348i	1.08677	−	0.627445i
$782$	−5.22523			−0.186854
$783$	0.851100	−	0.491383i	0.0304158	−	0.0175606i
$784$	4.89898	−	8.48528i	0.174964	−	0.303046i
$785$	3.85357			0.137540
$786$	−33.4393	−	19.3062i	−1.19274	−	0.688629i
$787$	−15.9989	+	9.23699i	−0.570301	+	0.329263i	−0.757269	−	0.653103i	$-0.773467\pi$
$787$	−15.9989	+	9.23699i	−0.570301	+	0.329263i	0.186969	+	0.982366i	$0.440134\pi$
$788$	11.4495	+	19.8311i	0.407871	+	0.706454i
$789$	−17.9722	−	31.1288i	−0.639827	−	1.10821i
$790$		−	1.66077i		−	0.0590877i
$791$	10.1865	−	5.88120i	0.362192	−	0.209111i
$792$	6.61507	+	11.4576i	0.235056	+	0.407130i
$793$	−7.50000	−	4.33013i	−0.266333	−	0.153767i
$794$	37.4722	+	21.6346i	1.32984	+	0.767783i
$795$		−	5.35557i		−	0.189943i
$796$	37.9665			1.34569
$797$	21.0959	−	36.5392i	0.747256	−	1.29428i	−0.201878	−	0.979411i	$-0.564704\pi$
$797$	21.0959	−	36.5392i	0.747256	−	1.29428i	0.949133	−	0.314874i	$-0.101962\pi$
$798$	11.8887	+	6.86397i	0.420857	+	0.242982i
$799$	2.87654	−	1.66077i	0.101765	−	0.0587540i
$800$	−24.0000	+	13.8564i	−0.848528	+	0.489898i
$801$		−	12.4422i		−	0.439623i
$802$	0.674235	−	0.389270i	0.0238081	−	0.0137456i
$803$	−3.78696	−	6.55921i	−0.133639	−	0.231469i
$804$	47.0908	−	27.1879i	1.66077	−	0.958843i
$805$	2.27526	−	3.94086i	0.0801922	−	0.138897i
$806$	18.0244			0.634882
$807$	−9.27612	+	16.0667i	−0.326535	+	0.565575i
$808$	46.0454	−	26.5843i	1.61987	−	0.935233i
$809$	42.7423			1.50274			0.751370	−	0.659881i	$-0.229393\pi$
$809$	42.7423			1.50274			0.751370	+	0.659881i	$0.229393\pi$
$810$	−2.52781	−	4.37829i	−0.0888181	−	0.153837i
$811$	12.6914	−	21.9822i	0.445656	−	0.771898i	−0.552442	−	0.833551i	$-0.686304\pi$
$811$	12.6914	−	21.9822i	0.445656	−	0.771898i	0.998098	+	0.0616532i	$0.0196373\pi$
$812$	1.17434	+	0.678008i	0.0412114	+	0.0237934i
$813$			27.1879i			0.953521i
$814$	22.0753	+	12.7452i	0.773738	+	0.446718i
$815$			5.66033i			0.198273i
$816$	−4.69738			−0.164441
$817$	13.4217	−	3.94086i	0.469565	−	0.137873i
$818$	−44.6969			−1.56279
$819$	11.4093			0.398674
$820$	−4.04541	−	2.33562i	−0.141272	−	0.0815633i
$821$	16.0454			0.559989			0.279994	−	0.960002i	$-0.409667\pi$
$821$	16.0454			0.559989			0.279994	+	0.960002i	$0.409667\pi$
$822$	−23.0341	+	39.8963i	−0.803407	+	1.39154i
$823$	26.7133	+	15.4230i	0.931168	+	0.537610i	0.887181	−	0.461422i	$-0.152660\pi$
$823$	26.7133	+	15.4230i	0.931168	+	0.537610i	0.0439875	+	0.999032i	$0.485994\pi$
$824$	18.0244	+	31.2192i	0.627909	+	1.08757i
$825$			31.5269i			1.09762i
$826$	−20.2474	−	35.0696i	−0.704499	−	1.22023i
$827$	14.8246	+	8.55899i	0.515502	+	0.297625i	0.735092	−	0.677967i	$-0.237139\pi$
$827$	14.8246	+	8.55899i	0.515502	+	0.297625i	−0.219590	+	0.975592i	$0.570472\pi$
$828$		−	20.8128i		−	0.723294i
$829$	12.1515	+	7.01569i	0.422040	+	0.243665i	0.695950	−	0.718090i	$-0.254984\pi$
$829$	12.1515	+	7.01569i	0.422040	+	0.243665i	−0.273910	+	0.961755i	$0.588317\pi$
$830$	6.66351	−	3.84718i	0.231294	−	0.133537i
$831$	35.9895	−	20.7785i	1.24846	−	0.720799i
$832$	−13.7980	−	23.8988i	−0.478358	−	0.828541i
$833$	1.34847			0.0467217
$834$	−8.07832	−	13.9921i	−0.279729	−	0.484505i
$835$	−0.802668	−	1.39026i	−0.0277775	−	0.0481120i
$836$	−11.1464	−	6.43539i	−0.385507	−	0.222573i
$837$	−9.89388	−	5.71223i	−0.341982	−	0.197444i
$838$			18.1007i			0.625280i
$839$	−2.87654			−0.0993093			−0.0496547	−	0.998766i	$-0.515812\pi$
$839$	−2.87654			−0.0993093			−0.0496547	+	0.998766i	$0.515812\pi$
$840$	2.04541	−	3.54275i	0.0705733	−	0.122236i
$841$	−14.4495	+	25.0273i	−0.498258	+	0.863009i
$842$	17.8207	+	30.8663i	0.614141	+	1.06372i
$843$	20.0498	+	34.7273i	0.690553	+	1.19607i
$844$	−39.8842			−1.37287
$845$	0.303062	−	0.174973i	0.0104256	−	0.00601924i
$846$	6.61507	+	11.4576i	0.227431	+	0.393922i
$847$	2.02544	+	3.50817i	0.0695951	+	0.120542i
$848$	−15.7980	+	27.3629i	−0.542504	+	0.939645i
$849$			46.4941i			1.59567i
$850$	−3.30306	−	1.90702i	−0.113294	−	0.0654104i
$851$	−20.0498	−	34.7273i	−0.687299	−	1.19044i
$852$	−49.5959			−1.69913
$853$	15.0732	+	26.1076i	0.516097	+	0.893906i	0.999825	+	0.0186881i	$0.00594894\pi$
$853$	15.0732	+	26.1076i	0.516097	+	0.893906i	−0.483728	+	0.875218i	$0.660718\pi$
$854$	−3.78696	+	6.55921i	−0.129587	+	0.224452i
$855$	−0.910416	−	0.525629i	−0.0311356	−	0.0179761i
$856$	17.0655			0.583288
$857$	14.7247	−	25.5040i	0.502988	−	0.871200i	−0.497006	−	0.867747i	$-0.665567\pi$
$857$	14.7247	−	25.5040i	0.502988	−	0.871200i	0.999994	−	0.00345335i	$-0.00109924\pi$
$858$	−31.3939			−1.07177
$859$	−52.6833			−1.79753			−0.898766	−	0.438429i	$-0.855535\pi$
$859$	−52.6833			−1.79753			−0.898766	+	0.438429i	$0.855535\pi$
$860$	−1.17434	−	3.99956i	−0.0400448	−	0.136384i
$861$	−33.4393			−1.13961
$862$	17.0655			0.581255
$863$	−14.8246	+	25.6770i	−0.504635	+	0.874054i	0.495350	+	0.868693i	$0.335040\pi$
$863$	−14.8246	+	25.6770i	−0.504635	+	0.874054i	−0.999986	+	0.00536060i	$0.998294\pi$
$864$			17.4912i			0.595064i
$865$	−1.28036	−	0.739215i	−0.0435335	−	0.0251341i
$866$	−13.7753	+	23.8594i	−0.468102	+	0.810777i
$867$	17.8089	+	30.8459i	0.604822	+	1.04758i
$868$		−	15.7634i		−	0.535046i
$869$	5.57321	+	9.65309i	0.189058	+	0.327459i
$870$	−0.263928	−	0.152379i	−0.00894799	−	0.00516613i
$871$			43.9643i			1.48967i
$872$	−42.2474	−	24.3916i	−1.43068	−	0.826003i
$873$	5.00000	+	8.66025i	0.169224	+	0.293105i
$874$	10.1237	+	17.5348i	0.342440	+	0.593124i
$875$	5.81241	−	3.35579i	0.196495	−	0.113447i
$876$			10.7111i			0.361896i
$877$	−12.8485	−	22.2542i	−0.433862	−	0.751471i	0.563340	−	0.826225i	$-0.309516\pi$
$877$	−12.8485	−	22.2542i	−0.433862	−	0.751471i	−0.997202	+	0.0747542i	$0.976183\pi$
$878$	−2.61262	−	4.52518i	−0.0881715	−	0.152718i
$879$	−14.2374	+	24.6599i	−0.480217	+	0.831759i
$880$	−1.91770	+	3.32155i	−0.0646455	+	0.111969i
$881$	16.0454			0.540584			0.270292	−	0.962778i	$-0.412880\pi$
$881$	16.0454			0.540584			0.270292	+	0.962778i	$0.412880\pi$
$882$			5.37113i			0.180855i
$883$	−4.63806	−	2.67779i	−0.156083	−	0.0901147i	0.419924	−	0.907559i	$-0.362057\pi$
$883$	−4.63806	−	2.67779i	−0.156083	−	0.0901147i	−0.576007	+	0.817445i	$0.695390\pi$
$884$	1.89898	−	3.28913i	0.0638696	−	0.110625i
$885$	4.55051	+	7.88171i	0.152964	+	0.264941i
$886$	−3.57146	−	6.18596i	−0.119986	−	0.207821i
$887$	31.3514			1.05268			0.526338	−	0.850275i	$-0.323564\pi$
$887$	31.3514			1.05268			0.526338	+	0.850275i	$0.323564\pi$
$888$	−18.0244	−	31.2192i	−0.604859	−	1.04765i
$889$		0			0
$890$	3.12372	−	1.80348i	0.104707	−	0.0604529i
$891$	29.3853	+	16.9656i	0.984444	+	0.568369i
$892$	22.8186			0.764024
$893$	−11.1464	−	6.43539i	−0.373001	−	0.215352i
$894$	14.9808	+	25.9475i	0.501032	+	0.867813i
$895$			0.373250i			0.0124764i
$896$	−20.9009	+	12.0672i	−0.698251	+	0.403135i
$897$	42.7702	+	24.6934i	1.42805	+	0.824487i
$898$	−14.4722	+	25.0666i	−0.482943	+	0.836482i
$899$	−1.17434			−0.0391666
$900$	7.59592	−	13.1565i	0.253197	−	0.438551i
$901$	−4.34847			−0.144869
$902$	31.3514			1.04389
$903$	−21.5959	−	20.5919i	−0.718665	−	0.685255i
$904$	15.5959			0.518713
$905$		−	6.96031i		−	0.231369i
$906$	−16.1566	−	9.32804i	−0.536768	−	0.309903i
$907$			40.2695i			1.33713i	0.743655	+	0.668564i	$0.233091\pi$
$907$			40.2695i			1.33713i	−0.743655	+	0.668564i	$0.766909\pi$
$908$	4.05089	−	7.01635i	0.134433	−	0.232846i
$909$	−14.5732	+	25.2415i	−0.483363	+	0.837209i
$910$	1.65377	+	2.86441i	0.0548219	+	0.0949543i
$911$	−28.4749			−0.943414			−0.471707	−	0.881755i	$-0.656362\pi$
$911$	−28.4749			−0.943414			−0.471707	+	0.881755i	$0.656362\pi$
$912$	9.10102	+	15.7634i	0.301365	+	0.521979i
$913$	−25.8207	+	44.7227i	−0.854539	+	1.48011i
$914$	−18.0000			−0.595387
$915$	0.851100	−	1.47415i	0.0281365	−	0.0487338i
$916$	11.0000	+	19.0526i	0.363450	+	0.629514i
$917$	−13.6515	−	23.6451i	−0.450813	−	0.780831i
$918$	−2.08476	+	1.20364i	−0.0688074	+	0.0397259i
$919$			53.3879i			1.76111i	0.473948	+	0.880553i	$0.342828\pi$
$919$			53.3879i			1.76111i	−0.473948	+	0.880553i	$0.657172\pi$
$920$	5.22523	−	3.01679i	0.172271	−	0.0994606i
$921$	50.8485	−	29.3574i	1.67551	−	0.967358i
$922$	20.3258	+	11.7351i	0.669393	+	0.386474i
$923$	20.0498	−	34.7273i	0.659948	−	1.14306i
$924$			27.4559i			0.903232i
$925$		−	29.2699i		−	0.962388i
$926$	−21.8113	−	12.5928i	−0.716765	−	0.413825i
$927$	−17.1140	−	9.88076i	−0.562097	−	0.324527i
$928$	0.898979	+	1.55708i	0.0295104	+	0.0511136i
$929$	−7.99490	+	4.61586i	−0.262304	+	0.151441i	−0.625385	−	0.780316i	$-0.715058\pi$
$929$	−7.99490	+	4.61586i	−0.262304	+	0.151441i	0.363081	+	0.931758i	$0.381725\pi$
$930$			3.54275i			0.116171i
$931$	−2.61262	−	4.52518i	−0.0856250	−	0.148307i
$932$	29.2020	−	16.8598i	0.956545	−	0.552261i
$933$	42.7702	−	24.6934i	1.40023	−	0.808424i
$934$	1.43827	+	0.830387i	0.0470617	+	0.0271711i
$935$	−0.527856			−0.0172627
$936$	13.1010	+	7.56388i	0.428220	+	0.247233i
$937$	−18.5227	+	10.6941i	−0.605110	+	0.349361i	−0.771049	−	0.636775i	$-0.780268\pi$
$937$	−18.5227	+	10.6941i	−0.605110	+	0.349361i	0.165939	+	0.986136i	$0.446935\pi$
$938$	38.4495			1.25542
$939$	−53.7499	+	31.0325i	−1.75406	+	1.01271i
$940$	−1.91770	+	3.32155i	−0.0625484	+	0.108337i
$941$	−15.2753	+	26.4575i	−0.497959	+	0.862490i	−0.999997	−	0.00235504i	$-0.999250\pi$
$941$	−15.2753	+	26.4575i	−0.497959	+	0.862490i	0.502038	+	0.864845i	$0.332584\pi$
$942$	36.5766			1.19173
$943$	−42.7123	−	24.6599i	−1.39090	−	0.803038i
$944$		−	53.6927i		−	1.74755i
$945$		−	2.09643i		−	0.0681968i
$946$	20.2474	+	19.3062i	0.658301	+	0.627698i
$947$			34.2359i			1.11252i	0.831009	+	0.556259i	$0.187764\pi$
$947$			34.2359i			1.11252i	−0.831009	+	0.556259i	$0.812236\pi$
$948$		−	15.7634i		−	0.511972i
$949$	−7.50000	−	4.33013i	−0.243460	−	0.140562i
$950$			14.7792i			0.479500i
$951$	31.3514	−	54.3022i	1.01664	−	1.76087i
$952$	−2.87654	−	1.66077i	−0.0932293	−	0.0538260i
$953$	−45.6464	+	26.3540i	−1.47863	+	0.853689i	−0.999708	−	0.0241668i	$-0.992307\pi$
$953$	−45.6464	+	26.3540i	−1.47863	+	0.853689i	−0.478925	+	0.877856i	$0.658973\pi$
$954$		−	17.3205i		−	0.560772i
$955$	−4.63806	+	2.67779i	−0.150084	+	0.0866511i
$956$	−45.3249	−	26.1683i	−1.46591	−	0.846345i
$957$	2.04541			0.0661186
$958$	18.5038	−	32.0495i	0.597831	−	1.03547i
$959$	−28.2109	+	16.2876i	−0.910978	+	0.525954i
$960$	4.69738	−	2.71203i	0.151607	−	0.0875305i
$961$	−8.67423	−	15.0242i	−0.279814	−	0.484652i
$962$	29.1464			0.939719
$963$	−8.10178	+	4.67756i	−0.261076	+	0.150732i
$964$	0.303062	−	0.174973i	0.00976096	−	0.00563549i
$965$	0.921683	+	0.532134i	0.0296700	+	0.0171300i
$966$	21.5959	−	37.4051i	0.694835	−	1.20349i
$967$		−	40.2695i		−	1.29498i	−0.762074	−	0.647490i	$-0.775819\pi$
$967$		−	40.2695i		−	1.29498i	0.762074	−	0.647490i	$-0.224181\pi$
$968$			5.37113i			0.172634i
$969$	−1.25255	+	2.16948i	−0.0402377	+	0.0696938i
$970$	−1.44949	+	2.51059i	−0.0465403	+	0.0806102i
$971$	13.6503	−	7.88098i	0.438058	−	0.252913i	−0.264716	−	0.964326i	$-0.585278\pi$
$971$	13.6503	−	7.88098i	0.438058	−	0.252913i	0.702773	+	0.711414i	$0.251945\pi$
$972$	−14.7169	−	25.4903i	−0.472043	−	0.817603i
$973$		−	11.4245i		−	0.366252i
$974$	19.4627	+	33.7103i	0.623624	+	1.08015i
$975$	18.0244	+	31.2192i	0.577242	+	0.999813i
$976$	−8.69694	+	5.02118i	−0.278382	+	0.160724i
$977$	−6.94949	+	12.0369i	−0.222334	+	0.385094i	−0.955516	−	0.294939i	$-0.904701\pi$
$977$	−6.94949	+	12.0369i	−0.222334	+	0.385094i	0.733182	+	0.680032i	$0.238034\pi$
$978$			53.7257i			1.71796i
$979$	−12.1042	+	20.9651i	−0.386853	+	0.670049i
$980$	−1.34847	+	0.778539i	−0.0430753	+	0.0248695i
$981$	26.7423			0.853817
$982$	−14.2374	+	8.21998i	−0.454335	+	0.262310i
$983$	26.4494	−	45.8117i	0.843605	−	1.46117i	−0.0432219	−	0.999065i	$-0.513762\pi$
$983$	26.4494	−	45.8117i	0.843605	−	1.46117i	0.886827	−	0.462102i	$-0.152904\pi$
$984$	−38.3975	−	22.1688i	−1.22407	−	0.706715i
$985$		−	3.63907i		−	0.115951i
$986$	−0.123724	+	0.214297i	−0.00394019	+	0.00682460i
$987$			27.4559i			0.873930i
$988$	−14.7169			−0.468205
$989$	−12.3990	−	42.2282i	−0.394265	−	1.34278i
$990$		−	2.10252i		−	0.0668224i
$991$	−39.8842			−1.26696			−0.633481	−	0.773758i	$-0.718375\pi$
$991$	−39.8842			−1.26696			−0.633481	+	0.773758i	$0.718375\pi$
$992$	10.4505	−	18.1007i	0.331803	−	0.574699i
$993$	−4.55051			−0.144406
$994$	−30.3712	−	17.5348i	−0.963315	−	0.556170i
$995$	−5.22523	−	3.01679i	−0.165651	−	0.0956387i
$996$	63.2474	−	36.5159i	2.00407	−	1.15705i
$997$		−	21.2132i		−	0.671829i	−0.941893	−	0.335914i	$-0.890955\pi$
$997$		−	21.2132i		−	0.671829i	0.941893	−	0.335914i	$-0.109045\pi$
$998$	21.8113	−	12.5928i	0.690426	−	0.398618i
$999$	−15.9989	−	9.23699i	−0.506184	−	0.292246i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	172.2.f.a.123.1	yes	8
4.3	odd	2	inner	172.2.f.a.123.2	yes	8
43.7	odd	6	inner	172.2.f.a.7.4	yes	8
172.7	even	6	inner	172.2.f.a.7.3	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
172.2.f.a.7.3	✓	8	172.7	even	6	inner
172.2.f.a.7.4	yes	8	43.7	odd	6	inner
172.2.f.a.123.1	yes	8	1.1	even	1	trivial
172.2.f.a.123.2	yes	8	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 172 = 2^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	172.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +(-1.06660 + 1.84740i) q^{3} -2.00000 q^{4} +(0.275255 + 0.158919i) q^{5} +(2.61262 + 1.50839i) q^{6} +(1.06660 + 1.84740i) q^{7} +2.82843i q^{8} +(-0.775255 - 1.34278i) q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +(-1.06660 + 1.84740i) q^{3} -2.00000 q^{4} +(0.275255 + 0.158919i) q^{5} +(2.61262 + 1.50839i) q^{6} +(1.06660 + 1.84740i) q^{7} +2.82843i q^{8} +(-0.775255 - 1.34278i) q^{9} +(0.224745 - 0.389270i) q^{10} +3.01679i q^{11} +(2.13319 - 3.69480i) q^{12} +(1.72474 + 2.98735i) q^{13} +(2.61262 - 1.50839i) q^{14} +(-0.587172 + 0.339004i) q^{15} +4.00000 q^{16} +(0.275255 + 0.476756i) q^{17} +(-1.89898 + 1.09638i) q^{18} +(1.06660 - 1.84740i) q^{19} +(-0.550510 - 0.317837i) q^{20} -4.55051 q^{21} +4.26639 q^{22} +(-5.81241 - 3.35579i) q^{23} +(-5.22523 - 3.01679i) q^{24} +(-2.44949 - 4.24264i) q^{25} +(4.22474 - 2.43916i) q^{26} -3.09204 q^{27} +(-2.13319 - 3.69480i) q^{28} +(-0.275255 + 0.158919i) q^{29} +(0.479424 + 0.830387i) q^{30} +(3.19979 + 1.84740i) q^{31} -5.65685i q^{32} +(-5.57321 - 3.21770i) q^{33} +(0.674235 - 0.389270i) q^{34} +0.678008i q^{35} +(1.55051 + 2.68556i) q^{36} +(5.17423 + 2.98735i) q^{37} +(-2.61262 - 1.50839i) q^{38} -7.35843 q^{39} +(-0.449490 + 0.778539i) q^{40} +7.34847 q^{41} +6.43539i q^{42} +(4.74581 + 4.52518i) q^{43} -6.03358i q^{44} -0.492810i q^{45} +(-4.74581 + 8.21998i) q^{46} -6.03358i q^{47} +(-4.26639 + 7.38960i) q^{48} +(1.22474 - 2.12132i) q^{49} +(-6.00000 + 3.46410i) q^{50} -1.17434 q^{51} +(-3.44949 - 5.97469i) q^{52} +(-3.94949 + 6.84072i) q^{53} +4.37281i q^{54} +(-0.479424 + 0.830387i) q^{55} +(-5.22523 + 3.01679i) q^{56} +(2.27526 + 3.94086i) q^{57} +(0.224745 + 0.389270i) q^{58} -13.4232i q^{59} +(1.17434 - 0.678008i) q^{60} +(-2.17423 + 1.25529i) q^{61} +(2.61262 - 4.52518i) q^{62} +(1.65377 - 2.86441i) q^{63} -8.00000 q^{64} +1.09638i q^{65} +(-4.55051 + 7.88171i) q^{66} +(11.0376 + 6.37258i) q^{67} +(-0.550510 - 0.953512i) q^{68} +(12.3990 - 7.15855i) q^{69} +0.958848 q^{70} +(-5.81241 - 10.0674i) q^{71} +(3.79796 - 2.19275i) q^{72} +(-2.17423 + 1.25529i) q^{73} +(4.22474 - 7.31747i) q^{74} +10.4505 q^{75} +(-2.13319 + 3.69480i) q^{76} +(-5.57321 + 3.21770i) q^{77} +10.4064i q^{78} +(3.19979 - 1.84740i) q^{79} +(1.10102 + 0.635674i) q^{80} +(5.62372 - 9.74058i) q^{81} -10.3923i q^{82} +(14.8246 + 8.55899i) q^{83} +9.10102 q^{84} +0.174973i q^{85} +(6.39958 - 6.71159i) q^{86} -0.678008i q^{87} -8.53277 q^{88} +(6.94949 + 4.01229i) q^{89} -0.696938 q^{90} +(-3.67921 + 6.37258i) q^{91} +(11.6248 + 6.71159i) q^{92} +(-6.82577 + 3.94086i) q^{93} -8.53277 q^{94} +(0.587172 - 0.339004i) q^{95} +(10.4505 + 6.03358i) q^{96} -6.44949 q^{97} +(-3.00000 - 1.73205i) q^{98} +(4.05089 - 2.33878i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 16 q^{4} + 12 q^{5} - 16 q^{9}+O(q^{10}) \) 8 * q - 16 * q^4 + 12 * q^5 - 16 * q^9	\( 8 q - 16 q^{4} + 12 q^{5} - 16 q^{9} - 8 q^{10} + 4 q^{13} + 32 q^{16} + 12 q^{17} + 24 q^{18} - 24 q^{20} - 56 q^{21} + 24 q^{26} - 12 q^{29} + 24 q^{33} - 24 q^{34} + 32 q^{36} + 12 q^{37} + 16 q^{40} - 48 q^{50} - 8 q^{52} - 12 q^{53} + 28 q^{57} - 8 q^{58} + 12 q^{61} - 64 q^{64} - 56 q^{66} - 24 q^{68} + 60 q^{69} - 48 q^{72} + 12 q^{73} + 24 q^{74} + 24 q^{77} + 48 q^{80} - 4 q^{81} + 112 q^{84} + 36 q^{89} + 112 q^{90} - 84 q^{93} - 32 q^{97} - 24 q^{98}+O(q^{100}) \) 8 * q - 16 * q^4 + 12 * q^5 - 16 * q^9 - 8 * q^10 + 4 * q^13 + 32 * q^16 + 12 * q^17 + 24 * q^18 - 24 * q^20 - 56 * q^21 + 24 * q^26 - 12 * q^29 + 24 * q^33 - 24 * q^34 + 32 * q^36 + 12 * q^37 + 16 * q^40 - 48 * q^50 - 8 * q^52 - 12 * q^53 + 28 * q^57 - 8 * q^58 + 12 * q^61 - 64 * q^64 - 56 * q^66 - 24 * q^68 + 60 * q^69 - 48 * q^72 + 12 * q^73 + 24 * q^74 + 24 * q^77 + 48 * q^80 - 4 * q^81 + 112 * q^84 + 36 * q^89 + 112 * q^90 - 84 * q^93 - 32 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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