LMFDB - Embedded newform 690.2.i.e.323.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(47,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("690.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.i (of order $4$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.2
Character	$\chi$	$=$	690.323
Dual form			690.2.i.e.47.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-1.35428 - 1.07978i) q^{3} +1.00000i q^{4} +(-1.85580 - 1.24740i) q^{5} +(0.194102 + 1.72114i) q^{6} +(-2.75926 + 2.75926i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.668152 + 2.92465i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.35428 - 1.07978i) q^{3} +1.00000i q^{4} +(-1.85580 - 1.24740i) q^{5} +(0.194102 + 1.72114i) q^{6} +(-2.75926 + 2.75926i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.668152 + 2.92465i) q^{9} +(0.430209 + 2.19429i) q^{10} -2.29656i q^{11} +(1.07978 - 1.35428i) q^{12} +(-4.98025 - 4.98025i) q^{13} +3.90218 q^{14} +(1.16637 + 3.69318i) q^{15} -1.00000 q^{16} +(3.92051 + 3.92051i) q^{17} +(1.59558 - 2.54049i) q^{18} +4.71936i q^{19} +(1.24740 - 1.85580i) q^{20} +(6.71621 - 0.757420i) q^{21} +(-1.62391 + 1.62391i) q^{22} +(0.707107 - 0.707107i) q^{23} +(-1.72114 + 0.194102i) q^{24} +(1.88801 + 4.62984i) q^{25} +7.04313i q^{26} +(2.25311 - 4.68225i) q^{27} +(-2.75926 - 2.75926i) q^{28} +6.12518 q^{29} +(1.78673 - 3.43622i) q^{30} +0.118966 q^{31} +(0.707107 + 0.707107i) q^{32} +(-2.47977 + 3.11018i) q^{33} -5.54444i q^{34} +(8.56254 - 1.67875i) q^{35} +(-2.92465 + 0.668152i) q^{36} +(0.206348 - 0.206348i) q^{37} +(3.33709 - 3.33709i) q^{38} +(1.36708 + 12.1222i) q^{39} +(-2.19429 + 0.430209i) q^{40} -5.80237i q^{41} +(-5.28465 - 4.21350i) q^{42} +(5.81015 + 5.81015i) q^{43} +2.29656 q^{44} +(2.40824 - 6.26102i) q^{45} -1.00000 q^{46} +(-7.73361 - 7.73361i) q^{47} +(1.35428 + 1.07978i) q^{48} -8.22705i q^{49} +(1.93877 - 4.60881i) q^{50} +(-1.07618 - 9.54276i) q^{51} +(4.98025 - 4.98025i) q^{52} +(3.05759 - 3.05759i) q^{53} +(-4.90404 + 1.71766i) q^{54} +(-2.86471 + 4.26196i) q^{55} +3.90218i q^{56} +(5.09587 - 6.39134i) q^{57} +(-4.33116 - 4.33116i) q^{58} +9.92337 q^{59} +(-3.69318 + 1.16637i) q^{60} +9.71148 q^{61} +(-0.0841220 - 0.0841220i) q^{62} +(-9.91348 - 6.22627i) q^{63} -1.00000i q^{64} +(3.03002 + 15.4547i) q^{65} +(3.95270 - 0.445765i) q^{66} +(-0.772079 + 0.772079i) q^{67} +(-3.92051 + 3.92051i) q^{68} +(-1.72114 + 0.194102i) q^{69} +(-7.24169 - 4.86757i) q^{70} +6.32014i q^{71} +(2.54049 + 1.59558i) q^{72} +(-0.302682 - 0.302682i) q^{73} -0.291820 q^{74} +(2.44232 - 8.30874i) q^{75} -4.71936 q^{76} +(6.33680 + 6.33680i) q^{77} +(7.60503 - 9.53838i) q^{78} +14.8422i q^{79} +(1.85580 + 1.24740i) q^{80} +(-8.10715 + 3.90822i) q^{81} +(-4.10289 + 4.10289i) q^{82} +(-9.99409 + 9.99409i) q^{83} +(0.757420 + 6.71621i) q^{84} +(-2.38527 - 12.1661i) q^{85} -8.21679i q^{86} +(-8.29522 - 6.61385i) q^{87} +(-1.62391 - 1.62391i) q^{88} -5.52293 q^{89} +(-6.13009 + 2.72433i) q^{90} +27.4836 q^{91} +(0.707107 + 0.707107i) q^{92} +(-0.161114 - 0.128458i) q^{93} +10.9370i q^{94} +(5.88691 - 8.75820i) q^{95} +(-0.194102 - 1.72114i) q^{96} +(1.89710 - 1.89710i) q^{97} +(-5.81740 + 5.81740i) q^{98} +(6.71662 - 1.53445i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{3} - 4 q^{6} - 8 q^{7}+O(q^{10}) $ 32 * q + 4 * q^3 - 4 * q^6 - 8 * q^7	$ 32 q + 4 q^{3} - 4 q^{6} - 8 q^{7} - 8 q^{10} - 4 q^{12} - 4 q^{15} - 32 q^{16} + 8 q^{18} - 32 q^{21} - 8 q^{22} + 4 q^{27} - 8 q^{28} + 20 q^{30} - 24 q^{31} + 20 q^{36} - 32 q^{37} - 16 q^{40} + 8 q^{42} + 144 q^{43} + 36 q^{45} - 32 q^{46} - 4 q^{48} + 12 q^{51} - 64 q^{55} + 52 q^{57} + 16 q^{58} + 4 q^{60} - 24 q^{61} - 116 q^{63} + 12 q^{66} - 16 q^{67} - 80 q^{70} - 8 q^{72} + 40 q^{73} + 44 q^{75} + 24 q^{76} - 36 q^{78} - 108 q^{81} - 32 q^{82} - 80 q^{85} + 68 q^{87} - 8 q^{88} + 16 q^{90} + 120 q^{91} + 12 q^{93} + 4 q^{96} - 8 q^{97}+O(q^{100}) $ 32 * q + 4 * q^3 - 4 * q^6 - 8 * q^7 - 8 * q^10 - 4 * q^12 - 4 * q^15 - 32 * q^16 + 8 * q^18 - 32 * q^21 - 8 * q^22 + 4 * q^27 - 8 * q^28 + 20 * q^30 - 24 * q^31 + 20 * q^36 - 32 * q^37 - 16 * q^40 + 8 * q^42 + 144 * q^43 + 36 * q^45 - 32 * q^46 - 4 * q^48 + 12 * q^51 - 64 * q^55 + 52 * q^57 + 16 * q^58 + 4 * q^60 - 24 * q^61 - 116 * q^63 + 12 * q^66 - 16 * q^67 - 80 * q^70 - 8 * q^72 + 40 * q^73 + 44 * q^75 + 24 * q^76 - 36 * q^78 - 108 * q^81 - 32 * q^82 - 80 * q^85 + 68 * q^87 - 8 * q^88 + 16 * q^90 + 120 * q^91 + 12 * q^93 + 4 * q^96 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−1.35428	−	1.07978i	−0.781894	−	0.623411i
$3$	−1.35428	−	1.07978i	−0.781894	−	0.623411i
$4$			1.00000i			0.500000i
$5$	−1.85580	−	1.24740i	−0.829940	−	0.557852i
$5$	−1.85580	−	1.24740i	−0.829940	−	0.557852i
$6$	0.194102	+	1.72114i	0.0792416	+	0.702653i
$7$	−2.75926	+	2.75926i	−1.04290	+	1.04290i	−0.0438654	+	0.999037i	$0.513967\pi$
$7$	−2.75926	+	2.75926i	−1.04290	+	1.04290i	−0.999037	+	0.0438654i	$0.986033\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	0.668152	+	2.92465i	0.222717	+	0.974883i
$10$	0.430209	+	2.19429i	0.136044	+	0.693896i
$11$		−	2.29656i		−	0.692438i	−0.938154	−	0.346219i	$-0.887465\pi$
$11$		−	2.29656i		−	0.692438i	0.938154	−	0.346219i	$-0.112535\pi$
$12$	1.07978	−	1.35428i	0.311706	−	0.390947i
$13$	−4.98025	−	4.98025i	−1.38127	−	1.38127i	−0.842366	−	0.538907i	$-0.818838\pi$
$13$	−4.98025	−	4.98025i	−1.38127	−	1.38127i	−0.538907	−	0.842366i	$-0.681162\pi$
$14$	3.90218			1.04290
$15$	1.16637	+	3.69318i	0.301154	+	0.953575i
$16$	−1.00000			−0.250000
$17$	3.92051	+	3.92051i	0.950864	+	0.950864i	0.998848	−	0.0479844i	$-0.0152798\pi$
$17$	3.92051	+	3.92051i	0.950864	+	0.950864i	−0.0479844	+	0.998848i	$0.515280\pi$
$18$	1.59558	−	2.54049i	0.376083	−	0.598800i
$19$			4.71936i			1.08270i	0.840799	+	0.541348i	$0.182086\pi$
$19$			4.71936i			1.08270i	−0.840799	+	0.541348i	$0.817914\pi$
$20$	1.24740	−	1.85580i	0.278926	−	0.414970i
$21$	6.71621	−	0.757420i	1.46560	−	0.165283i
$22$	−1.62391	+	1.62391i	−0.346219	+	0.346219i
$23$	0.707107	−	0.707107i	0.147442	−	0.147442i
$23$	0.707107	−	0.707107i	0.147442	−	0.147442i
$24$	−1.72114	+	0.194102i	−0.351326	+	0.0396208i
$25$	1.88801	+	4.62984i	0.377602	+	0.925968i
$26$			7.04313i			1.38127i
$27$	2.25311	−	4.68225i	0.433611	−	0.901100i
$28$	−2.75926	−	2.75926i	−0.521451	−	0.521451i
$29$	6.12518			1.13742			0.568709	−	0.822539i	$-0.307443\pi$
$29$	6.12518			1.13742			0.568709	+	0.822539i	$0.307443\pi$
$30$	1.78673	−	3.43622i	0.326211	−	0.627365i
$31$	0.118966			0.0213670			0.0106835	−	0.999943i	$-0.496599\pi$
$31$	0.118966			0.0213670			0.0106835	+	0.999943i	$0.496599\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−2.47977	+	3.11018i	−0.431673	+	0.541413i
$34$		−	5.54444i		−	0.950864i
$35$	8.56254	−	1.67875i	1.44733	−	0.283761i
$36$	−2.92465	+	0.668152i	−0.487442	+	0.111359i
$37$	0.206348	−	0.206348i	0.0339234	−	0.0339234i	−0.689942	−	0.723865i	$-0.742364\pi$
$37$	0.206348	−	0.206348i	0.0339234	−	0.0339234i	0.723865	+	0.689942i	$0.242364\pi$
$38$	3.33709	−	3.33709i	0.541348	−	0.541348i
$39$	1.36708	+	12.1222i	0.218909	+	1.94111i
$40$	−2.19429	+	0.430209i	−0.346948	+	0.0680220i
$41$		−	5.80237i		−	0.906178i	−0.891465	−	0.453089i	$-0.850322\pi$
$41$		−	5.80237i		−	0.906178i	0.891465	−	0.453089i	$-0.149678\pi$
$42$	−5.28465	−	4.21350i	−0.815440	−	0.650157i
$43$	5.81015	+	5.81015i	0.886040	+	0.886040i	0.994140	−	0.108100i	$-0.0344768\pi$
$43$	5.81015	+	5.81015i	0.886040	+	0.886040i	−0.108100	+	0.994140i	$0.534477\pi$
$44$	2.29656			0.346219
$45$	2.40824	−	6.26102i	0.358999	−	0.933338i
$46$	−1.00000			−0.147442
$47$	−7.73361	−	7.73361i	−1.12806	−	1.12806i	−0.990492	−	0.137572i	$-0.956070\pi$
$47$	−7.73361	−	7.73361i	−1.12806	−	1.12806i	−0.137572	−	0.990492i	$-0.543930\pi$
$48$	1.35428	+	1.07978i	0.195474	+	0.155853i
$49$		−	8.22705i		−	1.17529i
$50$	1.93877	−	4.60881i	0.274183	−	0.651785i
$51$	−1.07618	−	9.54276i	−0.150696	−	1.33625i
$52$	4.98025	−	4.98025i	0.690636	−	0.690636i
$53$	3.05759	−	3.05759i	0.419993	−	0.419993i	−0.465209	−	0.885201i	$-0.654021\pi$
$53$	3.05759	−	3.05759i	0.419993	−	0.419993i	0.885201	+	0.465209i	$0.154021\pi$
$54$	−4.90404	+	1.71766i	−0.667356	+	0.233744i
$55$	−2.86471	+	4.26196i	−0.386278	+	0.574682i
$56$			3.90218i			0.521451i
$57$	5.09587	−	6.39134i	0.674964	−	0.846554i
$58$	−4.33116	−	4.33116i	−0.568709	−	0.568709i
$59$	9.92337			1.29191			0.645956	−	0.763374i	$-0.276459\pi$
$59$	9.92337			1.29191			0.645956	+	0.763374i	$0.276459\pi$
$60$	−3.69318	+	1.16637i	−0.476788	+	0.150577i
$61$	9.71148			1.24343			0.621714	−	0.783244i	$-0.286437\pi$
$61$	9.71148			1.24343			0.621714	+	0.783244i	$0.286437\pi$
$62$	−0.0841220	−	0.0841220i	−0.0106835	−	0.0106835i
$63$	−9.91348	−	6.22627i	−1.24898	−	0.784436i
$64$		−	1.00000i		−	0.125000i
$65$	3.03002	+	15.4547i	0.375827	+	1.91692i
$66$	3.95270	−	0.445765i	0.486543	−	0.0548699i
$67$	−0.772079	+	0.772079i	−0.0943245	+	0.0943245i	−0.752694	−	0.658370i	$-0.771246\pi$
$67$	−0.772079	+	0.772079i	−0.0943245	+	0.0943245i	0.658370	+	0.752694i	$0.271246\pi$
$68$	−3.92051	+	3.92051i	−0.475432	+	0.475432i
$69$	−1.72114	+	0.194102i	−0.207201	+	0.0233671i
$70$	−7.24169	−	4.86757i	−0.865547	−	0.581786i
$71$			6.32014i			0.750063i	0.927012	+	0.375031i	$0.122368\pi$
$71$			6.32014i			0.750063i	−0.927012	+	0.375031i	$0.877632\pi$
$72$	2.54049	+	1.59558i	0.299400	+	0.188041i
$73$	−0.302682	−	0.302682i	−0.0354262	−	0.0354262i	0.689172	−	0.724598i	$-0.257975\pi$
$73$	−0.302682	−	0.302682i	−0.0354262	−	0.0354262i	−0.724598	+	0.689172i	$0.757975\pi$
$74$	−0.291820			−0.0339234
$75$	2.44232	−	8.30874i	0.282014	−	0.959410i
$76$	−4.71936			−0.541348
$77$	6.33680	+	6.33680i	0.722145	+	0.722145i
$78$	7.60503	−	9.53838i	0.861100	−	1.08001i
$79$			14.8422i			1.66987i	0.550346	+	0.834937i	$0.314496\pi$
$79$			14.8422i			1.66987i	−0.550346	+	0.834937i	$0.685504\pi$
$80$	1.85580	+	1.24740i	0.207485	+	0.139463i
$81$	−8.10715	+	3.90822i	−0.900794	+	0.434247i
$82$	−4.10289	+	4.10289i	−0.453089	+	0.453089i
$83$	−9.99409	+	9.99409i	−1.09699	+	1.09699i	−0.102234	+	0.994760i	$0.532599\pi$
$83$	−9.99409	+	9.99409i	−1.09699	+	1.09699i	−0.994760	+	0.102234i	$0.967401\pi$
$84$	0.757420	+	6.71621i	0.0826413	+	0.732798i
$85$	−2.38527	−	12.1661i	−0.258718	−	1.31960i
$86$		−	8.21679i		−	0.886040i
$87$	−8.29522	−	6.61385i	−0.889340	−	0.709079i
$88$	−1.62391	−	1.62391i	−0.173109	−	0.173109i
$89$	−5.52293			−0.585429			−0.292715	−	0.956200i	$-0.594559\pi$
$89$	−5.52293			−0.585429			−0.292715	+	0.956200i	$0.594559\pi$
$90$	−6.13009	+	2.72433i	−0.646168	+	0.287170i
$91$	27.4836			2.88107
$92$	0.707107	+	0.707107i	0.0737210	+	0.0737210i
$93$	−0.161114	−	0.128458i	−0.0167067	−	0.0133204i
$94$			10.9370i			1.12806i
$95$	5.88691	−	8.75820i	0.603984	−	0.898573i
$96$	−0.194102	−	1.72114i	−0.0198104	−	0.175663i
$97$	1.89710	−	1.89710i	0.192621	−	0.192621i	−0.604207	−	0.796828i	$-0.706510\pi$
$97$	1.89710	−	1.89710i	0.192621	−	0.192621i	0.796828	+	0.604207i	$0.206510\pi$
$98$	−5.81740	+	5.81740i	−0.587646	+	0.587646i
$99$	6.71662	−	1.53445i	0.675046	−	0.154218i
$100$	−4.62984	+	1.88801i	−0.462984	+	0.188801i
$101$			11.6939i			1.16359i	0.813336	+	0.581795i	$0.197649\pi$
$101$			11.6939i			1.16359i	−0.813336	+	0.581795i	$0.802351\pi$
$102$	−5.98677	+	7.50873i	−0.592779	+	0.743475i
$103$	8.74638	+	8.74638i	0.861806	+	0.861806i	0.991548	−	0.129742i	$-0.0414148\pi$
$103$	8.74638	+	8.74638i	0.861806	+	0.861806i	−0.129742	+	0.991548i	$0.541415\pi$
$104$	−7.04313			−0.690636
$105$	−13.4088	−	6.97215i	−1.30856	−	0.680412i
$106$	−4.32409			−0.419993
$107$	8.79387	+	8.79387i	0.850135	+	0.850135i	0.990149	−	0.140014i	$-0.0447148\pi$
$107$	8.79387	+	8.79387i	0.850135	+	0.850135i	−0.140014	+	0.990149i	$0.544715\pi$
$108$	4.68225	+	2.25311i	0.450550	+	0.216806i
$109$		−	7.32345i		−	0.701459i	−0.936477	−	0.350729i	$-0.885934\pi$
$109$		−	7.32345i		−	0.701459i	0.936477	−	0.350729i	$-0.114066\pi$
$110$	5.03932	−	0.987998i	0.480480	−	0.0942020i
$111$	−0.502264	+	0.0566428i	−0.0476727	+	0.00537629i
$112$	2.75926	−	2.75926i	0.260726	−	0.260726i
$113$	7.59615	−	7.59615i	0.714586	−	0.714586i	−0.252905	−	0.967491i	$-0.581386\pi$
$113$	7.59615	−	7.59615i	0.714586	−	0.714586i	0.967491	+	0.252905i	$0.0813860\pi$
$114$	−8.12268	+	0.916035i	−0.760759	+	0.0857946i
$115$	−2.19429	+	0.430209i	−0.204619	+	0.0401172i
$116$			6.12518i			0.568709i
$117$	11.2379	−	17.8930i	1.03895	−	1.65421i
$118$	−7.01688	−	7.01688i	−0.645956	−	0.645956i
$119$	−21.6354			−1.98332
$120$	3.43622	+	1.78673i	0.313682	+	0.163105i
$121$	5.72583			0.520530
$122$	−6.86706	−	6.86706i	−0.621714	−	0.621714i
$123$	−6.26528	+	7.85804i	−0.564921	+	0.708535i
$124$			0.118966i			0.0106835i
$125$	2.27147	−	10.9472i	0.203167	−	0.979144i
$126$	2.60725	+	11.4125i	0.232273	+	1.01671i
$127$	−7.95989	+	7.95989i	−0.706326	+	0.706326i	−0.965761	−	0.259435i	$-0.916464\pi$
$127$	−7.95989	+	7.95989i	−0.706326	+	0.706326i	0.259435	+	0.965761i	$0.416464\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−1.59489	−	14.1423i	−0.140422	−	1.24516i
$130$	8.78557	−	13.0707i	0.770546	−	1.14637i
$131$		−	4.09045i		−	0.357385i	−0.983905	−	0.178692i	$-0.942813\pi$
$131$		−	4.09045i		−	0.357385i	0.983905	−	0.178692i	$-0.0571866\pi$
$132$	−3.11018	−	2.47977i	−0.270707	−	0.215837i
$133$	−13.0220	−	13.0220i	−1.12915	−	1.12915i
$134$	1.09188			0.0943245
$135$	−10.0220	+	5.87882i	−0.862552	+	0.505968i
$136$	5.54444			0.475432
$137$	−1.39973	−	1.39973i	−0.119587	−	0.119587i	0.644781	−	0.764367i	$-0.276949\pi$
$137$	−1.39973	−	1.39973i	−0.119587	−	0.119587i	−0.764367	+	0.644781i	$0.776949\pi$
$138$	1.35428	+	1.07978i	0.115284	+	0.0919169i
$139$			8.53836i			0.724214i	0.932136	+	0.362107i	$0.117943\pi$
$139$			8.53836i			0.724214i	−0.932136	+	0.362107i	$0.882057\pi$
$140$	1.67875	+	8.56254i	0.141881	+	0.723666i
$141$	2.12289	+	18.8241i	0.178779	+	1.58527i
$142$	4.46902	−	4.46902i	0.375031	−	0.375031i
$143$	−11.4374	+	11.4374i	−0.956445	+	0.956445i
$144$	−0.668152	−	2.92465i	−0.0556793	−	0.243721i
$145$	−11.3671	−	7.64053i	−0.943989	−	0.634511i
$146$			0.428056i			0.0354262i
$147$	−8.88340	+	11.1417i	−0.732690	+	0.918955i
$148$	0.206348	+	0.206348i	0.0169617	+	0.0169617i
$149$	−10.3546			−0.848285			−0.424142	−	0.905596i	$-0.639424\pi$
$149$	−10.3546			−0.848285			−0.424142	+	0.905596i	$0.639424\pi$
$150$	−7.60214	+	4.14819i	−0.620712	+	0.338698i
$151$	−5.40744			−0.440051			−0.220026	−	0.975494i	$-0.570614\pi$
$151$	−5.40744			−0.440051			−0.220026	+	0.975494i	$0.570614\pi$
$152$	3.33709	+	3.33709i	0.270674	+	0.270674i
$153$	−8.84662	+	14.0856i	−0.715207	+	1.13875i
$154$		−	8.96159i		−	0.722145i
$155$	−0.220778	−	0.148398i	−0.0177333	−	0.0119196i
$156$	−12.1222	+	1.36708i	−0.970555	+	0.109454i
$157$	−2.89675	+	2.89675i	−0.231186	+	0.231186i	−0.813188	−	0.582002i	$-0.802270\pi$
$157$	−2.89675	+	2.89675i	−0.231186	+	0.231186i	0.582002	+	0.813188i	$0.302270\pi$
$158$	10.4950	−	10.4950i	0.834937	−	0.834937i
$159$	−7.44236	+	0.839312i	−0.590218	+	0.0665618i
$160$	−0.430209	−	2.19429i	−0.0340110	−	0.173474i
$161$			3.90218i			0.307535i
$162$	8.49615	+	2.96909i	0.667520	+	0.233274i
$163$	9.47261	+	9.47261i	0.741952	+	0.741952i	0.972953	−	0.231001i	$-0.0742002\pi$
$163$	9.47261	+	9.47261i	0.741952	+	0.741952i	−0.231001	+	0.972953i	$0.574200\pi$
$164$	5.80237			0.453089
$165$	8.48160	−	2.67862i	0.660292	−	0.208531i
$166$	14.1338			1.09699
$167$	10.6533	+	10.6533i	0.824375	+	0.824375i	0.986732	−	0.162357i	$-0.0519097\pi$
$167$	10.6533	+	10.6533i	0.824375	+	0.824375i	−0.162357	+	0.986732i	$0.551910\pi$
$168$	4.21350	−	5.28465i	0.325079	−	0.407720i
$169$			36.6057i			2.81583i
$170$	−6.91611	+	10.2894i	−0.530442	+	0.789160i
$171$	−13.8025	+	3.15325i	−1.05550	+	0.241135i
$172$	−5.81015	+	5.81015i	−0.443020	+	0.443020i
$173$	1.44162	−	1.44162i	0.109604	−	0.109604i	−0.650178	−	0.759782i	$-0.725306\pi$
$173$	1.44162	−	1.44162i	0.109604	−	0.109604i	0.759782	+	0.650178i	$0.225306\pi$
$174$	1.18891	+	10.5423i	0.0901308	+	0.799210i
$175$	−17.9844	−	7.56543i	−1.35950	−	0.571893i
$176$			2.29656i			0.173109i
$177$	−13.4390	−	10.7150i	−1.01014	−	0.805392i
$178$	3.90530	+	3.90530i	0.292715	+	0.292715i
$179$	−4.69858			−0.351188			−0.175594	−	0.984463i	$-0.556185\pi$
$179$	−4.69858			−0.351188			−0.175594	+	0.984463i	$0.556185\pi$
$180$	6.26102	+	2.40824i	0.466669	+	0.179499i
$181$	0.531517			0.0395074			0.0197537	−	0.999805i	$-0.493712\pi$
$181$	0.531517			0.0395074			0.0197537	+	0.999805i	$0.493712\pi$
$182$	−19.4338	−	19.4338i	−1.44053	−	1.44053i
$183$	−13.1521	−	10.4863i	−0.972229	−	0.775167i
$184$		−	1.00000i		−	0.0737210i
$185$	−0.640339	+	0.125544i	−0.0470787	+	0.00923015i
$186$	0.0230916	+	0.204758i	0.00169316	+	0.0150136i
$187$	9.00367	−	9.00367i	0.658414	−	0.658414i
$188$	7.73361	−	7.73361i	0.564032	−	0.564032i
$189$	6.70264	+	19.1365i	0.487545	+	1.39197i
$190$	−10.3557	+	2.03031i	−0.751278	+	0.147294i
$191$			8.00136i			0.578958i	0.957184	+	0.289479i	$0.0934820\pi$
$191$			8.00136i			0.578958i	−0.957184	+	0.289479i	$0.906518\pi$
$192$	−1.07978	+	1.35428i	−0.0779264	+	0.0977368i
$193$	9.64199	+	9.64199i	0.694046	+	0.694046i	0.963120	−	0.269074i	$-0.0867176\pi$
$193$	9.64199	+	9.64199i	0.694046	+	0.694046i	−0.269074	+	0.963120i	$0.586718\pi$
$194$	−2.68290			−0.192621
$195$	12.5842	−	24.2017i	0.901171	−	1.73312i
$196$	8.22705			0.587646
$197$	−1.48807	−	1.48807i	−0.106020	−	0.106020i	0.652107	−	0.758127i	$-0.273885\pi$
$197$	−1.48807	−	1.48807i	−0.106020	−	0.106020i	−0.758127	+	0.652107i	$0.773885\pi$
$198$	−5.83439	−	3.66435i	−0.414632	−	0.260414i
$199$		−	9.98521i		−	0.707833i	−0.935277	−	0.353916i	$-0.884850\pi$
$199$		−	9.98521i		−	0.707833i	0.935277	−	0.353916i	$-0.115150\pi$
$200$	4.60881	+	1.93877i	0.325892	+	0.137092i
$201$	1.87929	−	0.211937i	0.132555	−	0.0149489i
$202$	8.26886	−	8.26886i	0.581795	−	0.581795i
$203$	−16.9010	+	16.9010i	−1.18622	+	1.18622i
$204$	9.54276	−	1.07618i	0.668127	−	0.0753480i
$205$	−7.23785	+	10.7681i	−0.505513	+	0.752073i
$206$		−	12.3692i		−	0.861806i
$207$	2.54049	+	1.59558i	0.176577	+	0.110901i
$208$	4.98025	+	4.98025i	0.345318	+	0.345318i
$209$	10.8383			0.749699
$210$	4.55137	+	14.4115i	0.314075	+	0.994487i
$211$	−13.6764			−0.941524			−0.470762	−	0.882260i	$-0.656021\pi$
$211$	−13.6764			−0.941524			−0.470762	+	0.882260i	$0.656021\pi$
$212$	3.05759	+	3.05759i	0.209996	+	0.209996i
$213$	6.82436	−	8.55925i	0.467597	−	0.586470i
$214$		−	12.4364i		−	0.850135i
$215$	−3.53494	−	18.0300i	−0.241081	−	1.22964i
$216$	−1.71766	−	4.90404i	−0.116872	−	0.333678i
$217$	−0.328260	+	0.328260i	−0.0222837	+	0.0222837i
$218$	−5.17846	+	5.17846i	−0.350729	+	0.350729i
$219$	0.0830864	+	0.736745i	0.00561446	+	0.0497846i
$220$	−4.26196	−	2.86471i	−0.287341	−	0.193139i
$221$		−	39.0502i		−	2.62680i
$222$	0.395206	+	0.315101i	0.0265245	+	0.0211482i
$223$	−7.47810	−	7.47810i	−0.500771	−	0.500771i	0.410907	−	0.911677i	$-0.365212\pi$
$223$	−7.47810	−	7.47810i	−0.500771	−	0.500771i	−0.911677	+	0.410907i	$0.865212\pi$
$224$	−3.90218			−0.260726
$225$	−12.2792	+	8.61520i	−0.818612	+	0.574347i
$226$	−10.7426			−0.714586
$227$	12.5076	+	12.5076i	0.830158	+	0.830158i	0.987538	−	0.157380i	$-0.0503049\pi$
$227$	12.5076	+	12.5076i	0.830158	+	0.830158i	−0.157380	+	0.987538i	$0.550305\pi$
$228$	6.39134	+	5.09587i	0.423277	+	0.337482i
$229$		−	10.3963i		−	0.687009i	−0.939151	−	0.343505i	$-0.888386\pi$
$229$		−	10.3963i		−	0.687009i	0.939151	−	0.343505i	$-0.111614\pi$
$230$	1.85580	+	1.24740i	0.122368	+	0.0822508i
$231$	−1.73946	−	15.4241i	−0.114448	−	1.01483i
$232$	4.33116	−	4.33116i	0.284354	−	0.284354i
$233$	1.28951	−	1.28951i	0.0844787	−	0.0844787i	−0.663605	−	0.748083i	$-0.730974\pi$
$233$	1.28951	−	1.28951i	0.0844787	−	0.0844787i	0.748083	+	0.663605i	$0.230974\pi$
$234$	−20.5987	+	4.70588i	−1.34658	+	0.307633i
$235$	4.70518	+	23.9989i	0.306932	+	1.56552i
$236$			9.92337i			0.645956i
$237$	16.0263	−	20.1005i	1.04102	−	1.30566i
$238$	15.2986	+	15.2986i	0.991658	+	0.991658i
$239$	11.7193			0.758057			0.379029	−	0.925385i	$-0.376258\pi$
$239$	11.7193			0.758057			0.379029	+	0.925385i	$0.376258\pi$
$240$	−1.16637	−	3.69318i	−0.0752886	−	0.238394i
$241$	−6.18044			−0.398117			−0.199059	−	0.979988i	$-0.563788\pi$
$241$	−6.18044			−0.398117			−0.199059	+	0.979988i	$0.563788\pi$
$242$	−4.04877	−	4.04877i	−0.260265	−	0.260265i
$243$	15.1994	+	3.46110i	0.975040	+	0.222030i
$244$			9.71148i			0.621714i
$245$	−10.2624	+	15.2678i	−0.655640	+	0.975423i
$246$	9.98669	−	1.12625i	0.636728	−	0.0718070i
$247$	23.5036	−	23.5036i	1.49550	−	1.49550i
$248$	0.0841220	−	0.0841220i	0.00534175	−	0.00534175i
$249$	24.3262	−	2.74339i	1.54161	−	0.173855i
$250$	−9.34699	+	6.13464i	−0.591155	+	0.387989i
$251$		−	20.8314i		−	1.31486i	−0.753514	−	0.657432i	$-0.771643\pi$
$251$		−	20.8314i		−	1.31486i	0.753514	−	0.657432i	$-0.228357\pi$
$252$	6.22627	−	9.91348i	0.392218	−	0.624490i
$253$	−1.62391	−	1.62391i	−0.102094	−	0.102094i
$254$	11.2570			0.706326
$255$	−9.90641	+	19.0519i	−0.620364	+	1.19308i
$256$	1.00000			0.0625000
$257$	13.3668	+	13.3668i	0.833798	+	0.833798i	0.988034	−	0.154236i	$-0.0492915\pi$
$257$	13.3668	+	13.3668i	0.833798	+	0.833798i	−0.154236	+	0.988034i	$0.549292\pi$
$258$	−8.87232	+	11.1278i	−0.552367	+	0.692789i
$259$			1.13874i			0.0707576i
$260$	−15.4547	+	3.03002i	−0.958460	+	0.187914i
$261$	4.09255	+	17.9140i	0.253323	+	1.10885i
$262$	−2.89239	+	2.89239i	−0.178692	+	0.178692i
$263$	−0.374059	+	0.374059i	−0.0230655	+	0.0230655i	−0.718545	−	0.695480i	$-0.755192\pi$
$263$	−0.374059	+	0.374059i	−0.0230655	+	0.0230655i	0.695480	+	0.718545i	$0.255192\pi$
$264$	0.445765	+	3.95270i	0.0274349	+	0.243272i
$265$	−9.48832	+	1.86026i	−0.582863	+	0.114275i
$266$			18.4158i			1.12915i
$267$	7.47960	+	5.96355i	0.457744	+	0.364963i
$268$	−0.772079	−	0.772079i	−0.0471622	−	0.0471622i
$269$	−29.3344			−1.78855			−0.894275	−	0.447517i	$-0.852308\pi$
$269$	−29.3344			−1.78855			−0.894275	+	0.447517i	$0.852308\pi$
$270$	11.2435	+	2.92964i	0.684260	+	0.178292i
$271$	15.2750			0.927892			0.463946	−	0.885864i	$-0.346433\pi$
$271$	15.2750			0.927892			0.463946	+	0.885864i	$0.346433\pi$
$272$	−3.92051	−	3.92051i	−0.237716	−	0.237716i
$273$	−37.2205	−	29.6762i	−2.25269	−	1.79609i
$274$			1.97951i			0.119587i
$275$	10.6327	−	4.33592i	0.641175	−	0.261466i
$276$	−0.194102	−	1.72114i	−0.0116835	−	0.103600i
$277$	12.5262	−	12.5262i	0.752629	−	0.752629i	−0.222341	−	0.974969i	$-0.571370\pi$
$277$	12.5262	−	12.5262i	0.752629	−	0.752629i	0.974969	+	0.222341i	$0.0713697\pi$
$278$	6.03753	−	6.03753i	0.362107	−	0.362107i
$279$	0.0794877	+	0.347935i	0.00475880	+	0.0208303i
$280$	4.86757	−	7.24169i	0.290893	−	0.432773i
$281$		−	28.4991i		−	1.70011i	−0.526690	−	0.850057i	$-0.676567\pi$
$281$		−	28.4991i		−	1.70011i	0.526690	−	0.850057i	$-0.323433\pi$
$282$	11.8095	−	14.8117i	0.703247	−	0.882026i
$283$	−4.81687	−	4.81687i	−0.286333	−	0.286333i	0.549295	−	0.835628i	$-0.314896\pi$
$283$	−4.81687	−	4.81687i	−0.286333	−	0.286333i	−0.835628	+	0.549295i	$0.814896\pi$
$284$	−6.32014			−0.375031
$285$	−17.4295	+	5.50450i	−1.03243	+	0.326058i
$286$	16.1750			0.956445
$287$	16.0103	+	16.0103i	0.945055	+	0.945055i
$288$	−1.59558	+	2.54049i	−0.0940207	+	0.149700i
$289$			13.7408i			0.808284i
$290$	2.63511	+	13.4404i	0.154739	+	0.789250i
$291$	−4.61765	+	0.520755i	−0.270691	+	0.0305272i
$292$	0.302682	−	0.302682i	0.0177131	−	0.0177131i
$293$	16.0270	−	16.0270i	0.936308	−	0.936308i	−0.0617818	−	0.998090i	$-0.519678\pi$
$293$	16.0270	−	16.0270i	0.936308	−	0.936308i	0.998090	+	0.0617818i	$0.0196783\pi$
$294$	14.1599	−	1.59688i	0.825822	−	0.0931321i
$295$	−18.4158	−	12.3784i	−1.07221	−	0.720696i
$296$		−	0.291820i		−	0.0169617i
$297$	−10.7531	−	5.17440i	−0.623956	−	0.300249i
$298$	7.32183	+	7.32183i	0.424142	+	0.424142i
$299$	−7.04313			−0.407315
$300$	8.30874	+	2.44232i	0.479705	+	0.141007i
$301$	−32.0634			−1.84811
$302$	3.82364	+	3.82364i	0.220026	+	0.220026i
$303$	12.6269	−	15.8369i	0.725395	−	0.909804i
$304$		−	4.71936i		−	0.270674i
$305$	−18.0226	−	12.1141i	−1.03197	−	0.693649i
$306$	16.2155	−	3.70453i	0.926981	−	0.211774i
$307$	−12.7225	+	12.7225i	−0.726114	+	0.726114i	−0.969843	−	0.243729i	$-0.921629\pi$
$307$	−12.7225	+	12.7225i	−0.726114	+	0.726114i	0.243729	+	0.969843i	$0.421629\pi$
$308$	−6.33680	+	6.33680i	−0.361073	+	0.361073i
$309$	−2.40089	−	21.2892i	−0.136582	−	1.21110i
$310$	0.0511804	+	0.261047i	0.00290685	+	0.0148265i
$311$			1.68845i			0.0957431i	0.998854	+	0.0478715i	$0.0152438\pi$
$311$			1.68845i			0.0957431i	−0.998854	+	0.0478715i	$0.984756\pi$
$312$	9.53838	+	7.60503i	0.540004	+	0.430550i
$313$	18.5203	+	18.5203i	1.04683	+	1.04683i	0.998848	+	0.0479796i	$0.0152782\pi$
$313$	18.5203	+	18.5203i	1.04683	+	1.04683i	0.0479796	+	0.998848i	$0.484722\pi$
$314$	4.09663			0.231186
$315$	10.6308	+	23.9208i	0.598980	+	1.34778i
$316$	−14.8422			−0.834937
$317$	14.5249	+	14.5249i	0.815797	+	0.815797i	0.985496	−	0.169699i	$-0.0542795\pi$
$317$	14.5249	+	14.5249i	0.815797	+	0.815797i	−0.169699	+	0.985496i	$0.554280\pi$
$318$	5.85603	+	4.66906i	0.328390	+	0.261828i
$319$		−	14.0668i		−	0.787591i
$320$	−1.24740	+	1.85580i	−0.0697315	+	0.103743i
$321$	−2.41393	−	21.4048i	−0.134732	−	1.19470i
$322$	2.75926	−	2.75926i	0.153768	−	0.153768i
$323$	−18.5023	+	18.5023i	−1.02950	+	1.02950i
$324$	−3.90822	−	8.10715i	−0.217123	−	0.450397i
$325$	13.6550	−	32.4605i	0.757444	−	1.80058i
$326$		−	13.3963i		−	0.741952i
$327$	−7.90771	+	9.91800i	−0.437297	+	0.548467i
$328$	−4.10289	−	4.10289i	−0.226544	−	0.226544i
$329$	42.6781			2.35292
$330$	−7.89147	−	4.10332i	−0.434411	−	0.225881i
$331$	14.4348			0.793410			0.396705	−	0.917946i	$-0.370154\pi$
$331$	14.4348			0.793410			0.396705	+	0.917946i	$0.370154\pi$
$332$	−9.99409	−	9.99409i	−0.548497	−	0.548497i
$333$	0.741368	+	0.465624i	0.0406267	+	0.0255160i
$334$		−	15.0660i		−	0.824375i
$335$	2.39591	−	0.469738i	0.130903	−	0.0256645i
$336$	−6.71621	+	0.757420i	−0.366399	+	0.0413207i
$337$	1.60419	−	1.60419i	0.0873858	−	0.0873858i	−0.662063	−	0.749448i	$-0.730319\pi$
$337$	1.60419	−	1.60419i	0.0873858	−	0.0873858i	0.749448	+	0.662063i	$0.230319\pi$
$338$	25.8842	−	25.8842i	1.40791	−	1.40791i
$339$	−18.4895	+	2.08515i	−1.00421	+	0.113250i
$340$	12.1661	−	2.38527i	0.659801	−	0.129359i
$341$		−	0.273213i		−	0.0147953i
$342$	11.9895	+	7.53014i	0.648318	+	0.407183i
$343$	3.38575	+	3.38575i	0.182813	+	0.182813i
$344$	8.21679			0.443020
$345$	3.43622	+	1.78673i	0.185000	+	0.0961943i
$346$	−2.03875			−0.109604
$347$	−13.2298	−	13.2298i	−0.710212	−	0.710212i	0.256368	−	0.966579i	$-0.417474\pi$
$347$	−13.2298	−	13.2298i	−0.710212	−	0.710212i	−0.966579	+	0.256368i	$0.917474\pi$
$348$	6.61385	−	8.29522i	0.354539	−	0.444670i
$349$		−	23.5499i		−	1.26060i	−0.776352	−	0.630300i	$-0.782932\pi$
$349$		−	23.5499i		−	1.26060i	0.776352	−	0.630300i	$-0.217068\pi$
$350$	7.36736	+	18.0665i	0.393802	+	0.965695i
$351$	−34.5398	+	12.0977i	−1.84360	+	0.645729i
$352$	1.62391	−	1.62391i	0.0865547	−	0.0865547i
$353$	4.64958	−	4.64958i	0.247472	−	0.247472i	−0.572460	−	0.819932i	$-0.694011\pi$
$353$	4.64958	−	4.64958i	0.247472	−	0.247472i	0.819932	+	0.572460i	$0.194011\pi$
$354$	1.92614	+	17.0795i	0.102373	+	0.907766i
$355$	7.88372	−	11.7289i	0.418424	−	0.622507i
$356$		−	5.52293i		−	0.292715i
$357$	29.3004	+	23.3615i	1.55074	+	1.23642i
$358$	3.32240	+	3.32240i	0.175594	+	0.175594i
$359$	29.0528			1.53335			0.766675	−	0.642036i	$-0.221910\pi$
$359$	29.0528			1.53335			0.766675	+	0.642036i	$0.221910\pi$
$360$	−2.72433	−	6.13009i	−0.143585	−	0.323084i
$361$	−3.27237			−0.172230
$362$	−0.375839	−	0.375839i	−0.0197537	−	0.0197537i
$363$	−7.75438	−	6.18263i	−0.406999	−	0.324504i
$364$			27.4836i			1.44053i
$365$	0.184154	+	0.939281i	0.00963904	+	0.0491642i
$366$	1.88501	+	16.7148i	0.0985313	+	0.873698i
$367$	−4.29029	+	4.29029i	−0.223952	+	0.223952i	−0.810160	−	0.586209i	$-0.800620\pi$
$367$	−4.29029	+	4.29029i	−0.223952	+	0.223952i	0.586209	+	0.810160i	$0.300620\pi$
$368$	−0.707107	+	0.707107i	−0.0368605	+	0.0368605i
$369$	16.9699	−	3.87686i	0.883417	−	0.201822i
$370$	0.541561	+	0.364015i	0.0281544	+	0.0189243i
$371$			16.8734i			0.876023i
$372$	0.128458	−	0.161114i	0.00666022	−	0.00835337i
$373$	9.50901	+	9.50901i	0.492358	+	0.492358i	0.909048	−	0.416691i	$-0.136810\pi$
$373$	9.50901	+	9.50901i	0.492358	+	0.492358i	−0.416691	+	0.909048i	$0.636810\pi$
$374$	−12.7331			−0.658414
$375$	−14.8967	+	12.3728i	−0.769264	+	0.638931i
$376$	−10.9370			−0.564032
$377$	−30.5049	−	30.5049i	−1.57108	−	1.57108i
$378$	8.79206	−	18.2710i	0.452215	−	0.939760i
$379$		−	7.21205i		−	0.370458i	−0.982695	−	0.185229i	$-0.940697\pi$
$379$		−	7.21205i		−	0.370458i	0.982695	−	0.185229i	$-0.0593027\pi$
$380$	8.75820	+	5.88691i	0.449286	+	0.301992i
$381$	19.3748	−	2.18500i	0.992603	−	0.111941i
$382$	5.65781	−	5.65781i	0.289479	−	0.289479i
$383$	9.29577	−	9.29577i	0.474992	−	0.474992i	−0.428534	−	0.903526i	$-0.640970\pi$
$383$	9.29577	−	9.29577i	0.474992	−	0.474992i	0.903526	+	0.428534i	$0.140970\pi$
$384$	1.72114	−	0.194102i	0.0878316	−	0.00990520i
$385$	−3.85535	−	19.6643i	−0.196487	−	1.00219i
$386$		−	13.6358i		−	0.694046i
$387$	−13.1106	+	20.8747i	−0.666449	+	1.06112i
$388$	1.89710	+	1.89710i	0.0963105	+	0.0963105i
$389$	0.585718			0.0296971			0.0148485	−	0.999890i	$-0.495273\pi$
$389$	0.585718			0.0296971			0.0148485	+	0.999890i	$0.495273\pi$
$390$	−26.0116	+	8.21487i	−1.31715	+	0.415976i
$391$	5.54444			0.280394
$392$	−5.81740	−	5.81740i	−0.293823	−	0.293823i
$393$	−4.41679	+	5.53962i	−0.222797	+	0.279437i
$394$			2.10444i			0.106020i
$395$	18.5141	−	27.5441i	0.931543	−	1.38590i
$396$	1.53445	+	6.71662i	0.0771090	+	0.337523i
$397$	−15.1819	+	15.1819i	−0.761960	+	0.761960i	−0.976676	−	0.214717i	$-0.931117\pi$
$397$	−15.1819	+	15.1819i	−0.761960	+	0.761960i	0.214717	+	0.976676i	$0.431117\pi$
$398$	−7.06061	+	7.06061i	−0.353916	+	0.353916i
$399$	3.57454	+	31.6962i	0.178951	+	1.58680i
$400$	−1.88801	−	4.62984i	−0.0944004	−	0.231492i
$401$			36.1259i			1.80404i	0.431692	+	0.902021i	$0.357917\pi$
$401$			36.1259i			1.80404i	−0.431692	+	0.902021i	$0.642083\pi$
$402$	−1.47872	−	1.17899i	−0.0737518	−	0.0588029i
$403$	−0.592483	−	0.592483i	−0.0295137	−	0.0295137i
$404$	−11.6939			−0.581795
$405$	19.9204	+	2.85993i	0.989851	+	0.142111i
$406$	23.9016			1.18622
$407$	−0.473890	−	0.473890i	−0.0234898	−	0.0234898i
$408$	−7.50873	−	5.98677i	−0.371737	−	0.296389i
$409$			12.5098i			0.618571i	0.950969	+	0.309286i	$0.100090\pi$
$409$			12.5098i			0.618571i	−0.950969	+	0.309286i	$0.899910\pi$
$410$	12.7321	−	2.49623i	0.628793	−	0.123280i
$411$	0.384226	+	3.40702i	0.0189525	+	0.168056i
$412$	−8.74638	+	8.74638i	−0.430903	+	0.430903i
$413$	−27.3812	+	27.3812i	−1.34734	+	1.34734i
$414$	−0.668152	−	2.92465i	−0.0328379	−	0.143739i
$415$	31.0136	−	6.08047i	1.52240	−	0.298479i
$416$		−	7.04313i		−	0.345318i
$417$	9.21955	−	11.5633i	0.451483	−	0.566259i
$418$	−7.66382	−	7.66382i	−0.374850	−	0.374850i
$419$	−25.5177			−1.24662			−0.623310	−	0.781975i	$-0.714213\pi$
$419$	−25.5177			−1.24662			−0.623310	+	0.781975i	$0.714213\pi$
$420$	6.97215	−	13.4088i	0.340206	−	0.654281i
$421$	28.7694			1.40213			0.701067	−	0.713095i	$-0.252707\pi$
$421$	28.7694			1.40213			0.701067	+	0.713095i	$0.252707\pi$
$422$	9.67069	+	9.67069i	0.470762	+	0.470762i
$423$	17.4509	−	27.7853i	0.848491	−	1.35097i
$424$		−	4.32409i		−	0.209996i
$425$	−10.7494	+	25.5533i	−0.521422	+	1.23952i
$426$	−10.8779	+	1.22675i	−0.527034	+	0.0594362i
$427$	−26.7965	+	26.7965i	−1.29677	+	1.29677i
$428$	−8.79387	+	8.79387i	−0.425068	+	0.425068i
$429$	27.8394	−	3.13958i	1.34410	−	0.151581i
$430$	−10.2496	+	15.2487i	−0.494279	+	0.735360i
$431$			11.0573i			0.532612i	0.963888	+	0.266306i	$0.0858032\pi$
$431$			11.0573i			0.532612i	−0.963888	+	0.266306i	$0.914197\pi$
$432$	−2.25311	+	4.68225i	−0.108403	+	0.225275i
$433$	6.59432	+	6.59432i	0.316903	+	0.316903i	0.847576	−	0.530674i	$-0.178061\pi$
$433$	6.59432	+	6.59432i	0.316903	+	0.316903i	−0.530674	+	0.847576i	$0.678061\pi$
$434$	0.464229			0.0222837
$435$	7.14420	+	22.6214i	0.342538	+	1.08461i
$436$	7.32345			0.350729
$437$	3.33709	+	3.33709i	0.159635	+	0.159635i
$438$	0.462206	−	0.579708i	0.0220851	−	0.0276995i
$439$			6.00909i			0.286798i	0.989665	+	0.143399i	$0.0458032\pi$
$439$			6.00909i			0.286798i	−0.989665	+	0.143399i	$0.954197\pi$
$440$	0.987998	+	5.03932i	0.0471010	+	0.240240i
$441$	24.0612	−	5.49692i	1.14577	−	0.261758i
$442$	−27.6127	+	27.6127i	−1.31340	+	1.31340i
$443$	23.1363	−	23.1363i	1.09924	−	1.09924i	0.104739	−	0.994500i	$-0.466599\pi$
$443$	23.1363	−	23.1363i	1.09924	−	1.09924i	0.994500	−	0.104739i	$-0.0334008\pi$
$444$	−0.0566428	−	0.502264i	−0.00268815	−	0.0238364i
$445$	10.2495	+	6.88928i	0.485871	+	0.326583i
$446$			10.5756i			0.500771i
$447$	14.0231	+	11.1807i	0.663269	+	0.528830i
$448$	2.75926	+	2.75926i	0.130363	+	0.130363i
$449$	3.93638			0.185769			0.0928846	−	0.995677i	$-0.470391\pi$
$449$	3.93638			0.185769			0.0928846	+	0.995677i	$0.470391\pi$
$450$	14.7746	+	2.59083i	0.696479	+	0.122133i
$451$	−13.3255			−0.627472
$452$	7.59615	+	7.59615i	0.357293	+	0.357293i
$453$	7.32320	+	5.83885i	0.344074	+	0.274333i
$454$		−	17.6884i		−	0.830158i
$455$	−51.0042	−	34.2829i	−2.39111	−	1.60721i
$456$	−0.916035	−	8.12268i	−0.0428973	−	0.380379i
$457$	−10.1175	+	10.1175i	−0.473279	+	0.473279i	−0.902974	−	0.429695i	$-0.858621\pi$
$457$	−10.1175	+	10.1175i	−0.473279	+	0.473279i	0.429695	+	0.902974i	$0.358621\pi$
$458$	−7.35132	+	7.35132i	−0.343505	+	0.343505i
$459$	27.1902	−	9.52348i	1.26913	−	0.444518i
$460$	−0.430209	−	2.19429i	−0.0200586	−	0.102309i
$461$		−	25.5669i		−	1.19077i	−0.803441	−	0.595385i	$-0.797000\pi$
$461$		−	25.5669i		−	1.19077i	0.803441	−	0.595385i	$-0.203000\pi$
$462$	−9.67654	+	12.1365i	−0.450193	+	0.564641i
$463$	−12.8718	−	12.8718i	−0.598204	−	0.598204i	0.341630	−	0.939835i	$-0.389021\pi$
$463$	−12.8718	−	12.8718i	−0.598204	−	0.598204i	−0.939835	+	0.341630i	$0.889021\pi$
$464$	−6.12518			−0.284354
$465$	0.138758	+	0.439365i	0.00643477	+	0.0203751i
$466$	−1.82365			−0.0844787
$467$	−8.99881	−	8.99881i	−0.416415	−	0.416415i	0.467551	−	0.883966i	$-0.345136\pi$
$467$	−8.99881	−	8.99881i	−0.416415	−	0.416415i	−0.883966	+	0.467551i	$0.845136\pi$
$468$	17.8930	+	11.2379i	0.827106	+	0.519473i
$469$		−	4.26074i		−	0.196743i
$470$	13.6427	−	20.2969i	0.629293	−	0.936225i
$471$	7.05088	−	0.795162i	0.324887	−	0.0366391i
$472$	7.01688	−	7.01688i	0.322978	−	0.322978i
$473$	13.3433	−	13.3433i	0.613527	−	0.613527i
$474$	−25.5454	+	2.88089i	−1.17334	+	0.132324i
$475$	−21.8499	+	8.91019i	−1.00254	+	0.408828i
$476$		−	21.6354i		−	0.991658i
$477$	10.9853	+	6.89945i	0.502983	+	0.315904i
$478$	−8.28678	−	8.28678i	−0.379029	−	0.379029i
$479$	−13.1616			−0.601368			−0.300684	−	0.953724i	$-0.597215\pi$
$479$	−13.1616			−0.601368			−0.300684	+	0.953724i	$0.597215\pi$
$480$	−1.78673	+	3.43622i	−0.0815527	+	0.156841i
$481$	−2.05533			−0.0937149
$482$	4.37023	+	4.37023i	0.199059	+	0.199059i
$483$	4.21350	−	5.28465i	0.191721	−	0.240460i
$484$			5.72583i			0.260265i
$485$	−5.88707	+	1.15421i	−0.267318	+	0.0524099i
$486$	−8.30021	−	13.1949i	−0.376505	−	0.598535i
$487$	−22.8385	+	22.8385i	−1.03491	+	1.03491i	−0.0355411	+	0.999368i	$0.511315\pi$
$487$	−22.8385	+	22.8385i	−1.03491	+	1.03491i	−0.999368	+	0.0355411i	$0.988685\pi$
$488$	6.86706	−	6.86706i	0.310857	−	0.310857i
$489$	−2.60024	−	23.0569i	−0.117587	−	1.04267i
$490$	18.0526	−	3.53935i	0.815531	−	0.159891i
$491$		−	33.7238i		−	1.52193i	−0.648791	−	0.760966i	$-0.724725\pi$
$491$		−	33.7238i		−	1.52193i	0.648791	−	0.760966i	$-0.275275\pi$
$492$	−7.85804	−	6.26528i	−0.354268	−	0.282461i
$493$	24.0138	+	24.0138i	1.08153	+	1.08153i
$494$	−33.2391			−1.49550
$495$	−14.3788	−	5.53065i	−0.646278	−	0.248584i
$496$	−0.118966			−0.00534175
$497$	−17.4389	−	17.4389i	−0.782243	−	0.782243i
$498$	−19.1411	−	15.2614i	−0.857733	−	0.683878i
$499$			22.0549i			0.987314i	0.869657	+	0.493657i	$0.164340\pi$
$499$			22.0549i			0.987314i	−0.869657	+	0.493657i	$0.835660\pi$
$500$	10.9472	+	2.27147i	0.489572	+	0.101583i
$501$	−2.92433	−	25.9307i	−0.130650	−	1.15850i
$502$	−14.7300	+	14.7300i	−0.657432	+	0.657432i
$503$	−7.81907	+	7.81907i	−0.348635	+	0.348635i	−0.859601	−	0.510966i	$-0.829288\pi$
$503$	−7.81907	+	7.81907i	−0.348635	+	0.348635i	0.510966	+	0.859601i	$0.329288\pi$
$504$	−11.4125	+	2.60725i	−0.508354	+	0.116136i
$505$	14.5870	−	21.7016i	0.649111	−	0.965710i
$506$			2.29656i			0.102094i
$507$	39.5261	−	49.5744i	1.75542	−	2.20168i
$508$	−7.95989	−	7.95989i	−0.353163	−	0.353163i
$509$	−38.3147			−1.69827			−0.849134	−	0.528177i	$-0.822876\pi$
$509$	−38.3147			−1.69827			−0.849134	+	0.528177i	$0.822876\pi$
$510$	20.4766	−	6.46684i	0.906720	−	0.286357i
$511$	1.67035			0.0738921
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	22.0972	+	10.6332i	0.975617	+	0.469469i
$514$		−	18.9035i		−	0.833798i
$515$	−5.32136	−	27.1417i	−0.234487	−	1.19601i
$516$	14.1423	−	1.59489i	0.622578	−	0.0702112i
$517$	−17.7607	+	17.7607i	−0.781114	+	0.781114i
$518$	0.805208	−	0.805208i	0.0353788	−	0.0353788i
$519$	−3.50898	+	0.395725i	−0.154027	+	0.0173704i
$520$	13.0707	+	8.78557i	0.573187	+	0.385273i
$521$		−	1.36254i		−	0.0596941i	−0.999554	−	0.0298470i	$-0.990498\pi$
$521$		−	1.36254i		−	0.0596941i	0.999554	−	0.0298470i	$-0.00950202\pi$
$522$	9.77324	−	15.5610i	0.427763	−	0.681086i
$523$	4.54945	+	4.54945i	0.198933	+	0.198933i	0.799543	−	0.600609i	$-0.205075\pi$
$523$	4.54945	+	4.54945i	0.198933	+	0.198933i	−0.600609	+	0.799543i	$0.705075\pi$
$524$	4.09045			0.178692
$525$	16.1870	+	29.6650i	0.706458	+	1.29469i
$526$	0.528999			0.0230655
$527$	0.466409	+	0.466409i	0.0203171	+	0.0203171i
$528$	2.47977	−	3.11018i	0.107918	−	0.135353i
$529$		−	1.00000i		−	0.0434783i
$530$	8.02466	+	5.39385i	0.348569	+	0.234294i
$531$	6.63032	+	29.0224i	0.287731	+	1.25946i
$532$	13.0220	−	13.0220i	0.564573	−	0.564573i
$533$	−28.8972	+	28.8972i	−1.25168	+	1.25168i
$534$	−1.07201	−	9.50574i	−0.0463904	−	0.411354i
$535$	−5.35025	−	27.2891i	−0.231311	−	1.17981i
$536$			1.09188i			0.0471622i
$537$	6.36320	+	5.07343i	0.274592	+	0.218935i
$538$	20.7426	+	20.7426i	0.894275	+	0.894275i
$539$	−18.8939			−0.813817
$540$	−5.87882	−	10.0220i	−0.252984	−	0.431276i
$541$	28.0473			1.20585			0.602923	−	0.797799i	$-0.294003\pi$
$541$	28.0473			1.20585			0.602923	+	0.797799i	$0.294003\pi$
$542$	−10.8011	−	10.8011i	−0.463946	−	0.463946i
$543$	−0.719824	−	0.573921i	−0.0308906	−	0.0246293i
$544$			5.54444i			0.237716i
$545$	−9.13524	+	13.5909i	−0.391310	+	0.582169i
$546$	5.33461	+	47.3032i	0.228300	+	2.02439i
$547$	−14.0079	+	14.0079i	−0.598936	+	0.598936i	−0.940029	−	0.341093i	$-0.889203\pi$
$547$	−14.0079	+	14.0079i	−0.598936	+	0.598936i	0.341093	+	0.940029i	$0.389203\pi$
$548$	1.39973	−	1.39973i	0.0597933	−	0.0597933i
$549$	6.48875	+	28.4027i	0.276933	+	1.21220i
$550$	−10.5844	−	4.45249i	−0.451320	−	0.189855i
$551$			28.9069i			1.23148i
$552$	−1.07978	+	1.35428i	−0.0459585	+	0.0576420i
$553$	−40.9534	−	40.9534i	−1.74152	−	1.74152i
$554$	−17.7148			−0.752629
$555$	1.00276	+	0.521404i	0.0425647	+	0.0221324i
$556$	−8.53836			−0.362107
$557$	32.8676	+	32.8676i	1.39265	+	1.39265i	0.819346	+	0.573299i	$0.194337\pi$
$557$	32.8676	+	32.8676i	1.39265	+	1.39265i	0.573299	+	0.819346i	$0.305663\pi$
$558$	0.189821	−	0.302234i	0.00803577	−	0.0127946i
$559$		−	57.8720i		−	2.44772i
$560$	−8.56254	+	1.67875i	−0.361833	+	0.0709403i
$561$	−21.9155	+	2.47152i	−0.925273	+	0.104348i
$562$	−20.1519	+	20.1519i	−0.850057	+	0.850057i
$563$	7.29079	−	7.29079i	0.307270	−	0.307270i	−0.536580	−	0.843850i	$-0.680284\pi$
$563$	7.29079	−	7.29079i	0.307270	−	0.307270i	0.843850	+	0.536580i	$0.180284\pi$
$564$	−18.8241	+	2.12289i	−0.792637	+	0.0893896i
$565$	−23.5724	+	4.62155i	−0.991697	+	0.194430i
$566$			6.81208i			0.286333i
$567$	11.5859	−	33.1535i	0.486563	−	1.39232i
$568$	4.46902	+	4.46902i	0.187516	+	0.187516i
$569$	29.3461			1.23025			0.615126	−	0.788429i	$-0.289105\pi$
$569$	29.3461			1.23025			0.615126	+	0.788429i	$0.289105\pi$
$570$	16.2168	+	8.43222i	0.679245	+	0.353187i
$571$	−18.0793			−0.756594			−0.378297	−	0.925684i	$-0.623490\pi$
$571$	−18.0793			−0.756594			−0.378297	+	0.925684i	$0.623490\pi$
$572$	−11.4374	−	11.4374i	−0.478222	−	0.478222i
$573$	8.63970	−	10.8361i	0.360929	−	0.452684i
$574$		−	22.6419i		−	0.945055i
$575$	4.60881	+	1.93877i	0.192201	+	0.0808523i
$576$	2.92465	−	0.668152i	0.121860	−	0.0278397i
$577$	−8.11640	+	8.11640i	−0.337890	+	0.337890i	−0.855573	−	0.517683i	$-0.826795\pi$
$577$	−8.11640	+	8.11640i	−0.337890	+	0.337890i	0.517683	+	0.855573i	$0.326795\pi$
$578$	9.71623	−	9.71623i	0.404142	−	0.404142i
$579$	−2.64674	−	23.4692i	−0.109995	−	0.975346i
$580$	7.64053	−	11.3671i	0.317256	−	0.471994i
$581$		−	55.1526i		−	2.28812i
$582$	3.63340	+	2.89694i	0.150609	+	0.120082i
$583$	−7.02193	−	7.02193i	−0.290819	−	0.290819i
$584$	−0.428056			−0.0177131
$585$	−43.1751	+	19.1878i	−1.78507	+	0.793319i
$586$	−22.6656			−0.936308
$587$	0.974523	+	0.974523i	0.0402229	+	0.0402229i	0.726932	−	0.686709i	$-0.240945\pi$
$587$	0.974523	+	0.974523i	0.0402229	+	0.0402229i	−0.686709	+	0.726932i	$0.740945\pi$
$588$	−11.1417	−	8.88340i	−0.459477	−	0.366345i
$589$			0.561446i			0.0231340i
$590$	4.26912	+	21.7748i	0.175757	+	0.896453i
$591$	0.408475	+	3.62204i	0.0168024	+	0.148991i
$592$	−0.206348	+	0.206348i	−0.00848085	+	0.00848085i
$593$	−9.81152	+	9.81152i	−0.402911	+	0.402911i	−0.879258	−	0.476347i	$-0.841961\pi$
$593$	−9.81152	+	9.81152i	−0.402911	+	0.402911i	0.476347	+	0.879258i	$0.341961\pi$
$594$	3.94471	+	11.2624i	0.161853	+	0.462102i
$595$	40.1511	+	26.9879i	1.64603	+	1.10640i
$596$		−	10.3546i		−	0.424142i
$597$	−10.7818	+	13.5228i	−0.441271	+	0.553450i
$598$	4.98025	+	4.98025i	0.203657	+	0.203657i
$599$	21.3996			0.874363			0.437181	−	0.899373i	$-0.355977\pi$
$599$	21.3996			0.874363			0.437181	+	0.899373i	$0.355977\pi$
$600$	−4.14819	−	7.60214i	−0.169349	−	0.310356i
$601$	−5.22276			−0.213041			−0.106520	−	0.994311i	$-0.533971\pi$
$601$	−5.22276			−0.213041			−0.106520	+	0.994311i	$0.533971\pi$
$602$	22.6723	+	22.6723i	0.924053	+	0.924053i
$603$	−2.77393	−	1.74219i	−0.112963	−	0.0709476i
$604$		−	5.40744i		−	0.220026i
$605$	−10.6260	−	7.14238i	−0.432009	−	0.290379i
$606$	−20.1269	+	2.26981i	−0.817599	+	0.0922048i
$607$	0.566086	−	0.566086i	0.0229767	−	0.0229767i	−0.695525	−	0.718502i	$-0.744828\pi$
$607$	0.566086	−	0.566086i	0.0229767	−	0.0229767i	0.718502	+	0.695525i	$0.244828\pi$
$608$	−3.33709	+	3.33709i	−0.135337	+	0.135337i
$609$	41.1380	−	4.63934i	1.66700	−	0.187995i
$610$	4.17796	+	21.3098i	0.169161	+	0.862810i
$611$			77.0306i			3.11632i
$612$	−14.0856	−	8.84662i	−0.569377	−	0.357604i
$613$	−0.767442	−	0.767442i	−0.0309967	−	0.0309967i	0.691439	−	0.722435i	$-0.256977\pi$
$613$	−0.767442	−	0.767442i	−0.0309967	−	0.0309967i	−0.722435	+	0.691439i	$0.756977\pi$
$614$	17.9924			0.726114
$615$	21.4292	−	6.76768i	0.864109	−	0.272899i
$616$	8.96159			0.361073
$617$	−0.569528	−	0.569528i	−0.0229284	−	0.0229284i	0.695550	−	0.718478i	$-0.255161\pi$
$617$	−0.569528	−	0.569528i	−0.0229284	−	0.0229284i	−0.718478	+	0.695550i	$0.755161\pi$
$618$	−13.3561	+	16.7514i	−0.537260	+	0.673841i
$619$		−	6.59095i		−	0.264913i	−0.991189	−	0.132456i	$-0.957714\pi$
$619$		−	6.59095i		−	0.264913i	0.991189	−	0.132456i	$-0.0422864\pi$
$620$	0.148398	−	0.220778i	0.00595982	−	0.00886667i
$621$	−1.71766	−	4.90404i	−0.0689274	−	0.196792i
$622$	1.19391	−	1.19391i	0.0478715	−	0.0478715i
$623$	15.2392	−	15.2392i	0.610546	−	0.610546i
$624$	−1.36708	−	12.1222i	−0.0547271	−	0.485277i
$625$	−17.8709	+	17.4824i	−0.714834	+	0.699294i
$626$		−	26.1916i		−	1.04683i
$627$	−14.6781	−	11.7029i	−0.586186	−	0.467371i
$628$	−2.89675	−	2.89675i	−0.115593	−	0.115593i
$629$	1.61798			0.0645131
$630$	9.39738	−	24.4317i	0.374401	−	0.973381i
$631$	2.32089			0.0923930			0.0461965	−	0.998932i	$-0.485290\pi$
$631$	2.32089			0.0923930			0.0461965	+	0.998932i	$0.485290\pi$
$632$	10.4950	+	10.4950i	0.417468	+	0.417468i
$633$	18.5217	+	14.7675i	0.736172	+	0.586956i
$634$		−	20.5412i		−	0.815797i
$635$	24.7011	−	4.84285i	0.980234	−	0.192183i
$636$	−0.839312	−	7.44236i	−0.0332809	−	0.295109i
$637$	−40.9727	+	40.9727i	−1.62340	+	1.62340i
$638$	−9.94675	+	9.94675i	−0.393795	+	0.393795i
$639$	−18.4842	+	4.22282i	−0.731224	+	0.167052i
$640$	2.19429	−	0.430209i	0.0867370	−	0.0170055i
$641$			25.2939i			0.999051i	0.866299	+	0.499525i	$0.166492\pi$
$641$			25.2939i			0.999051i	−0.866299	+	0.499525i	$0.833508\pi$
$642$	−13.4286	+	16.8424i	−0.529984	+	0.664716i
$643$	−5.65542	−	5.65542i	−0.223028	−	0.223028i	0.586744	−	0.809772i	$-0.300409\pi$
$643$	−5.65542	−	5.65542i	−0.223028	−	0.223028i	−0.809772	+	0.586744i	$0.800409\pi$
$644$	−3.90218			−0.153768
$645$	−14.6812	+	28.2347i	−0.578071	+	1.11174i
$646$	26.1662			1.02950
$647$	−19.3089	−	19.3089i	−0.759110	−	0.759110i	0.217051	−	0.976160i	$-0.430356\pi$
$647$	−19.3089	−	19.3089i	−0.759110	−	0.759110i	−0.976160	+	0.217051i	$0.930356\pi$
$648$	−2.96909	+	8.49615i	−0.116637	+	0.333760i
$649$		−	22.7896i		−	0.894569i
$650$	−32.6086	+	13.2975i	−1.27901	+	0.521570i
$651$	0.799004	−	0.0901076i	0.0313154	−	0.00353160i
$652$	−9.47261	+	9.47261i	−0.370976	+	0.370976i
$653$	−5.44785	+	5.44785i	−0.213191	+	0.213191i	−0.805622	−	0.592431i	$-0.798168\pi$
$653$	−5.44785	+	5.44785i	−0.213191	+	0.213191i	0.592431	+	0.805622i	$0.298168\pi$
$654$	12.6047	−	1.42149i	0.492882	−	0.0555848i
$655$	−5.10241	+	7.59107i	−0.199368	+	0.296608i
$656$			5.80237i			0.226544i
$657$	0.683000	−	1.08747i	0.0266464	−	0.0424264i
$658$	−30.1780	−	30.1780i	−1.17646	−	1.17646i
$659$	−15.1034			−0.588344			−0.294172	−	0.955753i	$-0.595044\pi$
$659$	−15.1034			−0.588344			−0.294172	+	0.955753i	$0.595044\pi$
$660$	2.67862	+	8.48160i	0.104265	+	0.330146i
$661$	32.0911			1.24820			0.624099	−	0.781346i	$-0.285466\pi$
$661$	32.0911			1.24820			0.624099	+	0.781346i	$0.285466\pi$
$662$	−10.2070	−	10.2070i	−0.396705	−	0.396705i
$663$	−42.1656	+	52.8850i	−1.63758	+	2.05388i
$664$			14.1338i			0.548497i
$665$	7.92265	+	40.4097i	0.307227	+	1.56702i
$666$	−0.194980	−	0.853472i	−0.00755533	−	0.0330714i
$667$	4.33116	−	4.33116i	0.167703	−	0.167703i
$668$	−10.6533	+	10.6533i	−0.412187	+	0.412187i
$669$	2.05275	+	18.2021i	0.0793638	+	0.703736i
$670$	−2.02632	−	1.36201i	−0.0782837	−	0.0526191i
$671$		−	22.3030i		−	0.860996i
$672$	5.28465	+	4.21350i	0.203860	+	0.162539i
$673$	14.5895	+	14.5895i	0.562384	+	0.562384i	0.929984	−	0.367600i	$-0.119820\pi$
$673$	14.5895	+	14.5895i	0.562384	+	0.562384i	−0.367600	+	0.929984i	$0.619820\pi$
$674$	−2.26867			−0.0873858
$675$	25.9320	+	1.59142i	0.998122	+	0.0612536i
$676$	−36.6057			−1.40791
$677$	17.6118	+	17.6118i	0.676875	+	0.676875i	0.959292	−	0.282417i	$-0.0911361\pi$
$677$	17.6118	+	17.6118i	0.676875	+	0.676875i	−0.282417	+	0.959292i	$0.591136\pi$
$678$	14.5485	+	11.5996i	0.558731	+	0.445481i
$679$			10.4692i			0.401770i
$680$	−10.2894	−	6.91611i	−0.394580	−	0.265221i
$681$	−3.43335	−	30.4442i	−0.131566	−	1.16663i
$682$	−0.193191	+	0.193191i	−0.00739766	+	0.00739766i
$683$	−16.1721	+	16.1721i	−0.618807	+	0.618807i	−0.945225	−	0.326419i	$-0.894158\pi$
$683$	−16.1721	+	16.1721i	−0.618807	+	0.618807i	0.326419	+	0.945225i	$0.394158\pi$
$684$	−3.15325	−	13.8025i	−0.120568	−	0.527751i
$685$	0.851603	+	4.34362i	0.0325381	+	0.165961i
$686$		−	4.78817i		−	0.182813i
$687$	−11.2258	+	14.0796i	−0.428289	+	0.537169i
$688$	−5.81015	−	5.81015i	−0.221510	−	0.221510i
$689$	−30.4551			−1.16025
$690$	−1.16637	−	3.69318i	−0.0444028	−	0.140597i
$691$	23.3495			0.888258			0.444129	−	0.895963i	$-0.353513\pi$
$691$	23.3495			0.888258			0.444129	+	0.895963i	$0.353513\pi$
$692$	1.44162	+	1.44162i	0.0548020	+	0.0548020i
$693$	−14.2990	+	22.7669i	−0.543173	+	0.864841i
$694$			18.7097i			0.710212i
$695$	10.6507	−	15.8455i	0.404005	−	0.601055i
$696$	−10.5423	+	1.18891i	−0.399605	+	0.0450654i
$697$	22.7483	−	22.7483i	0.861651	−	0.861651i
$698$	−16.6523	+	16.6523i	−0.630300	+	0.630300i
$699$	−3.13875	+	0.353972i	−0.118718	+	0.0133885i
$700$	7.56543	−	17.9844i	0.285947	−	0.679748i
$701$			38.7525i			1.46366i	0.681486	+	0.731831i	$0.261334\pi$
$701$			38.7525i			1.46366i	−0.681486	+	0.731831i	$0.738666\pi$
$702$	32.9777	+	15.8690i	1.24466	+	0.598935i
$703$	0.973831	+	0.973831i	0.0367287	+	0.0367287i
$704$	−2.29656			−0.0865547
$705$	19.5414	−	37.5819i	0.735972	−	1.41541i
$706$	−6.57549			−0.247472
$707$	−32.2666	−	32.2666i	−1.21351	−	1.21351i
$708$	10.7150	−	13.4390i	0.402696	−	0.505069i
$709$			46.6007i			1.75013i	0.484009	+	0.875063i	$0.339180\pi$
$709$			46.6007i			1.75013i	−0.484009	+	0.875063i	$0.660820\pi$
$710$	−13.8682	+	2.71898i	−0.520466	+	0.102042i
$711$	−43.4081	+	9.91682i	−1.62793	+	0.371910i
$712$	−3.90530	+	3.90530i	−0.146357	+	0.146357i
$713$	0.0841220	−	0.0841220i	0.00315039	−	0.00315039i
$714$	−4.19947	−	37.2376i	−0.157161	−	1.39358i
$715$	35.4926	−	6.95861i	1.32735	−	0.260237i
$716$		−	4.69858i		−	0.175594i
$717$	−15.8712	−	12.6542i	−0.592721	−	0.472581i
$718$	−20.5434	−	20.5434i	−0.766675	−	0.766675i
$719$	7.22663			0.269508			0.134754	−	0.990879i	$-0.456976\pi$
$719$	7.22663			0.269508			0.134754	+	0.990879i	$0.456976\pi$
$720$	−2.40824	+	6.26102i	−0.0897497	+	0.233335i
$721$	−48.2671			−1.79756
$722$	2.31391	+	2.31391i	0.0861149	+	0.0861149i
$723$	8.37005	+	6.67351i	0.311285	+	0.248191i
$724$			0.531517i			0.0197537i
$725$	11.5644	+	28.3586i	0.429491	+	1.05321i
$726$	1.11139	+	9.85496i	0.0412476	+	0.365752i
$727$	24.7001	−	24.7001i	0.916076	−	0.916076i	−0.0806651	−	0.996741i	$-0.525704\pi$
$727$	24.7001	−	24.7001i	0.916076	−	0.916076i	0.996741	+	0.0806651i	$0.0257044\pi$
$728$	19.4338	−	19.4338i	0.720266	−	0.720266i
$729$	−16.8470	−	21.0993i	−0.623962	−	0.781454i
$730$	0.533956	−	0.794388i	0.0197626	−	0.0294016i
$731$			45.5575i			1.68501i
$732$	10.4863	−	13.1521i	0.387583	−	0.486115i
$733$	−5.85260	−	5.85260i	−0.216171	−	0.216171i	0.590712	−	0.806883i	$-0.298847\pi$
$733$	−5.85260	−	5.85260i	−0.216171	−	0.216171i	−0.806883	+	0.590712i	$0.798847\pi$
$734$	6.06739			0.223952
$735$	30.3840	−	9.59574i	1.12073	−	0.353944i
$736$	1.00000			0.0368605
$737$	1.77312	+	1.77312i	0.0653138	+	0.0653138i
$738$	−14.7409	−	9.25817i	−0.542619	−	0.340798i
$739$		−	5.34376i		−	0.196573i	−0.995158	−	0.0982866i	$-0.968664\pi$
$739$		−	5.34376i		−	0.196573i	0.995158	−	0.0982866i	$-0.0313362\pi$
$740$	−0.125544	−	0.640339i	−0.00461507	−	0.0235393i
$741$	−57.2091	+	6.45176i	−2.10163	+	0.237011i
$742$	11.9313	−	11.9313i	0.438011	−	0.438011i
$743$	−1.16720	+	1.16720i	−0.0428205	+	0.0428205i	−0.728193	−	0.685372i	$-0.759639\pi$
$743$	−1.16720	+	1.16720i	−0.0428205	+	0.0428205i	0.685372	+	0.728193i	$0.259639\pi$
$744$	−0.204758	+	0.0230916i	−0.00750679	+	0.000846578i
$745$	19.2162	+	12.9163i	0.704026	+	0.473218i
$746$		−	13.4478i		−	0.492358i
$747$	−35.9068	−	22.5516i	−1.31376	−	0.825121i
$748$	9.00367	+	9.00367i	0.329207	+	0.329207i
$749$	−48.5292			−1.77322
$750$	19.2825	+	1.78466i	0.704098	+	0.0651667i
$751$	−40.0709			−1.46221			−0.731104	−	0.682266i	$-0.760995\pi$
$751$	−40.0709			−1.46221			−0.731104	+	0.682266i	$0.760995\pi$
$752$	7.73361	+	7.73361i	0.282016	+	0.282016i
$753$	−22.4933	+	28.2115i	−0.819701	+	1.02808i
$754$			43.1405i			1.57108i
$755$	10.0351	+	6.74522i	0.365216	+	0.245484i
$756$	−19.1365	+	6.70264i	−0.695987	+	0.243773i
$757$	25.7687	−	25.7687i	0.936578	−	0.936578i	−0.0615277	−	0.998105i	$-0.519597\pi$
$757$	25.7687	−	25.7687i	0.936578	−	0.936578i	0.998105	+	0.0615277i	$0.0195973\pi$
$758$	−5.09969	+	5.09969i	−0.185229	+	0.185229i
$759$	0.445765	+	3.95270i	0.0161803	+	0.143474i
$760$	−2.03031	−	10.3557i	−0.0736471	−	0.375639i
$761$		−	9.26851i		−	0.335983i	−0.985788	−	0.167992i	$-0.946272\pi$
$761$		−	9.26851i		−	0.335983i	0.985788	−	0.167992i	$-0.0537281\pi$
$762$	−15.2451	−	12.1551i	−0.552272	−	0.440331i
$763$	20.2073	+	20.2073i	0.731553	+	0.731553i
$764$	−8.00136			−0.289479
$765$	33.9879	−	15.1049i	1.22884	−	0.546119i
$766$	−13.1462			−0.474992
$767$	−49.4208	−	49.4208i	−1.78448	−	1.78448i
$768$	−1.35428	−	1.07978i	−0.0488684	−	0.0389632i
$769$			24.5139i			0.883993i	0.897017	+	0.441996i	$0.145730\pi$
$769$			24.5139i			0.883993i	−0.897017	+	0.441996i	$0.854270\pi$
$770$	−11.1786	+	16.6309i	−0.402850	+	0.599337i
$771$	−3.66920	−	32.5356i	−0.132143	−	1.17174i
$772$	−9.64199	+	9.64199i	−0.347023	+	0.347023i
$773$	−3.24223	+	3.24223i	−0.116615	+	0.116615i	−0.763006	−	0.646391i	$-0.776277\pi$
$773$	−3.24223	+	3.24223i	−0.116615	+	0.116615i	0.646391	+	0.763006i	$0.276277\pi$
$774$	24.0312	−	5.49007i	0.863785	−	0.197336i
$775$	0.224610	+	0.550796i	0.00806822	+	0.0197852i
$776$		−	2.68290i		−	0.0963105i
$777$	1.22958	−	1.54217i	0.0441111	−	0.0553250i
$778$	−0.414165	−	0.414165i	−0.0148485	−	0.0148485i
$779$	27.3835			0.981115
$780$	24.2017	+	12.5842i	0.866562	+	0.450586i
$781$	14.5146			0.519372
$782$	−3.92051	−	3.92051i	−0.140197	−	0.140197i
$783$	13.8007	−	28.6797i	0.493197	−	1.02493i
$784$			8.22705i			0.293823i
$785$	8.98920	−	1.76241i	0.320838	−	0.0629030i
$786$	7.04024	−	0.793963i	0.251117	−	0.0283197i
$787$	17.5477	−	17.5477i	0.625509	−	0.625509i	−0.321426	−	0.946935i	$-0.604162\pi$
$787$	17.5477	−	17.5477i	0.625509	−	0.625509i	0.946935	+	0.321426i	$0.104162\pi$
$788$	1.48807	−	1.48807i	0.0530101	−	0.0530101i
$789$	0.910482	−	0.102680i	0.0324140	−	0.00365549i
$790$	−32.5681	+	6.38523i	−1.15872	+	0.227176i
$791$			41.9195i			1.49049i
$792$	3.66435	−	5.83439i	0.130207	−	0.207316i
$793$	−48.3656	−	48.3656i	−1.71751	−	1.71751i
$794$	21.4705			0.761960
$795$	14.8585	+	7.72598i	0.526977	+	0.274012i
$796$	9.98521			0.353916
$797$	−18.9143	−	18.9143i	−0.669977	−	0.669977i	0.287733	−	0.957711i	$-0.407098\pi$
$797$	−18.9143	−	18.9143i	−0.669977	−	0.669977i	−0.957711	+	0.287733i	$0.907098\pi$
$798$	19.8850	−	24.9402i	0.703922	−	0.882873i
$799$		−	60.6394i		−	2.14527i
$800$	−1.93877	+	4.60881i	−0.0685458	+	0.162946i
$801$	−3.69016	−	16.1526i	−0.130385	−	0.570725i
$802$	25.5449	−	25.5449i	0.902021	−	0.902021i
$803$	−0.695125	+	0.695125i	−0.0245304	+	0.0245304i
$804$	0.211937	+	1.87929i	0.00747443	+	0.0662773i
$805$	4.86757	−	7.24169i	0.171559	−	0.255236i
$806$			0.837897i			0.0295137i
$807$	39.7270	+	31.6747i	1.39846	+	1.11500i
$808$	8.26886	+	8.26886i	0.290897	+	0.290897i
$809$	−41.9673			−1.47549			−0.737745	−	0.675079i	$-0.764110\pi$
$809$	−41.9673			−1.47549			−0.737745	+	0.675079i	$0.764110\pi$
$810$	−12.0635	−	16.1081i	−0.423870	−	0.565981i
$811$	52.4673			1.84237			0.921187	−	0.389119i	$-0.127221\pi$
$811$	52.4673			1.84237			0.921187	+	0.389119i	$0.127221\pi$
$812$	−16.9010	−	16.9010i	−0.593108	−	0.593108i
$813$	−20.6867	−	16.4937i	−0.725513	−	0.578458i
$814$			0.670181i			0.0234898i
$815$	−5.76320	−	29.3954i	−0.201876	−	1.02968i
$816$	1.07618	+	9.54276i	0.0376740	+	0.334063i
$817$	−27.4202	+	27.4202i	−0.959311	+	0.959311i
$818$	8.84579	−	8.84579i	0.309286	−	0.309286i
$819$	18.3632	+	80.3799i	0.641663	+	2.80870i
$820$	−10.7681	−	7.23785i	−0.376037	−	0.252757i
$821$		−	10.9501i		−	0.382162i	−0.981574	−	0.191081i	$-0.938801\pi$
$821$		−	10.9501i		−	0.382162i	0.981574	−	0.191081i	$-0.0611993\pi$
$822$	2.13743	−	2.68081i	0.0745516	−	0.0935041i
$823$	26.5462	+	26.5462i	0.925341	+	0.925341i	0.997400	−	0.0720592i	$-0.0229570\pi$
$823$	26.5462	+	26.5462i	0.925341	+	0.925341i	−0.0720592	+	0.997400i	$0.522957\pi$
$824$	12.3692			0.430903
$825$	−19.0815	−	5.60891i	−0.664332	−	0.195277i
$826$	38.7228			1.34734
$827$	10.2837	+	10.2837i	0.357598	+	0.357598i	0.862927	−	0.505329i	$-0.168629\pi$
$827$	10.2837	+	10.2837i	0.357598	+	0.357598i	−0.505329	+	0.862927i	$0.668629\pi$
$828$	−1.59558	+	2.54049i	−0.0554504	+	0.0882883i
$829$		−	53.7277i		−	1.86604i	−0.359826	−	0.933019i	$-0.617164\pi$
$829$		−	53.7277i		−	1.86604i	0.359826	−	0.933019i	$-0.382836\pi$
$830$	−26.2295	−	17.6304i	−0.910439	−	0.611961i
$831$	−30.4896	+	3.43847i	−1.05767	+	0.119279i
$832$	−4.98025	+	4.98025i	−0.172659	+	0.172659i
$833$	32.2542	−	32.2542i	1.11754	−	1.11754i
$834$	−14.6957	+	1.65731i	−0.508871	+	0.0573879i
$835$	−6.48152	−	33.0592i	−0.224302	−	1.14406i
$836$			10.8383i			0.374850i
$837$	0.268045	−	0.557031i	0.00926498	−	0.0192538i
$838$	18.0437	+	18.0437i	0.623310	+	0.623310i
$839$	49.7271			1.71677			0.858385	−	0.513007i	$-0.171468\pi$
$839$	49.7271			1.71677			0.858385	+	0.513007i	$0.171468\pi$
$840$	−14.4115	+	4.55137i	−0.497243	+	0.157037i
$841$	8.51785			0.293719
$842$	−20.3430	−	20.3430i	−0.701067	−	0.701067i
$843$	−30.7728	+	38.5958i	−1.05987	+	1.32931i
$844$		−	13.6764i		−	0.470762i
$845$	45.6618	−	67.9330i	1.57081	−	2.33697i
$846$	−31.9868	+	7.30757i	−1.09973	+	0.251239i
$847$	−15.7991	+	15.7991i	−0.542862	+	0.542862i
$848$	−3.05759	+	3.05759i	−0.104998	+	0.104998i
$849$	1.32224	+	11.7245i	0.0453790	+	0.402385i
$850$	25.6699	−	10.4679i	0.880470	−	0.359048i
$851$		−	0.291820i		−	0.0100035i
$852$	8.55925	+	6.82436i	0.293235	+	0.233799i
$853$	−5.16107	−	5.16107i	−0.176712	−	0.176712i	0.613209	−	0.789921i	$-0.289878\pi$
$853$	−5.16107	−	5.16107i	−0.176712	−	0.176712i	−0.789921	+	0.613209i	$0.789878\pi$
$854$	37.8960			1.29677
$855$	29.5480	+	11.3653i	1.01052	+	0.388686i
$856$	12.4364			0.425068
$857$	25.8824	+	25.8824i	0.884124	+	0.884124i	0.993951	−	0.109826i	$-0.0350295\pi$
$857$	25.8824	+	25.8824i	0.884124	+	0.884124i	−0.109826	+	0.993951i	$0.535029\pi$
$858$	−21.9054	−	17.4654i	−0.747839	−	0.596258i
$859$			13.4931i			0.460379i	0.973146	+	0.230189i	$0.0739345\pi$
$859$			13.4931i			0.460379i	−0.973146	+	0.230189i	$0.926065\pi$
$860$	18.0300	−	3.53494i	0.614820	−	0.120540i
$861$	−4.39483	−	38.9699i	−0.149775	−	1.32809i
$862$	7.81871	−	7.81871i	0.266306	−	0.266306i
$863$	12.4757	−	12.4757i	0.424677	−	0.424677i	−0.462134	−	0.886810i	$-0.652916\pi$
$863$	12.4757	−	12.4757i	0.424677	−	0.424677i	0.886810	+	0.462134i	$0.152916\pi$
$864$	4.90404	−	1.71766i	0.166839	−	0.0584361i
$865$	−4.47362	+	0.877090i	−0.152108	+	0.0298219i
$866$		−	9.32577i		−	0.316903i
$867$	14.8371	−	18.6089i	0.503893	−	0.631992i
$868$	−0.328260	−	0.328260i	−0.0111419	−	0.0111419i
$869$	34.0859			1.15628
$870$	10.9440	−	21.0475i	0.371038	−	0.713576i
$871$	7.69029			0.260576
$872$	−5.17846	−	5.17846i	−0.175365	−	0.175365i
$873$	6.81589	+	4.28079i	0.230683	+	0.144883i
$874$		−	4.71936i		−	0.159635i
$875$	23.9385	+	36.4737i	0.809269	+	1.23304i
$876$	−0.736745	+	0.0830864i	−0.0248923	+	0.00280723i
$877$	3.16095	−	3.16095i	0.106738	−	0.106738i	−0.651721	−	0.758459i	$-0.725953\pi$
$877$	3.16095	−	3.16095i	0.106738	−	0.106738i	0.758459	+	0.651721i	$0.225953\pi$
$878$	4.24907	−	4.24907i	0.143399	−	0.143399i
$879$	−39.0107	+	4.39943i	−1.31580	+	0.148389i
$880$	2.86471	−	4.26196i	0.0965695	−	0.143670i
$881$			0.944479i			0.0318203i	0.999873	+	0.0159102i	$0.00506458\pi$
$881$			0.944479i			0.0318203i	−0.999873	+	0.0159102i	$0.994935\pi$
$882$	−20.9008	−	13.1269i	−0.703765	−	0.442007i
$883$	19.2808	+	19.2808i	0.648850	+	0.648850i	0.952715	−	0.303865i	$-0.0982773\pi$
$883$	19.2808	+	19.2808i	0.648850	+	0.648850i	−0.303865	+	0.952715i	$0.598277\pi$
$884$	39.0502			1.31340
$885$	11.5743	+	36.6488i	0.389065	+	1.23194i
$886$	−32.7197			−1.09924
$887$	1.81183	+	1.81183i	0.0608352	+	0.0608352i	0.736870	−	0.676035i	$-0.236303\pi$
$887$	1.81183	+	1.81183i	0.0608352	+	0.0608352i	−0.676035	+	0.736870i	$0.736303\pi$
$888$	−0.315101	+	0.395206i	−0.0105741	+	0.0132623i
$889$		−	43.9268i		−	1.47326i
$890$	−2.37601	−	12.1189i	−0.0796441	−	0.406227i
$891$	8.97545	+	18.6185i	0.300689	+	0.623744i
$892$	7.47810	−	7.47810i	0.250385	−	0.250385i
$893$	36.4977	−	36.4977i	1.22135	−	1.22135i
$894$	−2.00985	−	17.8218i	−0.0672195	−	0.596050i
$895$	8.71964	+	5.86099i	0.291465	+	0.195911i
$896$		−	3.90218i		−	0.130363i
$897$	9.53838	+	7.60503i	0.318477	+	0.253925i
$898$	−2.78344	−	2.78344i	−0.0928846	−	0.0928846i
$899$	0.728691			0.0243032
$900$	−8.61520	−	12.2792i	−0.287173	−	0.409306i
$901$	23.9747			0.798711
$902$	9.42253	+	9.42253i	0.313736	+	0.313736i
$903$	43.4229	+	34.6215i	1.44502	+	1.15213i
$904$		−	10.7426i		−	0.357293i
$905$	−0.986391	−	0.663012i	−0.0327888	−	0.0220393i
$906$	−1.04959	−	9.30697i	−0.0348704	−	0.309203i
$907$	34.8575	−	34.8575i	1.15742	−	1.15742i	0.172396	−	0.985028i	$-0.444849\pi$
$907$	34.8575	−	34.8575i	1.15742	−	1.15742i	0.985028	−	0.172396i	$-0.0551510\pi$
$908$	−12.5076	+	12.5076i	−0.415079	+	0.415079i
$909$	−34.2006	+	7.81333i	−1.13436	+	0.259152i
$910$	11.8237	+	60.3071i	0.391951	+	1.99916i
$911$			14.7929i			0.490112i	0.969509	+	0.245056i	$0.0788064\pi$
$911$			14.7929i			0.490112i	−0.969509	+	0.245056i	$0.921194\pi$
$912$	−5.09587	+	6.39134i	−0.168741	+	0.211638i
$913$	22.9520	+	22.9520i	0.759600	+	0.759600i
$914$	14.3084			0.473279
$915$	11.3271	+	35.8663i	0.374464	+	1.18570i
$916$	10.3963			0.343505
$917$	11.2866	+	11.2866i	0.372717	+	0.372717i
$918$	−25.9605	−	12.4922i	−0.856823	−	0.412305i
$919$		−	29.3405i		−	0.967853i	−0.875109	−	0.483926i	$-0.839210\pi$
$919$		−	29.3405i		−	0.967853i	0.875109	−	0.483926i	$-0.160790\pi$
$920$	−1.24740	+	1.85580i	−0.0411254	+	0.0611840i
$921$	30.9674	−	3.49235i	1.02041	−	0.115077i
$922$	−18.0785	+	18.0785i	−0.595385	+	0.595385i
$923$	31.4759	−	31.4759i	1.03604	−	1.03604i
$924$	15.4241	−	1.73946i	0.507417	−	0.0572240i
$925$	1.34495	+	0.565772i	0.0442215	+	0.0186025i
$926$			18.2035i			0.598204i
$927$	−19.7362	+	31.4240i	−0.648221	+	1.03210i
$928$	4.33116	+	4.33116i	0.142177	+	0.142177i
$929$	−9.92612			−0.325666			−0.162833	−	0.986654i	$-0.552063\pi$
$929$	−9.92612			−0.325666			−0.162833	+	0.986654i	$0.552063\pi$
$930$	0.212561	−	0.408795i	0.00697015	−	0.0134049i
$931$	38.8264			1.27248
$932$	1.28951	+	1.28951i	0.0422394	+	0.0422394i
$933$	1.82315	−	2.28663i	0.0596873	−	0.0748610i
$934$			12.7262i			0.416415i
$935$	−27.9402	+	5.47790i	−0.913742	+	0.179146i
$936$	−4.70588	−	20.5987i	−0.153817	−	0.673289i
$937$	−29.5880	+	29.5880i	−0.966598	+	0.966598i	−0.999460	−	0.0328624i	$-0.989538\pi$
$937$	−29.5880	+	29.5880i	−0.966598	+	0.966598i	0.0328624	+	0.999460i	$0.489538\pi$
$938$	−3.01280	+	3.01280i	−0.0983713	+	0.0983713i
$939$	−5.08384	−	45.0795i	−0.165905	−	1.47111i
$940$	−23.9989	+	4.70518i	−0.782759	+	0.153466i
$941$		−	8.15267i		−	0.265770i	−0.991131	−	0.132885i	$-0.957576\pi$
$941$		−	8.15267i		−	0.265770i	0.991131	−	0.132885i	$-0.0424240\pi$
$942$	−5.54799	−	4.42346i	−0.180763	−	0.144124i
$943$	−4.10289	−	4.10289i	−0.133609	−	0.133609i
$944$	−9.92337			−0.322978
$945$	11.4320	−	43.8744i	0.371883	−	1.42723i
$946$	−18.8703			−0.613527
$947$	5.31126	+	5.31126i	0.172593	+	0.172593i	0.788118	−	0.615525i	$-0.211056\pi$
$947$	5.31126	+	5.31126i	0.172593	+	0.172593i	−0.615525	+	0.788118i	$0.711056\pi$
$948$	20.1005	+	16.0263i	0.652832	+	0.520509i
$949$			3.01486i			0.0978664i
$950$	21.7507	+	9.14975i	0.705685	+	0.296857i
$951$	−3.98709	−	35.3544i	−0.129290	−	1.14644i
$952$	−15.2986	+	15.2986i	−0.495829	+	0.495829i
$953$	−35.3013	+	35.3013i	−1.14352	+	1.14352i	−0.155722	+	0.987801i	$0.549770\pi$
$953$	−35.3013	+	35.3013i	−1.14352	+	1.14352i	−0.987801	+	0.155722i	$0.950230\pi$
$954$	−2.88915	−	12.6464i	−0.0935397	−	0.409444i
$955$	9.98086	−	14.8489i	0.322973	−	0.480500i
$956$			11.7193i			0.379029i
$957$	−15.1891	+	19.0504i	−0.490993	+	0.615813i
$958$	9.30664	+	9.30664i	0.300684	+	0.300684i
$959$	7.72442			0.249434
$960$	3.69318	−	1.16637i	0.119197	−	0.0376443i
$961$	−30.9858			−0.999543
$962$	1.45334	+	1.45334i	0.0468575	+	0.0468575i
$963$	−19.8433	+	31.5946i	−0.639443	+	1.01812i
$964$		−	6.18044i		−	0.199059i
$965$	−5.86626	−	29.9210i	−0.188841	−	0.963191i
$966$	−6.71621	+	0.757420i	−0.216090	+	0.0243696i
$967$	−35.9105	+	35.9105i	−1.15480	+	1.15480i	−0.169228	+	0.985577i	$0.554127\pi$
$967$	−35.9105	+	35.9105i	−1.15480	+	1.15480i	−0.985577	+	0.169228i	$0.945873\pi$
$968$	4.04877	−	4.04877i	0.130133	−	0.130133i
$969$	45.0357	−	5.07890i	1.44676	−	0.163158i
$970$	4.97893	+	3.34664i	0.159864	+	0.107454i
$971$			1.64414i			0.0527629i	0.999652	+	0.0263815i	$0.00839845\pi$
$971$			1.64414i			0.0527629i	−0.999652	+	0.0263815i	$0.991602\pi$
$972$	−3.46110	+	15.1994i	−0.111015	+	0.487520i
$973$	−23.5596	−	23.5596i	−0.755285	−	0.755285i
$974$	32.2985			1.03491
$975$	−53.5429	+	29.2162i	−1.71475	+	0.935668i
$976$	−9.71148			−0.310857
$977$	−11.1434	−	11.1434i	−0.356509	−	0.356509i	0.506016	−	0.862524i	$-0.331118\pi$
$977$	−11.1434	−	11.1434i	−0.356509	−	0.356509i	−0.862524	+	0.506016i	$0.831118\pi$
$978$	−14.4650	+	18.1423i	−0.462541	+	0.580128i
$979$			12.6837i			0.405373i
$980$	−15.2678	−	10.2624i	−0.487711	−	0.327820i
$981$	21.4185	−	4.89318i	0.683840	−	0.156227i
$982$	−23.8463	+	23.8463i	−0.760966	+	0.760966i
$983$	−12.3382	+	12.3382i	−0.393527	+	0.393527i	−0.875943	−	0.482415i	$-0.839760\pi$
$983$	−12.3382	+	12.3382i	−0.393527	+	0.393527i	0.482415	+	0.875943i	$0.339760\pi$
$984$	1.12625	+	9.98669i	0.0359035	+	0.318364i
$985$	0.905349	+	4.61776i	0.0288468	+	0.147134i
$986$		−	33.9607i		−	1.08153i
$987$	−57.7982	−	46.0830i	−1.83974	−	1.46684i
$988$	23.5036	+	23.5036i	0.747749	+	0.747749i
$989$	8.21679			0.261279
$990$	6.25658	+	14.0781i	0.198847	+	0.447431i
$991$	−47.3048			−1.50269			−0.751343	−	0.659912i	$-0.770594\pi$
$991$	−47.3048			−1.50269			−0.751343	+	0.659912i	$0.770594\pi$
$992$	0.0841220	+	0.0841220i	0.00267088	+	0.00267088i
$993$	−19.5488	−	15.5864i	−0.620363	−	0.494621i
$994$			24.6624i			0.782243i
$995$	−12.4555	+	18.5306i	−0.394866	+	0.587459i
$996$	2.74339	+	24.3262i	0.0869276	+	0.770806i
$997$	−24.0238	+	24.0238i	−0.760842	+	0.760842i	−0.976475	−	0.215633i	$-0.930819\pi$
$997$	−24.0238	+	24.0238i	−0.760842	+	0.760842i	0.215633	+	0.976475i	$0.430819\pi$
$998$	15.5952	−	15.5952i	0.493657	−	0.493657i
$999$	−0.501249	−	1.43110i	−0.0158588	−	0.0452780i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.i.e.323.2	yes	32
3.2	odd	2	inner	690.2.i.e.323.11	yes	32
5.2	odd	4	inner	690.2.i.e.47.11	yes	32
15.2	even	4	inner	690.2.i.e.47.2	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.i.e.47.2	✓	32	15.2	even	4	inner
690.2.i.e.47.11	yes	32	5.2	odd	4	inner
690.2.i.e.323.2	yes	32	1.1	even	1	trivial
690.2.i.e.323.11	yes	32	3.2	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.35428 - 1.07978i) q^{3} +1.00000i q^{4} +(-1.85580 - 1.24740i) q^{5} +(0.194102 + 1.72114i) q^{6} +(-2.75926 + 2.75926i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.668152 + 2.92465i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.35428 - 1.07978i) q^{3} +1.00000i q^{4} +(-1.85580 - 1.24740i) q^{5} +(0.194102 + 1.72114i) q^{6} +(-2.75926 + 2.75926i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.668152 + 2.92465i) q^{9} +(0.430209 + 2.19429i) q^{10} -2.29656i q^{11} +(1.07978 - 1.35428i) q^{12} +(-4.98025 - 4.98025i) q^{13} +3.90218 q^{14} +(1.16637 + 3.69318i) q^{15} -1.00000 q^{16} +(3.92051 + 3.92051i) q^{17} +(1.59558 - 2.54049i) q^{18} +4.71936i q^{19} +(1.24740 - 1.85580i) q^{20} +(6.71621 - 0.757420i) q^{21} +(-1.62391 + 1.62391i) q^{22} +(0.707107 - 0.707107i) q^{23} +(-1.72114 + 0.194102i) q^{24} +(1.88801 + 4.62984i) q^{25} +7.04313i q^{26} +(2.25311 - 4.68225i) q^{27} +(-2.75926 - 2.75926i) q^{28} +6.12518 q^{29} +(1.78673 - 3.43622i) q^{30} +0.118966 q^{31} +(0.707107 + 0.707107i) q^{32} +(-2.47977 + 3.11018i) q^{33} -5.54444i q^{34} +(8.56254 - 1.67875i) q^{35} +(-2.92465 + 0.668152i) q^{36} +(0.206348 - 0.206348i) q^{37} +(3.33709 - 3.33709i) q^{38} +(1.36708 + 12.1222i) q^{39} +(-2.19429 + 0.430209i) q^{40} -5.80237i q^{41} +(-5.28465 - 4.21350i) q^{42} +(5.81015 + 5.81015i) q^{43} +2.29656 q^{44} +(2.40824 - 6.26102i) q^{45} -1.00000 q^{46} +(-7.73361 - 7.73361i) q^{47} +(1.35428 + 1.07978i) q^{48} -8.22705i q^{49} +(1.93877 - 4.60881i) q^{50} +(-1.07618 - 9.54276i) q^{51} +(4.98025 - 4.98025i) q^{52} +(3.05759 - 3.05759i) q^{53} +(-4.90404 + 1.71766i) q^{54} +(-2.86471 + 4.26196i) q^{55} +3.90218i q^{56} +(5.09587 - 6.39134i) q^{57} +(-4.33116 - 4.33116i) q^{58} +9.92337 q^{59} +(-3.69318 + 1.16637i) q^{60} +9.71148 q^{61} +(-0.0841220 - 0.0841220i) q^{62} +(-9.91348 - 6.22627i) q^{63} -1.00000i q^{64} +(3.03002 + 15.4547i) q^{65} +(3.95270 - 0.445765i) q^{66} +(-0.772079 + 0.772079i) q^{67} +(-3.92051 + 3.92051i) q^{68} +(-1.72114 + 0.194102i) q^{69} +(-7.24169 - 4.86757i) q^{70} +6.32014i q^{71} +(2.54049 + 1.59558i) q^{72} +(-0.302682 - 0.302682i) q^{73} -0.291820 q^{74} +(2.44232 - 8.30874i) q^{75} -4.71936 q^{76} +(6.33680 + 6.33680i) q^{77} +(7.60503 - 9.53838i) q^{78} +14.8422i q^{79} +(1.85580 + 1.24740i) q^{80} +(-8.10715 + 3.90822i) q^{81} +(-4.10289 + 4.10289i) q^{82} +(-9.99409 + 9.99409i) q^{83} +(0.757420 + 6.71621i) q^{84} +(-2.38527 - 12.1661i) q^{85} -8.21679i q^{86} +(-8.29522 - 6.61385i) q^{87} +(-1.62391 - 1.62391i) q^{88} -5.52293 q^{89} +(-6.13009 + 2.72433i) q^{90} +27.4836 q^{91} +(0.707107 + 0.707107i) q^{92} +(-0.161114 - 0.128458i) q^{93} +10.9370i q^{94} +(5.88691 - 8.75820i) q^{95} +(-0.194102 - 1.72114i) q^{96} +(1.89710 - 1.89710i) q^{97} +(-5.81740 + 5.81740i) q^{98} +(6.71662 - 1.53445i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{3} - 4 q^{6} - 8 q^{7}+O(q^{10}) \) 32 * q + 4 * q^3 - 4 * q^6 - 8 * q^7	\( 32 q + 4 q^{3} - 4 q^{6} - 8 q^{7} - 8 q^{10} - 4 q^{12} - 4 q^{15} - 32 q^{16} + 8 q^{18} - 32 q^{21} - 8 q^{22} + 4 q^{27} - 8 q^{28} + 20 q^{30} - 24 q^{31} + 20 q^{36} - 32 q^{37} - 16 q^{40} + 8 q^{42} + 144 q^{43} + 36 q^{45} - 32 q^{46} - 4 q^{48} + 12 q^{51} - 64 q^{55} + 52 q^{57} + 16 q^{58} + 4 q^{60} - 24 q^{61} - 116 q^{63} + 12 q^{66} - 16 q^{67} - 80 q^{70} - 8 q^{72} + 40 q^{73} + 44 q^{75} + 24 q^{76} - 36 q^{78} - 108 q^{81} - 32 q^{82} - 80 q^{85} + 68 q^{87} - 8 q^{88} + 16 q^{90} + 120 q^{91} + 12 q^{93} + 4 q^{96} - 8 q^{97}+O(q^{100}) \) 32 * q + 4 * q^3 - 4 * q^6 - 8 * q^7 - 8 * q^10 - 4 * q^12 - 4 * q^15 - 32 * q^16 + 8 * q^18 - 32 * q^21 - 8 * q^22 + 4 * q^27 - 8 * q^28 + 20 * q^30 - 24 * q^31 + 20 * q^36 - 32 * q^37 - 16 * q^40 + 8 * q^42 + 144 * q^43 + 36 * q^45 - 32 * q^46 - 4 * q^48 + 12 * q^51 - 64 * q^55 + 52 * q^57 + 16 * q^58 + 4 * q^60 - 24 * q^61 - 116 * q^63 + 12 * q^66 - 16 * q^67 - 80 * q^70 - 8 * q^72 + 40 * q^73 + 44 * q^75 + 24 * q^76 - 36 * q^78 - 108 * q^81 - 32 * q^82 - 80 * q^85 + 68 * q^87 - 8 * q^88 + 16 * q^90 + 120 * q^91 + 12 * q^93 + 4 * q^96 - 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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