LMFDB - Embedded newform 690.2.i.e.323.11

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			323.11
Character	$\chi$	$=$	690.323
Dual form			690.2.i.e.47.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-1.07978 - 1.35428i) q^{3} +1.00000i q^{4} +(1.85580 + 1.24740i) q^{5} +(0.194102 - 1.72114i) q^{6} +(-2.75926 + 2.75926i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.668152 + 2.92465i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-1.07978 - 1.35428i) 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} +(1.35428 - 1.07978i) q^{12} +(-4.98025 - 4.98025i) q^{13} -3.90218 q^{14} +(-0.314534 - 3.86019i) q^{15} -1.00000 q^{16} +(-3.92051 - 3.92051i) q^{17} +(-2.54049 + 1.59558i) 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} +(4.68225 - 2.25311i) q^{27} +(-2.75926 - 2.75926i) q^{28} -6.12518 q^{29} +(2.50716 - 2.95198i) q^{30} +0.118966 q^{31} +(-0.707107 - 0.707107i) q^{32} +(3.11018 - 2.47977i) 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} +(4.21350 + 5.28465i) q^{42} +(5.81015 + 5.81015i) q^{43} -2.29656 q^{44} +(-4.88815 + 4.59412i) q^{45} -1.00000 q^{46} +(7.73361 + 7.73361i) q^{47} +(1.07978 + 1.35428i) 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} +(6.39134 - 5.09587i) q^{57} +(-4.33116 - 4.33116i) q^{58} -9.92337 q^{59} +(3.86019 - 0.314534i) q^{60} +9.71148 q^{61} +(0.0841220 + 0.0841220i) q^{62} +(-6.22627 - 9.91348i) 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} +(-1.59558 - 2.54049i) q^{72} +(-0.302682 - 0.302682i) q^{73} +0.291820 q^{74} +(4.23147 - 7.55610i) q^{75} -4.71936 q^{76} +(-6.33680 - 6.33680i) q^{77} +(-9.53838 + 7.60503i) 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} +(6.61385 + 8.29522i) q^{87} +(-1.62391 - 1.62391i) q^{88} +5.52293 q^{89} +(-6.70498 - 0.207912i) q^{90} +27.4836 q^{91} +(-0.707107 - 0.707107i) q^{92} +(-0.128458 - 0.161114i) 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
$3$	−1.07978	−	1.35428i	−0.623411	−	0.781894i
$3$	−1.07978	−	1.35428i	−0.623411	−	0.781894i
$4$			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	$0.112535\pi$
$11$			2.29656i			0.692438i	−0.938154	+	0.346219i	$0.887465\pi$
$12$	1.35428	−	1.07978i	0.390947	−	0.311706i
$13$	−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
$15$	−0.314534	−	3.86019i	−0.0812123	−	0.996697i
$16$	−1.00000			−0.250000
$17$	−3.92051	−	3.92051i	−0.950864	−	0.950864i	0.0479844	−	0.998848i	$-0.484720\pi$
$17$	−3.92051	−	3.92051i	−0.950864	−	0.950864i	−0.998848	+	0.0479844i	$0.984720\pi$
$18$	−2.54049	+	1.59558i	−0.598800	+	0.376083i
$19$			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
$27$	4.68225	−	2.25311i	0.901100	−	0.433611i
$28$	−2.75926	−	2.75926i	−0.521451	−	0.521451i
$29$	−6.12518			−1.13742			−0.568709	−	0.822539i	$-0.692557\pi$
$29$	−6.12518			−1.13742			−0.568709	+	0.822539i	$0.692557\pi$
$30$	2.50716	−	2.95198i	0.457742	−	0.538955i
$31$	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
$33$	3.11018	−	2.47977i	0.541413	−	0.431673i
$34$		−	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	$0.149678\pi$
$41$			5.80237i			0.906178i	−0.891465	+	0.453089i	$0.850322\pi$
$42$	4.21350	+	5.28465i	0.650157	+	0.815440i
$43$	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
$45$	−4.88815	+	4.59412i	−0.728683	+	0.684851i
$46$	−1.00000			−0.147442
$47$	7.73361	+	7.73361i	1.12806	+	1.12806i	0.990492	+	0.137572i	$0.0439297\pi$
$47$	7.73361	+	7.73361i	1.12806	+	1.12806i	0.137572	+	0.990492i	$0.456070\pi$
$48$	1.07978	+	1.35428i	0.155853	+	0.195474i
$49$		−	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	−0.885201	−	0.465209i	$-0.845979\pi$
$53$	−3.05759	+	3.05759i	−0.419993	+	0.419993i	0.465209	+	0.885201i	$0.345979\pi$
$54$	4.90404	+	1.71766i	0.667356	+	0.233744i
$55$	−2.86471	+	4.26196i	−0.386278	+	0.574682i
$56$		−	3.90218i		−	0.521451i
$57$	6.39134	−	5.09587i	0.846554	−	0.674964i
$58$	−4.33116	−	4.33116i	−0.568709	−	0.568709i
$59$	−9.92337			−1.29191			−0.645956	−	0.763374i	$-0.723541\pi$
$59$	−9.92337			−1.29191			−0.645956	+	0.763374i	$0.723541\pi$
$60$	3.86019	−	0.314534i	0.498348	−	0.0406062i
$61$	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
$63$	−6.22627	−	9.91348i	−0.784436	−	1.24898i
$64$		−	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	$-0.877632\pi$
$71$		−	6.32014i		−	0.750063i	0.927012	−	0.375031i	$-0.122368\pi$
$72$	−1.59558	−	2.54049i	−0.188041	−	0.299400i
$73$	−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
$75$	4.23147	−	7.55610i	0.488608	−	0.872503i
$76$	−4.71936			−0.541348
$77$	−6.33680	−	6.33680i	−0.722145	−	0.722145i
$78$	−9.53838	+	7.60503i	−1.08001	+	0.861100i
$79$			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	$-0.467401\pi$
$83$	9.99409	−	9.99409i	1.09699	−	1.09699i	0.994760	−	0.102234i	$-0.0325989\pi$
$84$	−0.757420	+	6.71621i	−0.0826413	+	0.732798i
$85$	−2.38527	−	12.1661i	−0.258718	−	1.31960i
$86$			8.21679i			0.886040i
$87$	6.61385	+	8.29522i	0.709079	+	0.889340i
$88$	−1.62391	−	1.62391i	−0.173109	−	0.173109i
$89$	5.52293			0.585429			0.292715	−	0.956200i	$-0.405441\pi$
$89$	5.52293			0.585429			0.292715	+	0.956200i	$0.405441\pi$
$90$	−6.70498	−	0.207912i	−0.706767	−	0.0219158i
$91$	27.4836			2.88107
$92$	−0.707107	−	0.707107i	−0.0737210	−	0.0737210i
$93$	−0.128458	−	0.161114i	−0.0133204	−	0.0167067i
$94$			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	$-0.802351\pi$
$101$		−	11.6939i		−	1.16359i	0.813336	−	0.581795i	$-0.197649\pi$
$102$	−7.50873	+	5.98677i	−0.743475	+	0.592779i
$103$	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
$105$	11.5192	+	9.78339i	1.12415	+	0.954761i
$106$	−4.32409			−0.419993
$107$	−8.79387	−	8.79387i	−0.850135	−	0.850135i	0.140014	−	0.990149i	$-0.455285\pi$
$107$	−8.79387	−	8.79387i	−0.850135	−	0.850135i	−0.990149	+	0.140014i	$0.955285\pi$
$108$	2.25311	+	4.68225i	0.216806	+	0.450550i
$109$		−	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	−0.967491	−	0.252905i	$-0.918614\pi$
$113$	−7.59615	+	7.59615i	−0.714586	+	0.714586i	0.252905	+	0.967491i	$0.418614\pi$
$114$	8.12268	+	0.916035i	0.760759	+	0.0857946i
$115$	−2.19429	+	0.430209i	−0.204619	+	0.0401172i
$116$		−	6.12518i		−	0.568709i
$117$	17.8930	−	11.2379i	1.65421	−	1.03895i
$118$	−7.01688	−	7.01688i	−0.645956	−	0.645956i
$119$	21.6354			1.98332
$120$	2.95198	+	2.50716i	0.269477	+	0.228871i
$121$	5.72583			0.520530
$122$	6.86706	+	6.86706i	0.621714	+	0.621714i
$123$	7.85804	−	6.26528i	0.708535	−	0.564921i
$124$			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	$0.0571866\pi$
$131$			4.09045i			0.357385i	−0.983905	+	0.178692i	$0.942813\pi$
$132$	2.47977	+	3.11018i	0.215837	+	0.270707i
$133$	−13.0220	−	13.0220i	−1.12915	−	1.12915i
$134$	−1.09188			−0.0943245
$135$	11.4999	+	1.65929i	0.989750	+	0.142809i
$136$	5.54444			0.475432
$137$	1.39973	+	1.39973i	0.119587	+	0.119587i	0.764367	−	0.644781i	$-0.223051\pi$
$137$	1.39973	+	1.39973i	0.119587	+	0.119587i	−0.644781	+	0.764367i	$0.723051\pi$
$138$	1.07978	+	1.35428i	0.0919169	+	0.115284i
$139$			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
$147$	−11.1417	+	8.88340i	−0.918955	+	0.732690i
$148$	0.206348	+	0.206348i	0.0169617	+	0.0169617i
$149$	10.3546			0.848285			0.424142	−	0.905596i	$-0.360576\pi$
$149$	10.3546			0.848285			0.424142	+	0.905596i	$0.360576\pi$
$150$	8.33507	−	2.35087i	0.680556	−	0.191947i
$151$	−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
$153$	14.0856	−	8.84662i	1.13875	−	0.715207i
$154$		−	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
$162$	−2.96909	−	8.49615i	−0.233274	−	0.667520i
$163$	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
$165$	8.86514	−	0.722345i	0.690150	−	0.0562345i
$166$	14.1338			1.09699
$167$	−10.6533	−	10.6533i	−0.824375	−	0.824375i	0.162357	−	0.986732i	$-0.448090\pi$
$167$	−10.6533	−	10.6533i	−0.824375	−	0.824375i	−0.986732	+	0.162357i	$0.948090\pi$
$168$	−5.28465	+	4.21350i	−0.407720	+	0.325079i
$169$			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	−0.759782	−	0.650178i	$-0.774694\pi$
$173$	−1.44162	+	1.44162i	−0.109604	+	0.109604i	0.650178	+	0.759782i	$0.274694\pi$
$174$	−1.18891	+	10.5423i	−0.0901308	+	0.799210i
$175$	−17.9844	−	7.56543i	−1.35950	−	0.571893i
$176$		−	2.29656i		−	0.173109i
$177$	10.7150	+	13.4390i	0.805392	+	1.01014i
$178$	3.90530	+	3.90530i	0.292715	+	0.292715i
$179$	4.69858			0.351188			0.175594	−	0.984463i	$-0.443815\pi$
$179$	4.69858			0.351188			0.175594	+	0.984463i	$0.443815\pi$
$180$	−4.59412	−	4.88815i	−0.342426	−	0.364341i
$181$	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
$183$	−10.4863	−	13.1521i	−0.775167	−	0.972229i
$184$		−	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	$-0.906518\pi$
$191$		−	8.00136i		−	0.578958i	0.957184	−	0.289479i	$-0.0934820\pi$
$192$	−1.35428	+	1.07978i	−0.0977368	+	0.0779264i
$193$	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
$195$	−17.6582	+	20.7912i	−1.26453	+	1.48889i
$196$	8.22705			0.587646
$197$	1.48807	+	1.48807i	0.106020	+	0.106020i	0.758127	−	0.652107i	$-0.226115\pi$
$197$	1.48807	+	1.48807i	0.106020	+	0.106020i	−0.652107	+	0.758127i	$0.726115\pi$
$198$	−3.66435	−	5.83439i	−0.260414	−	0.414632i
$199$		−	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
$207$	−1.59558	−	2.54049i	−0.110901	−	0.176577i
$208$	4.98025	+	4.98025i	0.345318	+	0.345318i
$209$	−10.8383			−0.749699
$210$	1.22737	+	15.0632i	0.0846966	+	1.03946i
$211$	−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
$213$	−8.55925	+	6.82436i	−0.586470	+	0.467597i
$214$		−	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
$222$	−0.315101	−	0.395206i	−0.0211482	−	0.0265245i
$223$	−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
$225$	−14.8021	+	2.42832i	−0.986809	+	0.161888i
$226$	−10.7426			−0.714586
$227$	−12.5076	−	12.5076i	−0.830158	−	0.830158i	0.157380	−	0.987538i	$-0.449695\pi$
$227$	−12.5076	−	12.5076i	−0.830158	−	0.830158i	−0.987538	+	0.157380i	$0.949695\pi$
$228$	5.09587	+	6.39134i	0.337482	+	0.423277i
$229$		−	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	−0.748083	−	0.663605i	$-0.769026\pi$
$233$	−1.28951	+	1.28951i	−0.0844787	+	0.0844787i	0.663605	+	0.748083i	$0.269026\pi$
$234$	20.5987	+	4.70588i	1.34658	+	0.307633i
$235$	4.70518	+	23.9989i	0.306932	+	1.56552i
$236$		−	9.92337i		−	0.645956i
$237$	20.1005	−	16.0263i	1.30566	−	1.04102i
$238$	15.2986	+	15.2986i	0.991658	+	0.991658i
$239$	−11.7193			−0.758057			−0.379029	−	0.925385i	$-0.623742\pi$
$239$	−11.7193			−0.758057			−0.379029	+	0.925385i	$0.623742\pi$
$240$	0.314534	+	3.86019i	0.0203031	+	0.249174i
$241$	−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
$243$	3.46110	+	15.1994i	0.222030	+	0.975040i
$244$			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	$0.228357\pi$
$251$			20.8314i			1.31486i	−0.753514	+	0.657432i	$0.771643\pi$
$252$	9.91348	−	6.22627i	0.624490	−	0.392218i
$253$	−1.62391	−	1.62391i	−0.102094	−	0.102094i
$254$	−11.2570			−0.706326
$255$	−13.9008	+	16.3671i	−0.870501	+	1.02494i
$256$	1.00000			0.0625000
$257$	−13.3668	−	13.3668i	−0.833798	−	0.833798i	0.154236	−	0.988034i	$-0.450708\pi$
$257$	−13.3668	−	13.3668i	−0.833798	−	0.833798i	−0.988034	+	0.154236i	$0.950708\pi$
$258$	11.1278	−	8.87232i	0.692789	−	0.552367i
$259$			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	−0.695480	−	0.718545i	$-0.744808\pi$
$263$	0.374059	−	0.374059i	0.0230655	−	0.0230655i	0.718545	+	0.695480i	$0.244808\pi$
$264$	−0.445765	+	3.95270i	−0.0274349	+	0.243272i
$265$	−9.48832	+	1.86026i	−0.582863	+	0.114275i
$266$		−	18.4158i		−	1.12915i
$267$	−5.96355	−	7.47960i	−0.364963	−	0.457744i
$268$	−0.772079	−	0.772079i	−0.0471622	−	0.0471622i
$269$	29.3344			1.78855			0.894275	−	0.447517i	$-0.147692\pi$
$269$	29.3344			1.78855			0.894275	+	0.447517i	$0.147692\pi$
$270$	6.95833	+	9.30493i	0.423471	+	0.566280i
$271$	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
$273$	−29.6762	−	37.2205i	−1.79609	−	2.25269i
$274$			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	$0.323433\pi$
$281$			28.4991i			1.70011i	−0.526690	+	0.850057i	$0.676567\pi$
$282$	14.8117	−	11.8095i	0.882026	−	0.703247i
$283$	−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
$285$	18.2176	−	1.48440i	1.07912	−	0.0879282i
$286$	16.1750			0.956445
$287$	−16.0103	−	16.0103i	−0.945055	−	0.945055i
$288$	2.54049	−	1.59558i	0.149700	−	0.0940207i
$289$			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	−0.998090	−	0.0617818i	$-0.980322\pi$
$293$	−16.0270	+	16.0270i	−0.936308	+	0.936308i	0.0617818	+	0.998090i	$0.480322\pi$
$294$	−14.1599	−	1.59688i	−0.825822	−	0.0931321i
$295$	−18.4158	−	12.3784i	−1.07221	−	0.720696i
$296$			0.291820i			0.0169617i
$297$	5.17440	+	10.7531i	0.300249	+	0.623956i
$298$	7.32183	+	7.32183i	0.424142	+	0.424142i
$299$	7.04313			0.407315
$300$	7.55610	+	4.23147i	0.436252	+	0.244304i
$301$	−32.0634			−1.84811
$302$	−3.82364	−	3.82364i	−0.220026	−	0.220026i
$303$	−15.8369	+	12.6269i	−0.909804	+	0.725395i
$304$		−	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	$-0.984756\pi$
$311$		−	1.68845i		−	0.0957431i	0.998854	−	0.0478715i	$-0.0152438\pi$
$312$	−7.60503	−	9.53838i	−0.430550	−	0.540004i
$313$	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
$315$	0.811311	−	26.1641i	0.0457122	−	1.47418i
$316$	−14.8422			−0.834937
$317$	−14.5249	−	14.5249i	−0.815797	−	0.815797i	0.169699	−	0.985496i	$-0.445720\pi$
$317$	−14.5249	−	14.5249i	−0.815797	−	0.815797i	−0.985496	+	0.169699i	$0.945720\pi$
$318$	4.66906	+	5.85603i	0.261828	+	0.328390i
$319$		−	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
$327$	−9.91800	+	7.90771i	−0.548467	+	0.437297i
$328$	−4.10289	−	4.10289i	−0.226544	−	0.226544i
$329$	−42.6781			−2.35292
$330$	6.77938	+	5.75783i	0.373192	+	0.316958i
$331$	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
$333$	0.465624	+	0.741368i	0.0255160	+	0.0406267i
$334$		−	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
$342$	−7.53014	−	11.9895i	−0.407183	−	0.648318i
$343$	3.38575	+	3.38575i	0.182813	+	0.182813i
$344$	−8.21679			−0.443020
$345$	2.95198	+	2.50716i	0.158929	+	0.134981i
$346$	−2.03875			−0.109604
$347$	13.2298	+	13.2298i	0.710212	+	0.710212i	0.966579	−	0.256368i	$-0.0825258\pi$
$347$	13.2298	+	13.2298i	0.710212	+	0.710212i	−0.256368	+	0.966579i	$0.582526\pi$
$348$	−8.29522	+	6.61385i	−0.444670	+	0.354539i
$349$		−	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	−0.819932	−	0.572460i	$-0.805989\pi$
$353$	−4.64958	+	4.64958i	−0.247472	+	0.247472i	0.572460	+	0.819932i	$0.305989\pi$
$354$	−1.92614	+	17.0795i	−0.102373	+	0.907766i
$355$	7.88372	−	11.7289i	0.418424	−	0.622507i
$356$			5.52293i			0.292715i
$357$	−23.3615	−	29.3004i	−1.23642	−	1.55074i
$358$	3.32240	+	3.32240i	0.175594	+	0.175594i
$359$	−29.0528			−1.53335			−0.766675	−	0.642036i	$-0.778090\pi$
$359$	−29.0528			−1.53335			−0.766675	+	0.642036i	$0.778090\pi$
$360$	0.207912	−	6.70498i	0.0109579	−	0.353384i
$361$	−3.27237			−0.172230
$362$	0.375839	+	0.375839i	0.0197537	+	0.0197537i
$363$	−6.18263	−	7.75438i	−0.324504	−	0.406999i
$364$			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
$372$	0.161114	−	0.128458i	0.00835337	−	0.00666022i
$373$	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
$375$	17.2782	−	8.74431i	0.892244	−	0.451554i
$376$	−10.9370			−0.564032
$377$	30.5049	+	30.5049i	1.57108	+	1.57108i
$378$	−18.2710	+	8.79206i	−0.939760	+	0.452215i
$379$		−	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	−0.903526	−	0.428534i	$-0.859030\pi$
$383$	−9.29577	+	9.29577i	−0.474992	+	0.474992i	0.428534	+	0.903526i	$0.359030\pi$
$384$	−1.72114	−	0.194102i	−0.0878316	−	0.00990520i
$385$	−3.85535	−	19.6643i	−0.196487	−	1.00219i
$386$			13.6358i			0.694046i
$387$	−20.8747	+	13.1106i	−1.06112	+	0.666449i
$388$	1.89710	+	1.89710i	0.0963105	+	0.0963105i
$389$	−0.585718			−0.0296971			−0.0148485	−	0.999890i	$-0.504727\pi$
$389$	−0.585718			−0.0296971			−0.0148485	+	0.999890i	$0.504727\pi$
$390$	−27.1878	+	2.21530i	−1.37671	+	0.112176i
$391$	5.54444			0.280394
$392$	5.81740	+	5.81740i	0.293823	+	0.293823i
$393$	5.53962	−	4.41679i	0.279437	−	0.222797i
$394$			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	$-0.642083\pi$
$401$		−	36.1259i		−	1.80404i	0.431692	−	0.902021i	$-0.357917\pi$
$402$	1.17899	+	1.47872i	0.0588029	+	0.0737518i
$403$	−0.592483	−	0.592483i	−0.0295137	−	0.0295137i
$404$	11.6939			0.581795
$405$	−10.1702	−	17.3657i	−0.505360	−	0.862909i
$406$	23.9016			1.18622
$407$	0.473890	+	0.473890i	0.0234898	+	0.0234898i
$408$	−5.98677	−	7.50873i	−0.296389	−	0.371737i
$409$			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
$417$	11.5633	−	9.21955i	0.566259	−	0.451483i
$418$	−7.66382	−	7.66382i	−0.374850	−	0.374850i
$419$	25.5177			1.24662			0.623310	−	0.781975i	$-0.285787\pi$
$419$	25.5177			1.24662			0.623310	+	0.781975i	$0.285787\pi$
$420$	−9.78339	+	11.5192i	−0.477381	+	0.562077i
$421$	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
$423$	−27.7853	+	17.4509i	−1.35097	+	0.848491i
$424$		−	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	$-0.914197\pi$
$431$		−	11.0573i		−	0.532612i	0.963888	−	0.266306i	$-0.0858032\pi$
$432$	−4.68225	+	2.25311i	−0.225275	+	0.108403i
$433$	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
$435$	1.92658	+	23.6444i	0.0923723	+	1.13366i
$436$	7.32345			0.350729
$437$	−3.33709	−	3.33709i	−0.159635	−	0.159635i
$438$	−0.579708	+	0.462206i	−0.0276995	+	0.0220851i
$439$			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	$0.533401\pi$
$443$	−23.1363	+	23.1363i	−1.09924	+	1.09924i	−0.994500	+	0.104739i	$0.966599\pi$
$444$	0.0566428	−	0.502264i	0.00268815	−	0.0238364i
$445$	10.2495	+	6.88928i	0.485871	+	0.326583i
$446$		−	10.5756i		−	0.500771i
$447$	−11.1807	−	14.0231i	−0.528830	−	0.663269i
$448$	2.75926	+	2.75926i	0.130363	+	0.130363i
$449$	−3.93638			−0.185769			−0.0928846	−	0.995677i	$-0.529609\pi$
$449$	−3.93638			−0.185769			−0.0928846	+	0.995677i	$0.529609\pi$
$450$	−12.1838	−	8.74961i	−0.574349	−	0.412460i
$451$	−13.3255			−0.627472
$452$	−7.59615	−	7.59615i	−0.357293	−	0.357293i
$453$	5.83885	+	7.32320i	0.274333	+	0.344074i
$454$		−	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	$0.203000\pi$
$461$			25.5669i			1.19077i	−0.803441	+	0.595385i	$0.797000\pi$
$462$	−12.1365	+	9.67654i	−0.564641	+	0.450193i
$463$	−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
$465$	−0.0374190	−	0.459233i	−0.00173526	−	0.0212964i
$466$	−1.82365			−0.0844787
$467$	8.99881	+	8.99881i	0.416415	+	0.416415i	0.883966	−	0.467551i	$-0.154864\pi$
$467$	8.99881	+	8.99881i	0.416415	+	0.416415i	−0.467551	+	0.883966i	$0.654864\pi$
$468$	11.2379	+	17.8930i	0.519473	+	0.827106i
$469$		−	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
$477$	−6.89945	−	10.9853i	−0.315904	−	0.502983i
$478$	−8.28678	−	8.28678i	−0.379029	−	0.379029i
$479$	13.1616			0.601368			0.300684	−	0.953724i	$-0.402785\pi$
$479$	13.1616			0.601368			0.300684	+	0.953724i	$0.402785\pi$
$480$	−2.50716	+	2.95198i	−0.114436	+	0.134739i
$481$	−2.05533			−0.0937149
$482$	−4.37023	−	4.37023i	−0.199059	−	0.199059i
$483$	−5.28465	+	4.21350i	−0.240460	+	0.191721i
$484$			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	$0.275275\pi$
$491$			33.7238i			1.52193i	−0.648791	+	0.760966i	$0.724725\pi$
$492$	6.26528	+	7.85804i	0.282461	+	0.354268i
$493$	24.0138	+	24.0138i	1.08153	+	1.08153i
$494$	33.2391			1.49550
$495$	−10.5507	−	11.2259i	−0.474217	−	0.504568i
$496$	−0.118966			−0.00534175
$497$	17.4389	+	17.4389i	0.782243	+	0.782243i
$498$	−15.2614	−	19.1411i	−0.683878	−	0.857733i
$499$			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	−0.510966	−	0.859601i	$-0.670712\pi$
$503$	7.81907	−	7.81907i	0.348635	−	0.348635i	0.859601	+	0.510966i	$0.170712\pi$
$504$	11.4125	+	2.60725i	0.508354	+	0.116136i
$505$	14.5870	−	21.7016i	0.649111	−	0.965710i
$506$		−	2.29656i		−	0.102094i
$507$	49.5744	−	39.5261i	2.20168	−	1.75542i
$508$	−7.95989	−	7.95989i	−0.353163	−	0.353163i
$509$	38.3147			1.69827			0.849134	−	0.528177i	$-0.177124\pi$
$509$	38.3147			1.69827			0.849134	+	0.528177i	$0.177124\pi$
$510$	−21.4026	+	1.74391i	−0.947723	+	0.0772219i
$511$	1.67035			0.0738921
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	10.6332	+	22.0972i	0.469469	+	0.975617i
$514$		−	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	$0.00950202\pi$
$521$			1.36254i			0.0596941i	−0.999554	+	0.0298470i	$0.990498\pi$
$522$	15.5610	−	9.77324i	0.681086	−	0.427763i
$523$	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
$525$	9.17352	+	32.5250i	0.400365	+	1.41951i
$526$	0.528999			0.0230655
$527$	−0.466409	−	0.466409i	−0.0203171	−	0.0203171i
$528$	−3.11018	+	2.47977i	−0.135353	+	0.107918i
$529$		−	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
$537$	−5.07343	−	6.36320i	−0.218935	−	0.274592i
$538$	20.7426	+	20.7426i	0.894275	+	0.894275i
$539$	18.8939			0.813817
$540$	−1.65929	+	11.4999i	−0.0714046	+	0.494875i
$541$	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
$543$	−0.573921	−	0.719824i	−0.0246293	−	0.0308906i
$544$			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
$552$	−1.35428	+	1.07978i	−0.0576420	+	0.0459585i
$553$	−40.9534	−	40.9534i	−1.74152	−	1.74152i
$554$	17.7148			0.752629
$555$	−0.861446	−	0.731639i	−0.0365664	−	0.0310564i
$556$	−8.53836			−0.362107
$557$	−32.8676	−	32.8676i	−1.39265	−	1.39265i	−0.819346	−	0.573299i	$-0.805663\pi$
$557$	−32.8676	−	32.8676i	−1.39265	−	1.39265i	−0.573299	−	0.819346i	$-0.694337\pi$
$558$	−0.302234	+	0.189821i	−0.0127946	+	0.00803577i
$559$		−	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	−0.843850	−	0.536580i	$-0.819716\pi$
$563$	−7.29079	+	7.29079i	−0.307270	+	0.307270i	0.536580	+	0.843850i	$0.319716\pi$
$564$	18.8241	+	2.12289i	0.792637	+	0.0893896i
$565$	−23.5724	+	4.62155i	−0.991697	+	0.194430i
$566$		−	6.81208i		−	0.286333i
$567$	33.1535	−	11.5859i	1.39232	−	0.486563i
$568$	4.46902	+	4.46902i	0.187516	+	0.187516i
$569$	−29.3461			−1.23025			−0.615126	−	0.788429i	$-0.710895\pi$
$569$	−29.3461			−1.23025			−0.615126	+	0.788429i	$0.710895\pi$
$570$	13.9314	+	11.8322i	0.583524	+	0.495596i
$571$	−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
$573$	−10.8361	+	8.63970i	−0.452684	+	0.360929i
$574$		−	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
$582$	−2.89694	−	3.63340i	−0.120082	−	0.150609i
$583$	−7.02193	−	7.02193i	−0.290819	−	0.290819i
$584$	0.428056			0.0177131
$585$	47.2241	+	1.46435i	1.95248	+	0.0605435i
$586$	−22.6656			−0.936308
$587$	−0.974523	−	0.974523i	−0.0402229	−	0.0402229i	0.686709	−	0.726932i	$-0.259055\pi$
$587$	−0.974523	−	0.974523i	−0.0402229	−	0.0402229i	−0.726932	+	0.686709i	$0.759055\pi$
$588$	−8.88340	−	11.1417i	−0.366345	−	0.459477i
$589$			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	−0.476347	−	0.879258i	$-0.658039\pi$
$593$	9.81152	−	9.81152i	0.402911	−	0.402911i	0.879258	+	0.476347i	$0.158039\pi$
$594$	−3.94471	+	11.2624i	−0.161853	+	0.462102i
$595$	40.1511	+	26.9879i	1.64603	+	1.10640i
$596$			10.3546i			0.424142i
$597$	−13.5228	+	10.7818i	−0.553450	+	0.441271i
$598$	4.98025	+	4.98025i	0.203657	+	0.203657i
$599$	−21.3996			−0.874363			−0.437181	−	0.899373i	$-0.644023\pi$
$599$	−21.3996			−0.874363			−0.437181	+	0.899373i	$0.644023\pi$
$600$	2.35087	+	8.33507i	0.0959737	+	0.340278i
$601$	−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
$603$	−1.74219	−	2.77393i	−0.0709476	−	0.112963i
$604$		−	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
$612$	8.84662	+	14.0856i	0.357604	+	0.569377i
$613$	−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
$615$	22.3982	−	1.82504i	0.903184	−	0.0735928i
$616$	8.96159			0.361073
$617$	0.569528	+	0.569528i	0.0229284	+	0.0229284i	0.718478	−	0.695550i	$-0.244839\pi$
$617$	0.569528	+	0.569528i	0.0229284	+	0.0229284i	−0.695550	+	0.718478i	$0.744839\pi$
$618$	16.7514	−	13.3561i	0.673841	−	0.537260i
$619$		−	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
$627$	11.7029	+	14.6781i	0.467371	+	0.586186i
$628$	−2.89675	−	2.89675i	−0.115593	−	0.115593i
$629$	−1.61798			−0.0645131
$630$	19.0745	−	17.9271i	0.759945	−	0.714233i
$631$	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
$633$	14.7675	+	18.5217i	0.586956	+	0.736172i
$634$		−	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	$-0.833508\pi$
$641$		−	25.2939i		−	0.999051i	0.866299	−	0.499525i	$-0.166492\pi$
$642$	−16.8424	+	13.4286i	−0.664716	+	0.529984i
$643$	−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
$645$	20.6008	−	24.2558i	0.811155	−	0.955070i
$646$	26.1662			1.02950
$647$	19.3089	+	19.3089i	0.759110	+	0.759110i	0.976160	−	0.217051i	$-0.0696436\pi$
$647$	19.3089	+	19.3089i	0.759110	+	0.759110i	−0.217051	+	0.976160i	$0.569644\pi$
$648$	8.49615	−	2.96909i	0.333760	−	0.116637i
$649$		−	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	−0.592431	−	0.805622i	$-0.701832\pi$
$653$	5.44785	−	5.44785i	0.213191	−	0.213191i	0.805622	+	0.592431i	$0.201832\pi$
$654$	−12.6047	−	1.42149i	−0.492882	−	0.0555848i
$655$	−5.10241	+	7.59107i	−0.199368	+	0.296608i
$656$		−	5.80237i		−	0.226544i
$657$	1.08747	−	0.683000i	0.0424264	−	0.0266464i
$658$	−30.1780	−	30.1780i	−1.17646	−	1.17646i
$659$	15.1034			0.588344			0.294172	−	0.955753i	$-0.404956\pi$
$659$	15.1034			0.588344			0.294172	+	0.955753i	$0.404956\pi$
$660$	0.722345	+	8.86514i	0.0281172	+	0.345075i
$661$	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
$663$	52.8850	−	42.1656i	2.05388	−	1.63758i
$664$			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
$672$	−4.21350	−	5.28465i	−0.162539	−	0.203860i
$673$	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
$675$	19.2717	+	17.4242i	0.741767	+	0.670658i
$676$	−36.6057			−1.40791
$677$	−17.6118	−	17.6118i	−0.676875	−	0.676875i	0.282417	−	0.959292i	$-0.408864\pi$
$677$	−17.6118	−	17.6118i	−0.676875	−	0.676875i	−0.959292	+	0.282417i	$0.908864\pi$
$678$	11.5996	+	14.5485i	0.445481	+	0.558731i
$679$			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	−0.326419	−	0.945225i	$-0.605842\pi$
$683$	16.1721	−	16.1721i	0.618807	−	0.618807i	0.945225	+	0.326419i	$0.105842\pi$
$684$	3.15325	−	13.8025i	0.120568	−	0.527751i
$685$	0.851603	+	4.34362i	0.0325381	+	0.165961i
$686$			4.78817i			0.182813i
$687$	−14.0796	+	11.2258i	−0.537169	+	0.428289i
$688$	−5.81015	−	5.81015i	−0.221510	−	0.221510i
$689$	30.4551			1.16025
$690$	0.314534	+	3.86019i	0.0119741	+	0.146955i
$691$	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
$693$	22.7669	−	14.2990i	0.864841	−	0.543173i
$694$			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	$-0.738666\pi$
$701$		−	38.7525i		−	1.46366i	0.681486	−	0.731831i	$-0.261334\pi$
$702$	−15.8690	−	32.9777i	−0.598935	−	1.24466i
$703$	0.973831	+	0.973831i	0.0367287	+	0.0367287i
$704$	2.29656			0.0865547
$705$	27.4207	−	32.2857i	1.03272	−	1.21595i
$706$	−6.57549			−0.247472
$707$	32.2666	+	32.2666i	1.21351	+	1.21351i
$708$	−13.4390	+	10.7150i	−0.505069	+	0.402696i
$709$			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
$717$	12.6542	+	15.8712i	0.472581	+	0.592721i
$718$	−20.5434	−	20.5434i	−0.766675	−	0.766675i
$719$	−7.22663			−0.269508			−0.134754	−	0.990879i	$-0.543024\pi$
$719$	−7.22663			−0.269508			−0.134754	+	0.990879i	$0.543024\pi$
$720$	4.88815	−	4.59412i	0.182171	−	0.171213i
$721$	−48.2671			−1.79756
$722$	−2.31391	−	2.31391i	−0.0861149	−	0.0861149i
$723$	6.67351	+	8.37005i	0.248191	+	0.311285i
$724$			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
$732$	13.1521	−	10.4863i	0.486115	−	0.387583i
$733$	−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
$735$	−31.7580	+	2.58769i	−1.17141	+	0.0954482i
$736$	1.00000			0.0368605
$737$	−1.77312	−	1.77312i	−0.0653138	−	0.0653138i
$738$	−9.25817	−	14.7409i	−0.340798	−	0.542619i
$739$		−	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	−0.685372	−	0.728193i	$-0.740361\pi$
$743$	1.16720	−	1.16720i	0.0428205	−	0.0428205i	0.728193	+	0.685372i	$0.240361\pi$
$744$	0.204758	+	0.0230916i	0.00750679	+	0.000846578i
$745$	19.2162	+	12.9163i	0.704026	+	0.473218i
$746$			13.4478i			0.492358i
$747$	22.5516	+	35.9068i	0.825121	+	1.31376i
$748$	9.00367	+	9.00367i	0.329207	+	0.329207i
$749$	48.5292			1.77322
$750$	18.4007	+	6.03439i	0.671899	+	0.220345i
$751$	−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
$753$	28.2115	−	22.4933i	1.02808	−	0.819701i
$754$			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	$0.0537281\pi$
$761$			9.26851i			0.335983i	−0.985788	+	0.167992i	$0.946272\pi$
$762$	12.1551	+	15.2451i	0.440331	+	0.552272i
$763$	20.2073	+	20.2073i	0.731553	+	0.731553i
$764$	8.00136			0.289479
$765$	37.1754	+	1.15275i	1.34408	+	0.0416779i
$766$	−13.1462			−0.474992
$767$	49.4208	+	49.4208i	1.78448	+	1.78448i
$768$	−1.07978	−	1.35428i	−0.0389632	−	0.0488684i
$769$			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	−0.646391	−	0.763006i	$-0.723723\pi$
$773$	3.24223	−	3.24223i	0.116615	−	0.116615i	0.763006	+	0.646391i	$0.223723\pi$
$774$	−24.0312	−	5.49007i	−0.863785	−	0.197336i
$775$	0.224610	+	0.550796i	0.00806822	+	0.0197852i
$776$			2.68290i			0.0963105i
$777$	1.54217	−	1.22958i	0.0553250	−	0.0441111i
$778$	−0.414165	−	0.414165i	−0.0148485	−	0.0148485i
$779$	−27.3835			−0.981115
$780$	−20.7912	−	17.6582i	−0.744443	−	0.632267i
$781$	14.5146			0.519372
$782$	3.92051	+	3.92051i	0.140197	+	0.140197i
$783$	−28.6797	+	13.8007i	−1.02493	+	0.493197i
$784$			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
$792$	5.83439	−	3.66435i	0.207316	−	0.130207i
$793$	−48.3656	−	48.3656i	−1.71751	−	1.71751i
$794$	−21.4705			−0.761960
$795$	12.7646	+	10.8412i	0.452714	+	0.384497i
$796$	9.98521			0.353916
$797$	18.9143	+	18.9143i	0.669977	+	0.669977i	0.957711	−	0.287733i	$-0.0929016\pi$
$797$	18.9143	+	18.9143i	0.669977	+	0.669977i	−0.287733	+	0.957711i	$0.592902\pi$
$798$	−24.9402	+	19.8850i	−0.882873	+	0.703922i
$799$		−	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
$807$	−31.6747	−	39.7270i	−1.11500	−	1.39846i
$808$	8.26886	+	8.26886i	0.290897	+	0.290897i
$809$	41.9673			1.47549			0.737745	−	0.675079i	$-0.235890\pi$
$809$	41.9673			1.47549			0.737745	+	0.675079i	$0.235890\pi$
$810$	5.08802	−	19.4708i	0.178775	−	0.684134i
$811$	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
$813$	−16.4937	−	20.6867i	−0.578458	−	0.725513i
$814$			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	$0.0611993\pi$
$821$			10.9501i			0.382162i	−0.981574	+	0.191081i	$0.938801\pi$
$822$	2.68081	−	2.13743i	0.0935041	−	0.0745516i
$823$	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
$825$	17.3530	+	9.71781i	0.604154	+	0.338331i
$826$	38.7228			1.34734
$827$	−10.2837	−	10.2837i	−0.357598	−	0.357598i	0.505329	−	0.862927i	$-0.331371\pi$
$827$	−10.2837	−	10.2837i	−0.357598	−	0.357598i	−0.862927	+	0.505329i	$0.831371\pi$
$828$	2.54049	−	1.59558i	0.0882883	−	0.0554504i
$829$		−	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
$837$	0.557031	−	0.268045i	0.0192538	−	0.00926498i
$838$	18.0437	+	18.0437i	0.623310	+	0.623310i
$839$	−49.7271			−1.71677			−0.858385	−	0.513007i	$-0.828532\pi$
$839$	−49.7271			−1.71677			−0.858385	+	0.513007i	$0.828532\pi$
$840$	−15.0632	+	1.22737i	−0.519729	+	0.0423483i
$841$	8.51785			0.293719
$842$	20.3430	+	20.3430i	0.701067	+	0.701067i
$843$	38.5958	−	30.7728i	1.32931	−	1.05987i
$844$		−	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
$852$	−6.82436	−	8.55925i	−0.233799	−	0.293235i
$853$	−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
$855$	−21.6813	−	23.0690i	−0.741485	−	0.788942i
$856$	12.4364			0.425068
$857$	−25.8824	−	25.8824i	−0.884124	−	0.884124i	0.109826	−	0.993951i	$-0.464971\pi$
$857$	−25.8824	−	25.8824i	−0.884124	−	0.884124i	−0.993951	+	0.109826i	$0.964971\pi$
$858$	−17.4654	−	21.9054i	−0.596258	−	0.747839i
$859$			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	−0.886810	−	0.462134i	$-0.847084\pi$
$863$	−12.4757	+	12.4757i	−0.424677	+	0.424677i	0.462134	+	0.886810i	$0.347084\pi$
$864$	−4.90404	−	1.71766i	−0.166839	−	0.0584361i
$865$	−4.47362	+	0.877090i	−0.152108	+	0.0298219i
$866$			9.32577i			0.316903i
$867$	18.6089	−	14.8371i	0.631992	−	0.503893i
$868$	−0.328260	−	0.328260i	−0.0111419	−	0.0111419i
$869$	−34.0859			−1.15628
$870$	−15.3568	+	18.0814i	−0.520644	+	0.613016i
$871$	7.69029			0.260576
$872$	5.17846	+	5.17846i	0.175365	+	0.175365i
$873$	4.28079	+	6.81589i	0.144883	+	0.230683i
$874$		−	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	$-0.994935\pi$
$881$		−	0.944479i		−	0.0318203i	0.999873	−	0.0159102i	$-0.00506458\pi$
$882$	13.1269	+	20.9008i	0.442007	+	0.703765i
$883$	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
$885$	3.12124	+	38.3061i	0.104919	+	1.28764i
$886$	−32.7197			−1.09924
$887$	−1.81183	−	1.81183i	−0.0608352	−	0.0608352i	0.676035	−	0.736870i	$-0.263697\pi$
$887$	−1.81183	−	1.81183i	−0.0608352	−	0.0608352i	−0.736870	+	0.676035i	$0.763697\pi$
$888$	0.395206	−	0.315101i	0.0132623	−	0.0105741i
$889$		−	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
$897$	−7.60503	−	9.53838i	−0.253925	−	0.318477i
$898$	−2.78344	−	2.78344i	−0.0928846	−	0.0928846i
$899$	−0.728691			−0.0243032
$900$	−2.42832	−	14.8021i	−0.0809441	−	0.493405i
$901$	23.9747			0.798711
$902$	−9.42253	−	9.42253i	−0.313736	−	0.313736i
$903$	34.6215	+	43.4229i	1.15213	+	1.44502i
$904$		−	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	$-0.921194\pi$
$911$		−	14.7929i		−	0.490112i	0.969509	−	0.245056i	$-0.0788064\pi$
$912$	−6.39134	+	5.09587i	−0.211638	+	0.168741i
$913$	22.9520	+	22.9520i	0.759600	+	0.759600i
$914$	−14.3084			−0.473279
$915$	−3.05459	−	37.4882i	−0.100982	−	1.23932i
$916$	10.3963			0.343505
$917$	−11.2866	−	11.2866i	−0.372717	−	0.372717i
$918$	−12.4922	−	25.9605i	−0.412305	−	0.856823i
$919$		−	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
$927$	−31.4240	+	19.7362i	−1.03210	+	0.648221i
$928$	4.33116	+	4.33116i	0.142177	+	0.142177i
$929$	9.92612			0.325666			0.162833	−	0.986654i	$-0.447937\pi$
$929$	9.92612			0.325666			0.162833	+	0.986654i	$0.447937\pi$
$930$	0.298268	−	0.351186i	0.00978058	−	0.0115158i
$931$	38.8264			1.27248
$932$	−1.28951	−	1.28951i	−0.0422394	−	0.0422394i
$933$	−2.28663	+	1.82315i	−0.0748610	+	0.0596873i
$934$			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	$0.0424240\pi$
$941$			8.15267i			0.265770i	−0.991131	+	0.132885i	$0.957576\pi$
$942$	4.42346	+	5.54799i	0.144124	+	0.180763i
$943$	−4.10289	−	4.10289i	−0.133609	−	0.133609i
$944$	9.92337			0.322978
$945$	−36.3095	+	27.1527i	−1.18115	+	0.883277i
$946$	−18.8703			−0.613527
$947$	−5.31126	−	5.31126i	−0.172593	−	0.172593i	0.615525	−	0.788118i	$-0.288944\pi$
$947$	−5.31126	−	5.31126i	−0.172593	−	0.172593i	−0.788118	+	0.615525i	$0.788944\pi$
$948$	16.0263	+	20.1005i	0.520509	+	0.652832i
$949$			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	$-0.450230\pi$
$953$	35.3013	−	35.3013i	1.14352	−	1.14352i	0.987801	−	0.155722i	$-0.0497703\pi$
$954$	2.88915	−	12.6464i	0.0935397	−	0.409444i
$955$	9.98086	−	14.8489i	0.322973	−	0.480500i
$956$		−	11.7193i		−	0.379029i
$957$	−19.0504	+	15.1891i	−0.615813	+	0.490993i
$958$	9.30664	+	9.30664i	0.300684	+	0.300684i
$959$	−7.72442			−0.249434
$960$	−3.86019	+	0.314534i	−0.124587	+	0.0101515i
$961$	−30.9858			−0.999543
$962$	−1.45334	−	1.45334i	−0.0468575	−	0.0468575i
$963$	31.5946	−	19.8433i	1.01812	−	0.639443i
$964$		−	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	$-0.991602\pi$
$971$		−	1.64414i		−	0.0527629i	0.999652	−	0.0263815i	$-0.00839845\pi$
$972$	−15.1994	+	3.46110i	−0.487520	+	0.111015i
$973$	−23.5596	−	23.5596i	−0.755285	−	0.755285i
$974$	−32.2985			−1.03491
$975$	−58.7050	+	16.5575i	−1.88007	+	0.530263i
$976$	−9.71148			−0.310857
$977$	11.1434	+	11.1434i	0.356509	+	0.356509i	0.862524	−	0.506016i	$-0.168882\pi$
$977$	11.1434	+	11.1434i	0.356509	+	0.356509i	−0.506016	+	0.862524i	$0.668882\pi$
$978$	18.1423	−	14.4650i	0.580128	−	0.462541i
$979$			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	−0.482415	−	0.875943i	$-0.660240\pi$
$983$	12.3382	−	12.3382i	0.393527	−	0.393527i	0.875943	+	0.482415i	$0.160240\pi$
$984$	−1.12625	+	9.98669i	−0.0359035	+	0.318364i
$985$	0.905349	+	4.61776i	0.0288468	+	0.147134i
$986$			33.9607i			1.08153i
$987$	46.0830	+	57.7982i	1.46684	+	1.83974i
$988$	23.5036	+	23.5036i	0.747749	+	0.747749i
$989$	−8.21679			−0.261279
$990$	0.477481	−	15.3984i	0.0151754	−	0.489392i
$991$	−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
$993$	−15.5864	−	19.5488i	−0.494621	−	0.620363i
$994$			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.323.11	yes	32
3.2	odd	2	inner	690.2.i.e.323.2	yes	32
5.2	odd	4	inner	690.2.i.e.47.2	✓	32
15.2	even	4	inner	690.2.i.e.47.11	yes	32

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.07978 - 1.35428i) q^{3} +1.00000i q^{4} +(1.85580 + 1.24740i) q^{5} +(0.194102 - 1.72114i) q^{6} +(-2.75926 + 2.75926i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.668152 + 2.92465i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.07978 - 1.35428i) 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} +(1.35428 - 1.07978i) q^{12} +(-4.98025 - 4.98025i) q^{13} -3.90218 q^{14} +(-0.314534 - 3.86019i) q^{15} -1.00000 q^{16} +(-3.92051 - 3.92051i) q^{17} +(-2.54049 + 1.59558i) 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} +(4.68225 - 2.25311i) q^{27} +(-2.75926 - 2.75926i) q^{28} -6.12518 q^{29} +(2.50716 - 2.95198i) q^{30} +0.118966 q^{31} +(-0.707107 - 0.707107i) q^{32} +(3.11018 - 2.47977i) 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} +(4.21350 + 5.28465i) q^{42} +(5.81015 + 5.81015i) q^{43} -2.29656 q^{44} +(-4.88815 + 4.59412i) q^{45} -1.00000 q^{46} +(7.73361 + 7.73361i) q^{47} +(1.07978 + 1.35428i) 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} +(6.39134 - 5.09587i) q^{57} +(-4.33116 - 4.33116i) q^{58} -9.92337 q^{59} +(3.86019 - 0.314534i) q^{60} +9.71148 q^{61} +(0.0841220 + 0.0841220i) q^{62} +(-6.22627 - 9.91348i) 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} +(-1.59558 - 2.54049i) q^{72} +(-0.302682 - 0.302682i) q^{73} +0.291820 q^{74} +(4.23147 - 7.55610i) q^{75} -4.71936 q^{76} +(-6.33680 - 6.33680i) q^{77} +(-9.53838 + 7.60503i) 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} +(6.61385 + 8.29522i) q^{87} +(-1.62391 - 1.62391i) q^{88} +5.52293 q^{89} +(-6.70498 - 0.207912i) q^{90} +27.4836 q^{91} +(-0.707107 - 0.707107i) q^{92} +(-0.128458 - 0.161114i) 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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