LMFDB - Embedded newform 155.2.x.a.43.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [155,2,Mod(3,155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(155, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([45, 2]))

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

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

chi := DirichletCharacter("155.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 155 = 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	155.x (of order $60$, degree $16$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.23768123133$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$14$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			43.12
Character	$\chi$	$=$	155.43
Dual form			155.2.x.a.137.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.60231 - 0.253782i) q^{2} +(1.85797 - 0.713206i) q^{3} +(0.600894 - 0.195242i) q^{4} +(-1.30841 + 1.81330i) q^{5} +(2.79605 - 1.61430i) q^{6} +(-0.210014 - 4.00730i) q^{7} +(-1.97767 + 1.00767i) q^{8} +(0.713938 - 0.642832i) q^{9} +O(q^{10})$	\(q+(1.60231 - 0.253782i) q^{2} +(1.85797 - 0.713206i) q^{3} +(0.600894 - 0.195242i) q^{4} +(-1.30841 + 1.81330i) q^{5} +(2.79605 - 1.61430i) q^{6} +(-0.210014 - 4.00730i) q^{7} +(-1.97767 + 1.00767i) q^{8} +(0.713938 - 0.642832i) q^{9} +(-1.63630 + 3.23753i) q^{10} +(-0.662578 + 3.11718i) q^{11} +(0.977192 - 0.791314i) q^{12} +(2.05991 + 1.66809i) q^{13} +(-1.35349 - 6.36766i) q^{14} +(-1.13772 + 4.30222i) q^{15} +(-3.93542 + 2.85925i) q^{16} +(-5.41247 - 3.51490i) q^{17} +(0.980813 - 1.21120i) q^{18} +(7.25023 + 0.762030i) q^{19} +(-0.432180 + 1.34506i) q^{20} +(-3.24823 - 7.29564i) q^{21} +(-0.270574 + 5.16286i) q^{22} +(-2.54070 - 4.98641i) q^{23} +(-2.95576 + 3.28270i) q^{24} +(-1.57614 - 4.74508i) q^{25} +(3.72396 + 2.15003i) q^{26} +(-1.84253 + 3.61617i) q^{27} +(-0.908590 - 2.36696i) q^{28} +(2.44832 + 1.77881i) q^{29} +(-0.731153 + 7.18224i) q^{30} +(5.55421 + 0.388290i) q^{31} +(-2.44118 + 2.44118i) q^{32} +(0.992147 + 6.26417i) q^{33} +(-9.56450 - 4.25839i) q^{34} +(7.54124 + 4.86236i) q^{35} +(0.303493 - 0.525665i) q^{36} +(0.764693 - 2.85387i) q^{37} +(11.8105 - 0.618964i) q^{38} +(5.01694 + 1.63010i) q^{39} +(0.760378 - 4.90455i) q^{40} +(-6.64855 + 2.96013i) q^{41} +(-7.05619 - 10.8656i) q^{42} +(0.565683 + 0.698561i) q^{43} +(0.210467 + 2.00246i) q^{44} +(0.231529 + 2.13567i) q^{45} +(-5.33646 - 7.34501i) q^{46} +(0.800413 - 5.05361i) q^{47} +(-5.27263 + 8.11914i) q^{48} +(-9.05270 + 0.951477i) q^{49} +(-3.72969 - 7.20311i) q^{50} +(-12.5630 - 2.67035i) q^{51} +(1.56347 + 0.600160i) q^{52} +(7.90579 + 0.414325i) q^{53} +(-2.03459 + 6.26184i) q^{54} +(-4.78548 - 5.28000i) q^{55} +(4.45338 + 7.71348i) q^{56} +(14.0142 - 3.75508i) q^{57} +(4.37441 + 2.22887i) q^{58} +(-0.943742 + 2.11968i) q^{59} +(0.156329 + 2.80731i) q^{60} -0.0552325i q^{61} +(8.99813 - 0.787393i) q^{62} +(-2.72596 - 2.72596i) q^{63} +(2.42648 - 3.33977i) q^{64} +(-5.71995 + 1.55272i) q^{65} +(3.17946 + 9.78538i) q^{66} +(2.24549 + 8.38027i) q^{67} +(-3.93858 - 1.05534i) q^{68} +(-8.27687 - 7.45253i) q^{69} +(13.3174 + 5.87720i) q^{70} +(-3.86036 - 4.28737i) q^{71} +(-0.764166 + 1.99072i) q^{72} +(2.35785 - 1.53121i) q^{73} +(0.501018 - 4.76687i) q^{74} +(-6.31264 - 7.69208i) q^{75} +(4.50540 - 0.957652i) q^{76} +(12.6306 + 2.00050i) q^{77} +(8.45240 + 1.33873i) q^{78} +(1.74872 - 0.371703i) q^{79} +(-0.0355583 - 10.8772i) q^{80} +(-1.14554 + 10.8991i) q^{81} +(-9.90185 + 6.43034i) q^{82} +(0.120320 - 0.313444i) q^{83} +(-3.37626 - 3.74971i) q^{84} +(13.4553 - 5.21553i) q^{85} +(1.08368 + 0.975754i) q^{86} +(5.81755 + 1.55881i) q^{87} +(-1.83074 - 6.83241i) q^{88} +(0.194560 + 0.598794i) q^{89} +(0.912977 + 3.36326i) q^{90} +(6.25191 - 8.60502i) q^{91} +(-2.50025 - 2.50025i) q^{92} +(10.5965 - 3.23987i) q^{93} -8.30060i q^{94} +(-10.8680 + 12.1498i) q^{95} +(-2.79456 + 6.27669i) q^{96} +(-7.63007 - 3.88771i) q^{97} +(-14.2638 + 3.82197i) q^{98} +(1.53079 + 2.65140i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 12 q^{2} - 14 q^{3} - 8 q^{5} - 36 q^{6} + 6 q^{7} - 40 q^{8}+O(q^{10}) $ 224 * q - 12 * q^2 - 14 * q^3 - 8 * q^5 - 36 * q^6 + 6 * q^7 - 40 * q^8	$ 224 q - 12 q^{2} - 14 q^{3} - 8 q^{5} - 36 q^{6} + 6 q^{7} - 40 q^{8} - 10 q^{10} - 28 q^{11} - 40 q^{12} - 14 q^{13} - 20 q^{15} + 24 q^{16} - 14 q^{17} - 40 q^{18} - 44 q^{20} - 44 q^{21} + 30 q^{22} - 30 q^{23} - 22 q^{25} - 48 q^{26} + 100 q^{27} - 48 q^{28} - 44 q^{31} + 28 q^{32} + 20 q^{33} - 72 q^{35} + 16 q^{36} + 30 q^{37} + 38 q^{38} - 4 q^{40} - 20 q^{41} - 130 q^{42} + 22 q^{43} - 34 q^{45} - 28 q^{47} - 156 q^{48} + 158 q^{50} - 36 q^{51} - 10 q^{52} + 26 q^{53} + 98 q^{55} - 48 q^{56} - 20 q^{58} + 260 q^{60} + 30 q^{62} + 152 q^{63} + 32 q^{65} - 152 q^{66} + 38 q^{67} - 126 q^{68} + 166 q^{70} - 128 q^{71} - 156 q^{72} - 30 q^{73} + 26 q^{75} + 128 q^{76} + 30 q^{78} + 154 q^{80} - 64 q^{81} + 8 q^{82} - 82 q^{83} + 60 q^{85} - 28 q^{86} - 24 q^{87} + 252 q^{88} + 38 q^{90} + 194 q^{93} - 74 q^{95} + 60 q^{96} - 38 q^{97} + 174 q^{98}+O(q^{100}) $ 224 * q - 12 * q^2 - 14 * q^3 - 8 * q^5 - 36 * q^6 + 6 * q^7 - 40 * q^8 - 10 * q^10 - 28 * q^11 - 40 * q^12 - 14 * q^13 - 20 * q^15 + 24 * q^16 - 14 * q^17 - 40 * q^18 - 44 * q^20 - 44 * q^21 + 30 * q^22 - 30 * q^23 - 22 * q^25 - 48 * q^26 + 100 * q^27 - 48 * q^28 - 44 * q^31 + 28 * q^32 + 20 * q^33 - 72 * q^35 + 16 * q^36 + 30 * q^37 + 38 * q^38 - 4 * q^40 - 20 * q^41 - 130 * q^42 + 22 * q^43 - 34 * q^45 - 28 * q^47 - 156 * q^48 + 158 * q^50 - 36 * q^51 - 10 * q^52 + 26 * q^53 + 98 * q^55 - 48 * q^56 - 20 * q^58 + 260 * q^60 + 30 * q^62 + 152 * q^63 + 32 * q^65 - 152 * q^66 + 38 * q^67 - 126 * q^68 + 166 * q^70 - 128 * q^71 - 156 * q^72 - 30 * q^73 + 26 * q^75 + 128 * q^76 + 30 * q^78 + 154 * q^80 - 64 * q^81 + 8 * q^82 - 82 * q^83 + 60 * q^85 - 28 * q^86 - 24 * q^87 + 252 * q^88 + 38 * q^90 + 194 * q^93 - 74 * q^95 + 60 * q^96 - 38 * q^97 + 174 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/155\mathbb{Z}\right)^\times$.

$n$	$32$	$96$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{19}{30}\right)$

Coefficient data

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

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

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

$2$	1.60231	−	0.253782i	1.13301	−	0.179451i	0.438359	−	0.898800i	$-0.355560\pi$
$2$	1.60231	−	0.253782i	1.13301	−	0.179451i	0.694649	+	0.719349i	$0.255560\pi$
$3$	1.85797	−	0.713206i	1.07270	−	0.411770i	0.243024	−	0.970020i	$-0.421861\pi$
$3$	1.85797	−	0.713206i	1.07270	−	0.411770i	0.829672	+	0.558251i	$0.188527\pi$
$4$	0.600894	−	0.195242i	0.300447	−	0.0976211i
$5$	−1.30841	+	1.81330i	−0.585137	+	0.810934i
$5$	−1.30841	+	1.81330i	−0.585137	+	0.810934i
$6$	2.79605	−	1.61430i	1.14148	−	0.659034i
$7$	−0.210014	−	4.00730i	−0.0793777	−	1.51462i	−0.690646	−	0.723193i	$-0.742674\pi$
$7$	−0.210014	−	4.00730i	−0.0793777	−	1.51462i	0.611268	−	0.791424i	$-0.290660\pi$
$8$	−1.97767	+	1.00767i	−0.699210	+	0.356266i
$9$	0.713938	−	0.642832i	0.237979	−	0.214277i
$10$	−1.63630	+	3.23753i	−0.517442	+	1.02380i
$11$	−0.662578	+	3.11718i	−0.199775	+	0.939866i	0.757980	+	0.652278i	$0.226187\pi$
$11$	−0.662578	+	3.11718i	−0.199775	+	0.939866i	−0.957754	+	0.287588i	$0.907147\pi$
$12$	0.977192	−	0.791314i	0.282091	−	0.228433i
$13$	2.05991	+	1.66809i	0.571317	+	0.462644i	0.870923	−	0.491419i	$-0.163522\pi$
$13$	2.05991	+	1.66809i	0.571317	+	0.462644i	−0.299606	+	0.954063i	$0.596855\pi$
$14$	−1.35349	−	6.36766i	−0.361735	−	1.70183i
$15$	−1.13772	+	4.30222i	−0.293757	+	1.11083i
$16$	−3.93542	+	2.85925i	−0.983854	+	0.714812i
$17$	−5.41247	−	3.51490i	−1.31272	−	0.852488i	−0.317319	−	0.948319i	$-0.602783\pi$
$17$	−5.41247	−	3.51490i	−1.31272	−	0.852488i	−0.995398	+	0.0958305i	$0.969449\pi$
$18$	0.980813	−	1.21120i	0.231180	−	0.285483i
$19$	7.25023	+	0.762030i	1.66332	+	0.174822i	0.888978	−	0.457950i	$-0.151416\pi$
$19$	7.25023	+	0.762030i	1.66332	+	0.174822i	0.774338	+	0.632772i	$0.218083\pi$
$20$	−0.432180	+	1.34506i	−0.0966384	+	0.300764i
$21$	−3.24823	−	7.29564i	−0.708822	−	1.59204i
$22$	−0.270574	+	5.16286i	−0.0576865	+	1.10072i
$23$	−2.54070	−	4.98641i	−0.529773	−	1.03974i	−0.988508	−	0.151165i	$-0.951697\pi$
$23$	−2.54070	−	4.98641i	−0.529773	−	1.03974i	0.458735	−	0.888573i	$-0.348303\pi$
$24$	−2.95576	+	3.28270i	−0.603341	+	0.670079i
$25$	−1.57614	−	4.74508i	−0.315228	−	0.949016i
$26$	3.72396	+	2.15003i	0.730329	+	0.421655i
$27$	−1.84253	+	3.61617i	−0.354595	+	0.695931i
$28$	−0.908590	−	2.36696i	−0.171707	−	0.447313i
$29$	2.44832	+	1.77881i	0.454641	+	0.330316i	0.791426	−	0.611266i	$-0.209339\pi$
$29$	2.44832	+	1.77881i	0.454641	+	0.330316i	−0.336784	+	0.941582i	$0.609339\pi$
$30$	−0.731153	+	7.18224i	−0.133490	+	1.31129i
$31$	5.55421	+	0.388290i	0.997565	+	0.0697390i
$31$	5.55421	+	0.388290i	0.997565	+	0.0697390i
$32$	−2.44118	+	2.44118i	−0.431544	+	0.431544i
$33$	0.992147	+	6.26417i	0.172711	+	1.09045i
$34$	−9.56450	−	4.25839i	−1.64030	−	0.730308i
$35$	7.54124	+	4.86236i	1.27470	+	0.821889i
$36$	0.303493	−	0.525665i	0.0505821	−	0.0876108i
$37$	0.764693	−	2.85387i	0.125715	−	0.469174i	−0.874149	−	0.485657i	$-0.838580\pi$
$37$	0.764693	−	2.85387i	0.125715	−	0.469174i	0.999864	+	0.0164831i	$0.00524699\pi$
$38$	11.8105	−	0.618964i	1.91592	−	0.100409i
$39$	5.01694	+	1.63010i	0.803353	+	0.261025i
$40$	0.760378	−	4.90455i	0.120226	−	0.775478i
$41$	−6.64855	+	2.96013i	−1.03833	+	0.462294i	−0.853837	−	0.520540i	$-0.825731\pi$
$41$	−6.64855	+	2.96013i	−1.03833	+	0.462294i	−0.184492	+	0.982834i	$0.559064\pi$
$42$	−7.05619	−	10.8656i	−1.08879	−	1.67659i
$43$	0.565683	+	0.698561i	0.0862659	+	0.106529i	0.818451	−	0.574576i	$-0.194833\pi$
$43$	0.565683	+	0.698561i	0.0862659	+	0.106529i	−0.732186	+	0.681105i	$0.761500\pi$
$44$	0.210467	+	2.00246i	0.0317291	+	0.301882i
$45$	0.231529	+	2.13567i	0.0345144	+	0.318367i
$46$	−5.33646	−	7.34501i	−0.786819	−	1.08296i
$47$	0.800413	−	5.05361i	0.116752	−	0.737144i	−0.857966	−	0.513707i	$-0.828272\pi$
$47$	0.800413	−	5.05361i	0.116752	−	0.737144i	0.974718	−	0.223438i	$-0.0717280\pi$
$48$	−5.27263	+	8.11914i	−0.761039	+	1.17190i
$49$	−9.05270	+	0.951477i	−1.29324	+	0.135925i
$50$	−3.72969	−	7.20311i	−0.527458	−	1.01867i
$51$	−12.5630	−	2.67035i	−1.75918	−	0.373924i
$52$	1.56347	+	0.600160i	0.216814	+	0.0832272i
$53$	7.90579	+	0.414325i	1.08594	+	0.0569119i	0.586896	−	0.809662i	$-0.300350\pi$
$53$	7.90579	+	0.414325i	1.08594	+	0.0569119i	0.499048	+	0.866574i	$0.333683\pi$
$54$	−2.03459	+	6.26184i	−0.276873	+	0.852128i
$55$	−4.78548	−	5.28000i	−0.645274	−	0.711955i
$56$	4.45338	+	7.71348i	0.595108	+	1.03076i
$57$	14.0142	−	3.75508i	1.85622	−	0.497373i
$58$	4.37441	+	2.22887i	0.574388	+	0.292665i
$59$	−0.943742	+	2.11968i	−0.122865	+	0.275959i	−0.964498	−	0.264091i	$-0.914928\pi$
$59$	−0.943742	+	2.11968i	−0.122865	+	0.275959i	0.841633	+	0.540050i	$0.181595\pi$
$60$	0.156329	+	2.80731i	0.0201820	+	0.362422i
$61$		−	0.0552325i		−	0.00707180i	−0.999994	−	0.00353590i	$-0.998874\pi$
$61$		−	0.0552325i		−	0.00707180i	0.999994	−	0.00353590i	$-0.00112551\pi$
$62$	8.99813	−	0.787393i	1.14276	−	0.0999990i
$63$	−2.72596	−	2.72596i	−0.343439	−	0.343439i
$64$	2.42648	−	3.33977i	0.303310	−	0.417471i
$65$	−5.71995	+	1.55272i	−0.709473	+	0.192591i
$66$	3.17946	+	9.78538i	0.391365	+	1.20450i
$67$	2.24549	+	8.38027i	0.274330	+	1.02381i	0.956289	+	0.292423i	$0.0944614\pi$
$67$	2.24549	+	8.38027i	0.274330	+	1.02381i	−0.681959	+	0.731390i	$0.738872\pi$
$68$	−3.93858	−	1.05534i	−0.477623	−	0.127979i
$69$	−8.27687	−	7.45253i	−0.996419	−	0.897179i
$70$	13.3174	+	5.87720i	1.59174	+	0.702460i
$71$	−3.86036	−	4.28737i	−0.458141	−	0.508817i	0.469171	−	0.883108i	$-0.344553\pi$
$71$	−3.86036	−	4.28737i	−0.458141	−	0.508817i	−0.927312	+	0.374290i	$0.877886\pi$
$72$	−0.764166	+	1.99072i	−0.0900579	+	0.234609i
$73$	2.35785	−	1.53121i	0.275966	−	0.179214i	−0.399234	−	0.916849i	$-0.630724\pi$
$73$	2.35785	−	1.53121i	0.275966	−	0.179214i	0.675200	+	0.737635i	$0.264057\pi$
$74$	0.501018	−	4.76687i	0.0582422	−	0.554137i
$75$	−6.31264	−	7.69208i	−0.728921	−	0.888205i
$76$	4.50540	−	0.957652i	0.516804	−	0.109850i
$77$	12.6306	+	2.00050i	1.43939	+	0.227978i
$78$	8.45240	+	1.33873i	0.957046	+	0.151581i
$79$	1.74872	−	0.371703i	0.196747	−	0.0418198i	−0.108484	−	0.994098i	$-0.534600\pi$
$79$	1.74872	−	0.371703i	0.196747	−	0.0418198i	0.305231	+	0.952278i	$0.401266\pi$
$80$	−0.0355583	−	10.8772i	−0.00397554	−	1.21610i
$81$	−1.14554	+	10.8991i	−0.127283	+	1.21101i
$82$	−9.90185	+	6.43034i	−1.09348	+	0.710112i
$83$	0.120320	−	0.313444i	0.0132068	−	0.0344050i	−0.926819	−	0.375510i	$-0.877468\pi$
$83$	0.120320	−	0.313444i	0.0132068	−	0.0344050i	0.940025	+	0.341105i	$0.110801\pi$
$84$	−3.37626	−	3.74971i	−0.368380	−	0.409127i
$85$	13.4553	−	5.21553i	1.45943	−	0.565704i
$86$	1.08368	+	0.975754i	0.116857	+	0.105218i
$87$	5.81755	+	1.55881i	0.623706	+	0.167122i
$88$	−1.83074	−	6.83241i	−0.195157	−	0.728337i
$89$	0.194560	+	0.598794i	0.0206233	+	0.0634720i	0.960839	−	0.277109i	$-0.0893763\pi$
$89$	0.194560	+	0.598794i	0.0206233	+	0.0634720i	−0.940215	+	0.340581i	$0.889376\pi$
$90$	0.912977	+	3.36326i	0.0962363	+	0.354519i
$91$	6.25191	−	8.60502i	0.655378	−	0.902051i
$92$	−2.50025	−	2.50025i	−0.260669	−	0.260669i
$93$	10.5965	−	3.23987i	1.09880	−	0.335958i
$94$		−	8.30060i		−	0.856141i
$95$	−10.8680	+	12.1498i	−1.11504	+	1.24655i
$96$	−2.79456	+	6.27669i	−0.285219	+	0.640612i
$97$	−7.63007	−	3.88771i	−0.774716	−	0.394737i	0.0214855	−	0.999769i	$-0.493160\pi$
$97$	−7.63007	−	3.88771i	−0.774716	−	0.394737i	−0.796201	+	0.605032i	$0.793160\pi$
$98$	−14.2638	+	3.82197i	−1.44086	+	0.386078i
$99$	1.53079	+	2.65140i	0.153850	+	0.266476i
$100$	−1.87353	−	2.54356i	−0.187353	−	0.254356i
$101$	0.213444	−	0.656913i	0.0212385	−	0.0653653i	−0.939876	−	0.341517i	$-0.889059\pi$
$101$	0.213444	−	0.656913i	0.0212385	−	0.0653653i	0.961114	+	0.276152i	$0.0890593\pi$
$102$	−20.8076	−	1.09048i	−2.06026	−	0.107974i
$103$	−7.96862	−	3.05887i	−0.785171	−	0.301399i	−0.0674438	−	0.997723i	$-0.521484\pi$
$103$	−7.96862	−	3.05887i	−0.785171	−	0.301399i	−0.717728	+	0.696324i	$0.754818\pi$
$104$	−5.75470	−	1.22320i	−0.564295	−	0.119945i
$105$	17.4792	+	3.65564i	1.70580	+	0.356754i
$106$	12.7727	−	1.34247i	1.24060	−	0.130392i
$107$	0.888188	−	1.36769i	0.0858643	−	0.132219i	−0.793129	−	0.609054i	$-0.791549\pi$
$107$	0.888188	−	1.36769i	0.0858643	−	0.132219i	0.878993	+	0.476835i	$0.158216\pi$
$108$	−0.401136	+	2.53267i	−0.0385993	+	0.243706i
$109$	−2.99838	−	4.12691i	−0.287192	−	0.395286i	0.640907	−	0.767618i	$-0.278558\pi$
$109$	−2.99838	−	4.12691i	−0.287192	−	0.395286i	−0.928100	+	0.372332i	$0.878558\pi$
$110$	−9.00781	−	7.24575i	−0.858861	−	0.690855i
$111$	−0.614627	−	5.84778i	−0.0583378	−	0.555047i
$112$	12.2844	+	15.1699i	1.16076	+	1.43342i
$113$	2.61593	+	4.02819i	0.246086	+	0.378940i	0.940031	−	0.341088i	$-0.110796\pi$
$113$	2.61593	+	4.02819i	0.246086	+	0.378940i	−0.693945	+	0.720028i	$0.744129\pi$
$114$	21.5021	−	9.57336i	2.01386	−	0.896627i
$115$	12.3661	+	1.91719i	1.15315	+	0.178779i
$116$	1.81848	+	0.590859i	0.168841	+	0.0548599i
$117$	2.54295	−	0.133270i	0.235096	−	0.0123208i
$118$	−0.974236	+	3.63590i	−0.0896857	+	0.334712i
$119$	−12.9486	+	22.4276i	−1.18699	+	2.05593i
$120$	−2.08520	−	9.65480i	−0.190352	−	0.881358i
$121$	0.771182	+	0.343352i	0.0701074	+	0.0312138i
$122$	−0.0140170	−	0.0884999i	−0.00126904	−	0.00801240i
$123$	−10.2416	+	10.2416i	−0.923454	+	0.923454i
$124$	3.41330	−	0.851095i	0.306523	−	0.0764306i
$125$	10.6665	+	3.35047i	0.954041	+	0.299675i
$126$	−5.05964	−	3.67604i	−0.450749	−	0.327488i
$127$	4.57605	+	11.9210i	0.406058	+	1.05782i	0.972332	+	0.233601i	$0.0750510\pi$
$127$	4.57605	+	11.9210i	0.406058	+	1.05782i	−0.566274	+	0.824217i	$0.691616\pi$
$128$	6.17508	−	12.1193i	0.545805	−	1.07120i
$129$	1.54924	+	0.894453i	0.136403	+	0.0787522i
$130$	−8.77111	+	3.93956i	−0.769277	+	0.345522i
$131$	−8.62134	+	9.57497i	−0.753250	+	0.836569i	−0.990874	−	0.134788i	$-0.956965\pi$
$131$	−8.62134	+	9.57497i	−0.753250	+	0.836569i	0.237624	+	0.971357i	$0.423631\pi$
$132$	1.81921	+	3.57039i	0.158342	+	0.310763i
$133$	1.53103	−	29.2139i	0.132758	−	2.53316i
$134$	5.72473	+	12.8580i	0.494542	+	1.11076i
$135$	−4.14643	−	8.07248i	−0.356868	−	0.694769i
$136$	14.2459	+	1.49731i	1.22158	+	0.128393i
$137$	9.64396	−	11.9093i	0.823939	−	1.01748i	−0.175516	−	0.984477i	$-0.556159\pi$
$137$	9.64396	−	11.9093i	0.823939	−	1.01748i	0.999455	−	0.0330033i	$-0.0105072\pi$
$138$	−15.1535	−	9.84078i	−1.28995	−	0.837703i
$139$	−14.8612	+	10.7973i	−1.26051	+	0.915813i	−0.998783	−	0.0493298i	$-0.984291\pi$
$139$	−14.8612	+	10.7973i	−1.26051	+	0.915813i	−0.261725	+	0.965142i	$0.584291\pi$
$140$	5.48082	+	1.44939i	0.463214	+	0.122496i
$141$	−2.11712	−	9.96029i	−0.178294	−	0.838807i
$142$	−7.27357	−	5.89002i	−0.610385	−	0.494280i
$143$	−6.56458	+	5.31589i	−0.548958	+	0.444537i
$144$	−0.971625	+	4.57114i	−0.0809687	+	0.380928i
$145$	−6.42892	+	2.11214i	−0.533892	+	0.175404i
$146$	3.38943	−	3.05186i	0.280511	−	0.252573i
$147$	−16.1410	+	8.22425i	−1.33129	+	0.678325i
$148$	−0.0976973	−	1.86418i	−0.00803067	−	0.153234i
$149$	−3.49085	+	2.01544i	−0.285981	+	0.165111i	−0.636128	−	0.771583i	$-0.719465\pi$
$149$	−3.49085	+	2.01544i	−0.285981	+	0.165111i	0.350147	+	0.936695i	$0.386132\pi$
$150$	−12.0669	−	10.7231i	−0.985261	−	0.875537i
$151$	9.51838	−	3.09271i	0.774595	−	0.251681i	0.105064	−	0.994465i	$-0.466495\pi$
$151$	9.51838	−	3.09271i	0.774595	−	0.251681i	0.669531	+	0.742784i	$0.266495\pi$
$152$	−15.1064	+	5.79880i	−1.22529	+	0.470345i
$153$	−6.12366	+	0.969892i	−0.495068	+	0.0784111i
$154$	20.7459			1.67176
$155$	−7.97125	+	9.56343i	−0.640266	+	0.768153i
$156$	3.33291			0.266846
$157$	−11.4983	+	1.82115i	−0.917663	+	0.145344i	−0.597362	−	0.801972i	$-0.703784\pi$
$157$	−11.4983	+	1.82115i	−0.917663	+	0.145344i	−0.320302	+	0.947316i	$0.603784\pi$
$158$	2.70767	−	1.03938i	0.215411	−	0.0826885i
$159$	14.9842	−	4.86866i	1.18832	−	0.386110i
$160$	−1.23254	−	7.62066i	−0.0974412	−	0.602466i
$161$	−19.4485	+	11.2286i	−1.53275	+	0.884936i
$162$	0.930476	+	17.7545i	0.0731051	+	1.39493i
$163$	−20.7606	+	10.5781i	−1.62610	+	0.828538i	−0.627337	+	0.778748i	$0.715855\pi$
$163$	−20.7606	+	10.5781i	−1.62610	+	0.828538i	−0.998760	+	0.0497898i	$0.984145\pi$
$164$	−3.41713	+	3.07680i	−0.266833	+	0.240258i
$165$	−12.6570	−	6.39702i	−0.985344	−	0.498007i
$166$	0.113244	−	0.532771i	0.00878944	−	0.0413511i
$167$	−3.07448	+	2.48967i	−0.237911	+	0.192656i	−0.740860	−	0.671660i	$-0.765582\pi$
$167$	−3.07448	+	2.48967i	−0.237911	+	0.192656i	0.502949	+	0.864316i	$0.332248\pi$
$168$	13.7755	+	11.1552i	1.06280	+	0.860642i
$169$	−1.24212	−	5.84369i	−0.0955474	−	0.449515i
$170$	20.2360	−	11.7716i	1.55203	−	0.902843i
$171$	5.66607	−	4.11664i	0.433295	−	0.314807i
$172$	0.476304	+	0.309315i	0.0363178	+	0.0235851i
$173$	−12.7070	+	15.6918i	−0.966096	+	1.19303i	0.0150751	+	0.999886i	$0.495201\pi$
$173$	−12.7070	+	15.6918i	−0.966096	+	1.19303i	−0.981171	+	0.193142i	$0.938132\pi$
$174$	9.71714	+	1.02131i	0.736654	+	0.0774255i
$175$	−18.6839	+	7.31261i	−1.41237	+	0.552781i
$176$	−6.30528	−	14.1619i	−0.475278	−	1.06749i
$177$	−0.241672	+	4.61137i	−0.0181652	+	0.346612i
$178$	0.463709	+	0.910080i	0.0347565	+	0.0682134i
$179$	7.55741	−	8.39335i	0.564867	−	0.627349i	−0.391267	−	0.920277i	$-0.627963\pi$
$179$	7.55741	−	8.39335i	0.564867	−	0.627349i	0.956134	+	0.292929i	$0.0946298\pi$
$180$	0.556098	+	1.23811i	0.0414491	+	0.0922831i
$181$	−4.60198	−	2.65696i	−0.342063	−	0.197490i	0.319121	−	0.947714i	$-0.396612\pi$
$181$	−4.60198	−	2.65696i	−0.342063	−	0.197490i	−0.661184	+	0.750224i	$0.729946\pi$
$182$	7.83373	−	15.3746i	0.580675	−	1.13964i
$183$	−0.0393922	−	0.102620i	−0.00291195	−	0.00758590i
$184$	10.0493	+	7.30126i	0.740846	+	0.538256i
$185$	4.17441	+	5.12065i	0.306909	+	0.376478i
$186$	16.1566	−	7.88047i	1.18466	−	0.577824i
$187$	14.5428	−	14.5428i	1.06347	−	1.06347i
$188$	−0.505714	−	3.19296i	−0.0368830	−	0.232870i
$189$	14.8780	+	6.62412i	1.08222	+	0.481834i
$190$	−14.3306	+	22.2259i	−1.03965	+	1.61244i
$191$	2.52575	−	4.37473i	0.182757	−	0.316545i	−0.760061	−	0.649851i	$-0.774831\pi$
$191$	2.52575	−	4.37473i	0.182757	−	0.316545i	0.942818	+	0.333307i	$0.108164\pi$
$192$	2.12638	−	7.93575i	0.153458	−	0.572713i
$193$	−6.54766	+	0.343148i	−0.471311	+	0.0247003i	−0.286513	−	0.958076i	$-0.592496\pi$
$193$	−6.54766	+	0.343148i	−0.471311	+	0.0247003i	−0.184797	+	0.982777i	$0.559163\pi$
$194$	−13.2124	−	4.29297i	−0.948595	−	0.308217i
$195$	−9.52007	+	6.96440i	−0.681746	+	0.498731i
$196$	−5.25394	+	2.33921i	−0.375282	+	0.167086i
$197$	1.76939	+	2.72462i	0.126064	+	0.194121i	0.896067	−	0.443919i	$-0.146412\pi$
$197$	1.76939	+	2.72462i	0.126064	+	0.194121i	−0.770003	+	0.638040i	$0.779745\pi$
$198$	3.12568	+	3.85989i	0.222132	+	0.274311i
$199$	−1.03167	−	9.81570i	−0.0731333	−	0.695817i	−0.968250	−	0.249985i	$-0.919574\pi$
$199$	−1.03167	−	9.81570i	−0.0731333	−	0.695817i	0.895117	−	0.445832i	$-0.147092\pi$
$200$	7.89856	+	7.79595i	0.558513	+	0.551257i
$201$	10.1489	+	13.9688i	0.715848	+	0.985280i
$202$	0.175292	−	1.10675i	0.0123335	−	0.0778707i
$203$	6.61404	−	10.1847i	0.464214	−	0.714827i
$204$	−8.07041	+	0.848234i	−0.565042	+	0.0593883i
$205$	3.33140	−	15.9289i	0.232675	−	1.11252i
$206$	−13.5445	−	2.87898i	−0.943691	−	0.200588i
$207$	−5.01933	−	1.92674i	−0.348867	−	0.133918i
$208$	−12.8761	−	0.674807i	−0.892796	−	0.0467894i
$209$	−7.17922	+	22.0954i	−0.496597	+	1.52837i
$210$	28.9349	+	1.42158i	1.99670	+	0.0980985i
$211$	4.10381	+	7.10801i	0.282518	+	0.489335i	0.972004	−	0.234963i	$-0.0754970\pi$
$211$	4.10381	+	7.10801i	0.282518	+	0.489335i	−0.689486	+	0.724299i	$0.742164\pi$
$212$	4.83143	−	1.29458i	0.331824	−	0.0889121i
$213$	−10.2302	−	5.21255i	−0.700962	−	0.357158i
$214$	1.07606	−	2.41687i	0.0735580	−	0.165214i
$215$	−2.00685	+	0.111754i	−0.136866	+	0.00762156i
$216$		−	9.00823i		−	0.612932i
$217$	0.389536	−	22.3389i	0.0264434	−	1.51647i
$218$	−5.85168	−	5.85168i	−0.396326	−	0.396326i
$219$	3.28874	−	4.52657i	0.222233	−	0.305877i
$220$	−3.90644	−	2.23839i	−0.263372	−	0.150912i
$221$	−5.28607	−	16.2689i	−0.355580	−	1.09436i
$222$	−2.46889	−	9.21401i	−0.165701	−	0.618404i
$223$	14.1855	+	3.80101i	0.949935	+	0.254534i	0.700335	−	0.713815i	$-0.253034\pi$
$223$	14.1855	+	3.80101i	0.949935	+	0.254534i	0.249600	+	0.968349i	$0.419701\pi$
$224$	10.2952	+	9.26986i	0.687879	+	0.619369i
$225$	−4.17556	−	2.37449i	−0.278370	−	0.158300i
$226$	5.21383	+	5.79054i	0.346819	+	0.385181i
$227$	−2.16005	+	5.62712i	−0.143368	+	0.373485i	−0.986397	−	0.164383i	$-0.947437\pi$
$227$	−2.16005	+	5.62712i	−0.143368	+	0.373485i	0.843029	+	0.537868i	$0.180770\pi$
$228$	7.68787	−	4.99256i	0.509141	−	0.330640i
$229$	1.20047	−	11.4217i	0.0793294	−	0.754769i	−0.880474	−	0.474095i	$-0.842775\pi$
$229$	1.20047	−	11.4217i	0.0793294	−	0.754769i	0.959803	−	0.280674i	$-0.0905580\pi$
$230$	20.3010	−	0.0663656i	1.33861	−	0.00437602i
$231$	24.8941	−	5.29139i	1.63791	−	0.348148i
$232$	−6.63441	−	1.05079i	−0.435570	−	0.0689876i
$233$	20.5862	+	3.26054i	1.34865	+	0.213605i	0.788626	−	0.614873i	$-0.210793\pi$
$233$	20.5862	+	3.26054i	1.34865	+	0.213605i	0.560022	+	0.828478i	$0.310793\pi$
$234$	4.04078	−	0.858895i	0.264154	−	0.0561477i
$235$	8.11646	+	8.06357i	0.529460	+	0.526009i
$236$	−0.153238	+	1.45796i	−0.00997493	+	0.0949052i
$237$	2.98397	−	1.93781i	0.193830	−	0.125874i
$238$	−15.0560	+	39.2221i	−0.975933	+	2.54239i
$239$	−1.73606	−	1.92809i	−0.112296	−	0.124718i	0.684376	−	0.729129i	$-0.260075\pi$
$239$	−1.73606	−	1.92809i	−0.112296	−	0.124718i	−0.796672	+	0.604412i	$0.793408\pi$
$240$	−7.82372	−	20.1840i	−0.505019	−	1.30287i
$241$	2.09986	+	1.89072i	0.135264	+	0.121792i	0.733986	−	0.679165i	$-0.237658\pi$
$241$	2.09986	+	1.89072i	0.135264	+	0.121792i	−0.598722	+	0.800957i	$0.704325\pi$
$242$	1.32281	+	0.354446i	0.0850336	+	0.0227847i
$243$	2.49367	+	9.30651i	0.159969	+	0.597013i
$244$	−0.0107837	−	0.0331889i	−0.000690357	−	0.00212470i
$245$	10.1193	−	17.6602i	0.646498	−	1.12827i
$246$	−13.8111	+	19.0094i	−0.880566	+	1.21200i
$247$	13.6637	+	13.6637i	0.869401	+	0.869401i
$248$	−11.3756	+	4.82891i	−0.722354	+	0.306636i
$249$		−	0.668181i		−	0.0423443i
$250$	17.9414	+	2.66154i	1.13471	+	0.168331i
$251$	−9.10914	+	20.4595i	−0.574964	+	1.29139i	0.358771	+	0.933426i	$0.383196\pi$
$251$	−9.10914	+	20.4595i	−0.574964	+	1.29139i	−0.933735	+	0.357965i	$0.883471\pi$
$252$	−2.17023	−	1.10579i	−0.136712	−	0.0696582i
$253$	17.2270	−	4.61595i	1.08305	−	0.290202i
$254$	10.3576	+	17.9399i	0.649894	+	1.12565i
$255$	21.2797	−	19.2867i	1.33259	−	1.20778i
$256$	4.26742	−	13.1338i	0.266714	−	0.820861i
$257$	−0.615025	−	0.0322321i	−0.0383642	−	0.00201058i	0.0331442	−	0.999451i	$-0.489448\pi$
$257$	−0.615025	−	0.0322321i	−0.0383642	−	0.00201058i	−0.0715084	+	0.997440i	$0.522781\pi$
$258$	2.70936	+	1.04003i	0.168677	+	0.0647492i
$259$	−11.5969	−	2.46500i	−0.720598	−	0.153168i
$260$	−3.13393	+	2.04979i	−0.194358	+	0.127123i
$261$	2.89142	−	0.303901i	0.178974	−	0.0188110i
$262$	−11.3841	+	17.5300i	−0.703315	+	1.08301i
$263$	4.89504	−	30.9061i	0.301841	−	1.90575i	−0.108996	−	0.994042i	$-0.534764\pi$
$263$	4.89504	−	30.9061i	0.301841	−	1.90575i	0.410838	−	0.911708i	$-0.365236\pi$
$264$	−8.27436	−	11.3887i	−0.509252	−	0.700925i
$265$	−11.0953	+	13.7935i	−0.681578	+	0.847328i
$266$	−4.96075	−	47.1984i	−0.304163	−	2.89392i
$267$	0.788549	+	0.973777i	0.0482584	+	0.0595942i
$268$	2.98548	+	4.59724i	0.182367	+	0.280821i
$269$	23.1958	−	10.3274i	1.41427	−	0.629674i	0.449623	−	0.893218i	$-0.351558\pi$
$269$	23.1958	−	10.3274i	1.41427	−	0.629674i	0.964647	+	0.263545i	$0.0848917\pi$
$270$	−8.69253	−	11.8824i	−0.529011	−	0.723138i
$271$	−3.31533	−	1.07722i	−0.201392	−	0.0654363i	0.206584	−	0.978429i	$-0.433765\pi$
$271$	−3.31533	−	1.07722i	−0.201392	−	0.0654363i	−0.407976	+	0.912993i	$0.633765\pi$
$272$	31.3503	−	1.64300i	1.90089	−	0.0996214i
$273$	5.47868	−	20.4467i	0.331585	−	1.23749i
$274$	12.4303	−	21.5299i	0.750941	−	1.30067i
$275$	15.8356	−	1.76914i	0.954922	−	0.106683i
$276$	−6.42857	−	2.86218i	−0.386954	−	0.172283i
$277$	3.46797	+	21.8959i	0.208370	+	1.31560i	0.840955	+	0.541105i	$0.181994\pi$
$277$	3.46797	+	21.8959i	0.208370	+	1.31560i	−0.632585	+	0.774491i	$0.718006\pi$
$278$	−21.0721	+	21.0721i	−1.26382	+	1.26382i
$279$	4.21496	−	3.29321i	0.252343	−	0.197159i
$280$	−19.8137	−	2.01704i	−1.18410	−	0.120541i
$281$	−3.60384	−	2.61834i	−0.214987	−	0.156197i	0.475080	−	0.879943i	$-0.342419\pi$
$281$	−3.60384	−	2.61834i	−0.214987	−	0.156197i	−0.690067	+	0.723745i	$0.742419\pi$
$282$	−5.92004	−	15.4222i	−0.352533	−	0.918380i
$283$	−7.22770	+	14.1852i	−0.429642	+	0.843220i	0.570123	+	0.821559i	$0.306895\pi$
$283$	−7.22770	+	14.1852i	−0.429642	+	0.843220i	−0.999765	+	0.0216610i	$0.993105\pi$
$284$	−3.15674	−	1.82255i	−0.187318	−	0.108148i
$285$	−11.5271	+	30.3251i	−0.682807	+	1.79630i
$286$	−9.16945	+	10.1837i	−0.542201	+	0.602175i
$287$	13.2584	+	26.0211i	0.782619	+	1.53598i
$288$	−0.173581	+	3.31212i	−0.0102283	+	0.195169i
$289$	10.0258	+	22.5183i	0.589753	+	1.32461i
$290$	−9.76512	+	5.01586i	−0.573428	+	0.294541i
$291$	−16.9491	−	1.78143i	−0.993576	−	0.104429i
$292$	1.11786	−	1.38045i	0.0654180	−	0.0807845i
$293$	3.85779	+	2.50528i	0.225374	+	0.146360i	0.652387	−	0.757886i	$-0.273768\pi$
$293$	3.85779	+	2.50528i	0.225374	+	0.146360i	−0.427013	+	0.904245i	$0.640434\pi$
$294$	−23.7758	+	17.2741i	−1.38663	+	1.00745i
$295$	−2.60882	−	4.48470i	−0.151892	−	0.261109i
$296$	1.36346	+	6.41457i	0.0792494	+	0.372839i
$297$	−10.0514	−	8.13949i	−0.583243	−	0.472301i
$298$	−5.08195	+	4.11528i	−0.294390	+	0.238392i
$299$	3.08413	−	14.5097i	0.178360	−	0.839117i
$300$	−5.29504	−	3.38963i	−0.305709	−	0.195700i
$301$	2.68054	−	2.41357i	0.154504	−	0.139116i
$302$	14.4666	−	7.37108i	0.832457	−	0.424158i
$303$	−0.0719429	−	1.37275i	−0.00413301	−	0.0788625i
$304$	−30.7115	+	17.7313i	−1.76142	+	1.01696i
$305$	0.100153	+	0.0722666i	0.00573477	+	0.00413798i
$306$	−9.56588	+	3.10814i	−0.546845	+	0.177681i
$307$	−16.7611	+	6.43398i	−0.956606	+	0.367206i	−0.786065	−	0.618144i	$-0.787885\pi$
$307$	−16.7611	+	6.43398i	−0.956606	+	0.367206i	−0.170541	+	0.985351i	$0.554551\pi$
$308$	7.98025	−	1.26395i	0.454717	−	0.0720201i
$309$	−16.9870			−0.966358
$310$	−10.3454	+	17.3466i	−0.587581	+	0.985219i
$311$	21.2003			1.20216			0.601081	−	0.799188i	$-0.294737\pi$
$311$	21.2003			1.20216			0.601081	+	0.799188i	$0.294737\pi$
$312$	−11.5644	+	1.83163i	−0.654707	+	0.103695i
$313$	5.77020	−	2.21497i	0.326151	−	0.125198i	−0.189783	−	0.981826i	$-0.560778\pi$
$313$	5.77020	−	2.21497i	0.326151	−	0.125198i	0.515934	+	0.856628i	$0.327445\pi$
$314$	−17.9617	+	5.83611i	−1.01364	+	0.329351i
$315$	8.50966	−	1.37633i	0.479465	−	0.0775473i
$316$	0.978225	−	0.564779i	0.0550295	−	0.0317713i
$317$	−1.50079	−	28.6368i	−0.0842928	−	1.60840i	−0.634195	−	0.773173i	$-0.718668\pi$
$317$	−1.50079	−	28.6368i	−0.0842928	−	1.60840i	0.549902	−	0.835229i	$-0.314665\pi$
$318$	22.7738	−	11.6038i	1.27709	−	0.650711i
$319$	−7.16707	+	6.45326i	−0.401279	+	0.361313i
$320$	2.88118	+	8.76972i	0.161063	+	0.490242i
$321$	0.674778	−	3.17458i	0.0376624	−	0.177188i
$322$	−28.3129	+	22.9274i	−1.57782	+	1.27769i
$323$	−36.5632	−	29.6083i	−2.03443	−	1.64745i
$324$	1.43962	+	6.77287i	0.0799788	+	0.376271i
$325$	4.66848	−	12.4036i	0.258961	−	0.688028i
$326$	−30.5805	+	22.2180i	−1.69370	+	1.23054i
$327$	−8.51422	−	5.52920i	−0.470837	−	0.305765i
$328$	10.1658	−	12.5537i	0.561312	−	0.693162i
$329$	−20.4194	−	2.14617i	−1.12576	−	0.118322i
$330$	−21.9039	−	7.03793i	−1.20577	−	0.387425i
$331$	−8.41203	−	18.8937i	−0.462367	−	1.03849i	−0.982814	−	0.184600i	$-0.940901\pi$
$331$	−8.41203	−	18.8937i	−0.462367	−	1.03849i	0.520447	−	0.853894i	$-0.325765\pi$
$332$	0.0111020	−	0.211838i	0.000609300	−	0.0116261i
$333$	−1.28862	−	2.52906i	−0.0706159	−	0.138592i
$334$	−4.29446	+	4.76948i	−0.234982	+	0.260974i
$335$	−18.1340	−	6.89305i	−0.990765	−	0.376608i
$336$	33.6432	+	19.4239i	1.83539	+	1.05966i
$337$	13.6162	−	26.7234i	0.741724	−	1.45572i	−0.143059	−	0.989714i	$-0.545694\pi$
$337$	13.6162	−	26.7234i	0.741724	−	1.45572i	0.884784	−	0.466002i	$-0.154306\pi$
$338$	−3.47328	−	9.04821i	−0.188922	−	0.492158i
$339$	7.73324	+	5.61853i	0.420012	+	0.305157i
$340$	7.06691	−	5.76102i	0.383257	−	0.312435i
$341$	−4.89047	+	17.0562i	−0.264834	+	0.923646i
$342$	8.03409	−	8.03409i	0.434434	−	0.434434i
$343$	1.31986	+	8.33329i	0.0712659	+	0.449955i
$344$	−1.82265	−	0.811497i	−0.0982708	−	0.0437530i
$345$	24.3432	−	5.25755i	1.31060	−	0.283057i
$346$	−16.3783	+	28.3681i	−0.880504	+	1.52508i
$347$	3.76094	−	14.0360i	0.201898	−	0.753494i	−0.788475	−	0.615067i	$-0.789129\pi$
$347$	3.76094	−	14.0360i	0.201898	−	0.753494i	0.990373	−	0.138427i	$-0.0442045\pi$
$348$	3.80007	−	0.199153i	0.203705	−	0.0106757i
$349$	−32.5479	−	10.5755i	−1.74225	−	0.566092i	−0.747124	−	0.664685i	$-0.768566\pi$
$349$	−32.5479	−	10.5755i	−1.74225	−	0.566092i	−0.995128	+	0.0985931i	$0.968566\pi$
$350$	−28.0818	+	16.4587i	−1.50103	+	0.879757i
$351$	−9.82752	+	4.37550i	−0.524554	+	0.233547i
$352$	−5.99213	−	9.22708i	−0.319382	−	0.491805i
$353$	−3.57657	−	4.41670i	−0.190362	−	0.235077i	0.673025	−	0.739620i	$-0.264995\pi$
$353$	−3.57657	−	4.41670i	−0.190362	−	0.235077i	−0.863387	+	0.504542i	$0.831661\pi$
$354$	0.783048	+	7.45020i	0.0416185	+	0.395974i
$355$	12.8252	−	1.39039i	0.680693	−	0.0737943i
$356$	0.233820	+	0.321825i	0.0123924	+	0.0170567i
$357$	−8.06250	+	50.9046i	−0.426713	+	2.69416i
$358$	9.97927	−	15.3667i	0.527421	−	0.812157i
$359$	33.3312	−	3.50325i	1.75915	−	0.184895i	0.830795	−	0.556579i	$-0.187886\pi$
$359$	33.3312	−	3.50325i	1.75915	−	0.184895i	0.928359	+	0.371684i	$0.121220\pi$
$360$	−2.60994	−	3.99034i	−0.137556	−	0.210309i
$361$	33.4003	+	7.09945i	1.75791	+	0.373655i
$362$	−8.04811	−	3.08938i	−0.422999	−	0.162374i
$363$	1.67771	+	0.0879250i	0.0880569	+	0.00461487i
$364$	2.07667	−	6.39134i	0.108847	−	0.334997i
$365$	−0.308486	+	6.27895i	−0.0161469	+	0.328655i
$366$	−0.0891618	−	0.154433i	−0.00466056	−	0.00807233i
$367$	12.7043	−	3.40412i	0.663161	−	0.177693i	0.0884888	−	0.996077i	$-0.471796\pi$
$367$	12.7043	−	3.40412i	0.663161	−	0.177693i	0.574672	+	0.818384i	$0.305130\pi$
$368$	24.2561	+	12.3591i	1.26444	+	0.644263i
$369$	−2.84379	+	6.38725i	−0.148042	+	0.332507i
$370$	7.98825	+	7.14550i	0.415289	+	0.371477i
$371$		−	31.7679i		−	1.64931i
$372$	5.73479	−	4.01569i	0.297335	−	0.208204i
$373$	11.6267	+	11.6267i	0.602007	+	0.602007i	0.940845	−	0.338838i	$-0.110034\pi$
$373$	11.6267	+	11.6267i	0.602007	+	0.602007i	−0.338838	+	0.940845i	$0.610034\pi$
$374$	19.6114	−	26.9928i	1.01408	−	1.39576i
$375$	22.2076	−	1.38236i	1.14679	−	0.0713848i
$376$	3.50943	+	10.8009i	0.180985	+	0.557014i
$377$	2.07612	+	7.74819i	0.106926	+	0.399052i
$378$	25.5203	+	6.83816i	1.31263	+	0.351717i
$379$	−2.54809	−	2.29431i	−0.130887	−	0.117851i	0.601088	−	0.799183i	$-0.294734\pi$
$379$	−2.54809	−	2.29431i	−0.130887	−	0.117851i	−0.731974	+	0.681332i	$0.761401\pi$
$380$	−4.15838	+	9.42265i	−0.213320	+	0.483372i
$381$	17.0043	+	18.8852i	0.871155	+	0.967516i
$382$	2.93683	−	7.65069i	0.150261	−	0.391443i
$383$	26.7201	−	17.3523i	1.36534	−	0.886659i	0.366297	−	0.930498i	$-0.380625\pi$
$383$	26.7201	−	17.3523i	1.36534	−	0.886659i	0.999039	+	0.0438386i	$0.0139587\pi$
$384$	2.82954	−	26.9213i	0.144395	−	1.37382i
$385$	−20.1535	+	20.2857i	−1.02712	+	1.03386i
$386$	−10.4043	+	2.21151i	−0.529566	+	0.112563i
$387$	0.852920	+	0.135089i	0.0433563	+	0.00686697i
$388$	−5.34390	−	0.846391i	−0.271296	−	0.0429690i
$389$	8.41432	−	1.78852i	0.426623	−	0.0906815i	0.0104038	−	0.999946i	$-0.496688\pi$
$389$	8.41432	−	1.78852i	0.426623	−	0.0906815i	0.416219	+	0.909264i	$0.363355\pi$
$390$	−13.4867	+	13.5752i	−0.682926	+	0.687405i
$391$	−3.77525	+	35.9191i	−0.190923	+	1.81651i
$392$	16.9444	−	11.0038i	0.855823	−	0.555778i
$393$	−9.18922	+	23.9387i	−0.463535	+	1.20755i
$394$	3.52658	+	3.91667i	0.177667	+	0.197319i
$395$	−1.61403	+	3.65731i	−0.0812108	+	0.184019i
$396$	1.43751	+	1.29434i	0.0722374	+	0.0650428i
$397$	−22.2269	−	5.95568i	−1.11554	−	0.298907i	−0.346461	−	0.938064i	$-0.612617\pi$
$397$	−22.2269	−	5.95568i	−1.11554	−	0.298907i	−0.769076	+	0.639157i	$0.779283\pi$
$398$	−4.14411	−	15.4660i	−0.207725	−	0.775242i
$399$	−17.9909	−	55.3703i	−0.900672	−	2.77198i
$400$	19.7701	+	14.1673i	0.988506	+	0.708364i
$401$	5.69752	−	7.84197i	0.284521	−	0.391609i	−0.642704	−	0.766115i	$-0.722188\pi$
$401$	5.69752	−	7.84197i	0.284521	−	0.391609i	0.927225	+	0.374505i	$0.122188\pi$
$402$	19.8067	+	19.8067i	0.987870	+	0.987870i
$403$	10.7935	+	10.0647i	0.537662	+	0.501360i
$404$		−	0.436408i		−	0.0217121i
$405$	−18.2646	−	16.3377i	−0.907574	−	0.811827i
$406$	8.01307	−	17.9976i	0.397682	−	0.893208i
$407$	8.38938	+	4.27460i	0.415846	+	0.211884i
$408$	27.5363	−	7.37833i	1.36325	−	0.365282i
$409$	−4.50565	−	7.80401i	−0.222790	−	0.385883i	0.732864	−	0.680375i	$-0.238183\pi$
$409$	−4.50565	−	7.80401i	−0.222790	−	0.385883i	−0.955654	+	0.294491i	$0.904850\pi$
$410$	1.29549	−	26.3686i	0.0639799	−	1.30225i
$411$	9.42436	−	29.0052i	0.464869	−	1.43072i
$412$	−5.38551	−	0.282243i	−0.265325	−	0.0139051i
$413$	8.69239	+	3.33670i	0.427725	+	0.164188i
$414$	−8.53151	−	1.81343i	−0.419301	−	0.0891252i
$415$	0.410942	+	0.628289i	0.0201724	+	0.0308415i
$416$	−9.10072	+	0.956524i	−0.446199	+	0.0468975i
$417$	−19.9109	+	30.6600i	−0.975039	+	1.50143i
$418$	−5.89597	+	37.2257i	−0.288381	+	1.82077i
$419$	0.281689	+	0.387712i	0.0137614	+	0.0189410i	0.815842	−	0.578274i	$-0.196274\pi$
$419$	0.281689	+	0.387712i	0.0137614	+	0.0189410i	−0.802081	+	0.597215i	$0.796274\pi$
$420$	11.2169	−	1.21603i	0.547328	−	0.0593362i
$421$	0.524251	+	4.98792i	0.0255504	+	0.243096i	0.999842	+	0.0178033i	$0.00566726\pi$
$421$	0.524251	+	4.98792i	0.0255504	+	0.243096i	−0.974291	+	0.225293i	$0.927666\pi$
$422$	8.37948	+	10.3478i	0.407906	+	0.503723i
$423$	−2.67718	−	4.12249i	−0.130169	−	0.200442i
$424$	−16.0525	+	7.14704i	−0.779579	+	0.347091i
$425$	−8.14765	+	31.2226i	−0.395219	+	1.51452i
$426$	−17.7148	−	5.75590i	−0.858287	−	0.278874i
$427$	−0.221333	+	0.0115996i	−0.0107111	+	0.000561344i
$428$	0.266676	−	0.995247i	0.0128903	−	0.0481071i
$429$	−8.40543	+	14.5586i	−0.405818	+	0.702898i
$430$	−3.18724	+	0.688366i	−0.153702	+	0.0331960i
$431$	12.0308	+	5.35646i	0.579504	+	0.258012i	0.675488	−	0.737371i	$-0.263933\pi$
$431$	12.0308	+	5.35646i	0.579504	+	0.258012i	−0.0959839	+	0.995383i	$0.530600\pi$
$432$	−3.08840	−	19.4994i	−0.148590	−	0.938163i
$433$	16.6940	−	16.6940i	0.802264	−	0.802264i	−0.181185	−	0.983449i	$-0.557993\pi$
$433$	16.6940	−	16.6940i	0.802264	−	0.802264i	0.983449	+	0.181185i	$0.0579932\pi$
$434$	−5.04505	−	35.8928i	−0.242170	−	1.72291i
$435$	−10.4383	+	8.50943i	−0.500479	+	0.407996i
$436$	−2.60745	−	1.89443i	−0.124874	−	0.0907265i
$437$	−14.6209	−	38.0887i	−0.699412	−	1.82203i
$438$	4.12084	−	8.08761i	0.196901	−	0.386441i
$439$	−26.0876	−	15.0617i	−1.24509	−	0.718856i	−0.274967	−	0.961454i	$-0.588667\pi$
$439$	−26.0876	−	15.0617i	−1.24509	−	0.718856i	−0.970127	+	0.242598i	$0.922000\pi$
$440$	14.7846	+	5.61988i	0.704827	+	0.267917i
$441$	−5.85142	+	6.49866i	−0.278639	+	0.309460i
$442$	−12.5987	−	24.7263i	−0.599258	−	1.17611i
$443$	−1.22981	+	23.4663i	−0.0584302	+	1.11492i	0.799339	+	0.600880i	$0.205183\pi$
$443$	−1.22981	+	23.4663i	−0.0584302	+	1.11492i	−0.857769	+	0.514035i	$0.828150\pi$
$444$	−1.51106	−	3.39390i	−0.0717117	−	0.161067i
$445$	−1.34036	−	0.430670i	−0.0635391	−	0.0204157i
$446$	23.6943	+	2.49038i	1.12196	+	0.117923i
$447$	−5.04845	+	6.23431i	−0.238783	+	0.294873i
$448$	−13.8930	−	9.02225i	−0.656384	−	0.426261i
$449$	−0.457247	+	0.332209i	−0.0215788	+	0.0156779i	−0.598522	−	0.801106i	$-0.704245\pi$
$449$	−0.457247	+	0.332209i	−0.0215788	+	0.0156779i	0.576944	+	0.816784i	$0.304245\pi$
$450$	−7.29316	−	2.74501i	−0.343803	−	0.129401i
$451$	−4.82207	−	22.6861i	−0.227063	−	1.06825i
$452$	2.35837	+	1.90977i	0.110928	+	0.0898281i
$453$	15.4791	−	12.5347i	0.727271	−	0.588932i
$454$	−2.03302	+	9.56460i	−0.0954143	+	0.448889i
$455$	7.42347	+	22.5955i	0.348017	+	1.05929i
$456$	−23.9314	+	21.5480i	−1.12069	+	1.00908i
$457$	5.31611	−	2.70869i	0.248677	−	0.126707i	−0.325210	−	0.945642i	$-0.605435\pi$
$457$	5.31611	−	2.70869i	0.248677	−	0.126707i	0.573887	+	0.818935i	$0.305435\pi$
$458$	−0.975091	−	18.6059i	−0.0455630	−	0.869394i
$459$	22.6831	−	13.0961i	1.05876	−	0.611273i
$460$	7.80506	−	1.26237i	0.363913	−	0.0588582i
$461$	−29.3680	+	9.54223i	−1.36780	+	0.444426i	−0.898640	−	0.438687i	$-0.855444\pi$
$461$	−29.3680	+	9.54223i	−1.36780	+	0.444426i	−0.469162	+	0.883112i	$0.655444\pi$
$462$	38.5452	−	14.7961i	1.79329	−	0.688378i
$463$	−30.9374	+	4.90000i	−1.43778	+	0.227722i	−0.826164	−	0.563430i	$-0.809482\pi$
$463$	−30.9374	+	4.90000i	−1.43778	+	0.227722i	−0.611619	+	0.791152i	$0.709482\pi$
$464$	−14.7212			−0.683415
$465$	−7.98962	+	23.4537i	−0.370510	+	1.08764i
$466$	33.8130			1.56636
$467$	17.2170	−	2.72691i	0.796709	−	0.126186i	0.255208	−	0.966886i	$-0.417856\pi$
$467$	17.2170	−	2.72691i	0.796709	−	0.126186i	0.541501	+	0.840700i	$0.317856\pi$
$468$	1.50202	−	0.576572i	0.0694310	−	0.0266521i
$469$	33.1107	−	10.7583i	1.52891	−	0.496773i
$470$	15.0515	+	10.8606i	0.694274	+	0.500960i
$471$	−20.0646	+	11.5843i	−0.924526	+	0.533775i
$472$	−0.269533	−	5.14300i	−0.0124063	−	0.236726i
$473$	−2.55235	+	1.30049i	−0.117357	+	0.0597965i
$474$	4.28947	−	3.86226i	0.197022	−	0.177399i
$475$	−7.81150	−	35.6040i	−0.358416	−	1.63362i
$476$	−3.40190	+	16.0047i	−0.155926	+	0.733574i
$477$	5.91058	−	4.78630i	0.270627	−	0.219149i
$478$	−3.27102	−	2.64882i	−0.149613	−	0.121154i
$479$	2.20790	+	10.3873i	0.100881	+	0.474610i	0.999366	+	0.0356047i	$0.0113357\pi$
$479$	2.20790	+	10.3873i	0.100881	+	0.474610i	−0.898484	+	0.439005i	$0.855331\pi$
$480$	−7.72513	−	13.2799i	−0.352602	−	0.606140i
$481$	6.33571	−	4.60316i	0.288883	−	0.209886i
$482$	3.84447	+	2.49663i	0.175111	+	0.113718i
$483$	−28.1263	+	34.7331i	−1.27979	+	1.58041i
$484$	0.530435	+	0.0557510i	0.0241107	+	0.00253414i
$485$	17.0328	−	8.74892i	0.773421	−	0.397268i
$486$	6.35747	+	14.2791i	0.288381	+	0.647713i
$487$	0.0675629	−	1.28918i	0.00306157	−	0.0584182i	−0.996671	−	0.0815227i	$-0.974022\pi$
$487$	0.0675629	−	1.28918i	0.00306157	−	0.0584182i	0.999733	+	0.0231045i	$0.00735504\pi$
$488$	0.0556562	+	0.109231i	0.00251944	+	0.00494468i
$489$	−31.0282	+	34.4603i	−1.40314	+	1.55835i
$490$	11.7325	−	30.8653i	0.530018	−	1.39435i
$491$	14.5025	+	8.37300i	0.654487	+	0.377868i	0.790173	−	0.612884i	$-0.209991\pi$
$491$	14.5025	+	8.37300i	0.654487	+	0.377868i	−0.135686	+	0.990752i	$0.543324\pi$
$492$	−4.15452	+	8.15371i	−0.187300	+	0.367598i
$493$	−6.99912	−	18.2333i	−0.315225	−	0.821188i
$494$	25.3612	+	18.4260i	1.14105	+	0.829023i
$495$	−6.81069	−	0.693329i	−0.306118	−	0.0311628i
$496$	−22.9683	+	14.3528i	−1.03131	+	0.644458i
$497$	−16.3700	+	16.3700i	−0.734297	+	0.734297i
$498$	−0.169572	−	1.07064i	−0.00759871	−	0.0479764i
$499$	25.7854	+	11.4804i	1.15431	+	0.513934i	0.892439	−	0.451168i	$-0.148993\pi$
$499$	25.7854	+	11.4804i	1.15431	+	0.513934i	0.261875	+	0.965102i	$0.415659\pi$
$500$	7.06359	−	0.0692763i	0.315893	−	0.00309813i
$501$	−3.93664	+	6.81845i	−0.175876	+	0.304626i
$502$	−9.40347	+	35.0942i	−0.419698	+	1.56633i
$503$	−1.60869	+	0.0843079i	−0.0717280	+	0.00375910i	−0.0881662	−	0.996106i	$-0.528101\pi$
$503$	−1.60869	+	0.0843079i	−0.0717280	+	0.00375910i	0.0164382	+	0.999865i	$0.494767\pi$
$504$	8.13790	+	2.64417i	0.362491	+	0.117780i
$505$	0.911912	+	1.24655i	0.0405795	+	0.0554707i
$506$	26.4316	−	11.7681i	1.17503	−	0.523155i
$507$	−6.47557	−	9.97150i	−0.287590	−	0.442850i
$508$	5.07720	+	6.26982i	0.225264	+	0.278178i
$509$	0.274959	+	2.61606i	0.0121873	+	0.115955i	0.998924	−	0.0463734i	$-0.0147664\pi$
$509$	0.274959	+	2.61606i	0.0121873	+	0.115955i	−0.986737	+	0.162328i	$0.948100\pi$
$510$	29.2022	−	36.3037i	1.29309	−	1.60756i
$511$	−6.63119	−	9.12705i	−0.293347	−	0.403757i
$512$	−0.750938	+	4.74124i	−0.0331871	+	0.209535i
$513$	−16.1144	+	24.8140i	−0.711467	+	1.09556i
$514$	−0.993643	+	0.104436i	−0.0438277	+	0.00460648i
$515$	15.9728	−	10.4473i	0.703848	−	0.460362i
$516$	1.10556	+	0.234994i	0.0486697	+	0.0103451i
$517$	15.2227	+	5.84344i	0.669493	+	0.256994i
$518$	−19.2075	−	1.00662i	−0.843929	−	0.0442285i
$519$	−12.4177	+	38.2176i	−0.545075	+	1.67757i
$520$	9.74753	−	8.83458i	0.427457	−	0.387422i
$521$	−16.6462	−	28.8320i	−0.729281	−	1.26315i	−0.957187	−	0.289469i	$-0.906521\pi$
$521$	−16.6462	−	28.8320i	−0.729281	−	1.26315i	0.227906	−	0.973683i	$-0.426812\pi$
$522$	4.55584	−	1.22073i	0.199404	−	0.0534301i
$523$	34.7563	+	17.7092i	1.51978	+	0.774369i	0.996948	−	0.0780638i	$-0.0248738\pi$
$523$	34.7563	+	17.7092i	1.51978	+	0.774369i	0.522837	+	0.852433i	$0.324874\pi$
$524$	−3.31107	+	7.43679i	−0.144645	+	0.324878i
$525$	−29.4987	+	26.9121i	−1.28743	+	1.17454i
$526$		−	50.7635i		−	2.21340i
$527$	−28.6972	−	21.6241i	−1.25007	−	0.941960i
$528$	−21.8153	−	21.8153i	−0.949390	−	0.949390i
$529$	−4.89005	+	6.73057i	−0.212611	+	0.292634i
$530$	−14.2776	+	24.9173i	−0.620180	+	1.08234i
$531$	0.688826	+	2.11999i	0.0298925	+	0.0919996i
$532$	−4.78379	−	17.8534i	−0.207404	−	0.774041i
$533$	−18.6332	−	4.99275i	−0.807093	−	0.216260i
$534$	1.51063	+	1.36018i	0.0653714	+	0.0588606i
$535$	1.31792	+	3.40005i	0.0569789	+	0.146997i
$536$	−12.8854	−	14.3107i	−0.556563	−	0.618126i
$537$	8.05521	−	20.9845i	0.347608	−	0.905550i
$538$	34.5460	−	22.4344i	1.48938	−	0.967217i
$539$	3.03219	−	28.8493i	0.130606	−	1.24263i
$540$	−4.06765	−	4.04114i	−0.175044	−	0.173903i
$541$	−9.35840	+	1.98919i	−0.402349	+	0.0855220i	−0.404641	−	0.914475i	$-0.632604\pi$
$541$	−9.35840	+	1.98919i	−0.402349	+	0.0855220i	0.00229230	+	0.999997i	$0.499270\pi$
$542$	−5.58559	−	0.884670i	−0.239921	−	0.0379998i
$543$	−10.4453	−	1.65437i	−0.448250	−	0.0709958i
$544$	21.7933	−	4.63231i	0.934381	−	0.198609i
$545$	11.4064	−	0.0372886i	0.488598	−	0.00159727i
$546$	3.58957	−	34.1525i	0.153619	−	1.46159i
$547$	0.619799	−	0.402502i	0.0265007	−	0.0172098i	−0.531321	−	0.847171i	$-0.678304\pi$
$547$	0.619799	−	0.402502i	0.0265007	−	0.0172098i	0.557821	+	0.829961i	$0.311637\pi$
$548$	3.46980	−	9.03913i	0.148222	−	0.386132i
$549$	−0.0355053	−	0.0394326i	−0.00151533	−	0.00168294i
$550$	24.9246	−	6.85350i	1.06279	−	0.292234i
$551$	16.3954	+	14.7625i	0.698466	+	0.628902i
$552$	23.8786	+	6.39825i	1.01634	+	0.272328i
$553$	−1.85678	−	6.92960i	−0.0789584	−	0.294677i
$554$	11.1135	+	34.2040i	0.472169	+	1.45319i
$555$	11.4080	+	6.53678i	0.484242	+	0.277471i
$556$	−6.82190	+	9.38954i	−0.289313	+	0.398205i
$557$	−19.6255	−	19.6255i	−0.831561	−	0.831561i	0.156169	−	0.987730i	$-0.450085\pi$
$557$	−19.6255	−	19.6255i	−0.831561	−	0.831561i	−0.987730	+	0.156169i	$0.950085\pi$
$558$	5.91794	−	6.34644i	0.250526	−	0.268666i
$559$			2.38258i			0.100773i
$560$	−43.5806	+	2.42685i	−1.84162	+	0.102553i
$561$	16.6480	−	37.3919i	0.702878	−	1.57869i
$562$	−6.43898	−	3.28082i	−0.271612	−	0.138393i
$563$	14.5693	−	3.90384i	0.614024	−	0.164527i	0.0616145	−	0.998100i	$-0.480375\pi$
$563$	14.5693	−	3.90384i	0.614024	−	0.164527i	0.552410	+	0.833573i	$0.313708\pi$
$564$	−3.21684	−	5.57172i	−0.135453	−	0.234612i
$565$	−10.7270	−	0.527022i	−0.451290	−	0.0221720i
$566$	−7.98111	+	24.5633i	−0.335471	+	1.03247i
$567$	43.9166	+	2.30157i	1.84432	+	0.0966570i
$568$	11.9548	+	4.58901i	0.501611	+	0.192550i
$569$	−9.13735	−	1.94220i	−0.383057	−	0.0814214i	0.0123583	−	0.999924i	$-0.496066\pi$
$569$	−9.13735	−	1.94220i	−0.383057	−	0.0814214i	−0.395416	+	0.918502i	$0.629399\pi$
$570$	−10.7741	+	51.5157i	−0.451278	+	2.15776i
$571$	31.6855	−	3.33028i	1.32600	−	0.139368i	0.585085	−	0.810972i	$-0.301061\pi$
$571$	31.6855	−	3.33028i	1.32600	−	0.139368i	0.740910	+	0.671604i	$0.234394\pi$
$572$	−2.90673	+	4.47597i	−0.121536	+	0.187150i
$573$	1.57268	−	9.92949i	0.0656995	−	0.414810i
$574$	27.8478	+	38.3292i	1.16235	+	1.59983i
$575$	−19.6564	+	19.9151i	−0.819728	+	0.830518i
$576$	−0.414553	−	3.94420i	−0.0172730	−	0.164342i
$577$	20.9624	+	25.8865i	0.872678	+	1.07767i	0.996352	+	0.0853444i	$0.0271991\pi$
$577$	20.9624	+	25.8865i	0.872678	+	1.07767i	−0.123674	+	0.992323i	$0.539468\pi$
$578$	21.7792	+	33.5370i	0.905896	+	1.39496i
$579$	−11.9206	+	5.30739i	−0.495403	+	0.220567i
$580$	−3.45072	+	2.52437i	−0.143283	+	0.104819i
$581$	−1.28133	−	0.416331i	−0.0531587	−	0.0172723i
$582$	−27.6099	+	1.44698i	−1.14447	+	0.0599791i
$583$	−6.52973	+	24.3693i	−0.270434	+	1.00927i
$584$	−3.12009	+	5.40416i	−0.129110	+	0.223626i
$585$	−3.08555	+	4.78551i	−0.127572	+	0.197857i
$586$	6.81718	+	3.03520i	0.281615	+	0.125383i
$587$	−3.00926	−	18.9997i	−0.124205	−	0.784201i	−0.968626	−	0.248521i	$-0.920055\pi$
$587$	−3.00926	−	18.9997i	−0.124205	−	0.784201i	0.844421	−	0.535680i	$-0.179945\pi$
$588$	−8.09331	+	8.09331i	−0.333762	+	0.333762i
$589$	39.9734	+	7.04766i	1.64707	+	0.290394i
$590$	−5.31829	−	6.52382i	−0.218951	−	0.268581i
$591$	5.23069	+	3.80032i	0.215162	+	0.156324i
$592$	5.15055	+	13.4176i	0.211686	+	0.551461i
$593$	−5.47279	+	10.7410i	−0.224741	+	0.441078i	−0.975652	−	0.219325i	$-0.929615\pi$
$593$	−5.47279	+	10.7410i	−0.224741	+	0.441078i	0.750911	+	0.660403i	$0.229615\pi$
$594$	−18.1712	−	10.4912i	−0.745574	−	0.430457i
$595$	−23.7260	−	52.8241i	−0.972672	−	2.16558i
$596$	−1.70413	+	1.89263i	−0.0698038	+	0.0775250i
$597$	−8.91743	−	17.5014i	−0.364966	−	0.716286i
$598$	1.25945	−	24.0318i	0.0515028	−	0.982732i
$599$	0.542792	+	1.21913i	0.0221779	+	0.0498124i	0.924295	−	0.381679i	$-0.124654\pi$
$599$	0.542792	+	1.21913i	0.0221779	+	0.0498124i	−0.902117	+	0.431492i	$0.857987\pi$
$600$	20.2354	+	8.85130i	0.826106	+	0.361353i
$601$	−47.6751	−	5.01085i	−1.94471	−	0.204397i	−0.950406	−	0.311013i	$-0.899332\pi$
$601$	−47.6751	−	5.01085i	−1.94471	−	0.204397i	−0.994300	+	0.106616i	$0.965999\pi$
$602$	3.68255	−	4.54757i	0.150090	−	0.185345i
$603$	6.99024	+	4.53952i	0.284665	+	0.184863i
$604$	5.11571	−	3.71678i	0.208155	−	0.151234i
$605$	−1.63162	+	0.949142i	−0.0663348	+	0.0385881i
$606$	−0.463654	−	2.18132i	−0.0188347	−	0.0886102i
$607$	−20.7250	−	16.7828i	−0.841202	−	0.681192i	0.108586	−	0.994087i	$-0.465368\pi$
$607$	−20.7250	−	16.7828i	−0.841202	−	0.681192i	−0.949788	+	0.312895i	$0.898701\pi$
$608$	−19.5594	+	15.8389i	−0.793237	+	0.642351i
$609$	5.02484	−	23.6400i	0.203617	−	0.957942i
$610$	0.178817	+	0.0903768i	0.00724010	+	0.00365925i
$611$	10.0786	−	9.07484i	0.407738	−	0.367129i
$612$	−3.49030	+	1.77840i	−0.141087	+	0.0718875i
$613$	−0.573799	−	10.9487i	−0.0231755	−	0.442215i	−0.985432	−	0.170070i	$-0.945600\pi$
$613$	−0.573799	−	10.9487i	−0.0231755	−	0.442215i	0.962256	−	0.272144i	$-0.0877329\pi$
$614$	−25.2237	+	14.5629i	−1.01795	+	0.587711i
$615$	−5.17095	−	31.9713i	−0.208513	−	1.28921i
$616$	−26.9950	+	8.77121i	−1.08766	+	0.353402i
$617$	−30.5053	+	11.7099i	−1.22810	+	0.471423i	−0.883989	−	0.467507i	$-0.845152\pi$
$617$	−30.5053	+	11.7099i	−1.22810	+	0.471423i	−0.344109	+	0.938930i	$0.611819\pi$
$618$	−27.2185	+	4.31099i	−1.09489	+	0.173414i
$619$	35.5738			1.42983			0.714916	−	0.699210i	$-0.246465\pi$
$619$	35.5738			1.42983			0.714916	+	0.699210i	$0.246465\pi$
$620$	−2.92269	+	7.30293i	−0.117378	+	0.293293i
$621$	22.7130			0.911441
$622$	33.9696	−	5.38026i	1.36206	−	0.215729i
$623$	2.35869	−	0.905415i	0.0944988	−	0.0362747i
$624$	−24.4046	+	7.92953i	−0.976966	+	0.317435i
$625$	−20.0316	+	14.9578i	−0.801262	+	0.598314i
$626$	8.68356	−	5.01346i	0.347065	−	0.200378i
$627$	2.41981	+	46.1727i	0.0966379	+	1.84396i
$628$	−6.55368	+	3.33927i	−0.261520	+	0.133251i
$629$	−14.1700	+	12.7587i	−0.564993	+	0.508722i
$630$	13.2859	−	4.36491i	0.529321	−	0.173902i
$631$	−4.91530	+	23.1247i	−0.195675	+	0.920579i	0.765242	+	0.643743i	$0.222619\pi$
$631$	−4.91530	+	23.1247i	−0.195675	+	0.920579i	−0.960917	+	0.276836i	$0.910714\pi$
$632$	−3.08384	+	2.49724i	−0.122668	+	0.0993350i
$633$	12.6942	+	10.2796i	0.504549	+	0.408576i
$634$	−9.67223	−	45.5043i	−0.384133	−	1.80721i
$635$	−27.6037	−	7.29977i	−1.09542	−	0.289682i
$636$	8.05334	−	5.85109i	0.319336	−	0.232011i
$637$	−20.2349	−	13.1407i	−0.801737	−	0.520654i
$638$	−9.84618	+	12.1590i	−0.389814	+	0.481380i
$639$	−5.51212	−	0.579347i	−0.218056	−	0.0229186i
$640$	13.8964	+	27.0543i	0.549304	+	1.06941i
$641$	11.9488	+	26.8375i	0.471950	+	1.06002i	0.980056	+	0.198723i	$0.0636793\pi$
$641$	11.9488	+	26.8375i	0.471950	+	1.06002i	−0.508105	+	0.861295i	$0.669654\pi$
$642$	0.275556	−	5.25792i	0.0108753	−	0.207514i
$643$	20.4872	+	40.2085i	0.807938	+	1.58567i	0.810549	+	0.585671i	$0.199169\pi$
$643$	20.4872	+	40.2085i	0.807938	+	1.58567i	−0.00261103	+	0.999997i	$0.500831\pi$
$644$	−9.49417	+	10.5443i	−0.374123	+	0.415505i
$645$	−3.64895	+	1.63893i	−0.143677	+	0.0645328i
$646$	−66.0998	−	38.1627i	−2.60066	−	1.50149i
$647$	−21.7585	+	42.7034i	−0.855413	+	1.67884i	−0.128936	+	0.991653i	$0.541156\pi$
$647$	−21.7585	+	42.7034i	−0.855413	+	1.67884i	−0.726477	+	0.687190i	$0.758844\pi$
$648$	−8.71722	−	22.7091i	−0.342445	−	0.892099i
$649$	−5.98213	−	4.34627i	−0.234819	−	0.170606i
$650$	4.33257	−	21.0592i	0.169937	−	0.826011i
$651$	−15.2085	−	41.7828i	−0.596069	−	1.63760i
$652$	−10.4096	+	10.4096i	−0.407673	+	0.407673i
$653$	3.57138	+	22.5488i	0.139759	+	0.882404i	0.953548	+	0.301243i	$0.0974014\pi$
$653$	3.57138	+	22.5488i	0.139759	+	0.882404i	−0.813788	+	0.581161i	$0.802599\pi$
$654$	−15.0457	−	6.69876i	−0.588332	−	0.261942i
$655$	−6.08211	−	28.1611i	−0.237648	−	1.10034i
$656$	17.7011	−	30.6592i	0.691112	−	1.19704i
$657$	0.699050	−	2.60889i	0.0272725	−	0.101783i
$658$	−33.2630	+	1.74324i	−1.29673	+	0.0679586i
$659$	39.7581	+	12.9182i	1.54876	+	0.503221i	0.953776	−	0.300520i	$-0.0971601\pi$
$659$	39.7581	+	12.9182i	1.54876	+	0.503221i	0.594980	+	0.803741i	$0.297160\pi$
$660$	−8.85447	−	1.37275i	−0.344660	−	0.0534343i
$661$	−12.9810	+	5.77953i	−0.504904	+	0.224798i	−0.643350	−	0.765572i	$-0.722456\pi$
$661$	−12.9810	+	5.77953i	−0.504904	+	0.224798i	0.138446	+	0.990370i	$0.455789\pi$
$662$	−18.2736	−	28.1389i	−0.710224	−	1.09365i
$663$	−21.4244	−	26.4569i	−0.832054	−	1.02750i
$664$	0.0778960	+	0.741131i	0.00302295	+	0.0287615i
$665$	50.9704	+	40.9999i	1.97655	+	1.58991i
$666$	−2.70660	−	3.72532i	−0.104879	−	0.144353i
$667$	2.64941	−	16.7277i	0.102586	−	0.647701i
$668$	−1.36135	+	2.09629i	−0.0526722	+	0.0811080i
$669$	29.0672	−	3.05508i	1.12380	−	0.118116i
$670$	−30.8057	−	6.44276i	−1.19013	−	0.248906i
$671$	0.172170	+	0.0365958i	0.00664655	+	0.00141277i
$672$	25.7395	+	9.88047i	0.992922	+	0.381147i
$673$	−4.64366	−	0.243364i	−0.179000	−	0.00938099i	−0.0373746	−	0.999301i	$-0.511899\pi$
$673$	−4.64366	−	0.243364i	−0.179000	−	0.00938099i	−0.141625	+	0.989920i	$0.545233\pi$
$674$	15.0356	−	46.2748i	0.579150	−	1.78244i
$675$	20.0631	+	3.04335i	0.772228	+	0.117139i
$676$	−1.88732	−	3.26893i	−0.0725890	−	0.125728i
$677$	−8.88520	+	2.38078i	−0.341486	+	0.0915009i	−0.425486	−	0.904965i	$-0.639897\pi$
$677$	−8.88520	+	2.38078i	−0.341486	+	0.0915009i	0.0840004	+	0.996466i	$0.473230\pi$
$678$	13.8170	+	7.04009i	0.530637	+	0.270373i
$679$	−13.9768	+	31.3924i	−0.536381	+	1.20473i
$680$	−21.3545	+	23.8731i	−0.818909	+	0.915491i
$681$			11.9956i			0.459671i
$682$	−3.50751	+	28.5705i	−0.134310	+	1.09402i
$683$	−22.7037	−	22.7037i	−0.868733	−	0.868733i	0.123600	−	0.992332i	$-0.460556\pi$
$683$	−22.7037	−	22.7037i	−0.868733	−	0.868733i	−0.992332	+	0.123600i	$0.960556\pi$
$684$	2.60096	−	3.57992i	0.0994503	−	0.136882i
$685$	8.97695	+	33.0696i	0.342992	+	1.26353i
$686$	4.22967	+	13.0176i	0.161490	+	0.497014i
$687$	−5.91561	−	22.0774i	−0.225695	−	0.842303i
$688$	−4.22356	−	1.13170i	−0.161022	−	0.0431456i
$689$	15.5941	+	14.0410i	0.594089	+	0.534920i
$690$	37.6712	−	14.6021i	1.43412	−	0.555893i
$691$	25.1579	+	27.9406i	0.957050	+	1.06291i	0.997966	+	0.0637494i	$0.0203058\pi$
$691$	25.1579	+	27.9406i	0.957050	+	1.06291i	−0.0409157	+	0.999163i	$0.513028\pi$
$692$	−4.57185	+	11.9101i	−0.173796	+	0.452753i
$693$	10.3035	−	6.69115i	0.391396	−	0.254176i
$694$	2.46413	−	23.4446i	0.0935370	−	0.889945i
$695$	−0.134278	−	41.0750i	−0.00509344	−	1.55807i
$696$	−13.0759	+	2.77937i	−0.495642	+	0.105352i
$697$	46.3897	+	7.34740i	1.75713	+	0.278303i
$698$	−54.8359	−	8.68515i	−2.07557	−	0.328738i
$699$	40.5739	−	8.62425i	1.53465	−	0.326199i
$700$	−9.79934	+	8.04200i	−0.370380	+	0.303959i
$701$	0.207861	−	1.97767i	0.00785081	−	0.0746955i	−0.989895	−	0.141802i	$-0.954710\pi$
$701$	0.207861	−	1.97767i	0.00785081	−	0.0746955i	0.997746	+	0.0671070i	$0.0213769\pi$
$702$	−14.6364	+	9.50497i	−0.552414	+	0.358742i
$703$	7.71894	−	20.1085i	0.291125	−	0.758407i
$704$	8.80293	+	9.77664i	0.331773	+	0.368471i
$705$	20.8311	+	9.19312i	0.784544	+	0.346233i
$706$	−6.85167	−	6.16927i	−0.257866	−	0.232183i
$707$	−2.67728	−	0.717374i	−0.100689	−	0.0269796i
$708$	0.755116	+	2.81813i	0.0283790	+	0.105912i
$709$	−11.5255	−	35.4719i	−0.432850	−	1.33218i	−0.895274	−	0.445517i	$-0.853020\pi$
$709$	−11.5255	−	35.4719i	−0.432850	−	1.33218i	0.462423	−	0.886659i	$-0.346980\pi$
$710$	20.1972	−	5.48265i	0.757987	−	0.205760i
$711$	1.00954	−	1.38951i	0.0378606	−	0.0521107i
$712$	−0.988162	−	0.988162i	−0.0370329	−	0.0370329i
$713$	−12.1754	−	28.6821i	−0.455973	−	1.07415i
$714$			83.6114i			3.12908i
$715$	−1.05019	−	18.8589i	−0.0392747	−	0.705284i
$716$	2.90246	−	6.51904i	0.108470	−	0.243628i
$717$	−4.60065	−	2.34415i	−0.171815	−	0.0875439i
$718$	52.5180	−	14.0722i	1.95996	−	0.525168i
$719$	−4.71384	−	8.16461i	−0.175797	−	0.304489i	0.764640	−	0.644458i	$-0.222917\pi$
$719$	−4.71384	−	8.16461i	−0.175797	−	0.304489i	−0.940437	+	0.339969i	$0.889583\pi$
$720$	−7.01758	−	7.74276i	−0.261530	−	0.288556i
$721$	−10.5843	+	32.5751i	−0.394179	+	1.21316i
$722$	55.3195	+	2.89917i	2.05878	+	0.107896i
$723$	5.24994	+	2.01526i	0.195247	+	0.0749484i
$724$	−3.28405	−	0.698047i	−0.122051	−	0.0259427i
$725$	4.58168	−	14.4211i	0.170159	−	0.535587i
$726$	2.71053	−	0.284888i	0.100597	−	0.0105732i
$727$	−8.68222	+	13.3695i	−0.322006	+	0.495845i	−0.962191	−	0.272375i	$-0.912191\pi$
$727$	−8.68222	+	13.3695i	−0.322006	+	0.495845i	0.640185	+	0.768220i	$0.278858\pi$
$728$	−3.69316	+	23.3177i	−0.136878	+	0.864212i
$729$	−8.05427	−	11.0858i	−0.298306	−	0.410584i
$730$	1.09919	+	10.1391i	0.0406828	+	0.375266i
$731$	−0.606373	−	5.76926i	−0.0224275	−	0.213384i
$732$	−0.0437063	−	0.0539728i	−0.00161543	−	0.00199489i
$733$	−26.2157	−	40.3687i	−0.968300	−	1.49105i	−0.868285	−	0.496065i	$-0.834778\pi$
$733$	−26.2157	−	40.3687i	−0.968300	−	1.49105i	−0.100014	−	0.994986i	$-0.531889\pi$
$734$	19.4924	−	8.67859i	0.719479	−	0.320333i
$735$	6.20593	−	40.0292i	0.228909	−	1.47650i
$736$	18.3750	+	5.97041i	0.677313	+	0.220072i
$737$	−27.6106	+	1.44701i	−1.01705	+	0.0533014i
$738$	−2.93567	+	10.9561i	−0.108064	+	0.403299i
$739$	−10.3532	+	17.9323i	−0.380850	+	0.659651i	−0.991184	−	0.132493i	$-0.957702\pi$
$739$	−10.3532	+	17.9323i	−0.380850	+	0.659651i	0.610334	+	0.792144i	$0.291035\pi$
$740$	3.50815	+	2.26195i	0.128962	+	0.0831508i
$741$	35.1317	+	15.6417i	1.29060	+	0.574611i
$742$	−8.06211	−	50.9022i	−0.295969	−	1.86868i
$743$	−24.9325	+	24.9325i	−0.914685	+	0.914685i	−0.996636	−	0.0819514i	$-0.973885\pi$
$743$	−24.9325	+	24.9325i	−0.914685	+	0.914685i	0.0819514	+	0.996636i	$0.473885\pi$
$744$	−17.6915	+	17.0851i	−0.648603	+	0.626371i
$745$	0.912841	−	8.96698i	0.0334439	−	0.328525i
$746$	21.5803	+	15.6790i	0.790110	+	0.574048i
$747$	−0.115591	−	0.301125i	−0.00422926	−	0.0110176i
$748$	5.89929	−	11.5780i	0.215700	−	0.423334i
$749$	−5.66727	−	3.27200i	−0.207078	−	0.119556i
$750$	35.2327	−	7.85085i	1.28652	−	0.286673i
$751$	−7.57948	+	8.41787i	−0.276579	+	0.307172i	−0.865390	−	0.501098i	$-0.832929\pi$
$751$	−7.57948	+	8.41787i	−0.276579	+	0.307172i	0.588811	+	0.808271i	$0.299596\pi$
$752$	11.2996	+	22.1766i	0.412052	+	0.808698i
$753$	−2.33265	+	44.5097i	−0.0850066	+	1.62202i
$754$	5.29295	+	11.8882i	0.192758	+	0.432941i
$755$	−6.84589	+	21.3062i	−0.249148	+	0.775414i
$756$	10.2334	+	1.07558i	0.372186	+	0.0391183i
$757$	−12.5991	+	15.5586i	−0.457923	+	0.565488i	−0.952848	−	0.303448i	$-0.901862\pi$
$757$	−12.5991	+	15.5586i	−0.457923	+	0.565488i	0.494925	+	0.868936i	$0.335195\pi$
$758$	−4.66510	−	3.02955i	−0.169444	−	0.110038i
$759$	28.7150	−	20.8626i	1.04229	−	0.757266i
$760$	9.25033	−	34.9797i	0.335545	−	1.26885i
$761$	4.18709	+	19.6987i	0.151782	+	0.714078i	0.986548	+	0.163473i	$0.0522696\pi$
$761$	4.18709	+	19.6987i	0.151782	+	0.714078i	−0.834766	+	0.550605i	$0.814397\pi$
$762$	32.0389	+	25.9446i	1.16065	+	0.939873i
$763$	−15.9081	+	12.8821i	−0.575911	+	0.466364i
$764$	0.663577	−	3.12188i	0.0240074	−	0.112946i
$765$	6.25353	−	12.3731i	0.226097	−	0.447349i
$766$	38.4104	−	34.5849i	1.38782	−	1.24960i
$767$	−5.47983	+	2.79212i	−0.197865	+	0.100817i
$768$	−1.43836	−	27.4456i	−0.0519025	−	0.990359i
$769$	28.7493	−	16.5984i	1.03672	−	0.598553i	0.117821	−	0.993035i	$-0.462409\pi$
$769$	28.7493	−	16.5984i	1.03672	−	0.598553i	0.918904	+	0.394482i	$0.129076\pi$
$770$	−27.1441	+	37.6187i	−0.978207	+	1.35568i
$771$	−1.16568	+	0.378753i	−0.0419810	+	0.0136405i
$772$	−3.86745	+	1.48457i	−0.139193	+	0.0534310i
$773$	51.8861	−	8.21795i	1.86621	−	0.295579i	0.881824	−	0.471579i	$-0.156316\pi$
$773$	51.8861	−	8.21795i	1.86621	−	0.295579i	0.984390	+	0.176000i	$0.0563158\pi$
$774$	1.40093			0.0503554
$775$	−6.91176	−	26.9672i	−0.248278	−	0.968689i
$776$	19.0073			0.682321
$777$	−23.3047	+	3.69111i	−0.836053	+	0.132418i
$778$	13.0285	−	5.00117i	0.467094	−	0.179301i
$779$	−50.4592	+	16.3952i	−1.80789	+	0.587419i
$780$	−4.36080	+	6.04358i	−0.156142	+	0.216395i
$781$	15.9223	−	9.19275i	0.569745	−	0.328942i
$782$	3.06647	+	58.5118i	0.109657	+	2.09238i
$783$	−10.9436	+	5.57602i	−0.391091	+	0.199271i
$784$	32.9056	−	29.6284i	1.17520	−	1.05816i
$785$	11.7421	−	23.2327i	0.419095	−	0.829210i
$786$	−8.64881	+	40.6895i	−0.308493	+	1.45135i
$787$	4.79068	−	3.87942i	0.170769	−	0.138286i	−0.540126	−	0.841584i	$-0.681623\pi$
$787$	4.79068	−	3.87942i	0.170769	−	0.138286i	0.710895	+	0.703298i	$0.248290\pi$
$788$	1.59518	+	1.29175i	0.0568259	+	0.0460167i
$789$	−12.9476	−	60.9136i	−0.460946	−	2.16858i
$790$	−1.65803	+	6.26977i	−0.0589901	+	0.223068i
$791$	15.5928	−	11.3288i	0.554415	−	0.402806i
$792$	−5.69912	−	3.70105i	−0.202510	−	0.131511i
$793$	0.0921326	−	0.113774i	0.00327172	−	0.00404024i
$794$	−37.1260	−	3.90210i	−1.31755	−	0.138480i
$795$	−10.7771	+	33.5411i	−0.382223	+	1.18958i
$796$	−2.53637	−	5.69677i	−0.0898991	−	0.201917i
$797$	−2.40908	+	45.9679i	−0.0853339	+	1.62827i	0.535648	+	0.844442i	$0.320068\pi$
$797$	−2.40908	+	45.9679i	−0.0853339	+	1.62827i	−0.620981	+	0.783825i	$0.713266\pi$
$798$	−42.8791	−	84.1549i	−1.51790	−	2.97905i
$799$	−22.0951	+	24.5391i	−0.781670	+	0.868132i
$800$	15.4312	+	7.73595i	0.545577	+	0.273507i
$801$	0.523828	+	0.302432i	0.0185085	+	0.0106859i
$802$	7.13907	−	14.0112i	0.252089	−	0.494753i
$803$	3.21079	+	8.36440i	0.113306	+	0.295173i
$804$	8.82570	+	6.41224i	0.311258	+	0.226142i
$805$	5.08568	−	49.9575i	0.179247	−	1.76077i
$806$	19.8488	+	13.3877i	0.699145	+	0.471561i
$807$	35.7313	−	35.7313i	1.25780	−	1.25780i
$808$	0.239831	+	1.51424i	0.00843724	+	0.0532707i
$809$	−45.7559	−	20.3718i	−1.60869	−	0.716236i	−0.611508	−	0.791238i	$-0.709437\pi$
$809$	−45.7559	−	20.3718i	−1.60869	−	0.716236i	−0.997183	+	0.0750027i	$0.976103\pi$
$810$	−33.4118	−	21.5429i	−1.17397	−	0.756941i
$811$	5.45027	−	9.44015i	0.191385	−	0.331488i	−0.754325	−	0.656502i	$-0.772035\pi$
$811$	5.45027	−	9.44015i	0.191385	−	0.331488i	0.945709	+	0.325013i	$0.105369\pi$
$812$	1.98585	−	7.41127i	0.0696895	−	0.260085i
$813$	−6.92805	+	0.363084i	−0.242977	+	0.0127339i
$814$	14.5272	+	4.72019i	0.509180	+	0.165442i
$815$	7.98209	−	51.4857i	0.279600	−	1.80347i
$816$	57.0759	−	25.4118i	1.99806	−	0.889593i
$817$	3.56901	+	5.49579i	0.124864	+	0.192273i
$818$	−9.19998	−	11.3610i	−0.321670	−	0.397229i
$819$	−1.06811	−	10.1624i	−0.0373227	−	0.355102i
$820$	−1.10817	−	10.2220i	−0.0386991	−	0.356968i
$821$	−7.57657	−	10.4282i	−0.264424	−	0.363948i	0.656073	−	0.754697i	$-0.272216\pi$
$821$	−7.57657	−	10.4282i	−0.264424	−	0.363948i	−0.920497	+	0.390749i	$0.872216\pi$
$822$	7.73980	−	48.8672i	0.269956	−	1.70444i
$823$	−11.0261	+	16.9787i	−0.384345	+	0.591839i	−0.976902	−	0.213690i	$-0.931452\pi$
$823$	−11.0261	+	16.9787i	−0.384345	+	0.591839i	0.592557	+	0.805529i	$0.298119\pi$
$824$	18.8416	−	1.98033i	0.656378	−	0.0689881i
$825$	28.1602	−	14.5810i	0.980413	−	0.507647i
$826$	14.7747	+	3.14047i	0.514079	+	0.109271i
$827$	−26.3823	−	10.1272i	−0.917402	−	0.352158i	−0.146573	−	0.989200i	$-0.546824\pi$
$827$	−26.3823	−	10.1272i	−0.917402	−	0.352158i	−0.770829	+	0.637042i	$0.780158\pi$
$828$	−3.39226	−	0.177781i	−0.117889	−	0.00617832i
$829$	−10.0075	+	30.8000i	−0.347576	+	1.06973i	0.612615	+	0.790382i	$0.290118\pi$
$829$	−10.0075	+	30.8000i	−0.347576	+	1.06973i	−0.960190	+	0.279346i	$0.909882\pi$
$830$	0.817907	+	0.902427i	0.0283900	+	0.0313237i
$831$	22.0596	+	38.2084i	0.765240	+	1.32544i
$832$	10.5694	−	2.83205i	0.366427	−	0.0981837i
$833$	52.3418	+	26.6695i	1.81354	+	0.924043i
$834$	−24.1225	+	54.1800i	−0.835294	+	1.87610i
$835$	−0.491848	−	8.83247i	−0.0170211	−	0.305660i
$836$			14.6787i			0.507672i
$837$	−11.6379	+	19.3695i	−0.402265	+	0.669508i
$838$	0.549749	+	0.549749i	0.0189908	+	0.0189908i
$839$	−11.2536	+	15.4892i	−0.388516	+	0.534746i	−0.957815	−	0.287384i	$-0.907214\pi$
$839$	−11.2536	+	15.4892i	−0.388516	+	0.534746i	0.569300	+	0.822130i	$0.307214\pi$
$840$	−38.2517	+	10.3837i	−1.31981	+	0.358271i
$841$	−6.13139	−	18.8705i	−0.211427	−	0.650706i
$842$	2.10586	+	7.85917i	0.0725726	+	0.270845i
$843$	−8.56323	−	2.29451i	−0.294933	−	0.0790272i
$844$	3.85374	+	3.46992i	0.132651	+	0.119440i
$845$	12.2216	+	5.39360i	0.420435	+	0.185545i
$846$	−5.33589	−	5.92611i	−0.183452	−	0.203744i
$847$	1.21396	−	3.16247i	0.0417120	−	0.108664i
$848$	−32.2972	+	20.9741i	−1.10909	+	0.720253i
$849$	−3.31187	+	31.5104i	−0.113663	+	1.08143i
$850$	−5.13138	+	52.0961i	−0.176005	+	1.78688i
$851$	−16.1734	+	3.43777i	−0.554419	+	0.117845i
$852$	−7.16497	−	1.13482i	−0.245468	−	0.0388783i
$853$	−15.2099	−	2.40902i	−0.520778	−	0.0824832i	−0.109489	−	0.993988i	$-0.534921\pi$
$853$	−15.2099	−	2.40902i	−0.520778	−	0.0824832i	−0.411289	+	0.911505i	$0.634921\pi$
$854$	−0.351702	+	0.0747566i	−0.0120350	+	0.00255812i
$855$	0.0511955	+	15.6605i	0.00175085	+	0.535579i
$856$	−0.378358	+	3.59983i	−0.0129320	+	0.123040i
$857$	27.2652	−	17.7062i	0.931361	−	0.604833i	0.0127172	−	0.999919i	$-0.495952\pi$
$857$	27.2652	−	17.7062i	0.931361	−	0.604833i	0.918644	+	0.395086i	$0.129285\pi$
$858$	−9.77343	+	25.4607i	−0.333660	+	0.869213i
$859$	31.9180	+	35.4485i	1.08903	+	1.20949i	0.976427	+	0.215848i	$0.0692514\pi$
$859$	31.9180	+	35.4485i	1.08903	+	1.20949i	0.112601	+	0.993640i	$0.464082\pi$
$860$	−1.18408	+	0.458973i	−0.0403769	+	0.0156509i
$861$	43.1921	+	38.8903i	1.47198	+	1.32538i
$862$	20.6365	+	5.52954i	0.702883	+	0.188337i
$863$	5.51519	+	20.5830i	0.187739	+	0.700653i	0.994028	+	0.109130i	$0.0348064\pi$
$863$	5.51519	+	20.5830i	0.187739	+	0.700653i	−0.806288	+	0.591523i	$0.798527\pi$
$864$	−4.32977	−	13.3257i	−0.147302	−	0.453348i
$865$	−11.8281	−	43.5730i	−0.402169	−	1.48153i
$866$	22.5125	−	30.9857i	0.765004	−	1.05294i
$867$	34.6878	+	34.6878i	1.17806	+	1.17806i
$868$	−4.12743	−	13.4994i	−0.140094	−	0.458199i
$869$			5.69737i			0.193270i
$870$	−14.5659	+	16.2838i	−0.493831	+	0.552074i
$871$	−9.35349	+	21.0083i	−0.316931	+	0.711839i
$872$	10.0884	+	5.14027i	0.341635	+	0.174072i
$873$	−7.94654	+	2.12927i	−0.268950	+	0.0720648i
$874$	−33.0935	−	57.3196i	−1.11940	−	1.93886i
$875$	11.1862	−	43.4475i	0.378163	−	1.46879i
$876$	1.09241	−	3.36209i	0.0369091	−	0.113594i
$877$	−14.0794	−	0.737870i	−0.475427	−	0.0249161i	−0.186882	−	0.982382i	$-0.559838\pi$
$877$	−14.0794	−	0.737870i	−0.475427	−	0.0249161i	−0.288545	+	0.957466i	$0.593172\pi$
$878$	−45.6230	−	17.5130i	−1.53970	−	0.591036i
$879$	8.95441	+	1.90332i	0.302025	+	0.0641973i
$880$	33.9297	+	7.09612i	1.14377	+	0.239210i
$881$	−32.1970	+	3.38404i	−1.08475	+	0.114011i	−0.629989	−	0.776604i	$-0.716941\pi$
$881$	−32.1970	+	3.38404i	−1.08475	+	0.114011i	−0.454757	+	0.890616i	$0.650274\pi$
$882$	−7.72658	+	11.8979i	−0.260167	+	0.400623i
$883$	4.74984	−	29.9893i	0.159845	−	1.00922i	−0.769134	−	0.639087i	$-0.779312\pi$
$883$	4.74984	−	29.9893i	0.159845	−	1.00922i	0.928979	−	0.370133i	$-0.120688\pi$
$884$	−6.35273	−	8.74379i	−0.213666	−	0.294085i
$885$	−8.04562	−	6.47178i	−0.270450	−	0.217546i
$886$	3.98476	+	37.9124i	0.133871	+	1.27369i
$887$	−6.75721	−	8.34445i	−0.226885	−	0.280179i	0.650973	−	0.759101i	$-0.274361\pi$
$887$	−6.75721	−	8.34445i	−0.226885	−	0.280179i	−0.877858	+	0.478922i	$0.841028\pi$
$888$	7.10817	+	10.9456i	0.238535	+	0.367311i
$889$	46.8100	−	20.8412i	1.56996	−	0.698990i
$890$	−2.25697	−	0.349910i	−0.0756539	−	0.0117290i
$891$	−33.2155	−	10.7924i	−1.11276	−	0.361558i
$892$	9.26612	−	0.485617i	0.310253	−	0.0162597i
$893$	9.65417	−	36.0299i	0.323065	−	1.20569i
$894$	−6.50705	+	11.2705i	−0.217628	+	0.376943i
$895$	5.33153	+	24.6858i	0.178214	+	0.825155i
$896$	−49.8625	−	22.2002i	−1.66579	−	0.741657i
$897$	−4.61819	−	29.1581i	−0.154197	−	0.973561i
$898$	−0.648345	+	0.648345i	−0.0216355	+	0.0216355i
$899$	12.9078	+	10.8305i	0.430498	+	0.361218i
$900$	−2.97267	−	0.611574i	−0.0990889	−	0.0203858i
$901$	−41.3336	−	30.0306i	−1.37702	−	1.00046i
$902$	−13.4838	−	35.1265i	−0.448961	−	1.16958i
$903$	3.25898	−	6.39611i	0.108452	−	0.212849i
$904$	−9.23253	−	5.33040i	−0.307069	−	0.177287i
$905$	10.8391	−	4.86841i	0.360305	−	0.161832i
$906$	21.6213	−	24.0129i	0.718319	−	0.797774i
$907$	−6.65568	−	13.0625i	−0.220998	−	0.433733i	0.753712	−	0.657204i	$-0.228261\pi$
$907$	−6.65568	−	13.0625i	−0.220998	−	0.433733i	−0.974711	+	0.223471i	$0.928261\pi$
$908$	−0.199309	+	3.80304i	−0.00661429	+	0.126208i
$909$	−0.269899	−	0.606204i	−0.00895200	−	0.0201065i
$910$	17.6290	+	34.3211i	0.584397	+	1.13773i
$911$	−5.68010	−	0.597003i	−0.188190	−	0.0197796i	0.00996450	−	0.999950i	$-0.496828\pi$
$911$	−5.68010	−	0.597003i	−0.188190	−	0.0197796i	−0.198155	+	0.980171i	$0.563495\pi$
$912$	−44.4148	+	54.8477i	−1.47072	+	1.81619i
$913$	0.897341	+	0.582740i	0.0296977	+	0.0192859i
$914$	7.83066	−	5.68931i	0.259015	−	0.188186i
$915$	0.237622	+	0.0628389i	0.00785556	+	0.00207739i
$916$	−1.50865	−	7.09763i	−0.0498471	−	0.234512i
$917$	40.1804	+	32.5374i	1.32687	+	1.07448i
$918$	33.0219	−	26.7406i	1.08989	−	0.882571i
$919$	−11.9034	+	56.0010i	−0.392656	+	1.84730i	0.125605	+	0.992080i	$0.459913\pi$
$919$	−11.9034	+	56.0010i	−0.392656	+	1.84730i	−0.518262	+	0.855222i	$0.673421\pi$
$920$	−26.3880	+	8.66946i	−0.869987	+	0.285823i
$921$	−26.5528	+	23.9082i	−0.874943	+	0.787802i
$922$	−44.6351	+	22.7427i	−1.46998	+	0.748991i
$923$	−0.800321	−	15.2710i	−0.0263429	−	0.502652i
$924$	13.9256	−	8.03994i	0.458118	−	0.264494i
$925$	−14.7471	+	0.869582i	−0.484883	+	0.0285917i
$926$	−48.3279	+	15.7027i	−1.58815	+	0.516023i
$927$	−7.65543	+	2.93865i	−0.251437	+	0.0965178i
$928$	−10.3192	+	1.63440i	−0.338744	+	0.0536517i
$929$	−25.6193			−0.840540			−0.420270	−	0.907399i	$-0.638065\pi$
$929$	−25.6193			−0.840540			−0.420270	+	0.907399i	$0.638065\pi$
$930$	−6.84977	+	39.6078i	−0.224613	+	1.29879i
$931$	−66.3592			−2.17483
$932$	13.0067	−	2.06006i	0.426049	−	0.0674796i
$933$	39.3895	−	15.1202i	1.28955	−	0.495014i
$934$	26.8951	−	8.73874i	0.880033	−	0.285940i
$935$	7.34260	+	45.3983i	0.240129	+	1.48468i
$936$	−4.89481	+	2.82602i	−0.159992	+	0.0923714i
$937$	1.35971	+	25.9448i	0.0444198	+	0.847580i	0.926457	+	0.376400i	$0.122838\pi$
$937$	1.35971	+	25.9448i	0.0444198	+	0.847580i	−0.882037	+	0.471180i	$0.843828\pi$
$938$	50.3234	−	25.6411i	1.64312	−	0.837211i
$939$	9.14110	−	8.23069i	0.298309	−	0.268598i
$940$	6.45148	+	3.26067i	0.210424	+	0.106351i
$941$	2.90693	−	13.6761i	0.0947634	−	0.445827i	−0.905027	−	0.425354i	$-0.860150\pi$
$941$	2.90693	−	13.6761i	0.0947634	−	0.445827i	0.999790	−	0.0204726i	$-0.00651707\pi$
$942$	−29.2099	+	23.6537i	−0.951709	+	0.770679i
$943$	31.6524	+	25.6316i	1.03074	+	0.834680i
$944$	−2.34667	−	11.0402i	−0.0763776	−	0.359328i
$945$	−31.4780	+	18.3113i	−1.02398	+	0.595667i
$946$	−3.75963	+	2.73153i	−0.122236	+	0.0888097i
$947$	13.0495	+	8.47447i	0.424053	+	0.275383i	0.738973	−	0.673735i	$-0.235311\pi$
$947$	13.0495	+	8.47447i	0.424053	+	0.275383i	−0.314920	+	0.949118i	$0.601978\pi$
$948$	1.41471	−	1.74702i	0.0459475	−	0.0567404i
$949$	7.41116	+	0.778944i	0.240576	+	0.0252856i
$950$	−21.5521	−	55.0663i	−0.699243	−	1.78659i
$951$	−23.2124	−	52.1358i	−0.752712	−	1.69062i
$952$	3.00832	−	57.4021i	0.0975002	−	1.86041i
$953$	4.20747	+	8.25763i	0.136293	+	0.267491i	0.949058	−	0.315101i	$-0.102039\pi$
$953$	4.20747	+	8.25763i	0.136293	+	0.267491i	−0.812765	+	0.582592i	$0.802039\pi$
$954$	8.25594	−	9.16915i	0.267296	−	0.296862i
$955$	4.62801	+	10.3039i	0.149759	+	0.333426i
$956$	−1.41963	−	0.819623i	−0.0459141	−	0.0265085i
$957$	−8.71366	+	17.1015i	−0.281673	+	0.552814i
$958$	6.17387	+	16.0835i	0.199469	+	0.519633i
$959$	−49.7495	−	36.1451i	−1.60649	−	1.16719i
$960$	11.6078	+	14.2390i	0.374639	+	0.459560i
$961$	30.6985	+	4.31329i	0.990273	+	0.139138i
$962$	8.98360	−	8.98360i	0.289643	−	0.289643i
$963$	−0.245084	−	1.54740i	−0.00789772	−	0.0498643i
$964$	1.63094	+	0.726142i	0.0525291	+	0.0233875i
$965$	7.94477	−	12.3219i	0.255751	−	0.396655i
$966$	−36.2525	+	62.7912i	−1.16641	+	2.02027i
$967$	2.29440	−	8.56283i	0.0737830	−	0.275362i	−0.919172	−	0.393857i	$-0.871140\pi$
$967$	2.29440	−	8.56283i	0.0737830	−	0.275362i	0.992955	+	0.118495i	$0.0378071\pi$
$968$	−1.87113	+	0.0980615i	−0.0601403	+	0.00315182i
$969$	−89.0499	−	28.9341i	−2.86070	−	0.929496i
$970$	25.0716	−	18.3411i	0.805002	−	0.588899i
$971$	−35.7630	+	15.9227i	−1.14769	+	0.510985i	−0.890323	−	0.455329i	$-0.849522\pi$
$971$	−35.7630	+	15.9227i	−1.14769	+	0.510985i	−0.257367	+	0.966314i	$0.582855\pi$
$972$	3.31545	+	5.10535i	0.106343	+	0.163754i
$973$	46.3890	+	57.2856i	1.48716	+	1.83649i
$974$	−0.218912	−	2.08281i	−0.00701441	−	0.0667376i
$975$	−0.172446	−	26.3750i	−0.00552269	−	0.844677i
$976$	0.157923	+	0.217363i	0.00505501	+	0.00695762i
$977$	6.29313	−	39.7332i	0.201335	−	1.27118i	−0.655345	−	0.755330i	$-0.727477\pi$
$977$	6.29313	−	39.7332i	0.201335	−	1.27118i	0.856680	−	0.515849i	$-0.172523\pi$
$978$	−40.9715	+	63.0906i	−1.31012	+	2.01741i
$979$	−1.99546	+	0.209731i	−0.0637752	+	0.00670304i
$980$	2.63260	−	12.5876i	0.0840954	−	0.402097i
$981$	−4.79357	−	1.01890i	−0.153047	−	0.0325311i
$982$	25.3624	+	9.73572i	0.809347	+	0.310679i
$983$	7.83723	+	0.410732i	0.249969	+	0.0131003i	0.176909	−	0.984227i	$-0.443390\pi$
$983$	7.83723	+	0.410732i	0.249969	+	0.0131003i	0.0730600	+	0.997328i	$0.476724\pi$
$984$	9.93430	−	30.5746i	0.316694	−	0.974684i
$985$	−7.25566	−	0.356472i	−0.231184	−	0.0113582i
$986$	−15.8421	−	27.4393i	−0.504515	−	0.873845i
$987$	−39.4692	+	10.5758i	−1.25632	+	0.336630i
$988$	10.8782	+	5.54271i	0.346081	+	0.176337i
$989$	2.04608	−	4.59556i	0.0650614	−	0.146130i
$990$	−11.0888	+	0.617496i	−0.352426	+	0.0196253i
$991$			28.0248i			0.890237i	0.895472	+	0.445119i	$0.146839\pi$
$991$			28.0248i			0.890237i	−0.895472	+	0.445119i	$0.853161\pi$
$992$	−14.5067	+	12.6109i	−0.460589	+	0.400398i
$993$	−29.1044	−	29.1044i	−0.923600	−	0.923600i
$994$	−22.0755	+	30.3844i	−0.700194	+	0.963734i
$995$	19.1487	+	10.9722i	0.607055	+	0.347842i
$996$	−0.130457	−	0.401506i	−0.00413369	−	0.0127222i
$997$	2.97807	+	11.1143i	0.0943163	+	0.351993i	0.996915	−	0.0784899i	$-0.0250098\pi$
$997$	2.97807	+	11.1143i	0.0943163	+	0.351993i	−0.902599	+	0.430483i	$0.858343\pi$
$998$	44.2299	+	11.8514i	1.40007	+	0.375148i
$999$	8.91111	+	8.02360i	0.281935	+	0.253856i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	155.2.x.a.43.12	yes	224
5.2	odd	4	inner	155.2.x.a.12.12	✓	224
5.3	odd	4		775.2.df.b.632.3		224
5.4	even	2		775.2.df.b.43.3		224
31.13	odd	30	inner	155.2.x.a.13.12	yes	224
155.13	even	60		775.2.df.b.757.3		224
155.44	odd	30		775.2.df.b.168.3		224
155.137	even	60	inner	155.2.x.a.137.12	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.x.a.12.12	✓	224	5.2	odd	4	inner
155.2.x.a.13.12	yes	224	31.13	odd	30	inner
155.2.x.a.43.12	yes	224	1.1	even	1	trivial
155.2.x.a.137.12	yes	224	155.137	even	60	inner
775.2.df.b.43.3		224	5.4	even	2
775.2.df.b.168.3		224	155.44	odd	30
775.2.df.b.632.3		224	5.3	odd	4
775.2.df.b.757.3		224	155.13	even	60

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:	\( N \)	\(=\)	\( 155 = 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	155.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.60231 - 0.253782i) q^{2} +(1.85797 - 0.713206i) q^{3} +(0.600894 - 0.195242i) q^{4} +(-1.30841 + 1.81330i) q^{5} +(2.79605 - 1.61430i) q^{6} +(-0.210014 - 4.00730i) q^{7} +(-1.97767 + 1.00767i) q^{8} +(0.713938 - 0.642832i) q^{9} +O(q^{10})\)	\(q+(1.60231 - 0.253782i) q^{2} +(1.85797 - 0.713206i) q^{3} +(0.600894 - 0.195242i) q^{4} +(-1.30841 + 1.81330i) q^{5} +(2.79605 - 1.61430i) q^{6} +(-0.210014 - 4.00730i) q^{7} +(-1.97767 + 1.00767i) q^{8} +(0.713938 - 0.642832i) q^{9} +(-1.63630 + 3.23753i) q^{10} +(-0.662578 + 3.11718i) q^{11} +(0.977192 - 0.791314i) q^{12} +(2.05991 + 1.66809i) q^{13} +(-1.35349 - 6.36766i) q^{14} +(-1.13772 + 4.30222i) q^{15} +(-3.93542 + 2.85925i) q^{16} +(-5.41247 - 3.51490i) q^{17} +(0.980813 - 1.21120i) q^{18} +(7.25023 + 0.762030i) q^{19} +(-0.432180 + 1.34506i) q^{20} +(-3.24823 - 7.29564i) q^{21} +(-0.270574 + 5.16286i) q^{22} +(-2.54070 - 4.98641i) q^{23} +(-2.95576 + 3.28270i) q^{24} +(-1.57614 - 4.74508i) q^{25} +(3.72396 + 2.15003i) q^{26} +(-1.84253 + 3.61617i) q^{27} +(-0.908590 - 2.36696i) q^{28} +(2.44832 + 1.77881i) q^{29} +(-0.731153 + 7.18224i) q^{30} +(5.55421 + 0.388290i) q^{31} +(-2.44118 + 2.44118i) q^{32} +(0.992147 + 6.26417i) q^{33} +(-9.56450 - 4.25839i) q^{34} +(7.54124 + 4.86236i) q^{35} +(0.303493 - 0.525665i) q^{36} +(0.764693 - 2.85387i) q^{37} +(11.8105 - 0.618964i) q^{38} +(5.01694 + 1.63010i) q^{39} +(0.760378 - 4.90455i) q^{40} +(-6.64855 + 2.96013i) q^{41} +(-7.05619 - 10.8656i) q^{42} +(0.565683 + 0.698561i) q^{43} +(0.210467 + 2.00246i) q^{44} +(0.231529 + 2.13567i) q^{45} +(-5.33646 - 7.34501i) q^{46} +(0.800413 - 5.05361i) q^{47} +(-5.27263 + 8.11914i) q^{48} +(-9.05270 + 0.951477i) q^{49} +(-3.72969 - 7.20311i) q^{50} +(-12.5630 - 2.67035i) q^{51} +(1.56347 + 0.600160i) q^{52} +(7.90579 + 0.414325i) q^{53} +(-2.03459 + 6.26184i) q^{54} +(-4.78548 - 5.28000i) q^{55} +(4.45338 + 7.71348i) q^{56} +(14.0142 - 3.75508i) q^{57} +(4.37441 + 2.22887i) q^{58} +(-0.943742 + 2.11968i) q^{59} +(0.156329 + 2.80731i) q^{60} -0.0552325i q^{61} +(8.99813 - 0.787393i) q^{62} +(-2.72596 - 2.72596i) q^{63} +(2.42648 - 3.33977i) q^{64} +(-5.71995 + 1.55272i) q^{65} +(3.17946 + 9.78538i) q^{66} +(2.24549 + 8.38027i) q^{67} +(-3.93858 - 1.05534i) q^{68} +(-8.27687 - 7.45253i) q^{69} +(13.3174 + 5.87720i) q^{70} +(-3.86036 - 4.28737i) q^{71} +(-0.764166 + 1.99072i) q^{72} +(2.35785 - 1.53121i) q^{73} +(0.501018 - 4.76687i) q^{74} +(-6.31264 - 7.69208i) q^{75} +(4.50540 - 0.957652i) q^{76} +(12.6306 + 2.00050i) q^{77} +(8.45240 + 1.33873i) q^{78} +(1.74872 - 0.371703i) q^{79} +(-0.0355583 - 10.8772i) q^{80} +(-1.14554 + 10.8991i) q^{81} +(-9.90185 + 6.43034i) q^{82} +(0.120320 - 0.313444i) q^{83} +(-3.37626 - 3.74971i) q^{84} +(13.4553 - 5.21553i) q^{85} +(1.08368 + 0.975754i) q^{86} +(5.81755 + 1.55881i) q^{87} +(-1.83074 - 6.83241i) q^{88} +(0.194560 + 0.598794i) q^{89} +(0.912977 + 3.36326i) q^{90} +(6.25191 - 8.60502i) q^{91} +(-2.50025 - 2.50025i) q^{92} +(10.5965 - 3.23987i) q^{93} -8.30060i q^{94} +(-10.8680 + 12.1498i) q^{95} +(-2.79456 + 6.27669i) q^{96} +(-7.63007 - 3.88771i) q^{97} +(-14.2638 + 3.82197i) q^{98} +(1.53079 + 2.65140i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 12 q^{2} - 14 q^{3} - 8 q^{5} - 36 q^{6} + 6 q^{7} - 40 q^{8}+O(q^{10}) \) 224 * q - 12 * q^2 - 14 * q^3 - 8 * q^5 - 36 * q^6 + 6 * q^7 - 40 * q^8	\( 224 q - 12 q^{2} - 14 q^{3} - 8 q^{5} - 36 q^{6} + 6 q^{7} - 40 q^{8} - 10 q^{10} - 28 q^{11} - 40 q^{12} - 14 q^{13} - 20 q^{15} + 24 q^{16} - 14 q^{17} - 40 q^{18} - 44 q^{20} - 44 q^{21} + 30 q^{22} - 30 q^{23} - 22 q^{25} - 48 q^{26} + 100 q^{27} - 48 q^{28} - 44 q^{31} + 28 q^{32} + 20 q^{33} - 72 q^{35} + 16 q^{36} + 30 q^{37} + 38 q^{38} - 4 q^{40} - 20 q^{41} - 130 q^{42} + 22 q^{43} - 34 q^{45} - 28 q^{47} - 156 q^{48} + 158 q^{50} - 36 q^{51} - 10 q^{52} + 26 q^{53} + 98 q^{55} - 48 q^{56} - 20 q^{58} + 260 q^{60} + 30 q^{62} + 152 q^{63} + 32 q^{65} - 152 q^{66} + 38 q^{67} - 126 q^{68} + 166 q^{70} - 128 q^{71} - 156 q^{72} - 30 q^{73} + 26 q^{75} + 128 q^{76} + 30 q^{78} + 154 q^{80} - 64 q^{81} + 8 q^{82} - 82 q^{83} + 60 q^{85} - 28 q^{86} - 24 q^{87} + 252 q^{88} + 38 q^{90} + 194 q^{93} - 74 q^{95} + 60 q^{96} - 38 q^{97} + 174 q^{98}+O(q^{100}) \) 224 * q - 12 * q^2 - 14 * q^3 - 8 * q^5 - 36 * q^6 + 6 * q^7 - 40 * q^8 - 10 * q^10 - 28 * q^11 - 40 * q^12 - 14 * q^13 - 20 * q^15 + 24 * q^16 - 14 * q^17 - 40 * q^18 - 44 * q^20 - 44 * q^21 + 30 * q^22 - 30 * q^23 - 22 * q^25 - 48 * q^26 + 100 * q^27 - 48 * q^28 - 44 * q^31 + 28 * q^32 + 20 * q^33 - 72 * q^35 + 16 * q^36 + 30 * q^37 + 38 * q^38 - 4 * q^40 - 20 * q^41 - 130 * q^42 + 22 * q^43 - 34 * q^45 - 28 * q^47 - 156 * q^48 + 158 * q^50 - 36 * q^51 - 10 * q^52 + 26 * q^53 + 98 * q^55 - 48 * q^56 - 20 * q^58 + 260 * q^60 + 30 * q^62 + 152 * q^63 + 32 * q^65 - 152 * q^66 + 38 * q^67 - 126 * q^68 + 166 * q^70 - 128 * q^71 - 156 * q^72 - 30 * q^73 + 26 * q^75 + 128 * q^76 + 30 * q^78 + 154 * q^80 - 64 * q^81 + 8 * q^82 - 82 * q^83 + 60 * q^85 - 28 * q^86 - 24 * q^87 + 252 * q^88 + 38 * q^90 + 194 * q^93 - 74 * q^95 + 60 * q^96 - 38 * q^97 + 174 * q^98

Introduction

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