LMFDB - Embedded newform 361.2.e.j.62.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [361,2,Mod(28,361)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(361, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("361.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	361.e (of order $9$, degree $6$, not 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:	$2.88259951297$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.6053445140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{9} + 17x^{6} + 4x^{3} + 1 $ x^12 - 4x^9 + 17x^6 + 4*x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			62.2
Root			$-0.580762 + 0.211380i$ of defining polynomial
Character	$\chi$	$=$	361.62
Dual form			361.2.e.j.99.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.580762 - 0.211380i) q^{2} +(0.454617 - 2.57826i) q^{3} +(-1.23949 + 1.04005i) q^{4} +(-0.946883 - 0.794529i) q^{5} +(-0.280969 - 1.59345i) q^{6} +(-1.50000 - 2.59808i) q^{7} +(-1.11803 + 1.93649i) q^{8} +(-3.62167 - 1.31818i) q^{9} +O(q^{10})$	\(q+(0.580762 - 0.211380i) q^{2} +(0.454617 - 2.57826i) q^{3} +(-1.23949 + 1.04005i) q^{4} +(-0.946883 - 0.794529i) q^{5} +(-0.280969 - 1.59345i) q^{6} +(-1.50000 - 2.59808i) q^{7} +(-1.11803 + 1.93649i) q^{8} +(-3.62167 - 1.31818i) q^{9} +(-0.717861 - 0.261280i) q^{10} +(-0.309017 + 0.535233i) q^{11} +(2.11803 + 3.66854i) q^{12} +(-0.173648 - 0.984808i) q^{13} +(-1.42032 - 1.19179i) q^{14} +(-2.47897 + 2.08010i) q^{15} +(0.321961 - 1.82593i) q^{16} +(-4.92029 + 1.79084i) q^{17} -2.38197 q^{18} +2.00000 q^{20} +(-7.38044 + 2.68626i) q^{21} +(-0.0663277 + 0.376163i) q^{22} +(5.83575 - 4.89678i) q^{23} +(4.48450 + 3.76294i) q^{24} +(-0.602930 - 3.41939i) q^{25} +(-0.309017 - 0.535233i) q^{26} +(-1.11803 + 1.93649i) q^{27} +(4.56136 + 1.66020i) q^{28} +(1.29862 + 0.472660i) q^{29} +(-1.00000 + 1.73205i) q^{30} +(1.07295 + 1.85840i) q^{31} +(-0.975561 - 5.53268i) q^{32} +(1.23949 + 1.04005i) q^{33} +(-2.47897 + 2.08010i) q^{34} +(-0.643923 + 3.65187i) q^{35} +(5.85999 - 2.13286i) q^{36} +2.14590 q^{37} -2.61803 q^{39} +(2.59725 - 0.945320i) q^{40} +(-0.520945 + 2.95442i) q^{41} +(-3.71846 + 3.12016i) q^{42} +(-5.25055 - 4.40573i) q^{43} +(-0.173648 - 0.984808i) q^{44} +(2.38197 + 4.12569i) q^{45} +(2.35410 - 4.07742i) q^{46} +(-2.81908 - 1.02606i) q^{47} +(-4.56136 - 1.66020i) q^{48} +(-1.00000 + 1.73205i) q^{49} +(-1.07295 - 1.85840i) q^{50} +(2.38040 + 13.4999i) q^{51} +(1.23949 + 1.04005i) q^{52} +(7.14431 - 5.99479i) q^{53} +(-0.239976 + 1.36097i) q^{54} +(0.717861 - 0.261280i) q^{55} +6.70820 q^{56} +0.854102 q^{58} +(14.4020 - 5.24188i) q^{59} +(0.909234 - 5.15652i) q^{60} +(-4.41543 + 3.70498i) q^{61} +(1.01596 + 0.852489i) q^{62} +(2.00777 + 11.3866i) q^{63} +(0.118034 + 0.204441i) q^{64} +(-0.618034 + 1.07047i) q^{65} +(0.939693 + 0.342020i) q^{66} +(6.57785 + 2.39414i) q^{67} +(4.23607 - 7.33708i) q^{68} +(-9.97214 - 17.2722i) q^{69} +(0.397966 + 2.25698i) q^{70} +(1.12772 + 0.946271i) q^{71} +(6.60180 - 5.53957i) q^{72} +(1.85946 - 10.5455i) q^{73} +(1.24626 - 0.453600i) q^{74} -9.09017 q^{75} +1.85410 q^{77} +(-1.52045 + 0.553400i) q^{78} +(-2.32973 + 13.2126i) q^{79} +(-1.75562 + 1.47314i) q^{80} +(-4.37274 - 3.66916i) q^{81} +(0.321961 + 1.82593i) q^{82} +(0.236068 + 0.408882i) q^{83} +(6.35410 - 11.0056i) q^{84} +(6.08182 + 2.21360i) q^{85} +(-3.98060 - 1.44882i) q^{86} +(1.80902 - 3.13331i) q^{87} +(-0.690983 - 1.19682i) q^{88} +(-2.12477 - 12.0502i) q^{89} +(2.25544 + 1.89254i) q^{90} +(-2.29813 + 1.92836i) q^{91} +(-2.14043 + 12.1390i) q^{92} +(5.27923 - 1.92148i) q^{93} -1.85410 q^{94} -14.7082 q^{96} +(-6.71495 + 2.44404i) q^{97} +(-0.214641 + 1.21729i) q^{98} +(1.82469 - 1.53110i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 18 q^{7}+O(q^{10}) $ 12 * q - 18 * q^7	$ 12 q - 18 q^{7} + 3 q^{11} + 12 q^{12} - 42 q^{18} + 24 q^{20} + 3 q^{26} - 12 q^{30} + 33 q^{31} + 66 q^{37} - 18 q^{39} + 42 q^{45} - 12 q^{46} - 12 q^{49} - 33 q^{50} - 30 q^{58} - 12 q^{64} + 6 q^{65} + 24 q^{68} - 66 q^{69} - 42 q^{75} - 18 q^{77} - 24 q^{83} + 36 q^{84} + 15 q^{87} - 15 q^{88} + 18 q^{94} - 96 q^{96}+O(q^{100}) $ 12 * q - 18 * q^7 + 3 * q^11 + 12 * q^12 - 42 * q^18 + 24 * q^20 + 3 * q^26 - 12 * q^30 + 33 * q^31 + 66 * q^37 - 18 * q^39 + 42 * q^45 - 12 * q^46 - 12 * q^49 - 33 * q^50 - 30 * q^58 - 12 * q^64 + 6 * q^65 + 24 * q^68 - 66 * q^69 - 42 * q^75 - 18 * q^77 - 24 * q^83 + 36 * q^84 + 15 * q^87 - 15 * q^88 + 18 * q^94 - 96 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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 $

$2$	0.580762	−	0.211380i	0.410661	−	0.149468i	−0.128425	−	0.991719i	$-0.540992\pi$
$2$	0.580762	−	0.211380i	0.410661	−	0.149468i	0.539086	+	0.842251i	$0.318770\pi$
$3$	0.454617	−	2.57826i	0.262473	−	1.48856i	−0.513662	−	0.857993i	$-0.671711\pi$
$3$	0.454617	−	2.57826i	0.262473	−	1.48856i	0.776135	−	0.630567i	$-0.217177\pi$
$4$	−1.23949	+	1.04005i	−0.619743	+	0.520026i
$5$	−0.946883	−	0.794529i	−0.423459	−	0.355324i	0.406018	−	0.913865i	$-0.366917\pi$
$5$	−0.946883	−	0.794529i	−0.423459	−	0.355324i	−0.829477	+	0.558541i	$0.811361\pi$
$6$	−0.280969	−	1.59345i	−0.114705	−	0.650524i
$7$	−1.50000	−	2.59808i	−0.566947	−	0.981981i	−0.996866	−	0.0791130i	$-0.974791\pi$
$7$	−1.50000	−	2.59808i	−0.566947	−	0.981981i	0.429919	−	0.902867i	$-0.358542\pi$
$8$	−1.11803	+	1.93649i	−0.395285	+	0.684653i
$9$	−3.62167	−	1.31818i	−1.20722	−	0.439394i
$10$	−0.717861	−	0.261280i	−0.227008	−	0.0826240i
$11$	−0.309017	+	0.535233i	−0.0931721	+	0.161379i	−0.908844	−	0.417136i	$-0.863034\pi$
$11$	−0.309017	+	0.535233i	−0.0931721	+	0.161379i	0.815672	+	0.578514i	$0.196367\pi$
$12$	2.11803	+	3.66854i	0.611424	+	1.05902i
$13$	−0.173648	−	0.984808i	−0.0481613	−	0.273137i	0.951212	−	0.308539i	$-0.0998399\pi$
$13$	−0.173648	−	0.984808i	−0.0481613	−	0.273137i	−0.999373	+	0.0354021i	$0.988729\pi$
$14$	−1.42032	−	1.19179i	−0.379598	−	0.318520i
$15$	−2.47897	+	2.08010i	−0.640068	+	0.537081i
$16$	0.321961	−	1.82593i	0.0804904	−	0.456483i
$17$	−4.92029	+	1.79084i	−1.19335	+	0.434343i	−0.860897	−	0.508778i	$-0.830097\pi$
$17$	−4.92029	+	1.79084i	−1.19335	+	0.434343i	−0.332449	+	0.943121i	$0.607875\pi$
$18$	−2.38197			−0.561435
$19$		0			0
$19$		0			0
$20$	2.00000			0.447214
$21$	−7.38044	+	2.68626i	−1.61054	+	0.586190i
$22$	−0.0663277	+	0.376163i	−0.0141411	+	0.0801982i
$23$	5.83575	−	4.89678i	1.21684	−	1.02105i	0.217855	−	0.975981i	$-0.430094\pi$
$23$	5.83575	−	4.89678i	1.21684	−	1.02105i	0.998984	−	0.0450675i	$-0.0143503\pi$
$24$	4.48450	+	3.76294i	0.915395	+	0.768108i
$25$	−0.602930	−	3.41939i	−0.120586	−	0.683877i
$26$	−0.309017	−	0.535233i	−0.0606032	−	0.104968i
$27$	−1.11803	+	1.93649i	−0.215166	+	0.372678i
$28$	4.56136	+	1.66020i	0.862017	+	0.313748i
$29$	1.29862	+	0.472660i	0.241148	+	0.0877708i	0.459767	−	0.888040i	$-0.347933\pi$
$29$	1.29862	+	0.472660i	0.241148	+	0.0877708i	−0.218619	+	0.975810i	$0.570155\pi$
$30$	−1.00000	+	1.73205i	−0.182574	+	0.316228i
$31$	1.07295	+	1.85840i	0.192707	+	0.333779i	0.946147	−	0.323739i	$-0.104940\pi$
$31$	1.07295	+	1.85840i	0.192707	+	0.333779i	−0.753439	+	0.657518i	$0.771607\pi$
$32$	−0.975561	−	5.53268i	−0.172457	−	0.978049i
$33$	1.23949	+	1.04005i	0.215767	+	0.181050i
$34$	−2.47897	+	2.08010i	−0.425140	+	0.356735i
$35$	−0.643923	+	3.65187i	−0.108843	+	0.617278i
$36$	5.85999	−	2.13286i	0.976665	−	0.355477i
$37$	2.14590			0.352783			0.176392	−	0.984320i	$-0.443557\pi$
$37$	2.14590			0.352783			0.176392	+	0.984320i	$0.443557\pi$
$38$		0			0
$39$	−2.61803			−0.419221
$40$	2.59725	−	0.945320i	0.410661	−	0.149468i
$41$	−0.520945	+	2.95442i	−0.0813579	+	0.461403i	0.916725	+	0.399518i	$0.130822\pi$
$41$	−0.520945	+	2.95442i	−0.0813579	+	0.461403i	−0.998083	+	0.0618855i	$0.980289\pi$
$42$	−3.71846	+	3.12016i	−0.573771	+	0.481451i
$43$	−5.25055	−	4.40573i	−0.800701	−	0.671868i	0.147668	−	0.989037i	$-0.452823\pi$
$43$	−5.25055	−	4.40573i	−0.800701	−	0.671868i	−0.948369	+	0.317169i	$0.897268\pi$
$44$	−0.173648	−	0.984808i	−0.0261784	−	0.148465i
$45$	2.38197	+	4.12569i	0.355083	+	0.615021i
$46$	2.35410	−	4.07742i	0.347093	−	0.601183i
$47$	−2.81908	−	1.02606i	−0.411205	−	0.149666i	0.128131	−	0.991757i	$-0.459102\pi$
$47$	−2.81908	−	1.02606i	−0.411205	−	0.149666i	−0.539335	+	0.842091i	$0.681325\pi$
$48$	−4.56136	−	1.66020i	−0.658376	−	0.239629i
$49$	−1.00000	+	1.73205i	−0.142857	+	0.247436i
$50$	−1.07295	−	1.85840i	−0.151738	−	0.262818i
$51$	2.38040	+	13.4999i	0.333323	+	1.89037i
$52$	1.23949	+	1.04005i	0.171886	+	0.144229i
$53$	7.14431	−	5.99479i	0.981347	−	0.823448i	−0.00294522	−	0.999996i	$-0.500937\pi$
$53$	7.14431	−	5.99479i	0.981347	−	0.823448i	0.984292	+	0.176548i	$0.0564931\pi$
$54$	−0.239976	+	1.36097i	−0.0326566	+	0.185205i
$55$	0.717861	−	0.261280i	0.0967964	−	0.0352310i
$56$	6.70820			0.896421
$57$		0			0
$58$	0.854102			0.112149
$59$	14.4020	−	5.24188i	1.87497	−	0.682435i	0.914069	−	0.405559i	$-0.132923\pi$
$59$	14.4020	−	5.24188i	1.87497	−	0.682435i	0.960906	−	0.276876i	$-0.0892991\pi$
$60$	0.909234	−	5.15652i	0.117382	−	0.665704i
$61$	−4.41543	+	3.70498i	−0.565338	+	0.474375i	−0.880095	−	0.474798i	$-0.842521\pi$
$61$	−4.41543	+	3.70498i	−0.565338	+	0.474375i	0.314757	+	0.949172i	$0.398077\pi$
$62$	1.01596	+	0.852489i	0.129027	+	0.108266i
$63$	2.00777	+	11.3866i	0.252956	+	1.43458i
$64$	0.118034	+	0.204441i	0.0147542	+	0.0255551i
$65$	−0.618034	+	1.07047i	−0.0766577	+	0.132775i
$66$	0.939693	+	0.342020i	0.115668	+	0.0420998i
$67$	6.57785	+	2.39414i	0.803612	+	0.292491i	0.710982	−	0.703210i	$-0.248251\pi$
$67$	6.57785	+	2.39414i	0.803612	+	0.292491i	0.0926296	+	0.995701i	$0.470473\pi$
$68$	4.23607	−	7.33708i	0.513699	−	0.889752i
$69$	−9.97214	−	17.2722i	−1.20050	−	2.07933i
$70$	0.397966	+	2.25698i	0.0475661	+	0.269761i
$71$	1.12772	+	0.946271i	0.133836	+	0.112302i	0.707248	−	0.706965i	$-0.249936\pi$
$71$	1.12772	+	0.946271i	0.133836	+	0.112302i	−0.573412	+	0.819267i	$0.694381\pi$
$72$	6.60180	−	5.53957i	0.778029	−	0.652844i
$73$	1.85946	−	10.5455i	0.217633	−	1.23426i	−0.658645	−	0.752454i	$-0.728870\pi$
$73$	1.85946	−	10.5455i	0.217633	−	1.23426i	0.876278	−	0.481806i	$-0.160019\pi$
$74$	1.24626	−	0.453600i	0.144874	−	0.0527299i
$75$	−9.09017			−1.04964
$76$		0			0
$77$	1.85410			0.211295
$78$	−1.52045	+	0.553400i	−0.172158	+	0.0626602i
$79$	−2.32973	+	13.2126i	−0.262116	+	1.48653i	0.515009	+	0.857185i	$0.327789\pi$
$79$	−2.32973	+	13.2126i	−0.262116	+	1.48653i	−0.777125	+	0.629347i	$0.783322\pi$
$80$	−1.75562	+	1.47314i	−0.196284	+	0.164702i
$81$	−4.37274	−	3.66916i	−0.485860	−	0.407685i
$82$	0.321961	+	1.82593i	0.0355547	+	0.201641i
$83$	0.236068	+	0.408882i	0.0259118	+	0.0448806i	0.878691	−	0.477392i	$-0.158418\pi$
$83$	0.236068	+	0.408882i	0.0259118	+	0.0448806i	−0.852779	+	0.522272i	$0.825084\pi$
$84$	6.35410	−	11.0056i	0.693289	−	1.20081i
$85$	6.08182	+	2.21360i	0.659666	+	0.240099i
$86$	−3.98060	−	1.44882i	−0.429239	−	0.156230i
$87$	1.80902	−	3.13331i	0.193947	−	0.335926i
$88$	−0.690983	−	1.19682i	−0.0736590	−	0.127581i
$89$	−2.12477	−	12.0502i	−0.225225	−	1.27732i	−0.862254	−	0.506476i	$-0.830948\pi$
$89$	−2.12477	−	12.0502i	−0.225225	−	1.27732i	0.637029	−	0.770840i	$-0.280163\pi$
$90$	2.25544	+	1.89254i	0.237745	+	0.199491i
$91$	−2.29813	+	1.92836i	−0.240910	+	0.202147i
$92$	−2.14043	+	12.1390i	−0.223155	+	1.26558i
$93$	5.27923	−	1.92148i	0.547430	−	0.199248i
$94$	−1.85410			−0.191236
$95$		0			0
$96$	−14.7082			−1.50115
$97$	−6.71495	+	2.44404i	−0.681800	+	0.248155i	−0.659620	−	0.751599i	$-0.729283\pi$
$97$	−6.71495	+	2.44404i	−0.681800	+	0.248155i	−0.0221796	+	0.999754i	$0.507061\pi$
$98$	−0.214641	+	1.21729i	−0.0216820	+	0.122965i
$99$	1.82469	−	1.53110i	0.183388	−	0.153881i
$100$	4.30366	+	3.61120i	0.430366	+	0.361120i
$101$	2.28874	+	12.9801i	0.227738	+	1.29157i	0.857381	+	0.514683i	$0.172090\pi$
$101$	2.28874	+	12.9801i	0.227738	+	1.29157i	−0.629642	+	0.776885i	$0.716798\pi$
$102$	4.23607	+	7.33708i	0.419433	+	0.726480i
$103$	0.663119	−	1.14856i	0.0653391	−	0.113171i	−0.831505	−	0.555517i	$-0.812520\pi$
$103$	0.663119	−	1.14856i	0.0653391	−	0.113171i	0.896844	+	0.442346i	$0.145854\pi$
$104$	2.10122	+	0.764780i	0.206041	+	0.0749929i
$105$	9.12273	+	3.32040i	0.890287	+	0.324038i
$106$	2.88197	−	4.99171i	0.279921	−	0.484838i
$107$	5.20820	+	9.02087i	0.503496	+	0.872081i	0.999992	+	0.00404164i	$0.00128650\pi$
$107$	5.20820	+	9.02087i	0.503496	+	0.872081i	−0.496496	+	0.868039i	$0.665380\pi$
$108$	−0.628265	−	3.56307i	−0.0604548	−	0.342856i
$109$	−12.7992	−	10.7398i	−1.22594	−	1.02869i	−0.998492	−	0.0548994i	$-0.982516\pi$
$109$	−12.7992	−	10.7398i	−1.22594	−	1.02869i	−0.227452	−	0.973789i	$-0.573039\pi$
$110$	0.361677	−	0.303483i	0.0344846	−	0.0289360i
$111$	0.975561	−	5.53268i	0.0925962	−	0.525139i
$112$	−5.22686	+	1.90242i	−0.493892	+	0.179762i
$113$	11.2361			1.05700			0.528500	−	0.848933i	$-0.322755\pi$
$113$	11.2361			1.05700			0.528500	+	0.848933i	$0.322755\pi$
$114$		0			0
$115$	−9.41641			−0.878085
$116$	−2.10122	+	0.764780i	−0.195093	+	0.0710081i
$117$	−0.669258	+	3.79555i	−0.0618729	+	0.350899i
$118$	7.25608	−	6.08857i	0.667976	−	0.560498i
$119$	12.0332	+	10.0970i	1.10308	+	0.925594i
$120$	−1.25653	−	7.12614i	−0.114705	−	0.650524i
$121$	5.30902	+	9.19549i	0.482638	+	0.835953i
$122$	−1.78115	+	3.08505i	−0.161258	+	0.279307i
$123$	7.38044	+	2.68626i	0.665472	+	0.242212i
$124$	−3.26274	−	1.18754i	−0.293003	−	0.106644i
$125$	−5.23607	+	9.06914i	−0.468328	+	0.811168i
$126$	3.57295	+	6.18853i	0.318304	+	0.551318i
$127$	1.77747	+	10.0806i	0.157725	+	0.894505i	0.956252	+	0.292545i	$0.0945022\pi$
$127$	1.77747	+	10.0806i	0.157725	+	0.894505i	−0.798526	+	0.601960i	$0.794387\pi$
$128$	8.71909	+	7.31619i	0.770666	+	0.646666i
$129$	−13.7461	+	11.5344i	−1.21028	+	1.01554i
$130$	−0.132655	+	0.752326i	−0.0116346	+	0.0659834i
$131$	−3.67404	+	1.33724i	−0.321002	+	0.116835i	−0.497495	−	0.867467i	$-0.665747\pi$
$131$	−3.67404	+	1.33724i	−0.321002	+	0.116835i	0.176493	+	0.984302i	$0.443525\pi$
$132$	−2.61803			−0.227871
$133$		0			0
$134$	4.32624			0.373730
$135$	2.59725	−	0.945320i	0.223535	−	0.0813602i
$136$	2.03311	−	11.5303i	0.174338	−	0.988718i
$137$	−1.12772	+	0.946271i	−0.0963478	+	0.0808454i	−0.689689	−	0.724106i	$-0.742253\pi$
$137$	−1.12772	+	0.946271i	−0.0963478	+	0.0808454i	0.593341	+	0.804951i	$0.297808\pi$
$138$	−9.44245	−	7.92315i	−0.803794	−	0.674464i
$139$	−1.70147	−	9.64951i	−0.144317	−	0.818461i	−0.967913	−	0.251285i	$-0.919147\pi$
$139$	−1.70147	−	9.64951i	−0.144317	−	0.818461i	0.823596	−	0.567176i	$-0.191964\pi$
$140$	−3.00000	−	5.19615i	−0.253546	−	0.439155i
$141$	−3.92705	+	6.80185i	−0.330717	+	0.572819i
$142$	0.854961	+	0.311180i	0.0717467	+	0.0261137i
$143$	0.580762	+	0.211380i	0.0485658	+	0.0176765i
$144$	−3.57295	+	6.18853i	−0.297746	+	0.515711i
$145$	−0.854102	−	1.47935i	−0.0709293	−	0.122853i
$146$	−1.14921	−	6.51749i	−0.0951093	−	0.539391i
$147$	4.01106	+	3.36568i	0.330827	+	0.277597i
$148$	−2.65981	+	2.23185i	−0.218635	+	0.183457i
$149$	−2.27308	+	12.8913i	−0.186218	+	1.05610i	0.738162	+	0.674624i	$0.235694\pi$
$149$	−2.27308	+	12.8913i	−0.186218	+	1.05610i	−0.924380	+	0.381473i	$0.875417\pi$
$150$	−5.27923	+	1.92148i	−0.431047	+	0.156888i
$151$	−9.90983			−0.806451			−0.403225	−	0.915101i	$-0.632111\pi$
$151$	−9.90983			−0.806451			−0.403225	+	0.915101i	$0.632111\pi$
$152$		0			0
$153$	20.1803			1.63148
$154$	1.07679	−	0.391920i	0.0867704	−	0.0315818i
$155$	0.460598	−	2.61218i	0.0369961	−	0.209815i
$156$	3.24502	−	2.72289i	0.259809	−	0.218006i
$157$	−8.53825	−	7.16445i	−0.681427	−	0.571785i	0.234996	−	0.971996i	$-0.424492\pi$
$157$	−8.53825	−	7.16445i	−0.681427	−	0.571785i	−0.916423	+	0.400211i	$0.868937\pi$
$158$	1.43986	+	8.16583i	0.114549	+	0.649638i
$159$	−12.2082	−	21.1452i	−0.968174	−	1.67693i
$160$	−3.47214	+	6.01392i	−0.274496	+	0.475442i
$161$	−21.4758	−	7.81656i	−1.69253	−	0.616031i
$162$	−3.31511	−	1.20660i	−0.260459	−	0.0947995i
$163$	−3.11803	+	5.40059i	−0.244223	+	0.423007i	−0.961913	−	0.273356i	$-0.911866\pi$
$163$	−3.11803	+	5.40059i	−0.244223	+	0.423007i	0.717690	+	0.696363i	$0.245200\pi$
$164$	−2.42705	−	4.20378i	−0.189521	−	0.328260i
$165$	−0.347296	−	1.96962i	−0.0270370	−	0.153334i
$166$	0.223529	+	0.187563i	0.0173492	+	0.0145577i
$167$	12.0759	−	10.1329i	0.934459	−	0.784104i	−0.0421535	−	0.999111i	$-0.513422\pi$
$167$	12.0759	−	10.1329i	0.934459	−	0.784104i	0.976613	+	0.215007i	$0.0689774\pi$
$168$	3.04966	−	17.2955i	0.235287	−	1.33438i
$169$	11.2763	−	4.10424i	0.867409	−	0.315711i
$170$	4.00000			0.306786
$171$		0			0
$172$	11.0902			0.845618
$173$	−7.96120	+	2.89764i	−0.605279	+	0.220304i	−0.626436	−	0.779473i	$-0.715487\pi$
$173$	−7.96120	+	2.89764i	−0.605279	+	0.220304i	0.0211572	+	0.999776i	$0.493265\pi$
$174$	0.388289	−	2.20210i	0.0294361	−	0.166941i
$175$	−7.97943	+	6.69554i	−0.603188	+	0.506135i
$176$	0.877809	+	0.736569i	0.0661673	+	0.0555210i
$177$	−6.96757	−	39.5150i	−0.523714	−	2.97013i
$178$	−3.78115	−	6.54915i	−0.283409	−	0.490879i
$179$	−3.88197	+	6.72376i	−0.290152	+	0.502558i	−0.973845	−	0.227212i	$-0.927039\pi$
$179$	−3.88197	+	6.72376i	−0.290152	+	0.502558i	0.683694	+	0.729769i	$0.260372\pi$
$180$	−7.24334	−	2.63636i	−0.539887	−	0.196503i
$181$	−11.2763	−	4.10424i	−0.838162	−	0.305066i	−0.112958	−	0.993600i	$-0.536032\pi$
$181$	−11.2763	−	4.10424i	−0.838162	−	0.305066i	−0.725204	+	0.688534i	$0.758255\pi$
$182$	−0.927051	+	1.60570i	−0.0687176	+	0.119022i
$183$	7.54508	+	13.0685i	0.557749	+	0.966049i
$184$	2.95800	+	16.7757i	0.218067	+	1.23672i
$185$	−2.03191	−	1.70498i	−0.149389	−	0.125353i
$186$	2.65981	−	2.23185i	0.195027	−	0.163647i
$187$	0.561937	−	3.18690i	0.0410929	−	0.233050i
$188$	4.56136	−	1.66020i	0.332672	−	0.121083i
$189$	6.70820			0.487950
$190$		0			0
$191$	9.76393			0.706493			0.353247	−	0.935530i	$-0.385078\pi$
$191$	9.76393			0.706493			0.353247	+	0.935530i	$0.385078\pi$
$192$	0.580762	−	0.211380i	0.0419129	−	0.0152550i
$193$	3.98423	−	22.5957i	0.286791	−	1.62647i	−0.412025	−	0.911173i	$-0.635178\pi$
$193$	3.98423	−	22.5957i	0.286791	−	1.62647i	0.698816	−	0.715301i	$-0.253711\pi$
$194$	−3.38316	+	2.83881i	−0.242897	+	0.203815i
$195$	2.47897	+	2.08010i	0.177523	+	0.148959i
$196$	−0.561937	−	3.18690i	−0.0401384	−	0.227636i
$197$	−1.50000	−	2.59808i	−0.106871	−	0.185105i	0.807630	−	0.589689i	$-0.200750\pi$
$197$	−1.50000	−	2.59808i	−0.106871	−	0.185105i	−0.914501	+	0.404584i	$0.867416\pi$
$198$	0.736068	−	1.27491i	0.0523101	−	0.0906037i
$199$	−12.6073	−	4.58868i	−0.893708	−	0.325283i	−0.145979	−	0.989288i	$-0.546633\pi$
$199$	−12.6073	−	4.58868i	−0.893708	−	0.325283i	−0.747728	+	0.664005i	$0.768856\pi$
$200$	7.29571	+	2.65542i	0.515885	+	0.187767i
$201$	9.16312	−	15.8710i	0.646317	−	1.11945i
$202$	4.07295	+	7.05455i	0.286572	+	0.496357i
$203$	−0.719928	−	4.08291i	−0.0505290	−	0.286564i
$204$	−16.9911	−	14.2572i	−1.18962	−	0.998207i
$205$	2.84065	−	2.38359i	0.198400	−	0.166477i
$206$	0.142332	−	0.807208i	0.00991677	−	0.0562408i
$207$	−27.5900	+	10.0419i	−1.91764	+	0.697963i
$208$	−1.85410			−0.128559
$209$		0			0
$210$	6.00000			0.414039
$211$	−2.68198	+	0.976160i	−0.184635	+	0.0672017i	−0.432683	−	0.901546i	$-0.642433\pi$
$211$	−2.68198	+	0.976160i	−0.184635	+	0.0672017i	0.248048	+	0.968748i	$0.420211\pi$
$212$	−2.62038	+	14.8609i	−0.179968	+	1.02065i
$213$	2.95241	−	2.47737i	0.202296	−	0.169747i
$214$	4.93156	+	4.13807i	0.337114	+	0.282873i
$215$	1.47117	+	8.34343i	0.100333	+	0.569017i
$216$	−2.50000	−	4.33013i	−0.170103	−	0.294628i
$217$	3.21885	−	5.57521i	0.218510	−	0.378470i
$218$	−9.70349	−	3.53178i	−0.657203	−	0.239202i
$219$	−26.3438	−	9.58834i	−1.78015	−	0.647920i
$220$	−0.618034	+	1.07047i	−0.0416678	+	0.0721708i
$221$	2.61803	+	4.53457i	0.176108	+	0.305028i
$222$	−0.602930	−	3.41939i	−0.0404660	−	0.229494i
$223$	15.0547	+	12.6324i	1.00814	+	0.845926i	0.988091	−	0.153873i	$-0.0491747\pi$
$223$	15.0547	+	12.6324i	1.00814	+	0.845926i	0.0200447	+	0.999799i	$0.493619\pi$
$224$	−12.9110	+	10.8336i	−0.862652	+	0.723851i
$225$	−2.32375	+	13.1787i	−0.154917	+	0.878578i
$226$	6.52548	−	2.37508i	0.434069	−	0.157988i
$227$	−10.4164			−0.691361			−0.345681	−	0.938352i	$-0.612352\pi$
$227$	−10.4164			−0.691361			−0.345681	+	0.938352i	$0.612352\pi$
$228$		0			0
$229$	−11.3820			−0.752141			−0.376071	−	0.926591i	$-0.622725\pi$
$229$	−11.3820			−0.752141			−0.376071	+	0.926591i	$0.622725\pi$
$230$	−5.46869	+	1.99044i	−0.360595	+	0.131246i
$231$	0.842906	−	4.78036i	0.0554591	−	0.314524i
$232$	−2.36721	+	1.98632i	−0.155415	+	0.130408i
$233$	10.3203	+	8.65972i	0.676102	+	0.567317i	0.914865	−	0.403761i	$-0.132297\pi$
$233$	10.3203	+	8.65972i	0.676102	+	0.567317i	−0.238762	+	0.971078i	$0.576742\pi$
$234$	0.413624	+	2.34578i	0.0270395	+	0.153348i
$235$	1.85410	+	3.21140i	0.120948	+	0.209489i
$236$	−12.3992	+	21.4760i	−0.807118	+	1.39797i
$237$	33.0063	+	12.0133i	2.14399	+	0.780349i
$238$	9.12273	+	3.32040i	0.591339	+	0.215230i
$239$	−7.66312	+	13.2729i	−0.495686	+	0.858553i	−0.999988	−	0.00497428i	$-0.998417\pi$
$239$	−7.66312	+	13.2729i	−0.495686	+	0.858553i	0.504302	+	0.863528i	$0.331750\pi$
$240$	3.00000	+	5.19615i	0.193649	+	0.335410i
$241$	−3.33063	−	18.8889i	−0.214545	−	1.21674i	−0.881695	−	0.471821i	$-0.843597\pi$
$241$	−3.33063	−	18.8889i	−0.214545	−	1.21674i	0.667150	−	0.744924i	$-0.267514\pi$
$242$	5.02702	+	4.21817i	0.323149	+	0.271154i
$243$	−16.5868	+	13.9179i	−1.06404	+	0.892836i
$244$	1.61948	−	9.18455i	0.103677	−	0.587981i
$245$	2.32305	−	0.845520i	0.148414	−	0.0540183i
$246$	4.85410			0.309486
$247$		0			0
$248$	−4.79837			−0.304697
$249$	1.16152	−	0.422760i	0.0736086	−	0.0267913i
$250$	−1.12387	+	6.37381i	−0.0710801	+	0.403115i
$251$	14.8311	−	12.4448i	0.936133	−	0.785509i	−0.0407749	−	0.999168i	$-0.512983\pi$
$251$	14.8311	−	12.4448i	0.936133	−	0.785509i	0.976908	+	0.213659i	$0.0685382\pi$
$252$	−14.3313	−	12.0254i	−0.902788	−	0.757529i
$253$	0.817571	+	4.63668i	0.0514003	+	0.291505i
$254$	3.16312	+	5.47868i	0.198472	+	0.343763i
$255$	8.47214	−	14.6742i	0.530546	−	0.918932i
$256$	6.16655	+	2.24444i	0.385409	+	0.140278i
$257$	22.8916	+	8.33184i	1.42794	+	0.519726i	0.936339	−	0.351097i	$-0.114191\pi$
$257$	22.8916	+	8.33184i	1.42794	+	0.519726i	0.491597	+	0.870823i	$0.336413\pi$
$258$	−5.54508	+	9.60437i	−0.345222	+	0.597942i
$259$	−3.21885	−	5.57521i	−0.200009	−	0.346426i
$260$	−0.347296	−	1.96962i	−0.0215384	−	0.122150i
$261$	−4.08013	−	3.42364i	−0.252554	−	0.211918i
$262$	−1.85108	+	1.55324i	−0.114360	+	0.0959593i
$263$	0.511267	−	2.89954i	0.0315261	−	0.178793i	−0.964979	−	0.262328i	$-0.915510\pi$
$263$	0.511267	−	2.89954i	0.0315261	−	0.178793i	0.996505	+	0.0835345i	$0.0266209\pi$
$264$	−3.39984	+	1.23744i	−0.209246	+	0.0761592i
$265$	−11.5279			−0.708151
$266$		0			0
$267$	−32.0344			−1.96048
$268$	−10.6432	+	3.87380i	−0.650136	+	0.236630i
$269$	2.54807	−	14.4508i	0.155359	−	0.881083i	−0.803098	−	0.595846i	$-0.796817\pi$
$269$	2.54807	−	14.4508i	0.155359	−	0.881083i	0.958457	−	0.285237i	$-0.0920722\pi$
$270$	1.30856	−	1.09801i	0.0796364	−	0.0668229i
$271$	6.01659	+	5.04852i	0.365482	+	0.306676i	0.806971	−	0.590591i	$-0.201105\pi$
$271$	6.01659	+	5.04852i	0.365482	+	0.306676i	−0.441489	+	0.897267i	$0.645550\pi$
$272$	1.68581	+	9.56071i	0.102217	+	0.579703i
$273$	3.92705	+	6.80185i	0.237676	+	0.411667i
$274$	−0.454915	+	0.787936i	−0.0274824	+	0.0476010i
$275$	2.01648	+	0.733940i	0.121599	+	0.0442583i
$276$	30.3244	+	11.0372i	1.82531	+	0.664359i
$277$	7.70820	−	13.3510i	0.463141	−	0.802184i	−0.535974	−	0.844234i	$-0.680056\pi$
$277$	7.70820	−	13.3510i	0.463141	−	0.802184i	0.999115	+	0.0420503i	$0.0133890\pi$
$278$	−3.02786	−	5.24441i	−0.181599	−	0.314539i
$279$	−1.43616	−	8.14486i	−0.0859806	−	0.487620i
$280$	−6.35188	−	5.32986i	−0.379598	−	0.318520i
$281$	6.51642	−	5.46792i	0.388737	−	0.326189i	−0.427384	−	0.904070i	$-0.640565\pi$
$281$	6.51642	−	5.46792i	0.388737	−	0.326189i	0.816121	+	0.577881i	$0.196120\pi$
$282$	−0.842906	+	4.78036i	−0.0501943	+	0.284666i
$283$	2.85144	−	1.03784i	0.169501	−	0.0616932i	−0.255876	−	0.966710i	$-0.582364\pi$
$283$	2.85144	−	1.03784i	0.169501	−	0.0616932i	0.425377	+	0.905016i	$0.360142\pi$
$284$	−2.38197			−0.141344
$285$		0			0
$286$	0.381966			0.0225861
$287$	8.45723	−	3.07818i	0.499215	−	0.181699i
$288$	−3.75991	+	21.3235i	−0.221555	+	1.25650i
$289$	7.97943	−	6.69554i	0.469378	−	0.393855i
$290$	−0.808735	−	0.678609i	−0.0474905	−	0.0398493i
$291$	3.24865	+	18.4240i	0.190439	+	1.08003i
$292$	8.66312	+	15.0050i	0.506971	+	0.878099i
$293$	8.42705	−	14.5961i	0.492314	−	0.852712i	−0.507647	−	0.861565i	$-0.669485\pi$
$293$	8.42705	−	14.5961i	0.492314	−	0.852712i	0.999961	+	0.00885289i	$0.00281800\pi$
$294$	3.04091	+	1.10680i	0.177349	+	0.0645499i
$295$	−17.8018	−	6.47932i	−1.03646	−	0.377241i
$296$	−2.39919	+	4.15551i	−0.139450	+	0.241534i
$297$	−0.690983	−	1.19682i	−0.0400949	−	0.0694464i
$298$	1.40484	+	7.96726i	0.0813804	+	0.461531i
$299$	−5.83575	−	4.89678i	−0.337490	−	0.283188i
$300$	11.2671	−	9.45425i	0.650509	−	0.545841i
$301$	−3.57061	+	20.2499i	−0.205806	+	1.16719i
$302$	−5.75525	+	2.09474i	−0.331178	+	0.120539i
$303$	34.5066			1.98235
$304$		0			0
$305$	7.12461			0.407954
$306$	11.7200	−	4.26572i	0.669986	−	0.243855i
$307$	−0.290646	+	1.64833i	−0.0165880	+	0.0940754i	−0.991978	−	0.126412i	$-0.959654\pi$
$307$	−0.290646	+	1.64833i	−0.0165880	+	0.0940754i	0.975390	+	0.220488i	$0.0707649\pi$
$308$	−2.29813	+	1.92836i	−0.130948	+	0.109879i
$309$	−2.65981	−	2.23185i	−0.151311	−	0.126965i
$310$	−0.284665	−	1.61442i	−0.0161679	−	0.0916926i
$311$	9.32624	+	16.1535i	0.528842	+	0.915982i	0.999434	+	0.0336310i	$0.0107071\pi$
$311$	9.32624	+	16.1535i	0.528842	+	0.915982i	−0.470592	+	0.882351i	$0.655960\pi$
$312$	2.92705	−	5.06980i	0.165712	−	0.287021i
$313$	−4.06533	−	1.47966i	−0.229786	−	0.0836354i	0.224561	−	0.974460i	$-0.427905\pi$
$313$	−4.06533	−	1.47966i	−0.229786	−	0.0836354i	−0.454347	+	0.890825i	$0.650127\pi$
$314$	−6.47311	−	2.35602i	−0.365299	−	0.132958i
$315$	7.14590	−	12.3771i	0.402626	−	0.697368i
$316$	−10.8541	−	18.7999i	−0.610591	−	1.05757i
$317$	3.12567	+	17.7265i	0.175555	+	0.995622i	0.937501	+	0.347982i	$0.113133\pi$
$317$	3.12567	+	17.7265i	0.175555	+	0.995622i	−0.761946	+	0.647640i	$0.775756\pi$
$318$	−11.5597	−	9.69977i	−0.648238	−	0.543936i
$319$	−0.654280	+	0.549006i	−0.0366327	+	0.0307384i
$320$	0.0506699	−	0.287363i	0.00283253	−	0.0160641i
$321$	25.6259	−	9.32706i	1.43030	−	0.520586i
$322$	−14.1246			−0.787134
$323$		0			0
$324$	9.23607			0.513115
$325$	−3.26274	+	1.18754i	−0.180984	+	0.0658729i
$326$	−0.669258	+	3.79555i	−0.0370668	+	0.210216i
$327$	−33.5088	+	28.1172i	−1.85304	+	1.55489i
$328$	−5.13878	−	4.31195i	−0.283742	−	0.238088i
$329$	1.56283	+	8.86327i	0.0861618	+	0.488648i
$330$	−0.618034	−	1.07047i	−0.0340217	−	0.0589272i
$331$	3.47214	−	6.01392i	0.190846	−	0.330555i	−0.754685	−	0.656087i	$-0.772210\pi$
$331$	3.47214	−	6.01392i	0.190846	−	0.330555i	0.945531	+	0.325533i	$0.105544\pi$
$332$	−0.717861	−	0.261280i	−0.0393978	−	0.0143396i
$333$	−7.77174	−	2.82868i	−0.425889	−	0.155011i
$334$	4.87132	−	8.43738i	0.266547	−	0.461673i
$335$	−4.32624	−	7.49326i	−0.236368	−	0.409401i
$336$	2.52872	+	14.3411i	0.137953	+	0.782370i
$337$	17.7145	+	14.8642i	0.964969	+	0.809705i	0.981754	−	0.190154i	$-0.0608987\pi$
$337$	17.7145	+	14.8642i	0.964969	+	0.809705i	−0.0167851	+	0.999859i	$0.505343\pi$
$338$	5.68130	−	4.76718i	0.309022	−	0.259300i
$339$	5.10811	−	28.9695i	0.277434	−	1.57341i
$340$	−9.84059	+	3.58168i	−0.533681	+	0.194244i
$341$	−1.32624			−0.0718198
$342$		0			0
$343$	−15.0000			−0.809924
$344$	14.4020	−	5.24188i	0.776501	−	0.282623i
$345$	−4.28086	+	24.2779i	−0.230474	+	1.30708i
$346$	−4.01106	+	3.36568i	−0.215636	+	0.180940i
$347$	1.08503	+	0.910449i	0.0582475	+	0.0488755i	0.671447	−	0.741053i	$-0.265673\pi$
$347$	1.08503	+	0.910449i	0.0582475	+	0.0488755i	−0.613199	+	0.789928i	$0.710118\pi$
$348$	1.01655	+	5.76517i	0.0544930	+	0.309045i
$349$	−12.9894	−	22.4982i	−0.695304	−	1.20430i	−0.970078	−	0.242793i	$-0.921936\pi$
$349$	−12.9894	−	22.4982i	−0.695304	−	1.20430i	0.274774	−	0.961509i	$-0.411397\pi$
$350$	−3.21885	+	5.57521i	−0.172055	+	0.298007i
$351$	2.10122	+	0.764780i	0.112155	+	0.0408210i
$352$	3.26274	+	1.18754i	0.173905	+	0.0632961i
$353$	15.7254	−	27.2372i	0.836980	−	1.44969i	−0.0554283	−	0.998463i	$-0.517652\pi$
$353$	15.7254	−	27.2372i	0.836980	−	1.44969i	0.892408	−	0.451229i	$-0.149014\pi$
$354$	−12.3992	−	21.4760i	−0.659009	−	1.14144i
$355$	−0.315981	−	1.79202i	−0.0167705	−	0.0951103i
$356$	15.1664	+	12.7261i	0.803819	+	0.674485i
$357$	31.5033	−	26.4344i	1.66733	−	1.39906i
$358$	−0.833229	+	4.72548i	−0.0440375	+	0.249749i
$359$	20.7056	−	7.53622i	1.09280	−	0.397747i	0.268143	−	0.963379i	$-0.413590\pi$
$359$	20.7056	−	7.53622i	1.09280	−	0.397747i	0.824657	+	0.565633i	$0.191368\pi$
$360$	−10.6525			−0.561435
$361$		0			0
$362$	−7.41641			−0.389798
$363$	26.1219	−	9.50760i	1.37105	−	0.499020i
$364$	0.842906	−	4.78036i	0.0441803	−	0.250559i
$365$	−10.1394	+	8.50798i	−0.530721	+	0.445328i
$366$	7.14431	+	5.99479i	0.373439	+	0.313353i
$367$	0.337619	+	1.91473i	0.0176236	+	0.0999483i	0.992351	−	0.123450i	$-0.0393960\pi$
$367$	0.337619	+	1.91473i	0.0176236	+	0.0999483i	−0.974727	+	0.223399i	$0.928285\pi$
$368$	−7.06231	−	12.2323i	−0.368148	−	0.637651i
$369$	5.78115	−	10.0133i	0.300955	−	0.521269i
$370$	−1.54046	−	0.560681i	−0.0800846	−	0.0291484i
$371$	−26.2914	−	9.56928i	−1.36498	−	0.496812i
$372$	−4.54508	+	7.87232i	−0.235652	+	0.408161i
$373$	−1.73607	−	3.00696i	−0.0898902	−	0.155694i	0.817574	−	0.575823i	$-0.195318\pi$
$373$	−1.73607	−	3.00696i	−0.0898902	−	0.155694i	−0.907465	+	0.420129i	$0.861985\pi$
$374$	−0.347296	−	1.96962i	−0.0179583	−	0.101846i
$375$	21.0022	+	17.6229i	1.08455	+	0.910044i
$376$	5.13878	−	4.31195i	0.265012	−	0.222372i
$377$	0.239976	−	1.36097i	0.0123594	−	0.0700936i
$378$	3.89587	−	1.41798i	0.200382	−	0.0729331i
$379$	25.1246			1.29056			0.645282	−	0.763944i	$-0.276740\pi$
$379$	25.1246			1.29056			0.645282	+	0.763944i	$0.276740\pi$
$380$		0			0
$381$	26.7984			1.37292
$382$	5.67052	−	2.06390i	0.290129	−	0.105598i
$383$	0.454617	−	2.57826i	0.0232298	−	0.131743i	−0.970987	−	0.239131i	$-0.923138\pi$
$383$	0.454617	−	2.57826i	0.0232298	−	0.131743i	0.994217	+	0.107388i	$0.0342486\pi$
$384$	22.8269	−	19.1540i	1.16488	−	0.977450i
$385$	−1.75562	−	1.47314i	−0.0894746	−	0.0750781i
$386$	−2.46239	−	13.9649i	−0.125332	−	0.710795i
$387$	13.2082	+	22.8773i	0.671411	+	1.16292i
$388$	5.78115	−	10.0133i	0.293494	−	0.508346i
$389$	22.8068	+	8.30100i	1.15635	+	0.420878i	0.847793	−	0.530328i	$-0.177931\pi$
$389$	22.8068	+	8.30100i	1.15635	+	0.420878i	0.308559	+	0.951205i	$0.400153\pi$
$390$	1.87939	+	0.684040i	0.0951664	+	0.0346377i
$391$	−19.9443	+	34.5445i	−1.00863	+	1.74699i
$392$	−2.23607	−	3.87298i	−0.112938	−	0.195615i
$393$	1.77747	+	10.0806i	0.0896617	+	0.508497i
$394$	−1.42032	−	1.19179i	−0.0715549	−	0.0600417i
$395$	12.7038	−	10.6597i	0.639196	−	0.536349i
$396$	−0.669258	+	3.79555i	−0.0336315	+	0.190734i
$397$	2.37542	−	0.864580i	0.119219	−	0.0433920i	−0.281722	−	0.959496i	$-0.590906\pi$
$397$	2.37542	−	0.864580i	0.119219	−	0.0433920i	0.400941	+	0.916104i	$0.368683\pi$
$398$	−8.29180			−0.415630
$399$		0			0
$400$	−6.43769			−0.321885
$401$	0.104735	−	0.0381203i	0.00523019	−	0.00190363i	−0.339404	−	0.940641i	$-0.610225\pi$
$401$	0.104735	−	0.0381203i	0.00523019	−	0.00190363i	0.344634	+	0.938737i	$0.388003\pi$
$402$	1.96678	−	11.1542i	0.0980941	−	0.556319i
$403$	1.64385	−	1.37936i	0.0818862	−	0.0687106i
$404$	−16.3368	−	13.7082i	−0.812788	−	0.682011i
$405$	1.22521	+	6.94854i	0.0608814	+	0.345276i
$406$	−1.28115	−	2.21902i	−0.0635826	−	0.110128i
$407$	−0.663119	+	1.14856i	−0.0328696	+	0.0569318i
$408$	−28.8039	−	10.4838i	−1.42601	−	0.519024i
$409$	20.3990	+	7.42464i	1.00867	+	0.367125i	0.792921	−	0.609324i	$-0.208559\pi$
$409$	20.3990	+	7.42464i	1.00867	+	0.367125i	0.215747	+	0.976449i	$0.430782\pi$
$410$	1.14590	−	1.98475i	0.0565919	−	0.0980200i
$411$	1.92705	+	3.33775i	0.0950544	+	0.164639i
$412$	0.372631	+	2.11330i	0.0183582	+	0.104115i
$413$	−35.2217	−	29.5545i	−1.73315	−	1.45428i
$414$	−13.9006	+	11.6640i	−0.683175	+	0.573252i
$415$	0.101340	−	0.574726i	0.00497457	−	0.0282122i
$416$	−5.27923	+	1.92148i	−0.258835	+	0.0942083i
$417$	−25.6525			−1.25621
$418$		0			0
$419$	8.94427			0.436956			0.218478	−	0.975842i	$-0.429891\pi$
$419$	8.94427			0.436956			0.218478	+	0.975842i	$0.429891\pi$
$420$	−14.7609	+	5.37252i	−0.720257	+	0.262152i
$421$	−3.21733	+	18.2464i	−0.156803	+	0.889274i	0.800316	+	0.599579i	$0.204665\pi$
$421$	−3.21733	+	18.2464i	−0.156803	+	0.889274i	−0.957119	+	0.289696i	$0.906446\pi$
$422$	−1.35125	+	1.13383i	−0.0657778	+	0.0551942i
$423$	8.85724	+	7.43211i	0.430654	+	0.361361i
$424$	3.62128	+	20.5373i	0.175865	+	0.997379i
$425$	9.09017	+	15.7446i	0.440938	+	0.763727i
$426$	1.19098	−	2.06284i	0.0577033	−	0.0999451i
$427$	16.2490	+	5.91414i	0.786343	+	0.286205i
$428$	−15.8377	−	5.76444i	−0.765543	−	0.278635i
$429$	0.809017	−	1.40126i	0.0390597	−	0.0676534i
$430$	2.61803	+	4.53457i	0.126253	+	0.218676i
$431$	−0.634246	−	3.59699i	−0.0305505	−	0.173261i	0.965715	−	0.259605i	$-0.0835925\pi$
$431$	−0.634246	−	3.59699i	−0.0305505	−	0.173261i	−0.996265	+	0.0863446i	$0.972481\pi$
$432$	3.17594	+	2.66493i	0.152803	+	0.128217i
$433$	−18.0498	+	15.1456i	−0.867417	+	0.727849i	−0.963553	−	0.267519i	$-0.913796\pi$
$433$	−18.0498	+	15.1456i	−0.867417	+	0.727849i	0.0961358	+	0.995368i	$0.469352\pi$
$434$	0.690896	−	3.91827i	0.0331641	−	0.188083i
$435$	−4.20243	+	1.52956i	−0.201491	+	0.0733368i
$436$	27.0344			1.29471
$437$		0			0
$438$	−17.3262			−0.827880
$439$	−13.7165	+	4.99238i	−0.654651	+	0.238273i	−0.647925	−	0.761704i	$-0.724363\pi$
$439$	−13.7165	+	4.99238i	−0.654651	+	0.238273i	−0.00672557	+	0.999977i	$0.502141\pi$
$440$	−0.296626	+	1.68225i	−0.0141411	+	0.0801982i
$441$	5.90483	−	4.95474i	0.281182	−	0.235940i
$442$	2.47897	+	2.08010i	0.117913	+	0.0989405i
$443$	−5.97635	−	33.8935i	−0.283945	−	1.61033i	−0.709030	−	0.705178i	$-0.750867\pi$
$443$	−5.97635	−	33.8935i	−0.283945	−	1.61033i	0.425086	−	0.905153i	$-0.360244\pi$
$444$	4.54508	+	7.87232i	0.215700	+	0.373604i
$445$	−7.56231	+	13.0983i	−0.358488	+	0.620919i
$446$	11.4134	+	4.15414i	0.540441	+	0.196704i
$447$	32.2037	+	11.7212i	1.52318	+	0.554394i
$448$	0.354102	−	0.613323i	0.0167297	−	0.0289768i
$449$	16.4443	+	28.4823i	0.776053	+	1.34416i	0.934201	+	0.356748i	$0.116115\pi$
$449$	16.4443	+	28.4823i	0.776053	+	1.34416i	−0.158147	+	0.987416i	$0.550552\pi$
$450$	1.43616	+	8.14486i	0.0677012	+	0.383952i
$451$	−1.42032	−	1.19179i	−0.0668805	−	0.0561194i
$452$	−13.9269	+	11.6861i	−0.655069	+	0.549668i
$453$	−4.50518	+	25.5501i	−0.211672	+	1.20045i
$454$	−6.04945	+	2.20182i	−0.283915	+	0.103337i
$455$	3.70820			0.173843
$456$		0			0
$457$	6.29180			0.294318			0.147159	−	0.989113i	$-0.452987\pi$
$457$	6.29180			0.294318			0.147159	+	0.989113i	$0.452987\pi$
$458$	−6.61021	+	2.40592i	−0.308875	+	0.112421i
$459$	2.03311	−	11.5303i	0.0948974	−	0.538190i
$460$	11.6715	−	9.79356i	0.544187	−	0.456627i
$461$	2.34082	+	1.96418i	0.109023	+	0.0914812i	0.695670	−	0.718362i	$-0.255108\pi$
$461$	2.34082	+	1.96418i	0.109023	+	0.0914812i	−0.586647	+	0.809843i	$0.699552\pi$
$462$	−0.520945	−	2.95442i	−0.0242365	−	0.137452i
$463$	2.63525	+	4.56440i	0.122471	+	0.212125i	0.920741	−	0.390173i	$-0.127585\pi$
$463$	2.63525	+	4.56440i	0.122471	+	0.212125i	−0.798271	+	0.602299i	$0.794252\pi$
$464$	1.28115	−	2.21902i	0.0594760	−	0.103016i
$465$	−6.52548	−	2.37508i	−0.302612	−	0.110142i
$466$	7.82410	+	2.84774i	0.362445	+	0.131919i
$467$	−0.972136	+	1.68379i	−0.0449851	+	0.0779165i	−0.887641	−	0.460536i	$-0.847657\pi$
$467$	−0.972136	+	1.68379i	−0.0449851	+	0.0779165i	0.842656	+	0.538452i	$0.180991\pi$
$468$	−3.11803	−	5.40059i	−0.144131	−	0.249643i
$469$	−3.64661	−	20.6810i	−0.168385	−	0.954958i
$470$	1.75562	+	1.47314i	0.0809806	+	0.0679508i
$471$	−22.3534	+	18.7568i	−1.02999	+	0.864266i
$472$	−5.95101	+	33.7499i	−0.273918	+	1.55346i
$473$	3.98060	−	1.44882i	0.183028	−	0.0666168i
$474$	21.7082			0.997091
$475$		0			0
$476$	−25.4164			−1.16496
$477$	−33.7766	+	12.2937i	−1.54652	+	0.562888i
$478$	−1.64482	+	9.32823i	−0.0752323	+	0.426663i
$479$	9.12346	−	7.65549i	0.416861	−	0.349788i	−0.410106	−	0.912038i	$-0.634508\pi$
$479$	9.12346	−	7.65549i	0.416861	−	0.349788i	0.826968	+	0.562249i	$0.190064\pi$
$480$	13.9269	+	11.6861i	0.635675	+	0.533395i
$481$	−0.372631	−	2.11330i	−0.0169905	−	0.0963581i
$482$	−5.92705	−	10.2660i	−0.269970	−	0.467601i
$483$	−29.9164	+	51.8167i	−1.36124	+	2.35774i
$484$	−16.1442	−	5.87602i	−0.733829	−	0.267092i
$485$	8.30013	+	3.02100i	0.376890	+	0.137177i
$486$	−6.69098	+	11.5891i	−0.303509	+	0.525693i
$487$	9.09017	+	15.7446i	0.411915	+	0.713458i	0.995099	−	0.0988824i	$-0.0315268\pi$
$487$	9.09017	+	15.7446i	0.411915	+	0.713458i	−0.583184	+	0.812340i	$0.698193\pi$
$488$	−2.23807	−	12.6927i	−0.101313	−	0.574573i
$489$	12.5066	+	10.4943i	0.565569	+	0.474569i
$490$	1.17041	−	0.982092i	0.0528738	−	0.0443664i
$491$	5.24674	−	29.7558i	0.236782	−	1.34286i	−0.602046	−	0.798462i	$-0.705648\pi$
$491$	5.24674	−	29.7558i	0.236782	−	1.34286i	0.838828	−	0.544397i	$-0.183241\pi$
$492$	−11.9418	+	4.34646i	−0.538378	+	0.195954i
$493$	−7.23607			−0.325896
$494$		0			0
$495$	−2.94427			−0.132335
$496$	3.73877	−	1.36080i	0.167876	−	0.0611017i
$497$	0.766901	−	4.34931i	0.0344002	−	0.195093i
$498$	0.585206	−	0.491046i	0.0262237	−	0.0220043i
$499$	−11.5861	−	9.72191i	−0.518666	−	0.435213i	0.345500	−	0.938419i	$-0.387709\pi$
$499$	−11.5861	−	9.72191i	−0.518666	−	0.435213i	−0.864166	+	0.503206i	$0.832154\pi$
$500$	−2.94234	−	16.6869i	−0.131586	−	0.746259i
$501$	−20.6353	−	35.7413i	−0.921915	−	1.59680i
$502$	5.98278	−	10.3625i	0.267024	−	0.462500i
$503$	16.7574	+	6.09918i	0.747174	+	0.271949i	0.687416	−	0.726264i	$-0.258745\pi$
$503$	16.7574	+	6.09918i	0.747174	+	0.271949i	0.0597579	+	0.998213i	$0.480967\pi$
$504$	−24.2949	−	8.84262i	−1.08218	−	0.393882i
$505$	8.14590	−	14.1091i	0.362488	−	0.627847i
$506$	1.45492	+	2.51999i	0.0646789	+	0.112027i
$507$	−5.45540	−	30.9391i	−0.242283	−	1.37405i
$508$	−12.6875	−	10.6460i	−0.562915	−	0.472342i
$509$	−20.7096	+	17.3774i	−0.917936	+	0.770240i	−0.973612	−	0.228209i	$-0.926713\pi$
$509$	−20.7096	+	17.3774i	−0.917936	+	0.770240i	0.0556760	+	0.998449i	$0.482269\pi$
$510$	1.81847	−	10.3130i	0.0805231	−	0.456669i
$511$	−30.1873	+	10.9873i	−1.33541	+	0.486048i
$512$	−18.7082			−0.826794
$513$		0			0
$514$	15.0557			0.664080
$515$	−1.54046	+	0.560681i	−0.0678807	+	0.0247065i
$516$	5.04178	−	28.5933i	0.221952	−	1.25875i
$517$	1.42032	−	1.19179i	0.0624658	−	0.0524150i
$518$	−3.04787	−	2.55747i	−0.133916	−	0.112369i
$519$	3.85158	+	21.8434i	0.169065	+	0.958818i
$520$	−1.38197	−	2.39364i	−0.0606032	−	0.104968i
$521$	13.6353	−	23.6170i	0.597371	−	1.03468i	−0.395836	−	0.918321i	$-0.629545\pi$
$521$	13.6353	−	23.6170i	0.597371	−	1.03468i	0.993208	−	0.116356i	$-0.0371215\pi$
$522$	−3.09328	−	1.12586i	−0.135389	−	0.0492776i
$523$	−21.0645	−	7.66686i	−0.921088	−	0.335249i	−0.162417	−	0.986722i	$-0.551929\pi$
$523$	−21.0645	−	7.66686i	−0.921088	−	0.335249i	−0.758671	+	0.651474i	$0.774151\pi$
$524$	3.16312	−	5.47868i	0.138181	−	0.239337i
$525$	13.6353	+	23.6170i	0.595091	+	1.03073i
$526$	−0.315981	−	1.79202i	−0.0137774	−	0.0781356i
$527$	−8.60733	−	7.22241i	−0.374941	−	0.314613i
$528$	2.29813	−	1.92836i	0.100013	−	0.0839212i
$529$	6.08367	−	34.5022i	0.264507	−	1.50010i
$530$	−6.69495	+	2.43676i	−0.290810	+	0.105846i
$531$	−59.0689			−2.56337
$532$		0			0
$533$	3.00000			0.129944
$534$	−18.6044	+	6.77144i	−0.805091	+	0.293029i
$535$	2.23579	−	12.6798i	0.0966615	−	0.548195i
$536$	−11.9905	+	10.0612i	−0.517910	+	0.434578i
$537$	15.5708	+	13.0655i	0.671930	+	0.563816i
$538$	−1.57480	−	8.93111i	−0.0678942	−	0.385047i
$539$	−0.618034	−	1.07047i	−0.0266206	−	0.0461082i
$540$	−2.23607	+	3.87298i	−0.0962250	+	0.166667i
$541$	−22.3955	−	8.15130i	−0.962859	−	0.350452i	−0.187706	−	0.982225i	$-0.560105\pi$
$541$	−22.3955	−	8.15130i	−0.962859	−	0.350452i	−0.775153	+	0.631773i	$0.782327\pi$
$542$	4.56136	+	1.66020i	0.195927	+	0.0713117i
$543$	−15.7082	+	27.2074i	−0.674104	+	1.16758i
$544$	14.7082	+	25.4754i	0.630609	+	1.09225i
$545$	3.58626	+	20.3387i	0.153619	+	0.871215i
$546$	3.71846	+	3.12016i	0.159135	+	0.133530i
$547$	29.0507	−	24.3764i	1.24212	−	1.04226i	0.244762	−	0.969583i	$-0.421290\pi$
$547$	29.0507	−	24.3764i	1.24212	−	1.04226i	0.997355	−	0.0726776i	$-0.0231544\pi$
$548$	0.413624	−	2.34578i	0.0176691	−	0.100207i
$549$	20.8751	−	7.59790i	0.890926	−	0.324271i
$550$	1.32624			0.0565510
$551$		0			0
$552$	44.5967			1.89816
$553$	37.8219	−	13.7660i	1.60835	−	0.585392i
$554$	1.65450	−	9.38311i	0.0702928	−	0.398650i
$555$	−5.31962	+	4.46369i	−0.225805	+	0.189473i
$556$	12.1449	+	10.1908i	0.515060	+	0.432187i
$557$	−4.02522	−	22.8282i	−0.170554	−	0.967261i	−0.943151	−	0.332364i	$-0.892154\pi$
$557$	−4.02522	−	22.8282i	−0.170554	−	0.967261i	0.772597	−	0.634897i	$-0.218957\pi$
$558$	−2.55573	−	4.42665i	−0.108193	−	0.187395i
$559$	−3.42705	+	5.93583i	−0.144949	+	0.251059i
$560$	6.46075	+	2.35152i	0.273017	+	0.0993699i
$561$	−7.96120	−	2.89764i	−0.336122	−	0.122339i
$562$	2.62868	−	4.55300i	0.110884	−	0.192057i
$563$	−10.4164	−	18.0417i	−0.438999	−	0.760369i	0.558613	−	0.829428i	$-0.311334\pi$
$563$	−10.4164	−	18.0417i	−0.438999	−	0.760369i	−0.997613	+	0.0690592i	$0.978000\pi$
$564$	−2.20676	−	12.5151i	−0.0929212	−	0.526982i
$565$	−10.6392	−	8.92738i	−0.447596	−	0.375578i
$566$	1.43663	−	1.20548i	0.0603861	−	0.0506699i
$567$	−2.97366	+	16.8645i	−0.124882	+	0.708240i
$568$	−3.09328	+	1.12586i	−0.129791	+	0.0472401i
$569$	28.0902			1.17760			0.588801	−	0.808278i	$-0.299600\pi$
$569$	28.0902			1.17760			0.588801	+	0.808278i	$0.299600\pi$
$570$		0			0
$571$	22.3262			0.934324			0.467162	−	0.884172i	$-0.345276\pi$
$571$	22.3262			0.934324			0.467162	+	0.884172i	$0.345276\pi$
$572$	−0.939693	+	0.342020i	−0.0392905	+	0.0143006i
$573$	4.43885	−	25.1740i	0.185436	−	1.05166i
$574$	4.26097	−	3.57538i	0.177850	−	0.149234i
$575$	−20.2625	−	17.0023i	−0.845006	−	0.709044i
$576$	−0.157990	−	0.896008i	−0.00658293	−	0.0373337i
$577$	−14.0623	−	24.3566i	−0.585421	−	1.01398i	−0.994823	−	0.101625i	$-0.967596\pi$
$577$	−14.0623	−	24.3566i	−0.585421	−	1.01398i	0.409401	−	0.912354i	$-0.365738\pi$
$578$	3.21885	−	5.57521i	0.133886	−	0.231898i
$579$	−56.4463	−	20.5448i	−2.34583	−	0.853811i
$580$	2.59725	+	0.945320i	0.107845	+	0.0392523i
$581$	0.708204	−	1.22665i	0.0293812	−	0.0508898i
$582$	5.78115	+	10.0133i	0.239636	+	0.415063i
$583$	1.00090	+	5.67636i	0.0414529	+	0.235091i
$584$	18.3424	+	15.3911i	0.759013	+	0.636887i
$585$	3.64938	−	3.06220i	0.150883	−	0.126606i
$586$	1.80879	−	10.2582i	0.0747204	−	0.423761i
$587$	−35.8254	+	13.0394i	−1.47867	+	0.538193i	−0.950440	−	0.310907i	$-0.899367\pi$
$587$	−35.8254	+	13.0394i	−1.47867	+	0.538193i	−0.528233	+	0.849100i	$0.677145\pi$
$588$	−8.47214			−0.349385
$589$		0			0
$590$	−11.7082			−0.482019
$591$	−7.38044	+	2.68626i	−0.303591	+	0.110498i
$592$	0.690896	−	3.91827i	0.0283957	−	0.161040i
$593$	−9.73505	+	8.16868i	−0.399771	+	0.335447i	−0.820405	−	0.571783i	$-0.806252\pi$
$593$	−9.73505	+	8.16868i	−0.399771	+	0.335447i	0.420634	+	0.907230i	$0.361808\pi$
$594$	−0.654280	−	0.549006i	−0.0268454	−	0.0225260i
$595$	−3.37162	−	19.1214i	−0.138223	−	0.783902i
$596$	−10.5902	−	18.3427i	−0.433790	−	0.751347i
$597$	−17.5623	+	30.4188i	−0.718777	+	1.24496i
$598$	−4.42426	−	1.61030i	−0.180922	−	0.0658501i
$599$	−1.48809	−	0.541620i	−0.0608017	−	0.0221300i	0.311440	−	0.950266i	$-0.399189\pi$
$599$	−1.48809	−	0.541620i	−0.0608017	−	0.0221300i	−0.372242	+	0.928136i	$0.621411\pi$
$600$	10.1631	−	17.6030i	0.414908	−	0.718641i
$601$	−16.8541	−	29.1922i	−0.687493	−	1.19077i	−0.972646	−	0.232291i	$-0.925378\pi$
$601$	−16.8541	−	29.1922i	−0.687493	−	1.19077i	0.285153	−	0.958482i	$-0.407956\pi$
$602$	2.20676	+	12.5151i	0.0899407	+	0.510079i
$603$	−20.6669	−	17.3416i	−0.841621	−	0.706204i
$604$	12.2831	−	10.3067i	0.499792	−	0.419375i
$605$	2.27906	−	12.9252i	0.0926572	−	0.525485i
$606$	20.0401	−	7.29400i	0.814074	−	0.296299i
$607$	27.2705			1.10688			0.553438	−	0.832890i	$-0.313316\pi$
$607$	27.2705			1.10688			0.553438	+	0.832890i	$0.313316\pi$
$608$		0			0
$609$	−10.8541			−0.439830
$610$	4.13770	−	1.50600i	0.167531	−	0.0609762i
$611$	−0.520945	+	2.95442i	−0.0210752	+	0.119523i
$612$	−25.0132	+	20.9886i	−1.01110	+	0.848414i
$613$	−1.57478	−	1.32140i	−0.0636047	−	0.0533707i	0.610431	−	0.792069i	$-0.290996\pi$
$613$	−1.57478	−	1.32140i	−0.0636047	−	0.0533707i	−0.674036	+	0.738699i	$0.735441\pi$
$614$	0.179629	+	1.01873i	0.00724923	+	0.0411124i
$615$	−4.85410	−	8.40755i	−0.195736	−	0.339025i
$616$	−2.07295	+	3.59045i	−0.0835215	+	0.144663i
$617$	−21.9195	−	7.97804i	−0.882446	−	0.321184i	−0.139249	−	0.990257i	$-0.544469\pi$
$617$	−21.9195	−	7.97804i	−0.882446	−	0.321184i	−0.743196	+	0.669073i	$0.766691\pi$
$618$	−2.01648	−	0.733940i	−0.0811149	−	0.0295234i
$619$	15.0623	−	26.0887i	0.605405	−	1.04859i	−0.386582	−	0.922255i	$-0.626344\pi$
$619$	15.0623	−	26.0887i	0.605405	−	1.04859i	0.991987	−	0.126338i	$-0.0403222\pi$
$620$	2.14590	+	3.71680i	0.0861813	+	0.149270i
$621$	2.95800	+	16.7757i	0.118700	+	0.673184i
$622$	8.83086	+	7.40997i	0.354085	+	0.297113i
$623$	−28.1201	+	23.5956i	−1.12661	+	0.945337i
$624$	−0.842906	+	4.78036i	−0.0337432	+	0.191367i
$625$	−4.15007	+	1.51050i	−0.166003	+	0.0604200i
$626$	−2.67376			−0.106865
$627$		0			0
$628$	18.0344			0.719653
$629$	−10.5585	+	3.84296i	−0.420993	+	0.153229i
$630$	1.53380	−	8.69863i	0.0611081	−	0.346562i
$631$	−11.7670	+	9.87365i	−0.468435	+	0.393064i	−0.846223	−	0.532828i	$-0.821129\pi$
$631$	−11.7670	+	9.87365i	−0.468435	+	0.393064i	0.377788	+	0.925892i	$0.376685\pi$
$632$	−22.9813	−	19.2836i	−0.914148	−	0.767062i
$633$	1.29752	+	7.35862i	0.0515719	+	0.292479i
$634$	5.56231	+	9.63420i	0.220907	+	0.382623i
$635$	6.32624	−	10.9574i	0.251049	−	0.434830i
$636$	37.1240	+	13.5120i	1.47206	+	0.535787i
$637$	1.87939	+	0.684040i	0.0744640	+	0.0271027i
$638$	−0.263932	+	0.457144i	−0.0104492	+	0.0180985i
$639$	−2.83688	−	4.91362i	−0.112225	−	0.194380i
$640$	−2.44304	−	13.8551i	−0.0965695	−	0.547673i
$641$	−1.14403	−	0.959953i	−0.0451864	−	0.0379159i	0.619915	−	0.784669i	$-0.287167\pi$
$641$	−1.14403	−	0.959953i	−0.0451864	−	0.0379159i	−0.665101	+	0.746753i	$0.731612\pi$
$642$	12.9110	−	10.8336i	0.509556	−	0.427568i
$643$	−6.54796	+	37.1353i	−0.258226	+	1.46447i	0.529427	+	0.848356i	$0.322407\pi$
$643$	−6.54796	+	37.1353i	−0.258226	+	1.46447i	−0.787653	+	0.616119i	$0.788704\pi$
$644$	34.7486	−	12.6475i	1.36929	−	0.498380i
$645$	22.1803			0.873350
$646$		0			0
$647$	−1.47214			−0.0578756			−0.0289378	−	0.999581i	$-0.509212\pi$
$647$	−1.47214			−0.0578756			−0.0289378	+	0.999581i	$0.509212\pi$
$648$	11.9942	−	4.36552i	0.471176	−	0.171494i
$649$	−1.64482	+	9.32823i	−0.0645648	+	0.366165i
$650$	−1.64385	+	1.37936i	−0.0644772	+	0.0541028i
$651$	−12.9110	−	10.8336i	−0.506022	−	0.424603i
$652$	−1.75214	−	9.93688i	−0.0686191	−	0.389158i
$653$	1.71885	+	2.97713i	0.0672637	+	0.116504i	0.897696	−	0.440616i	$-0.145240\pi$
$653$	1.71885	+	2.97713i	0.0672637	+	0.116504i	−0.830432	+	0.557120i	$0.811906\pi$
$654$	−13.5172	+	23.4125i	−0.528565	+	0.915502i
$655$	4.54136	+	1.65292i	0.177446	+	0.0645849i
$656$	5.22686	+	1.90242i	0.204075	+	0.0742770i
$657$	−20.6353	+	35.7413i	−0.805058	+	1.39440i
$658$	2.78115	+	4.81710i	0.108421	+	0.187790i
$659$	7.94911	+	45.0816i	0.309653	+	1.75613i	0.600750	+	0.799437i	$0.294869\pi$
$659$	7.94911	+	45.0816i	0.309653	+	1.75613i	−0.291096	+	0.956694i	$0.594020\pi$
$660$	2.47897	+	2.08010i	0.0964939	+	0.0809680i
$661$	−16.4059	+	13.7662i	−0.638116	+	0.535443i	−0.903439	−	0.428716i	$-0.858966\pi$
$661$	−16.4059	+	13.7662i	−0.638116	+	0.535443i	0.265323	+	0.964160i	$0.414521\pi$
$662$	0.745263	−	4.22659i	0.0289655	−	0.164271i
$663$	12.8815	−	4.68848i	0.500276	−	0.182086i
$664$	−1.05573			−0.0409702
$665$		0			0
$666$	−5.11146			−0.198065
$667$	9.89296	−	3.60074i	0.383057	−	0.139421i
$668$	−4.42917	+	25.1191i	−0.171370	+	0.971886i
$669$	39.4136	−	33.0720i	1.52382	−	1.27864i
$670$	−4.09644	−	3.43732i	−0.158259	−	0.132795i
$671$	−0.618588	−	3.50819i	−0.0238803	−	0.135432i
$672$	22.0623	+	38.2130i	0.851072	+	1.47410i
$673$	3.06231	−	5.30407i	0.118043	−	0.204457i	−0.800949	−	0.598733i	$-0.795671\pi$
$673$	3.06231	−	5.30407i	0.118043	−	0.204457i	0.918992	+	0.394276i	$0.129005\pi$
$674$	13.4299	+	4.88808i	0.517300	+	0.188282i
$675$	7.29571	+	2.65542i	0.280812	+	0.102207i
$676$	−9.70820	+	16.8151i	−0.373392	+	0.646735i
$677$	−5.87132	−	10.1694i	−0.225653	−	0.390843i	0.730862	−	0.682525i	$-0.239118\pi$
$677$	−5.87132	−	10.1694i	−0.225653	−	0.390843i	−0.956515	+	0.291682i	$0.905785\pi$
$678$	−3.15698	−	17.9041i	−0.121243	−	0.687604i
$679$	16.4222	+	13.7799i	0.630227	+	0.528823i
$680$	−11.0863	+	9.30251i	−0.425140	+	0.356735i
$681$	−4.73547	+	26.8562i	−0.181464	+	1.02913i
$682$	−0.770229	+	0.280340i	−0.0294936	+	0.0107348i
$683$	−21.6525			−0.828509			−0.414254	−	0.910161i	$-0.635958\pi$
$683$	−21.6525			−0.828509			−0.414254	+	0.910161i	$0.635958\pi$
$684$		0			0
$685$	1.81966			0.0695256
$686$	−8.71143	+	3.17070i	−0.332604	+	0.121058i
$687$	−5.17443	+	29.3457i	−0.197417	+	1.11961i
$688$	−9.73505	+	8.16868i	−0.371145	+	0.311428i
$689$	−7.14431	−	5.99479i	−0.272177	−	0.228383i
$690$	2.64572	+	15.0046i	0.100721	+	0.571215i
$691$	8.40983	+	14.5663i	0.319925	+	0.554126i	0.980472	−	0.196658i	$-0.0630089\pi$
$691$	8.40983	+	14.5663i	0.319925	+	0.554126i	−0.660547	+	0.750785i	$0.729676\pi$
$692$	6.85410	−	11.8717i	0.260554	−	0.451293i
$693$	−6.71495	−	2.44404i	−0.255080	−	0.0928414i
$694$	0.822596	+	0.299400i	0.0312253	+	0.0113651i
$695$	−6.05573	+	10.4888i	−0.229707	+	0.397864i
$696$	4.04508	+	7.00629i	0.153329	+	0.265573i
$697$	−2.72770	−	15.4696i	−0.103319	−	0.585951i
$698$	−12.2994	−	10.3204i	−0.465539	−	0.390634i
$699$	27.0188	−	22.6714i	1.02194	−	0.857513i
$700$	2.92668	−	16.5981i	0.110618	−	0.627347i
$701$	−36.3014	+	13.2126i	−1.37109	+	0.499035i	−0.919464	−	0.393174i	$-0.871377\pi$
$701$	−36.3014	+	13.2126i	−1.37109	+	0.499035i	−0.451623	+	0.892209i	$0.649155\pi$
$702$	1.38197			0.0521589
$703$		0			0
$704$	−0.145898			−0.00549874
$705$	9.12273	−	3.32040i	0.343582	−	0.125054i
$706$	3.37532	−	19.1424i	0.127032	−	0.720433i
$707$	30.2902	−	25.4165i	1.13918	−	0.955885i
$708$	49.7339	+	41.7317i	1.86911	+	1.56837i
$709$	7.53918	+	42.7568i	0.283140	+	1.60577i	0.711855	+	0.702326i	$0.247855\pi$
$709$	7.53918	+	42.7568i	0.283140	+	1.60577i	−0.428715	+	0.903440i	$0.641034\pi$
$710$	−0.562306	−	0.973942i	−0.0211030	−	0.0365514i
$711$	25.8541	−	44.7806i	0.969605	−	1.67940i
$712$	25.7106	+	9.35790i	0.963547	+	0.350702i
$713$	15.3616	+	5.59118i	0.575298	+	0.209391i
$714$	12.7082	−	22.0113i	0.475593	−	0.823751i
$715$	−0.381966	−	0.661585i	−0.0142847	−	0.0247419i
$716$	−2.18142	−	12.3715i	−0.0815236	−	0.462343i
$717$	30.7372	+	25.7916i	1.14790	+	0.963205i
$718$	10.4320	−	8.75350i	0.389320	−	0.326678i
$719$	3.11969	−	17.6926i	0.116345	−	0.659823i	−0.869731	−	0.493526i	$-0.835708\pi$
$719$	3.11969	−	17.6926i	0.116345	−	0.659823i	0.986076	−	0.166297i	$-0.0531811\pi$
$720$	8.30013	−	3.02100i	0.309328	−	0.112586i
$721$	−3.97871			−0.148175
$722$		0			0
$723$	−50.2148			−1.86751
$724$	18.2455	−	6.64080i	0.678087	−	0.246803i
$725$	0.833229	−	4.72548i	0.0309453	−	0.175500i
$726$	13.1609	−	11.0433i	0.488447	−	0.409856i
$727$	32.2266	+	27.0414i	1.19522	+	1.00291i	0.999754	+	0.0221980i	$0.00706641\pi$
$727$	32.2266	+	27.0414i	1.19522	+	1.00291i	0.195466	+	0.980710i	$0.437378\pi$
$728$	−1.16487	−	6.60629i	−0.0431729	−	0.244845i
$729$	19.7812	+	34.2620i	0.732635	+	1.26896i
$730$	−4.09017	+	7.08438i	−0.151384	+	0.262205i
$731$	33.7242	+	12.2746i	1.24733	+	0.453993i
$732$	−22.9439	−	8.35090i	−0.848032	−	0.308658i
$733$	−20.4787	+	35.4702i	−0.756399	+	1.31012i	0.188277	+	0.982116i	$0.439710\pi$
$733$	−20.4787	+	35.4702i	−0.756399	+	1.31012i	−0.944676	+	0.328005i	$0.893624\pi$
$734$	0.600813	+	1.04064i	0.0221764	+	0.0384107i
$735$	−1.12387	−	6.37381i	−0.0414547	−	0.235102i
$736$	−32.7855	−	27.5103i	−1.20849	−	1.01404i
$737$	−3.31409	+	2.78085i	−0.122076	+	0.102434i
$738$	1.24087	−	7.03734i	0.0456771	−	0.259048i
$739$	23.4923	−	8.55050i	0.864179	−	0.314535i	0.128371	−	0.991726i	$-0.459025\pi$
$739$	23.4923	−	8.55050i	0.864179	−	0.314535i	0.735807	+	0.677191i	$0.236803\pi$
$740$	4.29180			0.157770
$741$		0			0
$742$	−17.2918			−0.634802
$743$	−38.8663	+	14.1462i	−1.42587	+	0.518973i	−0.935744	−	0.352680i	$-0.885270\pi$
$743$	−38.8663	+	14.1462i	−1.42587	+	0.518973i	−0.490123	+	0.871653i	$0.663048\pi$
$744$	−2.18142	+	12.3715i	−0.0799748	+	0.453560i
$745$	12.3949	−	10.4005i	0.454113	−	0.381046i
$746$	−1.64385	−	1.37936i	−0.0601857	−	0.0505018i
$747$	−0.315981	−	1.79202i	−0.0115611	−	0.0655664i
$748$	2.61803	+	4.53457i	0.0957248	+	0.165800i
$749$	15.6246	−	27.0626i	0.570911	−	0.988847i
$750$	15.9224	+	5.79528i	0.581404	+	0.211614i
$751$	22.4155	+	8.15858i	0.817954	+	0.297711i	0.716905	−	0.697171i	$-0.245558\pi$
$751$	22.4155	+	8.15858i	0.817954	+	0.297711i	0.101049	+	0.994881i	$0.467780\pi$
$752$	−2.78115	+	4.81710i	−0.101418	+	0.175661i
$753$	−25.3435	−	43.8962i	−0.923567	−	1.59966i
$754$	−0.148313	−	0.841126i	−0.00540125	−	0.0306320i
$755$	9.38345	+	7.87365i	0.341499	+	0.286551i
$756$	−8.31472	+	6.97688i	−0.302404	+	0.253747i
$757$	−2.73368	+	15.5035i	−0.0993574	+	0.563484i	0.893967	+	0.448132i	$0.147911\pi$
$757$	−2.73368	+	15.5035i	−0.0993574	+	0.563484i	−0.993325	+	0.115352i	$0.963201\pi$
$758$	14.5914	−	5.31084i	0.529984	−	0.192898i
$759$	12.3262			0.447414
$760$		0			0
$761$	−30.8885			−1.11971			−0.559854	−	0.828591i	$-0.689143\pi$
$761$	−30.8885			−1.11971			−0.559854	+	0.828591i	$0.689143\pi$
$762$	15.5635	−	5.66464i	0.563805	−	0.205208i
$763$	−8.70405	+	49.3631i	−0.315108	+	1.78706i
$764$	−12.1023	+	10.1550i	−0.437844	+	0.367395i
$765$	−19.1084	−	16.0339i	−0.690866	−	0.579706i
$766$	−0.280969	−	1.59345i	−0.0101518	−	0.0575738i
$767$	−7.66312	−	13.2729i	−0.276699	−	0.479257i
$768$	8.59017	−	14.8786i	0.309971	−	0.536886i
$769$	39.1205	+	14.2387i	1.41072	+	0.513461i	0.931342	−	0.364146i	$-0.118639\pi$
$769$	39.1205	+	14.2387i	1.41072	+	0.513461i	0.479380	+	0.877607i	$0.340861\pi$
$770$	−1.33099	−	0.484440i	−0.0479655	−	0.0174580i
$771$	31.8885	−	55.2326i	1.14844	−	1.98915i
$772$	18.5623	+	32.1509i	0.668072	+	1.15713i
$773$	5.02242	+	28.4836i	0.180644	+	1.02448i	0.931425	+	0.363932i	$0.118566\pi$
$773$	5.02242	+	28.4836i	0.180644	+	1.02448i	−0.750781	+	0.660551i	$0.770323\pi$
$774$	12.5066	+	10.4943i	0.449541	+	0.377210i
$775$	5.70768	−	4.78931i	0.205026	−	0.172037i
$776$	2.77467	−	15.7360i	0.0996050	−	0.564888i
$777$	−15.8377	+	5.76444i	−0.568173	+	0.206798i
$778$	15.0000			0.537776
$779$		0			0
$780$	−5.23607			−0.187481
$781$	−0.854961	+	0.311180i	−0.0305929	+	0.0111349i
$782$	−4.28086	+	24.2779i	−0.153083	+	0.868178i
$783$	−2.36721	+	1.98632i	−0.0845971	+	0.0709854i
$784$	2.84065	+	2.38359i	0.101452	+	0.0851281i
$785$	2.39237	+	13.5678i	0.0853872	+	0.484255i
$786$	3.16312	+	5.47868i	0.112825	+	0.195418i
$787$	−19.0000	+	32.9090i	−0.677277	+	1.17308i	0.298521	+	0.954403i	$0.403507\pi$
$787$	−19.0000	+	32.9090i	−0.677277	+	1.17308i	−0.975798	+	0.218675i	$0.929827\pi$
$788$	4.56136	+	1.66020i	0.162492	+	0.0591422i
$789$	−7.24334	−	2.63636i	−0.257870	−	0.0938569i
$790$	5.12461	−	8.87609i	0.182326	−	0.315797i
$791$	−16.8541	−	29.1922i	−0.599263	−	1.03795i
$792$	0.924892	+	5.24532i	0.0328646	+	0.186384i
$793$	4.41543	+	3.70498i	0.156796	+	0.131568i
$794$	1.19680	−	1.00423i	0.0424727	−	0.0356388i
$795$	−5.24076	+	29.7218i	−0.185871	+	1.05412i
$796$	20.3990	−	7.42464i	0.723025	−	0.263159i
$797$	−33.7082			−1.19401			−0.597003	−	0.802239i	$-0.703642\pi$
$797$	−33.7082			−1.19401			−0.597003	+	0.802239i	$0.703642\pi$
$798$		0			0
$799$	15.7082			0.555716
$800$	−18.3302	+	6.67164i	−0.648070	+	0.235878i
$801$	−8.18908	+	46.4426i	−0.289347	+	1.64097i
$802$	0.0527680	−	0.0442776i	0.00186330	−	0.00156350i
$803$	5.06971	+	4.25399i	0.178906	+	0.150120i
$804$	5.14910	+	29.2020i	0.181595	+	1.02987i
$805$	14.1246	+	24.4645i	0.497827	+	0.862262i
$806$	0.663119	−	1.14856i	0.0233574	−	0.0404562i
$807$	−36.0996	−	13.1392i	−1.27077	−	0.462521i
$808$	−27.6947	−	10.0801i	−0.974298	−	0.354615i
$809$	0.100813	−	0.174613i	0.00354440	−	0.00613908i	−0.864248	−	0.503066i	$-0.832205\pi$
$809$	0.100813	−	0.174613i	0.00354440	−	0.00613908i	0.867792	+	0.496927i	$0.165538\pi$
$810$	2.18034	+	3.77646i	0.0766093	+	0.132691i
$811$	−4.16386	−	23.6144i	−0.146213	−	0.829215i	−0.966385	−	0.257098i	$-0.917234\pi$
$811$	−4.16386	−	23.6144i	−0.146213	−	0.829215i	0.820172	−	0.572116i	$-0.193877\pi$
$812$	5.13878	+	4.31195i	0.180336	+	0.151320i
$813$	15.7516	−	13.2172i	0.552434	−	0.463547i
$814$	−0.142332	+	0.807208i	−0.00498875	+	0.0282926i
$815$	7.24334	−	2.63636i	0.253723	−	0.0923477i
$816$	25.4164			0.889752
$817$		0			0
$818$	13.4164			0.469094
$819$	10.8650	−	3.95454i	0.379654	−	0.138183i
$820$	−1.04189	+	5.90885i	−0.0363843	+	0.206346i
$821$	−40.6368	+	34.0983i	−1.41823	+	1.19004i	−0.465957	+	0.884807i	$0.654290\pi$
$821$	−40.6368	+	34.0983i	−1.41823	+	1.19004i	−0.952278	+	0.305233i	$0.901266\pi$
$822$	1.82469	+	1.53110i	0.0636434	+	0.0534032i
$823$	4.09753	+	23.2383i	0.142831	+	0.810035i	0.969083	+	0.246734i	$0.0793575\pi$
$823$	4.09753	+	23.2383i	0.142831	+	0.810035i	−0.826252	+	0.563300i	$0.809531\pi$
$824$	1.48278	+	2.56825i	0.0516551	+	0.0894692i
$825$	2.80902	−	4.86536i	0.0977974	−	0.169390i
$826$	−26.7027	−	9.71898i	−0.929105	−	0.338167i
$827$	15.5958	+	5.67642i	0.542321	+	0.197389i	0.598631	−	0.801025i	$-0.295712\pi$
$827$	15.5958	+	5.67642i	0.542321	+	0.197389i	−0.0563107	+	0.998413i	$0.517934\pi$
$828$	23.7533	−	41.1419i	0.825484	−	1.42978i
$829$	−10.1631	−	17.6030i	−0.352980	−	0.611379i	0.633790	−	0.773505i	$-0.281498\pi$
$829$	−10.1631	−	17.6030i	−0.352980	−	0.611379i	−0.986770	+	0.162126i	$0.948165\pi$
$830$	−0.0626314	−	0.355200i	−0.00217397	−	0.0123292i
$831$	−30.9181	−	25.9433i	−1.07254	−	0.899965i
$832$	0.180839	−	0.151742i	0.00626945	−	0.00526069i
$833$	1.81847	−	10.3130i	0.0630062	−	0.357326i
$834$	−14.8980	+	5.42242i	−0.515875	+	0.187763i
$835$	−19.4853			−0.674316
$836$		0			0
$837$	−4.79837			−0.165856
$838$	5.19449	−	1.89064i	0.179441	−	0.0653111i
$839$	6.91092	−	39.1937i	0.238591	−	1.35312i	−0.596326	−	0.802743i	$-0.703373\pi$
$839$	6.91092	−	39.1937i	0.238591	−	1.35312i	0.834917	−	0.550376i	$-0.185516\pi$
$840$	−16.6294	+	13.9538i	−0.573771	+	0.481451i
$841$	−20.7523	−	17.4132i	−0.715596	−	0.600456i
$842$	1.98842	+	11.2769i	0.0685255	+	0.388627i
$843$	−11.1353	−	19.2868i	−0.383519	−	0.664274i
$844$	2.30902	−	3.99933i	0.0794796	−	0.137663i
$845$	−13.9383	−	5.07312i	−0.479492	−	0.174521i
$846$	6.71495	+	2.44404i	0.230865	+	0.0840279i
$847$	15.9271	−	27.5865i	0.547260	−	0.947882i
$848$	−8.64590	−	14.9751i	−0.296901	−	0.514248i
$849$	−1.37951	−	7.82358i	−0.0473446	−	0.268505i
$850$	8.60733	+	7.22241i	0.295229	+	0.247726i
$851$	12.5229	−	10.5080i	0.429281	−	0.360209i
$852$	−1.08288	+	6.14133i	−0.0370989	+	0.210398i
$853$	−16.2490	+	5.91414i	−0.556354	+	0.202496i	−0.604867	−	0.796326i	$-0.706774\pi$
$853$	−16.2490	+	5.91414i	−0.556354	+	0.202496i	0.0485132	+	0.998823i	$0.484552\pi$
$854$	10.6869			0.365699
$855$		0			0
$856$	−23.2918			−0.796097
$857$	7.87647	−	2.86680i	0.269055	−	0.0979281i	−0.203970	−	0.978977i	$-0.565384\pi$
$857$	7.87647	−	2.86680i	0.269055	−	0.0979281i	0.473025	+	0.881049i	$0.343162\pi$
$858$	0.173648	−	0.984808i	0.00592825	−	0.0336208i
$859$	14.2032	−	11.9179i	0.484608	−	0.406635i	−0.367481	−	0.930031i	$-0.619780\pi$
$859$	14.2032	−	11.9179i	0.484608	−	0.406635i	0.852089	+	0.523396i	$0.175335\pi$
$860$	−10.5011	−	8.81146i	−0.358084	−	0.300468i
$861$	−4.09155	−	23.2043i	−0.139440	−	0.790802i
$862$	−1.12868	−	1.95493i	−0.0384429	−	0.0665850i
$863$	22.4721	−	38.9229i	0.764960	−	1.32495i	−0.175307	−	0.984514i	$-0.556092\pi$
$863$	22.4721	−	38.9229i	0.764960	−	1.32495i	0.940268	−	0.340436i	$-0.110575\pi$
$864$	11.8047	+	4.29656i	0.401604	+	0.146172i
$865$	9.84059	+	3.58168i	0.334590	+	0.121781i
$866$	−7.28115	+	12.6113i	−0.247424	+	0.428550i
$867$	−13.6353	−	23.6170i	−0.463078	−	0.802074i
$868$	1.80879	+	10.2582i	0.0613943	+	0.348185i
$869$	−6.35188	−	5.32986i	−0.215473	−	0.180803i
$870$	−2.11729	+	1.77662i	−0.0717830	+	0.0602331i
$871$	1.21554	−	6.89365i	0.0411869	−	0.233583i
$872$	35.1076	−	12.7781i	1.18889	−	0.432721i
$873$	27.5410			0.932122
$874$		0			0
$875$	31.4164			1.06207
$876$	42.6251	−	15.5143i	1.44017	−	0.524178i
$877$	5.93535	−	33.6611i	0.200423	−	1.13665i	−0.704059	−	0.710141i	$-0.748631\pi$
$877$	5.93535	−	33.6611i	0.200423	−	1.13665i	0.904482	−	0.426512i	$-0.140258\pi$
$878$	−6.91071	+	5.79877i	−0.233225	+	0.195699i
$879$	−33.8014	−	28.3628i	−1.14009	−	0.956652i
$880$	−0.245957	−	1.39489i	−0.00829120	−	0.0470217i
$881$	11.7254	+	20.3090i	0.395040	+	0.684229i	0.993106	−	0.117218i	$-0.0373975\pi$
$881$	11.7254	+	20.3090i	0.395040	+	0.684229i	−0.598067	+	0.801446i	$0.704064\pi$
$882$	2.38197	−	4.12569i	0.0802050	−	0.138919i
$883$	−13.0833	−	4.76194i	−0.440289	−	0.160252i	0.112358	−	0.993668i	$-0.464160\pi$
$883$	−13.0833	−	4.76194i	−0.440289	−	0.160252i	−0.552647	+	0.833416i	$0.686382\pi$
$884$	−7.96120	−	2.89764i	−0.267764	−	0.0974582i
$885$	−24.7984	+	42.9520i	−0.833588	+	1.44382i
$886$	−10.6353	−	18.4208i	−0.357298	−	0.618859i
$887$	10.1849	+	57.7614i	0.341975	+	1.93944i	0.342717	+	0.939439i	$0.388653\pi$
$887$	10.1849	+	57.7614i	0.341975	+	1.93944i	−0.000741626		1.00000i	$0.500236\pi$
$888$	9.62328	+	8.07489i	0.322936	+	0.270976i
$889$	23.5238	−	19.7389i	0.788965	−	0.662020i
$890$	−1.62318	+	9.20551i	−0.0544091	+	0.308570i
$891$	3.31511	−	1.20660i	0.111060	−	0.0404226i
$892$	−31.7984			−1.06469
$893$		0			0
$894$	21.1803			0.708377
$895$	9.01799	−	3.28228i	0.301438	−	0.109715i
$896$	5.92937	−	33.6271i	0.198086	−	1.12340i
$897$	−15.2782	+	12.8199i	−0.510124	+	0.428045i
$898$	15.5708	+	13.0655i	0.519604	+	0.436000i
$899$	0.514964	+	2.92050i	0.0171750	+	0.0974043i
$900$	−10.8262	−	18.7516i	−0.360875	−	0.625053i
$901$	−24.4164	+	42.2905i	−0.813428	+	1.40890i
$902$	−1.07679	−	0.391920i	−0.0358532	−	0.0130495i
$903$	50.5863	+	18.4119i	1.68341	+	0.612710i
$904$	−12.5623	+	21.7586i	−0.417816	+	0.723679i
$905$	7.41641	+	12.8456i	0.246530	+	0.427002i
$906$	2.78435	+	15.7908i	0.0925039	+	0.524616i
$907$	−13.4271	−	11.2667i	−0.445840	−	0.374104i	0.392049	−	0.919944i	$-0.371766\pi$
$907$	−13.4271	−	11.2667i	−0.445840	−	0.374104i	−0.837890	+	0.545840i	$0.816211\pi$
$908$	12.9110	−	10.8336i	0.428466	−	0.359526i
$909$	8.82105	−	50.0266i	0.292576	−	1.65928i
$910$	2.15358	−	0.783840i	0.0713906	−	0.0259841i
$911$	5.61803			0.186134			0.0930669	−	0.995660i	$-0.470333\pi$
$911$	5.61803			0.186134			0.0930669	+	0.995660i	$0.470333\pi$
$912$		0			0
$913$	−0.291796			−0.00965704
$914$	3.65404	−	1.32996i	0.120865	−	0.0439912i
$915$	3.23897	−	18.3691i	0.107077	−	0.607264i
$916$	14.1078	−	11.8378i	0.466134	−	0.391133i
$917$	8.98531	+	7.53957i	0.296721	+	0.248979i
$918$	−1.25653	−	7.12614i	−0.0414717	−	0.235198i
$919$	−18.3541	−	31.7902i	−0.605446	−	1.04866i	−0.991981	−	0.126388i	$-0.959661\pi$
$919$	−18.3541	−	31.7902i	−0.605446	−	1.04866i	0.386535	−	0.922275i	$-0.373672\pi$
$920$	10.5279	−	18.2348i	0.347093	−	0.601183i
$921$	4.11770	+	1.49872i	0.135683	+	0.0493845i
$922$	1.77465	+	0.645920i	0.0584450	+	0.0212722i
$923$	0.736068	−	1.27491i	0.0242280	−	0.0419641i
$924$	3.92705	+	6.80185i	0.129190	+	0.223764i
$925$	−1.29383	−	7.33765i	−0.0425408	−	0.241261i
$926$	2.49528	+	2.09379i	0.0819999	+	0.0688061i
$927$	−3.91560	+	3.28558i	−0.128605	+	0.107913i
$928$	1.34819	−	7.64598i	0.0442566	−	0.250992i
$929$	−17.4952	+	6.36774i	−0.574000	+	0.208919i	−0.612678	−	0.790333i	$-0.709908\pi$
$929$	−17.4952	+	6.36774i	−0.574000	+	0.208919i	0.0386778	+	0.999252i	$0.487685\pi$
$930$	−4.29180			−0.140734
$931$		0			0
$932$	−21.7984			−0.714029
$933$	45.8878	−	16.7018i	1.50230	−	0.546793i
$934$	−0.208660	+	1.18337i	−0.00682757	+	0.0387211i
$935$	−3.06418	+	2.57115i	−0.100209	+	0.0840856i
$936$	−6.60180	−	5.53957i	−0.215786	−	0.181066i
$937$	3.54897	+	20.1272i	0.115940	+	0.657527i	0.986281	+	0.165077i	$0.0527873\pi$
$937$	3.54897	+	20.1272i	0.115940	+	0.657527i	−0.870341	+	0.492450i	$0.836102\pi$
$938$	−6.48936	−	11.2399i	−0.211885	−	0.366996i
$939$	−5.66312	+	9.80881i	−0.184809	+	0.320098i
$940$	−5.63816	−	2.05212i	−0.183896	−	0.0669328i
$941$	−46.6904	−	16.9939i	−1.52206	−	0.553986i	−0.560402	−	0.828221i	$-0.689353\pi$
$941$	−46.6904	−	16.9939i	−1.52206	−	0.553986i	−0.961663	+	0.274235i	$0.911575\pi$
$942$	−9.01722	+	15.6183i	−0.293797	+	0.508871i
$943$	11.4271	+	19.7922i	0.372116	+	0.644524i
$944$	−4.93446	−	27.9847i	−0.160603	−	0.910824i
$945$	−6.35188	−	5.32986i	−0.206627	−	0.173380i
$946$	2.00553	−	1.68284i	0.0652054	−	0.0547138i
$947$	−0.233995	+	1.32705i	−0.00760382	+	0.0431234i	−0.988374	−	0.152045i	$-0.951414\pi$
$947$	−0.233995	+	1.32705i	−0.00760382	+	0.0431234i	0.980770	+	0.195168i	$0.0625253\pi$
$948$	−53.4054	+	19.4380i	−1.73453	+	0.631316i
$949$	−10.7082			−0.347603
$950$		0			0
$951$	47.1246			1.52812
$952$	−33.0063	+	12.0133i	−1.06974	+	0.389354i
$953$	5.33242	−	30.2417i	0.172734	−	0.979624i	−0.767993	−	0.640459i	$-0.778744\pi$
$953$	5.33242	−	30.2417i	0.172734	−	0.979624i	0.940727	−	0.339165i	$-0.110145\pi$
$954$	−17.0175	+	14.2794i	−0.550962	+	0.462312i
$955$	−9.24530	−	7.75773i	−0.299171	−	0.251034i
$956$	−4.30619	−	24.4216i	−0.139272	−	0.789852i
$957$	1.11803	+	1.93649i	0.0361409	+	0.0625979i
$958$	3.68034	−	6.37454i	0.118906	−	0.205952i
$959$	4.15007	+	1.51050i	0.134013	+	0.0487766i
$960$	−0.717861	−	0.261280i	−0.0231689	−	0.00843278i
$961$	13.1976	−	22.8588i	0.425728	−	0.737382i
$962$	−0.663119	−	1.14856i	−0.0213798	−	0.0370309i
$963$	−6.97126	−	39.5360i	−0.224646	−	1.27403i
$964$	23.7738	+	19.9486i	0.765701	+	0.642500i
$965$	−21.7255	+	18.2299i	−0.699370	+	0.586841i
$966$	−6.42129	+	36.4169i	−0.206601	+	1.17170i
$967$	56.8899	−	20.7062i	1.82946	−	0.665868i	0.836417	−	0.548093i	$-0.184646\pi$
$967$	56.8899	−	20.7062i	1.82946	−	0.665868i	0.993040	−	0.117775i	$-0.0375760\pi$
$968$	−23.7426			−0.763118
$969$		0			0
$970$	5.45898			0.175277
$971$	13.6317	−	4.96154i	0.437463	−	0.159223i	−0.113894	−	0.993493i	$-0.536332\pi$
$971$	13.6317	−	4.96154i	0.437463	−	0.159223i	0.551357	+	0.834269i	$0.314110\pi$
$972$	6.08367	−	34.5022i	0.195134	−	1.10666i
$973$	−22.5180	+	18.8948i	−0.721893	+	0.605740i
$974$	8.60733	+	7.22241i	0.275797	+	0.231421i
$975$	1.57849	+	8.95207i	0.0505522	+	0.286696i
$976$	5.34346	+	9.25514i	0.171040	+	0.296250i
$977$	−27.6803	+	47.9438i	−0.885573	+	1.53386i	−0.0405165	+	0.999179i	$0.512900\pi$
$977$	−27.6803	+	47.9438i	−0.885573	+	1.53386i	−0.845056	+	0.534678i	$0.820433\pi$
$978$	9.48166	+	3.45104i	0.303190	+	0.110352i
$979$	7.10624	+	2.58646i	0.227117	+	0.0826637i
$980$	−2.00000	+	3.46410i	−0.0638877	+	0.110657i
$981$	32.1976	+	55.7678i	1.02799	+	1.78053i
$982$	−3.24266	−	18.3901i	−0.103478	−	0.586851i
$983$	23.2739	+	19.5292i	0.742323	+	0.622883i	0.933461	−	0.358680i	$-0.116773\pi$
$983$	23.2739	+	19.5292i	0.742323	+	0.622883i	−0.191137	+	0.981563i	$0.561218\pi$
$984$	−13.4535	+	11.2888i	−0.428882	+	0.359875i
$985$	−0.643923	+	3.65187i	−0.0205171	+	0.116358i
$986$	−4.20243	+	1.52956i	−0.133833	+	0.0487111i
$987$	23.5623			0.749996
$988$		0			0
$989$	−52.2148			−1.66033
$990$	−1.70992	+	0.622360i	−0.0543449	+	0.0197799i
$991$	−8.41340	+	47.7148i	−0.267261	+	1.51571i	0.495260	+	0.868745i	$0.335073\pi$
$991$	−8.41340	+	47.7148i	−0.267261	+	1.51571i	−0.762520	+	0.646965i	$0.776038\pi$
$992$	9.23522	−	7.74927i	0.293219	−	0.246040i
$993$	−13.9269	−	11.6861i	−0.441958	−	0.370847i
$994$	−0.473971	−	2.68802i	−0.0150334	−	0.0852589i
$995$	8.29180	+	14.3618i	0.262868	+	0.455300i
$996$	−1.00000	+	1.73205i	−0.0316862	+	0.0548821i
$997$	−24.7062	−	8.99232i	−0.782453	−	0.284790i	−0.0802581	−	0.996774i	$-0.525574\pi$
$997$	−24.7062	−	8.99232i	−0.782453	−	0.284790i	−0.702195	+	0.711984i	$0.747797\pi$
$998$	−8.78380	−	3.19704i	−0.278046	−	0.101201i
$999$	−2.39919	+	4.15551i	−0.0759069	+	0.131475i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.2.e.j.62.2		12
19.2	odd	18		361.2.a.c.1.2	✓	2
19.3	odd	18		361.2.c.g.292.1		4
19.4	even	9	inner	361.2.e.j.99.2		12
19.5	even	9		361.2.c.d.68.2		4
19.6	even	9	inner	361.2.e.j.28.1		12
19.7	even	3	inner	361.2.e.j.245.1		12
19.8	odd	6		361.2.e.i.54.2		12
19.9	even	9	inner	361.2.e.j.234.1		12
19.10	odd	18		361.2.e.i.234.2		12
19.11	even	3	inner	361.2.e.j.54.1		12
19.12	odd	6		361.2.e.i.245.2		12
19.13	odd	18		361.2.e.i.28.2		12
19.14	odd	18		361.2.c.g.68.1		4
19.15	odd	18		361.2.e.i.99.1		12
19.16	even	9		361.2.c.d.292.2		4
19.17	even	9		361.2.a.f.1.1	yes	2
19.18	odd	2		361.2.e.i.62.1		12
57.2	even	18		3249.2.a.o.1.1		2
57.17	odd	18		3249.2.a.i.1.2		2
76.55	odd	18		5776.2.a.s.1.1		2
76.59	even	18		5776.2.a.bg.1.2		2
95.59	odd	18		9025.2.a.s.1.1		2
95.74	even	18		9025.2.a.n.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
361.2.a.c.1.2	✓	2	19.2	odd	18
361.2.a.f.1.1	yes	2	19.17	even	9
361.2.c.d.68.2		4	19.5	even	9
361.2.c.d.292.2		4	19.16	even	9
361.2.c.g.68.1		4	19.14	odd	18
361.2.c.g.292.1		4	19.3	odd	18
361.2.e.i.28.2		12	19.13	odd	18
361.2.e.i.54.2		12	19.8	odd	6
361.2.e.i.62.1		12	19.18	odd	2
361.2.e.i.99.1		12	19.15	odd	18
361.2.e.i.234.2		12	19.10	odd	18
361.2.e.i.245.2		12	19.12	odd	6
361.2.e.j.28.1		12	19.6	even	9	inner
361.2.e.j.54.1		12	19.11	even	3	inner
361.2.e.j.62.2		12	1.1	even	1	trivial
361.2.e.j.99.2		12	19.4	even	9	inner
361.2.e.j.234.1		12	19.9	even	9	inner
361.2.e.j.245.1		12	19.7	even	3	inner
3249.2.a.i.1.2		2	57.17	odd	18
3249.2.a.o.1.1		2	57.2	even	18
5776.2.a.s.1.1		2	76.55	odd	18
5776.2.a.bg.1.2		2	76.59	even	18
9025.2.a.n.1.2		2	95.74	even	18
9025.2.a.s.1.1		2	95.59	odd	18

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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:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	361.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.580762 - 0.211380i) q^{2} +(0.454617 - 2.57826i) q^{3} +(-1.23949 + 1.04005i) q^{4} +(-0.946883 - 0.794529i) q^{5} +(-0.280969 - 1.59345i) q^{6} +(-1.50000 - 2.59808i) q^{7} +(-1.11803 + 1.93649i) q^{8} +(-3.62167 - 1.31818i) q^{9} +O(q^{10})\)	\(q+(0.580762 - 0.211380i) q^{2} +(0.454617 - 2.57826i) q^{3} +(-1.23949 + 1.04005i) q^{4} +(-0.946883 - 0.794529i) q^{5} +(-0.280969 - 1.59345i) q^{6} +(-1.50000 - 2.59808i) q^{7} +(-1.11803 + 1.93649i) q^{8} +(-3.62167 - 1.31818i) q^{9} +(-0.717861 - 0.261280i) q^{10} +(-0.309017 + 0.535233i) q^{11} +(2.11803 + 3.66854i) q^{12} +(-0.173648 - 0.984808i) q^{13} +(-1.42032 - 1.19179i) q^{14} +(-2.47897 + 2.08010i) q^{15} +(0.321961 - 1.82593i) q^{16} +(-4.92029 + 1.79084i) q^{17} -2.38197 q^{18} +2.00000 q^{20} +(-7.38044 + 2.68626i) q^{21} +(-0.0663277 + 0.376163i) q^{22} +(5.83575 - 4.89678i) q^{23} +(4.48450 + 3.76294i) q^{24} +(-0.602930 - 3.41939i) q^{25} +(-0.309017 - 0.535233i) q^{26} +(-1.11803 + 1.93649i) q^{27} +(4.56136 + 1.66020i) q^{28} +(1.29862 + 0.472660i) q^{29} +(-1.00000 + 1.73205i) q^{30} +(1.07295 + 1.85840i) q^{31} +(-0.975561 - 5.53268i) q^{32} +(1.23949 + 1.04005i) q^{33} +(-2.47897 + 2.08010i) q^{34} +(-0.643923 + 3.65187i) q^{35} +(5.85999 - 2.13286i) q^{36} +2.14590 q^{37} -2.61803 q^{39} +(2.59725 - 0.945320i) q^{40} +(-0.520945 + 2.95442i) q^{41} +(-3.71846 + 3.12016i) q^{42} +(-5.25055 - 4.40573i) q^{43} +(-0.173648 - 0.984808i) q^{44} +(2.38197 + 4.12569i) q^{45} +(2.35410 - 4.07742i) q^{46} +(-2.81908 - 1.02606i) q^{47} +(-4.56136 - 1.66020i) q^{48} +(-1.00000 + 1.73205i) q^{49} +(-1.07295 - 1.85840i) q^{50} +(2.38040 + 13.4999i) q^{51} +(1.23949 + 1.04005i) q^{52} +(7.14431 - 5.99479i) q^{53} +(-0.239976 + 1.36097i) q^{54} +(0.717861 - 0.261280i) q^{55} +6.70820 q^{56} +0.854102 q^{58} +(14.4020 - 5.24188i) q^{59} +(0.909234 - 5.15652i) q^{60} +(-4.41543 + 3.70498i) q^{61} +(1.01596 + 0.852489i) q^{62} +(2.00777 + 11.3866i) q^{63} +(0.118034 + 0.204441i) q^{64} +(-0.618034 + 1.07047i) q^{65} +(0.939693 + 0.342020i) q^{66} +(6.57785 + 2.39414i) q^{67} +(4.23607 - 7.33708i) q^{68} +(-9.97214 - 17.2722i) q^{69} +(0.397966 + 2.25698i) q^{70} +(1.12772 + 0.946271i) q^{71} +(6.60180 - 5.53957i) q^{72} +(1.85946 - 10.5455i) q^{73} +(1.24626 - 0.453600i) q^{74} -9.09017 q^{75} +1.85410 q^{77} +(-1.52045 + 0.553400i) q^{78} +(-2.32973 + 13.2126i) q^{79} +(-1.75562 + 1.47314i) q^{80} +(-4.37274 - 3.66916i) q^{81} +(0.321961 + 1.82593i) q^{82} +(0.236068 + 0.408882i) q^{83} +(6.35410 - 11.0056i) q^{84} +(6.08182 + 2.21360i) q^{85} +(-3.98060 - 1.44882i) q^{86} +(1.80902 - 3.13331i) q^{87} +(-0.690983 - 1.19682i) q^{88} +(-2.12477 - 12.0502i) q^{89} +(2.25544 + 1.89254i) q^{90} +(-2.29813 + 1.92836i) q^{91} +(-2.14043 + 12.1390i) q^{92} +(5.27923 - 1.92148i) q^{93} -1.85410 q^{94} -14.7082 q^{96} +(-6.71495 + 2.44404i) q^{97} +(-0.214641 + 1.21729i) q^{98} +(1.82469 - 1.53110i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 18 q^{7}+O(q^{10}) \) 12 * q - 18 * q^7	\( 12 q - 18 q^{7} + 3 q^{11} + 12 q^{12} - 42 q^{18} + 24 q^{20} + 3 q^{26} - 12 q^{30} + 33 q^{31} + 66 q^{37} - 18 q^{39} + 42 q^{45} - 12 q^{46} - 12 q^{49} - 33 q^{50} - 30 q^{58} - 12 q^{64} + 6 q^{65} + 24 q^{68} - 66 q^{69} - 42 q^{75} - 18 q^{77} - 24 q^{83} + 36 q^{84} + 15 q^{87} - 15 q^{88} + 18 q^{94} - 96 q^{96}+O(q^{100}) \) 12 * q - 18 * q^7 + 3 * q^11 + 12 * q^12 - 42 * q^18 + 24 * q^20 + 3 * q^26 - 12 * q^30 + 33 * q^31 + 66 * q^37 - 18 * q^39 + 42 * q^45 - 12 * q^46 - 12 * q^49 - 33 * q^50 - 30 * q^58 - 12 * q^64 + 6 * q^65 + 24 * q^68 - 66 * q^69 - 42 * q^75 - 18 * q^77 - 24 * q^83 + 36 * q^84 + 15 * q^87 - 15 * q^88 + 18 * q^94 - 96 * q^96

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