LMFDB - Embedded newform 490.2.p.a.239.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,2,Mod(29,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 6]))

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

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

chi := DirichletCharacter("490.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.p (of order $14$, degree $6$, 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:	$3.91266969904$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$28$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			239.17
Character	$\chi$	$=$	490.239
Dual form			490.2.p.a.449.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.781831 + 0.623490i) q^{2} +(-0.864658 + 1.79548i) q^{3} +(0.222521 + 0.974928i) q^{4} +(2.20292 + 0.383576i) q^{5} +(-1.79548 + 0.864658i) q^{6} +(-2.09628 + 1.61419i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(-0.605651 - 0.759462i) q^{9} +O(q^{10})$	\(q+(0.781831 + 0.623490i) q^{2} +(-0.864658 + 1.79548i) q^{3} +(0.222521 + 0.974928i) q^{4} +(2.20292 + 0.383576i) q^{5} +(-1.79548 + 0.864658i) q^{6} +(-2.09628 + 1.61419i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(-0.605651 - 0.759462i) q^{9} +(1.48316 + 1.67339i) q^{10} +(-0.709829 + 0.890098i) q^{11} +(-1.94287 - 0.443447i) q^{12} +(-1.60170 - 1.27731i) q^{13} +(-2.64537 - 0.0449900i) q^{14} +(-2.59348 + 3.62365i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(0.405486 + 0.0925496i) q^{17} -0.971389i q^{18} +3.74683 q^{19} +(0.116238 + 2.23304i) q^{20} +(-1.08567 - 5.15956i) q^{21} +(-1.10993 + 0.253335i) q^{22} +(0.412963 - 0.0942561i) q^{23} +(-1.24251 - 1.55806i) q^{24} +(4.70574 + 1.68997i) q^{25} +(-0.455867 - 1.99728i) q^{26} +(-3.94133 + 0.899582i) q^{27} +(-2.04018 - 1.68454i) q^{28} +(0.276073 - 1.20955i) q^{29} +(-4.28697 + 1.21607i) q^{30} -2.98785 q^{31} +(-0.974928 - 0.222521i) q^{32} +(-0.984394 - 2.04412i) q^{33} +(0.259318 + 0.325175i) q^{34} +(-5.23711 + 2.75184i) q^{35} +(0.605651 - 0.759462i) q^{36} +(2.53123 + 0.577738i) q^{37} +(2.92939 + 2.33611i) q^{38} +(3.67831 - 1.77138i) q^{39} +(-1.30140 + 1.81834i) q^{40} +(-8.98068 - 4.32487i) q^{41} +(2.36812 - 4.71081i) q^{42} +(4.11060 + 8.53575i) q^{43} +(-1.02573 - 0.493967i) q^{44} +(-1.04289 - 1.90535i) q^{45} +(0.381635 + 0.183786i) q^{46} +(0.165799 + 0.132221i) q^{47} -1.99283i q^{48} +(1.78881 - 6.76758i) q^{49} +(2.62541 + 4.25526i) q^{50} +(-0.516778 + 0.648019i) q^{51} +(0.888875 - 1.84577i) q^{52} +(12.9637 - 2.95888i) q^{53} +(-3.64233 - 1.75406i) q^{54} +(-1.90512 + 1.68854i) q^{55} +(-0.544788 - 2.58906i) q^{56} +(-3.23973 + 6.72737i) q^{57} +(0.969986 - 0.773538i) q^{58} +(3.09745 - 1.49165i) q^{59} +(-4.10990 - 1.72212i) q^{60} +(-0.440971 + 1.93202i) q^{61} +(-2.33599 - 1.86289i) q^{62} +(2.49553 + 0.614415i) q^{63} +(-0.623490 - 0.781831i) q^{64} +(-3.03847 - 3.42819i) q^{65} +(0.504855 - 2.21191i) q^{66} +4.24431i q^{67} +0.415914i q^{68} +(-0.187837 + 0.822967i) q^{69} +(-5.81029 - 1.11381i) q^{70} +(1.57739 + 6.91101i) q^{71} +(0.947034 - 0.216154i) q^{72} +(4.40064 - 3.50939i) q^{73} +(1.61879 + 2.02989i) q^{74} +(-7.10318 + 6.98782i) q^{75} +(0.833748 + 3.65289i) q^{76} +(0.0512201 - 3.01169i) q^{77} +(3.98025 + 0.908467i) q^{78} +11.7903 q^{79} +(-2.15119 + 0.610223i) q^{80} +(2.44118 - 10.6955i) q^{81} +(-4.32487 - 8.98068i) q^{82} +(4.28750 - 3.41917i) q^{83} +(4.78861 - 2.20656i) q^{84} +(0.857755 + 0.359414i) q^{85} +(-2.10816 + 9.23644i) q^{86} +(1.93302 + 1.54153i) q^{87} +(-0.493967 - 1.02573i) q^{88} +(10.4406 + 13.0920i) q^{89} +(0.372601 - 2.13989i) q^{90} +(5.41943 + 0.0921687i) q^{91} +(0.183786 + 0.381635i) q^{92} +(2.58347 - 5.36463i) q^{93} +(0.0471890 + 0.206749i) q^{94} +(8.25398 + 1.43719i) q^{95} +(1.24251 - 1.55806i) q^{96} +4.55800i q^{97} +(5.61806 - 4.17580i) q^{98} +1.10590 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q + 28 q^{4} - 4 q^{5} + 14 q^{6} + 18 q^{9}+O(q^{10}) $ 168 * q + 28 * q^4 - 4 * q^5 + 14 * q^6 + 18 * q^9	$ 168 q + 28 q^{4} - 4 q^{5} + 14 q^{6} + 18 q^{9} - 4 q^{10} - 24 q^{11} + 4 q^{14} - 2 q^{15} - 28 q^{16} + 44 q^{19} - 10 q^{20} + 22 q^{26} - 2 q^{29} - 12 q^{30} - 16 q^{31} - 8 q^{34} - 4 q^{35} - 18 q^{36} - 80 q^{39} - 10 q^{40} + 52 q^{41} - 18 q^{44} - 72 q^{45} + 26 q^{46} - 52 q^{49} - 8 q^{50} + 64 q^{51} - 42 q^{54} - 60 q^{55} + 10 q^{56} - 58 q^{59} + 2 q^{60} + 32 q^{61} + 28 q^{64} + 4 q^{65} + 48 q^{66} - 48 q^{69} + 18 q^{70} - 68 q^{71} - 10 q^{74} - 16 q^{76} - 4 q^{80} + 34 q^{81} + 84 q^{84} - 48 q^{85} - 64 q^{86} + 100 q^{89} + 54 q^{90} + 78 q^{91} - 86 q^{94} - 64 q^{95} - 212 q^{99}+O(q^{100}) $ 168 * q + 28 * q^4 - 4 * q^5 + 14 * q^6 + 18 * q^9 - 4 * q^10 - 24 * q^11 + 4 * q^14 - 2 * q^15 - 28 * q^16 + 44 * q^19 - 10 * q^20 + 22 * q^26 - 2 * q^29 - 12 * q^30 - 16 * q^31 - 8 * q^34 - 4 * q^35 - 18 * q^36 - 80 * q^39 - 10 * q^40 + 52 * q^41 - 18 * q^44 - 72 * q^45 + 26 * q^46 - 52 * q^49 - 8 * q^50 + 64 * q^51 - 42 * q^54 - 60 * q^55 + 10 * q^56 - 58 * q^59 + 2 * q^60 + 32 * q^61 + 28 * q^64 + 4 * q^65 + 48 * q^66 - 48 * q^69 + 18 * q^70 - 68 * q^71 - 10 * q^74 - 16 * q^76 - 4 * q^80 + 34 * q^81 + 84 * q^84 - 48 * q^85 - 64 * q^86 + 100 * q^89 + 54 * q^90 + 78 * q^91 - 86 * q^94 - 64 * q^95 - 212 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{1}{7}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.781831	+	0.623490i	0.552838	+	0.440874i
$2$	0.781831	+	0.623490i	0.552838	+	0.440874i
$3$	−0.864658	+	1.79548i	−0.499211	+	1.03662i	0.487347	+	0.873208i	$0.337965\pi$
$3$	−0.864658	+	1.79548i	−0.499211	+	1.03662i	−0.986558	+	0.163413i	$0.947750\pi$
$4$	0.222521	+	0.974928i	0.111260	+	0.487464i
$5$	2.20292	+	0.383576i	0.985177	+	0.171540i
$5$	2.20292	+	0.383576i	0.985177	+	0.171540i
$6$	−1.79548	+	0.864658i	−0.733002	+	0.352995i
$7$	−2.09628	+	1.61419i	−0.792321	+	0.610105i
$7$	−2.09628	+	1.61419i	−0.792321	+	0.610105i
$8$	−0.433884	+	0.900969i	−0.153401	+	0.318541i
$9$	−0.605651	−	0.759462i	−0.201884	−	0.253154i
$10$	1.48316	+	1.67339i	0.469016	+	0.529173i
$11$	−0.709829	+	0.890098i	−0.214022	+	0.268374i	−0.877241	−	0.480051i	$-0.840618\pi$
$11$	−0.709829	+	0.890098i	−0.214022	+	0.268374i	0.663219	+	0.748425i	$0.269190\pi$
$12$	−1.94287	−	0.443447i	−0.560858	−	0.128012i
$13$	−1.60170	−	1.27731i	−0.444231	−	0.354262i	0.375684	−	0.926748i	$-0.377408\pi$
$13$	−1.60170	−	1.27731i	−0.444231	−	0.354262i	−0.819915	+	0.572486i	$0.805979\pi$
$14$	−2.64537	−	0.0449900i	−0.707005	−	0.0120241i
$15$	−2.59348	+	3.62365i	−0.669633	+	0.935621i
$16$	−0.900969	+	0.433884i	−0.225242	+	0.108471i
$17$	0.405486	+	0.0925496i	0.0983448	+	0.0224466i	0.271410	−	0.962464i	$-0.412510\pi$
$17$	0.405486	+	0.0925496i	0.0983448	+	0.0224466i	−0.173065	+	0.984910i	$0.555367\pi$
$18$		−	0.971389i		−	0.228959i
$19$	3.74683			0.859582			0.429791	−	0.902928i	$-0.358587\pi$
$19$	3.74683			0.859582			0.429791	+	0.902928i	$0.358587\pi$
$20$	0.116238	+	2.23304i	0.0259916	+	0.499324i
$21$	−1.08567	−	5.15956i	−0.236913	−	1.12591i
$22$	−1.10993	+	0.253335i	−0.236639	+	0.0540112i
$23$	0.412963	−	0.0942561i	0.0861087	−	0.0196538i	−0.179249	−	0.983804i	$-0.557367\pi$
$23$	0.412963	−	0.0942561i	0.0861087	−	0.0196538i	0.265358	+	0.964150i	$0.414510\pi$
$24$	−1.24251	−	1.55806i	−0.253627	−	0.318038i
$25$	4.70574	+	1.68997i	0.941148	+	0.337995i
$26$	−0.455867	−	1.99728i	−0.0894028	−	0.391699i
$27$	−3.94133	+	0.899582i	−0.758509	+	0.173125i
$28$	−2.04018	−	1.68454i	−0.385558	−	0.318347i
$29$	0.276073	−	1.20955i	0.0512654	−	0.224608i	−0.942805	−	0.333344i	$-0.891823\pi$
$29$	0.276073	−	1.20955i	0.0512654	−	0.224608i	0.994071	+	0.108735i	$0.0346801\pi$
$30$	−4.28697	+	1.21607i	−0.782690	+	0.222024i
$31$	−2.98785			−0.536634			−0.268317	−	0.963331i	$-0.586467\pi$
$31$	−2.98785			−0.536634			−0.268317	+	0.963331i	$0.586467\pi$
$32$	−0.974928	−	0.222521i	−0.172345	−	0.0393365i
$33$	−0.984394	−	2.04412i	−0.171361	−	0.355835i
$34$	0.259318	+	0.325175i	0.0444727	+	0.0557670i
$35$	−5.23711	+	2.75184i	−0.885234	+	0.465147i
$36$	0.605651	−	0.759462i	0.100942	−	0.126577i
$37$	2.53123	+	0.577738i	0.416132	+	0.0949795i	0.425460	−	0.904977i	$-0.360112\pi$
$37$	2.53123	+	0.577738i	0.416132	+	0.0949795i	−0.00932815	+	0.999956i	$0.502969\pi$
$38$	2.92939	+	2.33611i	0.475210	+	0.378967i
$39$	3.67831	−	1.77138i	0.589001	−	0.283648i
$40$	−1.30140	+	1.81834i	−0.205770	+	0.287504i
$41$	−8.98068	−	4.32487i	−1.40255	−	0.675431i	−0.428870	−	0.903366i	$-0.641088\pi$
$41$	−8.98068	−	4.32487i	−1.40255	−	0.675431i	−0.973676	+	0.227935i	$0.926803\pi$
$42$	2.36812	−	4.71081i	0.365409	−	0.726894i
$43$	4.11060	+	8.53575i	0.626861	+	1.30169i	0.936444	+	0.350817i	$0.114096\pi$
$43$	4.11060	+	8.53575i	0.626861	+	1.30169i	−0.309583	+	0.950872i	$0.600190\pi$
$44$	−1.02573	−	0.493967i	−0.154635	−	0.0744683i
$45$	−1.04289	−	1.90535i	−0.155465	−	0.284033i
$46$	0.381635	+	0.183786i	0.0562690	+	0.0270977i
$47$	0.165799	+	0.132221i	0.0241843	+	0.0192864i	0.635507	−	0.772095i	$-0.280791\pi$
$47$	0.165799	+	0.132221i	0.0241843	+	0.0192864i	−0.611323	+	0.791381i	$0.709362\pi$
$48$		−	1.99283i		−	0.287641i
$49$	1.78881	−	6.76758i	0.255544	−	0.966797i
$50$	2.62541	+	4.25526i	0.371290	+	0.601784i
$51$	−0.516778	+	0.648019i	−0.0723634	+	0.0907408i
$52$	0.888875	−	1.84577i	0.123265	−	0.255962i
$53$	12.9637	−	2.95888i	1.78070	−	0.406433i	0.799694	−	0.600408i	$-0.204995\pi$
$53$	12.9637	−	2.95888i	1.78070	−	0.406433i	0.981007	+	0.193974i	$0.0621379\pi$
$54$	−3.64233	−	1.75406i	−0.495659	−	0.238697i
$55$	−1.90512	+	1.68854i	−0.256886	+	0.227683i
$56$	−0.544788	−	2.58906i	−0.0728003	−	0.345977i
$57$	−3.23973	+	6.72737i	−0.429112	+	0.891061i
$58$	0.969986	−	0.773538i	0.127365	−	0.101571i
$59$	3.09745	−	1.49165i	0.403254	−	0.194197i	−0.221252	−	0.975217i	$-0.571014\pi$
$59$	3.09745	−	1.49165i	0.403254	−	0.194197i	0.624506	+	0.781020i	$0.285300\pi$
$60$	−4.10990	−	1.72212i	−0.530585	−	0.222324i
$61$	−0.440971	+	1.93202i	−0.0564605	+	0.247370i	−0.995281	−	0.0970381i	$-0.969063\pi$
$61$	−0.440971	+	1.93202i	−0.0564605	+	0.247370i	0.938820	+	0.344408i	$0.111920\pi$
$62$	−2.33599	−	1.86289i	−0.296672	−	0.236588i
$63$	2.49553	+	0.614415i	0.314407	+	0.0774090i
$64$	−0.623490	−	0.781831i	−0.0779362	−	0.0977289i
$65$	−3.03847	−	3.42819i	−0.376876	−	0.425214i
$66$	0.504855	−	2.21191i	0.0621433	−	0.272268i
$67$			4.24431i			0.518525i	0.965807	+	0.259262i	$0.0834794\pi$
$67$			4.24431i			0.518525i	−0.965807	+	0.259262i	$0.916521\pi$
$68$			0.415914i			0.0504370i
$69$	−0.187837	+	0.822967i	−0.0226129	+	0.0990736i
$70$	−5.81029	−	1.11381i	−0.694462	−	0.133126i
$71$	1.57739	+	6.91101i	0.187202	+	0.820186i	0.978083	+	0.208216i	$0.0667656\pi$
$71$	1.57739	+	6.91101i	0.187202	+	0.820186i	−0.790881	+	0.611970i	$0.790377\pi$
$72$	0.947034	−	0.216154i	0.111609	−	0.0254740i
$73$	4.40064	−	3.50939i	0.515056	−	0.410743i	−0.331167	−	0.943572i	$-0.607442\pi$
$73$	4.40064	−	3.50939i	0.515056	−	0.410743i	0.846223	+	0.532829i	$0.178871\pi$
$74$	1.61879	+	2.02989i	0.188180	+	0.235970i
$75$	−7.10318	+	6.98782i	−0.820204	+	0.806884i
$76$	0.833748	+	3.65289i	0.0956375	+	0.419015i
$77$	0.0512201	−	3.01169i	0.00583707	−	0.343214i
$78$	3.98025	+	0.908467i	0.450675	+	0.102864i
$79$	11.7903			1.32651			0.663255	−	0.748394i	$-0.269175\pi$
$79$	11.7903			1.32651			0.663255	+	0.748394i	$0.269175\pi$
$80$	−2.15119	+	0.610223i	−0.240511	+	0.0682250i
$81$	2.44118	−	10.6955i	0.271242	−	1.18839i
$82$	−4.32487	−	8.98068i	−0.477602	−	0.991750i
$83$	4.28750	−	3.41917i	0.470614	−	0.375303i	−0.359274	−	0.933232i	$-0.616976\pi$
$83$	4.28750	−	3.41917i	0.470614	−	0.375303i	0.829888	+	0.557930i	$0.188404\pi$
$84$	4.78861	−	2.20656i	0.522480	−	0.240756i
$85$	0.857755	+	0.359414i	0.0930366	+	0.0389839i
$86$	−2.10816	+	9.23644i	−0.227328	+	0.995990i
$87$	1.93302	+	1.54153i	0.207242	+	0.165270i
$88$	−0.493967	−	1.02573i	−0.0526570	−	0.109343i
$89$	10.4406	+	13.0920i	1.10670	+	1.38775i	0.913620	+	0.406570i	$0.133275\pi$
$89$	10.4406	+	13.0920i	1.10670	+	1.38775i	0.193077	+	0.981184i	$0.438153\pi$
$90$	0.372601	−	2.13989i	0.0392756	−	0.225565i
$91$	5.41943	+	0.0921687i	0.568110	+	0.00966190i
$92$	0.183786	+	0.381635i	0.0191610	+	0.0397882i
$93$	2.58347	−	5.36463i	0.267893	−	0.556286i
$94$	0.0471890	+	0.206749i	0.00486717	+	0.0213245i
$95$	8.25398	+	1.43719i	0.846840	+	0.147453i
$96$	1.24251	−	1.55806i	0.126813	−	0.159019i
$97$			4.55800i			0.462795i	0.972859	+	0.231397i	$0.0743297\pi$
$97$			4.55800i			0.462795i	−0.972859	+	0.231397i	$0.925670\pi$
$98$	5.61806	−	4.17580i	0.567510	−	0.421820i
$99$	1.10590			0.111148
$100$	−0.600478	+	4.96381i	−0.0600478	+	0.496381i
$101$	−1.49609	−	0.720480i	−0.148867	−	0.0716904i	0.357967	−	0.933734i	$-0.383470\pi$
$101$	−1.49609	−	0.720480i	−0.148867	−	0.0716904i	−0.506834	+	0.862044i	$0.669184\pi$
$102$	−0.808067	+	0.184436i	−0.0800105	+	0.0182619i
$103$	3.32473	−	6.90388i	0.327596	−	0.680260i	−0.670502	−	0.741908i	$-0.733921\pi$
$103$	3.32473	−	6.90388i	0.327596	−	0.680260i	0.998098	+	0.0616480i	$0.0196356\pi$
$104$	1.84577	−	0.888875i	0.180992	−	0.0871613i
$105$	−0.412572	−	11.7825i	−0.0402629	−	1.14986i
$106$	11.9803	+	5.76939i	1.16363	+	0.560372i
$107$	3.19275	−	2.54613i	0.308655	−	0.246144i	−0.456895	−	0.889521i	$-0.651038\pi$
$107$	3.19275	−	2.54613i	0.308655	−	0.246144i	0.765550	+	0.643377i	$0.222467\pi$
$108$	−1.75406	−	3.64233i	−0.168784	−	0.350484i
$109$	6.31458	−	7.91823i	0.604827	−	0.758429i	−0.381295	−	0.924454i	$-0.624522\pi$
$109$	6.31458	−	7.91823i	0.604827	−	0.758429i	0.986122	+	0.166025i	$0.0530931\pi$
$110$	−2.54227	+	0.132334i	−0.242396	+	0.0126176i
$111$	−3.22597	+	4.04524i	−0.306196	+	0.383957i
$112$	1.18832	−	2.36387i	0.112285	−	0.223365i
$113$	10.9783	−	8.75492i	1.03275	−	0.823594i	0.0482287	−	0.998836i	$-0.484642\pi$
$113$	10.9783	−	8.75492i	1.03275	−	0.823594i	0.984525	+	0.175242i	$0.0560709\pi$
$114$	−6.72737	+	3.23973i	−0.630075	+	0.303428i
$115$	0.945880	−	0.0492364i	0.0882038	−	0.00459132i
$116$	1.24066			0.115192
$117$			1.99003i			0.183979i
$118$	3.35172	+	0.765007i	0.308551	+	0.0704246i
$119$	−0.999406	+	0.460520i	−0.0916154	+	0.0422158i
$120$	−2.13952	−	3.90888i	−0.195311	−	0.356831i
$121$	2.15931	+	9.46057i	0.196301	+	0.860052i
$122$	−1.54936	+	1.23557i	−0.140272	+	0.111863i
$123$	15.5304	−	12.3851i	1.40033	−	1.11673i
$124$	−0.664859	−	2.91294i	−0.0597061	−	0.261590i
$125$	9.71815	+	5.52789i	0.869218	+	0.494430i
$126$	1.56800	+	2.03631i	0.139689	+	0.181409i
$127$	−15.9013	−	3.62936i	−1.41101	−	0.322054i	−0.551928	−	0.833892i	$-0.686107\pi$
$127$	−15.9013	−	3.62936i	−1.41101	−	0.322054i	−0.859082	+	0.511838i	$0.828965\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−18.8800			−1.66230
$130$	−0.238131	−	4.57472i	−0.0208854	−	0.401230i
$131$	−10.8117	+	5.20664i	−0.944622	+	0.454906i	−0.841798	−	0.539793i	$-0.818502\pi$
$131$	−10.8117	+	5.20664i	−0.944622	+	0.454906i	−0.102825	+	0.994699i	$0.532788\pi$
$132$	1.77382	−	1.41457i	0.154391	−	0.123123i
$133$	−7.85442	+	6.04808i	−0.681064	+	0.524435i
$134$	−2.64628	+	3.31833i	−0.228604	+	0.286660i
$135$	−9.02750	+	0.469914i	−0.776963	+	0.0404437i
$136$	−0.259318	+	0.325175i	−0.0222363	+	0.0278835i
$137$	5.85831	+	12.1649i	0.500509	+	1.03932i	0.986257	+	0.165219i	$0.0528330\pi$
$137$	5.85831	+	12.1649i	0.500509	+	1.03932i	−0.485748	+	0.874099i	$0.661453\pi$
$138$	−0.659968	+	0.526307i	−0.0561802	+	0.0448022i
$139$	−14.7531	−	7.10473i	−1.25134	−	0.602616i	−0.313472	−	0.949597i	$-0.601492\pi$
$139$	−14.7531	−	7.10473i	−1.25134	−	0.602616i	−0.937872	+	0.346982i	$0.887207\pi$
$140$	−3.84822	−	4.49346i	−0.325234	−	0.379767i
$141$	−0.380760	+	0.183364i	−0.0320658	+	0.0154421i
$142$	−3.07569	+	6.38673i	−0.258106	+	0.535963i
$143$	2.27386	−	0.518994i	0.190150	−	0.0434005i
$144$	0.875191	+	0.421470i	0.0729326	+	0.0351225i
$145$	1.07212	−	2.55866i	0.0890349	−	0.212485i
$146$	5.62863			0.465829
$147$	10.6044	+	9.06342i	0.874633	+	0.747538i
$148$			2.59633i			0.213417i
$149$	−10.4673	+	13.1256i	−0.857516	+	1.07529i	0.138866	+	0.990311i	$0.455654\pi$
$149$	−10.4673	+	13.1256i	−0.857516	+	1.07529i	−0.996383	+	0.0849801i	$0.972917\pi$
$150$	−9.91032	+	1.03454i	−0.809174	+	0.0844697i
$151$	−0.794295	−	3.48003i	−0.0646388	−	0.283201i	0.932271	−	0.361762i	$-0.117825\pi$
$151$	−0.794295	−	3.48003i	−0.0646388	−	0.283201i	−0.996909	+	0.0785608i	$0.974968\pi$
$152$	−1.62569	+	3.37578i	−0.131861	+	0.273812i
$153$	−0.175295	−	0.364004i	−0.0141718	−	0.0294280i
$154$	1.91781	−	2.32270i	0.154541	−	0.187169i
$155$	−6.58200	−	1.14607i	−0.528679	−	0.0920542i
$156$	2.54547	+	3.19192i	0.203801	+	0.255558i
$157$	−8.78208	−	18.2362i	−0.700887	−	1.45541i	−0.881662	−	0.471882i	$-0.843575\pi$
$157$	−8.78208	−	18.2362i	−0.700887	−	1.45541i	0.180775	−	0.983524i	$-0.442139\pi$
$158$	9.21801	+	7.35111i	0.733345	+	0.584823i
$159$	−5.89656	+	25.8345i	−0.467627	+	2.04881i
$160$	−2.06234	−	0.864155i	−0.163042	−	0.0683175i
$161$	−0.713541	+	0.864187i	−0.0562349	+	0.0681074i
$162$	8.57714	−	6.84004i	0.673884	−	0.537404i
$163$	−8.98077	−	18.6488i	−0.703428	−	1.46068i	−0.879299	−	0.476270i	$-0.841989\pi$
$163$	−8.98077	−	18.6488i	−0.703428	−	1.46068i	0.175871	−	0.984413i	$-0.443726\pi$
$164$	2.21804	−	9.71789i	0.173200	−	0.758840i
$165$	−1.38447	−	4.88062i	−0.107781	−	0.379956i
$166$	5.48392			0.425635
$167$	1.92873	+	0.440220i	0.149250	+	0.0340652i	0.296493	−	0.955035i	$-0.404183\pi$
$167$	1.92873	+	0.440220i	0.149250	+	0.0340652i	−0.147243	+	0.989100i	$0.547040\pi$
$168$	5.11966	+	1.26049i	0.394990	+	0.0972490i
$169$	−1.95886	−	8.58233i	−0.150682	−	0.660180i
$170$	0.446529	+	0.815803i	0.0342472	+	0.0625692i
$171$	−2.26927	−	2.84558i	−0.173536	−	0.217607i
$172$	−7.40705	+	5.90692i	−0.564782	+	0.450399i
$173$	−5.12885	+	1.17063i	−0.389939	+	0.0890011i	−0.412995	−	0.910733i	$-0.635517\pi$
$173$	−5.12885	+	1.17063i	−0.389939	+	0.0890011i	0.0230562	+	0.999734i	$0.492660\pi$
$174$	0.550167	+	2.41044i	0.0417080	+	0.182735i
$175$	−12.5925	+	4.05327i	−0.951903	+	0.306399i
$176$	0.253335	−	1.10993i	0.0190958	−	0.0836644i
$177$			6.85119i			0.514967i
$178$			16.7453i			1.25512i
$179$	3.71600	−	16.2809i	0.277747	−	1.21689i	−0.622887	−	0.782312i	$-0.714040\pi$
$179$	3.71600	−	16.2809i	0.277747	−	1.21689i	0.900634	−	0.434578i	$-0.143103\pi$
$180$	1.62551	−	1.44072i	0.121159	−	0.107385i
$181$	−12.2420	−	15.3510i	−0.909943	−	1.14103i	−0.989548	−	0.144206i	$-0.953937\pi$
$181$	−12.2420	−	15.3510i	−0.909943	−	1.14103i	0.0796046	−	0.996827i	$-0.474634\pi$
$182$	4.17961	+	3.45102i	0.309813	+	0.255806i
$183$	−3.08762	−	2.46229i	−0.228243	−	0.182018i
$184$	−0.0942561	+	0.412963i	−0.00694865	+	0.0304440i
$185$	5.35451	+	2.24363i	0.393671	+	0.164955i
$186$	5.36463	−	2.58347i	0.393354	−	0.189429i
$187$	−0.370204	+	0.295228i	−0.0270720	+	0.0215892i
$188$	−0.0920118	+	0.191064i	−0.00671065	+	0.0139348i
$189$	6.81005	−	8.24781i	0.495358	−	0.599940i
$190$	5.55715	+	6.26991i	0.403158	+	0.454867i
$191$	10.5782	+	5.09419i	0.765411	+	0.368602i	0.775501	−	0.631347i	$-0.217498\pi$
$191$	10.5782	+	5.09419i	0.765411	+	0.368602i	−0.0100900	+	0.999949i	$0.503212\pi$
$192$	1.94287	−	0.443447i	0.140215	−	0.0320031i
$193$	−6.81123	+	14.1437i	−0.490283	+	1.01808i	0.498244	+	0.867037i	$0.333978\pi$
$193$	−6.81123	+	14.1437i	−0.490283	+	1.01808i	−0.988527	+	0.151046i	$0.951736\pi$
$194$	−2.84187	+	3.56359i	−0.204034	+	0.255851i
$195$	8.78249	−	2.49130i	0.628927	−	0.178406i
$196$	6.99595	+	0.238030i	0.499711	+	0.0170022i
$197$		−	8.60206i		−	0.612872i	−0.951891	−	0.306436i	$-0.900864\pi$
$197$		−	8.60206i		−	0.612872i	0.951891	−	0.306436i	$-0.0991365\pi$
$198$	0.864631	+	0.689520i	0.0614466	+	0.0490021i
$199$	−16.8130	−	8.09671i	−1.19184	−	0.573960i	−0.270502	−	0.962720i	$-0.587190\pi$
$199$	−16.8130	−	8.09671i	−1.19184	−	0.573960i	−0.921339	+	0.388759i	$0.872904\pi$
$200$	−3.56436	+	3.50647i	−0.252038	+	0.247945i
$201$	−7.62057	−	3.66988i	−0.537514	−	0.258853i
$202$	−0.720480	−	1.49609i	−0.0506928	−	0.105265i
$203$	1.37372	+	2.98120i	0.0964160	+	0.209239i
$204$	−0.746766	−	0.359624i	−0.0522841	−	0.0251787i
$205$	−18.1248	−	12.9721i	−1.26589	−	0.906012i
$206$	6.90388	−	3.32473i	0.481016	−	0.231645i
$207$	−0.321695	−	0.256544i	−0.0223594	−	0.0178310i
$208$	1.99728	+	0.455867i	0.138487	+	0.0316087i
$209$	−2.65961	+	3.33504i	−0.183969	+	0.230690i
$210$	7.02374	−	9.46920i	0.484684	−	0.653437i
$211$	14.2220	+	17.8338i	0.979081	+	1.22773i	0.973721	+	0.227743i	$0.0731346\pi$
$211$	14.2220	+	17.8338i	0.979081	+	1.22773i	0.00535977	+	0.999986i	$0.498294\pi$
$212$	5.76939	+	11.9803i	0.396243	+	0.822807i
$213$	−13.7725	−	3.14348i	−0.943676	−	0.215388i
$214$	4.08368			0.279155
$215$	5.78123	+	20.3803i	0.394277	+	1.38993i
$216$	0.899582	−	3.94133i	0.0612088	−	0.268173i
$217$	6.26338	−	4.82294i	0.425186	−	0.327403i
$218$	9.87387	−	2.25365i	0.668743	−	0.152636i
$219$	2.49600	+	10.9357i	0.168664	+	0.738966i
$220$	−2.07014	−	1.48162i	−0.139569	−	0.0998906i
$221$	−0.531251	−	0.666168i	−0.0357358	−	0.0448113i
$222$	−5.04433	+	1.15134i	−0.338553	+	0.0772726i
$223$	9.82360	−	2.24217i	0.657837	−	0.150147i	0.119444	−	0.992841i	$-0.461889\pi$
$223$	9.82360	−	2.24217i	0.657837	−	0.150147i	0.538393	+	0.842694i	$0.319032\pi$
$224$	2.40292	−	1.10725i	0.160552	−	0.0739811i
$225$	−1.56656	−	4.59737i	−0.104438	−	0.306491i
$226$	14.0418			0.934047
$227$		−	17.6353i		−	1.17050i	−0.810854	−	0.585248i	$-0.800997\pi$
$227$		−	17.6353i		−	1.17050i	0.810854	−	0.585248i	$-0.199003\pi$
$228$	−7.27960	−	1.66152i	−0.482104	−	0.110037i
$229$	8.27740	−	3.98618i	0.546986	−	0.263414i	−0.139918	−	0.990163i	$-0.544684\pi$
$229$	8.27740	−	3.98618i	0.546986	−	0.263414i	0.686903	+	0.726749i	$0.258970\pi$
$230$	0.770217	+	0.551252i	0.0507866	+	0.0363485i
$231$	5.36315	+	2.69605i	0.352869	+	0.177387i
$232$	0.969986	+	0.773538i	0.0636827	+	0.0507853i
$233$	−14.2645	−	3.25579i	−0.934501	−	0.213294i	−0.271951	−	0.962311i	$-0.587669\pi$
$233$	−14.2645	−	3.25579i	−0.934501	−	0.213294i	−0.662550	+	0.749017i	$0.730526\pi$
$234$	−1.24077	+	1.55587i	−0.0811114	+	0.101710i
$235$	0.314527	+	0.354869i	0.0205175	+	0.0231491i
$236$	2.14350	+	2.68787i	0.139530	+	0.174965i
$237$	−10.1946	+	21.1692i	−0.662208	+	1.37509i
$238$	−1.06850	−	0.263071i	−0.0692604	−	0.0170523i
$239$	7.80381	−	3.75812i	0.504786	−	0.243092i	−0.164118	−	0.986441i	$-0.552478\pi$
$239$	7.80381	−	3.75812i	0.504786	−	0.243092i	0.668904	+	0.743348i	$0.266764\pi$
$240$	0.764403	−	4.39006i	0.0493420	−	0.283377i
$241$	0.876514	+	3.84026i	0.0564612	+	0.247373i	0.995281	−	0.0970365i	$-0.0309363\pi$
$241$	0.876514	+	3.84026i	0.0564612	+	0.247373i	−0.938820	+	0.344409i	$0.888079\pi$
$242$	−4.21035	+	8.74288i	−0.270652	+	0.562014i
$243$	7.61072	+	6.06934i	0.488228	+	0.389349i
$244$	−1.98170			−0.126866
$245$	6.53649	−	14.2223i	0.417601	−	0.908631i
$246$	19.8642			1.26649
$247$	−6.00129	−	4.78587i	−0.381853	−	0.304517i
$248$	1.29638	−	2.69196i	0.0823202	−	0.170940i
$249$	2.43183	+	10.6545i	0.154111	+	0.675204i
$250$	4.15137	+	10.3810i	0.262556	+	0.656555i
$251$	−23.6820	+	11.4046i	−1.49479	+	0.719854i	−0.989693	−	0.143207i	$-0.954258\pi$
$251$	−23.6820	+	11.4046i	−1.49479	+	0.719854i	−0.505099	+	0.863061i	$0.668544\pi$
$252$	−0.0437028	+	2.56968i	−0.00275302	+	0.161875i
$253$	−0.209236	+	0.434483i	−0.0131546	+	0.0273157i
$254$	−10.1692	−	12.7518i	−0.638075	−	0.800121i
$255$	−1.38699	+	1.22931i	−0.0868565	+	0.0769826i
$256$	0.623490	−	0.781831i	0.0389681	−	0.0488645i
$257$	29.2317	+	6.67193i	1.82342	+	0.416184i	0.990535	−	0.137262i	$-0.0438301\pi$
$257$	29.2317	+	6.67193i	1.82342	+	0.416184i	0.832885	+	0.553445i	$0.186687\pi$
$258$	−14.7610	−	11.7715i	−0.918981	−	0.732863i
$259$	−6.23876	+	2.87478i	−0.387658	+	0.178630i
$260$	2.66611	−	3.72513i	0.165345	−	0.231023i
$261$	−1.08581	+	0.522900i	−0.0672102	+	0.0323667i
$262$	−11.6992	−	2.67027i	−0.722780	−	0.164970i
$263$			10.1868i			0.628145i	0.949399	+	0.314072i	$0.101693\pi$
$263$			10.1868i			0.628145i	−0.949399	+	0.314072i	$0.898307\pi$
$264$	2.26880			0.139635
$265$	29.6930	−	1.54563i	1.82403	−	0.0949470i
$266$	−9.91175	−	0.168570i	−0.607728	−	0.0103357i
$267$	−32.5340	+	7.42568i	−1.99105	+	0.454444i
$268$	−4.13789	+	0.944447i	−0.252762	+	0.0576913i
$269$	1.17853	+	1.47783i	0.0718562	+	0.0901048i	0.816460	−	0.577401i	$-0.195933\pi$
$269$	1.17853	+	1.47783i	0.0718562	+	0.0901048i	−0.744604	+	0.667506i	$0.767362\pi$
$270$	−7.35097	−	5.26116i	−0.447366	−	0.320184i
$271$	−5.67759	−	24.8751i	−0.344889	−	1.51106i	−0.788611	−	0.614893i	$-0.789199\pi$
$271$	−5.67759	−	24.8751i	−0.344889	−	1.51106i	0.443722	−	0.896165i	$-0.353658\pi$
$272$	−0.405486	+	0.0925496i	−0.0245862	+	0.00561164i
$273$	−4.85144	+	9.65079i	−0.293623	+	0.584092i
$274$	−3.00448	+	13.1635i	−0.181507	+	0.795236i
$275$	−4.84451	+	2.98897i	−0.292135	+	0.180242i
$276$	−0.844131			−0.0508107
$277$	−32.1919	−	7.34759i	−1.93422	−	0.441474i	−0.995233	−	0.0975284i	$-0.968906\pi$
$277$	−32.1919	−	7.34759i	−1.93422	−	0.441474i	−0.938990	−	0.343945i	$-0.888237\pi$
$278$	−7.10473	−	14.7531i	−0.426114	−	0.884834i
$279$	1.80959	+	2.26916i	0.108338	+	0.135851i
$280$	−0.207028	−	5.91246i	−0.0123723	−	0.353337i
$281$	1.30568	−	1.63727i	0.0778902	−	0.0976712i	−0.741360	−	0.671108i	$-0.765819\pi$
$281$	1.30568	−	1.63727i	0.0778902	−	0.0976712i	0.819250	+	0.573437i	$0.194390\pi$
$282$	−0.412016	−	0.0940399i	−0.0245352	−	0.00559999i
$283$	9.14149	+	7.29009i	0.543405	+	0.433351i	0.856332	−	0.516426i	$-0.172738\pi$
$283$	9.14149	+	7.29009i	0.543405	+	0.433351i	−0.312927	+	0.949777i	$0.601309\pi$
$284$	−6.38673	+	3.07569i	−0.378983	+	0.182509i
$285$	−9.71732	+	13.5772i	−0.575605	+	0.804243i
$286$	2.10136	+	1.01196i	0.124256	+	0.0598387i
$287$	25.8072	−	5.43034i	1.52335	−	0.320543i
$288$	0.421470	+	0.875191i	0.0248353	+	0.0515711i
$289$	−15.1606	−	7.30097i	−0.891801	−	0.429469i
$290$	2.43352	−	1.33198i	0.142901	−	0.0782167i
$291$	−8.18380	−	3.94111i	−0.479743	−	0.231032i
$292$	4.40064	+	3.50939i	0.257528	+	0.205372i
$293$			24.7113i			1.44365i	0.692076	+	0.721824i	$0.256696\pi$
$293$			24.7113i			1.44365i	−0.692076	+	0.721824i	$0.743304\pi$
$294$	2.63987	+	13.6978i	0.153961	+	0.798871i
$295$	7.39561	−	2.09789i	0.430589	−	0.122144i
$296$	−1.61879	+	2.02989i	−0.0940900	+	0.117985i
$297$	1.99695	−	4.14672i	0.115875	−	0.240617i
$298$	−16.3674	+	3.73574i	−0.948136	+	0.216406i
$299$	−0.781836	−	0.376512i	−0.0452147	−	0.0217743i
$300$	−8.39322	−	5.37015i	−0.484583	−	0.310046i
$301$	−22.3953	−	11.2581i	−1.29084	−	0.648905i
$302$	1.54876	−	3.21603i	0.0891212	−	0.185062i
$303$	2.58722	−	2.06324i	0.148632	−	0.118530i
$304$	−3.37578	+	1.62569i	−0.193614	+	0.0932396i
$305$	−1.71250	+	4.08694i	−0.0980575	+	0.234018i
$306$	0.0899016	−	0.393885i	0.00513933	−	0.0225169i
$307$	−8.59300	−	6.85269i	−0.490428	−	0.391104i	0.346815	−	0.937933i	$-0.387263\pi$
$307$	−8.59300	−	6.85269i	−0.490428	−	0.391104i	−0.837244	+	0.546830i	$0.815834\pi$
$308$	2.94758	−	0.620229i	0.167954	−	0.0353408i
$309$	9.52103	+	11.9390i	0.541633	+	0.679186i
$310$	−4.43146	−	4.99984i	−0.251690	−	0.283972i
$311$	5.03566	−	22.0627i	0.285546	−	1.25106i	−0.605022	−	0.796209i	$-0.706836\pi$
$311$	5.03566	−	22.0627i	0.285546	−	1.25106i	0.890568	−	0.454850i	$-0.150307\pi$
$312$			4.08261i			0.231133i
$313$			7.86633i			0.444631i	0.974975	+	0.222316i	$0.0713615\pi$
$313$			7.86633i			0.444631i	−0.974975	+	0.222316i	$0.928638\pi$
$314$	4.50397	−	19.7332i	0.254173	−	1.11361i
$315$	5.26178	+	2.31073i	0.296468	+	0.130195i
$316$	2.62358	+	11.4947i	0.147588	+	0.646625i
$317$	−5.02410	+	1.14672i	−0.282181	+	0.0644060i	−0.361269	−	0.932462i	$-0.617656\pi$
$317$	−5.02410	+	1.14672i	−0.282181	+	0.0644060i	0.0790877	+	0.996868i	$0.474799\pi$
$318$	−20.7177	+	16.5218i	−1.16179	+	0.926496i
$319$	0.880656	+	1.10431i	0.0493073	+	0.0618293i
$320$	−1.07361	−	1.96147i	−0.0600165	−	0.109650i
$321$	1.81090	+	7.93407i	0.101075	+	0.442836i
$322$	−1.09668	+	0.230763i	−0.0611156	+	0.0128599i
$323$	1.51929	+	0.346768i	0.0845354	+	0.0192947i
$324$	10.9706			0.609476
$325$	−5.37855	−	8.71752i	−0.298348	−	0.483561i
$326$	4.60586	−	20.1796i	0.255095	−	1.11764i
$327$	8.75709	+	18.1843i	0.484268	+	1.00559i
$328$	7.79314	−	6.21482i	0.430304	−	0.343156i
$329$	−0.560991	−	0.00954083i	−0.0309285	−	0.000526003i
$330$	1.96059	−	4.67903i	0.107927	−	0.257572i
$331$	−2.23495	+	9.79197i	−0.122844	+	0.538215i	0.875629	+	0.482984i	$0.160447\pi$
$331$	−2.23495	+	9.79197i	−0.122844	+	0.538215i	−0.998474	+	0.0552319i	$0.982410\pi$
$332$	4.28750	+	3.41917i	0.235307	+	0.187651i
$333$	−1.09427	−	2.27228i	−0.0599659	−	0.124520i
$334$	1.23347	+	1.54672i	0.0674924	+	0.0846328i
$335$	−1.62801	+	9.34988i	−0.0889478	+	0.510838i
$336$	3.21681	+	4.17755i	0.175491	+	0.227904i
$337$	−5.57448	−	11.5755i	−0.303661	−	0.630559i	0.692174	−	0.721731i	$-0.256653\pi$
$337$	−5.57448	−	11.5755i	−0.303661	−	0.630559i	−0.995835	+	0.0911718i	$0.970939\pi$
$338$	3.81950	−	7.93127i	0.207753	−	0.431404i
$339$	6.22680	+	27.2814i	0.338193	+	1.48172i
$340$	−0.159534	+	0.916227i	−0.00865197	+	0.0496894i
$341$	2.12086	−	2.65948i	0.114851	−	0.144019i
$342$		−	3.63963i		−	0.196809i
$343$	7.17429	+	17.0742i	0.387375	+	0.921922i
$344$	−9.47397			−0.510802
$345$	−0.729460	+	1.74088i	−0.0392728	+	0.0937260i
$346$	−4.73977	−	2.28255i	−0.254812	−	0.122711i
$347$	0.192270	−	0.0438844i	0.0103216	−	0.00235584i	−0.217357	−	0.976092i	$-0.569744\pi$
$347$	0.192270	−	0.0438844i	0.0103216	−	0.00235584i	0.227679	+	0.973736i	$0.426886\pi$
$348$	−1.07275	+	2.22758i	−0.0575052	+	0.119411i
$349$	−16.8169	+	8.09860i	−0.900188	+	0.433508i	−0.825957	−	0.563733i	$-0.809365\pi$
$349$	−16.8169	+	8.09860i	−0.900188	+	0.433508i	−0.0742314	+	0.997241i	$0.523650\pi$
$350$	−12.3724	−	4.68232i	−0.661332	−	0.250280i
$351$	7.46186	+	3.59344i	0.398285	+	0.191804i
$352$	0.890098	−	0.709829i	0.0474424	−	0.0378340i
$353$	1.80154	+	3.74094i	0.0958864	+	0.199110i	0.943395	−	0.331672i	$-0.107613\pi$
$353$	1.80154	+	3.74094i	0.0958864	+	0.199110i	−0.847508	+	0.530782i	$0.821898\pi$
$354$	−4.27165	+	5.35648i	−0.227035	+	0.284693i
$355$	0.823981	+	15.8295i	0.0437323	+	0.840141i
$356$	−10.4406	+	13.0920i	−0.553348	+	0.693877i
$357$	0.0372899	−	2.19261i	0.00197359	−	0.116045i
$358$	13.0563	−	10.4120i	0.690044	−	0.550292i
$359$	7.65046	−	3.68427i	0.403776	−	0.194448i	−0.220962	−	0.975282i	$-0.570920\pi$
$359$	7.65046	−	3.68427i	0.403776	−	0.194448i	0.624739	+	0.780834i	$0.285206\pi$
$360$	2.16915	−	0.112912i	0.114324	−	0.00595100i
$361$	−4.96126			−0.261119
$362$		−	19.6347i		−	1.03198i
$363$	−18.8534	−	4.30316i	−0.989544	−	0.225857i
$364$	1.11608	+	5.30406i	0.0584984	+	0.278008i
$365$	11.0404	−	6.04294i	0.577880	−	0.316302i
$366$	−0.878782	−	3.85019i	−0.0459347	−	0.201253i
$367$	14.9036	−	11.8852i	0.777960	−	0.620402i	−0.151867	−	0.988401i	$-0.548528\pi$
$367$	14.9036	−	11.8852i	0.777960	−	0.620402i	0.929826	+	0.367999i	$0.119957\pi$
$368$	−0.331171	+	0.264100i	−0.0172635	+	0.0137672i
$369$	2.15458	+	9.43985i	0.112163	+	0.491419i
$370$	2.78744	+	5.09262i	0.144912	+	0.264753i
$371$	−22.3994	+	27.1285i	−1.16292	+	1.40844i
$372$	5.80500	+	1.32495i	0.300975	+	0.0686957i
$373$			0.129544i			0.00670755i	0.999994	+	0.00335378i	$0.00106754\pi$
$373$			0.129544i			0.00670755i	−0.999994	+	0.00335378i	$0.998932\pi$
$374$	−0.473509			−0.0244846
$375$	−18.3281	+	12.6690i	−0.946459	+	0.654225i
$376$	−0.191064	+	0.0920118i	−0.00985339	+	0.00474514i
$377$	−1.98716	+	1.58471i	−0.102344	+	0.0816166i
$378$	10.4667	−	2.20241i	0.538351	−	0.113280i
$379$	16.4577	−	20.6374i	0.845378	−	1.06007i	−0.152049	−	0.988373i	$-0.548587\pi$
$379$	16.4577	−	20.6374i	0.845378	−	1.06007i	0.997426	−	0.0716969i	$-0.0228414\pi$
$380$	0.435524	+	8.36684i	0.0223419	+	0.429210i
$381$	20.2656	−	25.4123i	1.03824	−	1.30191i
$382$	5.09419	+	10.5782i	0.260641	+	0.541227i
$383$	2.79056	−	2.22540i	0.142591	−	0.113713i	−0.549596	−	0.835430i	$-0.685219\pi$
$383$	2.79056	−	2.22540i	0.142591	−	0.113713i	0.692188	+	0.721718i	$0.256647\pi$
$384$	1.79548	+	0.864658i	0.0916253	+	0.0441244i
$385$	1.26805	−	6.61488i	0.0646256	−	0.337126i
$386$	−14.1437	+	6.81123i	−0.719893	+	0.346682i
$387$	3.99299	−	8.29153i	0.202975	−	0.421482i
$388$	−4.44372	+	1.01425i	−0.225596	+	0.0514907i
$389$	9.36815	+	4.51146i	0.474984	+	0.228740i	0.656031	−	0.754734i	$-0.272234\pi$
$389$	9.36815	+	4.51146i	0.474984	+	0.228740i	−0.181047	+	0.983475i	$0.557948\pi$
$390$	8.41973	+	3.52801i	0.426350	+	0.178648i
$391$	0.176174			0.00890951
$392$	5.32125	+	4.54800i	0.268764	+	0.229709i
$393$		−	23.9142i		−	1.20631i
$394$	5.36330	−	6.72536i	0.270199	−	0.338819i
$395$	25.9731	+	4.52246i	1.30685	+	0.227550i
$396$	0.246087	+	1.07818i	0.0123663	+	0.0541804i
$397$	15.7477	−	32.7004i	0.790354	−	1.64119i	0.0231929	−	0.999731i	$-0.492617\pi$
$397$	15.7477	−	32.7004i	0.790354	−	1.64119i	0.767161	−	0.641455i	$-0.221669\pi$
$398$	−8.09671	−	16.8130i	−0.405851	−	0.842759i
$399$	−4.06783	−	19.3320i	−0.203646	−	0.967810i
$400$	−4.97298	+	0.519129i	−0.248649	+	0.0259565i
$401$	−23.7837	−	29.8239i	−1.18770	−	1.48933i	−0.832037	−	0.554720i	$-0.812826\pi$
$401$	−23.7837	−	29.8239i	−1.18770	−	1.48933i	−0.355666	−	0.934613i	$-0.615746\pi$
$402$	−3.66988	−	7.62057i	−0.183037	−	0.380080i
$403$	4.78563	+	3.81641i	0.238389	+	0.190109i
$404$	0.369504	−	1.61890i	0.0183835	−	0.0805435i
$405$	9.48027	−	22.6250i	0.471079	−	1.12425i
$406$	−0.784732	+	3.18729i	−0.0389456	+	0.158183i
$407$	−2.31099	+	1.84295i	−0.114551	+	0.0913517i
$408$	−0.359624	−	0.746766i	−0.0178040	−	0.0369704i
$409$	−6.61825	+	28.9965i	−0.327251	+	1.43378i	0.497095	+	0.867696i	$0.334400\pi$
$409$	−6.61825	+	28.9965i	−0.327251	+	1.43378i	−0.824346	+	0.566086i	$0.808457\pi$
$410$	−6.08258	−	21.4427i	−0.300397	−	1.05898i
$411$	−26.9073			−1.32724
$412$	7.47061	+	1.70512i	0.368050	+	0.0840051i
$413$	−4.08533	+	8.12679i	−0.201026	+	0.399893i
$414$	−0.0915593	−	0.401148i	−0.00449990	−	0.0197153i
$415$	10.7565	−	5.88758i	0.528018	−	0.289010i
$416$	1.27731	+	1.60170i	0.0626253	+	0.0785296i
$417$	25.5128	−	20.3458i	1.24937	−	0.996339i
$418$	−4.15873	+	0.949203i	−0.203410	+	0.0464271i
$419$	7.51021	+	32.9044i	0.366898	+	1.60748i	0.735249	+	0.677797i	$0.237065\pi$
$419$	7.51021	+	32.9044i	0.366898	+	1.60748i	−0.368351	+	0.929687i	$0.620078\pi$
$420$	11.3953	−	3.02409i	0.556035	−	0.147561i
$421$	0.135355	−	0.593028i	0.00659678	−	0.0289024i	−0.971522	−	0.236948i	$-0.923853\pi$
$421$	0.135355	−	0.593028i	0.00659678	−	0.0289024i	0.978119	+	0.208045i	$0.0667101\pi$
$422$			22.8103i			1.11039i
$423$		−	0.205998i		−	0.0100160i
$424$	−2.95888	+	12.9637i	−0.143696	+	0.629573i
$425$	1.75171	+	1.12078i	0.0849702	+	0.0543656i
$426$	−8.80784	−	11.0447i	−0.426741	−	0.535117i
$427$	−2.19424	−	4.76187i	−0.106187	−	0.230443i
$428$	3.19275	+	2.54613i	0.154328	+	0.123072i
$429$	−1.03427	+	4.53143i	−0.0499350	+	0.218780i
$430$	−8.18698	+	19.5385i	−0.394811	+	0.942231i
$431$	18.4449	−	8.88262i	0.888462	−	0.427861i	0.0667539	−	0.997769i	$-0.478736\pi$
$431$	18.4449	−	8.88262i	0.888462	−	0.427861i	0.821708	+	0.569909i	$0.193021\pi$
$432$	3.16070	−	2.52057i	0.152069	−	0.121271i
$433$	−3.40933	+	7.07955i	−0.163842	+	0.340221i	−0.966685	−	0.255969i	$-0.917605\pi$
$433$	−3.40933	+	7.07955i	−0.163842	+	0.340221i	0.802843	+	0.596191i	$0.203320\pi$
$434$	7.90396	+	0.134423i	0.379402	+	0.00645253i
$435$	3.66700	+	4.13734i	0.175819	+	0.198370i
$436$	9.12483	+	4.39429i	0.437000	+	0.210448i
$437$	1.54730	−	0.353162i	0.0740175	−	0.0168940i
$438$	−4.86684	+	10.1061i	−0.232547	+	0.482888i
$439$	14.4458	−	18.1145i	0.689462	−	0.864557i	−0.306726	−	0.951798i	$-0.599233\pi$
$439$	14.4458	−	18.1145i	0.689462	−	0.864557i	0.996187	+	0.0872405i	$0.0278049\pi$
$440$	−0.694725	−	2.44908i	−0.0331197	−	0.116755i
$441$	−6.22312	+	2.74026i	−0.296339	+	0.130489i
$442$		−	0.852061i		−	0.0405284i
$443$	−12.4601	−	9.93660i	−0.591997	−	0.472102i	0.281080	−	0.959684i	$-0.409307\pi$
$443$	−12.4601	−	9.93660i	−0.591997	−	0.472102i	−0.873077	+	0.487582i	$0.837879\pi$
$444$	−4.66166	−	2.24494i	−0.221233	−	0.106540i
$445$	17.9780	+	32.8455i	0.852237	+	1.55703i
$446$	9.07837	+	4.37191i	0.429873	+	0.207016i
$447$	−14.5161	−	30.1430i	−0.686589	−	1.42572i
$448$	2.56903	+	0.632512i	0.121375	+	0.0298834i
$449$	−11.4361	−	5.50732i	−0.539701	−	0.259906i	0.144115	−	0.989561i	$-0.453967\pi$
$449$	−11.4361	−	5.50732i	−0.539701	−	0.259906i	−0.683816	+	0.729655i	$0.739681\pi$
$450$	1.64162	−	4.57110i	0.0773868	−	0.215484i
$451$	10.2243	−	4.92376i	0.481444	−	0.231851i
$452$	10.9783	+	8.75492i	0.516377	+	0.411797i
$453$	6.93513	+	1.58290i	0.325841	+	0.0743711i
$454$	10.9954	−	13.7878i	0.516041	−	0.647095i
$455$	11.9032	+	2.28180i	0.558032	+	0.106972i
$456$	−4.65548	−	5.83779i	−0.218013	−	0.273380i
$457$	12.8456	+	26.6742i	0.600893	+	1.24777i	0.950457	+	0.310856i	$0.100616\pi$
$457$	12.8456	+	26.6742i	0.600893	+	1.24777i	−0.349564	+	0.936913i	$0.613670\pi$
$458$	8.95688	+	2.04435i	0.418527	+	0.0955261i
$459$	−1.68141			−0.0784815
$460$	0.258480	+	0.911209i	0.0120517	+	0.0424853i
$461$	−1.67282	+	7.32910i	−0.0779109	+	0.341350i	−0.998828	−	0.0484095i	$-0.984585\pi$
$461$	−1.67282	+	7.32910i	−0.0779109	+	0.341350i	0.920917	+	0.389760i	$0.127442\pi$
$462$	2.51212	+	5.45173i	0.116874	+	0.253637i
$463$	−10.0762	+	2.29983i	−0.468282	+	0.106882i	−0.450149	−	0.892953i	$-0.648629\pi$
$463$	−10.0762	+	2.29983i	−0.468282	+	0.106882i	−0.0181325	+	0.999836i	$0.505772\pi$
$464$	0.276073	+	1.20955i	0.0128163	+	0.0561521i
$465$	7.74892	−	10.8269i	0.359348	−	0.502086i
$466$	−9.12252	−	11.4393i	−0.422592	−	0.529914i
$467$	−8.46983	+	1.93318i	−0.391937	+	0.0894570i	−0.413948	−	0.910301i	$-0.635850\pi$
$467$	−8.46983	+	1.93318i	−0.391937	+	0.0894570i	0.0220108	+	0.999758i	$0.492993\pi$
$468$	−1.94014	+	0.442824i	−0.0896829	+	0.0204695i
$469$	−6.85110	−	8.89727i	−0.316354	−	0.410838i
$470$	0.0246501	+	0.473552i	0.00113702	+	0.0218433i
$471$	40.3362			1.85860
$472$			3.43791i			0.158243i
$473$	−10.5155	−	2.40009i	−0.483502	−	0.110356i
$474$	−21.1692	+	10.1946i	−0.972334	+	0.468252i
$475$	17.6316	+	6.33205i	0.808994	+	0.290534i
$476$	−0.671363	−	0.871874i	−0.0307719	−	0.0399623i
$477$	−10.0986	−	8.05339i	−0.462385	−	0.368739i
$478$	8.44441	+	1.92738i	0.386238	+	0.0881564i
$479$	24.5992	−	30.8464i	1.12396	−	1.40941i	0.223377	−	0.974732i	$-0.428292\pi$
$479$	24.5992	−	30.8464i	1.12396	−	1.40941i	0.900588	−	0.434674i	$-0.143137\pi$
$480$	3.33479	−	2.95569i	0.152212	−	0.134908i
$481$	−3.31632	−	4.15853i	−0.151211	−	0.189613i
$482$	−1.70908	+	3.54893i	−0.0778463	+	0.161650i
$483$	−0.934662	−	2.02838i	−0.0425286	−	0.0922943i
$484$	−8.74288	+	4.21035i	−0.397404	+	0.191380i
$485$	−1.74834	+	10.0409i	−0.0793879	+	0.455935i
$486$	2.16612	+	9.49041i	0.0982574	+	0.430494i
$487$	−8.26389	+	17.1601i	−0.374473	+	0.777601i	−0.999997	−	0.00260442i	$-0.999171\pi$
$487$	−8.26389	+	17.1601i	−0.374473	+	0.777601i	0.625524	+	0.780205i	$0.284885\pi$
$488$	−1.54936	−	1.23557i	−0.0701362	−	0.0559317i
$489$	41.2488			1.86533
$490$	13.9779	−	7.04402i	0.631457	−	0.318217i
$491$	−24.0478			−1.08526			−0.542630	−	0.839972i	$-0.682571\pi$
$491$	−24.0478			−1.08526			−0.542630	+	0.839972i	$0.682571\pi$
$492$	15.5304	+	12.3851i	0.700166	+	0.558364i
$493$	0.223887	−	0.464907i	0.0100834	−	0.0209383i
$494$	−1.70806	−	7.48348i	−0.0768491	−	0.336698i
$495$	2.43622	+	0.424198i	0.109500	+	0.0190663i
$496$	2.69196	−	1.29638i	0.120873	−	0.0582091i
$497$	−14.4623	−	11.9412i	−0.648723	−	0.535637i
$498$	−4.74172	+	9.84628i	−0.212481	+	0.441222i
$499$	−7.96881	−	9.99257i	−0.356733	−	0.447329i	0.570790	−	0.821096i	$-0.306637\pi$
$499$	−7.96881	−	9.99257i	−0.356733	−	0.447329i	−0.927522	+	0.373768i	$0.878066\pi$
$500$	−3.22680	+	10.7046i	−0.144307	+	0.478723i
$501$	−2.45810	+	3.08236i	−0.109820	+	0.137710i
$502$	−25.6260	−	5.84896i	−1.14374	−	0.261052i
$503$	−10.3307	−	8.23849i	−0.460625	−	0.367336i	0.365511	−	0.930807i	$-0.380894\pi$
$503$	−10.3307	−	8.23849i	−0.460625	−	0.367336i	−0.826136	+	0.563471i	$0.809466\pi$
$504$	−1.63634	+	1.98181i	−0.0728883	+	0.0882768i
$505$	−3.01942	−	2.16103i	−0.134362	−	0.0961644i
$506$	−0.434483	+	0.209236i	−0.0193151	+	0.00930168i
$507$	17.1032	+	3.90369i	0.759578	+	0.173369i
$508$		−	16.3102i		−	0.723648i
$509$	21.1020			0.935329			0.467664	−	0.883906i	$-0.345096\pi$
$509$	21.1020			0.935329			0.467664	+	0.883906i	$0.345096\pi$
$510$	−1.85085	+	0.0963436i	−0.0819572	+	0.00426617i
$511$	−3.56018	+	14.4601i	−0.157493	+	0.639679i
$512$	0.974928	−	0.222521i	0.0430861	−	0.00983413i
$513$	−14.7675	+	3.37058i	−0.652000	+	0.148815i
$514$	18.6943	+	23.4420i	0.824572	+	1.03398i
$515$	9.97229	−	13.9334i	0.439432	−	0.613980i
$516$	−4.20121	−	18.4067i	−0.184948	−	0.810309i
$517$	−0.235379	+	0.0537236i	−0.0103519	+	0.00236276i
$518$	−6.67006	−	1.64221i	−0.293065	−	0.0721545i
$519$	2.33286	−	10.2209i	0.102401	−	0.448650i
$520$	4.40703	−	1.25013i	0.193261	−	0.0548219i
$521$	39.1693			1.71604			0.858019	−	0.513617i	$-0.171695\pi$
$521$	39.1693			1.71604			0.858019	+	0.513617i	$0.171695\pi$
$522$	−1.17495	−	0.268174i	−0.0514260	−	0.0117376i
$523$	−8.39449	−	17.4313i	−0.367065	−	0.762219i	0.632862	−	0.774264i	$-0.281880\pi$
$523$	−8.39449	−	17.4313i	−0.367065	−	0.762219i	−0.999927	+	0.0120455i	$0.996166\pi$
$524$	−7.48193	−	9.38204i	−0.326849	−	0.409856i
$525$	3.61063	−	26.1143i	0.157581	−	1.13972i
$526$	−6.35137	+	7.96436i	−0.276933	+	0.347263i
$527$	−1.21153	−	0.276524i	−0.0527752	−	0.0120456i
$528$	1.77382	+	1.41457i	0.0771955	+	0.0615613i
$529$	−20.5606	+	9.90148i	−0.893940	+	0.430499i
$530$	24.1786	+	17.3049i	1.05025	+	0.751675i
$531$	−3.00883	−	1.44898i	−0.130572	−	0.0628802i
$532$	−7.64421	−	6.31167i	−0.331419	−	0.273645i
$533$	8.86013	+	18.3982i	0.383775	+	0.796916i
$534$	−30.0660	−	14.4790i	−1.30108	−	0.626568i
$535$	8.01002	−	4.38428i	0.346303	−	0.189549i
$536$	−3.82399	−	1.84154i	−0.165171	−	0.0795422i
$537$	26.0189	+	20.7494i	1.12280	+	0.895403i
$538$			1.89021i			0.0814929i
$539$	4.75406	+	6.39604i	0.204772	+	0.275497i
$540$	−2.46694	−	8.69660i	−0.106160	−	0.374242i
$541$	−1.89333	+	2.37416i	−0.0814007	+	0.102073i	−0.820864	−	0.571123i	$-0.806508\pi$
$541$	−1.89333	+	2.37416i	−0.0814007	+	0.102073i	0.739464	+	0.673197i	$0.235079\pi$
$542$	11.0705	−	22.9881i	0.475518	−	0.987423i
$543$	38.1477	−	8.70695i	1.63707	−	0.373651i
$544$	−0.374726	−	0.180458i	−0.0160662	−	0.00773709i
$545$	16.9478	−	15.0211i	0.725963	−	0.643435i
$546$	−9.81018	+	4.52047i	−0.419837	+	0.193458i
$547$	−6.60323	+	13.7118i	−0.282334	+	0.586272i	−0.993115	−	0.117141i	$-0.962627\pi$
$547$	−6.60323	+	13.7118i	−0.282334	+	0.586272i	0.710782	+	0.703413i	$0.248341\pi$
$548$	−10.5563	+	8.41837i	−0.450943	+	0.359615i
$549$	1.73437	−	0.835229i	0.0740211	−	0.0356467i
$550$	−5.65119	−	0.683631i	−0.240967	−	0.0291501i
$551$	1.03440	−	4.53199i	0.0440668	−	0.193069i
$552$	−0.659968	−	0.526307i	−0.0280901	−	0.0224011i
$553$	−24.7158	+	19.0317i	−1.05102	+	0.809310i
$554$	−20.5875	−	25.8159i	−0.874678	−	1.09681i
$555$	−8.65822	+	7.67395i	−0.367521	+	0.325741i
$556$	3.64372	−	15.9642i	0.154528	−	0.677033i
$557$		−	22.8554i		−	0.968413i	−0.874954	−	0.484206i	$-0.839108\pi$
$557$		−	22.8554i		−	0.968413i	0.874954	−	0.484206i	$-0.160892\pi$
$558$			2.90236i			0.122867i
$559$	4.31887	−	18.9222i	0.182669	−	0.800324i
$560$	3.52450	−	4.75162i	0.148937	−	0.200793i
$561$	−0.209976	−	0.919966i	−0.00886520	−	0.0388410i
$562$	2.04164	−	0.465991i	0.0861214	−	0.0196566i
$563$	3.13855	−	2.50291i	0.132274	−	0.105485i	−0.555118	−	0.831772i	$-0.687327\pi$
$563$	3.13855	−	2.50291i	0.132274	−	0.105485i	0.687392	+	0.726287i	$0.258755\pi$
$564$	−0.263494	−	0.330411i	−0.0110951	−	0.0139128i
$565$	27.5426	−	15.0754i	1.15873	−	0.634227i
$566$	2.60180	+	11.3993i	0.109362	+	0.479146i
$567$	12.1471	+	26.3614i	0.510132	+	1.10707i
$568$	−6.91101	−	1.57739i	−0.289979	−	0.0661859i
$569$	27.6639			1.15973			0.579865	−	0.814712i	$-0.303105\pi$
$569$	27.6639			1.15973			0.579865	+	0.814712i	$0.303105\pi$
$570$	−16.0625	+	4.55642i	−0.672786	+	0.190847i
$571$	4.83177	−	21.1694i	0.202203	−	0.885911i	−0.767388	−	0.641183i	$-0.778444\pi$
$571$	4.83177	−	21.1694i	0.202203	−	0.885911i	0.969592	−	0.244728i	$-0.0786988\pi$
$572$	1.01196	+	2.10136i	0.0423123	+	0.0878625i
$573$	−18.2930	+	14.5882i	−0.764202	+	0.609431i
$574$	23.5626	+	11.8449i	0.983485	+	0.494397i
$575$	2.10259	+	0.254352i	0.0876839	+	0.0106072i
$576$	−0.216154	+	0.947034i	−0.00900643	+	0.0394598i
$577$	6.06757	+	4.83873i	0.252596	+	0.201439i	0.741599	−	0.670843i	$-0.234068\pi$
$577$	6.06757	+	4.83873i	0.252596	+	0.201439i	−0.489003	+	0.872282i	$0.662639\pi$
$578$	−7.30097	−	15.1606i	−0.303680	−	0.630599i
$579$	−19.5053	−	24.4589i	−0.810612	−	1.01648i
$580$	2.73308	+	0.475886i	0.113485	+	0.0197601i
$581$	−3.46865	+	14.0884i	−0.143904	+	0.584484i
$582$	−3.94111	−	8.18380i	−0.163364	−	0.339230i
$583$	−6.56832	+	13.6393i	−0.272032	+	0.564880i
$584$	1.25249	+	5.48751i	0.0518283	+	0.227075i
$585$	−0.763328	+	4.38389i	−0.0315597	+	0.181252i
$586$	−15.4072	+	19.3201i	−0.636467	+	0.798104i
$587$			24.4031i			1.00722i	0.863930	+	0.503612i	$0.167996\pi$
$587$			24.4031i			1.00722i	−0.863930	+	0.503612i	$0.832004\pi$
$588$	−6.47649	+	12.3553i	−0.267086	+	0.509524i
$589$	−11.1950			−0.461280
$590$	7.09014	+	2.97089i	0.291896	+	0.122310i
$591$	15.4448	+	7.43785i	0.635316	+	0.305952i
$592$	−2.53123	+	0.577738i	−0.104033	+	0.0237449i
$593$	3.92536	−	8.15109i	0.161195	−	0.334725i	−0.804690	−	0.593695i	$-0.797669\pi$
$593$	3.92536	−	8.15109i	0.161195	−	0.334725i	0.965885	+	0.258970i	$0.0833830\pi$
$594$	4.14672	−	1.99695i	0.170142	−	0.0819360i
$595$	−2.37826	+	0.631142i	−0.0974991	+	0.0258743i
$596$	−15.1257	−	7.28416i	−0.619573	−	0.298371i
$597$	29.0750	−	23.1865i	1.18996	−	0.948961i
$598$	−0.376512	−	0.781836i	−0.0153967	−	0.0319716i
$599$	−8.83498	+	11.0787i	−0.360987	+	0.452664i	−0.928848	−	0.370461i	$-0.879200\pi$
$599$	−8.83498	+	11.0787i	−0.360987	+	0.452664i	0.567861	+	0.823125i	$0.307771\pi$
$600$	−3.21385	−	9.43164i	−0.131205	−	0.385045i
$601$	5.71192	−	7.16252i	0.232994	−	0.292165i	−0.651566	−	0.758592i	$-0.725888\pi$
$601$	5.71192	−	7.16252i	0.232994	−	0.292165i	0.884560	+	0.466427i	$0.154459\pi$
$602$	−10.4900	−	22.7651i	−0.427542	−	0.927838i
$603$	3.22339	−	2.57057i	0.131267	−	0.104682i
$604$	3.21603	−	1.54876i	0.130859	−	0.0630182i
$605$	1.12796	+	21.6692i	0.0458580	+	0.880977i
$606$	3.30918			0.134426
$607$		−	44.7844i		−	1.81774i	−0.417074	−	0.908872i	$-0.636945\pi$
$607$		−	44.7844i		−	1.81774i	0.417074	−	0.908872i	$-0.363055\pi$
$608$	−3.65289	−	0.833748i	−0.148144	−	0.0338130i
$609$	−6.54048	−	0.111235i	−0.265034	−	0.00450745i
$610$	−3.88705	+	2.12758i	−0.157382	+	0.0861430i
$611$	−0.0966736	−	0.423555i	−0.00391100	−	0.0171352i
$612$	0.315871	−	0.251899i	0.0127683	−	0.0101824i
$613$	3.70105	−	2.95149i	0.149484	−	0.119209i	−0.545892	−	0.837855i	$-0.683809\pi$
$613$	3.70105	−	2.95149i	0.149484	−	0.119209i	0.695376	+	0.718646i	$0.255238\pi$
$614$	−2.44570	−	10.7153i	−0.0987003	−	0.432434i
$615$	38.9630	−	21.3264i	1.57114	−	0.859962i
$616$	2.69122	+	1.35287i	0.108432	+	0.0545088i
$617$	41.9170	+	9.56728i	1.68751	+	0.385164i	0.955237	−	0.295842i	$-0.0956003\pi$
$617$	41.9170	+	9.56728i	1.68751	+	0.385164i	0.732278	+	0.681006i	$0.238457\pi$
$618$			15.2706i			0.614272i
$619$	−30.7235			−1.23488			−0.617441	−	0.786617i	$-0.711830\pi$
$619$	−30.7235			−1.23488			−0.617441	+	0.786617i	$0.711830\pi$
$620$	−0.347302	−	6.67200i	−0.0139480	−	0.267954i
$621$	−1.54283	+	0.742988i	−0.0619117	+	0.0298151i
$622$	17.6929	−	14.1096i	0.709420	−	0.565743i
$623$	−43.0193	−	10.5916i	−1.72353	−	0.424345i
$624$	−2.54547	+	3.19192i	−0.101900	+	0.127779i
$625$	19.2880	+	15.9052i	0.771519	+	0.636207i
$626$	−4.90458	+	6.15014i	−0.196026	+	0.245809i
$627$	−3.68836	−	7.65895i	−0.147299	−	0.305869i
$628$	15.8248	−	12.6198i	0.631477	−	0.503586i
$629$	0.972911	+	0.468529i	0.0387925	+	0.0186815i
$630$	2.67311	+	5.08727i	0.106499	+	0.202682i
$631$	−6.56411	+	3.16111i	−0.261313	+	0.125842i	−0.559954	−	0.828524i	$-0.689181\pi$
$631$	−6.56411	+	3.16111i	−0.261313	+	0.125842i	0.298641	+	0.954366i	$0.403467\pi$
$632$	−5.11561	+	10.6227i	−0.203488	+	0.422547i
$633$	−44.3174	+	10.1152i	−1.76146	+	0.402041i
$634$	−4.64296	−	2.23593i	−0.184396	−	0.0888002i
$635$	−33.6371	−	14.0945i	−1.33485	−	0.559325i
$636$	−26.4989			−1.05075
$637$	−11.5094	+	8.55475i	−0.456020	+	0.338952i
$638$			1.41246i			0.0559199i
$639$	4.29330	−	5.38363i	0.169840	−	0.212973i
$640$	0.383576	−	2.20292i	0.0151622	−	0.0870782i
$641$	1.99672	+	8.74820i	0.0788657	+	0.345533i	0.998931	−	0.0462326i	$-0.0147215\pi$
$641$	1.99672	+	8.74820i	0.0788657	+	0.345533i	−0.920065	+	0.391766i	$0.871864\pi$
$642$	−3.53099	+	7.33218i	−0.139357	+	0.289378i
$643$	−5.14797	−	10.6899i	−0.203016	−	0.421567i	0.774457	−	0.632626i	$-0.218023\pi$
$643$	−5.14797	−	10.6899i	−0.203016	−	0.421567i	−0.977473	+	0.211059i	$0.932309\pi$
$644$	−1.00130	−	0.503351i	−0.0394566	−	0.0198348i
$645$	−41.5913	−	7.24192i	−1.63766	−	0.285151i
$646$	0.971621	+	1.21837i	0.0382279	+	0.0479363i
$647$	15.8896	+	32.9950i	0.624684	+	1.29717i	0.937708	+	0.347424i	$0.112943\pi$
$647$	15.8896	+	32.9950i	0.624684	+	1.29717i	−0.313025	+	0.949745i	$0.601342\pi$
$648$	8.57714	+	6.84004i	0.336942	+	0.268702i
$649$	−0.870944	+	3.81585i	−0.0341875	+	0.149785i
$650$	1.23017	−	10.1691i	0.0482511	−	0.398865i
$651$	3.24382	+	15.4160i	0.127136	+	0.604200i
$652$	16.1828	−	12.9053i	0.633767	−	0.505412i
$653$	1.30502	+	2.70991i	0.0510695	+	0.106047i	0.924942	−	0.380108i	$-0.124113\pi$
$653$	1.30502	+	2.70991i	0.0510695	+	0.106047i	−0.873872	+	0.486155i	$0.838399\pi$
$654$	−4.49115	+	19.6770i	−0.175618	+	0.769431i
$655$	−25.8145	+	7.32272i	−1.00865	+	0.286122i
$656$	9.96780			0.389177
$657$	−5.33050	−	1.21665i	−0.207963	−	0.0474661i
$658$	−0.432652	−	0.357232i	−0.0168665	−	0.0139263i
$659$	−5.75792	−	25.2271i	−0.224297	−	0.982708i	−0.954203	−	0.299161i	$-0.903293\pi$
$659$	−5.75792	−	25.2271i	−0.224297	−	0.982708i	0.729906	−	0.683548i	$-0.239564\pi$
$660$	4.45018	−	2.43580i	0.173223	−	0.0948134i
$661$	17.5408	+	21.9954i	0.682257	+	0.855523i	0.995560	−	0.0941304i	$-0.0300071\pi$
$661$	17.5408	+	21.9954i	0.682257	+	0.855523i	−0.313303	+	0.949653i	$0.601436\pi$
$662$	−7.85255	+	6.26220i	−0.305198	+	0.243387i
$663$	1.65544	−	0.377844i	0.0642921	−	0.0146743i
$664$	1.22029	+	5.34643i	0.0473563	+	0.207482i
$665$	−19.6226	+	10.3107i	−0.760931	+	0.399832i
$666$	0.561208	−	2.45881i	0.0217464	−	0.0952770i
$667$		−	0.525522i		−	0.0203483i
$668$			1.97833i			0.0765439i
$669$	−4.46828	+	19.5768i	−0.172754	+	0.756883i
$670$	−7.10239	+	6.29498i	−0.274389	+	0.243196i
$671$	−1.40667	−	1.76391i	−0.0543040	−	0.0680950i
$672$	−0.0896576	+	5.27178i	−0.00345862	+	0.203363i
$673$	−18.8177	−	15.0066i	−0.725369	−	0.578463i	0.189660	−	0.981850i	$-0.439261\pi$
$673$	−18.8177	−	15.0066i	−0.725369	−	0.578463i	−0.915029	+	0.403387i	$0.867833\pi$
$674$	2.85892	−	12.5257i	0.110121	−	0.482473i
$675$	−20.0671	−	2.42754i	−0.772384	−	0.0934362i
$676$	7.93127	−	3.81950i	0.305049	−	0.146904i
$677$	−14.6836	+	11.7098i	−0.564337	+	0.450044i	−0.863636	−	0.504115i	$-0.831819\pi$
$677$	−14.6836	+	11.7098i	−0.564337	+	0.450044i	0.299299	+	0.954159i	$0.403247\pi$
$678$	−12.1414	+	25.2118i	−0.466286	+	0.968254i
$679$	−7.35746	−	9.55486i	−0.282353	−	0.366682i
$680$	−0.695987	+	0.616867i	−0.0266899	+	0.0236558i
$681$	31.6639	+	15.2485i	1.21336	+	0.584324i
$682$	3.31631	−	0.756927i	0.126988	−	0.0289842i
$683$	−21.8765	+	45.4271i	−0.837082	+	1.73822i	−0.181068	+	0.983471i	$0.557955\pi$
$683$	−21.8765	+	45.4271i	−0.837082	+	1.73822i	−0.656014	+	0.754749i	$0.727759\pi$
$684$	2.26927	−	2.84558i	0.0867678	−	0.108803i
$685$	8.23924	+	29.0454i	0.314805	+	1.10977i
$686$	−5.03653	+	17.8223i	−0.192296	+	0.680457i
$687$			18.3086i			0.698517i
$688$	−7.40705	−	5.90692i	−0.282391	−	0.225199i
$689$	−24.5433	−	11.8194i	−0.935026	−	0.450285i
$690$	−1.65574	+	0.906266i	−0.0630329	+	0.0345010i
$691$	−43.4030	−	20.9018i	−1.65113	−	0.795141i	−0.999324	−	0.0367528i	$-0.988299\pi$
$691$	−43.4030	−	20.9018i	−1.65113	−	0.795141i	−0.651803	−	0.758388i	$-0.725987\pi$
$692$	−2.28255	−	4.73977i	−0.0867696	−	0.180179i
$693$	−2.31829	+	1.78513i	−0.0880645	+	0.0678117i
$694$	0.177684	+	0.0855682i	0.00674480	+	0.00324812i
$695$	−29.7748	−	21.3101i	−1.12942	−	0.808339i
$696$	−2.22758	+	1.07275i	−0.0844362	+	0.0406623i
$697$	−3.24128	−	2.58483i	−0.122772	−	0.0979075i
$698$	−18.1974	−	4.15343i	−0.688781	−	0.157210i
$699$	18.1797	−	22.7966i	0.687618	−	0.862246i
$700$	−6.75374	−	11.3748i	−0.255267	−	0.429929i
$701$	9.26864	+	11.6225i	0.350072	+	0.438976i	0.925426	−	0.378928i	$-0.123707\pi$
$701$	9.26864	+	11.6225i	0.350072	+	0.438976i	−0.575354	+	0.817904i	$0.695136\pi$
$702$	3.59344	+	7.46186i	0.135626	+	0.281630i
$703$	9.48410	+	2.16469i	0.357700	+	0.0816426i
$704$	1.13848			0.0429080
$705$	−0.909118	+	0.257887i	−0.0342394	+	0.00971259i
$706$	−0.923936	+	4.04803i	−0.0347728	+	0.152350i
$707$	4.29922	−	0.904640i	0.161689	−	0.0340225i
$708$	−6.67942	+	1.52453i	−0.251028	+	0.0572955i
$709$	8.05945	+	35.3108i	0.302679	+	1.32612i	0.866066	+	0.499930i	$0.166641\pi$
$709$	8.05945	+	35.3108i	0.302679	+	1.32612i	−0.563387	+	0.826193i	$0.690502\pi$
$710$	−9.22530	+	12.8897i	−0.346219	+	0.483743i
$711$	−7.14079	−	8.95427i	−0.267801	−	0.335811i
$712$	−16.3255	+	3.72619i	−0.611824	+	0.139645i
$713$	−1.23387	+	0.281623i	−0.0462088	+	0.0105469i
$714$	1.39622	−	1.69100i	0.0522523	−	0.0632841i
$715$	5.20822	−	0.271106i	0.194776	−	0.0101388i
$716$	16.6996			0.624092
$717$			17.2611i			0.644627i
$718$	8.27848	+	1.88951i	0.308950	+	0.0705158i
$719$	27.7053	−	13.3422i	1.03323	−	0.497578i	0.161146	−	0.986931i	$-0.448481\pi$
$719$	27.7053	−	13.3422i	1.03323	−	0.497578i	0.872086	+	0.489352i	$0.162767\pi$
$720$	1.76631	+	1.26417i	0.0658266	+	0.0471127i
$721$	4.17456	+	19.8392i	0.155469	+	0.738851i
$722$	−3.87887	−	3.09330i	−0.144357	−	0.115121i
$723$	−7.65300	−	1.74675i	−0.284618	−	0.0649622i
$724$	12.2420	−	15.3510i	0.454972	−	0.570516i
$725$	3.34324	−	5.22529i	0.124165	−	0.194062i
$726$	−12.0572	−	15.1192i	−0.447484	−	0.561127i
$727$	−19.0893	+	39.6393i	−0.707982	+	1.47014i	0.166986	+	0.985959i	$0.446597\pi$
$727$	−19.0893	+	39.6393i	−0.707982	+	1.47014i	−0.874968	+	0.484181i	$0.839118\pi$
$728$	−2.43444	+	4.84274i	−0.0902264	+	0.179484i
$729$	12.1744	−	5.86286i	0.450902	−	0.217143i
$730$	12.3994	+	2.15900i	0.458924	+	0.0799083i
$731$	0.876812	+	3.84156i	0.0324301	+	0.142085i
$732$	1.71350	−	3.55811i	0.0633327	−	0.131512i
$733$	−15.6783	−	12.5030i	−0.579091	−	0.461809i	0.289611	−	0.957144i	$-0.406474\pi$
$733$	−15.6783	−	12.5030i	−0.579091	−	0.461809i	−0.868702	+	0.495335i	$0.835045\pi$
$734$	19.0624			0.703605
$735$	19.8841	+	24.0336i	0.733436	+	0.886492i
$736$	−0.423583			−0.0156135
$737$	−3.77785	−	3.01273i	−0.139159	−	0.110975i
$738$	−4.20113	+	8.72373i	−0.154646	+	0.321125i
$739$	−4.46546	−	19.5645i	−0.164265	−	0.719691i	−0.988220	−	0.153037i	$-0.951095\pi$
$739$	−4.46546	−	19.5645i	−0.164265	−	0.719691i	0.823956	−	0.566654i	$-0.191762\pi$
$740$	−0.995889	+	5.71951i	−0.0366096	+	0.210254i
$741$	13.7820	−	6.63706i	0.506294	−	0.243818i
$742$	−34.4269	+	7.24409i	−1.26385	+	0.265939i
$743$	−10.3889	+	21.5727i	−0.381131	+	0.791426i	0.618852	+	0.785508i	$0.287598\pi$
$743$	−10.3889	+	21.5727i	−0.381131	+	0.791426i	−0.999982	+	0.00591834i	$0.998116\pi$
$744$	3.71244	+	4.65525i	0.136105	+	0.170670i
$745$	−28.0934	+	24.8997i	−1.02926	+	0.912254i
$746$	−0.0807696	+	0.101282i	−0.00295718	+	0.00370819i
$747$	−5.19346	−	1.18537i	−0.190019	−	0.0433705i
$748$	−0.370204	−	0.295228i	−0.0135360	−	0.0107946i
$749$	−2.58298	+	10.4911i	−0.0943800	+	0.383337i
$750$	−22.2285	−	1.52235i	−0.811670	−	0.0555883i
$751$	39.0481	−	18.8046i	1.42488	−	0.686188i	0.446846	−	0.894611i	$-0.352547\pi$
$751$	39.0481	−	18.8046i	1.42488	−	0.686188i	0.978039	+	0.208422i	$0.0668329\pi$
$752$	−0.206749	−	0.0471890i	−0.00753934	−	0.00172081i
$753$		−	52.3816i		−	1.90889i
$754$	−2.54167			−0.0925622
$755$	−0.414915	−	7.97092i	−0.0151003	−	0.290091i
$756$	9.55640	+	4.80399i	0.347563	+	0.174720i
$757$	−31.9623	+	7.29518i	−1.16169	+	0.265148i	−0.759561	−	0.650436i	$-0.774586\pi$
$757$	−31.9623	+	7.29518i	−1.16169	+	0.265148i	−0.402128	+	0.915584i	$0.631729\pi$
$758$	25.7344	−	5.87370i	0.934714	−	0.213342i
$759$	−0.599189	−	0.751359i	−0.0217492	−	0.0272726i
$760$	−4.87613	+	6.81300i	−0.176876	+	0.247134i
$761$	5.64616	+	24.7374i	0.204673	+	0.896732i	0.968046	+	0.250773i	$0.0806849\pi$
$761$	5.64616	+	24.7374i	0.204673	+	0.896732i	−0.763373	+	0.645958i	$0.776458\pi$
$762$	31.6886	−	7.23271i	1.14796	−	0.262014i
$763$	−0.455650	+	26.7918i	−0.0164956	+	0.969927i
$764$	−2.61260	+	11.4465i	−0.0945204	+	0.414121i
$765$	−0.246539	−	0.869112i	−0.00891363	−	0.0314228i
$766$	3.56927			0.128963
$767$	−6.86648	−	1.56723i	−0.247934	−	0.0565894i
$768$	0.864658	+	1.79548i	0.0312007	+	0.0647889i
$769$	7.50008	+	9.40480i	0.270460	+	0.339146i	0.898450	−	0.439075i	$-0.144694\pi$
$769$	7.50008	+	9.40480i	0.270460	+	0.339146i	−0.627991	+	0.778221i	$0.716122\pi$
$770$	5.11571	−	4.38111i	0.184357	−	0.157884i
$771$	−37.2547	+	46.7160i	−1.34170	+	1.68243i
$772$	−15.3047	−	3.49319i	−0.550828	−	0.125723i
$773$	−26.1712	−	20.8708i	−0.941311	−	0.750671i	0.0272028	−	0.999630i	$-0.491340\pi$
$773$	−26.1712	−	20.8708i	−0.941311	−	0.750671i	−0.968514	+	0.248959i	$0.919911\pi$
$774$	8.29153	−	3.99299i	0.298033	−	0.143525i
$775$	−14.0600	−	5.04939i	−0.505052	−	0.181379i
$776$	−4.10661	−	1.97764i	−0.147419	−	0.0709932i
$777$	0.232781	−	13.6873i	0.00835096	−	0.491029i
$778$	4.51146	+	9.36815i	0.161744	+	0.335864i
$779$	−33.6491	−	16.2045i	−1.20560	−	0.580588i
$780$	4.38313	+	8.00793i	0.156941	+	0.286730i
$781$	−7.27115	−	3.50160i	−0.260182	−	0.125297i
$782$	0.137739	+	0.109843i	0.00492552	+	0.00392797i
$783$			5.01559i			0.179243i
$784$	1.32468	+	6.87352i	0.0473101	+	0.245483i
$785$	−12.3513	−	43.5415i	−0.440837	−	1.55406i
$786$	14.9102	−	18.6968i	0.531831	−	0.666895i
$787$	−10.5358	+	21.8779i	−0.375562	+	0.779862i	−0.999999	−	0.00121290i	$-0.999614\pi$
$787$	−10.5358	+	21.8779i	−0.375562	+	0.779862i	0.624438	+	0.781075i	$0.285328\pi$
$788$	8.38639	−	1.91414i	0.298753	−	0.0681884i
$789$	−18.2902	−	8.80810i	−0.651149	−	0.313577i
$790$	17.4868	+	19.7297i	0.622154	+	0.701953i
$791$	−8.88161	+	36.0739i	−0.315794	+	1.28264i
$792$	−0.479834	+	0.996385i	−0.0170502	+	0.0354050i
$793$	3.17409	−	2.53125i	0.112715	−	0.0898874i
$794$	32.7004	−	15.7477i	1.16049	−	0.558864i
$795$	−22.8991	+	54.6496i	−0.812149	+	1.93822i
$796$	4.15246	−	18.1931i	0.147180	−	0.644839i
$797$	−0.740920	−	0.590864i	−0.0262447	−	0.0209295i	0.610280	−	0.792186i	$-0.291057\pi$
$797$	−0.740920	−	0.590864i	−0.0262447	−	0.0209295i	−0.636524	+	0.771257i	$0.719629\pi$
$798$	8.87294	−	17.6506i	0.314099	−	0.624825i
$799$	0.0549924	+	0.0689583i	0.00194549	+	0.00243957i
$800$	−4.21170	−	2.69473i	−0.148906	−	0.0952731i
$801$	3.61958	−	15.8584i	0.127892	−	0.560330i
$802$		−	38.1462i		−	1.34699i
$803$			6.40807i			0.226136i
$804$	1.88213	−	8.24613i	0.0663775	−	0.290819i
$805$	−1.90336	+	1.63004i	−0.0670845	+	0.0574514i
$806$	1.36206	+	5.96758i	0.0479766	+	0.210199i
$807$	−3.67244	+	0.838210i	−0.129276	+	0.0295064i
$808$	1.29826	−	1.03533i	0.0456726	−	0.0364227i
$809$	29.0147	+	36.3833i	1.02010	+	1.27917i	0.959709	+	0.280994i	$0.0906642\pi$
$809$	29.0147	+	36.3833i	1.02010	+	1.27917i	0.0603938	+	0.998175i	$0.480764\pi$
$810$	21.5184	−	11.7781i	0.756081	−	0.413840i
$811$	6.38510	+	27.9749i	0.224211	+	0.982333i	0.954269	+	0.298948i	$0.0966358\pi$
$811$	6.38510	+	27.9749i	0.224211	+	0.982333i	−0.730058	+	0.683385i	$0.760507\pi$
$812$	−2.60077	+	2.00265i	−0.0912692	+	0.0702794i
$813$	49.5720	+	11.3145i	1.73857	+	0.396817i
$814$	−2.95586			−0.103603
$815$	−12.6307	−	44.5266i	−0.442435	−	1.55970i
$816$	0.184436	−	0.808067i	0.00645655	−	0.0282880i
$817$	15.4017	+	31.9820i	0.538838	+	1.11891i
$818$	−23.2534	+	18.5439i	−0.813034	+	0.648373i
$819$	−3.21228	−	4.17167i	−0.112246	−	0.145770i
$820$	8.61373	−	20.5570i	0.300804	−	0.717881i
$821$	6.94527	−	30.4292i	0.242392	−	1.06199i	−0.696441	−	0.717614i	$-0.745234\pi$
$821$	6.94527	−	30.4292i	0.242392	−	1.06199i	0.938833	−	0.344373i	$-0.111909\pi$
$822$	−21.0370	−	16.7764i	−0.733749	−	0.585145i
$823$	14.0050	+	29.0818i	0.488185	+	1.01373i	0.988965	+	0.148152i	$0.0473324\pi$
$823$	14.0050	+	29.0818i	0.488185	+	1.01373i	−0.500780	+	0.865575i	$0.666953\pi$
$824$	4.77763	+	5.99096i	0.166437	+	0.208705i
$825$	−1.17780	−	11.2827i	−0.0410057	−	0.392812i
$826$	−8.26101	+	3.80662i	−0.287437	+	0.132449i
$827$	0.726447	+	1.50848i	0.0252610	+	0.0524551i	0.913218	−	0.407472i	$-0.133590\pi$
$827$	0.726447	+	1.50848i	0.0252610	+	0.0524551i	−0.887957	+	0.459927i	$0.847875\pi$
$828$	0.178527	−	0.370716i	0.00620426	−	0.0128833i
$829$	7.42115	+	32.5142i	0.257747	+	1.12926i	0.923653	+	0.383229i	$0.125188\pi$
$829$	7.42115	+	32.5142i	0.257747	+	1.12926i	−0.665906	+	0.746036i	$0.731955\pi$
$830$	12.0807	+	2.10350i	0.419326	+	0.0730135i
$831$	41.0274	−	51.4468i	1.42323	−	1.78467i
$832$			2.04865i			0.0710241i
$833$	1.35167	−	2.57861i	0.0468327	−	0.0893435i
$834$	32.6321			1.12996
$835$	4.07998	+	1.70958i	0.141194	+	0.0591626i
$836$	−3.84325	−	1.85081i	−0.132921	−	0.0640116i
$837$	11.7761	−	2.68782i	0.407041	−	0.0929045i
$838$	−14.6438	+	30.4082i	−0.505863	+	1.05043i
$839$	11.1577	−	5.37326i	0.385206	−	0.185506i	−0.231251	−	0.972894i	$-0.574282\pi$
$839$	11.1577	−	5.37326i	0.385206	−	0.185506i	0.616457	+	0.787389i	$0.288567\pi$
$840$	10.7947	+	4.74054i	0.372453	+	0.163564i
$841$	24.7413	+	11.9148i	0.853148	+	0.410854i
$842$	0.475571	−	0.379255i	0.0163893	−	0.0130700i
$843$	1.81072	+	3.76000i	0.0623645	+	0.129501i
$844$	−14.2220	+	17.8338i	−0.489541	+	0.613864i
$845$	−1.02325	−	19.6576i	−0.0352008	−	0.676242i
$846$	0.128438	−	0.161056i	0.00441578	−	0.00553721i
$847$	−19.7977	−	16.3465i	−0.680256	−	0.561673i
$848$	−10.3961	+	8.29060i	−0.357003	+	0.284700i
$849$	−20.9935	+	10.1099i	−0.720495	+	0.346972i
$850$	0.670747	+	1.96843i	0.0230064	+	0.0675165i
$851$	1.09976			0.0376993
$852$		−	14.1267i		−	0.483972i
$853$	37.4091	+	8.53839i	1.28086	+	0.292349i	0.808207	−	0.588898i	$-0.200438\pi$
$853$	37.4091	+	8.53839i	1.28086	+	0.292349i	0.472656	+	0.881247i	$0.343295\pi$
$854$	1.25345	−	5.09106i	0.0428922	−	0.174213i
$855$	−3.90754	−	7.13902i	−0.133635	−	0.244149i
$856$	0.908705	+	3.98130i	0.0310589	+	0.136078i
$857$	−38.7182	+	30.8767i	−1.32259	+	1.05473i	−0.328689	+	0.944438i	$0.606607\pi$
$857$	−38.7182	+	30.8767i	−1.32259	+	1.05473i	−0.993899	+	0.110291i	$0.964822\pi$
$858$	−3.63392	+	2.89796i	−0.124060	+	0.0989347i
$859$	−1.29852	−	5.68919i	−0.0443049	−	0.194112i	0.947932	−	0.318472i	$-0.103170\pi$
$859$	−1.29852	−	5.68919i	−0.0443049	−	0.194112i	−0.992237	+	0.124359i	$0.960312\pi$
$860$	−18.5829	+	10.1713i	−0.633672	+	0.346840i
$861$	−12.5643	+	51.0317i	−0.428191	+	1.73916i
$862$	19.9591	+	4.55553i	0.679808	+	0.155162i
$863$		−	12.2565i		−	0.417216i	−0.977999	−	0.208608i	$-0.933107\pi$
$863$		−	12.2565i		−	0.417216i	0.977999	−	0.208608i	$-0.0668932\pi$
$864$	4.04269			0.137535
$865$	−11.7475	+	0.611499i	−0.399426	+	0.0207916i
$866$	−7.07955	+	3.40933i	−0.240573	+	0.115854i
$867$	26.2175	−	20.9078i	0.890393	−	0.710065i
$868$	6.09576	+	5.03314i	0.206903	+	0.170836i
$869$	−8.36908	+	10.4945i	−0.283902	+	0.356001i
$870$	0.287390	+	5.52104i	0.00974343	+	0.187181i
$871$	5.42130	−	6.79809i	0.183694	−	0.230345i
$872$	4.39429	+	9.12483i	0.148809	+	0.309006i
$873$	3.46163	−	2.76056i	0.117158	−	0.0934307i
$874$	1.42992	+	0.688614i	0.0483678	+	0.0232927i
$875$	−29.2950	+	4.09887i	−0.990353	+	0.138567i
$876$	−10.1061	+	4.86684i	−0.341454	+	0.164435i
$877$	11.8055	−	24.5144i	0.398643	−	0.827792i	−0.600950	−	0.799286i	$-0.705211\pi$
$877$	11.8055	−	24.5144i	0.398643	−	0.827792i	0.999594	−	0.0285051i	$-0.00907468\pi$
$878$	22.5884	−	5.15565i	0.762322	−	0.173995i
$879$	−44.3687	−	21.3668i	−1.49652	−	0.720685i
$880$	0.983821	−	2.34792i	0.0331646	−	0.0791485i
$881$	−25.0893			−0.845279			−0.422640	−	0.906298i	$-0.638896\pi$
$881$	−25.0893			−0.845279			−0.422640	+	0.906298i	$0.638896\pi$
$882$	−6.57395	−	1.73763i	−0.221357	−	0.0585090i
$883$		−	20.0959i		−	0.676280i	−0.941096	−	0.338140i	$-0.890202\pi$
$883$		−	20.0959i		−	0.676280i	0.941096	−	0.338140i	$-0.109798\pi$
$884$	0.531251	−	0.666168i	0.0178679	−	0.0224057i
$885$	−2.62795	+	15.0926i	−0.0883375	+	0.507334i
$886$	−3.54633	−	15.5375i	−0.119141	−	0.521992i
$887$	−15.0549	+	31.2619i	−0.505496	+	1.04967i	0.479572	+	0.877503i	$0.340792\pi$
$887$	−15.0549	+	31.2619i	−0.505496	+	1.04967i	−0.985067	+	0.172170i	$0.944922\pi$
$888$	−2.24494	−	4.66166i	−0.0753352	−	0.156435i
$889$	39.1920	−	18.0594i	1.31446	−	0.605694i
$890$	−6.42311	+	36.8887i	−0.215303	+	1.23651i
$891$	7.78723	+	9.76488i	0.260882	+	0.327136i
$892$	4.37191	+	9.07837i	0.146382	+	0.303966i
$893$	0.621222	+	0.495408i	0.0207884	+	0.0165782i
$894$	7.44472	−	32.6174i	0.248989	−	1.09089i
$895$	14.4310	−	34.4402i	0.482376	−	1.15121i
$896$	1.61419	+	2.09628i	0.0539262	+	0.0700319i
$897$	1.35204	−	1.07822i	0.0451434	−	0.0360006i
$898$	−5.50732	−	11.4361i	−0.183782	−	0.381626i
$899$	−0.824863	+	3.61396i	−0.0275107	+	0.120532i
$900$	4.13351	−	2.55030i	0.137784	−	0.0850099i
$901$	5.53044			0.184246
$902$	11.0636	+	2.52519i	0.368378	+	0.0840798i
$903$	39.5779	−	30.4759i	1.31707	−	1.01417i
$904$	3.12460	+	13.6897i	0.103923	+	0.455314i
$905$	−21.0800	−	38.5129i	−0.700722	−	1.28021i
$906$	4.43518	+	5.56154i	0.147349	+	0.184770i
$907$	14.0710	−	11.2212i	0.467220	−	0.372595i	−0.361397	−	0.932412i	$-0.617700\pi$
$907$	14.0710	−	11.2212i	0.467220	−	0.372595i	0.828616	+	0.559817i	$0.189129\pi$
$908$	17.1931	−	3.92422i	0.570575	−	0.130230i
$909$	0.358932	+	1.57259i	0.0119050	+	0.0521594i
$910$	7.88364	+	9.20552i	0.261340	+	0.305160i
$911$	−4.92427	+	21.5746i	−0.163148	+	0.714799i	0.825481	+	0.564429i	$0.190904\pi$
$911$	−4.92427	+	21.5746i	−0.163148	+	0.714799i	−0.988630	+	0.150370i	$0.951953\pi$
$912$		−	7.46681i		−	0.247251i
$913$			6.24332i			0.206624i
$914$	−6.58799	+	28.8639i	−0.217911	+	0.954732i
$915$	−5.85731	−	6.60857i	−0.193637	−	0.218473i
$916$	5.72814	+	7.18286i	0.189263	+	0.237328i
$917$	14.2599	−	28.3667i	0.470903	−	0.936750i
$918$	−1.31458	−	1.04834i	−0.0433876	−	0.0346004i
$919$	10.4880	−	45.9508i	0.345966	−	1.51578i	−0.440279	−	0.897861i	$-0.645120\pi$
$919$	10.4880	−	45.9508i	0.345966	−	1.51578i	0.786245	−	0.617915i	$-0.212023\pi$
$920$	−0.366041	+	0.873571i	−0.0120680	+	0.0288008i
$921$	19.7339	−	9.50334i	0.650254	−	0.313146i
$922$	−5.87748	+	4.68713i	−0.193564	+	0.154363i
$923$	6.30100	−	13.0842i	0.207400	−	0.430670i
$924$	−1.43504	+	5.82861i	−0.0472094	+	0.191747i
$925$	10.9350	+	6.99641i	0.359539	+	0.230040i
$926$	−9.31183	−	4.48434i	−0.306006	−	0.147365i
$927$	−7.25687	+	1.65633i	−0.238347	+	0.0544011i
$928$	−0.538302	+	1.11780i	−0.0176706	+	0.0366934i
$929$	−4.82501	+	6.05037i	−0.158303	+	0.198506i	−0.854658	−	0.519192i	$-0.826233\pi$
$929$	−4.82501	+	6.05037i	−0.158303	+	0.198506i	0.696354	+	0.717698i	$0.254804\pi$
$930$	12.8088	−	3.63344i	0.420018	−	0.119145i
$931$	6.70236	−	25.3570i	0.219661	−	0.831041i
$932$		−	14.6314i		−	0.479267i
$933$	35.2590	+	28.1181i	1.15433	+	0.920545i
$934$	−7.82730	−	3.76943i	−0.256117	−	0.123339i
$935$	−0.928773	+	0.508363i	−0.0303741	+	0.0166252i
$936$	−1.79296	−	0.863443i	−0.0586047	−	0.0282225i
$937$	−13.2690	−	27.5535i	−0.433481	−	0.900132i	−0.997244	−	0.0741956i	$-0.976361\pi$
$937$	−13.2690	−	27.5535i	−0.433481	−	0.900132i	0.563763	−	0.825937i	$-0.309353\pi$
$938$	0.190951	−	11.2278i	0.00623478	−	0.366599i
$939$	−14.1238	−	6.80169i	−0.460914	−	0.221965i
$940$	−0.275982	+	0.385607i	−0.00900156	+	0.0125771i
$941$	5.17034	−	2.48990i	0.168548	−	0.0811685i	−0.347707	−	0.937603i	$-0.613040\pi$
$941$	5.17034	−	2.48990i	0.168548	−	0.0811685i	0.516256	+	0.856435i	$0.327325\pi$
$942$	31.5361	+	25.1492i	1.02750	+	0.819406i
$943$	−4.11633	−	0.939526i	−0.134046	−	0.0305952i
$944$	−2.14350	+	2.68787i	−0.0697651	+	0.0874827i
$945$	18.1657	−	15.5571i	0.590929	−	0.506074i
$946$	−6.72490	−	8.43276i	−0.218645	−	0.274173i
$947$	−16.4916	−	34.2452i	−0.535906	−	1.11282i	−0.976580	−	0.215153i	$-0.930975\pi$
$947$	−16.4916	−	34.2452i	−0.535906	−	1.11282i	0.440675	−	0.897667i	$-0.354739\pi$
$948$	−22.9070	−	5.22836i	−0.743984	−	0.169809i
$949$	−11.5311			−0.374315
$950$	9.83698	+	15.9437i	0.319154	+	0.517283i
$951$	2.28522	−	10.0122i	0.0741032	−	0.324668i
$952$	0.0187120	−	1.10025i	0.000606459	−	0.0356592i
$953$	12.5713	−	2.86933i	0.407226	−	0.0929466i	−0.0140011	−	0.999902i	$-0.504457\pi$
$953$	12.5713	−	2.86933i	0.407226	−	0.0929466i	0.421227	+	0.906955i	$0.361600\pi$
$954$	−2.87422	−	12.5928i	−0.0930564	−	0.407707i
$955$	21.3489	+	15.2796i	0.690835	+	0.494437i
$956$	5.40040	+	6.77189i	0.174661	+	0.219019i
$957$	−2.74423	+	0.626353i	−0.0887084	+	0.0202471i
$958$	38.4648	−	8.77934i	1.24274	−	0.283648i
$959$	−31.9171	−	16.0447i	−1.03066	−	0.518110i
$960$	4.45009	−	0.231643i	0.143626	−	0.00747625i
$961$	−22.0728			−0.712024
$962$		−	5.31896i		−	0.171490i
$963$	−3.86739	−	0.882706i	−0.124625	−	0.0284448i
$964$	−3.54893	+	1.70908i	−0.114303	+	0.0550456i
$965$	−20.4298	+	28.5448i	−0.657657	+	0.918889i
$966$	0.533923	−	2.16860i	0.0171787	−	0.0697736i
$967$	11.3098	+	9.01926i	0.363699	+	0.290040i	0.788239	−	0.615369i	$-0.210993\pi$
$967$	11.3098	+	9.01926i	0.363699	+	0.290040i	−0.424541	+	0.905409i	$0.639564\pi$
$968$	−9.46057	−	2.15931i	−0.304074	−	0.0694030i
$969$	−1.93628	+	2.42802i	−0.0622023	+	0.0779992i
$970$	−7.62732	+	6.76024i	−0.244898	+	0.217058i
$971$	−21.1594	−	26.5331i	−0.679038	−	0.851487i	0.316227	−	0.948684i	$-0.397584\pi$
$971$	−21.1594	−	26.5331i	−0.679038	−	0.851487i	−0.995265	+	0.0971966i	$0.969012\pi$
$972$	−4.22363	+	8.77046i	−0.135473	+	0.281312i
$973$	42.3951	−	8.92076i	1.35912	−	0.285986i
$974$	−17.1601	+	8.26389i	−0.549847	+	0.264792i
$975$	20.3027	−	2.11940i	0.650208	−	0.0678753i
$976$	−0.440971	−	1.93202i	−0.0141151	−	0.0618424i
$977$	−7.27171	+	15.0999i	−0.232643	+	0.483087i	−0.984308	−	0.176457i	$-0.943536\pi$
$977$	−7.27171	+	15.0999i	−0.232643	+	0.483087i	0.751666	+	0.659544i	$0.229251\pi$
$978$	32.2496	+	25.7182i	1.03123	+	0.822377i
$979$	−19.0642			−0.609295
$980$	15.3202	+	3.20784i	0.489387	+	0.102471i
$981$	−9.83803			−0.314104
$982$	−18.8013	−	14.9935i	−0.599974	−	0.478463i
$983$	3.90130	−	8.10112i	0.124432	−	0.258386i	−0.829442	−	0.558593i	$-0.811341\pi$
$983$	3.90130	−	8.10112i	0.124432	−	0.258386i	0.953874	+	0.300207i	$0.0970558\pi$
$984$	4.42020	+	19.3661i	0.140911	+	0.617370i
$985$	3.29954	−	18.9497i	0.105132	−	0.603787i
$986$	0.464907	−	0.223887i	0.0148056	−	0.00713002i
$987$	0.502196	−	0.999000i	0.0159851	−	0.0317985i
$988$	3.33046	−	6.91578i	0.105956	−	0.220020i
$989$	2.50207	+	3.13750i	0.0795613	+	0.0997667i
$990$	1.64023	+	1.85061i	0.0521300	+	0.0588163i
$991$	−20.4986	+	25.7044i	−0.651159	+	0.816527i	−0.992349	−	0.123467i	$-0.960599\pi$
$991$	−20.4986	+	25.7044i	−0.651159	+	0.816527i	0.341190	+	0.939994i	$0.389170\pi$
$992$	2.91294	+	0.664859i	0.0924859	+	0.0211093i
$993$	−15.6488	−	12.4795i	−0.496601	−	0.396026i
$994$	−3.86186	−	18.3531i	−0.122491	−	0.582126i
$995$	−33.9320	−	24.2855i	−1.07572	−	0.769901i
$996$	−9.84628	+	4.74172i	−0.311991	+	0.150247i
$997$	−12.2412	−	2.79398i	−0.387683	−	0.0884861i	0.0242368	−	0.999706i	$-0.492284\pi$
$997$	−12.2412	−	2.79398i	−0.387683	−	0.0884861i	−0.411920	+	0.911220i	$0.635142\pi$
$998$		−	12.7810i		−	0.404575i
$999$	−10.4961			−0.332083

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.p.a.239.17	yes	168
5.4	even	2	inner	490.2.p.a.239.12	✓	168
49.8	even	7	inner	490.2.p.a.449.12	yes	168
245.204	even	14	inner	490.2.p.a.449.17	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.2.p.a.239.12	✓	168	5.4	even	2	inner
490.2.p.a.239.17	yes	168	1.1	even	1	trivial
490.2.p.a.449.12	yes	168	49.8	even	7	inner
490.2.p.a.449.17	yes	168	245.204	even	14	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.p (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.781831 + 0.623490i) q^{2} +(-0.864658 + 1.79548i) q^{3} +(0.222521 + 0.974928i) q^{4} +(2.20292 + 0.383576i) q^{5} +(-1.79548 + 0.864658i) q^{6} +(-2.09628 + 1.61419i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(-0.605651 - 0.759462i) q^{9} +O(q^{10})\)	\(q+(0.781831 + 0.623490i) q^{2} +(-0.864658 + 1.79548i) q^{3} +(0.222521 + 0.974928i) q^{4} +(2.20292 + 0.383576i) q^{5} +(-1.79548 + 0.864658i) q^{6} +(-2.09628 + 1.61419i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(-0.605651 - 0.759462i) q^{9} +(1.48316 + 1.67339i) q^{10} +(-0.709829 + 0.890098i) q^{11} +(-1.94287 - 0.443447i) q^{12} +(-1.60170 - 1.27731i) q^{13} +(-2.64537 - 0.0449900i) q^{14} +(-2.59348 + 3.62365i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(0.405486 + 0.0925496i) q^{17} -0.971389i q^{18} +3.74683 q^{19} +(0.116238 + 2.23304i) q^{20} +(-1.08567 - 5.15956i) q^{21} +(-1.10993 + 0.253335i) q^{22} +(0.412963 - 0.0942561i) q^{23} +(-1.24251 - 1.55806i) q^{24} +(4.70574 + 1.68997i) q^{25} +(-0.455867 - 1.99728i) q^{26} +(-3.94133 + 0.899582i) q^{27} +(-2.04018 - 1.68454i) q^{28} +(0.276073 - 1.20955i) q^{29} +(-4.28697 + 1.21607i) q^{30} -2.98785 q^{31} +(-0.974928 - 0.222521i) q^{32} +(-0.984394 - 2.04412i) q^{33} +(0.259318 + 0.325175i) q^{34} +(-5.23711 + 2.75184i) q^{35} +(0.605651 - 0.759462i) q^{36} +(2.53123 + 0.577738i) q^{37} +(2.92939 + 2.33611i) q^{38} +(3.67831 - 1.77138i) q^{39} +(-1.30140 + 1.81834i) q^{40} +(-8.98068 - 4.32487i) q^{41} +(2.36812 - 4.71081i) q^{42} +(4.11060 + 8.53575i) q^{43} +(-1.02573 - 0.493967i) q^{44} +(-1.04289 - 1.90535i) q^{45} +(0.381635 + 0.183786i) q^{46} +(0.165799 + 0.132221i) q^{47} -1.99283i q^{48} +(1.78881 - 6.76758i) q^{49} +(2.62541 + 4.25526i) q^{50} +(-0.516778 + 0.648019i) q^{51} +(0.888875 - 1.84577i) q^{52} +(12.9637 - 2.95888i) q^{53} +(-3.64233 - 1.75406i) q^{54} +(-1.90512 + 1.68854i) q^{55} +(-0.544788 - 2.58906i) q^{56} +(-3.23973 + 6.72737i) q^{57} +(0.969986 - 0.773538i) q^{58} +(3.09745 - 1.49165i) q^{59} +(-4.10990 - 1.72212i) q^{60} +(-0.440971 + 1.93202i) q^{61} +(-2.33599 - 1.86289i) q^{62} +(2.49553 + 0.614415i) q^{63} +(-0.623490 - 0.781831i) q^{64} +(-3.03847 - 3.42819i) q^{65} +(0.504855 - 2.21191i) q^{66} +4.24431i q^{67} +0.415914i q^{68} +(-0.187837 + 0.822967i) q^{69} +(-5.81029 - 1.11381i) q^{70} +(1.57739 + 6.91101i) q^{71} +(0.947034 - 0.216154i) q^{72} +(4.40064 - 3.50939i) q^{73} +(1.61879 + 2.02989i) q^{74} +(-7.10318 + 6.98782i) q^{75} +(0.833748 + 3.65289i) q^{76} +(0.0512201 - 3.01169i) q^{77} +(3.98025 + 0.908467i) q^{78} +11.7903 q^{79} +(-2.15119 + 0.610223i) q^{80} +(2.44118 - 10.6955i) q^{81} +(-4.32487 - 8.98068i) q^{82} +(4.28750 - 3.41917i) q^{83} +(4.78861 - 2.20656i) q^{84} +(0.857755 + 0.359414i) q^{85} +(-2.10816 + 9.23644i) q^{86} +(1.93302 + 1.54153i) q^{87} +(-0.493967 - 1.02573i) q^{88} +(10.4406 + 13.0920i) q^{89} +(0.372601 - 2.13989i) q^{90} +(5.41943 + 0.0921687i) q^{91} +(0.183786 + 0.381635i) q^{92} +(2.58347 - 5.36463i) q^{93} +(0.0471890 + 0.206749i) q^{94} +(8.25398 + 1.43719i) q^{95} +(1.24251 - 1.55806i) q^{96} +4.55800i q^{97} +(5.61806 - 4.17580i) q^{98} +1.10590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q + 28 q^{4} - 4 q^{5} + 14 q^{6} + 18 q^{9}+O(q^{10}) \) 168 * q + 28 * q^4 - 4 * q^5 + 14 * q^6 + 18 * q^9	\( 168 q + 28 q^{4} - 4 q^{5} + 14 q^{6} + 18 q^{9} - 4 q^{10} - 24 q^{11} + 4 q^{14} - 2 q^{15} - 28 q^{16} + 44 q^{19} - 10 q^{20} + 22 q^{26} - 2 q^{29} - 12 q^{30} - 16 q^{31} - 8 q^{34} - 4 q^{35} - 18 q^{36} - 80 q^{39} - 10 q^{40} + 52 q^{41} - 18 q^{44} - 72 q^{45} + 26 q^{46} - 52 q^{49} - 8 q^{50} + 64 q^{51} - 42 q^{54} - 60 q^{55} + 10 q^{56} - 58 q^{59} + 2 q^{60} + 32 q^{61} + 28 q^{64} + 4 q^{65} + 48 q^{66} - 48 q^{69} + 18 q^{70} - 68 q^{71} - 10 q^{74} - 16 q^{76} - 4 q^{80} + 34 q^{81} + 84 q^{84} - 48 q^{85} - 64 q^{86} + 100 q^{89} + 54 q^{90} + 78 q^{91} - 86 q^{94} - 64 q^{95} - 212 q^{99}+O(q^{100}) \) 168 * q + 28 * q^4 - 4 * q^5 + 14 * q^6 + 18 * q^9 - 4 * q^10 - 24 * q^11 + 4 * q^14 - 2 * q^15 - 28 * q^16 + 44 * q^19 - 10 * q^20 + 22 * q^26 - 2 * q^29 - 12 * q^30 - 16 * q^31 - 8 * q^34 - 4 * q^35 - 18 * q^36 - 80 * q^39 - 10 * q^40 + 52 * q^41 - 18 * q^44 - 72 * q^45 + 26 * q^46 - 52 * q^49 - 8 * q^50 + 64 * q^51 - 42 * q^54 - 60 * q^55 + 10 * q^56 - 58 * q^59 + 2 * q^60 + 32 * q^61 + 28 * q^64 + 4 * q^65 + 48 * q^66 - 48 * q^69 + 18 * q^70 - 68 * q^71 - 10 * q^74 - 16 * q^76 - 4 * q^80 + 34 * q^81 + 84 * q^84 - 48 * q^85 - 64 * q^86 + 100 * q^89 + 54 * q^90 + 78 * q^91 - 86 * q^94 - 64 * q^95 - 212 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more