LMFDB - Embedded newform 400.2.q.f.349.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(149,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("400.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.q (of order $4$, degree $2$, 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:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.4767670494822400.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + \cdots + 64 $ x^12 - 4x^11 + 7x^10 - 4x^9 - 8x^8 + 24x^7 - 38x^6 + 48x^5 - 32x^4 - 32x^3 + 112x^2 - 128*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			349.4
Root			$1.35979 - 0.388551i$ of defining polynomial
Character	$\chi$	$=$	400.349
Dual form			400.2.q.f.149.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.388551 - 1.35979i) q^{2} +(-1.03997 + 1.03997i) q^{3} +(-1.69806 - 1.05670i) q^{4} +(1.01006 + 1.81822i) q^{6} -1.49668 q^{7} +(-2.09667 + 1.89842i) q^{8} +0.836925i q^{9} +O(q^{10})$	\(q+(0.388551 - 1.35979i) q^{2} +(-1.03997 + 1.03997i) q^{3} +(-1.69806 - 1.05670i) q^{4} +(1.01006 + 1.81822i) q^{6} -1.49668 q^{7} +(-2.09667 + 1.89842i) q^{8} +0.836925i q^{9} +(0.423260 - 0.423260i) q^{11} +(2.86486 - 0.666995i) q^{12} +(-1.85704 + 1.85704i) q^{13} +(-0.581538 + 2.03517i) q^{14} +(1.76679 + 3.58866i) q^{16} +6.50950i q^{17} +(1.13804 + 0.325188i) q^{18} +(1.75725 + 1.75725i) q^{19} +(1.55650 - 1.55650i) q^{21} +(-0.411086 - 0.740003i) q^{22} -7.19295 q^{23} +(0.206172 - 4.15477i) q^{24} +(1.80363 + 3.24674i) q^{26} +(-3.99029 - 3.99029i) q^{27} +(2.54145 + 1.58154i) q^{28} +(6.57892 + 6.57892i) q^{29} -6.75252 q^{31} +(5.56631 - 1.00808i) q^{32} +0.880355i q^{33} +(8.85156 + 2.52928i) q^{34} +(0.884375 - 1.42115i) q^{36} +(1.95300 + 1.95300i) q^{37} +(3.07227 - 1.70671i) q^{38} -3.86254i q^{39} -7.70745i q^{41} +(-1.51174 - 2.72130i) q^{42} +(6.13581 + 6.13581i) q^{43} +(-1.16598 + 0.271462i) q^{44} +(-2.79483 + 9.78090i) q^{46} -6.65476i q^{47} +(-5.56950 - 1.89469i) q^{48} -4.75994 q^{49} +(-6.76969 - 6.76969i) q^{51} +(5.11569 - 1.19103i) q^{52} +(-5.29390 - 5.29390i) q^{53} +(-6.97638 + 3.87552i) q^{54} +(3.13804 - 2.84133i) q^{56} -3.65497 q^{57} +(11.5022 - 6.38970i) q^{58} +(-5.91841 + 5.91841i) q^{59} +(-1.43686 - 1.43686i) q^{61} +(-2.62370 + 9.18201i) q^{62} -1.25261i q^{63} +(0.792016 - 7.96070i) q^{64} +(1.19710 + 0.342063i) q^{66} +(6.35614 - 6.35614i) q^{67} +(6.87857 - 11.0535i) q^{68} +(7.48045 - 7.48045i) q^{69} +4.08932i q^{71} +(-1.58883 - 1.75475i) q^{72} +2.43800 q^{73} +(3.41451 - 1.89683i) q^{74} +(-1.12703 - 4.84079i) q^{76} +(-0.633485 + 0.633485i) q^{77} +(-5.25224 - 1.50079i) q^{78} -11.6722 q^{79} +5.78878 q^{81} +(-10.4805 - 2.99474i) q^{82} +(2.81439 - 2.81439i) q^{83} +(-4.28778 + 0.998279i) q^{84} +(10.7275 - 5.95933i) q^{86} -13.6838 q^{87} +(-0.0839103 + 1.69096i) q^{88} -10.5543i q^{89} +(2.77940 - 2.77940i) q^{91} +(12.2140 + 7.60076i) q^{92} +(7.02242 - 7.02242i) q^{93} +(-9.04907 - 2.58572i) q^{94} +(-4.74042 + 6.83717i) q^{96} +18.1512i q^{97} +(-1.84948 + 6.47252i) q^{98} +(0.354237 + 0.354237i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 6 q^{6} + 12 q^{7} + 2 q^{8}+O(q^{10}) $ 12 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 6 * q^6 + 12 * q^7 + 2 * q^8	$ 12 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 6 q^{6} + 12 q^{7} + 2 q^{8} - 2 q^{11} - 6 q^{12} + 4 q^{13} - 14 q^{14} + 2 q^{16} - 18 q^{18} + 14 q^{19} - 20 q^{21} - 20 q^{22} + 12 q^{23} + 14 q^{24} - 16 q^{26} + 10 q^{27} - 10 q^{28} - 4 q^{31} + 2 q^{32} + 6 q^{34} + 2 q^{36} - 8 q^{37} + 28 q^{38} + 10 q^{42} + 44 q^{44} - 10 q^{46} - 58 q^{48} - 4 q^{49} + 10 q^{51} - 16 q^{53} - 10 q^{54} + 6 q^{56} - 16 q^{57} + 4 q^{58} - 20 q^{59} + 4 q^{61} + 22 q^{62} - 38 q^{64} + 32 q^{66} + 50 q^{67} + 50 q^{68} - 54 q^{72} + 40 q^{73} - 10 q^{74} + 60 q^{76} - 8 q^{77} - 48 q^{78} - 12 q^{79} - 8 q^{81} - 12 q^{82} + 2 q^{83} - 34 q^{84} + 6 q^{86} - 64 q^{87} + 56 q^{88} + 50 q^{92} + 44 q^{93} - 32 q^{94} - 34 q^{96} - 30 q^{98} - 12 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 6 * q^6 + 12 * q^7 + 2 * q^8 - 2 * q^11 - 6 * q^12 + 4 * q^13 - 14 * q^14 + 2 * q^16 - 18 * q^18 + 14 * q^19 - 20 * q^21 - 20 * q^22 + 12 * q^23 + 14 * q^24 - 16 * q^26 + 10 * q^27 - 10 * q^28 - 4 * q^31 + 2 * q^32 + 6 * q^34 + 2 * q^36 - 8 * q^37 + 28 * q^38 + 10 * q^42 + 44 * q^44 - 10 * q^46 - 58 * q^48 - 4 * q^49 + 10 * q^51 - 16 * q^53 - 10 * q^54 + 6 * q^56 - 16 * q^57 + 4 * q^58 - 20 * q^59 + 4 * q^61 + 22 * q^62 - 38 * q^64 + 32 * q^66 + 50 * q^67 + 50 * q^68 - 54 * q^72 + 40 * q^73 - 10 * q^74 + 60 * q^76 - 8 * q^77 - 48 * q^78 - 12 * q^79 - 8 * q^81 - 12 * q^82 + 2 * q^83 - 34 * q^84 + 6 * q^86 - 64 * q^87 + 56 * q^88 + 50 * q^92 + 44 * q^93 - 32 * q^94 - 34 * q^96 - 30 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.388551	−	1.35979i	0.274747	−	0.961516i
$2$	0.388551	−	1.35979i	0.274747	−	0.961516i
$3$	−1.03997	+	1.03997i	−0.600427	+	0.600427i	−0.940426	−	0.339999i	$-0.889573\pi$
$3$	−1.03997	+	1.03997i	−0.600427	+	0.600427i	0.339999	+	0.940426i	$0.389573\pi$
$4$	−1.69806	−	1.05670i	−0.849028	−	0.528348i
$5$		0			0
$5$		0			0
$6$	1.01006	+	1.81822i	0.412355	+	0.742286i
$7$	−1.49668			−0.565693			−0.282846	−	0.959165i	$-0.591279\pi$
$7$	−1.49668			−0.565693			−0.282846	+	0.959165i	$0.591279\pi$
$8$	−2.09667	+	1.89842i	−0.741283	+	0.671192i
$9$			0.836925i			0.278975i
$10$		0			0
$11$	0.423260	−	0.423260i	0.127618	−	0.127618i	−0.640413	−	0.768031i	$-0.721237\pi$
$11$	0.423260	−	0.423260i	0.127618	−	0.127618i	0.768031	+	0.640413i	$0.221237\pi$
$12$	2.86486	−	0.666995i	0.827014	−	0.192545i
$13$	−1.85704	+	1.85704i	−0.515051	+	0.515051i	−0.916070	−	0.401019i	$-0.868656\pi$
$13$	−1.85704	+	1.85704i	−0.515051	+	0.515051i	0.401019	+	0.916070i	$0.368656\pi$
$14$	−0.581538	+	2.03517i	−0.155422	+	0.543923i
$15$		0			0
$16$	1.76679	+	3.58866i	0.441697	+	0.897164i
$17$			6.50950i			1.57879i	0.613888	+	0.789393i	$0.289605\pi$
$17$			6.50950i			1.57879i	−0.613888	+	0.789393i	$0.710395\pi$
$18$	1.13804	+	0.325188i	0.268239	+	0.0766476i
$19$	1.75725	+	1.75725i	0.403141	+	0.403141i	0.879338	−	0.476198i	$-0.157985\pi$
$19$	1.75725	+	1.75725i	0.403141	+	0.403141i	−0.476198	+	0.879338i	$0.657985\pi$
$20$		0			0
$21$	1.55650	−	1.55650i	0.339657	−	0.339657i
$22$	−0.411086	−	0.740003i	−0.0876439	−	0.157769i
$23$	−7.19295			−1.49983			−0.749917	−	0.661532i	$-0.769906\pi$
$23$	−7.19295			−1.49983			−0.749917	+	0.661532i	$0.769906\pi$
$24$	0.206172	−	4.15477i	0.0420846	−	0.848088i
$25$		0			0
$26$	1.80363	+	3.24674i	0.353721	+	0.636739i
$27$	−3.99029	−	3.99029i	−0.767931	−	0.767931i
$28$	2.54145	+	1.58154i	0.480289	+	0.298883i
$29$	6.57892	+	6.57892i	1.22167	+	1.22167i	0.967036	+	0.254639i	$0.0819565\pi$
$29$	6.57892	+	6.57892i	1.22167	+	1.22167i	0.254639	+	0.967036i	$0.418043\pi$
$30$		0			0
$31$	−6.75252			−1.21279			−0.606394	−	0.795164i	$-0.707385\pi$
$31$	−6.75252			−1.21279			−0.606394	+	0.795164i	$0.707385\pi$
$32$	5.56631	−	1.00808i	0.983993	−	0.178205i
$33$			0.880355i			0.153250i
$34$	8.85156	+	2.52928i	1.51803	+	0.433767i
$35$		0			0
$36$	0.884375	−	1.42115i	0.147396	−	0.236858i
$37$	1.95300	+	1.95300i	0.321071	+	0.321071i	0.849178	−	0.528107i	$-0.177098\pi$
$37$	1.95300	+	1.95300i	0.321071	+	0.321071i	−0.528107	+	0.849178i	$0.677098\pi$
$38$	3.07227	−	1.70671i	0.498388	−	0.276865i
$39$		−	3.86254i		−	0.618501i
$40$		0			0
$41$		−	7.70745i		−	1.20370i	−0.798609	−	0.601851i	$-0.794430\pi$
$41$		−	7.70745i		−	1.20370i	0.798609	−	0.601851i	$-0.205570\pi$
$42$	−1.51174	−	2.72130i	−0.233266	−	0.419906i
$43$	6.13581	+	6.13581i	0.935702	+	0.935702i	0.998054	−	0.0623522i	$-0.0198602\pi$
$43$	6.13581	+	6.13581i	0.935702	+	0.935702i	−0.0623522	+	0.998054i	$0.519860\pi$
$44$	−1.16598	+	0.271462i	−0.175778	+	0.0409244i
$45$		0			0
$46$	−2.79483	+	9.78090i	−0.412075	+	1.44211i
$47$		−	6.65476i		−	0.970697i	−0.874321	−	0.485348i	$-0.838693\pi$
$47$		−	6.65476i		−	0.970697i	0.874321	−	0.485348i	$-0.161307\pi$
$48$	−5.56950	−	1.89469i	−0.803888	−	0.273475i
$49$	−4.75994			−0.679992
$50$		0			0
$51$	−6.76969	−	6.76969i	−0.947946	−	0.947946i
$52$	5.11569	−	1.19103i	0.709419	−	0.165167i
$53$	−5.29390	−	5.29390i	−0.727173	−	0.727173i	0.242882	−	0.970056i	$-0.421907\pi$
$53$	−5.29390	−	5.29390i	−0.727173	−	0.727173i	−0.970056	+	0.242882i	$0.921907\pi$
$54$	−6.97638	+	3.87552i	−0.949365	+	0.527391i
$55$		0			0
$56$	3.13804	−	2.84133i	0.419338	−	0.379688i
$57$	−3.65497			−0.484113
$58$	11.5022	−	6.38970i	1.51031	−	0.839009i
$59$	−5.91841	+	5.91841i	−0.770511	+	0.770511i	−0.978196	−	0.207685i	$-0.933407\pi$
$59$	−5.91841	+	5.91841i	−0.770511	+	0.770511i	0.207685	+	0.978196i	$0.433407\pi$
$60$		0			0
$61$	−1.43686	−	1.43686i	−0.183971	−	0.183971i	0.609113	−	0.793084i	$-0.291526\pi$
$61$	−1.43686	−	1.43686i	−0.183971	−	0.183971i	−0.793084	+	0.609113i	$0.791526\pi$
$62$	−2.62370	+	9.18201i	−0.333210	+	1.16612i
$63$		−	1.25261i		−	0.157814i
$64$	0.792016	−	7.96070i	0.0990020	−	0.995087i
$65$		0			0
$66$	1.19710	+	0.342063i	0.147353	+	0.0421051i
$67$	6.35614	−	6.35614i	0.776526	−	0.776526i	−0.202712	−	0.979238i	$-0.564976\pi$
$67$	6.35614	−	6.35614i	0.776526	−	0.776526i	0.979238	+	0.202712i	$0.0649756\pi$
$68$	6.87857	−	11.0535i	0.834149	−	1.34043i
$69$	7.48045	−	7.48045i	0.900540	−	0.900540i
$70$		0			0
$71$			4.08932i			0.485313i	0.970112	+	0.242657i	$0.0780188\pi$
$71$			4.08932i			0.485313i	−0.970112	+	0.242657i	$0.921981\pi$
$72$	−1.58883	−	1.75475i	−0.187246	−	0.206799i
$73$	2.43800			0.285346			0.142673	−	0.989770i	$-0.454430\pi$
$73$	2.43800			0.285346			0.142673	+	0.989770i	$0.454430\pi$
$74$	3.41451	−	1.89683i	0.396929	−	0.220502i
$75$		0			0
$76$	−1.12703	−	4.84079i	−0.129279	−	0.555276i
$77$	−0.633485	+	0.633485i	−0.0721924	+	0.0721924i
$78$	−5.25224	−	1.50079i	−0.594699	−	0.169931i
$79$	−11.6722			−1.31323			−0.656615	−	0.754226i	$-0.728012\pi$
$79$	−11.6722			−1.31323			−0.656615	+	0.754226i	$0.728012\pi$
$80$		0			0
$81$	5.78878			0.643198
$82$	−10.4805	−	2.99474i	−1.15738	−	0.330714i
$83$	2.81439	−	2.81439i	0.308919	−	0.308919i	−0.535571	−	0.844490i	$-0.679904\pi$
$83$	2.81439	−	2.81439i	0.308919	−	0.308919i	0.844490	+	0.535571i	$0.179904\pi$
$84$	−4.28778	+	0.998279i	−0.467835	+	0.108921i
$85$		0			0
$86$	10.7275	−	5.95933i	1.15677	−	0.642611i
$87$	−13.6838			−1.46705
$88$	−0.0839103	+	1.69096i	−0.00894487	+	0.180257i
$89$		−	10.5543i		−	1.11876i	−0.828912	−	0.559379i	$-0.811040\pi$
$89$		−	10.5543i		−	1.11876i	0.828912	−	0.559379i	$-0.188960\pi$
$90$		0			0
$91$	2.77940	−	2.77940i	0.291360	−	0.291360i
$92$	12.2140	+	7.60076i	1.27340	+	0.792434i
$93$	7.02242	−	7.02242i	0.728191	−	0.728191i
$94$	−9.04907	−	2.58572i	−0.933341	−	0.266696i
$95$		0			0
$96$	−4.74042	+	6.83717i	−0.483817	+	0.697815i
$97$			18.1512i			1.84298i	0.388407	+	0.921488i	$0.373025\pi$
$97$			18.1512i			1.84298i	−0.388407	+	0.921488i	$0.626975\pi$
$98$	−1.84948	+	6.47252i	−0.186826	+	0.653823i
$99$	0.354237	+	0.354237i	0.0356021	+	0.0356021i
$100$		0			0
$101$	−1.04036	+	1.04036i	−0.103520	+	0.103520i	−0.756970	−	0.653450i	$-0.773321\pi$
$101$	−1.04036	+	1.04036i	−0.103520	+	0.103520i	0.653450	+	0.756970i	$0.273321\pi$
$102$	−11.8357	+	6.57498i	−1.17191	+	0.651020i
$103$	−0.955267			−0.0941253			−0.0470626	−	0.998892i	$-0.514986\pi$
$103$	−0.955267			−0.0941253			−0.0470626	+	0.998892i	$0.514986\pi$
$104$	0.368154	−	7.41904i	0.0361005	−	0.727497i
$105$		0			0
$106$	−9.25555	+	5.14164i	−0.898978	+	0.499400i
$107$	7.20266	+	7.20266i	0.696308	+	0.696308i	0.963612	−	0.267305i	$-0.0861330\pi$
$107$	7.20266	+	7.20266i	0.696308	+	0.696308i	−0.267305	+	0.963612i	$0.586133\pi$
$108$	2.55921	+	10.9922i	0.246260	+	1.05773i
$109$	5.67807	+	5.67807i	0.543861	+	0.543861i	0.924658	−	0.380798i	$-0.124351\pi$
$109$	5.67807	+	5.67807i	0.543861	+	0.543861i	−0.380798	+	0.924658i	$0.624351\pi$
$110$		0			0
$111$	−4.06212			−0.385560
$112$	−2.64432	−	5.37108i	−0.249865	−	0.507519i
$113$		−	1.94751i		−	0.183206i	−0.995796	−	0.0916029i	$-0.970801\pi$
$113$		−	1.94751i		−	0.183206i	0.995796	−	0.0916029i	$-0.0291991\pi$
$114$	−1.42014	+	4.97000i	−0.133009	+	0.465483i
$115$		0			0
$116$	−4.21946	−	18.1233i	−0.391767	−	1.68271i
$117$	−1.55420	−	1.55420i	−0.143686	−	0.143686i
$118$	5.74818	+	10.3474i	0.529163	+	0.952555i
$119$		−	9.74266i		−	0.893108i
$120$		0			0
$121$			10.6417i			0.967427i
$122$	−2.51212	+	1.39553i	−0.227437	+	0.126346i
$123$	8.01552	+	8.01552i	0.722735	+	0.722735i
$124$	11.4662	+	7.13536i	1.02969	+	0.640774i
$125$		0			0
$126$	−1.70329	−	0.486703i	−0.151741	−	0.0433590i
$127$		−	1.31796i		−	0.116950i	−0.998289	−	0.0584750i	$-0.981376\pi$
$127$		−	1.31796i		−	0.116950i	0.998289	−	0.0584750i	$-0.0186238\pi$
$128$	−10.5171	−	4.17011i	−0.929592	−	0.368589i
$129$	−12.7621			−1.12364
$130$		0			0
$131$	1.03026	+	1.03026i	0.0900139	+	0.0900139i	0.750680	−	0.660666i	$-0.229726\pi$
$131$	1.03026	+	1.03026i	0.0900139	+	0.0900139i	−0.660666	+	0.750680i	$0.729726\pi$
$132$	0.930268	−	1.49489i	0.0809694	−	0.130114i
$133$	−2.63004	−	2.63004i	−0.228054	−	0.228054i
$134$	−6.17333	−	11.1127i	−0.533294	−	0.959991i
$135$		0			0
$136$	−12.3578	−	13.6483i	−1.05967	−	1.17033i
$137$	3.75559			0.320862			0.160431	−	0.987047i	$-0.448712\pi$
$137$	3.75559			0.320862			0.160431	+	0.987047i	$0.448712\pi$
$138$	−7.26530	−	13.0784i	−0.618463	−	1.11331i
$139$	−12.9485	+	12.9485i	−1.09828	+	1.09828i	−0.103669	+	0.994612i	$0.533058\pi$
$139$	−12.9485	+	12.9485i	−1.09828	+	1.09828i	−0.994612	+	0.103669i	$0.966942\pi$
$140$		0			0
$141$	6.92075	+	6.92075i	0.582832	+	0.582832i
$142$	5.56062	+	1.58891i	0.466637	+	0.133338i
$143$			1.57202i			0.131459i
$144$	−3.00344	+	1.47867i	−0.250286	+	0.123222i
$145$		0			0
$146$	0.947288	−	3.31517i	0.0783982	−	0.274365i
$147$	4.95020	−	4.95020i	0.408285	−	0.408285i
$148$	−1.25258	−	5.38003i	−0.102961	−	0.442236i
$149$	15.8472	−	15.8472i	1.29825	−	1.29825i	0.368709	−	0.929545i	$-0.379800\pi$
$149$	15.8472	−	15.8472i	1.29825	−	1.29825i	0.929545	−	0.368709i	$-0.120200\pi$
$150$		0			0
$151$			11.5316i			0.938424i	0.883085	+	0.469212i	$0.155462\pi$
$151$			11.5316i			0.938424i	−0.883085	+	0.469212i	$0.844538\pi$
$152$	−7.02036	−	0.348371i	−0.569427	−	0.0282566i
$153$	−5.44797			−0.440442
$154$	0.615265	+	1.10755i	0.0495795	+	0.0892488i
$155$		0			0
$156$	−4.08153	+	6.55880i	−0.326784	+	0.525125i
$157$	5.41891	−	5.41891i	0.432476	−	0.432476i	−0.456994	−	0.889470i	$-0.651074\pi$
$157$	5.41891	−	5.41891i	0.432476	−	0.432476i	0.889470	+	0.456994i	$0.151074\pi$
$158$	−4.53526	+	15.8718i	−0.360806	+	1.26269i
$159$	11.0110			0.873229
$160$		0			0
$161$	10.7656			0.848445
$162$	2.24924	−	7.87153i	0.176717	−	0.618446i
$163$	6.47288	−	6.47288i	0.506995	−	0.506995i	−0.406608	−	0.913603i	$-0.633289\pi$
$163$	6.47288	−	6.47288i	0.506995	−	0.506995i	0.913603	+	0.406608i	$0.133289\pi$
$164$	−8.14443	+	13.0877i	−0.635973	+	1.02198i
$165$		0			0
$166$	−2.73344	−	4.92051i	−0.212156	−	0.381906i
$167$	8.29734			0.642068			0.321034	−	0.947068i	$-0.395970\pi$
$167$	8.29734			0.642068			0.321034	+	0.947068i	$0.395970\pi$
$168$	−0.308573	+	6.21837i	−0.0238069	+	0.479757i
$169$			6.10279i			0.469445i
$170$		0			0
$171$	−1.47069	+	1.47069i	−0.112466	+	0.112466i
$172$	−3.93526	−	16.9026i	−0.300061	−	1.28881i
$173$	11.9420	−	11.9420i	0.907935	−	0.907935i	−0.0881700	−	0.996105i	$-0.528102\pi$
$173$	11.9420	−	11.9420i	0.907935	−	0.907935i	0.996105	+	0.0881700i	$0.0281019\pi$
$174$	−5.31684	+	18.6070i	−0.403069	+	1.41060i
$175$		0			0
$176$	2.26675	+	0.771125i	0.170862	+	0.0581257i
$177$		−	12.3099i		−	0.925271i
$178$	−14.3517	−	4.10090i	−1.07570	−	0.307376i
$179$	10.8703	+	10.8703i	0.812481	+	0.812481i	0.985005	−	0.172524i	$-0.0551922\pi$
$179$	10.8703	+	10.8703i	0.812481	+	0.812481i	−0.172524	+	0.985005i	$0.555192\pi$
$180$		0			0
$181$	−4.09403	+	4.09403i	−0.304307	+	0.304307i	−0.842696	−	0.538389i	$-0.819033\pi$
$181$	−4.09403	+	4.09403i	−0.304307	+	0.304307i	0.538389	+	0.842696i	$0.319033\pi$
$182$	−2.69946	−	4.85934i	−0.200097	−	0.360198i
$183$	2.98858			0.220922
$184$	15.0812	−	13.6552i	1.11180	−	1.00668i
$185$		0			0
$186$	−6.82044	−	12.2776i	−0.500099	−	0.900236i
$187$	2.75521	+	2.75521i	0.201481	+	0.201481i
$188$	−7.03206	+	11.3002i	−0.512866	+	0.824148i
$189$	5.97219	+	5.97219i	0.434413	+	0.434413i
$190$		0			0
$191$	19.2542			1.39319			0.696594	−	0.717466i	$-0.254698\pi$
$191$	19.2542			1.39319			0.696594	+	0.717466i	$0.254698\pi$
$192$	7.45521	+	9.10256i	0.538034	+	0.656921i
$193$			24.8152i			1.78624i	0.449820	+	0.893119i	$0.351488\pi$
$193$			24.8152i			1.78624i	−0.449820	+	0.893119i	$0.648512\pi$
$194$	24.6818	+	7.05267i	1.77205	+	0.506352i
$195$		0			0
$196$	8.08265	+	5.02981i	0.577332	+	0.359272i
$197$	−2.81324	−	2.81324i	−0.200435	−	0.200435i	0.599751	−	0.800186i	$-0.295266\pi$
$197$	−2.81324	−	2.81324i	−0.200435	−	0.200435i	−0.800186	+	0.599751i	$0.795266\pi$
$198$	0.619327	−	0.344048i	0.0440136	−	0.0244505i
$199$		−	21.2194i		−	1.50420i	−0.659048	−	0.752101i	$-0.729041\pi$
$199$		−	21.2194i		−	1.50420i	0.659048	−	0.752101i	$-0.270959\pi$
$200$		0			0
$201$			13.2204i			0.932495i
$202$	1.01044	+	1.81891i	0.0710944	+	0.127978i
$203$	−9.84655	−	9.84655i	−0.691092	−	0.691092i
$204$	4.34181	+	18.6488i	0.303987	+	1.30568i
$205$		0			0
$206$	−0.371170	+	1.29896i	−0.0258607	+	0.0905030i
$207$		−	6.01996i		−	0.418416i
$208$	−9.94529	−	3.38329i	−0.689582	−	0.234589i
$209$	1.48755			0.102896
$210$		0			0
$211$	15.5715	+	15.5715i	1.07199	+	1.07199i	0.997200	+	0.0747872i	$0.0238278\pi$
$211$	15.5715	+	15.5715i	1.07199	+	1.07199i	0.0747872	+	0.997200i	$0.476172\pi$
$212$	3.39530	+	14.5834i	0.233190	+	1.00159i
$213$	−4.25277	−	4.25277i	−0.291395	−	0.291395i
$214$	12.5927	−	6.99550i	0.860820	−	0.478203i
$215$		0			0
$216$	15.9415	+	0.791065i	1.08468	+	0.0538251i
$217$	10.1064			0.686065
$218$	9.92721	−	5.51476i	0.672355	−	0.373507i
$219$	−2.53545	+	2.53545i	−0.171330	+	0.171330i
$220$		0			0
$221$	−12.0884	−	12.0884i	−0.813155	−	0.813155i
$222$	−1.57834	+	5.52363i	−0.105931	+	0.370722i
$223$			7.88779i			0.528205i	0.964495	+	0.264103i	$0.0850758\pi$
$223$			7.88779i			0.528205i	−0.964495	+	0.264103i	$0.914924\pi$
$224$	−8.33099	+	1.50878i	−0.556638	+	0.100809i
$225$		0			0
$226$	−2.64820	−	0.756705i	−0.176155	−	0.0503353i
$227$	5.98838	−	5.98838i	0.397463	−	0.397463i	−0.479874	−	0.877337i	$-0.659318\pi$
$227$	5.98838	−	5.98838i	0.397463	−	0.397463i	0.877337	+	0.479874i	$0.159318\pi$
$228$	6.20635	+	3.86220i	0.411026	+	0.255780i
$229$	−19.4584	+	19.4584i	−1.28585	+	1.28585i	−0.348563	+	0.937286i	$0.613330\pi$
$229$	−19.4584	+	19.4584i	−1.28585	+	1.28585i	−0.937286	+	0.348563i	$0.886670\pi$
$230$		0			0
$231$		−	1.31761i		−	0.0866925i
$232$	−26.2833	−	1.30426i	−1.72559	−	0.0856286i
$233$	−2.68717			−0.176042			−0.0880212	−	0.996119i	$-0.528054\pi$
$233$	−2.68717			−0.176042			−0.0880212	+	0.996119i	$0.528054\pi$
$234$	−2.71728	+	1.50950i	−0.177634	+	0.0986793i
$235$		0			0
$236$	16.3037	−	3.79583i	1.06128	−	0.247087i
$237$	12.1388	−	12.1388i	0.788499	−	0.788499i
$238$	−13.2480	−	3.78552i	−0.858738	−	0.245379i
$239$	12.6359			0.817346			0.408673	−	0.912681i	$-0.365992\pi$
$239$	12.6359			0.817346			0.408673	+	0.912681i	$0.365992\pi$
$240$		0			0
$241$	7.53314			0.485252			0.242626	−	0.970120i	$-0.421991\pi$
$241$	7.53314			0.485252			0.242626	+	0.970120i	$0.421991\pi$
$242$	14.4705	+	4.13485i	0.930197	+	0.265798i
$243$	5.95070	−	5.95070i	0.381738	−	0.381738i
$244$	0.921544	+	3.95819i	0.0589958	+	0.253397i
$245$		0			0
$246$	14.0139	−	7.78498i	0.893491	−	0.496352i
$247$	−6.52658			−0.415276
$248$	14.1578	−	12.8191i	0.899020	−	0.814014i
$249$			5.85376i			0.370967i
$250$		0			0
$251$	−9.95683	+	9.95683i	−0.628470	+	0.628470i	−0.947683	−	0.319213i	$-0.896581\pi$
$251$	−9.95683	+	9.95683i	−0.628470	+	0.628470i	0.319213	+	0.947683i	$0.396581\pi$
$252$	−1.32363	+	2.12700i	−0.0833807	+	0.133989i
$253$	−3.04449	+	3.04449i	−0.191405	+	0.191405i
$254$	−1.79215	−	0.512094i	−0.112449	−	0.0321317i
$255$		0			0
$256$	−9.75692	+	12.6808i	−0.609808	+	0.792549i
$257$			4.51630i			0.281719i	0.990030	+	0.140860i	$0.0449866\pi$
$257$			4.51630i			0.281719i	−0.990030	+	0.140860i	$0.955013\pi$
$258$	−4.95874	+	17.3538i	−0.308717	+	1.08040i
$259$	−2.92302	−	2.92302i	−0.181628	−	0.181628i
$260$		0			0
$261$	−5.50606	+	5.50606i	−0.340817	+	0.340817i
$262$	1.80124	−	1.00062i	0.111281	−	0.0618188i
$263$	−20.2127			−1.24637			−0.623185	−	0.782075i	$-0.714162\pi$
$263$	−20.2127			−1.24637			−0.623185	+	0.782075i	$0.714162\pi$
$264$	−1.67128	−	1.84581i	−0.102860	−	0.113602i
$265$		0			0
$266$	−4.59821	+	2.55440i	−0.281935	+	0.156620i
$267$	10.9762	+	10.9762i	0.671732	+	0.671732i
$268$	−17.5096	+	4.07657i	−1.06957	+	0.249016i
$269$	−16.9430	−	16.9430i	−1.03304	−	1.03304i	−0.999435	−	0.0335999i	$-0.989303\pi$
$269$	−16.9430	−	16.9430i	−1.03304	−	1.03304i	−0.0335999	−	0.999435i	$-0.510697\pi$
$270$		0			0
$271$	−3.64054			−0.221147			−0.110573	−	0.993868i	$-0.535269\pi$
$271$	−3.64054			−0.221147			−0.110573	+	0.993868i	$0.535269\pi$
$272$	−23.3604	+	11.5009i	−1.41643	+	0.697345i
$273$			5.78099i			0.349881i
$274$	1.45924	−	5.10681i	0.0881559	−	0.308514i
$275$		0			0
$276$	−20.6068	+	4.79766i	−1.24038	+	0.288785i
$277$	−16.0090	−	16.0090i	−0.961888	−	0.961888i	0.0374115	−	0.999300i	$-0.488089\pi$
$277$	−16.0090	−	16.0090i	−0.961888	−	0.961888i	−0.999300	+	0.0374115i	$0.988089\pi$
$278$	12.5761	+	22.6385i	0.754266	+	1.35777i
$279$		−	5.65135i		−	0.338338i
$280$		0			0
$281$		−	5.51857i		−	0.329210i	−0.986360	−	0.164605i	$-0.947365\pi$
$281$		−	5.51857i		−	0.329210i	0.986360	−	0.164605i	$-0.0526350\pi$
$282$	12.0998	−	6.72170i	0.720535	−	0.400271i
$283$	−2.36694	−	2.36694i	−0.140700	−	0.140700i	0.633249	−	0.773949i	$-0.281721\pi$
$283$	−2.36694	−	2.36694i	−0.140700	−	0.140700i	−0.773949	+	0.633249i	$0.781721\pi$
$284$	4.32117	−	6.94389i	0.256414	−	0.412044i
$285$		0			0
$286$	2.13762	+	0.610812i	0.126400	+	0.0361180i
$287$			11.5356i			0.680925i
$288$	0.843689	+	4.65858i	0.0497148	+	0.274509i
$289$	−25.3736			−1.49257
$290$		0			0
$291$	−18.8767	−	18.8767i	−1.10657	−	1.10657i
$292$	−4.13986	−	2.57623i	−0.242267	−	0.150762i
$293$	19.1812	+	19.1812i	1.12058	+	1.12058i	0.991655	+	0.128922i	$0.0411517\pi$
$293$	19.1812	+	19.1812i	1.12058	+	1.12058i	0.128922	+	0.991655i	$0.458848\pi$
$294$	−4.80782	−	8.65463i	−0.280398	−	0.504749i
$295$		0			0
$296$	−7.80240	−	0.387177i	−0.453505	−	0.0225042i
$297$	−3.37786			−0.196003
$298$	−15.3914	−	27.7063i	−0.891601	−	1.60498i
$299$	13.3576	−	13.3576i	0.772491	−	0.772491i
$300$		0			0
$301$	−9.18335	−	9.18335i	−0.529320	−	0.529320i
$302$	15.6805	+	4.48060i	0.902311	+	0.257829i
$303$		−	2.16390i		−	0.124313i
$304$	−3.20148	+	9.41086i	−0.183618	+	0.539750i
$305$		0			0
$306$	−2.11681	+	7.40809i	−0.121010	+	0.423492i
$307$	−19.9292	+	19.9292i	−1.13742	+	1.13742i	−0.148507	+	0.988911i	$0.547447\pi$
$307$	−19.9292	+	19.9292i	−1.13742	+	1.13742i	−0.988911	+	0.148507i	$0.952553\pi$
$308$	1.74510	−	0.406292i	0.0994360	−	0.0231506i
$309$	0.993449	−	0.993449i	0.0565153	−	0.0565153i
$310$		0			0
$311$			5.73314i			0.325096i	0.986701	+	0.162548i	$0.0519713\pi$
$311$			5.73314i			0.325096i	−0.986701	+	0.162548i	$0.948029\pi$
$312$	7.33271	+	8.09845i	0.415133	+	0.458484i
$313$	−0.212621			−0.0120180			−0.00600902	−	0.999982i	$-0.501913\pi$
$313$	−0.212621			−0.0120180			−0.00600902	+	0.999982i	$0.501913\pi$
$314$	−5.26306	−	9.47411i	−0.297011	−	0.534655i
$315$		0			0
$316$	19.8201	+	12.3340i	1.11497	+	0.693842i
$317$	3.21582	−	3.21582i	0.180618	−	0.180618i	−0.611007	−	0.791625i	$-0.709235\pi$
$317$	3.21582	−	3.21582i	0.180618	−	0.180618i	0.791625	+	0.611007i	$0.209235\pi$
$318$	4.27834	−	14.9726i	0.239917	−	0.839624i
$319$	5.56919			0.311815
$320$		0			0
$321$	−14.9811			−0.836164
$322$	4.18297	−	14.6389i	0.233108	−	0.815793i
$323$	−11.4388	+	11.4388i	−0.636473	+	0.636473i
$324$	−9.82968	−	6.11698i	−0.546093	−	0.339832i
$325$		0			0
$326$	−6.28671	−	11.3168i	−0.348188	−	0.626779i
$327$	−11.8101			−0.653097
$328$	14.6320	+	16.1599i	0.807915	+	0.892284i
$329$			9.96006i			0.549116i
$330$		0			0
$331$	22.0295	−	22.0295i	1.21085	−	1.21085i	0.240106	−	0.970747i	$-0.422818\pi$
$331$	22.0295	−	22.0295i	1.21085	−	1.21085i	0.970747	−	0.240106i	$-0.0771824\pi$
$332$	−7.75295	+	1.80504i	−0.425498	+	0.0990643i
$333$	−1.63451	+	1.63451i	−0.0895708	+	0.0895708i
$334$	3.22394	−	11.2826i	0.176406	−	0.617359i
$335$		0			0
$336$	8.33577	+	2.83575i	0.454754	+	0.154703i
$337$		−	11.2122i		−	0.610767i	−0.952229	−	0.305384i	$-0.901215\pi$
$337$		−	11.2122i		−	0.610767i	0.952229	−	0.305384i	$-0.0987847\pi$
$338$	8.29851	+	2.37125i	0.451379	+	0.128979i
$339$	2.02535	+	2.02535i	0.110002	+	0.110002i
$340$		0			0
$341$	−2.85807	+	2.85807i	−0.154773	+	0.154773i
$342$	1.42839	+	2.57126i	0.0772383	+	0.139038i
$343$	17.6009			0.950359
$344$	−24.5131	−	1.21641i	−1.32166	−	0.0655844i
$345$		0			0
$346$	−11.5986	−	20.8787i	−0.623542	−	1.12245i
$347$	1.23653	+	1.23653i	0.0663803	+	0.0663803i	0.739518	−	0.673137i	$-0.235054\pi$
$347$	1.23653	+	1.23653i	0.0663803	+	0.0663803i	−0.673137	+	0.739518i	$0.735054\pi$
$348$	23.2358	+	14.4596i	1.24557	+	0.775115i
$349$	5.61778	+	5.61778i	0.300713	+	0.300713i	0.841293	−	0.540580i	$-0.181795\pi$
$349$	5.61778	+	5.61778i	0.300713	+	0.300713i	−0.540580	+	0.841293i	$0.681795\pi$
$350$		0			0
$351$	14.8203			0.791047
$352$	1.92931	−	2.78268i	0.102833	−	0.148317i
$353$		−	0.748709i		−	0.0398497i	−0.999801	−	0.0199249i	$-0.993657\pi$
$353$		−	0.748709i		−	0.0398497i	0.999801	−	0.0199249i	$-0.00634270\pi$
$354$	−16.7389	−	4.78304i	−0.889663	−	0.254216i
$355$		0			0
$356$	−11.1527	+	17.9219i	−0.591093	+	0.949856i
$357$	10.1321	+	10.1321i	0.536246	+	0.536246i
$358$	19.0049	−	10.5576i	1.00444	−	0.557987i
$359$		−	2.69883i		−	0.142439i	−0.997461	−	0.0712195i	$-0.977311\pi$
$359$		−	2.69883i		−	0.142439i	0.997461	−	0.0712195i	$-0.0226891\pi$
$360$		0			0
$361$		−	12.8241i		−	0.674955i
$362$	3.97628	+	7.15776i	0.208989	+	0.376204i
$363$	−11.0671	−	11.0671i	−0.580870	−	0.580870i
$364$	−7.65656	+	1.78260i	−0.401313	+	0.0934335i
$365$		0			0
$366$	1.16122	−	4.06384i	0.0606978	−	0.212420i
$367$			20.6101i			1.07584i	0.842996	+	0.537920i	$0.180790\pi$
$367$			20.6101i			1.07584i	−0.842996	+	0.537920i	$0.819210\pi$
$368$	−12.7084	−	25.8130i	−0.662472	−	1.34560i
$369$	6.45056			0.335802
$370$		0			0
$371$	7.92329	+	7.92329i	0.411357	+	0.411357i
$372$	−19.3450	+	4.50390i	−1.00299	+	0.233516i
$373$	−5.24143	−	5.24143i	−0.271391	−	0.271391i	0.558269	−	0.829660i	$-0.311466\pi$
$373$	−5.24143	−	5.24143i	−0.271391	−	0.271391i	−0.829660	+	0.558269i	$0.811466\pi$
$374$	4.81705	−	2.67597i	0.249084	−	0.138371i
$375$		0			0
$376$	12.6335	+	13.9528i	0.651524	+	0.719561i
$377$	−24.4347			−1.25845
$378$	10.4414	−	5.80042i	0.537049	−	0.298341i
$379$	−5.41344	+	5.41344i	−0.278070	+	0.278070i	−0.832338	−	0.554268i	$-0.812998\pi$
$379$	−5.41344	+	5.41344i	−0.278070	+	0.278070i	0.554268	+	0.832338i	$0.312998\pi$
$380$		0			0
$381$	1.37064	+	1.37064i	0.0702199	+	0.0702199i
$382$	7.48125	−	26.1817i	0.382774	−	1.33957i
$383$		−	29.5087i		−	1.50782i	−0.656975	−	0.753912i	$-0.728164\pi$
$383$		−	29.5087i		−	1.50782i	0.656975	−	0.753912i	$-0.271836\pi$
$384$	15.2743	−	6.60071i	0.779463	−	0.336841i
$385$		0			0
$386$	33.7435	+	9.64199i	1.71750	+	0.490764i
$387$	−5.13521	+	5.13521i	−0.261037	+	0.261037i
$388$	19.1803	−	30.8218i	0.973732	−	1.56474i
$389$	−1.37884	+	1.37884i	−0.0699099	+	0.0699099i	−0.741197	−	0.671287i	$-0.765742\pi$
$389$	−1.37884	+	1.37884i	−0.0699099	+	0.0699099i	0.671287	+	0.741197i	$0.265742\pi$
$390$		0			0
$391$		−	46.8225i		−	2.36792i
$392$	9.98001	−	9.03636i	0.504067	−	0.456405i
$393$	−2.14287			−0.108094
$394$	−4.91850	+	2.73232i	−0.247790	+	0.137652i
$395$		0			0
$396$	−0.227193	−	0.975834i	−0.0114169	−	0.0490375i
$397$	−21.9750	+	21.9750i	−1.10289	+	1.10289i	−0.108832	+	0.994060i	$0.534711\pi$
$397$	−21.9750	+	21.9750i	−1.10289	+	1.10289i	−0.994060	+	0.108832i	$0.965289\pi$
$398$	−28.8539	−	8.24482i	−1.44632	−	0.413275i
$399$	5.47033			0.273859
$400$		0			0
$401$	−31.4584			−1.57096			−0.785479	−	0.618889i	$-0.787583\pi$
$401$	−31.4584			−1.57096			−0.785479	+	0.618889i	$0.787583\pi$
$402$	17.9770	+	5.13680i	0.896609	+	0.256200i
$403$	12.5397	−	12.5397i	0.624648	−	0.624648i
$404$	2.86595	−	0.667248i	0.142586	−	0.0331968i
$405$		0			0
$406$	−17.2151	+	9.56335i	−0.854372	+	0.474621i
$407$	1.65325			0.0819487
$408$	27.0455	+	1.34207i	1.33895	+	0.0664426i
$409$		−	12.8017i		−	0.633003i	−0.948592	−	0.316502i	$-0.897492\pi$
$409$		−	12.8017i		−	0.633003i	0.948592	−	0.316502i	$-0.102508\pi$
$410$		0			0
$411$	−3.90570	+	3.90570i	−0.192654	+	0.192654i
$412$	1.62210	+	1.00943i	0.0799150	+	0.0497309i
$413$	8.85797	−	8.85797i	0.435872	−	0.435872i
$414$	−8.18588	−	2.33906i	−0.402314	−	0.114959i
$415$		0			0
$416$	−8.46482	+	12.2089i	−0.415022	+	0.598592i
$417$		−	26.9322i		−	1.31888i
$418$	0.577988	−	2.02275i	0.0282703	−	0.0989360i
$419$	11.4979	+	11.4979i	0.561709	+	0.561709i	0.929793	−	0.368084i	$-0.119986\pi$
$419$	11.4979	+	11.4979i	0.561709	+	0.561709i	−0.368084	+	0.929793i	$0.619986\pi$
$420$		0			0
$421$	12.5714	−	12.5714i	0.612690	−	0.612690i	−0.330956	−	0.943646i	$-0.607371\pi$
$421$	12.5714	−	12.5714i	0.612690	−	0.612690i	0.943646	+	0.330956i	$0.107371\pi$
$422$	27.2243	−	15.1236i	1.32526	−	0.736208i
$423$	5.56953			0.270800
$424$	21.1496	+	1.04950i	1.02711	+	0.0509684i
$425$		0			0
$426$	−7.43529	+	4.13045i	−0.360241	+	0.200121i
$427$	2.15052	+	2.15052i	0.104071	+	0.104071i
$428$	−4.61950	−	19.8415i	−0.223292	−	0.959077i
$429$	−1.63486	−	1.63486i	−0.0789316	−	0.0789316i
$430$		0			0
$431$	−15.2579			−0.734946			−0.367473	−	0.930034i	$-0.619777\pi$
$431$	−15.2579			−0.734946			−0.367473	+	0.930034i	$0.619777\pi$
$432$	7.26978	−	21.3698i	0.349768	−	1.02815i
$433$		−	12.1705i		−	0.584877i	−0.956284	−	0.292439i	$-0.905533\pi$
$433$		−	12.1705i		−	0.584877i	0.956284	−	0.292439i	$-0.0944667\pi$
$434$	3.92684	−	13.7425i	0.188495	−	0.659663i
$435$		0			0
$436$	−3.64169	−	15.6417i	−0.174405	−	0.749101i
$437$	−12.6398	−	12.6398i	−0.604644	−	0.604644i
$438$	2.46252	+	4.43283i	0.117664	+	0.211809i
$439$			39.7535i			1.89733i	0.316283	+	0.948665i	$0.397565\pi$
$439$			39.7535i			1.89733i	−0.316283	+	0.948665i	$0.602435\pi$
$440$		0			0
$441$		−	3.98371i		−	0.189701i
$442$	−21.1347	+	11.7407i	−1.00527	+	0.558450i
$443$	3.62318	+	3.62318i	0.172142	+	0.172142i	0.787920	−	0.615778i	$-0.211158\pi$
$443$	3.62318	+	3.62318i	0.172142	+	0.172142i	−0.615778	+	0.787920i	$0.711158\pi$
$444$	6.89771	+	4.29243i	0.327351	+	0.203710i
$445$		0			0
$446$	10.7257	+	3.06481i	0.507878	+	0.145123i
$447$			32.9612i			1.55901i
$448$	−1.18540	+	11.9146i	−0.0560047	+	0.562913i
$449$	5.38425			0.254098			0.127049	−	0.991896i	$-0.459449\pi$
$449$	5.38425			0.254098			0.127049	+	0.991896i	$0.459449\pi$
$450$		0			0
$451$	−3.26225	−	3.26225i	−0.153614	−	0.153614i
$452$	−2.05792	+	3.30697i	−0.0967964	+	0.155547i
$453$	−11.9925	−	11.9925i	−0.563455	−	0.563455i
$454$	−5.81615	−	10.4697i	−0.272965	−	0.491369i
$455$		0			0
$456$	7.66326	−	6.93867i	0.358865	−	0.324933i
$457$	14.3039			0.669108			0.334554	−	0.942377i	$-0.391414\pi$
$457$	14.3039			0.669108			0.334554	+	0.942377i	$0.391414\pi$
$458$	18.8988	+	34.0199i	0.883081	+	1.58965i
$459$	25.9748	−	25.9748i	1.21240	−	1.21240i
$460$		0			0
$461$	−4.50363	−	4.50363i	−0.209755	−	0.209755i	0.594408	−	0.804163i	$-0.297386\pi$
$461$	−4.50363	−	4.50363i	−0.209755	−	0.209755i	−0.804163	+	0.594408i	$0.797386\pi$
$462$	−1.79167	−	0.511960i	−0.0833563	−	0.0238185i
$463$			19.3500i			0.899271i	0.893212	+	0.449636i	$0.148446\pi$
$463$			19.3500i			0.899271i	−0.893212	+	0.449636i	$0.851554\pi$
$464$	−11.9859	+	35.2330i	−0.556433	+	1.63565i
$465$		0			0
$466$	−1.04410	+	3.65399i	−0.0483672	+	0.169268i
$467$	−17.1773	+	17.1773i	−0.794871	+	0.794871i	−0.982282	−	0.187410i	$-0.939991\pi$
$467$	−17.1773	+	17.1773i	−0.794871	+	0.794871i	0.187410	+	0.982282i	$0.439991\pi$
$468$	0.996805	+	4.28145i	0.0460773	+	0.197910i
$469$	−9.51312	+	9.51312i	−0.439275	+	0.439275i
$470$		0			0
$471$			11.2710i			0.519341i
$472$	1.17331	−	23.6445i	0.0540060	−	1.08833i
$473$	5.19408			0.238824
$474$	−11.7897	−	21.2227i	−0.541517	−	0.974792i
$475$		0			0
$476$	−10.2950	+	16.5436i	−0.471872	+	0.758273i
$477$	4.43060	−	4.43060i	0.202863	−	0.202863i
$478$	4.90968	−	17.1821i	0.224564	−	0.785892i
$479$	−5.54474			−0.253346			−0.126673	−	0.991945i	$-0.540430\pi$
$479$	−5.54474			−0.253346			−0.126673	+	0.991945i	$0.540430\pi$
$480$		0			0
$481$	−7.25361			−0.330736
$482$	2.92701	−	10.2435i	0.133322	−	0.466578i
$483$	−11.1959	+	11.1959i	−0.509429	+	0.509429i
$484$	11.2450	−	18.0702i	0.511138	−	0.821373i
$485$		0			0
$486$	−5.77955	−	10.4039i	−0.262166	−	0.471928i
$487$	31.7138			1.43709			0.718546	−	0.695480i	$-0.244808\pi$
$487$	31.7138			1.43709			0.718546	+	0.695480i	$0.244808\pi$
$488$	5.74037	+	0.284854i	0.259855	+	0.0128947i
$489$			13.4632i			0.608827i
$490$		0			0
$491$	7.39419	−	7.39419i	0.333695	−	0.333695i	−0.520293	−	0.853988i	$-0.674177\pi$
$491$	7.39419	−	7.39419i	0.333695	−	0.333695i	0.853988	+	0.520293i	$0.174177\pi$
$492$	−5.14083	−	22.0808i	−0.231767	−	0.995477i
$493$	−42.8255	+	42.8255i	−1.92876	+	1.92876i
$494$	−2.53591	+	8.87477i	−0.114096	+	0.399295i
$495$		0			0
$496$	−11.9303	−	24.2325i	−0.535685	−	1.08807i
$497$		−	6.12041i		−	0.274538i
$498$	7.95988	+	2.27449i	0.356691	+	0.101922i
$499$	−14.0103	−	14.0103i	−0.627189	−	0.627189i	0.320171	−	0.947360i	$-0.396260\pi$
$499$	−14.0103	−	14.0103i	−0.627189	−	0.627189i	−0.947360	+	0.320171i	$0.896260\pi$
$500$		0			0
$501$	−8.62899	+	8.62899i	−0.385515	+	0.385515i
$502$	9.67046	+	17.4079i	0.431614	+	0.776954i
$503$	−8.43795			−0.376230			−0.188115	−	0.982147i	$-0.560238\pi$
$503$	−8.43795			−0.376230			−0.188115	+	0.982147i	$0.560238\pi$
$504$	2.37798	+	2.62631i	0.105924	+	0.116985i
$505$		0			0
$506$	2.95692	+	5.32280i	0.131451	+	0.236627i
$507$	−6.34671	−	6.34671i	−0.281868	−	0.281868i
$508$	−1.39268	+	2.23797i	−0.0617902	+	0.0992937i
$509$	−2.09367	−	2.09367i	−0.0928004	−	0.0928004i	0.659183	−	0.751983i	$-0.270902\pi$
$509$	−2.09367	−	2.09367i	−0.0928004	−	0.0928004i	−0.751983	+	0.659183i	$0.770902\pi$
$510$		0			0
$511$	−3.64891			−0.161418
$512$	13.4521	+	18.1945i	0.594506	+	0.804091i
$513$		−	14.0239i		−	0.619169i
$514$	6.14122	+	1.75481i	0.270878	+	0.0774016i
$515$		0			0
$516$	21.6708	+	13.4857i	0.954003	+	0.593674i
$517$	−2.81669	−	2.81669i	−0.123878	−	0.123878i
$518$	−5.11043	+	2.83895i	−0.224540	+	0.124736i
$519$			24.8387i			1.09030i
$520$		0			0
$521$		−	28.2558i		−	1.23791i	−0.785428	−	0.618954i	$-0.787557\pi$
$521$		−	28.2558i		−	1.23791i	0.785428	−	0.618954i	$-0.212443\pi$
$522$	5.34770	+	9.62647i	0.234062	+	0.421339i
$523$	10.1929	+	10.1929i	0.445703	+	0.445703i	0.893923	−	0.448220i	$-0.147942\pi$
$523$	10.1929	+	10.1929i	0.445703	+	0.445703i	−0.448220	+	0.893923i	$0.647942\pi$
$524$	−0.660765	−	2.83810i	−0.0288657	−	0.123983i
$525$		0			0
$526$	−7.85368	+	27.4851i	−0.342437	+	1.19841i
$527$		−	43.9555i		−	1.91473i
$528$	−3.15929	+	1.55540i	−0.137491	+	0.0676901i
$529$	28.7385			1.24950
$530$		0			0
$531$	−4.95326	−	4.95326i	−0.214953	−	0.214953i
$532$	1.68681	+	7.24512i	0.0731323	+	0.314116i
$533$	14.3131	+	14.3131i	0.619967	+	0.619967i
$534$	19.1901	−	10.6605i	0.830438	−	0.461325i
$535$		0			0
$536$	−1.26009	+	25.3933i	−0.0544276	+	1.09682i
$537$	−22.6095			−0.975671
$538$	−29.6222	+	16.4557i	−1.27710	+	0.709457i
$539$	−2.01469	+	2.01469i	−0.0867790	+	0.0867790i
$540$		0			0
$541$	3.86053	+	3.86053i	0.165977	+	0.165977i	0.785209	−	0.619231i	$-0.212556\pi$
$541$	3.86053	+	3.86053i	0.165977	+	0.165977i	−0.619231	+	0.785209i	$0.712556\pi$
$542$	−1.41453	+	4.95036i	−0.0607595	+	0.212636i
$543$		−	8.51534i		−	0.365428i
$544$	6.56211	+	36.2339i	0.281348	+	1.55352i
$545$		0			0
$546$	7.86093	+	2.24621i	0.336417	+	0.0961289i
$547$	20.6231	−	20.6231i	0.881781	−	0.881781i	−0.111935	−	0.993716i	$-0.535705\pi$
$547$	20.6231	−	20.6231i	0.881781	−	0.881781i	0.993716	+	0.111935i	$0.0357048\pi$
$548$	−6.37720	−	3.96852i	−0.272421	−	0.169527i
$549$	1.20254	−	1.20254i	0.0513233	−	0.0513233i
$550$		0			0
$551$			23.1216i			0.985014i
$552$	−1.48298	+	29.8850i	−0.0631199	+	1.27199i
$553$	17.4696			0.742884
$554$	−27.9892	+	15.5486i	−1.18915	+	0.660595i
$555$		0			0
$556$	35.6700	−	8.30468i	1.51275	−	0.352197i
$557$	−1.28512	+	1.28512i	−0.0544523	+	0.0544523i	−0.733809	−	0.679356i	$-0.762259\pi$
$557$	−1.28512	+	1.28512i	−0.0544523	+	0.0544523i	0.679356	+	0.733809i	$0.262259\pi$
$558$	−7.68465	−	2.19584i	−0.325317	−	0.0929573i
$559$	−22.7889			−0.963868
$560$		0			0
$561$	−5.73068			−0.241949
$562$	−7.50409	−	2.14425i	−0.316541	−	0.0904496i
$563$	−21.9152	+	21.9152i	−0.923615	+	0.923615i	−0.997283	−	0.0736677i	$-0.976530\pi$
$563$	−21.9152	+	21.9152i	−0.923615	+	0.923615i	0.0736677	+	0.997283i	$0.476530\pi$
$564$	−4.43869	−	19.0650i	−0.186903	−	0.802779i
$565$		0			0
$566$	−4.13822	+	2.29886i	−0.173942	+	0.0966284i
$567$	−8.66397			−0.363852
$568$	−7.76324	−	8.57394i	−0.325738	−	0.359754i
$569$		−	35.6668i		−	1.49523i	−0.664132	−	0.747615i	$-0.731199\pi$
$569$		−	35.6668i		−	1.49523i	0.664132	−	0.747615i	$-0.268801\pi$
$570$		0			0
$571$	5.60524	−	5.60524i	0.234572	−	0.234572i	−0.580026	−	0.814598i	$-0.696958\pi$
$571$	5.60524	−	5.60524i	0.234572	−	0.234572i	0.814598	+	0.580026i	$0.196958\pi$
$572$	1.66115	−	2.66938i	0.0694562	−	0.111613i
$573$	−20.0238	+	20.0238i	−0.836507	+	0.836507i
$574$	15.6860	+	4.48217i	0.654720	+	0.187082i
$575$		0			0
$576$	6.66251	+	0.662858i	0.277604	+	0.0276191i
$577$			2.43681i			0.101446i	0.998713	+	0.0507230i	$0.0161526\pi$
$577$			2.43681i			0.101446i	−0.998713	+	0.0507230i	$0.983847\pi$
$578$	−9.85896	+	34.5028i	−0.410079	+	1.43513i
$579$	−25.8071	−	25.8071i	−1.07251	−	1.07251i
$580$		0			0
$581$	−4.21225	+	4.21225i	−0.174753	+	0.174753i
$582$	−33.0029	+	18.3338i	−1.36802	+	0.759960i
$583$	−4.48139			−0.185600
$584$	−5.11167	+	4.62835i	−0.211523	+	0.191522i
$585$		0			0
$586$	33.5353	−	18.6295i	1.38533	−	0.769578i
$587$	−0.415982	−	0.415982i	−0.0171694	−	0.0171694i	0.698470	−	0.715639i	$-0.253865\pi$
$587$	−0.415982	−	0.415982i	−0.0171694	−	0.0171694i	−0.715639	+	0.698470i	$0.753865\pi$
$588$	−13.6366	+	3.17486i	−0.562363	+	0.130929i
$589$	−11.8659	−	11.8659i	−0.488924	−	0.488924i
$590$		0			0
$591$	5.85136			0.240693
$592$	−3.55811	+	10.4592i	−0.146237	+	0.429870i
$593$		−	15.3439i		−	0.630098i	−0.949075	−	0.315049i	$-0.897979\pi$
$593$		−	15.3439i		−	0.630098i	0.949075	−	0.315049i	$-0.102021\pi$
$594$	−1.31247	+	4.59318i	−0.0538513	+	0.188460i
$595$		0			0
$596$	−43.6551	+	10.1638i	−1.78818	+	0.416324i
$597$	22.0675	+	22.0675i	0.903163	+	0.903163i
$598$	−12.9734	−	23.3537i	−0.530523	−	0.955002i
$599$			43.3487i			1.77118i	0.464468	+	0.885590i	$0.346246\pi$
$599$			43.3487i			1.77118i	−0.464468	+	0.885590i	$0.653754\pi$
$600$		0			0
$601$			38.7291i			1.57979i	0.613239	+	0.789897i	$0.289866\pi$
$601$			38.7291i			1.57979i	−0.613239	+	0.789897i	$0.710134\pi$
$602$	−16.0556	+	8.91923i	−0.654379	+	0.363520i
$603$	5.31961	+	5.31961i	0.216631	+	0.216631i
$604$	12.1853	−	19.5812i	0.495815	−	0.796748i
$605$		0			0
$606$	−2.94244	−	0.840784i	−0.119529	−	0.0341545i
$607$			34.9068i			1.41682i	0.705800	+	0.708412i	$0.250588\pi$
$607$			34.9068i			1.41682i	−0.705800	+	0.708412i	$0.749412\pi$
$608$	11.5528	+	8.00994i	0.468530	+	0.324846i
$609$	20.4802			0.829901
$610$		0			0
$611$	12.3582	+	12.3582i	0.499958	+	0.499958i
$612$	9.25095	+	5.75684i	0.373947	+	0.232707i
$613$	−0.151779	−	0.151779i	−0.00613031	−	0.00613031i	0.704035	−	0.710165i	$-0.251380\pi$
$613$	−0.151779	−	0.151779i	−0.00613031	−	0.00613031i	−0.710165	+	0.704035i	$0.751380\pi$
$614$	19.3560	+	34.8430i	0.781144	+	1.40615i
$615$		0			0
$616$	0.125587	−	2.53083i	0.00506004	−	0.101970i
$617$	−0.288199			−0.0116025			−0.00580123	−	0.999983i	$-0.501847\pi$
$617$	−0.288199			−0.0116025			−0.00580123	+	0.999983i	$0.501847\pi$
$618$	−0.964876	−	1.73689i	−0.0388130	−	0.0698679i
$619$	11.5307	−	11.5307i	0.463460	−	0.463460i	−0.436328	−	0.899788i	$-0.643721\pi$
$619$	11.5307	−	11.5307i	0.463460	−	0.463460i	0.899788	+	0.436328i	$0.143721\pi$
$620$		0			0
$621$	28.7019	+	28.7019i	1.15177	+	1.15177i
$622$	7.79586	+	2.22762i	0.312585	+	0.0893193i
$623$			15.7965i			0.632873i
$624$	13.8613	−	6.82428i	0.554897	−	0.273190i
$625$		0			0
$626$	−0.0826141	+	0.289120i	−0.00330192	+	0.0115555i
$627$	−1.54700	+	1.54700i	−0.0617814	+	0.0617814i
$628$	−14.9278	+	3.47547i	−0.595682	+	0.138686i
$629$	−12.7131	+	12.7131i	−0.506903	+	0.506903i
$630$		0			0
$631$		−	14.2062i		−	0.565541i	−0.959188	−	0.282771i	$-0.908746\pi$
$631$		−	14.2062i		−	0.565541i	0.959188	−	0.282771i	$-0.0912536\pi$
$632$	24.4728	−	22.1588i	0.973475	−	0.881430i
$633$	−32.3878			−1.28730
$634$	−3.12332	−	5.62234i	−0.124043	−	0.223292i
$635$		0			0
$636$	−18.6973	−	11.6353i	−0.741396	−	0.461369i
$637$	8.83942	−	8.83942i	0.350230	−	0.350230i
$638$	2.16391	−	7.57292i	0.0856702	−	0.299815i
$639$	−3.42245			−0.135390
$640$		0			0
$641$	19.7372			0.779572			0.389786	−	0.920905i	$-0.372549\pi$
$641$	19.7372			0.779572			0.389786	+	0.920905i	$0.372549\pi$
$642$	−5.82093	+	20.3712i	−0.229734	+	0.803985i
$643$	5.80043	−	5.80043i	0.228747	−	0.228747i	−0.583422	−	0.812169i	$-0.698287\pi$
$643$	5.80043	−	5.80043i	0.228747	−	0.228747i	0.812169	+	0.583422i	$0.198287\pi$
$644$	−18.2805	−	11.3759i	−0.720353	−	0.448274i
$645$		0			0
$646$	11.1098	+	19.9990i	0.437110	+	0.786849i
$647$	46.3186			1.82097			0.910485	−	0.413541i	$-0.135708\pi$
$647$	46.3186			1.82097			0.910485	+	0.413541i	$0.135708\pi$
$648$	−12.1371	+	10.9895i	−0.476792	+	0.431710i
$649$			5.01005i			0.196662i
$650$		0			0
$651$	−10.5103	+	10.5103i	−0.411932	+	0.411932i
$652$	−17.8312	+	4.15144i	−0.698322	+	0.162583i
$653$	4.42354	−	4.42354i	0.173106	−	0.173106i	−0.615236	−	0.788343i	$-0.710939\pi$
$653$	4.42354	−	4.42354i	0.173106	−	0.173106i	0.788343	+	0.615236i	$0.210939\pi$
$654$	−4.58881	+	16.0592i	−0.179437	+	0.627964i
$655$		0			0
$656$	27.6594	−	13.6174i	1.07992	−	0.531671i
$657$			2.04042i			0.0796045i
$658$	13.5436	+	3.86999i	0.527984	+	0.150868i
$659$	15.2461	+	15.2461i	0.593905	+	0.593905i	0.938684	−	0.344779i	$-0.112046\pi$
$659$	15.2461	+	15.2461i	0.593905	+	0.593905i	−0.344779	+	0.938684i	$0.612046\pi$
$660$		0			0
$661$	19.1271	−	19.1271i	0.743958	−	0.743958i	−0.229379	−	0.973337i	$-0.573670\pi$
$661$	19.1271	−	19.1271i	0.743958	−	0.743958i	0.973337	+	0.229379i	$0.0736696\pi$
$662$	−21.3959	−	38.5151i	−0.831577	−	1.49693i
$663$	25.1432			0.976481
$664$	−0.557946	+	11.2437i	−0.0216525	+	0.436341i
$665$		0			0
$666$	1.58750	+	2.85769i	0.0615145	+	0.110733i
$667$	−47.3218	−	47.3218i	−1.83231	−	1.83231i
$668$	−14.0894	−	8.76777i	−0.545133	−	0.339235i
$669$	−8.20306	−	8.20306i	−0.317149	−	0.317149i
$670$		0			0
$671$	−1.21633			−0.0469559
$672$	7.09490	−	10.2331i	0.273692	−	0.394749i
$673$		−	18.5586i		−	0.715382i	−0.933840	−	0.357691i	$-0.883564\pi$
$673$		−	18.5586i		−	0.715382i	0.933840	−	0.357691i	$-0.116436\pi$
$674$	−15.2462	−	4.35651i	−0.587263	−	0.167807i
$675$		0			0
$676$	6.44879	−	10.3629i	0.248030	−	0.398572i
$677$	2.71844	+	2.71844i	0.104478	+	0.104478i	0.757414	−	0.652935i	$-0.226463\pi$
$677$	2.71844	+	2.71844i	0.104478	+	0.104478i	−0.652935	+	0.757414i	$0.726463\pi$
$678$	3.54100	−	1.96709i	0.135991	−	0.0755458i
$679$		−	27.1666i		−	1.04256i
$680$		0			0
$681$			12.4555i			0.477295i
$682$	2.77587	+	4.99688i	0.106293	+	0.191340i
$683$	−12.6646	−	12.6646i	−0.484598	−	0.484598i	0.421999	−	0.906596i	$-0.361329\pi$
$683$	−12.6646	−	12.6646i	−0.484598	−	0.484598i	−0.906596	+	0.421999i	$0.861329\pi$
$684$	4.05138	−	0.943239i	0.154908	−	0.0360657i
$685$		0			0
$686$	6.83885	−	23.9335i	0.261108	−	0.913786i
$687$		−	40.4723i		−	1.54412i
$688$	−11.1786	+	32.8600i	−0.426182	+	1.25278i
$689$	19.6620			0.749063
$690$		0			0
$691$	26.8892	+	26.8892i	1.02291	+	1.02291i	0.999731	+	0.0231826i	$0.00737991\pi$
$691$	26.8892	+	26.8892i	1.02291	+	1.02291i	0.0231826	+	0.999731i	$0.492620\pi$
$692$	−32.8973	+	7.65914i	−1.25057	+	0.291157i
$693$	−0.530180	−	0.530180i	−0.0201399	−	0.0201399i
$694$	2.16187	−	1.20096i	0.0820636	−	0.0455880i
$695$		0			0
$696$	28.6903	−	25.9775i	1.08750	−	0.984675i
$697$	50.1717			1.90039
$698$	9.82180	−	5.45621i	0.371761	−	0.206521i
$699$	2.79458	−	2.79458i	0.105701	−	0.105701i
$700$		0			0
$701$	25.3725	+	25.3725i	0.958305	+	0.958305i	0.999165	−	0.0408602i	$-0.0130098\pi$
$701$	25.3725	+	25.3725i	0.958305	+	0.958305i	−0.0408602	+	0.999165i	$0.513010\pi$
$702$	5.75843	−	20.1524i	0.217338	−	0.760605i
$703$			6.86382i			0.258874i
$704$	−3.03422	−	3.70467i	−0.114356	−	0.139625i
$705$		0			0
$706$	−1.01809	−	0.290912i	−0.0383162	−	0.0109486i
$707$	1.55709	−	1.55709i	0.0585606	−	0.0585606i
$708$	−13.0079	+	20.9029i	−0.488865	+	0.785581i
$709$	−16.1117	+	16.1117i	−0.605089	+	0.605089i	−0.941659	−	0.336570i	$-0.890733\pi$
$709$	−16.1117	+	16.1117i	−0.605089	+	0.605089i	0.336570	+	0.941659i	$0.390733\pi$
$710$		0			0
$711$		−	9.76879i		−	0.366358i
$712$	20.0365	+	22.1289i	0.750901	+	0.829316i
$713$	48.5705			1.81898
$714$	17.7143	−	9.84066i	0.662941	−	0.368277i
$715$		0			0
$716$	−6.97175	−	29.9449i	−0.260546	−	1.11909i
$717$	−13.1409	+	13.1409i	−0.490757	+	0.490757i
$718$	−3.66985	−	1.04864i	−0.136958	−	0.0391347i
$719$	−29.1676			−1.08777			−0.543884	−	0.839160i	$-0.683047\pi$
$719$	−29.1676			−1.08777			−0.543884	+	0.839160i	$0.683047\pi$
$720$		0			0
$721$	1.42973			0.0532460
$722$	−17.4381	−	4.98284i	−0.648980	−	0.185442i
$723$	−7.83424	+	7.83424i	−0.291358	+	0.291358i
$724$	11.2780	−	2.62575i	0.419145	−	0.0975852i
$725$		0			0
$726$	−19.3490	+	10.7487i	−0.718108	+	0.398923i
$727$	−4.13463			−0.153345			−0.0766724	−	0.997056i	$-0.524430\pi$
$727$	−4.13463			−0.153345			−0.0766724	+	0.997056i	$0.524430\pi$
$728$	−0.551010	+	11.1039i	−0.0204218	+	0.411540i
$729$			29.7434i			1.10161i
$730$		0			0
$731$	−39.9411	+	39.9411i	−1.47727	+	1.47727i
$732$	−5.07478	−	3.15802i	−0.187569	−	0.116724i
$733$	19.3838	−	19.3838i	0.715957	−	0.715957i	−0.251817	−	0.967775i	$-0.581028\pi$
$733$	19.3838	−	19.3838i	0.715957	−	0.715957i	0.967775	+	0.251817i	$0.0810282\pi$
$734$	28.0255	+	8.00809i	1.03444	+	0.295584i
$735$		0			0
$736$	−40.0382	+	7.25108i	−1.47583	+	0.267278i
$737$		−	5.38060i		−	0.198197i
$738$	2.50637	−	8.77140i	0.0922608	−	0.322880i
$739$	−23.9820	−	23.9820i	−0.882194	−	0.882194i	0.111564	−	0.993757i	$-0.464414\pi$
$739$	−23.9820	−	23.9820i	−0.882194	−	0.882194i	−0.993757	+	0.111564i	$0.964414\pi$
$740$		0			0
$741$	6.78744	−	6.78744i	0.249343	−	0.249343i
$742$	13.8526	−	7.69540i	0.508545	−	0.282507i
$743$	10.3473			0.379604			0.189802	−	0.981822i	$-0.439215\pi$
$743$	10.3473			0.379604			0.189802	+	0.981822i	$0.439215\pi$
$744$	−1.39218	+	28.0551i	−0.0510397	+	1.02855i
$745$		0			0
$746$	−9.16380	+	5.09068i	−0.335511	+	0.186383i
$747$	2.35543	+	2.35543i	0.0861808	+	0.0861808i
$748$	−1.76708	−	7.58993i	−0.0646109	−	0.277515i
$749$	−10.7801	−	10.7801i	−0.393896	−	0.393896i
$750$		0			0
$751$	−37.0217			−1.35094			−0.675470	−	0.737387i	$-0.736059\pi$
$751$	−37.0217			−1.35094			−0.675470	+	0.737387i	$0.736059\pi$
$752$	23.8817	−	11.7575i	0.870874	−	0.428754i
$753$		−	20.7096i		−	0.754700i
$754$	−9.49412	+	33.2260i	−0.345756	+	1.21002i
$755$		0			0
$756$	−3.83032	−	16.4519i	−0.139308	−	0.598350i
$757$	30.4305	+	30.4305i	1.10601	+	1.10601i	0.993669	+	0.112345i	$0.0358361\pi$
$757$	30.4305	+	30.4305i	1.10601	+	1.10601i	0.112345	+	0.993669i	$0.464164\pi$
$758$	5.25774	+	9.46454i	0.190970	+	0.343768i
$759$		−	6.33235i		−	0.229850i
$760$		0			0
$761$		−	43.1054i		−	1.56257i	−0.624174	−	0.781285i	$-0.714564\pi$
$761$		−	43.1054i		−	1.56257i	0.624174	−	0.781285i	$-0.285436\pi$
$762$	2.39634	−	1.33122i	0.0868103	−	0.0482249i
$763$	−8.49827	−	8.49827i	−0.307658	−	0.307658i
$764$	−32.6948	−	20.3459i	−1.18285	−	0.736088i
$765$		0			0
$766$	−40.1256	−	11.4656i	−1.44980	−	0.414271i
$767$		−	21.9815i		−	0.793705i
$768$	−3.04073	−	23.3345i	−0.109723	−	0.842013i
$769$	31.2507			1.12693			0.563465	−	0.826140i	$-0.309468\pi$
$769$	31.2507			1.12693			0.563465	+	0.826140i	$0.309468\pi$
$770$		0			0
$771$	−4.69682	−	4.69682i	−0.169152	−	0.169152i
$772$	26.2221	−	42.1376i	0.943756	−	1.51657i
$773$	24.4047	+	24.4047i	0.877778	+	0.877778i	0.993304	−	0.115527i	$-0.0368556\pi$
$773$	24.4047	+	24.4047i	0.877778	+	0.877778i	−0.115527	+	0.993304i	$0.536856\pi$
$774$	4.98751	+	8.97810i	0.179272	+	0.322711i
$775$		0			0
$776$	−34.4586	−	38.0570i	−1.23699	−	1.36617i
$777$	6.07970			0.218108
$778$	1.33918	+	2.41068i	0.0480120	+	0.0864271i
$779$	13.5439	−	13.5439i	0.485261	−	0.485261i
$780$		0			0
$781$	1.73085	+	1.73085i	0.0619345	+	0.0619345i
$782$	−63.6688	−	18.1929i	−2.27679	−	0.650579i
$783$		−	52.5036i		−	1.87632i
$784$	−8.40981	−	17.0818i	−0.300350	−	0.610065i
$785$		0			0
$786$	−0.832616	+	2.91386i	−0.0296984	+	0.103934i
$787$	−17.2122	+	17.2122i	−0.613549	+	0.613549i	−0.943869	−	0.330320i	$-0.892843\pi$
$787$	−17.2122	+	17.2122i	−0.613549	+	0.613549i	0.330320	+	0.943869i	$0.392843\pi$
$788$	1.80430	+	7.74977i	0.0642754	+	0.276074i
$789$	21.0206	−	21.0206i	0.748354	−	0.748354i
$790$		0			0
$791$			2.91480i			0.103638i
$792$	−1.41521	−	0.0702266i	−0.0502871	−	0.00249539i
$793$	5.33662			0.189509
$794$	21.3429	+	38.4197i	0.757432	+	1.36347i
$795$		0			0
$796$	−22.4224	+	36.0317i	−0.794742	+	1.27711i
$797$	−20.3220	+	20.3220i	−0.719841	+	0.719841i	−0.968573	−	0.248731i	$-0.919986\pi$
$797$	−20.3220	+	20.3220i	−0.719841	+	0.719841i	0.248731	+	0.968573i	$0.419986\pi$
$798$	2.12551	−	7.43850i	0.0752421	−	0.263320i
$799$	43.3192			1.53252
$800$		0			0
$801$	8.83319			0.312105
$802$	−12.2232	+	42.7768i	−0.431616	+	1.51050i
$803$	1.03191	−	1.03191i	0.0364153	−	0.0364153i
$804$	13.9699	−	22.4490i	0.492682	−	0.791714i
$805$		0			0
$806$	−12.1791	−	21.9237i	−0.428989	−	0.772229i
$807$	35.2405			1.24052
$808$	0.206250	−	4.15634i	0.00725584	−	0.146220i
$809$		−	2.80407i		−	0.0985859i	−0.998784	−	0.0492930i	$-0.984303\pi$
$809$		−	2.80407i		−	0.0985859i	0.998784	−	0.0492930i	$-0.0156968\pi$
$810$		0			0
$811$	−7.29902	+	7.29902i	−0.256303	+	0.256303i	−0.823549	−	0.567246i	$-0.808009\pi$
$811$	−7.29902	+	7.29902i	−0.256303	+	0.256303i	0.567246	+	0.823549i	$0.308009\pi$
$812$	6.31518	+	27.1248i	0.221619	+	0.951894i
$813$	3.78605	−	3.78605i	0.132782	−	0.132782i
$814$	0.642373	−	2.24808i	0.0225152	−	0.0787950i
$815$		0			0
$816$	12.3335	−	36.2547i	0.431759	−	1.26917i
$817$			21.5643i			0.754439i
$818$	−17.4076	−	4.97411i	−0.608643	−	0.173916i
$819$	2.32615	+	2.32615i	0.0812823	+	0.0812823i
$820$		0			0
$821$	−10.0517	+	10.0517i	−0.350806	+	0.350806i	−0.860409	−	0.509603i	$-0.829792\pi$
$821$	−10.0517	+	10.0517i	−0.350806	+	0.350806i	0.509603	+	0.860409i	$0.329792\pi$
$822$	3.79337	+	6.82850i	0.132309	+	0.238171i
$823$	34.2064			1.19236			0.596179	−	0.802851i	$-0.296685\pi$
$823$	34.2064			1.19236			0.596179	+	0.802851i	$0.296685\pi$
$824$	2.00288	−	1.81350i	0.0697735	−	0.0631761i
$825$		0			0
$826$	−8.60320	−	15.4868i	−0.299344	−	0.538853i
$827$	−31.3455	−	31.3455i	−1.08999	−	1.08999i	−0.995529	−	0.0944595i	$-0.969888\pi$
$827$	−31.3455	−	31.3455i	−1.08999	−	1.08999i	−0.0944595	−	0.995529i	$-0.530112\pi$
$828$	−6.36126	+	10.2222i	−0.221069	+	0.355247i
$829$	3.87895	+	3.87895i	0.134722	+	0.134722i	0.771252	−	0.636530i	$-0.219631\pi$
$829$	3.87895	+	3.87895i	0.134722	+	0.134722i	−0.636530	+	0.771252i	$0.719631\pi$
$830$		0			0
$831$	33.2978			1.15509
$832$	13.3125	+	16.2542i	0.461530	+	0.563512i
$833$		−	30.9849i		−	1.07356i
$834$	−36.6221	−	10.4645i	−1.26812	−	0.362357i
$835$		0			0
$836$	−2.52594	−	1.57189i	−0.0873614	−	0.0543648i
$837$	26.9445	+	26.9445i	0.931338	+	0.931338i
$838$	20.1022	−	11.1672i	0.694421	−	0.385765i
$839$			32.9463i			1.13743i	0.822533	+	0.568717i	$0.192560\pi$
$839$			32.9463i			1.13743i	−0.822533	+	0.568717i	$0.807440\pi$
$840$		0			0
$841$			57.5644i			1.98498i
$842$	−12.2098	−	21.9790i	−0.420777	−	0.757447i
$843$	5.73915	+	5.73915i	0.197667	+	0.197667i
$844$	−9.98694	−	42.8956i	−0.343765	−	1.47653i
$845$		0			0
$846$	2.16405	−	7.57340i	0.0744016	−	0.260379i
$847$		−	15.9272i		−	0.547267i
$848$	9.64480	−	28.3512i	0.331204	−	0.973584i
$849$	4.92309			0.168960
$850$		0			0
$851$	−14.0478	−	14.0478i	−0.481553	−	0.481553i
$852$	2.72756	+	11.7153i	0.0934446	+	0.401361i
$853$	1.87566	+	1.87566i	0.0642212	+	0.0642212i	0.738488	−	0.674267i	$-0.235540\pi$
$853$	1.87566	+	1.87566i	0.0642212	+	0.0642212i	−0.674267	+	0.738488i	$0.735540\pi$
$854$	3.75984	−	2.08867i	0.128659	−	0.0714728i
$855$		0			0
$856$	−28.7752	−	1.42791i	−0.983517	−	0.0488050i
$857$	−23.1714			−0.791521			−0.395760	−	0.918354i	$-0.629519\pi$
$857$	−23.1714			−0.791521			−0.395760	+	0.918354i	$0.629519\pi$
$858$	−2.85829	+	1.58784i	−0.0975803	+	0.0542078i
$859$	10.5073	−	10.5073i	0.358506	−	0.358506i	−0.504756	−	0.863262i	$-0.668418\pi$
$859$	10.5073	−	10.5073i	0.358506	−	0.358506i	0.863262	+	0.504756i	$0.168418\pi$
$860$		0			0
$861$	−11.9967	−	11.9967i	−0.408846	−	0.408846i
$862$	−5.92847	+	20.7475i	−0.201924	+	0.706663i
$863$			25.2777i			0.860463i	0.902719	+	0.430231i	$0.141568\pi$
$863$			25.2777i			0.860463i	−0.902719	+	0.430231i	$0.858432\pi$
$864$	−26.2337	−	18.1886i	−0.892488	−	0.618790i
$865$		0			0
$866$	−16.5493	−	4.72887i	−0.562369	−	0.160693i
$867$	26.3878	−	26.3878i	0.896177	−	0.896177i
$868$	−17.1612	−	10.6794i	−0.582489	−	0.362481i
$869$	−4.94039	+	4.94039i	−0.167591	+	0.167591i
$870$		0			0
$871$			23.6073i			0.799901i
$872$	−22.6844	−	1.12566i	−0.768190	−	0.0381198i
$873$	−15.1912			−0.514144
$874$	−22.0987	+	12.2763i	−0.747500	+	0.415251i
$875$		0			0
$876$	6.98453	−	1.62613i	0.235985	−	0.0549420i
$877$	−16.7350	+	16.7350i	−0.565101	+	0.565101i	−0.930752	−	0.365651i	$-0.880846\pi$
$877$	−16.7350	+	16.7350i	−0.565101	+	0.565101i	0.365651	+	0.930752i	$0.380846\pi$
$878$	54.0564	+	15.4463i	1.82431	+	0.521286i
$879$	−39.8957			−1.34565
$880$		0			0
$881$	9.38791			0.316287			0.158143	−	0.987416i	$-0.449449\pi$
$881$	9.38791			0.316287			0.158143	+	0.987416i	$0.449449\pi$
$882$	−5.41701	−	1.54788i	−0.182400	−	0.0521197i
$883$	21.5593	−	21.5593i	0.725527	−	0.725527i	−0.244198	−	0.969725i	$-0.578525\pi$
$883$	21.5593	−	21.5593i	0.725527	−	0.725527i	0.969725	+	0.244198i	$0.0785248\pi$
$884$	7.75303	+	33.3006i	0.260763	+	1.12002i
$885$		0			0
$886$	6.33455	−	3.51897i	0.212813	−	0.118222i
$887$	−48.2072			−1.61864			−0.809320	−	0.587368i	$-0.800164\pi$
$887$	−48.2072			−1.61864			−0.809320	+	0.587368i	$0.800164\pi$
$888$	8.51691	−	7.71161i	0.285809	−	0.258785i
$889$			1.97256i			0.0661577i
$890$		0			0
$891$	2.45016	−	2.45016i	0.0820834	−	0.0820834i
$892$	8.33500	−	13.3939i	0.279076	−	0.448461i
$893$	11.6941	−	11.6941i	0.391327	−	0.391327i
$894$	44.8204	+	12.8071i	1.49902	+	0.428335i
$895$		0			0
$896$	15.7408	+	6.24133i	0.525863	+	0.208508i
$897$			27.7830i			0.927648i
$898$	2.09206	−	7.32144i	0.0698128	−	0.244320i
$899$	−44.4243	−	44.4243i	−1.48163	−	1.48163i
$900$		0			0
$901$	34.4607	−	34.4607i	1.14805	−	1.14805i
$902$	−5.70353	+	3.16843i	−0.189907	+	0.105497i
$903$	19.1008			0.635636
$904$	3.69718	+	4.08327i	0.122966	+	0.135807i
$905$		0			0
$906$	−20.9669	+	11.6475i	−0.696579	+	0.386964i
$907$	31.8381	+	31.8381i	1.05717	+	1.05717i	0.998264	+	0.0589044i	$0.0187607\pi$
$907$	31.8381	+	31.8381i	1.05717	+	1.05717i	0.0589044	+	0.998264i	$0.481239\pi$
$908$	−16.4965	+	3.84071i	−0.547456	+	0.127458i
$909$	−0.870707	−	0.870707i	−0.0288795	−	0.0288795i
$910$		0			0
$911$	14.8669			0.492561			0.246281	−	0.969199i	$-0.420791\pi$
$911$	14.8669			0.492561			0.246281	+	0.969199i	$0.420791\pi$
$912$	−6.45756	−	13.1165i	−0.213831	−	0.434329i
$913$		−	2.38244i		−	0.0788472i
$914$	5.55780	−	19.4503i	0.183836	−	0.643358i
$915$		0			0
$916$	53.6031	−	12.4798i	1.77110	−	0.412346i
$917$	−1.54197	−	1.54197i	−0.0509202	−	0.0509202i
$918$	−25.2277	−	45.4128i	−0.832638	−	1.49885i
$919$			5.27591i			0.174036i	0.996207	+	0.0870181i	$0.0277338\pi$
$919$			5.27591i			0.174036i	−0.996207	+	0.0870181i	$0.972266\pi$
$920$		0			0
$921$		−	41.4515i		−	1.36587i
$922$	−7.87389	+	4.37410i	−0.259313	+	0.144053i
$923$	−7.59404	−	7.59404i	−0.249961	−	0.249961i
$924$	−1.39231	+	2.23738i	−0.0458038	+	0.0736043i
$925$		0			0
$926$	26.3119	+	7.51847i	0.864664	+	0.247072i
$927$		−	0.799487i		−	0.0262586i
$928$	43.2524	+	29.9882i	1.41983	+	0.984411i
$929$	9.13997			0.299873			0.149936	−	0.988696i	$-0.452093\pi$
$929$	9.13997			0.299873			0.149936	+	0.988696i	$0.452093\pi$
$930$		0			0
$931$	−8.36441	−	8.36441i	−0.274133	−	0.274133i
$932$	4.56297	+	2.83952i	0.149465	+	0.0930116i
$933$	−5.96229	−	5.96229i	−0.195197	−	0.195197i
$934$	16.6833	+	30.0318i	0.545893	+	0.982671i
$935$		0			0
$936$	6.20918	+	0.308117i	0.202953	+	0.0100711i
$937$	19.0036			0.620819			0.310410	−	0.950603i	$-0.399534\pi$
$937$	19.0036			0.620819			0.310410	+	0.950603i	$0.399534\pi$
$938$	9.23951	+	16.6322i	0.301681	+	0.543060i
$939$	0.221119	−	0.221119i	0.00721596	−	0.00721596i
$940$		0			0
$941$	1.48322	+	1.48322i	0.0483517	+	0.0483517i	0.730869	−	0.682518i	$-0.239115\pi$
$941$	1.48322	+	1.48322i	0.0483517	+	0.0483517i	−0.682518	+	0.730869i	$0.739115\pi$
$942$	15.3262	+	4.37937i	0.499355	+	0.142687i
$943$			55.4393i			1.80535i
$944$	−31.6957	−	10.7826i	−1.03161	−	0.350943i
$945$		0			0
$946$	2.01817	−	7.06286i	0.0656163	−	0.229633i
$947$	−3.97577	+	3.97577i	−0.129195	+	0.129195i	−0.768748	−	0.639552i	$-0.779120\pi$
$947$	−3.97577	+	3.97577i	−0.129195	+	0.129195i	0.639552	+	0.768748i	$0.279120\pi$
$948$	−33.4393	+	7.78533i	−1.08606	+	0.252856i
$949$	−4.52747	+	4.52747i	−0.146968	+	0.146968i
$950$		0			0
$951$			6.68870i			0.216896i
$952$	18.4956	+	20.4271i	0.599447	+	0.662046i
$953$	16.5970			0.537628			0.268814	−	0.963192i	$-0.413368\pi$
$953$	16.5970			0.537628			0.268814	+	0.963192i	$0.413368\pi$
$954$	−4.30317	−	7.74620i	−0.139320	−	0.250792i
$955$		0			0
$956$	−21.4564	−	13.3523i	−0.693950	−	0.431843i
$957$	−5.79179	+	5.79179i	−0.187222	+	0.187222i
$958$	−2.15442	+	7.53968i	−0.0696060	+	0.243596i
$959$	−5.62092			−0.181509
$960$		0			0
$961$	14.5965			0.470855
$962$	−2.81840	+	9.86338i	−0.0908688	+	0.318008i
$963$	−6.02809	+	6.02809i	−0.194252	+	0.194252i
$964$	−12.7917	−	7.96024i	−0.411993	−	0.256382i
$965$		0			0
$966$	10.8738	+	19.5742i	0.349860	+	0.629789i
$967$	−8.72635			−0.280621			−0.140310	−	0.990108i	$-0.544810\pi$
$967$	−8.72635			−0.280621			−0.140310	+	0.990108i	$0.544810\pi$
$968$	−20.2024	−	22.3121i	−0.649330	−	0.717138i
$969$		−	23.7921i		−	0.764311i
$970$		0			0
$971$	−14.5421	+	14.5421i	−0.466677	+	0.466677i	−0.900836	−	0.434159i	$-0.857045\pi$
$971$	−14.5421	+	14.5421i	−0.466677	+	0.466677i	0.434159	+	0.900836i	$0.357045\pi$
$972$	−16.3927	+	3.81654i	−0.525796	+	0.122416i
$973$	19.3799	−	19.3799i	0.621289	−	0.621289i
$974$	12.3225	−	43.1242i	0.394837	−	1.38179i
$975$		0			0
$976$	2.61777	−	7.69502i	0.0837928	−	0.246312i
$977$		−	25.2020i		−	0.806284i	−0.915137	−	0.403142i	$-0.867918\pi$
$977$		−	25.2020i		−	0.806284i	0.915137	−	0.403142i	$-0.132082\pi$
$978$	18.3071	+	5.23114i	0.585397	+	0.167273i
$979$	−4.46723	−	4.46723i	−0.142773	−	0.142773i
$980$		0			0
$981$	−4.75212	+	4.75212i	−0.151724	+	0.151724i
$982$	−7.18152	−	12.9276i	−0.229171	−	0.412535i
$983$	−4.00157			−0.127630			−0.0638151	−	0.997962i	$-0.520327\pi$
$983$	−4.00157			−0.127630			−0.0638151	+	0.997962i	$0.520327\pi$
$984$	−32.0227	−	1.58906i	−1.02085	−	0.0506573i
$985$		0			0
$986$	41.5938	+	74.8736i	1.32462	+	2.38446i
$987$	−10.3582	−	10.3582i	−0.329704	−	0.329704i
$988$	11.0825	+	6.89661i	0.352581	+	0.219410i
$989$	−44.1346	−	44.1346i	−1.40340	−	1.40340i
$990$		0			0
$991$	−62.3391			−1.98027			−0.990134	−	0.140127i	$-0.955249\pi$
$991$	−62.3391			−1.98027			−0.990134	+	0.140127i	$0.955249\pi$
$992$	−37.5866	+	6.80709i	−1.19338	+	0.216125i
$993$			45.8201i			1.45406i
$994$	−8.32247	−	2.37809i	−0.263973	−	0.0754285i
$995$		0			0
$996$	6.18565	−	9.94001i	0.196000	−	0.314961i
$997$	−21.6855	−	21.6855i	−0.686787	−	0.686787i	0.274733	−	0.961521i	$-0.411410\pi$
$997$	−21.6855	−	21.6855i	−0.686787	−	0.686787i	−0.961521	+	0.274733i	$0.911410\pi$
$998$	−24.4949	+	13.6074i	−0.775371	+	0.430734i
$999$		−	15.5861i		−	0.493121i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.q.f.349.4		12
4.3	odd	2		1600.2.q.f.849.5		12
5.2	odd	4		400.2.l.g.301.6	yes	12
5.3	odd	4		400.2.l.f.301.1	yes	12
5.4	even	2		400.2.q.e.349.3		12
16.5	even	4		400.2.q.e.149.3		12
16.11	odd	4		1600.2.q.e.49.2		12
20.3	even	4		1600.2.l.g.401.5		12
20.7	even	4		1600.2.l.f.401.2		12
20.19	odd	2		1600.2.q.e.849.2		12
80.27	even	4		1600.2.l.f.1201.2		12
80.37	odd	4		400.2.l.g.101.6	yes	12
80.43	even	4		1600.2.l.g.1201.5		12
80.53	odd	4		400.2.l.f.101.1	✓	12
80.59	odd	4		1600.2.q.f.49.5		12
80.69	even	4	inner	400.2.q.f.149.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.l.f.101.1	✓	12	80.53	odd	4
400.2.l.f.301.1	yes	12	5.3	odd	4
400.2.l.g.101.6	yes	12	80.37	odd	4
400.2.l.g.301.6	yes	12	5.2	odd	4
400.2.q.e.149.3		12	16.5	even	4
400.2.q.e.349.3		12	5.4	even	2
400.2.q.f.149.4		12	80.69	even	4	inner
400.2.q.f.349.4		12	1.1	even	1	trivial
1600.2.l.f.401.2		12	20.7	even	4
1600.2.l.f.1201.2		12	80.27	even	4
1600.2.l.g.401.5		12	20.3	even	4
1600.2.l.g.1201.5		12	80.43	even	4
1600.2.q.e.49.2		12	16.11	odd	4
1600.2.q.e.849.2		12	20.19	odd	2
1600.2.q.f.49.5		12	80.59	odd	4
1600.2.q.f.849.5		12	4.3	odd	2

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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.q (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.388551 - 1.35979i) q^{2} +(-1.03997 + 1.03997i) q^{3} +(-1.69806 - 1.05670i) q^{4} +(1.01006 + 1.81822i) q^{6} -1.49668 q^{7} +(-2.09667 + 1.89842i) q^{8} +0.836925i q^{9} +O(q^{10})\)	\(q+(0.388551 - 1.35979i) q^{2} +(-1.03997 + 1.03997i) q^{3} +(-1.69806 - 1.05670i) q^{4} +(1.01006 + 1.81822i) q^{6} -1.49668 q^{7} +(-2.09667 + 1.89842i) q^{8} +0.836925i q^{9} +(0.423260 - 0.423260i) q^{11} +(2.86486 - 0.666995i) q^{12} +(-1.85704 + 1.85704i) q^{13} +(-0.581538 + 2.03517i) q^{14} +(1.76679 + 3.58866i) q^{16} +6.50950i q^{17} +(1.13804 + 0.325188i) q^{18} +(1.75725 + 1.75725i) q^{19} +(1.55650 - 1.55650i) q^{21} +(-0.411086 - 0.740003i) q^{22} -7.19295 q^{23} +(0.206172 - 4.15477i) q^{24} +(1.80363 + 3.24674i) q^{26} +(-3.99029 - 3.99029i) q^{27} +(2.54145 + 1.58154i) q^{28} +(6.57892 + 6.57892i) q^{29} -6.75252 q^{31} +(5.56631 - 1.00808i) q^{32} +0.880355i q^{33} +(8.85156 + 2.52928i) q^{34} +(0.884375 - 1.42115i) q^{36} +(1.95300 + 1.95300i) q^{37} +(3.07227 - 1.70671i) q^{38} -3.86254i q^{39} -7.70745i q^{41} +(-1.51174 - 2.72130i) q^{42} +(6.13581 + 6.13581i) q^{43} +(-1.16598 + 0.271462i) q^{44} +(-2.79483 + 9.78090i) q^{46} -6.65476i q^{47} +(-5.56950 - 1.89469i) q^{48} -4.75994 q^{49} +(-6.76969 - 6.76969i) q^{51} +(5.11569 - 1.19103i) q^{52} +(-5.29390 - 5.29390i) q^{53} +(-6.97638 + 3.87552i) q^{54} +(3.13804 - 2.84133i) q^{56} -3.65497 q^{57} +(11.5022 - 6.38970i) q^{58} +(-5.91841 + 5.91841i) q^{59} +(-1.43686 - 1.43686i) q^{61} +(-2.62370 + 9.18201i) q^{62} -1.25261i q^{63} +(0.792016 - 7.96070i) q^{64} +(1.19710 + 0.342063i) q^{66} +(6.35614 - 6.35614i) q^{67} +(6.87857 - 11.0535i) q^{68} +(7.48045 - 7.48045i) q^{69} +4.08932i q^{71} +(-1.58883 - 1.75475i) q^{72} +2.43800 q^{73} +(3.41451 - 1.89683i) q^{74} +(-1.12703 - 4.84079i) q^{76} +(-0.633485 + 0.633485i) q^{77} +(-5.25224 - 1.50079i) q^{78} -11.6722 q^{79} +5.78878 q^{81} +(-10.4805 - 2.99474i) q^{82} +(2.81439 - 2.81439i) q^{83} +(-4.28778 + 0.998279i) q^{84} +(10.7275 - 5.95933i) q^{86} -13.6838 q^{87} +(-0.0839103 + 1.69096i) q^{88} -10.5543i q^{89} +(2.77940 - 2.77940i) q^{91} +(12.2140 + 7.60076i) q^{92} +(7.02242 - 7.02242i) q^{93} +(-9.04907 - 2.58572i) q^{94} +(-4.74042 + 6.83717i) q^{96} +18.1512i q^{97} +(-1.84948 + 6.47252i) q^{98} +(0.354237 + 0.354237i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 6 q^{6} + 12 q^{7} + 2 q^{8}+O(q^{10}) \) 12 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 6 * q^6 + 12 * q^7 + 2 * q^8	\( 12 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 6 q^{6} + 12 q^{7} + 2 q^{8} - 2 q^{11} - 6 q^{12} + 4 q^{13} - 14 q^{14} + 2 q^{16} - 18 q^{18} + 14 q^{19} - 20 q^{21} - 20 q^{22} + 12 q^{23} + 14 q^{24} - 16 q^{26} + 10 q^{27} - 10 q^{28} - 4 q^{31} + 2 q^{32} + 6 q^{34} + 2 q^{36} - 8 q^{37} + 28 q^{38} + 10 q^{42} + 44 q^{44} - 10 q^{46} - 58 q^{48} - 4 q^{49} + 10 q^{51} - 16 q^{53} - 10 q^{54} + 6 q^{56} - 16 q^{57} + 4 q^{58} - 20 q^{59} + 4 q^{61} + 22 q^{62} - 38 q^{64} + 32 q^{66} + 50 q^{67} + 50 q^{68} - 54 q^{72} + 40 q^{73} - 10 q^{74} + 60 q^{76} - 8 q^{77} - 48 q^{78} - 12 q^{79} - 8 q^{81} - 12 q^{82} + 2 q^{83} - 34 q^{84} + 6 q^{86} - 64 q^{87} + 56 q^{88} + 50 q^{92} + 44 q^{93} - 32 q^{94} - 34 q^{96} - 30 q^{98} - 12 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 6 * q^6 + 12 * q^7 + 2 * q^8 - 2 * q^11 - 6 * q^12 + 4 * q^13 - 14 * q^14 + 2 * q^16 - 18 * q^18 + 14 * q^19 - 20 * q^21 - 20 * q^22 + 12 * q^23 + 14 * q^24 - 16 * q^26 + 10 * q^27 - 10 * q^28 - 4 * q^31 + 2 * q^32 + 6 * q^34 + 2 * q^36 - 8 * q^37 + 28 * q^38 + 10 * q^42 + 44 * q^44 - 10 * q^46 - 58 * q^48 - 4 * q^49 + 10 * q^51 - 16 * q^53 - 10 * q^54 + 6 * q^56 - 16 * q^57 + 4 * q^58 - 20 * q^59 + 4 * q^61 + 22 * q^62 - 38 * q^64 + 32 * q^66 + 50 * q^67 + 50 * q^68 - 54 * q^72 + 40 * q^73 - 10 * q^74 + 60 * q^76 - 8 * q^77 - 48 * q^78 - 12 * q^79 - 8 * q^81 - 12 * q^82 + 2 * q^83 - 34 * q^84 + 6 * q^86 - 64 * q^87 + 56 * q^88 + 50 * q^92 + 44 * q^93 - 32 * q^94 - 34 * q^96 - 30 * q^98 - 12 * q^99

Introduction

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