LMFDB - Embedded newform 400.2.q.f.149.4

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			149.4
Root			$1.35979 + 0.388551i$ of defining polynomial
Character	$\chi$	$=$	400.149
Dual form			400.2.q.f.349.4

$q$-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 $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

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

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	0.339999	−	0.940426i	$-0.389573\pi$
$3$	−1.03997	−	1.03997i	−0.600427	−	0.600427i	−0.940426	+	0.339999i	$0.889573\pi$
$4$	−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	0.768031	−	0.640413i	$-0.221237\pi$
$11$	0.423260	+	0.423260i	0.127618	+	0.127618i	−0.640413	+	0.768031i	$0.721237\pi$
$12$	2.86486	+	0.666995i	0.827014	+	0.192545i
$13$	−1.85704	−	1.85704i	−0.515051	−	0.515051i	0.401019	−	0.916070i	$-0.368656\pi$
$13$	−1.85704	−	1.85704i	−0.515051	−	0.515051i	−0.916070	+	0.401019i	$0.868656\pi$
$14$	−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	$-0.710395\pi$
$17$		−	6.50950i		−	1.57879i	0.613888	−	0.789393i	$-0.289605\pi$
$18$	1.13804	−	0.325188i	0.268239	−	0.0766476i
$19$	1.75725	−	1.75725i	0.403141	−	0.403141i	−0.476198	−	0.879338i	$-0.657985\pi$
$19$	1.75725	−	1.75725i	0.403141	−	0.403141i	0.879338	+	0.476198i	$0.157985\pi$
$20$		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	0.254639	−	0.967036i	$-0.418043\pi$
$29$	6.57892	−	6.57892i	1.22167	−	1.22167i	0.967036	−	0.254639i	$-0.0819565\pi$
$30$		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	−0.528107	−	0.849178i	$-0.677098\pi$
$37$	1.95300	−	1.95300i	0.321071	−	0.321071i	0.849178	+	0.528107i	$0.177098\pi$
$38$	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	$0.205570\pi$
$41$			7.70745i			1.20370i	−0.798609	+	0.601851i	$0.794430\pi$
$42$	−1.51174	+	2.72130i	−0.233266	+	0.419906i
$43$	6.13581	−	6.13581i	0.935702	−	0.935702i	−0.0623522	−	0.998054i	$-0.519860\pi$
$43$	6.13581	−	6.13581i	0.935702	−	0.935702i	0.998054	+	0.0623522i	$0.0198602\pi$
$44$	−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	$0.161307\pi$
$47$			6.65476i			0.970697i	−0.874321	+	0.485348i	$0.838693\pi$
$48$	−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	−0.970056	−	0.242882i	$-0.921907\pi$
$53$	−5.29390	+	5.29390i	−0.727173	+	0.727173i	0.242882	+	0.970056i	$0.421907\pi$
$54$	−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	0.207685	−	0.978196i	$-0.433407\pi$
$59$	−5.91841	−	5.91841i	−0.770511	−	0.770511i	−0.978196	+	0.207685i	$0.933407\pi$
$60$		0			0
$61$	−1.43686	+	1.43686i	−0.183971	+	0.183971i	−0.793084	−	0.609113i	$-0.791526\pi$
$61$	−1.43686	+	1.43686i	−0.183971	+	0.183971i	0.609113	+	0.793084i	$0.291526\pi$
$62$	−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	0.979238	−	0.202712i	$-0.0649756\pi$
$67$	6.35614	+	6.35614i	0.776526	+	0.776526i	−0.202712	+	0.979238i	$0.564976\pi$
$68$	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	$-0.921981\pi$
$71$		−	4.08932i		−	0.485313i	0.970112	−	0.242657i	$-0.0780188\pi$
$72$	−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	0.844490	−	0.535571i	$-0.179904\pi$
$83$	2.81439	+	2.81439i	0.308919	+	0.308919i	−0.535571	+	0.844490i	$0.679904\pi$
$84$	−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	$0.188960\pi$
$89$			10.5543i			1.11876i	−0.828912	+	0.559379i	$0.811040\pi$
$90$		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	$-0.626975\pi$
$97$		−	18.1512i		−	1.84298i	0.388407	−	0.921488i	$-0.373025\pi$
$98$	−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	0.653450	−	0.756970i	$-0.273321\pi$
$101$	−1.04036	−	1.04036i	−0.103520	−	0.103520i	−0.756970	+	0.653450i	$0.773321\pi$
$102$	−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	−0.267305	−	0.963612i	$-0.586133\pi$
$107$	7.20266	−	7.20266i	0.696308	−	0.696308i	0.963612	+	0.267305i	$0.0861330\pi$
$108$	2.55921	−	10.9922i	0.246260	−	1.05773i
$109$	5.67807	−	5.67807i	0.543861	−	0.543861i	−0.380798	−	0.924658i	$-0.624351\pi$
$109$	5.67807	−	5.67807i	0.543861	−	0.543861i	0.924658	+	0.380798i	$0.124351\pi$
$110$		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	$0.0291991\pi$
$113$			1.94751i			0.183206i	−0.995796	+	0.0916029i	$0.970801\pi$
$114$	−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	$0.0186238\pi$
$127$			1.31796i			0.116950i	−0.998289	+	0.0584750i	$0.981376\pi$
$128$	−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	−0.660666	−	0.750680i	$-0.729726\pi$
$131$	1.03026	−	1.03026i	0.0900139	−	0.0900139i	0.750680	+	0.660666i	$0.229726\pi$
$132$	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	−0.994612	−	0.103669i	$-0.966942\pi$
$139$	−12.9485	−	12.9485i	−1.09828	−	1.09828i	−0.103669	−	0.994612i	$-0.533058\pi$
$140$		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	0.929545	+	0.368709i	$0.120200\pi$
$149$	15.8472	+	15.8472i	1.29825	+	1.29825i	0.368709	+	0.929545i	$0.379800\pi$
$150$		0			0
$151$		−	11.5316i		−	0.938424i	−0.883085	−	0.469212i	$-0.844538\pi$
$151$		−	11.5316i		−	0.938424i	0.883085	−	0.469212i	$-0.155462\pi$
$152$	−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	0.889470	−	0.456994i	$-0.151074\pi$
$157$	5.41891	+	5.41891i	0.432476	+	0.432476i	−0.456994	+	0.889470i	$0.651074\pi$
$158$	−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	0.913603	−	0.406608i	$-0.133289\pi$
$163$	6.47288	+	6.47288i	0.506995	+	0.506995i	−0.406608	+	0.913603i	$0.633289\pi$
$164$	−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	0.996105	−	0.0881700i	$-0.0281019\pi$
$173$	11.9420	+	11.9420i	0.907935	+	0.907935i	−0.0881700	+	0.996105i	$0.528102\pi$
$174$	−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	−0.172524	−	0.985005i	$-0.555192\pi$
$179$	10.8703	−	10.8703i	0.812481	−	0.812481i	0.985005	+	0.172524i	$0.0551922\pi$
$180$		0			0
$181$	−4.09403	−	4.09403i	−0.304307	−	0.304307i	0.538389	−	0.842696i	$-0.319033\pi$
$181$	−4.09403	−	4.09403i	−0.304307	−	0.304307i	−0.842696	+	0.538389i	$0.819033\pi$
$182$	−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	$-0.648512\pi$
$193$		−	24.8152i		−	1.78624i	0.449820	−	0.893119i	$-0.351488\pi$
$194$	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	−0.800186	−	0.599751i	$-0.795266\pi$
$197$	−2.81324	+	2.81324i	−0.200435	+	0.200435i	0.599751	+	0.800186i	$0.295266\pi$
$198$	0.619327	+	0.344048i	0.0440136	+	0.0244505i
$199$			21.2194i			1.50420i	0.659048	+	0.752101i	$0.270959\pi$
$199$			21.2194i			1.50420i	−0.659048	+	0.752101i	$0.729041\pi$
$200$		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	0.0747872	−	0.997200i	$-0.476172\pi$
$211$	15.5715	−	15.5715i	1.07199	−	1.07199i	0.997200	−	0.0747872i	$-0.0238278\pi$
$212$	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	$-0.914924\pi$
$223$		−	7.88779i		−	0.528205i	0.964495	−	0.264103i	$-0.0850758\pi$
$224$	−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	0.877337	−	0.479874i	$-0.159318\pi$
$227$	5.98838	+	5.98838i	0.397463	+	0.397463i	−0.479874	+	0.877337i	$0.659318\pi$
$228$	6.20635	−	3.86220i	0.411026	−	0.255780i
$229$	−19.4584	−	19.4584i	−1.28585	−	1.28585i	−0.937286	−	0.348563i	$-0.886670\pi$
$229$	−19.4584	−	19.4584i	−1.28585	−	1.28585i	−0.348563	−	0.937286i	$-0.613330\pi$
$230$		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	0.319213	−	0.947683i	$-0.396581\pi$
$251$	−9.95683	−	9.95683i	−0.628470	−	0.628470i	−0.947683	+	0.319213i	$0.896581\pi$
$252$	−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	$-0.955013\pi$
$257$		−	4.51630i		−	0.281719i	0.990030	−	0.140860i	$-0.0449866\pi$
$258$	−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	−0.0335999	+	0.999435i	$0.510697\pi$
$269$	−16.9430	+	16.9430i	−1.03304	+	1.03304i	−0.999435	+	0.0335999i	$0.989303\pi$
$270$		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	−0.999300	−	0.0374115i	$-0.988089\pi$
$277$	−16.0090	+	16.0090i	−0.961888	+	0.961888i	0.0374115	+	0.999300i	$0.488089\pi$
$278$	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	$0.0526350\pi$
$281$			5.51857i			0.329210i	−0.986360	+	0.164605i	$0.947365\pi$
$282$	12.0998	+	6.72170i	0.720535	+	0.400271i
$283$	−2.36694	+	2.36694i	−0.140700	+	0.140700i	−0.773949	−	0.633249i	$-0.781721\pi$
$283$	−2.36694	+	2.36694i	−0.140700	+	0.140700i	0.633249	+	0.773949i	$0.281721\pi$
$284$	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	0.128922	−	0.991655i	$-0.458848\pi$
$293$	19.1812	−	19.1812i	1.12058	−	1.12058i	0.991655	−	0.128922i	$-0.0411517\pi$
$294$	−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	−0.988911	−	0.148507i	$-0.952553\pi$
$307$	−19.9292	−	19.9292i	−1.13742	−	1.13742i	−0.148507	−	0.988911i	$-0.547447\pi$
$308$	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	$-0.948029\pi$
$311$		−	5.73314i		−	0.325096i	0.986701	−	0.162548i	$-0.0519713\pi$
$312$	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	0.791625	−	0.611007i	$-0.209235\pi$
$317$	3.21582	+	3.21582i	0.180618	+	0.180618i	−0.611007	+	0.791625i	$0.709235\pi$
$318$	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	0.970747	+	0.240106i	$0.0771824\pi$
$331$	22.0295	+	22.0295i	1.21085	+	1.21085i	0.240106	+	0.970747i	$0.422818\pi$
$332$	−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	$0.0987847\pi$
$337$			11.2122i			0.610767i	−0.952229	+	0.305384i	$0.901215\pi$
$338$	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	−0.673137	−	0.739518i	$-0.735054\pi$
$347$	1.23653	−	1.23653i	0.0663803	−	0.0663803i	0.739518	+	0.673137i	$0.235054\pi$
$348$	23.2358	−	14.4596i	1.24557	−	0.775115i
$349$	5.61778	−	5.61778i	0.300713	−	0.300713i	−0.540580	−	0.841293i	$-0.681795\pi$
$349$	5.61778	−	5.61778i	0.300713	−	0.300713i	0.841293	+	0.540580i	$0.181795\pi$
$350$		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	$0.00634270\pi$
$353$			0.748709i			0.0398497i	−0.999801	+	0.0199249i	$0.993657\pi$
$354$	−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	$0.0226891\pi$
$359$			2.69883i			0.142439i	−0.997461	+	0.0712195i	$0.977311\pi$
$360$		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	$-0.819210\pi$
$367$		−	20.6101i		−	1.07584i	0.842996	−	0.537920i	$-0.180790\pi$
$368$	−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	−0.829660	−	0.558269i	$-0.811466\pi$
$373$	−5.24143	+	5.24143i	−0.271391	+	0.271391i	0.558269	+	0.829660i	$0.311466\pi$
$374$	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	0.554268	−	0.832338i	$-0.312998\pi$
$379$	−5.41344	−	5.41344i	−0.278070	−	0.278070i	−0.832338	+	0.554268i	$0.812998\pi$
$380$		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	$0.271836\pi$
$383$			29.5087i			1.50782i	−0.656975	+	0.753912i	$0.728164\pi$
$384$	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	0.671287	−	0.741197i	$-0.265742\pi$
$389$	−1.37884	−	1.37884i	−0.0699099	−	0.0699099i	−0.741197	+	0.671287i	$0.765742\pi$
$390$		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	−0.994060	−	0.108832i	$-0.965289\pi$
$397$	−21.9750	−	21.9750i	−1.10289	−	1.10289i	−0.108832	−	0.994060i	$-0.534711\pi$
$398$	−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	$0.102508\pi$
$409$			12.8017i			0.633003i	−0.948592	+	0.316502i	$0.897492\pi$
$410$		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	−0.368084	−	0.929793i	$-0.619986\pi$
$419$	11.4979	−	11.4979i	0.561709	−	0.561709i	0.929793	+	0.368084i	$0.119986\pi$
$420$		0			0
$421$	12.5714	+	12.5714i	0.612690	+	0.612690i	0.943646	−	0.330956i	$-0.107371\pi$
$421$	12.5714	+	12.5714i	0.612690	+	0.612690i	−0.330956	+	0.943646i	$0.607371\pi$
$422$	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	$0.0944667\pi$
$433$			12.1705i			0.584877i	−0.956284	+	0.292439i	$0.905533\pi$
$434$	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	$-0.602435\pi$
$439$		−	39.7535i		−	1.89733i	0.316283	−	0.948665i	$-0.397565\pi$
$440$		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	−0.615778	−	0.787920i	$-0.711158\pi$
$443$	3.62318	−	3.62318i	0.172142	−	0.172142i	0.787920	+	0.615778i	$0.211158\pi$
$444$	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	−0.804163	−	0.594408i	$-0.797386\pi$
$461$	−4.50363	+	4.50363i	−0.209755	+	0.209755i	0.594408	+	0.804163i	$0.297386\pi$
$462$	−1.79167	+	0.511960i	−0.0833563	+	0.0238185i
$463$		−	19.3500i		−	0.899271i	−0.893212	−	0.449636i	$-0.851554\pi$
$463$		−	19.3500i		−	0.899271i	0.893212	−	0.449636i	$-0.148446\pi$
$464$	−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	0.187410	−	0.982282i	$-0.439991\pi$
$467$	−17.1773	−	17.1773i	−0.794871	−	0.794871i	−0.982282	+	0.187410i	$0.939991\pi$
$468$	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	0.853988	−	0.520293i	$-0.174177\pi$
$491$	7.39419	+	7.39419i	0.333695	+	0.333695i	−0.520293	+	0.853988i	$0.674177\pi$
$492$	−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	−0.947360	−	0.320171i	$-0.896260\pi$
$499$	−14.0103	+	14.0103i	−0.627189	+	0.627189i	0.320171	+	0.947360i	$0.396260\pi$
$500$		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	−0.751983	−	0.659183i	$-0.770902\pi$
$509$	−2.09367	+	2.09367i	−0.0928004	+	0.0928004i	0.659183	+	0.751983i	$0.270902\pi$
$510$		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	$0.212443\pi$
$521$			28.2558i			1.23791i	−0.785428	+	0.618954i	$0.787557\pi$
$522$	5.34770	−	9.62647i	0.234062	−	0.421339i
$523$	10.1929	−	10.1929i	0.445703	−	0.445703i	−0.448220	−	0.893923i	$-0.647942\pi$
$523$	10.1929	−	10.1929i	0.445703	−	0.445703i	0.893923	+	0.448220i	$0.147942\pi$
$524$	−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	−0.619231	−	0.785209i	$-0.712556\pi$
$541$	3.86053	−	3.86053i	0.165977	−	0.165977i	0.785209	+	0.619231i	$0.212556\pi$
$542$	−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	0.993716	−	0.111935i	$-0.0357048\pi$
$547$	20.6231	+	20.6231i	0.881781	+	0.881781i	−0.111935	+	0.993716i	$0.535705\pi$
$548$	−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	0.679356	−	0.733809i	$-0.262259\pi$
$557$	−1.28512	−	1.28512i	−0.0544523	−	0.0544523i	−0.733809	+	0.679356i	$0.762259\pi$
$558$	−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	0.0736677	−	0.997283i	$-0.476530\pi$
$563$	−21.9152	−	21.9152i	−0.923615	−	0.923615i	−0.997283	+	0.0736677i	$0.976530\pi$
$564$	−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	$0.268801\pi$
$569$			35.6668i			1.49523i	−0.664132	+	0.747615i	$0.731199\pi$
$570$		0			0
$571$	5.60524	+	5.60524i	0.234572	+	0.234572i	0.814598	−	0.580026i	$-0.196958\pi$
$571$	5.60524	+	5.60524i	0.234572	+	0.234572i	−0.580026	+	0.814598i	$0.696958\pi$
$572$	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	$-0.983847\pi$
$577$		−	2.43681i		−	0.101446i	0.998713	−	0.0507230i	$-0.0161526\pi$
$578$	−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	−0.715639	−	0.698470i	$-0.753865\pi$
$587$	−0.415982	+	0.415982i	−0.0171694	+	0.0171694i	0.698470	+	0.715639i	$0.253865\pi$
$588$	−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	$0.102021\pi$
$593$			15.3439i			0.630098i	−0.949075	+	0.315049i	$0.897979\pi$
$594$	−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	$-0.653754\pi$
$599$		−	43.3487i		−	1.77118i	0.464468	−	0.885590i	$-0.346246\pi$
$600$		0			0
$601$		−	38.7291i		−	1.57979i	−0.613239	−	0.789897i	$-0.710134\pi$
$601$		−	38.7291i		−	1.57979i	0.613239	−	0.789897i	$-0.289866\pi$
$602$	−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	$-0.749412\pi$
$607$		−	34.9068i		−	1.41682i	0.705800	−	0.708412i	$-0.250588\pi$
$608$	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	−0.710165	−	0.704035i	$-0.751380\pi$
$613$	−0.151779	+	0.151779i	−0.00613031	+	0.00613031i	0.704035	+	0.710165i	$0.251380\pi$
$614$	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	0.899788	−	0.436328i	$-0.143721\pi$
$619$	11.5307	+	11.5307i	0.463460	+	0.463460i	−0.436328	+	0.899788i	$0.643721\pi$
$620$		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	$0.0912536\pi$
$631$			14.2062i			0.565541i	−0.959188	+	0.282771i	$0.908746\pi$
$632$	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	0.812169	−	0.583422i	$-0.198287\pi$
$643$	5.80043	+	5.80043i	0.228747	+	0.228747i	−0.583422	+	0.812169i	$0.698287\pi$
$644$	−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	0.788343	−	0.615236i	$-0.210939\pi$
$653$	4.42354	+	4.42354i	0.173106	+	0.173106i	−0.615236	+	0.788343i	$0.710939\pi$
$654$	−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	−0.344779	−	0.938684i	$-0.612046\pi$
$659$	15.2461	−	15.2461i	0.593905	−	0.593905i	0.938684	+	0.344779i	$0.112046\pi$
$660$		0			0
$661$	19.1271	+	19.1271i	0.743958	+	0.743958i	0.973337	−	0.229379i	$-0.0736696\pi$
$661$	19.1271	+	19.1271i	0.743958	+	0.743958i	−0.229379	+	0.973337i	$0.573670\pi$
$662$	−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	$0.116436\pi$
$673$			18.5586i			0.715382i	−0.933840	+	0.357691i	$0.883564\pi$
$674$	−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	−0.652935	−	0.757414i	$-0.726463\pi$
$677$	2.71844	−	2.71844i	0.104478	−	0.104478i	0.757414	+	0.652935i	$0.226463\pi$
$678$	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	−0.906596	−	0.421999i	$-0.861329\pi$
$683$	−12.6646	+	12.6646i	−0.484598	+	0.484598i	0.421999	+	0.906596i	$0.361329\pi$
$684$	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	0.0231826	−	0.999731i	$-0.492620\pi$
$691$	26.8892	−	26.8892i	1.02291	−	1.02291i	0.999731	−	0.0231826i	$-0.00737991\pi$
$692$	−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	−0.0408602	−	0.999165i	$-0.513010\pi$
$701$	25.3725	−	25.3725i	0.958305	−	0.958305i	0.999165	+	0.0408602i	$0.0130098\pi$
$702$	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	0.336570	−	0.941659i	$-0.390733\pi$
$709$	−16.1117	−	16.1117i	−0.605089	−	0.605089i	−0.941659	+	0.336570i	$0.890733\pi$
$710$		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	0.967775	−	0.251817i	$-0.0810282\pi$
$733$	19.3838	+	19.3838i	0.715957	+	0.715957i	−0.251817	+	0.967775i	$0.581028\pi$
$734$	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	−0.993757	−	0.111564i	$-0.964414\pi$
$739$	−23.9820	+	23.9820i	−0.882194	+	0.882194i	0.111564	+	0.993757i	$0.464414\pi$
$740$		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	0.112345	−	0.993669i	$-0.464164\pi$
$757$	30.4305	−	30.4305i	1.10601	−	1.10601i	0.993669	−	0.112345i	$-0.0358361\pi$
$758$	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	$0.285436\pi$
$761$			43.1054i			1.56257i	−0.624174	+	0.781285i	$0.714564\pi$
$762$	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	−0.115527	−	0.993304i	$-0.536856\pi$
$773$	24.4047	−	24.4047i	0.877778	−	0.877778i	0.993304	+	0.115527i	$0.0368556\pi$
$774$	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	0.330320	−	0.943869i	$-0.392843\pi$
$787$	−17.2122	−	17.2122i	−0.613549	−	0.613549i	−0.943869	+	0.330320i	$0.892843\pi$
$788$	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	0.248731	−	0.968573i	$-0.419986\pi$
$797$	−20.3220	−	20.3220i	−0.719841	−	0.719841i	−0.968573	+	0.248731i	$0.919986\pi$
$798$	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	$0.0156968\pi$
$809$			2.80407i			0.0985859i	−0.998784	+	0.0492930i	$0.984303\pi$
$810$		0			0
$811$	−7.29902	−	7.29902i	−0.256303	−	0.256303i	0.567246	−	0.823549i	$-0.308009\pi$
$811$	−7.29902	−	7.29902i	−0.256303	−	0.256303i	−0.823549	+	0.567246i	$0.808009\pi$
$812$	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	0.509603	−	0.860409i	$-0.329792\pi$
$821$	−10.0517	−	10.0517i	−0.350806	−	0.350806i	−0.860409	+	0.509603i	$0.829792\pi$
$822$	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	−0.0944595	+	0.995529i	$0.530112\pi$
$827$	−31.3455	+	31.3455i	−1.08999	+	1.08999i	−0.995529	+	0.0944595i	$0.969888\pi$
$828$	−6.36126	−	10.2222i	−0.221069	−	0.355247i
$829$	3.87895	−	3.87895i	0.134722	−	0.134722i	−0.636530	−	0.771252i	$-0.719631\pi$
$829$	3.87895	−	3.87895i	0.134722	−	0.134722i	0.771252	+	0.636530i	$0.219631\pi$
$830$		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	$-0.807440\pi$
$839$		−	32.9463i		−	1.13743i	0.822533	−	0.568717i	$-0.192560\pi$
$840$		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	−0.674267	−	0.738488i	$-0.735540\pi$
$853$	1.87566	−	1.87566i	0.0642212	−	0.0642212i	0.738488	+	0.674267i	$0.235540\pi$
$854$	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	0.863262	−	0.504756i	$-0.168418\pi$
$859$	10.5073	+	10.5073i	0.358506	+	0.358506i	−0.504756	+	0.863262i	$0.668418\pi$
$860$		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	$-0.858432\pi$
$863$		−	25.2777i		−	0.860463i	0.902719	−	0.430231i	$-0.141568\pi$
$864$	−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	0.365651	−	0.930752i	$-0.380846\pi$
$877$	−16.7350	−	16.7350i	−0.565101	−	0.565101i	−0.930752	+	0.365651i	$0.880846\pi$
$878$	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	0.969725	−	0.244198i	$-0.0785248\pi$
$883$	21.5593	+	21.5593i	0.725527	+	0.725527i	−0.244198	+	0.969725i	$0.578525\pi$
$884$	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	0.0589044	−	0.998264i	$-0.481239\pi$
$907$	31.8381	−	31.8381i	1.05717	−	1.05717i	0.998264	−	0.0589044i	$-0.0187607\pi$
$908$	−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	$-0.972266\pi$
$919$		−	5.27591i		−	0.174036i	0.996207	−	0.0870181i	$-0.0277338\pi$
$920$		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	−0.682518	−	0.730869i	$-0.739115\pi$
$941$	1.48322	−	1.48322i	0.0483517	−	0.0483517i	0.730869	+	0.682518i	$0.239115\pi$
$942$	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	0.639552	−	0.768748i	$-0.279120\pi$
$947$	−3.97577	−	3.97577i	−0.129195	−	0.129195i	−0.768748	+	0.639552i	$0.779120\pi$
$948$	−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	0.434159	−	0.900836i	$-0.357045\pi$
$971$	−14.5421	−	14.5421i	−0.466677	−	0.466677i	−0.900836	+	0.434159i	$0.857045\pi$
$972$	−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	$0.132082\pi$
$977$			25.2020i			0.806284i	−0.915137	+	0.403142i	$0.867918\pi$
$978$	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	−0.961521	−	0.274733i	$-0.911410\pi$
$997$	−21.6855	+	21.6855i	−0.686787	+	0.686787i	0.274733	+	0.961521i	$0.411410\pi$
$998$	−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.149.4		12
4.3	odd	2		1600.2.q.f.49.5		12
5.2	odd	4		400.2.l.f.101.1	✓	12
5.3	odd	4		400.2.l.g.101.6	yes	12
5.4	even	2		400.2.q.e.149.3		12
16.3	odd	4		1600.2.q.e.849.2		12
16.13	even	4		400.2.q.e.349.3		12
20.3	even	4		1600.2.l.f.1201.2		12
20.7	even	4		1600.2.l.g.1201.5		12
20.19	odd	2		1600.2.q.e.49.2		12
80.3	even	4		1600.2.l.f.401.2		12
80.13	odd	4		400.2.l.g.301.6	yes	12
80.19	odd	4		1600.2.q.f.849.5		12
80.29	even	4	inner	400.2.q.f.349.4		12
80.67	even	4		1600.2.l.g.401.5		12
80.77	odd	4		400.2.l.f.301.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.l.f.101.1	✓	12	5.2	odd	4
400.2.l.f.301.1	yes	12	80.77	odd	4
400.2.l.g.101.6	yes	12	5.3	odd	4
400.2.l.g.301.6	yes	12	80.13	odd	4
400.2.q.e.149.3		12	5.4	even	2
400.2.q.e.349.3		12	16.13	even	4
400.2.q.f.149.4		12	1.1	even	1	trivial
400.2.q.f.349.4		12	80.29	even	4	inner
1600.2.l.f.401.2		12	80.3	even	4
1600.2.l.f.1201.2		12	20.3	even	4
1600.2.l.g.401.5		12	80.67	even	4
1600.2.l.g.1201.5		12	20.7	even	4
1600.2.q.e.49.2		12	20.19	odd	2
1600.2.q.e.849.2		12	16.3	odd	4
1600.2.q.f.49.5		12	4.3	odd	2
1600.2.q.f.849.5		12	80.19	odd	4

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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more