LMFDB - Embedded newform 507.2.p.a.25.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(25,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("507.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.p (of order $26$, degree $12$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$14$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			25.2
Character	$\chi$	$=$	507.25
Dual form			507.2.p.a.142.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.23311 - 0.846906i) q^{2} +(0.568065 + 0.822984i) q^{3} +(2.77250 + 2.45622i) q^{4} +(0.980994 + 0.119114i) q^{5} +(-0.571560 - 2.31891i) q^{6} +(1.47491 + 2.81021i) q^{7} +(-1.89129 - 3.60355i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(-2.08979 - 1.09680i) q^{10} +(1.93416 - 0.733529i) q^{11} +(-0.446470 + 3.67701i) q^{12} +(1.22146 + 3.39235i) q^{13} +(-0.913654 - 7.52462i) q^{14} +(0.459239 + 0.875007i) q^{15} +(0.278644 + 2.29484i) q^{16} +(0.841746 - 0.441782i) q^{17} +(1.58374 - 1.78767i) q^{18} +1.80701i q^{19} +(2.42723 + 2.73978i) q^{20} +(-1.47491 + 2.81021i) q^{21} -4.94041 q^{22} -5.08440 q^{23} +(1.89129 - 3.60355i) q^{24} +(-3.90655 - 0.962877i) q^{25} +(0.145355 - 8.60994i) q^{26} +(-0.970942 + 0.239316i) q^{27} +(-2.81330 + 11.4140i) q^{28} +(1.17080 - 3.08714i) q^{29} +(-0.284482 - 2.34292i) q^{30} +(0.0195969 + 0.0795079i) q^{31} +(-0.626619 + 2.54229i) q^{32} +(1.70241 + 1.17509i) q^{33} +(-2.25386 + 0.273668i) q^{34} +(1.11215 + 2.93249i) q^{35} +(-3.27974 + 1.72134i) q^{36} +(0.866242 + 3.51448i) q^{37} +(1.53037 - 4.03525i) q^{38} +(-2.09798 + 2.93231i) q^{39} +(-1.42611 - 3.76034i) q^{40} +(-5.86348 + 4.04727i) q^{41} +(5.67363 - 5.02639i) q^{42} +(4.53280 + 1.11723i) q^{43} +(7.16415 + 2.71700i) q^{44} +(-0.459239 + 0.875007i) q^{45} +(11.3540 + 4.30601i) q^{46} +(1.15472 + 1.30341i) q^{47} +(-1.73033 + 1.53294i) q^{48} +(-1.74548 + 2.52876i) q^{49} +(7.90827 + 5.45869i) q^{50} +(0.841746 + 0.441782i) q^{51} +(-4.94586 + 12.4054i) q^{52} +(5.24511 - 2.75285i) q^{53} +(2.37089 + 0.287879i) q^{54} +(1.98477 - 0.489202i) q^{55} +(7.33726 - 10.6299i) q^{56} +(-1.48714 + 1.02650i) q^{57} +(-5.22904 + 5.90236i) q^{58} +(6.10129 + 0.740831i) q^{59} +(-0.875969 + 3.55394i) q^{60} +(0.134221 + 0.0704445i) q^{61} +(0.0235736 - 0.194146i) q^{62} +(-3.15061 + 0.382553i) q^{63} +(6.17878 - 8.95151i) q^{64} +(0.794166 + 3.47337i) q^{65} +(-2.80647 - 4.06588i) q^{66} +(7.45846 + 8.41886i) q^{67} +(3.41885 + 0.842671i) q^{68} +(-2.88827 - 4.18438i) q^{69} -7.49044i q^{70} +(-3.25036 + 2.24356i) q^{71} +(4.04004 - 0.490550i) q^{72} +(11.4839 - 4.35528i) q^{73} +(1.04202 - 8.58184i) q^{74} +(-1.42674 - 3.76200i) q^{75} +(-4.43842 + 5.00994i) q^{76} +(4.91409 + 4.35350i) q^{77} +(7.16841 - 4.77138i) q^{78} +(1.79258 - 1.58809i) q^{79} +2.28442i q^{80} +(-0.748511 - 0.663123i) q^{81} +(16.5214 - 4.07217i) q^{82} +(2.42199 + 1.67178i) q^{83} +(-10.9917 + 4.16860i) q^{84} +(0.878371 - 0.333122i) q^{85} +(-9.17602 - 6.33375i) q^{86} +(3.20576 - 0.790148i) q^{87} +(-6.30136 - 5.58252i) q^{88} +16.1650i q^{89} +(1.76658 - 1.56505i) q^{90} +(-7.73168 + 8.43598i) q^{91} +(-14.0965 - 12.4884i) q^{92} +(-0.0543014 + 0.0612936i) q^{93} +(-1.47474 - 3.88858i) q^{94} +(-0.215241 + 1.77267i) q^{95} +(-2.44823 + 0.928490i) q^{96} +(-16.6424 + 2.02076i) q^{97} +(6.03946 - 4.16874i) q^{98} +2.06858i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9} - 4 q^{10} + 12 q^{12} + 13 q^{13} + 2 q^{14} - 8 q^{16} - 4 q^{17} - 72 q^{22} + 48 q^{23} - 44 q^{25} - 39 q^{26} - 14 q^{27} + 45 q^{29} - 4 q^{30} - 26 q^{31}+ \cdots - 104 q^{98}+O(q^{100}) $ 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9 - 4 * q^10 + 12 * q^12 + 13 * q^13 + 2 * q^14 - 8 * q^16 - 4 * q^17 - 72 * q^22 + 48 * q^23 - 44 * q^25 - 39 * q^26 - 14 * q^27 + 45 * q^29 - 4 * q^30 - 26 * q^31 + 130 * q^32 + 13 * q^33 - 65 * q^34 - 35 * q^35 + 12 * q^36 + 61 * q^38 + 12 * q^40 - 63 * q^42 + 72 * q^43 - 39 * q^44 - 8 * q^48 - 68 * q^49 - 52 * q^50 - 4 * q^51 + 65 * q^52 - q^53 + 53 * q^55 - 14 * q^56 - 13 * q^57 - 26 * q^58 - 104 * q^59 + 117 * q^60 + 12 * q^61 + 49 * q^62 - 32 * q^64 - 52 * q^65 - 46 * q^66 + 26 * q^67 - 84 * q^68 - 4 * q^69 - 39 * q^71 - 52 * q^73 + 29 * q^74 + 8 * q^75 - 130 * q^76 + 60 * q^77 + 65 * q^78 + 14 * q^79 - 14 * q^81 + 45 * q^82 + 78 * q^83 - 13 * q^85 - 13 * q^86 - 46 * q^87 - 26 * q^88 - 4 * q^90 - 208 * q^91 + 82 * q^92 - 39 * q^93 + 25 * q^94 - 66 * q^95 + 65 * q^96 + 26 * q^97 - 104 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{3}{26}\right)$

Coefficient data

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

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

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

$2$	−2.23311	−	0.846906i	−1.57904	−	0.598853i	−0.599553	−	0.800335i	$-0.704655\pi$
$2$	−2.23311	−	0.846906i	−1.57904	−	0.598853i	−0.979492	+	0.201482i	$0.935424\pi$
$3$	0.568065	+	0.822984i	0.327972	+	0.475150i
$3$	0.568065	+	0.822984i	0.327972	+	0.475150i
$4$	2.77250	+	2.45622i	1.38625	+	1.22811i
$5$	0.980994	+	0.119114i	0.438714	+	0.0532695i	0.336914	−	0.941535i	$-0.390617\pi$
$5$	0.980994	+	0.119114i	0.438714	+	0.0532695i	0.101800	+	0.994805i	$0.467540\pi$
$6$	−0.571560	−	2.31891i	−0.233338	−	0.946690i
$7$	1.47491	+	2.81021i	0.557465	+	1.06216i	0.987242	+	0.159226i	$0.0508998\pi$
$7$	1.47491	+	2.81021i	0.557465	+	1.06216i	−0.429777	+	0.902935i	$0.641408\pi$
$8$	−1.89129	−	3.60355i	−0.668672	−	1.27405i
$9$	−0.354605	+	0.935016i	−0.118202	+	0.311672i
$10$	−2.08979	−	1.09680i	−0.660849	−	0.346840i
$11$	1.93416	−	0.733529i	0.583171	−	0.221167i	−0.0453359	−	0.998972i	$-0.514436\pi$
$11$	1.93416	−	0.733529i	0.583171	−	0.221167i	0.628506	+	0.777804i	$0.283667\pi$
$12$	−0.446470	+	3.67701i	−0.128885	+	1.06146i
$13$	1.22146	+	3.39235i	0.338771	+	0.940869i
$13$	1.22146	+	3.39235i	0.338771	+	0.940869i
$14$	−0.913654	−	7.52462i	−0.244184	−	2.01104i
$15$	0.459239	+	0.875007i	0.118575	+	0.225926i
$16$	0.278644	+	2.29484i	0.0696611	+	0.573711i
$17$	0.841746	−	0.441782i	0.204153	−	0.107148i	−0.359548	−	0.933127i	$-0.617069\pi$
$17$	0.841746	−	0.441782i	0.204153	−	0.107148i	0.563702	+	0.825979i	$0.309377\pi$
$18$	1.58374	−	1.78767i	0.373291	−	0.421359i
$19$			1.80701i			0.414557i	0.978282	+	0.207279i	$0.0664607\pi$
$19$			1.80701i			0.414557i	−0.978282	+	0.207279i	$0.933539\pi$
$20$	2.42723	+	2.73978i	0.542746	+	0.612633i
$21$	−1.47491	+	2.81021i	−0.321853	+	0.613239i
$22$	−4.94041			−1.05330
$23$	−5.08440			−1.06017			−0.530086	−	0.847944i	$-0.677840\pi$
$23$	−5.08440			−1.06017			−0.530086	+	0.847944i	$0.677840\pi$
$24$	1.89129	−	3.60355i	0.386058	−	0.735572i
$25$	−3.90655	−	0.962877i	−0.781309	−	0.192575i
$26$	0.145355	−	8.60994i	0.0285065	−	1.68855i
$27$	−0.970942	+	0.239316i	−0.186858	+	0.0460563i
$28$	−2.81330	+	11.4140i	−0.531664	+	2.15705i
$29$	1.17080	−	3.08714i	0.217412	−	0.573268i	−0.781292	−	0.624166i	$-0.785439\pi$
$29$	1.17080	−	3.08714i	0.217412	−	0.573268i	0.998704	+	0.0508977i	$0.0162082\pi$
$30$	−0.284482	−	2.34292i	−0.0519390	−	0.427756i
$31$	0.0195969	+	0.0795079i	0.00351972	+	0.0142800i	0.972675	−	0.232169i	$-0.0745823\pi$
$31$	0.0195969	+	0.0795079i	0.00351972	+	0.0142800i	−0.969156	+	0.246449i	$0.920736\pi$
$32$	−0.626619	+	2.54229i	−0.110772	+	0.449418i
$33$	1.70241	+	1.17509i	0.296351	+	0.204557i
$34$	−2.25386	+	0.273668i	−0.386533	+	0.0469336i
$35$	1.11215	+	2.93249i	0.187987	+	0.495681i
$36$	−3.27974	+	1.72134i	−0.546624	+	0.286890i
$37$	0.866242	+	3.51448i	0.142409	+	0.577777i	0.998174	+	0.0604113i	$0.0192412\pi$
$37$	0.866242	+	3.51448i	0.142409	+	0.577777i	−0.855764	+	0.517366i	$0.826913\pi$
$38$	1.53037	−	4.03525i	0.248259	−	0.654605i
$39$	−2.09798	+	2.93231i	−0.335946	+	0.469546i
$40$	−1.42611	−	3.76034i	−0.225488	−	0.594563i
$41$	−5.86348	+	4.04727i	−0.915722	+	0.632077i	−0.929896	−	0.367823i	$-0.880103\pi$
$41$	−5.86348	+	4.04727i	−0.915722	+	0.632077i	0.0141744	+	0.999900i	$0.495488\pi$
$42$	5.67363	−	5.02639i	0.875460	−	0.775589i
$43$	4.53280	+	1.11723i	0.691245	+	0.170377i	0.569263	−	0.822156i	$-0.307229\pi$
$43$	4.53280	+	1.11723i	0.691245	+	0.170377i	0.121982	+	0.992532i	$0.461075\pi$
$44$	7.16415	+	2.71700i	1.08004	+	0.409604i
$45$	−0.459239	+	0.875007i	−0.0684593	+	0.130438i
$46$	11.3540	+	4.30601i	1.67406	+	0.634887i
$47$	1.15472	+	1.30341i	0.168433	+	0.190121i	0.826666	−	0.562693i	$-0.190235\pi$
$47$	1.15472	+	1.30341i	0.168433	+	0.190121i	−0.658234	+	0.752814i	$0.728696\pi$
$48$	−1.73033	+	1.53294i	−0.249752	+	0.221261i
$49$	−1.74548	+	2.52876i	−0.249354	+	0.361251i
$50$	7.90827	+	5.45869i	1.11840	+	0.771975i
$51$	0.841746	+	0.441782i	0.117868	+	0.0618619i
$52$	−4.94586	+	12.4054i	−0.685867	+	1.72032i
$53$	5.24511	−	2.75285i	0.720471	−	0.378133i	−0.0642894	−	0.997931i	$-0.520478\pi$
$53$	5.24511	−	2.75285i	0.720471	−	0.378133i	0.784761	+	0.619799i	$0.212786\pi$
$54$	2.37089	+	0.287879i	0.322638	+	0.0391753i
$55$	1.98477	−	0.489202i	0.267627	−	0.0659640i
$56$	7.33726	−	10.6299i	0.980483	−	1.42047i
$57$	−1.48714	+	1.02650i	−0.196977	+	0.135963i
$58$	−5.22904	+	5.90236i	−0.686606	+	0.775018i
$59$	6.10129	+	0.740831i	0.794320	+	0.0964480i	0.507630	−	0.861575i	$-0.330522\pi$
$59$	6.10129	+	0.740831i	0.794320	+	0.0964480i	0.286691	+	0.958023i	$0.407445\pi$
$60$	−0.875969	+	3.55394i	−0.113087	+	0.458812i
$61$	0.134221	+	0.0704445i	0.0171852	+	0.00901949i	0.473294	−	0.880905i	$-0.343065\pi$
$61$	0.134221	+	0.0704445i	0.0171852	+	0.00901949i	−0.456109	+	0.889924i	$0.650757\pi$
$62$	0.0235736	−	0.194146i	0.00299386	−	0.0246566i
$63$	−3.15061	+	0.382553i	−0.396939	+	0.0481971i
$64$	6.17878	−	8.95151i	0.772347	−	1.11894i
$65$	0.794166	+	3.47337i	0.0985042	+	0.430818i
$66$	−2.80647	−	4.06588i	−0.345453	−	0.500475i
$67$	7.45846	+	8.41886i	0.911196	+	1.02853i	0.999474	+	0.0324318i	$0.0103252\pi$
$67$	7.45846	+	8.41886i	0.911196	+	1.02853i	−0.0882779	+	0.996096i	$0.528136\pi$
$68$	3.41885	+	0.842671i	0.414597	+	0.102189i
$69$	−2.88827	−	4.18438i	−0.347707	−	0.503741i
$70$		−	7.49044i		−	0.895279i
$71$	−3.25036	+	2.24356i	−0.385747	+	0.266262i	−0.745118	−	0.666933i	$-0.767607\pi$
$71$	−3.25036	+	2.24356i	−0.385747	+	0.266262i	0.359371	+	0.933195i	$0.382991\pi$
$72$	4.04004	−	0.490550i	0.476123	−	0.0578118i
$73$	11.4839	−	4.35528i	1.34409	−	0.509747i	0.425503	−	0.904957i	$-0.360097\pi$
$73$	11.4839	−	4.35528i	1.34409	−	0.509747i	0.918591	+	0.395210i	$0.129328\pi$
$74$	1.04202	−	8.58184i	0.121133	−	0.997618i
$75$	−1.42674	−	3.76200i	−0.164746	−	0.434399i
$76$	−4.43842	+	5.00994i	−0.509121	+	0.574679i
$77$	4.91409	+	4.35350i	0.560013	+	0.496128i
$78$	7.16841	−	4.77138i	0.811663	−	0.540252i
$79$	1.79258	−	1.58809i	0.201681	−	0.178674i	−0.556237	−	0.831024i	$-0.687755\pi$
$79$	1.79258	−	1.58809i	0.201681	−	0.178674i	0.757918	+	0.652350i	$0.226217\pi$
$80$			2.28442i			0.255406i
$81$	−0.748511	−	0.663123i	−0.0831679	−	0.0736803i
$82$	16.5214	−	4.07217i	1.82449	−	0.449696i
$83$	2.42199	+	1.67178i	0.265848	+	0.183502i	0.693530	−	0.720427i	$-0.256054\pi$
$83$	2.42199	+	1.67178i	0.265848	+	0.183502i	−0.427682	+	0.903929i	$0.640670\pi$
$84$	−10.9917	+	4.16860i	−1.19929	+	0.454831i
$85$	0.878371	−	0.333122i	0.0952727	−	0.0361322i
$86$	−9.17602	−	6.33375i	−0.989476	−	0.682986i
$87$	3.20576	−	0.790148i	0.343693	−	0.0847128i
$88$	−6.30136	−	5.58252i	−0.671728	−	0.595099i
$89$			16.1650i			1.71349i	0.515743	+	0.856743i	$0.327516\pi$
$89$			16.1650i			1.71349i	−0.515743	+	0.856743i	$0.672484\pi$
$90$	1.76658	−	1.56505i	0.186214	−	0.164971i
$91$	−7.73168	+	8.43598i	−0.810501	+	0.884331i
$92$	−14.0965	−	12.4884i	−1.46966	−	1.30201i
$93$	−0.0543014	+	0.0612936i	−0.00563079	+	0.00635585i
$94$	−1.47474	−	3.88858i	−0.152108	−	0.401076i
$95$	−0.215241	+	1.77267i	−0.0220833	+	0.181872i
$96$	−2.44823	+	0.928490i	−0.249871	+	0.0947636i
$97$	−16.6424	+	2.02076i	−1.68978	+	0.205177i	−0.908174	−	0.418592i	$-0.862524\pi$
$97$	−16.6424	+	2.02076i	−1.68978	+	0.205177i	−0.781609	+	0.623769i	$0.785601\pi$
$98$	6.03946	−	4.16874i	0.610077	−	0.421106i
$99$			2.06858i			0.207900i
$100$	−8.46585	−	12.2649i	−0.846585	−	1.22649i
$101$	−16.2635	−	4.00859i	−1.61828	−	0.398870i	−0.676860	−	0.736112i	$-0.736660\pi$
$101$	−16.2635	−	4.00859i	−1.61828	−	0.398870i	−0.941418	+	0.337242i	$0.890506\pi$
$102$	−1.50556	−	1.69943i	−0.149073	−	0.168268i
$103$	−3.42965	−	4.96870i	−0.337933	−	0.489581i	0.616769	−	0.787144i	$-0.288441\pi$
$103$	−3.42965	−	4.96870i	−0.337933	−	0.489581i	−0.954702	+	0.297564i	$0.903826\pi$
$104$	9.91438	−	10.8175i	0.972185	−	1.06074i
$105$	−1.78162	+	2.58112i	−0.173868	+	0.251892i
$106$	−14.0443	+	1.70529i	−1.36410	+	0.165632i
$107$	−0.914392	+	7.53070i	−0.0883976	+	0.728020i	0.879364	+	0.476151i	$0.157968\pi$
$107$	−0.914392	+	7.53070i	−0.0883976	+	0.728020i	−0.967761	+	0.251869i	$0.918955\pi$
$108$	−3.27974	−	1.72134i	−0.315593	−	0.165636i
$109$	4.22407	−	17.1377i	0.404593	−	1.64150i	−0.316453	−	0.948608i	$-0.602492\pi$
$109$	4.22407	−	17.1377i	0.404593	−	1.64150i	0.721045	−	0.692888i	$-0.243662\pi$
$110$	−4.84652	−	0.588474i	−0.462097	−	0.0561088i
$111$	−2.40028	+	2.70936i	−0.227825	+	0.257161i
$112$	−6.03802	+	4.16775i	−0.570539	+	0.393815i
$113$	4.52329	−	6.55311i	0.425515	−	0.616465i	−0.550325	−	0.834950i	$-0.685496\pi$
$113$	4.52329	−	6.55311i	0.425515	−	0.616465i	0.975840	+	0.218485i	$0.0701116\pi$
$114$	4.19030	−	1.03282i	0.392457	−	0.0967321i
$115$	−4.98777	−	0.605625i	−0.465112	−	0.0564748i
$116$	10.8287	−	5.68335i	1.00542	−	0.527686i
$117$	−3.60504	−	0.0608611i	−0.333286	−	0.00562661i
$118$	−12.9974	−	6.82157i	−1.19651	−	0.627977i
$119$	2.48301	+	1.71390i	0.227617	+	0.157113i
$120$	2.28458	−	3.30978i	0.208553	−	0.302141i
$121$	−5.03072	+	4.45683i	−0.457338	+	0.405166i
$122$	−0.240070	−	0.270982i	−0.0217349	−	0.0245336i
$123$	−6.66167	−	2.52644i	−0.600663	−	0.227801i
$124$	−0.140956	+	0.268570i	−0.0126582	+	0.0241183i
$125$	−8.33752	−	3.16200i	−0.745731	−	0.282818i
$126$	7.35963	+	1.81399i	0.655648	+	0.161603i
$127$	10.7952	−	9.56373i	0.957920	−	0.848643i	−0.0306306	−	0.999531i	$-0.509752\pi$
$127$	10.7952	−	9.56373i	0.957920	−	0.848643i	0.988551	+	0.150887i	$0.0482131\pi$
$128$	−17.0692	+	11.7820i	−1.50872	+	1.04139i
$129$	1.65546	+	4.36508i	0.145755	+	0.384324i
$130$	1.16816	−	8.42899i	0.102454	−	0.739271i
$131$	0.897277	−	2.36593i	0.0783955	−	0.206712i	−0.890089	−	0.455788i	$-0.849358\pi$
$131$	0.897277	−	2.36593i	0.0783955	−	0.206712i	0.968484	+	0.249076i	$0.0801268\pi$
$132$	1.83365	+	7.43941i	0.159599	+	0.647518i
$133$	−5.07809	+	2.66519i	−0.440327	+	0.231101i
$134$	−9.52556	−	25.1168i	−0.822883	−	2.16976i
$135$	−0.980994	+	0.119114i	−0.0844306	+	0.0102517i
$136$	−3.18397	−	2.19774i	−0.273023	−	0.188454i
$137$	1.52011	−	6.16731i	0.129871	−	0.526909i	−0.869580	−	0.493792i	$-0.835610\pi$
$137$	1.52011	−	6.16731i	0.129871	−	0.526909i	0.999451	−	0.0331170i	$-0.0105434\pi$
$138$	2.90604	+	11.7903i	0.247379	+	1.00365i
$139$	−2.15122	−	17.7169i	−0.182464	−	1.50273i	−0.740018	−	0.672587i	$-0.765183\pi$
$139$	−2.15122	−	17.7169i	−0.182464	−	1.50273i	0.557554	−	0.830141i	$-0.311740\pi$
$140$	−4.11940	+	10.8620i	−0.348153	+	0.918005i
$141$	−0.416728	+	1.69073i	−0.0350948	+	0.142385i
$142$	9.15849	−	2.25737i	0.768564	−	0.189434i
$143$	4.85088	+	5.66537i	0.405651	+	0.473762i
$144$	−2.24452	−	0.553225i	−0.187044	−	0.0461021i
$145$	1.51627	−	2.88901i	0.125919	−	0.239919i
$146$	−29.3334			−2.42765
$147$	−3.07267			−0.253430
$148$	−6.23068	+	11.8716i	−0.512158	+	0.975836i
$149$	−2.02091	−	2.28114i	−0.165559	−	0.186878i	0.659876	−	0.751375i	$-0.270609\pi$
$149$	−2.02091	−	2.28114i	−0.165559	−	0.186878i	−0.825435	+	0.564497i	$0.809070\pi$
$150$			9.60927i			0.784593i
$151$	13.3243	−	15.0400i	1.08431	−	1.22394i	0.111154	−	0.993803i	$-0.464545\pi$
$151$	13.3243	−	15.0400i	1.08431	−	1.22394i	0.973159	−	0.230134i	$-0.0739163\pi$
$152$	6.51167	−	3.41759i	0.528166	−	0.277203i
$153$	0.114586	+	0.943705i	0.00926377	+	0.0762940i
$154$	−7.28668	−	13.8836i	−0.587178	−	1.11877i
$155$	0.00975396	+	0.0803311i	0.000783457	+	0.00645235i
$156$	−13.0190	+	2.97673i	−1.04236	+	0.238329i
$157$	−2.30553	+	18.9878i	−0.184002	+	1.51539i	0.549380	+	0.835573i	$0.314864\pi$
$157$	−2.30553	+	18.9878i	−0.184002	+	1.51539i	−0.733381	+	0.679817i	$0.762059\pi$
$158$	−5.34798	+	2.02822i	−0.425462	+	0.161357i
$159$	5.24511	+	2.75285i	0.415964	+	0.218315i
$160$	−0.917534	+	2.41934i	−0.0725374	+	0.191265i
$161$	−7.49906	−	14.2883i	−0.591009	−	1.12607i
$162$	1.10990	+	2.11474i	0.0872021	+	0.166150i
$163$	2.10472	+	8.53920i	0.164855	+	0.668842i	0.993959	+	0.109748i	$0.0350045\pi$
$163$	2.10472	+	8.53920i	0.164855	+	0.668842i	−0.829105	+	0.559093i	$0.811149\pi$
$164$	−26.1974	−	3.18094i	−2.04568	−	0.248390i
$165$	1.53008	+	1.35554i	0.119117	+	0.105528i
$166$	−3.99273	−	5.78447i	−0.309896	−	0.448962i
$167$	14.4411	+	5.47678i	1.11748	+	0.423806i	0.843069	−	0.537805i	$-0.180746\pi$
$167$	14.4411	+	5.47678i	1.11748	+	0.423806i	0.274416	+	0.961611i	$0.411516\pi$
$168$	12.9162			0.996510
$169$	−10.0161	+	8.28723i	−0.770468	+	0.637479i
$170$	−2.24362			−0.172078
$171$	−1.68959	−	0.640776i	−0.129206	−	0.0490014i
$172$	9.82299	+	14.2311i	0.748996	+	1.08511i
$173$	−1.56794	−	1.38907i	−0.119208	−	0.105609i	0.601413	−	0.798938i	$-0.294605\pi$
$173$	−1.56794	−	1.38907i	−0.119208	−	0.105609i	−0.720621	+	0.693329i	$0.756143\pi$
$174$	−7.82798	−	0.950489i	−0.593438	−	0.0720564i
$175$	−3.05593	−	12.3984i	−0.231007	−	0.937230i
$176$	2.22228	+	4.23419i	0.167510	+	0.319164i
$177$	2.85624	+	5.44210i	0.214688	+	0.409054i
$178$	13.6902	−	36.0982i	1.02613	−	2.70567i
$179$	3.51531	+	1.84498i	0.262747	+	0.137900i	0.590953	−	0.806706i	$-0.298752\pi$
$179$	3.51531	+	1.84498i	0.262747	+	0.137900i	−0.328206	+	0.944606i	$0.606444\pi$
$180$	−3.42245	+	1.29796i	−0.255094	+	0.0967444i
$181$	−0.0631595	+	0.520165i	−0.00469461	+	0.0386636i	−0.994868	−	0.101182i	$-0.967738\pi$
$181$	−0.0631595	+	0.520165i	−0.00469461	+	0.0386636i	0.990173	+	0.139846i	$0.0446606\pi$
$182$	24.4102	−	12.2904i	1.80940	−	0.911028i
$183$	0.0182714	+	0.150479i	0.00135066	+	0.0111237i
$184$	9.61608	+	18.3219i	0.708907	+	1.35071i
$185$	0.431153	+	3.55087i	0.0316990	+	0.261065i
$186$	0.173171	−	0.0908870i	0.0126975	−	0.00666416i
$187$	1.30401	−	1.47192i	0.0953586	−	0.107638i
$188$			6.44992i			0.470409i
$189$	−2.10458	−	2.37558i	−0.153086	−	0.172798i
$190$	1.98194	−	3.77627i	0.143785	−	0.273960i
$191$	−11.7428			−0.849682			−0.424841	−	0.905268i	$-0.639670\pi$
$191$	−11.7428			−0.849682			−0.424841	+	0.905268i	$0.639670\pi$
$192$	10.8769			0.784972
$193$	10.6210	−	20.2367i	0.764518	−	1.45667i	−0.121291	−	0.992617i	$-0.538703\pi$
$193$	10.6210	−	20.2367i	0.764518	−	1.45667i	0.885809	−	0.464050i	$-0.153604\pi$
$194$	38.8757	+	9.58201i	2.79111	+	0.687948i
$195$	−2.40739	+	2.62668i	−0.172397	+	0.188101i
$196$	−11.0505	+	2.72371i	−0.789322	+	0.194550i
$197$	−2.99196	+	12.1388i	−0.213168	+	0.864857i	0.762745	+	0.646699i	$0.223851\pi$
$197$	−2.99196	+	12.1388i	−0.213168	+	0.864857i	−0.975913	+	0.218158i	$0.929995\pi$
$198$	1.75189	−	4.61936i	0.124502	−	0.328284i
$199$	0.0875498	+	0.721038i	0.00620624	+	0.0511130i	0.995483	−	0.0949402i	$-0.0302660\pi$
$199$	0.0875498	+	0.721038i	0.00620624	+	0.0511130i	−0.989277	+	0.146053i	$0.953343\pi$
$200$	3.91863	+	15.8985i	0.277089	+	1.12420i
$201$	−2.69170	+	10.9207i	−0.189858	+	0.770283i
$202$	32.9232	+	22.7253i	2.31647	+	1.59894i
$203$	10.4024	−	1.26308i	0.730102	−	0.0886505i
$204$	1.24862	+	3.29235i	0.0874212	+	0.230511i
$205$	−6.23413	+	3.27192i	−0.435410	+	0.228521i
$206$	3.45075	+	14.0002i	0.240425	+	0.975442i
$207$	1.80295	−	4.75400i	0.125314	−	0.330426i
$208$	−7.44456	+	3.74831i	−0.516187	+	0.259899i
$209$	1.32550	+	3.49505i	0.0916866	+	0.241758i
$210$	6.16451	−	4.25505i	0.425392	−	0.293627i
$211$	18.3024	−	16.2145i	1.25999	−	1.11625i	0.271903	−	0.962325i	$-0.412347\pi$
$211$	18.3024	−	16.2145i	1.25999	−	1.11625i	0.988082	−	0.153925i	$-0.0491915\pi$
$212$	21.3036	+	5.25087i	1.46314	+	0.360631i
$213$	−3.69283	−	1.40051i	−0.253029	−	0.0959612i
$214$	8.41972	−	16.0424i	0.575560	−	1.09664i
$215$	4.31357	+	1.63592i	0.294183	+	0.111569i
$216$	2.69872	+	3.04622i	0.183625	+	0.207269i
$217$	−0.194530	+	0.172339i	−0.0132056	+	0.0116991i
$218$	−23.9468	+	34.6930i	−1.62188	+	2.34971i
$219$	10.1080	+	6.97701i	0.683032	+	0.471463i
$220$	6.70436	+	3.51872i	0.452008	+	0.237232i
$221$	2.52684	+	2.31588i	0.169974	+	0.155783i
$222$	7.65465	−	4.01747i	0.513747	−	0.269635i
$223$	−9.82484	−	1.19295i	−0.657920	−	0.0798860i	−0.215234	−	0.976563i	$-0.569051\pi$
$223$	−9.82484	−	1.19295i	−0.657920	−	0.0798860i	−0.442686	+	0.896677i	$0.645974\pi$
$224$	−8.06860	+	1.98873i	−0.539106	+	0.132878i
$225$	2.28559	−	3.31124i	0.152372	−	0.220750i
$226$	−15.6509	+	10.8030i	−1.04108	+	0.718605i
$227$	15.1205	−	17.0675i	1.00358	−	1.13281i	0.0124521	−	0.999922i	$-0.496036\pi$
$227$	15.1205	−	17.0675i	1.00358	−	1.13281i	0.991131	−	0.132889i	$-0.0424253\pi$
$228$	−6.64440	−	0.806777i	−0.440036	−	0.0534301i
$229$	4.34373	−	17.6232i	0.287041	−	1.16457i	−0.633442	−	0.773791i	$-0.718358\pi$
$229$	4.34373	−	17.6232i	0.287041	−	1.16457i	0.920483	−	0.390782i	$-0.127796\pi$
$230$	10.6253	+	5.57660i	0.700613	+	0.367710i
$231$	−0.791342	+	6.51729i	−0.0520665	+	0.428806i
$232$	−13.3390	+	1.61965i	−0.875748	+	0.106335i
$233$	6.54549	−	9.48278i	0.428809	−	0.621237i	−0.547710	−	0.836668i	$-0.684500\pi$
$233$	6.54549	−	9.48278i	0.428809	−	0.621237i	0.976519	+	0.215431i	$0.0691156\pi$
$234$	7.99889	+	3.18904i	0.522904	+	0.208474i
$235$	0.977516	+	1.41618i	0.0637661	+	0.0923812i
$236$	15.0962	+	17.0400i	0.982676	+	1.10921i
$237$	2.32527	+	0.573127i	0.151042	+	0.0372286i
$238$	−4.09331	−	5.93018i	−0.265330	−	0.384397i
$239$		−	3.75404i		−	0.242829i	−0.992602	−	0.121414i	$-0.961257\pi$
$239$		−	3.75404i		−	0.242829i	0.992602	−	0.121414i	$-0.0387430\pi$
$240$	−1.88004	+	1.29770i	−0.121356	+	0.0837660i
$241$	1.40167	−	0.170193i	0.0902893	−	0.0109631i	−0.0752673	−	0.997163i	$-0.523981\pi$
$241$	1.40167	−	0.170193i	0.0902893	−	0.0109631i	0.165557	+	0.986200i	$0.447058\pi$
$242$	15.0086	−	5.69203i	0.964792	−	0.365897i
$243$	0.120537	−	0.992709i	0.00773243	−	0.0636823i
$244$	0.199100	+	0.524982i	0.0127460	+	0.0336086i
$245$	−2.01351	+	2.27279i	−0.128639	+	0.145203i
$246$	12.7366	+	11.2836i	0.812054	+	0.719417i
$247$	−6.13002	+	2.20719i	−0.390044	+	0.140440i
$248$	0.249447	−	0.220991i	0.0158399	−	0.0140330i
$249$			2.94294i			0.186501i
$250$	15.9407	+	14.1222i	1.00818	+	0.893166i
$251$	4.23953	−	1.04495i	0.267597	−	0.0659567i	−0.103234	−	0.994657i	$-0.532919\pi$
$251$	4.23953	−	1.04495i	0.267597	−	0.0659567i	0.370831	+	0.928700i	$0.379073\pi$
$252$	−9.67468	−	6.67795i	−0.609447	−	0.420671i
$253$	−9.83404	+	3.72956i	−0.618261	+	0.234475i
$254$	−32.2064	+	12.2143i	−2.02081	+	0.766393i
$255$	0.773126	+	0.533650i	0.0484150	+	0.0334185i
$256$	26.9739	−	6.64847i	1.68587	−	0.415529i
$257$	15.5996	+	13.8200i	0.973074	+	0.862069i	0.990463	−	0.137780i	$-0.0439967\pi$
$257$	15.5996	+	13.8200i	0.973074	+	0.862069i	−0.0173885	+	0.999849i	$0.505535\pi$
$258$		−	11.1497i		−	0.694150i
$259$	−8.59881	+	7.61788i	−0.534304	+	0.473352i
$260$	−6.32953	+	11.5805i	−0.392541	+	0.718195i
$261$	2.47136	+	2.18943i	0.152973	+	0.135522i
$262$	−4.00743	+	4.52345i	−0.247580	+	0.279460i
$263$	−6.52876	−	17.2149i	−0.402581	−	1.06152i	−0.971063	−	0.238823i	$-0.923239\pi$
$263$	−6.52876	−	17.2149i	−0.402581	−	1.06152i	0.568483	−	0.822695i	$-0.307531\pi$
$264$	1.01474	−	8.35715i	0.0624531	−	0.514347i
$265$	5.47333	−	2.07576i	0.336224	−	0.127513i
$266$	13.5971	−	1.65099i	0.833691	−	0.101228i
$267$	−13.3035	+	9.18276i	−0.814163	+	0.561976i
$268$			41.6608i			2.54484i
$269$	−15.7599	−	22.8322i	−0.960899	−	1.39210i	−0.919557	−	0.392957i	$-0.871452\pi$
$269$	−15.7599	−	22.8322i	−0.960899	−	1.39210i	−0.0413421	−	0.999145i	$-0.513163\pi$
$270$	2.29154	+	0.564815i	0.139459	+	0.0343735i
$271$	−9.01293	−	10.1735i	−0.547497	−	0.617996i	0.408006	−	0.912979i	$-0.366224\pi$
$271$	−9.01293	−	10.1735i	−0.547497	−	0.617996i	−0.955502	+	0.294983i	$0.904686\pi$
$272$	1.24837	+	1.80857i	0.0756935	+	0.109661i
$273$	−11.3348	−	1.57087i	−0.686012	−	0.0950732i
$274$	−8.61769	+	12.4849i	−0.520614	+	0.754239i
$275$	−8.26218	+	1.00321i	−0.498228	+	0.0604958i
$276$	2.27003	−	18.6954i	0.136640	−	1.12533i
$277$	22.7886	+	11.9604i	1.36924	+	0.718630i	0.979338	−	0.202228i	$-0.0648183\pi$
$277$	22.7886	+	11.9604i	1.36924	+	0.718630i	0.389897	+	0.920858i	$0.372511\pi$
$278$	−10.2006	+	41.3856i	−0.611794	+	2.48214i
$279$	−0.0812904	−	0.00987044i	−0.00486673	−	0.000590928i
$280$	8.46398	−	9.55386i	0.505820	−	0.570952i
$281$	−4.75931	+	3.28511i	−0.283916	+	0.195973i	−0.701508	−	0.712661i	$-0.747490\pi$
$281$	−4.75931	+	3.28511i	−0.283916	+	0.195973i	0.417592	+	0.908635i	$0.362874\pi$
$282$	2.36249	−	3.42265i	0.140684	−	0.203816i
$283$	−6.26832	+	1.54500i	−0.372613	+	0.0918408i	−0.421175	−	0.906979i	$-0.638382\pi$
$283$	−6.26832	+	1.54500i	−0.372613	+	0.0918408i	0.0485623	+	0.998820i	$0.484536\pi$
$284$	−14.5223	−	1.76333i	−0.861740	−	0.104634i
$285$	−1.58115	+	0.829851i	−0.0936592	+	0.0491562i
$286$	−6.03450	−	16.7596i	−0.356828	−	0.991016i
$287$	−20.0218	−	10.5083i	−1.18185	−	0.620283i
$288$	−2.15488	−	1.48741i	−0.126978	−	0.0876464i
$289$	−9.14374	+	13.2470i	−0.537867	+	0.779235i
$290$	−5.83271	+	5.16733i	−0.342509	+	0.303436i
$291$	−11.1170	−	12.5485i	−0.651692	−	0.735608i
$292$	42.5367	+	16.1320i	2.48927	+	0.944056i
$293$	−9.82184	+	18.7139i	−0.573798	+	1.09328i	0.409676	+	0.912231i	$0.365642\pi$
$293$	−9.82184	+	18.7139i	−0.573798	+	1.09328i	−0.983474	+	0.181049i	$0.942051\pi$
$294$	6.86161	+	2.60226i	0.400177	+	0.151767i
$295$	5.89709	+	1.45350i	0.343342	+	0.0846262i
$296$	11.0263	−	9.76845i	0.640891	−	0.567780i
$297$	−1.70241	+	1.17509i	−0.0987838	+	0.0681856i
$298$	2.58100	+	6.80554i	0.149513	+	0.394234i
$299$	−6.21039	−	17.2481i	−0.359156	−	0.997482i
$300$	5.28466	−	13.9345i	0.305110	−	0.804509i
$301$	3.54582	+	14.3859i	0.204378	+	0.829192i
$302$	−42.4920	+	22.3015i	−2.44514	+	1.28331i
$303$	−5.93971	−	15.6617i	−0.341227	−	0.899743i
$304$	−4.14681	+	0.503514i	−0.237836	+	0.0288785i
$305$	0.123279	+	0.0850933i	0.00705893	+	0.00487243i
$306$	0.543345	−	2.20444i	0.0310610	−	0.126019i
$307$	2.24317	+	9.10091i	0.128025	+	0.519416i	0.999576	+	0.0291123i	$0.00926803\pi$
$307$	2.24317	+	9.10091i	0.128025	+	0.519416i	−0.871552	+	0.490304i	$0.836886\pi$
$308$	2.93114	+	24.1401i	0.167017	+	1.37551i
$309$	2.14090	−	5.64509i	0.121792	−	0.321138i
$310$	0.0462512	−	0.187649i	0.00262689	−	0.0106577i
$311$	28.1555	−	6.93971i	1.59655	−	0.393515i	0.662046	−	0.749463i	$-0.269688\pi$
$311$	28.1555	−	6.93971i	1.59655	−	0.393515i	0.934506	+	0.355948i	$0.115842\pi$
$312$	14.5346	+	2.01433i	0.822862	+	0.114039i
$313$	−9.78250	−	2.41117i	−0.552940	−	0.136287i	−0.0470611	−	0.998892i	$-0.514986\pi$
$313$	−9.78250	−	2.41117i	−0.552940	−	0.136287i	−0.505879	+	0.862605i	$0.668832\pi$
$314$	21.2294	−	40.4492i	1.19804	−	2.28268i
$315$	−3.13630			−0.176710
$316$	8.87060			0.499010
$317$	2.36722	−	4.51037i	0.132957	−	0.253328i	−0.809871	−	0.586608i	$-0.800463\pi$
$317$	2.36722	−	4.51037i	0.132957	−	0.253328i	0.942828	+	0.333280i	$0.108155\pi$
$318$	−9.38149	−	10.5895i	−0.526088	−	0.593831i
$319$		−	6.82984i		−	0.382397i
$320$	7.12760	−	8.04540i	0.398445	−	0.449751i
$321$	−6.71707	+	3.52539i	−0.374911	+	0.196768i
$322$	4.64539	+	38.2582i	0.258877	+	2.13205i
$323$	0.798307	+	1.52105i	0.0444190	+	0.0846333i
$324$	−0.446470	−	3.67701i	−0.0248039	−	0.204278i
$325$	−1.50527	−	14.4285i	−0.0834971	−	0.800349i
$326$	2.53182	−	20.8515i	0.140225	−	1.15486i
$327$	16.5036	−	6.25900i	0.912652	−	0.346123i
$328$	25.6741	+	13.4748i	1.41761	+	0.744021i
$329$	−1.95974	+	5.16741i	−0.108044	+	0.284888i
$330$	−2.26883	−	4.32290i	−0.124895	−	0.237968i
$331$	−14.4598	−	27.5509i	−0.794785	−	1.51434i	−0.856445	−	0.516238i	$-0.827332\pi$
$331$	−14.4598	−	27.5509i	−0.794785	−	1.51434i	0.0616602	−	0.998097i	$-0.480360\pi$
$332$	2.60871	+	10.5840i	0.143172	+	0.580870i
$333$	−3.59327	−	0.436302i	−0.196910	−	0.0239092i
$334$	−27.6102	−	24.4605i	−1.51076	−	1.33842i
$335$	6.31390	+	9.14727i	0.344965	+	0.499769i
$336$	−6.85997	−	2.60165i	−0.374242	−	0.141931i
$337$	−5.98562			−0.326058			−0.163029	−	0.986621i	$-0.552126\pi$
$337$	−5.98562			−0.326058			−0.163029	+	0.986621i	$0.552126\pi$
$338$	29.3855	−	10.0236i	1.59836	−	0.545211i
$339$	7.96263			0.432471
$340$	3.25350	+	1.23389i	0.176446	+	0.0669170i
$341$	0.0962250	+	0.139406i	0.00521088	+	0.00754926i
$342$	3.23035	+	2.86184i	0.174677	+	0.154751i
$343$	12.3735	+	1.50241i	0.668104	+	0.0811226i
$344$	−4.54682	−	18.4472i	−0.245148	−	0.994605i
$345$	−2.33496	−	4.44889i	−0.125710	−	0.239520i
$346$	2.32496	+	4.42984i	0.124991	+	0.238150i
$347$	1.35798	−	3.58069i	0.0729000	−	0.192222i	−0.893613	−	0.448837i	$-0.851838\pi$
$347$	1.35798	−	3.58069i	0.0729000	−	0.192222i	0.966513	+	0.256616i	$0.0826075\pi$
$348$	10.8287	+	5.68335i	0.580481	+	0.304660i
$349$	−12.9338	+	4.90514i	−0.692329	+	0.262566i	−0.675572	−	0.737294i	$-0.736103\pi$
$349$	−12.9338	+	4.90514i	−0.692329	+	0.262566i	−0.0167570	+	0.999860i	$0.505334\pi$
$350$	−3.67605	+	30.2750i	−0.196493	+	1.61827i
$351$	−1.99781	−	3.00146i	−0.106635	−	0.160206i
$352$	0.652867	+	5.37684i	0.0347979	+	0.286587i
$353$	−11.6360	−	22.1705i	−0.619322	−	1.18002i	−0.969904	−	0.243487i	$-0.921709\pi$
$353$	−11.6360	−	22.1705i	−0.619322	−	1.18002i	0.350583	−	0.936532i	$-0.385984\pi$
$354$	−1.76933	−	14.5718i	−0.0940390	−	0.774480i
$355$	−3.45583	+	1.81376i	−0.183416	+	0.0962643i
$356$	−39.7047	+	44.8174i	−2.10435	+	2.37532i
$357$			3.01708i			0.159681i
$358$	−6.28755	−	7.09717i	−0.332307	−	0.375097i
$359$	−10.8018	+	20.5811i	−0.570096	+	1.08623i	0.414280	+	0.910150i	$0.364034\pi$
$359$	−10.8018	+	20.5811i	−0.570096	+	1.08623i	−0.984376	+	0.176078i	$0.943659\pi$
$360$	4.02169			0.211962
$361$	15.7347			0.828142
$362$	0.581573	−	1.10809i	0.0305668	−	0.0582401i
$363$	−6.52567	−	1.60843i	−0.342509	−	0.0844208i
$364$	−42.1567	+	4.39803i	−2.20961	+	0.230519i
$365$	11.7845	−	2.90461i	0.616827	−	0.152034i
$366$	0.0866392	−	0.351509i	0.00452870	−	0.0183737i
$367$	−6.79211	+	17.9093i	−0.354545	+	0.934858i	0.632521	+	0.774543i	$0.282020\pi$
$367$	−6.79211	+	17.9093i	−0.354545	+	0.934858i	−0.987066	+	0.160315i	$0.948749\pi$
$368$	−1.41674	−	11.6679i	−0.0738527	−	0.608232i
$369$	−1.70504	−	6.91763i	−0.0887610	−	0.360117i
$370$	2.04444	−	8.29461i	0.106285	−	0.431216i
$371$	15.4722	+	10.6797i	0.803275	+	0.554461i
$372$	−0.301101	+	0.0365603i	−0.0156113	+	0.00189556i
$373$	3.73391	+	9.84551i	0.193335	+	0.509781i	0.996271	−	0.0862839i	$-0.0274992\pi$
$373$	3.73391	+	9.84551i	0.193335	+	0.509781i	−0.802936	+	0.596065i	$0.796730\pi$
$374$	−4.15857	+	2.18259i	−0.215035	+	0.112859i
$375$	−2.13397	−	8.65787i	−0.110198	−	0.447090i
$376$	2.51298	−	6.62620i	0.129597	−	0.341720i
$377$	11.9028	+	0.200945i	0.613023	+	0.0103492i
$378$	2.68786	+	7.08732i	0.138249	+	0.364532i
$379$	16.1824	−	11.1699i	0.831235	−	0.573760i	−0.0746862	−	0.997207i	$-0.523796\pi$
$379$	16.1824	−	11.1699i	0.831235	−	0.573760i	0.905921	+	0.423447i	$0.139180\pi$
$380$	−4.95082	+	4.38604i	−0.253972	+	0.224999i
$381$	14.0032	+	3.45147i	0.717404	+	0.176824i
$382$	26.2230	+	9.94508i	1.34169	+	0.508835i
$383$	14.4184	−	27.4720i	0.736746	−	1.40375i	−0.171444	−	0.985194i	$-0.554843\pi$
$383$	14.4184	−	27.4720i	0.736746	−	1.40375i	0.908190	−	0.418558i	$-0.137464\pi$
$384$	−19.3928	−	7.35472i	−0.989635	−	0.375319i
$385$	4.30213	+	4.85610i	0.219257	+	0.247490i
$386$	−40.8564	+	36.1956i	−2.07954	+	1.84231i
$387$	−2.65198	+	3.84206i	−0.134808	+	0.195303i
$388$	−51.1045	−	35.2749i	−2.59444	−	1.79081i
$389$	−23.2210	−	12.1873i	−1.17735	−	0.617922i	−0.241530	−	0.970393i	$-0.577649\pi$
$389$	−23.2210	−	12.1873i	−1.17735	−	0.617922i	−0.935823	+	0.352471i	$0.885341\pi$
$390$	7.60051	−	3.82684i	0.384867	−	0.193779i
$391$	−4.27978	+	2.24620i	−0.216438	+	0.113595i
$392$	12.4137	+	1.50730i	0.626987	+	0.0761301i
$393$	2.45683	−	0.605554i	0.123931	−	0.0305462i
$394$	16.9618	−	24.5734i	0.854524	−	1.23799i
$395$	1.94767	−	1.34438i	0.0979981	−	0.0676432i
$396$	−5.08089	+	5.73513i	−0.255324	+	0.288201i
$397$	−20.2450	−	2.45819i	−1.01607	−	0.123373i	−0.404478	−	0.914548i	$-0.632547\pi$
$397$	−20.2450	−	2.45819i	−1.01607	−	0.123373i	−0.611590	+	0.791175i	$0.709470\pi$
$398$	0.415143	−	1.68430i	0.0208092	−	0.0844264i
$399$	−5.07809	−	2.66519i	−0.254223	−	0.133426i
$400$	1.12111	−	9.23321i	0.0560557	−	0.461661i
$401$	35.9312	−	4.36284i	1.79432	−	0.217870i	0.845562	−	0.533878i	$-0.179266\pi$
$401$	35.9312	−	4.36284i	1.79432	−	0.217870i	0.948757	+	0.316008i	$0.102343\pi$
$402$	15.2596	−	22.1074i	0.761080	−	1.10262i
$403$	−0.245782	+	0.163595i	−0.0122433	+	0.00814926i
$404$	−35.2445	−	51.0605i	−1.75348	−	2.54035i
$405$	−0.655297	−	0.739678i	−0.0325620	−	0.0367549i
$406$	−24.2993	−	5.98924i	−1.20595	−	0.297241i
$407$	4.25342	+	6.16215i	0.210834	+	0.305446i
$408$		−	3.86881i		−	0.191535i
$409$	−13.3768	+	9.23333i	−0.661440	+	0.456559i	−0.850899	−	0.525330i	$-0.823942\pi$
$409$	−13.3768	+	9.23333i	−0.661440	+	0.456559i	0.189459	+	0.981889i	$0.439327\pi$
$410$	16.6925	−	2.02683i	0.824383	−	0.100098i
$411$	5.93911	−	2.25241i	0.292955	−	0.111103i
$412$	2.69553	−	22.1997i	0.132799	−	1.09370i
$413$	6.91699	+	18.2386i	0.340363	+	0.897463i
$414$	−8.05238	+	9.08926i	−0.395753	+	0.446713i
$415$	2.17683	+	1.92850i	0.106856	+	0.0946665i
$416$	−9.38974	+	0.979593i	−0.460370	+	0.0480285i
$417$	13.3587	−	11.8348i	0.654178	−	0.579551i
$418$		−	8.92739i		−	0.436653i
$419$	17.9134	+	15.8699i	0.875128	+	0.775295i	0.975580	−	0.219646i	$-0.0704904\pi$
$419$	17.9134	+	15.8699i	0.875128	+	0.775295i	−0.100452	+	0.994942i	$0.532029\pi$
$420$	−11.2793	+	2.78010i	−0.550374	+	0.135655i
$421$	14.0829	+	9.72074i	0.686360	+	0.473760i	0.859499	−	0.511137i	$-0.170776\pi$
$421$	14.0829	+	9.72074i	0.686360	+	0.473760i	−0.173139	+	0.984897i	$0.555391\pi$
$422$	−54.6032	+	20.7083i	−2.65804	+	1.00806i
$423$	−1.62817	+	0.617485i	−0.0791645	+	0.0300231i
$424$	−19.8401	−	13.6946i	−0.963518	−	0.665068i
$425$	−3.71370	+	0.915346i	−0.180141	+	0.0444008i
$426$	7.06039	+	6.25496i	0.342077	+	0.303054i
$427$			0.481089i			0.0232815i
$428$	−21.0322	+	18.6329i	−1.01663	+	0.900654i
$429$	−1.90689	+	7.21049i	−0.0920655	+	0.348126i
$430$	−8.24719	−	7.30637i	−0.397715	−	0.352345i
$431$	22.1874	−	25.0444i	1.06873	−	1.20634i	0.0911351	−	0.995839i	$-0.470950\pi$
$431$	22.1874	−	25.0444i	1.06873	−	1.20634i	0.977593	−	0.210506i	$-0.0675111\pi$
$432$	−0.819739	−	2.16147i	−0.0394397	−	0.103994i
$433$	2.43897	−	20.0867i	0.117210	−	0.965307i	−0.808872	−	0.587984i	$-0.799922\pi$
$433$	2.43897	−	20.0867i	0.117210	−	0.965307i	0.926082	−	0.377323i	$-0.123155\pi$
$434$	0.580362	−	0.220102i	0.0278583	−	0.0105653i
$435$	3.23895	−	0.393280i	0.155296	−	0.0188563i
$436$	53.8052	−	37.1390i	2.57680	−	1.77864i
$437$		−	9.18759i		−	0.439502i
$438$	−16.6633	−	24.1409i	−0.796201	−	1.15350i
$439$	−19.0823	−	4.70336i	−0.910749	−	0.224479i	−0.244011	−	0.969772i	$-0.578463\pi$
$439$	−19.0823	−	4.70336i	−0.910749	−	0.224479i	−0.666737	+	0.745293i	$0.732310\pi$
$440$	−5.51664	−	6.22700i	−0.262996	−	0.296861i
$441$	−1.74548	−	2.52876i	−0.0831179	−	0.120417i
$442$	−3.68137	−	7.31160i	−0.175105	−	0.347777i
$443$	3.38135	−	4.89873i	0.160653	−	0.232746i	−0.734388	−	0.678730i	$-0.762531\pi$
$443$	3.38135	−	4.89873i	0.160653	−	0.232746i	0.895041	+	0.445984i	$0.147146\pi$
$444$	−13.3095	+	1.61607i	−0.631642	+	0.0766953i
$445$	−1.92548	+	15.8578i	−0.0912766	+	0.751730i
$446$	20.9296	+	10.9847i	0.991045	+	0.520141i
$447$	0.729330	−	2.95901i	0.0344961	−	0.139956i
$448$	34.2688	+	4.16099i	1.61905	+	0.196588i
$449$	−0.0792575	+	0.0894632i	−0.00374039	+	0.00422203i	−0.750378	−	0.661009i	$-0.770128\pi$
$449$	−0.0792575	+	0.0894632i	−0.00374039	+	0.00422203i	0.746638	+	0.665231i	$0.231667\pi$
$450$	−7.90827	+	5.45869i	−0.372799	+	0.257325i
$451$	−8.37210	+	12.1291i	−0.394227	+	0.571136i
$452$	28.6367	−	7.05830i	1.34695	−	0.331995i
$453$	19.9467	+	2.42197i	0.937178	+	0.113794i
$454$	−48.2203	+	25.3080i	−2.26309	+	1.18776i
$455$	−8.58958	+	7.35470i	−0.402686	+	0.344794i
$456$	6.51167	+	3.41759i	0.304937	+	0.160043i
$457$	1.54422	+	1.06590i	0.0722357	+	0.0498607i	0.603635	−	0.797261i	$-0.293718\pi$
$457$	1.54422	+	1.06590i	0.0722357	+	0.0498607i	−0.531400	+	0.847121i	$0.678334\pi$
$458$	−24.6252	+	35.6757i	−1.15066	+	1.66702i
$459$	−0.711561	+	0.630388i	−0.0332128	+	0.0294240i
$460$	−12.3410	−	13.9301i	−0.575403	−	0.649496i
$461$	1.57275	+	0.596466i	0.0732504	+	0.0277802i	0.390958	−	0.920409i	$-0.372144\pi$
$461$	1.57275	+	0.596466i	0.0732504	+	0.0277802i	−0.317708	+	0.948189i	$0.602913\pi$
$462$	7.28668	−	13.8836i	0.339007	−	0.645924i
$463$	−8.03591	−	3.04762i	−0.373461	−	0.141635i	0.160731	−	0.986998i	$-0.448615\pi$
$463$	−8.03591	−	3.04762i	−0.373461	−	0.141635i	−0.534192	+	0.845363i	$0.679384\pi$
$464$	7.41074	+	1.82658i	0.344035	+	0.0847970i
$465$	−0.0605703	+	0.0536606i	−0.00280888	+	0.00248845i
$466$	−22.6478	+	15.6326i	−1.04914	+	0.724168i
$467$	−8.74427	−	23.0568i	−0.404637	−	1.06694i	−0.970215	−	0.242245i	$-0.922116\pi$
$467$	−8.74427	−	23.0568i	−0.404637	−	1.06694i	0.565578	−	0.824695i	$-0.308653\pi$
$468$	−9.84546	−	9.02349i	−0.455107	−	0.417111i
$469$	−12.6582	+	33.3770i	−0.584502	+	1.54121i
$470$	−0.983530	−	3.99034i	−0.0453668	−	0.184060i
$471$	−16.9363	+	8.88887i	−0.780385	+	0.409578i
$472$	−8.86969	−	23.3874i	−0.408260	−	1.07649i
$473$	9.58667	−	1.16403i	0.440795	−	0.0535222i
$474$	−4.70719	−	3.24914i	−0.216208	−	0.149238i
$475$	1.73993	−	7.05918i	0.0798336	−	0.323898i
$476$	2.67442	+	10.8506i	0.122582	+	0.497335i
$477$	0.714014	+	5.88044i	0.0326925	+	0.269247i
$478$	−3.17932	+	8.38317i	−0.145419	+	0.383437i
$479$	1.66347	−	6.74898i	0.0760061	−	0.308369i	−0.920618	−	0.390463i	$-0.872315\pi$
$479$	1.66347	−	6.74898i	0.0760061	−	0.308369i	0.996625	+	0.0820945i	$0.0261609\pi$
$480$	−2.51229	+	0.619225i	−0.114670	+	0.0282636i
$481$	−10.8643	+	7.23139i	−0.495368	+	0.329723i
$482$	−3.27421	−	0.807020i	−0.149136	−	0.0367587i
$483$	7.49906	−	14.2883i	0.341219	−	0.650139i
$484$	−24.8946			−1.13157
$485$	−16.5668			−0.752261
$486$	−1.10990	+	2.11474i	−0.0503462	+	0.0959266i
$487$	19.0663	+	21.5213i	0.863974	+	0.975225i	0.999880	−	0.0154964i	$-0.00493285\pi$
$487$	19.0663	+	21.5213i	0.863974	+	0.975225i	−0.135906	+	0.990722i	$0.543394\pi$
$488$		−	0.616903i		−	0.0279259i
$489$	−5.83201	+	6.58297i	−0.263732	+	0.297692i
$490$	6.42123	−	3.37012i	0.290082	−	0.152247i
$491$	1.34039	+	11.0391i	0.0604909	+	0.498188i	0.991195	+	0.132414i	$0.0422727\pi$
$491$	1.34039	+	11.0391i	0.0604909	+	0.498188i	−0.930704	+	0.365774i	$0.880804\pi$
$492$	−12.2640	−	23.3670i	−0.552903	−	1.05347i
$493$	−0.378330	−	3.11583i	−0.0170391	−	0.140330i
$494$	15.5583	+	0.262658i	0.700000	+	0.0118176i
$495$	−0.246398	+	2.02927i	−0.0110748	+	0.0912088i
$496$	−0.176998	+	0.0671263i	−0.00794743	+	0.00301406i
$497$	−11.0989	−	5.82515i	−0.497854	−	0.261294i
$498$	2.49240	−	6.57191i	0.111687	−	0.294494i
$499$	4.25346	+	8.10430i	0.190411	+	0.362798i	0.961881	−	0.273467i	$-0.0881706\pi$
$499$	4.25346	+	8.10430i	0.190411	+	0.362798i	−0.771470	+	0.636266i	$0.780478\pi$
$500$	−15.3492	−	29.2454i	−0.686436	−	1.30789i
$501$	3.69617	+	14.9959i	0.165133	+	0.669970i
$502$	−10.3523	−	1.25700i	−0.462046	−	0.0561026i
$503$	−3.82400	−	3.38777i	−0.170504	−	0.151053i	0.573556	−	0.819167i	$-0.305564\pi$
$503$	−3.82400	−	3.38777i	−0.170504	−	0.151053i	−0.744060	+	0.668113i	$0.767102\pi$
$504$	7.33726	+	10.6299i	0.326828	+	0.473491i
$505$	−15.4769	−	5.86962i	−0.688714	−	0.261195i
$506$	25.1191			1.11668
$507$	−12.5100	−	3.53539i	−0.555590	−	0.157012i
$508$	53.4203			2.37014
$509$	3.11057	+	1.17968i	0.137874	+	0.0522885i	0.422577	−	0.906327i	$-0.361126\pi$
$509$	3.11057	+	1.17968i	0.137874	+	0.0522885i	−0.284703	+	0.958616i	$0.591895\pi$
$510$	−1.27452	−	1.84646i	−0.0564367	−	0.0817627i
$511$	29.1771	+	25.8487i	1.29072	+	1.14348i
$512$	−24.6875	−	2.99760i	−1.09104	−	0.132477i
$513$	−0.432447	−	1.75450i	−0.0190930	−	0.0774633i
$514$	−23.1313	−	44.0729i	−1.02028	−	1.94397i
$515$	−2.77262	−	5.28279i	−0.122176	−	0.232788i
$516$	−6.13183	+	16.1683i	−0.269939	+	0.711770i
$517$	3.18949	+	1.67397i	0.140274	+	0.0736212i
$518$	25.6537	−	9.72916i	1.12716	−	0.427475i
$519$	0.252494	−	2.07947i	0.0110832	−	0.0912787i
$520$	11.0145	−	9.43097i	0.483016	−	0.413575i
$521$	3.90836	+	32.1883i	0.171228	+	1.41019i	0.784406	+	0.620248i	$0.212968\pi$
$521$	3.90836	+	32.1883i	0.171228	+	1.41019i	−0.613177	+	0.789945i	$0.710109\pi$
$522$	−3.66456	−	6.98224i	−0.160394	−	0.305604i
$523$	−0.220171	−	1.81327i	−0.00962741	−	0.0792888i	0.987103	−	0.160085i	$-0.0511768\pi$
$523$	−0.220171	−	1.81327i	−0.00962741	−	0.0792888i	−0.996731	+	0.0807961i	$0.974254\pi$
$524$	8.29892	−	4.35561i	0.362540	−	0.190276i
$525$	8.46771	−	9.55807i	0.369561	−	0.417148i
$526$			43.9720i			1.91727i
$527$	0.0516209	+	0.0582679i	0.00224864	+	0.00253819i
$528$	−2.22228	+	4.23419i	−0.0967122	+	0.184270i
$529$	2.85117			0.123964
$530$	−13.9805			−0.607274
$531$	−2.85624	+	5.44210i	−0.123950	+	0.236167i
$532$	−20.6253	−	5.08367i	−0.894219	−	0.220405i
$533$	−20.8917	−	14.9474i	−0.904922	−	0.647444i
$534$	37.4851	−	9.23926i	1.62214	−	0.399822i
$535$	−1.79403	+	7.27865i	−0.0775625	+	0.314684i
$536$	16.2317	−	42.7995i	0.701102	−	1.84866i
$537$	0.478538	+	3.94111i	0.0206504	+	0.170072i
$538$	15.8569	+	64.3338i	0.683638	+	2.77363i
$539$	−1.52111	+	6.17138i	−0.0655188	+	0.265820i
$540$	−3.01237	−	2.07929i	−0.129632	−	0.0894784i
$541$	16.0193	−	1.94510i	0.688726	−	0.0836264i	0.231311	−	0.972880i	$-0.425699\pi$
$541$	16.0193	−	1.94510i	0.688726	−	0.0836264i	0.457415	+	0.889253i	$0.348776\pi$
$542$	11.5108	+	30.3516i	0.494433	+	1.30371i
$543$	−0.463966	+	0.243508i	−0.0199107	+	0.0104499i
$544$	0.595687	+	2.41680i	0.0255399	+	0.103619i
$545$	6.18514	−	16.3089i	0.264942	−	0.698595i
$546$	23.9814	+	13.1074i	1.02631	+	0.560945i
$547$	3.38162	+	8.91659i	0.144587	+	0.381246i	0.987672	−	0.156534i	$-0.0500322\pi$
$547$	3.38162	+	8.91659i	0.144587	+	0.381246i	−0.843085	+	0.537780i	$0.819263\pi$
$548$	19.3627	−	13.3651i	0.827135	−	0.570930i
$549$	−0.113462	+	0.100519i	−0.00484244	+	0.00429003i
$550$	19.2999	+	4.75701i	0.822953	+	0.202840i
$551$	5.57851	+	2.11565i	0.237652	+	0.0901297i
$552$	−9.61608	+	18.3219i	−0.409288	+	0.779833i
$553$	7.10676	+	2.69524i	0.302210	+	0.114613i
$554$	−40.7601	−	46.0086i	−1.73173	−	1.95472i
$555$	−2.67738	+	2.37196i	−0.113649	+	0.100684i
$556$	37.5523	−	54.4039i	1.59257	−	2.30724i
$557$	−8.52600	−	5.88507i	−0.361258	−	0.249358i	0.373584	−	0.927596i	$-0.378129\pi$
$557$	−8.52600	−	5.88507i	−0.361258	−	0.249358i	−0.734843	+	0.678238i	$0.762744\pi$
$558$	0.173171	+	0.0908870i	0.00733090	+	0.00384755i
$559$	1.74657	+	16.7415i	0.0738721	+	0.708089i
$560$	−6.41970	+	3.36932i	−0.271282	+	0.142380i
$561$	1.95213	+	0.237032i	0.0824190	+	0.0100075i
$562$	13.4102	−	3.30532i	0.565676	−	0.139427i
$563$	7.20679	−	10.4408i	0.303730	−	0.440029i	−0.641165	−	0.767403i	$-0.721548\pi$
$563$	7.20679	−	10.4408i	0.303730	−	0.440029i	0.944895	+	0.327375i	$0.106164\pi$
$564$	−5.30818	+	3.66397i	−0.223515	+	0.154281i
$565$	5.21789	−	5.88978i	0.219518	−	0.247785i
$566$	15.3063	+	1.85852i	0.643371	+	0.0781194i
$567$	0.759527	−	3.08152i	0.0318972	−	0.129412i
$568$	14.2322	+	7.46962i	0.597169	+	0.313418i
$569$	3.41866	−	28.1552i	0.143318	−	1.18033i	−0.726576	−	0.687087i	$-0.758889\pi$
$569$	3.41866	−	28.1552i	0.143318	−	1.18033i	0.869893	−	0.493240i	$-0.164188\pi$
$570$	4.23368	−	0.514062i	0.177329	−	0.0215317i
$571$	22.8405	−	33.0902i	0.955846	−	1.38478i	0.0330662	−	0.999453i	$-0.489473\pi$
$571$	22.8405	−	33.0902i	0.955846	−	1.38478i	0.922780	−	0.385328i	$-0.125912\pi$
$572$	−0.466321	+	27.6220i	−0.0194979	+	1.15493i
$573$	−6.67070	−	9.66417i	−0.278672	−	0.403727i
$574$	35.8113	+	40.4227i	1.49474	+	1.68721i
$575$	19.8625	+	4.89566i	0.828322	+	0.204163i
$576$	6.17878	+	8.95151i	0.257449	+	0.372979i
$577$			15.2678i			0.635605i	0.948157	+	0.317803i	$0.102945\pi$
$577$			15.2678i			0.635605i	−0.948157	+	0.317803i	$0.897055\pi$
$578$	31.6379	−	21.8381i	1.31596	−	0.908343i
$579$	22.6879	−	2.75481i	0.942876	−	0.114486i
$580$	11.2999	−	4.28548i	0.469202	−	0.177945i
$581$	−1.12583	+	9.27206i	−0.0467074	+	0.384670i
$582$	14.1981	+	37.4373i	0.588530	+	1.55183i
$583$	8.12558	−	9.17188i	0.336527	−	0.379861i
$584$	−37.4140	−	33.1459i	−1.54820	−	1.37159i
$585$	−3.52927	−	0.489116i	−0.145917	−	0.0202225i
$586$	37.7822	−	33.4721i	1.56077	−	1.38272i
$587$		−	29.0477i		−	1.19893i	−0.800402	−	0.599463i	$-0.795381\pi$
$587$		−	29.0477i		−	1.19893i	0.800402	−	0.599463i	$-0.204619\pi$
$588$	−8.51897	−	7.54715i	−0.351316	−	0.311239i
$589$	−0.143672	+	0.0354119i	−0.00591990	+	0.00145912i
$590$	−11.9379	−	8.24010i	−0.491474	−	0.339240i
$591$	−11.6897	+	4.43332i	−0.480850	+	0.182362i
$592$	−7.82381	+	2.96718i	−0.321557	+	0.121950i
$593$	27.7658	+	19.1653i	1.14020	+	0.787025i	0.979791	−	0.200025i	$-0.0641023\pi$
$593$	27.7658	+	19.1653i	1.14020	+	0.787025i	0.160412	+	0.987050i	$0.448718\pi$
$594$	4.79685	−	1.18232i	0.196817	−	0.0485111i
$595$	2.23167	+	1.97708i	0.0914894	+	0.0810525i
$596$		−	11.2882i		−	0.462384i
$597$	−0.543668	+	0.481648i	−0.0222509	+	0.0197125i
$598$	−0.739043	+	43.7764i	−0.0302217	+	1.79015i
$599$	25.7719	+	22.8319i	1.05301	+	0.932885i	0.997847	−	0.0655922i	$-0.0208936\pi$
$599$	25.7719	+	22.8319i	1.05301	+	0.932885i	0.0551631	+	0.998477i	$0.482432\pi$
$600$	−10.8582	+	12.2564i	−0.443284	+	0.500364i
$601$	−2.21360	−	5.83679i	−0.0902948	−	0.238088i	0.882260	−	0.470763i	$-0.156021\pi$
$601$	−2.21360	−	5.83679i	−0.0902948	−	0.238088i	−0.972554	+	0.232675i	$0.925252\pi$
$602$	4.26535	−	35.1283i	0.173843	−	1.43172i
$603$	−10.5166	+	3.98841i	−0.428268	+	0.162421i
$604$	73.8829	−	8.97101i	3.00625	−	0.365025i
$605$	−5.46598	+	3.77289i	−0.222224	+	0.153390i
$606$			40.0047i			1.62508i
$607$	11.6330	+	16.8533i	0.472168	+	0.684053i	0.984629	−	0.174657i	$-0.0558817\pi$
$607$	11.6330	+	16.8533i	0.472168	+	0.684053i	−0.512462	+	0.858710i	$0.671266\pi$
$608$	−4.59396	−	1.13231i	−0.186310	−	0.0459212i
$609$	6.94870	+	7.84346i	0.281576	+	0.317833i
$610$	−0.203229	−	0.294428i	−0.00822850	−	0.0119210i
$611$	−3.01117	+	5.50926i	−0.121819	+	0.222881i
$612$	−2.00025	+	2.89787i	−0.0808554	+	0.117139i
$613$	−39.8667	+	4.84069i	−1.61020	+	0.195514i	−0.875617	−	0.483006i	$-0.839545\pi$
$613$	−39.8667	+	4.84069i	−1.61020	+	0.195514i	−0.734582	+	0.678520i	$0.762622\pi$
$614$	2.69837	−	22.2230i	0.108897	−	0.896849i
$615$	−6.23413	−	3.27192i	−0.251384	−	0.131937i
$616$	6.39411	−	25.9419i	0.257626	−	1.04523i
$617$	−44.2777	−	5.37628i	−1.78255	−	0.216441i	−0.838196	−	0.545369i	$-0.816390\pi$
$617$	−44.2777	−	5.37628i	−1.78255	−	0.216441i	−0.944355	+	0.328928i	$0.893313\pi$
$618$	−9.56172	+	10.7929i	−0.384629	+	0.434156i
$619$	−15.4003	+	10.6301i	−0.618991	+	0.427258i	−0.835860	−	0.548942i	$-0.815031\pi$
$619$	−15.4003	+	10.6301i	−0.618991	+	0.427258i	0.216870	+	0.976201i	$0.430415\pi$
$620$	−0.170268	+	0.246675i	−0.00683812	+	0.00990673i
$621$	4.93666	−	1.21678i	0.198101	−	0.0488276i
$622$	−68.7515	−	8.34795i	−2.75668	−	0.334722i
$623$	−45.4271	+	23.8420i	−1.82000	+	0.955209i
$624$	−7.31379	−	3.99747i	−0.292786	−	0.160027i
$625$	10.0106	+	5.25395i	0.400423	+	0.210158i
$626$	19.8033	+	13.6693i	0.791501	+	0.546333i
$627$	−2.12340	+	3.07628i	−0.0848005	+	0.122855i
$628$	−53.0302	+	46.9806i	−2.11613	+	1.87473i
$629$	2.28179	+	2.57561i	0.0909810	+	0.102696i
$630$	7.00368	+	2.65615i	0.279033	+	0.105823i
$631$	−6.96225	+	13.2655i	−0.277163	+	0.528090i	−0.983752	−	0.179535i	$-0.942541\pi$
$631$	−6.96225	+	13.2655i	−0.277163	+	0.528090i	0.706589	+	0.707624i	$0.250233\pi$
$632$	−9.11303	−	3.45612i	−0.362497	−	0.137477i
$633$	23.7412	+	5.85167i	0.943627	+	0.232583i
$634$	−9.10612	+	8.06732i	−0.361650	+	0.320394i
$635$	11.7292	−	8.09610i	0.465460	−	0.321284i
$636$	7.78046	+	20.5154i	0.308515	+	0.813488i
$637$	−10.7105	−	2.83250i	−0.424364	−	0.112228i
$638$	−5.78423	+	15.2518i	−0.229000	+	0.603823i
$639$	−0.945174	−	3.83472i	−0.0373905	−	0.151699i
$640$	−18.1482	+	9.52490i	−0.717370	+	0.376505i
$641$	−1.27173	−	3.35329i	−0.0502305	−	0.132447i	0.907553	−	0.419938i	$-0.137948\pi$
$641$	−1.27173	−	3.35329i	−0.0502305	−	0.132447i	−0.957783	+	0.287491i	$0.907179\pi$
$642$	17.9856	−	2.18385i	0.709836	−	0.0861897i
$643$	−28.3695	−	19.5820i	−1.11878	−	0.772239i	−0.142727	−	0.989762i	$-0.545587\pi$
$643$	−28.3695	−	19.5820i	−1.11878	−	0.772239i	−0.976055	+	0.217523i	$0.930202\pi$
$644$	14.3040	−	58.0335i	0.563655	−	2.28684i
$645$	1.10405	+	4.47931i	0.0434719	+	0.176373i
$646$	−0.494521	−	4.07275i	−0.0194567	−	0.160240i
$647$	0.0479516	−	0.126438i	0.00188517	−	0.00497079i	−0.934070	−	0.357089i	$-0.883769\pi$
$647$	0.0479516	−	0.126438i	0.00188517	−	0.00497079i	0.935956	+	0.352118i	$0.114539\pi$
$648$	−0.973946	+	3.95145i	−0.0382602	+	0.155228i
$649$	12.3443	−	3.04259i	0.484555	−	0.119432i
$650$	−8.85815	+	33.4952i	−0.347445	+	1.31379i
$651$	−0.252338	−	0.0621958i	−0.00988991	−	0.00243764i
$652$	−15.1388	+	28.8446i	−0.592881	+	1.12964i
$653$	−41.9480			−1.64155			−0.820776	−	0.571250i	$-0.806459\pi$
$653$	−41.9480			−1.64155			−0.820776	+	0.571250i	$0.806459\pi$
$654$	−42.1551			−1.64840
$655$	1.16204	−	2.21408i	0.0454046	−	0.0865113i
$656$	−10.9217	−	12.3280i	−0.426419	−	0.481328i
$657$			12.2821i			0.479169i
$658$	8.75262	−	9.87966i	0.341213	−	0.385149i
$659$	−4.44168	+	2.33117i	−0.173023	+	0.0908095i	−0.549011	−	0.835815i	$-0.684996\pi$
$659$	−4.44168	+	2.33117i	−0.173023	+	0.0908095i	0.375988	+	0.926624i	$0.377303\pi$
$660$	0.912661	+	7.51644i	0.0355253	+	0.292577i
$661$	−5.65739	−	10.7793i	−0.220047	−	0.419264i	0.750259	−	0.661143i	$-0.229929\pi$
$661$	−5.65739	−	10.7793i	−0.220047	−	0.419264i	−0.970306	+	0.241879i	$0.922236\pi$
$662$	8.95733	+	73.7703i	0.348137	+	2.86716i
$663$	−0.470523	+	3.39512i	−0.0182736	+	0.131855i
$664$	1.44366	−	11.8896i	0.0560249	−	0.461406i
$665$	−5.29904	+	2.00966i	−0.205488	+	0.0779314i
$666$	7.65465	+	4.01747i	0.296612	+	0.155674i
$667$	−5.95282	+	15.6963i	−0.230494	+	0.607763i
$668$	26.5857	+	50.6548i	1.02863	+	1.95989i
$669$	−4.59937	−	8.76336i	−0.177822	−	0.338811i
$670$	−6.35275	−	25.7741i	−0.245428	−	0.995740i
$671$	0.311277	+	0.0377959i	0.0120167	+	0.00145909i
$672$	−6.22018	−	5.51060i	−0.239949	−	0.212576i
$673$	−4.73800	−	6.86418i	−0.182637	−	0.264595i	0.720962	−	0.692974i	$-0.243700\pi$
$673$	−4.73800	−	6.86418i	−0.182637	−	0.264595i	−0.903599	+	0.428380i	$0.859085\pi$
$674$	13.3665	+	5.06926i	0.514859	+	0.195260i
$675$	4.02346			0.154863
$676$	−48.1248	−	1.62537i	−1.85095	−	0.0625142i
$677$	34.2318			1.31563			0.657817	−	0.753177i	$-0.271480\pi$
$677$	34.2318			1.31563			0.657817	+	0.753177i	$0.271480\pi$
$678$	−17.7814	−	6.74359i	−0.682890	−	0.258986i
$679$	−30.2249	−	43.7884i	−1.15993	−	1.68044i
$680$	−2.86168	−	2.53522i	−0.109740	−	0.0972214i
$681$	22.6357	+	2.74847i	0.867403	+	0.105322i
$682$	−0.0968170	−	0.392802i	−0.00370731	−	0.0150412i
$683$	14.6449	+	27.9035i	0.560371	+	1.06770i	0.986611	+	0.163088i	$0.0521456\pi$
$683$	14.6449	+	27.9035i	0.560371	+	1.06770i	−0.426240	+	0.904610i	$0.640162\pi$
$684$	−3.11049	−	5.92654i	−0.118932	−	0.226607i
$685$	2.22583	−	5.86903i	0.0850446	−	0.224244i
$686$	−26.3589	−	13.8342i	−1.00639	−	0.528192i
$687$	16.9711	−	6.43630i	0.647488	−	0.245560i
$688$	−1.30084	+	10.7134i	−0.0495940	+	0.408443i
$689$	15.7453	+	14.4308i	0.599848	+	0.549768i
$690$	1.44642	+	11.9123i	0.0550643	+	0.453495i
$691$	9.18742	+	17.5052i	0.349506	+	0.665928i	0.995221	−	0.0976508i	$-0.0311328\pi$
$691$	9.18742	+	17.5052i	0.349506	+	0.665928i	−0.645715	+	0.763579i	$0.723441\pi$
$692$	−0.935240	−	7.70240i	−0.0355525	−	0.292801i
$693$	−5.81316	+	3.05098i	−0.220824	+	0.115897i
$694$	−6.06501	+	6.84599i	−0.230225	+	0.259870i
$695$		−	17.6364i		−	0.668988i
$696$	−8.91036	−	10.0577i	−0.337746	−	0.381237i
$697$	−3.14755	+	5.99715i	−0.119222	+	0.227158i
$698$	33.0367			1.25046
$699$	11.5224			0.435819
$700$	21.9806	−	41.8805i	0.830788	−	1.58293i
$701$	−30.3356	−	7.47705i	−1.14576	−	0.282404i	−0.379659	−	0.925126i	$-0.623959\pi$
$701$	−30.3356	−	7.47705i	−1.14576	−	0.282404i	−0.766099	+	0.642722i	$0.777805\pi$
$702$	1.91936	+	8.39454i	0.0724417	+	0.316831i
$703$	−6.35072	+	1.56531i	−0.239522	+	0.0590368i
$704$	5.38454	−	21.8459i	0.202938	−	0.823350i
$705$	−0.610198	+	1.60896i	−0.0229814	+	0.0605969i
$706$	7.20807	+	59.3638i	0.271279	+	2.23419i
$707$	−12.7223	−	51.6162i	−0.478470	−	1.94123i
$708$	−5.44808	+	22.1037i	−0.204751	+	0.830709i
$709$	−21.0987	−	14.5634i	−0.792378	−	0.546939i	0.101719	−	0.994813i	$-0.467566\pi$
$709$	−21.0987	−	14.5634i	−0.792378	−	0.546939i	−0.894097	+	0.447874i	$0.852181\pi$
$710$	9.25332	−	1.12356i	0.347271	−	0.0421663i
$711$	0.849229	+	2.23923i	0.0318486	+	0.0839778i
$712$	58.2514	−	30.5727i	2.18306	−	1.14576i
$713$	−0.0996388	−	0.404251i	−0.00373150	−	0.0151393i
$714$	2.55518	−	6.73746i	0.0956252	−	0.252143i
$715$	4.08386	+	6.13550i	0.152728	+	0.229455i
$716$	5.21452	+	13.7496i	0.194876	+	0.513845i
$717$	3.08951	−	2.13254i	0.115380	−	0.0796411i
$718$	41.5518	−	36.8117i	1.55070	−	1.37380i
$719$	47.0355	+	11.5932i	1.75413	+	0.432354i	0.979726	−	0.200340i	$-0.0642047\pi$
$719$	47.0355	+	11.5932i	1.75413	+	0.432354i	0.774402	+	0.632694i	$0.218051\pi$
$720$	−2.13597	−	0.810066i	−0.0796028	−	0.0301894i
$721$	8.90468	−	16.9665i	0.331628	−	0.631864i
$722$	−35.1373	−	13.3258i	−1.30767	−	0.495935i
$723$	0.936304	+	1.05687i	0.0348215	+	0.0393054i
$724$	−1.45275	+	1.28702i	−0.0539909	+	0.0478318i
$725$	−7.54632	+	10.9327i	−0.280263	+	0.406032i
$726$	13.2103	+	9.11843i	0.490281	+	0.338417i
$727$	−36.9497	−	19.3927i	−1.37039	−	0.719236i	−0.390844	−	0.920457i	$-0.627817\pi$
$727$	−36.9497	−	19.3927i	−1.37039	−	0.719236i	−0.979546	+	0.201220i	$0.935509\pi$
$728$	45.0224	+	11.9066i	1.66864	+	0.441289i
$729$	0.885456	−	0.464723i	0.0327947	−	0.0172120i
$730$	−28.7759	−	3.49402i	−1.06504	−	0.129320i
$731$	4.30904	−	1.06208i	0.159376	−	0.0392825i
$732$	−0.318951	+	0.462080i	−0.0117888	+	0.0170790i
$733$	11.4891	−	7.93036i	0.424360	−	0.292914i	−0.336681	−	0.941619i	$-0.609304\pi$
$733$	11.4891	−	7.93036i	0.424360	−	0.292914i	0.761040	+	0.648705i	$0.224689\pi$
$734$	30.3350	−	34.2411i	1.11969	−	1.26386i
$735$	−3.01427	−	0.365999i	−0.111183	−	0.0135001i
$736$	3.18599	−	12.9261i	0.117437	−	0.476461i
$737$	20.6013	+	10.8124i	0.758860	+	0.398280i
$738$	−2.05104	+	16.8918i	−0.0754997	+	0.621796i
$739$	10.5672	−	1.28309i	0.388721	−	0.0471993i	0.0761569	−	0.997096i	$-0.475735\pi$
$739$	10.5672	−	1.28309i	0.388721	−	0.0471993i	0.312565	+	0.949897i	$0.398812\pi$
$740$	−7.52633	+	10.9038i	−0.276673	+	0.400831i
$741$	−5.29873	−	3.79108i	−0.194654	−	0.139269i
$742$	−25.5063	−	36.9523i	−0.936367	−	1.35656i
$743$	17.5548	+	19.8153i	0.644023	+	0.726952i	0.976346	−	0.216214i	$-0.0693709\pi$
$743$	17.5548	+	19.8153i	0.644023	+	0.726952i	−0.332323	+	0.943166i	$0.607832\pi$
$744$	0.323574	+	0.0797539i	0.0118628	+	0.00292392i
$745$	−1.71079	−	2.47850i	−0.0626784	−	0.0908053i
$746$		−	25.1483i		−	0.920746i
$747$	−2.42199	+	1.67178i	−0.0886162	+	0.0611673i
$748$	7.23072	−	0.877968i	0.264381	−	0.0321017i
$749$	−22.5115	+	8.53749i	−0.822553	+	0.311953i
$750$	−2.56701	+	21.1412i	−0.0937339	+	0.771968i
$751$	−17.1416	−	45.1987i	−0.625506	−	1.64932i	−0.753421	−	0.657539i	$-0.771598\pi$
$751$	−17.1416	−	45.1987i	−0.625506	−	1.64932i	0.127915	−	0.991785i	$-0.459172\pi$
$752$	−2.66935	+	3.01308i	−0.0973413	+	0.109876i
$753$	3.26831	+	2.89547i	0.119104	+	0.105517i
$754$	−26.4099	−	10.5292i	−0.961793	−	0.383452i
$755$	14.8625	−	13.1670i	0.540902	−	0.479197i
$756$		−	11.7556i		−	0.427547i
$757$	−16.0902	−	14.2547i	−0.584808	−	0.518095i	0.318027	−	0.948082i	$-0.396980\pi$
$757$	−16.0902	−	14.2547i	−0.584808	−	0.518095i	−0.902835	+	0.429987i	$0.858518\pi$
$758$	−45.5969	+	11.2386i	−1.65615	+	0.408205i
$759$	−8.65574	−	5.97463i	−0.314183	−	0.216865i
$760$	6.79499	−	2.57700i	0.246480	−	0.0934776i
$761$	−49.8158	+	18.8926i	−1.80582	+	0.684858i	−0.810786	+	0.585343i	$0.800960\pi$
$761$	−49.8158	+	18.8926i	−1.80582	+	0.684858i	−0.995036	+	0.0995150i	$0.968271\pi$
$762$	−28.3475	−	19.5669i	−1.02692	−	0.708833i
$763$	54.3908	−	13.4061i	1.96908	−	0.485334i
$764$	−32.5570	−	28.8430i	−1.17787	−	1.04350i
$765$			0.939418i			0.0339647i
$766$	−55.4640	+	49.1368i	−2.00400	+	1.77539i
$767$	4.93931	+	21.6026i	0.178348	+	0.780025i
$768$	20.7945	+	18.4223i	0.750357	+	0.664759i
$769$	8.30512	−	9.37454i	0.299490	−	0.338055i	−0.579431	−	0.815021i	$-0.696725\pi$
$769$	8.30512	−	9.37454i	0.299490	−	0.338055i	0.878921	+	0.476967i	$0.158264\pi$

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.p (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.23311 - 0.846906i) q^{2} +(0.568065 + 0.822984i) q^{3} +(2.77250 + 2.45622i) q^{4} +(0.980994 + 0.119114i) q^{5} +(-0.571560 - 2.31891i) q^{6} +(1.47491 + 2.81021i) q^{7} +(-1.89129 - 3.60355i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(-2.08979 - 1.09680i) q^{10} +(1.93416 - 0.733529i) q^{11} +(-0.446470 + 3.67701i) q^{12} +(1.22146 + 3.39235i) q^{13} +(-0.913654 - 7.52462i) q^{14} +(0.459239 + 0.875007i) q^{15} +(0.278644 + 2.29484i) q^{16} +(0.841746 - 0.441782i) q^{17} +(1.58374 - 1.78767i) q^{18} +1.80701i q^{19} +(2.42723 + 2.73978i) q^{20} +(-1.47491 + 2.81021i) q^{21} -4.94041 q^{22} -5.08440 q^{23} +(1.89129 - 3.60355i) q^{24} +(-3.90655 - 0.962877i) q^{25} +(0.145355 - 8.60994i) q^{26} +(-0.970942 + 0.239316i) q^{27} +(-2.81330 + 11.4140i) q^{28} +(1.17080 - 3.08714i) q^{29} +(-0.284482 - 2.34292i) q^{30} +(0.0195969 + 0.0795079i) q^{31} +(-0.626619 + 2.54229i) q^{32} +(1.70241 + 1.17509i) q^{33} +(-2.25386 + 0.273668i) q^{34} +(1.11215 + 2.93249i) q^{35} +(-3.27974 + 1.72134i) q^{36} +(0.866242 + 3.51448i) q^{37} +(1.53037 - 4.03525i) q^{38} +(-2.09798 + 2.93231i) q^{39} +(-1.42611 - 3.76034i) q^{40} +(-5.86348 + 4.04727i) q^{41} +(5.67363 - 5.02639i) q^{42} +(4.53280 + 1.11723i) q^{43} +(7.16415 + 2.71700i) q^{44} +(-0.459239 + 0.875007i) q^{45} +(11.3540 + 4.30601i) q^{46} +(1.15472 + 1.30341i) q^{47} +(-1.73033 + 1.53294i) q^{48} +(-1.74548 + 2.52876i) q^{49} +(7.90827 + 5.45869i) q^{50} +(0.841746 + 0.441782i) q^{51} +(-4.94586 + 12.4054i) q^{52} +(5.24511 - 2.75285i) q^{53} +(2.37089 + 0.287879i) q^{54} +(1.98477 - 0.489202i) q^{55} +(7.33726 - 10.6299i) q^{56} +(-1.48714 + 1.02650i) q^{57} +(-5.22904 + 5.90236i) q^{58} +(6.10129 + 0.740831i) q^{59} +(-0.875969 + 3.55394i) q^{60} +(0.134221 + 0.0704445i) q^{61} +(0.0235736 - 0.194146i) q^{62} +(-3.15061 + 0.382553i) q^{63} +(6.17878 - 8.95151i) q^{64} +(0.794166 + 3.47337i) q^{65} +(-2.80647 - 4.06588i) q^{66} +(7.45846 + 8.41886i) q^{67} +(3.41885 + 0.842671i) q^{68} +(-2.88827 - 4.18438i) q^{69} -7.49044i q^{70} +(-3.25036 + 2.24356i) q^{71} +(4.04004 - 0.490550i) q^{72} +(11.4839 - 4.35528i) q^{73} +(1.04202 - 8.58184i) q^{74} +(-1.42674 - 3.76200i) q^{75} +(-4.43842 + 5.00994i) q^{76} +(4.91409 + 4.35350i) q^{77} +(7.16841 - 4.77138i) q^{78} +(1.79258 - 1.58809i) q^{79} +2.28442i q^{80} +(-0.748511 - 0.663123i) q^{81} +(16.5214 - 4.07217i) q^{82} +(2.42199 + 1.67178i) q^{83} +(-10.9917 + 4.16860i) q^{84} +(0.878371 - 0.333122i) q^{85} +(-9.17602 - 6.33375i) q^{86} +(3.20576 - 0.790148i) q^{87} +(-6.30136 - 5.58252i) q^{88} +16.1650i q^{89} +(1.76658 - 1.56505i) q^{90} +(-7.73168 + 8.43598i) q^{91} +(-14.0965 - 12.4884i) q^{92} +(-0.0543014 + 0.0612936i) q^{93} +(-1.47474 - 3.88858i) q^{94} +(-0.215241 + 1.77267i) q^{95} +(-2.44823 + 0.928490i) q^{96} +(-16.6424 + 2.02076i) q^{97} +(6.03946 - 4.16874i) q^{98} +2.06858i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9} - 4 q^{10} + 12 q^{12} + 13 q^{13} + 2 q^{14} - 8 q^{16} - 4 q^{17} - 72 q^{22} + 48 q^{23} - 44 q^{25} - 39 q^{26} - 14 q^{27} + 45 q^{29} - 4 q^{30} - 26 q^{31}+ \cdots - 104 q^{98}+O(q^{100}) \) 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9 - 4 * q^10 + 12 * q^12 + 13 * q^13 + 2 * q^14 - 8 * q^16 - 4 * q^17 - 72 * q^22 + 48 * q^23 - 44 * q^25 - 39 * q^26 - 14 * q^27 + 45 * q^29 - 4 * q^30 - 26 * q^31 + 130 * q^32 + 13 * q^33 - 65 * q^34 - 35 * q^35 + 12 * q^36 + 61 * q^38 + 12 * q^40 - 63 * q^42 + 72 * q^43 - 39 * q^44 - 8 * q^48 - 68 * q^49 - 52 * q^50 - 4 * q^51 + 65 * q^52 - q^53 + 53 * q^55 - 14 * q^56 - 13 * q^57 - 26 * q^58 - 104 * q^59 + 117 * q^60 + 12 * q^61 + 49 * q^62 - 32 * q^64 - 52 * q^65 - 46 * q^66 + 26 * q^67 - 84 * q^68 - 4 * q^69 - 39 * q^71 - 52 * q^73 + 29 * q^74 + 8 * q^75 - 130 * q^76 + 60 * q^77 + 65 * q^78 + 14 * q^79 - 14 * q^81 + 45 * q^82 + 78 * q^83 - 13 * q^85 - 13 * q^86 - 46 * q^87 - 26 * q^88 - 4 * q^90 - 208 * q^91 + 82 * q^92 - 39 * q^93 + 25 * q^94 - 66 * q^95 + 65 * q^96 + 26 * q^97 - 104 * q^98

Introduction

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