LMFDB - Embedded newform 304.2.m.a.227.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,2,Mod(75,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 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("304.75");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	304.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.42745222145$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			227.1
Character	$\chi$	$=$	304.227
Dual form			304.2.m.a.75.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41289 + 0.0612206i) q^{2} +(-1.42780 - 1.42780i) q^{3} +(1.99250 - 0.172996i) q^{4} +(0.391081 - 0.391081i) q^{5} +(2.10473 + 1.92991i) q^{6} -3.36082 q^{7} +(-2.80459 + 0.366406i) q^{8} +1.07723i q^{9} +O(q^{10})$	\(q+(-1.41289 + 0.0612206i) q^{2} +(-1.42780 - 1.42780i) q^{3} +(1.99250 - 0.172996i) q^{4} +(0.391081 - 0.391081i) q^{5} +(2.10473 + 1.92991i) q^{6} -3.36082 q^{7} +(-2.80459 + 0.366406i) q^{8} +1.07723i q^{9} +(-0.528611 + 0.576495i) q^{10} +(-0.0339409 - 0.0339409i) q^{11} +(-3.09190 - 2.59790i) q^{12} +(-0.227848 + 0.227848i) q^{13} +(4.74847 - 0.205752i) q^{14} -1.11677 q^{15} +(3.94014 - 0.689389i) q^{16} +0.208245 q^{17} +(-0.0659488 - 1.52201i) q^{18} +(0.442793 + 4.33635i) q^{19} +(0.711574 - 0.846885i) q^{20} +(4.79859 + 4.79859i) q^{21} +(0.0500326 + 0.0458768i) q^{22} -8.50857 q^{23} +(4.52756 + 3.48125i) q^{24} +4.69411i q^{25} +(0.307975 - 0.335873i) q^{26} +(-2.74533 + 2.74533i) q^{27} +(-6.69645 + 0.581408i) q^{28} +(-2.09323 + 2.09323i) q^{29} +(1.57787 - 0.0683694i) q^{30} -0.695564 q^{31} +(-5.52478 + 1.21525i) q^{32} +0.0969217i q^{33} +(-0.294227 + 0.0127489i) q^{34} +(-1.31435 + 1.31435i) q^{35} +(0.186357 + 2.14639i) q^{36} +(3.52688 + 3.52688i) q^{37} +(-0.891091 - 6.09967i) q^{38} +0.650644 q^{39} +(-0.953528 + 1.24012i) q^{40} -7.19785 q^{41} +(-7.07364 - 6.48609i) q^{42} +(5.14249 + 5.14249i) q^{43} +(-0.0734990 - 0.0617557i) q^{44} +(0.421285 + 0.421285i) q^{45} +(12.0217 - 0.520900i) q^{46} -6.18843i q^{47} +(-6.61005 - 4.64143i) q^{48} +4.29513 q^{49} +(-0.287376 - 6.63225i) q^{50} +(-0.297333 - 0.297333i) q^{51} +(-0.414572 + 0.493405i) q^{52} +(-2.19113 - 2.19113i) q^{53} +(3.71077 - 4.04691i) q^{54} -0.0265472 q^{55} +(9.42574 - 1.23142i) q^{56} +(5.55923 - 6.82367i) q^{57} +(2.82935 - 3.08565i) q^{58} +(1.98964 - 1.98964i) q^{59} +(-2.22517 + 0.193197i) q^{60} +(-5.48730 - 5.48730i) q^{61} +(0.982753 - 0.0425828i) q^{62} -3.62039i q^{63} +(7.73149 - 2.05524i) q^{64} +0.178214i q^{65} +(-0.00593360 - 0.136939i) q^{66} +(0.280654 + 0.280654i) q^{67} +(0.414930 - 0.0360255i) q^{68} +(12.1485 + 12.1485i) q^{69} +(1.77657 - 1.93750i) q^{70} -12.8008i q^{71} +(-0.394704 - 3.02120i) q^{72} -7.46524i q^{73} +(-5.19900 - 4.76717i) q^{74} +(6.70226 - 6.70226i) q^{75} +(1.63244 + 8.56359i) q^{76} +(0.114069 + 0.114069i) q^{77} +(-0.919287 + 0.0398328i) q^{78} -8.31193 q^{79} +(1.27131 - 1.81052i) q^{80} +11.0713 q^{81} +(10.1698 - 0.440657i) q^{82} +(-9.37194 + 9.37194i) q^{83} +(10.3913 + 8.73107i) q^{84} +(0.0814407 - 0.0814407i) q^{85} +(-7.58058 - 6.95093i) q^{86} +5.97744 q^{87} +(0.107627 + 0.0827543i) q^{88} -7.02497 q^{89} +(-0.621020 - 0.569437i) q^{90} +(0.765758 - 0.765758i) q^{91} +(-16.9534 + 1.47195i) q^{92} +(0.993127 + 0.993127i) q^{93} +(0.378859 + 8.74356i) q^{94} +(1.86903 + 1.52269i) q^{95} +(9.62342 + 6.15315i) q^{96} +5.52597i q^{97} +(-6.06854 + 0.262951i) q^{98} +(0.0365622 - 0.0365622i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 4 q^{4} - 4 q^{5} - 4 q^{6} - 8 q^{7}+O(q^{10}) $ 76 * q - 4 * q^4 - 4 * q^5 - 4 * q^6 - 8 * q^7	$ 76 q - 4 q^{4} - 4 q^{5} - 4 q^{6} - 8 q^{7} - 4 q^{11} + 4 q^{16} - 8 q^{17} + 6 q^{19} - 32 q^{20} - 8 q^{23} - 12 q^{24} - 8 q^{26} - 40 q^{30} + 44 q^{36} - 12 q^{38} - 8 q^{39} + 12 q^{42} - 4 q^{43} - 76 q^{44} + 4 q^{45} + 44 q^{49} + 96 q^{54} - 8 q^{55} + 24 q^{58} + 28 q^{61} + 20 q^{62} - 64 q^{64} + 12 q^{66} - 80 q^{74} + 12 q^{76} - 32 q^{77} - 16 q^{80} - 52 q^{81} + 68 q^{82} + 36 q^{83} - 56 q^{85} - 120 q^{87} - 8 q^{92} - 16 q^{93} + 48 q^{96} + 76 q^{99}+O(q^{100}) $ 76 * q - 4 * q^4 - 4 * q^5 - 4 * q^6 - 8 * q^7 - 4 * q^11 + 4 * q^16 - 8 * q^17 + 6 * q^19 - 32 * q^20 - 8 * q^23 - 12 * q^24 - 8 * q^26 - 40 * q^30 + 44 * q^36 - 12 * q^38 - 8 * q^39 + 12 * q^42 - 4 * q^43 - 76 * q^44 + 4 * q^45 + 44 * q^49 + 96 * q^54 - 8 * q^55 + 24 * q^58 + 28 * q^61 + 20 * q^62 - 64 * q^64 + 12 * q^66 - 80 * q^74 + 12 * q^76 - 32 * q^77 - 16 * q^80 - 52 * q^81 + 68 * q^82 + 36 * q^83 - 56 * q^85 - 120 * q^87 - 8 * q^92 - 16 * q^93 + 48 * q^96 + 76 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.41289	+	0.0612206i	−0.999063	+	0.0432895i
$2$	−1.41289	+	0.0612206i	−0.999063	+	0.0432895i
$3$	−1.42780	−	1.42780i	−0.824341	−	0.824341i	0.162386	−	0.986727i	$-0.448081\pi$
$3$	−1.42780	−	1.42780i	−0.824341	−	0.824341i	−0.986727	+	0.162386i	$0.948081\pi$
$4$	1.99250	−	0.172996i	0.996252	−	0.0864978i
$5$	0.391081	−	0.391081i	0.174897	−	0.174897i	−0.614230	−	0.789127i	$-0.710533\pi$
$5$	0.391081	−	0.391081i	0.174897	−	0.174897i	0.789127	+	0.614230i	$0.210533\pi$
$6$	2.10473	+	1.92991i	0.859254	+	0.787883i
$7$	−3.36082			−1.27027			−0.635136	−	0.772400i	$-0.719056\pi$
$7$	−3.36082			−1.27027			−0.635136	+	0.772400i	$0.719056\pi$
$8$	−2.80459	+	0.366406i	−0.991574	+	0.129544i
$9$			1.07723i			0.359078i
$10$	−0.528611	+	0.576495i	−0.167161	+	0.182304i
$11$	−0.0339409	−	0.0339409i	−0.0102336	−	0.0102336i	0.701971	−	0.712205i	$-0.252303\pi$
$11$	−0.0339409	−	0.0339409i	−0.0102336	−	0.0102336i	−0.712205	+	0.701971i	$0.752303\pi$
$12$	−3.09190	−	2.59790i	−0.892556	−	0.749948i
$13$	−0.227848	+	0.227848i	−0.0631937	+	0.0631937i	−0.737997	−	0.674804i	$-0.764228\pi$
$13$	−0.227848	+	0.227848i	−0.0631937	+	0.0631937i	0.674804	+	0.737997i	$0.264228\pi$
$14$	4.74847	−	0.205752i	1.26908	−	0.0549894i
$15$	−1.11677			−0.288349
$16$	3.94014	−	0.689389i	0.985036	−	0.172347i
$17$	0.208245			0.0505069			0.0252534	−	0.999681i	$-0.491961\pi$
$17$	0.208245			0.0505069			0.0252534	+	0.999681i	$0.491961\pi$
$18$	−0.0659488	−	1.52201i	−0.0155443	−	0.358741i
$19$	0.442793	+	4.33635i	0.101584	+	0.994827i
$19$	0.442793	+	4.33635i	0.101584	+	0.994827i
$20$	0.711574	−	0.846885i	0.159113	−	0.189369i
$21$	4.79859	+	4.79859i	1.04714	+	1.04714i
$22$	0.0500326	+	0.0458768i	0.0106670	+	0.00978096i
$23$	−8.50857			−1.77416			−0.887079	−	0.461617i	$-0.847270\pi$
$23$	−8.50857			−1.77416			−0.887079	+	0.461617i	$0.847270\pi$
$24$	4.52756	+	3.48125i	0.924184	+	0.710607i
$25$			4.69411i			0.938822i
$26$	0.307975	−	0.335873i	0.0603989	−	0.0658701i
$27$	−2.74533	+	2.74533i	−0.528339	+	0.528339i
$28$	−6.69645	+	0.581408i	−1.26551	+	0.109876i
$29$	−2.09323	+	2.09323i	−0.388703	+	0.388703i	−0.874225	−	0.485521i	$-0.838630\pi$
$29$	−2.09323	+	2.09323i	−0.388703	+	0.388703i	0.485521	+	0.874225i	$0.338630\pi$
$30$	1.57787	−	0.0683694i	0.288079	−	0.0124825i
$31$	−0.695564			−0.124927			−0.0624635	−	0.998047i	$-0.519896\pi$
$31$	−0.695564			−0.124927			−0.0624635	+	0.998047i	$0.519896\pi$
$32$	−5.52478	+	1.21525i	−0.976652	+	0.214827i
$33$			0.0969217i			0.0168719i
$34$	−0.294227	+	0.0127489i	−0.0504595	+	0.00218642i
$35$	−1.31435	+	1.31435i	−0.222166	+	0.222166i
$36$	0.186357	+	2.14639i	0.0310594	+	0.357732i
$37$	3.52688	+	3.52688i	0.579815	+	0.579815i	0.934852	−	0.355037i	$-0.115532\pi$
$37$	3.52688	+	3.52688i	0.579815	+	0.579815i	−0.355037	+	0.934852i	$0.615532\pi$
$38$	−0.891091	−	6.09967i	−0.144554	−	0.989497i
$39$	0.650644			0.104186
$40$	−0.953528	+	1.24012i	−0.150766	+	0.196080i
$41$	−7.19785			−1.12412			−0.562058	−	0.827098i	$-0.689990\pi$
$41$	−7.19785			−1.12412			−0.562058	+	0.827098i	$0.689990\pi$
$42$	−7.07364	−	6.48609i	−1.09149	−	1.00083i
$43$	5.14249	+	5.14249i	0.784222	+	0.784222i	0.980540	−	0.196318i	$-0.0628986\pi$
$43$	5.14249	+	5.14249i	0.784222	+	0.784222i	−0.196318	+	0.980540i	$0.562899\pi$
$44$	−0.0734990	−	0.0617557i	−0.0110804	−	0.00931003i
$45$	0.421285	+	0.421285i	0.0628014	+	0.0628014i
$46$	12.0217	−	0.520900i	1.77250	−	0.0768025i
$47$		−	6.18843i		−	0.902675i	−0.892353	−	0.451338i	$-0.850947\pi$
$47$		−	6.18843i		−	0.902675i	0.892353	−	0.451338i	$-0.149053\pi$
$48$	−6.61005	−	4.64143i	−0.954079	−	0.669933i
$49$	4.29513			0.613590
$50$	−0.287376	−	6.63225i	−0.0406411	−	0.937942i
$51$	−0.297333	−	0.297333i	−0.0416349	−	0.0416349i
$52$	−0.414572	+	0.493405i	−0.0574908	+	0.0684230i
$53$	−2.19113	−	2.19113i	−0.300975	−	0.300975i	0.540421	−	0.841395i	$-0.318265\pi$
$53$	−2.19113	−	2.19113i	−0.300975	−	0.300975i	−0.841395	+	0.540421i	$0.818265\pi$
$54$	3.71077	−	4.04691i	0.504972	−	0.550715i
$55$	−0.0265472			−0.00357963
$56$	9.42574	−	1.23142i	1.25957	−	0.164556i
$57$	5.55923	−	6.82367i	0.736337	−	0.903817i
$58$	2.82935	−	3.08565i	0.371512	−	0.405166i
$59$	1.98964	−	1.98964i	0.259029	−	0.259029i	−0.565630	−	0.824659i	$-0.691367\pi$
$59$	1.98964	−	1.98964i	0.259029	−	0.259029i	0.824659	+	0.565630i	$0.191367\pi$
$60$	−2.22517	+	0.193197i	−0.287268	+	0.0249416i
$61$	−5.48730	−	5.48730i	−0.702577	−	0.702577i	0.262386	−	0.964963i	$-0.415491\pi$
$61$	−5.48730	−	5.48730i	−0.702577	−	0.702577i	−0.964963	+	0.262386i	$0.915491\pi$
$62$	0.982753	−	0.0425828i	0.124810	−	0.00540802i
$63$		−	3.62039i		−	0.456126i
$64$	7.73149	−	2.05524i	0.966437	−	0.256905i
$65$			0.178214i			0.0221047i
$66$	−0.00593360	−	0.136939i	−0.000730376	−	0.0168561i
$67$	0.280654	+	0.280654i	0.0342873	+	0.0342873i	0.724043	−	0.689755i	$-0.242282\pi$
$67$	0.280654	+	0.280654i	0.0342873	+	0.0342873i	−0.689755	+	0.724043i	$0.742282\pi$
$68$	0.414930	−	0.0360255i	0.0503176	−	0.00436874i
$69$	12.1485	+	12.1485i	1.46251	+	1.46251i
$70$	1.77657	−	1.93750i	0.212340	−	0.231575i
$71$		−	12.8008i		−	1.51917i	−0.650407	−	0.759586i	$-0.725402\pi$
$71$		−	12.8008i		−	1.51917i	0.650407	−	0.759586i	$-0.274598\pi$
$72$	−0.394704	−	3.02120i	−0.0465164	−	0.356052i
$73$		−	7.46524i		−	0.873741i	−0.899525	−	0.436870i	$-0.856087\pi$
$73$		−	7.46524i		−	0.873741i	0.899525	−	0.436870i	$-0.143913\pi$
$74$	−5.19900	−	4.76717i	−0.604372	−	0.554172i
$75$	6.70226	−	6.70226i	0.773910	−	0.773910i
$76$	1.63244	+	8.56359i	0.187253	+	0.982312i
$77$	0.114069	+	0.114069i	0.0129994	+	0.0129994i
$78$	−0.919287	+	0.0398328i	−0.104089	+	0.00451018i
$79$	−8.31193			−0.935165			−0.467582	−	0.883949i	$-0.654875\pi$
$79$	−8.31193			−0.935165			−0.467582	+	0.883949i	$0.654875\pi$
$80$	1.27131	−	1.81052i	0.142137	−	0.202422i
$81$	11.0713			1.23014
$82$	10.1698	−	0.440657i	1.12306	−	0.0486624i
$83$	−9.37194	+	9.37194i	−1.02870	+	1.02870i	−0.0291285	+	0.999576i	$0.509273\pi$
$83$	−9.37194	+	9.37194i	−1.02870	+	1.02870i	−0.999576	+	0.0291285i	$0.990727\pi$
$84$	10.3913	+	8.73107i	1.13379	+	0.952638i
$85$	0.0814407	−	0.0814407i	0.00883348	−	0.00883348i
$86$	−7.58058	−	6.95093i	−0.817435	−	0.749538i
$87$	5.97744			0.640849
$88$	0.107627	+	0.0827543i	0.0114730	+	0.00882164i
$89$	−7.02497			−0.744645			−0.372323	−	0.928103i	$-0.621439\pi$
$89$	−7.02497			−0.744645			−0.372323	+	0.928103i	$0.621439\pi$
$90$	−0.621020	−	0.569437i	−0.0654612	−	0.0600239i
$91$	0.765758	−	0.765758i	0.0802732	−	0.0802732i
$92$	−16.9534	+	1.47195i	−1.76751	+	0.153461i
$93$	0.993127	+	0.993127i	0.102982	+	0.102982i
$94$	0.378859	+	8.74356i	0.0390764	+	0.901829i
$95$	1.86903	+	1.52269i	0.191758	+	0.156225i
$96$	9.62342	+	6.15315i	0.982186	+	0.628004i
$97$			5.52597i			0.561078i	0.959843	+	0.280539i	$0.0905132\pi$
$97$			5.52597i			0.561078i	−0.959843	+	0.280539i	$0.909487\pi$
$98$	−6.06854	+	0.262951i	−0.613015	+	0.0265620i
$99$	0.0365622	−	0.0365622i	0.00367464	−	0.00367464i
$100$	0.812061	+	9.35304i	0.0812061	+	0.935304i
$101$	−7.26755	+	7.26755i	−0.723148	+	0.723148i	−0.969245	−	0.246097i	$-0.920852\pi$
$101$	−7.26755	+	7.26755i	−0.723148	+	0.723148i	0.246097	+	0.969245i	$0.420852\pi$
$102$	0.438301	+	0.401895i	0.0433983	+	0.0397935i
$103$		−	11.1653i		−	1.10015i	−0.835116	−	0.550074i	$-0.814599\pi$
$103$		−	11.1653i		−	1.10015i	0.835116	−	0.550074i	$-0.185401\pi$
$104$	0.555537	−	0.722507i	0.0544749	−	0.0708476i
$105$	3.75327			0.366282
$106$	3.22996	+	2.96168i	0.313721	+	0.287663i
$107$	11.7682	−	11.7682i	1.13767	−	1.13767i	0.148805	−	0.988867i	$-0.452457\pi$
$107$	11.7682	−	11.7682i	1.13767	−	1.13767i	0.988867	−	0.148805i	$-0.0475427\pi$
$108$	−4.99515	+	5.94501i	−0.480658	+	0.572059i
$109$	−1.56316	+	1.56316i	−0.149723	+	0.149723i	−0.777995	−	0.628271i	$-0.783763\pi$
$109$	−1.56316	+	1.56316i	−0.149723	+	0.149723i	0.628271	+	0.777995i	$0.283763\pi$
$110$	0.0375083	−	0.00162524i	0.00357627	−	0.000154960i
$111$		−	10.0714i		−	0.955931i
$112$	−13.2421	+	2.31691i	−1.25126	+	0.218928i
$113$		−	7.29553i		−	0.686306i	−0.939280	−	0.343153i	$-0.888505\pi$
$113$		−	7.29553i		−	0.686306i	0.939280	−	0.343153i	$-0.111495\pi$
$114$	−7.43681	+	9.98142i	−0.696521	+	0.934845i
$115$	−3.32754	+	3.32754i	−0.310294	+	0.310294i
$116$	−3.80865	+	4.53289i	−0.353624	+	0.420868i
$117$	−0.245446	−	0.245446i	−0.0226915	−	0.0226915i
$118$	−2.68933	+	2.93295i	−0.247573	+	0.270000i
$119$	−0.699875			−0.0641575
$120$	3.13209	−	0.409191i	0.285919	−	0.0373539i
$121$		−	10.9977i		−	0.999791i
$122$	8.08887	+	7.41700i	0.732332	+	0.671504i
$123$	10.2771	+	10.2771i	0.926655	+	0.926655i
$124$	−1.38591	+	0.120329i	−0.124459	+	0.0108059i
$125$	3.79118	+	3.79118i	0.339093	+	0.339093i
$126$	0.221642	+	5.11520i	0.0197455	+	0.455699i
$127$	−13.3941			−1.18853			−0.594265	−	0.804269i	$-0.702557\pi$
$127$	−13.3941			−1.18853			−0.594265	+	0.804269i	$0.702557\pi$
$128$	−10.7979	+	3.37715i	−0.954409	+	0.298501i
$129$		−	14.6849i		−	1.29293i
$130$	−0.0109104	−	0.251797i	−0.000956903	−	0.0220840i
$131$	14.3341	−	14.3341i	1.25237	−	1.25237i	0.297720	−	0.954653i	$-0.403774\pi$
$131$	14.3341	−	14.3341i	1.25237	−	1.25237i	0.954653	−	0.297720i	$-0.0962261\pi$
$132$	0.0167670	+	0.193117i	0.00145938	+	0.0168087i
$133$	−1.48815	−	14.5737i	−0.129039	−	1.26370i
$134$	−0.413714	−	0.379350i	−0.0357394	−	0.0327709i
$135$			2.14729i			0.184809i
$136$	−0.584043	+	0.0763023i	−0.0500813	+	0.00654287i
$137$			3.35195i			0.286376i	0.989695	+	0.143188i	$0.0457354\pi$
$137$			3.35195i			0.286376i	−0.989695	+	0.143188i	$0.954265\pi$
$138$	−17.9083	−	16.4208i	−1.52445	−	1.39783i
$139$	1.43256	+	1.43256i	0.121508	+	0.121508i	0.765246	−	0.643738i	$-0.222617\pi$
$139$	1.43256	+	1.43256i	0.121508	+	0.121508i	−0.643738	+	0.765246i	$0.722617\pi$
$140$	−2.39148	+	2.84623i	−0.202117	+	0.240550i
$141$	−8.83585	+	8.83585i	−0.744113	+	0.744113i
$142$	0.783670	+	18.0860i	0.0657642	+	1.51775i
$143$	0.0154667			0.00129339
$144$	0.742633	+	4.24445i	0.0618861	+	0.353705i
$145$			1.63724i			0.135966i
$146$	0.457027	+	10.5476i	0.0378238	+	0.872922i
$147$	−6.13260	−	6.13260i	−0.505808	−	0.505808i
$148$	7.63745	+	6.41718i	0.627795	+	0.527489i
$149$	−12.5414	+	12.5414i	−1.02743	+	1.02743i	−0.0278206	+	0.999613i	$0.508857\pi$
$149$	−12.5414	+	12.5414i	−1.02743	+	1.02743i	−0.999613	+	0.0278206i	$0.991143\pi$
$150$	−9.05922	+	9.87986i	−0.739683	+	0.806687i
$151$			22.5956i			1.83880i	0.393320	+	0.919402i	$0.371327\pi$
$151$			22.5956i			1.83880i	−0.393320	+	0.919402i	$0.628673\pi$
$152$	−2.83072	−	11.9995i	−0.229602	−	0.973285i
$153$			0.224329i			0.0181359i
$154$	−0.168151	−	0.154184i	−0.0135500	−	0.0124245i
$155$	−0.272021	+	0.272021i	−0.0218493	+	0.0218493i
$156$	1.29641	−	0.112559i	0.103796	−	0.00901190i
$157$	−5.87676	−	5.87676i	−0.469016	−	0.469016i	0.432580	−	0.901596i	$-0.357603\pi$
$157$	−5.87676	−	5.87676i	−0.469016	−	0.469016i	−0.901596	+	0.432580i	$0.857603\pi$
$158$	11.7438	−	0.508861i	0.934288	−	0.0404828i
$159$			6.25699i			0.496212i
$160$	−1.68537	+	2.63589i	−0.133241	+	0.208386i
$161$	28.5958			2.25366
$162$	−15.6425	+	0.677790i	−1.22899	+	0.0532522i
$163$	−2.16820	+	2.16820i	−0.169826	+	0.169826i	−0.786903	−	0.617077i	$-0.788317\pi$
$163$	−2.16820	+	2.16820i	−0.169826	+	0.169826i	0.617077	+	0.786903i	$0.288317\pi$
$164$	−14.3418	+	1.24520i	−1.11990	+	0.0972336i
$165$	0.0379042	+	0.0379042i	0.00295084	+	0.00295084i
$166$	12.6677	−	13.8153i	0.983208	−	1.07227i
$167$			15.0475i			1.16441i	0.813042	+	0.582205i	$0.197810\pi$
$167$			15.0475i			1.16441i	−0.813042	+	0.582205i	$0.802190\pi$
$168$	−15.2163	−	11.6999i	−1.17396	−	0.902664i
$169$			12.8962i			0.992013i
$170$	−0.110081	+	0.120052i	−0.00844280	+	0.00920760i
$171$	−4.67126	+	0.476992i	−0.357220	+	0.0364765i
$172$	11.1361	+	9.35680i	0.849116	+	0.713449i
$173$	−1.84859	+	1.84859i	−0.140546	+	0.140546i	−0.773879	−	0.633333i	$-0.781686\pi$
$173$	−1.84859	+	1.84859i	−0.140546	+	0.140546i	0.633333	+	0.773879i	$0.281686\pi$
$174$	−8.44545	+	0.365942i	−0.640248	+	0.0277420i
$175$		−	15.7761i		−	1.19256i
$176$	−0.157131	−	0.110334i	−0.0118442	−	0.00831670i
$177$	−5.68162			−0.427057
$178$	9.92549	−	0.430073i	0.743947	−	0.0322353i
$179$	−7.79254	−	7.79254i	−0.582442	−	0.582442i	0.353132	−	0.935574i	$-0.385117\pi$
$179$	−7.79254	−	7.79254i	−0.582442	−	0.582442i	−0.935574	+	0.353132i	$0.885117\pi$
$180$	0.912292	+	0.766531i	0.0679983	+	0.0571339i
$181$	−14.9191	−	14.9191i	−1.10893	−	1.10893i	−0.993291	−	0.115639i	$-0.963108\pi$
$181$	−14.9191	−	14.9191i	−1.10893	−	1.10893i	−0.115639	−	0.993291i	$-0.536892\pi$
$182$	−1.03505	+	1.12881i	−0.0767230	+	0.0836730i
$183$			15.6695i			1.15833i
$184$	23.8631	−	3.11759i	1.75921	−	0.229832i
$185$	2.75859			0.202815
$186$	−1.46398	−	1.34238i	−0.107344	−	0.0984278i
$187$	−0.00706803	−	0.00706803i	−0.000516866	−	0.000516866i
$188$	−1.07057	−	12.3305i	−0.0780795	−	0.899292i
$189$	9.22657	−	9.22657i	0.671134	−	0.671134i
$190$	−2.73395	−	2.03697i	−0.198342	−	0.147778i
$191$			17.0723i			1.23531i	0.786451	+	0.617653i	$0.211916\pi$
$191$			17.0723i			1.23531i	−0.786451	+	0.617653i	$0.788084\pi$
$192$	−13.9735	−	8.10456i	−1.00845	−	0.584897i
$193$		−	7.75896i		−	0.558502i	−0.960218	−	0.279251i	$-0.909914\pi$
$193$		−	7.75896i		−	0.558502i	0.960218	−	0.279251i	$-0.0900862\pi$
$194$	−0.338303	−	7.80758i	−0.0242888	−	0.560552i
$195$	0.254454	−	0.254454i	0.0182219	−	0.0182219i
$196$	8.55807	−	0.743039i	0.611291	−	0.0530742i
$197$	−1.33234	+	1.33234i	−0.0949256	+	0.0949256i	−0.752975	−	0.658049i	$-0.771382\pi$
$197$	−1.33234	+	1.33234i	−0.0949256	+	0.0949256i	0.658049	+	0.752975i	$0.271382\pi$
$198$	−0.0494200	+	0.0538967i	−0.00351213	+	0.00383027i
$199$	13.5183			0.958287			0.479144	−	0.877736i	$-0.340947\pi$
$199$	13.5183			0.958287			0.479144	+	0.877736i	$0.340947\pi$
$200$	−1.71995	−	13.1651i	−0.121619	−	0.930912i
$201$		−	0.801435i		−	0.0565289i
$202$	9.82331	−	10.7132i	0.691166	−	0.753775i
$203$	7.03498	−	7.03498i	0.493759	−	0.493759i
$204$	−0.643874	−	0.541000i	−0.0450802	−	0.0378775i
$205$	−2.81494	+	2.81494i	−0.196604	+	0.196604i
$206$	0.683546	+	15.7753i	0.0476249	+	1.09912i
$207$		−	9.16571i		−	0.637061i
$208$	−0.740679	+	1.05483i	−0.0513569	+	0.0731394i
$209$	0.132151	−	0.162208i	0.00914106	−	0.0112202i
$210$	−5.30295	+	0.229777i	−0.365938	+	0.0158561i
$211$	13.4797	+	13.4797i	0.927978	+	0.927978i	0.997575	−	0.0695975i	$-0.0221715\pi$
$211$	13.4797	+	13.4797i	0.927978	+	0.927978i	−0.0695975	+	0.997575i	$0.522172\pi$
$212$	−4.74489	−	3.98678i	−0.325880	−	0.273813i
$213$	−18.2769	+	18.2769i	−1.25232	+	1.25232i
$214$	−15.9066	+	17.3476i	−1.08736	+	1.18585i
$215$	4.02225			0.274315
$216$	6.69363	−	8.70544i	0.455444	−	0.592330i
$217$	2.33767			0.158691
$218$	2.11287	−	2.30426i	0.143102	−	0.156065i
$219$	−10.6589	+	10.6589i	−0.720261	+	0.720261i
$220$	−0.0528955	+	0.00459256i	−0.00356621	+	0.000309630i
$221$	−0.0474483	+	0.0474483i	−0.00319172	+	0.00319172i
$222$	0.616575	+	14.2297i	0.0413818	+	0.955035i
$223$	−14.2160			−0.951974			−0.475987	−	0.879452i	$-0.657909\pi$
$223$	−14.2160			−0.951974			−0.475987	+	0.879452i	$0.657909\pi$
$224$	18.5678	−	4.08423i	1.24061	−	0.272889i
$225$	−5.05665			−0.337110
$226$	0.446637	+	10.3078i	0.0297098	+	0.685663i
$227$	20.6970	+	20.6970i	1.37371	+	1.37371i	0.854875	+	0.518833i	$0.173633\pi$
$227$	20.6970	+	20.6970i	1.37371	+	1.37371i	0.518833	+	0.854875i	$0.326367\pi$
$228$	9.89631	−	14.5579i	0.655399	−	0.964121i
$229$	7.77653	−	7.77653i	0.513888	−	0.513888i	−0.401828	−	0.915715i	$-0.631625\pi$
$229$	7.77653	−	7.77653i	0.513888	−	0.513888i	0.915715	+	0.401828i	$0.131625\pi$
$230$	4.49772	−	4.90515i	0.296571	−	0.323436i
$231$		−	0.325737i		−	0.0214319i
$232$	5.10369	−	6.63764i	0.335074	−	0.435782i
$233$		−	7.39228i		−	0.484284i	−0.970241	−	0.242142i	$-0.922150\pi$
$233$		−	7.39228i		−	0.484284i	0.970241	−	0.242142i	$-0.0778501\pi$
$234$	0.361814	+	0.331761i	0.0236525	+	0.0216879i
$235$	−2.42017	−	2.42017i	−0.157875	−	0.157875i
$236$	3.62017	−	4.30857i	0.235653	−	0.280464i
$237$	11.8678	+	11.8678i	0.770895	+	0.770895i
$238$	0.988846	−	0.0428468i	0.0640973	−	0.00277735i
$239$			11.6463i			0.753334i	0.926349	+	0.376667i	$0.122930\pi$
$239$			11.6463i			0.753334i	−0.926349	+	0.376667i	$0.877070\pi$
$240$	−4.40024	+	0.769890i	−0.284034	+	0.0496962i
$241$		−	0.0825153i		−	0.00531528i	−0.999996	−	0.00265764i	$-0.999154\pi$
$241$		−	0.0825153i		−	0.00531528i	0.999996	−	0.00265764i	$-0.000845954\pi$
$242$	0.673285	+	15.5385i	0.0432804	+	0.998853i
$243$	−7.57158	−	7.57158i	−0.485717	−	0.485717i
$244$	−11.8827	−	9.98419i	−0.760715	−	0.639172i
$245$	1.67974	−	1.67974i	0.107315	−	0.107315i
$246$	−15.1496	−	13.8912i	−0.965901	−	0.885672i
$247$	−1.08892	−	0.887140i	−0.0692863	−	0.0564474i
$248$	1.95077	−	0.254859i	0.123874	−	0.0161835i
$249$	26.7625			1.69601
$250$	−5.58861	−	5.12441i	−0.353455	−	0.324096i
$251$	−6.69566	−	6.69566i	−0.422627	−	0.422627i	0.463481	−	0.886107i	$-0.346600\pi$
$251$	−6.69566	−	6.69566i	−0.422627	−	0.422627i	−0.886107	+	0.463481i	$0.846600\pi$
$252$	−0.626312	−	7.21364i	−0.0394539	−	0.454417i
$253$	0.288788	+	0.288788i	0.0181560	+	0.0181560i
$254$	18.9243	−	0.819992i	1.18742	−	0.0514509i
$255$	−0.232562			−0.0145636
$256$	15.0495	−	5.43259i	0.940593	−	0.339537i
$257$		−	12.6163i		−	0.786985i	−0.919328	−	0.393492i	$-0.871267\pi$
$257$		−	12.6163i		−	0.786985i	0.919328	−	0.393492i	$-0.128733\pi$
$258$	0.899018	+	20.7481i	0.0559704	+	1.29172i
$259$	−11.8532	−	11.8532i	−0.736523	−	0.736523i
$260$	0.0308303	+	0.355092i	0.00191201	+	0.0220219i
$261$	−2.25490	−	2.25490i	−0.139575	−	0.139575i
$262$	−19.3749	+	21.1300i	−1.19698	+	1.30541i
$263$	−9.15663			−0.564622			−0.282311	−	0.959323i	$-0.591101\pi$
$263$	−9.15663			−0.564622			−0.282311	+	0.959323i	$0.591101\pi$
$264$	−0.0355127	−	0.271826i	−0.00218565	−	0.0167297i
$265$	−1.71382			−0.105279
$266$	2.99480	+	20.4999i	0.183623	+	1.25693i
$267$	10.0303	+	10.0303i	0.613842	+	0.613842i
$268$	0.607755	+	0.510652i	0.0371246	+	0.0311930i
$269$	8.20751	−	8.20751i	0.500421	−	0.500421i	−0.411148	−	0.911569i	$-0.634872\pi$
$269$	8.20751	−	8.20751i	0.500421	−	0.500421i	0.911569	+	0.411148i	$0.134872\pi$
$270$	−0.131458	−	3.03388i	−0.00800030	−	0.184636i
$271$		−	18.4575i		−	1.12121i	−0.828082	−	0.560607i	$-0.810568\pi$
$271$		−	18.4575i		−	1.12121i	0.828082	−	0.560607i	$-0.189432\pi$
$272$	0.820517	−	0.143562i	0.0497511	−	0.00870473i
$273$	−2.18670			−0.132345
$274$	−0.205208	−	4.73593i	−0.0123971	−	0.286108i
$275$	0.159322	−	0.159322i	0.00960750	−	0.00960750i
$276$	26.3077	+	22.1044i	1.58354	+	1.33053i
$277$	12.2403	−	12.2403i	0.735447	−	0.735447i	−0.236246	−	0.971693i	$-0.575917\pi$
$277$	12.2403	−	12.2403i	0.735447	−	0.735447i	0.971693	+	0.236246i	$0.0759172\pi$
$278$	−2.11174	−	1.93634i	−0.126654	−	0.116134i
$279$		−	0.749284i		−	0.0448585i
$280$	3.20464	−	4.16781i	0.191514	−	0.249074i
$281$	−23.8640			−1.42361			−0.711803	−	0.702379i	$-0.752121\pi$
$281$	−23.8640			−1.42361			−0.711803	+	0.702379i	$0.752121\pi$
$282$	11.9431	−	13.0250i	0.711203	−	0.775627i
$283$	−17.8694	−	17.8694i	−1.06223	−	1.06223i	−0.997931	−	0.0642941i	$-0.979520\pi$
$283$	−17.8694	−	17.8694i	−1.06223	−	1.06223i	−0.0642941	−	0.997931i	$-0.520480\pi$
$284$	−2.21448	−	25.5056i	−0.131405	−	1.51348i
$285$	−0.494499	−	4.84271i	−0.0292916	−	0.286857i
$286$	−0.0218528		0.000946884i	−0.00129218		5.59904e-5i
$287$	24.1907			1.42793
$288$	−1.30910	−	5.95147i	−0.0771397	−	0.350694i
$289$	−16.9566			−0.997449
$290$	−0.100233	−	2.31324i	−0.00588589	−	0.135838i
$291$	7.88999	−	7.88999i	0.462520	−	0.462520i
$292$	−1.29145	−	14.8745i	−0.0755767	−	0.870466i
$293$	6.09548	+	6.09548i	0.356102	+	0.356102i	0.862374	−	0.506272i	$-0.168977\pi$
$293$	6.09548	+	6.09548i	0.356102	+	0.356102i	−0.506272	+	0.862374i	$0.668977\pi$
$294$	9.04011	+	8.28923i	0.527230	+	0.483438i
$295$		−	1.55622i		−	0.0906066i
$296$	−11.1837	−	8.59919i	−0.650041	−	0.499818i
$297$	0.186358			0.0108136
$298$	16.9518	−	18.4874i	0.981993	−	1.07095i
$299$	1.93866	−	1.93866i	0.112116	−	0.112116i
$300$	12.1948	−	14.5137i	0.704068	−	0.837951i
$301$	−17.2830	−	17.2830i	−0.996175	−	0.996175i
$302$	−1.38332	−	31.9250i	−0.0796009	−	1.83708i
$303$	20.7532			1.19224
$304$	4.73410	+	16.7806i	0.271519	+	0.962433i
$305$	−4.29195			−0.245756
$306$	−0.0137335	−	0.316951i	−0.000785094	−	0.0181189i
$307$	24.0824	+	24.0824i	1.37446	+	1.37446i	0.853715	+	0.520741i	$0.174344\pi$
$307$	24.0824	+	24.0824i	1.37446	+	1.37446i	0.520741	+	0.853715i	$0.325656\pi$
$308$	0.247017	+	0.207550i	0.0140751	+	0.0118263i
$309$	−15.9418	+	15.9418i	−0.906898	+	0.906898i
$310$	0.367682	−	0.400989i	0.0208830	−	0.0227747i
$311$	−20.4747			−1.16101			−0.580506	−	0.814256i	$-0.697145\pi$
$311$	−20.4747			−1.16101			−0.580506	+	0.814256i	$0.697145\pi$
$312$	−1.82479	+	0.238400i	−0.103309	+	0.0134967i
$313$		−	14.4919i		−	0.819132i	−0.912280	−	0.409566i	$-0.865680\pi$
$313$		−	14.4919i		−	0.819132i	0.912280	−	0.409566i	$-0.134320\pi$
$314$	8.66297	+	7.94342i	0.488880	+	0.448273i
$315$	−1.41586	−	1.41586i	−0.0797749	−	0.0797749i
$316$	−16.5615	+	1.43793i	−0.931660	+	0.0808897i
$317$	12.4605	−	12.4605i	0.699853	−	0.699853i	−0.264525	−	0.964379i	$-0.585215\pi$
$317$	12.4605	−	12.4605i	0.699853	−	0.699853i	0.964379	+	0.264525i	$0.0852153\pi$
$318$	−0.383057	−	8.84043i	−0.0214808	−	0.495746i
$319$	0.142092			0.00795564
$320$	2.21987	−	3.82740i	0.124095	−	0.213958i
$321$	−33.6052			−1.87566
$322$	−40.4026	+	1.75065i	−2.25155	+	0.0975600i
$323$	0.0922096	+	0.903024i	0.00513068	+	0.0502456i
$324$	22.0595	−	1.91528i	1.22553	−	0.106405i
$325$	−1.06955	−	1.06955i	−0.0593277	−	0.0593277i
$326$	2.93068	−	3.19616i	0.162315	−	0.177019i
$327$	4.46376			0.246846
$328$	20.1871	−	2.63734i	1.11464	−	0.145622i
$329$			20.7982i			1.14664i
$330$	−0.0558749	−	0.0512339i	−0.00307581	−	0.00282033i
$331$	−0.432281	+	0.432281i	−0.0237603	+	0.0237603i	−0.718887	−	0.695127i	$-0.755348\pi$
$331$	−0.432281	+	0.432281i	−0.0237603	+	0.0237603i	0.695127	+	0.718887i	$0.255348\pi$
$332$	−17.0523	+	20.2949i	−0.935868	+	1.11383i
$333$	−3.79927	+	3.79927i	−0.208199	+	0.208199i
$334$	−0.921217	−	21.2604i	−0.0504068	−	1.16332i
$335$	0.219516			0.0119935
$336$	22.2152	+	15.5990i	1.21194	+	0.850997i
$337$			32.7369i			1.78329i	0.452730	+	0.891647i	$0.350450\pi$
$337$			32.7369i			1.78329i	−0.452730	+	0.891647i	$0.649550\pi$
$338$	−0.789511	−	18.2208i	−0.0429437	−	0.991083i
$339$	−10.4166	+	10.4166i	−0.565751	+	0.565751i
$340$	0.148182	−	0.176360i	0.00803630	−	0.00956445i
$341$	0.0236080	+	0.0236080i	0.00127845	+	0.00127845i
$342$	6.57076	−	0.959913i	0.355306	−	0.0519061i
$343$	9.09058			0.490845
$344$	−16.3068	−	12.5383i	−0.879205	−	0.676023i
$345$	9.50212			0.511577
$346$	2.49868	−	2.72503i	0.134330	−	0.146498i
$347$	6.24400	+	6.24400i	0.335195	+	0.335195i	0.854555	−	0.519360i	$-0.173830\pi$
$347$	6.24400	+	6.24400i	0.335195	+	0.335195i	−0.519360	+	0.854555i	$0.673830\pi$
$348$	11.9101	−	1.03407i	0.638447	−	0.0554320i
$349$	−17.4921	−	17.4921i	−0.936330	−	0.936330i	0.0617611	−	0.998091i	$-0.480328\pi$
$349$	−17.4921	−	17.4921i	−0.936330	−	0.936330i	−0.998091	+	0.0617611i	$0.980328\pi$
$350$	0.965821	+	22.2898i	0.0516253	+	1.19144i
$351$		−	1.25104i		−	0.0667754i
$352$	0.228762	+	0.146269i	0.0121931	+	0.00779618i
$353$	−23.8572			−1.26979			−0.634894	−	0.772599i	$-0.718956\pi$
$353$	−23.8572			−1.26979			−0.634894	+	0.772599i	$0.718956\pi$
$354$	8.02750	−	0.347832i	0.426657	−	0.0184871i
$355$	−5.00613	−	5.00613i	−0.265698	−	0.265698i
$356$	−13.9973	+	1.21529i	−0.741854	+	0.0644102i
$357$	0.999283	+	0.999283i	0.0528877	+	0.0528877i
$358$	11.4871	+	10.5329i	0.607110	+	0.556683i
$359$	23.8006			1.25615			0.628073	−	0.778155i	$-0.283844\pi$
$359$	23.8006			1.25615			0.628073	+	0.778155i	$0.283844\pi$
$360$	−1.33589	−	1.02717i	−0.0704078	−	0.0541367i
$361$	−18.6079	+	3.84021i	−0.979361	+	0.202117i
$362$	21.9924	+	20.1657i	1.15590	+	1.05989i
$363$	−15.7025	+	15.7025i	−0.824169	+	0.824169i
$364$	1.39330	−	1.65825i	0.0730289	−	0.0869158i
$365$	−2.91951	−	2.91951i	−0.152814	−	0.152814i
$366$	−0.959299	−	22.1393i	−0.0501434	−	1.15724i
$367$			9.92689i			0.518180i	0.965853	+	0.259090i	$0.0834226\pi$
$367$			9.92689i			0.518180i	−0.965853	+	0.259090i	$0.916577\pi$
$368$	−33.5250	+	5.86571i	−1.74761	+	0.305771i
$369$		−	7.75377i		−	0.403645i
$370$	−3.89757	+	0.168882i	−0.202625	+	0.00877978i
$371$	7.36399	+	7.36399i	0.382319	+	0.382319i
$372$	2.15062	+	1.80700i	0.111504	+	0.0936887i
$373$	5.23630	+	5.23630i	0.271125	+	0.271125i	0.829553	−	0.558428i	$-0.188595\pi$
$373$	5.23630	+	5.23630i	0.271125	+	0.271125i	−0.558428	+	0.829553i	$0.688595\pi$
$374$	0.0104190	+	0.00955362i	0.000538756	+	0.000494006i
$375$		−	10.8261i		−	0.559057i
$376$	2.26748	+	17.3560i	0.116936	+	0.895069i
$377$		−	0.953878i		−	0.0491272i
$378$	−12.4712	+	13.6010i	−0.641452	+	0.699558i
$379$	−21.4183	+	21.4183i	−1.10019	+	1.10019i	−0.105799	+	0.994388i	$0.533740\pi$
$379$	−21.4183	+	21.4183i	−1.10019	+	1.10019i	−0.994388	+	0.105799i	$0.966260\pi$
$380$	3.98747	+	2.71064i	0.204553	+	0.139053i
$381$	19.1241	+	19.1241i	0.979755	+	0.979755i
$382$	−1.04517	−	24.1212i	−0.0534757	−	1.23415i
$383$	29.1110			1.48750			0.743751	−	0.668457i	$-0.233045\pi$
$383$	29.1110			1.48750			0.743751	+	0.668457i	$0.233045\pi$
$384$	20.2392	+	10.5954i	1.03283	+	0.540693i
$385$	0.0892206			0.00454710
$386$	0.475008	+	10.9625i	0.0241773	+	0.557979i
$387$	−5.53966	+	5.53966i	−0.281597	+	0.281597i
$388$	0.955970	+	11.0105i	0.0485320	+	0.558975i
$389$	−10.3932	+	10.3932i	−0.526958	+	0.526958i	−0.919664	−	0.392706i	$-0.871539\pi$
$389$	−10.3932	+	10.3932i	−0.526958	+	0.526958i	0.392706	+	0.919664i	$0.371539\pi$
$390$	−0.343938	+	0.375093i	−0.0174160	+	0.0189936i
$391$	−1.77187			−0.0896073
$392$	−12.0461	+	1.57376i	−0.608420	+	0.0794869i
$393$	−40.9324			−2.06477
$394$	1.80089	−	1.96402i	0.0907274	−	0.0989459i
$395$	−3.25063	+	3.25063i	−0.163557	+	0.163557i
$396$	0.0665253	−	0.0791755i	0.00334302	−	0.00397872i
$397$	9.67384	+	9.67384i	0.485516	+	0.485516i	0.906888	−	0.421372i	$-0.138451\pi$
$397$	9.67384	+	9.67384i	0.485516	+	0.485516i	−0.421372	+	0.906888i	$0.638451\pi$
$398$	−19.0999	+	0.827599i	−0.957389	+	0.0414838i
$399$	−18.6836	+	22.9331i	−0.935349	+	1.14809i
$400$	3.23607	+	18.4955i	0.161803	+	0.924774i
$401$			26.1540i			1.30607i	0.757329	+	0.653034i	$0.226504\pi$
$401$			26.1540i			1.30607i	−0.757329	+	0.653034i	$0.773496\pi$
$402$	0.0490643	+	1.13234i	0.00244711	+	0.0564759i
$403$	0.158483	−	0.158483i	0.00789460	−	0.00789460i
$404$	−13.2234	+	15.7379i	−0.657887	+	0.782989i
$405$	4.32976	−	4.32976i	0.215147	−	0.215147i
$406$	−9.50895	+	10.3703i	−0.471921	+	0.514671i
$407$		−	0.239411i		−	0.0118672i
$408$	0.942842	+	0.724953i	0.0466777	+	0.0358905i
$409$	19.2365			0.951183			0.475591	−	0.879666i	$-0.342234\pi$
$409$	19.2365			0.951183			0.475591	+	0.879666i	$0.342234\pi$
$410$	3.80486	−	4.14953i	0.187909	−	0.204931i
$411$	4.78592	−	4.78592i	0.236072	−	0.236072i
$412$	−1.93155	−	22.2469i	−0.0951605	−	1.09603i
$413$	−6.68683	+	6.68683i	−0.329037	+	0.329037i
$414$	0.561130	+	12.9501i	0.0275780	+	0.636464i
$415$			7.33037i			0.359834i
$416$	0.981919	−	1.53570i	0.0481426	−	0.0752941i
$417$		−	4.09081i		−	0.200328i
$418$	−0.176784	+	0.237273i	−0.00864678	+	0.0116054i
$419$	17.6810	−	17.6810i	0.863772	−	0.863772i	−0.128002	−	0.991774i	$-0.540856\pi$
$419$	17.6810	−	17.6810i	0.863772	−	0.863772i	0.991774	+	0.128002i	$0.0408563\pi$
$420$	7.47840	−	0.649299i	0.364909	−	0.0316826i
$421$	12.0531	+	12.0531i	0.587430	+	0.587430i	0.936935	−	0.349505i	$-0.113650\pi$
$421$	12.0531	+	12.0531i	0.587430	+	0.587430i	−0.349505	+	0.936935i	$0.613650\pi$
$422$	−19.8705	−	18.2200i	−0.967279	−	0.886936i
$423$	6.66638			0.324131
$424$	6.94807	+	5.34238i	0.337428	+	0.259449i
$425$			0.977527i			0.0474170i
$426$	24.7044	−	26.9422i	1.19693	−	1.30535i
$427$	18.4418	+	18.4418i	0.892463	+	0.892463i
$428$	21.4123	−	25.4840i	1.03500	−	1.23181i
$429$	−0.0220834	−	0.0220834i	−0.00106620	−	0.00106620i
$430$	−5.68299	+	0.246245i	−0.274058	+	0.0118750i
$431$	−31.5058			−1.51758			−0.758790	−	0.651335i	$-0.774209\pi$
$431$	−31.5058			−1.51758			−0.758790	+	0.651335i	$0.774209\pi$
$432$	−8.92440	+	12.7096i	−0.429375	+	0.611491i
$433$		−	34.7567i		−	1.67030i	−0.550022	−	0.835150i	$-0.685381\pi$
$433$		−	34.7567i		−	1.67030i	0.550022	−	0.835150i	$-0.314619\pi$
$434$	−3.30286	+	0.143113i	−0.158542	+	0.00686966i
$435$	2.33766	−	2.33766i	0.112082	−	0.112082i
$436$	−2.84418	+	3.38502i	−0.136212	+	0.162113i
$437$	−3.76754	−	36.8961i	−0.180226	−	1.76498i
$438$	14.4073	−	15.7124i	0.688406	−	0.750765i
$439$		−	35.4732i		−	1.69304i	−0.532355	−	0.846521i	$-0.678693\pi$
$439$		−	35.4732i		−	1.69304i	0.532355	−	0.846521i	$-0.321307\pi$
$440$	0.0744543	−	0.00972706i	0.00354947	−	0.000463720i
$441$			4.62686i			0.220327i
$442$	0.0641344	−	0.0699440i	0.00305056	−	0.00332690i
$443$	−8.00113	−	8.00113i	−0.380145	−	0.380145i	0.491009	−	0.871154i	$-0.336628\pi$
$443$	−8.00113	−	8.00113i	−0.380145	−	0.380145i	−0.871154	+	0.491009i	$0.836628\pi$
$444$	−1.74230	−	20.0672i	−0.0826860	−	0.952349i
$445$	−2.74733	+	2.74733i	−0.130236	+	0.130236i
$446$	20.0856	−	0.870312i	0.951082	−	0.0412105i
$447$	35.8133			1.69391
$448$	−25.9842	+	6.90729i	−1.22764	+	0.326339i
$449$			12.0121i			0.566887i	0.958989	+	0.283443i	$0.0914768\pi$
$449$			12.0121i			0.566887i	−0.958989	+	0.283443i	$0.908523\pi$
$450$	7.14448	−	0.309571i	0.336794	−	0.0145933i
$451$	0.244302	+	0.244302i	0.0115037	+	0.0115037i
$452$	−1.26210	−	14.5364i	−0.0593640	−	0.683734i
$453$	32.2620	−	32.2620i	1.51580	−	1.51580i
$454$	−30.5096	−	27.9755i	−1.43189	−	1.31295i
$455$		−	0.598946i		−	0.0280790i
$456$	−13.0911	+	21.1745i	−0.613049	+	0.991589i
$457$			23.9022i			1.11810i	0.829134	+	0.559050i	$0.188834\pi$
$457$			23.9022i			1.11810i	−0.829134	+	0.559050i	$0.811166\pi$
$458$	−10.5113	+	11.4635i	−0.491160	+	0.535652i
$459$	−0.571702	+	0.571702i	−0.0266848	+	0.0266848i
$460$	−6.05448	+	7.20578i	−0.282292	+	0.335971i
$461$	11.0824	+	11.0824i	0.516159	+	0.516159i	0.916407	−	0.400248i	$-0.131076\pi$
$461$	11.0824	+	11.0824i	0.516159	+	0.516159i	−0.400248	+	0.916407i	$0.631076\pi$
$462$	0.0199418	+	0.460229i	0.000927776	+	0.0214118i
$463$			15.7394i			0.731471i	0.930719	+	0.365735i	$0.119183\pi$
$463$			15.7394i			0.731471i	−0.930719	+	0.365735i	$0.880817\pi$
$464$	−6.80458	+	9.69069i	−0.315895	+	0.449879i
$465$	0.776785			0.0360225
$466$	0.452560	+	10.4445i	0.0209644	+	0.483831i
$467$	13.3513	−	13.3513i	0.617827	−	0.617827i	−0.327147	−	0.944974i	$-0.606087\pi$
$467$	13.3513	−	13.3513i	0.617827	−	0.617827i	0.944974	+	0.327147i	$0.106087\pi$
$468$	−0.531513	−	0.446591i	−0.0245692	−	0.0206437i
$469$	−0.943227	−	0.943227i	−0.0435542	−	0.0435542i
$470$	3.56760	+	3.27127i	0.164561	+	0.150892i
$471$			16.7817i			0.773259i
$472$	−4.85112	+	6.30915i	−0.223291	+	0.290402i
$473$		−	0.349081i		−	0.0160508i
$474$	−17.4944	−	16.0413i	−0.803544	−	0.736801i
$475$	−20.3553	+	2.07852i	−0.933966	+	0.0953691i
$476$	−1.39450	+	0.121075i	−0.0639170	+	0.00554948i
$477$	2.36036	−	2.36036i	0.108073	−	0.108073i
$478$	−0.712991	−	16.4549i	−0.0326115	−	0.752628i
$479$		−	24.4414i		−	1.11676i	−0.829586	−	0.558379i	$-0.811423\pi$
$479$		−	24.4414i		−	1.11676i	0.829586	−	0.558379i	$-0.188577\pi$
$480$	6.16991	−	1.35715i	0.281617	−	0.0619453i
$481$	−1.60719			−0.0732814
$482$	0.00505164	+	0.116585i	0.000230096	+	0.00531030i
$483$	−40.8291	−	40.8291i	−1.85779	−	1.85779i
$484$	−1.90255	−	21.9130i	−0.0864797	−	0.996043i
$485$	2.16110	+	2.16110i	0.0981306	+	0.0981306i
$486$	11.1613	+	10.2343i	0.506288	+	0.464235i
$487$		−	17.1665i		−	0.777887i	−0.921262	−	0.388943i	$-0.872840\pi$
$487$		−	17.1665i		−	0.777887i	0.921262	−	0.388943i	$-0.127160\pi$
$488$	17.4002	+	13.3791i	0.787671	+	0.605642i
$489$	6.19151			0.279990
$490$	−2.27045	+	2.47612i	−0.102569	+	0.111860i
$491$	19.4343	+	19.4343i	0.877058	+	0.877058i	0.993229	−	0.116171i	$-0.0370621\pi$
$491$	19.4343	+	19.4343i	0.877058	+	0.877058i	−0.116171	+	0.993229i	$0.537062\pi$
$492$	22.2551	+	18.6993i	1.00334	+	0.843029i
$493$	−0.435906	+	0.435906i	−0.0196322	+	0.0196322i
$494$	1.59283	+	1.18677i	0.0716649	+	0.0533951i
$495$		−	0.0285976i		−	0.00128537i
$496$	−2.74062	+	0.479514i	−0.123058	+	0.0215308i
$497$			43.0211i			1.92976i
$498$	−37.8125	+	1.63842i	−1.69442	+	0.0734193i
$499$	6.65603	−	6.65603i	0.297965	−	0.297965i	−0.542252	−	0.840216i	$-0.682428\pi$
$499$	6.65603	−	6.65603i	0.297965	−	0.297965i	0.840216	+	0.542252i	$0.182428\pi$
$500$	8.20980	+	6.89808i	0.367153	+	0.308492i
$501$	21.4848	−	21.4848i	0.959872	−	0.959872i
$502$	9.87013	+	9.05031i	0.440526	+	0.403935i
$503$	−28.5575			−1.27332			−0.636658	−	0.771146i	$-0.719684\pi$
$503$	−28.5575			−1.27332			−0.636658	+	0.771146i	$0.719684\pi$
$504$	1.32653	+	10.1537i	0.0590884	+	0.452283i
$505$			5.68440i			0.252952i
$506$	−0.425705	−	0.390346i	−0.0189249	−	0.0173530i
$507$	18.4132	−	18.4132i	0.817758	−	0.817758i
$508$	−26.6877	+	2.31711i	−1.18408	+	0.102805i
$509$	1.48878	−	1.48878i	0.0659888	−	0.0659888i	−0.673342	−	0.739331i	$-0.735142\pi$
$509$	1.48878	−	1.48878i	0.0659888	−	0.0659888i	0.739331	+	0.673342i	$0.235142\pi$
$510$	0.328584	−	0.0142376i	0.0145500	−	0.000630451i
$511$			25.0894i			1.10989i
$512$	−20.9306	+	8.59697i	−0.925013	+	0.379936i
$513$	−13.1203	−	10.6891i	−0.579276	−	0.471935i
$514$	0.772379	+	17.8255i	0.0340682	+	0.786247i
$515$	−4.36653	−	4.36653i	−0.192412	−	0.192412i
$516$	−2.54042	−	29.2597i	−0.111836	−	1.28809i
$517$	−0.210041	+	0.210041i	−0.00923758	+	0.00923758i
$518$	17.4729	+	16.0216i	0.767716	+	0.703949i
$519$	5.27885			0.231716
$520$	−0.0652987	−	0.499818i	−0.00286354	−	0.0219185i
$521$	−16.4787			−0.721944			−0.360972	−	0.932577i	$-0.617555\pi$
$521$	−16.4787			−0.721944			−0.360972	+	0.932577i	$0.617555\pi$
$522$	3.32396	+	3.04787i	0.145486	+	0.133402i
$523$	−15.8511	+	15.8511i	−0.693121	+	0.693121i	−0.962917	−	0.269796i	$-0.913044\pi$
$523$	−15.8511	+	15.8511i	−0.693121	+	0.693121i	0.269796	+	0.962917i	$0.413044\pi$
$524$	26.0810	−	31.0404i	1.13935	−	1.35601i
$525$	−22.5251	+	22.5251i	−0.983076	+	0.983076i
$526$	12.9373	−	0.560575i	0.564093	−	0.0244422i
$527$	−0.144848			−0.00630967
$528$	0.0668168	+	0.381886i	0.00290783	+	0.0166194i
$529$	49.3957			2.14764
$530$	2.42143	−	0.104921i	0.105180	−	0.00455747i
$531$	2.14331	+	2.14331i	0.0930116	+	0.0930116i
$532$	−5.48633	−	28.7807i	−0.237863	−	1.24780i
$533$	1.64002	−	1.64002i	0.0710371	−	0.0710371i
$534$	−14.7857	−	13.5576i	−0.639839	−	0.586694i
$535$		−	9.20460i		−	0.397950i
$536$	−0.889953	−	0.684286i	−0.0384401	−	0.0295567i
$537$			22.2524i			0.960262i
$538$	−11.0938	+	12.0988i	−0.478289	+	0.521614i
$539$	−0.145781	−	0.145781i	−0.00627922	−	0.00627922i
$540$	0.371472	+	4.27848i	0.0159856	+	0.184117i
$541$	−30.6392	−	30.6392i	−1.31728	−	1.31728i	−0.915918	−	0.401365i	$-0.868536\pi$
$541$	−30.6392	−	30.6392i	−1.31728	−	1.31728i	−0.401365	−	0.915918i	$-0.631464\pi$
$542$	1.12998	+	26.0784i	0.0485368	+	1.12016i
$543$			42.6031i			1.82827i
$544$	−1.15051	+	0.253070i	−0.0493277	+	0.0108503i
$545$			1.22264i			0.0523722i
$546$	3.08956	−	0.133871i	0.132221	−	0.00572915i
$547$	−8.05019	−	8.05019i	−0.344201	−	0.344201i	0.513743	−	0.857944i	$-0.328259\pi$
$547$	−8.05019	−	8.05019i	−0.344201	−	0.344201i	−0.857944	+	0.513743i	$0.828259\pi$
$548$	0.579872	+	6.67877i	0.0247709	+	0.285303i
$549$	5.91110	−	5.91110i	0.252280	−	0.252280i
$550$	−0.215351	+	0.234858i	−0.00918259	+	0.0100144i
$551$	−10.0039	−	8.15012i	−0.426178	−	0.347207i
$552$	−38.5230	−	29.6204i	−1.63965	−	1.26073i
$553$	27.9349			1.18791
$554$	−16.5448	+	18.0435i	−0.702920	+	0.766595i
$555$	−3.93871	−	3.93871i	−0.167189	−	0.167189i
$556$	3.10220	+	2.60655i	0.131563	+	0.110542i
$557$	32.1846	+	32.1846i	1.36371	+	1.36371i	0.869140	+	0.494567i	$0.164673\pi$
$557$	32.1846	+	32.1846i	1.36371	+	1.36371i	0.494567	+	0.869140i	$0.335327\pi$
$558$	0.0458716	+	1.05865i	0.00194190	+	0.0448164i
$559$	−2.34341			−0.0991158
$560$	−4.27264	+	6.08484i	−0.180552	+	0.257131i
$561$			0.0201835i			0.000852147i
$562$	33.7171	−	1.46097i	1.42227	−	0.0616272i
$563$	−9.57128	−	9.57128i	−0.403382	−	0.403382i	0.476041	−	0.879423i	$-0.342071\pi$
$563$	−9.57128	−	9.57128i	−0.403382	−	0.403382i	−0.879423	+	0.476041i	$0.842071\pi$
$564$	−16.0769	+	19.1340i	−0.676960	+	0.805688i
$565$	−2.85314	−	2.85314i	−0.120033	−	0.120033i
$566$	26.3414	+	24.1535i	1.10721	+	1.01525i
$567$	−37.2086			−1.56261
$568$	4.69027	+	35.9009i	0.196800	+	1.50637i
$569$	18.8139			0.788719			0.394360	−	0.918956i	$-0.370966\pi$
$569$	18.8139			0.788719			0.394360	+	0.918956i	$0.370966\pi$
$570$	0.995145	+	6.81193i	0.0416820	+	0.285320i
$571$	−30.0078	−	30.0078i	−1.25579	−	1.25579i	−0.953085	−	0.302703i	$-0.902111\pi$
$571$	−30.0078	−	30.0078i	−1.25579	−	1.25579i	−0.302703	−	0.953085i	$-0.597889\pi$
$572$	0.0308176	−	0.00267568i	0.00128855	−	0.000111876i
$573$	24.3758	−	24.3758i	1.01831	−	1.01831i
$574$	−34.1788	+	1.48097i	−1.42659	+	0.0618145i
$575$		−	39.9402i		−	1.66562i
$576$	2.21397	+	8.32862i	0.0922488	+	0.347026i
$577$	17.8466			0.742965			0.371483	−	0.928440i	$-0.378850\pi$
$577$	17.8466			0.742965			0.371483	+	0.928440i	$0.378850\pi$
$578$	23.9578	−	1.03810i	0.996514	−	0.0431791i
$579$	−11.0783	+	11.0783i	−0.460397	+	0.460397i
$580$	0.283236	+	3.26222i	0.0117607	+	0.135456i
$581$	31.4974	−	31.4974i	1.30673	−	1.30673i
$582$	−10.6646	+	11.6307i	−0.442064	+	0.482108i
$583$			0.148738i			0.00616008i
$584$	2.73531	+	20.9370i	0.113188	+	0.866378i
$585$	−0.191978			−0.00793732
$586$	−8.98540	−	8.23906i	−0.371183	−	0.340353i
$587$	−23.8089	−	23.8089i	−0.982699	−	0.982699i	0.0171537	−	0.999853i	$-0.494540\pi$
$587$	−23.8089	−	23.8089i	−0.982699	−	0.982699i	−0.999853	+	0.0171537i	$0.994540\pi$
$588$	−13.2801	−	11.1583i	−0.547663	−	0.460161i
$589$	−0.307991	−	3.01621i	−0.0126905	−	0.124281i
$590$	0.0952727	+	2.19876i	0.00392232	+	0.0905217i
$591$	3.80465			0.156502
$592$	16.3278	+	11.4650i	0.671069	+	0.471209i
$593$	7.67085			0.315004			0.157502	−	0.987519i	$-0.449656\pi$
$593$	7.67085			0.315004			0.157502	+	0.987519i	$0.449656\pi$
$594$	−0.263303	+	0.0114089i	−0.0108034	+	0.000468114i
$595$	−0.273708	+	0.273708i	−0.0112209	+	0.0112209i
$596$	−22.8192	+	27.1585i	−0.934712	+	1.11245i
$597$	−19.3015	−	19.3015i	−0.789956	−	0.789956i
$598$	−2.62043	+	2.85780i	−0.107157	+	0.116864i
$599$		−	4.82507i		−	0.197147i	−0.995130	−	0.0985735i	$-0.968572\pi$
$599$		−	4.82507i		−	0.197147i	0.995130	−	0.0985735i	$-0.0314280\pi$
$600$	−16.3414	+	21.2529i	−0.667134	+	0.867644i
$601$	36.8204			1.50193			0.750967	−	0.660339i	$-0.229588\pi$
$601$	36.8204			1.50193			0.750967	+	0.660339i	$0.229588\pi$
$602$	25.4770	+	23.3608i	1.03836	+	0.952117i
$603$	−0.302329	+	0.302329i	−0.0123118	+	0.0123118i
$604$	3.90894	+	45.0218i	0.159053	+	1.83191i
$605$	−4.30099	−	4.30099i	−0.174860	−	0.174860i
$606$	−29.3220	+	1.27053i	−1.19112	+	0.0516116i
$607$	0.0490249			0.00198986			0.000994930	−	1.00000i	$-0.499683\pi$
$607$	0.0490249			0.00198986			0.000994930		1.00000i	$0.499683\pi$
$608$	−7.71607	−	23.4193i	−0.312928	−	0.949777i
$609$	−20.0891			−0.814052
$610$	6.06405	−	0.262756i	0.245526	−	0.0106387i
$611$	1.41002	+	1.41002i	0.0570434	+	0.0570434i
$612$	0.0388079	+	0.446976i	0.00156872	+	0.0180679i
$613$	−19.9661	+	19.9661i	−0.806425	+	0.806425i	−0.984091	−	0.177666i	$-0.943145\pi$
$613$	−19.9661	+	19.9661i	−0.806425	+	0.806425i	0.177666	+	0.984091i	$0.443145\pi$
$614$	−35.5001	−	32.5514i	−1.43267	−	1.31367i
$615$	8.03835			0.324138
$616$	−0.361714	−	0.278122i	−0.0145739	−	0.0112059i
$617$			20.0577i			0.807492i	0.914871	+	0.403746i	$0.132292\pi$
$617$			20.0577i			0.807492i	−0.914871	+	0.403746i	$0.867708\pi$
$618$	21.5480	−	23.5000i	0.866789	−	0.945307i
$619$	−18.3760	−	18.3760i	−0.738595	−	0.738595i	0.233711	−	0.972306i	$-0.424913\pi$
$619$	−18.3760	−	18.3760i	−0.738595	−	0.738595i	−0.972306	+	0.233711i	$0.924913\pi$
$620$	−0.494945	+	0.589062i	−0.0198775	+	0.0236573i
$621$	23.3588	−	23.3588i	0.937357	−	0.937357i
$622$	28.9284	−	1.25347i	1.15992	−	0.0502596i
$623$	23.6097			0.945902
$624$	2.56363	−	0.448547i	0.102627	−	0.0179563i
$625$	−20.5052			−0.820210
$626$	0.887204	+	20.4755i	0.0354598	+	0.818364i
$627$	−0.420286	+	0.0429163i	−0.0167846	+	0.00171391i
$628$	−12.7261	−	10.6928i	−0.507827	−	0.426689i
$629$	0.734456	+	0.734456i	0.0292847	+	0.0292847i
$630$	2.08714	+	1.91378i	0.0831535	+	0.0762467i
$631$	27.1080			1.07915			0.539576	−	0.841937i	$-0.318584\pi$
$631$	27.1080			1.07915			0.539576	+	0.841937i	$0.318584\pi$
$632$	23.3116	−	3.04554i	0.927285	−	0.121145i
$633$		−	38.4925i		−	1.52994i
$634$	−16.8425	+	18.3682i	−0.668901	+	0.729493i
$635$	−5.23816	+	5.23816i	−0.207870	+	0.207870i
$636$	1.08243	+	12.4671i	0.0429212	+	0.494352i
$637$	−0.978639	+	0.978639i	−0.0387751	+	0.0387751i
$638$	−0.200760	+	0.00869897i	−0.00794818	+	0.000344396i
$639$	13.7894			0.545500
$640$	−2.90212	+	5.54359i	−0.114716	+	0.219130i
$641$			22.9476i			0.906377i	0.891415	+	0.453188i	$0.149714\pi$
$641$			22.9476i			0.906377i	−0.891415	+	0.453188i	$0.850286\pi$
$642$	47.4804	−	2.05733i	1.87390	−	0.0811964i
$643$	−22.9092	+	22.9092i	−0.903450	+	0.903450i	−0.995733	−	0.0922826i	$-0.970584\pi$
$643$	−22.9092	+	22.9092i	−0.903450	+	0.903450i	0.0922826	+	0.995733i	$0.470584\pi$
$644$	56.9772	−	4.94695i	2.24522	−	0.194937i
$645$	−5.74298	−	5.74298i	−0.226130	−	0.226130i
$646$	−0.185566	−	1.27023i	−0.00730098	−	0.0499764i
$647$	28.0774			1.10384			0.551918	−	0.833899i	$-0.313896\pi$
$647$	28.0774			1.10384			0.551918	+	0.833899i	$0.313896\pi$
$648$	−31.0504	+	4.05658i	−1.21978	+	0.159357i
$649$	−0.135060			−0.00530158
$650$	1.57663	+	1.44567i	0.0618404	+	0.0567038i
$651$	−3.33772	−	3.33772i	−0.130816	−	0.130816i
$652$	−3.94505	+	4.69523i	−0.154500	+	0.183879i
$653$	16.6430	+	16.6430i	0.651289	+	0.651289i	0.953303	−	0.302014i	$-0.0976589\pi$
$653$	16.6430	+	16.6430i	0.651289	+	0.651289i	−0.302014	+	0.953303i	$0.597659\pi$
$654$	−6.30679	+	0.273274i	−0.246615	+	0.0106859i
$655$		−	11.2116i		−	0.438072i
$656$	−28.3606	+	4.96212i	−1.10729	+	0.193738i
$657$	8.04181			0.313741
$658$	−1.27328	−	29.3855i	−0.0496376	−	1.14557i
$659$	9.17630	+	9.17630i	0.357458	+	0.357458i	0.862875	−	0.505417i	$-0.168661\pi$
$659$	9.17630	+	9.17630i	0.357458	+	0.357458i	−0.505417	+	0.862875i	$0.668661\pi$
$660$	0.0820815	+	0.0689670i	0.00319502	+	0.00268454i
$661$	−7.86073	−	7.86073i	−0.305747	−	0.305747i	0.537510	−	0.843257i	$-0.319365\pi$
$661$	−7.86073	−	7.86073i	−0.305747	−	0.305747i	−0.843257	+	0.537510i	$0.819365\pi$
$662$	0.584300	−	0.637230i	0.0227095	−	0.0247666i
$663$	0.135494			0.00526213
$664$	22.8506	−	29.7184i	0.886774	−	1.15330i
$665$	−6.28148	−	5.11751i	−0.243585	−	0.198448i
$666$	5.13535	−	5.60054i	0.198991	−	0.217016i
$667$	17.8104	−	17.8104i	0.689621	−	0.689621i
$668$	2.60315	+	29.9822i	0.100719	+	1.16005i
$669$	20.2976	+	20.2976i	0.784752	+	0.784752i
$670$	−0.310152	+	0.0134389i	−0.0119822	+	0.000519191i
$671$			0.372488i			0.0143797i
$672$	−32.3426	−	20.6797i	−1.24764	−	0.797735i
$673$		−	36.0914i		−	1.39122i	−0.718420	−	0.695610i	$-0.755134\pi$
$673$		−	36.0914i		−	1.39122i	0.718420	−	0.695610i	$-0.244866\pi$
$674$	−2.00418	−	46.2536i	−0.0771979	−	1.78162i
$675$	−12.8869	−	12.8869i	−0.496016	−	0.496016i
$676$	2.23098	+	25.6957i	0.0858070	+	0.988295i
$677$	23.8574	+	23.8574i	0.916916	+	0.916916i	0.996804	−	0.0798883i	$-0.0254564\pi$
$677$	23.8574	+	23.8574i	0.916916	+	0.916916i	−0.0798883	+	0.996804i	$0.525456\pi$
$678$	14.0797	−	15.3552i	0.540729	−	0.589711i
$679$		−	18.5718i		−	0.712721i
$680$	−0.198568	+	0.258248i	−0.00761472	+	0.00990337i
$681$		−	59.1024i		−	2.26481i
$682$	−0.0348008	−	0.0319102i	−0.00133259	−	0.00122191i
$683$	18.3167	−	18.3167i	0.700867	−	0.700867i	−0.263729	−	0.964597i	$-0.584953\pi$
$683$	18.3167	−	18.3167i	0.700867	−	0.700867i	0.964597	+	0.263729i	$0.0849525\pi$
$684$	−9.22499	+	1.75852i	−0.352726	+	0.0672385i
$685$	1.31088	+	1.31088i	0.0500862	+	0.0500862i
$686$	−12.8440	+	0.556531i	−0.490385	+	0.0212484i
$687$	−22.2067			−0.847238
$688$	23.8073	+	16.7170i	0.907645	+	0.637328i
$689$	0.998489			0.0380394
$690$	−13.4254	+	0.581725i	−0.511097	+	0.0221459i
$691$	4.95717	−	4.95717i	0.188580	−	0.188580i	−0.606502	−	0.795082i	$-0.707428\pi$
$691$	4.95717	−	4.95717i	0.188580	−	0.188580i	0.795082	+	0.606502i	$0.207428\pi$
$692$	−3.36353	+	4.00313i	−0.127862	+	0.152176i
$693$	−0.122879	+	0.122879i	−0.00466780	+	0.00466780i
$694$	−9.20433	−	8.43981i	−0.349392	−	0.320371i
$695$	1.12049			0.0425026
$696$	−16.7643	+	2.19017i	−0.635449	+	0.0830181i
$697$	−1.49892			−0.0567756
$698$	25.7852	+	23.6435i	0.975985	+	0.894919i
$699$	−10.5547	+	10.5547i	−0.399216	+	0.399216i
$700$	−2.72919	−	31.4339i	−0.103154	−	1.18809i
$701$	10.4645	+	10.4645i	0.395239	+	0.395239i	0.876550	−	0.481311i	$-0.159839\pi$
$701$	10.4645	+	10.4645i	0.395239	+	0.395239i	−0.481311	+	0.876550i	$0.659839\pi$
$702$	0.0765892	+	1.76758i	0.00289067	+	0.0667128i
$703$	−13.7321	+	16.8555i	−0.517916	+	0.635716i
$704$	−0.332170	−	0.192657i	−0.0125191	−	0.00726104i
$705$			6.91106i			0.260285i
$706$	33.7075	−	1.46055i	1.26860	−	0.0549685i
$707$	24.4250	−	24.4250i	0.918595	−	0.918595i
$708$	−11.3207	+	0.982896i	−0.425456	+	0.0369395i
$709$	14.5542	−	14.5542i	0.546596	−	0.546596i	−0.378859	−	0.925454i	$-0.623683\pi$
$709$	14.5542	−	14.5542i	0.546596	−	0.546596i	0.925454	+	0.378859i	$0.123683\pi$
$710$	7.37958	+	6.76662i	0.276951	+	0.253947i
$711$		−	8.95388i		−	0.335797i
$712$	19.7022	−	2.57399i	0.738371	−	0.0964643i
$713$	5.91825			0.221640
$714$	−1.47305	−	1.35070i	−0.0551276	−	0.0505486i
$715$	0.00604875	−	0.00604875i	0.000226210	−	0.000226210i
$716$	−16.8748	−	14.1786i	−0.630639	−	0.529879i
$717$	16.6286	−	16.6286i	0.621005	−	0.621005i
$718$	−33.6275	+	1.45708i	−1.25497	+	0.0543779i
$719$			31.7846i			1.18537i	0.805435	+	0.592684i	$0.201932\pi$
$719$			31.7846i			1.18537i	−0.805435	+	0.592684i	$0.798068\pi$
$720$	1.95035	+	1.36949i	0.0726854	+	0.0510380i
$721$			37.5246i			1.39749i
$722$	26.0557	−	6.56498i	0.969694	−	0.244323i
$723$	−0.117816	+	0.117816i	−0.00438161	+	0.00438161i
$724$	−32.3074	−	27.1455i	−1.20069	−	1.00885i
$725$	−9.82586	−	9.82586i	−0.364923	−	0.364923i
$726$	21.2246	−	23.1472i	0.787718	−	0.859074i
$727$	3.56457			0.132202			0.0661012	−	0.997813i	$-0.478944\pi$
$727$	3.56457			0.132202			0.0661012	+	0.997813i	$0.478944\pi$
$728$	−1.86706	+	2.42822i	−0.0691979	+	0.0899957i
$729$		−	11.5924i		−	0.429347i
$730$	4.30368	+	3.94621i	0.159286	+	0.146056i
$731$	1.07090	+	1.07090i	0.0396086	+	0.0396086i
$732$	2.71076	+	31.2216i	0.100193	+	1.15398i
$733$	4.71576	+	4.71576i	0.174181	+	0.174181i	0.788813	−	0.614633i	$-0.210696\pi$
$733$	4.71576	+	4.71576i	0.174181	+	0.174181i	−0.614633	+	0.788813i	$0.710696\pi$
$734$	−0.607730	−	14.0256i	−0.0224317	−	0.517694i
$735$	−4.79668			−0.176928
$736$	47.0079	−	10.3400i	1.73274	−	0.381138i
$737$		−	0.0190513i		−	0.000701762i
$738$	0.474690	+	10.9552i	0.0174736	+	0.403267i
$739$	−0.427759	+	0.427759i	−0.0157354	+	0.0157354i	−0.714931	−	0.699195i	$-0.753542\pi$
$739$	−0.427759	+	0.427759i	−0.0157354	+	0.0157354i	0.699195	+	0.714931i	$0.253542\pi$
$740$	5.49650	−	0.477224i	0.202055	−	0.0175431i
$741$	0.288101	+	2.82142i	0.0105837	+	0.103647i
$742$	−10.8553	−	9.95367i	−0.398511	−	0.365411i
$743$			21.7535i			0.798057i	0.916939	+	0.399028i	$0.130653\pi$
$743$			21.7535i			0.798057i	−0.916939	+	0.399028i	$0.869347\pi$
$744$	−3.14920	−	2.42143i	−0.115455	−	0.0887739i
$745$			9.80942i			0.359389i
$746$	−7.71887	−	7.07773i	−0.282608	−	0.259134i
$747$	−10.0958	−	10.0958i	−0.369385	−	0.369385i
$748$	−0.0153058	−	0.0128603i	−0.000559636	−	0.000470221i
$749$	−39.5507	+	39.5507i	−1.44515	+	1.44515i
$750$	0.662780	+	15.2961i	0.0242013	+	0.558533i
$751$	9.54520			0.348309			0.174155	−	0.984718i	$-0.444281\pi$
$751$	9.54520			0.348309			0.174155	+	0.984718i	$0.444281\pi$
$752$	−4.26624	−	24.3833i	−0.155574	−	0.889168i
$753$			19.1202i			0.696777i
$754$	0.0583970	+	1.34772i	0.00212669	+	0.0490812i
$755$	8.83670	+	8.83670i	0.321600	+	0.321600i
$756$	16.7878	−	19.9801i	0.610567	−	0.726670i
$757$	−5.51918	+	5.51918i	−0.200598	+	0.200598i	−0.800256	−	0.599658i	$-0.795303\pi$
$757$	−5.51918	+	5.51918i	−0.200598	+	0.200598i	0.599658	+	0.800256i	$0.295303\pi$
$758$	28.9505	−	31.5730i	1.05153	−	1.14678i
$759$		−	0.824665i		−	0.0299334i
$760$	−5.79980	−	3.58572i	−0.210381	−	0.130068i
$761$		−	12.7422i		−	0.461905i	−0.972965	−	0.230953i	$-0.925816\pi$
$761$		−	12.7422i		−	0.461905i	0.972965	−	0.230953i	$-0.0741843\pi$
$762$	−28.1909	−	25.8494i	−1.02125	−	0.936423i
$763$	5.25350	−	5.25350i	0.190189	−	0.190189i
$764$	2.95343	+	34.0165i	0.106851	+	1.23068i
$765$	0.0877306	+	0.0877306i	0.00317191	+	0.00317191i
$766$	−41.1306	+	1.78219i	−1.48611	+	0.0643932i
$767$			0.906673i			0.0327381i
$768$	−29.2443	−	13.7310i	−1.05526	−	0.495476i
$769$	19.7867			0.713526			0.356763	−	0.934195i	$-0.383880\pi$
$769$	19.7867			0.713526			0.356763	+	0.934195i	$0.383880\pi$
$770$	−0.126059	+	0.00546214i	−0.00454284	+	0.000196842i
$771$	−18.0136	+	18.0136i	−0.648744	+	0.648744i
$772$	−1.34227	−	15.4598i	−0.0483092	−	0.556409i
$773$	−16.6933	−	16.6933i	−0.600416	−	0.600416i	0.340007	−	0.940423i	$-0.389571\pi$
$773$	−16.6933	−	16.6933i	−0.600416	−	0.600416i	−0.940423	+	0.340007i	$0.889571\pi$
$774$	7.48777	−	8.16605i	0.269142	−	0.293523i
$775$		−	3.26505i		−	0.117284i
$776$	−2.02475	−	15.4981i	−0.0726842	−	0.556350i
$777$			33.8481i			1.21429i
$778$	14.0482	−	15.3208i	0.503652	−	0.549276i
$779$	−3.18716	−	31.2124i	−0.114192	−	1.11830i
$780$	0.462982	−	0.551021i	0.0165774	−	0.0197297i
$781$	−0.434469	+	0.434469i	−0.0155465	+	0.0155465i
$782$	2.50345	−	0.108475i	0.0895233	−	0.00387905i
$783$		−	11.4932i		−	0.410734i
$784$	16.9234	−	2.96102i	0.604409	−	0.105751i
$785$	−4.59657			−0.164059
$786$	57.8329	−	2.50591i	2.06283	−	0.0893827i
$787$	−19.6818	−	19.6818i	−0.701579	−	0.701579i	0.263171	−	0.964749i	$-0.415232\pi$
$787$	−19.6818	−	19.6818i	−0.701579	−	0.701579i	−0.964749	+	0.263171i	$0.915232\pi$
$788$	−2.42421	+	2.88519i	−0.0863590	+	0.102781i
$789$	13.0739	+	13.0739i	0.465441	+	0.465441i
$790$	4.39378	−	4.79179i	0.156324	−	0.170484i
$791$			24.5190i			0.871795i
$792$	−0.0891456	+	0.115939i	−0.00316765	+	0.00411971i
$793$	2.50054			0.0887969
$794$	−14.2603	−	13.0758i	−0.506079	−	0.464043i
$795$	2.44699	+	2.44699i	0.0867857	+	0.0867857i
$796$	26.9353	−	2.33861i	0.954696	−	0.0828898i
$797$	4.73949	−	4.73949i	0.167881	−	0.167881i	−0.618166	−	0.786047i	$-0.712124\pi$
$797$	4.73949	−	4.73949i	0.167881	−	0.167881i	0.786047	+	0.618166i	$0.212124\pi$
$798$	24.9938	−	33.5458i	0.884771	−	1.18751i
$799$		−	1.28871i		−	0.0455913i
$800$	−5.70451	−	25.9339i	−0.201685	−	0.916903i
$801$		−	7.56753i		−	0.267385i
$802$	−1.60116	−	36.9526i	−0.0565390	−	1.30484i
$803$	−0.253377	+	0.253377i	−0.00894148	+	0.00894148i
$804$	−0.138645	−	1.59686i	−0.00488963	−	0.0563170i
$805$	11.1833	−	11.1833i	0.394158	−	0.394158i
$806$	−0.214216	+	0.233621i	−0.00754545	+	0.00822895i
$807$	−23.4374			−0.825035
$808$	17.7197	−	23.0454i	0.623375	−	0.810735i
$809$		−	15.0096i		−	0.527711i	−0.964562	−	0.263855i	$-0.915006\pi$
$809$		−	15.0096i		−	0.527711i	0.964562	−	0.263855i	$-0.0849942\pi$
$810$	−5.85239	+	6.38253i	−0.205632	+	0.224259i
$811$	−27.7594	+	27.7594i	−0.974765	+	0.974765i	−0.999689	−	0.0249239i	$-0.992066\pi$
$811$	−27.7594	+	27.7594i	−0.974765	+	0.974765i	0.0249239	+	0.999689i	$0.492066\pi$
$812$	12.8002	−	15.2342i	0.449199	−	0.534617i
$813$	−26.3537	+	26.3537i	−0.924263	+	0.924263i
$814$	0.0146569	+	0.338261i	0.000513723	+	0.0118560i
$815$			1.69588i			0.0594041i
$816$	−1.37651	−	0.966556i	−0.0481876	−	0.0338362i
$817$	−20.0226	+	24.5767i	−0.700501	+	0.859829i
$818$	−27.1790	+	1.17767i	−0.950291	+	0.0411762i
$819$	0.824900	+	0.824900i	0.0288243	+	0.0288243i
$820$	−5.12181	+	6.09575i	−0.178861	+	0.212873i
$821$	−35.2556	+	35.2556i	−1.23043	+	1.23043i	−0.266628	+	0.963799i	$0.585910\pi$
$821$	−35.2556	+	35.2556i	−1.23043	+	1.23043i	−0.963799	+	0.266628i	$0.914090\pi$
$822$	−6.46897	+	7.05496i	−0.225631	+	0.246070i
$823$	27.9107			0.972905			0.486452	−	0.873707i	$-0.338291\pi$
$823$	27.9107			0.972905			0.486452	+	0.873707i	$0.338291\pi$
$824$	4.09103	+	31.3141i	0.142518	+	1.09088i
$825$	−0.454961			−0.0158397
$826$	9.03837	−	9.85711i	0.314485	−	0.342973i
$827$	18.5819	−	18.5819i	0.646157	−	0.646157i	−0.305905	−	0.952062i	$-0.598959\pi$
$827$	18.5819	−	18.5819i	0.646157	−	0.646157i	0.952062	+	0.305905i	$0.0989590\pi$
$828$	−1.58563	−	18.2627i	−0.0551044	−	0.634673i
$829$	21.6563	−	21.6563i	0.752155	−	0.752155i	−0.222726	−	0.974881i	$-0.571496\pi$
$829$	21.6563	−	21.6563i	0.752155	−	0.752155i	0.974881	+	0.222726i	$0.0714955\pi$
$830$	−0.448770	−	10.3570i	−0.0155770	−	0.359496i
$831$	−34.9534			−1.21252
$832$	−1.29333	+	2.22989i	−0.0448380	+	0.0773075i
$833$	0.894441			0.0309905
$834$	0.250442	+	5.77986i	0.00867209	+	0.200140i
$835$	5.88479	+	5.88479i	0.203651	+	0.203651i
$836$	0.235250	−	0.346062i	0.00813628	−	0.0119688i
$837$	1.90955	−	1.90955i	0.0660037	−	0.0660037i
$838$	−23.8988	+	26.0637i	−0.825570	+	0.900355i
$839$			20.0753i			0.693075i	0.938036	+	0.346538i	$0.112643\pi$
$839$			20.0753i			0.693075i	−0.938036	+	0.346538i	$0.887357\pi$
$840$	−10.5264	+	1.37522i	−0.363195	+	0.0474496i
$841$			20.2368i			0.697819i
$842$	−17.7675	−	16.2917i	−0.612309	−	0.561450i
$843$	34.0730	+	34.0730i	1.17354	+	1.17354i
$844$	29.1902	+	24.5263i	1.00477	+	0.844232i
$845$	5.04344	+	5.04344i	0.173500	+	0.173500i
$846$	−9.41885	+	0.408120i	−0.323827	+	0.0140314i
$847$			36.9613i			1.27001i
$848$	−10.1439	−	7.12282i	−0.348343	−	0.244599i
$849$			51.0279i			1.75127i
$850$	−0.0598448	−	1.38114i	−0.00205266	−	0.0473726i
$851$	−30.0087	−	30.0087i	−1.02868	−	1.02868i
$852$	−33.2551	+	39.5787i	−1.13930	+	1.35594i
$853$	−11.2092	+	11.2092i	−0.383795	+	0.383795i	−0.872467	−	0.488673i	$-0.837481\pi$
$853$	−11.2092	+	11.2092i	−0.383795	+	0.383795i	0.488673	+	0.872467i	$0.337481\pi$
$854$	−27.1853	−	24.9272i	−0.930261	−	0.852992i
$855$	−1.64030	+	2.01338i	−0.0560970	+	0.0688562i
$856$	−28.6930	+	37.3169i	−0.980707	+	1.27546i
$857$	−42.4625			−1.45049			−0.725246	−	0.688489i	$-0.758274\pi$
$857$	−42.4625			−1.45049			−0.725246	+	0.688489i	$0.758274\pi$
$858$	0.0325534	+	0.0298495i	0.00111135	+	0.00101904i
$859$	14.0616	+	14.0616i	0.479775	+	0.479775i	0.905060	−	0.425285i	$-0.139826\pi$
$859$	14.0616	+	14.0616i	0.479775	+	0.479775i	−0.425285	+	0.905060i	$0.639826\pi$
$860$	8.01436	−	0.695832i	0.273287	−	0.0237277i
$861$	−34.5395	−	34.5395i	−1.17710	−	1.17710i
$862$	44.5142	−	1.92880i	1.51616	−	0.0656953i
$863$	8.27957			0.281840			0.140920	−	0.990021i	$-0.454994\pi$
$863$	8.27957			0.281840			0.140920	+	0.990021i	$0.454994\pi$
$864$	11.8311	−	18.5036i	0.402502	−	0.629505i
$865$			1.44590i			0.0491620i
$866$	2.12783	+	49.1073i	0.0723065	+	1.66873i
$867$	24.2107	+	24.2107i	0.822239	+	0.822239i
$868$	4.65781	−	0.404406i	0.158096	−	0.0137264i
$869$	0.282114	+	0.282114i	0.00957007	+	0.00957007i
$870$	−3.15974	+	3.44596i	−0.107125	+	0.116829i
$871$	−0.127893			−0.00433349
$872$	3.81127	−	4.95677i	0.129066	−	0.167858i
$873$	−5.95276			−0.201470
$874$	7.58191	+	51.8994i	0.256462	+	1.75552i
$875$	−12.7415	−	12.7415i	−0.430741	−	0.430741i
$876$	−19.3939	+	23.0818i	−0.655260	+	0.779862i
$877$	−26.3319	+	26.3319i	−0.889165	+	0.889165i	−0.994443	−	0.105278i	$-0.966427\pi$
$877$	−26.3319	+	26.3319i	−0.889165	+	0.889165i	0.105278	+	0.994443i	$0.466427\pi$
$878$	2.17169	+	50.1196i	0.0732909	+	1.69145i
$879$		−	17.4063i		−	0.587099i
$880$	−0.104600	+	0.0183014i	−0.00352607	+	0.000616940i
$881$	18.1146			0.610296			0.305148	−	0.952305i	$-0.401294\pi$
$881$	18.1146			0.610296			0.305148	+	0.952305i	$0.401294\pi$
$882$	−0.283259	−	6.53723i	−0.00953783	−	0.220120i
$883$	−32.8628	+	32.8628i	−1.10592	+	1.10592i	−0.112241	+	0.993681i	$0.535803\pi$
$883$	−32.8628	+	32.8628i	−1.10592	+	1.10592i	−0.993681	+	0.112241i	$0.964197\pi$
$884$	−0.0863326	+	0.102749i	−0.00290368	+	0.00345583i
$885$	−2.22197	+	2.22197i	−0.0746908	+	0.0746908i
$886$	11.7945	+	10.8149i	0.396245	+	0.363332i
$887$		−	55.0667i		−	1.84896i	−0.381231	−	0.924480i	$-0.624500\pi$
$887$		−	55.0667i		−	1.84896i	0.381231	−	0.924480i	$-0.375500\pi$
$888$	3.69021	+	28.2461i	0.123835	+	0.947876i
$889$	45.0151			1.50976
$890$	3.71347	−	4.04986i	0.124476	−	0.135752i
$891$	−0.375769	−	0.375769i	−0.0125887	−	0.0125887i
$892$	−28.3254	+	2.45931i	−0.948406	+	0.0823437i
$893$	26.8352	−	2.74020i	0.898006	−	0.0916971i
$894$	−50.6002	+	2.19251i	−1.69232	+	0.0733286i
$895$	−6.09503			−0.203734
$896$	36.2899	−	11.3500i	1.21236	−	0.379177i
$897$	−5.53605			−0.184843
$898$	−0.735389	−	16.9718i	−0.0245403	−	0.566356i
$899$	1.45598	−	1.45598i	0.0485595	−	0.0485595i
$900$	−10.0754	+	0.874779i	−0.335847	+	0.0291593i
$901$	−0.456292	−	0.456292i	−0.0152013	−	0.0152013i
$902$	−0.360127	−	0.330214i	−0.0119909	−	0.0109949i
$903$			49.3533i			1.64238i
$904$	2.67313	+	20.4610i	0.0889068	+	0.680523i
$905$	−11.6692			−0.387896
$906$	−43.6075	+	47.5577i	−1.44876	+	1.58000i
$907$	16.1329	−	16.1329i	0.535683	−	0.535683i	−0.386575	−	0.922258i	$-0.626342\pi$
$907$	16.1329	−	16.1329i	0.535683	−	0.535683i	0.922258	+	0.386575i	$0.126342\pi$
$908$	44.8194	+	37.6584i	1.48738	+	1.24974i
$909$	−7.82885	−	7.82885i	−0.259666	−	0.259666i
$910$	0.0366678	+	0.846244i	0.00121553	+	0.0280527i
$911$	−14.8774			−0.492910			−0.246455	−	0.969154i	$-0.579266\pi$
$911$	−14.8774			−0.492910			−0.246455	+	0.969154i	$0.579266\pi$
$912$	17.2000	−	30.7187i	0.569549	−	1.01720i
$913$	0.636184			0.0210546
$914$	−1.46331	−	33.7712i	−0.0484020	−	1.11705i
$915$	6.12806	+	6.12806i	0.202587	+	0.202587i
$916$	14.1495	−	16.8401i	0.467512	−	0.556412i
$917$	−48.1743	+	48.1743i	−1.59085	+	1.59085i
$918$	0.772751	−	0.842750i	0.0255046	−	0.0278149i
$919$	38.8587			1.28183			0.640915	−	0.767612i	$-0.278555\pi$
$919$	38.8587			1.28183			0.640915	+	0.767612i	$0.278555\pi$
$920$	8.11316	−	10.5516i	0.267483	−	0.347876i
$921$		−	68.7698i		−	2.26604i
$922$	−16.3367	−	14.9797i	−0.538020	−	0.493331i
$923$	2.91663	+	2.91663i	0.0960021	+	0.0960021i
$924$	−0.0563510	−	0.649032i	−0.00185381	−	0.0213516i
$925$	−16.5556	+	16.5556i	−0.544344	+	0.544344i
$926$	−0.963574	−	22.2380i	−0.0316650	−	0.730785i
$927$	12.0276			0.395039
$928$	9.02084	−	14.1084i	0.296124	−	0.463132i
$929$	−28.4046			−0.931923			−0.465962	−	0.884805i	$-0.654292\pi$
$929$	−28.4046			−0.931923			−0.465962	+	0.884805i	$0.654292\pi$
$930$	−1.09751	+	0.0475552i	−0.0359888	+	0.00155940i
$931$	1.90186	+	18.6252i	0.0623308	+	0.610416i
$932$	−1.27883	−	14.7292i	−0.0418896	−	0.482469i
$933$	29.2337	+	29.2337i	0.957070	+	0.957070i
$934$	−18.0466	+	19.6813i	−0.590502	+	0.643993i
$935$	−0.00552834			−0.000180796
$936$	0.778308	+	0.598443i	0.0254398	+	0.0195607i
$937$			37.4859i			1.22461i	0.790621	+	0.612305i	$0.209758\pi$
$937$			37.4859i			1.22461i	−0.790621	+	0.612305i	$0.790242\pi$
$938$	1.39042	+	1.27493i	0.0453988	+	0.0416279i
$939$	−20.6916	+	20.6916i	−0.675245	+	0.675245i
$940$	−5.24089	−	4.40353i	−0.170939	−	0.143627i
$941$	−24.3100	+	24.3100i	−0.792483	+	0.792483i	−0.981897	−	0.189414i	$-0.939341\pi$
$941$	−24.3100	+	24.3100i	−0.792483	+	0.792483i	0.189414	+	0.981897i	$0.439341\pi$
$942$	−1.02738	−	23.7106i	−0.0334740	−	0.772534i
$943$	61.2434			1.99436
$944$	6.46784	−	9.21111i	0.210510	−	0.299796i
$945$		−	7.21666i		−	0.234758i
$946$	0.0213710	+	0.493213i	0.000694830	+	0.0160357i
$947$	−30.4449	+	30.4449i	−0.989325	+	0.989325i	−0.999944	−	0.0106182i	$-0.996620\pi$
$947$	−30.4449	+	30.4449i	−0.989325	+	0.989325i	0.0106182	+	0.999944i	$0.496620\pi$
$948$	25.6997	+	21.5935i	0.834687	+	0.701325i
$949$	1.70094	+	1.70094i	0.0552149	+	0.0552149i
$950$	28.6325	−	4.18288i	0.928962	−	0.135711i
$951$	−35.5823			−1.15384
$952$	1.96287	−	0.256438i	0.0636169	−	0.00831122i
$953$	−1.20456			−0.0390194			−0.0195097	−	0.999810i	$-0.506211\pi$
$953$	−1.20456			−0.0390194			−0.0195097	+	0.999810i	$0.506211\pi$
$954$	−3.19041	+	3.47942i	−0.103293	+	0.112650i
$955$	6.67663	+	6.67663i	0.216051	+	0.216051i
$956$	2.01475	+	23.2052i	0.0651618	+	0.750511i
$957$	−0.202880	−	0.202880i	−0.00655816	−	0.00655816i
$958$	1.49632	+	34.5330i	0.0483439	+	1.11571i
$959$		−	11.2653i		−	0.363776i
$960$	−8.63431	+	2.29523i	−0.278671	+	0.0740782i
$961$	−30.5162			−0.984393
$962$	2.27077	−	0.0983929i	0.0732127	−	0.00317231i
$963$	12.6771	+	12.6771i	0.408512	+	0.408512i
$964$	−0.0142748	−	0.164412i	−0.000459760	−	0.00529536i
$965$	−3.03438	−	3.03438i	−0.0976801	−	0.0976801i
$966$	60.1865	+	55.1874i	1.93647	+	1.77562i
$967$	1.00120			0.0321964			0.0160982	−	0.999870i	$-0.494876\pi$
$967$	1.00120			0.0321964			0.0160982	+	0.999870i	$0.494876\pi$
$968$	4.02962	+	30.8441i	0.129517	+	0.991366i
$969$	1.15768	−	1.42100i	0.0371901	−	0.0456490i
$970$	−3.18570	−	2.92109i	−0.102287	−	0.0937905i
$971$	−2.06733	+	2.06733i	−0.0663439	+	0.0663439i	−0.739500	−	0.673156i	$-0.764938\pi$
$971$	−2.06733	+	2.06733i	−0.0663439	+	0.0663439i	0.673156	+	0.739500i	$0.264938\pi$
$972$	−16.3963	−	13.7766i	−0.525910	−	0.441883i
$973$	−4.81457	−	4.81457i	−0.154348	−	0.154348i
$974$	1.05094	+	24.2543i	0.0336743	+	0.777157i
$975$			3.05420i			0.0978126i
$976$	−25.4036	−	17.8379i	−0.813151	−	0.570976i
$977$		−	12.8363i		−	0.410671i	−0.978692	−	0.205336i	$-0.934171\pi$
$977$		−	12.8363i		−	0.410671i	0.978692	−	0.205336i	$-0.0658286\pi$
$978$	−8.74791	+	0.379048i	−0.279727	+	0.0121206i
$979$	0.238434	+	0.238434i	0.00762037	+	0.00762037i
$980$	3.05631	−	3.63748i	0.0976301	−	0.116195i
$981$	−1.68389	−	1.68389i	−0.0537623	−	0.0537623i
$982$	−28.6483	−	26.2687i	−0.914203	−	0.838269i
$983$			16.1390i			0.514755i	0.966311	+	0.257378i	$0.0828584\pi$
$983$			16.1390i			0.514755i	−0.966311	+	0.257378i	$0.917142\pi$
$984$	−32.5887	−	25.0575i	−1.03889	−	0.798804i
$985$			1.04211i			0.0332043i
$986$	0.589199	−	0.642572i	0.0187639	−	0.0204637i
$987$	29.6957	−	29.6957i	0.945225	−	0.945225i
$988$	−2.32315	−	1.57925i	−0.0739092	−	0.0502427i
$989$	−43.7552	−	43.7552i	−1.39133	−	1.39133i
$990$	0.00175076	+	0.0404052i	5.56428e−5	+	0.00128416i
$991$	−45.2181			−1.43640			−0.718200	−	0.695837i	$-0.755034\pi$
$991$	−45.2181			−1.43640			−0.718200	+	0.695837i	$0.755034\pi$
$992$	3.84283	−	0.845282i	0.122010	−	0.0268377i
$993$	1.23442			0.0391732
$994$	−2.63378	−	60.7840i	−0.0835384	−	1.92795i
$995$	5.28675	−	5.28675i	0.167601	−	0.167601i
$996$	53.3245	−	4.62980i	1.68965	−	0.146701i
$997$	−28.2400	+	28.2400i	−0.894368	+	0.894368i	−0.994931	−	0.100562i	$-0.967936\pi$
$997$	−28.2400	+	28.2400i	−0.894368	+	0.894368i	0.100562	+	0.994931i	$0.467936\pi$
$998$	−8.99673	+	9.81170i	−0.284787	+	0.310584i
$999$	−19.3649			−0.612678

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.2.m.a.227.1	yes	76
4.3	odd	2		1216.2.m.a.303.31		76
16.5	even	4		1216.2.m.a.911.8		76
16.11	odd	4	inner	304.2.m.a.75.38	yes	76
19.18	odd	2	inner	304.2.m.a.227.38	yes	76
76.75	even	2		1216.2.m.a.303.8		76
304.37	odd	4		1216.2.m.a.911.31		76
304.75	even	4	inner	304.2.m.a.75.1	✓	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
304.2.m.a.75.1	✓	76	304.75	even	4	inner
304.2.m.a.75.38	yes	76	16.11	odd	4	inner
304.2.m.a.227.1	yes	76	1.1	even	1	trivial
304.2.m.a.227.38	yes	76	19.18	odd	2	inner
1216.2.m.a.303.8		76	76.75	even	2
1216.2.m.a.303.31		76	4.3	odd	2
1216.2.m.a.911.8		76	16.5	even	4
1216.2.m.a.911.31		76	304.37	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:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	304.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41289 + 0.0612206i) q^{2} +(-1.42780 - 1.42780i) q^{3} +(1.99250 - 0.172996i) q^{4} +(0.391081 - 0.391081i) q^{5} +(2.10473 + 1.92991i) q^{6} -3.36082 q^{7} +(-2.80459 + 0.366406i) q^{8} +1.07723i q^{9} +O(q^{10})\)	\(q+(-1.41289 + 0.0612206i) q^{2} +(-1.42780 - 1.42780i) q^{3} +(1.99250 - 0.172996i) q^{4} +(0.391081 - 0.391081i) q^{5} +(2.10473 + 1.92991i) q^{6} -3.36082 q^{7} +(-2.80459 + 0.366406i) q^{8} +1.07723i q^{9} +(-0.528611 + 0.576495i) q^{10} +(-0.0339409 - 0.0339409i) q^{11} +(-3.09190 - 2.59790i) q^{12} +(-0.227848 + 0.227848i) q^{13} +(4.74847 - 0.205752i) q^{14} -1.11677 q^{15} +(3.94014 - 0.689389i) q^{16} +0.208245 q^{17} +(-0.0659488 - 1.52201i) q^{18} +(0.442793 + 4.33635i) q^{19} +(0.711574 - 0.846885i) q^{20} +(4.79859 + 4.79859i) q^{21} +(0.0500326 + 0.0458768i) q^{22} -8.50857 q^{23} +(4.52756 + 3.48125i) q^{24} +4.69411i q^{25} +(0.307975 - 0.335873i) q^{26} +(-2.74533 + 2.74533i) q^{27} +(-6.69645 + 0.581408i) q^{28} +(-2.09323 + 2.09323i) q^{29} +(1.57787 - 0.0683694i) q^{30} -0.695564 q^{31} +(-5.52478 + 1.21525i) q^{32} +0.0969217i q^{33} +(-0.294227 + 0.0127489i) q^{34} +(-1.31435 + 1.31435i) q^{35} +(0.186357 + 2.14639i) q^{36} +(3.52688 + 3.52688i) q^{37} +(-0.891091 - 6.09967i) q^{38} +0.650644 q^{39} +(-0.953528 + 1.24012i) q^{40} -7.19785 q^{41} +(-7.07364 - 6.48609i) q^{42} +(5.14249 + 5.14249i) q^{43} +(-0.0734990 - 0.0617557i) q^{44} +(0.421285 + 0.421285i) q^{45} +(12.0217 - 0.520900i) q^{46} -6.18843i q^{47} +(-6.61005 - 4.64143i) q^{48} +4.29513 q^{49} +(-0.287376 - 6.63225i) q^{50} +(-0.297333 - 0.297333i) q^{51} +(-0.414572 + 0.493405i) q^{52} +(-2.19113 - 2.19113i) q^{53} +(3.71077 - 4.04691i) q^{54} -0.0265472 q^{55} +(9.42574 - 1.23142i) q^{56} +(5.55923 - 6.82367i) q^{57} +(2.82935 - 3.08565i) q^{58} +(1.98964 - 1.98964i) q^{59} +(-2.22517 + 0.193197i) q^{60} +(-5.48730 - 5.48730i) q^{61} +(0.982753 - 0.0425828i) q^{62} -3.62039i q^{63} +(7.73149 - 2.05524i) q^{64} +0.178214i q^{65} +(-0.00593360 - 0.136939i) q^{66} +(0.280654 + 0.280654i) q^{67} +(0.414930 - 0.0360255i) q^{68} +(12.1485 + 12.1485i) q^{69} +(1.77657 - 1.93750i) q^{70} -12.8008i q^{71} +(-0.394704 - 3.02120i) q^{72} -7.46524i q^{73} +(-5.19900 - 4.76717i) q^{74} +(6.70226 - 6.70226i) q^{75} +(1.63244 + 8.56359i) q^{76} +(0.114069 + 0.114069i) q^{77} +(-0.919287 + 0.0398328i) q^{78} -8.31193 q^{79} +(1.27131 - 1.81052i) q^{80} +11.0713 q^{81} +(10.1698 - 0.440657i) q^{82} +(-9.37194 + 9.37194i) q^{83} +(10.3913 + 8.73107i) q^{84} +(0.0814407 - 0.0814407i) q^{85} +(-7.58058 - 6.95093i) q^{86} +5.97744 q^{87} +(0.107627 + 0.0827543i) q^{88} -7.02497 q^{89} +(-0.621020 - 0.569437i) q^{90} +(0.765758 - 0.765758i) q^{91} +(-16.9534 + 1.47195i) q^{92} +(0.993127 + 0.993127i) q^{93} +(0.378859 + 8.74356i) q^{94} +(1.86903 + 1.52269i) q^{95} +(9.62342 + 6.15315i) q^{96} +5.52597i q^{97} +(-6.06854 + 0.262951i) q^{98} +(0.0365622 - 0.0365622i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 4 q^{4} - 4 q^{5} - 4 q^{6} - 8 q^{7}+O(q^{10}) \) 76 * q - 4 * q^4 - 4 * q^5 - 4 * q^6 - 8 * q^7	\( 76 q - 4 q^{4} - 4 q^{5} - 4 q^{6} - 8 q^{7} - 4 q^{11} + 4 q^{16} - 8 q^{17} + 6 q^{19} - 32 q^{20} - 8 q^{23} - 12 q^{24} - 8 q^{26} - 40 q^{30} + 44 q^{36} - 12 q^{38} - 8 q^{39} + 12 q^{42} - 4 q^{43} - 76 q^{44} + 4 q^{45} + 44 q^{49} + 96 q^{54} - 8 q^{55} + 24 q^{58} + 28 q^{61} + 20 q^{62} - 64 q^{64} + 12 q^{66} - 80 q^{74} + 12 q^{76} - 32 q^{77} - 16 q^{80} - 52 q^{81} + 68 q^{82} + 36 q^{83} - 56 q^{85} - 120 q^{87} - 8 q^{92} - 16 q^{93} + 48 q^{96} + 76 q^{99}+O(q^{100}) \) 76 * q - 4 * q^4 - 4 * q^5 - 4 * q^6 - 8 * q^7 - 4 * q^11 + 4 * q^16 - 8 * q^17 + 6 * q^19 - 32 * q^20 - 8 * q^23 - 12 * q^24 - 8 * q^26 - 40 * q^30 + 44 * q^36 - 12 * q^38 - 8 * q^39 + 12 * q^42 - 4 * q^43 - 76 * q^44 + 4 * q^45 + 44 * q^49 + 96 * q^54 - 8 * q^55 + 24 * q^58 + 28 * q^61 + 20 * q^62 - 64 * q^64 + 12 * q^66 - 80 * q^74 + 12 * q^76 - 32 * q^77 - 16 * q^80 - 52 * q^81 + 68 * q^82 + 36 * q^83 - 56 * q^85 - 120 * q^87 - 8 * q^92 - 16 * q^93 + 48 * q^96 + 76 * q^99

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