LMFDB - Embedded newform 370.2.r.f.23.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(23,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 5]))

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

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

chi := DirichletCharacter("370.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$370 = 2 \cdot 5 \cdot 37$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	370.r (of order $12$ , degree $4$ , 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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.4
Character	$\chi$	$=$	370.23
Dual form			370.2.r.f.177.4

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-1.56225 - 0.418603i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.20578 + 0.366816i) q^{5} +(1.14364 + 1.14364i) q^{6} +(1.11476 + 0.298699i) q^{7} -1.00000i q^{8} +(-0.332689 - 0.192078i) q^{9} +(-1.72685 - 1.42056i) q^{10} +5.41958i q^{11} +(-0.418603 - 1.56225i) q^{12} +(-3.53236 + 2.03941i) q^{13} +(-0.816061 - 0.816061i) q^{14} +(-3.29242 - 1.49640i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.94729 - 3.37280i) q^{17} +(0.192078 + 0.332689i) q^{18} +(5.80123 + 1.55443i) q^{19} +(0.785216 + 2.09367i) q^{20} +(-1.61650 - 0.933284i) q^{21} +(2.70979 - 4.69349i) q^{22} +0.383468i q^{23} +(-0.418603 + 1.56225i) q^{24} +(4.73089 + 1.61823i) q^{25} +4.07882 q^{26} +(3.87027 + 3.87027i) q^{27} +(0.298699 + 1.11476i) q^{28} +(5.82137 + 5.82137i) q^{29} +(2.10312 + 2.94213i) q^{30} +(-3.43124 + 3.43124i) q^{31} +(0.866025 - 0.500000i) q^{32} +(2.26865 - 8.46672i) q^{33} +(-3.37280 + 1.94729i) q^{34} +(2.34934 + 1.06778i) q^{35} -0.384156i q^{36} +(2.71702 - 5.44223i) q^{37} +(-4.24679 - 4.24679i) q^{38} +(6.37212 - 1.70740i) q^{39} +(0.366816 - 2.20578i) q^{40} +(7.78143 - 4.49261i) q^{41} +(0.933284 + 1.61650i) q^{42} +1.57247i q^{43} +(-4.69349 + 2.70979i) q^{44} +(-0.663380 - 0.545717i) q^{45} +(0.191734 - 0.332093i) q^{46} +(-3.06744 + 3.06744i) q^{47} +(1.14364 - 1.14364i) q^{48} +(-4.90871 - 2.83404i) q^{49} +(-3.28796 - 3.76687i) q^{50} +(-4.45401 + 4.45401i) q^{51} +(-3.53236 - 2.03941i) q^{52} +(7.61884 - 2.04146i) q^{53} +(-1.41662 - 5.28689i) q^{54} +(-1.98799 + 11.9544i) q^{55} +(0.298699 - 1.11476i) q^{56} +(-8.41226 - 4.85682i) q^{57} +(-2.13077 - 7.95215i) q^{58} +(2.84475 + 10.6168i) q^{59} +(-0.350287 - 3.59952i) q^{60} +(-8.58880 - 2.30136i) q^{61} +(4.68716 - 1.25592i) q^{62} +(-0.313495 - 0.313495i) q^{63} -1.00000 q^{64} +(-8.53968 + 3.20275i) q^{65} +(-6.19807 + 6.19807i) q^{66} +(2.68457 - 10.0190i) q^{67} +3.89458 q^{68} +(0.160521 - 0.599071i) q^{69} +(-1.50070 - 2.09939i) q^{70} +(2.42276 + 4.19634i) q^{71} +(-0.192078 + 0.332689i) q^{72} +(-9.61059 + 9.61059i) q^{73} +(-5.07412 + 3.35460i) q^{74} +(-6.71343 - 4.50843i) q^{75} +(1.55443 + 5.80123i) q^{76} +(-1.61882 + 6.04153i) q^{77} +(-6.37212 - 1.70740i) q^{78} +(-8.53421 - 2.28673i) q^{79} +(-1.42056 + 1.72685i) q^{80} +(-3.84998 - 6.66836i) q^{81} -8.98522 q^{82} +(-12.0271 + 3.22265i) q^{83} -1.86657i q^{84} +(5.53248 - 6.72535i) q^{85} +(0.786233 - 1.36180i) q^{86} +(-6.65758 - 11.5313i) q^{87} +5.41958 q^{88} +(14.3038 - 3.83268i) q^{89} +(0.301646 + 0.804295i) q^{90} +(-4.54690 + 1.21834i) q^{91} +(-0.332093 + 0.191734i) q^{92} +(6.79677 - 3.92412i) q^{93} +(4.19020 - 1.12276i) q^{94} +(12.2260 + 5.55672i) q^{95} +(-1.56225 + 0.418603i) q^{96} -4.38333 q^{97} +(2.83404 + 4.90871i) q^{98} +(1.04098 - 1.80304i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$32 q - 10 q^{3} + 16 q^{4} + 6 q^{5} + 8 q^{6} + 2 q^{7} - 12 q^{9} + 6 q^{10} - 2 q^{12} + 12 q^{13} + 8 q^{14} - 8 q^{15} - 16 q^{16} - 6 q^{17} - 24 q^{18} - 2 q^{19} + 6 q^{20} - 54 q^{21} + 12 q^{22}+ \cdots + 26 q^{99}+O(q^{100})$ 32 * q - 10 * q^3 + 16 * q^4 + 6 * q^5 + 8 * q^6 + 2 * q^7 - 12 * q^9 + 6 * q^10 - 2 * q^12 + 12 * q^13 + 8 * q^14 - 8 * q^15 - 16 * q^16 - 6 * q^17 - 24 * q^18 - 2 * q^19 + 6 * q^20 - 54 * q^21 + 12 * q^22 - 2 * q^24 - 14 * q^25 + 20 * q^26 - 40 * q^27 + 10 * q^28 - 6 * q^29 - 8 * q^30 - 4 * q^31 - 22 * q^33 + 12 * q^34 + 24 * q^37 - 26 * q^38 + 58 * q^39 + 18 * q^41 - 2 * q^42 - 6 * q^44 - 18 * q^45 + 6 * q^46 + 18 * q^47 + 8 * q^48 + 12 * q^49 + 24 * q^50 - 4 * q^51 + 12 * q^52 - 20 * q^54 + 42 * q^55 + 10 * q^56 + 36 * q^57 + 30 * q^58 - 42 * q^59 - 16 * q^60 - 46 * q^61 - 10 * q^62 - 32 * q^64 - 18 * q^65 + 4 * q^66 + 46 * q^67 - 12 * q^68 + 66 * q^69 + 12 * q^70 - 12 * q^71 + 24 * q^72 + 28 * q^73 - 16 * q^74 - 20 * q^75 - 28 * q^76 + 24 * q^77 - 58 * q^78 - 38 * q^79 + 56 * q^81 - 48 * q^82 + 12 * q^83 + 8 * q^85 - 16 * q^86 - 2 * q^87 + 24 * q^88 - 18 * q^89 + 52 * q^90 + 4 * q^91 - 12 * q^92 + 36 * q^93 - 30 * q^94 + 30 * q^95 - 10 * q^96 - 12 * q^97 - 16 * q^98 + 26 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$ .

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{3}{4}\right)$

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

)

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−1.56225	−	0.418603i	−0.901964	−	0.241680i	−0.222104	−	0.975023i	$-0.571293\pi$
$3$	−1.56225	−	0.418603i	−0.901964	−	0.241680i	−0.679859	+	0.733342i	$0.737959\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	2.20578	+	0.366816i	0.986453	+	0.164045i
$5$	2.20578	+	0.366816i	0.986453	+	0.164045i
$6$	1.14364	+	1.14364i	0.466891	+	0.466891i
$7$	1.11476	+	0.298699i	0.421340	+	0.112898i	0.463258	−	0.886223i	$-0.346680\pi$
$7$	1.11476	+	0.298699i	0.421340	+	0.112898i	−0.0419183	+	0.999121i	$0.513347\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.332689	−	0.192078i	−0.110896	−	0.0640260i
$10$	−1.72685	−	1.42056i	−0.546078	−	0.449220i
$11$			5.41958i			1.63406i	0.576592	+	0.817032i	$0.304382\pi$
$11$			5.41958i			1.63406i	−0.576592	+	0.817032i	$0.695618\pi$
$12$	−0.418603	−	1.56225i	−0.120840	−	0.450982i
$13$	−3.53236	+	2.03941i	−0.979700	+	0.565630i	−0.902179	−	0.431361i	$-0.858034\pi$
$13$	−3.53236	+	2.03941i	−0.979700	+	0.565630i	−0.0775203	+	0.996991i	$0.524700\pi$
$14$	−0.816061	−	0.816061i	−0.218102	−	0.218102i
$15$	−3.29242	−	1.49640i	−0.850098	−	0.386369i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.94729	−	3.37280i	0.472287	−	0.818025i	−0.527210	−	0.849735i	$-0.676762\pi$
$17$	1.94729	−	3.37280i	0.472287	−	0.818025i	0.999497	+	0.0317102i	$0.0100953\pi$
$18$	0.192078	+	0.332689i	0.0452732	+	0.0784156i
$19$	5.80123	+	1.55443i	1.33089	+	0.356612i	0.853048	−	0.521833i	$-0.174751\pi$
$19$	5.80123	+	1.55443i	1.33089	+	0.356612i	0.477845	+	0.878444i	$0.341418\pi$
$20$	0.785216	+	2.09367i	0.175580	+	0.468158i
$21$	−1.61650	−	0.933284i	−0.352748	−	0.203659i
$22$	2.70979	−	4.69349i	0.577729	−	1.00066i
$23$			0.383468i			0.0799586i	0.999201	+	0.0399793i	$0.0127292\pi$
$23$			0.383468i			0.0799586i	−0.999201	+	0.0399793i	$0.987271\pi$
$24$	−0.418603	+	1.56225i	−0.0854469	+	0.318892i
$25$	4.73089	+	1.61823i	0.946178	+	0.323645i
$26$	4.07882			0.799922
$27$	3.87027	+	3.87027i	0.744834	+	0.744834i
$28$	0.298699	+	1.11476i	0.0564488	+	0.210670i
$29$	5.82137	+	5.82137i	1.08100	+	1.08100i	0.996416	+	0.0845860i	$0.0269568\pi$
$29$	5.82137	+	5.82137i	1.08100	+	1.08100i	0.0845860	+	0.996416i	$0.473043\pi$
$30$	2.10312	+	2.94213i	0.383975	+	0.537157i
$31$	−3.43124	+	3.43124i	−0.616269	+	0.616269i	−0.944572	−	0.328304i	$-0.893523\pi$
$31$	−3.43124	+	3.43124i	−0.616269	+	0.616269i	0.328304	+	0.944572i	$0.393523\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	2.26865	−	8.46672i	0.394922	−	1.47387i
$34$	−3.37280	+	1.94729i	−0.578431	+	0.333957i
$35$	2.34934	+	1.06778i	0.397112	+	0.180487i
$36$		−	0.384156i		−	0.0640260i
$37$	2.71702	−	5.44223i	0.446675	−	0.894696i
$37$	2.71702	−	5.44223i	0.446675	−	0.894696i
$38$	−4.24679	−	4.24679i	−0.688921	−	0.688921i
$39$	6.37212	−	1.70740i	1.02036	−	0.273403i
$40$	0.366816	−	2.20578i	0.0579987	−	0.348764i
$41$	7.78143	−	4.49261i	1.21526	−	0.701628i	0.251356	−	0.967895i	$-0.419123\pi$
$41$	7.78143	−	4.49261i	1.21526	−	0.701628i	0.963899	+	0.266267i	$0.0857901\pi$
$42$	0.933284	+	1.61650i	0.144009	+	0.249431i
$43$			1.57247i			0.239799i	0.992786	+	0.119899i	$0.0382572\pi$
$43$			1.57247i			0.239799i	−0.992786	+	0.119899i	$0.961743\pi$
$44$	−4.69349	+	2.70979i	−0.707571	+	0.408516i
$45$	−0.663380	−	0.545717i	−0.0988909	−	0.0813507i
$46$	0.191734	−	0.332093i	0.0282696	−	0.0489644i
$47$	−3.06744	+	3.06744i	−0.447432	+	0.447432i	−0.894500	−	0.447068i	$-0.852468\pi$
$47$	−3.06744	+	3.06744i	−0.447432	+	0.447432i	0.447068	+	0.894500i	$0.352468\pi$
$48$	1.14364	−	1.14364i	0.165071	−	0.165071i
$49$	−4.90871	−	2.83404i	−0.701244	−	0.404863i
$50$	−3.28796	−	3.76687i	−0.464988	−	0.532716i
$51$	−4.45401	+	4.45401i	−0.623686	+	0.623686i
$52$	−3.53236	−	2.03941i	−0.489850	−	0.282815i
$53$	7.61884	−	2.04146i	1.04653	−	0.280416i	0.305712	−	0.952124i	$-0.401106\pi$
$53$	7.61884	−	2.04146i	1.04653	−	0.280416i	0.740816	+	0.671708i	$0.234439\pi$
$54$	−1.41662	−	5.28689i	−0.192777	−	0.719454i
$55$	−1.98799	+	11.9544i	−0.268060	+	1.61193i
$56$	0.298699	−	1.11476i	0.0399154	−	0.148966i
$57$	−8.41226	−	4.85682i	−1.11423	−	0.643302i
$58$	−2.13077	−	7.95215i	−0.279784	−	1.04417i
$59$	2.84475	+	10.6168i	0.370355	+	1.38218i	0.860014	+	0.510270i	$0.170454\pi$
$59$	2.84475	+	10.6168i	0.370355	+	1.38218i	−0.489659	+	0.871914i	$0.662879\pi$
$60$	−0.350287	−	3.59952i	−0.0452219	−	0.464696i
$61$	−8.58880	−	2.30136i	−1.09968	−	0.294659i	−0.337047	−	0.941488i	$-0.609428\pi$
$61$	−8.58880	−	2.30136i	−1.09968	−	0.294659i	−0.762635	+	0.646829i	$0.776095\pi$
$62$	4.68716	−	1.25592i	0.595270	−	0.159502i
$63$	−0.313495	−	0.313495i	−0.0394967	−	0.0394967i
$64$	−1.00000			−0.125000
$65$	−8.53968	+	3.20275i	−1.05922	+	0.397252i
$66$	−6.19807	+	6.19807i	−0.762930	+	0.762930i
$67$	2.68457	−	10.0190i	0.327973	−	1.22401i	−0.583317	−	0.812245i	$-0.698245\pi$
$67$	2.68457	−	10.0190i	0.327973	−	1.22401i	0.911290	−	0.411766i	$-0.135088\pi$
$68$	3.89458			0.472287
$69$	0.160521	−	0.599071i	0.0193244	−	0.0721197i
$70$	−1.50070	−	2.09939i	−0.179368	−	0.250925i
$71$	2.42276	+	4.19634i	0.287528	+	0.498013i	0.973219	−	0.229879i	$-0.0738332\pi$
$71$	2.42276	+	4.19634i	0.287528	+	0.498013i	−0.685691	+	0.727893i	$0.740500\pi$
$72$	−0.192078	+	0.332689i	−0.0226366	+	0.0392078i
$73$	−9.61059	+	9.61059i	−1.12483	+	1.12483i	−0.133830	+	0.991004i	$0.542728\pi$
$73$	−9.61059	+	9.61059i	−1.12483	+	1.12483i	−0.991004	+	0.133830i	$0.957272\pi$
$74$	−5.07412	+	3.35460i	−0.589854	+	0.389964i
$75$	−6.71343	−	4.50843i	−0.775200	−	0.520589i
$76$	1.55443	+	5.80123i	0.178306	+	0.665446i
$77$	−1.61882	+	6.04153i	−0.184482	+	0.688497i
$78$	−6.37212	−	1.70740i	−0.721500	−	0.193325i
$79$	−8.53421	−	2.28673i	−0.960174	−	0.257278i	−0.255500	−	0.966809i	$-0.582240\pi$
$79$	−8.53421	−	2.28673i	−0.960174	−	0.257278i	−0.704674	+	0.709531i	$0.748907\pi$
$80$	−1.42056	+	1.72685i	−0.158823	+	0.193068i
$81$	−3.84998	−	6.66836i	−0.427775	−	0.740929i
$82$	−8.98522			−0.992252
$83$	−12.0271	+	3.22265i	−1.32014	+	0.353731i	−0.849032	−	0.528342i	$-0.822814\pi$
$83$	−12.0271	+	3.22265i	−1.32014	+	0.353731i	−0.471112	+	0.882073i	$0.656147\pi$
$84$		−	1.86657i		−	0.203659i
$85$	5.53248	−	6.72535i	0.600081	−	0.729466i
$86$	0.786233	−	1.36180i	0.0847817	−	0.146846i
$87$	−6.65758	−	11.5313i	−0.713768	−	1.23628i
$88$	5.41958			0.577729
$89$	14.3038	−	3.83268i	1.51620	−	0.406264i	0.597709	−	0.801713i	$-0.296078\pi$
$89$	14.3038	−	3.83268i	1.51620	−	0.406264i	0.918488	+	0.395449i	$0.129411\pi$
$90$	0.301646	+	0.804295i	0.0317962	+	0.0847801i
$91$	−4.54690	+	1.21834i	−0.476645	+	0.127717i
$92$	−0.332093	+	0.191734i	−0.0346231	+	0.0199896i
$93$	6.79677	−	3.92412i	0.704792	−	0.406912i
$94$	4.19020	−	1.12276i	0.432186	−	0.115804i
$95$	12.2260	+	5.55672i	1.25436	+	0.570107i
$96$	−1.56225	+	0.418603i	−0.159446	+	0.0427235i
$97$	−4.38333			−0.445060			−0.222530	−	0.974926i	$-0.571431\pi$
$97$	−4.38333			−0.445060			−0.222530	+	0.974926i	$0.571431\pi$
$98$	2.83404	+	4.90871i	0.286282	+	0.495854i
$99$	1.04098	−	1.80304i	0.104623	−	0.181212i
$100$	0.964021	+	4.90619i	0.0964021	+	0.490619i
$101$		−	7.97874i		−	0.793914i	−0.917837	−	0.396957i	$-0.870066\pi$
$101$		−	7.97874i		−	0.793914i	0.917837	−	0.396957i	$-0.129934\pi$
$102$	6.08429	−	1.63028i	0.602434	−	0.161422i
$103$	4.69150			0.462267			0.231134	−	0.972922i	$-0.425757\pi$
$103$	4.69150			0.462267			0.231134	+	0.972922i	$0.425757\pi$
$104$	2.03941	+	3.53236i	0.199980	+	0.346376i
$105$	−3.22328	−	2.65157i	−0.314560	−	0.258767i
$106$	−7.61884	−	2.04146i	−0.740007	−	0.198284i
$107$	3.24023	+	0.868218i	0.313245	+	0.0839338i	0.412017	−	0.911176i	$-0.364825\pi$
$107$	3.24023	+	0.868218i	0.313245	+	0.0839338i	−0.0987714	+	0.995110i	$0.531491\pi$
$108$	−1.41662	+	5.28689i	−0.136314	+	0.508731i
$109$	−2.16115	−	8.06551i	−0.207000	−	0.772536i	−0.988831	−	0.149044i	$-0.952380\pi$
$109$	−2.16115	−	8.06551i	−0.207000	−	0.772536i	0.781830	−	0.623491i	$-0.214286\pi$
$110$	7.69884	−	9.35880i	0.734055	−	0.892327i
$111$	−6.52278	+	7.36475i	−0.619115	+	0.699031i
$112$	−0.816061	+	0.816061i	−0.0771106	+	0.0771106i
$113$	−3.40830	+	5.90335i	−0.320626	+	0.555340i	−0.980617	−	0.195933i	$-0.937227\pi$
$113$	−3.40830	+	5.90335i	−0.320626	+	0.555340i	0.659992	+	0.751273i	$0.270560\pi$
$114$	4.85682	+	8.41226i	0.454883	+	0.787880i
$115$	−0.140662	+	0.845844i	−0.0131168	+	0.0788753i
$116$	−2.13077	+	7.95215i	−0.197837	+	0.738338i
$117$	1.56690			0.144860
$118$	2.84475	−	10.6168i	0.261881	−	0.977351i
$119$	3.17821	−	3.17821i	0.291346	−	0.291346i
$120$	−1.49640	+	3.29242i	−0.136602	+	0.300555i
$121$	−18.3719			−1.67017
$122$	6.28744	+	6.28744i	0.569238	+	0.569238i
$123$	−14.0371	+	3.76124i	−1.26569	+	0.339140i
$124$	−4.68716	−	1.25592i	−0.420919	−	0.112785i
$125$	9.84170	+	5.30481i	0.880268	+	0.474477i
$126$	0.114747	+	0.428242i	0.0102225	+	0.0381508i
$127$	−0.401127	−	1.49703i	−0.0355943	−	0.132840i	0.945842	−	0.324626i	$-0.105239\pi$
$127$	−0.401127	−	1.49703i	−0.0355943	−	0.132840i	−0.981437	+	0.191787i	$0.938572\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	0.658239	−	2.45658i	0.0579547	−	0.216290i
$130$	8.99695	+	1.49617i	0.789085	+	0.131223i
$131$	−3.77026	−	14.0708i	−0.329409	−	1.22937i	−0.909805	−	0.415036i	$-0.863769\pi$
$131$	−3.77026	−	14.0708i	−0.329409	−	1.22937i	0.580396	−	0.814334i	$-0.302898\pi$
$132$	8.46672	−	2.26865i	0.736934	−	0.197461i
$133$	6.00267	+	3.46564i	0.520498	+	0.300509i
$134$	−7.33439	+	7.33439i	−0.633595	+	0.633595i
$135$	7.11727	+	9.95662i	0.612557	+	0.856930i
$136$	−3.37280	−	1.94729i	−0.289215	−	0.166979i
$137$	−8.51418	+	8.51418i	−0.727416	+	0.727416i	−0.970104	−	0.242689i	$-0.921971\pi$
$137$	−8.51418	+	8.51418i	−0.727416	+	0.727416i	0.242689	+	0.970104i	$0.421971\pi$
$138$	−0.438551	+	0.438551i	−0.0373319	+	0.0373319i
$139$	5.04939	−	8.74580i	0.428284	−	0.741809i	−0.568437	−	0.822727i	$-0.692452\pi$
$139$	5.04939	−	8.74580i	0.428284	−	0.741809i	0.996721	+	0.0809175i	$0.0257850\pi$
$140$	0.249952	+	2.56848i	0.0211248	+	0.217076i
$141$	6.07614	−	3.50806i	0.511703	−	0.295432i
$142$		−	4.84551i		−	0.406626i
$143$	−11.0527	−	19.1439i	−0.924276	−	1.60089i
$144$	0.332689	−	0.192078i	0.0277241	−	0.0160065i
$145$	10.7053	+	14.9760i	0.889025	+	1.24369i
$146$	13.1283	−	3.51772i	1.08651	−	0.291128i
$147$	6.48228	+	6.48228i	0.534649	+	0.534649i
$148$	6.07161	−	0.368107i	0.499084	−	0.0302582i
$149$		−	7.20201i		−	0.590012i	−0.955495	−	0.295006i	$-0.904678\pi$
$149$		−	7.20201i		−	0.590012i	0.955495	−	0.295006i	$-0.0953216\pi$
$150$	3.55978	+	7.26113i	0.290655	+	0.592869i
$151$	5.82441	−	3.36272i	0.473984	−	0.273655i	−0.243922	−	0.969795i	$-0.578434\pi$
$151$	5.82441	−	3.36272i	0.473984	−	0.273655i	0.717906	+	0.696140i	$0.245101\pi$
$152$	1.55443	−	5.80123i	0.126081	−	0.470542i
$153$	−1.29568	+	0.748063i	−0.104750	+	0.0604773i
$154$	4.42271	−	4.42271i	0.356392	−	0.356392i
$155$	−8.82717	+	6.30991i	−0.709016	+	0.506824i
$156$	4.66471	+	4.66471i	0.373476	+	0.373476i
$157$	−3.44829	−	12.8692i	−0.275204	−	1.02707i	−0.955705	−	0.294327i	$-0.904905\pi$
$157$	−3.44829	−	12.8692i	−0.275204	−	1.02707i	0.680501	−	0.732747i	$-0.261762\pi$
$158$	6.24748	+	6.24748i	0.497022	+	0.497022i
$159$	−12.7571			−1.01170
$160$	2.09367	−	0.785216i	0.165519	−	0.0620768i
$161$	−0.114542	+	0.427475i	−0.00902714	+	0.0336897i
$162$			7.69996i			0.604966i
$163$	−2.24597	+	3.89013i	−0.175918	+	0.304699i	−0.940479	−	0.339853i	$-0.889623\pi$
$163$	−2.24597	+	3.89013i	−0.175918	+	0.304699i	0.764561	+	0.644552i	$0.222956\pi$
$164$	7.78143	+	4.49261i	0.607628	+	0.350814i
$165$	8.10986	−	17.8435i	0.631352	−	1.38912i
$166$	12.0271	+	3.22265i	0.933483	+	0.250126i
$167$	−2.20707	−	3.82275i	−0.170788	−	0.295813i	0.767908	−	0.640561i	$-0.221298\pi$
$167$	−2.20707	−	3.82275i	−0.170788	−	0.295813i	−0.938696	+	0.344747i	$0.887965\pi$
$168$	−0.933284	+	1.61650i	−0.0720044	+	0.124715i
$169$	1.81837	−	3.14951i	0.139874	−	0.242270i
$170$	−8.15394	+	3.05808i	−0.625379	+	0.234544i
$171$	−1.63143	−	1.63143i	−0.124759	−	0.124759i
$172$	−1.36180	+	0.786233i	−0.103836	+	0.0599497i
$173$	5.27554	+	19.6886i	0.401092	+	1.49690i	0.811151	+	0.584837i	$0.198842\pi$
$173$	5.27554	+	19.6886i	0.401092	+	1.49690i	−0.410058	+	0.912059i	$0.634492\pi$
$174$			13.3152i			1.00942i
$175$	4.79045	+	3.21705i	0.362124	+	0.243186i
$176$	−4.69349	−	2.70979i	−0.353785	−	0.204258i
$177$		−	17.7768i		−	1.33619i
$178$	−14.3038	−	3.83268i	−1.07211	−	0.287272i
$179$	−14.7689	−	14.7689i	−1.10388	−	1.10388i	−0.993938	−	0.109943i	$-0.964933\pi$
$179$	−14.7689	−	14.7689i	−1.10388	−	1.10388i	−0.109943	−	0.993938i	$-0.535067\pi$
$180$	0.140915	−	0.847362i	0.0105032	−	0.0631587i
$181$	−2.80922	−	4.86571i	−0.208808	−	0.361665i	0.742532	−	0.669811i	$-0.233625\pi$
$181$	−2.80922	−	4.86571i	−0.208808	−	0.361665i	−0.951339	+	0.308146i	$0.900292\pi$
$182$	4.54690	+	1.21834i	0.337039	+	0.0903093i
$183$	12.4545	+	7.19059i	0.920661	+	0.531544i
$184$	0.383468			0.0282696
$185$	7.98942	−	11.0077i	0.587394	−	0.809301i
$186$	−7.84823			−0.575460
$187$	18.2792	+	10.5535i	1.33671	+	0.771747i
$188$	−4.19020	−	1.12276i	−0.305602	−	0.0818857i
$189$	3.15838	+	5.47047i	0.229738	+	0.397918i
$190$	−7.80968	−	10.9253i	−0.566574	−	0.792602i
$191$	6.46180	+	6.46180i	0.467559	+	0.467559i	0.901123	−	0.433564i	$-0.142744\pi$
$191$	6.46180	+	6.46180i	0.467559	+	0.467559i	−0.433564	+	0.901123i	$0.642744\pi$
$192$	1.56225	+	0.418603i	0.112745	+	0.0302101i
$193$			10.6806i			0.768808i	0.923165	+	0.384404i	$0.125593\pi$
$193$			10.6806i			0.768808i	−0.923165	+	0.384404i	$0.874407\pi$
$194$	3.79607	+	2.19166i	0.272542	+	0.157352i
$195$	14.6818	−	1.42876i	1.05138	−	0.102315i
$196$		−	5.66809i		−	0.404863i
$197$	0.449673	+	1.67820i	0.0320379	+	0.119567i	0.980093	−	0.198539i	$-0.0636198\pi$
$197$	0.449673	+	1.67820i	0.0320379	+	0.119567i	−0.948055	+	0.318106i	$0.896953\pi$
$198$	−1.80304	+	1.04098i	−0.128136	+	0.0739794i
$199$	−10.8607	−	10.8607i	−0.769891	−	0.769891i	0.208196	−	0.978087i	$-0.433241\pi$
$199$	−10.8607	−	10.8607i	−0.769891	−	0.769891i	−0.978087	+	0.208196i	$0.933241\pi$
$200$	1.61823	−	4.73089i	0.114426	−	0.334525i
$201$	−8.38793	+	14.5283i	−0.591639	+	1.02475i
$202$	−3.98937	+	6.90979i	−0.280691	+	0.486171i
$203$	4.75060	+	8.22828i	0.333427	+	0.577512i
$204$	−6.08429	−	1.63028i	−0.425985	−	0.114142i
$205$	18.8121	−	7.05534i	1.31389	−	0.492766i
$206$	−4.06296	−	2.34575i	−0.283080	−	0.163436i
$207$	0.0736558	−	0.127576i	0.00511943	−	0.00886711i
$208$		−	4.07882i		−	0.282815i
$209$	−8.42438	+	31.4402i	−0.582727	+	2.17477i
$210$	1.46566	+	3.90797i	0.101140	+	0.269675i
$211$	15.7228			1.08240			0.541200	−	0.840894i	$-0.317970\pi$
$211$	15.7228			1.08240			0.541200	+	0.840894i	$0.317970\pi$
$212$	5.57738	+	5.57738i	0.383056	+	0.383056i
$213$	−2.02834	−	7.56989i	−0.138980	−	0.518680i
$214$	−2.37202	−	2.37202i	−0.162148	−	0.162148i
$215$	−0.576806	+	3.46851i	−0.0393378	+	0.236550i
$216$	3.87027	−	3.87027i	0.263339	−	0.263339i
$217$	−4.84992	+	2.80010i	−0.329234	+	0.190083i
$218$	−2.16115	+	8.06551i	−0.146371	+	0.546265i
$219$	19.0371	−	10.9911i	1.28641	−	0.742709i
$220$	−11.3468	+	4.25554i	−0.765000	+	0.286909i
$221$			15.8853i			1.06856i
$222$	9.33127	−	3.11667i	0.626274	−	0.209177i
$223$	−7.88096	−	7.88096i	−0.527748	−	0.527748i	0.392152	−	0.919900i	$-0.371731\pi$
$223$	−7.88096	−	7.88096i	−0.527748	−	0.527748i	−0.919900	+	0.392152i	$0.871731\pi$
$224$	1.11476	−	0.298699i	0.0744831	−	0.0199577i
$225$	−1.26309	−	1.44707i	−0.0842060	−	0.0964711i
$226$	5.90335	−	3.40830i	0.392685	−	0.226717i
$227$	−1.77796	−	3.07951i	−0.118007	−	0.204394i	0.800971	−	0.598704i	$-0.204317\pi$
$227$	−1.77796	−	3.07951i	−0.118007	−	0.204394i	−0.918978	+	0.394309i	$0.870984\pi$
$228$		−	9.71364i		−	0.643302i
$229$	−11.7656	+	6.79287i	−0.777492	+	0.448885i	−0.835541	−	0.549428i	$-0.814846\pi$
$229$	−11.7656	+	6.79287i	−0.777492	+	0.448885i	0.0580484	+	0.998314i	$0.481512\pi$
$230$	0.544739	−	0.662191i	0.0359190	−	0.0436636i
$231$	5.05801	−	8.76072i	0.332792	−	0.576413i
$232$	5.82137	−	5.82137i	0.382192	−	0.382192i
$233$	7.60963	−	7.60963i	0.498523	−	0.498523i	−0.412455	−	0.910978i	$-0.635328\pi$
$233$	7.60963	−	7.60963i	0.498523	−	0.498523i	0.910978	+	0.412455i	$0.135328\pi$
$234$	−1.35698	−	0.783451i	−0.0887084	−	0.0512158i
$235$	−7.89127	+	5.64090i	−0.514770	+	0.367972i
$236$	−7.77200	+	7.77200i	−0.505914	+	0.505914i
$237$	12.3753	+	7.14489i	0.803863	+	0.464110i
$238$	−4.34152	+	1.16331i	−0.281419	+	0.0754060i
$239$	5.53867	+	20.6706i	0.358267	+	1.33707i	0.876323	+	0.481724i	$0.159989\pi$
$239$	5.53867	+	20.6706i	0.358267	+	1.33707i	−0.518056	+	0.855347i	$0.673344\pi$
$240$	2.94213	−	2.10312i	0.189914	−	0.135756i
$241$	−1.88845	+	7.04781i	−0.121646	+	0.453989i	−0.999698	−	0.0245762i	$-0.992176\pi$
$241$	−1.88845	+	7.04781i	−0.121646	+	0.453989i	0.878052	+	0.478565i	$0.158843\pi$
$242$	15.9105	+	9.18593i	1.02277	+	0.590494i
$243$	−1.02663	−	3.83143i	−0.0658583	−	0.245786i
$244$	−2.30136	−	8.58880i	−0.147330	−	0.549841i
$245$	−9.78794	−	8.05186i	−0.625328	−	0.514414i
$246$	14.0371	+	3.76124i	0.894975	+	0.239808i
$247$	−23.6621	+	6.34025i	−1.50559	+	0.403420i
$248$	3.43124	+	3.43124i	0.217884	+	0.217884i
$249$	20.1383			1.27621
$250$	−5.87075	−	9.51495i	−0.371299	−	0.601778i
$251$	4.53943	−	4.53943i	0.286526	−	0.286526i	−0.549179	−	0.835705i	$-0.685059\pi$
$251$	4.53943	−	4.53943i	0.286526	−	0.286526i	0.835705	+	0.549179i	$0.185059\pi$
$252$	0.114747	−	0.428242i	0.00722839	−	0.0269767i
$253$	−2.07823			−0.130657
$254$	−0.401127	+	1.49703i	−0.0251690	+	0.0939319i
$255$	−11.4583	+	8.19074i	−0.717549	+	0.512924i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.27813	−	10.8740i	0.391619	−	0.678304i	−0.601044	−	0.799216i	$-0.705248\pi$
$257$	6.27813	−	10.8740i	0.391619	−	0.678304i	0.992663	+	0.120912i	$0.0385818\pi$
$258$	−1.79834	+	1.79834i	−0.111960	+	0.111960i
$259$	4.65441	−	5.25521i	0.289211	−	0.326543i
$260$	−7.04350	−	5.79420i	−0.436819	−	0.359341i
$261$	−0.818549	−	3.05487i	−0.0506669	−	0.189091i
$262$	−3.77026	+	14.0708i	−0.232927	+	0.869296i
$263$	6.67077	+	1.78743i	0.411337	+	0.110218i	0.458553	−	0.888667i	$-0.348368\pi$
$263$	6.67077	+	1.78743i	0.411337	+	0.110218i	−0.0472153	+	0.998885i	$0.515035\pi$
$264$	−8.46672	−	2.26865i	−0.521091	−	0.139626i
$265$	17.5543	−	1.70830i	1.07835	−	0.104940i
$266$	−3.46564	−	6.00267i	−0.212492	−	0.368047i
$267$	−23.9504			−1.46574
$268$	10.0190	−	2.68457i	0.612005	−	0.163986i
$269$		−	25.0622i		−	1.52807i	−0.645174	−	0.764036i	$-0.723215\pi$
$269$		−	25.0622i		−	1.52807i	0.645174	−	0.764036i	$-0.276785\pi$
$270$	−1.18543	−	12.1813i	−0.0721427	−	0.741332i
$271$	8.90741	−	15.4281i	0.541087	−	0.937189i	−0.457755	−	0.889078i	$-0.651346\pi$
$271$	8.90741	−	15.4281i	0.541087	−	0.937189i	0.998842	−	0.0481113i	$-0.0153202\pi$
$272$	1.94729	+	3.37280i	0.118072	+	0.204506i
$273$	7.61339			0.460783
$274$	11.6306	−	3.11641i	0.702629	−	0.188269i
$275$	−8.77011	+	25.6395i	−0.528858	+	1.54612i
$276$	0.599071	−	0.160521i	0.0360599	−	0.00966221i
$277$	−13.6809	+	7.89869i	−0.822008	+	0.474586i	−0.851108	−	0.524990i	$-0.824069\pi$
$277$	−13.6809	+	7.89869i	−0.822008	+	0.474586i	0.0291008	+	0.999576i	$0.490736\pi$
$278$	−8.74580	+	5.04939i	−0.524538	+	0.302842i
$279$	1.80060	−	0.482470i	0.107799	−	0.0288847i
$280$	1.06778	−	2.34934i	0.0638118	−	0.140400i
$281$	9.74564	−	2.61134i	0.581376	−	0.155779i	0.0438671	−	0.999037i	$-0.486032\pi$
$281$	9.74564	−	2.61134i	0.581376	−	0.155779i	0.537509	+	0.843258i	$0.319366\pi$
$282$	−7.01612			−0.417804
$283$	−9.26316	−	16.0443i	−0.550638	−	0.953733i	−0.998229	−	0.0594941i	$-0.981051\pi$
$283$	−9.26316	−	16.0443i	−0.550638	−	0.953733i	0.447591	−	0.894238i	$-0.352282\pi$
$284$	−2.42276	+	4.19634i	−0.143764	+	0.249007i
$285$	−16.7740	−	13.7988i	−0.993606	−	0.817371i
$286$			22.1055i			1.30712i
$287$	10.0164	−	2.68388i	0.591248	−	0.158424i
$288$	−0.384156			−0.0226366
$289$	0.916138	+	1.58680i	0.0538905	+	0.0933410i
$290$	−1.78303	−	18.3223i	−0.104703	−	1.07592i
$291$	6.84784	+	1.83487i	0.401428	+	0.107562i
$292$	−13.1283	−	3.51772i	−0.768276	−	0.205859i
$293$	2.37105	−	8.84889i	0.138518	−	0.516957i	−0.861440	−	0.507859i	$-0.830437\pi$
$293$	2.37105	−	8.84889i	0.138518	−	0.516957i	0.999959	−	0.00909855i	$-0.00289620\pi$
$294$	−2.37268	−	8.85495i	−0.138377	−	0.516431i
$295$	2.38049	+	24.4617i	0.138597	+	1.42421i
$296$	−5.44223	−	2.71702i	−0.316323	−	0.157923i
$297$	−20.9752	+	20.9752i	−1.21711	+	1.21711i
$298$	−3.60101	+	6.23713i	−0.208601	+	0.361307i
$299$	−0.782047	−	1.35455i	−0.0452270	−	0.0783354i
$300$	0.547705	−	8.06822i	0.0316218	−	0.465819i
$301$	−0.469695	+	1.75292i	−0.0270727	+	0.101037i
$302$	−6.72545			−0.387006
$303$	−3.33992	+	12.4648i	−0.191874	+	0.716082i
$304$	−4.24679	+	4.24679i	−0.243570	+	0.243570i
$305$	−18.1008	−	8.22679i	−1.03645	−	0.471065i
$306$	1.49613			0.0855278
$307$	24.1075	+	24.1075i	1.37589	+	1.37589i	0.851450	+	0.524435i	$0.175724\pi$
$307$	24.1075	+	24.1075i	1.37589	+	1.37589i	0.524435	+	0.851450i	$0.324276\pi$
$308$	−6.04153	+	1.61882i	−0.344248	+	0.0922411i
$309$	−7.32928	−	1.96388i	−0.416948	−	0.111721i
$310$	10.7995	−	1.05095i	0.613371	−	0.0596902i
$311$	−6.07987	−	22.6904i	−0.344758	−	1.28665i	−0.892895	−	0.450266i	$-0.851329\pi$
$311$	−6.07987	−	22.6904i	−0.344758	−	1.28665i	0.548137	−	0.836389i	$-0.315337\pi$
$312$	−1.70740	−	6.37212i	−0.0966627	−	0.360750i
$313$	−10.4495	−	6.03304i	−0.590643	−	0.341008i	0.174709	−	0.984620i	$-0.444102\pi$
$313$	−10.4495	−	6.03304i	−0.590643	−	0.341008i	−0.765352	+	0.643612i	$0.777435\pi$
$314$	−3.44829	+	12.8692i	−0.194598	+	0.726251i
$315$	−0.576505	−	0.806495i	−0.0324824	−	0.0454408i
$316$	−2.28673	−	8.53421i	−0.128639	−	0.480087i
$317$	15.3111	−	4.10260i	0.859959	−	0.230425i	0.198218	−	0.980158i	$-0.436485\pi$
$317$	15.3111	−	4.10260i	0.859959	−	0.230425i	0.661741	+	0.749733i	$0.269818\pi$
$318$	11.0479	+	6.37854i	0.619538	+	0.357691i
$319$	−31.5494	+	31.5494i	−1.76643	+	1.76643i
$320$	−2.20578	−	0.366816i	−0.123307	−	0.0205056i
$321$	−4.69861	−	2.71274i	−0.262251	−	0.151410i
$322$	0.312933	−	0.312933i	0.0174391	−	0.0174391i
$323$	16.5395	−	16.5395i	0.920280	−	0.920280i
$324$	3.84998	−	6.66836i	0.213888	−	0.370464i
$325$	−20.0114	+	3.93206i	−1.11003	+	0.218112i
$326$	3.89013	−	2.24597i	0.215454	−	0.124393i
$327$			13.5050i			0.746827i
$328$	−4.49261	−	7.78143i	−0.248063	−	0.429658i
$329$	−4.33570	+	2.50322i	−0.239035	+	0.138007i
$330$	−15.9451	+	11.3980i	−0.877749	+	0.627439i
$331$	0.522368	−	0.139968i	0.0287119	−	0.00769334i	−0.244434	−	0.969666i	$-0.578602\pi$
$331$	0.522368	−	0.139968i	0.0287119	−	0.00769334i	0.273146	+	0.961972i	$0.411936\pi$
$332$	−8.80443	−	8.80443i	−0.483206	−	0.483206i
$333$	−1.94925	+	1.28869i	−0.106818	+	0.0706197i
$334$			4.41413i			0.241531i
$335$	9.59668	−	21.1148i	0.524322	−	1.15363i
$336$	1.61650	−	0.933284i	0.0881870	−	0.0509148i
$337$	7.13180	−	26.6162i	0.388494	−	1.44988i	−0.444092	−	0.895981i	$-0.646474\pi$
$337$	7.13180	−	26.6162i	0.388494	−	1.44988i	0.832585	−	0.553897i	$-0.186860\pi$
$338$	−3.14951	+	1.81837i	−0.171311	+	0.0989062i
$339$	7.79576	−	7.79576i	0.423408	−	0.423408i
$340$	8.59056	+	1.42859i	0.465889	+	0.0774763i
$341$	−18.5959	−	18.5959i	−1.00702	−	1.00702i
$342$	0.597146	+	2.22858i	0.0322899	+	0.120508i
$343$	−10.3379	−	10.3379i	−0.558196	−	0.558196i
$344$	1.57247			0.0847817
$345$	0.573821	−	1.26254i	0.0308935	−	0.0679726i
$346$	5.27554	−	19.6886i	0.283615	−	1.05847i
$347$		−	2.69381i		−	0.144611i	−0.997383	−	0.0723056i	$-0.976964\pi$
$347$		−	2.69381i		−	0.144611i	0.997383	−	0.0723056i	$-0.0230357\pi$
$348$	6.65758	−	11.5313i	0.356884	−	0.618141i
$349$	13.6101	+	7.85782i	0.728535	+	0.420620i	0.817886	−	0.575381i	$-0.195146\pi$
$349$	13.6101	+	7.85782i	0.728535	+	0.420620i	−0.0893513	+	0.996000i	$0.528479\pi$
$350$	−2.54013	−	5.18127i	−0.135775	−	0.276951i
$351$	−21.5642	−	5.77812i	−1.15101	−	0.308413i
$352$	2.70979	+	4.69349i	0.144432	+	0.250164i
$353$	5.89584	−	10.2119i	0.313804	−	0.543525i	−0.665378	−	0.746506i	$-0.731730\pi$
$353$	5.89584	−	10.2119i	0.313804	−	0.543525i	0.979183	+	0.202982i	$0.0650632\pi$
$354$	−8.88841	+	15.3952i	−0.472413	+	0.818244i
$355$	3.80477	+	10.1449i	0.201936	+	0.538434i
$356$	10.4711	+	10.4711i	0.554967	+	0.554967i
$357$	−6.29556	+	3.63475i	−0.333197	+	0.192371i
$358$	5.40580	+	20.1747i	0.285705	+	1.06627i
$359$			12.6671i			0.668543i	0.942477	+	0.334272i	$0.108490\pi$
$359$			12.6671i			0.668543i	−0.942477	+	0.334272i	$0.891510\pi$
$360$	−0.545717	+	0.663380i	−0.0287618	+	0.0349632i
$361$	14.7835	+	8.53525i	0.778079	+	0.449224i
$362$			5.61844i			0.295299i
$363$	28.7014	+	7.69051i	1.50643	+	0.403647i
$364$	−3.32856	−	3.32856i	−0.174464	−	0.174464i
$365$	−24.7241	+	17.6735i	−1.29412	+	0.925072i
$366$	−7.19059	−	12.4545i	−0.375858	−	0.651005i
$367$	−19.9349	−	5.34154i	−1.04059	−	0.278826i	−0.302234	−	0.953234i	$-0.597732\pi$
$367$	−19.9349	−	5.34154i	−1.04059	−	0.278826i	−0.738359	+	0.674408i	$0.764399\pi$
$368$	−0.332093	−	0.191734i	−0.0173115	−	0.00999482i
$369$	−3.45173			−0.179690
$370$	−12.4229	+	5.53822i	−0.645835	+	0.287918i
$371$	9.10297			0.472603
$372$	6.79677	+	3.92412i	0.352396	+	0.203456i
$373$	33.3290	+	8.93048i	1.72571	+	0.462403i	0.979188	−	0.202957i	$-0.0650553\pi$
$373$	33.3290	+	8.93048i	1.72571	+	0.462403i	0.746523	+	0.665360i	$0.231722\pi$
$374$	−10.5535	−	18.2792i	−0.545708	−	0.945193i
$375$	−13.1546	−	12.4072i	−0.679298	−	0.640704i
$376$	3.06744	+	3.06744i	0.158191	+	0.158191i
$377$	−32.4353	−	8.69102i	−1.67050	−	0.447610i
$378$		−	6.31676i		−	0.324899i
$379$	−4.64897	−	2.68408i	−0.238802	−	0.137872i	0.375824	−	0.926691i	$-0.377360\pi$
$379$	−4.64897	−	2.68408i	−0.238802	−	0.137872i	−0.614626	+	0.788819i	$0.710693\pi$
$380$	1.30075	+	13.3664i	0.0667271	+	0.685682i
$381$			2.50664i			0.128419i
$382$	−2.36518	−	8.82698i	−0.121013	−	0.451628i
$383$	−29.4786	+	17.0195i	−1.50629	+	0.869656i	−0.506314	+	0.862349i	$0.668992\pi$
$383$	−29.4786	+	17.0195i	−1.50629	+	0.869656i	−0.999973	+	0.00730659i	$0.997674\pi$
$384$	−1.14364	−	1.14364i	−0.0583613	−	0.0583613i
$385$	−5.78689	+	12.7325i	−0.294927	+	0.648906i
$386$	5.34031	−	9.24969i	0.271815	−	0.470797i
$387$	0.302036	−	0.523143i	0.0153534	−	0.0265928i
$388$	−2.19166	−	3.79607i	−0.111265	−	0.192716i
$389$	−17.5552	−	4.70391i	−0.890086	−	0.238498i	−0.215332	−	0.976541i	$-0.569083\pi$
$389$	−17.5552	−	4.70391i	−0.890086	−	0.238498i	−0.674754	+	0.738043i	$0.735750\pi$
$390$	−13.4292	−	6.10354i	−0.680012	−	0.309065i
$391$	1.29336	+	0.746722i	0.0654081	+	0.0377634i
$392$	−2.83404	+	4.90871i	−0.143141	+	0.247927i
$393$			23.5603i			1.18846i
$394$	0.449673	−	1.67820i	0.0226542	−	0.0845466i
$395$	−17.9857	−	8.17451i	−0.904961	−	0.411304i
$396$	2.08197			0.104623
$397$	22.8690	+	22.8690i	1.14776	+	1.14776i	0.986992	+	0.160770i	$0.0513979\pi$
$397$	22.8690	+	22.8690i	1.14776	+	1.14776i	0.160770	+	0.986992i	$0.448602\pi$
$398$	3.97528	+	14.8359i	0.199263	+	0.743658i
$399$	−7.92693	−	7.92693i	−0.396843	−	0.396843i
$400$	−3.76687	+	3.28796i	−0.188344	+	0.164398i
$401$	18.7127	−	18.7127i	0.934468	−	0.934468i	−0.0635130	−	0.997981i	$-0.520230\pi$
$401$	18.7127	−	18.7127i	0.934468	−	0.934468i	0.997981	+	0.0635130i	$0.0202304\pi$
$402$	14.5283	−	8.38793i	0.724607	−	0.418352i
$403$	5.12267	−	19.1181i	0.255178	−	0.952338i
$404$	6.90979	−	3.98937i	0.343775	−	0.198479i
$405$	−6.04613	−	16.1211i	−0.300435	−	0.801065i
$406$		−	9.50120i		−	0.471537i
$407$	29.4946	+	14.7251i	1.46199	+	0.729896i
$408$	4.45401	+	4.45401i	0.220506	+	0.220506i
$409$	33.4605	−	8.96573i	1.65452	−	0.443327i	0.693645	−	0.720317i	$-0.256004\pi$
$409$	33.4605	−	8.96573i	1.65452	−	0.443327i	0.960873	+	0.276990i	$0.0893370\pi$
$410$	−19.8194	−	3.29592i	−0.978810	−	0.162774i
$411$	16.8653	−	9.73719i	0.831905	−	0.480300i
$412$	2.34575	+	4.06296i	0.115567	+	0.200168i
$413$			12.6849i			0.624181i
$414$	−0.127576	+	0.0736558i	−0.00626999	+	0.00361998i
$415$	−27.7112	+	2.69671i	−1.36029	+	0.132376i
$416$	−2.03941	+	3.53236i	−0.0999902	+	0.173188i
$417$	−11.5494	+	11.5494i	−0.565577	+	0.565577i
$418$	23.0158	−	23.0158i	1.12574	−	1.12574i
$419$	15.3378	+	8.85527i	0.749300	+	0.432608i	0.825441	−	0.564489i	$-0.190927\pi$
$419$	15.3378	+	8.85527i	0.749300	+	0.432608i	−0.0761412	+	0.997097i	$0.524260\pi$
$420$	0.684687	−	4.11723i	0.0334093	−	0.200900i
$421$	−12.5994	+	12.5994i	−0.614057	+	0.614057i	−0.944001	−	0.329944i	$-0.892970\pi$
$421$	−12.5994	+	12.5994i	−0.614057	+	0.614057i	0.329944	+	0.944001i	$0.392970\pi$
$422$	−13.6163	−	7.86139i	−0.662832	−	0.382686i
$423$	1.60969	−	0.431315i	0.0782659	−	0.0209713i
$424$	−2.04146	−	7.61884i	−0.0991422	−	0.370004i
$425$	14.6704	−	12.8052i	0.711617	−	0.621144i
$426$	−2.02834	+	7.56989i	−0.0982736	+	0.366762i
$427$	−8.88704	−	5.13093i	−0.430074	−	0.248303i
$428$	0.868218	+	3.24023i	0.0419669	+	0.156623i
$429$	9.25341	+	34.5342i	0.446759	+	1.66733i
$430$	2.23378	−	2.71541i	0.107723	−	0.130949i
$431$	−10.8241	−	2.90031i	−0.521380	−	0.139703i	−0.0114749	−	0.999934i	$-0.503653\pi$
$431$	−10.8241	−	2.90031i	−0.521380	−	0.139703i	−0.509905	+	0.860231i	$0.670319\pi$
$432$	−5.28689	+	1.41662i	−0.254366	+	0.0681570i
$433$	−3.62400	−	3.62400i	−0.174158	−	0.174158i	0.614645	−	0.788804i	$-0.289299\pi$
$433$	−3.62400	−	3.62400i	−0.174158	−	0.174158i	−0.788804	+	0.614645i	$0.789299\pi$
$434$	5.60020			0.268818
$435$	−10.4553	−	27.8775i	−0.501292	−	1.33662i
$436$	5.90436	−	5.90436i	0.282768	−	0.282768i
$437$	−0.596075	+	2.22458i	−0.0285142	+	0.106416i
$438$	−21.9822			−1.05035
$439$	4.65935	−	17.3889i	0.222378	−	0.829928i	−0.761059	−	0.648682i	$-0.775320\pi$
$439$	4.65935	−	17.3889i	0.222378	−	0.829928i	0.983438	−	0.181245i	$-0.0580129\pi$
$440$	11.9544	+	1.98799i	0.569903	+	0.0947736i
$441$	1.08872	+	1.88571i	0.0518436	+	0.0897957i
$442$	7.94263	−	13.7570i	0.377792	−	0.654356i
$443$	9.53895	−	9.53895i	0.453209	−	0.453209i	−0.443209	−	0.896418i	$-0.646160\pi$
$443$	9.53895	−	9.53895i	0.453209	−	0.453209i	0.896418	+	0.443209i	$0.146160\pi$
$444$	−9.63945	−	1.96652i	−0.457468	−	0.0933270i
$445$	32.9568	−	3.20719i	1.56230	−	0.152035i
$446$	2.88463	+	10.7656i	0.136591	+	0.509766i
$447$	−3.01478	+	11.2513i	−0.142594	+	0.532169i
$448$	−1.11476	−	0.298699i	−0.0526675	−	0.0141122i
$449$	−20.0298	−	5.36698i	−0.945267	−	0.253283i	−0.246914	−	0.969037i	$-0.579417\pi$
$449$	−20.0298	−	5.36698i	−0.945267	−	0.253283i	−0.698353	+	0.715754i	$0.746083\pi$
$450$	0.370335	+	1.88474i	0.0174577	+	0.0888476i
$451$	24.3481	+	42.1721i	1.14651	+	1.98581i
$452$	−6.81660			−0.320626
$453$	−10.5068	+	2.81529i	−0.493653	+	0.132274i
$454$			3.55591i			0.166887i
$455$	−10.4764	+	1.01951i	−0.491139	+	0.0477952i
$456$	−4.85682	+	8.41226i	−0.227441	+	0.393940i
$457$	2.12756	+	3.68504i	0.0995230	+	0.172379i	0.911487	−	0.411328i	$-0.134935\pi$
$457$	2.12756	+	3.68504i	0.0995230	+	0.172379i	−0.811964	+	0.583707i	$0.801602\pi$
$458$	13.5857			0.634820
$459$	20.5902	−	5.51712i	0.961068	−	0.257517i
$460$	−0.802853	+	0.301105i	−0.0374332	+	0.0140391i
$461$	22.9371	−	6.14596i	1.06829	−	0.286246i	0.318497	−	0.947924i	$-0.396822\pi$
$461$	22.9371	−	6.14596i	1.06829	−	0.286246i	0.749788	+	0.661678i	$0.230155\pi$
$462$	−8.76072	+	5.05801i	−0.407586	+	0.235320i
$463$	22.8418	−	13.1877i	1.06155	−	0.612886i	0.135689	−	0.990752i	$-0.456675\pi$
$463$	22.8418	−	13.1877i	1.06155	−	0.612886i	0.925860	+	0.377866i	$0.123342\pi$
$464$	−7.95215	+	2.13077i	−0.369169	+	0.0989186i
$465$	16.4316	−	6.16256i	0.761996	−	0.285782i
$466$	−10.3949	+	2.78532i	−0.481537	+	0.129027i
$467$	4.82320			0.223191			0.111596	−	0.993754i	$-0.464404\pi$
$467$	4.82320			0.223191			0.111596	+	0.993754i	$0.464404\pi$
$468$	0.783451	+	1.35698i	0.0362150	+	0.0627263i
$469$	5.98531	−	10.3669i	0.276376	−	0.478697i
$470$	9.65449	−	0.939526i	0.445328	−	0.0433371i
$471$			21.5483i			0.992895i
$472$	10.6168	−	2.84475i	0.488676	−	0.130940i
$473$	−8.52211			−0.391847
$474$	−7.14489	−	12.3753i	−0.328176	−	0.568417i
$475$	24.9296	+	16.7416i	1.14385	+	0.768156i
$476$	4.34152	+	1.16331i	0.198993	+	0.0533201i
$477$	−2.92683	−	0.784240i	−0.134010	−	0.0359079i
$478$	5.53867	−	20.6706i	0.253333	−	0.945452i
$479$	−10.5344	−	39.3150i	−0.481330	−	1.79635i	−0.596046	−	0.802950i	$-0.703262\pi$
$479$	−10.5344	−	39.3150i	−0.481330	−	1.79635i	0.114716	−	0.993398i	$-0.463404\pi$
$480$	−3.59952	+	0.350287i	−0.164295	+	0.0159883i
$481$	1.50144	+	24.7650i	0.0684598	+	1.12919i
$482$	5.15935	−	5.15935i	0.235002	−	0.235002i
$483$	0.357884	−	0.619874i	0.0162843	−	0.0282052i
$484$	−9.18593	−	15.9105i	−0.417542	−	0.723204i
$485$	−9.66864	−	1.60787i	−0.439030	−	0.0730098i
$486$	−1.02663	+	3.83143i	−0.0465688	+	0.173797i
$487$	−14.0068			−0.634709			−0.317355	−	0.948307i	$-0.602795\pi$
$487$	−14.0068			−0.634709			−0.317355	+	0.948307i	$0.602795\pi$
$488$	−2.30136	+	8.58880i	−0.104178	+	0.388797i
$489$	5.13718	−	5.13718i	0.232311	−	0.232311i
$490$	4.45067	+	11.8671i	0.201061	+	0.536100i
$491$	14.8170			0.668683			0.334342	−	0.942452i	$-0.391486\pi$
$491$	14.8170			0.668683			0.334342	+	0.942452i	$0.391486\pi$
$492$	−10.2759	−	10.2759i	−0.463273	−	0.463273i
$493$	30.9702	−	8.29845i	1.39483	−	0.373743i
$494$	23.6621	+	6.34025i	1.06461	+	0.285261i
$495$	2.95756	−	3.59524i	0.132932	−	0.161594i
$496$	−1.25592	−	4.68716i	−0.0563925	−	0.210460i
$497$	1.44735	+	5.40159i	0.0649225	+	0.242294i
$498$	−17.4403	−	10.0691i	−0.781517	−	0.451209i
$499$	−8.81869	+	32.9118i	−0.394779	+	1.47333i	0.427378	+	0.904073i	$0.359437\pi$
$499$	−8.81869	+	32.9118i	−0.394779	+	1.47333i	−0.822157	+	0.569261i	$0.807229\pi$
$500$	0.326747	+	11.1756i	0.0146126	+	0.499786i
$501$	1.84777	+	6.89596i	0.0825522	+	0.308089i
$502$	−6.20098	+	1.66155i	−0.276763	+	0.0741585i
$503$	−12.3607	−	7.13645i	−0.551136	−	0.318199i	0.198444	−	0.980112i	$-0.436411\pi$
$503$	−12.3607	−	7.13645i	−0.551136	−	0.318199i	−0.749580	+	0.661914i	$0.769745\pi$
$504$	−0.313495	+	0.313495i	−0.0139642	+	0.0139642i
$505$	2.92673	−	17.5993i	0.130238	−	0.783159i
$506$	1.79980	+	1.03912i	0.0800110	+	0.0461944i
$507$	−4.15913	+	4.15913i	−0.184714	+	0.184714i
$508$	1.09590	−	1.09590i	0.0486227	−	0.0486227i
$509$	−8.11064	+	14.0480i	−0.359498	+	0.622669i	−0.987877	−	0.155239i	$-0.950385\pi$
$509$	−8.11064	+	14.0480i	−0.359498	+	0.622669i	0.628379	+	0.777907i	$0.283719\pi$
$510$	14.0186	−	1.36422i	0.620754	−	0.0604087i
$511$	−13.5842	+	7.84283i	−0.600929	+	0.346946i
$512$			1.00000i			0.0441942i
$513$	16.4362	+	28.4684i	0.725678	+	1.25691i
$514$	−10.8740	+	6.27813i	−0.479633	+	0.276917i
$515$	10.3484	+	1.72092i	0.456005	+	0.0758326i
$516$	2.45658	−	0.658239i	0.108145	−	0.0289774i
$517$	−16.6242	−	16.6242i	−0.731133	−	0.731133i
$518$	−6.65844	+	2.22394i	−0.292555	+	0.0977142i
$519$		−	32.9668i		−	1.44708i
$520$	3.20275	+	8.53968i	0.140450	+	0.374490i
$521$	−13.4673	+	7.77533i	−0.590012	+	0.340643i	−0.765102	−	0.643909i	$-0.777312\pi$
$521$	−13.4673	+	7.77533i	−0.590012	+	0.340643i	0.175090	+	0.984552i	$0.443978\pi$
$522$	−0.818549	+	3.05487i	−0.0358269	+	0.133708i
$523$	24.0862	−	13.9061i	1.05321	−	0.608073i	0.129666	−	0.991558i	$-0.458609\pi$
$523$	24.0862	−	13.9061i	1.05321	−	0.608073i	0.923547	+	0.383484i	$0.125276\pi$
$524$	10.3005	−	10.3005i	0.449981	−	0.449981i
$525$	−6.13720	−	7.03112i	−0.267849	−	0.306863i
$526$	−4.88334	−	4.88334i	−0.212924	−	0.212924i
$527$	4.89128	+	18.2545i	0.213067	+	0.795178i
$528$	6.19807	+	6.19807i	0.269736	+	0.269736i
$529$	22.8530			0.993607
$530$	−16.0566	−	7.29772i	−0.697455	−	0.316993i
$531$	1.09283	−	4.07849i	0.0474247	−	0.176991i
$532$			6.93129i			0.300509i
$533$	−18.3245	+	31.7390i	−0.793724	+	1.37477i
$534$	20.7417	+	11.9752i	0.897579	+	0.518217i
$535$	6.82875	+	3.10366i	0.295233	+	0.134183i
$536$	−10.0190	−	2.68457i	−0.432753	−	0.115956i
$537$	16.8904	+	29.2550i	0.728874	+	1.26245i
$538$	−12.5311	+	21.7045i	−0.540255	+	0.935749i
$539$	15.3593	−	26.6031i	0.661573	−	1.14588i
$540$	−5.06405	+	11.1421i	−0.217922	+	0.479478i
$541$	1.73685	+	1.73685i	0.0746729	+	0.0746729i	0.743457	−	0.668784i	$-0.233185\pi$
$541$	1.73685	+	1.73685i	0.0746729	+	0.0746729i	−0.668784	+	0.743457i	$0.733185\pi$
$542$	−15.4281	+	8.90741i	−0.662693	+	0.382606i
$543$	2.35189	+	8.77739i	0.100929	+	0.376674i
$544$		−	3.89458i		−	0.166979i
$545$	−1.80845	−	18.5834i	−0.0774654	−	0.796027i
$546$	−6.59339	−	3.80669i	−0.282171	−	0.162911i
$547$			7.95342i			0.340064i	0.985439	+	0.170032i	$0.0543870\pi$
$547$			7.95342i			0.340064i	−0.985439	+	0.170032i	$0.945613\pi$
$548$	−11.6306	−	3.11641i	−0.496834	−	0.133126i
$549$	2.41536	+	2.41536i	0.103085	+	0.103085i
$550$	20.4149	−	17.8194i	0.870493	−	0.759820i
$551$	24.7222	+	42.8201i	1.05320	+	1.82420i
$552$	−0.599071	−	0.160521i	−0.0254982	−	0.00683221i
$553$	−8.83056	−	5.09832i	−0.375513	−	0.216803i
$554$	15.7974			0.671166
$555$	−17.0893	+	13.8523i	−0.725400	+	0.587998i
$556$	10.0988			0.428284
$557$	23.7183	+	13.6937i	1.00498	+	0.580223i	0.909716	−	0.415230i	$-0.136299\pi$
$557$	23.7183	+	13.6937i	1.00498	+	0.580223i	0.0952586	+	0.995453i	$0.469632\pi$
$558$	−1.80060	−	0.482470i	−0.0762255	−	0.0204246i
$559$	−3.20690	−	5.55452i	−0.135637	−	0.234931i
$560$	−2.09939	+	1.50070i	−0.0887155	+	0.0634163i
$561$	−24.1389	−	24.1389i	−1.01914	−	1.01914i
$562$	−9.74564	−	2.61134i	−0.411095	−	0.110153i
$563$		−	3.30187i		−	0.139157i	−0.997576	−	0.0695785i	$-0.977835\pi$
$563$		−	3.30187i		−	0.139157i	0.997576	−	0.0695785i	$-0.0221654\pi$
$564$	6.07614	+	3.50806i	0.255851	+	0.147716i
$565$	−9.68338	+	11.7712i	−0.407383	+	0.495220i
$566$			18.5263i			0.778719i
$567$	−2.29997	−	8.58361i	−0.0965897	−	0.360478i
$568$	4.19634	−	2.42276i	0.176074	−	0.101657i
$569$	−9.43733	−	9.43733i	−0.395633	−	0.395633i	0.481056	−	0.876690i	$-0.340253\pi$
$569$	−9.43733	−	9.43733i	−0.395633	−	0.395633i	−0.876690	+	0.481056i	$0.840253\pi$
$570$	7.62731	+	20.3371i	0.319473	+	0.851828i
$571$	−3.05157	+	5.28548i	−0.127704	+	0.221190i	−0.922787	−	0.385311i	$-0.874094\pi$
$571$	−3.05157	+	5.28548i	−0.127704	+	0.221190i	0.795083	+	0.606501i	$0.207428\pi$
$572$	11.0527	−	19.1439i	0.462138	−	0.800447i
$573$	−7.39000	−	12.7999i	−0.308722	−	0.534722i
$574$	−10.0164	−	2.68388i	−0.418075	−	0.112023i
$575$	−0.620538	+	1.81414i	−0.0258782	+	0.0756551i
$576$	0.332689	+	0.192078i	0.0138620	+	0.00800325i
$577$	−0.722081	+	1.25068i	−0.0300606	+	0.0520665i	−0.880664	−	0.473741i	$-0.842903\pi$
$577$	−0.722081	+	1.25068i	−0.0300606	+	0.0520665i	0.850604	+	0.525807i	$0.176237\pi$
$578$		−	1.83228i		−	0.0762126i
$579$	4.47094	−	16.6858i	0.185806	−	0.693437i
$580$	−7.61698	+	16.7590i	−0.316278	+	0.695882i
$581$	−14.3699			−0.596165
$582$	−5.01297	−	5.01297i	−0.207794	−	0.207794i
$583$	11.0639	+	41.2909i	0.458219	+	1.71010i
$584$	9.61059	+	9.61059i	0.397689	+	0.397689i
$585$	3.45624	+	0.574765i	0.142898	+	0.0237636i
$586$	−6.47783	+	6.47783i	−0.267597	+	0.267597i
$587$	7.89250	−	4.55674i	0.325758	−	0.188077i	−0.328198	−	0.944609i	$-0.606441\pi$
$587$	7.89250	−	4.55674i	0.325758	−	0.188077i	0.653956	+	0.756532i	$0.273108\pi$
$588$	−2.37268	+	8.85495i	−0.0978476	+	0.365172i
$589$	−25.2390	+	14.5718i	−1.03996	+	0.600419i
$590$	10.1693	−	22.3747i	0.418662	−	0.921151i
$591$		−	2.81000i		−	0.115588i
$592$	3.35460	+	5.07412i	0.137873	+	0.208545i
$593$	−12.0803	−	12.0803i	−0.496078	−	0.496078i	0.414136	−	0.910215i	$-0.364084\pi$
$593$	−12.0803	−	12.0803i	−0.496078	−	0.496078i	−0.910215	+	0.414136i	$0.864084\pi$
$594$	28.6527	−	7.67747i	1.17564	−	0.315010i
$595$	8.17624	−	5.84461i	0.335193	−	0.239606i
$596$	6.23713	−	3.60101i	0.255483	−	0.147503i
$597$	12.4207	+	21.5133i	0.508346	+	0.880482i
$598$			1.56409i			0.0639606i
$599$	17.9905	−	10.3868i	0.735073	−	0.424395i	−0.0852021	−	0.996364i	$-0.527154\pi$
$599$	17.9905	−	10.3868i	0.735073	−	0.424395i	0.820275	+	0.571969i	$0.193820\pi$
$600$	−4.50843	+	6.71343i	−0.184056	+	0.274075i
$601$	14.4319	−	24.9968i	0.588690	−	1.01964i	−0.405715	−	0.914000i	$-0.632977\pi$
$601$	14.4319	−	24.9968i	0.588690	−	1.01964i	0.994404	−	0.105641i	$-0.0336893\pi$
$602$	1.28323	−	1.28323i	0.0523005	−	0.0523005i
$603$	−2.81755	+	2.81755i	−0.114740	+	0.114740i
$604$	5.82441	+	3.36272i	0.236992	+	0.136827i
$605$	−40.5242	−	6.73909i	−1.64754	−	0.273983i
$606$	9.12484	−	9.12484i	0.370671	−	0.370671i
$607$	−38.4145	−	22.1786i	−1.55920	−	0.900203i	−0.997334	−	0.0729719i	$-0.976752\pi$
$607$	−38.4145	−	22.1786i	−1.55920	−	0.900203i	−0.561863	−	0.827231i	$-0.689915\pi$
$608$	5.80123	−	1.55443i	0.235271	−	0.0630406i
$609$	−3.97723	−	14.8432i	−0.161165	−	0.601478i
$610$	11.5623	+	16.1750i	0.468146	+	0.654907i
$611$	4.57953	−	17.0911i	0.185268	−	0.691430i
$612$	−1.29568	−	0.748063i	−0.0523749	−	0.0302386i
$613$	2.95989	+	11.0465i	0.119549	+	0.446163i	0.999587	−	0.0287405i	$-0.00914963\pi$
$613$	2.95989	+	11.0465i	0.119549	+	0.446163i	−0.880038	+	0.474903i	$0.842483\pi$
$614$	−8.82394	−	32.9314i	−0.356105	−	1.32900i
$615$	−32.3425	+	3.14741i	−1.30417	+	0.126916i
$616$	6.04153	+	1.61882i	0.243420	+	0.0652243i
$617$	6.80561	−	1.82356i	0.273983	−	0.0734136i	−0.119211	−	0.992869i	$-0.538037\pi$
$617$	6.80561	−	1.82356i	0.273983	−	0.0734136i	0.393195	+	0.919455i	$0.371370\pi$
$618$	5.36541	+	5.36541i	0.215828	+	0.215828i
$619$	−16.6861			−0.670672			−0.335336	−	0.942099i	$-0.608850\pi$
$619$	−16.6861			−0.670672			−0.335336	+	0.942099i	$0.608850\pi$
$620$	−9.87813	−	4.48960i	−0.396715	−	0.180307i
$621$	−1.48412	+	1.48412i	−0.0595558	+	0.0595558i
$622$	−6.07987	+	22.6904i	−0.243781	+	0.909802i
$623$	17.0901			0.684700
$624$	−1.70740	+	6.37212i	−0.0683508	+	0.255089i
$625$	19.7627	+	15.3113i	0.790507	+	0.612453i
$626$	6.03304	+	10.4495i	0.241129	+	0.417647i
$627$	26.3219	−	45.5909i	1.05120	−	1.82073i
$628$	9.42091	−	9.42091i	0.375935	−	0.375935i
$629$	−13.0647	−	19.7615i	−0.520925	−	0.787944i
$630$	0.0960205	+	0.986697i	0.00382555	+	0.0393110i
$631$	0.508184	+	1.89657i	0.0202305	+	0.0755012i	0.975303	−	0.220871i	$-0.0708899\pi$
$631$	0.508184	+	1.89657i	0.0202305	+	0.0755012i	−0.955073	+	0.296372i	$0.904223\pi$
$632$	−2.28673	+	8.53421i	−0.0909614	+	0.339473i
$633$	−24.5629	−	6.58160i	−0.976286	−	0.261595i
$634$	−15.3111	−	4.10260i	−0.608083	−	0.162935i
$635$	−0.335664	−	3.44925i	−0.0133204	−	0.136879i
$636$	−6.37854	−	11.0479i	−0.252925	−	0.438080i
$637$	23.1191			0.916011
$638$	43.0973	−	11.5479i	1.70624	−	0.457185i
$639$		−	1.86143i		−	0.0736372i
$640$	1.72685	+	1.42056i	0.0682597	+	0.0561525i
$641$	−0.691853	+	1.19832i	−0.0273265	+	0.0473309i	−0.879365	−	0.476148i	$-0.842033\pi$
$641$	−0.691853	+	1.19832i	−0.0273265	+	0.0473309i	0.852039	+	0.523479i	$0.175366\pi$
$642$	2.71274	+	4.69861i	0.107063	+	0.185439i
$643$	−5.02728			−0.198256			−0.0991282	−	0.995075i	$-0.531605\pi$
$643$	−5.02728			−0.198256			−0.0991282	+	0.995075i	$0.531605\pi$
$644$	−0.427475	+	0.114542i	−0.0168449	+	0.00451357i
$645$	2.35304	−	5.17722i	0.0926509	−	0.203853i
$646$	−22.5933	+	6.05386i	−0.888922	+	0.238186i
$647$	−33.9690	+	19.6120i	−1.33546	+	0.771029i	−0.986131	−	0.165971i	$-0.946924\pi$
$647$	−33.9690	+	19.6120i	−1.33546	+	0.771029i	−0.349330	+	0.937000i	$0.613591\pi$
$648$	−6.66836	+	3.84998i	−0.261958	+	0.151241i
$649$	−57.5384	+	15.4174i	−2.25858	+	0.605184i
$650$	19.2964	+	6.60045i	0.756869	+	0.258891i
$651$	8.74890	−	2.34426i	0.342896	−	0.0918788i
$652$	−4.49194			−0.175918
$653$	−5.72522	−	9.91638i	−0.224045	−	0.388058i	0.731987	−	0.681318i	$-0.238593\pi$
$653$	−5.72522	−	9.91638i	−0.224045	−	0.388058i	−0.956033	+	0.293260i	$0.905260\pi$
$654$	6.75249	−	11.6957i	0.264043	−	0.457336i
$655$	−3.15495	−	32.4200i	−0.123274	−	1.26675i
$656$			8.98522i			0.350814i
$657$	5.04332	−	1.35135i	0.196759	−	0.0527213i
$658$	5.00644			0.195171
$659$	21.5298	+	37.2907i	0.838683	+	1.45264i	0.890996	+	0.454010i	$0.150007\pi$
$659$	21.5298	+	37.2907i	0.838683	+	1.45264i	−0.0523138	+	0.998631i	$0.516660\pi$
$660$	19.5079	−	1.89841i	0.759343	−	0.0738955i
$661$	−35.8756	−	9.61285i	−1.39540	−	0.373896i	−0.518710	−	0.854950i	$-0.673587\pi$
$661$	−35.8756	−	9.61285i	−1.39540	−	0.373896i	−0.876691	+	0.481054i	$0.840254\pi$
$662$	−0.522368	−	0.139968i	−0.0203024	−	0.00544001i
$663$	6.64961	−	24.8167i	0.258250	−	0.963801i
$664$	3.22265	+	12.0271i	0.125063	+	0.466741i
$665$	11.9693	+	9.84631i	0.464149	+	0.381823i
$666$	2.33245	−	0.141411i	0.0903805	−	0.00547955i
$667$	−2.23231	+	2.23231i	−0.0864354	+	0.0864354i
$668$	2.20707	−	3.82275i	0.0853939	−	0.147907i
$669$	9.01302	+	15.6110i	0.348463	+	0.603556i
$670$	−18.8684	+	13.4876i	−0.728949	+	0.521073i
$671$	12.4724	−	46.5477i	0.481492	−	1.79695i
$672$	−1.86657			−0.0720044
$673$	−6.31935	+	23.5841i	−0.243593	+	0.909102i	0.730492	+	0.682921i	$0.239291\pi$
$673$	−6.31935	+	23.5841i	−0.243593	+	0.909102i	−0.974085	+	0.226181i	$0.927376\pi$
$674$	−19.4844	+	19.4844i	−0.750512	+	0.750512i
$675$	12.0469	+	24.5728i	0.463684	+	0.945808i
$676$	3.63674			0.139874
$677$	26.0351	+	26.0351i	1.00061	+	1.00061i	1.00000		0.000608497i	$0.000193691\pi$
$677$	26.0351	+	26.0351i	1.00061	+	1.00061i	0.000608497		1.00000i	$0.499806\pi$
$678$	−10.6492	+	2.85345i	−0.408980	+	0.109586i
$679$	−4.88636	−	1.30930i	−0.187521	−	0.0502462i
$680$	−6.72535	−	5.53248i	−0.257905	−	0.212161i
$681$	1.48851	+	5.55521i	0.0570400	+	0.212876i
$682$	6.80656	+	25.4024i	0.260637	+	0.972710i
$683$	−44.1277	−	25.4771i	−1.68850	−	0.974855i	−0.955669	−	0.294442i	$-0.904866\pi$
$683$	−44.1277	−	25.4771i	−1.68850	−	0.974855i	−0.732829	−	0.680413i	$-0.761801\pi$
$684$	0.597146	−	2.22858i	0.0228324	−	0.0852118i
$685$	−21.9035	+	15.6572i	−0.836890	+	0.598232i
$686$	3.78395	+	14.1219i	0.144472	+	0.539176i
$687$	21.2243	−	5.68703i	0.809757	−	0.216974i
$688$	−1.36180	−	0.786233i	−0.0519180	−	0.0299749i
$689$	−22.7491	+	22.7491i	−0.866672	+	0.866672i
$690$	−1.12821	+	0.806477i	−0.0429503	+	0.0307021i
$691$	15.6154	+	9.01555i	0.594038	+	0.342968i	0.766692	−	0.642015i	$-0.221901\pi$
$691$	15.6154	+	9.01555i	0.594038	+	0.342968i	−0.172655	+	0.984982i	$0.555234\pi$
$692$	−14.4131	+	14.4131i	−0.547902	+	0.547902i
$693$	1.69901	−	1.69901i	0.0645401	−	0.0645401i
$694$	−1.34690	+	2.33291i	−0.0511278	+	0.0885559i
$695$	14.3459	−	17.4391i	0.544172	−	0.661502i
$696$	−11.5313	+	6.65758i	−0.437092	+	0.252355i
$697$		−	34.9936i		−	1.32548i
$698$	−7.85782	−	13.6101i	−0.297423	−	0.515152i
$699$	−15.0735	+	8.70271i	−0.570133	+	0.329167i
$700$	−0.390822	+	5.75718i	−0.0147717	+	0.217601i
$701$	−6.34539	+	1.70024i	−0.239662	+	0.0642173i	−0.376651	−	0.926355i	$-0.622924\pi$
$701$	−6.34539	+	1.70024i	−0.239662	+	0.0642173i	0.136989	+	0.990573i	$0.456258\pi$
$702$	15.7861	+	15.7861i	0.595809	+	0.595809i
$703$	24.2216	−	27.3482i	0.913536	−	1.03146i
$704$		−	5.41958i		−	0.204258i
$705$	14.6894	−	5.50917i	0.553235	−	0.207487i
$706$	−10.2119	+	5.89584i	−0.384330	+	0.221893i
$707$	2.38324	−	8.89438i	0.0896311	−	0.334508i
$708$	15.3952	−	8.88841i	0.578586	−	0.334047i
$709$	2.12914	−	2.12914i	0.0799615	−	0.0799615i	−0.665995	−	0.745956i	$-0.731993\pi$
$709$	2.12914	−	2.12914i	0.0799615	−	0.0799615i	0.745956	+	0.665995i	$0.231993\pi$
$710$	1.77741	−	10.6881i	0.0667050	−	0.401118i
$711$	2.40001	+	2.40001i	0.0900073	+	0.0900073i
$712$	−3.83268	−	14.3038i	−0.143636	−	0.536056i
$713$	−1.31577	−	1.31577i	−0.0492759	−	0.0492759i
$714$	7.26949			0.272054
$715$	−17.3576	−	46.2815i	−0.649136	−	1.73083i
$716$	5.40580	−	20.1747i	0.202024	−	0.753964i
$717$		−	34.6111i		−	1.29258i
$718$	6.33354	−	10.9700i	0.236366	−	0.409397i
$719$	14.1884	+	8.19165i	0.529137	+	0.305497i	0.740665	−	0.671875i	$-0.234511\pi$
$719$	14.1884	+	8.19165i	0.529137	+	0.305497i	−0.211528	+	0.977372i	$0.567844\pi$
$720$	0.804295	−	0.301646i	0.0299743	−	0.0112417i
$721$	5.22990	+	1.40135i	0.194772	+	0.0521889i
$722$	−8.53525	−	14.7835i	−0.317649	−	0.550185i
$723$	5.90046	−	10.2199i	0.219441	−	0.380082i
$724$	2.80922	−	4.86571i	0.104404	−	0.180833i
$725$	18.1200	+	36.9606i	0.672960	+	1.37268i
$726$	−21.0109	−	21.0109i	−0.779786	−	0.779786i
$727$	−17.3691	+	10.0281i	−0.644184	+	0.371920i	−0.786225	−	0.617941i	$-0.787967\pi$
$727$	−17.3691	+	10.0281i	−0.644184	+	0.371920i	0.142040	+	0.989861i	$0.454634\pi$
$728$	1.21834	+	4.54690i	0.0451546	+	0.168519i
$729$			29.5153i			1.09316i
$730$	30.2484	−	2.94363i	1.11955	−	0.108949i
$731$	5.30362	+	3.06205i	0.196161	+	0.113254i
$732$			14.3812i			0.531544i
$733$	9.75335	+	2.61340i	0.360248	+	0.0965283i	0.434403	−	0.900718i	$-0.356959\pi$
$733$	9.75335	+	2.61340i	0.360248	+	0.0965283i	−0.0741549	+	0.997247i	$0.523626\pi$
$734$	14.5934	+	14.5934i	0.538651	+	0.538651i
$735$	11.9206	+	16.6762i	0.439700	+	0.615113i
$736$	0.191734	+	0.332093i	0.00706740	+	0.0122411i
$737$	54.2986	+	14.5493i	2.00011	+	0.535929i
$738$	2.98929	+	1.72586i	0.110037	+	0.0635300i
$739$	10.7871			0.396811			0.198405	−	0.980120i	$-0.436424\pi$
$739$	10.7871			0.396811			0.198405	+	0.980120i	$0.436424\pi$
$740$	13.5276	+	1.41520i	0.497286	+	0.0520239i
$741$	39.6201			1.45548
$742$	−7.88340	−	4.55148i	−0.289409	−	0.167090i
$743$	−26.6221	−	7.13337i	−0.976669	−	0.261698i	−0.265028	−	0.964241i	$-0.585381\pi$
$743$	−26.6221	−	7.13337i	−0.976669	−	0.261698i	−0.711641	+	0.702543i	$0.752048\pi$
$744$	−3.92412	−	6.79677i	−0.143865	−	0.249182i
$745$	2.64181	−	15.8860i	0.0967885	−	0.582019i
$746$	−24.3985	−	24.3985i	−0.893293	−	0.893293i
$747$	4.62028	+	1.23800i	0.169047	+	0.0452960i
$748$			21.1070i			0.771747i
$749$	3.35275	+	1.93571i	0.122507	+	0.0707293i
$750$	5.18858	+	17.3222i	0.189460	+	0.632518i
$751$		−	21.2874i		−	0.776790i	−0.921493	−	0.388395i	$-0.873030\pi$
$751$		−	21.2874i		−	0.776790i	0.921493	−	0.388395i	$-0.126970\pi$
$752$	−1.12276	−	4.19020i	−0.0409429	−	0.152801i
$753$	−8.99193	+	5.19149i	−0.327684	+	0.189188i
$754$	23.7443	+	23.7443i	0.864717	+	0.864717i
$755$	14.0808	−	5.28093i	0.512454	−	0.192193i
$756$	−3.15838	+	5.47047i	−0.114869	+	0.198959i
$757$	15.0584	−	26.0820i	0.547308	−	0.947966i	−0.451149	−	0.892448i	$-0.648986\pi$
$757$	15.0584	−	26.0820i	0.547308	−	0.947966i	0.998458	−	0.0555175i	$-0.0176809\pi$
$758$	2.68408	+	4.64897i	0.0974904	+	0.168858i
$759$	3.24672	+	0.869955i	0.117848	+	0.0315774i
$760$	5.55672	−	12.2260i	0.201563	−	0.443484i
$761$	−38.3547	−	22.1441i	−1.39036	−	0.802723i	−0.397003	−	0.917817i	$-0.629950\pi$
$761$	−38.3547	−	22.1441i	−1.39036	−	0.802723i	−0.993355	+	0.115094i	$0.963283\pi$
$762$	1.25332	−	2.17081i	0.0454030	−	0.0786403i
$763$		−	9.63664i		−	0.348870i
$764$	−2.36518	+	8.82698i	−0.0855693	+	0.319349i
$765$	−3.13239	+	1.17478i	−0.113252	+	0.0424743i
$766$	34.0390			1.22988
$767$	−31.7006	−	31.7006i	−1.14464	−	1.14464i
$768$	0.418603	+	1.56225i	0.0151050	+	0.0563727i
$769$	−17.1063	−	17.1063i	−0.616870	−	0.616870i	0.327857	−	0.944727i	$-0.393673\pi$
$769$	−17.1063	−	17.1063i	−0.616870	−	0.616870i	−0.944727	+	0.327857i	$0.893673\pi$
$770$	11.3778	−	8.13319i	0.410028	−	0.293100i
$771$	−14.3599	+	14.3599i	−0.517159	+	0.517159i
$772$	−9.24969	+	5.34031i	−0.332904	+	0.192202i
$773$	−2.68374	+	10.0159i	−0.0965276	+	0.360246i	−0.997247	−	0.0741563i	$-0.976374\pi$
$773$	−2.68374	+	10.0159i	−0.0965276	+	0.360246i	0.900719	+	0.434402i	$0.143040\pi$
$774$	−0.523143	+	0.302036i	−0.0188040	+	0.0108565i
$775$	−21.7853	+	10.6803i	−0.782553	+	0.383648i
$776$			4.38333i			0.157352i
$777$	−9.47119	+	6.26158i	−0.339777	+	0.224633i
$778$	12.8513	+	12.8513i	0.460742	+	0.460742i
$779$	52.1253	−	13.9669i	1.86758	−	0.500418i
$780$	8.57822	+	12.0004i	0.307150	+	0.429683i
$781$	−22.7424	+	13.1303i	−0.813786	+	0.469840i
$782$	−0.746722	−	1.29336i	−0.0267027	−	0.0462505i
$783$			45.0606i			1.61033i
$784$	4.90871	−	2.83404i	0.175311	−	0.101216i
$785$	−2.88553	−	29.6515i	−0.102989	−	1.05831i
$786$	11.7801	−	20.4038i	0.420184	−	0.727779i
$787$	24.1983	−	24.1983i	0.862577	−	0.862577i	−0.129060	−	0.991637i	$-0.541196\pi$
$787$	24.1983	−	24.1983i	0.862577	−	0.862577i	0.991637	+	0.129060i	$0.0411959\pi$
$788$	−1.22853	+	1.22853i	−0.0437645	+	0.0437645i
$789$	−9.67317	−	5.58481i	−0.344374	−	0.198824i
$790$	11.4889	+	16.0722i	0.408755	+	0.571823i
$791$	−5.56276	+	5.56276i	−0.197789	+	0.197789i
$792$	−1.80304	−	1.04098i	−0.0640681	−	0.0369897i
$793$	35.0321	−	9.38683i	1.24403	−	0.333336i
$794$	−8.37064	−	31.2396i	−0.297063	−	1.10865i
$795$	−28.1392	−	4.67950i	−0.997996	−	0.165965i
$796$	3.97528	−	14.8359i	0.140900	−	0.525846i
$797$	−34.9981	−	20.2061i	−1.23969	−	0.715738i	−0.270663	−	0.962674i	$-0.587243\pi$
$797$	−34.9981	−	20.2061i	−1.23969	−	0.715738i	−0.969032	+	0.246936i	$0.920576\pi$
$798$	2.90146	+	10.8284i	0.102710	+	0.383321i
$799$	4.37268	+	16.3191i	0.154694	+	0.577327i
$800$	4.90619	−	0.964021i	0.173460	−	0.0340833i
$801$	−5.49488	−	1.47235i	−0.194152	−	0.0520229i
$802$	−25.5620	+	6.84933i	−0.902627	+	0.241858i
$803$	−52.0853	−	52.0853i	−1.83805	−	1.83805i
$804$	−16.7759			−0.591639
$805$	−0.409457	+	0.900898i	−0.0144315	+	0.0317525i
$806$	−13.9954	+	13.9954i	−0.492967	+	0.492967i
$807$	−10.4911	+	39.1534i	−0.369305	+	1.37826i
$808$	−7.97874			−0.280691
$809$	−11.8811	+	44.3407i	−0.417716	+	1.55894i	0.361618	+	0.932327i	$0.382225\pi$
$809$	−11.8811	+	44.3407i	−0.417716	+	1.55894i	−0.779333	+	0.626610i	$0.784442\pi$
$810$	−2.82447	+	16.9844i	−0.0992416	+	0.596770i
$811$	−19.0531	−	33.0009i	−0.669044	−	1.15882i	−0.978172	−	0.207798i	$-0.933370\pi$
$811$	−19.0531	−	33.0009i	−0.669044	−	1.15882i	0.309128	−	0.951021i	$-0.399963\pi$
$812$	−4.75060	+	8.22828i	−0.166713	+	0.288756i
$813$	−20.3738	+	20.3738i	−0.714541	+	0.714541i
$814$	−18.1805	−	27.4996i	−0.637226	−	0.963860i
$815$	−6.38106	+	7.75690i	−0.223519	+	0.271712i
$816$	−1.63028	−	6.08429i	−0.0570712	−	0.212993i
$817$	−2.44430	+	9.12224i	−0.0855151	+	0.319147i
$818$	−33.4605	−	8.96573i	−1.16992	−	0.313479i
$819$	1.74672	+	0.468032i	0.0610354	+	0.0163544i
$820$	15.5161	+	12.7640i	0.541847	+	0.445740i
$821$	17.6107	+	30.5026i	0.614618	+	1.06455i	0.990451	+	0.137862i	$0.0440231\pi$
$821$	17.6107	+	30.5026i	0.614618	+	1.06455i	−0.375834	+	0.926687i	$0.622644\pi$
$822$	−19.4744			−0.679247
$823$	−7.57375	+	2.02938i	−0.264004	+	0.0707397i	−0.388393	−	0.921494i	$-0.626970\pi$
$823$	−7.57375	+	2.02938i	−0.264004	+	0.0707397i	0.124389	+	0.992234i	$0.460303\pi$
$824$		−	4.69150i		−	0.163436i
$825$	24.4338	−	36.3840i	0.850677	−	1.26673i
$826$	6.34243	−	10.9854i	0.220681	−	0.382231i
$827$	−11.7277	−	20.3129i	−0.407811	−	0.706349i	0.586834	−	0.809708i	$-0.300374\pi$
$827$	−11.7277	−	20.3129i	−0.407811	−	0.706349i	−0.994644	+	0.103359i	$0.967041\pi$
$828$	0.147312			0.00511943
$829$	−22.4913	+	6.02652i	−0.781155	+	0.209310i	−0.627294	−	0.778783i	$-0.715837\pi$
$829$	−22.4913	+	6.02652i	−0.781155	+	0.209310i	−0.153861	+	0.988093i	$0.549171\pi$
$830$	25.3469	+	11.5202i	0.879805	+	0.399871i
$831$	24.6794	−	6.61283i	0.856119	−	0.229396i
$832$	3.53236	−	2.03941i	0.122462	−	0.0707037i
$833$	−19.1173	+	11.0374i	−0.662376	+	0.382423i
$834$	15.7768	−	4.22738i	0.546306	−	0.146382i
$835$	−3.46605	−	9.24172i	−0.119947	−	0.319823i
$836$	−31.4402	+	8.42438i	−1.08738	+	0.291363i
$837$	−26.5596			−0.918036
$838$	−8.85527	−	15.3378i	−0.305900	−	0.529835i
$839$	−13.6978	+	23.7253i	−0.472900	+	0.819087i	−0.999519	−	0.0310147i	$-0.990126\pi$
$839$	−13.6978	+	23.7253i	−0.472900	+	0.819087i	0.526619	+	0.850101i	$0.323459\pi$
$840$	−2.65157	+	3.22328i	−0.0914879	+	0.111214i
$841$			38.7768i			1.33713i
$842$	17.2111	−	4.61170i	0.593133	−	0.158930i
$843$	−16.3182			−0.562029
$844$	7.86139	+	13.6163i	0.270600	+	0.468693i
$845$	5.16620	−	6.28010i	0.177723	−	0.216042i
$846$	−1.60969	−	0.431315i	−0.0553423	−	0.0148289i
$847$	−20.4802	−	5.48766i	−0.703709	−	0.188558i
$848$	−2.04146	+	7.61884i	−0.0701041	+	0.261632i
$849$	7.75517	+	28.9427i	0.266157	+	0.993310i
$850$	−19.1075	+	3.75445i	−0.655382	+	0.128777i
$851$	2.08692	+	1.04189i	0.0715386	+	0.0357155i
$852$	5.54154	−	5.54154i	0.189850	−	0.189850i
$853$	−9.40340	+	16.2872i	−0.321966	+	0.557662i	−0.980894	−	0.194544i	$-0.937677\pi$
$853$	−9.40340	+	16.2872i	−0.321966	+	0.557662i	0.658927	+	0.752207i	$0.271010\pi$
$854$	5.13093	+	8.88704i	0.175577	+	0.304108i
$855$	−3.00014	−	4.19701i	−0.102603	−	0.143535i
$856$	0.868218	−	3.24023i	0.0296751	−	0.110749i
$857$	33.0001			1.12726			0.563631	−	0.826027i	$-0.309404\pi$
$857$	33.0001			1.12726			0.563631	+	0.826027i	$0.309404\pi$
$858$	9.25341	−	34.5342i	0.315906	−	1.17898i
$859$	−14.9683	+	14.9683i	−0.510713	+	0.510713i	−0.914745	−	0.404032i	$-0.867608\pi$
$859$	−14.9683	+	14.9683i	−0.510713	+	0.510713i	0.404032	+	0.914745i	$0.367608\pi$
$860$	−3.29222	+	1.23473i	−0.112264	+	0.0421038i
$861$	−16.7715			−0.571572
$862$	7.92381	+	7.92381i	0.269886	+	0.269886i
$863$	−9.75362	+	2.61347i	−0.332017	+	0.0889637i	−0.420977	−	0.907072i	$-0.638313\pi$
$863$	−9.75362	+	2.61347i	−0.332017	+	0.0889637i	0.0889594	+	0.996035i	$0.471646\pi$
$864$	5.28689	+	1.41662i	0.179864	+	0.0481943i
$865$	4.41458	+	45.3638i	0.150100	+	1.54241i
$866$	1.32648	+	4.95048i	0.0450755	+	0.168224i
$867$	−0.766996	−	2.86247i	−0.0260485	−	0.0972145i
$868$	−4.84992	−	2.80010i	−0.164617	−	0.0950416i
$869$	12.3931	−	46.2518i	0.420409	−	1.56899i
$870$	−4.88421	+	29.3703i	−0.165590	+	0.995745i
$871$	10.9499	+	40.8655i	0.371022	+	1.38467i
$872$	−8.06551	+	2.16115i	−0.273133	+	0.0731857i
$873$	1.45829	+	0.841941i	0.0493555	+	0.0284954i
$874$	1.62851	−	1.62851i	0.0550851	−	0.0550851i
$875$	9.38659	+	8.85330i	0.317325	+	0.299296i
$876$	19.0371	+	10.9911i	0.643205	+	0.371355i
$877$	12.2589	−	12.2589i	0.413952	−	0.413952i	−0.469161	−	0.883113i	$-0.655444\pi$
$877$	12.2589	−	12.2589i	0.413952	−	0.413952i	0.883113	+	0.469161i	$0.155444\pi$
$878$	−12.7296	+	12.7296i	−0.429602	+	0.429602i
$879$	−7.40834	+	12.8316i	−0.249877	+	0.432800i
$880$	−9.35880	−	7.69884i	−0.315485	−	0.259528i
$881$	−4.48347	+	2.58853i	−0.151052	+	0.0872099i	−0.573621	−	0.819121i	$-0.694462\pi$
$881$	−4.48347	+	2.58853i	−0.151052	+	0.0872099i	0.422569	+	0.906331i	$0.361128\pi$
$882$		−	2.17743i		−	0.0733179i
$883$	16.0468	+	27.7939i	0.540017	+	0.935338i	0.998902	+	0.0468420i	$0.0149157\pi$
$883$	16.0468	+	27.7939i	0.540017	+	0.935338i	−0.458885	+	0.888496i	$0.651751\pi$
$884$	−13.7570	+	7.94263i	−0.462699	+	0.267140i
$885$	6.52082	−	39.2117i	0.219195	−	1.31809i
$886$	−13.0304	+	3.49150i	−0.437766	+	0.117299i
$887$	−28.3782	−	28.3782i	−0.952845	−	0.952845i	0.0460918	−	0.998937i	$-0.485323\pi$
$887$	−28.3782	−	28.3782i	−0.952845	−	0.952845i	−0.998937	+	0.0460918i	$0.985323\pi$
$888$	7.36475	+	6.52278i	0.247145	+	0.218890i
$889$		−	1.78864i		−	0.0599892i
$890$	−30.1450	−	13.7009i	−1.01046	−	0.459255i
$891$	36.1397	−	20.8653i	1.21073	−	0.699013i
$892$	2.88463	−	10.7656i	0.0965846	−	0.360459i
$893$	−22.5630	+	13.0268i	−0.755043	+	0.435925i
$894$	8.23654	−	8.23654i	0.275471	−	0.275471i
$895$	−27.1594	−	37.9944i	−0.907840	−	1.27001i
$896$	0.816061	+	0.816061i	0.0272627	+	0.0272627i
$897$	0.654734	+	2.44350i	0.0218609	+	0.0815861i
$898$	14.6629	+	14.6629i	0.489306	+	0.489306i
$899$	−39.9491			−1.33238
$900$	0.621652	−	1.81740i	0.0207217	−	0.0605801i
$901$	7.95063	−	29.6722i	0.264874	−	0.988523i
$902$		−	48.6961i		−	1.62140i
$903$	1.46756	−	2.54188i	0.0488373	−	0.0845886i
$904$	5.90335	+	3.40830i	0.196342	+	0.113358i
$905$	−4.41169	−	11.7631i	−0.146649	−	0.391020i
$906$	10.5068	+	2.81529i	0.349065	+	0.0935318i
$907$	0.958632	+	1.66040i	0.0318308	+	0.0551326i	0.881502	−	0.472180i	$-0.156533\pi$
$907$	0.958632	+	1.66040i	0.0318308	+	0.0551326i	−0.849671	+	0.527313i	$0.823200\pi$
$908$	1.77796	−	3.07951i	0.0590035	−	0.102197i
$909$	−1.53254	+	2.65444i	−0.0508312	+	0.0880422i
$910$	9.58254	+	4.35526i	0.317658	+	0.144375i
$911$	−16.5788	−	16.5788i	−0.549281	−	0.549281i	0.376952	−	0.926233i	$-0.376972\pi$
$911$	−16.5788	−	16.5788i	−0.549281	−	0.549281i	−0.926233	+	0.376952i	$0.876972\pi$
$912$	8.41226	−	4.85682i	0.278558	−	0.160825i
$913$	−17.4654	−	65.1817i	−0.578020	−	2.15720i
$914$		−	4.25512i		−	0.140747i
$915$	24.8341	+	20.4293i	0.820991	+	0.675373i
$916$	−11.7656	−	6.79287i	−0.388746	−	0.224443i
$917$		−	16.8117i		−	0.555172i
$918$	−20.5902	−	5.51712i	−0.679577	−	0.182092i
$919$	−36.7182	−	36.7182i	−1.21122	−	1.21122i	−0.970626	−	0.240594i	$-0.922658\pi$
$919$	−36.7182	−	36.7182i	−1.21122	−	1.21122i	−0.240594	−	0.970626i	$-0.577342\pi$
$920$	0.845844	+	0.140662i	0.0278866	+	0.00463749i
$921$	−27.5704	−	47.7533i	−0.908474	−	1.57352i
$922$	−22.9371	−	6.14596i	−0.755392	−	0.202407i
$923$	−17.1161	−	9.88197i	−0.563383	−	0.325269i
$924$	10.1160			0.332792
$925$	21.6607	−	21.3498i	0.712198	−	0.701978i
$926$	−26.3755			−0.866751
$927$	−1.56081	−	0.901135i	−0.0512638	−	0.0295971i
$928$	7.95215	+	2.13077i	0.261042	+	0.0699460i
$929$	10.8007	+	18.7074i	0.354360	+	0.613770i	0.987008	−	0.160670i	$-0.0513654\pi$
$929$	10.8007	+	18.7074i	0.354360	+	0.613770i	−0.632648	+	0.774439i	$0.718032\pi$
$930$	−17.3114	−	2.87886i	−0.567664	−	0.0944014i
$931$	−24.0712	−	24.0712i	−0.788902	−	0.788902i
$932$	10.3949	+	2.78532i	0.340498	+	0.0912361i
$933$			37.9931i			1.24384i
$934$	−4.17701	−	2.41160i	−0.136676	−	0.0789100i
$935$	36.4486	+	29.9837i	1.19200	+	0.980572i
$936$		−	1.56690i		−	0.0512158i
$937$	2.72206	+	10.1589i	0.0889258	+	0.331876i	0.996029	−	0.0890335i	$-0.0283778\pi$
$937$	2.72206	+	10.1589i	0.0889258	+	0.331876i	−0.907103	+	0.420909i	$0.861711\pi$
$938$	−10.3669	+	5.98531i	−0.338490	+	0.195427i
$939$	13.7993	+	13.7993i	0.450323	+	0.450323i
$940$	−8.83079	−	4.01359i	−0.288029	−	0.130909i
$941$	−20.8136	+	36.0502i	−0.678504	+	1.17520i	0.296927	+	0.954900i	$0.404038\pi$
$941$	−20.8136	+	36.0502i	−0.678504	+	1.17520i	−0.975431	+	0.220304i	$0.929295\pi$
$942$	10.7742	−	18.6614i	0.351041	−	0.608021i
$943$	1.72277	+	2.98393i	0.0561012	+	0.0971701i
$944$	−10.6168	−	2.84475i	−0.345546	−	0.0925887i
$945$	4.96002	+	13.2252i	0.161349	+	0.430215i
$946$	7.38036	+	4.26106i	0.239956	+	0.138539i
$947$	−11.6606	+	20.1967i	−0.378917	+	0.656304i	−0.990905	−	0.134564i	$-0.957037\pi$
$947$	−11.6606	+	20.1967i	−0.378917	+	0.656304i	0.611988	+	0.790867i	$0.290370\pi$
$948$			14.2898i			0.464110i
$949$	14.3481	−	53.5479i	0.465760	−	1.73824i
$950$	−13.2188	−	26.9634i	−0.428876	−	0.874808i
$951$	−25.6371			−0.831341
$952$	−3.17821	−	3.17821i	−0.103006	−	0.103006i
$953$	−2.68937	−	10.0369i	−0.0871174	−	0.325126i	0.908589	−	0.417690i	$-0.137160\pi$
$953$	−2.68937	−	10.0369i	−0.0871174	−	0.325126i	−0.995707	+	0.0925641i	$0.970494\pi$
$954$	2.14258	+	2.14258i	0.0693687	+	0.0693687i
$955$	11.8830	+	16.6236i	0.384524	+	0.537926i
$956$	−15.1319	+	15.1319i	−0.489402	+	0.489402i
$957$	62.4946	−	36.0813i	2.02016	−	1.16634i
$958$	−10.5344	+	39.3150i	−0.340352	+	1.27021i
$959$	−12.0345	+	6.94809i	−0.388613	+	0.224366i
$960$	3.29242	+	1.49640i	0.106262	+	0.0482961i
$961$			7.45320i			0.240426i
$962$	11.0822	−	22.1978i	0.357305	−	0.715687i
$963$	−0.911225	−	0.911225i	−0.0293638	−	0.0293638i
$964$	−7.04781	+	1.88845i	−0.226995	+	0.0608230i
$965$	−3.91782	+	23.5591i	−0.126119	+	0.758393i
$966$	−0.619874	+	0.357884i	−0.0199441	+	0.0115147i
$967$	11.1090	+	19.2414i	0.357242	+	0.618761i	0.987499	−	0.157625i	$-0.0503838\pi$
$967$	11.1090	+	19.2414i	0.357242	+	0.618761i	−0.630257	+	0.776387i	$0.717050\pi$
$968$			18.3719i			0.590494i
$969$	−32.7622	+	18.9153i	−1.05247	+	0.607646i
$970$	7.56935	+	6.22678i	0.243037	+	0.199930i
$971$	−5.81973	+	10.0801i	−0.186764	+	0.323485i	−0.944170	−	0.329460i	$-0.893133\pi$
$971$	−5.81973	+	10.0801i	−0.186764	+	0.323485i	0.757405	+	0.652945i	$0.226467\pi$
$972$	2.80480	−	2.80480i	0.0899641	−	0.0899641i
$973$	8.24123	−	8.24123i	0.264202	−	0.264202i
$974$	12.1303	+	7.00341i	0.388679	+	0.224404i
$975$	32.9088	+	2.23399i	1.05392	+	0.0715449i
$976$	6.28744	−	6.28744i	0.201256	−	0.201256i
$977$	47.1628	+	27.2295i	1.50887	+	0.871147i	0.999947	+	0.0103367i	$0.00329033\pi$
$977$	47.1628	+	27.2295i	1.50887	+	0.871147i	0.508925	+	0.860811i	$0.330043\pi$
$978$	−7.01751	+	1.88034i	−0.224395	+	0.0601266i
$979$	20.7715	+	77.5204i	0.663861	+	2.47756i
$980$	2.07914	−	12.5025i	0.0664158	−	0.399379i
$981$	−0.830218	+	3.09842i	−0.0265068	+	0.0989248i
$982$	−12.8319	−	7.40852i	−0.409483	−	0.236415i
$983$	−4.14789	−	15.4801i	−0.132297	−	0.493740i	0.867697	−	0.497093i	$-0.165599\pi$
$983$	−4.14789	−	15.4801i	−0.132297	−	0.493740i	−0.999994	+	0.00335334i	$0.998933\pi$
$984$	3.76124	+	14.0371i	0.119904	+	0.447488i
$985$	0.376286	+	3.86668i	0.0119895	+	0.123203i
$986$	−30.9702	−	8.29845i	−0.986293	−	0.264277i
$987$	7.82129	−	2.09571i	0.248954	−	0.0667071i
$988$	−17.3219	−	17.3219i	−0.551083	−	0.551083i
$989$	−0.602990			−0.0191740
$990$	−4.35894	+	1.63479i	−0.138536	+	0.0519571i
$991$	−18.9057	+	18.9057i	−0.600559	+	0.600559i	−0.940461	−	0.339902i	$-0.889606\pi$
$991$	−18.9057	+	18.9057i	−0.600559	+	0.600559i	0.339902	+	0.940461i	$0.389606\pi$
$992$	−1.25592	+	4.68716i	−0.0398755	+	0.148817i
$993$	−0.874659			−0.0277565
$994$	1.44735	−	5.40159i	0.0459072	−	0.171328i
$995$	−19.9723	−	27.9400i	−0.633165	−	0.885758i
$996$	10.0691	+	17.4403i	0.319053	+	0.552616i
$997$	12.9756	−	22.4744i	0.410942	−	0.711772i	−0.584051	−	0.811717i	$-0.698533\pi$
$997$	12.9756	−	22.4744i	0.410942	−	0.711772i	0.994993	+	0.0999446i	$0.0318666\pi$
$998$	24.0931	−	24.0931i	0.762654	−	0.762654i
$999$	31.5785	−	10.5473i	0.999099	−	0.333702i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.r.f.23.4	yes	32
5.2	odd	4		370.2.q.f.97.4	✓	32
37.29	odd	12		370.2.q.f.103.4	yes	32
185.177	even	12	inner	370.2.r.f.177.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.q.f.97.4	✓	32	5.2	odd	4
370.2.q.f.103.4	yes	32	37.29	odd	12
370.2.r.f.23.4	yes	32	1.1	even	1	trivial
370.2.r.f.177.4	yes	32	185.177	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	370.2.r.f.23.4

Level	$370$
Weight	$2$
Character	370.23
Analytic conductor	$2.954$
Analytic rank	$0$
Dimension	$32$
Inner twists	$2$