LMFDB - Embedded newform 735.2.u.b.106.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(106,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("735.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.u (of order $7$, degree $6$, 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:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			106.1
Character	$\chi$	$=$	735.106
Dual form			735.2.u.b.631.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.50084 - 1.88200i) q^{2} +(-0.900969 + 0.433884i) q^{3} +(-0.844346 + 3.69932i) q^{4} +(-0.900969 + 0.433884i) q^{5} +(2.16878 + 1.04443i) q^{6} +(-2.16503 + 1.52074i) q^{7} +(3.89178 - 1.87418i) q^{8} +(0.623490 - 0.781831i) q^{9} +(2.16878 + 1.04443i) q^{10} +(-2.93244 - 3.67717i) q^{11} +(-0.844346 - 3.69932i) q^{12} +(2.81613 + 3.53131i) q^{13} +(6.11140 + 1.79219i) q^{14} +(0.623490 - 0.781831i) q^{15} +(-2.53080 - 1.21877i) q^{16} +(1.61025 + 7.05496i) q^{17} -2.40717 q^{18} +2.14887 q^{19} +(-0.844346 - 3.69932i) q^{20} +(1.29080 - 2.30951i) q^{21} +(-2.51929 + 11.0377i) q^{22} +(0.660647 - 2.89448i) q^{23} +(-2.69320 + 3.37716i) q^{24} +(0.623490 - 0.781831i) q^{25} +(2.41936 - 10.5999i) q^{26} +(-0.222521 + 0.974928i) q^{27} +(-3.79767 - 9.29317i) q^{28} +(-1.59837 - 7.00292i) q^{29} -2.40717 q^{30} -8.49514 q^{31} +(-0.417766 - 1.83035i) q^{32} +(4.23750 + 2.04067i) q^{33} +(10.8607 - 13.6189i) q^{34} +(1.29080 - 2.30951i) q^{35} +(2.36580 + 2.96662i) q^{36} +(-0.0872805 - 0.382401i) q^{37} +(-3.22512 - 4.04417i) q^{38} +(-4.06942 - 1.95973i) q^{39} +(-2.69320 + 3.37716i) q^{40} +(4.88280 - 2.35143i) q^{41} +(-6.28379 + 1.03693i) q^{42} +(-5.84672 - 2.81563i) q^{43} +(16.0790 - 7.74324i) q^{44} +(-0.222521 + 0.974928i) q^{45} +(-6.43894 + 3.10083i) q^{46} +(-3.63290 - 4.55551i) q^{47} +2.80898 q^{48} +(2.37470 - 6.58489i) q^{49} -2.40717 q^{50} +(-4.51181 - 5.65764i) q^{51} +(-15.4413 + 7.43611i) q^{52} +(-0.226187 + 0.990992i) q^{53} +(2.16878 - 1.04443i) q^{54} +(4.23750 + 2.04067i) q^{55} +(-5.57568 + 9.97606i) q^{56} +(-1.93606 + 0.932359i) q^{57} +(-10.7806 + 13.5184i) q^{58} +(-2.11761 - 1.01979i) q^{59} +(2.36580 + 2.96662i) q^{60} +(-2.52071 - 11.0440i) q^{61} +(12.7499 + 15.9878i) q^{62} +(-0.160911 + 2.64085i) q^{63} +(-6.32046 + 7.92561i) q^{64} +(-4.06942 - 1.95973i) q^{65} +(-2.51929 - 11.0377i) q^{66} +2.09747 q^{67} -27.4582 q^{68} +(0.660647 + 2.89448i) q^{69} +(-6.28379 + 1.03693i) q^{70} +(0.395941 - 1.73473i) q^{71} +(0.961191 - 4.21125i) q^{72} +(0.932407 - 1.16920i) q^{73} +(-0.588684 + 0.738186i) q^{74} +(-0.222521 + 0.974928i) q^{75} +(-1.81439 + 7.94935i) q^{76} +(11.9408 + 3.50169i) q^{77} +(2.41936 + 10.5999i) q^{78} +15.9492 q^{79} +2.80898 q^{80} +(-0.222521 - 0.974928i) q^{81} +(-11.7537 - 5.66029i) q^{82} +(5.06550 - 6.35193i) q^{83} +(7.45374 + 6.72511i) q^{84} +(-4.51181 - 5.65764i) q^{85} +(3.47600 + 15.2294i) q^{86} +(4.47854 + 5.61591i) q^{87} +(-18.3041 - 8.81480i) q^{88} +(-7.24944 + 9.09051i) q^{89} +(2.16878 - 1.04443i) q^{90} +(-11.4672 - 3.36280i) q^{91} +(10.1498 + 4.88789i) q^{92} +(7.65386 - 3.68590i) q^{93} +(-3.12105 + 13.6742i) q^{94} +(-1.93606 + 0.932359i) q^{95} +(1.17055 + 1.46783i) q^{96} -17.4331 q^{97} +(-15.9568 + 5.41371i) q^{98} -4.70327 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + q^{2} - 8 q^{3} - q^{4} - 8 q^{5} + q^{6} - q^{7} + 15 q^{8} - 8 q^{9} + q^{10} + 10 q^{11} - q^{12} + 20 q^{13} - q^{14} - 8 q^{15} - 15 q^{16} + 7 q^{17} - 6 q^{18} - 2 q^{19} - q^{20}+ \cdots - 32 q^{99}+O(q^{100}) $ 48 * q + q^2 - 8 * q^3 - q^4 - 8 * q^5 + q^6 - q^7 + 15 * q^8 - 8 * q^9 + q^10 + 10 * q^11 - q^12 + 20 * q^13 - q^14 - 8 * q^15 - 15 * q^16 + 7 * q^17 - 6 * q^18 - 2 * q^19 - q^20 - q^21 - 17 * q^22 + 12 * q^23 - 6 * q^24 - 8 * q^25 - 12 * q^26 - 8 * q^27 + 29 * q^28 + 12 * q^29 - 6 * q^30 - 58 * q^31 + 9 * q^32 + 3 * q^33 + 36 * q^34 - q^35 - q^36 - 15 * q^37 - 5 * q^38 - 8 * q^39 - 6 * q^40 - 2 * q^41 + 6 * q^42 + 30 * q^43 + 33 * q^44 - 8 * q^45 + 52 * q^46 + 6 * q^47 + 6 * q^48 + 13 * q^49 - 6 * q^50 - 7 * q^51 + 3 * q^53 + q^54 + 3 * q^55 - 67 * q^56 + 19 * q^57 + 36 * q^58 + 9 * q^59 - q^60 - 7 * q^61 + 14 * q^62 - 15 * q^63 + 19 * q^64 - 8 * q^65 - 17 * q^66 + 14 * q^67 + 22 * q^68 + 12 * q^69 + 6 * q^70 - 24 * q^71 - 6 * q^72 + 2 * q^73 + 2 * q^74 - 8 * q^75 + 62 * q^76 + 42 * q^77 - 12 * q^78 + 22 * q^79 + 6 * q^80 - 8 * q^81 - 51 * q^82 + 53 * q^83 + 50 * q^84 - 7 * q^85 - 35 * q^86 + 19 * q^87 + 11 * q^88 - 51 * q^89 + q^90 - q^91 + 29 * q^92 + 26 * q^93 - 4 * q^94 + 19 * q^95 + 9 * q^96 - 102 * q^97 + 90 * q^98 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{6}{7}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.50084	−	1.88200i	−1.06126	−	1.33077i	−0.941141	−	0.338015i	$-0.890245\pi$
$2$	−1.50084	−	1.88200i	−1.06126	−	1.33077i	−0.120116	−	0.992760i	$-0.538327\pi$
$3$	−0.900969	+	0.433884i	−0.520175	+	0.250503i
$3$	−0.900969	+	0.433884i	−0.520175	+	0.250503i
$4$	−0.844346	+	3.69932i	−0.422173	+	1.84966i
$5$	−0.900969	+	0.433884i	−0.402926	+	0.194039i
$5$	−0.900969	+	0.433884i	−0.402926	+	0.194039i
$6$	2.16878	+	1.04443i	0.885402	+	0.426387i
$7$	−2.16503	+	1.52074i	−0.818304	+	0.574786i
$7$	−2.16503	+	1.52074i	−0.818304	+	0.574786i
$8$	3.89178	−	1.87418i	1.37595	−	0.662624i
$9$	0.623490	−	0.781831i	0.207830	−	0.260610i
$10$	2.16878	+	1.04443i	0.685829	+	0.330278i
$11$	−2.93244	−	3.67717i	−0.884165	−	1.10871i	−0.993401	−	0.114692i	$-0.963412\pi$
$11$	−2.93244	−	3.67717i	−0.884165	−	1.10871i	0.109237	−	0.994016i	$-0.465159\pi$
$12$	−0.844346	−	3.69932i	−0.243742	−	1.06790i
$13$	2.81613	+	3.53131i	0.781054	+	0.979410i	0.999993	+	0.00367197i	$0.00116883\pi$
$13$	2.81613	+	3.53131i	0.781054	+	0.979410i	−0.218940	+	0.975738i	$0.570260\pi$
$14$	6.11140	+	1.79219i	1.63334	+	0.478983i
$15$	0.623490	−	0.781831i	0.160984	−	0.201868i
$16$	−2.53080	−	1.21877i	−0.632701	−	0.304693i
$17$	1.61025	+	7.05496i	0.390542	+	1.71108i	0.662751	+	0.748840i	$0.269389\pi$
$17$	1.61025	+	7.05496i	0.390542	+	1.71108i	−0.272208	+	0.962238i	$0.587754\pi$
$18$	−2.40717			−0.567375
$19$	2.14887			0.492984			0.246492	−	0.969145i	$-0.420722\pi$
$19$	2.14887			0.492984			0.246492	+	0.969145i	$0.420722\pi$
$20$	−0.844346	−	3.69932i	−0.188801	−	0.827193i
$21$	1.29080	−	2.30951i	0.281675	−	0.503976i
$22$	−2.51929	+	11.0377i	−0.537113	+	2.35325i
$23$	0.660647	−	2.89448i	0.137754	−	0.603542i	−0.858171	−	0.513364i	$-0.828399\pi$
$23$	0.660647	−	2.89448i	0.137754	−	0.603542i	0.995926	−	0.0901780i	$-0.0287436\pi$
$24$	−2.69320	+	3.37716i	−0.549747	+	0.689361i
$25$	0.623490	−	0.781831i	0.124698	−	0.156366i
$26$	2.41936	−	10.5999i	0.474475	−	2.07881i
$27$	−0.222521	+	0.974928i	−0.0428242	+	0.187625i
$28$	−3.79767	−	9.29317i	−0.717692	−	1.75624i
$29$	−1.59837	−	7.00292i	−0.296810	−	1.30041i	−0.874847	−	0.484399i	$-0.839038\pi$
$29$	−1.59837	−	7.00292i	−0.296810	−	1.30041i	0.578037	−	0.816011i	$-0.303819\pi$
$30$	−2.40717			−0.439487
$31$	−8.49514			−1.52577			−0.762886	−	0.646533i	$-0.776218\pi$
$31$	−8.49514			−1.52577			−0.762886	+	0.646533i	$0.776218\pi$
$32$	−0.417766	−	1.83035i	−0.0738512	−	0.323563i
$33$	4.23750	+	2.04067i	0.737654	+	0.355236i
$34$	10.8607	−	13.6189i	1.86259	−	2.33562i
$35$	1.29080	−	2.30951i	0.218185	−	0.390378i
$36$	2.36580	+	2.96662i	0.394301	+	0.494437i
$37$	−0.0872805	−	0.382401i	−0.0143488	−	0.0628663i	0.967247	−	0.253838i	$-0.0816931\pi$
$37$	−0.0872805	−	0.382401i	−0.0143488	−	0.0628663i	−0.981595	+	0.190972i	$0.938836\pi$
$38$	−3.22512	−	4.04417i	−0.523183	−	0.656051i
$39$	−4.06942	−	1.95973i	−0.651629	−	0.313808i
$40$	−2.69320	+	3.37716i	−0.425832	+	0.533976i
$41$	4.88280	−	2.35143i	0.762565	−	0.367232i	−0.0118335	−	0.999930i	$-0.503767\pi$
$41$	4.88280	−	2.35143i	0.762565	−	0.367232i	0.774399	+	0.632698i	$0.218053\pi$
$42$	−6.28379	+	1.03693i	−0.969609	+	0.160002i
$43$	−5.84672	−	2.81563i	−0.891617	−	0.429380i	−0.0687629	−	0.997633i	$-0.521905\pi$
$43$	−5.84672	−	2.81563i	−0.891617	−	0.429380i	−0.822854	+	0.568253i	$0.807619\pi$
$44$	16.0790	−	7.74324i	2.42400	−	1.16734i
$45$	−0.222521	+	0.974928i	−0.0331715	+	0.145334i
$46$	−6.43894	+	3.10083i	−0.949371	+	0.457193i
$47$	−3.63290	−	4.55551i	−0.529912	−	0.664489i	0.442768	−	0.896636i	$-0.353996\pi$
$47$	−3.63290	−	4.55551i	−0.529912	−	0.664489i	−0.972681	+	0.232147i	$0.925425\pi$
$48$	2.80898			0.405441
$49$	2.37470	−	6.58489i	0.339243	−	0.940699i
$50$	−2.40717			−0.340425
$51$	−4.51181	−	5.65764i	−0.631780	−	0.792228i
$52$	−15.4413	+	7.43611i	−2.14132	+	1.03120i
$53$	−0.226187	+	0.990992i	−0.0310692	+	0.136123i	−0.988084	−	0.153916i	$-0.950811\pi$
$53$	−0.226187	+	0.990992i	−0.0310692	+	0.136123i	0.957015	+	0.290040i	$0.0936685\pi$
$54$	2.16878	−	1.04443i	0.295134	−	0.142129i
$55$	4.23750	+	2.04067i	0.571385	+	0.275164i
$56$	−5.57568	+	9.97606i	−0.745081	+	1.33311i
$57$	−1.93606	+	0.932359i	−0.256438	+	0.123494i
$58$	−10.7806	+	13.5184i	−1.41556	+	1.77506i
$59$	−2.11761	−	1.01979i	−0.275690	−	0.132765i	0.290931	−	0.956744i	$-0.406035\pi$
$59$	−2.11761	−	1.01979i	−0.275690	−	0.132765i	−0.566620	+	0.823979i	$0.691749\pi$
$60$	2.36580	+	2.96662i	0.305424	+	0.382990i
$61$	−2.52071	−	11.0440i	−0.322744	−	1.41403i	−0.832648	−	0.553802i	$-0.813176\pi$
$61$	−2.52071	−	11.0440i	−0.322744	−	1.41403i	0.509904	−	0.860231i	$-0.329681\pi$
$62$	12.7499	+	15.9878i	1.61924	+	2.03046i
$63$	−0.160911	+	2.64085i	−0.0202729	+	0.332716i
$64$	−6.32046	+	7.92561i	−0.790057	+	0.990701i
$65$	−4.06942	−	1.95973i	−0.504750	−	0.243075i
$66$	−2.51929	−	11.0377i	−0.310103	−	1.35865i
$67$	2.09747			0.256247			0.128123	−	0.991758i	$-0.459105\pi$
$67$	2.09747			0.256247			0.128123	+	0.991758i	$0.459105\pi$
$68$	−27.4582			−3.32979
$69$	0.660647	+	2.89448i	0.0795325	+	0.348455i
$70$	−6.28379	+	1.03693i	−0.751056	+	0.123937i
$71$	0.395941	−	1.73473i	0.0469895	−	0.205875i	−0.945984	−	0.324214i	$-0.894900\pi$
$71$	0.395941	−	1.73473i	0.0469895	−	0.205875i	0.992973	+	0.118340i	$0.0377572\pi$
$72$	0.961191	−	4.21125i	0.113277	−	0.496301i
$73$	0.932407	−	1.16920i	0.109130	−	0.136845i	−0.724267	−	0.689520i	$-0.757822\pi$
$73$	0.932407	−	1.16920i	0.109130	−	0.136845i	0.833397	+	0.552675i	$0.186393\pi$
$74$	−0.588684	+	0.738186i	−0.0684331	+	0.0858124i
$75$	−0.222521	+	0.974928i	−0.0256945	+	0.112575i
$76$	−1.81439	+	7.94935i	−0.208125	+	0.911853i
$77$	11.9408	+	3.50169i	1.36078	+	0.399054i
$78$	2.41936	+	10.5999i	0.273939	+	1.20020i
$79$	15.9492			1.79443			0.897215	−	0.441594i	$-0.145587\pi$
$79$	15.9492			1.79443			0.897215	+	0.441594i	$0.145587\pi$
$80$	2.80898			0.314054
$81$	−0.222521	−	0.974928i	−0.0247245	−	0.108325i
$82$	−11.7537	−	5.66029i	−1.29798	−	0.625075i
$83$	5.06550	−	6.35193i	0.556011	−	0.697215i	−0.421804	−	0.906687i	$-0.638603\pi$
$83$	5.06550	−	6.35193i	0.556011	−	0.697215i	0.977815	+	0.209472i	$0.0671744\pi$
$84$	7.45374	+	6.72511i	0.813269	+	0.733769i
$85$	−4.51181	−	5.65764i	−0.489375	−	0.613657i
$86$	3.47600	+	15.2294i	0.374827	+	1.64222i
$87$	4.47854	+	5.61591i	0.480149	+	0.602088i
$88$	−18.3041	−	8.81480i	−1.95123	−	0.939661i
$89$	−7.24944	+	9.09051i	−0.768439	+	0.963592i	−0.999957	−	0.00923877i	$-0.997059\pi$
$89$	−7.24944	+	9.09051i	−0.768439	+	0.963592i	0.231519	+	0.972830i	$0.425631\pi$
$90$	2.16878	−	1.04443i	0.228610	−	0.110093i
$91$	−11.4672	−	3.36280i	−1.20209	−	0.352517i
$92$	10.1498	+	4.88789i	1.05819	+	0.509598i
$93$	7.65386	−	3.68590i	0.793668	−	0.382210i
$94$	−3.12105	+	13.6742i	−0.321912	+	1.41039i
$95$	−1.93606	+	0.932359i	−0.198636	+	0.0956580i
$96$	1.17055	+	1.46783i	0.119469	+	0.149810i
$97$	−17.4331			−1.77006			−0.885031	−	0.465531i	$-0.845863\pi$
$97$	−17.4331			−1.77006			−0.885031	+	0.465531i	$0.845863\pi$
$98$	−15.9568	+	5.41371i	−1.61188	+	0.546868i
$99$	−4.70327			−0.472697
$100$	2.36580	+	2.96662i	0.236580	+	0.296662i
$101$	9.55824	−	4.60301i	0.951081	−	0.458016i	0.107016	−	0.994257i	$-0.465870\pi$
$101$	9.55824	−	4.60301i	0.951081	−	0.458016i	0.844065	+	0.536241i	$0.180156\pi$
$102$	−3.87614	+	16.9825i	−0.383795	+	1.68151i
$103$	12.4658	−	6.00321i	1.22829	−	0.591514i	0.296683	−	0.954976i	$-0.404120\pi$
$103$	12.4658	−	6.00321i	1.22829	−	0.591514i	0.931609	+	0.363462i	$0.118405\pi$
$104$	17.5781	+	8.46517i	1.72367	+	0.830078i
$105$	−0.160911	+	2.64085i	−0.0157033	+	0.257721i
$106$	2.20452	−	1.06164i	0.214122	−	0.103116i
$107$	6.28761	−	7.88442i	0.607846	−	0.762215i	−0.378732	−	0.925507i	$-0.623640\pi$
$107$	6.28761	−	7.88442i	0.607846	−	0.762215i	0.986578	+	0.163291i	$0.0522111\pi$
$108$	−3.41869	−	1.64635i	−0.328963	−	0.158420i
$109$	3.29270	+	4.12891i	0.315383	+	0.395478i	0.914104	−	0.405480i	$-0.132895\pi$
$109$	3.29270	+	4.12891i	0.315383	+	0.395478i	−0.598721	+	0.800958i	$0.704324\pi$
$110$	−2.51929	−	11.0377i	−0.240204	−	1.05240i
$111$	0.244555	+	0.306662i	0.0232121	+	0.0291070i
$112$	7.33270	−	1.21002i	0.692875	−	0.114336i
$113$	0.981934	−	1.23131i	0.0923726	−	0.115832i	−0.733497	−	0.679693i	$-0.762113\pi$
$113$	0.981934	−	1.23131i	0.0923726	−	0.115832i	0.825870	+	0.563861i	$0.190685\pi$
$114$	4.66043	+	2.24434i	0.436489	+	0.210202i
$115$	0.660647	+	2.89448i	0.0616056	+	0.269912i
$116$	27.2556			2.53062
$117$	4.51672			0.417571
$118$	1.25897	+	5.51589i	0.115897	+	0.507779i
$119$	−14.2150	−	12.8254i	−1.30309	−	1.17570i
$120$	0.961191	−	4.21125i	0.0877444	−	0.384433i
$121$	−2.47460	+	10.8419i	−0.224964	+	0.985632i
$122$	−17.0015	+	21.3192i	−1.53925	+	1.93015i
$123$	−3.37900	+	4.23714i	−0.304674	+	0.382050i
$124$	7.17283	−	31.4262i	0.644140	−	2.82216i
$125$	−0.222521	+	0.974928i	−0.0199029	+	0.0872002i
$126$	5.21159	−	3.66068i	0.464285	−	0.326119i
$127$	−3.96369	−	17.3661i	−0.351721	−	1.54099i	−0.773206	−	0.634155i	$-0.781348\pi$
$127$	−3.96369	−	17.3661i	−0.351721	−	1.54099i	0.421485	−	0.906835i	$-0.361509\pi$
$128$	20.6472			1.82497
$129$	6.48937			0.571357
$130$	2.41936	+	10.5999i	0.212192	+	0.929673i
$131$	−10.3327	−	4.97599i	−0.902776	−	0.434754i	−0.0758854	−	0.997117i	$-0.524178\pi$
$131$	−10.3327	−	4.97599i	−0.902776	−	0.434754i	−0.826891	+	0.562362i	$0.809893\pi$
$132$	−11.1270	+	13.9528i	−0.968483	+	1.21444i
$133$	−4.65236	+	3.26787i	−0.403411	+	0.283360i
$134$	−3.14798	−	3.94744i	−0.271944	−	0.341007i
$135$	−0.222521	−	0.974928i	−0.0191516	−	0.0839084i
$136$	19.4890	+	24.4385i	1.67117	+	2.09558i
$137$	−7.59978	−	3.65986i	−0.649293	−	0.312683i	0.0800912	−	0.996788i	$-0.474479\pi$
$137$	−7.59978	−	3.65986i	−0.649293	−	0.312683i	−0.729384	+	0.684105i	$0.760193\pi$
$138$	4.45589	−	5.58751i	0.379310	−	0.475640i
$139$	7.46773	−	3.59627i	0.633405	−	0.305032i	−0.0894923	−	0.995988i	$-0.528524\pi$
$139$	7.46773	−	3.59627i	0.633405	−	0.305032i	0.722897	+	0.690956i	$0.242810\pi$
$140$	7.45374	+	6.72511i	0.629956	+	0.568375i
$141$	5.24969	+	2.52812i	0.442103	+	0.212906i
$142$	−3.85901	+	1.85840i	−0.323841	+	0.155953i
$143$	4.72709	−	20.7108i	0.395299	−	1.73192i
$144$	−2.53080	+	1.21877i	−0.210900	+	0.101564i
$145$	4.47854	+	5.61591i	0.371922	+	0.466376i
$146$	−3.59983			−0.297924
$147$	0.717547	+	6.96313i	0.0591823	+	0.574309i
$148$	1.48832			0.122339
$149$	−4.45441	−	5.58565i	−0.364919	−	0.457594i	0.565145	−	0.824992i	$-0.308820\pi$
$149$	−4.45441	−	5.58565i	−0.364919	−	0.457594i	−0.930064	+	0.367398i	$0.880249\pi$
$150$	2.16878	−	1.04443i	0.177080	−	0.0852774i
$151$	−4.62988	+	20.2848i	−0.376775	+	1.65076i	0.330490	+	0.943809i	$0.392786\pi$
$151$	−4.62988	+	20.2848i	−0.376775	+	1.65076i	−0.707265	+	0.706948i	$0.750071\pi$
$152$	8.36293	−	4.02737i	0.678323	−	0.326663i
$153$	6.51976	+	3.13975i	0.527091	+	0.253834i
$154$	−11.3312	−	27.7281i	−0.913091	−	2.23440i
$155$	7.65386	−	3.68590i	0.614772	−	0.296059i
$156$	10.6857	−	13.3994i	0.855539	−	1.07281i
$157$	12.5505	+	6.04399i	1.00164	+	0.482363i	0.861494	−	0.507768i	$-0.169529\pi$
$157$	12.5505	+	6.04399i	1.00164	+	0.482363i	0.140144	+	0.990131i	$0.455244\pi$
$158$	−23.9373	−	30.0165i	−1.90435	−	2.38798i
$159$	−0.226187	−	0.990992i	−0.0179378	−	0.0785908i
$160$	1.17055	+	1.46783i	0.0925404	+	0.116042i
$161$	2.97144	+	7.27131i	0.234182	+	0.573060i
$162$	−1.50084	+	1.88200i	−0.117917	+	0.147864i
$163$	−9.12027	−	4.39209i	−0.714354	−	0.344015i	0.0411550	−	0.999153i	$-0.486896\pi$
$163$	−9.12027	−	4.39209i	−0.714354	−	0.344015i	−0.755509	+	0.655138i	$0.772611\pi$
$164$	4.57593	+	20.0485i	0.357320	+	1.56552i
$165$	−4.70327			−0.366149
$166$	−19.5569			−1.51791
$167$	−0.928650	−	4.06868i	−0.0718611	−	0.314844i	0.926204	−	0.377023i	$-0.123052\pi$
$167$	−0.928650	−	4.06868i	−0.0718611	−	0.314844i	−0.998065	+	0.0621788i	$0.980195\pi$
$168$	0.695064	−	11.4073i	0.0536253	−	0.880093i
$169$	−1.64683	+	7.21521i	−0.126679	+	0.555016i
$170$	−3.87614	+	16.9825i	−0.297286	+	1.30250i
$171$	1.33980	−	1.68005i	0.102457	−	0.128477i
$172$	15.3526	−	19.2515i	1.17062	−	1.46792i
$173$	−2.58441	+	11.3230i	−0.196489	+	0.860875i	0.776517	+	0.630096i	$0.216985\pi$
$173$	−2.58441	+	11.3230i	−0.196489	+	0.860875i	−0.973006	+	0.230779i	$0.925873\pi$
$174$	3.84755	−	16.8572i	0.291682	−	1.27794i
$175$	−0.160911	+	2.64085i	−0.0121637	+	0.199630i
$176$	2.93981	+	12.8802i	0.221597	+	0.970879i
$177$	2.35037			0.176665
$178$	27.9886			2.09783
$179$	1.25807	+	5.51197i	0.0940326	+	0.411984i	0.999934	−	0.0115052i	$-0.00366231\pi$
$179$	1.25807	+	5.51197i	0.0940326	+	0.411984i	−0.905901	+	0.423489i	$0.860805\pi$
$180$	−3.41869	−	1.64635i	−0.254814	−	0.122712i
$181$	14.8784	−	18.6569i	1.10590	−	1.38676i	0.191723	−	0.981449i	$-0.438592\pi$
$181$	14.8784	−	18.6569i	1.10590	−	1.38676i	0.914180	−	0.405309i	$-0.132836\pi$
$182$	10.8817	+	26.6283i	0.806607	+	1.97382i
$183$	7.06287	+	8.85656i	0.522103	+	0.654696i
$184$	−2.85370	−	12.5029i	−0.210378	−	0.921725i
$185$	0.244555	+	0.306662i	0.0179800	+	0.0225462i
$186$	−18.4241	−	8.87258i	−1.35092	−	0.650569i
$187$	21.2203	−	26.6094i	1.55178	−	1.94587i
$188$	19.9197	−	9.59282i	1.45279	−	0.699629i
$189$	−1.00085	−	2.44914i	−0.0728010	−	0.178149i
$190$	4.66043	+	2.24434i	0.338103	+	0.162822i
$191$	10.7848	−	5.19369i	0.780362	−	0.375803i	−0.000904956	−	1.00000i	$-0.500288\pi$
$191$	10.7848	−	5.19369i	0.780362	−	0.375803i	0.781267	+	0.624197i	$0.214574\pi$
$192$	2.25575	−	9.88307i	0.162794	−	0.713249i
$193$	12.9723	−	6.24715i	0.933770	−	0.449680i	0.0958026	−	0.995400i	$-0.469458\pi$
$193$	12.9723	−	6.24715i	0.933770	−	0.449680i	0.837967	+	0.545720i	$0.183744\pi$
$194$	26.1644	+	32.8091i	1.87849	+	2.35555i
$195$	4.51672			0.323449
$196$	22.3546	+	14.3447i	1.59675	+	1.02462i
$197$	−16.0155			−1.14106			−0.570529	−	0.821277i	$-0.693262\pi$
$197$	−16.0155			−1.14106			−0.570529	+	0.821277i	$0.693262\pi$
$198$	7.05888	+	8.85156i	0.501653	+	0.629053i
$199$	23.8491	−	11.4851i	1.69062	−	0.814158i	0.695169	−	0.718846i	$-0.255329\pi$
$199$	23.8491	−	11.4851i	1.69062	−	0.814158i	0.995447	−	0.0953120i	$-0.0303849\pi$
$200$	0.961191	−	4.21125i	0.0679665	−	0.297781i
$201$	−1.88975	+	0.910058i	−0.133293	+	0.0641905i
$202$	−23.0083	−	11.0802i	−1.61886	−	0.779601i
$203$	14.1101	+	12.7308i	0.990338	+	0.893528i
$204$	24.7389	−	11.9136i	1.73207	−	0.834122i
$205$	−3.37900	+	4.23714i	−0.236000	+	0.295934i
$206$	−30.0073	−	14.4507i	−2.09071	−	1.00683i
$207$	−1.85109	−	2.32120i	−0.128660	−	0.161334i
$208$	−2.82321	−	12.3693i	−0.195754	−	0.857655i
$209$	−6.30143	−	7.90174i	−0.435879	−	0.546575i
$210$	5.21159	−	3.66068i	0.359634	−	0.252611i
$211$	2.84439	−	3.56676i	0.195816	−	0.245546i	−0.674224	−	0.738527i	$-0.735522\pi$
$211$	2.84439	−	3.56676i	0.195816	−	0.245546i	0.870040	+	0.492982i	$0.164093\pi$
$212$	−3.47502	−	1.67348i	−0.238665	−	0.114935i
$213$	0.395941	+	1.73473i	0.0271294	+	0.118862i
$214$	−24.2752			−1.65942
$215$	6.48937			0.442572
$216$	0.961191	+	4.21125i	0.0654008	+	0.286540i
$217$	18.3922	−	12.9189i	1.24855	−	0.876992i
$218$	2.82878	−	12.3937i	0.191589	−	0.839408i
$219$	−0.332772	+	1.45797i	−0.0224867	+	0.0985205i
$220$	−11.1270	+	13.9528i	−0.750184	+	0.940701i
$221$	−20.3786	+	25.5540i	−1.37081	+	1.71895i
$222$	0.210099	−	0.920503i	0.0141009	−	0.0617801i
$223$	−0.275935	+	1.20895i	−0.0184780	+	0.0809574i	−0.983326	−	0.181850i	$-0.941791\pi$
$223$	−0.275935	+	1.20895i	−0.0184780	+	0.0809574i	0.964848	+	0.262808i	$0.0846485\pi$
$224$	3.68796	+	3.32745i	0.246412	+	0.222325i
$225$	−0.222521	−	0.974928i	−0.0148347	−	0.0649952i
$226$	−3.79105			−0.252177
$227$	−16.3139			−1.08279			−0.541396	−	0.840767i	$-0.682104\pi$
$227$	−16.3139			−1.08279			−0.541396	+	0.840767i	$0.682104\pi$
$228$	−1.81439	−	7.94935i	−0.120161	−	0.526459i
$229$	13.0686	+	6.29352i	0.863599	+	0.415887i	0.812607	−	0.582812i	$-0.198048\pi$
$229$	13.0686	+	6.29352i	0.863599	+	0.415887i	0.0509916	+	0.998699i	$0.483762\pi$
$230$	4.45589	−	5.58751i	0.293813	−	0.368429i
$231$	−12.2776	+	2.02602i	−0.807810	+	0.133302i
$232$	−19.3453	−	24.2582i	−1.27008	−	1.59263i
$233$	4.99065	+	21.8655i	0.326948	+	1.43245i	0.824915	+	0.565257i	$0.191223\pi$
$233$	4.99065	+	21.8655i	0.326948	+	1.43245i	−0.497966	+	0.867196i	$0.665920\pi$
$234$	−6.77889	−	8.50047i	−0.443150	−	0.555693i
$235$	5.24969	+	2.52812i	0.342452	+	0.164916i
$236$	5.56052	−	6.97267i	0.361959	−	0.453882i
$237$	−14.3698	+	6.92012i	−0.933417	+	0.449510i
$238$	−2.80294	+	46.0016i	−0.181688	+	2.98184i
$239$	−1.02075	−	0.491568i	−0.0660269	−	0.0317969i	0.400579	−	0.916262i	$-0.368809\pi$
$239$	−1.02075	−	0.491568i	−0.0660269	−	0.0317969i	−0.466606	+	0.884465i	$0.654523\pi$
$240$	−2.53080	+	1.21877i	−0.163363	+	0.0786713i
$241$	−0.336193	+	1.47296i	−0.0216561	+	0.0948816i	−0.984601	−	0.174817i	$-0.944067\pi$
$241$	−0.336193	+	1.47296i	−0.0216561	+	0.0948816i	0.962945	+	0.269698i	$0.0869239\pi$
$242$	24.1185	−	11.6149i	1.55040	−	0.746632i
$243$	0.623490	+	0.781831i	0.0399969	+	0.0501545i
$244$	42.9835			2.75174
$245$	0.717547	+	6.96313i	0.0458424	+	0.444858i
$246$	13.0456			0.831760
$247$	6.05149	+	7.58833i	0.385047	+	0.482834i
$248$	−33.0612	+	15.9215i	−2.09939	+	1.01101i
$249$	−1.80786	+	7.92073i	−0.114568	+	0.501956i
$250$	2.16878	−	1.04443i	0.137166	−	0.0660556i
$251$	−8.49078	−	4.08894i	−0.535933	−	0.258092i	0.146282	−	0.989243i	$-0.453269\pi$
$251$	−8.49078	−	4.08894i	−0.535933	−	0.258092i	−0.682216	+	0.731151i	$0.738983\pi$
$252$	−9.63350	−	2.82505i	−0.606853	−	0.177962i
$253$	−12.5808	+	6.05860i	−0.790949	+	0.380901i
$254$	−26.7341	+	33.5234i	−1.67744	+	2.10345i
$255$	6.51976	+	3.13975i	0.408283	+	0.196619i
$256$	−18.3473	−	23.0067i	−1.14670	−	1.43792i
$257$	−5.13066	−	22.4789i	−0.320042	−	1.40219i	−0.837477	−	0.546472i	$-0.815971\pi$
$257$	−5.13066	−	22.4789i	−0.320042	−	1.40219i	0.517436	−	0.855722i	$-0.326887\pi$
$258$	−9.73954	−	12.2130i	−0.606357	−	0.760348i
$259$	0.770497	+	0.695178i	0.0478764	+	0.0431963i
$260$	10.6857	−	13.3994i	0.662698	−	0.830996i
$261$	−6.47167	−	3.11659i	−0.400586	−	0.192912i
$262$	6.14304	+	26.9144i	0.379518	+	1.66278i
$263$	−23.1735			−1.42894			−0.714470	−	0.699666i	$-0.753332\pi$
$263$	−23.1735			−1.42894			−0.714470	+	0.699666i	$0.753332\pi$
$264$	20.3160			1.25037
$265$	−0.226187	−	0.990992i	−0.0138946	−	0.0608761i
$266$	13.1326	+	3.85118i	0.805211	+	0.236131i
$267$	2.58729	−	11.3357i	0.158340	−	0.693732i
$268$	−1.77099	+	7.75921i	−0.108180	+	0.473969i
$269$	4.55696	−	5.71424i	0.277842	−	0.348403i	−0.623256	−	0.782018i	$-0.714191\pi$
$269$	4.55696	−	5.71424i	0.277842	−	0.348403i	0.901099	+	0.433614i	$0.142762\pi$
$270$	−1.50084	+	1.88200i	−0.0913385	+	0.114535i
$271$	−3.83027	+	16.7815i	−0.232672	+	1.01940i	0.714740	+	0.699390i	$0.246545\pi$
$271$	−3.83027	+	16.7815i	−0.232672	+	1.01940i	−0.947413	+	0.320014i	$0.896312\pi$
$272$	4.52316	−	19.8172i	0.274257	−	1.20160i
$273$	11.7907	−	1.94566i	0.713603	−	0.117757i
$274$	4.51823	+	19.7957i	0.272956	+	1.19590i
$275$	−4.70327			−0.283618
$276$	−11.2654			−0.678100
$277$	−6.82113	−	29.8853i	−0.409842	−	1.79563i	−0.584933	−	0.811082i	$-0.698879\pi$
$277$	−6.82113	−	29.8853i	−0.409842	−	1.79563i	0.175091	−	0.984552i	$-0.443978\pi$
$278$	−17.9761	−	8.65682i	−1.07813	−	0.519202i
$279$	−5.29663	+	6.64177i	−0.317101	+	0.397632i
$280$	0.695064	−	11.4073i	0.0415380	−	0.681717i
$281$	−8.68451	−	10.8900i	−0.518074	−	0.649645i	0.452124	−	0.891955i	$-0.350666\pi$
$281$	−8.68451	−	10.8900i	−0.518074	−	0.649645i	−0.970199	+	0.242310i	$0.922095\pi$
$282$	−3.12105	−	13.6742i	−0.185856	−	0.814288i
$283$	4.93204	+	6.18459i	0.293180	+	0.367636i	0.906505	−	0.422195i	$-0.138740\pi$
$283$	4.93204	+	6.18459i	0.293180	+	0.367636i	−0.613326	+	0.789830i	$0.710169\pi$
$284$	6.08301	+	2.92942i	0.360960	+	0.173829i
$285$	1.33980	−	1.68005i	0.0793627	−	0.0995177i
$286$	−46.0723	+	22.1872i	−2.72431	+	1.31196i
$287$	−6.99549	+	12.5164i	−0.412930	+	0.738819i
$288$	−1.69150	−	0.814583i	−0.0996725	−	0.0479998i
$289$	−31.8630	+	15.3444i	−1.87430	+	0.902614i
$290$	3.84755	−	16.8572i	0.225936	−	0.989889i
$291$	15.7067	−	7.56394i	0.920742	−	0.443406i
$292$	3.53798	+	4.43648i	0.207044	+	0.259625i
$293$	−4.97077			−0.290395			−0.145198	−	0.989403i	$-0.546382\pi$
$293$	−4.97077			−0.290395			−0.145198	+	0.989403i	$0.546382\pi$
$294$	12.0277	−	11.8010i	0.701468	−	0.688248i
$295$	2.35037			0.136844
$296$	−1.05637	−	1.32464i	−0.0614001	−	0.0769933i
$297$	4.23750	−	2.04067i	0.245885	−	0.118412i
$298$	−3.82682	+	16.7664i	−0.221682	+	0.971250i
$299$	12.0818	−	5.81829i	0.698708	−	0.336480i
$300$	−3.41869	−	1.64635i	−0.197378	−	0.0950522i
$301$	16.9402	−	2.79542i	0.976415	−	0.161125i
$302$	45.1248	−	21.7310i	2.59664	−	1.25048i
$303$	−6.61451	+	8.29433i	−0.379994	+	0.476497i
$304$	−5.43836	−	2.61898i	−0.311912	−	0.150209i
$305$	7.06287	+	8.85656i	0.404419	+	0.507125i
$306$	−3.87614	−	16.9825i	−0.221584	−	0.970823i
$307$	−10.8094	−	13.5545i	−0.616924	−	0.773598i	0.370984	−	0.928639i	$-0.379021\pi$
$307$	−10.8094	−	13.5545i	−0.616924	−	0.773598i	−0.987908	+	0.155041i	$0.950449\pi$
$308$	−23.0361	+	41.2163i	−1.31260	+	2.34852i
$309$	−8.62660	+	10.8174i	−0.490750	+	0.615381i
$310$	−18.4241	−	8.87258i	−1.04642	−	0.503929i
$311$	−2.74590	−	12.0306i	−0.155706	−	0.682191i	−0.991165	−	0.132638i	$-0.957655\pi$
$311$	−2.74590	−	12.0306i	−0.155706	−	0.682191i	0.835459	−	0.549553i	$-0.185202\pi$
$312$	−19.5102			−1.10455
$313$	−2.61645			−0.147890			−0.0739452	−	0.997262i	$-0.523559\pi$
$313$	−2.61645			−0.147890			−0.0739452	+	0.997262i	$0.523559\pi$
$314$	−7.46153	−	32.6911i	−0.421078	−	1.84487i
$315$	−1.00085	−	2.44914i	−0.0563914	−	0.137994i
$316$	−13.4667	+	59.0013i	−0.757559	+	3.31908i
$317$	−5.01461	+	21.9704i	−0.281648	+	1.23398i	0.614031	+	0.789282i	$0.289547\pi$
$317$	−5.01461	+	21.9704i	−0.281648	+	1.23398i	−0.895679	+	0.444700i	$0.853310\pi$
$318$	−1.52557	+	1.91301i	−0.0855499	+	0.107276i
$319$	−21.0638	+	26.4131i	−1.17934	+	1.47885i
$320$	2.25575	−	9.88307i	0.126100	−	0.552480i
$321$	−2.24402	+	9.83170i	−0.125249	+	0.548752i
$322$	9.22494	−	16.5054i	0.514086	−	0.919807i
$323$	3.46021	+	15.1602i	0.192531	+	0.843534i
$324$	3.79446			0.210803
$325$	4.51672			0.250543
$326$	5.42219	+	23.7562i	0.300307	+	1.31573i
$327$	−4.75809	−	2.29137i	−0.263123	−	0.126713i
$328$	14.5958	−	18.3025i	0.805917	−	1.01059i
$329$	14.7931	+	4.33812i	0.815568	+	0.239168i
$330$	7.05888	+	8.85156i	0.388579	+	0.487262i
$331$	3.97324	+	17.4079i	0.218389	+	0.956825i	0.958668	+	0.284526i	$0.0918362\pi$
$331$	3.97324	+	17.4079i	0.218389	+	0.956825i	−0.740279	+	0.672300i	$0.765307\pi$
$332$	19.2208	+	24.1021i	1.05488	+	1.32278i
$333$	−0.353392	−	0.170184i	−0.0193657	−	0.00932605i
$334$	−6.26350	+	7.85418i	−0.342723	+	0.429762i
$335$	−1.88975	+	0.910058i	−0.103248	+	0.0497218i
$336$	−6.08152	+	4.27173i	−0.331774	+	0.233042i
$337$	−16.6239	−	8.00565i	−0.905562	−	0.436096i	−0.0776675	−	0.996979i	$-0.524747\pi$
$337$	−16.6239	−	8.00565i	−0.905562	−	0.436096i	−0.827895	+	0.560884i	$0.810462\pi$
$338$	16.0507	−	7.72959i	0.873041	−	0.420434i
$339$	−0.350448	+	1.53541i	−0.0190337	+	0.0833922i
$340$	24.7389	−	11.9136i	1.34166	−	0.646108i
$341$	24.9115	+	31.2380i	1.34903	+	1.69163i
$342$	−5.17268			−0.279707
$343$	4.87261	+	17.8678i	0.263096	+	0.964770i
$344$	−28.0312			−1.51134
$345$	−1.85109	−	2.32120i	−0.0996594	−	0.124969i
$346$	25.1888	−	12.1303i	1.35416	−	0.652127i
$347$	0.793395	−	3.47609i	0.0425917	−	0.186606i	−0.949157	−	0.314803i	$-0.898062\pi$
$347$	0.793395	−	3.47609i	0.0425917	−	0.186606i	0.991749	+	0.128196i	$0.0409188\pi$
$348$	−24.5565	+	11.8258i	−1.31636	+	0.633928i
$349$	2.71474	+	1.30735i	0.145317	+	0.0699808i	0.505129	−	0.863044i	$-0.331445\pi$
$349$	2.71474	+	1.30735i	0.145317	+	0.0699808i	−0.359812	+	0.933025i	$0.617159\pi$
$350$	5.21159	−	3.66068i	0.278571	−	0.195671i
$351$	−4.06942	+	1.95973i	−0.217210	+	0.104603i
$352$	−5.50543	+	6.90359i	−0.293440	+	0.367963i
$353$	−1.25533	−	0.604536i	−0.0668145	−	0.0321762i	0.400178	−	0.916437i	$-0.368948\pi$
$353$	−1.25533	−	0.604536i	−0.0668145	−	0.0321762i	−0.466993	+	0.884261i	$0.654663\pi$
$354$	−3.52754	−	4.42340i	−0.187487	−	0.235101i
$355$	0.395941	+	1.73473i	0.0210144	+	0.0920699i
$356$	−27.5077	−	34.4935i	−1.45790	−	1.82815i
$357$	18.3720	+	5.38765i	0.972349	+	0.285145i
$358$	8.48535	−	10.6403i	0.448465	−	0.562357i
$359$	2.37857	+	1.14546i	0.125536	+	0.0604551i	0.495598	−	0.868552i	$-0.334949\pi$
$359$	2.37857	+	1.14546i	0.125536	+	0.0604551i	−0.370061	+	0.929007i	$0.620663\pi$
$360$	0.961191	+	4.21125i	0.0506592	+	0.221953i
$361$	−14.3824			−0.756967
$362$	−57.4425			−3.01911
$363$	−2.47460	−	10.8419i	−0.129883	−	0.569055i
$364$	22.1224	−	39.5815i	1.15953	−	2.07464i
$365$	−0.332772	+	1.45797i	−0.0174181	+	0.0763136i
$366$	6.06777	−	26.5846i	0.317168	−	1.38960i
$367$	−9.45539	+	11.8567i	−0.493567	+	0.618914i	−0.964765	−	0.263114i	$-0.915250\pi$
$367$	−9.45539	+	11.8567i	−0.493567	+	0.618914i	0.471197	+	0.882028i	$0.343822\pi$
$368$	−5.19968	+	6.52019i	−0.271052	+	0.339889i
$369$	1.20595	−	5.28362i	0.0627794	−	0.275054i
$370$	0.210099	−	0.920503i	0.0109225	−	0.0478547i
$371$	−1.01734	−	2.48950i	−0.0528176	−	0.129248i
$372$	7.17283	+	31.4262i	0.371894	+	1.62937i
$373$	18.1618			0.940385			0.470192	−	0.882564i	$-0.344185\pi$
$373$	18.1618			0.940385			0.470192	+	0.882564i	$0.344185\pi$
$374$	−81.9272			−4.23636
$375$	−0.222521	−	0.974928i	−0.0114909	−	0.0503451i
$376$	−22.6763	−	10.9203i	−1.16944	−	0.563173i
$377$	20.2283	−	25.3655i	1.04181	−	1.30639i
$378$	−3.10717	+	5.55938i	−0.159816	+	0.285944i
$379$	−19.4892	−	24.4386i	−1.00109	−	1.25533i	−0.966698	−	0.255920i	$-0.917622\pi$
$379$	−19.4892	−	24.4386i	−1.00109	−	1.25533i	−0.0343929	−	0.999408i	$-0.510950\pi$
$380$	−1.81439	−	7.94935i	−0.0930761	−	0.407793i
$381$	11.1060	+	13.9265i	0.568979	+	0.713477i
$382$	−25.9609	−	12.5021i	−1.32827	−	0.639663i
$383$	−22.2839	+	27.9431i	−1.13865	+	1.42783i	−0.250597	+	0.968092i	$0.580627\pi$
$383$	−22.2839	+	27.9431i	−1.13865	+	1.42783i	−0.888056	+	0.459734i	$0.847945\pi$
$384$	−18.6025	+	8.95847i	−0.949303	+	0.457160i
$385$	−12.2776	+	2.02602i	−0.625727	+	0.103256i
$386$	−31.2266	−	15.0379i	−1.58939	−	0.765411i
$387$	−5.84672	+	2.81563i	−0.297206	+	0.143127i
$388$	14.7196	−	64.4906i	0.747273	−	3.27402i
$389$	−4.86541	+	2.34306i	−0.246686	+	0.118798i	−0.553142	−	0.833087i	$-0.686571\pi$
$389$	−4.86541	+	2.34306i	−0.246686	+	0.118798i	0.306456	+	0.951885i	$0.400857\pi$
$390$	−6.77889	−	8.50047i	−0.343263	−	0.430438i
$391$	21.4843			1.08651
$392$	−3.09948	−	30.0776i	−0.156548	−	1.51915i
$393$	11.4685			0.578508
$394$	24.0368	+	30.1412i	1.21096	+	1.51849i
$395$	−14.3698	+	6.92012i	−0.723021	+	0.348189i
$396$	3.97119	−	17.3989i	0.199560	−	0.874328i
$397$	31.1029	−	14.9784i	1.56101	−	0.751742i	0.563765	−	0.825935i	$-0.309352\pi$
$397$	31.1029	−	14.9784i	1.56101	−	0.751742i	0.997244	+	0.0741925i	$0.0236379\pi$
$398$	−57.4087	−	27.6466i	−2.87764	−	1.38580i
$399$	2.77376	−	4.96283i	0.138862	−	0.248452i
$400$	−2.53080	+	1.21877i	−0.126540	+	0.0609386i
$401$	15.0951	−	18.9287i	0.753814	−	0.945253i	−0.245897	−	0.969296i	$-0.579082\pi$
$401$	15.0951	−	18.9287i	0.753814	−	0.945253i	0.999711	+	0.0240431i	$0.00765390\pi$
$402$	4.54896	+	2.19066i	0.226881	+	0.109260i
$403$	−23.9234	−	29.9990i	−1.19171	−	1.49436i
$404$	8.95754	+	39.2455i	0.445654	+	1.95254i
$405$	0.623490	+	0.781831i	0.0309815	+	0.0388495i
$406$	2.78227	−	45.6623i	0.138082	−	2.26618i
$407$	−1.15021	+	1.44231i	−0.0570136	+	0.0714928i
$408$	−28.1625	−	13.5623i	−1.39425	−	0.671435i
$409$	1.00527	+	4.40439i	0.0497076	+	0.217783i	0.993681	−	0.112237i	$-0.0358016\pi$
$409$	1.00527	+	4.40439i	0.0497076	+	0.217783i	−0.943974	+	0.330020i	$0.892944\pi$
$410$	13.0456			0.644278
$411$	8.43511			0.416074
$412$	11.6824	+	51.1838i	0.575549	+	2.52164i
$413$	6.13552	−	1.01247i	0.301909	−	0.0498202i
$414$	−1.59029	+	6.96751i	−0.0781584	+	0.342434i
$415$	−1.80786	+	7.92073i	−0.0887441	+	0.388813i
$416$	5.28706	−	6.62977i	0.259220	−	0.325051i
$417$	−5.16783	+	6.48025i	−0.253070	+	0.317339i
$418$	−5.41361	+	23.7186i	−0.264788	+	1.16011i
$419$	−0.960375	+	4.20768i	−0.0469174	+	0.205559i	−0.992954	−	0.118502i	$-0.962191\pi$
$419$	−0.960375	+	4.20768i	−0.0469174	+	0.205559i	0.946036	+	0.324060i	$0.105048\pi$
$420$	−9.63350	−	2.82505i	−0.470067	−	0.137849i
$421$	2.70190	+	11.8378i	0.131683	+	0.576939i	0.997114	+	0.0759124i	$0.0241869\pi$
$421$	2.70190	+	11.8378i	0.131683	+	0.576939i	−0.865432	+	0.501026i	$0.832956\pi$
$422$	−10.9816			−0.534577
$423$	−5.82671			−0.283305
$424$	0.977029	+	4.28064i	0.0474487	+	0.207886i
$425$	6.51976	+	3.13975i	0.316255	+	0.152300i
$426$	2.67052	−	3.34872i	0.129387	−	0.162246i
$427$	22.2524	+	20.0771i	1.07687	+	0.971601i
$428$	23.8581	+	29.9171i	1.15322	+	1.44610i
$429$	4.72709	+	20.7108i	0.228226	+	0.999925i
$430$	−9.73954	−	12.2130i	−0.469682	−	0.588963i
$431$	−34.4002	−	16.5663i	−1.65700	−	0.797970i	−0.998989	−	0.0449627i	$-0.985683\pi$
$431$	−34.4002	−	16.5663i	−1.65700	−	0.797970i	−0.658012	−	0.753007i	$-0.728603\pi$
$432$	1.75137	−	2.19615i	0.0842629	−	0.105662i
$433$	−24.5767	+	11.8355i	−1.18108	+	0.568778i	−0.918226	−	0.396058i	$-0.870378\pi$
$433$	−24.5767	+	11.8355i	−1.18108	+	0.568778i	−0.262854	+	0.964836i	$0.584664\pi$
$434$	−51.9172	−	15.2249i	−2.49211	−	0.730818i
$435$	−6.47167	−	3.11659i	−0.310293	−	0.149429i
$436$	−18.0544	+	8.69452i	−0.864647	+	0.416392i
$437$	1.41964	−	6.21986i	0.0679107	−	0.297536i
$438$	3.24334	−	1.56191i	0.154973	−	0.0746309i
$439$	0.206103	+	0.258445i	0.00983676	+	0.0123349i	0.786726	−	0.617303i	$-0.211775\pi$
$439$	0.206103	+	0.258445i	0.00983676	+	0.0123349i	−0.776889	+	0.629638i	$0.783203\pi$
$440$	20.3160			0.968529
$441$	−3.66767	−	5.96223i	−0.174651	−	0.283916i
$442$	78.6777			3.74231
$443$	18.0876	+	22.6811i	0.859367	+	1.07761i	0.996207	+	0.0870190i	$0.0277341\pi$
$443$	18.0876	+	22.6811i	0.859367	+	1.07761i	−0.136840	+	0.990593i	$0.543694\pi$
$444$	−1.34093	+	0.645757i	−0.0636377	+	0.0306463i
$445$	2.58729	−	11.3357i	0.122649	−	0.537363i
$446$	2.68938	−	1.29514i	0.127346	−	0.0613266i
$447$	6.43680	+	3.09980i	0.304450	+	0.146616i
$448$	1.63119	−	26.7709i	0.0770666	−	1.26481i
$449$	24.8048	−	11.9454i	1.17061	−	0.563737i	0.255450	−	0.966822i	$-0.417776\pi$
$449$	24.8048	−	11.9454i	1.17061	−	0.563737i	0.915163	+	0.403085i	$0.132062\pi$
$450$	−1.50084	+	1.88200i	−0.0707505	+	0.0887183i
$451$	−22.9651	−	11.0594i	−1.08139	−	0.520768i
$452$	3.72590	+	4.67214i	0.175252	+	0.219759i
$453$	−4.62988	−	20.2848i	−0.217531	−	0.953065i
$454$	24.4847	+	30.7028i	1.14912	+	1.44095i
$455$	11.7907	−	1.94566i	0.552755	−	0.0912140i
$456$	−5.78733	+	7.25708i	−0.271016	+	0.339844i
$457$	−2.03035	−	0.977767i	−0.0949760	−	0.0457380i	0.385793	−	0.922586i	$-0.373928\pi$
$457$	−2.03035	−	0.977767i	−0.0949760	−	0.0457380i	−0.480769	+	0.876847i	$0.659642\pi$
$458$	−7.76957	−	34.0407i	−0.363048	−	1.59062i
$459$	−7.23639			−0.337766
$460$	−11.2654			−0.525254
$461$	2.27567	+	9.97034i	0.105988	+	0.464365i	0.999871	+	0.0160641i	$0.00511358\pi$
$461$	2.27567	+	9.97034i	0.105988	+	0.464365i	−0.893883	+	0.448301i	$0.852029\pi$
$462$	22.2398	+	20.0658i	1.03469	+	0.933545i
$463$	4.02703	−	17.6436i	0.187152	−	0.819966i	−0.790957	−	0.611872i	$-0.790417\pi$
$463$	4.02703	−	17.6436i	0.187152	−	0.819966i	0.978109	−	0.208094i	$-0.0667261\pi$
$464$	−4.48979	+	19.6711i	−0.208433	+	0.913206i
$465$	−5.29663	+	6.64177i	−0.245625	+	0.308005i
$466$	33.6606	−	42.2090i	1.55930	−	1.95530i
$467$	−0.585109	+	2.56353i	−0.0270756	+	0.118626i	−0.986660	−	0.162796i	$-0.947949\pi$
$467$	−0.585109	+	2.56353i	−0.0270756	+	0.118626i	0.959584	+	0.281422i	$0.0908060\pi$
$468$	−3.81367	+	16.7088i	−0.176287	+	0.772364i
$469$	−4.54108	+	3.18971i	−0.209688	+	0.147287i
$470$	−3.12105	−	13.6742i	−0.143963	−	0.630745i
$471$	−13.9300			−0.641860
$472$	−10.1526			−0.467309
$473$	6.79162	+	29.7561i	0.312279	+	1.36818i
$474$	34.5904	+	16.6579i	1.58879	+	0.765122i
$475$	1.33980	−	1.68005i	0.0614741	−	0.0770861i
$476$	59.4477	−	41.7567i	2.72478	−	1.91392i
$477$	0.633763	+	0.794714i	0.0290180	+	0.0363874i
$478$	0.606858	+	2.65882i	0.0277570	+	0.121612i
$479$	−8.93787	−	11.2077i	−0.408382	−	0.512094i	0.534525	−	0.845153i	$-0.320491\pi$
$479$	−8.93787	−	11.2077i	−0.408382	−	0.512094i	−0.942906	+	0.333059i	$0.891919\pi$
$480$	−1.69150	−	0.814583i	−0.0772060	−	0.0371804i
$481$	1.10458	−	1.38511i	0.0503647	−	0.0631554i
$482$	3.27668	−	1.57797i	0.149249	−	0.0718744i
$483$	−5.83208	−	5.26197i	−0.265369	−	0.239428i
$484$	−38.0184	−	18.3087i	−1.72811	−	0.832214i
$485$	15.7067	−	7.56394i	0.713204	−	0.343461i
$486$	0.535645	−	2.34681i	0.0242974	−	0.106454i
$487$	2.69632	−	1.29848i	0.122182	−	0.0588398i	−0.371794	−	0.928315i	$-0.621257\pi$
$487$	2.69632	−	1.29848i	0.122182	−	0.0588398i	0.493976	+	0.869475i	$0.335543\pi$
$488$	−30.5085	−	38.2564i	−1.38105	−	1.73179i
$489$	10.1227			0.457766
$490$	12.0277	−	11.8010i	0.543355	−	0.533114i
$491$	−36.1124			−1.62973			−0.814866	−	0.579649i	$-0.803190\pi$
$491$	−36.1124			−1.62973			−0.814866	+	0.579649i	$0.803190\pi$
$492$	−12.8215	−	16.0776i	−0.578037	−	0.724835i
$493$	46.8315	−	22.5529i	2.10919	−	1.01573i
$494$	5.19888	−	22.7778i	0.233909	−	1.02482i
$495$	4.23750	−	2.04067i	0.190462	−	0.0917214i
$496$	21.4995	+	10.3536i	0.965358	+	0.464892i
$497$	1.78085	+	4.35786i	0.0798820	+	0.195477i
$498$	17.6201	−	8.48540i	0.789577	−	0.380240i
$499$	9.92836	−	12.4498i	0.444454	−	0.557328i	−0.508257	−	0.861206i	$-0.669710\pi$
$499$	9.92836	−	12.4498i	0.444454	−	0.557328i	0.952711	+	0.303878i	$0.0982814\pi$
$500$	−3.41869	−	1.64635i	−0.152888	−	0.0736271i
$501$	2.60202	+	3.26283i	0.116250	+	0.145773i
$502$	5.04795	+	22.1165i	0.225301	+	0.987108i
$503$	20.4172	+	25.6023i	0.910356	+	1.14155i	0.989478	+	0.144685i	$0.0462169\pi$
$503$	20.4172	+	25.6023i	0.910356	+	1.14155i	−0.0791219	+	0.996865i	$0.525212\pi$
$504$	4.32322	+	10.5792i	0.192571	+	0.471235i
$505$	−6.61451	+	8.29433i	−0.294342	+	0.369093i
$506$	30.2841	+	14.5841i	1.34629	+	0.648340i
$507$	−1.64683	−	7.21521i	−0.0731381	−	0.320439i
$508$	67.5894			2.99879
$509$	27.4775			1.21792			0.608960	−	0.793201i	$-0.291587\pi$
$509$	27.4775			1.21792			0.608960	+	0.793201i	$0.291587\pi$
$510$	−3.87614	−	16.9825i	−0.171638	−	0.751996i
$511$	−0.240637	+	3.94930i	−0.0106451	+	0.174707i
$512$	−6.57343	+	28.8001i	−0.290507	+	1.27280i
$513$	−0.478168	+	2.09499i	−0.0211116	+	0.0924961i
$514$	−34.6049	+	43.3932i	−1.52636	+	1.91399i
$515$	−8.62660	+	10.8174i	−0.380134	+	0.476672i
$516$	−5.47927	+	24.0063i	−0.241212	+	1.05682i
$517$	−6.09810	+	26.7175i	−0.268194	+	1.17504i
$518$	0.151928	−	2.49343i	0.00667534	−	0.109555i
$519$	−2.58441	−	11.3230i	−0.113443	−	0.497027i
$520$	−19.5102			−0.855580
$521$	−23.3762			−1.02413			−0.512064	−	0.858947i	$-0.671119\pi$
$521$	−23.3762			−1.02413			−0.512064	+	0.858947i	$0.671119\pi$
$522$	3.84755	+	16.8572i	0.168403	+	0.737820i
$523$	−9.92607	−	4.78014i	−0.434037	−	0.209021i	0.204090	−	0.978952i	$-0.434576\pi$
$523$	−9.92607	−	4.78014i	−0.434037	−	0.209021i	−0.638127	+	0.769931i	$0.720291\pi$
$524$	27.1322	−	34.0227i	1.18528	−	1.48629i
$525$	−1.00085	−	2.44914i	−0.0436806	−	0.106889i
$526$	34.7798	+	43.6125i	1.51647	+	1.90160i
$527$	−13.6793	−	59.9328i	−0.595879	−	2.61072i
$528$	−8.23717	−	10.3291i	−0.358477	−	0.449516i
$529$	12.7807	+	6.15486i	0.555683	+	0.267603i
$530$	−1.52557	+	1.91301i	−0.0662667	+	0.0830958i
$531$	−2.11761	+	1.01979i	−0.0918965	+	0.0442550i
$532$	−8.16069	−	19.9698i	−0.353811	−	0.865800i
$533$	22.0542	+	10.6208i	0.955275	+	0.460036i
$534$	−25.2169	+	12.1438i	−1.09124	+	0.525514i
$535$	−2.24402	+	9.83170i	−0.0970176	+	0.425062i
$536$	8.16290	−	3.93104i	0.352584	−	0.169795i
$537$	−3.52504	−	4.42026i	−0.152117	−	0.190748i
$538$	−17.5935			−0.758509
$539$	−31.1774	+	10.5776i	−1.34291	+	0.455612i
$540$	3.79446			0.163287
$541$	−9.68983	−	12.1507i	−0.416598	−	0.522398i	0.528610	−	0.848865i	$-0.322713\pi$
$541$	−9.68983	−	12.1507i	−0.416598	−	0.522398i	−0.945209	+	0.326467i	$0.894142\pi$
$542$	37.3314	−	17.9779i	1.60352	−	0.772216i
$543$	−5.31004	+	23.2648i	−0.227876	+	0.998388i
$544$	12.2403	−	5.89464i	0.524800	−	0.252731i
$545$	−4.75809	−	2.29137i	−0.203814	−	0.0981517i
$546$	−21.3577	−	19.2699i	−0.914025	−	0.824675i
$547$	20.6229	−	9.93148i	0.881773	−	0.424639i	0.0625010	−	0.998045i	$-0.480092\pi$
$547$	20.6229	−	9.93148i	0.881773	−	0.424639i	0.819272	+	0.573406i	$0.194378\pi$
$548$	19.9558	−	25.0238i	0.852471	−	1.06896i
$549$	−10.2061	−	4.91502i	−0.435588	−	0.209768i
$550$	7.05888	+	8.85156i	0.300992	+	0.377432i
$551$	−3.43469	−	15.0484i	−0.146323	−	0.641081i
$552$	7.99589	+	10.0265i	0.340328	+	0.426758i
$553$	−34.5306	+	24.2546i	−1.46839	+	1.03141i
$554$	−46.0067	+	57.6905i	−1.95464	+	2.45104i
$555$	−0.353392	−	0.170184i	−0.0150006	−	0.00722393i
$556$	6.99841	+	30.6620i	0.296799	+	1.30036i
$557$	46.1042			1.95350			0.976748	−	0.214389i	$-0.0687760\pi$
$557$	46.1042			1.95350			0.976748	+	0.214389i	$0.0687760\pi$
$558$	20.4492			0.865685
$559$	−6.52224	−	28.5758i	−0.275861	−	1.20863i
$560$	−6.08152	+	4.27173i	−0.256991	+	0.180514i
$561$	−7.57343	+	33.1814i	−0.319751	+	1.40092i
$562$	−7.46093	+	32.6885i	−0.314720	+	1.37888i
$563$	−15.8224	+	19.8407i	−0.666835	+	0.836185i	−0.994068	−	0.108759i	$-0.965312\pi$
$563$	−15.8224	+	19.8407i	−0.666835	+	0.836185i	0.327233	+	0.944944i	$0.393884\pi$
$564$	−13.7849	+	17.2857i	−0.580447	+	0.727858i
$565$	−0.350448	+	1.53541i	−0.0147435	+	0.0645953i
$566$	4.23716	−	18.5642i	0.178101	−	0.780312i
$567$	1.96438	+	1.77235i	0.0824960	+	0.0744317i
$568$	−1.71029	−	7.49326i	−0.0717621	−	0.314410i
$569$	−30.9796			−1.29873			−0.649366	−	0.760476i	$-0.724966\pi$
$569$	−30.9796			−1.29873			−0.649366	+	0.760476i	$0.724966\pi$
$570$	−5.17268			−0.216660
$571$	−1.63310	−	7.15507i	−0.0683430	−	0.299430i	0.929192	−	0.369597i	$-0.120504\pi$
$571$	−1.63310	−	7.15507i	−0.0683430	−	0.299430i	−0.997535	+	0.0701664i	$0.977647\pi$
$572$	72.6244	+	34.9741i	3.03658	+	1.46234i
$573$	−7.46332	+	9.35871i	−0.311785	+	0.390966i
$574$	34.0550	−	5.61965i	1.42143	−	0.234560i
$575$	−1.85109	−	2.32120i	−0.0771959	−	0.0968005i
$576$	2.25575	+	9.88307i	0.0939894	+	0.411795i
$577$	−16.9370	−	21.2383i	−0.705097	−	0.884164i	0.292296	−	0.956328i	$-0.405581\pi$
$577$	−16.9370	−	21.2383i	−0.705097	−	0.884164i	−0.997393	+	0.0721640i	$0.977009\pi$
$578$	76.6997	+	36.9366i	3.19029	+	1.53636i
$579$	−8.97714	+	11.2570i	−0.373077	+	0.467824i
$580$	−24.5565	+	11.8258i	−1.01965	+	0.491038i
$581$	−1.30731	+	21.4554i	−0.0542364	+	0.890121i
$582$	−37.8086	−	18.2077i	−1.56722	−	0.754732i
$583$	4.30732	−	2.07430i	0.178391	−	0.0859086i
$584$	1.43743	−	6.29778i	0.0594812	−	0.260604i
$585$	−4.06942	+	1.95973i	−0.168250	+	0.0810249i
$586$	7.46035	+	9.35498i	0.308184	+	0.386451i
$587$	23.1434			0.955231			0.477615	−	0.878569i	$-0.341501\pi$
$587$	23.1434			0.955231			0.477615	+	0.878569i	$0.341501\pi$
$588$	−26.3647	−	3.22485i	−1.08726	−	0.132991i
$589$	−18.2549			−0.752181
$590$	−3.52754	−	4.42340i	−0.145227	−	0.182108i
$591$	14.4295	−	6.94887i	0.593549	−	0.285838i
$592$	−0.245169	+	1.07416i	−0.0100764	+	0.0441476i
$593$	0.0765713	−	0.0368748i	0.00314441	−	0.00151427i	−0.432311	−	0.901725i	$-0.642302\pi$
$593$	0.0765713	−	0.0368748i	0.00314441	−	0.00151427i	0.435455	+	0.900210i	$0.356587\pi$
$594$	−10.2004	−	4.91224i	−0.418527	−	0.201552i
$595$	18.3720	+	5.38765i	0.753179	+	0.220872i
$596$	24.4242	−	11.7621i	1.00045	−	0.481793i
$597$	−16.5041	+	20.6955i	−0.675467	+	0.847009i
$598$	−29.0829	−	14.0056i	−1.18929	−	0.572731i
$599$	5.02297	+	6.29860i	0.205233	+	0.257354i	0.873786	−	0.486310i	$-0.161658\pi$
$599$	5.02297	+	6.29860i	0.205233	+	0.257354i	−0.668553	+	0.743664i	$0.733086\pi$
$600$	0.961191	+	4.21125i	0.0392405	+	0.171924i
$601$	−23.4065	−	29.3508i	−0.954771	−	1.19725i	−0.980289	−	0.197571i	$-0.936695\pi$
$601$	−23.4065	−	29.3508i	−0.954771	−	1.19725i	0.0255173	−	0.999674i	$-0.491877\pi$
$602$	−30.6855	−	27.6859i	−1.25065	−	1.12839i
$603$	1.30775	−	1.63987i	0.0532557	−	0.0667806i
$604$	−71.1309	−	34.2549i	−2.89428	−	1.39381i
$605$	−2.47460	−	10.8419i	−0.100607	−	0.440788i
$606$	25.5373			1.03738
$607$	−42.6636			−1.73166			−0.865830	−	0.500337i	$-0.833209\pi$
$607$	−42.6636			−1.73166			−0.865830	+	0.500337i	$0.833209\pi$
$608$	−0.897723	−	3.93318i	−0.0364075	−	0.159512i
$609$	−18.2365	−	5.34791i	−0.738980	−	0.216708i
$610$	6.06777	−	26.5846i	0.245677	−	1.07638i
$611$	5.85623	−	25.6578i	0.236918	−	1.03800i
$612$	−17.1199	+	21.4676i	−0.692030	+	0.867778i
$613$	−13.7804	+	17.2800i	−0.556583	+	0.697934i	−0.977922	−	0.208970i	$-0.932989\pi$
$613$	−13.7804	+	17.2800i	−0.556583	+	0.697934i	0.421339	+	0.906903i	$0.361560\pi$
$614$	−9.28643	+	40.6865i	−0.374770	+	1.64197i
$615$	1.20595	−	5.28362i	0.0486287	−	0.213056i
$616$	53.0340	−	8.75151i	2.13680	−	0.352608i
$617$	−3.78644	−	16.5895i	−0.152437	−	0.667868i	−0.992173	−	0.124873i	$-0.960148\pi$
$617$	−3.78644	−	16.5895i	−0.152437	−	0.667868i	0.839736	−	0.542995i	$-0.182710\pi$
$618$	33.3056			1.33975
$619$	20.3092			0.816297			0.408149	−	0.912915i	$-0.366175\pi$
$619$	20.3092			0.816297			0.408149	+	0.912915i	$0.366175\pi$
$620$	7.17283	+	31.4262i	0.288068	+	1.26211i
$621$	2.67490	+	1.28817i	0.107340	+	0.0516923i
$622$	−18.5204	+	23.2238i	−0.742598	+	0.931189i
$623$	1.87094	−	30.7057i	0.0749578	−	1.23020i
$624$	7.91045	+	9.91939i	0.316672	+	0.397094i
$625$	−0.222521	−	0.974928i	−0.00890084	−	0.0389971i
$626$	3.92688	+	4.92415i	0.156950	+	0.196809i
$627$	9.10583	+	4.38514i	0.363652	+	0.175126i
$628$	−32.9556	+	41.3250i	−1.31507	+	1.64905i
$629$	2.55728	−	1.23152i	0.101965	−	0.0491039i
$630$	−3.10717	+	5.55938i	−0.123793	+	0.221491i
$631$	15.4520	+	7.44127i	0.615133	+	0.296232i	0.715386	−	0.698730i	$-0.246251\pi$
$631$	15.4520	+	7.44127i	0.615133	+	0.296232i	−0.100253	+	0.994962i	$0.531965\pi$
$632$	62.0710	−	29.8918i	2.46905	−	1.18903i
$633$	−1.01515	+	4.44767i	−0.0403487	+	0.176779i
$634$	48.8745	−	23.5367i	1.94105	−	0.934762i
$635$	11.1060	+	13.9265i	0.440729	+	0.552657i
$636$	3.85698			0.152939
$637$	29.9408	−	10.1581i	1.18630	−	0.402478i
$638$	81.3230			3.21961
$639$	−1.10940	−	1.39115i	−0.0438872	−	0.0550329i
$640$	−18.6025	+	8.95847i	−0.735327	+	0.354115i
$641$	0.803997	−	3.52254i	0.0317560	−	0.139132i	−0.956565	−	0.291520i	$-0.905839\pi$
$641$	0.803997	−	3.52254i	0.0317560	−	0.139132i	0.988321	+	0.152388i	$0.0486962\pi$
$642$	21.8712	−	10.5326i	0.863187	−	0.415689i
$643$	−4.10426	−	1.97651i	−0.161856	−	0.0779459i	0.351202	−	0.936300i	$-0.385773\pi$
$643$	−4.10426	−	1.97651i	−0.161856	−	0.0779459i	−0.513058	+	0.858354i	$0.671487\pi$
$644$	−29.4078	+	4.85280i	−1.15883	+	0.191227i
$645$	−5.84672	+	2.81563i	−0.230214	+	0.110865i
$646$	23.3382	−	29.2652i	0.918229	−	1.15142i
$647$	6.38502	+	3.07486i	0.251021	+	0.120885i	0.555164	−	0.831741i	$-0.312656\pi$
$647$	6.38502	+	3.07486i	0.251021	+	0.120885i	−0.304143	+	0.952627i	$0.598370\pi$
$648$	−2.69320	−	3.37716i	−0.105799	−	0.132668i
$649$	2.45984	+	10.7773i	0.0965573	+	0.423045i
$650$	−6.77889	−	8.50047i	−0.265890	−	0.333416i
$651$	−10.9655	+	19.6196i	−0.429773	+	0.768953i
$652$	23.9484	−	30.0303i	0.937892	−	1.17608i
$653$	20.8062	+	10.0197i	0.814208	+	0.392102i	0.794169	−	0.607697i	$-0.207907\pi$
$653$	20.8062	+	10.0197i	0.814208	+	0.392102i	0.0200393	+	0.999799i	$0.493621\pi$
$654$	2.82878	+	12.3937i	0.110614	+	0.484633i
$655$	11.4685			0.448111
$656$	−15.2233			−0.594369
$657$	−0.332772	−	1.45797i	−0.0129827	−	0.0568808i
$658$	−14.0378	−	34.3514i	−0.547249	−	1.33916i
$659$	6.07094	−	26.5985i	0.236490	−	1.03613i	−0.707644	−	0.706570i	$-0.750242\pi$
$659$	6.07094	−	26.5985i	0.236490	−	1.03613i	0.944134	−	0.329562i	$-0.106901\pi$
$660$	3.97119	−	17.3989i	0.154578	−	0.677252i
$661$	−17.2707	+	21.6568i	−0.671752	+	0.842350i	−0.994566	−	0.104112i	$-0.966800\pi$
$661$	−17.2707	+	21.6568i	−0.671752	+	0.842350i	0.322814	+	0.946463i	$0.395371\pi$
$662$	26.7985	−	33.6042i	1.04155	−	1.30606i
$663$	7.27304	−	31.8653i	0.282461	−	1.23754i
$664$	7.80913	−	34.2140i	0.303053	−	1.32776i
$665$	2.77376	−	4.96283i	0.107562	−	0.192450i
$666$	0.210099	+	0.920503i	0.00814116	+	0.0356688i
$667$	−21.3258			−0.825738
$668$	15.8355			0.612693
$669$	−0.275935	−	1.20895i	−0.0106683	−	0.0467408i
$670$	4.54896	+	2.19066i	0.175742	+	0.0846327i
$671$	−33.2186	+	41.6548i	−1.28239	+	1.60807i
$672$	−4.76647	−	1.39778i	−0.183870	−	0.0539206i
$673$	8.31116	+	10.4219i	0.320372	+	0.401733i	0.915774	−	0.401695i	$-0.131579\pi$
$673$	8.31116	+	10.4219i	0.320372	+	0.401733i	−0.595402	+	0.803428i	$0.703007\pi$
$674$	9.88327	+	43.3014i	0.380689	+	1.66791i
$675$	0.623490	+	0.781831i	0.0239981	+	0.0300927i
$676$	−25.3009	−	12.1843i	−0.973111	−	0.468626i
$677$	−9.15910	+	11.4852i	−0.352013	+	0.441410i	−0.926040	−	0.377426i	$-0.876809\pi$
$677$	−9.15910	+	11.4852i	−0.352013	+	0.441410i	0.574027	+	0.818837i	$0.305381\pi$
$678$	3.41562	−	1.64487i	0.131176	−	0.0631710i
$679$	37.7432	−	26.5112i	1.44845	−	1.01741i
$680$	−28.1625	−	13.5623i	−1.07998	−	0.520091i
$681$	14.6983	−	7.07835i	0.563241	−	0.271243i
$682$	21.4017	−	93.7669i	0.819513	−	3.59052i
$683$	3.48222	−	1.67695i	0.133243	−	0.0641666i	−0.366074	−	0.930586i	$-0.619298\pi$
$683$	3.48222	−	1.67695i	0.133243	−	0.0641666i	0.499318	+	0.866419i	$0.333584\pi$
$684$	5.08380	+	6.37488i	0.194384	+	0.243750i
$685$	8.43511			0.322289
$686$	26.3141	−	35.9870i	1.00468	−	1.37399i
$687$	−14.5051			−0.553403
$688$	11.3653	+	14.2516i	0.433298	+	0.543338i
$689$	−4.13648	+	1.99202i	−0.157587	+	0.0758900i
$690$	−1.59029	+	6.96751i	−0.0605412	+	0.265248i
$691$	−1.55697	+	0.749799i	−0.0592301	+	0.0285237i	−0.463264	−	0.886220i	$-0.653322\pi$
$691$	−1.55697	+	0.749799i	−0.0592301	+	0.0285237i	0.404034	+	0.914744i	$0.367608\pi$
$692$	−39.7054	−	19.1211i	−1.50937	−	0.726876i
$693$	10.1827	−	7.15245i	0.386810	−	0.271699i
$694$	−7.73276	+	3.72390i	−0.293532	+	0.141357i
$695$	−5.16783	+	6.48025i	−0.196027	+	0.245810i
$696$	27.9547	+	13.4623i	1.05962	+	0.510287i
$697$	24.4518	+	30.6616i	0.926177	+	1.16139i
$698$	−1.61397	−	7.07126i	−0.0610896	−	0.267651i
$699$	−13.9835	−	17.5347i	−0.528904	−	0.663225i
$700$	−9.63350	−	2.82505i	−0.364112	−	0.106777i
$701$	20.4620	−	25.6586i	0.772840	−	0.969111i	−0.227148	−	0.973860i	$-0.572940\pi$
$701$	20.4620	−	25.6586i	0.772840	−	0.969111i	0.999989	+	0.00474893i	$0.00151164\pi$
$702$	9.79579	+	4.71740i	0.369718	+	0.178047i
$703$	−0.187554	−	0.821729i	−0.00707374	−	0.0309921i
$704$	47.6782			1.79694
$705$	−5.82671			−0.219447
$706$	0.746321	+	3.26985i	0.0280882	+	0.123062i
$707$	−13.6939	+	24.5012i	−0.515012	+	0.921464i
$708$	−1.98453	+	8.69478i	−0.0745831	+	0.326770i
$709$	8.20189	−	35.9348i	0.308029	−	1.34956i	−0.549659	−	0.835389i	$-0.685242\pi$
$709$	8.20189	−	35.9348i	0.308029	−	1.34956i	0.857687	−	0.514172i	$-0.171901\pi$
$710$	2.67052	−	3.34872i	0.100223	−	0.125675i
$711$	9.94419	−	12.4696i	0.372936	−	0.467647i
$712$	−11.1760	+	48.9651i	−0.418837	+	1.83504i
$713$	−5.61229	+	24.5890i	−0.210182	+	0.920867i
$714$	−17.4340	−	42.6621i	−0.652450	−	1.59659i
$715$	4.72709	+	20.7108i	0.176783	+	0.774538i
$716$	−21.4528			−0.801728
$717$	1.13295			0.0423107
$718$	−1.41411	−	6.19563i	−0.0527742	−	0.231219i
$719$	−36.1652	−	17.4162i	−1.34873	−	0.649516i	−0.386639	−	0.922231i	$-0.626364\pi$
$719$	−36.1652	−	17.4162i	−1.34873	−	0.649516i	−0.962095	+	0.272715i	$0.912078\pi$
$720$	1.75137	−	2.19615i	0.0652697	−	0.0818457i
$721$	−17.8595	+	31.9544i	−0.665122	+	1.19004i
$722$	21.5857	+	27.0676i	0.803336	+	1.00735i
$723$	−0.336193	−	1.47296i	−0.0125032	−	0.0547799i
$724$	56.4554	+	70.7929i	2.09815	+	2.63100i
$725$	−6.47167	−	3.11659i	−0.240352	−	0.115747i
$726$	−16.6905	+	20.9293i	−0.619444	+	0.776759i
$727$	−31.5718	+	15.2042i	−1.17093	+	0.563892i	−0.915257	−	0.402870i	$-0.868013\pi$
$727$	−31.5718	+	15.2042i	−1.17093	+	0.563892i	−0.255677	+	0.966762i	$0.582298\pi$
$728$	−50.9304	+	8.40439i	−1.88761	+	0.311487i
$729$	−0.900969	−	0.433884i	−0.0333692	−	0.0160698i
$730$	3.24334	−	1.56191i	0.120041	−	0.0578088i
$731$	10.4495	−	45.7822i	0.386489	−	1.69332i
$732$	−38.7268	+	18.6498i	−1.43138	+	0.689318i
$733$	−31.0656	−	38.9550i	−1.14743	−	1.43884i	−0.879817	−	0.475312i	$-0.842335\pi$
$733$	−31.0656	−	38.9550i	−1.14743	−	1.43884i	−0.267617	−	0.963525i	$-0.586236\pi$
$734$	36.5053			1.34744
$735$	−3.66767	−	5.96223i	−0.135284	−	0.219920i
$736$	−5.57392			−0.205457
$737$	−6.15071	−	7.71274i	−0.226564	−	0.284103i
$738$	−11.7537	+	5.66029i	−0.432660	+	0.208358i
$739$	−3.38489	+	14.8302i	−0.124515	+	0.545537i	0.873735	+	0.486403i	$0.161691\pi$
$739$	−3.38489	+	14.8302i	−0.124515	+	0.545537i	−0.998250	+	0.0591346i	$0.981166\pi$
$740$	−1.34093	+	0.645757i	−0.0492935	+	0.0237385i
$741$	−8.74466	−	4.21120i	−0.321243	−	0.154702i
$742$	−3.15837	+	5.65098i	−0.115947	+	0.207454i
$743$	16.2230	−	7.81259i	0.595164	−	0.286616i	−0.111952	−	0.993714i	$-0.535710\pi$
$743$	16.2230	−	7.81259i	0.595164	−	0.286616i	0.707116	+	0.707098i	$0.249996\pi$
$744$	22.8791	−	28.6895i	0.838788	−	1.05181i
$745$	6.43680	+	3.09980i	0.235826	+	0.113568i
$746$	−27.2581	−	34.1806i	−0.997990	−	1.25144i
$747$	−1.80786	−	7.92073i	−0.0661460	−	0.289804i
$748$	80.5194	+	100.968i	2.94408	+	3.69176i
$749$	−1.62271	+	26.6318i	−0.0592927	+	0.973105i
$750$	−1.50084	+	1.88200i	−0.0548031	+	0.0687209i
$751$	4.52802	+	2.18058i	0.165230	+	0.0795705i	0.514671	−	0.857388i	$-0.327914\pi$
$751$	4.52802	+	2.18058i	0.165230	+	0.0795705i	−0.349441	+	0.936958i	$0.613628\pi$
$752$	3.64203	+	15.9568i	0.132811	+	0.581883i
$753$	9.42405			0.343432
$754$	−78.0973			−2.84414
$755$	−4.62988	−	20.2848i	−0.168499	−	0.738241i
$756$	9.90523	−	1.63453i	0.360250	−	0.0594474i
$757$	−4.10282	+	17.9756i	−0.149119	+	0.653335i	0.844011	+	0.536325i	$0.180188\pi$
$757$	−4.10282	+	17.9756i	−0.149119	+	0.653335i	−0.993131	+	0.117010i	$0.962669\pi$
$758$	−16.7433	+	73.3572i	−0.608144	+	2.66445i
$759$	8.70619	−	10.9172i	0.316015	−	0.396270i
$760$	−5.78733	+	7.25708i	−0.209928	+	0.263242i
$761$	−0.0229180	+	0.100410i	−0.000830777	+	0.00363987i	−0.975342	−	0.220701i	$-0.929166\pi$
$761$	−0.0229180	+	0.100410i	−0.000830777	+	0.00363987i	0.974511	+	0.224340i	$0.0720228\pi$
$762$	9.54127	−	41.8030i	0.345644	−	1.51436i
$763$	−13.4078	−	3.93188i	−0.485395	−	0.142344i
$764$	10.1070	+	44.2818i	0.365659	+	1.60206i
$765$	−7.23639			−0.261632
$766$	86.0335			3.10852
$767$	−2.36228	−	10.3498i	−0.0852969	−	0.373710i
$768$	26.5126	+	12.7678i	0.956690	+	0.460718i
$769$	−26.3285	+	33.0149i	−0.949431	+	1.19055i	0.0321465	+	0.999483i	$0.489766\pi$
$769$	−26.3285	+	33.0149i	−0.949431	+	1.19055i	−0.981577	+	0.191065i	$0.938806\pi$
$770$	22.2398	+	20.0658i	0.801467	+	0.723121i
$771$	14.3758	+	18.0267i	0.517731	+	0.649214i
$772$	12.1571	+	53.2636i	0.437543	+	1.91700i
$773$	−6.81750	−	8.54888i	−0.245209	−	0.307482i	0.643962	−	0.765057i	$-0.277289\pi$
$773$	−6.81750	−	8.54888i	−0.245209	−	0.307482i	−0.889171	+	0.457575i	$0.848718\pi$
$774$	14.0740	+	6.77770i	0.505881	+	0.243619i
$775$	−5.29663	+	6.64177i	−0.190261	+	0.238579i
$776$	−67.8459	+	32.6728i	−2.43552	+	1.17289i
$777$	−0.995820	−	0.292028i	−0.0357249	−	0.0104764i
$778$	11.7119	+	5.64013i	0.419890	+	0.202208i
$779$	10.4925	−	5.05292i	0.375933	−	0.181040i
$780$	−3.81367	+	16.7088i	−0.136551	+	0.598271i
$781$	−7.53996	+	3.63106i	−0.269801	+	0.129929i
$782$	−32.2445	−	40.4334i	−1.15306	−	1.44589i
$783$	7.18301			0.256700
$784$	−14.0354	+	13.7709i	−0.501263	+	0.491816i
$785$	−13.9300			−0.497183
$786$	−17.2124	−	21.5837i	−0.613946	−	0.769864i
$787$	−23.6208	+	11.3752i	−0.841990	+	0.405481i	−0.804598	−	0.593820i	$-0.797619\pi$
$787$	−23.6208	+	11.3752i	−0.841990	+	0.405481i	−0.0373916	+	0.999301i	$0.511905\pi$
$788$	13.5226	−	59.2465i	0.481724	−	2.11057i
$789$	20.8786	−	10.0546i	0.743298	−	0.357953i
$790$	34.5904	+	16.6579i	1.23067	+	0.592661i
$791$	−0.253419	+	4.15908i	−0.00901053	+	0.147880i
$792$	−18.3041	+	8.81480i	−0.650409	+	0.313220i
$793$	31.9010	−	40.0026i	1.13284	−	1.42053i
$794$	−74.8699	−	36.0554i	−2.65703	−	1.27956i
$795$	0.633763	+	0.794714i	0.0224773	+	0.0281856i
$796$	22.3502	+	97.9228i	0.792183	+	3.47078i
$797$	−0.319338	−	0.400438i	−0.0113115	−	0.0141842i	0.776144	−	0.630556i	$-0.217173\pi$
$797$	−0.319338	−	0.400438i	−0.0113115	−	0.0141842i	−0.787455	+	0.616372i	$0.788602\pi$
$798$	−13.5030	+	2.22823i	−0.478002	+	0.0788785i
$799$	26.2890	−	32.9654i	0.930040	−	1.16623i
$800$	−1.69150	−	0.814583i	−0.0598035	−	0.0287999i
$801$	2.58729	+	11.3357i	0.0914175	+	0.400526i
$802$	−58.2792			−2.05791
$803$	−7.03358			−0.248209
$804$	−1.77099	−	7.75921i	−0.0624580	−	0.273646i
$805$	−5.83208	−	5.26197i	−0.205554	−	0.185460i
$806$	−20.5528	+	90.0477i	−0.723941	+	3.17179i
$807$	−1.62636	+	7.12554i	−0.0572505	+	0.250831i
$808$	28.5717	−	35.8278i	1.00515	−	1.26042i
$809$	−24.7529	+	31.0392i	−0.870266	+	1.09128i	0.124812	+	0.992180i	$0.460167\pi$
$809$	−24.7529	+	31.0392i	−0.870266	+	1.09128i	−0.995078	+	0.0990985i	$0.968404\pi$
$810$	0.535645	−	2.34681i	0.0188207	−	0.0824587i
$811$	0.944768	−	4.13930i	0.0331753	−	0.145350i	−0.955628	−	0.294577i	$-0.904821\pi$
$811$	0.944768	−	4.13930i	0.0331753	−	0.145350i	0.988803	+	0.149227i	$0.0476784\pi$
$812$	−59.0092	+	41.4487i	−2.07082	+	1.45456i
$813$	−3.83027	−	16.7815i	−0.134333	−	0.588553i
$814$	4.44071			0.155647
$815$	10.1227			0.354584
$816$	4.52316	+	19.8172i	0.158342	+	0.693742i
$817$	−12.5638	−	6.05042i	−0.439553	−	0.211678i
$818$	6.78030	−	8.50223i	0.237068	−	0.297274i
$819$	−9.77883	+	6.86876i	−0.341700	+	0.240014i
$820$	−12.8215	−	16.0776i	−0.447745	−	0.561455i
$821$	9.73255	+	42.6411i	0.339668	+	1.48818i	0.799764	+	0.600315i	$0.204958\pi$
$821$	9.73255	+	42.6411i	0.339668	+	1.48818i	−0.460096	+	0.887869i	$0.652185\pi$
$822$	−12.6598	−	15.8749i	−0.441561	−	0.553700i
$823$	13.2464	+	6.37912i	0.461740	+	0.222362i	0.650267	−	0.759706i	$-0.274657\pi$
$823$	13.2464	+	6.37912i	0.461740	+	0.222362i	−0.188527	+	0.982068i	$0.560371\pi$
$824$	37.2631	−	46.7264i	1.29812	−	1.62779i
$825$	4.23750	−	2.04067i	0.147531	−	0.0710471i
$826$	−11.1139	−	10.0275i	−0.386703	−	0.348901i
$827$	−11.1405	−	5.36497i	−0.387392	−	0.186558i	0.230042	−	0.973181i	$-0.426114\pi$
$827$	−11.1405	−	5.36497i	−0.387392	−	0.186558i	−0.617434	+	0.786622i	$0.711828\pi$
$828$	10.1498	−	4.88789i	0.352730	−	0.169866i
$829$	3.41217	−	14.9497i	0.118510	−	0.519225i	−0.880472	−	0.474099i	$-0.842774\pi$
$829$	3.41217	−	14.9497i	0.118510	−	0.519225i	0.998981	−	0.0451259i	$-0.0143689\pi$
$830$	17.6201	−	8.48540i	0.611603	−	0.294533i
$831$	19.1124	+	23.9662i	0.663001	+	0.831377i
$832$	−45.7870			−1.58738
$833$	50.2800	+	6.15010i	1.74210	+	0.213088i
$834$	19.9519			0.690879
$835$	2.60202	+	3.26283i	0.0900466	+	0.112915i
$836$	34.5517	−	16.6392i	1.19499	−	0.575479i
$837$	1.89035	−	8.28215i	0.0653399	−	0.286273i
$838$	9.36022	−	4.50764i	0.323343	−	0.155714i
$839$	23.5295	+	11.3312i	0.812328	+	0.391197i	0.793458	−	0.608625i	$-0.208279\pi$
$839$	23.5295	+	11.3312i	0.812328	+	0.391197i	0.0188706	+	0.999822i	$0.493993\pi$
$840$	4.32322	+	10.5792i	0.149165	+	0.365017i
$841$	−20.3580	+	9.80390i	−0.702000	+	0.338066i
$842$	18.2236	−	22.8517i	0.628026	−	0.787520i
$843$	12.5495	+	6.04351i	0.432227	+	0.208150i
$844$	10.7929	+	13.5339i	0.371508	+	0.465856i
$845$	−1.64683	−	7.21521i	−0.0566525	−	0.248211i
$846$	8.74499	+	10.9659i	0.300659	+	0.377014i
$847$	−11.1302	−	27.2364i	−0.382438	−	0.935853i
$848$	1.78023	−	2.23234i	0.0611333	−	0.0766587i
$849$	−7.12701	−	3.43219i	−0.244598	−	0.117792i
$850$	−3.87614	−	16.9825i	−0.132950	−	0.582494i
$851$	−1.16451			−0.0399190
$852$	−6.75163			−0.231307
$853$	−4.10775	−	17.9972i	−0.140647	−	0.616213i	−0.995285	−	0.0969898i	$-0.969079\pi$
$853$	−4.10775	−	17.9972i	−0.140647	−	0.616213i	0.854639	−	0.519223i	$-0.173779\pi$
$854$	4.38777	−	72.0117i	0.150147	−	2.46419i
$855$	−0.478168	+	2.09499i	−0.0163530	+	0.0716472i
$856$	9.69318	−	42.4686i	0.331306	−	1.45155i
$857$	−3.42727	+	4.29766i	−0.117073	+	0.146805i	−0.836915	−	0.547333i	$-0.815643\pi$
$857$	−3.42727	+	4.29766i	−0.117073	+	0.146805i	0.719842	+	0.694138i	$0.244214\pi$
$858$	31.8830	−	39.9800i	1.08847	−	1.36489i
$859$	−3.38179	+	14.8166i	−0.115385	+	0.505535i	0.883898	+	0.467679i	$0.154910\pi$
$859$	−3.38179	+	14.8166i	−0.115385	+	0.505535i	−0.999283	+	0.0378556i	$0.987947\pi$
$860$	−5.47927	+	24.0063i	−0.186842	+	0.818607i
$861$	0.872057	−	14.3121i	0.0297196	−	0.487755i
$862$	20.4517	+	89.6046i	0.696587	+	3.05195i
$863$	−43.9440			−1.49587			−0.747936	−	0.663771i	$-0.768955\pi$
$863$	−43.9440			−1.49587			−0.747936	+	0.663771i	$0.768955\pi$
$864$	1.87742			0.0638712
$865$	−2.58441	−	11.3230i	−0.0878726	−	0.384995i
$866$	59.1602	+	28.4900i	2.01034	+	0.968131i
$867$	22.0499	−	27.6497i	0.748854	−	0.939034i
$868$	32.2617	+	78.9467i	1.09504	+	2.67963i
$869$	−46.7702	−	58.6480i	−1.58657	−	1.98950i
$870$	3.84755	+	16.8572i	0.130444	+	0.571513i
$871$	5.90675	+	7.40682i	0.200142	+	0.250971i
$872$	20.5528	+	9.89772i	0.696006	+	0.335179i
$873$	−10.8694	+	13.6297i	−0.367872	+	0.461297i
$874$	−13.8364	+	6.66328i	−0.468025	+	0.225389i
$875$	−1.00085	−	2.44914i	−0.0338348	−	0.0827962i
$876$	−5.11252	−	2.46206i	−0.172736	−	0.0831853i
$877$	−39.0312	+	18.7964i	−1.31799	+	0.634711i	−0.954868	−	0.297031i	$-0.904004\pi$
$877$	−39.0312	+	18.7964i	−1.31799	+	0.634711i	−0.363122	+	0.931742i	$0.618289\pi$
$878$	0.177065	−	0.775771i	0.00597565	−	0.0261810i
$879$	4.47851	−	2.15673i	0.151056	−	0.0727449i
$880$	−8.23717	−	10.3291i	−0.277675	−	0.348194i
$881$	−7.90585			−0.266355			−0.133177	−	0.991092i	$-0.542518\pi$
$881$	−7.90585			−0.266355			−0.133177	+	0.991092i	$0.542518\pi$
$882$	−5.71630	+	15.8509i	−0.192478	+	0.533729i
$883$	−39.4712			−1.32831			−0.664156	−	0.747594i	$-0.731209\pi$
$883$	−39.4712			−1.32831			−0.664156	+	0.747594i	$0.731209\pi$
$884$	−77.3257	−	96.9634i	−2.60074	−	3.26123i
$885$	−2.11761	+	1.01979i	−0.0711827	+	0.0342798i
$886$	15.5392	−	68.0816i	0.522049	−	2.28725i
$887$	−8.73197	+	4.20510i	−0.293191	+	0.141193i	−0.574697	−	0.818366i	$-0.694880\pi$
$887$	−8.73197	+	4.20510i	−0.293191	+	0.141193i	0.281506	+	0.959559i	$0.409166\pi$
$888$	1.52649	+	0.735121i	0.0512258	+	0.0246690i
$889$	34.9908	+	31.5703i	1.17355	+	1.05883i
$890$	−25.2169	+	12.1438i	−0.845271	+	0.407061i
$891$	−2.93244	+	3.67717i	−0.0982405	+	0.123190i
$892$	−4.23931	−	2.04155i	−0.141943	−	0.0683560i
$893$	−7.80661	−	9.78918i	−0.261238	−	0.327583i
$894$	−3.82682	−	16.7664i	−0.127988	−	0.560752i
$895$	−3.52504	−	4.42026i	−0.117829	−	0.147753i
$896$	−44.7017	+	31.3990i	−1.49338	+	1.04897i
$897$	−8.36086	+	10.4842i	−0.279161	+	0.350057i
$898$	−59.7094	−	28.7545i	−1.99253	−	0.959551i
$899$	13.5784	+	59.4908i	0.452864	+	1.98413i
$900$	3.79446			0.126482
$901$	−7.35562			−0.245051
$902$	13.6533	+	59.8189i	0.454604	+	1.99175i
$903$	−14.0497	+	9.86865i	−0.467544	+	0.328408i
$904$	1.51378	−	6.63230i	0.0503476	−	0.220587i
$905$	−5.31004	+	23.2648i	−0.176512	+	0.773348i
$906$	−31.2273	+	39.1578i	−1.03746	+	1.30093i
$907$	15.4833	−	19.4154i	0.514113	−	0.644677i	−0.455234	−	0.890372i	$-0.650445\pi$
$907$	15.4833	−	19.4154i	0.514113	−	0.644677i	0.969347	+	0.245694i	$0.0790159\pi$
$908$	13.7746	−	60.3504i	0.457126	−	2.00280i
$909$	2.36069	−	10.3429i	0.0782992	−	0.343051i
$910$	−21.3577	−	19.2699i	−0.708000	−	0.638791i
$911$	6.17335	+	27.0472i	0.204532	+	0.896114i	0.968135	+	0.250428i	$0.0805713\pi$
$911$	6.17335	+	27.0472i	0.204532	+	0.896114i	−0.763603	+	0.645686i	$0.776572\pi$
$912$	6.03613			0.199876
$913$	−38.2114			−1.26461
$914$	1.20709	+	5.28860i	0.0399270	+	0.174931i
$915$	−10.2061	−	4.91502i	−0.337405	−	0.162486i
$916$	−34.3162	+	43.0311i	−1.13384	+	1.42179i
$917$	29.9379	−	4.94026i	0.988636	−	0.163142i
$918$	10.8607	+	13.6189i	0.358456	+	0.449490i
$919$	2.59574	+	11.3727i	0.0856257	+	0.375151i	0.999526	−	0.0307881i	$-0.00980171\pi$
$919$	2.59574	+	11.3727i	0.0856257	+	0.375151i	−0.913900	+	0.405939i	$0.866945\pi$
$920$	7.99589	+	10.0265i	0.263617	+	0.330565i
$921$	15.6200	+	7.52220i	0.514697	+	0.247865i
$922$	15.3488	−	19.2467i	0.505484	−	0.633857i
$923$	7.24090	−	3.48703i	0.238337	−	0.114777i
$924$	2.87168	−	47.1296i	0.0944712	−	1.55045i
$925$	−0.353392	−	0.170184i	−0.0116194	−	0.00559563i
$926$	−39.2491	+	18.9014i	−1.28981	+	0.621138i
$927$	3.07880	−	13.4891i	0.101121	−	0.443040i
$928$	−12.1501	+	5.85116i	−0.398845	+	0.192074i
$929$	−31.1002	−	38.9985i	−1.02037	−	1.27950i	−0.959606	−	0.281346i	$-0.909219\pi$
$929$	−31.1002	−	38.9985i	−1.02037	−	1.27950i	−0.0607597	−	0.998152i	$-0.519352\pi$
$930$	20.4492			0.670556
$931$	5.10292	−	14.1501i	0.167241	−	0.463750i
$932$	−85.1012			−2.78758
$933$	7.69384	+	9.64777i	0.251885	+	0.315854i
$934$	5.70272	−	2.74629i	0.186599	−	0.0898612i
$935$	−7.57343	+	33.1814i	−0.247678	+	1.08515i
$936$	17.5781	−	8.46517i	0.574558	−	0.276693i
$937$	18.0337	+	8.68455i	0.589134	+	0.283712i	0.704606	−	0.709599i	$-0.251124\pi$
$937$	18.0337	+	8.68455i	0.589134	+	0.283712i	−0.115472	+	0.993311i	$0.536838\pi$
$938$	12.8185	+	3.75906i	0.418538	+	0.122738i
$939$	2.35734	−	1.13523i	0.0769288	−	0.0370470i
$940$	−13.7849	+	17.2857i	−0.449613	+	0.563796i
$941$	28.5124	+	13.7308i	0.929476	+	0.447612i	0.836445	−	0.548051i	$-0.184630\pi$
$941$	28.5124	+	13.7308i	0.929476	+	0.447612i	0.0930314	+	0.995663i	$0.470344\pi$
$942$	20.9067	+	26.2162i	0.681178	+	0.854171i
$943$	−3.58038	−	15.6867i	−0.116593	−	0.510828i
$944$	4.11637	+	5.16177i	0.133977	+	0.168001i
$945$	1.96438	+	1.77235i	0.0639012	+	0.0576546i
$946$	45.8077	−	57.4410i	1.48934	−	1.86757i
$947$	−2.14446	−	1.03272i	−0.0696855	−	0.0335588i	0.398716	−	0.917074i	$-0.369456\pi$
$947$	−2.14446	−	1.03272i	−0.0696855	−	0.0335588i	−0.468402	+	0.883515i	$0.655170\pi$
$948$	−13.4667	−	59.0013i	−0.437377	−	1.91627i
$949$	6.75459			0.219263
$950$	−5.17268			−0.167824
$951$	−5.01461	−	21.9704i	−0.162610	−	0.712440i
$952$	−79.3589	−	23.2722i	−2.57204	−	0.754258i
$953$	−0.148420	+	0.650270i	−0.00480779	+	0.0210643i	−0.977275	−	0.211976i	$-0.932010\pi$
$953$	−0.148420	+	0.650270i	−0.00480779	+	0.0210643i	0.972467	+	0.233040i	$0.0748673\pi$
$954$	0.544471	−	2.38548i	0.0176279	−	0.0772329i
$955$	−7.46332	+	9.35871i	−0.241508	+	0.302841i
$956$	2.68033	−	3.36103i	0.0866881	−	0.108703i
$957$	7.51757	−	32.9366i	0.243009	−	1.06469i
$958$	−7.67859	+	33.6421i	−0.248084	+	1.08693i
$959$	22.0194	−	3.63358i	0.711044	−	0.117334i
$960$	2.25575	+	9.88307i	0.0728039	+	0.318975i
$961$	41.1674			1.32798
$962$	−4.26458			−0.137495
$963$	−2.24402	−	9.83170i	−0.0723126	−	0.316822i
$964$	−5.16508	−	2.48737i	−0.166356	−	0.0801129i
$965$	−8.97714	+	11.2570i	−0.288984	+	0.362375i
$966$	−1.14998	+	18.8734i	−0.0370000	+	0.607240i
$967$	−20.2619	−	25.4077i	−0.651580	−	0.817055i	0.340818	−	0.940129i	$-0.389296\pi$
$967$	−20.2619	−	25.4077i	−0.651580	−	0.817055i	−0.992397	+	0.123074i	$0.960725\pi$
$968$	10.6892	+	46.8324i	0.343564	+	1.50525i
$969$	−9.69529	−	12.1575i	−0.311458	−	0.390556i
$970$	−37.8086	−	18.2077i	−1.21396	−	0.584613i
$971$	16.9429	−	21.2457i	0.543723	−	0.681808i	−0.431733	−	0.902002i	$-0.642098\pi$
$971$	16.9429	−	21.2457i	0.543723	−	0.681808i	0.975456	+	0.220194i	$0.0706690\pi$
$972$	−3.41869	+	1.64635i	−0.109654	+	0.0528068i
$973$	−10.6989	+	19.1425i	−0.342990	+	0.613680i
$974$	−6.49050	−	3.12566i	−0.207969	−	0.100153i
$975$	−4.06942	+	1.95973i	−0.130326	+	0.0627616i
$976$	−7.08063	+	31.0223i	−0.226645	+	0.992998i
$977$	−40.5471	+	19.5265i	−1.29722	+	0.624707i	−0.949757	−	0.312988i	$-0.898670\pi$
$977$	−40.5471	+	19.5265i	−1.29722	+	0.624707i	−0.347460	+	0.937695i	$0.612956\pi$
$978$	−15.1926	−	19.0510i	−0.485807	−	0.609183i
$979$	54.6859			1.74777
$980$	−26.3647	−	3.22485i	−0.842189	−	0.103014i
$981$	5.28108			0.168612
$982$	54.1992	+	67.9636i	1.72956	+	2.16881i
$983$	26.6675	−	12.8424i	0.850561	−	0.409609i	0.0427755	−	0.999085i	$-0.486380\pi$
$983$	26.6675	−	12.8424i	0.850561	−	0.409609i	0.807786	+	0.589476i	$0.200666\pi$
$984$	−5.20918	+	22.8229i	−0.166062	+	0.727567i
$985$	14.4295	−	6.94887i	0.459761	−	0.221409i
$986$	−112.731	−	54.2885i	−3.59010	−	1.72890i
$987$	−15.2103	+	2.50996i	−0.484150	+	0.0798931i
$988$	−33.1812	+	15.9792i	−1.05563	+	0.508367i
$989$	−12.0124	+	15.0631i	−0.381973	+	0.478979i
$990$	−10.2004	−	4.91224i	−0.324189	−	0.156121i
$991$	−29.9952	−	37.6128i	−0.952828	−	1.19481i	−0.980764	−	0.195199i	$-0.937465\pi$
$991$	−29.9952	−	37.6128i	−0.952828	−	1.19481i	0.0279354	−	0.999610i	$-0.491107\pi$
$992$	3.54898	+	15.5491i	0.112680	+	0.493684i
$993$	−11.1328	−	13.9601i	−0.353288	−	0.443009i
$994$	5.52872	−	9.89203i	0.175360	−	0.313756i
$995$	−16.5041	+	20.6955i	−0.523214	+	0.656090i
$996$	−27.7749	−	13.3757i	−0.880080	−	0.423824i
$997$	−4.33860	−	19.0086i	−0.137405	−	0.602009i	−0.996000	−	0.0893551i	$-0.971519\pi$
$997$	−4.33860	−	19.0086i	−0.137405	−	0.602009i	0.858595	−	0.512654i	$-0.171338\pi$
$998$	−38.3314			−1.21336
$999$	0.392235			0.0124098

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.u.b.106.1	✓	48
49.43	even	7	inner	735.2.u.b.631.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
735.2.u.b.106.1	✓	48	1.1	even	1	trivial
735.2.u.b.631.1	yes	48	49.43	even	7	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.u (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50084 - 1.88200i) q^{2} +(-0.900969 + 0.433884i) q^{3} +(-0.844346 + 3.69932i) q^{4} +(-0.900969 + 0.433884i) q^{5} +(2.16878 + 1.04443i) q^{6} +(-2.16503 + 1.52074i) q^{7} +(3.89178 - 1.87418i) q^{8} +(0.623490 - 0.781831i) q^{9} +(2.16878 + 1.04443i) q^{10} +(-2.93244 - 3.67717i) q^{11} +(-0.844346 - 3.69932i) q^{12} +(2.81613 + 3.53131i) q^{13} +(6.11140 + 1.79219i) q^{14} +(0.623490 - 0.781831i) q^{15} +(-2.53080 - 1.21877i) q^{16} +(1.61025 + 7.05496i) q^{17} -2.40717 q^{18} +2.14887 q^{19} +(-0.844346 - 3.69932i) q^{20} +(1.29080 - 2.30951i) q^{21} +(-2.51929 + 11.0377i) q^{22} +(0.660647 - 2.89448i) q^{23} +(-2.69320 + 3.37716i) q^{24} +(0.623490 - 0.781831i) q^{25} +(2.41936 - 10.5999i) q^{26} +(-0.222521 + 0.974928i) q^{27} +(-3.79767 - 9.29317i) q^{28} +(-1.59837 - 7.00292i) q^{29} -2.40717 q^{30} -8.49514 q^{31} +(-0.417766 - 1.83035i) q^{32} +(4.23750 + 2.04067i) q^{33} +(10.8607 - 13.6189i) q^{34} +(1.29080 - 2.30951i) q^{35} +(2.36580 + 2.96662i) q^{36} +(-0.0872805 - 0.382401i) q^{37} +(-3.22512 - 4.04417i) q^{38} +(-4.06942 - 1.95973i) q^{39} +(-2.69320 + 3.37716i) q^{40} +(4.88280 - 2.35143i) q^{41} +(-6.28379 + 1.03693i) q^{42} +(-5.84672 - 2.81563i) q^{43} +(16.0790 - 7.74324i) q^{44} +(-0.222521 + 0.974928i) q^{45} +(-6.43894 + 3.10083i) q^{46} +(-3.63290 - 4.55551i) q^{47} +2.80898 q^{48} +(2.37470 - 6.58489i) q^{49} -2.40717 q^{50} +(-4.51181 - 5.65764i) q^{51} +(-15.4413 + 7.43611i) q^{52} +(-0.226187 + 0.990992i) q^{53} +(2.16878 - 1.04443i) q^{54} +(4.23750 + 2.04067i) q^{55} +(-5.57568 + 9.97606i) q^{56} +(-1.93606 + 0.932359i) q^{57} +(-10.7806 + 13.5184i) q^{58} +(-2.11761 - 1.01979i) q^{59} +(2.36580 + 2.96662i) q^{60} +(-2.52071 - 11.0440i) q^{61} +(12.7499 + 15.9878i) q^{62} +(-0.160911 + 2.64085i) q^{63} +(-6.32046 + 7.92561i) q^{64} +(-4.06942 - 1.95973i) q^{65} +(-2.51929 - 11.0377i) q^{66} +2.09747 q^{67} -27.4582 q^{68} +(0.660647 + 2.89448i) q^{69} +(-6.28379 + 1.03693i) q^{70} +(0.395941 - 1.73473i) q^{71} +(0.961191 - 4.21125i) q^{72} +(0.932407 - 1.16920i) q^{73} +(-0.588684 + 0.738186i) q^{74} +(-0.222521 + 0.974928i) q^{75} +(-1.81439 + 7.94935i) q^{76} +(11.9408 + 3.50169i) q^{77} +(2.41936 + 10.5999i) q^{78} +15.9492 q^{79} +2.80898 q^{80} +(-0.222521 - 0.974928i) q^{81} +(-11.7537 - 5.66029i) q^{82} +(5.06550 - 6.35193i) q^{83} +(7.45374 + 6.72511i) q^{84} +(-4.51181 - 5.65764i) q^{85} +(3.47600 + 15.2294i) q^{86} +(4.47854 + 5.61591i) q^{87} +(-18.3041 - 8.81480i) q^{88} +(-7.24944 + 9.09051i) q^{89} +(2.16878 - 1.04443i) q^{90} +(-11.4672 - 3.36280i) q^{91} +(10.1498 + 4.88789i) q^{92} +(7.65386 - 3.68590i) q^{93} +(-3.12105 + 13.6742i) q^{94} +(-1.93606 + 0.932359i) q^{95} +(1.17055 + 1.46783i) q^{96} -17.4331 q^{97} +(-15.9568 + 5.41371i) q^{98} -4.70327 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} - 8 q^{3} - q^{4} - 8 q^{5} + q^{6} - q^{7} + 15 q^{8} - 8 q^{9} + q^{10} + 10 q^{11} - q^{12} + 20 q^{13} - q^{14} - 8 q^{15} - 15 q^{16} + 7 q^{17} - 6 q^{18} - 2 q^{19} - q^{20}+ \cdots - 32 q^{99}+O(q^{100}) \) 48 * q + q^2 - 8 * q^3 - q^4 - 8 * q^5 + q^6 - q^7 + 15 * q^8 - 8 * q^9 + q^10 + 10 * q^11 - q^12 + 20 * q^13 - q^14 - 8 * q^15 - 15 * q^16 + 7 * q^17 - 6 * q^18 - 2 * q^19 - q^20 - q^21 - 17 * q^22 + 12 * q^23 - 6 * q^24 - 8 * q^25 - 12 * q^26 - 8 * q^27 + 29 * q^28 + 12 * q^29 - 6 * q^30 - 58 * q^31 + 9 * q^32 + 3 * q^33 + 36 * q^34 - q^35 - q^36 - 15 * q^37 - 5 * q^38 - 8 * q^39 - 6 * q^40 - 2 * q^41 + 6 * q^42 + 30 * q^43 + 33 * q^44 - 8 * q^45 + 52 * q^46 + 6 * q^47 + 6 * q^48 + 13 * q^49 - 6 * q^50 - 7 * q^51 + 3 * q^53 + q^54 + 3 * q^55 - 67 * q^56 + 19 * q^57 + 36 * q^58 + 9 * q^59 - q^60 - 7 * q^61 + 14 * q^62 - 15 * q^63 + 19 * q^64 - 8 * q^65 - 17 * q^66 + 14 * q^67 + 22 * q^68 + 12 * q^69 + 6 * q^70 - 24 * q^71 - 6 * q^72 + 2 * q^73 + 2 * q^74 - 8 * q^75 + 62 * q^76 + 42 * q^77 - 12 * q^78 + 22 * q^79 + 6 * q^80 - 8 * q^81 - 51 * q^82 + 53 * q^83 + 50 * q^84 - 7 * q^85 - 35 * q^86 + 19 * q^87 + 11 * q^88 - 51 * q^89 + q^90 - q^91 + 29 * q^92 + 26 * q^93 - 4 * q^94 + 19 * q^95 + 9 * q^96 - 102 * q^97 + 90 * q^98 - 32 * q^99

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