LMFDB - Embedded newform 403.2.k.e.287.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(66,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("403.66");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.k (of order $5$, 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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			287.15
Character	$\chi$	$=$	403.287
Dual form			403.2.k.e.66.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.767174 - 2.36112i) q^{2} +(0.517972 + 1.59415i) q^{3} +(-3.36829 - 2.44720i) q^{4} +3.20234 q^{5} +4.16136 q^{6} +(-2.60176 - 1.89029i) q^{7} +(-4.34523 + 3.15699i) q^{8} +(0.154019 - 0.111901i) q^{9} +O(q^{10})$	\(q+(0.767174 - 2.36112i) q^{2} +(0.517972 + 1.59415i) q^{3} +(-3.36829 - 2.44720i) q^{4} +3.20234 q^{5} +4.16136 q^{6} +(-2.60176 - 1.89029i) q^{7} +(-4.34523 + 3.15699i) q^{8} +(0.154019 - 0.111901i) q^{9} +(2.45675 - 7.56111i) q^{10} +(0.903159 + 0.656183i) q^{11} +(2.15654 - 6.63715i) q^{12} +(0.309017 + 0.951057i) q^{13} +(-6.45920 + 4.69289i) q^{14} +(1.65872 + 5.10503i) q^{15} +(1.54734 + 4.76223i) q^{16} +(4.43884 - 3.22501i) q^{17} +(-0.146053 - 0.449505i) q^{18} +(1.47675 - 4.54497i) q^{19} +(-10.7864 - 7.83679i) q^{20} +(1.66578 - 5.12673i) q^{21} +(2.24221 - 1.62906i) q^{22} +(-4.73426 + 3.43964i) q^{23} +(-7.28344 - 5.29173i) q^{24} +5.25501 q^{25} +2.48263 q^{26} +(4.32637 + 3.14329i) q^{27} +(4.13756 + 12.7341i) q^{28} +(-2.63854 + 8.12060i) q^{29} +13.3261 q^{30} +(-5.20534 - 1.97596i) q^{31} +1.68928 q^{32} +(-0.578246 + 1.77966i) q^{33} +(-4.20926 - 12.9548i) q^{34} +(-8.33174 - 6.05336i) q^{35} -0.792627 q^{36} +4.97054 q^{37} +(-9.59828 - 6.97356i) q^{38} +(-1.35607 + 0.985241i) q^{39} +(-13.9149 + 10.1098i) q^{40} +(-1.25751 + 3.87020i) q^{41} +(-10.8269 - 7.86618i) q^{42} +(-2.09100 + 6.43544i) q^{43} +(-1.43628 - 4.42043i) q^{44} +(0.493222 - 0.358347i) q^{45} +(4.48940 + 13.8170i) q^{46} +(-0.568737 - 1.75039i) q^{47} +(-6.79025 + 4.93341i) q^{48} +(1.03285 + 3.17878i) q^{49} +(4.03151 - 12.4077i) q^{50} +(7.44036 + 5.40574i) q^{51} +(1.28657 - 3.95966i) q^{52} +(-6.66369 + 4.84145i) q^{53} +(10.7408 - 7.80362i) q^{54} +(2.89223 + 2.10132i) q^{55} +17.2729 q^{56} +8.01030 q^{57} +(17.1495 + 12.4598i) q^{58} +(3.79171 + 11.6697i) q^{59} +(6.90599 - 21.2545i) q^{60} +3.54653 q^{61} +(-8.65887 + 10.7745i) q^{62} -0.612248 q^{63} +(-1.79871 + 5.53587i) q^{64} +(0.989579 + 3.04561i) q^{65} +(3.75837 + 2.73061i) q^{66} -1.79487 q^{67} -22.8436 q^{68} +(-7.93554 - 5.76551i) q^{69} +(-20.6846 + 15.0282i) q^{70} +(1.28754 - 0.935454i) q^{71} +(-0.315976 + 0.972474i) q^{72} +(-0.0280883 - 0.0204074i) q^{73} +(3.81326 - 11.7360i) q^{74} +(2.72195 + 8.37730i) q^{75} +(-16.0966 + 11.6949i) q^{76} +(-1.10943 - 3.41447i) q^{77} +(1.28593 + 3.95769i) q^{78} +(-4.78075 + 3.47342i) q^{79} +(4.95513 + 15.2503i) q^{80} +(-2.59346 + 7.98186i) q^{81} +(8.17328 + 5.93824i) q^{82} +(3.45291 - 10.6270i) q^{83} +(-18.1570 + 13.1918i) q^{84} +(14.2147 - 10.3276i) q^{85} +(13.5907 + 9.87421i) q^{86} -14.3122 q^{87} -5.99599 q^{88} +(10.7589 + 7.81676i) q^{89} +(-0.467712 - 1.43947i) q^{90} +(0.993785 - 3.05856i) q^{91} +24.3639 q^{92} +(0.453754 - 9.32161i) q^{93} -4.56920 q^{94} +(4.72906 - 14.5546i) q^{95} +(0.875002 + 2.69298i) q^{96} +(-12.7754 - 9.28188i) q^{97} +8.29786 q^{98} +0.212532 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9}+O(q^{10}) $ 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9	\( 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9} - 13 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 3 q^{14} - 14 q^{15} + 9 q^{16} + 12 q^{17} - 19 q^{18} - 4 q^{19} - 53 q^{20} - 13 q^{21} - 14 q^{22} - 9 q^{23} + 2 q^{24} + 96 q^{25} + 12 q^{26} + 25 q^{27} - 25 q^{28} - 78 q^{30} - 2 q^{31} + 76 q^{32} + 29 q^{33} - 15 q^{34} - 36 q^{35} + 52 q^{36} + 24 q^{37} - 19 q^{38} + 3 q^{39} - 12 q^{40} - 40 q^{41} + 11 q^{42} - 22 q^{43} + 4 q^{44} + 63 q^{45} - 24 q^{46} + 3 q^{47} + 68 q^{48} + 33 q^{49} - 76 q^{50} - 59 q^{51} - 13 q^{52} - q^{53} + 18 q^{54} - 22 q^{55} + 78 q^{56} - 16 q^{57} + 5 q^{58} - 18 q^{59} + 43 q^{60} - 32 q^{61} - 39 q^{62} + 20 q^{63} + 23 q^{64} + 2 q^{65} + 11 q^{66} + 114 q^{67} + 98 q^{68} - 46 q^{69} + 32 q^{70} - 2 q^{71} + 28 q^{72} + 10 q^{73} - 43 q^{74} - 12 q^{75} - 35 q^{76} - 3 q^{77} - 6 q^{78} - 10 q^{79} + 68 q^{80} - 54 q^{81} - 80 q^{82} - 22 q^{83} - 14 q^{84} - 50 q^{85} - 66 q^{86} + 76 q^{87} - 34 q^{88} - 10 q^{89} - 63 q^{90} - 8 q^{91} - 64 q^{92} - 16 q^{93} + 30 q^{94} + 15 q^{95} + 34 q^{96} - 7 q^{97} + 138 q^{98} - 48 q^{99}+O(q^{100}) \) 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9 - 13 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 3 * q^14 - 14 * q^15 + 9 * q^16 + 12 * q^17 - 19 * q^18 - 4 * q^19 - 53 * q^20 - 13 * q^21 - 14 * q^22 - 9 * q^23 + 2 * q^24 + 96 * q^25 + 12 * q^26 + 25 * q^27 - 25 * q^28 - 78 * q^30 - 2 * q^31 + 76 * q^32 + 29 * q^33 - 15 * q^34 - 36 * q^35 + 52 * q^36 + 24 * q^37 - 19 * q^38 + 3 * q^39 - 12 * q^40 - 40 * q^41 + 11 * q^42 - 22 * q^43 + 4 * q^44 + 63 * q^45 - 24 * q^46 + 3 * q^47 + 68 * q^48 + 33 * q^49 - 76 * q^50 - 59 * q^51 - 13 * q^52 - q^53 + 18 * q^54 - 22 * q^55 + 78 * q^56 - 16 * q^57 + 5 * q^58 - 18 * q^59 + 43 * q^60 - 32 * q^61 - 39 * q^62 + 20 * q^63 + 23 * q^64 + 2 * q^65 + 11 * q^66 + 114 * q^67 + 98 * q^68 - 46 * q^69 + 32 * q^70 - 2 * q^71 + 28 * q^72 + 10 * q^73 - 43 * q^74 - 12 * q^75 - 35 * q^76 - 3 * q^77 - 6 * q^78 - 10 * q^79 + 68 * q^80 - 54 * q^81 - 80 * q^82 - 22 * q^83 - 14 * q^84 - 50 * q^85 - 66 * q^86 + 76 * q^87 - 34 * q^88 - 10 * q^89 - 63 * q^90 - 8 * q^91 - 64 * q^92 - 16 * q^93 + 30 * q^94 + 15 * q^95 + 34 * q^96 - 7 * q^97 + 138 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.767174	−	2.36112i	0.542474	−	1.66956i	−0.184448	−	0.982842i	$-0.559050\pi$
$2$	0.767174	−	2.36112i	0.542474	−	1.66956i	0.726922	−	0.686720i	$-0.240950\pi$
$3$	0.517972	+	1.59415i	0.299051	+	0.920385i	0.981830	+	0.189760i	$0.0607711\pi$
$3$	0.517972	+	1.59415i	0.299051	+	0.920385i	−0.682779	+	0.730625i	$0.739229\pi$
$4$	−3.36829	−	2.44720i	−1.68414	−	1.22360i
$5$	3.20234			1.43213			0.716066	−	0.698033i	$-0.245941\pi$
$5$	3.20234			1.43213			0.716066	+	0.698033i	$0.245941\pi$
$6$	4.16136			1.69887
$7$	−2.60176	−	1.89029i	−0.983374	−	0.714463i	−0.0249138	−	0.999690i	$-0.507931\pi$
$7$	−2.60176	−	1.89029i	−0.983374	−	0.714463i	−0.958460	+	0.285227i	$0.907931\pi$
$8$	−4.34523	+	3.15699i	−1.53627	+	1.11617i
$9$	0.154019	−	0.111901i	0.0513397	−	0.0373005i
$10$	2.45675	−	7.56111i	0.776894	−	2.39103i
$11$	0.903159	+	0.656183i	0.272313	+	0.197847i	0.715557	−	0.698554i	$-0.246173\pi$
$11$	0.903159	+	0.656183i	0.272313	+	0.197847i	−0.443245	+	0.896401i	$0.646173\pi$
$12$	2.15654	−	6.63715i	0.622540	−	1.91598i
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$14$	−6.45920	+	4.69289i	−1.72630	+	1.25423i
$15$	1.65872	+	5.10503i	0.428281	+	1.31811i
$16$	1.54734	+	4.76223i	0.386836	+	1.19056i
$17$	4.43884	−	3.22501i	1.07658	−	0.782180i	0.0994950	−	0.995038i	$-0.468277\pi$
$17$	4.43884	−	3.22501i	1.07658	−	0.782180i	0.977083	+	0.212858i	$0.0682773\pi$
$18$	−0.146053	−	0.449505i	−0.0344250	−	0.105949i
$19$	1.47675	−	4.54497i	0.338790	−	1.04269i	−0.626035	−	0.779795i	$-0.715323\pi$
$19$	1.47675	−	4.54497i	0.338790	−	1.04269i	0.964825	−	0.262893i	$-0.0846765\pi$
$20$	−10.7864	−	7.83679i	−2.41192	−	1.75236i
$21$	1.66578	−	5.12673i	0.363502	−	1.11874i
$22$	2.24221	−	1.62906i	0.478040	−	0.347316i
$23$	−4.73426	+	3.43964i	−0.987162	+	0.717216i	−0.959298	−	0.282396i	$-0.908871\pi$
$23$	−4.73426	+	3.43964i	−0.987162	+	0.717216i	−0.0278646	+	0.999612i	$0.508871\pi$
$24$	−7.28344	−	5.29173i	−1.48673	−	1.08017i
$25$	5.25501			1.05100
$26$	2.48263			0.486883
$27$	4.32637	+	3.14329i	0.832610	+	0.604927i
$28$	4.13756	+	12.7341i	0.781925	+	2.40652i
$29$	−2.63854	+	8.12060i	−0.489965	+	1.50796i	0.334694	+	0.942327i	$0.391367\pi$
$29$	−2.63854	+	8.12060i	−0.489965	+	1.50796i	−0.824659	+	0.565630i	$0.808633\pi$
$30$	13.3261			2.43300
$31$	−5.20534	−	1.97596i	−0.934907	−	0.354892i
$31$	−5.20534	−	1.97596i	−0.934907	−	0.354892i
$32$	1.68928			0.298626
$33$	−0.578246	+	1.77966i	−0.100660	+	0.309799i
$34$	−4.20926	−	12.9548i	−0.721883	−	2.22173i
$35$	−8.33174	−	6.05336i	−1.40832	−	1.02321i
$36$	−0.792627			−0.132104
$37$	4.97054			0.817151			0.408576	−	0.912725i	$-0.366026\pi$
$37$	4.97054			0.817151			0.408576	+	0.912725i	$0.366026\pi$
$38$	−9.59828	−	6.97356i	−1.55705	−	1.13126i
$39$	−1.35607	+	0.985241i	−0.217145	+	0.157765i
$40$	−13.9149	+	10.1098i	−2.20014	+	1.59850i
$41$	−1.25751	+	3.87020i	−0.196389	+	0.604424i	0.803568	+	0.595213i	$0.202932\pi$
$41$	−1.25751	+	3.87020i	−0.196389	+	0.604424i	−0.999958	+	0.00921169i	$0.997068\pi$
$42$	−10.8269	−	7.86618i	−1.67062	−	1.21378i
$43$	−2.09100	+	6.43544i	−0.318875	+	0.981396i	0.655255	+	0.755408i	$0.272561\pi$
$43$	−2.09100	+	6.43544i	−0.318875	+	0.981396i	−0.974130	+	0.225988i	$0.927439\pi$
$44$	−1.43628	−	4.42043i	−0.216528	−	0.666405i
$45$	0.493222	−	0.358347i	0.0735253	−	0.0534192i
$46$	4.48940	+	13.8170i	0.661926	+	2.03720i
$47$	−0.568737	−	1.75039i	−0.0829588	−	0.255321i	0.900970	−	0.433881i	$-0.142856\pi$
$47$	−0.568737	−	1.75039i	−0.0829588	−	0.255321i	−0.983929	+	0.178560i	$0.942856\pi$
$48$	−6.79025	+	4.93341i	−0.980089	+	0.712076i
$49$	1.03285	+	3.17878i	0.147550	+	0.454112i
$50$	4.03151	−	12.4077i	0.570141	−	1.75471i
$51$	7.44036	+	5.40574i	1.04186	+	0.756955i
$52$	1.28657	−	3.95966i	0.178415	−	0.549106i
$53$	−6.66369	+	4.84145i	−0.915328	+	0.665025i	−0.942357	−	0.334610i	$-0.891395\pi$
$53$	−6.66369	+	4.84145i	−0.915328	+	0.665025i	0.0270288	+	0.999635i	$0.491395\pi$
$54$	10.7408	−	7.80362i	1.46163	−	1.06194i
$55$	2.89223	+	2.10132i	0.389988	+	0.283343i
$56$	17.2729			2.30819
$57$	8.01030			1.06099
$58$	17.1495	+	12.4598i	2.25184	+	1.63605i
$59$	3.79171	+	11.6697i	0.493639	+	1.51926i	0.819067	+	0.573698i	$0.194492\pi$
$59$	3.79171	+	11.6697i	0.493639	+	1.51926i	−0.325428	+	0.945567i	$0.605508\pi$
$60$	6.90599	−	21.2545i	0.891560	−	2.74394i
$61$	3.54653			0.454086			0.227043	−	0.973885i	$-0.427094\pi$
$61$	3.54653			0.454086			0.227043	+	0.973885i	$0.427094\pi$
$62$	−8.65887	+	10.7745i	−1.09968	+	1.36837i
$63$	−0.612248			−0.0771360
$64$	−1.79871	+	5.53587i	−0.224839	+	0.691983i
$65$	0.989579	+	3.04561i	0.122742	+	0.377762i
$66$	3.75837	+	2.73061i	0.462623	+	0.336115i
$67$	−1.79487			−0.219279			−0.109639	−	0.993971i	$-0.534970\pi$
$67$	−1.79487			−0.219279			−0.109639	+	0.993971i	$0.534970\pi$
$68$	−22.8436			−2.77019
$69$	−7.93554	−	5.76551i	−0.955327	−	0.694086i
$70$	−20.6846	+	15.0282i	−2.47228	+	1.79622i
$71$	1.28754	−	0.935454i	0.152803	−	0.111018i	−0.508757	−	0.860910i	$-0.669895\pi$
$71$	1.28754	−	0.935454i	0.152803	−	0.111018i	0.661560	+	0.749892i	$0.269895\pi$
$72$	−0.315976	+	0.972474i	−0.0372381	+	0.114607i
$73$	−0.0280883	−	0.0204074i	−0.00328749	−	0.00238850i	0.586140	−	0.810210i	$-0.300647\pi$
$73$	−0.0280883	−	0.0204074i	−0.00328749	−	0.00238850i	−0.589428	+	0.807821i	$0.700647\pi$
$74$	3.81326	−	11.7360i	0.443283	−	1.36428i
$75$	2.72195	+	8.37730i	0.314304	+	0.967327i
$76$	−16.0966	+	11.6949i	−1.84641	+	1.34149i
$77$	−1.10943	−	3.41447i	−0.126431	−	0.389115i
$78$	1.28593	+	3.95769i	0.145603	+	0.448120i
$79$	−4.78075	+	3.47342i	−0.537877	+	0.390790i	−0.823296	−	0.567612i	$-0.807867\pi$
$79$	−4.78075	+	3.47342i	−0.537877	+	0.390790i	0.285419	+	0.958403i	$0.407867\pi$
$80$	4.95513	+	15.2503i	0.554000	+	1.70504i
$81$	−2.59346	+	7.98186i	−0.288163	+	0.886873i
$82$	8.17328	+	5.93824i	0.902588	+	0.655769i
$83$	3.45291	−	10.6270i	0.379006	−	1.16646i	−0.561730	−	0.827320i	$-0.689864\pi$
$83$	3.45291	−	10.6270i	0.379006	−	1.16646i	0.940736	−	0.339139i	$-0.110136\pi$
$84$	−18.1570	+	13.1918i	−1.98109	+	1.43934i
$85$	14.2147	−	10.3276i	1.54180	−	1.12018i
$86$	13.5907	+	9.87421i	1.46552	+	1.06476i
$87$	−14.3122			−1.53443
$88$	−5.99599			−0.639175
$89$	10.7589	+	7.81676i	1.14044	+	0.828575i	0.987180	−	0.159611i	$-0.0510240\pi$
$89$	10.7589	+	7.81676i	1.14044	+	0.828575i	0.153256	+	0.988186i	$0.451024\pi$
$90$	−0.467712	−	1.43947i	−0.0493012	−	0.151734i
$91$	0.993785	−	3.05856i	0.104177	−	0.320624i
$92$	24.3639			2.54011
$93$	0.453754	−	9.32161i	0.0470521	−	0.966606i
$94$	−4.56920			−0.471277
$95$	4.72906	−	14.5546i	0.485192	−	1.49327i
$96$	0.875002	+	2.69298i	0.0893045	+	0.274851i
$97$	−12.7754	−	9.28188i	−1.29715	−	0.942432i	−0.297223	−	0.954808i	$-0.596060\pi$
$97$	−12.7754	−	9.28188i	−1.29715	−	0.942432i	−0.999923	+	0.0123763i	$0.996060\pi$
$98$	8.29786			0.838210
$99$	0.212532			0.0213602
$100$	−17.7004	−	12.8601i	−1.77004	−	1.28601i
$101$	12.9038	−	9.37514i	1.28397	−	0.932862i	0.284309	−	0.958733i	$-0.408236\pi$
$101$	12.9038	−	9.37514i	1.28397	−	0.932862i	0.999665	+	0.0258711i	$0.00823595\pi$
$102$	18.4716	−	13.4204i	1.82896	−	1.32882i
$103$	−1.57598	+	4.85038i	−0.155286	+	0.477922i	−0.998190	−	0.0601429i	$-0.980844\pi$
$103$	−1.57598	+	4.85038i	−0.155286	+	0.477922i	0.842904	+	0.538065i	$0.180844\pi$
$104$	−4.34523	−	3.15699i	−0.426085	−	0.309569i
$105$	5.33439	−	16.4176i	0.520583	−	1.60219i
$106$	6.31903	+	19.4480i	0.613759	+	1.88896i
$107$	−0.784092	+	0.569676i	−0.0758011	+	0.0550727i	−0.625040	−	0.780592i	$-0.714918\pi$
$107$	−0.784092	+	0.569676i	−0.0758011	+	0.0550727i	0.549239	+	0.835665i	$0.314918\pi$
$108$	−6.88018	−	21.1750i	−0.662046	−	2.03757i
$109$	1.12311	+	3.45659i	0.107575	+	0.331081i	0.990326	−	0.138759i	$-0.0443114\pi$
$109$	1.12311	+	3.45659i	0.107575	+	0.331081i	−0.882751	+	0.469841i	$0.844311\pi$
$110$	7.18031	−	5.21680i	0.684616	−	0.497403i
$111$	2.57460	+	7.92380i	0.244370	+	0.752094i
$112$	4.97619	−	15.3151i	0.470206	−	1.44714i
$113$	−9.11121	−	6.61968i	−0.857111	−	0.622727i	0.0699867	−	0.997548i	$-0.477704\pi$
$113$	−9.11121	−	6.61968i	−0.857111	−	0.622727i	−0.927097	+	0.374821i	$0.877704\pi$
$114$	6.14529	−	18.9133i	0.575559	−	1.77139i
$115$	−15.1607	+	11.0149i	−1.41375	+	1.02715i
$116$	28.7601	−	20.8955i	2.67031	−	1.94010i
$117$	0.154019	+	0.111901i	0.0142391	+	0.0103453i
$118$	30.4624			2.80429
$119$	−17.6450			−1.61752
$120$	−23.3241	−	16.9459i	−2.12919	−	1.54694i
$121$	−3.01407	−	9.27635i	−0.274006	−	0.843304i
$122$	2.72080	−	8.37377i	0.246330	−	0.758125i
$123$	−6.82105			−0.615034
$124$	12.6975	+	19.3941i	1.14027	+	1.74164i
$125$	0.816635			0.0730420
$126$	−0.469700	+	1.44559i	−0.0418442	+	0.128783i
$127$	−1.64307	−	5.05686i	−0.145799	−	0.448723i	0.851314	−	0.524657i	$-0.175806\pi$
$127$	−1.64307	−	5.05686i	−0.145799	−	0.448723i	−0.997113	+	0.0759334i	$0.975806\pi$
$128$	14.4242	+	10.4798i	1.27493	+	0.926294i
$129$	−11.3422			−0.998622
$130$	7.95022			0.697281
$131$	6.99729	+	5.08383i	0.611356	+	0.444176i	0.849891	−	0.526958i	$-0.176667\pi$
$131$	6.99729	+	5.08383i	0.611356	+	0.444176i	−0.238536	+	0.971134i	$0.576667\pi$
$132$	6.30289	−	4.57932i	0.548596	−	0.398578i
$133$	−12.4335	+	9.03344i	−1.07812	+	0.783299i
$134$	−1.37698	+	4.23791i	−0.118953	+	0.366100i
$135$	13.8545	+	10.0659i	1.19241	+	0.866335i
$136$	−9.10646	+	28.0268i	−0.780872	+	2.40328i
$137$	0.231413	+	0.712216i	0.0197709	+	0.0608487i	0.960455	−	0.278434i	$-0.0898155\pi$
$137$	0.231413	+	0.712216i	0.0197709	+	0.0608487i	−0.940684	+	0.339283i	$0.889816\pi$
$138$	−19.7010	+	14.3136i	−1.67706	+	1.21845i
$139$	−5.93538	−	18.2672i	−0.503432	−	1.54940i	−0.803391	−	0.595452i	$-0.796973\pi$
$139$	−5.93538	−	18.2672i	−0.503432	−	1.54940i	0.299959	−	0.953952i	$-0.403027\pi$
$140$	13.2499	+	40.7789i	1.11982	+	3.44645i
$141$	2.49581	−	1.81331i	0.210185	−	0.152708i
$142$	−1.22095	−	3.75769i	−0.102460	−	0.315339i
$143$	−0.344976	+	1.06173i	−0.0288483	+	0.0887861i
$144$	0.771221	+	0.560325i	0.0642685	+	0.0466938i
$145$	−8.44952	+	26.0050i	−0.701695	+	2.15959i
$146$	−0.0697328	+	0.0506639i	−0.00577113	+	0.00419297i
$147$	−4.53248	+	3.29304i	−0.373833	+	0.271605i
$148$	−16.7422	−	12.1639i	−1.37620	−	0.999868i
$149$	14.8102			1.21330			0.606649	−	0.794970i	$-0.292513\pi$
$149$	14.8102			1.21330			0.606649	+	0.794970i	$0.292513\pi$
$150$	21.8680			1.78551
$151$	−2.84968	−	2.07041i	−0.231904	−	0.168488i	0.465765	−	0.884908i	$-0.345779\pi$
$151$	−2.84968	−	2.07041i	−0.231904	−	0.168488i	−0.697669	+	0.716421i	$0.745779\pi$
$152$	7.93162	+	24.4110i	0.643339	+	1.97999i
$153$	0.322784	−	0.993427i	0.0260955	−	0.0803138i
$154$	−8.91308			−0.718236
$155$	−16.6693	−	6.32769i	−1.33891	−	0.508252i
$156$	6.97872			0.558744
$157$	−5.28045	+	16.2515i	−0.421425	+	1.29701i	0.484950	+	0.874542i	$0.338838\pi$
$157$	−5.28045	+	16.2515i	−0.421425	+	1.29701i	−0.906376	+	0.422473i	$0.861162\pi$
$158$	4.53349	+	13.9526i	0.360665	+	1.11001i
$159$	−11.1696	−	8.11521i	−0.885809	−	0.643578i
$160$	5.40967			0.427672
$161$	18.8194			1.48317
$162$	16.8565	+	12.2469i	1.32437	+	0.962211i
$163$	20.1157	−	14.6149i	1.57558	−	1.14473i	0.654030	−	0.756469i	$-0.273077\pi$
$163$	20.1157	−	14.6149i	1.57558	−	1.14473i	0.921551	−	0.388257i	$-0.126923\pi$
$164$	13.7068	−	9.95859i	1.07032	−	0.777635i
$165$	−1.85174	+	5.69908i	−0.144158	+	0.443673i
$166$	−22.4425	−	16.3054i	−1.74188	−	1.26555i
$167$	−3.80885	+	11.7224i	−0.294737	+	0.907109i	0.688572	+	0.725168i	$0.258238\pi$
$167$	−3.80885	+	11.7224i	−0.294737	+	0.907109i	−0.983310	+	0.181941i	$0.941762\pi$
$168$	8.94687	+	27.5356i	0.690266	+	2.12442i
$169$	−0.809017	+	0.587785i	−0.0622321	+	0.0452143i
$170$	−13.4795	−	41.4857i	−1.03383	−	3.18181i
$171$	−0.281141	−	0.865263i	−0.0214994	−	0.0661683i
$172$	22.7919	−	16.5593i	1.73787	−	1.26264i
$173$	7.63956	+	23.5121i	0.580825	+	1.78759i	0.615427	+	0.788194i	$0.288984\pi$
$173$	7.63956	+	23.5121i	0.580825	+	1.78759i	−0.0346024	+	0.999401i	$0.511016\pi$
$174$	−10.9799	+	33.7927i	−0.832386	+	2.56182i
$175$	−13.6723	−	9.93350i	−1.03353	−	0.750902i
$176$	−1.72740	+	5.31639i	−0.130208	+	0.400738i
$177$	−16.6393	+	12.0891i	−1.25069	+	0.908676i
$178$	26.7102	−	19.4061i	2.00201	−	1.45455i
$179$	−17.0777	−	12.4077i	−1.27645	−	0.927395i	−0.277011	−	0.960867i	$-0.589344\pi$
$179$	−17.0777	−	12.4077i	−1.27645	−	0.927395i	−0.999440	+	0.0334715i	$0.989344\pi$
$180$	−2.53826			−0.189191
$181$	−7.66785			−0.569947			−0.284973	−	0.958535i	$-0.591985\pi$
$181$	−7.66785			−0.569947			−0.284973	+	0.958535i	$0.591985\pi$
$182$	−6.45920	−	4.69289i	−0.478788	−	0.347860i
$183$	1.83700	+	5.65371i	0.135795	+	0.417934i
$184$	9.71252	−	29.8921i	0.716017	−	2.20367i
$185$	15.9174			1.17027
$186$	−21.6613	−	8.22266i	−1.58828	−	0.602915i
$187$	6.12518			0.447917
$188$	−2.36790	+	7.28764i	−0.172697	+	0.531506i
$189$	−5.31445	−	16.3562i	−0.386570	−	1.18974i
$190$	−30.7370	−	22.3317i	−2.22990	−	1.62012i
$191$	−25.3126			−1.83156			−0.915779	−	0.401682i	$-0.868426\pi$
$191$	−25.3126			−1.83156			−0.915779	+	0.401682i	$0.868426\pi$
$192$	−9.75671			−0.704130
$193$	−11.6461	−	8.46138i	−0.838304	−	0.609063i	0.0835926	−	0.996500i	$-0.473361\pi$
$193$	−11.6461	−	8.46138i	−0.838304	−	0.609063i	−0.921896	+	0.387437i	$0.873361\pi$
$194$	−31.7166	+	23.0434i	−2.27712	+	1.65442i
$195$	−4.34260	+	3.15508i	−0.310980	+	0.225940i
$196$	4.30020	−	13.2347i	0.307157	−	0.945332i
$197$	−0.391505	−	0.284445i	−0.0278936	−	0.0202659i	0.573751	−	0.819030i	$-0.305488\pi$
$197$	−0.391505	−	0.284445i	−0.0278936	−	0.0202659i	−0.601645	+	0.798764i	$0.705488\pi$
$198$	0.163049	−	0.501812i	0.0115874	−	0.0356622i
$199$	5.48135	+	16.8699i	0.388563	+	1.19587i	0.933863	+	0.357632i	$0.116416\pi$
$199$	5.48135	+	16.8699i	0.388563	+	1.19587i	−0.545300	+	0.838241i	$0.683584\pi$
$200$	−22.8342	+	16.5900i	−1.61462	+	1.17309i
$201$	−0.929695	−	2.86131i	−0.0655756	−	0.201821i
$202$	−12.2364	−	37.6597i	−0.860949	−	2.64973i
$203$	22.2152	−	16.1403i	1.55920	−	1.13282i
$204$	−11.8323	−	36.4162i	−0.828429	−	2.54964i
$205$	−4.02697	+	12.3937i	−0.281256	+	0.865616i
$206$	10.2433	+	7.44216i	0.713681	+	0.518520i
$207$	−0.344266	+	1.05954i	−0.0239282	+	0.0736433i
$208$	−4.05100	+	2.94322i	−0.280886	+	0.204076i
$209$	4.31607	−	3.13581i	0.298549	−	0.216908i
$210$	−34.6714	−	25.1902i	−2.39255	−	1.73829i
$211$	13.0304			0.897050			0.448525	−	0.893770i	$-0.351950\pi$
$211$	13.0304			0.897050			0.448525	+	0.893770i	$0.351950\pi$
$212$	34.2932			2.35527
$213$	2.15817	+	1.56800i	0.147875	+	0.107438i
$214$	0.743538	+	2.28838i	0.0508272	+	0.156430i
$215$	−6.69611	+	20.6085i	−0.456671	+	1.40549i
$216$	−28.7224			−1.95431
$217$	9.80794	+	14.9806i	0.665806	+	1.01695i
$218$	9.02304			0.611118
$219$	0.0179835	−	0.0553476i	0.00121521	−	0.00374004i
$220$	−4.59948	−	14.1557i	−0.310097	−	0.954379i
$221$	4.43884	+	3.22501i	0.298589	+	0.216938i
$222$	20.6842			1.38823
$223$	−11.5636			−0.774356			−0.387178	−	0.922005i	$-0.626550\pi$
$223$	−11.5636			−0.774356			−0.387178	+	0.922005i	$0.626550\pi$
$224$	−4.39512	−	3.19324i	−0.293661	−	0.213357i
$225$	0.809372	−	0.588043i	0.0539582	−	0.0392029i
$226$	−22.6197	+	16.4342i	−1.50464	+	1.09319i
$227$	−0.499447	+	1.53714i	−0.0331495	+	0.102024i	−0.966262	−	0.257560i	$-0.917081\pi$
$227$	−0.499447	+	1.53714i	−0.0331495	+	0.102024i	0.933113	+	0.359584i	$0.117081\pi$
$228$	−26.9810	−	19.6028i	−1.78686	−	1.29823i
$229$	−0.900770	+	2.77229i	−0.0595246	+	0.183198i	−0.976397	−	0.215982i	$-0.930705\pi$
$229$	−0.900770	+	2.77229i	−0.0595246	+	0.183198i	0.916873	+	0.399179i	$0.130705\pi$
$230$	14.3766	+	44.2467i	0.947966	+	2.91754i
$231$	4.86853	−	3.53720i	0.320326	−	0.232730i
$232$	−14.1716	−	43.6157i	−0.930411	−	2.86351i
$233$	−8.31984	−	25.6058i	−0.545051	−	1.67749i	−0.720870	−	0.693071i	$-0.756257\pi$
$233$	−8.31984	−	25.6058i	−0.545051	−	1.67749i	0.175819	−	0.984422i	$-0.443743\pi$
$234$	0.382372	−	0.277810i	0.0249964	−	0.0181610i
$235$	−1.82129	−	5.60536i	−0.118808	−	0.365653i
$236$	15.7865	−	48.5860i	1.02762	−	3.16268i
$237$	−8.01346	−	5.82212i	−0.520530	−	0.378187i
$238$	−13.5368	+	41.6620i	−0.877461	+	2.70055i
$239$	12.5521	−	9.11960i	0.811925	−	0.589898i	−0.102463	−	0.994737i	$-0.532672\pi$
$239$	12.5521	−	9.11960i	0.811925	−	0.589898i	0.914388	+	0.404839i	$0.132672\pi$
$240$	−21.7447	+	15.7985i	−1.40362	+	1.01979i
$241$	−3.48538	−	2.53228i	−0.224513	−	0.163118i	0.469843	−	0.882750i	$-0.344311\pi$
$241$	−3.48538	−	2.53228i	−0.224513	−	0.163118i	−0.694356	+	0.719632i	$0.744311\pi$
$242$	−24.2149			−1.55659
$243$	1.97541			0.126723
$244$	−11.9457	−	8.67908i	−0.764747	−	0.555621i
$245$	3.30754	+	10.1796i	0.211311	+	0.650348i
$246$	−5.23293	+	16.1053i	−0.333640	+	1.02684i
$247$	4.77886			0.304072
$248$	28.8565	−	7.84726i	1.83239	−	0.498301i
$249$	18.7295			1.18693
$250$	0.626501	−	1.92817i	0.0396234	−	0.121948i
$251$	−7.67182	−	23.6114i	−0.484241	−	1.49034i	−0.833077	−	0.553157i	$-0.813423\pi$
$251$	−7.67182	−	23.6114i	−0.484241	−	1.49034i	0.348836	−	0.937184i	$-0.386577\pi$
$252$	2.06223	+	1.49830i	0.129908	+	0.0943837i
$253$	−6.53283			−0.410715
$254$	−13.2004			−0.828264
$255$	23.8266	+	17.3110i	1.49208	+	1.08406i
$256$	26.3918	−	19.1748i	1.64949	−	1.19842i
$257$	−1.76666	+	1.28355i	−0.110201	+	0.0800657i	−0.641521	−	0.767106i	$-0.721696\pi$
$257$	−1.76666	+	1.28355i	−0.110201	+	0.0800657i	0.531320	+	0.847171i	$0.321696\pi$
$258$	−8.70141	+	26.7802i	−0.541726	+	1.66726i
$259$	−12.9322	−	9.39576i	−0.803565	−	0.583824i
$260$	4.12005	−	12.6802i	0.255514	−	0.786392i
$261$	0.502321	+	1.54598i	0.0310929	+	0.0956940i
$262$	17.3716	−	12.6212i	1.07322	−	0.779743i
$263$	−0.594280	−	1.82900i	−0.0366449	−	0.112781i	0.931061	−	0.364864i	$-0.118885\pi$
$263$	−0.594280	−	1.82900i	−0.0366449	−	0.112781i	−0.967706	+	0.252083i	$0.918885\pi$
$264$	−3.10576	−	9.55854i	−0.191146	−	0.588287i
$265$	−21.3394	+	15.5040i	−1.31087	+	0.952403i
$266$	11.7904	+	36.2871i	0.722915	+	2.22491i
$267$	−6.88834	+	21.2001i	−0.421560	+	1.29743i
$268$	6.04565	+	4.39243i	0.369297	+	0.268310i
$269$	7.67560	−	23.6231i	0.467990	−	1.44032i	−0.387193	−	0.921999i	$-0.626555\pi$
$269$	7.67560	−	23.6231i	0.467990	−	1.44032i	0.855183	−	0.518326i	$-0.173445\pi$
$270$	34.3956	−	24.9899i	2.09325	−	1.52084i
$271$	0.0533848	−	0.0387863i	0.00324289	−	0.00235610i	−0.586163	−	0.810193i	$-0.699362\pi$
$271$	0.0533848	−	0.0387863i	0.00324289	−	0.00235610i	0.589406	+	0.807837i	$0.299362\pi$
$272$	22.2267	+	16.1486i	1.34769	+	0.979154i
$273$	5.39056			0.326252
$274$	1.85916			0.112316
$275$	4.74611	+	3.44825i	0.286201	+	0.207937i
$276$	12.6198	+	38.8398i	0.759623	+	2.33788i
$277$	−0.0798580	+	0.245778i	−0.00479820	+	0.0147674i	−0.953427	−	0.301624i	$-0.902471\pi$
$277$	−0.0798580	+	0.245778i	−0.00479820	+	0.0147674i	0.948629	+	0.316391i	$0.102471\pi$
$278$	−47.6845			−2.85993
$279$	−1.02283	+	0.278151i	−0.0612355	+	0.0166524i
$280$	55.3137			3.30563
$281$	−0.560185	+	1.72407i	−0.0334178	+	0.102850i	−0.966374	−	0.257140i	$-0.917220\pi$
$281$	−0.560185	+	1.72407i	−0.0334178	+	0.102850i	0.932956	+	0.359990i	$0.117220\pi$
$282$	−2.36672	−	7.28401i	−0.140936	−	0.433757i
$283$	−2.40054	−	1.74409i	−0.142697	−	0.103675i	0.514146	−	0.857702i	$-0.328109\pi$
$283$	−2.40054	−	1.74409i	−0.142697	−	0.103675i	−0.656843	+	0.754027i	$0.728109\pi$
$284$	−6.62606			−0.393184
$285$	25.6517			1.51948
$286$	2.24221	+	1.62906i	0.132584	+	0.0963282i
$287$	10.5875	−	7.69230i	0.624963	−	0.454062i
$288$	0.260182	−	0.189033i	0.0153314	−	0.0111389i
$289$	4.04937	−	12.4627i	0.238198	−	0.733099i
$290$	54.9185	+	39.9006i	3.22493	+	2.34305i
$291$	8.17944	−	25.1737i	0.479487	−	1.47571i
$292$	0.0446686	+	0.137476i	0.00261403	+	0.00804516i
$293$	6.16974	−	4.48258i	0.360440	−	0.261875i	−0.392796	−	0.919626i	$-0.628492\pi$
$293$	6.16974	−	4.48258i	0.360440	−	0.261875i	0.753236	+	0.657751i	$0.228492\pi$
$294$	4.29806	+	13.2281i	0.250668	+	0.771476i
$295$	12.1424	+	37.3704i	0.706956	+	2.17579i
$296$	−21.5981	+	15.6919i	−1.25536	+	0.912076i
$297$	1.84482	+	5.67778i	0.107048	+	0.329458i
$298$	11.3620	−	34.9686i	0.658182	−	2.02568i
$299$	−4.73426	−	3.43964i	−0.273790	−	0.198920i
$300$	11.3327	−	34.8783i	0.654291	−	2.01370i
$301$	17.6052	−	12.7909i	1.01474	−	0.737255i
$302$	−7.07469	+	5.14006i	−0.407103	+	0.295777i
$303$	21.6292	+	15.7145i	1.24257	+	0.902777i
$304$	23.9292			1.37244
$305$	11.3572			0.650312
$306$	−2.09797	−	1.52426i	−0.119933	−	0.0871362i
$307$	−1.61851	−	4.98127i	−0.0923735	−	0.284296i	0.894187	−	0.447694i	$-0.147755\pi$
$307$	−1.61851	−	4.98127i	−0.0923735	−	0.284296i	−0.986560	+	0.163398i	$0.947755\pi$
$308$	−4.61903	+	14.2159i	−0.263193	+	0.810026i
$309$	−8.54856			−0.486311
$310$	−27.7287	+	34.5038i	−1.57488	+	1.95968i
$311$	30.8613			1.74998			0.874991	−	0.484138i	$-0.160867\pi$
$311$	30.8613			1.74998			0.874991	+	0.484138i	$0.160867\pi$
$312$	2.78203	−	8.56219i	0.157501	−	0.484739i
$313$	0.895131	+	2.75493i	0.0505958	+	0.155718i	0.973162	−	0.230121i	$-0.0739121\pi$
$313$	0.895131	+	2.75493i	0.0505958	+	0.155718i	−0.922566	+	0.385839i	$0.873912\pi$
$314$	34.3208	+	24.9355i	1.93683	+	1.40719i
$315$	−1.96063			−0.110469
$316$	24.6031			1.38403
$317$	−14.6373	−	10.6346i	−0.822113	−	0.597300i	0.0952040	−	0.995458i	$-0.469650\pi$
$317$	−14.6373	−	10.6346i	−0.822113	−	0.597300i	−0.917317	+	0.398158i	$0.869650\pi$
$318$	−27.7300	+	20.1470i	−1.55502	+	1.12979i
$319$	−7.71162	+	5.60282i	−0.431768	+	0.313698i
$320$	−5.76010	+	17.7278i	−0.321999	+	0.991012i
$321$	−1.31429	−	0.954887i	−0.0733565	−	0.0532966i
$322$	14.4377	−	44.4347i	0.804583	−	2.47625i
$323$	−8.10250	−	24.9369i	−0.450835	−	1.38753i
$324$	28.2688	−	20.5385i	1.57049	−	1.14103i
$325$	1.62389	+	4.99781i	0.0900771	+	0.277229i
$326$	−19.0753	−	58.7076i	−1.05648	−	3.25151i
$327$	−4.92860	+	3.58084i	−0.272552	+	0.198021i
$328$	−6.75406	−	20.7869i	−0.372930	−	1.14776i
$329$	−1.82903	+	5.62918i	−0.100838	+	0.310347i
$330$	12.0356	+	8.74437i	0.662537	+	0.481362i
$331$	−2.79188	+	8.59253i	−0.153456	+	0.472288i	−0.998001	−	0.0631959i	$-0.979871\pi$
$331$	−2.79188	+	8.59253i	−0.153456	+	0.472288i	0.844545	+	0.535484i	$0.179871\pi$
$332$	−37.6367	+	27.3447i	−2.06558	+	1.50073i
$333$	0.765558	−	0.556210i	0.0419523	−	0.0304801i
$334$	24.7560	+	17.9863i	1.35459	+	0.984165i
$335$	−5.74781			−0.314036
$336$	26.9922			1.47255
$337$	−9.51826	−	6.91542i	−0.518492	−	0.376707i	0.297543	−	0.954708i	$-0.403833\pi$
$337$	−9.51826	−	6.91542i	−0.518492	−	0.376707i	−0.816036	+	0.578002i	$0.803833\pi$
$338$	0.767174	+	2.36112i	0.0417287	+	0.128428i
$339$	5.83344	−	17.9535i	0.316829	−	0.975099i
$340$	−73.1530			−3.96728
$341$	−3.40466	−	5.20026i	−0.184373	−	0.281610i
$342$	−2.25867			−0.122135
$343$	−3.63490	+	11.1871i	−0.196266	+	0.604045i
$344$	−11.2308	−	34.5647i	−0.605522	−	1.86361i
$345$	−25.4123	−	18.4631i	−1.36815	−	0.994022i
$346$	61.3758			3.29958
$347$	15.7148			0.843616			0.421808	−	0.906685i	$-0.361396\pi$
$347$	15.7148			0.843616			0.421808	+	0.906685i	$0.361396\pi$
$348$	48.2075	+	35.0248i	2.58419	+	1.87753i
$349$	18.1255	−	13.1689i	0.970235	−	0.704917i	0.0147302	−	0.999892i	$-0.495311\pi$
$349$	18.1255	−	13.1689i	0.970235	−	0.704917i	0.955505	+	0.294974i	$0.0953111\pi$
$350$	−33.9432	+	24.6612i	−1.81434	+	1.31820i
$351$	−1.65253	+	5.08595i	−0.0882053	+	0.271468i
$352$	1.52569	+	1.10848i	0.0813196	+	0.0590822i
$353$	1.06285	−	3.27111i	0.0565697	−	0.174104i	−0.918779	−	0.394772i	$-0.870824\pi$
$353$	1.06285	−	3.27111i	0.0565697	−	0.174104i	0.975349	+	0.220668i	$0.0708237\pi$
$354$	15.7787	+	48.5618i	0.838627	+	2.58103i
$355$	4.12315	−	2.99565i	0.218834	−	0.158992i
$356$	−17.1097	−	52.6582i	−0.906812	−	2.79088i
$357$	−9.13963	−	28.1289i	−0.483721	−	1.48874i
$358$	−42.3976	+	30.8037i	−2.24079	+	1.62803i
$359$	−5.34600	−	16.4533i	−0.282151	−	0.868372i	−0.987238	−	0.159251i	$-0.949092\pi$
$359$	−5.34600	−	16.4533i	−0.282151	−	0.868372i	0.705087	−	0.709121i	$-0.250908\pi$
$360$	−1.01186	+	3.11420i	−0.0533299	+	0.164133i
$361$	−3.10463	−	2.25564i	−0.163401	−	0.118718i
$362$	−5.88257	+	18.1047i	−0.309181	+	0.951561i
$363$	13.2267	−	9.60978i	0.694223	−	0.504382i
$364$	−10.8323	+	7.87010i	−0.567765	+	0.412505i
$365$	−0.0899485	−	0.0653514i	−0.00470812	−	0.00342065i
$366$	14.7584			0.771433
$367$	−14.7513			−0.770010			−0.385005	−	0.922915i	$-0.625800\pi$
$367$	−14.7513			−0.770010			−0.385005	+	0.922915i	$0.625800\pi$
$368$	−23.7059	−	17.2234i	−1.23576	−	0.897830i
$369$	0.239402	+	0.736802i	0.0124627	+	0.0383564i
$370$	12.2114	−	37.5828i	0.634840	−	1.95384i
$371$	26.4891			1.37525
$372$	−24.3403	+	30.2874i	−1.26198	+	1.57033i
$373$	−10.5984			−0.548763			−0.274382	−	0.961621i	$-0.588473\pi$
$373$	−10.5984			−0.548763			−0.274382	+	0.961621i	$0.588473\pi$
$374$	4.69908	−	14.4623i	0.242983	−	0.747826i
$375$	0.422994	+	1.30184i	0.0218433	+	0.0672268i
$376$	7.99727	+	5.81035i	0.412427	+	0.299646i
$377$	−8.53850			−0.439755
$378$	−42.6960			−2.19605
$379$	20.5184	+	14.9075i	1.05396	+	0.765747i	0.972961	−	0.230967i	$-0.0741891\pi$
$379$	20.5184	+	14.9075i	1.05396	+	0.765747i	0.0809986	+	0.996714i	$0.474189\pi$
$380$	−51.5468	+	37.4510i	−2.64430	+	1.92119i
$381$	7.21034	−	5.23862i	0.369397	−	0.268383i
$382$	−19.4192	+	59.7661i	−0.993572	+	3.05790i
$383$	−19.8588	−	14.4283i	−1.01474	−	0.737250i	−0.0495404	−	0.998772i	$-0.515776\pi$
$383$	−19.8588	−	14.4283i	−1.01474	−	0.737250i	−0.965198	+	0.261522i	$0.915776\pi$
$384$	−9.23509	+	28.4227i	−0.471276	+	1.45044i
$385$	−3.55277	−	10.9343i	−0.181066	−	0.557263i
$386$	−28.9129	+	21.0064i	−1.47163	+	1.06920i
$387$	0.398081	+	1.22517i	0.0202356	+	0.0622788i
$388$	20.3166	+	62.5281i	1.03142	+	3.17438i
$389$	8.15741	−	5.92670i	0.413597	−	0.300496i	−0.361459	−	0.932388i	$-0.617721\pi$
$389$	8.15741	−	5.92670i	0.413597	−	0.300496i	0.775056	+	0.631892i	$0.217721\pi$
$390$	4.11799	+	12.6739i	0.208523	+	0.641767i
$391$	−9.92178	+	30.5361i	−0.501766	+	1.54428i
$392$	−14.5234	−	10.5518i	−0.733540	−	0.532948i
$393$	−4.48000	+	13.7880i	−0.225986	+	0.695514i
$394$	−0.971960	+	0.706170i	−0.0489666	+	0.0355763i
$395$	−15.3096	+	11.1231i	−0.770310	+	0.559663i
$396$	−0.715868	−	0.520108i	−0.0359737	−	0.0261364i
$397$	4.20130			0.210857			0.105429	−	0.994427i	$-0.466379\pi$
$397$	4.20130			0.210857			0.105429	+	0.994427i	$0.466379\pi$
$398$	44.0369			2.20737
$399$	−20.8409	−	15.1418i	−1.04335	−	0.758038i
$400$	8.13131	+	25.0256i	0.406565	+	1.25128i
$401$	4.91880	−	15.1385i	0.245633	−	0.755980i	−0.749899	−	0.661553i	$-0.769898\pi$
$401$	4.91880	−	15.1385i	0.245633	−	0.755980i	0.995532	−	0.0944278i	$-0.0301022\pi$
$402$	−7.46912			−0.372526
$403$	0.270705	−	5.56118i	0.0134848	−	0.277022i
$404$	−66.4065			−3.30385
$405$	−8.30516	+	25.5607i	−0.412687	+	1.27012i
$406$	−21.0662	−	64.8350i	−1.04550	−	3.21771i
$407$	4.48918	+	3.26158i	0.222521	+	0.161671i
$408$	−49.3959			−2.44546
$409$	12.5214			0.619144			0.309572	−	0.950876i	$-0.399814\pi$
$409$	12.5214			0.619144			0.309572	+	0.950876i	$0.399814\pi$
$410$	26.1737	+	19.0163i	1.29263	+	0.939147i
$411$	−1.01552	+	0.737816i	−0.0500917	+	0.0363938i
$412$	17.1782	−	12.4807i	0.846310	−	0.614880i
$413$	12.1940	−	37.5292i	0.600026	−	1.84669i
$414$	2.23759	+	1.62571i	0.109972	+	0.0798991i
$415$	11.0574	−	34.0312i	0.542786	−	1.67052i
$416$	0.522018	+	1.60660i	0.0255940	+	0.0787703i
$417$	26.0464	−	18.9238i	1.27550	−	0.926703i
$418$	−4.09284	−	12.5965i	−0.200187	−	0.616113i
$419$	7.46274	+	22.9680i	0.364579	+	1.12206i	0.950244	+	0.311505i	$0.100833\pi$
$419$	7.46274	+	22.9680i	0.364579	+	1.12206i	−0.585666	+	0.810553i	$0.699167\pi$
$420$	−58.1449	+	42.2447i	−2.83718	+	2.06133i
$421$	−2.43546	−	7.49559i	−0.118697	−	0.365313i	0.874003	−	0.485921i	$-0.161516\pi$
$421$	−2.43546	−	7.49559i	−0.118697	−	0.365313i	−0.992700	+	0.120608i	$0.961516\pi$
$422$	9.99658	−	30.7663i	0.486626	−	1.49768i
$423$	−0.283468	−	0.205951i	−0.0137827	−	0.0100137i
$424$	13.6708	−	42.0744i	0.663913	−	2.04331i
$425$	23.3262	−	16.9475i	1.13149	−	0.822073i
$426$	5.35793	−	3.89276i	0.259592	−	0.188605i
$427$	−9.22722	−	6.70397i	−0.446537	−	0.324428i
$428$	4.03516			0.195047
$429$	−1.87124			−0.0903445
$430$	43.5220	+	31.6206i	2.09882	+	1.52488i
$431$	1.15927	+	3.56788i	0.0558403	+	0.171859i	0.975087	−	0.221824i	$-0.0712010\pi$
$431$	1.15927	+	3.56788i	0.0558403	+	0.171859i	−0.919246	+	0.393682i	$0.871201\pi$
$432$	−8.27471	+	25.4669i	−0.398117	+	1.22528i
$433$	−39.0709			−1.87763			−0.938813	−	0.344427i	$-0.888073\pi$
$433$	−39.0709			−1.87763			−0.938813	+	0.344427i	$0.888073\pi$
$434$	42.8953	−	11.6650i	2.05904	−	0.559937i
$435$	−45.8325			−2.19750
$436$	4.67601	−	14.3913i	0.223940	−	0.689218i
$437$	8.64175	+	26.5966i	0.413391	+	1.27229i
$438$	−0.116886	−	0.0849224i	−0.00558501	−	0.00405775i
$439$	35.7959			1.70845			0.854223	−	0.519907i	$-0.174033\pi$
$439$	35.7959			1.70845			0.854223	+	0.519907i	$0.174033\pi$
$440$	−19.2012			−0.915383
$441$	0.514789	+	0.374016i	0.0245138	+	0.0178103i
$442$	11.0200	−	8.00649i	0.524168	−	0.380830i
$443$	−13.2172	+	9.60283i	−0.627966	+	0.456244i	−0.855695	−	0.517480i	$-0.826870\pi$
$443$	−13.2172	+	9.60283i	−0.627966	+	0.456244i	0.227729	+	0.973725i	$0.426870\pi$
$444$	10.7192	−	32.9902i	0.508709	−	1.56565i
$445$	34.4536	+	25.0320i	1.63326	+	1.18663i
$446$	−8.87129	+	27.3030i	−0.420068	+	1.29284i
$447$	7.67126	+	23.6097i	0.362838	+	1.11670i
$448$	15.1442	−	11.0029i	0.715497	−	0.519839i
$449$	7.22326	+	22.2309i	0.340887	+	1.04914i	0.963749	+	0.266810i	$0.0859697\pi$
$449$	7.22326	+	22.2309i	0.340887	+	1.04914i	−0.622862	+	0.782332i	$0.714030\pi$
$450$	−0.767511	−	2.36216i	−0.0361808	−	0.111353i
$451$	−3.67529	+	2.67025i	−0.173063	+	0.125737i
$452$	14.4895	+	44.5940i	0.681527	+	2.09753i
$453$	1.82450	−	5.61524i	0.0857226	−	0.263827i
$454$	3.24621	+	2.35851i	0.152352	+	0.110690i
$455$	3.18244	−	9.79455i	0.149195	−	0.459176i
$456$	−34.8065	+	25.2884i	−1.62997	+	1.18424i
$457$	21.5200	−	15.6352i	1.00666	−	0.731382i	0.0431551	−	0.999068i	$-0.486259\pi$
$457$	21.5200	−	15.6352i	1.00666	−	0.731382i	0.963506	+	0.267686i	$0.0862590\pi$
$458$	5.85464	+	4.25365i	0.273570	+	0.198760i
$459$	29.3412			1.36953
$460$	78.0216			3.63777
$461$	1.79010	+	1.30059i	0.0833734	+	0.0605743i	0.628691	−	0.777655i	$-0.283591\pi$
$461$	1.79010	+	1.30059i	0.0833734	+	0.0605743i	−0.545318	+	0.838229i	$0.683591\pi$
$462$	−4.61673	−	14.2088i	−0.214790	−	0.661054i
$463$	−8.17468	+	25.1591i	−0.379909	+	1.16924i	0.560197	+	0.828360i	$0.310726\pi$
$463$	−8.17468	+	25.1591i	−0.379909	+	1.16924i	−0.940106	+	0.340882i	$0.889274\pi$
$464$	−42.7549			−1.98485
$465$	1.45308	−	29.8510i	0.0673848	−	1.38431i
$466$	−66.8411			−3.09636
$467$	4.46669	−	13.7471i	0.206694	−	0.636139i	−0.792946	−	0.609292i	$-0.791454\pi$
$467$	4.46669	−	13.7471i	0.206694	−	0.636139i	0.999640	−	0.0268462i	$-0.00854644\pi$
$468$	−0.244935	−	0.753833i	−0.0113221	−	0.0348459i
$469$	4.66984	+	3.39284i	0.215633	+	0.156667i
$470$	−14.6322			−0.674931
$471$	−28.6426			−1.31978
$472$	−53.3170	−	38.7370i	−2.45411	−	1.78302i
$473$	−6.11134	+	4.44015i	−0.281000	+	0.204158i
$474$	−19.8944	+	14.4542i	−0.913782	+	0.663901i
$475$	7.76034	−	23.8839i	0.356069	−	1.09587i
$476$	59.4335	+	43.1810i	2.72413	+	1.97920i
$477$	−0.484570	+	1.49135i	−0.0221869	+	0.0682844i
$478$	−11.9028	−	36.6332i	−0.544423	−	1.67556i
$479$	−4.83452	+	3.51248i	−0.220895	+	0.160489i	−0.692729	−	0.721198i	$-0.743592\pi$
$479$	−4.83452	+	3.51248i	−0.220895	+	0.160489i	0.471835	+	0.881687i	$0.343592\pi$
$480$	2.80206	+	8.62385i	0.127896	+	0.393623i
$481$	1.53598	+	4.72726i	0.0700347	+	0.215545i
$482$	−8.65291	+	6.28670i	−0.394129	+	0.286352i
$483$	9.74790	+	30.0010i	0.443545	+	1.36509i
$484$	−12.5489	+	38.6214i	−0.570403	+	1.75552i
$485$	−40.9113	−	29.7238i	−1.85768	−	1.34969i
$486$	1.51549	−	4.66419i	0.0687438	−	0.211572i
$487$	−7.90774	+	5.74531i	−0.358334	+	0.260345i	−0.752357	−	0.658756i	$-0.771083\pi$
$487$	−7.90774	+	5.74531i	−0.358334	+	0.260345i	0.394023	+	0.919101i	$0.371083\pi$
$488$	−15.4105	+	11.1964i	−0.697599	+	0.506835i
$489$	33.7177	+	24.4974i	1.52477	+	1.10781i
$490$	26.5726			1.20043
$491$	−11.2906			−0.509537			−0.254769	−	0.967002i	$-0.581999\pi$
$491$	−11.2906			−0.509537			−0.254769	+	0.967002i	$0.581999\pi$
$492$	22.9753	+	16.6925i	1.03581	+	0.752557i
$493$	14.4769	+	44.5554i	0.652008	+	2.00667i
$494$	3.66622	−	11.2835i	0.164951	−	0.507667i
$495$	0.680599			0.0305907
$496$	1.35550	−	27.8465i	0.0608640	−	1.25035i
$497$	−5.11816			−0.229581
$498$	14.3688	−	44.2226i	0.643881	−	1.98166i
$499$	6.26012	+	19.2667i	0.280242	+	0.862495i	0.987785	+	0.155825i	$0.0498035\pi$
$499$	6.26012	+	19.2667i	0.280242	+	0.862495i	−0.707543	+	0.706670i	$0.750197\pi$
$500$	−2.75066	−	1.99847i	−0.123013	−	0.0893744i
$501$	−20.6602			−0.923031
$502$	−61.6350			−2.75091
$503$	13.8933	+	10.0941i	0.619472	+	0.450073i	0.852737	−	0.522340i	$-0.174941\pi$
$503$	13.8933	+	10.0941i	0.619472	+	0.450073i	−0.233265	+	0.972413i	$0.574941\pi$
$504$	2.66035	−	1.93286i	0.118502	−	0.0860965i
$505$	41.3223	−	30.0224i	1.83882	−	1.33598i
$506$	−5.01182	+	15.4248i	−0.222802	+	0.685715i
$507$	−1.35607	−	0.985241i	−0.0602251	−	0.0437561i
$508$	−6.84082	+	21.0539i	−0.303512	+	0.934115i
$509$	2.04959	+	6.30799i	0.0908464	+	0.279597i	0.986149	−	0.165862i	$-0.0530407\pi$
$509$	2.04959	+	6.30799i	0.0908464	+	0.279597i	−0.895303	+	0.445459i	$0.853041\pi$
$510$	59.1525	−	42.9768i	2.61932	−	1.90305i
$511$	0.0345033	+	0.106190i	0.00152634	+	0.00469758i
$512$	−14.0076	−	43.1111i	−0.619056	−	1.90526i
$513$	20.6751	−	15.0214i	0.912829	−	0.663209i
$514$	1.67528	+	5.15599i	0.0738935	+	0.227421i
$515$	−5.04684	+	15.5326i	−0.222390	+	0.684447i
$516$	38.2037	+	27.7566i	1.68182	+	1.22192i
$517$	0.634918	−	1.95408i	0.0279237	−	0.0859402i
$518$	−32.1057	+	23.3262i	−1.41064	+	1.02489i
$519$	−33.5249	+	24.3573i	−1.47158	+	1.06917i
$520$	−13.9149	−	10.1098i	−0.610209	−	0.443343i
$521$	−41.4508			−1.81599			−0.907995	−	0.418981i	$-0.862388\pi$
$521$	−41.4508			−1.81599			−0.907995	+	0.418981i	$0.862388\pi$
$522$	4.03562			0.176634
$523$	18.8897	+	13.7241i	0.825987	+	0.600115i	0.918421	−	0.395604i	$-0.129465\pi$
$523$	18.8897	+	13.7241i	0.825987	+	0.600115i	−0.0924342	+	0.995719i	$0.529465\pi$
$524$	−11.1277	−	34.2476i	−0.486116	−	1.49611i
$525$	8.75367	−	26.9410i	0.382041	−	1.17580i
$526$	−4.77441			−0.208174
$527$	−29.4782	+	8.01633i	−1.28409	+	0.349197i
$528$	−9.36989			−0.407772
$529$	3.47472	−	10.6941i	0.151075	−	0.464960i
$530$	20.2357	+	62.2792i	0.878984	+	2.70523i
$531$	1.88985	+	1.37306i	0.0820126	+	0.0595856i
$532$	63.9862			2.77415
$533$	−4.06937			−0.176264
$534$	44.7715	+	32.5284i	1.93745	+	1.40764i
$535$	−2.51093	+	1.82430i	−0.108557	+	0.0788714i
$536$	7.79914	−	5.66640i	0.336871	−	0.244751i
$537$	10.9340	−	33.6514i	0.471837	−	1.45216i
$538$	−49.8884	−	36.2460i	−2.15084	−	1.56268i
$539$	−1.15304	+	3.54868i	−0.0496648	+	0.152853i
$540$	−22.0327	−	67.8097i	−0.948137	−	2.91807i
$541$	6.18280	−	4.49207i	0.265819	−	0.193129i	−0.446889	−	0.894589i	$-0.647468\pi$
$541$	6.18280	−	4.49207i	0.265819	−	0.193129i	0.712709	+	0.701460i	$0.247468\pi$
$542$	−0.0506237	−	0.155804i	−0.00217447	−	0.00669234i
$543$	−3.97173	−	12.2237i	−0.170443	−	0.524570i
$544$	7.49847	−	5.44796i	0.321494	−	0.233579i
$545$	3.59660	+	11.0692i	0.154061	+	0.474152i
$546$	4.13550	−	12.7278i	0.176983	−	0.544697i
$547$	24.5292	+	17.8215i	1.04879	+	0.761993i	0.971983	−	0.235053i	$-0.0755264\pi$
$547$	24.5292	+	17.8215i	1.04879	+	0.761993i	0.0768103	+	0.997046i	$0.475526\pi$
$548$	0.963473	−	2.96526i	0.0411575	−	0.126670i
$549$	0.546233	−	0.396862i	0.0233127	−	0.0169376i
$550$	11.7828	−	8.56072i	0.502421	−	0.365030i
$551$	33.0114	+	23.9842i	1.40633	+	1.02176i
$552$	52.6834			2.24235
$553$	19.0042			0.808139
$554$	0.519045	+	0.377108i	0.0220521	+	0.0160218i
$555$	8.24475	+	25.3747i	0.349970	+	1.07710i
$556$	−24.7115	+	76.0543i	−1.04800	+	3.22542i
$557$	41.5489			1.76048			0.880242	−	0.474525i	$-0.157380\pi$
$557$	41.5489			1.76048			0.880242	+	0.474525i	$0.157380\pi$
$558$	−0.127946	+	2.62842i	−0.00541637	+	0.111270i
$559$	−6.76663			−0.286198
$560$	15.9355	−	49.0443i	0.673396	−	2.07250i
$561$	3.17267	+	9.76448i	0.133950	+	0.412257i
$562$	3.64098	+	2.64533i	0.153585	+	0.111586i
$563$	−37.9883			−1.60101			−0.800507	−	0.599323i	$-0.795437\pi$
$563$	−37.9883			−1.60101			−0.800507	+	0.599323i	$0.795437\pi$
$564$	−12.8441			−0.540835
$565$	−29.1772	−	21.1985i	−1.22750	−	0.891828i
$566$	−5.95963	+	4.32993i	−0.250502	+	0.182000i
$567$	21.8356	−	15.8645i	0.917009	−	0.666246i
$568$	−2.64144	+	8.12952i	−0.110832	+	0.341107i
$569$	35.0631	+	25.4748i	1.46992	+	1.06796i	0.980637	+	0.195837i	$0.0627423\pi$
$569$	35.0631	+	25.4748i	1.46992	+	1.06796i	0.489285	+	0.872124i	$0.337258\pi$
$570$	19.6793	−	60.5667i	0.824276	−	2.53686i
$571$	2.06095	+	6.34295i	0.0862481	+	0.265444i	0.984874	−	0.173271i	$-0.0554336\pi$
$571$	2.06095	+	6.34295i	0.0862481	+	0.265444i	−0.898626	+	0.438715i	$0.855434\pi$
$572$	3.76024	−	2.73197i	0.157224	−	0.114230i
$573$	−13.1112	−	40.3522i	−0.547730	−	1.68574i
$574$	−10.0399	−	30.8998i	−0.419059	−	1.28973i
$575$	−24.8786	+	18.0754i	−1.03751	+	0.753795i
$576$	0.342436	+	1.05391i	0.0142681	+	0.0439128i
$577$	3.03924	−	9.35383i	0.126525	−	0.389405i	−0.867651	−	0.497175i	$-0.834371\pi$
$577$	3.03924	−	9.35383i	0.126525	−	0.389405i	0.994176	+	0.107770i	$0.0343709\pi$
$578$	−26.3193	−	19.1221i	−1.09474	−	0.795373i
$579$	7.45639	−	22.9484i	0.309877	−	0.953703i
$580$	92.0999	−	66.9145i	3.82424	−	2.77847i
$581$	−29.0717	+	21.1218i	−1.20610	+	0.876280i
$582$	−53.1631	−	38.6252i	−2.20368	−	1.60107i
$583$	−9.19525			−0.380828
$584$	0.186476			0.00771644
$585$	0.493222	+	0.358347i	0.0203922	+	0.0148158i
$586$	−5.85063	−	18.0064i	−0.241687	−	0.743837i
$587$	−8.57639	+	26.3954i	−0.353986	+	1.08946i	0.602610	+	0.798036i	$0.294128\pi$
$587$	−8.57639	+	26.3954i	−0.353986	+	1.08946i	−0.956595	+	0.291420i	$0.905872\pi$
$588$	23.3255			0.961926
$589$	−16.6676	+	20.7401i	−0.686778	+	0.854582i
$590$	97.5512			4.01612
$591$	0.250660	−	0.771453i	0.0103108	−	0.0317333i
$592$	7.69113	+	23.6709i	0.316103	+	0.972866i
$593$	−20.6943	−	15.0353i	−0.849813	−	0.617426i	0.0752812	−	0.997162i	$-0.476015\pi$
$593$	−20.6943	−	15.0353i	−0.849813	−	0.617426i	−0.925095	+	0.379737i	$0.876015\pi$
$594$	14.8212			0.608122
$595$	−56.5055			−2.31650
$596$	−49.8850	−	36.2436i	−2.04337	−	1.48459i
$597$	−24.0540	+	17.4762i	−0.984464	+	0.715255i
$598$	−11.7534	+	8.53935i	−0.480633	+	0.349200i
$599$	9.11487	−	28.0527i	0.372424	−	1.14620i	−0.572777	−	0.819711i	$-0.694134\pi$
$599$	9.11487	−	28.0527i	0.372424	−	1.14620i	0.945200	−	0.326491i	$-0.105866\pi$
$600$	−38.2745	−	27.8081i	−1.56255	−	1.13526i
$601$	13.6109	−	41.8899i	0.555199	−	1.70873i	−0.140219	−	0.990121i	$-0.544781\pi$
$601$	13.6109	−	41.8899i	0.555199	−	1.70873i	0.695418	−	0.718606i	$-0.255219\pi$
$602$	−16.6946	−	51.3807i	−0.680421	−	2.09412i
$603$	−0.276445	+	0.200849i	−0.0112577	+	0.00817921i
$604$	4.53182	+	13.9475i	0.184397	+	0.567516i
$605$	−9.65208	−	29.7061i	−0.392413	−	1.20772i
$606$	53.6973	−	39.0133i	2.18130	−	1.58481i
$607$	1.83432	+	5.64544i	0.0744526	+	0.229141i	0.981357	−	0.192196i	$-0.0615609\pi$
$607$	1.83432	+	5.64544i	0.0744526	+	0.229141i	−0.906904	+	0.421337i	$0.861561\pi$
$608$	2.49465	−	7.67774i	0.101171	−	0.311374i
$609$	37.2369	+	27.0542i	1.50891	+	1.09629i
$610$	8.71295	−	26.8157i	0.352777	−	1.08574i
$611$	1.48897	−	1.08180i	0.0602374	−	0.0437650i
$612$	−3.51835	+	2.55623i	−0.142221	+	0.103329i
$613$	−23.4056	−	17.0052i	−0.945344	−	0.686833i	0.00435671	−	0.999991i	$-0.498613\pi$
$613$	−23.4056	−	17.0052i	−0.945344	−	0.686833i	−0.949701	+	0.313158i	$0.898613\pi$
$614$	−13.0031			−0.524761
$615$	−21.8434			−0.880810
$616$	15.6002	+	11.3342i	0.628548	+	0.456667i
$617$	5.37106	+	16.5304i	0.216231	+	0.665490i	0.999064	+	0.0432581i	$0.0137738\pi$
$617$	5.37106	+	16.5304i	0.216231	+	0.665490i	−0.782833	+	0.622232i	$0.786226\pi$
$618$	−6.55823	+	20.1842i	−0.263811	+	0.811926i
$619$	−22.6748			−0.911379			−0.455689	−	0.890139i	$-0.650607\pi$
$619$	−22.6748			−0.911379			−0.455689	+	0.890139i	$0.650607\pi$
$620$	40.6619	+	62.1067i	1.63302	+	2.49426i
$621$	−31.2940			−1.25578
$622$	23.6760	−	72.8671i	0.949320	−	2.92171i
$623$	−13.2160	−	40.6747i	−0.529489	−	1.62960i
$624$	−6.79025	−	4.93341i	−0.271828	−	0.197494i
$625$	−23.6599			−0.946396
$626$	7.19144			0.287428
$627$	7.23457	+	5.25622i	0.288921	+	0.209913i
$628$	57.5569	−	41.8175i	2.29677	−	1.66870i
$629$	22.0634	−	16.0300i	0.879727	−	0.639159i
$630$	−1.50414	+	4.62927i	−0.0599265	+	0.184435i
$631$	21.4204	+	15.5629i	0.852734	+	0.619547i	0.925898	−	0.377772i	$-0.123310\pi$
$631$	21.4204	+	15.5629i	0.852734	+	0.619547i	−0.0731645	+	0.997320i	$0.523310\pi$
$632$	9.80789	−	30.1856i	0.390137	−	1.20072i
$633$	6.74938	+	20.7725i	0.268264	+	0.825631i
$634$	−36.3390	+	26.4018i	−1.44320	+	1.04855i
$635$	−5.26168	−	16.1938i	−0.208804	−	0.642631i
$636$	17.7629	+	54.6687i	0.704346	+	2.16776i
$637$	−2.70403	+	1.96460i	−0.107138	+	0.0778401i
$638$	7.31277	+	22.5064i	0.289515	+	0.891037i
$639$	0.0936275	−	0.288156i	0.00370384	−	0.0113993i
$640$	46.1914	+	33.5600i	1.82587	+	1.32657i
$641$	4.19111	−	12.8989i	0.165539	−	0.509476i	−0.833537	−	0.552464i	$-0.813688\pi$
$641$	4.19111	−	12.8989i	0.165539	−	0.509476i	0.999076	+	0.0429877i	$0.0136876\pi$
$642$	−3.26289	+	2.37063i	−0.128776	+	0.0935612i
$643$	14.3310	−	10.4121i	0.565158	−	0.410611i	−0.268185	−	0.963367i	$-0.586424\pi$
$643$	14.3310	−	10.4121i	0.565158	−	0.410611i	0.833343	+	0.552756i	$0.186424\pi$
$644$	−63.3890	−	46.0548i	−2.49788	−	1.81481i
$645$	−36.3215			−1.43016
$646$	−65.0951			−2.56113
$647$	−20.7044	−	15.0426i	−0.813974	−	0.591387i	0.101006	−	0.994886i	$-0.467794\pi$
$647$	−20.7044	−	15.0426i	−0.813974	−	0.591387i	−0.914980	+	0.403499i	$0.867794\pi$
$648$	−13.9295	−	42.8705i	−0.547202	−	1.68411i
$649$	−4.23294	+	13.0276i	−0.166157	+	0.511380i
$650$	13.0462			0.511715
$651$	−18.8011	+	23.3949i	−0.736874	+	0.916918i
$652$	−103.521			−4.05419
$653$	−2.73407	+	8.41460i	−0.106992	+	0.329289i	−0.990193	−	0.139707i	$-0.955384\pi$
$653$	−2.73407	+	8.41460i	−0.106992	+	0.329289i	0.883200	+	0.468996i	$0.155384\pi$
$654$	4.67368	+	14.3841i	0.182756	+	0.562464i
$655$	22.4077	+	16.2802i	0.875542	+	0.636119i
$656$	−20.3766			−0.795573
$657$	−0.00660976			−0.000257871
$658$	11.8880	+	8.63712i	0.463442	+	0.336710i
$659$	−2.90638	+	2.11161i	−0.113216	+	0.0822566i	−0.642953	−	0.765906i	$-0.722291\pi$
$659$	−2.90638	+	2.11161i	−0.113216	+	0.0822566i	0.529736	+	0.848162i	$0.322291\pi$
$660$	20.1840	−	14.6645i	0.785662	−	0.570817i
$661$	−12.4090	+	38.1910i	−0.482655	+	1.48546i	0.352695	+	0.935738i	$0.385265\pi$
$661$	−12.4090	+	38.1910i	−0.482655	+	1.48546i	−0.835349	+	0.549720i	$0.814735\pi$
$662$	18.1461	+	13.1839i	0.705269	+	0.512408i
$663$	−2.84196	+	8.74667i	−0.110373	+	0.339692i
$664$	18.5455	+	57.0773i	0.719707	+	2.21503i
$665$	−39.8162	+	28.9282i	−1.54401	+	1.12179i
$666$	−0.725962	−	2.23428i	−0.0281305	−	0.0865767i
$667$	−15.4404	−	47.5207i	−0.597855	−	1.84001i
$668$	41.5165	−	30.1635i	1.60632	−	1.16706i
$669$	−5.98962	−	18.4342i	−0.231572	−	0.712706i
$670$	−4.40957	+	13.5713i	−0.170356	+	0.524303i
$671$	3.20308	+	2.32717i	0.123653	+	0.0898395i
$672$	2.81397	−	8.66050i	0.108551	−	0.334086i
$673$	−7.05297	+	5.12429i	−0.271872	+	0.197527i	−0.715365	−	0.698751i	$-0.753739\pi$
$673$	−7.05297	+	5.12429i	−0.271872	+	0.197527i	0.443492	+	0.896278i	$0.353739\pi$
$674$	−23.6303	+	17.1684i	−0.910204	+	0.661302i
$675$	22.7351	+	16.5180i	0.875075	+	0.635780i
$676$	4.16343			0.160132
$677$	−34.7717			−1.33639			−0.668193	−	0.743988i	$-0.732932\pi$
$677$	−34.7717			−1.33639			−0.668193	+	0.743988i	$0.732932\pi$
$678$	−37.9150	−	27.5469i	−1.45612	−	1.05793i
$679$	15.6931	+	48.2985i	0.602247	+	1.85353i
$680$	−29.1620	+	89.7515i	−1.11831	+	3.44181i
$681$	−2.70914			−0.103814
$682$	−14.8904	+	4.04931i	−0.570183	+	0.155056i
$683$	48.5265			1.85681			0.928407	−	0.371565i	$-0.121179\pi$
$683$	48.5265			1.85681			0.928407	+	0.371565i	$0.121179\pi$
$684$	−1.17051	+	3.60246i	−0.0447556	+	0.137744i
$685$	0.741064	+	2.28076i	0.0283146	+	0.0871434i
$686$	23.6254	+	17.1648i	0.902021	+	0.655357i
$687$	−4.88602			−0.186413
$688$	−33.8826			−1.29176
$689$	−6.66369	−	4.84145i	−0.253866	−	0.184445i
$690$	−63.0893	+	45.8371i	−2.40177	+	1.74499i
$691$	9.57048	−	6.95336i	0.364078	−	0.264518i	−0.390673	−	0.920530i	$-0.627758\pi$
$691$	9.57048	−	6.95336i	0.364078	−	0.264518i	0.754751	+	0.656011i	$0.227758\pi$
$692$	31.8068	−	97.8912i	1.20911	−	3.72127i
$693$	−0.552957	−	0.401747i	−0.0210051	−	0.0152611i
$694$	12.0560	−	37.1046i	0.457640	−	1.40847i
$695$	−19.0071	−	58.4979i	−0.720981	−	2.21895i
$696$	62.1897	−	45.1834i	2.35729	−	1.71267i
$697$	6.89957	+	21.2347i	0.261340	+	0.804322i
$698$	−17.1880	−	52.8993i	−0.650576	−	2.00227i
$699$	36.5102	−	26.5262i	1.38094	−	1.00331i
$700$	21.7429	+	66.9178i	0.821805	+	2.52925i
$701$	12.7155	−	39.1343i	0.480258	−	1.47808i	−0.358475	−	0.933539i	$-0.616703\pi$
$701$	12.7155	−	39.1343i	0.480258	−	1.47808i	0.838733	−	0.544543i	$-0.183297\pi$
$702$	10.7408	+	7.80362i	0.405384	+	0.294529i
$703$	7.34024	−	22.5909i	0.276842	−	0.852033i
$704$	−5.25707	+	3.81948i	−0.198133	+	0.143952i
$705$	7.99243	−	5.80684i	0.301012	−	0.218698i
$706$	−6.90809	−	5.01902i	−0.259990	−	0.188893i
$707$	−51.2943			−1.92912
$708$	85.6305			3.21819
$709$	−2.83965	−	2.06313i	−0.106645	−	0.0774824i	0.533184	−	0.845999i	$-0.320995\pi$
$709$	−2.83965	−	2.06313i	−0.106645	−	0.0774824i	−0.639830	+	0.768517i	$0.720995\pi$
$710$	−3.90990	−	12.0334i	−0.146736	−	0.451607i
$711$	−0.347647	+	1.06995i	−0.0130378	+	0.0401261i
$712$	−71.4271			−2.67684
$713$	31.4401	−	8.54984i	1.17744	−	0.320194i
$714$	−73.4273			−2.74795
$715$	−1.10473	+	3.40002i	−0.0413146	+	0.127153i
$716$	27.1586	+	83.5854i	1.01496	+	3.12373i
$717$	21.0397	+	15.2862i	0.785740	+	0.570874i
$718$	−42.9495			−1.60286
$719$	28.5711			1.06552			0.532761	−	0.846266i	$-0.321155\pi$
$719$	28.5711			1.06552			0.532761	+	0.846266i	$0.321155\pi$
$720$	2.46972	+	1.79435i	0.0920409	+	0.0668716i
$721$	13.2690	−	9.64046i	0.494162	−	0.359029i
$722$	−7.70763	+	5.59992i	−0.286848	+	0.208408i
$723$	2.23151	−	6.86789i	0.0829908	−	0.255420i
$724$	25.8275	+	18.7648i	0.959872	+	0.697388i
$725$	−13.8656	+	42.6738i	−0.514954	+	1.58487i
$726$	−12.5426	−	38.6022i	−0.465500	−	1.43266i
$727$	5.73775	−	4.16872i	0.212802	−	0.154609i	−0.476279	−	0.879294i	$-0.658015\pi$
$727$	5.73775	−	4.16872i	0.212802	−	0.154609i	0.689080	+	0.724685i	$0.258015\pi$
$728$	5.33761	+	16.4275i	0.197825	+	0.608843i
$729$	8.80360	+	27.0947i	0.326059	+	1.00351i
$730$	−0.223309	+	0.162243i	−0.00826502	+	0.00600489i
$731$	11.4727	+	35.3094i	0.424334	+	1.30597i
$732$	7.64823	−	23.5388i	0.282687	−	0.870021i
$733$	−14.6578	−	10.6495i	−0.541398	−	0.393349i	0.283206	−	0.959059i	$-0.408602\pi$
$733$	−14.6578	−	10.6495i	−0.541398	−	0.393349i	−0.824604	+	0.565711i	$0.808602\pi$
$734$	−11.3168	+	34.8295i	−0.417710	+	1.28558i
$735$	−14.5146	+	10.5455i	−0.535378	+	0.388975i
$736$	−7.99752	+	5.81054i	−0.294792	+	0.214179i
$737$	−1.62106	−	1.17777i	−0.0597124	−	0.0433836i
$738$	1.92334			0.0707991
$739$	−14.8662			−0.546861			−0.273430	−	0.961892i	$-0.588158\pi$
$739$	−14.8662			−0.546861			−0.273430	+	0.961892i	$0.588158\pi$
$740$	−53.6143	−	38.9531i	−1.97090	−	1.43194i
$741$	2.47532	+	7.61824i	0.0909331	+	0.279863i
$742$	20.3217	−	62.5439i	0.746034	−	2.29606i
$743$	11.8867			0.436082			0.218041	−	0.975940i	$-0.430033\pi$
$743$	11.8867			0.436082			0.218041	+	0.975940i	$0.430033\pi$
$744$	27.4566	+	41.9370i	1.00661	+	1.53749i
$745$	47.4273			1.73760
$746$	−8.13080	+	25.0240i	−0.297690	+	0.916195i
$747$	−0.657358	−	2.02314i	−0.0240515	−	0.0740228i
$748$	−20.6314	−	14.9896i	−0.754357	−	0.548073i
$749$	3.11688			0.113888
$750$	3.39831			0.124089
$751$	−23.8434	−	17.3232i	−0.870057	−	0.632133i	0.0605454	−	0.998165i	$-0.480716\pi$
$751$	−23.8434	−	17.3232i	−0.870057	−	0.632133i	−0.930602	+	0.366032i	$0.880716\pi$
$752$	7.45575	−	5.41692i	0.271883	−	0.197535i
$753$	33.6665	−	24.4601i	1.22687	−	0.891377i
$754$	−6.55051	+	20.1604i	−0.238556	+	0.734199i
$755$	−9.12566	−	6.63018i	−0.332117	−	0.241297i
$756$	−22.1264	+	68.0980i	−0.804728	+	2.47670i
$757$	−8.85248	−	27.2451i	−0.321749	−	0.990241i	−0.972887	−	0.231282i	$-0.925708\pi$
$757$	−8.85248	−	27.2451i	−0.321749	−	0.990241i	0.651138	−	0.758959i	$-0.274292\pi$
$758$	50.9396	−	37.0097i	1.85021	−	1.34425i
$759$	−3.38382	−	10.4143i	−0.122825	−	0.378016i
$760$	25.3998	+	78.1725i	0.921347	+	2.83561i
$761$	−7.96008	+	5.78334i	−0.288553	+	0.209646i	−0.722639	−	0.691225i	$-0.757071\pi$
$761$	−7.96008	+	5.78334i	−0.288553	+	0.209646i	0.434087	+	0.900871i	$0.357071\pi$
$762$	−6.83742	−	21.0434i	−0.247693	−	0.762322i
$763$	3.61189	−	11.1162i	0.130759	−	0.402435i
$764$	85.2602	+	61.9452i	3.08461	+	2.24110i
$765$	1.03367	−	3.18129i	0.0373722	−	0.115020i
$766$	−49.3020	+	35.8200i	−1.78135	+	1.29423i
$767$	−9.92683	+	7.21227i	−0.358437	+	0.260420i
$768$	44.2377	+	32.1406i	1.59629	+	1.15977i
$769$	20.8754			0.752786			0.376393	−	0.926460i	$-0.377164\pi$
$769$	20.8754			0.752786			0.376393	+	0.926460i	$0.377164\pi$
$770$	−28.5428			−1.02861
$771$	−2.96125	−	2.15148i	−0.106647	−	0.0774836i
$772$	18.5207	+	57.0007i	0.666573	+	2.05150i
$773$	11.6089	−	35.7285i	0.417543	−	1.28506i	−0.492414	−	0.870361i	$-0.663885\pi$
$773$	11.6089	−	35.7285i	0.417543	−	1.28506i	0.909957	−	0.414703i	$-0.136115\pi$
$774$	3.19816			0.114956
$775$	−27.3541	−	10.3837i	−0.982590	−	0.372992i
$776$	84.8149			3.04468
$777$	8.27979	−	25.4826i	0.297036	−	0.914183i
$778$	−7.73550	−	23.8074i	−0.277331	−	0.853537i
$779$	15.7329	+	11.4306i	0.563691	+	0.409545i
$780$	22.3483			0.800196
$781$	1.77668			0.0635748
$782$	64.4876	+	46.8530i	2.30607	+	1.67546i
$783$	−36.9407	+	26.8390i	−1.32015	+	0.959148i
$784$	−13.5399	+	9.83734i	−0.483569	+	0.351334i
$785$	−16.9098	+	52.0430i	−0.603537	+	1.85750i
$786$	29.1182	+	21.1556i	1.03861	+	0.754596i
$787$	−12.8268	+	39.4769i	−0.457227	+	1.40720i	0.411274	+	0.911512i	$0.365084\pi$
$787$	−12.8268	+	39.4769i	−0.457227	+	1.40720i	−0.868501	+	0.495688i	$0.834916\pi$
$788$	0.622606	+	1.91618i	0.0221794	+	0.0682612i
$789$	2.60789	−	1.89475i	0.0928435	−	0.0674548i
$790$	14.5178	+	44.6812i	0.516520	+	1.58968i
$791$	11.1921	+	34.4457i	0.397945	+	1.22475i
$792$	−0.923498	+	0.670961i	−0.0328151	+	0.0238415i
$793$	1.09594	+	3.37295i	0.0389179	+	0.119777i
$794$	3.22313	−	9.91977i	0.114385	−	0.352040i
$795$	−35.7690	−	25.9877i	−1.26860	−	0.921688i
$796$	22.8212	−	70.2365i	0.808877	−	2.48947i
$797$	−44.3568	+	32.2271i	−1.57120	+	1.14154i	−0.645198	+	0.764015i	$0.723225\pi$
$797$	−44.3568	+	32.2271i	−1.57120	+	1.14154i	−0.925999	+	0.377526i	$0.876775\pi$
$798$	−51.7401	+	37.5914i	−1.83158	+	1.33072i
$799$	−8.16957	−	5.93554i	−0.289019	−	0.209984i
$800$	8.87721			0.313857
$801$	2.53178			0.0894559
$802$	−31.9702	−	23.2277i	−1.12891	−	0.820199i
$803$	−0.0119773	−	0.0368622i	−0.000422668	−	0.00130084i
$804$	−3.87072	+	11.9129i	−0.136510	+	0.420134i
$805$	60.2661			2.12410
$806$	−12.9229	−	4.90556i	−0.455191	−	0.172791i
$807$	41.6346			1.46561
$808$	−26.4726	+	81.4743i	−0.931302	+	2.86625i
$809$	−5.84030	−	17.9746i	−0.205334	−	0.631953i	−0.999700	−	0.0245130i	$-0.992196\pi$
$809$	−5.84030	−	17.9746i	−0.205334	−	0.631953i	0.794365	−	0.607440i	$-0.207804\pi$
$810$	53.9802	+	39.2189i	1.89667	+	1.37801i
$811$	−52.5654			−1.84582			−0.922910	−	0.385017i	$-0.874196\pi$
$811$	−52.5654			−1.84582			−0.922910	+	0.385017i	$0.874196\pi$
$812$	−114.326			−4.01204
$813$	0.0894832	+	0.0650133i	0.00313831	+	0.00228012i
$814$	11.1450	−	8.09729i	0.390631	−	0.283810i
$815$	64.4173	−	46.8019i	2.25644	−	1.63940i
$816$	−14.2306	+	43.7973i	−0.498170	+	1.53321i
$817$	26.1610	+	19.0071i	0.915258	+	0.664974i
$818$	9.60610	−	29.5645i	0.335870	−	1.03370i
$819$	−0.189195	−	0.582282i	−0.00661101	−	0.0203466i
$820$	43.8940	−	31.8908i	1.53284	−	1.11368i
$821$	14.5747	+	44.8563i	0.508661	+	1.56550i	0.794528	+	0.607228i	$0.207718\pi$
$821$	14.5747	+	44.8563i	0.508661	+	1.56550i	−0.285867	+	0.958269i	$0.592282\pi$
$822$	0.962993	+	2.96379i	0.0335882	+	0.103374i
$823$	9.50253	−	6.90399i	0.331237	−	0.240658i	−0.409718	−	0.912212i	$-0.634373\pi$
$823$	9.50253	−	6.90399i	0.331237	−	0.240658i	0.740956	+	0.671554i	$0.234373\pi$
$824$	−8.46459	−	26.0513i	−0.294878	−	0.907542i
$825$	−3.03869	+	9.35213i	−0.105794	+	0.325599i
$826$	−79.2560	−	57.5828i	−2.75767	−	2.00356i
$827$	−0.390610	+	1.20217i	−0.0135828	+	0.0418037i	−0.957618	−	0.288041i	$-0.906996\pi$
$827$	−0.390610	+	1.20217i	−0.0135828	+	0.0418037i	0.944035	+	0.329844i	$0.106996\pi$
$828$	3.75250	−	2.72635i	0.130409	−	0.0947474i
$829$	−42.9449	+	31.2013i	−1.49154	+	1.08367i	−0.517936	+	0.855419i	$0.673300\pi$
$829$	−42.9449	+	31.2013i	−1.49154	+	1.08367i	−0.973603	+	0.228248i	$0.926700\pi$
$830$	−71.8687	−	52.2156i	−2.49460	−	1.81243i
$831$	−0.433172			−0.0150266
$832$	−5.82076			−0.201798
$833$	14.8363	+	10.7792i	0.514046	+	0.373476i
$834$	−24.6992	−	76.0164i	−0.855265	−	2.63223i
$835$	−12.1972	+	37.5393i	−0.422103	+	1.29910i
$836$	−22.2117			−0.768209
$837$	−16.3092	−	24.9106i	−0.563730	−	0.861037i
$838$	59.9553			2.07112
$839$	12.5255	−	38.5496i	0.432429	−	1.33088i	−0.463269	−	0.886218i	$-0.653323\pi$
$839$	12.5255	−	38.5496i	0.432429	−	1.33088i	0.895698	−	0.444663i	$-0.146677\pi$
$840$	28.6510	+	88.1786i	0.988552	+	3.04245i
$841$	−35.5207	−	25.8073i	−1.22485	−	0.889908i
$842$	−19.5664			−0.674302
$843$	−3.03860			−0.104655
$844$	−43.8901	−	31.8881i	−1.51076	−	1.09763i
$845$	−2.59075	+	1.88229i	−0.0891246	+	0.0647528i
$846$	−0.703745	+	0.511300i	−0.0241952	+	0.0175789i
$847$	−9.69311	+	29.8323i	−0.333059	+	1.02505i
$848$	−33.3671	−	24.2426i	−1.14583	−	0.832496i
$849$	1.53694	−	4.73022i	0.0527476	−	0.162341i
$850$	−22.1197	−	68.0775i	−0.758700	−	2.33504i
$851$	−23.5318	+	17.0969i	−0.806661	+	0.586073i
$852$	−3.43211	−	10.5630i	−0.117582	−	0.361881i
$853$	7.33497	+	22.5747i	0.251145	+	0.772944i	0.994565	+	0.104119i	$0.0332023\pi$
$853$	7.33497	+	22.5747i	0.251145	+	0.772944i	−0.743420	+	0.668825i	$0.766798\pi$
$854$	−22.9077	+	16.6435i	−0.783887	+	0.569527i
$855$	−0.900310	−	2.77087i	−0.0307900	−	0.0947617i
$856$	1.60859	−	4.95075i	0.0549806	−	0.169213i
$857$	−32.2711	−	23.4463i	−1.10236	−	0.800912i	−0.120917	−	0.992663i	$-0.538583\pi$
$857$	−32.2711	−	23.4463i	−1.10236	−	0.800912i	−0.981444	+	0.191751i	$0.938583\pi$
$858$	−1.43557	+	4.41823i	−0.0490095	+	0.150836i
$859$	−12.5218	+	9.09764i	−0.427239	+	0.310407i	−0.780544	−	0.625101i	$-0.785058\pi$
$859$	−12.5218	+	9.09764i	−0.427239	+	0.310407i	0.353305	+	0.935508i	$0.385058\pi$
$860$	72.9877	−	53.0286i	2.48886	−	1.80826i
$861$	17.7468	+	12.8938i	0.604808	+	0.439419i
$862$	9.31355			0.317221
$863$	2.71157			0.0923028			0.0461514	−	0.998934i	$-0.485304\pi$
$863$	2.71157			0.0923028			0.0461514	+	0.998934i	$0.485304\pi$
$864$	7.30847	+	5.30991i	0.248639	+	0.180647i
$865$	24.4645	+	75.2940i	0.831818	+	2.56007i
$866$	−29.9741	+	92.2509i	−1.01856	+	3.13481i
$867$	21.9649			0.745967
$868$	3.62459	−	74.4609i	0.123026	−	2.52737i
$869$	−6.59698			−0.223787
$870$	−35.1615	+	108.216i	−1.19209	+	3.66887i
$871$	−0.554647	−	1.70703i	−0.0187935	−	0.0578404i
$872$	−15.7926	−	11.4740i	−0.534806	−	0.388559i
$873$	−3.00631			−0.101748
$874$	69.4274			2.34842
$875$	−2.12469	−	1.54368i	−0.0718276	−	0.0521858i
$876$	−0.196021	+	0.142417i	−0.00662292	+	0.00481183i
$877$	−29.3705	+	21.3389i	−0.991771	+	0.720563i	−0.960308	−	0.278941i	$-0.910016\pi$
$877$	−29.3705	+	21.3389i	−0.991771	+	0.720563i	−0.0314624	+	0.999505i	$0.510016\pi$
$878$	27.4617	−	84.5184i	0.926787	−	2.85236i
$879$	10.3417	+	7.51366i	0.348816	+	0.253429i
$880$	−5.53173	+	17.0249i	−0.186475	+	0.573910i
$881$	1.62171	+	4.99112i	0.0546369	+	0.168155i	0.974651	−	0.223730i	$-0.0718233\pi$
$881$	1.62171	+	4.99112i	0.0546369	+	0.168155i	−0.920014	+	0.391885i	$0.871823\pi$
$882$	1.27803	−	0.928542i	0.0430335	−	0.0312656i
$883$	8.83570	+	27.1935i	0.297345	+	0.915134i	0.982424	+	0.186665i	$0.0597678\pi$
$883$	8.83570	+	27.1935i	0.297345	+	0.915134i	−0.685079	+	0.728469i	$0.740232\pi$
$884$	−7.05905	−	21.7255i	−0.237422	−	0.730708i
$885$	−53.2847	+	38.7136i	−1.79115	+	1.30134i
$886$	12.5336	+	38.5743i	0.421073	+	1.29593i
$887$	12.1397	−	37.3622i	0.407612	−	1.25450i	−0.511083	−	0.859531i	$-0.670756\pi$
$887$	12.1397	−	37.3622i	0.407612	−	1.25450i	0.918695	−	0.394968i	$-0.129244\pi$
$888$	−36.2026	−	26.3027i	−1.21488	−	0.882661i
$889$	−5.28405	+	16.2626i	−0.177221	+	0.545431i
$890$	85.5353	−	62.1450i	2.86715	−	2.08311i
$891$	−7.57987	+	5.50710i	−0.253935	+	0.184495i
$892$	38.9495	+	28.2985i	1.30413	+	0.947504i
$893$	−8.79536			−0.294326
$894$	61.6305			2.06123
$895$	−54.6888	−	39.7337i	−1.82805	−	1.32815i
$896$	−17.7185	−	54.5320i	−0.591934	−	1.82179i
$897$	3.03111	−	9.32879i	0.101206	−	0.311479i
$898$	58.0313			1.93653
$899$	29.7805	−	37.0569i	0.993234	−	1.23592i
$900$	−4.16526			−0.138842
$901$	−13.9653	+	42.9809i	−0.465253	+	1.43190i
$902$	3.48520	+	10.7263i	0.116044	+	0.357148i
$903$	29.5096	+	21.4400i	0.982019	+	0.713479i
$904$	60.4886			2.01182
$905$	−24.5551			−0.816239
$906$	−11.8585	−	8.61574i	−0.393974	−	0.286239i
$907$	−0.214817	+	0.156074i	−0.00713290	+	0.00518235i	−0.591346	−	0.806418i	$-0.701403\pi$
$907$	−0.214817	+	0.156074i	−0.00713290	+	0.00518235i	0.584213	+	0.811600i	$0.301403\pi$
$908$	5.44398	−	3.95528i	0.180665	−	0.131261i
$909$	0.938337	−	2.88790i	0.0311227	−	0.0957857i
$910$	−20.6846	−	15.0282i	−0.685688	−	0.498181i
$911$	−0.373344	+	1.14904i	−0.0123694	+	0.0380692i	−0.957051	−	0.289920i	$-0.906371\pi$
$911$	−0.373344	+	1.14904i	−0.0123694	+	0.0380692i	0.944681	+	0.327990i	$0.106371\pi$
$912$	12.3947	+	38.1469i	0.410429	+	1.26317i
$913$	10.0918	−	7.33209i	0.333988	−	0.242657i
$914$	−20.4069	−	62.8060i	−0.675001	−	2.07744i
$915$	5.88271	+	18.1051i	0.194477	+	0.598537i
$916$	9.81840	−	7.13349i	0.324409	−	0.235697i
$917$	−8.59537	−	26.4538i	−0.283844	−	0.873582i
$918$	22.5098	−	69.2781i	0.742935	−	2.28652i
$919$	−16.3132	−	11.8522i	−0.538123	−	0.390969i	0.285265	−	0.958449i	$-0.407918\pi$
$919$	−16.3132	−	11.8522i	−0.538123	−	0.390969i	−0.823387	+	0.567480i	$0.807918\pi$
$920$	31.1028	−	95.7247i	1.02543	−	3.15595i
$921$	7.10257	−	5.16032i	0.234038	−	0.170038i
$922$	4.44415	−	3.22887i	0.146360	−	0.106337i
$923$	1.28754	+	0.935454i	0.0423800	+	0.0307908i
$924$	−25.0549			−0.824244
$925$	26.1202			0.858828
$926$	53.1321	+	38.6028i	1.74603	+	1.26857i
$927$	0.300033	+	0.923405i	0.00985436	+	0.0303286i
$928$	−4.45725	+	13.7180i	−0.146316	+	0.450315i
$929$	18.2381			0.598373			0.299187	−	0.954195i	$-0.403285\pi$
$929$	18.2381			0.598373			0.299187	+	0.954195i	$0.403285\pi$
$930$	−69.3670	−	26.3318i	−2.27463	−	0.863453i
$931$	15.9727			0.523485
$932$	−34.6391	+	106.608i	−1.13464	+	3.49207i
$933$	15.9853	+	49.1976i	0.523335	+	1.61066i
$934$	−29.0317	−	21.0928i	−0.949947	−	0.690177i
$935$	19.6149			0.641477
$936$	−1.02252			−0.0334221
$937$	−21.6559	−	15.7339i	−0.707466	−	0.514004i	0.174889	−	0.984588i	$-0.444043\pi$
$937$	−21.6559	−	15.7339i	−0.707466	−	0.514004i	−0.882355	+	0.470584i	$0.844043\pi$
$938$	11.5935	−	8.42314i	0.378540	−	0.275025i
$939$	−3.92813	+	2.85395i	−0.128190	+	0.0931353i
$940$	−7.58283	+	23.3375i	−0.247325	+	0.761187i
$941$	−1.15879	−	0.841909i	−0.0377754	−	0.0274454i	0.568737	−	0.822519i	$-0.307432\pi$
$941$	−1.15879	−	0.841909i	−0.0377754	−	0.0274454i	−0.606513	+	0.795074i	$0.707432\pi$
$942$	−21.9738	+	67.6285i	−0.715946	+	2.20346i
$943$	−7.35876	−	22.6479i	−0.239634	−	0.737519i
$944$	−49.7067	+	36.1140i	−1.61782	+	1.17541i
$945$	−17.0187	−	52.3782i	−0.553619	−	1.70386i
$946$	5.79525	+	17.8360i	0.188420	+	0.579897i
$947$	32.6932	−	23.7530i	1.06239	−	0.771868i	0.0878570	−	0.996133i	$-0.471998\pi$
$947$	32.6932	−	23.7530i	1.06239	−	0.771868i	0.974528	+	0.224265i	$0.0719981\pi$
$948$	12.7437	+	39.2212i	0.413897	+	1.27384i
$949$	0.0107288	−	0.0330198i	0.000348271	−	0.00107187i
$950$	−50.4391	−	36.6461i	−1.63646	−	1.18896i
$951$	9.37151	−	28.8426i	0.303892	−	0.935284i
$952$	76.6717	−	55.7052i	2.48494	−	1.80542i
$953$	−24.7033	+	17.9480i	−0.800219	+	0.581393i	−0.910978	−	0.412454i	$-0.864672\pi$
$953$	−24.7033	+	17.9480i	−0.800219	+	0.581393i	0.110760	+	0.993847i	$0.464672\pi$
$954$	3.14951	+	2.28825i	0.101969	+	0.0740849i
$955$	−81.0598			−2.62303
$956$	−64.5964			−2.08920
$957$	−12.9262	−	9.39141i	−0.417844	−	0.303581i
$958$	4.58447	+	14.1095i	0.148117	+	0.455859i
$959$	0.744214	−	2.29046i	0.0240319	−	0.0739627i
$960$	−31.2443			−1.00841
$961$	23.1912	+	20.5710i	0.748103	+	0.663582i
$962$	12.3400			0.397857
$963$	−0.0570176	+	0.175482i	−0.00183737	+	0.00565483i
$964$	5.54277	+	17.0589i	0.178521	+	0.549430i
$965$	−37.2948	−	27.0962i	−1.20056	−	0.872259i
$966$	78.3142			2.51972
$967$	−31.1563			−1.00192			−0.500960	−	0.865470i	$-0.667020\pi$
$967$	−31.1563			−1.00192			−0.500960	+	0.865470i	$0.667020\pi$
$968$	42.3822	+	30.7924i	1.36221	+	0.989707i
$969$	35.5565	−	25.8333i	1.14224	−	0.829884i
$970$	−101.567	+	73.7930i	−3.26113	+	2.36935i
$971$	0.830003	−	2.55449i	0.0266361	−	0.0819774i	−0.936855	−	0.349719i	$-0.886277\pi$
$971$	0.830003	−	2.55449i	0.0266361	−	0.0819774i	0.963491	+	0.267741i	$0.0862772\pi$
$972$	−6.65376	−	4.83424i	−0.213420	−	0.155058i
$973$	−19.0879	+	58.7465i	−0.611930	+	1.88333i
$974$	7.49874	+	23.0788i	0.240275	+	0.739491i
$975$	−7.12615	+	5.17745i	−0.228220	+	0.165811i
$976$	5.48770	+	16.8894i	0.175657	+	0.540616i
$977$	−11.2350	−	34.5778i	−0.359439	−	1.10624i	−0.953391	−	0.301739i	$-0.902433\pi$
$977$	−11.2350	−	34.5778i	−0.359439	−	1.10624i	0.593951	−	0.804501i	$-0.297567\pi$
$978$	83.7085	−	60.8178i	2.67670	−	1.94474i
$979$	4.58772	+	14.1196i	0.146624	+	0.451263i
$980$	13.7707	−	42.3819i	0.439889	−	1.35384i
$981$	0.559779	+	0.406703i	0.0178724	+	0.0129850i
$982$	−8.66184	+	26.6584i	−0.276411	+	0.850704i
$983$	−20.1150	+	14.6144i	−0.641570	+	0.466128i	−0.860389	−	0.509638i	$-0.829780\pi$
$983$	−20.1150	+	14.6144i	−0.641570	+	0.466128i	0.218819	+	0.975765i	$0.429780\pi$
$984$	29.6390	−	21.5340i	0.944858	−	0.686479i
$985$	−1.25373	−	0.910890i	−0.0399473	−	0.0290234i
$986$	116.307			3.70397
$987$	−9.92117			−0.315794
$988$	−16.0966	−	11.6949i	−0.512101	−	0.372063i
$989$	−12.2363	−	37.6594i	−0.389091	−	1.19750i
$990$	0.522138	−	1.60698i	0.0165946	−	0.0510730i
$991$	21.7496			0.690898			0.345449	−	0.938438i	$-0.387727\pi$
$991$	21.7496			0.690898			0.345449	+	0.938438i	$0.387727\pi$
$992$	−8.79331	−	3.33795i	−0.279188	−	0.105980i
$993$	−15.1439			−0.480578
$994$	−3.92652	+	12.0846i	−0.124542	+	0.383300i
$995$	17.5532	+	54.0231i	0.556473	+	1.71265i
$996$	−63.0864	−	45.8349i	−1.99897	−	1.45234i
$997$	−5.63438			−0.178443			−0.0892213	−	0.996012i	$-0.528438\pi$
$997$	−5.63438			−0.178443			−0.0892213	+	0.996012i	$0.528438\pi$
$998$	50.2935			1.59201
$999$	21.5044	+	15.6238i	0.680369	+	0.494317i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.k.e.287.15	yes	68
31.4	even	5	inner	403.2.k.e.66.15	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.k.e.66.15	✓	68	31.4	even	5	inner
403.2.k.e.287.15	yes	68	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.767174 - 2.36112i) q^{2} +(0.517972 + 1.59415i) q^{3} +(-3.36829 - 2.44720i) q^{4} +3.20234 q^{5} +4.16136 q^{6} +(-2.60176 - 1.89029i) q^{7} +(-4.34523 + 3.15699i) q^{8} +(0.154019 - 0.111901i) q^{9} +O(q^{10})\)	\(q+(0.767174 - 2.36112i) q^{2} +(0.517972 + 1.59415i) q^{3} +(-3.36829 - 2.44720i) q^{4} +3.20234 q^{5} +4.16136 q^{6} +(-2.60176 - 1.89029i) q^{7} +(-4.34523 + 3.15699i) q^{8} +(0.154019 - 0.111901i) q^{9} +(2.45675 - 7.56111i) q^{10} +(0.903159 + 0.656183i) q^{11} +(2.15654 - 6.63715i) q^{12} +(0.309017 + 0.951057i) q^{13} +(-6.45920 + 4.69289i) q^{14} +(1.65872 + 5.10503i) q^{15} +(1.54734 + 4.76223i) q^{16} +(4.43884 - 3.22501i) q^{17} +(-0.146053 - 0.449505i) q^{18} +(1.47675 - 4.54497i) q^{19} +(-10.7864 - 7.83679i) q^{20} +(1.66578 - 5.12673i) q^{21} +(2.24221 - 1.62906i) q^{22} +(-4.73426 + 3.43964i) q^{23} +(-7.28344 - 5.29173i) q^{24} +5.25501 q^{25} +2.48263 q^{26} +(4.32637 + 3.14329i) q^{27} +(4.13756 + 12.7341i) q^{28} +(-2.63854 + 8.12060i) q^{29} +13.3261 q^{30} +(-5.20534 - 1.97596i) q^{31} +1.68928 q^{32} +(-0.578246 + 1.77966i) q^{33} +(-4.20926 - 12.9548i) q^{34} +(-8.33174 - 6.05336i) q^{35} -0.792627 q^{36} +4.97054 q^{37} +(-9.59828 - 6.97356i) q^{38} +(-1.35607 + 0.985241i) q^{39} +(-13.9149 + 10.1098i) q^{40} +(-1.25751 + 3.87020i) q^{41} +(-10.8269 - 7.86618i) q^{42} +(-2.09100 + 6.43544i) q^{43} +(-1.43628 - 4.42043i) q^{44} +(0.493222 - 0.358347i) q^{45} +(4.48940 + 13.8170i) q^{46} +(-0.568737 - 1.75039i) q^{47} +(-6.79025 + 4.93341i) q^{48} +(1.03285 + 3.17878i) q^{49} +(4.03151 - 12.4077i) q^{50} +(7.44036 + 5.40574i) q^{51} +(1.28657 - 3.95966i) q^{52} +(-6.66369 + 4.84145i) q^{53} +(10.7408 - 7.80362i) q^{54} +(2.89223 + 2.10132i) q^{55} +17.2729 q^{56} +8.01030 q^{57} +(17.1495 + 12.4598i) q^{58} +(3.79171 + 11.6697i) q^{59} +(6.90599 - 21.2545i) q^{60} +3.54653 q^{61} +(-8.65887 + 10.7745i) q^{62} -0.612248 q^{63} +(-1.79871 + 5.53587i) q^{64} +(0.989579 + 3.04561i) q^{65} +(3.75837 + 2.73061i) q^{66} -1.79487 q^{67} -22.8436 q^{68} +(-7.93554 - 5.76551i) q^{69} +(-20.6846 + 15.0282i) q^{70} +(1.28754 - 0.935454i) q^{71} +(-0.315976 + 0.972474i) q^{72} +(-0.0280883 - 0.0204074i) q^{73} +(3.81326 - 11.7360i) q^{74} +(2.72195 + 8.37730i) q^{75} +(-16.0966 + 11.6949i) q^{76} +(-1.10943 - 3.41447i) q^{77} +(1.28593 + 3.95769i) q^{78} +(-4.78075 + 3.47342i) q^{79} +(4.95513 + 15.2503i) q^{80} +(-2.59346 + 7.98186i) q^{81} +(8.17328 + 5.93824i) q^{82} +(3.45291 - 10.6270i) q^{83} +(-18.1570 + 13.1918i) q^{84} +(14.2147 - 10.3276i) q^{85} +(13.5907 + 9.87421i) q^{86} -14.3122 q^{87} -5.99599 q^{88} +(10.7589 + 7.81676i) q^{89} +(-0.467712 - 1.43947i) q^{90} +(0.993785 - 3.05856i) q^{91} +24.3639 q^{92} +(0.453754 - 9.32161i) q^{93} -4.56920 q^{94} +(4.72906 - 14.5546i) q^{95} +(0.875002 + 2.69298i) q^{96} +(-12.7754 - 9.28188i) q^{97} +8.29786 q^{98} +0.212532 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9}+O(q^{10}) \) 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9	\( 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9} - 13 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 3 q^{14} - 14 q^{15} + 9 q^{16} + 12 q^{17} - 19 q^{18} - 4 q^{19} - 53 q^{20} - 13 q^{21} - 14 q^{22} - 9 q^{23} + 2 q^{24} + 96 q^{25} + 12 q^{26} + 25 q^{27} - 25 q^{28} - 78 q^{30} - 2 q^{31} + 76 q^{32} + 29 q^{33} - 15 q^{34} - 36 q^{35} + 52 q^{36} + 24 q^{37} - 19 q^{38} + 3 q^{39} - 12 q^{40} - 40 q^{41} + 11 q^{42} - 22 q^{43} + 4 q^{44} + 63 q^{45} - 24 q^{46} + 3 q^{47} + 68 q^{48} + 33 q^{49} - 76 q^{50} - 59 q^{51} - 13 q^{52} - q^{53} + 18 q^{54} - 22 q^{55} + 78 q^{56} - 16 q^{57} + 5 q^{58} - 18 q^{59} + 43 q^{60} - 32 q^{61} - 39 q^{62} + 20 q^{63} + 23 q^{64} + 2 q^{65} + 11 q^{66} + 114 q^{67} + 98 q^{68} - 46 q^{69} + 32 q^{70} - 2 q^{71} + 28 q^{72} + 10 q^{73} - 43 q^{74} - 12 q^{75} - 35 q^{76} - 3 q^{77} - 6 q^{78} - 10 q^{79} + 68 q^{80} - 54 q^{81} - 80 q^{82} - 22 q^{83} - 14 q^{84} - 50 q^{85} - 66 q^{86} + 76 q^{87} - 34 q^{88} - 10 q^{89} - 63 q^{90} - 8 q^{91} - 64 q^{92} - 16 q^{93} + 30 q^{94} + 15 q^{95} + 34 q^{96} - 7 q^{97} + 138 q^{98} - 48 q^{99}+O(q^{100}) \) 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9 - 13 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 3 * q^14 - 14 * q^15 + 9 * q^16 + 12 * q^17 - 19 * q^18 - 4 * q^19 - 53 * q^20 - 13 * q^21 - 14 * q^22 - 9 * q^23 + 2 * q^24 + 96 * q^25 + 12 * q^26 + 25 * q^27 - 25 * q^28 - 78 * q^30 - 2 * q^31 + 76 * q^32 + 29 * q^33 - 15 * q^34 - 36 * q^35 + 52 * q^36 + 24 * q^37 - 19 * q^38 + 3 * q^39 - 12 * q^40 - 40 * q^41 + 11 * q^42 - 22 * q^43 + 4 * q^44 + 63 * q^45 - 24 * q^46 + 3 * q^47 + 68 * q^48 + 33 * q^49 - 76 * q^50 - 59 * q^51 - 13 * q^52 - q^53 + 18 * q^54 - 22 * q^55 + 78 * q^56 - 16 * q^57 + 5 * q^58 - 18 * q^59 + 43 * q^60 - 32 * q^61 - 39 * q^62 + 20 * q^63 + 23 * q^64 + 2 * q^65 + 11 * q^66 + 114 * q^67 + 98 * q^68 - 46 * q^69 + 32 * q^70 - 2 * q^71 + 28 * q^72 + 10 * q^73 - 43 * q^74 - 12 * q^75 - 35 * q^76 - 3 * q^77 - 6 * q^78 - 10 * q^79 + 68 * q^80 - 54 * q^81 - 80 * q^82 - 22 * q^83 - 14 * q^84 - 50 * q^85 - 66 * q^86 + 76 * q^87 - 34 * q^88 - 10 * q^89 - 63 * q^90 - 8 * q^91 - 64 * q^92 - 16 * q^93 + 30 * q^94 + 15 * q^95 + 34 * q^96 - 7 * q^97 + 138 * q^98 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more