LMFDB - Embedded newform 91.2.h.b.16.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(16,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 2]))

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

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

chi := DirichletCharacter("91.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.h (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.726638658394$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 $ x^12 - x^11 + 7x^10 - 2x^9 + 33x^8 - 11x^7 + 55x^6 + 17x^5 + 47x^4 + x^3 + 8x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.1
Root			$-0.181721 - 0.314749i$ of defining polynomial
Character	$\chi$	$=$	91.16
Dual form			91.2.h.b.74.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.38804 q^{2} +(1.37574 - 2.38285i) q^{3} +3.70272 q^{4} +(-0.491140 + 0.850679i) q^{5} +(-3.28532 + 5.69033i) q^{6} +(-0.911766 - 2.48368i) q^{7} -4.06616 q^{8} +(-2.28532 - 3.95828i) q^{9} +O(q^{10})$	\(q-2.38804 q^{2} +(1.37574 - 2.38285i) q^{3} +3.70272 q^{4} +(-0.491140 + 0.850679i) q^{5} +(-3.28532 + 5.69033i) q^{6} +(-0.911766 - 2.48368i) q^{7} -4.06616 q^{8} +(-2.28532 - 3.95828i) q^{9} +(1.17286 - 2.03145i) q^{10} +(0.293901 - 0.509052i) q^{11} +(5.09398 - 8.82303i) q^{12} +(2.39227 - 2.69760i) q^{13} +(2.17733 + 5.93113i) q^{14} +(1.35136 + 2.34063i) q^{15} +2.30470 q^{16} -6.45420 q^{17} +(5.45742 + 9.45253i) q^{18} +(1.91345 + 3.31419i) q^{19} +(-1.81855 + 3.14983i) q^{20} +(-7.17260 - 1.24430i) q^{21} +(-0.701847 + 1.21563i) q^{22} +8.26001 q^{23} +(-5.59398 + 9.68906i) q^{24} +(2.01756 + 3.49452i) q^{25} +(-5.71283 + 6.44197i) q^{26} -4.32156 q^{27} +(-3.37601 - 9.19639i) q^{28} +(1.98009 + 3.42962i) q^{29} +(-3.22710 - 5.58950i) q^{30} +(1.49436 + 2.58831i) q^{31} +2.62861 q^{32} +(-0.808663 - 1.40065i) q^{33} +15.4129 q^{34} +(2.56062 + 0.444216i) q^{35} +(-8.46189 - 14.6564i) q^{36} +1.75588 q^{37} +(-4.56938 - 7.91440i) q^{38} +(-3.13683 - 9.41161i) q^{39} +(1.99705 - 3.45900i) q^{40} +(-1.83584 - 3.17977i) q^{41} +(17.1284 + 2.97143i) q^{42} +(-3.19042 + 5.52598i) q^{43} +(1.08823 - 1.88488i) q^{44} +4.48964 q^{45} -19.7252 q^{46} +(2.17030 - 3.75906i) q^{47} +(3.17067 - 5.49176i) q^{48} +(-5.33737 + 4.52907i) q^{49} +(-4.81802 - 8.34505i) q^{50} +(-8.87930 + 15.3794i) q^{51} +(8.85791 - 9.98846i) q^{52} +(-0.212770 - 0.368529i) q^{53} +10.3200 q^{54} +(0.288693 + 0.500031i) q^{55} +(3.70739 + 10.0991i) q^{56} +10.5296 q^{57} +(-4.72853 - 8.19006i) q^{58} +6.00863 q^{59} +(5.00371 + 8.66669i) q^{60} +(-1.10337 - 1.91109i) q^{61} +(-3.56859 - 6.18097i) q^{62} +(-7.74745 + 9.28503i) q^{63} -10.8866 q^{64} +(1.11985 + 3.35995i) q^{65} +(1.93112 + 3.34479i) q^{66} +(-3.50651 + 6.07346i) q^{67} -23.8981 q^{68} +(11.3636 - 19.6824i) q^{69} +(-6.11486 - 1.06080i) q^{70} +(-1.80127 + 3.11988i) q^{71} +(9.29247 + 16.0950i) q^{72} +(-2.46714 - 4.27321i) q^{73} -4.19311 q^{74} +11.1026 q^{75} +(7.08496 + 12.2715i) q^{76} +(-1.53229 - 0.265822i) q^{77} +(7.49088 + 22.4753i) q^{78} +(-1.39270 + 2.41223i) q^{79} +(-1.13193 + 1.96056i) q^{80} +(0.910609 - 1.57722i) q^{81} +(4.38406 + 7.59342i) q^{82} -2.86819 q^{83} +(-26.5581 - 4.60730i) q^{84} +(3.16992 - 5.49045i) q^{85} +(7.61885 - 13.1962i) q^{86} +10.8964 q^{87} +(-1.19505 + 2.06989i) q^{88} -2.09311 q^{89} -10.7214 q^{90} +(-8.88117 - 3.48206i) q^{91} +30.5845 q^{92} +8.22340 q^{93} +(-5.18275 + 8.97679i) q^{94} -3.75908 q^{95} +(3.61628 - 6.26357i) q^{96} +(-3.84852 + 6.66584i) q^{97} +(12.7458 - 10.8156i) q^{98} -2.68663 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} + q^{3} + 8 q^{4} + q^{5} - 9 q^{6} - 3 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 12 * q - 4 * q^2 + q^3 + 8 * q^4 + q^5 - 9 * q^6 - 3 * q^7 - 6 * q^8 + 3 * q^9	\( 12 q - 4 q^{2} + q^{3} + 8 q^{4} + q^{5} - 9 q^{6} - 3 q^{7} - 6 q^{8} + 3 q^{9} + 4 q^{10} + 4 q^{11} + 5 q^{12} - 2 q^{13} - 2 q^{14} - 2 q^{15} - 16 q^{16} - 10 q^{17} + 3 q^{18} - q^{19} - q^{20} - 9 q^{21} - 5 q^{22} + 2 q^{23} - 11 q^{24} + 7 q^{25} - 16 q^{26} - 8 q^{27} - q^{28} + 3 q^{29} - 5 q^{30} + 16 q^{31} - 16 q^{32} + 16 q^{33} + 32 q^{34} + 20 q^{35} - 21 q^{36} + 26 q^{37} - 17 q^{38} - 20 q^{39} - 5 q^{40} - 8 q^{41} + 50 q^{42} - 11 q^{43} + 21 q^{44} + 14 q^{45} - 32 q^{46} - q^{47} + 21 q^{48} - 3 q^{49} + 6 q^{50} - 20 q^{51} + 41 q^{52} - 2 q^{53} + 36 q^{54} + 9 q^{55} + 9 q^{56} + 42 q^{57} - 8 q^{58} - 26 q^{59} + 20 q^{60} - 5 q^{61} + 5 q^{62} - 40 q^{63} - 30 q^{64} - 5 q^{65} + 18 q^{66} - 11 q^{67} - 58 q^{68} + 23 q^{69} - 39 q^{70} + 6 q^{71} + 25 q^{72} - 30 q^{73} + 6 q^{74} + 6 q^{75} - 9 q^{76} + 11 q^{77} + 16 q^{78} + 7 q^{79} - 7 q^{80} - 6 q^{81} + q^{82} - 54 q^{83} - 46 q^{84} - q^{85} - 7 q^{86} - 32 q^{87} - 8 q^{89} - 16 q^{90} - 23 q^{91} + 54 q^{92} + 14 q^{93} + 45 q^{94} + 12 q^{95} + 19 q^{96} - 35 q^{97} + 20 q^{98} - 20 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 + q^3 + 8 * q^4 + q^5 - 9 * q^6 - 3 * q^7 - 6 * q^8 + 3 * q^9 + 4 * q^10 + 4 * q^11 + 5 * q^12 - 2 * q^13 - 2 * q^14 - 2 * q^15 - 16 * q^16 - 10 * q^17 + 3 * q^18 - q^19 - q^20 - 9 * q^21 - 5 * q^22 + 2 * q^23 - 11 * q^24 + 7 * q^25 - 16 * q^26 - 8 * q^27 - q^28 + 3 * q^29 - 5 * q^30 + 16 * q^31 - 16 * q^32 + 16 * q^33 + 32 * q^34 + 20 * q^35 - 21 * q^36 + 26 * q^37 - 17 * q^38 - 20 * q^39 - 5 * q^40 - 8 * q^41 + 50 * q^42 - 11 * q^43 + 21 * q^44 + 14 * q^45 - 32 * q^46 - q^47 + 21 * q^48 - 3 * q^49 + 6 * q^50 - 20 * q^51 + 41 * q^52 - 2 * q^53 + 36 * q^54 + 9 * q^55 + 9 * q^56 + 42 * q^57 - 8 * q^58 - 26 * q^59 + 20 * q^60 - 5 * q^61 + 5 * q^62 - 40 * q^63 - 30 * q^64 - 5 * q^65 + 18 * q^66 - 11 * q^67 - 58 * q^68 + 23 * q^69 - 39 * q^70 + 6 * q^71 + 25 * q^72 - 30 * q^73 + 6 * q^74 + 6 * q^75 - 9 * q^76 + 11 * q^77 + 16 * q^78 + 7 * q^79 - 7 * q^80 - 6 * q^81 + q^82 - 54 * q^83 - 46 * q^84 - q^85 - 7 * q^86 - 32 * q^87 - 8 * q^89 - 16 * q^90 - 23 * q^91 + 54 * q^92 + 14 * q^93 + 45 * q^94 + 12 * q^95 + 19 * q^96 - 35 * q^97 + 20 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−2.38804			−1.68860			−0.844299	−	0.535873i	$-0.819983\pi$
$2$	−2.38804			−1.68860			−0.844299	+	0.535873i	$0.819983\pi$
$3$	1.37574	−	2.38285i	0.794283	−	1.37574i	−0.129010	−	0.991643i	$-0.541180\pi$
$3$	1.37574	−	2.38285i	0.794283	−	1.37574i	0.923293	−	0.384096i	$-0.125487\pi$
$4$	3.70272			1.85136
$5$	−0.491140	+	0.850679i	−0.219644	+	0.380435i	−0.954699	−	0.297572i	$-0.903823\pi$
$5$	−0.491140	+	0.850679i	−0.219644	+	0.380435i	0.735055	+	0.678008i	$0.237156\pi$
$6$	−3.28532	+	5.69033i	−1.34122	+	2.32307i
$7$	−0.911766	−	2.48368i	−0.344615	−	0.938744i
$7$	−0.911766	−	2.48368i	−0.344615	−	0.938744i
$8$	−4.06616			−1.43761
$9$	−2.28532	−	3.95828i	−0.761772	−	1.31943i
$10$	1.17286	−	2.03145i	0.370891	−	0.642402i
$11$	0.293901	−	0.509052i	0.0886146	−	0.153485i	−0.818311	−	0.574775i	$-0.805089\pi$
$11$	0.293901	−	0.509052i	0.0886146	−	0.153485i	0.906926	+	0.421291i	$0.138423\pi$
$12$	5.09398	−	8.82303i	1.47051	−	2.54699i
$13$	2.39227	−	2.69760i	0.663496	−	0.748179i
$13$	2.39227	−	2.69760i	0.663496	−	0.748179i
$14$	2.17733	+	5.93113i	0.581916	+	1.58516i
$15$	1.35136	+	2.34063i	0.348920	+	0.604347i
$16$	2.30470			0.576176
$17$	−6.45420			−1.56537			−0.782687	−	0.622416i	$-0.786151\pi$
$17$	−6.45420			−1.56537			−0.782687	+	0.622416i	$0.786151\pi$
$18$	5.45742	+	9.45253i	1.28633	+	2.22798i
$19$	1.91345	+	3.31419i	0.438975	+	0.760327i	0.997611	−	0.0690863i	$-0.0220084\pi$
$19$	1.91345	+	3.31419i	0.438975	+	0.760327i	−0.558636	+	0.829413i	$0.688675\pi$
$20$	−1.81855	+	3.14983i	−0.406641	+	0.704323i
$21$	−7.17260	−	1.24430i	−1.56519	−	0.271528i
$22$	−0.701847	+	1.21563i	−0.149634	+	0.259174i
$23$	8.26001			1.72233			0.861166	−	0.508324i	$-0.169735\pi$
$23$	8.26001			1.72233			0.861166	+	0.508324i	$0.169735\pi$
$24$	−5.59398	+	9.68906i	−1.14187	+	1.97777i
$25$	2.01756	+	3.49452i	0.403513	+	0.698904i
$26$	−5.71283	+	6.44197i	−1.12038	+	1.26337i
$27$	−4.32156			−0.831685
$28$	−3.37601	−	9.19639i	−0.638007	−	1.73795i
$29$	1.98009	+	3.42962i	0.367694	+	0.636864i	0.989205	−	0.146541i	$-0.0468141\pi$
$29$	1.98009	+	3.42962i	0.367694	+	0.636864i	−0.621511	+	0.783406i	$0.713481\pi$
$30$	−3.22710	−	5.58950i	−0.589185	−	1.02050i
$31$	1.49436	+	2.58831i	0.268395	+	0.464874i	0.968448	−	0.249218i	$-0.0801734\pi$
$31$	1.49436	+	2.58831i	0.268395	+	0.464874i	−0.700053	+	0.714091i	$0.746840\pi$
$32$	2.62861			0.464676
$33$	−0.808663	−	1.40065i	−0.140770	−	0.243821i
$34$	15.4129			2.64329
$35$	2.56062	+	0.444216i	0.432824	+	0.0750862i
$36$	−8.46189	−	14.6564i	−1.41031	−	2.44274i
$37$	1.75588			0.288665			0.144333	−	0.989529i	$-0.453896\pi$
$37$	1.75588			0.288665			0.144333	+	0.989529i	$0.453896\pi$
$38$	−4.56938	−	7.91440i	−0.741252	−	1.28389i
$39$	−3.13683	−	9.41161i	−0.502295	−	1.50706i
$40$	1.99705	−	3.45900i	0.315762	−	0.546916i
$41$	−1.83584	−	3.17977i	−0.286710	−	0.496597i	0.686312	−	0.727307i	$-0.259228\pi$
$41$	−1.83584	−	3.17977i	−0.286710	−	0.496597i	−0.973023	+	0.230710i	$0.925895\pi$
$42$	17.1284	+	2.97143i	2.64297	+	0.458502i
$43$	−3.19042	+	5.52598i	−0.486535	+	0.842703i	−0.999880	−	0.0154788i	$-0.995073\pi$
$43$	−3.19042	+	5.52598i	−0.486535	+	0.842703i	0.513345	+	0.858182i	$0.328406\pi$
$44$	1.08823	−	1.88488i	0.164058	−	0.284156i
$45$	4.48964			0.669276
$46$	−19.7252			−2.90832
$47$	2.17030	−	3.75906i	0.316570	−	0.548316i	−0.663200	−	0.748442i	$-0.730802\pi$
$47$	2.17030	−	3.75906i	0.316570	−	0.548316i	0.979770	+	0.200127i	$0.0641353\pi$
$48$	3.17067	−	5.49176i	0.457647	−	0.792668i
$49$	−5.33737	+	4.52907i	−0.762481	+	0.647011i
$50$	−4.81802	−	8.34505i	−0.681370	−	1.18017i
$51$	−8.87930	+	15.3794i	−1.24335	+	2.15355i
$52$	8.85791	−	9.98846i	1.22837	−	1.38515i
$53$	−0.212770	−	0.368529i	−0.0292263	−	0.0506214i	0.851042	−	0.525097i	$-0.175971\pi$
$53$	−0.212770	−	0.368529i	−0.0292263	−	0.0506214i	−0.880269	+	0.474476i	$0.842638\pi$
$54$	10.3200			1.40438
$55$	0.288693	+	0.500031i	0.0389274	+	0.0674242i
$56$	3.70739	+	10.0991i	0.495420	+	1.34954i
$57$	10.5296			1.39468
$58$	−4.72853	−	8.19006i	−0.620887	−	1.07541i
$59$	6.00863			0.782256			0.391128	−	0.920336i	$-0.372085\pi$
$59$	6.00863			0.782256			0.391128	+	0.920336i	$0.372085\pi$
$60$	5.00371	+	8.66669i	0.645977	+	1.11886i
$61$	−1.10337	−	1.91109i	−0.141272	−	0.244691i	0.786704	−	0.617331i	$-0.211786\pi$
$61$	−1.10337	−	1.91109i	−0.141272	−	0.244691i	−0.927976	+	0.372640i	$0.878453\pi$
$62$	−3.56859	−	6.18097i	−0.453211	−	0.784985i
$63$	−7.74745	+	9.28503i	−0.976087	+	1.16980i
$64$	−10.8866			−1.36083
$65$	1.11985	+	3.35995i	0.138901	+	0.416751i
$66$	1.93112	+	3.34479i	0.237704	+	0.411716i
$67$	−3.50651	+	6.07346i	−0.428389	+	0.741991i	−0.996730	−	0.0808015i	$-0.974252\pi$
$67$	−3.50651	+	6.07346i	−0.428389	+	0.741991i	0.568341	+	0.822793i	$0.307585\pi$
$68$	−23.8981			−2.89807
$69$	11.3636	−	19.6824i	1.36802	−	2.36948i
$70$	−6.11486	−	1.06080i	−0.730866	−	0.126790i
$71$	−1.80127	+	3.11988i	−0.213771	+	0.370262i	−0.952892	−	0.303311i	$-0.901908\pi$
$71$	−1.80127	+	3.11988i	−0.213771	+	0.370262i	0.739121	+	0.673573i	$0.235241\pi$
$72$	9.29247	+	16.0950i	1.09513	+	1.89682i
$73$	−2.46714	−	4.27321i	−0.288756	−	0.500141i	0.684757	−	0.728772i	$-0.259908\pi$
$73$	−2.46714	−	4.27321i	−0.288756	−	0.500141i	−0.973513	+	0.228631i	$0.926575\pi$
$74$	−4.19311			−0.487439
$75$	11.1026			1.28201
$76$	7.08496	+	12.2715i	0.812701	+	1.40764i
$77$	−1.53229	−	0.265822i	−0.174621	−	0.0302932i
$78$	7.49088	+	22.4753i	0.848175	+	2.54483i
$79$	−1.39270	+	2.41223i	−0.156691	+	0.271397i	−0.933674	−	0.358125i	$-0.883416\pi$
$79$	−1.39270	+	2.41223i	−0.156691	+	0.271397i	0.776982	+	0.629522i	$0.216749\pi$
$80$	−1.13193	+	1.96056i	−0.126554	+	0.219198i
$81$	0.910609	−	1.57722i	0.101179	−	0.175247i
$82$	4.38406	+	7.59342i	0.484138	+	0.838552i
$83$	−2.86819			−0.314825			−0.157412	−	0.987533i	$-0.550315\pi$
$83$	−2.86819			−0.314825			−0.157412	+	0.987533i	$0.550315\pi$
$84$	−26.5581	−	4.60730i	−2.89773	−	0.502697i
$85$	3.16992	−	5.49045i	0.343826	−	0.595523i
$86$	7.61885	−	13.1962i	0.821562	−	1.42299i
$87$	10.8964			1.16821
$88$	−1.19505	+	2.06989i	−0.127393	+	0.220651i
$89$	−2.09311			−0.221870			−0.110935	−	0.993828i	$-0.535384\pi$
$89$	−2.09311			−0.221870			−0.110935	+	0.993828i	$0.535384\pi$
$90$	−10.7214			−1.13014
$91$	−8.88117	−	3.48206i	−0.931000	−	0.365020i
$92$	30.5845			3.18866
$93$	8.22340			0.852727
$94$	−5.18275	+	8.97679i	−0.534560	+	0.925885i
$95$	−3.75908			−0.385674
$96$	3.61628	−	6.26357i	0.369085	−	0.639273i
$97$	−3.84852	+	6.66584i	−0.390758	+	0.676813i	−0.992550	−	0.121840i	$-0.961120\pi$
$97$	−3.84852	+	6.66584i	−0.390758	+	0.676813i	0.601791	+	0.798653i	$0.294454\pi$
$98$	12.7458	−	10.8156i	1.28752	−	1.09254i
$99$	−2.68663			−0.270016
$100$	7.47047	+	12.9392i	0.747047	+	1.29392i
$101$	1.31866	−	2.28399i	0.131212	−	0.227265i	−0.792932	−	0.609310i	$-0.791447\pi$
$101$	1.31866	−	2.28399i	0.131212	−	0.227265i	0.924144	+	0.382045i	$0.124780\pi$
$102$	21.2041	−	36.7266i	2.09952	−	3.63647i
$103$	5.43095	−	9.40669i	0.535128	−	0.926868i	−0.464029	−	0.885820i	$-0.653597\pi$
$103$	5.43095	−	9.40669i	0.535128	−	0.926868i	0.999157	−	0.0410486i	$-0.0130699\pi$
$104$	−9.72736	+	10.9689i	−0.953846	+	1.07559i
$105$	4.58125	−	5.49045i	0.447084	−	0.535813i
$106$	0.508103	+	0.880061i	0.0493514	+	0.0854791i
$107$	−15.9805			−1.54489			−0.772446	−	0.635080i	$-0.780967\pi$
$107$	−15.9805			−1.54489			−0.772446	+	0.635080i	$0.780967\pi$
$108$	−16.0015			−1.53975
$109$	−4.61738	−	7.99754i	−0.442265	−	0.766026i	0.555592	−	0.831455i	$-0.312492\pi$
$109$	−4.61738	−	7.99754i	−0.442265	−	0.766026i	−0.997857	+	0.0654294i	$0.979158\pi$
$110$	−0.689410	−	1.19409i	−0.0657327	−	0.113852i
$111$	2.41564	−	4.18400i	0.229282	−	0.397128i
$112$	−2.10135	−	5.72416i	−0.198559	−	0.540882i
$113$	−5.09012	+	8.81635i	−0.478838	+	0.829372i	−0.999706	−	0.0242655i	$-0.992275\pi$
$113$	−5.09012	+	8.81635i	−0.478838	+	0.829372i	0.520867	+	0.853638i	$0.325609\pi$
$114$	−25.1451			−2.35506
$115$	−4.05682	+	7.02662i	−0.378301	+	0.655236i
$116$	7.33173	+	12.6989i	0.680734	+	1.17907i
$117$	−16.1450	−	3.30442i	−1.49260	−	0.305494i
$118$	−14.3488			−1.32092
$119$	5.88472	+	16.0302i	0.539451	+	1.46949i
$120$	−5.49485	−	9.51736i	−0.501609	−	0.868813i
$121$	5.32724	+	9.22706i	0.484295	+	0.838823i
$122$	2.63489	+	4.56376i	0.238552	+	0.413184i
$123$	−10.1026			−0.910917
$124$	5.53320	+	9.58378i	0.496896	+	0.860649i
$125$	−8.87502			−0.793806
$126$	18.5012	−	22.1730i	1.64822	−	1.97533i
$127$	−2.12513	−	3.68083i	−0.188575	−	0.326621i	0.756201	−	0.654340i	$-0.227053\pi$
$127$	−2.12513	−	3.68083i	−0.188575	−	0.326621i	−0.944775	+	0.327719i	$0.893720\pi$
$128$	20.7404			1.83321
$129$	8.77838	+	15.2046i	0.772893	+	1.33869i
$130$	−2.67425	−	8.02369i	−0.234547	−	0.703725i
$131$	1.08478	−	1.87890i	0.0947779	−	0.164160i	−0.814738	−	0.579829i	$-0.803119\pi$
$131$	1.08478	−	1.87890i	0.0947779	−	0.164160i	0.909516	+	0.415669i	$0.136453\pi$
$132$	−2.99425	−	5.18620i	−0.260616	−	0.451401i
$133$	6.48678	−	7.77416i	0.562475	−	0.674105i
$134$	8.37369	−	14.5037i	0.723376	−	1.25292i
$135$	2.12249	−	3.67626i	0.182675	−	0.316402i
$136$	26.2438			2.25039
$137$	8.36316			0.714513			0.357257	−	0.934006i	$-0.383712\pi$
$137$	8.36316			0.714513			0.357257	+	0.934006i	$0.383712\pi$
$138$	−27.1367	+	47.0022i	−2.31003	+	4.00110i
$139$	0.288457	−	0.499622i	0.0244666	−	0.0423774i	−0.853533	−	0.521039i	$-0.825545\pi$
$139$	0.288457	−	0.499622i	0.0244666	−	0.0423774i	0.877999	+	0.478662i	$0.158878\pi$
$140$	9.48127	+	1.64481i	0.801314	+	0.139012i
$141$	−5.97152	−	10.3430i	−0.502893	−	0.871036i
$142$	4.30149	−	7.45040i	0.360973	−	0.625224i
$143$	−0.670127	−	2.01062i	−0.0560388	−	0.168136i
$144$	−5.26698	−	9.12267i	−0.438915	−	0.760223i
$145$	−3.89001			−0.323048
$146$	5.89161	+	10.2046i	0.487593	+	0.844537i
$147$	3.44928	+	18.9490i	0.284492	+	1.56288i
$148$	6.50154			0.534423
$149$	−1.40331	−	2.43061i	−0.114964	−	0.199123i	0.802801	−	0.596246i	$-0.203342\pi$
$149$	−1.40331	−	2.43061i	−0.114964	−	0.199123i	−0.917765	+	0.397123i	$0.870009\pi$
$150$	−26.5133			−2.16480
$151$	11.5054	+	19.9280i	0.936300	+	1.62172i	0.772300	+	0.635258i	$0.219106\pi$
$151$	11.5054	+	19.9280i	0.936300	+	1.62172i	0.164000	+	0.986460i	$0.447560\pi$
$152$	−7.78039	−	13.4760i	−0.631073	−	1.09305i
$153$	14.7499	+	25.5476i	1.19246	+	2.06540i
$154$	3.65917	+	0.634792i	0.294864	+	0.0511530i
$155$	−2.93576			−0.235806
$156$	−11.6148	−	34.8486i	−0.929930	−	2.79012i
$157$	−11.2880	−	19.5513i	−0.900879	−	1.56037i	−0.826356	−	0.563148i	$-0.809590\pi$
$157$	−11.2880	−	19.5513i	−0.900879	−	1.56037i	−0.0745227	−	0.997219i	$-0.523743\pi$
$158$	3.32583	−	5.76050i	0.264588	−	0.458281i
$159$	−1.17087			−0.0928557
$160$	−1.29101	+	2.23610i	−0.102064	+	0.176779i
$161$	−7.53119	−	20.5153i	−0.593541	−	1.61683i
$162$	−2.17457	+	3.76646i	−0.170850	+	0.295921i
$163$	−4.08857	−	7.08161i	−0.320242	−	0.554675i	0.660296	−	0.751005i	$-0.270431\pi$
$163$	−4.08857	−	7.08161i	−0.320242	−	0.554675i	−0.980538	+	0.196331i	$0.937097\pi$
$164$	−6.79761	−	11.7738i	−0.530804	−	0.919380i
$165$	1.58867			0.123678
$166$	6.84934			0.531612
$167$	1.16386	+	2.01586i	0.0900619	+	0.155992i	0.907537	−	0.419972i	$-0.137960\pi$
$167$	1.16386	+	2.01586i	0.0900619	+	0.155992i	−0.817475	+	0.575964i	$0.804627\pi$
$168$	29.1649	+	5.05953i	2.25012	+	0.390351i
$169$	−1.55408	−	12.9068i	−0.119545	−	0.992829i
$170$	−7.56988	+	13.1114i	−0.580583	+	1.00560i
$171$	8.74566	−	15.1479i	0.668798	−	1.15839i
$172$	−11.8133	+	20.4611i	−0.900752	+	1.56015i
$173$	4.06686	+	7.04401i	0.309198	+	0.535546i	0.978187	−	0.207726i	$-0.0666061\pi$
$173$	4.06686	+	7.04401i	0.309198	+	0.535546i	−0.668989	+	0.743272i	$0.733273\pi$
$174$	−26.0209			−1.97264
$175$	6.83974	−	8.19717i	0.517036	−	0.619648i
$176$	0.677355	−	1.17321i	0.0510576	−	0.0884343i
$177$	8.26630	−	14.3177i	0.621333	−	1.07618i
$178$	4.99843			0.374648
$179$	10.4963	−	18.1801i	0.784528	−	1.35884i	−0.144752	−	0.989468i	$-0.546239\pi$
$179$	10.4963	−	18.1801i	0.784528	−	1.35884i	0.929281	−	0.369375i	$-0.120428\pi$
$180$	16.6239			1.23907
$181$	−1.60807			−0.119527			−0.0597635	−	0.998213i	$-0.519035\pi$
$181$	−1.60807			−0.119527			−0.0597635	+	0.998213i	$0.519035\pi$
$182$	21.2086	+	8.31530i	1.57208	+	0.616371i
$183$	−6.07180			−0.448841
$184$	−33.5865			−2.47603
$185$	−0.862384	+	1.49369i	−0.0634037	+	0.109818i
$186$	−19.6378			−1.43991
$187$	−1.89690	+	3.28552i	−0.138715	+	0.240261i
$188$	8.03601	−	13.9188i	0.586086	−	1.01513i
$189$	3.94025	+	10.7334i	0.286611	+	0.780739i
$190$	8.97683			0.651247
$191$	5.78111	+	10.0132i	0.418307	+	0.724529i	0.995769	−	0.0918886i	$-0.0292904\pi$
$191$	5.78111	+	10.0132i	0.418307	+	0.724529i	−0.577463	+	0.816417i	$0.695957\pi$
$192$	−14.9771	+	25.9412i	−1.08088	+	1.87214i
$193$	−11.7894	+	20.4199i	−0.848621	+	1.46985i	0.0338178	+	0.999428i	$0.489233\pi$
$193$	−11.7894	+	20.4199i	−0.848621	+	1.46985i	−0.882439	+	0.470427i	$0.844100\pi$
$194$	9.19041	−	15.9183i	0.659833	−	1.14286i
$195$	9.54689	+	1.95398i	0.683667	+	0.139927i
$196$	−19.7628	+	16.7699i	−1.41163	+	1.19785i
$197$	0.735472	+	1.27387i	0.0524002	+	0.0907598i	0.891036	−	0.453933i	$-0.149980\pi$
$197$	0.735472	+	1.27387i	0.0524002	+	0.0907598i	−0.838636	+	0.544693i	$0.816646\pi$
$198$	6.41577			0.455949
$199$	9.39399			0.665922			0.332961	−	0.942941i	$-0.391952\pi$
$199$	9.39399			0.665922			0.332961	+	0.942941i	$0.391952\pi$
$200$	−8.20374	−	14.2093i	−0.580092	−	1.00475i
$201$	9.64810	+	16.7110i	0.680524	+	1.17870i
$202$	−3.14901	+	5.45425i	−0.221564	+	0.383760i
$203$	6.71271	−	8.04493i	0.471140	−	0.564643i
$204$	−32.8776	+	56.9456i	−2.30189	+	3.98699i
$205$	3.60662			0.251897
$206$	−12.9693	+	22.4635i	−0.903615	+	1.56511i
$207$	−18.8767	−	32.6955i	−1.31202	−	2.27249i
$208$	5.51348	−	6.21717i	0.382291	−	0.431083i
$209$	2.24946			0.155598
$210$	−10.9402	+	13.1114i	−0.754945	+	0.904773i
$211$	4.47109	+	7.74416i	0.307803	+	0.533130i	0.977881	−	0.209160i	$-0.0670730\pi$
$211$	4.47109	+	7.74416i	0.307803	+	0.533130i	−0.670079	+	0.742290i	$0.733740\pi$
$212$	−0.787829	−	1.36456i	−0.0541083	−	0.0937184i
$213$	4.95615	+	8.58430i	0.339589	+	0.588186i
$214$	38.1620			2.60870
$215$	−3.13389	−	5.42805i	−0.213729	−	0.370190i
$216$	17.5722			1.19563
$217$	5.06603	−	6.07145i	0.343905	−	0.412157i
$218$	11.0265	+	19.0984i	0.746808	+	1.29351i
$219$	−13.5765			−0.917418
$220$	1.06895	+	1.85148i	0.0720686	+	0.124827i
$221$	−15.4402	+	17.4108i	−1.03862	+	1.17118i
$222$	−5.76863	+	9.99156i	−0.387165	+	0.670589i
$223$	−10.9098	−	18.8963i	−0.730574	−	1.26539i	−0.956638	−	0.291279i	$-0.905919\pi$
$223$	−10.9098	−	18.8963i	−0.730574	−	1.26539i	0.226064	−	0.974112i	$-0.427414\pi$
$224$	−2.39667	−	6.52862i	−0.160134	−	0.436212i
$225$	9.22154	−	15.9722i	0.614769	−	1.06481i
$226$	12.1554	−	21.0538i	0.808565	−	1.40048i
$227$	−18.5525			−1.23137			−0.615687	−	0.787990i	$-0.711122\pi$
$227$	−18.5525			−1.23137			−0.615687	+	0.787990i	$0.711122\pi$
$228$	38.9882			2.58206
$229$	−9.67525	+	16.7580i	−0.639359	+	1.10740i	0.346215	+	0.938155i	$0.387467\pi$
$229$	−9.67525	+	16.7580i	−0.639359	+	1.10740i	−0.985574	+	0.169247i	$0.945867\pi$
$230$	9.68784	−	16.7798i	0.638797	−	1.10643i
$231$	−2.74145	+	3.28552i	−0.180374	+	0.216172i
$232$	−8.05137	−	13.9454i	−0.528599	−	0.915560i
$233$	−8.08170	+	13.9979i	−0.529450	+	0.917034i	0.469960	+	0.882688i	$0.344268\pi$
$233$	−8.08170	+	13.9979i	−0.529450	+	0.917034i	−0.999410	+	0.0343462i	$0.989065\pi$
$234$	38.5548	+	7.89108i	2.52040	+	0.515856i
$235$	2.13184	+	3.69245i	0.139066	+	0.240869i
$236$	22.2483			1.44824
$237$	3.83199	+	6.63720i	0.248915	+	0.431133i
$238$	−14.0529	−	38.2807i	−0.910916	−	2.48137i
$239$	16.1037			1.04166			0.520831	−	0.853660i	$-0.325622\pi$
$239$	16.1037			1.04166			0.520831	+	0.853660i	$0.325622\pi$
$240$	3.11449	+	5.39445i	0.201039	+	0.348210i
$241$	−4.00600			−0.258049			−0.129025	−	0.991641i	$-0.541185\pi$
$241$	−4.00600			−0.258049			−0.129025	+	0.991641i	$0.541185\pi$
$242$	−12.7217	−	22.0346i	−0.817779	−	1.41643i
$243$	−8.98786	−	15.5674i	−0.576572	−	0.998651i
$244$	−4.08548	−	7.07625i	−0.261546	−	0.453011i
$245$	−1.23140	−	6.76480i	−0.0786710	−	0.432187i
$246$	24.1253			1.53817
$247$	13.5178	+	2.76672i	0.860119	+	0.176042i
$248$	−6.07631	−	10.5245i	−0.385846	−	0.668305i
$249$	−3.94588	+	6.83446i	−0.250060	+	0.433116i
$250$	21.1939			1.34042
$251$	−1.62344	+	2.81188i	−0.102471	+	0.177484i	−0.912702	−	0.408626i	$-0.866008\pi$
$251$	−1.62344	+	2.81188i	−0.102471	+	0.177484i	0.810231	+	0.586110i	$0.199341\pi$
$252$	−28.6867	+	34.3799i	−1.80709	+	2.16573i
$253$	2.42763	−	4.20477i	0.152624	−	0.264352i
$254$	5.07489	+	8.78996i	0.318427	+	0.551531i
$255$	−8.72195	−	15.1069i	−0.546190	−	0.946029i
$256$	−27.7557			−1.73473
$257$	−26.8924			−1.67750			−0.838751	−	0.544516i	$-0.816713\pi$
$257$	−26.8924			−1.67750			−0.838751	+	0.544516i	$0.816713\pi$
$258$	−20.9631	−	36.3092i	−1.30511	−	2.26051i
$259$	−1.60095	−	4.36106i	−0.0994784	−	0.270983i
$260$	4.14650	+	12.4410i	0.257155	+	0.771556i
$261$	9.05027	−	15.6755i	0.560198	−	0.970291i
$262$	−2.59050	+	4.48688i	−0.160042	+	0.277200i
$263$	1.90353	−	3.29701i	0.117377	−	0.203302i	−0.801351	−	0.598195i	$-0.795885\pi$
$263$	1.90353	−	3.29701i	0.117377	−	0.203302i	0.918727	+	0.394893i	$0.129218\pi$
$264$	3.28815	+	5.69525i	0.202372	+	0.350518i
$265$	0.418000			0.0256775
$266$	−15.4907	+	18.5650i	−0.949794	+	1.13829i
$267$	−2.87958	+	4.98757i	−0.176227	+	0.305235i
$268$	−12.9836	+	22.4883i	−0.793102	+	1.37369i
$269$	−23.8381			−1.45343			−0.726716	−	0.686938i	$-0.758954\pi$
$269$	−23.8381			−1.45343			−0.726716	+	0.686938i	$0.758954\pi$
$270$	−5.06859	+	8.77905i	−0.308464	+	0.534276i
$271$	9.90135			0.601464			0.300732	−	0.953709i	$-0.402769\pi$
$271$	9.90135			0.601464			0.300732	+	0.953709i	$0.402769\pi$
$272$	−14.8750			−0.901931
$273$	−20.5154	+	16.3721i	−1.24165	+	0.990884i
$274$	−19.9715			−1.20653
$275$	2.37186			0.143028
$276$	42.0763	−	72.8783i	2.53270	−	4.38676i
$277$	11.7858			0.708139			0.354069	−	0.935219i	$-0.384798\pi$
$277$	11.7858			0.708139			0.354069	+	0.935219i	$0.384798\pi$
$278$	−0.688846	+	1.19312i	−0.0413142	+	0.0715584i
$279$	6.83017	−	11.8302i	0.408912	−	0.708256i
$280$	−10.4119	−	1.80625i	−0.622231	−	0.107944i
$281$	12.9976			0.775372			0.387686	−	0.921791i	$-0.373274\pi$
$281$	12.9976			0.775372			0.387686	+	0.921791i	$0.373274\pi$
$282$	14.2602	+	24.6994i	0.849184	+	1.47083i
$283$	8.40249	−	14.5535i	0.499476	−	0.865118i	−0.500524	−	0.865723i	$-0.666859\pi$
$283$	8.40249	−	14.5535i	0.499476	−	0.865118i	1.00000		0.000604910i	$0.000192549\pi$
$284$	−6.66959	+	11.5521i	−0.395767	+	0.685489i
$285$	−5.17151	+	8.95733i	−0.306334	+	0.530586i
$286$	1.60029	+	4.80143i	0.0946270	+	0.283914i
$287$	−6.22369	+	7.45886i	−0.367373	+	0.440283i
$288$	−6.00719	−	10.4048i	−0.353977	−	0.613107i
$289$	24.6567			1.45039
$290$	9.28948			0.545497
$291$	10.5891	+	18.3409i	0.620746	+	1.07516i
$292$	−9.13512	−	15.8225i	−0.534592	−	0.925941i
$293$	7.04782	−	12.2072i	0.411738	−	0.713151i	−0.583342	−	0.812227i	$-0.698255\pi$
$293$	7.04782	−	12.2072i	0.411738	−	0.713151i	0.995080	+	0.0990757i	$0.0315886\pi$
$294$	−8.23701	−	45.2508i	−0.480392	−	2.63908i
$295$	−2.95108	+	5.11141i	−0.171818	+	0.297598i
$296$	−7.13970			−0.414987
$297$	−1.27011	+	2.19990i	−0.0736994	+	0.127651i
$298$	3.35116	+	5.80438i	0.194128	+	0.336239i
$299$	19.7602	−	22.2822i	1.14276	−	1.28861i
$300$	41.1097			2.37347
$301$	16.6337	+	2.88561i	0.958750	+	0.166324i
$302$	−27.4754	−	47.5888i	−1.58103	−	2.73843i
$303$	−3.62827	−	6.28434i	−0.208439	−	0.361026i
$304$	4.40993	+	7.63822i	0.252927	+	0.438082i
$305$	2.16764			0.124119
$306$	−35.2233	−	61.0085i	−2.01358	−	3.48762i
$307$	15.8786			0.906240			0.453120	−	0.891450i	$-0.350311\pi$
$307$	15.8786			0.906240			0.453120	+	0.891450i	$0.350311\pi$
$308$	−5.67365	−	0.984264i	−0.323286	−	0.0560836i
$309$	−14.9431	−	25.8823i	−0.850086	−	1.47239i
$310$	7.01070			0.398181
$311$	14.3017	+	24.7713i	0.810975	+	1.40465i	0.912183	+	0.409784i	$0.134396\pi$
$311$	14.3017	+	24.7713i	0.810975	+	1.40465i	−0.101208	+	0.994865i	$0.532271\pi$
$312$	12.7549	+	38.2692i	0.722103	+	2.16656i
$313$	9.28962	−	16.0901i	0.525080	−	0.909465i	−0.474493	−	0.880259i	$-0.657369\pi$
$313$	9.28962	−	16.0901i	0.525080	−	0.909465i	0.999573	−	0.0292063i	$-0.00929798\pi$
$314$	26.9561	+	46.6893i	1.52122	+	2.63483i
$315$	−4.09350	−	11.1508i	−0.230643	−	0.628279i
$316$	−5.15679	+	8.93182i	−0.290092	+	0.502454i
$317$	−15.3223	+	26.5389i	−0.860584	+	1.49057i	0.0107826	+	0.999942i	$0.496568\pi$
$317$	−15.3223	+	26.5389i	−0.860584	+	1.49057i	−0.871366	+	0.490633i	$0.836766\pi$
$318$	2.79607			0.156796
$319$	2.32781			0.130332
$320$	5.34685	−	9.26102i	0.298898	−	0.517707i
$321$	−21.9850	+	38.0791i	−1.22708	+	2.12537i
$322$	17.9848	+	48.9912i	1.00225	+	2.73017i
$323$	−12.3498	−	21.3904i	−0.687160	−	1.19020i
$324$	3.37173	−	5.84001i	0.187318	−	0.324445i
$325$	14.2534	+	2.91727i	0.790635	+	0.161821i
$326$	9.76366	+	16.9112i	0.540759	+	0.936622i
$327$	−25.4093			−1.40514
$328$	7.46483	+	12.9295i	0.412177	+	0.713911i
$329$	−11.3151	−	1.96295i	−0.623823	−	0.108221i
$330$	−3.79379			−0.208842
$331$	−13.6138	−	23.5799i	−0.748284	−	1.29607i	−0.948644	−	0.316344i	$-0.897545\pi$
$331$	−13.6138	−	23.5799i	−0.748284	−	1.29607i	0.200360	−	0.979722i	$-0.435789\pi$
$332$	−10.6201			−0.582854
$333$	−4.01275	−	6.95028i	−0.219897	−	0.380873i
$334$	−2.77933	−	4.81395i	−0.152078	−	0.263407i
$335$	−3.44438	−	5.96584i	−0.188187	−	0.325949i
$336$	−16.5307	−	2.86774i	−0.901824	−	0.156448i
$337$	−12.3160			−0.670898			−0.335449	−	0.942058i	$-0.608888\pi$
$337$	−12.3160			−0.670898			−0.335449	+	0.942058i	$0.608888\pi$
$338$	3.71121	+	30.8219i	0.201863	+	1.67649i
$339$	14.0054	+	24.2580i	0.760666	+	1.31751i
$340$	11.7373	−	20.3296i	0.636545	−	1.10253i
$341$	1.75678			0.0951348
$342$	−20.8850	+	36.1738i	−1.12933	+	1.95606i
$343$	16.1152	+	9.12688i	0.870140	+	0.492805i
$344$	12.9728	−	22.4695i	0.699445	−	1.21148i
$345$	11.1623	+	19.3336i	0.600956	+	1.04089i
$346$	−9.71182	−	16.8214i	−0.522111	−	0.904322i
$347$	6.14506			0.329884			0.164942	−	0.986303i	$-0.447256\pi$
$347$	6.14506			0.329884			0.164942	+	0.986303i	$0.447256\pi$
$348$	40.3462			2.16278
$349$	−6.51563	−	11.2854i	−0.348774	−	0.604094i	0.637258	−	0.770650i	$-0.280068\pi$
$349$	−6.51563	−	11.2854i	−0.348774	−	0.604094i	−0.986032	+	0.166557i	$0.946735\pi$
$350$	−16.3336	+	19.5752i	−0.873065	+	1.04634i
$351$	−10.3383	+	11.6578i	−0.551820	+	0.622249i
$352$	0.772550	−	1.33810i	0.0411771	−	0.0713208i
$353$	−15.8332	+	27.4240i	−0.842718	+	1.45963i	0.0448710	+	0.998993i	$0.485712\pi$
$353$	−15.8332	+	27.4240i	−0.842718	+	1.45963i	−0.887589	+	0.460637i	$0.847621\pi$
$354$	−19.7402	+	34.1911i	−1.04918	+	1.81724i
$355$	−1.76935	−	3.06460i	−0.0939072	−	0.162652i
$356$	−7.75021			−0.410761
$357$	46.2934	+	8.03096i	2.45011	+	0.425043i
$358$	−25.0655	+	43.4147i	−1.32475	+	2.29454i
$359$	−9.96610	+	17.2618i	−0.525991	+	0.911043i	0.473551	+	0.880767i	$0.342972\pi$
$359$	−9.96610	+	17.2618i	−0.525991	+	0.911043i	−0.999542	+	0.0302764i	$0.990361\pi$
$360$	−18.2556			−0.962155
$361$	2.17744	−	3.77144i	0.114602	−	0.198497i
$362$	3.84014			0.201833
$363$	29.3156			1.53867
$364$	−32.8845	−	12.8931i	−1.72362	−	0.675783i
$365$	4.84684			0.253695
$366$	14.4997			0.757911
$367$	−9.85950	+	17.0772i	−0.514662	+	0.891420i	0.485194	+	0.874407i	$0.338749\pi$
$367$	−9.85950	+	17.0772i	−0.514662	+	0.891420i	−0.999855	+	0.0170133i	$0.994584\pi$
$368$	19.0369			0.992366
$369$	−8.39096	+	14.5336i	−0.436816	+	0.756588i
$370$	2.05940	−	3.56699i	0.107063	−	0.185439i
$371$	−0.721313	+	0.864466i	−0.0374487	+	0.0448808i
$372$	30.4490			1.57870
$373$	−8.77345	−	15.1961i	−0.454272	−	0.786823i	0.544374	−	0.838843i	$-0.316767\pi$
$373$	−8.77345	−	15.1961i	−0.454272	−	0.786823i	−0.998646	+	0.0520202i	$0.983434\pi$
$374$	4.52986	−	7.84595i	0.234234	−	0.405704i
$375$	−12.2097	+	21.1478i	−0.630507	+	1.09207i
$376$	−8.82478	+	15.2850i	−0.455103	+	0.788262i
$377$	13.9887	+	2.86308i	0.720452	+	0.147456i
$378$	−9.40946	−	25.6317i	−0.483971	−	1.31835i
$379$	5.85068	+	10.1337i	0.300529	+	0.520532i	0.976256	−	0.216620i	$-0.0695034\pi$
$379$	5.85068	+	10.1337i	0.300529	+	0.520532i	−0.675727	+	0.737152i	$0.736170\pi$
$380$	−13.9188			−0.714021
$381$	−11.6945			−0.599127
$382$	−13.8055	−	23.9119i	−0.706352	−	1.22344i
$383$	10.7644	+	18.6445i	0.550036	+	0.952690i	0.998271	+	0.0587748i	$0.0187194\pi$
$383$	10.7644	+	18.6445i	0.550036	+	0.952690i	−0.448235	+	0.893916i	$0.647947\pi$
$384$	28.5334	−	49.4213i	1.45609	−	2.52202i
$385$	0.978699	−	1.17293i	0.0498791	−	0.0597783i
$386$	28.1536	−	48.7634i	1.43298	−	2.48199i
$387$	29.1645			1.48252
$388$	−14.2500	+	24.6817i	−0.723435	+	1.25303i
$389$	−13.2455	−	22.9419i	−0.671574	−	1.16320i	−0.977458	−	0.211131i	$-0.932285\pi$
$389$	−13.2455	−	22.9419i	−0.671574	−	1.16320i	0.305884	−	0.952069i	$-0.401048\pi$
$390$	−22.7983	−	4.66618i	−1.15444	−	0.236281i
$391$	−53.3118			−2.69609
$392$	21.7026	−	18.4160i	1.09615	−	0.930146i
$393$	−2.98476	−	5.16975i	−0.150561	−	0.260779i
$394$	−1.75633	−	3.04206i	−0.0884828	−	0.153257i
$395$	−1.36802	−	2.36949i	−0.0688327	−	0.119222i
$396$	−9.94784			−0.499898
$397$	16.8995	+	29.2707i	0.848160	+	1.46906i	0.882849	+	0.469658i	$0.155623\pi$
$397$	16.8995	+	29.2707i	0.848160	+	1.46906i	−0.0346887	+	0.999398i	$0.511044\pi$
$398$	−22.4332			−1.12447
$399$	−9.60054	−	26.1522i	−0.480628	−	1.30925i
$400$	4.64989	+	8.05384i	0.232494	+	0.402692i
$401$	21.6119			1.07925			0.539623	−	0.841907i	$-0.318567\pi$
$401$	21.6119			1.07925			0.539623	+	0.841907i	$0.318567\pi$
$402$	−23.0400	−	39.9065i	−1.14913	−	1.99035i
$403$	10.5571	+	2.16075i	0.525888	+	0.107635i
$404$	4.88264	−	8.45697i	0.242920	−	0.420750i
$405$	0.894473	+	1.54927i	0.0444467	+	0.0769839i
$406$	−16.0302	+	19.2116i	−0.795565	+	0.953455i
$407$	0.516056	−	0.893835i	0.0255799	−	0.0443058i
$408$	36.1047	−	62.5351i	1.78745	−	3.09595i
$409$	7.74217			0.382826			0.191413	−	0.981510i	$-0.438693\pi$
$409$	7.74217			0.382826			0.191413	+	0.981510i	$0.438693\pi$
$410$	−8.61275			−0.425353
$411$	11.5055	−	19.9282i	0.567526	−	0.982984i
$412$	20.1093	−	34.8303i	0.990714	−	1.71597i
$413$	−5.47846	−	14.9235i	−0.269577	−	0.734339i
$414$	45.0783	+	78.0780i	2.21548	+	3.83732i
$415$	1.40868	−	2.43991i	0.0691495	−	0.119770i
$416$	6.28834	−	7.09092i	0.308311	−	0.347661i
$417$	−0.793683	−	1.37470i	−0.0388668	−	0.0673193i
$418$	−5.37179			−0.262743
$419$	4.05097	+	7.01649i	0.197903	+	0.342778i	0.947848	−	0.318722i	$-0.103254\pi$
$419$	4.05097	+	7.01649i	0.197903	+	0.342778i	−0.749945	+	0.661500i	$0.769920\pi$
$420$	16.9631	−	20.3296i	0.827714	−	0.991984i
$421$	−32.1124			−1.56506			−0.782530	−	0.622612i	$-0.786071\pi$
$421$	−32.1124			−1.56506			−0.782530	+	0.622612i	$0.786071\pi$
$422$	−10.6771	−	18.4933i	−0.519755	−	0.900242i
$423$	−19.8393			−0.964618
$424$	0.865159	+	1.49850i	0.0420158	+	0.0727735i
$425$	−13.0218	−	22.5543i	−0.631648	−	1.09405i
$426$	−11.8355	−	20.4996i	−0.573430	−	0.993210i
$427$	−3.74054	+	4.48289i	−0.181017	+	0.216942i
$428$	−59.1713			−2.86015
$429$	−5.71292	−	1.16927i	−0.275822	−	0.0564531i
$430$	7.48384	+	12.9624i	0.360903	+	0.625102i
$431$	14.7640	−	25.5721i	0.711159	−	1.23176i	−0.253263	−	0.967397i	$-0.581504\pi$
$431$	14.7640	−	25.5721i	0.711159	−	1.23176i	0.964422	−	0.264366i	$-0.0851627\pi$
$432$	−9.95992			−0.479197
$433$	−11.0455	+	19.1314i	−0.530813	+	0.919395i	0.468540	+	0.883442i	$0.344780\pi$
$433$	−11.0455	+	19.1314i	−0.530813	+	0.919395i	−0.999353	+	0.0359531i	$0.988553\pi$
$434$	−12.0979	+	14.4988i	−0.580716	+	0.695967i
$435$	−5.35164	+	9.26931i	−0.256591	+	0.444429i
$436$	−17.0969	−	29.6127i	−0.818792	−	1.41819i
$437$	15.8051	+	27.3752i	0.756060	+	1.30953i
$438$	32.4213			1.54915
$439$	−6.35580			−0.303346			−0.151673	−	0.988431i	$-0.548466\pi$
$439$	−6.35580			−0.303346			−0.151673	+	0.988431i	$0.548466\pi$
$440$	−1.17387	−	2.03321i	−0.0559622	−	0.0969294i
$441$	30.1249	+	10.7764i	1.43452	+	0.513164i
$442$	36.8718	−	41.5777i	1.75381	−	1.97765i
$443$	6.78135	−	11.7456i	0.322192	−	0.558052i	−0.658748	−	0.752363i	$-0.728914\pi$
$443$	6.78135	−	11.7456i	0.322192	−	0.558052i	0.980940	+	0.194311i	$0.0622472\pi$
$444$	8.94443	−	15.4922i	0.424484	−	0.735227i
$445$	1.02801	−	1.78057i	0.0487324	−	0.0844070i
$446$	26.0530	+	45.1251i	1.23365	+	2.13674i
$447$	−7.72237			−0.365255
$448$	9.92604	+	27.0389i	0.468961	+	1.27747i
$449$	−10.9559	+	18.9762i	−0.517041	+	0.895541i	0.482763	+	0.875751i	$0.339633\pi$
$449$	−10.9559	+	18.9762i	−0.517041	+	0.895541i	−0.999804	+	0.0197900i	$0.993700\pi$
$450$	−22.0214	+	38.1421i	−1.03810	+	1.79804i
$451$	−2.15823			−0.101627
$452$	−18.8473	+	32.6445i	−0.886502	+	1.53547i
$453$	63.3139			2.97475
$454$	44.3041			2.07930
$455$	7.32402	−	5.84485i	0.343355	−	0.274011i
$456$	−42.8151			−2.00500
$457$	15.2146			0.711710			0.355855	−	0.934541i	$-0.384190\pi$
$457$	15.2146			0.711710			0.355855	+	0.934541i	$0.384190\pi$
$458$	23.1049	−	40.0188i	1.07962	−	1.86996i
$459$	27.8922			1.30190
$460$	−15.0213	+	26.0176i	−0.700371	+	1.21308i
$461$	8.10813	−	14.0437i	0.377633	−	0.654080i	−0.613084	−	0.790018i	$-0.710071\pi$
$461$	8.10813	−	14.0437i	0.377633	−	0.654080i	0.990717	+	0.135937i	$0.0434046\pi$
$462$	6.54668	−	7.84595i	0.304579	−	0.365027i
$463$	−1.44769			−0.0672799			−0.0336400	−	0.999434i	$-0.510710\pi$
$463$	−1.44769			−0.0672799			−0.0336400	+	0.999434i	$0.510710\pi$
$464$	4.56353	+	7.90426i	0.211856	+	0.366946i
$465$	−4.03884	+	6.99547i	−0.187297	+	0.324407i
$466$	19.2994	−	33.4275i	0.894027	−	1.54850i
$467$	−7.00337	+	12.1302i	−0.324078	+	0.561319i	−0.981325	−	0.192356i	$-0.938387\pi$
$467$	−7.00337	+	12.1302i	−0.324078	+	0.561319i	0.657248	+	0.753675i	$0.271721\pi$
$468$	−59.7803	−	12.2353i	−2.76334	−	0.565579i
$469$	18.2817	+	3.17150i	0.844169	+	0.146446i
$470$	−5.09091	−	8.81772i	−0.234826	−	0.406731i
$471$	−62.1172			−2.86221
$472$	−24.4320			−1.12458
$473$	1.87534	+	3.24818i	0.0862282	+	0.149352i
$474$	−9.15094	−	15.8499i	−0.420316	−	0.728009i
$475$	−7.72100	+	13.3732i	−0.354264	+	0.613603i
$476$	21.7895	+	59.3553i	0.998719	+	2.72055i
$477$	−0.972495	+	1.68441i	−0.0445275	+	0.0771239i
$478$	−38.4562			−1.75895
$479$	15.0122	−	26.0018i	0.685923	−	1.18805i	−0.287223	−	0.957864i	$-0.592732\pi$
$479$	15.0122	−	26.0018i	0.685923	−	1.18805i	0.973146	−	0.230189i	$-0.0739345\pi$
$480$	3.55219	+	6.15258i	0.162135	+	0.280826i
$481$	4.20055	−	4.73667i	0.191528	−	0.215973i
$482$	9.56649			0.435742
$483$	−59.2457	−	10.2779i	−2.69577	−	0.467662i
$484$	19.7253	+	34.1652i	0.896605	+	1.55296i
$485$	−3.78033	−	6.54772i	−0.171656	−	0.297317i
$486$	21.4633	+	37.1756i	0.973597	+	1.68632i
$487$	−28.4903			−1.29102			−0.645510	−	0.763752i	$-0.723355\pi$
$487$	−28.4903			−1.29102			−0.645510	+	0.763752i	$0.723355\pi$
$488$	4.48649	+	7.77082i	0.203094	+	0.351769i
$489$	−22.4992			−1.01745
$490$	2.94062	+	16.1546i	0.132844	+	0.729790i
$491$	14.2339	+	24.6538i	0.642365	+	1.11261i	0.984903	+	0.173105i	$0.0553799\pi$
$491$	14.2339	+	24.6538i	0.642365	+	1.11261i	−0.342539	+	0.939504i	$0.611287\pi$
$492$	−37.4070			−1.68644
$493$	−12.7799	−	22.1354i	−0.575578	−	0.996930i
$494$	−32.2811	−	6.60703i	−1.45239	−	0.297264i
$495$	1.31951	−	2.28546i	0.0593076	−	0.102724i
$496$	3.44406	+	5.96528i	0.154643	+	0.267849i
$497$	9.39114	+	1.62917i	0.421250	+	0.0730783i
$498$	9.42290	−	16.3209i	0.422250	−	0.731359i
$499$	13.1164	−	22.7183i	0.587172	−	1.01701i	−0.407429	−	0.913237i	$-0.633575\pi$
$499$	13.1164	−	22.7183i	0.587172	−	1.01701i	0.994601	−	0.103775i	$-0.0330921\pi$
$500$	−32.8617			−1.46962
$501$	6.40465			0.286139
$502$	3.87684	−	6.71488i	0.173032	−	0.299700i
$503$	−4.26588	+	7.38872i	−0.190206	+	0.329447i	−0.945318	−	0.326149i	$-0.894249\pi$
$503$	−4.26588	+	7.38872i	−0.190206	+	0.329447i	0.755112	+	0.655595i	$0.227582\pi$
$504$	31.5024	−	37.7544i	1.40323	−	1.68172i
$505$	1.29529	+	2.24352i	0.0576398	+	0.0998351i
$506$	−5.79726	+	10.0412i	−0.257720	+	0.446384i
$507$	−32.8929	−	14.0532i	−1.46083	−	0.624125i
$508$	−7.86876	−	13.6291i	−0.349120	−	0.604693i
$509$	−13.0260			−0.577366			−0.288683	−	0.957425i	$-0.593217\pi$
$509$	−13.0260			−0.577366			−0.288683	+	0.957425i	$0.593217\pi$
$510$	20.8283	+	36.0758i	0.922295	+	1.59746i
$511$	−8.36384	+	10.0237i	−0.369995	+	0.443425i
$512$	24.8008			1.09605
$513$	−8.26908	−	14.3225i	−0.365089	−	0.632352i
$514$	64.2200			2.83262
$515$	5.33472	+	9.24000i	0.235076	+	0.407163i
$516$	32.5039	+	56.2984i	1.43090	+	2.47840i
$517$	−1.27571	−	2.20959i	−0.0561055	−	0.0971775i
$518$	3.82313	+	10.4144i	0.167979	+	0.457581i
$519$	22.3798			0.982363
$520$	−4.55350	−	13.6621i	−0.199684	−	0.599124i
$521$	−2.23285	−	3.86741i	−0.0978230	−	0.169434i	0.812960	−	0.582319i	$-0.197855\pi$
$521$	−2.23285	−	3.86741i	−0.0978230	−	0.169434i	−0.910783	+	0.412885i	$0.864521\pi$
$522$	−21.6124	+	37.4337i	−0.945948	+	1.63843i
$523$	−2.90811			−0.127163			−0.0635815	−	0.997977i	$-0.520252\pi$
$523$	−2.90811			−0.127163			−0.0635815	+	0.997977i	$0.520252\pi$
$524$	4.01665	−	6.95704i	0.175468	−	0.303920i
$525$	−10.1229	−	27.5752i	−0.441801	−	1.20348i
$526$	−4.54570	+	7.87339i	−0.198202	+	0.343296i
$527$	−9.64490	−	16.7055i	−0.420138	−	0.727701i
$528$	−1.86373	−	3.22807i	−0.0811084	−	0.140484i
$529$	45.2278			1.96643
$530$	−0.998200			−0.0433590
$531$	−13.7316	−	23.7838i	−0.595901	−	1.03213i
$532$	24.0187	−	28.7855i	1.04134	−	1.24801i
$533$	−12.9696	−	2.65451i	−0.561775	−	0.114980i
$534$	6.87654	−	11.9105i	0.297577	−	0.515418i
$535$	7.84866	−	13.5943i	0.339327	−	0.587732i
$536$	14.2581	−	24.6957i	0.615854	−	1.06669i
$537$	−28.8803	−	50.0221i	−1.24628	−	2.15861i
$538$	56.9262			2.45426
$539$	0.736875	+	4.04810i	0.0317394	+	0.174364i
$540$	7.85899	−	13.6122i	0.338197	−	0.585775i
$541$	9.23193	−	15.9902i	0.396912	−	0.687471i	−0.596431	−	0.802664i	$-0.703415\pi$
$541$	9.23193	−	15.9902i	0.396912	−	0.687471i	0.993343	+	0.115193i	$0.0367486\pi$
$542$	−23.6448			−1.01563
$543$	−2.21229	+	3.83180i	−0.0949384	+	0.164438i
$544$	−16.9655			−0.727392
$545$	9.07112			0.388564
$546$	48.9916	−	39.0972i	2.09665	−	1.67320i
$547$	34.9817			1.49571			0.747856	−	0.663861i	$-0.231083\pi$
$547$	34.9817			1.49571			0.747856	+	0.663861i	$0.231083\pi$
$548$	30.9665			1.32282
$549$	−5.04310	+	8.73491i	−0.215234	+	0.372797i
$550$	−5.66408			−0.241517
$551$	−7.57760	+	13.1248i	−0.322817	+	0.559135i
$552$	−46.2063	+	80.0317i	−1.96667	+	3.40638i
$553$	7.26104	+	1.25964i	0.308771	+	0.0535655i
$554$	−28.1449			−1.19576
$555$	2.37283	+	4.10986i	0.100721	+	0.174454i
$556$	1.06808	−	1.84996i	0.0452965	−	0.0784559i
$557$	−0.0265706	+	0.0460217i	−0.00112583	+	0.00195000i	−0.866588	−	0.499025i	$-0.833692\pi$
$557$	−0.0265706	+	0.0460217i	−0.00112583	+	0.00195000i	0.865462	+	0.500975i	$0.167025\pi$
$558$	−16.3107	+	28.2510i	−0.690487	+	1.19596i
$559$	7.27451	+	21.8261i	0.307679	+	0.923146i
$560$	5.90148	+	1.02379i	0.249383	+	0.0432629i
$561$	5.21927	+	9.04004i	0.220358	+	0.381671i
$562$	−31.0388			−1.30929
$563$	7.98506			0.336530			0.168265	−	0.985742i	$-0.446184\pi$
$563$	7.98506			0.336530			0.168265	+	0.985742i	$0.446184\pi$
$564$	−22.1109	−	38.2972i	−0.931037	−	1.61260i
$565$	−4.99992	−	8.66012i	−0.210348	−	0.364334i
$566$	−20.0655	+	34.7544i	−0.843414	+	1.46084i
$567$	−4.74758	−	0.823608i	−0.199380	−	0.0345883i
$568$	7.32424	−	12.6860i	0.307318	−	0.532291i
$569$	−26.7241			−1.12033			−0.560167	−	0.828380i	$-0.689263\pi$
$569$	−26.7241			−1.12033			−0.560167	+	0.828380i	$0.689263\pi$
$570$	12.3498	−	21.3904i	0.517275	−	0.895946i
$571$	−6.74647	−	11.6852i	−0.282331	−	0.489012i	0.689627	−	0.724164i	$-0.257774\pi$
$571$	−6.74647	−	11.6852i	−0.282331	−	0.489012i	−0.971958	+	0.235153i	$0.924441\pi$
$572$	−2.48129	−	7.44476i	−0.103748	−	0.311281i
$573$	31.8132			1.32902
$574$	14.8624	−	17.8120i	0.620345	−	0.743460i
$575$	16.6651	+	28.8648i	0.694982	+	1.20374i
$576$	24.8794	+	43.0923i	1.03664	+	1.79551i
$577$	−6.00662	−	10.4038i	−0.250059	−	0.433115i	0.713483	−	0.700673i	$-0.247117\pi$
$577$	−6.00662	−	10.4038i	−0.250059	−	0.433115i	−0.963542	+	0.267558i	$0.913783\pi$
$578$	−58.8811			−2.44913
$579$	32.4383	+	56.1848i	1.34809	+	2.33496i
$580$	−14.4036			−0.598078
$581$	2.61512	+	7.12367i	0.108493	+	0.295540i
$582$	−25.2872	−	43.7988i	−1.04819	−	1.81552i
$583$	−0.250134			−0.0103595
$584$	10.0318	+	17.3756i	0.415118	+	0.719005i
$585$	10.7404	−	12.1112i	0.444062	−	0.500739i
$586$	−16.8305	+	29.1512i	−0.695260	+	1.20422i
$587$	−5.21177	−	9.02705i	−0.215113	−	0.372586i	0.738195	−	0.674588i	$-0.235679\pi$
$587$	−5.21177	−	9.02705i	−0.215113	−	0.372586i	−0.953307	+	0.302002i	$0.902345\pi$
$588$	12.7717	+	70.1628i	0.526697	+	2.89346i
$589$	−5.71876	+	9.90518i	−0.235637	+	0.408136i
$590$	7.04728	−	12.2062i	0.290132	−	0.502523i
$591$	4.04727			0.166482
$592$	4.04679			0.166322
$593$	11.1751	−	19.3558i	0.458905	−	0.794847i	−0.539998	−	0.841666i	$-0.681575\pi$
$593$	11.1751	−	19.3558i	0.458905	−	0.794847i	0.998903	+	0.0468194i	$0.0149085\pi$
$594$	3.03307	−	5.25344i	0.124449	−	0.215551i
$595$	−16.5268	−	2.86706i	−0.677532	−	0.117538i
$596$	−5.19607	−	8.99986i	−0.212839	−	0.368649i
$597$	12.9237	−	22.3845i	0.528931	−	0.916135i
$598$	−47.1880	+	53.2107i	−1.92966	+	2.17595i
$599$	−0.579463	−	1.00366i	−0.0236762	−	0.0410084i	0.853945	−	0.520364i	$-0.174204\pi$
$599$	−0.579463	−	1.00366i	−0.0236762	−	0.0410084i	−0.877621	+	0.479356i	$0.840870\pi$
$600$	−45.1448			−1.84303
$601$	−21.0907	−	36.5301i	−0.860306	−	1.49009i	−0.871633	−	0.490158i	$-0.836939\pi$
$601$	−21.0907	−	36.5301i	−0.860306	−	1.49009i	0.0113271	−	0.999936i	$-0.496394\pi$
$602$	−39.7219	−	6.89094i	−1.61894	−	0.280854i
$603$	32.0540			1.30534
$604$	42.6014	+	73.7879i	1.73343	+	3.00239i
$605$	−10.4657			−0.425491
$606$	8.66444	+	15.0072i	0.351969	+	0.609628i
$607$	9.07844	+	15.7243i	0.368482	+	0.638230i	0.989328	−	0.145702i	$-0.0465441\pi$
$607$	9.07844	+	15.7243i	0.368482	+	0.638230i	−0.620846	+	0.783932i	$0.713211\pi$
$608$	5.02970	+	8.71169i	0.203981	+	0.353306i
$609$	−9.93492	−	27.0631i	−0.402583	−	1.09665i
$610$	−5.17640			−0.209586
$611$	−4.94851	−	14.8473i	−0.200195	−	0.600657i
$612$	54.6147	+	94.5955i	2.20767	+	3.82380i
$613$	0.451323	−	0.781714i	0.0182288	−	0.0315731i	−0.856767	−	0.515703i	$-0.827531\pi$
$613$	0.451323	−	0.781714i	0.0182288	−	0.0315731i	0.874996	+	0.484130i	$0.160864\pi$
$614$	−37.9187			−1.53027
$615$	4.96177	−	8.59404i	0.200078	−	0.346545i
$616$	6.23055	+	1.08087i	0.251036	+	0.0435497i
$617$	13.0218	−	22.5544i	0.524238	−	0.908008i	−0.475363	−	0.879790i	$-0.657683\pi$
$617$	13.0218	−	22.5544i	0.524238	−	0.908008i	0.999602	−	0.0282180i	$-0.00898327\pi$
$618$	35.6848	+	61.8079i	1.43545	+	2.48628i
$619$	−13.4171	−	23.2390i	−0.539277	−	0.934056i	−0.998943	−	0.0459638i	$-0.985364\pi$
$619$	−13.4171	−	23.2390i	−0.539277	−	0.934056i	0.459666	−	0.888092i	$-0.347969\pi$
$620$	−10.8703			−0.436562
$621$	−35.6961			−1.43244
$622$	−34.1530	−	59.1547i	−1.36941	−	2.37189i
$623$	1.90843	+	5.19863i	0.0764596	+	0.208279i
$624$	−7.22948	−	21.6910i	−0.289411	−	0.868335i
$625$	−5.72894	+	9.92281i	−0.229158	+	0.396912i
$626$	−22.1839	+	38.4237i	−0.886649	+	1.53572i
$627$	3.09467	−	5.36012i	0.123589	−	0.214063i
$628$	−41.7962	−	72.3932i	−1.66785	−	2.88880i
$629$	−11.3328			−0.451869
$630$	9.77543	+	26.6286i	0.389462	+	1.06091i
$631$	16.8061	−	29.1089i	0.669039	−	1.15881i	−0.309135	−	0.951018i	$-0.600039\pi$
$631$	16.8061	−	29.1089i	0.669039	−	1.15881i	0.978173	−	0.207791i	$-0.0666273\pi$
$632$	5.66296	−	9.80853i	0.225260	−	0.390162i
$633$	24.6042			0.977930
$634$	36.5901	−	63.3760i	1.45318	−	2.51698i
$635$	4.17494			0.165678
$636$	−4.33539			−0.171909
$637$	−0.550800	+	25.2328i	−0.0218235	+	0.999762i
$638$	−5.55889			−0.220078
$639$	16.4659			0.651379
$640$	−10.1865	+	17.6435i	−0.402655	+	0.697419i
$641$	21.1841			0.836722			0.418361	−	0.908281i	$-0.362605\pi$
$641$	21.1841			0.836722			0.418361	+	0.908281i	$0.362605\pi$
$642$	52.5010	−	90.9343i	2.07205	−	3.58889i
$643$	−0.330770	+	0.572910i	−0.0130443	+	0.0225933i	−0.872474	−	0.488661i	$-0.837486\pi$
$643$	−0.330770	+	0.572910i	−0.0130443	+	0.0225933i	0.859430	+	0.511254i	$0.170819\pi$
$644$	−27.8859	−	75.9623i	−1.09886	−	2.99333i
$645$	−17.2457			−0.679047
$646$	29.4917	+	51.0811i	1.16034	+	2.00976i
$647$	20.0162	−	34.6690i	0.786916	−	1.36298i	−0.140931	−	0.990019i	$-0.545010\pi$
$647$	20.0162	−	34.6690i	0.786916	−	1.36298i	0.927848	−	0.372960i	$-0.121657\pi$
$648$	−3.70268	+	6.41323i	−0.145455	+	0.251936i
$649$	1.76594	−	3.05870i	0.0693193	−	0.120065i
$650$	−34.0376	−	6.96654i	−1.33506	−	0.273250i
$651$	−7.49781	−	20.4243i	−0.293862	−	0.800492i
$652$	−15.1388	−	26.2212i	−0.592883	−	1.02690i
$653$	12.7120			0.497460			0.248730	−	0.968573i	$-0.419987\pi$
$653$	12.7120			0.497460			0.248730	+	0.968573i	$0.419987\pi$
$654$	60.6782			2.37271
$655$	1.06556	+	1.84560i	0.0416349	+	0.0721138i
$656$	−4.23107	−	7.32844i	−0.165196	−	0.286127i
$657$	−11.2764	+	19.5313i	−0.439933	+	0.761987i
$658$	27.0209	+	4.68759i	1.05339	+	0.182741i
$659$	7.09522	−	12.2893i	0.276391	−	0.478723i	−0.694094	−	0.719884i	$-0.744195\pi$
$659$	7.09522	−	12.2893i	0.276391	−	0.478723i	0.970485	+	0.241161i	$0.0775283\pi$
$660$	5.88239			0.228972
$661$	−25.0890	+	43.4554i	−0.975848	+	1.69022i	−0.298742	+	0.954334i	$0.596567\pi$
$661$	−25.0890	+	43.4554i	−0.975848	+	1.69022i	−0.677106	+	0.735885i	$0.736766\pi$
$662$	32.5104	+	56.3096i	1.26355	+	2.18853i
$663$	20.2458	+	60.7444i	0.786280	+	2.35912i
$664$	11.6625			0.452594
$665$	3.42740	+	9.33637i	0.132909	+	0.362049i
$666$	9.58259	+	16.5975i	0.371318	+	0.643141i
$667$	16.3556	+	28.3287i	0.633290	+	1.09689i
$668$	4.30944	+	7.46417i	0.166737	+	0.288797i
$669$	−60.0362			−2.32113
$670$	8.22530	+	14.2466i	0.317771	+	0.550396i
$671$	−1.29713			−0.0500751
$672$	−18.8539	−	3.27077i	−0.727306	−	0.126173i
$673$	0.937137	+	1.62317i	0.0361240	+	0.0625685i	0.883522	−	0.468389i	$-0.155166\pi$
$673$	0.937137	+	1.62317i	0.0361240	+	0.0625685i	−0.847398	+	0.530958i	$0.821832\pi$
$674$	29.4112			1.13288
$675$	−8.71902	−	15.1018i	−0.335595	−	0.581268i
$676$	−5.75433	−	47.7902i	−0.221321	−	1.83808i
$677$	1.00439	−	1.73966i	0.0386020	−	0.0668607i	−0.846079	−	0.533058i	$-0.821043\pi$
$677$	1.00439	−	1.73966i	0.0386020	−	0.0668607i	0.884681	+	0.466197i	$0.154376\pi$
$678$	−33.4453	−	57.9290i	−1.28446	−	2.22475i
$679$	20.0648	+	3.48083i	0.770015	+	0.133582i
$680$	−12.8894	+	22.3251i	−0.494286	+	0.856128i
$681$	−25.5234	+	44.2079i	−0.978061	+	1.69405i
$682$	−4.19525			−0.160644
$683$	−14.1012			−0.539568			−0.269784	−	0.962921i	$-0.586952\pi$
$683$	−14.1012			−0.539568			−0.269784	+	0.962921i	$0.586952\pi$
$684$	32.3828	−	56.0886i	1.23819	−	2.14460i
$685$	−4.10748	+	7.11437i	−0.156939	+	0.271826i
$686$	−38.4837	−	21.7953i	−1.46932	−	0.832149i
$687$	26.6212	+	46.1094i	1.01566	+	1.75918i
$688$	−7.35298	+	12.7357i	−0.280330	+	0.485546i
$689$	−1.50315	−	0.307652i	−0.0572654	−	0.0117206i
$690$	−26.6559	−	46.1693i	−1.01477	−	1.75764i
$691$	−35.6920			−1.35779			−0.678895	−	0.734236i	$-0.737541\pi$
$691$	−35.6920			−1.35779			−0.678895	+	0.734236i	$0.737541\pi$
$692$	15.0585	+	26.0820i	0.572437	+	0.991489i
$693$	2.44958	+	6.67274i	0.0930517	+	0.253476i
$694$	−14.6746			−0.557041
$695$	0.283346	+	0.490769i	0.0107479	+	0.0186159i
$696$	−44.3064			−1.67943
$697$	11.8489	+	20.5229i	0.448809	+	0.777360i
$698$	15.5596	+	26.9500i	0.588938	+	1.02007i
$699$	22.2366	+	38.5150i	0.841066	+	1.45677i
$700$	25.3257	−	30.3518i	0.957220	−	1.14719i
$701$	−6.15865			−0.232609			−0.116305	−	0.993214i	$-0.537105\pi$
$701$	−6.15865			−0.232609			−0.116305	+	0.993214i	$0.537105\pi$
$702$	24.6883	−	27.8394i	0.931802	−	1.05073i
$703$	3.35979	+	5.81932i	0.126717	+	0.219480i
$704$	−3.19959	+	5.54185i	−0.120589	+	0.208866i
$705$	11.7314			0.441831
$706$	37.8103	−	65.4894i	1.42301	−	2.46473i
$707$	−6.87501	−	1.19268i	−0.258561	−	0.0448552i
$708$	30.6078	−	53.0143i	1.15031	−	1.99240i
$709$	−17.0185	−	29.4770i	−0.639144	−	1.10703i	−0.985621	−	0.168972i	$-0.945955\pi$
$709$	−17.0185	−	29.4770i	−0.639144	−	1.10703i	0.346477	−	0.938059i	$-0.387378\pi$
$710$	4.22527	+	7.31838i	0.158571	+	0.274654i
$711$	12.7311			0.477452
$712$	8.51094			0.318961
$713$	12.3434	+	21.3794i	0.462265	+	0.800667i
$714$	−110.550	−	19.1782i	−4.13724	−	0.717727i
$715$	2.03952	+	0.417432i	0.0762736	+	0.0156111i
$716$	38.8648	−	67.3158i	1.45244	−	2.51571i
$717$	22.1545	−	38.3727i	0.827375	−	1.43306i
$718$	23.7994	−	41.2218i	0.888187	−	1.53838i
$719$	11.4824	+	19.8881i	0.428222	+	0.741702i	0.996715	−	0.0809859i	$-0.0258069\pi$
$719$	11.4824	+	19.8881i	0.428222	+	0.741702i	−0.568493	+	0.822688i	$0.692474\pi$
$720$	10.3473			0.385621
$721$	−28.3150	−	4.91208i	−1.05451	−	0.182935i
$722$	−5.19981	+	9.00633i	−0.193517	+	0.335181i
$723$	−5.51122	+	9.54571i	−0.204964	+	0.355009i
$724$	−5.95424			−0.221288
$725$	−7.98992	+	13.8389i	−0.296738	+	0.513966i
$726$	−70.0067			−2.59819
$727$	1.06558			0.0395203			0.0197601	−	0.999805i	$-0.493710\pi$
$727$	1.06558			0.0395203			0.0197601	+	0.999805i	$0.493710\pi$
$728$	36.1123	+	14.1586i	1.33841	+	0.524754i
$729$	−43.9962			−1.62949
$730$	−11.5744			−0.428389
$731$	20.5916	−	35.6658i	0.761609	−	1.31915i
$732$	−22.4822			−0.830966
$733$	13.1689	−	22.8092i	0.486404	−	0.842476i	−0.513474	−	0.858105i	$-0.671642\pi$
$733$	13.1689	−	22.8092i	0.486404	−	0.842476i	0.999878	+	0.0156289i	$0.00497504\pi$
$734$	23.5448	−	40.7809i	0.869056	−	1.50525i
$735$	−17.8136	−	6.37236i	−0.657064	−	0.235048i
$736$	21.7123			0.800326
$737$	2.06114	+	3.57000i	0.0759230	+	0.131502i
$738$	20.0379	−	34.7067i	0.737606	−	1.27757i
$739$	−17.1075	+	29.6310i	−0.629308	+	1.08999i	0.358383	+	0.933575i	$0.383328\pi$
$739$	−17.1075	+	29.6310i	−0.629308	+	1.08999i	−0.987691	+	0.156419i	$0.950005\pi$
$740$	−3.19317	+	5.53073i	−0.117383	+	0.203314i
$741$	25.1897	−	28.4047i	0.925366	−	1.04347i
$742$	1.72252	−	2.06438i	0.0632358	−	0.0757857i
$743$	−11.2391	−	19.4667i	−0.412322	−	0.714163i	0.582821	−	0.812600i	$-0.301949\pi$
$743$	−11.2391	−	19.4667i	−0.412322	−	0.714163i	−0.995143	+	0.0984379i	$0.968615\pi$
$744$	−33.4377			−1.22588
$745$	2.75689			0.101005
$746$	20.9513	+	36.2888i	0.767083	+	1.32863i
$747$	6.55472	+	11.3531i	0.239825	+	0.415388i
$748$	−7.02368	+	12.1654i	−0.256811	+	0.444810i
$749$	14.5705	+	39.6905i	0.532393	+	1.45026i
$750$	29.1573	−	50.5018i	1.06467	−	1.84407i
$751$	−42.5424			−1.55239			−0.776197	−	0.630491i	$-0.782854\pi$
$751$	−42.5424			−1.55239			−0.776197	+	0.630491i	$0.782854\pi$
$752$	5.00189	−	8.66353i	0.182400	−	0.315927i
$753$	4.46686	+	7.73683i	0.162781	+	0.281946i
$754$	−33.4054	−	6.83715i	−1.21655	−	0.248994i
$755$	−22.6031			−0.822612
$756$	14.5896	+	39.7427i	0.530620	+	1.44543i
$757$	5.61902	+	9.73243i	0.204227	+	0.353731i	0.949886	−	0.312596i	$-0.101199\pi$
$757$	5.61902	+	9.73243i	0.204227	+	0.353731i	−0.745659	+	0.666327i	$0.767865\pi$
$758$	−13.9716	−	24.1996i	−0.507473	−	0.878969i
$759$	−6.67956	−	11.5693i	−0.242453	−	0.419941i
$760$	15.2850			0.554447
$761$	−6.40422	−	11.0924i	−0.232153	−	0.402101i	0.726289	−	0.687390i	$-0.241244\pi$
$761$	−6.40422	−	11.0924i	−0.232153	−	0.402101i	−0.958441	+	0.285289i	$0.907910\pi$
$762$	27.9269			1.01168
$763$	−15.6534	+	18.7600i	−0.566691	+	0.679158i
$764$	21.4059	+	37.0760i	0.774437	+	1.34136i
$765$	−28.9770			−1.04767
$766$	−25.7058	−	44.5238i	−0.928789	−	1.60871i
$767$	14.3743	−	16.2089i	0.519024	−	0.585268i
$768$	−38.1846	+	66.1377i	−1.37787	+	2.38654i
$769$	25.6759	+	44.4719i	0.925895	+	1.60370i	0.790115	+	0.612958i	$0.210021\pi$
$769$	25.6759	+	44.4719i	0.925895	+	1.60370i	0.135780	+	0.990739i	$0.456646\pi$
$770$	−2.33717	+	2.80101i	−0.0842258	+	0.100941i
$771$	−36.9969	+	64.0805i	−1.33241	+	2.30780i
$772$	−43.6529	+	75.6091i	−1.57110	+	2.72123i
$773$	20.0046			0.719517			0.359759	−	0.933045i	$-0.382859\pi$
$773$	20.0046			0.719517			0.359759	+	0.933045i	$0.382859\pi$
$774$	−69.6459			−2.50337
$775$	−6.02993	+	10.4441i	−0.216602	+	0.375165i
$776$	15.6487	−	27.1044i	0.561756	−	0.972990i
$777$	−12.5942	−	2.18484i	−0.451816	−	0.0783808i
$778$	31.6308	+	54.7861i	1.13402	+	1.96418i
$779$	7.02558	−	12.1687i	0.251717	−	0.435987i
$780$	35.3495	+	7.23504i	1.26571	+	0.259056i
$781$	1.05879	+	1.83388i	0.0378864	+	0.0656212i
$782$	127.310			4.55261
$783$	−8.55708	−	14.8213i	−0.305805	−	0.529670i
$784$	−12.3011	+	10.4382i	−0.439323	+	0.372792i
$785$	22.1759			0.791492
$786$	7.12771	+	12.3456i	0.254237	+	0.440351i
$787$	29.3192			1.04512			0.522558	−	0.852604i	$-0.324978\pi$
$787$	29.3192			1.04512			0.522558	+	0.852604i	$0.324978\pi$
$788$	2.72325	+	4.71680i	0.0970117	+	0.168029i
$789$	−5.23752	−	9.07166i	−0.186461	−	0.322959i
$790$	3.26689	+	5.65842i	0.116231	+	0.201318i
$791$	26.5380	+	4.60381i	0.943583	+	0.163693i
$792$	10.9243			0.388177
$793$	−7.79493	−	1.59540i	−0.276806	−	0.0566544i
$794$	−40.3566	−	69.8996i	−1.43220	−	2.48064i
$795$	0.575059	−	0.996031i	0.0203952	−	0.0353256i
$796$	34.7833			1.23286
$797$	−1.55050	+	2.68554i	−0.0549215	+	0.0951269i	−0.892179	−	0.451682i	$-0.850824\pi$
$797$	−1.55050	+	2.68554i	−0.0549215	+	0.0951269i	0.837258	+	0.546809i	$0.184158\pi$
$798$	22.9264	+	62.4525i	0.811588	+	2.21079i
$799$	−14.0075	+	24.2618i	−0.495551	+	0.858319i
$800$	5.30338	+	9.18572i	0.187503	+	0.324764i
$801$	4.78343	+	8.28514i	0.169014	+	0.292741i
$802$	−51.6100			−1.82241
$803$	−2.90038			−0.102352
$804$	35.7242	+	61.8762i	1.25990	+	2.18220i
$805$	21.1508	+	3.66923i	0.745467	+	0.129323i
$806$	−25.2108	−	5.15995i	−0.888013	−	0.181751i
$807$	−32.7950	+	56.8025i	−1.15444	+	1.99954i
$808$	−5.36189	+	9.28707i	−0.188631	+	0.326718i
$809$	−3.99501	+	6.91957i	−0.140457	+	0.243279i	−0.927669	−	0.373404i	$-0.878191\pi$
$809$	−3.99501	+	6.91957i	−0.140457	+	0.243279i	0.787212	+	0.616683i	$0.211524\pi$
$810$	−2.13603	−	3.69972i	−0.0750526	−	0.129995i
$811$	−48.2554			−1.69448			−0.847239	−	0.531213i	$-0.821737\pi$
$811$	−48.2554			−1.69448			−0.847239	+	0.531213i	$0.821737\pi$
$812$	24.8553	−	29.7881i	0.872250	−	1.04536i
$813$	13.6217	−	23.5934i	0.477733	−	0.827458i
$814$	−1.23236	+	2.13451i	−0.0431942	+	0.0748146i
$815$	8.03224			0.281357
$816$	−20.4642	+	35.4449i	−0.716389	+	1.24082i
$817$	−24.4188			−0.854307
$818$	−18.4886			−0.646439
$819$	6.51329	+	43.1118i	0.227593	+	1.50645i
$820$	13.3543			0.466353
$821$	−27.5519			−0.961569			−0.480785	−	0.876839i	$-0.659648\pi$
$821$	−27.5519			−0.961569			−0.480785	+	0.876839i	$0.659648\pi$
$822$	−27.4756	+	47.5892i	−0.958323	+	1.65986i
$823$	20.4274			0.712056			0.356028	−	0.934475i	$-0.384131\pi$
$823$	20.4274			0.712056			0.356028	+	0.934475i	$0.384131\pi$
$824$	−22.0831	+	38.2491i	−0.769303	+	1.33247i
$825$	3.26306	−	5.65178i	0.113605	−	0.196770i
$826$	13.0828	+	35.6379i	0.455207	+	1.24000i
$827$	−27.7142			−0.963719			−0.481859	−	0.876249i	$-0.660038\pi$
$827$	−27.7142			−0.963719			−0.481859	+	0.876249i	$0.660038\pi$
$828$	−69.8953	−	121.062i	−2.42903	−	4.20720i
$829$	−4.62832	+	8.01648i	−0.160748	+	0.278424i	−0.935137	−	0.354286i	$-0.884724\pi$
$829$	−4.62832	+	8.01648i	−0.160748	+	0.278424i	0.774389	+	0.632710i	$0.218057\pi$
$830$	−3.36398	+	5.82659i	−0.116766	+	0.202244i
$831$	16.2142	−	28.0837i	0.562463	−	0.974214i
$832$	−26.0437	+	29.3677i	−0.902904	+	1.01814i
$833$	34.4484	−	29.2315i	1.19357	−	1.01281i
$834$	1.89535	+	3.28283i	0.0656304	+	0.113675i
$835$	−2.28647			−0.0791264
$836$	8.32912			0.288069
$837$	−6.45797	−	11.1855i	−0.223220	−	0.386628i
$838$	−9.67387	−	16.7556i	−0.334178	−	0.578814i
$839$	15.1870	−	26.3046i	0.524312	−	0.908135i	−0.475287	−	0.879831i	$-0.657656\pi$
$839$	15.1870	−	26.3046i	0.524312	−	0.908135i	0.999599	−	0.0283045i	$-0.00901080\pi$
$840$	−18.6281	+	22.3251i	−0.642731	+	0.770288i
$841$	6.65848	−	11.5328i	0.229603	−	0.397683i
$842$	76.6855			2.64276
$843$	17.8813	−	30.9713i	0.615865	−	1.06671i
$844$	16.5552	+	28.6745i	0.569854	+	0.987016i
$845$	11.7428	+	5.01701i	0.403965	+	0.172590i
$846$	47.3769			1.62885
$847$	18.0599	−	21.6441i	0.620545	−	0.743700i
$848$	−0.490373	−	0.849350i	−0.0168395	−	0.0291668i
$849$	−23.1193	−	40.0437i	−0.793451	−	1.37430i
$850$	31.0964	+	53.8606i	1.06660	+	1.84740i
$851$	14.5036			0.497177
$852$	18.3512	+	31.7853i	0.628703	+	1.08894i
$853$	−5.30773			−0.181733			−0.0908666	−	0.995863i	$-0.528964\pi$
$853$	−5.30773			−0.181733			−0.0908666	+	0.995863i	$0.528964\pi$
$854$	8.93254	−	10.7053i	0.305665	−	0.366328i
$855$	8.59069	+	14.8795i	0.293795	+	0.508868i
$856$	64.9793			2.22095
$857$	8.31857	+	14.4082i	0.284157	+	0.492175i	0.972404	−	0.233302i	$-0.0749529\pi$
$857$	8.31857	+	14.4082i	0.284157	+	0.492175i	−0.688247	+	0.725476i	$0.741620\pi$
$858$	13.6427	+	2.79227i	0.465753	+	0.0953265i
$859$	5.29426	−	9.16993i	0.180638	−	0.312874i	−0.761460	−	0.648212i	$-0.775517\pi$
$859$	5.29426	−	9.16993i	0.180638	−	0.312874i	0.942098	+	0.335338i	$0.108850\pi$
$860$	−11.6039	−	20.0986i	−0.395690	−	0.685356i
$861$	9.21117	+	25.0916i	0.313916	+	0.855118i
$862$	−35.2571	+	61.0671i	−1.20086	+	2.07995i
$863$	28.0316	−	48.5522i	0.954207	−	1.65273i	0.218033	−	0.975941i	$-0.430036\pi$
$863$	28.0316	−	48.5522i	0.954207	−	1.65273i	0.736173	−	0.676793i	$-0.236631\pi$
$864$	−11.3597			−0.386464
$865$	−7.98959			−0.271654
$866$	26.3771	−	45.6864i	0.896329	−	1.55249i
$867$	33.9212	−	58.7532i	1.15202	−	1.99536i
$868$	18.7581	−	22.4809i	0.636691	−	0.763051i
$869$	0.818634	+	1.41792i	0.0277703	+	0.0480995i
$870$	12.7799	−	22.1354i	0.433279	−	0.750462i
$871$	7.99523	+	23.9885i	0.270908	+	0.812820i
$872$	18.7750	+	32.5193i	0.635803	+	1.10124i
$873$	35.1804			1.19067
$874$	−37.7432	−	65.3731i	−1.27668	−	2.21128i
$875$	8.09194	+	22.0427i	0.273558	+	0.745181i
$876$	−50.2702			−1.69847
$877$	1.83026	+	3.17010i	0.0618033	+	0.107047i	0.895272	−	0.445521i	$-0.146982\pi$
$877$	1.83026	+	3.17010i	0.0618033	+	0.107047i	−0.833468	+	0.552567i	$0.813648\pi$
$878$	15.1779			0.512229
$879$	−19.3919	−	33.5878i	−0.654073	−	1.13289i
$880$	0.665353	+	1.15242i	0.0224290	+	0.0388482i
$881$	−5.11493	−	8.85932i	−0.172326	−	0.298478i	0.766906	−	0.641759i	$-0.221795\pi$
$881$	−5.11493	−	8.85932i	−0.172326	−	0.298478i	−0.939233	+	0.343281i	$0.888462\pi$
$882$	−71.9395	−	25.7346i	−2.42233	−	0.866528i
$883$	−3.98979			−0.134267			−0.0671335	−	0.997744i	$-0.521385\pi$
$883$	−3.98979			−0.134267			−0.0671335	+	0.997744i	$0.521385\pi$
$884$	−57.1707	+	64.4675i	−1.92286	+	2.16828i
$885$	8.11982	+	14.0639i	0.272945	+	0.472754i
$886$	−16.1941	+	28.0490i	−0.544052	+	0.942325i
$887$	−14.2208			−0.477487			−0.238743	−	0.971083i	$-0.576735\pi$
$887$	−14.2208			−0.477487			−0.238743	+	0.971083i	$0.576735\pi$
$888$	−9.82237	+	17.0128i	−0.329617	+	0.570913i
$889$	−7.20440	+	8.63420i	−0.241628	+	0.289582i
$890$	−2.45493	+	4.25206i	−0.0822894	+	0.142529i
$891$	−0.535258	−	0.927094i	−0.0179318	−	0.0310588i
$892$	−40.3960	−	69.9678i	−1.35256	−	2.34270i
$893$	16.6110			0.555866
$894$	18.4413			0.616769
$895$	10.3103	+	17.8579i	0.344635	+	0.596924i
$896$	−18.9104	−	51.5127i	−0.631753	−	1.72092i
$897$	−25.9103	−	77.7400i	−0.865119	−	2.59566i
$898$	26.1631	−	45.3158i	0.873074	−	1.51221i
$899$	−5.91794	+	10.2502i	−0.197374	+	0.341862i
$900$	34.1448	−	59.1405i	1.13816	−	1.97135i
$901$	1.37326	+	2.37856i	0.0457500	+	0.0792413i
$902$	5.15392			0.171607
$903$	29.7596	−	35.6658i	0.990337	−	1.18688i
$904$	20.6973	−	35.8487i	0.688381	−	1.19231i
$905$	0.789789	−	1.36795i	0.0262535	−	0.0454723i
$906$	−151.196			−5.02315
$907$	−21.7126	+	37.6074i	−0.720956	+	1.24873i	0.239661	+	0.970857i	$0.422964\pi$
$907$	−21.7126	+	37.6074i	−0.720956	+	1.24873i	−0.960617	+	0.277876i	$0.910370\pi$
$908$	−68.6949			−2.27972
$909$	−12.0542			−0.399814
$910$	−17.4900	+	13.9577i	−0.579789	+	0.462694i
$911$	24.8617			0.823706			0.411853	−	0.911250i	$-0.364882\pi$
$911$	24.8617			0.823706			0.411853	+	0.911250i	$0.364882\pi$
$912$	24.2677			0.803582
$913$	−0.842964	+	1.46006i	−0.0278980	+	0.0483208i
$914$	−36.3331			−1.20179
$915$	2.98210	−	5.16516i	0.0985853	−	0.170755i
$916$	−35.8248	+	62.0503i	−1.18368	+	2.05020i
$917$	−5.65566	−	0.981142i	−0.186766	−	0.0324002i
$918$	−66.6076			−2.19838
$919$	0.831637	+	1.44044i	0.0274332	+	0.0475157i	0.879416	−	0.476054i	$-0.157933\pi$
$919$	0.831637	+	1.44044i	0.0274332	+	0.0475157i	−0.851983	+	0.523570i	$0.824600\pi$
$920$	16.4957	−	28.5714i	0.543847	−	0.941971i
$921$	21.8448	−	37.8363i	0.719811	−	1.24675i
$922$	−19.3625	+	33.5369i	−0.637671	+	1.10448i
$923$	4.10708	+	12.3227i	0.135186	+	0.405607i
$924$	−10.1508	+	12.1654i	−0.333937	+	0.400211i
$925$	3.54260	+	6.13597i	0.116480	+	0.201749i
$926$	3.45714			0.113609
$927$	−49.6458			−1.63058
$928$	5.20488	+	9.01512i	0.170859	+	0.295936i
$929$	−4.74761	−	8.22310i	−0.155764	−	0.269791i	0.777573	−	0.628793i	$-0.216451\pi$
$929$	−4.74761	−	8.22310i	−0.155764	−	0.269791i	−0.933337	+	0.359002i	$0.883117\pi$
$930$	9.64490	−	16.7055i	0.316269	−	0.547793i
$931$	−25.2230	−	9.02289i	−0.826649	−	0.295713i
$932$	−29.9243	+	51.8304i	−0.980202	+	1.69776i
$933$	78.7016			2.57657
$934$	16.7243	−	28.9674i	0.547236	−	0.947841i
$935$	−1.86328	−	3.22730i	−0.0609359	−	0.105544i
$936$	65.6480	+	13.4363i	2.14577	+	0.439179i
$937$	−6.41678			−0.209627			−0.104813	−	0.994492i	$-0.533425\pi$
$937$	−6.41678			−0.209627			−0.104813	+	0.994492i	$0.533425\pi$
$938$	−43.6573	−	7.57366i	−1.42546	−	0.247289i
$939$	−25.5602	−	44.2715i	−0.834125	−	1.44475i
$940$	7.89361	+	13.6721i	0.257461	+	0.445936i
$941$	25.7593	+	44.6164i	0.839730	+	1.45445i	0.890121	+	0.455725i	$0.150620\pi$
$941$	25.7593	+	44.6164i	0.839730	+	1.45445i	−0.0503911	+	0.998730i	$0.516047\pi$
$942$	148.338			4.83312
$943$	−15.1641	−	26.2650i	−0.493810	−	0.855305i
$944$	13.8481			0.450717
$945$	−11.0659	−	1.91971i	−0.359973	−	0.0624481i
$946$	−4.47838	−	7.75678i	−0.145605	−	0.252195i
$947$	−8.40219			−0.273034			−0.136517	−	0.990638i	$-0.543591\pi$
$947$	−8.40219			−0.273034			−0.136517	+	0.990638i	$0.543591\pi$
$948$	14.1888	+	24.5757i	0.460831	+	0.798182i
$949$	−17.4295	−	3.56732i	−0.565784	−	0.115800i
$950$	18.4380	−	31.9356i	0.598209	−	1.03613i
$951$	42.1589	+	73.0213i	1.36709	+	2.36788i
$952$	−23.9282	−	65.1814i	−0.775518	−	2.11254i
$953$	18.0455	−	31.2558i	0.584552	−	1.01247i	−0.410379	−	0.911915i	$-0.634604\pi$
$953$	18.0455	−	31.2558i	0.584552	−	1.01247i	0.994931	−	0.100559i	$-0.0320631\pi$
$954$	2.32235	−	4.02244i	0.0751890	−	0.130231i
$955$	−11.3573			−0.367515
$956$	59.6275			1.92849
$957$	3.20245	−	5.54681i	0.103521	−	0.179303i
$958$	−35.8496	+	62.0933i	−1.15825	+	2.00614i
$959$	−7.62524	−	20.7715i	−0.246232	−	0.670745i
$960$	−14.7117	−	25.4815i	−0.474820	−	0.822412i
$961$	11.0338	−	19.1111i	0.355928	−	0.616486i
$962$	−10.0311	+	11.3113i	−0.323414	+	0.364692i
$963$	36.5205	+	63.2553i	1.17686	+	2.03837i
$964$	−14.8331			−0.477743
$965$	−11.5805	−	20.0580i	−0.372790	−	0.645691i
$966$	141.481	+	24.5441i	4.55208	+	0.789693i
$967$	3.18338			0.102371			0.0511853	−	0.998689i	$-0.483700\pi$
$967$	3.18338			0.102371			0.0511853	+	0.998689i	$0.483700\pi$
$968$	−21.6614	−	37.5187i	−0.696225	−	1.20590i
$969$	−67.9602			−2.18320
$970$	9.02756	+	15.6362i	0.289857	+	0.502048i
$971$	−18.8738	−	32.6904i	−0.605690	−	1.04909i	−0.991942	−	0.126692i	$-0.959564\pi$
$971$	−18.8738	−	32.6904i	−0.605690	−	1.04909i	0.386253	−	0.922393i	$-0.373769\pi$
$972$	−33.2795	−	57.6419i	−1.06744	−	1.84886i
$973$	−1.50391	−	0.260898i	−0.0482131	−	0.00836399i
$974$	68.0359			2.18001
$975$	26.5603	−	29.9503i	0.850611	−	0.959176i
$976$	−2.54294	−	4.40451i	−0.0813977	−	0.140985i
$977$	10.6538	−	18.4530i	0.340846	−	0.590363i	−0.643744	−	0.765241i	$-0.722620\pi$
$977$	10.6538	−	18.4530i	0.340846	−	0.590363i	0.984590	+	0.174878i	$0.0559532\pi$
$978$	53.7290			1.71806
$979$	−0.615168	+	1.06550i	−0.0196609	+	0.0340536i
$980$	−4.55951	−	25.0482i	−0.145648	−	0.800134i
$981$	−21.1044	+	36.5538i	−0.673810	+	1.16707i
$982$	−33.9910	−	58.8741i	−1.08470	−	1.87875i
$983$	11.0158	+	19.0799i	0.351350	+	0.608556i	0.986486	−	0.163844i	$-0.0523895\pi$
$983$	11.0158	+	19.0799i	0.351350	+	0.608556i	−0.635136	+	0.772400i	$0.719056\pi$
$984$	41.0787			1.30954
$985$	−1.44488			−0.0460377
$986$	30.5189	+	52.8603i	0.971919	+	1.68341i
$987$	−20.2441	+	24.2618i	−0.644376	+	0.772260i
$988$	50.0528	+	10.2444i	1.59239	+	0.325918i
$989$	−26.3529	+	45.6446i	−0.837975	+	1.45141i
$990$	−3.15104	+	5.45776i	−0.100147	+	0.173459i
$991$	11.0129	−	19.0750i	0.349838	−	0.605937i	−0.636383	−	0.771374i	$-0.719570\pi$
$991$	11.0129	−	19.0750i	0.349838	−	0.605937i	0.986220	+	0.165437i	$0.0529033\pi$
$992$	3.92808	+	6.80364i	0.124717	+	0.216016i
$993$	−74.9164			−2.37740
$994$	−22.4264	−	3.89052i	−0.711322	−	0.123400i
$995$	−4.61376	+	7.99127i	−0.146266	+	0.253340i
$996$	−14.6105	+	25.3061i	−0.462951	+	0.801855i
$997$	10.0820			0.319301			0.159651	−	0.987174i	$-0.448963\pi$
$997$	10.0820			0.319301			0.159651	+	0.987174i	$0.448963\pi$
$998$	−31.3225	+	54.2522i	−0.991497	+	1.71732i
$999$	−7.58815			−0.240078

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.2.h.b.16.1	yes	12
3.2	odd	2		819.2.s.d.289.6		12
7.2	even	3		637.2.f.k.393.6		12
7.3	odd	6		637.2.g.l.263.6		12
7.4	even	3		91.2.g.b.81.6	yes	12
7.5	odd	6		637.2.f.j.393.6		12
7.6	odd	2		637.2.h.l.471.1		12
13.3	even	3		1183.2.e.h.170.6		12
13.9	even	3		91.2.g.b.9.6	✓	12
13.10	even	6		1183.2.e.g.170.1		12
21.11	odd	6		819.2.n.d.172.1		12
39.35	odd	6		819.2.n.d.100.1		12
91.9	even	3		637.2.f.k.295.6		12
91.16	even	3		8281.2.a.bz.1.1		6
91.23	even	6		8281.2.a.ce.1.6		6
91.48	odd	6		637.2.g.l.373.6		12
91.61	odd	6		637.2.f.j.295.6		12
91.68	odd	6		8281.2.a.ca.1.1		6
91.74	even	3	inner	91.2.h.b.74.1	yes	12
91.75	odd	6		8281.2.a.cf.1.6		6
91.81	even	3		1183.2.e.h.508.6		12
91.87	odd	6		637.2.h.l.165.1		12
91.88	even	6		1183.2.e.g.508.1		12
273.74	odd	6		819.2.s.d.802.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.6	✓	12	13.9	even	3
91.2.g.b.81.6	yes	12	7.4	even	3
91.2.h.b.16.1	yes	12	1.1	even	1	trivial
91.2.h.b.74.1	yes	12	91.74	even	3	inner
637.2.f.j.295.6		12	91.61	odd	6
637.2.f.j.393.6		12	7.5	odd	6
637.2.f.k.295.6		12	91.9	even	3
637.2.f.k.393.6		12	7.2	even	3
637.2.g.l.263.6		12	7.3	odd	6
637.2.g.l.373.6		12	91.48	odd	6
637.2.h.l.165.1		12	91.87	odd	6
637.2.h.l.471.1		12	7.6	odd	2
819.2.n.d.100.1		12	39.35	odd	6
819.2.n.d.172.1		12	21.11	odd	6
819.2.s.d.289.6		12	3.2	odd	2
819.2.s.d.802.6		12	273.74	odd	6
1183.2.e.g.170.1		12	13.10	even	6
1183.2.e.g.508.1		12	91.88	even	6
1183.2.e.h.170.6		12	13.3	even	3
1183.2.e.h.508.6		12	91.81	even	3
8281.2.a.bz.1.1		6	91.16	even	3
8281.2.a.ca.1.1		6	91.68	odd	6
8281.2.a.ce.1.6		6	91.23	even	6
8281.2.a.cf.1.6		6	91.75	odd	6

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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.38804 q^{2} +(1.37574 - 2.38285i) q^{3} +3.70272 q^{4} +(-0.491140 + 0.850679i) q^{5} +(-3.28532 + 5.69033i) q^{6} +(-0.911766 - 2.48368i) q^{7} -4.06616 q^{8} +(-2.28532 - 3.95828i) q^{9} +O(q^{10})\)	\(q-2.38804 q^{2} +(1.37574 - 2.38285i) q^{3} +3.70272 q^{4} +(-0.491140 + 0.850679i) q^{5} +(-3.28532 + 5.69033i) q^{6} +(-0.911766 - 2.48368i) q^{7} -4.06616 q^{8} +(-2.28532 - 3.95828i) q^{9} +(1.17286 - 2.03145i) q^{10} +(0.293901 - 0.509052i) q^{11} +(5.09398 - 8.82303i) q^{12} +(2.39227 - 2.69760i) q^{13} +(2.17733 + 5.93113i) q^{14} +(1.35136 + 2.34063i) q^{15} +2.30470 q^{16} -6.45420 q^{17} +(5.45742 + 9.45253i) q^{18} +(1.91345 + 3.31419i) q^{19} +(-1.81855 + 3.14983i) q^{20} +(-7.17260 - 1.24430i) q^{21} +(-0.701847 + 1.21563i) q^{22} +8.26001 q^{23} +(-5.59398 + 9.68906i) q^{24} +(2.01756 + 3.49452i) q^{25} +(-5.71283 + 6.44197i) q^{26} -4.32156 q^{27} +(-3.37601 - 9.19639i) q^{28} +(1.98009 + 3.42962i) q^{29} +(-3.22710 - 5.58950i) q^{30} +(1.49436 + 2.58831i) q^{31} +2.62861 q^{32} +(-0.808663 - 1.40065i) q^{33} +15.4129 q^{34} +(2.56062 + 0.444216i) q^{35} +(-8.46189 - 14.6564i) q^{36} +1.75588 q^{37} +(-4.56938 - 7.91440i) q^{38} +(-3.13683 - 9.41161i) q^{39} +(1.99705 - 3.45900i) q^{40} +(-1.83584 - 3.17977i) q^{41} +(17.1284 + 2.97143i) q^{42} +(-3.19042 + 5.52598i) q^{43} +(1.08823 - 1.88488i) q^{44} +4.48964 q^{45} -19.7252 q^{46} +(2.17030 - 3.75906i) q^{47} +(3.17067 - 5.49176i) q^{48} +(-5.33737 + 4.52907i) q^{49} +(-4.81802 - 8.34505i) q^{50} +(-8.87930 + 15.3794i) q^{51} +(8.85791 - 9.98846i) q^{52} +(-0.212770 - 0.368529i) q^{53} +10.3200 q^{54} +(0.288693 + 0.500031i) q^{55} +(3.70739 + 10.0991i) q^{56} +10.5296 q^{57} +(-4.72853 - 8.19006i) q^{58} +6.00863 q^{59} +(5.00371 + 8.66669i) q^{60} +(-1.10337 - 1.91109i) q^{61} +(-3.56859 - 6.18097i) q^{62} +(-7.74745 + 9.28503i) q^{63} -10.8866 q^{64} +(1.11985 + 3.35995i) q^{65} +(1.93112 + 3.34479i) q^{66} +(-3.50651 + 6.07346i) q^{67} -23.8981 q^{68} +(11.3636 - 19.6824i) q^{69} +(-6.11486 - 1.06080i) q^{70} +(-1.80127 + 3.11988i) q^{71} +(9.29247 + 16.0950i) q^{72} +(-2.46714 - 4.27321i) q^{73} -4.19311 q^{74} +11.1026 q^{75} +(7.08496 + 12.2715i) q^{76} +(-1.53229 - 0.265822i) q^{77} +(7.49088 + 22.4753i) q^{78} +(-1.39270 + 2.41223i) q^{79} +(-1.13193 + 1.96056i) q^{80} +(0.910609 - 1.57722i) q^{81} +(4.38406 + 7.59342i) q^{82} -2.86819 q^{83} +(-26.5581 - 4.60730i) q^{84} +(3.16992 - 5.49045i) q^{85} +(7.61885 - 13.1962i) q^{86} +10.8964 q^{87} +(-1.19505 + 2.06989i) q^{88} -2.09311 q^{89} -10.7214 q^{90} +(-8.88117 - 3.48206i) q^{91} +30.5845 q^{92} +8.22340 q^{93} +(-5.18275 + 8.97679i) q^{94} -3.75908 q^{95} +(3.61628 - 6.26357i) q^{96} +(-3.84852 + 6.66584i) q^{97} +(12.7458 - 10.8156i) q^{98} -2.68663 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} + q^{3} + 8 q^{4} + q^{5} - 9 q^{6} - 3 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 12 * q - 4 * q^2 + q^3 + 8 * q^4 + q^5 - 9 * q^6 - 3 * q^7 - 6 * q^8 + 3 * q^9	\( 12 q - 4 q^{2} + q^{3} + 8 q^{4} + q^{5} - 9 q^{6} - 3 q^{7} - 6 q^{8} + 3 q^{9} + 4 q^{10} + 4 q^{11} + 5 q^{12} - 2 q^{13} - 2 q^{14} - 2 q^{15} - 16 q^{16} - 10 q^{17} + 3 q^{18} - q^{19} - q^{20} - 9 q^{21} - 5 q^{22} + 2 q^{23} - 11 q^{24} + 7 q^{25} - 16 q^{26} - 8 q^{27} - q^{28} + 3 q^{29} - 5 q^{30} + 16 q^{31} - 16 q^{32} + 16 q^{33} + 32 q^{34} + 20 q^{35} - 21 q^{36} + 26 q^{37} - 17 q^{38} - 20 q^{39} - 5 q^{40} - 8 q^{41} + 50 q^{42} - 11 q^{43} + 21 q^{44} + 14 q^{45} - 32 q^{46} - q^{47} + 21 q^{48} - 3 q^{49} + 6 q^{50} - 20 q^{51} + 41 q^{52} - 2 q^{53} + 36 q^{54} + 9 q^{55} + 9 q^{56} + 42 q^{57} - 8 q^{58} - 26 q^{59} + 20 q^{60} - 5 q^{61} + 5 q^{62} - 40 q^{63} - 30 q^{64} - 5 q^{65} + 18 q^{66} - 11 q^{67} - 58 q^{68} + 23 q^{69} - 39 q^{70} + 6 q^{71} + 25 q^{72} - 30 q^{73} + 6 q^{74} + 6 q^{75} - 9 q^{76} + 11 q^{77} + 16 q^{78} + 7 q^{79} - 7 q^{80} - 6 q^{81} + q^{82} - 54 q^{83} - 46 q^{84} - q^{85} - 7 q^{86} - 32 q^{87} - 8 q^{89} - 16 q^{90} - 23 q^{91} + 54 q^{92} + 14 q^{93} + 45 q^{94} + 12 q^{95} + 19 q^{96} - 35 q^{97} + 20 q^{98} - 20 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 + q^3 + 8 * q^4 + q^5 - 9 * q^6 - 3 * q^7 - 6 * q^8 + 3 * q^9 + 4 * q^10 + 4 * q^11 + 5 * q^12 - 2 * q^13 - 2 * q^14 - 2 * q^15 - 16 * q^16 - 10 * q^17 + 3 * q^18 - q^19 - q^20 - 9 * q^21 - 5 * q^22 + 2 * q^23 - 11 * q^24 + 7 * q^25 - 16 * q^26 - 8 * q^27 - q^28 + 3 * q^29 - 5 * q^30 + 16 * q^31 - 16 * q^32 + 16 * q^33 + 32 * q^34 + 20 * q^35 - 21 * q^36 + 26 * q^37 - 17 * q^38 - 20 * q^39 - 5 * q^40 - 8 * q^41 + 50 * q^42 - 11 * q^43 + 21 * q^44 + 14 * q^45 - 32 * q^46 - q^47 + 21 * q^48 - 3 * q^49 + 6 * q^50 - 20 * q^51 + 41 * q^52 - 2 * q^53 + 36 * q^54 + 9 * q^55 + 9 * q^56 + 42 * q^57 - 8 * q^58 - 26 * q^59 + 20 * q^60 - 5 * q^61 + 5 * q^62 - 40 * q^63 - 30 * q^64 - 5 * q^65 + 18 * q^66 - 11 * q^67 - 58 * q^68 + 23 * q^69 - 39 * q^70 + 6 * q^71 + 25 * q^72 - 30 * q^73 + 6 * q^74 + 6 * q^75 - 9 * q^76 + 11 * q^77 + 16 * q^78 + 7 * q^79 - 7 * q^80 - 6 * q^81 + q^82 - 54 * q^83 - 46 * q^84 - q^85 - 7 * q^86 - 32 * q^87 - 8 * q^89 - 16 * q^90 - 23 * q^91 + 54 * q^92 + 14 * q^93 + 45 * q^94 + 12 * q^95 + 19 * q^96 - 35 * q^97 + 20 * q^98 - 20 * q^99

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