LMFDB - Embedded newform 151.2.g.a.2.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [151,2,Mod(2,151)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(151, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([14]))

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

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

chi := DirichletCharacter("151.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	151.g (of order $15$, degree $8$, 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:	$1.20574107052$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			2.4
Character	$\chi$	$=$	151.2
Dual form			151.2.g.a.76.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.579506 + 1.00373i) q^{2} +(2.23683 - 1.62515i) q^{3} +(0.328346 + 0.568712i) q^{4} +(2.59512 + 2.88217i) q^{5} +(0.334964 + 3.18697i) q^{6} +(-3.20705 - 3.56179i) q^{7} -3.07914 q^{8} +(1.43524 - 4.41720i) q^{9} +O(q^{10})$	\(q+(-0.579506 + 1.00373i) q^{2} +(2.23683 - 1.62515i) q^{3} +(0.328346 + 0.568712i) q^{4} +(2.59512 + 2.88217i) q^{5} +(0.334964 + 3.18697i) q^{6} +(-3.20705 - 3.56179i) q^{7} -3.07914 q^{8} +(1.43524 - 4.41720i) q^{9} +(-4.39682 + 0.934574i) q^{10} +(-2.36314 + 1.05214i) q^{11} +(1.65870 + 0.738499i) q^{12} +(-0.237336 - 0.105669i) q^{13} +(5.43359 - 1.15494i) q^{14} +(10.4888 + 2.22947i) q^{15} +(1.12769 - 1.95321i) q^{16} +(-0.923528 - 0.196302i) q^{17} +(3.60197 + 4.00039i) q^{18} -1.00249 q^{19} +(-0.787029 + 2.42223i) q^{20} +(-12.9621 - 2.75517i) q^{21} +(0.313388 - 2.98169i) q^{22} +(3.07236 - 5.32148i) q^{23} +(-6.88750 + 5.00406i) q^{24} +(-1.04963 + 9.98658i) q^{25} +(0.243601 - 0.176986i) q^{26} +(-1.40507 - 4.32435i) q^{27} +(0.972609 - 2.99338i) q^{28} +(6.26582 + 4.55238i) q^{29} +(-8.31612 + 9.23598i) q^{30} +(-4.24631 - 0.902581i) q^{31} +(-1.77214 - 3.06943i) q^{32} +(-3.57606 + 6.19393i) q^{33} +(0.732225 - 0.813218i) q^{34} +(1.94301 - 18.4865i) q^{35} +(2.98337 - 0.634135i) q^{36} +(-0.549079 - 5.22414i) q^{37} +(0.580950 - 1.00623i) q^{38} +(-0.702608 + 0.149344i) q^{39} +(-7.99073 - 8.87461i) q^{40} +(-1.12044 + 0.814048i) q^{41} +(10.2770 - 11.4138i) q^{42} +(-3.09752 + 3.44014i) q^{43} +(-1.37429 - 0.998483i) q^{44} +(16.4558 - 7.32658i) q^{45} +(3.56090 + 6.16765i) q^{46} +(2.26562 + 1.00872i) q^{47} +(-0.651820 - 6.20166i) q^{48} +(-1.66947 + 15.8840i) q^{49} +(-9.41559 - 6.84083i) q^{50} +(-2.38479 + 1.06178i) q^{51} +(-0.0178332 - 0.169672i) q^{52} +(-1.62964 - 1.18401i) q^{53} +(5.15474 + 1.09567i) q^{54} +(-9.16510 - 4.08056i) q^{55} +(9.87493 + 10.9672i) q^{56} +(-2.24240 + 1.62920i) q^{57} +(-8.20046 + 3.65108i) q^{58} +5.08482 q^{59} +(2.17604 + 6.69715i) q^{60} +(0.401456 - 3.81960i) q^{61} +(3.36671 - 3.73911i) q^{62} +(-20.3360 + 9.05417i) q^{63} +8.61860 q^{64} +(-0.311360 - 0.958267i) q^{65} +(-4.14470 - 7.17883i) q^{66} +(0.694374 + 2.13706i) q^{67} +(-0.191597 - 0.589676i) q^{68} +(-1.77587 - 16.8963i) q^{69} +(17.4296 + 12.6633i) q^{70} +(-12.5155 + 2.66025i) q^{71} +(-4.41929 + 13.6012i) q^{72} +(-0.923986 + 2.84374i) q^{73} +(5.56184 + 2.47629i) q^{74} +(13.8819 + 24.0441i) q^{75} +(-0.329164 - 0.570129i) q^{76} +(11.3262 + 5.04275i) q^{77} +(0.257264 - 0.791777i) q^{78} +(-1.03493 + 3.18520i) q^{79} +(8.55597 - 1.81863i) q^{80} +(1.10187 + 0.800552i) q^{81} +(-0.167785 - 1.59637i) q^{82} +(1.10634 + 3.40497i) q^{83} +(-2.68914 - 8.27632i) q^{84} +(-1.83089 - 3.17120i) q^{85} +(-1.65796 - 5.10266i) q^{86} +21.4139 q^{87} +(7.27645 - 3.23968i) q^{88} +(8.23084 - 9.14127i) q^{89} +(-2.18228 + 20.7630i) q^{90} +(0.384778 + 1.18422i) q^{91} +4.03518 q^{92} +(-10.9651 + 4.88198i) q^{93} +(-2.32542 + 1.68952i) q^{94} +(-2.60159 - 2.88936i) q^{95} +(-8.95225 - 3.98580i) q^{96} +(-1.31093 - 0.278648i) q^{97} +(-14.9758 - 10.8806i) q^{98} +(1.25584 + 11.9486i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 3 q^{2} - 4 q^{3} - 49 q^{4} - 9 q^{5} + 7 q^{6} - 7 q^{7} + 12 q^{8} - 32 q^{9}+O(q^{10}) $ 96 * q - 3 * q^2 - 4 * q^3 - 49 * q^4 - 9 * q^5 + 7 * q^6 - 7 * q^7 + 12 * q^8 - 32 * q^9	\( 96 q - 3 q^{2} - 4 q^{3} - 49 q^{4} - 9 q^{5} + 7 q^{6} - 7 q^{7} + 12 q^{8} - 32 q^{9} + 11 q^{10} - 7 q^{11} + 7 q^{12} - 8 q^{13} + 5 q^{14} + 10 q^{15} - 47 q^{16} - 26 q^{17} - 40 q^{18} - 20 q^{19} + 23 q^{20} - 2 q^{21} - 32 q^{22} - q^{23} + 95 q^{24} - 51 q^{25} + 41 q^{26} + 5 q^{27} - 2 q^{28} + 13 q^{29} + 19 q^{30} - 24 q^{31} - 60 q^{32} + 39 q^{33} + 47 q^{34} - 54 q^{35} + 11 q^{36} + 5 q^{37} + 8 q^{38} - 13 q^{39} - 74 q^{40} + 8 q^{41} + 166 q^{42} - 8 q^{43} + 18 q^{44} - 33 q^{45} + 21 q^{46} - 5 q^{47} + 8 q^{48} + 21 q^{49} - 72 q^{50} - 6 q^{51} + 96 q^{52} + 41 q^{53} - 60 q^{54} - 116 q^{55} - 85 q^{56} - 8 q^{57} - 58 q^{58} + 32 q^{59} - 6 q^{60} - 18 q^{61} + 38 q^{62} - 129 q^{63} + 160 q^{64} + 53 q^{65} + 43 q^{66} + 4 q^{67} + 10 q^{68} + 81 q^{69} + 33 q^{70} - 41 q^{71} - 40 q^{72} - 58 q^{73} - 20 q^{74} + 32 q^{75} - q^{76} - 22 q^{77} - 10 q^{78} + 32 q^{79} + 71 q^{80} - 66 q^{81} - 10 q^{82} + 80 q^{83} - 58 q^{84} - 2 q^{85} - 72 q^{86} + 72 q^{87} + 89 q^{88} + 9 q^{89} + 121 q^{90} - 138 q^{91} - 72 q^{92} - 85 q^{93} + 11 q^{94} - 47 q^{95} - 201 q^{96} + 54 q^{97} - 92 q^{98} - 21 q^{99}+O(q^{100}) \) 96 * q - 3 * q^2 - 4 * q^3 - 49 * q^4 - 9 * q^5 + 7 * q^6 - 7 * q^7 + 12 * q^8 - 32 * q^9 + 11 * q^10 - 7 * q^11 + 7 * q^12 - 8 * q^13 + 5 * q^14 + 10 * q^15 - 47 * q^16 - 26 * q^17 - 40 * q^18 - 20 * q^19 + 23 * q^20 - 2 * q^21 - 32 * q^22 - q^23 + 95 * q^24 - 51 * q^25 + 41 * q^26 + 5 * q^27 - 2 * q^28 + 13 * q^29 + 19 * q^30 - 24 * q^31 - 60 * q^32 + 39 * q^33 + 47 * q^34 - 54 * q^35 + 11 * q^36 + 5 * q^37 + 8 * q^38 - 13 * q^39 - 74 * q^40 + 8 * q^41 + 166 * q^42 - 8 * q^43 + 18 * q^44 - 33 * q^45 + 21 * q^46 - 5 * q^47 + 8 * q^48 + 21 * q^49 - 72 * q^50 - 6 * q^51 + 96 * q^52 + 41 * q^53 - 60 * q^54 - 116 * q^55 - 85 * q^56 - 8 * q^57 - 58 * q^58 + 32 * q^59 - 6 * q^60 - 18 * q^61 + 38 * q^62 - 129 * q^63 + 160 * q^64 + 53 * q^65 + 43 * q^66 + 4 * q^67 + 10 * q^68 + 81 * q^69 + 33 * q^70 - 41 * q^71 - 40 * q^72 - 58 * q^73 - 20 * q^74 + 32 * q^75 - q^76 - 22 * q^77 - 10 * q^78 + 32 * q^79 + 71 * q^80 - 66 * q^81 - 10 * q^82 + 80 * q^83 - 58 * q^84 - 2 * q^85 - 72 * q^86 + 72 * q^87 + 89 * q^88 + 9 * q^89 + 121 * q^90 - 138 * q^91 - 72 * q^92 - 85 * q^93 + 11 * q^94 - 47 * q^95 - 201 * q^96 + 54 * q^97 - 92 * q^98 - 21 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/151\mathbb{Z}\right)^\times$.

$n$	$6$
$\chi(n)$	$e\left(\frac{7}{15}\right)$

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 $

$2$	−0.579506	+	1.00373i	−0.409772	+	0.709747i	−0.994864	−	0.101220i	$-0.967725\pi$
$2$	−0.579506	+	1.00373i	−0.409772	+	0.709747i	0.585092	+	0.810967i	$0.301059\pi$
$3$	2.23683	−	1.62515i	1.29143	−	0.938282i	0.291601	−	0.956540i	$-0.405812\pi$
$3$	2.23683	−	1.62515i	1.29143	−	0.938282i	0.999833	+	0.0182585i	$0.00581218\pi$
$4$	0.328346	+	0.568712i	0.164173	+	0.284356i
$5$	2.59512	+	2.88217i	1.16057	+	1.28895i	0.950311	+	0.311303i	$0.100765\pi$
$5$	2.59512	+	2.88217i	1.16057	+	1.28895i	0.210263	+	0.977645i	$0.432568\pi$
$6$	0.334964	+	3.18697i	0.136748	+	1.30107i
$7$	−3.20705	−	3.56179i	−1.21215	−	1.34623i	−0.921006	−	0.389549i	$-0.872631\pi$
$7$	−3.20705	−	3.56179i	−1.21215	−	1.34623i	−0.291144	−	0.956679i	$-0.594036\pi$
$8$	−3.07914			−1.08864
$9$	1.43524	−	4.41720i	0.478412	−	1.47240i
$10$	−4.39682	+	0.934574i	−1.39040	+	0.295538i
$11$	−2.36314	+	1.05214i	−0.712515	+	0.317232i	−0.730791	−	0.682601i	$-0.760849\pi$
$11$	−2.36314	+	1.05214i	−0.712515	+	0.317232i	0.0182764	+	0.999833i	$0.494182\pi$
$12$	1.65870	+	0.738499i	0.478825	+	0.213186i
$13$	−0.237336	−	0.105669i	−0.0658252	−	0.0293073i	0.373560	−	0.927606i	$-0.378137\pi$
$13$	−0.237336	−	0.105669i	−0.0658252	−	0.0293073i	−0.439385	+	0.898299i	$0.644804\pi$
$14$	5.43359	−	1.15494i	1.45219	−	0.308672i
$15$	10.4888	+	2.22947i	2.70820	+	0.575646i
$16$	1.12769	−	1.95321i	0.281921	−	0.488302i
$17$	−0.923528	−	0.196302i	−0.223988	−	0.0476102i	0.0945502	−	0.995520i	$-0.469859\pi$
$17$	−0.923528	−	0.196302i	−0.223988	−	0.0476102i	−0.318539	+	0.947910i	$0.603192\pi$
$18$	3.60197	+	4.00039i	0.848992	+	0.942901i
$19$	−1.00249			−0.229987			−0.114994	−	0.993366i	$-0.536685\pi$
$19$	−1.00249			−0.229987			−0.114994	+	0.993366i	$0.536685\pi$
$20$	−0.787029	+	2.42223i	−0.175985	+	0.541626i
$21$	−12.9621	−	2.75517i	−2.82855	−	0.601227i
$22$	0.313388	−	2.98169i	0.0668146	−	0.635698i
$23$	3.07236	−	5.32148i	0.640630	−	1.10960i	−0.344662	−	0.938727i	$-0.612006\pi$
$23$	3.07236	−	5.32148i	0.640630	−	1.10960i	0.985292	−	0.170877i	$-0.0546602\pi$
$24$	−6.88750	+	5.00406i	−1.40591	+	1.02145i
$25$	−1.04963	+	9.98658i	−0.209926	+	1.99732i
$26$	0.243601	−	0.176986i	0.0477741	−	0.0347099i
$27$	−1.40507	−	4.32435i	−0.270405	−	0.832222i
$28$	0.972609	−	2.99338i	0.183806	−	0.565696i
$29$	6.26582	+	4.55238i	1.16353	+	0.845357i	0.990221	−	0.139510i	$-0.0445528\pi$
$29$	6.26582	+	4.55238i	1.16353	+	0.845357i	0.173313	+	0.984867i	$0.444553\pi$
$30$	−8.31612	+	9.23598i	−1.51831	+	1.68625i
$31$	−4.24631	−	0.902581i	−0.762660	−	0.162108i	−0.189868	−	0.981810i	$-0.560806\pi$
$31$	−4.24631	−	0.902581i	−0.762660	−	0.162108i	−0.572791	+	0.819701i	$0.694139\pi$
$32$	−1.77214	−	3.06943i	−0.313272	−	0.542604i
$33$	−3.57606	+	6.19393i	−0.622513	+	1.07822i
$34$	0.732225	−	0.813218i	0.125576	−	0.139466i
$35$	1.94301	−	18.4865i	0.328429	−	3.12479i
$36$	2.98337	−	0.634135i	0.497228	−	0.105689i
$37$	−0.549079	−	5.22414i	−0.0902680	−	0.858843i	−0.942169	−	0.335139i	$-0.891217\pi$
$37$	−0.549079	−	5.22414i	−0.0902680	−	0.858843i	0.851901	−	0.523704i	$-0.175450\pi$
$38$	0.580950	−	1.00623i	0.0942425	−	0.163233i
$39$	−0.702608	+	0.149344i	−0.112507	+	0.0239142i
$40$	−7.99073	−	8.87461i	−1.26345	−	1.40320i
$41$	−1.12044	+	0.814048i	−0.174983	+	0.127133i	−0.671830	−	0.740706i	$-0.734491\pi$
$41$	−1.12044	+	0.814048i	−0.174983	+	0.127133i	0.496846	+	0.867839i	$0.334491\pi$
$42$	10.2770	−	11.4138i	1.58578	−	1.76119i
$43$	−3.09752	+	3.44014i	−0.472367	+	0.524617i	−0.931495	−	0.363753i	$-0.881495\pi$
$43$	−3.09752	+	3.44014i	−0.472367	+	0.524617i	0.459128	+	0.888370i	$0.348162\pi$
$44$	−1.37429	−	0.998483i	−0.207183	−	0.150527i
$45$	16.4558	−	7.32658i	2.45308	−	1.09218i
$46$	3.56090	+	6.16765i	0.525025	+	0.909371i
$47$	2.26562	+	1.00872i	0.330474	+	0.147136i	0.565265	−	0.824909i	$-0.308774\pi$
$47$	2.26562	+	1.00872i	0.330474	+	0.147136i	−0.234791	+	0.972046i	$0.575441\pi$
$48$	−0.651820	−	6.20166i	−0.0940822	−	0.895132i
$49$	−1.66947	+	15.8840i	−0.238496	+	2.26914i
$50$	−9.41559	−	6.84083i	−1.33157	−	0.967439i
$51$	−2.38479	+	1.06178i	−0.333938	+	0.148679i
$52$	−0.0178332	−	0.169672i	−0.00247302	−	0.0235292i
$53$	−1.62964	−	1.18401i	−0.223849	−	0.162636i	0.470209	−	0.882555i	$-0.344179\pi$
$53$	−1.62964	−	1.18401i	−0.223849	−	0.162636i	−0.694057	+	0.719920i	$0.744179\pi$
$54$	5.15474	+	1.09567i	0.701472	+	0.149102i
$55$	−9.16510	−	4.08056i	−1.23582	−	0.550223i
$56$	9.87493	+	10.9672i	1.31959	+	1.46556i
$57$	−2.24240	+	1.62920i	−0.297013	+	0.215793i
$58$	−8.20046	+	3.65108i	−1.07677	+	0.479410i
$59$	5.08482			0.661987			0.330993	−	0.943633i	$-0.392616\pi$
$59$	5.08482			0.661987			0.330993	+	0.943633i	$0.392616\pi$
$60$	2.17604	+	6.69715i	0.280925	+	0.864598i
$61$	0.401456	−	3.81960i	0.0514012	−	0.489049i	−0.938292	−	0.345844i	$-0.887592\pi$
$61$	0.401456	−	3.81960i	0.0514012	−	0.489049i	0.989693	−	0.143205i	$-0.0457408\pi$
$62$	3.36671	−	3.73911i	0.427573	−	0.474868i
$63$	−20.3360	+	9.05417i	−2.56209	+	1.14072i
$64$	8.61860			1.07732
$65$	−0.311360	−	0.958267i	−0.0386194	−	0.118858i
$66$	−4.14470	−	7.17883i	−0.510177	−	0.883653i
$67$	0.694374	+	2.13706i	0.0848313	+	0.261084i	0.984470	−	0.175550i	$-0.0561704\pi$
$67$	0.694374	+	2.13706i	0.0848313	+	0.261084i	−0.899639	+	0.436634i	$0.856170\pi$
$68$	−0.191597	−	0.589676i	−0.0232346	−	0.0715088i
$69$	−1.77587	−	16.8963i	−0.213790	−	2.03407i
$70$	17.4296	+	12.6633i	2.08323	+	1.51356i
$71$	−12.5155	+	2.66025i	−1.48531	+	0.315713i	−0.877966	−	0.478723i	$-0.841100\pi$
$71$	−12.5155	+	2.66025i	−1.48531	+	0.315713i	−0.607348	+	0.794436i	$0.707767\pi$
$72$	−4.41929	+	13.6012i	−0.520818	+	1.60291i
$73$	−0.923986	+	2.84374i	−0.108144	+	0.332834i	−0.990456	−	0.137832i	$-0.955987\pi$
$73$	−0.923986	+	2.84374i	−0.108144	+	0.332834i	0.882311	+	0.470667i	$0.155987\pi$
$74$	5.56184	+	2.47629i	0.646550	+	0.287863i
$75$	13.8819	+	24.0441i	1.60294	+	2.77637i
$76$	−0.329164	−	0.570129i	−0.0377577	−	0.0653983i
$77$	11.3262	+	5.04275i	1.29074	+	0.574675i
$78$	0.257264	−	0.791777i	0.0291294	−	0.0896511i
$79$	−1.03493	+	3.18520i	−0.116439	+	0.358363i	−0.992244	−	0.124302i	$-0.960331\pi$
$79$	−1.03493	+	3.18520i	−0.116439	+	0.358363i	0.875805	+	0.482665i	$0.160331\pi$
$80$	8.55597	−	1.81863i	0.956587	−	0.203329i
$81$	1.10187	+	0.800552i	0.122429	+	0.0889502i
$82$	−0.167785	−	1.59637i	−0.0185288	−	0.176290i
$83$	1.10634	+	3.40497i	0.121437	+	0.373744i	0.993235	−	0.116121i	$-0.0370461\pi$
$83$	1.10634	+	3.40497i	0.121437	+	0.373744i	−0.871798	+	0.489865i	$0.837046\pi$
$84$	−2.68914	−	8.27632i	−0.293409	−	0.903021i
$85$	−1.83089	−	3.17120i	−0.198588	−	0.343965i
$86$	−1.65796	−	5.10266i	−0.178782	−	0.550234i
$87$	21.4139			2.29581
$88$	7.27645	−	3.23968i	0.775672	−	0.345351i
$89$	8.23084	−	9.14127i	0.872467	−	0.968973i	−0.127271	−	0.991868i	$-0.540622\pi$
$89$	8.23084	−	9.14127i	0.872467	−	0.968973i	0.999738	+	0.0228950i	$0.00728835\pi$
$90$	−2.18228	+	20.7630i	−0.230032	+	2.18861i
$91$	0.384778	+	1.18422i	0.0403357	+	0.124140i
$92$	4.03518			0.420697
$93$	−10.9651	+	4.88198i	−1.13703	+	0.506237i
$94$	−2.32542	+	1.68952i	−0.239849	+	0.174260i
$95$	−2.60159	−	2.88936i	−0.266917	−	0.296442i
$96$	−8.95225	−	3.98580i	−0.913686	−	0.406799i
$97$	−1.31093	−	0.278648i	−0.133105	−	0.0282924i	0.140877	−	0.990027i	$-0.455008\pi$
$97$	−1.31093	−	0.278648i	−0.133105	−	0.0282924i	−0.273982	+	0.961735i	$0.588341\pi$
$98$	−14.9758	−	10.8806i	−1.51278	−	1.09910i
$99$	1.25584	+	11.9486i	0.126217	+	1.20088i
$100$	−6.02413	+	2.68211i	−0.602413	+	0.268211i
$101$	10.5386	+	7.65672i	1.04863	+	0.761872i	0.971951	−	0.235184i	$-0.0755693\pi$
$101$	10.5386	+	7.65672i	1.04863	+	0.761872i	0.0766761	+	0.997056i	$0.475569\pi$
$102$	0.316259	−	3.00901i	0.0313143	−	0.297936i
$103$	−1.51531	−	14.4172i	−0.149307	−	1.42057i	−0.770766	−	0.637119i	$-0.780126\pi$
$103$	−1.51531	−	14.4172i	−0.149307	−	1.42057i	0.621458	−	0.783447i	$-0.286541\pi$
$104$	0.730790	+	0.325369i	0.0716599	+	0.0319050i
$105$	−25.6972	−	44.5089i	−2.50779	−	4.34362i
$106$	2.13281	−	0.949590i	0.207157	−	0.0922324i
$107$	13.0697	+	9.49567i	1.26349	+	0.917981i	0.998924	−	0.0463858i	$-0.0147704\pi$
$107$	13.0697	+	9.49567i	1.26349	+	0.917981i	0.264569	+	0.964367i	$0.414770\pi$
$108$	1.99796	−	2.21896i	0.192254	−	0.213520i
$109$	4.24720	−	4.71700i	0.406808	−	0.451806i	−0.504573	−	0.863369i	$-0.668350\pi$
$109$	4.24720	−	4.71700i	0.406808	−	0.451806i	0.911382	+	0.411562i	$0.135017\pi$
$110$	9.40703	−	6.83461i	0.896925	−	0.651654i
$111$	−9.71821	−	10.7932i	−0.922412	−	1.02444i
$112$	−10.5735	+	2.24746i	−0.999097	+	0.212365i
$113$	−7.22326	+	12.5111i	−0.679507	+	1.17694i	0.295622	+	0.955305i	$0.404473\pi$
$113$	−7.22326	+	12.5111i	−0.679507	+	1.17694i	−0.975129	+	0.221636i	$0.928860\pi$
$114$	−0.335798	−	3.19491i	−0.0314504	−	0.299230i
$115$	23.3106	−	4.95481i	2.17372	−	0.462039i
$116$	−0.531639	+	5.05820i	−0.0493614	+	0.469642i
$117$	−0.807394	+	0.896702i	−0.0746436	+	0.0829001i
$118$	−2.94668	+	5.10380i	−0.271264	+	0.469843i
$119$	2.26261	+	3.91896i	0.207413	+	0.359250i
$120$	−32.2965	−	6.86483i	−2.94825	−	0.626671i
$121$	−2.88298	+	3.20187i	−0.262089	+	0.291080i
$122$	3.60121	+	2.61643i	0.326039	+	0.236881i
$123$	−1.18328	+	3.64177i	−0.106693	+	0.328368i
$124$	−0.880950	−	2.71129i	−0.0791117	−	0.243481i
$125$	−15.8187	+	11.4930i	−1.41487	+	1.02796i
$126$	2.69686	−	25.6589i	0.240255	−	2.28587i
$127$	13.2114	−	9.59864i	1.17232	−	0.851741i	0.181037	−	0.983476i	$-0.442055\pi$
$127$	13.2114	−	9.59864i	1.17232	−	0.851741i	0.991285	+	0.131735i	$0.0420548\pi$
$128$	−1.45025	+	2.51191i	−0.128186	+	0.222024i
$129$	−1.33787	+	12.7289i	−0.117793	+	1.12072i
$130$	1.14228	+	0.242799i	0.100185	+	0.0212949i
$131$	2.17652	−	6.69864i	0.190163	−	0.585263i	−0.809836	−	0.586657i	$-0.800444\pi$
$131$	2.17652	−	6.69864i	0.190163	−	0.585263i	0.999999	+	0.00139413i	$0.000443765\pi$
$132$	−4.69675			−0.408799
$133$	3.21504	+	3.57066i	0.278779	+	0.309616i
$134$	−2.54744	−	0.541474i	−0.220065	−	0.0467763i
$135$	8.81722	−	15.2719i	0.758866	−	1.31439i
$136$	2.84367	+	0.604441i	0.243843	+	0.0518304i
$137$	−6.17015	+	1.31151i	−0.527152	+	0.112050i	−0.463797	−	0.885942i	$-0.653513\pi$
$137$	−6.17015	+	1.31151i	−0.527152	+	0.112050i	−0.0633547	+	0.997991i	$0.520180\pi$
$138$	17.9885	+	8.00899i	1.53128	+	0.681770i
$139$	−9.93769	−	4.42454i	−0.842904	−	0.375285i	−0.0605849	−	0.998163i	$-0.519297\pi$
$139$	−9.93769	−	4.42454i	−0.842904	−	0.375285i	−0.782319	+	0.622878i	$0.785963\pi$
$140$	11.1515	−	4.96496i	0.942473	−	0.419616i
$141$	6.70711	−	1.42564i	0.564841	−	0.120061i
$142$	4.58261	−	14.1038i	0.384564	−	1.18357i
$143$	0.672038			0.0561986
$144$	−7.00923	−	7.78453i	−0.584102	−	0.648711i
$145$	3.13980	+	29.8732i	0.260746	+	2.48083i
$146$	−2.31890	−	2.57540i	−0.191913	−	0.213141i
$147$	22.0795	+	38.2429i	1.82109	+	3.15422i
$148$	2.79074	−	2.02759i	0.229398	−	0.166667i
$149$	0.404986	−	0.701457i	0.0331778	−	0.0574656i	−0.848960	−	0.528458i	$-0.822771\pi$
$149$	0.404986	−	0.701457i	0.0331778	−	0.0574656i	0.882138	+	0.470992i	$0.156104\pi$
$150$	−32.1785			−2.62736
$151$	−2.49041	+	12.0332i	−0.202667	+	0.979248i
$151$	−2.49041	+	12.0332i	−0.202667	+	0.979248i
$152$	3.08681			0.250373
$153$	−2.19259	+	3.79767i	−0.177260	+	0.307024i
$154$	−11.6252	+	8.44619i	−0.936784	+	0.680614i
$155$	−8.41829	−	14.5809i	−0.676174	−	1.17117i
$156$	−0.315632	−	0.350545i	−0.0252708	−	0.0280661i
$157$	−1.46964	−	13.9827i	−0.117290	−	1.11594i	−0.881896	−	0.471443i	$-0.843733\pi$
$157$	−1.46964	−	13.9827i	−0.117290	−	1.11594i	0.764606	−	0.644498i	$-0.222933\pi$
$158$	−2.59734	−	2.88464i	−0.206633	−	0.229490i
$159$	−5.56942			−0.441684
$160$	4.24772	−	13.0731i	0.335812	−	1.03352i
$161$	−28.8071	+	6.12315i	−2.27032	+	0.482572i
$162$	−1.44208	+	0.642054i	−0.113300	+	0.0504446i
$163$	12.9592	+	5.76979i	1.01504	+	0.451925i	0.845715	−	0.533635i	$-0.179174\pi$
$163$	12.9592	+	5.76979i	1.01504	+	0.451925i	0.169326	+	0.985560i	$0.445841\pi$
$164$	−0.830851	−	0.369919i	−0.0648786	−	0.0288858i
$165$	−27.1323	+	5.76715i	−2.11225	+	0.448972i
$166$	−4.05881	−	0.862726i	−0.315025	−	0.0669606i
$167$	−9.46339	+	16.3911i	−0.732299	+	1.26838i	0.223599	+	0.974681i	$0.428219\pi$
$167$	−9.46339	+	16.3911i	−0.732299	+	1.26838i	−0.955898	+	0.293698i	$0.905114\pi$
$168$	39.9119	+	8.48355i	3.07927	+	0.654520i
$169$	−8.65354	−	9.61072i	−0.665657	−	0.739287i
$170$	4.24405			0.325504
$171$	−1.43881	+	4.42821i	−0.110029	+	0.338634i
$172$	−2.97351	−	0.632038i	−0.226728	−	0.0481925i
$173$	0.354814	−	3.37583i	0.0269760	−	0.256660i	−0.972719	−	0.231984i	$-0.925478\pi$
$173$	0.354814	−	3.37583i	0.0269760	−	0.256660i	0.999696	−	0.0246753i	$-0.00785518\pi$
$174$	−12.4095	+	21.4938i	−0.940760	+	1.62944i
$175$	38.9363	−	28.2888i	2.94330	−	2.13844i
$176$	−0.609836	+	5.80220i	−0.0459681	+	0.437357i
$177$	11.3739	−	8.26360i	0.854912	−	0.621130i
$178$	4.40558	+	13.5590i	0.330212	+	1.01629i
$179$	−5.16056	+	15.8826i	−0.385718	+	1.18712i	0.550239	+	0.835007i	$0.314537\pi$
$179$	−5.16056	+	15.8826i	−0.385718	+	1.18712i	−0.935958	+	0.352112i	$0.885463\pi$
$180$	9.56990	+	6.95294i	0.713298	+	0.518241i
$181$	−3.32696	+	3.69497i	−0.247291	+	0.274645i	−0.853993	−	0.520285i	$-0.825826\pi$
$181$	−3.32696	+	3.69497i	−0.247291	+	0.274645i	0.606701	+	0.794930i	$0.292492\pi$
$182$	−1.41163	−	0.300051i	−0.104637	−	0.0222412i
$183$	−5.30944	−	9.19622i	−0.392485	−	0.679804i
$184$	−9.46020	+	16.3856i	−0.697415	+	1.20796i
$185$	13.6320	−	15.1398i	1.00224	−	1.11310i
$186$	1.45414	−	13.8352i	0.106622	−	1.01444i
$187$	2.38897	−	0.507791i	0.174699	−	0.0371333i
$188$	0.170236	+	1.61969i	0.0124158	+	0.118128i
$189$	−10.8963	+	18.8730i	−0.792589	+	1.37281i
$190$	4.40778	−	0.936902i	0.319774	−	0.0679700i
$191$	−7.58229	−	8.42098i	−0.548635	−	0.609321i	0.403507	−	0.914977i	$-0.367791\pi$
$191$	−7.58229	−	8.42098i	−0.548635	−	0.609321i	−0.952142	+	0.305656i	$0.901124\pi$
$192$	19.2783	−	14.0065i	1.39129	−	1.01083i
$193$	14.0172	−	15.5677i	1.00898	−	1.12059i	0.0162960	−	0.999867i	$-0.494813\pi$
$193$	14.0172	−	15.5677i	1.00898	−	1.12059i	0.992686	−	0.120721i	$-0.0385207\pi$
$194$	1.03938	−	1.15435i	0.0746233	−	0.0828775i
$195$	−2.25379	−	1.63747i	−0.161397	−	0.117262i
$196$	−9.58157	+	4.26599i	−0.684398	+	0.304713i
$197$	−11.2471	−	19.4805i	−0.801321	−	1.38793i	−0.918747	−	0.394847i	$-0.870798\pi$
$197$	−11.2471	−	19.4805i	−0.801321	−	1.38793i	0.117426	−	0.993082i	$-0.462536\pi$
$198$	−12.7209	−	5.66373i	−0.904038	−	0.402504i
$199$	−0.277337	−	2.63869i	−0.0196599	−	0.187052i	0.980285	−	0.197591i	$-0.0633118\pi$
$199$	−0.277337	−	2.63869i	−0.0196599	−	0.187052i	−0.999944	+	0.0105394i	$0.996645\pi$
$200$	3.23196	−	30.7500i	0.228534	−	2.17436i
$201$	5.02625	+	3.65178i	0.354524	+	0.257577i
$202$	−13.7925	+	6.14080i	−0.970435	+	0.432065i
$203$	−3.88016	−	36.9172i	−0.272334	−	2.59108i
$204$	−1.38688	−	1.00763i	−0.0971013	−	0.0705482i
$205$	−5.25391	−	1.11675i	−0.366949	−	0.0779974i
$206$	15.3491	+	6.83387i	1.06942	+	0.476138i
$207$	−19.0965	−	21.2088i	−1.32730	−	1.47411i
$208$	−0.474034	+	0.344406i	−0.0328683	+	0.0238802i
$209$	2.36903	−	1.05476i	0.163869	−	0.0729594i
$210$	59.5668			4.11050
$211$	3.24395	+	9.98385i	0.223323	+	0.687317i	0.998458	+	0.0555209i	$0.0176820\pi$
$211$	3.24395	+	9.98385i	0.223323	+	0.687317i	−0.775135	+	0.631796i	$0.782318\pi$
$212$	0.138271	−	1.31556i	0.00949650	−	0.0903531i
$213$	−23.6717	+	26.2901i	−1.62196	+	1.80137i
$214$	−17.1051	+	7.61567i	−1.16928	+	0.520596i
$215$	−17.9535			−1.22442
$216$	4.32640	+	13.3153i	0.294374	+	0.905990i
$217$	10.4033	+	18.0191i	0.706223	+	1.22321i
$218$	2.27333	+	6.99659i	0.153969	+	0.473869i
$219$	2.55470	+	7.86257i	0.172631	+	0.531303i
$220$	−0.688657	−	6.55214i	−0.0464293	−	0.441745i
$221$	0.198444	+	0.144178i	0.0133488	+	0.00969844i
$222$	16.4652	−	3.49979i	1.10507	−	0.234891i
$223$	−5.72636	+	17.6239i	−0.383466	+	1.18019i	0.554121	+	0.832436i	$0.313054\pi$
$223$	−5.72636	+	17.6239i	−0.383466	+	1.18019i	−0.937587	+	0.347750i	$0.886946\pi$
$224$	−5.24933	+	16.1558i	−0.350735	+	1.07945i
$225$	42.6063	+	18.9695i	2.84042	+	1.26464i
$226$	−8.37185	−	14.5005i	−0.556887	−	0.964557i
$227$	4.38926	+	7.60242i	0.291325	+	0.504590i	0.974123	−	0.226017i	$-0.0725705\pi$
$227$	4.38926	+	7.60242i	0.291325	+	0.504590i	−0.682798	+	0.730607i	$0.739237\pi$
$228$	−1.66283	−	0.740340i	−0.110124	−	0.0490302i
$229$	8.04778	−	24.7685i	0.531812	−	1.63675i	−0.218625	−	0.975809i	$-0.570157\pi$
$229$	8.04778	−	24.7685i	0.531812	−	1.63675i	0.750437	−	0.660942i	$-0.229843\pi$
$230$	−8.53529	+	26.2689i	−0.562800	+	1.73212i
$231$	33.5300	−	7.12703i	2.20611	−	0.468924i
$232$	−19.2933	−	14.0174i	−1.26667	−	0.920289i
$233$	0.542550	+	5.16201i	0.0355436	+	0.338175i	0.997814	+	0.0660808i	$0.0210495\pi$
$233$	0.542550	+	5.16201i	0.0355436	+	0.338175i	−0.962271	+	0.272094i	$0.912284\pi$
$234$	−0.432160	−	1.33005i	−0.0282512	−	0.0869482i
$235$	2.97225	+	9.14764i	0.193888	+	0.596726i
$236$	1.66958	+	2.89180i	0.108680	+	0.188240i
$237$	2.86146	+	8.80667i	0.185872	+	0.572055i
$238$	−5.24479			−0.339969
$239$	16.6325	−	7.40528i	1.07587	−	0.479008i	0.209191	−	0.977875i	$-0.432917\pi$
$239$	16.6325	−	7.40528i	1.07587	−	0.479008i	0.866679	+	0.498867i	$0.166250\pi$
$240$	16.1827	−	17.9727i	1.04459	−	1.16013i
$241$	−0.717159	+	6.82331i	−0.0461963	+	0.439528i	0.946839	+	0.321709i	$0.104257\pi$
$241$	−0.717159	+	6.82331i	−0.0461963	+	0.439528i	−0.993035	+	0.117820i	$0.962410\pi$
$242$	−1.54312	−	4.74925i	−0.0991958	−	0.305293i
$243$	17.4064			1.11662
$244$	2.30407	−	1.02584i	0.147503	−	0.0656725i
$245$	−50.1128	+	36.4091i	−3.20159	+	2.32609i
$246$	−2.96965	−	3.29813i	−0.189338	−	0.210281i
$247$	0.237927	+	0.105932i	0.0151390	+	0.00674030i
$248$	13.0750	+	2.77917i	0.830261	+	0.176477i
$249$	8.00828	+	5.81836i	0.507504	+	0.368723i
$250$	−2.36884	−	22.5380i	−0.149819	−	1.42543i
$251$	−7.22638	+	3.21739i	−0.456125	+	0.203080i	−0.621921	−	0.783080i	$-0.713647\pi$
$251$	−7.22638	+	3.21739i	−0.456125	+	0.203080i	0.165796	+	0.986160i	$0.446981\pi$
$252$	−11.8265	−	8.59242i	−0.744997	−	0.541272i
$253$	−1.66148	+	15.8080i	−0.104457	+	0.993838i
$254$	1.97840	+	18.8232i	0.124136	+	1.18107i
$255$	−9.24906	−	4.11795i	−0.579199	−	0.257876i
$256$	6.93773	+	12.0165i	0.433608	+	0.751032i
$257$	−12.4786	+	5.55582i	−0.778393	+	0.346563i	−0.757175	−	0.653212i	$-0.773421\pi$
$257$	−12.4786	+	5.55582i	−0.778393	+	0.346563i	−0.0212178	+	0.999775i	$0.506754\pi$
$258$	−12.0012	−	8.71936i	−0.747160	−	0.542843i
$259$	−16.8463	+	18.7098i	−1.04678	+	1.16257i
$260$	0.442744	−	0.491717i	0.0274578	−	0.0304950i
$261$	29.1017	−	21.1437i	1.80135	−	1.30876i
$262$	5.46234	+	6.06654i	0.337465	+	0.374792i
$263$	9.56578	−	2.03327i	0.589851	−	0.125377i	0.0966899	−	0.995315i	$-0.469174\pi$
$263$	9.56578	−	2.03327i	0.589851	−	0.125377i	0.493161	+	0.869938i	$0.335841\pi$
$264$	11.0112	−	19.0719i	0.677692	−	1.17380i
$265$	−0.816613	−	7.76956i	−0.0501642	−	0.477280i
$266$	−5.44712	+	1.15782i	−0.333985	+	0.0709906i
$267$	3.55503	−	33.8238i	0.217564	−	2.06998i
$268$	−0.987379	+	1.09660i	−0.0603138	+	0.0669852i
$269$	6.04131	−	10.4639i	0.368345	−	0.637992i	−0.620962	−	0.783841i	$-0.713258\pi$
$269$	6.04131	−	10.4639i	0.368345	−	0.637992i	0.989307	+	0.145848i	$0.0465912\pi$
$270$	10.2193	+	17.7003i	0.621924	+	1.07720i
$271$	−1.95698	−	0.415970i	−0.118878	−	0.0252684i	0.148088	−	0.988974i	$-0.452688\pi$
$271$	−1.95698	−	0.415970i	−0.118878	−	0.0252684i	−0.266967	+	0.963706i	$0.586021\pi$
$272$	−1.42487	+	1.58248i	−0.0863953	+	0.0959517i
$273$	2.78523	+	2.02359i	0.168570	+	0.122473i
$274$	2.25924	−	6.95321i	0.136485	−	0.420059i
$275$	−8.02684	−	24.7041i	−0.484037	−	1.48971i
$276$	9.02601	−	6.55778i	0.543302	−	0.394732i
$277$	2.11621	−	20.1344i	0.127151	−	1.20976i	−0.725852	−	0.687851i	$-0.758554\pi$
$277$	2.11621	−	20.1344i	0.127151	−	1.20976i	0.853003	−	0.521907i	$-0.174779\pi$
$278$	10.2000	−	7.41074i	0.611756	−	0.444467i
$279$	−10.0813	+	17.4614i	−0.603554	+	1.04539i
$280$	−5.98280	+	56.9226i	−0.357541	+	3.40177i
$281$	7.01283	+	1.49062i	0.418350	+	0.0889231i	0.412277	−	0.911058i	$-0.364734\pi$
$281$	7.01283	+	1.49062i	0.418350	+	0.0889231i	0.00607301	+	0.999982i	$0.498067\pi$
$282$	−2.45585	+	7.55832i	−0.146244	+	0.450091i
$283$	9.90038			0.588516			0.294258	−	0.955726i	$-0.404927\pi$
$283$	9.90038			0.588516			0.294258	+	0.955726i	$0.404927\pi$
$284$	−5.62232	−	6.24422i	−0.333623	−	0.370526i
$285$	−10.5149	−	2.23502i	−0.622852	−	0.132391i
$286$	−0.389450	+	0.674547i	−0.0230287	+	0.0398868i
$287$	6.49277	+	1.38008i	0.383256	+	0.0814636i
$288$	−16.1017	+	3.42253i	−0.948803	+	0.201674i
$289$	−14.7159	−	6.55194i	−0.865641	−	0.385408i
$290$	−31.8042	−	14.1602i	−1.86761	−	0.831513i
$291$	−3.38518	+	1.50718i	−0.198443	+	0.0883524i
$292$	−1.92065	+	0.408248i	−0.112398	+	0.0238909i
$293$	−4.68153	+	14.4083i	−0.273498	+	0.841740i	0.716115	+	0.697982i	$0.245919\pi$
$293$	−4.68153	+	14.4083i	−0.273498	+	0.841740i	−0.989613	+	0.143758i	$0.954081\pi$
$294$	−51.1809			−2.98493
$295$	13.1957	+	14.6553i	0.768284	+	0.853266i
$296$	1.69069	+	16.0858i	0.0982693	+	0.934970i
$297$	7.87020	+	8.74075i	0.456676	+	0.507190i
$298$	0.469384	+	0.812997i	0.0271907	+	0.0470956i
$299$	−1.29149	+	0.938326i	−0.0746891	+	0.0542648i
$300$	−9.11610	+	15.7895i	−0.526318	+	0.911610i
$301$	22.1869			1.27883
$302$	−10.6349	−	9.47302i	−0.611971	−	0.545111i
$303$	36.0163			2.06908
$304$	−1.13050	+	1.95808i	−0.0648384	+	0.112303i
$305$	12.0506	−	8.75526i	0.690014	−	0.501324i
$306$	−2.54123	−	4.40155i	−0.145273	−	0.251620i
$307$	−12.3711	−	13.7395i	−0.706055	−	0.784153i	0.278273	−	0.960502i	$-0.410238\pi$
$307$	−12.3711	−	13.7395i	−0.706055	−	0.784153i	−0.984328	+	0.176349i	$0.943571\pi$
$308$	0.851042	+	8.09712i	0.0484926	+	0.461376i
$309$	−26.8196	−	29.7861i	−1.52571	−	1.69447i
$310$	19.5138			1.10831
$311$	−8.72501	+	26.8528i	−0.494750	+	1.52268i	0.322596	+	0.946537i	$0.395444\pi$
$311$	−8.72501	+	26.8528i	−0.494750	+	1.52268i	−0.817346	+	0.576147i	$0.804556\pi$
$312$	2.16343	−	0.459850i	0.122480	−	0.0260339i
$313$	15.7027	−	6.99127i	0.887566	−	0.395170i	0.0882627	−	0.996097i	$-0.471869\pi$
$313$	15.7027	−	6.99127i	0.887566	−	0.395170i	0.799304	+	0.600927i	$0.205202\pi$
$314$	14.8866	+	6.62793i	0.840098	+	0.374036i
$315$	−78.8701	−	35.1152i	−4.44383	−	1.97852i
$316$	−2.15128	+	0.457268i	−0.121019	+	0.0257233i
$317$	−6.88643	−	1.46376i	−0.386780	−	0.0822127i	0.0104175	−	0.999946i	$-0.496684\pi$
$317$	−6.88643	−	1.46376i	−0.386780	−	0.0822127i	−0.397198	+	0.917733i	$0.630017\pi$
$318$	3.22751	−	5.59022i	0.180990	−	0.313484i
$319$	−19.5968	−	4.16543i	−1.09721	−	0.233219i
$320$	22.3663	+	24.8403i	1.25031	+	1.38861i
$321$	44.6665			2.49304
$322$	10.5479	−	32.4631i	0.587811	−	1.80910i
$323$	0.925829	+	0.196791i	0.0515145	+	0.0109497i
$324$	−0.0934904	+	0.889502i	−0.00519391	+	0.0494168i
$325$	1.30438	−	2.25926i	0.0723543	−	0.125321i
$326$	−13.3012	+	9.66392i	−0.736688	+	0.535235i
$327$	1.83443	−	17.4535i	0.101444	−	0.965179i
$328$	3.44999	−	2.50656i	0.190494	−	0.138402i
$329$	−3.67310	−	11.3046i	−0.202505	−	0.623245i
$330$	9.93464	−	30.5757i	0.546884	−	1.68314i
$331$	−26.3543	−	19.1475i	−1.44856	−	1.05244i	−0.986164	−	0.165773i	$-0.946988\pi$
$331$	−26.3543	−	19.1475i	−1.44856	−	1.05244i	−0.462401	−	0.886671i	$-0.653012\pi$
$332$	−1.57318	+	1.74720i	−0.0863396	+	0.0958898i
$333$	−23.8641	−	5.07248i	−1.30775	−	0.277970i
$334$	−10.9682	−	18.9974i	−0.600152	−	1.03949i
$335$	−4.35740	+	7.54725i	−0.238070	+	0.412350i
$336$	−19.9985	+	22.2106i	−1.09101	+	1.21169i
$337$	1.06059	−	10.0908i	0.0577739	−	0.549682i	−0.926904	−	0.375299i	$-0.877540\pi$
$337$	1.06059	−	10.0908i	0.0577739	−	0.549682i	0.984678	−	0.174383i	$-0.0557932\pi$
$338$	14.6614	−	3.11637i	0.797474	−	0.169508i
$339$	4.17516	+	39.7240i	0.226764	+	2.15751i
$340$	1.20233	−	2.08250i	0.0652056	−	0.112939i
$341$	10.9843	−	2.33478i	0.594832	−	0.126436i
$342$	−3.61094	−	4.01036i	−0.195257	−	0.216855i
$343$	34.7868	−	25.2741i	1.87831	−	1.36467i
$344$	9.53768	−	10.5927i	0.514237	−	0.571118i
$345$	44.0894	−	48.9663i	2.37369	−	2.63625i
$346$	3.18282	+	2.31245i	0.171109	+	0.124318i
$347$	2.61120	−	1.16258i	0.140176	−	0.0624106i	−0.335450	−	0.942058i	$-0.608888\pi$
$347$	2.61120	−	1.16258i	0.140176	−	0.0624106i	0.475626	+	0.879648i	$0.342222\pi$
$348$	7.03116	+	12.1783i	0.376910	+	0.652827i
$349$	−4.38179	−	1.95090i	−0.234552	−	0.104429i	0.286095	−	0.958201i	$-0.407643\pi$
$349$	−4.38179	−	1.95090i	−0.234552	−	0.104429i	−0.520647	+	0.853772i	$0.674309\pi$
$350$	5.83068	+	55.4752i	0.311663	+	2.96527i
$351$	−0.123476	+	1.17480i	−0.00659067	+	0.0627060i
$352$	7.41728	+	5.38897i	0.395343	+	0.287233i
$353$	−18.4373	+	8.20879i	−0.981316	+	0.436910i	−0.833750	−	0.552142i	$-0.813811\pi$
$353$	−18.4373	+	8.20879i	−0.981316	+	0.436910i	−0.147566	+	0.989052i	$0.547144\pi$
$354$	1.70323	+	16.2051i	0.0905256	+	0.861293i
$355$	−40.1465	−	29.1681i	−2.13075	−	1.54808i
$356$	7.90131	+	1.67948i	0.418769	+	0.0890121i
$357$	11.4300	+	5.08895i	0.604939	+	0.269336i
$358$	−12.9513	−	14.3839i	−0.684497	−	0.760211i
$359$	19.4356	−	14.1208i	1.02577	−	0.745268i	0.0583145	−	0.998298i	$-0.481427\pi$
$359$	19.4356	−	14.1208i	1.02577	−	0.745268i	0.967458	+	0.253031i	$0.0814274\pi$
$360$	−50.6695	+	22.5595i	−2.67052	+	1.18899i
$361$	−17.9950			−0.947106
$362$	−1.78077	−	5.48064i	−0.0935950	−	0.288056i
$363$	−1.24520	+	11.8473i	−0.0653563	+	0.621823i
$364$	−0.547142	+	0.607663i	−0.0286781	+	0.0318502i
$365$	−10.5940	+	4.71675i	−0.554515	+	0.246886i
$366$	12.3074			0.643318
$367$	0.659747	+	2.03049i	0.0344385	+	0.105991i	0.966798	−	0.255541i	$-0.0822537\pi$
$367$	0.659747	+	2.03049i	0.0344385	+	0.105991i	−0.932360	+	0.361532i	$0.882254\pi$
$368$	−6.92930	−	12.0019i	−0.361215	−	0.625643i
$369$	1.98772	+	6.11757i	0.103476	+	0.318468i
$370$	7.29655	+	22.4565i	0.379329	+	1.16746i
$371$	1.00917	+	9.60160i	0.0523935	+	0.498490i
$372$	−6.37678	−	4.63301i	−0.330621	−	0.240210i
$373$	−8.39598	+	1.78462i	−0.434728	+	0.0924042i	−0.420077	−	0.907488i	$-0.637997\pi$
$373$	−8.39598	+	1.78462i	−0.434728	+	0.0924042i	−0.0146506	+	0.999893i	$0.504664\pi$
$374$	−0.874734	+	2.69215i	−0.0452314	+	0.139208i
$375$	−16.7060	+	51.4156i	−0.862692	+	2.65509i
$376$	−6.97614	−	3.10598i	−0.359767	−	0.160179i
$377$	−1.00606	−	1.74255i	−0.0518147	−	0.0897457i
$378$	−12.6289	−	21.8740i	−0.649563	−	1.12508i
$379$	−5.16268	−	2.29857i	−0.265189	−	0.118070i	0.269835	−	0.962907i	$-0.413031\pi$
$379$	−5.16268	−	2.29857i	−0.265189	−	0.118070i	−0.535024	+	0.844837i	$0.679697\pi$
$380$	0.788990	−	2.42826i	0.0404743	−	0.124567i
$381$	13.9524	−	42.9410i	0.714802	−	2.19994i
$382$	12.8464	−	2.73059i	0.657279	−	0.139709i
$383$	−7.82672	−	5.68644i	−0.399926	−	0.290564i	0.369585	−	0.929197i	$-0.379500\pi$
$383$	−7.82672	−	5.68644i	−0.399926	−	0.290564i	−0.769511	+	0.638634i	$0.779500\pi$
$384$	0.838270	+	7.97561i	0.0427778	+	0.407003i
$385$	14.8588	+	45.7307i	0.757274	+	2.33065i
$386$	7.50277	+	23.0911i	0.381881	+	1.17531i
$387$	10.7501	+	18.6198i	0.546460	+	0.946496i
$388$	−0.271970	−	0.837036i	−0.0138072	−	0.0424941i
$389$	−8.84098			−0.448255			−0.224128	−	0.974560i	$-0.571953\pi$
$389$	−8.84098			−0.448255			−0.224128	+	0.974560i	$0.571953\pi$
$390$	2.94967	−	1.31328i	0.149362	−	0.0665004i
$391$	−3.88202	+	4.31142i	−0.196322	+	0.218038i
$392$	5.14053	−	48.9089i	0.259636	−	2.47027i
$393$	−6.01780	−	18.5209i	−0.303558	−	0.934255i
$394$	26.0710			1.31344
$395$	−11.8661	+	5.28312i	−0.597047	+	0.265823i
$396$	−6.38294	+	4.63748i	−0.320755	+	0.233042i
$397$	5.21231	+	5.78885i	0.261598	+	0.290534i	0.859607	−	0.510955i	$-0.170708\pi$
$397$	5.21231	+	5.78885i	0.261598	+	0.290534i	−0.598009	+	0.801489i	$0.704041\pi$
$398$	2.80926	+	1.25076i	0.140815	+	0.0626951i
$399$	12.9944	+	2.76203i	0.650531	+	0.138275i
$400$	18.3222	+	13.3119i	0.916111	+	0.665593i
$401$	0.857082	+	8.15459i	0.0428006	+	0.407221i	0.994856	+	0.101296i	$0.0322989\pi$
$401$	0.857082	+	8.15459i	0.0428006	+	0.407221i	−0.952056	+	0.305925i	$0.901034\pi$
$402$	−6.57816	+	2.92878i	−0.328089	+	0.146074i
$403$	0.912428	+	0.662917i	0.0454513	+	0.0330223i
$404$	−0.894171	+	8.50746i	−0.0444866	+	0.423262i
$405$	0.552144	+	5.25330i	0.0274362	+	0.261038i
$406$	39.3036	+	17.4991i	1.95061	+	0.868466i
$407$	6.79408	+	11.7677i	0.336770	+	0.583303i
$408$	7.34311	−	3.26936i	0.363538	−	0.161858i
$409$	−17.6820	−	12.8467i	−0.874318	−	0.635229i	0.0574238	−	0.998350i	$-0.481711\pi$
$409$	−17.6820	−	12.8467i	−0.874318	−	0.635229i	−0.931742	+	0.363120i	$0.881711\pi$
$410$	4.16559	−	4.62636i	0.205724	−	0.228480i
$411$	−11.6702	+	12.9610i	−0.575647	+	0.639321i
$412$	7.70167	−	5.59559i	0.379434	−	0.275675i
$413$	−16.3072	−	18.1110i	−0.802427	−	0.891185i
$414$	32.3545	−	6.87716i	1.59014	−	0.337994i
$415$	−6.94262	+	12.0250i	−0.340800	+	0.590282i
$416$	0.0962488	+	0.915746i	0.00471898	+	0.0448981i
$417$	−29.4195	+	6.25330i	−1.44068	+	0.306225i
$418$	−0.314169	+	2.98912i	−0.0153665	+	0.146203i
$419$	13.2807	−	14.7497i	0.648806	−	0.720572i	−0.325565	−	0.945520i	$-0.605555\pi$
$419$	13.2807	−	14.7497i	0.648806	−	0.720572i	0.974371	+	0.224948i	$0.0722212\pi$
$420$	16.8752	−	29.2286i	0.823424	−	1.42621i
$421$	−10.3718	−	17.9645i	−0.505491	−	0.875537i	−0.999980	−	0.00635262i	$-0.997978\pi$
$421$	−10.3718	−	17.9645i	−0.505491	−	0.875537i	0.494488	−	0.869184i	$-0.335355\pi$
$422$	−11.9010	−	2.52964i	−0.579333	−	0.123141i
$423$	7.70740	−	8.55994i	0.374747	−	0.416198i
$424$	5.01790	+	3.64572i	0.243691	+	0.177052i
$425$	2.92975	−	9.01684i	0.142114	−	0.437381i
$426$	−12.6703	−	38.9953i	−0.613880	−	1.88933i
$427$	−14.8921	+	10.8197i	−0.720678	+	0.523603i
$428$	−1.10893	+	10.5507i	−0.0536020	+	0.509989i
$429$	1.50323	−	1.09216i	0.0725768	−	0.0527301i
$430$	10.4042	−	18.0205i	0.501734	−	0.869028i
$431$	3.97257	−	37.7965i	0.191352	−	1.82059i	−0.304868	−	0.952395i	$-0.598612\pi$
$431$	3.97257	−	37.7965i	0.191352	−	1.82059i	0.496220	−	0.868197i	$-0.334721\pi$
$432$	−10.0308	−	2.13212i	−0.482609	−	0.102582i
$433$	11.3270	−	34.8610i	0.544342	−	1.67531i	−0.178206	−	0.983993i	$-0.557029\pi$
$433$	11.3270	−	34.8610i	0.544342	−	1.67531i	0.722548	−	0.691321i	$-0.242971\pi$
$434$	−24.1151			−1.15756
$435$	55.5716	+	61.7185i	2.66446	+	2.95918i
$436$	4.07717	+	0.866628i	0.195261	+	0.0415040i
$437$	−3.08001	+	5.33474i	−0.147337	+	0.255195i
$438$	−9.37239	−	1.99216i	−0.447830	−	0.0951893i
$439$	−24.2132	+	5.14668i	−1.15563	+	0.245638i	−0.745576	−	0.666421i	$-0.767825\pi$
$439$	−24.2132	+	5.14668i	−1.15563	+	0.245638i	−0.410059	+	0.912059i	$0.634492\pi$
$440$	28.2206	+	12.5646i	1.34536	+	0.598995i
$441$	67.7666	+	30.1716i	3.22698	+	1.43674i
$442$	−0.259715	+	0.115633i	−0.0123534	+	0.00550008i
$443$	−3.71721	+	0.790117i	−0.176610	+	0.0375396i	−0.295368	−	0.955384i	$-0.595442\pi$
$443$	−3.71721	+	0.790117i	−0.176610	+	0.0375396i	0.118758	+	0.992923i	$0.462109\pi$
$444$	2.94727	−	9.07076i	0.139871	−	0.430479i
$445$	47.7068			2.26152
$446$	−14.3713	−	15.9609i	−0.680500	−	0.755771i
$447$	−0.234089	−	2.22720i	−0.0110720	−	0.105343i
$448$	−27.6402	−	30.6976i	−1.30588	−	1.45032i
$449$	11.3924	+	19.7322i	0.537641	+	0.931221i	0.999031	+	0.0440234i	$0.0140176\pi$
$449$	11.3924	+	19.7322i	0.537641	+	0.931221i	−0.461390	+	0.887197i	$0.652649\pi$
$450$	−43.7309	+	31.7724i	−2.06150	+	1.49776i
$451$	1.79127	−	3.10257i	0.0843477	−	0.146094i
$452$	−9.48692			−0.446227
$453$	13.9851	+	30.9635i	0.657079	+	1.45479i
$454$	−10.1744			−0.477508
$455$	−2.41460	+	4.18220i	−0.113198	+	0.196065i
$456$	6.90467	−	5.01653i	0.323341	−	0.234921i
$457$	13.3911	+	23.1940i	0.626408	+	1.08497i	0.988267	+	0.152737i	$0.0488088\pi$
$457$	13.3911	+	23.1940i	0.626408	+	1.08497i	−0.361859	+	0.932233i	$0.617858\pi$
$458$	20.1973	+	22.4313i	0.943756	+	1.04815i
$459$	0.448740	+	4.26948i	0.0209454	+	0.199282i
$460$	10.4718	+	11.6301i	0.488250	+	0.542256i
$461$	39.3473			1.83259			0.916294	−	0.400505i	$-0.131165\pi$
$461$	39.3473			1.83259			0.916294	+	0.400505i	$0.131165\pi$
$462$	−12.2772	+	37.7854i	−0.571188	+	1.75793i
$463$	3.07085	−	0.652730i	0.142715	−	0.0303349i	−0.136000	−	0.990709i	$-0.543425\pi$
$463$	3.07085	−	0.652730i	0.142715	−	0.0303349i	0.278715	+	0.960374i	$0.410092\pi$
$464$	15.9576	−	7.10480i	0.740815	−	0.329832i
$465$	−42.5265	−	18.9340i	−1.97212	−	0.878043i
$466$	−5.49570	−	2.44684i	−0.254583	−	0.113348i
$467$	1.96551	−	0.417783i	0.0909531	−	0.0193327i	−0.162210	−	0.986756i	$-0.551862\pi$
$467$	1.96551	−	0.417783i	0.0909531	−	0.0193327i	0.253163	+	0.967424i	$0.418529\pi$
$468$	−0.775070	−	0.164746i	−0.0358276	−	0.00761539i
$469$	5.38487	−	9.32687i	0.248650	−	0.430675i
$470$	−10.9042	−	2.31777i	−0.502975	−	0.106911i
$471$	−26.0113	−	28.8885i	−1.19854	−	1.33111i
$472$	−15.6568			−0.720665
$473$	3.70037	−	11.3886i	0.170143	−	0.523647i
$474$	−10.4978	−	2.23137i	−0.482179	−	0.102490i
$475$	1.05225	−	10.0115i	0.0482804	−	0.459357i
$476$	−1.48584	+	2.57355i	−0.0681033	+	0.117958i
$477$	−7.56892	+	5.49914i	−0.346557	+	0.251788i
$478$	−2.20572	+	20.9860i	−0.100887	+	0.959879i
$479$	−30.0524	+	21.8343i	−1.37313	+	0.997635i	−0.375642	+	0.926765i	$0.622578\pi$
$479$	−30.0524	+	21.8343i	−1.37313	+	0.997635i	−0.997486	+	0.0708705i	$0.977422\pi$
$480$	−11.7444	−	36.1456i	−0.536057	−	1.64981i
$481$	−0.421712	+	1.29790i	−0.0192284	+	0.0591790i
$482$	−6.43319	−	4.67399i	−0.293024	−	0.212894i
$483$	−54.4856	+	60.5124i	−2.47918	+	2.75341i
$484$	−2.76756	−	0.588263i	−0.125798	−	0.0267392i
$485$	−2.59892	−	4.50146i	−0.118011	−	0.204401i
$486$	−10.0871	+	17.4714i	−0.457560	+	0.792518i
$487$	−4.57647	+	5.08269i	−0.207380	+	0.230319i	−0.837858	−	0.545888i	$-0.816192\pi$
$487$	−4.57647	+	5.08269i	−0.207380	+	0.230319i	0.630478	+	0.776207i	$0.282859\pi$
$488$	−1.23614	+	11.7611i	−0.0559573	+	0.532398i
$489$	38.3642	−	8.15457i	1.73489	−	0.368762i
$490$	−7.50436	−	71.3992i	−0.339013	−	3.22549i
$491$	7.49949	−	12.9895i	0.338447	−	0.586207i	−0.645694	−	0.763596i	$-0.723432\pi$
$491$	7.49949	−	12.9895i	0.338447	−	0.586207i	0.984141	+	0.177389i	$0.0567651\pi$
$492$	−2.45965	+	0.522814i	−0.110889	+	0.0235703i
$493$	−4.89302	−	5.43425i	−0.220370	−	0.244746i
$494$	−0.244208	+	0.177427i	−0.0109874	+	0.00798284i
$495$	−31.1788	+	34.6275i	−1.40138	+	1.55639i
$496$	−6.55143	+	7.27610i	−0.294168	+	0.326707i
$497$	49.6129	+	36.0459i	2.22544	+	1.61688i
$498$	−10.4809	+	4.66641i	−0.469661	+	0.209107i
$499$	15.8997	+	27.5392i	0.711770	+	1.23282i	0.964192	+	0.265205i	$0.0854395\pi$
$499$	15.8997	+	27.5392i	0.711770	+	1.23282i	−0.252422	+	0.967617i	$0.581227\pi$
$500$	−11.7302	−	5.22262i	−0.524591	−	0.233563i
$501$	5.46999	+	52.0435i	0.244381	+	2.32513i
$502$	0.958325	−	9.11786i	0.0427721	−	0.406950i
$503$	−9.56710	−	6.95090i	−0.426576	−	0.309926i	0.353702	−	0.935358i	$-0.384923\pi$
$503$	−9.56710	−	6.95090i	−0.426576	−	0.309926i	−0.780278	+	0.625432i	$0.784923\pi$
$504$	62.6173	−	27.8790i	2.78920	−	1.24183i
$505$	5.28087	+	50.2441i	0.234996	+	2.23583i
$506$	−14.9041	−	10.8285i	−0.662570	−	0.481385i
$507$	−34.9754	−	7.43424i	−1.55331	−	0.330166i
$508$	9.79677	+	4.36180i	0.434661	+	0.193524i
$509$	24.8722	+	27.6233i	1.10244	+	1.22438i	0.972510	+	0.232860i	$0.0748084\pi$
$509$	24.8722	+	27.6233i	1.10244	+	1.22438i	0.129929	+	0.991523i	$0.458525\pi$
$510$	9.49321	−	6.89722i	0.420366	−	0.305414i
$511$	13.0920	−	5.82896i	0.579158	−	0.257858i
$512$	−21.8828			−0.967094
$513$	1.40857	+	4.33513i	0.0621898	+	0.191401i
$514$	1.65485	−	15.7448i	0.0729921	−	0.694474i
$515$	37.6204	−	41.7817i	1.65775	−	1.84112i
$516$	−7.67838	+	3.41864i	−0.338022	+	0.150497i
$517$	−6.41529			−0.282144
$518$	−9.01706	−	27.7516i	−0.396187	−	1.21934i
$519$	−4.69258	−	8.12778i	−0.205981	−	0.356770i
$520$	0.958720	+	2.95064i	0.0420426	+	0.129394i
$521$	−3.52993	−	10.8640i	−0.154649	−	0.475961i	0.843476	−	0.537167i	$-0.180505\pi$
$521$	−3.52993	−	10.8640i	−0.154649	−	0.475961i	−0.998125	+	0.0612057i	$0.980505\pi$
$522$	4.35796	+	41.4633i	0.190743	+	1.81480i
$523$	−31.8480	−	23.1389i	−1.39262	−	1.01179i	−0.995573	−	0.0939937i	$-0.970037\pi$
$523$	−31.8480	−	23.1389i	−1.39262	−	1.01179i	−0.397042	−	0.917800i	$-0.629963\pi$
$524$	4.52425	−	0.961658i	0.197643	−	0.0420102i
$525$	41.1201	−	126.555i	1.79463	−	5.52330i
$526$	−3.50257	+	10.7798i	−0.152719	+	0.470021i
$527$	3.74441	+	1.66712i	0.163109	+	0.0726208i
$528$	8.06536	+	13.9696i	0.351000	+	0.607949i
$529$	−7.37873	−	12.7803i	−0.320815	−	0.555667i
$530$	8.27180	+	3.68284i	0.359304	+	0.159972i
$531$	7.29791	−	22.4607i	0.316702	−	0.974710i
$532$	−0.975033	+	3.00084i	−0.0422730	+	0.130103i
$533$	0.351940	−	0.0748073i	0.0152442	−	0.00324026i
$534$	31.8900	+	23.1694i	1.38001	+	1.00264i
$535$	6.54920	+	62.3115i	0.283147	+	2.69396i
$536$	−2.13807	−	6.58031i	−0.0923507	−	0.284226i
$537$	14.2683	+	43.9133i	0.615722	+	1.89500i
$538$	7.00195	+	12.1277i	0.301875	+	0.522863i
$539$	−12.7669	−	39.2926i	−0.549911	−	1.69245i
$540$	11.5804			0.498341
$541$	−16.5901	+	7.38638i	−0.713263	+	0.317565i	−0.731095	−	0.682276i	$-0.760990\pi$
$541$	−16.5901	+	7.38638i	−0.713263	+	0.317565i	0.0178318	+	0.999841i	$0.494324\pi$
$542$	1.55161	−	1.72323i	0.0666472	−	0.0740192i
$543$	−1.43697	+	13.6718i	−0.0616661	+	0.586714i
$544$	1.03408	+	3.18258i	0.0443359	+	0.136452i
$545$	24.6172			1.05449
$546$	−3.64520	+	1.62295i	−0.156000	+	0.0694557i
$547$	−17.0916	+	12.4178i	−0.730784	+	0.530946i	−0.889811	−	0.456329i	$-0.849164\pi$
$547$	−17.0916	+	12.4178i	−0.730784	+	0.530946i	0.159027	+	0.987274i	$0.449164\pi$
$548$	−2.77181	−	3.07841i	−0.118406	−	0.131503i
$549$	−16.2958	−	7.25534i	−0.695486	−	0.309650i
$550$	29.4479	+	6.25935i	1.25566	+	0.266900i
$551$	−6.28143	−	4.56373i	−0.267598	−	0.194421i
$552$	5.46815	+	52.0259i	0.232740	+	2.21437i
$553$	14.6641	−	6.52887i	0.623580	−	0.277636i
$554$	18.9832	+	13.7921i	0.806519	+	0.585970i
$555$	5.88785	−	56.0192i	0.249925	−	2.37788i
$556$	−0.746709	−	7.10446i	−0.0316675	−	0.301296i
$557$	−18.7520	−	8.34891i	−0.794546	−	0.353755i	−0.0310094	−	0.999519i	$-0.509872\pi$
$557$	−18.7520	−	8.34891i	−0.794546	−	0.353755i	−0.763537	+	0.645764i	$0.776539\pi$
$558$	−11.6844	−	20.2380i	−0.494640	−	0.856741i
$559$	1.09867	−	0.489159i	0.0464687	−	0.0206892i
$560$	−33.9170	−	24.6421i	−1.43325	−	1.04132i
$561$	4.51848	−	5.01828i	0.190770	−	0.211872i
$562$	−5.56016	+	6.17518i	−0.234541	+	0.260484i
$563$	−13.0432	+	9.47646i	−0.549707	+	0.399385i	−0.827677	−	0.561204i	$-0.810338\pi$
$563$	−13.0432	+	9.47646i	−0.549707	+	0.399385i	0.277971	+	0.960590i	$0.410338\pi$
$564$	3.01303	+	3.34631i	0.126872	+	0.140905i
$565$	−54.8043	+	11.6490i	−2.30563	+	0.490078i
$566$	−5.73733	+	9.93734i	−0.241158	+	0.417698i
$567$	−0.682338	−	6.49201i	−0.0286555	−	0.272639i
$568$	38.5369	−	8.19126i	1.61697	−	0.343698i
$569$	2.98359	−	28.3870i	0.125079	−	1.19004i	−0.734344	−	0.678777i	$-0.762510\pi$
$569$	2.98359	−	28.3870i	0.125079	−	1.19004i	0.859423	−	0.511266i	$-0.170823\pi$
$570$	8.33684	−	9.25900i	0.349192	−	0.387817i
$571$	7.67617	−	13.2955i	0.321238	−	0.556400i	−0.659506	−	0.751699i	$-0.729235\pi$
$571$	7.67617	−	13.2955i	0.321238	−	0.556400i	0.980744	+	0.195299i	$0.0625678\pi$
$572$	0.220661	+	0.382196i	0.00922630	+	0.0159804i
$573$	−30.6457	−	6.51393i	−1.28024	−	0.272124i
$574$	−5.14783	+	5.71724i	−0.214866	+	0.238633i
$575$	49.9185	+	36.2679i	2.08174	+	1.51248i
$576$	12.3697	−	38.0701i	0.515405	−	1.58625i
$577$	5.20565	+	16.0213i	0.216714	+	0.666977i	0.999027	+	0.0440920i	$0.0140395\pi$
$577$	5.20565	+	16.0213i	0.216714	+	0.666977i	−0.782314	+	0.622885i	$0.785961\pi$
$578$	15.1044	−	10.9740i	0.628258	−	0.456456i
$579$	6.05426	−	57.6024i	0.251606	−	2.39388i
$580$	−15.9583	+	11.5944i	−0.662632	+	0.481430i
$581$	8.57967	−	14.8604i	0.355945	−	0.616514i
$582$	0.448925	−	4.27124i	0.0186085	−	0.177048i
$583$	5.09682	+	1.08336i	0.211089	+	0.0448683i
$584$	2.84508	−	8.75626i	0.117730	−	0.362336i
$585$	−4.67974			−0.193483
$586$	−11.7491	−	13.0487i	−0.485350	−	0.539036i
$587$	−22.4780	−	4.77786i	−0.927768	−	0.197203i	−0.280840	−	0.959755i	$-0.590613\pi$
$587$	−22.4780	−	4.77786i	−0.927768	−	0.197203i	−0.646928	+	0.762551i	$0.723946\pi$
$588$	−14.4994	+	25.1138i	−0.597947	+	1.03567i
$589$	4.25689	+	0.904830i	0.175402	+	0.0372829i
$590$	−22.3570	+	4.75214i	−0.920425	+	0.195642i
$591$	−56.8166	−	25.2964i	−2.33712	−	1.04055i
$592$	−10.8230	−	4.81872i	−0.444824	−	0.198048i
$593$	0.638564	−	0.284307i	0.0262227	−	0.0116751i	−0.393583	−	0.919289i	$-0.628765\pi$
$593$	0.638564	−	0.284307i	0.0262227	−	0.0116751i	0.419806	+	0.907614i	$0.362098\pi$
$594$	−13.3342	+	2.83427i	−0.547109	+	0.116292i
$595$	−5.42337	+	16.6914i	−0.222336	+	0.684281i
$596$	0.531903			0.0217876
$597$	−4.90863	−	5.45158i	−0.200897	−	0.223118i
$598$	−0.193400	−	1.84008i	−0.00790873	−	0.0752465i
$599$	−14.2507	−	15.8270i	−0.582267	−	0.646673i	0.377983	−	0.925812i	$-0.376618\pi$
$599$	−14.2507	−	15.8270i	−0.582267	−	0.646673i	−0.960251	+	0.279139i	$0.909951\pi$
$600$	−42.7441	−	74.0350i	−1.74502	−	3.02247i
$601$	−7.68765	+	5.58541i	−0.313586	+	0.227834i	−0.733434	−	0.679761i	$-0.762083\pi$
$601$	−7.68765	+	5.58541i	−0.313586	+	0.227834i	0.419848	+	0.907595i	$0.362083\pi$
$602$	−12.8575	+	22.2698i	−0.524031	+	0.907648i
$603$	10.4364			0.425004
$604$	−7.66114	+	2.53472i	−0.311727	+	0.103136i
$605$	−16.7100			−0.679360
$606$	−20.8717	+	36.1508i	−0.847853	+	1.46853i
$607$	−7.34942	+	5.33966i	−0.298304	+	0.216730i	−0.726862	−	0.686784i	$-0.759022\pi$
$607$	−7.34942	+	5.33966i	−0.298304	+	0.216730i	0.428558	+	0.903514i	$0.359022\pi$
$608$	1.77655	+	3.07708i	0.0720487	+	0.124792i
$609$	−68.6753	−	76.2717i	−2.78286	−	3.09068i
$610$	1.80456	+	17.1693i	0.0730647	+	0.695164i
$611$	−0.431122	−	0.478810i	−0.0174413	−	0.0193706i
$612$	−2.87971			−0.116405
$613$	−9.20147	+	28.3192i	−0.371644	+	1.14380i	0.574071	+	0.818806i	$0.305363\pi$
$613$	−9.20147	+	28.3192i	−0.371644	+	1.14380i	−0.945715	+	0.324997i	$0.894637\pi$
$614$	20.9599	−	4.45516i	0.845872	−	0.179796i
$615$	−13.5670	+	6.04041i	−0.547074	+	0.243573i
$616$	−34.8750	−	15.5273i	−1.40515	−	0.625614i
$617$	10.4998	+	4.67481i	0.422706	+	0.188201i	0.607055	−	0.794660i	$-0.292351\pi$
$617$	10.4998	+	4.67481i	0.422706	+	0.188201i	−0.184349	+	0.982861i	$0.559018\pi$
$618$	45.4394	−	9.65845i	1.82784	−	0.388520i
$619$	45.2211	+	9.61205i	1.81759	+	0.386341i	0.985688	−	0.168580i	$-0.0539181\pi$
$619$	45.2211	+	9.61205i	1.81759	+	0.386341i	0.831903	+	0.554921i	$0.187251\pi$
$620$	5.52823	−	9.57517i	0.222019	−	0.384548i
$621$	−27.3288	−	5.80892i	−1.09667	−	0.233104i
$622$	−21.8969	−	24.3190i	−0.877985	−	0.975101i
$623$	−58.9559			−2.36202
$624$	−0.500621	+	1.54075i	−0.0200409	+	0.0616795i
$625$	−25.0655	−	5.32784i	−1.00262	−	0.213114i
$626$	−2.08241	+	19.8128i	−0.0832297	+	0.791877i
$627$	3.58498	−	6.20936i	0.143170	−	0.247978i
$628$	7.46958	−	5.42697i	0.298069	−	0.216560i
$629$	−0.518419	+	4.93242i	−0.0206707	+	0.196669i
$630$	80.9520	−	58.8151i	3.22520	−	2.34325i
$631$	10.3801	+	31.9466i	0.413224	+	1.27177i	0.913830	+	0.406097i	$0.133111\pi$
$631$	10.3801	+	31.9466i	0.413224	+	1.27177i	−0.500606	+	0.865675i	$0.666889\pi$
$632$	3.18670	−	9.80767i	0.126760	−	0.390128i
$633$	23.4814	+	17.0603i	0.933303	+	0.678085i
$634$	5.45994	−	6.06388i	0.216842	−	0.240828i
$635$	61.9501	+	13.1679i	2.45842	+	0.522552i
$636$	−1.82870	−	3.16740i	−0.0725126	−	0.125596i
$637$	2.07467	−	3.59343i	0.0822013	−	0.142377i
$638$	15.5374	−	17.2561i	0.615133	−	0.683174i
$639$	−6.21182	+	59.1015i	−0.245736	+	2.33802i
$640$	−11.0034	+	2.33884i	−0.434946	+	0.0924506i
$641$	3.15435	+	30.0116i	0.124589	+	1.18539i	0.860911	+	0.508756i	$0.169895\pi$
$641$	3.15435	+	30.0116i	0.124589	+	1.18539i	−0.736321	+	0.676632i	$0.763439\pi$
$642$	−25.8845	+	44.8333i	−1.02158	+	1.76943i
$643$	−5.17411	+	1.09979i	−0.204047	+	0.0433715i	−0.308801	−	0.951127i	$-0.599928\pi$
$643$	−5.17411	+	1.09979i	−0.204047	+	0.0433715i	0.104754	+	0.994498i	$0.466594\pi$
$644$	−12.9410	−	14.3725i	−0.509947	−	0.566354i
$645$	−40.1590	+	29.1772i	−1.58126	+	1.14885i
$646$	−0.734049	+	0.815244i	−0.0288808	+	0.0320754i
$647$	7.10586	−	7.89185i	0.279360	−	0.310261i	−0.587093	−	0.809520i	$-0.699728\pi$
$647$	7.10586	−	7.89185i	0.279360	−	0.310261i	0.866453	+	0.499259i	$0.166394\pi$
$648$	−3.39279	−	2.46501i	−0.133282	−	0.0968347i
$649$	−12.0162	+	5.34994i	−0.471675	+	0.210003i
$650$	1.51180	+	2.61851i	0.0592976	+	0.102706i
$651$	52.5541	+	23.3986i	2.05976	+	0.917064i
$652$	0.973741	+	9.26452i	0.0381346	+	0.362827i
$653$	−2.07023	+	19.6970i	−0.0810145	+	0.770802i	0.876302	+	0.481761i	$0.160003\pi$
$653$	−2.07023	+	19.6970i	−0.0810145	+	0.770802i	−0.957317	+	0.289040i	$0.906664\pi$
$654$	16.4556	+	11.9557i	0.643464	+	0.467504i
$655$	24.9550	−	11.1107i	0.975071	−	0.434130i
$656$	0.326501	+	3.10645i	0.0127477	+	0.121286i
$657$	11.2352	+	8.16287i	0.438328	+	0.318464i
$658$	13.4754	+	2.86429i	0.525327	+	0.111662i
$659$	−37.5460	−	16.7166i	−1.46258	−	0.651184i	−0.487521	−	0.873111i	$-0.662099\pi$
$659$	−37.5460	−	16.7166i	−1.46258	−	0.651184i	−0.975063	+	0.221927i	$0.928765\pi$
$660$	−12.1886	−	13.5368i	−0.474442	−	0.526921i
$661$	32.6337	−	23.7098i	1.26930	−	0.922204i	0.270130	−	0.962824i	$-0.412933\pi$
$661$	32.6337	−	23.7098i	1.26930	−	0.922204i	0.999175	+	0.0406199i	$0.0129333\pi$
$662$	34.4915	−	15.3566i	1.34055	−	0.596852i
$663$	0.678195			0.0263389
$664$	−3.40657	−	10.4844i	−0.132201	−	0.406872i
$665$	−1.94785	+	18.5326i	−0.0755345	+	0.718663i
$666$	18.9208	−	21.0137i	0.733167	−	0.814265i
$667$	43.4762	−	19.3569i	1.68341	−	0.749501i
$668$	−12.4291			−0.480895
$669$	15.8327	+	48.7279i	0.612126	+	1.88393i
$670$	−5.05028	−	8.74735i	−0.195109	−	0.337939i
$671$	3.07005	+	9.44865i	0.118518	+	0.364761i
$672$	14.5137	+	44.6686i	0.559879	+	1.72313i
$673$	−1.37074	−	13.0417i	−0.0528381	−	0.502721i	−0.988652	−	0.150226i	$-0.952000\pi$
$673$	−1.37074	−	13.0417i	−0.0528381	−	0.502721i	0.935814	−	0.352495i	$-0.114667\pi$
$674$	9.51388	+	6.91224i	0.366461	+	0.266249i
$675$	44.6603	−	9.49284i	1.71898	−	0.365379i
$676$	2.62438	−	8.07701i	0.100938	−	0.310654i
$677$	−7.06332	+	21.7387i	−0.271466	+	0.835485i	0.718667	+	0.695354i	$0.244752\pi$
$677$	−7.06332	+	21.7387i	−0.271466	+	0.835485i	−0.990133	+	0.140131i	$0.955248\pi$
$678$	−42.2918	−	18.8295i	−1.62421	−	0.723144i
$679$	3.21174	+	5.56290i	0.123255	+	0.213485i
$680$	5.63756	+	9.76455i	0.216191	+	0.374453i
$681$	22.1731	+	9.87210i	0.849675	+	0.378300i
$682$	−4.02196	+	12.3783i	−0.154009	+	0.473990i
$683$	−1.15554	+	3.55639i	−0.0442156	+	0.136082i	−0.970727	−	0.240184i	$-0.922792\pi$
$683$	−1.15554	+	3.55639i	−0.0442156	+	0.136082i	0.926512	+	0.376266i	$0.122792\pi$
$684$	−2.99080	+	0.635715i	−0.114356	+	0.0243072i
$685$	−19.7923	−	14.3799i	−0.756224	−	0.549429i
$686$	5.20930	+	49.5632i	0.198892	+	1.89233i
$687$	−22.2511	−	68.4818i	−0.848932	−	2.61275i
$688$	3.22629	+	9.92950i	0.123001	+	0.378559i
$689$	0.261661	+	0.453210i	0.00996848	+	0.0172659i
$690$	23.5990	+	72.6302i	0.898398	+	2.76499i
$691$	5.44548			0.207156			0.103578	−	0.994621i	$-0.466971\pi$
$691$	5.44548			0.207156			0.103578	+	0.994621i	$0.466971\pi$
$692$	2.03638	−	0.906654i	0.0774115	−	0.0344658i
$693$	38.5307	−	42.7926i	1.46366	−	1.62556i
$694$	−0.346284	+	3.29467i	−0.0131447	+	0.125064i
$695$	−13.0372	−	40.1244i	−0.494529	−	1.52200i
$696$	−65.9363			−2.49931
$697$	1.19456	−	0.531851i	0.0452471	−	0.0201453i
$698$	4.49745	−	3.26759i	0.170231	−	0.123680i
$699$	9.60265	+	10.6648i	0.363205	+	0.403381i
$700$	28.8728	+	12.8550i	1.09129	+	0.485873i
$701$	−30.3546	−	6.45207i	−1.14648	−	0.243691i	−0.404772	−	0.914418i	$-0.632649\pi$
$701$	−30.3546	−	6.45207i	−1.14648	−	0.243691i	−0.741705	+	0.670726i	$0.765982\pi$
$702$	−1.10763	−	0.804739i	−0.0418047	−	0.0303729i
$703$	0.550447	+	5.23716i	0.0207605	+	0.197523i
$704$	−20.3670	+	9.06797i	−0.767610	+	0.341762i
$705$	21.5147	+	15.6314i	0.810291	+	0.588711i
$706$	2.44505	−	23.2631i	0.0920208	−	0.875520i
$707$	−6.52609	−	62.0916i	−0.245439	−	2.33519i
$708$	8.43417	+	3.75513i	0.316976	+	0.141127i
$709$	20.7086	+	35.8683i	0.777726	+	1.34706i	0.933250	+	0.359229i	$0.116960\pi$
$709$	20.7086	+	35.8683i	0.777726	+	1.34706i	−0.155524	+	0.987832i	$0.549706\pi$
$710$	52.5421	−	23.3933i	1.97187	−	0.877934i
$711$	12.5843	+	9.14303i	0.471948	+	0.342890i
$712$	−25.3439	+	28.1472i	−0.949802	+	1.05486i
$713$	−17.8492	+	19.8236i	−0.668459	+	0.742399i
$714$	−11.7317	+	8.52357i	−0.439048	+	0.318987i
$715$	1.74402	+	1.93693i	0.0652226	+	0.0724371i
$716$	−10.7271	+	2.28011i	−0.400889	+	0.0852116i
$717$	25.1694	−	43.5947i	0.939970	−	1.62808i
$718$	2.91047	+	27.6913i	0.108618	+	1.03343i
$719$	36.4390	−	7.74536i	1.35895	−	0.288853i	0.529913	−	0.848052i	$-0.322224\pi$
$719$	36.4390	−	7.74536i	1.35895	−	0.288853i	0.829034	+	0.559199i	$0.188891\pi$
$720$	4.24659	−	40.4036i	0.158261	−	1.50575i
$721$	−46.4912	+	51.6337i	−1.73142	+	1.92294i
$722$	10.4282	−	18.0622i	0.388098	−	0.672205i
$723$	9.48475	+	16.4281i	0.352742	+	0.610967i
$724$	−3.19377	−	0.678856i	−0.118695	−	0.0252295i
$725$	−52.0395	+	57.7958i	−1.93270	+	2.14648i
$726$	−11.1700	−	8.11545i	−0.414556	−	0.301193i
$727$	−10.5486	+	32.4654i	−0.391227	+	1.20407i	0.540634	+	0.841258i	$0.318185\pi$
$727$	−10.5486	+	32.4654i	−0.391227	+	1.20407i	−0.931861	+	0.362816i	$0.881815\pi$
$728$	−1.18478	−	3.64639i	−0.0439110	−	0.135144i
$729$	35.6295	−	25.8864i	1.31961	−	0.958754i
$730$	1.40492	−	13.3669i	0.0519985	−	0.494733i
$731$	3.53595	−	2.56902i	0.130782	−	0.0950186i
$732$	3.48667	−	6.03908i	0.128871	−	0.223211i
$733$	0.167131	−	1.59015i	0.00617314	−	0.0587335i	−0.991002	−	0.133850i	$-0.957266\pi$
$733$	0.167131	−	1.59015i	0.00617314	−	0.0587335i	0.997175	+	0.0751161i	$0.0239327\pi$
$734$	−2.42040	−	0.514472i	−0.0893387	−	0.0189895i
$735$	−52.9235	+	162.882i	−1.95211	+	6.00799i
$736$	−21.7785			−0.802767
$737$	−3.88940	−	4.31961i	−0.143268	−	0.159115i
$738$	−7.29230	−	1.55003i	−0.268433	−	0.0570572i
$739$	5.91166	−	10.2393i	0.217464	−	0.376658i	−0.736568	−	0.676363i	$-0.763555\pi$
$739$	5.91166	−	10.2393i	0.217464	−	0.376658i	0.954032	+	0.299705i	$0.0968882\pi$
$740$	13.0862	+	2.78156i	0.481058	+	0.102252i
$741$	0.704359	−	0.149716i	0.0258753	−	0.00549996i
$742$	−10.2223	−	4.55125i	−0.375271	−	0.167082i
$743$	2.59892	+	1.15711i	0.0953450	+	0.0424503i	0.453855	−	0.891076i	$-0.350048\pi$
$743$	2.59892	+	1.15711i	0.0953450	+	0.0424503i	−0.358510	+	0.933526i	$0.616715\pi$
$744$	33.7630	−	15.0323i	1.23781	−	0.551110i
$745$	3.07271	−	0.653125i	0.112575	−	0.0239286i
$746$	3.07424	−	9.46153i	0.112556	−	0.346411i
$747$	16.6283			0.608397
$748$	1.07319	+	1.19190i	0.0392399	+	0.0435803i
$749$	−8.09349	−	77.0044i	−0.295730	−	2.81368i
$750$	−41.9264	−	46.5640i	−1.53094	−	1.70028i
$751$	−7.51898	−	13.0233i	−0.274371	−	0.475225i	0.695605	−	0.718425i	$-0.255136\pi$
$751$	−7.51898	−	13.0233i	−0.274371	−	0.475225i	−0.969976	+	0.243199i	$0.921803\pi$
$752$	4.52514	−	3.28770i	0.165015	−	0.119890i
$753$	−10.9354	+	18.9407i	−0.398509	+	0.690238i
$754$	2.33207			0.0849290
$755$	−41.1447	+	24.0498i	−1.49741	+	0.875262i
$756$	−14.3110			−0.520487
$757$	17.4821	−	30.2798i	0.635396	−	1.10054i	−0.351035	−	0.936362i	$-0.614170\pi$
$757$	17.4821	−	30.2798i	0.635396	−	1.10054i	0.986431	−	0.164176i	$-0.0524965\pi$
$758$	5.29896	−	3.84992i	0.192467	−	0.139835i
$759$	21.9739	+	38.0599i	0.797601	+	1.38149i
$760$	8.01064	+	8.89672i	0.290577	+	0.322718i
$761$	2.72107	+	25.8892i	0.0986386	+	0.938484i	0.926181	+	0.377080i	$0.123072\pi$
$761$	2.72107	+	25.8892i	0.0986386	+	0.938484i	−0.827542	+	0.561404i	$0.810261\pi$
$762$	35.0159	+	38.8891i	1.26849	+	1.40880i
$763$	−30.4219			−1.10135
$764$	2.29950	−	7.07713i	0.0831930	−	0.256042i
$765$	−16.6356	+	3.53600i	−0.601461	+	0.127844i
$766$	10.2433	−	4.56061i	0.370105	−	0.164782i
$767$	−1.20681	−	0.537307i	−0.0435754	−	0.0194010i
$768$	35.0472	+	15.6040i	1.26466	+	0.563061i
$769$	41.7966	−	8.88413i	1.50722	−	0.320370i	0.621067	−	0.783758i	$-0.286699\pi$
$769$	41.7966	−	8.88413i	1.50722	−	0.320370i	0.886156	+	0.463387i	$0.153366\pi$
$770$	−54.5122	−	11.5869i	−1.96448	−	0.417564i
$771$	−18.8834	+	32.7070i	−0.680069	+	1.17791i
$772$	13.4560	+	2.86017i	0.484294	+	0.102940i
$773$	−6.04893	−	6.71802i	−0.217565	−	0.241630i	0.624476	−	0.781044i	$-0.285313\pi$
$773$	−6.04893	−	6.71802i	−0.217565	−	0.241630i	−0.842041	+	0.539414i	$0.818646\pi$
$774$	−24.9191			−0.895697
$775$	13.4708	−	41.4587i	0.483884	−	1.48924i
$776$	4.03654	+	0.857994i	0.144903	+	0.0308002i
$777$	−7.27620	+	69.2284i	−0.261032	+	2.48355i
$778$	5.12340	−	8.87399i	0.183683	−	0.318148i
$779$	1.12323	−	0.816076i	0.0402440	−	0.0292390i
$780$	0.191228	−	1.81941i	0.00684707	−	0.0651455i
$781$	26.7769	−	19.4546i	0.958154	−	0.696140i
$782$	−2.07786	−	6.39501i	−0.0743043	−	0.228685i
$783$	10.8822	−	33.4920i	0.388899	−	1.19691i
$784$	29.1421	+	21.1730i	1.04079	+	0.756177i
$785$	36.4867	−	40.5226i	1.30227	−	1.44631i
$786$	22.0774	+	4.69269i	0.787474	+	0.167383i
$787$	9.59893	+	16.6258i	0.342165	+	0.592647i	0.984835	−	0.173496i	$-0.0555065\pi$
$787$	9.59893	+	16.6258i	0.342165	+	0.592647i	−0.642670	+	0.766143i	$0.722173\pi$
$788$	7.38586	−	12.7927i	0.263111	−	0.455721i
$789$	18.0926	−	20.0939i	0.644115	−	0.715363i
$790$	1.57362	−	14.9720i	0.0559868	−	0.532679i
$791$	67.7270	−	14.3958i	2.40810	−	0.511857i
$792$	−3.86692	−	36.7913i	−0.137405	−	1.30732i
$793$	−0.498892	+	0.864107i	−0.0177162	+	0.0306853i
$794$	−8.83103	+	1.87709i	−0.313401	+	0.0666155i
$795$	−14.4533	−	16.0521i	−0.512607	−	0.569308i
$796$	1.40959	−	1.02413i	0.0499617	−	0.0362993i
$797$	−6.95942	+	7.72922i	−0.246515	+	0.273783i	−0.853686	−	0.520789i	$-0.825638\pi$
$797$	−6.95942	+	7.72922i	−0.246515	+	0.273783i	0.607170	+	0.794572i	$0.292305\pi$
$798$	−10.3027	+	11.4423i	−0.364710	+	0.405051i
$799$	−1.89435	−	1.37632i	−0.0670172	−	0.0486908i
$800$	32.5132	−	14.4758i	1.14951	−	0.511797i
$801$	−28.5657	−	49.4772i	−1.00932	−	1.74819i
$802$	−8.68172	−	3.86535i	−0.306562	−	0.136490i
$803$	−0.808496	−	7.69233i	−0.0285312	−	0.271456i
$804$	−0.426464	+	4.05754i	−0.0150402	+	0.143098i
$805$	−92.4060	−	67.1369i	−3.25688	−	2.36626i
$806$	−1.19415	+	0.531670i	−0.0420621	+	0.0187273i
$807$	−3.49197	−	33.2239i	−0.122923	−	1.16954i
$808$	−32.4497	−	23.5761i	−1.14158	−	0.829404i
$809$	5.42354	+	1.15281i	0.190681	+	0.0405306i	0.302262	−	0.953225i	$-0.402258\pi$
$809$	5.42354	+	1.15281i	0.190681	+	0.0405306i	−0.111581	+	0.993755i	$0.535591\pi$
$810$	−5.59288	−	2.49011i	−0.196514	−	0.0874936i
$811$	27.8269	+	30.9049i	0.977133	+	1.08522i	0.996347	+	0.0854012i	$0.0272172\pi$
$811$	27.8269	+	30.9049i	0.977133	+	1.08522i	−0.0192133	+	0.999815i	$0.506116\pi$
$812$	19.7212	−	14.3283i	0.692079	−	0.502825i
$813$	−5.05345	+	2.24994i	−0.177232	+	0.0789089i
$814$	−15.7488			−0.551996
$815$	17.0011	+	52.3239i	0.595521	+	1.83283i
$816$	−0.615423	+	5.85536i	−0.0215441	+	0.204978i
$817$	3.10524	−	3.44871i	0.108638	−	0.120655i
$818$	23.1415	−	10.3033i	0.809124	−	0.360245i
$819$	5.78321			0.202082
$820$	−1.08999	−	3.35464i	−0.0380641	−	0.117149i
$821$	20.3727	+	35.2866i	0.711013	+	1.23151i	0.964477	+	0.264166i	$0.0850966\pi$
$821$	20.3727	+	35.2866i	0.711013	+	1.23151i	−0.253464	+	0.967345i	$0.581570\pi$
$822$	−6.24650	−	19.2248i	−0.217872	−	0.670540i
$823$	−17.0220	−	52.3884i	−0.593351	−	1.82615i	−0.562770	−	0.826613i	$-0.690264\pi$
$823$	−17.0220	−	52.3884i	−0.593351	−	1.82615i	−0.0305805	−	0.999532i	$-0.509736\pi$
$824$	4.66583	+	44.3924i	0.162542	+	1.54648i
$825$	−58.1026	−	42.2140i	−2.02287	−	1.46970i
$826$	27.6288	−	5.87268i	0.961328	−	0.204337i
$827$	−7.06480	+	21.7432i	−0.245667	+	0.756086i	0.749859	+	0.661598i	$0.230121\pi$
$827$	−7.06480	+	21.7432i	−0.245667	+	0.756086i	−0.995526	+	0.0944882i	$0.969879\pi$
$828$	5.79144	−	17.8242i	0.201266	−	0.619434i
$829$	19.3936	+	8.63458i	0.673567	+	0.299891i	0.714872	−	0.699255i	$-0.246485\pi$
$829$	19.3936	+	8.63458i	0.673567	+	0.299891i	−0.0413049	+	0.999147i	$0.513152\pi$
$830$	−8.04657	−	13.9371i	−0.279301	−	0.483763i
$831$	−27.9878	−	48.4763i	−0.970887	−	1.68163i
$832$	−2.04550	−	0.910717i	−0.0709151	−	0.0315734i
$833$	4.65986	−	14.3416i	0.161455	−	0.496906i
$834$	10.7721	−	33.1531i	0.373008	−	1.14800i
$835$	−71.8006	+	15.2617i	−2.48476	+	0.528152i
$836$	1.37772	+	1.00097i	0.0476494	+	0.0346193i
$837$	2.06327	+	19.6307i	0.0713172	+	0.678537i
$838$	7.10855	+	21.8779i	0.245561	+	0.755758i
$839$	4.56942	+	14.0632i	0.157754	+	0.485517i	0.998430	−	0.0560224i	$-0.0178418\pi$
$839$	4.56942	+	14.0632i	0.157754	+	0.485517i	−0.840676	+	0.541539i	$0.817842\pi$
$840$	79.1253	+	137.049i	2.73008	+	4.72864i
$841$	9.57480	+	29.4682i	0.330166	+	1.01615i
$842$	24.0421			0.828546
$843$	18.1090	−	8.06264i	0.623706	−	0.277692i
$844$	−4.61280	+	5.12303i	−0.158779	+	0.176342i
$845$	5.24281	−	49.8820i	0.180358	−	1.71599i
$846$	4.12541	+	12.6967i	0.141835	+	0.436522i
$847$	20.6502			0.709551
$848$	−4.15034	+	1.84785i	−0.142523	+	0.0634554i
$849$	22.1455	−	16.0896i	0.760030	−	0.552194i
$850$	7.35270	+	8.16600i	0.252195	+	0.280091i
$851$	−29.4871	−	13.1285i	−1.01080	−	0.450039i
$852$	−22.7240	−	4.83013i	−0.778511	−	0.165478i
$853$	−1.57373	−	1.14338i	−0.0538835	−	0.0391487i	0.560517	−	0.828143i	$-0.310602\pi$
$853$	−1.57373	−	1.14338i	−0.0538835	−	0.0391487i	−0.614401	+	0.788994i	$0.710602\pi$
$854$	−2.23008	−	21.2178i	−0.0763117	−	0.726057i
$855$	−16.4968	+	7.34483i	−0.564177	+	0.251188i
$856$	−40.2433	−	29.2385i	−1.37549	−	0.999350i
$857$	4.13143	−	39.3079i	0.141127	−	1.34273i	−0.663154	−	0.748483i	$-0.730782\pi$
$857$	4.13143	−	39.3079i	0.141127	−	1.34273i	0.804281	−	0.594250i	$-0.202551\pi$
$858$	0.225108	+	2.14176i	0.00768507	+	0.0731185i
$859$	34.2494	+	15.2488i	1.16858	+	0.520284i	0.896955	−	0.442121i	$-0.145774\pi$
$859$	34.2494	+	15.2488i	1.16858	+	0.520284i	0.271620	+	0.962404i	$0.412440\pi$
$860$	−5.89497	−	10.2104i	−0.201017	−	0.348171i
$861$	16.7661	−	7.46473i	0.571386	−	0.254397i
$862$	35.6354	+	25.8907i	1.21375	+	0.881840i
$863$	22.0534	−	24.4928i	0.750708	−	0.833746i	−0.239854	−	0.970809i	$-0.577100\pi$
$863$	22.0534	−	24.4928i	0.750708	−	0.833746i	0.990562	+	0.137063i	$0.0437663\pi$
$864$	−10.7833	+	11.9761i	−0.366856	+	0.407435i
$865$	10.6505	−	7.73806i	0.362129	−	0.263102i
$866$	28.4271	+	31.5715i	0.965992	+	1.07284i
$867$	−43.5649	+	9.26000i	−1.47954	+	0.314486i
$868$	−6.83177	+	11.8330i	−0.231885	+	0.401637i
$869$	−0.905577	−	8.61599i	−0.0307196	−	0.292277i
$870$	−94.1531	+	20.0129i	−3.19209	+	0.678499i
$871$	0.0610210	−	0.580576i	0.00206762	−	0.0196721i
$872$	−13.0777	+	14.5243i	−0.442868	+	0.491854i
$873$	−3.11234	+	5.39074i	−0.105337	+	0.182449i
$874$	−3.56977	−	6.18302i	−0.120749	−	0.209144i
$875$	91.6669	+	19.4844i	3.09891	+	0.658693i
$876$	−3.63271	+	4.03453i	−0.122738	+	0.136314i
$877$	−37.1837	−	27.0155i	−1.25560	−	0.912250i	−0.257071	−	0.966393i	$-0.582757\pi$
$877$	−37.1837	−	27.0155i	−1.25560	−	0.912250i	−0.998533	+	0.0541429i	$0.982757\pi$
$878$	8.86582	−	27.2862i	0.299207	−	0.920864i
$879$	12.9438	+	39.8370i	0.436585	+	1.34367i
$880$	−18.3055	+	13.2998i	−0.617080	+	0.448335i
$881$	−2.20211	+	20.9517i	−0.0741910	+	0.705881i	0.892693	+	0.450665i	$0.148813\pi$
$881$	−2.20211	+	20.9517i	−0.0741910	+	0.705881i	−0.966884	+	0.255216i	$0.917854\pi$
$882$	−69.5554	+	50.5350i	−2.34205	+	1.70160i
$883$	−19.8043	+	34.3021i	−0.666469	+	1.15436i	0.312415	+	0.949946i	$0.398862\pi$
$883$	−19.8043	+	34.3021i	−0.666469	+	1.15436i	−0.978885	+	0.204413i	$0.934471\pi$
$884$	−0.0168374	+	0.160197i	−0.000566304	+	0.00538802i
$885$	53.3337	+	11.3364i	1.79279	+	0.381070i
$886$	1.36108	−	4.18896i	0.0457262	−	0.140731i
$887$	11.5371			0.387377			0.193688	−	0.981063i	$-0.437955\pi$
$887$	11.5371			0.387377			0.193688	+	0.981063i	$0.437955\pi$
$888$	29.9237	+	33.2336i	1.00417	+	1.11525i
$889$	−76.5578	−	16.2729i	−2.56767	−	0.545775i
$890$	−27.6464	+	47.8849i	−0.926708	+	1.60510i
$891$	−3.44616	−	0.732504i	−0.115451	−	0.0245398i
$892$	−11.9032	+	2.53010i	−0.398548	+	0.0847139i
$893$	−2.27126	−	1.01123i	−0.0760048	−	0.0338395i
$894$	2.37117	+	1.05572i	0.0793039	+	0.0353084i
$895$	−59.1686	+	26.3436i	−1.97779	+	0.880569i
$896$	13.5979	−	2.89033i	0.454275	−	0.0965591i
$897$	−1.36393	+	4.19775i	−0.0455403	+	0.140159i
$898$	−26.4078			−0.881241
$899$	−22.4977	−	24.9862i	−0.750341	−	0.833338i
$900$	3.20140	+	30.4593i	0.106713	+	1.01531i
$901$	1.27260	+	1.41336i	0.0423964	+	0.0470860i
$902$	2.07610	+	3.59592i	0.0691267	+	0.119731i
$903$	49.6284	−	36.0571i	1.65153	−	1.19991i
$904$	22.2414	−	38.5233i	0.739739	−	1.28126i
$905$	−19.2834			−0.641002
$906$	−39.1836	−	3.90618i	−1.30179	−	0.129774i
$907$	−6.26019			−0.207866			−0.103933	−	0.994584i	$-0.533143\pi$
$907$	−6.26019			−0.207866			−0.103933	+	0.994584i	$0.533143\pi$
$908$	−2.88239	+	4.99245i	−0.0956555	+	0.165680i
$909$	48.9466	−	35.5618i	1.62346	−	1.17951i
$910$	−2.79855	−	4.84722i	−0.0927709	−	0.160684i
$911$	17.7050	+	19.6634i	0.586594	+	0.651479i	0.961248	−	0.275686i	$-0.0889051\pi$
$911$	17.7050	+	19.6634i	0.586594	+	0.651479i	−0.374654	+	0.927165i	$0.622238\pi$
$912$	0.653444	+	6.21711i	0.0216377	+	0.205869i
$913$	−6.19694	−	6.88240i	−0.205089	−	0.227774i
$914$	−31.0408			−1.02674
$915$	12.7265	−	39.1680i	0.420724	−	1.29485i
$916$	16.7286	−	3.55578i	0.552729	−	0.117486i
$917$	−30.8393	+	13.7305i	−1.01840	+	0.453423i
$918$	−4.54547	−	2.02377i	−0.150023	−	0.0667945i
$919$	9.16559	+	4.08078i	0.302345	+	0.134613i	0.552302	−	0.833644i	$-0.313750\pi$
$919$	9.16559	+	4.08078i	0.302345	+	0.134613i	−0.249957	+	0.968257i	$0.580416\pi$
$920$	−71.7764	+	15.2565i	−2.36640	+	0.502993i
$921$	−50.0007	−	10.6280i	−1.64758	−	0.350204i
$922$	−22.8020	+	39.4943i	−0.750944	+	1.30067i
$923$	3.25148	+	0.691123i	0.107024	+	0.0227486i
$924$	15.0627	+	16.7288i	0.495526	+	0.550337i
$925$	52.7476			1.73433
$926$	−1.12441	+	3.46058i	−0.0369504	+	0.113722i
$927$	−65.8584	−	13.9986i	−2.16307	−	0.459775i
$928$	2.86934	−	27.2999i	0.0941907	−	0.896164i
$929$	7.08702	−	12.2751i	0.232517	−	0.402732i	−0.726031	−	0.687662i	$-0.758637\pi$
$929$	7.08702	−	12.2751i	0.232517	−	0.402732i	0.958548	+	0.284930i	$0.0919704\pi$
$930$	43.6490	−	31.7129i	1.43131	−	1.03991i
$931$	1.67363	−	15.9235i	0.0548511	−	0.521873i
$932$	−2.75756	+	2.00348i	−0.0903267	+	0.0656262i
$933$	24.1235	+	74.2446i	0.789769	+	2.43066i
$934$	−0.719684	+	2.21496i	−0.0235488	+	0.0724757i
$935$	7.66320	+	5.56764i	0.250614	+	0.182081i
$936$	2.48608	−	2.76107i	0.0812600	−	0.0902483i
$937$	21.4220	+	4.55339i	0.699827	+	0.148753i	0.544066	−	0.839042i	$-0.316884\pi$
$937$	21.4220	+	4.55339i	0.699827	+	0.148753i	0.155760	+	0.987795i	$0.450217\pi$
$938$	6.24113	+	10.8100i	0.203780	+	0.352958i
$939$	23.7623	−	41.1575i	0.775453	−	1.34312i
$940$	−4.22645	+	4.69394i	−0.137851	+	0.153100i
$941$	−5.95220	+	56.6314i	−0.194036	+	1.84613i	0.273149	+	0.961972i	$0.411935\pi$
$941$	−5.95220	+	56.6314i	−0.194036	+	1.84613i	−0.467185	+	0.884160i	$0.654732\pi$
$942$	44.0701	−	9.36739i	1.43588	−	0.305206i
$943$	0.889544	+	8.46344i	0.0289675	+	0.275608i
$944$	5.73408	−	9.93171i	0.186628	−	0.323250i
$945$	−82.6724	+	17.5726i	−2.68933	+	0.571635i
$946$	9.28671	+	10.3139i	0.301937	+	0.335335i
$947$	−10.0350	+	7.29086i	−0.326094	+	0.236921i	−0.738771	−	0.673956i	$-0.764594\pi$
$947$	−10.0350	+	7.29086i	−0.326094	+	0.236921i	0.412677	+	0.910877i	$0.364594\pi$
$948$	−4.06891	+	4.51898i	−0.132152	+	0.146770i
$949$	0.519790	−	0.577285i	0.0168731	−	0.0187395i
$950$	9.43905	+	6.85787i	0.306243	+	0.222499i
$951$	−17.7826	+	7.91732i	−0.576640	+	0.256737i
$952$	−6.96689	−	12.0670i	−0.225798	−	0.391094i
$953$	−15.9507	−	7.10169i	−0.516693	−	0.230046i	0.131787	−	0.991278i	$-0.457928\pi$
$953$	−15.9507	−	7.10169i	−0.516693	−	0.230046i	−0.648480	+	0.761232i	$0.724595\pi$
$954$	−1.13344	−	10.7840i	−0.0366965	−	0.349144i
$955$	4.59378	−	43.7069i	0.148651	−	1.41432i
$956$	9.67270	+	7.02763i	0.312837	+	0.227290i
$957$	−50.6041	+	22.5304i	−1.63580	+	0.728305i
$958$	−4.50032	−	42.8177i	−0.145399	−	1.38338i
$959$	24.4593	+	17.7707i	0.789831	+	0.573846i
$960$	90.3988	+	19.2149i	2.91761	+	0.620157i
$961$	−11.1034	−	4.94356i	−0.358175	−	0.159470i
$962$	−1.05836	−	1.17543i	−0.0341228	−	0.0378972i
$963$	60.7024	−	44.1028i	1.95611	−	1.42119i
$964$	−4.11597	+	1.83255i	−0.132567	+	0.0590225i
$965$	81.2453			2.61538
$966$	−29.1636	−	89.7563i	−0.938323	−	2.88786i
$967$	4.62067	−	43.9627i	0.148591	−	1.41375i	−0.625279	−	0.780401i	$-0.715015\pi$
$967$	4.62067	−	43.9627i	0.148591	−	1.41375i	0.773870	−	0.633345i	$-0.218319\pi$
$968$	8.87709	−	9.85901i	0.285321	−	0.316881i
$969$	2.39074	−	1.06442i	0.0768015	−	0.0341943i
$970$	6.02436			0.193431
$971$	−9.91057	−	30.5016i	−0.318045	−	0.978843i	−0.974483	−	0.224462i	$-0.927937\pi$
$971$	−9.91057	−	30.5016i	−0.318045	−	0.978843i	0.656437	−	0.754380i	$-0.272063\pi$
$972$	5.71532	+	9.89922i	0.183319	+	0.317518i
$973$	16.1114	+	49.5856i	0.516506	+	1.58964i
$974$	−2.44957	−	7.53901i	−0.0784894	−	0.241565i
$975$	−0.753955	−	7.17340i	−0.0241459	−	0.229733i
$976$	−7.00776	−	5.09143i	−0.224313	−	0.162973i
$977$	−15.0247	+	3.19359i	−0.480682	+	0.102172i	−0.441879	−	0.897075i	$-0.645688\pi$
$977$	−15.0247	+	3.19359i	−0.480682	+	0.102172i	−0.0388032	+	0.999247i	$0.512355\pi$
$978$	−14.0473	+	43.2331i	−0.449183	+	1.38244i
$979$	−9.83277	+	30.2621i	−0.314257	+	0.967182i
$980$	−37.1606	−	16.5450i	−1.18705	−	0.528510i
$981$	−14.7402	−	25.5308i	−0.470618	−	0.815135i
$982$	8.69199	+	15.0550i	0.277373	+	0.480423i
$983$	−1.87848	−	0.836352i	−0.0599141	−	0.0266755i	0.376561	−	0.926392i	$-0.377107\pi$
$983$	−1.87848	−	0.836352i	−0.0599141	−	0.0266755i	−0.436475	+	0.899716i	$0.643773\pi$
$984$	3.64349	−	11.2135i	0.116150	−	0.357474i
$985$	26.9587	−	82.9703i	0.858975	−	2.64365i
$986$	8.29007	−	1.76211i	0.264010	−	0.0561170i
$987$	−26.5878	−	19.3172i	−0.846300	−	0.614873i
$988$	0.0178777	+	0.170095i	0.000568764	+	0.00541143i
$989$	8.78995	+	27.0527i	0.279504	+	0.860226i
$990$	−16.6885	−	51.3620i	−0.530396	−	1.63239i
$991$	19.2753	+	33.3858i	0.612299	+	1.06053i	0.990852	+	0.134954i	$0.0430885\pi$
$991$	19.2753	+	33.3858i	0.612299	+	1.06053i	−0.378553	+	0.925580i	$0.623578\pi$
$992$	4.75463	+	14.6332i	0.150960	+	0.464606i
$993$	−90.0678			−2.85821
$994$	−64.9315	+	28.9094i	−2.05950	+	0.916949i
$995$	6.88544	−	7.64705i	0.218283	−	0.242428i
$996$	−0.679482	+	6.46484i	−0.0215302	+	0.204846i
$997$	13.0612	+	40.1982i	0.413652	+	1.27309i	0.913451	+	0.406948i	$0.133407\pi$
$997$	13.0612	+	40.1982i	0.413652	+	1.27309i	−0.499800	+	0.866141i	$0.666593\pi$
$998$	−36.8560			−1.16666
$999$	−21.8195	+	9.71468i	−0.690339	+	0.307359i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	151.2.g.a.2.4	✓	96
151.76	even	15	inner	151.2.g.a.76.4	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
151.2.g.a.2.4	✓	96	1.1	even	1	trivial
151.2.g.a.76.4	yes	96	151.76	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	151.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.579506 + 1.00373i) q^{2} +(2.23683 - 1.62515i) q^{3} +(0.328346 + 0.568712i) q^{4} +(2.59512 + 2.88217i) q^{5} +(0.334964 + 3.18697i) q^{6} +(-3.20705 - 3.56179i) q^{7} -3.07914 q^{8} +(1.43524 - 4.41720i) q^{9} +O(q^{10})\)	\(q+(-0.579506 + 1.00373i) q^{2} +(2.23683 - 1.62515i) q^{3} +(0.328346 + 0.568712i) q^{4} +(2.59512 + 2.88217i) q^{5} +(0.334964 + 3.18697i) q^{6} +(-3.20705 - 3.56179i) q^{7} -3.07914 q^{8} +(1.43524 - 4.41720i) q^{9} +(-4.39682 + 0.934574i) q^{10} +(-2.36314 + 1.05214i) q^{11} +(1.65870 + 0.738499i) q^{12} +(-0.237336 - 0.105669i) q^{13} +(5.43359 - 1.15494i) q^{14} +(10.4888 + 2.22947i) q^{15} +(1.12769 - 1.95321i) q^{16} +(-0.923528 - 0.196302i) q^{17} +(3.60197 + 4.00039i) q^{18} -1.00249 q^{19} +(-0.787029 + 2.42223i) q^{20} +(-12.9621 - 2.75517i) q^{21} +(0.313388 - 2.98169i) q^{22} +(3.07236 - 5.32148i) q^{23} +(-6.88750 + 5.00406i) q^{24} +(-1.04963 + 9.98658i) q^{25} +(0.243601 - 0.176986i) q^{26} +(-1.40507 - 4.32435i) q^{27} +(0.972609 - 2.99338i) q^{28} +(6.26582 + 4.55238i) q^{29} +(-8.31612 + 9.23598i) q^{30} +(-4.24631 - 0.902581i) q^{31} +(-1.77214 - 3.06943i) q^{32} +(-3.57606 + 6.19393i) q^{33} +(0.732225 - 0.813218i) q^{34} +(1.94301 - 18.4865i) q^{35} +(2.98337 - 0.634135i) q^{36} +(-0.549079 - 5.22414i) q^{37} +(0.580950 - 1.00623i) q^{38} +(-0.702608 + 0.149344i) q^{39} +(-7.99073 - 8.87461i) q^{40} +(-1.12044 + 0.814048i) q^{41} +(10.2770 - 11.4138i) q^{42} +(-3.09752 + 3.44014i) q^{43} +(-1.37429 - 0.998483i) q^{44} +(16.4558 - 7.32658i) q^{45} +(3.56090 + 6.16765i) q^{46} +(2.26562 + 1.00872i) q^{47} +(-0.651820 - 6.20166i) q^{48} +(-1.66947 + 15.8840i) q^{49} +(-9.41559 - 6.84083i) q^{50} +(-2.38479 + 1.06178i) q^{51} +(-0.0178332 - 0.169672i) q^{52} +(-1.62964 - 1.18401i) q^{53} +(5.15474 + 1.09567i) q^{54} +(-9.16510 - 4.08056i) q^{55} +(9.87493 + 10.9672i) q^{56} +(-2.24240 + 1.62920i) q^{57} +(-8.20046 + 3.65108i) q^{58} +5.08482 q^{59} +(2.17604 + 6.69715i) q^{60} +(0.401456 - 3.81960i) q^{61} +(3.36671 - 3.73911i) q^{62} +(-20.3360 + 9.05417i) q^{63} +8.61860 q^{64} +(-0.311360 - 0.958267i) q^{65} +(-4.14470 - 7.17883i) q^{66} +(0.694374 + 2.13706i) q^{67} +(-0.191597 - 0.589676i) q^{68} +(-1.77587 - 16.8963i) q^{69} +(17.4296 + 12.6633i) q^{70} +(-12.5155 + 2.66025i) q^{71} +(-4.41929 + 13.6012i) q^{72} +(-0.923986 + 2.84374i) q^{73} +(5.56184 + 2.47629i) q^{74} +(13.8819 + 24.0441i) q^{75} +(-0.329164 - 0.570129i) q^{76} +(11.3262 + 5.04275i) q^{77} +(0.257264 - 0.791777i) q^{78} +(-1.03493 + 3.18520i) q^{79} +(8.55597 - 1.81863i) q^{80} +(1.10187 + 0.800552i) q^{81} +(-0.167785 - 1.59637i) q^{82} +(1.10634 + 3.40497i) q^{83} +(-2.68914 - 8.27632i) q^{84} +(-1.83089 - 3.17120i) q^{85} +(-1.65796 - 5.10266i) q^{86} +21.4139 q^{87} +(7.27645 - 3.23968i) q^{88} +(8.23084 - 9.14127i) q^{89} +(-2.18228 + 20.7630i) q^{90} +(0.384778 + 1.18422i) q^{91} +4.03518 q^{92} +(-10.9651 + 4.88198i) q^{93} +(-2.32542 + 1.68952i) q^{94} +(-2.60159 - 2.88936i) q^{95} +(-8.95225 - 3.98580i) q^{96} +(-1.31093 - 0.278648i) q^{97} +(-14.9758 - 10.8806i) q^{98} +(1.25584 + 11.9486i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 3 q^{2} - 4 q^{3} - 49 q^{4} - 9 q^{5} + 7 q^{6} - 7 q^{7} + 12 q^{8} - 32 q^{9}+O(q^{10}) \) 96 * q - 3 * q^2 - 4 * q^3 - 49 * q^4 - 9 * q^5 + 7 * q^6 - 7 * q^7 + 12 * q^8 - 32 * q^9	\( 96 q - 3 q^{2} - 4 q^{3} - 49 q^{4} - 9 q^{5} + 7 q^{6} - 7 q^{7} + 12 q^{8} - 32 q^{9} + 11 q^{10} - 7 q^{11} + 7 q^{12} - 8 q^{13} + 5 q^{14} + 10 q^{15} - 47 q^{16} - 26 q^{17} - 40 q^{18} - 20 q^{19} + 23 q^{20} - 2 q^{21} - 32 q^{22} - q^{23} + 95 q^{24} - 51 q^{25} + 41 q^{26} + 5 q^{27} - 2 q^{28} + 13 q^{29} + 19 q^{30} - 24 q^{31} - 60 q^{32} + 39 q^{33} + 47 q^{34} - 54 q^{35} + 11 q^{36} + 5 q^{37} + 8 q^{38} - 13 q^{39} - 74 q^{40} + 8 q^{41} + 166 q^{42} - 8 q^{43} + 18 q^{44} - 33 q^{45} + 21 q^{46} - 5 q^{47} + 8 q^{48} + 21 q^{49} - 72 q^{50} - 6 q^{51} + 96 q^{52} + 41 q^{53} - 60 q^{54} - 116 q^{55} - 85 q^{56} - 8 q^{57} - 58 q^{58} + 32 q^{59} - 6 q^{60} - 18 q^{61} + 38 q^{62} - 129 q^{63} + 160 q^{64} + 53 q^{65} + 43 q^{66} + 4 q^{67} + 10 q^{68} + 81 q^{69} + 33 q^{70} - 41 q^{71} - 40 q^{72} - 58 q^{73} - 20 q^{74} + 32 q^{75} - q^{76} - 22 q^{77} - 10 q^{78} + 32 q^{79} + 71 q^{80} - 66 q^{81} - 10 q^{82} + 80 q^{83} - 58 q^{84} - 2 q^{85} - 72 q^{86} + 72 q^{87} + 89 q^{88} + 9 q^{89} + 121 q^{90} - 138 q^{91} - 72 q^{92} - 85 q^{93} + 11 q^{94} - 47 q^{95} - 201 q^{96} + 54 q^{97} - 92 q^{98} - 21 q^{99}+O(q^{100}) \) 96 * q - 3 * q^2 - 4 * q^3 - 49 * q^4 - 9 * q^5 + 7 * q^6 - 7 * q^7 + 12 * q^8 - 32 * q^9 + 11 * q^10 - 7 * q^11 + 7 * q^12 - 8 * q^13 + 5 * q^14 + 10 * q^15 - 47 * q^16 - 26 * q^17 - 40 * q^18 - 20 * q^19 + 23 * q^20 - 2 * q^21 - 32 * q^22 - q^23 + 95 * q^24 - 51 * q^25 + 41 * q^26 + 5 * q^27 - 2 * q^28 + 13 * q^29 + 19 * q^30 - 24 * q^31 - 60 * q^32 + 39 * q^33 + 47 * q^34 - 54 * q^35 + 11 * q^36 + 5 * q^37 + 8 * q^38 - 13 * q^39 - 74 * q^40 + 8 * q^41 + 166 * q^42 - 8 * q^43 + 18 * q^44 - 33 * q^45 + 21 * q^46 - 5 * q^47 + 8 * q^48 + 21 * q^49 - 72 * q^50 - 6 * q^51 + 96 * q^52 + 41 * q^53 - 60 * q^54 - 116 * q^55 - 85 * q^56 - 8 * q^57 - 58 * q^58 + 32 * q^59 - 6 * q^60 - 18 * q^61 + 38 * q^62 - 129 * q^63 + 160 * q^64 + 53 * q^65 + 43 * q^66 + 4 * q^67 + 10 * q^68 + 81 * q^69 + 33 * q^70 - 41 * q^71 - 40 * q^72 - 58 * q^73 - 20 * q^74 + 32 * q^75 - q^76 - 22 * q^77 - 10 * q^78 + 32 * q^79 + 71 * q^80 - 66 * q^81 - 10 * q^82 + 80 * q^83 - 58 * q^84 - 2 * q^85 - 72 * q^86 + 72 * q^87 + 89 * q^88 + 9 * q^89 + 121 * q^90 - 138 * q^91 - 72 * q^92 - 85 * q^93 + 11 * q^94 - 47 * q^95 - 201 * q^96 + 54 * q^97 - 92 * q^98 - 21 * q^99

Introduction

L-functions

Modular forms

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