LMFDB - Embedded newform 588.2.x.b.223.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,2,Mod(55,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 0, 9]))

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

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

chi := DirichletCharacter("588.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.x (of order $14$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$28$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			223.10
Character	$\chi$	$=$	588.223
Dual form			588.2.x.b.559.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.841658 + 1.13649i) q^{2} +(0.222521 - 0.974928i) q^{3} +(-0.583224 - 1.91307i) q^{4} +(2.57339 + 0.587359i) q^{5} +(0.920710 + 1.07345i) q^{6} +(2.51025 + 0.835852i) q^{7} +(2.66507 + 0.947324i) q^{8} +(-0.900969 - 0.433884i) q^{9} +O(q^{10})$	\(q+(-0.841658 + 1.13649i) q^{2} +(0.222521 - 0.974928i) q^{3} +(-0.583224 - 1.91307i) q^{4} +(2.57339 + 0.587359i) q^{5} +(0.920710 + 1.07345i) q^{6} +(2.51025 + 0.835852i) q^{7} +(2.66507 + 0.947324i) q^{8} +(-0.900969 - 0.433884i) q^{9} +(-2.83344 + 2.43028i) q^{10} +(-1.03750 - 2.15439i) q^{11} +(-1.99489 + 0.142903i) q^{12} +(1.89781 + 3.94084i) q^{13} +(-3.06271 + 2.14937i) q^{14} +(1.14527 - 2.37817i) q^{15} +(-3.31970 + 2.23150i) q^{16} +(-0.584700 + 0.466282i) q^{17} +(1.25141 - 0.658761i) q^{18} +5.65127 q^{19} +(-0.377201 - 5.26564i) q^{20} +(1.37348 - 2.26132i) q^{21} +(3.32167 + 0.634151i) q^{22} +(-6.32994 - 5.04796i) q^{23} +(1.51661 - 2.38745i) q^{24} +(1.77249 + 0.853588i) q^{25} +(-6.07604 - 1.16000i) q^{26} +(-0.623490 + 0.781831i) q^{27} +(0.135009 - 5.28978i) q^{28} +(1.27868 + 1.60341i) q^{29} +(1.73885 + 3.30319i) q^{30} -0.240610 q^{31} +(0.257970 - 5.65097i) q^{32} +(-2.33124 + 0.532091i) q^{33} +(-0.0378088 - 1.05696i) q^{34} +(5.96890 + 3.62539i) q^{35} +(-0.304585 + 1.97667i) q^{36} +(-1.99964 - 2.50747i) q^{37} +(-4.75643 + 6.42261i) q^{38} +(4.26434 - 0.973308i) q^{39} +(6.30183 + 4.00318i) q^{40} +(11.4238 + 2.60740i) q^{41} +(1.41397 + 3.46420i) q^{42} +(9.66372 - 2.20568i) q^{43} +(-3.51642 + 3.24131i) q^{44} +(-2.06370 - 1.64574i) q^{45} +(11.0646 - 2.94527i) q^{46} +(-2.94725 + 1.41932i) q^{47} +(1.43685 + 3.73302i) q^{48} +(5.60270 + 4.19639i) q^{49} +(-2.46193 + 1.29599i) q^{50} +(0.324484 + 0.673798i) q^{51} +(6.43227 - 5.92904i) q^{52} +(-7.68409 + 9.63554i) q^{53} +(-0.363779 - 1.36663i) q^{54} +(-1.40449 - 6.15347i) q^{55} +(5.89816 + 4.60562i) q^{56} +(1.25753 - 5.50958i) q^{57} +(-2.89847 + 0.103682i) q^{58} +(-0.367809 - 1.61148i) q^{59} +(-5.21756 - 0.803972i) q^{60} +(-1.02870 + 0.820364i) q^{61} +(0.202511 - 0.273451i) q^{62} +(-1.89899 - 1.84223i) q^{63} +(6.20515 + 5.04936i) q^{64} +(2.56911 + 11.2560i) q^{65} +(1.35739 - 3.09728i) q^{66} -9.89182i q^{67} +(1.23304 + 0.846626i) q^{68} +(-6.32994 + 5.04796i) q^{69} +(-9.14400 + 3.73226i) q^{70} +(-2.19839 - 1.75316i) q^{71} +(-1.99011 - 2.00984i) q^{72} +(-4.78064 + 9.92710i) q^{73} +(4.53273 - 0.162142i) q^{74} +(1.22660 - 1.53811i) q^{75} +(-3.29595 - 10.8113i) q^{76} +(-0.803632 - 6.27526i) q^{77} +(-2.48296 + 5.66558i) q^{78} +6.28692i q^{79} +(-9.85357 + 3.79266i) q^{80} +(0.623490 + 0.781831i) q^{81} +(-12.5782 + 10.7885i) q^{82} +(-5.85990 - 2.82198i) q^{83} +(-5.12711 - 1.30871i) q^{84} +(-1.77853 + 0.856497i) q^{85} +(-5.62681 + 12.8392i) q^{86} +(1.84774 - 0.889825i) q^{87} +(-0.724100 - 6.72445i) q^{88} +(6.43770 - 13.3680i) q^{89} +(3.60730 - 0.960221i) q^{90} +(1.47001 + 11.4788i) q^{91} +(-5.96535 + 15.0537i) q^{92} +(-0.0535407 + 0.234577i) q^{93} +(0.867530 - 4.54410i) q^{94} +(14.5429 + 3.31932i) q^{95} +(-5.45188 - 1.50896i) q^{96} -11.5887i q^{97} +(-9.48472 + 2.83549i) q^{98} +2.39120i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q + 28 q^{3} - 2 q^{7} + 6 q^{8} - 28 q^{9}+O(q^{10}) $ 168 * q + 28 * q^3 - 2 * q^7 + 6 * q^8 - 28 * q^9	$ 168 q + 28 q^{3} - 2 q^{7} + 6 q^{8} - 28 q^{9} - 20 q^{10} + 14 q^{14} - 20 q^{16} - 12 q^{19} + 25 q^{20} + 2 q^{21} - 6 q^{22} - 27 q^{24} + 32 q^{25} - 6 q^{26} + 28 q^{27} + 6 q^{28} - 8 q^{30} + 4 q^{31} - 45 q^{32} - 44 q^{34} + 12 q^{35} - 10 q^{37} - 35 q^{38} - 14 q^{39} + 40 q^{40} + 7 q^{42} + 20 q^{44} + 28 q^{46} + 8 q^{47} - 8 q^{48} - 8 q^{49} + 114 q^{50} - 20 q^{52} - 8 q^{53} + 23 q^{56} + 12 q^{57} - 6 q^{58} - 20 q^{59} + 10 q^{60} - 14 q^{61} + 16 q^{62} + 12 q^{63} - 42 q^{64} - 8 q^{65} + 6 q^{66} + 16 q^{68} + 19 q^{70} - 28 q^{71} - 15 q^{72} + 22 q^{74} - 18 q^{75} - 49 q^{76} + 8 q^{77} + 6 q^{78} - 26 q^{80} - 28 q^{81} - 12 q^{82} - 10 q^{83} - 27 q^{84} - 24 q^{85} - 34 q^{86} + 94 q^{88} - 20 q^{90} + 16 q^{91} + 7 q^{92} - 4 q^{93} + 11 q^{94} + 10 q^{96} - 150 q^{98}+O(q^{100}) $ 168 * q + 28 * q^3 - 2 * q^7 + 6 * q^8 - 28 * q^9 - 20 * q^10 + 14 * q^14 - 20 * q^16 - 12 * q^19 + 25 * q^20 + 2 * q^21 - 6 * q^22 - 27 * q^24 + 32 * q^25 - 6 * q^26 + 28 * q^27 + 6 * q^28 - 8 * q^30 + 4 * q^31 - 45 * q^32 - 44 * q^34 + 12 * q^35 - 10 * q^37 - 35 * q^38 - 14 * q^39 + 40 * q^40 + 7 * q^42 + 20 * q^44 + 28 * q^46 + 8 * q^47 - 8 * q^48 - 8 * q^49 + 114 * q^50 - 20 * q^52 - 8 * q^53 + 23 * q^56 + 12 * q^57 - 6 * q^58 - 20 * q^59 + 10 * q^60 - 14 * q^61 + 16 * q^62 + 12 * q^63 - 42 * q^64 - 8 * q^65 + 6 * q^66 + 16 * q^68 + 19 * q^70 - 28 * q^71 - 15 * q^72 + 22 * q^74 - 18 * q^75 - 49 * q^76 + 8 * q^77 + 6 * q^78 - 26 * q^80 - 28 * q^81 - 12 * q^82 - 10 * q^83 - 27 * q^84 - 24 * q^85 - 34 * q^86 + 94 * q^88 - 20 * q^90 + 16 * q^91 + 7 * q^92 - 4 * q^93 + 11 * q^94 + 10 * q^96 - 150 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{14}\right)$

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 $

$2$	−0.841658	+	1.13649i	−0.595142	+	0.803621i
$2$	−0.841658	+	1.13649i	−0.595142	+	0.803621i
$3$	0.222521	−	0.974928i	0.128473	−	0.562875i
$3$	0.222521	−	0.974928i	0.128473	−	0.562875i
$4$	−0.583224	−	1.91307i	−0.291612	−	0.956537i
$5$	2.57339	+	0.587359i	1.15085	+	0.262675i	0.755055	−	0.655662i	$-0.227610\pi$
$5$	2.57339	+	0.587359i	1.15085	+	0.262675i	0.395800	+	0.918337i	$0.370467\pi$
$6$	0.920710	+	1.07345i	0.375878	+	0.438234i
$7$	2.51025	+	0.835852i	0.948785	+	0.315922i
$7$	2.51025	+	0.835852i	0.948785	+	0.315922i
$8$	2.66507	+	0.947324i	0.942243	+	0.334930i
$9$	−0.900969	−	0.433884i	−0.300323	−	0.144628i
$10$	−2.83344	+	2.43028i	−0.896013	+	0.768521i
$11$	−1.03750	−	2.15439i	−0.312818	−	0.649574i	0.683983	−	0.729498i	$-0.260246\pi$
$11$	−1.03750	−	2.15439i	−0.312818	−	0.649574i	−0.996801	+	0.0799245i	$0.974532\pi$
$12$	−1.99489	+	0.142903i	−0.575875	+	0.0412524i
$13$	1.89781	+	3.94084i	0.526358	+	1.09299i	0.979479	+	0.201544i	$0.0645960\pi$
$13$	1.89781	+	3.94084i	0.526358	+	1.09299i	−0.453122	+	0.891449i	$0.649690\pi$
$14$	−3.06271	+	2.14937i	−0.818544	+	0.574444i
$15$	1.14527	−	2.37817i	0.295706	−	0.614040i
$16$	−3.31970	+	2.23150i	−0.829925	+	0.557875i
$17$	−0.584700	+	0.466282i	−0.141810	+	0.113090i	−0.691826	−	0.722065i	$-0.743193\pi$
$17$	−0.584700	+	0.466282i	−0.141810	+	0.113090i	0.550015	+	0.835155i	$0.314622\pi$
$18$	1.25141	−	0.658761i	0.294961	−	0.155272i
$19$	5.65127			1.29649			0.648245	−	0.761432i	$-0.275503\pi$
$19$	5.65127			1.29649			0.648245	+	0.761432i	$0.275503\pi$
$20$	−0.377201	−	5.26564i	−0.0843447	−	1.17743i
$21$	1.37348	−	2.26132i	0.299718	−	0.493460i
$22$	3.32167	+	0.634151i	0.708182	+	0.135201i
$23$	−6.32994	−	5.04796i	−1.31988	−	1.05257i	−0.994251	−	0.107077i	$-0.965851\pi$
$23$	−6.32994	−	5.04796i	−1.31988	−	1.05257i	−0.325634	−	0.945496i	$-0.605578\pi$
$24$	1.51661	−	2.38745i	0.309576	−	0.487336i
$25$	1.77249	+	0.853588i	0.354499	+	0.170718i
$26$	−6.07604	−	1.16000i	−1.19161	−	0.227494i
$27$	−0.623490	+	0.781831i	−0.119991	+	0.150464i
$28$	0.135009	−	5.28978i	0.0255142	−	0.999674i
$29$	1.27868	+	1.60341i	0.237444	+	0.297745i	0.886249	−	0.463209i	$-0.153302\pi$
$29$	1.27868	+	1.60341i	0.237444	+	0.297745i	−0.648805	+	0.760955i	$0.724731\pi$
$30$	1.73885	+	3.30319i	0.317468	+	0.603077i
$31$	−0.240610			−0.0432148			−0.0216074	−	0.999767i	$-0.506878\pi$
$31$	−0.240610			−0.0432148			−0.0216074	+	0.999767i	$0.506878\pi$
$32$	0.257970	−	5.65097i	0.0456031	−	0.998960i
$33$	−2.33124	+	0.532091i	−0.405817	+	0.0926252i
$34$	−0.0378088	−	1.05696i	−0.00648415	−	0.181266i
$35$	5.96890	+	3.62539i	1.00893	+	0.612803i
$36$	−0.304585	+	1.97667i	−0.0507641	+	0.329445i
$37$	−1.99964	−	2.50747i	−0.328739	−	0.412226i	0.589804	−	0.807546i	$-0.299205\pi$
$37$	−1.99964	−	2.50747i	−0.328739	−	0.412226i	−0.918543	+	0.395321i	$0.870633\pi$
$38$	−4.75643	+	6.42261i	−0.771595	+	1.04189i
$39$	4.26434	−	0.973308i	0.682841	−	0.155854i
$40$	6.30183	+	4.00318i	0.996407	+	0.632959i
$41$	11.4238	+	2.60740i	1.78409	+	0.407208i	0.981830	−	0.189763i	$-0.0607721\pi$
$41$	11.4238	+	2.60740i	1.78409	+	0.407208i	0.802263	+	0.596971i	$0.203629\pi$
$42$	1.41397	+	3.46420i	0.218180	+	0.534538i
$43$	9.66372	−	2.20568i	1.47370	−	0.336363i	0.591145	−	0.806565i	$-0.298676\pi$
$43$	9.66372	−	2.20568i	1.47370	−	0.336363i	0.882559	+	0.470202i	$0.155819\pi$
$44$	−3.51642	+	3.24131i	−0.530120	+	0.488646i
$45$	−2.06370	−	1.64574i	−0.307638	−	0.245333i
$46$	11.0646	−	2.94527i	1.63139	−	0.434256i
$47$	−2.94725	+	1.41932i	−0.429900	+	0.207029i	−0.636305	−	0.771438i	$-0.719538\pi$
$47$	−2.94725	+	1.41932i	−0.429900	+	0.207029i	0.206405	+	0.978467i	$0.433824\pi$
$48$	1.43685	+	3.73302i	0.207391	+	0.538815i
$49$	5.60270	+	4.19639i	0.800386	+	0.599485i
$50$	−2.46193	+	1.29599i	−0.348169	+	0.183281i
$51$	0.324484	+	0.673798i	0.0454368	+	0.0943505i
$52$	6.43227	−	5.92904i	0.891996	−	0.822210i
$53$	−7.68409	+	9.63554i	−1.05549	+	1.32354i	−0.111430	+	0.993772i	$0.535543\pi$
$53$	−7.68409	+	9.63554i	−1.05549	+	1.32354i	−0.944061	+	0.329771i	$0.893028\pi$
$54$	−0.363779	−	1.36663i	−0.0495041	−	0.185974i
$55$	−1.40449	−	6.15347i	−0.189381	−	0.829734i
$56$	5.89816	+	4.60562i	0.788174	+	0.615452i
$57$	1.25753	−	5.50958i	0.166563	−	0.729761i
$58$	−2.89847	+	0.103682i	−0.380587	+	0.0136141i
$59$	−0.367809	−	1.61148i	−0.0478847	−	0.209797i	0.945326	−	0.326127i	$-0.105744\pi$
$59$	−0.367809	−	1.61148i	−0.0478847	−	0.209797i	−0.993211	+	0.116331i	$0.962887\pi$
$60$	−5.21756	−	0.803972i	−0.673584	−	0.103792i
$61$	−1.02870	+	0.820364i	−0.131712	+	0.105037i	−0.687130	−	0.726535i	$-0.741130\pi$
$61$	−1.02870	+	0.820364i	−0.131712	+	0.105037i	0.555418	+	0.831571i	$0.312558\pi$
$62$	0.202511	−	0.273451i	0.0257189	−	0.0347283i
$63$	−1.89899	−	1.84223i	−0.239251	−	0.232100i
$64$	6.20515	+	5.04936i	0.775644	+	0.631170i
$65$	2.56911	+	11.2560i	0.318659	+	1.39614i
$66$	1.35739	−	3.09728i	0.167083	−	0.381248i
$67$		−	9.89182i		−	1.20848i	−0.796803	−	0.604239i	$-0.793477\pi$
$67$		−	9.89182i		−	1.20848i	0.796803	−	0.604239i	$-0.206523\pi$
$68$	1.23304	+	0.846626i	0.149528	+	0.102668i
$69$	−6.32994	+	5.04796i	−0.762036	+	0.607703i
$70$	−9.14400	+	3.73226i	−1.09292	+	0.446091i
$71$	−2.19839	−	1.75316i	−0.260901	−	0.208062i	0.484299	−	0.874902i	$-0.339075\pi$
$71$	−2.19839	−	1.75316i	−0.260901	−	0.208062i	−0.745200	+	0.666841i	$0.767646\pi$
$72$	−1.99011	−	2.00984i	−0.234537	−	0.236862i
$73$	−4.78064	+	9.92710i	−0.559532	+	1.16188i	0.408895	+	0.912581i	$0.365914\pi$
$73$	−4.78064	+	9.92710i	−0.559532	+	1.16188i	−0.968427	+	0.249298i	$0.919800\pi$
$74$	4.53273	−	0.162142i	0.526919	−	0.0188486i
$75$	1.22660	−	1.53811i	0.141636	−	0.177606i
$76$	−3.29595	−	10.8113i	−0.378072	−	1.24014i
$77$	−0.803632	−	6.27526i	−0.0915823	−	0.715132i
$78$	−2.48296	+	5.66558i	−0.281140	+	0.641500i
$79$			6.28692i			0.707334i	0.935371	+	0.353667i	$0.115065\pi$
$79$			6.28692i			0.707334i	−0.935371	+	0.353667i	$0.884935\pi$
$80$	−9.85357	+	3.79266i	−1.10166	+	0.424033i
$81$	0.623490	+	0.781831i	0.0692766	+	0.0868702i
$82$	−12.5782	+	10.7885i	−1.38903	+	1.19139i
$83$	−5.85990	−	2.82198i	−0.643208	−	0.309752i	0.0836967	−	0.996491i	$-0.473327\pi$
$83$	−5.85990	−	2.82198i	−0.643208	−	0.309752i	−0.726904	+	0.686739i	$0.759042\pi$
$84$	−5.12711	−	1.30871i	−0.559414	−	0.142792i
$85$	−1.77853	+	0.856497i	−0.192909	+	0.0929001i
$86$	−5.62681	+	12.8392i	−0.606755	+	1.38448i
$87$	1.84774	−	0.889825i	0.198098	−	0.0953992i
$88$	−0.724100	−	6.72445i	−0.0771893	−	0.716829i
$89$	6.43770	−	13.3680i	0.682395	−	1.41701i	−0.215369	−	0.976533i	$-0.569096\pi$
$89$	6.43770	−	13.3680i	0.682395	−	1.41701i	0.897765	−	0.440476i	$-0.145190\pi$
$90$	3.60730	−	0.960221i	0.380243	−	0.101216i
$91$	1.47001	+	11.4788i	0.154099	+	1.20330i
$92$	−5.96535	+	15.0537i	−0.621930	+	1.56946i
$93$	−0.0535407	+	0.234577i	−0.00555191	+	0.0243245i
$94$	0.867530	−	4.54410i	0.0894789	−	0.468688i
$95$	14.5429	+	3.31932i	1.49207	+	0.340555i
$96$	−5.45188	−	1.50896i	−0.556431	−	0.154008i
$97$		−	11.5887i		−	1.17665i	−0.808623	−	0.588326i	$-0.799787\pi$
$97$		−	11.5887i		−	1.17665i	0.808623	−	0.588326i	$-0.200213\pi$
$98$	−9.48472	+	2.83549i	−0.958102	+	0.286428i
$99$			2.39120i			0.240324i
$100$	0.599215	−	3.88874i	0.0599215	−	0.388874i
$101$	−17.2863	−	3.94548i	−1.72005	−	0.392590i	−0.755220	−	0.655471i	$-0.772470\pi$
$101$	−17.2863	−	3.94548i	−1.72005	−	0.392590i	−0.964828	+	0.262881i	$0.915327\pi$
$102$	−1.03887	−	0.198334i	−0.102863	−	0.0196380i
$103$	−0.783993	+	3.43490i	−0.0772491	+	0.338451i	−0.998753	−	0.0499178i	$-0.984104\pi$
$103$	−0.783993	+	3.43490i	−0.0772491	+	0.338451i	0.921504	+	0.388368i	$0.126961\pi$
$104$	1.32453	+	12.3004i	0.129881	+	1.20616i
$105$	4.86270	−	5.01252i	0.474551	−	0.489172i
$106$	−4.48333	−	16.8427i	−0.435460	−	1.63591i
$107$	−0.779414	+	1.61847i	−0.0753488	+	0.156463i	−0.935240	−	0.354013i	$-0.884817\pi$
$107$	−0.779414	+	1.61847i	−0.0753488	+	0.156463i	0.859892	+	0.510477i	$0.170531\pi$
$108$	1.85934	+	0.736799i	0.178915	+	0.0708985i
$109$	11.5268	−	5.55099i	1.10406	−	0.531689i	0.209129	−	0.977888i	$-0.432937\pi$
$109$	11.5268	−	5.55099i	1.10406	−	0.531689i	0.894934	+	0.446199i	$0.147223\pi$
$110$	8.17547	+	3.58293i	0.779500	+	0.341619i
$111$	−2.88956	+	1.39154i	−0.274265	+	0.132079i
$112$	−10.1985	+	2.82685i	−0.963666	+	0.267112i
$113$	−6.74224	−	3.24689i	−0.634257	−	0.305442i	0.0889891	−	0.996033i	$-0.471636\pi$
$113$	−6.74224	−	3.24689i	−0.634257	−	0.305442i	−0.723246	+	0.690591i	$0.757351\pi$
$114$	5.20318	+	6.06635i	0.487322	+	0.568165i
$115$	−13.3244	−	16.7083i	−1.24251	−	1.55806i
$116$	2.32168	−	3.38135i	0.215563	−	0.313950i
$117$		−	4.37401i		−	0.404377i
$118$	2.14100	+	0.938301i	0.197095	+	0.0863776i
$119$	−1.85748	+	0.681763i	−0.170275	+	0.0624971i
$120$	5.30510	−	5.25304i	0.484288	−	0.479535i
$121$	3.29339	−	4.12978i	0.299399	−	0.375434i
$122$	−0.0665196	−	1.85958i	−0.00602240	−	0.168358i
$123$	5.08405	−	10.5571i	0.458414	−	0.951906i
$124$	0.140329	+	0.460304i	0.0126019	+	0.0413365i
$125$	−6.25854	−	4.99102i	−0.559781	−	0.446410i
$126$	3.69198	−	0.607660i	0.328908	−	0.0541346i
$127$	−1.33618	+	1.06557i	−0.118567	+	0.0945541i	−0.680978	−	0.732304i	$-0.738445\pi$
$127$	−1.33618	+	1.06557i	−0.118567	+	0.0945541i	0.562411	+	0.826858i	$0.309874\pi$
$128$	−10.9612	+	2.80227i	−0.968840	+	0.247688i
$129$		−	9.91224i		−	0.872724i
$130$	−14.9547	−	6.55394i	−1.31161	−	0.574819i
$131$	−1.25085	−	5.48033i	−0.109287	−	0.478819i	−0.999719	−	0.0237021i	$-0.992455\pi$
$131$	−1.25085	−	5.48033i	−0.109287	−	0.478819i	0.890432	−	0.455117i	$-0.150402\pi$
$132$	2.37757	+	4.14951i	0.206941	+	0.361169i
$133$	14.1861	+	4.72362i	1.23009	+	0.409590i
$134$	11.2420	+	8.32553i	0.971158	+	0.719216i
$135$	−2.06370	+	1.64574i	−0.177615	+	0.141643i
$136$	−1.99998	+	0.688773i	−0.171497	+	0.0590618i
$137$	3.58829	+	15.7213i	0.306568	+	1.34316i	0.860011	+	0.510275i	$0.170457\pi$
$137$	3.58829	+	15.7213i	0.306568	+	1.34316i	−0.553443	+	0.832887i	$0.686686\pi$
$138$	−0.409317	−	11.4426i	−0.0348433	−	0.974057i
$139$	−3.44631	+	15.0993i	−0.292312	+	1.28070i	0.588987	+	0.808142i	$0.299527\pi$
$139$	−3.44631	+	15.0993i	−0.292312	+	1.28070i	−0.881299	+	0.472559i	$0.843330\pi$
$140$	3.45443	−	13.5334i	0.291953	−	1.14378i
$141$	0.727910	+	3.18918i	0.0613011	+	0.268578i
$142$	3.84274	−	1.02289i	0.322476	−	0.0858392i
$143$	6.52114	−	8.17725i	0.545325	−	0.683816i
$144$	3.95916	−	0.570149i	0.329930	−	0.0475124i
$145$	2.34875	+	4.87723i	0.195053	+	0.405032i
$146$	−7.25840	−	13.7884i	−0.600709	−	1.14113i
$147$	5.33790	−	4.52845i	0.440263	−	0.373500i
$148$	−3.63074	+	5.28788i	−0.298445	+	0.434661i
$149$	4.58673	−	2.20885i	0.375760	−	0.180956i	−0.236465	−	0.971640i	$-0.575989\pi$
$149$	4.58673	−	2.20885i	0.375760	−	0.180956i	0.612225	+	0.790684i	$0.290275\pi$
$150$	0.715670	+	2.68859i	0.0584342	+	0.219522i
$151$	−10.2339	−	8.16124i	−0.832821	−	0.664153i	0.111287	−	0.993788i	$-0.464503\pi$
$151$	−10.2339	−	8.16124i	−0.832821	−	0.664153i	−0.944108	+	0.329636i	$0.893074\pi$
$152$	15.0610	+	5.35358i	1.22161	+	0.434233i
$153$	0.729108	−	0.166414i	0.0589449	−	0.0134538i
$154$	7.80816	+	4.36830i	0.629199	+	0.352008i
$155$	−0.619182	−	0.141324i	−0.0497339	−	0.0113514i
$156$	−4.34907	−	7.59034i	−0.348205	−	0.607713i
$157$	−3.05369	+	0.696985i	−0.243711	+	0.0556254i	−0.342631	−	0.939470i	$-0.611318\pi$
$157$	−3.05369	+	0.696985i	−0.243711	+	0.0556254i	0.0989205	+	0.995095i	$0.468461\pi$
$158$	−7.14503	−	5.29144i	−0.568428	−	0.420964i
$159$	7.68409	+	9.63554i	0.609388	+	0.764148i
$160$	3.98301	−	14.3906i	0.314884	−	1.13768i
$161$	−11.6704	−	17.9625i	−0.919755	−	1.41565i
$162$	−1.41331	+	0.0505560i	−0.111040	+	0.00397205i
$163$	−22.9100	+	5.22906i	−1.79445	+	0.409572i	−0.984279	−	0.176619i	$-0.943484\pi$
$163$	−22.9100	+	5.22906i	−1.79445	+	0.409572i	−0.810173	+	0.586191i	$0.800627\pi$
$164$	−1.67447	−	23.3752i	−0.130754	−	1.82530i
$165$	−6.31172			−0.491367
$166$	8.13919	−	4.28458i	0.631723	−	0.332548i
$167$	8.69453	+	10.9026i	0.672803	+	0.843668i	0.994669	−	0.103117i	$-0.0328816\pi$
$167$	8.69453	+	10.9026i	0.672803	+	0.843668i	−0.321866	+	0.946785i	$0.604310\pi$
$168$	5.80261	−	4.72543i	0.447681	−	0.364575i
$169$	−3.82319	+	4.79413i	−0.294092	+	0.368779i
$170$	0.523516	−	2.74217i	0.0401519	−	0.210315i
$171$	−5.09162	−	2.45199i	−0.389366	−	0.187509i
$172$	−9.85575	−	17.2010i	−0.751494	−	1.31156i
$173$	−9.60754	−	7.66176i	−0.730448	−	0.582513i	0.186056	−	0.982539i	$-0.440430\pi$
$173$	−9.60754	−	7.66176i	−0.730448	−	0.582513i	−0.916504	+	0.400026i	$0.869001\pi$
$174$	−0.543887	+	2.84887i	−0.0412320	+	0.215972i
$175$	3.73593	+	3.62426i	0.282409	+	0.273968i
$176$	8.25172	+	4.83675i	0.621997	+	0.364584i
$177$	−1.65292			−0.124241
$178$	9.77430	+	18.5677i	0.732615	+	1.39171i
$179$	−11.1372	+	8.88166i	−0.832437	+	0.663846i	−0.944013	−	0.329910i	$-0.892982\pi$
$179$	−11.1372	+	8.88166i	−0.832437	+	0.663846i	0.111576	+	0.993756i	$0.464410\pi$
$180$	−1.94483	+	4.90784i	−0.144959	+	0.365809i
$181$	0.495218	−	1.02833i	0.0368093	−	0.0764353i	−0.881753	−	0.471711i	$-0.843637\pi$
$181$	0.495218	−	1.02833i	0.0368093	−	0.0764353i	0.918563	+	0.395276i	$0.129351\pi$
$182$	−14.2828	−	7.99055i	−1.05871	−	0.592299i
$183$	0.570887	+	1.18546i	0.0422012	+	0.0876317i
$184$	−12.0877	−	19.4497i	−0.891114	−	1.43385i
$185$	−3.67307	−	7.62720i	−0.270049	−	0.560763i
$186$	−0.221532	−	0.258282i	−0.0162435	−	0.0189382i
$187$	1.61118	+	0.775904i	0.117821	+	0.0567397i
$188$	4.43417	+	4.81052i	0.323395	+	0.350843i
$189$	−2.21861	+	1.44145i	−0.161380	+	0.104850i
$190$	−16.0125	+	13.7341i	−1.16167	+	0.996380i
$191$	−19.4936	−	4.44930i	−1.41051	−	0.321940i	−0.551618	−	0.834097i	$-0.685990\pi$
$191$	−19.4936	−	4.44930i	−1.41051	−	0.321940i	−0.858892	+	0.512157i	$0.828847\pi$
$192$	6.30354	−	4.92599i	0.454919	−	0.355503i
$193$	−2.19666	+	9.62418i	−0.158119	+	0.692764i	0.832260	+	0.554385i	$0.187046\pi$
$193$	−2.19666	+	9.62418i	−0.158119	+	0.692764i	−0.990379	+	0.138379i	$0.955811\pi$
$194$	13.1704	+	9.75371i	0.945583	+	0.700276i
$195$	11.5455			0.826789
$196$	4.76038	−	13.1658i	0.340027	−	0.940416i
$197$	0.917043			0.0653366			0.0326683	−	0.999466i	$-0.489600\pi$
$197$	0.917043			0.0653366			0.0326683	+	0.999466i	$0.489600\pi$
$198$	−2.71757	−	2.01257i	−0.193129	−	0.143027i
$199$	0.119882	−	0.525237i	0.00849821	−	0.0372331i	−0.970501	−	0.241097i	$-0.922493\pi$
$199$	0.119882	−	0.525237i	0.00849821	−	0.0372331i	0.978999	+	0.203864i	$0.0653500\pi$
$200$	3.91519	+	3.95399i	0.276845	+	0.279589i
$201$	−9.64381	−	2.20114i	−0.680222	−	0.155256i
$202$	19.0331	−	16.3250i	1.33917	−	1.14862i
$203$	1.86958	+	5.09374i	0.131219	+	0.357510i
$204$	1.09978	−	1.01374i	0.0769998	−	0.0709757i
$205$	27.8663	+	13.4197i	1.94627	+	0.937273i
$206$	−3.24388	−	3.78201i	−0.226012	−	0.263505i
$207$	3.51285	+	7.29452i	0.244160	+	0.507004i
$208$	−15.0942	−	8.84745i	−1.04659	−	0.613460i
$209$	−5.86319	−	12.1750i	−0.405566	−	0.842166i
$210$	1.60396	+	9.74524i	0.110684	+	0.672486i
$211$	−9.04895	+	18.7903i	−0.622955	+	1.29358i	0.315744	+	0.948844i	$0.397746\pi$
$211$	−9.04895	+	18.7903i	−0.622955	+	1.29358i	−0.938700	+	0.344736i	$0.887968\pi$
$212$	22.9150	+	9.08054i	1.57381	+	0.623654i
$213$	−2.19839	+	1.75316i	−0.150631	+	0.120124i
$214$	−1.18338	−	2.24799i	−0.0808939	−	0.153670i
$215$	26.1640			1.78437
$216$	−2.40229	+	1.49299i	−0.163455	+	0.101585i
$217$	−0.603990	−	0.201114i	−0.0410015	−	0.0136525i
$218$	−3.39293	+	17.7721i	−0.229798	+	1.20368i
$219$	8.61442	+	6.86977i	0.582108	+	0.464216i
$220$	−10.9529	+	6.27575i	−0.738445	+	0.423111i
$221$	−2.94719	−	1.41929i	−0.198250	−	0.0954720i
$222$	0.850551	−	4.45517i	0.0570852	−	0.299011i
$223$	−8.22903	+	10.3189i	−0.551057	+	0.691003i	−0.976876	−	0.213805i	$-0.931414\pi$
$223$	−8.22903	+	10.3189i	−0.551057	+	0.691003i	0.425820	+	0.904808i	$0.359986\pi$
$224$	5.37094	−	13.9697i	0.358861	−	0.933391i
$225$	−1.22660	−	1.53811i	−0.0817735	−	0.102541i
$226$	9.36472	−	4.92972i	0.622932	−	0.327920i
$227$	−20.4246			−1.35563			−0.677814	−	0.735233i	$-0.737073\pi$
$227$	−20.4246			−1.35563			−0.677814	+	0.735233i	$0.737073\pi$
$228$	−11.2736	+	0.807580i	−0.746615	+	0.0534833i
$229$	0.219924	−	0.0501962i	0.0145330	−	0.00331706i	−0.215248	−	0.976559i	$-0.569056\pi$
$229$	0.219924	−	0.0501962i	0.0145330	−	0.00331706i	0.229781	+	0.973242i	$0.426199\pi$
$230$	30.2035	−	1.08042i	1.99156	−	0.0712407i
$231$	−6.29675	−	0.612894i	−0.414296	−	0.0403254i
$232$	1.88881	+	5.48451i	0.124006	+	0.360076i
$233$	−0.802049	−	1.00574i	−0.0525440	−	0.0658881i	0.754865	−	0.655880i	$-0.227702\pi$
$233$	−0.802049	−	1.00574i	−0.0525440	−	0.0658881i	−0.807409	+	0.589992i	$0.799131\pi$
$234$	4.97102	+	3.68142i	0.324966	+	0.240662i
$235$	−8.41806	+	1.92137i	−0.549134	+	0.125336i
$236$	−2.86836	+	1.64350i	−0.186714	+	0.106983i
$237$	6.12929	+	1.39897i	0.398140	+	0.0908730i
$238$	0.788550	−	2.68483i	0.0511141	−	0.174031i
$239$	−10.2200	+	2.33264i	−0.661075	+	0.150886i	−0.539879	−	0.841743i	$-0.681530\pi$
$239$	−10.2200	+	2.33264i	−0.661075	+	0.150886i	−0.121196	+	0.992629i	$0.538673\pi$
$240$	1.50495	+	10.4505i	0.0971440	+	0.674575i
$241$	−10.4940	−	8.36870i	−0.675979	−	0.539076i	0.224228	−	0.974537i	$-0.428014\pi$
$241$	−10.4940	−	8.36870i	−0.675979	−	0.539076i	−0.900208	+	0.435461i	$0.856585\pi$
$242$	1.92155	+	7.21877i	0.123522	+	0.464040i
$243$	0.900969	−	0.433884i	0.0577972	−	0.0278337i
$244$	2.16938	+	1.48953i	0.138880	+	0.0953574i
$245$	11.9531	+	14.0898i	0.763658	+	0.900161i
$246$	7.71907	+	14.6635i	0.492150	+	0.934910i
$247$	10.7250	+	22.2708i	0.682417	+	1.41705i
$248$	−0.641241	−	0.227935i	−0.0407188	−	0.0144739i
$249$	−4.05518	+	5.08503i	−0.256986	+	0.322251i
$250$	10.9398	−	2.91204i	0.691893	−	0.184174i
$251$	−1.82478	−	7.99488i	−0.115179	−	0.504632i	−0.999301	−	0.0373765i	$-0.988100\pi$
$251$	−1.82478	−	7.99488i	−0.115179	−	0.504632i	0.884122	−	0.467256i	$-0.154757\pi$
$252$	−2.41679	+	4.70735i	−0.152243	+	0.296535i
$253$	−4.30797	+	18.8744i	−0.270840	+	1.18663i
$254$	−0.0864023	−	2.41541i	−0.00542136	−	0.151556i
$255$	0.439262	+	1.92453i	0.0275076	+	0.120519i
$256$	6.04081	−	14.8158i	0.377550	−	0.925989i
$257$	21.3595	−	17.0336i	1.33237	−	1.06253i	0.339842	−	0.940482i	$-0.389626\pi$
$257$	21.3595	−	17.0336i	1.33237	−	1.06253i	0.992525	−	0.122045i	$-0.0389451\pi$
$258$	11.2652	+	8.34272i	0.701339	+	0.519395i
$259$	−2.92372	−	7.96578i	−0.181671	−	0.494969i
$260$	20.0352	−	11.4797i	1.24253	−	0.711939i
$261$	−0.456354	−	1.99942i	−0.0282476	−	0.123761i
$262$	7.28114	+	3.19098i	0.449830	+	0.197140i
$263$			10.8080i			0.666449i	0.942848	+	0.333224i	$0.108137\pi$
$263$			10.8080i			0.666449i	−0.942848	+	0.333224i	$0.891863\pi$
$264$	−6.71698	−	0.790385i	−0.413402	−	0.0486449i
$265$	−25.4337	+	20.2827i	−1.56238	+	1.24595i
$266$	−17.3082	+	12.1467i	−1.06123	+	0.744761i
$267$	−11.6003	−	9.25096i	−0.709929	−	0.566150i
$268$	−18.9238	+	5.76915i	−1.15595	+	0.352407i
$269$	−2.63026	+	5.46178i	−0.160369	+	0.333011i	−0.965634	−	0.259905i	$-0.916309\pi$
$269$	−2.63026	+	5.46178i	−0.160369	+	0.333011i	0.805265	+	0.592915i	$0.202023\pi$
$270$	−0.133446	−	3.73053i	−0.00812127	−	0.227033i
$271$	−4.14757	+	5.20089i	−0.251947	+	0.315932i	−0.891681	−	0.452665i	$-0.850473\pi$
$271$	−4.14757	+	5.20089i	−0.251947	+	0.315932i	0.639733	+	0.768597i	$0.279045\pi$
$272$	0.900517	−	2.85267i	0.0546019	−	0.172969i
$273$	11.5181	+	1.12111i	0.697107	+	0.0678528i
$274$	−20.8872	−	9.15391i	−1.26184	−	0.553008i
$275$		−	4.70424i		−	0.283677i
$276$	13.3489	+	9.16555i	0.803509	+	0.551702i
$277$	−17.5646	−	22.0253i	−1.05536	−	1.32337i	−0.944128	−	0.329579i	$-0.893093\pi$
$277$	−17.5646	−	22.0253i	−1.05536	−	1.32337i	−0.111227	−	0.993795i	$-0.535478\pi$
$278$	−14.2596	−	16.6251i	−0.855231	−	0.997107i
$279$	0.216782	+	0.104397i	0.0129784	+	0.00625006i
$280$	12.4731	+	15.3164i	0.745410	+	0.915329i
$281$	−3.15435	+	1.51906i	−0.188173	+	0.0906192i	−0.525598	−	0.850733i	$-0.676158\pi$
$281$	−3.15435	+	1.51906i	−0.188173	+	0.0906192i	0.337425	+	0.941352i	$0.390444\pi$
$282$	−4.23713	−	1.85694i	−0.252317	−	0.110579i
$283$	17.1181	−	8.24363i	1.01756	−	0.490033i	0.150701	−	0.988579i	$-0.451847\pi$
$283$	17.1181	−	8.24363i	1.01756	−	0.490033i	0.866863	+	0.498547i	$0.166133\pi$
$284$	−2.07177	+	5.22817i	−0.122937	+	0.310235i
$285$	6.47220	−	13.4397i	0.383380	−	0.796097i
$286$	3.80481	+	14.2937i	0.224983	+	0.845202i
$287$	26.4971	+	16.0938i	1.56407	+	0.949987i
$288$	−2.68429	+	4.97942i	−0.158173	+	0.293415i
$289$	−3.65840	+	16.0285i	−0.215200	+	0.942853i
$290$	−7.51978	−	1.43563i	−0.441577	−	0.0843029i
$291$	−11.2981	−	2.57873i	−0.662308	−	0.151168i
$292$	21.7795	+	3.35599i	1.27455	+	0.196394i
$293$			17.5315i			1.02420i	0.858925	+	0.512101i	$0.171133\pi$
$293$			17.5315i			1.02420i	−0.858925	+	0.512101i	$0.828867\pi$
$294$	0.653852	+	9.87788i	0.0381334	+	0.576090i
$295$		−	4.36299i		−	0.254023i
$296$	−2.95379	−	8.57688i	−0.171685	−	0.498521i
$297$	2.33124	+	0.532091i	0.135272	+	0.0308751i
$298$	−1.35012	+	7.07188i	−0.0782101	+	0.409663i
$299$	7.88019	−	34.5254i	0.455723	−	1.99665i
$300$	−3.65790	−	1.44952i	−0.211189	−	0.0836880i
$301$	26.1020	+	2.54063i	1.50449	+	0.146440i
$302$	17.8886	−	4.76173i	1.02937	−	0.274007i
$303$	−7.69312	+	15.9749i	−0.441958	+	0.917735i
$304$	−18.7605	+	12.6108i	−1.07599	+	0.723279i
$305$	−3.12910	+	1.50690i	−0.179172	+	0.0862846i
$306$	−0.424532	+	0.968689i	−0.0242689	+	0.0553763i
$307$	−19.0864	+	9.19152i	−1.08932	+	0.524588i	−0.890284	−	0.455405i	$-0.849494\pi$
$307$	−19.0864	+	9.19152i	−1.08932	+	0.524588i	−0.199033	+	0.979993i	$0.563780\pi$
$308$	−11.5363	+	5.19729i	−0.657344	+	0.296143i
$309$	3.17432	+	1.52867i	0.180581	+	0.0869632i
$310$	0.681753	−	0.584748i	0.0387210	−	0.0332115i
$311$	13.1192	+	16.4510i	0.743922	+	0.932848i	0.999423	−	0.0339604i	$-0.0108120\pi$
$311$	13.1192	+	16.4510i	0.743922	+	0.932848i	−0.255502	+	0.966809i	$0.582241\pi$
$312$	12.2868	+	1.44578i	0.695602	+	0.0818513i
$313$		−	17.9475i		−	1.01445i	−0.861812	−	0.507227i	$-0.830670\pi$
$313$		−	17.9475i		−	1.01445i	0.861812	−	0.507227i	$-0.169330\pi$
$314$	1.77804	−	4.05711i	0.100341	−	0.228956i
$315$	−3.80480	−	5.85617i	−0.214376	−	0.329958i
$316$	12.0273	−	3.66668i	0.676591	−	0.206267i
$317$	9.83533	−	12.3331i	0.552407	−	0.692697i	−0.424727	−	0.905322i	$-0.639630\pi$
$317$	9.83533	−	12.3331i	0.552407	−	0.692697i	0.977134	+	0.212625i	$0.0682012\pi$
$318$	−17.4181	+	0.623068i	−0.976757	+	0.0349399i
$319$	2.12774	−	4.41831i	0.119131	−	0.247378i
$320$	13.0025	+	16.6386i	0.726861	+	0.930127i
$321$	1.40446	+	1.12002i	0.0783890	+	0.0625132i
$322$	30.2367	+	1.85502i	1.68503	+	0.103376i
$323$	−3.30429	+	2.63509i	−0.183856	+	0.146620i
$324$	1.13207	−	1.64876i	0.0628926	−	0.0915980i
$325$			8.60506i			0.477323i
$326$	13.3396	−	30.4381i	0.738813	−	1.68581i
$327$	−2.84687	−	12.4730i	−0.157432	−	0.689757i
$328$	27.9750	+	17.7709i	1.54466	+	0.981234i
$329$	−8.58467	+	1.09938i	−0.473288	+	0.0606109i
$330$	5.31231	−	7.17322i	0.292433	−	0.394873i
$331$	21.4744	−	17.1252i	1.18034	−	0.941288i	0.181227	−	0.983441i	$-0.441993\pi$
$331$	21.4744	−	17.1252i	1.18034	−	0.941288i	0.999111	+	0.0421528i	$0.0134216\pi$
$332$	−1.98102	+	12.8563i	−0.108723	+	0.705579i
$333$	0.713664	+	3.12676i	0.0391085	+	0.171346i
$334$	−19.7085	+	0.705001i	−1.07840	+	0.0385759i
$335$	5.81005	−	25.4555i	0.317437	−	1.39078i
$336$	0.486596	+	10.5718i	0.0265460	+	0.576740i
$337$	4.97482	+	21.7961i	0.270996	+	1.18731i	0.908840	+	0.417144i	$0.136969\pi$
$337$	4.97482	+	21.7961i	0.270996	+	1.18731i	−0.637845	+	0.770165i	$0.720174\pi$
$338$	−2.23067	−	8.38004i	−0.121332	−	0.455814i
$339$	−4.66578	+	5.85070i	−0.253410	+	0.317766i
$340$	2.67583	+	2.90294i	0.145117	+	0.157434i
$341$	0.249633	+	0.518368i	0.0135184	+	0.0280712i
$342$	7.07207	−	3.72284i	0.382414	−	0.201308i
$343$	10.5566	+	15.2170i	0.570004	+	0.821642i
$344$	27.8440	+	3.27639i	1.50125	+	0.176651i
$345$	−19.2544	+	9.27242i	−1.03662	+	0.499210i
$346$	16.7938	−	4.47031i	0.902840	−	0.240325i
$347$	7.49948	+	5.98063i	0.402593	+	0.321057i	0.803766	−	0.594945i	$-0.202826\pi$
$347$	7.49948	+	5.98063i	0.402593	+	0.321057i	−0.401174	+	0.916002i	$0.631398\pi$
$348$	−2.77995	−	3.01589i	−0.149021	−	0.161669i
$349$	−14.1748	+	3.23530i	−0.758758	+	0.173182i	−0.584361	−	0.811494i	$-0.698655\pi$
$349$	−14.1748	+	3.23530i	−0.758758	+	0.173182i	−0.174397	+	0.984675i	$0.555798\pi$
$350$	−7.26331	+	1.19546i	−0.388240	+	0.0639000i
$351$	−4.26434	−	0.973308i	−0.227614	−	0.0519513i
$352$	−12.4421	+	5.30712i	−0.663163	+	0.282870i
$353$	26.2175	−	5.98397i	1.39542	−	0.318494i	0.542286	−	0.840194i	$-0.317559\pi$
$353$	26.2175	−	5.98397i	1.39542	−	0.318494i	0.853129	+	0.521700i	$0.174702\pi$
$354$	1.39119	−	1.87853i	0.0739411	−	0.0998427i
$355$	−4.62758	−	5.80280i	−0.245607	−	0.307981i
$356$	−29.3286	−	4.51924i	−1.55442	−	0.239519i
$357$	0.251340	+	1.96262i	0.0133023	+	0.103873i
$358$	−0.720174	−	20.1327i	−0.0380624	−	1.06405i
$359$	6.70228	−	1.52975i	0.353733	−	0.0807372i	−0.0419622	−	0.999119i	$-0.513361\pi$
$359$	6.70228	−	1.52975i	0.353733	−	0.0807372i	0.395695	+	0.918382i	$0.370504\pi$
$360$	−3.94084	−	6.34101i	−0.207700	−	0.334200i
$361$	12.9368			0.680885
$362$	0.751885	+	1.42831i	0.0395182	+	0.0750705i
$363$	−3.29339	−	4.12978i	−0.172858	−	0.216757i
$364$	21.1024	−	9.50695i	1.10607	−	0.498299i
$365$	−18.1332	+	22.7383i	−0.949136	+	1.19018i
$366$	−1.82776	−	0.348943i	−0.0955384	−	0.0182396i
$367$	20.4900	+	9.86746i	1.06957	+	0.515077i	0.883968	−	0.467548i	$-0.154862\pi$
$367$	20.4900	+	9.86746i	1.06957	+	0.515077i	0.185602	+	0.982625i	$0.440577\pi$
$368$	32.2780	+	2.63244i	1.68261	+	0.137225i
$369$	−9.16115	−	7.30577i	−0.476910	−	0.380323i
$370$	11.7597	+	2.24509i	0.611358	+	0.116717i
$371$	−27.3429	+	17.7648i	−1.41957	+	0.922305i
$372$	0.479989	−	0.0343837i	0.0248863	−	0.00178271i
$373$	18.8643			0.976754			0.488377	−	0.872633i	$-0.337589\pi$
$373$	18.8643			0.976754			0.488377	+	0.872633i	$0.337589\pi$
$374$	−2.23787	+	1.17805i	−0.115718	+	0.0609154i
$375$	−6.25854	+	4.99102i	−0.323189	+	0.257735i
$376$	−9.19916	+	0.990581i	−0.474411	+	0.0510853i
$377$	−3.89210	+	8.08202i	−0.200453	+	0.416245i
$378$	0.229120	−	3.73464i	0.0117846	−	0.192089i
$379$	−12.1250	−	25.1779i	−0.622822	−	1.29330i	−0.938776	−	0.344528i	$-0.888039\pi$
$379$	−12.1250	−	25.1779i	−0.622822	−	1.29330i	0.315954	−	0.948774i	$-0.397675\pi$
$380$	−2.13166	−	29.7575i	−0.109352	−	1.52653i
$381$	0.741525	+	1.53979i	0.0379895	+	0.0788860i
$382$	21.4636	−	18.4096i	1.09817	−	0.941915i
$383$	2.49312	+	1.20062i	0.127392	+	0.0613490i	0.496494	−	0.868040i	$-0.334620\pi$
$383$	2.49312	+	1.20062i	0.127392	+	0.0613490i	−0.369102	+	0.929389i	$0.620335\pi$
$384$	0.292917	+	11.3099i	0.0149478	+	0.577157i
$385$	1.61777	−	16.6207i	0.0824494	−	0.847069i
$386$	−9.08897	−	10.5968i	−0.462616	−	0.539361i
$387$	−9.66372	−	2.20568i	−0.491235	−	0.112121i
$388$	−22.1700	+	6.75880i	−1.12551	+	0.343126i
$389$	−5.62109	+	24.6276i	−0.285001	+	1.24867i	0.606292	+	0.795242i	$0.292656\pi$
$389$	−5.62109	+	24.6276i	−0.285001	+	1.24867i	−0.891293	+	0.453428i	$0.850201\pi$
$390$	−9.71735	+	13.1213i	−0.492057	+	0.664425i
$391$	6.05489			0.306209
$392$	10.9562	+	16.4912i	0.553373	+	0.832934i
$393$	−5.62127			−0.283555
$394$	−0.771837	+	1.04221i	−0.0388846	+	0.0525059i
$395$	−3.69268	+	16.1787i	−0.185799	+	0.814038i
$396$	4.57453	−	1.39460i	0.229879	−	0.0700814i
$397$	−19.6796	−	4.49173i	−0.987689	−	0.225434i	−0.301984	−	0.953313i	$-0.597649\pi$
$397$	−19.6796	−	4.49173i	−0.987689	−	0.225434i	−0.685705	+	0.727879i	$0.740506\pi$
$398$	0.496028	+	0.578315i	0.0248636	+	0.0289883i
$399$	7.76189	−	12.7793i	0.388581	−	0.639766i
$400$	−7.78892	+	1.12167i	−0.389446	+	0.0560833i
$401$	14.8375	+	7.14538i	0.740951	+	0.356823i	0.765981	−	0.642864i	$-0.222254\pi$
$401$	14.8375	+	7.14538i	0.740951	+	0.356823i	−0.0250300	+	0.999687i	$0.507968\pi$
$402$	10.6184	−	9.10750i	0.529596	−	0.454241i
$403$	−0.456631	−	0.948205i	−0.0227464	−	0.0472335i
$404$	2.53378	+	35.3710i	0.126060	+	1.75977i
$405$	1.14527	+	2.37817i	0.0569087	+	0.118172i
$406$	−7.36254	−	2.16242i	−0.365397	−	0.107319i
$407$	−3.32745	+	6.90951i	−0.164935	+	0.342492i
$408$	0.226466	+	2.10311i	0.0112117	+	0.104119i
$409$	10.5952	−	8.44939i	0.523899	−	0.417795i	−0.325504	−	0.945541i	$-0.605534\pi$
$409$	10.5952	−	8.44939i	0.523899	−	0.417795i	0.849403	+	0.527745i	$0.176962\pi$
$410$	−38.7053	+	20.3750i	−1.91152	+	1.00625i
$411$	16.1256			0.795418
$412$	7.02846	−	0.503479i	0.346267	−	0.0248046i
$413$	0.423664	−	4.35265i	0.0208472	−	0.214180i
$414$	−11.2468	−	2.14716i	−0.552749	−	0.105527i
$415$	−13.4223	−	10.7039i	−0.658874	−	0.525434i
$416$	22.7592	−	9.70784i	1.11586	−	0.475966i
$417$	13.9538	+	6.71980i	0.683321	+	0.329070i
$418$	18.7716	+	3.58376i	0.918151	+	0.175287i
$419$	20.1801	−	25.3051i	0.985863	−	1.23623i	0.0141917	−	0.999899i	$-0.495482\pi$
$419$	20.1801	−	25.3051i	0.985863	−	1.23623i	0.971672	−	0.236334i	$-0.0759461\pi$
$420$	−12.4254	−	6.37928i	−0.606296	−	0.311277i
$421$	−23.6613	−	29.6704i	−1.15318	−	1.44604i	−0.874079	−	0.485783i	$-0.838534\pi$
$421$	−23.6613	−	29.6704i	−1.15318	−	1.44604i	−0.279103	−	0.960261i	$-0.590037\pi$
$422$	−13.7389	−	26.0991i	−0.668801	−	1.27048i
$423$	3.27120			0.159051
$424$	−29.6066	+	18.4000i	−1.43782	+	0.893585i
$425$	−1.43439	+	0.327390i	−0.0695781	+	0.0158807i
$426$	−0.142156	−	3.97401i	−0.00688747	−	0.192542i
$427$	−3.26801	+	1.19947i	−0.158150	+	0.0580466i
$428$	3.55082	+	0.547145i	0.171636	+	0.0264473i
$429$	−6.52114	−	8.17725i	−0.314844	−	0.394802i
$430$	−22.0212	+	29.7352i	−1.06195	+	1.43396i
$431$	−3.22583	+	0.736274i	−0.155383	+	0.0354651i	−0.299505	−	0.954095i	$-0.596821\pi$
$431$	−3.22583	+	0.736274i	−0.155383	+	0.0354651i	0.144122	+	0.989560i	$0.453964\pi$
$432$	0.325141	−	3.98676i	0.0156434	−	0.191813i
$433$	−9.73502	−	2.22196i	−0.467835	−	0.106780i	−0.0178968	−	0.999840i	$-0.505697\pi$
$433$	−9.73502	−	2.22196i	−0.467835	−	0.106780i	−0.449939	+	0.893059i	$0.648554\pi$
$434$	0.736918	−	0.517160i	0.0353732	−	0.0248245i
$435$	5.27760	−	1.20458i	0.253041	−	0.0577551i
$436$	−17.3421	−	18.8141i	−0.830538	−	0.901030i
$437$	−35.7722	−	28.5274i	−1.71122	−	1.36465i
$438$	−15.0578	+	4.00821i	−0.719490	+	0.191520i
$439$	−1.78933	+	0.861694i	−0.0853999	+	0.0411264i	−0.476096	−	0.879393i	$-0.657949\pi$
$439$	−1.78933	+	0.861694i	−0.0853999	+	0.0411264i	0.390696	+	0.920520i	$0.372234\pi$
$440$	2.08628	−	17.7299i	0.0994593	−	0.845241i
$441$	−3.22711	−	6.21174i	−0.153672	−	0.295797i
$442$	4.09354	−	2.15490i	0.194710	−	0.102498i
$443$	0.971121	+	2.01655i	0.0461394	+	0.0958094i	0.922764	−	0.385365i	$-0.125925\pi$
$443$	0.971121	+	2.01655i	0.0461394	+	0.0958094i	−0.876625	+	0.481175i	$0.840210\pi$
$444$	4.34738	+	4.71637i	0.206318	+	0.223829i
$445$	24.4185	−	30.6199i	1.15755	−	1.45152i
$446$	−4.80129	−	18.0372i	−0.227348	−	0.854086i
$447$	−1.13283	−	4.96325i	−0.0535810	−	0.234754i
$448$	11.3560	+	17.8618i	0.536519	+	0.843888i
$449$	5.83434	−	25.5619i	0.275340	−	1.20634i	−0.628274	−	0.777992i	$-0.716238\pi$
$449$	5.83434	−	25.5619i	0.275340	−	1.20634i	0.903613	−	0.428349i	$-0.140905\pi$
$450$	2.78043	−	0.0994598i	0.131071	−	0.00468858i
$451$	−6.23480	−	27.3165i	−0.293585	−	1.28628i
$452$	−2.27931	+	14.7921i	−0.107210	+	0.695760i
$453$	−10.2339	+	8.16124i	−0.480829	+	0.383449i
$454$	17.1905	−	23.2124i	0.806792	−	1.08941i
$455$	−2.95925	+	30.4028i	−0.138732	+	1.42531i
$456$	8.57074	−	13.4921i	0.401362	−	0.631826i
$457$	7.06795	+	30.9667i	0.330625	+	1.44856i	0.817924	+	0.575326i	$0.195125\pi$
$457$	7.06795	+	30.9667i	0.330625	+	1.44856i	−0.487299	+	0.873235i	$0.662018\pi$
$458$	−0.128053	+	0.292190i	−0.00598354	+	0.0136531i
$459$		−	0.747859i		−	0.0349071i
$460$	−24.1931	+	35.2353i	−1.12801	+	1.64286i
$461$	−3.31009	+	2.63971i	−0.154166	+	0.122944i	−0.697535	−	0.716550i	$-0.745720\pi$
$461$	−3.31009	+	2.63971i	−0.154166	+	0.122944i	0.543369	+	0.839494i	$0.317149\pi$
$462$	5.99626	−	6.64035i	0.278971	−	0.308937i
$463$	14.6687	+	11.6979i	0.681712	+	0.543647i	0.901972	−	0.431794i	$-0.142119\pi$
$463$	14.6687	+	11.6979i	0.681712	+	0.543647i	−0.220261	+	0.975441i	$0.570691\pi$
$464$	−7.82283	−	2.46947i	−0.363166	−	0.114642i
$465$	−0.275562	+	0.572210i	−0.0127789	+	0.0265356i
$466$	1.81806	−	0.0650346i	0.0842202	−	0.00301267i
$467$	−3.58845	+	4.49977i	−0.166054	+	0.208225i	−0.857895	−	0.513825i	$-0.828228\pi$
$467$	−3.58845	+	4.49977i	−0.166054	+	0.208225i	0.691842	+	0.722049i	$0.256800\pi$
$468$	−8.36779	+	2.55103i	−0.386801	+	0.117921i
$469$	8.26810	−	24.8309i	0.381785	−	1.14659i
$470$	4.90151	−	11.1842i	0.226090	−	0.515888i
$471$			3.13222i			0.144325i
$472$	0.546356	−	4.64313i	0.0251481	−	0.213717i
$473$	−14.7780	−	18.5311i	−0.679494	−	0.852059i
$474$	−6.74869	+	5.78843i	−0.309977	+	0.265872i
$475$	10.0168	+	4.82385i	0.459604	+	0.221333i
$476$	2.38759	+	3.15588i	0.109435	+	0.144650i
$477$	11.1038	−	5.34732i	0.508409	−	0.244837i
$478$	5.95069	−	13.5782i	0.272178	−	0.621052i
$479$	16.9367	−	8.15627i	0.773856	−	0.372669i	−0.00490686	−	0.999988i	$-0.501562\pi$
$479$	16.9367	−	8.15627i	0.773856	−	0.372669i	0.778763	+	0.627319i	$0.215848\pi$
$480$	−13.1435	−	7.08536i	−0.599917	−	0.323401i
$481$	6.08661	−	12.6390i	0.277525	−	0.576287i
$482$	18.3433	−	4.88278i	0.835516	−	0.222404i
$483$	−20.1091	+	7.38074i	−0.914995	+	0.335836i
$484$	−9.82135	−	3.89191i	−0.446425	−	0.176905i
$485$	6.80672	−	29.8222i	0.309077	−	1.35416i
$486$	−0.265203	+	1.38912i	−0.0120298	+	0.0630120i
$487$	−17.0498	−	3.89151i	−0.772601	−	0.176341i	−0.181993	−	0.983300i	$-0.558255\pi$
$487$	−17.0498	−	3.89151i	−0.772601	−	0.176341i	−0.590608	+	0.806959i	$0.701112\pi$
$488$	−3.51871	+	1.21181i	−0.159285	+	0.0548560i
$489$			23.4992i			1.06267i
$490$	−26.0733	+	1.72589i	−1.17787	+	0.0779676i
$491$		−	35.5537i		−	1.60451i	−0.596979	−	0.802257i	$-0.703632\pi$
$491$		−	35.5537i		−	1.60451i	0.596979	−	0.802257i	$-0.296368\pi$
$492$	−23.1617	−	3.56899i	−1.04421	−	0.160902i
$493$	−1.49528	−	0.341288i	−0.0673441	−	0.0153709i
$494$	−34.3373	−	6.55545i	−1.54491	−	0.294944i
$495$	−1.40449	+	6.15347i	−0.0631271	+	0.276578i
$496$	0.798752	−	0.536921i	0.0358650	−	0.0241085i
$497$	−4.05313	−	6.23840i	−0.181808	−	0.279830i
$498$	−2.36602	−	8.88853i	−0.106024	−	0.398304i
$499$	10.2078	−	21.1968i	0.456965	−	0.948898i	−0.537443	−	0.843300i	$-0.680610\pi$
$499$	10.2078	−	21.1968i	0.456965	−	0.948898i	0.994409	−	0.105599i	$-0.0336759\pi$
$500$	−5.89805	+	14.8839i	−0.263769	+	0.665629i
$501$	12.5640	−	6.05048i	0.561316	−	0.270316i
$502$	10.6219	+	4.65511i	0.474081	+	0.207768i
$503$	−4.75069	+	2.28781i	−0.211823	+	0.102008i	−0.536787	−	0.843718i	$-0.680362\pi$
$503$	−4.75069	+	2.28781i	−0.211823	+	0.102008i	0.324964	+	0.945726i	$0.394648\pi$
$504$	−3.31575	−	6.70864i	−0.147695	−	0.298826i
$505$	−42.1669	−	20.3065i	−1.87640	−	0.903627i
$506$	−17.8248	−	20.7818i	−0.792409	−	0.923864i
$507$	3.82319	+	4.79413i	0.169794	+	0.212915i
$508$	2.81781	+	1.93475i	0.125020	+	0.0858406i
$509$			4.10916i			0.182135i	0.995845	+	0.0910676i	$0.0290279\pi$
$509$			4.10916i			0.182135i	−0.995845	+	0.0910676i	$0.970972\pi$
$510$	−2.55692	−	1.12058i	−0.113222	−	0.0496201i
$511$	−20.2982	+	20.9236i	−0.897939	+	0.925605i
$512$	11.7538	+	19.3352i	0.519448	+	0.854502i
$513$	−3.52351	+	4.41834i	−0.155567	+	0.195074i
$514$	1.38118	+	38.6113i	0.0609212	+	1.70307i
$515$	−4.03504	+	8.37884i	−0.177805	+	0.369216i
$516$	−18.9628	+	5.78106i	−0.834793	+	0.254497i
$517$	6.11554	+	4.87698i	0.268961	+	0.214489i
$518$	11.5138	+	3.38168i	0.505888	+	0.148582i
$519$	−9.60754	+	7.66176i	−0.421724	+	0.336314i
$520$	−3.81624	+	32.4318i	−0.167353	+	1.42223i
$521$			3.57020i			0.156413i	0.996937	+	0.0782067i	$0.0249194\pi$
$521$			3.57020i			0.156413i	−0.996937	+	0.0782067i	$0.975081\pi$
$522$	2.65641	+	1.16418i	0.116268	+	0.0509549i
$523$	−0.550000	−	2.40971i	−0.0240498	−	0.105369i	0.961478	−	0.274880i	$-0.0886382\pi$
$523$	−0.550000	−	2.40971i	−0.0240498	−	0.105369i	−0.985528	+	0.169511i	$0.945781\pi$
$524$	−9.75475	+	5.58923i	−0.426138	+	0.244167i
$525$	4.36471	−	2.83578i	0.190492	−	0.123764i
$526$	−12.2832	−	9.09662i	−0.535572	−	0.396632i
$527$	0.140684	−	0.112192i	0.00612831	−	0.00488716i
$528$	6.55166	−	6.96855i	0.285125	−	0.303267i
$529$	9.46829	+	41.4833i	0.411665	+	1.80362i
$530$	−1.64463	−	45.9762i	−0.0714382	−	1.99708i
$531$	−0.367809	+	1.61148i	−0.0159616	+	0.0699322i
$532$	0.762970	−	29.8940i	0.0330789	−	1.29607i
$533$	11.4048	+	49.9676i	0.493996	+	2.16434i
$534$	20.2772	−	5.39754i	0.877478	−	0.233574i
$535$	−2.95636	+	3.70715i	−0.127814	+	0.160274i
$536$	9.37076	−	26.3623i	0.404755	−	1.13868i
$537$	6.18071	+	12.8344i	0.266717	+	0.553844i
$538$	−3.99349	−	7.58621i	−0.172172	−	0.327065i
$539$	3.22787	−	16.4242i	0.139034	−	0.707440i
$540$	4.35203	+	2.98817i	0.187281	+	0.128590i
$541$	2.51848	−	1.21284i	0.108278	−	0.0521439i	−0.378961	−	0.925413i	$-0.623718\pi$
$541$	2.51848	−	1.21284i	0.108278	−	0.0521439i	0.487239	+	0.873269i	$0.338004\pi$
$542$	−2.41993	−	9.09105i	−0.103945	−	0.390494i
$543$	−0.892353	−	0.711627i	−0.0382945	−	0.0305389i
$544$	2.48411	+	3.42441i	0.106505	+	0.146820i
$545$	32.9232	−	7.51451i	1.41028	−	0.321886i
$546$	−10.9684	+	12.1466i	−0.469406	+	0.519827i
$547$	−13.4255	−	3.06428i	−0.574032	−	0.131019i	−0.0743567	−	0.997232i	$-0.523690\pi$
$547$	−13.4255	−	3.06428i	−0.574032	−	0.131019i	−0.499676	+	0.866213i	$0.666547\pi$
$548$	27.9833	−	16.0337i	1.19539	−	0.684926i
$549$	1.28277	−	0.292784i	0.0547474	−	0.0124957i
$550$	5.34633	+	3.95936i	0.227968	+	0.168828i
$551$	7.22614	+	9.06129i	0.307844	+	0.386024i
$552$	−21.6518	+	7.45664i	−0.921561	+	0.317376i
$553$	−5.25494	+	15.7817i	−0.223463	+	0.671108i
$554$	39.8150	−	1.42424i	1.69158	−	0.0605100i
$555$	−8.25331	+	1.88376i	−0.350333	+	0.0799613i
$556$	30.8959	−	2.21321i	1.31028	−	0.0938611i
$557$	−12.1343			−0.514147			−0.257074	−	0.966392i	$-0.582758\pi$
$557$	−12.1343			−0.514147			−0.257074	+	0.966392i	$0.582758\pi$
$558$	−0.301102	+	0.158504i	−0.0127467	+	0.00671003i
$559$	27.0321	+	33.8972i	1.14334	+	1.43370i
$560$	−27.9050	+	1.28440i	−1.17920	+	0.0542759i
$561$	1.11497	−	1.39813i	0.0470742	−	0.0590291i
$562$	0.928491	−	4.86342i	0.0391660	−	0.205151i
$563$	28.9502	+	13.9417i	1.22010	+	0.587571i	0.929340	−	0.369224i	$-0.120376\pi$
$563$	28.9502	+	13.9417i	1.22010	+	0.587571i	0.290763	+	0.956795i	$0.406091\pi$
$564$	5.67660	−	3.25255i	0.239028	−	0.136957i
$565$	−15.4433	−	12.3156i	−0.649705	−	0.518122i
$566$	−5.03875	+	26.3928i	−0.211794	+	1.10937i
$567$	0.911619	+	2.48374i	0.0382844	+	0.104307i
$568$	−4.19805	−	6.75487i	−0.176146	−	0.283428i
$569$	45.2933			1.89880			0.949398	−	0.314077i	$-0.101695\pi$
$569$	45.2933			1.89880			0.949398	+	0.314077i	$0.101695\pi$
$570$	9.82668	+	18.6672i	0.411594	+	0.781883i
$571$	−11.3592	+	9.05862i	−0.475366	+	0.379092i	−0.831663	−	0.555281i	$-0.812611\pi$
$571$	−11.3592	+	9.05862i	−0.475366	+	0.379092i	0.356297	+	0.934373i	$0.384039\pi$
$572$	−19.4470	−	7.70625i	−0.813119	−	0.322215i
$573$	−8.67549	+	18.0148i	−0.362424	+	0.752580i
$574$	−40.5920	+	16.5682i	−1.69428	+	0.691545i
$575$	−6.91090	−	14.3506i	−0.288205	−	0.598463i
$576$	−3.39981	−	7.24163i	−0.141659	−	0.301735i
$577$	9.47811	+	19.6815i	0.394579	+	0.819351i	0.999730	+	0.0232407i	$0.00739842\pi$
$577$	9.47811	+	19.6815i	0.394579	+	0.819351i	−0.605151	+	0.796111i	$0.706887\pi$
$578$	−15.1371	−	17.6483i	−0.629622	−	0.734071i
$579$	8.89408	+	4.28317i	0.369626	+	0.178002i
$580$	7.96066	−	7.33786i	0.330548	−	0.304688i
$581$	−12.3511	−	11.9819i	−0.512408	−	0.497092i
$582$	12.4399	−	10.6698i	0.515649	−	0.442279i
$583$	28.7310	+	6.55766i	1.18992	+	0.271591i
$584$	−22.1449	+	21.9276i	−0.916363	+	0.907369i
$585$	2.56911	−	11.2560i	0.106220	−	0.465379i
$586$	−19.9244	−	14.7556i	−0.823071	−	0.609546i
$587$	−35.3839			−1.46045			−0.730225	−	0.683207i	$-0.760585\pi$
$587$	−35.3839			−1.46045			−0.730225	+	0.683207i	$0.760585\pi$
$588$	−11.7764	−	7.57070i	−0.485652	−	0.312210i
$589$	−1.35975			−0.0560275
$590$	4.95850	+	3.67215i	0.204138	+	0.151180i
$591$	0.204061	−	0.894051i	0.00839396	−	0.0367764i
$592$	12.2336	+	3.86185i	0.502799	+	0.158721i
$593$	3.91211	+	0.892914i	0.160651	+	0.0366676i	0.302090	−	0.953279i	$-0.402316\pi$
$593$	3.91211	+	0.892914i	0.160651	+	0.0366676i	−0.141439	+	0.989947i	$0.545173\pi$
$594$	−2.56683	+	2.20160i	−0.105318	+	0.0903327i
$595$	−5.18047	+	0.663429i	−0.212379	+	0.0271979i
$596$	−6.90079	−	7.48650i	−0.282667	−	0.306659i
$597$	−0.485392	−	0.233753i	−0.0198658	−	0.00956685i
$598$	32.6054	+	38.0143i	1.33333	+	1.55452i
$599$	0.793069	+	1.64683i	0.0324039	+	0.0672875i	0.916542	−	0.399937i	$-0.130968\pi$
$599$	0.793069	+	1.64683i	0.0324039	+	0.0672875i	−0.884139	+	0.467225i	$0.845254\pi$
$600$	4.72607	−	2.93718i	0.192941	−	0.119910i
$601$	−19.2202	−	39.9111i	−0.784007	−	1.62801i	−0.778194	−	0.628024i	$-0.783864\pi$
$601$	−19.2202	−	39.9111i	−0.784007	−	1.62801i	−0.00581301	−	0.999983i	$-0.501850\pi$
$602$	−24.8563	+	27.5263i	−1.01307	+	1.12189i
$603$	−4.29190	+	8.91222i	−0.174780	+	0.362934i
$604$	−9.64441	+	24.3380i	−0.392426	+	0.990299i
$605$	10.9008	−	8.69312i	0.443182	−	0.353426i
$606$	−11.6804	−	22.1886i	−0.474483	−	0.901349i
$607$	−5.42979			−0.220388			−0.110194	−	0.993910i	$-0.535147\pi$
$607$	−5.42979			−0.220388			−0.110194	+	0.993910i	$0.535147\pi$
$608$	1.45786	−	31.9351i	0.0591239	−	1.29514i
$609$	5.38205	−	0.689244i	0.218092	−	0.0279296i
$610$	0.921059	−	4.82449i	0.0372926	−	0.195338i
$611$	−11.1866	−	8.92104i	−0.452562	−	0.360907i
$612$	−0.743596	−	1.29778i	−0.0300581	−	0.0524597i
$613$	42.0070	+	20.2295i	1.69665	+	0.817061i	0.994466	+	0.105062i	$0.0335040\pi$
$613$	42.0070	+	20.2295i	1.69665	+	0.817061i	0.702180	+	0.712000i	$0.252210\pi$
$614$	5.61813	−	29.4276i	0.226729	−	1.18760i
$615$	19.2841	−	24.1815i	0.777609	−	0.975091i
$616$	3.80297	−	17.4853i	0.153226	−	0.704502i
$617$	−3.14118	−	3.93891i	−0.126459	−	0.158575i	0.714571	−	0.699563i	$-0.246622\pi$
$617$	−3.14118	−	3.93891i	−0.126459	−	0.158575i	−0.841030	+	0.540988i	$0.818050\pi$
$618$	−4.40902	+	2.32097i	−0.177357	+	0.0933631i
$619$	13.9091			0.559053			0.279526	−	0.960138i	$-0.409823\pi$
$619$	13.9091			0.559053			0.279526	+	0.960138i	$0.409823\pi$
$620$	0.0907582	+	1.26696i	0.00364494	+	0.0508825i
$621$	7.89331	−	1.80160i	0.316748	−	0.0722956i
$622$	−29.7382	+	1.06378i	−1.19240	+	0.0426536i
$623$	27.3339	−	28.1761i	1.09511	−	1.12885i
$624$	−11.9844	+	12.7470i	−0.479760	+	0.510287i
$625$	−19.3071	−	24.2104i	−0.772286	−	0.968416i
$626$	20.3972	+	15.1057i	0.815237	+	0.603745i
$627$	−13.1745	+	3.00699i	−0.526138	+	0.120088i
$628$	3.11437	+	5.43543i	0.124277	+	0.216897i
$629$	2.33838	+	0.533720i	0.0932373	+	0.0212808i
$630$	9.85782	+	0.604777i	0.392745	+	0.0240949i
$631$	37.5419	−	8.56869i	1.49452	−	0.341114i	0.604340	−	0.796727i	$-0.293437\pi$
$631$	37.5419	−	8.56869i	1.49452	−	0.341114i	0.890178	+	0.455613i	$0.150580\pi$
$632$	−5.95575	+	16.7551i	−0.236907	+	0.666480i
$633$	16.3056	+	13.0033i	0.648091	+	0.516835i
$634$	5.73849	+	21.5580i	0.227905	+	0.856179i
$635$	−4.06439	+	1.95731i	−0.161290	+	0.0776733i
$636$	13.9520	−	20.3199i	0.553231	−	0.805737i
$637$	−5.90447	+	30.0433i	−0.233943	+	1.19036i
$638$	3.23053	+	6.13686i	0.127898	+	0.242961i
$639$	1.22002	+	2.53339i	0.0482631	+	0.100219i
$640$	−29.8533	+	0.773173i	−1.18005	+	0.0305624i
$641$	−3.99746	+	5.01266i	−0.157890	+	0.197988i	−0.854484	−	0.519478i	$-0.826127\pi$
$641$	−3.99746	+	5.01266i	−0.157890	+	0.197988i	0.696594	+	0.717466i	$0.254698\pi$
$642$	−2.45496	+	0.653481i	−0.0968895	+	0.0257908i
$643$	−10.5471	−	46.2097i	−0.415936	−	1.82233i	−0.554754	−	0.832015i	$-0.687187\pi$
$643$	−10.5471	−	46.2097i	−0.415936	−	1.82233i	0.138818	−	0.990318i	$-0.455670\pi$
$644$	−27.5572	+	32.8025i	−1.08591	+	1.29260i
$645$	5.82205	−	25.5080i	0.229243	−	1.00438i
$646$	−0.213667	−	5.97314i	−0.00840663	−	0.235010i
$647$	−5.09918	−	22.3410i	−0.200470	−	0.878315i	−0.970652	−	0.240490i	$-0.922692\pi$
$647$	−5.09918	−	22.3410i	−0.200470	−	0.878315i	0.770182	−	0.637824i	$-0.220165\pi$
$648$	0.920994	+	2.67428i	0.0361800	+	0.105056i
$649$	−3.09015	+	2.46432i	−0.121299	+	0.0967328i
$650$	−9.77958	−	7.24252i	−0.383587	−	0.284075i
$651$	−0.330472	+	0.544095i	−0.0129522	+	0.0213248i
$652$	23.3653	+	40.7789i	0.915054	+	1.59702i
$653$	2.71804	+	11.9085i	0.106365	+	0.466015i	0.999857	+	0.0169355i	$0.00539098\pi$
$653$	2.71804	+	11.9085i	0.106365	+	0.466015i	−0.893492	+	0.449080i	$0.851752\pi$
$654$	16.5715	+	7.26252i	0.647997	+	0.283987i
$655$		−	14.8377i		−	0.579758i
$656$	−43.7419	+	16.8364i	−1.70783	+	0.657350i
$657$	8.61442	−	6.86977i	0.336080	−	0.268015i
$658$	5.97591	−	10.6817i	0.232965	−	0.416416i
$659$	8.46957	+	6.75426i	0.329928	+	0.263108i	0.774417	−	0.632676i	$-0.218043\pi$
$659$	8.46957	+	6.75426i	0.329928	+	0.263108i	−0.444489	+	0.895784i	$0.646615\pi$
$660$	3.68115	+	12.0748i	0.143289	+	0.470010i
$661$	13.9357	−	28.9378i	0.542036	−	1.12555i	−0.432566	−	0.901602i	$-0.642392\pi$
$661$	13.9357	−	28.9378i	0.542036	−	1.12555i	0.974601	−	0.223946i	$-0.0718941\pi$
$662$	1.38861	+	38.8190i	0.0539698	+	1.50874i
$663$	−2.03952	+	2.55748i	−0.0792084	+	0.0993243i
$664$	−12.9437	−	13.0720i	−0.502313	−	0.507291i
$665$	33.7318	+	20.4880i	1.30806	+	0.794492i
$666$	−4.15420	−	1.82059i	−0.160972	−	0.0705466i
$667$		−	16.6042i		−	0.642917i
$668$	15.7866	−	22.9919i	0.610802	−	0.889584i
$669$	8.22903	+	10.3189i	0.318153	+	0.398951i
$670$	24.0399	+	28.0279i	0.928741	+	1.08281i
$671$	2.83467	+	1.36510i	0.109431	+	0.0526992i
$672$	−12.4243	−	8.34484i	−0.479278	−	0.321909i
$673$	−21.4151	+	10.3130i	−0.825493	+	0.397536i	−0.798423	−	0.602097i	$-0.794332\pi$
$673$	−21.4151	+	10.3130i	−0.825493	+	0.397536i	−0.0270699	+	0.999634i	$0.508618\pi$
$674$	−28.9582	−	12.6910i	−1.11543	−	0.488840i
$675$	−1.77249	+	0.853588i	−0.0682233	+	0.0328546i
$676$	11.4013	+	4.51799i	0.438511	+	0.173769i
$677$	−15.7669	+	32.7403i	−0.605970	+	1.25831i	0.341924	+	0.939727i	$0.388921\pi$
$677$	−15.7669	+	32.7403i	−0.605970	+	1.25831i	−0.947895	+	0.318583i	$0.896793\pi$
$678$	−2.72228	−	10.2269i	−0.104548	−	0.392762i
$679$	9.68643	−	29.0905i	0.371731	−	1.11639i
$680$	−5.55129	+	0.597772i	−0.212882	+	0.0229235i
$681$	−4.54490	+	19.9125i	−0.174161	+	0.763049i
$682$	−0.799226	−	0.152583i	−0.0306039	−	0.00584270i
$683$	−4.47652	−	1.02174i	−0.171289	−	0.0390956i	0.136016	−	0.990707i	$-0.456570\pi$
$683$	−4.47652	−	1.02174i	−0.171289	−	0.0390956i	−0.307305	+	0.951611i	$0.599427\pi$
$684$	−1.72129	+	11.1707i	−0.0658151	+	0.427122i
$685$			42.5647i			1.62631i
$686$	−26.1791	−	0.810032i	−0.999522	−	0.0309272i
$687$		−	0.225580i		−	0.00860641i
$688$	−27.1587	+	28.8868i	−1.03541	+	1.10130i
$689$	−52.5551	−	11.9954i	−2.00219	−	0.456987i
$690$	5.66757	−	29.6866i	0.215761	−	1.13015i
$691$	−9.72102	+	42.5906i	−0.369805	+	1.62022i	0.357504	+	0.933912i	$0.383628\pi$
$691$	−9.72102	+	42.5906i	−0.369805	+	1.62022i	−0.727309	+	0.686310i	$0.759229\pi$
$692$	−9.05416	+	22.8485i	−0.344187	+	0.868568i
$693$	−1.99869	+	6.00250i	−0.0759238	+	0.228016i
$694$	−13.1089	+	3.48944i	−0.497608	+	0.132457i
$695$	−17.7374	+	36.8320i	−0.672817	+	1.39712i
$696$	5.76730	−	0.621033i	0.218609	−	0.0235402i
$697$	−7.89526	+	3.80216i	−0.299054	+	0.144017i
$698$	8.25342	−	18.8325i	0.312397	−	0.712821i
$699$	−1.15899	+	0.558142i	−0.0438372	+	0.0211109i
$700$	4.75459	−	9.26085i	0.179707	−	0.350027i
$701$	12.1120	+	5.83283i	0.457464	+	0.220303i	0.648401	−	0.761299i	$-0.275438\pi$
$701$	12.1120	+	5.83283i	0.457464	+	0.220303i	−0.190937	+	0.981602i	$0.561153\pi$
$702$	4.69527	−	4.02719i	0.177212	−	0.151997i
$703$	−11.3005	−	14.1704i	−0.426207	−	0.534446i
$704$	4.44046	−	18.6071i	0.167356	−	0.701280i
$705$			8.63455i			0.325196i
$706$	−15.2654	+	34.8324i	−0.574522	+	1.31093i
$707$	−40.0950	−	24.3529i	−1.50793	−	0.915885i
$708$	0.964023	+	3.16216i	0.0362302	+	0.118841i
$709$	2.42715	−	3.04355i	0.0911534	−	0.114303i	−0.734163	−	0.678973i	$-0.762425\pi$
$709$	2.42715	−	3.04355i	0.0911534	−	0.114303i	0.825317	+	0.564670i	$0.190997\pi$
$710$	10.4897	−	0.375230i	0.393670	−	0.0140821i
$711$	2.72779	−	5.66432i	0.102300	−	0.212429i
$712$	29.8208	−	29.5281i	1.11758	−	1.10661i
$713$	1.52305	+	1.21459i	0.0570385	+	0.0454867i
$714$	−2.44204	−	1.36621i	−0.0913912	−	0.0511291i
$715$	21.5844	−	17.2130i	0.807211	−	0.643730i
$716$	23.4868	+	16.1264i	0.877742	+	0.602671i
$717$			10.4828i			0.391487i
$718$	−3.90248	+	8.90460i	−0.145639	+	0.332317i
$719$	−3.97257	−	17.4050i	−0.148152	−	0.649096i	−0.993398	−	0.114719i	$-0.963403\pi$
$719$	−3.97257	−	17.4050i	−0.148152	−	0.649096i	0.845246	−	0.534377i	$-0.179454\pi$
$720$	10.5233	+	0.858232i	0.392181	+	0.0319844i
$721$	−4.83909	+	7.96715i	−0.180217	+	0.296712i
$722$	−10.8884	+	14.7026i	−0.405223	+	0.547173i
$723$	−10.4940	+	8.36870i	−0.390277	+	0.311235i
$724$	−2.25610	−	0.347641i	−0.0838472	−	0.0129200i
$725$	0.897794	+	3.93349i	0.0333432	+	0.146086i
$726$	7.46536	−	0.267046i	0.277066	−	0.00991101i
$727$	−3.13918	+	13.7536i	−0.116426	+	0.510094i	0.882763	+	0.469819i	$0.155681\pi$
$727$	−3.13918	+	13.7536i	−0.116426	+	0.510094i	−0.999189	+	0.0402754i	$0.987176\pi$
$728$	−6.95645	+	31.9843i	−0.257823	+	1.18542i
$729$	−0.222521	−	0.974928i	−0.00824152	−	0.0361084i
$730$	−10.5800	−	39.7461i	−0.391582	−	1.47107i
$731$	−4.62190	+	5.79568i	−0.170947	+	0.214361i
$732$	1.93492	−	1.78354i	0.0715166	−	0.0659215i
$733$	−21.6721	−	45.0026i	−0.800477	−	1.66221i	−0.748104	−	0.663581i	$-0.769036\pi$
$733$	−21.6721	−	45.0026i	−0.800477	−	1.66221i	−0.0523730	−	0.998628i	$-0.516678\pi$
$734$	−28.4599	+	14.9817i	−1.05047	+	0.552984i
$735$	16.3963	−	8.51818i	0.604787	−	0.314198i
$736$	−30.1588	+	34.4681i	−1.11167	+	1.27051i
$737$	−21.3109	+	10.2628i	−0.784996	+	0.378034i
$738$	16.0135	−	4.26260i	0.589465	−	0.156909i
$739$	−19.0718	−	15.2093i	−0.701567	−	0.559481i	0.206428	−	0.978462i	$-0.433816\pi$
$739$	−19.0718	−	15.2093i	−0.701567	−	0.559481i	−0.907995	+	0.418980i	$0.862388\pi$
$740$	−12.4492	+	11.4752i	−0.457641	+	0.421837i
$741$	24.0989	−	5.50042i	0.885296	−	0.202063i
$742$	2.82374	−	46.0268i	0.103663	−	1.68970i
$743$	15.9092	+	3.63118i	0.583654	+	0.133215i	0.504145	−	0.863619i	$-0.331808\pi$
$743$	15.9092	+	3.63118i	0.583654	+	0.133215i	0.0795086	+	0.996834i	$0.474665\pi$
$744$	−0.364910	+	0.574443i	−0.0133783	+	0.0210601i
$745$	13.1008	−	2.99018i	0.479977	−	0.109552i
$746$	−15.8773	+	21.4391i	−0.581307	+	0.784940i
$747$	4.05518	+	5.08503i	0.148371	+	0.186052i
$748$	0.544682	−	3.53483i	0.0199155	−	0.129246i
$749$	−3.30932	+	3.41129i	−0.120920	+	0.124646i
$750$	−0.404699	−	11.3135i	−0.0147775	−	0.413111i
$751$	48.0662	−	10.9708i	1.75396	−	0.400330i	0.779772	−	0.626063i	$-0.215335\pi$
$751$	48.0662	−	10.9708i	1.75396	−	0.400330i	0.974189	+	0.225733i	$0.0724776\pi$
$752$	6.61676	−	11.2885i	0.241288	−	0.411649i
$753$	−8.20048			−0.298842
$754$	−5.90933	−	11.2256i	−0.215205	−	0.408813i
$755$	−21.5422	−	27.0130i	−0.783999	−	0.983104i
$756$	4.05154	+	3.40368i	0.147353	+	0.123791i
$757$	5.16090	−	6.47157i	0.187576	−	0.235213i	−0.679147	−	0.734002i	$-0.737650\pi$
$757$	5.16090	−	6.47157i	0.187576	−	0.235213i	0.866724	+	0.498789i	$0.166222\pi$
$758$	38.8196	+	7.41118i	1.40999	+	0.269186i
$759$	17.4426	+	8.39992i	0.633127	+	0.304898i
$760$	35.6133	+	22.6231i	1.29183	+	0.820625i
$761$	31.0552	+	24.7657i	1.12575	+	0.897754i	0.995597	−	0.0937398i	$-0.0298822\pi$
$761$	31.0552	+	24.7657i	1.12575	+	0.897754i	0.130152	+	0.991494i	$0.458454\pi$
$762$	−2.37407	−	0.453242i	−0.0860036	−	0.0164192i
$763$	33.5748	−	4.29971i	1.21549	−	0.155660i
$764$	2.85733	+	39.8877i	0.103375	+	1.44309i
$765$	1.97402			0.0713710
$766$	−3.46285	+	1.82289i	−0.125118	+	0.0658638i
$767$	5.65255	−	4.50776i	0.204102	−	0.162766i
$768$	−13.1002	−	9.18618i	−0.472711	−	0.331478i
$769$	−7.63740	+	15.8592i	−0.275412	+	0.571898i	−0.992093	−	0.125502i	$-0.959946\pi$
$769$	−7.63740	+	15.8592i	−0.275412	+	0.571898i	0.716682	+	0.697400i	$0.245660\pi$
$770$	17.5277	+	15.8275i	0.631653	+	0.570385i
$771$	−11.8536	−	24.6143i	−0.426897	−	0.886461i
$772$	19.6929	−	1.41069i	0.708764	−	0.0507718i
$773$	−13.7267	−	28.5037i	−0.493714	−	1.02521i	−0.987790	−	0.155789i	$-0.950208\pi$
$773$	−13.7267	−	28.5037i	−0.493714	−	1.02521i	0.494076	−	0.869418i	$-0.335506\pi$
$774$	10.6403	−	9.12630i	0.382457	−	0.328038i
$775$	−0.426479	−	0.205381i	−0.0153196	−	0.00737752i
$776$	10.9782	−	30.8846i	0.394096	−	1.10869i
$777$	−8.41665	+	1.07787i	−0.301946	+	0.0386682i
$778$	−23.2580	−	27.1164i	−0.833841	−	0.972168i
$779$	64.5588	+	14.7351i	2.31306	+	0.527940i
$780$	−6.73360	−	22.0874i	−0.241102	−	0.790854i
$781$	−1.49616	+	6.55510i	−0.0535368	+	0.234560i
$782$	−5.09615	+	6.88133i	−0.182238	+	0.246076i
$783$	−2.05084			−0.0732909
$784$	−27.9635	−	1.42833i	−0.998698	−	0.0510119i
$785$	−8.26771			−0.295087
$786$	4.73118	−	6.38852i	0.168756	−	0.227871i
$787$	3.67981	−	16.1223i	0.131171	−	0.574698i	−0.866034	−	0.499985i	$-0.833339\pi$
$787$	3.67981	−	16.1223i	0.131171	−	0.574698i	0.997205	−	0.0747127i	$-0.0238040\pi$
$788$	−0.534842	−	1.75437i	−0.0190530	−	0.0624969i
$789$	10.5370	+	2.40500i	0.375127	+	0.0856203i
$790$	−15.2790	−	17.8136i	−0.543601	−	0.633780i
$791$	−14.2108	−	13.7860i	−0.505277	−	0.490175i
$792$	−2.26524	+	6.37269i	−0.0804917	+	0.226444i
$793$	−5.18521	−	2.49706i	−0.184132	−	0.0886734i
$794$	21.6683	−	18.5851i	0.768978	−	0.659562i
$795$	14.1146	+	29.3093i	0.500594	+	1.03949i
$796$	−1.07474	+	0.0769880i	−0.0380930	+	0.00272877i
$797$	6.44658	+	13.3865i	0.228350	+	0.474173i	0.983390	−	0.181506i	$-0.0580970\pi$
$797$	6.44658	+	13.3865i	0.228350	+	0.474173i	−0.755040	+	0.655678i	$0.772383\pi$
$798$	7.99071	+	19.5771i	0.282868	+	0.693023i
$799$	1.06145	−	2.20412i	0.0375514	−	0.0779763i
$800$	5.28085	−	9.79610i	0.186706	−	0.346344i
$801$	−11.6003	+	9.25096i	−0.409878	+	0.326867i
$802$	−20.6088	+	10.8488i	−0.727721	+	0.383083i
$803$	26.3468			0.929758
$804$	1.41357	+	19.7331i	0.0498526	+	0.695932i
$805$	−19.4820	−	53.0793i	−0.686649	−	1.87080i
$806$	1.46195	+	0.279107i	0.0514951	+	0.00983111i
$807$	4.73956	+	3.77967i	0.166840	+	0.133051i
$808$	−42.3314	−	26.8907i	−1.48921	−	0.946010i
$809$	36.9283	+	17.7837i	1.29833	+	0.625242i	0.950035	−	0.312143i	$-0.101047\pi$
$809$	36.9283	+	17.7837i	1.29833	+	0.625242i	0.348294	+	0.937385i	$0.386761\pi$
$810$	−3.66669	−	0.700020i	−0.128834	−	0.0245962i
$811$	14.2306	−	17.8446i	0.499703	−	0.626607i	−0.466460	−	0.884543i	$-0.654471\pi$
$811$	14.2306	−	17.8446i	0.499703	−	0.626607i	0.966162	+	0.257935i	$0.0830421\pi$
$812$	8.65431	−	6.54744i	0.303707	−	0.229770i
$813$	4.14757	+	5.20089i	0.145462	+	0.182403i
$814$	−5.05203	−	9.59706i	−0.177074	−	0.336377i
$815$	−62.0277			−2.17274
$816$	−2.58077	−	1.51272i	−0.0903450	−	0.0529558i
$817$	54.6123	−	12.4649i	1.91064	−	0.436091i
$818$	0.685123	+	19.1528i	0.0239548	+	0.669664i
$819$	3.65602	−	10.9798i	0.127752	−	0.383667i
$820$	9.42058	−	61.1370i	0.328981	−	2.13500i
$821$	−0.0238844	−	0.0299501i	−0.000833572	−	0.00104527i	0.781415	−	0.624012i	$-0.214498\pi$
$821$	−0.0238844	−	0.0299501i	−0.000833572	−	0.00104527i	−0.782248	+	0.622967i	$0.785927\pi$
$822$	−13.5723	+	18.3266i	−0.473387	+	0.639214i
$823$	−38.7006	+	8.83315i	−1.34902	+	0.307904i	−0.835177	−	0.549982i	$-0.814635\pi$
$823$	−38.7006	+	8.83315i	−1.34902	+	0.307904i	−0.513840	+	0.857886i	$0.671777\pi$
$824$	−5.34336	+	8.41154i	−0.186145	+	0.293030i
$825$	−4.58630	−	1.04679i	−0.159674	−	0.0364446i
$826$	4.59016	+	4.14493i	0.159712	+	0.144221i
$827$	32.7294	−	7.47027i	1.13811	−	0.259767i	0.388375	−	0.921501i	$-0.373037\pi$
$827$	32.7294	−	7.47027i	1.13811	−	0.259767i	0.749738	+	0.661735i	$0.230179\pi$
$828$	11.9062	−	10.9747i	0.413768	−	0.381397i
$829$	−12.8407	−	10.2401i	−0.445976	−	0.355654i	0.374605	−	0.927185i	$-0.377778\pi$
$829$	−12.8407	−	10.2401i	−0.445976	−	0.355654i	−0.820581	+	0.571531i	$0.806350\pi$
$830$	23.4619	−	6.24527i	0.814374	−	0.216777i
$831$	−25.3816	+	12.2231i	−0.880478	+	0.424016i
$832$	−8.12254	+	34.0363i	−0.281599	+	1.18000i
$833$	−5.23260	+	0.158811i	−0.181299	+	0.00550248i
$834$	−19.3813	+	10.2026i	−0.671120	+	0.353287i
$835$	15.9707	+	33.1634i	0.552688	+	1.14767i
$836$	−19.8722	+	18.3175i	−0.687294	+	0.633524i
$837$	0.150018	−	0.188116i	0.00518537	−	0.00650225i
$838$	11.7742	+	44.2327i	0.406734	+	1.52799i
$839$	2.94685	+	12.9110i	0.101737	+	0.445737i	0.999981	+	0.00623994i	$0.00198625\pi$
$839$	2.94685	+	12.9110i	0.101737	+	0.445737i	−0.898244	+	0.439497i	$0.855157\pi$
$840$	17.7079	−	8.75215i	0.610981	−	0.301978i
$841$	5.51720	−	24.1724i	0.190248	−	0.833532i
$842$	53.6348	−	1.91859i	1.84838	−	0.0661190i
$843$	0.779060	+	3.41329i	0.0268323	+	0.117560i
$844$	41.2249	+	6.35233i	1.41902	+	0.218656i
$845$	−12.6544	+	10.0916i	−0.435326	+	0.347161i
$846$	−2.75323	+	3.71769i	−0.0946580	+	0.127817i
$847$	11.7191	−	7.61399i	0.402673	−	0.261620i
$848$	4.00714	−	49.1341i	0.137606	−	1.68727i
$849$	−4.22781	−	18.5233i	−0.145098	−	0.635717i
$850$	0.835189	−	1.90572i	0.0286467	−	0.0653657i
$851$			25.9663i			0.890112i
$852$	4.63608	+	3.18320i	0.158829	+	0.109055i
$853$	17.7230	−	14.1337i	0.606825	−	0.483927i	−0.271212	−	0.962520i	$-0.587424\pi$
$853$	17.7230	−	14.1337i	0.606825	−	0.483927i	0.878037	+	0.478593i	$0.158853\pi$
$854$	1.38735	−	4.72360i	0.0474742	−	0.161638i
$855$	−11.6625	−	9.30054i	−0.398849	−	0.318072i
$856$	−3.61040	+	3.57497i	−0.123401	+	0.122190i
$857$	−2.03871	+	4.23342i	−0.0696410	+	0.144611i	−0.932883	−	0.360179i	$-0.882716\pi$
$857$	−2.03871	+	4.23342i	−0.0696410	+	0.144611i	0.863242	+	0.504790i	$0.168430\pi$
$858$	14.7819	−	0.528770i	0.504647	−	0.0180519i
$859$	−15.9026	+	19.9412i	−0.542588	+	0.680384i	−0.975233	−	0.221180i	$-0.929009\pi$
$859$	−15.9026	+	19.9412i	−0.542588	+	0.680384i	0.432645	+	0.901565i	$0.357580\pi$
$860$	−15.2595	−	50.0537i	−0.520345	−	1.70682i
$861$	21.5865	−	22.2516i	0.735665	−	0.758331i
$862$	1.87827	−	4.28581i	0.0639743	−	0.145975i
$863$			15.3968i			0.524115i	0.965052	+	0.262057i	$0.0844009\pi$
$863$			15.3968i			0.524115i	−0.965052	+	0.262057i	$0.915599\pi$
$864$	4.25726	+	3.72501i	0.144835	+	0.126727i
$865$	−20.2237	−	25.3598i	−0.687628	−	0.862258i
$866$	10.7188	−	9.19364i	0.364239	−	0.312413i
$867$	14.8126	+	7.13336i	0.503061	+	0.242261i
$868$	−0.0324844	+	1.27277i	−0.00110259	+	0.0432007i
$869$	13.5445	−	6.52268i	0.459466	−	0.221267i
$870$	−3.07294	+	7.01179i	−0.104182	+	0.237722i
$871$	38.9821	−	18.7728i	1.32086	−	0.636092i
$872$	35.9781	−	3.87419i	1.21837	−	0.131197i
$873$	−5.02814	+	10.4410i	−0.170177	+	0.353376i
$874$	62.5291	−	16.6445i	2.11508	−	0.563008i
$875$	−11.5387	−	17.7599i	−0.390080	−	0.600394i
$876$	8.11823	−	20.4866i	0.274290	−	0.692179i
$877$	−1.14958	+	5.03664i	−0.0388186	+	0.170075i	−0.990621	−	0.136635i	$-0.956371\pi$
$877$	−1.14958	+	5.03664i	−0.0388186	+	0.170075i	0.951803	+	0.306711i	$0.0992283\pi$
$878$	0.526693	−	2.75881i	0.0177750	−	0.0931052i
$879$	17.0920	+	3.90113i	0.576498	+	0.131582i
$880$	18.3940	+	17.2936i	0.620061	+	0.582966i
$881$		−	32.0721i		−	1.08054i	−0.841492	−	0.540269i	$-0.818322\pi$
$881$		−	32.0721i		−	1.08054i	0.841492	−	0.540269i	$-0.181678\pi$
$882$	9.77571	+	1.56058i	0.329165	+	0.0525473i
$883$			50.0789i			1.68529i	0.538471	+	0.842644i	$0.319002\pi$
$883$			50.0789i			1.68529i	−0.538471	+	0.842644i	$0.680998\pi$
$884$	−0.996339	+	6.46596i	−0.0335105	+	0.217474i
$885$	−4.25361	−	0.970858i	−0.142983	−	0.0326350i
$886$	−3.10915	−	0.593578i	−0.104454	−	0.0199416i
$887$	−5.08745	+	22.2896i	−0.170820	+	0.748410i	0.814843	+	0.579682i	$0.196823\pi$
$887$	−5.08745	+	22.2896i	−0.170820	+	0.748410i	−0.985663	+	0.168728i	$0.946034\pi$
$888$	−9.01912	+	0.971194i	−0.302662	+	0.0325911i
$889$	−4.24481	+	1.55800i	−0.142366	+	0.0522535i
$890$	14.2472	+	53.5229i	0.477566	+	1.79409i
$891$	1.03750	−	2.15439i	0.0347576	−	0.0721749i
$892$	24.5401	+	9.72452i	0.821665	+	0.325601i
$893$	−16.6557	+	8.02095i	−0.557361	+	0.268411i
$894$	6.59414	+	2.88991i	0.220541	+	0.0966529i
$895$	−33.8772	+	16.3144i	−1.13239	+	0.545330i
$896$	−29.8576	−	2.12753i	−0.997471	−	0.0710760i
$897$	−31.9063	−	15.3652i	−1.06532	−	0.513030i
$898$	24.1404	+	28.1451i	0.805575	+	0.939213i
$899$	−0.307662	−	0.385796i	−0.0102611	−	0.0128670i
$900$	−2.22714	+	3.24365i	−0.0742379	+	0.108122i
$901$		−	9.21685i		−	0.307058i
$902$	36.2925	+	15.9053i	1.20841	+	0.529589i
$903$	8.28517	−	24.8822i	0.275713	−	0.828028i
$904$	−14.8927	−	15.0403i	−0.495322	−	0.500232i
$905$	1.87839	−	2.35543i	0.0624398	−	0.0782970i
$906$	−0.661759	−	18.4997i	−0.0219855	−	0.614611i
$907$	−0.00210864	+	0.00437864i	−7.00163e−5	+	0.000145390i	−0.901004	−	0.433811i	$-0.857169\pi$
$907$	−0.00210864	+	0.00437864i	−7.00163e−5	+	0.000145390i	0.900934	+	0.433956i	$0.142883\pi$
$908$	11.9121	+	39.0738i	0.395318	+	1.29671i
$909$	13.8625	+	11.0550i	0.459791	+	0.366671i
$910$	−32.0618	−	28.9519i	−1.06284	−	0.959747i
$911$	−21.6568	+	17.2707i	−0.717521	+	0.572204i	−0.912733	−	0.408557i	$-0.866032\pi$
$911$	−21.6568	+	17.2707i	−0.717521	+	0.572204i	0.195212	+	0.980761i	$0.437461\pi$
$912$	8.12002	+	21.0963i	0.268881	+	0.698569i
$913$			15.5523i			0.514707i
$914$	−41.1422	−	18.0307i	−1.36086	−	0.596403i
$915$	0.772824	+	3.38596i	0.0255488	+	0.111937i
$916$	−0.224294	−	0.391455i	−0.00741089	−	0.0129340i
$917$	1.44080	−	14.8025i	0.0475795	−	0.488822i
$918$	0.849935	+	0.629441i	0.0280520	+	0.0207747i
$919$	34.1168	−	27.2072i	1.12541	−	0.897483i	0.129841	−	0.991535i	$-0.458553\pi$
$919$	34.1168	−	27.2072i	1.12541	−	0.897483i	0.995567	+	0.0940514i	$0.0299818\pi$
$920$	−19.6823	−	57.1513i	−0.648907	−	1.88422i
$921$	4.71395	+	20.6531i	0.155330	+	0.680544i
$922$	−0.214042	−	5.98362i	−0.00704911	−	0.197060i
$923$	2.73679	−	11.9907i	0.0900827	−	0.394678i
$924$	2.49991	+	12.4036i	0.0822409	+	0.408048i
$925$	−1.40400	−	6.15134i	−0.0461634	−	0.202255i
$926$	−25.6406	+	6.82521i	−0.842601	+	0.224290i
$927$	2.19670	−	2.75457i	0.0721491	−	0.0904721i
$928$	9.39067	−	6.81212i	0.308264	−	0.223619i
$929$	26.2768	+	54.5644i	0.862114	+	1.79020i	0.533732	+	0.845654i	$0.320789\pi$
$929$	26.2768	+	54.5644i	0.862114	+	1.79020i	0.328383	+	0.944545i	$0.393496\pi$
$930$	−0.418383	−	0.794779i	−0.0137193	−	0.0260618i
$931$	31.6624	+	23.7149i	1.03769	+	0.777226i
$932$	−1.45628	+	2.12095i	−0.0477019	+	0.0694740i
$933$	18.9578	−	9.12959i	0.620650	−	0.298889i
$934$	−2.09371	−	7.86551i	−0.0685081	−	0.257367i
$935$	3.69046	+	2.94304i	0.120691	+	0.0962479i
$936$	4.14360	−	11.6570i	0.135438	−	0.381021i
$937$	−15.5567	+	3.55071i	−0.508215	+	0.115997i	−0.468937	−	0.883232i	$-0.655363\pi$
$937$	−15.5567	+	3.55071i	−0.508215	+	0.115997i	−0.0392778	+	0.999228i	$0.512506\pi$
$938$	21.2612	+	30.2958i	0.694204	+	0.989192i
$939$	−17.4976	−	3.99370i	−0.571011	−	0.130330i
$940$	8.58533	+	14.9838i	0.280023	+	0.488717i
$941$	45.4140	−	10.3655i	1.48045	−	0.337904i	0.595414	−	0.803419i	$-0.296988\pi$
$941$	45.4140	−	10.3655i	1.48045	−	0.337904i	0.885040	+	0.465515i	$0.154131\pi$
$942$	−3.55974	−	2.63626i	−0.115983	−	0.0858939i
$943$	−59.1498	−	74.1714i	−1.92618	−	2.41535i
$944$	4.81703	+	4.52886i	0.156781	+	0.147402i
$945$	−6.55599	+	2.40628i	−0.213266	+	0.0782763i
$946$	33.4984	−	1.19828i	1.08913	−	0.0389596i
$947$	−22.4986	+	5.13516i	−0.731107	+	0.166870i	−0.571840	−	0.820365i	$-0.693770\pi$
$947$	−22.4986	+	5.13516i	−0.731107	+	0.166870i	−0.159267	+	0.987236i	$0.550913\pi$
$948$	−0.898417	−	12.5417i	−0.0291792	−	0.407336i
$949$	−48.1939			−1.56444
$950$	−13.9130	+	7.32400i	−0.451398	+	0.237622i
$951$	−9.83533	−	12.3331i	−0.318933	−	0.399929i
$952$	−5.59617	+	0.0573017i	−0.181373	+	0.00185716i
$953$	15.2751	−	19.1543i	0.494808	−	0.620469i	−0.470242	−	0.882538i	$-0.655833\pi$
$953$	15.2751	−	19.1543i	0.494808	−	0.620469i	0.965049	+	0.262069i	$0.0844047\pi$
$954$	−3.26844	+	17.1200i	−0.105820	+	0.554281i
$955$	−47.5514	−	22.8995i	−1.53873	−	0.741012i
$956$	10.4230	+	18.1911i	0.337105	+	0.588342i
$957$	−3.83406	−	3.05756i	−0.123938	−	0.0988370i
$958$	−4.98535	+	26.1132i	−0.161069	+	0.843678i
$959$	−4.13320	+	42.4637i	−0.133468	+	1.37122i
$960$	19.1148	−	8.97404i	0.616927	−	0.289636i
$961$	−30.9421			−0.998132
$962$	9.24124	+	17.5551i	0.297949	+	0.565998i
$963$	1.40446	−	1.12002i	0.0452579	−	0.0360920i
$964$	−9.88958	+	24.9567i	−0.318522	+	0.803800i
$965$	−11.3057	+	23.4765i	−0.363944	+	0.755737i
$966$	8.53682	−	29.0659i	0.274668	−	0.935179i
$967$	1.96545	+	4.08129i	0.0632045	+	0.131246i	0.930178	−	0.367109i	$-0.119652\pi$
$967$	1.96545	+	4.08129i	0.0632045	+	0.131246i	−0.866974	+	0.498354i	$0.833938\pi$
$968$	12.6893	−	7.88623i	0.407851	−	0.253473i
$969$	1.83374	+	3.80781i	0.0589084	+	0.122324i
$970$	28.1637	+	32.8359i	0.904283	+	1.05430i
$971$	18.3965	+	8.85927i	0.590370	+	0.284307i	0.705121	−	0.709087i	$-0.250893\pi$
$971$	18.3965	+	8.85927i	0.590370	+	0.284307i	−0.114751	+	0.993394i	$0.536607\pi$
$972$	−1.35552	−	1.47057i	−0.0434783	−	0.0471685i
$973$	−21.2718	+	35.0223i	−0.681943	+	1.12276i
$974$	18.7728	−	16.1017i	0.601519	−	0.515930i
$975$	8.38931	+	1.91481i	0.268673	+	0.0613229i
$976$	1.58434	−	5.01891i	0.0507136	−	0.160652i
$977$	−11.3043	+	49.5274i	−0.361657	+	1.58452i	0.387333	+	0.921940i	$0.373396\pi$
$977$	−11.3043	+	49.5274i	−0.361657	+	1.58452i	−0.748990	+	0.662582i	$0.769461\pi$
$978$	−26.7066	−	19.7783i	−0.853984	−	0.632440i
$979$	−35.4791			−1.13392
$980$	19.9834	−	31.0847i	0.638345	−	0.992965i
$981$	−12.7937			−0.408472
$982$	40.4064	+	29.9240i	1.28942	+	0.954914i
$983$	−8.78144	+	38.4740i	−0.280085	+	1.22713i	0.617600	+	0.786492i	$0.288105\pi$
$983$	−8.78144	+	38.4740i	−0.280085	+	1.22713i	−0.897685	+	0.440638i	$0.854752\pi$
$984$	23.5504	−	23.3192i	0.750759	−	0.743391i
$985$	2.35991	+	0.538634i	0.0751930	+	0.0171623i
$986$	1.64639	−	1.41213i	0.0524316	−	0.0449713i
$987$	−0.838449	+	8.61407i	−0.0266881	+	0.274189i
$988$	36.3505	−	33.5066i	1.15646	−	1.06599i
$989$	−72.3050	−	34.8203i	−2.29917	−	1.10722i
$990$	−5.81127	−	6.77531i	−0.184694	−	0.215334i
$991$	−4.14620	−	8.60967i	−0.131708	−	0.273495i	0.824677	−	0.565605i	$-0.191357\pi$
$991$	−4.14620	−	8.60967i	−0.131708	−	0.273495i	−0.956385	+	0.292109i	$0.905643\pi$
$992$	−0.0620701	+	1.35968i	−0.00197073	+	0.0431698i
$993$	−11.9174	−	24.7467i	−0.378187	−	0.785313i
$994$	10.5012	+	0.644250i	0.333079	+	0.0204344i
$995$	0.617006	−	1.28123i	0.0195604	−	0.0406176i
$996$	12.0931	+	4.79214i	0.383185	+	0.151845i
$997$	−8.45075	+	6.73925i	−0.267638	+	0.213434i	−0.748108	−	0.663577i	$-0.769038\pi$
$997$	−8.45075	+	6.73925i	−0.267638	+	0.213434i	0.480470	+	0.877011i	$0.340466\pi$
$998$	15.4985	+	29.4416i	0.490595	+	0.931956i
$999$	3.20717			0.101471

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.x.b.223.10	yes	168
4.3	odd	2		588.2.x.a.223.2	✓	168
49.20	odd	14		588.2.x.a.559.2	yes	168
196.167	even	14	inner	588.2.x.b.559.10	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.x.a.223.2	✓	168	4.3	odd	2
588.2.x.a.559.2	yes	168	49.20	odd	14
588.2.x.b.223.10	yes	168	1.1	even	1	trivial
588.2.x.b.559.10	yes	168	196.167	even	14	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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.x (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.841658 + 1.13649i) q^{2} +(0.222521 - 0.974928i) q^{3} +(-0.583224 - 1.91307i) q^{4} +(2.57339 + 0.587359i) q^{5} +(0.920710 + 1.07345i) q^{6} +(2.51025 + 0.835852i) q^{7} +(2.66507 + 0.947324i) q^{8} +(-0.900969 - 0.433884i) q^{9} +O(q^{10})\)	\(q+(-0.841658 + 1.13649i) q^{2} +(0.222521 - 0.974928i) q^{3} +(-0.583224 - 1.91307i) q^{4} +(2.57339 + 0.587359i) q^{5} +(0.920710 + 1.07345i) q^{6} +(2.51025 + 0.835852i) q^{7} +(2.66507 + 0.947324i) q^{8} +(-0.900969 - 0.433884i) q^{9} +(-2.83344 + 2.43028i) q^{10} +(-1.03750 - 2.15439i) q^{11} +(-1.99489 + 0.142903i) q^{12} +(1.89781 + 3.94084i) q^{13} +(-3.06271 + 2.14937i) q^{14} +(1.14527 - 2.37817i) q^{15} +(-3.31970 + 2.23150i) q^{16} +(-0.584700 + 0.466282i) q^{17} +(1.25141 - 0.658761i) q^{18} +5.65127 q^{19} +(-0.377201 - 5.26564i) q^{20} +(1.37348 - 2.26132i) q^{21} +(3.32167 + 0.634151i) q^{22} +(-6.32994 - 5.04796i) q^{23} +(1.51661 - 2.38745i) q^{24} +(1.77249 + 0.853588i) q^{25} +(-6.07604 - 1.16000i) q^{26} +(-0.623490 + 0.781831i) q^{27} +(0.135009 - 5.28978i) q^{28} +(1.27868 + 1.60341i) q^{29} +(1.73885 + 3.30319i) q^{30} -0.240610 q^{31} +(0.257970 - 5.65097i) q^{32} +(-2.33124 + 0.532091i) q^{33} +(-0.0378088 - 1.05696i) q^{34} +(5.96890 + 3.62539i) q^{35} +(-0.304585 + 1.97667i) q^{36} +(-1.99964 - 2.50747i) q^{37} +(-4.75643 + 6.42261i) q^{38} +(4.26434 - 0.973308i) q^{39} +(6.30183 + 4.00318i) q^{40} +(11.4238 + 2.60740i) q^{41} +(1.41397 + 3.46420i) q^{42} +(9.66372 - 2.20568i) q^{43} +(-3.51642 + 3.24131i) q^{44} +(-2.06370 - 1.64574i) q^{45} +(11.0646 - 2.94527i) q^{46} +(-2.94725 + 1.41932i) q^{47} +(1.43685 + 3.73302i) q^{48} +(5.60270 + 4.19639i) q^{49} +(-2.46193 + 1.29599i) q^{50} +(0.324484 + 0.673798i) q^{51} +(6.43227 - 5.92904i) q^{52} +(-7.68409 + 9.63554i) q^{53} +(-0.363779 - 1.36663i) q^{54} +(-1.40449 - 6.15347i) q^{55} +(5.89816 + 4.60562i) q^{56} +(1.25753 - 5.50958i) q^{57} +(-2.89847 + 0.103682i) q^{58} +(-0.367809 - 1.61148i) q^{59} +(-5.21756 - 0.803972i) q^{60} +(-1.02870 + 0.820364i) q^{61} +(0.202511 - 0.273451i) q^{62} +(-1.89899 - 1.84223i) q^{63} +(6.20515 + 5.04936i) q^{64} +(2.56911 + 11.2560i) q^{65} +(1.35739 - 3.09728i) q^{66} -9.89182i q^{67} +(1.23304 + 0.846626i) q^{68} +(-6.32994 + 5.04796i) q^{69} +(-9.14400 + 3.73226i) q^{70} +(-2.19839 - 1.75316i) q^{71} +(-1.99011 - 2.00984i) q^{72} +(-4.78064 + 9.92710i) q^{73} +(4.53273 - 0.162142i) q^{74} +(1.22660 - 1.53811i) q^{75} +(-3.29595 - 10.8113i) q^{76} +(-0.803632 - 6.27526i) q^{77} +(-2.48296 + 5.66558i) q^{78} +6.28692i q^{79} +(-9.85357 + 3.79266i) q^{80} +(0.623490 + 0.781831i) q^{81} +(-12.5782 + 10.7885i) q^{82} +(-5.85990 - 2.82198i) q^{83} +(-5.12711 - 1.30871i) q^{84} +(-1.77853 + 0.856497i) q^{85} +(-5.62681 + 12.8392i) q^{86} +(1.84774 - 0.889825i) q^{87} +(-0.724100 - 6.72445i) q^{88} +(6.43770 - 13.3680i) q^{89} +(3.60730 - 0.960221i) q^{90} +(1.47001 + 11.4788i) q^{91} +(-5.96535 + 15.0537i) q^{92} +(-0.0535407 + 0.234577i) q^{93} +(0.867530 - 4.54410i) q^{94} +(14.5429 + 3.31932i) q^{95} +(-5.45188 - 1.50896i) q^{96} -11.5887i q^{97} +(-9.48472 + 2.83549i) q^{98} +2.39120i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q + 28 q^{3} - 2 q^{7} + 6 q^{8} - 28 q^{9}+O(q^{10}) \) 168 * q + 28 * q^3 - 2 * q^7 + 6 * q^8 - 28 * q^9	\( 168 q + 28 q^{3} - 2 q^{7} + 6 q^{8} - 28 q^{9} - 20 q^{10} + 14 q^{14} - 20 q^{16} - 12 q^{19} + 25 q^{20} + 2 q^{21} - 6 q^{22} - 27 q^{24} + 32 q^{25} - 6 q^{26} + 28 q^{27} + 6 q^{28} - 8 q^{30} + 4 q^{31} - 45 q^{32} - 44 q^{34} + 12 q^{35} - 10 q^{37} - 35 q^{38} - 14 q^{39} + 40 q^{40} + 7 q^{42} + 20 q^{44} + 28 q^{46} + 8 q^{47} - 8 q^{48} - 8 q^{49} + 114 q^{50} - 20 q^{52} - 8 q^{53} + 23 q^{56} + 12 q^{57} - 6 q^{58} - 20 q^{59} + 10 q^{60} - 14 q^{61} + 16 q^{62} + 12 q^{63} - 42 q^{64} - 8 q^{65} + 6 q^{66} + 16 q^{68} + 19 q^{70} - 28 q^{71} - 15 q^{72} + 22 q^{74} - 18 q^{75} - 49 q^{76} + 8 q^{77} + 6 q^{78} - 26 q^{80} - 28 q^{81} - 12 q^{82} - 10 q^{83} - 27 q^{84} - 24 q^{85} - 34 q^{86} + 94 q^{88} - 20 q^{90} + 16 q^{91} + 7 q^{92} - 4 q^{93} + 11 q^{94} + 10 q^{96} - 150 q^{98}+O(q^{100}) \) 168 * q + 28 * q^3 - 2 * q^7 + 6 * q^8 - 28 * q^9 - 20 * q^10 + 14 * q^14 - 20 * q^16 - 12 * q^19 + 25 * q^20 + 2 * q^21 - 6 * q^22 - 27 * q^24 + 32 * q^25 - 6 * q^26 + 28 * q^27 + 6 * q^28 - 8 * q^30 + 4 * q^31 - 45 * q^32 - 44 * q^34 + 12 * q^35 - 10 * q^37 - 35 * q^38 - 14 * q^39 + 40 * q^40 + 7 * q^42 + 20 * q^44 + 28 * q^46 + 8 * q^47 - 8 * q^48 - 8 * q^49 + 114 * q^50 - 20 * q^52 - 8 * q^53 + 23 * q^56 + 12 * q^57 - 6 * q^58 - 20 * q^59 + 10 * q^60 - 14 * q^61 + 16 * q^62 + 12 * q^63 - 42 * q^64 - 8 * q^65 + 6 * q^66 + 16 * q^68 + 19 * q^70 - 28 * q^71 - 15 * q^72 + 22 * q^74 - 18 * q^75 - 49 * q^76 + 8 * q^77 + 6 * q^78 - 26 * q^80 - 28 * q^81 - 12 * q^82 - 10 * q^83 - 27 * q^84 - 24 * q^85 - 34 * q^86 + 94 * q^88 - 20 * q^90 + 16 * q^91 + 7 * q^92 - 4 * q^93 + 11 * q^94 + 10 * q^96 - 150 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more