LMFDB - Embedded newform 572.2.e.b.131.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(131,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("572.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.e (of order $2$, degree $1$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			131.2
Character	$\chi$	$=$	572.131
Dual form			572.2.e.b.131.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41398 + 0.0257972i) q^{2} -0.803304i q^{3} +(1.99867 - 0.0729533i) q^{4} -1.80361 q^{5} +(0.0207230 + 1.13585i) q^{6} +0.264488 q^{7} +(-2.82419 + 0.154714i) q^{8} +2.35470 q^{9} +O(q^{10})$	\(q+(-1.41398 + 0.0257972i) q^{2} -0.803304i q^{3} +(1.99867 - 0.0729533i) q^{4} -1.80361 q^{5} +(0.0207230 + 1.13585i) q^{6} +0.264488 q^{7} +(-2.82419 + 0.154714i) q^{8} +2.35470 q^{9} +(2.55027 - 0.0465281i) q^{10} +(-2.27957 - 2.40906i) q^{11} +(-0.0586037 - 1.60554i) q^{12} +1.00000i q^{13} +(-0.373980 + 0.00682304i) q^{14} +1.44885i q^{15} +(3.98936 - 0.291619i) q^{16} -1.04789i q^{17} +(-3.32950 + 0.0607446i) q^{18} -1.53543 q^{19} +(-3.60482 + 0.131579i) q^{20} -0.212464i q^{21} +(3.28540 + 3.34755i) q^{22} -8.18120i q^{23} +(0.124283 + 2.26869i) q^{24} -1.74698 q^{25} +(-0.0257972 - 1.41398i) q^{26} -4.30146i q^{27} +(0.528624 - 0.0192952i) q^{28} -4.03747i q^{29} +(-0.0373762 - 2.04864i) q^{30} +7.63885i q^{31} +(-5.63334 + 0.515257i) q^{32} +(-1.93521 + 1.83119i) q^{33} +(0.0270325 + 1.48169i) q^{34} -0.477033 q^{35} +(4.70627 - 0.171783i) q^{36} -2.46500 q^{37} +(2.17107 - 0.0396098i) q^{38} +0.803304 q^{39} +(5.09375 - 0.279045i) q^{40} -7.92708i q^{41} +(0.00548097 + 0.300420i) q^{42} -3.94737 q^{43} +(-4.73185 - 4.64861i) q^{44} -4.24697 q^{45} +(0.211052 + 11.5680i) q^{46} +1.28238i q^{47} +(-0.234259 - 3.20467i) q^{48} -6.93005 q^{49} +(2.47020 - 0.0450672i) q^{50} -0.841773 q^{51} +(0.0729533 + 1.99867i) q^{52} -10.4434 q^{53} +(0.110965 + 6.08216i) q^{54} +(4.11145 + 4.34501i) q^{55} +(-0.746964 + 0.0409201i) q^{56} +1.23342i q^{57} +(0.104155 + 5.70890i) q^{58} +0.310013i q^{59} +(0.105698 + 2.89577i) q^{60} -11.0454i q^{61} +(-0.197061 - 10.8012i) q^{62} +0.622790 q^{63} +(7.95213 - 0.873886i) q^{64} -1.80361i q^{65} +(2.68910 - 2.63918i) q^{66} -13.0013i q^{67} +(-0.0764468 - 2.09438i) q^{68} -6.57199 q^{69} +(0.674515 - 0.0123061i) q^{70} +8.11260i q^{71} +(-6.65013 + 0.364306i) q^{72} -14.5259i q^{73} +(3.48545 - 0.0635900i) q^{74} +1.40336i q^{75} +(-3.06882 + 0.112015i) q^{76} +(-0.602917 - 0.637167i) q^{77} +(-1.13585 + 0.0207230i) q^{78} +10.5958 q^{79} +(-7.19525 + 0.525967i) q^{80} +3.60873 q^{81} +(0.204496 + 11.2087i) q^{82} -7.26828 q^{83} +(-0.0155000 - 0.424646i) q^{84} +1.88998i q^{85} +(5.58149 - 0.101831i) q^{86} -3.24332 q^{87} +(6.81065 + 6.45097i) q^{88} -0.0793061 q^{89} +(6.00512 - 0.109560i) q^{90} +0.264488i q^{91} +(-0.596845 - 16.3515i) q^{92} +6.13632 q^{93} +(-0.0330817 - 1.81326i) q^{94} +2.76932 q^{95} +(0.413908 + 4.52529i) q^{96} -5.67474 q^{97} +(9.79893 - 0.178776i) q^{98} +(-5.36770 - 5.67262i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9}+O(q^{10}) $ 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9	$ 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9} - 8 q^{12} - 34 q^{14} + 26 q^{16} + 14 q^{20} - 8 q^{22} + 76 q^{25} + 2 q^{26} - 16 q^{33} + 32 q^{34} - 24 q^{36} - 32 q^{37} - 30 q^{38} + 54 q^{42} + 10 q^{44} + 12 q^{45} + 34 q^{48} - 36 q^{49} - 32 q^{53} - 36 q^{56} + 62 q^{58} + 4 q^{60} - 18 q^{64} - 30 q^{66} - 24 q^{69} - 30 q^{70} + 88 q^{77} - 10 q^{78} - 46 q^{80} + 64 q^{81} - 46 q^{82} + 98 q^{86} + 16 q^{88} + 24 q^{89} + 84 q^{92} + 8 q^{93} - 88 q^{97}+O(q^{100}) $ 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9 - 8 * q^12 - 34 * q^14 + 26 * q^16 + 14 * q^20 - 8 * q^22 + 76 * q^25 + 2 * q^26 - 16 * q^33 + 32 * q^34 - 24 * q^36 - 32 * q^37 - 30 * q^38 + 54 * q^42 + 10 * q^44 + 12 * q^45 + 34 * q^48 - 36 * q^49 - 32 * q^53 - 36 * q^56 + 62 * q^58 + 4 * q^60 - 18 * q^64 - 30 * q^66 - 24 * q^69 - 30 * q^70 + 88 * q^77 - 10 * q^78 - 46 * q^80 + 64 * q^81 - 46 * q^82 + 98 * q^86 + 16 * q^88 + 24 * q^89 + 84 * q^92 + 8 * q^93 - 88 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.41398	+	0.0257972i	−0.999834	+	0.0182414i
$2$	−1.41398	+	0.0257972i	−0.999834	+	0.0182414i
$3$		−	0.803304i		−	0.463788i	−0.972741	−	0.231894i	$-0.925508\pi$
$3$		−	0.803304i		−	0.463788i	0.972741	−	0.231894i	$-0.0744922\pi$
$4$	1.99867	−	0.0729533i	0.999335	−	0.0364766i
$5$	−1.80361			−0.806600			−0.403300	−	0.915068i	$-0.632137\pi$
$5$	−1.80361			−0.806600			−0.403300	+	0.915068i	$0.632137\pi$
$6$	0.0207230	+	1.13585i	0.00846012	+	0.463711i
$7$	0.264488			0.0999670			0.0499835	−	0.998750i	$-0.484083\pi$
$7$	0.264488			0.0999670			0.0499835	+	0.998750i	$0.484083\pi$
$8$	−2.82419	+	0.154714i	−0.998503	+	0.0546998i
$9$	2.35470			0.784901
$10$	2.55027	−	0.0465281i	0.806466	−	0.0147135i
$11$	−2.27957	−	2.40906i	−0.687315	−	0.726359i
$11$	−2.27957	−	2.40906i	−0.687315	−	0.726359i
$12$	−0.0586037	−	1.60554i	−0.0169174	−	0.463479i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	−0.373980	+	0.00682304i	−0.0999504	+	0.00182353i
$15$			1.44885i			0.374091i
$16$	3.98936	−	0.291619i	0.997339	−	0.0729047i
$17$		−	1.04789i		−	0.254150i	−0.991893	−	0.127075i	$-0.959441\pi$
$17$		−	1.04789i		−	0.254150i	0.991893	−	0.127075i	$-0.0405589\pi$
$18$	−3.32950	+	0.0607446i	−0.784770	+	0.0143177i
$19$	−1.53543			−0.352252			−0.176126	−	0.984368i	$-0.556357\pi$
$19$	−1.53543			−0.352252			−0.176126	+	0.984368i	$0.556357\pi$
$20$	−3.60482	+	0.131579i	−0.806063	+	0.0294220i
$21$		−	0.212464i		−	0.0463635i
$22$	3.28540	+	3.34755i	0.700450	+	0.713701i
$23$		−	8.18120i		−	1.70590i	−0.521995	−	0.852949i	$-0.674812\pi$
$23$		−	8.18120i		−	1.70590i	0.521995	−	0.852949i	$-0.325188\pi$
$24$	0.124283	+	2.26869i	0.0253691	+	0.463094i
$25$	−1.74698			−0.349397
$26$	−0.0257972	−	1.41398i	−0.00505924	−	0.277304i
$27$		−	4.30146i		−	0.827815i
$28$	0.528624	−	0.0192952i	0.0999005	−	0.00364646i
$29$		−	4.03747i		−	0.749740i	−0.927077	−	0.374870i	$-0.877687\pi$
$29$		−	4.03747i		−	0.749740i	0.927077	−	0.374870i	$-0.122313\pi$
$30$	−0.0373762	−	2.04864i	−0.00682393	−	0.374029i
$31$			7.63885i			1.37198i	0.727612	+	0.685989i	$0.240630\pi$
$31$			7.63885i			1.37198i	−0.727612	+	0.685989i	$0.759370\pi$
$32$	−5.63334	+	0.515257i	−0.995843	+	0.0910854i
$33$	−1.93521	+	1.83119i	−0.336877	+	0.318768i
$34$	0.0270325	+	1.48169i	0.00463604	+	0.254108i
$35$	−0.477033			−0.0806334
$36$	4.70627	−	0.171783i	0.784378	−	0.0286305i
$37$	−2.46500			−0.405243			−0.202622	−	0.979257i	$-0.564946\pi$
$37$	−2.46500			−0.405243			−0.202622	+	0.979257i	$0.564946\pi$
$38$	2.17107	−	0.0396098i	0.352193	−	0.00642555i
$39$	0.803304			0.128632
$40$	5.09375	−	0.279045i	0.805392	−	0.0441208i
$41$		−	7.92708i		−	1.23800i	−0.785390	−	0.619001i	$-0.787538\pi$
$41$		−	7.92708i		−	1.23800i	0.785390	−	0.619001i	$-0.212462\pi$
$42$	0.00548097	+	0.300420i	0.000845733	+	0.0463558i
$43$	−3.94737			−0.601968			−0.300984	−	0.953629i	$-0.597315\pi$
$43$	−3.94737			−0.601968			−0.300984	+	0.953629i	$0.597315\pi$
$44$	−4.73185	−	4.64861i	−0.713353	−	0.700805i
$45$	−4.24697			−0.633101
$46$	0.211052	+	11.5680i	0.0311179	+	1.70561i
$47$			1.28238i			0.187054i	0.995617	+	0.0935270i	$0.0298142\pi$
$47$			1.28238i			0.187054i	−0.995617	+	0.0935270i	$0.970186\pi$
$48$	−0.234259	−	3.20467i	−0.0338123	−	0.462554i
$49$	−6.93005			−0.990007
$50$	2.47020	−	0.0450672i	0.349339	−	0.00637347i
$51$	−0.841773			−0.117872
$52$	0.0729533	+	1.99867i	0.0101168	+	0.277166i
$53$	−10.4434			−1.43452			−0.717259	−	0.696807i	$-0.754604\pi$
$53$	−10.4434			−1.43452			−0.717259	+	0.696807i	$0.754604\pi$
$54$	0.110965	+	6.08216i	0.0151005	+	0.827678i
$55$	4.11145	+	4.34501i	0.554388	+	0.585881i
$56$	−0.746964	+	0.0409201i	−0.0998173	+	0.00546817i
$57$			1.23342i			0.163370i
$58$	0.104155	+	5.70890i	0.0136763	+	0.749615i
$59$			0.310013i			0.0403603i	0.999796	+	0.0201801i	$0.00642398\pi$
$59$			0.310013i			0.0403603i	−0.999796	+	0.0201801i	$0.993576\pi$
$60$	0.105698	+	2.89577i	0.0136456	+	0.373842i
$61$		−	11.0454i		−	1.41422i	−0.707105	−	0.707109i	$-0.749999\pi$
$61$		−	11.0454i		−	1.41422i	0.707105	−	0.707109i	$-0.250001\pi$
$62$	−0.197061	−	10.8012i	−0.0250267	−	1.37175i
$63$	0.622790			0.0784642
$64$	7.95213	−	0.873886i	0.994016	−	0.109236i
$65$		−	1.80361i		−	0.223711i
$66$	2.68910	−	2.63918i	0.331006	−	0.324861i
$67$		−	13.0013i		−	1.58836i	−0.607680	−	0.794182i	$-0.707900\pi$
$67$		−	13.0013i		−	1.58836i	0.607680	−	0.794182i	$-0.292100\pi$
$68$	−0.0764468	−	2.09438i	−0.00927054	−	0.253981i
$69$	−6.57199			−0.791175
$70$	0.674515	−	0.0123061i	0.0806199	−	0.00147086i
$71$			8.11260i			0.962789i	0.876504	+	0.481394i	$0.159870\pi$
$71$			8.11260i			0.962789i	−0.876504	+	0.481394i	$0.840130\pi$
$72$	−6.65013	+	0.364306i	−0.783726	+	0.0429339i
$73$		−	14.5259i		−	1.70013i	−0.526675	−	0.850067i	$-0.676562\pi$
$73$		−	14.5259i		−	1.70013i	0.526675	−	0.850067i	$-0.323438\pi$
$74$	3.48545	−	0.0635900i	0.405176	−	0.00739218i
$75$			1.40336i			0.162046i
$76$	−3.06882	+	0.112015i	−0.352018	+	0.0128490i
$77$	−0.602917	−	0.637167i	−0.0687088	−	0.0726120i
$78$	−1.13585	+	0.0207230i	−0.128610	+	0.00234642i
$79$	10.5958			1.19212			0.596061	−	0.802939i	$-0.296732\pi$
$79$	10.5958			1.19212			0.596061	+	0.802939i	$0.296732\pi$
$80$	−7.19525	+	0.525967i	−0.804453	+	0.0588049i
$81$	3.60873			0.400970
$82$	0.204496	+	11.2087i	0.0225828	+	1.23780i
$83$	−7.26828			−0.797798			−0.398899	−	0.916995i	$-0.630608\pi$
$83$	−7.26828			−0.797798			−0.398899	+	0.916995i	$0.630608\pi$
$84$	−0.0155000	−	0.424646i	−0.00169118	−	0.0463326i
$85$			1.88998i			0.204997i
$86$	5.58149	−	0.101831i	0.601868	−	0.0109807i
$87$	−3.24332			−0.347720
$88$	6.81065	+	6.45097i	0.726018	+	0.687676i
$89$	−0.0793061			−0.00840643			−0.00420321	−	0.999991i	$-0.501338\pi$
$89$	−0.0793061			−0.00840643			−0.00420321	+	0.999991i	$0.501338\pi$
$90$	6.00512	−	0.109560i	0.632995	−	0.0115486i
$91$			0.264488i			0.0277259i
$92$	−0.596845	−	16.3515i	−0.0622254	−	1.70476i
$93$	6.13632			0.636307
$94$	−0.0330817	−	1.81326i	−0.00341212	−	0.187023i
$95$	2.76932			0.284126
$96$	0.413908	+	4.52529i	0.0422443	+	0.461860i
$97$	−5.67474			−0.576183			−0.288091	−	0.957603i	$-0.593021\pi$
$97$	−5.67474			−0.576183			−0.288091	+	0.957603i	$0.593021\pi$
$98$	9.79893	−	0.178776i	0.989842	−	0.0180591i
$99$	−5.36770	−	5.67262i	−0.539474	−	0.570120i
$100$	−3.49164	+	0.127448i	−0.349164	+	0.0127448i
$101$			14.4857i			1.44138i	0.693258	+	0.720690i	$0.256175\pi$
$101$			14.4857i			1.44138i	−0.693258	+	0.720690i	$0.743825\pi$
$102$	1.19025	−	0.0217154i	0.117852	−	0.00215014i
$103$			9.20664i			0.907157i	0.891216	+	0.453579i	$0.149853\pi$
$103$			9.20664i			0.907157i	−0.891216	+	0.453579i	$0.850147\pi$
$104$	−0.154714	−	2.82419i	−0.0151710	−	0.276935i
$105$			0.383203i			0.0373968i
$106$	14.7668	−	0.269411i	1.43428	−	0.0261675i
$107$	−10.2166			−0.987681			−0.493840	−	0.869553i	$-0.664407\pi$
$107$	−10.2166			−0.987681			−0.493840	+	0.869553i	$0.664407\pi$
$108$	−0.313805	−	8.59719i	−0.0301959	−	0.827265i
$109$		−	3.96129i		−	0.379423i	−0.981840	−	0.189711i	$-0.939245\pi$
$109$		−	3.96129i		−	0.379423i	0.981840	−	0.189711i	$-0.0607553\pi$
$110$	−5.92559	−	6.03769i	−0.564983	−	0.575671i
$111$			1.98014i			0.187947i
$112$	1.05514	−	0.0771296i	0.0997010	−	0.00728807i
$113$	14.7844			1.39079			0.695397	−	0.718625i	$-0.255228\pi$
$113$	14.7844			1.39079			0.695397	+	0.718625i	$0.255228\pi$
$114$	−0.0318187	−	1.74403i	−0.00298009	−	0.163343i
$115$			14.7557i			1.37598i
$116$	−0.294547	−	8.06957i	−0.0273480	−	0.749241i
$117$			2.35470i			0.217692i
$118$	−0.00799746	−	0.438352i	−0.000736226	−	0.0403536i
$119$		−	0.277154i		−	0.0254066i
$120$	−0.224158	−	4.09183i	−0.0204627	−	0.373531i
$121$	−0.607156	+	10.9832i	−0.0551960	+	0.998476i
$122$	0.284940	+	15.6179i	0.0257972	+	1.41398i
$123$	−6.36786			−0.574170
$124$	0.557279	+	15.2675i	0.0500451	+	1.37106i
$125$	12.1689			1.08842
$126$	−0.880612	+	0.0160662i	−0.0784511	+	0.00143129i
$127$	10.7994			0.958295			0.479148	−	0.877734i	$-0.340946\pi$
$127$	10.7994			0.958295			0.479148	+	0.877734i	$0.340946\pi$
$128$	−11.2216	+	1.44080i	−0.991858	+	0.127350i
$129$			3.17094i			0.279186i
$130$	0.0465281	+	2.55027i	0.00408078	+	0.223673i
$131$	16.7772			1.46583			0.732915	−	0.680321i	$-0.238159\pi$
$131$	16.7772			1.46583			0.732915	+	0.680321i	$0.238159\pi$
$132$	−3.73425	+	3.80111i	−0.325025	+	0.330844i
$133$	−0.406103			−0.0352136
$134$	0.335397	+	18.3836i	0.0289739	+	1.58810i
$135$			7.75816i			0.667716i
$136$	0.162123	+	2.95944i	0.0139020	+	0.253770i
$137$	2.19285			0.187348			0.0936738	−	0.995603i	$-0.470139\pi$
$137$	2.19285			0.187348			0.0936738	+	0.995603i	$0.470139\pi$
$138$	9.29265	−	0.169539i	0.791043	−	0.0144321i
$139$	15.3564			1.30251			0.651257	−	0.758858i	$-0.274242\pi$
$139$	15.3564			1.30251			0.651257	+	0.758858i	$0.274242\pi$
$140$	−0.953432	+	0.0348011i	−0.0805797	+	0.00294123i
$141$	1.03014			0.0867534
$142$	−0.209282	−	11.4710i	−0.0175626	−	0.962629i
$143$	2.40906	−	2.27957i	0.201456	−	0.190627i
$144$	9.39374	−	0.686676i	0.782812	−	0.0572230i
$145$			7.28203i			0.604740i
$146$	0.374728	+	20.5394i	0.0310127	+	1.69985i
$147$			5.56694i			0.459153i
$148$	−4.92672	+	0.179830i	−0.404974	+	0.0147819i
$149$			8.57113i			0.702174i	0.936343	+	0.351087i	$0.114188\pi$
$149$			8.57113i			0.702174i	−0.936343	+	0.351087i	$0.885812\pi$
$150$	−0.0362027	−	1.98432i	−0.00295594	−	0.162019i
$151$	14.0059			1.13979			0.569893	−	0.821719i	$-0.306985\pi$
$151$	14.0059			1.13979			0.569893	+	0.821719i	$0.306985\pi$
$152$	4.33635	−	0.237553i	0.351725	−	0.0192681i
$153$		−	2.46746i		−	0.199483i
$154$	0.868949	+	0.885387i	0.0700219	+	0.0713465i
$155$		−	13.7775i		−	1.10664i
$156$	1.60554	−	0.0586037i	0.128546	−	0.00469205i
$157$	5.00850			0.399721			0.199861	−	0.979824i	$-0.435951\pi$
$157$	5.00850			0.399721			0.199861	+	0.979824i	$0.435951\pi$
$158$	−14.9823	+	0.273342i	−1.19192	+	0.0217459i
$159$			8.38927i			0.665312i
$160$	10.1604	−	0.929323i	0.803247	−	0.0734695i
$161$		−	2.16383i		−	0.170533i
$162$	−5.10266	+	0.0930950i	−0.400903	+	0.00731423i
$163$			0.197235i			0.0154486i	0.999970	+	0.00772430i	$0.00245875\pi$
$163$			0.197235i			0.0154486i	−0.999970	+	0.00772430i	$0.997541\pi$
$164$	−0.578306	−	15.8436i	−0.0451581	−	1.23718i
$165$	3.49037	−	3.30275i	0.271725	−	0.257119i
$166$	10.2772	−	0.187501i	0.797665	−	0.0145529i
$167$	3.17780			0.245905			0.122953	−	0.992413i	$-0.460764\pi$
$167$	3.17780			0.245905			0.122953	+	0.992413i	$0.460764\pi$
$168$	0.0328713	+	0.600040i	0.00253607	+	0.0462941i
$169$	−1.00000			−0.0769231
$170$	−0.0487562	−	2.67239i	−0.00373943	−	0.204963i
$171$	−3.61548			−0.276483
$172$	−7.88949	+	0.287974i	−0.601568	+	0.0219578i
$173$			20.6711i			1.57159i	0.618486	+	0.785796i	$0.287746\pi$
$173$			20.6711i			1.57159i	−0.618486	+	0.785796i	$0.712254\pi$
$174$	4.58598	−	0.0836684i	0.347662	−	0.00634289i
$175$	−0.462056			−0.0349281
$176$	−9.79653	−	8.94584i	−0.738441	−	0.674318i
$177$	0.249035			0.0187186
$178$	0.112137	−	0.00204587i	0.00840503	−	0.000153345i
$179$			3.93125i			0.293836i	0.989149	+	0.146918i	$0.0469353\pi$
$179$			3.93125i			0.293836i	−0.989149	+	0.146918i	$0.953065\pi$
$180$	−8.48829	+	0.309830i	−0.632679	+	0.0230934i
$181$	−8.16803			−0.607125			−0.303563	−	0.952811i	$-0.598176\pi$
$181$	−8.16803			−0.607125			−0.303563	+	0.952811i	$0.598176\pi$
$182$	−0.00682304	−	0.373980i	−0.000505757	−	0.0277212i
$183$	−8.87281			−0.655897
$184$	1.26575	+	23.1053i	0.0933122	+	1.70334i
$185$	4.44590			0.326869
$186$	−8.67662	+	0.158300i	−0.636201	+	0.0116071i
$187$	−2.52443	+	2.38873i	−0.184604	+	0.174681i
$188$	0.0935537	+	2.56305i	0.00682310	+	0.186930i
$189$		−	1.13768i		−	0.0827542i
$190$	−3.91576	+	0.0714407i	−0.284079	+	0.00518285i
$191$			3.48533i			0.252189i	0.992018	+	0.126095i	$0.0402443\pi$
$191$			3.48533i			0.252189i	−0.992018	+	0.126095i	$0.959756\pi$
$192$	−0.701997	−	6.38798i	−0.0506622	−	0.461013i
$193$		−	9.27878i		−	0.667901i	−0.942591	−	0.333951i	$-0.891618\pi$
$193$		−	9.27878i		−	0.667901i	0.942591	−	0.333951i	$-0.108382\pi$
$194$	8.02396	−	0.146392i	0.576087	−	0.0105104i
$195$	−1.44885			−0.103754
$196$	−13.8509	+	0.505570i	−0.989348	+	0.0361121i
$197$		−	18.6314i		−	1.32743i	−0.747986	−	0.663715i	$-0.768979\pi$
$197$		−	18.6314i		−	1.32743i	0.747986	−	0.663715i	$-0.231021\pi$
$198$	7.73615	+	7.88249i	0.549784	+	0.560184i
$199$		−	13.0891i		−	0.927858i	−0.885872	−	0.463929i	$-0.846439\pi$
$199$		−	13.0891i		−	0.927858i	0.885872	−	0.463929i	$-0.153561\pi$
$200$	4.93382	−	0.270283i	0.348874	−	0.0191119i
$201$	−10.4440			−0.736664
$202$	−0.373690	−	20.4824i	−0.0262927	−	1.44114i
$203$		−	1.06786i		−	0.0749492i
$204$	−1.68243	+	0.0614101i	−0.117793	+	0.00429957i
$205$			14.2974i			0.998572i
$206$	−0.237505	−	13.0180i	−0.0165478	−	0.907006i
$207$		−	19.2643i		−	1.33896i
$208$	0.291619	+	3.98936i	0.0202201	+	0.276612i
$209$	3.50012	+	3.69895i	0.242108	+	0.255862i
$210$	−0.00988555	−	0.541841i	−0.000682168	−	0.0373906i
$211$	−10.2972			−0.708888			−0.354444	−	0.935077i	$-0.615330\pi$
$211$	−10.2972			−0.708888			−0.354444	+	0.935077i	$0.615330\pi$
$212$	−20.8730	+	0.761884i	−1.43356	+	0.0523264i
$213$	6.51689			0.446530
$214$	14.4461	−	0.263561i	0.987516	−	0.0180166i
$215$	7.11952			0.485547
$216$	0.665497	+	12.1481i	0.0452813	+	0.826576i
$217$			2.02038i			0.137152i
$218$	0.102190	+	5.60118i	0.00692119	+	0.379360i
$219$	−11.6688			−0.788501
$220$	8.53442	+	8.38430i	0.575390	+	0.565269i
$221$	1.04789			0.0704886
$222$	−0.0510821	−	2.79988i	−0.00342841	−	0.187916i
$223$			2.98039i			0.199582i	0.995008	+	0.0997909i	$0.0318174\pi$
$223$			2.98039i			0.199582i	−0.995008	+	0.0997909i	$0.968183\pi$
$224$	−1.48995	+	0.136279i	−0.0995514	+	0.00910553i
$225$	−4.11363			−0.274242
$226$	−20.9048	+	0.381394i	−1.39056	+	0.0253700i
$227$	−9.72305			−0.645342			−0.322671	−	0.946511i	$-0.604581\pi$
$227$	−9.72305			−0.645342			−0.322671	+	0.946511i	$0.604581\pi$
$228$	0.0899819	+	2.46520i	0.00595920	+	0.163262i
$229$	26.0746			1.72306			0.861529	−	0.507709i	$-0.169507\pi$
$229$	26.0746			1.72306			0.861529	+	0.507709i	$0.169507\pi$
$230$	−0.380655	−	20.8642i	−0.0250997	−	1.37575i
$231$	−0.511839	+	0.484326i	−0.0336766	+	0.0318663i
$232$	0.624655	+	11.4026i	0.0410106	+	0.748617i
$233$			21.3493i			1.39864i	0.714809	+	0.699320i	$0.246514\pi$
$233$			21.3493i			1.39864i	−0.714809	+	0.699320i	$0.753486\pi$
$234$	−0.0607446	−	3.32950i	−0.00397100	−	0.217656i
$235$		−	2.31291i		−	0.150878i
$236$	0.0226165	+	0.619614i	0.00147221	+	0.0403334i
$237$		−	8.51166i		−	0.552892i
$238$	0.00714978	+	0.391889i	0.000463451	+	0.0254024i
$239$	6.41571			0.414998			0.207499	−	0.978235i	$-0.433468\pi$
$239$	6.41571			0.414998			0.207499	+	0.978235i	$0.433468\pi$
$240$	0.422512	+	5.77998i	0.0272730	+	0.373096i
$241$		−	6.48216i		−	0.417553i	−0.977963	−	0.208776i	$-0.933052\pi$
$241$		−	6.48216i		−	0.417553i	0.977963	−	0.208776i	$-0.0669480\pi$
$242$	0.575168	−	15.5457i	0.0369732	−	0.999316i
$243$		−	15.8033i		−	1.01378i
$244$	−0.805798	−	22.0761i	−0.0515859	−	1.41328i
$245$	12.4991			0.798539
$246$	9.00401	−	0.164273i	0.574075	−	0.0104736i
$247$		−	1.53543i		−	0.0976971i
$248$	−1.18184	−	21.5736i	−0.0750469	−	1.36992i
$249$			5.83864i			0.370009i
$250$	−17.2066	+	0.313924i	−1.08824	+	0.0198543i
$251$		−	18.3782i		−	1.16002i	−0.814609	−	0.580011i	$-0.803048\pi$
$251$		−	18.3782i		−	1.16002i	0.814609	−	0.580011i	$-0.196952\pi$
$252$	1.24475	−	0.0454346i	0.0784119	−	0.00286211i
$253$	−19.7090	+	18.6496i	−1.23909	+	1.17249i
$254$	−15.2702	+	0.278595i	−0.958136	+	0.0174806i
$255$	1.51823			0.0950753
$256$	15.8299	−	2.32674i	0.989370	−	0.145421i
$257$	−12.5253			−0.781305			−0.390653	−	0.920538i	$-0.627751\pi$
$257$	−12.5253			−0.781305			−0.390653	+	0.920538i	$0.627751\pi$
$258$	−0.0818012	−	4.48364i	−0.00509272	−	0.279139i
$259$	−0.651962			−0.0405109
$260$	−0.131579	−	3.60482i	−0.00816021	−	0.223562i
$261$		−	9.50704i		−	0.588471i
$262$	−23.7226	+	0.432804i	−1.46559	+	0.0267387i
$263$	−22.3685			−1.37930			−0.689650	−	0.724143i	$-0.742236\pi$
$263$	−22.3685			−1.37930			−0.689650	+	0.724143i	$0.742236\pi$
$264$	5.18209	−	5.47102i	0.318936	−	0.336718i
$265$	18.8359			1.15708
$266$	0.574220	−	0.0104763i	0.0352077	−	0.000642343i
$267$			0.0637069i			0.00389880i
$268$	−0.948489	−	25.9853i	−0.0579382	−	1.58731i
$269$	−6.25402			−0.381315			−0.190657	−	0.981657i	$-0.561062\pi$
$269$	−6.25402			−0.381315			−0.190657	+	0.981657i	$0.561062\pi$
$270$	−0.200138	−	10.9699i	−0.0121800	−	0.667605i
$271$	−8.24402			−0.500789			−0.250394	−	0.968144i	$-0.580560\pi$
$271$	−8.24402			−0.500789			−0.250394	+	0.968144i	$0.580560\pi$
$272$	−0.305584	−	4.18040i	−0.0185287	−	0.253474i
$273$	0.212464			0.0128589
$274$	−3.10064	+	0.0565692i	−0.187316	+	0.00341747i
$275$	3.98237	+	4.20859i	0.240146	+	0.253788i
$276$	−13.1352	+	0.479448i	−0.790648	+	0.0288594i
$277$		−	27.7071i		−	1.66476i	−0.554206	−	0.832380i	$-0.686978\pi$
$277$		−	27.7071i		−	1.66476i	0.554206	−	0.832380i	$-0.313022\pi$
$278$	−21.7136	+	0.396152i	−1.30230	+	0.0237596i
$279$			17.9872i			1.07687i
$280$	1.34723	−	0.0738039i	0.0805126	−	0.00441063i
$281$		−	22.9857i		−	1.37121i	−0.727973	−	0.685606i	$-0.759537\pi$
$281$		−	22.9857i		−	1.37121i	0.727973	−	0.685606i	$-0.240463\pi$
$282$	−1.45660	+	0.0265747i	−0.0867390	+	0.00158250i
$283$	−19.7335			−1.17303			−0.586517	−	0.809937i	$-0.699501\pi$
$283$	−19.7335			−1.17303			−0.586517	+	0.809937i	$0.699501\pi$
$284$	0.591841	+	16.2144i	0.0351193	+	0.962148i
$285$		−	2.22461i		−	0.131774i
$286$	−3.34755	+	3.28540i	−0.197945	+	0.194270i
$287$		−	2.09662i		−	0.123759i
$288$	−13.2648	+	1.21328i	−0.781638	+	0.0714930i
$289$	15.9019			0.935408
$290$	−0.187856	−	10.2966i	−0.0110313	−	0.604639i
$291$			4.55854i			0.267227i
$292$	−1.05972	−	29.0326i	−0.0620151	−	1.69900i
$293$			24.3035i			1.41983i	0.704289	+	0.709913i	$0.251266\pi$
$293$			24.3035i			1.41983i	−0.704289	+	0.709913i	$0.748734\pi$
$294$	−0.143611	−	7.87153i	−0.00837557	−	0.459077i
$295$		−	0.559144i		−	0.0325546i
$296$	6.96163	−	0.381371i	0.404636	−	0.0221667i
$297$	−10.3625	+	9.80545i	−0.601292	+	0.568970i
$298$	−0.221111	−	12.1194i	−0.0128086	−	0.702057i
$299$	8.18120			0.473131
$300$	0.102380	+	2.80485i	0.00591089	+	0.161938i
$301$	−1.04403			−0.0601770
$302$	−19.8041	+	0.361313i	−1.13960	+	0.0207913i
$303$	11.6364			0.668494
$304$	−6.12538	+	0.447761i	−0.351315	+	0.0256808i
$305$			19.9216i			1.14071i
$306$	0.0636536	+	3.48894i	0.00363883	+	0.199449i
$307$	32.2783			1.84222			0.921110	−	0.389302i	$-0.127284\pi$
$307$	32.2783			1.84222			0.921110	+	0.389302i	$0.127284\pi$
$308$	−1.25152	−	1.22950i	−0.0713117	−	0.0700574i
$309$	7.39573			0.420729
$310$	0.355421	+	19.4811i	0.0201865	+	1.10645i
$311$		−	9.85422i		−	0.558782i	−0.960177	−	0.279391i	$-0.909867\pi$
$311$		−	9.85422i		−	0.558782i	0.960177	−	0.279391i	$-0.0901325\pi$
$312$	−2.26869	+	0.124283i	−0.128439	+	0.00703612i
$313$	2.52118			0.142505			0.0712526	−	0.997458i	$-0.477300\pi$
$313$	2.52118			0.142505			0.0712526	+	0.997458i	$0.477300\pi$
$314$	−7.08190	+	0.129205i	−0.399655	+	0.00729146i
$315$	−1.12327			−0.0632892
$316$	21.1775	−	0.772999i	1.19133	−	0.0434846i
$317$	4.93139			0.276974			0.138487	−	0.990364i	$-0.455776\pi$
$317$	4.93139			0.276974			0.138487	+	0.990364i	$0.455776\pi$
$318$	−0.216419	−	11.8622i	−0.0121362	−	0.665201i
$319$	−9.72652	+	9.20368i	−0.544580	+	0.515307i
$320$	−14.3426	+	1.57615i	−0.801773	+	0.0881096i
$321$			8.20708i			0.458074i
$322$	0.0558206	+	3.05960i	0.00311076	+	0.170505i
$323$			1.60896i			0.0895249i
$324$	7.21265	−	0.263269i	0.400703	−	0.0146260i
$325$		−	1.74698i		−	0.0969052i
$326$	−0.00508809	−	0.278885i	−0.000281803	−	0.0154460i
$327$	−3.18212			−0.175972
$328$	1.22643	+	22.3876i	0.0677184	+	1.23615i
$329$			0.339173i			0.0186992i
$330$	−4.85010	+	4.76006i	−0.266989	+	0.262032i
$331$		−	11.0815i		−	0.609092i	−0.952498	−	0.304546i	$-0.901495\pi$
$331$		−	11.0815i		−	0.609092i	0.952498	−	0.304546i	$-0.0985048\pi$
$332$	−14.5269	+	0.530245i	−0.797267	+	0.0291010i
$333$	−5.80434			−0.318076
$334$	−4.49334	+	0.0819782i	−0.245864	+	0.00448565i
$335$			23.4493i			1.28117i
$336$	−0.0619586	−	0.847595i	−0.00338012	−	0.0462401i
$337$			6.63768i			0.361578i	0.983522	+	0.180789i	$0.0578651\pi$
$337$			6.63768i			0.361578i	−0.983522	+	0.180789i	$0.942135\pi$
$338$	1.41398	−	0.0257972i	0.0769103	−	0.00140318i
$339$		−	11.8763i		−	0.645034i
$340$	0.137880	+	3.77745i	0.00747762	+	0.204861i
$341$	18.4025	−	17.4133i	0.996549	−	0.942981i
$342$	5.11221	−	0.0932692i	0.276437	−	0.00504342i
$343$	−3.68433			−0.198935
$344$	11.1481	−	0.610715i	0.601067	−	0.0329275i
$345$	11.8533			0.638161
$346$	−0.533255	−	29.2284i	−0.0286680	−	1.57133i
$347$	−25.8541			−1.38792			−0.693961	−	0.720012i	$-0.744136\pi$
$347$	−25.8541			−1.38792			−0.693961	+	0.720012i	$0.744136\pi$
$348$	−6.48232	+	0.236611i	−0.347489	+	0.0126837i
$349$			15.2828i			0.818072i	0.912518	+	0.409036i	$0.134135\pi$
$349$			15.2828i			0.818072i	−0.912518	+	0.409036i	$0.865865\pi$
$350$	0.653337	−	0.0119197i	0.0349223	−	0.000637137i
$351$	4.30146			0.229595
$352$	14.0829	+	12.3965i	0.750619	+	0.660736i
$353$	24.7824			1.31903			0.659516	−	0.751691i	$-0.270761\pi$
$353$	24.7824			1.31903			0.659516	+	0.751691i	$0.270761\pi$
$354$	−0.352130	+	0.00642440i	−0.0187155	+	0.000341453i
$355$		−	14.6320i		−	0.776585i
$356$	−0.158507	+	0.00578564i	−0.00840083	+	0.000306638i
$357$	−0.222639			−0.0117833
$358$	−0.101415	−	5.55871i	−0.00535996	−	0.293787i
$359$	8.24579			0.435196			0.217598	−	0.976038i	$-0.430178\pi$
$359$	8.24579			0.435196			0.217598	+	0.976038i	$0.430178\pi$
$360$	11.9943	−	0.657067i	0.632153	−	0.0346305i
$361$	−16.6425			−0.875919
$362$	11.5494	−	0.210712i	0.607024	−	0.0110748i
$363$	8.82288	+	0.487731i	0.463081	+	0.0255992i
$364$	0.0192952	+	0.528624i	0.00101135	+	0.0277074i
$365$			26.1992i			1.37133i
$366$	12.5460	−	0.228893i	0.655788	−	0.0119645i
$367$			21.1333i			1.10315i	0.834125	+	0.551575i	$0.185973\pi$
$367$			21.1333i			1.10315i	−0.834125	+	0.551575i	$0.814027\pi$
$368$	−2.38579	−	32.6377i	−0.124368	−	1.70136i
$369$		−	18.6659i		−	0.971708i
$370$	−6.28641	+	0.114692i	−0.326815	+	0.00596253i
$371$	−2.76216			−0.143404
$372$	12.2645	−	0.447664i	0.635883	−	0.0232103i
$373$			17.2329i			0.892286i	0.894962	+	0.446143i	$0.147203\pi$
$373$			17.2329i			0.892286i	−0.894962	+	0.446143i	$0.852797\pi$
$374$	3.50786	−	3.44273i	0.181387	−	0.178020i
$375$		−	9.77536i		−	0.504798i
$376$	−0.198402	−	3.62168i	−0.0102318	−	0.186774i
$377$	4.03747			0.207940
$378$	0.0293490	+	1.60866i	0.00150955	+	0.0827405i
$379$			0.968179i			0.0497320i	0.999691	+	0.0248660i	$0.00791591\pi$
$379$			0.968179i			0.0497320i	−0.999691	+	0.0248660i	$0.992084\pi$
$380$	5.53496	−	0.202031i	0.283937	−	0.0103640i
$381$		−	8.67523i		−	0.444446i
$382$	−0.0899116	−	4.92818i	−0.00460028	−	0.252148i
$383$		−	5.85556i		−	0.299205i	−0.988746	−	0.149603i	$-0.952201\pi$
$383$		−	5.85556i		−	0.299205i	0.988746	−	0.149603i	$-0.0477994\pi$
$384$	1.15740	+	9.01435i	0.0590633	+	0.460012i
$385$	1.08743	+	1.14920i	0.0554205	+	0.0585688i
$386$	0.239366	+	13.1200i	0.0121834	+	0.667790i
$387$	−9.29488			−0.472485
$388$	−11.3419	+	0.413991i	−0.575799	+	0.0210172i
$389$	−2.34619			−0.118956			−0.0594782	−	0.998230i	$-0.518944\pi$
$389$	−2.34619			−0.118956			−0.0594782	+	0.998230i	$0.518944\pi$
$390$	2.04864	−	0.0373762i	0.103737	−	0.00189262i
$391$	−8.57298			−0.433554
$392$	19.5718	−	1.07218i	0.988524	−	0.0541531i
$393$		−	13.4772i		−	0.679834i
$394$	0.480636	+	26.3443i	0.0242141	+	1.32721i
$395$	−19.1107			−0.961566
$396$	−11.1421	−	10.9461i	−0.559911	−	0.550062i
$397$	−21.5414			−1.08113			−0.540566	−	0.841302i	$-0.681790\pi$
$397$	−21.5414			−1.08113			−0.540566	+	0.841302i	$0.681790\pi$
$398$	0.337661	+	18.5076i	0.0169254	+	0.927704i
$399$			0.326224i			0.0163316i
$400$	−6.96934	+	0.509453i	−0.348467	+	0.0254727i
$401$	16.6576			0.831842			0.415921	−	0.909401i	$-0.363459\pi$
$401$	16.6576			0.831842			0.415921	+	0.909401i	$0.363459\pi$
$402$	14.7676	−	0.269426i	0.736542	−	0.0134378i
$403$	−7.63885			−0.380518
$404$	1.05678	+	28.9521i	0.0525767	+	1.44042i
$405$	−6.50875			−0.323422
$406$	0.0275478	+	1.50993i	0.00136718	+	0.0749368i
$407$	5.61913	+	5.93833i	0.278530	+	0.294352i
$408$	2.37733	−	0.130234i	0.117695	−	0.00644756i
$409$			10.7500i			0.531554i	0.964035	+	0.265777i	$0.0856285\pi$
$409$			10.7500i			0.531554i	−0.964035	+	0.265777i	$0.914371\pi$
$410$	−0.368832	−	20.2162i	−0.0182153	−	0.998406i
$411$		−	1.76152i		−	0.0868896i
$412$	0.671655	+	18.4010i	0.0330900	+	0.906554i
$413$			0.0819947i			0.00403470i
$414$	0.496964	+	27.2393i	0.0244244	+	1.33874i
$415$	13.1092			0.643504
$416$	−0.515257	−	5.63334i	−0.0252625	−	0.276197i
$417$		−	12.3359i		−	0.604090i
$418$	−5.04451	−	5.13994i	−0.246735	−	0.251403i
$419$			14.5363i			0.710146i	0.934839	+	0.355073i	$0.115544\pi$
$419$			14.5363i			0.710146i	−0.934839	+	0.355073i	$0.884456\pi$
$420$	0.0279559	+	0.765896i	0.00136411	+	0.0373719i
$421$	−28.7737			−1.40234			−0.701171	−	0.712993i	$-0.747339\pi$
$421$	−28.7737			−1.40234			−0.701171	+	0.712993i	$0.747339\pi$
$422$	14.5600	−	0.265638i	0.708770	−	0.0129311i
$423$			3.01962i			0.146819i
$424$	29.4943	−	1.61575i	1.43237	−	0.0784678i
$425$			1.83064i			0.0887992i
$426$	−9.21474	+	0.168117i	−0.446456	+	0.00814531i
$427$		−	2.92137i		−	0.141375i
$428$	−20.4197	+	0.745338i	−0.987023	+	0.0360273i
$429$	−1.83119	−	1.93521i	−0.0884105	−	0.0934328i
$430$	−10.0669	+	0.183664i	−0.485467	+	0.00885704i
$431$	−29.9335			−1.44185			−0.720924	−	0.693015i	$-0.756282\pi$
$431$	−29.9335			−1.44185			−0.720924	+	0.693015i	$0.756282\pi$
$432$	−1.25439	−	17.1600i	−0.0603517	−	0.825613i
$433$	29.9547			1.43953			0.719767	−	0.694216i	$-0.244249\pi$
$433$	29.9547			1.43953			0.719767	+	0.694216i	$0.244249\pi$
$434$	−0.0521201	−	2.85678i	−0.00250185	−	0.137130i
$435$	5.84969			0.280471
$436$	−0.288989	−	7.91731i	−0.0138401	−	0.379170i
$437$			12.5617i			0.600906i
$438$	16.4994	−	0.301021i	0.788370	−	0.0143833i
$439$	17.4832			0.834426			0.417213	−	0.908809i	$-0.363007\pi$
$439$	17.4832			0.834426			0.417213	+	0.908809i	$0.363007\pi$
$440$	−12.2838	−	11.6351i	−0.585606	−	0.554679i
$441$	−16.3182			−0.777057
$442$	−1.48169	+	0.0270325i	−0.0704768	+	0.00128581i
$443$		−	19.2008i		−	0.912257i	−0.889914	−	0.456128i	$-0.849236\pi$
$443$		−	19.2008i		−	0.912257i	0.889914	−	0.456128i	$-0.150764\pi$
$444$	0.144458	+	3.95765i	0.00685567	+	0.187822i
$445$	0.143037			0.00678062
$446$	−0.0768857	−	4.21421i	−0.00364064	−	0.199549i
$447$	6.88522			0.325660
$448$	2.10324	−	0.231132i	0.0993688	−	0.0109200i
$449$	−21.2960			−1.00502			−0.502510	−	0.864572i	$-0.667590\pi$
$449$	−21.2960			−1.00502			−0.502510	+	0.864572i	$0.667590\pi$
$450$	5.81658	−	0.106120i	0.274196	−	0.00500254i
$451$	−19.0968	+	18.0703i	−0.899234	+	0.850897i
$452$	29.5490	−	1.07857i	1.38987	−	0.0507315i
$453$		−	11.2510i		−	0.528619i
$454$	13.7482	−	0.250827i	0.645234	−	0.0117719i
$455$		−	0.477033i		−	0.0223637i
$456$	−0.190828	−	3.48341i	−0.00893632	−	0.163126i
$457$		−	23.3910i		−	1.09419i	−0.837072	−	0.547093i	$-0.815734\pi$
$457$		−	23.3910i		−	1.09419i	0.837072	−	0.547093i	$-0.184266\pi$
$458$	−36.8689	+	0.672651i	−1.72277	+	0.0314309i
$459$	−4.50744			−0.210389
$460$	1.07648	+	29.4918i	0.0501910	+	1.37506i
$461$			12.0479i			0.561126i	0.959836	+	0.280563i	$0.0905212\pi$
$461$			12.0479i			0.561126i	−0.959836	+	0.280563i	$0.909479\pi$
$462$	0.711235	−	0.698031i	0.0330897	−	0.0324753i
$463$		−	27.7755i		−	1.29084i	−0.763829	−	0.645419i	$-0.776683\pi$
$463$		−	27.7755i		−	1.29084i	0.763829	−	0.645419i	$-0.223317\pi$
$464$	−1.17740	−	16.1069i	−0.0546596	−	0.747745i
$465$	−11.0675			−0.513245
$466$	−0.550752	−	30.1875i	−0.0255131	−	1.39841i
$467$		−	7.64285i		−	0.353669i	−0.984241	−	0.176834i	$-0.943414\pi$
$467$		−	7.64285i		−	0.353669i	0.984241	−	0.176834i	$-0.0565857\pi$
$468$	0.171783	+	4.70627i	0.00794068	+	0.217547i
$469$		−	3.43869i		−	0.158784i
$470$	0.0596666	+	3.27041i	0.00275222	+	0.150853i
$471$		−	4.02335i		−	0.185386i
$472$	−0.0479635	−	0.875537i	−0.00220770	−	0.0402999i
$473$	8.99829	+	9.50946i	0.413742	+	0.437245i
$474$	0.219577	+	12.0353i	0.0100855	+	0.552800i
$475$	2.68237			0.123076
$476$	−0.0202193	−	0.553938i	−0.000926748	−	0.0253897i
$477$	−24.5912			−1.12595
$478$	−9.07167	+	0.165507i	−0.414928	+	0.00757012i
$479$	18.5987			0.849795			0.424897	−	0.905241i	$-0.360310\pi$
$479$	18.5987			0.849795			0.424897	+	0.905241i	$0.360310\pi$
$480$	−0.746530	−	8.16186i	−0.0340743	−	0.372536i
$481$		−	2.46500i		−	0.112394i
$482$	0.167221	+	9.16563i	0.00761672	+	0.417483i
$483$	−1.73821			−0.0790914
$484$	−0.412240	+	21.9961i	−0.0187382	+	0.999824i
$485$	10.2350			0.464749
$486$	0.407680	+	22.3455i	0.0184927	+	1.01361i
$487$			14.2190i			0.644324i	0.946685	+	0.322162i	$0.104410\pi$
$487$			14.2190i			0.644324i	−0.946685	+	0.322162i	$0.895590\pi$
$488$	1.70888	+	31.1943i	0.0773574	+	1.41210i
$489$	0.158439			0.00716488
$490$	−17.6735	+	0.322442i	−0.798406	+	0.0145664i
$491$	−2.42924			−0.109630			−0.0548151	−	0.998497i	$-0.517457\pi$
$491$	−2.42924			−0.109630			−0.0548151	+	0.998497i	$0.517457\pi$
$492$	−12.7272	+	0.464556i	−0.573788	+	0.0209438i
$493$	−4.23082			−0.190546
$494$	0.0396098	+	2.17107i	0.00178213	+	0.0976809i
$495$	9.68125	+	10.2312i	0.435140	+	0.459859i
$496$	2.22763	+	30.4741i	0.100024	+	1.36833i
$497$			2.14568i			0.0962471i
$498$	−0.150620	−	8.25572i	−0.00674947	−	0.369947i
$499$			38.3109i			1.71503i	0.514457	+	0.857516i	$0.327993\pi$
$499$			38.3109i			1.71503i	−0.514457	+	0.857516i	$0.672007\pi$
$500$	24.3217	−	0.887764i	1.08770	−	0.0397020i
$501$		−	2.55274i		−	0.114048i
$502$	0.474105	+	25.9864i	0.0211604	+	1.15983i
$503$	25.1705			1.12230			0.561148	−	0.827716i	$-0.310360\pi$
$503$	25.1705			1.12230			0.561148	+	0.827716i	$0.310360\pi$
$504$	−1.75888	+	0.0963545i	−0.0783467	+	0.00429197i
$505$		−	26.1266i		−	1.16262i
$506$	27.3870	−	26.8785i	1.21750	−	1.19490i
$507$			0.803304i			0.0356760i
$508$	21.5845	−	0.787854i	0.957657	−	0.0349554i
$509$	34.4298			1.52607			0.763037	−	0.646355i	$-0.223707\pi$
$509$	34.4298			1.52607			0.763037	+	0.646355i	$0.223707\pi$
$510$	−2.14675	+	0.0391661i	−0.0950595	+	0.00173430i
$511$		−	3.84194i		−	0.169957i
$512$	−22.3231	+	3.69833i	−0.986553	+	0.163445i
$513$			6.60459i			0.291600i
$514$	17.7105	−	0.323117i	0.781175	−	0.0142521i
$515$		−	16.6052i		−	0.731713i
$516$	0.231330	+	6.33766i	0.0101838	+	0.279000i
$517$	3.08933	−	2.92327i	0.135869	−	0.128565i
$518$	0.921860	−	0.0168188i	0.0405042	−	0.000738974i
$519$	16.6052			0.728886
$520$	0.279045	+	5.09375i	0.0122369	+	0.223376i
$521$	−3.01951			−0.132287			−0.0661436	−	0.997810i	$-0.521070\pi$
$521$	−3.01951			−0.132287			−0.0661436	+	0.997810i	$0.521070\pi$
$522$	0.245255	+	13.4428i	0.0107345	+	0.588373i
$523$	−5.40710			−0.236436			−0.118218	−	0.992988i	$-0.537718\pi$
$523$	−5.40710			−0.236436			−0.118218	+	0.992988i	$0.537718\pi$
$524$	33.5320	−	1.22395i	1.46485	−	0.0534685i
$525$			0.371171i			0.0161993i
$526$	31.6285	−	0.577043i	1.37907	−	0.0251603i
$527$	8.00465			0.348688
$528$	−7.18623	+	7.86959i	−0.312741	+	0.342480i
$529$	−43.9320			−1.91009
$530$	−26.6336	+	0.485914i	−1.15689	+	0.0211067i
$531$			0.729989i			0.0316788i
$532$	−0.811665	+	0.0296265i	−0.0351901	+	0.00128447i
$533$	7.92708			0.343360
$534$	−0.00164346	−	0.0900802i	−7.11194e−5	−	0.00389815i
$535$	18.4269			0.796663
$536$	2.01149	+	36.7182i	0.0868832	+	1.58599i
$537$	3.15799			0.136277
$538$	8.84305	−	0.161336i	0.381251	−	0.00695569i
$539$	15.7975	+	16.6949i	0.680446	+	0.719101i
$540$	0.565983	+	15.5060i	0.0243560	+	0.667271i
$541$		−	17.8483i		−	0.767360i	−0.923466	−	0.383680i	$-0.874657\pi$
$541$		−	17.8483i		−	0.767360i	0.923466	−	0.383680i	$-0.125343\pi$
$542$	11.6569	−	0.212672i	0.500705	−	0.00913506i
$543$			6.56142i			0.281577i
$544$	0.539931	+	5.90311i	0.0231494	+	0.253094i
$545$			7.14463i			0.306043i
$546$	−0.300420	+	0.00548097i	−0.0128568	+	0.000234564i
$547$	32.4143			1.38594			0.692968	−	0.720969i	$-0.256303\pi$
$547$	32.4143			1.38594			0.692968	+	0.720969i	$0.256303\pi$
$548$	4.38278	−	0.159975i	0.187223	−	0.00683381i
$549$		−	26.0086i		−	1.11002i
$550$	−5.73955	−	5.84812i	−0.244735	−	0.249365i
$551$			6.19926i			0.264097i
$552$	18.5606	−	1.01678i	0.789990	−	0.0432771i
$553$	2.80246			0.119173
$554$	0.714765	+	39.1773i	0.0303675	+	1.66448i
$555$		−	3.57141i		−	0.151598i
$556$	30.6924	−	1.12030i	1.30165	−	0.0475113i
$557$		−	42.6654i		−	1.80779i	−0.427752	−	0.903896i	$-0.640694\pi$
$557$		−	42.6654i		−	1.80779i	0.427752	−	0.903896i	$-0.359306\pi$
$558$	−0.464019	−	25.4335i	−0.0196435	−	1.07669i
$559$		−	3.94737i		−	0.166956i
$560$	−1.90306	+	0.139112i	−0.0804188	+	0.00587855i
$561$	1.91888	+	2.02788i	0.0810150	+	0.0856173i
$562$	0.592966	+	32.5013i	0.0250128	+	1.37098i
$563$	33.8382			1.42611			0.713054	−	0.701109i	$-0.247311\pi$
$563$	33.8382			1.42611			0.713054	+	0.701109i	$0.247311\pi$
$564$	2.05891	−	0.0751521i	0.0866957	−	0.00316447i
$565$	−26.6652			−1.12181
$566$	27.9027	−	0.509068i	1.17284	−	0.0213977i
$567$	0.954465			0.0400838
$568$	−1.25514	−	22.9116i	−0.0526643	−	0.961347i
$569$			23.1175i			0.969134i	0.874754	+	0.484567i	$0.161023\pi$
$569$			23.1175i			0.969134i	−0.874754	+	0.484567i	$0.838977\pi$
$570$	0.0573886	+	3.14555i	0.00240374	+	0.131752i
$571$	−24.8235			−1.03883			−0.519416	−	0.854521i	$-0.673851\pi$
$571$	−24.8235			−1.03883			−0.519416	+	0.854521i	$0.673851\pi$
$572$	4.64861	−	4.73185i	0.194368	−	0.197848i
$573$	2.79978			0.116962
$574$	0.0540867	+	2.96457i	0.00225754	+	0.123739i
$575$			14.2924i			0.596035i
$576$	18.7249	−	2.05774i	0.780204	−	0.0857392i
$577$	−22.1076			−0.920352			−0.460176	−	0.887828i	$-0.652214\pi$
$577$	−22.1076			−0.920352			−0.460176	+	0.887828i	$0.652214\pi$
$578$	−22.4850	+	0.410225i	−0.935252	+	0.0170631i
$579$	−7.45368			−0.309765
$580$	0.531248	+	14.5544i	0.0220589	+	0.604337i
$581$	−1.92237			−0.0797535
$582$	−0.117598	−	6.44568i	−0.00487457	−	0.267182i
$583$	23.8065	+	25.1589i	0.985966	+	1.04198i
$584$	2.24737	+	41.0241i	0.0929969	+	1.69759i
$585$		−	4.24697i		−	0.175591i
$586$	−0.626962	−	34.3646i	−0.0258996	−	1.41959i
$587$		−	1.77144i		−	0.0731151i	−0.999332	−	0.0365576i	$-0.988361\pi$
$587$		−	1.77144i		−	0.0731151i	0.999332	−	0.0365576i	$-0.0116392\pi$
$588$	0.406126	+	11.1265i	0.0167484	+	0.458848i
$589$		−	11.7289i		−	0.483282i
$590$	0.0144243	+	0.790617i	0.000593840	+	0.0325492i
$591$	−14.9667			−0.615646
$592$	−9.83375	+	0.718840i	−0.404165	+	0.0295441i
$593$			9.81426i			0.403023i	0.979486	+	0.201512i	$0.0645854\pi$
$593$			9.81426i			0.403023i	−0.979486	+	0.201512i	$0.935415\pi$
$594$	14.3994	−	14.1320i	0.590813	−	0.579844i
$595$			0.499877i			0.0204930i
$596$	0.625292	+	17.1308i	0.0256129	+	0.701707i
$597$	−10.5145			−0.430330
$598$	−11.5680	+	0.211052i	−0.473052	+	0.00863055i
$599$			27.1945i			1.11114i	0.831471	+	0.555568i	$0.187499\pi$
$599$			27.1945i			1.11114i	−0.831471	+	0.555568i	$0.812501\pi$
$600$	−0.217120	−	3.96336i	−0.00886388	−	0.161803i
$601$		−	16.9318i		−	0.690661i	−0.938481	−	0.345331i	$-0.887767\pi$
$601$		−	16.9318i		−	0.690661i	0.938481	−	0.345331i	$-0.112233\pi$
$602$	1.47624	−	0.0269330i	0.0601669	−	0.00109771i
$603$		−	30.6142i		−	1.24671i
$604$	27.9932	−	1.02178i	1.13903	−	0.0415756i
$605$	1.09507	−	19.8095i	0.0445210	−	0.805370i
$606$	−16.4536	+	0.300186i	−0.668383	+	0.0121942i
$607$	13.1440			0.533497			0.266748	−	0.963766i	$-0.414051\pi$
$607$	13.1440			0.533497			0.266748	+	0.963766i	$0.414051\pi$
$608$	8.64960	−	0.791141i	0.350788	−	0.0320850i
$609$	−0.857818			−0.0347605
$610$	−0.513921	−	28.1687i	−0.0208081	−	1.14052i
$611$	−1.28238			−0.0518795
$612$	−0.180010	−	4.93164i	−0.00727645	−	0.199350i
$613$		−	32.1559i		−	1.29876i	−0.760462	−	0.649382i	$-0.775028\pi$
$613$		−	32.1559i		−	1.29876i	0.760462	−	0.649382i	$-0.224972\pi$
$614$	−45.6408	+	0.832689i	−1.84191	+	0.0336046i
$615$	11.4851			0.463126
$616$	1.80133	+	1.70620i	0.0725778	+	0.0687449i
$617$	−28.7052			−1.15563			−0.577814	−	0.816169i	$-0.696094\pi$
$617$	−28.7052			−1.15563			−0.577814	+	0.816169i	$0.696094\pi$
$618$	−10.4574	+	0.190789i	−0.420659	+	0.00767466i
$619$		−	11.1652i		−	0.448767i	−0.974501	−	0.224384i	$-0.927963\pi$
$619$		−	11.1652i		−	0.448767i	0.974501	−	0.224384i	$-0.0720368\pi$
$620$	−1.00511	−	27.5367i	−0.0403664	−	1.10590i
$621$	−35.1911			−1.41217
$622$	0.254211	+	13.9337i	0.0101929	+	0.558689i
$623$	−0.0209755			−0.000840365
$624$	3.20467	−	0.234259i	0.128289	−	0.00937785i
$625$	−13.2131			−0.528525
$626$	−3.56489	+	0.0650392i	−0.142482	+	0.00259949i
$627$	2.97138	−	2.81166i	0.118666	−	0.112287i
$628$	10.0103	−	0.365386i	0.399455	−	0.0145805i
$629$			2.58304i			0.102993i
$630$	1.58828	−	0.0289772i	0.0632786	−	0.00115448i
$631$			22.7984i			0.907589i	0.891106	+	0.453794i	$0.149930\pi$
$631$			22.7984i			0.907589i	−0.891106	+	0.453794i	$0.850070\pi$
$632$	−29.9246	+	1.63932i	−1.19034	+	0.0652088i
$633$			8.27178i			0.328774i
$634$	−6.97288	+	0.127216i	−0.276928	+	0.00505239i
$635$	−19.4780			−0.772961
$636$	0.612024	+	16.7674i	0.0242683	+	0.664869i
$637$		−	6.93005i		−	0.274578i
$638$	13.5157	−	13.2647i	0.535090	−	0.525156i
$639$			19.1028i			0.755694i
$640$	20.2394	−	2.59864i	0.800032	−	0.102720i
$641$	−46.5182			−1.83736			−0.918679	−	0.395006i	$-0.870743\pi$
$641$	−46.5182			−1.83736			−0.918679	+	0.395006i	$0.870743\pi$
$642$	−0.211719	−	11.6046i	−0.00835590	−	0.457998i
$643$		−	17.4415i		−	0.687826i	−0.939001	−	0.343913i	$-0.888247\pi$
$643$		−	17.4415i		−	0.687826i	0.939001	−	0.343913i	$-0.111753\pi$
$644$	−0.157858	−	4.32477i	−0.00622049	−	0.170420i
$645$		−	5.71914i		−	0.225191i
$646$	−0.0415066	−	2.27503i	−0.00163306	−	0.0895100i
$647$		−	41.3898i		−	1.62720i	−0.581426	−	0.813600i	$-0.697505\pi$
$647$		−	41.3898i		−	1.62720i	0.581426	−	0.813600i	$-0.302495\pi$
$648$	−10.1917	+	0.558322i	−0.400370	+	0.0219330i
$649$	0.746841	−	0.706696i	0.0293161	−	0.0277402i
$650$	0.0450672	+	2.47020i	0.00176768	+	0.0968891i
$651$	1.62298			0.0636097
$652$	0.0143889	+	0.394207i	0.000563513	+	0.0154383i
$653$	26.4465			1.03493			0.517466	−	0.855704i	$-0.326876\pi$
$653$	26.4465			1.03493			0.517466	+	0.855704i	$0.326876\pi$
$654$	4.49945	−	0.0820898i	0.175943	−	0.00320996i
$655$	−30.2595			−1.18234
$656$	−2.31169	−	31.6239i	−0.0902562	−	1.23471i
$657$		−	34.2043i		−	1.33444i
$658$	−0.00874971	−	0.479584i	−0.000341099	−	0.0186961i
$659$	10.2202			0.398123			0.199061	−	0.979987i	$-0.436211\pi$
$659$	10.2202			0.398123			0.199061	+	0.979987i	$0.436211\pi$
$660$	6.73514	−	6.85573i	0.262165	−	0.266859i
$661$	7.07892			0.275338			0.137669	−	0.990478i	$-0.456039\pi$
$661$	7.07892			0.275338			0.137669	+	0.990478i	$0.456039\pi$
$662$	0.285870	+	15.6689i	0.0111107	+	0.608991i
$663$		−	0.841773i		−	0.0326917i
$664$	20.5270	−	1.12451i	0.796603	−	0.0436394i
$665$	0.732452			0.0284033
$666$	8.20721	−	0.149735i	0.318023	−	0.00580213i
$667$	−33.0314			−1.27898
$668$	6.35137	−	0.231831i	0.245742	−	0.00896980i
$669$	2.39416			0.0925636
$670$	−0.604927	−	33.1569i	−0.0233704	−	1.28096i
$671$	−26.6090	+	25.1787i	−1.02723	+	0.972013i
$672$	0.109474	+	1.19688i	0.00422304	+	0.0461708i
$673$			17.5627i			0.676994i	0.940967	+	0.338497i	$0.109918\pi$
$673$			17.5627i			0.676994i	−0.940967	+	0.338497i	$0.890082\pi$
$674$	−0.171233	−	9.38554i	−0.00659567	−	0.361518i
$675$			7.51457i			0.289236i
$676$	−1.99867	+	0.0729533i	−0.0768719	+	0.00280589i
$677$			24.2167i			0.930723i	0.885121	+	0.465362i	$0.154076\pi$
$677$			24.2167i			0.930723i	−0.885121	+	0.465362i	$0.845924\pi$
$678$	0.306376	+	16.7929i	0.0117663	+	0.644927i
$679$	−1.50090			−0.0575992
$680$	−0.292407	−	5.33768i	−0.0112133	−	0.204691i
$681$			7.81057i			0.299302i
$682$	−25.5715	+	25.0967i	−0.979182	+	0.961002i
$683$		−	40.6917i		−	1.55702i	−0.627630	−	0.778512i	$-0.715975\pi$
$683$		−	40.6917i		−	1.55702i	0.627630	−	0.778512i	$-0.284025\pi$
$684$	−7.22615	+	0.263761i	−0.276299	+	0.0100852i
$685$	−3.95505			−0.151115
$686$	5.20956	−	0.0950452i	0.198902	−	0.00362884i
$687$		−	20.9458i		−	0.799133i
$688$	−15.7475	+	1.15113i	−0.600366	+	0.0438863i
$689$		−	10.4434i		−	0.397864i
$690$	−16.7603	+	0.305782i	−0.638055	+	0.0116409i
$691$		−	14.0717i		−	0.535314i	−0.963514	−	0.267657i	$-0.913751\pi$
$691$		−	14.0717i		−	0.535314i	0.963514	−	0.267657i	$-0.0862494\pi$
$692$	1.50802	+	41.3146i	0.0573264	+	1.57055i
$693$	−1.41969	−	1.50034i	−0.0539296	−	0.0569932i
$694$	36.5572	−	0.666963i	1.38769	−	0.0253176i
$695$	−27.6970			−1.05061
$696$	9.15976	−	0.501788i	0.347200	−	0.0190202i
$697$	−8.30669			−0.314638
$698$	−0.394254	−	21.6096i	−0.0149227	−	0.817935i
$699$	17.1500			0.648672
$700$	−0.923497	+	0.0337085i	−0.0349049	+	0.00127406i
$701$			1.35799i			0.0512906i	0.999671	+	0.0256453i	$0.00816405\pi$
$701$			1.35799i			0.0512906i	−0.999671	+	0.0256453i	$0.991836\pi$
$702$	−6.08216	+	0.110965i	−0.229557	+	0.00418812i
$703$	3.78483			0.142748
$704$	−20.2326	−	17.1651i	−0.762547	−	0.646933i
$705$	−1.85797			−0.0699753
$706$	−35.0417	+	0.639315i	−1.31881	+	0.0240609i
$707$			3.83129i			0.144090i
$708$	0.497739	−	0.0181679i	0.0187062	−	0.000682792i
$709$	48.7757			1.83181			0.915905	−	0.401395i	$-0.131475\pi$
$709$	48.7757			1.83181			0.915905	+	0.401395i	$0.131475\pi$
$710$	0.377464	+	20.6893i	0.0141660	+	0.776456i
$711$	24.9500			0.935698
$712$	0.223976	−	0.0122698i	0.00839384	−	0.000459830i
$713$	62.4949			2.34045
$714$	0.314806	−	0.00574345i	0.0117813	−	0.000214943i
$715$	−4.34501	+	4.11145i	−0.162494	+	0.153760i
$716$	0.286798	+	7.85727i	0.0107181	+	0.293640i
$717$		−	5.15376i		−	0.192471i
$718$	−11.6594	+	0.212718i	−0.435124	+	0.00793856i
$719$		−	15.2050i		−	0.567052i	−0.958965	−	0.283526i	$-0.908496\pi$
$719$		−	15.2050i		−	0.567052i	0.958965	−	0.283526i	$-0.0915042\pi$
$720$	−16.9427	+	1.23850i	−0.631416	+	0.0461560i
$721$			2.43504i			0.0906858i
$722$	23.5321	−	0.429328i	0.875773	−	0.0159779i
$723$	−5.20715			−0.193656
$724$	−16.3252	+	0.595885i	−0.606721	+	0.0221459i
$725$			7.05340i			0.261957i
$726$	−12.4879	−	0.462035i	−0.463471	−	0.0171477i
$727$			16.7618i			0.621659i	0.950466	+	0.310830i	$0.100607\pi$
$727$			16.7618i			0.621659i	−0.950466	+	0.310830i	$0.899393\pi$
$728$	−0.0409201	−	0.746964i	−0.00151660	−	0.0276843i
$729$	−1.86865			−0.0692093
$730$	−0.675864	−	37.0451i	−0.0250149	−	1.37110i
$731$			4.13640i			0.152990i
$732$	−17.7338	+	0.647301i	−0.655461	+	0.0239249i
$733$			9.29909i			0.343470i	0.985143	+	0.171735i	$0.0549373\pi$
$733$			9.29909i			0.343470i	−0.985143	+	0.171735i	$0.945063\pi$
$734$	−0.545180	−	29.8821i	−0.0201230	−	1.10297i
$735$		−	10.0406i		−	0.370353i
$736$	4.21542	+	46.0875i	0.155382	+	1.69881i
$737$	−31.3210	+	29.6374i	−1.15372	+	1.09171i
$738$	0.481528	+	26.3932i	0.0177253	+	0.971547i
$739$	−12.4802			−0.459092			−0.229546	−	0.973298i	$-0.573724\pi$
$739$	−12.4802			−0.459092			−0.229546	+	0.973298i	$0.573724\pi$
$740$	8.88588	−	0.324343i	0.326652	−	0.0119231i
$741$	−1.23342			−0.0453108
$742$	3.90564	−	0.0712560i	0.143381	−	0.00261589i
$743$	19.5810			0.718357			0.359179	−	0.933269i	$-0.383057\pi$
$743$	19.5810			0.718357			0.359179	+	0.933269i	$0.383057\pi$
$744$	−17.3301	+	0.949376i	−0.635354	+	0.0348058i
$745$		−	15.4590i		−	0.566373i
$746$	−0.444560	−	24.3669i	−0.0162765	−	0.892137i
$747$	−17.1146			−0.626192
$748$	−4.87123	+	4.95844i	−0.178110	+	0.181299i
$749$	−2.70218			−0.0987354
$750$	0.252177	+	13.8222i	0.00920819	+	0.504714i
$751$		−	36.3091i		−	1.32494i	−0.749090	−	0.662468i	$-0.769509\pi$
$751$		−	36.3091i		−	1.32494i	0.749090	−	0.662468i	$-0.230491\pi$
$752$	0.373966	+	5.11586i	0.0136371	+	0.186556i
$753$	−14.7633			−0.538004
$754$	−5.70890	+	0.104155i	−0.207906	+	0.00379311i
$755$	−25.2613			−0.919352
$756$	−0.0829977	−	2.27385i	−0.00301860	−	0.0826992i
$757$	−18.2625			−0.663763			−0.331882	−	0.943321i	$-0.607683\pi$
$757$	−18.2625			−0.663763			−0.331882	+	0.943321i	$0.607683\pi$
$758$	−0.0249763	−	1.36898i	−0.000907179	−	0.0497237i
$759$	14.9813	+	15.8323i	0.543786	+	0.574677i
$760$	−7.82110	+	0.428454i	−0.283701	+	0.0155417i
$761$			14.3858i			0.521483i	0.965409	+	0.260742i	$0.0839670\pi$
$761$			14.3858i			0.521483i	−0.965409	+	0.260742i	$0.916033\pi$
$762$	0.223796	+	12.2666i	0.00810729	+	0.444372i
$763$		−	1.04771i		−	0.0379298i
$764$	0.254266	+	6.96602i	0.00919902	+	0.252022i
$765$			4.45035i			0.160903i
$766$	0.151057	+	8.27964i	0.00545791	+	0.299155i
$767$	−0.310013			−0.0111939
$768$	−1.86908	−	12.7162i	−0.0674447	−	0.458858i
$769$			15.2983i			0.551669i	0.961205	+	0.275835i	$0.0889542\pi$
$769$			15.2983i			0.551669i	−0.961205	+	0.275835i	$0.911046\pi$
$770$	−1.56725	−	1.59690i	−0.0564797	−	0.0575481i
$771$			10.0616i			0.362360i
$772$	−0.676917	−	18.5452i	−0.0243628	−	0.667457i
$773$	10.6872			0.384393			0.192197	−	0.981356i	$-0.438439\pi$
$773$	10.6872			0.384393			0.192197	+	0.981356i	$0.438439\pi$
$774$	13.1428	−	0.239782i	0.472407	−	0.00861877i
$775$		−	13.3449i		−	0.479364i
$776$	16.0266	−	0.877964i	0.575320	−	0.0315171i
$777$			0.523724i			0.0187885i
$778$	3.31746	−	0.0605250i	0.118937	−	0.00216993i
$779$			12.1715i			0.436089i
$780$	−2.89577	+	0.105698i	−0.103685	+	0.00378461i
$781$	19.5438	−	18.4932i	0.699331	−	0.661739i
$782$	12.1220	−	0.221159i	0.433482	−	0.00790861i
$783$	−17.3670			−0.620646
$784$	−27.6464	+	2.02093i	−0.987372	+	0.0721762i
$785$	−9.03338			−0.322415
$786$	0.347673	+	19.0564i	0.0124011	+	0.679721i
$787$	39.8885			1.42187			0.710935	−	0.703257i	$-0.248272\pi$
$787$	39.8885			1.42187			0.710935	+	0.703257i	$0.248272\pi$
$788$	−1.35922	−	37.2379i	−0.0484202	−	1.32655i
$789$			17.9687i			0.639703i
$790$	27.0222	−	0.493003i	0.961406	−	0.0175403i
$791$	3.91028			0.139034
$792$	16.0371	+	15.1901i	0.569852	+	0.539757i
$793$	11.0454			0.392233
$794$	30.4591	−	0.555707i	1.08095	−	0.0197213i
$795$		−	15.1310i		−	0.536641i
$796$	−0.954889	−	26.1607i	−0.0338452	−	0.927241i
$797$	17.4052			0.616522			0.308261	−	0.951302i	$-0.400253\pi$
$797$	17.4052			0.616522			0.308261	+	0.951302i	$0.400253\pi$
$798$	−0.00841566	−	0.461274i	−0.000297911	−	0.0163289i
$799$	1.34379			0.0475398
$800$	9.84135	−	0.900145i	0.347944	−	0.0318249i
$801$	−0.186742			−0.00659821
$802$	−23.5535	+	0.429720i	−0.831704	+	0.0151739i
$803$	−34.9939	+	33.1129i	−1.23491	+	1.16853i
$804$	−20.8741	+	0.761925i	−0.736174	+	0.0268710i
$805$			3.90270i			0.137552i
$806$	10.8012	−	0.197061i	0.380455	−	0.00694116i
$807$			5.02388i			0.176849i
$808$	−2.24114	−	40.9104i	−0.0788431	−	1.43922i
$809$			5.37470i			0.188964i	0.995527	+	0.0944822i	$0.0301196\pi$
$809$			5.37470i			0.188964i	−0.995527	+	0.0944822i	$0.969880\pi$
$810$	9.20323	−	0.167907i	0.323368	−	0.00589966i
$811$	−0.288818			−0.0101418			−0.00507088	−	0.999987i	$-0.501614\pi$
$811$	−0.288818			−0.0101418			−0.00507088	+	0.999987i	$0.501614\pi$
$812$	−0.0779040	−	2.13430i	−0.00273390	−	0.0748993i
$813$			6.62246i			0.232260i
$814$	−8.09852	−	8.25172i	−0.283853	−	0.289222i
$815$		−	0.355735i		−	0.0124608i
$816$	−3.35813	+	0.245477i	−0.117558	+	0.00859341i
$817$	6.06091			0.212045
$818$	−0.277320	−	15.2003i	−0.00969627	−	0.531466i
$819$			0.622790i			0.0217620i
$820$	1.04304	+	28.5757i	0.0364245	+	0.997907i
$821$		−	22.3535i		−	0.780144i	−0.920784	−	0.390072i	$-0.872450\pi$
$821$		−	22.3535i		−	0.780144i	0.920784	−	0.390072i	$-0.127550\pi$
$822$	0.0454423	+	2.49076i	0.00158498	+	0.0868751i
$823$			35.5217i			1.23821i	0.785308	+	0.619105i	$0.212504\pi$
$823$			35.5217i			1.23821i	−0.785308	+	0.619105i	$0.787496\pi$
$824$	−1.42440	−	26.0013i	−0.0496213	−	0.905799i
$825$	3.38078	−	3.19905i	0.117704	−	0.111377i
$826$	−0.00211523	−	0.115939i	−7.35983e−5	−	0.00403403i
$827$	−36.3953			−1.26559			−0.632795	−	0.774319i	$-0.718092\pi$
$827$	−36.3953			−1.26559			−0.632795	+	0.774319i	$0.718092\pi$
$828$	−1.40539	−	38.5029i	−0.0488408	−	1.33807i
$829$	−45.7433			−1.58873			−0.794365	−	0.607441i	$-0.792196\pi$
$829$	−45.7433			−1.58873			−0.794365	+	0.607441i	$0.792196\pi$
$830$	−18.5361	+	0.338179i	−0.643397	+	0.0117384i
$831$	−22.2572			−0.772095
$832$	0.873886	+	7.95213i	0.0302966	+	0.275690i
$833$			7.26191i			0.251610i
$834$	0.318230	+	17.4426i	0.0110194	+	0.603989i
$835$	−5.73151			−0.198347
$836$	7.26542	+	7.13763i	0.251280	+	0.246860i
$837$	32.8582			1.13574
$838$	−0.374996	−	20.5540i	−0.0129540	−	0.710028i
$839$		−	2.18645i		−	0.0754847i	−0.999288	−	0.0377423i	$-0.987983\pi$
$839$		−	2.18645i		−	0.0754847i	0.999288	−	0.0377423i	$-0.0120166\pi$
$840$	−0.0592870	−	1.08224i	−0.00204560	−	0.0373408i
$841$	12.6988			0.437890
$842$	40.6853	−	0.742279i	1.40211	−	0.0255806i
$843$	−18.4645			−0.635952
$844$	−20.5807	+	0.751214i	−0.708416	+	0.0258578i
$845$	1.80361			0.0620461
$846$	−0.0778976	−	4.26968i	−0.00267818	−	0.146794i
$847$	−0.160585	+	2.90493i	−0.00551777	+	0.0998146i
$848$	−41.6626	+	3.04551i	−1.43070	+	0.104583i
$849$			15.8520i			0.544039i
$850$	−0.0472254	−	2.58849i	−0.00161982	−	0.0887844i
$851$			20.1666i			0.691303i
$852$	13.0251	−	0.475428i	0.446233	−	0.0162879i
$853$			33.3197i			1.14084i	0.821352	+	0.570422i	$0.193220\pi$
$853$			33.3197i			1.14084i	−0.821352	+	0.570422i	$0.806780\pi$
$854$	0.0753631	+	4.13076i	0.00257887	+	0.141352i
$855$	6.52093			0.223011
$856$	28.8538	−	1.58066i	0.986202	−	0.0540259i
$857$			9.61578i			0.328469i	0.986421	+	0.164234i	$0.0525153\pi$
$857$			9.61578i			0.328469i	−0.986421	+	0.164234i	$0.947485\pi$
$858$	2.63918	+	2.68910i	0.0901001	+	0.0918045i
$859$		−	53.7291i		−	1.83321i	−0.399789	−	0.916607i	$-0.630917\pi$
$859$		−	53.7291i		−	1.83321i	0.399789	−	0.916607i	$-0.369083\pi$
$860$	14.2296	−	0.519393i	0.485224	−	0.0177111i
$861$	−1.68422			−0.0573981
$862$	42.3254	−	0.772200i	1.44161	−	0.0263012i
$863$		−	17.6460i		−	0.600676i	−0.953833	−	0.300338i	$-0.902901\pi$
$863$		−	17.6460i		−	0.600676i	0.953833	−	0.300338i	$-0.0970995\pi$
$864$	2.21635	+	24.2316i	0.0754019	+	0.824374i
$865$		−	37.2826i		−	1.26765i
$866$	−42.3554	+	0.772748i	−1.43929	+	0.0262590i
$867$		−	12.7741i		−	0.433831i
$868$	0.147393	+	4.03807i	0.00500286	+	0.137061i
$869$	−24.1539	−	25.5260i	−0.819364	−	0.865909i
$870$	−8.27133	+	0.150905i	−0.280424	+	0.00511617i
$871$	13.0013			0.440533
$872$	0.612869	+	11.1875i	0.0207544	+	0.378855i
$873$	−13.3623			−0.452246
$874$	−0.324055	−	17.7619i	−0.0109613	−	0.600806i
$875$	3.21854			0.108806
$876$	−23.3220	+	0.851274i	−0.787977	+	0.0287619i
$877$			13.9917i			0.472468i	0.971696	+	0.236234i	$0.0759131\pi$
$877$			13.9917i			0.472468i	−0.971696	+	0.236234i	$0.924087\pi$
$878$	−24.7208	+	0.451016i	−0.834287	+	0.0152211i
$879$	19.5231			0.658499
$880$	17.6691	+	16.1348i	0.595626	+	0.543905i
$881$	35.0871			1.18212			0.591058	−	0.806629i	$-0.298711\pi$
$881$	35.0871			1.18212			0.591058	+	0.806629i	$0.298711\pi$
$882$	23.0736	−	0.420963i	0.776928	−	0.0141746i
$883$			32.9674i			1.10944i	0.832037	+	0.554720i	$0.187175\pi$
$883$			32.9674i			1.10944i	−0.832037	+	0.554720i	$0.812825\pi$
$884$	2.09438	−	0.0764468i	0.0704416	−	0.00257119i
$885$	−0.449162			−0.0150984
$886$	0.495326	+	27.1495i	0.0166408	+	0.912105i
$887$	48.3920			1.62485			0.812423	−	0.583069i	$-0.198148\pi$
$887$	48.3920			1.62485			0.812423	+	0.583069i	$0.198148\pi$
$888$	−0.306357	−	5.59231i	−0.0102807	−	0.187666i
$889$	2.85632			0.0957979
$890$	−0.202252	+	0.00368996i	−0.00677949	+	0.000123688i
$891$	−8.22634	−	8.69365i	−0.275593	−	0.291248i
$892$	0.217429	+	5.95682i	0.00728007	+	0.199449i
$893$		−	1.96900i		−	0.0658902i
$894$	−9.73556	+	0.177619i	−0.325606	+	0.00594048i
$895$		−	7.09045i		−	0.237008i
$896$	−2.96797	+	0.381074i	−0.0991530	+	0.0127308i
$897$		−	6.57199i		−	0.219432i
$898$	30.1121	−	0.549376i	1.00485	−	0.0183329i
$899$	30.8416			1.02863
$900$	−8.22178	+	0.300102i	−0.274059	+	0.0100034i
$901$			10.9436i			0.364583i
$902$	26.5363	−	26.0437i	0.883563	−	0.867159i
$903$			0.838675i			0.0279093i
$904$	−41.7539	+	2.28735i	−1.38871	+	0.0760762i
$905$	14.7320			0.489707
$906$	0.290245	+	15.9087i	0.00964273	+	0.528531i
$907$		−	33.5065i		−	1.11256i	−0.830994	−	0.556282i	$-0.812228\pi$
$907$		−	33.5065i		−	1.11256i	0.830994	−	0.556282i	$-0.187772\pi$
$908$	−19.4332	+	0.709328i	−0.644912	+	0.0235399i
$909$			34.1095i			1.13134i
$910$	0.0123061	+	0.674515i	0.000407944	+	0.0223599i
$911$		−	9.50419i		−	0.314888i	−0.987528	−	0.157444i	$-0.949675\pi$
$911$		−	9.50419i		−	0.314888i	0.987528	−	0.157444i	$-0.0503254\pi$
$912$	0.359688	+	4.92054i	0.0119105	+	0.162936i
$913$	16.5685	+	17.5097i	0.548339	+	0.579488i
$914$	0.603422	+	33.0744i	0.0199594	+	1.09400i
$915$	16.0031			0.529047
$916$	52.1145	−	1.90223i	1.72191	−	0.0628513i
$917$	4.43736			0.146535
$918$	6.37343	−	0.116279i	0.210354	−	0.00383779i
$919$	−50.2230			−1.65670			−0.828351	−	0.560209i	$-0.810721\pi$
$919$	−50.2230			−1.65670			−0.828351	+	0.560209i	$0.810721\pi$
$920$	−2.28292	−	41.6730i	−0.0752656	−	1.37392i
$921$		−	25.9293i		−	0.854399i
$922$	−0.310801	−	17.0355i	−0.0102357	−	0.561033i
$923$	−8.11260			−0.267030
$924$	−0.987664	+	1.00535i	−0.0324918	+	0.0330735i
$925$	4.30631			0.141591
$926$	0.716530	+	39.2740i	0.0235466	+	1.29062i
$927$			21.6789i			0.712028i
$928$	2.08033	+	22.7444i	0.0682903	+	0.746623i
$929$	12.2998			0.403543			0.201771	−	0.979433i	$-0.435330\pi$
$929$	12.2998			0.403543			0.201771	+	0.979433i	$0.435330\pi$
$930$	15.6493	−	0.285511i	0.513159	−	0.00936228i
$931$	10.6406			0.348732
$932$	1.55750	+	42.6702i	0.0510177	+	1.39771i
$933$	−7.91594			−0.259156
$934$	0.197164	+	10.8068i	0.00645140	+	0.353610i
$935$	4.55309	−	4.30834i	0.148902	−	0.140898i
$936$	−0.364306	−	6.65013i	−0.0119077	−	0.217366i
$937$		−	48.9011i		−	1.59753i	−0.601644	−	0.798764i	$-0.705488\pi$
$937$		−	48.9011i		−	1.59753i	0.601644	−	0.798764i	$-0.294512\pi$
$938$	0.0887085	+	4.86223i	0.00289644	+	0.158758i
$939$		−	2.02527i		−	0.0660922i
$940$	−0.168735	−	4.62275i	−0.00550351	−	0.150777i
$941$			4.96581i			0.161881i	0.996719	+	0.0809404i	$0.0257924\pi$
$941$			4.96581i			0.161881i	−0.996719	+	0.0809404i	$0.974208\pi$
$942$	0.103791	+	5.68892i	0.00338169	+	0.185355i
$943$	−64.8530			−2.11190
$944$	0.0904057	+	1.23675i	0.00294246	+	0.0402529i
$945$			2.05194i			0.0667495i
$946$	−12.9687	−	13.2140i	−0.421649	−	0.429625i
$947$			13.4095i			0.435751i	0.975977	+	0.217875i	$0.0699126\pi$
$947$			13.4095i			0.435751i	−0.975977	+	0.217875i	$0.930087\pi$
$948$	−0.620954	−	17.0120i	−0.0201676	−	0.552524i
$949$	14.5259			0.471532
$950$	−3.79282	+	0.0691976i	−0.123055	+	0.00224507i
$951$		−	3.96141i		−	0.128457i
$952$	0.0428796	+	0.782735i	0.00138974	+	0.0253686i
$953$		−	17.0757i		−	0.553135i	−0.960994	−	0.276568i	$-0.910803\pi$
$953$		−	17.0757i		−	0.553135i	0.960994	−	0.276568i	$-0.0891970\pi$
$954$	34.7714	−	0.634384i	1.12577	−	0.0205389i
$955$		−	6.28618i		−	0.203416i
$956$	12.8229	−	0.468047i	0.414721	−	0.0151377i
$957$	7.39336	+	7.81335i	0.238993	+	0.252570i
$958$	−26.2981	+	0.479793i	−0.849654	+	0.0155014i
$959$	0.579981			0.0187286
$960$	1.26613	+	11.5214i	0.0408641	+	0.371853i
$961$	−27.3520			−0.882322
$962$	0.0635900	+	3.48545i	0.00205022	+	0.112376i
$963$	−24.0572			−0.775231
$964$	−0.472895	−	12.9557i	−0.0152309	−	0.417275i
$965$			16.7353i			0.538729i
$966$	2.45779	−	0.0448409i	0.0790782	−	0.00144273i
$967$	−34.5799			−1.11201			−0.556007	−	0.831178i	$-0.687667\pi$
$967$	−34.5799			−1.11201			−0.556007	+	0.831178i	$0.687667\pi$
$968$	0.0154609	−	31.1127i	0.000496931	−	1.00000i
$969$	1.29248			0.0415206
$970$	−14.4721	+	0.264035i	−0.464672	+	0.00847765i
$971$		−	26.6683i		−	0.855826i	−0.903820	−	0.427913i	$-0.859249\pi$
$971$		−	26.6683i		−	0.855826i	0.903820	−	0.427913i	$-0.140751\pi$
$972$	−1.15290	−	31.5855i	−0.0369793	−	1.01311i
$973$	4.06158			0.130208
$974$	−0.366810	−	20.1053i	−0.0117533	−	0.644217i
$975$	−1.40336			−0.0449435
$976$	−3.22105	−	44.0640i	−0.103103	−	1.41045i
$977$	37.7226			1.20685			0.603426	−	0.797419i	$-0.293802\pi$
$977$	37.7226			1.20685			0.603426	+	0.797419i	$0.293802\pi$
$978$	−0.224030	+	0.00408729i	−0.00716368	+	0.000130697i
$979$	0.180783	+	0.191053i	0.00577786	+	0.00610609i
$980$	24.9816	−	0.911851i	0.798008	−	0.0291280i
$981$		−	9.32766i		−	0.297809i
$982$	3.43490	−	0.0626676i	0.109612	−	0.00199980i
$983$			44.7066i			1.42592i	0.701206	+	0.712959i	$0.252645\pi$
$983$			44.7066i			1.42592i	−0.701206	+	0.712959i	$0.747355\pi$
$984$	17.9841	−	0.985199i	0.573311	−	0.0314070i
$985$			33.6038i			1.07070i
$986$	5.98228	−	0.109143i	0.190515	−	0.00347582i
$987$	0.272459			0.00867248
$988$	−0.112015	−	3.06882i	−0.00356366	−	0.0976321i
$989$			32.2942i			1.02690i
$990$	−13.9530	−	14.2170i	−0.443456	−	0.451845i
$991$		−	55.3271i		−	1.75752i	−0.477259	−	0.878762i	$-0.658370\pi$
$991$		−	55.3271i		−	1.75752i	0.477259	−	0.878762i	$-0.341630\pi$
$992$	−3.93597	−	43.0322i	−0.124967	−	1.36627i
$993$	−8.90179			−0.282490
$994$	−0.0553526	−	3.03395i	−0.00175568	−	0.0962311i
$995$			23.6076i			0.748410i
$996$	0.425948	+	11.6695i	0.0134967	+	0.369763i
$997$			33.1820i			1.05089i	0.850829	+	0.525443i	$0.176100\pi$
$997$			33.1820i			1.05089i	−0.850829	+	0.525443i	$0.823900\pi$
$998$	−0.988313	−	54.1708i	−0.0312845	−	1.71475i
$999$			10.6031i			0.335467i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.e.b.131.2	yes	64
4.3	odd	2	inner	572.2.e.b.131.64	yes	64
11.10	odd	2	inner	572.2.e.b.131.63	yes	64
44.43	even	2	inner	572.2.e.b.131.1	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.e.b.131.1	✓	64	44.43	even	2	inner
572.2.e.b.131.2	yes	64	1.1	even	1	trivial
572.2.e.b.131.63	yes	64	11.10	odd	2	inner
572.2.e.b.131.64	yes	64	4.3	odd	2	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41398 + 0.0257972i) q^{2} -0.803304i q^{3} +(1.99867 - 0.0729533i) q^{4} -1.80361 q^{5} +(0.0207230 + 1.13585i) q^{6} +0.264488 q^{7} +(-2.82419 + 0.154714i) q^{8} +2.35470 q^{9} +O(q^{10})\)	\(q+(-1.41398 + 0.0257972i) q^{2} -0.803304i q^{3} +(1.99867 - 0.0729533i) q^{4} -1.80361 q^{5} +(0.0207230 + 1.13585i) q^{6} +0.264488 q^{7} +(-2.82419 + 0.154714i) q^{8} +2.35470 q^{9} +(2.55027 - 0.0465281i) q^{10} +(-2.27957 - 2.40906i) q^{11} +(-0.0586037 - 1.60554i) q^{12} +1.00000i q^{13} +(-0.373980 + 0.00682304i) q^{14} +1.44885i q^{15} +(3.98936 - 0.291619i) q^{16} -1.04789i q^{17} +(-3.32950 + 0.0607446i) q^{18} -1.53543 q^{19} +(-3.60482 + 0.131579i) q^{20} -0.212464i q^{21} +(3.28540 + 3.34755i) q^{22} -8.18120i q^{23} +(0.124283 + 2.26869i) q^{24} -1.74698 q^{25} +(-0.0257972 - 1.41398i) q^{26} -4.30146i q^{27} +(0.528624 - 0.0192952i) q^{28} -4.03747i q^{29} +(-0.0373762 - 2.04864i) q^{30} +7.63885i q^{31} +(-5.63334 + 0.515257i) q^{32} +(-1.93521 + 1.83119i) q^{33} +(0.0270325 + 1.48169i) q^{34} -0.477033 q^{35} +(4.70627 - 0.171783i) q^{36} -2.46500 q^{37} +(2.17107 - 0.0396098i) q^{38} +0.803304 q^{39} +(5.09375 - 0.279045i) q^{40} -7.92708i q^{41} +(0.00548097 + 0.300420i) q^{42} -3.94737 q^{43} +(-4.73185 - 4.64861i) q^{44} -4.24697 q^{45} +(0.211052 + 11.5680i) q^{46} +1.28238i q^{47} +(-0.234259 - 3.20467i) q^{48} -6.93005 q^{49} +(2.47020 - 0.0450672i) q^{50} -0.841773 q^{51} +(0.0729533 + 1.99867i) q^{52} -10.4434 q^{53} +(0.110965 + 6.08216i) q^{54} +(4.11145 + 4.34501i) q^{55} +(-0.746964 + 0.0409201i) q^{56} +1.23342i q^{57} +(0.104155 + 5.70890i) q^{58} +0.310013i q^{59} +(0.105698 + 2.89577i) q^{60} -11.0454i q^{61} +(-0.197061 - 10.8012i) q^{62} +0.622790 q^{63} +(7.95213 - 0.873886i) q^{64} -1.80361i q^{65} +(2.68910 - 2.63918i) q^{66} -13.0013i q^{67} +(-0.0764468 - 2.09438i) q^{68} -6.57199 q^{69} +(0.674515 - 0.0123061i) q^{70} +8.11260i q^{71} +(-6.65013 + 0.364306i) q^{72} -14.5259i q^{73} +(3.48545 - 0.0635900i) q^{74} +1.40336i q^{75} +(-3.06882 + 0.112015i) q^{76} +(-0.602917 - 0.637167i) q^{77} +(-1.13585 + 0.0207230i) q^{78} +10.5958 q^{79} +(-7.19525 + 0.525967i) q^{80} +3.60873 q^{81} +(0.204496 + 11.2087i) q^{82} -7.26828 q^{83} +(-0.0155000 - 0.424646i) q^{84} +1.88998i q^{85} +(5.58149 - 0.101831i) q^{86} -3.24332 q^{87} +(6.81065 + 6.45097i) q^{88} -0.0793061 q^{89} +(6.00512 - 0.109560i) q^{90} +0.264488i q^{91} +(-0.596845 - 16.3515i) q^{92} +6.13632 q^{93} +(-0.0330817 - 1.81326i) q^{94} +2.76932 q^{95} +(0.413908 + 4.52529i) q^{96} -5.67474 q^{97} +(9.79893 - 0.178776i) q^{98} +(-5.36770 - 5.67262i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9}+O(q^{10}) \) 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9	\( 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9} - 8 q^{12} - 34 q^{14} + 26 q^{16} + 14 q^{20} - 8 q^{22} + 76 q^{25} + 2 q^{26} - 16 q^{33} + 32 q^{34} - 24 q^{36} - 32 q^{37} - 30 q^{38} + 54 q^{42} + 10 q^{44} + 12 q^{45} + 34 q^{48} - 36 q^{49} - 32 q^{53} - 36 q^{56} + 62 q^{58} + 4 q^{60} - 18 q^{64} - 30 q^{66} - 24 q^{69} - 30 q^{70} + 88 q^{77} - 10 q^{78} - 46 q^{80} + 64 q^{81} - 46 q^{82} + 98 q^{86} + 16 q^{88} + 24 q^{89} + 84 q^{92} + 8 q^{93} - 88 q^{97}+O(q^{100}) \) 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9 - 8 * q^12 - 34 * q^14 + 26 * q^16 + 14 * q^20 - 8 * q^22 + 76 * q^25 + 2 * q^26 - 16 * q^33 + 32 * q^34 - 24 * q^36 - 32 * q^37 - 30 * q^38 + 54 * q^42 + 10 * q^44 + 12 * q^45 + 34 * q^48 - 36 * q^49 - 32 * q^53 - 36 * q^56 + 62 * q^58 + 4 * q^60 - 18 * q^64 - 30 * q^66 - 24 * q^69 - 30 * q^70 + 88 * q^77 - 10 * q^78 - 46 * q^80 + 64 * q^81 - 46 * q^82 + 98 * q^86 + 16 * q^88 + 24 * q^89 + 84 * q^92 + 8 * q^93 - 88 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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