LMFDB - Embedded newform 280.2.h.b.251.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(251,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("280.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.h (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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} - 2x^{12} + 6x^{11} - 12x^{9} + 8x^{8} - 24x^{7} + 48x^{5} - 32x^{4} - 128x + 256 $ x^16 - x^15 - 2x^12 + 6x^11 - 12x^9 + 8x^8 - 24x^7 + 48x^5 - 32x^4 - 128x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.6
Root			$-0.470943 - 1.33350i$ of defining polynomial
Character	$\chi$	$=$	280.251
Dual form			280.2.h.b.251.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.470943 + 1.33350i) q^{2} +0.528177i q^{3} +(-1.55642 - 1.25600i) q^{4} +1.00000 q^{5} +(-0.704322 - 0.248741i) q^{6} +(2.17448 - 1.50719i) q^{7} +(2.40786 - 1.48398i) q^{8} +2.72103 q^{9} +O(q^{10})$	\(q+(-0.470943 + 1.33350i) q^{2} +0.528177i q^{3} +(-1.55642 - 1.25600i) q^{4} +1.00000 q^{5} +(-0.704322 - 0.248741i) q^{6} +(2.17448 - 1.50719i) q^{7} +(2.40786 - 1.48398i) q^{8} +2.72103 q^{9} +(-0.470943 + 1.33350i) q^{10} +3.04781 q^{11} +(0.663391 - 0.822067i) q^{12} -4.75069 q^{13} +(0.985772 + 3.60947i) q^{14} +0.528177i q^{15} +(0.844916 + 3.90975i) q^{16} +6.78894i q^{17} +(-1.28145 + 3.62848i) q^{18} -0.584285i q^{19} +(-1.55642 - 1.25600i) q^{20} +(0.796062 + 1.14851i) q^{21} +(-1.43535 + 4.06425i) q^{22} -5.80481i q^{23} +(0.783804 + 1.27178i) q^{24} +1.00000 q^{25} +(2.23730 - 6.33502i) q^{26} +3.02172i q^{27} +(-5.27745 - 0.385331i) q^{28} -0.185682i q^{29} +(-0.704322 - 0.248741i) q^{30} +3.12589 q^{31} +(-5.61154 - 0.714577i) q^{32} +1.60978i q^{33} +(-9.05303 - 3.19721i) q^{34} +(2.17448 - 1.50719i) q^{35} +(-4.23508 - 3.41762i) q^{36} +7.04672i q^{37} +(0.779143 + 0.275165i) q^{38} -2.50920i q^{39} +(2.40786 - 1.48398i) q^{40} -3.83583i q^{41} +(-1.90644 + 0.520662i) q^{42} -1.43554 q^{43} +(-4.74369 - 3.82806i) q^{44} +2.72103 q^{45} +(7.74069 + 2.73374i) q^{46} +2.95871 q^{47} +(-2.06504 + 0.446265i) q^{48} +(2.45676 - 6.55472i) q^{49} +(-0.470943 + 1.33350i) q^{50} -3.58576 q^{51} +(7.39409 + 5.96688i) q^{52} -0.535513i q^{53} +(-4.02945 - 1.42306i) q^{54} +3.04781 q^{55} +(2.99922 - 6.85600i) q^{56} +0.308606 q^{57} +(0.247606 + 0.0874456i) q^{58} -1.52116i q^{59} +(0.663391 - 0.822067i) q^{60} -13.2354 q^{61} +(-1.47212 + 4.16837i) q^{62} +(5.91683 - 4.10111i) q^{63} +(3.59560 - 7.14644i) q^{64} -4.75069 q^{65} +(-2.14664 - 0.758117i) q^{66} -9.13242 q^{67} +(8.52693 - 10.5665i) q^{68} +3.06597 q^{69} +(0.985772 + 3.60947i) q^{70} -9.68233i q^{71} +(6.55186 - 4.03795i) q^{72} +12.4295i q^{73} +(-9.39678 - 3.31861i) q^{74} +0.528177i q^{75} +(-0.733864 + 0.909396i) q^{76} +(6.62742 - 4.59363i) q^{77} +(3.34601 + 1.18169i) q^{78} -2.81383i q^{79} +(0.844916 + 3.90975i) q^{80} +6.56709 q^{81} +(5.11507 + 1.80646i) q^{82} -13.4535i q^{83} +(0.203523 - 2.78743i) q^{84} +6.78894i q^{85} +(0.676056 - 1.91428i) q^{86} +0.0980728 q^{87} +(7.33871 - 4.52289i) q^{88} -3.10041i q^{89} +(-1.28145 + 3.62848i) q^{90} +(-10.3303 + 7.16019i) q^{91} +(-7.29085 + 9.03475i) q^{92} +1.65102i q^{93} +(-1.39338 + 3.94543i) q^{94} -0.584285i q^{95} +(0.377423 - 2.96389i) q^{96} -13.5027i q^{97} +(7.58370 + 6.36298i) q^{98} +8.29319 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{2} + q^{4} + 16 q^{5} + q^{8} - 16 q^{9}+O(q^{10}) $ 16 * q + q^2 + q^4 + 16 * q^5 + q^8 - 16 * q^9	$ 16 q + q^{2} + q^{4} + 16 q^{5} + q^{8} - 16 q^{9} + q^{10} - 4 q^{11} + 14 q^{12} - q^{14} + 9 q^{16} - 15 q^{18} + q^{20} - 4 q^{21} + 6 q^{22} + 22 q^{24} + 16 q^{25} - 20 q^{26} + q^{28} - 16 q^{31} - 19 q^{32} - 14 q^{34} + 15 q^{36} - 30 q^{38} + q^{40} + 44 q^{42} - 4 q^{43} - 20 q^{44} - 16 q^{45} + 6 q^{46} - 34 q^{48} - 8 q^{49} + q^{50} - 40 q^{51} - 38 q^{52} + 26 q^{54} - 4 q^{55} + 33 q^{56} - 16 q^{57} + 18 q^{58} + 14 q^{60} - 8 q^{61} + 28 q^{62} + 28 q^{63} - 23 q^{64} + 46 q^{66} + 20 q^{67} + 12 q^{68} - 40 q^{69} - q^{70} - 13 q^{72} - 28 q^{74} + 34 q^{76} - 4 q^{77} - 6 q^{78} + 9 q^{80} + 24 q^{81} - 16 q^{82} - 42 q^{84} - 24 q^{86} + 72 q^{87} - 44 q^{88} - 15 q^{90} - 32 q^{91} - 30 q^{92} - 58 q^{94} - 30 q^{96} + 5 q^{98} + 20 q^{99}+O(q^{100}) $ 16 * q + q^2 + q^4 + 16 * q^5 + q^8 - 16 * q^9 + q^10 - 4 * q^11 + 14 * q^12 - q^14 + 9 * q^16 - 15 * q^18 + q^20 - 4 * q^21 + 6 * q^22 + 22 * q^24 + 16 * q^25 - 20 * q^26 + q^28 - 16 * q^31 - 19 * q^32 - 14 * q^34 + 15 * q^36 - 30 * q^38 + q^40 + 44 * q^42 - 4 * q^43 - 20 * q^44 - 16 * q^45 + 6 * q^46 - 34 * q^48 - 8 * q^49 + q^50 - 40 * q^51 - 38 * q^52 + 26 * q^54 - 4 * q^55 + 33 * q^56 - 16 * q^57 + 18 * q^58 + 14 * q^60 - 8 * q^61 + 28 * q^62 + 28 * q^63 - 23 * q^64 + 46 * q^66 + 20 * q^67 + 12 * q^68 - 40 * q^69 - q^70 - 13 * q^72 - 28 * q^74 + 34 * q^76 - 4 * q^77 - 6 * q^78 + 9 * q^80 + 24 * q^81 - 16 * q^82 - 42 * q^84 - 24 * q^86 + 72 * q^87 - 44 * q^88 - 15 * q^90 - 32 * q^91 - 30 * q^92 - 58 * q^94 - 30 * q^96 + 5 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

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 $

$2$	−0.470943	+	1.33350i	−0.333007	+	0.942924i
$2$	−0.470943	+	1.33350i	−0.333007	+	0.942924i
$3$			0.528177i			0.304943i	0.988308	+	0.152472i	$0.0487232\pi$
$3$			0.528177i			0.304943i	−0.988308	+	0.152472i	$0.951277\pi$
$4$	−1.55642	−	1.25600i	−0.778212	−	0.628001i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−0.704322	−	0.248741i	−0.287538	−	0.101548i
$7$	2.17448	−	1.50719i	0.821878	−	0.569664i
$7$	2.17448	−	1.50719i	0.821878	−	0.569664i
$8$	2.40786	−	1.48398i	0.851308	−	0.524666i
$9$	2.72103			0.907010
$10$	−0.470943	+	1.33350i	−0.148925	+	0.421689i
$11$	3.04781			0.918950			0.459475	−	0.888191i	$-0.348038\pi$
$11$	3.04781			0.918950			0.459475	+	0.888191i	$0.348038\pi$
$12$	0.663391	−	0.822067i	0.191505	−	0.237310i
$13$	−4.75069			−1.31760			−0.658802	−	0.752317i	$-0.728936\pi$
$13$	−4.75069			−1.31760			−0.658802	+	0.752317i	$0.728936\pi$
$14$	0.985772	+	3.60947i	0.263459	+	0.964671i
$15$			0.528177i			0.136375i
$16$	0.844916	+	3.90975i	0.211229	+	0.977437i
$17$			6.78894i			1.64656i	0.567635	+	0.823280i	$0.307858\pi$
$17$			6.78894i			1.64656i	−0.567635	+	0.823280i	$0.692142\pi$
$18$	−1.28145	+	3.62848i	−0.302041	+	0.855242i
$19$		−	0.584285i		−	0.134044i	−0.997751	−	0.0670221i	$-0.978650\pi$
$19$		−	0.584285i		−	0.134044i	0.997751	−	0.0670221i	$-0.0213498\pi$
$20$	−1.55642	−	1.25600i	−0.348027	−	0.280851i
$21$	0.796062	+	1.14851i	0.173715	+	0.250626i
$22$	−1.43535	+	4.06425i	−0.306017	+	0.866500i
$23$		−	5.80481i		−	1.21039i	−0.796079	−	0.605193i	$-0.793096\pi$
$23$		−	5.80481i		−	1.21039i	0.796079	−	0.605193i	$-0.206904\pi$
$24$	0.783804	+	1.27178i	0.159993	+	0.259600i
$25$	1.00000			0.200000
$26$	2.23730	−	6.33502i	0.438772	−	1.24240i
$27$			3.02172i			0.581529i
$28$	−5.27745	−	0.385331i	−0.997345	−	0.0728206i
$29$		−	0.185682i		−	0.0344802i	−0.999851	−	0.0172401i	$-0.994512\pi$
$29$		−	0.185682i		−	0.0344802i	0.999851	−	0.0172401i	$-0.00548797\pi$
$30$	−0.704322	−	0.248741i	−0.128591	−	0.0454138i
$31$	3.12589			0.561427			0.280714	−	0.959792i	$-0.409429\pi$
$31$	3.12589			0.561427			0.280714	+	0.959792i	$0.409429\pi$
$32$	−5.61154	−	0.714577i	−0.991989	−	0.126321i
$33$			1.60978i			0.280227i
$34$	−9.05303	−	3.19721i	−1.55258	−	0.548317i
$35$	2.17448	−	1.50719i	0.367555	−	0.254761i
$36$	−4.23508	−	3.41762i	−0.705846	−	0.569603i
$37$			7.04672i			1.15847i	0.815159	+	0.579237i	$0.196649\pi$
$37$			7.04672i			1.15847i	−0.815159	+	0.579237i	$0.803351\pi$
$38$	0.779143	+	0.275165i	0.126394	+	0.0446377i
$39$		−	2.50920i		−	0.401794i
$40$	2.40786	−	1.48398i	0.380716	−	0.234638i
$41$		−	3.83583i		−	0.599056i	−0.954087	−	0.299528i	$-0.903171\pi$
$41$		−	3.83583i		−	0.599056i	0.954087	−	0.299528i	$-0.0968292\pi$
$42$	−1.90644	+	0.520662i	−0.294170	+	0.0803399i
$43$	−1.43554			−0.218917			−0.109459	−	0.993991i	$-0.534912\pi$
$43$	−1.43554			−0.218917			−0.109459	+	0.993991i	$0.534912\pi$
$44$	−4.74369	−	3.82806i	−0.715138	−	0.577102i
$45$	2.72103			0.405627
$46$	7.74069	+	2.73374i	1.14130	+	0.403067i
$47$	2.95871			0.431572			0.215786	−	0.976441i	$-0.430769\pi$
$47$	2.95871			0.431572			0.215786	+	0.976441i	$0.430769\pi$
$48$	−2.06504	+	0.446265i	−0.298062	+	0.0644128i
$49$	2.45676	−	6.55472i	0.350966	−	0.936388i
$50$	−0.470943	+	1.33350i	−0.0666014	+	0.188585i
$51$	−3.58576			−0.502107
$52$	7.39409	+	5.96688i	1.02538	+	0.827457i
$53$		−	0.535513i		−	0.0735584i	−0.999323	−	0.0367792i	$-0.988290\pi$
$53$		−	0.535513i		−	0.0735584i	0.999323	−	0.0367792i	$-0.0117098\pi$
$54$	−4.02945	−	1.42306i	−0.548338	−	0.193653i
$55$	3.04781			0.410967
$56$	2.99922	−	6.85600i	0.400787	−	0.916171i
$57$	0.308606			0.0408759
$58$	0.247606	+	0.0874456i	0.0325123	+	0.0114822i
$59$		−	1.52116i		−	0.198038i	−0.995086	−	0.0990188i	$-0.968430\pi$
$59$		−	1.52116i		−	0.198038i	0.995086	−	0.0990188i	$-0.0315704\pi$
$60$	0.663391	−	0.822067i	0.0856435	−	0.106128i
$61$	−13.2354			−1.69461			−0.847307	−	0.531103i	$-0.821778\pi$
$61$	−13.2354			−1.69461			−0.847307	+	0.531103i	$0.821778\pi$
$62$	−1.47212	+	4.16837i	−0.186959	+	0.529383i
$63$	5.91683	−	4.10111i	0.745451	−	0.516691i
$64$	3.59560	−	7.14644i	0.449450	−	0.893305i
$65$	−4.75069			−0.589250
$66$	−2.14664	−	0.758117i	−0.264233	−	0.0933177i
$67$	−9.13242			−1.11570			−0.557851	−	0.829941i	$-0.688374\pi$
$67$	−9.13242			−1.11570			−0.557851	+	0.829941i	$0.688374\pi$
$68$	8.52693	−	10.5665i	1.03404	−	1.28137i
$69$	3.06597			0.369099
$70$	0.985772	+	3.60947i	0.117822	+	0.431414i
$71$		−	9.68233i		−	1.14908i	−0.818476	−	0.574540i	$-0.805181\pi$
$71$		−	9.68233i		−	1.14908i	0.818476	−	0.574540i	$-0.194819\pi$
$72$	6.55186	−	4.03795i	0.772145	−	0.475878i
$73$			12.4295i			1.45476i	0.686235	+	0.727380i	$0.259262\pi$
$73$			12.4295i			1.45476i	−0.686235	+	0.727380i	$0.740738\pi$
$74$	−9.39678	−	3.31861i	−1.09235	−	0.385780i
$75$			0.528177i			0.0609886i
$76$	−0.733864	+	0.909396i	−0.0841800	+	0.104315i
$77$	6.62742	−	4.59363i	0.755264	−	0.523493i
$78$	3.34601	+	1.18169i	0.378861	+	0.133800i
$79$		−	2.81383i		−	0.316580i	−0.987393	−	0.158290i	$-0.949402\pi$
$79$		−	2.81383i		−	0.316580i	0.987393	−	0.158290i	$-0.0505982\pi$
$80$	0.844916	+	3.90975i	0.0944645	+	0.437123i
$81$	6.56709			0.729676
$82$	5.11507	+	1.80646i	0.564865	+	0.199490i
$83$		−	13.4535i		−	1.47671i	−0.674412	−	0.738355i	$-0.735603\pi$
$83$		−	13.4535i		−	1.47671i	0.674412	−	0.738355i	$-0.264397\pi$
$84$	0.203523	−	2.78743i	0.0222061	−	0.304133i
$85$			6.78894i			0.736364i
$86$	0.676056	−	1.91428i	0.0729010	−	0.206422i
$87$	0.0980728			0.0105145
$88$	7.33871	−	4.52289i	0.782309	−	0.482142i
$89$		−	3.10041i		−	0.328642i	−0.986407	−	0.164321i	$-0.947457\pi$
$89$		−	3.10041i		−	0.328642i	0.986407	−	0.164321i	$-0.0525434\pi$
$90$	−1.28145	+	3.62848i	−0.135077	+	0.382476i
$91$	−10.3303	+	7.16019i	−1.08291	+	0.750591i
$92$	−7.29085	+	9.03475i	−0.760124	+	0.941938i
$93$			1.65102i			0.171203i
$94$	−1.39338	+	3.94543i	−0.143717	+	0.406940i
$95$		−	0.584285i		−	0.0599464i
$96$	0.377423	−	2.96389i	0.0385206	−	0.302500i
$97$		−	13.5027i		−	1.37099i	−0.728077	−	0.685495i	$-0.759586\pi$
$97$		−	13.5027i		−	1.37099i	0.728077	−	0.685495i	$-0.240414\pi$
$98$	7.58370	+	6.36298i	0.766069	+	0.642758i
$99$	8.29319			0.833497
$100$	−1.55642	−	1.25600i	−0.155642	−	0.125600i
$101$	−1.29842			−0.129198			−0.0645988	−	0.997911i	$-0.520577\pi$
$101$	−1.29842			−0.129198			−0.0645988	+	0.997911i	$0.520577\pi$
$102$	1.68869	−	4.78160i	0.167205	−	0.473449i
$103$	−19.0846			−1.88046			−0.940232	−	0.340535i	$-0.889392\pi$
$103$	−19.0846			−1.88046			−0.940232	+	0.340535i	$0.889392\pi$
$104$	−11.4390	+	7.04993i	−1.12169	+	0.691302i
$105$	0.796062	+	1.14851i	0.0776877	+	0.112083i
$106$	0.714105	+	0.252196i	0.0693600	+	0.0244955i
$107$	−3.81102			−0.368425			−0.184213	−	0.982886i	$-0.558973\pi$
$107$	−3.81102			−0.368425			−0.184213	+	0.982886i	$0.558973\pi$
$108$	3.79528	−	4.70307i	0.365201	−	0.452553i
$109$			15.1487i			1.45098i	0.688233	+	0.725490i	$0.258387\pi$
$109$			15.1487i			1.45098i	−0.688233	+	0.725490i	$0.741613\pi$
$110$	−1.43535	+	4.06425i	−0.136855	+	0.387511i
$111$	−3.72192			−0.353269
$112$	7.72998	+	7.22823i	0.730415	+	0.683004i
$113$	−16.6411			−1.56546			−0.782732	−	0.622359i	$-0.786175\pi$
$113$	−16.6411			−1.56546			−0.782732	+	0.622359i	$0.786175\pi$
$114$	−0.145336	+	0.411525i	−0.0136120	+	0.0385429i
$115$		−	5.80481i		−	0.541301i
$116$	−0.233217	+	0.289000i	−0.0216536	+	0.0268330i
$117$	−12.9268			−1.19508
$118$	2.02846	+	0.716378i	0.186734	+	0.0659479i
$119$	10.2322	+	14.7624i	0.937986	+	1.35327i
$120$	0.783804	+	1.27178i	0.0715512	+	0.116097i
$121$	−1.71084			−0.155531
$122$	6.23311	−	17.6493i	0.564319	−	1.59789i
$123$	2.02600			0.182678
$124$	−4.86522	−	3.92613i	−0.436909	−	0.352577i
$125$	1.00000			0.0894427
$126$	2.68232	+	9.82147i	0.238960	+	0.874966i
$127$			15.9073i			1.41154i	0.708440	+	0.705771i	$0.249399\pi$
$127$			15.9073i			1.41154i	−0.708440	+	0.705771i	$0.750601\pi$
$128$	7.83643	+	8.16029i	0.692649	+	0.721275i
$129$		−	0.758217i		−	0.0667573i
$130$	2.23730	−	6.33502i	0.196225	−	0.555618i
$131$			20.2439i			1.76872i	0.466806	+	0.884360i	$0.345405\pi$
$131$			20.2439i			1.76872i	−0.466806	+	0.884360i	$0.654595\pi$
$132$	2.02189	−	2.50551i	0.175983	−	0.218076i
$133$	−0.880629	−	1.27052i	−0.0763602	−	0.110168i
$134$	4.30085	−	12.1780i	0.371537	−	1.05202i
$135$			3.02172i			0.260068i
$136$	10.0747	+	16.3468i	0.863895	+	1.40173i
$137$	6.38933			0.545877			0.272939	−	0.962031i	$-0.412004\pi$
$137$	6.38933			0.545877			0.272939	+	0.962031i	$0.412004\pi$
$138$	−1.44390	+	4.08845i	−0.122913	+	0.348032i
$139$		−	21.8128i		−	1.85014i	−0.379801	−	0.925068i	$-0.624008\pi$
$139$		−	21.8128i		−	1.85014i	0.379801	−	0.925068i	$-0.375992\pi$
$140$	−5.27745	−	0.385331i	−0.446026	−	0.0325664i
$141$			1.56272i			0.131605i
$142$	12.9113	+	4.55983i	1.08350	+	0.382652i
$143$	−14.4792			−1.21081
$144$	2.29904	+	10.6385i	0.191587	+	0.886545i
$145$		−	0.185682i		−	0.0154200i
$146$	−16.5747	−	5.85358i	−1.37173	−	0.484446i
$147$	3.46205	+	1.29760i	0.285545	+	0.107025i
$148$	8.85070	−	10.9677i	0.727523	−	0.901539i
$149$		−	11.5156i		−	0.943396i	−0.881760	−	0.471698i	$-0.843641\pi$
$149$		−	11.5156i		−	0.943396i	0.881760	−	0.471698i	$-0.156359\pi$
$150$	−0.704322	−	0.248741i	−0.0575076	−	0.0203096i
$151$			7.70970i			0.627407i	0.949521	+	0.313703i	$0.101570\pi$
$151$			7.70970i			0.627407i	−0.949521	+	0.313703i	$0.898430\pi$
$152$	−0.867068	−	1.40688i	−0.0703285	−	0.114113i
$153$			18.4729i			1.49345i
$154$	3.00445	+	11.0010i	0.242105	+	0.886484i
$155$	3.12589			0.251078
$156$	−3.15157	+	3.90539i	−0.252327	+	0.312681i
$157$	4.42111			0.352843			0.176422	−	0.984315i	$-0.443548\pi$
$157$	4.42111			0.352843			0.176422	+	0.984315i	$0.443548\pi$
$158$	3.75223	+	1.32515i	0.298511	+	0.105424i
$159$	0.282846			0.0224311
$160$	−5.61154	−	0.714577i	−0.443631	−	0.0564923i
$161$	−8.74895	−	12.6225i	−0.689514	−	0.994790i
$162$	−3.09273	+	8.75719i	−0.242988	+	0.688030i
$163$	17.5475			1.37443			0.687213	−	0.726456i	$-0.258834\pi$
$163$	17.5475			1.37443			0.687213	+	0.726456i	$0.258834\pi$
$164$	−4.81781	+	5.97018i	−0.376208	+	0.466193i
$165$			1.60978i			0.125321i
$166$	17.9402	+	6.33582i	1.39243	+	0.491755i
$167$	−1.57597			−0.121952			−0.0609760	−	0.998139i	$-0.519421\pi$
$167$	−1.57597			−0.121952			−0.0609760	+	0.998139i	$0.519421\pi$
$168$	3.62118	+	1.58412i	0.279380	+	0.122217i
$169$	9.56903			0.736079
$170$	−9.05303	−	3.19721i	−0.694336	−	0.245215i
$171$		−	1.58986i		−	0.121579i
$172$	2.23430	+	1.80304i	0.170364	+	0.137480i
$173$	0.208914			0.0158835			0.00794173	−	0.999968i	$-0.497472\pi$
$173$	0.208914			0.0158835			0.00794173	+	0.999968i	$0.497472\pi$
$174$	−0.0461867	+	0.130780i	−0.00350141	+	0.00991439i
$175$	2.17448	−	1.50719i	0.164376	−	0.113933i
$176$	2.57514	+	11.9162i	0.194109	+	0.898215i
$177$	0.803439			0.0603902
$178$	4.13438	+	1.46012i	0.309885	+	0.109440i
$179$	−5.84685			−0.437014			−0.218507	−	0.975835i	$-0.570119\pi$
$179$	−5.84685			−0.437014			−0.218507	+	0.975835i	$0.570119\pi$
$180$	−4.23508	−	3.41762i	−0.315664	−	0.254734i
$181$	8.66680			0.644198			0.322099	−	0.946706i	$-0.395612\pi$
$181$	8.66680			0.644198			0.322099	+	0.946706i	$0.395612\pi$
$182$	−4.68310	−	17.1475i	−0.347134	−	1.27105i
$183$		−	6.99061i		−	0.516761i
$184$	−8.61422	−	13.9772i	−0.635049	−	1.03041i
$185$			7.04672i			0.518085i
$186$	−2.20163	−	0.777539i	−0.161432	−	0.0570119i
$187$			20.6914i			1.51311i
$188$	−4.60501	−	3.71615i	−0.335855	−	0.271028i
$189$	4.55430	+	6.57067i	0.331276	+	0.477946i
$190$	0.779143	+	0.275165i	0.0565249	+	0.0199626i
$191$			12.9741i			0.938770i	0.882993	+	0.469385i	$0.155524\pi$
$191$			12.9741i			0.938770i	−0.882993	+	0.469385i	$0.844476\pi$
$192$	3.77459	+	1.89911i	0.272407	+	0.137057i
$193$	−24.5869			−1.76980			−0.884901	−	0.465780i	$-0.845774\pi$
$193$	−24.5869			−1.76980			−0.884901	+	0.465780i	$0.845774\pi$
$194$	18.0058	+	6.35900i	1.29274	+	0.456550i
$195$		−	2.50920i		−	0.179688i
$196$	−12.0565	+	7.11623i	−0.861179	+	0.508302i
$197$		−	7.21194i		−	0.513829i	−0.966434	−	0.256915i	$-0.917294\pi$
$197$		−	7.21194i		−	0.513829i	0.966434	−	0.256915i	$-0.0827059\pi$
$198$	−3.90562	+	11.0589i	−0.277560	+	0.785924i
$199$	6.32808			0.448585			0.224293	−	0.974522i	$-0.427993\pi$
$199$	6.32808			0.448585			0.224293	+	0.974522i	$0.427993\pi$
$200$	2.40786	−	1.48398i	0.170262	−	0.104933i
$201$		−	4.82353i		−	0.340226i
$202$	0.611482	−	1.73144i	0.0430237	−	0.121823i
$203$	−0.279858	−	0.403762i	−0.0196422	−	0.0283385i
$204$	5.58097	+	4.50373i	0.390746	+	0.315324i
$205$		−	3.83583i		−	0.267906i
$206$	8.98777	−	25.4493i	0.626208	−	1.77313i
$207$		−	15.7951i		−	1.09783i
$208$	−4.01393	−	18.5740i	−0.278316	−	1.28787i
$209$		−	1.78079i		−	0.123180i
$210$	−1.90644	+	0.520662i	−0.131557	+	0.0359291i
$211$	−10.2211			−0.703650			−0.351825	−	0.936066i	$-0.614439\pi$
$211$	−10.2211			−0.703650			−0.351825	+	0.936066i	$0.614439\pi$
$212$	−0.672606	+	0.833486i	−0.0461948	+	0.0572441i
$213$	5.11398			0.350404
$214$	1.79477	−	5.08198i	0.122688	−	0.347397i
$215$	−1.43554			−0.0979028
$216$	4.48417	+	7.27587i	0.305109	+	0.495061i
$217$	6.79721	−	4.71131i	0.461424	−	0.319825i
$218$	−20.2007	−	7.13417i	−1.36816	−	0.483187i
$219$	−6.56496			−0.443619
$220$	−4.74369	−	3.82806i	−0.319820	−	0.258088i
$221$		−	32.2521i		−	2.16951i
$222$	1.75281	−	4.96316i	0.117641	−	0.333106i
$223$	−2.64553			−0.177158			−0.0885790	−	0.996069i	$-0.528233\pi$
$223$	−2.64553			−0.177158			−0.0885790	+	0.996069i	$0.528233\pi$
$224$	−13.2792	+	6.90382i	−0.887254	+	0.461281i
$225$	2.72103			0.181402
$226$	7.83702	−	22.1909i	0.521311	−	1.47611i
$227$		−	16.2979i		−	1.08173i	−0.841109	−	0.540866i	$-0.818097\pi$
$227$		−	16.2979i		−	1.08173i	0.841109	−	0.540866i	$-0.181903\pi$
$228$	−0.480322	−	0.387610i	−0.0318101	−	0.0256701i
$229$	−5.51840			−0.364666			−0.182333	−	0.983237i	$-0.558365\pi$
$229$	−5.51840			−0.364666			−0.182333	+	0.983237i	$0.558365\pi$
$230$	7.74069	+	2.73374i	0.510406	+	0.180257i
$231$	2.42625	+	3.50045i	0.159635	+	0.230313i
$232$	−0.275548	−	0.447096i	−0.0180906	−	0.0293533i
$233$	18.6314			1.22058			0.610291	−	0.792177i	$-0.291053\pi$
$233$	18.6314			1.22058			0.610291	+	0.792177i	$0.291053\pi$
$234$	6.08777	−	17.2378i	0.397970	−	1.12687i
$235$	2.95871			0.193005
$236$	−1.91057	+	2.36756i	−0.124368	+	0.154115i
$237$	1.48620			0.0965390
$238$	−24.5045	+	6.69235i	−1.58839	+	0.433801i
$239$			5.77674i			0.373666i	0.982392	+	0.186833i	$0.0598223\pi$
$239$			5.77674i			0.373666i	−0.982392	+	0.186833i	$0.940178\pi$
$240$	−2.06504	+	0.446265i	−0.133298	+	0.0288063i
$241$		−	1.42853i		−	0.0920200i	−0.998941	−	0.0460100i	$-0.985349\pi$
$241$		−	1.42853i		−	0.0920200i	0.998941	−	0.0460100i	$-0.0146506\pi$
$242$	0.805710	−	2.28140i	0.0517930	−	0.146654i
$243$			12.5337i			0.804039i
$244$	20.5999	+	16.6237i	1.31877	+	1.06422i
$245$	2.45676	−	6.55472i	0.156957	−	0.418766i
$246$	−0.954130	+	2.70166i	−0.0608331	+	0.172252i
$247$			2.77576i			0.176617i
$248$	7.52672	−	4.63877i	0.477947	−	0.294562i
$249$	7.10581			0.450312
$250$	−0.470943	+	1.33350i	−0.0297851	+	0.0843377i
$251$			11.6354i			0.734419i	0.930138	+	0.367210i	$0.119687\pi$
$251$			11.6354i			0.734419i	−0.930138	+	0.367210i	$0.880313\pi$
$252$	−14.3601	−	1.04850i	−0.904602	−	0.0660490i
$253$		−	17.6920i		−	1.11228i
$254$	−21.2123	−	7.49142i	−1.33098	−	0.470054i
$255$	−3.58576			−0.224549
$256$	−14.5722	+	6.60681i	−0.910765	+	0.412926i
$257$		−	12.0011i		−	0.748611i	−0.927305	−	0.374306i	$-0.877881\pi$
$257$		−	12.0011i		−	0.748611i	0.927305	−	0.374306i	$-0.122119\pi$
$258$	1.01108	+	0.357077i	0.0629471	+	0.0222307i
$259$	10.6207	+	15.3230i	0.659941	+	0.952124i
$260$	7.39409	+	5.96688i	0.458562	+	0.370050i
$261$		−	0.505246i		−	0.0312739i
$262$	−26.9952	−	9.53374i	−1.66777	−	0.588996i
$263$			26.7775i			1.65117i	0.564277	+	0.825585i	$0.309155\pi$
$263$			26.7775i			1.65117i	−0.564277	+	0.825585i	$0.690845\pi$
$264$	2.38889	+	3.87614i	0.147026	+	0.238560i
$265$		−	0.535513i		−	0.0328963i
$266$	2.10896	−	0.575973i	0.129309	−	0.0353151i
$267$	1.63756			0.100217
$268$	14.2139	+	11.4703i	0.868253	+	0.700662i
$269$	19.0365			1.16067			0.580337	−	0.814376i	$-0.302921\pi$
$269$	19.0365			1.16067			0.580337	+	0.814376i	$0.302921\pi$
$270$	−4.02945	−	1.42306i	−0.245224	−	0.0866045i
$271$	2.47835			0.150549			0.0752745	−	0.997163i	$-0.476017\pi$
$271$	2.47835			0.150549			0.0752745	+	0.997163i	$0.476017\pi$
$272$	−26.5430	+	5.73608i	−1.60941	+	0.347801i
$273$	−3.78184	−	5.45622i	−0.228888	−	0.330226i
$274$	−3.00901	+	8.52015i	−0.181781	+	0.514721i
$275$	3.04781			0.183790
$276$	−4.77194	−	3.85086i	−0.287237	−	0.231795i
$277$		−	16.0967i		−	0.967159i	−0.875301	−	0.483579i	$-0.839336\pi$
$277$		−	16.0967i		−	0.967159i	0.875301	−	0.483579i	$-0.160664\pi$
$278$	29.0873	+	10.2726i	1.74454	+	0.616109i
$279$	8.50565			0.509220
$280$	2.99922	−	6.85600i	0.179238	−	0.409724i
$281$	17.4111			1.03866			0.519328	−	0.854575i	$-0.326182\pi$
$281$	17.4111			1.03866			0.519328	+	0.854575i	$0.326182\pi$
$282$	−2.08388	−	0.735954i	−0.124093	−	0.0438254i
$283$		−	29.4211i		−	1.74890i	−0.485114	−	0.874451i	$-0.661222\pi$
$283$		−	29.4211i		−	1.74890i	0.485114	−	0.874451i	$-0.338778\pi$
$284$	−12.1610	+	15.0698i	−0.721624	+	0.894229i
$285$	0.308606			0.0182802
$286$	6.81888	−	19.3080i	0.403209	−	1.14170i
$287$	−5.78132	−	8.34095i	−0.341261	−	0.492351i
$288$	−15.2692	−	1.94439i	−0.899744	−	0.114574i
$289$	−29.0897			−1.71116
$290$	0.247606	+	0.0874456i	0.0145399	+	0.00513498i
$291$	7.13181			0.418074
$292$	15.6115	−	19.3456i	0.913591	−	1.13211i
$293$	23.7367			1.38671			0.693357	−	0.720594i	$-0.256131\pi$
$293$	23.7367			1.38671			0.693357	+	0.720594i	$0.256131\pi$
$294$	−3.36078	+	4.00553i	−0.196005	+	0.233607i
$295$		−	1.52116i		−	0.0885651i
$296$	10.4572	+	16.9675i	0.607812	+	0.986218i
$297$			9.20962i			0.534396i
$298$	15.3560	+	5.42320i	0.889551	+	0.314158i
$299$			27.5768i			1.59481i
$300$	0.663391	−	0.822067i	0.0383009	−	0.0474621i
$301$	−3.12155	+	2.16362i	−0.179923	+	0.124709i
$302$	−10.2809	−	3.63083i	−0.591597	−	0.208931i
$303$		−	0.685795i		−	0.0393979i
$304$	2.28441	−	0.493672i	0.131020	−	0.0283140i
$305$	−13.2354			−0.757855
$306$	−24.6336	−	8.69969i	−1.40821	−	0.497328i
$307$		−	3.27590i		−	0.186965i	−0.995621	−	0.0934827i	$-0.970200\pi$
$307$		−	3.27590i		−	0.186965i	0.995621	−	0.0934827i	$-0.0298000\pi$
$308$	−16.0847	−	1.17442i	−0.916510	−	0.0669185i
$309$		−	10.0801i		−	0.573434i
$310$	−1.47212	+	4.16837i	−0.0836107	+	0.236747i
$311$	−20.9116			−1.18579			−0.592893	−	0.805282i	$-0.702014\pi$
$311$	−20.9116			−1.18579			−0.592893	+	0.805282i	$0.702014\pi$
$312$	−3.72361	−	6.04182i	−0.210808	−	0.342050i
$313$			13.8819i			0.784650i	0.919827	+	0.392325i	$0.128329\pi$
$313$			13.8819i			0.784650i	−0.919827	+	0.392325i	$0.871671\pi$
$314$	−2.08209	+	5.89554i	−0.117499	+	0.332704i
$315$	5.91683	−	4.10111i	0.333376	−	0.231071i
$316$	−3.53418	+	4.37951i	−0.198813	+	0.246367i
$317$		−	5.93227i		−	0.333190i	−0.986025	−	0.166595i	$-0.946723\pi$
$317$		−	5.93227i		−	0.333190i	0.986025	−	0.166595i	$-0.0532772\pi$
$318$	−0.133204	+	0.377174i	−0.00746973	+	0.0211509i
$319$		−	0.565923i		−	0.0316856i
$320$	3.59560	−	7.14644i	0.201000	−	0.399498i
$321$		−	2.01289i		−	0.112349i
$322$	20.9523	−	5.72222i	1.16762	−	0.318887i
$323$	3.96668			0.220712
$324$	−10.2212	−	8.24828i	−0.567843	−	0.458238i
$325$	−4.75069			−0.263521
$326$	−8.26388	+	23.3995i	−0.457694	+	1.29598i
$327$	−8.00118			−0.442466
$328$	−5.69230	−	9.23615i	−0.314305	−	0.509981i
$329$	6.43367	−	4.45934i	0.354700	−	0.245851i
$330$	−2.14664	−	0.758117i	−0.118169	−	0.0417330i
$331$	−7.33151			−0.402976			−0.201488	−	0.979491i	$-0.564578\pi$
$331$	−7.33151			−0.402976			−0.201488	+	0.979491i	$0.564578\pi$
$332$	−16.8976	+	20.9393i	−0.927376	+	1.14919i
$333$			19.1743i			1.05075i
$334$	0.742192	−	2.10155i	0.0406109	−	0.114992i
$335$	−9.13242			−0.498957
$336$	−3.81779	+	4.08280i	−0.208277	+	0.222735i
$337$	−16.5861			−0.903505			−0.451752	−	0.892143i	$-0.649201\pi$
$337$	−16.5861			−0.903505			−0.451752	+	0.892143i	$0.649201\pi$
$338$	−4.50647	+	12.7603i	−0.245120	+	0.694067i
$339$		−	8.78945i		−	0.477378i
$340$	8.52693	−	10.5665i	0.462438	−	0.573048i
$341$	9.52714			0.515923
$342$	2.12007	+	0.748733i	0.114640	+	0.0404868i
$343$	−4.53701	−	17.9559i	−0.244976	−	0.969529i
$344$	−3.45657	+	2.13031i	−0.186366	+	0.114859i
$345$	3.06597			0.165066
$346$	−0.0983868	+	0.278586i	−0.00528931	+	0.0149769i
$347$	28.9802			1.55574			0.777870	−	0.628425i	$-0.216300\pi$
$347$	28.9802			1.55574			0.777870	+	0.628425i	$0.216300\pi$
$348$	−0.152643	−	0.123180i	−0.00818252	−	0.00660313i
$349$	10.2706			0.549772			0.274886	−	0.961477i	$-0.411360\pi$
$349$	10.2706			0.549772			0.274886	+	0.961477i	$0.411360\pi$
$350$	0.985772	+	3.60947i	0.0526918	+	0.192934i
$351$		−	14.3552i		−	0.766225i
$352$	−17.1029	−	2.17790i	−0.911589	−	0.116082i
$353$			24.6097i			1.30984i	0.755697	+	0.654921i	$0.227298\pi$
$353$			24.6097i			1.30984i	−0.755697	+	0.654921i	$0.772702\pi$
$354$	−0.378374	+	1.07138i	−0.0201104	+	0.0569434i
$355$		−	9.68233i		−	0.513885i
$356$	−3.89412	+	4.82555i	−0.206388	+	0.255754i
$357$	−7.79718	+	5.40442i	−0.412671	+	0.286032i
$358$	2.75354	−	7.79676i	0.145529	−	0.412072i
$359$			5.06081i			0.267099i	0.991042	+	0.133550i	$0.0426375\pi$
$359$			5.06081i			0.267099i	−0.991042	+	0.133550i	$0.957362\pi$
$360$	6.55186	−	4.03795i	0.345314	−	0.212819i
$361$	18.6586			0.982032
$362$	−4.08157	+	11.5571i	−0.214523	+	0.607430i
$363$		−	0.903627i		−	0.0474281i
$364$	25.0715	+	1.83059i	1.31411	+	0.0959487i
$365$			12.4295i			0.650589i
$366$	9.32196	+	3.29218i	0.487266	+	0.172085i
$367$	−12.8106			−0.668708			−0.334354	−	0.942447i	$-0.608518\pi$
$367$	−12.8106			−0.668708			−0.334354	+	0.942447i	$0.608518\pi$
$368$	22.6953	−	4.90458i	1.18308	−	0.255669i
$369$		−	10.4374i		−	0.543350i
$370$	−9.39678	−	3.31861i	−0.488515	−	0.172526i
$371$	−0.807120	−	1.16447i	−0.0419036	−	0.0604560i
$372$	2.07369	−	2.56970i	0.107516	−	0.133232i
$373$			12.4155i			0.642849i	0.946935	+	0.321425i	$0.104162\pi$
$373$			12.4155i			0.642849i	−0.946935	+	0.321425i	$0.895838\pi$
$374$	−27.5919	−	9.74449i	−1.42674	−	0.503875i
$375$			0.528177i			0.0272749i
$376$	7.12417	−	4.39067i	0.367401	−	0.226431i
$377$			0.882116i			0.0454313i
$378$	−10.9068	+	2.97872i	−0.560984	+	0.153209i
$379$	9.41586			0.483660			0.241830	−	0.970319i	$-0.422252\pi$
$379$	9.41586			0.483660			0.241830	+	0.970319i	$0.422252\pi$
$380$	−0.733864	+	0.909396i	−0.0376464	+	0.0466511i
$381$	−8.40185			−0.430440
$382$	−17.3009	−	6.11005i	−0.885189	−	0.312617i
$383$	28.8384			1.47358			0.736788	−	0.676124i	$-0.236342\pi$
$383$	28.8384			1.47358			0.736788	+	0.676124i	$0.236342\pi$
$384$	−4.31008	+	4.13902i	−0.219948	+	0.211218i
$385$	6.62742	−	4.59363i	0.337765	−	0.234113i
$386$	11.5790	−	32.7865i	0.589357	−	1.66879i
$387$	−3.90614			−0.198560
$388$	−16.9594	+	21.0159i	−0.860984	+	1.06692i
$389$		−	4.35382i		−	0.220747i	−0.993890	−	0.110374i	$-0.964795\pi$
$389$		−	4.35382i		−	0.220747i	0.993890	−	0.110374i	$-0.0352048\pi$
$390$	3.34601	+	1.18169i	0.169432	+	0.0598373i
$391$	39.4085			1.99297
$392$	−3.81153	−	19.4286i	−0.192511	−	0.981295i
$393$	−10.6924			−0.539359
$394$	9.61709	+	3.39641i	0.484502	+	0.171109i
$395$		−	2.81383i		−	0.141579i
$396$	−12.9077	−	10.4163i	−0.648637	−	0.523437i
$397$	−16.9988			−0.853148			−0.426574	−	0.904453i	$-0.640280\pi$
$397$	−16.9988			−0.853148			−0.426574	+	0.904453i	$0.640280\pi$
$398$	−2.98017	+	8.43847i	−0.149382	+	0.422982i
$399$	0.671059	−	0.465128i	0.0335950	−	0.0232855i
$400$	0.844916	+	3.90975i	0.0422458	+	0.195487i
$401$	10.4337			0.521035			0.260518	−	0.965469i	$-0.416107\pi$
$401$	10.4337			0.521035			0.260518	+	0.965469i	$0.416107\pi$
$402$	6.43216	+	2.27161i	0.320807	+	0.113298i
$403$	−14.8501			−0.739738
$404$	2.02089	+	1.63082i	0.100543	+	0.0811362i
$405$	6.56709			0.326321
$406$	0.670212	−	0.183040i	0.0332621	−	0.00908412i
$407$			21.4771i			1.06458i
$408$	−8.63402	+	5.32120i	−0.427448	+	0.263439i
$409$			27.7527i			1.37228i	0.727469	+	0.686141i	$0.240697\pi$
$409$			27.7527i			1.37228i	−0.727469	+	0.686141i	$0.759303\pi$
$410$	5.11507	+	1.80646i	0.252615	+	0.0892147i
$411$			3.37470i			0.166461i
$412$	29.7038	+	23.9703i	1.46340	+	1.18093i
$413$	−2.29267	−	3.30773i	−0.112815	−	0.162763i
$414$	21.0626	+	7.43858i	1.03517	+	0.365586i
$415$		−	13.4535i		−	0.660405i
$416$	26.6587	+	3.39473i	1.30705	+	0.166440i
$417$	11.5210			0.564186
$418$	2.37468	+	0.838652i	0.116149	+	0.0410198i
$419$			30.1125i			1.47109i	0.677476	+	0.735545i	$0.263074\pi$
$419$			30.1125i			1.47109i	−0.677476	+	0.735545i	$0.736926\pi$
$420$	0.203523	−	2.78743i	0.00993089	−	0.136013i
$421$			27.1321i			1.32234i	0.750236	+	0.661170i	$0.229940\pi$
$421$			27.1321i			1.32234i	−0.750236	+	0.661170i	$0.770060\pi$
$422$	4.81356	−	13.6298i	0.234321	−	0.663489i
$423$	8.05074			0.391440
$424$	−0.794691	−	1.28944i	−0.0385936	−	0.0626209i
$425$			6.78894i			0.329312i
$426$	−2.40840	+	6.81948i	−0.116687	+	0.330405i
$427$	−28.7801	+	19.9482i	−1.39277	+	0.965361i
$428$	5.93156	+	4.78665i	0.286713	+	0.231371i
$429$		−	7.64758i		−	0.369229i
$430$	0.676056	−	1.91428i	0.0326023	−	0.0923149i
$431$			3.80266i			0.183167i	0.995797	+	0.0915837i	$0.0291929\pi$
$431$			3.80266i			0.183167i	−0.995797	+	0.0915837i	$0.970807\pi$
$432$	−11.8141	+	2.55309i	−0.568408	+	0.122836i
$433$		−	6.04283i		−	0.290400i	−0.989402	−	0.145200i	$-0.953617\pi$
$433$		−	6.04283i		−	0.290400i	0.989402	−	0.145200i	$-0.0463825\pi$
$434$	3.08142	+	11.2828i	0.147913	+	0.541592i
$435$	0.0980728			0.00470223
$436$	19.0268	−	23.5778i	0.911217	−	1.12917i
$437$	−3.39167			−0.162245
$438$	3.09173	−	8.75435i	0.147728	−	0.418299i
$439$	−20.7511			−0.990398			−0.495199	−	0.868780i	$-0.664905\pi$
$439$	−20.7511			−0.990398			−0.495199	+	0.868780i	$0.664905\pi$
$440$	7.33871	−	4.52289i	0.349859	−	0.215621i
$441$	6.68492	−	17.8356i	0.318329	−	0.849313i
$442$	43.0081	+	15.1889i	2.04569	+	0.722464i
$443$	40.9174			1.94404			0.972022	−	0.234891i	$-0.0754733\pi$
$443$	40.9174			1.94404			0.972022	+	0.234891i	$0.0754733\pi$
$444$	5.79288	+	4.67474i	0.274918	+	0.221853i
$445$		−	3.10041i		−	0.146973i
$446$	1.24590	−	3.52781i	0.0589949	−	0.167047i
$447$	6.08228			0.287682
$448$	−2.95246	−	20.9591i	−0.139491	−	0.990223i
$449$	9.64737			0.455288			0.227644	−	0.973744i	$-0.426898\pi$
$449$	9.64737			0.455288			0.227644	+	0.973744i	$0.426898\pi$
$450$	−1.28145	+	3.62848i	−0.0604082	+	0.171048i
$451$		−	11.6909i		−	0.550503i
$452$	25.9006	+	20.9013i	1.21826	+	0.983114i
$453$	−4.07209			−0.191323
$454$	21.7332	+	7.67540i	1.01999	+	0.360224i
$455$	−10.3303	+	7.16019i	−0.484292	+	0.335675i
$456$	0.743081	−	0.457965i	0.0347980	−	0.0214462i
$457$	8.31667			0.389037			0.194519	−	0.980899i	$-0.437686\pi$
$457$	8.31667			0.389037			0.194519	+	0.980899i	$0.437686\pi$
$458$	2.59886	−	7.35877i	0.121437	−	0.343853i
$459$	−20.5142			−0.957523
$460$	−7.29085	+	9.03475i	−0.339938	+	0.421247i
$461$	−14.8017			−0.689385			−0.344693	−	0.938716i	$-0.612017\pi$
$461$	−14.8017			−0.689385			−0.344693	+	0.938716i	$0.612017\pi$
$462$	−5.81046	+	1.58688i	−0.270327	+	0.0738284i
$463$		−	10.2328i		−	0.475556i	−0.971319	−	0.237778i	$-0.923581\pi$
$463$		−	10.2328i		−	0.475556i	0.971319	−	0.237778i	$-0.0764191\pi$
$464$	0.725969	−	0.156885i	0.0337023	−	0.00728323i
$465$			1.65102i			0.0765644i
$466$	−8.77432	+	24.8449i	−0.406463	+	1.15092i
$467$		−	1.49149i		−	0.0690179i	−0.999404	−	0.0345090i	$-0.989013\pi$
$467$		−	1.49149i		−	0.0690179i	0.999404	−	0.0345090i	$-0.0109867\pi$
$468$	20.1195	+	16.2360i	0.930026	+	0.750511i
$469$	−19.8583	+	13.7643i	−0.916971	+	0.635575i
$470$	−1.39338	+	3.94543i	−0.0642721	+	0.181989i
$471$			2.33513i			0.107597i
$472$	−2.25737	−	3.66273i	−0.103904	−	0.168591i
$473$	−4.37524			−0.201174
$474$	−0.699916	+	1.98184i	−0.0321482	+	0.0910290i
$475$		−	0.584285i		−	0.0268089i
$476$	2.61599	−	35.8283i	0.119904	−	1.64219i
$477$		−	1.45715i		−	0.0667182i
$478$	−7.70326	−	2.72052i	−0.352339	−	0.124434i
$479$	−33.0698			−1.51100			−0.755499	−	0.655150i	$-0.772605\pi$
$479$	−33.0698			−1.51100			−0.755499	+	0.655150i	$0.772605\pi$
$480$	0.377423	−	2.96389i	0.0172269	−	0.135282i
$481$		−	33.4768i		−	1.52641i
$482$	1.90494	+	0.672759i	0.0867679	+	0.0306433i
$483$	6.66689	−	4.62099i	0.303354	−	0.210262i
$484$	2.66280	+	2.14882i	0.121036	+	0.0976737i
$485$		−	13.5027i		−	0.613126i
$486$	−16.7137	−	5.90268i	−0.758148	−	0.267751i
$487$		−	30.3143i		−	1.37367i	−0.726811	−	0.686837i	$-0.758999\pi$
$487$		−	30.3143i		−	1.37367i	0.726811	−	0.686837i	$-0.241001\pi$
$488$	−31.8689	+	19.6410i	−1.44264	+	0.889107i
$489$			9.26819i			0.419122i
$490$	7.58370	+	6.36298i	0.342596	+	0.287450i
$491$	−24.0080			−1.08347			−0.541733	−	0.840551i	$-0.682232\pi$
$491$	−24.0080			−1.08347			−0.541733	+	0.840551i	$0.682232\pi$
$492$	−3.15331	−	2.54466i	−0.142162	−	0.114722i
$493$	1.26058			0.0567738
$494$	−3.70146	−	1.30722i	−0.166537	−	0.0588148i
$495$	8.29319			0.372751
$496$	2.64112	+	12.2215i	0.118590	+	0.548759i
$497$	−14.5931	−	21.0541i	−0.654590	−	0.944404i
$498$	−3.34643	+	9.47557i	−0.149957	+	0.424611i
$499$	−36.6238			−1.63951			−0.819754	−	0.572716i	$-0.805890\pi$
$499$	−36.6238			−1.63951			−0.819754	+	0.572716i	$0.805890\pi$
$500$	−1.55642	−	1.25600i	−0.0696054	−	0.0561701i
$501$		−	0.832390i		−	0.0371884i
$502$	−15.5157	−	5.47961i	−0.692502	−	0.244567i
$503$	−0.225539			−0.0100563			−0.00502815	−	0.999987i	$-0.501601\pi$
$503$	−0.225539			−0.0100563			−0.00502815	+	0.999987i	$0.501601\pi$
$504$	8.16096	−	18.6554i	0.363518	−	0.830976i
$505$	−1.29842			−0.0577789
$506$	23.5922	+	8.33191i	1.04880	+	0.370399i
$507$			5.05414i			0.224462i
$508$	19.9796	−	24.7585i	0.886450	−	1.09848i
$509$	11.4130			0.505871			0.252935	−	0.967483i	$-0.418604\pi$
$509$	11.4130			0.505871			0.252935	+	0.967483i	$0.418604\pi$
$510$	1.68869	−	4.78160i	0.0747765	−	0.211733i
$511$	18.7336	+	27.0277i	0.828725	+	1.19564i
$512$	−1.94746	−	22.5435i	−0.0860665	−	0.996289i
$513$	1.76554			0.0779507
$514$	16.0035	+	5.65186i	0.705884	+	0.249293i
$515$	−19.0846			−0.840969
$516$	−0.952322	+	1.18011i	−0.0419237	+	0.0519513i
$517$	9.01759			0.396593
$518$	−25.4349	+	6.94647i	−1.11755	+	0.305210i
$519$			0.110344i			0.00484355i
$520$	−11.4390	+	7.04993i	−0.501633	+	0.309160i
$521$			18.6069i			0.815183i	0.913164	+	0.407591i	$0.133631\pi$
$521$			18.6069i			0.815183i	−0.913164	+	0.407591i	$0.866369\pi$
$522$	0.673743	+	0.237942i	0.0294889	+	0.0104144i
$523$		−	35.5417i		−	1.55413i	−0.629420	−	0.777065i	$-0.716708\pi$
$523$		−	35.5417i		−	1.55413i	0.629420	−	0.777065i	$-0.283292\pi$
$524$	25.4264	−	31.5081i	1.11076	−	1.37644i
$525$	0.796062	+	1.14851i	0.0347430	+	0.0501252i
$526$	−35.7077	−	12.6107i	−1.55693	−	0.549852i
$527$			21.2215i			0.924424i
$528$	−6.29385	+	1.36013i	−0.273904	+	0.0591921i
$529$	−10.6958			−0.465035
$530$	0.714105	+	0.252196i	0.0310187	+	0.0109547i
$531$		−	4.13911i		−	0.179622i
$532$	−0.225143	+	3.08354i	−0.00976119	+	0.133688i
$533$			18.2228i			0.789319i
$534$	−0.771199	+	2.18368i	−0.0333731	+	0.0944972i
$535$	−3.81102			−0.164765
$536$	−21.9896	+	13.5523i	−0.949806	+	0.585371i
$537$		−	3.08817i		−	0.133265i
$538$	−8.96510	+	25.3851i	−0.386513	+	1.09443i
$539$	7.48775	−	19.9775i	0.322520	−	0.860494i
$540$	3.79528	−	4.70307i	0.163323	−	0.202388i
$541$			40.2046i			1.72853i	0.503035	+	0.864266i	$0.332216\pi$
$541$			40.2046i			1.72853i	−0.503035	+	0.864266i	$0.667784\pi$
$542$	−1.16716	+	3.30487i	−0.0501339	+	0.141956i
$543$			4.57760i			0.196444i
$544$	4.85122	−	38.0964i	0.207994	−	1.63337i
$545$			15.1487i			0.648898i
$546$	9.05689	−	2.47350i	0.387599	−	0.105856i
$547$	−6.38283			−0.272910			−0.136455	−	0.990646i	$-0.543571\pi$
$547$	−6.38283			−0.272910			−0.136455	+	0.990646i	$0.543571\pi$
$548$	−9.94451	−	8.02501i	−0.424808	−	0.342812i
$549$	−36.0138			−1.53703
$550$	−1.43535	+	4.06425i	−0.0612034	+	0.173300i
$551$	−0.108491			−0.00462188
$552$	7.38242	−	4.54983i	0.314217	−	0.193654i
$553$	−4.24097	−	6.11863i	−0.180344	−	0.260190i
$554$	21.4649	+	7.58065i	0.911957	+	0.322071i
$555$	−3.72192			−0.157987
$556$	−27.3969	+	33.9500i	−1.16189	+	1.43980i
$557$			33.9096i			1.43680i	0.695631	+	0.718399i	$0.255125\pi$
$557$			33.9096i			1.43680i	−0.695631	+	0.718399i	$0.744875\pi$
$558$	−4.00568	+	11.3422i	−0.169574	+	0.480156i
$559$	6.81978			0.288446
$560$	7.72998	+	7.22823i	0.326651	+	0.305449i
$561$	−10.9287			−0.461411
$562$	−8.19962	+	23.2176i	−0.345880	+	0.979375i
$563$		−	13.9112i		−	0.586288i	−0.956068	−	0.293144i	$-0.905298\pi$
$563$		−	13.9112i		−	0.586288i	0.956068	−	0.293144i	$-0.0947016\pi$
$564$	1.96278	−	2.43226i	0.0826481	−	0.102417i
$565$	−16.6411			−0.700097
$566$	39.2329	+	13.8557i	1.64908	+	0.582397i
$567$	14.2800	−	9.89784i	0.599705	−	0.415670i
$568$	−14.3684	−	23.3137i	−0.602884	−	0.978222i
$569$	−23.6948			−0.993336			−0.496668	−	0.867940i	$-0.665443\pi$
$569$	−23.6948			−0.993336			−0.496668	+	0.867940i	$0.665443\pi$
$570$	−0.145336	+	0.411525i	−0.00608745	+	0.0172369i
$571$	20.9646			0.877340			0.438670	−	0.898648i	$-0.355450\pi$
$571$	20.9646			0.877340			0.438670	+	0.898648i	$0.355450\pi$
$572$	22.5358	+	18.1859i	0.942269	+	0.760391i
$573$	−6.85260			−0.286271
$574$	13.8453	−	3.78126i	0.577892	−	0.157827i
$575$		−	5.80481i		−	0.242077i
$576$	9.78374	−	19.4457i	0.407656	−	0.810237i
$577$		−	11.5447i		−	0.480614i	−0.970697	−	0.240307i	$-0.922752\pi$
$577$		−	11.5447i		−	0.480614i	0.970697	−	0.240307i	$-0.0772481\pi$
$578$	13.6996	−	38.7911i	0.569829	−	1.61350i
$579$		−	12.9862i		−	0.539689i
$580$	−0.233217	+	0.289000i	−0.00968380	+	0.0120001i
$581$	−20.2769	−	29.2544i	−0.841229	−	1.21368i
$582$	−3.35868	+	9.51024i	−0.139222	+	0.394212i
$583$		−	1.63214i		−	0.0675965i
$584$	18.4451	+	29.9285i	0.763264	+	1.23845i
$585$	−12.9268			−0.534456
$586$	−11.1786	+	31.6528i	−0.461786	+	1.30757i
$587$		−	8.38593i		−	0.346124i	−0.984911	−	0.173062i	$-0.944634\pi$
$587$		−	8.38593i		−	0.346124i	0.984911	−	0.173062i	$-0.0553661\pi$
$588$	−3.75863	−	6.36797i	−0.155003	−	0.262611i
$589$		−	1.82641i		−	0.0752561i
$590$	2.02846	+	0.716378i	0.0835102	+	0.0294928i
$591$	3.80918			0.156689
$592$	−27.5509	+	5.95389i	−1.13234	+	0.244703i
$593$		−	26.8713i		−	1.10347i	−0.834018	−	0.551737i	$-0.813965\pi$
$593$		−	26.8713i		−	1.10347i	0.834018	−	0.551737i	$-0.186035\pi$
$594$	−12.2810	−	4.33721i	−0.503895	−	0.177958i
$595$	10.2322	+	14.7624i	0.419480	+	0.605201i
$596$	−14.4636	+	17.9232i	−0.592454	+	0.734162i
$597$			3.34234i			0.136793i
$598$	−36.7736	−	12.9871i	−1.50378	−	0.531083i
$599$		−	34.0473i		−	1.39113i	−0.718462	−	0.695566i	$-0.755153\pi$
$599$		−	34.0473i		−	1.39113i	0.718462	−	0.695566i	$-0.244847\pi$
$600$	0.783804	+	1.27178i	0.0319987	+	0.0519201i
$601$			24.5067i			0.999649i	0.866127	+	0.499825i	$0.166602\pi$
$601$			24.5067i			0.999649i	−0.866127	+	0.499825i	$0.833398\pi$
$602$	−1.41511	−	5.18152i	−0.0576757	−	0.211183i
$603$	−24.8496			−1.01195
$604$	9.68340	−	11.9996i	0.394012	−	0.488256i
$605$	−1.71084			−0.0695556
$606$	0.914505	+	0.322970i	0.0371492	+	0.0131198i
$607$	36.7082			1.48994			0.744971	−	0.667097i	$-0.232463\pi$
$607$	36.7082			1.48994			0.744971	+	0.667097i	$0.232463\pi$
$608$	−0.417517	+	3.27874i	−0.0169326	+	0.132971i
$609$	0.213258	−	0.147814i	0.00864164	−	0.00598974i
$610$	6.23311	−	17.6493i	0.252371	−	0.714600i
$611$	−14.0559			−0.568641
$612$	23.2020	−	28.7517i	0.937886	−	1.16222i
$613$			41.6702i			1.68304i	0.540224	+	0.841521i	$0.318339\pi$
$613$			41.6702i			1.68304i	−0.540224	+	0.841521i	$0.681661\pi$
$614$	4.36840	+	1.54276i	0.176294	+	0.0622608i
$615$	2.02600			0.0816961
$616$	9.14106	−	20.8958i	0.368304	−	0.841915i
$617$	18.6715			0.751688			0.375844	−	0.926683i	$-0.377353\pi$
$617$	18.6715			0.751688			0.375844	+	0.926683i	$0.377353\pi$
$618$	13.4417	+	4.74713i	0.540705	+	0.190958i
$619$		−	19.0302i		−	0.764888i	−0.923979	−	0.382444i	$-0.875083\pi$
$619$		−	19.0302i		−	0.764888i	0.923979	−	0.382444i	$-0.124917\pi$
$620$	−4.86522	−	3.92613i	−0.195392	−	0.157677i
$621$	17.5405			0.703875
$622$	9.84816	−	27.8855i	0.394875	−	1.11811i
$623$	−4.67290	−	6.74178i	−0.187216	−	0.270104i
$624$	9.81035	−	2.12007i	0.392728	−	0.0848705i
$625$	1.00000			0.0400000
$626$	−18.5114	−	6.53758i	−0.739866	−	0.261294i
$627$	0.940573			0.0375629
$628$	−6.88113	−	5.55293i	−0.274587	−	0.221586i
$629$	−47.8398			−1.90750
$630$	2.68232	+	9.82147i	0.106866	+	0.391297i
$631$		−	28.1199i		−	1.11944i	−0.828683	−	0.559718i	$-0.810910\pi$
$631$		−	28.1199i		−	1.11944i	0.828683	−	0.559718i	$-0.189090\pi$
$632$	−4.17567	−	6.77531i	−0.166099	−	0.269507i
$633$		−	5.39855i		−	0.214573i
$634$	7.91067	+	2.79377i	0.314173	+	0.110955i
$635$			15.9073i			0.631261i
$636$	−0.440228	−	0.355255i	−0.0174562	−	0.0140868i
$637$	−11.6713	+	31.1394i	−0.462434	+	1.23379i
$638$	0.754657	+	0.266518i	0.0298771	+	0.0105515i
$639$		−	26.3459i		−	1.04223i
$640$	7.83643	+	8.16029i	0.309762	+	0.322564i
$641$	−7.40297			−0.292400			−0.146200	−	0.989255i	$-0.546704\pi$
$641$	−7.40297			−0.292400			−0.146200	+	0.989255i	$0.546704\pi$
$642$	2.68418	+	0.947958i	0.105936	+	0.0374129i
$643$		−	10.9752i		−	0.432819i	−0.976303	−	0.216409i	$-0.930565\pi$
$643$		−	10.9752i		−	0.432819i	0.976303	−	0.216409i	$-0.0694346\pi$
$644$	−2.23677	+	30.6346i	−0.0881411	+	1.20717i
$645$		−	0.758217i		−	0.0298548i
$646$	−1.86808	+	5.28955i	−0.0734987	+	0.208115i
$647$	37.3313			1.46765			0.733823	−	0.679340i	$-0.237734\pi$
$647$	37.3313			1.46765			0.733823	+	0.679340i	$0.237734\pi$
$648$	15.8126	−	9.74543i	0.621179	−	0.382837i
$649$		−	4.63620i		−	0.181987i
$650$	2.23730	−	6.33502i	0.0877543	−	0.248480i
$651$	2.48841	+	3.59013i	0.0975283	+	0.140708i
$652$	−27.3114	−	22.0397i	−1.06960	−	0.863142i
$653$		−	27.0398i		−	1.05815i	−0.848575	−	0.529074i	$-0.822539\pi$
$653$		−	27.0398i		−	1.05815i	0.848575	−	0.529074i	$-0.177461\pi$
$654$	3.76810	−	10.6695i	0.147344	−	0.417212i
$655$			20.2439i			0.790995i
$656$	14.9971	−	3.24095i	0.585539	−	0.126538i
$657$			33.8210i			1.31948i
$658$	2.91662	+	10.6794i	0.113701	+	0.416325i
$659$	16.0036			0.623410			0.311705	−	0.950179i	$-0.399100\pi$
$659$	16.0036			0.623410			0.311705	+	0.950179i	$0.399100\pi$
$660$	2.02189	−	2.50551i	0.0787020	−	0.0975267i
$661$	28.7776			1.11932			0.559659	−	0.828723i	$-0.310932\pi$
$661$	28.7776			1.11932			0.559659	+	0.828723i	$0.310932\pi$
$662$	3.45273	−	9.77654i	0.134194	−	0.379976i
$663$	17.0348			0.661578
$664$	−19.9647	−	32.3941i	−0.774780	−	1.25714i
$665$	−0.880629	−	1.27052i	−0.0341493	−	0.0492686i
$666$	−25.5689	−	9.03003i	−0.990775	−	0.349907i
$667$	−1.07785			−0.0417344
$668$	2.45288	+	1.97942i	0.0949046	+	0.0765861i
$669$		−	1.39731i		−	0.0540231i
$670$	4.30085	−	12.1780i	0.166156	−	0.470479i
$671$	−40.3389			−1.55727
$672$	−3.64644	−	7.01377i	−0.140664	−	0.270562i
$673$	19.6820			0.758685			0.379342	−	0.925256i	$-0.376150\pi$
$673$	19.6820			0.758685			0.379342	+	0.925256i	$0.376150\pi$
$674$	7.81113	−	22.1176i	0.300874	−	0.851937i
$675$			3.02172i			0.116306i
$676$	−14.8935	−	12.0187i	−0.572826	−	0.462259i
$677$	41.7128			1.60315			0.801576	−	0.597893i	$-0.203995\pi$
$677$	41.7128			1.60315			0.801576	+	0.597893i	$0.203995\pi$
$678$	11.7207	+	4.13933i	0.450131	+	0.158970i
$679$	−20.3511	−	29.3614i	−0.781004	−	1.12679i
$680$	10.0747	+	16.3468i	0.386346	+	0.626873i
$681$	8.60819			0.329866
$682$	−4.48674	+	12.7044i	−0.171806	+	0.486477i
$683$	−22.1942			−0.849237			−0.424618	−	0.905372i	$-0.639592\pi$
$683$	−22.1942			−0.849237			−0.424618	+	0.905372i	$0.639592\pi$
$684$	−1.99687	+	2.47449i	−0.0763521	+	0.0946146i
$685$	6.38933			0.244124
$686$	26.0808	+	2.40614i	0.995771	+	0.0918668i
$687$		−	2.91469i		−	0.111202i
$688$	−1.21291	−	5.61258i	−0.0462417	−	0.213978i
$689$			2.54406i			0.0969208i
$690$	−1.44390	+	4.08845i	−0.0549682	+	0.155645i
$691$			7.35566i			0.279822i	0.990164	+	0.139911i	$0.0446817\pi$
$691$			7.35566i			0.279822i	−0.990164	+	0.139911i	$0.955318\pi$
$692$	−0.325159	−	0.262397i	−0.0123607	−	0.00997483i
$693$	18.0334	−	12.4994i	0.685032	−	0.474813i
$694$	−13.6481	+	38.6450i	−0.518073	+	1.46695i
$695$		−	21.8128i		−	0.827406i
$696$	0.236146	−	0.145538i	0.00895109	−	0.00551661i
$697$	26.0412			0.986382
$698$	−4.83687	+	13.6958i	−0.183078	+	0.518393i
$699$			9.84066i			0.372208i
$700$	−5.27745	−	0.385331i	−0.199469	−	0.0145641i
$701$		−	10.2820i		−	0.388346i	−0.980967	−	0.194173i	$-0.937798\pi$
$701$		−	10.2820i		−	0.388346i	0.980967	−	0.194173i	$-0.0622024\pi$
$702$	19.1426	+	6.76050i	0.722492	+	0.255159i
$703$	4.11730			0.155287
$704$	10.9587	−	21.7810i	0.413022	−	0.820903i
$705$			1.56272i			0.0588555i
$706$	−32.8169	−	11.5898i	−1.23508	−	0.436187i
$707$	−2.82339	+	1.95696i	−0.106185	+	0.0735992i
$708$	−1.25049	−	1.00912i	−0.0469964	−	0.0379251i
$709$		−	10.8180i		−	0.406277i	−0.979150	−	0.203139i	$-0.934886\pi$
$709$		−	10.8180i		−	0.406277i	0.979150	−	0.203139i	$-0.0651142\pi$
$710$	12.9113	+	4.55983i	0.484554	+	0.171127i
$711$		−	7.65651i		−	0.287142i
$712$	−4.60094	−	7.46535i	−0.172428	−	0.279776i
$713$		−	18.1452i		−	0.679544i
$714$	−3.53475	−	12.9427i	−0.132285	−	0.484368i
$715$	−14.4792			−0.541491
$716$	9.10019	+	7.34366i	0.340090	+	0.274446i
$717$	−3.05114			−0.113947
$718$	−6.74857	−	2.38335i	−0.251854	−	0.0889459i
$719$	29.4274			1.09746			0.548729	−	0.836000i	$-0.315112\pi$
$719$	29.4274			1.09746			0.548729	+	0.836000i	$0.315112\pi$
$720$	2.29904	+	10.6385i	0.0856802	+	0.396475i
$721$	−41.4992	+	28.7641i	−1.54551	+	1.07123i
$722$	−8.78715	+	24.8812i	−0.327024	+	0.925982i
$723$	0.754518			0.0280608
$724$	−13.4892	−	10.8855i	−0.501323	−	0.404557i
$725$		−	0.185682i		−	0.00689605i
$726$	1.20498	+	0.425557i	0.0447211	+	0.0157939i
$727$	−31.0932			−1.15318			−0.576591	−	0.817033i	$-0.695617\pi$
$727$	−31.0932			−1.15318			−0.576591	+	0.817033i	$0.695617\pi$
$728$	−14.2484	+	32.5707i	−0.528079	+	1.20715i
$729$	13.0812			0.484490
$730$	−16.5747	−	5.85358i	−0.613456	−	0.216651i
$731$		−	9.74577i		−	0.360460i
$732$	−8.78023	+	10.8804i	−0.324527	+	0.402150i
$733$	−10.0076			−0.369639			−0.184820	−	0.982772i	$-0.559170\pi$
$733$	−10.0076			−0.369639			−0.184820	+	0.982772i	$0.559170\pi$
$734$	6.03307	−	17.0829i	0.222685	−	0.630541i
$735$	3.46205	+	1.29760i	0.127700	+	0.0478629i
$736$	−4.14798	+	32.5739i	−0.152897	+	1.20069i
$737$	−27.8339			−1.02527
$738$	13.9182	+	4.91543i	0.512338	+	0.180939i
$739$	40.1592			1.47728			0.738641	−	0.674099i	$-0.235468\pi$
$739$	40.1592			1.47728			0.738641	+	0.674099i	$0.235468\pi$
$740$	8.85070	−	10.9677i	0.325358	−	0.403180i
$741$	−1.46609			−0.0538582
$742$	1.93292	−	0.527894i	0.0709596	−	0.0193796i
$743$			41.3554i			1.51718i	0.651567	+	0.758591i	$0.274112\pi$
$743$			41.3554i			1.51718i	−0.651567	+	0.758591i	$0.725888\pi$
$744$	2.45009	+	3.97544i	0.0898246	+	0.145747i
$745$		−	11.5156i		−	0.421899i
$746$	−16.5560	−	5.84699i	−0.606158	−	0.214073i
$747$		−	36.6073i		−	1.33939i
$748$	25.9885	−	32.2046i	0.950233	−	1.17752i
$749$	−8.28700	+	5.74393i	−0.302800	+	0.209878i
$750$	−0.704322	−	0.248741i	−0.0257182	−	0.00908275i
$751$		−	10.4171i		−	0.380126i	−0.981772	−	0.190063i	$-0.939131\pi$
$751$		−	10.4171i		−	0.380126i	0.981772	−	0.190063i	$-0.0608693\pi$
$752$	2.49986	+	11.5678i	0.0911605	+	0.421835i
$753$	−6.14554			−0.223956
$754$	−1.17630	−	0.415427i	−0.0428383	−	0.0151290i
$755$			7.70970i			0.280585i
$756$	1.16436	−	15.9470i	0.0423473	−	0.579985i
$757$		−	31.7145i		−	1.15268i	−0.817209	−	0.576341i	$-0.804480\pi$
$757$		−	31.7145i		−	1.15268i	0.817209	−	0.576341i	$-0.195520\pi$
$758$	−4.43434	+	12.5560i	−0.161062	+	0.456055i
$759$	9.34449			0.339183
$760$	−0.867068	−	1.40688i	−0.0314519	−	0.0510329i
$761$			11.9199i			0.432095i	0.976383	+	0.216047i	$0.0693166\pi$
$761$			11.9199i			0.432095i	−0.976383	+	0.216047i	$0.930683\pi$
$762$	3.95680	−	11.2038i	0.143340	−	0.405872i
$763$	22.8319	+	32.9406i	0.826571	+	1.19253i
$764$	16.2955	−	20.1932i	0.589549	−	0.730563i
$765$			18.4729i			0.667890i
$766$	−13.5813	+	38.4560i	−0.490711	+	1.38947i
$767$			7.22653i			0.260935i
$768$	−3.48957	−	7.69672i	−0.125919	−	0.277731i
$769$			9.56458i			0.344908i	0.985018	+	0.172454i	$0.0551695\pi$
$769$			9.56458i			0.344908i	−0.985018	+	0.172454i	$0.944830\pi$
$770$	3.00445	+	11.0010i	0.108273	+	0.396448i
$771$	6.33873			0.228284
$772$	38.2676	+	30.8812i	1.37728	+	1.11144i
$773$	30.6270			1.10158			0.550788	−	0.834645i	$-0.314327\pi$
$773$	30.6270			1.10158			0.550788	+	0.834645i	$0.314327\pi$
$774$	1.83957	−	5.20882i	0.0661219	−	0.187227i
$775$	3.12589			0.112285
$776$	−20.0377	−	32.5126i	−0.719313	−	1.16714i
$777$	−8.09325	+	5.60963i	−0.290344	+	0.201244i
$778$	5.80580	+	2.05040i	0.208148	+	0.0735105i
$779$	−2.24122			−0.0803001
$780$	−3.15157	+	3.90539i	−0.112844	+	0.139835i
$781$		−	29.5099i		−	1.05595i
$782$	−18.5592	+	52.5511i	−0.663675	+	1.87922i
$783$	0.561078			0.0200513
$784$	27.7030	+	4.06713i	0.989394	+	0.145255i
$785$	4.42111			0.157796
$786$	5.03550	−	14.2582i	0.179610	−	0.508574i
$787$			26.7295i			0.952804i	0.879228	+	0.476402i	$0.158059\pi$
$787$			26.7295i			0.952804i	−0.879228	+	0.476402i	$0.841941\pi$
$788$	−9.05821	+	11.2248i	−0.322685	+	0.399868i
$789$	−14.1432			−0.503513
$790$	3.75223	+	1.32515i	0.133498	+	0.0471469i
$791$	−36.1858	+	25.0813i	−1.28662	+	0.891789i
$792$	19.9689	−	12.3069i	0.709562	−	0.437308i
$793$	62.8771			2.23283
$794$	8.00549	−	22.6679i	0.284104	−	0.804454i
$795$	0.282846			0.0100315
$796$	−9.84918	−	7.94808i	−0.349095	−	0.281712i
$797$	1.38276			0.0489799			0.0244899	−	0.999700i	$-0.492204\pi$
$797$	1.38276			0.0489799			0.0244899	+	0.999700i	$0.492204\pi$
$798$	0.304215	+	1.11390i	0.0107691	+	0.0394318i
$799$			20.0865i			0.710610i
$800$	−5.61154	−	0.714577i	−0.198398	−	0.0252641i
$801$		−	8.43630i		−	0.298082i
$802$	−4.91369	+	13.9133i	−0.173508	+	0.491297i
$803$			37.8827i			1.33685i
$804$	−6.05837	+	7.50746i	−0.213662	+	0.264768i
$805$	−8.74895	−	12.6225i	−0.308360	−	0.444883i
$806$	6.99358	−	19.8026i	0.246338	−	0.697517i
$807$			10.0546i			0.353939i
$808$	−3.12641	+	1.92683i	−0.109987	+	0.0677856i
$809$	3.98813			0.140215			0.0701075	−	0.997539i	$-0.477666\pi$
$809$	3.98813			0.140215			0.0701075	+	0.997539i	$0.477666\pi$
$810$	−3.09273	+	8.75719i	−0.108667	+	0.307696i
$811$		−	19.2038i		−	0.674338i	−0.941444	−	0.337169i	$-0.890531\pi$
$811$		−	19.2038i		−	0.674338i	0.941444	−	0.337169i	$-0.109469\pi$
$812$	−0.0715489	+	0.979927i	−0.00251087	+	0.0343887i
$813$			1.30901i			0.0459089i
$814$	−28.6396	−	10.1145i	−1.00382	−	0.354513i
$815$	17.5475			0.614662
$816$	−3.02967	−	14.0194i	−0.106060	−	0.490778i
$817$			0.838763i			0.0293446i
$818$	−37.0081	−	13.0699i	−1.29396	−	0.456980i
$819$	−28.1090	+	19.4831i	−0.982209	+	0.680794i
$820$	−4.81781	+	5.97018i	−0.168245	+	0.208488i
$821$			39.4413i			1.37651i	0.725468	+	0.688256i	$0.241623\pi$
$821$			39.4413i			1.37651i	−0.725468	+	0.688256i	$0.758377\pi$
$822$	−4.50014	−	1.58929i	−0.156961	−	0.0554329i
$823$			0.408196i			0.0142288i	0.999975	+	0.00711440i	$0.00226460\pi$
$823$			0.408196i			0.0142288i	−0.999975	+	0.00711440i	$0.997735\pi$
$824$	−45.9531	+	28.3212i	−1.60085	+	0.986616i
$825$			1.60978i			0.0560455i
$826$	5.49056	−	1.49951i	0.191041	−	0.0521747i
$827$	33.9219			1.17958			0.589790	−	0.807557i	$-0.299211\pi$
$827$	33.9219			1.17958			0.589790	+	0.807557i	$0.299211\pi$
$828$	−19.8386	+	24.5838i	−0.689440	+	0.854347i
$829$	16.5466			0.574686			0.287343	−	0.957828i	$-0.407228\pi$
$829$	16.5466			0.574686			0.287343	+	0.957828i	$0.407228\pi$
$830$	17.9402	+	6.33582i	0.622712	+	0.219920i
$831$	8.50192			0.294928
$832$	−17.0816	+	33.9505i	−0.592197	+	1.17702i
$833$	44.4996	+	16.6788i	1.54182	+	0.577887i
$834$	−5.42574	+	15.3632i	−0.187878	+	0.531985i
$835$	−1.57597			−0.0545386
$836$	−2.23668	+	2.77167i	−0.0773572	+	0.0958602i
$837$			9.44556i			0.326486i
$838$	−40.1549	−	14.1813i	−1.38713	−	0.489884i
$839$	−33.4148			−1.15361			−0.576804	−	0.816883i	$-0.695700\pi$
$839$	−33.4148			−1.15361			−0.576804	+	0.816883i	$0.695700\pi$
$840$	3.62118	+	1.58412i	0.124943	+	0.0546573i
$841$	28.9655			0.998811
$842$	−36.1806	−	12.7777i	−1.24687	−	0.440349i
$843$			9.19612i			0.316731i
$844$	15.9084	+	12.8377i	0.547589	+	0.441893i
$845$	9.56903			0.329185
$846$	−3.79144	+	10.7356i	−0.130352	+	0.369098i
$847$	−3.72020	+	2.57856i	−0.127828	+	0.0886005i
$848$	2.09372	−	0.452464i	0.0718987	−	0.0155377i
$849$	15.5395			0.533315
$850$	−9.05303	−	3.19721i	−0.310516	−	0.109663i
$851$	40.9049			1.40220
$852$	−7.95953	−	6.42317i	−0.272689	−	0.220054i
$853$	−12.1851			−0.417211			−0.208606	−	0.978000i	$-0.566893\pi$
$853$	−12.1851			−0.417211			−0.208606	+	0.978000i	$0.566893\pi$
$854$	−13.0471	−	47.7726i	−0.446461	−	1.63475i
$855$		−	1.58986i		−	0.0543720i
$856$	−9.17641	+	5.65548i	−0.313643	+	0.193300i
$857$			16.0726i			0.549031i	0.961583	+	0.274515i	$0.0885174\pi$
$857$			16.0726i			0.549031i	−0.961583	+	0.274515i	$0.911483\pi$
$858$	10.1980	+	3.60158i	0.348155	+	0.122956i
$859$			21.5250i			0.734425i	0.930137	+	0.367212i	$0.119688\pi$
$859$			21.5250i			0.734425i	−0.930137	+	0.367212i	$0.880312\pi$
$860$	2.23430	+	1.80304i	0.0761891	+	0.0614831i
$861$	4.40550	−	3.05356i	0.150139	−	0.104065i
$862$	−5.07083	−	1.79084i	−0.172713	−	0.0609961i
$863$		−	3.22755i		−	0.109867i	−0.998490	−	0.0549336i	$-0.982505\pi$
$863$		−	3.22755i		−	0.109867i	0.998490	−	0.0549336i	$-0.0174947\pi$
$864$	2.15925	−	16.9565i	0.0734591	−	0.576871i
$865$	0.208914			0.00710330
$866$	8.05809	+	2.84583i	0.273825	+	0.0967052i
$867$		−	15.3645i		−	0.521807i
$868$	−16.4968	−	1.20450i	−0.559936	−	0.0408835i
$869$		−	8.57602i		−	0.290922i
$870$	−0.0461867	+	0.130780i	−0.00156588	+	0.00443385i
$871$	43.3853			1.47005
$872$	22.4803	+	36.4759i	0.761281	+	1.23523i
$873$		−	36.7412i		−	1.24350i
$874$	1.59728	−	4.52277i	0.0540289	−	0.152985i
$875$	2.17448	−	1.50719i	0.0735110	−	0.0509523i
$876$	10.2179	+	8.24561i	0.345230	+	0.278593i
$877$		−	27.5777i		−	0.931233i	−0.884987	−	0.465616i	$-0.845833\pi$
$877$		−	27.5777i		−	0.931233i	0.884987	−	0.465616i	$-0.154167\pi$
$878$	9.77261	−	27.6716i	0.329810	−	0.933870i
$879$			12.5372i			0.422869i
$880$	2.57514	+	11.9162i	0.0868081	+	0.401694i
$881$		−	20.1792i		−	0.679856i	−0.940452	−	0.339928i	$-0.889597\pi$
$881$		−	20.1792i		−	0.679856i	0.940452	−	0.339928i	$-0.110403\pi$
$882$	20.6355	+	17.3139i	0.694832	+	0.582988i
$883$	4.97245			0.167336			0.0836681	−	0.996494i	$-0.473336\pi$
$883$	4.97245			0.167336			0.0836681	+	0.996494i	$0.473336\pi$
$884$	−40.5088	+	50.1980i	−1.36246	+	1.68834i
$885$	0.803439			0.0270073
$886$	−19.2698	+	54.5632i	−0.647381	+	1.83309i
$887$	5.11354			0.171696			0.0858480	−	0.996308i	$-0.472640\pi$
$887$	5.11354			0.171696			0.0858480	+	0.996308i	$0.472640\pi$
$888$	−8.96186	+	5.52325i	−0.300740	+	0.185348i
$889$	23.9753	+	34.5901i	0.804105	+	1.16012i
$890$	4.13438	+	1.46012i	0.138585	+	0.0489432i
$891$	20.0152			0.670536
$892$	4.11757	+	3.32280i	0.137867	+	0.111255i
$893$		−	1.72873i		−	0.0578498i
$894$	−2.86441	+	8.11070i	−0.0958002	+	0.271262i
$895$	−5.84685			−0.195439
$896$	29.3393	+	5.93345i	0.980157	+	0.198223i
$897$	−14.5654			−0.486326
$898$	−4.54337	+	12.8647i	−0.151614	+	0.429302i
$899$		−	0.580422i		−	0.0193581i
$900$	−4.23508	−	3.41762i	−0.141169	−	0.113921i
$901$	3.63557			0.121118
$902$	15.5898	+	5.50575i	0.519082	+	0.183321i
$903$	−1.14278	−	1.64873i	−0.0380292	−	0.0548663i
$904$	−40.0695	+	24.6951i	−1.33269	+	0.821347i
$905$	8.66680			0.288094
$906$	1.91772	−	5.43011i	0.0637120	−	0.180403i
$907$	−26.8798			−0.892530			−0.446265	−	0.894901i	$-0.647246\pi$
$907$	−26.8798			−0.892530			−0.446265	+	0.894901i	$0.647246\pi$
$908$	−20.4702	+	25.3665i	−0.679329	+	0.841817i
$909$	−3.53304			−0.117183
$910$	−4.68310	−	17.1475i	−0.155243	−	0.568432i
$911$		−	43.0775i		−	1.42722i	−0.700543	−	0.713610i	$-0.747059\pi$
$911$		−	43.0775i		−	1.42722i	0.700543	−	0.713610i	$-0.252941\pi$
$912$	0.260746	+	1.20657i	0.00863417	+	0.0399536i
$913$		−	41.0036i		−	1.35702i
$914$	−3.91668	+	11.0902i	−0.129552	+	0.366833i
$915$		−	6.99061i		−	0.231103i
$916$	8.58898	+	6.93113i	0.283788	+	0.229011i
$917$	30.5114	+	44.0201i	1.00758	+	1.45367i
$918$	9.66105	−	27.3557i	0.318862	−	0.902872i
$919$		−	6.42394i		−	0.211906i	−0.994371	−	0.105953i	$-0.966211\pi$
$919$		−	6.42394i		−	0.211906i	0.994371	−	0.105953i	$-0.0337893\pi$
$920$	−8.61422	−	13.9772i	−0.284003	−	0.460814i
$921$	1.73025			0.0570138
$922$	6.97078	−	19.7381i	0.229570	−	0.650038i
$923$			45.9977i			1.51403i
$924$	0.620299	−	8.49556i	0.0204063	−	0.279483i
$925$			7.04672i			0.231695i
$926$	13.6453	+	4.81905i	0.448414	+	0.158364i
$927$	−51.9298			−1.70560
$928$	−0.132684	+	1.04196i	−0.00435556	+	0.0342040i
$929$		−	8.92552i		−	0.292837i	−0.989223	−	0.146418i	$-0.953225\pi$
$929$		−	8.92552i		−	0.292837i	0.989223	−	0.146418i	$-0.0467746\pi$
$930$	−2.20163	−	0.777539i	−0.0721945	−	0.0254965i
$931$	−3.82983	−	1.43545i	−0.125517	−	0.0470450i
$932$	−28.9983	−	23.4011i	−0.949872	−	0.766527i
$933$		−	11.0450i		−	0.361597i
$934$	1.98890	+	0.702407i	0.0650787	+	0.0229835i
$935$			20.6914i			0.676682i
$936$	−31.1259	+	19.1831i	−1.01738	+	0.627018i
$937$			23.5181i			0.768304i	0.923270	+	0.384152i	$0.125506\pi$
$937$			23.5181i			0.768304i	−0.923270	+	0.384152i	$0.874494\pi$
$938$	−9.00248	−	32.9632i	−0.293942	−	1.07629i
$939$	−7.33209			−0.239274
$940$	−4.60501	−	3.71615i	−0.150199	−	0.121207i
$941$	−0.932766			−0.0304073			−0.0152037	−	0.999884i	$-0.504840\pi$
$941$	−0.932766			−0.0304073			−0.0152037	+	0.999884i	$0.504840\pi$
$942$	−3.11389	−	1.09971i	−0.101456	−	0.0358306i
$943$	−22.2663			−0.725089
$944$	5.94733	−	1.28525i	0.193569	−	0.0418313i
$945$	4.55430	+	6.57067i	0.148151	+	0.213744i
$946$	2.06049	−	5.83437i	0.0669924	−	0.189692i
$947$	18.3452			0.596140			0.298070	−	0.954544i	$-0.403657\pi$
$947$	18.3452			0.596140			0.298070	+	0.954544i	$0.403657\pi$
$948$	−2.31316	−	1.86667i	−0.0751278	−	0.0606266i
$949$		−	59.0486i		−	1.91680i
$950$	0.779143	+	0.275165i	0.0252787	+	0.00892754i
$951$	3.13329			0.101604
$952$	46.5450	+	20.3615i	1.50853	+	0.659921i
$953$	−47.3388			−1.53345			−0.766727	−	0.641973i	$-0.778116\pi$
$953$	−47.3388			−1.53345			−0.766727	+	0.641973i	$0.778116\pi$
$954$	1.94310	+	0.686234i	0.0629102	+	0.0222176i
$955$			12.9741i			0.419831i
$956$	7.25560	−	8.99106i	0.234663	−	0.290792i
$957$	0.298908			0.00966231
$958$	15.5740	−	44.0984i	0.503173	−	1.42476i
$959$	13.8935	−	9.62993i	0.448644	−	0.310967i
$960$	3.77459	+	1.89911i	0.121824	+	0.0612937i
$961$	−21.2288			−0.684800
$962$	44.6412	+	15.7657i	1.43929	+	0.508306i
$963$	−10.3699			−0.334165
$964$	−1.79424	+	2.22341i	−0.0577886	+	0.0716111i
$965$	−24.5869			−0.791479
$966$	3.02234	+	11.0665i	0.0972423	+	0.356059i
$967$			6.55903i			0.210924i	0.994423	+	0.105462i	$0.0336322\pi$
$967$			6.55903i			0.210924i	−0.994423	+	0.105462i	$0.966368\pi$
$968$	−4.11947	+	2.53886i	−0.132405	+	0.0816019i
$969$			2.09511i			0.0673046i
$970$	18.0058	+	6.35900i	0.578131	+	0.204175i
$971$		−	40.6590i		−	1.30481i	−0.757871	−	0.652404i	$-0.773760\pi$
$971$		−	40.6590i		−	1.30481i	0.757871	−	0.652404i	$-0.226240\pi$
$972$	15.7424	−	19.5078i	0.504938	−	0.625713i
$973$	−32.8760	−	47.4316i	−1.05396	−	1.52059i
$974$	40.4241	+	14.2763i	1.29527	+	0.457443i
$975$		−	2.50920i		−	0.0803588i
$976$	−11.1828	−	51.7469i	−0.357952	−	1.65638i
$977$	5.28576			0.169106			0.0845532	−	0.996419i	$-0.473054\pi$
$977$	5.28576			0.169106			0.0845532	+	0.996419i	$0.473054\pi$
$978$	−12.3591	−	4.36479i	−0.395200	−	0.139571i
$979$		−	9.44946i		−	0.302006i
$980$	−12.0565	+	7.11623i	−0.385131	+	0.227320i
$981$			41.2200i			1.31605i
$982$	11.3064	−	32.0146i	0.360802	−	1.02163i
$983$	11.2577			0.359066			0.179533	−	0.983752i	$-0.442541\pi$
$983$	11.2577			0.359066			0.179533	+	0.983752i	$0.442541\pi$
$984$	4.87832	−	3.00654i	0.155515	−	0.0958450i
$985$		−	7.21194i		−	0.229791i
$986$	−0.593663	+	1.68098i	−0.0189061	+	0.0535334i
$987$	2.35532	+	3.39811i	0.0749706	+	0.108163i
$988$	3.48636	−	4.32026i	0.110916	−	0.137446i
$989$			8.33301i			0.264974i
$990$	−3.90562	+	11.0589i	−0.124129	+	0.351476i
$991$			14.3170i			0.454796i	0.973802	+	0.227398i	$0.0730218\pi$
$991$			14.3170i			0.454796i	−0.973802	+	0.227398i	$0.926978\pi$
$992$	−17.5411	−	2.23369i	−0.556930	−	0.0709198i
$993$		−	3.87233i		−	0.122885i
$994$	34.9480	−	9.54457i	1.10848	−	0.302735i
$995$	6.32808			0.200614
$996$	−11.0597	−	8.92492i	−0.350439	−	0.282797i
$997$	18.4076			0.582974			0.291487	−	0.956575i	$-0.405850\pi$
$997$	18.4076			0.582974			0.291487	+	0.956575i	$0.405850\pi$
$998$	17.2478	−	48.8378i	0.545968	−	1.54593i
$999$	−21.2932			−0.673687

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.h.b.251.6	yes	16
4.3	odd	2		1120.2.h.b.111.8		16
7.6	odd	2		280.2.h.a.251.6	yes	16
8.3	odd	2		280.2.h.a.251.5	✓	16
8.5	even	2		1120.2.h.a.111.8		16
28.27	even	2		1120.2.h.a.111.9		16
56.13	odd	2		1120.2.h.b.111.9		16
56.27	even	2	inner	280.2.h.b.251.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.h.a.251.5	✓	16	8.3	odd	2
280.2.h.a.251.6	yes	16	7.6	odd	2
280.2.h.b.251.5	yes	16	56.27	even	2	inner
280.2.h.b.251.6	yes	16	1.1	even	1	trivial
1120.2.h.a.111.8		16	8.5	even	2
1120.2.h.a.111.9		16	28.27	even	2
1120.2.h.b.111.8		16	4.3	odd	2
1120.2.h.b.111.9		16	56.13	odd	2

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.470943 + 1.33350i) q^{2} +0.528177i q^{3} +(-1.55642 - 1.25600i) q^{4} +1.00000 q^{5} +(-0.704322 - 0.248741i) q^{6} +(2.17448 - 1.50719i) q^{7} +(2.40786 - 1.48398i) q^{8} +2.72103 q^{9} +O(q^{10})\)	\(q+(-0.470943 + 1.33350i) q^{2} +0.528177i q^{3} +(-1.55642 - 1.25600i) q^{4} +1.00000 q^{5} +(-0.704322 - 0.248741i) q^{6} +(2.17448 - 1.50719i) q^{7} +(2.40786 - 1.48398i) q^{8} +2.72103 q^{9} +(-0.470943 + 1.33350i) q^{10} +3.04781 q^{11} +(0.663391 - 0.822067i) q^{12} -4.75069 q^{13} +(0.985772 + 3.60947i) q^{14} +0.528177i q^{15} +(0.844916 + 3.90975i) q^{16} +6.78894i q^{17} +(-1.28145 + 3.62848i) q^{18} -0.584285i q^{19} +(-1.55642 - 1.25600i) q^{20} +(0.796062 + 1.14851i) q^{21} +(-1.43535 + 4.06425i) q^{22} -5.80481i q^{23} +(0.783804 + 1.27178i) q^{24} +1.00000 q^{25} +(2.23730 - 6.33502i) q^{26} +3.02172i q^{27} +(-5.27745 - 0.385331i) q^{28} -0.185682i q^{29} +(-0.704322 - 0.248741i) q^{30} +3.12589 q^{31} +(-5.61154 - 0.714577i) q^{32} +1.60978i q^{33} +(-9.05303 - 3.19721i) q^{34} +(2.17448 - 1.50719i) q^{35} +(-4.23508 - 3.41762i) q^{36} +7.04672i q^{37} +(0.779143 + 0.275165i) q^{38} -2.50920i q^{39} +(2.40786 - 1.48398i) q^{40} -3.83583i q^{41} +(-1.90644 + 0.520662i) q^{42} -1.43554 q^{43} +(-4.74369 - 3.82806i) q^{44} +2.72103 q^{45} +(7.74069 + 2.73374i) q^{46} +2.95871 q^{47} +(-2.06504 + 0.446265i) q^{48} +(2.45676 - 6.55472i) q^{49} +(-0.470943 + 1.33350i) q^{50} -3.58576 q^{51} +(7.39409 + 5.96688i) q^{52} -0.535513i q^{53} +(-4.02945 - 1.42306i) q^{54} +3.04781 q^{55} +(2.99922 - 6.85600i) q^{56} +0.308606 q^{57} +(0.247606 + 0.0874456i) q^{58} -1.52116i q^{59} +(0.663391 - 0.822067i) q^{60} -13.2354 q^{61} +(-1.47212 + 4.16837i) q^{62} +(5.91683 - 4.10111i) q^{63} +(3.59560 - 7.14644i) q^{64} -4.75069 q^{65} +(-2.14664 - 0.758117i) q^{66} -9.13242 q^{67} +(8.52693 - 10.5665i) q^{68} +3.06597 q^{69} +(0.985772 + 3.60947i) q^{70} -9.68233i q^{71} +(6.55186 - 4.03795i) q^{72} +12.4295i q^{73} +(-9.39678 - 3.31861i) q^{74} +0.528177i q^{75} +(-0.733864 + 0.909396i) q^{76} +(6.62742 - 4.59363i) q^{77} +(3.34601 + 1.18169i) q^{78} -2.81383i q^{79} +(0.844916 + 3.90975i) q^{80} +6.56709 q^{81} +(5.11507 + 1.80646i) q^{82} -13.4535i q^{83} +(0.203523 - 2.78743i) q^{84} +6.78894i q^{85} +(0.676056 - 1.91428i) q^{86} +0.0980728 q^{87} +(7.33871 - 4.52289i) q^{88} -3.10041i q^{89} +(-1.28145 + 3.62848i) q^{90} +(-10.3303 + 7.16019i) q^{91} +(-7.29085 + 9.03475i) q^{92} +1.65102i q^{93} +(-1.39338 + 3.94543i) q^{94} -0.584285i q^{95} +(0.377423 - 2.96389i) q^{96} -13.5027i q^{97} +(7.58370 + 6.36298i) q^{98} +8.29319 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{2} + q^{4} + 16 q^{5} + q^{8} - 16 q^{9}+O(q^{10}) \) 16 * q + q^2 + q^4 + 16 * q^5 + q^8 - 16 * q^9	\( 16 q + q^{2} + q^{4} + 16 q^{5} + q^{8} - 16 q^{9} + q^{10} - 4 q^{11} + 14 q^{12} - q^{14} + 9 q^{16} - 15 q^{18} + q^{20} - 4 q^{21} + 6 q^{22} + 22 q^{24} + 16 q^{25} - 20 q^{26} + q^{28} - 16 q^{31} - 19 q^{32} - 14 q^{34} + 15 q^{36} - 30 q^{38} + q^{40} + 44 q^{42} - 4 q^{43} - 20 q^{44} - 16 q^{45} + 6 q^{46} - 34 q^{48} - 8 q^{49} + q^{50} - 40 q^{51} - 38 q^{52} + 26 q^{54} - 4 q^{55} + 33 q^{56} - 16 q^{57} + 18 q^{58} + 14 q^{60} - 8 q^{61} + 28 q^{62} + 28 q^{63} - 23 q^{64} + 46 q^{66} + 20 q^{67} + 12 q^{68} - 40 q^{69} - q^{70} - 13 q^{72} - 28 q^{74} + 34 q^{76} - 4 q^{77} - 6 q^{78} + 9 q^{80} + 24 q^{81} - 16 q^{82} - 42 q^{84} - 24 q^{86} + 72 q^{87} - 44 q^{88} - 15 q^{90} - 32 q^{91} - 30 q^{92} - 58 q^{94} - 30 q^{96} + 5 q^{98} + 20 q^{99}+O(q^{100}) \) 16 * q + q^2 + q^4 + 16 * q^5 + q^8 - 16 * q^9 + q^10 - 4 * q^11 + 14 * q^12 - q^14 + 9 * q^16 - 15 * q^18 + q^20 - 4 * q^21 + 6 * q^22 + 22 * q^24 + 16 * q^25 - 20 * q^26 + q^28 - 16 * q^31 - 19 * q^32 - 14 * q^34 + 15 * q^36 - 30 * q^38 + q^40 + 44 * q^42 - 4 * q^43 - 20 * q^44 - 16 * q^45 + 6 * q^46 - 34 * q^48 - 8 * q^49 + q^50 - 40 * q^51 - 38 * q^52 + 26 * q^54 - 4 * q^55 + 33 * q^56 - 16 * q^57 + 18 * q^58 + 14 * q^60 - 8 * q^61 + 28 * q^62 + 28 * q^63 - 23 * q^64 + 46 * q^66 + 20 * q^67 + 12 * q^68 - 40 * q^69 - q^70 - 13 * q^72 - 28 * q^74 + 34 * q^76 - 4 * q^77 - 6 * q^78 + 9 * q^80 + 24 * q^81 - 16 * q^82 - 42 * q^84 - 24 * q^86 + 72 * q^87 - 44 * q^88 - 15 * q^90 - 32 * q^91 - 30 * q^92 - 58 * q^94 - 30 * q^96 + 5 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more