LMFDB - Embedded newform 280.2.h.a.251.5

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

$q$-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} +(3.03389 + 2.18987i) 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} +(1.49139 - 5.07698i) 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} +(-1.15664 + 1.60243i) 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} +(-7.47250 + 0.402212i) 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} +(-3.03389 - 2.18987i) 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} +(2.68155 + 0.787716i) 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} +(-9.89769 - 0.189181i) 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} + 7 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} - 3 q^{28} + 16 q^{31} - 19 q^{32} + 14 q^{34} + 15 q^{36} + 30 q^{38} - q^{40} + 20 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} + 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} - 7 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} + 10 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} - 39 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 + 7 * 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 - 3 * q^28 + 16 * q^31 - 19 * q^32 + 14 * q^34 + 15 * q^36 + 30 * q^38 - q^40 + 20 * 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 + 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 - 7 * 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 + 10 * 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 - 39 * 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	$-0.271064\pi$
$13$	4.75069			1.31760			0.658802	+	0.752317i	$0.271064\pi$
$14$	3.03389	+	2.18987i	0.810841	+	0.585266i
$15$		−	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	$0.206904\pi$
$23$			5.80481i			1.21039i	−0.796079	+	0.605193i	$0.793096\pi$
$24$	−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
$28$	1.49139	−	5.07698i	0.281846	−	0.959460i
$29$			0.185682i			0.0344802i	0.999851	+	0.0172401i	$0.00548797\pi$
$29$			0.185682i			0.0344802i	−0.999851	+	0.0172401i	$0.994512\pi$
$30$	−0.704322	+	0.248741i	−0.128591	+	0.0454138i
$31$	−3.12589			−0.561427			−0.280714	−	0.959792i	$-0.590571\pi$
$31$	−3.12589			−0.561427			−0.280714	+	0.959792i	$0.590571\pi$
$32$	−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	$-0.803351\pi$
$37$		−	7.04672i		−	1.15847i	0.815159	−	0.579237i	$-0.196649\pi$
$38$	−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	$-0.0968292\pi$
$42$	−1.15664	+	1.60243i	−0.178473	+	0.247260i
$43$	−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	$-0.569231\pi$
$47$	−2.95871			−0.431572			−0.215786	+	0.976441i	$0.569231\pi$
$48$	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	$0.0117098\pi$
$53$			0.535513i			0.0735584i	−0.999323	+	0.0367792i	$0.988290\pi$
$54$	4.02945	−	1.42306i	0.548338	−	0.193653i
$55$	−3.04781			−0.410967
$56$	−7.47250	+	0.402212i	−0.998555	+	0.0537479i
$57$	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	$-0.178222\pi$
$61$	13.2354			1.69461			0.847307	+	0.531103i	$0.178222\pi$
$62$	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
$70$	−3.03389	−	2.18987i	−0.362619	−	0.261739i
$71$			9.68233i			1.14908i	0.818476	+	0.574540i	$0.194819\pi$
$71$			9.68233i			1.14908i	−0.818476	+	0.574540i	$0.805181\pi$
$72$	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	$0.0505982\pi$
$79$			2.81383i			0.316580i	−0.987393	+	0.158290i	$0.949402\pi$
$80$	−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	$-0.264397\pi$
$84$	2.68155	+	0.787716i	0.292581	+	0.0859469i
$85$		−	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	$-0.240414\pi$
$98$	−9.89769	−	0.189181i	−0.999817	−	0.0191102i
$99$	8.29319			0.833497
$100$	−1.55642	+	1.25600i	−0.155642	+	0.125600i
$101$	1.29842			0.129198			0.0645988	−	0.997911i	$-0.479423\pi$
$101$	1.29842			0.129198			0.0645988	+	0.997911i	$0.479423\pi$
$102$	1.68869	+	4.78160i	0.167205	+	0.473449i
$103$	19.0846			1.88046			0.940232	−	0.340535i	$-0.110608\pi$
$103$	19.0846			1.88046			0.940232	+	0.340535i	$0.110608\pi$
$104$	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	$-0.741613\pi$
$109$		−	15.1487i		−	1.45098i	0.688233	−	0.725490i	$-0.258387\pi$
$110$	1.43535	+	4.06425i	0.136855	+	0.387511i
$111$	3.72192			0.353269
$112$	4.05547	+	9.77513i	0.383206	+	0.923663i
$113$	−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
$126$	8.25530	+	5.95869i	0.735441	+	0.530842i
$127$		−	15.9073i		−	1.41154i	−0.708440	−	0.705771i	$-0.750601\pi$
$127$		−	15.9073i		−	1.41154i	0.708440	−	0.705771i	$-0.249399\pi$
$128$	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	$-0.375992\pi$
$140$	−1.49139	+	5.07698i	−0.126045	+	0.429083i
$141$		−	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	$0.156359\pi$
$149$			11.5156i			0.943396i	−0.881760	+	0.471698i	$0.843641\pi$
$150$	0.704322	−	0.248741i	0.0575076	−	0.0203096i
$151$		−	7.70970i		−	0.627407i	−0.949521	−	0.313703i	$-0.898430\pi$
$151$		−	7.70970i		−	0.627407i	0.949521	−	0.313703i	$-0.101570\pi$
$152$	0.867068	−	1.40688i	0.0703285	−	0.114113i
$153$			18.4729i			1.49345i
$154$	9.24673	+	6.67430i	0.745122	+	0.537830i
$155$	3.12589			0.251078
$156$	−3.15157	−	3.90539i	−0.252327	−	0.312681i
$157$	−4.42111			−0.352843			−0.176422	−	0.984315i	$-0.556452\pi$
$157$	−4.42111			−0.352843			−0.176422	+	0.984315i	$0.556452\pi$
$158$	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	$-0.480579\pi$
$167$	1.57597			0.121952			0.0609760	+	0.998139i	$0.480579\pi$
$168$	−0.212439	−	3.94680i	−0.0163900	−	0.304502i
$169$	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	$-0.502528\pi$
$173$	−0.208914			−0.0158835			−0.00794173	+	0.999968i	$0.502528\pi$
$174$	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	$-0.604388\pi$
$181$	−8.66680			−0.644198			−0.322099	+	0.946706i	$0.604388\pi$
$182$	14.4131	+	10.4034i	1.06837	+	0.771149i
$183$			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	$-0.844476\pi$
$191$		−	12.9741i		−	0.938770i	0.882993	−	0.469385i	$-0.155524\pi$
$192$	−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
$196$	4.40898	+	13.2876i	0.314927	+	0.949116i
$197$			7.21194i			0.513829i	0.966434	+	0.256915i	$0.0827059\pi$
$197$			7.21194i			0.513829i	−0.966434	+	0.256915i	$0.917294\pi$
$198$	−3.90562	−	11.0589i	−0.277560	−	0.785924i
$199$	−6.32808			−0.448585			−0.224293	−	0.974522i	$-0.572007\pi$
$199$	−6.32808			−0.448585			−0.224293	+	0.974522i	$0.572007\pi$
$200$	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
$210$	1.15664	−	1.60243i	0.0798155	−	0.110578i
$211$	−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	$-0.471767\pi$
$223$	2.64553			0.177158			0.0885790	+	0.996069i	$0.471767\pi$
$224$	11.1252	−	10.0115i	0.743334	−	0.668921i
$225$	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	$-0.441635\pi$
$229$	5.51840			0.364666			0.182333	+	0.983237i	$0.441635\pi$
$230$	−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
$238$	−14.8669	+	20.5969i	−0.963676	+	1.33510i
$239$		−	5.77674i		−	0.373666i	−0.982392	−	0.186833i	$-0.940178\pi$
$239$		−	5.77674i		−	0.373666i	0.982392	−	0.186833i	$-0.0598223\pi$
$240$	−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	$0.880313\pi$
$252$	4.05811	−	13.8146i	0.255637	−	0.870239i
$253$			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	$-0.690845\pi$
$263$		−	26.7775i		−	1.65117i	0.564277	−	0.825585i	$-0.309155\pi$
$264$	−2.38889	+	3.87614i	−0.147026	+	0.238560i
$265$		−	0.535513i		−	0.0328963i
$266$	1.27951	−	1.77266i	0.0784516	−	0.108689i
$267$	1.63756			0.100217
$268$	14.2139	−	11.4703i	0.868253	−	0.700662i
$269$	−19.0365			−1.16067			−0.580337	−	0.814376i	$-0.697079\pi$
$269$	−19.0365			−1.16067			−0.580337	+	0.814376i	$0.697079\pi$
$270$	−4.02945	+	1.42306i	−0.245224	+	0.0866045i
$271$	−2.47835			−0.150549			−0.0752745	−	0.997163i	$-0.523983\pi$
$271$	−2.47835			−0.150549			−0.0752745	+	0.997163i	$0.523983\pi$
$272$	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	$0.160664\pi$
$277$			16.0967i			0.967159i	−0.875301	+	0.483579i	$0.839336\pi$
$278$	−29.0873	+	10.2726i	−1.74454	+	0.616109i
$279$	−8.50565			−0.509220
$280$	7.47250	−	0.402212i	0.446567	−	0.0240368i
$281$	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	$-0.743869\pi$
$293$	−23.7367			−1.38671			−0.693357	+	0.720594i	$0.743869\pi$
$294$	0.0999211	−	5.22773i	0.00582752	−	0.304887i
$295$			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	$-0.0298000\pi$
$308$	4.54547	−	15.4737i	0.259002	−	0.881695i
$309$			10.0801i			0.573434i
$310$	−1.47212	−	4.16837i	−0.0836107	−	0.236747i
$311$	20.9116			1.18579			0.592893	−	0.805282i	$-0.297986\pi$
$311$	20.9116			1.18579			0.592893	+	0.805282i	$0.297986\pi$
$312$	−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	$0.0532772\pi$
$317$			5.93227i			0.333190i	−0.986025	+	0.166595i	$0.946723\pi$
$318$	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
$322$	−12.7118	+	17.6112i	−0.708398	+	0.981431i
$323$	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
$336$	−5.16300	+	2.14201i	−0.281665	+	0.116856i
$337$	−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	$-0.588640\pi$
$349$	−10.2706			−0.549772			−0.274886	+	0.961477i	$0.588640\pi$
$350$	3.03389	+	2.18987i	0.162168	+	0.117053i
$351$			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	$-0.957362\pi$
$359$		−	5.06081i		−	0.267099i	0.991042	−	0.133550i	$-0.0426375\pi$
$360$	−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
$364$	7.08511	−	24.1192i	0.371361	−	1.26419i
$365$		−	12.4295i		−	0.650589i
$366$	9.32196	−	3.29218i	0.487266	−	0.172085i
$367$	12.8106			0.668708			0.334354	−	0.942447i	$-0.391482\pi$
$367$	12.8106			0.668708			0.334354	+	0.942447i	$0.391482\pi$
$368$	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	$-0.895838\pi$
$373$		−	12.4155i		−	0.642849i	0.946935	−	0.321425i	$-0.104162\pi$
$374$	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
$378$	−6.61715	+	9.16755i	−0.340349	+	0.471528i
$379$	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	$-0.763658\pi$
$383$	−28.8384			−1.47358			−0.736788	+	0.676124i	$0.763658\pi$
$384$	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	$0.0352048\pi$
$389$			4.35382i			0.220747i	−0.993890	+	0.110374i	$0.964795\pi$
$390$	−3.34601	+	1.18169i	−0.169432	+	0.0598373i
$391$	−39.4085			−1.99297
$392$	15.6426	−	12.1371i	0.790071	−	0.613015i
$393$	−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	$-0.359720\pi$
$397$	16.9988			0.853148			0.426574	+	0.904453i	$0.359720\pi$
$398$	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
$406$	−0.406618	+	0.563338i	−0.0201801	+	0.0279580i
$407$		−	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	$0.736926\pi$
$420$	−2.68155	−	0.787716i	−0.130846	−	0.0384366i
$421$		−	27.1321i		−	1.32234i	−0.750236	−	0.661170i	$-0.770060\pi$
$421$		−	27.1321i		−	1.32234i	0.750236	−	0.661170i	$-0.229940\pi$
$422$	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	$-0.970807\pi$
$431$		−	3.80266i		−	0.183167i	0.995797	−	0.0915837i	$-0.0291929\pi$
$432$	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	$-0.0463825\pi$
$434$	−9.48362	−	6.84529i	−0.455228	−	0.328584i
$435$	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	$-0.335095\pi$
$439$	20.7511			0.990398			0.495199	+	0.868780i	$0.335095\pi$
$440$	−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
$448$	−18.5896	−	10.1206i	−0.878277	−	0.478152i
$449$	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	$-0.387983\pi$
$461$	14.8017			0.689385			0.344693	+	0.938716i	$0.387983\pi$
$462$	−3.52521	+	4.88391i	−0.164008	+	0.227220i
$463$			10.2328i			0.475556i	0.971319	+	0.237778i	$0.0764191\pi$
$463$			10.2328i			0.475556i	−0.971319	+	0.237778i	$0.923581\pi$
$464$	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
$476$	34.4674	+	10.1249i	1.57981	+	0.464076i
$477$			1.45715i			0.0667182i
$478$	−7.70326	+	2.72052i	−0.352339	+	0.124434i
$479$	33.0698			1.51100			0.755499	−	0.655150i	$-0.227395\pi$
$479$	33.0698			1.51100			0.755499	+	0.655150i	$0.227395\pi$
$480$	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	$0.241001\pi$
$487$			30.3143i			1.37367i	−0.726811	+	0.686837i	$0.758999\pi$
$488$	31.8689	+	19.6410i	1.44264	+	0.889107i
$489$			9.26819i			0.419122i
$490$	9.89769	+	0.189181i	0.447132	+	0.00854634i
$491$	−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	$-0.498399\pi$
$503$	0.225539			0.0100563			0.00502815	+	0.999987i	$0.498399\pi$
$504$	−20.3329	+	1.09443i	−0.905699	+	0.0487499i
$505$	−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	$-0.581396\pi$
$509$	−11.4130			−0.505871			−0.252935	+	0.967483i	$0.581396\pi$
$510$	−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
$518$	15.4314	−	21.3790i	0.678016	−	0.939339i
$519$		−	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
$532$	−2.96641	−	0.871396i	−0.128610	−	0.0377798i
$533$		−	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	$-0.667784\pi$
$541$		−	40.2046i		−	1.72853i	0.503035	−	0.864266i	$-0.332216\pi$
$542$	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
$546$	−5.49482	+	7.61265i	−0.235156	+	0.325791i
$547$	−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	$-0.744875\pi$
$557$		−	33.9096i		−	1.43680i	0.695631	−	0.718399i	$-0.255125\pi$
$558$	4.00568	+	11.3422i	0.169574	+	0.480156i
$559$	−6.81978			−0.288446
$560$	−4.05547	−	9.77513i	−0.171375	−	0.413075i
$561$	−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
$574$	8.39995	−	11.6375i	0.350607	−	0.485739i
$575$			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	$-0.0553661\pi$
$588$	−7.01821	+	2.32872i	−0.289426	+	0.0960348i
$589$			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	$0.244847\pi$
$599$			34.0473i			1.39113i	−0.718462	+	0.695566i	$0.755153\pi$
$600$	−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	$0.833398\pi$
$602$	−4.35526	−	3.14363i	−0.177507	−	0.128125i
$603$	−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	$-0.767537\pi$
$607$	−36.7082			−1.48994			−0.744971	+	0.667097i	$0.767537\pi$
$608$	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	$-0.681661\pi$
$613$		−	41.6702i		−	1.68304i	0.540224	−	0.841521i	$-0.318339\pi$
$614$	−4.36840	+	1.54276i	−0.176294	+	0.0622608i
$615$	−2.02600			−0.0816961
$616$	−22.7748	+	1.22587i	−0.917622	+	0.0493916i
$617$	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
$630$	−8.25530	−	5.95869i	−0.328899	−	0.237400i
$631$			28.1199i			1.11944i	0.828683	+	0.559718i	$0.189090\pi$
$631$			28.1199i			1.11944i	−0.828683	+	0.559718i	$0.810910\pi$
$632$	−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	$-0.0694346\pi$
$644$	29.4709	+	8.65722i	1.16132	+	0.341142i
$645$			0.758217i			0.0298548i
$646$	−1.86808	−	5.28955i	−0.0734987	−	0.208115i
$647$	−37.3313			−1.46765			−0.733823	−	0.679340i	$-0.762266\pi$
$647$	−37.3313			−1.46765			−0.733823	+	0.679340i	$0.762266\pi$
$648$	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	$0.177461\pi$
$653$			27.0398i			1.05815i	−0.848575	+	0.529074i	$0.822539\pi$
$654$	−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
$658$	−8.97640	−	6.47918i	−0.349937	−	0.252585i
$659$	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	$-0.689068\pi$
$661$	−28.7776			−1.11932			−0.559659	+	0.828723i	$0.689068\pi$
$662$	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
$672$	5.28784	+	5.87607i	0.203983	+	0.226674i
$673$	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	$-0.796005\pi$
$677$	−41.7128			−1.60315			−0.801576	+	0.597893i	$0.796005\pi$
$678$	−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
$686$	21.8075	−	14.5063i	0.832614	−	0.553854i
$687$			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
$700$	1.49139	−	5.07698i	0.0563691	−	0.191892i
$701$			10.2820i			0.388346i	0.980967	+	0.194173i	$0.0622024\pi$
$701$			10.2820i			0.388346i	−0.980967	+	0.194173i	$0.937798\pi$
$702$	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	$0.0651142\pi$
$709$			10.8180i			0.406277i	−0.979150	+	0.203139i	$0.934886\pi$
$710$	−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
$714$	−10.8788	−	7.85234i	−0.407129	−	0.293866i
$715$	−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	$-0.684888\pi$
$719$	−29.4274			−1.09746			−0.548729	+	0.836000i	$0.684888\pi$
$720$	−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	$-0.304383\pi$
$727$	31.0932			1.15318			0.576591	+	0.817033i	$0.304383\pi$
$728$	−35.4995	+	1.91079i	−1.31570	+	0.0708184i
$729$	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	$-0.440830\pi$
$733$	10.0076			0.369639			0.184820	+	0.982772i	$0.440830\pi$
$734$	−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
$742$	−1.17270	+	1.62469i	−0.0430513	+	0.0596442i
$743$		−	41.3554i		−	1.51718i	−0.651567	−	0.758591i	$-0.725888\pi$
$743$		−	41.3554i		−	1.51718i	0.651567	−	0.758591i	$-0.274112\pi$
$744$	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	$0.0608693\pi$
$751$			10.4171i			0.380126i	−0.981772	+	0.190063i	$0.939131\pi$
$752$	−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
$756$	15.3412	+	4.50655i	0.557954	+	0.163902i
$757$			31.7145i			1.15268i	0.817209	+	0.576341i	$0.195520\pi$
$757$			31.7145i			1.15268i	−0.817209	+	0.576341i	$0.804480\pi$
$758$	−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	$0.944830\pi$
$770$	−9.24673	−	6.67430i	−0.333229	−	0.240525i
$771$	6.33873			0.228284
$772$	38.2676	−	30.8812i	1.37728	−	1.11144i
$773$	−30.6270			−1.10158			−0.550788	−	0.834645i	$-0.685673\pi$
$773$	−30.6270			−1.10158			−0.550788	+	0.834645i	$0.685673\pi$
$774$	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
$784$	−23.5515	−	15.1435i	−0.841126	−	0.540839i
$785$	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	$-0.507796\pi$
$797$	−1.38276			−0.0489799			−0.0244899	+	0.999700i	$0.507796\pi$
$798$	0.936277	+	0.675806i	0.0331438	+	0.0239233i
$799$		−	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	$-0.109469\pi$
$812$	0.942704	+	0.276923i	0.0330824	+	0.00971811i
$813$		−	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	$-0.758377\pi$
$821$		−	39.4413i		−	1.37651i	0.725468	−	0.688256i	$-0.241623\pi$
$822$	4.50014	−	1.58929i	0.156961	−	0.0554329i
$823$		−	0.408196i		−	0.0142288i	−0.999975	−	0.00711440i	$-0.997735\pi$
$823$		−	0.408196i		−	0.0142288i	0.999975	−	0.00711440i	$-0.00226460\pi$
$824$	45.9531	+	28.3212i	1.60085	+	0.986616i
$825$			1.60978i			0.0560455i
$826$	3.33113	−	4.61502i	0.115905	−	0.160577i
$827$	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	$-0.592772\pi$
$829$	−16.5466			−0.574686			−0.287343	+	0.957828i	$0.592772\pi$
$830$	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	$-0.304300\pi$
$839$	33.4148			1.15361			0.576804	+	0.816883i	$0.304300\pi$
$840$	0.212439	+	3.94680i	0.00732985	+	0.136178i
$841$	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	$-0.433107\pi$
$853$	12.1851			0.417211			0.208606	+	0.978000i	$0.433107\pi$
$854$	40.1546	+	28.9837i	1.37406	+	0.991801i
$855$			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	$0.0174947\pi$
$863$			3.22755i			0.109867i	−0.998490	+	0.0549336i	$0.982505\pi$
$864$	−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
$868$	−4.66192	+	15.8701i	−0.158236	+	0.538667i
$869$			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	$0.154167\pi$
$877$			27.5777i			0.931233i	−0.884987	+	0.465616i	$0.845833\pi$
$878$	−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	$-0.110403\pi$
$882$	−26.9319	−	0.514768i	−0.906844	−	0.0173331i
$883$	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	$-0.527360\pi$
$887$	−5.11354			−0.171696			−0.0858480	+	0.996308i	$0.527360\pi$
$888$	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
$896$	−4.74108	+	29.5554i	−0.158388	+	0.987377i
$897$	−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
$910$	−14.4131	−	10.4034i	−0.477788	−	0.344868i
$911$			43.0775i			1.42722i	0.700543	+	0.713610i	$0.252941\pi$
$911$			43.0775i			1.42722i	−0.700543	+	0.713610i	$0.747059\pi$
$912$	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	$0.0337893\pi$
$919$			6.42394i			0.211906i	−0.994371	+	0.105953i	$0.966211\pi$
$920$	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
$924$	8.17285	+	2.40081i	0.268867	+	0.0789809i
$925$		−	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	$0.874494\pi$
$938$	−27.7067	−	19.9988i	−0.904657	−	0.652983i
$939$	−7.33209			−0.239274
$940$	−4.60501	+	3.71615i	−0.150199	+	0.121207i
$941$	0.932766			0.0304073			0.0152037	−	0.999884i	$-0.495160\pi$
$941$	0.932766			0.0304073			0.0152037	+	0.999884i	$0.495160\pi$
$942$	−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
$952$	−2.73060	−	50.7304i	−0.0884991	−	1.64418i
$953$	−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
$966$	−9.30180	−	6.71405i	−0.299281	−	0.216021i
$967$		−	6.55903i		−	0.210924i	−0.994423	−	0.105462i	$-0.966368\pi$
$967$		−	6.55903i		−	0.210924i	0.994423	−	0.105462i	$-0.0336322\pi$
$968$	−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
$980$	−4.40898	−	13.2876i	−0.140840	−	0.424458i
$981$		−	41.2200i		−	1.31605i
$982$	11.3064	+	32.0146i	0.360802	+	1.02163i
$983$	−11.2577			−0.359066			−0.179533	−	0.983752i	$-0.557459\pi$
$983$	−11.2577			−0.359066			−0.179533	+	0.983752i	$0.557459\pi$
$984$	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	$-0.926978\pi$
$991$		−	14.3170i		−	0.454796i	0.973802	−	0.227398i	$-0.0730218\pi$
$992$	17.5411	−	2.23369i	0.556930	−	0.0709198i
$993$		−	3.87233i		−	0.122885i
$994$	−21.2030	+	29.3751i	−0.672518	+	0.931722i
$995$	6.32808			0.200614
$996$	−11.0597	+	8.92492i	−0.350439	+	0.282797i
$997$	−18.4076			−0.582974			−0.291487	−	0.956575i	$-0.594150\pi$
$997$	−18.4076			−0.582974			−0.291487	+	0.956575i	$0.594150\pi$
$998$	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.a.251.5	✓	16
4.3	odd	2		1120.2.h.a.111.8		16
7.6	odd	2		280.2.h.b.251.5	yes	16
8.3	odd	2		280.2.h.b.251.6	yes	16
8.5	even	2		1120.2.h.b.111.8		16
28.27	even	2		1120.2.h.b.111.9		16
56.13	odd	2		1120.2.h.a.111.9		16
56.27	even	2	inner	280.2.h.a.251.6	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.h.a.251.5	✓	16	1.1	even	1	trivial
280.2.h.a.251.6	yes	16	56.27	even	2	inner
280.2.h.b.251.5	yes	16	7.6	odd	2
280.2.h.b.251.6	yes	16	8.3	odd	2
1120.2.h.a.111.8		16	4.3	odd	2
1120.2.h.a.111.9		16	56.13	odd	2
1120.2.h.b.111.8		16	8.5	even	2
1120.2.h.b.111.9		16	28.27	even	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} +(3.03389 + 2.18987i) 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} +(1.49139 - 5.07698i) 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} +(-1.15664 + 1.60243i) 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} +(-7.47250 + 0.402212i) 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} +(-3.03389 - 2.18987i) 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} +(2.68155 + 0.787716i) 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} +(-9.89769 - 0.189181i) 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	\( 16 q + q^{2} + q^{4} - 16 q^{5} + q^{8} - 16 q^{9} - q^{10} - 4 q^{11} - 14 q^{12} + 7 q^{14} + 9 q^{16} - 15 q^{18} - q^{20} + 4 q^{21} + 6 q^{22} - 22 q^{24} + 16 q^{25} + 20 q^{26} - 3 q^{28} + 16 q^{31} - 19 q^{32} + 14 q^{34} + 15 q^{36} + 30 q^{38} - q^{40} + 20 q^{42} - 4 q^{43} - 20 q^{44} + 16 q^{45} + 6 q^{46} + 34 q^{48} - 8 q^{49} + q^{50} - 40 q^{51} + 38 q^{52} - 26 q^{54} + 4 q^{55} + q^{56} - 16 q^{57} + 18 q^{58} + 14 q^{60} + 8 q^{61} - 28 q^{62} - 28 q^{63} - 23 q^{64} - 46 q^{66} + 20 q^{67} - 12 q^{68} + 40 q^{69} - 7 q^{70} - 13 q^{72} - 28 q^{74} - 34 q^{76} + 4 q^{77} - 6 q^{78} - 9 q^{80} + 24 q^{81} + 16 q^{82} + 10 q^{84} - 24 q^{86} - 72 q^{87} - 44 q^{88} + 15 q^{90} - 32 q^{91} - 30 q^{92} + 58 q^{94} + 30 q^{96} - 39 q^{98} + 20 q^{99}+O(q^{100}) \) 16 * q + q^2 + q^4 - 16 * q^5 + q^8 - 16 * q^9 - q^10 - 4 * q^11 - 14 * q^12 + 7 * 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 - 3 * q^28 + 16 * q^31 - 19 * q^32 + 14 * q^34 + 15 * q^36 + 30 * q^38 - q^40 + 20 * 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 + 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 - 7 * 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 + 10 * 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 - 39 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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