LMFDB - Embedded newform 935.2.i.b.166.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [935,2,Mod(166,935)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(935, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 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("935.166");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 935 = 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	935.i (of order $4$, degree $2$, 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:	$7.46601258899$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			166.16
Character	$\chi$	$=$	935.166
Dual form			935.2.i.b.276.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.570806i q^{2} +(2.39792 + 2.39792i) q^{3} +1.67418 q^{4} +(0.707107 + 0.707107i) q^{5} +(1.36875 - 1.36875i) q^{6} +(2.12451 - 2.12451i) q^{7} -2.09725i q^{8} +8.50005i q^{9} +O(q^{10})$	\(q-0.570806i q^{2} +(2.39792 + 2.39792i) q^{3} +1.67418 q^{4} +(0.707107 + 0.707107i) q^{5} +(1.36875 - 1.36875i) q^{6} +(2.12451 - 2.12451i) q^{7} -2.09725i q^{8} +8.50005i q^{9} +(0.403621 - 0.403621i) q^{10} +(0.707107 - 0.707107i) q^{11} +(4.01455 + 4.01455i) q^{12} -5.45773 q^{13} +(-1.21268 - 1.21268i) q^{14} +3.39117i q^{15} +2.15124 q^{16} +(-4.03065 - 0.868239i) q^{17} +4.85188 q^{18} +4.08195i q^{19} +(1.18382 + 1.18382i) q^{20} +10.1888 q^{21} +(-0.403621 - 0.403621i) q^{22} +(3.21936 - 3.21936i) q^{23} +(5.02903 - 5.02903i) q^{24} +1.00000i q^{25} +3.11531i q^{26} +(-13.1887 + 13.1887i) q^{27} +(3.55681 - 3.55681i) q^{28} +(-4.51060 - 4.51060i) q^{29} +1.93570 q^{30} +(-2.80133 - 2.80133i) q^{31} -5.42243i q^{32} +3.39117 q^{33} +(-0.495596 + 2.30072i) q^{34} +3.00451 q^{35} +14.2306i q^{36} +(-3.06274 - 3.06274i) q^{37} +2.33000 q^{38} +(-13.0872 - 13.0872i) q^{39} +(1.48298 - 1.48298i) q^{40} +(6.13639 - 6.13639i) q^{41} -5.81584i q^{42} +1.45353i q^{43} +(1.18382 - 1.18382i) q^{44} +(-6.01044 + 6.01044i) q^{45} +(-1.83763 - 1.83763i) q^{46} +6.73322 q^{47} +(5.15850 + 5.15850i) q^{48} -2.02710i q^{49} +0.570806 q^{50} +(-7.58322 - 11.7472i) q^{51} -9.13722 q^{52} -11.4789i q^{53} +(7.52819 + 7.52819i) q^{54} +1.00000 q^{55} +(-4.45562 - 4.45562i) q^{56} +(-9.78818 + 9.78818i) q^{57} +(-2.57468 + 2.57468i) q^{58} +12.7249i q^{59} +5.67743i q^{60} +(-1.87477 + 1.87477i) q^{61} +(-1.59902 + 1.59902i) q^{62} +(18.0585 + 18.0585i) q^{63} +1.20732 q^{64} +(-3.85920 - 3.85920i) q^{65} -1.93570i q^{66} -4.75293 q^{67} +(-6.74804 - 1.45359i) q^{68} +15.4395 q^{69} -1.71499i q^{70} +(-0.233147 - 0.233147i) q^{71} +17.8267 q^{72} +(4.03484 + 4.03484i) q^{73} +(-1.74823 + 1.74823i) q^{74} +(-2.39792 + 2.39792i) q^{75} +6.83391i q^{76} -3.00451i q^{77} +(-7.47026 + 7.47026i) q^{78} +(-3.35541 + 3.35541i) q^{79} +(1.52116 + 1.52116i) q^{80} -37.7507 q^{81} +(-3.50269 - 3.50269i) q^{82} +9.36021i q^{83} +17.0579 q^{84} +(-2.23616 - 3.46404i) q^{85} +0.829683 q^{86} -21.6321i q^{87} +(-1.48298 - 1.48298i) q^{88} -9.41784 q^{89} +(3.43080 + 3.43080i) q^{90} +(-11.5950 + 11.5950i) q^{91} +(5.38979 - 5.38979i) q^{92} -13.4347i q^{93} -3.84337i q^{94} +(-2.88637 + 2.88637i) q^{95} +(13.0026 - 13.0026i) q^{96} +(-2.69589 - 2.69589i) q^{97} -1.15708 q^{98} +(6.01044 + 6.01044i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 76 q^{4} - 4 q^{6}+O(q^{10}) $ 68 * q - 76 * q^4 - 4 * q^6	$ 68 q - 76 q^{4} - 4 q^{6} + 4 q^{10} + 20 q^{12} - 16 q^{13} + 20 q^{14} + 100 q^{16} - 8 q^{17} + 64 q^{18} - 32 q^{21} - 4 q^{22} + 4 q^{23} - 16 q^{24} + 24 q^{27} + 20 q^{28} + 28 q^{31} - 72 q^{34} + 20 q^{35} - 28 q^{37} - 24 q^{38} - 8 q^{39} + 8 q^{40} + 4 q^{41} - 8 q^{45} - 16 q^{46} + 4 q^{47} + 56 q^{48} + 12 q^{50} - 88 q^{51} + 124 q^{52} - 124 q^{54} + 68 q^{55} - 136 q^{56} + 28 q^{57} + 4 q^{58} + 16 q^{61} - 28 q^{62} + 36 q^{63} - 188 q^{64} + 52 q^{67} - 40 q^{68} + 160 q^{69} - 20 q^{71} - 164 q^{72} - 56 q^{73} - 64 q^{74} + 200 q^{78} - 180 q^{81} + 108 q^{82} + 152 q^{84} - 4 q^{85} + 296 q^{86} - 8 q^{88} - 180 q^{89} - 96 q^{91} - 48 q^{92} + 12 q^{95} + 104 q^{96} + 24 q^{97} - 180 q^{98} + 8 q^{99}+O(q^{100}) $ 68 * q - 76 * q^4 - 4 * q^6 + 4 * q^10 + 20 * q^12 - 16 * q^13 + 20 * q^14 + 100 * q^16 - 8 * q^17 + 64 * q^18 - 32 * q^21 - 4 * q^22 + 4 * q^23 - 16 * q^24 + 24 * q^27 + 20 * q^28 + 28 * q^31 - 72 * q^34 + 20 * q^35 - 28 * q^37 - 24 * q^38 - 8 * q^39 + 8 * q^40 + 4 * q^41 - 8 * q^45 - 16 * q^46 + 4 * q^47 + 56 * q^48 + 12 * q^50 - 88 * q^51 + 124 * q^52 - 124 * q^54 + 68 * q^55 - 136 * q^56 + 28 * q^57 + 4 * q^58 + 16 * q^61 - 28 * q^62 + 36 * q^63 - 188 * q^64 + 52 * q^67 - 40 * q^68 + 160 * q^69 - 20 * q^71 - 164 * q^72 - 56 * q^73 - 64 * q^74 + 200 * q^78 - 180 * q^81 + 108 * q^82 + 152 * q^84 - 4 * q^85 + 296 * q^86 - 8 * q^88 - 180 * q^89 - 96 * q^91 - 48 * q^92 + 12 * q^95 + 104 * q^96 + 24 * q^97 - 180 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/935\mathbb{Z}\right)^\times$.

$n$	$496$	$562$	$596$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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 $

$2$		−	0.570806i		−	0.403621i	−0.979425	−	0.201811i	$-0.935317\pi$
$2$		−	0.570806i		−	0.403621i	0.979425	−	0.201811i	$-0.0646825\pi$
$3$	2.39792	+	2.39792i	1.38444	+	1.38444i	0.836550	+	0.547890i	$0.184569\pi$
$3$	2.39792	+	2.39792i	1.38444	+	1.38444i	0.547890	+	0.836550i	$0.315431\pi$
$4$	1.67418			0.837090
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$6$	1.36875	−	1.36875i	0.558789	−	0.558789i
$7$	2.12451	−	2.12451i	0.802990	−	0.802990i	−0.180572	−	0.983562i	$-0.557795\pi$
$7$	2.12451	−	2.12451i	0.802990	−	0.802990i	0.983562	+	0.180572i	$0.0577949\pi$
$8$		−	2.09725i		−	0.741488i
$9$			8.50005i			2.83335i
$10$	0.403621	−	0.403621i	0.127636	−	0.127636i
$11$	0.707107	−	0.707107i	0.213201	−	0.213201i
$11$	0.707107	−	0.707107i	0.213201	−	0.213201i
$12$	4.01455	+	4.01455i	1.15890	+	1.15890i
$13$	−5.45773			−1.51370			−0.756851	−	0.653587i	$-0.773263\pi$
$13$	−5.45773			−1.51370			−0.756851	+	0.653587i	$0.773263\pi$
$14$	−1.21268	−	1.21268i	−0.324104	−	0.324104i
$15$			3.39117i			0.875597i
$16$	2.15124			0.537810
$17$	−4.03065	−	0.868239i	−0.977577	−	0.210579i
$17$	−4.03065	−	0.868239i	−0.977577	−	0.210579i
$18$	4.85188			1.14360
$19$			4.08195i			0.936462i	0.883606	+	0.468231i	$0.155109\pi$
$19$			4.08195i			0.936462i	−0.883606	+	0.468231i	$0.844891\pi$
$20$	1.18382	+	1.18382i	0.264711	+	0.264711i
$21$	10.1888			2.22338
$22$	−0.403621	−	0.403621i	−0.0860523	−	0.0860523i
$23$	3.21936	−	3.21936i	0.671283	−	0.671283i	−0.286729	−	0.958012i	$-0.592568\pi$
$23$	3.21936	−	3.21936i	0.671283	−	0.671283i	0.958012	+	0.286729i	$0.0925679\pi$
$24$	5.02903	−	5.02903i	1.02655	−	1.02655i
$25$			1.00000i			0.200000i
$26$			3.11531i			0.610962i
$27$	−13.1887	+	13.1887i	−2.53816	+	2.53816i
$28$	3.55681	−	3.55681i	0.672175	−	0.672175i
$29$	−4.51060	−	4.51060i	−0.837597	−	0.837597i	0.150945	−	0.988542i	$-0.451768\pi$
$29$	−4.51060	−	4.51060i	−0.837597	−	0.837597i	−0.988542	+	0.150945i	$0.951768\pi$
$30$	1.93570			0.353409
$31$	−2.80133	−	2.80133i	−0.503134	−	0.503134i	0.409276	−	0.912410i	$-0.365781\pi$
$31$	−2.80133	−	2.80133i	−0.503134	−	0.503134i	−0.912410	+	0.409276i	$0.865781\pi$
$32$		−	5.42243i		−	0.958560i
$33$	3.39117			0.590327
$34$	−0.495596	+	2.30072i	−0.0849940	+	0.394571i
$35$	3.00451			0.507855
$36$			14.2306i			2.37177i
$37$	−3.06274	−	3.06274i	−0.503511	−	0.503511i	0.409016	−	0.912527i	$-0.365872\pi$
$37$	−3.06274	−	3.06274i	−0.503511	−	0.503511i	−0.912527	+	0.409016i	$0.865872\pi$
$38$	2.33000			0.377976
$39$	−13.0872	−	13.0872i	−2.09563	−	2.09563i
$40$	1.48298	−	1.48298i	0.234479	−	0.234479i
$41$	6.13639	−	6.13639i	0.958343	−	0.958343i	−0.0408237	−	0.999166i	$-0.512998\pi$
$41$	6.13639	−	6.13639i	0.958343	−	0.958343i	0.999166	+	0.0408237i	$0.0129982\pi$
$42$		−	5.81584i		−	0.897404i
$43$			1.45353i			0.221661i	0.993839	+	0.110830i	$0.0353511\pi$
$43$			1.45353i			0.221661i	−0.993839	+	0.110830i	$0.964649\pi$
$44$	1.18382	−	1.18382i	0.178468	−	0.178468i
$45$	−6.01044	+	6.01044i	−0.895984	+	0.895984i
$46$	−1.83763	−	1.83763i	−0.270944	−	0.270944i
$47$	6.73322			0.982142			0.491071	−	0.871120i	$-0.336606\pi$
$47$	6.73322			0.982142			0.491071	+	0.871120i	$0.336606\pi$
$48$	5.15850	+	5.15850i	0.744566	+	0.744566i
$49$		−	2.02710i		−	0.289585i
$50$	0.570806			0.0807242
$51$	−7.58322	−	11.7472i	−1.06186	−	1.64493i
$52$	−9.13722			−1.26710
$53$		−	11.4789i		−	1.57674i	−0.615199	−	0.788372i	$-0.710924\pi$
$53$		−	11.4789i		−	1.57674i	0.615199	−	0.788372i	$-0.289076\pi$
$54$	7.52819	+	7.52819i	1.02446	+	1.02446i
$55$	1.00000			0.134840
$56$	−4.45562	−	4.45562i	−0.595407	−	0.595407i
$57$	−9.78818	+	9.78818i	−1.29648	+	1.29648i
$58$	−2.57468	+	2.57468i	−0.338072	+	0.338072i
$59$			12.7249i			1.65664i	0.560255	+	0.828320i	$0.310703\pi$
$59$			12.7249i			1.65664i	−0.560255	+	0.828320i	$0.689297\pi$
$60$			5.67743i			0.732954i
$61$	−1.87477	+	1.87477i	−0.240040	+	0.240040i	−0.816866	−	0.576827i	$-0.804291\pi$
$61$	−1.87477	+	1.87477i	−0.240040	+	0.240040i	0.576827	+	0.816866i	$0.304291\pi$
$62$	−1.59902	+	1.59902i	−0.203076	+	0.203076i
$63$	18.0585	+	18.0585i	2.27515	+	2.27515i
$64$	1.20732			0.150915
$65$	−3.85920	−	3.85920i	−0.478675	−	0.478675i
$66$		−	1.93570i		−	0.238269i
$67$	−4.75293			−0.580663			−0.290332	−	0.956926i	$-0.593766\pi$
$67$	−4.75293			−0.580663			−0.290332	+	0.956926i	$0.593766\pi$
$68$	−6.74804	−	1.45359i	−0.818320	−	0.176273i
$69$	15.4395			1.85870
$70$		−	1.71499i		−	0.204981i
$71$	−0.233147	−	0.233147i	−0.0276694	−	0.0276694i	0.693137	−	0.720806i	$-0.256228\pi$
$71$	−0.233147	−	0.233147i	−0.0276694	−	0.0276694i	−0.720806	+	0.693137i	$0.756228\pi$
$72$	17.8267			2.10090
$73$	4.03484	+	4.03484i	0.472242	+	0.472242i	0.902640	−	0.430397i	$-0.141627\pi$
$73$	4.03484	+	4.03484i	0.472242	+	0.472242i	−0.430397	+	0.902640i	$0.641627\pi$
$74$	−1.74823	+	1.74823i	−0.203227	+	0.203227i
$75$	−2.39792	+	2.39792i	−0.276888	+	0.276888i
$76$			6.83391i			0.783903i
$77$		−	3.00451i		−	0.342396i
$78$	−7.47026	+	7.47026i	−0.845840	+	0.845840i
$79$	−3.35541	+	3.35541i	−0.377513	+	0.377513i	−0.870204	−	0.492691i	$-0.836013\pi$
$79$	−3.35541	+	3.35541i	−0.377513	+	0.377513i	0.492691	+	0.870204i	$0.336013\pi$
$80$	1.52116	+	1.52116i	0.170070	+	0.170070i
$81$	−37.7507			−4.19453
$82$	−3.50269	−	3.50269i	−0.386807	−	0.386807i
$83$			9.36021i			1.02742i	0.857965	+	0.513708i	$0.171729\pi$
$83$			9.36021i			1.02742i	−0.857965	+	0.513708i	$0.828271\pi$
$84$	17.0579			1.86117
$85$	−2.23616	−	3.46404i	−0.242546	−	0.375728i
$86$	0.829683			0.0894670
$87$		−	21.6321i		−	2.31921i
$88$	−1.48298	−	1.48298i	−0.158086	−	0.158086i
$89$	−9.41784			−0.998289			−0.499144	−	0.866519i	$-0.666352\pi$
$89$	−9.41784			−0.998289			−0.499144	+	0.866519i	$0.666352\pi$
$90$	3.43080	+	3.43080i	0.361638	+	0.361638i
$91$	−11.5950	+	11.5950i	−1.21549	+	1.21549i
$92$	5.38979	−	5.38979i	0.561924	−	0.561924i
$93$		−	13.4347i		−	1.39312i
$94$		−	3.84337i		−	0.396413i
$95$	−2.88637	+	2.88637i	−0.296135	+	0.296135i
$96$	13.0026	−	13.0026i	1.32707	−	1.32707i
$97$	−2.69589	−	2.69589i	−0.273726	−	0.273726i	0.556872	−	0.830598i	$-0.312001\pi$
$97$	−2.69589	−	2.69589i	−0.273726	−	0.273726i	−0.830598	+	0.556872i	$0.812001\pi$
$98$	−1.15708			−0.116883
$99$	6.01044	+	6.01044i	0.604072	+	0.604072i
$100$			1.67418i			0.167418i
$101$	−4.16842			−0.414773			−0.207386	−	0.978259i	$-0.566496\pi$
$101$	−4.16842			−0.414773			−0.207386	+	0.978259i	$0.566496\pi$
$102$	−6.70535	+	4.32855i	−0.663929	+	0.428590i
$103$	5.65871			0.557569			0.278785	−	0.960354i	$-0.410068\pi$
$103$	5.65871			0.557569			0.278785	+	0.960354i	$0.410068\pi$
$104$			11.4462i			1.12239i
$105$	7.20458	+	7.20458i	0.703095	+	0.703095i
$106$	−6.55221			−0.636407
$107$	4.12356	+	4.12356i	0.398640	+	0.398640i	0.877753	−	0.479113i	$-0.159042\pi$
$107$	4.12356	+	4.12356i	0.398640	+	0.398640i	−0.479113	+	0.877753i	$0.659042\pi$
$108$	−22.0802	+	22.0802i	−2.12467	+	2.12467i
$109$	−4.29965	+	4.29965i	−0.411832	+	0.411832i	−0.882376	−	0.470544i	$-0.844058\pi$
$109$	−4.29965	+	4.29965i	−0.411832	+	0.411832i	0.470544	+	0.882376i	$0.344058\pi$
$110$		−	0.570806i		−	0.0544242i
$111$		−	14.6884i		−	1.39416i
$112$	4.57033	−	4.57033i	0.431856	−	0.431856i
$113$	11.1660	−	11.1660i	1.05041	−	1.05041i	0.0517535	−	0.998660i	$-0.483519\pi$
$113$	11.1660	−	11.1660i	1.05041	−	1.05041i	0.998660	−	0.0517535i	$-0.0164810\pi$
$114$	5.58716	+	5.58716i	0.523285	+	0.523285i
$115$	4.55286			0.424557
$116$	−7.55155	−	7.55155i	−0.701144	−	0.701144i
$117$		−	46.3910i		−	4.28885i
$118$	7.26345			0.668655
$119$	−10.4078	+	6.71858i	−0.954077	+	0.615892i
$120$	7.11212			0.649245
$121$		−	1.00000i		−	0.0909091i
$122$	1.07013	+	1.07013i	0.0968850	+	0.0968850i
$123$	29.4291			2.65354
$124$	−4.68993	−	4.68993i	−0.421169	−	0.421169i
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$	10.3079	−	10.3079i	0.918299	−	0.918299i
$127$			8.68961i			0.771078i	0.922692	+	0.385539i	$0.125984\pi$
$127$			8.68961i			0.771078i	−0.922692	+	0.385539i	$0.874016\pi$
$128$		−	11.5340i		−	1.01947i
$129$	−3.48545	+	3.48545i	−0.306876	+	0.306876i
$130$	−2.20285	+	2.20285i	−0.193203	+	0.193203i
$131$	11.1072	+	11.1072i	0.970443	+	0.970443i	0.999576	−	0.0291322i	$-0.00927439\pi$
$131$	11.1072	+	11.1072i	0.970443	+	0.970443i	−0.0291322	+	0.999576i	$0.509274\pi$
$132$	5.67743			0.494157
$133$	8.67214	+	8.67214i	0.751970	+	0.751970i
$134$			2.71300i			0.234368i
$135$	−18.6516			−1.60528
$136$	−1.82091	+	8.45327i	−0.156142	+	0.724862i
$137$	20.0165			1.71013			0.855063	−	0.518524i	$-0.173518\pi$
$137$	20.0165			1.71013			0.855063	+	0.518524i	$0.173518\pi$
$138$		−	8.81299i		−	0.750211i
$139$	3.92649	+	3.92649i	0.333040	+	0.333040i	0.853740	−	0.520700i	$-0.174329\pi$
$139$	3.92649	+	3.92649i	0.333040	+	0.333040i	−0.520700	+	0.853740i	$0.674329\pi$
$140$	5.03010			0.425121
$141$	16.1457	+	16.1457i	1.35972	+	1.35972i
$142$	−0.133082	+	0.133082i	−0.0111680	+	0.0111680i
$143$	−3.85920	+	3.85920i	−0.322722	+	0.322722i
$144$			18.2856i			1.52380i
$145$		−	6.37895i		−	0.529743i
$146$	2.30311	−	2.30311i	0.190607	−	0.190607i
$147$	4.86082	−	4.86082i	0.400914	−	0.400914i
$148$	−5.12757	−	5.12757i	−0.421484	−	0.421484i
$149$	2.07622			0.170090			0.0850451	−	0.996377i	$-0.472897\pi$
$149$	2.07622			0.170090			0.0850451	+	0.996377i	$0.472897\pi$
$150$	1.36875	+	1.36875i	0.111758	+	0.111758i
$151$		−	2.91626i		−	0.237322i	−0.992935	−	0.118661i	$-0.962140\pi$
$151$		−	2.91626i		−	0.237322i	0.992935	−	0.118661i	$-0.0378601\pi$
$152$	8.56084			0.694376
$153$	7.38008	−	34.2608i	0.596644	−	2.76982i
$154$	−1.71499			−0.138198
$155$		−	3.96168i		−	0.318210i
$156$	−21.9103	−	21.9103i	−1.75423	−	1.75423i
$157$	−16.6314			−1.32733			−0.663665	−	0.748029i	$-0.731000\pi$
$157$	−16.6314			−1.32733			−0.663665	+	0.748029i	$0.731000\pi$
$158$	1.91529	+	1.91529i	0.152372	+	0.152372i
$159$	27.5254	−	27.5254i	2.18291	−	2.18291i
$160$	3.83424	−	3.83424i	0.303123	−	0.303123i
$161$		−	13.6791i		−	1.07807i
$162$			21.5484i			1.69300i
$163$	−6.66022	+	6.66022i	−0.521669	+	0.521669i	−0.918075	−	0.396406i	$-0.870257\pi$
$163$	−6.66022	+	6.66022i	−0.521669	+	0.521669i	0.396406	+	0.918075i	$0.370257\pi$
$164$	10.2734	−	10.2734i	0.802219	−	0.802219i
$165$	2.39792	+	2.39792i	0.186678	+	0.186678i
$166$	5.34286			0.414687
$167$	−4.29734	−	4.29734i	−0.332538	−	0.332538i	0.521012	−	0.853550i	$-0.325555\pi$
$167$	−4.29734	−	4.29734i	−0.332538	−	0.332538i	−0.853550	+	0.521012i	$0.825555\pi$
$168$		−	21.3685i		−	1.64861i
$169$	16.7868			1.29129
$170$	−1.97730	+	1.27642i	−0.151652	+	0.0978967i
$171$	−34.6967			−2.65333
$172$			2.43347i			0.185550i
$173$	−12.4299	−	12.4299i	−0.945027	−	0.945027i	0.0535392	−	0.998566i	$-0.482950\pi$
$173$	−12.4299	−	12.4299i	−0.945027	−	0.945027i	−0.998566	+	0.0535392i	$0.982950\pi$
$174$	−12.3477			−0.936080
$175$	2.12451	+	2.12451i	0.160598	+	0.160598i
$176$	1.52116	−	1.52116i	0.114661	−	0.114661i
$177$	−30.5133	+	30.5133i	−2.29352	+	2.29352i
$178$			5.37576i			0.402930i
$179$		−	21.8022i		−	1.62958i	−0.579759	−	0.814788i	$-0.696853\pi$
$179$		−	21.8022i		−	1.62958i	0.579759	−	0.814788i	$-0.303147\pi$
$180$	−10.0626	+	10.0626i	−0.750019	+	0.750019i
$181$	7.45677	−	7.45677i	0.554257	−	0.554257i	−0.373410	−	0.927667i	$-0.621811\pi$
$181$	7.45677	−	7.45677i	0.554257	−	0.554257i	0.927667	+	0.373410i	$0.121811\pi$
$182$	6.61850	+	6.61850i	0.490596	+	0.490596i
$183$	−8.99110			−0.664641
$184$	−6.75179	−	6.75179i	−0.497748	−	0.497748i
$185$		−	4.33136i		−	0.318448i
$186$	−7.66864			−0.562292
$187$	−3.46404	+	2.23616i	−0.253316	+	0.163525i
$188$	11.2726			0.822141
$189$			56.0390i			4.07624i
$190$	1.64756	+	1.64756i	0.119526	+	0.119526i
$191$	4.23195			0.306213			0.153107	−	0.988210i	$-0.451072\pi$
$191$	4.23195			0.306213			0.153107	+	0.988210i	$0.451072\pi$
$192$	2.89506	+	2.89506i	0.208933	+	0.208933i
$193$	4.82636	−	4.82636i	0.347409	−	0.347409i	−0.511735	−	0.859143i	$-0.670997\pi$
$193$	4.82636	−	4.82636i	0.347409	−	0.347409i	0.859143	+	0.511735i	$0.170997\pi$
$194$	−1.53883	+	1.53883i	−0.110482	+	0.110482i
$195$		−	18.5081i		−	1.32539i
$196$		−	3.39373i		−	0.242409i
$197$	−4.30591	+	4.30591i	−0.306784	+	0.306784i	−0.843661	−	0.536877i	$-0.819604\pi$
$197$	−4.30591	+	4.30591i	−0.306784	+	0.306784i	0.536877	+	0.843661i	$0.319604\pi$
$198$	3.43080	−	3.43080i	0.243816	−	0.243816i
$199$	−1.52237	−	1.52237i	−0.107918	−	0.107918i	0.651086	−	0.759004i	$-0.274314\pi$
$199$	−1.52237	−	1.52237i	−0.107918	−	0.107918i	−0.759004	+	0.651086i	$0.774314\pi$
$200$	2.09725			0.148298
$201$	−11.3972	−	11.3972i	−0.803893	−	0.803893i
$202$			2.37936i			0.167411i
$203$	−19.1656			−1.34516
$204$	−12.6957	−	19.6669i	−0.888875	−	1.37696i
$205$	8.67816			0.606109
$206$		−	3.23003i		−	0.225047i
$207$	27.3647	+	27.3647i	1.90198	+	1.90198i
$208$	−11.7409			−0.814084
$209$	2.88637	+	2.88637i	0.199654	+	0.199654i
$210$	4.11242	−	4.11242i	0.283784	−	0.283784i
$211$	−17.3043	+	17.3043i	−1.19128	+	1.19128i	−0.214569	+	0.976709i	$0.568835\pi$
$211$	−17.3043	+	17.3043i	−1.19128	+	1.19128i	−0.976709	+	0.214569i	$0.931165\pi$
$212$		−	19.2177i		−	1.31988i
$213$		−	1.11814i		−	0.0766134i
$214$	2.35375	−	2.35375i	0.160899	−	0.160899i
$215$	−1.02780	+	1.02780i	−0.0700954	+	0.0700954i
$216$	27.6599	+	27.6599i	1.88202	+	1.88202i
$217$	−11.9029			−0.808023
$218$	2.45427	+	2.45427i	0.166224	+	0.166224i
$219$			19.3505i			1.30758i
$220$	1.67418			0.112873
$221$	21.9982	+	4.73861i	1.47976	+	0.318754i
$222$	−8.38423			−0.562713
$223$			6.46148i			0.432693i	0.976317	+	0.216346i	$0.0694140\pi$
$223$			6.46148i			0.432693i	−0.976317	+	0.216346i	$0.930586\pi$
$224$	−11.5200	−	11.5200i	−0.769714	−	0.769714i
$225$	−8.50005			−0.566670
$226$	−6.37365	−	6.37365i	−0.423969	−	0.423969i
$227$	10.1127	−	10.1127i	0.671205	−	0.671205i	−0.286789	−	0.957994i	$-0.592588\pi$
$227$	10.1127	−	10.1127i	0.671205	−	0.671205i	0.957994	+	0.286789i	$0.0925879\pi$
$228$	−16.3872	+	16.3872i	−1.08527	+	1.08527i
$229$			18.8701i			1.24697i	0.781836	+	0.623484i	$0.214284\pi$
$229$			18.8701i			1.24697i	−0.781836	+	0.623484i	$0.785716\pi$
$230$		−	2.59880i		−	0.171360i
$231$	7.20458	−	7.20458i	0.474027	−	0.474027i
$232$	−9.45983	+	9.45983i	−0.621068	+	0.621068i
$233$	−10.6874	−	10.6874i	−0.700152	−	0.700152i	0.264291	−	0.964443i	$-0.414862\pi$
$233$	−10.6874	−	10.6874i	−0.700152	−	0.700152i	−0.964443	+	0.264291i	$0.914862\pi$
$234$	−26.4803			−1.73107
$235$	4.76111	+	4.76111i	0.310580	+	0.310580i
$236$			21.3038i			1.38676i
$237$	−16.0920			−1.04529
$238$	3.83501	+	5.94081i	0.248587	+	0.385085i
$239$	−5.29289			−0.342369			−0.171184	−	0.985239i	$-0.554759\pi$
$239$	−5.29289			−0.342369			−0.171184	+	0.985239i	$0.554759\pi$
$240$			7.29522i			0.470905i
$241$	13.8350	+	13.8350i	0.891191	+	0.891191i	0.994635	−	0.103444i	$-0.0329864\pi$
$241$	13.8350	+	13.8350i	0.891191	+	0.891191i	−0.103444	+	0.994635i	$0.532986\pi$
$242$	−0.570806			−0.0366928
$243$	−50.9572	−	50.9572i	−3.26891	−	3.26891i
$244$	−3.13870	+	3.13870i	−0.200935	+	0.200935i
$245$	1.43337	−	1.43337i	0.0915749	−	0.0915749i
$246$		−	16.7983i		−	1.07102i
$247$		−	22.2782i		−	1.41753i
$248$	−5.87508	+	5.87508i	−0.373068	+	0.373068i
$249$	−22.4450	+	22.4450i	−1.42240	+	1.42240i
$250$	0.403621	+	0.403621i	0.0255272	+	0.0255272i
$251$	−11.8644			−0.748877			−0.374439	−	0.927252i	$-0.622165\pi$
$251$	−11.8644			−0.748877			−0.374439	+	0.927252i	$0.622165\pi$
$252$	30.2331	+	30.2331i	1.90451	+	1.90451i
$253$		−	4.55286i		−	0.286236i
$254$	4.96008			0.311223
$255$	2.94435	−	13.6686i	0.184382	−	0.855963i
$256$	−4.16904			−0.260565
$257$			6.43124i			0.401170i	0.979676	+	0.200585i	$0.0642842\pi$
$257$			6.43124i			0.401170i	−0.979676	+	0.200585i	$0.935716\pi$
$258$	1.98951	+	1.98951i	0.123862	+	0.123862i
$259$	−13.0136			−0.808628
$260$	−6.46099	−	6.46099i	−0.400694	−	0.400694i
$261$	38.3403	−	38.3403i	2.37321	−	2.37321i
$262$	6.34008	−	6.34008i	0.391691	−	0.391691i
$263$			20.1178i			1.24052i	0.784397	+	0.620260i	$0.212973\pi$
$263$			20.1178i			1.24052i	−0.784397	+	0.620260i	$0.787027\pi$
$264$		−	7.11212i		−	0.437721i
$265$	8.11679	−	8.11679i	0.498610	−	0.498610i
$266$	4.95011	−	4.95011i	0.303511	−	0.303511i
$267$	−22.5832	−	22.5832i	−1.38207	−	1.38207i
$268$	−7.95726			−0.486067
$269$	−13.6683	−	13.6683i	−0.833369	−	0.833369i	0.154607	−	0.987976i	$-0.450589\pi$
$269$	−13.6683	−	13.6683i	−0.833369	−	0.833369i	−0.987976	+	0.154607i	$0.950589\pi$
$270$			10.6465i			0.647923i
$271$	19.4648			1.18240			0.591201	−	0.806524i	$-0.298654\pi$
$271$	19.4648			1.18240			0.591201	+	0.806524i	$0.298654\pi$
$272$	−8.67090	−	1.86779i	−0.525751	−	0.113251i
$273$	−55.6078			−3.36554
$274$		−	11.4256i		−	0.690243i
$275$	0.707107	+	0.707107i	0.0426401	+	0.0426401i
$276$	25.8486			1.55590
$277$	1.38140	+	1.38140i	0.0830004	+	0.0830004i	0.747388	−	0.664388i	$-0.231308\pi$
$277$	1.38140	+	1.38140i	0.0830004	+	0.0830004i	−0.664388	+	0.747388i	$0.731308\pi$
$278$	2.24126	−	2.24126i	0.134422	−	0.134422i
$279$	23.8115	−	23.8115i	1.42556	−	1.42556i
$280$		−	6.30120i		−	0.376569i
$281$			31.9636i			1.90679i	0.301725	+	0.953395i	$0.402438\pi$
$281$			31.9636i			1.90679i	−0.301725	+	0.953395i	$0.597562\pi$
$282$	9.21609	−	9.21609i	0.548810	−	0.548810i
$283$	19.5144	−	19.5144i	1.16001	−	1.16001i	0.175539	−	0.984472i	$-0.443833\pi$
$283$	19.5144	−	19.5144i	1.16001	−	1.16001i	0.984472	−	0.175539i	$-0.0561668\pi$
$284$	−0.390330	−	0.390330i	−0.0231618	−	0.0231618i
$285$	−13.8426			−0.819964
$286$	2.20285	+	2.20285i	0.130258	+	0.130258i
$287$		−	26.0736i		−	1.53908i
$288$	46.0909			2.71594
$289$	15.4923	+	6.99914i	0.911313	+	0.411714i
$290$	−3.64114			−0.213815
$291$		−	12.9291i		−	0.757916i
$292$	6.75505	+	6.75505i	0.395309	+	0.395309i
$293$	0.718070			0.0419501			0.0209751	−	0.999780i	$-0.493323\pi$
$293$	0.718070			0.0419501			0.0209751	+	0.999780i	$0.493323\pi$
$294$	−2.77459	−	2.77459i	−0.161817	−	0.161817i
$295$	−8.99786	+	8.99786i	−0.523876	+	0.523876i
$296$	−6.42331	+	6.42331i	−0.373347	+	0.373347i
$297$			18.6516i			1.08228i
$298$		−	1.18512i		−	0.0686520i
$299$	−17.5704	+	17.5704i	−1.01612	+	1.01612i
$300$	−4.01455	+	4.01455i	−0.231780	+	0.231780i
$301$	3.08804	+	3.08804i	0.177992	+	0.177992i
$302$	−1.66462			−0.0957881
$303$	−9.99553	−	9.99553i	−0.574228	−	0.574228i
$304$			8.78124i			0.503639i
$305$	−2.65132			−0.151814
$306$	−19.5563	−	4.21259i	−1.11796	−	0.240818i
$307$	6.49749			0.370831			0.185416	−	0.982660i	$-0.440637\pi$
$307$	6.49749			0.370831			0.185416	+	0.982660i	$0.440637\pi$
$308$		−	5.03010i		−	0.286616i
$309$	13.5691	+	13.5691i	0.771921	+	0.771921i
$310$	−2.26135			−0.128436
$311$	−0.186127	−	0.186127i	−0.0105543	−	0.0105543i	0.701810	−	0.712364i	$-0.252376\pi$
$311$	−0.186127	−	0.186127i	−0.0105543	−	0.0105543i	−0.712364	+	0.701810i	$0.752376\pi$
$312$	−27.4471	+	27.4471i	−1.55389	+	1.55389i
$313$	−21.7993	+	21.7993i	−1.23217	+	1.23217i	−0.269042	+	0.963128i	$0.586707\pi$
$313$	−21.7993	+	21.7993i	−1.23217	+	1.23217i	−0.963128	+	0.269042i	$0.913293\pi$
$314$			9.49331i			0.535739i
$315$			25.5385i			1.43893i
$316$	−5.61756	+	5.61756i	−0.316012	+	0.316012i
$317$	−2.69129	+	2.69129i	−0.151158	+	0.151158i	−0.778635	−	0.627477i	$-0.784088\pi$
$317$	−2.69129	+	2.69129i	−0.151158	+	0.151158i	0.627477	+	0.778635i	$0.284088\pi$
$318$	−15.7117	−	15.7117i	−0.881068	−	0.881068i
$319$	−6.37895			−0.357153
$320$	0.853705	+	0.853705i	0.0477236	+	0.0477236i
$321$			19.7759i			1.10379i
$322$	−7.80814			−0.435130
$323$	3.54410	−	16.4529i	0.197199	−	0.915464i
$324$	−63.2015			−3.51120
$325$		−	5.45773i		−	0.302740i
$326$	3.80170	+	3.80170i	0.210556	+	0.210556i
$327$	−20.6205			−1.14031
$328$	−12.8695	−	12.8695i	−0.710600	−	0.710600i
$329$	14.3048	−	14.3048i	0.788650	−	0.788650i
$330$	1.36875	−	1.36875i	0.0753471	−	0.0753471i
$331$		−	32.0917i		−	1.76392i	−0.471324	−	0.881960i	$-0.656224\pi$
$331$		−	32.0917i		−	1.76392i	0.471324	−	0.881960i	$-0.343776\pi$
$332$			15.6707i			0.860040i
$333$	26.0334	−	26.0334i	1.42662	−	1.42662i
$334$	−2.45295	+	2.45295i	−0.134219	+	0.134219i
$335$	−3.36083	−	3.36083i	−0.183622	−	0.183622i
$336$	21.9186			1.19576
$337$	7.41359	+	7.41359i	0.403844	+	0.403844i	0.879585	−	0.475741i	$-0.157820\pi$
$337$	7.41359	+	7.41359i	0.403844	+	0.403844i	−0.475741	+	0.879585i	$0.657820\pi$
$338$		−	9.58202i		−	0.521193i
$339$	53.5506			2.90847
$340$	−3.74374	−	5.79943i	−0.203033	−	0.314518i
$341$	−3.96168			−0.214537
$342$			19.8051i			1.07094i
$343$	10.5650	+	10.5650i	0.570456	+	0.570456i
$344$	3.04841			0.164359
$345$	10.9174	+	10.9174i	0.587773	+	0.587773i
$346$	−7.09506	+	7.09506i	−0.381433	+	0.381433i
$347$	18.5506	−	18.5506i	0.995848	−	0.995848i	−0.00414313	−	0.999991i	$-0.501319\pi$
$347$	18.5506	−	18.5506i	0.995848	−	0.995848i	0.999991	+	0.00414313i	$0.00131880\pi$
$348$		−	36.2161i		−	1.94138i
$349$			11.3252i			0.606222i	0.952955	+	0.303111i	$0.0980253\pi$
$349$			11.3252i			0.606222i	−0.952955	+	0.303111i	$0.901975\pi$
$350$	1.21268	−	1.21268i	0.0648207	−	0.0648207i
$351$	71.9803	−	71.9803i	3.84203	−	3.84203i
$352$	−3.83424	−	3.83424i	−0.204366	−	0.204366i
$353$	−32.9459			−1.75353			−0.876766	−	0.480917i	$-0.840304\pi$
$353$	−32.9459			−1.75353			−0.876766	+	0.480917i	$0.840304\pi$
$354$	17.4172	+	17.4172i	0.925713	+	0.925713i
$355$		−	0.329719i		−	0.0174997i
$356$	−15.7672			−0.835657
$357$	−41.0676	−	8.84633i	−2.17353	−	0.468197i
$358$	−12.4449			−0.657731
$359$		−	10.4477i		−	0.551407i	−0.961243	−	0.275703i	$-0.911089\pi$
$359$		−	10.4477i		−	0.551407i	0.961243	−	0.275703i	$-0.0889108\pi$
$360$	12.6054	+	12.6054i	0.664362	+	0.664362i
$361$	2.33772			0.123038
$362$	−4.25637	−	4.25637i	−0.223710	−	0.223710i
$363$	2.39792	−	2.39792i	0.125858	−	0.125858i
$364$	−19.4121	+	19.4121i	−1.01747	+	1.01747i
$365$			5.70613i			0.298672i
$366$			5.13218i			0.268263i
$367$	19.5570	−	19.5570i	1.02087	−	1.02087i	0.0210900	−	0.999778i	$-0.493286\pi$
$367$	19.5570	−	19.5570i	1.02087	−	1.02087i	0.999778	−	0.0210900i	$-0.00671364\pi$
$368$	6.92562	−	6.92562i	0.361023	−	0.361023i
$369$	52.1596	+	52.1596i	2.71532	+	2.71532i
$370$	−2.47237			−0.128532
$371$	−24.3870	−	24.3870i	−1.26611	−	1.26611i
$372$		−	22.4922i		−	1.16617i
$373$	−16.9388			−0.877058			−0.438529	−	0.898717i	$-0.644500\pi$
$373$	−16.9388			−0.877058			−0.438529	+	0.898717i	$0.644500\pi$
$374$	1.27642	+	1.97730i	0.0660019	+	0.102244i
$375$	−3.39117			−0.175119
$376$		−	14.1212i		−	0.728246i
$377$	24.6176	+	24.6176i	1.26787	+	1.26787i
$378$	31.9874			1.64526
$379$	19.5132	+	19.5132i	1.00232	+	1.00232i	0.999997	+	0.00232677i	$0.000740635\pi$
$379$	19.5132	+	19.5132i	1.00232	+	1.00232i	0.00232677	+	0.999997i	$0.499259\pi$
$380$	−4.83231	+	4.83231i	−0.247892	+	0.247892i
$381$	−20.8370	+	20.8370i	−1.06751	+	1.06751i
$382$		−	2.41563i		−	0.123594i
$383$		−	9.11756i		−	0.465885i	−0.972490	−	0.232943i	$-0.925165\pi$
$383$		−	9.11756i		−	0.465885i	0.972490	−	0.232943i	$-0.0748355\pi$
$384$	27.6576	−	27.6576i	1.41140	−	1.41140i
$385$	2.12451	−	2.12451i	0.108275	−	0.108275i
$386$	−2.75491	−	2.75491i	−0.140221	−	0.140221i
$387$	−12.3551			−0.628043
$388$	−4.51341	−	4.51341i	−0.229134	−	0.229134i
$389$		−	22.3118i		−	1.13126i	−0.824661	−	0.565628i	$-0.808634\pi$
$389$		−	22.3118i		−	1.13126i	0.824661	−	0.565628i	$-0.191366\pi$
$390$	−10.5645			−0.534956
$391$	−15.7713	+	10.1809i	−0.797589	+	0.514873i
$392$	−4.25132			−0.214724
$393$			53.2685i			2.68704i
$394$	2.45784	+	2.45784i	0.123824	+	0.123824i
$395$	−4.74527			−0.238760
$396$	10.0626	+	10.0626i	0.505663	+	0.505663i
$397$	−10.7779	+	10.7779i	−0.540927	+	0.540927i	−0.923801	−	0.382873i	$-0.874935\pi$
$397$	−10.7779	+	10.7779i	−0.540927	+	0.540927i	0.382873	+	0.923801i	$0.374935\pi$
$398$	−0.868976	+	0.868976i	−0.0435578	+	0.0435578i
$399$			41.5902i			2.08211i
$400$			2.15124i			0.107562i
$401$	5.47798	−	5.47798i	0.273557	−	0.273557i	−0.556973	−	0.830531i	$-0.688037\pi$
$401$	5.47798	−	5.47798i	0.273557	−	0.273557i	0.830531	+	0.556973i	$0.188037\pi$
$402$	−6.50557	+	6.50557i	−0.324468	+	0.324468i
$403$	15.2889	+	15.2889i	0.761595	+	0.761595i
$404$	−6.97868			−0.347202
$405$	−26.6938	−	26.6938i	−1.32643	−	1.32643i
$406$			10.9399i			0.542936i
$407$	−4.33136			−0.214698
$408$	−24.6367	+	15.9039i	−1.21970	+	0.787359i
$409$	−9.69495			−0.479385			−0.239692	−	0.970849i	$-0.577047\pi$
$409$	−9.69495			−0.479385			−0.239692	+	0.970849i	$0.577047\pi$
$410$		−	4.95355i		−	0.244638i
$411$	47.9980	+	47.9980i	2.36757	+	2.36757i
$412$	9.47370			0.466736
$413$	27.0342	+	27.0342i	1.33027	+	1.33027i
$414$	15.6200	−	15.6200i	0.767679	−	0.767679i
$415$	−6.61867	+	6.61867i	−0.324897	+	0.324897i
$416$			29.5942i			1.45097i
$417$			18.8308i			0.922149i
$418$	1.64756	−	1.64756i	0.0805847	−	0.0805847i
$419$	−2.46277	+	2.46277i	−0.120314	+	0.120314i	−0.764700	−	0.644386i	$-0.777113\pi$
$419$	−2.46277	+	2.46277i	−0.120314	+	0.120314i	0.644386	+	0.764700i	$0.277113\pi$
$420$	12.0618	+	12.0618i	0.588554	+	0.588554i
$421$	26.3172			1.28262			0.641312	−	0.767280i	$-0.278390\pi$
$421$	26.3172			1.28262			0.641312	+	0.767280i	$0.278390\pi$
$422$	9.87741	+	9.87741i	0.480825	+	0.480825i
$423$			57.2327i			2.78275i
$424$	−24.0740			−1.16914
$425$	0.868239	−	4.03065i	0.0421158	−	0.195515i
$426$	−0.638239			−0.0309228
$427$			7.96594i			0.385499i
$428$	6.90358	+	6.90358i	0.333697	+	0.333697i
$429$	−18.5081			−0.893580
$430$	0.586675	+	0.586675i	0.0282920	+	0.0282920i
$431$	−2.27349	+	2.27349i	−0.109510	+	0.109510i	−0.759739	−	0.650228i	$-0.774673\pi$
$431$	−2.27349	+	2.27349i	−0.109510	+	0.109510i	0.650228	+	0.759739i	$0.274673\pi$
$432$	−28.3720	+	28.3720i	−1.36505	+	1.36505i
$433$		−	36.3543i		−	1.74708i	−0.486754	−	0.873539i	$-0.661819\pi$
$433$		−	36.3543i		−	1.74708i	0.486754	−	0.873539i	$-0.338181\pi$
$434$			6.79426i			0.326135i
$435$	15.2962	−	15.2962i	0.733397	−	0.733397i
$436$	−7.19839	+	7.19839i	−0.344740	+	0.344740i
$437$	13.1413	+	13.1413i	0.628631	+	0.628631i
$438$	11.0454			0.527768
$439$	12.6824	+	12.6824i	0.605297	+	0.605297i	0.941713	−	0.336417i	$-0.109215\pi$
$439$	12.6824	+	12.6824i	0.605297	+	0.605297i	−0.336417	+	0.941713i	$0.609215\pi$
$440$		−	2.09725i		−	0.0999822i
$441$	17.2304			0.820497
$442$	2.70483	−	12.5567i	0.128656	−	0.597262i
$443$	8.15822			0.387609			0.193804	−	0.981040i	$-0.437917\pi$
$443$	8.15822			0.387609			0.193804	+	0.981040i	$0.437917\pi$
$444$		−	24.5910i		−	1.16704i
$445$	−6.65942	−	6.65942i	−0.315687	−	0.315687i
$446$	3.68825			0.174644
$447$	4.97860	+	4.97860i	0.235480	+	0.235480i
$448$	2.56497	−	2.56497i	0.121183	−	0.121183i
$449$	−6.93972	+	6.93972i	−0.327506	+	0.327506i	−0.851637	−	0.524132i	$-0.824390\pi$
$449$	−6.93972	+	6.93972i	−0.327506	+	0.327506i	0.524132	+	0.851637i	$0.324390\pi$
$450$			4.85188i			0.228720i
$451$		−	8.67816i		−	0.408639i
$452$	18.6940	−	18.6940i	0.879291	−	0.879291i
$453$	6.99296	−	6.99296i	0.328558	−	0.328558i
$454$	−5.77240	−	5.77240i	−0.270912	−	0.270912i
$455$	−16.3978			−0.768742
$456$	20.5282	+	20.5282i	0.961322	+	0.961322i
$457$		−	25.4836i		−	1.19207i	−0.802958	−	0.596036i	$-0.796741\pi$
$457$		−	25.4836i		−	1.19207i	0.802958	−	0.596036i	$-0.203259\pi$
$458$	10.7712			0.503303
$459$	64.6100	−	41.7081i	3.01574	−	1.94677i
$460$	7.62231			0.355392
$461$			7.15713i			0.333341i	0.986013	+	0.166670i	$0.0533016\pi$
$461$			7.15713i			0.333341i	−0.986013	+	0.166670i	$0.946698\pi$
$462$	−4.11242	−	4.11242i	−0.191327	−	0.191327i
$463$	−31.4927			−1.46359			−0.731796	−	0.681524i	$-0.761317\pi$
$463$	−31.4927			−1.46359			−0.731796	+	0.681524i	$0.761317\pi$
$464$	−9.70338	−	9.70338i	−0.450468	−	0.450468i
$465$	9.49980	−	9.49980i	0.440543	−	0.440543i
$466$	−6.10041	+	6.10041i	−0.282596	+	0.282596i
$467$		−	17.3619i		−	0.803414i	−0.915768	−	0.401707i	$-0.868417\pi$
$467$		−	17.3619i		−	0.803414i	0.915768	−	0.401707i	$-0.131583\pi$
$468$		−	77.6669i		−	3.59015i
$469$	−10.0977	+	10.0977i	−0.466266	+	0.466266i
$470$	2.71767	−	2.71767i	0.125357	−	0.125357i
$471$	−39.8808	−	39.8808i	−1.83761	−	1.83761i
$472$	26.6872			1.22838
$473$	1.02780	+	1.02780i	0.0472583	+	0.0472583i
$474$			9.18542i			0.421901i
$475$	−4.08195			−0.187292
$476$	−17.4244	+	11.2481i	−0.798648	+	0.515557i
$477$	97.5710			4.46747
$478$			3.02122i			0.138187i
$479$	4.11314	+	4.11314i	0.187934	+	0.187934i	0.794802	−	0.606868i	$-0.207574\pi$
$479$	4.11314	+	4.11314i	0.187934	+	0.187934i	−0.606868	+	0.794802i	$0.707574\pi$
$480$	18.3884			0.839312
$481$	16.7156	+	16.7156i	0.762165	+	0.762165i
$482$	7.89711	−	7.89711i	0.359703	−	0.359703i
$483$	32.8015	−	32.8015i	1.49252	−	1.49252i
$484$		−	1.67418i		−	0.0760991i
$485$		−	3.81257i		−	0.173120i
$486$	−29.0867	+	29.0867i	−1.31940	+	1.31940i
$487$	17.6341	−	17.6341i	0.799079	−	0.799079i	−0.183871	−	0.982950i	$-0.558863\pi$
$487$	17.6341	−	17.6341i	0.799079	−	0.799079i	0.982950	+	0.183871i	$0.0588630\pi$
$488$	3.93185	+	3.93185i	0.177987	+	0.177987i
$489$	−31.9414			−1.44444
$490$	−0.818179	−	0.818179i	−0.0369616	−	0.0369616i
$491$			2.82546i			0.127511i	0.997966	+	0.0637557i	$0.0203078\pi$
$491$			2.82546i			0.127511i	−0.997966	+	0.0637557i	$0.979692\pi$
$492$	49.2697			2.22125
$493$	14.2644	+	22.0969i	0.642435	+	0.995196i
$494$	−12.7165			−0.572143
$495$			8.50005i			0.382049i
$496$	−6.02634	−	6.02634i	−0.270591	−	0.270591i
$497$	−0.990646			−0.0444365
$498$	12.8118	+	12.8118i	0.574109	+	0.574109i
$499$	−17.7104	+	17.7104i	−0.792826	+	0.792826i	−0.981953	−	0.189127i	$-0.939434\pi$
$499$	−17.7104	+	17.7104i	−0.792826	+	0.792826i	0.189127	+	0.981953i	$0.439434\pi$
$500$	−1.18382	+	1.18382i	−0.0529422	+	0.0529422i
$501$		−	20.6093i		−	0.920758i
$502$			6.77230i			0.302262i
$503$	23.3480	−	23.3480i	1.04103	−	1.04103i	0.0419127	−	0.999121i	$-0.486655\pi$
$503$	23.3480	−	23.3480i	1.04103	−	1.04103i	0.999121	−	0.0419127i	$-0.0133451\pi$
$504$	37.8730	−	37.8730i	1.68700	−	1.68700i
$505$	−2.94752	−	2.94752i	−0.131163	−	0.131163i
$506$	−2.59880			−0.115531
$507$	40.2535	+	40.2535i	1.78772	+	1.78772i
$508$			14.5480i			0.645462i
$509$	−24.2435			−1.07458			−0.537288	−	0.843399i	$-0.680551\pi$
$509$	−24.2435			−1.07458			−0.537288	+	0.843399i	$0.680551\pi$
$510$	−7.80215	−	1.68065i	−0.345485	−	0.0744205i
$511$	17.1441			0.758412
$512$		−	20.6883i		−	0.914302i
$513$	−53.8355	−	53.8355i	−2.37690	−	2.37690i
$514$	3.67099			0.161920
$515$	4.00131	+	4.00131i	0.176319	+	0.176319i
$516$	−5.83526	+	5.83526i	−0.256883	+	0.256883i
$517$	4.76111	−	4.76111i	0.209393	−	0.209393i
$518$			7.42826i			0.326379i
$519$		−	59.6118i		−	2.61667i
$520$	−8.09368	+	8.09368i	−0.354932	+	0.354932i
$521$	11.6837	−	11.6837i	0.511871	−	0.511871i	−0.403228	−	0.915099i	$-0.632112\pi$
$521$	11.6837	−	11.6837i	0.511871	−	0.511871i	0.915099	+	0.403228i	$0.132112\pi$
$522$	−21.8849	−	21.8849i	−0.957876	−	0.957876i
$523$	6.90566			0.301964			0.150982	−	0.988537i	$-0.451757\pi$
$523$	6.90566			0.301964			0.150982	+	0.988537i	$0.451757\pi$
$524$	18.5955	+	18.5955i	0.812349	+	0.812349i
$525$			10.1888i			0.444677i
$526$	11.4834			0.500700
$527$	8.85897	+	13.7234i	0.385903	+	0.597802i
$528$	7.29522			0.317484
$529$			2.27144i			0.0987582i
$530$	−4.63311	−	4.63311i	−0.201250	−	0.201250i
$531$	−108.162			−4.69384
$532$	14.5187	+	14.5187i	0.629466	+	0.629466i
$533$	−33.4907	+	33.4907i	−1.45065	+	1.45065i
$534$	−12.8906	+	12.8906i	−0.557833	+	0.557833i
$535$			5.83159i			0.252122i
$536$			9.96806i			0.430555i
$537$	52.2800	−	52.2800i	2.25605	−	2.25605i
$538$	−7.80193	+	7.80193i	−0.336365	+	0.336365i
$539$	−1.43337	−	1.43337i	−0.0617398	−	0.0617398i
$540$	−31.2262			−1.34376
$541$	−21.9237	−	21.9237i	−0.942575	−	0.942575i	0.0558635	−	0.998438i	$-0.482209\pi$
$541$	−21.9237	−	21.9237i	−0.942575	−	0.942575i	−0.998438	+	0.0558635i	$0.982209\pi$
$542$		−	11.1106i		−	0.477243i
$543$	35.7615			1.53467
$544$	−4.70797	+	21.8559i	−0.201852	+	0.937066i
$545$	−6.08063			−0.260465
$546$			31.7413i			1.35840i
$547$	−12.4537	−	12.4537i	−0.532482	−	0.532482i	0.388828	−	0.921310i	$-0.372880\pi$
$547$	−12.4537	−	12.4537i	−0.532482	−	0.532482i	−0.921310	+	0.388828i	$0.872880\pi$
$548$	33.5112			1.43153
$549$	−15.9356	−	15.9356i	−0.680116	−	0.680116i
$550$	0.403621	−	0.403621i	0.0172105	−	0.0172105i
$551$	18.4120	−	18.4120i	0.784378	−	0.784378i
$552$		−	32.3805i		−	1.37821i
$553$			14.2572i			0.606278i
$554$	0.788513	−	0.788513i	0.0335007	−	0.0335007i
$555$	10.3863	−	10.3863i	0.440872	−	0.440872i
$556$	6.57365	+	6.57365i	0.278785	+	0.278785i
$557$	7.31170			0.309807			0.154903	−	0.987930i	$-0.450493\pi$
$557$	7.31170			0.309807			0.154903	+	0.987930i	$0.450493\pi$
$558$	−13.5917	−	13.5917i	−0.575384	−	0.575384i
$559$		−	7.93297i		−	0.335529i
$560$	6.46343			0.273130
$561$	−13.6686	−	2.94435i	−0.577090	−	0.124310i
$562$	18.2450			0.769621
$563$			0.281946i			0.0118826i	0.999982	+	0.00594130i	$0.00189118\pi$
$563$			0.281946i			0.0118826i	−0.999982	+	0.00594130i	$0.998109\pi$
$564$	27.0309	+	27.0309i	1.13821	+	1.13821i
$565$	15.7912			0.664340
$566$	−11.1390	−	11.1390i	−0.468205	−	0.468205i
$567$	−80.2019	+	80.2019i	−3.36816	+	3.36816i
$568$	−0.488966	+	0.488966i	−0.0205166	+	0.0205166i
$569$			32.5637i			1.36514i	0.730821	+	0.682570i	$0.239138\pi$
$569$			32.5637i			1.36514i	−0.730821	+	0.682570i	$0.760862\pi$
$570$			7.90143i			0.330955i
$571$	−19.6174	+	19.6174i	−0.820963	+	0.820963i	−0.986246	−	0.165283i	$-0.947146\pi$
$571$	−19.6174	+	19.6174i	−0.820963	+	0.820963i	0.165283	+	0.986246i	$0.447146\pi$
$572$	−6.46099	+	6.46099i	−0.270148	+	0.270148i
$573$	10.1479	+	10.1479i	0.423934	+	0.423934i
$574$	−14.8830			−0.621205
$575$	3.21936	+	3.21936i	0.134257	+	0.134257i
$576$			10.2623i			0.427596i
$577$	28.9770			1.20633			0.603164	−	0.797617i	$-0.293906\pi$
$577$	28.9770			1.20633			0.603164	+	0.797617i	$0.293906\pi$
$578$	3.99515	−	8.84312i	0.166176	−	0.367825i
$579$	23.1464			0.961933
$580$		−	10.6795i		−	0.443442i
$581$	19.8859	+	19.8859i	0.825005	+	0.825005i
$582$	−7.38000			−0.305911
$583$	−8.11679	−	8.11679i	−0.336163	−	0.336163i
$584$	8.46205	−	8.46205i	0.350162	−	0.350162i
$585$	32.8034	−	32.8034i	1.35625	−	1.35625i
$586$		−	0.409879i		−	0.0169319i
$587$			22.7486i			0.938935i	0.882950	+	0.469467i	$0.155554\pi$
$587$			22.7486i			0.938935i	−0.882950	+	0.469467i	$0.844446\pi$
$588$	8.13789	−	8.13789i	0.335601	−	0.335601i
$589$	11.4349	−	11.4349i	0.471166	−	0.471166i
$590$	5.13603	+	5.13603i	0.211447	+	0.211447i
$591$	−20.6505			−0.849447
$592$	−6.58868	−	6.58868i	−0.270793	−	0.270793i
$593$			26.3460i			1.08190i	0.841055	+	0.540950i	$0.181935\pi$
$593$			26.3460i			1.08190i	−0.841055	+	0.540950i	$0.818065\pi$
$594$	10.6465			0.436830
$595$	−12.1101	−	2.60863i	−0.496468	−	0.106944i
$596$	3.47596			0.142381
$597$		−	7.30103i		−	0.298811i
$598$	10.0293	+	10.0293i	0.410128	+	0.410128i
$599$	−8.72306			−0.356414			−0.178207	−	0.983993i	$-0.557030\pi$
$599$	−8.72306			−0.356414			−0.178207	+	0.983993i	$0.557030\pi$
$600$	5.02903	+	5.02903i	0.205309	+	0.205309i
$601$	−7.25834	+	7.25834i	−0.296074	+	0.296074i	−0.839474	−	0.543400i	$-0.817137\pi$
$601$	−7.25834	+	7.25834i	−0.296074	+	0.296074i	0.543400	+	0.839474i	$0.317137\pi$
$602$	1.76267	−	1.76267i	0.0718411	−	0.0718411i
$603$		−	40.4002i		−	1.64522i
$604$		−	4.88234i		−	0.198660i
$605$	0.707107	−	0.707107i	0.0287480	−	0.0287480i
$606$	−5.70551	+	5.70551i	−0.231771	+	0.231771i
$607$	17.1319	+	17.1319i	0.695363	+	0.695363i	0.963407	−	0.268044i	$-0.0863771\pi$
$607$	17.1319	+	17.1319i	0.695363	+	0.695363i	−0.268044	+	0.963407i	$0.586377\pi$
$608$	22.1341			0.897655
$609$	−45.9577	−	45.9577i	−1.86230	−	1.86230i
$610$			1.51339i			0.0612755i
$611$	−36.7481			−1.48667
$612$	12.3556	−	57.3587i	0.499445	−	2.31859i
$613$	−20.1173			−0.812530			−0.406265	−	0.913755i	$-0.633169\pi$
$613$	−20.1173			−0.812530			−0.406265	+	0.913755i	$0.633169\pi$
$614$		−	3.70881i		−	0.149675i
$615$	20.8095	+	20.8095i	0.839122	+	0.839122i
$616$	−6.30120			−0.253883
$617$	0.750039	+	0.750039i	0.0301954	+	0.0301954i	0.722043	−	0.691848i	$-0.243203\pi$
$617$	0.750039	+	0.750039i	0.0301954	+	0.0301954i	−0.691848	+	0.722043i	$0.743203\pi$
$618$	7.74535	−	7.74535i	0.311564	−	0.311564i
$619$	−28.8817	+	28.8817i	−1.16085	+	1.16085i	−0.176565	+	0.984289i	$0.556499\pi$
$619$	−28.8817	+	28.8817i	−1.16085	+	1.16085i	−0.984289	+	0.176565i	$0.943501\pi$
$620$		−	6.63257i		−	0.266370i
$621$			84.9183i			3.40765i
$622$	−0.106242	+	0.106242i	−0.00425994	+	0.00425994i
$623$	−20.0083	+	20.0083i	−0.801616	+	0.801616i
$624$	−28.1537	−	28.1537i	−1.12705	−	1.12705i
$625$	−1.00000			−0.0400000
$626$	12.4432	+	12.4432i	0.497330	+	0.497330i
$627$			13.8426i			0.552819i
$628$	−27.8440			−1.11110
$629$	9.68564	+	15.0040i	0.386192	+	0.598249i
$630$	14.5775			0.580783
$631$			19.6651i			0.782855i	0.920209	+	0.391428i	$0.128019\pi$
$631$			19.6651i			0.782855i	−0.920209	+	0.391428i	$0.871981\pi$
$632$	7.03712	+	7.03712i	0.279921	+	0.279921i
$633$	−82.9888			−3.29851
$634$	1.53620	+	1.53620i	0.0610104	+	0.0610104i
$635$	−6.14448	+	6.14448i	−0.243836	+	0.243836i
$636$	46.0825	−	46.0825i	1.82729	−	1.82729i
$637$			11.0633i			0.438346i
$638$			3.64114i			0.144154i
$639$	1.98176	−	1.98176i	0.0783972	−	0.0783972i
$640$	8.15578	−	8.15578i	0.322385	−	0.322385i
$641$	1.81048	+	1.81048i	0.0715097	+	0.0715097i	0.741957	−	0.670447i	$-0.233898\pi$
$641$	1.81048	+	1.81048i	0.0715097	+	0.0715097i	−0.670447	+	0.741957i	$0.733898\pi$
$642$	11.2882			0.445511
$643$	3.23259	+	3.23259i	0.127481	+	0.127481i	0.767969	−	0.640488i	$-0.221268\pi$
$643$	3.23259	+	3.23259i	0.127481	+	0.127481i	−0.640488	+	0.767969i	$0.721268\pi$
$644$		−	22.9013i		−	0.902439i
$645$	−4.92917			−0.194086
$646$	−9.39142	−	2.02300i	−0.369501	−	0.0795937i
$647$	25.8561			1.01651			0.508254	−	0.861207i	$-0.330291\pi$
$647$	25.8561			1.01651			0.508254	+	0.861207i	$0.330291\pi$
$648$			79.1725i			3.11019i
$649$	8.99786	+	8.99786i	0.353197	+	0.353197i
$650$	−3.11531			−0.122192
$651$	−28.5423	−	28.5423i	−1.11866	−	1.11866i
$652$	−11.1504	+	11.1504i	−0.436684	+	0.436684i
$653$	10.6090	−	10.6090i	0.415162	−	0.415162i	−0.468370	−	0.883532i	$-0.655159\pi$
$653$	10.6090	−	10.6090i	0.415162	−	0.415162i	0.883532	+	0.468370i	$0.155159\pi$
$654$			11.7703i			0.460255i
$655$			15.7080i			0.613762i
$656$	13.2008	−	13.2008i	0.515406	−	0.515406i
$657$	−34.2964	+	34.2964i	−1.33803	+	1.33803i
$658$	−8.16528	−	8.16528i	−0.318316	−	0.318316i
$659$	−11.5188			−0.448708			−0.224354	−	0.974508i	$-0.572027\pi$
$659$	−11.5188			−0.448708			−0.224354	+	0.974508i	$0.572027\pi$
$660$	4.01455	+	4.01455i	0.156266	+	0.156266i
$661$			39.2320i			1.52595i	0.646430	+	0.762973i	$0.276261\pi$
$661$			39.2320i			1.52595i	−0.646430	+	0.762973i	$0.723739\pi$
$662$	−18.3182			−0.711955
$663$	41.3872	+	64.1128i	1.60734	+	2.48994i
$664$	19.6306			0.761817
$665$			12.2643i			0.475587i
$666$	−14.8600	−	14.8600i	−0.575815	−	0.575815i
$667$	−29.0425			−1.12453
$668$	−7.19452	−	7.19452i	−0.278364	−	0.278364i
$669$	−15.4941	+	15.4941i	−0.599037	+	0.599037i
$670$	−1.91838	+	1.91838i	−0.0741136	+	0.0741136i
$671$			2.65132i			0.102353i
$672$		−	55.2482i		−	2.13125i
$673$	3.02747	−	3.02747i	0.116700	−	0.116700i	−0.646345	−	0.763045i	$-0.723703\pi$
$673$	3.02747	−	3.02747i	0.116700	−	0.116700i	0.763045	+	0.646345i	$0.223703\pi$
$674$	4.23172	−	4.23172i	0.163000	−	0.163000i
$675$	−13.1887	−	13.1887i	−0.507633	−	0.507633i
$676$	28.1042			1.08093
$677$	−13.0368	−	13.0368i	−0.501046	−	0.501046i	0.410717	−	0.911763i	$-0.365278\pi$
$677$	−13.0368	−	13.0368i	−0.501046	−	0.501046i	−0.911763	+	0.410717i	$0.865278\pi$
$678$		−	30.5670i		−	1.17392i
$679$	−11.4549			−0.439599
$680$	−7.26494	+	4.68978i	−0.278598	+	0.179845i
$681$	48.4990			1.85849
$682$			2.26135i			0.0865917i
$683$	−12.8164	−	12.8164i	−0.490406	−	0.490406i	0.418028	−	0.908434i	$-0.362721\pi$
$683$	−12.8164	−	12.8164i	−0.490406	−	0.490406i	−0.908434	+	0.418028i	$0.862721\pi$
$684$	−58.0886			−2.22107
$685$	14.1538	+	14.1538i	0.540789	+	0.540789i
$686$	6.03056	−	6.03056i	0.230248	−	0.230248i
$687$	−45.2489	+	45.2489i	−1.72635	+	1.72635i
$688$			3.12689i			0.119211i
$689$			62.6486i			2.38672i
$690$	6.23172	−	6.23172i	0.237238	−	0.237238i
$691$	11.4097	−	11.4097i	0.434046	−	0.434046i	−0.455957	−	0.890002i	$-0.650703\pi$
$691$	11.4097	−	11.4097i	0.434046	−	0.434046i	0.890002	+	0.455957i	$0.150703\pi$
$692$	−20.8099	−	20.8099i	−0.791072	−	0.791072i
$693$	25.5385			0.970128
$694$	−10.5888	−	10.5888i	−0.401945	−	0.401945i
$695$			5.55289i			0.210633i
$696$	−45.3678			−1.71966
$697$	−30.0615	+	19.4058i	−1.13866	+	0.735047i
$698$	6.46447			0.244684
$699$		−	51.2549i		−	1.93864i
$700$	3.55681	+	3.55681i	0.134435	+	0.134435i
$701$	31.1713			1.17733			0.588663	−	0.808379i	$-0.299655\pi$
$701$	31.1713			1.17733			0.588663	+	0.808379i	$0.299655\pi$
$702$	−41.0868	−	41.0868i	−1.55072	−	1.55072i
$703$	12.5019	−	12.5019i	0.471519	−	0.471519i
$704$	0.853705	−	0.853705i	0.0321752	−	0.0321752i
$705$			22.8335i			0.859960i
$706$			18.8057i			0.707763i
$707$	−8.85585	+	8.85585i	−0.333058	+	0.333058i
$708$	−51.0848	+	51.0848i	−1.91988	+	1.91988i
$709$	3.38767	+	3.38767i	0.127227	+	0.127227i	0.767853	−	0.640626i	$-0.221325\pi$
$709$	3.38767	+	3.38767i	0.127227	+	0.127227i	−0.640626	+	0.767853i	$0.721325\pi$
$710$	−0.188206			−0.00706324
$711$	−28.5212	−	28.5212i	−1.06963	−	1.06963i
$712$			19.7515i			0.740219i
$713$	−18.0370			−0.675491
$714$	−5.04954	+	23.4416i	−0.188974	+	0.877282i
$715$	−5.45773			−0.204108
$716$		−	36.5009i		−	1.36410i
$717$	−12.6919	−	12.6919i	−0.473989	−	0.473989i
$718$	−5.96360			−0.222559
$719$	22.4746	+	22.4746i	0.838162	+	0.838162i	0.988617	−	0.150455i	$-0.0480737\pi$
$719$	22.4746	+	22.4746i	0.838162	+	0.838162i	−0.150455	+	0.988617i	$0.548074\pi$
$720$	−12.9299	+	12.9299i	−0.481869	+	0.481869i
$721$	12.0220	−	12.0220i	0.447722	−	0.447722i
$722$		−	1.33439i		−	0.0496607i
$723$			66.3505i			2.46760i
$724$	12.4840	−	12.4840i	0.463963	−	0.463963i
$725$	4.51060	−	4.51060i	0.167519	−	0.167519i
$726$	−1.36875	−	1.36875i	−0.0507990	−	0.0507990i
$727$	−15.3191			−0.568154			−0.284077	−	0.958802i	$-0.591687\pi$
$727$	−15.3191			−0.568154			−0.284077	+	0.958802i	$0.591687\pi$
$728$	24.3176	+	24.3176i	0.901269	+	0.901269i
$729$		−	131.131i		−	4.85669i
$730$	3.25709			0.120550
$731$	1.26201	−	5.85867i	0.0466771	−	0.216691i
$732$	−15.0527			−0.556365
$733$			25.5151i			0.942421i	0.882021	+	0.471210i	$0.156183\pi$
$733$			25.5151i			0.942421i	−0.882021	+	0.471210i	$0.843817\pi$
$734$	−11.1633	−	11.1633i	−0.412044	−	0.412044i
$735$	6.87424			0.253560
$736$	−17.4568	−	17.4568i	−0.643465	−	0.643465i
$737$	−3.36083	+	3.36083i	−0.123798	+	0.123798i
$738$	29.7730	−	29.7730i	1.09596	−	1.09596i
$739$		−	40.8978i		−	1.50445i	−0.658906	−	0.752225i	$-0.728981\pi$
$739$		−	40.8978i		−	1.50445i	0.658906	−	0.752225i	$-0.271019\pi$
$740$		−	7.25148i		−	0.266570i
$741$	53.4213	−	53.4213i	1.96248	−	1.96248i
$742$	−13.9202	+	13.9202i	−0.511028	+	0.511028i
$743$	36.7853	+	36.7853i	1.34952	+	1.34952i	0.886181	+	0.463339i	$0.153349\pi$
$743$	36.7853	+	36.7853i	1.34952	+	1.34952i	0.463339	+	0.886181i	$0.346651\pi$
$744$	−28.1760			−1.03298
$745$	1.46811	+	1.46811i	0.0537872	+	0.0537872i
$746$			9.66878i			0.353999i
$747$	−79.5622			−2.91103
$748$	−5.79943	+	3.74374i	−0.212048	+	0.136885i
$749$	17.5211			0.640207
$750$			1.93570i			0.0706819i
$751$	2.57255	+	2.57255i	0.0938738	+	0.0938738i	0.752484	−	0.658610i	$-0.228855\pi$
$751$	2.57255	+	2.57255i	0.0938738	+	0.0938738i	−0.658610	+	0.752484i	$0.728855\pi$
$752$	14.4848			0.528205
$753$	−28.4500	−	28.4500i	−1.03678	−	1.03678i
$754$	14.0519	−	14.0519i	0.511740	−	0.511740i
$755$	2.06211	−	2.06211i	0.0750478	−	0.0750478i
$756$			93.8195i			3.41218i
$757$			26.6994i			0.970407i	0.874401	+	0.485203i	$0.161254\pi$
$757$			26.6994i			0.970407i	−0.874401	+	0.485203i	$0.838746\pi$
$758$	11.1382	−	11.1382i	0.404559	−	0.404559i
$759$	10.9174	−	10.9174i	0.396277	−	0.396277i
$760$	6.05343	+	6.05343i	0.219581	+	0.219581i
$761$	−30.3647			−1.10072			−0.550360	−	0.834928i	$-0.685509\pi$
$761$	−30.3647			−1.10072			−0.550360	+	0.834928i	$0.685509\pi$
$762$	11.8939	+	11.8939i	0.430870	+	0.430870i
$763$			18.2693i			0.661394i
$764$	7.08505			0.256328
$765$	29.4445	−	19.0075i	1.06457	−	0.687218i
$766$	−5.20436			−0.188041
$767$		−	69.4490i		−	2.50766i
$768$	−9.99704	−	9.99704i	−0.360737	−	0.360737i
$769$	−17.4255			−0.628380			−0.314190	−	0.949360i	$-0.601733\pi$
$769$	−17.4255			−0.628380			−0.314190	+	0.949360i	$0.601733\pi$
$770$	−1.21268	−	1.21268i	−0.0437021	−	0.0437021i
$771$	−15.4216	+	15.4216i	−0.555395	+	0.555395i
$772$	8.08019	−	8.08019i	0.290812	−	0.290812i
$773$			25.6435i			0.922333i	0.887314	+	0.461166i	$0.152569\pi$
$773$			25.6435i			0.922333i	−0.887314	+	0.461166i	$0.847431\pi$
$774$			7.05235i			0.253491i
$775$	2.80133	−	2.80133i	0.100627	−	0.100627i
$776$	−5.65395	+	5.65395i	−0.202965	+	0.202965i
$777$	−31.2057	−	31.2057i	−1.11950	−	1.11950i
$778$	−12.7357			−0.456599
$779$	25.0484	+	25.0484i	0.897452	+	0.897452i
$780$		−	30.9859i		−	1.10947i
$781$	−0.329719			−0.0117983
$782$	5.81135	+	9.00236i	0.207813	+	0.321924i
$783$	118.978			4.25192
$784$		−	4.36077i		−	0.155742i
$785$	−11.7602	−	11.7602i	−0.419739	−	0.419739i
$786$	30.4060			1.08455
$787$	−16.9747	−	16.9747i	−0.605083	−	0.605083i	0.336574	−	0.941657i	$-0.390732\pi$
$787$	−16.9747	−	16.9747i	−0.605083	−	0.605083i	−0.941657	+	0.336574i	$0.890732\pi$
$788$	−7.20887	+	7.20887i	−0.256806	+	0.256806i
$789$	−48.2410	+	48.2410i	−1.71743	+	1.71743i
$790$			2.70863i			0.0963687i
$791$		−	47.4448i		−	1.68694i
$792$	12.6054	−	12.6054i	0.447913	−	0.447913i
$793$	10.2320	−	10.2320i	0.363349	−	0.363349i
$794$	6.15209	+	6.15209i	0.218330	+	0.218330i
$795$	38.9268			1.38059
$796$	−2.54871	−	2.54871i	−0.0903368	−	0.0903368i
$797$		−	21.2108i		−	0.751326i	−0.926756	−	0.375663i	$-0.877415\pi$
$797$		−	21.2108i		−	0.751326i	0.926756	−	0.375663i	$-0.122585\pi$
$798$	23.7400			0.840385
$799$	−27.1393	−	5.84605i	−0.960119	−	0.206818i
$800$	5.42243			0.191712
$801$		−	80.0521i		−	2.82850i
$802$	−3.12687	−	3.12687i	−0.110414	−	0.110414i
$803$	5.70613			0.201365
$804$	−19.0809	−	19.0809i	−0.672931	−	0.672931i
$805$	9.67261	−	9.67261i	0.340915	−	0.340915i
$806$	8.72701	−	8.72701i	0.307396	−	0.307396i
$807$		−	65.5508i		−	2.30750i
$808$			8.74219i			0.307549i
$809$	−0.315388	+	0.315388i	−0.0110885	+	0.0110885i	−0.712629	−	0.701541i	$-0.752496\pi$
$809$	−0.315388	+	0.315388i	−0.0110885	+	0.0110885i	0.701541	+	0.712629i	$0.252496\pi$
$810$	−15.2370	+	15.2370i	−0.535373	+	0.535373i
$811$	−14.6079	−	14.6079i	−0.512953	−	0.512953i	0.402477	−	0.915430i	$-0.368149\pi$
$811$	−14.6079	−	14.6079i	−0.512953	−	0.512953i	−0.915430	+	0.402477i	$0.868149\pi$
$812$	−32.0867			−1.12602
$813$	46.6751	+	46.6751i	1.63697	+	1.63697i
$814$			2.47237i			0.0866565i
$815$	−9.41897			−0.329932
$816$	−16.3133	−	25.2709i	−0.571080	−	0.884660i
$817$	−5.93322			−0.207577
$818$			5.53394i			0.193490i
$819$	−98.5582	−	98.5582i	−3.44390	−	3.44390i
$820$	14.5288			0.507368
$821$	−0.0632263	−	0.0632263i	−0.00220661	−	0.00220661i	0.706003	−	0.708209i	$-0.250497\pi$
$821$	−0.0632263	−	0.0632263i	−0.00220661	−	0.00220661i	−0.708209	+	0.706003i	$0.750497\pi$
$822$	27.3976	−	27.3976i	0.955600	−	0.955600i
$823$	−32.8578	+	32.8578i	−1.14535	+	1.14535i	−0.157897	+	0.987456i	$0.550471\pi$
$823$	−32.8578	+	32.8578i	−1.14535	+	1.14535i	−0.987456	+	0.157897i	$0.949529\pi$
$824$		−	11.8677i		−	0.413431i
$825$			3.39117i			0.118065i
$826$	15.4313	−	15.4313i	0.536923	−	0.536923i
$827$	−36.1207	+	36.1207i	−1.25604	+	1.25604i	−0.303074	+	0.952967i	$0.598013\pi$
$827$	−36.1207	+	36.1207i	−1.25604	+	1.25604i	−0.952967	+	0.303074i	$0.901987\pi$
$828$	45.8135	+	45.8135i	1.59213	+	1.59213i
$829$	4.39908			0.152786			0.0763932	−	0.997078i	$-0.475660\pi$
$829$	4.39908			0.152786			0.0763932	+	0.997078i	$0.475660\pi$
$830$	3.77798	+	3.77798i	0.131135	+	0.131135i
$831$			6.62499i			0.229818i
$832$	−6.58923			−0.228441
$833$	−1.76000	+	8.17052i	−0.0609805	+	0.283092i
$834$	10.7488			0.372199
$835$		−	6.07735i		−	0.210315i
$836$	4.83231	+	4.83231i	0.167129	+	0.167129i
$837$	73.8918			2.55407
$838$	1.40577	+	1.40577i	0.0485614	+	0.0485614i
$839$	−15.7548	+	15.7548i	−0.543916	+	0.543916i	−0.924675	−	0.380758i	$-0.875663\pi$
$839$	−15.7548	+	15.7548i	−0.543916	+	0.543916i	0.380758	+	0.924675i	$0.375663\pi$
$840$	15.1098	−	15.1098i	0.521337	−	0.521337i
$841$			11.6910i			0.403137i
$842$		−	15.0220i		−	0.517694i
$843$	−76.6463	+	76.6463i	−2.63984	+	2.63984i
$844$	−28.9705	+	28.9705i	−0.997207	+	0.997207i
$845$	11.8701	+	11.8701i	0.408343	+	0.408343i
$846$	32.6688			1.12318
$847$	−2.12451	−	2.12451i	−0.0729991	−	0.0729991i
$848$		−	24.6938i		−	0.847989i
$849$	93.5881			3.21193
$850$	−2.30072	−	0.495596i	−0.0789141	−	0.0169988i
$851$	−19.7201			−0.675996
$852$		−	1.87196i		−	0.0641323i
$853$	−17.1602	−	17.1602i	−0.587554	−	0.587554i	0.349414	−	0.936968i	$-0.386381\pi$
$853$	−17.1602	−	17.1602i	−0.587554	−	0.587554i	−0.936968	+	0.349414i	$0.886381\pi$
$854$	4.54701			0.155595
$855$	−24.5343	−	24.5343i	−0.839056	−	0.839056i
$856$	8.64812	−	8.64812i	0.295587	−	0.295587i
$857$	29.3704	−	29.3704i	1.00327	−	1.00327i	0.00328011	−	0.999995i	$-0.498956\pi$
$857$	29.3704	−	29.3704i	1.00327	−	1.00327i	0.999995	−	0.00328011i	$-0.00104409\pi$
$858$			10.5645i			0.360668i
$859$		−	8.05278i		−	0.274757i	−0.990519	−	0.137379i	$-0.956132\pi$
$859$		−	8.05278i		−	0.274757i	0.990519	−	0.137379i	$-0.0438677\pi$
$860$	−1.72072	+	1.72072i	−0.0586761	+	0.0586761i
$861$	62.5226	−	62.5226i	2.13076	−	2.13076i
$862$	1.29772	+	1.29772i	0.0442006	+	0.0442006i
$863$	−23.0206			−0.783630			−0.391815	−	0.920044i	$-0.628153\pi$
$863$	−23.0206			−0.783630			−0.391815	+	0.920044i	$0.628153\pi$
$864$	71.5148	+	71.5148i	2.43298	+	2.43298i
$865$		−	17.5785i		−	0.597687i
$866$	−20.7513			−0.705157
$867$	20.3660	+	53.9328i	0.691665	+	1.83165i
$868$	−19.9276			−0.676388
$869$			4.74527i			0.160972i
$870$	−8.73118	−	8.73118i	−0.296015	−	0.296015i
$871$	25.9402			0.878951
$872$	9.01742	+	9.01742i	0.305369	+	0.305369i
$873$	22.9152	−	22.9152i	0.775563	−	0.775563i
$874$	7.50111	−	7.50111i	0.253729	−	0.253729i
$875$			3.00451i			0.101571i
$876$			32.3962i			1.09456i
$877$	18.6190	−	18.6190i	0.628719	−	0.628719i	−0.319027	−	0.947746i	$-0.603356\pi$
$877$	18.6190	−	18.6190i	0.628719	−	0.628719i	0.947746	+	0.319027i	$0.103356\pi$
$878$	7.23918	−	7.23918i	0.244310	−	0.244310i
$879$	1.72188	+	1.72188i	0.0580774	+	0.0580774i
$880$	2.15124			0.0725183
$881$	−5.87311	−	5.87311i	−0.197870	−	0.197870i	0.601216	−	0.799086i	$-0.294683\pi$
$881$	−5.87311	−	5.87311i	−0.197870	−	0.197870i	−0.799086	+	0.601216i	$0.794683\pi$
$882$		−	9.83524i		−	0.331170i
$883$	−5.87449			−0.197692			−0.0988462	−	0.995103i	$-0.531515\pi$
$883$	−5.87449			−0.197692			−0.0988462	+	0.995103i	$0.531515\pi$
$884$	36.8290	+	7.93329i	1.23869	+	0.266826i
$885$	−43.1523			−1.45055
$886$		−	4.65676i		−	0.156447i
$887$	9.25898	+	9.25898i	0.310886	+	0.310886i	0.845253	−	0.534367i	$-0.179450\pi$
$887$	9.25898	+	9.25898i	0.310886	+	0.310886i	−0.534367	+	0.845253i	$0.679450\pi$
$888$	−30.8052			−1.03375
$889$	18.4612	+	18.4612i	0.619168	+	0.619168i
$890$	−3.80124	+	3.80124i	−0.127418	+	0.127418i
$891$	−26.6938	+	26.6938i	−0.894276	+	0.894276i
$892$			10.8177i			0.362203i
$893$			27.4847i			0.919739i
$894$	2.84182	−	2.84182i	0.0950446	−	0.0950446i
$895$	15.4165	−	15.4165i	0.515317	−	0.515317i
$896$	−24.5041	−	24.5041i	−0.818626	−	0.818626i
$897$	−84.2649			−2.81352
$898$	3.96124	+	3.96124i	0.132188	+	0.132188i
$899$			25.2714i			0.842847i
$900$	−14.2306			−0.474354
$901$	−9.96640	+	46.2673i	−0.332029	+	1.54139i
$902$	−4.95355			−0.164935
$903$			14.8097i			0.492837i
$904$	−23.4179	−	23.4179i	−0.778869	−	0.778869i
$905$	10.5455			0.350543
$906$	−3.99163	−	3.99163i	−0.132613	−	0.132613i
$907$	6.20585	−	6.20585i	0.206062	−	0.206062i	−0.596529	−	0.802591i	$-0.703454\pi$
$907$	6.20585	−	6.20585i	0.206062	−	0.206062i	0.802591	+	0.596529i	$0.203454\pi$
$908$	16.9305	−	16.9305i	0.561859	−	0.561859i
$909$		−	35.4318i		−	1.17520i
$910$			9.35998i			0.310280i
$911$	9.42234	−	9.42234i	0.312176	−	0.312176i	−0.533576	−	0.845752i	$-0.679152\pi$
$911$	9.42234	−	9.42234i	0.312176	−	0.312176i	0.845752	+	0.533576i	$0.179152\pi$
$912$	−21.0567	+	21.0567i	−0.697258	+	0.697258i
$913$	6.61867	+	6.61867i	0.219046	+	0.219046i
$914$	−14.5462			−0.481145
$915$	−6.35767	−	6.35767i	−0.210178	−	0.210178i
$916$			31.5919i			1.04383i
$917$	47.1949			1.55851
$918$	−23.8072	−	36.8798i	−0.785756	−	1.21721i
$919$	32.5419			1.07346			0.536729	−	0.843755i	$-0.319660\pi$
$919$	32.5419			1.07346			0.536729	+	0.843755i	$0.319660\pi$
$920$		−	9.54847i		−	0.314804i
$921$	15.5805	+	15.5805i	0.513394	+	0.513394i
$922$	4.08534			0.134543
$923$	1.27245	+	1.27245i	0.0418833	+	0.0418833i
$924$	12.0618	−	12.0618i	0.396803	−	0.396803i
$925$	3.06274	−	3.06274i	0.100702	−	0.100702i
$926$			17.9762i			0.590736i
$927$			48.0993i			1.57979i
$928$	−24.4584	+	24.4584i	−0.802887	+	0.802887i
$929$	32.7272	−	32.7272i	1.07374	−	1.07374i	0.0766886	−	0.997055i	$-0.475565\pi$
$929$	32.7272	−	32.7272i	1.07374	−	1.07374i	0.997055	−	0.0766886i	$-0.0244347\pi$
$930$	−5.42255	−	5.42255i	−0.177812	−	0.177812i
$931$	8.27450			0.271186
$932$	−17.8926	−	17.8926i	−0.586091	−	0.586091i
$933$		−	0.892636i		−	0.0292236i
$934$	−9.91029			−0.324275
$935$	−4.03065	−	0.868239i	−0.131816	−	0.0283944i
$936$	−97.2933			−3.18013
$937$		−	42.8436i		−	1.39964i	−0.714319	−	0.699820i	$-0.753263\pi$
$937$		−	42.8436i		−	1.39964i	0.714319	−	0.699820i	$-0.246737\pi$
$938$	5.76381	+	5.76381i	0.188195	+	0.188195i
$939$	−104.546			−3.41173
$940$	7.97095	+	7.97095i	0.259984	+	0.259984i
$941$	6.31563	−	6.31563i	0.205884	−	0.205884i	−0.596632	−	0.802515i	$-0.703495\pi$
$941$	6.31563	−	6.31563i	0.205884	−	0.205884i	0.802515	+	0.596632i	$0.203495\pi$
$942$	−22.7642	+	22.7642i	−0.741698	+	0.741698i
$943$		−	39.5105i		−	1.28664i
$944$			27.3743i			0.890957i
$945$	−39.6256	+	39.6256i	−1.28902	+	1.28902i
$946$	0.586675	−	0.586675i	0.0190744	−	0.0190744i
$947$	3.58846	+	3.58846i	0.116609	+	0.116609i	0.763004	−	0.646394i	$-0.223724\pi$
$947$	3.58846	+	3.58846i	0.116609	+	0.116609i	−0.646394	+	0.763004i	$0.723724\pi$
$948$	−26.9409			−0.875001
$949$	−22.0211	−	22.0211i	−0.714834	−	0.714834i
$950$			2.33000i			0.0755952i
$951$	−12.9070			−0.418538
$952$	14.0905	+	21.8276i	0.456676	+	0.707437i
$953$	5.19585			0.168310			0.0841550	−	0.996453i	$-0.473181\pi$
$953$	5.19585			0.168310			0.0841550	+	0.996453i	$0.473181\pi$
$954$		−	55.6941i		−	1.80316i
$955$	2.99244	+	2.99244i	0.0968332	+	0.0968332i
$956$	−8.86125			−0.286593
$957$	−15.2962	−	15.2962i	−0.494456	−	0.494456i
$958$	2.34781	−	2.34781i	0.0758542	−	0.0758542i
$959$	42.5253	−	42.5253i	1.37321	−	1.37321i
$960$			4.09423i			0.132141i
$961$		−	15.3051i		−	0.493712i
$962$	9.54136	−	9.54136i	0.307626	−	0.307626i
$963$	−35.0505	+	35.0505i	−1.12949	+	1.12949i
$964$	23.1623	+	23.1623i	0.746007	+	0.746007i
$965$	6.82550			0.219721
$966$	−18.7233	−	18.7233i	−0.602412	−	0.602412i
$967$		−	45.3416i		−	1.45809i	−0.684467	−	0.729044i	$-0.739965\pi$
$967$		−	45.3416i		−	1.45809i	0.684467	−	0.729044i	$-0.260035\pi$
$968$	−2.09725			−0.0674080
$969$	47.9512	−	30.9543i	1.54042	−	0.994395i
$970$	−2.17624			−0.0698748
$971$		−	0.829788i		−	0.0266292i	−0.999911	−	0.0133146i	$-0.995762\pi$
$971$		−	0.829788i		−	0.0266292i	0.999911	−	0.0133146i	$-0.00423829\pi$
$972$	−85.3115	−	85.3115i	−2.73637	−	2.73637i
$973$	16.6837			0.534856
$974$	−10.0657	−	10.0657i	−0.322525	−	0.322525i
$975$	13.0872	−	13.0872i	0.419126	−	0.419126i
$976$	−4.03308	+	4.03308i	−0.129096	+	0.129096i
$977$			59.6552i			1.90854i	0.298946	+	0.954270i	$0.403365\pi$
$977$			59.6552i			1.90854i	−0.298946	+	0.954270i	$0.596635\pi$
$978$			18.2323i			0.583006i
$979$	−6.65942	+	6.65942i	−0.212836	+	0.212836i
$980$	2.39973	−	2.39973i	0.0766564	−	0.0766564i
$981$	−36.5473	−	36.5473i	−1.16686	−	1.16686i
$982$	1.61279			0.0514663
$983$	14.4086	+	14.4086i	0.459564	+	0.459564i	0.898512	−	0.438948i	$-0.144649\pi$
$983$	14.4086	+	14.4086i	0.459564	+	0.459564i	−0.438948	+	0.898512i	$0.644649\pi$
$984$		−	61.7201i		−	1.96757i
$985$	−6.08948			−0.194027
$986$	12.6131	−	8.14220i	0.401682	−	0.259300i
$987$	68.6036			2.18368
$988$		−	37.2976i		−	1.18660i
$989$	4.67943	+	4.67943i	0.148797	+	0.148797i
$990$	4.85188			0.154203
$991$	1.19514	+	1.19514i	0.0379647	+	0.0379647i	0.725834	−	0.687870i	$-0.241454\pi$
$991$	1.19514	+	1.19514i	0.0379647	+	0.0379647i	−0.687870	+	0.725834i	$0.741454\pi$
$992$	−15.1900	+	15.1900i	−0.482284	+	0.482284i
$993$	76.9534	−	76.9534i	2.44204	−	2.44204i
$994$			0.565467i			0.0179355i
$995$		−	2.15295i		−	0.0682531i
$996$	−37.5770	+	37.5770i	−1.19067	+	1.19067i
$997$	−29.5756	+	29.5756i	−0.936669	+	0.936669i	−0.998111	−	0.0614415i	$-0.980430\pi$
$997$	−29.5756	+	29.5756i	−0.936669	+	0.936669i	0.0614415	+	0.998111i	$0.480430\pi$
$998$	10.1092	+	10.1092i	0.320001	+	0.320001i
$999$	80.7870			2.55599

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	935.2.i.b.166.16	✓	68
17.4	even	4	inner	935.2.i.b.276.19	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
935.2.i.b.166.16	✓	68	1.1	even	1	trivial
935.2.i.b.276.19	yes	68	17.4	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 935 = 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	935.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.570806i q^{2} +(2.39792 + 2.39792i) q^{3} +1.67418 q^{4} +(0.707107 + 0.707107i) q^{5} +(1.36875 - 1.36875i) q^{6} +(2.12451 - 2.12451i) q^{7} -2.09725i q^{8} +8.50005i q^{9} +O(q^{10})\)	\(q-0.570806i q^{2} +(2.39792 + 2.39792i) q^{3} +1.67418 q^{4} +(0.707107 + 0.707107i) q^{5} +(1.36875 - 1.36875i) q^{6} +(2.12451 - 2.12451i) q^{7} -2.09725i q^{8} +8.50005i q^{9} +(0.403621 - 0.403621i) q^{10} +(0.707107 - 0.707107i) q^{11} +(4.01455 + 4.01455i) q^{12} -5.45773 q^{13} +(-1.21268 - 1.21268i) q^{14} +3.39117i q^{15} +2.15124 q^{16} +(-4.03065 - 0.868239i) q^{17} +4.85188 q^{18} +4.08195i q^{19} +(1.18382 + 1.18382i) q^{20} +10.1888 q^{21} +(-0.403621 - 0.403621i) q^{22} +(3.21936 - 3.21936i) q^{23} +(5.02903 - 5.02903i) q^{24} +1.00000i q^{25} +3.11531i q^{26} +(-13.1887 + 13.1887i) q^{27} +(3.55681 - 3.55681i) q^{28} +(-4.51060 - 4.51060i) q^{29} +1.93570 q^{30} +(-2.80133 - 2.80133i) q^{31} -5.42243i q^{32} +3.39117 q^{33} +(-0.495596 + 2.30072i) q^{34} +3.00451 q^{35} +14.2306i q^{36} +(-3.06274 - 3.06274i) q^{37} +2.33000 q^{38} +(-13.0872 - 13.0872i) q^{39} +(1.48298 - 1.48298i) q^{40} +(6.13639 - 6.13639i) q^{41} -5.81584i q^{42} +1.45353i q^{43} +(1.18382 - 1.18382i) q^{44} +(-6.01044 + 6.01044i) q^{45} +(-1.83763 - 1.83763i) q^{46} +6.73322 q^{47} +(5.15850 + 5.15850i) q^{48} -2.02710i q^{49} +0.570806 q^{50} +(-7.58322 - 11.7472i) q^{51} -9.13722 q^{52} -11.4789i q^{53} +(7.52819 + 7.52819i) q^{54} +1.00000 q^{55} +(-4.45562 - 4.45562i) q^{56} +(-9.78818 + 9.78818i) q^{57} +(-2.57468 + 2.57468i) q^{58} +12.7249i q^{59} +5.67743i q^{60} +(-1.87477 + 1.87477i) q^{61} +(-1.59902 + 1.59902i) q^{62} +(18.0585 + 18.0585i) q^{63} +1.20732 q^{64} +(-3.85920 - 3.85920i) q^{65} -1.93570i q^{66} -4.75293 q^{67} +(-6.74804 - 1.45359i) q^{68} +15.4395 q^{69} -1.71499i q^{70} +(-0.233147 - 0.233147i) q^{71} +17.8267 q^{72} +(4.03484 + 4.03484i) q^{73} +(-1.74823 + 1.74823i) q^{74} +(-2.39792 + 2.39792i) q^{75} +6.83391i q^{76} -3.00451i q^{77} +(-7.47026 + 7.47026i) q^{78} +(-3.35541 + 3.35541i) q^{79} +(1.52116 + 1.52116i) q^{80} -37.7507 q^{81} +(-3.50269 - 3.50269i) q^{82} +9.36021i q^{83} +17.0579 q^{84} +(-2.23616 - 3.46404i) q^{85} +0.829683 q^{86} -21.6321i q^{87} +(-1.48298 - 1.48298i) q^{88} -9.41784 q^{89} +(3.43080 + 3.43080i) q^{90} +(-11.5950 + 11.5950i) q^{91} +(5.38979 - 5.38979i) q^{92} -13.4347i q^{93} -3.84337i q^{94} +(-2.88637 + 2.88637i) q^{95} +(13.0026 - 13.0026i) q^{96} +(-2.69589 - 2.69589i) q^{97} -1.15708 q^{98} +(6.01044 + 6.01044i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 76 q^{4} - 4 q^{6}+O(q^{10}) \) 68 * q - 76 * q^4 - 4 * q^6	\( 68 q - 76 q^{4} - 4 q^{6} + 4 q^{10} + 20 q^{12} - 16 q^{13} + 20 q^{14} + 100 q^{16} - 8 q^{17} + 64 q^{18} - 32 q^{21} - 4 q^{22} + 4 q^{23} - 16 q^{24} + 24 q^{27} + 20 q^{28} + 28 q^{31} - 72 q^{34} + 20 q^{35} - 28 q^{37} - 24 q^{38} - 8 q^{39} + 8 q^{40} + 4 q^{41} - 8 q^{45} - 16 q^{46} + 4 q^{47} + 56 q^{48} + 12 q^{50} - 88 q^{51} + 124 q^{52} - 124 q^{54} + 68 q^{55} - 136 q^{56} + 28 q^{57} + 4 q^{58} + 16 q^{61} - 28 q^{62} + 36 q^{63} - 188 q^{64} + 52 q^{67} - 40 q^{68} + 160 q^{69} - 20 q^{71} - 164 q^{72} - 56 q^{73} - 64 q^{74} + 200 q^{78} - 180 q^{81} + 108 q^{82} + 152 q^{84} - 4 q^{85} + 296 q^{86} - 8 q^{88} - 180 q^{89} - 96 q^{91} - 48 q^{92} + 12 q^{95} + 104 q^{96} + 24 q^{97} - 180 q^{98} + 8 q^{99}+O(q^{100}) \) 68 * q - 76 * q^4 - 4 * q^6 + 4 * q^10 + 20 * q^12 - 16 * q^13 + 20 * q^14 + 100 * q^16 - 8 * q^17 + 64 * q^18 - 32 * q^21 - 4 * q^22 + 4 * q^23 - 16 * q^24 + 24 * q^27 + 20 * q^28 + 28 * q^31 - 72 * q^34 + 20 * q^35 - 28 * q^37 - 24 * q^38 - 8 * q^39 + 8 * q^40 + 4 * q^41 - 8 * q^45 - 16 * q^46 + 4 * q^47 + 56 * q^48 + 12 * q^50 - 88 * q^51 + 124 * q^52 - 124 * q^54 + 68 * q^55 - 136 * q^56 + 28 * q^57 + 4 * q^58 + 16 * q^61 - 28 * q^62 + 36 * q^63 - 188 * q^64 + 52 * q^67 - 40 * q^68 + 160 * q^69 - 20 * q^71 - 164 * q^72 - 56 * q^73 - 64 * q^74 + 200 * q^78 - 180 * q^81 + 108 * q^82 + 152 * q^84 - 4 * q^85 + 296 * q^86 - 8 * q^88 - 180 * q^89 - 96 * q^91 - 48 * q^92 + 12 * q^95 + 104 * q^96 + 24 * q^97 - 180 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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