LMFDB - Embedded newform 91.2.e.b.53.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(53,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("91.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.e (of order $3$, 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:	$0.726638658394$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			53.1
Root			$-0.309017 - 0.535233i$ of defining polynomial
Character	$\chi$	$=$	91.53
Dual form			91.2.e.b.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.190983 + 0.330792i) q^{2} +(-1.11803 + 1.93649i) q^{3} +(0.927051 - 1.60570i) q^{4} +(1.11803 + 1.93649i) q^{5} -0.854102 q^{6} +(-2.00000 + 1.73205i) q^{7} +1.47214 q^{8} +(-1.00000 - 1.73205i) q^{9} +O(q^{10})$	\(q+(0.190983 + 0.330792i) q^{2} +(-1.11803 + 1.93649i) q^{3} +(0.927051 - 1.60570i) q^{4} +(1.11803 + 1.93649i) q^{5} -0.854102 q^{6} +(-2.00000 + 1.73205i) q^{7} +1.47214 q^{8} +(-1.00000 - 1.73205i) q^{9} +(-0.427051 + 0.739674i) q^{10} +(1.50000 - 2.59808i) q^{11} +(2.07295 + 3.59045i) q^{12} -1.00000 q^{13} +(-0.954915 - 0.330792i) q^{14} -5.00000 q^{15} +(-1.57295 - 2.72443i) q^{16} +(3.73607 - 6.47106i) q^{17} +(0.381966 - 0.661585i) q^{18} +(-1.50000 - 2.59808i) q^{19} +4.14590 q^{20} +(-1.11803 - 5.80948i) q^{21} +1.14590 q^{22} +(1.88197 + 3.25966i) q^{23} +(-1.64590 + 2.85078i) q^{24} +(-0.190983 - 0.330792i) q^{26} -2.23607 q^{27} +(0.927051 + 4.81710i) q^{28} -4.47214 q^{29} +(-0.954915 - 1.65396i) q^{30} +(-2.50000 + 4.33013i) q^{31} +(2.07295 - 3.59045i) q^{32} +(3.35410 + 5.80948i) q^{33} +2.85410 q^{34} +(-5.59017 - 1.93649i) q^{35} -3.70820 q^{36} +(4.35410 + 7.54153i) q^{37} +(0.572949 - 0.992377i) q^{38} +(1.11803 - 1.93649i) q^{39} +(1.64590 + 2.85078i) q^{40} +4.47214 q^{41} +(1.70820 - 1.47935i) q^{42} -8.00000 q^{43} +(-2.78115 - 4.81710i) q^{44} +(2.23607 - 3.87298i) q^{45} +(-0.718847 + 1.24508i) q^{46} +(-0.736068 - 1.27491i) q^{47} +7.03444 q^{48} +(1.00000 - 6.92820i) q^{49} +(8.35410 + 14.4697i) q^{51} +(-0.927051 + 1.60570i) q^{52} +(-0.736068 + 1.27491i) q^{53} +(-0.427051 - 0.739674i) q^{54} +6.70820 q^{55} +(-2.94427 + 2.54981i) q^{56} +6.70820 q^{57} +(-0.854102 - 1.47935i) q^{58} +(-3.73607 + 6.47106i) q^{59} +(-4.63525 + 8.02850i) q^{60} +(-1.50000 - 2.59808i) q^{61} -1.90983 q^{62} +(5.00000 + 1.73205i) q^{63} -4.70820 q^{64} +(-1.11803 - 1.93649i) q^{65} +(-1.28115 + 2.21902i) q^{66} +(1.50000 - 2.59808i) q^{67} +(-6.92705 - 11.9980i) q^{68} -8.41641 q^{69} +(-0.427051 - 2.21902i) q^{70} +8.94427 q^{71} +(-1.47214 - 2.54981i) q^{72} +(-5.35410 + 9.27358i) q^{73} +(-1.66312 + 2.88061i) q^{74} -5.56231 q^{76} +(1.50000 + 7.79423i) q^{77} +0.854102 q^{78} +(-5.35410 - 9.27358i) q^{79} +(3.51722 - 6.09201i) q^{80} +(5.50000 - 9.52628i) q^{81} +(0.854102 + 1.47935i) q^{82} +(-10.3647 - 3.59045i) q^{84} +16.7082 q^{85} +(-1.52786 - 2.64634i) q^{86} +(5.00000 - 8.66025i) q^{87} +(2.20820 - 3.82472i) q^{88} +(1.11803 + 1.93649i) q^{89} +1.70820 q^{90} +(2.00000 - 1.73205i) q^{91} +6.97871 q^{92} +(-5.59017 - 9.68246i) q^{93} +(0.281153 - 0.486971i) q^{94} +(3.35410 - 5.80948i) q^{95} +(4.63525 + 8.02850i) q^{96} -17.4164 q^{97} +(2.48278 - 0.992377i) q^{98} -6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} - 3 q^{4} + 10 q^{6} - 8 q^{7} - 12 q^{8} - 4 q^{9}+O(q^{10}) $ 4 * q + 3 * q^2 - 3 * q^4 + 10 * q^6 - 8 * q^7 - 12 * q^8 - 4 * q^9	$ 4 q + 3 q^{2} - 3 q^{4} + 10 q^{6} - 8 q^{7} - 12 q^{8} - 4 q^{9} + 5 q^{10} + 6 q^{11} + 15 q^{12} - 4 q^{13} - 15 q^{14} - 20 q^{15} - 13 q^{16} + 6 q^{17} + 6 q^{18} - 6 q^{19} + 30 q^{20} + 18 q^{22} + 12 q^{23} - 20 q^{24} - 3 q^{26} - 3 q^{28} - 15 q^{30} - 10 q^{31} + 15 q^{32} - 2 q^{34} + 12 q^{36} + 4 q^{37} + 9 q^{38} + 20 q^{40} - 20 q^{42} - 32 q^{43} + 9 q^{44} - 23 q^{46} + 6 q^{47} - 30 q^{48} + 4 q^{49} + 20 q^{51} + 3 q^{52} + 6 q^{53} + 5 q^{54} + 24 q^{56} + 10 q^{58} - 6 q^{59} + 15 q^{60} - 6 q^{61} - 30 q^{62} + 20 q^{63} + 8 q^{64} + 15 q^{66} + 6 q^{67} - 21 q^{68} + 20 q^{69} + 5 q^{70} + 12 q^{72} - 8 q^{73} + 9 q^{74} + 18 q^{76} + 6 q^{77} - 10 q^{78} - 8 q^{79} - 15 q^{80} + 22 q^{81} - 10 q^{82} - 75 q^{84} + 40 q^{85} - 24 q^{86} + 20 q^{87} - 18 q^{88} - 20 q^{90} + 8 q^{91} - 66 q^{92} - 19 q^{94} - 15 q^{96} - 16 q^{97} + 39 q^{98} - 24 q^{99}+O(q^{100}) $ 4 * q + 3 * q^2 - 3 * q^4 + 10 * q^6 - 8 * q^7 - 12 * q^8 - 4 * q^9 + 5 * q^10 + 6 * q^11 + 15 * q^12 - 4 * q^13 - 15 * q^14 - 20 * q^15 - 13 * q^16 + 6 * q^17 + 6 * q^18 - 6 * q^19 + 30 * q^20 + 18 * q^22 + 12 * q^23 - 20 * q^24 - 3 * q^26 - 3 * q^28 - 15 * q^30 - 10 * q^31 + 15 * q^32 - 2 * q^34 + 12 * q^36 + 4 * q^37 + 9 * q^38 + 20 * q^40 - 20 * q^42 - 32 * q^43 + 9 * q^44 - 23 * q^46 + 6 * q^47 - 30 * q^48 + 4 * q^49 + 20 * q^51 + 3 * q^52 + 6 * q^53 + 5 * q^54 + 24 * q^56 + 10 * q^58 - 6 * q^59 + 15 * q^60 - 6 * q^61 - 30 * q^62 + 20 * q^63 + 8 * q^64 + 15 * q^66 + 6 * q^67 - 21 * q^68 + 20 * q^69 + 5 * q^70 + 12 * q^72 - 8 * q^73 + 9 * q^74 + 18 * q^76 + 6 * q^77 - 10 * q^78 - 8 * q^79 - 15 * q^80 + 22 * q^81 - 10 * q^82 - 75 * q^84 + 40 * q^85 - 24 * q^86 + 20 * q^87 - 18 * q^88 - 20 * q^90 + 8 * q^91 - 66 * q^92 - 19 * q^94 - 15 * q^96 - 16 * q^97 + 39 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.190983	+	0.330792i	0.135045	+	0.233905i	0.925615	−	0.378467i	$-0.123549\pi$
$2$	0.190983	+	0.330792i	0.135045	+	0.233905i	−0.790569	+	0.612372i	$0.790215\pi$
$3$	−1.11803	+	1.93649i	−0.645497	+	1.11803i	0.338689	+	0.940898i	$0.390016\pi$
$3$	−1.11803	+	1.93649i	−0.645497	+	1.11803i	−0.984186	+	0.177136i	$0.943317\pi$
$4$	0.927051	−	1.60570i	0.463525	−	0.802850i
$5$	1.11803	+	1.93649i	0.500000	+	0.866025i	1.00000			$0$
$5$	1.11803	+	1.93649i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$6$	−0.854102			−0.348686
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$8$	1.47214			0.520479
$9$	−1.00000	−	1.73205i	−0.333333	−	0.577350i
$10$	−0.427051	+	0.739674i	−0.135045	+	0.233905i
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$	2.07295	+	3.59045i	0.598409	+	1.03647i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	−0.954915	−	0.330792i	−0.255212	−	0.0884080i
$15$	−5.00000			−1.29099
$16$	−1.57295	−	2.72443i	−0.393237	−	0.681107i
$17$	3.73607	−	6.47106i	0.906130	−	1.56946i	0.0867359	−	0.996231i	$-0.472356\pi$
$17$	3.73607	−	6.47106i	0.906130	−	1.56946i	0.819394	−	0.573231i	$-0.194310\pi$
$18$	0.381966	−	0.661585i	0.0900303	−	0.155937i
$19$	−1.50000	−	2.59808i	−0.344124	−	0.596040i	0.641071	−	0.767482i	$-0.278491\pi$
$19$	−1.50000	−	2.59808i	−0.344124	−	0.596040i	−0.985194	+	0.171442i	$0.945157\pi$
$20$	4.14590			0.927051
$21$	−1.11803	−	5.80948i	−0.243975	−	1.26773i
$22$	1.14590			0.244306
$23$	1.88197	+	3.25966i	0.392417	+	0.679686i	0.992768	−	0.120051i	$-0.0383057\pi$
$23$	1.88197	+	3.25966i	0.392417	+	0.679686i	−0.600351	+	0.799737i	$0.704972\pi$
$24$	−1.64590	+	2.85078i	−0.335968	+	0.581913i
$25$		0			0
$26$	−0.190983	−	0.330792i	−0.0374548	−	0.0648737i
$27$	−2.23607			−0.430331
$28$	0.927051	+	4.81710i	0.175196	+	0.910346i
$29$	−4.47214			−0.830455			−0.415227	−	0.909718i	$-0.636298\pi$
$29$	−4.47214			−0.830455			−0.415227	+	0.909718i	$0.636298\pi$
$30$	−0.954915	−	1.65396i	−0.174343	−	0.301971i
$31$	−2.50000	+	4.33013i	−0.449013	+	0.777714i	−0.998322	−	0.0579057i	$-0.981558\pi$
$31$	−2.50000	+	4.33013i	−0.449013	+	0.777714i	0.549309	+	0.835619i	$0.314891\pi$
$32$	2.07295	−	3.59045i	0.366449	−	0.634708i
$33$	3.35410	+	5.80948i	0.583874	+	1.01130i
$34$	2.85410			0.489474
$35$	−5.59017	−	1.93649i	−0.944911	−	0.327327i
$36$	−3.70820			−0.618034
$37$	4.35410	+	7.54153i	0.715810	+	1.23982i	0.962646	+	0.270762i	$0.0872757\pi$
$37$	4.35410	+	7.54153i	0.715810	+	1.23982i	−0.246836	+	0.969057i	$0.579391\pi$
$38$	0.572949	−	0.992377i	0.0929446	−	0.160985i
$39$	1.11803	−	1.93649i	0.179029	−	0.310087i
$40$	1.64590	+	2.85078i	0.260239	+	0.450748i
$41$	4.47214			0.698430			0.349215	−	0.937043i	$-0.386448\pi$
$41$	4.47214			0.698430			0.349215	+	0.937043i	$0.386448\pi$
$42$	1.70820	−	1.47935i	0.263582	−	0.228268i
$43$	−8.00000			−1.21999			−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000			−1.21999			−0.609994	+	0.792406i	$0.708828\pi$
$44$	−2.78115	−	4.81710i	−0.419275	−	0.726205i
$45$	2.23607	−	3.87298i	0.333333	−	0.577350i
$46$	−0.718847	+	1.24508i	−0.105988	+	0.183577i
$47$	−0.736068	−	1.27491i	−0.107367	−	0.185964i	0.807336	−	0.590092i	$-0.200909\pi$
$47$	−0.736068	−	1.27491i	−0.107367	−	0.185964i	−0.914703	+	0.404128i	$0.867575\pi$
$48$	7.03444			1.01533
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$		0			0
$51$	8.35410	+	14.4697i	1.16981	+	2.02617i
$52$	−0.927051	+	1.60570i	−0.128559	+	0.222670i
$53$	−0.736068	+	1.27491i	−0.101107	+	0.175122i	−0.912141	−	0.409877i	$-0.865572\pi$
$53$	−0.736068	+	1.27491i	−0.101107	+	0.175122i	0.811034	+	0.584999i	$0.198905\pi$
$54$	−0.427051	−	0.739674i	−0.0581143	−	0.100657i
$55$	6.70820			0.904534
$56$	−2.94427	+	2.54981i	−0.393445	+	0.340733i
$57$	6.70820			0.888523
$58$	−0.854102	−	1.47935i	−0.112149	−	0.194248i
$59$	−3.73607	+	6.47106i	−0.486395	+	0.842460i	−0.999878	−	0.0156395i	$-0.995022\pi$
$59$	−3.73607	+	6.47106i	−0.486395	+	0.842460i	0.513483	+	0.858100i	$0.328355\pi$
$60$	−4.63525	+	8.02850i	−0.598409	+	1.03647i
$61$	−1.50000	−	2.59808i	−0.192055	−	0.332650i	0.753876	−	0.657017i	$-0.228182\pi$
$61$	−1.50000	−	2.59808i	−0.192055	−	0.332650i	−0.945931	+	0.324367i	$0.894849\pi$
$62$	−1.90983			−0.242549
$63$	5.00000	+	1.73205i	0.629941	+	0.218218i
$64$	−4.70820			−0.588525
$65$	−1.11803	−	1.93649i	−0.138675	−	0.240192i
$66$	−1.28115	+	2.21902i	−0.157699	+	0.273143i
$67$	1.50000	−	2.59808i	0.183254	−	0.317406i	−0.759733	−	0.650236i	$-0.774670\pi$
$67$	1.50000	−	2.59808i	0.183254	−	0.317406i	0.942987	+	0.332830i	$0.108004\pi$
$68$	−6.92705	−	11.9980i	−0.840028	−	1.45497i
$69$	−8.41641			−1.01322
$70$	−0.427051	−	2.21902i	−0.0510424	−	0.265224i
$71$	8.94427			1.06149			0.530745	−	0.847532i	$-0.321912\pi$
$71$	8.94427			1.06149			0.530745	+	0.847532i	$0.321912\pi$
$72$	−1.47214	−	2.54981i	−0.173493	−	0.300498i
$73$	−5.35410	+	9.27358i	−0.626650	+	1.08539i	0.361569	+	0.932345i	$0.382241\pi$
$73$	−5.35410	+	9.27358i	−0.626650	+	1.08539i	−0.988219	+	0.153045i	$0.951092\pi$
$74$	−1.66312	+	2.88061i	−0.193334	+	0.334864i
$75$		0			0
$76$	−5.56231			−0.638040
$77$	1.50000	+	7.79423i	0.170941	+	0.888235i
$78$	0.854102			0.0967080
$79$	−5.35410	−	9.27358i	−0.602384	−	1.04336i	−0.992459	−	0.122576i	$-0.960884\pi$
$79$	−5.35410	−	9.27358i	−0.602384	−	1.04336i	0.390076	−	0.920783i	$-0.372449\pi$
$80$	3.51722	−	6.09201i	0.393237	−	0.681107i
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$	0.854102	+	1.47935i	0.0943198	+	0.163367i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$	−10.3647	−	3.59045i	−1.13089	−	0.391751i
$85$	16.7082			1.81226
$86$	−1.52786	−	2.64634i	−0.164754	−	0.285362i
$87$	5.00000	−	8.66025i	0.536056	−	0.928477i
$88$	2.20820	−	3.82472i	0.235395	−	0.407717i
$89$	1.11803	+	1.93649i	0.118511	+	0.205268i	0.919178	−	0.393842i	$-0.128854\pi$
$89$	1.11803	+	1.93649i	0.118511	+	0.205268i	−0.800667	+	0.599110i	$0.795521\pi$
$90$	1.70820			0.180061
$91$	2.00000	−	1.73205i	0.209657	−	0.181568i
$92$	6.97871			0.727581
$93$	−5.59017	−	9.68246i	−0.579674	−	1.00402i
$94$	0.281153	−	0.486971i	0.0289987	−	0.0502272i
$95$	3.35410	−	5.80948i	0.344124	−	0.596040i
$96$	4.63525	+	8.02850i	0.473084	+	0.819405i
$97$	−17.4164			−1.76837			−0.884184	−	0.467139i	$-0.845285\pi$
$97$	−17.4164			−1.76837			−0.884184	+	0.467139i	$0.845285\pi$
$98$	2.48278	−	0.992377i	0.250799	−	0.100245i
$99$	−6.00000			−0.603023
$100$		0			0
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	−0.550474	−	0.834853i	$-0.685553\pi$
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	0.998240	+	0.0592978i	$0.0188862\pi$
$102$	−3.19098	+	5.52694i	−0.315954	+	0.547249i
$103$	−5.35410	−	9.27358i	−0.527555	−	0.913753i	−0.999484	−	0.0321160i	$-0.989775\pi$
$103$	−5.35410	−	9.27358i	−0.527555	−	0.913753i	0.471929	−	0.881637i	$-0.343558\pi$
$104$	−1.47214			−0.144355
$105$	10.0000	−	8.66025i	0.975900	−	0.845154i
$106$	−0.562306			−0.0546160
$107$	7.11803	+	12.3288i	0.688126	+	1.19187i	0.972443	+	0.233139i	$0.0748999\pi$
$107$	7.11803	+	12.3288i	0.688126	+	1.19187i	−0.284317	+	0.958730i	$0.591767\pi$
$108$	−2.07295	+	3.59045i	−0.199470	+	0.345492i
$109$	−5.35410	+	9.27358i	−0.512830	+	0.888248i	0.487059	+	0.873369i	$0.338070\pi$
$109$	−5.35410	+	9.27358i	−0.512830	+	0.888248i	−0.999889	+	0.0148787i	$0.995264\pi$
$110$	1.28115	+	2.21902i	0.122153	+	0.211575i
$111$	−19.4721			−1.84821
$112$	7.86475	+	2.72443i	0.743149	+	0.257434i
$113$	−14.9443			−1.40584			−0.702919	−	0.711269i	$-0.748121\pi$
$113$	−14.9443			−1.40584			−0.702919	+	0.711269i	$0.748121\pi$
$114$	1.28115	+	2.21902i	0.119991	+	0.207830i
$115$	−4.20820	+	7.28882i	−0.392417	+	0.679686i
$116$	−4.14590	+	7.18091i	−0.384937	+	0.666730i
$117$	1.00000	+	1.73205i	0.0924500	+	0.160128i
$118$	−2.85410			−0.262741
$119$	3.73607	+	19.4132i	0.342485	+	1.77960i
$120$	−7.36068			−0.671935
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	0.572949	−	0.992377i	0.0518724	−	0.0898456i
$123$	−5.00000	+	8.66025i	−0.450835	+	0.780869i
$124$	4.63525	+	8.02850i	0.416258	+	0.720980i
$125$	11.1803			1.00000
$126$	0.381966	+	1.98475i	0.0340282	+	0.176816i
$127$	15.4164			1.36798			0.683992	−	0.729489i	$-0.260242\pi$
$127$	15.4164			1.36798			0.683992	+	0.729489i	$0.260242\pi$
$128$	−5.04508	−	8.73834i	−0.445927	−	0.772368i
$129$	8.94427	−	15.4919i	0.787499	−	1.36399i
$130$	0.427051	−	0.739674i	0.0374548	−	0.0648737i
$131$	1.88197	+	3.25966i	0.164428	+	0.284798i	0.936452	−	0.350796i	$-0.114089\pi$
$131$	1.88197	+	3.25966i	0.164428	+	0.284798i	−0.772024	+	0.635593i	$0.780755\pi$
$132$	12.4377			1.08256
$133$	7.50000	+	2.59808i	0.650332	+	0.225282i
$134$	1.14590			0.0989905
$135$	−2.50000	−	4.33013i	−0.215166	−	0.372678i
$136$	5.50000	−	9.52628i	0.471621	−	0.816872i
$137$	1.88197	−	3.25966i	0.160787	−	0.278492i	−0.774364	−	0.632740i	$-0.781930\pi$
$137$	1.88197	−	3.25966i	0.160787	−	0.278492i	0.935151	+	0.354249i	$0.115263\pi$
$138$	−1.60739	−	2.78408i	−0.136830	−	0.236997i
$139$	3.41641			0.289776			0.144888	−	0.989448i	$-0.453718\pi$
$139$	3.41641			0.289776			0.144888	+	0.989448i	$0.453718\pi$
$140$	−8.29180	+	7.18091i	−0.700785	+	0.606897i
$141$	3.29180			0.277219
$142$	1.70820	+	2.95870i	0.143349	+	0.248288i
$143$	−1.50000	+	2.59808i	−0.125436	+	0.217262i
$144$	−3.14590	+	5.44886i	−0.262158	+	0.454071i
$145$	−5.00000	−	8.66025i	−0.415227	−	0.719195i
$146$	−4.09017			−0.338505
$147$	12.2984	+	9.68246i	1.01435	+	0.798596i
$148$	16.1459			1.32718
$149$	6.35410	+	11.0056i	0.520548	+	0.901616i	0.999715	+	0.0238920i	$0.00760577\pi$
$149$	6.35410	+	11.0056i	0.520548	+	0.901616i	−0.479166	+	0.877724i	$0.659061\pi$
$150$		0			0
$151$	3.20820	−	5.55677i	0.261080	−	0.452204i	−0.705449	−	0.708760i	$-0.749255\pi$
$151$	3.20820	−	5.55677i	0.261080	−	0.452204i	0.966529	+	0.256557i	$0.0825880\pi$
$152$	−2.20820	−	3.82472i	−0.179109	−	0.310226i
$153$	−14.9443			−1.20817
$154$	−2.29180	+	1.98475i	−0.184678	+	0.159936i
$155$	−11.1803			−0.898027
$156$	−2.07295	−	3.59045i	−0.165969	−	0.287466i
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	−0.971219	−	0.238190i	$-0.923446\pi$
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	0.691888	+	0.722005i	$0.256779\pi$
$158$	2.04508	−	3.54219i	0.162698	−	0.281802i
$159$	−1.64590	−	2.85078i	−0.130528	−	0.226081i
$160$	9.27051			0.732898
$161$	−9.40983	−	3.25966i	−0.741598	−	0.256897i
$162$	4.20163			0.330111
$163$	−5.20820	−	9.02087i	−0.407938	−	0.706569i	0.586721	−	0.809789i	$-0.300419\pi$
$163$	−5.20820	−	9.02087i	−0.407938	−	0.706569i	−0.994659	+	0.103220i	$0.967085\pi$
$164$	4.14590	−	7.18091i	0.323740	−	0.560735i
$165$	−7.50000	+	12.9904i	−0.583874	+	1.01130i
$166$		0			0
$167$	13.5279			1.04682			0.523409	−	0.852082i	$-0.324660\pi$
$167$	13.5279			1.04682			0.523409	+	0.852082i	$0.324660\pi$
$168$	−1.64590	−	8.55234i	−0.126984	−	0.659827i
$169$	1.00000			0.0769231
$170$	3.19098	+	5.52694i	0.244737	+	0.423897i
$171$	−3.00000	+	5.19615i	−0.229416	+	0.397360i
$172$	−7.41641	+	12.8456i	−0.565496	+	0.979467i
$173$	−5.20820	−	9.02087i	−0.395972	−	0.685844i	0.597252	−	0.802053i	$-0.296259\pi$
$173$	−5.20820	−	9.02087i	−0.395972	−	0.685844i	−0.993225	+	0.116209i	$0.962926\pi$
$174$	3.81966			0.289568
$175$		0			0
$176$	−9.43769			−0.711393
$177$	−8.35410	−	14.4697i	−0.627933	−	1.08761i
$178$	−0.427051	+	0.739674i	−0.0320088	+	0.0554409i
$179$	−10.0623	+	17.4284i	−0.752092	+	1.30266i	0.194715	+	0.980860i	$0.437622\pi$
$179$	−10.0623	+	17.4284i	−0.752092	+	1.30266i	−0.946807	+	0.321802i	$0.895712\pi$
$180$	−4.14590	−	7.18091i	−0.309017	−	0.535233i
$181$	1.41641			0.105281			0.0526404	−	0.998614i	$-0.483236\pi$
$181$	1.41641			0.105281			0.0526404	+	0.998614i	$0.483236\pi$
$182$	0.954915	+	0.330792i	0.0707830	+	0.0245200i
$183$	6.70820			0.495885
$184$	2.77051	+	4.79866i	0.204245	+	0.353762i
$185$	−9.73607	+	16.8634i	−0.715810	+	1.23982i
$186$	2.13525	−	3.69837i	0.156564	−	0.271178i
$187$	−11.2082	−	19.4132i	−0.819625	−	1.41963i
$188$	−2.72949			−0.199069
$189$	4.47214	−	3.87298i	0.325300	−	0.281718i
$190$	2.56231			0.185889
$191$	5.59017	+	9.68246i	0.404491	+	0.700598i	0.994262	−	0.106972i	$-0.0341155\pi$
$191$	5.59017	+	9.68246i	0.404491	+	0.700598i	−0.589772	+	0.807570i	$0.700782\pi$
$192$	5.26393	−	9.11740i	0.379892	−	0.657992i
$193$	6.35410	−	11.0056i	0.457378	−	0.792202i	−0.541443	−	0.840737i	$-0.682122\pi$
$193$	6.35410	−	11.0056i	0.457378	−	0.792202i	0.998821	+	0.0485349i	$0.0154552\pi$
$194$	−3.32624	−	5.76121i	−0.238810	−	0.413631i
$195$	5.00000			0.358057
$196$	−10.1976	−	8.02850i	−0.728397	−	0.573464i
$197$	−26.9443			−1.91970			−0.959850	−	0.280514i	$-0.909495\pi$
$197$	−26.9443			−1.91970			−0.959850	+	0.280514i	$0.909495\pi$
$198$	−1.14590	−	1.98475i	−0.0814354	−	0.141050i
$199$	3.64590	−	6.31488i	0.258451	−	0.447650i	−0.707376	−	0.706837i	$-0.750121\pi$
$199$	3.64590	−	6.31488i	0.258451	−	0.447650i	0.965827	+	0.259187i	$0.0834547\pi$
$200$		0			0
$201$	3.35410	+	5.80948i	0.236580	+	0.409769i
$202$	3.43769			0.241875
$203$	8.94427	−	7.74597i	0.627765	−	0.543660i
$204$	30.9787			2.16894
$205$	5.00000	+	8.66025i	0.349215	+	0.604858i
$206$	2.04508	−	3.54219i	0.142488	−	0.246796i
$207$	3.76393	−	6.51932i	0.261611	−	0.453124i
$208$	1.57295	+	2.72443i	0.109064	+	0.188905i
$209$	−9.00000			−0.622543
$210$	4.77458	+	1.65396i	0.329477	+	0.114134i
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$	1.36475	+	2.36381i	0.0937311	+	0.162347i
$213$	−10.0000	+	17.3205i	−0.685189	+	1.18678i
$214$	−2.71885	+	4.70918i	−0.185857	+	0.321913i
$215$	−8.94427	−	15.4919i	−0.609994	−	1.05654i
$216$	−3.29180			−0.223978
$217$	−2.50000	−	12.9904i	−0.169711	−	0.881845i
$218$	−4.09017			−0.277021
$219$	−11.9721	−	20.7363i	−0.809002	−	1.40123i
$220$	6.21885	−	10.7714i	0.419275	−	0.726205i
$221$	−3.73607	+	6.47106i	−0.251315	+	0.435291i
$222$	−3.71885	−	6.44123i	−0.249593	−	0.432307i
$223$	−4.00000			−0.267860			−0.133930	−	0.990991i	$-0.542760\pi$
$223$	−4.00000			−0.267860			−0.133930	+	0.990991i	$0.542760\pi$
$224$	2.07295	+	10.7714i	0.138505	+	0.719692i
$225$		0			0
$226$	−2.85410	−	4.94345i	−0.189852	−	0.328833i
$227$	5.97214	−	10.3440i	0.396385	−	0.686558i	−0.596892	−	0.802321i	$-0.703598\pi$
$227$	5.97214	−	10.3440i	0.396385	−	0.686558i	0.993277	+	0.115763i	$0.0369314\pi$
$228$	6.21885	−	10.7714i	0.411853	−	0.713351i
$229$	8.06231	+	13.9643i	0.532772	+	0.922788i	0.999268	+	0.0382649i	$0.0121831\pi$
$229$	8.06231	+	13.9643i	0.532772	+	0.922788i	−0.466495	+	0.884524i	$0.654484\pi$
$230$	−3.21478			−0.211976
$231$	−16.7705	−	5.80948i	−1.10342	−	0.382235i
$232$	−6.58359			−0.432234
$233$	2.97214	+	5.14789i	0.194711	+	0.337250i	0.946806	−	0.321806i	$-0.104290\pi$
$233$	2.97214	+	5.14789i	0.194711	+	0.337250i	−0.752095	+	0.659055i	$0.770956\pi$
$234$	−0.381966	+	0.661585i	−0.0249699	+	0.0432491i
$235$	1.64590	−	2.85078i	0.107367	−	0.185964i
$236$	6.92705	+	11.9980i	0.450913	+	0.781004i
$237$	23.9443			1.55535
$238$	−5.70820	+	4.94345i	−0.370008	+	0.320436i
$239$	−7.41641			−0.479728			−0.239864	−	0.970807i	$-0.577103\pi$
$239$	−7.41641			−0.479728			−0.239864	+	0.970807i	$0.577103\pi$
$240$	7.86475	+	13.6221i	0.507667	+	0.879305i
$241$	4.35410	−	7.54153i	0.280472	−	0.485792i	−0.691029	−	0.722827i	$-0.742842\pi$
$241$	4.35410	−	7.54153i	0.280472	−	0.485792i	0.971501	+	0.237035i	$0.0761756\pi$
$242$	−0.381966	+	0.661585i	−0.0245537	+	0.0425283i
$243$	8.94427	+	15.4919i	0.573775	+	0.993808i
$244$	−5.56231			−0.356090
$245$	14.5344	−	5.80948i	0.928571	−	0.371154i
$246$	−3.81966			−0.243533
$247$	1.50000	+	2.59808i	0.0954427	+	0.165312i
$248$	−3.68034	+	6.37454i	−0.233702	+	0.404783i
$249$		0			0
$250$	2.13525	+	3.69837i	0.135045	+	0.233905i
$251$	10.4721			0.660995			0.330498	−	0.943807i	$-0.392783\pi$
$251$	10.4721			0.660995			0.330498	+	0.943807i	$0.392783\pi$
$252$	7.41641	−	6.42280i	0.467190	−	0.404598i
$253$	11.2918			0.709909
$254$	2.94427	+	5.09963i	0.184740	+	0.319979i
$255$	−18.6803	+	32.3553i	−1.16981	+	2.02617i
$256$	−2.78115	+	4.81710i	−0.173822	+	0.301069i
$257$	8.97214	+	15.5402i	0.559666	+	0.969371i	0.997524	+	0.0703264i	$0.0224041\pi$
$257$	8.97214	+	15.5402i	0.559666	+	0.969371i	−0.437858	+	0.899044i	$0.644263\pi$
$258$	6.83282			0.425393
$259$	−21.7705	−	7.54153i	−1.35275	−	0.468608i
$260$	−4.14590			−0.257118
$261$	4.47214	+	7.74597i	0.276818	+	0.479463i
$262$	−0.718847	+	1.24508i	−0.0444105	+	0.0769213i
$263$	7.06231	−	12.2323i	0.435480	−	0.754274i	−0.561854	−	0.827236i	$-0.689912\pi$
$263$	7.06231	−	12.2323i	0.435480	−	0.754274i	0.997335	+	0.0729620i	$0.0232452\pi$
$264$	4.93769	+	8.55234i	0.303894	+	0.526360i
$265$	−3.29180			−0.202213
$266$	0.572949	+	2.97713i	0.0351298	+	0.182540i
$267$	−5.00000			−0.305995
$268$	−2.78115	−	4.81710i	−0.169886	−	0.294251i
$269$	−2.26393	+	3.92125i	−0.138034	+	0.239083i	−0.926753	−	0.375672i	$-0.877412\pi$
$269$	−2.26393	+	3.92125i	−0.138034	+	0.239083i	0.788718	+	0.614755i	$0.210745\pi$
$270$	0.954915	−	1.65396i	0.0581143	−	0.100657i
$271$	−3.20820	−	5.55677i	−0.194885	−	0.337550i	0.751978	−	0.659188i	$-0.229100\pi$
$271$	−3.20820	−	5.55677i	−0.194885	−	0.337550i	−0.946863	+	0.321638i	$0.895767\pi$
$272$	−23.5066			−1.42530
$273$	1.11803	+	5.80948i	0.0676665	+	0.351605i
$274$	1.43769			0.0868543
$275$		0			0
$276$	−7.80244	+	13.5142i	−0.469652	+	0.813461i
$277$	−13.2082	+	22.8773i	−0.793604	+	1.37456i	0.130118	+	0.991499i	$0.458464\pi$
$277$	−13.2082	+	22.8773i	−0.793604	+	1.37456i	−0.923722	+	0.383064i	$0.874869\pi$
$278$	0.652476	+	1.13012i	0.0391329	+	0.0677802i
$279$	10.0000			0.598684
$280$	−8.22949	−	2.85078i	−0.491806	−	0.170367i
$281$	9.05573			0.540219			0.270110	−	0.962830i	$-0.412940\pi$
$281$	9.05573			0.540219			0.270110	+	0.962830i	$0.412940\pi$
$282$	0.628677	+	1.08890i	0.0374372	+	0.0648431i
$283$	7.06231	−	12.2323i	0.419811	−	0.727133i	−0.576110	−	0.817372i	$-0.695430\pi$
$283$	7.06231	−	12.2323i	0.419811	−	0.727133i	0.995920	+	0.0902393i	$0.0287632\pi$
$284$	8.29180	−	14.3618i	0.492028	−	0.852217i
$285$	7.50000	+	12.9904i	0.444262	+	0.769484i
$286$	−1.14590			−0.0677584
$287$	−8.94427	+	7.74597i	−0.527964	+	0.457230i
$288$	−8.29180			−0.488599
$289$	−19.4164	−	33.6302i	−1.14214	−	1.97825i
$290$	1.90983	−	3.30792i	0.112149	−	0.194248i
$291$	19.4721	−	33.7267i	1.14148	−	1.97710i
$292$	9.92705	+	17.1942i	0.580937	+	1.00621i
$293$	2.94427			0.172006			0.0860031	−	0.996295i	$-0.472591\pi$
$293$	2.94427			0.172006			0.0860031	+	0.996295i	$0.472591\pi$
$294$	−0.854102	+	5.91739i	−0.0498122	+	0.345109i
$295$	−16.7082			−0.972789
$296$	6.40983	+	11.1022i	0.372564	+	0.645299i
$297$	−3.35410	+	5.80948i	−0.194625	+	0.337100i
$298$	−2.42705	+	4.20378i	−0.140595	+	0.243518i
$299$	−1.88197	−	3.25966i	−0.108837	−	0.188511i
$300$		0			0
$301$	16.0000	−	13.8564i	0.922225	−	0.798670i
$302$	2.45085			0.141031
$303$	10.0623	+	17.4284i	0.578064	+	1.00124i
$304$	−4.71885	+	8.17328i	−0.270644	+	0.468770i
$305$	3.35410	−	5.80948i	0.192055	−	0.332650i
$306$	−2.85410	−	4.94345i	−0.163158	−	0.282598i
$307$	−7.41641			−0.423277			−0.211638	−	0.977348i	$-0.567880\pi$
$307$	−7.41641			−0.423277			−0.211638	+	0.977348i	$0.567880\pi$
$308$	13.9058	+	4.81710i	0.792354	+	0.274480i
$309$	23.9443			1.36214
$310$	−2.13525	−	3.69837i	−0.121274	−	0.210053i
$311$	16.1180	−	27.9173i	0.913970	−	1.58304i	0.105567	−	0.994412i	$-0.466334\pi$
$311$	16.1180	−	27.9173i	0.913970	−	1.58304i	0.808403	−	0.588630i	$-0.200333\pi$
$312$	1.64590	−	2.85078i	0.0931806	−	0.161394i
$313$	16.2082	+	28.0734i	0.916142	+	1.58680i	0.805221	+	0.592975i	$0.202047\pi$
$313$	16.2082	+	28.0734i	0.916142	+	1.58680i	0.110921	+	0.993829i	$0.464620\pi$
$314$	−2.67376			−0.150889
$315$	2.23607	+	11.6190i	0.125988	+	0.654654i
$316$	−19.8541			−1.11688
$317$	1.88197	+	3.25966i	0.105702	+	0.183081i	0.914025	−	0.405659i	$-0.132958\pi$
$317$	1.88197	+	3.25966i	0.105702	+	0.183081i	−0.808323	+	0.588739i	$0.799624\pi$
$318$	0.628677	−	1.08890i	0.0352545	−	0.0610625i
$319$	−6.70820	+	11.6190i	−0.375587	+	0.650536i
$320$	−5.26393	−	9.11740i	−0.294263	−	0.509678i
$321$	−31.8328			−1.77673
$322$	−0.718847	−	3.73524i	−0.0400598	−	0.208157i
$323$	−22.4164			−1.24728
$324$	−10.1976	−	17.6627i	−0.566531	−	0.981261i
$325$		0			0
$326$	1.98936	−	3.44567i	0.110180	−	0.190838i
$327$	−11.9721	−	20.7363i	−0.662061	−	1.14672i
$328$	6.58359			0.363518
$329$	3.68034	+	1.27491i	0.202904	+	0.0702879i
$330$	−5.72949			−0.315398
$331$	14.2082	+	24.6093i	0.780954	+	1.35265i	0.931387	+	0.364031i	$0.118600\pi$
$331$	14.2082	+	24.6093i	0.780954	+	1.35265i	−0.150433	+	0.988620i	$0.548067\pi$
$332$		0			0
$333$	8.70820	−	15.0831i	0.477207	−	0.826546i
$334$	2.58359	+	4.47491i	0.141368	+	0.244856i
$335$	6.70820			0.366508
$336$	−14.0689	+	12.1840i	−0.767521	+	0.664692i
$337$	18.0000			0.980522			0.490261	−	0.871576i	$-0.336901\pi$
$337$	18.0000			0.980522			0.490261	+	0.871576i	$0.336901\pi$
$338$	0.190983	+	0.330792i	0.0103881	+	0.0179927i
$339$	16.7082	−	28.9395i	0.907465	−	1.57178i
$340$	15.4894	−	26.8284i	0.840028	−	1.45497i
$341$	7.50000	+	12.9904i	0.406148	+	0.703469i
$342$	−2.29180			−0.123926
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	−11.7771			−0.634978
$345$	−9.40983	−	16.2983i	−0.506608	−	0.877471i
$346$	1.98936	−	3.44567i	0.106948	−	0.185240i
$347$	17.5344	−	30.3705i	0.941298	−	1.63038i	0.178299	−	0.983976i	$-0.442940\pi$
$347$	17.5344	−	30.3705i	0.941298	−	1.63038i	0.762999	−	0.646400i	$-0.223726\pi$
$348$	−9.27051	−	16.0570i	−0.496951	−	0.860745i
$349$	−2.58359			−0.138297			−0.0691483	−	0.997606i	$-0.522028\pi$
$349$	−2.58359			−0.138297			−0.0691483	+	0.997606i	$0.522028\pi$
$350$		0			0
$351$	2.23607			0.119352
$352$	−6.21885	−	10.7714i	−0.331466	−	0.574115i
$353$	−15.3541	+	26.5941i	−0.817216	+	1.41546i	0.0905091	+	0.995896i	$0.471151\pi$
$353$	−15.3541	+	26.5941i	−0.817216	+	1.41546i	−0.907725	+	0.419565i	$0.862183\pi$
$354$	3.19098	−	5.52694i	0.169599	−	0.293754i
$355$	10.0000	+	17.3205i	0.530745	+	0.919277i
$356$	4.14590			0.219732
$357$	−41.7705	−	14.4697i	−2.21073	−	0.765819i
$358$	−7.68692			−0.406266
$359$	2.97214	+	5.14789i	0.156863	+	0.271695i	0.933736	−	0.357963i	$-0.116528\pi$
$359$	2.97214	+	5.14789i	0.156863	+	0.271695i	−0.776873	+	0.629658i	$0.783195\pi$
$360$	3.29180	−	5.70156i	0.173493	−	0.300498i
$361$	5.00000	−	8.66025i	0.263158	−	0.455803i
$362$	0.270510	+	0.468537i	0.0142177	+	0.0246257i
$363$	−4.47214			−0.234726
$364$	−0.927051	−	4.81710i	−0.0485907	−	0.252485i
$365$	−23.9443			−1.25330
$366$	1.28115	+	2.21902i	0.0669669	+	0.115990i
$367$	−0.354102	+	0.613323i	−0.0184840	+	0.0320152i	−0.875119	−	0.483907i	$-0.839217\pi$
$367$	−0.354102	+	0.613323i	−0.0184840	+	0.0320152i	0.856635	+	0.515922i	$0.172551\pi$
$368$	5.92047	−	10.2546i	0.308626	−	0.534556i
$369$	−4.47214	−	7.74597i	−0.232810	−	0.403239i
$370$	−7.43769			−0.386667
$371$	−0.736068	−	3.82472i	−0.0382147	−	0.198570i
$372$	−20.7295			−1.07477
$373$	14.2082	+	24.6093i	0.735673	+	1.27422i	0.954427	+	0.298443i	$0.0964673\pi$
$373$	14.2082	+	24.6093i	0.735673	+	1.27422i	−0.218755	+	0.975780i	$0.570199\pi$
$374$	4.28115	−	7.41517i	0.221373	−	0.383430i
$375$	−12.5000	+	21.6506i	−0.645497	+	1.11803i
$376$	−1.08359	−	1.87684i	−0.0558820	−	0.0967905i
$377$	4.47214			0.230327
$378$	2.13525	+	0.739674i	0.109826	+	0.0380447i
$379$	11.4164			0.586421			0.293211	−	0.956048i	$-0.405276\pi$
$379$	11.4164			0.586421			0.293211	+	0.956048i	$0.405276\pi$
$380$	−6.21885	−	10.7714i	−0.319020	−	0.552559i
$381$	−17.2361	+	29.8537i	−0.883031	+	1.52945i
$382$	−2.13525	+	3.69837i	−0.109249	+	0.189225i
$383$	−7.50000	−	12.9904i	−0.383232	−	0.663777i	0.608290	−	0.793715i	$-0.291856\pi$
$383$	−7.50000	−	12.9904i	−0.383232	−	0.663777i	−0.991522	+	0.129937i	$0.958522\pi$
$384$	22.5623			1.15138
$385$	−13.4164	+	11.6190i	−0.683763	+	0.592157i
$386$	4.85410			0.247067
$387$	8.00000	+	13.8564i	0.406663	+	0.704361i
$388$	−16.1459	+	27.9655i	−0.819684	+	1.41973i
$389$	3.73607	−	6.47106i	0.189426	−	0.328096i	−0.755633	−	0.654995i	$-0.772671\pi$
$389$	3.73607	−	6.47106i	0.189426	−	0.328096i	0.945059	+	0.326900i	$0.106004\pi$
$390$	0.954915	+	1.65396i	0.0483540	+	0.0837516i
$391$	28.1246			1.42232
$392$	1.47214	−	10.1993i	0.0743541	−	0.515140i
$393$	−8.41641			−0.424552
$394$	−5.14590	−	8.91296i	−0.259247	−	0.449028i
$395$	11.9721	−	20.7363i	0.602384	−	1.04336i
$396$	−5.56231	+	9.63420i	−0.279516	+	0.484137i
$397$	−7.06231	−	12.2323i	−0.354447	−	0.613920i	0.632576	−	0.774498i	$-0.281998\pi$
$397$	−7.06231	−	12.2323i	−0.354447	−	0.613920i	−0.987023	+	0.160578i	$0.948664\pi$
$398$	2.78522			0.139610
$399$	−13.4164	+	11.6190i	−0.671660	+	0.581675i
$400$		0			0
$401$	−4.88197	−	8.45581i	−0.243794	−	0.422263i	0.717998	−	0.696045i	$-0.245059\pi$
$401$	−4.88197	−	8.45581i	−0.243794	−	0.422263i	−0.961792	+	0.273782i	$0.911725\pi$
$402$	−1.28115	+	2.21902i	−0.0638981	+	0.110675i
$403$	2.50000	−	4.33013i	0.124534	−	0.215699i
$404$	−8.34346	−	14.4513i	−0.415103	−	0.718979i
$405$	24.5967			1.22222
$406$	4.27051	+	1.47935i	0.211942	+	0.0734188i
$407$	26.1246			1.29495
$408$	12.2984	+	21.3014i	0.608860	+	1.05458i
$409$	2.35410	−	4.07742i	0.116403	−	0.201616i	−0.801937	−	0.597409i	$-0.796197\pi$
$409$	2.35410	−	4.07742i	0.116403	−	0.201616i	0.918340	+	0.395793i	$0.129530\pi$
$410$	−1.90983	+	3.30792i	−0.0943198	+	0.163367i
$411$	4.20820	+	7.28882i	0.207575	+	0.359531i
$412$	−19.8541			−0.978141
$413$	−3.73607	−	19.4132i	−0.183840	−	0.955260i
$414$	2.87539			0.141318
$415$		0			0
$416$	−2.07295	+	3.59045i	−0.101635	+	0.176036i
$417$	−3.81966	+	6.61585i	−0.187050	+	0.323979i
$418$	−1.71885	−	2.97713i	−0.0840716	−	0.145616i
$419$	15.0557			0.735520			0.367760	−	0.929921i	$-0.380125\pi$
$419$	15.0557			0.735520			0.367760	+	0.929921i	$0.380125\pi$
$420$	−4.63525	−	24.0855i	−0.226177	−	1.17525i
$421$	−13.4164			−0.653876			−0.326938	−	0.945046i	$-0.606017\pi$
$421$	−13.4164			−0.653876			−0.326938	+	0.945046i	$0.606017\pi$
$422$	0.763932	+	1.32317i	0.0371876	+	0.0644109i
$423$	−1.47214	+	2.54981i	−0.0715777	+	0.123976i
$424$	−1.08359	+	1.87684i	−0.0526239	+	0.0911472i
$425$		0			0
$426$	−7.63932			−0.370126
$427$	7.50000	+	2.59808i	0.362950	+	0.125730i
$428$	26.3951			1.27586
$429$	−3.35410	−	5.80948i	−0.161938	−	0.280484i
$430$	3.41641	−	5.91739i	0.164754	−	0.285362i
$431$	−6.68034	+	11.5707i	−0.321781	+	0.557340i	−0.980856	−	0.194737i	$-0.937615\pi$
$431$	−6.68034	+	11.5707i	−0.321781	+	0.557340i	0.659075	+	0.752077i	$0.270948\pi$
$432$	3.51722	+	6.09201i	0.169222	+	0.293102i
$433$	2.58359			0.124160			0.0620798	−	0.998071i	$-0.480227\pi$
$433$	2.58359			0.124160			0.0620798	+	0.998071i	$0.480227\pi$
$434$	3.81966	−	3.30792i	0.183350	−	0.158785i
$435$	22.3607			1.07211
$436$	9.92705	+	17.1942i	0.475420	+	0.823451i
$437$	5.64590	−	9.77898i	0.270080	−	0.467792i
$438$	4.57295	−	7.92058i	0.218504	−	0.378460i
$439$	8.06231	+	13.9643i	0.384793	+	0.666481i	0.991740	−	0.128261i	$-0.0409395\pi$
$439$	8.06231	+	13.9643i	0.384793	+	0.666481i	−0.606948	+	0.794742i	$0.707606\pi$
$440$	9.87539			0.470791
$441$	−13.0000	+	5.19615i	−0.619048	+	0.247436i
$442$	−2.85410			−0.135756
$443$	1.11803	+	1.93649i	0.0531194	+	0.0920055i	0.891362	−	0.453291i	$-0.149750\pi$
$443$	1.11803	+	1.93649i	0.0531194	+	0.0920055i	−0.838243	+	0.545297i	$0.816417\pi$
$444$	−18.0517	+	31.2664i	−0.856694	+	1.48384i
$445$	−2.50000	+	4.33013i	−0.118511	+	0.205268i
$446$	−0.763932	−	1.32317i	−0.0361732	−	0.0626539i
$447$	−28.4164			−1.34405
$448$	9.41641	−	8.15485i	0.444883	−	0.385280i
$449$	10.3607			0.488951			0.244475	−	0.969656i	$-0.421384\pi$
$449$	10.3607			0.488951			0.244475	+	0.969656i	$0.421384\pi$
$450$		0			0
$451$	6.70820	−	11.6190i	0.315877	−	0.547115i
$452$	−13.8541	+	23.9960i	−0.651642	+	1.12868i
$453$	7.17376	+	12.4253i	0.337053	+	0.583792i
$454$	4.56231			0.214120
$455$	5.59017	+	1.93649i	0.262071	+	0.0907841i
$456$	9.87539			0.462457
$457$	−17.0623	−	29.5528i	−0.798141	−	1.38242i	−0.920825	−	0.389975i	$-0.872484\pi$
$457$	−17.0623	−	29.5528i	−0.798141	−	1.38242i	0.122684	−	0.992446i	$-0.460850\pi$
$458$	−3.07953	+	5.33390i	−0.143897	+	0.249237i
$459$	−8.35410	+	14.4697i	−0.389936	+	0.675389i
$460$	7.80244	+	13.5142i	0.363791	+	0.630104i
$461$	−10.3607			−0.482545			−0.241272	−	0.970457i	$-0.577565\pi$
$461$	−10.3607			−0.482545			−0.241272	+	0.970457i	$0.577565\pi$
$462$	−1.28115	−	6.65707i	−0.0596046	−	0.309715i
$463$	−24.0000			−1.11537			−0.557687	−	0.830051i	$-0.688311\pi$
$463$	−24.0000			−1.11537			−0.557687	+	0.830051i	$0.688311\pi$
$464$	7.03444	+	12.1840i	0.326566	+	0.565628i
$465$	12.5000	−	21.6506i	0.579674	−	1.00402i
$466$	−1.13525	+	1.96632i	−0.0525897	+	0.0910880i
$467$	10.8262	+	18.7516i	0.500979	+	0.867720i	0.999999	+	0.00113029i	$0.000359784\pi$
$467$	10.8262	+	18.7516i	0.500979	+	0.867720i	−0.499021	+	0.866590i	$0.666307\pi$
$468$	3.70820			0.171412
$469$	1.50000	+	7.79423i	0.0692636	+	0.359904i
$470$	1.25735			0.0579974
$471$	−7.82624	−	13.5554i	−0.360614	−	0.624602i
$472$	−5.50000	+	9.52628i	−0.253158	+	0.438483i
$473$	−12.0000	+	20.7846i	−0.551761	+	0.955677i
$474$	4.57295	+	7.92058i	0.210043	+	0.363804i
$475$		0			0
$476$	34.6353	+	11.9980i	1.58750	+	0.549928i
$477$	2.94427			0.134809
$478$	−1.41641	−	2.45329i	−0.0647850	−	0.112211i
$479$	14.9164	−	25.8360i	0.681548	−	1.18048i	−0.292960	−	0.956125i	$-0.594640\pi$
$479$	14.9164	−	25.8360i	0.681548	−	1.18048i	0.974508	−	0.224351i	$-0.0720263\pi$
$480$	−10.3647	+	17.9523i	−0.473084	+	0.819405i
$481$	−4.35410	−	7.54153i	−0.198530	−	0.343864i
$482$	3.32624			0.151506
$483$	16.8328	−	14.5776i	0.765920	−	0.663306i
$484$	3.70820			0.168555
$485$	−19.4721	−	33.7267i	−0.884184	−	1.53145i
$486$	−3.41641	+	5.91739i	−0.154971	+	0.268418i
$487$	−15.9164	+	27.5680i	−0.721241	+	1.24923i	0.239261	+	0.970955i	$0.423095\pi$
$487$	−15.9164	+	27.5680i	−0.721241	+	1.24923i	−0.960503	+	0.278271i	$0.910239\pi$
$488$	−2.20820	−	3.82472i	−0.0999607	−	0.173137i
$489$	23.2918			1.05329
$490$	4.69756	+	3.69837i	0.212214	+	0.167075i
$491$	−34.4721			−1.55571			−0.777853	−	0.628446i	$-0.783691\pi$
$491$	−34.4721			−1.55571			−0.777853	+	0.628446i	$0.783691\pi$
$492$	9.27051	+	16.0570i	0.417947	+	0.723905i
$493$	−16.7082	+	28.9395i	−0.752500	+	1.30337i
$494$	−0.572949	+	0.992377i	−0.0257782	+	0.0446491i
$495$	−6.70820	−	11.6190i	−0.301511	−	0.522233i
$496$	15.7295			0.706275
$497$	−17.8885	+	15.4919i	−0.802411	+	0.694908i
$498$		0			0
$499$	0.208204	+	0.360620i	0.00932049	+	0.0161436i	0.870648	−	0.491907i	$-0.163700\pi$
$499$	0.208204	+	0.360620i	0.00932049	+	0.0161436i	−0.861328	+	0.508050i	$0.830366\pi$
$500$	10.3647	−	17.9523i	0.463525	−	0.802850i
$501$	−15.1246	+	26.1966i	−0.675718	+	1.17038i
$502$	2.00000	+	3.46410i	0.0892644	+	0.154610i
$503$	3.05573			0.136248			0.0681241	−	0.997677i	$-0.478299\pi$
$503$	3.05573			0.136248			0.0681241	+	0.997677i	$0.478299\pi$
$504$	7.36068	+	2.54981i	0.327871	+	0.113578i
$505$	20.1246			0.895533
$506$	2.15654	+	3.73524i	0.0958699	+	0.166052i
$507$	−1.11803	+	1.93649i	−0.0496536	+	0.0860026i
$508$	14.2918	−	24.7541i	0.634096	−	1.09829i
$509$	7.88197	+	13.6520i	0.349362	+	0.605113i	0.986136	−	0.165938i	$-0.0530650\pi$
$509$	7.88197	+	13.6520i	0.349362	+	0.605113i	−0.636774	+	0.771050i	$0.719732\pi$
$510$	−14.2705			−0.631909
$511$	−5.35410	−	27.8207i	−0.236852	−	1.23072i
$512$	−22.3050			−0.985749
$513$	3.35410	+	5.80948i	0.148087	+	0.256495i
$514$	−3.42705	+	5.93583i	−0.151161	+	0.261818i
$515$	11.9721	−	20.7363i	0.527555	−	0.913753i
$516$	−16.5836	−	28.7236i	−0.730052	−	1.26449i
$517$	−4.41641			−0.194233
$518$	−1.66312	−	8.64182i	−0.0730733	−	0.379700i
$519$	23.2918			1.02240
$520$	−1.64590	−	2.85078i	−0.0721774	−	0.125015i
$521$	0.0278640	−	0.0482619i	0.00122075	−	0.00211439i	−0.865414	−	0.501057i	$-0.832945\pi$
$521$	0.0278640	−	0.0482619i	0.00122075	−	0.00211439i	0.866635	+	0.498942i	$0.166278\pi$
$522$	−1.70820	+	2.95870i	−0.0747661	+	0.129499i
$523$	−9.64590	−	16.7072i	−0.421786	−	0.730554i	0.574329	−	0.818625i	$-0.305263\pi$
$523$	−9.64590	−	16.7072i	−0.421786	−	0.730554i	−0.996114	+	0.0880707i	$0.971930\pi$
$524$	6.97871			0.304867
$525$		0			0
$526$	5.39512			0.235238
$527$	18.6803	+	32.3553i	0.813728	+	1.40942i
$528$	10.5517	−	18.2760i	0.459202	−	0.795362i
$529$	4.41641	−	7.64944i	0.192018	−	0.332584i
$530$	−0.628677	−	1.08890i	−0.0273080	−	0.0472988i
$531$	14.9443			0.648526
$532$	11.1246	−	9.63420i	0.482313	−	0.417695i
$533$	−4.47214			−0.193710
$534$	−0.954915	−	1.65396i	−0.0413232	−	0.0715739i
$535$	−15.9164	+	27.5680i	−0.688126	+	1.19187i
$536$	2.20820	−	3.82472i	0.0953799	−	0.165203i
$537$	−22.5000	−	38.9711i	−0.970947	−	1.68173i
$538$	−1.72949			−0.0745636
$539$	−16.5000	−	12.9904i	−0.710705	−	0.559535i
$540$	−9.27051			−0.398939
$541$	−7.35410	−	12.7377i	−0.316178	−	0.547636i	0.663510	−	0.748168i	$-0.269066\pi$
$541$	−7.35410	−	12.7377i	−0.316178	−	0.547636i	−0.979687	+	0.200532i	$0.935733\pi$
$542$	1.22542	−	2.12250i	0.0526365	−	0.0911691i
$543$	−1.58359	+	2.74286i	−0.0679584	+	0.117707i
$544$	−15.4894	−	26.8284i	−0.664101	−	1.15026i
$545$	−23.9443			−1.02566
$546$	−1.70820	+	1.47935i	−0.0731044	+	0.0633102i
$547$	−31.4164			−1.34327			−0.671634	−	0.740883i	$-0.734407\pi$
$547$	−31.4164			−1.34327			−0.671634	+	0.740883i	$0.734407\pi$
$548$	−3.48936	−	6.04374i	−0.149058	−	0.258176i
$549$	−3.00000	+	5.19615i	−0.128037	+	0.221766i
$550$		0			0
$551$	6.70820	+	11.6190i	0.285779	+	0.494984i
$552$	−12.3901			−0.527358
$553$	26.7705	+	9.27358i	1.13840	+	0.394353i
$554$	−10.0902			−0.428690
$555$	−21.7705	−	37.7076i	−0.924107	−	1.60060i
$556$	3.16718	−	5.48572i	0.134319	−	0.232647i
$557$	2.64590	−	4.58283i	0.112110	−	0.194181i	−0.804511	−	0.593938i	$-0.797572\pi$
$557$	2.64590	−	4.58283i	0.112110	−	0.194181i	0.916621	+	0.399758i	$0.130906\pi$
$558$	1.90983	+	3.30792i	0.0808496	+	0.140036i
$559$	8.00000			0.338364
$560$	3.51722	+	18.2760i	0.148630	+	0.772303i
$561$	50.1246			2.11626
$562$	1.72949	+	2.99556i	0.0729541	+	0.126360i
$563$	18.2984	−	31.6937i	0.771185	−	1.33573i	−0.165730	−	0.986171i	$-0.552998\pi$
$563$	18.2984	−	31.6937i	0.771185	−	1.33573i	0.936914	−	0.349560i	$-0.113669\pi$
$564$	3.05166	−	5.28563i	0.128498	−	0.222565i
$565$	−16.7082	−	28.9395i	−0.702919	−	1.21749i
$566$	5.39512			0.226774
$567$	5.50000	+	28.5788i	0.230978	+	1.20020i
$568$	13.1672			0.552483
$569$	−8.26393	−	14.3136i	−0.346442	−	0.600055i	0.639173	−	0.769063i	$-0.279277\pi$
$569$	−8.26393	−	14.3136i	−0.346442	−	0.600055i	−0.985615	+	0.169008i	$0.945944\pi$
$570$	−2.86475	+	4.96188i	−0.119991	+	0.207830i
$571$	−2.06231	+	3.57202i	−0.0863048	+	0.149484i	−0.905946	−	0.423392i	$-0.860839\pi$
$571$	−2.06231	+	3.57202i	−0.0863048	+	0.149484i	0.819642	+	0.572877i	$0.194173\pi$
$572$	2.78115	+	4.81710i	0.116286	+	0.201413i
$573$	−25.0000			−1.04439
$574$	−4.27051	−	1.47935i	−0.178248	−	0.0617468i
$575$		0			0
$576$	4.70820	+	8.15485i	0.196175	+	0.339785i
$577$	16.3541	−	28.3261i	0.680830	−	1.17923i	−0.293898	−	0.955837i	$-0.594953\pi$
$577$	16.3541	−	28.3261i	0.680830	−	1.17923i	0.974728	−	0.223396i	$-0.0717142\pi$
$578$	7.41641	−	12.8456i	0.308482	−	0.534306i
$579$	14.2082	+	24.6093i	0.590473	+	1.02273i
$580$	−18.5410			−0.769874
$581$		0			0
$582$	14.8754			0.616605
$583$	2.20820	+	3.82472i	0.0914545	+	0.158404i
$584$	−7.88197	+	13.6520i	−0.326158	+	0.564922i
$585$	−2.23607	+	3.87298i	−0.0924500	+	0.160128i
$586$	0.562306	+	0.973942i	0.0232286	+	0.0402332i
$587$	−41.8885			−1.72893			−0.864463	−	0.502697i	$-0.832341\pi$
$587$	−41.8885			−1.72893			−0.864463	+	0.502697i	$0.832341\pi$
$588$	26.9483	−	10.7714i	1.11133	−	0.444203i
$589$	15.0000			0.618064
$590$	−3.19098	−	5.52694i	−0.131371	−	0.227541i
$591$	30.1246	−	52.1774i	1.23916	−	2.14629i
$592$	13.6976	−	23.7249i	0.562966	−	0.975086i
$593$	−16.1180	−	27.9173i	−0.661888	−	1.14642i	−0.980119	−	0.198411i	$-0.936422\pi$
$593$	−16.1180	−	27.9173i	−0.661888	−	1.14642i	0.318231	−	0.948013i	$-0.396911\pi$
$594$	−2.56231			−0.105133
$595$	−33.4164	+	28.9395i	−1.36994	+	1.18640i
$596$	23.5623			0.965150
$597$	8.15248	+	14.1205i	0.333659	+	0.577914i
$598$	0.718847	−	1.24508i	0.0293958	−	0.0509151i
$599$	−20.5344	+	35.5667i	−0.839015	+	1.45322i	0.0517049	+	0.998662i	$0.483534\pi$
$599$	−20.5344	+	35.5667i	−0.839015	+	1.45322i	−0.890719	+	0.454553i	$0.849799\pi$
$600$		0			0
$601$	−22.0000			−0.897399			−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000			−0.897399			−0.448699	+	0.893683i	$0.648113\pi$
$602$	7.63932	+	2.64634i	0.311355	+	0.107857i
$603$	−6.00000			−0.244339
$604$	−5.94834	−	10.3028i	−0.242034	−	0.419216i
$605$	−2.23607	+	3.87298i	−0.0909091	+	0.157459i
$606$	−3.84346	+	6.65707i	−0.156130	+	0.270425i
$607$	8.06231	+	13.9643i	0.327239	+	0.566794i	0.981963	−	0.189074i	$-0.0605485\pi$
$607$	8.06231	+	13.9643i	0.327239	+	0.566794i	−0.654724	+	0.755868i	$0.727215\pi$
$608$	−12.4377			−0.504415
$609$	5.00000	+	25.9808i	0.202610	+	1.05279i
$610$	2.56231			0.103745
$611$	0.736068	+	1.27491i	0.0297781	+	0.0515772i
$612$	−13.8541	+	23.9960i	−0.560019	+	0.969981i
$613$	−11.0623	+	19.1605i	−0.446802	+	0.773884i	−0.998176	−	0.0603742i	$-0.980771\pi$
$613$	−11.0623	+	19.1605i	−0.446802	+	0.773884i	0.551373	+	0.834259i	$0.314104\pi$
$614$	−1.41641	−	2.45329i	−0.0571616	−	0.0990067i
$615$	−22.3607			−0.901670
$616$	2.20820	+	11.4742i	0.0889711	+	0.462307i
$617$	4.47214			0.180041			0.0900207	−	0.995940i	$-0.471307\pi$
$617$	4.47214			0.180041			0.0900207	+	0.995940i	$0.471307\pi$
$618$	4.57295	+	7.92058i	0.183951	+	0.318612i
$619$	−8.50000	+	14.7224i	−0.341644	+	0.591744i	−0.984738	−	0.174042i	$-0.944317\pi$
$619$	−8.50000	+	14.7224i	−0.341644	+	0.591744i	0.643094	+	0.765787i	$0.277650\pi$
$620$	−10.3647	+	17.9523i	−0.416258	+	0.720980i
$621$	−4.20820	−	7.28882i	−0.168869	−	0.292490i
$622$	12.3131			0.493710
$623$	−5.59017	−	1.93649i	−0.223965	−	0.0775839i
$624$	−7.03444			−0.281603
$625$	12.5000	+	21.6506i	0.500000	+	0.866025i
$626$	−6.19098	+	10.7231i	−0.247441	+	0.428581i
$627$	10.0623	−	17.4284i	0.401850	−	0.696024i
$628$	6.48936	+	11.2399i	0.258954	+	0.448521i
$629$	65.0689			2.59447
$630$	−3.41641	+	2.95870i	−0.136113	+	0.117877i
$631$	−30.8328			−1.22744			−0.613718	−	0.789526i	$-0.710327\pi$
$631$	−30.8328			−1.22744			−0.613718	+	0.789526i	$0.710327\pi$
$632$	−7.88197	−	13.6520i	−0.313528	−	0.543046i
$633$	−4.47214	+	7.74597i	−0.177751	+	0.307875i
$634$	−0.718847	+	1.24508i	−0.0285491	+	0.0494484i
$635$	17.2361	+	29.8537i	0.683992	+	1.18471i
$636$	−6.10333			−0.242013
$637$	−1.00000	+	6.92820i	−0.0396214	+	0.274505i
$638$	−5.12461			−0.202885
$639$	−8.94427	−	15.4919i	−0.353830	−	0.612851i
$640$	11.2812	−	19.5395i	0.445927	−	0.772368i
$641$	2.97214	−	5.14789i	0.117392	−	0.203329i	−0.801341	−	0.598208i	$-0.795880\pi$
$641$	2.97214	−	5.14789i	0.117392	−	0.203329i	0.918734	+	0.394878i	$0.129213\pi$
$642$	−6.07953	−	10.5300i	−0.239940	−	0.415588i
$643$	−18.8328			−0.742694			−0.371347	−	0.928494i	$-0.621104\pi$
$643$	−18.8328			−0.742694			−0.371347	+	0.928494i	$0.621104\pi$
$644$	−13.9574	+	12.0875i	−0.550000	+	0.476314i
$645$	40.0000			1.57500
$646$	−4.28115	−	7.41517i	−0.168440	−	0.291746i
$647$	−7.88197	+	13.6520i	−0.309872	+	0.536714i	−0.978334	−	0.207032i	$-0.933620\pi$
$647$	−7.88197	+	13.6520i	−0.309872	+	0.536714i	0.668462	+	0.743746i	$0.266953\pi$
$648$	8.09675	−	14.0240i	0.318070	−	0.550914i
$649$	11.2082	+	19.4132i	0.439960	+	0.762034i
$650$		0			0
$651$	27.9508	+	9.68246i	1.09548	+	0.379485i
$652$	−19.3131			−0.756359
$653$	−6.73607	−	11.6672i	−0.263603	−	0.456573i	0.703594	−	0.710602i	$-0.251577\pi$
$653$	−6.73607	−	11.6672i	−0.263603	−	0.456573i	−0.967197	+	0.254029i	$0.918244\pi$
$654$	4.57295	−	7.92058i	0.178816	−	0.309719i
$655$	−4.20820	+	7.28882i	−0.164428	+	0.284798i
$656$	−7.03444	−	12.1840i	−0.274649	−	0.475706i
$657$	21.4164			0.835534
$658$	0.281153	+	1.46091i	0.0109605	+	0.0569523i
$659$	8.94427			0.348419			0.174210	−	0.984709i	$-0.444263\pi$
$659$	8.94427			0.348419			0.174210	+	0.984709i	$0.444263\pi$
$660$	13.9058	+	24.0855i	0.541281	+	0.937526i
$661$	−3.35410	+	5.80948i	−0.130459	+	0.225962i	−0.923854	−	0.382746i	$-0.874979\pi$
$661$	−3.35410	+	5.80948i	−0.130459	+	0.225962i	0.793394	+	0.608708i	$0.208312\pi$
$662$	−5.42705	+	9.39993i	−0.210928	+	0.365339i
$663$	−8.35410	−	14.4697i	−0.324446	−	0.561958i
$664$		0			0
$665$	3.35410	+	17.4284i	0.130066	+	0.675845i
$666$	6.65248			0.257778
$667$	−8.41641	−	14.5776i	−0.325885	−	0.564449i
$668$	12.5410	−	21.7217i	0.485227	−	0.840437i
$669$	4.47214	−	7.74597i	0.172903	−	0.299476i
$670$	1.28115	+	2.21902i	0.0494953	+	0.0857283i
$671$	−9.00000			−0.347441
$672$	−23.1763	−	8.02850i	−0.894044	−	0.309706i
$673$	17.4164			0.671353			0.335677	−	0.941977i	$-0.391035\pi$
$673$	17.4164			0.671353			0.335677	+	0.941977i	$0.391035\pi$
$674$	3.43769	+	5.95426i	0.132415	+	0.229350i
$675$		0			0
$676$	0.927051	−	1.60570i	0.0356558	−	0.0617577i
$677$	−16.4443	−	28.4823i	−0.632005	−	1.09466i	−0.987141	−	0.159850i	$-0.948899\pi$
$677$	−16.4443	−	28.4823i	−0.632005	−	1.09466i	0.355137	−	0.934814i	$-0.384434\pi$
$678$	12.7639			0.490196
$679$	34.8328	−	30.1661i	1.33676	−	1.15767i
$680$	24.5967			0.943242
$681$	13.3541	+	23.1300i	0.511730	+	0.886343i
$682$	−2.86475	+	4.96188i	−0.109697	+	0.190000i
$683$	2.26393	−	3.92125i	0.0866270	−	0.150042i	−0.819456	−	0.573142i	$-0.805725\pi$
$683$	2.26393	−	3.92125i	0.0866270	−	0.150042i	0.906083	+	0.423099i	$0.139058\pi$
$684$	5.56231	+	9.63420i	0.212680	+	0.368373i
$685$	8.41641			0.321574
$686$	−3.24671	+	6.28505i	−0.123960	+	0.239964i
$687$	−36.0557			−1.37561
$688$	12.5836	+	21.7954i	0.479745	+	0.830943i
$689$	0.736068	−	1.27491i	0.0280420	−	0.0485701i
$690$	3.59424	−	6.22540i	0.136830	−	0.236997i
$691$	−0.916408	−	1.58726i	−0.0348618	−	0.0603824i	0.848068	−	0.529887i	$-0.177766\pi$
$691$	−0.916408	−	1.58726i	−0.0348618	−	0.0603824i	−0.882930	+	0.469505i	$0.844432\pi$
$692$	−19.3131			−0.734173
$693$	12.0000	−	10.3923i	0.455842	−	0.394771i
$694$	13.3951			0.508472
$695$	3.81966	+	6.61585i	0.144888	+	0.250953i
$696$	7.36068	−	12.7491i	0.279006	−	0.483252i
$697$	16.7082	−	28.9395i	0.632868	−	1.09616i
$698$	−0.493422	−	0.854632i	−0.0186763	−	0.0323483i
$699$	−13.2918			−0.502742
$700$		0			0
$701$	22.3607			0.844551			0.422276	−	0.906467i	$-0.361231\pi$
$701$	22.3607			0.844551			0.422276	+	0.906467i	$0.361231\pi$
$702$	0.427051	+	0.739674i	0.0161180	+	0.0279172i
$703$	13.0623	−	22.6246i	0.492654	−	0.853302i
$704$	−7.06231	+	12.2323i	−0.266171	+	0.461021i
$705$	3.68034	+	6.37454i	0.138610	+	0.240079i
$706$	−11.7295			−0.441445
$707$	4.50000	+	23.3827i	0.169240	+	0.879396i
$708$	−30.9787			−1.16425
$709$	4.93769	+	8.55234i	0.185439	+	0.321190i	0.943724	−	0.330733i	$-0.107296\pi$
$709$	4.93769	+	8.55234i	0.185439	+	0.321190i	−0.758285	+	0.651923i	$0.773963\pi$
$710$	−3.81966	+	6.61585i	−0.143349	+	0.248288i
$711$	−10.7082	+	18.5472i	−0.401589	+	0.695573i
$712$	1.64590	+	2.85078i	0.0616826	+	0.106837i
$713$	−18.8197			−0.704802
$714$	−3.19098	−	16.5808i	−0.119420	−	0.620522i
$715$	−6.70820			−0.250873
$716$	18.6565	+	32.3141i	0.697228	+	1.20763i
$717$	8.29180	−	14.3618i	0.309663	−	0.536352i
$718$	−1.13525	+	1.96632i	−0.0423673	+	0.0733824i
$719$	−5.64590	−	9.77898i	−0.210556	−	0.364694i	0.741332	−	0.671138i	$-0.234194\pi$
$719$	−5.64590	−	9.77898i	−0.210556	−	0.364694i	−0.951889	+	0.306444i	$0.900861\pi$
$720$	−14.0689			−0.524316
$721$	26.7705	+	9.27358i	0.996986	+	0.345366i
$722$	3.81966			0.142153
$723$	9.73607	+	16.8634i	0.362088	+	0.627155i
$724$	1.31308	−	2.27433i	0.0488003	−	0.0845246i
$725$		0			0
$726$	−0.854102	−	1.47935i	−0.0316987	−	0.0549038i
$727$	14.8328			0.550119			0.275059	−	0.961427i	$-0.411302\pi$
$727$	14.8328			0.550119			0.275059	+	0.961427i	$0.411302\pi$
$728$	2.94427	−	2.54981i	0.109122	−	0.0945024i
$729$	−7.00000			−0.259259
$730$	−4.57295	−	7.92058i	−0.169252	−	0.293154i
$731$	−29.8885	+	51.7685i	−1.10547	+	1.91473i
$732$	6.21885	−	10.7714i	0.229855	−	0.398121i
$733$	−7.64590	−	13.2431i	−0.282408	−	0.489144i	0.689570	−	0.724219i	$-0.257800\pi$
$733$	−7.64590	−	13.2431i	−0.282408	−	0.489144i	−0.971977	+	0.235075i	$0.924466\pi$
$734$	−0.270510			−0.00998470
$735$	−5.00000	+	34.6410i	−0.184428	+	1.27775i
$736$	15.6049			0.575203
$737$	−4.50000	−	7.79423i	−0.165760	−	0.287104i
$738$	1.70820	−	2.95870i	0.0628799	−	0.108911i
$739$	−17.9164	+	31.0321i	−0.659066	+	1.14154i	0.321792	+	0.946810i	$0.395715\pi$
$739$	−17.9164	+	31.0321i	−0.659066	+	1.14154i	−0.980858	+	0.194725i	$0.937619\pi$
$740$	18.0517	+	31.2664i	0.663592	+	1.14938i
$741$	−6.70820			−0.246432
$742$	1.12461	−	0.973942i	0.0412858	−	0.0357545i
$743$	15.0557			0.552341			0.276171	−	0.961109i	$-0.410935\pi$
$743$	15.0557			0.552341			0.276171	+	0.961109i	$0.410935\pi$
$744$	−8.22949	−	14.2539i	−0.301708	−	0.522573i
$745$	−14.2082	+	24.6093i	−0.520548	+	0.901616i
$746$	−5.42705	+	9.39993i	−0.198698	+	0.344156i
$747$		0			0
$748$	−41.5623			−1.51967
$749$	−35.5902	−	12.3288i	−1.30044	−	0.450484i
$750$	−9.54915			−0.348686
$751$	−15.0623	−	26.0887i	−0.549631	−	0.951989i	−0.998300	−	0.0582911i	$-0.981435\pi$
$751$	−15.0623	−	26.0887i	−0.549631	−	0.951989i	0.448668	−	0.893698i	$-0.351898\pi$
$752$	−2.31559	+	4.01073i	−0.0844411	+	0.146256i
$753$	−11.7082	+	20.2792i	−0.426671	+	0.739015i
$754$	0.854102	+	1.47935i	0.0311046	+	0.0538747i
$755$	14.3475			0.522160
$756$	−2.07295	−	10.7714i	−0.0753924	−	0.391751i
$757$	0.832816			0.0302692			0.0151346	−	0.999885i	$-0.495182\pi$
$757$	0.832816			0.0302692			0.0151346	+	0.999885i	$0.495182\pi$
$758$	2.18034	+	3.77646i	0.0791935	+	0.137167i
$759$	−12.6246	+	21.8665i	−0.458244	+	0.793703i
$760$	4.93769	−	8.55234i	0.179109	−	0.310226i
$761$	−16.7705	−	29.0474i	−0.607931	−	1.05297i	−0.991581	−	0.129488i	$-0.958667\pi$
$761$	−16.7705	−	29.0474i	−0.607931	−	1.05297i	0.383650	−	0.923478i	$-0.374667\pi$
$762$	−13.1672			−0.476997
$763$	−5.35410	−	27.8207i	−0.193832	−	1.00718i
$764$	20.7295			0.749967
$765$	−16.7082	−	28.9395i	−0.604086	−	1.04631i
$766$	2.86475	−	4.96188i	0.103507	−	0.179280i
$767$	3.73607	−	6.47106i	0.134902	−	0.233656i
$768$	−6.21885	−	10.7714i	−0.224403	−	0.388678i
$769$	46.0000			1.65880			0.829401	−	0.558653i	$-0.188682\pi$
$769$	46.0000			1.65880			0.829401	+	0.558653i	$0.188682\pi$
$770$	−6.40576	−	2.21902i	−0.230848	−	0.0799680i
$771$

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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.190983 + 0.330792i) q^{2} +(-1.11803 + 1.93649i) q^{3} +(0.927051 - 1.60570i) q^{4} +(1.11803 + 1.93649i) q^{5} -0.854102 q^{6} +(-2.00000 + 1.73205i) q^{7} +1.47214 q^{8} +(-1.00000 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(0.190983 + 0.330792i) q^{2} +(-1.11803 + 1.93649i) q^{3} +(0.927051 - 1.60570i) q^{4} +(1.11803 + 1.93649i) q^{5} -0.854102 q^{6} +(-2.00000 + 1.73205i) q^{7} +1.47214 q^{8} +(-1.00000 - 1.73205i) q^{9} +(-0.427051 + 0.739674i) q^{10} +(1.50000 - 2.59808i) q^{11} +(2.07295 + 3.59045i) q^{12} -1.00000 q^{13} +(-0.954915 - 0.330792i) q^{14} -5.00000 q^{15} +(-1.57295 - 2.72443i) q^{16} +(3.73607 - 6.47106i) q^{17} +(0.381966 - 0.661585i) q^{18} +(-1.50000 - 2.59808i) q^{19} +4.14590 q^{20} +(-1.11803 - 5.80948i) q^{21} +1.14590 q^{22} +(1.88197 + 3.25966i) q^{23} +(-1.64590 + 2.85078i) q^{24} +(-0.190983 - 0.330792i) q^{26} -2.23607 q^{27} +(0.927051 + 4.81710i) q^{28} -4.47214 q^{29} +(-0.954915 - 1.65396i) q^{30} +(-2.50000 + 4.33013i) q^{31} +(2.07295 - 3.59045i) q^{32} +(3.35410 + 5.80948i) q^{33} +2.85410 q^{34} +(-5.59017 - 1.93649i) q^{35} -3.70820 q^{36} +(4.35410 + 7.54153i) q^{37} +(0.572949 - 0.992377i) q^{38} +(1.11803 - 1.93649i) q^{39} +(1.64590 + 2.85078i) q^{40} +4.47214 q^{41} +(1.70820 - 1.47935i) q^{42} -8.00000 q^{43} +(-2.78115 - 4.81710i) q^{44} +(2.23607 - 3.87298i) q^{45} +(-0.718847 + 1.24508i) q^{46} +(-0.736068 - 1.27491i) q^{47} +7.03444 q^{48} +(1.00000 - 6.92820i) q^{49} +(8.35410 + 14.4697i) q^{51} +(-0.927051 + 1.60570i) q^{52} +(-0.736068 + 1.27491i) q^{53} +(-0.427051 - 0.739674i) q^{54} +6.70820 q^{55} +(-2.94427 + 2.54981i) q^{56} +6.70820 q^{57} +(-0.854102 - 1.47935i) q^{58} +(-3.73607 + 6.47106i) q^{59} +(-4.63525 + 8.02850i) q^{60} +(-1.50000 - 2.59808i) q^{61} -1.90983 q^{62} +(5.00000 + 1.73205i) q^{63} -4.70820 q^{64} +(-1.11803 - 1.93649i) q^{65} +(-1.28115 + 2.21902i) q^{66} +(1.50000 - 2.59808i) q^{67} +(-6.92705 - 11.9980i) q^{68} -8.41641 q^{69} +(-0.427051 - 2.21902i) q^{70} +8.94427 q^{71} +(-1.47214 - 2.54981i) q^{72} +(-5.35410 + 9.27358i) q^{73} +(-1.66312 + 2.88061i) q^{74} -5.56231 q^{76} +(1.50000 + 7.79423i) q^{77} +0.854102 q^{78} +(-5.35410 - 9.27358i) q^{79} +(3.51722 - 6.09201i) q^{80} +(5.50000 - 9.52628i) q^{81} +(0.854102 + 1.47935i) q^{82} +(-10.3647 - 3.59045i) q^{84} +16.7082 q^{85} +(-1.52786 - 2.64634i) q^{86} +(5.00000 - 8.66025i) q^{87} +(2.20820 - 3.82472i) q^{88} +(1.11803 + 1.93649i) q^{89} +1.70820 q^{90} +(2.00000 - 1.73205i) q^{91} +6.97871 q^{92} +(-5.59017 - 9.68246i) q^{93} +(0.281153 - 0.486971i) q^{94} +(3.35410 - 5.80948i) q^{95} +(4.63525 + 8.02850i) q^{96} -17.4164 q^{97} +(2.48278 - 0.992377i) q^{98} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} - 3 q^{4} + 10 q^{6} - 8 q^{7} - 12 q^{8} - 4 q^{9}+O(q^{10}) \) 4 * q + 3 * q^2 - 3 * q^4 + 10 * q^6 - 8 * q^7 - 12 * q^8 - 4 * q^9	\( 4 q + 3 q^{2} - 3 q^{4} + 10 q^{6} - 8 q^{7} - 12 q^{8} - 4 q^{9} + 5 q^{10} + 6 q^{11} + 15 q^{12} - 4 q^{13} - 15 q^{14} - 20 q^{15} - 13 q^{16} + 6 q^{17} + 6 q^{18} - 6 q^{19} + 30 q^{20} + 18 q^{22} + 12 q^{23} - 20 q^{24} - 3 q^{26} - 3 q^{28} - 15 q^{30} - 10 q^{31} + 15 q^{32} - 2 q^{34} + 12 q^{36} + 4 q^{37} + 9 q^{38} + 20 q^{40} - 20 q^{42} - 32 q^{43} + 9 q^{44} - 23 q^{46} + 6 q^{47} - 30 q^{48} + 4 q^{49} + 20 q^{51} + 3 q^{52} + 6 q^{53} + 5 q^{54} + 24 q^{56} + 10 q^{58} - 6 q^{59} + 15 q^{60} - 6 q^{61} - 30 q^{62} + 20 q^{63} + 8 q^{64} + 15 q^{66} + 6 q^{67} - 21 q^{68} + 20 q^{69} + 5 q^{70} + 12 q^{72} - 8 q^{73} + 9 q^{74} + 18 q^{76} + 6 q^{77} - 10 q^{78} - 8 q^{79} - 15 q^{80} + 22 q^{81} - 10 q^{82} - 75 q^{84} + 40 q^{85} - 24 q^{86} + 20 q^{87} - 18 q^{88} - 20 q^{90} + 8 q^{91} - 66 q^{92} - 19 q^{94} - 15 q^{96} - 16 q^{97} + 39 q^{98} - 24 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 - 3 * q^4 + 10 * q^6 - 8 * q^7 - 12 * q^8 - 4 * q^9 + 5 * q^10 + 6 * q^11 + 15 * q^12 - 4 * q^13 - 15 * q^14 - 20 * q^15 - 13 * q^16 + 6 * q^17 + 6 * q^18 - 6 * q^19 + 30 * q^20 + 18 * q^22 + 12 * q^23 - 20 * q^24 - 3 * q^26 - 3 * q^28 - 15 * q^30 - 10 * q^31 + 15 * q^32 - 2 * q^34 + 12 * q^36 + 4 * q^37 + 9 * q^38 + 20 * q^40 - 20 * q^42 - 32 * q^43 + 9 * q^44 - 23 * q^46 + 6 * q^47 - 30 * q^48 + 4 * q^49 + 20 * q^51 + 3 * q^52 + 6 * q^53 + 5 * q^54 + 24 * q^56 + 10 * q^58 - 6 * q^59 + 15 * q^60 - 6 * q^61 - 30 * q^62 + 20 * q^63 + 8 * q^64 + 15 * q^66 + 6 * q^67 - 21 * q^68 + 20 * q^69 + 5 * q^70 + 12 * q^72 - 8 * q^73 + 9 * q^74 + 18 * q^76 + 6 * q^77 - 10 * q^78 - 8 * q^79 - 15 * q^80 + 22 * q^81 - 10 * q^82 - 75 * q^84 + 40 * q^85 - 24 * q^86 + 20 * q^87 - 18 * q^88 - 20 * q^90 + 8 * q^91 - 66 * q^92 - 19 * q^94 - 15 * q^96 - 16 * q^97 + 39 * q^98 - 24 * q^99

Introduction

L-functions

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