LMFDB - Embedded newform 37.3.d.a.31.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,3,Mod(6,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("37.6");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	37.d (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:	$1.00817697813$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 18 x^{10} + 8 x^{9} + 42 x^{8} - 268 x^{7} + 884 x^{6} + 704 x^{5} + 761 x^{4} + \cdots + 16 $ x^12 - 6x^11 + 18x^10 + 8x^9 + 42x^8 - 268x^7 + 884x^6 + 704x^5 + 761x^4 - 2054x^3 + 3042x^2 + 312*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.5
Root			$2.02961 + 2.02961i$ of defining polynomial
Character	$\chi$	$=$	37.31
Dual form			37.3.d.a.6.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.02961 + 1.02961i) q^{2} +3.18930i q^{3} -1.87979i q^{4} +(-0.460662 + 0.460662i) q^{5} +(-3.28375 + 3.28375i) q^{6} -2.31735 q^{7} +(6.05392 - 6.05392i) q^{8} -1.17160 q^{9} +O(q^{10})$	\(q+(1.02961 + 1.02961i) q^{2} +3.18930i q^{3} -1.87979i q^{4} +(-0.460662 + 0.460662i) q^{5} +(-3.28375 + 3.28375i) q^{6} -2.31735 q^{7} +(6.05392 - 6.05392i) q^{8} -1.17160 q^{9} -0.948609 q^{10} -17.2954i q^{11} +5.99520 q^{12} +(-10.2742 + 10.2742i) q^{13} +(-2.38597 - 2.38597i) q^{14} +(-1.46919 - 1.46919i) q^{15} +4.94725 q^{16} +(-12.3100 + 12.3100i) q^{17} +(-1.20630 - 1.20630i) q^{18} +(1.47612 - 1.47612i) q^{19} +(0.865947 + 0.865947i) q^{20} -7.39070i q^{21} +(17.8076 - 17.8076i) q^{22} +(5.39671 - 5.39671i) q^{23} +(19.3077 + 19.3077i) q^{24} +24.5756i q^{25} -21.1568 q^{26} +24.9671i q^{27} +4.35612i q^{28} +(5.59041 + 5.59041i) q^{29} -3.02540i q^{30} +(-3.08292 - 3.08292i) q^{31} +(-19.1219 - 19.1219i) q^{32} +55.1600 q^{33} -25.3490 q^{34} +(1.06751 - 1.06751i) q^{35} +2.20236i q^{36} +(3.81569 + 36.8027i) q^{37} +3.03967 q^{38} +(-32.7673 - 32.7673i) q^{39} +5.57762i q^{40} -65.3467i q^{41} +(7.60958 - 7.60958i) q^{42} +(41.3135 - 41.3135i) q^{43} -32.5116 q^{44} +(0.539714 - 0.539714i) q^{45} +11.1131 q^{46} -52.1282 q^{47} +15.7782i q^{48} -43.6299 q^{49} +(-25.3034 + 25.3034i) q^{50} +(-39.2601 - 39.2601i) q^{51} +(19.3132 + 19.3132i) q^{52} +63.5869 q^{53} +(-25.7065 + 25.7065i) q^{54} +(7.96733 + 7.96733i) q^{55} +(-14.0290 + 14.0290i) q^{56} +(4.70779 + 4.70779i) q^{57} +11.5119i q^{58} +(31.9694 - 31.9694i) q^{59} +(-2.76176 + 2.76176i) q^{60} +(83.9349 + 83.9349i) q^{61} -6.34844i q^{62} +2.71501 q^{63} -59.1654i q^{64} -9.46583i q^{65} +(56.7936 + 56.7936i) q^{66} +5.14012i q^{67} +(23.1401 + 23.1401i) q^{68} +(17.2117 + 17.2117i) q^{69} +2.19826 q^{70} +75.1898 q^{71} +(-7.09279 + 7.09279i) q^{72} -66.0866i q^{73} +(-33.9639 + 41.8213i) q^{74} -78.3788 q^{75} +(-2.77479 - 2.77479i) q^{76} +40.0794i q^{77} -67.4754i q^{78} +(-87.3354 + 87.3354i) q^{79} +(-2.27901 + 2.27901i) q^{80} -90.1718 q^{81} +(67.2819 - 67.2819i) q^{82} -74.2334 q^{83} -13.8929 q^{84} -11.3415i q^{85} +85.0740 q^{86} +(-17.8295 + 17.8295i) q^{87} +(-104.705 - 104.705i) q^{88} +(57.8946 + 57.8946i) q^{89} +1.11139 q^{90} +(23.8088 - 23.8088i) q^{91} +(-10.1447 - 10.1447i) q^{92} +(9.83235 - 9.83235i) q^{93} +(-53.6719 - 53.6719i) q^{94} +1.35999i q^{95} +(60.9854 - 60.9854i) q^{96} +(31.5767 - 31.5767i) q^{97} +(-44.9220 - 44.9220i) q^{98} +20.2633i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 6 q^{5} + 6 q^{6} - 4 q^{7} + 36 q^{8} - 60 q^{9}+O(q^{10}) $ 12 * q - 6 * q^2 - 6 * q^5 + 6 * q^6 - 4 * q^7 + 36 * q^8 - 60 * q^9	$ 12 q - 6 q^{2} - 6 q^{5} + 6 q^{6} - 4 q^{7} + 36 q^{8} - 60 q^{9} - 16 q^{10} + 64 q^{12} + 14 q^{13} - 70 q^{14} - 2 q^{15} - 96 q^{16} + 2 q^{17} + 132 q^{18} + 14 q^{19} - 24 q^{20} + 22 q^{22} + 56 q^{23} - 84 q^{24} - 48 q^{26} + 60 q^{29} + 72 q^{31} + 208 q^{32} + 56 q^{33} + 112 q^{34} - 154 q^{35} - 66 q^{37} - 336 q^{38} - 46 q^{39} + 90 q^{42} + 70 q^{43} + 80 q^{44} + 232 q^{45} - 424 q^{46} - 384 q^{47} + 144 q^{49} - 34 q^{50} - 126 q^{51} + 328 q^{52} - 56 q^{53} - 194 q^{54} + 70 q^{55} + 16 q^{56} - 94 q^{57} + 184 q^{59} + 276 q^{60} + 132 q^{61} - 400 q^{63} + 614 q^{66} + 116 q^{68} + 368 q^{69} + 556 q^{70} + 68 q^{71} - 692 q^{72} - 382 q^{74} + 116 q^{75} + 12 q^{76} - 2 q^{79} + 4 q^{80} - 76 q^{81} + 374 q^{82} + 108 q^{83} - 1436 q^{84} + 140 q^{86} - 420 q^{87} - 788 q^{88} + 278 q^{89} - 664 q^{90} - 450 q^{91} + 652 q^{92} + 584 q^{93} + 118 q^{94} + 1584 q^{96} - 244 q^{97} + 416 q^{98}+O(q^{100}) $ 12 * q - 6 * q^2 - 6 * q^5 + 6 * q^6 - 4 * q^7 + 36 * q^8 - 60 * q^9 - 16 * q^10 + 64 * q^12 + 14 * q^13 - 70 * q^14 - 2 * q^15 - 96 * q^16 + 2 * q^17 + 132 * q^18 + 14 * q^19 - 24 * q^20 + 22 * q^22 + 56 * q^23 - 84 * q^24 - 48 * q^26 + 60 * q^29 + 72 * q^31 + 208 * q^32 + 56 * q^33 + 112 * q^34 - 154 * q^35 - 66 * q^37 - 336 * q^38 - 46 * q^39 + 90 * q^42 + 70 * q^43 + 80 * q^44 + 232 * q^45 - 424 * q^46 - 384 * q^47 + 144 * q^49 - 34 * q^50 - 126 * q^51 + 328 * q^52 - 56 * q^53 - 194 * q^54 + 70 * q^55 + 16 * q^56 - 94 * q^57 + 184 * q^59 + 276 * q^60 + 132 * q^61 - 400 * q^63 + 614 * q^66 + 116 * q^68 + 368 * q^69 + 556 * q^70 + 68 * q^71 - 692 * q^72 - 382 * q^74 + 116 * q^75 + 12 * q^76 - 2 * q^79 + 4 * q^80 - 76 * q^81 + 374 * q^82 + 108 * q^83 - 1436 * q^84 + 140 * q^86 - 420 * q^87 - 788 * q^88 + 278 * q^89 - 664 * q^90 - 450 * q^91 + 652 * q^92 + 584 * q^93 + 118 * q^94 + 1584 * q^96 - 244 * q^97 + 416 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.02961	+	1.02961i	0.514807	+	0.514807i	0.915996	−	0.401188i	$-0.131403\pi$
$2$	1.02961	+	1.02961i	0.514807	+	0.514807i	−0.401188	+	0.915996i	$0.631403\pi$
$3$			3.18930i			1.06310i	0.847027	+	0.531549i	$0.178390\pi$
$3$			3.18930i			1.06310i	−0.847027	+	0.531549i	$0.821610\pi$
$4$		−	1.87979i		−	0.469947i
$5$	−0.460662	+	0.460662i	−0.0921325	+	0.0921325i	−0.751671	−	0.659538i	$-0.770752\pi$
$5$	−0.460662	+	0.460662i	−0.0921325	+	0.0921325i	0.659538	+	0.751671i	$0.270752\pi$
$6$	−3.28375	+	3.28375i	−0.547291	+	0.547291i
$7$	−2.31735			−0.331050			−0.165525	−	0.986206i	$-0.552932\pi$
$7$	−2.31735			−0.331050			−0.165525	+	0.986206i	$0.552932\pi$
$8$	6.05392	−	6.05392i	0.756739	−	0.756739i
$9$	−1.17160			−0.130178
$10$	−0.948609			−0.0948609
$11$		−	17.2954i		−	1.57231i	−0.618032	−	0.786153i	$-0.712070\pi$
$11$		−	17.2954i		−	1.57231i	0.618032	−	0.786153i	$-0.287930\pi$
$12$	5.99520			0.499600
$13$	−10.2742	+	10.2742i	−0.790319	+	0.790319i	−0.981546	−	0.191227i	$-0.938753\pi$
$13$	−10.2742	+	10.2742i	−0.790319	+	0.790319i	0.191227	+	0.981546i	$0.438753\pi$
$14$	−2.38597	−	2.38597i	−0.170427	−	0.170427i
$15$	−1.46919	−	1.46919i	−0.0979459	−	0.0979459i
$16$	4.94725			0.309203
$17$	−12.3100	+	12.3100i	−0.724115	+	0.724115i	−0.969441	−	0.245325i	$-0.921105\pi$
$17$	−12.3100	+	12.3100i	−0.724115	+	0.724115i	0.245325	+	0.969441i	$0.421105\pi$
$18$	−1.20630	−	1.20630i	−0.0670167	−	0.0670167i
$19$	1.47612	−	1.47612i	0.0776906	−	0.0776906i	−0.667194	−	0.744884i	$-0.732505\pi$
$19$	1.47612	−	1.47612i	0.0776906	−	0.0776906i	0.744884	+	0.667194i	$0.232505\pi$
$20$	0.865947	+	0.865947i	0.0432974	+	0.0432974i
$21$		−	7.39070i		−	0.351938i
$22$	17.8076	−	17.8076i	0.809435	−	0.809435i
$23$	5.39671	−	5.39671i	0.234640	−	0.234640i	−0.579987	−	0.814626i	$-0.696942\pi$
$23$	5.39671	−	5.39671i	0.234640	−	0.234640i	0.814626	+	0.579987i	$0.196942\pi$
$24$	19.3077	+	19.3077i	0.804488	+	0.804488i
$25$			24.5756i			0.983023i
$26$	−21.1568			−0.813724
$27$			24.9671i			0.924706i
$28$			4.35612i			0.155576i
$29$	5.59041	+	5.59041i	0.192773	+	0.192773i	0.796893	−	0.604120i	$-0.206475\pi$
$29$	5.59041	+	5.59041i	0.192773	+	0.192773i	−0.604120	+	0.796893i	$0.706475\pi$
$30$		−	3.02540i		−	0.100847i
$31$	−3.08292	−	3.08292i	−0.0994491	−	0.0994491i	0.655632	−	0.755081i	$-0.272402\pi$
$31$	−3.08292	−	3.08292i	−0.0994491	−	0.0994491i	−0.755081	+	0.655632i	$0.772402\pi$
$32$	−19.1219	−	19.1219i	−0.597559	−	0.597559i
$33$	55.1600			1.67152
$34$	−25.3490			−0.745560
$35$	1.06751	−	1.06751i	0.0305004	−	0.0305004i
$36$			2.20236i			0.0611768i
$37$	3.81569	+	36.8027i	0.103127	+	0.994668i
$37$	3.81569	+	36.8027i	0.103127	+	0.994668i
$38$	3.03967			0.0799914
$39$	−32.7673	−	32.7673i	−0.840187	−	0.840187i
$40$			5.57762i			0.139441i
$41$		−	65.3467i		−	1.59382i	−0.604097	−	0.796911i	$-0.706466\pi$
$41$		−	65.3467i		−	1.59382i	0.604097	−	0.796911i	$-0.293534\pi$
$42$	7.60958	−	7.60958i	0.181180	−	0.181180i
$43$	41.3135	−	41.3135i	0.960779	−	0.960779i	−0.0384801	−	0.999259i	$-0.512252\pi$
$43$	41.3135	−	41.3135i	0.960779	−	0.960779i	0.999259	+	0.0384801i	$0.0122516\pi$
$44$	−32.5116			−0.738900
$45$	0.539714	−	0.539714i	0.0119936	−	0.0119936i
$46$	11.1131			0.241588
$47$	−52.1282			−1.10911			−0.554555	−	0.832147i	$-0.687112\pi$
$47$	−52.1282			−1.10911			−0.554555	+	0.832147i	$0.687112\pi$
$48$			15.7782i			0.328713i
$49$	−43.6299			−0.890406
$50$	−25.3034	+	25.3034i	−0.506068	+	0.506068i
$51$	−39.2601	−	39.2601i	−0.769806	−	0.769806i
$52$	19.3132	+	19.3132i	0.371408	+	0.371408i
$53$	63.5869			1.19975			0.599876	−	0.800093i	$-0.295217\pi$
$53$	63.5869			1.19975			0.599876	+	0.800093i	$0.295217\pi$
$54$	−25.7065	+	25.7065i	−0.476046	+	0.476046i
$55$	7.96733	+	7.96733i	0.144860	+	0.144860i
$56$	−14.0290	+	14.0290i	−0.250518	+	0.250518i
$57$	4.70779	+	4.70779i	0.0825927	+	0.0825927i
$58$			11.5119i			0.198482i
$59$	31.9694	−	31.9694i	0.541853	−	0.541853i	−0.382219	−	0.924072i	$-0.624840\pi$
$59$	31.9694	−	31.9694i	0.541853	−	0.541853i	0.924072	+	0.382219i	$0.124840\pi$
$60$	−2.76176	+	2.76176i	−0.0460294	+	0.0460294i
$61$	83.9349	+	83.9349i	1.37598	+	1.37598i	0.851294	+	0.524688i	$0.175818\pi$
$61$	83.9349	+	83.9349i	1.37598	+	1.37598i	0.524688	+	0.851294i	$0.324182\pi$
$62$		−	6.34844i		−	0.102394i
$63$	2.71501			0.0430954
$64$		−	59.1654i		−	0.924459i
$65$		−	9.46583i		−	0.145628i
$66$	56.7936	+	56.7936i	0.860509	+	0.860509i
$67$			5.14012i			0.0767181i	0.999264	+	0.0383591i	$0.0122131\pi$
$67$			5.14012i			0.0767181i	−0.999264	+	0.0383591i	$0.987787\pi$
$68$	23.1401	+	23.1401i	0.340296	+	0.340296i
$69$	17.2117	+	17.2117i	0.249445	+	0.249445i
$70$	2.19826			0.0314037
$71$	75.1898			1.05901			0.529505	−	0.848307i	$-0.322378\pi$
$71$	75.1898			1.05901			0.529505	+	0.848307i	$0.322378\pi$
$72$	−7.09279	+	7.09279i	−0.0985109	+	0.0985109i
$73$		−	66.0866i		−	0.905296i	−0.891689	−	0.452648i	$-0.850479\pi$
$73$		−	66.0866i		−	0.905296i	0.891689	−	0.452648i	$-0.149521\pi$
$74$	−33.9639	+	41.8213i	−0.458972	+	0.565153i
$75$	−78.3788			−1.04505
$76$	−2.77479	−	2.77479i	−0.0365104	−	0.0365104i
$77$			40.0794i			0.520511i
$78$		−	67.4754i		−	0.865069i
$79$	−87.3354	+	87.3354i	−1.10551	+	1.10551i	−0.111778	+	0.993733i	$0.535654\pi$
$79$	−87.3354	+	87.3354i	−1.10551	+	1.10551i	−0.993733	+	0.111778i	$0.964346\pi$
$80$	−2.27901	+	2.27901i	−0.0284877	+	0.0284877i
$81$	−90.1718			−1.11323
$82$	67.2819	−	67.2819i	0.820511	−	0.820511i
$83$	−74.2334			−0.894379			−0.447189	−	0.894439i	$-0.647575\pi$
$83$	−74.2334			−0.894379			−0.447189	+	0.894439i	$0.647575\pi$
$84$	−13.8929			−0.165392
$85$		−	11.3415i		−	0.133429i
$86$	85.0740			0.989232
$87$	−17.8295	+	17.8295i	−0.204936	+	0.204936i
$88$	−104.705	−	104.705i	−1.18983	−	1.18983i
$89$	57.8946	+	57.8946i	0.650501	+	0.650501i	0.953114	−	0.302613i	$-0.0978589\pi$
$89$	57.8946	+	57.8946i	0.650501	+	0.650501i	−0.302613	+	0.953114i	$0.597859\pi$
$90$	1.11139			0.0123488
$91$	23.8088	−	23.8088i	0.261635	−	0.261635i
$92$	−10.1447	−	10.1447i	−0.110268	−	0.110268i
$93$	9.83235	−	9.83235i	0.105724	−	0.105724i
$94$	−53.6719	−	53.6719i	−0.570978	−	0.570978i
$95$			1.35999i			0.0143157i
$96$	60.9854	−	60.9854i	0.635264	−	0.635264i
$97$	31.5767	−	31.5767i	0.325533	−	0.325533i	−0.525352	−	0.850885i	$-0.676066\pi$
$97$	31.5767	−	31.5767i	0.325533	−	0.325533i	0.850885	+	0.525352i	$0.176066\pi$
$98$	−44.9220	−	44.9220i	−0.458388	−	0.458388i
$99$			20.2633i			0.204680i
$100$	46.1969			0.461969
$101$		−	4.86493i		−	0.0481677i	−0.999710	−	0.0240838i	$-0.992333\pi$
$101$		−	4.86493i		−	0.0481677i	0.999710	−	0.0240838i	$-0.00766686\pi$
$102$		−	80.8456i		−	0.792604i
$103$	−31.0988	−	31.0988i	−0.301930	−	0.301930i	0.539839	−	0.841768i	$-0.318485\pi$
$103$	−31.0988	−	31.0988i	−0.301930	−	0.301930i	−0.841768	+	0.539839i	$0.818485\pi$
$104$			124.398i			1.19613i
$105$	3.40462	+	3.40462i	0.0324249	+	0.0324249i
$106$	65.4700	+	65.4700i	0.617641	+	0.617641i
$107$	146.876			1.37267			0.686336	−	0.727285i	$-0.259218\pi$
$107$	146.876			1.37267			0.686336	+	0.727285i	$0.259218\pi$
$108$	46.9328			0.434563
$109$	−94.7493	+	94.7493i	−0.869260	+	0.869260i	−0.992390	−	0.123131i	$-0.960707\pi$
$109$	−94.7493	+	94.7493i	−0.869260	+	0.869260i	0.123131	+	0.992390i	$0.460707\pi$
$110$			16.4066i			0.149150i
$111$	−117.375	+	12.1694i	−1.05743	+	0.109634i
$112$	−11.4645			−0.102362
$113$	−50.9641	−	50.9641i	−0.451010	−	0.451010i	0.444680	−	0.895690i	$-0.353317\pi$
$113$	−50.9641	−	50.9641i	−0.451010	−	0.451010i	−0.895690	+	0.444680i	$0.853317\pi$
$114$			9.69441i			0.0850387i
$115$			4.97212i			0.0432358i
$116$	10.5088	−	10.5088i	0.0905930	−	0.0905930i
$117$	12.0372	−	12.0372i	0.102882	−	0.102882i
$118$	65.8322			0.557900
$119$	28.5265	−	28.5265i	0.239718	−	0.239718i
$120$	−17.7887			−0.148239
$121$	−178.130			−1.47215
$122$			172.841i			1.41673i
$123$	208.410			1.69439
$124$	−5.79524	+	5.79524i	−0.0467358	+	0.0467358i
$125$	−22.8376	−	22.8376i	−0.182701	−	0.182701i
$126$	2.79541	+	2.79541i	0.0221858	+	0.0221858i
$127$	−181.574			−1.42972			−0.714858	−	0.699269i	$-0.753509\pi$
$127$	−181.574			−1.42972			−0.714858	+	0.699269i	$0.753509\pi$
$128$	−15.5701	+	15.5701i	−0.121641	+	0.121641i
$129$	131.761	+	131.761i	1.02140	+	1.02140i
$130$	9.74616	−	9.74616i	0.0749704	−	0.0749704i
$131$	101.787	+	101.787i	0.776998	+	0.776998i	0.979319	−	0.202321i	$-0.0648485\pi$
$131$	101.787	+	101.787i	0.776998	+	0.776998i	−0.202321	+	0.979319i	$0.564848\pi$
$132$		−	103.689i		−	0.785524i
$133$	−3.42068	+	3.42068i	−0.0257194	+	0.0257194i
$134$	−5.29234	+	5.29234i	−0.0394951	+	0.0394951i
$135$	−11.5014	−	11.5014i	−0.0851955	−	0.0851955i
$136$			149.047i			1.09593i
$137$	−64.4553			−0.470476			−0.235238	−	0.971938i	$-0.575587\pi$
$137$	−64.4553			−0.470476			−0.235238	+	0.971938i	$0.575587\pi$
$138$			35.4428i			0.256832i
$139$		−	246.167i		−	1.77098i	−0.464655	−	0.885492i	$-0.653822\pi$
$139$		−	246.167i		−	1.77098i	0.464655	−	0.885492i	$-0.346178\pi$
$140$	−2.00670	−	2.00670i	−0.0143336	−	0.0143336i
$141$		−	166.252i		−	1.17909i
$142$	77.4165	+	77.4165i	0.545186	+	0.545186i
$143$	177.695	+	177.695i	1.24262	+	1.24262i
$144$	−5.79621			−0.0402515
$145$	−5.15059			−0.0355213
$146$	68.0437	−	68.0437i	0.466053	−	0.466053i
$147$		−	139.149i		−	0.946589i
$148$	69.1813	−	7.17269i	0.467441	−	0.0484641i
$149$	−70.3175			−0.471929			−0.235965	−	0.971762i	$-0.575825\pi$
$149$	−70.3175			−0.471929			−0.235965	+	0.971762i	$0.575825\pi$
$150$	−80.6999	−	80.6999i	−0.538000	−	0.538000i
$151$		−	114.317i		−	0.757067i	−0.925588	−	0.378533i	$-0.876429\pi$
$151$		−	114.317i		−	0.757067i	0.925588	−	0.378533i	$-0.123571\pi$
$152$		−	17.8726i		−	0.117583i
$153$	14.4224	−	14.4224i	0.0942640	−	0.0942640i
$154$	−41.2663	+	41.2663i	−0.267963	+	0.267963i
$155$	2.84037			0.0183250
$156$	−61.5956	+	61.5956i	−0.394843	+	0.394843i
$157$	−43.1093			−0.274581			−0.137291	−	0.990531i	$-0.543839\pi$
$157$	−43.1093			−0.274581			−0.137291	+	0.990531i	$0.543839\pi$
$158$	−179.844			−1.13825
$159$			202.797i			1.27545i
$160$	17.6175			0.110109
$161$	−12.5060	+	12.5060i	−0.0776773	+	0.0776773i
$162$	−92.8422	−	92.8422i	−0.573100	−	0.573100i
$163$	143.266	+	143.266i	0.878934	+	0.878934i	0.993424	−	0.114490i	$-0.0365234\pi$
$163$	143.266	+	143.266i	0.878934	+	0.878934i	−0.114490	+	0.993424i	$0.536523\pi$
$164$	−122.838			−0.749011
$165$	−25.4102	+	25.4102i	−0.154001	+	0.154001i
$166$	−76.4318	−	76.4318i	−0.460433	−	0.460433i
$167$	109.900	−	109.900i	0.658086	−	0.658086i	−0.296841	−	0.954927i	$-0.595933\pi$
$167$	109.900	−	109.900i	0.658086	−	0.658086i	0.954927	+	0.296841i	$0.0959330\pi$
$168$	−44.7427	−	44.7427i	−0.266326	−	0.266326i
$169$		−	42.1164i		−	0.249209i
$170$	11.6773	−	11.6773i	0.0686903	−	0.0686903i
$171$	−1.72943	+	1.72943i	−0.0101136	+	0.0101136i
$172$	−77.6606	−	77.6606i	−0.451515	−	0.451515i
$173$		−	286.598i		−	1.65663i	−0.560260	−	0.828317i	$-0.689299\pi$
$173$		−	286.598i		−	1.65663i	0.560260	−	0.828317i	$-0.310701\pi$
$174$	−36.7150			−0.211006
$175$		−	56.9501i		−	0.325429i
$176$		−	85.5645i		−	0.486162i
$177$	101.960	+	101.960i	0.576043	+	0.576043i
$178$			119.218i			0.669765i
$179$	−116.004	−	116.004i	−0.648066	−	0.648066i	0.304459	−	0.952525i	$-0.401524\pi$
$179$	−116.004	−	116.004i	−0.648066	−	0.648066i	−0.952525	+	0.304459i	$0.901524\pi$
$180$	−1.01455	−	1.01455i	−0.00563637	−	0.00563637i
$181$	99.6081			0.550321			0.275160	−	0.961398i	$-0.411269\pi$
$181$	99.6081			0.550321			0.275160	+	0.961398i	$0.411269\pi$
$182$	49.0277			0.269383
$183$	−267.693	+	267.693i	−1.46280	+	1.46280i
$184$		−	65.3424i		−	0.355122i
$185$	−18.7114	−	15.1959i	−0.101143	−	0.0821399i
$186$	20.2471			0.108855
$187$	212.905	+	212.905i	1.13853	+	1.13853i
$188$			97.9899i			0.521223i
$189$		−	57.8573i		−	0.306124i
$190$	−1.40026	+	1.40026i	−0.00736980	+	0.00736980i
$191$	−39.3256	+	39.3256i	−0.205893	+	0.205893i	−0.802519	−	0.596626i	$-0.796508\pi$
$191$	−39.3256	+	39.3256i	−0.205893	+	0.205893i	0.596626	+	0.802519i	$0.296508\pi$
$192$	188.696			0.982791
$193$	180.602	−	180.602i	0.935763	−	0.935763i	−0.0622950	−	0.998058i	$-0.519842\pi$
$193$	180.602	−	180.602i	0.935763	−	0.935763i	0.998058	+	0.0622950i	$0.0198420\pi$
$194$	65.0238			0.335174
$195$	30.1893			0.154817
$196$			82.0149i			0.418444i
$197$	−172.849			−0.877407			−0.438704	−	0.898632i	$-0.644562\pi$
$197$	−172.849			−0.877407			−0.438704	+	0.898632i	$0.644562\pi$
$198$	−20.8634	+	20.8634i	−0.105371	+	0.105371i
$199$	149.605	+	149.605i	0.751783	+	0.751783i	0.974812	−	0.223029i	$-0.0715945\pi$
$199$	149.605	+	149.605i	0.751783	+	0.751783i	−0.223029	+	0.974812i	$0.571595\pi$
$200$	148.778	+	148.778i	0.743892	+	0.743892i
$201$	−16.3933			−0.0815589
$202$	5.00901	−	5.00901i	0.0247971	−	0.0247971i
$203$	−12.9549	−	12.9549i	−0.0638174	−	0.0638174i
$204$	−73.8006	+	73.8006i	−0.361768	+	0.361768i
$205$	30.1028	+	30.1028i	0.146843	+	0.146843i
$206$		−	64.0395i		−	0.310871i
$207$	−6.32280	+	6.32280i	−0.0305449	+	0.0305449i
$208$	−50.8288	+	50.8288i	−0.244369	+	0.244369i
$209$	−25.5301	−	25.5301i	−0.122153	−	0.122153i
$210$			7.01089i			0.0333852i
$211$	−108.718			−0.515249			−0.257625	−	0.966245i	$-0.582940\pi$
$211$	−108.718			−0.515249			−0.257625	+	0.966245i	$0.582940\pi$
$212$		−	119.530i		−	0.563820i
$213$			239.802i			1.12583i
$214$	151.226	+	151.226i	0.706661	+	0.706661i
$215$			38.0632i			0.177038i
$216$	151.149	+	151.149i	0.699762	+	0.699762i
$217$	7.14420	+	7.14420i	0.0329226	+	0.0329226i
$218$	−195.111			−0.895003
$219$	210.770			0.962419
$220$	14.9769	−	14.9769i	0.0680767	−	0.0680767i
$221$		−	252.949i		−	1.14456i
$222$	−133.381	−	108.321i	−0.600813	−	0.487932i
$223$	−21.8699			−0.0980712			−0.0490356	−	0.998797i	$-0.515615\pi$
$223$	−21.8699			−0.0980712			−0.0490356	+	0.998797i	$0.515615\pi$
$224$	44.3121	+	44.3121i	0.197822	+	0.197822i
$225$		−	28.7928i		−	0.127968i
$226$		−	104.947i		−	0.464366i
$227$	−15.4392	+	15.4392i	−0.0680140	+	0.0680140i	−0.740296	−	0.672282i	$-0.765314\pi$
$227$	−15.4392	+	15.4392i	−0.0680140	+	0.0680140i	0.672282	+	0.740296i	$0.265314\pi$
$228$	8.84964	−	8.84964i	0.0388142	−	0.0388142i
$229$	31.9570			0.139550			0.0697751	−	0.997563i	$-0.477772\pi$
$229$	31.9570			0.139550			0.0697751	+	0.997563i	$0.477772\pi$
$230$	−5.11937	+	5.11937i	−0.0222581	+	0.0222581i
$231$	−127.825			−0.553355
$232$	67.6878			0.291758
$233$			3.55985i			0.0152783i	0.999971	+	0.00763915i	$0.00243164\pi$
$233$			3.55985i			0.0152783i	−0.999971	+	0.00763915i	$0.997568\pi$
$234$	24.7874			0.105929
$235$	24.0135	−	24.0135i	0.102185	−	0.102185i
$236$	−60.0956	−	60.0956i	−0.254642	−	0.254642i
$237$	−278.538	−	278.538i	−1.17527	−	1.17527i
$238$	58.7425			0.246817
$239$	−13.7258	+	13.7258i	−0.0574300	+	0.0574300i	−0.735239	−	0.677808i	$-0.762930\pi$
$239$	−13.7258	+	13.7258i	−0.0574300	+	0.0574300i	0.677808	+	0.735239i	$0.262930\pi$
$240$	−7.26844	−	7.26844i	−0.0302852	−	0.0302852i
$241$	−82.3328	+	82.3328i	−0.341630	+	0.341630i	−0.856980	−	0.515350i	$-0.827662\pi$
$241$	−82.3328	+	82.3328i	−0.341630	+	0.341630i	0.515350	+	0.856980i	$0.327662\pi$
$242$	−183.405	−	183.405i	−0.757872	−	0.757872i
$243$		−	62.8808i		−	0.258769i
$244$	157.780	−	157.780i	0.646639	−	0.646639i
$245$	20.0987	−	20.0987i	0.0820353	−	0.0820353i
$246$	214.582	+	214.582i	0.872284	+	0.872284i
$247$			30.3318i			0.122801i
$248$	−37.3275			−0.150514
$249$		−	236.752i		−	0.950812i
$250$		−	47.0279i		−	0.188111i
$251$	−140.696	−	140.696i	−0.560540	−	0.560540i	0.368921	−	0.929461i	$-0.379727\pi$
$251$	−140.696	−	140.696i	−0.560540	−	0.560540i	−0.929461	+	0.368921i	$0.879727\pi$
$252$		−	5.10364i		−	0.0202526i
$253$	−93.3381	−	93.3381i	−0.368925	−	0.368925i
$254$	−186.951	−	186.951i	−0.736029	−	0.736029i
$255$	36.1713			0.141848
$256$	−268.724			−1.04970
$257$	−142.782	+	142.782i	−0.555571	+	0.555571i	−0.928043	−	0.372472i	$-0.878510\pi$
$257$	−142.782	+	142.782i	−0.555571	+	0.555571i	0.372472	+	0.928043i	$0.378510\pi$
$258$			271.326i			1.05165i
$259$	−8.84228	−	85.2847i	−0.0341401	−	0.329284i
$260$	−17.7937			−0.0684375
$261$	−6.54975	−	6.54975i	−0.0250948	−	0.0250948i
$262$			209.602i			0.800009i
$263$			345.178i			1.31246i	0.754560	+	0.656231i	$0.227851\pi$
$263$			345.178i			1.31246i	−0.754560	+	0.656231i	$0.772149\pi$
$264$	333.934	−	333.934i	1.26490	−	1.26490i
$265$	−29.2921	+	29.2921i	−0.110536	+	0.110536i
$266$	−7.04397			−0.0264811
$267$	−184.643	+	184.643i	−0.691546	+	0.691546i
$268$	9.66232			0.0360534
$269$	175.284			0.651613			0.325806	−	0.945437i	$-0.394364\pi$
$269$	175.284			0.651613			0.325806	+	0.945437i	$0.394364\pi$
$270$		−	23.6840i		−	0.0877185i
$271$	−426.485			−1.57374			−0.786872	−	0.617116i	$-0.788301\pi$
$271$	−426.485			−1.57374			−0.786872	+	0.617116i	$0.788301\pi$
$272$	−60.9005	+	60.9005i	−0.223899	+	0.223899i
$273$	75.9332	+	75.9332i	0.278144	+	0.278144i
$274$	−66.3641	−	66.3641i	−0.242205	−	0.242205i
$275$	425.044			1.54561
$276$	32.3543	−	32.3543i	0.117226	−	0.117226i
$277$	350.918	+	350.918i	1.26685	+	1.26685i	0.947705	+	0.319148i	$0.103397\pi$
$277$	350.918	+	350.918i	1.26685	+	1.26685i	0.319148	+	0.947705i	$0.396603\pi$
$278$	253.457	−	253.457i	0.911715	−	0.911715i
$279$	3.61196	+	3.61196i	0.0129461	+	0.0129461i
$280$		−	12.9253i		−	0.0461617i
$281$	136.491	−	136.491i	0.485732	−	0.485732i	−0.421224	−	0.906957i	$-0.638399\pi$
$281$	136.491	−	136.491i	0.485732	−	0.485732i	0.906957	+	0.421224i	$0.138399\pi$
$282$	171.176	−	171.176i	0.607006	−	0.607006i
$283$	−129.122	−	129.122i	−0.456261	−	0.456261i	0.441165	−	0.897426i	$-0.354565\pi$
$283$	−129.122	−	129.122i	−0.456261	−	0.456261i	−0.897426	+	0.441165i	$0.854565\pi$
$284$		−	141.341i		−	0.497679i
$285$	−4.33740			−0.0152189
$286$			365.915i			1.27942i
$287$			151.431i			0.527634i
$288$	22.4033	+	22.4033i	0.0777892	+	0.0777892i
$289$		−	14.0704i		−	0.0486864i
$290$	−5.30312	−	5.30312i	−0.0182866	−	0.0182866i
$291$	100.708	+	100.708i	0.346074	+	0.346074i
$292$	−124.229			−0.425441
$293$	−360.811			−1.23144			−0.615719	−	0.787966i	$-0.711134\pi$
$293$	−360.811			−1.23144			−0.615719	+	0.787966i	$0.711134\pi$
$294$	143.269	−	143.269i	0.487311	−	0.487311i
$295$			29.4542i			0.0998446i
$296$	245.900	+	199.701i	0.830745	+	0.674665i
$297$	431.815			1.45392
$298$	−72.3999	−	72.3999i	−0.242953	−	0.242953i
$299$			110.893i			0.370880i
$300$			147.335i			0.491118i
$301$	−95.7377	+	95.7377i	−0.318066	+	0.318066i
$302$	117.703	−	117.703i	0.389744	−	0.389744i
$303$	15.5157			0.0512070
$304$	7.30274	−	7.30274i	0.0240222	−	0.0240222i
$305$	−77.3313			−0.253545
$306$	29.6990			0.0970556
$307$		−	71.7099i		−	0.233583i	−0.993156	−	0.116791i	$-0.962739\pi$
$307$		−	71.7099i		−	0.233583i	0.993156	−	0.116791i	$-0.0372609\pi$
$308$	75.3407			0.244613
$309$	99.1831	−	99.1831i	0.320981	−	0.320981i
$310$	2.92449	+	2.92449i	0.00943384	+	0.00943384i
$311$	−219.160	−	219.160i	−0.704693	−	0.704693i	0.260721	−	0.965414i	$-0.416040\pi$
$311$	−219.160	−	219.160i	−0.704693	−	0.704693i	−0.965414	+	0.260721i	$0.916040\pi$
$312$	−396.741			−1.27161
$313$	−295.783	+	295.783i	−0.944995	+	0.944995i	−0.998564	−	0.0535690i	$-0.982940\pi$
$313$	−295.783	+	295.783i	−0.944995	+	0.944995i	0.0535690	+	0.998564i	$0.482940\pi$
$314$	−44.3860	−	44.3860i	−0.141357	−	0.141357i
$315$	−1.25070	+	1.25070i	−0.00397049	+	0.00397049i
$316$	164.172	+	164.172i	0.519531	+	0.519531i
$317$			407.463i			1.28537i	0.766130	+	0.642686i	$0.222180\pi$
$317$			407.463i			1.28537i	−0.766130	+	0.642686i	$0.777820\pi$
$318$	−208.803	+	208.803i	−0.656613	+	0.656613i
$319$	96.6883	−	96.6883i	0.303098	−	0.303098i
$320$	27.2553	+	27.2553i	0.0851727	+	0.0851727i
$321$			468.430i			1.45929i
$322$	−25.7528			−0.0799777
$323$			36.3420i			0.112514i
$324$			169.504i			0.523160i
$325$	−252.493	−	252.493i	−0.776902	−	0.776902i
$326$			295.018i			0.904964i
$327$	−302.184	−	302.184i	−0.924109	−	0.924109i
$328$	−395.603	−	395.603i	−1.20611	−	1.20611i
$329$	120.799			0.367170
$330$	−52.3253			−0.158562
$331$	438.051	−	438.051i	1.32342	−	1.32342i	0.412428	−	0.910990i	$-0.364681\pi$
$331$	438.051	−	438.051i	1.32342	−	1.32342i	0.910990	−	0.412428i	$-0.135319\pi$
$332$			139.543i			0.420310i
$333$	−4.47047	−	43.1182i	−0.0134248	−	0.129484i
$334$	226.310			0.677575
$335$	−2.36786	−	2.36786i	−0.00706823	−	0.00706823i
$336$		−	36.5637i		−	0.108820i
$337$		−	315.899i		−	0.937386i	−0.883361	−	0.468693i	$-0.844725\pi$
$337$		−	315.899i		−	0.937386i	0.883361	−	0.468693i	$-0.155275\pi$
$338$	43.3637	−	43.3637i	0.128295	−	0.128295i
$339$	162.539	−	162.539i	0.479468	−	0.479468i
$340$	−21.3196			−0.0627046
$341$	−53.3203	+	53.3203i	−0.156364	+	0.156364i
$342$	−3.56129			−0.0104131
$343$	214.656			0.625818
$344$		−	500.217i		−	1.45412i
$345$	−15.8576			−0.0459640
$346$	295.085	−	295.085i	0.852847	−	0.852847i
$347$	246.659	+	246.659i	0.710833	+	0.710833i	0.966709	−	0.255876i	$-0.0823640\pi$
$347$	246.659	+	246.659i	0.710833	+	0.710833i	−0.255876	+	0.966709i	$0.582364\pi$
$348$	33.5156	+	33.5156i	0.0963093	+	0.0963093i
$349$	130.612			0.374247			0.187124	−	0.982336i	$-0.440084\pi$
$349$	130.612			0.374247			0.187124	+	0.982336i	$0.440084\pi$
$350$	58.6367	−	58.6367i	0.167533	−	0.167533i
$351$	−256.515	−	256.515i	−0.730813	−	0.730813i
$352$	−330.720	+	330.720i	−0.939546	+	0.939546i
$353$	−28.0902	−	28.0902i	−0.0795757	−	0.0795757i	0.666199	−	0.745774i	$-0.267920\pi$
$353$	−28.0902	−	28.0902i	−0.0795757	−	0.0795757i	−0.745774	+	0.666199i	$0.767920\pi$
$354$			209.958i			0.593103i
$355$	−34.6371	+	34.6371i	−0.0975693	+	0.0975693i
$356$	108.829	−	108.829i	0.305701	−	0.305701i
$357$	90.9793	+	90.9793i	0.254844	+	0.254844i
$358$		−	238.878i		−	0.667258i
$359$	−105.212			−0.293071			−0.146536	−	0.989205i	$-0.546812\pi$
$359$	−105.212			−0.293071			−0.146536	+	0.989205i	$0.546812\pi$
$360$		−	6.53476i		−	0.0181521i
$361$			356.642i			0.987928i
$362$	102.558	+	102.558i	0.283309	+	0.283309i
$363$		−	568.109i		−	1.56504i
$364$	−44.7554	−	44.7554i	−0.122954	−	0.122954i
$365$	30.4436	+	30.4436i	0.0834072	+	0.0834072i
$366$	−551.242			−1.50613
$367$	133.934			0.364944			0.182472	−	0.983211i	$-0.441590\pi$
$367$	133.934			0.364944			0.182472	+	0.983211i	$0.441590\pi$
$368$	26.6989	−	26.6989i	0.0725513	−	0.0725513i
$369$			76.5604i			0.207481i
$370$	−3.61960	−	34.9114i	−0.00978270	−	0.0943552i
$371$	−147.353			−0.397177
$372$	−18.4827	−	18.4827i	−0.0496847	−	0.0496847i
$373$		−	439.758i		−	1.17898i	−0.807777	−	0.589489i	$-0.799329\pi$
$373$		−	439.758i		−	1.17898i	0.807777	−	0.589489i	$-0.200671\pi$
$374$			438.421i			1.17225i
$375$	72.8359	−	72.8359i	0.194229	−	0.194229i
$376$	−315.580	+	315.580i	−0.839307	+	0.839307i
$377$	−114.873			−0.304704
$378$	59.5708	−	59.5708i	0.157595	−	0.157595i
$379$	146.226			0.385821			0.192911	−	0.981216i	$-0.438207\pi$
$379$	146.226			0.385821			0.192911	+	0.981216i	$0.438207\pi$
$380$	2.55649			0.00672760
$381$		−	579.093i		−	1.51993i
$382$	−80.9805			−0.211991
$383$	−317.388	+	317.388i	−0.828690	+	0.828690i	−0.987336	−	0.158646i	$-0.949287\pi$
$383$	−317.388	+	317.388i	−0.828690	+	0.828690i	0.158646	+	0.987336i	$0.449287\pi$
$384$	−49.6575	−	49.6575i	−0.129316	−	0.129316i
$385$	−18.4631	−	18.4631i	−0.0479560	−	0.0479560i
$386$	371.901			0.963475
$387$	−48.4030	+	48.4030i	−0.125072	+	0.125072i
$388$	−59.3576	−	59.3576i	−0.152983	−	0.152983i
$389$	161.952	−	161.952i	0.416328	−	0.416328i	−0.467608	−	0.883936i	$-0.654884\pi$
$389$	161.952	−	161.952i	0.416328	−	0.416328i	0.883936	+	0.467608i	$0.154884\pi$
$390$	31.0834	+	31.0834i	0.0797010	+	0.0797010i
$391$			132.867i			0.339812i
$392$	−264.132	+	264.132i	−0.673805	+	0.673805i
$393$	−324.628	+	324.628i	−0.826025	+	0.826025i
$394$	−177.968	−	177.968i	−0.451696	−	0.451696i
$395$		−	80.4642i		−	0.203707i
$396$	38.0907			0.0961887
$397$			332.442i			0.837385i	0.908128	+	0.418692i	$0.137511\pi$
$397$			332.442i			0.837385i	−0.908128	+	0.418692i	$0.862489\pi$
$398$			308.070i			0.774046i
$399$	−10.9096	−	10.9096i	−0.0273423	−	0.0273423i
$400$			121.582i			0.303954i
$401$	299.367	+	299.367i	0.746550	+	0.746550i	0.973830	−	0.227279i	$-0.0729830\pi$
$401$	299.367	+	299.367i	0.746550	+	0.746550i	−0.227279	+	0.973830i	$0.572983\pi$
$402$	−16.8788	−	16.8788i	−0.0419871	−	0.0419871i
$403$	63.3488			0.157193
$404$	−9.14504			−0.0226362
$405$	41.5387	−	41.5387i	0.102565	−	0.102565i
$406$		−	26.6772i		−	0.0657073i
$407$	636.517	−	65.9938i	1.56392	−	0.162147i
$408$	−475.355			−1.16509
$409$	98.0164	+	98.0164i	0.239649	+	0.239649i	0.816705	−	0.577056i	$-0.195799\pi$
$409$	98.0164	+	98.0164i	0.239649	+	0.239649i	−0.577056	+	0.816705i	$0.695799\pi$
$410$			61.9885i			0.151191i
$411$		−	205.567i		−	0.500163i
$412$	−58.4591	+	58.4591i	−0.141891	+	0.141891i
$413$	−74.0841	+	74.0841i	−0.179380	+	0.179380i
$414$	−13.0201			−0.0314495
$415$	34.1965	−	34.1965i	0.0824013	−	0.0824013i
$416$	392.923			0.944525
$417$	785.098			1.88273
$418$		−	52.5723i		−	0.125771i
$419$	285.321			0.680958			0.340479	−	0.940252i	$-0.389411\pi$
$419$	285.321			0.680958			0.340479	+	0.940252i	$0.389411\pi$
$420$	6.39996	−	6.39996i	0.0152380	−	0.0152380i
$421$	515.126	+	515.126i	1.22358	+	1.22358i	0.966351	+	0.257227i	$0.0828087\pi$
$421$	515.126	+	515.126i	1.22358	+	1.22358i	0.257227	+	0.966351i	$0.417191\pi$
$422$	−111.937	−	111.937i	−0.265254	−	0.265254i
$423$	61.0735			0.144382
$424$	384.949	−	384.949i	0.907900	−	0.907900i
$425$	−302.524	−	302.524i	−0.711822	−	0.711822i
$426$	−246.904	+	246.904i	−0.579587	+	0.579587i
$427$	−194.506	−	194.506i	−0.455518	−	0.455518i
$428$		−	276.095i		−	0.645083i
$429$	−566.723	+	566.723i	−1.32103	+	1.32103i
$430$	−39.1904	+	39.1904i	−0.0911404	+	0.0911404i
$431$	−200.649	−	200.649i	−0.465543	−	0.465543i	0.434924	−	0.900467i	$-0.356775\pi$
$431$	−200.649	−	200.649i	−0.465543	−	0.465543i	−0.900467	+	0.434924i	$0.856775\pi$
$432$			123.518i			0.285922i
$433$	764.775			1.76622			0.883112	−	0.469162i	$-0.155444\pi$
$433$	764.775			1.76622			0.883112	+	0.469162i	$0.155444\pi$
$434$			14.7115i			0.0338976i
$435$		−	16.4267i		−	0.0377626i
$436$	178.109	+	178.109i	0.408506	+	0.408506i
$437$		−	15.9324i		−	0.0364586i
$438$	217.012	+	217.012i	0.495460	+	0.495460i
$439$	−249.701	−	249.701i	−0.568796	−	0.568796i	0.362995	−	0.931791i	$-0.381754\pi$
$439$	−249.701	−	249.701i	−0.568796	−	0.568796i	−0.931791	+	0.362995i	$0.881754\pi$
$440$	96.4670			0.219243
$441$	51.1169			0.115911
$442$	260.440	−	260.440i	0.589230	−	0.589230i
$443$			370.301i			0.835894i	0.908472	+	0.417947i	$0.137250\pi$
$443$			370.301i			0.835894i	−0.908472	+	0.417947i	$0.862750\pi$
$444$	22.8758	+	220.640i	0.0515221	+	0.496936i
$445$	−53.3397			−0.119864
$446$	−22.5175	−	22.5175i	−0.0504878	−	0.0504878i
$447$		−	224.263i		−	0.501707i
$448$			137.107i			0.306042i
$449$	−348.300	+	348.300i	−0.775724	+	0.775724i	−0.979101	−	0.203377i	$-0.934808\pi$
$449$	−348.300	+	348.300i	−0.775724	+	0.775724i	0.203377	+	0.979101i	$0.434808\pi$
$450$	29.6455	−	29.6455i	0.0658789	−	0.0658789i
$451$	−1130.20			−2.50598
$452$	−95.8016	+	95.8016i	−0.211951	+	0.211951i
$453$	364.591			0.804837
$454$	−31.7928			−0.0700282
$455$			21.9356i			0.0482101i
$456$	57.0011			0.125002
$457$	303.849	−	303.849i	0.664878	−	0.664878i	−0.291648	−	0.956526i	$-0.594203\pi$
$457$	303.849	−	303.849i	0.664878	−	0.664878i	0.956526	+	0.291648i	$0.0942035\pi$
$458$	32.9034	+	32.9034i	0.0718414	+	0.0718414i
$459$	−307.344	−	307.344i	−0.669594	−	0.669594i
$460$	9.34653			0.0203185
$461$	344.896	−	344.896i	0.748147	−	0.748147i	−0.225984	−	0.974131i	$-0.572560\pi$
$461$	344.896	−	344.896i	0.748147	−	0.748147i	0.974131	+	0.225984i	$0.0725598\pi$
$462$	−131.610	−	131.610i	−0.284871	−	0.284871i
$463$	−187.728	+	187.728i	−0.405459	+	0.405459i	−0.880152	−	0.474693i	$-0.842559\pi$
$463$	−187.728	+	187.728i	−0.405459	+	0.405459i	0.474693	+	0.880152i	$0.342559\pi$
$464$	27.6572	+	27.6572i	0.0596060	+	0.0596060i
$465$			9.05879i			0.0194813i
$466$	−3.66527	+	3.66527i	−0.00786538	+	0.00786538i
$467$	−623.436	+	623.436i	−1.33498	+	1.33498i	−0.434129	+	0.900851i	$0.642944\pi$
$467$	−623.436	+	623.436i	−1.33498	+	1.33498i	−0.900851	+	0.434129i	$0.857056\pi$
$468$	−22.6274	−	22.6274i	−0.0483492	−	0.0483492i
$469$		−	11.9114i		−	0.0253975i
$470$	49.4493			0.105211
$471$		−	137.488i		−	0.291907i
$472$		−	387.079i		−	0.820084i
$473$	−714.532	−	714.532i	−1.51064	−	1.51064i
$474$		−	573.574i		−	1.21007i
$475$	36.2765	+	36.2765i	0.0763717	+	0.0763717i
$476$	−53.6237	−	53.6237i	−0.112655	−	0.112655i
$477$	−74.4986			−0.156181
$478$	−28.2645			−0.0591308
$479$	93.9576	−	93.9576i	0.196154	−	0.196154i	−0.602195	−	0.798349i	$-0.705707\pi$
$479$	93.9576	−	93.9576i	0.196154	−	0.196154i	0.798349	+	0.602195i	$0.205707\pi$
$480$			56.1873i			0.117057i
$481$	−417.320	−	338.914i	−0.867609	−	0.704603i
$482$	−169.542			−0.351747
$483$	−39.8855	−	39.8855i	−0.0825786	−	0.0825786i
$484$			334.846i			0.691831i
$485$			29.0924i			0.0599844i
$486$	64.7430	−	64.7430i	0.133216	−	0.133216i
$487$	294.207	−	294.207i	0.604121	−	0.604121i	−0.337282	−	0.941404i	$-0.609508\pi$
$487$	294.207	−	294.207i	0.604121	−	0.604121i	0.941404	+	0.337282i	$0.109508\pi$
$488$	1016.27			2.08252
$489$	−456.918	+	456.918i	−0.934394	+	0.934394i
$490$	41.3877			0.0844648
$491$	20.4034			0.0415549			0.0207774	−	0.999784i	$-0.493386\pi$
$491$	20.4034			0.0415549			0.0207774	+	0.999784i	$0.493386\pi$
$492$		−	391.766i		−	0.796273i
$493$	−137.636			−0.279180
$494$	−31.2301	+	31.2301i	−0.0632187	+	0.0632187i
$495$	−9.33455	−	9.33455i	−0.0188577	−	0.0188577i
$496$	−15.2520	−	15.2520i	−0.0307500	−	0.0307500i
$497$	−174.241			−0.350585
$498$	243.764	−	243.764i	0.489485	−	0.489485i
$499$	−203.414	−	203.414i	−0.407643	−	0.407643i	0.473273	−	0.880916i	$-0.343073\pi$
$499$	−203.414	−	203.414i	−0.407643	−	0.407643i	−0.880916	+	0.473273i	$0.843073\pi$
$500$	−42.9298	+	42.9298i	−0.0858597	+	0.0858597i
$501$	350.505	+	350.505i	0.699611	+	0.699611i
$502$		−	289.724i		−	0.577140i
$503$	−328.246	+	328.246i	−0.652577	+	0.652577i	−0.953613	−	0.301036i	$-0.902668\pi$
$503$	−328.246	+	328.246i	−0.652577	+	0.652577i	0.301036	+	0.953613i	$0.402668\pi$
$504$	16.4364	−	16.4364i	0.0326120	−	0.0326120i
$505$	2.24109	+	2.24109i	0.00443781	+	0.00443781i
$506$		−	192.205i		−	0.379851i
$507$	134.322			0.264934
$508$			341.321i			0.671891i
$509$			234.925i			0.461542i	0.973008	+	0.230771i	$0.0741248\pi$
$509$			234.925i			0.461542i	−0.973008	+	0.230771i	$0.925875\pi$
$510$	37.2425	+	37.2425i	0.0730245	+	0.0730245i
$511$			153.146i			0.299698i
$512$	−214.402	−	214.402i	−0.418753	−	0.418753i
$513$	36.8544	+	36.8544i	0.0718410	+	0.0718410i
$514$	−294.020			−0.572024
$515$	28.6521			0.0556351
$516$	247.683	−	247.683i	0.480005	−	0.480005i
$517$			901.576i			1.74386i
$518$	78.7062	−	96.9145i	0.151942	−	0.187094i
$519$	914.044			1.76116
$520$	−57.3053	−	57.3053i	−0.110203	−	0.110203i
$521$		−	1031.04i		−	1.97896i	−0.144678	−	0.989479i	$-0.546215\pi$
$521$		−	1031.04i		−	1.97896i	0.144678	−	0.989479i	$-0.453785\pi$
$522$		−	13.4874i		−	0.0258380i
$523$	−274.682	+	274.682i	−0.525204	+	0.525204i	−0.919139	−	0.393934i	$-0.871114\pi$
$523$	−274.682	+	274.682i	−0.525204	+	0.525204i	0.393934	+	0.919139i	$0.371114\pi$
$524$	191.337	−	191.337i	0.365148	−	0.365148i
$525$	181.631			0.345963
$526$	−355.400	+	355.400i	−0.675666	+	0.675666i
$527$	75.9013			0.144025
$528$	272.891			0.516838
$529$			470.751i			0.889889i
$530$	−60.3191			−0.113810
$531$	−37.4554	+	37.4554i	−0.0705375	+	0.0705375i
$532$	6.43016	+	6.43016i	0.0120868	+	0.0120868i
$533$	671.382	+	671.382i	1.25963	+	1.25963i
$534$	−380.222			−0.712026
$535$	−67.6602	+	67.6602i	−0.126468	+	0.126468i
$536$	31.1178	+	31.1178i	0.0580556	+	0.0580556i
$537$	369.970	−	369.970i	0.688958	−	0.688958i
$538$	180.475	+	180.475i	0.335455	+	0.335455i
$539$			754.595i			1.39999i
$540$	−21.6202	+	21.6202i	−0.0400373	+	0.0400373i
$541$	175.879	−	175.879i	0.325099	−	0.325099i	−0.525620	−	0.850719i	$-0.676167\pi$
$541$	175.879	−	175.879i	0.325099	−	0.325099i	0.850719	+	0.525620i	$0.176167\pi$
$542$	−439.115	−	439.115i	−0.810175	−	0.810175i
$543$			317.679i			0.585045i
$544$	470.780			0.865404
$545$		−	87.2949i		−	0.160174i
$546$			156.364i			0.286381i
$547$	−292.360	−	292.360i	−0.534480	−	0.534480i	0.387423	−	0.921902i	$-0.373365\pi$
$547$	−292.360	−	292.360i	−0.534480	−	0.534480i	−0.921902	+	0.387423i	$0.873365\pi$
$548$			121.162i			0.221099i
$549$	−98.3385	−	98.3385i	−0.179123	−	0.179123i
$550$	437.631	+	437.631i	0.795693	+	0.795693i
$551$	16.5043			0.0299533
$552$	208.396			0.377530
$553$	202.386	−	202.386i	0.365979	−	0.365979i
$554$			722.621i			1.30437i
$555$	48.4642	−	59.6761i	0.0873228	−	0.107524i
$556$	−462.741			−0.832268
$557$	−327.259	−	327.259i	−0.587539	−	0.587539i	0.349425	−	0.936964i	$-0.386377\pi$
$557$	−327.259	−	327.259i	−0.587539	−	0.587539i	−0.936964	+	0.349425i	$0.886377\pi$
$558$			7.43786i			0.0133295i
$559$			848.923i			1.51865i
$560$	5.28126	−	5.28126i	0.00943082	−	0.00943082i
$561$	−679.018	+	679.018i	−1.21037	+	1.21037i
$562$	281.066			0.500117
$563$	−42.5457	+	42.5457i	−0.0755696	+	0.0755696i	−0.743881	−	0.668312i	$-0.767017\pi$
$563$	−42.5457	+	42.5457i	−0.0755696	+	0.0755696i	0.668312	+	0.743881i	$0.267017\pi$
$564$	−312.519			−0.554111
$565$	46.9545			0.0831053
$566$		−	265.892i		−	0.469773i
$567$	208.959			0.368535
$568$	455.192	−	455.192i	0.801395	−	0.801395i
$569$	−641.876	−	641.876i	−1.12808	−	1.12808i	−0.990490	−	0.137587i	$-0.956065\pi$
$569$	−641.876	−	641.876i	−1.12808	−	1.12808i	−0.137587	−	0.990490i	$-0.543935\pi$
$570$	−4.46585	−	4.46585i	−0.00783483	−	0.00783483i
$571$	303.084			0.530794			0.265397	−	0.964139i	$-0.414497\pi$
$571$	303.084			0.530794			0.265397	+	0.964139i	$0.414497\pi$
$572$	334.029	−	334.029i	0.583967	−	0.583967i
$573$	−125.421	−	125.421i	−0.218885	−	0.218885i
$574$	−155.915	+	155.915i	−0.271630	+	0.271630i
$575$	132.627	+	132.627i	0.230656	+	0.230656i
$576$			69.3183i			0.120344i
$577$	155.193	−	155.193i	0.268965	−	0.268965i	−0.559718	−	0.828683i	$-0.689091\pi$
$577$	155.193	−	155.193i	0.268965	−	0.268965i	0.828683	+	0.559718i	$0.189091\pi$
$578$	14.4871	−	14.4871i	0.0250641	−	0.0250641i
$579$	575.994	+	575.994i	0.994808	+	0.994808i
$580$			9.68200i			0.0166931i
$581$	172.025			0.296084
$582$			207.380i			0.356323i
$583$		−	1099.76i		−	1.88638i
$584$	−400.083	−	400.083i	−0.685073	−	0.685073i
$585$			11.0902i			0.0189576i
$586$	−371.497	−	371.497i	−0.633954	−	0.633954i
$587$	−265.166	−	265.166i	−0.451730	−	0.451730i	0.444198	−	0.895929i	$-0.353489\pi$
$587$	−265.166	−	265.166i	−0.451730	−	0.451730i	−0.895929	+	0.444198i	$0.853489\pi$
$588$	−261.570			−0.444847
$589$	−9.10153			−0.0154525
$590$	−30.3264	+	30.3264i	−0.0514007	+	0.0514007i
$591$		−	551.267i		−	0.932770i
$592$	18.8772	+	182.072i	0.0318871	+	0.307555i
$593$	652.633			1.10056			0.550281	−	0.834980i	$-0.314521\pi$
$593$	652.633			1.10056			0.550281	+	0.834980i	$0.314521\pi$
$594$	444.603	+	444.603i	0.748489	+	0.748489i
$595$			26.2821i			0.0441716i
$596$			132.182i			0.221782i
$597$	−477.134	+	477.134i	−0.799219	+	0.799219i
$598$	−114.177	+	114.177i	−0.190932	+	0.190932i
$599$	−637.192			−1.06376			−0.531880	−	0.846820i	$-0.678514\pi$
$599$	−637.192			−1.06376			−0.531880	+	0.846820i	$0.678514\pi$
$600$	−474.498	+	474.498i	−0.790831	+	0.790831i
$601$	339.622			0.565094			0.282547	−	0.959253i	$-0.408821\pi$
$601$	339.622			0.565094			0.282547	+	0.959253i	$0.408821\pi$
$602$	−197.146			−0.327485
$603$		−	6.02218i		−	0.00998703i
$604$	−214.892			−0.355781
$605$	82.0577	−	82.0577i	0.135633	−	0.135633i
$606$	15.9752	+	15.9752i	0.0263617	+	0.0263617i
$607$	−386.313	−	386.313i	−0.636431	−	0.636431i	0.313242	−	0.949673i	$-0.398585\pi$
$607$	−386.313	−	386.313i	−0.636431	−	0.636431i	−0.949673	+	0.313242i	$0.898585\pi$
$608$	−56.4525			−0.0928495
$609$	41.3171	−	41.3171i	0.0678441	−	0.0678441i
$610$	−79.6215	−	79.6215i	−0.130527	−	0.130527i
$611$	535.573	−	535.573i	0.876551	−	0.876551i
$612$	−27.1110	−	27.1110i	−0.0442991	−	0.0442991i
$613$		−	289.345i		−	0.472015i	−0.971751	−	0.236008i	$-0.924161\pi$
$613$		−	289.345i		−	0.472015i	0.971751	−	0.236008i	$-0.0758390\pi$
$614$	73.8336	−	73.8336i	0.120250	−	0.120250i
$615$	−96.0066	+	96.0066i	−0.156108	+	0.156108i
$616$	242.637	+	242.637i	0.393891	+	0.393891i
$617$		−	645.129i		−	1.04559i	−0.852459	−	0.522795i	$-0.824889\pi$
$617$		−	645.129i		−	1.04559i	0.852459	−	0.522795i	$-0.175111\pi$
$618$	204.241			0.330487
$619$		−	304.651i		−	0.492166i	−0.969249	−	0.246083i	$-0.920856\pi$
$619$		−	304.651i		−	0.492166i	0.969249	−	0.246083i	$-0.0791435\pi$
$620$		−	5.33930i		−	0.00861177i
$621$	134.740	+	134.740i	0.216973	+	0.216973i
$622$		−	451.300i		−	0.725562i
$623$	−134.162	−	134.162i	−0.215348	−	0.215348i
$624$	−162.108	−	162.108i	−0.259789	−	0.259789i
$625$	−593.349			−0.949358
$626$	−609.086			−0.972981
$627$	81.4229	−	81.4229i	0.129861	−	0.129861i
$628$			81.0363i			0.129039i
$629$	−500.011	−	406.069i	−0.794930	−	0.645579i
$630$	−2.57549			−0.00408807
$631$	570.848	+	570.848i	0.904673	+	0.904673i	0.995836	−	0.0911634i	$-0.0290586\pi$
$631$	570.848	+	570.848i	0.904673	+	0.904673i	−0.0911634	+	0.995836i	$0.529059\pi$
$632$			1057.44i			1.67317i
$633$		−	346.733i		−	0.547761i
$634$	−419.530	+	419.530i	−0.661719	+	0.661719i
$635$	83.6443	−	83.6443i	0.131723	−	0.131723i
$636$	381.216			0.599396
$637$	448.260	−	448.260i	0.703705	−	0.703705i
$638$	199.103			0.312074
$639$	−88.0926			−0.137860
$640$		−	14.3451i		−	0.0224142i
$641$	142.943			0.223000			0.111500	−	0.993764i	$-0.464434\pi$
$641$	142.943			0.223000			0.111500	+	0.993764i	$0.464434\pi$
$642$	−482.303	+	482.303i	−0.751251	+	0.751251i
$643$	725.814	+	725.814i	1.12879	+	1.12879i	0.990374	+	0.138420i	$0.0442025\pi$
$643$	725.814	+	725.814i	1.12879	+	1.12879i	0.138420	+	0.990374i	$0.455798\pi$
$644$	23.5087	+	23.5087i	0.0365042	+	0.0365042i
$645$	−121.395			−0.188209
$646$	−37.4183	+	37.4183i	−0.0579230	+	0.0579230i
$647$	200.699	+	200.699i	0.310200	+	0.310200i	0.844987	−	0.534787i	$-0.179608\pi$
$647$	200.699	+	200.699i	0.310200	+	0.310200i	−0.534787	+	0.844987i	$0.679608\pi$
$648$	−545.892	+	545.892i	−0.842426	+	0.842426i
$649$	−552.922	−	552.922i	−0.851960	−	0.851960i
$650$		−	519.942i		−	0.799910i
$651$	−22.7850	+	22.7850i	−0.0349999	+	0.0349999i
$652$	269.310	−	269.310i	0.413052	−	0.413052i
$653$	−441.090	−	441.090i	−0.675482	−	0.675482i	0.283492	−	0.958975i	$-0.408507\pi$
$653$	−441.090	−	441.090i	−0.675482	−	0.675482i	−0.958975	+	0.283492i	$0.908507\pi$
$654$		−	622.265i		−	0.951476i
$655$	−93.7787			−0.143174
$656$		−	323.286i		−	0.492815i
$657$			77.4273i			0.117850i
$658$	124.376	+	124.376i	0.189022	+	0.189022i
$659$			652.584i			0.990264i	0.868818	+	0.495132i	$0.164880\pi$
$659$			652.584i			0.990264i	−0.868818	+	0.495132i	$0.835120\pi$
$660$	47.7657	+	47.7657i	0.0723723	+	0.0723723i
$661$	182.760	+	182.760i	0.276491	+	0.276491i	0.831706	−	0.555216i	$-0.187364\pi$
$661$	182.760	+	182.760i	0.276491	+	0.276491i	−0.555216	+	0.831706i	$0.687364\pi$
$662$	902.048			1.36261
$663$	806.729			1.21679
$664$	−449.403	+	449.403i	−0.676812	+	0.676812i
$665$		−	3.15156i		−	0.00473919i
$666$	39.7923	−	48.9980i	0.0597481	−	0.0735706i
$667$	60.3397			0.0904643
$668$	−206.589	−	206.589i	−0.309266	−	0.309266i
$669$		−	69.7495i		−	0.104259i
$670$		−	4.87596i		−	0.00727756i
$671$	1451.69	−	1451.69i	2.16347	−	2.16347i
$672$	−141.324	+	141.324i	−0.210304	+	0.210304i
$673$	−48.2331			−0.0716688			−0.0358344	−	0.999358i	$-0.511409\pi$
$673$	−48.2331			−0.0716688			−0.0358344	+	0.999358i	$0.511409\pi$
$674$	325.254	−	325.254i	0.482573	−	0.482573i
$675$	−613.580			−0.909008
$676$	−79.1699			−0.117115
$677$		−	65.2005i		−	0.0963080i	−0.998840	−	0.0481540i	$-0.984666\pi$
$677$		−	65.2005i		−	0.0963080i	0.998840	−	0.0481540i	$-0.0153338\pi$
$678$	334.706			0.493667
$679$	−73.1743	+	73.1743i	−0.107768	+	0.107768i
$680$	−68.6603	−	68.6603i	−0.100971	−	0.100971i
$681$	−49.2401	−	49.2401i	−0.0723056	−	0.0723056i
$682$	−109.799			−0.160995
$683$	−402.730	+	402.730i	−0.589648	+	0.589648i	−0.937536	−	0.347888i	$-0.886899\pi$
$683$	−402.730	+	402.730i	−0.589648	+	0.589648i	0.347888	+	0.937536i	$0.386899\pi$
$684$	3.25096	+	3.25096i	0.00475286	+	0.00475286i
$685$	29.6921	−	29.6921i	0.0433462	−	0.0433462i
$686$	221.013	+	221.013i	0.322176	+	0.322176i
$687$			101.920i			0.148356i
$688$	204.388	−	204.388i	0.297076	−	0.297076i
$689$	−653.301	+	653.301i	−0.948187	+	0.948187i
$690$	−16.3272	−	16.3272i	−0.0236626	−	0.0236626i
$691$			1143.83i			1.65532i	0.561227	+	0.827662i	$0.310329\pi$
$691$			1143.83i			1.65532i	−0.561227	+	0.827662i	$0.689671\pi$
$692$	−538.742			−0.778530
$693$		−	46.9571i		−	0.0677592i
$694$			507.928i			0.731884i
$695$	113.400	+	113.400i	0.163165	+	0.163165i
$696$			215.876i			0.310167i
$697$	804.415	+	804.415i	1.15411	+	1.15411i
$698$	134.480	+	134.480i	0.192665	+	0.192665i
$699$	−11.3534			−0.0162423
$700$	−107.054			−0.152934
$701$	−798.107	+	798.107i	−1.13853	+	1.13853i	−0.149811	+	0.988715i	$0.547867\pi$
$701$	−798.107	+	798.107i	−1.13853	+	1.13853i	−0.988715	+	0.149811i	$0.952133\pi$
$702$		−	528.224i		−	0.752456i
$703$	59.9577	+	48.6929i	0.0852883	+	0.0692644i
$704$	−1023.29			−1.45353
$705$	76.5861	+	76.5861i	0.108633	+	0.108633i
$706$		−	57.8442i		−	0.0819323i
$707$			11.2737i			0.0159459i
$708$	191.663	−	191.663i	0.270710	−	0.270710i
$709$	145.383	−	145.383i	0.205054	−	0.205054i	−0.597107	−	0.802161i	$-0.703683\pi$
$709$	145.383	−	145.383i	0.205054	−	0.205054i	0.802161	+	0.597107i	$0.203683\pi$
$710$	−71.3257			−0.100459
$711$	102.322	−	102.322i	0.143913	−	0.143913i
$712$	700.977			0.984519
$713$	−33.2753			−0.0466694
$714$			187.347i			0.262391i
$715$	−163.715			−0.228972
$716$	−218.063	+	218.063i	−0.304557	+	0.304557i
$717$	−43.7756	−	43.7756i	−0.0610538	−	0.0610538i
$718$	−108.328	−	108.328i	−0.150875	−	0.150875i
$719$	1231.32			1.71254			0.856269	−	0.516530i	$-0.172776\pi$
$719$	1231.32			1.71254			0.856269	+	0.516530i	$0.172776\pi$
$720$	2.67010	−	2.67010i	0.00370847	−	0.00370847i
$721$	72.0666	+	72.0666i	0.0999537	+	0.0999537i
$722$	−367.204	+	367.204i	−0.508593	+	0.508593i
$723$	−262.584	−	262.584i	−0.363186	−	0.363186i
$724$		−	187.242i		−	0.258621i
$725$	−137.388	+	137.388i	−0.189500	+	0.189500i
$726$	584.933	−	584.933i	0.805693	−	0.805693i
$727$	−26.4537	−	26.4537i	−0.0363875	−	0.0363875i	0.688679	−	0.725066i	$-0.258191\pi$
$727$	−26.4537	−	26.4537i	−0.0363875	−	0.0363875i	−0.725066	+	0.688679i	$0.758191\pi$
$728$		−	288.273i		−	0.395979i
$729$	−611.001			−0.838135
$730$			62.6904i			0.0858772i
$731$			1017.14i			1.39143i
$732$	503.206	+	503.206i	0.687441	+	0.687441i
$733$		−	666.104i		−	0.908736i	−0.890814	−	0.454368i	$-0.849865\pi$
$733$		−	666.104i		−	0.908736i	0.890814	−	0.454368i	$-0.150135\pi$
$734$	137.901	+	137.901i	0.187876	+	0.187876i
$735$	64.1005	+	64.1005i	0.0872116	+	0.0872116i
$736$	−206.391			−0.280422
$737$	88.9002			0.120624
$738$	−78.8277	+	78.8277i	−0.106813	+	0.106813i
$739$		−	650.489i		−	0.880229i	−0.897942	−	0.440114i	$-0.854938\pi$
$739$		−	650.489i		−	0.880229i	0.897942	−	0.440114i	$-0.145062\pi$
$740$	−28.5650	+	35.1734i	−0.0386014	+	0.0475316i
$741$	−96.7370			−0.130549
$742$	−151.717	−	151.717i	−0.204470	−	0.204470i
$743$			68.3034i			0.0919292i	0.998943	+	0.0459646i	$0.0146361\pi$
$743$			68.3034i			0.0919292i	−0.998943	+	0.0459646i	$0.985364\pi$
$744$		−	119.048i		−	0.160011i
$745$	32.3926	−	32.3926i	0.0434800	−	0.0434800i
$746$	452.782	−	452.782i	0.606946	−	0.606946i
$747$	86.9721			0.116429
$748$	400.217	−	400.217i	0.535049	−	0.535049i
$749$	−340.362			−0.454422
$750$	149.986			0.199981
$751$			484.624i			0.645305i	0.946518	+	0.322652i	$0.104574\pi$
$751$			484.624i			0.645305i	−0.946518	+	0.322652i	$0.895426\pi$
$752$	−257.891			−0.342940
$753$	448.719	−	448.719i	0.595909	−	0.595909i
$754$	−118.275	−	118.275i	−0.156864	−	0.156864i
$755$	52.6616	+	52.6616i	0.0697504	+	0.0697504i
$756$	−108.760			−0.143862
$757$	−454.129	+	454.129i	−0.599907	+	0.599907i	−0.940288	−	0.340381i	$-0.889444\pi$
$757$	−454.129	+	454.129i	−0.599907	+	0.599907i	0.340381	+	0.940288i	$0.389444\pi$
$758$	150.557	+	150.557i	0.198624	+	0.198624i
$759$	297.683	−	297.683i	0.392204	−	0.392204i
$760$	8.23325	+	8.23325i	0.0108332	+	0.0108332i
$761$		−	124.497i		−	0.163596i	−0.996649	−	0.0817982i	$-0.973934\pi$
$761$		−	124.497i		−	0.163596i	0.996649	−	0.0817982i	$-0.0260663\pi$
$762$	596.243	−	596.243i	0.782471	−	0.782471i
$763$	219.567	−	219.567i	0.287768	−	0.287768i
$764$	73.9238	+	73.9238i	0.0967589	+	0.0967589i
$765$			13.2877i			0.0173696i
$766$	−653.575			−0.853231
$767$			656.916i			0.856475i
$768$		−	857.040i		−	1.11594i
$769$	860.893	+	860.893i	1.11950	+	1.11950i	0.991815	+	0.127681i	$0.0407534\pi$
$769$	860.893	+	860.893i	1.11950	+	1.11950i	0.127681	+	0.991815i	$0.459247\pi$
$770$		−	38.0197i		−	0.0493762i
$771$	−455.373	−	455.373i	−0.590626	−	0.590626i
$772$	−339.494	−	339.494i	−0.439759	−	0.439759i
$773$	771.283			0.997778			0.498889	−	0.866666i	$-0.333741\pi$
$773$	771.283			0.997778			0.498889	+	0.866666i	$0.333741\pi$
$774$	−99.6730			−0.128776
$775$	75.7646	−	75.7646i	0.0977608	−	0.0977608i
$776$		−	382.326i		−	0.492688i
$777$	271.998	−	28.2006i	0.350062	−	0.0362942i
$778$	333.496			0.428657
$779$	−96.4596	−	96.4596i	−0.123825	−	0.123825i
$780$		−	56.7495i		−	0.0727558i
$781$		−	1300.43i		−	1.66509i
$782$	−136.801	+	136.801i	−0.174938	+	0.174938i
$783$	−139.576	+	139.576i	−0.178258	+	0.178258i
$784$	−215.848			−0.275316
$785$	19.8588	−	19.8588i	0.0252979	−	0.0252979i
$786$	−668.484			−0.850488
$787$	−623.639			−0.792425			−0.396213	−	0.918159i	$-0.629676\pi$
$787$	−623.639			−0.792425			−0.396213	+	0.918159i	$0.629676\pi$
$788$			324.920i			0.412335i
$789$	−1100.87			−1.39528
$790$	82.8471	−	82.8471i	0.104870	−	0.104870i
$791$	118.101	+	118.101i	0.149307	+	0.149307i
$792$	122.672	+	122.672i	0.154889	+	0.154889i
$793$	−1724.72			−2.17493
$794$	−342.287	+	342.287i	−0.431092	+	0.431092i
$795$	−93.4211	−	93.4211i	−0.117511	−	0.117511i
$796$	281.225	−	281.225i	0.353298	−	0.353298i
$797$	−701.754	−	701.754i	−0.880495	−	0.880495i	0.113090	−	0.993585i	$-0.463925\pi$
$797$	−701.754	−	701.754i	−0.880495	−	0.880495i	−0.993585	+	0.113090i	$0.963925\pi$
$798$		−	22.4653i		−	0.0281520i
$799$	641.696	−	641.696i	0.803124	−	0.803124i
$800$	469.932	−	469.932i	0.587415	−	0.587415i
$801$	−67.8294	−	67.8294i	−0.0846810	−	0.0846810i
$802$			616.465i			0.768659i
$803$	−1142.99			−1.42340
$804$			30.8160i			0.0383284i
$805$		−	11.5221i		−	0.0143132i
$806$	65.2249	+	65.2249i	0.0809242	+	0.0809242i
$807$			559.032i			0.692728i
$808$	−29.4519	−	29.4519i	−0.0364504	−	0.0364504i
$809$	132.202	+	132.202i	0.163414	+	0.163414i	0.784077	−	0.620663i	$-0.213137\pi$
$809$	132.202	+	132.202i	0.163414	+	0.163414i	−0.620663	+	0.784077i	$0.713137\pi$
$810$	85.5378			0.105602
$811$	−1153.23			−1.42199			−0.710995	−	0.703198i	$-0.751755\pi$
$811$	−1153.23			−1.42199			−0.710995	+	0.703198i	$0.751755\pi$
$812$	−24.3525	+	24.3525i	−0.0299908	+	0.0299908i
$813$		−	1360.19i		−	1.67305i
$814$	723.315	+	587.419i	0.888594	+	0.721645i
$815$	−131.995			−0.161957
$816$	−194.230	−	194.230i	−0.238026	−	0.238026i
$817$		−	121.968i		−	0.149287i
$818$			201.838i			0.246746i
$819$	−27.8944	+	27.8944i	−0.0340591	+	0.0340591i
$820$	56.5868	−	56.5868i	0.0690083	−	0.0690083i
$821$	1573.26			1.91628			0.958138	−	0.286307i	$-0.0924278\pi$
$821$	1573.26			1.91628			0.958138	+	0.286307i	$0.0924278\pi$
$822$	211.655	−	211.655i	0.257487	−	0.257487i
$823$	−664.845			−0.807831			−0.403915	−	0.914796i	$-0.632351\pi$
$823$	−664.845			−0.807831			−0.403915	+	0.914796i	$0.632351\pi$
$824$	−376.539			−0.456964
$825$			1355.59i			1.64314i
$826$	−152.556			−0.184693
$827$	−921.316	+	921.316i	−1.11405	+	1.11405i	−0.121448	+	0.992598i	$0.538754\pi$
$827$	−921.316	+	921.316i	−1.11405	+	1.11405i	−0.992598	+	0.121448i	$0.961246\pi$
$828$	11.8855	+	11.8855i	0.0143545	+	0.0143545i
$829$	−83.2492	−	83.2492i	−0.100421	−	0.100421i	0.655111	−	0.755532i	$-0.272622\pi$
$829$	−83.2492	−	83.2492i	−0.100421	−	0.100421i	−0.755532	+	0.655111i	$0.772622\pi$
$830$	70.4185			0.0848416
$831$	−1119.18	+	1119.18i	−1.34679	+	1.34679i
$832$	607.874	+	607.874i	0.730618	+	0.730618i
$833$	537.083	−	537.083i	0.644757	−	0.644757i
$834$	808.349	+	808.349i	0.969243	+	0.969243i
$835$			101.254i			0.121262i
$836$	−47.9911	+	47.9911i	−0.0574056	+	0.0574056i
$837$	76.9715	−	76.9715i	0.0919612	−	0.0919612i
$838$	293.771	+	293.771i	0.350562	+	0.350562i
$839$		−	799.534i		−	0.952960i	−0.879185	−	0.476480i	$-0.841912\pi$
$839$		−	799.534i		−	0.952960i	0.879185	−	0.476480i	$-0.158088\pi$
$840$	41.2225			0.0490745
$841$		−	778.495i		−	0.925677i
$842$			1060.76i			1.25981i
$843$	435.309	+	435.309i	0.516381	+	0.516381i
$844$			204.366i			0.242140i
$845$	19.4014	+	19.4014i	0.0229603	+	0.0229603i
$846$	62.8822	+	62.8822i	0.0743289	+	0.0743289i
$847$	412.789			0.487354
$848$	314.580			0.370967
$849$	411.808	−	411.808i	0.485050	−	0.485050i
$850$		−	622.967i		−	0.732903i
$851$	219.206	+	178.021i	0.257586	+	0.209191i
$852$	450.777			0.529081
$853$	−462.562	−	462.562i	−0.542276	−	0.542276i	0.381919	−	0.924196i	$-0.375263\pi$
$853$	−462.562	−	462.562i	−0.542276	−	0.542276i	−0.924196	+	0.381919i	$0.875263\pi$
$854$		−	400.533i		−	0.469008i
$855$		−	1.59337i		−	0.00186359i
$856$	889.174	−	889.174i	1.03875	−	1.03875i
$857$	325.901	−	325.901i	0.380282	−	0.380282i	−0.490922	−	0.871204i	$-0.663340\pi$
$857$	325.901	−	325.901i	0.380282	−	0.380282i	0.871204	+	0.490922i	$0.163340\pi$
$858$	−1167.01			−1.36015
$859$	661.306	−	661.306i	0.769856	−	0.769856i	−0.208225	−	0.978081i	$-0.566769\pi$
$859$	661.306	−	661.306i	0.769856	−	0.769856i	0.978081	+	0.208225i	$0.0667687\pi$
$860$	71.5506			0.0831984
$861$	−482.958			−0.560927
$862$		−	413.182i		−	0.479330i
$863$	1231.50			1.42699			0.713497	−	0.700658i	$-0.247110\pi$
$863$	1231.50			1.42699			0.713497	+	0.700658i	$0.247110\pi$
$864$	477.418	−	477.418i	0.552567	−	0.552567i
$865$	132.025	+	132.025i	0.152630	+	0.152630i
$866$	787.424	+	787.424i	0.909265	+	0.909265i
$867$	44.8745			0.0517584
$868$	13.4296	−	13.4296i	0.0154719	−	0.0154719i
$869$	1510.50	+	1510.50i	1.73820	+	1.73820i
$870$	16.9132	−	16.9132i	0.0194405	−	0.0194405i
$871$	−52.8103	−	52.8103i	−0.0606318	−	0.0606318i
$872$			1147.21i			1.31561i
$873$	−36.9954	+	36.9954i	−0.0423773	+	0.0423773i
$874$	16.4042	−	16.4042i	0.0187691	−	0.0187691i
$875$	52.9226	+	52.9226i	0.0604830	+	0.0604830i
$876$		−	396.202i		−	0.452286i
$877$	−63.0445			−0.0718866			−0.0359433	−	0.999354i	$-0.511444\pi$
$877$	−63.0445			−0.0718866			−0.0359433	+	0.999354i	$0.511444\pi$
$878$		−	514.192i		−	0.585640i
$879$		−	1150.73i		−	1.30914i
$880$	39.4164	+	39.4164i	0.0447913	+	0.0447913i
$881$			1196.99i			1.35867i	0.733827	+	0.679336i	$0.237732\pi$
$881$			1196.99i			1.35867i	−0.733827	+	0.679336i	$0.762268\pi$
$882$	52.6307	+	52.6307i	0.0596721	+	0.0596721i
$883$	420.334	+	420.334i	0.476030	+	0.476030i	0.903859	−	0.427830i	$-0.140722\pi$
$883$	420.334	+	420.334i	0.476030	+	0.476030i	−0.427830	+	0.903859i	$0.640722\pi$
$884$	−475.490			−0.537885
$885$	−93.9380			−0.106145
$886$	−381.267	+	381.267i	−0.430324	+	0.430324i
$887$			404.749i			0.456312i	0.973625	+	0.228156i	$0.0732696\pi$
$887$			404.749i			0.456312i	−0.973625	+	0.228156i	$0.926730\pi$
$888$	−636.904	+	784.249i	−0.717235	+	0.883163i
$889$	420.770			0.473307
$890$	−54.9193	−	54.9193i	−0.0617071	−	0.0617071i
$891$			1559.55i			1.75034i
$892$			41.1107i			0.0460882i
$893$	−76.9475	+	76.9475i	−0.0861674	+	0.0861674i
$894$	230.905	−	230.905i	0.258283	−	0.258283i
$895$	106.877			0.119416
$896$	36.0812	−	36.0812i	0.0402692	−	0.0402692i
$897$	−353.671			−0.394282
$898$	−717.230			−0.798697
$899$		−	34.4696i		−	0.0383422i
$900$	−54.1244			−0.0601382
$901$	−782.752	+	782.752i	−0.868759	+	0.868759i
$902$	−1163.67	−	1163.67i	−1.29009	−	1.29009i
$903$	−305.336	−	305.336i	−0.338135	−	0.338135i
$904$	−617.064			−0.682593
$905$	−45.8857	+	45.8857i	−0.0507024	+	0.0507024i
$906$	375.388	+	375.388i	0.414336	+	0.414336i
$907$	−268.378	+	268.378i	−0.295896	+	0.295896i	−0.839404	−	0.543508i	$-0.817096\pi$
$907$	−268.378	+	268.378i	−0.295896	+	0.295896i	0.543508	+	0.839404i	$0.317096\pi$
$908$	29.0224	+	29.0224i	0.0319630	+	0.0319630i
$909$			5.69977i			0.00627038i
$910$	−22.5852	+	22.5852i	−0.0248189	+	0.0248189i
$911$	1094.95	−	1094.95i	1.20192	−	1.20192i	0.228342	−	0.973581i	$-0.426669\pi$
$911$	1094.95	−	1094.95i	1.20192	−	1.20192i	0.973581	−	0.228342i	$-0.0733305\pi$
$912$	23.2906	+	23.2906i	0.0255379	+	0.0255379i
$913$			1283.89i			1.40624i
$914$	625.695			0.684568
$915$		−	246.632i		−	0.269544i
$916$		−	60.0723i		−	0.0655811i
$917$	−235.875	−	235.875i	−0.257225	−	0.257225i
$918$		−	632.891i		−	0.689424i
$919$	−544.251	−	544.251i	−0.592221	−	0.592221i	0.346010	−	0.938231i	$-0.387536\pi$
$919$	−544.251	−	544.251i	−0.592221	−	0.592221i	−0.938231	+	0.346010i	$0.887536\pi$
$920$	30.1008	+	30.1008i	0.0327183	+	0.0327183i
$921$	228.704			0.248321
$922$	710.219			0.770303
$923$	−772.511	+	772.511i	−0.836957	+	0.836957i
$924$			240.284i			0.260047i
$925$	−904.448	+	93.7728i	−0.977782	+	0.101376i
$926$	−386.574			−0.417467
$927$	36.4354	+	36.4354i	0.0393047	+	0.0393047i
$928$		−	213.799i		−	0.230386i
$929$		−	811.254i		−	0.873255i	−0.899642	−	0.436628i	$-0.856173\pi$
$929$		−	811.254i		−	0.873255i	0.899642	−	0.436628i	$-0.143827\pi$
$930$	−9.32706	+	9.32706i	−0.0100291	+	0.0100291i
$931$	−64.4030	+	64.4030i	−0.0691762	+	0.0691762i
$932$	6.69175			0.00717999
$933$	698.965	−	698.965i	0.749158	−	0.749158i
$934$	−1283.80			−1.37451
$935$	−196.155			−0.209791
$936$		−	145.745i		−	0.155710i
$937$	−734.830			−0.784237			−0.392119	−	0.919915i	$-0.628258\pi$
$937$	−734.830			−0.784237			−0.392119	+	0.919915i	$0.628258\pi$
$938$	12.2642	−	12.2642i	0.0130748	−	0.0130748i
$939$	−943.341	−	943.341i	−1.00462	−	1.00462i
$940$	−45.1403	−	45.1403i	−0.0480215	−	0.0480215i
$941$	1741.80			1.85101			0.925507	−	0.378730i	$-0.123639\pi$
$941$	1741.80			1.85101			0.925507	+	0.378730i	$0.123639\pi$
$942$	141.560	−	141.560i	0.150276	−	0.150276i
$943$	−352.657	−	352.657i	−0.373974	−	0.373974i
$944$	158.160	−	158.160i	0.167543	−	0.167543i
$945$	26.6527	+	26.6527i	0.0282039	+	0.0282039i
$946$		−	1471.39i		−	1.55538i
$947$	736.970	−	736.970i	0.778216	−	0.778216i	−0.201311	−	0.979527i	$-0.564520\pi$
$947$	736.970	−	736.970i	0.778216	−	0.778216i	0.979527	+	0.201311i	$0.0645203\pi$
$948$	−523.593	+	523.593i	−0.552313	+	0.552313i
$949$	678.984	+	678.984i	0.715473	+	0.715473i
$950$			74.7017i			0.0786334i
$951$	−1299.52			−1.36648
$952$		−	345.393i		−	0.362808i
$953$		−	100.144i		−	0.105083i	−0.998619	−	0.0525414i	$-0.983268\pi$
$953$		−	100.144i		−	0.105083i	0.998619	−	0.0525414i	$-0.0167321\pi$
$954$	−76.7048	−	76.7048i	−0.0804034	−	0.0804034i
$955$		−	36.2317i		−	0.0379389i
$956$	25.8015	+	25.8015i	0.0269891	+	0.0269891i
$957$	308.367	+	308.367i	0.322223	+	0.322223i
$958$	193.480			0.201963
$959$	149.365			0.155751
$960$	−86.9251	+	86.9251i	−0.0905470	+	0.0905470i
$961$		−	941.991i		−	0.980220i
$962$	−80.7279	−	778.629i	−0.0839168	−	0.809386i
$963$	−172.080			−0.178692
$964$	154.768	+	154.768i	0.160548	+	0.160548i
$965$			166.393i			0.172428i
$966$		−	82.1333i		−	0.0850241i
$967$	−121.105	+	121.105i	−0.125238	+	0.125238i	−0.766948	−	0.641710i	$-0.778225\pi$
$967$	−121.105	+	121.105i	−0.125238	+	0.125238i	0.641710	+	0.766948i	$0.278225\pi$
$968$	−1078.38	+	1078.38i	−1.11403	+	1.11403i
$969$	−115.905			−0.119613
$970$	−29.9540	+	29.9540i	−0.0308804	+	0.0308804i
$971$	−127.750			−0.131565			−0.0657826	−	0.997834i	$-0.520954\pi$
$971$	−127.750			−0.131565			−0.0657826	+	0.997834i	$0.520954\pi$
$972$	−118.203			−0.121608
$973$			570.454i			0.586283i
$974$	605.840			0.622012
$975$	805.275	−	805.275i	0.825924	−	0.825924i
$976$	415.247	+	415.247i	0.425458	+	0.425458i
$977$	−115.752	−	115.752i	−0.118477	−	0.118477i	0.645383	−	0.763860i	$-0.276698\pi$
$977$	−115.752	−	115.752i	−0.118477	−	0.118477i	−0.763860	+	0.645383i	$0.776698\pi$
$978$	−940.900			−0.962065
$979$	1001.31	−	1001.31i	1.02279	−	1.02279i
$980$	−37.7812	−	37.7812i	−0.0385522	−	0.0385522i
$981$	111.009	−	111.009i	0.113159	−	0.113159i
$982$	21.0077	+	21.0077i	0.0213927	+	0.0213927i
$983$		−	27.4845i		−	0.0279598i	−0.999902	−	0.0139799i	$-0.995550\pi$
$983$		−	27.4845i		−	0.0279598i	0.999902	−	0.0139799i	$-0.00445008\pi$
$984$	1261.70	−	1261.70i	1.28221	−	1.28221i
$985$	79.6251	−	79.6251i	0.0808377	−	0.0808377i
$986$	−141.712	−	141.712i	−0.143724	−	0.143724i
$987$			385.264i			0.390338i
$988$	57.0173			0.0577098
$989$		−	445.914i		−	0.450874i
$990$		−	19.2220i		−	0.0194161i
$991$	147.450	+	147.450i	0.148790	+	0.148790i	0.777577	−	0.628788i	$-0.216448\pi$
$991$	147.450	+	147.450i	0.148790	+	0.148790i	−0.628788	+	0.777577i	$0.716448\pi$
$992$			117.903i			0.118853i
$993$	1397.08	+	1397.08i	1.40692	+	1.40692i
$994$	−179.401	−	179.401i	−0.180484	−	0.180484i
$995$	−137.835			−0.138527
$996$	−445.044			−0.446831
$997$	−345.971	+	345.971i	−0.347012	+	0.347012i	−0.858995	−	0.511984i	$-0.828911\pi$
$997$	−345.971	+	345.971i	−0.347012	+	0.347012i	0.511984	+	0.858995i	$0.328911\pi$
$998$		−	418.876i		−	0.419716i
$999$	−918.856	+	95.2666i	−0.919776	+	0.0953620i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.3.d.a.31.5	yes	12
3.2	odd	2		333.3.i.a.253.2		12
4.3	odd	2		592.3.k.e.401.2		12
37.6	odd	4	inner	37.3.d.a.6.5	✓	12
111.80	even	4		333.3.i.a.154.2		12
148.43	even	4		592.3.k.e.561.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.3.d.a.6.5	✓	12	37.6	odd	4	inner
37.3.d.a.31.5	yes	12	1.1	even	1	trivial
333.3.i.a.154.2		12	111.80	even	4
333.3.i.a.253.2		12	3.2	odd	2
592.3.k.e.401.2		12	4.3	odd	2
592.3.k.e.561.5		12	148.43	even	4

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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	37.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.02961 + 1.02961i) q^{2} +3.18930i q^{3} -1.87979i q^{4} +(-0.460662 + 0.460662i) q^{5} +(-3.28375 + 3.28375i) q^{6} -2.31735 q^{7} +(6.05392 - 6.05392i) q^{8} -1.17160 q^{9} +O(q^{10})\)	\(q+(1.02961 + 1.02961i) q^{2} +3.18930i q^{3} -1.87979i q^{4} +(-0.460662 + 0.460662i) q^{5} +(-3.28375 + 3.28375i) q^{6} -2.31735 q^{7} +(6.05392 - 6.05392i) q^{8} -1.17160 q^{9} -0.948609 q^{10} -17.2954i q^{11} +5.99520 q^{12} +(-10.2742 + 10.2742i) q^{13} +(-2.38597 - 2.38597i) q^{14} +(-1.46919 - 1.46919i) q^{15} +4.94725 q^{16} +(-12.3100 + 12.3100i) q^{17} +(-1.20630 - 1.20630i) q^{18} +(1.47612 - 1.47612i) q^{19} +(0.865947 + 0.865947i) q^{20} -7.39070i q^{21} +(17.8076 - 17.8076i) q^{22} +(5.39671 - 5.39671i) q^{23} +(19.3077 + 19.3077i) q^{24} +24.5756i q^{25} -21.1568 q^{26} +24.9671i q^{27} +4.35612i q^{28} +(5.59041 + 5.59041i) q^{29} -3.02540i q^{30} +(-3.08292 - 3.08292i) q^{31} +(-19.1219 - 19.1219i) q^{32} +55.1600 q^{33} -25.3490 q^{34} +(1.06751 - 1.06751i) q^{35} +2.20236i q^{36} +(3.81569 + 36.8027i) q^{37} +3.03967 q^{38} +(-32.7673 - 32.7673i) q^{39} +5.57762i q^{40} -65.3467i q^{41} +(7.60958 - 7.60958i) q^{42} +(41.3135 - 41.3135i) q^{43} -32.5116 q^{44} +(0.539714 - 0.539714i) q^{45} +11.1131 q^{46} -52.1282 q^{47} +15.7782i q^{48} -43.6299 q^{49} +(-25.3034 + 25.3034i) q^{50} +(-39.2601 - 39.2601i) q^{51} +(19.3132 + 19.3132i) q^{52} +63.5869 q^{53} +(-25.7065 + 25.7065i) q^{54} +(7.96733 + 7.96733i) q^{55} +(-14.0290 + 14.0290i) q^{56} +(4.70779 + 4.70779i) q^{57} +11.5119i q^{58} +(31.9694 - 31.9694i) q^{59} +(-2.76176 + 2.76176i) q^{60} +(83.9349 + 83.9349i) q^{61} -6.34844i q^{62} +2.71501 q^{63} -59.1654i q^{64} -9.46583i q^{65} +(56.7936 + 56.7936i) q^{66} +5.14012i q^{67} +(23.1401 + 23.1401i) q^{68} +(17.2117 + 17.2117i) q^{69} +2.19826 q^{70} +75.1898 q^{71} +(-7.09279 + 7.09279i) q^{72} -66.0866i q^{73} +(-33.9639 + 41.8213i) q^{74} -78.3788 q^{75} +(-2.77479 - 2.77479i) q^{76} +40.0794i q^{77} -67.4754i q^{78} +(-87.3354 + 87.3354i) q^{79} +(-2.27901 + 2.27901i) q^{80} -90.1718 q^{81} +(67.2819 - 67.2819i) q^{82} -74.2334 q^{83} -13.8929 q^{84} -11.3415i q^{85} +85.0740 q^{86} +(-17.8295 + 17.8295i) q^{87} +(-104.705 - 104.705i) q^{88} +(57.8946 + 57.8946i) q^{89} +1.11139 q^{90} +(23.8088 - 23.8088i) q^{91} +(-10.1447 - 10.1447i) q^{92} +(9.83235 - 9.83235i) q^{93} +(-53.6719 - 53.6719i) q^{94} +1.35999i q^{95} +(60.9854 - 60.9854i) q^{96} +(31.5767 - 31.5767i) q^{97} +(-44.9220 - 44.9220i) q^{98} +20.2633i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 6 q^{5} + 6 q^{6} - 4 q^{7} + 36 q^{8} - 60 q^{9}+O(q^{10}) \) 12 * q - 6 * q^2 - 6 * q^5 + 6 * q^6 - 4 * q^7 + 36 * q^8 - 60 * q^9	\( 12 q - 6 q^{2} - 6 q^{5} + 6 q^{6} - 4 q^{7} + 36 q^{8} - 60 q^{9} - 16 q^{10} + 64 q^{12} + 14 q^{13} - 70 q^{14} - 2 q^{15} - 96 q^{16} + 2 q^{17} + 132 q^{18} + 14 q^{19} - 24 q^{20} + 22 q^{22} + 56 q^{23} - 84 q^{24} - 48 q^{26} + 60 q^{29} + 72 q^{31} + 208 q^{32} + 56 q^{33} + 112 q^{34} - 154 q^{35} - 66 q^{37} - 336 q^{38} - 46 q^{39} + 90 q^{42} + 70 q^{43} + 80 q^{44} + 232 q^{45} - 424 q^{46} - 384 q^{47} + 144 q^{49} - 34 q^{50} - 126 q^{51} + 328 q^{52} - 56 q^{53} - 194 q^{54} + 70 q^{55} + 16 q^{56} - 94 q^{57} + 184 q^{59} + 276 q^{60} + 132 q^{61} - 400 q^{63} + 614 q^{66} + 116 q^{68} + 368 q^{69} + 556 q^{70} + 68 q^{71} - 692 q^{72} - 382 q^{74} + 116 q^{75} + 12 q^{76} - 2 q^{79} + 4 q^{80} - 76 q^{81} + 374 q^{82} + 108 q^{83} - 1436 q^{84} + 140 q^{86} - 420 q^{87} - 788 q^{88} + 278 q^{89} - 664 q^{90} - 450 q^{91} + 652 q^{92} + 584 q^{93} + 118 q^{94} + 1584 q^{96} - 244 q^{97} + 416 q^{98}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^5 + 6 * q^6 - 4 * q^7 + 36 * q^8 - 60 * q^9 - 16 * q^10 + 64 * q^12 + 14 * q^13 - 70 * q^14 - 2 * q^15 - 96 * q^16 + 2 * q^17 + 132 * q^18 + 14 * q^19 - 24 * q^20 + 22 * q^22 + 56 * q^23 - 84 * q^24 - 48 * q^26 + 60 * q^29 + 72 * q^31 + 208 * q^32 + 56 * q^33 + 112 * q^34 - 154 * q^35 - 66 * q^37 - 336 * q^38 - 46 * q^39 + 90 * q^42 + 70 * q^43 + 80 * q^44 + 232 * q^45 - 424 * q^46 - 384 * q^47 + 144 * q^49 - 34 * q^50 - 126 * q^51 + 328 * q^52 - 56 * q^53 - 194 * q^54 + 70 * q^55 + 16 * q^56 - 94 * q^57 + 184 * q^59 + 276 * q^60 + 132 * q^61 - 400 * q^63 + 614 * q^66 + 116 * q^68 + 368 * q^69 + 556 * q^70 + 68 * q^71 - 692 * q^72 - 382 * q^74 + 116 * q^75 + 12 * q^76 - 2 * q^79 + 4 * q^80 - 76 * q^81 + 374 * q^82 + 108 * q^83 - 1436 * q^84 + 140 * q^86 - 420 * q^87 - 788 * q^88 + 278 * q^89 - 664 * q^90 - 450 * q^91 + 652 * q^92 + 584 * q^93 + 118 * q^94 + 1584 * q^96 - 244 * q^97 + 416 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more