LMFDB - Embedded newform 245.4.e.p.116.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,4,Mod(116,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("245.116");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	245.e (of order $3$, degree $2$, not 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:	$14.4554679514$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
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} - 2 x^{11} + 27 x^{10} + 22 x^{9} + 399 x^{8} + 492 x^{7} + 4046 x^{6} + 8784 x^{5} + 22536 x^{4} + \cdots + 784 $ x^12 - 2x^11 + 27x^10 + 22x^9 + 399x^8 + 492x^7 + 4046x^6 + 8784x^5 + 22536x^4 + 22736x^3 + 18792x^2 + 4256*x + 784
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			116.6
Root			$2.05188 - 3.55396i$ of defining polynomial
Character	$\chi$	$=$	245.116
Dual form			245.4.e.p.226.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.75899 + 4.77871i) q^{2} +(-1.93020 + 3.34320i) q^{3} +(-11.2240 + 19.4406i) q^{4} +(2.50000 + 4.33013i) q^{5} -21.3015 q^{6} -79.7239 q^{8} +(6.04869 + 10.4766i) q^{9} +O(q^{10})$	\(q+(2.75899 + 4.77871i) q^{2} +(-1.93020 + 3.34320i) q^{3} +(-11.2240 + 19.4406i) q^{4} +(2.50000 + 4.33013i) q^{5} -21.3015 q^{6} -79.7239 q^{8} +(6.04869 + 10.4766i) q^{9} +(-13.7949 + 23.8935i) q^{10} +(-17.2605 + 29.8961i) q^{11} +(-43.3291 - 75.0482i) q^{12} +68.8935 q^{13} -19.3020 q^{15} +(-130.165 - 225.452i) q^{16} +(45.7173 - 79.1847i) q^{17} +(-33.3765 + 57.8098i) q^{18} +(-5.91392 - 10.2432i) q^{19} -112.240 q^{20} -190.486 q^{22} +(0.0520827 + 0.0902099i) q^{23} +(153.883 - 266.533i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(190.076 + 329.222i) q^{26} -150.931 q^{27} +190.863 q^{29} +(-53.2538 - 92.2384i) q^{30} +(-79.9010 + 138.393i) q^{31} +(399.352 - 691.697i) q^{32} +(-66.6324 - 115.411i) q^{33} +504.534 q^{34} -271.562 q^{36} +(88.9538 + 154.073i) q^{37} +(32.6328 - 56.5217i) q^{38} +(-132.978 + 230.324i) q^{39} +(-199.310 - 345.215i) q^{40} +145.247 q^{41} +8.25729 q^{43} +(-387.465 - 671.109i) q^{44} +(-30.2435 + 52.3832i) q^{45} +(-0.287391 + 0.497776i) q^{46} +(-130.264 - 225.624i) q^{47} +1004.98 q^{48} -137.949 q^{50} +(176.487 + 305.684i) q^{51} +(-773.262 + 1339.33i) q^{52} +(-176.554 + 305.800i) q^{53} +(-416.417 - 721.256i) q^{54} -172.605 q^{55} +45.6601 q^{57} +(526.589 + 912.079i) q^{58} +(-120.247 + 208.274i) q^{59} +(216.645 - 375.241i) q^{60} +(-389.094 - 673.931i) q^{61} -881.783 q^{62} +2324.58 q^{64} +(172.234 + 298.318i) q^{65} +(367.676 - 636.833i) q^{66} +(-75.9723 + 131.588i) q^{67} +(1026.26 + 1777.54i) q^{68} -0.402119 q^{69} -311.449 q^{71} +(-482.225 - 835.238i) q^{72} +(-319.944 + 554.159i) q^{73} +(-490.845 + 850.168i) q^{74} +(-48.2549 - 83.5799i) q^{75} +265.512 q^{76} -1467.54 q^{78} +(-195.593 - 338.777i) q^{79} +(650.825 - 1127.26i) q^{80} +(128.012 - 221.723i) q^{81} +(400.736 + 694.095i) q^{82} +493.205 q^{83} +457.173 q^{85} +(22.7817 + 39.4591i) q^{86} +(-368.403 + 638.093i) q^{87} +(1376.08 - 2383.44i) q^{88} +(-236.925 - 410.366i) q^{89} -333.765 q^{90} -2.33831 q^{92} +(-308.449 - 534.249i) q^{93} +(718.795 - 1244.99i) q^{94} +(29.5696 - 51.2160i) q^{95} +(1541.65 + 2670.22i) q^{96} +839.005 q^{97} -417.615 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - 16 q^{3} - 14 q^{4} + 30 q^{5} + 48 q^{6} - 132 q^{8} - 70 q^{9}+O(q^{10}) $ 12 * q + 2 * q^2 - 16 * q^3 - 14 * q^4 + 30 * q^5 + 48 * q^6 - 132 * q^8 - 70 * q^9	\( 12 q + 2 q^{2} - 16 q^{3} - 14 q^{4} + 30 q^{5} + 48 q^{6} - 132 q^{8} - 70 q^{9} - 10 q^{10} + 16 q^{11} - 160 q^{12} + 336 q^{13} - 160 q^{15} - 298 q^{16} + 4 q^{17} - 354 q^{18} - 308 q^{19} - 140 q^{20} - 472 q^{22} + 336 q^{23} + 92 q^{24} - 150 q^{25} - 56 q^{26} + 1928 q^{27} + 352 q^{29} + 120 q^{30} - 392 q^{31} + 770 q^{32} - 188 q^{33} + 1624 q^{34} + 460 q^{36} + 140 q^{37} - 20 q^{38} - 140 q^{39} - 330 q^{40} + 1312 q^{41} - 776 q^{43} + 160 q^{44} + 350 q^{45} + 388 q^{46} - 628 q^{47} + 2792 q^{48} - 100 q^{50} - 744 q^{51} - 1520 q^{52} + 676 q^{53} - 2284 q^{54} + 160 q^{55} + 2936 q^{57} + 2012 q^{58} - 996 q^{59} + 800 q^{60} - 740 q^{61} - 728 q^{62} + 2852 q^{64} + 840 q^{65} + 3620 q^{66} - 1768 q^{67} + 2940 q^{68} - 2096 q^{69} - 448 q^{71} - 2858 q^{72} - 2640 q^{73} - 928 q^{74} - 400 q^{75} - 2680 q^{76} + 16 q^{78} - 1636 q^{79} + 1490 q^{80} - 4442 q^{81} + 1756 q^{82} + 280 q^{83} + 40 q^{85} - 1180 q^{86} - 1940 q^{87} + 5652 q^{88} + 1904 q^{89} - 3540 q^{90} - 3904 q^{92} + 1592 q^{93} + 3332 q^{94} + 1540 q^{95} + 6460 q^{96} + 1032 q^{97} - 5608 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 - 16 * q^3 - 14 * q^4 + 30 * q^5 + 48 * q^6 - 132 * q^8 - 70 * q^9 - 10 * q^10 + 16 * q^11 - 160 * q^12 + 336 * q^13 - 160 * q^15 - 298 * q^16 + 4 * q^17 - 354 * q^18 - 308 * q^19 - 140 * q^20 - 472 * q^22 + 336 * q^23 + 92 * q^24 - 150 * q^25 - 56 * q^26 + 1928 * q^27 + 352 * q^29 + 120 * q^30 - 392 * q^31 + 770 * q^32 - 188 * q^33 + 1624 * q^34 + 460 * q^36 + 140 * q^37 - 20 * q^38 - 140 * q^39 - 330 * q^40 + 1312 * q^41 - 776 * q^43 + 160 * q^44 + 350 * q^45 + 388 * q^46 - 628 * q^47 + 2792 * q^48 - 100 * q^50 - 744 * q^51 - 1520 * q^52 + 676 * q^53 - 2284 * q^54 + 160 * q^55 + 2936 * q^57 + 2012 * q^58 - 996 * q^59 + 800 * q^60 - 740 * q^61 - 728 * q^62 + 2852 * q^64 + 840 * q^65 + 3620 * q^66 - 1768 * q^67 + 2940 * q^68 - 2096 * q^69 - 448 * q^71 - 2858 * q^72 - 2640 * q^73 - 928 * q^74 - 400 * q^75 - 2680 * q^76 + 16 * q^78 - 1636 * q^79 + 1490 * q^80 - 4442 * q^81 + 1756 * q^82 + 280 * q^83 + 40 * q^85 - 1180 * q^86 - 1940 * q^87 + 5652 * q^88 + 1904 * q^89 - 3540 * q^90 - 3904 * q^92 + 1592 * q^93 + 3332 * q^94 + 1540 * q^95 + 6460 * q^96 + 1032 * q^97 - 5608 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	2.75899	+	4.77871i	0.975449	+	1.68953i	0.678445	+	0.734651i	$0.262654\pi$
$2$	2.75899	+	4.77871i	0.975449	+	1.68953i	0.297004	+	0.954876i	$0.404012\pi$
$3$	−1.93020	+	3.34320i	−0.371466	+	0.643398i	−0.989791	−	0.142524i	$-0.954478\pi$
$3$	−1.93020	+	3.34320i	−0.371466	+	0.643398i	0.618325	+	0.785922i	$0.287812\pi$
$4$	−11.2240	+	19.4406i	−1.40300	+	2.43007i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$6$	−21.3015			−1.44939
$7$		0			0
$7$		0			0
$8$	−79.7239			−3.52333
$9$	6.04869	+	10.4766i	0.224026	+	0.388024i
$10$	−13.7949	+	23.8935i	−0.436234	+	0.755580i
$11$	−17.2605	+	29.8961i	−0.473113	+	0.819456i	−0.999526	−	0.0307725i	$-0.990203\pi$
$11$	−17.2605	+	29.8961i	−0.473113	+	0.819456i	0.526413	+	0.850229i	$0.323537\pi$
$12$	−43.3291	−	75.0482i	−1.04234	−	1.80538i
$13$	68.8935			1.46982			0.734908	−	0.678167i	$-0.237225\pi$
$13$	68.8935			1.46982			0.734908	+	0.678167i	$0.237225\pi$
$14$		0			0
$15$	−19.3020			−0.332250
$16$	−130.165	−	225.452i	−2.03383	−	3.52269i
$17$	45.7173	−	79.1847i	0.652239	−	1.12971i	−0.330339	−	0.943862i	$-0.607163\pi$
$17$	45.7173	−	79.1847i	0.652239	−	1.12971i	0.982578	−	0.185849i	$-0.0595036\pi$
$18$	−33.3765	+	57.8098i	−0.437051	+	0.756995i
$19$	−5.91392	−	10.2432i	−0.0714077	−	0.123682i	0.828111	−	0.560564i	$-0.189416\pi$
$19$	−5.91392	−	10.2432i	−0.0714077	−	0.123682i	−0.899518	+	0.436883i	$0.856082\pi$
$20$	−112.240			−1.25488
$21$		0			0
$22$	−190.486			−1.84599
$23$	0.0520827	+	0.0902099i	0.000472174	+	0.000817829i	0.866261	−	0.499591i	$-0.166516\pi$
$23$	0.0520827	+	0.0902099i	0.000472174	+	0.000817829i	−0.865789	+	0.500409i	$0.833183\pi$
$24$	153.883	−	266.533i	1.30880	−	2.26691i
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	190.076	+	329.222i	1.43373	+	2.48330i
$27$	−150.931			−1.07580
$28$		0			0
$29$	190.863			1.22215			0.611076	−	0.791572i	$-0.290737\pi$
$29$	190.863			1.22215			0.611076	+	0.791572i	$0.290737\pi$
$30$	−53.2538	−	92.2384i	−0.324093	−	0.561345i
$31$	−79.9010	+	138.393i	−0.462924	+	0.801807i	−0.999105	−	0.0422954i	$-0.986533\pi$
$31$	−79.9010	+	138.393i	−0.462924	+	0.801807i	0.536181	+	0.844103i	$0.319866\pi$
$32$	399.352	−	691.697i	2.20613	−	3.82112i
$33$	−66.6324	−	115.411i	−0.351491	−	0.608801i
$34$	504.534			2.54491
$35$		0			0
$36$	−271.562			−1.25723
$37$	88.9538	+	154.073i	0.395241	+	0.684577i	0.993132	−	0.117000i	$-0.0373277\pi$
$37$	88.9538	+	154.073i	0.395241	+	0.684577i	−0.597891	+	0.801577i	$0.703994\pi$
$38$	32.6328	−	56.5217i	0.139309	−	0.241290i
$39$	−132.978	+	230.324i	−0.545987	+	0.945678i
$40$	−199.310	−	345.215i	−0.787841	−	1.36458i
$41$	145.247			0.553264			0.276632	−	0.960976i	$-0.410782\pi$
$41$	145.247			0.553264			0.276632	+	0.960976i	$0.410782\pi$
$42$		0			0
$43$	8.25729			0.0292843			0.0146421	−	0.999893i	$-0.495339\pi$
$43$	8.25729			0.0292843			0.0146421	+	0.999893i	$0.495339\pi$
$44$	−387.465	−	671.109i	−1.32756	−	2.29940i
$45$	−30.2435	+	52.3832i	−0.100187	+	0.173529i
$46$	−0.287391	+	0.497776i	−0.000921163	+	0.00159550i
$47$	−130.264	−	225.624i	−0.404277	−	0.700228i	0.589960	−	0.807432i	$-0.299143\pi$
$47$	−130.264	−	225.624i	−0.404277	−	0.700228i	−0.994237	+	0.107204i	$0.965810\pi$
$48$	1004.98			3.02199
$49$		0			0
$50$	−137.949			−0.390180
$51$	176.487	+	305.684i	0.484570	+	0.839300i
$52$	−773.262	+	1339.33i	−2.06216	+	3.57176i
$53$	−176.554	+	305.800i	−0.457576	+	0.792544i	−0.998832	−	0.0483132i	$-0.984615\pi$
$53$	−176.554	+	305.800i	−0.457576	+	0.792544i	0.541257	+	0.840857i	$0.317949\pi$
$54$	−416.417	−	721.256i	−1.04939	−	1.81760i
$55$	−172.605			−0.423165
$56$		0			0
$57$	45.6601			0.106102
$58$	526.589	+	912.079i	1.19215	+	2.06486i
$59$	−120.247	+	208.274i	−0.265337	+	0.459576i	−0.967652	−	0.252290i	$-0.918816\pi$
$59$	−120.247	+	208.274i	−0.265337	+	0.459576i	0.702315	+	0.711866i	$0.252150\pi$
$60$	216.645	−	375.241i	0.466147	−	0.807390i
$61$	−389.094	−	673.931i	−0.816695	−	1.41456i	−0.908104	−	0.418744i	$-0.862470\pi$
$61$	−389.094	−	673.931i	−0.816695	−	1.41456i	0.0914091	−	0.995813i	$-0.470863\pi$
$62$	−881.783			−1.80623
$63$		0			0
$64$	2324.58			4.54020
$65$	172.234	+	298.318i	0.328661	+	0.569257i
$66$	367.676	−	636.833i	0.685724	−	1.18771i
$67$	−75.9723	+	131.588i	−0.138530	+	0.239940i	−0.926940	−	0.375209i	$-0.877571\pi$
$67$	−75.9723	+	131.588i	−0.138530	+	0.239940i	0.788411	+	0.615149i	$0.210904\pi$
$68$	1026.26	+	1777.54i	1.83019	+	3.16998i
$69$	−0.402119			−0.000701587
$70$		0			0
$71$	−311.449			−0.520594			−0.260297	−	0.965529i	$-0.583820\pi$
$71$	−311.449			−0.520594			−0.260297	+	0.965529i	$0.583820\pi$
$72$	−482.225	−	835.238i	−0.789316	−	1.36714i
$73$	−319.944	+	554.159i	−0.512967	+	0.888485i	0.486920	+	0.873447i	$0.338120\pi$
$73$	−319.944	+	554.159i	−0.512967	+	0.888485i	−0.999887	+	0.0150383i	$0.995213\pi$
$74$	−490.845	+	850.168i	−0.771075	+	1.33554i
$75$	−48.2549	−	83.5799i	−0.0742933	−	0.128680i
$76$	265.512			0.400740
$77$		0			0
$78$	−1467.54			−2.13033
$79$	−195.593	−	338.777i	−0.278556	−	0.482473i	0.692470	−	0.721447i	$-0.256522\pi$
$79$	−195.593	−	338.777i	−0.278556	−	0.482473i	−0.971026	+	0.238973i	$0.923189\pi$
$80$	650.825	−	1127.26i	0.909556	−	1.57540i
$81$	128.012	−	221.723i	0.175599	−	0.304147i
$82$	400.736	+	694.095i	0.539681	+	0.934755i
$83$	493.205			0.652245			0.326122	−	0.945328i	$-0.394258\pi$
$83$	493.205			0.652245			0.326122	+	0.945328i	$0.394258\pi$
$84$		0			0
$85$	457.173			0.583381
$86$	22.7817	+	39.4591i	0.0285653	+	0.0494766i
$87$	−368.403	+	638.093i	−0.453988	+	0.786331i
$88$	1376.08	−	2383.44i	1.66694	−	2.88722i
$89$	−236.925	−	410.366i	−0.282180	−	0.488749i	0.689742	−	0.724056i	$-0.257724\pi$
$89$	−236.925	−	410.366i	−0.282180	−	0.488749i	−0.971921	+	0.235306i	$0.924391\pi$
$90$	−333.765			−0.390910
$91$		0			0
$92$	−2.33831			−0.00264984
$93$	−308.449	−	534.249i	−0.343921	−	0.595689i
$94$	718.795	−	1244.99i	0.788703	−	1.36607i
$95$	29.5696	−	51.2160i	0.0319345	−	0.0553121i
$96$	1541.65	+	2670.22i	1.63900	+	2.83884i
$97$	839.005			0.878227			0.439114	−	0.898431i	$-0.355293\pi$
$97$	839.005			0.878227			0.439114	+	0.898431i	$0.355293\pi$
$98$		0			0
$99$	−417.615			−0.423958
$100$	−280.600	−	486.014i	−0.280600	−	0.486014i
$101$	−443.720	+	768.546i	−0.437146	+	0.757160i	−0.997468	−	0.0711152i	$-0.977344\pi$
$101$	−443.720	+	768.546i	−0.437146	+	0.757160i	0.560322	+	0.828275i	$0.310678\pi$
$102$	−973.848	+	1686.75i	−0.945347	+	1.63739i
$103$	−309.544	−	536.145i	−0.296119	−	0.512893i	0.679126	−	0.734022i	$-0.262359\pi$
$103$	−309.544	−	536.145i	−0.296119	−	0.512893i	−0.975245	+	0.221129i	$0.929026\pi$
$104$	−5492.46			−5.17865
$105$		0			0
$106$	−1948.44			−1.78537
$107$	1075.65	+	1863.08i	0.971841	+	1.68328i	0.689990	+	0.723819i	$0.257615\pi$
$107$	1075.65	+	1863.08i	0.971841	+	1.68328i	0.281851	+	0.959458i	$0.409052\pi$
$108$	1694.05	−	2934.19i	1.50936	−	2.61428i
$109$	203.538	−	352.539i	0.178857	−	0.309790i	−0.762632	−	0.646832i	$-0.776093\pi$
$109$	203.538	−	352.539i	0.178857	−	0.309790i	0.941489	+	0.337043i	$0.109427\pi$
$110$	−476.216	−	824.830i	−0.412776	−	0.714950i
$111$	−686.793			−0.587275
$112$		0			0
$113$	−349.581			−0.291025			−0.145513	−	0.989356i	$-0.546483\pi$
$113$	−349.581			−0.291025			−0.145513	+	0.989356i	$0.546483\pi$
$114$	125.976	+	218.196i	0.103497	+	0.179263i
$115$	−0.260414	+	0.451050i	−0.000211163	+	0.000365744i
$116$	−2142.25	+	3710.49i	−1.71468	+	2.96992i
$117$	416.715	+	721.772i	0.329277	+	0.570324i
$118$	−1327.04			−1.03529
$119$		0			0
$120$	1538.83			1.17063
$121$	69.6478	+	120.633i	0.0523274	+	0.0906337i
$122$	2147.01	−	3718.73i	1.59329	−	2.75966i
$123$	−280.356	+	485.591i	−0.205519	+	0.355969i
$124$	−1793.62	−	3106.64i	−1.29897	−	2.24987i
$125$	−125.000			−0.0894427
$126$		0			0
$127$	1183.78			0.827114			0.413557	−	0.910478i	$-0.364286\pi$
$127$	1183.78			0.827114			0.413557	+	0.910478i	$0.364286\pi$
$128$	3218.68	+	5574.92i	2.22261	+	3.84967i
$129$	−15.9382	+	27.6057i	−0.0108781	+	0.0188415i
$130$	−950.381	+	1646.11i	−0.641184	+	1.11056i
$131$	−111.679	−	193.433i	−0.0744840	−	0.129010i	0.826378	−	0.563116i	$-0.190398\pi$
$131$	−111.679	−	193.433i	−0.0744840	−	0.129010i	−0.900862	+	0.434106i	$0.857064\pi$
$132$	2991.53			1.97257
$133$		0			0
$134$	−838.426			−0.540515
$135$	−377.328	−	653.551i	−0.240557	−	0.416657i
$136$	−3644.76	+	6312.91i	−2.29806	+	3.98035i
$137$	−1018.33	+	1763.80i	−0.635050	+	1.09994i	0.351454	+	0.936205i	$0.385687\pi$
$137$	−1018.33	+	1763.80i	−0.635050	+	1.09994i	−0.986504	+	0.163734i	$0.947646\pi$
$138$	−1.10944	−	1.92161i	−0.000684362	−	0.00118535i
$139$	2687.00			1.63963			0.819815	−	0.572629i	$-0.194076\pi$
$139$	2687.00			1.63963			0.819815	+	0.572629i	$0.194076\pi$
$140$		0			0
$141$	1005.74			0.600701
$142$	−859.283	−	1488.32i	−0.507813	−	0.879557i
$143$	−1189.14	+	2059.65i	−0.695390	+	1.20445i
$144$	1574.66	−	2727.38i	0.911259	−	1.57835i
$145$	477.158	+	826.462i	0.273282	+	0.473337i
$146$	−3530.88			−2.00149
$147$		0			0
$148$	−3993.68			−2.21810
$149$	−336.750	−	583.268i	−0.185152	−	0.320693i	0.758476	−	0.651701i	$-0.225944\pi$
$149$	−336.750	−	583.268i	−0.185152	−	0.320693i	−0.943628	+	0.331009i	$0.892611\pi$
$150$	266.269	−	461.192i	0.144939	−	0.251041i
$151$	1062.59	−	1840.46i	0.572664	−	0.991884i	−0.423627	−	0.905837i	$-0.639243\pi$
$151$	1062.59	−	1840.46i	0.572664	−	0.991884i	0.996291	−	0.0860467i	$-0.0274234\pi$
$152$	471.480	+	816.628i	0.251593	+	0.435772i
$153$	1106.12			0.584473
$154$		0			0
$155$	−799.010			−0.414052
$156$	−2985.09	−	5170.33i	−1.53204	−	2.65358i
$157$	1406.52	−	2436.16i	0.714983	−	1.23839i	−0.247984	−	0.968764i	$-0.579768\pi$
$157$	1406.52	−	2436.16i	0.714983	−	1.23839i	0.962966	−	0.269622i	$-0.0868988\pi$
$158$	1079.28	−	1869.36i	0.543435	−	0.941257i
$159$	−681.566	−	1180.51i	−0.339948	−	0.588807i
$160$	3993.52			1.97322
$161$		0			0
$162$	1412.73			0.685153
$163$	672.210	+	1164.30i	0.323016	+	0.559480i	0.981109	−	0.193457i	$-0.0619699\pi$
$163$	672.210	+	1164.30i	0.323016	+	0.559480i	−0.658093	+	0.752937i	$0.728637\pi$
$164$	−1630.26	+	2823.69i	−0.776231	+	1.34447i
$165$	333.162	−	577.054i	0.157192	−	0.272264i
$166$	1360.75	+	2356.88i	0.636232	+	1.10199i
$167$	1451.24			0.672456			0.336228	−	0.941781i	$-0.390849\pi$
$167$	1451.24			0.672456			0.336228	+	0.941781i	$0.390849\pi$
$168$		0			0
$169$	2549.31			1.16036
$170$	1261.33	+	2184.69i	0.569058	+	0.985638i
$171$	71.5429	−	123.916i	0.0319943	−	0.0554157i
$172$	−92.6799	+	160.526i	−0.0410859	+	0.0711629i
$173$	989.579	+	1714.00i	0.434892	+	0.753255i	0.997287	−	0.0736139i	$-0.0234532\pi$
$173$	989.579	+	1714.00i	0.434892	+	0.753255i	−0.562395	+	0.826869i	$0.690120\pi$
$174$	−4065.68			−1.77137
$175$		0			0
$176$	8986.87			3.84893
$177$	−464.201	−	804.020i	−0.197127	−	0.341434i
$178$	1307.35	−	2264.39i	0.550504	−	0.953501i
$179$	2179.33	−	3774.71i	0.910005	−	1.57617i	0.0959500	−	0.995386i	$-0.469411\pi$
$179$	2179.33	−	3774.71i	0.910005	−	1.57617i	0.814055	−	0.580788i	$-0.197256\pi$
$180$	−678.906	−	1175.90i	−0.281126	−	0.486924i
$181$	−377.923			−0.155198			−0.0775988	−	0.996985i	$-0.524725\pi$
$181$	−377.923			−0.155198			−0.0775988	+	0.996985i	$0.524725\pi$
$182$		0			0
$183$	3004.11			1.21350
$184$	−4.15224	−	7.19189i	−0.00166362	−	0.00288148i
$185$	−444.769	+	770.363i	−0.176757	+	0.306152i
$186$	1702.01	−	2947.97i	0.670955	−	1.16213i
$187$	1578.21	+	2733.54i	0.617166	+	1.06896i
$188$	5848.36			2.26880
$189$		0			0
$190$	326.328			0.124602
$191$	1212.97	+	2100.93i	0.459517	+	0.795906i	0.998935	−	0.0461315i	$-0.0146893\pi$
$191$	1212.97	+	2100.93i	0.459517	+	0.795906i	−0.539419	+	0.842038i	$0.681356\pi$
$192$	−4486.90	+	7771.54i	−1.68653	+	2.92116i
$193$	311.461	−	539.467i	0.116163	−	0.201200i	−0.802081	−	0.597215i	$-0.796274\pi$
$193$	311.461	−	539.467i	0.116163	−	0.201200i	0.918244	+	0.396015i	$0.129607\pi$
$194$	2314.80	+	4009.36i	0.856666	+	1.48379i
$195$	−1329.78			−0.488346
$196$		0			0
$197$	2842.29			1.02794			0.513971	−	0.857807i	$-0.328174\pi$
$197$	2842.29			1.02794			0.513971	+	0.857807i	$0.328174\pi$
$198$	−1152.19	−	1995.66i	−0.413550	−	0.716289i
$199$	433.682	−	751.159i	0.154487	−	0.267579i	−0.778385	−	0.627787i	$-0.783961\pi$
$199$	433.682	−	751.159i	0.154487	−	0.267579i	0.932872	+	0.360208i	$0.117294\pi$
$200$	996.549	−	1726.07i	0.352333	−	0.610259i
$201$	−293.283	−	507.980i	−0.102918	−	0.178260i
$202$	−4896.87			−1.70566
$203$		0			0
$204$	−7923.55			−2.71941
$205$	363.119	+	628.940i	0.123714	+	0.214278i
$206$	1708.05	−	2958.44i	0.577698	−	1.00060i
$207$	−0.630065	+	1.09130i	−0.000211558	+	0.000366429i
$208$	−8967.52	−	15532.2i	−2.98935	−	5.17771i
$209$	408.309			0.135136
$210$		0			0
$211$	−5975.92			−1.94976			−0.974880	−	0.222730i	$-0.928503\pi$
$211$	−5975.92			−1.94976			−0.974880	+	0.222730i	$0.928503\pi$
$212$	−3963.28	−	6864.61i	−1.28396	−	2.22388i
$213$	601.157	−	1041.23i	0.193383	−	0.334949i
$214$	−5935.40	+	10280.4i	−1.89596	+	3.28390i
$215$	20.6432	+	35.7551i	0.00654817	+	0.0113418i
$216$	12032.8			3.79042
$217$		0			0
$218$	2246.24			0.697864
$219$	−1235.11	−	2139.27i	−0.381100	−	0.660084i
$220$	1937.33	−	3355.55i	0.593702	−	1.02832i
$221$	3149.62	−	5455.31i	0.958672	−	1.66047i
$222$	−1894.85	−	3281.98i	−0.572857	−	0.992217i
$223$	−5181.58			−1.55598			−0.777992	−	0.628274i	$-0.783762\pi$
$223$	−5181.58			−1.55598			−0.777992	+	0.628274i	$0.783762\pi$
$224$		0			0
$225$	−302.435			−0.0896102
$226$	−964.491	−	1670.55i	−0.283880	−	0.491695i
$227$	−1876.53	+	3250.24i	−0.548677	+	0.950336i	0.449689	+	0.893185i	$0.351535\pi$
$227$	−1876.53	+	3250.24i	−0.548677	+	0.950336i	−0.998366	+	0.0571507i	$0.981798\pi$
$228$	−512.489	+	887.658i	−0.148862	+	0.257836i
$229$	3129.07	+	5419.71i	0.902947	+	1.56395i	0.823650	+	0.567099i	$0.191934\pi$
$229$	3129.07	+	5419.71i	0.902947	+	1.56395i	0.0792969	+	0.996851i	$0.474732\pi$
$230$	−2.87391			−0.000823913
$231$		0			0
$232$	−15216.4			−4.30605
$233$	−889.981	−	1541.49i	−0.250234	−	0.433419i	0.713356	−	0.700802i	$-0.247174\pi$
$233$	−889.981	−	1541.49i	−0.250234	−	0.433419i	−0.963590	+	0.267383i	$0.913841\pi$
$234$	−2299.42	+	3982.72i	−0.642385	+	1.11264i
$235$	651.322	−	1128.12i	0.180798	−	0.313151i
$236$	−2699.31	−	4675.35i	−0.744536	−	1.28957i
$237$	1510.13			0.413897
$238$		0			0
$239$	3519.46			0.952532			0.476266	−	0.879301i	$-0.341990\pi$
$239$	3519.46			0.952532			0.476266	+	0.879301i	$0.341990\pi$
$240$	2512.44	+	4351.67i	0.675739	+	1.17041i
$241$	−181.465	+	314.307i	−0.0485029	+	0.0840095i	−0.889258	−	0.457407i	$-0.848778\pi$
$241$	−181.465	+	314.307i	−0.0485029	+	0.0840095i	0.840755	+	0.541416i	$0.182112\pi$
$242$	−384.315	+	665.652i	−0.102085	+	0.176817i
$243$	−1543.39	−	2673.24i	−0.407444	−	0.705713i
$244$	17468.8			4.58330
$245$		0			0
$246$	−3093.99			−0.801894
$247$	−407.430	−	705.690i	−0.104956	−	0.181789i
$248$	6370.01	−	11033.2i	1.63103	−	2.82503i
$249$	−951.983	+	1648.88i	−0.242287	+	0.419653i
$250$	−344.873	−	597.338i	−0.0872468	−	0.151116i
$251$	−5333.85			−1.34131			−0.670656	−	0.741768i	$-0.733988\pi$
$251$	−5333.85			−1.34131			−0.670656	+	0.741768i	$0.733988\pi$
$252$		0			0
$253$	−3.59590			−0.000893567
$254$	3266.03	+	5656.93i	0.806807	+	1.39743i
$255$	−882.433	+	1528.42i	−0.216706	+	0.375346i
$256$	−8462.27	+	14657.1i	−2.06598	+	3.57839i
$257$	1219.39	+	2112.04i	0.295966	+	0.512629i	0.975209	−	0.221285i	$-0.0710250\pi$
$257$	1219.39	+	2112.04i	0.295966	+	0.512629i	−0.679243	+	0.733914i	$0.737692\pi$
$258$	−175.893			−0.0424442
$259$		0			0
$260$	−7732.62			−1.84445
$261$	1154.47	+	1999.61i	0.273793	+	0.474224i
$262$	616.239	−	1067.36i	0.145311	−	0.251685i
$263$	−763.126	+	1321.77i	−0.178921	+	0.309901i	−0.941511	−	0.336981i	$-0.890594\pi$
$263$	−763.126	+	1321.77i	−0.178921	+	0.309901i	0.762590	+	0.646882i	$0.223927\pi$
$264$	5312.19	+	9200.99i	1.23842	+	2.14501i
$265$	−1765.54			−0.409268
$266$		0			0
$267$	1829.25			0.419281
$268$	−1705.43	−	2953.89i	−0.388715	−	0.673274i
$269$	3782.06	−	6550.72i	0.857235	−	1.48478i	−0.0173203	−	0.999850i	$-0.505513\pi$
$269$	3782.06	−	6550.72i	0.857235	−	1.48478i	0.874556	−	0.484925i	$-0.161153\pi$
$270$	2082.09	−	3606.28i	0.469303	−	0.812856i
$271$	−2141.34	−	3708.91i	−0.479990	−	0.831367i	0.519747	−	0.854320i	$-0.326026\pi$
$271$	−2141.34	−	3708.91i	−0.479990	−	0.831367i	−0.999737	+	0.0229535i	$0.992693\pi$
$272$	−23803.2			−5.30617
$273$		0			0
$274$	−11238.2			−2.47784
$275$	−431.513	−	747.403i	−0.0946227	−	0.163891i
$276$	4.51339	−	7.81743i	0.000984328	−	0.00170491i
$277$	2004.20	−	3471.38i	0.434732	−	0.752979i	−0.562541	−	0.826769i	$-0.690176\pi$
$277$	2004.20	−	3471.38i	0.434732	−	0.752979i	0.997274	+	0.0737905i	$0.0235096\pi$
$278$	7413.40	+	12840.4i	1.59937	+	2.77020i
$279$	−1933.18			−0.414827
$280$		0			0
$281$	6935.44			1.47236			0.736181	−	0.676785i	$-0.236627\pi$
$281$	6935.44			1.47236			0.736181	+	0.676785i	$0.236627\pi$
$282$	2774.83	+	4806.15i	0.585953	+	1.01490i
$283$	1333.32	−	2309.38i	0.280062	−	0.485082i	−0.691338	−	0.722532i	$-0.742978\pi$
$283$	1333.32	−	2309.38i	0.280062	−	0.485082i	0.971400	+	0.237450i	$0.0763116\pi$
$284$	3495.71	−	6054.74i	0.730394	−	1.26508i
$285$	114.150	+	197.714i	0.0237252	+	0.0410932i
$286$	−13123.3			−2.71327
$287$		0			0
$288$	9662.22			1.97692
$289$	−1723.64	−	2985.43i	−0.350832	−	0.607660i
$290$	−2632.95	+	4560.40i	−0.533144	+	0.923433i
$291$	−1619.44	+	2804.96i	−0.326232	+	0.565050i
$292$	−7182.11	−	12439.8i	−1.43939	−	2.49309i
$293$	5939.10			1.18418			0.592092	−	0.805870i	$-0.298302\pi$
$293$	5939.10			1.18418			0.592092	+	0.805870i	$0.298302\pi$
$294$		0			0
$295$	−1202.47			−0.237324
$296$	−7091.74	−	12283.3i	−1.39256	−	2.41199i
$297$	2605.15	−	4512.26i	0.508977	−	0.881575i
$298$	1858.18	−	3218.46i	0.361213	−	0.625639i
$299$	3.58816	+	6.21488i	0.000694009	+	0.00120206i
$300$	2166.45			0.416934
$301$		0			0
$302$	11726.7			2.23442
$303$	−1712.93	−	2966.89i	−0.324770	−	0.562519i
$304$	−1539.57	+	2666.61i	−0.290462	+	0.503095i
$305$	1945.47	−	3369.65i	0.365237	−	0.632609i
$306$	3051.77	+	5285.82i	0.570124	+	0.987484i
$307$	10381.5			1.92998			0.964992	−	0.262278i	$-0.0844737\pi$
$307$	10381.5			1.92998			0.964992	+	0.262278i	$0.0844737\pi$
$308$		0			0
$309$	2389.92			0.439993
$310$	−2204.46	−	3818.23i	−0.403886	−	0.699551i
$311$	−2120.27	+	3672.42i	−0.386590	+	0.669594i	−0.991988	−	0.126329i	$-0.959681\pi$
$311$	−2120.27	+	3672.42i	−0.386590	+	0.669594i	0.605398	+	0.795923i	$0.293014\pi$
$312$	10601.5	−	18362.4i	1.92369	−	3.33194i
$313$	141.951	+	245.867i	0.0256344	+	0.0444001i	0.878558	−	0.477636i	$-0.158506\pi$
$313$	141.951	+	245.867i	0.0256344	+	0.0444001i	−0.852924	+	0.522036i	$0.825173\pi$
$314$	15522.2			2.78972
$315$		0			0
$316$	8781.36			1.56326
$317$	−869.746	−	1506.44i	−0.154100	−	0.266910i	0.778631	−	0.627482i	$-0.215915\pi$
$317$	−869.746	−	1506.44i	−0.154100	−	0.266910i	−0.932731	+	0.360573i	$0.882581\pi$
$318$	3760.86	−	6514.01i	0.663204	−	1.14870i
$319$	−3294.40	+	5706.07i	−0.578217	+	1.00150i
$320$	5811.46	+	10065.7i	1.01522	+	1.75841i
$321$	−8304.85			−1.44402
$322$		0			0
$323$	−1081.47			−0.186300
$324$	2873.62	+	4977.25i	0.492733	+	0.853438i
$325$	−861.169	+	1491.59i	−0.146982	+	0.254580i
$326$	−3709.24	+	6424.59i	−0.630171	+	1.09149i
$327$	785.737	+	1360.94i	0.132879	+	0.230153i
$328$	−11579.7			−1.94933
$329$		0			0
$330$	3676.76			0.613330
$331$	−2803.48	−	4855.77i	−0.465538	−	0.806336i	0.533687	−	0.845682i	$-0.320806\pi$
$331$	−2803.48	−	4855.77i	−0.465538	−	0.806336i	−0.999226	+	0.0393458i	$0.987473\pi$
$332$	−5535.75	+	9588.19i	−0.915101	+	1.58500i
$333$	−1076.11	+	1863.87i	−0.177088	+	0.306726i
$334$	4003.94	+	6935.04i	0.655946	+	1.13613i
$335$	−759.723			−0.123905
$336$		0			0
$337$	−9427.44			−1.52387			−0.761937	−	0.647652i	$-0.775751\pi$
$337$	−9427.44			−1.52387			−0.761937	+	0.647652i	$0.775751\pi$
$338$	7033.52	+	12182.4i	1.13187	+	1.96046i
$339$	674.760	−	1168.72i	0.108106	−	0.187245i
$340$	−5131.32	+	8887.70i	−0.818484	+	1.41766i
$341$	−2758.27	−	4777.46i	−0.438031	−	0.758692i
$342$	789.544			0.124835
$343$		0			0
$344$	−658.303			−0.103178
$345$	−1.00530	−	1.74123i	−0.000156880	−	0.000271723i
$346$	−5460.47	+	9457.81i	−0.848430	+	1.46952i
$347$	−5817.11	+	10075.5i	−0.899939	+	1.55874i	−0.0723679	+	0.997378i	$0.523056\pi$
$347$	−5817.11	+	10075.5i	−0.899939	+	1.55874i	−0.827571	+	0.561361i	$0.810278\pi$
$348$	−8269.93	−	14323.9i	−1.27389	−	2.20645i
$349$	−1317.10			−0.202013			−0.101006	−	0.994886i	$-0.532206\pi$
$349$	−1317.10			−0.202013			−0.101006	+	0.994886i	$0.532206\pi$
$350$		0			0
$351$	−10398.2			−1.58124
$352$	13786.0	+	23878.1i	2.08750	+	3.61565i
$353$	−2924.41	+	5065.23i	−0.440937	+	0.763725i	−0.997759	−	0.0669064i	$-0.978687\pi$
$353$	−2924.41	+	5065.23i	−0.440937	+	0.763725i	0.556822	+	0.830632i	$0.312020\pi$
$354$	2561.45	−	4436.56i	0.384575	−	0.666104i
$355$	−778.622	−	1348.61i	−0.116408	−	0.201625i
$356$	10637.0			1.58359
$357$		0			0
$358$	24051.0			3.55065
$359$	6211.00	+	10757.8i	0.913104	+	1.58154i	0.809654	+	0.586907i	$0.199655\pi$
$359$	6211.00	+	10757.8i	0.913104	+	1.58154i	0.103450	+	0.994635i	$0.467012\pi$
$360$	2411.13	−	4176.19i	0.352993	−	0.611402i
$361$	3359.55	−	5818.91i	0.489802	−	0.848362i
$362$	−1042.68	−	1805.98i	−0.151387	−	0.262211i
$363$	−537.735			−0.0777515
$364$		0			0
$365$	−3199.44			−0.458812
$366$	8288.30	+	14355.8i	1.18371	+	2.05024i
$367$	3295.39	−	5707.78i	0.468713	−	0.811836i	−0.530647	−	0.847593i	$-0.678051\pi$
$367$	3295.39	−	5707.78i	0.468713	−	0.811836i	0.999361	+	0.0357573i	$0.0113843\pi$
$368$	13.5587	−	23.4844i	0.00192064	−	0.00332665i
$369$	878.557	+	1521.71i	0.123945	+	0.214680i
$370$	−4908.45			−0.689670
$371$		0			0
$372$	13848.1			1.93009
$373$	−172.139	−	298.154i	−0.0238955	−	0.0413882i	0.853830	−	0.520551i	$-0.174274\pi$
$373$	−172.139	−	298.154i	−0.0238955	−	0.0413882i	−0.877726	+	0.479163i	$0.840940\pi$
$374$	−8708.52	+	15083.6i	−1.20403	+	2.08544i
$375$	241.274	−	417.900i	0.0332250	−	0.0575473i
$376$	10385.2	+	17987.7i	1.42440	+	2.46713i
$377$	13149.2			1.79634
$378$		0			0
$379$	5241.23			0.710353			0.355177	−	0.934799i	$-0.384421\pi$
$379$	5241.23			0.710353			0.355177	+	0.934799i	$0.384421\pi$
$380$	663.779	+	1149.70i	0.0896083	+	0.155206i
$381$	−2284.93	+	3957.61i	−0.307245	+	0.532164i
$382$	−6693.16	+	11592.9i	−0.896470	+	1.55273i
$383$	−3798.69	−	6579.52i	−0.506798	−	0.877801i	−0.999969	−	0.00786802i	$-0.997496\pi$
$383$	−3798.69	−	6579.52i	−0.506798	−	0.877801i	0.493171	−	0.869933i	$-0.335838\pi$
$384$	−24850.7			−3.30250
$385$		0			0
$386$	3437.27			0.453245
$387$	49.9458	+	86.5086i	0.00656043	+	0.0113630i
$388$	−9417.01	+	16310.7i	−1.23216	+	2.13416i
$389$	−1550.92	+	2686.27i	−0.202146	+	0.350127i	−0.949220	−	0.314614i	$-0.898125\pi$
$389$	−1550.92	+	2686.27i	−0.202146	+	0.350127i	0.747074	+	0.664741i	$0.231458\pi$
$390$	−3668.84	−	6354.62i	−0.476357	−	0.825074i
$391$	9.52432			0.00123188
$392$		0			0
$393$	862.246			0.110673
$394$	7841.84	+	13582.5i	1.00271	+	1.73674i
$395$	977.965	−	1693.89i	0.124574	−	0.215769i
$396$	4687.31	−	8118.67i	0.594814	−	1.03025i
$397$	1466.03	+	2539.24i	0.185335	+	0.321009i	0.943689	−	0.330833i	$-0.107330\pi$
$397$	1466.03	+	2539.24i	0.185335	+	0.321009i	−0.758355	+	0.651842i	$0.773996\pi$
$398$	4786.09			0.602777
$399$		0			0
$400$	6508.25			0.813531
$401$	−44.6187	−	77.2819i	−0.00555649	−	0.00962413i	0.863234	−	0.504804i	$-0.168435\pi$
$401$	−44.6187	−	77.2819i	−0.00555649	−	0.00962413i	−0.868790	+	0.495180i	$0.835102\pi$
$402$	1618.33	−	2803.02i	0.200783	−	0.347766i
$403$	−5504.65	+	9534.34i	−0.680413	+	1.17851i
$404$	−9960.64	−	17252.3i	−1.22663	−	2.12459i
$405$	1280.12			0.157061
$406$		0			0
$407$	−6141.56			−0.747975
$408$	−14070.2	−	24370.3i	−1.70730	−	2.95713i
$409$	−73.6942	+	127.642i	−0.00890940	+	0.0154315i	−0.870446	−	0.492264i	$-0.836169\pi$
$409$	−73.6942	+	127.642i	−0.00890940	+	0.0154315i	0.861536	+	0.507696i	$0.169503\pi$
$410$	−2003.68	+	3470.47i	−0.241353	+	0.418035i
$411$	−3931.16	−	6808.96i	−0.471800	−	0.817181i
$412$	13897.3			1.66182
$413$		0			0
$414$	−6.95336			−0.000825457
$415$	1233.01	+	2135.64i	0.145846	+	0.252613i
$416$	27512.7	−	47653.4i	3.24260	−	5.61635i
$417$	−5186.44	+	8983.17i	−0.609067	+	1.05493i
$418$	1126.52	+	1951.19i	0.131818	+	0.228315i
$419$	−3781.67			−0.440923			−0.220462	−	0.975396i	$-0.570756\pi$
$419$	−3781.67			−0.440923			−0.220462	+	0.975396i	$0.570756\pi$
$420$		0			0
$421$	−10899.2			−1.26175			−0.630874	−	0.775885i	$-0.717304\pi$
$421$	−10899.2			−1.26175			−0.630874	+	0.775885i	$0.717304\pi$
$422$	−16487.5	−	28557.2i	−1.90189	−	3.29417i
$423$	1575.86	−	2729.47i	0.181137	−	0.313738i
$424$	14075.5	−	24379.6i	1.61219	−	2.79240i
$425$	1142.93	+	1979.62i	0.130448	+	0.225942i
$426$	6634.33			0.754541
$427$		0			0
$428$	−48292.4			−5.45398
$429$	−4590.54	−	7951.05i	−0.516628	−	0.894826i
$430$	−113.909	+	197.296i	−0.0127748	+	0.0221266i
$431$	5641.69	−	9771.69i	0.630512	−	1.09208i	−0.356936	−	0.934129i	$-0.616178\pi$
$431$	5641.69	−	9771.69i	0.630512	−	1.09208i	0.987447	−	0.157949i	$-0.0504882\pi$
$432$	19646.0	+	34027.8i	2.18800	+	3.78973i
$433$	−8906.19			−0.988462			−0.494231	−	0.869331i	$-0.664550\pi$
$433$	−8906.19			−0.988462			−0.494231	+	0.869331i	$0.664550\pi$
$434$		0			0
$435$	−3684.03			−0.406059
$436$	4569.03	+	7913.80i	0.501874	+	0.869271i
$437$	0.616026	−	1.06699i	6.74337e−5	−	0.000116799i
$438$	6815.29	−	11804.4i	0.743487	−	1.28776i
$439$	−4074.74	−	7057.67i	−0.443000	−	0.767298i	0.554911	−	0.831910i	$-0.312752\pi$
$439$	−4074.74	−	7057.67i	−0.443000	−	0.767298i	−0.997910	+	0.0646116i	$0.979419\pi$
$440$	13760.8			1.49095
$441$		0			0
$442$	34759.1			3.74054
$443$	5736.39	+	9935.71i	0.615223	+	1.06560i	0.990345	+	0.138623i	$0.0442675\pi$
$443$	5736.39	+	9935.71i	0.615223	+	1.06560i	−0.375122	+	0.926975i	$0.622399\pi$
$444$	7708.58	−	13351.6i	0.823948	−	1.42712i
$445$	1184.62	−	2051.83i	0.126195	−	0.218575i
$446$	−14295.9	−	24761.3i	−1.51778	−	2.62888i
$447$	2599.97			0.275111
$448$		0			0
$449$	1963.80			0.206409			0.103204	−	0.994660i	$-0.467090\pi$
$449$	1963.80			0.206409			0.103204	+	0.994660i	$0.467090\pi$
$450$	−834.413	−	1445.25i	−0.0874102	−	0.151399i
$451$	−2507.05	+	4342.34i	−0.261757	+	0.453376i
$452$	3923.71	−	6796.06i	0.408309	−	0.707212i
$453$	4102.01	+	7104.89i	0.425451	+	0.736903i
$454$	−20709.3			−2.14083
$455$		0			0
$456$	−3640.20			−0.373833
$457$	−2794.93	−	4840.96i	−0.286086	−	0.495515i	0.686786	−	0.726860i	$-0.259021\pi$
$457$	−2794.93	−	4840.96i	−0.286086	−	0.495515i	−0.972872	+	0.231344i	$0.925688\pi$
$458$	−17266.1	+	29905.8i	−1.76156	+	3.05111i
$459$	−6900.16	+	11951.4i	−0.701682	+	1.21535i
$460$	−5.84577	−	10.1252i	−0.000592523	−	0.00102628i
$461$	−18790.9			−1.89844			−0.949219	−	0.314618i	$-0.898124\pi$
$461$	−18790.9			−1.89844			−0.949219	+	0.314618i	$0.898124\pi$
$462$		0			0
$463$	−7892.22			−0.792187			−0.396094	−	0.918210i	$-0.629634\pi$
$463$	−7892.22			−0.792187			−0.396094	+	0.918210i	$0.629634\pi$
$464$	−24843.7	−	43030.6i	−2.48565	−	4.30527i
$465$	1542.24	−	2671.25i	0.153806	−	0.266400i
$466$	4910.89	−	8505.91i	0.488182	−	0.845556i
$467$	−192.755	−	333.862i	−0.0190999	−	0.0330820i	0.856317	−	0.516450i	$-0.172747\pi$
$467$	−192.755	−	333.862i	−0.0190999	−	0.0330820i	−0.875417	+	0.483368i	$0.839413\pi$
$468$	−18708.9			−1.84790
$469$		0			0
$470$	7187.95			0.705437
$471$	5429.71	+	9404.53i	0.531184	+	0.920038i
$472$	9586.58	−	16604.4i	0.934869	−	1.61924i
$473$	−142.525	+	246.861i	−0.0138548	+	0.0239972i
$474$	4166.43	+	7216.47i	0.403735	+	0.699290i
$475$	295.696			0.0285631
$476$		0			0
$477$	−4271.67			−0.410035
$478$	9710.15	+	16818.5i	0.929146	+	1.60933i
$479$	−847.229	+	1467.44i	−0.0808160	+	0.139977i	−0.903601	−	0.428376i	$-0.859086\pi$
$479$	−847.229	+	1467.44i	−0.0808160	+	0.139977i	0.822785	+	0.568353i	$0.192419\pi$
$480$	−7708.27	+	13351.1i	−0.732985	+	1.26957i
$481$	6128.34	+	10614.6i	0.580932	+	1.00620i
$482$	−2002.64			−0.189248
$483$		0			0
$484$	−3126.91			−0.293662
$485$	2097.51	+	3633.00i	0.196378	+	0.340136i
$486$	8516.41	−	14750.9i	0.794881	−	1.37677i
$487$	−7855.58	+	13606.3i	−0.730945	+	1.26603i	0.225534	+	0.974235i	$0.427587\pi$
$487$	−7855.58	+	13606.3i	−0.730945	+	1.26603i	−0.956480	+	0.291799i	$0.905746\pi$
$488$	31020.1	+	53728.4i	2.87749	+	4.98395i
$489$	−5189.99			−0.479958
$490$		0			0
$491$	−2716.34			−0.249667			−0.124834	−	0.992178i	$-0.539840\pi$
$491$	−2716.34			−0.249667			−0.124834	+	0.992178i	$0.539840\pi$
$492$	−6293.44	−	10900.6i	−0.576687	−	0.998852i
$493$	8725.75	−	15113.4i	0.797136	−	1.38068i
$494$	2248.19	−	3893.98i	0.204759	−	0.354653i
$495$	−1044.04	−	1808.32i	−0.0947999	−	0.164198i
$496$	41601.2			3.76603
$497$		0			0
$498$	−10506.0			−0.945355
$499$	−2147.67	−	3719.87i	−0.192671	−	0.333716i	0.753463	−	0.657490i	$-0.228382\pi$
$499$	−2147.67	−	3719.87i	−0.192671	−	0.333716i	−0.946135	+	0.323774i	$0.895048\pi$
$500$	1403.00	−	2430.07i	0.125488	−	0.217352i
$501$	−2801.17	+	4851.77i	−0.249795	+	0.432657i
$502$	−14716.0	−	25488.9i	−1.30838	−	2.26619i
$503$	6515.26			0.577537			0.288769	−	0.957399i	$-0.406754\pi$
$503$	6515.26			0.577537			0.288769	+	0.957399i	$0.406754\pi$
$504$		0			0
$505$	−4437.20			−0.390996
$506$	−9.92105	−	17.1838i	−0.000871629	−	0.00150971i
$507$	−4920.67	+	8522.85i	−0.431035	+	0.746574i
$508$	−13286.8	+	23013.3i	−1.16044	+	2.00994i
$509$	−7195.88	−	12463.6i	−0.626624	−	1.08535i	−0.988224	−	0.153012i	$-0.951103\pi$
$509$	−7195.88	−	12463.6i	−0.626624	−	1.08535i	0.361600	−	0.932333i	$-0.382231\pi$
$510$	−9738.48			−0.845544
$511$		0			0
$512$	−41890.2			−3.61583
$513$	892.594	+	1546.02i	0.0768207	+	0.133057i
$514$	−6728.56	+	11654.2i	−0.577401	+	1.00009i
$515$	1547.72	−	2680.73i	0.132428	−	0.229373i
$516$	−357.781	−	619.695i	−0.0305241	−	0.0528692i
$517$	8993.73			0.765075
$518$		0			0
$519$	−7640.32			−0.646191
$520$	−13731.1	−	23783.0i	−1.15798	−	2.00568i
$521$	−1456.68	+	2523.05i	−0.122492	+	0.212163i	−0.920750	−	0.390153i	$-0.872422\pi$
$521$	−1456.68	+	2523.05i	−0.122492	+	0.212163i	0.798258	+	0.602316i	$0.205755\pi$
$522$	−6370.35	+	11033.8i	−0.534143	+	0.925163i
$523$	−8435.11	−	14610.0i	−0.705242	−	1.22151i	−0.966604	−	0.256274i	$-0.917505\pi$
$523$	−8435.11	−	14610.0i	−0.705242	−	1.22151i	0.261362	−	0.965241i	$-0.415828\pi$
$524$	5013.93			0.418005
$525$		0			0
$526$	−8421.82			−0.698115
$527$	7305.71	+	12653.9i	0.603874	+	1.04594i
$528$	−17346.4	+	30044.9i	−1.42975	+	2.47639i
$529$	6083.49	−	10536.9i	0.500000	−	0.866025i
$530$	−4871.09	−	8436.98i	−0.399220	−	0.691470i
$531$	−2909.35			−0.237769
$532$		0			0
$533$	10006.6			0.813197
$534$	5046.86	+	8741.43i	0.408987	+	0.708387i
$535$	−5378.25	+	9315.40i	−0.434620	+	0.752785i
$536$	6056.80	−	10490.7i	0.488086	−	0.845390i
$537$	8413.07	+	14571.9i	0.676072	+	1.17099i
$538$	41738.6			3.34476
$539$		0			0
$540$	16940.5			1.35001
$541$	1114.79	+	1930.88i	0.0885929	+	0.153447i	0.906917	−	0.421310i	$-0.138430\pi$
$541$	1114.79	+	1930.88i	0.0885929	+	0.153447i	−0.818324	+	0.574758i	$0.805096\pi$
$542$	11815.9	−	20465.7i	0.936412	−	1.62191i
$543$	729.465	−	1263.47i	0.0576507	−	0.0998539i
$544$	−36514.5	−	63245.0i	−2.87785	−	4.98457i
$545$	2035.38			0.159975
$546$		0			0
$547$	−1218.73			−0.0952639			−0.0476319	−	0.998865i	$-0.515167\pi$
$547$	−1218.73			−0.0952639			−0.0476319	+	0.998865i	$0.515167\pi$
$548$	−22859.5	−	39593.9i	−1.78195	−	3.08643i
$549$	4707.02	−	8152.80i	0.365921	−	0.633794i
$550$	2381.08	−	4124.15i	0.184599	−	0.319735i
$551$	−1128.75	−	1955.05i	−0.0872710	−	0.151158i
$552$	32.0585			0.00247192
$553$		0			0
$554$	22118.3			1.69624
$555$	−1716.98	−	2973.90i	−0.131319	−	0.227451i
$556$	−30158.9	+	52236.8i	−2.30040	+	3.98442i
$557$	11367.3	−	19688.7i	0.864714	−	1.49773i	−0.00261590	−	0.999997i	$-0.500833\pi$
$557$	11367.3	−	19688.7i	0.864714	−	1.49773i	0.867330	−	0.497733i	$-0.165834\pi$
$558$	−5333.63	−	9238.12i	−0.404643	−	0.700862i
$559$	568.873			0.0430425
$560$		0			0
$561$	−12185.0			−0.917026
$562$	19134.8	+	33142.4i	1.43621	+	2.48759i
$563$	−2151.06	+	3725.74i	−0.161023	+	0.278901i	−0.935236	−	0.354025i	$-0.884813\pi$
$563$	−2151.06	+	3725.74i	−0.161023	+	0.278901i	0.774213	+	0.632926i	$0.218146\pi$
$564$	−11288.5	+	19552.2i	−0.842784	+	1.45975i
$565$	−873.954	−	1513.73i	−0.0650752	−	0.112714i
$566$	14714.4			1.09275
$567$		0			0
$568$	24829.9			1.83422
$569$	−7433.46	−	12875.1i	−0.547675	−	0.948601i	−0.998433	−	0.0559547i	$-0.982180\pi$
$569$	−7433.46	−	12875.1i	−0.547675	−	0.948601i	0.450759	−	0.892646i	$-0.351154\pi$
$570$	−629.878	+	1090.98i	−0.0462854	+	0.0801686i
$571$	−8257.24	+	14302.0i	−0.605174	+	1.04819i	0.386850	+	0.922143i	$0.373563\pi$
$571$	−8257.24	+	14302.0i	−0.605174	+	1.04819i	−0.992024	+	0.126050i	$0.959770\pi$
$572$	−26693.8	−	46235.1i	−1.95127	−	3.37969i
$573$	−9365.10			−0.682780
$574$		0			0
$575$	−2.60414			−0.000188870
$576$	14060.7	+	24353.8i	1.01712	+	1.76171i
$577$	−933.984	+	1617.71i	−0.0673870	+	0.116718i	−0.897750	−	0.440505i	$-0.854800\pi$
$577$	−933.984	+	1617.71i	−0.0673870	+	0.116718i	0.830363	+	0.557222i	$0.188133\pi$
$578$	9511.00	−	16473.5i	0.684438	−	1.18548i
$579$	1202.36	+	2082.55i	0.0863014	+	0.149478i
$580$	−21422.5			−1.53366
$581$		0			0
$582$	−17872.1			−1.27289
$583$	−6094.82	−	10556.5i	−0.432970	−	0.749927i
$584$	25507.2	−	44179.7i	1.80735	−	3.13043i
$585$	−2083.58	+	3608.86i	−0.147257	+	0.255056i
$586$	16385.9	+	28381.2i	1.15511	+	2.00071i
$587$	3926.15			0.276064			0.138032	−	0.990428i	$-0.455922\pi$
$587$	3926.15			0.276064			0.138032	+	0.990428i	$0.455922\pi$
$588$		0			0
$589$	1890.11			0.132225
$590$	−3317.61	−	5746.26i	−0.231498	−	0.400966i
$591$	−5486.17	+	9502.33i	−0.381846	+	0.661377i
$592$	23157.3	−	40109.7i	1.60770	−	2.78463i
$593$	3777.09	+	6542.11i	0.261562	+	0.453039i	0.966657	−	0.256074i	$-0.0824289\pi$
$593$	3777.09	+	6542.11i	0.261562	+	0.453039i	−0.705095	+	0.709113i	$0.749096\pi$
$594$	28750.3			1.98593
$595$		0			0
$596$	15118.8			1.03907
$597$	1674.18	+	2899.77i	0.114773	+	0.198793i
$598$	−19.7994	+	34.2935i	−0.00135394	+	0.00234509i
$599$	−14105.5	+	24431.4i	−0.962160	+	1.66651i	−0.245099	+	0.969498i	$0.578821\pi$
$599$	−14105.5	+	24431.4i	−0.962160	+	1.66651i	−0.717060	+	0.697011i	$0.754513\pi$
$600$	3847.07	+	6663.32i	0.261760	+	0.453381i
$601$	−23181.4			−1.57336			−0.786679	−	0.617363i	$-0.788201\pi$
$601$	−23181.4			−1.57336			−0.786679	+	0.617363i	$0.788201\pi$
$602$		0			0
$603$	−1838.13			−0.124137
$604$	23853.0	+	41314.7i	1.60690	+	2.78323i
$605$	−348.239	+	603.167i	−0.0234015	+	0.0405326i
$606$	9451.92	−	16371.2i	0.633594	−	1.09742i
$607$	12431.8	+	21532.5i	0.831287	+	1.43983i	0.897018	+	0.441994i	$0.145729\pi$
$607$	12431.8	+	21532.5i	0.831287	+	1.43983i	−0.0657313	+	0.997837i	$0.520938\pi$
$608$	−9446.93			−0.630137
$609$		0			0
$610$	21470.1			1.42508
$611$	−8974.36	−	15544.1i	−0.594213	−	1.02921i
$612$	−12415.1	+	21503.6i	−0.820017	+	1.42031i
$613$	6396.36	−	11078.8i	0.421446	−	0.729966i	−0.574635	−	0.818410i	$-0.694856\pi$
$613$	6396.36	−	11078.8i	0.421446	−	0.729966i	0.996081	+	0.0884435i	$0.0281893\pi$
$614$	28642.5	+	49610.3i	1.88260	+	3.26076i
$615$	−2803.56			−0.183822
$616$		0			0
$617$	19793.3			1.29149			0.645744	−	0.763554i	$-0.276547\pi$
$617$	19793.3			1.29149			0.645744	+	0.763554i	$0.276547\pi$
$618$	6593.76	+	11420.7i	0.429191	+	0.743380i
$619$	10475.8	−	18144.7i	0.680226	−	1.17819i	−0.294686	−	0.955594i	$-0.595215\pi$
$619$	10475.8	−	18144.7i	0.680226	−	1.17819i	0.974912	−	0.222592i	$-0.0714517\pi$
$620$	8968.10	−	15533.2i	0.580915	−	1.00617i
$621$	−7.86091	−	13.6155i	−0.000507967	−	0.000879824i
$622$	−23399.2			−1.50840
$623$		0			0
$624$	69236.3			4.44178
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	−783.284	+	1356.69i	−0.0500101	+	0.0866200i
$627$	−788.117	+	1365.06i	−0.0501984	+	0.0869461i
$628$	31573.5	+	54687.0i	2.00624	+	3.47492i
$629$	16266.9			1.03117
$630$		0			0
$631$	23273.5			1.46831			0.734156	−	0.678981i	$-0.237578\pi$
$631$	23273.5			1.46831			0.734156	+	0.678981i	$0.237578\pi$
$632$	15593.4	+	27008.6i	0.981446	+	1.69991i
$633$	11534.7	−	19978.7i	0.724270	−	1.25447i
$634$	4799.24	−	8312.52i	0.300634	−	0.520713i
$635$	2959.45	+	5125.91i	0.184948	+	0.320340i
$636$	30599.6			1.90779
$637$		0			0
$638$	−36356.8			−2.25608
$639$	−1883.86	−	3262.94i	−0.116626	−	0.202003i
$640$	−16093.4	+	27874.6i	−0.993981	+	1.72163i
$641$	11058.9	−	19154.5i	0.681434	−	1.18028i	−0.293110	−	0.956079i	$-0.594690\pi$
$641$	11058.9	−	19154.5i	0.681434	−	1.18028i	0.974543	−	0.224199i	$-0.0719765\pi$
$642$	−22913.0	−	39686.5i	−1.40857	−	2.43972i
$643$	20269.9			1.24318			0.621591	−	0.783342i	$-0.286487\pi$
$643$	20269.9			1.24318			0.621591	+	0.783342i	$0.286487\pi$
$644$		0			0
$645$	−159.382			−0.00972969
$646$	−2983.77	−	5168.04i	−0.181726	−	0.314758i
$647$	1572.62	−	2723.87i	0.0955583	−	0.165512i	−0.814283	−	0.580468i	$-0.802870\pi$
$647$	1572.62	−	2723.87i	0.0955583	−	0.165512i	0.909841	+	0.414956i	$0.136203\pi$
$648$	−10205.6	+	17676.6i	−0.618695	+	1.07161i
$649$	−4151.06	−	7189.85i	−0.251069	−	0.434864i
$650$	−9503.81			−0.573493
$651$		0			0
$652$	−30179.6			−1.81277
$653$	2976.67	+	5155.75i	0.178386	+	0.308974i	0.941328	−	0.337493i	$-0.109579\pi$
$653$	2976.67	+	5155.75i	0.178386	+	0.308974i	−0.762942	+	0.646467i	$0.776246\pi$
$654$	−4335.68	+	7509.61i	−0.259233	+	0.449005i
$655$	558.393	−	967.165i	0.0333102	−	0.0576950i
$656$	−18906.1	−	32746.4i	−1.12524	−	1.94898i
$657$	−7740.96			−0.459671
$658$		0			0
$659$	26277.5			1.55330			0.776652	−	0.629930i	$-0.216916\pi$
$659$	26277.5			1.55330			0.776652	+	0.629930i	$0.216916\pi$
$660$	7478.83	+	12953.7i	0.441081	+	0.763974i
$661$	12002.2	−	20788.4i	0.706248	−	1.22326i	−0.259991	−	0.965611i	$-0.583720\pi$
$661$	12002.2	−	20788.4i	0.706248	−	1.22326i	0.966239	−	0.257647i	$-0.0829470\pi$
$662$	15469.5	−	26794.0i	0.908218	−	1.57308i
$663$	12158.8	+	21059.6i	0.712229	+	1.23362i
$664$	−39320.3			−2.29808
$665$		0			0
$666$	−11875.9			−0.690962
$667$	9.94068	+	17.2178i	0.000577068	+	0.000999512i
$668$	−16288.7	+	28212.9i	−0.943457	+	1.63412i
$669$	10001.5	−	17323.1i	0.577996	−	1.00112i
$670$	−2096.06	−	3630.49i	−0.120863	−	0.209340i
$671$	26863.9			1.54556
$672$		0			0
$673$	9205.36			0.527252			0.263626	−	0.964625i	$-0.415082\pi$
$673$	9205.36			0.527252			0.263626	+	0.964625i	$0.415082\pi$
$674$	−26010.2	−	45050.9i	−1.48646	−	2.57463i
$675$	1886.64	−	3267.76i	0.107580	−	0.186335i
$676$	−28613.5	+	49560.1i	−1.62799	+	2.81976i
$677$	9386.57	+	16258.0i	0.532873	+	0.922964i	0.999263	+	0.0383843i	$0.0122211\pi$
$677$	9386.57	+	16258.0i	0.532873	+	0.922964i	−0.466390	+	0.884579i	$0.654446\pi$
$678$	7446.62			0.421808
$679$		0			0
$680$	−36447.6			−2.05544
$681$	−7244.14	−	12547.2i	−0.407630	−	0.706036i
$682$	15220.0	−	26361.9i	0.854554	−	1.48013i
$683$	5111.12	−	8852.73i	0.286342	−	0.495959i	−0.686592	−	0.727043i	$-0.740894\pi$
$683$	5111.12	−	8852.73i	0.286342	−	0.495959i	0.972934	+	0.231084i	$0.0742272\pi$
$684$	1606.00	+	2781.67i	0.0897761	+	0.155497i
$685$	−10183.3			−0.568006
$686$		0			0
$687$	−24158.9			−1.34166
$688$	−1074.81	−	1861.63i	−0.0595592	−	0.103160i
$689$	−12163.4	+	21067.6i	−0.672552	+	1.16489i
$690$	5.54721	−	9.60805i	0.000306056	−	0.000530105i
$691$	−11177.6	−	19360.1i	−0.615361	−	1.06584i	−0.990321	−	0.138795i	$-0.955677\pi$
$691$	−11177.6	−	19360.1i	−0.615361	−	1.06584i	0.374961	−	0.927041i	$-0.377656\pi$
$692$	−44428.2			−2.44062
$693$		0			0
$694$	−64197.3			−3.51138
$695$	6717.50	+	11635.1i	0.366632	+	0.635026i
$696$	29370.5	−	50871.3i	1.59955	−	2.77050i
$697$	6640.32	−	11501.4i	0.360861	−	0.625029i
$698$	−3633.85	−	6294.01i	−0.197053	−	0.341307i
$699$	6871.35			0.371814
$700$		0			0
$701$	16217.3			0.873779			0.436890	−	0.899515i	$-0.356080\pi$
$701$	16217.3			0.873779			0.436890	+	0.899515i	$0.356080\pi$
$702$	−28688.4	−	49689.8i	−1.54241	−	2.67154i
$703$	1052.13	−	1822.34i	0.0564465	−	0.0977682i
$704$	−40123.5	+	69496.0i	−2.14803	+	3.72050i
$705$	2514.36	+	4354.99i	0.134321	+	0.232650i
$706$	−32273.7			−1.72045
$707$		0			0
$708$	20840.8			1.10628
$709$	−1961.46	−	3397.35i	−0.103899	−	0.179958i	0.809389	−	0.587273i	$-0.199798\pi$
$709$	−1961.46	−	3397.35i	−0.103899	−	0.179958i	−0.913288	+	0.407315i	$0.866465\pi$
$710$	4296.41	−	7441.61i	0.227101	−	0.393350i
$711$	2366.16	−	4098.32i	0.124807	−	0.216173i
$712$	18888.6	+	32716.0i	0.994212	+	1.72203i
$713$	−16.6458			−0.000874322
$714$		0			0
$715$	−11891.4			−0.621976
$716$	48921.7	+	84734.9i	2.55348	+	4.42275i
$717$	−6793.25	+	11766.3i	−0.353833	+	0.612857i
$718$	−34272.2	+	59361.1i	−1.78137	+	3.08543i
$719$	−11954.3	−	20705.4i	−0.620055	−	1.07397i	−0.989475	−	0.144705i	$-0.953777\pi$
$719$	−11954.3	−	20705.4i	−0.620055	−	1.07397i	0.369420	−	0.929263i	$-0.379556\pi$
$720$	15746.6			0.815055
$721$		0			0
$722$	37075.8			1.91111
$723$	−700.527	−	1213.35i	−0.0360344	−	0.0624134i
$724$	4241.81	−	7347.03i	0.217743	−	0.377141i
$725$	−2385.79	+	4132.31i	−0.122215	+	0.211683i
$726$	−1483.60	−	2569.68i	−0.0758426	−	0.131363i
$727$	−26906.4			−1.37263			−0.686315	−	0.727305i	$-0.740773\pi$
$727$	−26906.4			−1.37263			−0.686315	+	0.727305i	$0.740773\pi$
$728$		0			0
$729$	18828.9			0.956605
$730$	−8827.21	−	15289.2i	−0.447547	−	0.775175i
$731$	377.501	−	653.850i	0.0191004	−	0.0330828i
$732$	−33718.2	+	58401.6i	−1.70254	+	2.94889i
$733$	−13818.7	−	23934.7i	−0.696325	−	1.20607i	−0.969732	−	0.244172i	$-0.921484\pi$
$733$	−13818.7	−	23934.7i	−0.696325	−	1.20607i	0.273407	−	0.961899i	$-0.411850\pi$
$734$	36367.7			1.82882
$735$		0			0
$736$	83.1973			0.00416670
$737$	−2622.64	−	4542.55i	−0.131080	−	0.227038i
$738$	−4847.85	+	8396.73i	−0.241805	+	0.418818i
$739$	7019.44	−	12158.0i	0.349410	−	0.605197i	−0.636734	−	0.771083i	$-0.719715\pi$
$739$	7019.44	−	12158.0i	0.349410	−	0.605197i	0.986145	+	0.165887i	$0.0530486\pi$
$740$	−9984.19	−	17293.1i	−0.495981	−	0.859065i
$741$	3145.68			0.155951
$742$		0			0
$743$	17698.7			0.873893			0.436946	−	0.899488i	$-0.356060\pi$
$743$	17698.7			0.873893			0.436946	+	0.899488i	$0.356060\pi$
$744$	24590.7	+	42592.4i	1.21175	+	2.09881i
$745$	1683.75	−	2916.34i	0.0828025	−	0.143418i
$746$	949.859	−	1645.20i	0.0466177	−	0.0807442i
$747$	2983.25	+	5167.14i	0.146120	+	0.253087i
$748$	−70855.4			−3.46354
$749$		0			0
$750$	2662.69			0.129637
$751$	−8599.83	−	14895.3i	−0.417859	−	0.723754i	0.577865	−	0.816133i	$-0.303886\pi$
$751$	−8599.83	−	14895.3i	−0.417859	−	0.723754i	−0.995724	+	0.0923791i	$0.970553\pi$
$752$	−33911.7	+	58736.8i	−1.64446	+	2.84829i
$753$	10295.4	−	17832.1i	0.498253	−	0.862999i
$754$	36278.6	+	62836.3i	1.75224	+	3.03496i
$755$	10625.9			0.512206
$756$		0			0
$757$	−19200.7			−0.921879			−0.460939	−	0.887432i	$-0.652487\pi$
$757$	−19200.7			−0.921879			−0.460939	+	0.887432i	$0.652487\pi$
$758$	14460.5	+	25046.3i	0.692914	+	1.20016i
$759$	6.94080	−	12.0218i	0.000331930	−	0.000574920i
$760$	−2357.40	+	4083.14i	−0.112516	+	0.194883i
$761$	13959.4	+	24178.3i	0.664949	+	1.15173i	0.979299	+	0.202419i	$0.0648801\pi$
$761$	13959.4	+	24178.3i	0.664949	+	1.15173i	−0.314350	+	0.949307i	$0.601787\pi$
$762$	−25216.3			−1.19881
$763$		0			0
$764$	−54457.7			−2.57881
$765$	2765.30	+	4789.64i	0.130692	+	0.226366i
$766$	20961.1	−	36305.6i	0.988712	−	1.71250i
$767$	−8284.25	+	14348.7i	−0.389996	+	0.675493i
$768$	−32667.7	−	56582.1i	−1.53489	−	2.65850i
$769$	−7436.29			−0.348712			−0.174356	−	0.984683i	$-0.555784\pi$
$769$	−7436.29			−0.348712			−0.174356	+	0.984683i	$0.555784\pi$
$770$		0			0
$771$	−9414.64			−0.439766
$772$	6991.70	+	12110.0i	0.325954	+	0.564569i
$773$	−2494.92	+	4321.33i	−0.116088	+	0.201070i	−0.918214	−	0.396084i	$-0.870369\pi$
$773$	−2494.92	+	4321.33i	−0.116088	+	0.201070i	0.802126	+	0.597155i	$0.203702\pi$
$774$	−275.600	+	477.352i	−0.0127987	+	0.0221681i
$775$	−1997.52	−	3459.81i	−0.0925847	−	0.160361i
$776$	−66888.7			−3.09429
$777$		0			0
$778$	−17115.9			−0.788731
$779$	−858.981	−	1487.80i	−0.0395073	−	0.0684287i
$780$	14925.5	−	25851.7i	0.685150	−	1.18672i
$781$	5375.77	−	9311.11i	0.246300	−	0.426604i
$782$	26.2775	+	45.5139i	0.00120164	+	0.00208130i
$783$	−28807.2			−1.31480
$784$		0			0
$785$	14065.2			0.639500
$786$	2378.92	+	4120.42i	0.107956	+	0.186985i
$787$	1435.35	−	2486.09i	0.0650122	−	0.112604i	−0.831687	−	0.555244i	$-0.812625\pi$
$787$	1435.35	−	2486.09i	0.0650122	−	0.112604i	0.896699	+	0.442640i	$0.145958\pi$
$788$	−31901.9	+	55255.7i	−1.44221	+	2.49797i
$789$	−2945.96	−	5102.56i	−0.132927	−	0.230236i
$790$	10792.8			0.486063
$791$		0			0
$792$	33293.9			1.49374
$793$	−26806.1	−	46429.4i	−1.20039	−	2.07914i
$794$	−8089.50	+	14011.4i	−0.361569	+	0.626256i
$795$	3407.83	−	5902.54i	0.152029	−	0.263322i
$796$	9735.31	+	16862.0i	0.433491	+	0.750828i
$797$	4676.61			0.207847			0.103923	−	0.994585i	$-0.466860\pi$
$797$	4676.61			0.207847			0.103923	+	0.994585i	$0.466860\pi$
$798$		0			0
$799$	−23821.3			−1.05474
$800$	9983.79	+	17292.4i	0.441225	+	0.764225i
$801$	2866.17	−	4964.35i	0.126431	−	0.218985i
$802$	246.205	−	426.440i	0.0108402	−	0.0187757i
$803$	−11044.8	−	19130.2i	−0.485383	−	0.840708i
$804$	13167.2			0.577578
$805$		0			0
$806$	−60749.1			−2.65483
$807$	14600.2	+	25288.3i	0.636868	+	1.10309i
$808$	35375.1	−	61271.4i	1.54021	−	2.66772i
$809$	7688.45	−	13316.8i	0.334131	−	0.578731i	−0.649187	−	0.760629i	$-0.724891\pi$
$809$	7688.45	−	13316.8i	0.334131	−	0.578731i	0.983317	+	0.181898i	$0.0582240\pi$
$810$	3531.83	+	6117.32i	0.153205	+	0.265359i
$811$	36422.9			1.57704			0.788522	−	0.615007i	$-0.210847\pi$
$811$	36422.9			1.57704			0.788522	+	0.615007i	$0.210847\pi$
$812$		0			0
$813$	16532.8			0.713200
$814$	−16944.5	−	29348.7i	−0.729612	−	1.26372i
$815$	−3361.05	+	5821.51i	−0.144457	+	0.250207i
$816$	45944.8	−	79578.6i	1.97106	−	3.41398i
$817$	−48.8329	−	84.5811i	−0.00209112	−	0.00362193i
$818$	−813.285			−0.0347627
$819$		0			0
$820$	−16302.6			−0.694282
$821$	12739.5	+	22065.5i	0.541550	+	0.937991i	0.998815	+	0.0486612i	$0.0154955\pi$
$821$	12739.5	+	22065.5i	0.541550	+	0.937991i	−0.457266	+	0.889330i	$0.651171\pi$
$822$	21692.0	−	37571.7i	0.920433	−	1.59424i
$823$	8966.65	−	15530.7i	0.379779	−	0.657796i	−0.611251	−	0.791437i	$-0.709334\pi$
$823$	8966.65	−	15530.7i	0.379779	−	0.657796i	0.991030	+	0.133641i	$0.0426668\pi$
$824$	24678.0	+	42743.6i	1.04333	+	1.80709i
$825$	3331.62			0.140597
$826$		0			0
$827$	13021.6			0.547529			0.273764	−	0.961797i	$-0.411731\pi$
$827$	13021.6			0.547529			0.273764	+	0.961797i	$0.411731\pi$
$828$	−14.1437	−	24.4976i	−0.000593633	−	0.00102820i
$829$	5698.80	−	9870.61i	0.238754	−	0.413535i	−0.721603	−	0.692307i	$-0.756594\pi$
$829$	5698.80	−	9870.61i	0.238754	−	0.413535i	0.960357	+	0.278773i	$0.0899276\pi$
$830$	−6803.74	+	11784.4i	−0.284532	+	0.492823i
$831$	7737.01	+	13400.9i	0.322977	+	0.559412i
$832$	160149.			6.67326
$833$		0			0
$834$	−57237.2			−2.37646
$835$	3628.09	+	6284.04i	0.150366	+	0.260441i
$836$	−4582.87	+	7937.77i	−0.189596	+	0.328389i
$837$	12059.5	−	20887.7i	0.498015	−	0.862588i
$838$	−10433.6	−	18071.5i	−0.430098	−	0.744952i
$839$	−37681.2			−1.55053			−0.775267	−	0.631633i	$-0.782385\pi$
$839$	−37681.2			−1.55053			−0.775267	+	0.631633i	$0.782385\pi$
$840$		0			0
$841$	12039.8			0.493656
$842$	−30070.8	−	52084.2i	−1.23077	−	2.13176i
$843$	−13386.7	+	23186.5i	−0.546932	+	0.947315i
$844$	67073.9	−	116175.i	2.73552	−	4.73806i
$845$	6373.28	+	11038.8i	0.259465	+	0.449406i
$846$	17391.1			0.706758
$847$		0			0
$848$	91924.4			3.72252
$849$	5147.13	+	8915.09i	0.208067	+	0.360383i
$850$	−6306.67	+	10923.5i	−0.254491	+	0.440791i
$851$	−9.26591	+	16.0490i	−0.000373245	+	0.000646479i
$852$	13494.8	+	23373.7i	0.542634	+	0.939869i
$853$	21771.6			0.873911			0.436956	−	0.899483i	$-0.356057\pi$
$853$	21771.6			0.873911			0.436956	+	0.899483i	$0.356057\pi$
$854$		0			0
$855$	715.429			0.0286166
$856$	−85754.9	−	148532.i	−3.42412	−	5.93074i
$857$	−14930.1	+	25859.7i	−0.595103	+	1.03075i	0.398429	+	0.917199i	$0.369555\pi$
$857$	−14930.1	+	25859.7i	−0.595103	+	1.03075i	−0.993532	+	0.113550i	$0.963778\pi$
$858$	25330.5	−	43873.7i	1.00789	−	1.74571i
$859$	−9265.32	−	16048.0i	−0.368019	−	0.637428i	0.621236	−	0.783623i	$-0.286631\pi$
$859$	−9265.32	−	16048.0i	−0.368019	−	0.637428i	−0.989256	+	0.146195i	$0.953297\pi$
$860$	−926.799			−0.0367484
$861$		0			0
$862$	62261.4			2.46013
$863$	10648.2	+	18443.3i	0.420012	+	0.727482i	0.995940	−	0.0900182i	$-0.0286925\pi$
$863$	10648.2	+	18443.3i	0.420012	+	0.727482i	−0.575928	+	0.817500i	$0.695359\pi$
$864$	−60274.6	+	104399.i	−2.37336	+	4.11078i
$865$	−4947.90	+	8570.01i	−0.194490	+	0.336866i
$866$	−24572.1	−	42560.1i	−0.964195	−	1.67003i
$867$	13307.8			0.521290
$868$		0			0
$869$	13504.2			0.527155
$870$	−10164.2	−	17604.9i	−0.396090	−	0.686049i
$871$	−5233.99	+	9065.54i	−0.203613	+	0.352668i
$872$	−16226.9	+	28105.7i	−0.630173	+	1.09149i
$873$	5074.88	+	8789.96i	0.196745	+	0.340773i
$874$	6.79843			0.000263112
$875$		0			0
$876$	55451.5			2.13874
$877$	9396.72	+	16275.6i	0.361807	+	0.626668i	0.988258	−	0.152793i	$-0.0488266\pi$
$877$	9396.72	+	16275.6i	0.361807	+	0.626668i	−0.626451	+	0.779460i	$0.715493\pi$
$878$	22484.3	−	38944.0i	0.864248	−	1.49692i
$879$	−11463.6	+	19855.6i	−0.439885	+	0.761902i
$880$	22467.2	+	38914.3i	0.860646	+	1.49068i
$881$	1638.62			0.0626634			0.0313317	−	0.999509i	$-0.490025\pi$
$881$	1638.62			0.0626634			0.0313317	+	0.999509i	$0.490025\pi$
$882$		0			0
$883$	−35424.1			−1.35008			−0.675038	−	0.737783i	$-0.735873\pi$
$883$	−35424.1			−1.35008			−0.675038	+	0.737783i	$0.735873\pi$
$884$	70702.8	+	122461.i	2.69004	+	4.65928i
$885$	2321.01	−	4020.10i	0.0881580	−	0.152694i
$886$	−31653.2	+	54825.0i	−1.20024	+	2.07887i
$887$	2565.71	+	4443.93i	0.0971229	+	0.168222i	0.910493	−	0.413525i	$-0.135703\pi$
$887$	2565.71	+	4443.93i	0.0971229	+	0.168222i	−0.813370	+	0.581747i	$0.802369\pi$
$888$	54753.8			2.06916
$889$		0			0
$890$	13073.5			0.492386
$891$	4419.11	+	7654.13i	0.166157	+	0.287792i
$892$	58158.2	−	100733.i	2.18305	−	3.78115i
$893$	−1540.74	+	2668.65i	−0.0577369	+	0.100003i
$894$	7173.30	+	12424.5i	0.268357	+	0.464807i
$895$	21793.3			0.813933
$896$		0			0
$897$	−27.7034			−0.00103120
$898$	5418.10	+	9384.43i	0.201341	+	0.348733i
$899$	−15250.2	+	26414.0i	−0.565763	+	0.979931i
$900$	3394.53	−	5879.50i	0.125723	−	0.217759i
$901$	16143.1	+	27960.7i	0.596898	+	1.03386i
$902$	−27667.7			−1.02132
$903$		0			0
$904$	27870.0			1.02538
$905$	−944.807	−	1636.45i	−0.0347032	−	0.0601078i
$906$	−22634.8	+	39204.6i	−0.830011	+	1.43762i
$907$	9967.28	−	17263.8i	0.364893	−	0.632014i	−0.623866	−	0.781532i	$-0.714439\pi$
$907$	9967.28	−	17263.8i	0.364893	−	0.632014i	0.988759	+	0.149518i	$0.0477721\pi$
$908$	−42124.4	−	72961.6i	−1.53959	−	2.66665i
$909$	−10735.7			−0.391728
$910$		0			0
$911$	48387.4			1.75976			0.879882	−	0.475193i	$-0.157622\pi$
$911$	48387.4			1.75976			0.879882	+	0.475193i	$0.157622\pi$
$912$	−5943.34	−	10294.2i	−0.215794	−	0.373765i
$913$	−8512.99	+	14744.9i	−0.308586	+	0.534486i
$914$	15422.3	−	26712.3i	0.558124	−	0.966700i
$915$	7510.28	+	13008.2i	0.271347	+	0.469986i
$916$	−140483.			−5.06735
$917$		0			0
$918$	−76149.8			−2.73782
$919$	7215.87	+	12498.2i	0.259009	+	0.448617i	0.965977	−	0.258629i	$-0.0832706\pi$
$919$	7215.87	+	12498.2i	0.259009	+	0.448617i	−0.706968	+	0.707246i	$0.749937\pi$
$920$	20.7612	−	35.9594i	0.000743996	−	0.00128864i
$921$	−20038.4	+	34707.5i	−0.716924	+	1.24175i
$922$	−51843.8	−	89796.2i	−1.85183	−	3.20746i
$923$	−21456.8			−0.765177
$924$		0			0
$925$	−4447.69			−0.158096
$926$	−21774.5	−	37714.6i	−0.772738	−	1.33842i
$927$	3744.67	−	6485.96i	0.132676	−	0.229802i
$928$	76221.5	−	132020.i	2.69622	−	4.66999i
$929$	−2774.91	−	4806.28i	−0.0979998	−	0.169741i	0.812857	−	0.582464i	$-0.197911\pi$
$929$	−2774.91	−	4806.28i	−0.0979998	−	0.169741i	−0.910857	+	0.412723i	$0.864578\pi$
$930$	17020.1			0.600120
$931$		0			0
$932$	39956.7			1.40432
$933$	−8185.08	−	14177.0i	−0.287211	−	0.497463i
$934$	1063.62	−	1842.24i	0.0372620	−	0.0645396i
$935$	−7891.05	+	13667.7i	−0.276005	+	0.478055i
$936$	−33222.2	−	57542.5i	−1.16015	−	2.00944i
$937$	26231.9			0.914576			0.457288	−	0.889319i	$-0.348821\pi$
$937$	26231.9			0.914576			0.457288	+	0.889319i	$0.348821\pi$
$938$		0			0
$939$	−1095.98			−0.0380893
$940$	14620.9	+	25324.1i	0.507320	+	0.878704i
$941$	−1418.40	+	2456.74i	−0.0491376	+	0.0851089i	−0.889548	−	0.456842i	$-0.848981\pi$
$941$	−1418.40	+	2456.74i	−0.0491376	+	0.0851089i	0.840410	+	0.541950i	$0.182314\pi$
$942$	−29961.0	+	51893.9i	−1.03629	+	1.79490i
$943$	7.56488	+	13.1028i	0.000261237	+	0.000452476i
$944$	62607.9			2.15860
$945$		0			0
$946$	−1572.90			−0.0540586
$947$	20136.4	+	34877.3i	0.690967	+	1.19679i	0.971521	+	0.236952i	$0.0761486\pi$
$947$	20136.4	+	34877.3i	0.690967	+	1.19679i	−0.280554	+	0.959838i	$0.590518\pi$
$948$	−16949.7	+	29357.8i	−0.580698	+	1.00580i
$949$	−22042.0	+	38177.9i	−0.753967	+	1.30591i
$950$	815.821	+	1413.04i	0.0278618	+	0.0482581i
$951$	6715.12			0.228972
$952$		0			0
$953$	17770.1			0.604019			0.302010	−	0.953305i	$-0.402343\pi$
$953$	17770.1			0.604019			0.302010	+	0.953305i	$0.402343\pi$
$954$	−11785.5	−	20413.1i	−0.399968	−	0.692765i
$955$	−6064.87	+	10504.7i	−0.205502	+	0.355940i
$956$	−39502.5	+	68420.3i	−1.33640	+	2.31472i
$957$	−12717.7	−	22027.7i	−0.429576	−	0.744047i
$958$	−9349.97			−0.315328
$959$		0			0
$960$	−44869.0			−1.50848
$961$	2127.18	+	3684.38i	0.0714033	+	0.123674i
$962$	−33816.0	+	58571.0i	−1.13334	+	1.96300i
$963$	−13012.5	+	22538.4i	−0.435434	+	0.754194i
$964$	−4073.54	−	7055.57i	−0.136099	−	0.235731i
$965$	3114.61			0.103899
$966$		0			0
$967$	−3530.14			−0.117396			−0.0586978	−	0.998276i	$-0.518695\pi$
$967$	−3530.14			−0.117396			−0.0586978	+	0.998276i	$0.518695\pi$
$968$	−5552.59	−	9617.37i	−0.184367	−	0.319333i
$969$	2087.45	−	3615.58i	0.0692040	−	0.119865i
$970$	−11574.0	+	20046.8i	−0.383113	+	0.663571i
$971$	−8825.36	−	15286.0i	−0.291678	−	0.505201i	0.682529	−	0.730859i	$-0.260880\pi$
$971$	−8825.36	−	15286.0i	−0.291678	−	0.505201i	−0.974207	+	0.225658i	$0.927547\pi$
$972$	69292.3			2.28658
$973$		0			0
$974$	−86693.8			−2.85200
$975$	−3324.45	−	5758.11i	−0.109197	−	0.189136i
$976$	−101293.	+	175444.i	−3.32204	+	5.75393i
$977$	7238.82	−	12538.0i	0.237042	−	0.410569i	−0.722822	−	0.691034i	$-0.757155\pi$
$977$	7238.82	−	12538.0i	0.237042	−	0.410569i	0.959864	+	0.280465i	$0.0904886\pi$
$978$	−14319.1	−	24801.4i	−0.468175	−	0.810902i
$979$	16357.8			0.534012
$980$		0			0
$981$	4924.56			0.160274
$982$	−7494.34	−	12980.6i	−0.243538	−	0.421820i
$983$	4382.05	−	7589.93i	0.142183	−	0.246268i	−0.786136	−	0.618054i	$-0.787921\pi$
$983$	4382.05	−	7589.93i	0.142183	−	0.246268i	0.928318	+	0.371786i	$0.121255\pi$
$984$	22351.1	−	38713.2i	0.724112	−	1.25420i
$985$	7105.72	+	12307.5i	0.229855	+	0.398120i
$986$	96296.9			3.11026
$987$		0			0
$988$	18292.0			0.589015
$989$	0.430062	+	0.744889i	1.38273e−5	+	2.39495e-5i
$990$	5760.97	−	9978.29i	0.184945	−	0.320334i
$991$	−16812.1	+	29119.3i	−0.538903	+	0.933407i	0.460061	+	0.887887i	$0.347828\pi$
$991$	−16812.1	+	29119.3i	−0.538903	+	0.933407i	−0.998963	+	0.0455192i	$0.985506\pi$
$992$	63817.1	+	110535.i	2.04254	+	3.53778i
$993$	21645.1			0.691727
$994$		0			0
$995$	4336.82			0.138177
$996$	−21370.1	−	37014.2i	−0.679858	−	1.17755i
$997$	−8315.63	+	14403.1i	−0.264151	+	0.457523i	−0.967341	−	0.253479i	$-0.918425\pi$
$997$	−8315.63	+	14403.1i	−0.264151	+	0.457523i	0.703190	+	0.711002i	$0.251758\pi$
$998$	11850.8	−	20526.2i	0.375882	−	0.651046i
$999$	−13425.9	−	23254.3i	−0.425202	−	0.736471i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.4.e.p.116.6		12
7.2	even	3	inner	245.4.e.p.226.6		12
7.3	odd	6		245.4.a.o.1.1	✓	6
7.4	even	3		245.4.a.p.1.1	yes	6
7.5	odd	6		245.4.e.q.226.6		12
7.6	odd	2		245.4.e.q.116.6		12
21.11	odd	6		2205.4.a.ca.1.6		6
21.17	even	6		2205.4.a.bz.1.6		6
35.4	even	6		1225.4.a.bi.1.6		6
35.24	odd	6		1225.4.a.bj.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.4.a.o.1.1	✓	6	7.3	odd	6
245.4.a.p.1.1	yes	6	7.4	even	3
245.4.e.p.116.6		12	1.1	even	1	trivial
245.4.e.p.226.6		12	7.2	even	3	inner
245.4.e.q.116.6		12	7.6	odd	2
245.4.e.q.226.6		12	7.5	odd	6
1225.4.a.bi.1.6		6	35.4	even	6
1225.4.a.bj.1.6		6	35.24	odd	6
2205.4.a.bz.1.6		6	21.17	even	6
2205.4.a.ca.1.6		6	21.11	odd	6

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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	245.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.75899 + 4.77871i) q^{2} +(-1.93020 + 3.34320i) q^{3} +(-11.2240 + 19.4406i) q^{4} +(2.50000 + 4.33013i) q^{5} -21.3015 q^{6} -79.7239 q^{8} +(6.04869 + 10.4766i) q^{9} +O(q^{10})\)	\(q+(2.75899 + 4.77871i) q^{2} +(-1.93020 + 3.34320i) q^{3} +(-11.2240 + 19.4406i) q^{4} +(2.50000 + 4.33013i) q^{5} -21.3015 q^{6} -79.7239 q^{8} +(6.04869 + 10.4766i) q^{9} +(-13.7949 + 23.8935i) q^{10} +(-17.2605 + 29.8961i) q^{11} +(-43.3291 - 75.0482i) q^{12} +68.8935 q^{13} -19.3020 q^{15} +(-130.165 - 225.452i) q^{16} +(45.7173 - 79.1847i) q^{17} +(-33.3765 + 57.8098i) q^{18} +(-5.91392 - 10.2432i) q^{19} -112.240 q^{20} -190.486 q^{22} +(0.0520827 + 0.0902099i) q^{23} +(153.883 - 266.533i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(190.076 + 329.222i) q^{26} -150.931 q^{27} +190.863 q^{29} +(-53.2538 - 92.2384i) q^{30} +(-79.9010 + 138.393i) q^{31} +(399.352 - 691.697i) q^{32} +(-66.6324 - 115.411i) q^{33} +504.534 q^{34} -271.562 q^{36} +(88.9538 + 154.073i) q^{37} +(32.6328 - 56.5217i) q^{38} +(-132.978 + 230.324i) q^{39} +(-199.310 - 345.215i) q^{40} +145.247 q^{41} +8.25729 q^{43} +(-387.465 - 671.109i) q^{44} +(-30.2435 + 52.3832i) q^{45} +(-0.287391 + 0.497776i) q^{46} +(-130.264 - 225.624i) q^{47} +1004.98 q^{48} -137.949 q^{50} +(176.487 + 305.684i) q^{51} +(-773.262 + 1339.33i) q^{52} +(-176.554 + 305.800i) q^{53} +(-416.417 - 721.256i) q^{54} -172.605 q^{55} +45.6601 q^{57} +(526.589 + 912.079i) q^{58} +(-120.247 + 208.274i) q^{59} +(216.645 - 375.241i) q^{60} +(-389.094 - 673.931i) q^{61} -881.783 q^{62} +2324.58 q^{64} +(172.234 + 298.318i) q^{65} +(367.676 - 636.833i) q^{66} +(-75.9723 + 131.588i) q^{67} +(1026.26 + 1777.54i) q^{68} -0.402119 q^{69} -311.449 q^{71} +(-482.225 - 835.238i) q^{72} +(-319.944 + 554.159i) q^{73} +(-490.845 + 850.168i) q^{74} +(-48.2549 - 83.5799i) q^{75} +265.512 q^{76} -1467.54 q^{78} +(-195.593 - 338.777i) q^{79} +(650.825 - 1127.26i) q^{80} +(128.012 - 221.723i) q^{81} +(400.736 + 694.095i) q^{82} +493.205 q^{83} +457.173 q^{85} +(22.7817 + 39.4591i) q^{86} +(-368.403 + 638.093i) q^{87} +(1376.08 - 2383.44i) q^{88} +(-236.925 - 410.366i) q^{89} -333.765 q^{90} -2.33831 q^{92} +(-308.449 - 534.249i) q^{93} +(718.795 - 1244.99i) q^{94} +(29.5696 - 51.2160i) q^{95} +(1541.65 + 2670.22i) q^{96} +839.005 q^{97} -417.615 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 16 q^{3} - 14 q^{4} + 30 q^{5} + 48 q^{6} - 132 q^{8} - 70 q^{9}+O(q^{10}) \) 12 * q + 2 * q^2 - 16 * q^3 - 14 * q^4 + 30 * q^5 + 48 * q^6 - 132 * q^8 - 70 * q^9	\( 12 q + 2 q^{2} - 16 q^{3} - 14 q^{4} + 30 q^{5} + 48 q^{6} - 132 q^{8} - 70 q^{9} - 10 q^{10} + 16 q^{11} - 160 q^{12} + 336 q^{13} - 160 q^{15} - 298 q^{16} + 4 q^{17} - 354 q^{18} - 308 q^{19} - 140 q^{20} - 472 q^{22} + 336 q^{23} + 92 q^{24} - 150 q^{25} - 56 q^{26} + 1928 q^{27} + 352 q^{29} + 120 q^{30} - 392 q^{31} + 770 q^{32} - 188 q^{33} + 1624 q^{34} + 460 q^{36} + 140 q^{37} - 20 q^{38} - 140 q^{39} - 330 q^{40} + 1312 q^{41} - 776 q^{43} + 160 q^{44} + 350 q^{45} + 388 q^{46} - 628 q^{47} + 2792 q^{48} - 100 q^{50} - 744 q^{51} - 1520 q^{52} + 676 q^{53} - 2284 q^{54} + 160 q^{55} + 2936 q^{57} + 2012 q^{58} - 996 q^{59} + 800 q^{60} - 740 q^{61} - 728 q^{62} + 2852 q^{64} + 840 q^{65} + 3620 q^{66} - 1768 q^{67} + 2940 q^{68} - 2096 q^{69} - 448 q^{71} - 2858 q^{72} - 2640 q^{73} - 928 q^{74} - 400 q^{75} - 2680 q^{76} + 16 q^{78} - 1636 q^{79} + 1490 q^{80} - 4442 q^{81} + 1756 q^{82} + 280 q^{83} + 40 q^{85} - 1180 q^{86} - 1940 q^{87} + 5652 q^{88} + 1904 q^{89} - 3540 q^{90} - 3904 q^{92} + 1592 q^{93} + 3332 q^{94} + 1540 q^{95} + 6460 q^{96} + 1032 q^{97} - 5608 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 - 16 * q^3 - 14 * q^4 + 30 * q^5 + 48 * q^6 - 132 * q^8 - 70 * q^9 - 10 * q^10 + 16 * q^11 - 160 * q^12 + 336 * q^13 - 160 * q^15 - 298 * q^16 + 4 * q^17 - 354 * q^18 - 308 * q^19 - 140 * q^20 - 472 * q^22 + 336 * q^23 + 92 * q^24 - 150 * q^25 - 56 * q^26 + 1928 * q^27 + 352 * q^29 + 120 * q^30 - 392 * q^31 + 770 * q^32 - 188 * q^33 + 1624 * q^34 + 460 * q^36 + 140 * q^37 - 20 * q^38 - 140 * q^39 - 330 * q^40 + 1312 * q^41 - 776 * q^43 + 160 * q^44 + 350 * q^45 + 388 * q^46 - 628 * q^47 + 2792 * q^48 - 100 * q^50 - 744 * q^51 - 1520 * q^52 + 676 * q^53 - 2284 * q^54 + 160 * q^55 + 2936 * q^57 + 2012 * q^58 - 996 * q^59 + 800 * q^60 - 740 * q^61 - 728 * q^62 + 2852 * q^64 + 840 * q^65 + 3620 * q^66 - 1768 * q^67 + 2940 * q^68 - 2096 * q^69 - 448 * q^71 - 2858 * q^72 - 2640 * q^73 - 928 * q^74 - 400 * q^75 - 2680 * q^76 + 16 * q^78 - 1636 * q^79 + 1490 * q^80 - 4442 * q^81 + 1756 * q^82 + 280 * q^83 + 40 * q^85 - 1180 * q^86 - 1940 * q^87 + 5652 * q^88 + 1904 * q^89 - 3540 * q^90 - 3904 * q^92 + 1592 * q^93 + 3332 * q^94 + 1540 * q^95 + 6460 * q^96 + 1032 * q^97 - 5608 * q^99

Introduction

L-functions

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