LMFDB - Embedded newform 245.4.e.p.226.3

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			226.3
Root			$-1.02943 - 1.78303i$ of defining polynomial
Character	$\chi$	$=$	245.226
Dual form			245.4.e.p.116.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.322324 + 0.558282i) q^{2} +(2.09344 + 3.62594i) q^{3} +(3.79221 + 6.56831i) q^{4} +(2.50000 - 4.33013i) q^{5} -2.69906 q^{6} -10.0465 q^{8} +(4.73504 - 8.20133i) q^{9} +O(q^{10})$	\(q+(-0.322324 + 0.558282i) q^{2} +(2.09344 + 3.62594i) q^{3} +(3.79221 + 6.56831i) q^{4} +(2.50000 - 4.33013i) q^{5} -2.69906 q^{6} -10.0465 q^{8} +(4.73504 - 8.20133i) q^{9} +(1.61162 + 2.79141i) q^{10} +(23.8507 + 41.3106i) q^{11} +(-15.8775 + 27.5007i) q^{12} +57.2256 q^{13} +20.9344 q^{15} +(-27.0995 + 46.9377i) q^{16} +(18.4843 + 32.0157i) q^{17} +(3.05244 + 5.28697i) q^{18} +(-15.3830 + 26.6441i) q^{19} +37.9221 q^{20} -30.7506 q^{22} +(-26.5641 + 46.0104i) q^{23} +(-21.0317 - 36.4279i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(-18.4452 + 31.9480i) q^{26} +152.696 q^{27} -195.663 q^{29} +(-6.74765 + 11.6873i) q^{30} +(-128.935 - 223.322i) q^{31} +(-57.6555 - 99.8623i) q^{32} +(-99.8597 + 172.962i) q^{33} -23.8317 q^{34} +71.8252 q^{36} +(-173.212 + 300.011i) q^{37} +(-9.91660 - 17.1760i) q^{38} +(119.798 + 207.497i) q^{39} +(-25.1162 + 43.5025i) q^{40} +267.050 q^{41} -176.859 q^{43} +(-180.894 + 313.317i) q^{44} +(-23.6752 - 41.0067i) q^{45} +(-17.1245 - 29.6605i) q^{46} +(155.799 - 269.852i) q^{47} -226.924 q^{48} +16.1162 q^{50} +(-77.3914 + 134.046i) q^{51} +(217.012 + 375.875i) q^{52} +(246.135 + 426.318i) q^{53} +(-49.2175 + 85.2472i) q^{54} +238.507 q^{55} -128.813 q^{57} +(63.0668 - 109.235i) q^{58} +(-49.3827 - 85.5333i) q^{59} +(79.3876 + 137.503i) q^{60} +(-41.0841 + 71.1597i) q^{61} +166.235 q^{62} -359.257 q^{64} +(143.064 - 247.794i) q^{65} +(-64.3744 - 111.500i) q^{66} +(-327.334 - 566.959i) q^{67} +(-140.193 + 242.821i) q^{68} -222.441 q^{69} +779.658 q^{71} +(-47.5705 + 82.3945i) q^{72} +(414.836 + 718.518i) q^{73} +(-111.660 - 193.402i) q^{74} +(52.3359 - 90.6485i) q^{75} -233.342 q^{76} -154.455 q^{78} +(384.713 - 666.343i) q^{79} +(135.497 + 234.689i) q^{80} +(191.813 + 332.229i) q^{81} +(-86.0765 + 149.089i) q^{82} +613.203 q^{83} +184.843 q^{85} +(57.0059 - 98.7372i) q^{86} +(-409.608 - 709.461i) q^{87} +(-239.615 - 415.025i) q^{88} +(228.833 - 396.350i) q^{89} +30.5244 q^{90} -402.947 q^{92} +(539.835 - 935.022i) q^{93} +(100.436 + 173.960i) q^{94} +(76.9148 + 133.220i) q^{95} +(241.396 - 418.111i) q^{96} -1412.11 q^{97} +451.736 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 $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.322324	+	0.558282i	−0.113959	+	0.197382i	−0.917363	−	0.398052i	$-0.869687\pi$
$2$	−0.322324	+	0.558282i	−0.113959	+	0.197382i	0.803404	+	0.595434i	$0.203020\pi$
$3$	2.09344	+	3.62594i	0.402882	+	0.697812i	0.994072	−	0.108720i	$-0.0346751\pi$
$3$	2.09344	+	3.62594i	0.402882	+	0.697812i	−0.591190	+	0.806532i	$0.701342\pi$
$4$	3.79221	+	6.56831i	0.474027	+	0.821039i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$6$	−2.69906			−0.183648
$7$		0			0
$7$		0			0
$8$	−10.0465			−0.443995
$9$	4.73504	−	8.20133i	0.175372	−	0.303753i
$10$	1.61162	+	2.79141i	0.0509639	+	0.0882721i
$11$	23.8507	+	41.3106i	0.653750	+	1.13233i	0.982206	+	0.187808i	$0.0601383\pi$
$11$	23.8507	+	41.3106i	0.653750	+	1.13233i	−0.328456	+	0.944519i	$0.606528\pi$
$12$	−15.8775	+	27.5007i	−0.381954	+	0.661564i
$13$	57.2256			1.22089			0.610443	−	0.792060i	$-0.290991\pi$
$13$	57.2256			1.22089			0.610443	+	0.792060i	$0.290991\pi$
$14$		0			0
$15$	20.9344			0.360349
$16$	−27.0995	+	46.9377i	−0.423430	+	0.733402i
$17$	18.4843	+	32.0157i	0.263712	+	0.456762i	0.967225	−	0.253920i	$-0.0817199\pi$
$17$	18.4843	+	32.0157i	0.263712	+	0.456762i	−0.703514	+	0.710682i	$0.748387\pi$
$18$	3.05244	+	5.28697i	0.0399703	+	0.0692306i
$19$	−15.3830	+	26.6441i	−0.185742	+	0.321714i	−0.943826	−	0.330442i	$-0.892802\pi$
$19$	−15.3830	+	26.6441i	−0.185742	+	0.321714i	0.758084	+	0.652156i	$0.226135\pi$
$20$	37.9221			0.423982
$21$		0			0
$22$	−30.7506			−0.298002
$23$	−26.5641	+	46.0104i	−0.240826	+	0.417123i	−0.960950	−	0.276723i	$-0.910752\pi$
$23$	−26.5641	+	46.0104i	−0.240826	+	0.417123i	0.720124	+	0.693846i	$0.244085\pi$
$24$	−21.0317	−	36.4279i	−0.178878	−	0.309826i
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	−18.4452	+	31.9480i	−0.139131	+	0.240981i
$27$	152.696			1.08838
$28$		0			0
$29$	−195.663			−1.25288			−0.626442	−	0.779468i	$-0.715490\pi$
$29$	−195.663			−1.25288			−0.626442	+	0.779468i	$0.715490\pi$
$30$	−6.74765	+	11.6873i	−0.0410649	+	0.0711265i
$31$	−128.935	−	223.322i	−0.747014	−	1.29387i	−0.949248	−	0.314529i	$-0.898154\pi$
$31$	−128.935	−	223.322i	−0.747014	−	1.29387i	0.202234	−	0.979337i	$-0.435180\pi$
$32$	−57.6555	−	99.8623i	−0.318505	−	0.551666i
$33$	−99.8597	+	172.962i	−0.526768	+	0.912389i
$34$	−23.8317			−0.120209
$35$		0			0
$36$	71.8252			0.332524
$37$	−173.212	+	300.011i	−0.769616	+	1.33301i	0.168155	+	0.985761i	$0.446219\pi$
$37$	−173.212	+	300.011i	−0.769616	+	1.33301i	−0.937771	+	0.347254i	$0.887114\pi$
$38$	−9.91660	−	17.1760i	−0.0423338	−	0.0733243i
$39$	119.798	+	207.497i	0.491873	+	0.851950i
$40$	−25.1162	+	43.5025i	−0.0992804	+	0.171959i
$41$	267.050			1.01722			0.508611	−	0.860996i	$-0.330159\pi$
$41$	267.050			1.01722			0.508611	+	0.860996i	$0.330159\pi$
$42$		0			0
$43$	−176.859			−0.627227			−0.313614	−	0.949551i	$-0.601540\pi$
$43$	−176.859			−0.627227			−0.313614	+	0.949551i	$0.601540\pi$
$44$	−180.894	+	313.317i	−0.619790	+	1.07351i
$45$	−23.6752	−	41.0067i	−0.0784287	−	0.135843i
$46$	−17.1245	−	29.6605i	−0.0548884	−	0.0950696i
$47$	155.799	−	269.852i	0.483524	−	0.837489i	−0.516297	−	0.856410i	$-0.672690\pi$
$47$	155.799	−	269.852i	0.483524	−	0.837489i	0.999821	+	0.0189211i	$0.00602314\pi$
$48$	−226.924			−0.682369
$49$		0			0
$50$	16.1162			0.0455835
$51$	−77.3914	+	134.046i	−0.212489	+	0.368042i
$52$	217.012	+	375.875i	0.578733	+	1.00240i
$53$	246.135	+	426.318i	0.637910	+	1.10489i	0.985891	+	0.167391i	$0.0535343\pi$
$53$	246.135	+	426.318i	0.637910	+	1.10489i	−0.347980	+	0.937502i	$0.613132\pi$
$54$	−49.2175	+	85.2472i	−0.124031	+	0.214827i
$55$	238.507			0.584731
$56$		0			0
$57$	−128.813			−0.299328
$58$	63.0668	−	109.235i	0.142777	−	0.247297i
$59$	−49.3827	−	85.5333i	−0.108967	−	0.188737i	0.806385	−	0.591391i	$-0.201421\pi$
$59$	−49.3827	−	85.5333i	−0.108967	−	0.188737i	−0.915352	+	0.402654i	$0.868088\pi$
$60$	79.3876	+	137.503i	0.170815	+	0.295860i
$61$	−41.0841	+	71.1597i	−0.0862340	+	0.149362i	−0.905916	−	0.423457i	$-0.860817\pi$
$61$	−41.0841	+	71.1597i	−0.0862340	+	0.149362i	0.819682	+	0.572818i	$0.194150\pi$
$62$	166.235			0.340515
$63$		0			0
$64$	−359.257			−0.701674
$65$	143.064	−	247.794i	0.272999	−	0.472847i
$66$	−64.3744	−	111.500i	−0.120060	−	0.207949i
$67$	−327.334	−	566.959i	−0.596869	−	1.03381i	−0.993280	−	0.115734i	$-0.963078\pi$
$67$	−327.334	−	566.959i	−0.596869	−	1.03381i	0.396411	−	0.918073i	$-0.370255\pi$
$68$	−140.193	+	242.821i	−0.250013	+	0.433035i
$69$	−222.441			−0.388098
$70$		0			0
$71$	779.658			1.30322			0.651608	−	0.758556i	$-0.274095\pi$
$71$	779.658			1.30322			0.651608	+	0.758556i	$0.274095\pi$
$72$	−47.5705	+	82.3945i	−0.0778643	+	0.134865i
$73$	414.836	+	718.518i	0.665109	+	1.15200i	0.979256	+	0.202628i	$0.0649481\pi$
$73$	414.836	+	718.518i	0.665109	+	1.15200i	−0.314147	+	0.949374i	$0.601719\pi$
$74$	−111.660	−	193.402i	−0.175409	−	0.303817i
$75$	52.3359	−	90.6485i	0.0805764	−	0.139562i
$76$	−233.342			−0.352186
$77$		0			0
$78$	−154.455			−0.224213
$79$	384.713	−	666.343i	0.547894	−	0.948980i	−0.450525	−	0.892764i	$-0.648763\pi$
$79$	384.713	−	666.343i	0.547894	−	0.948980i	0.998419	−	0.0562159i	$-0.0179035\pi$
$80$	135.497	+	234.689i	0.189363	+	0.327987i
$81$	191.813	+	332.229i	0.263117	+	0.455733i
$82$	−86.0765	+	149.089i	−0.115921	+	0.200782i
$83$	613.203			0.810937			0.405469	−	0.914109i	$-0.367108\pi$
$83$	613.203			0.810937			0.405469	+	0.914109i	$0.367108\pi$
$84$		0			0
$85$	184.843			0.235871
$86$	57.0059	−	98.7372i	0.0714780	−	0.123804i
$87$	−409.608	−	709.461i	−0.504765	−	0.874278i
$88$	−239.615	−	415.025i	−0.290262	−	0.502748i
$89$	228.833	−	396.350i	0.272542	−	0.472057i	−0.696970	−	0.717100i	$-0.745469\pi$
$89$	228.833	−	396.350i	0.272542	−	0.472057i	0.969512	+	0.245043i	$0.0788022\pi$
$90$	30.5244			0.0357506
$91$		0			0
$92$	−402.947			−0.456632
$93$	539.835	−	935.022i	0.601917	−	1.04255i
$94$	100.436	+	173.960i	0.110204	+	0.190878i
$95$	76.9148	+	133.220i	0.0830662	+	0.143875i
$96$	241.396	−	418.111i	0.256640	−	0.444513i
$97$	−1412.11			−1.47813			−0.739063	−	0.673636i	$-0.764732\pi$
$97$	−1412.11			−1.47813			−0.739063	+	0.673636i	$0.764732\pi$
$98$		0			0
$99$	451.736			0.458597
$100$	94.8054	−	164.208i	0.0948054	−	0.164208i
$101$	−911.895	−	1579.45i	−0.898386	−	1.55605i	−0.829558	−	0.558421i	$-0.811407\pi$
$101$	−911.895	−	1579.45i	−0.898386	−	1.55605i	−0.0688279	−	0.997629i	$-0.521926\pi$
$102$	−49.8902	−	86.4124i	−0.0484301	−	0.0838833i
$103$	−203.887	+	353.143i	−0.195045	+	0.337828i	−0.946915	−	0.321483i	$-0.895819\pi$
$103$	−203.887	+	353.143i	−0.195045	+	0.337828i	0.751870	+	0.659311i	$0.229152\pi$
$104$	−574.915			−0.542068
$105$		0			0
$106$	−317.341			−0.290782
$107$	185.054	−	320.524i	0.167195	−	0.289591i	−0.770237	−	0.637757i	$-0.779862\pi$
$107$	185.054	−	320.524i	0.167195	−	0.289591i	0.937433	+	0.348167i	$0.113196\pi$
$108$	579.055	+	1002.95i	0.515922	+	0.893603i
$109$	−487.785	−	844.869i	−0.428636	−	0.742420i	0.568116	−	0.822948i	$-0.307672\pi$
$109$	−487.785	−	844.869i	−0.428636	−	0.742420i	−0.996752	+	0.0805287i	$0.974339\pi$
$110$	−76.8764	+	133.154i	−0.0666352	+	0.115416i
$111$	−1450.43			−1.24026
$112$		0			0
$113$	1978.85			1.64739			0.823693	−	0.567036i	$-0.191910\pi$
$113$	1978.85			1.64739			0.823693	+	0.567036i	$0.191910\pi$
$114$	41.5195	−	71.9139i	0.0341111	−	0.0590821i
$115$	132.820	+	230.052i	0.107701	+	0.186543i
$116$	−741.995	−	1285.17i	−0.593901	−	1.02867i
$117$	270.966	−	469.326i	0.214109	−	0.370848i
$118$	63.6689			0.0496711
$119$		0			0
$120$	−210.317			−0.159993
$121$	−472.208	+	817.888i	−0.354777	+	0.614492i
$122$	−26.4848	−	45.8730i	−0.0196542	−	0.0340422i
$123$	559.052	+	968.306i	0.409821	+	0.709831i
$124$	977.899	−	1693.77i	0.708209	−	1.22665i
$125$	−125.000			−0.0894427
$126$		0			0
$127$	1392.38			0.972867			0.486433	−	0.873718i	$-0.338298\pi$
$127$	1392.38			0.972867			0.486433	+	0.873718i	$0.338298\pi$
$128$	577.041	−	999.465i	0.398467	−	0.690164i
$129$	−370.243	−	641.280i	−0.252699	−	0.437687i
$130$	92.2259	+	159.740i	0.0622211	+	0.107770i
$131$	888.509	−	1538.94i	0.592591	−	1.02640i	−0.401291	−	0.915951i	$-0.631438\pi$
$131$	888.509	−	1538.94i	0.592591	−	1.02640i	0.993882	−	0.110447i	$-0.0352282\pi$
$132$	−1514.76			−0.998809
$133$		0			0
$134$	422.031			0.272074
$135$	381.739	−	661.192i	0.243369	−	0.421528i
$136$	−185.702	−	321.645i	−0.117087	−	0.202800i
$137$	990.240	+	1715.15i	0.617532	+	1.06960i	0.989935	+	0.141526i	$0.0452009\pi$
$137$	990.240	+	1715.15i	0.617532	+	1.06960i	−0.372402	+	0.928071i	$0.621466\pi$
$138$	71.6981	−	124.185i	0.0442271	−	0.0766037i
$139$	2182.09			1.33153			0.665763	−	0.746163i	$-0.268106\pi$
$139$	2182.09			1.33153			0.665763	+	0.746163i	$0.268106\pi$
$140$		0			0
$141$	1304.62			0.779213
$142$	−251.302	+	435.268i	−0.148513	+	0.257232i
$143$	1364.87	+	2364.02i	0.798154	+	1.38244i
$144$	256.635	+	444.504i	0.148515	+	0.257236i
$145$	−489.157	+	847.244i	−0.280153	+	0.485240i
$146$	−534.847			−0.303180
$147$		0			0
$148$	−2627.42			−1.45928
$149$	−335.077	+	580.370i	−0.184232	+	0.319099i	−0.943317	−	0.331892i	$-0.892313\pi$
$149$	−335.077	+	580.370i	−0.184232	+	0.319099i	0.759085	+	0.650991i	$0.225646\pi$
$150$	33.7383	+	58.4364i	0.0183648	+	0.0318087i
$151$	−1674.42	−	2900.18i	−0.902401	−	1.56300i	−0.824369	−	0.566053i	$-0.808470\pi$
$151$	−1674.42	−	2900.18i	−0.902401	−	1.56300i	−0.0780315	−	0.996951i	$-0.524863\pi$
$152$	154.544	−	267.679i	0.0824685	−	0.142840i
$153$	350.096			0.184990
$154$		0			0
$155$	−1289.35			−0.668149
$156$	−908.601	+	1573.74i	−0.466322	+	0.807694i
$157$	−1204.20	−	2085.74i	−0.612140	−	1.06026i	−0.990879	−	0.134754i	$-0.956975\pi$
$157$	−1204.20	−	2085.74i	−0.612140	−	1.06026i	0.378739	−	0.925504i	$-0.376358\pi$
$158$	248.005	+	429.556i	0.124875	+	0.216289i
$159$	−1030.54	+	1784.94i	−0.514005	+	0.890284i
$160$	−576.555			−0.284879
$161$		0			0
$162$	−247.303			−0.119938
$163$	1905.52	−	3300.45i	0.915654	−	1.58596i	0.109712	−	0.993963i	$-0.465007\pi$
$163$	1905.52	−	3300.45i	0.915654	−	1.58596i	0.805942	−	0.591995i	$-0.201659\pi$
$164$	1012.71	+	1754.06i	0.482191	+	0.835179i
$165$	499.299	+	864.810i	0.235578	+	0.408033i
$166$	−197.650	+	342.340i	−0.0924134	+	0.160065i
$167$	1207.15			0.559354			0.279677	−	0.960094i	$-0.409773\pi$
$167$	1207.15			0.559354			0.279677	+	0.960094i	$0.409773\pi$
$168$		0			0
$169$	1077.77			0.490564
$170$	−59.5793	+	103.194i	−0.0268795	+	0.0465567i
$171$	145.678	+	252.322i	0.0651478	+	0.112839i
$172$	−670.688	−	1161.67i	−0.297322	−	0.514978i
$173$	−1621.64	+	2808.76i	−0.712665	+	1.23437i	0.251188	+	0.967938i	$0.419179\pi$
$173$	−1621.64	+	2808.76i	−0.712665	+	1.23437i	−0.963853	+	0.266434i	$0.914155\pi$
$174$	528.105			0.230089
$175$		0			0
$176$	−2585.36			−1.10727
$177$	206.759	−	358.117i	0.0878020	−	0.152078i
$178$	147.517	+	255.507i	0.0621171	+	0.107590i
$179$	−429.864	−	744.546i	−0.179495	−	0.310894i	0.762213	−	0.647326i	$-0.224113\pi$
$179$	−429.864	−	744.546i	−0.179495	−	0.310894i	−0.941708	+	0.336433i	$0.890780\pi$
$180$	179.563	−	311.012i	0.0743546	−	0.128786i
$181$	−290.504			−0.119298			−0.0596491	−	0.998219i	$-0.518998\pi$
$181$	−290.504			−0.119298			−0.0596491	+	0.998219i	$0.518998\pi$
$182$		0			0
$183$	−344.028			−0.138969
$184$	266.875	−	462.242i	0.106926	−	0.185201i
$185$	866.058	+	1500.06i	0.344183	+	0.596142i
$186$	348.004	+	602.760i	0.137187	+	0.237616i
$187$	−881.725	+	1527.19i	−0.344803	+	0.597216i
$188$	2363.30			0.916814
$189$		0			0
$190$	−99.1660			−0.0378645
$191$	−2447.81	+	4239.73i	−0.927315	+	1.60616i	−0.139519	+	0.990219i	$0.544556\pi$
$191$	−2447.81	+	4239.73i	−0.927315	+	1.60616i	−0.787795	+	0.615937i	$0.788778\pi$
$192$	−752.082	−	1302.64i	−0.282692	−	0.489637i
$193$	1774.36	+	3073.29i	0.661770	+	1.14622i	0.980150	+	0.198256i	$0.0635276\pi$
$193$	1774.36	+	3073.29i	0.661770	+	1.14622i	−0.318381	+	0.947963i	$0.603139\pi$
$194$	455.158	−	788.356i	0.168445	−	0.291756i
$195$	1197.98			0.439945
$196$		0			0
$197$	−650.107			−0.235118			−0.117559	−	0.993066i	$-0.537507\pi$
$197$	−650.107			−0.235118			−0.117559	+	0.993066i	$0.537507\pi$
$198$	−145.605	+	252.196i	−0.0522612	+	0.0905190i
$199$	−2027.55	−	3511.81i	−0.722256	−	1.25098i	−0.960094	−	0.279679i	$-0.909772\pi$
$199$	−2027.55	−	3511.81i	−0.722256	−	1.25098i	0.237838	−	0.971305i	$-0.423561\pi$
$200$	125.581	+	217.512i	0.0443995	+	0.0769023i
$201$	1370.51	−	2373.79i	0.480936	−	0.833005i
$202$	1175.70			0.409516
$203$		0			0
$204$	−1173.94			−0.402903
$205$	667.624	−	1156.36i	0.227458	−	0.393969i
$206$	−131.436	−	227.653i	−0.0444541	−	0.0769968i
$207$	251.564	+	435.722i	0.0844682	+	0.146303i
$208$	−1550.79	+	2686.04i	−0.516960	+	0.895400i
$209$	−1467.58			−0.485714
$210$		0			0
$211$	−1569.67			−0.512134			−0.256067	−	0.966659i	$-0.582427\pi$
$211$	−1569.67			−0.512134			−0.256067	+	0.966659i	$0.582427\pi$
$212$	−1866.79	+	3233.38i	−0.604773	+	1.04750i
$213$	1632.16	+	2826.99i	0.525042	+	0.909400i
$214$	119.295	+	206.625i	0.0381067	+	0.0660027i
$215$	−442.148	+	765.822i	−0.140252	+	0.242924i
$216$	−1534.05			−0.483236
$217$		0			0
$218$	628.900			0.195387
$219$	−1736.87	+	3008.34i	−0.535921	+	0.928242i
$220$	904.468	+	1566.58i	0.277178	+	0.480087i
$221$	1057.77	+	1832.12i	0.321962	+	0.557655i
$222$	467.508	−	809.748i	0.141338	−	0.244805i
$223$	4723.86			1.41853			0.709267	−	0.704940i	$-0.249026\pi$
$223$	4723.86			1.41853			0.709267	+	0.704940i	$0.249026\pi$
$224$		0			0
$225$	−236.752			−0.0701488
$226$	−637.831	+	1104.76i	−0.187734	+	0.325165i
$227$	−1842.51	−	3191.32i	−0.538730	−	0.933108i	−0.998973	−	0.0453145i	$-0.985571\pi$
$227$	−1842.51	−	3191.32i	−0.538730	−	0.933108i	0.460243	−	0.887793i	$-0.347762\pi$
$228$	−488.487	−	846.084i	−0.141890	−	0.245760i
$229$	−1678.39	+	2907.05i	−0.484328	+	0.838880i	−0.999838	−	0.0180032i	$-0.994269\pi$
$229$	−1678.39	+	2907.05i	−0.484328	+	0.838880i	0.515510	+	0.856883i	$0.327602\pi$
$230$	−171.245			−0.0490937
$231$		0			0
$232$	1965.72			0.556275
$233$	−1157.01	+	2004.00i	−0.325314	+	0.563460i	−0.981576	−	0.191073i	$-0.938803\pi$
$233$	−1157.01	+	2004.00i	−0.325314	+	0.563460i	0.656262	+	0.754533i	$0.272137\pi$
$234$	174.677	+	302.550i	0.0487992	+	0.0845228i
$235$	−778.996	−	1349.26i	−0.216239	−	0.374536i
$236$	374.539	−	648.721i	0.103307	−	0.178933i
$237$	3221.49			0.882946
$238$		0			0
$239$	941.179			0.254727			0.127364	−	0.991856i	$-0.459348\pi$
$239$	941.179			0.254727			0.127364	+	0.991856i	$0.459348\pi$
$240$	−567.311	+	982.611i	−0.152582	+	0.264280i
$241$	−2819.12	−	4882.86i	−0.753509	−	1.30512i	−0.946112	−	0.323838i	$-0.895027\pi$
$241$	−2819.12	−	4882.86i	−0.753509	−	1.30512i	0.192604	−	0.981277i	$-0.438307\pi$
$242$	−304.408	−	527.250i	−0.0808599	−	0.140053i
$243$	1258.30	−	2179.43i	0.332180	−	0.575353i
$244$	−623.199			−0.163509
$245$		0			0
$246$	−720.783			−0.186811
$247$	−880.299	+	1524.72i	−0.226770	+	0.392777i
$248$	1295.34	+	2243.60i	0.331671	+	0.574471i
$249$	1283.70	+	2223.44i	0.326712	+	0.565882i
$250$	40.2905	−	69.7852i	0.0101928	−	0.0176544i
$251$	365.822			0.0919940			0.0459970	−	0.998942i	$-0.485354\pi$
$251$	365.822			0.0919940			0.0459970	+	0.998942i	$0.485354\pi$
$252$		0			0
$253$	−2534.28			−0.629759
$254$	−448.799	+	777.342i	−0.110867	+	0.192027i
$255$	386.957	+	670.229i	0.0950282	+	0.164594i
$256$	−1065.04	−	1844.70i	−0.260019	−	0.450367i
$257$	3138.23	−	5435.57i	0.761702	−	1.31931i	−0.180271	−	0.983617i	$-0.557697\pi$
$257$	3138.23	−	5435.57i	0.761702	−	1.31931i	0.941973	−	0.335689i	$-0.108969\pi$
$258$	477.353			0.115189
$259$		0			0
$260$	2170.12			0.517635
$261$	−926.471	+	1604.69i	−0.219721	+	0.380568i
$262$	572.776	+	992.076i	0.135062	+	0.233934i
$263$	2112.99	+	3659.80i	0.495408	+	0.858072i	0.999986	−	0.00529397i	$-0.00168513\pi$
$263$	2112.99	+	3659.80i	0.495408	+	0.858072i	−0.504578	+	0.863366i	$0.668352\pi$
$264$	1003.24	−	1737.66i	0.233883	−	0.405097i
$265$	2461.35			0.570564
$266$		0			0
$267$	1916.19			0.439210
$268$	2482.64	−	4300.06i	0.565864	−	0.980105i
$269$	−490.796	−	850.083i	−0.111243	−	0.192678i	0.805029	−	0.593236i	$-0.202150\pi$
$269$	−490.796	−	850.083i	−0.111243	−	0.192678i	−0.916272	+	0.400557i	$0.868816\pi$
$270$	246.087	+	426.236i	0.0554681	+	0.0960737i
$271$	−1942.21	+	3364.01i	−0.435354	+	0.754055i	−0.997324	−	0.0731021i	$-0.976710\pi$
$271$	−1942.21	+	3364.01i	−0.435354	+	0.754055i	0.561971	+	0.827157i	$0.310043\pi$
$272$	−2003.66			−0.446653
$273$		0			0
$274$	−1276.71			−0.281493
$275$	596.267	−	1032.76i	0.130750	−	0.226465i
$276$	−843.544	−	1461.06i	−0.183969	−	0.318643i
$277$	−1807.46	−	3130.62i	−0.392058	−	0.679064i	0.600663	−	0.799502i	$-0.294903\pi$
$277$	−1807.46	−	3130.62i	−0.392058	−	0.679064i	−0.992721	+	0.120438i	$0.961570\pi$
$278$	−703.339	+	1218.22i	−0.151739	+	0.262820i
$279$	−2442.05			−0.524021
$280$		0			0
$281$	72.6835			0.0154304			0.00771518	−	0.999970i	$-0.497544\pi$
$281$	72.6835			0.0154304			0.00771518	+	0.999970i	$0.497544\pi$
$282$	−420.511	+	728.347i	−0.0887982	+	0.153803i
$283$	−871.522	−	1509.52i	−0.183062	−	0.317073i	0.759860	−	0.650087i	$-0.225268\pi$
$283$	−871.522	−	1509.52i	−0.183062	−	0.317073i	−0.942922	+	0.333014i	$0.891934\pi$
$284$	2956.63	+	5121.03i	0.617759	+	1.06999i
$285$	−322.033	+	557.777i	−0.0669318	+	0.115929i
$286$	−1759.72			−0.363827
$287$		0			0
$288$	−1092.01			−0.223427
$289$	1773.16	−	3071.21i	0.360912	−	0.625119i
$290$	−315.334	−	546.174i	−0.0638519	−	0.110595i
$291$	−2956.17	−	5120.23i	−0.595511	−	1.03145i
$292$	−3146.30	+	5449.55i	−0.630559	+	1.09216i
$293$	−4989.29			−0.994804			−0.497402	−	0.867520i	$-0.665713\pi$
$293$	−4989.29			−0.994804			−0.497402	+	0.867520i	$0.665713\pi$
$294$		0			0
$295$	−493.827			−0.0974634
$296$	1740.17	−	3014.05i	0.341706	−	0.591853i
$297$	3641.89	+	6307.94i	0.711529	+	1.23240i
$298$	−216.007	−	374.135i	−0.0419897	−	0.0727283i
$299$	−1520.15	+	2632.97i	−0.294021	+	0.509260i
$300$	793.876			0.152782
$301$		0			0
$302$	2158.82			0.411346
$303$	3817.99	−	6612.95i	0.723887	−	1.25381i
$304$	−833.741	−	1444.08i	−0.157297	−	0.272447i
$305$	205.420	+	355.799i	0.0385650	+	0.0667966i
$306$	−112.844	+	195.452i	−0.0210813	+	0.0365139i
$307$	1664.61			0.309461			0.154731	−	0.987957i	$-0.450549\pi$
$307$	1664.61			0.309461			0.154731	+	0.987957i	$0.450549\pi$
$308$		0			0
$309$	−1707.30			−0.314320
$310$	415.589	−	719.821i	0.0761415	−	0.131881i
$311$	−272.812	−	472.524i	−0.0497419	−	0.0861555i	0.840082	−	0.542459i	$-0.182507\pi$
$311$	−272.812	−	472.524i	−0.0497419	−	0.0861555i	−0.889824	+	0.456303i	$0.849173\pi$
$312$	−1203.55	−	2084.61i	−0.218390	−	0.378262i
$313$	−106.782	+	184.952i	−0.0192833	+	0.0333997i	−0.875506	−	0.483207i	$-0.839472\pi$
$313$	−106.782	+	184.952i	−0.0192833	+	0.0333997i	0.856223	+	0.516607i	$0.172805\pi$
$314$	1552.58			0.279035
$315$		0			0
$316$	5835.66			1.03887
$317$	1341.97	−	2324.35i	0.237767	−	0.411825i	−0.722306	−	0.691574i	$-0.756918\pi$
$317$	1341.97	−	2324.35i	0.237767	−	0.411825i	0.960073	+	0.279748i	$0.0902511\pi$
$318$	−664.333	−	1150.66i	−0.117151	−	0.202911i
$319$	−4666.68	−	8082.93i	−0.819073	−	1.41868i
$320$	−898.142	+	1555.63i	−0.156899	+	0.271757i
$321$	1549.60			0.269440
$322$		0			0
$323$	−1137.37			−0.195929
$324$	−1454.79	+	2519.77i	−0.249449	+	0.432059i
$325$	−715.320	−	1238.97i	−0.122089	−	0.211464i
$326$	1228.39	+	2127.63i	0.208693	+	0.361468i
$327$	2042.30	−	3537.36i	0.345380	−	0.598215i
$328$	−2682.91			−0.451642
$329$		0			0
$330$	−643.744			−0.107385
$331$	2533.76	−	4388.61i	0.420750	−	0.728760i	−0.575263	−	0.817968i	$-0.695100\pi$
$331$	2533.76	−	4388.61i	0.420750	−	0.728760i	0.996013	+	0.0892084i	$0.0284337\pi$
$332$	2325.40	+	4027.71i	0.384406	+	0.665811i
$333$	1640.33	+	2841.13i	0.269938	+	0.467547i
$334$	−389.093	+	673.930i	−0.0637433	+	0.110407i
$335$	−3273.34			−0.533856
$336$		0			0
$337$	−9353.21			−1.51187			−0.755937	−	0.654644i	$-0.772818\pi$
$337$	−9353.21			−1.51187			−0.755937	+	0.654644i	$0.772818\pi$
$338$	−347.391	+	601.699i	−0.0559041	+	0.0968287i
$339$	4142.60	+	7175.19i	0.663703	+	1.14957i
$340$	700.964	+	1214.10i	0.111809	+	0.193659i
$341$	6150.37	−	10652.8i	0.976720	−	1.69173i
$342$	−187.822			−0.0296966
$343$		0			0
$344$	1776.81			0.278486
$345$	−556.103	+	963.198i	−0.0867813	+	0.150310i
$346$	−1045.39	−	1810.66i	−0.162429	−	0.281335i
$347$	−1174.67	−	2034.59i	−0.181728	−	0.314762i	0.760741	−	0.649055i	$-0.224836\pi$
$347$	−1174.67	−	2034.59i	−0.181728	−	0.314762i	−0.942469	+	0.334293i	$0.891502\pi$
$348$	3106.64	−	5380.86i	0.478544	−	0.828863i
$349$	−10472.6			−1.60626			−0.803128	−	0.595806i	$-0.796833\pi$
$349$	−10472.6			−1.60626			−0.803128	+	0.595806i	$0.796833\pi$
$350$		0			0
$351$	8738.10			1.32879
$352$	2750.24	−	4763.56i	0.416445	−	0.721303i
$353$	3587.31	+	6213.41i	0.540888	+	0.936845i	0.998853	+	0.0478752i	$0.0152450\pi$
$353$	3587.31	+	6213.41i	0.540888	+	0.936845i	−0.457966	+	0.888970i	$0.651422\pi$
$354$	133.287	+	230.859i	0.0200116	+	0.0346611i
$355$	1949.14	−	3376.02i	0.291408	−	0.504733i
$356$	3471.14			0.516769
$357$		0			0
$358$	554.222			0.0818199
$359$	3767.06	−	6524.74i	0.553811	−	0.959228i	−0.444185	−	0.895935i	$-0.646507\pi$
$359$	3767.06	−	6524.74i	0.553811	−	0.959228i	0.997995	−	0.0632926i	$-0.0201601\pi$
$360$	237.852	+	411.972i	0.0348220	+	0.0603135i
$361$	2956.23	+	5120.34i	0.431000	+	0.746514i
$362$	93.6364	−	162.183i	0.0135951	−	0.0235474i
$363$	−3954.15			−0.571733
$364$		0			0
$365$	4148.36			0.594891
$366$	110.888	−	192.064i	0.0158367	−	0.0274300i
$367$	−2726.53	−	4722.49i	−0.387803	−	0.671694i	0.604351	−	0.796718i	$-0.293433\pi$
$367$	−2726.53	−	4722.49i	−0.387803	−	0.671694i	−0.992154	+	0.125024i	$0.960099\pi$
$368$	−1439.75	−	2493.71i	−0.203946	−	0.353244i
$369$	1264.49	−	2190.16i	0.178392	−	0.308985i
$370$	−1116.60			−0.156891
$371$		0			0
$372$	8188.68			1.14130
$373$	−4115.65	+	7128.51i	−0.571314	+	0.989545i	0.425117	+	0.905138i	$0.360233\pi$
$373$	−4115.65	+	7128.51i	−0.571314	+	0.989545i	−0.996431	+	0.0844067i	$0.973101\pi$
$374$	−568.402	−	984.501i	−0.0785866	−	0.136116i
$375$	−261.680	−	453.242i	−0.0360349	−	0.0624142i
$376$	−1565.23	+	2711.06i	−0.214683	+	0.371841i
$377$	−11196.9			−1.52963
$378$		0			0
$379$	1670.06			0.226346			0.113173	−	0.993575i	$-0.463898\pi$
$379$	1670.06			0.226346			0.113173	+	0.993575i	$0.463898\pi$
$380$	−583.355	+	1010.40i	−0.0787512	+	0.136401i
$381$	2914.87	+	5048.70i	0.391951	+	0.678879i
$382$	−1577.97	−	2733.13i	−0.211351	−	0.366071i
$383$	−1610.07	+	2788.72i	−0.214806	+	0.372055i	−0.953213	−	0.302301i	$-0.902245\pi$
$383$	−1610.07	+	2788.72i	−0.214806	+	0.372055i	0.738407	+	0.674356i	$0.235579\pi$
$384$	4832.00			0.642140
$385$		0			0
$386$	−2287.68			−0.301658
$387$	−837.435	+	1450.48i	−0.109998	+	0.190522i
$388$	−5355.03	−	9275.19i	−0.700672	−	1.21360i
$389$	−1761.11	−	3050.34i	−0.229543	−	0.397579i	0.728130	−	0.685439i	$-0.240390\pi$
$389$	−1761.11	−	3050.34i	−0.229543	−	0.397579i	−0.957673	+	0.287860i	$0.907056\pi$
$390$	−386.138	+	668.811i	−0.0501356	+	0.0868374i
$391$	−1964.07			−0.254034
$392$		0			0
$393$	7440.15			0.954977
$394$	209.545	−	362.943i	0.0267937	−	0.0464081i
$395$	−1923.57	−	3331.71i	−0.245026	−	0.424397i
$396$	1713.08	+	2967.14i	0.217387	+	0.376526i
$397$	2727.58	−	4724.31i	0.344819	−	0.597245i	−0.640502	−	0.767957i	$-0.721274\pi$
$397$	2727.58	−	4724.31i	0.344819	−	0.597245i	0.985321	+	0.170712i	$0.0546068\pi$
$398$	2614.11			0.329229
$399$		0			0
$400$	1354.97			0.169372
$401$	580.899	−	1006.15i	0.0723409	−	0.125298i	−0.827586	−	0.561339i	$-0.810286\pi$
$401$	580.899	−	1006.15i	0.0723409	−	0.125298i	0.899927	+	0.436041i	$0.143620\pi$
$402$	883.494	+	1530.26i	0.109614	+	0.189856i
$403$	−7378.39	−	12779.7i	−0.912019	−	1.57966i
$404$	6916.20	−	11979.2i	0.851718	−	1.47522i
$405$	1918.13			0.235339
$406$		0			0
$407$	−16524.8			−2.01255
$408$	777.510	−	1346.69i	0.0943443	−	0.163409i
$409$	3699.32	+	6407.42i	0.447237	+	0.774637i	0.998205	−	0.0598896i	$-0.0190749\pi$
$409$	3699.32	+	6407.42i	0.447237	+	0.774637i	−0.550968	+	0.834526i	$0.685742\pi$
$410$	430.382	+	745.444i	0.0518416	+	0.0897924i
$411$	−4146.01	+	7181.10i	−0.497586	+	0.861843i
$412$	−3092.74			−0.369826
$413$		0			0
$414$	−324.341			−0.0385036
$415$	1533.01	−	2655.25i	0.181331	−	0.314075i
$416$	−3299.37	−	5714.68i	−0.388858	−	0.673522i
$417$	4568.06	+	7912.11i	0.536448	+	0.929155i
$418$	473.035	−	819.320i	0.0553514	−	0.0958714i
$419$	2134.46			0.248867			0.124433	−	0.992228i	$-0.460289\pi$
$419$	2134.46			0.248867			0.124433	+	0.992228i	$0.460289\pi$
$420$		0			0
$421$	−3902.36			−0.451756			−0.225878	−	0.974156i	$-0.572525\pi$
$421$	−3902.36			−0.451756			−0.225878	+	0.974156i	$0.572525\pi$
$422$	505.941	−	876.316i	0.0583621	−	0.101086i
$423$	−1475.43	−	2555.52i	−0.169593	−	0.293744i
$424$	−2472.79	−	4283.00i	−0.283229	−	0.490568i
$425$	462.107	−	800.393i	0.0527423	−	0.0913524i
$426$	−2104.34			−0.239333
$427$		0			0
$428$	2807.06			0.317020
$429$	−5714.53	+	9897.86i	−0.643124	+	1.11392i
$430$	−285.030	−	493.686i	−0.0319659	−	0.0553666i
$431$	1809.07	+	3133.39i	0.202180	+	0.350186i	0.949231	−	0.314581i	$-0.101864\pi$
$431$	1809.07	+	3133.39i	0.202180	+	0.350186i	−0.747050	+	0.664767i	$0.768531\pi$
$432$	−4137.98	+	7167.18i	−0.460853	+	0.798221i
$433$	4222.37			0.468624			0.234312	−	0.972161i	$-0.424716\pi$
$433$	4222.37			0.468624			0.234312	+	0.972161i	$0.424716\pi$
$434$		0			0
$435$	−4096.08			−0.451475
$436$	3699.57	−	6407.85i	0.406370	−	0.703854i
$437$	−817.269	−	1415.55i	−0.0894629	−	0.154954i
$438$	−1119.67	−	1939.32i	−0.122146	−	0.211563i
$439$	−6758.98	+	11706.9i	−0.734826	+	1.27276i	0.219974	+	0.975506i	$0.429403\pi$
$439$	−6758.98	+	11706.9i	−0.734826	+	1.27276i	−0.954800	+	0.297250i	$0.903931\pi$
$440$	−2396.15			−0.259618
$441$		0			0
$442$	−1363.78			−0.146762
$443$	−8295.58	+	14368.4i	−0.889695	+	1.54100i	−0.0494599	+	0.998776i	$0.515750\pi$
$443$	−8295.58	+	14368.4i	−0.889695	+	1.54100i	−0.840236	+	0.542222i	$0.817583\pi$
$444$	−5500.34	−	9526.87i	−0.587916	−	1.01830i
$445$	−1144.17	−	1981.75i	−0.121885	−	0.211110i
$446$	−1522.61	+	2637.24i	−0.161654	+	0.279993i
$447$	−2805.85			−0.296895
$448$		0			0
$449$	8354.32			0.878095			0.439048	−	0.898464i	$-0.355316\pi$
$449$	8354.32			0.878095			0.439048	+	0.898464i	$0.355316\pi$
$450$	76.3109	−	132.174i	0.00799407	−	0.0138461i
$451$	6369.31	+	11032.0i	0.665009	+	1.15183i
$452$	7504.23	+	12997.7i	0.780905	+	1.35257i
$453$	7010.59	−	12142.7i	0.727122	−	1.25941i
$454$	2375.54			0.245572
$455$		0			0
$456$	1294.12			0.132900
$457$	640.168	−	1108.80i	0.0655269	−	0.113496i	−0.831401	−	0.555673i	$-0.812461\pi$
$457$	640.168	−	1108.80i	0.0655269	−	0.113496i	0.896928	+	0.442177i	$0.145794\pi$
$458$	−1081.97	−	1874.03i	−0.110387	−	0.191195i
$459$	2822.47	+	4888.66i	0.287019	+	0.497131i
$460$	−1007.37	+	1744.81i	−0.102106	+	0.176853i
$461$	6986.72			0.705865			0.352932	−	0.935649i	$-0.385185\pi$
$461$	6986.72			0.705865			0.352932	+	0.935649i	$0.385185\pi$
$462$		0			0
$463$	−5587.32			−0.560831			−0.280416	−	0.959879i	$-0.590472\pi$
$463$	−5587.32			−0.560831			−0.280416	+	0.959879i	$0.590472\pi$
$464$	5302.36	−	9183.96i	0.530508	−	0.918867i
$465$	−2699.18	−	4675.11i	−0.269185	−	0.466243i
$466$	−745.863	−	1291.87i	−0.0741447	−	0.128422i
$467$	−4966.92	+	8602.95i	−0.492166	+	0.852456i	−0.999959	−	0.00902263i	$-0.997128\pi$
$467$	−4966.92	+	8602.95i	−0.492166	+	0.852456i	0.507793	+	0.861479i	$0.330461\pi$
$468$	4110.24			0.405974
$469$		0			0
$470$	1004.36			0.0985691
$471$	5041.85	−	8732.75i	0.493241	−	0.854318i
$472$	496.121	+	859.308i	0.0483810	+	0.0837984i
$473$	−4218.21	−	7306.15i	−0.410049	−	0.710226i
$474$	−1038.36	+	1798.50i	−0.100619	+	0.174278i
$475$	769.148			0.0742967
$476$		0			0
$477$	4661.84			0.447486
$478$	−303.365	+	525.443i	−0.0290284	+	0.0502787i
$479$	2534.31	+	4389.55i	0.241744	+	0.418714i	0.961211	−	0.275813i	$-0.0889471\pi$
$479$	2534.31	+	4389.55i	0.241744	+	0.418714i	−0.719467	+	0.694527i	$0.755614\pi$
$480$	−1206.98	−	2090.55i	−0.114773	−	0.198792i
$481$	−9912.14	+	17168.3i	−0.939614	+	1.62746i
$482$	3634.68			0.343476
$483$		0			0
$484$	−7162.86			−0.672695
$485$	−3530.28	+	6114.62i	−0.330519	+	0.572476i
$486$	811.158	+	1404.97i	0.0757096	+	0.131133i
$487$	−132.177	−	228.937i	−0.0122988	−	0.0213021i	0.859811	−	0.510613i	$-0.170582\pi$
$487$	−132.177	−	228.937i	−0.0122988	−	0.0213021i	−0.872109	+	0.489311i	$0.837248\pi$
$488$	412.750	−	714.904i	0.0382875	−	0.0663159i
$489$	15956.3			1.47560
$490$		0			0
$491$	−7459.47			−0.685623			−0.342812	−	0.939404i	$-0.611379\pi$
$491$	−7459.47			−0.685623			−0.342812	+	0.939404i	$0.611379\pi$
$492$	−4240.09	+	7344.05i	−0.388532	+	0.672958i
$493$	−3616.68	−	6264.28i	−0.330400	−	0.572270i
$494$	−567.483	−	982.910i	−0.0516848	−	0.0895206i
$495$	1129.34	−	1956.07i	0.102545	−	0.177614i
$496$	13976.3			1.26523
$497$		0			0
$498$	−1655.07			−0.148927
$499$	−3603.34	+	6241.16i	−0.323261	+	0.559905i	−0.981159	−	0.193202i	$-0.938113\pi$
$499$	−3603.34	+	6241.16i	−0.323261	+	0.559905i	0.657897	+	0.753108i	$0.271446\pi$
$500$	−474.027	−	821.039i	−0.0423982	−	0.0734359i
$501$	2527.09	+	4377.05i	0.225354	+	0.390324i
$502$	−117.913	+	204.232i	−0.0104835	+	0.0181580i
$503$	−10886.7			−0.965037			−0.482519	−	0.875886i	$-0.660278\pi$
$503$	−10886.7			−0.965037			−0.482519	+	0.875886i	$0.660278\pi$
$504$		0			0
$505$	−9118.95			−0.803541
$506$	816.861	−	1414.84i	0.0717666	−	0.124303i
$507$	2256.24	+	3907.93i	0.197640	+	0.342322i
$508$	5280.22	+	9145.61i	0.461165	+	0.798761i
$509$	3752.48	−	6499.49i	0.326770	−	0.565982i	−0.655099	−	0.755543i	$-0.727373\pi$
$509$	3752.48	−	6499.49i	0.326770	−	0.565982i	0.981869	+	0.189561i	$0.0607064\pi$
$510$	−498.902			−0.0433172
$511$		0			0
$512$	10605.8			0.915459
$513$	−2348.91	+	4068.43i	−0.202158	+	0.350148i
$514$	2023.05	+	3504.03i	0.173605	+	0.300693i
$515$	1019.44	+	1765.72i	0.0872267	+	0.151081i
$516$	2808.09	−	4863.75i	0.239572	−	0.414951i
$517$	14863.7			1.26442
$518$		0			0
$519$	−13579.2			−1.14848
$520$	−1437.29	+	2489.46i	−0.121210	+	0.209942i
$521$	11132.4	+	19281.8i	0.936120	+	1.62141i	0.772625	+	0.634863i	$0.218944\pi$
$521$	11132.4	+	19281.8i	0.936120	+	1.62141i	0.163495	+	0.986544i	$0.447723\pi$
$522$	−597.248	−	1034.46i	−0.0500782	−	0.0867380i
$523$	−5643.33	+	9774.54i	−0.471828	+	0.817229i	−0.999480	−	0.0322308i	$-0.989739\pi$
$523$	−5643.33	+	9774.54i	−0.471828	+	0.817229i	0.527653	+	0.849460i	$0.323072\pi$
$524$	13477.7			1.12362
$525$		0			0
$526$	−2724.27			−0.225824
$527$	4766.55	−	8255.90i	0.393992	−	0.682415i
$528$	−5412.30	−	9374.37i	−0.446098	−	0.772665i
$529$	4672.20	+	8092.48i	0.384006	+	0.665118i
$530$	−793.352	+	1374.13i	−0.0650208	+	0.112619i
$531$	−935.316			−0.0764393
$532$		0			0
$533$	15282.1			1.24191
$534$	−617.634	+	1069.77i	−0.0500518	+	0.0866922i
$535$	−925.272	−	1602.62i	−0.0747720	−	0.129509i
$536$	3288.55	+	5695.94i	0.265007	+	0.459006i
$537$	1799.79	−	3117.32i	0.144630	−	0.250507i
$538$	632.781			0.0507084
$539$		0			0
$540$	5790.55			0.461455
$541$	−8203.38	+	14208.7i	−0.651924	+	1.12917i	0.330732	+	0.943725i	$0.392705\pi$
$541$	−8203.38	+	14208.7i	−0.651924	+	1.12917i	−0.982655	+	0.185440i	$0.940629\pi$
$542$	−1252.04	−	2168.60i	−0.0992248	−	0.171862i
$543$	−608.152	−	1053.35i	−0.0480631	−	0.0832478i
$544$	2131.44	−	3691.77i	0.167987	−	0.290962i
$545$	−4877.85			−0.383384
$546$		0			0
$547$	−8692.48			−0.679458			−0.339729	−	0.940523i	$-0.610335\pi$
$547$	−8692.48			−0.679458			−0.339729	+	0.940523i	$0.610335\pi$
$548$	−7510.41	+	13008.4i	−0.585454	+	1.01404i
$549$	389.070	+	673.888i	0.0302461	+	0.0523877i
$550$	384.382	+	665.769i	0.0298002	+	0.0516154i
$551$	3009.87	−	5213.25i	0.232713	−	0.403071i
$552$	2234.75			0.172314
$553$		0			0
$554$	2330.36			0.178714
$555$	−3626.08	+	6280.55i	−0.277330	+	0.480350i
$556$	8274.94	+	14332.6i	0.631179	+	1.09323i
$557$	6967.85	+	12068.7i	0.530049	+	0.918071i	0.999385	+	0.0350521i	$0.0111597\pi$
$557$	6967.85	+	12068.7i	0.530049	+	0.918071i	−0.469337	+	0.883019i	$0.655507\pi$
$558$	787.132	−	1363.35i	0.0597168	−	0.103432i
$559$	−10120.9			−0.765773
$560$		0			0
$561$	−7383.34			−0.555659
$562$	−23.4276	+	40.5778i	−0.00175843	+	0.00304568i
$563$	−11131.8	−	19280.9i	−0.833304	−	1.44332i	−0.895404	−	0.445255i	$-0.853113\pi$
$563$	−11131.8	−	19280.9i	−0.833304	−	1.44332i	0.0621002	−	0.998070i	$-0.480220\pi$
$564$	4947.41	+	8569.17i	0.369368	+	0.639764i
$565$	4947.13	−	8568.68i	0.368367	−	0.638030i
$566$	1123.65			0.0834462
$567$		0			0
$568$	−7832.81			−0.578622
$569$	−4762.83	+	8249.47i	−0.350911	+	0.607795i	−0.986409	−	0.164307i	$-0.947461\pi$
$569$	−4762.83	+	8249.47i	−0.350911	+	0.607795i	0.635498	+	0.772102i	$0.280795\pi$
$570$	−207.598	−	359.570i	−0.0152549	−	0.0264223i
$571$	−3835.00	−	6642.41i	−0.281068	−	0.486823i	0.690580	−	0.723256i	$-0.257355\pi$
$571$	−3835.00	−	6642.41i	−0.281068	−	0.486823i	−0.971648	+	0.236432i	$0.924022\pi$
$572$	−10351.7	+	17929.8i	−0.756693	+	1.31063i
$573$	−20497.3			−1.49439
$574$		0			0
$575$	1328.20			0.0963304
$576$	−1701.10	+	2946.39i	−0.123054	+	0.213136i
$577$	1953.57	+	3383.69i	0.140950	+	0.244133i	0.927855	−	0.372942i	$-0.121651\pi$
$577$	1953.57	+	3383.69i	0.140950	+	0.244133i	−0.786904	+	0.617075i	$0.788318\pi$
$578$	1143.07	+	1979.85i	0.0822582	+	0.142475i
$579$	−7429.04	+	12867.5i	−0.533230	+	0.923582i
$580$	−7419.95			−0.531201
$581$		0			0
$582$	3811.38			0.271455
$583$	−11741.0	+	20336.0i	−0.834067	+	1.44465i
$584$	−4167.64	−	7218.57i	−0.295305	−	0.511484i
$585$	−1354.83	−	2346.63i	−0.0957526	−	0.165848i
$586$	1608.17	−	2785.43i	0.113367	−	0.196357i
$587$	19891.6			1.39866			0.699331	−	0.714798i	$-0.253481\pi$
$587$	19891.6			1.39866			0.699331	+	0.714798i	$0.253481\pi$
$588$		0			0
$589$	7933.61			0.555007
$590$	159.172	−	275.694i	0.0111068	−	0.0192375i
$591$	−1360.96	−	2357.25i	−0.0947248	−	0.164068i
$592$	−9387.89	−	16260.3i	−0.651757	−	1.12888i
$593$	2390.18	−	4139.91i	0.165519	−	0.286688i	−0.771320	−	0.636447i	$-0.780403\pi$
$593$	2390.18	−	4139.91i	0.165519	−	0.286688i	0.936840	+	0.349759i	$0.113737\pi$
$594$	−4695.48			−0.324340
$595$		0			0
$596$	−5082.74			−0.349324
$597$	8489.08	−	14703.5i	0.581968	−	1.00800i
$598$	−979.959	−	1697.34i	−0.0670126	−	0.116069i
$599$	−5542.80	−	9600.42i	−0.378085	−	0.654862i	0.612699	−	0.790317i	$-0.290084\pi$
$599$	−5542.80	−	9600.42i	−0.378085	−	0.654862i	−0.990784	+	0.135454i	$0.956751\pi$
$600$	−525.791	+	910.697i	−0.0357756	+	0.0619651i
$601$	1573.44			0.106792			0.0533958	−	0.998573i	$-0.482995\pi$
$601$	1573.44			0.106792			0.0533958	+	0.998573i	$0.482995\pi$
$602$		0			0
$603$	−6199.76			−0.418696
$604$	12699.5	−	21996.2i	0.855524	−	1.48181i
$605$	2361.04	+	4089.44i	0.158661	+	0.274809i
$606$	2461.26	+	4263.03i	0.164987	+	0.285765i
$607$	4271.36	−	7398.22i	0.285617	−	0.494702i	−0.687142	−	0.726523i	$-0.741135\pi$
$607$	4271.36	−	7398.22i	0.285617	−	0.494702i	0.972759	+	0.231821i	$0.0744683\pi$
$608$	3547.65			0.236639
$609$		0			0
$610$	−264.848			−0.0175793
$611$	8915.70	−	15442.4i	0.590328	−	1.02248i
$612$	1327.64	+	2299.54i	0.0876904	+	0.151884i
$613$	−7534.08	−	13049.4i	−0.496409	−	0.859805i	0.503583	−	0.863947i	$-0.332015\pi$
$613$	−7534.08	−	13049.4i	−0.496409	−	0.859805i	−0.999991	+	0.00414209i	$0.998682\pi$
$614$	−536.545	+	929.323i	−0.0352658	+	0.0610822i
$615$	5590.52			0.366555
$616$		0			0
$617$	2524.58			0.164725			0.0823627	−	0.996602i	$-0.473753\pi$
$617$	2524.58			0.164725			0.0823627	+	0.996602i	$0.473753\pi$
$618$	550.304	−	953.155i	0.0358196	−	0.0620413i
$619$	−10619.5	−	18393.4i	−0.689551	−	1.19434i	−0.971983	−	0.235050i	$-0.924475\pi$
$619$	−10619.5	−	18393.4i	−0.689551	−	1.19434i	0.282433	−	0.959287i	$-0.408859\pi$
$620$	−4889.50	−	8468.85i	−0.316721	−	0.548576i
$621$	−4056.22	+	7025.58i	−0.262110	+	0.453988i
$622$	351.735			0.0226741
$623$		0			0
$624$	−12985.9			−0.833095
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	−68.8369	−	119.229i	−0.00439501	−	0.00761238i
$627$	−3072.28	−	5321.34i	−0.195686	−	0.338937i
$628$	9133.21	−	15819.2i	0.580342	−	1.00518i
$629$	−12806.8			−0.811827
$630$		0			0
$631$	−8885.83			−0.560601			−0.280300	−	0.959912i	$-0.590434\pi$
$631$	−8885.83			−0.560601			−0.280300	+	0.959912i	$0.590434\pi$
$632$	−3865.01	+	6694.39i	−0.243262	+	0.421343i
$633$	−3286.00	−	5691.51i	−0.206330	−	0.357373i
$634$	865.095	+	1498.39i	0.0541914	+	0.0938622i
$635$	3480.96	−	6029.20i	0.217540	−	0.376790i
$636$	−15632.1			−0.974609
$637$		0			0
$638$	6016.74			0.373362
$639$	3691.71	−	6394.23i	0.228547	−	0.395856i
$640$	−2885.21	−	4997.32i	−0.178200	−	0.308651i
$641$	−1827.82	−	3165.87i	−0.112628	−	0.195077i	0.804201	−	0.594357i	$-0.202593\pi$
$641$	−1827.82	−	3165.87i	−0.112628	−	0.195077i	−0.916829	+	0.399280i	$0.869260\pi$
$642$	−499.473	+	865.112i	−0.0307050	+	0.0531827i
$643$	−4221.22			−0.258894			−0.129447	−	0.991586i	$-0.541320\pi$
$643$	−4221.22			−0.258894			−0.129447	+	0.991586i	$0.541320\pi$
$644$		0			0
$645$	−3702.43			−0.226020
$646$	366.602	−	634.974i	0.0223278	−	0.0386729i
$647$	51.8393	+	89.7884i	0.00314995	+	0.00545587i	0.867596	−	0.497270i	$-0.165664\pi$
$647$	51.8393	+	89.7884i	0.00314995	+	0.00545587i	−0.864446	+	0.502725i	$0.832331\pi$
$648$	−1927.04	−	3337.73i	−0.116823	−	0.202343i
$649$	2355.62	−	4080.05i	0.142475	−	0.246773i
$650$	922.259			0.0556523
$651$		0			0
$652$	28904.5			1.73618
$653$	−2238.05	+	3876.42i	−0.134122	+	0.232307i	−0.925262	−	0.379329i	$-0.876155\pi$
$653$	−2238.05	+	3876.42i	−0.134122	+	0.232307i	0.791140	+	0.611636i	$0.209488\pi$
$654$	1316.56	+	2280.35i	0.0787181	+	0.136344i
$655$	−4442.55	−	7694.71i	−0.265015	−	0.459019i
$656$	−7236.91	+	12534.7i	−0.430722	+	0.746033i
$657$	7857.07			0.466566
$658$		0			0
$659$	12022.0			0.710641			0.355321	−	0.934745i	$-0.384372\pi$
$659$	12022.0			0.710641			0.355321	+	0.934745i	$0.384372\pi$
$660$	−3786.89	+	6559.09i	−0.223340	+	0.386837i
$661$	6725.51	+	11648.9i	0.395752	+	0.685462i	0.993197	−	0.116448i	$-0.0371507\pi$
$661$	6725.51	+	11648.9i	0.395752	+	0.685462i	−0.597445	+	0.801910i	$0.703817\pi$
$662$	1633.38	+	2829.11i	0.0958962	+	0.166097i
$663$	−4428.77	+	7670.85i	−0.259426	+	0.449338i
$664$	−6160.53			−0.360053
$665$		0			0
$666$	−2114.87			−0.123047
$667$	5197.60	−	9002.51i	0.301727	−	0.522606i
$668$	4577.77	+	7928.93i	0.265149	+	0.459251i
$669$	9889.10	+	17128.4i	0.571502	+	0.989870i
$670$	1055.08	−	1827.45i	0.0608375	−	0.105374i
$671$	−3919.53			−0.225502
$672$		0			0
$673$	9774.83			0.559869			0.279935	−	0.960019i	$-0.409687\pi$
$673$	9774.83			0.559869			0.279935	+	0.960019i	$0.409687\pi$
$674$	3014.76	−	5221.72i	0.172291	−	0.298417i
$675$	−1908.70	−	3305.96i	−0.108838	−	0.188513i
$676$	4087.13	+	7079.13i	0.232541	+	0.402772i
$677$	11928.7	−	20661.1i	0.677190	−	1.17293i	−0.298634	−	0.954368i	$-0.596531\pi$
$677$	11928.7	−	20661.1i	0.677190	−	1.17293i	0.975824	−	0.218560i	$-0.0701358\pi$
$678$	−5341.04			−0.302539
$679$		0			0
$680$	−1857.02			−0.104726
$681$	7714.36	−	13361.7i	0.434089	−	0.751865i
$682$	3964.83	+	6867.28i	0.222612	+	0.385574i
$683$	−5959.68	−	10322.5i	−0.333881	−	0.578299i	0.649388	−	0.760457i	$-0.275025\pi$
$683$	−5959.68	−	10322.5i	−0.333881	−	0.578299i	−0.983269	+	0.182158i	$0.941692\pi$
$684$	−1104.88	+	1913.72i	−0.0617636	+	0.106978i
$685$	9902.40			0.552338
$686$		0			0
$687$	−14054.4			−0.780508
$688$	4792.79	−	8301.36i	0.265587	−	0.460009i
$689$	14085.2	+	24396.3i	0.778816	+	1.34895i
$690$	−358.490	−	620.924i	−0.0197790	−	0.0342582i
$691$	−4101.79	+	7104.51i	−0.225817	+	0.391126i	−0.956564	−	0.291522i	$-0.905838\pi$
$691$	−4101.79	+	7104.51i	−0.225817	+	0.391126i	0.730747	+	0.682648i	$0.239172\pi$
$692$	−24598.4			−1.35129
$693$		0			0
$694$	1514.50			0.0828380
$695$	5455.21	−	9448.71i	0.297738	−	0.515698i
$696$	4115.11	+	7127.58i	0.224113	+	0.388176i
$697$	4936.22	+	8549.79i	0.268254	+	0.464629i
$698$	3375.56	−	5846.64i	0.183047	−	0.317047i
$699$	−9688.49			−0.524252
$700$		0			0
$701$	449.084			0.0241964			0.0120982	−	0.999927i	$-0.496149\pi$
$701$	449.084			0.0241964			0.0120982	+	0.999927i	$0.496149\pi$
$702$	−2816.50	+	4878.32i	−0.151427	+	0.262280i
$703$	−5329.01	−	9230.12i	−0.285900	−	0.495193i
$704$	−8568.51	−	14841.1i	−0.458719	−	0.794524i
$705$	3261.56	−	5649.18i	0.174237	−	0.301788i
$706$	−4625.11			−0.246556
$707$		0			0
$708$	3136.30			0.166482
$709$	−948.819	+	1643.40i	−0.0502590	+	0.0870512i	−0.890060	−	0.455843i	$-0.849338\pi$
$709$	−948.819	+	1643.40i	−0.0502590	+	0.0870512i	0.839801	+	0.542894i	$0.182671\pi$
$710$	1256.51	+	2176.34i	0.0664170	+	0.115038i
$711$	−3643.27	−	6310.32i	−0.192170	−	0.332849i
$712$	−2298.96	+	3981.92i	−0.121007	+	0.209591i
$713$	13700.2			0.719601
$714$		0			0
$715$	13648.7			0.713891
$716$	3260.27	−	5646.96i	0.170171	−	0.294744i
$717$	1970.30	+	3412.66i	0.102625	+	0.177752i
$718$	2428.43	+	4206.16i	0.126223	+	0.218625i
$719$	3247.35	−	5624.58i	0.168436	−	0.291740i	−0.769434	−	0.638726i	$-0.779462\pi$
$719$	3247.35	−	5624.58i	0.168436	−	0.291740i	0.937870	+	0.346986i	$0.112795\pi$
$720$	2566.35			0.132836
$721$		0			0
$722$	−3811.45			−0.196465
$723$	11803.3	−	20443.9i	0.607150	−	1.05162i
$724$	−1101.65	−	1908.12i	−0.0565506	−	0.0979485i
$725$	2445.78	+	4236.22i	0.125288	+	0.217006i
$726$	1274.52	−	2207.53i	0.0651540	−	0.112850i
$727$	18311.2			0.934148			0.467074	−	0.884218i	$-0.345308\pi$
$727$	18311.2			0.934148			0.467074	+	0.884218i	$0.345308\pi$
$728$		0			0
$729$	20894.5			1.06155
$730$	−1337.12	+	2315.96i	−0.0677931	+	0.117421i
$731$	−3269.11	−	5662.27i	−0.165407	−	0.286493i
$732$	−1304.63	−	2259.68i	−0.0658749	−	0.114099i
$733$	10616.6	−	18388.5i	0.534972	−	0.926598i	−0.464193	−	0.885734i	$-0.653656\pi$
$733$	10616.6	−	18388.5i	0.534972	−	0.926598i	0.999165	−	0.0408640i	$-0.0130111\pi$
$734$	3515.30			0.176774
$735$		0			0
$736$	6126.27			0.306817
$737$	15614.3	−	27044.7i	0.780406	−	1.35170i
$738$	815.152	+	1411.88i	0.0406587	+	0.0704230i
$739$	11011.8	+	19072.9i	0.548138	+	0.949404i	0.998402	+	0.0565080i	$0.0179966\pi$
$739$	11011.8	+	19072.9i	0.548138	+	0.949404i	−0.450264	+	0.892896i	$0.648670\pi$
$740$	−6568.55	+	11377.1i	−0.326304	+	0.565175i
$741$	−7371.40			−0.365446
$742$		0			0
$743$	9436.77			0.465951			0.232975	−	0.972483i	$-0.425154\pi$
$743$	9436.77			0.465951			0.232975	+	0.972483i	$0.425154\pi$
$744$	−5423.44	+	9393.67i	−0.267248	+	0.462888i
$745$	1675.38	+	2901.85i	0.0823911	+	0.142706i
$746$	−2653.14	−	4595.38i	−0.130212	−	0.225535i
$747$	2903.54	−	5029.08i	0.142216	−	0.246325i
$748$	−13374.8			−0.653783
$749$		0			0
$750$	337.383			0.0164260
$751$	19580.9	−	33915.1i	0.951421	−	1.64791i	0.209067	−	0.977901i	$-0.432957\pi$
$751$	19580.9	−	33915.1i	0.951421	−	1.64791i	0.742354	−	0.670008i	$-0.233709\pi$
$752$	8444.16	+	14625.7i	0.409477	+	0.709235i
$753$	765.826	+	1326.45i	0.0370627	+	0.0641946i
$754$	3609.03	−	6251.03i	0.174315	−	0.301922i
$755$	−16744.2			−0.807132
$756$		0			0
$757$	20340.6			0.976607			0.488303	−	0.872674i	$-0.337616\pi$
$757$	20340.6			0.976607			0.488303	+	0.872674i	$0.337616\pi$
$758$	−538.301	+	932.365i	−0.0257942	+	0.0446768i
$759$	−5305.36	−	9189.16i	−0.253719	−	0.439454i
$760$	−772.722	−	1338.39i	−0.0368810	−	0.0638798i
$761$	1653.95	−	2864.72i	0.0787852	−	0.136460i	−0.823941	−	0.566676i	$-0.808229\pi$
$761$	1653.95	−	2864.72i	0.0787852	−	0.136460i	0.902726	+	0.430216i	$0.141563\pi$
$762$	−3758.13			−0.178665
$763$		0			0
$764$	−37130.4			−1.75829
$765$	875.239	−	1515.96i	0.0413651	−	0.0716465i
$766$	−1037.93	−	1797.74i	−0.0489580	−	0.0847978i
$767$	−2825.95	−	4894.69i	−0.133037	−	0.230427i
$768$	4459.19	−	7723.54i	0.209514	−	0.362889i
$769$	−17234.0			−0.808159			−0.404079	−	0.914724i	$-0.632408\pi$
$769$	−17234.0			−0.808159			−0.404079	+	0.914724i	$0.632408\pi$
$770$		0			0
$771$	26278.7			1.22750
$772$	−13457.5	+	23309.1i	−0.627393	+	1.08668i
$773$	−4363.17	−	7557.23i	−0.203017	−	0.351636i	0.746482	−	0.665406i	$-0.231741\pi$
$773$	−4363.17	−	7557.23i	−0.203017	−	0.351636i	−0.949499	+	0.313770i	$0.898408\pi$
$774$	−539.851	−	935.049i	−0.0250705	−	0.0434233i
$775$	−3223.38	+	5583.05i	−0.149403	+	0.258773i
$776$	14186.7			0.656281
$777$		0			0
$778$	2270.60			0.104634
$779$	−4108.01	+	7115.29i	−0.188941	+	0.327255i
$780$	4543.00	+	7868.72i	0.208546	+	0.361212i
$781$	18595.3	+	32208.1i	0.851977	+	1.47567i
$782$	633.068	−	1096.51i	0.0289494	−	0.0501419i
$783$	−29876.8			−1.36362
$784$		0			0
$785$	−12042.0			−0.547515
$786$	−2398.14	+	4153.70i	−0.108828	+	0.188496i
$787$	−5321.03	−	9216.30i	−0.241009	−	0.417440i	0.719993	−	0.693982i	$-0.244145\pi$
$787$	−5321.03	−	9216.30i	−0.241009	−	0.417440i	−0.961002	+	0.276541i	$0.910812\pi$
$788$	−2465.35	−	4270.11i	−0.111452	−	0.193041i
$789$	−8846.81	+	15323.1i	−0.399182	+	0.691404i
$790$	2480.05			0.111691
$791$		0			0
$792$	−4538.35			−0.203615
$793$	−2351.06	+	4072.16i	−0.105282	+	0.182354i
$794$	1758.33	+	3045.51i	0.0785904	+	0.136123i
$795$	5152.68	+	8924.71i	0.229870	+	0.398147i
$796$	15377.8	−	26635.1i	0.684737	−	1.18600i
$797$	−29234.1			−1.29928			−0.649640	−	0.760242i	$-0.725080\pi$
$797$	−29234.1			−1.29928			−0.649640	+	0.760242i	$0.725080\pi$
$798$		0			0
$799$	11519.3			0.510044
$800$	−1441.39	+	2496.56i	−0.0637010	+	0.110333i
$801$	−2167.07	−	3753.47i	−0.0955925	−	0.165571i
$802$	374.475	+	648.610i	0.0164878	+	0.0285576i
$803$	−19788.2	+	34274.2i	−0.869629	+	1.50624i
$804$	20789.0			0.911906
$805$		0			0
$806$	9512.93			0.415730
$807$	2054.90	−	3559.19i	0.0896355	−	0.155253i
$808$	9161.33	+	15867.9i	0.398879	+	0.690879i
$809$	−18105.6	−	31359.8i	−0.786846	−	1.36286i	−0.927890	−	0.372853i	$-0.878379\pi$
$809$	−18105.6	−	31359.8i	−0.786846	−	1.36286i	0.141045	−	0.990003i	$-0.454954\pi$
$810$	−618.258	+	1070.85i	−0.0268190	+	0.0464518i
$811$	27995.2			1.21214			0.606069	−	0.795412i	$-0.292746\pi$
$811$	27995.2			1.21214			0.606069	+	0.795412i	$0.292746\pi$
$812$		0			0
$813$	−16263.6			−0.701585
$814$	5326.35	−	9225.51i	0.229347	−	0.397241i
$815$	−9527.58	−	16502.3i	−0.409493	−	0.709262i
$816$	−4194.53	−	7265.15i	−0.179949	−	0.311680i
$817$	2720.62	−	4712.25i	0.116502	−	0.201788i
$818$	−4769.52			−0.203866
$819$		0			0
$820$	10127.1			0.431285
$821$	−22402.9	+	38802.9i	−0.952333	+	1.64949i	−0.211977	+	0.977275i	$0.567990\pi$
$821$	−22402.9	+	38802.9i	−0.952333	+	1.64949i	−0.740356	+	0.672215i	$0.765343\pi$
$822$	−2672.72	−	4629.28i	−0.113408	−	0.196429i
$823$	7925.47	+	13727.3i	0.335680	+	0.581415i	0.983615	−	0.180281i	$-0.0577007\pi$
$823$	7925.47	+	13727.3i	0.335680	+	0.581415i	−0.647935	+	0.761695i	$0.724367\pi$
$824$	2048.35	−	3547.85i	0.0865991	−	0.149994i
$825$	4992.99			0.210707
$826$		0			0
$827$	−45013.9			−1.89273			−0.946363	−	0.323104i	$-0.895274\pi$
$827$	−45013.9			−1.89273			−0.946363	+	0.323104i	$0.895274\pi$
$828$	−1907.97	+	3304.70i	−0.0800804	+	0.138703i
$829$	2827.91	+	4898.09i	0.118477	+	0.205208i	0.919164	−	0.393874i	$-0.128865\pi$
$829$	2827.91	+	4898.09i	0.118477	+	0.205208i	−0.800687	+	0.599083i	$0.795532\pi$
$830$	988.251	+	1711.70i	0.0413285	+	0.0715831i
$831$	7567.63	−	13107.5i	0.315906	−	0.547166i
$832$	−20558.7			−0.856664
$833$		0			0
$834$	−5889.58			−0.244532
$835$	3017.88	−	5227.11i	0.125075	−	0.216637i
$836$	−5565.36	−	9639.49i	−0.230242	−	0.398790i
$837$	−19687.8	−	34100.3i	−0.813036	−	1.40822i
$838$	−687.987	+	1191.63i	−0.0283605	+	0.0491219i
$839$	22037.0			0.906797			0.453398	−	0.891308i	$-0.350211\pi$
$839$	22037.0			0.906797			0.453398	+	0.891308i	$0.350211\pi$
$840$		0			0
$841$	13894.9			0.569719
$842$	1257.82	−	2178.62i	0.0514816	−	0.0891687i
$843$	152.158	+	263.546i	0.00621662	+	0.0107675i
$844$	−5952.51	−	10310.1i	−0.242765	−	0.420482i
$845$	2694.42	−	4666.88i	0.109694	−	0.189995i
$846$	1902.27			0.0773065
$847$		0			0
$848$	−26680.5			−1.08044
$849$	3648.95	−	6320.17i	0.147505	−	0.255486i
$850$	297.896	+	515.972i	0.0120209	+	0.0208208i
$851$	−9202.42	−	15939.1i	−0.370687	−	0.642049i
$852$	−12379.0	+	21441.1i	−0.497768	+	0.862160i
$853$	44486.7			1.78569			0.892846	−	0.450362i	$-0.148705\pi$
$853$	44486.7			1.78569			0.892846	+	0.450362i	$0.148705\pi$
$854$		0			0
$855$	1456.78			0.0582699
$856$	−1859.14	+	3220.13i	−0.0742339	+	0.128577i
$857$	−19279.8	−	33393.6i	−0.768478	−	1.33104i	−0.938388	−	0.345583i	$-0.887681\pi$
$857$	−19279.8	−	33393.6i	−0.768478	−	1.33104i	0.169910	−	0.985460i	$-0.445652\pi$
$858$	−3683.86	−	6380.64i	−0.146579	−	0.253883i
$859$	4213.01	−	7297.14i	0.167341	−	0.289843i	−0.770143	−	0.637871i	$-0.779815\pi$
$859$	4213.01	−	7297.14i	0.167341	−	0.289843i	0.937484	+	0.348028i	$0.113149\pi$
$860$	−6706.88			−0.265933
$861$		0			0
$862$	−2332.42			−0.0921608
$863$	10027.2	−	17367.6i	0.395514	−	0.685051i	−0.597652	−	0.801755i	$-0.703900\pi$
$863$	10027.2	−	17367.6i	0.395514	−	0.685051i	0.993167	+	0.116704i	$0.0372330\pi$
$864$	−8803.75	−	15248.5i	−0.346655	−	0.600423i
$865$	8108.20	+	14043.8i	0.318713	+	0.552028i
$866$	−1360.97	+	2357.27i	−0.0534038	+	0.0924981i
$867$	14848.0			0.581621
$868$		0			0
$869$	36702.6			1.43274
$870$	1320.26	−	2286.76i	0.0514496	−	0.0891133i
$871$	−18731.9	−	32444.6i	−0.728709	−	1.26216i
$872$	4900.52	+	8487.95i	0.190313	+	0.329631i
$873$	−6686.41	+	11581.2i	−0.259222	+	0.448985i
$874$	1053.70			0.0407803
$875$		0			0
$876$	−26346.3			−1.01616
$877$	−23541.1	+	40774.3i	−0.906414	+	1.56995i	−0.0874057	+	0.996173i	$0.527858\pi$
$877$	−23541.1	+	40774.3i	−0.906414	+	1.56995i	−0.819008	+	0.573782i	$0.805476\pi$
$878$	−4357.16	−	7546.83i	−0.167480	−	0.290083i
$879$	−10444.8	−	18090.9i	−0.400789	−	0.694186i
$880$	−6463.41	+	11195.0i	−0.247593	+	0.428843i
$881$	9467.24			0.362042			0.181021	−	0.983479i	$-0.442060\pi$
$881$	9467.24			0.362042			0.181021	+	0.983479i	$0.442060\pi$
$882$		0			0
$883$	−3049.49			−0.116221			−0.0581106	−	0.998310i	$-0.518508\pi$
$883$	−3049.49			−0.116221			−0.0581106	+	0.998310i	$0.518508\pi$
$884$	−8022.62	+	13895.6i	−0.305237	+	0.528686i
$885$	−1033.79	−	1790.59i	−0.0392663	−	0.0680112i
$886$	−5347.73	−	9262.54i	−0.202777	−	0.351220i
$887$	−9734.29	+	16860.3i	−0.368484	+	0.638233i	−0.989329	−	0.145700i	$-0.953456\pi$
$887$	−9734.29	+	16860.3i	−0.368484	+	0.638233i	0.620845	+	0.783934i	$0.286790\pi$
$888$	14571.7			0.550669
$889$		0			0
$890$	1475.17			0.0555592
$891$	−9149.71	+	15847.8i	−0.344026	+	0.595870i
$892$	17913.9	+	31027.8i	0.672423	+	1.16467i
$893$	4793.30	+	8302.25i	0.179621	+	0.311113i
$894$	904.393	−	1566.45i	0.0338338	−	0.0586019i
$895$	−4298.64			−0.160545
$896$		0			0
$897$	−12729.3			−0.473823
$898$	−2692.80	+	4664.06i	−0.100067	+	0.173321i
$899$	25227.8	+	43695.8i	0.935922	+	1.62106i
$900$	−897.815	−	1555.06i	−0.0332524	−	0.0575948i
$901$	−9099.26	+	15760.4i	−0.336449	+	0.582746i
$902$	−8211.92			−0.303134
$903$		0			0
$904$	−19880.5			−0.731432
$905$	−726.260	+	1257.92i	−0.0266759	+	0.0462040i
$906$	4519.36	+	7827.77i	0.165724	+	0.287042i
$907$	16007.1	+	27725.1i	0.586006	+	1.01499i	0.994749	+	0.102343i	$0.0326339\pi$
$907$	16007.1	+	27725.1i	0.586006	+	1.01499i	−0.408743	+	0.912649i	$0.634033\pi$
$908$	13974.4	−	24204.3i	0.510745	−	0.884636i
$909$	−17271.4			−0.630206
$910$		0			0
$911$	20921.1			0.760866			0.380433	−	0.924809i	$-0.375775\pi$
$911$	20921.1			0.760866			0.380433	+	0.924809i	$0.375775\pi$
$912$	3490.77	−	6046.19i	0.126744	−	0.219528i
$913$	14625.3	+	25331.8i	0.530150	+	0.918247i
$914$	412.683	+	714.788i	0.0149347	+	0.0258677i
$915$	−860.069	+	1489.68i	−0.0310743	+	0.0538223i
$916$	−25459.2			−0.918337
$917$		0			0
$918$	−3639.00			−0.130833
$919$	−21733.7	+	37643.9i	−0.780118	+	1.35120i	0.151754	+	0.988418i	$0.451508\pi$
$919$	−21733.7	+	37643.9i	−0.780118	+	1.35120i	−0.931872	+	0.362786i	$0.881826\pi$
$920$	−1334.38	−	2311.21i	−0.0478186	−	0.0828242i
$921$	3484.77	+	6035.79i	0.124676	+	0.215946i
$922$	−2251.99	+	3900.55i	−0.0804395	+	0.139325i
$923$	44616.4			1.59108
$924$		0			0
$925$	8660.58			0.307847
$926$	1800.93	−	3119.30i	0.0639116	−	0.110698i
$927$	1930.83	+	3344.30i	0.0684108	+	0.118491i
$928$	11281.0	+	19539.3i	0.399050	+	0.691174i
$929$	−9271.05	+	16057.9i	−0.327420	+	0.567108i	−0.981999	−	0.188885i	$-0.939513\pi$
$929$	−9271.05	+	16057.9i	−0.327420	+	0.567108i	0.654579	+	0.755993i	$0.272846\pi$
$930$	3480.04			0.122704
$931$		0			0
$932$	−17550.5			−0.616830
$933$	1142.23	−	1978.40i	0.0400803	−	0.0694210i
$934$	−3201.91	−	5545.87i	−0.112173	−	0.194290i
$935$	4408.62	+	7635.96i	0.154200	+	0.267083i
$936$	−2722.25	+	4715.07i	−0.0950635	+	0.164655i
$937$	−13842.5			−0.482619			−0.241309	−	0.970448i	$-0.577577\pi$
$937$	−13842.5			−0.482619			−0.241309	+	0.970448i	$0.577577\pi$
$938$		0			0
$939$	−894.167			−0.0310757
$940$	5908.24	−	10233.4i	0.205006	−	0.355081i
$941$	−26696.6	−	46239.8i	−0.924850	−	1.60189i	−0.791803	−	0.610777i	$-0.790857\pi$
$941$	−26696.6	−	46239.8i	−0.924850	−	1.60189i	−0.133047	−	0.991110i	$-0.542476\pi$
$942$	3250.22	+	5629.55i	0.112418	+	0.194714i
$943$	−7093.93	+	12287.0i	−0.244974	+	0.424307i
$944$	5352.98			0.184560
$945$		0			0
$946$	5438.52			0.186915
$947$	−11172.1	+	19350.7i	−0.383364	+	0.664005i	−0.991541	−	0.129796i	$-0.958568\pi$
$947$	−11172.1	+	19350.7i	−0.383364	+	0.664005i	0.608177	+	0.793801i	$0.291901\pi$
$948$	12216.6	+	21159.7i	0.418540	+	0.724933i
$949$	23739.3	+	41117.6i	0.812022	+	1.40646i
$950$	−247.915	+	429.401i	−0.00846676	+	0.0146649i
$951$	11237.3			0.383169
$952$		0			0
$953$	−8902.63			−0.302607			−0.151304	−	0.988487i	$-0.548347\pi$
$953$	−8902.63			−0.302607			−0.151304	+	0.988487i	$0.548347\pi$
$954$	−1502.62	+	2602.62i	−0.0509950	+	0.0883259i
$955$	12239.0	+	21198.6i	0.414708	+	0.718295i
$956$	3569.15	+	6181.96i	0.120748	+	0.209141i
$957$	19538.8	−	33842.2i	0.659979	−	1.14312i
$958$	−3267.48			−0.110196
$959$		0			0
$960$	−7520.82			−0.252847
$961$	−18353.0	+	31788.4i	−0.616059	+	1.06705i
$962$	−6389.84	−	11067.5i	−0.214155	−	0.370927i
$963$	−1752.48	−	3035.39i	−0.0586427	−	0.101572i
$964$	21381.4	−	37033.7i	0.714366	−	1.23732i
$965$	17743.6			0.591905
$966$		0			0
$967$	−2225.57			−0.0740119			−0.0370059	−	0.999315i	$-0.511782\pi$
$967$	−2225.57			−0.0740119			−0.0370059	+	0.999315i	$0.511782\pi$
$968$	4744.02	−	8216.89i	0.157519	−	0.272831i
$969$	−2381.02	−	4124.04i	−0.0789363	−	0.136722i
$970$	−2275.79	−	3941.78i	−0.0753311	−	0.130477i
$971$	−5662.41	+	9807.59i	−0.187143	+	0.324141i	−0.944296	−	0.329096i	$-0.893256\pi$
$971$	−5662.41	+	9807.59i	−0.187143	+	0.324141i	0.757154	+	0.653237i	$0.226589\pi$
$972$	19086.9			0.629849
$973$		0			0
$974$	170.415			0.00560621
$975$	2994.96	−	5187.41i	0.0983747	−	0.170390i
$976$	−2226.72	−	3856.78i	−0.0730281	−	0.126488i
$977$	28847.9	+	49966.1i	0.944654	+	1.63619i	0.756442	+	0.654061i	$0.226936\pi$
$977$	28847.9	+	49966.1i	0.944654	+	1.63619i	0.188213	+	0.982128i	$0.439731\pi$
$978$	−5143.10	+	8908.11i	−0.168158	+	0.291258i
$979$	21831.3			0.712697
$980$		0			0
$981$	−9238.73			−0.300683
$982$	2404.36	−	4164.48i	0.0781328	−	0.135330i
$983$	29828.6	+	51664.7i	0.967839	+	1.67635i	0.701786	+	0.712388i	$0.252386\pi$
$983$	29828.6	+	51664.7i	0.967839	+	1.67635i	0.266054	+	0.963958i	$0.414280\pi$
$984$	−5616.49	−	9728.05i	−0.181959	−	0.315162i
$985$	−1625.27	+	2815.05i	−0.0525740	+	0.0910608i
$986$	4662.98			0.150608
$987$		0			0
$988$	−13353.1			−0.429980
$989$	4698.10	−	8137.35i	0.151053	−	0.261631i
$990$	728.026	+	1260.98i	0.0233719	+	0.0404813i
$991$	−1445.30	−	2503.33i	−0.0463284	−	0.0802431i	0.841931	−	0.539585i	$-0.181419\pi$
$991$	−1445.30	−	2503.33i	−0.0463284	−	0.0802431i	−0.888260	+	0.459342i	$0.848085\pi$
$992$	−14867.6	+	25751.5i	−0.475855	+	0.824205i
$993$	21217.1			0.678050
$994$		0			0
$995$	−20275.5			−0.646005
$996$	−9736.15	+	16863.5i	−0.309741	+	0.536487i
$997$	−5309.79	−	9196.83i	−0.168669	−	0.292143i	0.769283	−	0.638908i	$-0.220613\pi$
$997$	−5309.79	−	9196.83i	−0.168669	−	0.292143i	−0.937952	+	0.346765i	$0.887280\pi$
$998$	−2322.88	−	4023.35i	−0.0736769	−	0.127612i
$999$	−26448.7	+	45810.4i	−0.837636	+	1.45083i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.4.e.p.226.3		12
7.2	even	3		245.4.a.p.1.4	yes	6
7.3	odd	6		245.4.e.q.116.3		12
7.4	even	3	inner	245.4.e.p.116.3		12
7.5	odd	6		245.4.a.o.1.4	✓	6
7.6	odd	2		245.4.e.q.226.3		12
21.2	odd	6		2205.4.a.ca.1.3		6
21.5	even	6		2205.4.a.bz.1.3		6
35.9	even	6		1225.4.a.bi.1.3		6
35.19	odd	6		1225.4.a.bj.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.4.a.o.1.4	✓	6	7.5	odd	6
245.4.a.p.1.4	yes	6	7.2	even	3
245.4.e.p.116.3		12	7.4	even	3	inner
245.4.e.p.226.3		12	1.1	even	1	trivial
245.4.e.q.116.3		12	7.3	odd	6
245.4.e.q.226.3		12	7.6	odd	2
1225.4.a.bi.1.3		6	35.9	even	6
1225.4.a.bj.1.3		6	35.19	odd	6
2205.4.a.bz.1.3		6	21.5	even	6
2205.4.a.ca.1.3		6	21.2	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)

\(f(q)\)	\(=\)	\(q+(-0.322324 + 0.558282i) q^{2} +(2.09344 + 3.62594i) q^{3} +(3.79221 + 6.56831i) q^{4} +(2.50000 - 4.33013i) q^{5} -2.69906 q^{6} -10.0465 q^{8} +(4.73504 - 8.20133i) q^{9} +O(q^{10})\)	\(q+(-0.322324 + 0.558282i) q^{2} +(2.09344 + 3.62594i) q^{3} +(3.79221 + 6.56831i) q^{4} +(2.50000 - 4.33013i) q^{5} -2.69906 q^{6} -10.0465 q^{8} +(4.73504 - 8.20133i) q^{9} +(1.61162 + 2.79141i) q^{10} +(23.8507 + 41.3106i) q^{11} +(-15.8775 + 27.5007i) q^{12} +57.2256 q^{13} +20.9344 q^{15} +(-27.0995 + 46.9377i) q^{16} +(18.4843 + 32.0157i) q^{17} +(3.05244 + 5.28697i) q^{18} +(-15.3830 + 26.6441i) q^{19} +37.9221 q^{20} -30.7506 q^{22} +(-26.5641 + 46.0104i) q^{23} +(-21.0317 - 36.4279i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(-18.4452 + 31.9480i) q^{26} +152.696 q^{27} -195.663 q^{29} +(-6.74765 + 11.6873i) q^{30} +(-128.935 - 223.322i) q^{31} +(-57.6555 - 99.8623i) q^{32} +(-99.8597 + 172.962i) q^{33} -23.8317 q^{34} +71.8252 q^{36} +(-173.212 + 300.011i) q^{37} +(-9.91660 - 17.1760i) q^{38} +(119.798 + 207.497i) q^{39} +(-25.1162 + 43.5025i) q^{40} +267.050 q^{41} -176.859 q^{43} +(-180.894 + 313.317i) q^{44} +(-23.6752 - 41.0067i) q^{45} +(-17.1245 - 29.6605i) q^{46} +(155.799 - 269.852i) q^{47} -226.924 q^{48} +16.1162 q^{50} +(-77.3914 + 134.046i) q^{51} +(217.012 + 375.875i) q^{52} +(246.135 + 426.318i) q^{53} +(-49.2175 + 85.2472i) q^{54} +238.507 q^{55} -128.813 q^{57} +(63.0668 - 109.235i) q^{58} +(-49.3827 - 85.5333i) q^{59} +(79.3876 + 137.503i) q^{60} +(-41.0841 + 71.1597i) q^{61} +166.235 q^{62} -359.257 q^{64} +(143.064 - 247.794i) q^{65} +(-64.3744 - 111.500i) q^{66} +(-327.334 - 566.959i) q^{67} +(-140.193 + 242.821i) q^{68} -222.441 q^{69} +779.658 q^{71} +(-47.5705 + 82.3945i) q^{72} +(414.836 + 718.518i) q^{73} +(-111.660 - 193.402i) q^{74} +(52.3359 - 90.6485i) q^{75} -233.342 q^{76} -154.455 q^{78} +(384.713 - 666.343i) q^{79} +(135.497 + 234.689i) q^{80} +(191.813 + 332.229i) q^{81} +(-86.0765 + 149.089i) q^{82} +613.203 q^{83} +184.843 q^{85} +(57.0059 - 98.7372i) q^{86} +(-409.608 - 709.461i) q^{87} +(-239.615 - 415.025i) q^{88} +(228.833 - 396.350i) q^{89} +30.5244 q^{90} -402.947 q^{92} +(539.835 - 935.022i) q^{93} +(100.436 + 173.960i) q^{94} +(76.9148 + 133.220i) q^{95} +(241.396 - 418.111i) q^{96} -1412.11 q^{97} +451.736 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more