LMFDB - Embedded newform 169.4.c.h.22.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,4,Mod(22,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("169.22");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	169.c (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:	$9.97132279097$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	169.22
Dual form			169.4.c.h.146.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 1.50000i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(2.50000 + 4.33013i) q^{4} -1.73205 q^{5} +(1.73205 + 3.00000i) q^{6} +(-6.92820 - 12.0000i) q^{7} +22.5167 q^{8} +(11.5000 + 19.9186i) q^{9} +(-1.50000 + 2.59808i) q^{10} +(-6.92820 + 12.0000i) q^{11} -10.0000 q^{12} -24.0000 q^{14} +(1.73205 - 3.00000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(58.5000 + 101.325i) q^{17} +39.8372 q^{18} +(57.1577 + 99.0000i) q^{19} +(-4.33013 - 7.50000i) q^{20} +27.7128 q^{21} +(12.0000 + 20.7846i) q^{22} +(-39.0000 + 67.5500i) q^{23} +(-22.5167 + 39.0000i) q^{24} -122.000 q^{25} -100.000 q^{27} +(34.6410 - 60.0000i) q^{28} +(70.5000 - 122.110i) q^{29} +(-3.00000 - 5.19615i) q^{30} +155.885 q^{31} +(90.9327 + 157.500i) q^{32} +(-13.8564 - 24.0000i) q^{33} +202.650 q^{34} +(12.0000 + 20.7846i) q^{35} +(-57.5000 + 99.5929i) q^{36} +(71.8801 - 124.500i) q^{37} +198.000 q^{38} -39.0000 q^{40} +(135.966 - 235.500i) q^{41} +(24.0000 - 41.5692i) q^{42} +(52.0000 + 90.0666i) q^{43} -69.2820 q^{44} +(-19.9186 - 34.5000i) q^{45} +(67.5500 + 117.000i) q^{46} -301.377 q^{47} +(-1.00000 - 1.73205i) q^{48} +(75.5000 - 130.770i) q^{49} +(-105.655 + 183.000i) q^{50} -234.000 q^{51} +93.0000 q^{53} +(-86.6025 + 150.000i) q^{54} +(12.0000 - 20.7846i) q^{55} +(-156.000 - 270.200i) q^{56} -228.631 q^{57} +(-122.110 - 211.500i) q^{58} +(-142.028 - 246.000i) q^{59} +17.3205 q^{60} +(-72.5000 - 125.574i) q^{61} +(135.000 - 233.827i) q^{62} +(159.349 - 276.000i) q^{63} +307.000 q^{64} -48.0000 q^{66} +(-393.176 + 681.000i) q^{67} +(-292.500 + 506.625i) q^{68} +(-78.0000 - 135.100i) q^{69} +41.5692 q^{70} +(-528.275 - 915.000i) q^{71} +(258.942 + 448.500i) q^{72} -458.993 q^{73} +(-124.500 - 215.640i) q^{74} +(122.000 - 211.310i) q^{75} +(-285.788 + 495.000i) q^{76} +192.000 q^{77} +1276.00 q^{79} +(0.866025 - 1.50000i) q^{80} +(-210.500 + 364.597i) q^{81} +(-235.500 - 407.898i) q^{82} -789.815 q^{83} +(69.2820 + 120.000i) q^{84} +(-101.325 - 175.500i) q^{85} +180.133 q^{86} +(141.000 + 244.219i) q^{87} +(-156.000 + 270.200i) q^{88} +(488.438 - 846.000i) q^{89} -69.0000 q^{90} -390.000 q^{92} +(-155.885 + 270.000i) q^{93} +(-261.000 + 452.065i) q^{94} +(-99.0000 - 171.473i) q^{95} -363.731 q^{96} +(-100.459 - 174.000i) q^{97} +(-130.770 - 226.500i) q^{98} -318.697 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} + 10 q^{4} + 46 q^{9} - 6 q^{10} - 40 q^{12} - 96 q^{14} - 2 q^{16} + 234 q^{17} + 48 q^{22} - 156 q^{23} - 488 q^{25} - 400 q^{27} + 282 q^{29} - 12 q^{30} + 48 q^{35} - 230 q^{36} + 792 q^{38}+ \cdots - 396 q^{95}+O(q^{100}) $ 4 * q - 4 * q^3 + 10 * q^4 + 46 * q^9 - 6 * q^10 - 40 * q^12 - 96 * q^14 - 2 * q^16 + 234 * q^17 + 48 * q^22 - 156 * q^23 - 488 * q^25 - 400 * q^27 + 282 * q^29 - 12 * q^30 + 48 * q^35 - 230 * q^36 + 792 * q^38 - 156 * q^40 + 96 * q^42 + 208 * q^43 - 4 * q^48 + 302 * q^49 - 936 * q^51 + 372 * q^53 + 48 * q^55 - 624 * q^56 - 290 * q^61 + 540 * q^62 + 1228 * q^64 - 192 * q^66 - 1170 * q^68 - 312 * q^69 - 498 * q^74 + 488 * q^75 + 768 * q^77 + 5104 * q^79 - 842 * q^81 - 942 * q^82 + 564 * q^87 - 624 * q^88 - 276 * q^90 - 1560 * q^92 - 1044 * q^94 - 396 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.866025	−	1.50000i	0.306186	−	0.530330i	−0.671339	−	0.741151i	$-0.734280\pi$
$2$	0.866025	−	1.50000i	0.306186	−	0.530330i	0.977525	+	0.210821i	$0.0676136\pi$
$3$	−1.00000	+	1.73205i	−0.192450	+	0.333333i	−0.946062	−	0.323987i	$-0.894977\pi$
$3$	−1.00000	+	1.73205i	−0.192450	+	0.333333i	0.753612	+	0.657320i	$0.228310\pi$
$4$	2.50000	+	4.33013i	0.312500	+	0.541266i
$5$	−1.73205			−0.154919			−0.0774597	−	0.996995i	$-0.524681\pi$
$5$	−1.73205			−0.154919			−0.0774597	+	0.996995i	$0.524681\pi$
$6$	1.73205	+	3.00000i	0.117851	+	0.204124i
$7$	−6.92820	−	12.0000i	−0.374088	−	0.647939i	0.616102	−	0.787666i	$-0.288711\pi$
$7$	−6.92820	−	12.0000i	−0.374088	−	0.647939i	−0.990190	+	0.139727i	$0.955377\pi$
$8$	22.5167			0.995105
$9$	11.5000	+	19.9186i	0.425926	+	0.737725i
$10$	−1.50000	+	2.59808i	−0.0474342	+	0.0821584i
$11$	−6.92820	+	12.0000i	−0.189903	+	0.328921i	−0.945218	−	0.326441i	$-0.894151\pi$
$11$	−6.92820	+	12.0000i	−0.189903	+	0.328921i	0.755315	+	0.655362i	$0.227484\pi$
$12$	−10.0000			−0.240563
$13$		0			0
$13$		0			0
$14$	−24.0000			−0.458162
$15$	1.73205	−	3.00000i	0.0298142	−	0.0516398i
$16$	−0.500000	+	0.866025i	−0.00781250	+	0.0135316i
$17$	58.5000	+	101.325i	0.834608	+	1.44558i	0.894349	+	0.447369i	$0.147639\pi$
$17$	58.5000	+	101.325i	0.834608	+	1.44558i	−0.0597414	+	0.998214i	$0.519028\pi$
$18$	39.8372			0.521651
$19$	57.1577	+	99.0000i	0.690151	+	1.19538i	0.971788	+	0.235856i	$0.0757893\pi$
$19$	57.1577	+	99.0000i	0.690151	+	1.19538i	−0.281637	+	0.959521i	$0.590877\pi$
$20$	−4.33013	−	7.50000i	−0.0484123	−	0.0838525i
$21$	27.7128			0.287973
$22$	12.0000	+	20.7846i	0.116291	+	0.201422i
$23$	−39.0000	+	67.5500i	−0.353568	+	0.612398i	−0.986872	−	0.161506i	$-0.948365\pi$
$23$	−39.0000	+	67.5500i	−0.353568	+	0.612398i	0.633304	+	0.773903i	$0.281698\pi$
$24$	−22.5167	+	39.0000i	−0.191508	+	0.331702i
$25$	−122.000			−0.976000
$26$		0			0
$27$	−100.000			−0.712778
$28$	34.6410	−	60.0000i	0.233805	−	0.404962i
$29$	70.5000	−	122.110i	0.451432	−	0.781903i	−0.547043	−	0.837104i	$-0.684247\pi$
$29$	70.5000	−	122.110i	0.451432	−	0.781903i	0.998475	+	0.0552014i	$0.0175801\pi$
$30$	−3.00000	−	5.19615i	−0.0182574	−	0.0316228i
$31$	155.885			0.903151			0.451576	−	0.892233i	$-0.350862\pi$
$31$	155.885			0.903151			0.451576	+	0.892233i	$0.350862\pi$
$32$	90.9327	+	157.500i	0.502337	+	0.870073i
$33$	−13.8564	−	24.0000i	−0.0730937	−	0.126602i
$34$	202.650			1.02218
$35$	12.0000	+	20.7846i	0.0579534	+	0.100378i
$36$	−57.5000	+	99.5929i	−0.266204	+	0.461078i
$37$	71.8801	−	124.500i	0.319379	−	0.553180i	−0.660980	−	0.750404i	$-0.729859\pi$
$37$	71.8801	−	124.500i	0.319379	−	0.553180i	0.980359	+	0.197223i	$0.0631924\pi$
$38$	198.000			0.845259
$39$		0			0
$40$	−39.0000			−0.154161
$41$	135.966	−	235.500i	0.517910	−	0.897047i	−0.481873	−	0.876241i	$-0.660043\pi$
$41$	135.966	−	235.500i	0.517910	−	0.897047i	0.999784	−	0.0208059i	$-0.00662322\pi$
$42$	24.0000	−	41.5692i	0.0881733	−	0.152721i
$43$	52.0000	+	90.0666i	0.184417	+	0.319419i	0.943380	−	0.331714i	$-0.107627\pi$
$43$	52.0000	+	90.0666i	0.184417	+	0.319419i	−0.758963	+	0.651134i	$0.774294\pi$
$44$	−69.2820			−0.237379
$45$	−19.9186	−	34.5000i	−0.0659842	−	0.114288i
$46$	67.5500	+	117.000i	0.216515	+	0.375015i
$47$	−301.377			−0.935326			−0.467663	−	0.883907i	$-0.654904\pi$
$47$	−301.377			−0.935326			−0.467663	+	0.883907i	$0.654904\pi$
$48$	−1.00000	−	1.73205i	−0.00300703	−	0.00520833i
$49$	75.5000	−	130.770i	0.220117	−	0.381253i
$50$	−105.655	+	183.000i	−0.298838	+	0.517602i
$51$	−234.000			−0.642481
$52$		0			0
$53$	93.0000			0.241029			0.120514	−	0.992712i	$-0.461546\pi$
$53$	93.0000			0.241029			0.120514	+	0.992712i	$0.461546\pi$
$54$	−86.6025	+	150.000i	−0.218243	+	0.378008i
$55$	12.0000	−	20.7846i	0.0294196	−	0.0509563i
$56$	−156.000	−	270.200i	−0.372257	−	0.644768i
$57$	−228.631			−0.531279
$58$	−122.110	−	211.500i	−0.276444	−	0.478816i
$59$	−142.028	−	246.000i	−0.313398	−	0.542822i	0.665698	−	0.746222i	$-0.268134\pi$
$59$	−142.028	−	246.000i	−0.313398	−	0.542822i	−0.979096	+	0.203400i	$0.934801\pi$
$60$	17.3205			0.0372678
$61$	−72.5000	−	125.574i	−0.152175	−	0.263575i	0.779852	−	0.625964i	$-0.215294\pi$
$61$	−72.5000	−	125.574i	−0.152175	−	0.263575i	−0.932027	+	0.362389i	$0.881961\pi$
$62$	135.000	−	233.827i	0.276533	−	0.478968i
$63$	159.349	−	276.000i	0.318667	−	0.551948i
$64$	307.000			0.599609
$65$		0			0
$66$	−48.0000			−0.0895211
$67$	−393.176	+	681.000i	−0.716926	+	1.24175i	0.245286	+	0.969451i	$0.421118\pi$
$67$	−393.176	+	681.000i	−0.716926	+	1.24175i	−0.962212	+	0.272301i	$0.912215\pi$
$68$	−292.500	+	506.625i	−0.521630	+	0.903490i
$69$	−78.0000	−	135.100i	−0.136088	−	0.235712i
$70$	41.5692			0.0709782
$71$	−528.275	−	915.000i	−0.883025	−	1.52944i	−0.847961	−	0.530059i	$-0.822170\pi$
$71$	−528.275	−	915.000i	−0.883025	−	1.52944i	−0.0350641	−	0.999385i	$-0.511164\pi$
$72$	258.942	+	448.500i	0.423841	+	0.734114i
$73$	−458.993			−0.735906			−0.367953	−	0.929844i	$-0.619941\pi$
$73$	−458.993			−0.735906			−0.367953	+	0.929844i	$0.619941\pi$
$74$	−124.500	−	215.640i	−0.195579	−	0.338752i
$75$	122.000	−	211.310i	0.187831	−	0.325333i
$76$	−285.788	+	495.000i	−0.431344	+	0.747110i
$77$	192.000			0.284161
$78$		0			0
$79$	1276.00			1.81723			0.908615	−	0.417634i	$-0.137141\pi$
$79$	1276.00			1.81723			0.908615	+	0.417634i	$0.137141\pi$
$80$	0.866025	−	1.50000i	0.00121031	−	0.00209631i
$81$	−210.500	+	364.597i	−0.288752	+	0.500133i
$82$	−235.500	−	407.898i	−0.317154	−	0.549327i
$83$	−789.815			−1.04450			−0.522250	−	0.852793i	$-0.674907\pi$
$83$	−789.815			−1.04450			−0.522250	+	0.852793i	$0.674907\pi$
$84$	69.2820	+	120.000i	0.0899915	+	0.155870i
$85$	−101.325	−	175.500i	−0.129297	−	0.223949i
$86$	180.133			0.225864
$87$	141.000	+	244.219i	0.173756	+	0.300955i
$88$	−156.000	+	270.200i	−0.188973	+	0.327311i
$89$	488.438	−	846.000i	0.581734	−	1.00759i	−0.413540	−	0.910486i	$-0.635708\pi$
$89$	488.438	−	846.000i	0.581734	−	1.00759i	0.995274	−	0.0971073i	$-0.0309590\pi$
$90$	−69.0000			−0.0808138
$91$		0			0
$92$	−390.000			−0.441960
$93$	−155.885	+	270.000i	−0.173812	+	0.301050i
$94$	−261.000	+	452.065i	−0.286384	+	0.496032i
$95$	−99.0000	−	171.473i	−0.106918	−	0.185187i
$96$	−363.731			−0.386699
$97$	−100.459	−	174.000i	−0.105155	−	0.182134i	0.808646	−	0.588295i	$-0.200201\pi$
$97$	−100.459	−	174.000i	−0.105155	−	0.182134i	−0.913802	+	0.406161i	$0.866867\pi$
$98$	−130.770	−	226.500i	−0.134793	−	0.233469i
$99$	−318.697			−0.323538
$100$	−305.000	−	528.275i	−0.305000	−	0.528275i
$101$	214.500	−	371.525i	0.211322	−	0.366021i	−0.740806	−	0.671719i	$-0.765556\pi$
$101$	214.500	−	371.525i	0.211322	−	0.366021i	0.952129	+	0.305698i	$0.0988897\pi$
$102$	−202.650	+	351.000i	−0.196719	+	0.340727i
$103$	−182.000			−0.174107			−0.0870534	−	0.996204i	$-0.527745\pi$
$103$	−182.000			−0.174107			−0.0870534	+	0.996204i	$0.527745\pi$
$104$		0			0
$105$	−48.0000			−0.0446126
$106$	80.5404	−	139.500i	0.0737997	−	0.127825i
$107$	753.000	−	1304.23i	0.680330	−	1.17837i	−0.294551	−	0.955636i	$-0.595170\pi$
$107$	753.000	−	1304.23i	0.680330	−	1.17837i	0.974880	−	0.222729i	$-0.0714967\pi$
$108$	−250.000	−	433.013i	−0.222743	−	0.385802i
$109$	1551.92			1.36373			0.681866	−	0.731477i	$-0.261169\pi$
$109$	1551.92			1.36373			0.681866	+	0.731477i	$0.261169\pi$
$110$	−20.7846	−	36.0000i	−0.0180158	−	0.0312042i
$111$	143.760	+	249.000i	0.122929	+	0.212919i
$112$	13.8564			0.0116902
$113$	343.500	+	594.959i	0.285962	+	0.495302i	0.972842	−	0.231470i	$-0.0743534\pi$
$113$	343.500	+	594.959i	0.285962	+	0.495302i	−0.686880	+	0.726771i	$0.741020\pi$
$114$	−198.000	+	342.946i	−0.162670	+	0.281753i
$115$	67.5500	−	117.000i	0.0547745	−	0.0948722i
$116$	705.000			0.564290
$117$		0			0
$118$	−492.000			−0.383833
$119$	810.600	−	1404.00i	0.624433	−	1.08155i
$120$	39.0000	−	67.5500i	0.0296683	−	0.0513870i
$121$	569.500	+	986.403i	0.427874	+	0.741099i
$122$	−251.147			−0.186376
$123$	271.932	+	471.000i	0.199344	+	0.345273i
$124$	389.711	+	675.000i	0.282235	+	0.488845i
$125$	427.817			0.306121
$126$	−276.000	−	478.046i	−0.195143	−	0.337998i
$127$	143.000	−	247.683i	0.0999149	−	0.173058i	−0.811734	−	0.584027i	$-0.801476\pi$
$127$	143.000	−	247.683i	0.0999149	−	0.173058i	0.911649	+	0.410969i	$0.134810\pi$
$128$	−461.592	+	799.500i	−0.318745	+	0.552082i
$129$	−208.000			−0.141964
$130$		0			0
$131$	−1974.00			−1.31656			−0.658279	−	0.752774i	$-0.728715\pi$
$131$	−1974.00			−1.31656			−0.658279	+	0.752774i	$0.728715\pi$
$132$	69.2820	−	120.000i	0.0456835	−	0.0791262i
$133$	792.000	−	1371.78i	0.516354	−	0.894352i
$134$	681.000	+	1179.53i	0.439026	+	0.760415i
$135$	173.205			0.110423
$136$	1317.22	+	2281.50i	0.830523	+	1.43851i
$137$	−423.486	−	733.500i	−0.264094	−	0.457424i	0.703232	−	0.710961i	$-0.251740\pi$
$137$	−423.486	−	733.500i	−0.264094	−	0.457424i	−0.967326	+	0.253536i	$0.918406\pi$
$138$	−270.200			−0.166674
$139$	−118.000	−	204.382i	−0.0720045	−	0.124716i	0.827775	−	0.561060i	$-0.189606\pi$
$139$	−118.000	−	204.382i	−0.0720045	−	0.124716i	−0.899780	+	0.436344i	$0.856273\pi$
$140$	−60.0000	+	103.923i	−0.0362209	+	0.0627364i
$141$	301.377	−	522.000i	0.180004	−	0.311775i
$142$	−1830.00			−1.08148
$143$		0			0
$144$	−23.0000			−0.0133102
$145$	−122.110	+	211.500i	−0.0699355	+	0.121132i
$146$	−397.500	+	688.490i	−0.225324	+	0.390273i
$147$	151.000	+	261.540i	0.0847229	+	0.146744i
$148$	718.801			0.399224
$149$	23.3827	+	40.5000i	0.0128563	+	0.0222677i	0.872382	−	0.488825i	$-0.162574\pi$
$149$	23.3827	+	40.5000i	0.0128563	+	0.0222677i	−0.859526	+	0.511093i	$0.829241\pi$
$150$	−211.310	−	366.000i	−0.115023	−	0.199225i
$151$	1770.16			0.953995			0.476998	−	0.878905i	$-0.341725\pi$
$151$	1770.16			0.953995			0.476998	+	0.878905i	$0.341725\pi$
$152$	1287.00	+	2229.15i	0.686773	+	1.18953i
$153$	−1345.50	+	2330.47i	−0.710962	+	1.23142i
$154$	166.277	−	288.000i	0.0870063	−	0.150699i
$155$	−270.000			−0.139916
$156$		0			0
$157$	1211.00			0.615594			0.307797	−	0.951452i	$-0.400408\pi$
$157$	1211.00			0.615594			0.307797	+	0.951452i	$0.400408\pi$
$158$	1105.05	−	1914.00i	0.556411	−	0.963732i
$159$	−93.0000	+	161.081i	−0.0463860	+	0.0803430i
$160$	−157.500	−	272.798i	−0.0778217	−	0.134791i
$161$	1080.80			0.529062
$162$	364.597	+	631.500i	0.176824	+	0.306267i
$163$	−502.295	−	870.000i	−0.241367	−	0.418059i	0.719737	−	0.694247i	$-0.244262\pi$
$163$	−502.295	−	870.000i	−0.241367	−	0.418059i	−0.961104	+	0.276187i	$0.910929\pi$
$164$	1359.66			0.647388
$165$	24.0000	+	41.5692i	0.0113236	+	0.0196131i
$166$	−684.000	+	1184.72i	−0.319811	+	0.553930i
$167$	−457.261	+	792.000i	−0.211880	+	0.366987i	−0.952303	−	0.305154i	$-0.901292\pi$
$167$	−457.261	+	792.000i	−0.211880	+	0.366987i	0.740423	+	0.672141i	$0.234625\pi$
$168$	624.000			0.286563
$169$		0			0
$170$	−351.000			−0.158356
$171$	−1314.63	+	2277.00i	−0.587906	+	1.01828i
$172$	−260.000	+	450.333i	−0.115261	+	0.199637i
$173$	1287.00	+	2229.15i	0.565600	+	0.979648i	0.996994	+	0.0774841i	$0.0246887\pi$
$173$	1287.00	+	2229.15i	0.565600	+	0.979648i	−0.431394	+	0.902164i	$0.641978\pi$
$174$	488.438			0.212807
$175$	845.241	+	1464.00i	0.365110	+	0.632389i
$176$	−6.92820	−	12.0000i	−0.00296723	−	0.00513940i
$177$	568.113			0.241254
$178$	−846.000	−	1465.31i	−0.356238	−	0.617022i
$179$	1872.00	−	3242.40i	0.781675	−	1.35390i	−0.149290	−	0.988793i	$-0.547699\pi$
$179$	1872.00	−	3242.40i	0.781675	−	1.35390i	0.930965	−	0.365108i	$-0.118968\pi$
$180$	99.5929	−	172.500i	0.0412401	−	0.0714299i
$181$	637.000			0.261590			0.130795	−	0.991409i	$-0.458247\pi$
$181$	637.000			0.261590			0.130795	+	0.991409i	$0.458247\pi$
$182$		0			0
$183$	290.000			0.117144
$184$	−878.150	+	1521.00i	−0.351837	+	0.609400i
$185$	−124.500	+	215.640i	−0.0494780	+	0.0856983i
$186$	270.000	+	467.654i	0.106437	+	0.184355i
$187$	−1621.20			−0.633978
$188$	−753.442	−	1305.00i	−0.292289	−	0.506260i
$189$	692.820	+	1200.00i	0.266642	+	0.461837i
$190$	−342.946			−0.130947
$191$	1299.00	+	2249.93i	0.492106	+	0.852353i	0.999959	−	0.00909077i	$-0.00289372\pi$
$191$	1299.00	+	2249.93i	0.492106	+	0.852353i	−0.507852	+	0.861444i	$0.669560\pi$
$192$	−307.000	+	531.740i	−0.115395	+	0.199870i
$193$	−558.586	+	967.500i	−0.208331	+	0.360840i	−0.951189	−	0.308609i	$-0.900137\pi$
$193$	−558.586	+	967.500i	−0.208331	+	0.360840i	0.742858	+	0.669449i	$0.233470\pi$
$194$	−348.000			−0.128788
$195$		0			0
$196$	755.000			0.275146
$197$	1025.37	−	1776.00i	0.370837	−	0.642308i	−0.618858	−	0.785503i	$-0.712404\pi$
$197$	1025.37	−	1776.00i	0.370837	−	0.642308i	0.989695	+	0.143195i	$0.0457375\pi$
$198$	−276.000	+	478.046i	−0.0990630	+	0.171582i
$199$	−1261.00	−	2184.12i	−0.449196	−	0.778030i	0.549138	−	0.835732i	$-0.314956\pi$
$199$	−1261.00	−	2184.12i	−0.449196	−	0.778030i	−0.998334	+	0.0577019i	$0.981623\pi$
$200$	−2747.03			−0.971223
$201$	−786.351	−	1362.00i	−0.275945	−	0.477951i
$202$	−371.525	−	643.500i	−0.129408	−	0.224141i
$203$	−1953.75			−0.675500
$204$	−585.000	−	1013.25i	−0.200775	−	0.347753i
$205$	−235.500	+	407.898i	−0.0802343	+	0.138970i
$206$	−157.617	+	273.000i	−0.0533091	+	0.0923340i
$207$	−1794.00			−0.602375
$208$		0			0
$209$	−1584.00			−0.524247
$210$	−41.5692	+	72.0000i	−0.0136598	+	0.0236594i
$211$	−521.000	+	902.398i	−0.169986	+	0.294425i	−0.938415	−	0.345511i	$-0.887706\pi$
$211$	−521.000	+	902.398i	−0.169986	+	0.294425i	0.768428	+	0.639936i	$0.221039\pi$
$212$	232.500	+	402.702i	0.0753215	+	0.130461i
$213$	2113.10			0.679753
$214$	−1304.23	−	2259.00i	−0.416615	−	0.721598i
$215$	−90.0666	−	156.000i	−0.0285697	−	0.0494842i
$216$	−2251.67			−0.709289
$217$	−1080.00	−	1870.61i	−0.337858	−	0.585187i
$218$	1344.00	−	2327.88i	0.417556	−	0.723228i
$219$	458.993	−	795.000i	0.141625	−	0.245302i
$220$	120.000			0.0367745
$221$		0			0
$222$	498.000			0.150557
$223$	−1203.78	+	2085.00i	−0.361483	+	0.626107i	−0.988205	−	0.153136i	$-0.951063\pi$
$223$	−1203.78	+	2085.00i	−0.361483	+	0.626107i	0.626722	+	0.779243i	$0.284396\pi$
$224$	1260.00	−	2182.38i	0.375836	−	0.650967i
$225$	−1403.00	−	2430.07i	−0.415704	−	0.720020i
$226$	1189.92			0.350231
$227$	−1203.78	−	2085.00i	−0.351971	−	0.609631i	0.634624	−	0.772821i	$-0.281155\pi$
$227$	−1203.78	−	2085.00i	−0.351971	−	0.609631i	−0.986595	+	0.163190i	$0.947822\pi$
$228$	−571.577	−	990.000i	−0.166025	−	0.287563i
$229$	−2508.01			−0.723729			−0.361864	−	0.932231i	$-0.617860\pi$
$229$	−2508.01			−0.723729			−0.361864	+	0.932231i	$0.617860\pi$
$230$	−117.000	−	202.650i	−0.0335424	−	0.0580971i
$231$	−192.000	+	332.554i	−0.0546869	+	0.0947205i
$232$	1587.42	−	2749.50i	0.449222	−	0.778076i
$233$	5850.00			1.64483			0.822417	−	0.568885i	$-0.192625\pi$
$233$	5850.00			1.64483			0.822417	+	0.568885i	$0.192625\pi$
$234$		0			0
$235$	522.000			0.144900
$236$	710.141	−	1230.00i	0.195874	−	0.339263i
$237$	−1276.00	+	2210.10i	−0.349726	+	0.605744i
$238$	−1404.00	−	2431.80i	−0.382386	−	0.662312i
$239$	−5383.21			−1.45695			−0.728475	−	0.685072i	$-0.759771\pi$
$239$	−5383.21			−1.45695			−0.728475	+	0.685072i	$0.759771\pi$
$240$	1.73205	+	3.00000i	0.000465847	+	0.000806872i
$241$	2458.65	+	4258.50i	0.657159	+	1.13823i	0.981348	+	0.192240i	$0.0615753\pi$
$241$	2458.65	+	4258.50i	0.657159	+	1.13823i	−0.324189	+	0.945992i	$0.605091\pi$
$242$	1972.81			0.524036
$243$	−1771.00	−	3067.46i	−0.467530	−	0.809785i
$244$	362.500	−	627.868i	0.0951094	−	0.164734i
$245$	−130.770	+	226.500i	−0.0341003	+	0.0590635i
$246$	942.000			0.244145
$247$		0			0
$248$	3510.00			0.898731
$249$	789.815	−	1368.00i	0.201014	−	0.348167i
$250$	370.500	−	641.725i	0.0937299	−	0.162345i
$251$	−1989.00	−	3445.05i	−0.500178	−	0.866333i	−1.00000		0.000205037i	$-0.999935\pi$
$251$	−1989.00	−	3445.05i	−0.500178	−	0.866333i	0.499822	−	0.866128i	$-0.333399\pi$
$252$	1593.49			0.398334
$253$	−540.400	−	936.000i	−0.134287	−	0.232592i
$254$	−247.683	−	429.000i	−0.0611852	−	0.105976i
$255$	405.300			0.0995328
$256$	2027.50	+	3511.73i	0.494995	+	0.857357i
$257$	1033.50	−	1790.07i	0.250848	−	0.434482i	−0.712911	−	0.701254i	$-0.752624\pi$
$257$	1033.50	−	1790.07i	0.250848	−	0.434482i	0.963760	+	0.266772i	$0.0859572\pi$
$258$	−180.133	+	312.000i	−0.0434675	+	0.0752879i
$259$	−1992.00			−0.477903
$260$		0			0
$261$	3243.00			0.769106
$262$	−1709.53	+	2961.00i	−0.403112	+	0.698211i
$263$	1026.00	−	1777.08i	0.240555	−	0.416653i	−0.720318	−	0.693644i	$-0.756004\pi$
$263$	1026.00	−	1777.08i	0.240555	−	0.416653i	0.960872	+	0.276991i	$0.0893373\pi$
$264$	−312.000	−	540.400i	−0.0727359	−	0.125982i
$265$	−161.081			−0.0373400
$266$	−1371.78	−	2376.00i	−0.316201	−	0.547676i
$267$	976.877	+	1692.00i	0.223910	+	0.387823i
$268$	−3931.76			−0.896157
$269$	−1665.00	−	2883.86i	−0.377386	−	0.653652i	0.613295	−	0.789854i	$-0.289844\pi$
$269$	−1665.00	−	2883.86i	−0.377386	−	0.653652i	−0.990681	+	0.136202i	$0.956510\pi$
$270$	150.000	−	259.808i	0.0338100	−	0.0585607i
$271$	−1402.96	+	2430.00i	−0.314479	+	0.544694i	−0.979327	−	0.202285i	$-0.935163\pi$
$271$	−1402.96	+	2430.00i	−0.314479	+	0.544694i	0.664848	+	0.746979i	$0.268496\pi$
$272$	−117.000			−0.0260815
$273$		0			0
$274$	−1467.00			−0.323448
$275$	845.241	−	1464.00i	0.185345	−	0.321027i
$276$	390.000	−	675.500i	0.0850552	−	0.147320i
$277$	188.500	+	326.492i	0.0408876	+	0.0708194i	0.885745	−	0.464172i	$-0.153648\pi$
$277$	188.500	+	326.492i	0.0408876	+	0.0708194i	−0.844857	+	0.534992i	$0.820315\pi$
$278$	−408.764			−0.0881872
$279$	1792.67	+	3105.00i	0.384676	+	0.666278i
$280$	270.200	+	468.000i	0.0576698	+	0.0998870i
$281$	36.3731			0.00772183			0.00386092	−	0.999993i	$-0.498771\pi$
$281$	36.3731			0.00772183			0.00386092	+	0.999993i	$0.498771\pi$
$282$	−522.000	−	904.131i	−0.110229	−	0.190923i
$283$	−3562.00	+	6169.56i	−0.748194	+	1.29591i	0.200493	+	0.979695i	$0.435745\pi$
$283$	−3562.00	+	6169.56i	−0.748194	+	1.29591i	−0.948688	+	0.316215i	$0.897588\pi$
$284$	2641.38	−	4575.00i	0.551891	−	0.955902i
$285$	396.000			0.0823053
$286$		0			0
$287$	−3768.00			−0.774976
$288$	−2091.45	+	3622.50i	−0.427917	+	0.741173i
$289$	−4388.00	+	7600.24i	−0.893141	+	1.54696i
$290$	211.500	+	366.329i	0.0428266	+	0.0741778i
$291$	401.836			0.0809486
$292$	−1147.48	−	1987.50i	−0.229971	−	0.398321i
$293$	−4161.25	−	7207.50i	−0.829703	−	1.43709i	−0.898271	−	0.439441i	$-0.855177\pi$
$293$	−4161.25	−	7207.50i	−0.829703	−	1.43709i	0.0685685	−	0.997646i	$-0.478157\pi$
$294$	523.079			0.103764
$295$	246.000	+	426.084i	0.0485514	+	0.0840936i
$296$	1618.50	−	2803.32i	0.317816	−	0.550473i
$297$	692.820	−	1200.00i	0.135359	−	0.234448i
$298$	81.0000			0.0157457
$299$		0			0
$300$	1220.00			0.234789
$301$	720.533	−	1248.00i	0.137976	−	0.238982i
$302$	1533.00	−	2655.23i	0.292100	−	0.505932i
$303$	429.000	+	743.050i	0.0813380	+	0.140882i
$304$	−114.315			−0.0215672
$305$	125.574	+	217.500i	0.0235748	+	0.0408328i
$306$	2330.47	+	4036.50i	0.435374	+	0.754089i
$307$	2220.49			0.412801			0.206401	−	0.978468i	$-0.433825\pi$
$307$	2220.49			0.412801			0.206401	+	0.978468i	$0.433825\pi$
$308$	480.000	+	831.384i	0.0888004	+	0.153807i
$309$	182.000	−	315.233i	0.0335069	−	0.0580356i
$310$	−233.827	+	405.000i	−0.0428402	+	0.0742015i
$311$	−4914.00			−0.895972			−0.447986	−	0.894041i	$-0.647859\pi$
$311$	−4914.00			−0.895972			−0.447986	+	0.894041i	$0.647859\pi$
$312$		0			0
$313$	−518.000			−0.0935434			−0.0467717	−	0.998906i	$-0.514893\pi$
$313$	−518.000			−0.0935434			−0.0467717	+	0.998906i	$0.514893\pi$
$314$	1048.76	−	1816.50i	0.188487	−	0.326468i
$315$	−276.000	+	478.046i	−0.0493677	+	0.0855074i
$316$	3190.00	+	5525.24i	0.567885	+	0.983605i
$317$	3916.17			0.693861			0.346930	−	0.937891i	$-0.387224\pi$
$317$	3916.17			0.693861			0.346930	+	0.937891i	$0.387224\pi$
$318$	161.081	+	279.000i	0.0284055	+	0.0491998i
$319$	976.877	+	1692.00i	0.171456	+	0.296971i
$320$	−531.740			−0.0928911
$321$	1506.00	+	2608.47i	0.261859	+	0.453553i
$322$	936.000	−	1621.20i	0.161991	−	0.280577i
$323$	−6687.45	+	11583.0i	−1.15201	+	1.99534i
$324$	−2105.00			−0.360940
$325$		0			0
$326$	−1740.00			−0.295613
$327$	−1551.92	+	2688.00i	−0.262450	+	0.454577i
$328$	3061.50	−	5302.67i	0.515375	−	0.892656i
$329$	2088.00	+	3616.52i	0.349894	+	0.606034i
$330$	83.1384			0.0138685
$331$	3727.37	+	6456.00i	0.618958	+	1.07207i	0.989676	+	0.143321i	$0.0457781\pi$
$331$	3727.37	+	6456.00i	0.618958	+	1.07207i	−0.370719	+	0.928745i	$0.620889\pi$
$332$	−1974.54	−	3420.00i	−0.326406	−	0.565352i
$333$	3306.48			0.544127
$334$	792.000	+	1371.78i	0.129749	+	0.224733i
$335$	681.000	−	1179.53i	0.111066	−	0.192371i
$336$	−13.8564	+	24.0000i	−0.00224979	+	0.00389675i
$337$	3575.00			0.577871			0.288936	−	0.957349i	$-0.406699\pi$
$337$	3575.00			0.577871			0.288936	+	0.957349i	$0.406699\pi$
$338$		0			0
$339$	−1374.00			−0.220134
$340$	506.625	−	877.500i	0.0808106	−	0.139968i
$341$	−1080.00	+	1870.61i	−0.171511	+	0.297066i
$342$	2277.00	+	3943.88i	0.360018	+	0.623569i
$343$	−6845.06			−1.07755
$344$	1170.87	+	2028.00i	0.183514	+	0.317856i
$345$	135.100	+	234.000i	0.0210827	+	0.0365163i
$346$	4458.30			0.692716
$347$	3483.00	+	6032.73i	0.538839	+	0.933297i	0.998967	+	0.0454442i	$0.0144703\pi$
$347$	3483.00	+	6032.73i	0.538839	+	0.933297i	−0.460128	+	0.887853i	$0.652196\pi$
$348$	−705.000	+	1221.10i	−0.108598	+	0.188097i
$349$	3325.54	−	5760.00i	0.510063	−	0.883455i	−0.489869	−	0.871796i	$-0.662955\pi$
$349$	3325.54	−	5760.00i	0.510063	−	0.883455i	0.999932	−	0.0116588i	$-0.00371121\pi$
$350$	2928.00			0.447166
$351$		0			0
$352$	−2520.00			−0.381581
$353$	2815.45	−	4876.50i	0.424508	−	0.735269i	−0.571867	−	0.820347i	$-0.693781\pi$
$353$	2815.45	−	4876.50i	0.424508	−	0.735269i	0.996374	+	0.0850777i	$0.0271139\pi$
$354$	492.000	−	852.169i	0.0738687	−	0.127944i
$355$	915.000	+	1584.83i	0.136798	+	0.236940i
$356$	4884.38			0.727168
$357$	1621.20	+	2808.00i	0.240344	+	0.416289i
$358$	−3242.40	−	5616.00i	−0.478676	−	0.829092i
$359$	7129.12			1.04808			0.524040	−	0.851694i	$-0.324424\pi$
$359$	7129.12			1.04808			0.524040	+	0.851694i	$0.324424\pi$
$360$	−448.500	−	776.825i	−0.0656612	−	0.113729i
$361$	−3104.50	+	5377.15i	−0.452617	+	0.783956i
$362$	551.658	−	955.500i	0.0800953	−	0.138729i
$363$	−2278.00			−0.329377
$364$		0			0
$365$	795.000			0.114006
$366$	251.147	−	435.000i	0.0358680	−	0.0621252i
$367$	−1.00000	+	1.73205i	−0.000142233	+	0.000246355i	−0.866097	−	0.499877i	$-0.833379\pi$
$367$	−1.00000	+	1.73205i	−0.000142233	+	0.000246355i	0.865954	+	0.500123i	$0.166712\pi$
$368$	−39.0000	−	67.5500i	−0.00552450	−	0.00956871i
$369$	6254.44			0.882366
$370$	215.640	+	373.500i	0.0302989	+	0.0524793i
$371$	−644.323	−	1116.00i	−0.0901660	−	0.156172i
$372$	−1558.85			−0.217264
$373$	−1749.50	−	3030.22i	−0.242857	−	0.420641i	0.718670	−	0.695351i	$-0.244751\pi$
$373$	−1749.50	−	3030.22i	−0.242857	−	0.420641i	−0.961527	+	0.274711i	$0.911418\pi$
$374$	−1404.00	+	2431.80i	−0.194115	+	0.336218i
$375$	−427.817	+	741.000i	−0.0589129	+	0.102040i
$376$	−6786.00			−0.930748
$377$		0			0
$378$	2400.00			0.326568
$379$	2759.16	−	4779.00i	0.373953	−	0.647706i	−0.616216	−	0.787577i	$-0.711335\pi$
$379$	2759.16	−	4779.00i	0.373953	−	0.647706i	0.990170	+	0.139871i	$0.0446686\pi$
$380$	495.000	−	857.365i	0.0668236	−	0.115742i
$381$	286.000	+	495.367i	0.0384573	+	0.0666100i
$382$	4499.87			0.602705
$383$	3682.34	+	6378.00i	0.491276	+	0.850915i	0.999950	−	0.0100443i	$-0.00319724\pi$
$383$	3682.34	+	6378.00i	0.491276	+	0.850915i	−0.508673	+	0.860960i	$0.669864\pi$
$384$	−923.183	−	1599.00i	−0.122685	−	0.212496i
$385$	−332.554			−0.0440221
$386$	967.500	+	1675.76i	0.127576	+	0.220969i
$387$	−1196.00	+	2071.53i	−0.157096	+	0.272098i
$388$	502.295	−	870.000i	0.0657220	−	0.113834i
$389$	1209.00			0.157580			0.0787901	−	0.996891i	$-0.474894\pi$
$389$	1209.00			0.157580			0.0787901	+	0.996891i	$0.474894\pi$
$390$		0			0
$391$	−9126.00			−1.18036
$392$	1700.01	−	2944.50i	0.219039	−	0.379387i
$393$	1974.00	−	3419.07i	0.253372	−	0.438853i
$394$	−1776.00	−	3076.12i	−0.227090	−	0.393332i
$395$	−2210.10			−0.281524
$396$	−796.743	−	1380.00i	−0.101106	−	0.175120i
$397$	5847.40	+	10128.0i	0.739226	+	1.28038i	0.952844	+	0.303460i	$0.0981419\pi$
$397$	5847.40	+	10128.0i	0.739226	+	1.28038i	−0.213618	+	0.976917i	$0.568525\pi$
$398$	−4368.23			−0.550150
$399$	1584.00	+	2743.57i	0.198745	+	0.344236i
$400$	61.0000	−	105.655i	0.00762500	−	0.0132069i
$401$	1490.43	−	2581.50i	0.185607	−	0.321481i	−0.758174	−	0.652053i	$-0.773908\pi$
$401$	1490.43	−	2581.50i	0.185607	−	0.321481i	0.943781	+	0.330571i	$0.107241\pi$
$402$	−2724.00			−0.337962
$403$		0			0
$404$	2145.00			0.264153
$405$	364.597	−	631.500i	0.0447332	−	0.0774802i
$406$	−1692.00	+	2930.63i	−0.206829	+	0.358238i
$407$	996.000	+	1725.12i	0.121302	+	0.210101i
$408$	−5268.90			−0.639337
$409$	−21.6506	−	37.5000i	−0.00261749	−	0.00453363i	0.864714	−	0.502265i	$-0.167500\pi$
$409$	−21.6506	−	37.5000i	−0.00261749	−	0.00453363i	−0.867331	+	0.497731i	$0.834167\pi$
$410$	407.898	+	706.500i	0.0491333	+	0.0851013i
$411$	1693.95			0.203300
$412$	−455.000	−	788.083i	−0.0544084	−	0.0942380i
$413$	−1968.00	+	3408.68i	−0.234477	+	0.406126i
$414$	−1553.65	+	2691.00i	−0.184439	+	0.319458i
$415$	1368.00			0.161813
$416$		0			0
$417$	472.000			0.0554291
$418$	−1371.78	+	2376.00i	−0.160517	+	0.278024i
$419$	4731.00	−	8194.33i	0.551610	−	0.955416i	−0.446549	−	0.894759i	$-0.647347\pi$
$419$	4731.00	−	8194.33i	0.551610	−	0.955416i	0.998159	−	0.0606569i	$-0.0193195\pi$
$420$	−120.000	−	207.846i	−0.0139414	−	0.0241473i
$421$	7068.50			0.818284			0.409142	−	0.912471i	$-0.365828\pi$
$421$	7068.50			0.818284			0.409142	+	0.912471i	$0.365828\pi$
$422$	902.398	+	1563.00i	0.104095	+	0.180298i
$423$	−3465.83	−	6003.00i	−0.398380	−	0.690014i
$424$	2094.05			0.239849
$425$	−7137.00	−	12361.6i	−0.814577	−	1.41089i
$426$	1830.00	−	3169.65i	0.208131	−	0.360493i
$427$	−1004.59	+	1740.00i	−0.113854	+	0.197200i
$428$	7530.00			0.850412
$429$		0			0
$430$	−312.000			−0.0349906
$431$	−4964.06	+	8598.00i	−0.554780	+	0.960907i	0.443140	+	0.896452i	$0.353864\pi$
$431$	−4964.06	+	8598.00i	−0.554780	+	0.960907i	−0.997921	+	0.0644552i	$0.979469\pi$
$432$	50.0000	−	86.6025i	0.00556858	−	0.00964506i
$433$	−3308.50	−	5730.49i	−0.367197	−	0.636004i	0.621929	−	0.783074i	$-0.286349\pi$
$433$	−3308.50	−	5730.49i	−0.367197	−	0.636004i	−0.989126	+	0.147070i	$0.953016\pi$
$434$	−3741.23			−0.413790
$435$	−244.219	−	423.000i	−0.0269182	−	0.0466237i
$436$	3879.79	+	6720.00i	0.426166	+	0.738141i
$437$	−8916.60			−0.976061
$438$	−795.000	−	1376.98i	−0.0867273	−	0.150216i
$439$	6994.00	−	12114.0i	0.760377	−	1.31701i	−0.182280	−	0.983247i	$-0.558348\pi$
$439$	6994.00	−	12114.0i	0.760377	−	1.31701i	0.942656	−	0.333765i	$-0.108319\pi$
$440$	270.200	−	468.000i	0.0292756	−	0.0507069i
$441$	3473.00			0.375013
$442$		0			0
$443$	2004.00			0.214928			0.107464	−	0.994209i	$-0.465727\pi$
$443$	2004.00			0.214928			0.107464	+	0.994209i	$0.465727\pi$
$444$	−718.801	+	1245.00i	−0.0768306	+	0.133075i
$445$	−846.000	+	1465.31i	−0.0901219	+	0.156096i
$446$	2085.00	+	3611.33i	0.221362	+	0.383411i
$447$	−93.5307			−0.00989676
$448$	−2126.96	−	3684.00i	−0.224307	−	0.388510i
$449$	4541.44	+	7866.00i	0.477336	+	0.826769i	0.999663	−	0.0259758i	$-0.00826929\pi$
$449$	4541.44	+	7866.00i	0.477336	+	0.826769i	−0.522327	+	0.852745i	$0.674936\pi$
$450$	−4860.13			−0.509131
$451$	1884.00	+	3263.18i	0.196705	+	0.340704i
$452$	−1717.50	+	2974.80i	−0.178727	+	0.309563i
$453$	−1770.16	+	3066.00i	−0.183596	+	0.317998i
$454$	−4170.00			−0.431074
$455$		0			0
$456$	−5148.00			−0.528678
$457$	1261.80	−	2185.50i	0.129156	−	0.223705i	−0.794194	−	0.607665i	$-0.792106\pi$
$457$	1261.80	−	2185.50i	0.129156	−	0.223705i	0.923350	+	0.383959i	$0.125440\pi$
$458$	−2172.00	+	3762.01i	−0.221596	+	0.383815i
$459$	−5850.00	−	10132.5i	−0.594890	−	1.03038i
$460$	675.500			0.0684681
$461$	−9793.88	−	16963.5i	−0.989472	−	1.71382i	−0.620072	−	0.784545i	$-0.712897\pi$
$461$	−9793.88	−	16963.5i	−0.989472	−	1.71382i	−0.369400	−	0.929270i	$-0.620437\pi$
$462$	332.554	+	576.000i	0.0334887	+	0.0580042i
$463$	−8632.54			−0.866497			−0.433249	−	0.901274i	$-0.642633\pi$
$463$	−8632.54			−0.866497			−0.433249	+	0.901274i	$0.642633\pi$
$464$	70.5000	+	122.110i	0.00705362	+	0.0122172i
$465$	270.000	−	467.654i	0.0269268	−	0.0466385i
$466$	5066.25	−	8775.00i	0.503625	−	0.872305i
$467$	−5460.00			−0.541025			−0.270512	−	0.962716i	$-0.587193\pi$
$467$	−5460.00			−0.541025			−0.270512	+	0.962716i	$0.587193\pi$
$468$		0			0
$469$	10896.0			1.07277
$470$	452.065	−	783.000i	0.0443664	−	0.0768449i
$471$	−1211.00	+	2097.51i	−0.118471	+	0.205198i
$472$	−3198.00	−	5539.10i	−0.311864	−	0.540165i
$473$	−1441.07			−0.140085
$474$	2210.10	+	3828.00i	0.214163	+	0.370941i
$475$	−6973.24	−	12078.0i	−0.673587	−	1.16669i
$476$	8106.00			0.780542
$477$	1069.50	+	1852.43i	0.102660	+	0.177813i
$478$	−4662.00	+	8074.82i	−0.446098	+	0.772665i
$479$	1276.52	−	2211.00i	0.121766	−	0.210904i	−0.798698	−	0.601732i	$-0.794478\pi$
$479$	1276.52	−	2211.00i	0.121766	−	0.210904i	0.920464	+	0.390827i	$0.127811\pi$
$480$	630.000			0.0599072
$481$		0			0
$482$	8517.00			0.804852
$483$	−1080.80	+	1872.00i	−0.101818	+	0.176354i
$484$	−2847.50	+	4932.01i	−0.267421	+	0.463187i
$485$	174.000	+	301.377i	0.0162906	+	0.0282161i
$486$	−6134.92			−0.572605
$487$	−5414.39	−	9378.00i	−0.503798	−	0.872603i	−0.999990	−	0.00439074i	$-0.998602\pi$
$487$	−5414.39	−	9378.00i	−0.503798	−	0.872603i	0.496193	−	0.868212i	$-0.334731\pi$
$488$	−1632.46	−	2827.50i	−0.151430	−	0.262285i
$489$	2009.18			0.185804
$490$	226.500	+	392.310i	0.0208821	+	0.0361689i
$491$	5694.00	−	9862.30i	0.523354	−	0.906475i	−0.476277	−	0.879295i	$-0.658014\pi$
$491$	5694.00	−	9862.30i	0.523354	−	0.906475i	0.999631	−	0.0271797i	$-0.00865264\pi$
$492$	−1359.66	+	2355.00i	−0.124590	+	0.215796i
$493$	16497.0			1.50707
$494$		0			0
$495$	552.000			0.0501223
$496$	−77.9423	+	135.000i	−0.00705587	+	0.0122211i
$497$	−7320.00	+	12678.6i	−0.660658	+	1.14429i
$498$	−1368.00	−	2369.45i	−0.123095	−	0.213208i
$499$	−17677.3			−1.58586			−0.792931	−	0.609311i	$-0.791446\pi$
$499$	−17677.3			−1.58586			−0.792931	+	0.609311i	$0.791446\pi$
$500$	1069.54	+	1852.50i	0.0956627	+	0.165693i
$501$	−914.523	−	1584.00i	−0.0815526	−	0.141253i
$502$	−6890.10			−0.612590
$503$	−1938.00	−	3356.71i	−0.171792	−	0.297552i	0.767255	−	0.641343i	$-0.221622\pi$
$503$	−1938.00	−	3356.71i	−0.171792	−	0.297552i	−0.939046	+	0.343791i	$0.888289\pi$
$504$	3588.00	−	6214.60i	0.317108	−	0.549246i
$505$	−371.525	+	643.500i	−0.0327379	+	0.0567037i
$506$	−1872.00			−0.164467
$507$		0			0
$508$	1430.00			0.124894
$509$	−8532.95	+	14779.5i	−0.743058	+	1.28701i	0.208039	+	0.978120i	$0.433292\pi$
$509$	−8532.95	+	14779.5i	−0.743058	+	1.28701i	−0.951097	+	0.308893i	$0.900042\pi$
$510$	351.000	−	607.950i	0.0304756	−	0.0527852i
$511$	3180.00	+	5507.92i	0.275293	+	0.476822i
$512$	−361.999			−0.0312465
$513$	−5715.77	−	9900.00i	−0.491925	−	0.852038i
$514$	−1790.07	−	3100.50i	−0.153612	−	0.266065i
$515$	315.233			0.0269725
$516$	−520.000	−	900.666i	−0.0443638	−	0.0768404i
$517$	2088.00	−	3616.52i	0.177621	−	0.307649i
$518$	−1725.12	+	2988.00i	−0.146327	+	0.253446i
$519$	−5148.00			−0.435399
$520$		0			0
$521$	2121.00			0.178355			0.0891773	−	0.996016i	$-0.471576\pi$
$521$	2121.00			0.178355			0.0891773	+	0.996016i	$0.471576\pi$
$522$	2808.52	−	4864.50i	0.235490	−	0.407880i
$523$	5732.00	−	9928.12i	0.479241	−	0.830069i	−0.520476	−	0.853876i	$-0.674245\pi$
$523$	5732.00	−	9928.12i	0.479241	−	0.830069i	0.999717	+	0.0238072i	$0.00757878\pi$
$524$	−4935.00	−	8547.67i	−0.411425	−	0.712608i
$525$	−3380.96			−0.281062
$526$	−1777.08	−	3078.00i	−0.147309	−	0.255147i
$527$	9119.25	+	15795.0i	0.753777	+	1.30558i
$528$	27.7128			0.00228418
$529$	3041.50	+	5268.03i	0.249979	+	0.432977i
$530$	−139.500	+	241.621i	−0.0114330	+	0.0198025i
$531$	3266.65	−	5658.00i	0.266969	−	0.462404i
$532$	7920.00			0.645443
$533$		0			0
$534$	3384.00			0.274232
$535$	−1304.23	+	2259.00i	−0.105396	+	0.182552i
$536$	−8853.00	+	15333.8i	−0.713417	+	1.23567i
$537$	3744.00	+	6484.80i	0.300867	+	0.521117i
$538$	−5767.73			−0.462202
$539$	1046.16	+	1812.00i	0.0836016	+	0.144802i
$540$	433.013	+	750.000i	0.0345072	+	0.0597683i
$541$	4764.87			0.378665			0.189333	−	0.981913i	$-0.439368\pi$
$541$	4764.87			0.378665			0.189333	+	0.981913i	$0.439368\pi$
$542$	2430.00	+	4208.88i	0.192578	+	0.333555i
$543$	−637.000	+	1103.32i	−0.0503431	+	0.0871968i
$544$	−10639.1	+	18427.5i	−0.838508	+	1.45234i
$545$	−2688.00			−0.211268
$546$		0			0
$547$	6554.00			0.512301			0.256151	−	0.966637i	$-0.417546\pi$
$547$	6554.00			0.512301			0.256151	+	0.966637i	$0.417546\pi$
$548$	2117.43	−	3667.50i	0.165059	−	0.285890i
$549$	1667.50	−	2888.19i	0.129631	−	0.224527i
$550$	−1464.00	−	2535.72i	−0.113500	−	0.196588i
$551$	16118.5			1.24622
$552$	−1756.30	−	3042.00i	−0.135422	−	0.234558i
$553$	−8840.39	−	15312.0i	−0.679804	−	1.17745i
$554$	652.983			0.0500769
$555$	−249.000	−	431.281i	−0.0190441	−	0.0329853i
$556$	590.000	−	1021.91i	0.0450028	−	0.0779472i
$557$	9056.03	−	15685.5i	0.688898	−	1.19321i	−0.283297	−	0.959032i	$-0.591428\pi$
$557$	9056.03	−	15685.5i	0.688898	−	1.19321i	0.972195	−	0.234174i	$-0.0752386\pi$
$558$	6210.00			0.471130
$559$		0			0
$560$	−24.0000			−0.00181104
$561$	1621.20	−	2808.00i	0.122009	−	0.211326i
$562$	31.5000	−	54.5596i	0.00236432	−	0.00409512i
$563$	−6084.00	−	10537.8i	−0.455435	−	0.788837i	0.543278	−	0.839553i	$-0.317183\pi$
$563$	−6084.00	−	10537.8i	−0.455435	−	0.788837i	−0.998713	+	0.0507160i	$0.983850\pi$
$564$	3013.77			0.225005
$565$	−594.959	−	1030.50i	−0.0443011	−	0.0767318i
$566$	6169.56	+	10686.0i	0.458173	+	0.793580i
$567$	5833.55			0.432074
$568$	−11895.0	−	20602.7i	−0.878703	−	1.52196i
$569$	−3861.00	+	6687.45i	−0.284467	+	0.492711i	−0.972480	−	0.232988i	$-0.925150\pi$
$569$	−3861.00	+	6687.45i	−0.284467	+	0.492711i	0.688013	+	0.725698i	$0.258483\pi$
$570$	342.946	−	594.000i	0.0252008	−	0.0436490i
$571$	−11440.0			−0.838440			−0.419220	−	0.907885i	$-0.637696\pi$
$571$	−11440.0			−0.838440			−0.419220	+	0.907885i	$0.637696\pi$
$572$		0			0
$573$	−5196.00			−0.378824
$574$	−3263.18	+	5652.00i	−0.237287	+	0.410993i
$575$	4758.00	−	8241.10i	0.345082	−	0.597700i
$576$	3530.50	+	6115.01i	0.255389	+	0.442347i
$577$	15444.7			1.11433			0.557167	−	0.830400i	$-0.311888\pi$
$577$	15444.7			1.11433			0.557167	+	0.830400i	$0.311888\pi$
$578$	7600.24	+	13164.0i	0.546935	+	0.947319i
$579$	−1117.17	−	1935.00i	−0.0801867	−	0.138887i
$580$	−1221.10			−0.0874194
$581$	5472.00	+	9477.78i	0.390735	+	0.676772i
$582$	348.000	−	602.754i	0.0247853	−	0.0429295i
$583$	−644.323	+	1116.00i	−0.0457721	+	0.0792796i
$584$	−10335.0			−0.732304
$585$		0			0
$586$	−14415.0			−1.01617
$587$	−7035.59	+	12186.0i	−0.494702	+	0.856848i	−0.999981	−	0.00610719i	$-0.998056\pi$
$587$	−7035.59	+	12186.0i	−0.494702	+	0.856848i	0.505280	+	0.862956i	$0.331389\pi$
$588$	−755.000	+	1307.70i	−0.0529518	+	0.0917153i
$589$	8910.00	+	15432.6i	0.623311	+	1.07961i
$590$	852.169			0.0594631
$591$	2050.75	+	3552.00i	0.142735	+	0.247225i
$592$	71.8801	+	124.500i	0.00499029	+	0.00864344i
$593$	−26938.6			−1.86549			−0.932745	−	0.360538i	$-0.882593\pi$
$593$	−26938.6			−1.86549			−0.932745	+	0.360538i	$0.882593\pi$
$594$	−1200.00	−	2078.46i	−0.0828899	−	0.143570i
$595$	−1404.00	+	2431.80i	−0.0967368	+	0.167553i
$596$	−116.913	+	202.500i	−0.00803517	+	0.0139173i
$597$	5044.00			0.345791
$598$		0			0
$599$	−10554.0			−0.719908			−0.359954	−	0.932970i	$-0.617208\pi$
$599$	−10554.0			−0.719908			−0.359954	+	0.932970i	$0.617208\pi$
$600$	2747.03	−	4758.00i	0.186912	−	0.323741i
$601$	7415.50	−	12844.0i	0.503302	−	0.871745i	−0.496691	−	0.867928i	$-0.665452\pi$
$601$	7415.50	−	12844.0i	0.503302	−	0.871745i	0.999993	−	0.00381713i	$-0.00121503\pi$
$602$	−1248.00	−	2161.60i	−0.0844928	−	0.146346i
$603$	−18086.1			−1.22143
$604$	4425.39	+	7665.00i	0.298123	+	0.516365i
$605$	−986.403	−	1708.50i	−0.0662859	−	0.114811i
$606$	1486.10			0.0996183
$607$	3977.00	+	6888.37i	0.265933	+	0.460610i	0.967808	−	0.251691i	$-0.0809866\pi$
$607$	3977.00	+	6888.37i	0.265933	+	0.460610i	−0.701874	+	0.712301i	$0.747653\pi$
$608$	−10395.0	+	18004.7i	−0.693377	+	1.20096i
$609$	1953.75	−	3384.00i	0.130000	−	0.225167i
$610$	435.000			0.0288732
$611$		0			0
$612$	−13455.0			−0.888703
$613$	12610.2	−	21841.5i	0.830866	−	1.43910i	−0.0664859	−	0.997787i	$-0.521179\pi$
$613$	12610.2	−	21841.5i	0.830866	−	1.43910i	0.897352	−	0.441315i	$-0.145488\pi$
$614$	1923.00	−	3330.73i	0.126394	−	0.218921i
$615$	−471.000	−	815.796i	−0.0308822	−	0.0534895i
$616$	4323.20			0.282771
$617$	8692.30	+	15055.5i	0.567162	+	0.982353i	0.996845	+	0.0793731i	$0.0252918\pi$
$617$	8692.30	+	15055.5i	0.567162	+	0.982353i	−0.429683	+	0.902980i	$0.641375\pi$
$618$	−315.233	−	546.000i	−0.0205187	−	0.0355394i
$619$	8209.92			0.533093			0.266547	−	0.963822i	$-0.414117\pi$
$619$	8209.92			0.533093			0.266547	+	0.963822i	$0.414117\pi$
$620$	−675.000	−	1169.13i	−0.0437236	−	0.0757316i
$621$	3900.00	−	6755.00i	0.252015	−	0.436504i
$622$	−4255.65	+	7371.00i	−0.274334	+	0.475161i
$623$	−13536.0			−0.870479
$624$		0			0
$625$	14509.0			0.928576
$626$	−448.601	+	777.000i	−0.0286417	+	0.0496089i
$627$	1584.00	−	2743.57i	0.100891	−	0.174749i
$628$	3027.50	+	5243.78i	0.192373	+	0.333200i
$629$	16819.9			1.06622
$630$	478.046	+	828.000i	0.0302314	+	0.0523624i
$631$	6432.84	+	11142.0i	0.405843	+	0.702941i	0.994419	−	0.105501i	$-0.0336445\pi$
$631$	6432.84	+	11142.0i	0.405843	+	0.702941i	−0.588576	+	0.808442i	$0.700311\pi$
$632$	28731.3			1.80834
$633$	−1042.00	−	1804.80i	−0.0654278	−	0.113324i
$634$	3391.50	−	5874.25i	0.212451	−	0.367975i
$635$	−247.683	+	429.000i	−0.0154788	+	0.0268100i
$636$	−930.000			−0.0579825
$637$		0			0
$638$	3384.00			0.209990
$639$	12150.3	−	21045.0i	0.752206	−	1.30286i
$640$	799.500	−	1384.77i	0.0493797	−	0.0855282i
$641$	3100.50	+	5370.22i	0.191049	+	0.330907i	0.945598	−	0.325337i	$-0.105478\pi$
$641$	3100.50	+	5370.22i	0.191049	+	0.330907i	−0.754549	+	0.656244i	$0.772144\pi$
$642$	5216.94			0.320710
$643$	8410.84	+	14568.0i	0.515849	+	0.893477i	0.999831	+	0.0183989i	$0.00585689\pi$
$643$	8410.84	+	14568.0i	0.515849	+	0.893477i	−0.483981	+	0.875078i	$0.660810\pi$
$644$	2702.00	+	4680.00i	0.165332	+	0.286363i
$645$	360.267			0.0219930
$646$	11583.0	+	20062.3i	0.705460	+	1.22189i
$647$	−6747.00	+	11686.1i	−0.409972	+	0.710092i	−0.994886	−	0.101003i	$-0.967795\pi$
$647$	−6747.00	+	11686.1i	−0.409972	+	0.710092i	0.584914	+	0.811095i	$0.301128\pi$
$648$	−4739.76	+	8209.50i	−0.287338	+	0.497685i
$649$	3936.00			0.238061
$650$		0			0
$651$	4320.00			0.260083
$652$	2511.47	−	4350.00i	0.150854	−	0.261287i
$653$	5667.00	−	9815.53i	0.339612	−	0.588226i	−0.644747	−	0.764396i	$-0.723037\pi$
$653$	5667.00	−	9815.53i	0.339612	−	0.588226i	0.984360	+	0.176170i	$0.0563708\pi$
$654$	2688.00	+	4655.75i	0.160717	+	0.278371i
$655$	3419.07			0.203960
$656$	135.966	+	235.500i	0.00809235	+	0.0140164i
$657$	−5278.42	−	9142.50i	−0.313441	−	0.542896i
$658$	7233.04			0.428531
$659$	−6618.00	−	11462.7i	−0.391200	−	0.677578i	0.601408	−	0.798942i	$-0.294607\pi$
$659$	−6618.00	−	11462.7i	−0.391200	−	0.677578i	−0.992608	+	0.121364i	$0.961273\pi$
$660$	−120.000	+	207.846i	−0.00707726	+	0.0122582i
$661$	5926.21	−	10264.5i	0.348718	−	0.603998i	−0.637304	−	0.770613i	$-0.719950\pi$
$661$	5926.21	−	10264.5i	0.348718	−	0.603998i	0.986022	+	0.166615i	$0.0532836\pi$
$662$	12912.0			0.758065
$663$		0			0
$664$	−17784.0			−1.03939
$665$	−1371.78	+	2376.00i	−0.0799932	+	0.138552i
$666$	2863.50	−	4959.73i	0.166604	−	0.288567i
$667$	5499.00	+	9524.55i	0.319224	+	0.552911i
$668$	−4572.61			−0.264850
$669$	−2407.55	−	4170.00i	−0.139135	−	0.240989i
$670$	−1179.53	−	2043.00i	−0.0680136	−	0.117803i
$671$	2009.18			0.115594
$672$	2520.00	+	4364.77i	0.144659	+	0.250557i
$673$	4010.50	−	6946.39i	0.229708	−	0.397866i	−0.728014	−	0.685563i	$-0.759556\pi$
$673$	4010.50	−	6946.39i	0.229708	−	0.397866i	0.957722	+	0.287697i	$0.0928896\pi$
$674$	3096.04	−	5362.50i	0.176936	−	0.306463i
$675$	12200.0			0.695671
$676$		0			0
$677$	−21630.0			−1.22793			−0.613965	−	0.789333i	$-0.710426\pi$
$677$	−21630.0			−1.22793			−0.613965	+	0.789333i	$0.710426\pi$
$678$	−1189.92	+	2061.00i	−0.0674020	+	0.116744i
$679$	−1392.00	+	2411.01i	−0.0786746	+	0.136268i
$680$	−2281.50	−	3951.67i	−0.128664	−	0.222853i
$681$	4815.10			0.270947
$682$	1870.61	+	3240.00i	0.105029	+	0.181915i
$683$	−13269.2	−	22983.0i	−0.743387	−	1.28758i	−0.950945	−	0.309361i	$-0.899885\pi$
$683$	−13269.2	−	22983.0i	−0.743387	−	1.28758i	0.207557	−	0.978223i	$-0.433449\pi$
$684$	−13146.3			−0.734883
$685$	733.500	+	1270.46i	0.0409133	+	0.0708639i
$686$	−5928.00	+	10267.6i	−0.329930	+	0.571456i
$687$	2508.01	−	4344.00i	0.139282	−	0.241243i
$688$	−104.000			−0.00576303
$689$		0			0
$690$	468.000			0.0258210
$691$	−415.692	+	720.000i	−0.0228852	+	0.0396383i	−0.877241	−	0.480050i	$-0.840619\pi$
$691$	−415.692	+	720.000i	−0.0228852	+	0.0396383i	0.854356	+	0.519688i	$0.173952\pi$
$692$	−6435.00	+	11145.7i	−0.353500	+	0.612280i
$693$	2208.00	+	3824.37i	0.121032	+	0.209633i
$694$	12065.5			0.659941
$695$	204.382	+	354.000i	0.0111549	+	0.0193208i
$696$	3174.85	+	5499.00i	0.172906	+	0.299481i
$697$	31816.0			1.72901
$698$	−5760.00	−	9976.61i	−0.312348	−	0.541003i
$699$	−5850.00	+	10132.5i	−0.316548	+	0.548278i
$700$	−4226.20	+	7320.00i	−0.228194	+	0.395243i
$701$	−30186.0			−1.62640			−0.813202	−	0.581981i	$-0.802278\pi$
$701$	−30186.0			−1.62640			−0.813202	+	0.581981i	$0.802278\pi$
$702$		0			0
$703$	16434.0			0.881679
$704$	−2126.96	+	3684.00i	−0.113868	+	0.197224i
$705$	−522.000	+	904.131i	−0.0278860	+	0.0483000i
$706$	−4876.50	−	8446.35i	−0.259957	−	0.450258i
$707$	−5944.40			−0.316212
$708$	1420.28	+	2460.00i	0.0753919	+	0.130583i
$709$	−5940.07	−	10288.5i	−0.314646	−	0.544983i	0.664716	−	0.747096i	$-0.268552\pi$
$709$	−5940.07	−	10288.5i	−0.314646	−	0.544983i	−0.979362	+	0.202113i	$0.935219\pi$
$710$	3169.65			0.167542
$711$	14674.0	+	25416.1i	0.774006	+	1.34062i
$712$	10998.0	−	19049.1i	0.578887	−	1.00266i
$713$	−6079.50	+	10530.0i	−0.319325	+	0.553088i
$714$	5616.00			0.294361
$715$		0			0
$716$	18720.0			0.977094
$717$	5383.21	−	9324.00i	0.280390	−	0.485650i
$718$	6174.00	−	10693.7i	0.320908	−	0.555828i
$719$	9204.00	+	15941.8i	0.477401	+	0.826883i	0.999665	−	0.0259014i	$-0.00824561\pi$
$719$	9204.00	+	15941.8i	0.477401	+	0.826883i	−0.522264	+	0.852784i	$0.674912\pi$
$720$	39.8372			0.00206201
$721$	1260.93	+	2184.00i	0.0651312	+	0.112811i
$722$	5377.15	+	9313.50i	0.277170	+	0.480073i
$723$	−9834.58			−0.505881
$724$	1592.50	+	2758.29i	0.0817470	+	0.141590i
$725$	−8601.00	+	14897.4i	−0.440597	+	0.763137i
$726$	−1972.81	+	3417.00i	−0.100851	+	0.174679i
$727$	−21112.0			−1.07703			−0.538515	−	0.842616i	$-0.681014\pi$
$727$	−21112.0			−1.07703			−0.538515	+	0.842616i	$0.681014\pi$
$728$		0			0
$729$	−4283.00			−0.217599
$730$	688.490	−	1192.50i	0.0349071	−	0.0604608i
$731$	−6084.00	+	10537.8i	−0.307832	+	0.533180i
$732$	725.000	+	1255.74i	0.0366076	+	0.0634062i
$733$	−23959.5			−1.20732			−0.603658	−	0.797243i	$-0.706291\pi$
$733$	−23959.5			−1.20732			−0.603658	+	0.797243i	$0.706291\pi$
$734$	1.73205	+	3.00000i	8.70997e−5	+	0.000150861i
$735$	−261.540	−	453.000i	−0.0131252	−	0.0227335i
$736$	−14185.5			−0.710441
$737$	−5448.00	−	9436.21i	−0.272293	−	0.471625i
$738$	5416.50	−	9381.65i	0.270168	−	0.467945i
$739$	−1583.09	+	2742.00i	−0.0788025	+	0.136490i	−0.902734	−	0.430200i	$-0.858443\pi$
$739$	−1583.09	+	2742.00i	−0.0788025	+	0.136490i	0.823931	+	0.566690i	$0.191776\pi$
$740$	−1245.00			−0.0618474
$741$		0			0
$742$	−2232.00			−0.110430
$743$	−15051.5	+	26070.0i	−0.743185	+	1.28723i	0.207852	+	0.978160i	$0.433353\pi$
$743$	−15051.5	+	26070.0i	−0.743185	+	1.28723i	−0.951038	+	0.309075i	$0.899981\pi$
$744$	−3510.00	+	6079.50i	−0.172961	+	0.299577i
$745$	−40.5000	−	70.1481i	−0.00199168	−	0.00344970i
$746$	−6060.45			−0.297438
$747$	−9082.87	−	15732.0i	−0.444880	−	0.770554i
$748$	−4053.00	−	7020.00i	−0.198118	−	0.343151i
$749$	−20867.7			−1.01801
$750$	741.000	+	1283.45i	0.0360767	+	0.0624866i
$751$	14248.0	−	24678.3i	0.692299	−	1.19910i	−0.278783	−	0.960354i	$-0.589931\pi$
$751$	14248.0	−	24678.3i	0.692299	−	1.19910i	0.971083	−	0.238744i	$-0.0767356\pi$
$752$	150.688	−	261.000i	0.00730724	−	0.0126565i
$753$	7956.00			0.385037
$754$		0			0
$755$	−3066.00			−0.147792
$756$	−3464.10	+	6000.00i	−0.166651	+	0.288648i
$757$	−8711.00	+	15087.9i	−0.418239	+	0.724411i	−0.995762	−	0.0919633i	$-0.970686\pi$
$757$	−8711.00	+	15087.9i	−0.418239	+	0.724411i	0.577524	+	0.816374i	$0.304019\pi$
$758$	−4779.00	−	8277.47i	−0.228999	−	0.396638i
$759$	2161.60			0.103374
$760$	−2229.15	−	3861.00i	−0.106394	−	0.184281i
$761$	20663.4	+	35790.0i	0.984292	+	1.70484i	0.645040	+	0.764149i	$0.276841\pi$
$761$	20663.4	+	35790.0i	0.984292	+	1.70484i	0.339252	+	0.940695i	$0.389826\pi$
$762$	990.733			0.0471004
$763$	−10752.0	−	18623.0i	−0.510155	−	0.883615i
$764$	−6495.00	+	11249.7i	−0.307567	+	0.532721i
$765$	2330.47	−	4036.50i	0.110142	−	0.190771i
$766$	12756.0			0.601688
$767$		0			0
$768$	−8110.00			−0.381047
$769$	−7035.59	+	12186.0i	−0.329922	+	0.571441i	−0.982496	−	0.186283i	$-0.940356\pi$
$769$	−7035.59	+	12186.0i	−0.329922	+	0.571441i	0.652574	+	0.757725i	$0.273689\pi$
$770$	−288.000	+	498.831i	−0.0134790	+	0.0233462i
$771$	2067.00	+	3580.15i	0.0965515	+	0.167232i
$772$	−5585.86			−0.260414
$773$	−100.459	−	174.000i	−0.00467433	−	0.00809618i	0.863679	−	0.504043i	$-0.168155\pi$
$773$	−100.459	−	174.000i	−0.00467433	−	0.00809618i	−0.868353	+	0.495946i	$0.834821\pi$
$774$	2071.53	+	3588.00i	0.0962012	+	0.166625i
$775$	−19017.9			−0.881476
$776$	−2262.00	−	3917.90i	−0.104641	−	0.181243i
$777$	1992.00	−	3450.25i	0.0919725	−	0.159301i
$778$	1047.02	−	1813.50i	0.0482489	−	0.0835696i
$779$	31086.0			1.42975
$780$		0			0
$781$	14640.0			0.670756
$782$	−7903.35	+	13689.0i	−0.361411	+	0.625982i
$783$	−7050.00	+	12211.0i	−0.321771	+	0.557323i
$784$	75.5000	+	130.770i	0.00343932	+	0.00595708i
$785$	−2097.51			−0.0953675
$786$	−3419.07	−	5922.00i	−0.155158	−	0.268741i
$787$	−3451.98	−	5979.00i	−0.156353	−	0.270811i	0.777198	−	0.629256i	$-0.216640\pi$
$787$	−3451.98	−	5979.00i	−0.156353	−	0.270811i	−0.933551	+	0.358445i	$0.883307\pi$
$788$	10253.7			0.463546
$789$	2052.00	+	3554.17i	0.0925895	+	0.160370i
$790$	−1914.00	+	3315.15i	−0.0861988	+	0.149301i
$791$	4759.68	−	8244.00i	0.213950	−	0.370573i
$792$	−7176.00			−0.321955
$793$		0			0
$794$	20256.0			0.905363
$795$	161.081	−	279.000i	0.00718609	−	0.0124467i
$796$	6305.00	−	10920.6i	0.280747	−	0.486268i
$797$	−15639.0	−	27087.5i	−0.695059	−	1.20388i	−0.970161	−	0.242462i	$-0.922045\pi$
$797$	−15639.0	−	27087.5i	−0.695059	−	1.20388i	0.275102	−	0.961415i	$-0.411288\pi$
$798$	5487.14			0.243412
$799$	−17630.5	−	30537.0i	−0.780631	−	1.35209i
$800$	−11093.8	−	19215.0i	−0.490281	−	0.849191i
$801$	22468.2			0.991103
$802$	−2581.50	−	4471.29i	−0.113661	−	0.196866i
$803$	3180.00	−	5507.92i	0.139751	−	0.242055i
$804$	3931.76	−	6810.00i	0.172466	−	0.298719i
$805$	−1872.00			−0.0819619
$806$		0			0
$807$	6660.00			0.290512
$808$	4829.82	−	8365.50i	0.210288	−	0.364229i
$809$	−4024.50	+	6970.64i	−0.174900	+	0.302935i	−0.940127	−	0.340826i	$-0.889293\pi$
$809$	−4024.50	+	6970.64i	−0.174900	+	0.302935i	0.765227	+	0.643761i	$0.222627\pi$
$810$	−631.500	−	1093.79i	−0.0273934	−	0.0474467i
$811$	14026.1			0.607305			0.303653	−	0.952783i	$-0.401794\pi$
$811$	14026.1			0.607305			0.303653	+	0.952783i	$0.401794\pi$
$812$	−4884.38	−	8460.00i	−0.211094	−	0.365625i
$813$	−2805.92	−	4860.00i	−0.121043	−	0.209653i
$814$	3450.25			0.148564
$815$	870.000	+	1506.88i	0.0373924	+	0.0647655i
$816$	117.000	−	202.650i	0.00501939	−	0.00869383i
$817$	−5944.40	+	10296.0i	−0.254551	+	0.440895i
$818$	−75.0000			−0.00320576
$819$		0			0
$820$	−2355.00			−0.100293
$821$	−4018.36	+	6960.00i	−0.170818	+	0.295866i	−0.938706	−	0.344718i	$-0.887974\pi$
$821$	−4018.36	+	6960.00i	−0.170818	+	0.295866i	0.767888	+	0.640584i	$0.221308\pi$
$822$	1467.00	−	2540.92i	0.0622476	−	0.107816i
$823$	−20150.0	−	34900.8i	−0.853445	−	1.47821i	−0.878081	−	0.478513i	$-0.841176\pi$
$823$	−20150.0	−	34900.8i	−0.853445	−	1.47821i	0.0246361	−	0.999696i	$-0.492157\pi$
$824$	−4098.03			−0.173255
$825$	1690.48	+	2928.00i	0.0713394	+	0.123563i
$826$	3408.68	+	5904.00i	0.143587	+	0.248700i
$827$	−39525.4			−1.66195			−0.830975	−	0.556310i	$-0.812217\pi$
$827$	−39525.4			−1.66195			−0.830975	+	0.556310i	$0.812217\pi$
$828$	−4485.00	−	7768.25i	−0.188242	−	0.326045i
$829$	−6155.50	+	10661.6i	−0.257888	+	0.446676i	−0.965676	−	0.259750i	$-0.916360\pi$
$829$	−6155.50	+	10661.6i	−0.257888	+	0.446676i	0.707788	+	0.706425i	$0.249693\pi$
$830$	1184.72	−	2052.00i	0.0495450	−	0.0858144i
$831$	−754.000			−0.0314753
$832$		0			0
$833$	17667.0			0.734844
$834$	408.764	−	708.000i	0.0169716	−	0.0293957i
$835$	792.000	−	1371.78i	0.0328243	−	0.0568534i
$836$	−3960.00	−	6858.92i	−0.163827	−	0.283757i
$837$	−15588.5			−0.643747
$838$	−8194.33	−	14193.0i	−0.337791	−	0.585070i
$839$	10733.5	+	18591.0i	0.441671	+	0.764997i	0.997814	−	0.0660899i	$-0.0210524\pi$
$839$	10733.5	+	18591.0i	0.441671	+	0.764997i	−0.556142	+	0.831087i	$0.687719\pi$
$840$	−1080.80			−0.0443942
$841$	2254.00	+	3904.04i	0.0924187	+	0.160074i
$842$	6121.50	−	10602.7i	0.250547	−	0.433961i
$843$	−36.3731	+	63.0000i	−0.00148607	+	0.00257394i
$844$	−5210.00			−0.212483
$845$		0			0
$846$	−12006.0			−0.487913
$847$	7891.22	−	13668.0i	0.320125	−	0.554472i
$848$	−46.5000	+	80.5404i	−0.00188304	+	0.00326152i
$849$	−7124.00	−	12339.1i	−0.287980	−	0.498796i
$850$	−24723.3			−0.997649
$851$	5606.65	+	9711.00i	0.225844	+	0.391174i
$852$	5282.75	+	9150.00i	0.212423	+	0.367927i
$853$	−774.227			−0.0310774			−0.0155387	−	0.999879i	$-0.504946\pi$
$853$	−774.227			−0.0310774			−0.0155387	+	0.999879i	$0.504946\pi$
$854$	1740.00	+	3013.77i	0.0697208	+	0.120760i
$855$	2277.00	−	3943.88i	0.0910781	−	0.157752i
$856$	16955.0	−	29367.0i	0.676999	−	1.17260i
$857$	−13923.0			−0.554960			−0.277480	−	0.960731i	$-0.589499\pi$
$857$	−13923.0			−0.554960			−0.277480	+	0.960731i	$0.589499\pi$
$858$		0			0
$859$	−22358.0			−0.888062			−0.444031	−	0.896011i	$-0.646452\pi$
$859$	−22358.0			−0.888062			−0.444031	+	0.896011i	$0.646452\pi$
$860$	450.333	−	780.000i	0.0178561	−	0.0309277i
$861$	3768.00	−	6526.37i	0.149144	−	0.258325i
$862$	8598.00	+	14892.2i	0.339732	+	0.588433i
$863$	−2230.88			−0.0879955			−0.0439977	−	0.999032i	$-0.514009\pi$
$863$	−2230.88			−0.0879955			−0.0439977	+	0.999032i	$0.514009\pi$
$864$	−9093.27	−	15750.0i	−0.358055	−	0.620169i
$865$	−2229.15	−	3861.00i	−0.0876224	−	0.151766i
$866$	−11461.0			−0.449723
$867$	−8776.00	−	15200.5i	−0.343770	−	0.595427i
$868$	5400.00	−	9353.07i	0.211161	−	0.365742i
$869$	−8840.39	+	15312.0i	−0.345097	+	0.597726i
$870$	−846.000			−0.0329679
$871$		0			0
$872$	34944.0			1.35706
$873$	2310.56	−	4002.00i	0.0895767	−	0.155151i
$874$	−7722.00	+	13374.9i	−0.298856	+	0.517635i
$875$	−2964.00	−	5133.80i	−0.114516	−	0.198348i
$876$	4589.93			0.177031
$877$	8377.06	+	14509.5i	0.322547	+	0.558667i	0.981013	−	0.193943i	$-0.0621278\pi$
$877$	8377.06	+	14509.5i	0.322547	+	0.558667i	−0.658466	+	0.752610i	$0.728794\pi$
$878$	−12114.0	−	20982.0i	−0.465634	−	0.806501i
$879$	16645.0			0.638706
$880$	12.0000	+	20.7846i	0.000459682	+	0.000796192i
$881$	8677.50	−	15029.9i	0.331842	−	0.574766i	−0.651031	−	0.759051i	$-0.725663\pi$
$881$	8677.50	−	15029.9i	0.331842	−	0.574766i	0.982873	+	0.184284i	$0.0589967\pi$
$882$	3007.71	−	5209.50i	0.114824	−	0.198881i
$883$	46982.0			1.79057			0.895283	−	0.445497i	$-0.146973\pi$
$883$	46982.0			1.79057			0.895283	+	0.445497i	$0.146973\pi$
$884$		0			0
$885$	−984.000			−0.0373749
$886$	1735.51	−	3006.00i	0.0658079	−	0.113983i
$887$	4458.00	−	7721.48i	0.168754	−	0.292291i	−0.769228	−	0.638975i	$-0.779359\pi$
$887$	4458.00	−	7721.48i	0.168754	−	0.292291i	0.937982	+	0.346684i	$0.112692\pi$
$888$	3237.00	+	5606.65i	0.122327	+	0.211877i
$889$	−3962.93			−0.149508
$890$	1465.31	+	2538.00i	0.0551882	+	0.0955887i
$891$	−2916.77	−	5052.00i	−0.109670	−	0.189953i
$892$	−12037.8			−0.451854
$893$	−17226.0	−	29836.3i	−0.645516	−	1.11807i
$894$	−81.0000	+	140.296i	−0.00303025	+	0.00524855i
$895$	−3242.40	+	5616.00i	−0.121097	+	0.209745i
$896$	12792.0			0.476954
$897$		0			0
$898$	15732.0			0.584614
$899$	10989.9	−	19035.0i	0.407711	−	0.706177i
$900$	7015.00	−	12150.3i	0.259815	−	0.450012i
$901$	5440.50	+	9423.22i	0.201165	+	0.348427i
$902$	6526.37			0.240914
$903$	1441.07	+	2496.00i	0.0531071	+	0.0919841i
$904$	7734.47	+	13396.5i	0.284563	+	0.492877i
$905$	−1103.32			−0.0405254
$906$	3066.00	+	5310.47i	0.112429	+	0.194733i
$907$	−15418.0	+	26704.8i	−0.564439	+	0.977637i	0.432662	+	0.901556i	$0.357574\pi$
$907$	−15418.0	+	26704.8i	−0.564439	+	0.977637i	−0.997102	+	0.0760813i	$0.975759\pi$
$908$	6018.88	−	10425.0i	0.219982	−	0.381020i
$909$	9867.00			0.360031
$910$		0			0
$911$	−27480.0			−0.999400			−0.499700	−	0.866199i	$-0.666556\pi$
$911$	−27480.0			−0.999400			−0.499700	+	0.866199i	$0.666556\pi$
$912$	114.315	−	198.000i	0.00415061	−	0.00718907i
$913$	5472.00	−	9477.78i	0.198354	−	0.343558i
$914$	−2185.50	−	3785.40i	−0.0790918	−	0.136991i
$915$	−502.295			−0.0181479
$916$	−6270.02	−	10860.0i	−0.226165	−	0.391730i
$917$	13676.3	+	23688.0i	0.492509	+	0.853050i
$918$	−20265.0			−0.728589
$919$	14221.0	+	24631.5i	0.510454	+	0.884133i	0.999927	+	0.0121140i	$0.00385609\pi$
$919$	14221.0	+	24631.5i	0.510454	+	0.884133i	−0.489472	+	0.872019i	$0.662811\pi$
$920$	1521.00	−	2634.45i	0.0545064	−	0.0944078i
$921$	−2220.49	+	3846.00i	−0.0794437	+	0.137600i
$922$	−33927.0			−1.21185
$923$		0			0
$924$	−1920.00			−0.0683586
$925$	−8769.37	+	15189.0i	−0.311714	+	0.539904i
$926$	−7476.00	+	12948.8i	−0.265310	+	0.459530i
$927$	−2093.00	−	3625.18i	−0.0741566	−	0.128443i
$928$	25643.0			0.907083
$929$	−3489.22	−	6043.50i	−0.123227	−	0.213435i	0.797812	−	0.602907i	$-0.205991\pi$
$929$	−3489.22	−	6043.50i	−0.123227	−	0.213435i	−0.921038	+	0.389472i	$0.872658\pi$
$930$	−467.654	−	810.000i	−0.0164892	−	0.0285602i
$931$	17261.6			0.607655
$932$	14625.0	+	25331.2i	0.514011	+	0.890292i
$933$	4914.00	−	8511.30i	0.172430	−	0.298657i
$934$	−4728.50	+	8190.00i	−0.165654	+	0.286922i
$935$	2808.00			0.0982154
$936$		0			0
$937$	−38465.0			−1.34109			−0.670543	−	0.741871i	$-0.733939\pi$
$937$	−38465.0			−1.34109			−0.670543	+	0.741871i	$0.733939\pi$
$938$	9436.21	−	16344.0i	0.328468	−	0.568924i
$939$	518.000	−	897.202i	0.0180024	−	0.0311811i
$940$	1305.00	+	2260.33i	0.0452813	+	0.0784295i
$941$	4884.38			0.169210			0.0846049	−	0.996415i	$-0.473037\pi$
$941$	4884.38			0.169210			0.0846049	+	0.996415i	$0.473037\pi$
$942$	2097.51	+	3633.00i	0.0725485	+	0.125658i
$943$	10605.3	+	18369.0i	0.366233	+	0.634334i
$944$	284.056			0.00979369
$945$	−1200.00	−	2078.46i	−0.0413079	−	0.0715475i
$946$	−1248.00	+	2161.60i	−0.0428922	+	0.0742914i
$947$	−10882.5	+	18849.0i	−0.373424	+	0.646790i	−0.990090	−	0.140435i	$-0.955150\pi$
$947$	−10882.5	+	18849.0i	−0.373424	+	0.646790i	0.616665	+	0.787225i	$0.288483\pi$
$948$	−12760.0			−0.437158
$949$		0			0
$950$	−24156.0			−0.824973
$951$	−3916.17	+	6783.00i	−0.133534	+	0.231287i
$952$	18252.0	−	31613.4i	0.621377	−	1.07626i
$953$	3237.00	+	5606.65i	0.110028	+	0.190574i	0.915781	−	0.401677i	$-0.131573\pi$
$953$	3237.00	+	5606.65i	0.110028	+	0.190574i	−0.805753	+	0.592251i	$0.798239\pi$
$954$	3704.86			0.125733
$955$	−2249.93	−	3897.00i	−0.0762368	−	0.132046i
$956$	−13458.0	−	23310.0i	−0.455297	−	0.788598i
$957$	−3907.51			−0.131987
$958$	−2211.00	−	3829.56i	−0.0745659	−	0.129152i
$959$	−5868.00	+	10163.7i	−0.197589	+	0.342234i
$960$	531.740	−	921.000i	0.0178769	−	0.0309637i
$961$	−5491.00			−0.184317
$962$		0			0
$963$	34638.0			1.15908
$964$	−12293.2	+	21292.5i	−0.410724	+	0.711395i
$965$	967.500	−	1675.76i	0.0322745	−	0.0559011i
$966$	1872.00	+	3242.40i	0.0623505	+	0.107994i
$967$	7541.35			0.250789			0.125395	−	0.992107i	$-0.459980\pi$
$967$	7541.35			0.250789			0.125395	+	0.992107i	$0.459980\pi$
$968$	12823.2	+	22210.5i	0.425779	+	0.737472i
$969$	−13374.9	−	23166.0i	−0.443409	−	0.768007i
$970$	602.754			0.0199518
$971$	−17499.0	−	30309.2i	−0.578342	−	1.00172i	−0.995670	−	0.0929611i	$-0.970367\pi$
$971$	−17499.0	−	30309.2i	−0.578342	−	1.00172i	0.417328	−	0.908756i	$-0.362967\pi$
$972$	8855.00	−	15337.3i	0.292206	−	0.506116i
$973$	−1635.06	+	2832.00i	−0.0538720	+	0.0933091i
$974$	−18756.0			−0.617024
$975$		0			0
$976$	145.000			0.00475547
$977$	−12608.5	+	21838.5i	−0.412877	+	0.715123i	−0.995203	−	0.0978318i	$-0.968809\pi$
$977$	−12608.5	+	21838.5i	−0.412877	+	0.715123i	0.582326	+	0.812955i	$0.302143\pi$
$978$	1740.00	−	3013.77i	0.0568907	−	0.0985375i
$979$	6768.00	+	11722.5i	0.220946	+	0.382690i
$980$	−1307.70			−0.0426254
$981$	17847.1	+	30912.0i	0.580849	+	1.00606i
$982$	−9862.30	−	17082.0i	−0.320487	−	0.555100i
$983$	56440.6			1.83131			0.915654	−	0.401967i	$-0.131673\pi$
$983$	56440.6			1.83131			0.915654	+	0.401967i	$0.131673\pi$
$984$	6123.00	+	10605.3i	0.198368	+	0.343583i
$985$	−1776.00	+	3076.12i	−0.0574498	+	0.0995060i
$986$	14286.8	−	24745.5i	0.461445	−	0.799247i
$987$	−8352.00			−0.269349
$988$		0			0
$989$	−8112.00			−0.260816
$990$	478.046	−	828.000i	0.0153468	−	0.0265814i
$991$	−29641.0	+	51339.7i	−0.950129	+	1.64567i	−0.204987	+	0.978765i	$0.565715\pi$
$991$	−29641.0	+	51339.7i	−0.950129	+	1.64567i	−0.745142	+	0.666906i	$0.767618\pi$
$992$	14175.0	+	24551.8i	0.453686	+	0.785808i
$993$	−14909.5			−0.476474
$994$	12678.6	+	21960.0i	0.404569	+	0.700733i
$995$	2184.12	+	3783.00i	0.0695891	+	0.120532i
$996$	7898.15			0.251268
$997$	18855.5	+	32658.7i	0.598957	+	1.03742i	0.992975	+	0.118321i	$0.0377511\pi$
$997$	18855.5	+	32658.7i	0.598957	+	1.03742i	−0.394019	+	0.919102i	$0.628916\pi$
$998$	−15309.0	+	26516.0i	−0.485569	+	0.841030i
$999$	−7188.01	+	12450.0i	−0.227646	+	0.394295i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.4.c.h.22.2		4
13.2	odd	12		13.4.e.b.10.1	yes	2
13.3	even	3	inner	169.4.c.h.146.2		4
13.4	even	6		169.4.a.i.1.2		2
13.5	odd	4		169.4.e.a.147.1		2
13.6	odd	12		169.4.b.d.168.2		2
13.7	odd	12		169.4.b.d.168.1		2
13.8	odd	4		13.4.e.b.4.1	✓	2
13.9	even	3		169.4.a.i.1.1		2
13.10	even	6	inner	169.4.c.h.146.1		4
13.11	odd	12		169.4.e.a.23.1		2
13.12	even	2	inner	169.4.c.h.22.1		4
39.2	even	12		117.4.q.a.10.1		2
39.8	even	4		117.4.q.a.82.1		2
39.17	odd	6		1521.4.a.o.1.1		2
39.35	odd	6		1521.4.a.o.1.2		2
52.15	even	12		208.4.w.b.49.1		2
52.47	even	4		208.4.w.b.17.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.4.e.b.4.1	✓	2	13.8	odd	4
13.4.e.b.10.1	yes	2	13.2	odd	12
117.4.q.a.10.1		2	39.2	even	12
117.4.q.a.82.1		2	39.8	even	4
169.4.a.i.1.1		2	13.9	even	3
169.4.a.i.1.2		2	13.4	even	6
169.4.b.d.168.1		2	13.7	odd	12
169.4.b.d.168.2		2	13.6	odd	12
169.4.c.h.22.1		4	13.12	even	2	inner
169.4.c.h.22.2		4	1.1	even	1	trivial
169.4.c.h.146.1		4	13.10	even	6	inner
169.4.c.h.146.2		4	13.3	even	3	inner
169.4.e.a.23.1		2	13.11	odd	12
169.4.e.a.147.1		2	13.5	odd	4
208.4.w.b.17.1		2	52.47	even	4
208.4.w.b.49.1		2	52.15	even	12
1521.4.a.o.1.1		2	39.17	odd	6
1521.4.a.o.1.2		2	39.35	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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	169.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 1.50000i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(2.50000 + 4.33013i) q^{4} -1.73205 q^{5} +(1.73205 + 3.00000i) q^{6} +(-6.92820 - 12.0000i) q^{7} +22.5167 q^{8} +(11.5000 + 19.9186i) q^{9} +(-1.50000 + 2.59808i) q^{10} +(-6.92820 + 12.0000i) q^{11} -10.0000 q^{12} -24.0000 q^{14} +(1.73205 - 3.00000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(58.5000 + 101.325i) q^{17} +39.8372 q^{18} +(57.1577 + 99.0000i) q^{19} +(-4.33013 - 7.50000i) q^{20} +27.7128 q^{21} +(12.0000 + 20.7846i) q^{22} +(-39.0000 + 67.5500i) q^{23} +(-22.5167 + 39.0000i) q^{24} -122.000 q^{25} -100.000 q^{27} +(34.6410 - 60.0000i) q^{28} +(70.5000 - 122.110i) q^{29} +(-3.00000 - 5.19615i) q^{30} +155.885 q^{31} +(90.9327 + 157.500i) q^{32} +(-13.8564 - 24.0000i) q^{33} +202.650 q^{34} +(12.0000 + 20.7846i) q^{35} +(-57.5000 + 99.5929i) q^{36} +(71.8801 - 124.500i) q^{37} +198.000 q^{38} -39.0000 q^{40} +(135.966 - 235.500i) q^{41} +(24.0000 - 41.5692i) q^{42} +(52.0000 + 90.0666i) q^{43} -69.2820 q^{44} +(-19.9186 - 34.5000i) q^{45} +(67.5500 + 117.000i) q^{46} -301.377 q^{47} +(-1.00000 - 1.73205i) q^{48} +(75.5000 - 130.770i) q^{49} +(-105.655 + 183.000i) q^{50} -234.000 q^{51} +93.0000 q^{53} +(-86.6025 + 150.000i) q^{54} +(12.0000 - 20.7846i) q^{55} +(-156.000 - 270.200i) q^{56} -228.631 q^{57} +(-122.110 - 211.500i) q^{58} +(-142.028 - 246.000i) q^{59} +17.3205 q^{60} +(-72.5000 - 125.574i) q^{61} +(135.000 - 233.827i) q^{62} +(159.349 - 276.000i) q^{63} +307.000 q^{64} -48.0000 q^{66} +(-393.176 + 681.000i) q^{67} +(-292.500 + 506.625i) q^{68} +(-78.0000 - 135.100i) q^{69} +41.5692 q^{70} +(-528.275 - 915.000i) q^{71} +(258.942 + 448.500i) q^{72} -458.993 q^{73} +(-124.500 - 215.640i) q^{74} +(122.000 - 211.310i) q^{75} +(-285.788 + 495.000i) q^{76} +192.000 q^{77} +1276.00 q^{79} +(0.866025 - 1.50000i) q^{80} +(-210.500 + 364.597i) q^{81} +(-235.500 - 407.898i) q^{82} -789.815 q^{83} +(69.2820 + 120.000i) q^{84} +(-101.325 - 175.500i) q^{85} +180.133 q^{86} +(141.000 + 244.219i) q^{87} +(-156.000 + 270.200i) q^{88} +(488.438 - 846.000i) q^{89} -69.0000 q^{90} -390.000 q^{92} +(-155.885 + 270.000i) q^{93} +(-261.000 + 452.065i) q^{94} +(-99.0000 - 171.473i) q^{95} -363.731 q^{96} +(-100.459 - 174.000i) q^{97} +(-130.770 - 226.500i) q^{98} -318.697 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 10 q^{4} + 46 q^{9} - 6 q^{10} - 40 q^{12} - 96 q^{14} - 2 q^{16} + 234 q^{17} + 48 q^{22} - 156 q^{23} - 488 q^{25} - 400 q^{27} + 282 q^{29} - 12 q^{30} + 48 q^{35} - 230 q^{36} + 792 q^{38}+ \cdots - 396 q^{95}+O(q^{100}) \) 4 * q - 4 * q^3 + 10 * q^4 + 46 * q^9 - 6 * q^10 - 40 * q^12 - 96 * q^14 - 2 * q^16 + 234 * q^17 + 48 * q^22 - 156 * q^23 - 488 * q^25 - 400 * q^27 + 282 * q^29 - 12 * q^30 + 48 * q^35 - 230 * q^36 + 792 * q^38 - 156 * q^40 + 96 * q^42 + 208 * q^43 - 4 * q^48 + 302 * q^49 - 936 * q^51 + 372 * q^53 + 48 * q^55 - 624 * q^56 - 290 * q^61 + 540 * q^62 + 1228 * q^64 - 192 * q^66 - 1170 * q^68 - 312 * q^69 - 498 * q^74 + 488 * q^75 + 768 * q^77 + 5104 * q^79 - 842 * q^81 - 942 * q^82 + 564 * q^87 - 624 * q^88 - 276 * q^90 - 1560 * q^92 - 1044 * q^94 - 396 * q^95

Introduction

L-functions

Modular forms

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Database

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