LMFDB - Embedded newform 169.4.c.h.22.1

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			22.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	169.22
Dual form			169.4.c.h.146.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 1.50000i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(2.50000 + 4.33013i) q^{4} +1.73205 q^{5} +(-1.73205 - 3.00000i) q^{6} +(6.92820 + 12.0000i) q^{7} -22.5167 q^{8} +(11.5000 + 19.9186i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 4 * q - 4 * q^3 + 10 * q^4 + 46 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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	−0.977525	−	0.210821i	$-0.932386\pi$
$2$	−0.866025	+	1.50000i	−0.306186	+	0.530330i	0.671339	+	0.741151i	$0.265720\pi$
$3$	−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	$-0.475319\pi$
$5$	1.73205			0.154919			0.0774597	+	0.996995i	$0.475319\pi$
$6$	−1.73205	−	3.00000i	−0.117851	−	0.204124i
$7$	6.92820	+	12.0000i	0.374088	+	0.647939i	0.990190	−	0.139727i	$-0.0446225\pi$
$7$	6.92820	+	12.0000i	0.374088	+	0.647939i	−0.616102	+	0.787666i	$0.711289\pi$
$8$	−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	−0.755315	−	0.655362i	$-0.772516\pi$
$11$	6.92820	−	12.0000i	0.189903	−	0.328921i	0.945218	+	0.326441i	$0.105849\pi$
$12$	−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	$-0.924211\pi$
$19$	−57.1577	−	99.0000i	−0.690151	−	1.19538i	0.281637	−	0.959521i	$-0.409123\pi$
$20$	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	$-0.649138\pi$
$31$	−155.885			−0.903151			−0.451576	+	0.892233i	$0.649138\pi$
$32$	−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	−0.980359	−	0.197223i	$-0.936808\pi$
$37$	−71.8801	+	124.500i	−0.319379	+	0.553180i	0.660980	+	0.750404i	$0.270141\pi$
$38$	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	$0.339957\pi$
$41$	−135.966	+	235.500i	−0.517910	+	0.897047i	−0.999784	+	0.0208059i	$0.993377\pi$
$42$	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	$-0.345096\pi$
$47$	301.377			0.935326			0.467663	+	0.883907i	$0.345096\pi$
$48$	−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	0.979096	−	0.203400i	$-0.0651992\pi$
$59$	142.028	+	246.000i	0.313398	+	0.542822i	−0.665698	+	0.746222i	$0.731866\pi$
$60$	−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	$-0.578882\pi$
$67$	393.176	−	681.000i	0.716926	−	1.24175i	0.962212	−	0.272301i	$-0.0877848\pi$
$68$	−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	$0.177830\pi$
$71$	528.275	+	915.000i	0.883025	+	1.52944i	0.0350641	+	0.999385i	$0.488836\pi$
$72$	−258.942	−	448.500i	−0.423841	−	0.734114i
$73$	458.993			0.735906			0.367953	−	0.929844i	$-0.380059\pi$
$73$	458.993			0.735906			0.367953	+	0.929844i	$0.380059\pi$
$74$	−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	$-0.325093\pi$
$83$	789.815			1.04450			0.522250	+	0.852793i	$0.325093\pi$
$84$	−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	$0.364292\pi$
$89$	−488.438	+	846.000i	−0.581734	+	1.00759i	−0.995274	+	0.0971073i	$0.969041\pi$
$90$	−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	0.913802	−	0.406161i	$-0.133133\pi$
$97$	100.459	+	174.000i	0.105155	+	0.182134i	−0.808646	+	0.588295i	$0.799799\pi$
$98$	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	$-0.738831\pi$
$109$	−1551.92			−1.36373			−0.681866	+	0.731477i	$0.738831\pi$
$110$	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	0.967326	−	0.253536i	$-0.0815937\pi$
$137$	423.486	+	733.500i	0.264094	+	0.457424i	−0.703232	+	0.710961i	$0.748260\pi$
$138$	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	0.859526	−	0.511093i	$-0.170759\pi$
$149$	−23.3827	−	40.5000i	−0.0128563	−	0.0222677i	−0.872382	+	0.488825i	$0.837426\pi$
$150$	211.310	+	366.000i	0.115023	+	0.199225i
$151$	−1770.16			−0.953995			−0.476998	−	0.878905i	$-0.658275\pi$
$151$	−1770.16			−0.953995			−0.476998	+	0.878905i	$0.658275\pi$
$152$	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	0.961104	−	0.276187i	$-0.0890710\pi$
$163$	502.295	+	870.000i	0.241367	+	0.418059i	−0.719737	+	0.694247i	$0.755738\pi$
$164$	−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	−0.740423	−	0.672141i	$-0.765375\pi$
$167$	457.261	−	792.000i	0.211880	−	0.366987i	0.952303	+	0.305154i	$0.0987081\pi$
$168$	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	−0.742858	−	0.669449i	$-0.766530\pi$
$193$	558.586	−	967.500i	0.208331	−	0.360840i	0.951189	+	0.308609i	$0.0998635\pi$
$194$	−348.000			−0.128788
$195$		0			0
$196$	755.000			0.275146
$197$	−1025.37	+	1776.00i	−0.370837	+	0.642308i	−0.989695	−	0.143195i	$-0.954262\pi$
$197$	−1025.37	+	1776.00i	−0.370837	+	0.642308i	0.618858	+	0.785503i	$0.287596\pi$
$198$	−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	−0.626722	−	0.779243i	$-0.715604\pi$
$223$	1203.78	−	2085.00i	0.361483	−	0.626107i	0.988205	+	0.153136i	$0.0489371\pi$
$224$	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	0.986595	−	0.163190i	$-0.0521783\pi$
$227$	1203.78	+	2085.00i	0.351971	+	0.609631i	−0.634624	+	0.772821i	$0.718845\pi$
$228$	571.577	+	990.000i	0.166025	+	0.287563i
$229$	2508.01			0.723729			0.361864	−	0.932231i	$-0.382140\pi$
$229$	2508.01			0.723729			0.361864	+	0.932231i	$0.382140\pi$
$230$	−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	$-0.240229\pi$
$239$	5383.21			1.45695			0.728475	+	0.685072i	$0.240229\pi$
$240$	−1.73205	−	3.00000i	−0.000465847	−	0.000806872i
$241$	−2458.65	−	4258.50i	−0.657159	−	1.13823i	−0.981348	−	0.192240i	$-0.938425\pi$
$241$	−2458.65	−	4258.50i	−0.657159	−	1.13823i	0.324189	−	0.945992i	$-0.394909\pi$
$242$	−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	−0.664848	−	0.746979i	$-0.731504\pi$
$271$	1402.96	−	2430.00i	0.314479	−	0.544694i	0.979327	+	0.202285i	$0.0648369\pi$
$272$	−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	$-0.501229\pi$
$281$	−36.3731			−0.00772183			−0.00386092	+	0.999993i	$0.501229\pi$
$282$	−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	$0.144823\pi$
$293$	4161.25	+	7207.50i	0.829703	+	1.43709i	−0.0685685	+	0.997646i	$0.521843\pi$
$294$	−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	$-0.566175\pi$
$307$	−2220.49			−0.412801			−0.206401	+	0.978468i	$0.566175\pi$
$308$	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	$-0.612776\pi$
$317$	−3916.17			−0.693861			−0.346930	+	0.937891i	$0.612776\pi$
$318$	−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	$-0.954222\pi$
$331$	−3727.37	−	6456.00i	−0.618958	−	1.07207i	0.370719	−	0.928745i	$-0.379111\pi$
$332$	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	$0.337045\pi$
$349$	−3325.54	+	5760.00i	−0.510063	+	0.883455i	−0.999932	+	0.0116588i	$0.996289\pi$
$350$	2928.00			0.447166
$351$		0			0
$352$	−2520.00			−0.381581
$353$	−2815.45	+	4876.50i	−0.424508	+	0.735269i	−0.996374	−	0.0850777i	$-0.972886\pi$
$353$	−2815.45	+	4876.50i	−0.424508	+	0.735269i	0.571867	+	0.820347i	$0.306219\pi$
$354$	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	$-0.675576\pi$
$359$	−7129.12			−1.04808			−0.524040	+	0.851694i	$0.675576\pi$
$360$	−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	−0.990170	−	0.139871i	$-0.955331\pi$
$379$	−2759.16	+	4779.00i	−0.373953	+	0.647706i	0.616216	+	0.787577i	$0.288665\pi$
$380$	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	0.508673	−	0.860960i	$-0.330136\pi$
$383$	−3682.34	−	6378.00i	−0.491276	−	0.850915i	−0.999950	+	0.0100443i	$0.996803\pi$
$384$	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	$-0.901858\pi$
$397$	−5847.40	−	10128.0i	−0.739226	−	1.28038i	0.213618	−	0.976917i	$-0.431475\pi$
$398$	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	−0.943781	−	0.330571i	$-0.892759\pi$
$401$	−1490.43	+	2581.50i	−0.185607	+	0.321481i	0.758174	+	0.652053i	$0.226092\pi$
$402$	−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	0.867331	−	0.497731i	$-0.165833\pi$
$409$	21.6506	+	37.5000i	0.00261749	+	0.00453363i	−0.864714	+	0.502265i	$0.832500\pi$
$410$	−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	$-0.634172\pi$
$421$	−7068.50			−0.818284			−0.409142	+	0.912471i	$0.634172\pi$
$422$	−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	$-0.646136\pi$
$431$	4964.06	−	8598.00i	0.554780	−	0.960907i	0.997921	−	0.0644552i	$-0.0205310\pi$
$432$	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	0.522327	−	0.852745i	$-0.325064\pi$
$449$	−4541.44	−	7866.00i	−0.477336	−	0.826769i	−0.999663	+	0.0259758i	$0.991731\pi$
$450$	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	−0.923350	−	0.383959i	$-0.874560\pi$
$457$	−1261.80	+	2185.50i	−0.129156	+	0.223705i	0.794194	+	0.607665i	$0.207894\pi$
$458$	−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	$0.287103\pi$
$461$	9793.88	+	16963.5i	0.989472	+	1.71382i	0.369400	+	0.929270i	$0.379563\pi$
$462$	−332.554	−	576.000i	−0.0334887	−	0.0580042i
$463$	8632.54			0.866497			0.433249	−	0.901274i	$-0.357367\pi$
$463$	8632.54			0.866497			0.433249	+	0.901274i	$0.357367\pi$
$464$	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	−0.920464	−	0.390827i	$-0.872189\pi$
$479$	−1276.52	+	2211.00i	−0.121766	+	0.210904i	0.798698	+	0.601732i	$0.205522\pi$
$480$	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	$0.00139762\pi$
$487$	5414.39	+	9378.00i	0.503798	+	0.872603i	−0.496193	+	0.868212i	$0.665269\pi$
$488$	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	$-0.208554\pi$
$499$	17677.3			1.58586			0.792931	+	0.609311i	$0.208554\pi$
$500$	−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	$-0.566708\pi$
$509$	8532.95	−	14779.5i	0.743058	−	1.28701i	0.951097	−	0.308893i	$-0.0999585\pi$
$510$	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	$-0.560632\pi$
$541$	−4764.87			−0.378665			−0.189333	+	0.981913i	$0.560632\pi$
$542$	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	$0.408572\pi$
$557$	−9056.03	+	15685.5i	−0.688898	+	1.19321i	−0.972195	+	0.234174i	$0.924761\pi$
$558$	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	$-0.688112\pi$
$577$	−15444.7			−1.11433			−0.557167	+	0.830400i	$0.688112\pi$
$578$	−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	−0.505280	−	0.862956i	$-0.668611\pi$
$587$	7035.59	−	12186.0i	0.494702	−	0.856848i	0.999981	+	0.00610719i	$0.00194399\pi$
$588$	−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	$-0.117407\pi$
$593$	26938.6			1.86549			0.932745	+	0.360538i	$0.117407\pi$
$594$	−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	$0.478821\pi$
$613$	−12610.2	+	21841.5i	−0.830866	+	1.43910i	−0.897352	+	0.441315i	$0.854512\pi$
$614$	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	$-0.974708\pi$
$617$	−8692.30	−	15055.5i	−0.567162	−	0.982353i	0.429683	−	0.902980i	$-0.358625\pi$
$618$	315.233	+	546.000i	0.0205187	+	0.0355394i
$619$	−8209.92			−0.533093			−0.266547	−	0.963822i	$-0.585883\pi$
$619$	−8209.92			−0.533093			−0.266547	+	0.963822i	$0.585883\pi$
$620$	−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	0.588576	−	0.808442i	$-0.299689\pi$
$631$	−6432.84	−	11142.0i	−0.405843	−	0.702941i	−0.994419	+	0.105501i	$0.966355\pi$
$632$	−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	$-0.994143\pi$
$643$	−8410.84	−	14568.0i	−0.515849	−	0.893477i	0.483981	−	0.875078i	$-0.339190\pi$
$644$	−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	−0.986022	−	0.166615i	$-0.946716\pi$
$661$	−5926.21	+	10264.5i	−0.348718	+	0.603998i	0.637304	+	0.770613i	$0.280050\pi$
$662$	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	$0.100115\pi$
$683$	13269.2	+	22983.0i	0.743387	+	1.28758i	−0.207557	+	0.978223i	$0.566551\pi$
$684$	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	−0.854356	−	0.519688i	$-0.826048\pi$
$691$	415.692	−	720.000i	0.0228852	−	0.0396383i	0.877241	+	0.480050i	$0.159381\pi$
$692$	−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	0.979362	−	0.202113i	$-0.0647809\pi$
$709$	5940.07	+	10288.5i	0.314646	+	0.544983i	−0.664716	+	0.747096i	$0.731448\pi$
$710$	−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	$-0.293709\pi$
$733$	23959.5			1.20732			0.603658	+	0.797243i	$0.293709\pi$
$734$	−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	−0.823931	−	0.566690i	$-0.808224\pi$
$739$	1583.09	−	2742.00i	0.0788025	−	0.136490i	0.902734	+	0.430200i	$0.141557\pi$
$740$	−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	$-0.566647\pi$
$743$	15051.5	−	26070.0i	0.743185	−	1.28723i	0.951038	−	0.309075i	$-0.100019\pi$
$744$	−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	$-0.723159\pi$
$761$	−20663.4	−	35790.0i	−0.984292	−	1.70484i	−0.339252	−	0.940695i	$-0.610174\pi$
$762$	−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	−0.652574	−	0.757725i	$-0.726311\pi$
$769$	7035.59	−	12186.0i	0.329922	−	0.571441i	0.982496	+	0.186283i	$0.0596443\pi$
$770$	−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	0.868353	−	0.495946i	$-0.165179\pi$
$773$	100.459	+	174.000i	0.00467433	+	0.00809618i	−0.863679	+	0.504043i	$0.831845\pi$
$774$	−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	0.933551	−	0.358445i	$-0.116693\pi$
$787$	3451.98	+	5979.00i	0.156353	+	0.270811i	−0.777198	+	0.629256i	$0.783360\pi$
$788$	−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	$-0.598206\pi$
$811$	−14026.1			−0.607305			−0.303653	+	0.952783i	$0.598206\pi$
$812$	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	−0.767888	−	0.640584i	$-0.778692\pi$
$821$	4018.36	−	6960.00i	0.170818	−	0.295866i	0.938706	+	0.344718i	$0.112026\pi$
$822$	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	$-0.187783\pi$
$827$	39525.4			1.66195			0.830975	+	0.556310i	$0.187783\pi$
$828$	−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	0.556142	−	0.831087i	$-0.312281\pi$
$839$	−10733.5	−	18591.0i	−0.441671	−	0.764997i	−0.997814	+	0.0660899i	$0.978948\pi$
$840$	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	$-0.495054\pi$
$853$	774.227			0.0310774			0.0155387	+	0.999879i	$0.495054\pi$
$854$	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	$-0.485991\pi$
$863$	2230.88			0.0879955			0.0439977	+	0.999032i	$0.485991\pi$
$864$	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	0.658466	−	0.752610i	$-0.271206\pi$
$877$	−8377.06	−	14509.5i	−0.322547	−	0.558667i	−0.981013	+	0.193943i	$0.937872\pi$
$878$	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	0.921038	−	0.389472i	$-0.127342\pi$
$929$	3489.22	+	6043.50i	0.123227	+	0.213435i	−0.797812	+	0.602907i	$0.794009\pi$
$930$	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	$-0.526963\pi$
$941$	−4884.38			−0.169210			−0.0846049	+	0.996415i	$0.526963\pi$
$942$	−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	−0.616665	−	0.787225i	$-0.711517\pi$
$947$	10882.5	−	18849.0i	0.373424	−	0.646790i	0.990090	+	0.140435i	$0.0448502\pi$
$948$	−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	$-0.540020\pi$
$967$	−7541.35			−0.250789			−0.125395	+	0.992107i	$0.540020\pi$
$968$	−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	−0.582326	−	0.812955i	$-0.697857\pi$
$977$	12608.5	−	21838.5i	0.412877	−	0.715123i	0.995203	+	0.0978318i	$0.0311907\pi$
$978$	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	$-0.868327\pi$
$983$	−56440.6			−1.83131			−0.915654	+	0.401967i	$0.868327\pi$
$984$	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.22.1		4
13.2	odd	12		169.4.e.a.23.1		2
13.3	even	3	inner	169.4.c.h.146.1		4
13.4	even	6		169.4.a.i.1.1		2
13.5	odd	4		13.4.e.b.4.1	✓	2
13.6	odd	12		169.4.b.d.168.1		2
13.7	odd	12		169.4.b.d.168.2		2
13.8	odd	4		169.4.e.a.147.1		2
13.9	even	3		169.4.a.i.1.2		2
13.10	even	6	inner	169.4.c.h.146.2		4
13.11	odd	12		13.4.e.b.10.1	yes	2
13.12	even	2	inner	169.4.c.h.22.2		4
39.5	even	4		117.4.q.a.82.1		2
39.11	even	12		117.4.q.a.10.1		2
39.17	odd	6		1521.4.a.o.1.2		2
39.35	odd	6		1521.4.a.o.1.1		2
52.11	even	12		208.4.w.b.49.1		2
52.31	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	13.5	odd	4
13.4.e.b.10.1	yes	2	13.11	odd	12
117.4.q.a.10.1		2	39.11	even	12
117.4.q.a.82.1		2	39.5	even	4
169.4.a.i.1.1		2	13.4	even	6
169.4.a.i.1.2		2	13.9	even	3
169.4.b.d.168.1		2	13.6	odd	12
169.4.b.d.168.2		2	13.7	odd	12
169.4.c.h.22.1		4	1.1	even	1	trivial
169.4.c.h.22.2		4	13.12	even	2	inner
169.4.c.h.146.1		4	13.3	even	3	inner
169.4.c.h.146.2		4	13.10	even	6	inner
169.4.e.a.23.1		2	13.2	odd	12
169.4.e.a.147.1		2	13.8	odd	4
208.4.w.b.17.1		2	52.31	even	4
208.4.w.b.49.1		2	52.11	even	12
1521.4.a.o.1.1		2	39.35	odd	6
1521.4.a.o.1.2		2	39.17	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 1.50000i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(2.50000 + 4.33013i) q^{4} +1.73205 q^{5} +(-1.73205 - 3.00000i) q^{6} +(6.92820 + 12.0000i) q^{7} -22.5167 q^{8} +(11.5000 + 19.9186i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 10 q^{4} + 46 q^{9}+O(q^{10}) \) 4 * q - 4 * q^3 + 10 * q^4 + 46 * q^9	\( 4 q - 4 q^{3} + 10 q^{4} + 46 q^{9} - 6 q^{10} - 40 q^{12} - 96 q^{14} - 2 q^{16} + 234 q^{17} + 48 q^{22} - 156 q^{23} - 488 q^{25} - 400 q^{27} + 282 q^{29} - 12 q^{30} + 48 q^{35} - 230 q^{36} + 792 q^{38} - 156 q^{40} + 96 q^{42} + 208 q^{43} - 4 q^{48} + 302 q^{49} - 936 q^{51} + 372 q^{53} + 48 q^{55} - 624 q^{56} - 290 q^{61} + 540 q^{62} + 1228 q^{64} - 192 q^{66} - 1170 q^{68} - 312 q^{69} - 498 q^{74} + 488 q^{75} + 768 q^{77} + 5104 q^{79} - 842 q^{81} - 942 q^{82} + 564 q^{87} - 624 q^{88} - 276 q^{90} - 1560 q^{92} - 1044 q^{94} - 396 q^{95}+O(q^{100}) \) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more