LMFDB - Embedded newform 980.4.i.t.961.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,4,Mod(361,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("980.361");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	980.i (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:	$57.8218718056$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-83})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 20x^{2} - 21x + 441 $ x^4 - x^3 - 20x^2 - 21x + 441
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.2
Root			$4.19493 + 1.84460i$ of defining polynomial
Character	$\chi$	$=$	980.961
Dual form			980.4.i.t.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.69493 + 6.39981i) q^{3} +(2.50000 - 4.33013i) q^{5} +(-13.8051 + 23.9111i) q^{9} +O(q^{10})$	\(q+(3.69493 + 6.39981i) q^{3} +(2.50000 - 4.33013i) q^{5} +(-13.8051 + 23.9111i) q^{9} +(31.4747 + 54.5157i) q^{11} +78.1696 q^{13} +36.9493 q^{15} +(-10.5253 - 18.2304i) q^{17} +(70.5595 - 122.213i) q^{19} +(101.119 - 175.143i) q^{23} +(-12.5000 - 21.6506i) q^{25} -4.50880 q^{27} +47.7291 q^{29} +(-19.7291 - 34.1717i) q^{31} +(-232.594 + 402.864i) q^{33} +(154.187 - 267.060i) q^{37} +(288.831 + 500.271i) q^{39} -233.899 q^{41} -457.220 q^{43} +(69.0253 + 119.555i) q^{45} +(-36.6949 + 63.5575i) q^{47} +(77.7808 - 134.720i) q^{51} +(182.255 + 315.676i) q^{53} +314.747 q^{55} +1042.85 q^{57} +(196.661 + 340.626i) q^{59} +(-200.830 + 347.848i) q^{61} +(195.424 - 338.484i) q^{65} +(-253.628 - 439.296i) q^{67} +1494.51 q^{69} +742.441 q^{71} +(64.7467 + 112.145i) q^{73} +(92.3733 - 159.995i) q^{75} +(13.8821 - 24.0446i) q^{79} +(356.077 + 616.744i) q^{81} -508.445 q^{83} -105.253 q^{85} +(176.356 + 305.457i) q^{87} +(147.255 - 255.054i) q^{89} +(145.795 - 252.525i) q^{93} +(-352.797 - 611.063i) q^{95} +1181.73 q^{97} -1738.04 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{3} + 10 q^{5} - 71 q^{9}+O(q^{10}) $ 4 * q - q^3 + 10 * q^5 - 71 * q^9	$ 4 q - q^{3} + 10 q^{5} - 71 q^{9} + 47 q^{11} + 218 q^{13} - 10 q^{15} - 121 q^{17} + 156 q^{19} + 152 q^{23} - 50 q^{25} + 266 q^{27} - 30 q^{29} + 142 q^{31} - 599 q^{33} - 46 q^{37} + 319 q^{39} - 620 q^{41} - 1892 q^{43} + 355 q^{45} - 131 q^{47} - 683 q^{51} - 344 q^{53} + 470 q^{55} + 1836 q^{57} + 976 q^{59} - 898 q^{61} + 545 q^{65} - 478 q^{67} + 3832 q^{69} + 3096 q^{71} - 530 q^{73} - 25 q^{75} - 623 q^{79} + 730 q^{81} + 1564 q^{83} - 1210 q^{85} + 879 q^{87} - 484 q^{89} + 1814 q^{93} - 780 q^{95} + 4506 q^{97} - 2092 q^{99}+O(q^{100}) $ 4 * q - q^3 + 10 * q^5 - 71 * q^9 + 47 * q^11 + 218 * q^13 - 10 * q^15 - 121 * q^17 + 156 * q^19 + 152 * q^23 - 50 * q^25 + 266 * q^27 - 30 * q^29 + 142 * q^31 - 599 * q^33 - 46 * q^37 + 319 * q^39 - 620 * q^41 - 1892 * q^43 + 355 * q^45 - 131 * q^47 - 683 * q^51 - 344 * q^53 + 470 * q^55 + 1836 * q^57 + 976 * q^59 - 898 * q^61 + 545 * q^65 - 478 * q^67 + 3832 * q^69 + 3096 * q^71 - 530 * q^73 - 25 * q^75 - 623 * q^79 + 730 * q^81 + 1564 * q^83 - 1210 * q^85 + 879 * q^87 - 484 * q^89 + 1814 * q^93 - 780 * q^95 + 4506 * q^97 - 2092 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	3.69493	+	6.39981i	0.711090	+	1.23164i	0.964448	+	0.264272i	$0.0851316\pi$
$3$	3.69493	+	6.39981i	0.711090	+	1.23164i	−0.253358	+	0.967373i	$0.581535\pi$
$4$		0			0
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−13.8051	+	23.9111i	−0.511299	+	0.885595i
$10$		0			0
$11$	31.4747	+	54.5157i	0.862724	+	1.49428i	0.869289	+	0.494304i	$0.164577\pi$
$11$	31.4747	+	54.5157i	0.862724	+	1.49428i	−0.00656453	+	0.999978i	$0.502090\pi$
$12$		0			0
$13$	78.1696			1.66772			0.833859	−	0.551977i	$-0.186126\pi$
$13$	78.1696			1.66772			0.833859	+	0.551977i	$0.186126\pi$
$14$		0			0
$15$	36.9493			0.636018
$16$		0			0
$17$	−10.5253	−	18.2304i	−0.150163	−	0.260090i	0.781124	−	0.624375i	$-0.214646\pi$
$17$	−10.5253	−	18.2304i	−0.150163	−	0.260090i	−0.931287	+	0.364286i	$0.881313\pi$
$18$		0			0
$19$	70.5595	−	122.213i	0.851971	−	1.47566i	−0.0274555	−	0.999623i	$-0.508740\pi$
$19$	70.5595	−	122.213i	0.851971	−	1.47566i	0.879427	−	0.476034i	$-0.157926\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	101.119	−	175.143i	0.916729	−	1.58782i	0.112378	−	0.993666i	$-0.464153\pi$
$23$	101.119	−	175.143i	0.916729	−	1.58782i	0.804351	−	0.594155i	$-0.202513\pi$
$24$		0			0
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$		0			0
$27$	−4.50880			−0.0321378
$28$		0			0
$29$	47.7291			0.305623			0.152811	−	0.988255i	$-0.451167\pi$
$29$	47.7291			0.305623			0.152811	+	0.988255i	$0.451167\pi$
$30$		0			0
$31$	−19.7291	−	34.1717i	−0.114305	−	0.197982i	0.803197	−	0.595714i	$-0.203131\pi$
$31$	−19.7291	−	34.1717i	−0.114305	−	0.197982i	−0.917502	+	0.397732i	$0.869797\pi$
$32$		0			0
$33$	−232.594	+	402.864i	−1.22695	+	2.12514i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	154.187	−	267.060i	0.685087	−	1.18661i	−0.288322	−	0.957533i	$-0.593097\pi$
$37$	154.187	−	267.060i	0.685087	−	1.18661i	0.973409	−	0.229072i	$-0.0735692\pi$
$38$		0			0
$39$	288.831	+	500.271i	1.18590	+	2.05404i
$40$		0			0
$41$	−233.899			−0.890947			−0.445474	−	0.895295i	$-0.646965\pi$
$41$	−233.899			−0.890947			−0.445474	+	0.895295i	$0.646965\pi$
$42$		0			0
$43$	−457.220			−1.62152			−0.810761	−	0.585377i	$-0.800946\pi$
$43$	−457.220			−1.62152			−0.810761	+	0.585377i	$0.800946\pi$
$44$		0			0
$45$	69.0253	+	119.555i	0.228660	+	0.396050i
$46$		0			0
$47$	−36.6949	+	63.5575i	−0.113883	+	0.197251i	−0.917333	−	0.398121i	$-0.869662\pi$
$47$	−36.6949	+	63.5575i	−0.113883	+	0.197251i	0.803450	+	0.595373i	$0.202996\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	77.7808	−	134.720i	0.213559	−	0.369894i
$52$		0			0
$53$	182.255	+	315.676i	0.472353	+	0.818140i	0.999499	−	0.0316349i	$-0.0100714\pi$
$53$	182.255	+	315.676i	0.472353	+	0.818140i	−0.527146	+	0.849774i	$0.676738\pi$
$54$		0			0
$55$	314.747			0.771644
$56$		0			0
$57$	1042.85			2.42331
$58$		0			0
$59$	196.661	+	340.626i	0.433950	+	0.751624i	0.997209	−	0.0746567i	$-0.0237861\pi$
$59$	196.661	+	340.626i	0.433950	+	0.751624i	−0.563259	+	0.826280i	$0.690453\pi$
$60$		0			0
$61$	−200.830	+	347.848i	−0.421536	+	0.730122i	−0.996090	−	0.0883449i	$-0.971842\pi$
$61$	−200.830	+	347.848i	−0.421536	+	0.730122i	0.574554	+	0.818467i	$0.305176\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	195.424	−	338.484i	0.372913	−	0.645905i
$66$		0			0
$67$	−253.628	−	439.296i	−0.462471	−	0.801023i	0.536612	−	0.843829i	$-0.319704\pi$
$67$	−253.628	−	439.296i	−0.462471	−	0.801023i	−0.999083	+	0.0428055i	$0.986370\pi$
$68$		0			0
$69$	1494.51			2.60751
$70$		0			0
$71$	742.441			1.24101			0.620503	−	0.784204i	$-0.286928\pi$
$71$	742.441			1.24101			0.620503	+	0.784204i	$0.286928\pi$
$72$		0			0
$73$	64.7467	+	112.145i	0.103809	+	0.179802i	0.913251	−	0.407398i	$-0.133564\pi$
$73$	64.7467	+	112.145i	0.103809	+	0.179802i	−0.809442	+	0.587199i	$0.800230\pi$
$74$		0			0
$75$	92.3733	−	159.995i	0.142218	−	0.246329i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	13.8821	−	24.0446i	0.0197704	−	0.0342434i	−0.855971	−	0.517024i	$-0.827040\pi$
$79$	13.8821	−	24.0446i	0.0197704	−	0.0342434i	0.875741	+	0.482781i	$0.160373\pi$
$80$		0			0
$81$	356.077	+	616.744i	0.488446	+	0.846013i
$82$		0			0
$83$	−508.445			−0.672398			−0.336199	−	0.941791i	$-0.609142\pi$
$83$	−508.445			−0.672398			−0.336199	+	0.941791i	$0.609142\pi$
$84$		0			0
$85$	−105.253			−0.134310
$86$		0			0
$87$	176.356	+	305.457i	0.217326	+	0.376419i
$88$		0			0
$89$	147.255	−	255.054i	0.175383	−	0.303772i	−0.764911	−	0.644136i	$-0.777217\pi$
$89$	147.255	−	255.054i	0.175383	−	0.303772i	0.940294	+	0.340364i	$0.110550\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	145.795	−	252.525i	0.162562	−	0.281565i
$94$		0			0
$95$	−352.797	−	611.063i	−0.381013	−	0.659934i
$96$		0			0
$97$	1181.73			1.23697			0.618487	−	0.785795i	$-0.287746\pi$
$97$	1181.73			1.23697			0.618487	+	0.785795i	$0.287746\pi$
$98$		0			0
$99$	−1738.04			−1.76444
$100$		0			0
$101$	532.291	+	921.955i	0.524405	+	0.908296i	0.999596	+	0.0284135i	$0.00904553\pi$
$101$	532.291	+	921.955i	0.524405	+	0.908296i	−0.475191	+	0.879883i	$0.657621\pi$
$102$		0			0
$103$	−440.492	+	762.955i	−0.421388	+	0.729866i	−0.996076	−	0.0885072i	$-0.971790\pi$
$103$	−440.492	+	762.955i	−0.421388	+	0.729866i	0.574687	+	0.818373i	$0.305124\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	111.390	−	192.933i	0.100640	−	0.174313i	−0.811309	−	0.584618i	$-0.801244\pi$
$107$	111.390	−	192.933i	0.100640	−	0.174313i	0.911948	+	0.410305i	$0.134578\pi$
$108$		0			0
$109$	−376.713	−	652.485i	−0.331032	−	0.573365i	0.651682	−	0.758492i	$-0.274064\pi$
$109$	−376.713	−	652.485i	−0.331032	−	0.573365i	−0.982715	+	0.185127i	$0.940730\pi$
$110$		0			0
$111$	2278.85			1.94863
$112$		0			0
$113$	40.6475			0.0338389			0.0169194	−	0.999857i	$-0.494614\pi$
$113$	40.6475			0.0338389			0.0169194	+	0.999857i	$0.494614\pi$
$114$		0			0
$115$	−505.595	−	875.716i	−0.409973	−	0.710095i
$116$		0			0
$117$	−1079.14	+	1869.12i	−0.852703	+	1.47692i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−1315.81	+	2279.05i	−0.988587	+	1.71228i
$122$		0			0
$123$	−864.240	−	1496.91i	−0.633544	−	1.09733i
$124$		0			0
$125$	−125.000			−0.0894427
$126$		0			0
$127$	−678.515			−0.474083			−0.237041	−	0.971500i	$-0.576178\pi$
$127$	−678.515			−0.474083			−0.237041	+	0.971500i	$0.576178\pi$
$128$		0			0
$129$	−1689.40	−	2926.12i	−1.15305	−	1.99714i
$130$		0			0
$131$	−1429.82	+	2476.52i	−0.953616	+	1.65171i	−0.216112	+	0.976369i	$0.569338\pi$
$131$	−1429.82	+	2476.52i	−0.953616	+	1.65171i	−0.737504	+	0.675343i	$0.763996\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−11.2720	+	19.5237i	−0.00718622	+	0.0124469i
$136$		0			0
$137$	237.438	+	411.255i	0.148071	+	0.256467i	0.930514	−	0.366255i	$-0.119360\pi$
$137$	237.438	+	411.255i	0.148071	+	0.256467i	−0.782443	+	0.622722i	$0.786027\pi$
$138$		0			0
$139$	1624.18			0.991088			0.495544	−	0.868583i	$-0.334969\pi$
$139$	1624.18			0.991088			0.495544	+	0.868583i	$0.334969\pi$
$140$		0			0
$141$	−542.341			−0.323925
$142$		0			0
$143$	2460.36	+	4261.47i	1.43878	+	2.49204i
$144$		0			0
$145$	119.323	−	206.673i	0.0683394	−	0.118367i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1124.36	+	1947.45i	−0.618196	+	1.07075i	0.371618	+	0.928386i	$0.378803\pi$
$149$	−1124.36	+	1947.45i	−0.618196	+	1.07075i	−0.989815	+	0.142362i	$0.954530\pi$
$150$		0			0
$151$	−1107.72	−	1918.62i	−0.596985	−	1.03401i	−0.993263	−	0.115878i	$-0.963032\pi$
$151$	−1107.72	−	1918.62i	−0.596985	−	1.03401i	0.396279	−	0.918130i	$-0.370301\pi$
$152$		0			0
$153$	581.212			0.307112
$154$		0			0
$155$	−197.291			−0.102237
$156$		0			0
$157$	1365.61	+	2365.31i	0.694189	+	1.20237i	0.970453	+	0.241289i	$0.0775703\pi$
$157$	1365.61	+	2365.31i	0.694189	+	1.20237i	−0.276264	+	0.961082i	$0.589096\pi$
$158$		0			0
$159$	−1346.84	+	2332.80i	−0.671771	+	1.16354i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−1370.61	+	2373.97i	−0.658617	+	1.14076i	0.322356	+	0.946618i	$0.395525\pi$
$163$	−1370.61	+	2373.97i	−0.658617	+	1.14076i	−0.980974	+	0.194140i	$0.937808\pi$
$164$		0			0
$165$	1162.97	+	2014.32i	0.548709	+	0.950391i
$166$		0			0
$167$	1010.07			0.468033			0.234016	−	0.972233i	$-0.424813\pi$
$167$	1010.07			0.468033			0.234016	+	0.972233i	$0.424813\pi$
$168$		0			0
$169$	3913.49			1.78129
$170$		0			0
$171$	1948.16	+	3374.31i	0.871224	+	1.50900i
$172$		0			0
$173$	−318.849	+	552.263i	−0.140125	+	0.242704i	−0.927544	−	0.373715i	$-0.878084\pi$
$173$	−318.849	+	552.263i	−0.140125	+	0.242704i	0.787418	+	0.616419i	$0.211417\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1453.30	+	2517.18i	−0.617155	+	1.06894i
$178$		0			0
$179$	−1590.41	−	2754.68i	−0.664096	−	1.15025i	−0.979530	−	0.201300i	$-0.935483\pi$
$179$	−1590.41	−	2754.68i	−0.664096	−	1.15025i	0.315434	−	0.948948i	$-0.397850\pi$
$180$		0			0
$181$	−891.365			−0.366048			−0.183024	−	0.983108i	$-0.558589\pi$
$181$	−891.365			−0.366048			−0.183024	+	0.983108i	$0.558589\pi$
$182$		0			0
$183$	−2968.22			−1.19900
$184$		0			0
$185$	−770.936	−	1335.30i	−0.306380	−	0.530666i
$186$		0			0
$187$	662.563	−	1147.59i	0.259098	−	0.448771i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	2258.94	−	3912.59i	0.855764	−	1.48223i	−0.0201701	−	0.999797i	$-0.506421\pi$
$191$	2258.94	−	3912.59i	0.855764	−	1.48223i	0.875934	−	0.482430i	$-0.160246\pi$
$192$		0			0
$193$	15.8128	+	27.3886i	0.00589756	+	0.0102149i	0.868959	−	0.494884i	$-0.164789\pi$
$193$	15.8128	+	27.3886i	0.00589756	+	0.0102149i	−0.863062	+	0.505099i	$0.831456\pi$
$194$		0			0
$195$	2888.31			1.06070
$196$		0			0
$197$	−3253.32			−1.17660			−0.588298	−	0.808644i	$-0.700202\pi$
$197$	−3253.32			−1.17660			−0.588298	+	0.808644i	$0.700202\pi$
$198$		0			0
$199$	−2528.89	−	4380.17i	−0.900846	−	1.56031i	−0.826398	−	0.563086i	$-0.809614\pi$
$199$	−2528.89	−	4380.17i	−0.900846	−	1.56031i	−0.0744482	−	0.997225i	$-0.523720\pi$
$200$		0			0
$201$	1874.28	−	3246.34i	0.657717	−	1.13920i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−584.747	+	1012.81i	−0.199222	+	0.345062i
$206$		0			0
$207$	2791.91	+	4835.73i	0.937444	+	1.62370i
$208$		0			0
$209$	8883.34			2.94007
$210$		0			0
$211$	−3717.12			−1.21278			−0.606391	−	0.795166i	$-0.707384\pi$
$211$	−3717.12			−1.21278			−0.606391	+	0.795166i	$0.707384\pi$
$212$		0			0
$213$	2743.27	+	4751.48i	0.882468	+	1.52848i
$214$		0			0
$215$	−1143.05	+	1979.82i	−0.362583	+	0.628013i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−478.469	+	828.733i	−0.147635	+	0.255710i
$220$		0			0
$221$	−822.761	−	1425.06i	−0.250429	−	0.433756i
$222$		0			0
$223$	−1589.75			−0.477387			−0.238693	−	0.971095i	$-0.576719\pi$
$223$	−1589.75			−0.477387			−0.238693	+	0.971095i	$0.576719\pi$
$224$		0			0
$225$	690.253			0.204520
$226$		0			0
$227$	−1107.53	−	1918.29i	−0.323828	−	0.560887i	0.657446	−	0.753502i	$-0.271637\pi$
$227$	−1107.53	−	1918.29i	−0.323828	−	0.560887i	−0.981275	+	0.192614i	$0.938303\pi$
$228$		0			0
$229$	195.577	−	338.749i	0.0564371	−	0.0977519i	−0.836427	−	0.548079i	$-0.815359\pi$
$229$	195.577	−	338.749i	0.0564371	−	0.0977519i	0.892864	+	0.450327i	$0.148693\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1347.76	−	2334.38i	0.378946	−	0.656353i	−0.611963	−	0.790886i	$-0.709620\pi$
$233$	1347.76	−	2334.38i	0.378946	−	0.656353i	0.990909	+	0.134533i	$0.0429533\pi$
$234$		0			0
$235$	183.475	+	317.787i	0.0509301	+	0.0882135i
$236$		0			0
$237$	205.174			0.0562342
$238$		0			0
$239$	−1045.99			−0.283095			−0.141547	−	0.989931i	$-0.545208\pi$
$239$	−1045.99			−0.283095			−0.141547	+	0.989931i	$0.545208\pi$
$240$		0			0
$241$	−790.471	−	1369.14i	−0.211281	−	0.365950i	0.740835	−	0.671687i	$-0.234430\pi$
$241$	−790.471	−	1369.14i	−0.211281	−	0.365950i	−0.952116	+	0.305738i	$0.901097\pi$
$242$		0			0
$243$	−2692.23	+	4663.08i	−0.710727	+	1.23102i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	5515.61	−	9553.31i	1.42085	−	2.46098i
$248$		0			0
$249$	−1878.67	−	3253.95i	−0.478136	−	0.828156i
$250$		0			0
$251$	−6004.18			−1.50988			−0.754941	−	0.655792i	$-0.772335\pi$
$251$	−6004.18			−1.50988			−0.754941	+	0.655792i	$0.772335\pi$
$252$		0			0
$253$	12730.7			3.16354
$254$		0			0
$255$	−388.904	−	673.602i	−0.0955063	−	0.165422i
$256$		0			0
$257$	−1832.76	+	3174.43i	−0.444841	+	0.770487i	−0.998041	−	0.0625612i	$-0.980073\pi$
$257$	−1832.76	+	3174.43i	−0.444841	+	0.770487i	0.553200	+	0.833048i	$0.313406\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−658.903	+	1141.25i	−0.156265	+	0.270658i
$262$		0			0
$263$	−975.971	−	1690.43i	−0.228825	−	0.396336i	0.728635	−	0.684902i	$-0.240155\pi$
$263$	−975.971	−	1690.43i	−0.228825	−	0.396336i	−0.957460	+	0.288566i	$0.906822\pi$
$264$		0			0
$265$	1822.55			0.422485
$266$		0			0
$267$	2176.40			0.498851
$268$		0			0
$269$	−2982.91	−	5166.56i	−0.676102	−	1.17104i	−0.976145	−	0.217118i	$-0.930334\pi$
$269$	−2982.91	−	5166.56i	−0.676102	−	1.17104i	0.300043	−	0.953926i	$-0.402999\pi$
$270$		0			0
$271$	−3707.94	+	6422.34i	−0.831148	+	1.43959i	0.0659799	+	0.997821i	$0.478983\pi$
$271$	−3707.94	+	6422.34i	−0.831148	+	1.43959i	−0.897128	+	0.441770i	$0.854351\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	786.867	−	1362.89i	0.172545	−	0.298857i
$276$		0			0
$277$	3496.53	+	6056.17i	0.758434	+	1.31365i	0.943649	+	0.330948i	$0.107368\pi$
$277$	3496.53	+	6056.17i	0.758434	+	1.31365i	−0.185215	+	0.982698i	$0.559298\pi$
$278$		0			0
$279$	1089.44			0.233775
$280$		0			0
$281$	4144.50			0.879859			0.439929	−	0.898032i	$-0.355003\pi$
$281$	4144.50			0.879859			0.439929	+	0.898032i	$0.355003\pi$
$282$		0			0
$283$	2205.47	+	3819.98i	0.463256	+	0.802383i	0.999121	−	0.0419208i	$-0.0133477\pi$
$283$	2205.47	+	3819.98i	0.463256	+	0.802383i	−0.535865	+	0.844304i	$0.680014\pi$
$284$		0			0
$285$	2607.13	−	4515.67i	0.541869	−	0.938545i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	2234.93	−	3871.02i	0.454902	−	0.787914i
$290$		0			0
$291$	4366.41	+	7562.84i	0.879600	+	1.52351i
$292$		0			0
$293$	−4045.10			−0.806544			−0.403272	−	0.915080i	$-0.632127\pi$
$293$	−4045.10			−0.806544			−0.403272	+	0.915080i	$0.632127\pi$
$294$		0			0
$295$	1966.61			0.388137
$296$		0			0
$297$	−141.913	−	245.801i	−0.0277260	−	0.0480229i
$298$		0			0
$299$	7904.43	−	13690.9i	1.52885	−	2.64804i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−3933.56	+	6813.12i	−0.745799	+	1.29176i
$304$		0			0
$305$	1004.15	+	1739.24i	0.188517	+	0.326520i
$306$		0			0
$307$	−5552.20			−1.03219			−0.516093	−	0.856533i	$-0.672614\pi$
$307$	−5552.20			−1.03219			−0.516093	+	0.856533i	$0.672614\pi$
$308$		0			0
$309$	−6510.36			−1.19858
$310$		0			0
$311$	3452.58	+	5980.04i	0.629511	+	1.09034i	0.987650	+	0.156676i	$0.0500779\pi$
$311$	3452.58	+	5980.04i	0.629511	+	1.09034i	−0.358139	+	0.933668i	$0.616589\pi$
$312$		0			0
$313$	−3346.09	+	5795.60i	−0.604256	+	1.04660i	0.387912	+	0.921696i	$0.373196\pi$
$313$	−3346.09	+	5795.60i	−0.604256	+	1.04660i	−0.992169	+	0.124906i	$0.960137\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2144.02	−	3713.55i	0.379875	−	0.657962i	−0.611169	−	0.791500i	$-0.709300\pi$
$317$	2144.02	−	3713.55i	0.379875	−	0.657962i	0.991044	+	0.133538i	$0.0426338\pi$
$318$		0			0
$319$	1502.26	+	2601.98i	0.263668	+	0.456687i
$320$		0			0
$321$	1646.31			0.286256
$322$		0			0
$323$	−2970.65			−0.511738
$324$		0			0
$325$	−977.120	−	1692.42i	−0.166772	−	0.288857i
$326$		0			0
$327$	2783.86	−	4821.78i	0.470788	−	0.815428i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	2755.23	−	4772.20i	0.457527	−	0.792459i	−0.541303	−	0.840828i	$-0.682069\pi$
$331$	2755.23	−	4772.20i	0.457527	−	0.792459i	0.998830	+	0.0483683i	$0.0154021\pi$
$332$		0			0
$333$	4257.13	+	7373.56i	0.700568	+	1.21342i
$334$		0			0
$335$	−2536.28			−0.413647
$336$		0			0
$337$	7747.05			1.25225			0.626126	−	0.779722i	$-0.284640\pi$
$337$	7747.05			1.25225			0.626126	+	0.779722i	$0.284640\pi$
$338$		0			0
$339$	150.190	+	260.136i	0.0240625	+	0.0416775i
$340$		0			0
$341$	1241.93	−	2151.09i	0.197227	−	0.341607i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	3736.28	−	6471.42i	0.583056	−	1.00988i
$346$		0			0
$347$	−4702.01	−	8144.13i	−0.727427	−	1.25994i	−0.957967	−	0.286878i	$-0.907383\pi$
$347$	−4702.01	−	8144.13i	−0.727427	−	1.25994i	0.230540	−	0.973063i	$-0.425951\pi$
$348$		0			0
$349$	1067.45			0.163723			0.0818617	−	0.996644i	$-0.473913\pi$
$349$	1067.45			0.163723			0.0818617	+	0.996644i	$0.473913\pi$
$350$		0			0
$351$	−352.451			−0.0535967
$352$		0			0
$353$	−3565.68	−	6175.93i	−0.537625	−	0.931194i	−0.999031	−	0.0440053i	$-0.985988\pi$
$353$	−3565.68	−	6175.93i	−0.537625	−	0.931194i	0.461406	−	0.887189i	$-0.347345\pi$
$354$		0			0
$355$	1856.10	−	3214.86i	0.277498	−	0.480640i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−3239.12	+	5610.32i	−0.476195	+	0.824795i	−0.999628	−	0.0272724i	$-0.991318\pi$
$359$	−3239.12	+	5610.32i	−0.476195	+	0.824795i	0.523433	+	0.852067i	$0.324651\pi$
$360$		0			0
$361$	−6527.78	−	11306.4i	−0.951710	−	1.64841i
$362$		0			0
$363$	−19447.3			−2.81190
$364$		0			0
$365$	647.467			0.0928492
$366$		0			0
$367$	5061.79	+	8767.28i	0.719955	+	1.24700i	0.961017	+	0.276489i	$0.0891709\pi$
$367$	5061.79	+	8767.28i	0.719955	+	1.24700i	−0.241062	+	0.970510i	$0.577496\pi$
$368$		0			0
$369$	3228.99	−	5592.77i	0.455540	−	0.789019i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−933.786	+	1617.37i	−0.129624	+	0.224515i	−0.923531	−	0.383524i	$-0.874710\pi$
$373$	−933.786	+	1617.37i	−0.129624	+	0.224515i	0.793907	+	0.608039i	$0.208044\pi$
$374$		0			0
$375$	−461.867	−	799.977i	−0.0636018	−	0.110162i
$376$		0			0
$377$	3730.96			0.509693
$378$		0			0
$379$	−7476.27			−1.01327			−0.506636	−	0.862160i	$-0.669111\pi$
$379$	−7476.27			−1.01327			−0.506636	+	0.862160i	$0.669111\pi$
$380$		0			0
$381$	−2507.07	−	4342.37i	−0.337116	−	0.583901i
$382$		0			0
$383$	4732.92	−	8197.66i	0.631438	−	1.09368i	−0.355819	−	0.934555i	$-0.615798\pi$
$383$	4732.92	−	8197.66i	0.631438	−	1.09368i	0.987258	−	0.159129i	$-0.0508685\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	6311.96	−	10932.6i	0.829082	−	1.43601i
$388$		0			0
$389$	−1480.71	−	2564.66i	−0.192995	−	0.334276i	0.753247	−	0.657738i	$-0.228487\pi$
$389$	−1480.71	−	2564.66i	−0.192995	−	0.334276i	−0.946241	+	0.323462i	$0.895153\pi$
$390$		0			0
$391$	−4257.24			−0.550634
$392$		0			0
$393$	−21132.3			−2.71243
$394$		0			0
$395$	−69.4107	−	120.223i	−0.00884160	−	0.0153141i
$396$		0			0
$397$	−856.889	+	1484.17i	−0.108327	+	0.187629i	−0.915093	−	0.403243i	$-0.867883\pi$
$397$	−856.889	+	1484.17i	−0.108327	+	0.187629i	0.806765	+	0.590872i	$0.201216\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−4156.04	+	7198.47i	−0.517563	+	0.896445i	0.482229	+	0.876045i	$0.339827\pi$
$401$	−4156.04	+	7198.47i	−0.517563	+	0.896445i	−0.999792	+	0.0203998i	$0.993506\pi$
$402$		0			0
$403$	−1542.21	−	2671.19i	−0.190628	−	0.330178i
$404$		0			0
$405$	3560.77			0.436879
$406$		0			0
$407$	19412.0			2.36417
$408$		0			0
$409$	−3511.86	−	6082.72i	−0.424573	−	0.735382i	0.571807	−	0.820388i	$-0.306242\pi$
$409$	−3511.86	−	6082.72i	−0.424573	−	0.735382i	−0.996380	+	0.0850058i	$0.972909\pi$
$410$		0			0
$411$	−1754.64	+	3039.12i	−0.210584	+	0.364742i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−1271.11	+	2201.63i	−0.150353	+	0.260419i
$416$		0			0
$417$	6001.24	+	10394.4i	0.704753	+	1.22067i
$418$		0			0
$419$	5194.97			0.605706			0.302853	−	0.953037i	$-0.402061\pi$
$419$	5194.97			0.605706			0.302853	+	0.953037i	$0.402061\pi$
$420$		0			0
$421$	−8581.61			−0.993449			−0.496725	−	0.867908i	$-0.665464\pi$
$421$	−8581.61			−0.993449			−0.496725	+	0.867908i	$0.665464\pi$
$422$		0			0
$423$	−1013.15	−	1754.83i	−0.116457	−	0.201709i
$424$		0			0
$425$	−263.133	+	455.760i	−0.0300326	+	0.0520179i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−18181.7	+	31491.7i	−2.04621	+	3.54414i
$430$		0			0
$431$	2946.82	+	5104.05i	0.329335	+	0.570425i	0.982380	−	0.186894i	$-0.0598421\pi$
$431$	2946.82	+	5104.05i	0.329335	+	0.570425i	−0.653045	+	0.757319i	$0.726509\pi$
$432$		0			0
$433$	−8696.77			−0.965220			−0.482610	−	0.875835i	$-0.660311\pi$
$433$	−8696.77			−0.965220			−0.482610	+	0.875835i	$0.660311\pi$
$434$		0			0
$435$	1763.56			0.194382
$436$		0			0
$437$	−14269.8	−	24716.0i	−1.56205	−	2.70555i
$438$		0			0
$439$	−4309.78	+	7464.75i	−0.468552	+	0.811556i	−0.999354	−	0.0359400i	$-0.988557\pi$
$439$	−4309.78	+	7464.75i	−0.468552	+	0.811556i	0.530802	+	0.847496i	$0.321891\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	655.985	−	1136.20i	0.0703539	−	0.121857i	−0.828703	−	0.559689i	$-0.810920\pi$
$443$	655.985	−	1136.20i	0.0703539	−	0.121857i	0.899056	+	0.437833i	$0.144254\pi$
$444$		0			0
$445$	−736.277	−	1275.27i	−0.0784335	−	0.135851i
$446$		0			0
$447$	−16617.8			−1.75837
$448$		0			0
$449$	−1279.20			−0.134452			−0.0672260	−	0.997738i	$-0.521415\pi$
$449$	−1279.20			−0.134452			−0.0672260	+	0.997738i	$0.521415\pi$
$450$		0			0
$451$	−7361.88	−	12751.2i	−0.768642	−	1.33133i
$452$		0			0
$453$	8185.88	−	14178.4i	0.849020	−	1.47055i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	3140.74	−	5439.91i	0.321482	−	0.556824i	−0.659312	−	0.751870i	$-0.729152\pi$
$457$	3140.74	−	5439.91i	0.321482	−	0.556824i	0.980794	+	0.195046i	$0.0624856\pi$
$458$		0			0
$459$	47.4566	+	82.1973i	0.00482590	+	0.00835870i
$460$		0			0
$461$	−8283.03			−0.836831			−0.418415	−	0.908256i	$-0.637414\pi$
$461$	−8283.03			−0.836831			−0.418415	+	0.908256i	$0.637414\pi$
$462$		0			0
$463$	64.4483			0.00646904			0.00323452	−	0.999995i	$-0.498970\pi$
$463$	64.4483			0.00646904			0.00323452	+	0.999995i	$0.498970\pi$
$464$		0			0
$465$	−728.976	−	1262.62i	−0.0726999	−	0.125920i
$466$		0			0
$467$	1936.65	−	3354.38i	0.191901	−	0.332382i	−0.753979	−	0.656898i	$-0.771868\pi$
$467$	1936.65	−	3354.38i	0.191901	−	0.332382i	0.945880	+	0.324516i	$0.105202\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−10091.7	+	17479.3i	−0.987263	+	1.70999i
$472$		0			0
$473$	−14390.9	−	24925.7i	−1.39893	−	2.42301i
$474$		0			0
$475$	−3527.97			−0.340788
$476$		0			0
$477$	−10064.2			−0.966054
$478$		0			0
$479$	2938.62	+	5089.84i	0.280311	+	0.485513i	0.971461	−	0.237198i	$-0.0762290\pi$
$479$	2938.62	+	5089.84i	0.280311	+	0.485513i	−0.691150	+	0.722711i	$0.742896\pi$
$480$		0			0
$481$	12052.8	−	20876.0i	1.14253	−	1.97892i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	2954.32	−	5117.04i	0.276596	−	0.479078i
$486$		0			0
$487$	−957.136	−	1657.81i	−0.0890595	−	0.154256i	0.818054	−	0.575141i	$-0.195053\pi$
$487$	−957.136	−	1657.81i	−0.0890595	−	0.154256i	−0.907114	+	0.420885i	$0.861719\pi$
$488$		0			0
$489$	−20257.3			−1.87335
$490$		0			0
$491$	8907.18			0.818687			0.409343	−	0.912380i	$-0.365758\pi$
$491$	8907.18			0.818687			0.409343	+	0.912380i	$0.365758\pi$
$492$		0			0
$493$	−502.364	−	870.121i	−0.0458932	−	0.0794894i
$494$		0			0
$495$	−4345.10	+	7525.93i	−0.394541	+	0.683365i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−7237.08	+	12535.0i	−0.649251	+	1.12454i	0.334051	+	0.942555i	$0.391584\pi$
$499$	−7237.08	+	12535.0i	−0.649251	+	1.12454i	−0.983302	+	0.181981i	$0.941749\pi$
$500$		0			0
$501$	3732.14	+	6464.25i	0.332813	+	0.576450i
$502$		0			0
$503$	16856.9			1.49426			0.747130	−	0.664678i	$-0.231431\pi$
$503$	16856.9			1.49426			0.747130	+	0.664678i	$0.231431\pi$
$504$		0			0
$505$	5322.91			0.469042
$506$		0			0
$507$	14460.1	+	25045.6i	1.26666	+	2.19391i
$508$		0			0
$509$	−1933.96	+	3349.72i	−0.168411	+	0.291697i	−0.937861	−	0.347010i	$-0.887197\pi$
$509$	−1933.96	+	3349.72i	−0.168411	+	0.291697i	0.769450	+	0.638707i	$0.220530\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−318.139	+	551.032i	−0.0273804	+	0.0474243i
$514$		0			0
$515$	2202.46	+	3814.77i	0.188451	+	0.326406i
$516$		0			0
$517$	−4619.84			−0.392999
$518$		0			0
$519$	−4712.50			−0.398566
$520$		0			0
$521$	11418.7	+	19777.7i	0.960194	+	1.66310i	0.722008	+	0.691884i	$0.243219\pi$
$521$	11418.7	+	19777.7i	0.960194	+	1.66310i	0.238185	+	0.971220i	$0.423447\pi$
$522$		0			0
$523$	−3123.73	+	5410.46i	−0.261169	+	0.452357i	−0.966553	−	0.256468i	$-0.917441\pi$
$523$	−3123.73	+	5410.46i	−0.261169	+	0.452357i	0.705384	+	0.708825i	$0.250775\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−415.310	+	719.338i	−0.0343286	+	0.0594589i
$528$		0			0
$529$	−14366.6	−	24883.6i	−1.18078	−	2.04517i
$530$		0			0
$531$	−10859.7			−0.887513
$532$		0			0
$533$	−18283.8			−1.48585
$534$		0			0
$535$	−556.949	−	964.665i	−0.0450075	−	0.0779553i
$536$		0			0
$537$	11752.9	−	20356.7i	0.944464	−	1.63586i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	4047.24	−	7010.03i	0.321635	−	0.557089i	−0.659190	−	0.751976i	$-0.729101\pi$
$541$	4047.24	−	7010.03i	0.321635	−	0.557089i	0.980826	+	0.194888i	$0.0624342\pi$
$542$		0			0
$543$	−3293.54	−	5704.57i	−0.260293	−	0.450841i
$544$		0			0
$545$	−3767.13			−0.296084
$546$		0			0
$547$	2748.01			0.214801			0.107401	−	0.994216i	$-0.465747\pi$
$547$	2748.01			0.214801			0.107401	+	0.994216i	$0.465747\pi$
$548$		0			0
$549$	−5544.95	−	9604.14i	−0.431062	−	0.746621i
$550$		0			0
$551$	3367.74	−	5833.09i	0.260382	−	0.450995i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	5697.11	−	9867.69i	0.435728	−	0.754703i
$556$		0			0
$557$	9484.54	+	16427.7i	0.721495	+	1.24967i	0.960400	+	0.278623i	$0.0898781\pi$
$557$	9484.54	+	16427.7i	0.721495	+	1.24967i	−0.238905	+	0.971043i	$0.576789\pi$
$558$		0			0
$559$	−35740.7			−2.70424
$560$		0			0
$561$	9792.50			0.736969
$562$		0			0
$563$	7724.62	+	13379.4i	0.578249	+	1.00156i	0.995680	+	0.0928479i	$0.0295970\pi$
$563$	7724.62	+	13379.4i	0.578249	+	1.00156i	−0.417432	+	0.908708i	$0.637070\pi$
$564$		0			0
$565$	101.619	−	176.009i	0.00756661	−	0.0131057i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	12497.8	−	21646.9i	0.920802	−	1.59488i	0.122626	−	0.992453i	$-0.460869\pi$
$569$	12497.8	−	21646.9i	0.920802	−	1.59488i	0.798177	−	0.602423i	$-0.205798\pi$
$570$		0			0
$571$	−10228.7	−	17716.7i	−0.749666	−	1.29846i	−0.947983	−	0.318321i	$-0.896881\pi$
$571$	−10228.7	−	17716.7i	−0.749666	−	1.29846i	0.198317	−	0.980138i	$-0.436452\pi$
$572$		0			0
$573$	33386.5			2.43410
$574$		0			0
$575$	−5055.95			−0.366691
$576$		0			0
$577$	−12432.2	−	21533.3i	−0.896985	−	1.55362i	−0.831328	−	0.555782i	$-0.812419\pi$
$577$	−12432.2	−	21533.3i	−0.896985	−	1.55362i	−0.0656574	−	0.997842i	$-0.520914\pi$
$578$		0			0
$579$	−116.854	+	202.398i	−0.00838740	+	0.0145274i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−11472.9	+	19871.6i	−0.815021	+	1.41166i
$584$		0			0
$585$	5395.68	+	9345.60i	0.381340	+	0.660501i
$586$		0			0
$587$	12122.0			0.852349			0.426175	−	0.904641i	$-0.359861\pi$
$587$	12122.0			0.852349			0.426175	+	0.904641i	$0.359861\pi$
$588$		0			0
$589$	−5568.29			−0.389537
$590$		0			0
$591$	−12020.8	−	20820.6i	−0.836667	−	1.44915i
$592$		0			0
$593$	3665.46	−	6348.77i	0.253832	−	0.439650i	−0.710745	−	0.703449i	$-0.751642\pi$
$593$	3665.46	−	6348.77i	0.253832	−	0.439650i	0.964578	+	0.263799i	$0.0849755\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	18688.2	−	32368.9i	1.28117	−	2.21904i
$598$		0			0
$599$	−12211.0	−	21150.0i	−0.832934	−	1.44268i	−0.895702	−	0.444655i	$-0.853326\pi$
$599$	−12211.0	−	21150.0i	−0.832934	−	1.44268i	0.0627682	−	0.998028i	$-0.480007\pi$
$600$		0			0
$601$	25156.9			1.70744			0.853719	−	0.520733i	$-0.174341\pi$
$601$	25156.9			1.70744			0.853719	+	0.520733i	$0.174341\pi$
$602$		0			0
$603$	14005.4			0.945843
$604$		0			0
$605$	6579.05	+	11395.2i	0.442110	+	0.765756i
$606$		0			0
$607$	−7218.65	+	12503.1i	−0.482695	+	0.836053i	−0.999803	−	0.0198677i	$-0.993676\pi$
$607$	−7218.65	+	12503.1i	−0.482695	+	0.836053i	0.517107	+	0.855921i	$0.327009\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−2868.43	+	4968.26i	−0.189925	+	0.328960i
$612$		0			0
$613$	4686.79	+	8117.75i	0.308805	+	0.534866i	0.978101	−	0.208130i	$-0.0667376\pi$
$613$	4686.79	+	8117.75i	0.308805	+	0.534866i	−0.669296	+	0.742996i	$0.733404\pi$
$614$		0			0
$615$	−8642.40			−0.566659
$616$		0			0
$617$	17763.9			1.15907			0.579535	−	0.814947i	$-0.303234\pi$
$617$	17763.9			1.15907			0.579535	+	0.814947i	$0.303234\pi$
$618$		0			0
$619$	7258.78	+	12572.6i	0.471333	+	0.816372i	0.999462	−	0.0327918i	$-0.0104398\pi$
$619$	7258.78	+	12572.6i	0.471333	+	0.816372i	−0.528130	+	0.849164i	$0.677106\pi$
$620$		0			0
$621$	−455.925	+	789.686i	−0.0294616	+	0.0510290i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	32823.4	+	56851.7i	2.09065	+	3.62112i
$628$		0			0
$629$	−6491.49			−0.411498
$630$		0			0
$631$	−4206.50			−0.265385			−0.132693	−	0.991157i	$-0.542362\pi$
$631$	−4206.50			−0.265385			−0.132693	+	0.991157i	$0.542362\pi$
$632$		0			0
$633$	−13734.5	−	23788.9i	−0.862398	−	1.49372i
$634$		0			0
$635$	−1696.29	+	2938.06i	−0.106008	+	0.183611i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−10249.4	+	17752.6i	−0.634525	+	1.09903i
$640$		0			0
$641$	948.079	+	1642.12i	0.0584195	+	0.101186i	0.893756	−	0.448553i	$-0.148061\pi$
$641$	948.079	+	1642.12i	0.0584195	+	0.101186i	−0.835337	+	0.549739i	$0.814727\pi$
$642$		0			0
$643$	1655.83			0.101555			0.0507774	−	0.998710i	$-0.483830\pi$
$643$	1655.83			0.101555			0.0507774	+	0.998710i	$0.483830\pi$
$644$		0			0
$645$	−16894.0			−1.03132
$646$		0			0
$647$	3343.12	+	5790.45i	0.203140	+	0.351849i	0.949538	−	0.313651i	$-0.101552\pi$
$647$	3343.12	+	5790.45i	0.203140	+	0.351849i	−0.746399	+	0.665499i	$0.768219\pi$
$648$		0			0
$649$	−12379.7	+	21442.2i	−0.748759	+	1.29689i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	2331.55	−	4038.35i	0.139725	−	0.242011i	−0.787668	−	0.616101i	$-0.788711\pi$
$653$	2331.55	−	4038.35i	0.139725	−	0.242011i	0.927392	+	0.374090i	$0.122045\pi$
$654$		0			0
$655$	7149.09	+	12382.6i	0.426470	+	0.738668i
$656$		0			0
$657$	−3575.33			−0.212309
$658$		0			0
$659$	11637.3			0.687900			0.343950	−	0.938988i	$-0.388235\pi$
$659$	11637.3			0.687900			0.343950	+	0.938988i	$0.388235\pi$
$660$		0			0
$661$	−5671.48	−	9823.29i	−0.333729	−	0.578036i	0.649511	−	0.760352i	$-0.274974\pi$
$661$	−5671.48	−	9823.29i	−0.333729	−	0.578036i	−0.983240	+	0.182317i	$0.941640\pi$
$662$		0			0
$663$	6080.09	−	10531.0i	0.356156	−	0.616880i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	4826.31	−	8359.42i	0.280173	−	0.485274i
$668$		0			0
$669$	−5874.01	−	10174.1i	−0.339465	−	0.587971i
$670$		0			0
$671$	−25284.3			−1.45468
$672$		0			0
$673$	32719.8			1.87408			0.937040	−	0.349223i	$-0.113555\pi$
$673$	32719.8			1.87408			0.937040	+	0.349223i	$0.113555\pi$
$674$		0			0
$675$	56.3600	+	97.6184i	0.00321378	+	0.00556642i
$676$		0			0
$677$	−5122.45	+	8872.34i	−0.290800	+	0.503680i	−0.973999	−	0.226552i	$-0.927255\pi$
$677$	−5122.45	+	8872.34i	−0.290800	+	0.503680i	0.683199	+	0.730232i	$0.260588\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	8184.46	−	14175.9i	0.460542	−	0.797683i
$682$		0			0
$683$	10912.2	+	18900.5i	0.611337	+	1.05887i	0.991015	+	0.133748i	$0.0427014\pi$
$683$	10912.2	+	18900.5i	0.611337	+	1.05887i	−0.379678	+	0.925119i	$0.623965\pi$
$684$		0			0
$685$	2374.38			0.132439
$686$		0			0
$687$	2890.58			0.160528
$688$		0			0
$689$	14246.8	+	24676.2i	0.787752	+	1.36443i
$690$		0			0
$691$	−9944.96	+	17225.2i	−0.547502	+	0.948302i	0.450942	+	0.892553i	$0.351088\pi$
$691$	−9944.96	+	17225.2i	−0.547502	+	0.948302i	−0.998445	+	0.0557490i	$0.982245\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	4060.45	−	7032.91i	0.221614	−	0.383847i
$696$		0			0
$697$	2461.86	+	4264.07i	0.133787	+	0.231726i
$698$		0			0
$699$	19919.5			1.07786
$700$		0			0
$701$	775.059			0.0417597			0.0208799	−	0.999782i	$-0.493353\pi$
$701$	775.059			0.0417597			0.0208799	+	0.999782i	$0.493353\pi$
$702$		0			0
$703$	−21758.7	−	37687.2i	−1.16735	−	2.02191i
$704$		0			0
$705$	−1355.85	+	2348.41i	−0.0724318	+	0.125455i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−2537.47	+	4395.02i	−0.134410	+	0.232805i	−0.925372	−	0.379061i	$-0.876247\pi$
$709$	−2537.47	+	4395.02i	−0.134410	+	0.232805i	0.790962	+	0.611865i	$0.209581\pi$
$710$		0			0
$711$	383.288	+	663.874i	0.0202172	+	0.0350172i
$712$		0			0
$713$	−7979.93			−0.419145
$714$		0			0
$715$	24603.6			1.28689
$716$		0			0
$717$	−3864.88	−	6694.16i	−0.201306	−	0.348672i
$718$		0			0
$719$	−7228.26	+	12519.7i	−0.374921	+	0.649383i	−0.990315	−	0.138837i	$-0.955664\pi$
$719$	−7228.26	+	12519.7i	−0.374921	+	0.649383i	0.615394	+	0.788220i	$0.288997\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	5841.48	−	10117.7i	0.300480	−	0.520446i
$724$		0			0
$725$	−596.613	−	1033.36i	−0.0305623	−	0.0529354i
$726$		0			0
$727$	22164.7			1.13073			0.565366	−	0.824840i	$-0.308735\pi$
$727$	22164.7			1.13073			0.565366	+	0.824840i	$0.308735\pi$
$728$		0			0
$729$	−20562.3			−1.04467
$730$		0			0
$731$	4812.40	+	8335.31i	0.243492	+	0.421741i
$732$		0			0
$733$	2911.76	−	5043.32i	0.146723	−	0.254133i	−0.783291	−	0.621655i	$-0.786461\pi$
$733$	2911.76	−	5043.32i	0.146723	−	0.254133i	0.930015	+	0.367523i	$0.119794\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	15965.7	−	27653.4i	0.797970	−	1.38212i
$738$		0			0
$739$	−8963.03	−	15524.4i	−0.446158	−	0.772768i	0.551974	−	0.833861i	$-0.313875\pi$
$739$	−8963.03	−	15524.4i	−0.446158	−	0.772768i	−0.998132	+	0.0610934i	$0.980541\pi$
$740$		0			0
$741$	81519.2			4.04141
$742$		0			0
$743$	11438.2			0.564775			0.282388	−	0.959300i	$-0.408874\pi$
$743$	11438.2			0.564775			0.282388	+	0.959300i	$0.408874\pi$
$744$		0			0
$745$	5621.81	+	9737.25i	0.276466	+	0.478853i
$746$		0			0
$747$	7019.11	−	12157.5i	0.343796	−	0.595473i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	15630.9	−	27073.6i	0.759496	−	1.31549i	−0.183612	−	0.982999i	$-0.558779\pi$
$751$	15630.9	−	27073.6i	0.759496	−	1.31549i	0.943108	−	0.332486i	$-0.107888\pi$
$752$		0			0
$753$	−22185.0	−	38425.6i	−1.07366	−	1.85964i
$754$		0			0
$755$	−11077.2			−0.533960
$756$		0			0
$757$	−19384.1			−0.930684			−0.465342	−	0.885131i	$-0.654069\pi$
$757$	−19384.1			−0.930684			−0.465342	+	0.885131i	$0.654069\pi$
$758$		0			0
$759$	47039.2	+	81474.3i	2.24956	+	3.89635i
$760$		0			0
$761$	5071.48	−	8784.06i	0.241578	−	0.418426i	−0.719586	−	0.694403i	$-0.755668\pi$
$761$	5071.48	−	8784.06i	0.241578	−	0.418426i	0.961164	+	0.275978i	$0.0890017\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	1453.03	−	2516.72i	0.0686724	−	0.118944i
$766$		0			0
$767$	15372.9	+	26626.6i	0.723707	+	1.25350i
$768$		0			0
$769$	12899.6			0.604906			0.302453	−	0.953164i	$-0.402195\pi$
$769$	12899.6			0.604906			0.302453	+	0.953164i	$0.402195\pi$
$770$		0			0
$771$	−27087.6			−1.26529
$772$		0			0
$773$	−15474.3	−	26802.2i	−0.720015	−	1.24710i	−0.960993	−	0.276572i	$-0.910802\pi$
$773$	−15474.3	−	26802.2i	−0.720015	−	1.24710i	0.240979	−	0.970530i	$-0.422532\pi$
$774$		0			0
$775$	−493.227	+	854.294i	−0.0228609	+	0.0395963i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−16503.8	+	28585.4i	−0.759061	+	1.31473i
$780$		0			0
$781$	23368.1	+	40474.7i	1.07065	+	1.85441i
$782$		0			0
$783$	−215.201			−0.00982204
$784$		0			0
$785$	13656.1			0.620902
$786$		0			0
$787$	6201.76	+	10741.8i	0.280901	+	0.486534i	0.971607	−	0.236601i	$-0.0760335\pi$
$787$	6201.76	+	10741.8i	0.280901	+	0.486534i	−0.690706	+	0.723135i	$0.742700\pi$
$788$		0			0
$789$	7212.30	−	12492.1i	0.325430	−	0.563662i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−15698.8	+	27191.2i	−0.703004	+	1.21764i
$794$		0			0
$795$	6734.22	+	11664.0i	0.300425	+	0.520352i
$796$		0			0
$797$	10324.8			0.458874			0.229437	−	0.973324i	$-0.426312\pi$
$797$	10324.8			0.458874			0.229437	+	0.973324i	$0.426312\pi$
$798$		0			0
$799$	1544.91			0.0684040
$800$		0			0
$801$	4065.74	+	7042.07i	0.179346	+	0.310636i
$802$		0			0
$803$	−4075.76	+	7059.42i	−0.179116	+	0.310239i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	22043.3	−	38180.2i	0.961539	−	1.66543i
$808$		0			0
$809$	11362.8	+	19681.0i	0.493815	+	0.855312i	0.999975	−	0.00712746i	$-0.00226876\pi$
$809$	11362.8	+	19681.0i	0.493815	+	0.855312i	−0.506160	+	0.862440i	$0.668935\pi$
$810$		0			0
$811$	−21908.3			−0.948588			−0.474294	−	0.880366i	$-0.657297\pi$
$811$	−21908.3			−0.948588			−0.474294	+	0.880366i	$0.657297\pi$
$812$		0			0
$813$	−54802.3			−2.36409
$814$		0			0
$815$	6853.06	+	11869.9i	0.294543	+	0.510163i
$816$		0			0
$817$	−32261.2	+	55878.1i	−1.38149	+	2.39281i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−10882.3	+	18848.7i	−0.462600	+	0.801246i	−0.999090	−	0.0426606i	$-0.986417\pi$
$821$	−10882.3	+	18848.7i	−0.462600	+	0.801246i	0.536490	+	0.843907i	$0.319750\pi$
$822$		0			0
$823$	−488.223	−	845.627i	−0.0206785	−	0.0358162i	0.855501	−	0.517801i	$-0.173249\pi$
$823$	−488.223	−	845.627i	−0.0206785	−	0.0358162i	−0.876179	+	0.481985i	$0.839916\pi$
$824$		0			0
$825$	11629.7			0.490780
$826$		0			0
$827$	−11223.0			−0.471900			−0.235950	−	0.971765i	$-0.575820\pi$
$827$	−11223.0			−0.471900			−0.235950	+	0.971765i	$0.575820\pi$
$828$		0			0
$829$	2484.70	+	4303.63i	0.104098	+	0.180303i	0.913369	−	0.407132i	$-0.133471\pi$
$829$	2484.70	+	4303.63i	0.104098	+	0.180303i	−0.809271	+	0.587435i	$0.800138\pi$
$830$		0			0
$831$	−25838.9	+	44754.3i	−1.07863	+	1.86824i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	2525.17	−	4373.72i	0.104655	−	0.181268i
$836$		0			0
$837$	88.9545	+	154.074i	0.00367350	+	0.00636268i
$838$		0			0
$839$	−25800.4			−1.06166			−0.530828	−	0.847480i	$-0.678119\pi$
$839$	−25800.4			−1.06166			−0.530828	+	0.847480i	$0.678119\pi$
$840$		0			0
$841$	−22110.9			−0.906595
$842$		0			0
$843$	15313.7	+	26524.0i	0.625659	+	1.08367i
$844$		0			0
$845$	9783.72	−	16945.9i	0.398308	−	0.689889i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−16298.1	+	28229.2i	−0.658834	+	1.14113i
$850$		0			0
$851$	−31182.5	−	54009.7i	−1.25608	−	2.17559i
$852$		0			0
$853$	43349.3			1.74004			0.870019	−	0.493018i	$-0.164106\pi$
$853$	43349.3			1.74004			0.870019	+	0.493018i	$0.164106\pi$
$854$		0			0
$855$	19481.6			0.779246
$856$		0			0
$857$	13328.1	+	23084.9i	0.531247	+	0.920147i	0.999335	+	0.0364648i	$0.0116097\pi$
$857$	13328.1	+	23084.9i	0.531247	+	0.920147i	−0.468088	+	0.883682i	$0.655057\pi$
$858$		0			0
$859$	−4540.67	+	7864.67i	−0.180356	+	0.312385i	−0.942002	−	0.335608i	$-0.891058\pi$
$859$	−4540.67	+	7864.67i	−0.180356	+	0.312385i	0.761646	+	0.647993i	$0.224392\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−12057.8	+	20884.7i	−0.475610	+	0.823781i	−0.999610	−	0.0279373i	$-0.991106\pi$
$863$	−12057.8	+	20884.7i	−0.475610	+	0.823781i	0.523999	+	0.851719i	$0.324439\pi$
$864$		0			0
$865$	1594.25	+	2761.31i	0.0626659	+	0.108540i
$866$		0			0
$867$	33031.7			1.29391
$868$		0			0
$869$	1747.74			0.0682257
$870$		0			0
$871$	−19826.0	−	34339.6i	−0.771272	−	1.33588i
$872$		0			0
$873$	−16313.8	+	28256.4i	−0.632463	+	1.09546i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	14026.4	−	24294.5i	0.540067	−	0.935423i	−0.458833	−	0.888523i	$-0.651732\pi$
$877$	14026.4	−	24294.5i	0.540067	−	0.935423i	0.998900	−	0.0469002i	$-0.0149343\pi$
$878$		0			0
$879$	−14946.4	−	25887.9i	−0.573526	−	0.993376i
$880$		0			0
$881$	27264.1			1.04262			0.521312	−	0.853366i	$-0.325443\pi$
$881$	27264.1			1.04262			0.521312	+	0.853366i	$0.325443\pi$
$882$		0			0
$883$	11307.9			0.430965			0.215482	−	0.976508i	$-0.430868\pi$
$883$	11307.9			0.430965			0.215482	+	0.976508i	$0.430868\pi$
$884$		0			0
$885$	7266.49	+	12585.9i	0.276000	+	0.478046i
$886$		0			0
$887$	20530.5	−	35559.9i	0.777167	−	1.34609i	−0.156401	−	0.987694i	$-0.549989\pi$
$887$	20530.5	−	35559.9i	0.777167	−	1.34609i	0.933568	−	0.358399i	$-0.116677\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−22414.8	+	38823.6i	−0.842788	+	1.45975i
$892$		0			0
$893$	5178.35	+	8969.17i	0.194050	+	0.336105i
$894$		0			0
$895$	−15904.1			−0.593985
$896$		0			0
$897$	116825.			4.34859
$898$		0			0
$899$	−941.650	−	1630.99i	−0.0349341	−	0.0605077i
$900$		0			0
$901$	3836.60	−	6645.18i	0.141860	−	0.245708i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−2228.41	+	3859.73i	−0.0818508	+	0.141770i
$906$		0			0
$907$	−25695.8	−	44506.4i	−0.940700	−	1.62934i	−0.764139	−	0.645051i	$-0.776836\pi$
$907$	−25695.8	−	44506.4i	−0.940700	−	1.62934i	−0.176561	−	0.984290i	$-0.556497\pi$
$908$		0			0
$909$	−29393.2			−1.07251
$910$		0			0
$911$	10350.4			0.376427			0.188214	−	0.982128i	$-0.439730\pi$
$911$	10350.4			0.376427			0.188214	+	0.982128i	$0.439730\pi$
$912$		0			0
$913$	−16003.1	−	27718.2i	−0.580095	−	1.00475i
$914$		0			0
$915$	−7420.55	+	12852.8i	−0.268105	+	0.464371i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−11214.7	+	19424.5i	−0.402546	+	0.697230i	−0.994032	−	0.109085i	$-0.965208\pi$
$919$	−11214.7	+	19424.5i	−0.402546	+	0.697230i	0.591487	+	0.806315i	$0.298541\pi$
$920$		0			0
$921$	−20515.0	−	35533.1i	−0.733977	−	1.27129i
$922$		0			0
$923$	58036.3			2.06965
$924$		0			0
$925$	−7709.36			−0.274035
$926$		0			0
$927$	−12162.1	−	21065.3i	−0.430911	−	0.746359i
$928$		0			0
$929$	−10298.1	+	17836.9i	−0.363692	+	0.629934i	−0.988565	−	0.150793i	$-0.951817\pi$
$929$	−10298.1	+	17836.9i	−0.363692	+	0.629934i	0.624873	+	0.780726i	$0.285151\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−25514.1	+	44191.7i	−0.895278	+	1.55067i
$934$		0			0
$935$	−3312.81	−	5737.96i	−0.115872	−	0.200697i
$936$		0			0
$937$	−36416.3			−1.26966			−0.634828	−	0.772653i	$-0.718929\pi$
$937$	−36416.3			−1.26966			−0.634828	+	0.772653i	$0.718929\pi$
$938$		0			0
$939$	−49454.3			−1.71872
$940$		0			0
$941$	−6131.95	−	10620.8i	−0.212429	−	0.367938i	0.740045	−	0.672557i	$-0.234804\pi$
$941$	−6131.95	−	10620.8i	−0.212429	−	0.367938i	−0.952474	+	0.304619i	$0.901471\pi$
$942$		0			0
$943$	−23651.6	+	40965.7i	−0.816757	+	1.41466i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1413.63	−	2448.48i	0.0485076	−	0.0840177i	−0.840752	−	0.541420i	$-0.817887\pi$
$947$	1413.63	−	2448.48i	0.0485076	−	0.0840177i	0.889260	+	0.457403i	$0.151220\pi$
$948$		0			0
$949$	5061.22	+	8766.29i	0.173124	+	0.299859i
$950$		0			0
$951$	31688.1			1.08050
$952$		0			0
$953$	−30378.5			−1.03259			−0.516293	−	0.856412i	$-0.672689\pi$
$953$	−30378.5			−1.03259			−0.516293	+	0.856412i	$0.672689\pi$
$954$		0			0
$955$	−11294.7	−	19563.0i	−0.382709	−	0.662872i
$956$		0			0
$957$	−11101.5	+	19228.3i	−0.374984	+	0.649491i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	14117.0	−	24451.4i	0.473869	−	0.820765i
$962$		0			0
$963$	3075.49	+	5326.90i	0.102914	+	0.178252i
$964$		0			0
$965$	158.128			0.00527494
$966$		0			0
$967$	−19686.0			−0.654665			−0.327332	−	0.944909i	$-0.606150\pi$
$967$	−19686.0			−0.654665			−0.327332	+	0.944909i	$0.606150\pi$
$968$		0			0
$969$	−10976.3	−	19011.6i	−0.363892	−	0.630279i
$970$		0			0
$971$	6356.43	−	11009.7i	0.210080	−	0.363869i	−0.741659	−	0.670777i	$-0.765961\pi$
$971$	6356.43	−	11009.7i	0.210080	−	0.363869i	0.951739	+	0.306908i	$0.0992943\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	7220.79	−	12506.8i	0.237180	−	0.410807i
$976$		0			0
$977$	−3297.99	−	5712.29i	−0.107996	−	0.187055i	0.806962	−	0.590603i	$-0.201110\pi$
$977$	−3297.99	−	5712.29i	−0.107996	−	0.187055i	−0.914958	+	0.403548i	$0.867777\pi$
$978$		0			0
$979$	18539.3			0.605227
$980$		0			0
$981$	20802.2			0.677026
$982$		0			0
$983$	4418.80	+	7653.58i	0.143375	+	0.248333i	0.928766	−	0.370668i	$-0.120871\pi$
$983$	4418.80	+	7653.58i	0.143375	+	0.248333i	−0.785390	+	0.619001i	$0.787538\pi$
$984$		0			0
$985$	−8133.30	+	14087.3i	−0.263095	+	0.455694i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−46233.6	+	80079.0i	−1.48650	+	2.57469i
$990$		0			0
$991$	7019.31	+	12157.8i	0.225001	+	0.389713i	0.956320	−	0.292323i	$-0.0944282\pi$
$991$	7019.31	+	12157.8i	0.225001	+	0.389713i	−0.731319	+	0.682036i	$0.761095\pi$
$992$		0			0
$993$	40721.6			1.30137
$994$		0			0
$995$	−25288.9			−0.805741
$996$		0			0
$997$	−13607.2	−	23568.4i	−0.432241	−	0.748663i	0.564825	−	0.825211i	$-0.308944\pi$
$997$	−13607.2	−	23568.4i	−0.432241	−	0.748663i	−0.997066	+	0.0765474i	$0.975610\pi$
$998$		0			0
$999$	−695.200	+	1204.12i	−0.0220172	+	0.0381348i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.4.i.t.961.2		4
7.2	even	3		980.4.a.s.1.1	yes	2
7.3	odd	6		980.4.i.v.361.1		4
7.4	even	3	inner	980.4.i.t.361.2		4
7.5	odd	6		980.4.a.p.1.2	✓	2
7.6	odd	2		980.4.i.v.961.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
980.4.a.p.1.2	✓	2	7.5	odd	6
980.4.a.s.1.1	yes	2	7.2	even	3
980.4.i.t.361.2		4	7.4	even	3	inner
980.4.i.t.961.2		4	1.1	even	1	trivial
980.4.i.v.361.1		4	7.3	odd	6
980.4.i.v.961.1		4	7.6	odd	2

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:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	980.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.69493 + 6.39981i) q^{3} +(2.50000 - 4.33013i) q^{5} +(-13.8051 + 23.9111i) q^{9} +O(q^{10})\)	\(q+(3.69493 + 6.39981i) q^{3} +(2.50000 - 4.33013i) q^{5} +(-13.8051 + 23.9111i) q^{9} +(31.4747 + 54.5157i) q^{11} +78.1696 q^{13} +36.9493 q^{15} +(-10.5253 - 18.2304i) q^{17} +(70.5595 - 122.213i) q^{19} +(101.119 - 175.143i) q^{23} +(-12.5000 - 21.6506i) q^{25} -4.50880 q^{27} +47.7291 q^{29} +(-19.7291 - 34.1717i) q^{31} +(-232.594 + 402.864i) q^{33} +(154.187 - 267.060i) q^{37} +(288.831 + 500.271i) q^{39} -233.899 q^{41} -457.220 q^{43} +(69.0253 + 119.555i) q^{45} +(-36.6949 + 63.5575i) q^{47} +(77.7808 - 134.720i) q^{51} +(182.255 + 315.676i) q^{53} +314.747 q^{55} +1042.85 q^{57} +(196.661 + 340.626i) q^{59} +(-200.830 + 347.848i) q^{61} +(195.424 - 338.484i) q^{65} +(-253.628 - 439.296i) q^{67} +1494.51 q^{69} +742.441 q^{71} +(64.7467 + 112.145i) q^{73} +(92.3733 - 159.995i) q^{75} +(13.8821 - 24.0446i) q^{79} +(356.077 + 616.744i) q^{81} -508.445 q^{83} -105.253 q^{85} +(176.356 + 305.457i) q^{87} +(147.255 - 255.054i) q^{89} +(145.795 - 252.525i) q^{93} +(-352.797 - 611.063i) q^{95} +1181.73 q^{97} -1738.04 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{3} + 10 q^{5} - 71 q^{9}+O(q^{10}) \) 4 * q - q^3 + 10 * q^5 - 71 * q^9	\( 4 q - q^{3} + 10 q^{5} - 71 q^{9} + 47 q^{11} + 218 q^{13} - 10 q^{15} - 121 q^{17} + 156 q^{19} + 152 q^{23} - 50 q^{25} + 266 q^{27} - 30 q^{29} + 142 q^{31} - 599 q^{33} - 46 q^{37} + 319 q^{39} - 620 q^{41} - 1892 q^{43} + 355 q^{45} - 131 q^{47} - 683 q^{51} - 344 q^{53} + 470 q^{55} + 1836 q^{57} + 976 q^{59} - 898 q^{61} + 545 q^{65} - 478 q^{67} + 3832 q^{69} + 3096 q^{71} - 530 q^{73} - 25 q^{75} - 623 q^{79} + 730 q^{81} + 1564 q^{83} - 1210 q^{85} + 879 q^{87} - 484 q^{89} + 1814 q^{93} - 780 q^{95} + 4506 q^{97} - 2092 q^{99}+O(q^{100}) \) 4 * q - q^3 + 10 * q^5 - 71 * q^9 + 47 * q^11 + 218 * q^13 - 10 * q^15 - 121 * q^17 + 156 * q^19 + 152 * q^23 - 50 * q^25 + 266 * q^27 - 30 * q^29 + 142 * q^31 - 599 * q^33 - 46 * q^37 + 319 * q^39 - 620 * q^41 - 1892 * q^43 + 355 * q^45 - 131 * q^47 - 683 * q^51 - 344 * q^53 + 470 * q^55 + 1836 * q^57 + 976 * q^59 - 898 * q^61 + 545 * q^65 - 478 * q^67 + 3832 * q^69 + 3096 * q^71 - 530 * q^73 - 25 * q^75 - 623 * q^79 + 730 * q^81 + 1564 * q^83 - 1210 * q^85 + 879 * q^87 - 484 * q^89 + 1814 * q^93 - 780 * q^95 + 4506 * q^97 - 2092 * q^99

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