LMFDB - Embedded newform 100.4.g.a.61.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,4,Mod(21,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("100.21");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	100.g (of order $5$, degree $4$, 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:	$5.90019100057$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			61.1
Character	$\chi$	$=$	100.61
Dual form			100.4.g.a.41.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.65908 + 8.18380i) q^{3} +(-1.44907 + 11.0860i) q^{5} +17.7526 q^{7} +(-38.0604 - 27.6525i) q^{9} +O(q^{10})$	\(q+(-2.65908 + 8.18380i) q^{3} +(-1.44907 + 11.0860i) q^{5} +17.7526 q^{7} +(-38.0604 - 27.6525i) q^{9} +(-23.4721 + 17.0535i) q^{11} +(-44.1893 - 32.1054i) q^{13} +(-86.8727 - 41.3375i) q^{15} +(21.1298 + 65.0309i) q^{17} +(-16.6150 - 51.1357i) q^{19} +(-47.2055 + 145.284i) q^{21} +(134.843 - 97.9692i) q^{23} +(-120.800 - 32.1289i) q^{25} +(139.546 - 101.386i) q^{27} +(-78.8623 + 242.713i) q^{29} +(63.8593 + 196.539i) q^{31} +(-77.1482 - 237.438i) q^{33} +(-25.7247 + 196.806i) q^{35} +(197.157 + 143.243i) q^{37} +(380.247 - 276.266i) q^{39} +(38.2337 + 27.7784i) q^{41} -35.8364 q^{43} +(361.709 - 381.869i) q^{45} +(144.580 - 444.972i) q^{47} -27.8456 q^{49} -588.385 q^{51} +(-208.142 + 640.594i) q^{53} +(-155.043 - 284.925i) q^{55} +462.665 q^{57} +(267.341 + 194.235i) q^{59} +(320.417 - 232.797i) q^{61} +(-675.671 - 490.904i) q^{63} +(419.955 - 443.361i) q^{65} +(110.149 + 339.004i) q^{67} +(443.202 + 1364.04i) q^{69} +(-104.255 + 320.863i) q^{71} +(-588.829 + 427.809i) q^{73} +(584.154 - 903.173i) q^{75} +(-416.691 + 302.744i) q^{77} +(-392.901 + 1209.22i) q^{79} +(66.1401 + 203.558i) q^{81} +(19.8749 + 61.1687i) q^{83} +(-751.553 + 140.012i) q^{85} +(-1776.61 - 1290.79i) q^{87} +(565.265 - 410.689i) q^{89} +(-784.474 - 569.954i) q^{91} -1778.24 q^{93} +(590.968 - 110.095i) q^{95} +(298.019 - 917.209i) q^{97} +1364.93 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{3} - 25 q^{5} + 16 q^{7} - 13 q^{9}+O(q^{10}) $ 28 * q - 4 * q^3 - 25 * q^5 + 16 * q^7 - 13 * q^9	$ 28 q - 4 q^{3} - 25 q^{5} + 16 q^{7} - 13 q^{9} - 20 q^{11} - 86 q^{13} - 240 q^{15} - 178 q^{17} + 2 q^{19} + 108 q^{21} + 102 q^{23} + 95 q^{25} + 92 q^{27} + 192 q^{29} + 378 q^{31} + 560 q^{33} - 350 q^{35} - 399 q^{37} + 592 q^{39} + 298 q^{41} - 180 q^{43} - 535 q^{45} - 78 q^{47} + 144 q^{49} - 1664 q^{51} - 657 q^{53} + 610 q^{55} + 384 q^{57} + 144 q^{59} + 516 q^{61} + 584 q^{63} - 505 q^{65} - 134 q^{67} + 2996 q^{69} - 2026 q^{71} - 1346 q^{73} + 3770 q^{75} + 2320 q^{77} + 896 q^{79} - 2203 q^{81} + 2082 q^{83} - 195 q^{85} - 4316 q^{87} - 167 q^{89} + 2212 q^{91} - 5664 q^{93} - 3740 q^{95} + 1156 q^{97} - 2100 q^{99}+O(q^{100}) $ 28 * q - 4 * q^3 - 25 * q^5 + 16 * q^7 - 13 * q^9 - 20 * q^11 - 86 * q^13 - 240 * q^15 - 178 * q^17 + 2 * q^19 + 108 * q^21 + 102 * q^23 + 95 * q^25 + 92 * q^27 + 192 * q^29 + 378 * q^31 + 560 * q^33 - 350 * q^35 - 399 * q^37 + 592 * q^39 + 298 * q^41 - 180 * q^43 - 535 * q^45 - 78 * q^47 + 144 * q^49 - 1664 * q^51 - 657 * q^53 + 610 * q^55 + 384 * q^57 + 144 * q^59 + 516 * q^61 + 584 * q^63 - 505 * q^65 - 134 * q^67 + 2996 * q^69 - 2026 * q^71 - 1346 * q^73 + 3770 * q^75 + 2320 * q^77 + 896 * q^79 - 2203 * q^81 + 2082 * q^83 - 195 * q^85 - 4316 * q^87 - 167 * q^89 + 2212 * q^91 - 5664 * q^93 - 3740 * q^95 + 1156 * q^97 - 2100 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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			0
$2$		0			0
$3$	−2.65908	+	8.18380i	−0.511740	+	1.57497i	0.277397	+	0.960755i	$0.410528\pi$
$3$	−2.65908	+	8.18380i	−0.511740	+	1.57497i	−0.789137	+	0.614217i	$0.789472\pi$
$4$		0			0
$5$	−1.44907	+	11.0860i	−0.129609	+	0.991565i
$5$	−1.44907	+	11.0860i	−0.129609	+	0.991565i
$6$		0			0
$7$	17.7526			0.958550			0.479275	−	0.877665i	$-0.340900\pi$
$7$	17.7526			0.958550			0.479275	+	0.877665i	$0.340900\pi$
$8$		0			0
$9$	−38.0604	−	27.6525i	−1.40964	−	1.02417i
$10$		0			0
$11$	−23.4721	+	17.0535i	−0.643374	+	0.467439i	−0.861008	−	0.508592i	$-0.830166\pi$
$11$	−23.4721	+	17.0535i	−0.643374	+	0.467439i	0.217634	+	0.976031i	$0.430166\pi$
$12$		0			0
$13$	−44.1893	−	32.1054i	−0.942762	−	0.684957i	0.00632198	−	0.999980i	$-0.497988\pi$
$13$	−44.1893	−	32.1054i	−0.942762	−	0.684957i	−0.949084	+	0.315023i	$0.897988\pi$
$14$		0			0
$15$	−86.8727	−	41.3375i	−1.49536	−	0.711554i
$16$		0			0
$17$	21.1298	+	65.0309i	0.301455	+	0.927782i	0.980976	+	0.194127i	$0.0621874\pi$
$17$	21.1298	+	65.0309i	0.301455	+	0.927782i	−0.679522	+	0.733655i	$0.737813\pi$
$18$		0			0
$19$	−16.6150	−	51.1357i	−0.200618	−	0.617438i	−0.999865	−	0.0164357i	$-0.994768\pi$
$19$	−16.6150	−	51.1357i	−0.200618	−	0.617438i	0.799247	−	0.601003i	$-0.205232\pi$
$20$		0			0
$21$	−47.2055	+	145.284i	−0.490528	+	1.50969i
$22$		0			0
$23$	134.843	−	97.9692i	1.22247	−	0.888173i	0.226163	−	0.974089i	$-0.427382\pi$
$23$	134.843	−	97.9692i	1.22247	−	0.888173i	0.996302	+	0.0859161i	$0.0273817\pi$
$24$		0			0
$25$	−120.800	−	32.1289i	−0.966403	−	0.257031i
$26$		0			0
$27$	139.546	−	101.386i	0.994654	−	0.722659i
$28$		0			0
$29$	−78.8623	+	242.713i	−0.504978	+	1.55416i	0.295830	+	0.955241i	$0.404404\pi$
$29$	−78.8623	+	242.713i	−0.504978	+	1.55416i	−0.800808	+	0.598921i	$0.795596\pi$
$30$		0			0
$31$	63.8593	+	196.539i	0.369983	+	1.13869i	0.946802	+	0.321818i	$0.104294\pi$
$31$	63.8593	+	196.539i	0.369983	+	1.13869i	−0.576819	+	0.816872i	$0.695706\pi$
$32$		0			0
$33$	−77.1482	−	237.438i	−0.406963	−	1.25250i
$34$		0			0
$35$	−25.7247	+	196.806i	−0.124236	+	0.950465i
$36$		0			0
$37$	197.157	+	143.243i	0.876011	+	0.636459i	0.932193	−	0.361961i	$-0.117893\pi$
$37$	197.157	+	143.243i	0.876011	+	0.636459i	−0.0561822	+	0.998421i	$0.517893\pi$
$38$		0			0
$39$	380.247	−	276.266i	1.56124	−	1.13430i
$40$		0			0
$41$	38.2337	+	27.7784i	0.145636	+	0.105811i	0.658218	−	0.752828i	$-0.271311\pi$
$41$	38.2337	+	27.7784i	0.145636	+	0.105811i	−0.512581	+	0.858639i	$0.671311\pi$
$42$		0			0
$43$	−35.8364			−0.127093			−0.0635464	−	0.997979i	$-0.520241\pi$
$43$	−35.8364			−0.127093			−0.0635464	+	0.997979i	$0.520241\pi$
$44$		0			0
$45$	361.709	−	381.869i	1.19823	−	1.26501i
$46$		0			0
$47$	144.580	−	444.972i	0.448706	−	1.38098i	−0.429662	−	0.902990i	$-0.641367\pi$
$47$	144.580	−	444.972i	0.448706	−	1.38098i	0.878368	−	0.477985i	$-0.158633\pi$
$48$		0			0
$49$	−27.8456			−0.0811824
$50$		0			0
$51$	−588.385			−1.61550
$52$		0			0
$53$	−208.142	+	640.594i	−0.539442	+	1.66023i	0.194407	+	0.980921i	$0.437722\pi$
$53$	−208.142	+	640.594i	−0.539442	+	1.66023i	−0.733849	+	0.679312i	$0.762278\pi$
$54$		0			0
$55$	−155.043	−	284.925i	−0.380109	−	0.698531i
$56$		0			0
$57$	462.665			1.07511
$58$		0			0
$59$	267.341	+	194.235i	0.589913	+	0.428597i	0.842284	−	0.539034i	$-0.181210\pi$
$59$	267.341	+	194.235i	0.589913	+	0.428597i	−0.252371	+	0.967630i	$0.581210\pi$
$60$		0			0
$61$	320.417	−	232.797i	0.672545	−	0.488633i	−0.198331	−	0.980135i	$-0.563552\pi$
$61$	320.417	−	232.797i	0.672545	−	0.488633i	0.870876	+	0.491502i	$0.163552\pi$
$62$		0			0
$63$	−675.671	−	490.904i	−1.35121	−	0.981715i
$64$		0			0
$65$	419.955	−	443.361i	0.801369	−	0.846034i
$66$		0			0
$67$	110.149	+	339.004i	0.200849	+	0.618149i	0.999858	+	0.0168306i	$0.00535760\pi$
$67$	110.149	+	339.004i	0.200849	+	0.618149i	−0.799010	+	0.601318i	$0.794642\pi$
$68$		0			0
$69$	443.202	+	1364.04i	0.773265	+	2.37986i
$70$		0			0
$71$	−104.255	+	320.863i	−0.174264	+	0.536331i	−0.999599	−	0.0283132i	$-0.990986\pi$
$71$	−104.255	+	320.863i	−0.174264	+	0.536331i	0.825335	+	0.564644i	$0.190986\pi$
$72$		0			0
$73$	−588.829	+	427.809i	−0.944072	+	0.685908i	−0.949397	−	0.314077i	$-0.898305\pi$
$73$	−588.829	+	427.809i	−0.944072	+	0.685908i	0.00532550	+	0.999986i	$0.498305\pi$
$74$		0			0
$75$	584.154	−	903.173i	0.899364	−	1.39053i
$76$		0			0
$77$	−416.691	+	302.744i	−0.616706	+	0.448063i
$78$		0			0
$79$	−392.901	+	1209.22i	−0.559554	+	1.72213i	0.124047	+	0.992276i	$0.460413\pi$
$79$	−392.901	+	1209.22i	−0.559554	+	1.72213i	−0.683602	+	0.729855i	$0.739587\pi$
$80$		0			0
$81$	66.1401	+	203.558i	0.0907272	+	0.279230i
$82$		0			0
$83$	19.8749	+	61.1687i	0.0262838	+	0.0808932i	0.963338	−	0.268291i	$-0.0864588\pi$
$83$	19.8749	+	61.1687i	0.0262838	+	0.0808932i	−0.937054	+	0.349184i	$0.886459\pi$
$84$		0			0
$85$	−751.553	+	140.012i	−0.959028	+	0.178663i
$86$		0			0
$87$	−1776.61	−	1290.79i	−2.18935	−	1.59065i
$88$		0			0
$89$	565.265	−	410.689i	0.673236	−	0.489134i	−0.197871	−	0.980228i	$-0.563403\pi$
$89$	565.265	−	410.689i	0.673236	−	0.489134i	0.871107	+	0.491094i	$0.163403\pi$
$90$		0			0
$91$	−784.474	−	569.954i	−0.903684	−	0.656565i
$92$		0			0
$93$	−1778.24			−1.98274
$94$		0			0
$95$	590.968	−	110.095i	0.638232	−	0.118900i
$96$		0			0
$97$	298.019	−	917.209i	0.311951	−	0.960088i	−0.665040	−	0.746808i	$-0.731585\pi$
$97$	298.019	−	917.209i	0.311951	−	0.960088i	0.976991	−	0.213280i	$-0.0684146\pi$
$98$		0			0
$99$	1364.93			1.38566
$100$		0			0
$101$	−45.8510			−0.0451718			−0.0225859	−	0.999745i	$-0.507190\pi$
$101$	−45.8510			−0.0451718			−0.0225859	+	0.999745i	$0.507190\pi$
$102$		0			0
$103$	351.665	−	1082.31i	0.336413	−	1.03537i	−0.629608	−	0.776913i	$-0.716785\pi$
$103$	351.665	−	1082.31i	0.336413	−	1.03537i	0.966022	−	0.258461i	$-0.0832154\pi$
$104$		0			0
$105$	−1542.22	−	733.848i	−1.43338	−	0.682059i
$106$		0			0
$107$	1828.84			1.65234			0.826169	−	0.563422i	$-0.190516\pi$
$107$	1828.84			1.65234			0.826169	+	0.563422i	$0.190516\pi$
$108$		0			0
$109$	−1699.65	−	1234.87i	−1.49355	−	1.08513i	−0.972864	−	0.231376i	$-0.925677\pi$
$109$	−1699.65	−	1234.87i	−1.49355	−	1.08513i	−0.520683	−	0.853750i	$-0.674323\pi$
$110$		0			0
$111$	−1696.53	+	1232.60i	−1.45070	+	1.05399i
$112$		0			0
$113$	1209.74	+	878.927i	1.00710	+	0.731704i	0.963600	−	0.267349i	$-0.0861478\pi$
$113$	1209.74	+	878.927i	1.00710	+	0.731704i	0.0435042	+	0.999053i	$0.486148\pi$
$114$		0			0
$115$	890.693	+	1636.84i	0.722239	+	1.32727i
$116$		0			0
$117$	794.068	+	2443.89i	0.627450	+	1.93109i
$118$		0			0
$119$	375.109	+	1154.47i	0.288959	+	0.889326i
$120$		0			0
$121$	−151.183	+	465.292i	−0.113586	+	0.349581i
$122$		0			0
$123$	−328.999	+	239.032i	−0.241178	+	0.175226i
$124$		0			0
$125$	531.230	−	1292.64i	0.380117	−	0.924938i
$126$		0			0
$127$	1640.51	−	1191.90i	1.14623	−	0.832787i	0.158257	−	0.987398i	$-0.449412\pi$
$127$	1640.51	−	1191.90i	1.14623	−	0.832787i	0.987975	+	0.154611i	$0.0494124\pi$
$128$		0			0
$129$	95.2917	−	293.278i	0.0650385	−	0.200168i
$130$		0			0
$131$	−106.950	−	329.158i	−0.0713303	−	0.219532i	0.909036	−	0.416718i	$-0.136820\pi$
$131$	−106.950	−	329.158i	−0.0713303	−	0.219532i	−0.980366	+	0.197186i	$0.936820\pi$
$132$		0			0
$133$	−294.959	−	907.791i	−0.192302	−	0.591845i
$134$		0			0
$135$	921.759	+	1693.93i	0.587647	+	1.07993i
$136$		0			0
$137$	610.585	+	443.616i	0.380772	+	0.276647i	0.761664	−	0.647973i	$-0.224383\pi$
$137$	610.585	+	443.616i	0.380772	+	0.276647i	−0.380892	+	0.924620i	$0.624383\pi$
$138$		0			0
$139$	1619.65	−	1176.75i	0.988325	−	0.718060i	0.0287710	−	0.999586i	$-0.490841\pi$
$139$	1619.65	−	1176.75i	0.988325	−	0.718060i	0.959554	+	0.281526i	$0.0908407\pi$
$140$		0			0
$141$	3257.11	+	2366.43i	1.94538	+	1.41340i
$142$		0			0
$143$	1584.73			0.926724
$144$		0			0
$145$	−2576.45	−	1225.98i	−1.47560	−	0.702151i
$146$		0			0
$147$	74.0435	−	227.882i	0.0415442	−	0.127860i
$148$		0			0
$149$	−1066.44			−0.586348			−0.293174	−	0.956059i	$-0.594711\pi$
$149$	−1066.44			−0.586348			−0.293174	+	0.956059i	$0.594711\pi$
$150$		0			0
$151$	763.019			0.411216			0.205608	−	0.978634i	$-0.434083\pi$
$151$	763.019			0.411216			0.205608	+	0.978634i	$0.434083\pi$
$152$		0			0
$153$	994.057	−	3059.39i	0.525260	−	1.61658i
$154$		0			0
$155$	−2271.37	+	423.148i	−1.17704	+	0.219278i
$156$		0			0
$157$	62.3483			0.0316939			0.0158469	−	0.999874i	$-0.494956\pi$
$157$	62.3483			0.0316939			0.0158469	+	0.999874i	$0.494956\pi$
$158$		0			0
$159$	−4689.03	−	3406.78i	−2.33877	−	1.69921i
$160$		0			0
$161$	2393.81	−	1739.21i	1.17179	−	0.851358i
$162$		0			0
$163$	292.802	+	212.733i	0.140700	+	0.102224i	0.655909	−	0.754840i	$-0.272286\pi$
$163$	292.802	+	212.733i	0.140700	+	0.102224i	−0.515209	+	0.857065i	$0.672286\pi$
$164$		0			0
$165$	2744.04	−	511.204i	1.29468	−	0.241195i
$166$		0			0
$167$	449.335	+	1382.91i	0.208207	+	0.640795i	0.999566	+	0.0294442i	$0.00937373\pi$
$167$	449.335	+	1382.91i	0.208207	+	0.640795i	−0.791359	+	0.611351i	$0.790626\pi$
$168$		0			0
$169$	243.027	+	747.959i	0.110617	+	0.340446i
$170$		0			0
$171$	−781.656	+	2405.69i	−0.349560	+	1.07583i
$172$		0			0
$173$	1636.62	−	1189.07i	0.719248	−	0.522564i	−0.166896	−	0.985974i	$-0.553374\pi$
$173$	1636.62	−	1189.07i	0.719248	−	0.522564i	0.886144	+	0.463411i	$0.153374\pi$
$174$		0			0
$175$	−2144.52	−	570.371i	−0.926345	−	0.246377i
$176$		0			0
$177$	−2300.46	+	1671.38i	−0.976910	+	0.709767i
$178$		0			0
$179$	−393.779	+	1211.93i	−0.164427	+	0.506054i	−0.998994	−	0.0448528i	$-0.985718\pi$
$179$	−393.779	+	1211.93i	−0.164427	+	0.506054i	0.834567	+	0.550907i	$0.185718\pi$
$180$		0			0
$181$	−1331.48	−	4097.87i	−0.546784	−	1.68283i	−0.716709	−	0.697372i	$-0.754353\pi$
$181$	−1331.48	−	4097.87i	−0.546784	−	1.68283i	0.169925	−	0.985457i	$-0.445647\pi$
$182$		0			0
$183$	1053.15	+	3241.26i	0.425415	+	1.30929i
$184$		0			0
$185$	−1873.69	+	1978.12i	−0.744629	+	0.786131i
$186$		0			0
$187$	−1604.97	−	1166.08i	−0.627630	−	0.456000i
$188$		0			0
$189$	2477.31	−	1799.87i	0.953426	−	0.692704i
$190$		0			0
$191$	251.826	+	182.962i	0.0954004	+	0.0693124i	0.634463	−	0.772953i	$-0.281221\pi$
$191$	251.826	+	182.962i	0.0954004	+	0.0693124i	−0.539062	+	0.842266i	$0.681221\pi$
$192$		0			0
$193$	2675.32			0.997790			0.498895	−	0.866662i	$-0.333739\pi$
$193$	2675.32			0.997790			0.498895	+	0.866662i	$0.333739\pi$
$194$		0			0
$195$	2511.69	+	4615.76i	0.922387	+	1.69508i
$196$		0			0
$197$	286.433	−	881.549i	0.103591	−	0.318821i	−0.885806	−	0.464056i	$-0.846394\pi$
$197$	286.433	−	881.549i	0.103591	−	0.318821i	0.989397	+	0.145235i	$0.0463937\pi$
$198$		0			0
$199$	−444.199			−0.158233			−0.0791166	−	0.996865i	$-0.525210\pi$
$199$	−444.199			−0.158233			−0.0791166	+	0.996865i	$0.525210\pi$
$200$		0			0
$201$	−3067.24			−1.07635
$202$		0			0
$203$	−1400.01	+	4308.79i	−0.484046	+	1.48974i
$204$		0			0
$205$	−363.355	+	383.607i	−0.123794	+	0.130694i
$206$		0			0
$207$	−7841.27			−2.63288
$208$		0			0
$209$	1262.03	+	916.920i	0.417687	+	0.303467i
$210$		0			0
$211$	785.213	−	570.491i	0.256191	−	0.186134i	−0.452275	−	0.891878i	$-0.649387\pi$
$211$	785.213	−	570.491i	0.256191	−	0.186134i	0.708466	+	0.705745i	$0.249387\pi$
$212$		0			0
$213$	−2348.66	−	1706.40i	−0.755528	−	0.548923i
$214$		0			0
$215$	51.9294	−	397.283i	0.0164723	−	0.126021i
$216$		0			0
$217$	1133.67	+	3489.07i	0.354647	+	1.09149i
$218$		0			0
$219$	−1935.36	−	5956.44i	−0.597168	−	1.83789i
$220$		0			0
$221$	1154.13	−	3552.05i	0.351291	−	1.08116i
$222$		0			0
$223$	−3058.75	+	2222.31i	−0.918517	+	0.667342i	−0.943154	−	0.332355i	$-0.892157\pi$
$223$	−3058.75	+	2222.31i	−0.918517	+	0.667342i	0.0246375	+	0.999696i	$0.492157\pi$
$224$		0			0
$225$	3709.27	+	4563.27i	1.09904	+	1.35208i
$226$		0			0
$227$	3663.59	−	2661.76i	1.07120	−	0.778269i	0.0950686	−	0.995471i	$-0.469693\pi$
$227$	3663.59	−	2661.76i	1.07120	−	0.778269i	0.976127	+	0.217202i	$0.0696930\pi$
$228$		0			0
$229$	−1260.02	+	3877.95i	−0.363601	+	1.11905i	0.587251	+	0.809405i	$0.300210\pi$
$229$	−1260.02	+	3877.95i	−0.363601	+	1.11905i	−0.950852	+	0.309644i	$0.899790\pi$
$230$		0			0
$231$	−1369.58	−	4215.14i	−0.390094	−	1.20059i
$232$		0			0
$233$	−206.237	−	634.732i	−0.0579873	−	0.178466i	0.917867	−	0.396887i	$-0.129910\pi$
$233$	−206.237	−	634.732i	−0.0579873	−	0.178466i	−0.975855	+	0.218421i	$0.929910\pi$
$234$		0			0
$235$	4723.47	+	2247.62i	1.31117	+	0.623908i
$236$		0			0
$237$	−8851.30	−	6430.84i	−2.42596	−	1.76257i
$238$		0			0
$239$	−2791.34	+	2028.03i	−0.755468	+	0.548880i	−0.897517	−	0.440980i	$-0.854631\pi$
$239$	−2791.34	+	2028.03i	−0.755468	+	0.548880i	0.142049	+	0.989860i	$0.454631\pi$
$240$		0			0
$241$	−1805.47	−	1311.75i	−0.482575	−	0.350611i	0.319747	−	0.947503i	$-0.396402\pi$
$241$	−1805.47	−	1311.75i	−0.482575	−	0.350611i	−0.802322	+	0.596892i	$0.796402\pi$
$242$		0			0
$243$	2815.44			0.743252
$244$		0			0
$245$	40.3502	−	308.697i	0.0105219	−	0.0804976i
$246$		0			0
$247$	−907.527	+	2793.08i	−0.233784	+	0.719512i
$248$		0			0
$249$	−553.441			−0.140855
$250$		0			0
$251$	433.464			0.109004			0.0545021	−	0.998514i	$-0.482643\pi$
$251$	433.464			0.109004			0.0545021	+	0.998514i	$0.482643\pi$
$252$		0			0
$253$	−1494.34	+	4599.09i	−0.371336	+	1.14286i
$254$		0			0
$255$	852.611	−	6522.86i	0.209383	−	1.60187i
$256$		0			0
$257$	−5696.10			−1.38254			−0.691270	−	0.722596i	$-0.742949\pi$
$257$	−5696.10			−1.38254			−0.691270	+	0.722596i	$0.742949\pi$
$258$		0			0
$259$	3500.05	+	2542.93i	0.839700	+	0.610078i
$260$		0			0
$261$	9713.16	−	7057.02i	2.30356	−	1.67363i
$262$		0			0
$263$	2961.39	+	2151.57i	0.694323	+	0.504455i	0.878078	−	0.478517i	$-0.158825\pi$
$263$	2961.39	+	2151.57i	0.694323	+	0.504455i	−0.183755	+	0.982972i	$0.558825\pi$
$264$		0			0
$265$	−6800.04	−	3235.73i	−1.57631	−	0.750073i
$266$		0			0
$267$	1857.91	+	5718.07i	0.425852	+	1.31064i
$268$		0			0
$269$	786.765	+	2421.41i	0.178327	+	0.548833i	0.999770	−	0.0214573i	$-0.00683060\pi$
$269$	786.765	+	2421.41i	0.178327	+	0.548833i	−0.821443	+	0.570291i	$0.806831\pi$
$270$		0			0
$271$	1452.10	−	4469.10i	0.325493	−	1.00177i	−0.645724	−	0.763571i	$-0.723444\pi$
$271$	1452.10	−	4469.10i	0.325493	−	1.00177i	0.971217	−	0.238195i	$-0.0765557\pi$
$272$		0			0
$273$	6750.37	−	4904.43i	1.49652	−	1.08729i
$274$		0			0
$275$	3383.35	−	1305.94i	0.741905	−	0.286367i
$276$		0			0
$277$	−54.1557	+	39.3464i	−0.0117469	+	0.00853465i	−0.593643	−	0.804728i	$-0.702311\pi$
$277$	−54.1557	+	39.3464i	−0.0117469	+	0.00853465i	0.581896	+	0.813263i	$0.302311\pi$
$278$		0			0
$279$	3004.27	−	9246.21i	0.644664	−	1.98407i
$280$		0			0
$281$	1462.28	+	4500.43i	0.310435	+	0.955420i	0.977593	+	0.210504i	$0.0675104\pi$
$281$	1462.28	+	4500.43i	0.310435	+	0.955420i	−0.667158	+	0.744916i	$0.732490\pi$
$282$		0			0
$283$	1158.06	+	3564.15i	0.243250	+	0.748645i	0.995919	+	0.0902471i	$0.0287657\pi$
$283$	1158.06	+	3564.15i	0.243250	+	0.748645i	−0.752670	+	0.658398i	$0.771234\pi$
$284$		0			0
$285$	−670.433	+	5129.12i	−0.139344	+	1.06604i
$286$		0			0
$287$	678.747	+	493.138i	0.139600	+	0.101425i
$288$		0			0
$289$	192.156	−	139.609i	0.0391117	−	0.0284163i
$290$		0			0
$291$	6713.80	+	4877.86i	1.35247	+	0.982630i
$292$		0			0
$293$	−1309.24			−0.261046			−0.130523	−	0.991445i	$-0.541666\pi$
$293$	−1309.24			−0.261046			−0.130523	+	0.991445i	$0.541666\pi$
$294$		0			0
$295$	−2540.69	+	2682.29i	−0.501440	+	0.529387i
$296$		0			0
$297$	−1546.46	+	4759.50i	−0.302136	+	0.929880i
$298$		0			0
$299$	−9103.96			−1.76085
$300$		0			0
$301$	−636.188			−0.121825
$302$		0			0
$303$	121.921	−	375.236i	0.0231162	−	0.0711443i
$304$		0			0
$305$	2116.49	+	3889.50i	0.397343	+	0.730203i
$306$		0			0
$307$	5371.12			0.998521			0.499260	−	0.866452i	$-0.333605\pi$
$307$	5371.12			0.998521			0.499260	+	0.866452i	$0.333605\pi$
$308$		0			0
$309$	7922.33	+	5755.91i	1.45853	+	1.05968i
$310$		0			0
$311$	−3016.82	+	2191.85i	−0.550058	+	0.399640i	−0.827807	−	0.561013i	$-0.810412\pi$
$311$	−3016.82	+	2191.85i	−0.550058	+	0.399640i	0.277749	+	0.960654i	$0.410412\pi$
$312$		0			0
$313$	2357.81	+	1713.05i	0.425787	+	0.309352i	0.779962	−	0.625827i	$-0.215238\pi$
$313$	2357.81	+	1713.05i	0.425787	+	0.309352i	−0.354175	+	0.935179i	$0.615238\pi$
$314$		0			0
$315$	6421.27	−	6779.16i	1.14856	−	1.21258i
$316$		0			0
$317$	−1117.90	−	3440.56i	−0.198069	−	0.609593i	−0.999927	−	0.0120786i	$-0.996155\pi$
$317$	−1117.90	−	3440.56i	−0.198069	−	0.609593i	0.801858	−	0.597514i	$-0.203845\pi$
$318$		0			0
$319$	−2288.04	−	7041.87i	−0.401586	−	1.23595i
$320$		0			0
$321$	−4863.02	+	14966.8i	−0.845567	+	2.60239i
$322$		0			0
$323$	2974.33	−	2160.97i	0.512371	−	0.372259i
$324$		0			0
$325$	4306.57	+	5298.10i	0.735033	+	0.904263i
$326$		0			0
$327$	14625.4	−	10626.0i	2.47335	−	1.79699i
$328$		0			0
$329$	2566.67	−	7899.41i	0.430107	−	1.32373i
$330$		0			0
$331$	−3240.51	−	9973.25i	−0.538110	−	1.65613i	−0.736832	−	0.676076i	$-0.763679\pi$
$331$	−3240.51	−	9973.25i	−0.538110	−	1.65613i	0.198722	−	0.980056i	$-0.436321\pi$
$332$		0			0
$333$	−3542.85	−	10903.8i	−0.583024	−	1.79436i
$334$		0			0
$335$	−3917.83	+	729.877i	−0.638967	+	0.119037i
$336$		0			0
$337$	7558.32	+	5491.44i	1.22175	+	0.887650i	0.996244	−	0.0865929i	$-0.0275979\pi$
$337$	7558.32	+	5491.44i	1.22175	+	0.887650i	0.225502	+	0.974243i	$0.427598\pi$
$338$		0			0
$339$	−10409.8	+	7563.13i	−1.66779	+	1.21172i
$340$		0			0
$341$	−4850.58	−	3524.16i	−0.770305	−	0.559659i
$342$		0			0
$343$	−6583.47			−1.03637
$344$		0			0
$345$	−15764.0	+	2936.77i	−2.46001	+	0.458291i
$346$		0			0
$347$	−355.778	+	1094.97i	−0.0550408	+	0.169398i	−0.974798	−	0.223090i	$-0.928386\pi$
$347$	−355.778	+	1094.97i	−0.0550408	+	0.169398i	0.919757	+	0.392488i	$0.128386\pi$
$348$		0			0
$349$	8519.22			1.30666			0.653329	−	0.757074i	$-0.273372\pi$
$349$	8519.22			1.30666			0.653329	+	0.757074i	$0.273372\pi$
$350$		0			0
$351$	−9421.49			−1.43271
$352$		0			0
$353$	1970.86	−	6065.69i	0.297163	−	0.914572i	−0.685324	−	0.728238i	$-0.740339\pi$
$353$	1970.86	−	6065.69i	0.297163	−	0.914572i	0.982486	−	0.186334i	$-0.0596606\pi$
$354$		0			0
$355$	−3406.03	−	1620.73i	−0.509221	−	0.242308i
$356$		0			0
$357$	−10445.4			−1.54854
$358$		0			0
$359$	−4907.70	−	3565.65i	−0.721500	−	0.524200i	0.165363	−	0.986233i	$-0.447120\pi$
$359$	−4907.70	−	3565.65i	−0.721500	−	0.524200i	−0.886863	+	0.462032i	$0.847120\pi$
$360$		0			0
$361$	3210.25	−	2332.38i	0.468034	−	0.340047i
$362$		0			0
$363$	−3405.85	−	2474.50i	−0.492454	−	0.357789i
$364$		0			0
$365$	−3889.46	−	7147.71i	−0.557763	−	1.02501i
$366$		0			0
$367$	95.8646	+	295.041i	0.0136351	+	0.0419646i	0.957643	−	0.287959i	$-0.0929768\pi$
$367$	95.8646	+	295.041i	0.0136351	+	0.0419646i	−0.944007	+	0.329924i	$0.892977\pi$
$368$		0			0
$369$	−687.047	−	2114.51i	−0.0969275	−	0.298312i
$370$		0			0
$371$	−3695.05	+	11372.2i	−0.517082	+	1.59142i
$372$		0			0
$373$	−3550.51	+	2579.60i	−0.492865	+	0.358087i	−0.806285	−	0.591527i	$-0.798525\pi$
$373$	−3550.51	+	2579.60i	−0.492865	+	0.358087i	0.313420	+	0.949615i	$0.398525\pi$
$374$		0			0
$375$	9166.13	+	7784.71i	1.26223	+	1.07200i
$376$		0			0
$377$	11277.3	−	8193.42i	1.54061	−	1.11932i
$378$		0			0
$379$	498.339	−	1533.73i	0.0675408	−	0.207869i	−0.911590	−	0.411101i	$-0.865144\pi$
$379$	498.339	−	1533.73i	0.0675408	−	0.207869i	0.979131	+	0.203232i	$0.0651444\pi$
$380$		0			0
$381$	5392.02	+	16594.9i	0.725044	+	2.23146i
$382$		0			0
$383$	1552.99	+	4779.61i	0.207191	+	0.637667i	0.999616	+	0.0276987i	$0.00881791\pi$
$383$	1552.99	+	4779.61i	0.207191	+	0.637667i	−0.792426	+	0.609968i	$0.791182\pi$
$384$		0			0
$385$	−2752.41	−	5058.15i	−0.364353	−	0.669577i
$386$		0			0
$387$	1363.95	+	990.965i	0.179156	+	0.130164i
$388$		0			0
$389$	−9215.13	+	6695.18i	−1.20109	+	0.872646i	−0.994392	−	0.105758i	$-0.966273\pi$
$389$	−9215.13	+	6695.18i	−1.20109	+	0.872646i	−0.206702	+	0.978404i	$0.566273\pi$
$390$		0			0
$391$	9220.23	+	6698.89i	1.19255	+	0.866438i
$392$		0			0
$393$	2978.15			0.382259
$394$		0			0
$395$	−12836.2	−	6107.96i	−1.63508	−	0.778038i
$396$		0			0
$397$	−2459.89	+	7570.75i	−0.310978	+	0.957091i	0.666401	+	0.745594i	$0.267834\pi$
$397$	−2459.89	+	7570.75i	−0.310978	+	0.957091i	−0.977379	+	0.211498i	$0.932166\pi$
$398$		0			0
$399$	8213.49			1.03055
$400$		0			0
$401$	−7624.87			−0.949546			−0.474773	−	0.880108i	$-0.657470\pi$
$401$	−7624.87			−0.949546			−0.474773	+	0.880108i	$0.657470\pi$
$402$		0			0
$403$	3488.05	−	10735.1i	0.431147	−	1.32694i
$404$		0			0
$405$	−2352.50	+	438.262i	−0.288633	+	0.0537714i
$406$		0			0
$407$	−7070.49			−0.861108
$408$		0			0
$409$	8492.31	+	6170.03i	1.02669	+	0.745937i	0.967644	−	0.252318i	$-0.0811930\pi$
$409$	8492.31	+	6170.03i	1.02669	+	0.745937i	0.0590496	+	0.998255i	$0.481193\pi$
$410$		0			0
$411$	−5254.05	+	3817.29i	−0.630568	+	0.458134i
$412$		0			0
$413$	4746.00	+	3448.17i	0.565461	+	0.410831i
$414$		0			0
$415$	−706.918	+	131.696i	−0.0836175	+	0.0155776i
$416$		0			0
$417$	5323.47	+	16384.0i	0.625160	+	1.92404i
$418$		0			0
$419$	1278.02	+	3933.33i	0.149010	+	0.458605i	0.997505	−	0.0705983i	$-0.0224908\pi$
$419$	1278.02	+	3933.33i	0.149010	+	0.458605i	−0.848495	+	0.529203i	$0.822491\pi$
$420$		0			0
$421$	1907.69	−	5871.26i	0.220843	−	0.679685i	−0.777844	−	0.628458i	$-0.783687\pi$
$421$	1907.69	−	5871.26i	0.220843	−	0.679685i	0.998687	−	0.0512278i	$-0.0163135\pi$
$422$		0			0
$423$	−17807.4	+	12937.8i	−2.04687	+	1.48713i
$424$		0			0
$425$	−463.120	−	8534.63i	−0.0528580	−	0.974095i
$426$		0			0
$427$	5688.24	−	4132.75i	0.644668	−	0.468379i
$428$		0			0
$429$	−4213.91	+	12969.1i	−0.474241	+	1.45956i
$430$		0			0
$431$	−3461.82	−	10654.4i	−0.386891	−	1.19073i	−0.935099	−	0.354387i	$-0.884690\pi$
$431$	−3461.82	−	10654.4i	−0.386891	−	1.19073i	0.548207	−	0.836342i	$-0.315310\pi$
$432$		0			0
$433$	−4184.71	−	12879.2i	−0.464444	−	1.42941i	−0.859681	−	0.510832i	$-0.829338\pi$
$433$	−4184.71	−	12879.2i	−0.464444	−	1.42941i	0.395237	−	0.918579i	$-0.370662\pi$
$434$		0			0
$435$	16884.1	−	17825.2i	1.86099	−	1.96472i
$436$		0			0
$437$	−7250.13	−	5267.53i	−0.793641	−	0.576614i
$438$		0			0
$439$	1753.39	−	1273.91i	0.190626	−	0.138498i	−0.488379	−	0.872632i	$-0.662412\pi$
$439$	1753.39	−	1273.91i	0.190626	−	0.138498i	0.679005	+	0.734134i	$0.262412\pi$
$440$		0			0
$441$	1059.81	+	769.999i	0.114438	+	0.0831443i
$442$		0			0
$443$	−13212.9			−1.41708			−0.708539	−	0.705672i	$-0.750645\pi$
$443$	−13212.9			−1.41708			−0.708539	+	0.705672i	$0.750645\pi$
$444$		0			0
$445$	3733.81	+	6861.67i	0.397751	+	0.730953i
$446$		0			0
$447$	2835.74	−	8727.50i	0.300057	−	0.923482i
$448$		0			0
$449$	−1921.34			−0.201946			−0.100973	−	0.994889i	$-0.532195\pi$
$449$	−1921.34			−0.201946			−0.100973	+	0.994889i	$0.532195\pi$
$450$		0			0
$451$	−1371.14			−0.143159
$452$		0			0
$453$	−2028.93	+	6244.39i	−0.210435	+	0.647654i
$454$		0			0
$455$	7455.29	−	7870.81i	0.768152	−	0.810965i
$456$		0			0
$457$	−117.313			−0.0120080			−0.00600399	−	0.999982i	$-0.501911\pi$
$457$	−117.313			−0.0120080			−0.00600399	+	0.999982i	$0.501911\pi$
$458$		0			0
$459$	9541.82	+	6932.53i	0.970313	+	0.704974i
$460$		0			0
$461$	7795.85	−	5664.02i	0.787611	−	0.572233i	−0.119642	−	0.992817i	$-0.538175\pi$
$461$	7795.85	−	5664.02i	0.787611	−	0.572233i	0.907254	+	0.420584i	$0.138175\pi$
$462$		0			0
$463$	−5132.47	−	3728.95i	−0.515175	−	0.374296i	0.299608	−	0.954062i	$-0.403144\pi$
$463$	−5132.47	−	3728.95i	−0.515175	−	0.374296i	−0.814783	+	0.579766i	$0.803144\pi$
$464$		0			0
$465$	2576.79	−	19713.6i	0.256980	−	1.96602i
$466$		0			0
$467$	−3277.59	−	10087.4i	−0.324773	−	0.999548i	−0.971543	−	0.236863i	$-0.923881\pi$
$467$	−3277.59	−	10087.4i	−0.324773	−	0.999548i	0.646770	−	0.762685i	$-0.276119\pi$
$468$		0			0
$469$	1955.43	+	6018.21i	0.192524	+	0.592526i
$470$		0			0
$471$	−165.789	+	510.246i	−0.0162190	+	0.0499170i
$472$		0			0
$473$	841.156	−	611.136i	0.0817683	−	0.0594081i
$474$		0			0
$475$	364.165	+	6711.03i	0.0351769	+	0.648259i
$476$		0			0
$477$	25636.0	−	18625.6i	2.46078	−	1.78786i
$478$		0			0
$479$	2570.20	−	7910.25i	0.245168	−	0.754548i	−0.750441	−	0.660937i	$-0.770159\pi$
$479$	2570.20	−	7910.25i	0.245168	−	0.754548i	0.995609	−	0.0936111i	$-0.0298410\pi$
$480$		0			0
$481$	−4113.36	−	12659.6i	−0.389923	−	1.20006i
$482$		0			0
$483$	7867.98	+	24215.2i	0.741213	+	2.28122i
$484$		0			0
$485$	9736.37	+	4632.95i	0.911558	+	0.433756i
$486$		0			0
$487$	1805.83	+	1312.02i	0.168029	+	0.122080i	0.668622	−	0.743603i	$-0.266885\pi$
$487$	1805.83	+	1312.02i	0.168029	+	0.122080i	−0.500593	+	0.865683i	$0.666885\pi$
$488$		0			0
$489$	−2519.55	+	1830.56i	−0.233002	+	0.169286i
$490$		0			0
$491$	6421.33	+	4665.37i	0.590205	+	0.428809i	0.842389	−	0.538871i	$-0.181149\pi$
$491$	6421.33	+	4665.37i	0.590205	+	0.428809i	−0.252184	+	0.967679i	$0.581149\pi$
$492$		0			0
$493$	−17450.2			−1.59415
$494$		0			0
$495$	−1977.88	+	15131.7i	−0.179594	+	1.37398i
$496$		0			0
$497$	−1850.79	+	5696.16i	−0.167041	+	0.514100i
$498$		0			0
$499$	16900.0			1.51612			0.758062	−	0.652182i	$-0.226146\pi$
$499$	16900.0			1.51612			0.758062	+	0.652182i	$0.226146\pi$
$500$		0			0
$501$	−12512.3			−1.11578
$502$		0			0
$503$	−80.8923	+	248.961i	−0.00717059	+	0.0220688i	−0.954578	−	0.297962i	$-0.903693\pi$
$503$	−80.8923	+	248.961i	−0.00717059	+	0.0220688i	0.947407	+	0.320031i	$0.103693\pi$
$504$		0			0
$505$	66.4413	−	508.306i	0.00585465	−	0.0447907i
$506$		0			0
$507$	−6767.37			−0.592800
$508$		0			0
$509$	15761.2	+	11451.2i	1.37250	+	0.997181i	0.997537	+	0.0701412i	$0.0223450\pi$
$509$	15761.2	+	11451.2i	1.37250	+	0.997181i	0.374964	+	0.927039i	$0.377655\pi$
$510$		0			0
$511$	−10453.2	+	7594.73i	−0.904940	+	0.657477i
$512$		0			0
$513$	−7503.01	−	5451.26i	−0.645743	−	0.469159i
$514$		0			0
$515$	11489.0	+	5466.92i	0.983038	+	0.467769i
$516$		0			0
$517$	4194.73	+	12910.0i	0.356835	+	1.09823i
$518$		0			0
$519$	5379.24	+	16555.6i	0.454956	+	1.40021i
$520$		0			0
$521$	−3787.38	+	11656.3i	−0.318480	+	0.980180i	0.655819	+	0.754918i	$0.272324\pi$
$521$	−3787.38	+	11656.3i	−0.318480	+	0.980180i	−0.974298	+	0.225261i	$0.927676\pi$
$522$		0			0
$523$	9567.80	−	6951.42i	0.799944	−	0.581193i	−0.110954	−	0.993826i	$-0.535390\pi$
$523$	9567.80	−	6951.42i	0.799944	−	0.581193i	0.910898	+	0.412632i	$0.135390\pi$
$524$		0			0
$525$	10370.2	−	16033.7i	0.862085	−	1.33289i
$526$		0			0
$527$	−11431.7	+	8305.65i	−0.944923	+	0.686527i
$528$		0			0
$529$	4824.87	−	14849.4i	0.396553	−	1.22047i
$530$		0			0
$531$	−4804.04	−	14785.3i	−0.392613	−	1.20834i
$532$		0			0
$533$	−797.683	−	2455.01i	−0.0648245	−	0.199509i
$534$		0			0
$535$	−2650.11	+	20274.5i	−0.214157	+	1.63840i
$536$		0			0
$537$	−8871.08	−	6445.22i	−0.712878	−	0.517936i
$538$		0			0
$539$	653.595	−	474.864i	0.0522306	−	0.0379478i
$540$		0			0
$541$	−675.028	−	490.436i	−0.0536446	−	0.0389751i	0.560640	−	0.828060i	$-0.310555\pi$
$541$	−675.028	−	490.436i	−0.0536446	−	0.0389751i	−0.614284	+	0.789085i	$0.710555\pi$
$542$		0			0
$543$	37076.6			2.93022
$544$		0			0
$545$	16152.7	−	17052.9i	1.26955	−	1.34031i
$546$		0			0
$547$	3979.68	−	12248.2i	0.311077	−	0.957396i	−0.666263	−	0.745717i	$-0.732107\pi$
$547$	3979.68	−	12248.2i	0.311077	−	0.957396i	0.977339	−	0.211679i	$-0.0678930\pi$
$548$		0			0
$549$	−18632.6			−1.44849
$550$		0			0
$551$	13721.6			1.06091
$552$		0			0
$553$	−6975.01	+	21466.9i	−0.536361	+	1.65075i
$554$		0			0
$555$	−11206.2	−	20593.9i	−0.857079	−	1.57507i
$556$		0			0
$557$	−10133.4			−0.770852			−0.385426	−	0.922739i	$-0.625945\pi$
$557$	−10133.4			−0.770852			−0.385426	+	0.922739i	$0.625945\pi$
$558$		0			0
$559$	1583.58	+	1150.54i	0.119818	+	0.0870531i
$560$		0			0
$561$	13810.7	−	10034.0i	1.03937	−	0.755146i
$562$		0			0
$563$	−15648.3	−	11369.2i	−1.17140	−	0.851073i	−0.180226	−	0.983625i	$-0.557683\pi$
$563$	−15648.3	−	11369.2i	−1.17140	−	0.851073i	−0.991176	+	0.132552i	$0.957683\pi$
$564$		0			0
$565$	−11496.8	+	12137.6i	−0.856061	+	0.903774i
$566$		0			0
$567$	1174.16	+	3613.69i	0.0869666	+	0.267656i
$568$		0			0
$569$	−5265.90	−	16206.8i	−0.387975	−	1.19407i	−0.934299	−	0.356491i	$-0.883973\pi$
$569$	−5265.90	−	16206.8i	−0.387975	−	1.19407i	0.546323	−	0.837574i	$-0.316027\pi$
$570$		0			0
$571$	−5894.02	+	18139.9i	−0.431974	+	1.32948i	0.464182	+	0.885740i	$0.346348\pi$
$571$	−5894.02	+	18139.9i	−0.431974	+	1.32948i	−0.896156	+	0.443739i	$0.853652\pi$
$572$		0			0
$573$	−2166.95	+	1574.38i	−0.157985	+	0.114783i
$574$		0			0
$575$	−19436.7	+	7502.36i	−1.40968	+	0.544122i
$576$		0			0
$577$	−7797.16	+	5664.97i	−0.562565	+	0.408727i	−0.832397	−	0.554180i	$-0.813032\pi$
$577$	−7797.16	+	5664.97i	−0.562565	+	0.408727i	0.269832	+	0.962907i	$0.413032\pi$
$578$		0			0
$579$	−7113.88	+	21894.3i	−0.510609	+	1.57149i
$580$		0			0
$581$	352.831	+	1085.90i	0.0251943	+	0.0775401i
$582$		0			0
$583$	−6038.84	−	18585.7i	−0.428994	−	1.32031i
$584$		0			0
$585$	−28243.7	+	5261.70i	−1.99613	+	0.371871i
$586$		0			0
$587$	−57.2082	−	41.5642i	−0.00402255	−	0.00292255i	0.585772	−	0.810476i	$-0.300791\pi$
$587$	−57.2082	−	41.5642i	−0.00402255	−	0.00292255i	−0.589795	+	0.807553i	$0.700791\pi$
$588$		0			0
$589$	8989.11	−	6530.97i	0.628845	−	0.456883i
$590$		0			0
$591$	6452.78	+	4688.22i	0.449123	+	0.326307i
$592$		0			0
$593$	10023.6			0.694134			0.347067	−	0.937840i	$-0.387178\pi$
$593$	10023.6			0.694134			0.347067	+	0.937840i	$0.387178\pi$
$594$		0			0
$595$	−13342.0	+	2485.57i	−0.919276	+	0.171258i
$596$		0			0
$597$	1181.16	−	3635.23i	0.0809742	−	0.249213i
$598$		0			0
$599$	−20888.2			−1.42483			−0.712413	−	0.701761i	$-0.752398\pi$
$599$	−20888.2			−1.42483			−0.712413	+	0.701761i	$0.752398\pi$
$600$		0			0
$601$	15619.9			1.06015			0.530073	−	0.847952i	$-0.322165\pi$
$601$	15619.9			1.06015			0.530073	+	0.847952i	$0.322165\pi$
$602$		0			0
$603$	5182.00	−	15948.5i	0.349962	−	1.07707i
$604$		0			0
$605$	−4939.17	−	2350.26i	−0.331910	−	0.157936i
$606$		0			0
$607$	12370.5			0.827190			0.413595	−	0.910461i	$-0.364273\pi$
$607$	12370.5			0.827190			0.413595	+	0.910461i	$0.364273\pi$
$608$		0			0
$609$	−31539.5	−	22914.8i	−2.09860	−	1.52472i
$610$		0			0
$611$	−20674.9	+	15021.2i	−1.36893	+	0.994587i
$612$		0			0
$613$	−1900.10	−	1380.50i	−0.125194	−	0.0909591i	0.523426	−	0.852071i	$-0.324654\pi$
$613$	−1900.10	−	1380.50i	−0.125194	−	0.0909591i	−0.648620	+	0.761112i	$0.724654\pi$
$614$		0			0
$615$	−2173.17	−	3993.67i	−0.142489	−	0.261854i
$616$		0			0
$617$	1528.69	+	4704.81i	0.0997449	+	0.306983i	0.988461	−	0.151474i	$-0.0484021\pi$
$617$	1528.69	+	4704.81i	0.0997449	+	0.306983i	−0.888716	+	0.458458i	$0.848402\pi$
$618$		0			0
$619$	−3757.04	−	11563.0i	−0.243955	−	0.750816i	−0.995807	−	0.0914835i	$-0.970839\pi$
$619$	−3757.04	−	11563.0i	−0.243955	−	0.750816i	0.751852	−	0.659332i	$-0.229161\pi$
$620$		0			0
$621$	8884.10	−	27342.4i	0.574085	−	1.76685i
$622$		0			0
$623$	10034.9	−	7290.80i	0.645330	−	0.468860i
$624$		0			0
$625$	13560.5	+	7762.36i	0.867870	+	0.496791i
$626$		0			0
$627$	−10859.7	+	7890.05i	−0.691700	+	0.502549i
$628$		0			0
$629$	−5149.32	+	15848.0i	−0.326418	+	1.00461i
$630$		0			0
$631$	−569.989	−	1754.25i	−0.0359603	−	0.110674i	0.931465	−	0.363831i	$-0.118531\pi$
$631$	−569.989	−	1754.25i	−0.0359603	−	0.110674i	−0.967425	+	0.253156i	$0.918531\pi$
$632$		0			0
$633$	2580.84	+	7943.01i	0.162052	+	0.498746i
$634$		0			0
$635$	10836.2	+	19913.9i	0.677201	+	1.24450i
$636$		0			0
$637$	1230.48	+	893.993i	0.0765357	+	0.0556064i
$638$		0			0
$639$	12840.7	−	9329.28i	0.794943	−	0.577560i
$640$		0			0
$641$	10619.6	+	7715.58i	0.654365	+	0.475424i	0.864755	−	0.502193i	$-0.167473\pi$
$641$	10619.6	+	7715.58i	0.654365	+	0.475424i	−0.210390	+	0.977618i	$0.567473\pi$
$642$		0			0
$643$	−16752.9			−1.02748			−0.513740	−	0.857946i	$-0.671740\pi$
$643$	−16752.9			−1.02748			−0.513740	+	0.857946i	$0.671740\pi$
$644$		0			0
$645$	3113.20	+	1481.39i	0.190050	+	0.0904334i
$646$		0			0
$647$	−2408.91	+	7413.87i	−0.146374	+	0.450493i	−0.997185	−	0.0749785i	$-0.976111\pi$
$647$	−2408.91	+	7413.87i	−0.146374	+	0.450493i	0.850811	+	0.525472i	$0.176111\pi$
$648$		0			0
$649$	−9587.45			−0.579877
$650$		0			0
$651$	−31568.3			−1.90055
$652$		0			0
$653$	−3725.85	+	11467.0i	−0.223283	+	0.687194i	0.775178	+	0.631742i	$0.217660\pi$
$653$	−3725.85	+	11467.0i	−0.223283	+	0.687194i	−0.998461	+	0.0554519i	$0.982340\pi$
$654$		0			0
$655$	3804.04	−	708.678i	0.226925	−	0.0422753i
$656$		0			0
$657$	34241.1			2.03329
$658$		0			0
$659$	−17896.8	−	13002.8i	−1.05791	−	0.768615i	−0.0842072	−	0.996448i	$-0.526836\pi$
$659$	−17896.8	−	13002.8i	−1.05791	−	0.768615i	−0.973700	+	0.227834i	$0.926836\pi$
$660$		0			0
$661$	5644.88	−	4101.24i	0.332164	−	0.241331i	−0.409184	−	0.912452i	$-0.634187\pi$
$661$	5644.88	−	4101.24i	0.332164	−	0.241331i	0.741348	+	0.671121i	$0.234187\pi$
$662$		0			0
$663$	26000.3	+	18890.3i	1.52303	+	1.10655i
$664$		0			0
$665$	10491.2	−	1954.47i	0.611777	−	0.113972i
$666$		0			0
$667$	13144.4	+	40454.2i	0.763047	+	2.34842i
$668$		0			0
$669$	−10053.5	−	30941.5i	−0.581003	−	1.78814i
$670$		0			0
$671$	−3550.88	+	10928.5i	−0.204292	+	0.628747i
$672$		0			0
$673$	4422.80	−	3213.35i	0.253323	−	0.184050i	−0.453875	−	0.891065i	$-0.649959\pi$
$673$	4422.80	−	3213.35i	0.253323	−	0.184050i	0.707198	+	0.707015i	$0.249959\pi$
$674$		0			0
$675$	−20114.7	+	7764.03i	−1.14698	+	0.442723i
$676$		0			0
$677$	1310.83	−	952.371i	0.0744153	−	0.0540659i	−0.549956	−	0.835194i	$-0.685355\pi$
$677$	1310.83	−	952.371i	0.0744153	−	0.0540659i	0.624371	+	0.781128i	$0.285355\pi$
$678$		0			0
$679$	5290.62	−	16282.8i	0.299021	−	0.920292i
$680$		0			0
$681$	12041.5	+	37059.9i	0.677579	+	2.08537i
$682$		0			0
$683$	709.376	+	2183.24i	0.0397416	+	0.122312i	0.968959	−	0.247221i	$-0.0795175\pi$
$683$	709.376	+	2183.24i	0.0397416	+	0.122312i	−0.929217	+	0.369534i	$0.879517\pi$
$684$		0			0
$685$	−5802.72	+	6126.13i	−0.323665	+	0.341704i
$686$		0			0
$687$	−28385.9	−	20623.5i	−1.57640	−	1.14532i
$688$		0			0
$689$	29764.2	−	21624.9i	1.64575	−	1.19571i
$690$		0			0
$691$	−20404.4	−	14824.6i	−1.12333	−	0.816144i	−0.138616	−	0.990346i	$-0.544266\pi$
$691$	−20404.4	−	14824.6i	−1.12333	−	0.816144i	−0.984710	+	0.174202i	$0.944266\pi$
$692$		0			0
$693$	24231.1			1.32823
$694$		0			0
$695$	10698.5	+	19660.7i	0.583908	+	1.07306i
$696$		0			0
$697$	−998.582	+	3073.32i	−0.0542669	+	0.167016i
$698$		0			0
$699$	5742.92			0.310754
$700$		0			0
$701$	9744.88			0.525049			0.262524	−	0.964925i	$-0.415445\pi$
$701$	9744.88			0.525049			0.262524	+	0.964925i	$0.415445\pi$
$702$		0			0
$703$	4049.06	−	12461.7i	0.217231	−	0.668568i
$704$		0			0
$705$	−30954.1	+	32679.3i	−1.65362	+	1.74578i
$706$		0			0
$707$	−813.974			−0.0432994
$708$		0			0
$709$	−26149.3	−	18998.6i	−1.38513	−	1.00636i	−0.996380	−	0.0850142i	$-0.972906\pi$
$709$	−26149.3	−	18998.6i	−1.38513	−	1.00636i	−0.388752	−	0.921343i	$-0.627094\pi$
$710$		0			0
$711$	48392.1	−	35158.9i	2.55252	−	1.85452i
$712$		0			0
$713$	27865.7	+	20245.6i	1.46364	+	1.06340i
$714$		0			0
$715$	−2296.38	+	17568.3i	−0.120111	+	0.918907i
$716$		0			0
$717$	−9174.58	−	28236.5i	−0.477867	−	1.47072i
$718$		0			0
$719$	11657.9	+	35879.3i	0.604681	+	1.86102i	0.498970	+	0.866619i	$0.333712\pi$
$719$	11657.9	+	35879.3i	0.604681	+	1.86102i	0.105711	+	0.994397i	$0.466288\pi$
$720$		0			0
$721$	6242.96	−	19213.9i	0.322469	−	0.992457i
$722$		0			0
$723$	15536.0	−	11287.5i	0.799155	−	0.580620i
$724$		0			0
$725$	17324.7	−	26786.1i	0.887480	−	1.37215i
$726$		0			0
$727$	−14187.1	+	10307.5i	−0.723756	+	0.525840i	−0.887582	−	0.460650i	$-0.847616\pi$
$727$	−14187.1	+	10307.5i	−0.723756	+	0.525840i	0.163826	+	0.986489i	$0.447616\pi$
$728$		0			0
$729$	−9272.25	+	28537.0i	−0.471079	+	1.44983i
$730$		0			0
$731$	−757.216	−	2330.47i	−0.0383128	−	0.117915i
$732$		0			0
$733$	−4004.96	−	12326.0i	−0.201810	−	0.621107i	−0.999829	−	0.0184751i	$-0.994119\pi$
$733$	−4004.96	−	12326.0i	−0.201810	−	0.621107i	0.798020	−	0.602632i	$-0.205881\pi$
$734$		0			0
$735$	2419.02	+	1151.07i	0.121397	+	0.0577656i
$736$		0			0
$737$	−8366.65	−	6078.73i	−0.418168	−	0.303816i
$738$		0			0
$739$	14750.5	−	10716.9i	0.734245	−	0.533460i	−0.156659	−	0.987653i	$-0.550072\pi$
$739$	14750.5	−	10716.9i	0.734245	−	0.533460i	0.890903	+	0.454193i	$0.150072\pi$
$740$		0			0
$741$	−20444.8	−	14854.0i	−1.01358	−	0.736406i
$742$		0			0
$743$	11715.5			0.578464			0.289232	−	0.957259i	$-0.406600\pi$
$743$	11715.5			0.578464			0.289232	+	0.957259i	$0.406600\pi$
$744$		0			0
$745$	1545.34	−	11822.5i	0.0759958	−	0.581402i
$746$		0			0
$747$	935.020	−	2877.70i	0.0457973	−	0.140950i
$748$		0			0
$749$	32466.6			1.58385
$750$		0			0
$751$	37841.6			1.83870			0.919348	−	0.393444i	$-0.128717\pi$
$751$	37841.6			1.83870			0.919348	+	0.393444i	$0.128717\pi$
$752$		0			0
$753$	−1152.62	+	3547.39i	−0.0557817	+	0.171679i
$754$		0			0
$755$	−1105.67	+	8458.85i	−0.0532972	+	0.407747i
$756$		0			0
$757$	−19408.2			−0.931841			−0.465921	−	0.884826i	$-0.654277\pi$
$757$	−19408.2			−0.931841			−0.465921	+	0.884826i	$0.654277\pi$
$758$		0			0
$759$	−33664.5	−	24458.7i	−1.60994	−	1.16969i
$760$		0			0
$761$	−16492.9	+	11982.8i	−0.785635	+	0.570797i	−0.906665	−	0.421852i	$-0.861380\pi$
$761$	−16492.9	+	11982.8i	−0.785635	+	0.570797i	0.121030	+	0.992649i	$0.461380\pi$
$762$		0			0
$763$	−30173.1	−	21922.1i	−1.43164	−	1.04015i
$764$		0			0
$765$	32476.1	+	15453.4i	1.53487	+	0.730353i
$766$		0			0
$767$	−5577.63	−	17166.2i	−0.262577	−	0.808130i
$768$		0			0
$769$	9147.67	+	28153.6i	0.428964	+	1.32022i	0.899147	+	0.437647i	$0.144188\pi$
$769$	9147.67	+	28153.6i	0.428964	+	1.32022i	−0.470183	+	0.882569i	$0.655812\pi$
$770$		0			0
$771$	15146.4	−	46615.7i	0.707501	−	2.17746i
$772$		0			0
$773$	3627.57	−	2635.58i	0.168790	−	0.122633i	−0.500183	−	0.865920i	$-0.666734\pi$
$773$	3627.57	−	2635.58i	0.168790	−	0.122633i	0.668973	+	0.743287i	$0.266734\pi$
$774$		0			0
$775$	−1399.66	−	25793.7i	−0.0648738	−	1.19553i
$776$		0			0
$777$	−30117.7	+	21881.8i	−1.39056	+	1.01030i
$778$		0			0
$779$	785.215	−	2416.64i	0.0361145	−	0.111149i
$780$		0			0
$781$	−3024.76	−	9309.26i	−0.138584	−	0.426519i
$782$		0			0
$783$	13602.8	+	41865.2i	0.620850	+	1.91078i
$784$		0			0
$785$	−90.3470	+	691.196i	−0.00410780	+	0.0314265i
$786$		0			0
$787$	−7659.76	−	5565.14i	−0.346939	−	0.252066i	0.400645	−	0.916233i	$-0.368786\pi$
$787$	−7659.76	−	5565.14i	−0.346939	−	0.252066i	−0.747584	+	0.664168i	$0.768786\pi$
$788$		0			0
$789$	−25482.6	+	18514.2i	−1.14982	+	0.835390i
$790$		0			0
$791$	21476.0	+	15603.2i	0.965359	+	0.701374i
$792$		0			0
$793$	−21633.1			−0.968742
$794$		0			0
$795$	44562.4	−	47046.1i	1.98801	−	2.09881i
$796$		0			0
$797$	530.071	−	1631.39i	0.0235584	−	0.0725054i	−0.938586	−	0.345045i	$-0.887864\pi$
$797$	530.071	−	1631.39i	0.0235584	−	0.0725054i	0.962145	+	0.272540i	$0.0878636\pi$
$798$		0			0
$799$	31991.9			1.41651
$800$		0			0
$801$	−32870.8			−1.44998
$802$		0			0
$803$	6525.43	−	20083.2i	0.286771	−	0.882591i
$804$		0			0
$805$	15812.1	+	29058.1i	0.692302	+	1.27225i
$806$		0			0
$807$	−21908.4			−0.955654
$808$		0			0
$809$	−1951.87	−	1418.12i	−0.0848260	−	0.0616297i	0.544564	−	0.838719i	$-0.316695\pi$
$809$	−1951.87	−	1418.12i	−0.0848260	−	0.0616297i	−0.629390	+	0.777090i	$0.716695\pi$
$810$		0			0
$811$	14561.4	−	10579.5i	0.630481	−	0.458071i	−0.226086	−	0.974107i	$-0.572593\pi$
$811$	14561.4	−	10579.5i	0.630481	−	0.458071i	0.856567	+	0.516036i	$0.172593\pi$
$812$		0			0
$813$	32713.0	+	23767.4i	1.41119	+	1.02529i
$814$		0			0
$815$	−2782.66	+	2937.75i	−0.119598	+	0.126264i
$816$		0			0
$817$	595.421	+	1832.52i	0.0254971	+	0.0784720i
$818$		0			0
$819$	14096.8	+	43385.4i	0.601442	+	1.85105i
$820$		0			0
$821$	−7847.92	+	24153.4i	−0.333610	+	1.02675i	0.633792	+	0.773503i	$0.281497\pi$
$821$	−7847.92	+	24153.4i	−0.333610	+	1.02675i	−0.967402	+	0.253244i	$0.918503\pi$
$822$		0			0
$823$	−28270.1	+	20539.4i	−1.19737	+	0.869939i	−0.994023	−	0.109168i	$-0.965181\pi$
$823$	−28270.1	+	20539.4i	−1.19737	+	0.869939i	−0.203345	+	0.979107i	$0.565181\pi$
$824$		0			0
$825$	1690.92	+	31161.3i	0.0713581	+	1.31503i
$826$		0			0
$827$	−2941.52	+	2137.14i	−0.123684	+	0.0898617i	−0.647907	−	0.761719i	$-0.724356\pi$
$827$	−2941.52	+	2137.14i	−0.123684	+	0.0898617i	0.524223	+	0.851581i	$0.324356\pi$
$828$		0			0
$829$	2810.25	−	8649.07i	0.117737	−	0.362358i	−0.874771	−	0.484537i	$-0.838988\pi$
$829$	2810.25	−	8649.07i	0.117737	−	0.362358i	0.992508	+	0.122179i	$0.0389882\pi$
$830$		0			0
$831$	−177.999	−	547.825i	−0.00743047	−	0.0228686i
$832$		0			0
$833$	−588.371	−	1810.82i	−0.0244728	−	0.0753196i
$834$		0			0
$835$	−15982.1	+	2977.41i	−0.662376	+	0.123398i
$836$		0			0
$837$	28837.6	+	20951.8i	1.19089	+	0.865231i
$838$		0			0
$839$	1495.42	−	1086.49i	0.0615349	−	0.0447077i	−0.556593	−	0.830786i	$-0.687892\pi$
$839$	1495.42	−	1086.49i	0.0615349	−	0.0447077i	0.618127	+	0.786078i	$0.287892\pi$
$840$		0			0
$841$	−32959.3	−	23946.3i	−1.35140	−	0.981850i
$842$		0			0
$843$	−40718.9			−1.66362
$844$		0			0
$845$	−8644.06	+	1610.36i	−0.351911	+	0.0655597i
$846$		0			0
$847$	−2683.88	+	8260.14i	−0.108878	+	0.335091i
$848$		0			0
$849$	−32247.6			−1.30358
$850$		0			0
$851$	40618.6			1.63618
$852$		0			0
$853$	−7487.34	+	23043.7i	−0.300541	+	0.924970i	0.680762	+	0.732504i	$0.261649\pi$
$853$	−7487.34	+	23043.7i	−0.300541	+	0.924970i	−0.981304	+	0.192466i	$0.938351\pi$
$854$		0			0
$855$	−25536.9	−	12151.5i	−1.02145	−	0.486049i
$856$		0			0
$857$	−34.5262			−0.00137619			−0.000688093	−	1.00000i	$-0.500219\pi$
$857$	−34.5262			−0.00137619			−0.000688093		1.00000i	$0.500219\pi$
$858$		0			0
$859$	13264.5	+	9637.23i	0.526868	+	0.382792i	0.819185	−	0.573530i	$-0.194426\pi$
$859$	13264.5	+	9637.23i	0.526868	+	0.382792i	−0.292317	+	0.956321i	$0.594426\pi$
$860$		0			0
$861$	−5840.58	+	4243.43i	−0.231181	+	0.167963i
$862$		0			0
$863$	29990.7	+	21789.5i	1.18296	+	0.859470i	0.992502	−	0.122225i	$-0.0390031\pi$
$863$	29990.7	+	21789.5i	1.18296	+	0.859470i	0.190457	+	0.981696i	$0.439003\pi$
$864$		0			0
$865$	10810.5	+	19866.7i	0.424935	+	0.780910i
$866$		0			0
$867$	631.578	+	1943.80i	0.0247399	+	0.0761416i
$868$		0			0
$869$	−11399.3	−	35083.4i	−0.444988	−	1.36953i
$870$		0			0
$871$	6016.46	−	18516.7i	0.234053	−	0.720340i
$872$		0			0
$873$	−36705.9	+	26668.4i	−1.42303	+	1.03389i
$874$		0			0
$875$	9430.71	−	22947.7i	0.364361	−	0.886599i
$876$		0			0
$877$	−23502.3	+	17075.4i	−0.904922	+	0.657464i	−0.939725	−	0.341930i	$-0.888919\pi$
$877$	−23502.3	+	17075.4i	−0.904922	+	0.657464i	0.0348035	+	0.999394i	$0.488919\pi$
$878$		0			0
$879$	3481.37	−	10714.6i	0.133588	−	0.411141i
$880$		0			0
$881$	−11842.9	−	36448.7i	−0.452891	−	1.39386i	−0.873593	−	0.486657i	$-0.838216\pi$
$881$	−11842.9	−	36448.7i	−0.452891	−	1.39386i	0.420702	−	0.907199i	$-0.361784\pi$
$882$		0			0
$883$	−2481.19	−	7636.32i	−0.0945625	−	0.291033i	0.892577	−	0.450895i	$-0.148895\pi$
$883$	−2481.19	−	7636.32i	−0.0945625	−	0.291033i	−0.987139	+	0.159862i	$0.948895\pi$
$884$		0			0
$885$	−15195.5	−	27924.9i	−0.577164	−	1.06066i
$886$		0			0
$887$	−3281.46	−	2384.12i	−0.124217	−	0.0902491i	0.523942	−	0.851754i	$-0.324461\pi$
$887$	−3281.46	−	2384.12i	−0.124217	−	0.0902491i	−0.648159	+	0.761505i	$0.724461\pi$
$888$		0			0
$889$	29123.3	−	21159.3i	1.09872	−	0.798268i
$890$		0			0
$891$	−5023.83	−	3650.03i	−0.188894	−	0.137240i
$892$		0			0
$893$	−25156.1			−0.942686
$894$		0			0
$895$	−12864.9	−	6121.62i	−0.480475	−	0.228629i
$896$		0			0
$897$	24208.1	−	74504.9i	0.901099	−	2.77330i
$898$		0			0
$899$	−52738.6			−1.95654
$900$		0			0
$901$	−46056.4			−1.70295
$902$		0			0
$903$	1691.67	−	5206.44i	0.0623426	−	0.191871i
$904$		0			0
$905$	47358.5	−	8822.71i	1.73950	−	0.324063i
$906$		0			0
$907$	30499.8			1.11657			0.558285	−	0.829649i	$-0.311460\pi$
$907$	30499.8			1.11657			0.558285	+	0.829649i	$0.311460\pi$
$908$		0			0
$909$	1745.11	+	1267.90i	0.0636761	+	0.0462634i
$910$		0			0
$911$	−26299.5	+	19107.7i	−0.956468	+	0.694915i	−0.952328	−	0.305076i	$-0.901318\pi$
$911$	−26299.5	+	19107.7i	−0.956468	+	0.694915i	−0.00414055	+	0.999991i	$0.501318\pi$
$912$		0			0
$913$	−1509.65	−	1096.82i	−0.0547229	−	0.0397585i
$914$		0			0
$915$	−37458.8	+	6978.43i	−1.35339	+	0.252131i
$916$		0			0
$917$	−1898.64	−	5843.41i	−0.0683736	−	0.210432i
$918$		0			0
$919$	−5998.77	−	18462.3i	−0.215322	−	0.662694i	−0.999131	−	0.0416910i	$-0.986725\pi$
$919$	−5998.77	−	18462.3i	−0.215322	−	0.662694i	0.783808	−	0.621003i	$-0.213275\pi$
$920$		0			0
$921$	−14282.2	+	43956.2i	−0.510983	+	1.57264i
$922$		0			0
$923$	14908.4	−	10831.6i	0.531653	−	0.386269i
$924$		0			0
$925$	−19214.4	−	23638.2i	−0.682990	−	0.840238i
$926$		0			0
$927$	−43313.2	+	31468.9i	−1.53462	+	1.11497i
$928$		0			0
$929$	−7828.35	+	24093.2i	−0.276469	+	0.850884i	0.712358	+	0.701816i	$0.247627\pi$
$929$	−7828.35	+	24093.2i	−0.276469	+	0.850884i	−0.988827	+	0.149068i	$0.952373\pi$
$930$		0			0
$931$	462.654	+	1423.90i	0.0162866	+	0.0501251i
$932$		0			0
$933$	−9915.67	−	30517.3i	−0.347936	−	1.07084i
$934$		0			0
$935$	15252.9	−	16103.0i	0.533500	−	0.563234i
$936$		0			0
$937$	−4141.28	−	3008.82i	−0.144386	−	0.104903i	0.513247	−	0.858241i	$-0.328442\pi$
$937$	−4141.28	−	3008.82i	−0.144386	−	0.104903i	−0.657633	+	0.753338i	$0.728442\pi$
$938$		0			0
$939$	−20288.9	+	14740.7i	−0.705114	+	0.512295i
$940$		0			0
$941$	19877.8	+	14442.1i	0.688627	+	0.500317i	0.876208	−	0.481932i	$-0.160065\pi$
$941$	19877.8	+	14442.1i	0.688627	+	0.500317i	−0.187582	+	0.982249i	$0.560065\pi$
$942$		0			0
$943$	7876.97			0.272014
$944$		0			0
$945$	16363.6	+	30071.6i	0.563289	+	1.03516i
$946$		0			0
$947$	2235.20	−	6879.24i	0.0766994	−	0.236056i	−0.905355	−	0.424656i	$-0.860395\pi$
$947$	2235.20	−	6879.24i	0.0766994	−	0.236056i	0.982054	+	0.188600i	$0.0603949\pi$
$948$		0			0
$949$	39754.9			1.35985
$950$		0			0
$951$	31129.4			1.06145
$952$		0			0
$953$	7417.92	−	22830.0i	0.252141	−	0.776009i	−0.742239	−	0.670135i	$-0.766236\pi$
$953$	7417.92	−	22830.0i	0.252141	−	0.776009i	0.994380	−	0.105874i	$-0.0337639\pi$
$954$		0			0
$955$	−2393.24	+	2526.62i	−0.0810925	+	0.0856122i
$956$		0			0
$957$	63713.4			2.15210
$958$		0			0
$959$	10839.5	+	7875.33i	0.364989	+	0.265180i
$960$		0			0
$961$	−10448.0	+	7590.91i	−0.350709	+	0.254805i
$962$		0			0
$963$	−69606.2	−	50571.9i	−2.32921	−	1.69227i
$964$		0			0
$965$	−3876.72	+	29658.7i	−0.129322	+	0.989374i
$966$		0			0
$967$	−4876.55	−	15008.5i	−0.162171	−	0.499111i	0.836646	−	0.547744i	$-0.184513\pi$
$967$	−4876.55	−	15008.5i	−0.162171	−	0.499111i	−0.998817	+	0.0486335i	$0.984513\pi$
$968$		0			0
$969$	9776.01	+	30087.5i	0.324098	+	0.997471i
$970$		0			0
$971$	5684.38	−	17494.7i	0.187869	−	0.578200i	−0.812117	−	0.583494i	$-0.801685\pi$
$971$	5684.38	−	17494.7i	0.187869	−	0.578200i	0.999986	+	0.00529403i	$0.00168515\pi$
$972$		0			0
$973$	28753.0	−	20890.3i	0.947358	−	0.688296i
$974$		0			0
$975$	−54810.1	+	21156.1i	−1.80034	+	0.694910i
$976$		0			0
$977$	602.540	−	437.771i	0.0197308	−	0.0143352i	−0.577876	−	0.816124i	$-0.696118\pi$
$977$	602.540	−	437.771i	0.0197308	−	0.0143352i	0.597607	+	0.801789i	$0.296118\pi$
$978$		0			0
$979$	−6264.29	+	19279.5i	−0.204502	+	0.629393i
$980$		0			0
$981$	30542.1	+	93999.0i	0.994022	+	3.05928i
$982$		0			0
$983$	−4149.20	−	12769.9i	−0.134627	−	0.414341i	0.860904	−	0.508767i	$-0.169898\pi$
$983$	−4149.20	−	12769.9i	−0.134627	−	0.414341i	−0.995532	+	0.0944260i	$0.969898\pi$
$984$		0			0
$985$	9357.83	+	4452.83i	0.302706	+	0.144040i
$986$		0			0
$987$	57822.2	+	42010.3i	1.86474	+	1.35481i
$988$		0			0
$989$	−4832.28	+	3510.86i	−0.155367	+	0.112881i
$990$		0			0
$991$	10603.6	+	7704.00i	0.339895	+	0.246948i	0.744617	−	0.667491i	$-0.232632\pi$
$991$	10603.6	+	7704.00i	0.339895	+	0.246948i	−0.404723	+	0.914439i	$0.632632\pi$
$992$		0			0
$993$	90235.9			2.88373
$994$		0			0
$995$	643.675	−	4924.40i	0.0205084	−	0.156899i
$996$		0			0
$997$	−8446.56	+	25995.8i	−0.268310	+	0.825774i	0.722602	+	0.691264i	$0.242946\pi$
$997$	−8446.56	+	25995.8i	−0.268310	+	0.825774i	−0.990912	+	0.134510i	$0.957054\pi$
$998$		0			0
$999$	42035.3			1.33127

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.4.g.a.61.1	yes	28
5.2	odd	4		500.4.i.b.449.14		56
5.3	odd	4		500.4.i.b.449.1		56
5.4	even	2		500.4.g.a.301.7		28
25.4	even	10		2500.4.a.d.1.13		14
25.9	even	10		500.4.g.a.201.7		28
25.12	odd	20		500.4.i.b.49.1		56
25.13	odd	20		500.4.i.b.49.14		56
25.16	even	5	inner	100.4.g.a.41.1	✓	28
25.21	even	5		2500.4.a.c.1.2		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.4.g.a.41.1	✓	28	25.16	even	5	inner
100.4.g.a.61.1	yes	28	1.1	even	1	trivial
500.4.g.a.201.7		28	25.9	even	10
500.4.g.a.301.7		28	5.4	even	2
500.4.i.b.49.1		56	25.12	odd	20
500.4.i.b.49.14		56	25.13	odd	20
500.4.i.b.449.1		56	5.3	odd	4
500.4.i.b.449.14		56	5.2	odd	4
2500.4.a.c.1.2		14	25.21	even	5
2500.4.a.d.1.13		14	25.4	even	10

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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	100.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.65908 + 8.18380i) q^{3} +(-1.44907 + 11.0860i) q^{5} +17.7526 q^{7} +(-38.0604 - 27.6525i) q^{9} +O(q^{10})\)	\(q+(-2.65908 + 8.18380i) q^{3} +(-1.44907 + 11.0860i) q^{5} +17.7526 q^{7} +(-38.0604 - 27.6525i) q^{9} +(-23.4721 + 17.0535i) q^{11} +(-44.1893 - 32.1054i) q^{13} +(-86.8727 - 41.3375i) q^{15} +(21.1298 + 65.0309i) q^{17} +(-16.6150 - 51.1357i) q^{19} +(-47.2055 + 145.284i) q^{21} +(134.843 - 97.9692i) q^{23} +(-120.800 - 32.1289i) q^{25} +(139.546 - 101.386i) q^{27} +(-78.8623 + 242.713i) q^{29} +(63.8593 + 196.539i) q^{31} +(-77.1482 - 237.438i) q^{33} +(-25.7247 + 196.806i) q^{35} +(197.157 + 143.243i) q^{37} +(380.247 - 276.266i) q^{39} +(38.2337 + 27.7784i) q^{41} -35.8364 q^{43} +(361.709 - 381.869i) q^{45} +(144.580 - 444.972i) q^{47} -27.8456 q^{49} -588.385 q^{51} +(-208.142 + 640.594i) q^{53} +(-155.043 - 284.925i) q^{55} +462.665 q^{57} +(267.341 + 194.235i) q^{59} +(320.417 - 232.797i) q^{61} +(-675.671 - 490.904i) q^{63} +(419.955 - 443.361i) q^{65} +(110.149 + 339.004i) q^{67} +(443.202 + 1364.04i) q^{69} +(-104.255 + 320.863i) q^{71} +(-588.829 + 427.809i) q^{73} +(584.154 - 903.173i) q^{75} +(-416.691 + 302.744i) q^{77} +(-392.901 + 1209.22i) q^{79} +(66.1401 + 203.558i) q^{81} +(19.8749 + 61.1687i) q^{83} +(-751.553 + 140.012i) q^{85} +(-1776.61 - 1290.79i) q^{87} +(565.265 - 410.689i) q^{89} +(-784.474 - 569.954i) q^{91} -1778.24 q^{93} +(590.968 - 110.095i) q^{95} +(298.019 - 917.209i) q^{97} +1364.93 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{3} - 25 q^{5} + 16 q^{7} - 13 q^{9}+O(q^{10}) \) 28 * q - 4 * q^3 - 25 * q^5 + 16 * q^7 - 13 * q^9	\( 28 q - 4 q^{3} - 25 q^{5} + 16 q^{7} - 13 q^{9} - 20 q^{11} - 86 q^{13} - 240 q^{15} - 178 q^{17} + 2 q^{19} + 108 q^{21} + 102 q^{23} + 95 q^{25} + 92 q^{27} + 192 q^{29} + 378 q^{31} + 560 q^{33} - 350 q^{35} - 399 q^{37} + 592 q^{39} + 298 q^{41} - 180 q^{43} - 535 q^{45} - 78 q^{47} + 144 q^{49} - 1664 q^{51} - 657 q^{53} + 610 q^{55} + 384 q^{57} + 144 q^{59} + 516 q^{61} + 584 q^{63} - 505 q^{65} - 134 q^{67} + 2996 q^{69} - 2026 q^{71} - 1346 q^{73} + 3770 q^{75} + 2320 q^{77} + 896 q^{79} - 2203 q^{81} + 2082 q^{83} - 195 q^{85} - 4316 q^{87} - 167 q^{89} + 2212 q^{91} - 5664 q^{93} - 3740 q^{95} + 1156 q^{97} - 2100 q^{99}+O(q^{100}) \) 28 * q - 4 * q^3 - 25 * q^5 + 16 * q^7 - 13 * q^9 - 20 * q^11 - 86 * q^13 - 240 * q^15 - 178 * q^17 + 2 * q^19 + 108 * q^21 + 102 * q^23 + 95 * q^25 + 92 * q^27 + 192 * q^29 + 378 * q^31 + 560 * q^33 - 350 * q^35 - 399 * q^37 + 592 * q^39 + 298 * q^41 - 180 * q^43 - 535 * q^45 - 78 * q^47 + 144 * q^49 - 1664 * q^51 - 657 * q^53 + 610 * q^55 + 384 * q^57 + 144 * q^59 + 516 * q^61 + 584 * q^63 - 505 * q^65 - 134 * q^67 + 2996 * q^69 - 2026 * q^71 - 1346 * q^73 + 3770 * q^75 + 2320 * q^77 + 896 * q^79 - 2203 * q^81 + 2082 * q^83 - 195 * q^85 - 4316 * q^87 - 167 * q^89 + 2212 * q^91 - 5664 * q^93 - 3740 * q^95 + 1156 * q^97 - 2100 * q^99

Introduction

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