LMFDB - Embedded newform 84.4.e.a.71.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [84,4,Mod(71,84)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("84.71"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(84, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	84.e (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.95616044048$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.13
Character	$\chi$	$=$	84.71
Dual form			84.4.e.a.71.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.15015 - 2.58402i) q^{2} +(-4.86546 + 1.82409i) q^{3} +(-5.35430 + 5.94403i) q^{4} -2.77918i q^{5} +(10.3095 + 10.4745i) q^{6} +7.00000i q^{7} +(21.5177 + 6.99905i) q^{8} +(20.3454 - 17.7500i) q^{9} +(-7.18146 + 3.19649i) q^{10} +21.0494 q^{11} +(15.2087 - 38.6871i) q^{12} +60.3058 q^{13} +(18.0881 - 8.05107i) q^{14} +(5.06947 + 13.5220i) q^{15} +(-6.66302 - 63.6522i) q^{16} +36.6043i q^{17} +(-69.2668 - 32.1577i) q^{18} -6.48327i q^{19} +(16.5196 + 14.8806i) q^{20} +(-12.7686 - 34.0582i) q^{21} +(-24.2101 - 54.3921i) q^{22} +60.1080 q^{23} +(-117.461 + 5.19660i) q^{24} +117.276 q^{25} +(-69.3608 - 155.831i) q^{26} +(-66.6123 + 123.474i) q^{27} +(-41.6082 - 37.4801i) q^{28} +163.642i q^{29} +(29.1104 - 28.6520i) q^{30} +109.330i q^{31} +(-156.815 + 90.4271i) q^{32} +(-102.415 + 38.3960i) q^{33} +(94.5861 - 42.1005i) q^{34} +19.4543 q^{35} +(-3.42864 + 215.973i) q^{36} +314.337 q^{37} +(-16.7529 + 7.45675i) q^{38} +(-293.415 + 110.003i) q^{39} +(19.4517 - 59.8018i) q^{40} +322.625i q^{41} +(-73.3212 + 72.1665i) q^{42} -370.111i q^{43} +(-112.705 + 125.118i) q^{44} +(-49.3306 - 56.5437i) q^{45} +(-69.1334 - 155.320i) q^{46} -259.967 q^{47} +(148.526 + 297.543i) q^{48} -49.0000 q^{49} +(-134.885 - 303.044i) q^{50} +(-66.7693 - 178.097i) q^{51} +(-322.895 + 358.459i) q^{52} -689.547i q^{53} +(395.673 + 30.1134i) q^{54} -58.5002i q^{55} +(-48.9934 + 150.624i) q^{56} +(11.8260 + 31.5441i) q^{57} +(422.853 - 188.213i) q^{58} +684.084 q^{59} +(-107.519 - 42.2678i) q^{60} -742.139 q^{61} +(282.512 - 125.747i) q^{62} +(124.250 + 142.418i) q^{63} +(414.027 + 301.208i) q^{64} -167.601i q^{65} +(217.009 + 220.481i) q^{66} -466.825i q^{67} +(-217.577 - 195.990i) q^{68} +(-292.453 + 109.642i) q^{69} +(-22.3754 - 50.2702i) q^{70} +442.245 q^{71} +(562.021 - 239.542i) q^{72} -83.8943 q^{73} +(-361.535 - 812.252i) q^{74} +(-570.602 + 213.922i) q^{75} +(38.5368 + 34.7134i) q^{76} +147.346i q^{77} +(621.722 + 631.670i) q^{78} +786.303i q^{79} +(-176.901 + 18.5178i) q^{80} +(98.8724 - 722.264i) q^{81} +(833.668 - 371.068i) q^{82} +1366.97 q^{83} +(270.810 + 106.461i) q^{84} +101.730 q^{85} +(-956.373 + 425.684i) q^{86} +(-298.497 - 796.193i) q^{87} +(452.936 + 147.326i) q^{88} +329.799i q^{89} +(-89.3721 + 192.505i) q^{90} +422.140i q^{91} +(-321.836 + 357.284i) q^{92} +(-199.428 - 531.943i) q^{93} +(299.001 + 671.758i) q^{94} -18.0182 q^{95} +(598.030 - 726.014i) q^{96} -1244.82 q^{97} +(56.3575 + 126.617i) q^{98} +(428.260 - 373.628i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 12 q^{4} + 30 q^{6} + 20 q^{9} - 132 q^{10} - 78 q^{12} + 324 q^{16} + 424 q^{18} - 240 q^{22} - 382 q^{24} - 900 q^{25} + 168 q^{28} + 476 q^{30} + 848 q^{33} - 576 q^{34} + 412 q^{36} + 528 q^{37}+ \cdots - 72 q^{97}+O(q^{100}) $ 36 * q + 12 * q^4 + 30 * q^6 + 20 * q^9 - 132 * q^10 - 78 * q^12 + 324 * q^16 + 424 * q^18 - 240 * q^22 - 382 * q^24 - 900 * q^25 + 168 * q^28 + 476 * q^30 + 848 * q^33 - 576 * q^34 + 412 * q^36 + 528 * q^37 - 1068 * q^40 + 70 * q^42 - 984 * q^45 + 288 * q^46 + 526 * q^48 - 1764 * q^49 + 468 * q^52 - 1826 * q^54 + 1840 * q^57 + 1536 * q^58 + 652 * q^60 + 2448 * q^61 - 2604 * q^64 - 1188 * q^66 - 744 * q^69 + 252 * q^70 + 1888 * q^72 - 1656 * q^73 - 972 * q^76 - 1348 * q^78 + 2452 * q^81 + 888 * q^82 + 490 * q^84 + 2904 * q^85 + 4008 * q^88 + 3184 * q^90 - 6744 * q^93 + 3264 * q^94 - 1330 * q^96 - 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−1.15015	−	2.58402i	−0.406640	−	0.913588i
$2$	−1.15015	−	2.58402i	−0.406640	−	0.913588i
$3$	−4.86546	+	1.82409i	−0.936358	+	0.351045i
$3$	−4.86546	+	1.82409i	−0.936358	+	0.351045i
$4$	−5.35430	+	5.94403i	−0.669287	+	0.743004i
$5$		−	2.77918i		−	0.248578i	−0.992246	−	0.124289i	$-0.960335\pi$
$5$		−	2.77918i		−	0.248578i	0.992246	−	0.124289i	$-0.0396649\pi$
$6$	10.3095	+	10.4745i	0.701472	+	0.712697i
$7$			7.00000i			0.377964i
$7$			7.00000i			0.377964i
$8$	21.5177	+	6.99905i	0.950959	+	0.309317i
$9$	20.3454	−	17.7500i	0.753534	−	0.657409i
$10$	−7.18146	+	3.19649i	−0.227098	+	0.101082i
$11$	21.0494			0.576967			0.288484	−	0.957485i	$-0.406849\pi$
$11$	21.0494			0.576967			0.288484	+	0.957485i	$0.406849\pi$
$12$	15.2087	−	38.6871i	0.365864	−	0.930668i
$13$	60.3058			1.28660			0.643300	−	0.765614i	$-0.277565\pi$
$13$	60.3058			1.28660			0.643300	+	0.765614i	$0.277565\pi$
$14$	18.0881	−	8.05107i	0.345304	−	0.153696i
$15$	5.06947	+	13.5220i	0.0872621	+	0.232758i
$16$	−6.66302	−	63.6522i	−0.104110	−	0.994566i
$17$			36.6043i			0.522226i	0.965308	+	0.261113i	$0.0840895\pi$
$17$			36.6043i			0.522226i	−0.965308	+	0.261113i	$0.915911\pi$
$18$	−69.2668	−	32.1577i	−0.907018	−	0.421091i
$19$		−	6.48327i		−	0.0782823i	−0.999234	−	0.0391412i	$-0.987538\pi$
$19$		−	6.48327i		−	0.0782823i	0.999234	−	0.0391412i	$-0.0124622\pi$
$20$	16.5196	+	14.8806i	0.184694	+	0.166370i
$21$	−12.7686	−	34.0582i	−0.132683	−	0.353910i
$22$	−24.2101	−	54.3921i	−0.234618	−	0.527111i
$23$	60.1080			0.544930			0.272465	−	0.962166i	$-0.412161\pi$
$23$	60.1080			0.544930			0.272465	+	0.962166i	$0.412161\pi$
$24$	−117.461	+	5.19660i	−0.999023	+	0.0441980i
$25$	117.276			0.938209
$26$	−69.3608	−	155.831i	−0.523184	−	1.17542i
$27$	−66.6123	+	123.474i	−0.474798	+	0.880095i
$28$	−41.6082	−	37.4801i	−0.280829	−	0.252967i
$29$			163.642i			1.04785i	0.851766	+	0.523923i	$0.175532\pi$
$29$			163.642i			1.04785i	−0.851766	+	0.523923i	$0.824468\pi$
$30$	29.1104	−	28.6520i	0.177161	−	0.174370i
$31$			109.330i			0.633430i	0.948521	+	0.316715i	$0.102580\pi$
$31$			109.330i			0.633430i	−0.948521	+	0.316715i	$0.897420\pi$
$32$	−156.815	+	90.4271i	−0.866288	+	0.499544i
$33$	−102.415	+	38.3960i	−0.540248	+	0.202542i
$34$	94.5861	−	42.1005i	0.477099	−	0.212358i
$35$	19.4543			0.0939536
$36$	−3.42864	+	215.973i	−0.0158733	+	0.999874i
$37$	314.337			1.39667			0.698333	−	0.715773i	$-0.253926\pi$
$37$	314.337			1.39667			0.698333	+	0.715773i	$0.253926\pi$
$38$	−16.7529	+	7.45675i	−0.0715178	+	0.0318328i
$39$	−293.415	+	110.003i	−1.20472	+	0.451655i
$40$	19.4517	−	59.8018i	0.0768894	−	0.236387i
$41$			322.625i			1.22891i	0.788950	+	0.614457i	$0.210625\pi$
$41$			322.625i			1.22891i	−0.788950	+	0.614457i	$0.789375\pi$
$42$	−73.3212	+	72.1665i	−0.269374	+	0.265132i
$43$		−	370.111i		−	1.31259i	−0.754504	−	0.656295i	$-0.772123\pi$
$43$		−	370.111i		−	1.31259i	0.754504	−	0.656295i	$-0.227877\pi$
$44$	−112.705	+	125.118i	−0.386157	+	0.428689i
$45$	−49.3306	−	56.5437i	−0.163417	−	0.187312i
$46$	−69.1334	−	155.320i	−0.221590	−	0.497841i
$47$	−259.967			−0.806809			−0.403404	−	0.915022i	$-0.632173\pi$
$47$	−259.967			−0.806809			−0.403404	+	0.915022i	$0.632173\pi$
$48$	148.526	+	297.543i	0.446622	+	0.894723i
$49$	−49.0000			−0.142857
$50$	−134.885	−	303.044i	−0.381514	−	0.857137i
$51$	−66.7693	−	178.097i	−0.183325	−	0.488990i
$52$	−322.895	+	358.459i	−0.861105	+	0.955949i
$53$		−	689.547i		−	1.78711i	−0.448958	−	0.893553i	$-0.648205\pi$
$53$		−	689.547i		−	1.78711i	0.448958	−	0.893553i	$-0.351795\pi$
$54$	395.673	+	30.1134i	0.997116	+	0.0758873i
$55$		−	58.5002i		−	0.143421i
$56$	−48.9934	+	150.624i	−0.116911	+	0.359429i
$57$	11.8260	+	31.5441i	0.0274807	+	0.0733003i
$58$	422.853	−	188.213i	0.957299	−	0.426096i
$59$	684.084			1.50949			0.754747	−	0.656016i	$-0.227760\pi$
$59$	684.084			1.50949			0.754747	+	0.656016i	$0.227760\pi$
$60$	−107.519	−	42.2678i	−0.231343	−	0.0909457i
$61$	−742.139			−1.55772			−0.778862	−	0.627196i	$-0.784203\pi$
$61$	−742.139			−1.55772			−0.778862	+	0.627196i	$0.784203\pi$
$62$	282.512	−	125.747i	0.578694	−	0.257578i
$63$	124.250	+	142.418i	0.248477	+	0.284809i
$64$	414.027	+	301.208i	0.808646	+	0.588296i
$65$		−	167.601i		−	0.319820i
$66$	217.009	+	220.481i	0.404727	+	0.411203i
$67$		−	466.825i		−	0.851220i	−0.904907	−	0.425610i	$-0.860060\pi$
$67$		−	466.825i		−	0.851220i	0.904907	−	0.425610i	$-0.139940\pi$
$68$	−217.577	−	195.990i	−0.388016	−	0.349519i
$69$	−292.453	+	109.642i	−0.510249	+	0.191295i
$70$	−22.3754	−	50.2702i	−0.0382053	−	0.0858349i
$71$	442.245			0.739223			0.369612	−	0.929186i	$-0.379491\pi$
$71$	442.245			0.739223			0.369612	+	0.929186i	$0.379491\pi$
$72$	562.021	−	239.542i	0.919928	−	0.392088i
$73$	−83.8943			−0.134508			−0.0672540	−	0.997736i	$-0.521424\pi$
$73$	−83.8943			−0.134508			−0.0672540	+	0.997736i	$0.521424\pi$
$74$	−361.535	−	812.252i	−0.567941	−	1.27598i
$75$	−570.602	+	213.922i	−0.878500	+	0.329354i
$76$	38.5368	+	34.7134i	0.0581641	+	0.0523933i
$77$			147.346i			0.218073i
$78$	621.722	+	631.670i	0.902515	+	0.916956i
$79$			786.303i			1.11982i	0.828553	+	0.559911i	$0.189165\pi$
$79$			786.303i			1.11982i	−0.828553	+	0.559911i	$0.810835\pi$
$80$	−176.901	+	18.5178i	−0.247227	+	0.0258794i
$81$	98.8724	−	722.264i	0.135627	−	0.990760i
$82$	833.668	−	371.068i	1.12272	−	0.499726i
$83$	1366.97			1.80776			0.903879	−	0.427788i	$-0.140707\pi$
$83$	1366.97			1.80776			0.903879	+	0.427788i	$0.140707\pi$
$84$	270.810	+	106.461i	0.351760	+	0.138284i
$85$	101.730			0.129814
$86$	−956.373	+	425.684i	−1.19917	+	0.533752i
$87$	−298.497	−	796.193i	−0.367841	−	0.981159i
$88$	452.936	+	147.326i	0.548672	+	0.178466i
$89$			329.799i			0.392793i	0.980525	+	0.196397i	$0.0629241\pi$
$89$			329.799i			0.392793i	−0.980525	+	0.196397i	$0.937076\pi$
$90$	−89.3721	+	192.505i	−0.104674	+	0.225465i
$91$			422.140i			0.486289i
$92$	−321.836	+	357.284i	−0.364714	+	0.404885i
$93$	−199.428	−	531.943i	−0.222363	−	0.593117i
$94$	299.001	+	671.758i	0.328081	+	0.737091i
$95$	−18.0182			−0.0194592
$96$	598.030	−	726.014i	0.635794	−	0.771859i
$97$	−1244.82			−1.30301			−0.651507	−	0.758643i	$-0.725863\pi$
$97$	−1244.82			−1.30301			−0.651507	+	0.758643i	$0.725863\pi$
$98$	56.3575	+	126.617i	0.0580915	+	0.130513i
$99$	428.260	−	373.628i	0.434765	−	0.379303i
$100$	−627.931	+	697.093i	−0.627931	+	0.697093i
$101$			166.013i			0.163554i	0.996651	+	0.0817768i	$0.0260595\pi$
$101$			166.013i			0.163554i	−0.996651	+	0.0817768i	$0.973941\pi$
$102$	−383.410	+	377.371i	−0.372189	+	0.366327i
$103$			235.134i			0.224936i	0.993655	+	0.112468i	$0.0358756\pi$
$103$			235.134i			0.224936i	−0.993655	+	0.112468i	$0.964124\pi$
$104$	1297.64	+	422.083i	1.22350	+	0.397968i
$105$	−94.6541	+	35.4863i	−0.0879742	+	0.0329820i
$106$	−1781.80	+	793.085i	−1.63268	+	0.726710i
$107$	−1050.49			−0.949112			−0.474556	−	0.880225i	$-0.657391\pi$
$107$	−1050.49			−0.949112			−0.474556	+	0.880225i	$0.657391\pi$
$108$	−377.271	−	1057.06i	−0.336138	−	0.941813i
$109$	949.313			0.834199			0.417100	−	0.908861i	$-0.363047\pi$
$109$	949.313			0.834199			0.417100	+	0.908861i	$0.363047\pi$
$110$	−151.166	+	67.2842i	−0.131028	+	0.0583209i
$111$	−1529.39	+	573.377i	−1.30778	+	0.490293i
$112$	445.565	−	46.6411i	0.375911	−	0.0393498i
$113$			1672.27i			1.39216i	0.717966	+	0.696078i	$0.245073\pi$
$113$			1672.27i			1.39216i	−0.717966	+	0.696078i	$0.754927\pi$
$114$	67.9088	−	66.8392i	0.0557916	−	0.0549129i
$115$		−	167.051i		−	0.135457i
$116$	−972.692	−	876.187i	−0.778553	−	0.701309i
$117$	1226.95	−	1070.43i	0.969497	−	0.845822i
$118$	−786.801	−	1767.68i	−0.613821	−	1.37906i
$119$	−256.230			−0.197383
$120$	14.4423	+	326.445i	0.0109866	+	0.248335i
$121$	−887.921			−0.667109
$122$	853.573	+	1917.70i	0.633433	+	1.42312i
$123$	−588.495	−	1569.72i	−0.431405	−	1.15070i
$124$	−649.863	−	585.387i	−0.470641	−	0.423946i
$125$		−	673.330i		−	0.481796i
$126$	225.104	−	484.867i	0.159157	−	0.342821i
$127$		−	2480.62i		−	1.73322i	−0.498985	−	0.866610i	$-0.666294\pi$
$127$		−	2480.62i		−	1.73322i	0.498985	−	0.866610i	$-0.333706\pi$
$128$	302.132	−	1416.29i	0.208632	−	0.977994i
$129$	675.114	+	1800.76i	0.460779	+	1.22905i
$130$	−433.083	+	192.767i	−0.292184	+	0.130052i
$131$	−779.191			−0.519681			−0.259840	−	0.965652i	$-0.583670\pi$
$131$	−779.191			−0.519681			−0.259840	+	0.965652i	$0.583670\pi$
$132$	320.134	−	814.343i	0.211092	−	0.536965i
$133$	45.3829			0.0295879
$134$	−1206.28	+	536.920i	−0.777664	+	0.346140i
$135$	343.157	+	185.128i	0.218772	+	0.118024i
$136$	−256.195	+	787.641i	−0.161533	+	0.496615i
$137$			1291.69i			0.805524i	0.915305	+	0.402762i	$0.131950\pi$
$137$			1291.69i			0.805524i	−0.915305	+	0.402762i	$0.868050\pi$
$138$	619.683	+	629.599i	0.382253	+	0.388370i
$139$			2958.50i			1.80530i	0.430376	+	0.902650i	$0.358381\pi$
$139$			2958.50i			1.80530i	−0.430376	+	0.902650i	$0.641619\pi$
$140$	−104.164	+	115.637i	−0.0628819	+	0.0698079i
$141$	1264.86	−	474.201i	0.755462	−	0.283227i
$142$	−508.650	−	1142.77i	−0.300598	−	0.675346i
$143$	1269.40			0.742327
$144$	−1265.39	−	1176.76i	−0.732287	−	0.680997i
$145$	454.791			0.260471
$146$	96.4913	+	216.784i	0.0546964	+	0.122885i
$147$	238.408	−	89.3802i	0.133765	−	0.0501494i
$148$	−1683.05	+	1868.43i	−0.934770	+	1.03773i
$149$		−	360.309i		−	0.198105i	−0.995082	−	0.0990527i	$-0.968419\pi$
$149$		−	360.309i		−	0.198105i	0.995082	−	0.0990527i	$-0.0315812\pi$
$150$	1209.06	+	1228.40i	0.658128	+	0.668659i
$151$			718.412i			0.387176i	0.981083	+	0.193588i	$0.0620125\pi$
$151$			718.412i			0.387176i	−0.981083	+	0.193588i	$0.937988\pi$
$152$	45.3767	−	139.505i	0.0242141	−	0.0744433i
$153$	649.727	+	744.729i	0.343316	+	0.393515i
$154$	380.745	−	169.470i	0.199229	−	0.0886774i
$155$	303.849			0.157457
$156$	917.172	−	2333.06i	0.470721	−	1.19740i
$157$	2096.78			1.06587			0.532935	−	0.846156i	$-0.321089\pi$
$157$	2096.78			1.06587			0.532935	+	0.846156i	$0.321089\pi$
$158$	2031.82	−	904.368i	1.02306	−	0.455365i
$159$	1257.79	+	3354.97i	0.627356	+	1.67337i
$160$	251.314	+	435.818i	0.124176	+	0.215340i
$161$			420.756i			0.205964i
$162$	−1980.06	+	575.226i	−0.960298	+	0.278975i
$163$			1555.24i			0.747336i	0.927563	+	0.373668i	$0.121900\pi$
$163$			1555.24i			0.747336i	−0.927563	+	0.373668i	$0.878100\pi$
$164$	−1917.69	−	1727.43i	−0.913088	−	0.822497i
$165$	106.709	+	284.631i	0.0503474	+	0.134294i
$166$	−1572.22	−	3532.26i	−0.735108	−	1.65155i
$167$	−669.611			−0.310276			−0.155138	−	0.987893i	$-0.549582\pi$
$167$	−669.611			−0.310276			−0.155138	+	0.987893i	$0.549582\pi$
$168$	−36.3762	−	822.224i	−0.0167053	−	0.377595i
$169$	1439.78			0.655341
$170$	−117.005	−	262.872i	−0.0527875	−	0.118596i
$171$	−115.078	−	131.905i	−0.0514635	−	0.0589884i
$172$	2199.95	+	1981.68i	0.975260	+	0.878499i
$173$		−	3555.69i		−	1.56263i	−0.624140	−	0.781313i	$-0.714550\pi$
$173$		−	3555.69i		−	1.56263i	0.624140	−	0.781313i	$-0.285450\pi$
$174$	−1714.06	+	1687.06i	−0.746796	+	0.735034i
$175$			820.933i			0.354610i
$176$	−140.253	−	1339.84i	−0.0600679	−	0.573832i
$177$	−3328.38	+	1247.83i	−1.41343	+	0.529901i
$178$	852.206	−	379.319i	0.358852	−	0.159726i
$179$	−658.864			−0.275116			−0.137558	−	0.990494i	$-0.543925\pi$
$179$	−658.864			−0.275116			−0.137558	+	0.990494i	$0.543925\pi$
$180$	600.228	+	9.52882i	0.248546	+	0.00394576i
$181$	729.720			0.299667			0.149833	−	0.988711i	$-0.452126\pi$
$181$	729.720			0.299667			0.149833	+	0.988711i	$0.452126\pi$
$182$	1090.82	−	485.526i	0.444268	−	0.197745i
$183$	3610.85	−	1353.72i	1.45859	−	0.546832i
$184$	1293.39	+	420.699i	0.518206	+	0.168556i
$185$		−	873.599i		−	0.347180i
$186$	−1145.18	+	1127.14i	−0.451443	+	0.444333i
$187$			770.499i			0.301307i
$188$	1391.94	−	1545.25i	0.539987	−	0.599462i
$189$	−864.317	−	466.286i	−0.332645	−	0.179457i
$190$	20.7237	+	46.5593i	0.00791292	+	0.0177777i
$191$	−1025.66			−0.388556			−0.194278	−	0.980947i	$-0.562236\pi$
$191$	−1025.66			−0.388556			−0.194278	+	0.980947i	$0.562236\pi$
$192$	−2563.86	−	710.294i	−0.963701	−	0.266985i
$193$	61.1644			0.0228120			0.0114060	−	0.999935i	$-0.496369\pi$
$193$	61.1644			0.0228120			0.0114060	+	0.999935i	$0.496369\pi$
$194$	1431.73	+	3216.64i	0.529858	+	1.19042i
$195$	305.718	+	815.455i	0.112271	+	0.299466i
$196$	262.361	−	291.258i	0.0956124	−	0.106143i
$197$		−	2548.32i		−	0.921626i	−0.887497	−	0.460813i	$-0.847558\pi$
$197$		−	2548.32i		−	0.921626i	0.887497	−	0.460813i	$-0.152442\pi$
$198$	−1458.03	−	676.901i	−0.523320	−	0.242956i
$199$		−	4685.87i		−	1.66921i	−0.550849	−	0.834605i	$-0.685696\pi$
$199$		−	4685.87i		−	1.66921i	0.550849	−	0.834605i	$-0.314304\pi$
$200$	2523.52	+	820.822i	0.892198	+	0.290204i
$201$	851.528	+	2271.32i	0.298817	+	0.797047i
$202$	428.981	−	190.940i	0.149421	−	0.0665075i
$203$	−1145.49			−0.396048
$204$	1416.11	+	556.703i	0.486019	+	0.191064i
$205$	896.633			0.305481
$206$	607.590	−	270.440i	0.205499	−	0.0914681i
$207$	1222.92	−	1066.92i	0.410623	−	0.358241i
$208$	−401.819	−	3838.59i	−0.133948	−	1.27961i
$209$		−	136.469i		−	0.0451664i
$210$	200.564	+	203.773i	0.0659058	+	0.0669604i
$211$		−	4682.02i		−	1.52760i	−0.645453	−	0.763800i	$-0.723331\pi$
$211$		−	4682.02i		−	1.52760i	0.645453	−	0.763800i	$-0.276669\pi$
$212$	4098.69	+	3692.04i	1.32783	+	1.19609i
$213$	−2151.73	+	806.693i	−0.692178	+	0.259501i
$214$	1208.23	+	2714.49i	0.385947	+	0.867097i
$215$	−1028.61			−0.326281
$216$	−2297.55	+	2190.66i	−0.723742	+	0.690071i
$217$	−765.313			−0.239414
$218$	−1091.86	−	2453.04i	−0.339219	−	0.762115i
$219$	408.184	−	153.030i	0.125948	−	0.0472184i
$220$	347.727	+	313.228i	0.106563	+	0.0959900i
$221$			2207.45i			0.671896i
$222$	3240.65	+	3292.51i	0.979722	+	0.995399i
$223$		−	902.711i		−	0.271076i	−0.990772	−	0.135538i	$-0.956724\pi$
$223$		−	902.711i		−	0.271076i	0.990772	−	0.135538i	$-0.0432763\pi$
$224$	−632.990	−	1097.70i	−0.188810	−	0.327426i
$225$	2386.03	−	2081.66i	0.706973	−	0.616787i
$226$	4321.17	−	1923.36i	1.27186	−	0.566107i
$227$	−1530.62			−0.447536			−0.223768	−	0.974642i	$-0.571836\pi$
$227$	−1530.62			−0.447536			−0.223768	+	0.974642i	$0.571836\pi$
$228$	−250.819	−	98.6021i	−0.0728549	−	0.0286407i
$229$	−6127.92			−1.76832			−0.884158	−	0.467189i	$-0.845267\pi$
$229$	−6127.92			−1.76832			−0.884158	+	0.467189i	$0.845267\pi$
$230$	−431.663	+	192.134i	−0.123752	+	0.0550824i
$231$	−268.772	−	716.906i	−0.0765536	−	0.204195i
$232$	−1145.34	+	3521.20i	−0.324117	+	0.996458i
$233$			223.774i			0.0629180i	0.999505	+	0.0314590i	$0.0100154\pi$
$233$			223.774i			0.0629180i	−0.999505	+	0.0314590i	$0.989985\pi$
$234$	−4177.18	−	1939.29i	−1.16697	−	0.541776i
$235$			722.495i			0.200555i
$236$	−3662.79	+	4066.22i	−1.01028	+	1.12156i
$237$	−1434.28	−	3825.73i	−0.393109	−	1.04856i
$238$	294.704	+	662.102i	0.0802638	+	0.180327i
$239$	−2877.67			−0.778831			−0.389416	−	0.921062i	$-0.627323\pi$
$239$	−2877.67			−0.778831			−0.389416	+	0.921062i	$0.627323\pi$
$240$	826.928	−	412.780i	0.222408	−	0.111020i
$241$	−1524.33			−0.407430			−0.203715	−	0.979030i	$-0.565302\pi$
$241$	−1524.33			−0.407430			−0.203715	+	0.979030i	$0.565302\pi$
$242$	1021.25	+	2294.40i	0.271273	+	0.609463i
$243$	836.412	+	3694.50i	0.220806	+	0.975318i
$244$	3973.63	−	4411.30i	1.04256	−	1.15739i
$245$			136.180i			0.0355111i
$246$	−3379.32	+	3326.10i	−0.875843	+	0.862050i
$247$		−	390.979i		−	0.100718i
$248$	−765.209	+	2352.54i	−0.195931	+	0.602366i
$249$	−6650.92	+	2493.46i	−1.69271	+	0.634605i
$250$	−1739.90	+	774.432i	−0.440163	+	0.195918i
$251$	−5527.05			−1.38990			−0.694949	−	0.719059i	$-0.744573\pi$
$251$	−5527.05			−1.38990			−0.694949	+	0.719059i	$0.744573\pi$
$252$	−1511.81	−	24.0005i	−0.377917	−	0.00599955i
$253$	1265.24			0.314407
$254$	−6409.96	+	2853.09i	−1.58345	+	0.704798i
$255$	−494.963	+	185.564i	−0.121552	+	0.0455705i
$256$	−4007.21	+	848.232i	−0.978322	+	0.207088i
$257$			2212.18i			0.536935i	0.963289	+	0.268467i	$0.0865171\pi$
$257$			2212.18i			0.536935i	−0.963289	+	0.268467i	$0.913483\pi$
$258$	3876.71	−	3815.66i	0.935479	−	0.920745i
$259$			2200.36i			0.527890i
$260$	996.224	+	897.384i	0.237628	+	0.214052i
$261$	2904.65	+	3329.36i	0.688863	+	0.789587i
$262$	896.188	+	2013.44i	0.211323	+	0.474774i
$263$	4772.68			1.11900			0.559498	−	0.828832i	$-0.310994\pi$
$263$	4772.68			1.11900			0.559498	+	0.828832i	$0.310994\pi$
$264$	−2472.48	+	109.385i	−0.576404	+	0.0255008i
$265$	−1916.38			−0.444235
$266$	−52.1973	−	117.270i	−0.0120317	−	0.0270312i
$267$	−601.582	−	1604.62i	−0.137888	−	0.367795i
$268$	2774.82	+	2499.52i	0.632460	+	0.569710i
$269$		−	7632.46i		−	1.72996i	−0.501806	−	0.864980i	$-0.667331\pi$
$269$		−	7632.46i		−	1.72996i	0.501806	−	0.864980i	$-0.332669\pi$
$270$	83.6907	−	1099.65i	0.0188639	−	0.247861i
$271$		−	2086.22i		−	0.467635i	−0.972280	−	0.233818i	$-0.924878\pi$
$271$		−	2086.22i		−	0.467635i	0.972280	−	0.233818i	$-0.0751218\pi$
$272$	2329.94	−	243.895i	0.519388	−	0.0543688i
$273$	−770.020	−	2053.91i	−0.170710	−	0.455341i
$274$	3337.76	−	1485.65i	0.735918	−	0.327559i
$275$	2468.60			0.541316
$276$	914.164	−	2325.41i	0.199370	−	0.507149i
$277$	−313.820			−0.0680707			−0.0340354	−	0.999421i	$-0.510836\pi$
$277$	−313.820			−0.0680707			−0.0340354	+	0.999421i	$0.510836\pi$
$278$	7644.82	−	3402.73i	1.64930	−	0.734108i
$279$	1940.62	+	2224.37i	0.416422	+	0.477311i
$280$	418.612	+	136.162i	0.0893460	+	0.0290615i
$281$			7607.09i			1.61495i	0.589901	+	0.807475i	$0.299167\pi$
$281$			7607.09i			1.61495i	−0.589901	+	0.807475i	$0.700833\pi$
$282$	−2680.12	−	2723.01i	−0.565954	−	0.575010i
$283$			3721.02i			0.781597i	0.920476	+	0.390798i	$0.127801\pi$
$283$			3721.02i			0.781597i	−0.920476	+	0.390798i	$0.872199\pi$
$284$	−2367.91	+	2628.72i	−0.494753	+	0.549246i
$285$	87.6668	−	32.8667i	0.0182208	−	0.00683108i
$286$	−1460.01	−	3280.16i	−0.301860	−	0.678181i
$287$	−2258.37			−0.464486
$288$	−1585.38	+	4623.25i	−0.324373	+	0.945929i
$289$	3573.13			0.727280
$290$	−523.079	−	1175.19i	−0.105918	−	0.237963i
$291$	6056.63	−	2270.66i	1.22009	−	0.457417i
$292$	449.195	−	498.670i	0.0900245	−	0.0999400i
$293$		−	2124.17i		−	0.423534i	−0.977320	−	0.211767i	$-0.932078\pi$
$293$		−	2124.17i		−	0.423534i	0.977320	−	0.211767i	$-0.0679218\pi$
$294$	−505.165	−	513.249i	−0.100210	−	0.101814i
$295$		−	1901.19i		−	0.375227i
$296$	6763.82	+	2200.06i	1.32817	+	0.432013i
$297$	−1402.15	+	2599.06i	−0.273943	+	0.507786i
$298$	−931.046	+	414.411i	−0.180987	+	0.0805576i
$299$	3624.86			0.701107
$300$	1783.62	−	4537.08i	0.343257	−	0.873161i
$301$	2590.78			0.496112
$302$	1856.39	−	826.284i	0.353719	−	0.157441i
$303$	−302.822	−	807.730i	−0.0574148	−	0.153145i
$304$	−412.675	+	43.1982i	−0.0778569	+	0.00814995i
$305$			2062.54i			0.387215i
$306$	1177.11	−	2535.46i	0.219905	−	0.473668i
$307$		−	4751.00i		−	0.883237i	−0.897203	−	0.441618i	$-0.854404\pi$
$307$		−	4751.00i		−	0.883237i	0.897203	−	0.441618i	$-0.145596\pi$
$308$	−875.829	−	788.934i	−0.162029	−	0.145954i
$309$	−428.904	−	1144.03i	−0.0789628	−	0.210621i
$310$	−349.473	−	785.152i	−0.0640282	−	0.143850i
$311$	1076.60			0.196297			0.0981487	−	0.995172i	$-0.468708\pi$
$311$	1076.60			0.196297			0.0981487	+	0.995172i	$0.468708\pi$
$312$	−7083.55	+	313.385i	−1.28534	+	0.0568651i
$313$	−2767.10			−0.499698			−0.249849	−	0.968285i	$-0.580381\pi$
$313$	−2767.10			−0.499698			−0.249849	+	0.968285i	$0.580381\pi$
$314$	−2411.62	−	5418.13i	−0.433426	−	0.973766i
$315$	395.806	−	345.314i	0.0707972	−	0.0617659i
$316$	−4673.81	−	4210.10i	−0.832032	−	0.749483i
$317$		−	3636.57i		−	0.644322i	−0.946685	−	0.322161i	$-0.895591\pi$
$317$		−	3636.57i		−	0.644322i	0.946685	−	0.322161i	$-0.104409\pi$
$318$	7222.64	−	7108.89i	1.27366	−	1.25361i
$319$			3444.57i			0.604573i
$320$	837.111	−	1150.66i	0.146237	−	0.201011i
$321$	5111.13	−	1916.19i	0.888709	−	0.333181i
$322$	1087.24	−	483.934i	0.188166	−	0.0837533i
$323$	237.315			0.0408810
$324$	3763.77	+	4454.92i	0.645365	+	0.763874i
$325$	7072.43			1.20710
$326$	4018.77	−	1788.76i	0.682757	−	0.303897i
$327$	−4618.85	+	1731.63i	−0.781110	+	0.292842i
$328$	−2258.07	+	6942.15i	−0.380125	+	1.16865i
$329$		−	1819.77i		−	0.304945i
$330$	612.758	−	603.108i	0.102216	−	0.100606i
$331$			8280.06i			1.37496i	0.726202	+	0.687482i	$0.241284\pi$
$331$			8280.06i			1.37496i	−0.726202	+	0.687482i	$0.758716\pi$
$332$	−7319.14	+	8125.28i	−1.20991	+	1.34317i
$333$	6395.31	−	5579.49i	1.05244	−	0.918180i
$334$	770.155	+	1730.29i	0.126171	+	0.283464i
$335$	−1297.39			−0.211594
$336$	−2082.80	+	1039.68i	−0.338173	+	0.168807i
$337$	−4146.36			−0.670228			−0.335114	−	0.942178i	$-0.608775\pi$
$337$	−4146.36			−0.670228			−0.335114	+	0.942178i	$0.608775\pi$
$338$	−1655.97	−	3720.43i	−0.266488	−	0.598712i
$339$	−3050.36	−	8136.35i	−0.488710	−	1.30356i
$340$	−544.692	+	604.686i	−0.0868826	+	0.0964521i
$341$			2301.34i			0.365468i
$342$	−208.487	+	449.075i	−0.0329640	+	0.0710035i
$343$		−	343.000i		−	0.0539949i
$344$	2590.42	−	7963.95i	0.406007	−	1.24822i
$345$	304.716	+	812.781i	0.0475517	+	0.126837i
$346$	−9187.97	+	4089.59i	−1.42760	+	0.635427i
$347$	−4589.27			−0.709986			−0.354993	−	0.934869i	$-0.615517\pi$
$347$	−4589.27			−0.709986			−0.354993	+	0.934869i	$0.615517\pi$
$348$	6330.83	+	2488.78i	0.975196	+	0.383369i
$349$	−103.000			−0.0157979			−0.00789895	−	0.999969i	$-0.502514\pi$
$349$	−103.000			−0.0157979			−0.00789895	+	0.999969i	$0.502514\pi$
$350$	2121.31	−	944.198i	0.323967	−	0.144199i
$351$	−4017.10	+	7446.19i	−0.610875	+	1.13233i
$352$	−3300.87	+	1903.44i	−0.499820	+	0.288221i
$353$		−	7919.90i		−	1.19415i	−0.802187	−	0.597073i	$-0.796330\pi$
$353$		−	7919.90i		−	1.19415i	0.802187	−	0.597073i	$-0.203670\pi$
$354$	7052.56	+	7165.41i	1.05887	+	1.07581i
$355$		−	1229.08i		−	0.183754i
$356$	−1960.34	−	1765.84i	−0.291847	−	0.262892i
$357$	1246.68	−	467.385i	0.184821	−	0.0692903i
$358$	757.794	+	1702.52i	0.111873	+	0.251343i
$359$	1194.25			0.175571			0.0877857	−	0.996139i	$-0.472021\pi$
$359$	1194.25			0.175571			0.0877857	+	0.996139i	$0.472021\pi$
$360$	−665.731	−	1561.96i	−0.0974642	−	0.228674i
$361$	6816.97			0.993872
$362$	−839.289	−	1885.61i	−0.121857	−	0.273772i
$363$	4320.15	−	1619.64i	0.624653	−	0.234185i
$364$	−2509.22	−	2260.26i	−0.361315	−	0.325467i
$365$			233.158i			0.0334357i
$366$	−7651.08	−	7773.50i	−1.09270	−	1.11018i
$367$			5789.97i			0.823526i	0.911291	+	0.411763i	$0.135087\pi$
$367$			5789.97i			0.823526i	−0.911291	+	0.411763i	$0.864913\pi$
$368$	−400.501	−	3826.01i	−0.0567325	−	0.541968i
$369$	5726.60	+	6563.93i	0.807899	+	0.926029i
$370$	−2257.40	+	1004.77i	−0.317180	+	0.141177i
$371$	4826.83			0.675463
$372$	4229.68	+	1662.77i	0.589513	+	0.231749i
$373$	−83.8497			−0.0116396			−0.00581980	−	0.999983i	$-0.501853\pi$
$373$	−83.8497			−0.0116396			−0.00581980	+	0.999983i	$0.501853\pi$
$374$	1990.98	−	886.192i	0.275271	−	0.122524i
$375$	1228.21	+	3276.06i	0.169132	+	0.451133i
$376$	−5593.89	−	1819.52i	−0.767242	−	0.249560i
$377$			9868.54i			1.34816i
$378$	−210.794	+	2769.71i	−0.0286827	+	0.376875i
$379$			3388.99i			0.459316i	0.973271	+	0.229658i	$0.0737607\pi$
$379$			3388.99i			0.459316i	−0.973271	+	0.229658i	$0.926239\pi$
$380$	96.4748	−	107.101i	0.0130238	−	0.0144583i
$381$	4524.86	+	12069.3i	0.608439	+	1.62292i
$382$	1179.67	+	2650.32i	0.158003	+	0.354980i
$383$	−2179.76			−0.290810			−0.145405	−	0.989372i	$-0.546449\pi$
$383$	−2179.76			−0.290810			−0.145405	+	0.989372i	$0.546449\pi$
$384$	1113.42	+	7442.00i	0.147966	+	0.988992i
$385$	409.502			0.0542081
$386$	−70.3485	−	158.050i	−0.00927627	−	0.0208408i
$387$	−6569.48	−	7530.06i	−0.862908	−	0.989081i
$388$	6665.14	−	7399.25i	0.872090	−	0.968145i
$389$			10887.9i			1.41912i	0.704645	+	0.709560i	$0.251106\pi$
$389$			10887.9i			1.41912i	−0.704645	+	0.709560i	$0.748894\pi$
$390$	1755.53	−	1727.88i	0.227935	−	0.224345i
$391$			2200.21i			0.284576i
$392$	−1054.37	−	342.954i	−0.135851	−	0.0441882i
$393$	3791.12	−	1421.31i	0.486608	−	0.182432i
$394$	−6584.91	+	2930.96i	−0.841987	+	0.374771i
$395$	2185.28			0.278363
$396$	−72.1709	+	4546.10i	−0.00915839	+	0.576895i
$397$	−4539.66			−0.573902			−0.286951	−	0.957945i	$-0.592642\pi$
$397$	−4539.66			−0.573902			−0.286951	+	0.957945i	$0.592642\pi$
$398$	−12108.4	+	5389.47i	−1.52497	+	0.678768i
$399$	−220.809	+	82.7823i	−0.0277049	+	0.0103867i
$400$	−781.413	−	7464.89i	−0.0976767	−	0.933111i
$401$		−	9637.64i		−	1.20020i	−0.799925	−	0.600100i	$-0.795127\pi$
$401$		−	9637.64i		−	1.20020i	0.799925	−	0.600100i	$-0.204873\pi$
$402$	4889.74	−	4812.73i	0.606661	−	0.597107i
$403$			6593.25i			0.814971i
$404$	−986.787	−	888.883i	−0.121521	−	0.109464i
$405$	−2007.30	−	274.784i	−0.246281	−	0.0337140i
$406$	1317.49	+	2959.97i	0.161049	+	0.361825i
$407$	6616.61			0.805831
$408$	−190.218	−	4299.56i	−0.0230813	−	0.521715i
$409$	−2660.40			−0.321634			−0.160817	−	0.986984i	$-0.551413\pi$
$409$	−2660.40			−0.321634			−0.160817	+	0.986984i	$0.551413\pi$
$410$	−1031.27	−	2316.92i	−0.124221	−	0.279084i
$411$	−2356.16	−	6284.69i	−0.282776	−	0.754260i
$412$	−1397.64	−	1258.98i	−0.167128	−	0.150547i
$413$			4788.59i			0.570535i
$414$	−4163.48	−	1932.93i	−0.494261	−	0.229465i
$415$		−	3799.05i		−	0.449368i
$416$	−9456.84	+	5453.28i	−1.11457	+	0.642714i
$417$	−5396.56	−	14394.5i	−0.633742	−	1.69041i
$418$	−352.639	+	156.960i	−0.0412635	+	0.0183665i
$419$	−3543.42			−0.413145			−0.206572	−	0.978431i	$-0.566231\pi$
$419$	−3543.42			−0.413145			−0.206572	+	0.978431i	$0.566231\pi$
$420$	295.874	−	752.631i	0.0343743	−	0.0874396i
$421$	−9464.22			−1.09562			−0.547812	−	0.836601i	$-0.684539\pi$
$421$	−9464.22			−1.09562			−0.547812	+	0.836601i	$0.684539\pi$
$422$	−12098.4	+	5385.04i	−1.39560	+	0.621184i
$423$	−5289.13	+	4614.42i	−0.607958	+	0.530403i
$424$	4826.18	−	14837.5i	0.552783	−	1.69946i
$425$			4292.81i			0.489957i
$426$	4559.33	+	4632.28i	0.518545	+	0.526842i
$427$		−	5194.97i		−	0.588764i
$428$	5624.65	−	6244.16i	0.635228	−	0.705194i
$429$	−6176.23	+	2315.50i	−0.695084	+	0.260590i
$430$	1183.05	+	2657.94i	0.132679	+	0.298086i
$431$	−10281.2			−1.14902			−0.574510	−	0.818497i	$-0.694808\pi$
$431$	−10281.2			−1.14902			−0.574510	+	0.818497i	$0.694808\pi$
$432$	8303.23	+	3417.31i	0.924743	+	0.380591i
$433$	858.183			0.0952463			0.0476232	−	0.998865i	$-0.484835\pi$
$433$	858.183			0.0952463			0.0476232	+	0.998865i	$0.484835\pi$
$434$	880.227	+	1977.58i	0.0973554	+	0.218726i
$435$	−2212.77	+	829.577i	−0.243894	+	0.0914372i
$436$	−5082.91	+	5642.75i	−0.558319	+	0.619813i
$437$		−	389.696i		−	0.0426584i
$438$	−864.908	−	878.747i	−0.0943536	−	0.0958634i
$439$		−	16181.2i		−	1.75920i	−0.475716	−	0.879599i	$-0.657811\pi$
$439$		−	16181.2i		−	1.75920i	0.475716	−	0.879599i	$-0.342189\pi$
$440$	409.446	−	1258.79i	0.0443627	−	0.136388i
$441$	−996.926	+	869.752i	−0.107648	+	0.0939155i
$442$	5704.08	−	2538.90i	0.613836	−	0.273220i
$443$	17918.4			1.92174			0.960868	−	0.277007i	$-0.0893427\pi$
$443$	17918.4			1.92174			0.960868	+	0.277007i	$0.0893427\pi$
$444$	4780.65	−	12160.8i	0.510990	−	1.29983i
$445$	916.572			0.0976397
$446$	−2332.62	+	1038.26i	−0.247652	+	0.110231i
$447$	657.235	+	1753.07i	0.0695440	+	0.185498i
$448$	−2108.45	+	2898.19i	−0.222355	+	0.305639i
$449$		−	2372.17i		−	0.249331i	−0.992199	−	0.124666i	$-0.960214\pi$
$449$		−	2372.17i		−	0.249331i	0.992199	−	0.124666i	$-0.0397858\pi$
$450$	−8123.34	−	3771.33i	−0.850973	−	0.395071i
$451$			6791.06i			0.709044i
$452$	−9940.01	−	8953.82i	−1.03438	−	0.931752i
$453$	−1310.45	−	3495.41i	−0.135916	−	0.362535i
$454$	1760.45	+	3955.15i	0.181986	+	0.408864i
$455$	1173.21			0.120881
$456$	33.6909	+	761.529i	0.00345992	+	0.0782058i
$457$	−10118.7			−1.03574			−0.517868	−	0.855461i	$-0.673274\pi$
$457$	−10118.7			−1.03574			−0.517868	+	0.855461i	$0.673274\pi$
$458$	7048.04	+	15834.6i	0.719069	+	1.61551i
$459$	−4519.67	−	2438.29i	−0.459608	−	0.247952i
$460$	992.957	+	894.441i	0.100645	+	0.0906599i
$461$			10415.1i			1.05223i	0.850412	+	0.526117i	$0.176353\pi$
$461$			10415.1i			1.05223i	−0.850412	+	0.526117i	$0.823647\pi$
$462$	−1543.37	+	1519.06i	−0.155420	+	0.152972i
$463$			5667.94i			0.568923i	0.958687	+	0.284462i	$0.0918148\pi$
$463$			5667.94i			0.568923i	−0.958687	+	0.284462i	$0.908185\pi$
$464$	10416.2	−	1090.35i	1.04215	−	0.109091i
$465$	−1478.37	+	554.247i	−0.147436	+	0.0552744i
$466$	578.235	−	257.374i	0.0574812	−	0.0255850i
$467$	13362.7			1.32409			0.662046	−	0.749463i	$-0.269688\pi$
$467$	13362.7			1.32409			0.662046	+	0.749463i	$0.269688\pi$
$468$	−206.767	+	13024.4i	−0.0204226	+	1.28644i
$469$	3267.77			0.321731
$470$	1866.94	−	830.980i	0.183224	−	0.0815537i
$471$	−10201.8	+	3824.71i	−0.998036	+	0.374169i
$472$	14719.9	+	4787.94i	1.43547	+	0.466913i
$473$		−	7790.62i		−	0.757322i
$474$	−8236.10	+	8106.38i	−0.798094	+	0.785524i
$475$		−	760.333i		−	0.0734452i
$476$	1371.93	−	1523.04i	0.132106	−	0.146656i
$477$	−12239.5	−	14029.1i	−1.17486	−	1.34665i
$478$	3309.76	+	7435.94i	0.316704	+	0.711531i
$479$	17751.9			1.69333			0.846663	−	0.532129i	$-0.178608\pi$
$479$	17751.9			1.69333			0.846663	+	0.532129i	$0.178608\pi$
$480$	−2017.73	−	1662.04i	−0.191867	−	0.158044i
$481$	18956.3			1.79695
$482$	1753.21	+	3938.89i	0.165677	+	0.372223i
$483$	−767.495	−	2047.17i	−0.0723027	−	0.192856i
$484$	4754.19	−	5277.83i	0.446487	−	0.495664i
$485$			3459.58i			0.323900i
$486$	8584.65	−	6410.54i	0.801250	−	0.598329i
$487$		−	16029.6i		−	1.49152i	−0.666213	−	0.745762i	$-0.732086\pi$
$487$		−	16029.6i		−	1.49152i	0.666213	−	0.745762i	$-0.267914\pi$
$488$	−15969.2	−	5194.27i	−1.48133	−	0.481831i
$489$	−2836.89	−	7566.96i	−0.262349	−	0.699774i
$490$	351.892	−	156.628i	0.0324425	−	0.0144403i
$491$	−15909.2			−1.46226			−0.731131	−	0.682237i	$-0.761007\pi$
$491$	−15909.2			−1.46226			−0.731131	+	0.682237i	$0.761007\pi$
$492$	12481.4	+	4906.70i	1.14371	+	0.449616i
$493$	−5989.99			−0.547212
$494$	−1010.30	+	449.685i	−0.0920149	+	0.0409561i
$495$	−1038.38	−	1190.21i	−0.0942864	−	0.108073i
$496$	6959.12	−	728.471i	0.629987	−	0.0659462i
$497$			3095.72i			0.279400i
$498$	14092.7	+	14318.2i	1.26809	+	1.28838i
$499$		−	11163.4i		−	1.00149i	−0.865596	−	0.500743i	$-0.833060\pi$
$499$		−	11163.4i		−	1.00149i	0.865596	−	0.500743i	$-0.166940\pi$
$500$	4002.29	+	3605.21i	0.357976	+	0.322460i
$501$	3257.97	−	1221.43i	0.290529	−	0.108921i
$502$	6356.96	+	14282.0i	0.565189	+	1.26980i
$503$	4480.16			0.397138			0.198569	−	0.980087i	$-0.436371\pi$
$503$	4480.16			0.397138			0.198569	+	0.980087i	$0.436371\pi$
$504$	1676.79	+	3934.15i	0.148195	+	0.347700i
$505$	461.381			0.0406558
$506$	−1455.22	−	3269.40i	−0.127850	−	0.287238i
$507$	−7005.21	+	2626.29i	−0.613634	+	0.230054i
$508$	14744.9	+	13282.0i	1.28779	+	1.16002i
$509$		−	21223.7i		−	1.84818i	−0.382174	−	0.924091i	$-0.624824\pi$
$509$		−	21223.7i		−	1.84818i	0.382174	−	0.924091i	$-0.375176\pi$
$510$	1048.78	+	1065.57i	0.0910607	+	0.0925178i
$511$		−	587.260i		−	0.0508392i
$512$	6800.75	+	9379.10i	0.587019	+	0.809573i
$513$	800.515	+	431.865i	0.0688959	+	0.0371683i
$514$	5716.32	−	2544.35i	0.490537	−	0.218339i
$515$	653.480			0.0559141
$516$	−14318.5	−	5628.90i	−1.22159	−	0.480230i
$517$	−5472.15			−0.465503
$518$	5685.76	−	2530.75i	0.482274	−	0.214661i
$519$	6485.89	+	17300.1i	0.548553	+	1.46318i
$520$	1173.05	−	3606.39i	0.0989259	−	0.304136i
$521$		−	6630.60i		−	0.557566i	−0.960354	−	0.278783i	$-0.910069\pi$
$521$		−	6630.60i		−	0.557566i	0.960354	−	0.278783i	$-0.0899309\pi$
$522$	5262.34	−	11334.9i	0.441238	−	0.950415i
$523$			3096.39i			0.258883i	0.991587	+	0.129441i	$0.0413184\pi$
$523$			3096.39i			0.258883i	−0.991587	+	0.129441i	$0.958682\pi$
$524$	4172.02	−	4631.53i	0.347816	−	0.386125i
$525$	−1497.45	−	3994.22i	−0.124484	−	0.332042i
$526$	−5489.31	−	12332.7i	−0.455029	−	1.02230i
$527$	−4001.96			−0.330793
$528$	3126.38	+	6263.12i	0.257686	+	0.516226i
$529$	−8554.03			−0.703052
$530$	2204.13	+	4951.96i	0.180644	+	0.405848i
$531$	13918.0	−	12142.5i	1.13746	−	0.992354i
$532$	−242.993	+	269.757i	−0.0198028	+	0.0219840i
$533$			19456.1i			1.58112i
$534$	−3454.47	+	3400.06i	−0.279943	+	0.275534i
$535$			2919.51i			0.235928i
$536$	3267.33	−	10045.0i	0.263297	−	0.809475i
$537$	3205.67	−	1201.82i	0.257607	−	0.0965782i
$538$	−19722.4	+	8778.50i	−1.58047	+	0.703472i
$539$	−1031.42			−0.0824239
$540$	−2937.77	+	1048.51i	−0.234114	+	0.0835565i
$541$	13892.9			1.10407			0.552035	−	0.833821i	$-0.313851\pi$
$541$	13892.9			1.10407			0.552035	+	0.833821i	$0.313851\pi$
$542$	−5390.84	+	2399.48i	−0.427226	+	0.190159i
$543$	−3550.42	+	1331.07i	−0.280595	+	0.105197i
$544$	−3310.02	−	5740.10i	−0.260875	−	0.452398i
$545$		−	2638.32i		−	0.207363i
$546$	−4421.69	+	4352.05i	−0.346577	+	0.341118i
$547$			23586.8i			1.84369i	0.387560	+	0.921845i	$0.373318\pi$
$547$			23586.8i			1.84369i	−0.387560	+	0.921845i	$0.626682\pi$
$548$	−7677.87	−	6916.11i	−0.598508	−	0.539127i
$549$	−15099.1	+	13173.0i	−1.17380	+	1.02406i
$550$	−2839.26	−	6378.90i	−0.220121	−	0.494540i
$551$	1060.93			0.0820278
$552$	−7060.32	+	312.357i	−0.544397	+	0.0240848i
$553$	−5504.12			−0.423253
$554$	360.941	+	810.915i	0.0276803	+	0.0621886i
$555$	1593.52	+	4250.46i	0.121876	+	0.325085i
$556$	−17585.4	−	15840.7i	−1.34134	−	1.20826i
$557$			2755.82i			0.209637i	0.994491	+	0.104819i	$0.0334262\pi$
$557$			2755.82i			0.209637i	−0.994491	+	0.104819i	$0.966574\pi$
$558$	3515.81	−	7572.96i	0.266731	−	0.574532i
$559$		−	22319.8i		−	1.68878i
$560$	−129.624	−	1238.31i	−0.00978148	−	0.0934430i
$561$	−1405.46	−	3748.83i	−0.105773	−	0.282132i
$562$	19656.9	−	8749.32i	1.47540	−	0.656704i
$563$	−6818.92			−0.510450			−0.255225	−	0.966882i	$-0.582149\pi$
$563$	−6818.92			−0.510450			−0.255225	+	0.966882i	$0.582149\pi$
$564$	−3953.75	+	10057.4i	−0.295183	+	0.750871i
$565$	4647.54			0.346059
$566$	9615.19	−	4279.75i	0.714058	−	0.317829i
$567$	5055.85	+	692.107i	0.374472	+	0.0512623i
$568$	9516.12	+	3095.30i	0.702971	+	0.228655i
$569$		−	3532.38i		−	0.260255i	−0.991497	−	0.130127i	$-0.958461\pi$
$569$		−	3532.38i		−	0.260255i	0.991497	−	0.130127i	$-0.0415386\pi$
$570$	−185.759	−	188.731i	−0.0136501	−	0.0138685i
$571$			9371.56i			0.686843i	0.939181	+	0.343422i	$0.111586\pi$
$571$			9371.56i			0.686843i	−0.939181	+	0.343422i	$0.888414\pi$
$572$	−6796.75	+	7545.36i	−0.496830	+	0.551552i
$573$	4990.31	−	1870.89i	0.363828	−	0.136401i
$574$	2597.47	+	5835.67i	0.188879	+	0.424349i
$575$	7049.23			0.511258
$576$	13770.0	−	1220.79i	0.996093	−	0.0883095i
$577$	−12404.2			−0.894965			−0.447482	−	0.894293i	$-0.647679\pi$
$577$	−12404.2			−0.894965			−0.447482	+	0.894293i	$0.647679\pi$
$578$	−4109.64	−	9233.03i	−0.295742	−	0.664435i
$579$	−297.593	+	111.569i	−0.0213602	+	0.00800804i
$580$	−2435.08	+	2703.29i	−0.174330	+	0.193531i
$581$			9568.76i			0.683268i
$582$	−12833.5	−	13038.8i	−0.914028	−	0.928654i
$583$		−	14514.6i		−	1.03110i
$584$	−1805.22	−	587.181i	−0.127912	−	0.0416057i
$585$	−2974.92	−	3409.91i	−0.210253	−	0.240995i
$586$	−5488.90	+	2443.12i	−0.386936	+	0.172226i
$587$	20073.0			1.41142			0.705710	−	0.708501i	$-0.250628\pi$
$587$	20073.0			1.41142			0.705710	+	0.708501i	$0.250628\pi$
$588$	−745.226	+	1895.67i	−0.0522663	+	0.132953i
$589$	708.819			0.0495863
$590$	−4912.72	+	2186.66i	−0.342803	+	0.152582i
$591$	4648.36	+	12398.8i	0.323533	+	0.862973i
$592$	−2094.43	−	20008.2i	−0.145406	−	1.38908i
$593$		−	15891.1i		−	1.10045i	−0.835015	−	0.550227i	$-0.814541\pi$
$593$		−	15891.1i		−	1.10045i	0.835015	−	0.550227i	$-0.185459\pi$
$594$	8328.69	+	633.870i	0.575304	+	0.0437845i
$595$			712.110i			0.0490650i
$596$	2141.69	+	1929.20i	0.147193	+	0.132589i
$597$	8547.43	+	22798.9i	0.585968	+	1.56298i
$598$	−4169.14	−	9366.70i	−0.285098	−	0.640523i
$599$	−14685.5			−1.00172			−0.500861	−	0.865528i	$-0.666983\pi$
$599$	−14685.5			−1.00172			−0.500861	+	0.865528i	$0.666983\pi$
$600$	−13775.3	+	609.437i	−0.937292	+	0.0414669i
$601$	21995.5			1.49287			0.746435	−	0.665458i	$-0.231764\pi$
$601$	21995.5			1.49287			0.746435	+	0.665458i	$0.231764\pi$
$602$	−2979.79	−	6694.61i	−0.201739	−	0.453242i
$603$	−8286.16	−	9497.75i	−0.559599	−	0.641423i
$604$	−4270.26	−	3846.59i	−0.287673	−	0.259132i
$605$			2467.70i			0.165828i
$606$	−1738.90	+	1711.51i	−0.116564	+	0.114728i
$607$		−	4511.18i		−	0.301653i	−0.988560	−	0.150826i	$-0.951807\pi$
$607$		−	4511.18i		−	0.301653i	0.988560	−	0.150826i	$-0.0481935\pi$
$608$	586.264	+	1016.67i	0.0391055	+	0.0678151i
$609$	5573.35	−	2089.48i	0.370843	−	0.139031i
$610$	5329.64	−	2372.24i	0.353755	−	0.157457i
$611$	−15677.5			−1.03804
$612$	−7905.52	−	125.503i	−0.522160	−	0.00828946i
$613$	−5257.74			−0.346425			−0.173212	−	0.984885i	$-0.555415\pi$
$613$	−5257.74			−0.346425			−0.173212	+	0.984885i	$0.555415\pi$
$614$	−12276.7	+	5464.37i	−0.806915	+	0.359160i
$615$	−4362.53	+	1635.54i	−0.286040	+	0.107238i
$616$	−1031.28	+	3170.55i	−0.0674538	+	0.207379i
$617$			5062.66i			0.330332i	0.986266	+	0.165166i	$0.0528160\pi$
$617$			5062.66i			0.330332i	−0.986266	+	0.165166i	$0.947184\pi$
$618$	−2462.90	+	2424.11i	−0.160311	+	0.157786i
$619$		−	11042.8i		−	0.717037i	−0.933523	−	0.358518i	$-0.883282\pi$
$619$		−	11042.8i		−	0.717037i	0.933523	−	0.358518i	$-0.116718\pi$
$620$	−1626.90	+	1806.09i	−0.105384	+	0.116991i
$621$	−4003.93	+	7421.77i	−0.258731	+	0.479590i
$622$	−1238.26	−	2781.96i	−0.0798225	−	0.179335i
$623$	−2308.59			−0.148462
$624$	8956.96	+	17943.6i	0.574624	+	1.15115i
$625$	12788.2			0.818445
$626$	3182.58	+	7150.23i	0.203198	+	0.456518i
$627$	248.931	+	663.985i	0.0158554	+	0.0422919i
$628$	−11226.8	+	12463.4i	−0.713373	+	0.791946i
$629$			11506.1i			0.729375i
$630$	−1347.54	−	625.605i	−0.0852176	−	0.0395630i
$631$			23354.2i			1.47340i	0.676221	+	0.736699i	$0.263617\pi$
$631$			23354.2i			1.47340i	−0.676221	+	0.736699i	$0.736383\pi$
$632$	−5503.37	+	16919.5i	−0.346380	+	1.06491i
$633$	8540.41	+	22780.2i	0.536257	+	1.43038i
$634$	−9396.96	+	4182.61i	−0.588645	+	0.262008i
$635$	−6894.09			−0.430840
$636$	−26676.6	−	10487.1i	−1.66320	−	0.653838i
$637$	−2954.98			−0.183800
$638$	8900.82	−	3961.78i	0.552331	−	0.245844i
$639$	8997.67	−	7849.87i	0.557030	−	0.485972i
$640$	−3936.12	−	839.680i	−0.243108	−	0.0518614i
$641$		−	7436.09i		−	0.458203i	−0.973403	−	0.229101i	$-0.926421\pi$
$641$		−	7436.09i		−	0.458203i	0.973403	−	0.229101i	$-0.0735787\pi$
$642$	−10830.0	−	11003.3i	−0.665776	−	0.676429i
$643$			17484.0i			1.07232i	0.844117	+	0.536160i	$0.180125\pi$
$643$			17484.0i			1.07232i	−0.844117	+	0.536160i	$0.819875\pi$
$644$	−2500.99	−	2252.85i	−0.153032	−	0.137849i
$645$	5004.64	−	1876.27i	0.305516	−	0.114539i
$646$	−272.949	−	613.227i	−0.0166239	−	0.0373484i
$647$	−9157.80			−0.556461			−0.278230	−	0.960514i	$-0.589748\pi$
$647$	−9157.80			−0.556461			−0.278230	+	0.960514i	$0.589748\pi$
$648$	7182.67	−	14849.5i	0.435435	−	0.900220i
$649$	14399.6			0.870929
$650$	−8134.37	−	18275.3i	−0.490856	−	1.10279i
$651$	3723.60	−	1396.00i	0.224177	−	0.0840452i
$652$	−9244.39	−	8327.21i	−0.555274	−	0.500182i
$653$		−	1608.20i		−	0.0963762i	−0.998838	−	0.0481881i	$-0.984655\pi$
$653$		−	1608.20i		−	0.0963762i	0.998838	−	0.0481881i	$-0.0153447\pi$
$654$	9786.94	+	9943.55i	0.585168	+	0.594531i
$655$			2165.51i			0.129181i
$656$	20535.8	−	2149.65i	1.22224	−	0.127942i
$657$	−1706.86	+	1489.13i	−0.101356	+	0.0884267i
$658$	−4702.31	+	2093.01i	−0.278594	+	0.124003i
$659$	−22526.0			−1.33154			−0.665772	−	0.746155i	$-0.731898\pi$
$659$	−22526.0			−1.33154			−0.665772	+	0.746155i	$0.731898\pi$
$660$	−2263.21	−	889.712i	−0.133478	−	0.0524727i
$661$	−1132.54			−0.0666424			−0.0333212	−	0.999445i	$-0.510608\pi$
$661$	−1132.54			−0.0666424			−0.0333212	+	0.999445i	$0.510608\pi$
$662$	21395.8	−	9523.33i	1.25615	−	0.559116i
$663$	−4026.57	−	10740.3i	−0.235866	−	0.629135i
$664$	29414.0	+	9567.46i	1.71910	+	0.559171i
$665$		−	126.127i		−	0.00735490i
$666$	−21773.1	−	10108.3i	−1.26680	−	0.588123i
$667$			9836.18i			0.571002i
$668$	3585.30	−	3980.19i	0.207664	−	0.230536i
$669$	1646.62	+	4392.10i	0.0951600	+	0.253824i
$670$	1492.20	+	3352.48i	0.0860428	+	0.193310i
$671$	−15621.6			−0.898756
$672$	5082.10	+	4186.21i	0.291735	+	0.240307i
$673$	17389.4			0.996004			0.498002	−	0.867176i	$-0.334067\pi$
$673$	17389.4			0.996004			0.498002	+	0.867176i	$0.334067\pi$
$674$	4768.95	+	10714.3i	0.272542	+	0.612312i
$675$	−7812.03	+	14480.5i	−0.445459	+	0.825713i
$676$	−7709.03	+	8558.12i	−0.438611	+	0.486921i
$677$			14631.4i			0.830621i	0.909680	+	0.415311i	$0.136327\pi$
$677$			14631.4i			0.830621i	−0.909680	+	0.415311i	$0.863673\pi$
$678$	−17516.1	+	17240.2i	−0.992186	+	0.976559i
$679$		−	8713.74i		−	0.492493i
$680$	2189.00	+	712.013i	0.123447	+	0.0401536i
$681$	7447.17	−	2791.98i	0.419054	−	0.157106i
$682$	5946.71	−	2646.90i	0.333888	−	0.148614i
$683$	−15627.9			−0.875526			−0.437763	−	0.899090i	$-0.644229\pi$
$683$	−15627.9			−0.875526			−0.437763	+	0.899090i	$0.644229\pi$
$684$	1400.21	+	22.2288i	0.0782725	+	0.00124260i
$685$	3589.85			0.200235
$686$	−886.318	+	394.502i	−0.0493291	+	0.0219565i
$687$	29815.1	−	11177.8i	1.65578	−	0.620759i
$688$	−23558.4	+	2466.06i	−1.30546	+	0.136653i
$689$		−	41583.7i		−	2.29929i
$690$	1749.77	−	1722.21i	0.0965400	−	0.0950196i
$691$			14315.9i			0.788134i	0.919082	+	0.394067i	$0.128932\pi$
$691$			14315.9i			0.788134i	−0.919082	+	0.394067i	$0.871068\pi$
$692$	21135.1	+	19038.2i	1.16104	+	1.04584i
$693$	2615.40	+	2997.82i	0.143363	+	0.164326i
$694$	5278.37	+	11858.8i	0.288709	+	0.648635i
$695$	8222.21			0.448757
$696$	−850.380	−	19221.5i	−0.0463126	−	1.04682i
$697$	−11809.4			−0.641771
$698$	118.466	+	266.154i	0.00642406	+	0.0144328i
$699$	−408.182	−	1088.76i	−0.0220871	−	0.0589138i
$700$	−4879.65	−	4395.52i	−0.263476	−	0.237336i
$701$		−	9735.48i		−	0.524542i	−0.964994	−	0.262271i	$-0.915529\pi$
$701$		−	9735.48i		−	0.524542i	0.964994	−	0.262271i	$-0.0844714\pi$
$702$	23861.4	+	1816.01i	1.28289	+	0.0976367i
$703$		−	2037.93i		−	0.109334i
$704$	8715.02	+	6340.25i	0.466562	+	0.339428i
$705$	−1317.89	−	3515.27i	−0.0704038	−	0.187791i
$706$	−20465.2	+	9109.09i	−1.09096	+	0.485588i
$707$	−1162.09			−0.0618175
$708$	10404.0	−	26465.3i	0.552270	−	1.40484i
$709$	−4631.15			−0.245313			−0.122656	−	0.992449i	$-0.539141\pi$
$709$	−4631.15			−0.245313			−0.122656	+	0.992449i	$0.539141\pi$
$710$	−3175.97	+	1413.63i	−0.167876	+	0.0747220i
$711$	13956.9	+	15997.7i	0.736181	+	0.843824i
$712$	−2308.28	+	7096.53i	−0.121498	+	0.373530i
$713$			6571.63i			0.345175i
$714$	−2641.60	−	2683.87i	−0.138459	−	0.140674i
$715$		−	3527.90i		−	0.184526i
$716$	3527.75	−	3916.31i	0.184132	−	0.204412i
$717$	14001.2	−	5249.11i	0.729265	−	0.273405i
$718$	−1373.57	−	3085.96i	−0.0713944	−	0.160400i
$719$	1311.54			0.0680281			0.0340141	−	0.999421i	$-0.489171\pi$
$719$	1311.54			0.0680281			0.0340141	+	0.999421i	$0.489171\pi$
$720$	−3270.44	+	3516.75i	−0.169281	+	0.182030i
$721$	−1645.94			−0.0850178
$722$	−7840.56	−	17615.2i	−0.404149	−	0.907990i
$723$	7416.55	−	2780.50i	0.381500	−	0.143026i
$724$	−3907.14	+	4337.48i	−0.200563	+	0.222653i
$725$			19191.3i			0.983098i
$726$	−9154.02	−	9300.50i	−0.467958	−	0.475446i
$727$		−	5347.22i		−	0.272788i	−0.990655	−	0.136394i	$-0.956449\pi$
$727$		−	5347.22i		−	0.272788i	0.990655	−	0.136394i	$-0.0435514\pi$
$728$	−2954.58	+	9083.51i	−0.150418	+	0.462441i
$729$	−10808.6	−	16449.8i	−0.549134	−	0.835734i
$730$	602.484	−	268.167i	0.0305465	−	0.0135963i
$731$	13547.6			0.685468
$732$	−11287.0	+	28711.2i	−0.569915	+	1.44972i
$733$	−18277.7			−0.921013			−0.460507	−	0.887656i	$-0.652332\pi$
$733$	−18277.7			−0.921013			−0.460507	+	0.887656i	$0.652332\pi$
$734$	14961.4	−	6659.35i	0.752364	−	0.334879i
$735$	−248.404	−	662.578i	−0.0124660	−	0.0332511i
$736$	−9425.83	+	5435.39i	−0.472066	+	0.272216i
$737$		−	9826.39i		−	0.491126i
$738$	10374.9	−	22347.2i	0.517485	−	1.11465i
$739$			199.208i			0.00991611i	0.999988	+	0.00495805i	$0.00157820\pi$
$739$			199.208i			0.00991611i	−0.999988	+	0.00495805i	$0.998422\pi$
$740$	5192.70	+	4677.51i	0.257956	+	0.232363i
$741$	713.178	+	1902.29i	0.0353566	+	0.0943082i
$742$	−5551.60	−	12472.6i	−0.274670	−	0.617095i
$743$	−1088.16			−0.0537290			−0.0268645	−	0.999639i	$-0.508552\pi$
$743$	−1088.16			−0.0537290			−0.0268645	+	0.999639i	$0.508552\pi$
$744$	−568.146	−	12842.0i	−0.0279963	−	0.632811i
$745$	−1001.37			−0.0492446
$746$	96.4400	+	216.669i	0.00473313	+	0.0106338i
$747$	27811.5	−	24263.7i	1.36221	−	1.18844i
$748$	−4579.87	−	4125.48i	−0.223872	−	0.201661i
$749$		−	7353.45i		−	0.358730i
$750$	7052.77	−	6941.69i	0.343374	−	0.337966i
$751$		−	12860.5i		−	0.624881i	−0.949937	−	0.312441i	$-0.898853\pi$
$751$		−	12860.5i		−	0.624881i	0.949937	−	0.312441i	$-0.101147\pi$
$752$	1732.16	+	16547.4i	0.0839966	+	0.802425i
$753$	26891.7	−	10081.8i	1.30144	−	0.487918i
$754$	25500.5	−	11350.3i	1.23166	−	0.548216i
$755$	1996.60			0.0962433
$756$	7399.43	−	2640.90i	0.355972	−	0.127048i
$757$	−24735.4			−1.18761			−0.593807	−	0.804608i	$-0.702376\pi$
$757$	−24735.4			−1.18761			−0.593807	+	0.804608i	$0.702376\pi$
$758$	8757.21	−	3897.86i	0.419626	−	0.186776i
$759$	−6155.97	+	2307.90i	−0.294397	+	0.110371i
$760$	−387.711	−	126.110i	−0.0185049	−	0.00601908i
$761$			24495.3i			1.16682i	0.812176	+	0.583412i	$0.198283\pi$
$761$			24495.3i			1.16682i	−0.812176	+	0.583412i	$0.801717\pi$
$762$	25983.1	−	25573.9i	1.23526	−	1.21581i
$763$			6645.19i			0.315298i
$764$	5491.69	−	6096.56i	0.260055	−	0.288699i
$765$	2069.74	−	1805.71i	0.0978191	−	0.0853407i
$766$	2507.05	+	5632.53i	0.118255	+	0.265681i
$767$	41254.2			1.94212
$768$	17949.7	−	11436.5i	0.843363	−	0.537344i
$769$	−2688.38			−0.126067			−0.0630335	−	0.998011i	$-0.520078\pi$
$769$	−2688.38			−0.126067			−0.0630335	+	0.998011i	$0.520078\pi$
$770$	−470.990	−	1058.16i	−0.0220432	−	0.0495239i
$771$	−4035.21	−	10763.3i	−0.188488	−	0.502763i
$772$	−327.493	+	363.563i	−0.0152678	+	0.0169494i
$773$		−	10282.0i		−	0.478417i	−0.970968	−	0.239208i	$-0.923112\pi$
$773$		−	10282.0i		−	0.478417i	0.970968	−	0.239208i	$-0.0768879\pi$
$774$	−11901.9	+	25636.4i	−0.552720	+	1.19054i
$775$			12821.8i			0.594289i
$776$	−26785.7	−	8712.56i	−1.23911	−	0.403045i
$777$	−4013.64	−	10705.8i	−0.185313	−	0.494294i
$778$	28134.5	−	12522.7i	1.29649	−	0.577072i
$779$	2091.66			0.0962023
$780$	−6484.00	−	2548.99i	−0.297647	−	0.117011i
$781$	9309.01			0.426508
$782$	5685.38	−	2530.58i	0.259986	−	0.115720i
$783$	−20205.5	−	10900.5i	−0.922203	−	0.497515i
$784$	326.488	+	3118.96i	0.0148728	+	0.142081i
$785$		−	5827.35i		−	0.264952i
$786$	−8033.06	−	8161.60i	−0.364542	−	0.370375i
$787$			5994.41i			0.271509i	0.990742	+	0.135755i	$0.0433459\pi$
$787$			5994.41i			0.271509i	−0.990742	+	0.135755i	$0.956654\pi$
$788$	15147.3	+	13644.5i	0.684772	+	0.616833i
$789$	−23221.3	+	8705.77i	−1.04778	+	0.392818i
$790$	−2513.41	−	5646.80i	−0.113194	−	0.254309i
$791$	−11705.9			−0.526186
$792$	11830.2	−	5042.22i	0.530768	−	0.226222i
$793$	−44755.2			−2.00417
$794$	5221.30	+	11730.6i	0.233372	+	0.524310i
$795$	9324.07	−	3495.64i	0.415963	−	0.155947i
$796$	27853.0	+	25089.5i	1.24023	+	1.11718i
$797$		−	25490.8i		−	1.13291i	−0.824093	−	0.566455i	$-0.808315\pi$
$797$		−	25490.8i		−	1.13291i	0.824093	−	0.566455i	$-0.191685\pi$
$798$	467.875	+	475.361i	0.0207551	+	0.0210872i
$799$		−	9515.88i		−	0.421336i
$800$	−18390.7	+	10604.9i	−0.812760	+	0.468677i
$801$	5853.94	+	6709.90i	0.258226	+	0.295983i
$802$	−24903.8	+	11084.8i	−1.09649	+	0.488050i
$803$	−1765.93			−0.0776067
$804$	−18060.1	−	7099.80i	−0.792203	−	0.311431i
$805$	1169.36			0.0511981
$806$	17037.1	−	7583.25i	0.744548	−	0.331400i
$807$	13922.3	+	37135.5i	0.607295	+	1.61986i
$808$	−1161.93	+	3572.23i	−0.0505900	+	0.155533i
$809$			27306.9i			1.18672i	0.804935	+	0.593362i	$0.202200\pi$
$809$			27306.9i			1.18672i	−0.804935	+	0.593362i	$0.797800\pi$
$810$	1598.66	+	5502.95i	0.0693471	+	0.238709i
$811$			15093.4i			0.653515i	0.945108	+	0.326757i	$0.105956\pi$
$811$			15093.4i			0.653515i	−0.945108	+	0.326757i	$0.894044\pi$
$812$	6133.31	−	6808.84i	0.265070	−	0.294265i
$813$	3805.45	+	10150.4i	0.164161	+	0.437874i
$814$	−7610.11	−	17097.4i	−0.327683	−	0.736198i
$815$	4322.30			0.185771
$816$	−10891.4	+	5436.68i	−0.467247	+	0.233237i
$817$	−2399.53			−0.102753
$818$	3059.87	+	6874.53i	0.130790	+	0.293841i
$819$	7493.01	+	8588.62i	0.319691	+	0.366436i
$820$	−4800.84	+	5329.61i	−0.204454	+	0.226973i
$821$			1092.37i			0.0464358i	0.999730	+	0.0232179i	$0.00739115\pi$
$821$			1092.37i			0.0464358i	−0.999730	+	0.0232179i	$0.992609\pi$
$822$	−13529.8	+	13316.7i	−0.574095	+	0.565053i
$823$		−	9262.37i		−	0.392304i	−0.980574	−	0.196152i	$-0.937155\pi$
$823$		−	9262.37i		−	0.392304i	0.980574	−	0.196152i	$-0.0628446\pi$
$824$	−1645.71	+	5059.55i	−0.0695766	+	0.213905i
$825$	−12010.9	+	4502.93i	−0.506866	+	0.190027i
$826$	12373.8	−	5507.61i	0.521234	−	0.232003i
$827$	−27259.0			−1.14618			−0.573088	−	0.819494i	$-0.694255\pi$
$827$	−27259.0			−1.14618			−0.573088	+	0.819494i	$0.694255\pi$
$828$	−206.089	+	12981.7i	−0.00864984	+	0.544861i
$829$	6431.75			0.269462			0.134731	−	0.990882i	$-0.456983\pi$
$829$	6431.75			0.269462			0.134731	+	0.990882i	$0.456983\pi$
$830$	−9816.81	+	4369.49i	−0.410538	+	0.182731i
$831$	1526.88	−	572.434i	0.0637386	−	0.0238959i
$832$	24968.2	+	18164.6i	1.04040	+	0.756902i
$833$		−	1793.61i		−	0.0746037i
$834$	−30988.7	+	30500.6i	−1.28663	+	1.26637i
$835$			1860.97i			0.0771277i
$836$	811.177	+	730.696i	0.0335588	+	0.0302293i
$837$	−13499.5	−	7282.75i	−0.557478	−	0.300751i
$838$	4075.48	+	9156.27i	0.168001	+	0.377444i
$839$	−22454.5			−0.923977			−0.461988	−	0.886886i	$-0.652864\pi$
$839$	−22454.5			−0.923977			−0.461988	+	0.886886i	$0.652864\pi$
$840$	−2285.11	+	101.096i	−0.0938617	+	0.00415255i
$841$	−2389.63			−0.0979799
$842$	10885.3	+	24455.7i	0.445525	+	1.00095i
$843$	−13876.0	−	37012.0i	−0.566921	−	1.51217i
$844$	27830.1	+	25068.9i	1.13501	+	1.02240i
$845$		−	4001.42i		−	0.162903i
$846$	18007.0	+	8359.92i	0.731791	+	0.339740i
$847$		−	6215.45i		−	0.252143i
$848$	−43891.2	+	4594.47i	−1.77739	+	0.186055i
$849$	−6787.47	−	18104.5i	−0.274376	−	0.731855i
$850$	11092.7	−	4937.38i	0.447619	−	0.199236i
$851$	18894.1			0.761084
$852$	6725.98	−	17109.2i	0.270456	−	0.687972i
$853$	−20109.9			−0.807210			−0.403605	−	0.914933i	$-0.632243\pi$
$853$	−20109.9			−0.807210			−0.403605	+	0.914933i	$0.632243\pi$
$854$	−13423.9	+	5975.01i	−0.537888	+	0.239415i
$855$	−366.588	+	319.824i	−0.0146632	+	0.0127927i
$856$	−22604.2	−	7352.45i	−0.902566	−	0.293577i
$857$		−	4520.19i		−	0.180171i	−0.995934	−	0.0900857i	$-0.971286\pi$
$857$		−	4520.19i		−	0.180171i	0.995934	−	0.0900857i	$-0.0287141\pi$
$858$	13086.9	+	13296.3i	0.520722	+	0.529054i
$859$			12336.2i			0.489996i	0.969524	+	0.244998i	$0.0787873\pi$
$859$			12336.2i			0.489996i	−0.969524	+	0.244998i	$0.921213\pi$
$860$	5507.46	−	6114.07i	0.218375	−	0.242428i
$861$	10988.0	−	4119.46i	0.434925	−	0.163056i
$862$	11825.0	+	26566.8i	0.467238	+	1.04973i
$863$	−28532.3			−1.12543			−0.562717	−	0.826650i	$-0.690244\pi$
$863$	−28532.3			−1.12543			−0.562717	+	0.826650i	$0.690244\pi$
$864$	−719.593	−	25386.1i	−0.0283346	−	0.999598i
$865$	−9881.92			−0.388434
$866$	−987.042	−	2217.56i	−0.0387310	−	0.0870159i
$867$	−17384.9	+	6517.69i	−0.680995	+	0.255308i
$868$	4097.71	−	4549.04i	0.160237	−	0.177885i
$869$			16551.2i			0.646101i
$870$	4688.66	+	4763.69i	0.182713	+	0.185637i
$871$		−	28152.2i		−	1.09518i
$872$	20427.1	+	6644.29i	0.793289	+	0.258032i
$873$	−25326.4	+	22095.6i	−0.981866	+	0.856613i
$874$	−1006.98	+	448.210i	−0.0389722	+	0.0173466i
$875$	4713.31			0.182102
$876$	−1275.92	+	3245.63i	−0.0492117	+	0.125182i
$877$	−4206.94			−0.161982			−0.0809910	−	0.996715i	$-0.525809\pi$
$877$	−4206.94			−0.161982			−0.0809910	+	0.996715i	$0.525809\pi$
$878$	−41812.6	+	18610.9i	−1.60718	+	0.715361i
$879$	3874.67	+	10335.1i	0.148680	+	0.396580i
$880$	−3723.67	+	389.788i	−0.142642	+	0.0149315i
$881$		−	34208.7i		−	1.30819i	−0.756410	−	0.654097i	$-0.773049\pi$
$881$		−	34208.7i		−	1.30819i	0.756410	−	0.654097i	$-0.226951\pi$
$882$	3394.07	+	1575.73i	0.129574	+	0.0601558i
$883$		−	38065.3i		−	1.45074i	−0.688361	−	0.725368i	$-0.741670\pi$
$883$		−	38065.3i		−	1.45074i	0.688361	−	0.725368i	$-0.258330\pi$
$884$	−13121.1	−	11819.3i	−0.499221	−	0.449691i
$885$	3467.94	+	9250.19i	0.131722	+	0.351347i
$886$	−20608.9	−	46301.5i	−0.781455	−	1.75568i
$887$	−48539.2			−1.83742			−0.918708	−	0.394939i	$-0.870766\pi$
$887$	−48539.2			−1.83742			−0.918708	+	0.394939i	$0.870766\pi$
$888$	−36922.2	+	1633.48i	−1.39530	+	0.0617298i
$889$	17364.3			0.655096
$890$	−1054.20	−	2368.44i	−0.0397043	−	0.0892025i
$891$	2081.21	−	15203.2i	0.0782526	−	0.571636i
$892$	5365.74	+	4833.38i	0.201411	+	0.181428i
$893$			1685.43i			0.0631589i
$894$	3774.05	−	3714.61i	0.141189	−	0.138965i
$895$			1831.10i			0.0683877i
$896$	9914.01	+	2114.92i	0.369647	+	0.0788556i
$897$	−17636.6	+	6612.05i	−0.656487	+	0.246120i
$898$	−6129.74	+	2728.36i	−0.227786	+	0.101388i
$899$	−17891.0			−0.663736
$900$	−402.097	+	25328.5i	−0.0148925	+	0.938091i
$901$	25240.4			0.933273
$902$	17548.2	−	7810.76i	0.647774	−	0.288326i
$903$	−12605.3	+	4725.80i	−0.464539	+	0.174158i
$904$	−11704.3	+	35983.4i	−0.430618	+	1.32388i
$905$		−	2028.03i		−	0.0744904i
$906$	−7524.98	+	7406.47i	−0.275939	+	0.271593i
$907$		−	29490.5i		−	1.07962i	−0.841787	−	0.539810i	$-0.818496\pi$
$907$		−	29490.5i		−	1.07962i	0.841787	−	0.539810i	$-0.181504\pi$
$908$	8195.39	−	9098.05i	0.299530	−	0.332521i
$909$	2946.74	+	3377.61i	0.107522	+	0.123243i
$910$	−1349.37	−	3031.58i	−0.0491550	−	0.110435i
$911$	24195.6			0.879950			0.439975	−	0.898010i	$-0.354987\pi$
$911$	24195.6			0.879950			0.439975	+	0.898010i	$0.354987\pi$
$912$	1929.05	−	962.933i	0.0700410	−	0.0349626i
$913$	28773.8			1.04302
$914$	11638.0	+	26146.8i	0.421172	+	0.946236i
$915$	−3762.25	−	10035.2i	−0.135930	−	0.362572i
$916$	32810.7	−	36424.5i	1.18351	−	1.31387i
$917$		−	5454.33i		−	0.196421i
$918$	−1102.28	+	14483.3i	−0.0396303	+	0.520720i
$919$			23199.3i			0.832726i	0.909198	+	0.416363i	$0.136696\pi$
$919$			23199.3i			0.832726i	−0.909198	+	0.416363i	$0.863304\pi$
$920$	1169.20	−	3594.56i	0.0418993	−	0.128814i
$921$	8666.23	+	23115.8i	0.310056	+	0.827026i
$922$	26912.8	−	11979.0i	0.961309	−	0.427881i
$923$	26669.9			0.951085
$924$	5700.40	+	2240.94i	0.202954	+	0.0797852i
$925$	36864.2			1.31036
$926$	14646.1	−	6519.00i	0.519762	−	0.231347i
$927$	4173.63	+	4783.89i	0.147875	+	0.169497i
$928$	−14797.7	−	25661.5i	−0.523445	−	0.907736i
$929$			6362.94i			0.224716i	0.993668	+	0.112358i	$0.0358403\pi$
$929$			6362.94i			0.224716i	−0.993668	+	0.112358i	$0.964160\pi$
$930$	3132.53	+	3182.66i	0.110451	+	0.112219i
$931$			317.680i			0.0111832i
$932$	−1330.12	−	1198.15i	−0.0467483	−	0.0421102i
$933$	−5238.17	+	1963.81i	−0.183805	+	0.0689093i
$934$	−15369.1	−	34529.4i	−0.538429	−	1.20967i
$935$	2141.36			0.0748983
$936$	33893.1	−	14445.8i	1.18358	−	0.504460i
$937$	−16368.1			−0.570677			−0.285338	−	0.958427i	$-0.592106\pi$
$937$	−16368.1			−0.570677			−0.285338	+	0.958427i	$0.592106\pi$
$938$	−3758.44	−	8443.98i	−0.130829	−	0.293929i
$939$	13463.2	−	5047.42i	0.467897	−	0.175417i
$940$	−4294.53	−	3868.45i	−0.149013	−	0.134229i
$941$		−	2253.45i		−	0.0780662i	−0.999238	−	0.0390331i	$-0.987572\pi$
$941$		−	2253.45i		−	0.0780662i	0.999238	−	0.0390331i	$-0.0124278\pi$
$942$	21616.8	+	21962.7i	0.747678	+	0.759642i
$943$			19392.3i			0.669672i
$944$	−4558.07	−	43543.5i	−0.157153	−	1.50129i
$945$	−1295.89	+	2402.10i	−0.0446089	+	0.0826881i
$946$	−20131.1	+	8960.41i	−0.691880	+	0.307958i
$947$	38973.7			1.33736			0.668678	−	0.743552i	$-0.266861\pi$
$947$	38973.7			1.33736			0.668678	+	0.743552i	$0.266861\pi$
$948$	30419.8	+	11958.6i	1.04218	+	0.409703i
$949$	−5059.31			−0.173058
$950$	−1964.71	+	874.499i	−0.0670987	+	0.0298658i
$951$	6633.42	+	17693.6i	0.226186	+	0.603317i
$952$	−5513.49	−	1793.37i	−0.187703	−	0.0610539i
$953$			31617.7i			1.07471i	0.843357	+	0.537354i	$0.180576\pi$
$953$			31617.7i			1.07471i	−0.843357	+	0.537354i	$0.819424\pi$
$954$	−22174.2	+	47762.7i	−0.752534	+	1.62094i
$955$			2850.50i			0.0965863i
$956$	15407.9	−	17104.9i	0.521262	−	0.578675i
$957$	−6283.18	−	16759.4i	−0.212233	−	0.566097i
$958$	−20417.4	−	45871.1i	−0.688575	−	1.54700i
$959$	−9041.86			−0.304460
$960$	−1974.04	+	7125.43i	−0.0663664	+	0.239555i
$961$	17837.9			0.598767
$962$	−21802.7	−	48983.4i	−0.730713	−	1.64167i
$963$	−21372.7	+	18646.3i	−0.715188	+	0.623954i
$964$	8161.70	−	9060.65i	0.272687	−	0.302722i
$965$		−	169.987i		−	0.00567055i
$966$	−4407.19	+	4337.78i	−0.146790	+	0.144478i
$967$		−	39611.3i		−	1.31728i	−0.752457	−	0.658642i	$-0.771131\pi$
$967$		−	39611.3i		−	1.31728i	0.752457	−	0.658642i	$-0.228869\pi$
$968$	−19106.1	−	6214.61i	−0.634393	−	0.206348i
$969$	−1154.65	+	432.884i	−0.0382793	+	0.0143511i
$970$	8939.63	−	3979.05i	0.295912	−	0.131711i
$971$	59595.6			1.96963			0.984817	−	0.173596i	$-0.0555388\pi$
$971$	59595.6			1.96963			0.984817	+	0.173596i	$0.0555388\pi$
$972$	−26438.6	−	14809.8i	−0.872447	−	0.488708i
$973$	−20709.5			−0.682339
$974$	−41420.9	+	18436.5i	−1.36264	+	0.606514i
$975$	−34410.6	+	12900.7i	−1.13028	+	0.423747i
$976$	4944.89	+	47238.8i	0.162174	+	1.54926i
$977$		−	15842.7i		−	0.518785i	−0.965772	−	0.259392i	$-0.916478\pi$
$977$		−	15842.7i		−	0.518785i	0.965772	−	0.259392i	$-0.0835223\pi$
$978$	−16290.3	+	16033.7i	−0.532624	+	0.524235i
$979$			6942.08i			0.226629i
$980$	−809.458	−	729.148i	−0.0263849	−	0.0237671i
$981$	19314.2	−	16850.3i	0.628598	−	0.548410i
$982$	18298.0	+	41109.6i	0.594615	+	1.33590i
$983$	54041.1			1.75345			0.876726	−	0.480990i	$-0.159723\pi$
$983$	54041.1			1.75345			0.876726	+	0.480990i	$0.159723\pi$
$984$	−1676.55	−	37895.7i	−0.0543155	−	1.22771i
$985$	−7082.25			−0.229096
$986$	6889.40	+	15478.2i	0.222518	+	0.499926i
$987$	3319.41	+	8854.00i	0.107050	+	0.285538i
$988$	2323.99	+	2093.41i	0.0748339	+	0.0674093i
$989$		−	22246.6i		−	0.715269i
$990$	−1881.23	+	4052.12i	−0.0603934	+	0.130086i
$991$			18418.5i			0.590397i	0.955436	+	0.295199i	$0.0953858\pi$
$991$			18418.5i			0.590397i	−0.955436	+	0.295199i	$0.904614\pi$
$992$	−9886.44	−	17144.6i	−0.316426	−	0.548733i
$993$	−15103.5	−	40286.3i	−0.482675	−	1.28746i
$994$	7999.39	−	3560.55i	0.255257	−	0.113615i
$995$	−13022.9			−0.414928
$996$	20789.8	−	52884.0i	0.661394	−	1.68242i
$997$	−3283.99			−0.104318			−0.0521590	−	0.998639i	$-0.516610\pi$
$997$	−3283.99			−0.104318			−0.0521590	+	0.998639i	$0.516610\pi$
$998$	−28846.4	+	12839.6i	−0.914947	+	0.407245i
$999$	−20938.7	+	38812.4i	−0.663134	+	1.22920i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.4.e.a.71.13	✓	36
3.2	odd	2	inner	84.4.e.a.71.24	yes	36
4.3	odd	2	inner	84.4.e.a.71.23	yes	36
12.11	even	2	inner	84.4.e.a.71.14	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.4.e.a.71.13	✓	36	1.1	even	1	trivial
84.4.e.a.71.14	yes	36	12.11	even	2	inner
84.4.e.a.71.23	yes	36	4.3	odd	2	inner
84.4.e.a.71.24	yes	36	3.2	odd	2	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	84.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.15015 - 2.58402i) q^{2} +(-4.86546 + 1.82409i) q^{3} +(-5.35430 + 5.94403i) q^{4} -2.77918i q^{5} +(10.3095 + 10.4745i) q^{6} +7.00000i q^{7} +(21.5177 + 6.99905i) q^{8} +(20.3454 - 17.7500i) q^{9} +(-7.18146 + 3.19649i) q^{10} +21.0494 q^{11} +(15.2087 - 38.6871i) q^{12} +60.3058 q^{13} +(18.0881 - 8.05107i) q^{14} +(5.06947 + 13.5220i) q^{15} +(-6.66302 - 63.6522i) q^{16} +36.6043i q^{17} +(-69.2668 - 32.1577i) q^{18} -6.48327i q^{19} +(16.5196 + 14.8806i) q^{20} +(-12.7686 - 34.0582i) q^{21} +(-24.2101 - 54.3921i) q^{22} +60.1080 q^{23} +(-117.461 + 5.19660i) q^{24} +117.276 q^{25} +(-69.3608 - 155.831i) q^{26} +(-66.6123 + 123.474i) q^{27} +(-41.6082 - 37.4801i) q^{28} +163.642i q^{29} +(29.1104 - 28.6520i) q^{30} +109.330i q^{31} +(-156.815 + 90.4271i) q^{32} +(-102.415 + 38.3960i) q^{33} +(94.5861 - 42.1005i) q^{34} +19.4543 q^{35} +(-3.42864 + 215.973i) q^{36} +314.337 q^{37} +(-16.7529 + 7.45675i) q^{38} +(-293.415 + 110.003i) q^{39} +(19.4517 - 59.8018i) q^{40} +322.625i q^{41} +(-73.3212 + 72.1665i) q^{42} -370.111i q^{43} +(-112.705 + 125.118i) q^{44} +(-49.3306 - 56.5437i) q^{45} +(-69.1334 - 155.320i) q^{46} -259.967 q^{47} +(148.526 + 297.543i) q^{48} -49.0000 q^{49} +(-134.885 - 303.044i) q^{50} +(-66.7693 - 178.097i) q^{51} +(-322.895 + 358.459i) q^{52} -689.547i q^{53} +(395.673 + 30.1134i) q^{54} -58.5002i q^{55} +(-48.9934 + 150.624i) q^{56} +(11.8260 + 31.5441i) q^{57} +(422.853 - 188.213i) q^{58} +684.084 q^{59} +(-107.519 - 42.2678i) q^{60} -742.139 q^{61} +(282.512 - 125.747i) q^{62} +(124.250 + 142.418i) q^{63} +(414.027 + 301.208i) q^{64} -167.601i q^{65} +(217.009 + 220.481i) q^{66} -466.825i q^{67} +(-217.577 - 195.990i) q^{68} +(-292.453 + 109.642i) q^{69} +(-22.3754 - 50.2702i) q^{70} +442.245 q^{71} +(562.021 - 239.542i) q^{72} -83.8943 q^{73} +(-361.535 - 812.252i) q^{74} +(-570.602 + 213.922i) q^{75} +(38.5368 + 34.7134i) q^{76} +147.346i q^{77} +(621.722 + 631.670i) q^{78} +786.303i q^{79} +(-176.901 + 18.5178i) q^{80} +(98.8724 - 722.264i) q^{81} +(833.668 - 371.068i) q^{82} +1366.97 q^{83} +(270.810 + 106.461i) q^{84} +101.730 q^{85} +(-956.373 + 425.684i) q^{86} +(-298.497 - 796.193i) q^{87} +(452.936 + 147.326i) q^{88} +329.799i q^{89} +(-89.3721 + 192.505i) q^{90} +422.140i q^{91} +(-321.836 + 357.284i) q^{92} +(-199.428 - 531.943i) q^{93} +(299.001 + 671.758i) q^{94} -18.0182 q^{95} +(598.030 - 726.014i) q^{96} -1244.82 q^{97} +(56.3575 + 126.617i) q^{98} +(428.260 - 373.628i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 12 q^{4} + 30 q^{6} + 20 q^{9} - 132 q^{10} - 78 q^{12} + 324 q^{16} + 424 q^{18} - 240 q^{22} - 382 q^{24} - 900 q^{25} + 168 q^{28} + 476 q^{30} + 848 q^{33} - 576 q^{34} + 412 q^{36} + 528 q^{37}+ \cdots - 72 q^{97}+O(q^{100}) \) 36 * q + 12 * q^4 + 30 * q^6 + 20 * q^9 - 132 * q^10 - 78 * q^12 + 324 * q^16 + 424 * q^18 - 240 * q^22 - 382 * q^24 - 900 * q^25 + 168 * q^28 + 476 * q^30 + 848 * q^33 - 576 * q^34 + 412 * q^36 + 528 * q^37 - 1068 * q^40 + 70 * q^42 - 984 * q^45 + 288 * q^46 + 526 * q^48 - 1764 * q^49 + 468 * q^52 - 1826 * q^54 + 1840 * q^57 + 1536 * q^58 + 652 * q^60 + 2448 * q^61 - 2604 * q^64 - 1188 * q^66 - 744 * q^69 + 252 * q^70 + 1888 * q^72 - 1656 * q^73 - 972 * q^76 - 1348 * q^78 + 2452 * q^81 + 888 * q^82 + 490 * q^84 + 2904 * q^85 + 4008 * q^88 + 3184 * q^90 - 6744 * q^93 + 3264 * q^94 - 1330 * q^96 - 72 * q^97

Introduction

L-functions

Modular forms

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Representations

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Database

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