LMFDB - Embedded newform 162.4.e.b.19.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,4,Mod(19,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.19");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	162.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$9.55830942093$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			19.4
Character	$\chi$	$=$	162.19
Dual form			162.4.e.b.145.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.87939 + 0.684040i) q^{2} +(3.06418 - 2.57115i) q^{4} +(2.36712 + 13.4246i) q^{5} +(-10.7136 - 8.98975i) q^{7} +(-4.00000 + 6.92820i) q^{8} +O(q^{10})$	\(q+(-1.87939 + 0.684040i) q^{2} +(3.06418 - 2.57115i) q^{4} +(2.36712 + 13.4246i) q^{5} +(-10.7136 - 8.98975i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(-13.6317 - 23.6108i) q^{10} +(-5.21774 + 29.5913i) q^{11} +(9.46670 + 3.44560i) q^{13} +(26.2843 + 9.56669i) q^{14} +(2.77837 - 15.7569i) q^{16} +(-45.9801 - 79.6399i) q^{17} +(-21.7919 + 37.7447i) q^{19} +(41.7700 + 35.0492i) q^{20} +(-10.4355 - 59.1825i) q^{22} +(-85.9596 + 72.1286i) q^{23} +(-57.1553 + 20.8028i) q^{25} -20.1485 q^{26} -55.9423 q^{28} +(-271.740 + 98.9052i) q^{29} +(-142.315 + 119.417i) q^{31} +(5.55674 + 31.5138i) q^{32} +(140.891 + 118.222i) q^{34} +(95.3236 - 165.105i) q^{35} +(-195.634 - 338.848i) q^{37} +(15.1365 - 85.8435i) q^{38} +(-102.477 - 37.2985i) q^{40} +(-345.291 - 125.676i) q^{41} +(-32.5874 + 184.812i) q^{43} +(60.0955 + 104.088i) q^{44} +(112.212 - 194.357i) q^{46} +(257.618 + 216.167i) q^{47} +(-25.5964 - 145.164i) q^{49} +(93.1868 - 78.1930i) q^{50} +(37.8668 - 13.7824i) q^{52} +366.522 q^{53} -409.602 q^{55} +(105.137 - 38.2668i) q^{56} +(443.048 - 371.762i) q^{58} +(65.6208 + 372.154i) q^{59} +(675.933 + 567.175i) q^{61} +(185.779 - 321.779i) q^{62} +(-32.0000 - 55.4256i) q^{64} +(-23.8470 + 135.243i) q^{65} +(897.489 + 326.659i) q^{67} +(-345.657 - 125.809i) q^{68} +(-66.2111 + 375.502i) q^{70} +(-341.031 - 590.683i) q^{71} +(-410.162 + 710.421i) q^{73} +(599.458 + 503.005i) q^{74} +(30.2730 + 171.687i) q^{76} +(321.919 - 270.122i) q^{77} +(-132.267 + 48.1413i) q^{79} +218.107 q^{80} +734.903 q^{82} +(241.086 - 87.7482i) q^{83} +(960.294 - 805.782i) q^{85} +(-65.1748 - 369.625i) q^{86} +(-184.143 - 154.515i) q^{88} +(470.400 - 814.757i) q^{89} +(-70.4471 - 122.018i) q^{91} +(-77.9418 + 442.030i) q^{92} +(-632.030 - 230.040i) q^{94} +(-558.292 - 203.202i) q^{95} +(40.0173 - 226.949i) q^{97} +(147.404 + 255.311i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 12 q^{5} + 33 q^{7} - 120 q^{8}+O(q^{10}) $ 30 * q + 12 * q^5 + 33 * q^7 - 120 * q^8	$ 30 q + 12 q^{5} + 33 q^{7} - 120 q^{8} - 30 q^{10} + 39 q^{11} - 60 q^{13} + 66 q^{14} - 102 q^{17} - 171 q^{19} - 96 q^{20} + 78 q^{22} - 48 q^{23} - 432 q^{25} + 468 q^{26} + 336 q^{28} + 381 q^{29} - 801 q^{31} - 222 q^{34} - 624 q^{35} - 555 q^{37} - 606 q^{38} + 96 q^{40} - 1401 q^{41} + 648 q^{43} - 132 q^{44} - 348 q^{46} - 540 q^{47} + 15 q^{49} + 828 q^{50} - 240 q^{52} + 1794 q^{53} + 3906 q^{55} + 264 q^{56} - 444 q^{58} + 1500 q^{59} - 378 q^{61} - 744 q^{62} - 960 q^{64} - 3666 q^{65} + 3087 q^{67} + 24 q^{68} + 2118 q^{70} - 120 q^{71} - 2604 q^{73} + 1974 q^{74} - 1212 q^{76} + 6504 q^{77} - 2625 q^{79} + 480 q^{80} + 3408 q^{82} + 5211 q^{83} - 1395 q^{85} + 1296 q^{86} - 912 q^{88} - 2604 q^{89} - 3399 q^{91} - 372 q^{92} + 4500 q^{94} - 7545 q^{95} + 8940 q^{97} - 4002 q^{98}+O(q^{100}) $ 30 * q + 12 * q^5 + 33 * q^7 - 120 * q^8 - 30 * q^10 + 39 * q^11 - 60 * q^13 + 66 * q^14 - 102 * q^17 - 171 * q^19 - 96 * q^20 + 78 * q^22 - 48 * q^23 - 432 * q^25 + 468 * q^26 + 336 * q^28 + 381 * q^29 - 801 * q^31 - 222 * q^34 - 624 * q^35 - 555 * q^37 - 606 * q^38 + 96 * q^40 - 1401 * q^41 + 648 * q^43 - 132 * q^44 - 348 * q^46 - 540 * q^47 + 15 * q^49 + 828 * q^50 - 240 * q^52 + 1794 * q^53 + 3906 * q^55 + 264 * q^56 - 444 * q^58 + 1500 * q^59 - 378 * q^61 - 744 * q^62 - 960 * q^64 - 3666 * q^65 + 3087 * q^67 + 24 * q^68 + 2118 * q^70 - 120 * q^71 - 2604 * q^73 + 1974 * q^74 - 1212 * q^76 + 6504 * q^77 - 2625 * q^79 + 480 * q^80 + 3408 * q^82 + 5211 * q^83 - 1395 * q^85 + 1296 * q^86 - 912 * q^88 - 2604 * q^89 - 3399 * q^91 - 372 * q^92 + 4500 * q^94 - 7545 * q^95 + 8940 * q^97 - 4002 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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 $

$2$	−1.87939	+	0.684040i	−0.664463	+	0.241845i
$2$	−1.87939	+	0.684040i	−0.664463	+	0.241845i
$3$		0			0
$3$		0			0
$4$	3.06418	−	2.57115i	0.383022	−	0.321394i
$5$	2.36712	+	13.4246i	0.211722	+	1.20073i	0.886506	+	0.462718i	$0.153126\pi$
$5$	2.36712	+	13.4246i	0.211722	+	1.20073i	−0.674784	+	0.738015i	$0.735763\pi$
$6$		0			0
$7$	−10.7136	−	8.98975i	−0.578478	−	0.485401i	0.305969	−	0.952042i	$-0.401020\pi$
$7$	−10.7136	−	8.98975i	−0.578478	−	0.485401i	−0.884447	+	0.466641i	$0.845464\pi$
$8$	−4.00000	+	6.92820i	−0.176777	+	0.306186i
$9$		0			0
$10$	−13.6317	−	23.6108i	−0.431072	−	0.746639i
$11$	−5.21774	+	29.5913i	−0.143019	+	0.811100i	0.825918	+	0.563791i	$0.190658\pi$
$11$	−5.21774	+	29.5913i	−0.143019	+	0.811100i	−0.968937	+	0.247309i	$0.920454\pi$
$12$		0			0
$13$	9.46670	+	3.44560i	0.201969	+	0.0735106i	0.441024	−	0.897495i	$-0.354615\pi$
$13$	9.46670	+	3.44560i	0.201969	+	0.0735106i	−0.239055	+	0.971006i	$0.576838\pi$
$14$	26.2843	+	9.56669i	0.501769	+	0.182629i
$15$		0			0
$16$	2.77837	−	15.7569i	0.0434120	−	0.246202i
$17$	−45.9801	−	79.6399i	−0.655989	−	1.13621i	−0.981645	−	0.190718i	$-0.938918\pi$
$17$	−45.9801	−	79.6399i	−0.655989	−	1.13621i	0.325656	−	0.945488i	$-0.394415\pi$
$18$		0			0
$19$	−21.7919	+	37.7447i	−0.263127	+	0.455749i	−0.967071	−	0.254506i	$-0.918087\pi$
$19$	−21.7919	+	37.7447i	−0.263127	+	0.455749i	0.703944	+	0.710255i	$0.251420\pi$
$20$	41.7700	+	35.0492i	0.467002	+	0.391862i
$21$		0			0
$22$	−10.4355	−	59.1825i	−0.101130	−	0.573534i
$23$	−85.9596	+	72.1286i	−0.779296	+	0.653907i	−0.943071	−	0.332591i	$-0.892077\pi$
$23$	−85.9596	+	72.1286i	−0.779296	+	0.653907i	0.163775	+	0.986498i	$0.447633\pi$
$24$		0			0
$25$	−57.1553	+	20.8028i	−0.457242	+	0.166423i
$26$	−20.1485			−0.151979
$27$		0			0
$28$	−55.9423			−0.377575
$29$	−271.740	+	98.9052i	−1.74003	+	0.633318i	−0.999261	−	0.0384441i	$-0.987760\pi$
$29$	−271.740	+	98.9052i	−1.74003	+	0.633318i	−0.740767	+	0.671762i	$0.765538\pi$
$30$		0			0
$31$	−142.315	+	119.417i	−0.824535	+	0.691867i	−0.954029	−	0.299713i	$-0.903109\pi$
$31$	−142.315	+	119.417i	−0.824535	+	0.691867i	0.129495	+	0.991580i	$0.458665\pi$
$32$	5.55674	+	31.5138i	0.0306970	+	0.174091i
$33$		0			0
$34$	140.891	+	118.222i	0.710666	+	0.596320i
$35$	95.3236	−	165.105i	0.460361	−	0.797368i
$36$		0			0
$37$	−195.634	−	338.848i	−0.869245	−	1.50558i	−0.862770	−	0.505597i	$-0.831272\pi$
$37$	−195.634	−	338.848i	−0.869245	−	1.50558i	−0.00647463	−	0.999979i	$-0.502061\pi$
$38$	15.1365	−	85.8435i	0.0646176	−	0.366464i
$39$		0			0
$40$	−102.477	−	37.2985i	−0.405076	−	0.147435i
$41$	−345.291	−	125.676i	−1.31525	−	0.478714i	−0.413320	−	0.910586i	$-0.635631\pi$
$41$	−345.291	−	125.676i	−1.31525	−	0.478714i	−0.901935	+	0.431872i	$0.857853\pi$
$42$		0			0
$43$	−32.5874	+	184.812i	−0.115570	+	0.655433i	0.870896	+	0.491468i	$0.163539\pi$
$43$	−32.5874	+	184.812i	−0.115570	+	0.655433i	−0.986466	+	0.163965i	$0.947572\pi$
$44$	60.0955	+	104.088i	0.205903	+	0.356635i
$45$		0			0
$46$	112.212	−	194.357i	0.359669	−	0.622966i
$47$	257.618	+	216.167i	0.799520	+	0.670877i	0.948082	−	0.318026i	$-0.103020\pi$
$47$	257.618	+	216.167i	0.799520	+	0.670877i	−0.148562	+	0.988903i	$0.547465\pi$
$48$		0			0
$49$	−25.5964	−	145.164i	−0.0746251	−	0.423220i
$50$	93.1868	−	78.1930i	0.263572	−	0.221163i
$51$		0			0
$52$	37.8668	−	13.7824i	0.100984	−	0.0367553i
$53$	366.522			0.949917			0.474959	−	0.880008i	$-0.342463\pi$
$53$	366.522			0.949917			0.474959	+	0.880008i	$0.342463\pi$
$54$		0			0
$55$	−409.602			−1.00420
$56$	105.137	−	38.2668i	0.250885	−	0.0913145i
$57$		0			0
$58$	443.048	−	371.762i	1.00302	−	0.841633i
$59$	65.6208	+	372.154i	0.144798	+	0.821193i	0.967529	+	0.252761i	$0.0813386\pi$
$59$	65.6208	+	372.154i	0.144798	+	0.821193i	−0.822730	+	0.568432i	$0.807550\pi$
$60$		0			0
$61$	675.933	+	567.175i	1.41876	+	1.19048i	0.952000	+	0.306098i	$0.0990235\pi$
$61$	675.933	+	567.175i	1.41876	+	1.19048i	0.466761	+	0.884384i	$0.345421\pi$
$62$	185.779	−	321.779i	0.380548	−	0.659129i
$63$		0			0
$64$	−32.0000	−	55.4256i	−0.0625000	−	0.108253i
$65$	−23.8470	+	135.243i	−0.0455054	+	0.258074i
$66$		0			0
$67$	897.489	+	326.659i	1.63650	+	0.595638i	0.986423	−	0.164227i	$-0.0525130\pi$
$67$	897.489	+	326.659i	1.63650	+	0.595638i	0.650080	+	0.759866i	$0.274735\pi$
$68$	−345.657	−	125.809i	−0.616428	−	0.224361i
$69$		0			0
$70$	−66.2111	+	375.502i	−0.113053	+	0.641158i
$71$	−341.031	−	590.683i	−0.570041	−	0.987341i	−0.996561	−	0.0828623i	$-0.973594\pi$
$71$	−341.031	−	590.683i	−0.570041	−	0.987341i	0.426520	−	0.904478i	$-0.359740\pi$
$72$		0			0
$73$	−410.162	+	710.421i	−0.657614	+	1.13902i	0.323618	+	0.946188i	$0.395101\pi$
$73$	−410.162	+	710.421i	−0.657614	+	1.13902i	−0.981232	+	0.192833i	$0.938233\pi$
$74$	599.458	+	503.005i	0.941696	+	0.790177i
$75$		0			0
$76$	30.2730	+	171.687i	0.0456915	+	0.259129i
$77$	321.919	−	270.122i	0.476442	−	0.399782i
$78$		0			0
$79$	−132.267	+	48.1413i	−0.188370	+	0.0685611i	−0.434483	−	0.900680i	$-0.643069\pi$
$79$	−132.267	+	48.1413i	−0.188370	+	0.0685611i	0.246113	+	0.969241i	$0.420847\pi$
$80$	218.107			0.304814
$81$		0			0
$82$	734.903			0.989712
$83$	241.086	−	87.7482i	0.318827	−	0.116044i	−0.177649	−	0.984094i	$-0.556849\pi$
$83$	241.086	−	87.7482i	0.318827	−	0.116044i	0.496476	+	0.868050i	$0.334627\pi$
$84$		0			0
$85$	960.294	−	805.782i	1.22539	−	1.02823i
$86$	−65.1748	−	369.625i	−0.0817207	−	0.463461i
$87$		0			0
$88$	−184.143	−	154.515i	−0.223065	−	0.187174i
$89$	470.400	−	814.757i	0.560251	−	0.970383i	−0.437223	−	0.899353i	$-0.644038\pi$
$89$	470.400	−	814.757i	0.560251	−	0.970383i	0.997474	−	0.0710302i	$-0.0226287\pi$
$90$		0			0
$91$	−70.4471	−	122.018i	−0.0811524	−	0.140560i
$92$	−77.9418	+	442.030i	−0.0883260	+	0.500922i
$93$		0			0
$94$	−632.030	−	230.040i	−0.693499	−	0.252413i
$95$	−558.292	−	203.202i	−0.602943	−	0.219453i
$96$		0			0
$97$	40.0173	−	226.949i	0.0418880	−	0.237559i	−0.956674	−	0.291160i	$-0.905959\pi$
$97$	40.0173	−	226.949i	0.0418880	−	0.237559i	0.998562	+	0.0536011i	$0.0170699\pi$
$98$	147.404	+	255.311i	0.151939	+	0.263166i
$99$		0			0
$100$	−121.647	+	210.698i	−0.121647	+	0.210698i
$101$	−417.730	−	350.517i	−0.411541	−	0.345324i	0.413393	−	0.910553i	$-0.364344\pi$
$101$	−417.730	−	350.517i	−0.411541	−	0.345324i	−0.824934	+	0.565228i	$0.808788\pi$
$102$		0			0
$103$	−25.6065	−	145.222i	−0.0244959	−	0.138923i	0.970107	−	0.242677i	$-0.0780256\pi$
$103$	−25.6065	−	145.222i	−0.0244959	−	0.138923i	−0.994603	+	0.103754i	$0.966915\pi$
$104$	−61.7386	+	51.8049i	−0.0582113	+	0.0488450i
$105$		0			0
$106$	−688.835	+	250.716i	−0.631185	+	0.229733i
$107$	46.8265			0.0423074			0.0211537	−	0.999776i	$-0.493266\pi$
$107$	46.8265			0.0423074			0.0211537	+	0.999776i	$0.493266\pi$
$108$		0			0
$109$	−99.9132			−0.0877977			−0.0438988	−	0.999036i	$-0.513978\pi$
$109$	−99.9132			−0.0877977			−0.0438988	+	0.999036i	$0.513978\pi$
$110$	769.800	−	280.184i	0.667251	−	0.242859i
$111$		0			0
$112$	−171.417	+	143.836i	−0.144620	+	0.121350i
$113$	118.789	+	673.684i	0.0988911	+	0.560840i	0.993485	+	0.113960i	$0.0363536\pi$
$113$	118.789	+	673.684i	0.0988911	+	0.560840i	−0.894594	+	0.446879i	$0.852535\pi$
$114$		0			0
$115$	−1171.78	−	983.236i	−0.950162	−	0.797281i
$116$	−578.359	+	1001.75i	−0.462925	+	0.801809i
$117$		0			0
$118$	−377.895	−	654.534i	−0.294814	−	0.510633i
$119$	−223.332	+	1266.58i	−0.172040	+	0.975689i
$120$		0			0
$121$	402.313	+	146.430i	0.302264	+	0.110015i
$122$	−1658.31	−	603.576i	−1.23063	−	0.447911i
$123$		0			0
$124$	−129.041	+	731.828i	−0.0934534	+	0.530001i
$125$	437.418	+	757.631i	0.312991	+	0.542116i
$126$		0			0
$127$	−977.697	+	1693.42i	−0.683123	+	1.18320i	0.290900	+	0.956753i	$0.406045\pi$
$127$	−977.697	+	1693.42i	−0.683123	+	1.18320i	−0.974023	+	0.226450i	$0.927288\pi$
$128$	98.0537	+	82.2768i	0.0677094	+	0.0568149i
$129$		0			0
$130$	−47.6940	−	270.486i	−0.0321772	−	0.182486i
$131$	−942.503	+	790.854i	−0.628602	+	0.527460i	−0.900494	−	0.434868i	$-0.856795\pi$
$131$	−942.503	+	790.854i	−0.628602	+	0.527460i	0.271892	+	0.962328i	$0.412351\pi$
$132$		0			0
$133$	572.785	−	208.477i	0.373434	−	0.135919i
$134$	−1910.17			−1.23145
$135$		0			0
$136$	735.682			0.463854
$137$	1495.42	−	544.290i	0.932575	−	0.339429i	0.169345	−	0.985557i	$-0.445835\pi$
$137$	1495.42	−	544.290i	0.932575	−	0.339429i	0.763230	+	0.646127i	$0.223613\pi$
$138$		0			0
$139$	−588.065	+	493.446i	−0.358842	+	0.301104i	−0.804329	−	0.594184i	$-0.797475\pi$
$139$	−588.065	+	493.446i	−0.358842	+	0.301104i	0.445487	+	0.895288i	$0.353031\pi$
$140$	−132.422	−	751.003i	−0.0799408	−	0.453367i
$141$		0			0
$142$	1044.98	+	876.842i	0.617555	+	0.518190i
$143$	−151.354	+	262.154i	−0.0885097	+	0.153303i
$144$		0			0
$145$	−1971.00	−	3413.88i	−1.12885	−	1.95522i
$146$	284.895	−	1615.72i	0.161494	−	0.915877i
$147$		0			0
$148$	−1470.69	−	535.286i	−0.816823	−	0.297299i
$149$	97.1961	+	35.3765i	0.0534404	+	0.0194507i	0.368602	−	0.929587i	$-0.379837\pi$
$149$	97.1961	+	35.3765i	0.0534404	+	0.0194507i	−0.315162	+	0.949038i	$0.602059\pi$
$150$		0			0
$151$	124.452	−	705.804i	0.0670714	−	0.380381i	−0.932732	−	0.360570i	$-0.882582\pi$
$151$	124.452	−	705.804i	0.0670714	−	0.380381i	0.999804	−	0.0198113i	$-0.00630655\pi$
$152$	−174.335	−	301.958i	−0.0930294	−	0.161132i
$153$		0			0
$154$	−420.235	+	727.868i	−0.219893	+	0.380866i
$155$	−1940.00	−	1627.85i	−1.00532	−	0.843563i
$156$		0			0
$157$	−87.1115	−	494.034i	−0.0442819	−	0.251135i	0.954629	−	0.297798i	$-0.0962523\pi$
$157$	−87.1115	−	494.034i	−0.0442819	−	0.251135i	−0.998911	+	0.0466633i	$0.985141\pi$
$158$	215.650	−	180.952i	0.108584	−	0.0911126i
$159$		0			0
$160$	−409.908	+	149.194i	−0.202538	+	0.0737177i
$161$	1569.35			0.768213
$162$		0			0
$163$	3228.18			1.55123			0.775616	−	0.631205i	$-0.217439\pi$
$163$	3228.18			1.55123			0.775616	+	0.631205i	$0.217439\pi$
$164$	−1381.17	+	502.703i	−0.657627	+	0.239357i
$165$		0			0
$166$	−393.071	+	329.825i	−0.183784	+	0.154213i
$167$	494.267	+	2803.13i	0.229027	+	1.29888i	0.854835	+	0.518900i	$0.173658\pi$
$167$	494.267	+	2803.13i	0.229027	+	1.29888i	−0.625807	+	0.779978i	$0.715230\pi$
$168$		0			0
$169$	−1605.25	−	1346.97i	−0.730657	−	0.613094i
$170$	−1253.57	+	2171.25i	−0.565557	+	0.979574i
$171$		0			0
$172$	375.327	+	650.085i	0.166386	+	0.288189i
$173$	−275.917	+	1564.80i	−0.121258	+	0.687686i	0.862203	+	0.506563i	$0.169084\pi$
$173$	−275.917	+	1564.80i	−0.121258	+	0.687686i	−0.983460	+	0.181123i	$0.942027\pi$
$174$		0			0
$175$	799.349	+	290.939i	0.345286	+	0.125674i
$176$	451.770	+	164.431i	0.193486	+	0.0704230i
$177$		0			0
$178$	−326.737	+	1853.02i	−0.137584	+	0.780278i
$179$	−107.489	−	186.177i	−0.0448833	−	0.0777402i	0.842711	−	0.538366i	$-0.180958\pi$
$179$	−107.489	−	186.177i	−0.0448833	−	0.0777402i	−0.887594	+	0.460626i	$0.847625\pi$
$180$		0			0
$181$	−228.843	+	396.368i	−0.0939768	+	0.162773i	−0.909181	−	0.416401i	$-0.863291\pi$
$181$	−228.843	+	396.368i	−0.0939768	+	0.162773i	0.815204	+	0.579173i	$0.196625\pi$
$182$	215.863	+	181.130i	0.0879165	+	0.0737707i
$183$		0			0
$184$	−155.884	−	884.060i	−0.0624559	−	0.354205i
$185$	4085.82	−	3428.41i	1.62376	−	1.36249i
$186$		0			0
$187$	2596.56	−	945.069i	1.01540	−	0.369574i
$188$	1345.18			0.521849
$189$		0			0
$190$	1188.24			0.453707
$191$	−3170.71	+	1154.04i	−1.20117	+	0.437192i	−0.863634	−	0.504119i	$-0.831817\pi$
$191$	−3170.71	+	1154.04i	−1.20117	+	0.437192i	−0.337541	+	0.941311i	$0.609595\pi$
$192$		0			0
$193$	−2029.66	+	1703.09i	−0.756987	+	0.635187i	−0.937341	−	0.348414i	$-0.886720\pi$
$193$	−2029.66	+	1703.09i	−0.756987	+	0.635187i	0.180354	+	0.983602i	$0.442276\pi$
$194$	80.0346	+	453.899i	0.0296193	+	0.167980i
$195$		0			0
$196$	−451.671	−	378.997i	−0.164603	−	0.138119i
$197$	439.042	−	760.444i	0.158784	−	0.275022i	−0.775646	−	0.631168i	$-0.782576\pi$
$197$	439.042	−	760.444i	0.158784	−	0.275022i	0.934430	+	0.356146i	$0.115909\pi$
$198$		0			0
$199$	1019.47	+	1765.78i	0.363159	+	0.629010i	0.988479	−	0.151359i	$-0.0483648\pi$
$199$	1019.47	+	1765.78i	0.363159	+	0.629010i	−0.625320	+	0.780369i	$0.715031\pi$
$200$	84.4950	−	479.195i	0.0298735	−	0.169421i
$201$		0			0
$202$	1024.84	+	373.012i	0.356969	+	0.129926i
$203$	3800.44	+	1383.25i	1.31398	+	0.478250i
$204$		0			0
$205$	869.802	−	4932.89i	0.296339	−	1.68062i
$206$	147.462	+	255.411i	0.0498745	+	0.0863852i
$207$		0			0
$208$	80.5941	−	139.593i	0.0268663	−	0.0465338i
$209$	−1003.21	−	841.793i	−0.332026	−	0.278603i
$210$		0			0
$211$	825.849	+	4683.62i	0.269449	+	1.52812i	0.756059	+	0.654503i	$0.227122\pi$
$211$	825.849	+	4683.62i	0.269449	+	1.52812i	−0.486610	+	0.873619i	$0.661767\pi$
$212$	1123.09	−	942.382i	0.363839	−	0.305298i
$213$		0			0
$214$	−88.0050	+	32.0312i	−0.0281117	+	0.0102318i
$215$	−2558.17			−0.811469
$216$		0			0
$217$	2598.23			0.812808
$218$	187.775	−	68.3446i	0.0583383	−	0.0212334i
$219$		0			0
$220$	−1255.09	+	1053.15i	−0.384629	+	0.322742i
$221$	−160.873	−	912.356i	−0.0489660	−	0.277700i
$222$		0			0
$223$	363.298	+	304.843i	0.109095	+	0.0915417i	0.695704	−	0.718329i	$-0.255093\pi$
$223$	363.298	+	304.843i	0.109095	+	0.0915417i	−0.586608	+	0.809871i	$0.699537\pi$
$224$	223.769	−	387.580i	0.0667465	−	0.115608i
$225$		0			0
$226$	−684.077	−	1184.86i	−0.201346	−	0.348741i
$227$	598.561	−	3394.61i	0.175013	−	0.992547i	−0.763116	−	0.646261i	$-0.776332\pi$
$227$	598.561	−	3394.61i	0.175013	−	0.992547i	0.938129	−	0.346286i	$-0.112557\pi$
$228$		0			0
$229$	−1846.48	−	672.063i	−0.532833	−	0.193935i	0.0615699	−	0.998103i	$-0.480389\pi$
$229$	−1846.48	−	672.063i	−0.532833	−	0.193935i	−0.594403	+	0.804167i	$0.702612\pi$
$230$	2874.79	+	1046.34i	0.824166	+	0.299972i
$231$		0			0
$232$	401.724	−	2278.29i	0.113683	−	0.644728i
$233$	−506.552	−	877.373i	−0.142426	−	0.246689i	0.785984	−	0.618247i	$-0.212157\pi$
$233$	−506.552	−	877.373i	−0.142426	−	0.246689i	−0.928410	+	0.371558i	$0.878824\pi$
$234$		0			0
$235$	−2292.15	+	3970.11i	−0.636268	+	1.10205i
$236$	1157.94	+	971.626i	0.319387	+	0.267998i
$237$		0			0
$238$	−446.663	−	2533.15i	−0.121651	−	0.689916i
$239$	−1786.08	+	1498.70i	−0.483396	+	0.405617i	−0.851653	−	0.524107i	$-0.824399\pi$
$239$	−1786.08	+	1498.70i	−0.483396	+	0.405617i	0.368257	+	0.929724i	$0.379955\pi$
$240$		0			0
$241$	107.717	−	39.2058i	0.0287912	−	0.0104791i	−0.327584	−	0.944822i	$-0.606235\pi$
$241$	107.717	−	39.2058i	0.0287912	−	0.0104791i	0.356376	+	0.934343i	$0.384012\pi$
$242$	−856.265			−0.227450
$243$		0			0
$244$	3529.47			0.926030
$245$	1888.19	−	687.243i	0.492374	−	0.179210i
$246$		0			0
$247$	−336.351	+	282.232i	−0.0866458	+	0.0727044i
$248$	−258.082	−	1463.66i	−0.0660815	−	0.374767i
$249$		0			0
$250$	−1340.33	−	1124.67i	−0.339079	−	0.284521i
$251$	1104.76	−	1913.51i	0.277817	−	0.481193i	−0.693025	−	0.720914i	$-0.743722\pi$
$251$	1104.76	−	1913.51i	0.277817	−	0.481193i	0.970842	+	0.239721i	$0.0770558\pi$
$252$		0			0
$253$	−1685.86	−	2920.00i	−0.418930	−	0.725608i
$254$	679.101	−	3851.37i	0.167758	−	0.951404i
$255$		0			0
$256$	−240.561	−	87.5572i	−0.0587308	−	0.0213763i
$257$	3470.53	+	1263.17i	0.842356	+	0.306592i	0.726920	−	0.686723i	$-0.240951\pi$
$257$	3470.53	+	1263.17i	0.842356	+	0.306592i	0.115436	+	0.993315i	$0.463173\pi$
$258$		0			0
$259$	−950.222	+	5388.98i	−0.227969	+	1.29288i
$260$	274.659	+	475.723i	0.0655139	+	0.113473i
$261$		0			0
$262$	1230.35	−	2131.03i	0.290119	−	0.502502i
$263$	−4332.96	−	3635.78i	−1.01590	−	0.852441i	−0.0267931	−	0.999641i	$-0.508530\pi$
$263$	−4332.96	−	3635.78i	−1.01590	−	0.852441i	−0.989107	+	0.147200i	$0.952974\pi$
$264$		0			0
$265$	867.601	+	4920.41i	0.201118	+	1.14060i
$266$	−933.878	+	783.616i	−0.215262	+	0.180626i
$267$		0			0
$268$	3589.95	−	1306.64i	0.818251	−	0.297819i
$269$	−3513.37			−0.796334			−0.398167	−	0.917313i	$-0.630354\pi$
$269$	−3513.37			−0.796334			−0.398167	+	0.917313i	$0.630354\pi$
$270$		0			0
$271$	7422.16			1.66371			0.831853	−	0.554996i	$-0.187280\pi$
$271$	7422.16			1.66371			0.831853	+	0.554996i	$0.187280\pi$
$272$	−1382.63	+	503.236i	−0.308214	+	0.112181i
$273$		0			0
$274$	−2438.16	+	2045.86i	−0.537572	+	0.451077i
$275$	−317.360	−	1799.84i	−0.0695911	−	0.394671i
$276$		0			0
$277$	3349.18	+	2810.30i	0.726473	+	0.609583i	0.929168	−	0.369659i	$-0.120525\pi$
$277$	3349.18	+	2810.30i	0.726473	+	0.609583i	−0.202695	+	0.979242i	$0.564970\pi$
$278$	767.665	−	1329.63i	0.165617	−	0.286857i
$279$		0			0
$280$	762.589	+	1320.84i	0.162762	+	0.281912i
$281$	825.061	−	4679.15i	0.175157	−	0.993363i	−0.762806	−	0.646627i	$-0.776179\pi$
$281$	825.061	−	4679.15i	0.175157	−	0.993363i	0.937963	−	0.346736i	$-0.112710\pi$
$282$		0			0
$283$	−3705.05	−	1348.53i	−0.778242	−	0.283257i	−0.0778025	−	0.996969i	$-0.524790\pi$
$283$	−3705.05	−	1348.53i	−0.778242	−	0.283257i	−0.700439	+	0.713712i	$0.747013\pi$
$284$	−2563.71	−	933.116i	−0.535664	−	0.194966i
$285$		0			0
$286$	105.130	−	596.220i	0.0217358	−	0.123270i
$287$	2569.51	+	4450.52i	0.528478	+	0.915351i
$288$		0			0
$289$	−1771.84	+	3068.92i	−0.360643	+	0.624652i
$290$	6039.51	+	5067.75i	1.22294	+	1.02617i
$291$		0			0
$292$	569.791	+	3231.44i	0.114193	+	0.647623i
$293$	−2812.23	+	2359.74i	−0.560725	+	0.470504i	−0.878553	−	0.477644i	$-0.841491\pi$
$293$	−2812.23	+	2359.74i	−0.560725	+	0.470504i	0.317828	+	0.948148i	$0.397046\pi$
$294$		0			0
$295$	−4840.69	+	1761.87i	−0.955377	+	0.347729i
$296$	3130.15			0.614649
$297$		0			0
$298$	−206.868			−0.0402132
$299$	−1062.28	+	386.638i	−0.205462	+	0.0747822i
$300$		0			0
$301$	2010.54	−	1687.05i	0.385003	−	0.323056i
$302$	248.905	+	1411.61i	0.0474267	+	0.268970i
$303$		0			0
$304$	534.195	+	448.243i	0.100783	+	0.0845674i
$305$	−6014.09	+	10416.7i	−1.12907	+	1.95560i
$306$		0			0
$307$	−3084.69	−	5342.84i	−0.573461	−	0.993263i	−0.996207	−	0.0870152i	$-0.972267\pi$
$307$	−3084.69	−	5342.84i	−0.573461	−	0.993263i	0.422746	−	0.906248i	$-0.361066\pi$
$308$	291.892	−	1655.40i	0.0540003	−	0.306251i
$309$		0			0
$310$	4759.52	+	1732.32i	0.872009	+	0.317385i
$311$	65.7962	+	23.9479i	0.0119967	+	0.00436643i	0.348012	−	0.937490i	$-0.386857\pi$
$311$	65.7962	+	23.9479i	0.0119967	+	0.00436643i	−0.336015	+	0.941857i	$0.609079\pi$
$312$		0			0
$313$	1258.00	−	7134.48i	0.227177	−	1.28839i	−0.631302	−	0.775537i	$-0.717479\pi$
$313$	1258.00	−	7134.48i	0.227177	−	1.28839i	0.858479	−	0.512849i	$-0.171410\pi$
$314$	501.655	+	868.892i	0.0901594	+	0.156161i
$315$		0			0
$316$	−281.512	+	487.593i	−0.0501148	+	0.0868013i
$317$	3258.40	+	2734.12i	0.577319	+	0.484428i	0.884065	−	0.467363i	$-0.154796\pi$
$317$	3258.40	+	2734.12i	0.577319	+	0.484428i	−0.306747	+	0.951791i	$0.599240\pi$
$318$		0			0
$319$	−1508.86	−	8557.18i	−0.264828	−	1.50191i
$320$	668.319	−	560.787i	0.116751	−	0.0979654i
$321$		0			0
$322$	−2949.42	+	1073.50i	−0.510449	+	0.185788i
$323$	4007.98			0.690434
$324$		0			0
$325$	−612.750			−0.104582
$326$	−6067.00	+	2208.21i	−1.03074	+	0.375157i
$327$		0			0
$328$	2251.87	−	1889.55i	0.379082	−	0.318087i
$329$	−816.719	−	4631.84i	−0.136861	−	0.776175i
$330$		0			0
$331$	−5161.18	−	4330.75i	−0.857052	−	0.719152i	0.104279	−	0.994548i	$-0.466747\pi$
$331$	−5161.18	−	4330.75i	−0.857052	−	0.719152i	−0.961331	+	0.275396i	$0.911191\pi$
$332$	513.117	−	888.745i	0.0848222	−	0.146916i
$333$		0			0
$334$	−2846.37	−	4930.06i	−0.466307	−	0.807667i
$335$	−2260.81	+	12821.7i	−0.368720	+	2.09111i
$336$		0			0
$337$	−6180.42	−	2249.49i	−0.999018	−	0.363613i	−0.209812	−	0.977742i	$-0.567285\pi$
$337$	−6180.42	−	2249.49i	−0.999018	−	0.363613i	−0.789206	+	0.614129i	$0.789508\pi$
$338$	3938.27	+	1433.41i	0.633768	+	0.230673i
$339$		0			0
$340$	870.724	−	4938.12i	0.138887	−	0.787668i
$341$	−2791.13	−	4834.37i	−0.443249	−	0.767730i
$342$		0			0
$343$	−3429.29	+	5939.70i	−0.539837	+	0.935026i
$344$	−1150.07	−	965.021i	−0.180254	−	0.151251i
$345$		0			0
$346$	−551.834	−	3129.60i	−0.0857421	−	0.486267i
$347$	−5441.48	+	4565.94i	−0.841827	+	0.706377i	−0.957974	−	0.286856i	$-0.907390\pi$
$347$	−5441.48	+	4565.94i	−0.841827	+	0.706377i	0.116147	+	0.993232i	$0.462946\pi$
$348$		0			0
$349$	−3203.97	+	1166.15i	−0.491417	+	0.178861i	−0.575829	−	0.817570i	$-0.695321\pi$
$349$	−3203.97	+	1166.15i	−0.491417	+	0.178861i	0.0844129	+	0.996431i	$0.473099\pi$
$350$	−1701.30			−0.259824
$351$		0			0
$352$	−961.528			−0.145596
$353$	8496.09	−	3092.32i	1.28102	−	0.466254i	0.390253	−	0.920708i	$-0.372388\pi$
$353$	8496.09	−	3092.32i	1.28102	−	0.466254i	0.890770	+	0.454454i	$0.150165\pi$
$354$		0			0
$355$	7122.43	−	5976.43i	1.06484	−	0.893509i
$356$	−653.473	−	3706.03i	−0.0972866	−	0.551740i
$357$		0			0
$358$	329.366	+	276.371i	0.0486244	+	0.0408007i
$359$	689.648	−	1194.51i	0.101388	−	0.175609i	−0.810869	−	0.585228i	$-0.801005\pi$
$359$	689.648	−	1194.51i	0.101388	−	0.175609i	0.912257	+	0.409619i	$0.134338\pi$
$360$		0			0
$361$	2479.72	+	4295.01i	0.361528	+	0.626186i
$362$	158.953	−	901.467i	0.0230784	−	0.130884i
$363$		0			0
$364$	−529.589	−	192.755i	−0.0762583	−	0.0277557i
$365$	−10508.0	−	3824.61i	−1.50689	−	0.548464i
$366$		0			0
$367$	−1729.63	+	9809.20i	−0.246010	+	1.39519i	0.572124	+	0.820167i	$0.306120\pi$
$367$	−1729.63	+	9809.20i	−0.246010	+	1.39519i	−0.818134	+	0.575027i	$0.804991\pi$
$368$	897.698	+	1554.86i	0.127162	+	0.220252i
$369$		0			0
$370$	−5333.65	+	9238.16i	−0.749415	+	1.29802i
$371$	−3926.75	−	3294.94i	−0.549507	−	0.461091i
$372$		0			0
$373$	304.924	+	1729.31i	0.0423281	+	0.240055i	0.998630	−	0.0523264i	$-0.0166636\pi$
$373$	304.924	+	1729.31i	0.0423281	+	0.240055i	−0.956302	+	0.292381i	$0.905552\pi$
$374$	−4233.46	+	3552.30i	−0.585313	+	0.491136i
$375$		0			0
$376$	−2528.12	+	920.161i	−0.346750	+	0.126207i
$377$	−2913.27			−0.397986
$378$		0			0
$379$	−10726.5			−1.45378			−0.726889	−	0.686755i	$-0.759034\pi$
$379$	−10726.5			−1.45378			−0.726889	+	0.686755i	$0.759034\pi$
$380$	−2233.17	+	812.807i	−0.301472	+	0.109727i
$381$		0			0
$382$	5169.57	−	4337.78i	0.692404	−	0.580996i
$383$	−1327.45	−	7528.34i	−0.177100	−	1.00439i	−0.935691	−	0.352819i	$-0.885223\pi$
$383$	−1327.45	−	7528.34i	−0.177100	−	1.00439i	0.758591	−	0.651567i	$-0.225888\pi$
$384$		0			0
$385$	4388.30	+	3682.22i	0.580905	+	0.487437i
$386$	2649.54	−	4589.14i	0.349373	−	0.605132i
$387$		0			0
$388$	−460.901	−	798.304i	−0.0603059	−	0.104453i
$389$	−2030.47	+	11515.3i	−0.264650	+	1.50090i	0.505381	+	0.862896i	$0.331352\pi$
$389$	−2030.47	+	11515.3i	−0.264650	+	1.50090i	−0.770031	+	0.638007i	$0.779759\pi$
$390$		0			0
$391$	9696.75	+	3529.33i	1.25418	+	0.456485i
$392$	1108.11	+	403.320i	0.142776	+	0.0519662i
$393$		0			0
$394$	−304.956	+	1729.49i	−0.0389935	+	0.221143i
$395$	−959.371	−	1661.68i	−0.122206	−	0.211666i
$396$		0			0
$397$	6856.19	−	11875.3i	0.866756	−	1.50127i	0.00146341	−	0.999999i	$-0.499534\pi$
$397$	6856.19	−	11875.3i	0.866756	−	1.50127i	0.865293	−	0.501267i	$-0.167132\pi$
$398$	−3123.85	−	2621.22i	−0.393429	−	0.330126i
$399$		0			0
$400$	168.990	+	958.389i	0.0211237	+	0.119799i
$401$	1824.82	−	1531.21i	0.227250	−	0.190686i	−0.522052	−	0.852914i	$-0.674833\pi$
$401$	1824.82	−	1531.21i	0.227250	−	0.190686i	0.749302	+	0.662228i	$0.230389\pi$
$402$		0			0
$403$	−1758.72	+	640.121i	−0.217390	+	0.0791233i
$404$	−2181.23			−0.268615
$405$		0			0
$406$	−8088.68			−0.988755
$407$	11047.7	−	4021.04i	1.34549	−	0.489719i
$408$		0			0
$409$	−7880.45	+	6612.48i	−0.952722	+	0.799428i	−0.979754	−	0.200206i	$-0.935839\pi$
$409$	−7880.45	+	6612.48i	−0.952722	+	0.799428i	0.0270322	+	0.999635i	$0.491394\pi$
$410$	1739.60	+	9865.78i	0.209544	+	1.18838i
$411$		0			0
$412$	−451.849	−	379.146i	−0.0540316	−	0.0453379i
$413$	2642.54	−	4577.02i	0.314845	−	0.545327i
$414$		0			0
$415$	1748.67	+	3028.78i	0.206840	+	0.358257i
$416$	−55.9800	+	317.479i	−0.00659771	+	0.0374175i
$417$		0			0
$418$	2461.24	+	895.817i	0.287998	+	0.104823i
$419$	−1986.26	−	722.938i	−0.231587	−	0.0842907i	0.223620	−	0.974676i	$-0.428213\pi$
$419$	−1986.26	−	722.938i	−0.231587	−	0.0842907i	−0.455207	+	0.890386i	$0.650435\pi$
$420$		0			0
$421$	−2008.91	+	11393.1i	−0.232561	+	1.31892i	0.615127	+	0.788428i	$0.289105\pi$
$421$	−2008.91	+	11393.1i	−0.232561	+	1.31892i	−0.847689	+	0.530494i	$0.822007\pi$
$422$	−4755.87	−	8237.41i	−0.548607	−	0.950216i
$423$		0			0
$424$	−1466.09	+	2539.34i	−0.167923	+	0.290852i
$425$	4284.74	+	3595.32i	0.489036	+	0.410350i
$426$		0			0
$427$	−2142.89	−	12152.9i	−0.242861	−	1.37734i
$428$	143.485	−	120.398i	0.0162047	−	0.0135973i
$429$		0			0
$430$	4807.79	−	1749.89i	0.539191	−	0.196250i
$431$	8465.46			0.946095			0.473047	−	0.881037i	$-0.343154\pi$
$431$	8465.46			0.946095			0.473047	+	0.881037i	$0.343154\pi$
$432$		0			0
$433$	3944.98			0.437838			0.218919	−	0.975743i	$-0.429747\pi$
$433$	3944.98			0.437838			0.218919	+	0.975743i	$0.429747\pi$
$434$	−4883.08	+	1777.29i	−0.540081	+	0.196573i
$435$		0			0
$436$	−306.152	+	256.892i	−0.0336285	+	0.0282176i
$437$	−849.251	−	4816.34i	−0.0929638	−	0.527224i
$438$		0			0
$439$	171.954	+	144.287i	0.0186946	+	0.0156866i	0.652087	−	0.758144i	$-0.273894\pi$
$439$	171.954	+	144.287i	0.0186946	+	0.0156866i	−0.633392	+	0.773831i	$0.718338\pi$
$440$	1638.41	−	2837.81i	0.177518	−	0.307471i
$441$		0			0
$442$	926.431	+	1604.63i	0.0996964	+	0.172679i
$443$	−365.239	+	2071.38i	−0.0391717	+	0.222154i	−0.998109	−	0.0614633i	$-0.980423\pi$
$443$	−365.239	+	2071.38i	−0.0391717	+	0.222154i	0.958938	+	0.283617i	$0.0915344\pi$
$444$		0			0
$445$	12051.3	+	4386.31i	1.28379	+	0.467261i
$446$	−891.302	−	324.407i	−0.0946286	−	0.0344420i
$447$		0			0
$448$	−155.428	+	881.478i	−0.0163913	+	0.0929597i
$449$	1643.98	+	2847.45i	0.172793	+	0.299287i	0.939395	−	0.342836i	$-0.111387\pi$
$449$	1643.98	+	2847.45i	0.172793	+	0.299287i	−0.766602	+	0.642122i	$0.778054\pi$
$450$		0			0
$451$	5520.54	−	9561.86i	0.576391	−	0.998338i
$452$	2096.13	+	1758.86i	0.218128	+	0.183031i
$453$		0			0
$454$	1197.12	+	6789.22i	0.123753	+	0.701837i
$455$	1471.29	−	1234.56i	0.151593	−	0.127202i
$456$		0			0
$457$	4214.92	−	1534.11i	0.431435	−	0.157030i	−0.117169	−	0.993112i	$-0.537382\pi$
$457$	4214.92	−	1534.11i	0.431435	−	0.157030i	0.548604	+	0.836083i	$0.315160\pi$
$458$	3929.96			0.400950
$459$		0			0
$460$	−6118.58			−0.620174
$461$	16717.2	−	6084.56i	1.68893	−	0.614721i	0.694441	−	0.719550i	$-0.255652\pi$
$461$	16717.2	−	6084.56i	1.68893	−	0.614721i	0.994490	+	0.104829i	$0.0334295\pi$
$462$		0			0
$463$	6606.76	−	5543.73i	0.663158	−	0.556456i	−0.247873	−	0.968792i	$-0.579732\pi$
$463$	6606.76	−	5543.73i	0.663158	−	0.556456i	0.911032	+	0.412337i	$0.135287\pi$
$464$	803.448	+	4556.58i	0.0803860	+	0.455892i
$465$		0			0
$466$	1552.16	+	1302.42i	0.154297	+	0.129471i
$467$	5697.43	−	9868.24i	0.564552	−	0.977832i	−0.432540	−	0.901615i	$-0.642382\pi$
$467$	5697.43	−	9868.24i	0.564552	−	0.977832i	0.997091	−	0.0762171i	$-0.0242842\pi$
$468$		0			0
$469$	−6678.72	−	11567.9i	−0.657558	−	1.13892i
$470$	1592.11	−	9029.29i	0.156252	−	0.886149i
$471$		0			0
$472$	−2840.84	−	1033.98i	−0.277035	−	0.100832i
$473$	−5298.80	−	1928.60i	−0.515093	−	0.187478i
$474$		0			0
$475$	460.327	−	2610.65i	0.0444658	−	0.252178i
$476$	2572.23	+	4455.24i	0.247685	+	0.429003i
$477$		0			0
$478$	2331.56	−	4038.37i	0.223102	−	0.386424i
$479$	3357.15	+	2816.98i	0.320234	+	0.268708i	0.788707	−	0.614770i	$-0.210751\pi$
$479$	3357.15	+	2816.98i	0.320234	+	0.268708i	−0.468473	+	0.883478i	$0.655196\pi$
$480$		0			0
$481$	−684.475	−	3881.85i	−0.0648844	−	0.367978i
$482$	−175.624	+	147.366i	−0.0165963	+	0.0139260i
$483$		0			0
$484$	1609.25	−	585.720i	0.151132	−	0.0550075i
$485$	3141.43			0.294114
$486$		0			0
$487$	10670.3			0.992846			0.496423	−	0.868081i	$-0.334647\pi$
$487$	10670.3			0.992846			0.496423	+	0.868081i	$0.334647\pi$
$488$	−6633.24	+	2414.30i	−0.615313	+	0.223956i
$489$		0			0
$490$	−3078.53	+	2583.19i	−0.283824	+	0.238156i
$491$	1187.10	+	6732.38i	0.109110	+	0.618794i	0.989499	+	0.144541i	$0.0461707\pi$
$491$	1187.10	+	6732.38i	0.109110	+	0.618794i	−0.880389	+	0.474253i	$0.842718\pi$
$492$		0			0
$493$	20371.4	+	17093.6i	1.86102	+	1.56158i
$494$	439.075	−	760.500i	0.0399897	−	0.0692642i
$495$		0			0
$496$	1486.24	+	2574.23i	0.134544	+	0.233037i
$497$	−1656.43	+	9394.11i	−0.149500	+	0.847854i
$498$		0			0
$499$	−16228.8	−	5906.82i	−1.45592	−	0.529911i	−0.511680	−	0.859176i	$-0.670977\pi$
$499$	−16228.8	−	5906.82i	−1.45592	−	0.529911i	−0.944237	+	0.329265i	$0.893199\pi$
$500$	3288.31	+	1196.85i	0.294115	+	0.107049i
$501$		0			0
$502$	−767.360	+	4351.92i	−0.0682250	+	0.386923i
$503$	456.976	+	791.505i	0.0405080	+	0.0701619i	0.885569	−	0.464509i	$-0.153769\pi$
$503$	456.976	+	791.505i	0.0405080	+	0.0701619i	−0.845061	+	0.534671i	$0.820436\pi$
$504$		0			0
$505$	3716.74	−	6437.58i	0.327510	−	0.567264i
$506$	5165.78	+	4334.61i	0.453848	+	0.380824i
$507$		0			0
$508$	1358.20	+	7702.75i	0.118623	+	0.672745i
$509$	−9349.80	+	7845.41i	−0.814190	+	0.683186i	−0.951604	−	0.307327i	$-0.900565\pi$
$509$	−9349.80	+	7845.41i	−0.814190	+	0.683186i	0.137414	+	0.990514i	$0.456121\pi$
$510$		0			0
$511$	10780.8	−	3923.89i	0.933297	−	0.339692i
$512$	512.000			0.0441942
$513$		0			0
$514$	−7386.51			−0.633862
$515$	1888.93	−	687.514i	0.161624	−	0.0588262i
$516$		0			0
$517$	−7740.84	+	6495.33i	−0.658495	+	0.552543i
$518$	−1900.44	−	10778.0i	−0.161198	−	0.914201i
$519$		0			0
$520$	−841.603	−	706.189i	−0.0709745	−	0.0595547i
$521$	−3427.08	+	5935.88i	−0.288183	+	0.499147i	−0.973376	−	0.229214i	$-0.926384\pi$
$521$	−3427.08	+	5935.88i	−0.288183	+	0.499147i	0.685193	+	0.728361i	$0.259718\pi$
$522$		0			0
$523$	7318.65	+	12676.3i	0.611897	+	1.05984i	0.990920	+	0.134450i	$0.0429268\pi$
$523$	7318.65	+	12676.3i	0.611897	+	1.05984i	−0.379023	+	0.925387i	$0.623740\pi$
$524$	−854.592	+	4846.63i	−0.0712463	+	0.404058i
$525$		0			0
$526$	10630.3	+	3869.12i	0.881186	+	0.320726i
$527$	16054.0	+	5843.18i	1.32699	+	0.482985i
$528$		0			0
$529$	73.7286	−	418.136i	0.00605972	−	0.0343664i
$530$	−4996.31	−	8653.87i	−0.409483	−	0.709245i
$531$		0			0
$532$	1219.09	−	2111.53i	0.0993502	−	0.172080i
$533$	−2835.74	−	2379.47i	−0.230450	−	0.193370i
$534$		0			0
$535$	110.844	+	628.627i	0.00895739	+	0.0507999i
$536$	−5853.12	+	4911.35i	−0.471672	+	0.395780i
$537$		0			0
$538$	6602.98	−	2403.29i	0.529135	−	0.192589i
$539$	4429.15			0.353946
$540$		0			0
$541$	−15158.8			−1.20468			−0.602338	−	0.798241i	$-0.705764\pi$
$541$	−15158.8			−1.20468			−0.602338	+	0.798241i	$0.705764\pi$
$542$	−13949.1	+	5077.06i	−1.10547	+	0.402359i
$543$		0			0
$544$	2254.26	−	1891.55i	0.177666	−	0.149080i
$545$	−236.507	−	1341.30i	−0.0185887	−	0.105422i
$546$		0			0
$547$	−13101.5	−	10993.5i	−1.02409	−	0.859317i	−0.0339575	−	0.999423i	$-0.510811\pi$
$547$	−13101.5	−	10993.5i	−1.02409	−	0.859317i	−0.990136	+	0.140106i	$0.955256\pi$
$548$	3182.79	−	5512.76i	0.248106	−	0.429733i
$549$		0			0
$550$	1827.61	+	3165.51i	0.141690	+	0.245414i
$551$	2188.58	−	12412.1i	0.169214	−	0.959659i
$552$		0			0
$553$	1849.83	+	673.284i	0.142248	+	0.0517739i
$554$	−8216.77	−	2990.66i	−0.630139	−	0.229352i
$555$		0			0
$556$	−533.214	+	3024.01i	−0.0406715	+	0.230659i
$557$	−114.961	−	199.118i	−0.00874515	−	0.0151470i	0.861620	−	0.507554i	$-0.169450\pi$
$557$	−114.961	−	199.118i	−0.00874515	−	0.0151470i	−0.870365	+	0.492407i	$0.836117\pi$
$558$		0			0
$559$	−945.284	+	1637.28i	−0.0715228	+	0.123881i
$560$	−2336.71	−	1960.73i	−0.176328	−	0.147957i
$561$		0			0
$562$	1650.12	+	9358.31i	0.123854	+	0.702413i
$563$	18764.0	−	15744.9i	1.40463	−	1.17863i	0.445637	−	0.895214i	$-0.352977\pi$
$563$	18764.0	−	15744.9i	1.40463	−	1.17863i	0.958997	−	0.283415i	$-0.0914673\pi$
$564$		0			0
$565$	−8762.76	+	3189.38i	−0.652481	+	0.237484i
$566$	7885.67			0.585617
$567$		0			0
$568$	5456.50			0.403080
$569$	−15826.9	+	5760.53i	−1.16608	+	0.424418i	−0.851266	−	0.524735i	$-0.824164\pi$
$569$	−15826.9	+	5760.53i	−1.16608	+	0.424418i	−0.314814	+	0.949153i	$0.601942\pi$
$570$		0			0
$571$	8220.49	−	6897.81i	0.602482	−	0.505542i	−0.289761	−	0.957099i	$-0.593576\pi$
$571$	8220.49	−	6897.81i	0.602482	−	0.505542i	0.892242	+	0.451557i	$0.149131\pi$
$572$	210.259	+	1192.44i	0.0153696	+	0.0871651i
$573$		0			0
$574$	−7873.43	−	6606.59i	−0.572527	−	0.480407i
$575$	3412.56	−	5910.73i	0.247502	−	0.428686i
$576$		0			0
$577$	107.375	+	185.980i	0.00774714	+	0.0134184i	0.869873	−	0.493276i	$-0.164201\pi$
$577$	107.375	+	185.980i	0.00774714	+	0.0134184i	−0.862126	+	0.506694i	$0.830867\pi$
$578$	1230.71	−	6979.69i	0.0885652	−	0.502278i
$579$		0			0
$580$	−14817.1	−	5392.98i	−1.06077	−	0.386089i
$581$	−3371.73	−	1227.21i	−0.240762	−	0.0876303i
$582$		0			0
$583$	−1912.41	+	10845.8i	−0.135856	+	0.770478i
$584$	−3281.29	−	5683.37i	−0.232502	−	0.402705i
$585$		0			0
$586$	3671.11	−	6358.55i	0.258792	−	0.448241i
$587$	−11462.3	−	9618.02i	−0.805963	−	0.676283i	0.143678	−	0.989625i	$-0.454107\pi$
$587$	−11462.3	−	9618.02i	−0.805963	−	0.676283i	−0.949640	+	0.313342i	$0.898552\pi$
$588$		0			0
$589$	−1406.03	−	7973.97i	−0.0983605	−	0.557830i
$590$	7892.34	−	6622.46i	0.550716	−	0.462106i
$591$		0			0
$592$	−5882.75	+	2141.15i	−0.408411	+	0.148650i
$593$	−25508.9			−1.76649			−0.883243	−	0.468915i	$-0.844645\pi$
$593$	−25508.9			−1.76649			−0.883243	+	0.468915i	$0.844645\pi$
$594$		0			0
$595$	−17532.0			−1.20797
$596$	388.784	−	141.506i	0.0267202	−	0.00972535i
$597$		0			0
$598$	1731.96	−	1453.28i	0.118436	−	0.0993800i
$599$	3902.95	+	22134.7i	0.266227	+	1.50985i	0.765517	+	0.643415i	$0.222483\pi$
$599$	3902.95	+	22134.7i	0.266227	+	1.50985i	−0.499290	+	0.866435i	$0.666406\pi$
$600$		0			0
$601$	−7214.07	−	6053.32i	−0.489631	−	0.410849i	0.364263	−	0.931296i	$-0.381321\pi$
$601$	−7214.07	−	6053.32i	−0.489631	−	0.410849i	−0.853894	+	0.520447i	$0.825765\pi$
$602$	−2624.58	+	4545.90i	−0.177691	+	0.307769i
$603$		0			0
$604$	−1433.38	−	2482.69i	−0.0965622	−	0.167251i
$605$	−1013.44	+	5747.51i	−0.0681029	+	0.386231i
$606$		0			0
$607$	5578.70	+	2030.48i	0.373036	+	0.135774i	0.521733	−	0.853109i	$-0.325286\pi$
$607$	5578.70	+	2030.48i	0.373036	+	0.135774i	−0.148697	+	0.988883i	$0.547508\pi$
$608$	−1310.57	−	477.010i	−0.0874191	−	0.0318179i
$609$		0			0
$610$	4177.35	−	23690.9i	0.277272	−	1.57249i
$611$	1693.97	+	2934.04i	0.112161	+	0.194269i
$612$		0			0
$613$	−3249.14	+	5627.68i	−0.214081	+	0.370799i	−0.952988	−	0.303008i	$-0.902009\pi$
$613$	−3249.14	+	5627.68i	−0.214081	+	0.370799i	0.738907	+	0.673808i	$0.235342\pi$
$614$	9452.03	+	7931.20i	0.621259	+	0.521298i
$615$		0			0
$616$	583.784	+	3310.81i	0.0381840	+	0.216552i
$617$	14232.3	−	11942.3i	0.928642	−	0.779223i	−0.0469312	−	0.998898i	$-0.514944\pi$
$617$	14232.3	−	11942.3i	0.928642	−	0.779223i	0.975573	+	0.219675i	$0.0704997\pi$
$618$		0			0
$619$	−9848.48	+	3584.55i	−0.639489	+	0.232755i	−0.641356	−	0.767243i	$-0.721628\pi$
$619$	−9848.48	+	3584.55i	−0.639489	+	0.232755i	0.00186717	+	0.999998i	$0.499406\pi$
$620$	−10130.0			−0.656176
$621$		0			0
$622$	−140.038			−0.00902734
$623$	−12364.1	+	4500.18i	−0.795118	+	0.289399i
$624$		0			0
$625$	−14959.7	+	12552.6i	−0.957418	+	0.803369i
$626$	2516.00	+	14269.0i	0.160639	+	0.911026i
$627$		0			0
$628$	−1537.16	−	1289.83i	−0.0976742	−	0.0819584i
$629$	−17990.6	+	31160.6i	−1.14043	+	1.97528i
$630$		0			0
$631$	9533.76	+	16513.0i	0.601479	+	1.04179i	0.992597	+	0.121452i	$0.0387549\pi$
$631$	9533.76	+	16513.0i	0.601479	+	1.04179i	−0.391119	+	0.920340i	$0.627912\pi$
$632$	195.536	−	1108.94i	0.0123070	−	0.0697963i
$633$		0			0
$634$	−7994.04	−	2909.59i	−0.500763	−	0.182263i
$635$	−25047.8	−	9116.67i	−1.56534	−	0.569739i
$636$		0			0
$637$	257.865	−	1462.42i	0.0160392	−	0.0909628i
$638$	8689.19	+	15050.1i	0.539198	+	0.933918i
$639$		0			0
$640$	−872.429	+	1511.09i	−0.0538840	+	0.0933299i
$641$	−1544.55	−	1296.03i	−0.0951733	−	0.0798599i	0.593960	−	0.804495i	$-0.297564\pi$
$641$	−1544.55	−	1296.03i	−0.0951733	−	0.0798599i	−0.689133	+	0.724635i	$0.742008\pi$
$642$		0			0
$643$	166.947	+	946.806i	0.0102391	+	0.0580690i	0.989499	−	0.144538i	$-0.0461697\pi$
$643$	166.947	+	946.806i	0.0102391	+	0.0580690i	−0.979260	+	0.202607i	$0.935059\pi$
$644$	4808.77	−	4035.04i	0.294243	−	0.246899i
$645$		0			0
$646$	−7532.54	+	2741.62i	−0.458768	+	0.166978i
$647$	−26668.0			−1.62044			−0.810222	−	0.586123i	$-0.800654\pi$
$647$	−26668.0			−1.62044			−0.810222	+	0.586123i	$0.800654\pi$
$648$		0			0
$649$	−11354.9			−0.686778
$650$	1151.59	−	419.146i	0.0694911	−	0.0252927i
$651$		0			0
$652$	9891.73	−	8300.15i	0.594157	−	0.498557i
$653$	−1144.56	−	6491.14i	−0.0685915	−	0.389001i	−0.999705	−	0.0242730i	$-0.992273\pi$
$653$	−1144.56	−	6491.14i	−0.0685915	−	0.389001i	0.931114	−	0.364729i	$-0.118838\pi$
$654$		0			0
$655$	−12847.9	−	10780.7i	−0.766427	−	0.643109i
$656$	−2939.61	+	5091.56i	−0.174958	+	0.303036i
$657$		0			0
$658$	4703.30	+	8146.35i	0.278653	+	0.482641i
$659$	1182.81	−	6708.06i	0.0699177	−	0.396523i	−0.929685	−	0.368354i	$-0.879921\pi$
$659$	1182.81	−	6708.06i	0.0699177	−	0.396523i	0.999603	−	0.0281687i	$-0.00896757\pi$
$660$		0			0
$661$	−17402.5	−	6334.00i	−1.02402	−	0.372714i	−0.225221	−	0.974308i	$-0.572310\pi$
$661$	−17402.5	−	6334.00i	−1.02402	−	0.372714i	−0.798802	+	0.601594i	$0.794533\pi$
$662$	12662.3	+	4608.69i	0.743403	+	0.270576i
$663$		0			0
$664$	−356.407	+	2021.29i	−0.0208303	+	0.118134i
$665$	4154.57	+	7195.93i	0.242267	+	0.419618i
$666$		0			0
$667$	16224.7	−	28102.1i	0.941865	−	1.63136i
$668$	8721.79	+	7318.45i	0.505174	+	0.423891i
$669$		0			0
$670$	−4521.61	−	25643.4i	−0.260724	−	1.47864i
$671$	−20310.3	+	17042.4i	−1.16851	+	0.980496i
$672$		0			0
$673$	18481.6	−	6726.75i	1.05856	−	0.385285i	0.246675	−	0.969098i	$-0.420662\pi$
$673$	18481.6	−	6726.75i	1.05856	−	0.385285i	0.811888	+	0.583813i	$0.198440\pi$
$674$	13154.1			0.751748
$675$		0			0
$676$	−8382.04			−0.476902
$677$	3049.50	−	1109.93i	0.173120	−	0.0630104i	−0.254006	−	0.967203i	$-0.581748\pi$
$677$	3049.50	−	1109.93i	0.173120	−	0.0630104i	0.427126	+	0.904192i	$0.359526\pi$
$678$		0			0
$679$	−2468.95	+	2071.69i	−0.139543	+	0.117090i
$680$	1741.45	+	9876.24i	0.0982080	+	0.556965i
$681$		0			0
$682$	8552.51	+	7176.41i	0.480194	+	0.402931i
$683$	9465.62	−	16394.9i	0.530295	−	0.918499i	−0.469080	−	0.883156i	$-0.655414\pi$
$683$	9465.62	−	16394.9i	0.530295	−	0.918499i	0.999375	−	0.0353428i	$-0.0112523\pi$
$684$		0			0
$685$	10846.7	+	18787.1i	0.605011	+	1.04791i
$686$	2381.96	−	13508.8i	0.132571	−	0.751847i
$687$		0			0
$688$	2821.53	+	1026.95i	0.156352	+	0.0569074i
$689$	3469.75	+	1262.89i	0.191853	+	0.0698289i
$690$		0			0
$691$	6138.35	−	34812.3i	0.337936	−	1.91653i	−0.0581275	−	0.998309i	$-0.518513\pi$
$691$	6138.35	−	34812.3i	0.337936	−	1.91653i	0.396064	−	0.918223i	$-0.370376\pi$
$692$	3177.88	+	5504.25i	0.174574	+	0.302370i
$693$		0			0
$694$	7103.35	−	12303.4i	0.388529	−	0.672952i
$695$	−8016.34	−	6726.50i	−0.437521	−	0.367124i
$696$		0			0
$697$	5867.73	+	33277.5i	0.318875	+	1.80843i
$698$	5223.79	−	4383.28i	0.283272	−	0.237693i
$699$		0			0
$700$	3197.40	−	1163.76i	0.172643	−	0.0628370i
$701$	28373.2			1.52873			0.764366	−	0.644783i	$-0.223052\pi$
$701$	28373.2			1.52873			0.764366	+	0.644783i	$0.223052\pi$
$702$		0			0
$703$	17053.0			0.914887
$704$	1807.08	−	657.724i	0.0967428	−	0.0352115i
$705$		0			0
$706$	−13852.1	+	11623.3i	−0.738431	+	0.619617i
$707$	1324.32	+	7510.58i	0.0704471	+	0.399525i
$708$		0			0
$709$	−264.073	−	221.583i	−0.0139880	−	0.0117373i	0.635767	−	0.771881i	$-0.280684\pi$
$709$	−264.073	−	221.583i	−0.0139880	−	0.0117373i	−0.649755	+	0.760144i	$0.725128\pi$
$710$	−9297.67	+	16104.0i	−0.491458	+	0.851231i
$711$		0			0
$712$	3763.20	+	6518.06i	0.198079	+	0.343082i
$713$	3619.99	−	20530.0i	0.190140	−	1.07834i
$714$		0			0
$715$	−3877.58	−	1411.32i	−0.202816	−	0.0738189i
$716$	−808.054	−	294.108i	−0.0421765	−	0.0153510i
$717$		0			0
$718$	−479.024	+	2716.68i	−0.0248984	+	0.141206i
$719$	3527.69	+	6110.14i	0.182977	+	0.316926i	0.942893	−	0.333095i	$-0.108093\pi$
$719$	3527.69	+	6110.14i	0.182977	+	0.316926i	−0.759916	+	0.650022i	$0.774760\pi$
$720$		0			0
$721$	−1031.17	+	1786.04i	−0.0532631	+	0.0922545i
$722$	−7598.31	−	6375.74i	−0.391662	−	0.328643i
$723$		0			0
$724$	317.906	+	1802.93i	0.0163189	+	0.0925491i
$725$	13473.9	−	11305.9i	0.690216	−	0.579160i
$726$		0			0
$727$	−19307.0	+	7027.19i	−0.984950	+	0.358492i	−0.783763	−	0.621060i	$-0.786702\pi$
$727$	−19307.0	+	7027.19i	−0.984950	+	0.358492i	−0.201187	+	0.979553i	$0.564480\pi$
$728$	1127.15			0.0573834
$729$		0			0
$730$	22364.8			1.13392
$731$	16216.8	−	5902.43i	0.820520	−	0.298645i
$732$		0			0
$733$	−8309.67	+	6972.64i	−0.418724	+	0.351351i	−0.827677	−	0.561204i	$-0.810338\pi$
$733$	−8309.67	+	6972.64i	−0.418724	+	0.351351i	0.408954	+	0.912555i	$0.365894\pi$
$734$	−3459.25	−	19618.4i	−0.173956	−	0.986551i
$735$		0			0
$736$	−2750.71	−	2308.12i	−0.137761	−	0.115596i
$737$	−14349.1	+	24853.4i	−0.717173	+	1.24218i
$738$		0			0
$739$	18216.6	+	31552.1i	0.906778	+	1.57059i	0.818512	+	0.574490i	$0.194799\pi$
$739$	18216.6	+	31552.1i	0.906778	+	1.57059i	0.0882666	+	0.996097i	$0.471867\pi$
$740$	3704.72	−	21010.5i	0.184038	−	1.04373i
$741$		0			0
$742$	9633.76	+	3506.40i	0.476639	+	0.173482i
$743$	4552.00	+	1656.79i	0.224760	+	0.0818060i	0.451946	−	0.892046i	$-0.350730\pi$
$743$	4552.00	+	1656.79i	0.224760	+	0.0818060i	−0.227185	+	0.973852i	$0.572952\pi$
$744$		0			0
$745$	−244.841	+	1388.56i	−0.0120406	+	0.0682858i
$746$	−1755.99	−	3041.46i	−0.0861814	−	0.149271i
$747$		0			0
$748$	5526.40	−	9572.00i	0.270140	−	0.467897i
$749$	−501.679	−	420.959i	−0.0244739	−	0.0205360i
$750$		0			0
$751$	2063.74	+	11704.1i	0.100276	+	0.568691i	0.993003	+	0.118093i	$0.0376781\pi$
$751$	2063.74	+	11704.1i	0.100276	+	0.568691i	−0.892727	+	0.450598i	$0.851211\pi$
$752$	4121.89	−	3458.67i	0.199880	−	0.167719i
$753$		0			0
$754$	5475.15	−	1992.79i	0.264447	−	0.0962509i
$755$	9769.74			0.470937
$756$		0			0
$757$	−12324.2			−0.591720			−0.295860	−	0.955231i	$-0.595606\pi$
$757$	−12324.2			−0.591720			−0.295860	+	0.955231i	$0.595606\pi$
$758$	20159.2	−	7337.34i	0.965981	−	0.351588i
$759$		0			0
$760$	3640.99	−	3055.16i	0.173780	−	0.145819i
$761$	−3601.53	−	20425.3i	−0.171558	−	0.972951i	−0.942043	−	0.335493i	$-0.891097\pi$
$761$	−3601.53	−	20425.3i	−0.171558	−	0.972951i	0.770485	−	0.637458i	$-0.220014\pi$
$762$		0			0
$763$	1070.43	+	898.195i	0.0507891	+	0.0426171i
$764$	−6748.40	+	11688.6i	−0.319566	+	0.553504i
$765$		0			0
$766$	7644.47	+	13240.6i	0.360582	+	0.624547i
$767$	−661.081	+	3749.18i	−0.0311216	+	0.176499i
$768$		0			0
$769$	15352.3	+	5587.78i	0.719920	+	0.262029i	0.675892	−	0.737001i	$-0.263759\pi$
$769$	15352.3	+	5587.78i	0.719920	+	0.262029i	0.0440282	+	0.999030i	$0.485981\pi$
$770$	−10766.1	−	3918.54i	−0.503874	−	0.183395i
$771$		0			0
$772$	−1840.35	+	10437.1i	−0.0857975	+	0.486582i
$773$	−4283.52	−	7419.27i	−0.199311	−	0.345217i	0.748994	−	0.662577i	$-0.230537\pi$
$773$	−4283.52	−	7419.27i	−0.199311	−	0.345217i	−0.948305	+	0.317360i	$0.897204\pi$
$774$		0			0
$775$	5649.87	−	9785.85i	0.261870	−	0.453572i
$776$	1412.28	+	1185.05i	0.0653324	+	0.0548204i
$777$		0			0
$778$	−4060.93	−	23030.7i	−0.187136	−	1.06130i
$779$	12268.2	−	10294.2i	0.564252	−	0.473464i
$780$		0			0
$781$	19258.5	−	7009.51i	0.882359	−	0.321152i
$782$	−20638.1			−0.943757
$783$		0			0
$784$	−2358.46			−0.107437
$785$	6426.01	−	2338.88i	0.292171	−	0.106341i
$786$		0			0
$787$	−12808.3	+	10747.4i	−0.580133	+	0.486790i	−0.884991	−	0.465608i	$-0.845836\pi$
$787$	−12808.3	+	10747.4i	−0.580133	+	0.486790i	0.304858	+	0.952398i	$0.401391\pi$
$788$	−609.911	−	3458.98i	−0.0275726	−	0.156372i
$789$		0			0
$790$	2939.68	+	2466.69i	0.132391	+	0.111090i
$791$	4783.60	−	8285.44i	0.215026	−	0.372435i
$792$		0			0
$793$	4444.60	+	7698.28i	0.199032	+	0.344734i
$794$	−4762.26	+	27008.1i	−0.212854	+	1.20716i
$795$		0			0
$796$	7663.94	+	2789.45i	0.341258	+	0.124208i
$797$	12736.2	+	4635.61i	0.566049	+	0.206025i	0.609163	−	0.793045i	$-0.291506\pi$
$797$	12736.2	+	4635.61i	0.566049	+	0.206025i	−0.0431140	+	0.999070i	$0.513728\pi$
$798$		0			0
$799$	5370.22	−	30456.0i	0.237778	−	1.34851i
$800$	−973.174	−	1685.59i	−0.0430086	−	0.0744931i
$801$		0			0
$802$	−2382.14	+	4125.99i	−0.104883	+	0.181663i
$803$	−18882.1	−	15844.0i	−0.829808	−	0.696292i
$804$		0			0
$805$	3714.85	+	21067.9i	0.162647	+	0.922419i
$806$	2867.44	−	2406.07i	0.125312	−	0.105149i
$807$		0			0
$808$	4099.37	−	1492.05i	0.178484	−	0.0649630i
$809$	−5028.45			−0.218530			−0.109265	−	0.994013i	$-0.534850\pi$
$809$	−5028.45			−0.218530			−0.109265	+	0.994013i	$0.534850\pi$
$810$		0			0
$811$	−8280.59			−0.358534			−0.179267	−	0.983800i	$-0.557373\pi$
$811$	−8280.59			−0.358534			−0.179267	+	0.983800i	$0.557373\pi$
$812$	15201.7	−	5532.98i	0.656991	−	0.239125i
$813$		0			0
$814$	−18012.4	+	15114.2i	−0.775593	+	0.650800i
$815$	7641.50	+	43337.1i	0.328430	+	1.86262i
$816$		0			0
$817$	−6265.55	−	5257.42i	−0.268303	−	0.225133i
$818$	10287.2	−	17817.9i	0.439711	−	0.761601i
$819$		0			0
$820$	−10018.0	−	17351.6i	−0.426638	−	0.738958i
$821$	−4485.93	+	25441.0i	−0.190695	+	1.08148i	0.727723	+	0.685871i	$0.240578\pi$
$821$	−4485.93	+	25441.0i	−0.190695	+	1.08148i	−0.918418	+	0.395612i	$0.870533\pi$
$822$		0			0
$823$	18089.9	+	6584.17i	0.766188	+	0.278870i	0.695401	−	0.718622i	$-0.255227\pi$
$823$	18089.9	+	6584.17i	0.766188	+	0.278870i	0.0707871	+	0.997491i	$0.477449\pi$
$824$	1108.55	+	403.479i	0.0468667	+	0.0170581i
$825$		0			0
$826$	−1835.49	+	10409.6i	−0.0773182	+	0.438494i
$827$	−8014.75	−	13882.0i	−0.337001	−	0.583704i	0.646866	−	0.762604i	$-0.276079\pi$
$827$	−8014.75	−	13882.0i	−0.337001	−	0.583704i	−0.983867	+	0.178900i	$0.942746\pi$
$828$		0			0
$829$	−558.740	+	967.767i	−0.0234087	+	0.0405451i	−0.877492	−	0.479590i	$-0.840785\pi$
$829$	−558.740	+	967.767i	−0.0234087	+	0.0405451i	0.854084	+	0.520136i	$0.174119\pi$
$830$	−5358.22	−	4496.08i	−0.224080	−	0.188026i
$831$		0			0
$832$	−111.960	−	634.957i	−0.00466529	−	0.0264581i
$833$	−10383.9	+	8713.17i	−0.431912	+	0.362417i
$834$		0			0
$835$	−36460.9	+	13270.7i	−1.51112	+	0.550001i
$836$	−5238.39			−0.216715
$837$		0			0
$838$	4227.46			0.174266
$839$	−18881.8	+	6872.40i	−0.776962	+	0.282791i	−0.699905	−	0.714236i	$-0.746774\pi$
$839$	−18881.8	+	6872.40i	−0.776962	+	0.282791i	−0.0770567	+	0.997027i	$0.524552\pi$
$840$		0			0
$841$	45377.2	−	38076.0i	1.86056	−	1.56119i
$842$	−4017.82	−	22786.2i	−0.164446	−	0.932618i
$843$		0			0
$844$	14572.8	+	12228.1i	0.594334	+	0.498705i
$845$	14282.7	−	24738.3i	0.581467	−	1.00713i
$846$		0			0
$847$	−2993.84	−	5185.48i	−0.121452	−	0.210360i
$848$	1018.33	−	5775.25i	0.0412378	−	0.233871i
$849$		0			0
$850$	−10512.0	−	3826.06i	−0.424188	−	0.154392i
$851$	41257.3	+	15016.4i	1.66191	+	0.604884i
$852$		0			0
$853$	−693.586	+	3933.52i	−0.0278405	+	0.157891i	−0.995559	−	0.0941437i	$-0.969989\pi$
$853$	−693.586	+	3933.52i	−0.0278405	+	0.157891i	0.967718	+	0.252035i	$0.0810998\pi$
$854$	12340.4	+	21374.2i	0.494474	+	0.856454i
$855$		0			0
$856$	−187.306	+	324.423i	−0.00747895	+	0.0129539i
$857$	6999.89	+	5873.60i	0.279010	+	0.234117i	0.771544	−	0.636176i	$-0.219485\pi$
$857$	6999.89	+	5873.60i	0.279010	+	0.234117i	−0.492534	+	0.870293i	$0.663929\pi$
$858$		0			0
$859$	−7009.80	−	39754.5i	−0.278430	−	1.57905i	−0.727852	−	0.685735i	$-0.759481\pi$
$859$	−7009.80	−	39754.5i	−0.278430	−	1.57905i	0.449422	−	0.893320i	$-0.351630\pi$
$860$	−7838.69	+	6577.44i	−0.310811	+	0.260801i
$861$		0			0
$862$	−15909.9	+	5790.72i	−0.628645	+	0.228808i
$863$	15362.0			0.605942			0.302971	−	0.953000i	$-0.402021\pi$
$863$	15362.0			0.605942			0.302971	+	0.953000i	$0.402021\pi$
$864$		0			0
$865$	−21660.0			−0.851401
$866$	−7414.14	+	2698.53i	−0.290927	+	0.105889i
$867$		0			0
$868$	7961.44	−	6680.44i	0.311324	−	0.261232i
$869$	−734.427	−	4165.14i	−0.0286694	−	0.162592i
$870$		0			0
$871$	7370.72	+	6184.77i	0.286736	+	0.240600i
$872$	399.653	−	692.219i	0.0155206	−	0.0268824i
$873$		0			0
$874$	4890.64	+	8470.84i	0.189277	+	0.327838i
$875$	2124.60	−	12049.2i	0.0820853	−	0.465529i
$876$		0			0
$877$	−13031.3	−	4742.99i	−0.501749	−	0.182622i	0.0787313	−	0.996896i	$-0.474913\pi$
$877$	−13031.3	−	4742.99i	−0.501749	−	0.182622i	−0.580481	+	0.814274i	$0.697135\pi$
$878$	−421.866	−	153.547i	−0.0162156	−	0.00590199i
$879$		0			0
$880$	−1138.03	+	6454.07i	−0.0435942	+	0.247235i
$881$	−13715.9	−	23756.7i	−0.524519	−	0.908493i	−0.999592	−	0.0285473i	$-0.990912\pi$
$881$	−13715.9	−	23756.7i	−0.524519	−	0.908493i	0.475074	−	0.879946i	$-0.342421\pi$
$882$		0			0
$883$	−16573.0	+	28705.2i	−0.631625	+	1.09401i	0.355594	+	0.934640i	$0.384279\pi$
$883$	−16573.0	+	28705.2i	−0.631625	+	1.09401i	−0.987219	+	0.159367i	$0.949055\pi$
$884$	−2838.75	−	2381.99i	−0.108006	−	0.0906279i
$885$		0			0
$886$	−730.479	−	4142.75i	−0.0276985	−	0.157086i
$887$	1184.80	−	994.161i	0.0448495	−	0.0376332i	−0.620087	−	0.784533i	$-0.712903\pi$
$887$	1184.80	−	994.161i	0.0448495	−	0.0376332i	0.664937	+	0.746900i	$0.268458\pi$
$888$		0			0
$889$	25698.1	−	9353.33i	0.969500	−	0.352869i
$890$	−25649.4			−0.966035
$891$		0			0
$892$	1897.01			0.0712068
$893$	−13773.2	+	5013.02i	−0.516127	+	0.187855i
$894$		0			0
$895$	2244.91	−	1883.70i	0.0838425	−	0.0703522i
$896$	−310.857	−	1762.96i	−0.0115904	−	0.0657324i
$897$		0			0
$898$	−5037.44	−	4226.92i	−0.187196	−	0.157076i
$899$	26861.8	−	46526.0i	0.996541	−	1.72606i
$900$		0			0
$901$	−16852.7	−	29189.7i	−0.623135	−	1.07930i
$902$	−3834.53	+	21746.7i	−0.141548	+	0.802756i
$903$		0			0
$904$	−5142.57	−	1871.74i	−0.189203	−	0.0688643i
$905$	−5862.79	−	2133.88i	−0.215343	−	0.0783786i
$906$		0			0
$907$	−1304.18	+	7396.39i	−0.0477450	+	0.270775i	−0.999330	−	0.0366118i	$-0.988343\pi$
$907$	−1304.18	+	7396.39i	−0.0477450	+	0.270775i	0.951585	+	0.307387i	$0.0994546\pi$
$908$	−6893.96	−	11940.7i	−0.251965	−	0.436416i
$909$		0			0
$910$	−1920.63	+	3326.63i	−0.0699651	+	0.121183i
$911$	−5556.53	−	4662.49i	−0.202081	−	0.169566i	0.536131	−	0.844135i	$-0.319885\pi$
$911$	−5556.53	−	4662.49i	−0.202081	−	0.169566i	−0.738212	+	0.674568i	$0.764330\pi$
$912$		0			0
$913$	1338.66	+	7591.89i	0.0485247	+	0.275197i
$914$	−6872.08	+	5766.36i	−0.248696	+	0.208681i
$915$		0			0
$916$	−7385.91	+	2688.25i	−0.266416	+	0.0969677i
$917$	17207.2			0.619662
$918$		0			0
$919$	−19172.9			−0.688202			−0.344101	−	0.938933i	$-0.611816\pi$
$919$	−19172.9			−0.688202			−0.344101	+	0.938933i	$0.611816\pi$
$920$	11499.2	−	4185.35i	0.412083	−	0.149986i
$921$		0			0
$922$	−27256.0	+	22870.5i	−0.973565	+	0.816918i
$923$	−1193.18	−	6766.88i	−0.0425505	−	0.241316i
$924$		0			0
$925$	18230.5	+	15297.2i	0.648017	+	0.543751i
$926$	−8624.52	+	14938.1i	−0.306068	+	0.530126i
$927$		0			0
$928$	−4626.87	−	8013.97i	−0.163669	−	0.283482i
$929$	−6367.84	+	36113.8i	−0.224889	+	1.27541i	0.638007	+	0.770030i	$0.279759\pi$
$929$	−6367.84	+	36113.8i	−0.224889	+	1.27541i	−0.862897	+	0.505380i	$0.831352\pi$
$930$		0			0
$931$	6036.99	+	2197.28i	0.212518	+	0.0773502i
$932$	−3808.02	−	1386.01i	−0.133837	−	0.0487126i
$933$		0			0
$934$	−3957.39	+	22443.5i	−0.138640	+	0.786267i
$935$	18833.5	+	32620.7i	0.658741	+	1.14097i
$936$		0			0
$937$	19987.7	−	34619.7i	0.696873	−	1.20702i	−0.272672	−	0.962107i	$-0.587907\pi$
$937$	19987.7	−	34619.7i	0.696873	−	1.20702i	0.969545	−	0.244913i	$-0.0787593\pi$
$938$	20464.8	+	17172.0i	0.712366	+	0.597746i
$939$		0			0
$940$	3184.22	+	18058.6i	0.110487	+	0.626602i
$941$	−10544.1	+	8847.51i	−0.365278	+	0.306504i	−0.806890	−	0.590702i	$-0.798851\pi$
$941$	−10544.1	+	8847.51i	−0.365278	+	0.306504i	0.441612	+	0.897206i	$0.354407\pi$
$942$		0			0
$943$	38745.9	−	14102.4i	1.33801	−	0.486995i
$944$	6046.33			0.208465
$945$		0			0
$946$	11277.7			0.387601
$947$	5520.57	−	2009.32i	0.189434	−	0.0689485i	−0.245561	−	0.969381i	$-0.578972\pi$
$947$	5520.57	−	2009.32i	0.189434	−	0.0689485i	0.434996	+	0.900433i	$0.356750\pi$
$948$		0			0
$949$	−6330.71	+	5312.09i	−0.216547	+	0.181705i
$950$	920.654	+	5221.29i	0.0314421	+	0.178317i
$951$		0			0
$952$	−7881.78	−	6613.60i	−0.268330	−	0.225155i
$953$	−13856.6	+	24000.4i	−0.470997	+	0.815791i	−0.999450	−	0.0331716i	$-0.989439\pi$
$953$	−13856.6	+	24000.4i	−0.470997	+	0.815791i	0.528452	+	0.848963i	$0.322773\pi$
$954$		0			0
$955$	−22998.0	−	39833.8i	−0.779266	−	1.34973i
$956$	−1619.48	+	9184.54i	−0.0547885	+	0.310721i
$957$		0			0
$958$	−8236.30	−	2997.77i	−0.277769	−	0.101100i
$959$	−20914.4	−	7612.21i	−0.704234	−	0.256320i
$960$		0			0
$961$	820.136	−	4651.22i	0.0275297	−	0.156128i
$962$	3941.74	+	6827.29i	0.132107	+	0.228816i
$963$		0			0
$964$	229.260	−	397.091i	0.00765973	−	0.0132670i
$965$	−27667.8	−	23216.0i	−0.922961	−	0.774457i
$966$		0			0
$967$	3821.01	+	21670.0i	0.127069	+	0.720643i	0.980058	+	0.198713i	$0.0636763\pi$
$967$	3821.01	+	21670.0i	0.127069	+	0.720643i	−0.852989	+	0.521929i	$0.825213\pi$
$968$	−2623.75	+	2201.59i	−0.0871182	+	0.0731009i
$969$		0			0
$970$	−5903.96	+	2148.87i	−0.195428	+	0.0711298i
$971$	−11228.0			−0.371087			−0.185543	−	0.982636i	$-0.559405\pi$
$971$	−11228.0			−0.371087			−0.185543	+	0.982636i	$0.559405\pi$
$972$		0			0
$973$	10736.2			0.353739
$974$	−20053.5	+	7298.89i	−0.659709	+	0.240115i
$975$		0			0
$976$	10814.9	−	9074.81i	0.354690	−	0.297620i
$977$	−868.492	−	4925.46i	−0.0284396	−	0.161289i	0.967280	−	0.253710i	$-0.0816507\pi$
$977$	−868.492	−	4925.46i	−0.0284396	−	0.161289i	−0.995720	+	0.0924204i	$0.970540\pi$
$978$		0			0
$979$	21655.3	+	18170.9i	0.706952	+	0.593203i
$980$	4018.73	−	6960.64i	0.130993	−	0.226887i
$981$		0			0
$982$	−6836.24	−	11840.7i	−0.222152	−	0.384778i
$983$	−5935.82	+	33663.7i	−0.192597	+	1.09227i	0.723202	+	0.690637i	$0.242670\pi$
$983$	−5935.82	+	33663.7i	−0.192597	+	1.09227i	−0.915799	+	0.401637i	$0.868441\pi$
$984$		0			0
$985$	11247.9	+	4093.91i	0.363846	+	0.132429i
$986$	−49978.5	−	18190.7i	−1.61424	−	0.587535i
$987$		0			0
$988$	−304.978	+	1729.62i	−0.00982050	+	0.0556948i
$989$	−10529.1	−	18236.9i	−0.338528	−	0.586349i
$990$		0			0
$991$	−26384.4	+	45699.0i	−0.845738	+	1.46486i	0.0392403	+	0.999230i	$0.487506\pi$
$991$	−26384.4	+	45699.0i	−0.845738	+	1.46486i	−0.884979	+	0.465632i	$0.845827\pi$
$992$	−4554.09	−	3821.33i	−0.145759	−	0.122306i
$993$		0			0
$994$	−3312.87	−	18788.2i	−0.105712	−	0.599523i
$995$	−21291.7	+	17865.9i	−0.678385	+	0.569232i
$996$		0			0
$997$	−4395.56	+	1599.85i	−0.139628	+	0.0508203i	−0.410889	−	0.911686i	$-0.634782\pi$
$997$	−4395.56	+	1599.85i	−0.139628	+	0.0508203i	0.271261	+	0.962506i	$0.412559\pi$
$998$	34540.8			1.09556
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.4.e.b.19.4		30
3.2	odd	2		54.4.e.b.7.1	✓	30
27.2	odd	18		1458.4.a.i.1.4		15
27.4	even	9	inner	162.4.e.b.145.4		30
27.23	odd	18		54.4.e.b.31.1	yes	30
27.25	even	9		1458.4.a.j.1.12		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.4.e.b.7.1	✓	30	3.2	odd	2
54.4.e.b.31.1	yes	30	27.23	odd	18
162.4.e.b.19.4		30	1.1	even	1	trivial
162.4.e.b.145.4		30	27.4	even	9	inner
1458.4.a.i.1.4		15	27.2	odd	18
1458.4.a.j.1.12		15	27.25	even	9

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	162.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.87939 + 0.684040i) q^{2} +(3.06418 - 2.57115i) q^{4} +(2.36712 + 13.4246i) q^{5} +(-10.7136 - 8.98975i) q^{7} +(-4.00000 + 6.92820i) q^{8} +O(q^{10})\)	\(q+(-1.87939 + 0.684040i) q^{2} +(3.06418 - 2.57115i) q^{4} +(2.36712 + 13.4246i) q^{5} +(-10.7136 - 8.98975i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(-13.6317 - 23.6108i) q^{10} +(-5.21774 + 29.5913i) q^{11} +(9.46670 + 3.44560i) q^{13} +(26.2843 + 9.56669i) q^{14} +(2.77837 - 15.7569i) q^{16} +(-45.9801 - 79.6399i) q^{17} +(-21.7919 + 37.7447i) q^{19} +(41.7700 + 35.0492i) q^{20} +(-10.4355 - 59.1825i) q^{22} +(-85.9596 + 72.1286i) q^{23} +(-57.1553 + 20.8028i) q^{25} -20.1485 q^{26} -55.9423 q^{28} +(-271.740 + 98.9052i) q^{29} +(-142.315 + 119.417i) q^{31} +(5.55674 + 31.5138i) q^{32} +(140.891 + 118.222i) q^{34} +(95.3236 - 165.105i) q^{35} +(-195.634 - 338.848i) q^{37} +(15.1365 - 85.8435i) q^{38} +(-102.477 - 37.2985i) q^{40} +(-345.291 - 125.676i) q^{41} +(-32.5874 + 184.812i) q^{43} +(60.0955 + 104.088i) q^{44} +(112.212 - 194.357i) q^{46} +(257.618 + 216.167i) q^{47} +(-25.5964 - 145.164i) q^{49} +(93.1868 - 78.1930i) q^{50} +(37.8668 - 13.7824i) q^{52} +366.522 q^{53} -409.602 q^{55} +(105.137 - 38.2668i) q^{56} +(443.048 - 371.762i) q^{58} +(65.6208 + 372.154i) q^{59} +(675.933 + 567.175i) q^{61} +(185.779 - 321.779i) q^{62} +(-32.0000 - 55.4256i) q^{64} +(-23.8470 + 135.243i) q^{65} +(897.489 + 326.659i) q^{67} +(-345.657 - 125.809i) q^{68} +(-66.2111 + 375.502i) q^{70} +(-341.031 - 590.683i) q^{71} +(-410.162 + 710.421i) q^{73} +(599.458 + 503.005i) q^{74} +(30.2730 + 171.687i) q^{76} +(321.919 - 270.122i) q^{77} +(-132.267 + 48.1413i) q^{79} +218.107 q^{80} +734.903 q^{82} +(241.086 - 87.7482i) q^{83} +(960.294 - 805.782i) q^{85} +(-65.1748 - 369.625i) q^{86} +(-184.143 - 154.515i) q^{88} +(470.400 - 814.757i) q^{89} +(-70.4471 - 122.018i) q^{91} +(-77.9418 + 442.030i) q^{92} +(-632.030 - 230.040i) q^{94} +(-558.292 - 203.202i) q^{95} +(40.0173 - 226.949i) q^{97} +(147.404 + 255.311i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 12 q^{5} + 33 q^{7} - 120 q^{8}+O(q^{10}) \) 30 * q + 12 * q^5 + 33 * q^7 - 120 * q^8	\( 30 q + 12 q^{5} + 33 q^{7} - 120 q^{8} - 30 q^{10} + 39 q^{11} - 60 q^{13} + 66 q^{14} - 102 q^{17} - 171 q^{19} - 96 q^{20} + 78 q^{22} - 48 q^{23} - 432 q^{25} + 468 q^{26} + 336 q^{28} + 381 q^{29} - 801 q^{31} - 222 q^{34} - 624 q^{35} - 555 q^{37} - 606 q^{38} + 96 q^{40} - 1401 q^{41} + 648 q^{43} - 132 q^{44} - 348 q^{46} - 540 q^{47} + 15 q^{49} + 828 q^{50} - 240 q^{52} + 1794 q^{53} + 3906 q^{55} + 264 q^{56} - 444 q^{58} + 1500 q^{59} - 378 q^{61} - 744 q^{62} - 960 q^{64} - 3666 q^{65} + 3087 q^{67} + 24 q^{68} + 2118 q^{70} - 120 q^{71} - 2604 q^{73} + 1974 q^{74} - 1212 q^{76} + 6504 q^{77} - 2625 q^{79} + 480 q^{80} + 3408 q^{82} + 5211 q^{83} - 1395 q^{85} + 1296 q^{86} - 912 q^{88} - 2604 q^{89} - 3399 q^{91} - 372 q^{92} + 4500 q^{94} - 7545 q^{95} + 8940 q^{97} - 4002 q^{98}+O(q^{100}) \) 30 * q + 12 * q^5 + 33 * q^7 - 120 * q^8 - 30 * q^10 + 39 * q^11 - 60 * q^13 + 66 * q^14 - 102 * q^17 - 171 * q^19 - 96 * q^20 + 78 * q^22 - 48 * q^23 - 432 * q^25 + 468 * q^26 + 336 * q^28 + 381 * q^29 - 801 * q^31 - 222 * q^34 - 624 * q^35 - 555 * q^37 - 606 * q^38 + 96 * q^40 - 1401 * q^41 + 648 * q^43 - 132 * q^44 - 348 * q^46 - 540 * q^47 + 15 * q^49 + 828 * q^50 - 240 * q^52 + 1794 * q^53 + 3906 * q^55 + 264 * q^56 - 444 * q^58 + 1500 * q^59 - 378 * q^61 - 744 * q^62 - 960 * q^64 - 3666 * q^65 + 3087 * q^67 + 24 * q^68 + 2118 * q^70 - 120 * q^71 - 2604 * q^73 + 1974 * q^74 - 1212 * q^76 + 6504 * q^77 - 2625 * q^79 + 480 * q^80 + 3408 * q^82 + 5211 * q^83 - 1395 * q^85 + 1296 * q^86 - 912 * q^88 - 2604 * q^89 - 3399 * q^91 - 372 * q^92 + 4500 * q^94 - 7545 * q^95 + 8940 * q^97 - 4002 * q^98

Introduction

L-functions

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