LMFDB - Embedded newform 312.4.m.a.181.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [312,4,Mod(181,312)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(312, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))

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

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

chi := DirichletCharacter("312.181");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	312.m (of order $2$, degree $1$, 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:	$18.4085959218$
Analytic rank:	$0$
Dimension:	$84$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.15
Character	$\chi$	$=$	312.181
Dual form			312.4.m.a.181.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.32798 - 1.60640i) q^{2} -3.00000i q^{3} +(2.83895 + 7.47933i) q^{4} +6.73184 q^{5} +(-4.81920 + 6.98393i) q^{6} +30.2729i q^{7} +(5.40578 - 21.9722i) q^{8} -9.00000 q^{9} +(-15.6716 - 10.8140i) q^{10} +17.0865 q^{11} +(22.4380 - 8.51686i) q^{12} +(28.4288 + 37.2667i) q^{13} +(48.6304 - 70.4746i) q^{14} -20.1955i q^{15} +(-47.8807 + 42.4669i) q^{16} -138.010 q^{17} +(20.9518 + 14.4576i) q^{18} -72.5929 q^{19} +(19.1114 + 50.3496i) q^{20} +90.8187 q^{21} +(-39.7769 - 27.4477i) q^{22} -90.4018 q^{23} +(-65.9166 - 16.2173i) q^{24} -79.6824 q^{25} +(-6.31642 - 132.424i) q^{26} +27.0000i q^{27} +(-226.421 + 85.9433i) q^{28} -265.087i q^{29} +(-32.4421 + 47.0147i) q^{30} -37.6473i q^{31} +(179.684 - 21.9464i) q^{32} -51.2595i q^{33} +(321.284 + 221.699i) q^{34} +203.792i q^{35} +(-25.5506 - 67.3140i) q^{36} -274.672 q^{37} +(168.995 + 116.613i) q^{38} +(111.800 - 85.2864i) q^{39} +(36.3908 - 147.913i) q^{40} +70.0720i q^{41} +(-211.424 - 145.891i) q^{42} -273.572i q^{43} +(48.5077 + 127.795i) q^{44} -60.5865 q^{45} +(210.453 + 145.222i) q^{46} +419.905i q^{47} +(127.401 + 143.642i) q^{48} -573.448 q^{49} +(185.499 + 128.002i) q^{50} +414.030i q^{51} +(-198.021 + 318.427i) q^{52} +426.970i q^{53} +(43.3728 - 62.8554i) q^{54} +115.023 q^{55} +(665.162 + 163.649i) q^{56} +217.779i q^{57} +(-425.837 + 617.117i) q^{58} -162.748 q^{59} +(151.049 - 57.3341i) q^{60} +629.954i q^{61} +(-60.4766 + 87.6419i) q^{62} -272.456i q^{63} +(-453.555 - 237.554i) q^{64} +(191.378 + 250.873i) q^{65} +(-82.3432 + 119.331i) q^{66} +180.038 q^{67} +(-391.804 - 1032.22i) q^{68} +271.206i q^{69} +(327.372 - 474.423i) q^{70} -690.958i q^{71} +(-48.6520 + 197.750i) q^{72} -63.7166i q^{73} +(639.431 + 441.234i) q^{74} +239.047i q^{75} +(-206.088 - 542.946i) q^{76} +517.257i q^{77} +(-397.272 + 18.9493i) q^{78} +27.2982 q^{79} +(-322.325 + 285.880i) q^{80} +81.0000 q^{81} +(112.564 - 163.126i) q^{82} +1090.69 q^{83} +(257.830 + 679.262i) q^{84} -929.060 q^{85} +(-439.467 + 636.870i) q^{86} -795.262 q^{87} +(92.3658 - 375.428i) q^{88} +1265.75i q^{89} +(141.044 + 97.3263i) q^{90} +(-1128.17 + 860.622i) q^{91} +(-256.647 - 676.145i) q^{92} -112.942 q^{93} +(674.536 - 977.530i) q^{94} -488.684 q^{95} +(-65.8393 - 539.052i) q^{96} +580.675i q^{97} +(1334.97 + 921.187i) q^{98} -153.778 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52}+ \cdots + 2480 q^{95}+O(q^{100}) $ 84 * q - 756 * q^9 - 36 * q^10 + 12 * q^12 - 208 * q^14 - 148 * q^16 - 104 * q^17 + 620 * q^22 + 2188 * q^25 + 444 * q^26 - 204 * q^30 - 40 * q^38 - 1924 * q^40 + 192 * q^42 + 624 * q^48 - 3396 * q^49 - 1292 * q^52 - 1616 * q^55 + 608 * q^56 - 2120 * q^62 - 2856 * q^64 + 696 * q^65 - 396 * q^66 - 2536 * q^68 - 3936 * q^74 - 156 * q^78 + 3160 * q^79 + 6804 * q^81 + 4276 * q^82 - 2088 * q^87 + 1780 * q^88 + 324 * q^90 + 4792 * q^92 - 860 * q^94 + 2480 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$1$	$-1$	$-1$	$1$

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 $

$2$	−2.32798	−	1.60640i	−0.823064	−	0.567948i
$2$	−2.32798	−	1.60640i	−0.823064	−	0.567948i
$3$		−	3.00000i		−	0.577350i
$3$		−	3.00000i		−	0.577350i
$4$	2.83895	+	7.47933i	0.354869	+	0.934916i
$5$	6.73184			0.602114			0.301057	−	0.953606i	$-0.402661\pi$
$5$	6.73184			0.602114			0.301057	+	0.953606i	$0.402661\pi$
$6$	−4.81920	+	6.98393i	−0.327905	+	0.475196i
$7$			30.2729i			1.63458i	0.576225	+	0.817291i	$0.304525\pi$
$7$			30.2729i			1.63458i	−0.576225	+	0.817291i	$0.695475\pi$
$8$	5.40578	−	21.9722i	0.238904	−	0.971043i
$9$	−9.00000			−0.333333
$10$	−15.6716	−	10.8140i	−0.495578	−	0.341970i
$11$	17.0865			0.468343			0.234171	−	0.972195i	$-0.424762\pi$
$11$	17.0865			0.468343			0.234171	+	0.972195i	$0.424762\pi$
$12$	22.4380	−	8.51686i	0.539774	−	0.204884i
$13$	28.4288	+	37.2667i	0.606518	+	0.795070i
$13$	28.4288	+	37.2667i	0.606518	+	0.795070i
$14$	48.6304	−	70.4746i	0.928358	−	1.34537i
$15$		−	20.1955i		−	0.347631i
$16$	−47.8807	+	42.4669i	−0.748136	+	0.663546i
$17$	−138.010			−1.96896			−0.984480	−	0.175497i	$-0.943847\pi$
$17$	−138.010			−1.96896			−0.984480	+	0.175497i	$0.943847\pi$
$18$	20.9518	+	14.4576i	0.274355	+	0.189316i
$19$	−72.5929			−0.876524			−0.438262	−	0.898847i	$-0.644406\pi$
$19$	−72.5929			−0.876524			−0.438262	+	0.898847i	$0.644406\pi$
$20$	19.1114	+	50.3496i	0.213672	+	0.562926i
$21$	90.8187			0.943726
$22$	−39.7769	−	27.4477i	−0.385476	−	0.265995i
$23$	−90.4018			−0.819569			−0.409784	−	0.912182i	$-0.634396\pi$
$23$	−90.4018			−0.819569			−0.409784	+	0.912182i	$0.634396\pi$
$24$	−65.9166	−	16.2173i	−0.560632	−	0.137931i
$25$	−79.6824			−0.637459
$26$	−6.31642	−	132.424i	−0.0476443	−	0.998864i
$27$			27.0000i			0.192450i
$28$	−226.421	+	85.9433i	−1.52820	+	0.580063i
$29$		−	265.087i		−	1.69743i	−0.528850	−	0.848715i	$-0.677377\pi$
$29$		−	265.087i		−	1.69743i	0.528850	−	0.848715i	$-0.322623\pi$
$30$	−32.4421	+	47.0147i	−0.197436	+	0.286122i
$31$		−	37.6473i		−	0.218118i	−0.994035	−	0.109059i	$-0.965216\pi$
$31$		−	37.6473i		−	0.218118i	0.994035	−	0.109059i	$-0.0347837\pi$
$32$	179.684	−	21.9464i	0.992623	−	0.121238i
$33$		−	51.2595i		−	0.270398i
$34$	321.284	+	221.699i	1.62058	+	1.11827i
$35$			203.792i			0.984205i
$36$	−25.5506	−	67.3140i	−0.118290	−	0.311639i
$37$	−274.672			−1.22043			−0.610214	−	0.792237i	$-0.708917\pi$
$37$	−274.672			−1.22043			−0.610214	+	0.792237i	$0.708917\pi$
$38$	168.995	+	116.613i	0.721435	+	0.497820i
$39$	111.800	−	85.2864i	0.459034	−	0.350173i
$40$	36.3908	−	147.913i	0.143847	−	0.584679i
$41$			70.0720i			0.266912i	0.991055	+	0.133456i	$0.0426075\pi$
$41$			70.0720i			0.266912i	−0.991055	+	0.133456i	$0.957392\pi$
$42$	−211.424	−	145.891i	−0.776747	−	0.535988i
$43$		−	273.572i		−	0.970219i	−0.874454	−	0.485109i	$-0.838780\pi$
$43$		−	273.572i		−	0.970219i	0.874454	−	0.485109i	$-0.161220\pi$
$44$	48.5077	+	127.795i	0.166200	+	0.437861i
$45$	−60.5865			−0.200705
$46$	210.453	+	145.222i	0.674558	+	0.465473i
$47$			419.905i			1.30318i	0.758571	+	0.651590i	$0.225898\pi$
$47$			419.905i			1.30318i	−0.758571	+	0.651590i	$0.774102\pi$
$48$	127.401	+	143.642i	0.383098	+	0.431936i
$49$	−573.448			−1.67186
$50$	185.499	+	128.002i	0.524669	+	0.362044i
$51$			414.030i			1.13678i
$52$	−198.021	+	318.427i	−0.528089	+	0.849189i
$53$			426.970i			1.10658i	0.832988	+	0.553291i	$0.186628\pi$
$53$			426.970i			1.10658i	−0.832988	+	0.553291i	$0.813372\pi$
$54$	43.3728	−	62.8554i	0.109302	−	0.158399i
$55$	115.023			0.281996
$56$	665.162	+	163.649i	1.58725	+	0.390508i
$57$			217.779i			0.506061i
$58$	−425.837	+	617.117i	−0.964053	+	1.39709i
$59$	−162.748			−0.359119			−0.179559	−	0.983747i	$-0.557467\pi$
$59$	−162.748			−0.359119			−0.179559	+	0.983747i	$0.557467\pi$
$60$	151.049	−	57.3341i	0.325005	−	0.123363i
$61$			629.954i			1.32225i	0.750275	+	0.661126i	$0.229921\pi$
$61$			629.954i			1.32225i	−0.750275	+	0.661126i	$0.770079\pi$
$62$	−60.4766	+	87.6419i	−0.123880	+	0.179525i
$63$		−	272.456i		−	0.544861i
$64$	−453.555	−	237.554i	−0.885850	−	0.463972i
$65$	191.378	+	250.873i	0.365193	+	0.478723i
$66$	−82.3432	+	119.331i	−0.153572	+	0.222555i
$67$	180.038			0.328286			0.164143	−	0.986437i	$-0.447514\pi$
$67$	180.038			0.328286			0.164143	+	0.986437i	$0.447514\pi$
$68$	−391.804	−	1032.22i	−0.698723	−	1.84081i
$69$			271.206i			0.473178i
$70$	327.372	−	474.423i	0.558977	−	0.810064i
$71$		−	690.958i		−	1.15495i	−0.816408	−	0.577476i	$-0.804038\pi$
$71$		−	690.958i		−	1.15495i	0.816408	−	0.577476i	$-0.195962\pi$
$72$	−48.6520	+	197.750i	−0.0796347	+	0.323681i
$73$		−	63.7166i		−	0.102157i	−0.998695	−	0.0510785i	$-0.983734\pi$
$73$		−	63.7166i		−	0.102157i	0.998695	−	0.0510785i	$-0.0162659\pi$
$74$	639.431	+	441.234i	1.00449	+	0.693140i
$75$			239.047i			0.368037i
$76$	−206.088	−	542.946i	−0.311051	−	0.819476i
$77$			517.257i			0.765545i
$78$	−397.272	+	18.9493i	−0.576695	+	0.0275074i
$79$	27.2982			0.0388770			0.0194385	−	0.999811i	$-0.493812\pi$
$79$	27.2982			0.0388770			0.0194385	+	0.999811i	$0.493812\pi$
$80$	−322.325	+	285.880i	−0.450463	+	0.399530i
$81$	81.0000			0.111111
$82$	112.564	−	163.126i	0.151592	−	0.219686i
$83$	1090.69			1.44240			0.721200	−	0.692727i	$-0.243591\pi$
$83$	1090.69			1.44240			0.721200	+	0.692727i	$0.243591\pi$
$84$	257.830	+	679.262i	0.334899	+	0.882305i
$85$	−929.060			−1.18554
$86$	−439.467	+	636.870i	−0.551034	+	0.798552i
$87$	−795.262			−0.980012
$88$	92.3658	−	375.428i	0.111889	−	0.454781i
$89$			1265.75i			1.50752i	0.657147	+	0.753762i	$0.271763\pi$
$89$			1265.75i			1.50752i	−0.657147	+	0.753762i	$0.728237\pi$
$90$	141.044	+	97.3263i	0.165193	+	0.113990i
$91$	−1128.17	+	860.622i	−1.29961	+	0.991403i
$92$	−256.647	−	676.145i	−0.290840	−	0.766228i
$93$	−112.942			−0.125930
$94$	674.536	−	977.530i	0.740140	−	1.07260i
$95$	−488.684			−0.527767
$96$	−65.8393	−	539.052i	−0.0699968	−	0.573091i
$97$			580.675i			0.607821i	0.952701	+	0.303911i	$0.0982924\pi$
$97$			580.675i			0.607821i	−0.952701	+	0.303911i	$0.901708\pi$
$98$	1334.97	+	921.187i	1.37605	+	0.949530i
$99$	−153.778			−0.156114
$100$	−226.214	−	595.970i	−0.226214	−	0.595970i
$101$		−	737.605i		−	0.726678i	−0.931657	−	0.363339i	$-0.881637\pi$
$101$		−	737.605i		−	0.726678i	0.931657	−	0.363339i	$-0.118363\pi$
$102$	665.098	−	963.852i	0.645632	−	0.935642i
$103$	2022.15			1.93445			0.967227	−	0.253913i	$-0.0817178\pi$
$103$	2022.15			1.93445			0.967227	+	0.253913i	$0.0817178\pi$
$104$	972.510	−	423.188i	0.916947	−	0.399010i
$105$	611.376			0.568231
$106$	685.885	−	993.976i	0.628481	−	0.910788i
$107$			633.950i			0.572769i	0.958115	+	0.286384i	$0.0924535\pi$
$107$			633.950i			0.572769i	−0.958115	+	0.286384i	$0.907547\pi$
$108$	−201.942	+	76.6517i	−0.179925	+	0.0682946i
$109$	−1806.68			−1.58760			−0.793800	−	0.608180i	$-0.791900\pi$
$109$	−1806.68			−1.58760			−0.793800	+	0.608180i	$0.791900\pi$
$110$	−267.772	−	184.774i	−0.232101	−	0.160159i
$111$			824.017i			0.704614i
$112$	−1285.60	−	1449.49i	−1.08462	−	1.22289i
$113$	−49.6150			−0.0413043			−0.0206522	−	0.999787i	$-0.506574\pi$
$113$	−49.6150			−0.0413043			−0.0206522	+	0.999787i	$0.506574\pi$
$114$	349.840	−	506.984i	0.287417	−	0.416521i
$115$	−608.571			−0.493474
$116$	1982.68	−	752.571i	1.58695	−	0.602366i
$117$	−255.859	−	335.400i	−0.202173	−	0.265023i
$118$	378.874	+	261.439i	0.295578	+	0.203961i
$119$		−	4177.96i		−	3.21843i
$120$	−443.740	−	109.173i	−0.337564	−	0.0830504i
$121$	−1039.05			−0.780655
$122$	1011.96	−	1466.52i	0.750971	−	1.08830i
$123$	210.216			0.154102
$124$	281.576	−	106.879i	0.203922	−	0.0774032i
$125$	−1377.89			−0.985937
$126$	−437.673	+	634.271i	−0.309453	+	0.448455i
$127$	−1107.91			−0.774102			−0.387051	−	0.922058i	$-0.626506\pi$
$127$	−1107.91			−0.774102			−0.387051	+	0.922058i	$0.626506\pi$
$128$	674.259	+	1281.61i	0.465599	+	0.884996i
$129$	−820.717			−0.560156
$130$	−42.5211	−	891.457i	−0.0286873	−	0.601430i
$131$		−	203.564i		−	0.135767i	−0.997693	−	0.0678835i	$-0.978375\pi$
$131$		−	203.564i		−	0.135767i	0.997693	−	0.0678835i	$-0.0216246\pi$
$132$	383.386	−	145.523i	0.252799	−	0.0959558i
$133$		−	2197.60i		−	1.43275i
$134$	−419.125	−	289.213i	−0.270200	−	0.186449i
$135$			181.760i			0.115877i
$136$	−746.051	+	3032.38i	−0.470392	+	1.91195i
$137$		−	2321.77i		−	1.44790i	−0.689853	−	0.723949i	$-0.742325\pi$
$137$		−	2321.77i		−	1.44790i	0.689853	−	0.723949i	$-0.257675\pi$
$138$	435.665	−	631.360i	0.268741	−	0.389456i
$139$			1031.99i			0.629729i	0.949137	+	0.314864i	$0.101959\pi$
$139$			1031.99i			0.629729i	−0.949137	+	0.314864i	$0.898041\pi$
$140$	−1524.23	+	578.556i	−0.920149	+	0.349264i
$141$	1259.72			0.752392
$142$	−1109.95	+	1608.53i	−0.655953	+	0.950600i
$143$	485.748	+	636.756i	0.284058	+	0.372365i
$144$	430.926	−	382.202i	0.249379	−	0.221182i
$145$		−	1784.53i		−	1.02205i
$146$	−102.354	+	148.331i	−0.0580200	+	0.0840818i
$147$			1720.34i			0.965248i
$148$	−779.781	−	2054.36i	−0.433092	−	1.14100i
$149$	597.622			0.328585			0.164292	−	0.986412i	$-0.447466\pi$
$149$	597.622			0.328585			0.164292	+	0.986412i	$0.447466\pi$
$150$	384.005	−	556.496i	0.209026	−	0.302918i
$151$			154.542i			0.0832878i	0.999133	+	0.0416439i	$0.0132595\pi$
$151$			154.542i			0.0832878i	−0.999133	+	0.0416439i	$0.986741\pi$
$152$	−392.421	+	1595.03i	−0.209405	+	0.851142i
$153$	1242.09			0.656320
$154$	830.922	−	1204.16i	0.434790	−	0.630092i
$155$		−	253.435i		−	0.131332i
$156$	955.280	+	594.064i	0.490279	+	0.304892i
$157$		−	379.317i		−	0.192820i	−0.995342	−	0.0964101i	$-0.969264\pi$
$157$		−	379.317i		−	0.192820i	0.995342	−	0.0964101i	$-0.0307360\pi$
$158$	−63.5495	−	43.8518i	−0.0319983	−	0.0220801i
$159$	1280.91			0.638885
$160$	1209.60	−	147.740i	0.597672	−	0.0729991i
$161$		−	2736.72i		−	1.33965i
$162$	−188.566	−	130.118i	−0.0914516	−	0.0631054i
$163$	3124.72			1.50152			0.750758	−	0.660577i	$-0.229688\pi$
$163$	3124.72			1.50152			0.750758	+	0.660577i	$0.229688\pi$
$164$	−524.091	+	198.931i	−0.249540	+	0.0947189i
$165$		−	345.070i		−	0.162810i
$166$	−2539.11	−	1752.09i	−1.18719	−	0.819208i
$167$			1062.01i			0.492101i	0.969257	+	0.246050i	$0.0791329\pi$
$167$			1062.01i			0.492101i	−0.969257	+	0.246050i	$0.920867\pi$
$168$	490.946	−	1995.49i	0.225460	−	0.916399i
$169$	−580.606	+	2118.89i	−0.264272	+	0.964448i
$170$	2162.83	+	1492.44i	0.975774	+	0.673325i
$171$	653.336			0.292175
$172$	2046.14	−	776.659i	0.907073	−	0.344301i
$173$			754.609i			0.331629i	0.986157	+	0.165815i	$0.0530253\pi$
$173$			754.609i			0.331629i	−0.986157	+	0.165815i	$0.946975\pi$
$174$	1851.35	+	1277.51i	0.806613	+	0.556596i
$175$		−	2412.21i		−	1.04198i
$176$	−818.113	+	725.611i	−0.350384	+	0.310767i
$177$			488.245i			0.207337i
$178$	2033.31	−	2946.65i	0.856196	−	1.24079i
$179$			3541.04i			1.47860i	0.673375	+	0.739301i	$0.264844\pi$
$179$			3541.04i			1.47860i	−0.673375	+	0.739301i	$0.735156\pi$
$180$	−172.002	−	453.147i	−0.0712239	−	0.187642i
$181$		−	1913.16i		−	0.785659i	−0.919611	−	0.392830i	$-0.871496\pi$
$181$		−	1913.16i		−	0.785659i	0.919611	−	0.392830i	$-0.128504\pi$
$182$	4008.85	−	191.216i	1.63273	−	0.0778785i
$183$	1889.86			0.763402
$184$	−488.693	+	1986.33i	−0.195798	+	0.795837i
$185$	−1849.05			−0.734837
$186$	262.926	+	181.430i	0.103649	+	0.0715219i
$187$	−2358.10			−0.922148
$188$	−3140.61	+	1192.09i	−1.21836	+	0.462459i
$189$	−817.368			−0.314575
$190$	1137.64	+	785.022i	0.434386	+	0.299745i
$191$	−3968.38			−1.50336			−0.751681	−	0.659527i	$-0.770757\pi$
$191$	−3968.38			−1.50336			−0.751681	+	0.659527i	$0.770757\pi$
$192$	−712.661	+	1360.67i	−0.267875	+	0.511446i
$193$			4077.07i			1.52059i	0.649578	+	0.760295i	$0.274946\pi$
$193$			4077.07i			1.52059i	−0.649578	+	0.760295i	$0.725054\pi$
$194$	932.798	−	1351.80i	0.345211	−	0.500276i
$195$	752.619	−	574.134i	0.276391	−	0.210844i
$196$	−1627.99	−	4289.00i	−0.593291	−	1.56305i
$197$	−876.471			−0.316985			−0.158492	−	0.987360i	$-0.550663\pi$
$197$	−876.471			−0.316985			−0.158492	+	0.987360i	$0.550663\pi$
$198$	357.993	+	247.030i	0.128492	+	0.0886648i
$199$	4791.02			1.70667			0.853333	−	0.521366i	$-0.174577\pi$
$199$	4791.02			1.70667			0.853333	+	0.521366i	$0.174577\pi$
$200$	−430.745	+	1750.80i	−0.152291	+	0.619000i
$201$		−	540.114i		−	0.189536i
$202$	−1184.89	+	1717.13i	−0.412716	+	0.598103i
$203$	8024.96			2.77459
$204$	−3096.66	+	1175.41i	−1.06279	+	0.403408i
$205$			471.713i			0.160712i
$206$	−4707.53	−	3248.39i	−1.59218	−	1.09867i
$207$	813.617			0.273190
$208$	−2943.79	−	577.069i	−0.981323	−	0.192368i
$209$	−1240.36			−0.410513
$210$	−1423.27	−	982.116i	−0.467690	−	0.322726i
$211$		−	1450.27i		−	0.473179i	−0.971610	−	0.236590i	$-0.923970\pi$
$211$		−	1450.27i		−	0.473179i	0.971610	−	0.236590i	$-0.0760297\pi$
$212$	−3193.45	+	1212.15i	−1.03456	+	0.392692i
$213$	−2072.87			−0.666812
$214$	1018.38	−	1475.82i	0.325303	−	0.471426i
$215$		−	1841.65i		−	0.584182i
$216$	593.249	+	145.956i	0.186877	+	0.0459771i
$217$	1139.69			0.356531
$218$	4205.90	+	2902.25i	1.30670	+	0.901674i
$219$	−191.150			−0.0589804
$220$	326.546	+	860.298i	0.100072	+	0.263642i
$221$	−3923.46	−	5143.17i	−1.19421	−	1.56546i
$222$	1323.70	−	1918.29i	0.400185	−	0.579943i
$223$			249.795i			0.0750113i	0.999296	+	0.0375056i	$0.0119412\pi$
$223$			249.795i			0.0750113i	−0.999296	+	0.0375056i	$0.988059\pi$
$224$	664.382	+	5439.55i	0.198174	+	1.62252i
$225$	717.141			0.212486
$226$	115.503	+	79.7016i	0.0339961	+	0.0234587i
$227$	485.137			0.141849			0.0709243	−	0.997482i	$-0.477405\pi$
$227$	485.137			0.141849			0.0709243	+	0.997482i	$0.477405\pi$
$228$	−1628.84	+	618.263i	−0.473125	+	0.179586i
$229$	720.569			0.207933			0.103966	−	0.994581i	$-0.466847\pi$
$229$	720.569			0.207933			0.103966	+	0.994581i	$0.466847\pi$
$230$	1416.74	+	977.608i	0.406161	+	0.280268i
$231$	1551.77			0.441987
$232$	−5824.55	−	1433.00i	−1.64828	−	0.405523i
$233$	−4035.27			−1.13459			−0.567295	−	0.823514i	$-0.692010\pi$
$233$	−4035.27			−1.13459			−0.567295	+	0.823514i	$0.692010\pi$
$234$	56.8478	+	1191.82i	0.0158814	+	0.332955i
$235$			2826.74i			0.784663i
$236$	−462.035	−	1217.25i	−0.127440	−	0.335746i
$237$		−	81.8945i		−	0.0224457i
$238$	−6711.47	+	9726.19i	−1.82790	+	2.64897i
$239$			3900.35i			1.05562i	0.849363	+	0.527808i	$0.176986\pi$
$239$			3900.35i			1.05562i	−0.849363	+	0.527808i	$0.823014\pi$
$240$	857.641	+	966.975i	0.230669	+	0.260075i
$241$			6662.45i			1.78077i	0.455207	+	0.890386i	$0.349565\pi$
$241$			6662.45i			1.78077i	−0.455207	+	0.890386i	$0.650435\pi$
$242$	2418.89	+	1669.13i	0.642529	+	0.443372i
$243$		−	243.000i		−	0.0641500i
$244$	−4711.63	+	1788.41i	−1.23619	+	0.469226i
$245$	−3860.36			−1.00665
$246$	−489.378	−	337.691i	−0.126836	−	0.0875219i
$247$	−2063.73	−	2705.29i	−0.531627	−	0.696898i
$248$	−827.193	−	203.513i	−0.211802	−	0.0521092i
$249$		−	3272.08i		−	0.832769i
$250$	3207.69	+	2213.44i	0.811489	+	0.559961i
$251$		−	3768.47i		−	0.947663i	−0.880615	−	0.473832i	$-0.842870\pi$
$251$		−	3768.47i		−	0.947663i	0.880615	−	0.473832i	$-0.157130\pi$
$252$	2037.79	−	773.490i	0.509399	−	0.193354i
$253$	−1544.65			−0.383839
$254$	2579.18	+	1779.74i	0.637135	+	0.439650i
$255$			2787.18i			0.684471i
$256$	489.121	−	4066.69i	0.119414	−	0.992845i
$257$	−201.599			−0.0489316			−0.0244658	−	0.999701i	$-0.507788\pi$
$257$	−201.599			−0.0489316			−0.0244658	+	0.999701i	$0.507788\pi$
$258$	1910.61	+	1318.40i	0.461044	+	0.318140i
$259$		−	8315.12i		−	1.99489i
$260$	−1333.05	+	2143.60i	−0.317970	+	0.511308i
$261$			2385.79i			0.565810i
$262$	−327.005	+	473.892i	−0.0771086	+	0.111745i
$263$	−1000.31			−0.234532			−0.117266	−	0.993101i	$-0.537413\pi$
$263$	−1000.31			−0.234532			−0.117266	+	0.993101i	$0.537413\pi$
$264$	−1126.28	−	277.097i	−0.262568	−	0.0645991i
$265$			2874.29i			0.666288i
$266$	−3530.22	+	5115.95i	−0.813728	+	1.17925i
$267$	3797.26			0.870370
$268$	511.120	+	1346.56i	0.116499	+	0.306920i
$269$		−	3570.59i		−	0.809303i	−0.914471	−	0.404652i	$-0.867393\pi$
$269$		−	3570.59i		−	0.809303i	0.914471	−	0.404652i	$-0.132607\pi$
$270$	291.979	−	423.132i	0.0658121	−	0.0953741i
$271$			4154.87i			0.931330i	0.884961	+	0.465665i	$0.154185\pi$
$271$			4154.87i			0.931330i	−0.884961	+	0.465665i	$0.845815\pi$
$272$	6608.01	−	5860.86i	1.47305	−	1.30649i
$273$	2581.87	+	3384.51i	0.572387	+	0.750329i
$274$	−3729.69	+	5405.03i	−0.822332	+	1.19171i
$275$	−1361.49			−0.298549
$276$	−2028.43	+	769.940i	−0.442382	+	0.167916i
$277$			2425.77i			0.526176i	0.964772	+	0.263088i	$0.0847409\pi$
$277$			2425.77i			0.526176i	−0.964772	+	0.263088i	$0.915259\pi$
$278$	1657.79	−	2402.45i	0.357654	−	0.518307i
$279$			338.825i			0.0727059i
$280$	4477.76	+	1101.66i	0.955705	+	0.235130i
$281$		−	922.711i		−	0.195887i	−0.995192	−	0.0979436i	$-0.968774\pi$
$281$		−	922.711i		−	0.195887i	0.995192	−	0.0979436i	$-0.0312265\pi$
$282$	−2932.59	−	2023.61i	−0.619267	−	0.427320i
$283$			6115.89i			1.28464i	0.766438	+	0.642318i	$0.222027\pi$
$283$			6115.89i			1.28464i	−0.766438	+	0.642318i	$0.777973\pi$
$284$	5167.90	−	1961.60i	1.07978	−	0.409857i
$285$			1466.05i			0.304707i
$286$	−107.925	−	2262.66i	−0.0223139	−	0.467811i
$287$	−2121.28			−0.436290
$288$	−1617.16	+	197.518i	−0.330874	+	0.0404127i
$289$	14133.7			2.87680
$290$	−2866.66	+	4154.33i	−0.580470	+	0.841210i
$291$	1742.03			0.350926
$292$	476.558	−	180.889i	0.0955083	−	0.0362524i
$293$	4447.28			0.886734			0.443367	−	0.896340i	$-0.353784\pi$
$293$	4447.28			0.886734			0.443367	+	0.896340i	$0.353784\pi$
$294$	2763.56	−	4004.92i	0.548211	−	0.794461i
$295$	−1095.59			−0.216230
$296$	−1484.82	+	6035.15i	−0.291565	+	1.18509i
$297$			461.335i			0.0901326i
$298$	−1391.25	−	960.021i	−0.270446	−	0.186619i
$299$	−2570.02	−	3368.97i	−0.497083	−	0.651615i
$300$	−1787.91	+	678.643i	−0.344084	+	0.130605i
$301$	8281.83			1.58590
$302$	248.256	−	359.770i	0.0473032	−	0.0685512i
$303$	−2212.82			−0.419548
$304$	3475.80	−	3082.80i	0.655759	−	0.581614i
$305$			4240.75i			0.796146i
$306$	−2891.55	−	1995.29i	−0.540193	−	0.372756i
$307$	3534.70			0.657120			0.328560	−	0.944483i	$-0.393437\pi$
$307$	3534.70			0.657120			0.328560	+	0.944483i	$0.393437\pi$
$308$	−3868.74	+	1468.47i	−0.715720	+	0.271668i
$309$		−	6066.46i		−	1.11686i
$310$	−407.119	+	589.991i	−0.0745896	+	0.108094i
$311$	3103.31			0.565829			0.282914	−	0.959145i	$-0.408699\pi$
$311$	3103.31			0.565829			0.282914	+	0.959145i	$0.408699\pi$
$312$	−1269.56	−	2917.53i	−0.230368	−	0.529399i
$313$	−4535.21			−0.818994			−0.409497	−	0.912311i	$-0.634296\pi$
$313$	−4535.21			−0.818994			−0.409497	+	0.912311i	$0.634296\pi$
$314$	−609.335	+	883.040i	−0.109512	+	0.158703i
$315$		−	1834.13i		−	0.328068i
$316$	77.4982	+	204.172i	0.0137963	+	0.0363467i
$317$	10326.9			1.82971			0.914856	−	0.403781i	$-0.132304\pi$
$317$	10326.9			1.82971			0.914856	+	0.403781i	$0.132304\pi$
$318$	−2981.93	−	2057.65i	−0.525844	−	0.362854i
$319$		−	4529.41i		−	0.794979i
$320$	−3053.26	−	1599.17i	−0.533382	−	0.279364i
$321$	1901.85			0.330688
$322$	−4396.28	+	6371.03i	−0.760854	+	1.10262i
$323$	10018.5			1.72584
$324$	229.955	+	605.826i	0.0394299	+	0.103880i
$325$	−2265.27	−	2969.49i	−0.386630	−	0.506824i
$326$	−7274.28	−	5019.56i	−1.23584	−	0.852784i
$327$			5420.03i			0.916601i
$328$	1539.63	+	378.794i	0.259183	+	0.0637664i
$329$	−12711.7			−2.13016
$330$	−554.321	+	803.316i	−0.0924678	+	0.134003i
$331$	−1221.58			−0.202851			−0.101426	−	0.994843i	$-0.532340\pi$
$331$	−1221.58			−0.202851			−0.101426	+	0.994843i	$0.532340\pi$
$332$	3096.43	+	8157.65i	0.511863	+	1.34852i
$333$	2472.05			0.406809
$334$	1706.01	−	2472.34i	0.279488	−	0.405031i
$335$	1211.99			0.197666
$336$	−4348.46	+	3856.79i	−0.706036	+	0.626206i
$337$	−10166.5			−1.64333			−0.821667	−	0.569968i	$-0.806956\pi$
$337$	−10166.5			−1.64333			−0.821667	+	0.569968i	$0.806956\pi$
$338$	4755.43	−	4000.05i	0.765270	−	0.643710i
$339$			148.845i			0.0238471i
$340$	−2637.56	−	6948.75i	−0.420711	−	1.10838i
$341$		−	643.259i		−	0.102154i
$342$	−1520.95	−	1049.52i	−0.240478	−	0.165940i
$343$		−	6976.31i		−	1.09821i
$344$	−6010.99	−	1478.87i	−0.942124	−	0.231789i
$345$			1825.71i			0.284907i
$346$	1212.20	−	1756.71i	0.188348	−	0.272952i
$347$			6327.78i			0.978942i	0.872020	+	0.489471i	$0.162810\pi$
$347$			6327.78i			0.978942i	−0.872020	+	0.489471i	$0.837190\pi$
$348$	−2257.71	−	5948.03i	−0.347776	−	0.916229i
$349$	1706.72			0.261773			0.130886	−	0.991397i	$-0.458218\pi$
$349$	1706.72			0.261773			0.130886	+	0.991397i	$0.458218\pi$
$350$	−3874.98	+	5615.58i	−0.591790	+	0.857615i
$351$	−1006.20	+	767.578i	−0.153011	+	0.116724i
$352$	3070.17	−	374.987i	0.464888	−	0.0567810i
$353$			2307.75i			0.347958i	0.984749	+	0.173979i	$0.0556624\pi$
$353$			2307.75i			0.347958i	−0.984749	+	0.173979i	$0.944338\pi$
$354$	784.317	−	1136.62i	0.117757	−	0.170652i
$355$		−	4651.42i		−	0.695413i
$356$	−9466.99	+	3593.42i	−1.40941	+	0.534974i
$357$	−12533.9			−1.85816
$358$	5688.33	−	8243.46i	0.839770	−	1.21698i
$359$		−	9345.50i		−	1.37392i	−0.726696	−	0.686959i	$-0.758945\pi$
$359$		−	9345.50i		−	1.37392i	0.726696	−	0.686959i	$-0.241055\pi$
$360$	−327.518	+	1331.22i	−0.0479491	+	0.194893i
$361$	−1589.27			−0.231706
$362$	−3073.31	+	4453.80i	−0.446214	+	0.646648i
$363$			3117.16i			0.450711i
$364$	−9639.69	−	5994.68i	−1.38807	−	0.863205i
$365$		−	428.930i		−	0.0615102i
$366$	−4399.55	−	3035.88i	−0.628329	−	0.433573i
$367$	9711.75			1.38133			0.690666	−	0.723174i	$-0.257317\pi$
$367$	9711.75			1.38133			0.690666	+	0.723174i	$0.257317\pi$
$368$	4328.50	−	3839.09i	0.613149	−	0.543821i
$369$		−	630.648i		−	0.0889707i
$370$	4304.54	+	2970.31i	0.604818	+	0.417349i
$371$	−12925.6			−1.80880
$372$	−320.636	−	844.728i	−0.0446888	−	0.117734i
$373$			3122.79i			0.433490i	0.976228	+	0.216745i	$0.0695440\pi$
$373$			3122.79i			0.433490i	−0.976228	+	0.216745i	$0.930456\pi$
$374$	5489.61	+	3788.06i	0.758987	+	0.523733i
$375$			4133.67i			0.569231i
$376$	9226.25	+	2269.92i	1.26544	+	0.311335i
$377$	9878.92	−	7536.12i	1.34958	−	1.02952i
$378$	1902.81	+	1313.02i	0.258916	+	0.178663i
$379$	427.606			0.0579543			0.0289771	−	0.999580i	$-0.490775\pi$
$379$	427.606			0.0579543			0.0289771	+	0.999580i	$0.490775\pi$
$380$	−1387.35	−	3655.02i	−0.187288	−	0.493418i
$381$			3323.72i			0.446928i
$382$	9238.31	+	6374.82i	1.23736	+	0.853832i
$383$			2619.58i			0.349489i	0.984614	+	0.174745i	$0.0559100\pi$
$383$			2619.58i			0.349489i	−0.984614	+	0.174745i	$0.944090\pi$
$384$	3844.83	−	2022.78i	0.510953	−	0.268814i
$385$			3482.09i			0.460945i
$386$	6549.41	−	9491.32i	0.863617	−	1.25154i
$387$			2462.15i			0.323406i
$388$	−4343.06	+	1648.51i	−0.568262	+	0.215697i
$389$		−	7796.02i		−	1.01613i	−0.861319	−	0.508064i	$-0.830361\pi$
$389$		−	7796.02i		−	1.01613i	0.861319	−	0.508064i	$-0.169639\pi$
$390$	−2674.37	+	127.563i	−0.347236	+	0.0165626i
$391$	12476.3			1.61370
$392$	−3099.93	+	12599.9i	−0.399414	+	1.62345i
$393$	−610.692			−0.0783851
$394$	2040.40	+	1407.96i	0.260899	+	0.180031i
$395$	183.767			0.0234084
$396$	−436.570	−	1150.16i	−0.0554001	−	0.145954i
$397$	11701.4			1.47928			0.739640	−	0.673003i	$-0.234996\pi$
$397$	11701.4			1.47928			0.739640	+	0.673003i	$0.234996\pi$
$398$	−11153.4	−	7696.30i	−1.40470	−	0.969298i
$399$	−6592.79			−0.827199
$400$	3815.25	−	3383.86i	0.476906	−	0.422983i
$401$		−	12230.8i		−	1.52313i	−0.648087	−	0.761567i	$-0.724431\pi$
$401$		−	12230.8i		−	1.52313i	0.648087	−	0.761567i	$-0.275569\pi$
$402$	−867.640	+	1257.37i	−0.107647	+	0.156000i
$403$	1402.99	−	1070.27i	0.173419	−	0.132292i
$404$	5516.79	−	2094.03i	0.679383	−	0.257876i
$405$	545.279			0.0669015
$406$	−18681.9	−	12891.3i	−2.28367	−	1.57582i
$407$	−4693.18			−0.571579
$408$	9097.14	+	2238.15i	1.10386	+	0.271581i
$409$		−	2580.82i		−	0.312013i	−0.987756	−	0.156006i	$-0.950138\pi$
$409$		−	2580.82i		−	0.312013i	0.987756	−	0.156006i	$-0.0498620\pi$
$410$	757.760	−	1098.14i	0.0912759	−	0.132276i
$411$	−6965.31			−0.835945
$412$	5740.80	+	15124.4i	0.686478	+	1.80855i
$413$		−	4926.86i		−	0.587009i
$414$	−1894.08	−	1306.99i	−0.224853	−	0.155158i
$415$	7342.37			0.868489
$416$	5926.07	+	6072.31i	0.698436	+	0.715672i
$417$	3095.97			0.363574
$418$	2887.52	+	1992.51i	0.337879	+	0.233151i
$419$		−	8491.73i		−	0.990091i	−0.868867	−	0.495046i	$-0.835151\pi$
$419$		−	8491.73i		−	0.990091i	0.868867	−	0.495046i	$-0.164849\pi$
$420$	1735.67	+	4572.69i	0.201648	+	0.531248i
$421$	−4939.11			−0.571776			−0.285888	−	0.958263i	$-0.592288\pi$
$421$	−4939.11			−0.571776			−0.285888	+	0.958263i	$0.592288\pi$
$422$	−2329.72	+	3376.20i	−0.268741	+	0.389457i
$423$		−	3779.15i		−	0.434394i
$424$	9381.47	+	2308.11i	1.07454	+	0.264367i
$425$	10997.0			1.25513
$426$	4825.60	+	3329.86i	0.548829	+	0.378715i
$427$	−19070.5			−2.16133
$428$	−4741.52	+	1799.75i	−0.535491	+	0.203258i
$429$	1910.27	−	1457.25i	0.214985	−	0.164001i
$430$	−2958.42	+	4287.31i	−0.331785	+	0.480819i
$431$			5600.99i			0.625963i	0.949759	+	0.312981i	$0.101328\pi$
$431$			5600.99i			0.625963i	−0.949759	+	0.312981i	$0.898672\pi$
$432$	−1146.61	−	1292.78i	−0.127699	−	0.143979i
$433$	−4894.40			−0.543210			−0.271605	−	0.962409i	$-0.587554\pi$
$433$	−4894.40			−0.543210			−0.271605	+	0.962409i	$0.587554\pi$
$434$	−2653.17	−	1830.80i	−0.293448	−	0.202491i
$435$	−5353.58			−0.590079
$436$	−5129.07	−	13512.7i	−0.563390	−	1.48427i
$437$	6562.53			0.718372
$438$	444.993	+	307.063i	0.0485447	+	0.0334978i
$439$	−9177.47			−0.997760			−0.498880	−	0.866671i	$-0.666255\pi$
$439$	−9177.47			−0.997760			−0.498880	+	0.866671i	$0.666255\pi$
$440$	621.792	−	2527.32i	0.0673699	−	0.273830i
$441$	5161.03			0.557286
$442$	871.728	+	18275.8i	0.0938097	+	1.96672i
$443$		−	2378.64i		−	0.255107i	−0.991832	−	0.127554i	$-0.959287\pi$
$443$		−	2378.64i		−	0.255107i	0.991832	−	0.127554i	$-0.0407125\pi$
$444$	−6163.09	+	2339.34i	−0.658755	+	0.250046i
$445$			8520.86i			0.907702i
$446$	401.271	−	581.517i	0.0426025	−	0.0617391i
$447$		−	1792.87i		−	0.189708i
$448$	7191.44	−	13730.4i	0.758401	−	1.44799i
$449$		−	6013.75i		−	0.632086i	−0.948745	−	0.316043i	$-0.897646\pi$
$449$		−	6013.75i		−	0.632086i	0.948745	−	0.316043i	$-0.102354\pi$
$450$	−1669.49	−	1152.02i	−0.174890	−	0.120681i
$451$			1197.28i			0.125006i
$452$	−140.855	−	371.087i	−0.0146576	−	0.0386161i
$453$	463.626			0.0480862
$454$	−1129.39	−	779.324i	−0.116751	−	0.0805627i
$455$	−7594.65	+	5793.57i	−0.782512	+	0.596938i
$456$	4785.08	+	1177.26i	0.491407	+	0.120900i
$457$			15592.7i			1.59606i	0.602620	+	0.798028i	$0.294123\pi$
$457$			15592.7i			1.59606i	−0.602620	+	0.798028i	$0.705877\pi$
$458$	−1677.47	−	1157.52i	−0.171142	−	0.118095i
$459$		−	3726.27i		−	0.378927i
$460$	−1727.70	−	4551.70i	−0.175119	−	0.461357i
$461$	−5143.01			−0.519596			−0.259798	−	0.965663i	$-0.583656\pi$
$461$	−5143.01			−0.519596			−0.259798	+	0.965663i	$0.583656\pi$
$462$	−3612.49	−	2492.77i	−0.363784	−	0.251026i
$463$		−	14322.0i		−	1.43758i	−0.695229	−	0.718788i	$-0.744697\pi$
$463$		−	14322.0i		−	1.43758i	0.695229	−	0.718788i	$-0.255303\pi$
$464$	11257.4	+	12692.6i	1.12632	+	1.26991i
$465$	−760.306			−0.0758244
$466$	9394.03	+	6482.27i	0.933841	+	0.644389i
$467$		−	1729.83i		−	0.171407i	−0.996321	−	0.0857036i	$-0.972686\pi$
$467$		−	1729.83i		−	0.171407i	0.996321	−	0.0857036i	$-0.0273138\pi$
$468$	1782.19	−	2865.84i	0.176030	−	0.283063i
$469$			5450.27i			0.536610i
$470$	4540.87	−	6580.57i	0.445648	−	0.645828i
$471$	−1137.95			−0.111325
$472$	−879.781	+	3575.94i	−0.0857949	+	0.348720i
$473$		−	4674.39i		−	0.454395i
$474$	−131.555	+	190.649i	−0.0127480	+	0.0184742i
$475$	5784.37			0.558748
$476$	31248.3	−	11861.0i	3.00896	−	1.14212i
$477$		−	3842.73i		−	0.368861i
$478$	6265.52	−	9079.92i	0.599536	−	0.868840i
$479$		−	7282.92i		−	0.694708i	−0.937734	−	0.347354i	$-0.887080\pi$
$479$		−	7282.92i		−	0.694708i	0.937734	−	0.347354i	$-0.112920\pi$
$480$	−443.219	−	3628.81i	−0.0421461	−	0.345066i
$481$	−7808.60	−	10236.1i	−0.740211	−	0.970326i
$482$	10702.6	−	15510.0i	1.01139	−	1.46569i
$483$	−8210.17			−0.773449
$484$	−2949.82	−	7771.41i	−0.277030	−	0.729847i
$485$			3909.01i			0.365978i
$486$	−390.355	+	565.698i	−0.0364339	+	0.0527996i
$487$			10707.6i			0.996324i	0.867084	+	0.498162i	$0.165992\pi$
$487$			10707.6i			0.996324i	−0.867084	+	0.498162i	$0.834008\pi$
$488$	13841.5	+	3405.39i	1.28396	+	0.315891i
$489$		−	9374.16i		−	0.866901i
$490$	8986.82	+	6201.28i	0.828537	+	0.571725i
$491$			11047.7i			1.01543i	0.861526	+	0.507713i	$0.169509\pi$
$491$			11047.7i			1.01543i	−0.861526	+	0.507713i	$0.830491\pi$
$492$	596.793	+	1572.27i	0.0546860	+	0.144072i
$493$			36584.7i			3.34217i
$494$	458.527	+	9613.04i	0.0417614	+	0.875528i
$495$	−1035.21			−0.0939986
$496$	1598.76	+	1802.58i	0.144731	+	0.163182i
$497$	20917.3			1.88786
$498$	−5256.27	+	7617.32i	−0.472970	+	0.685423i
$499$	−3115.74			−0.279518			−0.139759	−	0.990186i	$-0.544633\pi$
$499$	−3115.74			−0.279518			−0.139759	+	0.990186i	$0.544633\pi$
$500$	−3911.76	−	10305.7i	−0.349879	−	0.921768i
$501$	3186.03			0.284115
$502$	−6053.67	+	8772.90i	−0.538224	+	0.779988i
$503$	−18379.5			−1.62923			−0.814615	−	0.580002i	$-0.803052\pi$
$503$	−18379.5			−1.62923			−0.814615	+	0.580002i	$0.803052\pi$
$504$	−5986.46	−	1472.84i	−0.529083	−	0.130169i
$505$		−	4965.44i		−	0.437543i
$506$	3595.91	+	2481.33i	0.315924	+	0.218001i
$507$	6356.68	+	1741.82i	0.556824	+	0.152578i
$508$	−3145.30	−	8286.41i	−0.274705	−	0.723720i
$509$	−17510.5			−1.52483			−0.762415	−	0.647089i	$-0.775986\pi$
$509$	−17510.5			−1.52483			−0.762415	+	0.647089i	$0.775986\pi$
$510$	4477.33	−	6488.49i	0.388744	−	0.563363i
$511$	1928.89			0.166984
$512$	−7671.40	+	8681.44i	−0.662170	+	0.749354i
$513$		−	1960.01i		−	0.168687i
$514$	469.318	+	323.849i	0.0402738	+	0.0277906i
$515$	13612.8			1.16476
$516$	−2329.98	−	6138.41i	−0.198782	−	0.523699i
$517$			7174.71i			0.610335i
$518$	−13357.4	+	19357.4i	−1.13299	+	1.64192i
$519$	2263.83			0.191466
$520$	6546.78	−	2848.83i	0.552106	−	0.240249i
$521$	−2070.02			−0.174067			−0.0870337	−	0.996205i	$-0.527739\pi$
$521$	−2070.02			−0.174067			−0.0870337	+	0.996205i	$0.527739\pi$
$522$	3832.53	−	5554.06i	0.321351	−	0.465698i
$523$		−	14029.5i		−	1.17297i	−0.809959	−	0.586487i	$-0.800510\pi$
$523$		−	14029.5i		−	1.17297i	0.809959	−	0.586487i	$-0.199490\pi$
$524$	1522.52	−	577.908i	0.126931	−	0.0481795i
$525$	−7236.64			−0.601587
$526$	2328.71	+	1606.91i	0.193035	+	0.133202i
$527$			5195.69i			0.429465i
$528$	2176.83	+	2454.34i	0.179421	+	0.202294i
$529$	−3994.51			−0.328307
$530$	4617.27	−	6691.29i	0.378417	−	0.548398i
$531$	1464.73			0.119706
$532$	16436.5	−	6238.87i	1.33950	−	0.508439i
$533$	−2611.35	+	1992.06i	−0.212214	+	0.161887i
$534$	−8839.94	−	6099.93i	−0.716370	−	0.494325i
$535$			4267.65i			0.344872i
$536$	973.247	−	3955.83i	0.0784288	−	0.318780i
$537$	10623.1			0.853672
$538$	−5735.80	+	8312.25i	−0.459643	+	0.666109i
$539$	−9798.20			−0.783003
$540$	−1359.44	+	516.007i	−0.108335	+	0.0411211i
$541$	24526.4			1.94911			0.974557	−	0.224139i	$-0.0719569\pi$
$541$	24526.4			1.94911			0.974557	+	0.224139i	$0.0719569\pi$
$542$	6674.39	−	9672.45i	0.528948	−	0.766545i
$543$	−5739.49			−0.453600
$544$	−24798.2	+	3028.83i	−1.95444	+	0.238713i
$545$	−12162.3			−0.955915
$546$	−573.649	−	12026.6i	−0.0449632	−	0.942655i
$547$			19964.2i			1.56052i	0.625453	+	0.780262i	$0.284914\pi$
$547$			19964.2i			1.56052i	−0.625453	+	0.780262i	$0.715086\pi$
$548$	17365.3	−	6591.39i	1.35366	−	0.513815i
$549$		−	5669.59i		−	0.440750i
$550$	3169.52	+	2187.10i	0.245725	+	0.169561i
$551$			19243.5i			1.48784i
$552$	5958.98	+	1466.08i	0.459477	+	0.113044i
$553$			826.394i			0.0635477i
$554$	3896.77	−	5647.15i	0.298841	−	0.433076i
$555$			5547.15i			0.424258i
$556$	−7718.60	+	2929.77i	−0.588744	+	0.223471i
$557$	−14803.3			−1.12610			−0.563049	−	0.826424i	$-0.690372\pi$
$557$	−14803.3			−1.12610			−0.563049	+	0.826424i	$0.690372\pi$
$558$	544.289	−	788.777i	0.0412932	−	0.0598416i
$559$	10195.1	−	7777.34i	0.771392	−	0.588455i
$560$	−8654.43	−	9757.71i	−0.653065	−	0.736319i
$561$			7074.31i			0.532402i
$562$	−1482.24	+	2148.05i	−0.111254	+	0.161228i
$563$		−	14929.0i		−	1.11755i	−0.829318	−	0.558777i	$-0.811271\pi$
$563$		−	14929.0i		−	1.11755i	0.829318	−	0.558777i	$-0.188729\pi$
$564$	3576.28	+	9421.83i	0.267001	+	0.703423i
$565$	−334.000			−0.0248699
$566$	9824.58	−	14237.7i	0.729607	−	1.05734i
$567$			2452.10i			0.181620i
$568$	−15181.9	−	3735.17i	−1.12151	−	0.275923i
$569$	2044.26			0.150615			0.0753073	−	0.997160i	$-0.476006\pi$
$569$	2044.26			0.150615			0.0753073	+	0.997160i	$0.476006\pi$
$570$	2355.07	−	3412.93i	0.173058	−	0.250793i
$571$		−	4689.23i		−	0.343674i	−0.985125	−	0.171837i	$-0.945030\pi$
$571$		−	4689.23i		−	0.343674i	0.985125	−	0.171837i	$-0.0549703\pi$
$572$	−3383.49	+	5440.79i	−0.247327	+	0.397711i
$573$			11905.2i			0.867967i
$574$	4938.29	+	3407.63i	0.359095	+	0.247790i
$575$	7203.43			0.522441
$576$	4082.00	+	2137.98i	0.295283	+	0.154657i
$577$		−	14221.4i		−	1.02607i	−0.858367	−	0.513037i	$-0.828520\pi$
$577$		−	14221.4i		−	1.02607i	0.858367	−	0.513037i	$-0.171480\pi$
$578$	−32903.0	−	22704.4i	−2.36779	−	1.63388i
$579$	12231.2			0.877913
$580$	13347.0	−	5066.18i	0.955528	−	0.362693i
$581$			33018.4i			2.35772i
$582$	−4055.40	−	2798.39i	−0.288834	−	0.199308i
$583$			7295.42i			0.518260i
$584$	−1399.99	−	344.438i	−0.0991989	−	0.0244057i
$585$	−1722.40	−	2257.86i	−0.121731	−	0.159574i
$586$	−10353.2	−	7144.12i	−0.729839	−	0.503619i
$587$	−19391.9			−1.36352			−0.681762	−	0.731574i	$-0.738786\pi$
$587$	−19391.9			−1.36352			−0.681762	+	0.731574i	$0.738786\pi$
$588$	−12867.0	+	4883.97i	−0.902426	+	0.342537i
$589$			2732.92i			0.191185i
$590$	2550.52	+	1759.96i	0.177972	+	0.122808i
$591$			2629.41i			0.183011i
$592$	13151.5	−	11664.5i	0.913046	−	0.809810i
$593$			15694.8i			1.08686i	0.839454	+	0.543431i	$0.182875\pi$
$593$			15694.8i			1.08686i	−0.839454	+	0.543431i	$0.817125\pi$
$594$	741.089	−	1073.98i	0.0511907	−	0.0741849i
$595$		−	28125.3i		−	1.93786i
$596$	1696.62	+	4469.81i	0.116605	+	0.307199i
$597$		−	14373.1i		−	0.985344i
$598$	571.016	+	11971.4i	0.0390478	+	0.818638i
$599$	4716.77			0.321740			0.160870	−	0.986976i	$-0.448570\pi$
$599$	4716.77			0.321740			0.160870	+	0.986976i	$0.448570\pi$
$600$	5252.39	+	1292.24i	0.357380	+	0.0879255i
$601$	−16446.9			−1.11628			−0.558140	−	0.829747i	$-0.688485\pi$
$601$	−16446.9			−1.11628			−0.558140	+	0.829747i	$0.688485\pi$
$602$	−19279.9	−	13303.9i	−1.30530	−	0.900711i
$603$	−1620.34			−0.109429
$604$	−1155.87	+	438.738i	−0.0778671	+	0.0295563i
$605$	−6994.73			−0.470043
$606$	5151.38	+	3554.67i	0.345315	+	0.238281i
$607$	−12626.9			−0.844331			−0.422165	−	0.906519i	$-0.638730\pi$
$607$	−12626.9			−0.844331			−0.422165	+	0.906519i	$0.638730\pi$
$608$	−13043.8	+	1593.15i	−0.870058	+	0.106268i
$609$		−	24074.9i		−	1.60191i
$610$	6812.34	−	9872.36i	0.452170	−	0.655279i
$611$	−15648.5	+	11937.4i	−1.03612	+	0.790402i
$612$	3526.23	+	9289.99i	0.232908	+	0.613604i
$613$	20622.8			1.35880			0.679402	−	0.733767i	$-0.262239\pi$
$613$	20622.8			1.35880			0.679402	+	0.733767i	$0.262239\pi$
$614$	−8228.70	−	5678.14i	−0.540852	−	0.373210i
$615$	1415.14			0.0927869
$616$	11365.3	+	2796.18i	0.743377	+	0.182892i
$617$		−	5795.05i		−	0.378120i	−0.981966	−	0.189060i	$-0.939456\pi$
$617$		−	5795.05i		−	0.378120i	0.981966	−	0.189060i	$-0.0605440\pi$
$618$	−9745.17	+	14122.6i	−0.634317	+	0.919245i
$619$	−3388.09			−0.219998			−0.109999	−	0.993932i	$-0.535085\pi$
$619$	−3388.09			−0.219998			−0.109999	+	0.993932i	$0.535085\pi$
$620$	1895.52	−	719.491i	0.122784	−	0.0466055i
$621$		−	2440.85i		−	0.157726i
$622$	−7224.44	−	4985.16i	−0.465713	−	0.321361i
$623$	−38318.0			−2.46417
$624$	−1731.21	+	8831.37i	−0.111064	+	0.566567i
$625$	684.572			0.0438126
$626$	10557.9	+	7285.37i	0.674085	+	0.465147i
$627$			3721.07i			0.237010i
$628$	2837.03	−	1076.86i	0.180271	−	0.0684259i
$629$	37907.5			2.40297
$630$	−2946.35	+	4269.81i	−0.186326	+	0.270021i
$631$		−	5179.44i		−	0.326768i	−0.986563	−	0.163384i	$-0.947759\pi$
$631$		−	5179.44i		−	0.326768i	0.986563	−	0.163384i	$-0.0522409\pi$
$632$	147.568	−	599.801i	0.00928787	−	0.0377513i
$633$	−4350.82			−0.273190
$634$	−24040.9	−	16589.2i	−1.50597	−	1.03918i
$635$	−7458.26			−0.466098
$636$	3636.44	+	9580.35i	0.226721	+	0.597304i
$637$	−16302.4	−	21370.5i	−1.01401	−	1.32924i
$638$	−7276.05	+	10544.4i	−0.451507	+	0.654319i
$639$			6218.62i			0.384984i
$640$	4539.00	+	8627.60i	0.280344	+	0.532868i
$641$	10964.8			0.675639			0.337820	−	0.941211i	$-0.390311\pi$
$641$	10964.8			0.675639			0.337820	+	0.941211i	$0.390311\pi$
$642$	−4427.46	−	3055.13i	−0.272178	−	0.187814i
$643$	−23689.7			−1.45293			−0.726463	−	0.687206i	$-0.758837\pi$
$643$	−23689.7			−1.45293			−0.726463	+	0.687206i	$0.758837\pi$
$644$	20468.9	−	7769.43i	1.25246	−	0.475401i
$645$	−5524.94			−0.337278
$646$	−23322.9	−	16093.8i	−1.42048	−	0.980188i
$647$	16797.2			1.02066			0.510329	−	0.859979i	$-0.329524\pi$
$647$	16797.2			1.02066			0.510329	+	0.859979i	$0.329524\pi$
$648$	437.868	−	1779.75i	0.0265449	−	0.107894i
$649$	−2780.80			−0.168191
$650$	503.307	+	10551.9i	0.0303713	+	0.636735i
$651$		−	3419.07i		−	0.205843i
$652$	8870.94	+	23370.8i	0.532842	+	1.40379i
$653$			7732.84i			0.463414i	0.972786	+	0.231707i	$0.0744311\pi$
$653$			7732.84i			0.463414i	−0.972786	+	0.231707i	$0.925569\pi$
$654$	8706.74	−	12617.7i	0.520582	−	0.754421i
$655$		−	1370.36i		−	0.0817471i
$656$	−2975.74	−	3355.09i	−0.177108	−	0.199687i
$657$			573.450i			0.0340524i
$658$	29592.7	+	20420.2i	1.75326	+	1.20982i
$659$			1290.92i			0.0763081i	0.999272	+	0.0381540i	$0.0121478\pi$
$659$			1290.92i			0.0763081i	−0.999272	+	0.0381540i	$0.987852\pi$
$660$	2580.89	−	979.639i	0.152214	−	0.0577763i
$661$	−5515.38			−0.324544			−0.162272	−	0.986746i	$-0.551882\pi$
$661$	−5515.38			−0.324544			−0.162272	+	0.986746i	$0.551882\pi$
$662$	2843.80	+	1962.34i	0.166960	+	0.115209i
$663$	−15429.5	+	11770.4i	−0.903819	+	0.689477i
$664$	5896.05	−	23964.9i	0.344595	−	1.40063i
$665$		−	14793.9i		−	0.862679i
$666$	−5754.87	−	3971.10i	−0.334830	−	0.231047i
$667$			23964.4i			1.39116i
$668$	−7943.13	+	3015.00i	−0.460073	+	0.174631i
$669$	749.385			0.0433078
$670$	−2821.48	−	1946.94i	−0.162691	−	0.112264i
$671$			10763.7i			0.619267i
$672$	16318.7	−	1993.15i	0.936765	−	0.114416i
$673$	33159.3			1.89925			0.949625	−	0.313388i	$-0.101464\pi$
$673$	33159.3			1.89925			0.949625	+	0.313388i	$0.101464\pi$
$674$	23667.3	+	16331.4i	1.35257	+	0.933329i
$675$		−	2151.42i		−	0.122679i
$676$	−17496.2	+	1672.89i	−0.995460	+	0.0951804i
$677$		−	5403.55i		−	0.306758i	−0.988167	−	0.153379i	$-0.950984\pi$
$677$		−	5403.55i		−	0.306758i	0.988167	−	0.153379i	$-0.0490156\pi$
$678$	239.105	−	346.508i	0.0135439	−	0.0196277i
$679$	−17578.7			−0.993534
$680$	−5022.30	+	20413.5i	−0.283230	+	1.15121i
$681$		−	1455.41i		−	0.0818964i
$682$	−1033.33	+	1497.49i	−0.0580181	+	0.0840791i
$683$	9734.72			0.545372			0.272686	−	0.962103i	$-0.412088\pi$
$683$	9734.72			0.545372			0.272686	+	0.962103i	$0.412088\pi$
$684$	1854.79	+	4886.51i	0.103684	+	0.273159i
$685$		−	15629.8i		−	0.871800i
$686$	−11206.8	+	16240.7i	−0.623726	+	0.903896i
$687$		−	2161.71i		−	0.120050i
$688$	11617.8	+	13098.8i	0.643784	+	0.725855i
$689$	−15911.7	+	12138.2i	−0.879810	+	0.671162i
$690$	2932.82	−	4250.21i	0.161813	−	0.234497i
$691$	−23352.7			−1.28564			−0.642820	−	0.766017i	$-0.722236\pi$
$691$	−23352.7			−1.28564			−0.642820	+	0.766017i	$0.722236\pi$
$692$	−5643.97	+	2142.30i	−0.310045	+	0.117685i
$693$		−	4655.32i		−	0.255182i
$694$	10164.9	−	14730.9i	0.555988	−	0.805732i
$695$			6947.20i			0.379169i
$696$	−4299.01	+	17473.7i	−0.234129	+	0.951634i
$697$		−	9670.62i		−	0.525539i
$698$	−3973.21	−	2741.68i	−0.215456	−	0.148674i
$699$			12105.8i			0.655056i
$700$	18041.7	−	6848.16i	0.974163	−	0.369766i
$701$		−	18936.4i		−	1.02028i	−0.860090	−	0.510142i	$-0.829593\pi$
$701$		−	18936.4i		−	1.02028i	0.860090	−	0.510142i	$-0.170407\pi$
$702$	3575.45	−	170.543i	0.192232	−	0.00916915i
$703$	19939.2			1.06973
$704$	−7749.66	−	4058.96i	−0.414881	−	0.217298i
$705$	8480.21			0.453026
$706$	3707.17	−	5372.38i	0.197622	−	0.286391i
$707$	22329.4			1.18781
$708$	−3651.74	+	1386.10i	−0.193843	+	0.0735776i
$709$	10430.2			0.552488			0.276244	−	0.961088i	$-0.410910\pi$
$709$	10430.2			0.552488			0.276244	+	0.961088i	$0.410910\pi$
$710$	−7472.04	+	10828.4i	−0.394959	+	0.572369i
$711$	−245.684			−0.0129590
$712$	27811.4	+	6842.39i	1.46387	+	0.360154i
$713$			3403.38i			0.178762i
$714$	29178.6	+	20134.4i	1.52938	+	1.05534i
$715$	3269.98	+	4286.54i	0.171035	+	0.224206i
$716$	−26484.6	+	10052.9i	−1.38237	+	0.524710i
$717$	11701.0			0.609461
$718$	−15012.6	+	21756.1i	−0.780314	+	1.13082i
$719$	18026.5			0.935013			0.467507	−	0.883990i	$-0.345152\pi$
$719$	18026.5			0.935013			0.467507	+	0.883990i	$0.345152\pi$
$720$	2900.93	−	2572.92i	0.150154	−	0.133177i
$721$			61216.4i			3.16202i
$722$	3699.79	+	2553.01i	0.190709	+	0.131597i
$723$	19987.3			1.02813
$724$	14309.2	−	5431.38i	0.734525	−	0.278806i
$725$			21122.8i			1.08204i
$726$	5007.40	−	7256.67i	0.255981	−	0.370964i
$727$	−25211.7			−1.28618			−0.643088	−	0.765792i	$-0.722347\pi$
$727$	−25211.7			−1.28618			−0.643088	+	0.765792i	$0.722347\pi$
$728$	12811.1	+	29440.7i	0.652214	+	1.49882i
$729$	−729.000			−0.0370370
$730$	−689.034	+	998.539i	−0.0349346	+	0.0506268i
$731$			37755.7i			1.91032i
$732$	5365.23	+	14134.9i	0.270908	+	0.713717i
$733$	20215.1			1.01864			0.509319	−	0.860578i	$-0.329897\pi$
$733$	20215.1			1.01864			0.509319	+	0.860578i	$0.329897\pi$
$734$	−22608.7	−	15601.0i	−1.13693	−	0.784526i
$735$			11581.1i			0.581189i
$736$	−16243.8	+	1984.00i	−0.813523	+	0.0993629i
$737$	3076.22			0.153750
$738$	−1013.07	+	1468.13i	−0.0505308	+	0.0732286i
$739$	−9885.57			−0.492079			−0.246040	−	0.969260i	$-0.579129\pi$
$739$	−9885.57			−0.492079			−0.246040	+	0.969260i	$0.579129\pi$
$740$	−5249.36	−	13829.6i	−0.260771	−	0.687011i
$741$	−8115.88	+	6191.19i	−0.402354	+	0.306935i
$742$	30090.5	+	20763.7i	1.48876	+	1.02730i
$743$			17167.0i			0.847638i	0.905747	+	0.423819i	$0.139311\pi$
$743$			17167.0i			0.847638i	−0.905747	+	0.423819i	$0.860689\pi$
$744$	−610.538	+	2481.58i	−0.0300852	+	0.122284i
$745$	4023.10			0.197845
$746$	5016.45	−	7269.78i	0.246200	−	0.356790i
$747$	−9816.24			−0.480800
$748$	−6694.55	−	17637.0i	−0.327242	−	0.862131i
$749$	−19191.5			−0.936238
$750$	6640.32	−	9623.08i	0.323294	−	0.468513i
$751$	6314.05			0.306795			0.153397	−	0.988165i	$-0.450979\pi$
$751$	6314.05			0.306795			0.153397	+	0.988165i	$0.450979\pi$
$752$	−17832.1	−	20105.4i	−0.864720	−	0.974956i
$753$	−11305.4			−0.547134
$754$	−35103.9	+	1674.40i	−1.69550	+	0.0808729i
$755$			1040.35i			0.0501487i
$756$	−2320.47	−	6113.36i	−0.111633	−	0.294102i
$757$			19510.4i			0.936749i	0.883530	+	0.468375i	$0.155160\pi$
$757$			19510.4i			0.936749i	−0.883530	+	0.468375i	$0.844840\pi$
$758$	−995.458	−	686.907i	−0.0477001	−	0.0329150i
$759$			4633.95i			0.221610i
$760$	−2641.72	+	10737.5i	−0.126086	+	0.512485i
$761$		−	22481.2i		−	1.07089i	−0.844571	−	0.535443i	$-0.820145\pi$
$761$		−	22481.2i		−	1.07089i	0.844571	−	0.535443i	$-0.179855\pi$
$762$	5339.23	−	7737.55i	0.253832	−	0.367850i
$763$		−	54693.3i		−	2.59506i
$764$	−11266.1	−	29680.9i	−0.533497	−	1.40552i
$765$	8361.54			0.395179
$766$	4208.10	−	6098.33i	0.198492	−	0.287652i
$767$	−4626.74	−	6065.08i	−0.217812	−	0.285525i
$768$	−12200.1	−	1467.36i	−0.573219	−	0.0689439i
$769$		−	7820.77i		−	0.366741i	−0.983044	−	0.183371i	$-0.941299\pi$
$769$		−	7820.77i		−	0.366741i	0.983044	−	0.183371i	$-0.0587008\pi$
$770$	5593.64	−	8106.23i	0.261793	−	0.379387i
$771$			604.798i			0.0282507i
$772$	−30493.7	+	11574.6i	−1.42162	+	0.539610i
$773$	−2592.26			−0.120617			−0.0603085	−	0.998180i	$-0.519208\pi$
$773$	−2592.26			−0.120617			−0.0603085	+	0.998180i	$0.519208\pi$
$774$	3955.20	−	5731.83i	0.183678	−	0.266184i

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:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	312.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.32798 - 1.60640i) q^{2} -3.00000i q^{3} +(2.83895 + 7.47933i) q^{4} +6.73184 q^{5} +(-4.81920 + 6.98393i) q^{6} +30.2729i q^{7} +(5.40578 - 21.9722i) q^{8} -9.00000 q^{9} +(-15.6716 - 10.8140i) q^{10} +17.0865 q^{11} +(22.4380 - 8.51686i) q^{12} +(28.4288 + 37.2667i) q^{13} +(48.6304 - 70.4746i) q^{14} -20.1955i q^{15} +(-47.8807 + 42.4669i) q^{16} -138.010 q^{17} +(20.9518 + 14.4576i) q^{18} -72.5929 q^{19} +(19.1114 + 50.3496i) q^{20} +90.8187 q^{21} +(-39.7769 - 27.4477i) q^{22} -90.4018 q^{23} +(-65.9166 - 16.2173i) q^{24} -79.6824 q^{25} +(-6.31642 - 132.424i) q^{26} +27.0000i q^{27} +(-226.421 + 85.9433i) q^{28} -265.087i q^{29} +(-32.4421 + 47.0147i) q^{30} -37.6473i q^{31} +(179.684 - 21.9464i) q^{32} -51.2595i q^{33} +(321.284 + 221.699i) q^{34} +203.792i q^{35} +(-25.5506 - 67.3140i) q^{36} -274.672 q^{37} +(168.995 + 116.613i) q^{38} +(111.800 - 85.2864i) q^{39} +(36.3908 - 147.913i) q^{40} +70.0720i q^{41} +(-211.424 - 145.891i) q^{42} -273.572i q^{43} +(48.5077 + 127.795i) q^{44} -60.5865 q^{45} +(210.453 + 145.222i) q^{46} +419.905i q^{47} +(127.401 + 143.642i) q^{48} -573.448 q^{49} +(185.499 + 128.002i) q^{50} +414.030i q^{51} +(-198.021 + 318.427i) q^{52} +426.970i q^{53} +(43.3728 - 62.8554i) q^{54} +115.023 q^{55} +(665.162 + 163.649i) q^{56} +217.779i q^{57} +(-425.837 + 617.117i) q^{58} -162.748 q^{59} +(151.049 - 57.3341i) q^{60} +629.954i q^{61} +(-60.4766 + 87.6419i) q^{62} -272.456i q^{63} +(-453.555 - 237.554i) q^{64} +(191.378 + 250.873i) q^{65} +(-82.3432 + 119.331i) q^{66} +180.038 q^{67} +(-391.804 - 1032.22i) q^{68} +271.206i q^{69} +(327.372 - 474.423i) q^{70} -690.958i q^{71} +(-48.6520 + 197.750i) q^{72} -63.7166i q^{73} +(639.431 + 441.234i) q^{74} +239.047i q^{75} +(-206.088 - 542.946i) q^{76} +517.257i q^{77} +(-397.272 + 18.9493i) q^{78} +27.2982 q^{79} +(-322.325 + 285.880i) q^{80} +81.0000 q^{81} +(112.564 - 163.126i) q^{82} +1090.69 q^{83} +(257.830 + 679.262i) q^{84} -929.060 q^{85} +(-439.467 + 636.870i) q^{86} -795.262 q^{87} +(92.3658 - 375.428i) q^{88} +1265.75i q^{89} +(141.044 + 97.3263i) q^{90} +(-1128.17 + 860.622i) q^{91} +(-256.647 - 676.145i) q^{92} -112.942 q^{93} +(674.536 - 977.530i) q^{94} -488.684 q^{95} +(-65.8393 - 539.052i) q^{96} +580.675i q^{97} +(1334.97 + 921.187i) q^{98} -153.778 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52}+ \cdots + 2480 q^{95}+O(q^{100}) \) 84 * q - 756 * q^9 - 36 * q^10 + 12 * q^12 - 208 * q^14 - 148 * q^16 - 104 * q^17 + 620 * q^22 + 2188 * q^25 + 444 * q^26 - 204 * q^30 - 40 * q^38 - 1924 * q^40 + 192 * q^42 + 624 * q^48 - 3396 * q^49 - 1292 * q^52 - 1616 * q^55 + 608 * q^56 - 2120 * q^62 - 2856 * q^64 + 696 * q^65 - 396 * q^66 - 2536 * q^68 - 3936 * q^74 - 156 * q^78 + 3160 * q^79 + 6804 * q^81 + 4276 * q^82 - 2088 * q^87 + 1780 * q^88 + 324 * q^90 + 4792 * q^92 - 860 * q^94 + 2480 * q^95

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