LMFDB - Embedded newform 315.3.ca.b.37.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,3,Mod(37,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("315.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	315.ca (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.58312832735$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.10
Character	$\chi$	$=$	315.37
Dual form			315.3.ca.b.298.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.445275 - 0.119311i) q^{2} +(-3.28007 + 1.89375i) q^{4} +(-4.59550 + 1.97013i) q^{5} +(-0.171680 - 6.99789i) q^{7} +(-2.53844 + 2.53844i) q^{8} +O(q^{10})$	\(q+(0.445275 - 0.119311i) q^{2} +(-3.28007 + 1.89375i) q^{4} +(-4.59550 + 1.97013i) q^{5} +(-0.171680 - 6.99789i) q^{7} +(-2.53844 + 2.53844i) q^{8} +(-1.81120 + 1.42554i) q^{10} +(7.70109 + 13.3387i) q^{11} +(17.1139 - 17.1139i) q^{13} +(-0.911371 - 3.09550i) q^{14} +(6.74755 - 11.6871i) q^{16} +(5.59776 - 20.8911i) q^{17} +(-15.6219 - 9.01929i) q^{19} +(11.3426 - 15.1649i) q^{20} +(5.02055 + 5.02055i) q^{22} +(-2.98781 - 11.1507i) q^{23} +(17.2372 - 18.1075i) q^{25} +(5.57852 - 9.66228i) q^{26} +(13.8154 + 22.6284i) q^{28} +1.87676i q^{29} +(9.52708 + 16.5014i) q^{31} +(5.32665 - 19.8793i) q^{32} -9.97017i q^{34} +(14.5757 + 31.8206i) q^{35} +(-4.95991 + 1.32900i) q^{37} +(-8.03212 - 2.15220i) q^{38} +(6.66433 - 16.6665i) q^{40} +51.4301 q^{41} +(18.4492 - 18.4492i) q^{43} +(-50.5202 - 29.1678i) q^{44} +(-2.66080 - 4.60863i) q^{46} +(-22.4470 + 6.01467i) q^{47} +(-48.9411 + 2.40280i) q^{49} +(5.51485 - 10.1194i) q^{50} +(-23.7254 + 88.5443i) q^{52} +(-75.2491 - 20.1629i) q^{53} +(-61.6693 - 46.1257i) q^{55} +(18.1995 + 17.3279i) q^{56} +(0.223918 + 0.835675i) q^{58} +(40.1729 - 23.1938i) q^{59} +(12.3169 - 21.3335i) q^{61} +(6.21097 + 6.21097i) q^{62} +44.4931i q^{64} +(-44.9303 + 112.364i) q^{65} +(29.9876 - 111.915i) q^{67} +(21.2015 + 79.1251i) q^{68} +(10.2867 + 12.4298i) q^{70} -63.9145 q^{71} +(13.3047 + 3.56497i) q^{73} +(-2.04996 + 1.18354i) q^{74} +68.3210 q^{76} +(92.0205 - 56.1814i) q^{77} +(45.3292 + 26.1708i) q^{79} +(-7.98321 + 67.0016i) q^{80} +(22.9005 - 6.13617i) q^{82} +(34.3710 - 34.3710i) q^{83} +(15.4338 + 107.033i) q^{85} +(6.01376 - 10.4161i) q^{86} +(-53.4082 - 14.3107i) q^{88} +(-44.5648 - 25.7295i) q^{89} +(-122.700 - 116.823i) q^{91} +(30.9168 + 30.9168i) q^{92} +(-9.27748 + 5.35636i) q^{94} +(89.5594 + 10.6710i) q^{95} +(39.0134 + 39.0134i) q^{97} +(-21.5055 + 6.90911i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8}+O(q^{10}) $ 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8	$ 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8} - 16 q^{10} - 16 q^{11} + 80 q^{16} - 56 q^{17} - 96 q^{22} - 72 q^{23} - 4 q^{25} + 288 q^{26} - 380 q^{28} - 136 q^{31} + 48 q^{32} - 76 q^{35} - 28 q^{37} + 68 q^{38} + 164 q^{40} - 128 q^{41} + 344 q^{43} + 240 q^{46} - 412 q^{47} + 72 q^{50} + 388 q^{52} + 40 q^{53} - 8 q^{55} + 864 q^{56} + 56 q^{58} - 216 q^{61} + 912 q^{62} - 20 q^{65} - 368 q^{67} + 492 q^{68} + 416 q^{70} - 784 q^{71} - 316 q^{73} - 32 q^{76} - 844 q^{77} - 908 q^{80} + 556 q^{82} - 1408 q^{83} - 536 q^{85} - 1024 q^{86} + 372 q^{88} - 1064 q^{91} + 1704 q^{92} - 260 q^{95} + 352 q^{97} - 272 q^{98}+O(q^{100}) $ 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8 - 16 * q^10 - 16 * q^11 + 80 * q^16 - 56 * q^17 - 96 * q^22 - 72 * q^23 - 4 * q^25 + 288 * q^26 - 380 * q^28 - 136 * q^31 + 48 * q^32 - 76 * q^35 - 28 * q^37 + 68 * q^38 + 164 * q^40 - 128 * q^41 + 344 * q^43 + 240 * q^46 - 412 * q^47 + 72 * q^50 + 388 * q^52 + 40 * q^53 - 8 * q^55 + 864 * q^56 + 56 * q^58 - 216 * q^61 + 912 * q^62 - 20 * q^65 - 368 * q^67 + 492 * q^68 + 416 * q^70 - 784 * q^71 - 316 * q^73 - 32 * q^76 - 844 * q^77 - 908 * q^80 + 556 * q^82 - 1408 * q^83 - 536 * q^85 - 1024 * q^86 + 372 * q^88 - 1064 * q^91 + 1704 * q^92 - 260 * q^95 + 352 * q^97 - 272 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.445275	−	0.119311i	0.222637	−	0.0596555i	−0.145776	−	0.989318i	$-0.546568\pi$
$2$	0.445275	−	0.119311i	0.222637	−	0.0596555i	0.368413	+	0.929662i	$0.379901\pi$
$3$		0			0
$3$		0			0
$4$	−3.28007	+	1.89375i	−0.820017	+	0.473437i
$5$	−4.59550	+	1.97013i	−0.919099	+	0.394026i
$5$	−4.59550	+	1.97013i	−0.919099	+	0.394026i
$6$		0			0
$7$	−0.171680	−	6.99789i	−0.0245257	−	0.999699i
$7$	−0.171680	−	6.99789i	−0.0245257	−	0.999699i
$8$	−2.53844	+	2.53844i	−0.317305	+	0.317305i
$9$		0			0
$10$	−1.81120	+	1.42554i	−0.181120	+	0.142554i
$11$	7.70109	+	13.3387i	0.700099	+	1.21261i	0.968431	+	0.249280i	$0.0801941\pi$
$11$	7.70109	+	13.3387i	0.700099	+	1.21261i	−0.268333	+	0.963326i	$0.586473\pi$
$12$		0			0
$13$	17.1139	−	17.1139i	1.31646	−	1.31646i	0.399894	−	0.916561i	$-0.369047\pi$
$13$	17.1139	−	17.1139i	1.31646	−	1.31646i	0.916561	−	0.399894i	$-0.130953\pi$
$14$	−0.911371	−	3.09550i	−0.0650979	−	0.221107i
$15$		0			0
$16$	6.74755	−	11.6871i	0.421722	−	0.730444i
$17$	5.59776	−	20.8911i	0.329280	−	1.22889i	−0.580658	−	0.814147i	$-0.697205\pi$
$17$	5.59776	−	20.8911i	0.329280	−	1.22889i	0.909938	−	0.414743i	$-0.136129\pi$
$18$		0			0
$19$	−15.6219	−	9.01929i	−0.822203	−	0.474699i	0.0289723	−	0.999580i	$-0.490777\pi$
$19$	−15.6219	−	9.01929i	−0.822203	−	0.474699i	−0.851176	+	0.524881i	$0.824110\pi$
$20$	11.3426	−	15.1649i	0.567130	−	0.758244i
$21$		0			0
$22$	5.02055	+	5.02055i	0.228207	+	0.228207i
$23$	−2.98781	−	11.1507i	−0.129905	−	0.484812i	0.870062	−	0.492942i	$-0.164079\pi$
$23$	−2.98781	−	11.1507i	−0.129905	−	0.484812i	−0.999967	+	0.00813035i	$0.997412\pi$
$24$		0			0
$25$	17.2372	−	18.1075i	0.689486	−	0.724299i
$26$	5.57852	−	9.66228i	0.214558	−	0.371626i
$27$		0			0
$28$	13.8154	+	22.6284i	0.493406	+	0.808159i
$29$			1.87676i			0.0647160i	0.999476	+	0.0323580i	$0.0103017\pi$
$29$			1.87676i			0.0647160i	−0.999476	+	0.0323580i	$0.989698\pi$
$30$		0			0
$31$	9.52708	+	16.5014i	0.307325	+	0.532303i	0.977776	−	0.209651i	$-0.0672327\pi$
$31$	9.52708	+	16.5014i	0.307325	+	0.532303i	−0.670451	+	0.741954i	$0.733899\pi$
$32$	5.32665	−	19.8793i	0.166458	−	0.621229i
$33$		0			0
$34$		−	9.97017i		−	0.293240i
$35$	14.5757	+	31.8206i	0.416449	+	0.909159i
$36$		0			0
$37$	−4.95991	+	1.32900i	−0.134052	+	0.0359190i	−0.325221	−	0.945638i	$-0.605439\pi$
$37$	−4.95991	+	1.32900i	−0.134052	+	0.0359190i	0.191169	+	0.981557i	$0.438772\pi$
$38$	−8.03212	−	2.15220i	−0.211372	−	0.0566369i
$39$		0			0
$40$	6.66433	−	16.6665i	0.166608	−	0.416661i
$41$	51.4301			1.25439			0.627196	−	0.778861i	$-0.284203\pi$
$41$	51.4301			1.25439			0.627196	+	0.778861i	$0.284203\pi$
$42$		0			0
$43$	18.4492	−	18.4492i	0.429051	−	0.429051i	−0.459254	−	0.888305i	$-0.651883\pi$
$43$	18.4492	−	18.4492i	0.429051	−	0.429051i	0.888305	+	0.459254i	$0.151883\pi$
$44$	−50.5202	−	29.1678i	−1.14819	−	0.662905i
$45$		0			0
$46$	−2.66080	−	4.60863i	−0.0578434	−	0.100188i
$47$	−22.4470	+	6.01467i	−0.477597	+	0.127972i	−0.489583	−	0.871957i	$-0.662851\pi$
$47$	−22.4470	+	6.01467i	−0.477597	+	0.127972i	0.0119867	+	0.999928i	$0.496184\pi$
$48$		0			0
$49$	−48.9411	+	2.40280i	−0.998797	+	0.0490367i
$50$	5.51485	−	10.1194i	0.110297	−	0.202388i
$51$		0			0
$52$	−23.7254	+	88.5443i	−0.456257	+	1.70277i
$53$	−75.2491	−	20.1629i	−1.41979	−	0.380433i	−0.534384	−	0.845242i	$-0.679456\pi$
$53$	−75.2491	−	20.1629i	−1.41979	−	0.380433i	−0.885411	+	0.464809i	$0.846123\pi$
$54$		0			0
$55$	−61.6693	−	46.1257i	−1.12126	−	0.838648i
$56$	18.1995	+	17.3279i	0.324992	+	0.309428i
$57$		0			0
$58$	0.223918	+	0.835675i	0.00386066	+	0.0144082i
$59$	40.1729	−	23.1938i	0.680897	−	0.393116i	−0.119296	−	0.992859i	$-0.538064\pi$
$59$	40.1729	−	23.1938i	0.680897	−	0.393116i	0.800193	+	0.599743i	$0.204730\pi$
$60$		0			0
$61$	12.3169	−	21.3335i	0.201917	−	0.349730i	−0.747229	−	0.664566i	$-0.768616\pi$
$61$	12.3169	−	21.3335i	0.201917	−	0.349730i	0.949146	+	0.314836i	$0.101950\pi$
$62$	6.21097	+	6.21097i	0.100177	+	0.100177i
$63$		0			0
$64$			44.4931i			0.695205i
$65$	−44.9303	+	112.364i	−0.691235	+	1.72867i
$66$		0			0
$67$	29.9876	−	111.915i	0.447576	−	1.67038i	−0.261467	−	0.965212i	$-0.584206\pi$
$67$	29.9876	−	111.915i	0.447576	−	1.67038i	0.709043	−	0.705165i	$-0.249127\pi$
$68$	21.2015	+	79.1251i	0.311787	+	1.16360i
$69$		0			0
$70$	10.2867	+	12.4298i	0.146954	+	0.177569i
$71$	−63.9145			−0.900204			−0.450102	−	0.892977i	$-0.648612\pi$
$71$	−63.9145			−0.900204			−0.450102	+	0.892977i	$0.648612\pi$
$72$		0			0
$73$	13.3047	+	3.56497i	0.182256	+	0.0488352i	0.348792	−	0.937200i	$-0.386592\pi$
$73$	13.3047	+	3.56497i	0.182256	+	0.0488352i	−0.166537	+	0.986035i	$0.553258\pi$
$74$	−2.04996	+	1.18354i	−0.0277021	+	0.0159938i
$75$		0			0
$76$	68.3210			0.898961
$77$	92.0205	−	56.1814i	1.19507	−	0.729628i
$78$		0			0
$79$	45.3292	+	26.1708i	0.573788	+	0.331276i	0.758661	−	0.651486i	$-0.225854\pi$
$79$	45.3292	+	26.1708i	0.573788	+	0.331276i	−0.184873	+	0.982762i	$0.559187\pi$
$80$	−7.98321	+	67.0016i	−0.0997901	+	0.837520i
$81$		0			0
$82$	22.9005	−	6.13617i	0.279274	−	0.0748314i
$83$	34.3710	−	34.3710i	0.414109	−	0.414109i	−0.469058	−	0.883167i	$-0.655407\pi$
$83$	34.3710	−	34.3710i	0.414109	−	0.414109i	0.883167	+	0.469058i	$0.155407\pi$
$84$		0			0
$85$	15.4338	+	107.033i	0.181574	+	1.25922i
$86$	6.01376	−	10.4161i	0.0699275	−	0.121118i
$87$		0			0
$88$	−53.4082	−	14.3107i	−0.606911	−	0.162621i
$89$	−44.5648	−	25.7295i	−0.500728	−	0.289095i	0.228286	−	0.973594i	$-0.426688\pi$
$89$	−44.5648	−	25.7295i	−0.500728	−	0.289095i	−0.729014	+	0.684499i	$0.760021\pi$
$90$		0			0
$91$	−122.700	−	116.823i	−1.34835	−	1.28377i
$92$	30.9168	+	30.9168i	0.336052	+	0.336052i
$93$		0			0
$94$	−9.27748	+	5.35636i	−0.0986966	+	0.0569825i
$95$	89.5594	+	10.6710i	0.942731	+	0.112326i
$96$		0			0
$97$	39.0134	+	39.0134i	0.402200	+	0.402200i	0.879008	−	0.476808i	$-0.158206\pi$
$97$	39.0134	+	39.0134i	0.402200	+	0.402200i	−0.476808	+	0.879008i	$0.658206\pi$
$98$	−21.5055	+	6.90911i	−0.219444	+	0.0705011i
$99$		0			0
$100$	−22.2481	+	92.0365i	−0.222481	+	0.920365i
$101$	−79.6712	−	137.995i	−0.788824	−	1.36628i	−0.926688	−	0.375832i	$-0.877357\pi$
$101$	−79.6712	−	137.995i	−0.788824	−	1.36628i	0.137864	−	0.990451i	$-0.455976\pi$
$102$		0			0
$103$	26.2481	+	97.9591i	0.254835	+	0.951059i	0.968182	+	0.250247i	$0.0805119\pi$
$103$	26.2481	+	97.9591i	0.254835	+	0.951059i	−0.713346	+	0.700812i	$0.752821\pi$
$104$			86.8854i			0.835436i
$105$		0			0
$106$	−35.9122			−0.338794
$107$	9.51326	−	2.54907i	0.0889090	−	0.0238231i	−0.214090	−	0.976814i	$-0.568679\pi$
$107$	9.51326	−	2.54907i	0.0889090	−	0.0238231i	0.302999	+	0.952991i	$0.402012\pi$
$108$		0			0
$109$	−38.6718	+	22.3271i	−0.354787	+	0.204836i	−0.666792	−	0.745244i	$-0.732333\pi$
$109$	−38.6718	+	22.3271i	−0.354787	+	0.204836i	0.312005	+	0.950081i	$0.399000\pi$
$110$	−32.9631	−	13.1808i	−0.299664	−	0.119825i
$111$		0			0
$112$	−82.9435	−	45.2122i	−0.740567	−	0.403680i
$113$	−34.1599	+	34.1599i	−0.302300	+	0.302300i	−0.841913	−	0.539613i	$-0.818571\pi$
$113$	−34.1599	+	34.1599i	−0.302300	+	0.302300i	0.539613	+	0.841913i	$0.318571\pi$
$114$		0			0
$115$	35.6988	+	45.3565i	0.310424	+	0.394404i
$116$	−3.55412	−	6.15591i	−0.0306389	−	0.0530682i
$117$		0			0
$118$	15.1207	−	15.1207i	0.128141	−	0.128141i
$119$	−147.155	−	35.5860i	−1.23660	−	0.299042i
$120$		0			0
$121$	−58.1135	+	100.655i	−0.480277	+	0.831863i
$122$	2.93909	−	10.9688i	0.0240909	−	0.0899084i
$123$		0			0
$124$	−62.4989	−	36.0838i	−0.504024	−	0.290998i
$125$	−43.5392	+	117.172i	−0.348314	+	0.937378i
$126$		0			0
$127$	44.4734	+	44.4734i	0.350184	+	0.350184i	0.860178	−	0.509994i	$-0.170352\pi$
$127$	44.4734	+	44.4734i	0.350184	+	0.350184i	−0.509994	+	0.860178i	$0.670352\pi$
$128$	26.6151	+	99.3290i	0.207931	+	0.776008i
$129$		0			0
$130$	−6.60009	+	55.3934i	−0.0507700	+	0.426103i
$131$	112.718	−	195.234i	0.860446	−	1.49034i	−0.0110531	−	0.999939i	$-0.503518\pi$
$131$	112.718	−	195.234i	0.860446	−	1.49034i	0.871499	−	0.490397i	$-0.163148\pi$
$132$		0			0
$133$	−60.4341	+	110.869i	−0.454391	+	0.833598i
$134$		−	53.4109i		−	0.398589i
$135$		0			0
$136$	38.8213	+	67.2405i	0.285451	+	0.494416i
$137$	−9.15488	+	34.1665i	−0.0668239	+	0.249390i	−0.991255	−	0.131958i	$-0.957874\pi$
$137$	−9.15488	+	34.1665i	−0.0668239	+	0.249390i	0.924431	+	0.381349i	$0.124540\pi$
$138$		0			0
$139$			56.7049i			0.407949i	0.978976	+	0.203974i	$0.0653859\pi$
$139$			56.7049i			0.407949i	−0.978976	+	0.203974i	$0.934614\pi$
$140$	−108.069	−	76.7708i	−0.771925	−	0.548363i
$141$		0			0
$142$	−28.4595	+	7.62570i	−0.200419	+	0.0537021i
$143$	360.073	+	96.4812i	2.51799	+	0.674694i
$144$		0			0
$145$	−3.69747	−	8.62466i	−0.0254998	−	0.0594804i
$146$	6.34957			0.0434902
$147$		0			0
$148$	13.7520	−	13.7520i	0.0929191	−	0.0929191i
$149$	−79.1387	−	45.6907i	−0.531132	−	0.306649i	0.210345	−	0.977627i	$-0.432541\pi$
$149$	−79.1387	−	45.6907i	−0.531132	−	0.306649i	−0.741477	+	0.670978i	$0.765875\pi$
$150$		0			0
$151$	−45.6835	−	79.1262i	−0.302540	−	0.524015i	0.674171	−	0.738576i	$-0.264501\pi$
$151$	−45.6835	−	79.1262i	−0.302540	−	0.524015i	−0.976711	+	0.214561i	$0.931168\pi$
$152$	62.5501	−	16.7603i	0.411514	−	0.110265i
$153$		0			0
$154$	34.2713	−	35.9952i	0.222541	−	0.233735i
$155$	−76.2916	−	57.0625i	−0.492204	−	0.368145i
$156$		0			0
$157$	46.7269	−	174.387i	0.297623	−	1.11075i	−0.641488	−	0.767133i	$-0.721683\pi$
$157$	46.7269	−	174.387i	0.297623	−	1.11075i	0.939112	−	0.343613i	$-0.111651\pi$
$158$	23.3064	+	6.24494i	0.147509	+	0.0395249i
$159$		0			0
$160$	14.6863	+	101.850i	0.0917894	+	0.636560i
$161$	−77.5183	+	22.8228i	−0.481480	+	0.141756i
$162$		0			0
$163$	20.5517	+	76.7000i	0.126084	+	0.470552i	0.999876	−	0.0157477i	$-0.00501286\pi$
$163$	20.5517	+	76.7000i	0.126084	+	0.470552i	−0.873792	+	0.486300i	$0.838346\pi$
$164$	−168.694	+	97.3956i	−1.02862	+	0.593875i
$165$		0			0
$166$	11.2037	−	19.4054i	0.0674922	−	0.116900i
$167$	−15.2411	−	15.2411i	−0.0912643	−	0.0912643i	0.660001	−	0.751265i	$-0.270556\pi$
$167$	−15.2411	−	15.2411i	−0.0912643	−	0.0912643i	−0.751265	+	0.660001i	$0.770556\pi$
$168$		0			0
$169$		−	416.773i		−	2.46611i
$170$	19.6426	+	45.8179i	0.115544	+	0.269517i
$171$		0			0
$172$	−25.5765	+	95.4527i	−0.148700	+	0.554957i
$173$	−1.14313	−	4.26621i	−0.00660768	−	0.0246602i	0.962543	−	0.271128i	$-0.0873967\pi$
$173$	−1.14313	−	4.26621i	−0.00660768	−	0.0246602i	−0.969151	+	0.246468i	$0.920730\pi$
$174$		0			0
$175$	−129.673	−	117.515i	−0.740991	−	0.671515i
$176$	207.854			1.18099
$177$		0			0
$178$	−22.9134	−	6.13962i	−0.128727	−	0.0344923i
$179$	−9.12125	+	5.26616i	−0.0509567	+	0.0294199i	−0.525262	−	0.850941i	$-0.676033\pi$
$179$	−9.12125	+	5.26616i	−0.0509567	+	0.0294199i	0.474305	+	0.880360i	$0.342699\pi$
$180$		0			0
$181$	325.032			1.79575			0.897877	−	0.440246i	$-0.145109\pi$
$181$	325.032			1.79575			0.897877	+	0.440246i	$0.145109\pi$
$182$	−68.5733	−	37.3791i	−0.376776	−	0.205379i
$183$		0			0
$184$	35.8897	+	20.7209i	0.195053	+	0.112614i
$185$	20.1749	−	15.8791i	0.109054	−	0.0858330i
$186$		0			0
$187$	321.769	−	86.2177i	1.72069	−	0.461057i
$188$	62.2375	−	62.2375i	0.331051	−	0.331051i
$189$		0			0
$190$	41.1517	−	5.93391i	0.216588	−	0.0312311i
$191$	−119.545	+	207.058i	−0.625891	+	1.08408i	0.362477	+	0.931993i	$0.381931\pi$
$191$	−119.545	+	207.058i	−0.625891	+	1.08408i	−0.988368	+	0.152082i	$0.951402\pi$
$192$		0			0
$193$	−184.527	−	49.4439i	−0.956100	−	0.256186i	−0.253151	−	0.967427i	$-0.581467\pi$
$193$	−184.527	−	49.4439i	−0.956100	−	0.256186i	−0.702949	+	0.711241i	$0.748134\pi$
$194$	22.0264	+	12.7170i	0.113538	+	0.0655513i
$195$		0			0
$196$	155.980	−	100.563i	0.795815	−	0.513078i
$197$	60.9439	+	60.9439i	0.309360	+	0.309360i	0.844661	−	0.535301i	$-0.179802\pi$
$197$	60.9439	+	60.9439i	0.309360	+	0.309360i	−0.535301	+	0.844661i	$0.679802\pi$
$198$		0			0
$199$	−48.7356	+	28.1375i	−0.244903	+	0.141395i	−0.617428	−	0.786627i	$-0.711825\pi$
$199$	−48.7356	+	28.1375i	−0.244903	+	0.141395i	0.372525	+	0.928022i	$0.378492\pi$
$200$	2.20922	+	89.7202i	0.0110461	+	0.448601i
$201$		0			0
$202$	−51.9399	−	51.9399i	−0.257128	−	0.257128i
$203$	13.1334	−	0.322203i	0.0646965	−	0.00158721i
$204$		0			0
$205$	−236.347	+	101.324i	−1.15291	+	0.494264i
$206$	23.3752	+	40.4870i	0.113472	+	0.196539i
$207$		0			0
$208$	−84.5351	−	315.489i	−0.406419	−	1.51678i
$209$		−	277.833i		−	1.32935i
$210$		0			0
$211$	−57.8783			−0.274305			−0.137152	−	0.990550i	$-0.543795\pi$
$211$	−57.8783			−0.274305			−0.137152	+	0.990550i	$0.543795\pi$
$212$	285.006	−	76.3670i	1.34437	−	0.360222i
$213$		0			0
$214$	3.93188	−	2.27007i	0.0183733	−	0.0106078i
$215$	−48.4358	+	121.130i	−0.225283	+	0.563398i
$216$		0			0
$217$	113.839	−	69.5025i	0.524605	−	0.320288i
$218$	−14.5557	+	14.5557i	−0.0667692	+	0.0667692i
$219$		0			0
$220$	289.630	+	34.5092i	1.31650	+	0.156860i
$221$	−261.730	−	453.329i	−1.18430	−	2.05126i
$222$		0			0
$223$	118.966	−	118.966i	0.533481	−	0.533481i	−0.388125	−	0.921607i	$-0.626877\pi$
$223$	118.966	−	118.966i	0.533481	−	0.533481i	0.921607	+	0.388125i	$0.126877\pi$
$224$	−140.028	−	33.8624i	−0.625125	−	0.151172i
$225$		0			0
$226$	−11.1349	+	19.2862i	−0.0492694	+	0.0853371i
$227$	−87.4561	+	326.391i	−0.385269	+	1.43784i	0.452473	+	0.891778i	$0.350542\pi$
$227$	−87.4561	+	326.391i	−0.385269	+	1.43784i	−0.837742	+	0.546066i	$0.816125\pi$
$228$		0			0
$229$	−6.66275	−	3.84674i	−0.0290950	−	0.0167980i	0.485382	−	0.874302i	$-0.338681\pi$
$229$	−6.66275	−	3.84674i	−0.0290950	−	0.0167980i	−0.514477	+	0.857504i	$0.672014\pi$
$230$	21.3073	+	15.9368i	0.0926404	+	0.0692906i
$231$		0			0
$232$	−4.76405	−	4.76405i	−0.0205347	−	0.0205347i
$233$	−66.8075	−	249.329i	−0.286728	−	1.07008i	−0.947568	−	0.319555i	$-0.896466\pi$
$233$	−66.8075	−	249.329i	−0.286728	−	1.07008i	0.660840	−	0.750527i	$-0.270200\pi$
$234$		0			0
$235$	91.3056	−	71.8640i	0.388534	−	0.305804i
$236$	−87.8465	+	152.155i	−0.372231	+	0.644723i
$237$		0			0
$238$	−69.7702	+	1.71168i	−0.293152	+	0.00719193i
$239$			252.435i			1.05621i	0.849178	+	0.528107i	$0.177098\pi$
$239$			252.435i			1.05621i	−0.849178	+	0.528107i	$0.822902\pi$
$240$		0			0
$241$	7.25757	+	12.5705i	0.0301144	+	0.0521597i	0.880690	−	0.473693i	$-0.157080\pi$
$241$	7.25757	+	12.5705i	0.0301144	+	0.0521597i	−0.850575	+	0.525853i	$0.823746\pi$
$242$	−13.8672	+	51.7529i	−0.0573023	+	0.213855i
$243$		0			0
$244$			93.3005i			0.382379i
$245$	220.175	−	107.462i	0.898672	−	0.438622i
$246$		0			0
$247$	−421.707	+	112.996i	−1.70732	+	0.457474i
$248$	−66.0717	−	17.7039i	−0.266418	−	0.0713866i
$249$		0			0
$250$	−5.40696	+	57.3685i	−0.0216279	+	0.229474i
$251$	211.955			0.844443			0.422221	−	0.906493i	$-0.361251\pi$
$251$	211.955			0.844443			0.422221	+	0.906493i	$0.361251\pi$
$252$		0			0
$253$	125.726	−	125.726i	0.496940	−	0.496940i
$254$	25.1090	+	14.4967i	0.0988545	+	0.0570736i
$255$		0			0
$256$	−65.2842	−	113.076i	−0.255016	−	0.441701i
$257$	309.551	−	82.9440i	1.20448	−	0.322739i	0.399886	−	0.916565i	$-0.369050\pi$
$257$	309.551	−	82.9440i	1.20448	−	0.322739i	0.804594	+	0.593825i	$0.202383\pi$
$258$		0			0
$259$	10.1517	+	34.4807i	0.0391959	+	0.133130i
$260$	−65.4141	−	453.647i	−0.251593	−	1.74480i
$261$		0			0
$262$	26.8971	−	100.381i	0.102661	−	0.383135i
$263$	−125.573	−	33.6471i	−0.477462	−	0.127936i	0.0120584	−	0.999927i	$-0.496162\pi$
$263$	−125.573	−	33.6471i	−0.477462	−	0.127936i	−0.489521	+	0.871992i	$0.662828\pi$
$264$		0			0
$265$	385.531	−	55.5920i	1.45483	−	0.209781i
$266$	−13.6819	+	56.5774i	−0.0514358	+	0.212697i
$267$		0			0
$268$	113.578	+	423.879i	0.423798	+	1.58164i
$269$	−59.9735	+	34.6257i	−0.222950	+	0.128720i	−0.607315	−	0.794461i	$-0.707754\pi$
$269$	−59.9735	+	34.6257i	−0.222950	+	0.128720i	0.384366	+	0.923181i	$0.374420\pi$
$270$		0			0
$271$	−207.020	+	358.570i	−0.763913	+	1.32314i	0.176907	+	0.984228i	$0.443391\pi$
$271$	−207.020	+	358.570i	−0.763913	+	1.32314i	−0.940820	+	0.338908i	$0.889943\pi$
$272$	−206.386	−	206.386i	−0.758771	−	0.758771i
$273$		0			0
$274$			16.3057i			0.0595100i
$275$	374.274	+	90.4737i	1.36100	+	0.328995i
$276$		0			0
$277$	−13.5956	+	50.7395i	−0.0490816	+	0.183175i	−0.986115	−	0.166065i	$-0.946894\pi$
$277$	−13.5956	+	50.7395i	−0.0490816	+	0.183175i	0.937033	+	0.349241i	$0.113560\pi$
$278$	6.76551	+	25.2492i	0.0243364	+	0.0908246i
$279$		0			0
$280$	−117.774	−	43.7750i	−0.420622	−	0.156339i
$281$	460.003			1.63702			0.818511	−	0.574491i	$-0.194800\pi$
$281$	460.003			1.63702			0.818511	+	0.574491i	$0.194800\pi$
$282$		0			0
$283$	177.279	+	47.5016i	0.626426	+	0.167850i	0.558047	−	0.829809i	$-0.311551\pi$
$283$	177.279	+	47.5016i	0.626426	+	0.167850i	0.0683786	+	0.997659i	$0.478217\pi$
$284$	209.644	−	121.038i	0.738182	−	0.426190i
$285$		0			0
$286$	171.843			0.600848
$287$	−8.82952	−	359.902i	−0.0307649	−	1.25401i
$288$		0			0
$289$	−154.823	−	89.3874i	−0.535721	−	0.309299i
$290$	−2.67541	−	3.39919i	−0.00922554	−	0.0117214i
$291$		0			0
$292$	−50.3913	+	13.5023i	−0.172573	+	0.0462408i
$293$	−2.24023	+	2.24023i	−0.00764585	+	0.00764585i	−0.710919	−	0.703274i	$-0.751721\pi$
$293$	−2.24023	+	2.24023i	−0.00764585	+	0.00764585i	0.703274	+	0.710919i	$0.251721\pi$
$294$		0			0
$295$	−138.919	+	185.733i	−0.470913	+	0.629604i
$296$	9.21683	−	15.9640i	0.0311379	−	0.0539325i
$297$		0			0
$298$	−40.6899	−	10.9028i	−0.136543	−	0.0365866i
$299$	−241.965	−	139.699i	−0.809248	−	0.467219i
$300$		0			0
$301$	−132.273	−	125.938i	−0.439445	−	0.418399i
$302$	−29.7823	−	29.7823i	−0.0986170	−	0.0986170i
$303$		0			0
$304$	−210.819	+	121.716i	−0.693482	+	0.400382i
$305$	−14.5725	+	122.304i	−0.0477786	+	0.400997i
$306$		0			0
$307$	71.4036	+	71.4036i	0.232585	+	0.232585i	0.813771	−	0.581186i	$-0.197411\pi$
$307$	71.4036	+	71.4036i	0.232585	+	0.232585i	−0.581186	+	0.813771i	$0.697411\pi$
$308$	−195.440	+	358.542i	−0.634546	+	1.16410i
$309$		0			0
$310$	−40.7789	−	16.3060i	−0.131545	−	0.0526001i
$311$	−47.7241	−	82.6605i	−0.153454	−	0.265789i	0.779041	−	0.626973i	$-0.215706\pi$
$311$	−47.7241	−	82.6605i	−0.153454	−	0.265789i	−0.932495	+	0.361183i	$0.882373\pi$
$312$		0			0
$313$	−37.5811	−	140.255i	−0.120067	−	0.448098i	0.879549	−	0.475809i	$-0.157845\pi$
$313$	−37.5811	−	140.255i	−0.120067	−	0.448098i	−0.999616	+	0.0277115i	$0.991178\pi$
$314$		−	83.2252i		−	0.265048i
$315$		0			0
$316$	−198.244			−0.627354
$317$	−444.564	+	119.121i	−1.40241	+	0.375775i	−0.879210	−	0.476434i	$-0.841929\pi$
$317$	−444.564	+	119.121i	−1.40241	+	0.375775i	−0.523201	+	0.852209i	$0.675262\pi$
$318$		0			0
$319$	−25.0335	+	14.4531i	−0.0784750	+	0.0453076i
$320$	−87.6573	−	204.468i	−0.273929	−	0.638962i
$321$		0			0
$322$	−31.7939	+	19.4112i	−0.0987389	+	0.0602832i
$323$	−275.871	+	275.871i	−0.854089	+	0.854089i
$324$		0			0
$325$	−14.8943	−	604.885i	−0.0458287	−	1.86119i
$326$	18.3023	+	31.7005i	0.0561421	+	0.0972409i
$327$		0			0
$328$	−130.552	+	130.552i	−0.398025	+	0.398025i
$329$	45.9437	+	156.049i	0.139647	+	0.474314i
$330$		0			0
$331$	23.3963	−	40.5235i	0.0706836	−	0.122428i	−0.828517	−	0.559963i	$-0.810815\pi$
$331$	23.3963	−	40.5235i	0.0706836	−	0.122428i	0.899201	+	0.437536i	$0.144149\pi$
$332$	−47.6492	+	177.829i	−0.143522	+	0.535630i
$333$		0			0
$334$	−8.60493	−	4.96806i	−0.0257633	−	0.0148744i
$335$	82.6799	+	573.386i	0.246806	+	1.71160i
$336$		0			0
$337$	391.846	+	391.846i	1.16275	+	1.16275i	0.983872	+	0.178877i	$0.0572463\pi$
$337$	391.846	+	391.846i	1.16275	+	1.16275i	0.178877	+	0.983872i	$0.442754\pi$
$338$	−49.7256	−	185.578i	−0.147117	−	0.549048i
$339$		0			0
$340$	−253.318	−	321.849i	−0.745054	−	0.946616i
$341$	−146.738	+	254.157i	−0.430316	+	0.745329i
$342$		0			0
$343$	25.2167	+	342.072i	0.0735182	+	0.997294i
$344$			93.6643i			0.272280i
$345$		0			0
$346$	−1.01801	−	1.76325i	−0.00294223	−	0.00509609i
$347$	8.37062	−	31.2396i	0.0241228	−	0.0900276i	−0.952815	−	0.303552i	$-0.901828\pi$
$347$	8.37062	−	31.2396i	0.0241228	−	0.0900276i	0.976938	+	0.213524i	$0.0684942\pi$
$348$		0			0
$349$		−	214.001i		−	0.613183i	−0.951841	−	0.306592i	$-0.900811\pi$
$349$		−	214.001i		−	0.613183i	0.951841	−	0.306592i	$-0.0991886\pi$
$350$	−71.7611	−	36.8551i	−0.205032	−	0.105300i
$351$		0			0
$352$	306.185	−	82.0420i	0.869843	−	0.233074i
$353$	154.485	+	41.3943i	0.437636	+	0.117264i	0.470908	−	0.882182i	$-0.343926\pi$
$353$	154.485	+	41.3943i	0.437636	+	0.117264i	−0.0332725	+	0.999446i	$0.510593\pi$
$354$		0			0
$355$	293.719	−	125.920i	0.827376	−	0.354704i
$356$	194.901			0.547474
$357$		0			0
$358$	−3.43315	+	3.43315i	−0.00958981	+	0.00958981i
$359$	422.373	+	243.857i	1.17653	+	0.679267i	0.955208	−	0.295935i	$-0.0956311\pi$
$359$	422.373	+	243.857i	1.17653	+	0.679267i	0.221317	+	0.975202i	$0.428964\pi$
$360$		0			0
$361$	−17.8049	−	30.8390i	−0.0493210	−	0.0854265i
$362$	144.728	−	38.7798i	0.399802	−	0.107127i
$363$		0			0
$364$	623.697	+	150.826i	1.71345	+	0.414358i
$365$	−68.1650	+	9.82912i	−0.186753	+	0.0269291i
$366$		0			0
$367$	−67.9239	+	253.495i	−0.185079	+	0.690723i	0.809535	+	0.587072i	$0.199719\pi$
$367$	−67.9239	+	253.495i	−0.185079	+	0.690723i	−0.994614	+	0.103652i	$0.966947\pi$
$368$	−150.480	−	40.3209i	−0.408912	−	0.109568i
$369$		0			0
$370$	7.08883	−	9.47765i	0.0191590	−	0.0256153i
$371$	−128.179	+	530.047i	−0.345497	+	1.42870i
$372$		0			0
$373$	−35.7315	−	133.352i	−0.0957949	−	0.357512i	0.901344	−	0.433104i	$-0.142582\pi$
$373$	−35.7315	−	133.352i	−0.0957949	−	0.357512i	−0.997139	+	0.0755927i	$0.975915\pi$
$374$	132.989	−	76.7811i	0.355585	−	0.205297i
$375$		0			0
$376$	41.7126	−	72.2484i	0.110938	−	0.192150i
$377$	32.1188	+	32.1188i	0.0851957	+	0.0851957i
$378$		0			0
$379$			535.154i			1.41202i	0.708204	+	0.706008i	$0.249506\pi$
$379$			535.154i			1.41202i	−0.708204	+	0.706008i	$0.750494\pi$
$380$	−313.969	+	134.601i	−0.826234	+	0.354214i
$381$		0			0
$382$	−28.5261	+	106.461i	−0.0746757	+	0.278693i
$383$	−33.3533	−	124.476i	−0.0870845	−	0.325004i	0.908616	−	0.417632i	$-0.137140\pi$
$383$	−33.3533	−	124.476i	−0.0870845	−	0.325004i	−0.995701	+	0.0926283i	$0.970473\pi$
$384$		0			0
$385$	−312.195	+	439.474i	−0.810896	+	1.14149i
$386$	−88.0645			−0.228146
$387$		0			0
$388$	−201.848	−	54.0850i	−0.520227	−	0.139394i
$389$	128.234	−	74.0357i	0.329649	−	0.190323i	−0.326036	−	0.945357i	$-0.605713\pi$
$389$	128.234	−	74.0357i	0.329649	−	0.190323i	0.655685	+	0.755034i	$0.272380\pi$
$390$		0			0
$391$	−249.675			−0.638556
$392$	118.135	−	130.333i	0.301364	−	0.332483i
$393$		0			0
$394$	34.4080	+	19.8655i	0.0873300	+	0.0504200i
$395$	−259.870	−	30.9634i	−0.657899	−	0.0783884i
$396$		0			0
$397$	−462.699	+	123.980i	−1.16549	+	0.312292i	−0.789156	−	0.614193i	$-0.789482\pi$
$397$	−462.699	+	123.980i	−1.16549	+	0.312292i	−0.376333	+	0.926485i	$0.622815\pi$
$398$	−18.3436	+	18.3436i	−0.0460895	+	0.0460895i
$399$		0			0
$400$	−95.3152	−	323.633i	−0.238288	−	0.809084i
$401$	−233.401	+	404.263i	−0.582048	+	1.00814i	0.413189	+	0.910645i	$0.364415\pi$
$401$	−233.401	+	404.263i	−0.582048	+	1.00814i	−0.995236	+	0.0974907i	$0.968918\pi$
$402$		0			0
$403$	445.449	+	119.358i	1.10533	+	0.296173i
$404$	522.654	+	301.754i	1.29370	+	0.746917i
$405$		0			0
$406$	5.80952	−	1.71043i	0.0143092	−	0.00421287i
$407$	−55.9238	−	55.9238i	−0.137405	−	0.137405i
$408$		0			0
$409$	−556.548	+	321.323i	−1.36075	+	0.785631i	−0.989724	−	0.142990i	$-0.954328\pi$
$409$	−556.548	+	321.323i	−1.36075	+	0.785631i	−0.371029	+	0.928621i	$0.620995\pi$
$410$	−93.1501	+	73.3158i	−0.227195	+	0.178819i
$411$		0			0
$412$	−271.605	−	271.605i	−0.659236	−	0.659236i
$413$	−169.205	−	277.144i	−0.409697	−	0.671050i
$414$		0			0
$415$	−90.2364	+	225.667i	−0.217437	+	0.543777i
$416$	−249.053	−	431.373i	−0.598686	−	1.03695i
$417$		0			0
$418$	−33.1486	−	123.712i	−0.0793028	−	0.295962i
$419$		−	476.798i		−	1.13794i	−0.822358	−	0.568971i	$-0.807342\pi$
$419$		−	476.798i		−	1.13794i	0.822358	−	0.568971i	$-0.192658\pi$
$420$		0			0
$421$	−478.207			−1.13588			−0.567942	−	0.823069i	$-0.692260\pi$
$421$	−478.207			−1.13588			−0.567942	+	0.823069i	$0.692260\pi$
$422$	−25.7717	+	6.90552i	−0.0610705	+	0.0163638i
$423$		0			0
$424$	242.198	−	139.833i	0.571221	−	0.329795i
$425$	−281.796	−	461.465i	−0.663050	−	1.08580i
$426$		0			0
$427$	−151.404	−	82.5299i	−0.354577	−	0.193279i
$428$	−26.3768	+	26.3768i	−0.0616281	+	0.0616281i
$429$		0			0
$430$	−7.11505	+	59.7153i	−0.0165466	+	0.138873i
$431$	104.378	+	180.788i	0.242176	+	0.419461i	0.961334	−	0.275386i	$-0.0888055\pi$
$431$	104.378	+	180.788i	0.242176	+	0.419461i	−0.719158	+	0.694847i	$0.755472\pi$
$432$		0			0
$433$	−258.656	+	258.656i	−0.597358	+	0.597358i	−0.939609	−	0.342251i	$-0.888811\pi$
$433$	−258.656	+	258.656i	−0.597358	+	0.597358i	0.342251	+	0.939609i	$0.388811\pi$
$434$	42.3974	−	44.5300i	0.0976898	−	0.102604i
$435$		0			0
$436$	84.5640	−	146.469i	0.193954	−	0.335938i
$437$	−53.8959	+	201.142i	−0.123332	+	0.460280i
$438$		0			0
$439$	447.029	+	258.092i	1.01829	+	0.587910i	0.913608	−	0.406596i	$-0.133284\pi$
$439$	447.029	+	258.092i	1.01829	+	0.587910i	0.104681	+	0.994506i	$0.466618\pi$
$440$	273.631	−	39.4565i	0.621889	−	0.0896739i
$441$		0			0
$442$	−170.629	−	170.629i	−0.386038	−	0.386038i
$443$	−125.295	−	467.609i	−0.282834	−	1.05555i	−0.950408	−	0.311007i	$-0.899334\pi$
$443$	−125.295	−	467.609i	−0.282834	−	1.05555i	0.667574	−	0.744544i	$-0.267333\pi$
$444$		0			0
$445$	255.488	+	30.4413i	0.574130	+	0.0684073i
$446$	38.7787	−	67.1667i	0.0869478	−	0.150598i
$447$		0			0
$448$	311.358	−	7.63858i	0.694996	−	0.0170504i
$449$			290.894i			0.647871i	0.946079	+	0.323936i	$0.105006\pi$
$449$			290.894i			0.647871i	−0.946079	+	0.323936i	$0.894994\pi$
$450$		0			0
$451$	396.067	+	686.009i	0.878198	+	1.52108i
$452$	47.3565	−	176.737i	0.104771	−	0.391011i
$453$		0			0
$454$			155.768i			0.343101i
$455$	794.023	+	295.127i	1.74510	+	0.648630i
$456$		0			0
$457$	80.7582	−	21.6391i	0.176714	−	0.0473503i	−0.169377	−	0.985551i	$-0.554176\pi$
$457$	80.7582	−	21.6391i	0.176714	−	0.0473503i	0.346091	+	0.938201i	$0.387509\pi$
$458$	−3.42571	−	0.917917i	−0.00747972	−	0.00200419i
$459$		0			0
$460$	−202.988	−	81.1678i	−0.441279	−	0.176452i
$461$	−579.921			−1.25796			−0.628982	−	0.777420i	$-0.716528\pi$
$461$	−579.921			−1.25796			−0.628982	+	0.777420i	$0.716528\pi$
$462$		0			0
$463$	340.706	−	340.706i	0.735865	−	0.735865i	−0.235910	−	0.971775i	$-0.575807\pi$
$463$	340.706	−	340.706i	0.735865	−	0.735865i	0.971775	+	0.235910i	$0.0758069\pi$
$464$	21.9339	+	12.6636i	0.0472714	+	0.0272921i
$465$		0			0
$466$	−59.4954	−	103.049i	−0.127673	−	0.221135i
$467$	−393.823	+	105.524i	−0.843304	+	0.225963i	−0.654509	−	0.756054i	$-0.727125\pi$
$467$	−393.823	+	105.524i	−0.843304	+	0.225963i	−0.188794	+	0.982017i	$0.560458\pi$
$468$		0			0
$469$	−788.320	−	190.636i	−1.68085	−	0.406474i
$470$	32.0819	−	42.8930i	0.0682594	−	0.0912617i
$471$		0			0
$472$	−43.1004	+	160.853i	−0.0913143	+	0.340790i
$473$	388.166	+	104.009i	0.820648	+	0.219892i
$474$		0			0
$475$	−432.593	+	127.405i	−0.910722	+	0.268222i
$476$	550.069	−	161.950i	1.15561	−	0.340231i
$477$		0			0
$478$	30.1183	+	112.403i	0.0630089	+	0.235152i
$479$	547.299	−	315.983i	1.14259	−	0.659673i	0.195517	−	0.980700i	$-0.437361\pi$
$479$	547.299	−	315.983i	1.14259	−	0.659673i	0.947070	+	0.321027i	$0.104028\pi$
$480$		0			0
$481$	−62.1390	+	107.628i	−0.129187	+	0.223759i
$482$	4.73141	+	4.73141i	0.00981620	+	0.00981620i
$483$		0			0
$484$		−	440.209i		−	0.909523i
$485$	−256.147	−	102.424i	−0.528139	−	0.211184i
$486$		0			0
$487$	−14.3646	+	53.6096i	−0.0294962	+	0.110081i	−0.979104	−	0.203358i	$-0.934815\pi$
$487$	−14.3646	+	53.6096i	−0.0294962	+	0.110081i	0.949608	+	0.313439i	$0.101481\pi$
$488$	22.8881	+	85.4196i	0.0469019	+	0.175040i
$489$		0			0
$490$	85.2167	−	74.1195i	0.173912	−	0.151264i
$491$	−328.623			−0.669293			−0.334646	−	0.942344i	$-0.608617\pi$
$491$	−328.623			−0.669293			−0.334646	+	0.942344i	$0.608617\pi$
$492$		0			0
$493$	39.2077	+	10.5057i	0.0795288	+	0.0213097i
$494$	−174.294	+	100.629i	−0.352821	+	0.203701i
$495$		0			0
$496$	257.138			0.518423
$497$	10.9728	+	447.267i	0.0220782	+	0.899933i
$498$		0			0
$499$	794.743	+	458.845i	1.59267	+	0.919529i	0.992846	+	0.119398i	$0.0380965\pi$
$499$	794.743	+	458.845i	1.59267	+	0.919529i	0.599825	+	0.800131i	$0.295237\pi$
$500$	−79.0832	−	466.785i	−0.158166	−	0.933570i
$501$		0			0
$502$	94.3782	−	25.2886i	0.188004	−	0.0503756i
$503$	−268.947	+	268.947i	−0.534685	+	0.534685i	−0.921963	−	0.387278i	$-0.873415\pi$
$503$	−268.947	+	268.947i	−0.534685	+	0.534685i	0.387278	+	0.921963i	$0.373415\pi$
$504$		0			0
$505$	637.996	+	477.191i	1.26336	+	0.944932i
$506$	40.9821	−	70.9830i	0.0809922	−	0.140283i
$507$		0			0
$508$	−230.097	−	61.6543i	−0.452947	−	0.121367i
$509$	288.616	+	166.632i	0.567025	+	0.327372i	0.755960	−	0.654618i	$-0.227170\pi$
$509$	288.616	+	166.632i	0.567025	+	0.327372i	−0.188935	+	0.981990i	$0.560504\pi$
$510$		0			0
$511$	22.6632	−	93.7166i	0.0443506	−	0.183398i
$512$	−333.416	−	333.416i	−0.651203	−	0.651203i
$513$		0			0
$514$	127.939	−	73.8658i	0.248909	−	0.143708i
$515$	−313.615	−	398.458i	−0.608961	−	0.773706i
$516$		0			0
$517$	−253.094	−	253.094i	−0.489544	−	0.489544i
$518$	8.63424	+	14.1422i	0.0166684	+	0.0273015i
$519$		0			0
$520$	−171.176	−	399.281i	−0.329184	−	0.767849i
$521$	−186.745	−	323.451i	−0.358435	−	0.620828i	0.629264	−	0.777191i	$-0.283356\pi$
$521$	−186.745	−	323.451i	−0.358435	−	0.620828i	−0.987700	+	0.156363i	$0.950023\pi$
$522$		0			0
$523$	−48.0280	−	179.243i	−0.0918317	−	0.342721i	0.904688	−	0.426074i	$-0.140104\pi$
$523$	−48.0280	−	179.243i	−0.0918317	−	0.342721i	−0.996520	+	0.0833533i	$0.973437\pi$
$524$			853.841i			1.62947i
$525$		0			0
$526$	−59.9288			−0.113933
$527$	398.063	−	106.661i	0.755338	−	0.202392i
$528$		0			0
$529$	342.717	−	197.868i	0.647858	−	0.374041i
$530$	165.034	−	70.7517i	0.311385	−	0.133494i
$531$		0			0
$532$	−11.7294	−	478.103i	−0.0220477	−	0.898690i
$533$	880.170	−	880.170i	1.65135	−	1.65135i
$534$		0			0
$535$	−38.6962	+	30.4566i	−0.0723293	+	0.0569283i
$536$	207.969	+	360.212i	0.388001	+	0.672037i
$537$		0			0
$538$	−22.5735	+	22.5735i	−0.0419581	+	0.0419581i
$539$	−408.949	−	634.305i	−0.758719	−	1.17682i
$540$		0			0
$541$	493.154	−	854.168i	0.911560	−	1.57887i	0.0996992	−	0.995018i	$-0.468212\pi$
$541$	493.154	−	854.168i	0.911560	−	1.57887i	0.811861	−	0.583851i	$-0.198455\pi$
$542$	−49.3996	+	184.362i	−0.0911432	+	0.340151i
$543$		0			0
$544$	−385.484	−	222.560i	−0.708611	−	0.409117i
$545$	133.728	−	178.793i	0.245373	−	0.328060i
$546$		0			0
$547$	414.571	+	414.571i	0.757899	+	0.757899i	0.975940	−	0.218040i	$-0.0699664\pi$
$547$	414.571	+	414.571i	0.757899	+	0.757899i	−0.218040	+	0.975940i	$0.569966\pi$
$548$	−34.6741	−	129.405i	−0.0632738	−	0.236141i
$549$		0			0
$550$	177.449	−	4.36941i	0.322635	−	0.00794438i
$551$	16.9271	−	29.3185i	0.0307206	−	0.0532097i
$552$		0			0
$553$	175.359	−	321.702i	0.317104	−	0.581740i
$554$			24.2151i			0.0437096i
$555$		0			0
$556$	−107.385	−	185.996i	−0.193138	−	0.334525i
$557$	−231.777	+	865.003i	−0.416116	+	1.55297i	0.366472	+	0.930429i	$0.380565\pi$
$557$	−231.777	+	865.003i	−0.416116	+	1.55297i	−0.782589	+	0.622539i	$0.786101\pi$
$558$		0			0
$559$		−	631.476i		−	1.12965i
$560$	470.241	+	44.3628i	0.839715	+	0.0792193i
$561$		0			0
$562$	204.828	−	54.8834i	0.364462	−	0.0976574i
$563$	787.593	+	211.035i	1.39892	+	0.374840i	0.877958	−	0.478738i	$-0.158906\pi$
$563$	787.593	+	211.035i	1.39892	+	0.374840i	0.520964	+	0.853578i	$0.325572\pi$
$564$		0			0
$565$	89.6822	−	224.281i	0.158729	−	0.396958i
$566$	84.6051			0.149479
$567$		0			0
$568$	162.243	−	162.243i	0.285639	−	0.285639i
$569$	161.663	+	93.3360i	0.284117	+	0.164035i	0.635286	−	0.772277i	$-0.280882\pi$
$569$	161.663	+	93.3360i	0.284117	+	0.164035i	−0.351169	+	0.936312i	$0.614216\pi$
$570$		0			0
$571$	399.962	+	692.755i	0.700459	+	1.21323i	0.968305	+	0.249769i	$0.0803548\pi$
$571$	399.962	+	692.755i	0.700459	+	1.21323i	−0.267846	+	0.963462i	$0.586312\pi$
$572$	−1363.77	+	365.422i	−2.38422	+	0.638850i
$573$		0			0
$574$	−46.8718	−	159.202i	−0.0816583	−	0.277355i
$575$	−253.412	−	138.104i	−0.440716	−	0.240181i
$576$		0			0
$577$	38.8655	−	145.048i	0.0673579	−	0.251383i	−0.924034	−	0.382310i	$-0.875129\pi$
$577$	38.8655	−	145.048i	0.0673579	−	0.251383i	0.991392	+	0.130927i	$0.0417953\pi$
$578$	−79.6039	−	21.3298i	−0.137723	−	0.0369027i
$579$		0			0
$580$	28.4609	+	21.2874i	0.0490705	+	0.0367024i
$581$	−246.426	−	234.624i	−0.424140	−	0.403828i
$582$		0			0
$583$	−310.553	−	1159.00i	−0.532681	−	1.98799i
$584$	−42.8226	+	24.7236i	−0.0733263	+	0.0423350i
$585$		0			0
$586$	−0.730235	+	1.26480i	−0.00124613	+	0.00215837i
$587$	−153.429	−	153.429i	−0.261378	−	0.261378i	0.564236	−	0.825614i	$-0.309171\pi$
$587$	−153.429	−	153.429i	−0.261378	−	0.261378i	−0.825614	+	0.564236i	$0.809171\pi$
$588$		0			0
$589$		−	343.710i		−	0.583548i
$590$	−39.6973	+	99.2769i	−0.0672836	+	0.168266i
$591$		0			0
$592$	−17.9350	+	66.9344i	−0.0302957	+	0.113065i
$593$	−0.220820	−	0.824110i	−0.000372377	−	0.00138973i	0.965739	−	0.259514i	$-0.0835623\pi$
$593$	−0.220820	−	0.824110i	−0.000372377	−	0.00138973i	−0.966112	+	0.258124i	$0.916896\pi$
$594$		0			0
$595$	746.359	−	126.380i	1.25439	−	0.212403i
$596$	346.107			0.580716
$597$		0			0
$598$	−124.408	−	33.3352i	−0.208041	−	0.0557444i
$599$	696.721	−	402.252i	1.16314	−	0.671539i	0.211085	−	0.977468i	$-0.432300\pi$
$599$	696.721	−	402.252i	1.16314	−	0.671539i	0.952054	+	0.305929i	$0.0989669\pi$
$600$		0			0
$601$	−635.940			−1.05814			−0.529068	−	0.848579i	$-0.677458\pi$
$601$	−635.940			−1.05814			−0.529068	+	0.848579i	$0.677458\pi$
$602$	−73.9235	−	40.2954i	−0.122797	−	0.0669360i
$603$		0			0
$604$	299.690	+	173.026i	0.496176	+	0.286467i
$605$	68.7556	−	577.053i	0.113646	−	0.953807i
$606$		0			0
$607$	−248.787	+	66.6623i	−0.409864	+	0.109823i	−0.457859	−	0.889025i	$-0.651383\pi$
$607$	−248.787	+	66.6623i	−0.409864	+	0.109823i	0.0479951	+	0.998848i	$0.484717\pi$
$608$	−262.510	+	262.510i	−0.431759	+	0.431759i
$609$		0			0
$610$	8.10346	+	56.1976i	0.0132844	+	0.0921271i
$611$	−281.222	+	487.091i	−0.460266	+	0.797204i
$612$		0			0
$613$	−1115.56	−	298.914i	−1.81984	−	0.487624i	−0.823069	−	0.567941i	$-0.807740\pi$
$613$	−1115.56	−	298.914i	−1.81984	−	0.487624i	−0.996769	+	0.0803163i	$0.974407\pi$
$614$	40.3134	+	23.2750i	0.0656571	+	0.0379071i
$615$		0			0
$616$	−90.9755	+	376.202i	−0.147687	+	0.610717i
$617$	265.010	+	265.010i	0.429514	+	0.429514i	0.888463	−	0.458949i	$-0.151774\pi$
$617$	265.010	+	265.010i	0.429514	+	0.429514i	−0.458949	+	0.888463i	$0.651774\pi$
$618$		0			0
$619$	758.758	−	438.069i	1.22578	−	0.707704i	0.259635	−	0.965707i	$-0.416398\pi$
$619$	758.758	−	438.069i	1.22578	−	0.707704i	0.966144	+	0.258003i	$0.0830643\pi$
$620$	358.303	+	42.6917i	0.577909	+	0.0688576i
$621$		0			0
$622$	−31.1126	−	31.1126i	−0.0500203	−	0.0500203i
$623$	−172.401	+	316.277i	−0.276728	+	0.507668i
$624$		0			0
$625$	−30.7606	−	624.243i	−0.0492170	−	0.998788i
$626$	−33.4678	−	57.9680i	−0.0534630	−	0.0926006i
$627$		0			0
$628$	176.978	+	660.490i	0.281812	+	1.05174i
$629$			111.058i			0.176562i
$630$		0			0
$631$	247.281			0.391888			0.195944	−	0.980615i	$-0.437223\pi$
$631$	247.281			0.391888			0.195944	+	0.980615i	$0.437223\pi$
$632$	−181.499	+	48.6324i	−0.287181	+	0.0769500i
$633$		0			0
$634$	−183.741	+	106.083i	−0.289812	+	0.167323i
$635$	−291.996	−	116.759i	−0.459836	−	0.183872i
$636$		0			0
$637$	−796.452	+	878.695i	−1.25032	+	1.37943i
$638$	−9.42238	+	9.42238i	−0.0147686	+	0.0147686i
$639$		0			0
$640$	−318.001	−	404.031i	−0.496876	−	0.631298i
$641$	540.040	+	935.377i	0.842497	+	1.45925i	0.887778	+	0.460273i	$0.152248\pi$
$641$	540.040	+	935.377i	0.842497	+	1.45925i	−0.0452811	+	0.998974i	$0.514418\pi$
$642$		0			0
$643$	−40.2830	+	40.2830i	−0.0626485	+	0.0626485i	−0.737737	−	0.675088i	$-0.764105\pi$
$643$	−40.2830	+	40.2830i	−0.0626485	+	0.0626485i	0.675088	+	0.737737i	$0.264105\pi$
$644$	211.045	−	221.660i	0.327709	−	0.344193i
$645$		0			0
$646$	−89.9238	+	155.753i	−0.139201	+	0.241103i
$647$	71.9712	−	268.600i	0.111238	−	0.415147i	−0.887740	−	0.460346i	$-0.847725\pi$
$647$	71.9712	−	268.600i	0.111238	−	0.415147i	0.998978	+	0.0451988i	$0.0143921\pi$
$648$		0			0
$649$	618.750	+	357.235i	0.953390	+	0.550440i
$650$	−78.8015	−	267.563i	−0.121233	−	0.411635i
$651$		0			0
$652$	−212.662	−	212.662i	−0.326168	−	0.326168i
$653$	−228.842	−	854.052i	−0.350448	−	1.30789i	−0.886117	−	0.463461i	$-0.846607\pi$
$653$	−228.842	−	854.052i	−0.350448	−	1.30789i	0.535669	−	0.844428i	$-0.320059\pi$
$654$		0			0
$655$	−133.360	+	1119.27i	−0.203603	+	1.70881i
$656$	347.027	−	601.068i	0.529005	−	0.916263i
$657$		0			0
$658$	39.0760	+	64.0033i	0.0593860	+	0.0972694i
$659$			431.384i			0.654604i	0.944920	+	0.327302i	$0.106139\pi$
$659$			431.384i			0.654604i	−0.944920	+	0.327302i	$0.893861\pi$
$660$		0			0
$661$	−185.671	−	321.591i	−0.280894	−	0.486522i	0.690711	−	0.723130i	$-0.257297\pi$
$661$	−185.671	−	321.591i	−0.280894	−	0.486522i	−0.971605	+	0.236608i	$0.923964\pi$
$662$	5.58286	−	20.8355i	0.00843333	−	0.0314736i
$663$		0			0
$664$			174.498i			0.262798i
$665$	59.2987	−	628.559i	0.0891710	−	0.945202i
$666$		0			0
$667$	20.9272	−	5.60742i	0.0313751	−	0.00840693i
$668$	78.8548	+	21.1291i	0.118046	+	0.0316304i
$669$		0			0
$670$	105.227	+	245.450i	0.157054	+	0.366343i
$671$	379.414			0.565446
$672$		0			0
$673$	−306.397	+	306.397i	−0.455271	+	0.455271i	−0.897100	−	0.441828i	$-0.854330\pi$
$673$	−306.397	+	306.397i	−0.455271	+	0.455271i	0.441828	+	0.897100i	$0.354330\pi$
$674$	221.231	+	127.728i	0.328235	+	0.189507i
$675$		0			0
$676$	789.262	+	1367.04i	1.16755	+	2.02225i
$677$	1114.67	−	298.674i	1.64648	−	0.441173i	0.687856	−	0.725847i	$-0.258552\pi$
$677$	1114.67	−	298.674i	1.64648	−	0.441173i	0.958624	+	0.284674i	$0.0918855\pi$
$678$		0			0
$679$	266.314	−	279.709i	0.392215	−	0.411943i
$680$	−310.876	−	232.520i	−0.457170	−	0.341942i
$681$		0			0
$682$	−35.0149	+	130.677i	−0.0513414	+	0.191609i
$683$	−890.075	−	238.495i	−1.30318	−	0.349187i	−0.460531	−	0.887644i	$-0.652341\pi$
$683$	−890.075	−	238.495i	−1.30318	−	0.349187i	−0.842653	+	0.538456i	$0.819008\pi$
$684$		0			0
$685$	−25.2413	−	175.048i	−0.0368485	−	0.255545i
$686$	52.0413	+	149.307i	0.0758620	+	0.217649i
$687$		0			0
$688$	−91.1307	−	340.104i	−0.132457	−	0.494338i
$689$	−1632.87	+	942.741i	−2.36992	+	1.36827i
$690$		0			0
$691$	84.0700	−	145.613i	0.121664	−	0.210729i	−0.798760	−	0.601650i	$-0.794510\pi$
$691$	84.0700	−	145.613i	0.121664	−	0.210729i	0.920424	+	0.390921i	$0.127844\pi$
$692$	11.8287	+	11.8287i	0.0170934	+	0.0170934i
$693$		0			0
$694$		−	14.9089i		−	0.0214826i
$695$	−111.716	−	260.587i	−0.160743	−	0.374945i
$696$		0			0
$697$	287.893	−	1074.43i	0.413046	−	1.54151i
$698$	−25.5327	−	95.2892i	−0.0365797	−	0.136517i
$699$		0			0
$700$	647.882	+	139.889i	0.925545	+	0.199841i
$701$	−958.494			−1.36732			−0.683662	−	0.729799i	$-0.739614\pi$
$701$	−958.494			−1.36732			−0.683662	+	0.729799i	$0.739614\pi$
$702$		0			0
$703$	89.4696	+	23.9733i	0.127268	+	0.0341014i
$704$	−593.479	+	342.645i	−0.843010	+	0.486712i
$705$		0			0
$706$	73.7273			0.104430
$707$	−951.994	+	581.222i	−1.34653	+	0.822096i
$708$		0			0
$709$	30.6249	+	17.6813i	0.0431945	+	0.0249383i	0.521442	−	0.853287i	$-0.325394\pi$
$709$	30.6249	+	17.6813i	0.0431945	+	0.0249383i	−0.478247	+	0.878225i	$0.658728\pi$
$710$	115.762	−	91.1128i	0.163045	−	0.128328i
$711$		0			0
$712$	178.438	−	47.8123i	0.250615	−	0.0671521i
$713$	155.537	−	155.537i	0.218144	−	0.218144i
$714$		0			0
$715$	−1844.79	+	266.012i	−2.58013	+	0.372045i
$716$	19.9456	−	34.5467i	0.0278569	−	0.0482496i
$717$		0			0
$718$	217.167	+	58.1896i	0.302460	+	0.0810440i
$719$	983.525	+	567.839i	1.36791	+	0.789762i	0.990661	−	0.136351i	$-0.0435375\pi$
$719$	983.525	+	567.839i	1.36791	+	0.789762i	0.377247	+	0.926113i	$0.376871\pi$
$720$		0			0
$721$	681.001	−	200.499i	0.944523	−	0.278084i
$722$	−11.6075	−	11.6075i	−0.0160769	−	0.0160769i
$723$		0			0
$724$	−1066.13	+	615.528i	−1.47255	+	0.850177i
$725$	33.9834	+	32.3501i	0.0468737	+	0.0446208i
$726$		0			0
$727$	−12.8697	−	12.8697i	−0.0177025	−	0.0177025i	0.698200	−	0.715903i	$-0.253985\pi$
$727$	−12.8697	−	12.8697i	−0.0177025	−	0.0177025i	−0.715903	+	0.698200i	$0.753985\pi$
$728$	608.015	−	14.9165i	0.835185	−	0.0204897i
$729$		0			0
$730$	−29.1794	+	12.5095i	−0.0399718	+	0.0171363i
$731$	−282.150	−	488.699i	−0.385979	−	0.668535i
$732$		0			0
$733$	141.743	+	528.993i	0.193374	+	0.721682i	0.992682	+	0.120760i	$0.0385332\pi$
$733$	141.743	+	528.993i	0.193374	+	0.721682i	−0.799308	+	0.600922i	$0.794800\pi$
$734$			120.979i			0.164822i
$735$		0			0
$736$	−237.583			−0.322803
$737$	1723.74	−	461.874i	2.33886	−	0.626695i
$738$		0			0
$739$	−312.563	+	180.459i	−0.422955	+	0.244193i	−0.696341	−	0.717711i	$-0.745190\pi$
$739$	−312.563	+	180.459i	−0.422955	+	0.244193i	0.273386	+	0.961904i	$0.411856\pi$
$740$	−36.1041	+	90.2907i	−0.0487893	+	0.122014i
$741$		0			0
$742$	6.16541	+	251.310i	0.00830918	+	0.338692i
$743$	−416.926	+	416.926i	−0.561138	+	0.561138i	−0.929631	−	0.368492i	$-0.879874\pi$
$743$	−416.926	+	416.926i	−0.561138	+	0.561138i	0.368492	+	0.929631i	$0.379874\pi$
$744$		0			0
$745$	453.698	+	54.0579i	0.608991	+	0.0725610i
$746$	−31.8207	−	55.1150i	−0.0426551	−	0.0738807i
$747$		0			0
$748$	−892.149	+	892.149i	−1.19271	+	1.19271i
$749$	−19.4714	−	66.1352i	−0.0259965	−	0.0882980i
$750$		0			0
$751$	−521.992	+	904.116i	−0.695062	+	1.20388i	0.275097	+	0.961416i	$0.411290\pi$
$751$	−521.992	+	904.116i	−0.695062	+	1.20388i	−0.970160	+	0.242467i	$0.922043\pi$
$752$	−81.1685	+	302.925i	−0.107937	+	0.402826i
$753$		0			0
$754$	18.1338	+	10.4696i	0.0240501	+	0.0138854i
$755$	365.828	+	273.621i	0.484540	+	0.362413i
$756$		0			0
$757$	−691.527	−	691.527i	−0.913510	−	0.913510i	0.0830364	−	0.996547i	$-0.473538\pi$
$757$	−691.527	−	691.527i	−0.913510	−	0.913510i	−0.996547	+	0.0830364i	$0.973538\pi$
$758$	63.8497	+	238.291i	0.0842345	+	0.314367i
$759$		0			0
$760$	−254.429	+	200.254i	−0.334775	+	0.263492i
$761$	−553.925	+	959.427i	−0.727891	+	1.26074i	0.229881	+	0.973219i	$0.426166\pi$
$761$	−553.925	+	959.427i	−0.727891	+	1.26074i	−0.957773	+	0.287526i	$0.907167\pi$
$762$		0			0
$763$	162.882	+	266.788i	0.213476	+	0.349656i
$764$		−	905.554i		−	1.18528i
$765$		0			0
$766$	−29.7028	−	51.4468i	−0.0387765	−	0.0671629i
$767$	290.578	−	1084.45i	0.378851	−	1.41389i
$768$		0			0
$769$			671.432i			0.873124i	0.899674	+	0.436562i	$0.143804\pi$
$769$			671.432i			0.873124i	−0.899674	+	0.436562i	$0.856196\pi$
$770$	−86.5785	+	232.935i	−0.112440	+	0.302513i
$771$		0			0
$772$	698.896	−	187.269i	0.905306	−	0.242576i
$773$	1110.22	+	297.482i	1.43625	+	0.384841i	0.891217	−	0.453577i	$-0.149852\pi$
$773$	1110.22	+	297.482i	1.43625	+	0.384841i	0.545028	+	0.838418i	$0.316519\pi$
$774$		0			0
$775$	463.018	+	111.926i	0.597443	+	0.144420i
$776$	−198.066			−0.255240
$777$		0			0
$778$	48.2659	−	48.2659i	0.0620384	−	0.0620384i
$779$	−803.434	−	463.863i	−1.03137	−	0.595459i
$780$		0			0
$781$	−492.211	−	852.534i	−0.630231	−	1.09159i
$782$	−111.174	+	29.7890i	−0.142166	+	0.0380934i
$783$		0			0
$784$	−302.151	+	588.192i	−0.385396	+	0.750245i
$785$	128.832	+	893.453i	0.164118	+	1.13816i
$786$		0			0
$787$	218.012	−	813.633i	0.277017	−	1.03384i	−0.677461	−	0.735559i	$-0.736920\pi$
$787$	218.012	−	813.633i	0.277017	−	1.03384i	0.954478	−	0.298282i	$-0.0964137\pi$
$788$	−315.312	−	84.4877i	−0.400142	−	0.107218i
$789$		0			0
$790$	−119.408	+	17.2181i	−0.151149	+	0.0217951i
$791$	244.912	+	233.183i	0.309623	+	0.294795i
$792$		0			0
$793$	−154.310	−	575.891i	−0.194590	−	0.726218i
$794$	−191.236	+	110.410i	−0.240851	+	0.139056i
$795$		0			0
$796$	106.571	−	184.586i	0.133883	−	0.231892i
$797$	−704.301	−	704.301i	−0.883690	−	0.883690i	0.110218	−	0.993907i	$-0.464845\pi$
$797$	−704.301	−	704.301i	−0.883690	−	0.883690i	−0.993907	+	0.110218i	$0.964845\pi$
$798$		0			0
$799$			502.613i			0.629053i
$800$	−268.148	−	439.115i	−0.335185	−	0.548894i
$801$		0			0
$802$	−55.6946	+	207.855i	−0.0694447	+	0.259171i
$803$	54.9083	+	204.921i	0.0683790	+	0.255194i
$804$		0			0
$805$	311.271	−	257.603i	0.386672	−	0.320004i
$806$	212.588			0.263757
$807$		0			0
$808$	552.532	+	148.050i	0.683827	+	0.183231i
$809$	98.2739	−	56.7385i	0.121476	−	0.0701341i	−0.438031	−	0.898960i	$-0.644324\pi$
$809$	98.2739	−	56.7385i	0.121476	−	0.0701341i	0.559507	+	0.828826i	$0.310991\pi$
$810$		0			0
$811$	−624.622			−0.770187			−0.385094	−	0.922878i	$-0.625831\pi$
$811$	−624.622			−0.770187			−0.385094	+	0.922878i	$0.625831\pi$
$812$	−42.4682	+	25.9282i	−0.0523008	+	0.0319312i
$813$		0			0
$814$	−31.5738	−	18.2291i	−0.0387884	−	0.0223945i
$815$	−245.555	−	311.985i	−0.301294	−	0.382804i
$816$		0			0
$817$	−454.609	+	121.812i	−0.556437	+	0.149097i
$818$	−209.479	+	209.479i	−0.256087	+	0.256087i
$819$		0			0
$820$	583.351	−	779.931i	0.711403	−	0.951135i
$821$	662.006	−	1146.63i	0.806341	−	1.39662i	−0.109041	−	0.994037i	$-0.534778\pi$
$821$	662.006	−	1146.63i	0.806341	−	1.39662i	0.915382	−	0.402586i	$-0.131889\pi$
$822$		0			0
$823$	809.040	+	216.782i	0.983038	+	0.263404i	0.714324	−	0.699816i	$-0.246734\pi$
$823$	809.040	+	216.782i	0.983038	+	0.263404i	0.268715	+	0.963220i	$0.413401\pi$
$824$	−315.292	−	182.034i	−0.382636	−	0.220915i
$825$		0			0
$826$	−108.409	−	103.217i	−0.131246	−	0.124960i
$827$	387.240	+	387.240i	0.468247	+	0.468247i	0.901346	−	0.433100i	$-0.142580\pi$
$827$	387.240	+	387.240i	0.468247	+	0.468247i	−0.433100	+	0.901346i	$0.642580\pi$
$828$		0			0
$829$	120.871	−	69.7852i	0.145804	−	0.0841799i	−0.425323	−	0.905041i	$-0.639840\pi$
$829$	120.871	−	69.7852i	0.145804	−	0.0841799i	0.571127	+	0.820862i	$0.306506\pi$
$830$	−13.2554	+	111.250i	−0.0159704	+	0.134036i
$831$		0			0
$832$	761.452	+	761.452i	0.915207	+	0.915207i
$833$	−223.763	+	1035.88i	−0.268623	+	1.24356i
$834$		0			0
$835$	100.068	+	40.0135i	0.119841	+	0.0479204i
$836$	526.146	+	911.312i	0.629361	+	1.09009i
$837$		0			0
$838$	−56.8872	−	212.306i	−0.0678845	−	0.253348i
$839$		−	1564.83i		−	1.86511i	−0.361031	−	0.932554i	$-0.617575\pi$
$839$		−	1564.83i		−	1.86511i	0.361031	−	0.932554i	$-0.382425\pi$
$840$		0			0
$841$	837.478			0.995812
$842$	−212.933	+	57.0553i	−0.252890	+	0.0677617i
$843$		0			0
$844$	189.845	−	109.607i	0.224935	−	0.129866i
$845$	821.097	+	1915.28i	0.971713	+	2.26660i
$846$		0			0
$847$	714.353	+	389.391i	0.843392	+	0.459730i
$848$	−743.394	+	743.394i	−0.876643	+	0.876643i
$849$		0			0
$850$	−180.535	−	171.857i	−0.212394	−	0.202185i
$851$	29.6386	+	51.3355i	0.0348279	+	0.0603237i
$852$		0			0
$853$	156.700	−	156.700i	0.183704	−	0.183704i	−0.609264	−	0.792968i	$-0.708535\pi$
$853$	156.700	−	156.700i	0.183704	−	0.183704i	0.792968	+	0.609264i	$0.208535\pi$
$854$	−77.2632	−	18.6843i	−0.0904722	−	0.0218786i
$855$		0			0
$856$	−17.6782	+	30.6195i	−0.0206521	+	0.0357705i
$857$	−38.1030	+	142.202i	−0.0444610	+	0.165931i	−0.984587	−	0.174897i	$-0.944041\pi$
$857$	−38.1030	+	142.202i	−0.0444610	+	0.165931i	0.940126	+	0.340828i	$0.110707\pi$
$858$		0			0
$859$	−539.821	−	311.666i	−0.628429	−	0.362824i	0.151714	−	0.988424i	$-0.451521\pi$
$859$	−539.821	−	311.666i	−0.628429	−	0.362824i	−0.780143	+	0.625601i	$0.784854\pi$
$860$	−70.5178	−	489.041i	−0.0819975	−	0.568653i
$861$		0			0
$862$	68.0468	+	68.0468i	0.0789406	+	0.0789406i
$863$	−119.937	−	447.609i	−0.138976	−	0.518667i	−0.999950	−	0.0100170i	$-0.996811\pi$
$863$	−119.937	−	447.609i	−0.138976	−	0.518667i	0.860973	−	0.508650i	$-0.169855\pi$
$864$		0			0
$865$	13.6582	+	17.3532i	0.0157899	+	0.0200616i
$866$	−84.3125	+	146.033i	−0.0973585	+	0.168630i
$867$		0			0
$868$	−241.781	+	443.556i	−0.278549	+	0.511009i
$869$			806.176i			0.927705i
$870$		0			0
$871$	−1402.10	−	2428.52i	−1.60976	−	2.78819i
$872$	41.4898	−	154.842i	0.0475801	−	0.177571i
$873$		0			0
$874$			95.9940i			0.109833i
$875$	827.434	+	284.567i	0.945639	+	0.325219i
$876$		0			0
$877$	486.738	−	130.421i	0.555004	−	0.148713i	0.0295939	−	0.999562i	$-0.490579\pi$
$877$	486.738	−	130.421i	0.555004	−	0.148713i	0.525410	+	0.850849i	$0.323912\pi$
$878$	229.844	+	61.5865i	0.261781	+	0.0701441i
$879$		0			0
$880$	−955.192	+	409.500i	−1.08545	+	0.465340i
$881$	−1417.05			−1.60845			−0.804227	−	0.594322i	$-0.797420\pi$
$881$	−1417.05			−1.60845			−0.804227	+	0.594322i	$0.797420\pi$
$882$		0			0
$883$	−1107.55	+	1107.55i	−1.25430	+	1.25430i	−0.300530	+	0.953772i	$0.597164\pi$
$883$	−1107.55	+	1107.55i	−1.25430	+	1.25430i	−0.953772	+	0.300530i	$0.902836\pi$
$884$	1716.98	+	991.300i	1.94229	+	1.12138i
$885$		0			0
$886$	−111.582	−	193.265i	−0.125939	−	0.218132i
$887$	−609.740	+	163.379i	−0.687419	+	0.184193i	−0.585588	−	0.810609i	$-0.699137\pi$
$887$	−609.740	+	163.379i	−0.687419	+	0.184193i	−0.101830	+	0.994802i	$0.532470\pi$
$888$		0			0
$889$	303.585	−	318.855i	0.341490	−	0.358667i
$890$	117.394	−	16.9278i	0.131904	−	0.0190200i
$891$		0			0
$892$	−164.925	+	615.510i	−0.184894	+	0.690033i
$893$	404.913	+	108.496i	0.453430	+	0.121496i
$894$		0			0
$895$	31.5417	−	42.1707i	0.0352421	−	0.0471181i
$896$	690.524	−	203.303i	0.770674	−	0.226900i
$897$		0			0
$898$	34.7069	+	129.528i	0.0386491	+	0.144240i
$899$	−30.9692	+	17.8801i	−0.0344485	+	0.0198888i
$900$		0			0
$901$	−842.454	+	1459.17i	−0.935021	+	1.61950i
$902$	258.207	+	258.207i	0.286261	+	0.286261i
$903$		0			0
$904$		−	173.426i		−	0.191843i
$905$	−1493.68	+	640.355i	−1.65048	+	0.707575i
$906$		0			0
$907$	−271.289	+	1012.47i	−0.299106	+	1.11628i	0.638795	+	0.769377i	$0.279433\pi$
$907$	−271.289	+	1012.47i	−0.299106	+	1.11628i	−0.937901	+	0.346902i	$0.887234\pi$
$908$	−331.240	−	1236.20i	−0.364801	−	1.36146i
$909$		0			0
$910$	388.770	+	36.6768i	0.427220	+	0.0403042i
$911$	164.682			0.180771			0.0903853	−	0.995907i	$-0.471190\pi$
$911$	164.682			0.180771			0.0903853	+	0.995907i	$0.471190\pi$
$912$		0			0
$913$	723.158	+	193.770i	0.792068	+	0.212234i
$914$	33.3778	−	19.2707i	0.0365184	−	0.0210839i
$915$		0			0
$916$	29.1390			0.0318112
$917$	−1385.58	−	755.274i	−1.51099	−	0.823636i
$918$		0			0
$919$	−1440.17	−	831.481i	−1.56710	−	0.904767i	−0.996505	−	0.0835384i	$-0.973378\pi$
$919$	−1440.17	−	831.481i	−1.56710	−	0.904767i	−0.570599	−	0.821229i	$-0.693289\pi$
$920$	−205.754	−	24.5155i	−0.223646	−	0.0266473i
$921$		0			0
$922$	−258.224	+	69.1910i	−0.280070	+	0.0750444i
$923$	−1093.83	+	1093.83i	−1.18508	+	1.18508i
$924$		0			0
$925$	−61.4298	+	112.720i	−0.0664106	+	0.121859i
$926$	111.058	−	192.358i	0.119933	−	0.207730i
$927$		0			0
$928$	37.3088	+	9.99686i	0.0402034	+	0.0107725i
$929$	−683.395	−	394.558i	−0.735624	−	0.424713i	0.0848519	−	0.996394i	$-0.472958\pi$
$929$	−683.395	−	394.558i	−0.735624	−	0.424713i	−0.820476	+	0.571681i	$0.806292\pi$
$930$		0			0
$931$	786.222	+	403.877i	0.844492	+	0.433810i
$932$	691.300	+	691.300i	0.741738	+	0.741738i
$933$		0			0
$934$	−162.769	+	93.9748i	−0.174271	+	0.100615i
$935$	−1308.83	+	1030.14i	−1.39982	+	1.10175i
$936$		0			0
$937$	−545.274	−	545.274i	−0.581936	−	0.581936i	0.353499	−	0.935435i	$-0.384992\pi$
$937$	−545.274	−	545.274i	−0.581936	−	0.581936i	−0.935435	+	0.353499i	$0.884992\pi$
$938$	−373.764	+	9.16959i	−0.398469	+	0.00977568i
$939$		0			0
$940$	−163.396	+	408.629i	−0.173826	+	0.434711i
$941$	207.612	+	359.595i	0.220630	+	0.382142i	0.954999	−	0.296608i	$-0.0958555\pi$
$941$	207.612	+	359.595i	0.220630	+	0.382142i	−0.734370	+	0.678750i	$0.762522\pi$
$942$		0			0
$943$	−153.664	−	573.480i	−0.162952	−	0.608144i
$944$		−	626.006i		−	0.663142i
$945$		0			0
$946$	185.250			0.195825
$947$	1265.60	−	339.117i	1.33643	−	0.358096i	0.481322	−	0.876544i	$-0.340157\pi$
$947$	1265.60	−	339.117i	1.33643	−	0.358096i	0.855109	+	0.518448i	$0.173490\pi$
$948$		0			0
$949$	288.706	−	166.684i	0.304221	−	0.175642i
$950$	−177.422	+	108.344i	−0.186760	+	0.114046i
$951$		0			0
$952$	463.877	−	283.211i	0.487266	−	0.297491i
$953$	1215.33	−	1215.33i	1.27526	−	1.27526i	0.331976	−	0.943288i	$-0.392285\pi$
$953$	1215.33	−	1215.33i	1.27526	−	1.27526i	0.943288	−	0.331976i	$-0.107715\pi$
$954$		0			0
$955$	141.437	−	1187.06i	0.148102	−	1.24299i
$956$	−478.048	−	828.003i	−0.500050	−	0.866112i
$957$		0			0
$958$	205.998	−	205.998i	0.215029	−	0.215029i
$959$	240.665	+	58.1992i	0.250954	+	0.0606874i
$960$		0			0
$961$	298.969	−	517.830i	0.311102	−	0.538845i
$962$	−14.8277	+	55.3378i	−0.0154134	+	0.0575237i
$963$		0			0
$964$	−47.6106	−	27.4880i	−0.0493886	−	0.0285145i
$965$	945.405	−	136.324i	0.979695	−	0.141268i
$966$		0			0
$967$	837.149	+	837.149i	0.865717	+	0.865717i	0.991995	−	0.126278i	$-0.0403030\pi$
$967$	837.149	+	837.149i	0.865717	+	0.865717i	−0.126278	+	0.991995i	$0.540303\pi$
$968$	−107.990	−	403.026i	−0.111560	−	0.416349i
$969$		0			0
$970$	−126.276	−	15.0458i	−0.130182	−	0.0155111i
$971$	261.220	−	452.447i	0.269022	−	0.465959i	−0.699588	−	0.714547i	$-0.746633\pi$
$971$	261.220	−	452.447i	0.269022	−	0.465959i	0.968609	+	0.248587i	$0.0799663\pi$
$972$		0			0
$973$	396.815	−	9.73510i	0.407826	−	0.0100052i
$974$			25.5848i			0.0262678i
$975$		0			0
$976$	−166.218	−	287.898i	−0.170305	−	0.294978i
$977$	324.676	−	1211.71i	0.332320	−	1.24023i	−0.574427	−	0.818556i	$-0.694775\pi$
$977$	324.676	−	1211.71i	0.332320	−	1.24023i	0.906746	−	0.421677i	$-0.138558\pi$
$978$		0			0
$979$		−	792.580i		−	0.809582i
$980$	−518.681	+	769.439i	−0.529266	+	0.785142i
$981$		0			0
$982$	−146.327	+	39.2083i	−0.149010	+	0.0399270i
$983$	−748.307	−	200.508i	−0.761248	−	0.203976i	−0.142746	−	0.989759i	$-0.545593\pi$
$983$	−748.307	−	200.508i	−0.761248	−	0.203976i	−0.618502	+	0.785784i	$0.712260\pi$
$984$		0			0
$985$	−400.135	−	160.000i	−0.406228	−	0.162436i
$986$	18.7116			0.0189773
$987$		0			0
$988$	1169.24	−	1169.24i	1.18344	−	1.18344i
$989$	−260.844	−	150.598i	−0.263745	−	0.152273i
$990$		0			0
$991$	172.628	+	299.000i	0.174195	+	0.301715i	0.939882	−	0.341498i	$-0.110934\pi$
$991$	172.628	+	299.000i	0.174195	+	0.301715i	−0.765687	+	0.643213i	$0.777601\pi$
$992$	378.784	−	101.495i	0.381839	−	0.102313i
$993$		0			0
$994$	58.2498	+	197.847i	0.0586014	+	0.199042i
$995$	168.530	−	225.321i	0.169377	−	0.226454i
$996$		0			0
$997$	−195.060	+	727.975i	−0.195647	+	0.730166i	0.796451	+	0.604703i	$0.206708\pi$
$997$	−195.060	+	727.975i	−0.195647	+	0.730166i	−0.992098	+	0.125463i	$0.959958\pi$
$998$	408.624	+	109.491i	0.409443	+	0.109710i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.3.ca.b.37.10		64
3.2	odd	2		105.3.v.a.37.7	✓	64
5.3	odd	4	inner	315.3.ca.b.163.7		64
7.4	even	3	inner	315.3.ca.b.172.7		64
15.8	even	4		105.3.v.a.58.10	yes	64
21.11	odd	6		105.3.v.a.67.10	yes	64
35.18	odd	12	inner	315.3.ca.b.298.10		64
105.53	even	12		105.3.v.a.88.7	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.v.a.37.7	✓	64	3.2	odd	2
105.3.v.a.58.10	yes	64	15.8	even	4
105.3.v.a.67.10	yes	64	21.11	odd	6
105.3.v.a.88.7	yes	64	105.53	even	12
315.3.ca.b.37.10		64	1.1	even	1	trivial
315.3.ca.b.163.7		64	5.3	odd	4	inner
315.3.ca.b.172.7		64	7.4	even	3	inner
315.3.ca.b.298.10		64	35.18	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	315.ca (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.445275 - 0.119311i) q^{2} +(-3.28007 + 1.89375i) q^{4} +(-4.59550 + 1.97013i) q^{5} +(-0.171680 - 6.99789i) q^{7} +(-2.53844 + 2.53844i) q^{8} +O(q^{10})\)	\(q+(0.445275 - 0.119311i) q^{2} +(-3.28007 + 1.89375i) q^{4} +(-4.59550 + 1.97013i) q^{5} +(-0.171680 - 6.99789i) q^{7} +(-2.53844 + 2.53844i) q^{8} +(-1.81120 + 1.42554i) q^{10} +(7.70109 + 13.3387i) q^{11} +(17.1139 - 17.1139i) q^{13} +(-0.911371 - 3.09550i) q^{14} +(6.74755 - 11.6871i) q^{16} +(5.59776 - 20.8911i) q^{17} +(-15.6219 - 9.01929i) q^{19} +(11.3426 - 15.1649i) q^{20} +(5.02055 + 5.02055i) q^{22} +(-2.98781 - 11.1507i) q^{23} +(17.2372 - 18.1075i) q^{25} +(5.57852 - 9.66228i) q^{26} +(13.8154 + 22.6284i) q^{28} +1.87676i q^{29} +(9.52708 + 16.5014i) q^{31} +(5.32665 - 19.8793i) q^{32} -9.97017i q^{34} +(14.5757 + 31.8206i) q^{35} +(-4.95991 + 1.32900i) q^{37} +(-8.03212 - 2.15220i) q^{38} +(6.66433 - 16.6665i) q^{40} +51.4301 q^{41} +(18.4492 - 18.4492i) q^{43} +(-50.5202 - 29.1678i) q^{44} +(-2.66080 - 4.60863i) q^{46} +(-22.4470 + 6.01467i) q^{47} +(-48.9411 + 2.40280i) q^{49} +(5.51485 - 10.1194i) q^{50} +(-23.7254 + 88.5443i) q^{52} +(-75.2491 - 20.1629i) q^{53} +(-61.6693 - 46.1257i) q^{55} +(18.1995 + 17.3279i) q^{56} +(0.223918 + 0.835675i) q^{58} +(40.1729 - 23.1938i) q^{59} +(12.3169 - 21.3335i) q^{61} +(6.21097 + 6.21097i) q^{62} +44.4931i q^{64} +(-44.9303 + 112.364i) q^{65} +(29.9876 - 111.915i) q^{67} +(21.2015 + 79.1251i) q^{68} +(10.2867 + 12.4298i) q^{70} -63.9145 q^{71} +(13.3047 + 3.56497i) q^{73} +(-2.04996 + 1.18354i) q^{74} +68.3210 q^{76} +(92.0205 - 56.1814i) q^{77} +(45.3292 + 26.1708i) q^{79} +(-7.98321 + 67.0016i) q^{80} +(22.9005 - 6.13617i) q^{82} +(34.3710 - 34.3710i) q^{83} +(15.4338 + 107.033i) q^{85} +(6.01376 - 10.4161i) q^{86} +(-53.4082 - 14.3107i) q^{88} +(-44.5648 - 25.7295i) q^{89} +(-122.700 - 116.823i) q^{91} +(30.9168 + 30.9168i) q^{92} +(-9.27748 + 5.35636i) q^{94} +(89.5594 + 10.6710i) q^{95} +(39.0134 + 39.0134i) q^{97} +(-21.5055 + 6.90911i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8}+O(q^{10}) \) 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8	\( 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8} - 16 q^{10} - 16 q^{11} + 80 q^{16} - 56 q^{17} - 96 q^{22} - 72 q^{23} - 4 q^{25} + 288 q^{26} - 380 q^{28} - 136 q^{31} + 48 q^{32} - 76 q^{35} - 28 q^{37} + 68 q^{38} + 164 q^{40} - 128 q^{41} + 344 q^{43} + 240 q^{46} - 412 q^{47} + 72 q^{50} + 388 q^{52} + 40 q^{53} - 8 q^{55} + 864 q^{56} + 56 q^{58} - 216 q^{61} + 912 q^{62} - 20 q^{65} - 368 q^{67} + 492 q^{68} + 416 q^{70} - 784 q^{71} - 316 q^{73} - 32 q^{76} - 844 q^{77} - 908 q^{80} + 556 q^{82} - 1408 q^{83} - 536 q^{85} - 1024 q^{86} + 372 q^{88} - 1064 q^{91} + 1704 q^{92} - 260 q^{95} + 352 q^{97} - 272 q^{98}+O(q^{100}) \) 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8 - 16 * q^10 - 16 * q^11 + 80 * q^16 - 56 * q^17 - 96 * q^22 - 72 * q^23 - 4 * q^25 + 288 * q^26 - 380 * q^28 - 136 * q^31 + 48 * q^32 - 76 * q^35 - 28 * q^37 + 68 * q^38 + 164 * q^40 - 128 * q^41 + 344 * q^43 + 240 * q^46 - 412 * q^47 + 72 * q^50 + 388 * q^52 + 40 * q^53 - 8 * q^55 + 864 * q^56 + 56 * q^58 - 216 * q^61 + 912 * q^62 - 20 * q^65 - 368 * q^67 + 492 * q^68 + 416 * q^70 - 784 * q^71 - 316 * q^73 - 32 * q^76 - 844 * q^77 - 908 * q^80 + 556 * q^82 - 1408 * q^83 - 536 * q^85 - 1024 * q^86 + 372 * q^88 - 1064 * q^91 + 1704 * q^92 - 260 * q^95 + 352 * q^97 - 272 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more