LMFDB - Embedded newform 315.3.ca.b.298.10

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			298.10
Character	$\chi$	$=$	315.298
Dual form			315.3.ca.b.37.10

$q$-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 $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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	0.368413	−	0.929662i	$-0.379901\pi$
$2$	0.445275	+	0.119311i	0.222637	+	0.0596555i	−0.145776	+	0.989318i	$0.546568\pi$
$3$		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	−0.268333	−	0.963326i	$-0.586473\pi$
$11$	7.70109	−	13.3387i	0.700099	−	1.21261i	0.968431	−	0.249280i	$-0.0801941\pi$
$12$		0			0
$13$	17.1139	+	17.1139i	1.31646	+	1.31646i	0.916561	+	0.399894i	$0.130953\pi$
$13$	17.1139	+	17.1139i	1.31646	+	1.31646i	0.399894	+	0.916561i	$0.369047\pi$
$14$	−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	0.909938	+	0.414743i	$0.136129\pi$
$17$	5.59776	+	20.8911i	0.329280	+	1.22889i	−0.580658	+	0.814147i	$0.697205\pi$
$18$		0			0
$19$	−15.6219	+	9.01929i	−0.822203	+	0.474699i	−0.851176	−	0.524881i	$-0.824110\pi$
$19$	−15.6219	+	9.01929i	−0.822203	+	0.474699i	0.0289723	+	0.999580i	$0.490777\pi$
$20$	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	−0.999967	−	0.00813035i	$-0.997412\pi$
$23$	−2.98781	+	11.1507i	−0.129905	+	0.484812i	0.870062	+	0.492942i	$0.164079\pi$
$24$		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	$-0.989698\pi$
$29$		−	1.87676i		−	0.0647160i	0.999476	−	0.0323580i	$-0.0103017\pi$
$30$		0			0
$31$	9.52708	−	16.5014i	0.307325	−	0.532303i	−0.670451	−	0.741954i	$-0.733899\pi$
$31$	9.52708	−	16.5014i	0.307325	−	0.532303i	0.977776	+	0.209651i	$0.0672327\pi$
$32$	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	0.191169	−	0.981557i	$-0.438772\pi$
$37$	−4.95991	−	1.32900i	−0.134052	−	0.0359190i	−0.325221	+	0.945638i	$0.605439\pi$
$38$	−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	0.888305	−	0.459254i	$-0.151883\pi$
$43$	18.4492	+	18.4492i	0.429051	+	0.429051i	−0.459254	+	0.888305i	$0.651883\pi$
$44$	−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	0.0119867	−	0.999928i	$-0.496184\pi$
$47$	−22.4470	−	6.01467i	−0.477597	−	0.127972i	−0.489583	+	0.871957i	$0.662851\pi$
$48$		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	−0.885411	−	0.464809i	$-0.846123\pi$
$53$	−75.2491	+	20.1629i	−1.41979	+	0.380433i	−0.534384	+	0.845242i	$0.679456\pi$
$54$		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	0.800193	−	0.599743i	$-0.204730\pi$
$59$	40.1729	+	23.1938i	0.680897	+	0.393116i	−0.119296	+	0.992859i	$0.538064\pi$
$60$		0			0
$61$	12.3169	+	21.3335i	0.201917	+	0.349730i	0.949146	−	0.314836i	$-0.101950\pi$
$61$	12.3169	+	21.3335i	0.201917	+	0.349730i	−0.747229	+	0.664566i	$0.768616\pi$
$62$	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	0.709043	+	0.705165i	$0.249127\pi$
$67$	29.9876	+	111.915i	0.447576	+	1.67038i	−0.261467	+	0.965212i	$0.584206\pi$
$68$	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	−0.166537	−	0.986035i	$-0.553258\pi$
$73$	13.3047	−	3.56497i	0.182256	−	0.0488352i	0.348792	+	0.937200i	$0.386592\pi$
$74$	−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	−0.184873	−	0.982762i	$-0.559187\pi$
$79$	45.3292	−	26.1708i	0.573788	−	0.331276i	0.758661	+	0.651486i	$0.225854\pi$
$80$	−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	0.883167	−	0.469058i	$-0.155407\pi$
$83$	34.3710	+	34.3710i	0.414109	+	0.414109i	−0.469058	+	0.883167i	$0.655407\pi$
$84$		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	−0.729014	−	0.684499i	$-0.760021\pi$
$89$	−44.5648	+	25.7295i	−0.500728	+	0.289095i	0.228286	+	0.973594i	$0.426688\pi$
$90$		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	−0.476808	−	0.879008i	$-0.658206\pi$
$97$	39.0134	−	39.0134i	0.402200	−	0.402200i	0.879008	+	0.476808i	$0.158206\pi$
$98$	−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	0.137864	+	0.990451i	$0.455976\pi$
$101$	−79.6712	+	137.995i	−0.788824	+	1.36628i	−0.926688	+	0.375832i	$0.877357\pi$
$102$		0			0
$103$	26.2481	−	97.9591i	0.254835	−	0.951059i	−0.713346	−	0.700812i	$-0.752821\pi$
$103$	26.2481	−	97.9591i	0.254835	−	0.951059i	0.968182	−	0.250247i	$-0.0805119\pi$
$104$		−	86.8854i		−	0.835436i
$105$		0			0
$106$	−35.9122			−0.338794
$107$	9.51326	+	2.54907i	0.0889090	+	0.0238231i	0.302999	−	0.952991i	$-0.402012\pi$
$107$	9.51326	+	2.54907i	0.0889090	+	0.0238231i	−0.214090	+	0.976814i	$0.568679\pi$
$108$		0			0
$109$	−38.6718	−	22.3271i	−0.354787	−	0.204836i	0.312005	−	0.950081i	$-0.399000\pi$
$109$	−38.6718	−	22.3271i	−0.354787	−	0.204836i	−0.666792	+	0.745244i	$0.732333\pi$
$110$	−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	0.539613	−	0.841913i	$-0.318571\pi$
$113$	−34.1599	−	34.1599i	−0.302300	−	0.302300i	−0.841913	+	0.539613i	$0.818571\pi$
$114$		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	−0.509994	−	0.860178i	$-0.670352\pi$
$127$	44.4734	−	44.4734i	0.350184	−	0.350184i	0.860178	+	0.509994i	$0.170352\pi$
$128$	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	0.871499	+	0.490397i	$0.163148\pi$
$131$	112.718	+	195.234i	0.860446	+	1.49034i	−0.0110531	+	0.999939i	$0.503518\pi$
$132$		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	0.924431	−	0.381349i	$-0.124540\pi$
$137$	−9.15488	−	34.1665i	−0.0668239	−	0.249390i	−0.991255	+	0.131958i	$0.957874\pi$
$138$		0			0
$139$		−	56.7049i		−	0.407949i	−0.978976	−	0.203974i	$-0.934614\pi$
$139$		−	56.7049i		−	0.407949i	0.978976	−	0.203974i	$-0.0653859\pi$
$140$	−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	−0.741477	−	0.670978i	$-0.765875\pi$
$149$	−79.1387	+	45.6907i	−0.531132	+	0.306649i	0.210345	+	0.977627i	$0.432541\pi$
$150$		0			0
$151$	−45.6835	+	79.1262i	−0.302540	+	0.524015i	−0.976711	−	0.214561i	$-0.931168\pi$
$151$	−45.6835	+	79.1262i	−0.302540	+	0.524015i	0.674171	+	0.738576i	$0.264501\pi$
$152$	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	0.939112	+	0.343613i	$0.111651\pi$
$157$	46.7269	+	174.387i	0.297623	+	1.11075i	−0.641488	+	0.767133i	$0.721683\pi$
$158$	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	−0.873792	−	0.486300i	$-0.838346\pi$
$163$	20.5517	−	76.7000i	0.126084	−	0.470552i	0.999876	+	0.0157477i	$0.00501286\pi$
$164$	−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	−0.751265	−	0.660001i	$-0.770556\pi$
$167$	−15.2411	+	15.2411i	−0.0912643	+	0.0912643i	0.660001	+	0.751265i	$0.270556\pi$
$168$		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	−0.969151	−	0.246468i	$-0.920730\pi$
$173$	−1.14313	+	4.26621i	−0.00660768	+	0.0246602i	0.962543	+	0.271128i	$0.0873967\pi$
$174$		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	0.474305	−	0.880360i	$-0.342699\pi$
$179$	−9.12125	−	5.26616i	−0.0509567	−	0.0294199i	−0.525262	+	0.850941i	$0.676033\pi$
$180$		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	−0.988368	−	0.152082i	$-0.951402\pi$
$191$	−119.545	−	207.058i	−0.625891	−	1.08408i	0.362477	−	0.931993i	$-0.381931\pi$
$192$		0			0
$193$	−184.527	+	49.4439i	−0.956100	+	0.256186i	−0.702949	−	0.711241i	$-0.748134\pi$
$193$	−184.527	+	49.4439i	−0.956100	+	0.256186i	−0.253151	+	0.967427i	$0.581467\pi$
$194$	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	−0.535301	−	0.844661i	$-0.679802\pi$
$197$	60.9439	−	60.9439i	0.309360	−	0.309360i	0.844661	+	0.535301i	$0.179802\pi$
$198$		0			0
$199$	−48.7356	−	28.1375i	−0.244903	−	0.141395i	0.372525	−	0.928022i	$-0.378492\pi$
$199$	−48.7356	−	28.1375i	−0.244903	−	0.141395i	−0.617428	+	0.786627i	$0.711825\pi$
$200$	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	0.921607	−	0.388125i	$-0.126877\pi$
$223$	118.966	+	118.966i	0.533481	+	0.533481i	−0.388125	+	0.921607i	$0.626877\pi$
$224$	−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	−0.837742	−	0.546066i	$-0.816125\pi$
$227$	−87.4561	−	326.391i	−0.385269	−	1.43784i	0.452473	−	0.891778i	$-0.350542\pi$
$228$		0			0
$229$	−6.66275	+	3.84674i	−0.0290950	+	0.0167980i	−0.514477	−	0.857504i	$-0.672014\pi$
$229$	−6.66275	+	3.84674i	−0.0290950	+	0.0167980i	0.485382	+	0.874302i	$0.338681\pi$
$230$	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	0.660840	+	0.750527i	$0.270200\pi$
$233$	−66.8075	+	249.329i	−0.286728	+	1.07008i	−0.947568	+	0.319555i	$0.896466\pi$
$234$		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	$-0.822902\pi$
$239$		−	252.435i		−	1.05621i	0.849178	−	0.528107i	$-0.177098\pi$
$240$		0			0
$241$	7.25757	−	12.5705i	0.0301144	−	0.0521597i	−0.850575	−	0.525853i	$-0.823746\pi$
$241$	7.25757	−	12.5705i	0.0301144	−	0.0521597i	0.880690	+	0.473693i	$0.157080\pi$
$242$	−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	0.804594	−	0.593825i	$-0.202383\pi$
$257$	309.551	+	82.9440i	1.20448	+	0.322739i	0.399886	+	0.916565i	$0.369050\pi$
$258$		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	−0.489521	−	0.871992i	$-0.662828\pi$
$263$	−125.573	+	33.6471i	−0.477462	+	0.127936i	0.0120584	+	0.999927i	$0.496162\pi$
$264$		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	0.384366	−	0.923181i	$-0.374420\pi$
$269$	−59.9735	−	34.6257i	−0.222950	−	0.128720i	−0.607315	+	0.794461i	$0.707754\pi$
$270$		0			0
$271$	−207.020	−	358.570i	−0.763913	−	1.32314i	−0.940820	−	0.338908i	$-0.889943\pi$
$271$	−207.020	−	358.570i	−0.763913	−	1.32314i	0.176907	−	0.984228i	$-0.443391\pi$
$272$	−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	0.937033	−	0.349241i	$-0.113560\pi$
$277$	−13.5956	−	50.7395i	−0.0490816	−	0.183175i	−0.986115	+	0.166065i	$0.946894\pi$
$278$	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	0.0683786	−	0.997659i	$-0.478217\pi$
$283$	177.279	−	47.5016i	0.626426	−	0.167850i	0.558047	+	0.829809i	$0.311551\pi$
$284$	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	0.703274	−	0.710919i	$-0.251721\pi$
$293$	−2.24023	−	2.24023i	−0.00764585	−	0.00764585i	−0.710919	+	0.703274i	$0.751721\pi$
$294$		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	−0.581186	−	0.813771i	$-0.697411\pi$
$307$	71.4036	−	71.4036i	0.232585	−	0.232585i	0.813771	+	0.581186i	$0.197411\pi$
$308$	−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	−0.932495	−	0.361183i	$-0.882373\pi$
$311$	−47.7241	+	82.6605i	−0.153454	+	0.265789i	0.779041	+	0.626973i	$0.215706\pi$
$312$		0			0
$313$	−37.5811	+	140.255i	−0.120067	+	0.448098i	−0.999616	−	0.0277115i	$-0.991178\pi$
$313$	−37.5811	+	140.255i	−0.120067	+	0.448098i	0.879549	+	0.475809i	$0.157845\pi$
$314$			83.2252i			0.265048i
$315$		0			0
$316$	−198.244			−0.627354
$317$	−444.564	−	119.121i	−1.40241	−	0.375775i	−0.523201	−	0.852209i	$-0.675262\pi$
$317$	−444.564	−	119.121i	−1.40241	−	0.375775i	−0.879210	+	0.476434i	$0.841929\pi$
$318$		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	0.899201	−	0.437536i	$-0.144149\pi$
$331$	23.3963	+	40.5235i	0.0706836	+	0.122428i	−0.828517	+	0.559963i	$0.810815\pi$
$332$	−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	0.178877	−	0.983872i	$-0.442754\pi$
$337$	391.846	−	391.846i	1.16275	−	1.16275i	0.983872	−	0.178877i	$-0.0572463\pi$
$338$	−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	0.976938	−	0.213524i	$-0.0684942\pi$
$347$	8.37062	+	31.2396i	0.0241228	+	0.0900276i	−0.952815	+	0.303552i	$0.901828\pi$
$348$		0			0
$349$			214.001i			0.613183i	0.951841	+	0.306592i	$0.0991886\pi$
$349$			214.001i			0.613183i	−0.951841	+	0.306592i	$0.900811\pi$
$350$	−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	−0.0332725	−	0.999446i	$-0.510593\pi$
$353$	154.485	−	41.3943i	0.437636	−	0.117264i	0.470908	+	0.882182i	$0.343926\pi$
$354$		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	0.221317	−	0.975202i	$-0.428964\pi$
$359$	422.373	−	243.857i	1.17653	−	0.679267i	0.955208	+	0.295935i	$0.0956311\pi$
$360$		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	−0.994614	−	0.103652i	$-0.966947\pi$
$367$	−67.9239	−	253.495i	−0.185079	−	0.690723i	0.809535	−	0.587072i	$-0.199719\pi$
$368$	−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	−0.997139	−	0.0755927i	$-0.975915\pi$
$373$	−35.7315	+	133.352i	−0.0957949	+	0.357512i	0.901344	+	0.433104i	$0.142582\pi$
$374$	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	$-0.750494\pi$
$379$		−	535.154i		−	1.41202i	0.708204	−	0.706008i	$-0.249506\pi$
$380$	−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	−0.995701	−	0.0926283i	$-0.970473\pi$
$383$	−33.3533	+	124.476i	−0.0870845	+	0.325004i	0.908616	+	0.417632i	$0.137140\pi$
$384$		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	0.655685	−	0.755034i	$-0.272380\pi$
$389$	128.234	+	74.0357i	0.329649	+	0.190323i	−0.326036	+	0.945357i	$0.605713\pi$
$390$		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	−0.376333	−	0.926485i	$-0.622815\pi$
$397$	−462.699	−	123.980i	−1.16549	−	0.312292i	−0.789156	+	0.614193i	$0.789482\pi$
$398$	−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	−0.995236	−	0.0974907i	$-0.968918\pi$
$401$	−233.401	−	404.263i	−0.582048	−	1.00814i	0.413189	−	0.910645i	$-0.364415\pi$
$402$		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	−0.371029	−	0.928621i	$-0.620995\pi$
$409$	−556.548	−	321.323i	−1.36075	−	0.785631i	−0.989724	+	0.142990i	$0.954328\pi$
$410$	−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	$0.192658\pi$
$419$			476.798i			1.13794i	−0.822358	+	0.568971i	$0.807342\pi$
$420$		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	−0.719158	−	0.694847i	$-0.755472\pi$
$431$	104.378	−	180.788i	0.242176	−	0.419461i	0.961334	+	0.275386i	$0.0888055\pi$
$432$		0			0
$433$	−258.656	−	258.656i	−0.597358	−	0.597358i	0.342251	−	0.939609i	$-0.388811\pi$
$433$	−258.656	−	258.656i	−0.597358	−	0.597358i	−0.939609	+	0.342251i	$0.888811\pi$
$434$	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	0.104681	−	0.994506i	$-0.466618\pi$
$439$	447.029	−	258.092i	1.01829	−	0.587910i	0.913608	+	0.406596i	$0.133284\pi$
$440$	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	0.667574	+	0.744544i	$0.267333\pi$
$443$	−125.295	+	467.609i	−0.282834	+	1.05555i	−0.950408	+	0.311007i	$0.899334\pi$
$444$		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	$-0.894994\pi$
$449$		−	290.894i		−	0.647871i	0.946079	−	0.323936i	$-0.105006\pi$
$450$		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	0.346091	−	0.938201i	$-0.387509\pi$
$457$	80.7582	+	21.6391i	0.176714	+	0.0473503i	−0.169377	+	0.985551i	$0.554176\pi$
$458$	−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	0.971775	−	0.235910i	$-0.0758069\pi$
$463$	340.706	+	340.706i	0.735865	+	0.735865i	−0.235910	+	0.971775i	$0.575807\pi$
$464$	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	−0.188794	−	0.982017i	$-0.560458\pi$
$467$	−393.823	−	105.524i	−0.843304	−	0.225963i	−0.654509	+	0.756054i	$0.727125\pi$
$468$		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	0.947070	−	0.321027i	$-0.104028\pi$
$479$	547.299	+	315.983i	1.14259	+	0.659673i	0.195517	+	0.980700i	$0.437361\pi$
$480$		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	0.949608	−	0.313439i	$-0.101481\pi$
$487$	−14.3646	−	53.6096i	−0.0294962	−	0.110081i	−0.979104	+	0.203358i	$0.934815\pi$
$488$	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	0.599825	−	0.800131i	$-0.295237\pi$
$499$	794.743	−	458.845i	1.59267	−	0.919529i	0.992846	−	0.119398i	$-0.0380965\pi$
$500$	−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	0.387278	−	0.921963i	$-0.373415\pi$
$503$	−268.947	−	268.947i	−0.534685	−	0.534685i	−0.921963	+	0.387278i	$0.873415\pi$
$504$		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	−0.188935	−	0.981990i	$-0.560504\pi$
$509$	288.616	−	166.632i	0.567025	−	0.327372i	0.755960	+	0.654618i	$0.227170\pi$
$510$		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	−0.987700	−	0.156363i	$-0.950023\pi$
$521$	−186.745	+	323.451i	−0.358435	+	0.620828i	0.629264	+	0.777191i	$0.283356\pi$
$522$		0			0
$523$	−48.0280	+	179.243i	−0.0918317	+	0.342721i	−0.996520	−	0.0833533i	$-0.973437\pi$
$523$	−48.0280	+	179.243i	−0.0918317	+	0.342721i	0.904688	+	0.426074i	$0.140104\pi$
$524$		−	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	0.811861	+	0.583851i	$0.198455\pi$
$541$	493.154	+	854.168i	0.911560	+	1.57887i	0.0996992	+	0.995018i	$0.468212\pi$
$542$	−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	−0.218040	−	0.975940i	$-0.569966\pi$
$547$	414.571	−	414.571i	0.757899	−	0.757899i	0.975940	+	0.218040i	$0.0699664\pi$
$548$	−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	−0.782589	−	0.622539i	$-0.786101\pi$
$557$	−231.777	−	865.003i	−0.416116	−	1.55297i	0.366472	−	0.930429i	$-0.380565\pi$
$558$		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	0.520964	−	0.853578i	$-0.325572\pi$
$563$	787.593	−	211.035i	1.39892	−	0.374840i	0.877958	+	0.478738i	$0.158906\pi$
$564$		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	−0.351169	−	0.936312i	$-0.614216\pi$
$569$	161.663	−	93.3360i	0.284117	−	0.164035i	0.635286	+	0.772277i	$0.280882\pi$
$570$		0			0
$571$	399.962	−	692.755i	0.700459	−	1.21323i	−0.267846	−	0.963462i	$-0.586312\pi$
$571$	399.962	−	692.755i	0.700459	−	1.21323i	0.968305	−	0.249769i	$-0.0803548\pi$
$572$	−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	0.991392	−	0.130927i	$-0.0417953\pi$
$577$	38.8655	+	145.048i	0.0673579	+	0.251383i	−0.924034	+	0.382310i	$0.875129\pi$
$578$	−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	−0.825614	−	0.564236i	$-0.809171\pi$
$587$	−153.429	+	153.429i	−0.261378	+	0.261378i	0.564236	+	0.825614i	$0.309171\pi$
$588$		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	−0.966112	−	0.258124i	$-0.916896\pi$
$593$	−0.220820	+	0.824110i	−0.000372377	+	0.00138973i	0.965739	+	0.259514i	$0.0835623\pi$
$594$		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	0.952054	−	0.305929i	$-0.0989669\pi$
$599$	696.721	+	402.252i	1.16314	+	0.671539i	0.211085	+	0.977468i	$0.432300\pi$
$600$		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	0.0479951	−	0.998848i	$-0.484717\pi$
$607$	−248.787	−	66.6623i	−0.409864	−	0.109823i	−0.457859	+	0.889025i	$0.651383\pi$
$608$	−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	−0.996769	−	0.0803163i	$-0.974407\pi$
$613$	−1115.56	+	298.914i	−1.81984	+	0.487624i	−0.823069	+	0.567941i	$0.807740\pi$
$614$	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	−0.458949	−	0.888463i	$-0.651774\pi$
$617$	265.010	−	265.010i	0.429514	−	0.429514i	0.888463	+	0.458949i	$0.151774\pi$
$618$		0			0
$619$	758.758	+	438.069i	1.22578	+	0.707704i	0.966144	−	0.258003i	$-0.0830643\pi$
$619$	758.758	+	438.069i	1.22578	+	0.707704i	0.259635	+	0.965707i	$0.416398\pi$
$620$	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	−0.0452811	−	0.998974i	$-0.514418\pi$
$641$	540.040	−	935.377i	0.842497	−	1.45925i	0.887778	−	0.460273i	$-0.152248\pi$
$642$		0			0
$643$	−40.2830	−	40.2830i	−0.0626485	−	0.0626485i	0.675088	−	0.737737i	$-0.264105\pi$
$643$	−40.2830	−	40.2830i	−0.0626485	−	0.0626485i	−0.737737	+	0.675088i	$0.764105\pi$
$644$	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	0.998978	−	0.0451988i	$-0.0143921\pi$
$647$	71.9712	+	268.600i	0.111238	+	0.415147i	−0.887740	+	0.460346i	$0.847725\pi$
$648$		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	0.535669	+	0.844428i	$0.320059\pi$
$653$	−228.842	+	854.052i	−0.350448	+	1.30789i	−0.886117	+	0.463461i	$0.846607\pi$
$654$		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	$-0.893861\pi$
$659$		−	431.384i		−	0.654604i	0.944920	−	0.327302i	$-0.106139\pi$
$660$		0			0
$661$	−185.671	+	321.591i	−0.280894	+	0.486522i	−0.971605	−	0.236608i	$-0.923964\pi$
$661$	−185.671	+	321.591i	−0.280894	+	0.486522i	0.690711	+	0.723130i	$0.257297\pi$
$662$	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	0.441828	−	0.897100i	$-0.354330\pi$
$673$	−306.397	−	306.397i	−0.455271	−	0.455271i	−0.897100	+	0.441828i	$0.854330\pi$
$674$	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	0.958624	−	0.284674i	$-0.0918855\pi$
$677$	1114.67	+	298.674i	1.64648	+	0.441173i	0.687856	+	0.725847i	$0.258552\pi$
$678$		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	−0.842653	−	0.538456i	$-0.819008\pi$
$683$	−890.075	+	238.495i	−1.30318	+	0.349187i	−0.460531	+	0.887644i	$0.652341\pi$
$684$		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	0.920424	−	0.390921i	$-0.127844\pi$
$691$	84.0700	+	145.613i	0.121664	+	0.210729i	−0.798760	+	0.601650i	$0.794510\pi$
$692$	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	−0.478247	−	0.878225i	$-0.658728\pi$
$709$	30.6249	−	17.6813i	0.0431945	−	0.0249383i	0.521442	+	0.853287i	$0.325394\pi$
$710$	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	0.377247	−	0.926113i	$-0.376871\pi$
$719$	983.525	−	567.839i	1.36791	−	0.789762i	0.990661	+	0.136351i	$0.0435375\pi$
$720$		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	−0.715903	−	0.698200i	$-0.753985\pi$
$727$	−12.8697	+	12.8697i	−0.0177025	+	0.0177025i	0.698200	+	0.715903i	$0.253985\pi$
$728$	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	−0.799308	−	0.600922i	$-0.794800\pi$
$733$	141.743	−	528.993i	0.193374	−	0.721682i	0.992682	−	0.120760i	$-0.0385332\pi$
$734$		−	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	0.273386	−	0.961904i	$-0.411856\pi$
$739$	−312.563	−	180.459i	−0.422955	−	0.244193i	−0.696341	+	0.717711i	$0.745190\pi$
$740$	−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	0.368492	−	0.929631i	$-0.379874\pi$
$743$	−416.926	−	416.926i	−0.561138	−	0.561138i	−0.929631	+	0.368492i	$0.879874\pi$
$744$		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	−0.970160	−	0.242467i	$-0.922043\pi$
$751$	−521.992	−	904.116i	−0.695062	−	1.20388i	0.275097	−	0.961416i	$-0.411290\pi$
$752$	−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	−0.996547	−	0.0830364i	$-0.973538\pi$
$757$	−691.527	+	691.527i	−0.913510	+	0.913510i	0.0830364	+	0.996547i	$0.473538\pi$
$758$	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	−0.957773	−	0.287526i	$-0.907167\pi$
$761$	−553.925	−	959.427i	−0.727891	−	1.26074i	0.229881	−	0.973219i	$-0.426166\pi$
$762$		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	$-0.856196\pi$
$769$		−	671.432i		−	0.873124i	0.899674	−	0.436562i	$-0.143804\pi$
$770$	−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	0.545028	−	0.838418i	$-0.316519\pi$
$773$	1110.22	−	297.482i	1.43625	−	0.384841i	0.891217	+	0.453577i	$0.149852\pi$
$774$		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	0.954478	+	0.298282i	$0.0964137\pi$
$787$	218.012	+	813.633i	0.277017	+	1.03384i	−0.677461	+	0.735559i	$0.736920\pi$
$788$	−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	−0.993907	−	0.110218i	$-0.964845\pi$
$797$	−704.301	+	704.301i	−0.883690	+	0.883690i	0.110218	+	0.993907i	$0.464845\pi$
$798$		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	0.559507	−	0.828826i	$-0.310991\pi$
$809$	98.2739	+	56.7385i	0.121476	+	0.0701341i	−0.438031	+	0.898960i	$0.644324\pi$
$810$		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	0.915382	+	0.402586i	$0.131889\pi$
$821$	662.006	+	1146.63i	0.806341	+	1.39662i	−0.109041	+	0.994037i	$0.534778\pi$
$822$		0			0
$823$	809.040	−	216.782i	0.983038	−	0.263404i	0.268715	−	0.963220i	$-0.413401\pi$
$823$	809.040	−	216.782i	0.983038	−	0.263404i	0.714324	+	0.699816i	$0.246734\pi$
$824$	−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	−0.433100	−	0.901346i	$-0.642580\pi$
$827$	387.240	−	387.240i	0.468247	−	0.468247i	0.901346	+	0.433100i	$0.142580\pi$
$828$		0			0
$829$	120.871	+	69.7852i	0.145804	+	0.0841799i	0.571127	−	0.820862i	$-0.306506\pi$
$829$	120.871	+	69.7852i	0.145804	+	0.0841799i	−0.425323	+	0.905041i	$0.639840\pi$
$830$	−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	$0.382425\pi$
$839$			1564.83i			1.86511i	−0.361031	+	0.932554i	$0.617575\pi$
$840$		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	0.792968	−	0.609264i	$-0.208535\pi$
$853$	156.700	+	156.700i	0.183704	+	0.183704i	−0.609264	+	0.792968i	$0.708535\pi$
$854$	−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	0.940126	−	0.340828i	$-0.110707\pi$
$857$	−38.1030	−	142.202i	−0.0444610	−	0.165931i	−0.984587	+	0.174897i	$0.944041\pi$
$858$		0			0
$859$	−539.821	+	311.666i	−0.628429	+	0.362824i	−0.780143	−	0.625601i	$-0.784854\pi$
$859$	−539.821	+	311.666i	−0.628429	+	0.362824i	0.151714	+	0.988424i	$0.451521\pi$
$860$	−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	0.860973	+	0.508650i	$0.169855\pi$
$863$	−119.937	+	447.609i	−0.138976	+	0.518667i	−0.999950	+	0.0100170i	$0.996811\pi$
$864$		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	0.525410	−	0.850849i	$-0.323912\pi$
$877$	486.738	+	130.421i	0.555004	+	0.148713i	0.0295939	+	0.999562i	$0.490579\pi$
$878$	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	−0.953772	−	0.300530i	$-0.902836\pi$
$883$	−1107.55	−	1107.55i	−1.25430	−	1.25430i	−0.300530	−	0.953772i	$-0.597164\pi$
$884$	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	−0.101830	−	0.994802i	$-0.532470\pi$
$887$	−609.740	−	163.379i	−0.687419	−	0.184193i	−0.585588	+	0.810609i	$0.699137\pi$
$888$		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	−0.937901	−	0.346902i	$-0.887234\pi$
$907$	−271.289	−	1012.47i	−0.299106	−	1.11628i	0.638795	−	0.769377i	$-0.279433\pi$
$908$	−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	−0.570599	+	0.821229i	$0.693289\pi$
$919$	−1440.17	+	831.481i	−1.56710	+	0.904767i	−0.996505	+	0.0835384i	$0.973378\pi$
$920$	−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	−0.820476	−	0.571681i	$-0.806292\pi$
$929$	−683.395	+	394.558i	−0.735624	+	0.424713i	0.0848519	+	0.996394i	$0.472958\pi$
$930$		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	−0.935435	−	0.353499i	$-0.884992\pi$
$937$	−545.274	+	545.274i	−0.581936	+	0.581936i	0.353499	+	0.935435i	$0.384992\pi$
$938$	−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	−0.734370	−	0.678750i	$-0.762522\pi$
$941$	207.612	−	359.595i	0.220630	−	0.382142i	0.954999	+	0.296608i	$0.0958555\pi$
$942$		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	0.855109	−	0.518448i	$-0.173490\pi$
$947$	1265.60	+	339.117i	1.33643	+	0.358096i	0.481322	+	0.876544i	$0.340157\pi$
$948$		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	0.943288	+	0.331976i	$0.107715\pi$
$953$	1215.33	+	1215.33i	1.27526	+	1.27526i	0.331976	+	0.943288i	$0.392285\pi$
$954$		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	−0.126278	−	0.991995i	$-0.540303\pi$
$967$	837.149	−	837.149i	0.865717	−	0.865717i	0.991995	+	0.126278i	$0.0403030\pi$
$968$	−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	0.968609	−	0.248587i	$-0.0799663\pi$
$971$	261.220	+	452.447i	0.269022	+	0.465959i	−0.699588	+	0.714547i	$0.746633\pi$
$972$		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	0.906746	+	0.421677i	$0.138558\pi$
$977$	324.676	+	1211.71i	0.332320	+	1.24023i	−0.574427	+	0.818556i	$0.694775\pi$
$978$		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	−0.618502	−	0.785784i	$-0.712260\pi$
$983$	−748.307	+	200.508i	−0.761248	+	0.203976i	−0.142746	+	0.989759i	$0.545593\pi$
$984$		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	−0.765687	−	0.643213i	$-0.777601\pi$
$991$	172.628	−	299.000i	0.174195	−	0.301715i	0.939882	+	0.341498i	$0.110934\pi$
$992$	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	−0.992098	−	0.125463i	$-0.959958\pi$
$997$	−195.060	−	727.975i	−0.195647	−	0.730166i	0.796451	−	0.604703i	$-0.206708\pi$
$998$	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.298.10		64
3.2	odd	2		105.3.v.a.88.7	yes	64
5.2	odd	4	inner	315.3.ca.b.172.7		64
7.2	even	3	inner	315.3.ca.b.163.7		64
15.2	even	4		105.3.v.a.67.10	yes	64
21.2	odd	6		105.3.v.a.58.10	yes	64
35.2	odd	12	inner	315.3.ca.b.37.10		64
105.2	even	12		105.3.v.a.37.7	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.v.a.37.7	✓	64	105.2	even	12
105.3.v.a.58.10	yes	64	21.2	odd	6
105.3.v.a.67.10	yes	64	15.2	even	4
105.3.v.a.88.7	yes	64	3.2	odd	2
315.3.ca.b.37.10		64	35.2	odd	12	inner
315.3.ca.b.163.7		64	7.2	even	3	inner
315.3.ca.b.172.7		64	5.2	odd	4	inner
315.3.ca.b.298.10		64	1.1	even	1	trivial

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