LMFDB - Embedded newform 775.2.e.g.676.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [775,2,Mod(501,775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(775, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("775.501");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.e (of order $3$, degree $2$, 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:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} + 3x^{5} + 23x^{4} + x^{3} + 16x^{2} + 3x + 9 $ x^8 - x^7 + 6x^6 + 3x^5 + 23x^4 + x^3 + 16x^2 + 3*x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 155)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			676.1
Root			$-0.844316 + 1.46240i$ of defining polynomial
Character	$\chi$	$=$	775.676
Dual form			775.2.e.g.501.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.68863 q^{2} +(-1.34432 - 2.32842i) q^{3} +0.851477 q^{4} +(2.27005 + 3.93185i) q^{6} +(2.52642 + 4.37588i) q^{7} +1.93943 q^{8} +(-2.11437 + 3.66220i) q^{9} +O(q^{10})$	\(q-1.68863 q^{2} +(-1.34432 - 2.32842i) q^{3} +0.851477 q^{4} +(2.27005 + 3.93185i) q^{6} +(2.52642 + 4.37588i) q^{7} +1.93943 q^{8} +(-2.11437 + 3.66220i) q^{9} +(-0.726077 + 1.25760i) q^{11} +(-1.14465 - 1.98260i) q^{12} +(-0.381761 + 0.661230i) q^{13} +(-4.26619 - 7.38925i) q^{14} -4.97794 q^{16} +(-2.68476 - 4.65015i) q^{17} +(3.57039 - 6.18410i) q^{18} +(0.756362 + 1.31006i) q^{19} +(6.79260 - 11.7651i) q^{21} +(1.22608 - 2.12363i) q^{22} -3.39159 q^{23} +(-2.60721 - 4.51582i) q^{24} +(0.644655 - 1.11657i) q^{26} +3.30363 q^{27} +(2.15119 + 3.72596i) q^{28} -5.39159 q^{29} +(1.61171 - 5.32939i) q^{31} +4.52705 q^{32} +3.90431 q^{33} +(4.53358 + 7.85239i) q^{34} +(-1.80034 + 3.11828i) q^{36} +(-4.95869 - 8.58870i) q^{37} +(-1.27722 - 2.21220i) q^{38} +2.05283 q^{39} +(-0.604545 + 1.04710i) q^{41} +(-11.4702 + 19.8670i) q^{42} +(2.92840 + 5.07214i) q^{43} +(-0.618239 + 1.07082i) q^{44} +5.72714 q^{46} -5.15511 q^{47} +(6.69193 + 11.5908i) q^{48} +(-9.26556 + 16.0484i) q^{49} +(-7.21834 + 12.5025i) q^{51} +(-0.325061 + 0.563023i) q^{52} +(0.783748 - 1.35749i) q^{53} -5.57862 q^{54} +(4.89981 + 8.48672i) q^{56} +(2.03358 - 3.52226i) q^{57} +9.10440 q^{58} +(-5.78544 - 10.0207i) q^{59} -11.7742 q^{61} +(-2.72158 + 8.99938i) q^{62} -21.3671 q^{63} +2.31137 q^{64} -6.59294 q^{66} +(-2.64795 + 4.58638i) q^{67} +(-2.28602 - 3.95950i) q^{68} +(4.55936 + 7.89705i) q^{69} +(6.09681 - 10.5600i) q^{71} +(-4.10068 + 7.10258i) q^{72} +(-2.08795 + 3.61644i) q^{73} +(8.37340 + 14.5031i) q^{74} +(0.644025 + 1.11548i) q^{76} -7.33749 q^{77} -3.46648 q^{78} +(-0.868068 - 1.50354i) q^{79} +(1.90199 + 3.29434i) q^{81} +(1.02085 - 1.76817i) q^{82} +(4.88772 - 8.46578i) q^{83} +(5.78375 - 10.0177i) q^{84} +(-4.94499 - 8.56498i) q^{86} +(7.24800 + 12.5539i) q^{87} +(-1.40818 + 2.43904i) q^{88} +11.9649 q^{89} -3.85795 q^{91} -2.88786 q^{92} +(-14.5757 + 3.41165i) q^{93} +8.70508 q^{94} +(-6.08578 - 10.5409i) q^{96} +2.12840 q^{97} +(15.6461 - 27.0999i) q^{98} +(-3.07039 - 5.31808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 3 q^{3} + 6 q^{4} + 10 q^{6} + q^{7} + 18 q^{8} - q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 - 3 * q^3 + 6 * q^4 + 10 * q^6 + q^7 + 18 * q^8 - q^9	$ 8 q + 2 q^{2} - 3 q^{3} + 6 q^{4} + 10 q^{6} + q^{7} + 18 q^{8} - q^{9} + 4 q^{11} + 8 q^{12} - q^{13} - 8 q^{14} + 10 q^{16} + 12 q^{17} + 11 q^{18} - 5 q^{19} + 9 q^{21} - 10 q^{23} + 2 q^{24} - 12 q^{26} + 6 q^{27} - 4 q^{28} - 26 q^{29} + 19 q^{31} + 28 q^{32} - 8 q^{33} + 24 q^{34} - 5 q^{36} - 16 q^{37} - 9 q^{38} - 22 q^{39} - 4 q^{41} - 6 q^{42} + q^{43} - 7 q^{44} - 22 q^{46} - 20 q^{47} + 27 q^{48} - 37 q^{49} - 12 q^{51} - 21 q^{52} + q^{53} + 24 q^{54} - 29 q^{56} + 4 q^{57} - 26 q^{58} + 6 q^{59} - 2 q^{61} + 17 q^{62} - 24 q^{63} + 34 q^{64} + 2 q^{66} + 7 q^{67} + 5 q^{68} - 6 q^{69} + 12 q^{71} - 14 q^{72} - 20 q^{73} + 18 q^{74} - 23 q^{76} - 58 q^{77} - 22 q^{78} - 2 q^{79} + 12 q^{81} + 18 q^{82} + 4 q^{83} + 41 q^{84} - 13 q^{86} + 10 q^{88} + 54 q^{89} - 44 q^{91} - 86 q^{92} - 55 q^{93} - 48 q^{94} + 13 q^{96} + 18 q^{97} + 46 q^{98} - 7 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 - 3 * q^3 + 6 * q^4 + 10 * q^6 + q^7 + 18 * q^8 - q^9 + 4 * q^11 + 8 * q^12 - q^13 - 8 * q^14 + 10 * q^16 + 12 * q^17 + 11 * q^18 - 5 * q^19 + 9 * q^21 - 10 * q^23 + 2 * q^24 - 12 * q^26 + 6 * q^27 - 4 * q^28 - 26 * q^29 + 19 * q^31 + 28 * q^32 - 8 * q^33 + 24 * q^34 - 5 * q^36 - 16 * q^37 - 9 * q^38 - 22 * q^39 - 4 * q^41 - 6 * q^42 + q^43 - 7 * q^44 - 22 * q^46 - 20 * q^47 + 27 * q^48 - 37 * q^49 - 12 * q^51 - 21 * q^52 + q^53 + 24 * q^54 - 29 * q^56 + 4 * q^57 - 26 * q^58 + 6 * q^59 - 2 * q^61 + 17 * q^62 - 24 * q^63 + 34 * q^64 + 2 * q^66 + 7 * q^67 + 5 * q^68 - 6 * q^69 + 12 * q^71 - 14 * q^72 - 20 * q^73 + 18 * q^74 - 23 * q^76 - 58 * q^77 - 22 * q^78 - 2 * q^79 + 12 * q^81 + 18 * q^82 + 4 * q^83 + 41 * q^84 - 13 * q^86 + 10 * q^88 + 54 * q^89 - 44 * q^91 - 86 * q^92 - 55 * q^93 - 48 * q^94 + 13 * q^96 + 18 * q^97 + 46 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/775\mathbb{Z}\right)^\times$.

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−1.68863			−1.19404			−0.597022	−	0.802225i	$-0.703649\pi$
$2$	−1.68863			−1.19404			−0.597022	+	0.802225i	$0.703649\pi$
$3$	−1.34432	−	2.32842i	−0.776141	−	1.34432i	−0.934151	−	0.356878i	$-0.883841\pi$
$3$	−1.34432	−	2.32842i	−0.776141	−	1.34432i	0.158010	−	0.987438i	$-0.449492\pi$
$4$	0.851477			0.425739
$5$		0			0
$5$		0			0
$6$	2.27005	+	3.93185i	0.926746	+	1.60517i
$7$	2.52642	+	4.37588i	0.954896	+	1.65393i	0.734607	+	0.678493i	$0.237367\pi$
$7$	2.52642	+	4.37588i	0.954896	+	1.65393i	0.220288	+	0.975435i	$0.429300\pi$
$8$	1.93943			0.685693
$9$	−2.11437	+	3.66220i	−0.704790	+	1.22073i
$10$		0			0
$11$	−0.726077	+	1.25760i	−0.218921	+	0.379182i	−0.954478	−	0.298281i	$-0.903587\pi$
$11$	−0.726077	+	1.25760i	−0.218921	+	0.379182i	0.735558	+	0.677462i	$0.236920\pi$
$12$	−1.14465	−	1.98260i	−0.330433	−	0.572327i
$13$	−0.381761	+	0.661230i	−0.105882	+	0.183392i	−0.914098	−	0.405493i	$-0.867100\pi$
$13$	−0.381761	+	0.661230i	−0.105882	+	0.183392i	0.808216	+	0.588886i	$0.200433\pi$
$14$	−4.26619	−	7.38925i	−1.14019	−	1.97486i
$15$		0			0
$16$	−4.97794			−1.24449
$17$	−2.68476	−	4.65015i	−0.651151	−	1.12783i	−0.982844	−	0.184439i	$-0.940953\pi$
$17$	−2.68476	−	4.65015i	−0.651151	−	1.12783i	0.331693	−	0.943387i	$-0.392380\pi$
$18$	3.57039	−	6.18410i	0.841550	−	1.45761i
$19$	0.756362	+	1.31006i	0.173521	+	0.300548i	0.939649	−	0.342141i	$-0.111152\pi$
$19$	0.756362	+	1.31006i	0.173521	+	0.300548i	−0.766127	+	0.642689i	$0.777819\pi$
$20$		0			0
$21$	6.79260	−	11.7651i	1.48227	−	2.56736i
$22$	1.22608	−	2.12363i	0.261401	−	0.452759i
$23$	−3.39159			−0.707195			−0.353597	−	0.935398i	$-0.615042\pi$
$23$	−3.39159			−0.707195			−0.353597	+	0.935398i	$0.615042\pi$
$24$	−2.60721	−	4.51582i	−0.532194	−	0.921788i
$25$		0			0
$26$	0.644655	−	1.11657i	0.126427	−	0.218978i
$27$	3.30363			0.635784
$28$	2.15119	+	3.72596i	0.406536	+	0.704141i
$29$	−5.39159			−1.00119			−0.500596	−	0.865681i	$-0.666886\pi$
$29$	−5.39159			−1.00119			−0.500596	+	0.865681i	$0.666886\pi$
$30$		0			0
$31$	1.61171	−	5.32939i	0.289471	−	0.957187i
$31$	1.61171	−	5.32939i	0.289471	−	0.957187i
$32$	4.52705			0.800276
$33$	3.90431			0.679653
$34$	4.53358	+	7.85239i	0.777502	+	1.34667i
$35$		0			0
$36$	−1.80034	+	3.11828i	−0.300056	+	0.519713i
$37$	−4.95869	−	8.58870i	−0.815203	−	1.41197i	−0.909182	−	0.416399i	$-0.863292\pi$
$37$	−4.95869	−	8.58870i	−0.815203	−	1.41197i	0.0939790	−	0.995574i	$-0.470041\pi$
$38$	−1.27722	−	2.21220i	−0.207192	−	0.358867i
$39$	2.05283			0.328716
$40$		0			0
$41$	−0.604545	+	1.04710i	−0.0944141	+	0.163530i	−0.909364	−	0.416001i	$-0.863431\pi$
$41$	−0.604545	+	1.04710i	−0.0944141	+	0.163530i	0.814950	+	0.579532i	$0.196764\pi$
$42$	−11.4702	+	19.8670i	−1.76989	+	3.06554i
$43$	2.92840	+	5.07214i	0.446577	+	0.773494i	0.998161	−	0.0606254i	$-0.0193095\pi$
$43$	2.92840	+	5.07214i	0.446577	+	0.773494i	−0.551583	+	0.834120i	$0.685976\pi$
$44$	−0.618239	+	1.07082i	−0.0932030	+	0.161432i
$45$		0			0
$46$	5.72714			0.844421
$47$	−5.15511			−0.751950			−0.375975	−	0.926630i	$-0.622692\pi$
$47$	−5.15511			−0.751950			−0.375975	+	0.926630i	$0.622692\pi$
$48$	6.69193	+	11.5908i	0.965896	+	1.67298i
$49$	−9.26556	+	16.0484i	−1.32365	+	2.29263i
$50$		0			0
$51$	−7.21834	+	12.5025i	−1.01077	+	1.75070i
$52$	−0.325061	+	0.563023i	−0.0450779	+	0.0780772i
$53$	0.783748	−	1.35749i	0.107656	−	0.186466i	−0.807164	−	0.590327i	$-0.798999\pi$
$53$	0.783748	−	1.35749i	0.107656	−	0.186466i	0.914820	+	0.403861i	$0.132332\pi$
$54$	−5.57862			−0.759154
$55$		0			0
$56$	4.89981	+	8.48672i	0.654765	+	1.13409i
$57$	2.03358	−	3.52226i	0.269354	−	0.466535i
$58$	9.10440			1.19547
$59$	−5.78544	−	10.0207i	−0.753200	−	1.30458i	−0.946264	−	0.323395i	$-0.895176\pi$
$59$	−5.78544	−	10.0207i	−0.753200	−	1.30458i	0.193064	−	0.981186i	$-0.438158\pi$
$60$		0			0
$61$	−11.7742			−1.50753			−0.753764	−	0.657145i	$-0.771764\pi$
$61$	−11.7742			−1.50753			−0.753764	+	0.657145i	$0.771764\pi$
$62$	−2.72158	+	8.99938i	−0.345641	+	1.14292i
$63$	−21.3671			−2.69200
$64$	2.31137			0.288921
$65$		0			0
$66$	−6.59294			−0.811535
$67$	−2.64795	+	4.58638i	−0.323498	+	0.560316i	−0.981207	−	0.192957i	$-0.938192\pi$
$67$	−2.64795	+	4.58638i	−0.323498	+	0.560316i	0.657709	+	0.753272i	$0.271526\pi$
$68$	−2.28602	−	3.95950i	−0.277220	−	0.480159i
$69$	4.55936	+	7.89705i	0.548883	+	0.950693i
$70$		0			0
$71$	6.09681	−	10.5600i	0.723558	−	1.25324i	−0.236007	−	0.971751i	$-0.575839\pi$
$71$	6.09681	−	10.5600i	0.723558	−	1.25324i	0.959565	−	0.281488i	$-0.0908280\pi$
$72$	−4.10068	+	7.10258i	−0.483269	+	0.837047i
$73$	−2.08795	+	3.61644i	−0.244377	+	0.423273i	−0.961956	−	0.273204i	$-0.911917\pi$
$73$	−2.08795	+	3.61644i	−0.244377	+	0.423273i	0.717580	+	0.696477i	$0.245250\pi$
$74$	8.37340	+	14.5031i	0.973387	+	1.68596i
$75$		0			0
$76$	0.644025	+	1.11548i	0.0738747	+	0.127955i
$77$	−7.33749			−0.836185
$78$	−3.46648			−0.392501
$79$	−0.868068	−	1.50354i	−0.0976653	−	0.169161i	0.813053	−	0.582190i	$-0.197804\pi$
$79$	−0.868068	−	1.50354i	−0.0976653	−	0.169161i	−0.910718	+	0.413029i	$0.864471\pi$
$80$		0			0
$81$	1.90199	+	3.29434i	0.211332	+	0.366037i
$82$	1.02085	−	1.76817i	0.112735	−	0.195262i
$83$	4.88772	−	8.46578i	0.536497	−	0.929240i	−0.462592	−	0.886571i	$-0.653081\pi$
$83$	4.88772	−	8.46578i	0.536497	−	0.929240i	0.999089	−	0.0426687i	$-0.0135860\pi$
$84$	5.78375	−	10.0177i	0.631059	−	1.09303i
$85$		0			0
$86$	−4.94499	−	8.56498i	−0.533232	−	0.923586i
$87$	7.24800	+	12.5539i	0.777067	+	1.34592i
$88$	−1.40818	+	2.43904i	−0.150112	+	0.260002i
$89$	11.9649			1.26827			0.634137	−	0.773220i	$-0.281355\pi$
$89$	11.9649			1.26827			0.634137	+	0.773220i	$0.281355\pi$
$90$		0			0
$91$	−3.85795			−0.404423
$92$	−2.88786			−0.301080
$93$	−14.5757	+	3.41165i	−1.51143	+	0.353771i
$94$	8.70508			0.897861
$95$		0			0
$96$	−6.08578	−	10.5409i	−0.621127	−	1.07582i
$97$	2.12840			0.216107			0.108053	−	0.994145i	$-0.465538\pi$
$97$	2.12840			0.216107			0.108053	+	0.994145i	$0.465538\pi$
$98$	15.6461	−	27.0999i	1.58050	−	2.73750i
$99$	−3.07039	−	5.31808i	−0.308586	−	0.534487i
$100$		0			0
$101$	−2.30943			−0.229797			−0.114898	−	0.993377i	$-0.536654\pi$
$101$	−2.30943			−0.229797			−0.114898	+	0.993377i	$0.536654\pi$
$102$	12.1891	−	21.1122i	1.20690	−	2.09042i
$103$	1.19313	−	2.06656i	0.117563	−	0.203624i	−0.801239	−	0.598345i	$-0.795825\pi$
$103$	1.19313	−	2.06656i	0.117563	−	0.203624i	0.918801	+	0.394721i	$0.129159\pi$
$104$	−0.740400	+	1.28241i	−0.0726022	+	0.125751i
$105$		0			0
$106$	−1.32346	+	2.29230i	−0.128546	+	0.222648i
$107$	−9.25249	−	16.0258i	−0.894472	−	1.54927i	−0.834456	−	0.551074i	$-0.814218\pi$
$107$	−9.25249	−	16.0258i	−0.894472	−	1.54927i	−0.0600160	−	0.998197i	$-0.519115\pi$
$108$	2.81297			0.270678
$109$	−15.6732			−1.50122			−0.750608	−	0.660748i	$-0.770239\pi$
$109$	−15.6732			−1.50122			−0.750608	+	0.660748i	$0.770239\pi$
$110$		0			0
$111$	−13.3321	+	23.0918i	−1.26543	+	2.19178i
$112$	−12.5764	−	21.7829i	−1.18835	−	2.05829i
$113$	−10.0142	+	17.3451i	−0.942055	+	1.63169i	−0.180512	+	0.983573i	$0.557775\pi$
$113$	−10.0142	+	17.3451i	−0.942055	+	1.63169i	−0.761543	+	0.648114i	$0.775558\pi$
$114$	−3.43396	+	5.94780i	−0.321620	+	0.557062i
$115$		0			0
$116$	−4.59081			−0.426246
$117$	−1.61437	−	2.79617i	−0.149249	−	0.258506i
$118$	9.76948	+	16.9212i	0.899354	+	1.55773i
$119$	13.5657	−	23.4964i	1.24356	−	2.15391i
$120$		0			0
$121$	4.44562	+	7.70005i	0.404148	+	0.700004i
$122$	19.8823			1.80005
$123$	3.25080			0.293115
$124$	1.37233	−	4.53786i	0.123239	−	0.407511i
$125$		0			0
$126$	36.0812			3.21437
$127$	−2.89835	−	5.02009i	−0.257187	−	0.445461i	0.708300	−	0.705911i	$-0.249462\pi$
$127$	−2.89835	−	5.02009i	−0.257187	−	0.445461i	−0.965487	+	0.260450i	$0.916129\pi$
$128$	−12.9571			−1.14526
$129$	7.87340	−	13.6371i	0.693214	−	1.20068i
$130$		0			0
$131$	−3.06033	−	5.30065i	−0.267383	−	0.463120i	0.700802	−	0.713355i	$-0.252825\pi$
$131$	−3.06033	−	5.30065i	−0.267383	−	0.463120i	−0.968185	+	0.250235i	$0.919492\pi$
$132$	3.32443			0.289355
$133$	−3.82177	+	6.61950i	−0.331389	+	0.573983i
$134$	4.47141	−	7.74471i	0.386271	−	0.669041i
$135$		0			0
$136$	−5.20692	−	9.01864i	−0.446489	−	0.773342i
$137$	−2.12153	+	3.67460i	−0.181255	+	0.313942i	−0.942308	−	0.334747i	$-0.891349\pi$
$137$	−2.12153	+	3.67460i	−0.181255	+	0.313942i	0.761053	+	0.648689i	$0.224683\pi$
$138$	−7.69909	−	13.3352i	−0.655390	−	1.13517i
$139$	−19.1134			−1.62118			−0.810589	−	0.585616i	$-0.800853\pi$
$139$	−19.1134			−1.62118			−0.810589	+	0.585616i	$0.800853\pi$
$140$		0			0
$141$	6.93010	+	12.0033i	0.583619	+	1.01086i
$142$	−10.2953	+	17.8319i	−0.863960	+	1.49642i
$143$	−0.554377	−	0.960209i	−0.0463593	−	0.0802967i
$144$	10.5252	−	18.2302i	0.877101	−	1.51918i
$145$		0			0
$146$	3.52579	−	6.10684i	0.291796	−	0.505406i
$147$	49.8233			4.10936
$148$	−4.22221	−	7.31308i	−0.347063	−	0.601132i
$149$	3.21931	+	5.57601i	0.263736	+	0.456805i	0.967232	−	0.253895i	$-0.0817118\pi$
$149$	3.21931	+	5.57601i	0.263736	+	0.456805i	−0.703495	+	0.710700i	$0.748378\pi$
$150$		0			0
$151$	−5.45748			−0.444124			−0.222062	−	0.975033i	$-0.571279\pi$
$151$	−5.45748			−0.444124			−0.222062	+	0.975033i	$0.571279\pi$
$152$	1.46691	+	2.54077i	0.118982	+	0.206083i
$153$	22.7063			1.83570
$154$	12.3903			0.998441
$155$		0			0
$156$	1.74794			0.139947
$157$	13.8491			1.10528			0.552638	−	0.833421i	$-0.313621\pi$
$157$	13.8491			1.10528			0.552638	+	0.833421i	$0.313621\pi$
$158$	1.46585	+	2.53892i	0.116617	+	0.201986i
$159$	−4.21442			−0.334225
$160$		0			0
$161$	−8.56856	−	14.8412i	−0.675297	−	1.16965i
$162$	−3.21175	−	5.56292i	−0.252339	−	0.437064i
$163$	−0.560908			−0.0439337			−0.0219669	−	0.999759i	$-0.506993\pi$
$163$	−0.560908			−0.0439337			−0.0219669	+	0.999759i	$0.506993\pi$
$164$	−0.514757	+	0.891585i	−0.0401957	+	0.0696211i
$165$		0			0
$166$	−8.25356	+	14.2956i	−0.640600	+	1.10955i
$167$	0.628638	+	1.08883i	0.0486455	+	0.0842564i	0.889323	−	0.457280i	$-0.151176\pi$
$167$	0.628638	+	1.08883i	0.0486455	+	0.0842564i	−0.840677	+	0.541536i	$0.817843\pi$
$168$	13.1738	−	22.8177i	1.01638	−	1.76042i
$169$	6.20852	+	10.7535i	0.477578	+	0.827190i
$170$		0			0
$171$	−6.39691			−0.489184
$172$	2.49347	+	4.31881i	0.190125	+	0.329306i
$173$	0.421815	−	0.730606i	0.0320700	−	0.0555469i	−0.849545	−	0.527516i	$-0.823123\pi$
$173$	0.421815	−	0.730606i	0.0320700	−	0.0555469i	0.881615	+	0.471969i	$0.156457\pi$
$174$	−12.2392	−	21.1989i	−0.927851	−	1.60709i
$175$		0			0
$176$	3.61437	−	6.26027i	0.272443	−	0.471886i
$177$	−15.5549	+	26.9419i	−1.16918	+	2.02508i
$178$	−20.2043			−1.51437
$179$	−1.78108	−	3.08493i	−0.133124	−	0.230578i	0.791755	−	0.610839i	$-0.209168\pi$
$179$	−1.78108	−	3.08493i	−0.133124	−	0.230578i	−0.924879	+	0.380260i	$0.875834\pi$
$180$		0			0
$181$	5.23943	−	9.07496i	0.389444	−	0.674536i	−0.602931	−	0.797793i	$-0.706001\pi$
$181$	5.23943	−	9.07496i	0.389444	−	0.674536i	0.992375	+	0.123257i	$0.0393339\pi$
$182$	6.51466			0.482899
$183$	15.8282	+	27.4153i	1.17006	+	2.02660i
$184$	−6.57775			−0.484918
$185$		0			0
$186$	24.6130	−	5.76102i	1.80471	−	0.422418i
$187$	7.79739			0.570201
$188$	−4.38946			−0.320134
$189$	8.34635	+	14.4563i	0.607108	+	1.05154i
$190$		0			0
$191$	0.191295	−	0.331333i	0.0138417	−	0.0239744i	−0.859022	−	0.511939i	$-0.828927\pi$
$191$	0.191295	−	0.331333i	0.0138417	−	0.0239744i	0.872863	+	0.487965i	$0.162261\pi$
$192$	−3.10721	−	5.38184i	−0.224243	−	0.388401i
$193$	−3.24960	−	5.62846i	−0.233911	−	0.405146i	0.725045	−	0.688702i	$-0.241819\pi$
$193$	−3.24960	−	5.62846i	−0.233911	−	0.405146i	−0.958956	+	0.283556i	$0.908486\pi$
$194$	−3.59409			−0.258041
$195$		0			0
$196$	−7.88941	+	13.6649i	−0.563529	+	0.976062i
$197$	−4.52642	+	7.83998i	−0.322494	+	0.558576i	−0.981002	−	0.193998i	$-0.937854\pi$
$197$	−4.52642	+	7.83998i	−0.322494	+	0.558576i	0.658508	+	0.752574i	$0.271188\pi$
$198$	5.18476	+	8.98027i	0.368465	+	0.638200i
$199$	−4.71447	+	8.16571i	−0.334200	+	0.578852i	−0.983331	−	0.181825i	$-0.941799\pi$
$199$	−4.71447	+	8.16571i	−0.334200	+	0.578852i	0.649131	+	0.760677i	$0.275133\pi$
$200$		0			0
$201$	14.2387			1.00432
$202$	3.89977			0.274387
$203$	−13.6214	−	23.5929i	−0.956034	−	1.65590i
$204$	−6.14625	+	10.6456i	−0.430324	+	0.745343i
$205$		0			0
$206$	−2.01476	+	3.48966i	−0.140375	+	0.243136i
$207$	7.17107	−	12.4207i	0.498424	−	0.863295i
$208$	1.90039	−	3.29157i	0.131768	−	0.228229i
$209$	−2.19671			−0.151949
$210$		0			0
$211$	−1.82675	−	3.16403i	−0.125759	−	0.217821i	0.796270	−	0.604941i	$-0.206803\pi$
$211$	−1.82675	−	3.16403i	−0.125759	−	0.217821i	−0.922029	+	0.387120i	$0.873470\pi$
$212$	0.667343	−	1.15587i	0.0458333	−	0.0793857i
$213$	−32.7842			−2.24633
$214$	15.6241	+	27.0617i	1.06804	+	1.84990i
$215$		0			0
$216$	6.40717			0.435953
$217$	27.3926	−	6.41162i	1.85953	−	0.435249i
$218$	26.4662			1.79252
$219$	11.2275			0.758683
$220$		0			0
$221$	4.09976			0.275780
$222$	22.5130	−	38.9936i	1.51097	−	2.61708i
$223$	8.06323	+	13.9659i	0.539954	+	0.935228i	0.998906	+	0.0467665i	$0.0148917\pi$
$223$	8.06323	+	13.9659i	0.539954	+	0.935228i	−0.458952	+	0.888461i	$0.651775\pi$
$224$	11.4372	+	19.8098i	0.764180	+	1.32360i
$225$		0			0
$226$	16.9103	−	29.2894i	1.12485	−	1.94830i
$227$	−0.425739	+	0.737401i	−0.0282573	+	0.0489430i	−0.879808	−	0.475329i	$-0.842329\pi$
$227$	−0.425739	+	0.737401i	−0.0282573	+	0.0489430i	0.851551	+	0.524272i	$0.175662\pi$
$228$	1.73155	−	2.99912i	0.114674	−	0.198622i
$229$	9.65182	+	16.7174i	0.637810	+	1.10472i	0.985912	+	0.167263i	$0.0534928\pi$
$229$	9.65182	+	16.7174i	0.637810	+	1.10472i	−0.348102	+	0.937457i	$0.613174\pi$
$230$		0			0
$231$	9.86391	+	17.0848i	0.648998	+	1.12410i
$232$	−10.4566			−0.686510
$233$	−15.0790			−0.987855			−0.493928	−	0.869503i	$-0.664439\pi$
$233$	−15.0790			−0.987855			−0.493928	+	0.869503i	$0.664439\pi$
$234$	2.72608	+	4.72170i	0.178209	+	0.308667i
$235$		0			0
$236$	−4.92617	−	8.53238i	−0.320667	−	0.555411i
$237$	−2.33392	+	4.04246i	−0.151604	+	0.262586i
$238$	−22.9074	+	39.6768i	−1.48487	+	2.57186i
$239$	0.530859	−	0.919474i	0.0343384	−	0.0594758i	−0.848345	−	0.529443i	$-0.822401\pi$
$239$	0.530859	−	0.919474i	0.0343384	−	0.0594758i	0.882684	+	0.469967i	$0.155734\pi$
$240$		0			0
$241$	−1.39096	−	2.40921i	−0.0895994	−	0.155191i	0.817742	−	0.575584i	$-0.195225\pi$
$241$	−1.39096	−	2.40921i	−0.0895994	−	0.155191i	−0.907342	+	0.420394i	$0.861892\pi$
$242$	−7.50702	−	13.0025i	−0.482570	−	0.835835i
$243$	10.0692	−	17.4403i	0.645939	−	1.11880i
$244$	−10.0254			−0.641813
$245$		0			0
$246$	−5.48940			−0.349992
$247$	−1.15500			−0.0734908
$248$	3.12580	−	10.3360i	0.198488	−	0.656336i
$249$	−26.2826			−1.66559
$250$		0			0
$251$	2.13193	+	3.69261i	0.134566	+	0.233076i	0.925432	−	0.378914i	$-0.123703\pi$
$251$	2.13193	+	3.69261i	0.134566	+	0.233076i	−0.790865	+	0.611990i	$0.790369\pi$
$252$	−18.1936			−1.14609
$253$	2.46255	−	4.26527i	0.154819	−	0.268155i
$254$	4.89425	+	8.47709i	0.307093	+	0.531900i
$255$		0			0
$256$	17.2571			1.07857
$257$	−0.777216	+	1.34618i	−0.0484814	+	0.0839723i	−0.889248	−	0.457426i	$-0.848771\pi$
$257$	−0.777216	+	1.34618i	−0.0484814	+	0.0839723i	0.840766	+	0.541398i	$0.182105\pi$
$258$	−13.2953	+	23.0281i	−0.827727	+	1.43367i
$259$	25.0554	−	43.3972i	1.55687	−	2.69657i
$260$		0			0
$261$	11.3998	−	19.7451i	0.705631	−	1.22219i
$262$	5.16778	+	8.95085i	0.319266	+	0.552986i
$263$	3.20261			0.197482			0.0987408	−	0.995113i	$-0.468519\pi$
$263$	3.20261			0.197482			0.0987408	+	0.995113i	$0.468519\pi$
$264$	7.57214			0.466033
$265$		0			0
$266$	6.45356	−	11.1779i	0.395693	−	0.685361i
$267$	−16.0846	−	27.8593i	−0.984360	−	1.70496i
$268$	−2.25467	+	3.90520i	−0.137726	+	0.238548i
$269$	0.598014	−	1.03579i	0.0364615	−	0.0631532i	−0.847219	−	0.531244i	$-0.821725\pi$
$269$	0.598014	−	1.03579i	0.0364615	−	0.0631532i	0.883680	+	0.468091i	$0.155058\pi$
$270$		0			0
$271$	3.80930			0.231398			0.115699	−	0.993284i	$-0.463089\pi$
$271$	3.80930			0.231398			0.115699	+	0.993284i	$0.463089\pi$
$272$	13.3646	+	23.1482i	0.810348	+	1.40356i
$273$	5.18631	+	8.98295i	0.313890	+	0.543673i
$274$	3.58249	−	6.20505i	0.216426	−	0.374861i
$275$		0			0
$276$	3.88220	+	6.72416i	0.233681	+	0.404747i
$277$	−25.7035			−1.54437			−0.772186	−	0.635397i	$-0.780837\pi$
$277$	−25.7035			−1.54437			−0.772186	+	0.635397i	$0.780837\pi$
$278$	32.2755			1.93576
$279$	16.1095	+	17.1707i	0.964452	+	1.02798i
$280$		0			0
$281$	−26.2727			−1.56730			−0.783649	−	0.621204i	$-0.786644\pi$
$281$	−26.2727			−1.56730			−0.783649	+	0.621204i	$0.786644\pi$
$282$	−11.7024	−	20.2691i	−0.696867	−	1.20701i
$283$	−1.41771			−0.0842743			−0.0421371	−	0.999112i	$-0.513417\pi$
$283$	−1.41771			−0.0842743			−0.0421371	+	0.999112i	$0.513417\pi$
$284$	5.19130	−	8.99159i	0.308047	−	0.533553i
$285$		0			0
$286$	0.936138	+	1.62144i	0.0553550	+	0.0958777i
$287$	−6.10933			−0.360623
$288$	−9.57185	+	16.5789i	−0.564027	+	0.976923i
$289$	−5.91591	+	10.2467i	−0.347995	+	0.602745i
$290$		0			0
$291$	−2.86125	−	4.95583i	−0.167729	−	0.290516i
$292$	−1.77785	+	3.07932i	−0.104041	+	0.180204i
$293$	3.54277	+	6.13626i	0.206971	+	0.358484i	0.950759	−	0.309931i	$-0.100306\pi$
$293$	3.54277	+	6.13626i	0.206971	+	0.358484i	−0.743788	+	0.668416i	$0.766973\pi$
$294$	−84.1333			−4.90675
$295$		0			0
$296$	−9.61703	−	16.6572i	−0.558979	−	0.968180i
$297$	−2.39869	+	4.15466i	−0.139186	+	0.241078i
$298$	−5.43623	−	9.41583i	−0.314912	−	0.545444i
$299$	1.29478	−	2.24262i	0.0748789	−	0.129694i
$300$		0			0
$301$	−14.7967	+	25.6287i	−0.852869	+	1.47721i
$302$	9.21568			0.530303
$303$	3.10460	+	5.37733i	0.178355	+	0.308919i
$304$	−3.76512	−	6.52138i	−0.215945	−	0.374027i
$305$		0			0
$306$	−38.3427			−2.19190
$307$	3.86503	+	6.69443i	0.220589	+	0.382071i	0.954987	−	0.296648i	$-0.0958688\pi$
$307$	3.86503	+	6.69443i	0.220589	+	0.382071i	−0.734398	+	0.678719i	$0.762535\pi$
$308$	−6.24771			−0.355996
$309$	−6.41577			−0.364981
$310$		0			0
$311$	−0.887749			−0.0503396			−0.0251698	−	0.999683i	$-0.508013\pi$
$311$	−0.887749			−0.0503396			−0.0251698	+	0.999683i	$0.508013\pi$
$312$	3.98133			0.225398
$313$	−7.23551	−	12.5323i	−0.408975	−	0.708366i	0.585800	−	0.810456i	$-0.300780\pi$
$313$	−7.23551	−	12.5323i	−0.408975	−	0.708366i	−0.994775	+	0.102090i	$0.967447\pi$
$314$	−23.3860			−1.31975
$315$		0			0
$316$	−0.739141	−	1.28023i	−0.0415799	−	0.0720185i
$317$	4.83125	+	8.36798i	0.271350	+	0.469992i	0.969208	−	0.246244i	$-0.0791965\pi$
$317$	4.83125	+	8.36798i	0.271350	+	0.469992i	−0.697858	+	0.716236i	$0.745863\pi$
$318$	7.11660			0.399079
$319$	3.91471	−	6.78048i	0.219182	−	0.379634i
$320$		0			0
$321$	−24.8765	+	43.0874i	−1.38847	+	2.40491i
$322$	14.4691	+	25.0613i	0.806334	+	1.39661i
$323$	4.06130	−	7.03438i	0.225977	−	0.391404i
$324$	1.61950	+	2.80505i	0.0899721	+	0.155836i
$325$		0			0
$326$	0.947168			0.0524588
$327$	21.0697	+	36.4938i	1.16516	+	2.01811i
$328$	−1.17247	+	2.03079i	−0.0647391	+	0.112131i
$329$	−13.0240	−	22.5581i	−0.718034	−	1.24367i
$330$		0			0
$331$	15.1144	−	26.1789i	0.830761	−	1.43892i	−0.0666747	−	0.997775i	$-0.521239\pi$
$331$	15.1144	−	26.1789i	0.830761	−	1.43892i	0.897436	−	0.441145i	$-0.145428\pi$
$332$	4.16178	−	7.20842i	0.228407	−	0.395613i
$333$	41.9380			2.29819
$334$	−1.06154	−	1.83864i	−0.0580848	−	0.100606i
$335$		0			0
$336$	−33.8132	+	58.5661i	−1.84466	+	3.19504i
$337$	−10.1170			−0.551108			−0.275554	−	0.961286i	$-0.588861\pi$
$337$	−10.1170			−0.551108			−0.275554	+	0.961286i	$0.588861\pi$
$338$	−10.4839	−	18.1586i	−0.570249	−	0.987700i
$339$	53.8489			2.92467
$340$		0			0
$341$	5.53203	+	5.89644i	0.299576	+	0.319310i
$342$	10.8020			0.584107
$343$	−58.2648			−3.14600
$344$	5.67944	+	9.83707i	0.306215	+	0.530379i
$345$		0			0
$346$	−0.712291	+	1.23372i	−0.0382930	+	0.0663254i
$347$	−3.24960	−	5.62846i	−0.174447	−	0.302152i	0.765522	−	0.643409i	$-0.222481\pi$
$347$	−3.24960	−	5.62846i	−0.174447	−	0.302152i	−0.939970	+	0.341257i	$0.889147\pi$
$348$	6.17150	+	10.6894i	0.330827	+	0.573010i
$349$	−15.0765			−0.807029			−0.403515	−	0.914973i	$-0.632212\pi$
$349$	−15.0765			−0.807029			−0.403515	+	0.914973i	$0.632212\pi$
$350$		0			0
$351$	−1.26120	+	2.18446i	−0.0673179	+	0.116598i
$352$	−3.28699	+	5.69323i	−0.175197	+	0.303450i
$353$	−4.55670	−	7.89244i	−0.242529	−	0.420072i	0.718905	−	0.695108i	$-0.244644\pi$
$353$	−4.55670	−	7.89244i	−0.242529	−	0.420072i	−0.961434	+	0.275036i	$0.911310\pi$
$354$	26.2665	−	45.4950i	1.39605	−	2.41803i
$355$		0			0
$356$	10.1878			0.539954
$357$	−72.9461			−3.86072
$358$	3.00760	+	5.20931i	0.158956	+	0.275320i
$359$	−10.6398	+	18.4287i	−0.561548	+	0.972630i	0.435814	+	0.900037i	$0.356461\pi$
$359$	−10.6398	+	18.4287i	−0.561548	+	0.972630i	−0.997362	+	0.0725928i	$0.976873\pi$
$360$		0			0
$361$	8.35583	−	14.4727i	0.439781	−	0.761723i
$362$	−8.84747	+	15.3243i	−0.465013	+	0.805426i
$363$	11.9526	−	20.7026i	0.627351	−	1.08660i
$364$	−3.28496			−0.172179
$365$		0			0
$366$	−26.7280	−	46.2943i	−1.39710	−	2.41984i
$367$	−7.95215	+	13.7735i	−0.415099	+	0.718973i	−0.995439	−	0.0954017i	$-0.969586\pi$
$367$	−7.95215	+	13.7735i	−0.415099	+	0.718973i	0.580340	+	0.814374i	$0.302920\pi$
$368$	16.8831			0.880093
$369$	−2.55647	−	4.42793i	−0.133084	−	0.230509i
$370$		0			0
$371$	7.92029			0.411201
$372$	−12.4109	+	2.90494i	−0.643475	+	0.150614i
$373$	26.7444			1.38477			0.692386	−	0.721527i	$-0.256560\pi$
$373$	26.7444			1.38477			0.692386	+	0.721527i	$0.256560\pi$
$374$	−13.1669			−0.680845
$375$		0			0
$376$	−9.99798			−0.515607
$377$	2.05830	−	3.56508i	0.106008	−	0.183611i
$378$	−14.0939	−	24.4114i	−0.724913	−	1.25559i
$379$	4.36778	+	7.56521i	0.224358	+	0.388599i	0.956127	−	0.292954i	$-0.0946383\pi$
$379$	4.36778	+	7.56521i	0.224358	+	0.388599i	−0.731769	+	0.681553i	$0.761305\pi$
$380$		0			0
$381$	−7.79260	+	13.4972i	−0.399227	+	0.691482i
$382$	−0.323028	+	0.559500i	−0.0165275	+	0.0286265i
$383$	6.86174	−	11.8849i	0.350618	−	0.607289i	−0.635740	−	0.771904i	$-0.719305\pi$
$383$	6.86174	−	11.8849i	0.350618	−	0.607289i	0.986358	+	0.164615i	$0.0526381\pi$
$384$	17.4185	+	30.1697i	0.888884	+	1.53959i
$385$		0			0
$386$	5.48737	+	9.50440i	0.279300	+	0.483761i
$387$	−24.7669			−1.25897
$388$	1.81229			0.0920050
$389$	−5.54340	−	9.60146i	−0.281062	−	0.486813i	0.690585	−	0.723251i	$-0.257353\pi$
$389$	−5.54340	−	9.60146i	−0.281062	−	0.486813i	−0.971647	+	0.236438i	$0.924020\pi$
$390$		0			0
$391$	9.10561	+	15.7714i	0.460490	+	0.797593i
$392$	−17.9699	+	31.1248i	−0.907618	+	1.57204i
$393$	−8.22811	+	14.2515i	−0.415053	+	0.718893i
$394$	7.64345	−	13.2388i	0.385071	−	0.666963i
$395$		0			0
$396$	−2.61437	−	4.52822i	−0.131377	−	0.227552i
$397$	−8.38016	−	14.5149i	−0.420588	−	0.728480i	0.575409	−	0.817866i	$-0.304843\pi$
$397$	−8.38016	−	14.5149i	−0.420588	−	0.728480i	−0.995997	+	0.0893857i	$0.971510\pi$
$398$	7.96101	−	13.7889i	0.399049	−	0.691174i
$399$	20.5507			1.02882
$400$		0			0
$401$	−27.3990			−1.36824			−0.684121	−	0.729368i	$-0.739814\pi$
$401$	−27.3990			−1.36824			−0.684121	+	0.729368i	$0.739814\pi$
$402$	−24.0439			−1.19920
$403$	2.90867	+	3.10027i	0.144891	+	0.154435i
$404$	−1.96643			−0.0978333
$405$		0			0
$406$	23.0015	+	39.8398i	1.14155	+	1.97722i
$407$	14.4016			0.713859
$408$	−13.9995	+	24.2478i	−0.693078	+	1.20045i
$409$	−9.19662	−	15.9290i	−0.454744	−	0.787639i	0.543930	−	0.839131i	$-0.316936\pi$
$409$	−9.19662	−	15.9290i	−0.454744	−	0.787639i	−0.998673	+	0.0514916i	$0.983602\pi$
$410$		0			0
$411$	11.4080			0.562717
$412$	1.01592	−	1.75963i	0.0500509	−	0.0866908i
$413$	29.2329	−	50.6328i	1.43846	−	2.49148i
$414$	−12.1093	+	20.9739i	−0.595140	+	1.03081i
$415$		0			0
$416$	−1.72825	+	2.99342i	−0.0847345	+	0.146764i
$417$	25.6944	+	44.5041i	1.25826	+	2.17937i
$418$	3.70943			0.181434
$419$	−15.8228			−0.772996			−0.386498	−	0.922290i	$-0.626315\pi$
$419$	−15.8228			−0.772996			−0.386498	+	0.922290i	$0.626315\pi$
$420$		0			0
$421$	−9.26106	+	16.0406i	−0.451356	+	0.781772i	−0.998471	−	0.0552858i	$-0.982393\pi$
$421$	−9.26106	+	16.0406i	−0.451356	+	0.781772i	0.547114	+	0.837058i	$0.315726\pi$
$422$	3.08472	+	5.34289i	0.150162	+	0.260088i
$423$	10.8998	−	18.8790i	0.529967	−	0.917930i
$424$	1.52003	−	2.63276i	0.0738190	−	0.127858i
$425$		0			0
$426$	55.3604			2.68222
$427$	−29.7465	−	51.5224i	−1.43953	−	2.49334i
$428$	−7.87829	−	13.6456i	−0.380811	−	0.659585i
$429$	−1.49052	+	2.58165i	−0.0719627	+	0.124643i
$430$		0			0
$431$	12.3808	+	21.4441i	0.596360	+	1.03293i	0.993353	+	0.115104i	$0.0367203\pi$
$431$	12.3808	+	21.4441i	0.596360	+	1.03293i	−0.396993	+	0.917821i	$0.629946\pi$
$432$	−16.4453			−0.791224
$433$	10.5147			0.505302			0.252651	−	0.967557i	$-0.418697\pi$
$433$	10.5147			0.505302			0.252651	+	0.967557i	$0.418697\pi$
$434$	−46.2561	+	10.8269i	−2.22036	+	0.519706i
$435$		0			0
$436$	−13.3453			−0.639126
$437$	−2.56527	−	4.44317i	−0.122713	−	0.212546i
$438$	−18.9591			−0.905900
$439$	−2.06861	+	3.58295i	−0.0987296	+	0.171005i	−0.911159	−	0.412055i	$-0.864811\pi$
$439$	−2.06861	+	3.58295i	−0.0987296	+	0.171005i	0.812429	+	0.583059i	$0.198145\pi$
$440$		0			0
$441$	−39.1816	−	67.8646i	−1.86579	−	3.23165i
$442$	−6.92298			−0.329293
$443$	−3.41431	+	5.91376i	−0.162219	+	0.280971i	−0.935664	−	0.352892i	$-0.885198\pi$
$443$	−3.41431	+	5.91376i	−0.162219	+	0.280971i	0.773445	+	0.633863i	$0.218532\pi$
$444$	−11.3520	+	19.6622i	−0.538740	+	0.933126i
$445$		0			0
$446$	−13.6158	−	23.5833i	−0.644728	−	1.11670i
$447$	8.65554	−	14.9918i	0.409393	−	0.709090i
$448$	5.83948	+	10.1143i	0.275889	+	0.477854i
$449$	39.2979			1.85458			0.927290	−	0.374343i	$-0.122132\pi$
$449$	39.2979			1.85458			0.927290	+	0.374343i	$0.122132\pi$
$450$		0			0
$451$	−0.877894	−	1.52056i	−0.0413384	−	0.0716002i
$452$	−8.52685	+	14.7689i	−0.401069	+	0.694672i
$453$	7.33658	+	12.7073i	0.344703	+	0.597042i
$454$	0.718916	−	1.24520i	0.0337404	−	0.0584401i
$455$		0			0
$456$	3.94399	−	6.83118i	0.184694	−	0.319899i
$457$	−1.04056			−0.0486754			−0.0243377	−	0.999704i	$-0.507748\pi$
$457$	−1.04056			−0.0486754			−0.0243377	+	0.999704i	$0.507748\pi$
$458$	−16.2984	−	28.2296i	−0.761573	−	1.31908i
$459$	−8.86947	−	15.3624i	−0.413992	−	0.717054i
$460$		0			0
$461$	32.0205			1.49134			0.745672	−	0.666313i	$-0.232129\pi$
$461$	32.0205			1.49134			0.745672	+	0.666313i	$0.232129\pi$
$462$	−16.6565	−	28.8499i	−0.774931	−	1.34222i
$463$	30.3869			1.41220			0.706099	−	0.708113i	$-0.250453\pi$
$463$	30.3869			1.41220			0.706099	+	0.708113i	$0.250453\pi$
$464$	26.8390			1.24597
$465$		0			0
$466$	25.4628			1.17954
$467$	20.3582			0.942067			0.471033	−	0.882115i	$-0.343881\pi$
$467$	20.3582			0.942067			0.471033	+	0.882115i	$0.343881\pi$
$468$	−1.37460	−	2.38088i	−0.0635409	−	0.110056i
$469$	−26.7593			−1.23563
$470$		0			0
$471$	−18.6175	−	32.2465i	−0.857850	−	1.48584i
$472$	−11.2205	−	19.4344i	−0.516464	−	0.894542i
$473$	−8.50499			−0.391060
$474$	3.94113	−	6.82623i	0.181022	−	0.313539i
$475$		0			0
$476$	11.5509	−	20.0067i	0.529433	−	0.917004i
$477$	3.31427	+	5.74048i	0.151750	+	0.262838i
$478$	−0.896425	+	1.55265i	−0.0410015	+	0.0710167i
$479$	−8.73702	−	15.1330i	−0.399205	−	0.691443i	0.594423	−	0.804152i	$-0.297380\pi$
$479$	−8.73702	−	15.1330i	−0.399205	−	0.691443i	−0.993628	+	0.112709i	$0.964047\pi$
$480$		0			0
$481$	7.57214			0.345260
$482$	2.34881	+	4.06826i	0.106986	+	0.185304i
$483$	−23.0377	+	39.9025i	−1.04825	+	1.81563i
$484$	3.78535	+	6.55641i	0.172061	+	0.298019i
$485$		0			0
$486$	−17.0032	+	29.4503i	−0.771279	+	1.33589i
$487$	19.1585	−	33.1835i	0.868154	−	1.50369i	0.00427372	−	0.999991i	$-0.498640\pi$
$487$	19.1585	−	33.1835i	0.868154	−	1.50369i	0.863881	−	0.503697i	$-0.168027\pi$
$488$	−22.8352			−1.03370
$489$	0.754038	+	1.30603i	0.0340988	+	0.0590608i
$490$		0			0
$491$	−2.57475	+	4.45960i	−0.116197	+	0.201259i	−0.918258	−	0.395984i	$-0.870404\pi$
$491$	−2.57475	+	4.45960i	−0.116197	+	0.201259i	0.802061	+	0.597243i	$0.203737\pi$
$492$	2.76798			0.124790
$493$	14.4751	+	25.0717i	0.651927	+	1.12917i
$494$	1.95037			0.0877512
$495$		0			0
$496$	−8.02298	+	26.5294i	−0.360243	+	1.19120i
$497$	61.6123			2.76369
$498$	44.3816			1.98878
$499$	14.5305	+	25.1676i	0.650476	+	1.12666i	0.983007	+	0.183566i	$0.0587640\pi$
$499$	14.5305	+	25.1676i	0.650476	+	1.12666i	−0.332531	+	0.943092i	$0.607903\pi$
$500$		0			0
$501$	1.69018	−	2.92747i	0.0755115	−	0.130790i
$502$	−3.60005	−	6.23547i	−0.160678	−	0.278302i
$503$	4.81970	+	8.34796i	0.214900	+	0.372217i	0.953242	−	0.302209i	$-0.0977242\pi$
$503$	4.81970	+	8.34796i	0.214900	+	0.372217i	−0.738342	+	0.674427i	$0.764391\pi$
$504$	−41.4401			−1.84589
$505$		0			0
$506$	−4.15835	+	7.20247i	−0.184861	+	0.320189i
$507$	16.6924	−	28.9121i	0.741336	−	1.28403i
$508$	−2.46788	−	4.27450i	−0.109495	−	0.189650i
$509$	−8.27407	+	14.3311i	−0.366742	+	0.635215i	−0.989054	−	0.147554i	$-0.952860\pi$
$509$	−8.27407	+	14.3311i	−0.366742	+	0.635215i	0.622312	+	0.782769i	$0.286193\pi$
$510$		0			0
$511$	−21.1002			−0.933416
$512$	−3.22661			−0.142598
$513$	2.49874	+	4.32795i	0.110322	+	0.191083i
$514$	1.31243	−	2.27320i	0.0578889	−	0.100266i
$515$		0			0
$516$	6.70402	−	11.6117i	0.295128	−	0.511177i
$517$	3.74301	−	6.48308i	0.164617	−	0.285126i
$518$	−42.3094	+	73.2820i	−1.85897	+	3.21982i
$519$	−2.26821			−0.0995635
$520$		0			0
$521$	11.9890	+	20.7656i	0.525249	+	0.909758i	0.999568	+	0.0294044i	$0.00936106\pi$
$521$	11.9890	+	20.7656i	0.525249	+	0.909758i	−0.474319	+	0.880353i	$0.657306\pi$
$522$	−19.2501	+	33.3421i	−0.842553	+	1.45935i
$523$	0.165254			0.00722607			0.00361303	−	0.999993i	$-0.498850\pi$
$523$	0.165254			0.00722607			0.00361303	+	0.999993i	$0.498850\pi$
$524$	−2.60581	−	4.51339i	−0.113835	−	0.197168i
$525$		0			0
$526$	−5.40804			−0.235802
$527$	−29.1095	+	6.81348i	−1.26803	+	0.296800i
$528$	−19.4354			−0.845818
$529$	−11.4971			−0.499876
$530$		0			0
$531$	48.9303			2.12339
$532$	−3.25415	+	5.63635i	−0.141085	+	0.244367i
$533$	−0.461584	−	0.799487i	−0.0199934	−	0.0346296i
$534$	27.1609	+	47.0441i	1.17537	+	2.03580i
$535$		0			0
$536$	−5.13551	+	8.89497i	−0.221820	+	0.384204i
$537$	−4.78868	+	8.29424i	−0.206647	+	0.357923i
$538$	−1.00983	+	1.74907i	−0.0435367	+	0.0754077i
$539$	−13.4550	−	23.3048i	−0.579549	−	1.00381i
$540$		0			0
$541$	4.96527	+	8.60011i	0.213474	+	0.369747i	0.952799	−	0.303601i	$-0.0981889\pi$
$541$	4.96527	+	8.60011i	0.213474	+	0.369747i	−0.739326	+	0.673348i	$0.764856\pi$
$542$	−6.43250			−0.276300
$543$	−28.1738			−1.20905
$544$	−12.1540	−	21.0514i	−0.521101	−	0.902573i
$545$		0			0
$546$	−8.75777	−	15.1689i	−0.374798	−	0.649169i
$547$	5.24630	−	9.08686i	0.224316	−	0.388526i	−0.731798	−	0.681521i	$-0.761319\pi$
$547$	5.24630	−	9.08686i	0.224316	−	0.388526i	0.956114	+	0.292995i	$0.0946520\pi$
$548$	−1.80644	+	3.12884i	−0.0771671	+	0.133657i
$549$	24.8950	−	43.1194i	1.06249	−	1.84029i
$550$		0			0
$551$	−4.07799	−	7.06328i	−0.173728	−	0.300906i
$552$	8.84258	+	15.3158i	0.376365	+	0.651883i
$553$	4.38620	−	7.59713i	0.186520	−	0.323063i
$554$	43.4037			1.84405
$555$		0			0
$556$	−16.2746			−0.690198
$557$	−34.7858			−1.47392			−0.736961	−	0.675935i	$-0.763740\pi$
$557$	−34.7858			−1.47392			−0.736961	+	0.675935i	$0.763740\pi$
$558$	−27.2031	−	28.9950i	−1.15160	−	1.22746i
$559$	−4.47181			−0.189137
$560$		0			0
$561$	−10.4821	−	18.1556i	−0.442557	−	0.766531i
$562$	44.3649			1.87142
$563$	1.93546	−	3.35231i	0.0815698	−	0.141283i	−0.822355	−	0.568975i	$-0.807340\pi$
$563$	1.93546	−	3.35231i	0.0815698	−	0.141283i	0.903924	+	0.427692i	$0.140673\pi$
$564$	5.90082	+	10.2205i	0.248469	+	0.430362i
$565$		0			0
$566$	2.39400			0.100627
$567$	−9.61042	+	16.6457i	−0.403600	+	0.699055i
$568$	11.8243	−	20.4804i	0.496139	−	0.859337i
$569$	−11.2153	+	19.4255i	−0.470171	+	0.814361i	−0.999418	−	0.0341072i	$-0.989141\pi$
$569$	−11.2153	+	19.4255i	−0.470171	+	0.814361i	0.529247	+	0.848468i	$0.322475\pi$
$570$		0			0
$571$	17.3765	−	30.0969i	0.727182	−	1.25952i	−0.230888	−	0.972980i	$-0.574163\pi$
$571$	17.3765	−	30.0969i	0.727182	−	1.25952i	0.958070	−	0.286536i	$-0.0925037\pi$
$572$	−0.472039	−	0.817596i	−0.0197370	−	0.0341854i
$573$	−1.02865			−0.0429723
$574$	10.3164			0.430599
$575$		0			0
$576$	−4.88709	+	8.46469i	−0.203629	+	0.352695i
$577$	21.0346	+	36.4329i	0.875680	+	1.51672i	0.856037	+	0.516915i	$0.172920\pi$
$577$	21.0346	+	36.4329i	0.875680	+	1.51672i	0.0196434	+	0.999807i	$0.493747\pi$
$578$	9.98980	−	17.3028i	0.415521	−	0.719703i
$579$	−8.73697	+	15.1329i	−0.363096	+	0.628901i
$580$		0			0
$581$	49.3936			2.04919
$582$	4.83159	+	8.36856i	0.200276	+	0.346888i
$583$	1.13812	+	1.97129i	0.0471362	+	0.0816424i
$584$	−4.04945	+	7.01384i	−0.167567	+	0.290235i
$585$		0			0
$586$	−5.98244	−	10.3619i	−0.247132	−	0.428046i
$587$	23.7112			0.978666			0.489333	−	0.872097i	$-0.337240\pi$
$587$	23.7112			0.978666			0.489333	+	0.872097i	$0.337240\pi$
$588$	42.4234			1.74951
$589$	8.20084	−	1.91952i	0.337910	−	0.0790924i
$590$		0			0
$591$	24.3397			1.00120
$592$	24.6840	+	42.7540i	1.01451	+	1.75718i
$593$	−20.2727			−0.832500			−0.416250	−	0.909250i	$-0.636656\pi$
$593$	−20.2727			−0.832500			−0.416250	+	0.909250i	$0.636656\pi$
$594$	4.05051	−	7.01569i	0.166194	−	0.287857i
$595$		0			0
$596$	2.74117	+	4.74785i	0.112283	+	0.194479i
$597$	25.3510			1.03755
$598$	−2.18640	+	3.78696i	−0.0894086	+	0.154860i
$599$	−2.92637	+	5.06862i	−0.119568	+	0.207098i	−0.919597	−	0.392864i	$-0.871484\pi$
$599$	−2.92637	+	5.06862i	−0.119568	+	0.207098i	0.800028	+	0.599962i	$0.204818\pi$
$600$		0			0
$601$	10.6156	+	18.3867i	0.433018	+	0.750010i	0.997132	−	0.0756877i	$-0.0241152\pi$
$601$	10.6156	+	18.3867i	0.433018	+	0.750010i	−0.564113	+	0.825697i	$0.690782\pi$
$602$	24.9862	−	43.2774i	1.01836	−	1.76386i
$603$	−11.1975	−	19.3946i	−0.455997	−	0.789810i
$604$	−4.64692			−0.189081
$605$		0			0
$606$	−5.24253	−	9.08032i	−0.212963	−	0.368863i
$607$	−10.1879	+	17.6460i	−0.413515	+	0.716229i	−0.995271	−	0.0971344i	$-0.969032\pi$
$607$	−10.1879	+	17.6460i	−0.413515	+	0.716229i	0.581756	+	0.813363i	$0.302366\pi$
$608$	3.42408	+	5.93069i	0.138865	+	0.240521i
$609$	−36.6229	+	63.4327i	−1.48404	+	2.57042i
$610$		0			0
$611$	1.96802	−	3.40871i	0.0796177	−	0.137902i
$612$	19.3339			0.781528
$613$	3.62792	+	6.28375i	0.146530	+	0.253798i	0.929943	−	0.367704i	$-0.119856\pi$
$613$	3.62792	+	6.28375i	0.146530	+	0.253798i	−0.783412	+	0.621502i	$0.786523\pi$
$614$	−6.52661	−	11.3044i	−0.263393	−	0.456209i
$615$		0			0
$616$	−14.2306			−0.573366
$617$	−9.03880	−	15.6557i	−0.363888	−	0.630273i	0.624709	−	0.780858i	$-0.285218\pi$
$617$	−9.03880	−	15.6557i	−0.363888	−	0.630273i	−0.988597	+	0.150585i	$0.951884\pi$
$618$	10.8339			0.435802
$619$	16.9820			0.682565			0.341282	−	0.939961i	$-0.389139\pi$
$619$	16.9820			0.682565			0.341282	+	0.939961i	$0.389139\pi$
$620$		0			0
$621$	−11.2046			−0.449623
$622$	1.49908			0.0601076
$623$	30.2283	+	52.3569i	1.21107	+	2.09763i
$624$	−10.2189			−0.409083
$625$		0			0
$626$	12.2181	+	21.1624i	0.488334	+	0.845819i
$627$	2.95307	+	5.11487i	0.117934	+	0.204268i
$628$	11.7922			0.470559
$629$	−26.6258	+	46.1172i	−1.06164	+	1.83881i
$630$		0			0
$631$	−3.31414	+	5.74025i	−0.131934	+	0.228516i	−0.924422	−	0.381371i	$-0.875452\pi$
$631$	−3.31414	+	5.74025i	−0.131934	+	0.228516i	0.792488	+	0.609887i	$0.208785\pi$
$632$	−1.68356	−	2.91601i	−0.0669684	−	0.115993i
$633$	−4.91147	+	8.50692i	−0.195213	+	0.338120i
$634$	−8.15821	−	14.1304i	−0.324004	−	0.561191i
$635$		0			0
$636$	−3.58848			−0.142293
$637$	−7.07447	−	12.2533i	−0.280301	−	0.485495i
$638$	−6.61050	+	11.4497i	−0.261712	+	0.453299i
$639$	25.7818	+	44.6554i	1.01991	+	1.76654i
$640$		0			0
$641$	0.312538	−	0.541331i	0.0123445	−	0.0213813i	−0.859787	−	0.510653i	$-0.829404\pi$
$641$	0.312538	−	0.541331i	0.0123445	−	0.0213813i	0.872132	+	0.489271i	$0.162737\pi$
$642$	42.0073	−	72.7588i	1.65790	−	2.87156i
$643$	29.4044			1.15960			0.579798	−	0.814761i	$-0.303132\pi$
$643$	29.4044			1.15960			0.579798	+	0.814761i	$0.303132\pi$
$644$	−7.29593	−	12.6369i	−0.287500	−	0.497965i
$645$		0			0
$646$	−6.85805	+	11.8785i	−0.269826	+	0.467353i
$647$	−18.1462			−0.713402			−0.356701	−	0.934219i	$-0.616098\pi$
$647$	−18.1462			−0.713402			−0.356701	+	0.934219i	$0.616098\pi$
$648$	3.68877	+	6.38914i	0.144909	+	0.250989i
$649$	16.8027			0.659564
$650$		0			0
$651$	−51.7533	−	55.1624i	−2.02837	−	2.16198i
$652$	−0.477601			−0.0187043
$653$	33.0841			1.29468			0.647341	−	0.762201i	$-0.275881\pi$
$653$	33.0841			1.29468			0.647341	+	0.762201i	$0.275881\pi$
$654$	−35.5789	−	61.6245i	−1.39125	−	2.40971i
$655$		0			0
$656$	3.00939	−	5.21242i	0.117497	−	0.203511i
$657$	−8.82942	−	15.2930i	−0.344468	−	0.596637i
$658$	21.9927	+	38.0924i	0.857363	+	1.48500i
$659$	−6.45456			−0.251434			−0.125717	−	0.992066i	$-0.540123\pi$
$659$	−6.45456			−0.251434			−0.125717	+	0.992066i	$0.540123\pi$
$660$		0			0
$661$	22.8001	−	39.4909i	0.886820	−	1.53602i	0.0432069	−	0.999066i	$-0.486243\pi$
$661$	22.8001	−	39.4909i	0.886820	−	1.53602i	0.843613	−	0.536951i	$-0.180424\pi$
$662$	−25.5226	+	44.2065i	−0.991964	+	1.71813i
$663$	−5.51137	−	9.54597i	−0.214044	−	0.370735i
$664$	9.47940	−	16.4188i	0.367872	−	0.637173i
$665$		0			0
$666$	−70.8178			−2.74414
$667$	18.2860			0.708038
$668$	0.535271	+	0.927117i	0.0207103	+	0.0358712i
$669$	21.6791	−	37.5492i	0.838161	−	1.45174i
$670$		0			0
$671$	8.54896	−	14.8072i	0.330029	−	0.571627i
$672$	30.7504	−	53.2613i	1.18622	−	2.05460i
$673$	−2.68307	+	4.64721i	−0.103425	+	0.179137i	−0.913094	−	0.407750i	$-0.866313\pi$
$673$	−2.68307	+	4.64721i	−0.103425	+	0.179137i	0.809669	+	0.586887i	$0.199647\pi$
$674$	17.0839			0.658047
$675$		0			0
$676$	5.28641	+	9.15633i	0.203324	+	0.352167i
$677$	−19.1193	+	33.1156i	−0.734814	+	1.27274i	0.219990	+	0.975502i	$0.429397\pi$
$677$	−19.1193	+	33.1156i	−0.734814	+	1.27274i	−0.954805	+	0.297234i	$0.903936\pi$
$678$	−90.9310			−3.49218
$679$	5.37723	+	9.31364i	0.206359	+	0.357425i
$680$		0			0
$681$	2.28931			0.0877265
$682$	−9.34157	−	9.95691i	−0.357707	−	0.381270i
$683$	−42.6582			−1.63227			−0.816134	−	0.577862i	$-0.803887\pi$
$683$	−42.6582			−1.63227			−0.816134	+	0.577862i	$0.803887\pi$
$684$	−5.44683			−0.208265
$685$		0			0
$686$	98.3878			3.75646
$687$	25.9502	−	44.9470i	0.990061	−	1.71484i
$688$	−14.5774	−	25.2488i	−0.555759	−	0.962602i
$689$	0.598409	+	1.03648i	0.0227976	+	0.0394866i
$690$		0			0
$691$	9.20083	−	15.9363i	0.350016	−	0.606246i	−0.636236	−	0.771495i	$-0.719509\pi$
$691$	9.20083	−	15.9363i	0.350016	−	0.606246i	0.986252	+	0.165249i	$0.0528428\pi$
$692$	0.359166	−	0.622094i	0.0136535	−	0.0236485i
$693$	15.5142	−	26.8714i	0.589335	−	1.02076i
$694$	5.48737	+	9.50440i	0.208298	+	0.360782i
$695$		0			0
$696$	14.0570	+	24.3474i	0.532829	+	0.922887i
$697$	6.49225			0.245911
$698$	25.4587			0.963628
$699$	20.2709	+	35.1102i	0.766715	+	1.32799i
$700$		0			0
$701$	−0.808075	−	1.39963i	−0.0305206	−	0.0528632i	0.850362	−	0.526199i	$-0.176383\pi$
$701$	−0.808075	−	1.39963i	−0.0305206	−	0.0528632i	−0.880882	+	0.473335i	$0.843050\pi$
$702$	2.12970	−	3.68875i	0.0803804	−	0.139223i
$703$	7.50112	−	12.9923i	0.282910	−	0.490015i
$704$	−1.67823	+	2.90678i	−0.0632508	+	0.109554i
$705$		0			0
$706$	7.69459	+	13.3274i	0.289590	+	0.501584i
$707$	−5.83458	−	10.1058i	−0.219432	−	0.380067i
$708$	−13.2447	+	22.9404i	−0.497765	+	0.862154i
$709$	0.837154			0.0314400			0.0157200	−	0.999876i	$-0.494996\pi$
$709$	0.837154			0.0314400			0.0157200	+	0.999876i	$0.494996\pi$
$710$		0			0
$711$	7.34167			0.275334
$712$	23.2051			0.869647
$713$	−5.46624	+	18.0751i	−0.204712	+	0.676917i
$714$	123.179			4.60986
$715$		0			0
$716$	−1.51655	−	2.62675i	−0.0566762	−	0.0981661i
$717$	−2.85457			−0.106606
$718$	17.9667	−	31.1193i	0.670513	−	1.16136i
$719$	−20.3021	−	35.1642i	−0.757140	−	1.31141i	−0.944303	−	0.329076i	$-0.893263\pi$
$719$	−20.3021	−	35.1642i	−0.757140	−	1.31141i	0.187163	−	0.982329i	$-0.440071\pi$
$720$		0			0
$721$	12.0574			0.449040
$722$	−14.1099	+	24.4391i	−0.525117	+	0.909530i
$723$	−3.73977	+	6.47747i	−0.139084	+	0.240900i
$724$	4.46126	−	7.72712i	0.165801	−	0.287176i
$725$		0			0
$726$	−20.1836	+	34.9590i	−0.749084	+	1.29745i
$727$	20.8247	+	36.0694i	0.772345	+	1.33774i	0.936275	+	0.351269i	$0.114250\pi$
$727$	20.8247	+	36.0694i	0.772345	+	1.33774i	−0.163930	+	0.986472i	$0.552417\pi$
$728$	−7.48224			−0.277310
$729$	−42.7328			−1.58270
$730$		0			0
$731$	15.7241	−	27.2350i	0.581578	−	1.00732i
$732$	13.4774	+	23.3435i	0.498138	+	0.862800i
$733$	20.9344	−	36.2594i	0.773228	−	1.33927i	−0.162557	−	0.986699i	$-0.551974\pi$
$733$	20.9344	−	36.2594i	0.773228	−	1.33927i	0.935785	−	0.352571i	$-0.114693\pi$
$734$	13.4283	−	23.2584i	0.495646	−	0.858484i
$735$		0			0
$736$	−15.3539			−0.565951
$737$	−3.84523	−	6.66013i	−0.141641	−	0.245329i
$738$	4.31693	+	7.47714i	0.158908	+	0.275237i
$739$	−10.4543	+	18.1074i	−0.384568	+	0.666091i	−0.991709	−	0.128503i	$-0.958983\pi$
$739$	−10.4543	+	18.1074i	−0.384568	+	0.666091i	0.607141	+	0.794594i	$0.292316\pi$
$740$		0			0
$741$	1.55268	+	2.68933i	0.0570392	+	0.0987949i
$742$	−13.3745			−0.490992
$743$	−39.2816			−1.44110			−0.720551	−	0.693402i	$-0.756111\pi$
$743$	−39.2816			−1.44110			−0.720551	+	0.693402i	$0.756111\pi$
$744$	−28.2686	+	6.61666i	−1.03638	+	0.242578i
$745$		0			0
$746$	−45.1614			−1.65348
$747$	20.6689	+	35.7996i	0.756235	+	1.30984i
$748$	6.63930			0.242757
$749$	46.7513	−	80.9756i	1.70826	−	2.95878i
$750$		0			0
$751$	21.6008	+	37.4138i	0.788226	+	1.36525i	0.927053	+	0.374931i	$0.122334\pi$
$751$	21.6008	+	37.4138i	0.788226	+	1.36525i	−0.138827	+	0.990317i	$0.544333\pi$
$752$	25.6618			0.935791
$753$	5.73198	−	9.92808i	0.208885	−	0.361799i
$754$	−3.47571	+	6.02011i	−0.126578	+	0.219239i
$755$		0			0
$756$	7.10673	+	12.3092i	0.258469	+	0.447682i
$757$	16.0865	−	27.8627i	0.584674	−	1.01269i	−0.410242	−	0.911977i	$-0.634556\pi$
$757$	16.0865	−	27.8627i	0.584674	−	1.01269i	0.994916	−	0.100709i	$-0.0321110\pi$
$758$	−7.37557	−	12.7749i	−0.267893	−	0.464004i
$759$	−13.2418			−0.480647
$760$		0			0
$761$	−16.4054	−	28.4150i	−0.594696	−	1.03004i	−0.993590	−	0.113047i	$-0.963939\pi$
$761$	−16.4054	−	28.4150i	−0.594696	−	1.03004i	0.398893	−	0.916997i	$-0.369394\pi$
$762$	13.1588	−	22.7918i	0.476694	−	0.825659i
$763$	−39.5969	−	68.5839i	−1.43350	−	2.48290i
$764$	0.162884	−	0.282123i	0.00589293	−	0.0102068i
$765$		0			0
$766$	−11.5869	+	20.0692i	−0.418653	+	0.725129i
$767$	8.83463			0.319000
$768$	−23.1990	−	40.1818i	−0.837122	−	1.44994i
$769$	−23.5633	−	40.8128i	−0.849713	−	1.47175i	−0.881465	−	0.472250i	$-0.843442\pi$
$769$	−23.5633	−	40.8128i	−0.849713	−	1.47175i	0.0317522	−	0.999496i	$-0.489891\pi$
$770$		0			0
$771$	4.17930			0.150514
$772$	−2.76696	−	4.79251i	−0.0995850	−	0.172486i
$773$	−9.17775			−0.330101			−0.165050	−	0.986285i	$-0.552779\pi$
$773$	−9.17775			−0.330101			−0.165050	+	0.986285i	$0.552779\pi$
$774$	41.8222			1.50327
$775$		0			0
$776$	4.12789			0.148183
$777$	−134.730			−4.83340
$778$	9.36077	+	16.2133i	0.335600	+	0.581276i
$779$	−1.82902			−0.0655314
$780$		0			0
$781$	8.85351	+	15.3347i	0.316804	+	0.548720i
$782$	−15.3760	−	26.6320i	−0.549845	−	0.952360i
$783$	−17.8118			−0.636542
$784$	46.1234	−	79.8881i	1.64726	−	2.85315i
$785$		0			0
$786$	13.8943	−	24.0655i	0.495591	−	0.858390i
$787$	−9.40852	−	16.2960i	−0.335377	−	0.580891i	0.648180	−	0.761487i	$-0.275531\pi$
$787$	−9.40852	−	16.2960i	−0.335377	−	0.580891i	−0.983557	+	0.180597i	$0.942197\pi$
$788$	−3.85414	+	6.67557i	−0.137298	+	0.237807i
$789$	−4.30533	−	7.45704i	−0.153274	−	0.265478i
$790$		0			0
$791$	−101.200			−3.59826
$792$	−5.95482	−	10.3140i	−0.211595	−	0.366494i
$793$	4.49493	−	7.78544i	0.159620	−	0.276469i
$794$	14.1510	+	24.5103i	0.502200	+	0.869837i
$795$		0			0
$796$	−4.01427	+	6.95292i	−0.142282	+	0.246440i
$797$	−11.9938	+	20.7738i	−0.424841	+	0.735847i	−0.996406	−	0.0847104i	$-0.973003\pi$
$797$	−11.9938	+	20.7738i	−0.424841	+	0.735847i	0.571564	+	0.820557i	$0.306337\pi$
$798$	−34.7025			−1.22845
$799$	13.8403	+	23.9720i	0.489633	+	0.848069i
$800$		0			0
$801$	−25.2982	+	43.8177i	−0.893867	+	1.54822i
$802$	46.2669			1.63374
$803$	−3.03203	−	5.25164i	−0.106998	−	0.185326i
$804$	12.1239			0.427579
$805$		0			0
$806$	−4.91167	−	5.23521i	−0.173006	−	0.184402i
$807$	−3.21568			−0.113197
$808$	−4.47898			−0.157570
$809$	−3.99501	−	6.91957i	−0.140457	−	0.243279i	0.787212	−	0.616683i	$-0.211524\pi$
$809$	−3.99501	−	6.91957i	−0.140457	−	0.243279i	−0.927669	+	0.373404i	$0.878191\pi$
$810$		0			0
$811$	3.70038	−	6.40925i	0.129938	−	0.225059i	−0.793714	−	0.608291i	$-0.791855\pi$
$811$	3.70038	−	6.40925i	0.129938	−	0.225059i	0.923652	+	0.383231i	$0.125189\pi$
$812$	−11.5983	−	20.0889i	−0.407021	−	0.704981i
$813$	−5.12090	−	8.86966i	−0.179598	−	0.311073i
$814$	−24.3189			−0.852378
$815$		0			0
$816$	35.9325	−	62.2369i	1.25789	−	2.17873i
$817$	−4.42986	+	7.67275i	−0.154981	+	0.268435i
$818$	15.5297	+	26.8982i	0.542984	+	0.940475i
$819$	8.15714	−	14.1286i	0.285034	−	0.493693i
$820$		0			0
$821$	44.9331			1.56818			0.784088	−	0.620650i	$-0.213131\pi$
$821$	44.9331			1.56818			0.784088	+	0.620650i	$0.213131\pi$
$822$	−19.2640			−0.671908
$823$	−12.4658	−	21.5914i	−0.434530	−	0.752628i	0.562727	−	0.826643i	$-0.309752\pi$
$823$	−12.4658	−	21.5914i	−0.434530	−	0.752628i	−0.997257	+	0.0740144i	$0.976419\pi$
$824$	2.31399	−	4.00795i	0.0806118	−	0.139624i
$825$		0			0
$826$	−49.3635	+	85.5002i	−1.71758	+	2.97493i
$827$	20.7838	−	35.9986i	0.722723	−	1.25179i	−0.237181	−	0.971465i	$-0.576224\pi$
$827$	20.7838	−	35.9986i	0.722723	−	1.25179i	0.959904	−	0.280328i	$-0.0904431\pi$
$828$	6.10600	−	10.5759i	0.212198	−	0.367538i
$829$	−37.5957			−1.30575			−0.652876	−	0.757465i	$-0.726438\pi$
$829$	−37.5957			−1.30575			−0.652876	+	0.757465i	$0.726438\pi$
$830$		0			0
$831$	34.5536	+	59.8485i	1.19865	+	2.07612i
$832$	−0.882391	+	1.52835i	−0.0305914	+	0.0529859i
$833$	99.5033			3.44759
$834$	−43.3885	−	75.1510i	−1.50242	−	2.60227i
$835$		0			0
$836$	−1.87045			−0.0646908
$837$	5.32449	−	17.6063i	0.184041	−	0.608564i
$838$	26.7189			0.922990
$839$	45.2985			1.56388			0.781940	−	0.623354i	$-0.214231\pi$
$839$	45.2985			1.56388			0.781940	+	0.623354i	$0.214231\pi$
$840$		0			0
$841$	0.0692062			0.00238642
$842$	15.6385	−	27.0867i	0.538939	−	0.933470i
$843$	35.3188	+	61.1739i	1.21644	+	2.10694i
$844$	−1.55544	−	2.69410i	−0.0535405	−	0.0927348i
$845$		0			0
$846$	−18.4058	+	31.8797i	−0.632803	+	1.09605i
$847$	−22.4630	+	38.9070i	−0.771837	+	1.33686i
$848$	−3.90145	+	6.75751i	−0.133976	+	0.232054i
$849$	1.90585	+	3.30104i	0.0654087	+	0.113291i
$850$		0			0
$851$	16.8178	+	29.1293i	0.576507	+	0.998540i
$852$	−27.9150			−0.956351
$853$	−29.5952			−1.01332			−0.506660	−	0.862146i	$-0.669120\pi$
$853$	−29.5952			−1.01332			−0.506660	+	0.862146i	$0.669120\pi$
$854$	50.2308	+	87.0024i	1.71886	+	2.97716i
$855$		0			0
$856$	−17.9446	−	31.0809i	−0.613333	−	1.06232i
$857$	18.9100	−	32.7531i	0.645954	−	1.11883i	−0.338126	−	0.941101i	$-0.609793\pi$
$857$	18.9100	−	32.7531i	0.645954	−	1.11883i	0.984080	−	0.177724i	$-0.0568736\pi$
$858$	2.51693	−	4.35945i	0.0859266	−	0.148829i
$859$	19.9946	−	34.6316i	0.682207	−	1.18162i	−0.292099	−	0.956388i	$-0.594354\pi$
$859$	19.9946	−	34.6316i	0.682207	−	1.18162i	0.974306	−	0.225228i	$-0.0723128\pi$
$860$		0			0
$861$	8.21287	+	14.2251i	0.279894	+	0.484791i
$862$	−20.9065	−	36.2112i	−0.712080	−	1.23336i
$863$	−20.9482	+	36.2833i	−0.713085	+	1.23510i	0.250608	+	0.968089i	$0.419369\pi$
$863$	−20.9482	+	36.2833i	−0.713085	+	1.23510i	−0.963693	+	0.267011i	$0.913964\pi$
$864$	14.9557			0.508803
$865$		0			0
$866$	−17.7554			−0.603353
$867$	31.8114			1.08037
$868$	23.3242	−	5.45935i	0.791675	−	0.185302i
$869$	2.52114			0.0855238
$870$		0			0
$871$	−2.02177	−	3.50181i	−0.0685050	−	0.118654i
$872$	−30.3970			−1.02937
$873$	−4.50023	+	7.79463i	−0.152310	+	0.263808i
$874$	4.33179	+	7.50288i	0.146525	+	0.253789i
$875$		0			0
$876$	9.55995			0.323001
$877$	3.68356	−	6.38011i	0.124385	−	0.215441i	−0.797107	−	0.603838i	$-0.793638\pi$
$877$	3.68356	−	6.38011i	0.124385	−	0.215441i	0.921492	+	0.388396i	$0.126971\pi$
$878$	3.49313	−	6.05028i	0.117887	−	0.204187i
$879$	9.52521	−	16.4982i	0.321277	−	0.556469i
$880$		0			0
$881$	−7.39305	+	12.8051i	−0.249078	+	0.431416i	−0.963270	−	0.268534i	$-0.913461\pi$
$881$	−7.39305	+	12.8051i	−0.249078	+	0.431416i	0.714192	+	0.699950i	$0.246794\pi$
$882$	66.1634	+	114.598i	2.22784	+	3.85873i
$883$	−26.9381			−0.906540			−0.453270	−	0.891373i	$-0.649743\pi$
$883$	−26.9381			−0.906540			−0.453270	+	0.891373i	$0.649743\pi$
$884$	3.49085			0.117410
$885$		0			0
$886$	5.76552	−	9.98617i	0.193696	−	0.335492i
$887$	24.7570	+	42.8803i	0.831257	+	1.43978i	0.897042	+	0.441946i	$0.145712\pi$
$887$	24.7570	+	42.8803i	0.831257	+	1.43978i	−0.0657844	+	0.997834i	$0.520955\pi$
$888$	−25.8567	+	44.7851i	−0.867693	+	1.50289i
$889$	14.6449	−	25.3657i	0.491174	−	0.850738i
$890$		0			0
$891$	−5.52396			−0.185060
$892$	6.86566	+	11.8917i	0.229879	+	0.398163i
$893$	−3.89913	−	6.75349i	−0.130479	−	0.225997i
$894$	−14.6160	+	25.3157i	−0.488833	+	0.846684i
$895$		0			0
$896$	−32.7351	−	56.6989i	−1.09360	−	1.89418i
$897$	−6.96236			−0.232466
$898$	−66.3596			−2.21445
$899$	−8.68966	+	28.7339i	−0.289816	+	0.958328i
$900$		0			0
$901$	−8.41671			−0.280401
$902$	1.48244	+	2.56766i	0.0493598	+	0.0854937i
$903$	79.5659			2.64779
$904$	−19.4218	+	33.6396i	−0.645960	+	1.11884i
$905$		0			0
$906$	−12.3888	−	21.4580i	−0.411590	−	0.712894i
$907$	−45.9931			−1.52718			−0.763588	−	0.645703i	$-0.776564\pi$
$907$	−45.9931			−1.52718			−0.763588	+	0.645703i	$0.776564\pi$
$908$	−0.362507	+	0.627880i	−0.0120302	+	0.0208369i
$909$	4.88299	−	8.45758i	0.161958	−	0.280520i
$910$		0			0
$911$	21.8197	+	37.7929i	0.722920	+	1.25213i	0.959824	+	0.280602i	$0.0905340\pi$
$911$	21.8197	+	37.7929i	0.722920	+	1.25213i	−0.236904	+	0.971533i	$0.576133\pi$
$912$	−10.1230	+	17.5336i	−0.335207	+	0.580596i
$913$	7.09772	+	12.2936i	0.234900	+	0.406859i
$914$	1.75712			0.0581205
$915$		0			0
$916$	8.21830	+	14.2345i	0.271540	+	0.470322i
$917$	15.4634	−	26.7833i	0.510645	−	0.884463i
$918$	14.9773	+	25.9414i	0.494324	+	0.856194i
$919$	5.89866	−	10.2168i	0.194579	−	0.337021i	−0.752183	−	0.658954i	$-0.770999\pi$
$919$	5.89866	−	10.2168i	0.194579	−	0.337021i	0.946762	+	0.321933i	$0.104333\pi$
$920$		0			0
$921$	10.3916	−	17.9989i	0.342416	−	0.593082i
$922$	−54.0709			−1.78073
$923$	4.65505	+	8.06279i	0.153223	+	0.265390i
$924$	8.39890	+	14.5473i	0.276303	+	0.478572i
$925$		0			0
$926$	−51.3123			−1.68623
$927$	5.04544	+	8.73895i	0.165714	+	0.287025i
$928$	−24.4080			−0.801231
$929$	−6.37136			−0.209037			−0.104519	−	0.994523i	$-0.533330\pi$
$929$	−6.37136			−0.209037			−0.104519	+	0.994523i	$0.533330\pi$
$930$		0			0
$931$	−28.0324			−0.918726
$932$	−12.8394			−0.420568
$933$	1.19341	+	2.06705i	0.0390706	+	0.0676723i
$934$	−34.3776			−1.12487
$935$		0			0
$936$	−3.13096	−	5.42298i	−0.102339	−	0.177256i
$937$	22.0463	+	38.1853i	0.720221	+	1.24746i	0.960911	+	0.276858i	$0.0892931\pi$
$937$	22.0463	+	38.1853i	0.720221	+	1.24746i	−0.240690	+	0.970602i	$0.577374\pi$
$938$	45.1866			1.47539
$939$	−19.4536	+	33.6946i	−0.634845	+	1.09958i
$940$		0			0
$941$	−13.8396	+	23.9709i	−0.451158	+	0.781428i	−0.998458	−	0.0555083i	$-0.982322\pi$
$941$	−13.8396	+	23.9709i	−0.451158	+	0.781428i	0.547301	+	0.836936i	$0.315655\pi$
$942$	31.4381	+	54.4525i	1.02431	+	1.77416i
$943$	2.05037	−	3.55134i	0.0667692	−	0.115648i
$944$	28.7996	+	49.8823i	0.937347	+	1.62353i
$945$		0			0
$946$	14.3618			0.466942
$947$	5.45505	+	9.44843i	0.177265	+	0.307033i	0.940943	−	0.338565i	$-0.109942\pi$
$947$	5.45505	+	9.44843i	0.177265	+	0.307033i	−0.763678	+	0.645598i	$0.776608\pi$
$948$	−1.98728	+	3.44206i	−0.0645438	+	0.111793i
$949$	−1.59420	−	2.76124i	−0.0517500	−	0.0896336i
$950$		0			0
$951$	12.9895	−	22.4984i	0.421212	−	0.729561i
$952$	26.3097	−	45.5697i	0.852701	−	1.47692i
$953$	−48.5218			−1.57178			−0.785888	−	0.618369i	$-0.787794\pi$
$953$	−48.5218			−1.57178			−0.785888	+	0.618369i	$0.787794\pi$
$954$	−5.59658	−	9.69355i	−0.181196	−	0.313840i
$955$		0			0
$956$	0.452014	−	0.782911i	0.0146192	−	0.0253212i
$957$	−21.0504			−0.680464
$958$	14.7536	+	25.5540i	0.476668	+	0.825612i
$959$	−21.4395			−0.692317
$960$		0			0
$961$	−25.8048	−	17.1788i	−0.832413	−	0.554156i
$962$	−12.7866			−0.412255
$963$	78.2528			2.52166
$964$	−1.18437	−	2.05139i	−0.0381459	−	0.0660707i
$965$		0			0
$966$	38.9022	−	67.3806i	1.25166	−	2.16793i
$967$	7.10358	+	12.3038i	0.228436	+	0.395662i	0.957345	−	0.288948i	$-0.0933056\pi$
$967$	7.10358	+	12.3038i	0.228436	+	0.395662i	−0.728909	+	0.684611i	$0.759972\pi$
$968$	8.62198	+	14.9337i	0.277121	+	0.479988i
$969$	−21.8387			−0.701560
$970$		0			0
$971$	−2.74960	+	4.76244i	−0.0882387	+	0.152834i	−0.906767	−	0.421633i	$-0.861457\pi$
$971$	−2.74960	+	4.76244i	−0.0882387	+	0.152834i	0.818528	+	0.574467i	$0.194791\pi$
$972$	8.57369	−	14.8501i	0.275001	−	0.476316i
$973$	−48.2884	−	83.6380i	−1.54806	−	2.68131i
$974$	−32.3516	+	56.0347i	−1.03661	+	1.79547i
$975$		0			0
$976$	58.6112			1.87610
$977$	−20.4950			−0.655694			−0.327847	−	0.944731i	$-0.606323\pi$
$977$	−20.4950			−0.655694			−0.327847	+	0.944731i	$0.606323\pi$
$978$	−1.27329	−	2.20541i	−0.0407154	−	0.0705212i
$979$	−8.68743	+	15.0471i	−0.277651	+	0.480906i
$980$		0			0
$981$	33.1389	−	57.3982i	1.05804	−	1.83258i
$982$	4.34781	−	7.53062i	0.138744	−	0.240312i
$983$	−9.63150	+	16.6822i	−0.307197	+	0.532081i	−0.977748	−	0.209782i	$-0.932724\pi$
$983$	−9.63150	+	16.6822i	−0.307197	+	0.532081i	0.670551	+	0.741864i	$0.266058\pi$
$984$	6.30470			0.200987
$985$		0			0
$986$	−24.4432	−	42.3368i	−0.778429	−	1.34828i
$987$	−35.0166	+	60.6506i	−1.11459	+	1.93053i
$988$	−0.983455			−0.0312879
$989$	−9.93193	−	17.2026i	−0.315817	−	0.547011i
$990$		0			0
$991$	−32.6303			−1.03654			−0.518268	−	0.855218i	$-0.673423\pi$
$991$	−32.6303			−1.03654			−0.518268	+	0.855218i	$0.673423\pi$
$992$	7.29627	−	24.1264i	0.231657	−	0.766014i
$993$	−81.2740			−2.57915
$994$	−104.041			−3.29996
$995$		0			0
$996$	−22.3790			−0.709106
$997$	−16.4797	+	28.5437i	−0.521919	+	0.903990i	0.477756	+	0.878492i	$0.341450\pi$
$997$	−16.4797	+	28.5437i	−0.521919	+	0.903990i	−0.999675	+	0.0254971i	$0.991883\pi$
$998$	−24.5367	−	42.4989i	−0.776697	−	1.34528i
$999$	−16.3817	−	28.3739i	−0.518293	−	0.897710i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.e.g.676.1		8
5.2	odd	4		775.2.o.e.149.2		16
5.3	odd	4		775.2.o.e.149.7		16
5.4	even	2		155.2.e.c.56.4	yes	8
31.5	even	3	inner	775.2.e.g.501.1		8
155.67	odd	12		775.2.o.e.749.2		16
155.98	odd	12		775.2.o.e.749.7		16
155.99	odd	6		4805.2.a.k.1.4		4
155.129	even	6		155.2.e.c.36.4	✓	8
155.149	even	6		4805.2.a.i.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.e.c.36.4	✓	8	155.129	even	6
155.2.e.c.56.4	yes	8	5.4	even	2
775.2.e.g.501.1		8	31.5	even	3	inner
775.2.e.g.676.1		8	1.1	even	1	trivial
775.2.o.e.149.2		16	5.2	odd	4
775.2.o.e.149.7		16	5.3	odd	4
775.2.o.e.749.2		16	155.67	odd	12
775.2.o.e.749.7		16	155.98	odd	12
4805.2.a.i.1.4		4	155.149	even	6
4805.2.a.k.1.4		4	155.99	odd	6

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:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.68863 q^{2} +(-1.34432 - 2.32842i) q^{3} +0.851477 q^{4} +(2.27005 + 3.93185i) q^{6} +(2.52642 + 4.37588i) q^{7} +1.93943 q^{8} +(-2.11437 + 3.66220i) q^{9} +O(q^{10})\)	\(q-1.68863 q^{2} +(-1.34432 - 2.32842i) q^{3} +0.851477 q^{4} +(2.27005 + 3.93185i) q^{6} +(2.52642 + 4.37588i) q^{7} +1.93943 q^{8} +(-2.11437 + 3.66220i) q^{9} +(-0.726077 + 1.25760i) q^{11} +(-1.14465 - 1.98260i) q^{12} +(-0.381761 + 0.661230i) q^{13} +(-4.26619 - 7.38925i) q^{14} -4.97794 q^{16} +(-2.68476 - 4.65015i) q^{17} +(3.57039 - 6.18410i) q^{18} +(0.756362 + 1.31006i) q^{19} +(6.79260 - 11.7651i) q^{21} +(1.22608 - 2.12363i) q^{22} -3.39159 q^{23} +(-2.60721 - 4.51582i) q^{24} +(0.644655 - 1.11657i) q^{26} +3.30363 q^{27} +(2.15119 + 3.72596i) q^{28} -5.39159 q^{29} +(1.61171 - 5.32939i) q^{31} +4.52705 q^{32} +3.90431 q^{33} +(4.53358 + 7.85239i) q^{34} +(-1.80034 + 3.11828i) q^{36} +(-4.95869 - 8.58870i) q^{37} +(-1.27722 - 2.21220i) q^{38} +2.05283 q^{39} +(-0.604545 + 1.04710i) q^{41} +(-11.4702 + 19.8670i) q^{42} +(2.92840 + 5.07214i) q^{43} +(-0.618239 + 1.07082i) q^{44} +5.72714 q^{46} -5.15511 q^{47} +(6.69193 + 11.5908i) q^{48} +(-9.26556 + 16.0484i) q^{49} +(-7.21834 + 12.5025i) q^{51} +(-0.325061 + 0.563023i) q^{52} +(0.783748 - 1.35749i) q^{53} -5.57862 q^{54} +(4.89981 + 8.48672i) q^{56} +(2.03358 - 3.52226i) q^{57} +9.10440 q^{58} +(-5.78544 - 10.0207i) q^{59} -11.7742 q^{61} +(-2.72158 + 8.99938i) q^{62} -21.3671 q^{63} +2.31137 q^{64} -6.59294 q^{66} +(-2.64795 + 4.58638i) q^{67} +(-2.28602 - 3.95950i) q^{68} +(4.55936 + 7.89705i) q^{69} +(6.09681 - 10.5600i) q^{71} +(-4.10068 + 7.10258i) q^{72} +(-2.08795 + 3.61644i) q^{73} +(8.37340 + 14.5031i) q^{74} +(0.644025 + 1.11548i) q^{76} -7.33749 q^{77} -3.46648 q^{78} +(-0.868068 - 1.50354i) q^{79} +(1.90199 + 3.29434i) q^{81} +(1.02085 - 1.76817i) q^{82} +(4.88772 - 8.46578i) q^{83} +(5.78375 - 10.0177i) q^{84} +(-4.94499 - 8.56498i) q^{86} +(7.24800 + 12.5539i) q^{87} +(-1.40818 + 2.43904i) q^{88} +11.9649 q^{89} -3.85795 q^{91} -2.88786 q^{92} +(-14.5757 + 3.41165i) q^{93} +8.70508 q^{94} +(-6.08578 - 10.5409i) q^{96} +2.12840 q^{97} +(15.6461 - 27.0999i) q^{98} +(-3.07039 - 5.31808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 3 q^{3} + 6 q^{4} + 10 q^{6} + q^{7} + 18 q^{8} - q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - 3 * q^3 + 6 * q^4 + 10 * q^6 + q^7 + 18 * q^8 - q^9	\( 8 q + 2 q^{2} - 3 q^{3} + 6 q^{4} + 10 q^{6} + q^{7} + 18 q^{8} - q^{9} + 4 q^{11} + 8 q^{12} - q^{13} - 8 q^{14} + 10 q^{16} + 12 q^{17} + 11 q^{18} - 5 q^{19} + 9 q^{21} - 10 q^{23} + 2 q^{24} - 12 q^{26} + 6 q^{27} - 4 q^{28} - 26 q^{29} + 19 q^{31} + 28 q^{32} - 8 q^{33} + 24 q^{34} - 5 q^{36} - 16 q^{37} - 9 q^{38} - 22 q^{39} - 4 q^{41} - 6 q^{42} + q^{43} - 7 q^{44} - 22 q^{46} - 20 q^{47} + 27 q^{48} - 37 q^{49} - 12 q^{51} - 21 q^{52} + q^{53} + 24 q^{54} - 29 q^{56} + 4 q^{57} - 26 q^{58} + 6 q^{59} - 2 q^{61} + 17 q^{62} - 24 q^{63} + 34 q^{64} + 2 q^{66} + 7 q^{67} + 5 q^{68} - 6 q^{69} + 12 q^{71} - 14 q^{72} - 20 q^{73} + 18 q^{74} - 23 q^{76} - 58 q^{77} - 22 q^{78} - 2 q^{79} + 12 q^{81} + 18 q^{82} + 4 q^{83} + 41 q^{84} - 13 q^{86} + 10 q^{88} + 54 q^{89} - 44 q^{91} - 86 q^{92} - 55 q^{93} - 48 q^{94} + 13 q^{96} + 18 q^{97} + 46 q^{98} - 7 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 3 * q^3 + 6 * q^4 + 10 * q^6 + q^7 + 18 * q^8 - q^9 + 4 * q^11 + 8 * q^12 - q^13 - 8 * q^14 + 10 * q^16 + 12 * q^17 + 11 * q^18 - 5 * q^19 + 9 * q^21 - 10 * q^23 + 2 * q^24 - 12 * q^26 + 6 * q^27 - 4 * q^28 - 26 * q^29 + 19 * q^31 + 28 * q^32 - 8 * q^33 + 24 * q^34 - 5 * q^36 - 16 * q^37 - 9 * q^38 - 22 * q^39 - 4 * q^41 - 6 * q^42 + q^43 - 7 * q^44 - 22 * q^46 - 20 * q^47 + 27 * q^48 - 37 * q^49 - 12 * q^51 - 21 * q^52 + q^53 + 24 * q^54 - 29 * q^56 + 4 * q^57 - 26 * q^58 + 6 * q^59 - 2 * q^61 + 17 * q^62 - 24 * q^63 + 34 * q^64 + 2 * q^66 + 7 * q^67 + 5 * q^68 - 6 * q^69 + 12 * q^71 - 14 * q^72 - 20 * q^73 + 18 * q^74 - 23 * q^76 - 58 * q^77 - 22 * q^78 - 2 * q^79 + 12 * q^81 + 18 * q^82 + 4 * q^83 + 41 * q^84 - 13 * q^86 + 10 * q^88 + 54 * q^89 - 44 * q^91 - 86 * q^92 - 55 * q^93 - 48 * q^94 + 13 * q^96 + 18 * q^97 + 46 * q^98 - 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more