LMFDB - Embedded newform 775.2.o.d.749.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [775,2,Mod(149,775)]

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([3, 2]))

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

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

chi := DirichletCharacter("775.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			749.2
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	775.749
Dual form			775.2.o.d.149.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.414214i q^{2} +(-0.358719 - 0.207107i) q^{3} +1.82843 q^{4} +(-0.0857864 + 0.148586i) q^{6} +(-0.358719 - 0.207107i) q^{7} -1.58579i q^{8} +(-1.41421 - 2.44949i) q^{9} +O(q^{10})$	\(q-0.414214i q^{2} +(-0.358719 - 0.207107i) q^{3} +1.82843 q^{4} +(-0.0857864 + 0.148586i) q^{6} +(-0.358719 - 0.207107i) q^{7} -1.58579i q^{8} +(-1.41421 - 2.44949i) q^{9} +(-1.62132 - 2.80821i) q^{11} +(-0.655892 - 0.378680i) q^{12} +(-3.31552 + 1.91421i) q^{13} +(-0.0857864 + 0.148586i) q^{14} +3.00000 q^{16} +(-5.04757 - 2.91421i) q^{17} +(-1.01461 + 0.585786i) q^{18} +(2.20711 - 3.82282i) q^{19} +(0.0857864 + 0.148586i) q^{21} +(-1.16320 + 0.671573i) q^{22} -4.00000i q^{23} +(-0.328427 + 0.568852i) q^{24} +(0.792893 + 1.37333i) q^{26} +2.41421i q^{27} +(-0.655892 - 0.378680i) q^{28} +6.82843 q^{29} +(-5.00000 + 2.44949i) q^{31} -4.41421i q^{32} +1.34315i q^{33} +(-1.20711 + 2.09077i) q^{34} +(-2.58579 - 4.47871i) q^{36} +(0.866025 + 0.500000i) q^{37} +(-1.58346 - 0.914214i) q^{38} +1.58579 q^{39} +(3.74264 + 6.48244i) q^{41} +(0.0615465 - 0.0355339i) q^{42} +(9.43924 + 5.44975i) q^{43} +(-2.96447 - 5.13461i) q^{44} -1.65685 q^{46} -9.65685i q^{47} +(-1.07616 - 0.621320i) q^{48} +(-3.41421 - 5.91359i) q^{49} +(1.20711 + 2.09077i) q^{51} +(-6.06218 + 3.50000i) q^{52} +(5.04757 - 2.91421i) q^{53} +1.00000 q^{54} +(-0.328427 + 0.568852i) q^{56} +(-1.58346 + 0.914214i) q^{57} -2.82843i q^{58} +(2.03553 - 3.52565i) q^{59} -2.82843 q^{61} +(1.01461 + 2.07107i) q^{62} +1.17157i q^{63} +4.17157 q^{64} +0.556349 q^{66} +(-2.80821 + 1.62132i) q^{67} +(-9.22911 - 5.32843i) q^{68} +(-0.828427 + 1.43488i) q^{69} +(-0.0355339 - 0.0615465i) q^{71} +(-3.88437 + 2.24264i) q^{72} +(-1.58346 + 0.914214i) q^{73} +(0.207107 - 0.358719i) q^{74} +(4.03553 - 6.98975i) q^{76} +1.34315i q^{77} -0.656854i q^{78} +(-3.37868 + 5.85204i) q^{79} +(-3.74264 + 6.48244i) q^{81} +(2.68512 - 1.55025i) q^{82} +(-8.72180 + 5.03553i) q^{83} +(0.156854 + 0.271680i) q^{84} +(2.25736 - 3.90986i) q^{86} +(-2.44949 - 1.41421i) q^{87} +(-4.45322 + 2.57107i) q^{88} -4.48528 q^{89} +1.58579 q^{91} -7.31371i q^{92} +(2.30090 + 0.156854i) q^{93} -4.00000 q^{94} +(-0.914214 + 1.58346i) q^{96} -5.17157i q^{97} +(-2.44949 + 1.41421i) q^{98} +(-4.58579 + 7.94282i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 12 q^{6}+O(q^{10}) $ 8 * q - 8 * q^4 - 12 * q^6	$ 8 q - 8 q^{4} - 12 q^{6} + 4 q^{11} - 12 q^{14} + 24 q^{16} + 12 q^{19} + 12 q^{21} + 20 q^{24} + 12 q^{26} + 32 q^{29} - 40 q^{31} - 4 q^{34} - 32 q^{36} + 24 q^{39} - 4 q^{41} - 52 q^{44} + 32 q^{46} - 16 q^{49} + 4 q^{51} + 8 q^{54} + 20 q^{56} - 12 q^{59} + 56 q^{64} - 120 q^{66} + 16 q^{69} + 28 q^{71} - 4 q^{74} + 4 q^{76} - 44 q^{79} + 4 q^{81} - 44 q^{84} + 52 q^{86} + 32 q^{89} + 24 q^{91} - 32 q^{94} + 4 q^{96} - 48 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 - 12 * q^6 + 4 * q^11 - 12 * q^14 + 24 * q^16 + 12 * q^19 + 12 * q^21 + 20 * q^24 + 12 * q^26 + 32 * q^29 - 40 * q^31 - 4 * q^34 - 32 * q^36 + 24 * q^39 - 4 * q^41 - 52 * q^44 + 32 * q^46 - 16 * q^49 + 4 * q^51 + 8 * q^54 + 20 * q^56 - 12 * q^59 + 56 * q^64 - 120 * q^66 + 16 * q^69 + 28 * q^71 - 4 * q^74 + 4 * q^76 - 44 * q^79 + 4 * q^81 - 44 * q^84 + 52 * q^86 + 32 * q^89 + 24 * q^91 - 32 * q^94 + 4 * q^96 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$		−	0.414214i		−	0.292893i	−0.989219	−	0.146447i	$-0.953216\pi$
$2$		−	0.414214i		−	0.292893i	0.989219	−	0.146447i	$-0.0467837\pi$
$3$	−0.358719	−	0.207107i	−0.207107	−	0.119573i	0.392859	−	0.919599i	$-0.371486\pi$
$3$	−0.358719	−	0.207107i	−0.207107	−	0.119573i	−0.599966	+	0.800025i	$0.704819\pi$
$4$	1.82843			0.914214
$5$		0			0
$5$		0			0
$6$	−0.0857864	+	0.148586i	−0.0350222	+	0.0606602i
$7$	−0.358719	−	0.207107i	−0.135583	−	0.0782790i	0.430674	−	0.902507i	$-0.358276\pi$
$7$	−0.358719	−	0.207107i	−0.135583	−	0.0782790i	−0.566257	+	0.824228i	$0.691609\pi$
$8$		−	1.58579i		−	0.560660i
$9$	−1.41421	−	2.44949i	−0.471405	−	0.816497i
$10$		0			0
$11$	−1.62132	−	2.80821i	−0.488846	−	0.846707i	0.511071	−	0.859538i	$-0.329249\pi$
$11$	−1.62132	−	2.80821i	−0.488846	−	0.846707i	−0.999918	+	0.0128314i	$0.995916\pi$
$12$	−0.655892	−	0.378680i	−0.189340	−	0.109315i
$13$	−3.31552	+	1.91421i	−0.919558	+	0.530907i	−0.883494	−	0.468442i	$-0.844815\pi$
$13$	−3.31552	+	1.91421i	−0.919558	+	0.530907i	−0.0360643	+	0.999349i	$0.511482\pi$
$14$	−0.0857864	+	0.148586i	−0.0229274	+	0.0397114i
$15$		0			0
$16$	3.00000			0.750000
$17$	−5.04757	−	2.91421i	−1.22421	−	0.706801i	−0.258401	−	0.966038i	$-0.583196\pi$
$17$	−5.04757	−	2.91421i	−1.22421	−	0.706801i	−0.965814	+	0.259237i	$0.916529\pi$
$18$	−1.01461	+	0.585786i	−0.239146	+	0.138071i
$19$	2.20711	−	3.82282i	0.506345	−	0.877015i	−0.493628	−	0.869673i	$-0.664330\pi$
$19$	2.20711	−	3.82282i	0.506345	−	0.877015i	0.999973	−	0.00734216i	$-0.00233710\pi$
$20$		0			0
$21$	0.0857864	+	0.148586i	0.0187201	+	0.0324242i
$22$	−1.16320	+	0.671573i	−0.247995	+	0.143180i
$23$		−	4.00000i		−	0.834058i	−0.908893	−	0.417029i	$-0.863071\pi$
$23$		−	4.00000i		−	0.834058i	0.908893	−	0.417029i	$-0.136929\pi$
$24$	−0.328427	+	0.568852i	−0.0670399	+	0.116117i
$25$		0			0
$26$	0.792893	+	1.37333i	0.155499	+	0.269332i
$27$			2.41421i			0.464616i
$28$	−0.655892	−	0.378680i	−0.123952	−	0.0715637i
$29$	6.82843			1.26801			0.634004	−	0.773330i	$-0.281410\pi$
$29$	6.82843			1.26801			0.634004	+	0.773330i	$0.281410\pi$
$30$		0			0
$31$	−5.00000	+	2.44949i	−0.898027	+	0.439941i
$31$	−5.00000	+	2.44949i	−0.898027	+	0.439941i
$32$		−	4.41421i		−	0.780330i
$33$			1.34315i			0.233812i
$34$	−1.20711	+	2.09077i	−0.207017	+	0.358564i
$35$		0			0
$36$	−2.58579	−	4.47871i	−0.430964	−	0.746452i
$37$	0.866025	+	0.500000i	0.142374	+	0.0821995i	0.569495	−	0.821995i	$-0.307139\pi$
$37$	0.866025	+	0.500000i	0.142374	+	0.0821995i	−0.427121	+	0.904194i	$0.640472\pi$
$38$	−1.58346	−	0.914214i	−0.256872	−	0.148305i
$39$	1.58579			0.253929
$40$		0			0
$41$	3.74264	+	6.48244i	0.584502	+	1.01239i	0.994937	+	0.100498i	$0.0320435\pi$
$41$	3.74264	+	6.48244i	0.584502	+	1.01239i	−0.410435	+	0.911890i	$0.634623\pi$
$42$	0.0615465	−	0.0355339i	0.00949684	−	0.00548300i
$43$	9.43924	+	5.44975i	1.43947	+	0.831079i	0.997813	−	0.0661049i	$-0.0210572\pi$
$43$	9.43924	+	5.44975i	1.43947	+	0.831079i	0.441658	+	0.897184i	$0.354391\pi$
$44$	−2.96447	−	5.13461i	−0.446910	−	0.774071i
$45$		0			0
$46$	−1.65685			−0.244290
$47$		−	9.65685i		−	1.40860i	−0.709904	−	0.704298i	$-0.751262\pi$
$47$		−	9.65685i		−	1.40860i	0.709904	−	0.704298i	$-0.248738\pi$
$48$	−1.07616	−	0.621320i	−0.155330	−	0.0896799i
$49$	−3.41421	−	5.91359i	−0.487745	−	0.844799i
$50$		0			0
$51$	1.20711	+	2.09077i	0.169029	+	0.292766i
$52$	−6.06218	+	3.50000i	−0.840673	+	0.485363i
$53$	5.04757	−	2.91421i	0.693337	−	0.400298i	−0.111524	−	0.993762i	$-0.535573\pi$
$53$	5.04757	−	2.91421i	0.693337	−	0.400298i	0.804861	+	0.593464i	$0.202240\pi$
$54$	1.00000			0.136083
$55$		0			0
$56$	−0.328427	+	0.568852i	−0.0438879	+	0.0760161i
$57$	−1.58346	+	0.914214i	−0.209735	+	0.121091i
$58$		−	2.82843i		−	0.371391i
$59$	2.03553	−	3.52565i	0.265004	−	0.459000i	−0.702561	−	0.711624i	$-0.747960\pi$
$59$	2.03553	−	3.52565i	0.265004	−	0.459000i	0.967565	+	0.252624i	$0.0812934\pi$
$60$		0			0
$61$	−2.82843			−0.362143			−0.181071	−	0.983470i	$-0.557957\pi$
$61$	−2.82843			−0.362143			−0.181071	+	0.983470i	$0.557957\pi$
$62$	1.01461	+	2.07107i	0.128856	+	0.263026i
$63$			1.17157i			0.147604i
$64$	4.17157			0.521447
$65$		0			0
$66$	0.556349			0.0684819
$67$	−2.80821	+	1.62132i	−0.343077	+	0.198076i	−0.661632	−	0.749829i	$-0.730136\pi$
$67$	−2.80821	+	1.62132i	−0.343077	+	0.198076i	0.318555	+	0.947904i	$0.396803\pi$
$68$	−9.22911	−	5.32843i	−1.11919	−	0.646167i
$69$	−0.828427	+	1.43488i	−0.0997309	+	0.172739i
$70$		0			0
$71$	−0.0355339	−	0.0615465i	−0.00421710	−	0.00730423i	0.863909	−	0.503648i	$-0.168009\pi$
$71$	−0.0355339	−	0.0615465i	−0.00421710	−	0.00730423i	−0.868126	+	0.496343i	$0.834676\pi$
$72$	−3.88437	+	2.24264i	−0.457777	+	0.264298i
$73$	−1.58346	+	0.914214i	−0.185330	+	0.107001i	−0.589795	−	0.807553i	$-0.700791\pi$
$73$	−1.58346	+	0.914214i	−0.185330	+	0.107001i	0.404464	+	0.914554i	$0.367458\pi$
$74$	0.207107	−	0.358719i	0.0240757	−	0.0417003i
$75$		0			0
$76$	4.03553	−	6.98975i	0.462907	−	0.801779i
$77$			1.34315i			0.153066i
$78$		−	0.656854i		−	0.0743741i
$79$	−3.37868	+	5.85204i	−0.380131	+	0.658406i	−0.991081	−	0.133263i	$-0.957454\pi$
$79$	−3.37868	+	5.85204i	−0.380131	+	0.658406i	0.610950	+	0.791670i	$0.290788\pi$
$80$		0			0
$81$	−3.74264	+	6.48244i	−0.415849	+	0.720272i
$82$	2.68512	−	1.55025i	0.296521	−	0.171197i
$83$	−8.72180	+	5.03553i	−0.957342	+	0.552722i	−0.895354	−	0.445355i	$-0.853077\pi$
$83$	−8.72180	+	5.03553i	−0.957342	+	0.552722i	−0.0619880	+	0.998077i	$0.519744\pi$
$84$	0.156854	+	0.271680i	0.0171142	+	0.0296427i
$85$		0			0
$86$	2.25736	−	3.90986i	0.243417	−	0.421611i
$87$	−2.44949	−	1.41421i	−0.262613	−	0.151620i
$88$	−4.45322	+	2.57107i	−0.474715	+	0.274077i
$89$	−4.48528			−0.475439			−0.237719	−	0.971334i	$-0.576400\pi$
$89$	−4.48528			−0.475439			−0.237719	+	0.971334i	$0.576400\pi$
$90$		0			0
$91$	1.58579			0.166236
$92$		−	7.31371i		−	0.762507i
$93$	2.30090	+	0.156854i	0.238593	+	0.0162650i
$94$	−4.00000			−0.412568
$95$		0			0
$96$	−0.914214	+	1.58346i	−0.0933065	+	0.161612i
$97$		−	5.17157i		−	0.525094i	−0.964919	−	0.262547i	$-0.915438\pi$
$97$		−	5.17157i		−	0.525094i	0.964919	−	0.262547i	$-0.0845624\pi$
$98$	−2.44949	+	1.41421i	−0.247436	+	0.142857i
$99$	−4.58579	+	7.94282i	−0.460889	+	0.798283i
$100$		0			0
$101$	−8.48528			−0.844317			−0.422159	−	0.906522i	$-0.638727\pi$
$101$	−8.48528			−0.844317			−0.422159	+	0.906522i	$0.638727\pi$
$102$	0.866025	−	0.500000i	0.0857493	−	0.0495074i
$103$	1.79360	−	1.03553i	0.176728	−	0.102034i	−0.409026	−	0.912523i	$-0.634132\pi$
$103$	1.79360	−	1.03553i	0.176728	−	0.102034i	0.585755	+	0.810488i	$0.300798\pi$
$104$	3.03553	+	5.25770i	0.297659	+	0.515560i
$105$		0			0
$106$	−1.20711	−	2.09077i	−0.117245	−	0.203074i
$107$	10.7510	+	6.20711i	1.03934	+	0.600064i	0.919646	−	0.392747i	$-0.128475\pi$
$107$	10.7510	+	6.20711i	1.03934	+	0.600064i	0.119694	+	0.992811i	$0.461809\pi$
$108$			4.41421i			0.424758i
$109$	10.8284			1.03718			0.518588	−	0.855024i	$-0.326458\pi$
$109$	10.8284			1.03718			0.518588	+	0.855024i	$0.326458\pi$
$110$		0			0
$111$	−0.207107	−	0.358719i	−0.0196577	−	0.0340481i
$112$	−1.07616	−	0.621320i	−0.101687	−	0.0587093i
$113$	14.4253	−	8.32843i	1.35701	−	0.783473i	0.367794	−	0.929907i	$-0.380113\pi$
$113$	14.4253	−	8.32843i	1.35701	−	0.783473i	0.989220	+	0.146435i	$0.0467799\pi$
$114$	0.378680	+	0.655892i	0.0354666	+	0.0614300i
$115$		0			0
$116$	12.4853			1.15923
$117$	9.37769	+	5.41421i	0.866968	+	0.500544i
$118$	−1.46037	−	0.843146i	−0.134438	−	0.0776179i
$119$	1.20711	+	2.09077i	0.110655	+	0.191661i
$120$		0			0
$121$	0.242641	−	0.420266i	0.0220582	−	0.0382060i
$122$			1.17157i			0.106069i
$123$		−	3.10051i		−	0.279563i
$124$	−9.14214	+	4.47871i	−0.820988	+	0.402200i
$125$		0			0
$126$	0.485281			0.0432323
$127$	7.70719	+	4.44975i	0.683902	+	0.394851i	0.801324	−	0.598231i	$-0.204129\pi$
$127$	7.70719	+	4.44975i	0.683902	+	0.394851i	−0.117421	+	0.993082i	$0.537463\pi$
$128$		−	10.5563i		−	0.933058i
$129$	−2.25736	−	3.90986i	−0.198749	−	0.344244i
$130$		0			0
$131$	6.62132	−	11.4685i	0.578507	−	1.00200i	−0.417143	−	0.908841i	$-0.636969\pi$
$131$	6.62132	−	11.4685i	0.578507	−	1.00200i	0.995651	−	0.0931636i	$-0.0296980\pi$
$132$			2.45584i			0.213754i
$133$	−1.58346	+	0.914214i	−0.137304	+	0.0792724i
$134$	0.671573	+	1.16320i	0.0580151	+	0.100485i
$135$		0			0
$136$	−4.62132	+	8.00436i	−0.396275	+	0.686368i
$137$	−8.21449	+	4.74264i	−0.701812	+	0.405191i	−0.808022	−	0.589153i	$-0.799462\pi$
$137$	−8.21449	+	4.74264i	−0.701812	+	0.405191i	0.106210	+	0.994344i	$0.466128\pi$
$138$	0.594346	+	0.343146i	0.0505941	+	0.0292105i
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$		0			0
$141$	−2.00000	+	3.46410i	−0.168430	+	0.291730i
$142$	−0.0254934	+	0.0147186i	−0.00213936	+	0.00123516i
$143$	10.7510	+	6.20711i	0.899046	+	0.519064i
$144$	−4.24264	−	7.34847i	−0.353553	−	0.612372i
$145$		0			0
$146$	0.378680	+	0.655892i	0.0313398	+	0.0542820i
$147$			2.82843i			0.233285i
$148$	1.58346	+	0.914214i	0.130160	+	0.0751479i
$149$	0.500000	−	0.866025i	0.0409616	−	0.0709476i	−0.844818	−	0.535054i	$-0.820291\pi$
$149$	0.500000	−	0.866025i	0.0409616	−	0.0709476i	0.885779	+	0.464107i	$0.153625\pi$
$150$		0			0
$151$	5.31371			0.432423			0.216212	−	0.976346i	$-0.430630\pi$
$151$	5.31371			0.432423			0.216212	+	0.976346i	$0.430630\pi$
$152$	−6.06218	−	3.50000i	−0.491708	−	0.283887i
$153$			16.4853i			1.33276i
$154$	0.556349			0.0448319
$155$		0			0
$156$	2.89949			0.232145
$157$		−	9.17157i		−	0.731971i	−0.930621	−	0.365986i	$-0.880732\pi$
$157$		−	9.17157i		−	0.731971i	0.930621	−	0.365986i	$-0.119268\pi$
$158$	2.42400	+	1.39949i	0.192843	+	0.111338i
$159$	−2.41421			−0.191460
$160$		0			0
$161$	−0.828427	+	1.43488i	−0.0652892	+	0.113084i
$162$	2.68512	+	1.55025i	0.210963	+	0.121799i
$163$			20.9706i			1.64254i	0.570539	+	0.821271i	$0.306734\pi$
$163$			20.9706i			1.64254i	−0.570539	+	0.821271i	$0.693266\pi$
$164$	6.84315	+	11.8527i	0.534360	+	0.925539i
$165$		0			0
$166$	2.08579	+	3.61269i	0.161888	+	0.280399i
$167$	19.5344	+	11.2782i	1.51162	+	0.872731i	0.999908	+	0.0135714i	$0.00432005\pi$
$167$	19.5344	+	11.2782i	1.51162	+	0.872731i	0.511707	+	0.859160i	$0.329013\pi$
$168$	0.235626	−	0.136039i	0.0181790	−	0.0104956i
$169$	0.828427	−	1.43488i	0.0637252	−	0.110375i
$170$		0			0
$171$	−12.4853			−0.954773
$172$	17.2590	+	9.96447i	1.31598	+	0.759783i
$173$	7.19988	−	4.15685i	0.547397	−	0.316040i	−0.200674	−	0.979658i	$-0.564313\pi$
$173$	7.19988	−	4.15685i	0.547397	−	0.316040i	0.748071	+	0.663618i	$0.230980\pi$
$174$	−0.585786	+	1.01461i	−0.0444084	+	0.0769175i
$175$		0			0
$176$	−4.86396	−	8.42463i	−0.366635	−	0.635030i
$177$	−1.46037	+	0.843146i	−0.109768	+	0.0633747i
$178$			1.85786i			0.139253i
$179$	−7.62132	+	13.2005i	−0.569644	+	0.986653i	0.426957	+	0.904272i	$0.359586\pi$
$179$	−7.62132	+	13.2005i	−0.569644	+	0.986653i	−0.996601	+	0.0823807i	$0.973748\pi$
$180$		0			0
$181$	−6.15685	−	10.6640i	−0.457635	−	0.792648i	0.541200	−	0.840894i	$-0.317970\pi$
$181$	−6.15685	−	10.6640i	−0.457635	−	0.792648i	−0.998835	+	0.0482461i	$0.984637\pi$
$182$		−	0.656854i		−	0.0486893i
$183$	1.01461	+	0.585786i	0.0750023	+	0.0433026i
$184$	−6.34315			−0.467623
$185$		0			0
$186$	0.0649712	−	0.953065i	0.00476392	−	0.0698821i
$187$			18.8995i			1.38207i
$188$		−	17.6569i		−	1.28776i
$189$	0.500000	−	0.866025i	0.0363696	−	0.0629941i
$190$		0			0
$191$	10.4497	+	18.0995i	0.756117	+	1.30963i	0.944817	+	0.327599i	$0.106239\pi$
$191$	10.4497	+	18.0995i	0.756117	+	1.30963i	−0.188700	+	0.982035i	$0.560427\pi$
$192$	−1.49642	−	0.863961i	−0.107995	−	0.0623510i
$193$	−6.18527	−	3.57107i	−0.445226	−	0.257051i	0.260586	−	0.965451i	$-0.416084\pi$
$193$	−6.18527	−	3.57107i	−0.445226	−	0.257051i	−0.705812	+	0.708400i	$0.749418\pi$
$194$	−2.14214			−0.153796
$195$		0			0
$196$	−6.24264	−	10.8126i	−0.445903	−	0.772326i
$197$	11.6786	−	6.74264i	0.832066	−	0.480393i	−0.0224938	−	0.999747i	$-0.507161\pi$
$197$	11.6786	−	6.74264i	0.832066	−	0.480393i	0.854559	+	0.519354i	$0.173827\pi$
$198$	3.29002	+	1.89949i	0.233812	+	0.134991i
$199$	9.20711	+	15.9472i	0.652674	+	1.13047i	0.982471	+	0.186413i	$0.0596864\pi$
$199$	9.20711	+	15.9472i	0.652674	+	1.13047i	−0.329797	+	0.944052i	$0.606980\pi$
$200$		0			0
$201$	1.34315			0.0947382
$202$			3.51472i			0.247295i
$203$	−2.44949	−	1.41421i	−0.171920	−	0.0992583i
$204$	2.20711	+	3.82282i	0.154528	+	0.267651i
$205$		0			0
$206$	−0.428932	−	0.742932i	−0.0298851	−	0.0517625i
$207$	−9.79796	+	5.65685i	−0.681005	+	0.393179i
$208$	−9.94655	+	5.74264i	−0.689669	+	0.398180i
$209$	−14.3137			−0.990100
$210$		0			0
$211$	−5.20711	+	9.01897i	−0.358472	+	0.620892i	−0.987706	−	0.156324i	$-0.950035\pi$
$211$	−5.20711	+	9.01897i	−0.358472	+	0.620892i	0.629234	+	0.777216i	$0.283369\pi$
$212$	9.22911	−	5.32843i	0.633858	−	0.365958i
$213$			0.0294373i			0.00201701i
$214$	2.57107	−	4.45322i	0.175755	−	0.304416i
$215$		0			0
$216$	3.82843			0.260491
$217$	2.30090	+	0.156854i	0.156195	+	0.0106480i
$218$		−	4.48528i		−	0.303782i
$219$	0.757359			0.0511776
$220$		0			0
$221$	22.3137			1.50098
$222$	−0.148586	+	0.0857864i	−0.00997247	+	0.00575761i
$223$	20.5490	+	11.8640i	1.37606	+	0.794470i	0.991683	−	0.128706i	$-0.0410823\pi$
$223$	20.5490	+	11.8640i	1.37606	+	0.794470i	0.384379	+	0.923175i	$0.374416\pi$
$224$	−0.914214	+	1.58346i	−0.0610835	+	0.105800i
$225$		0			0
$226$	−3.44975	−	5.97514i	−0.229474	−	0.397460i
$227$	15.9472	−	9.20711i	1.05845	−	0.611097i	0.133448	−	0.991056i	$-0.457395\pi$
$227$	15.9472	−	9.20711i	1.05845	−	0.611097i	0.925003	+	0.379959i	$0.124062\pi$
$228$	−2.89525	+	1.67157i	−0.191743	+	0.110703i
$229$	−2.74264	+	4.75039i	−0.181239	+	0.313915i	−0.942303	−	0.334762i	$-0.891344\pi$
$229$	−2.74264	+	4.75039i	−0.181239	+	0.313915i	0.761064	+	0.648677i	$0.224677\pi$
$230$		0			0
$231$	0.278175	−	0.481813i	0.0183025	−	0.0317009i
$232$		−	10.8284i		−	0.710921i
$233$		−	9.17157i		−	0.600850i	−0.953805	−	0.300425i	$-0.902872\pi$
$233$		−	9.17157i		−	0.600850i	0.953805	−	0.300425i	$-0.0971285\pi$
$234$	2.24264	−	3.88437i	0.146606	−	0.253929i
$235$		0			0
$236$	3.72183	−	6.44639i	0.242270	−	0.419624i
$237$	2.42400	−	1.39949i	0.157455	−	0.0909070i
$238$	0.866025	−	0.500000i	0.0561361	−	0.0324102i
$239$	−10.6213	−	18.3967i	−0.687036	−	1.18998i	−0.972792	−	0.231679i	$-0.925578\pi$
$239$	−10.6213	−	18.3967i	−0.687036	−	1.18998i	0.285756	−	0.958302i	$-0.407755\pi$
$240$		0			0
$241$	−6.67157	+	11.5555i	−0.429754	+	0.744355i	−0.996851	−	0.0792954i	$-0.974733\pi$
$241$	−6.67157	+	11.5555i	−0.429754	+	0.744355i	0.567097	+	0.823651i	$0.308066\pi$
$242$	−0.174080	−	0.100505i	−0.0111903	−	0.00646071i
$243$	8.95743	−	5.17157i	0.574619	−	0.331757i
$244$	−5.17157			−0.331076
$245$		0			0
$246$	−1.28427			−0.0818821
$247$			16.8995i			1.07529i
$248$	3.88437	+	7.92893i	0.246658	+	0.503488i
$249$	4.17157			0.264363
$250$		0			0
$251$	−3.20711	+	5.55487i	−0.202431	+	0.350620i	−0.949311	−	0.314338i	$-0.898217\pi$
$251$	−3.20711	+	5.55487i	−0.202431	+	0.350620i	0.746880	+	0.664958i	$0.231551\pi$
$252$			2.14214i			0.134942i
$253$	−11.2328	+	6.48528i	−0.706202	+	0.407726i
$254$	1.84315	−	3.19242i	0.115649	−	0.200310i
$255$		0			0
$256$	3.97056			0.248160
$257$	−19.3242	+	11.1569i	−1.20541	+	0.695945i	−0.961754	−	0.273915i	$-0.911681\pi$
$257$	−19.3242	+	11.1569i	−1.20541	+	0.695945i	−0.243659	+	0.969861i	$0.578348\pi$
$258$	−1.61952	+	0.935029i	−0.100827	+	0.0582124i
$259$	−0.207107	−	0.358719i	−0.0128690	−	0.0222897i
$260$		0			0
$261$	−9.65685	−	16.7262i	−0.597744	−	1.03532i
$262$	−4.75039	−	2.74264i	−0.293480	−	0.169441i
$263$		−	23.3137i		−	1.43758i	−0.695225	−	0.718792i	$-0.744695\pi$
$263$		−	23.3137i		−	1.43758i	0.695225	−	0.718792i	$-0.255305\pi$
$264$	2.12994			0.131089
$265$		0			0
$266$	0.378680	+	0.655892i	0.0232183	+	0.0402153i
$267$	1.60896	+	0.928932i	0.0984666	+	0.0568497i
$268$	−5.13461	+	2.96447i	−0.313646	+	0.181084i
$269$	−13.0858	−	22.6652i	−0.797854	−	1.38192i	−0.921011	−	0.389537i	$-0.872635\pi$
$269$	−13.0858	−	22.6652i	−0.797854	−	1.38192i	0.123156	−	0.992387i	$-0.460698\pi$
$270$		0			0
$271$	−0.686292			−0.0416892			−0.0208446	−	0.999783i	$-0.506636\pi$
$271$	−0.686292			−0.0416892			−0.0208446	+	0.999783i	$0.506636\pi$
$272$	−15.1427	−	8.74264i	−0.918161	−	0.530100i
$273$	−0.568852	−	0.328427i	−0.0344285	−	0.0198773i
$274$	1.96447	+	3.40256i	0.118678	+	0.205556i
$275$		0			0
$276$	−1.51472	+	2.62357i	−0.0911753	+	0.157920i
$277$		−	14.1421i		−	0.849719i	−0.905259	−	0.424859i	$-0.860324\pi$
$277$		−	14.1421i		−	0.849719i	0.905259	−	0.424859i	$-0.139676\pi$
$278$		0			0
$279$	13.0711	+	8.78335i	0.782544	+	0.525845i
$280$		0			0
$281$	2.00000			0.119310			0.0596550	−	0.998219i	$-0.481000\pi$
$281$	2.00000			0.119310			0.0596550	+	0.998219i	$0.481000\pi$
$282$	1.43488	+	0.828427i	0.0854457	+	0.0493321i
$283$		−	13.6569i		−	0.811816i	−0.913914	−	0.405908i	$-0.866955\pi$
$283$		−	13.6569i		−	0.811816i	0.913914	−	0.405908i	$-0.133045\pi$
$284$	−0.0649712	−	0.112533i	−0.00385533	−	0.00667763i
$285$		0			0
$286$	2.57107	−	4.45322i	0.152030	−	0.263324i
$287$		−	3.10051i		−	0.183017i
$288$	−10.8126	+	6.24264i	−0.637137	+	0.367851i
$289$	8.48528	+	14.6969i	0.499134	+	0.864526i
$290$		0			0
$291$	−1.07107	+	1.85514i	−0.0627871	+	0.108750i
$292$	−2.89525	+	1.67157i	−0.169432	+	0.0978214i
$293$	−12.8163	−	7.39949i	−0.748736	−	0.432283i	0.0765008	−	0.997070i	$-0.475625\pi$
$293$	−12.8163	−	7.39949i	−0.748736	−	0.432283i	−0.825237	+	0.564786i	$0.808959\pi$
$294$	1.17157			0.0683275
$295$		0			0
$296$	0.792893	−	1.37333i	0.0460860	−	0.0798233i
$297$	6.77962	−	3.91421i	0.393393	−	0.227126i
$298$	−0.358719	−	0.207107i	−0.0207801	−	0.0119974i
$299$	7.65685	+	13.2621i	0.442807	+	0.766965i
$300$		0			0
$301$	−2.25736	−	3.90986i	−0.130112	−	0.225361i
$302$		−	2.20101i		−	0.126654i
$303$	3.04384	+	1.75736i	0.174864	+	0.100958i
$304$	6.62132	−	11.4685i	0.379759	−	0.657761i
$305$		0			0
$306$	6.82843			0.390355
$307$	−9.73641	−	5.62132i	−0.555686	−	0.320826i	0.195726	−	0.980659i	$-0.437294\pi$
$307$	−9.73641	−	5.62132i	−0.555686	−	0.320826i	−0.751412	+	0.659833i	$0.770627\pi$
$308$			2.45584i			0.139935i
$309$	−0.857864			−0.0488022
$310$		0			0
$311$	11.3137			0.641542			0.320771	−	0.947157i	$-0.396058\pi$
$311$	11.3137			0.641542			0.320771	+	0.947157i	$0.396058\pi$
$312$		−	2.51472i		−	0.142368i
$313$	1.58346	+	0.914214i	0.0895027	+	0.0516744i	0.544083	−	0.839031i	$-0.316878\pi$
$313$	1.58346	+	0.914214i	0.0895027	+	0.0516744i	−0.454581	+	0.890706i	$0.650211\pi$
$314$	−3.79899			−0.214389
$315$		0			0
$316$	−6.17767	+	10.7000i	−0.347521	+	0.601924i
$317$	−6.77962	−	3.91421i	−0.380781	−	0.219844i	0.297377	−	0.954760i	$-0.403888\pi$
$317$	−6.77962	−	3.91421i	−0.380781	−	0.219844i	−0.678158	+	0.734916i	$0.737222\pi$
$318$			1.00000i			0.0560772i
$319$	−11.0711	−	19.1757i	−0.619861	−	1.07363i
$320$		0			0
$321$	−2.57107	−	4.45322i	−0.143503	−	0.248555i
$322$	0.594346	+	0.343146i	0.0331216	+	0.0191228i
$323$	−22.2810	+	12.8640i	−1.23975	+	0.715770i
$324$	−6.84315	+	11.8527i	−0.380175	+	0.658482i
$325$		0			0
$326$	8.68629			0.481089
$327$	−3.88437	−	2.24264i	−0.214806	−	0.124018i
$328$	10.2798	−	5.93503i	0.567605	−	0.327707i
$329$	−2.00000	+	3.46410i	−0.110264	+	0.190982i
$330$		0			0
$331$	−4.62132	−	8.00436i	−0.254011	−	0.439960i	0.710616	−	0.703580i	$-0.248417\pi$
$331$	−4.62132	−	8.00436i	−0.254011	−	0.439960i	−0.964626	+	0.263621i	$0.915083\pi$
$332$	−15.9472	+	9.20711i	−0.875215	+	0.505306i
$333$		−	2.82843i		−	0.154997i
$334$	4.67157	−	8.09140i	0.255617	−	0.442742i
$335$		0			0
$336$	0.257359	+	0.445759i	0.0140401	+	0.0243182i
$337$		−	9.31371i		−	0.507350i	−0.967290	−	0.253675i	$-0.918361\pi$
$337$		−	9.31371i		−	0.507350i	0.967290	−	0.253675i	$-0.0816394\pi$
$338$	−0.594346	−	0.343146i	−0.0323282	−	0.0186647i
$339$	−6.89949			−0.374729
$340$		0			0
$341$	14.9853	+	10.0696i	0.811498	+	0.545301i
$342$			5.17157i			0.279647i
$343$			5.72792i			0.309279i
$344$	8.64214	−	14.9686i	0.465953	−	0.807054i
$345$		0			0
$346$	−1.72183	−	2.98229i	−0.0925659	−	0.160329i
$347$	−7.41002	−	4.27817i	−0.397790	−	0.229664i	0.287740	−	0.957709i	$-0.407096\pi$
$347$	−7.41002	−	4.27817i	−0.397790	−	0.229664i	−0.685530	+	0.728044i	$0.740430\pi$
$348$	−4.47871	−	2.58579i	−0.240084	−	0.138613i
$349$	27.1127			1.45131			0.725655	−	0.688059i	$-0.241537\pi$
$349$	27.1127			1.45131			0.725655	+	0.688059i	$0.241537\pi$
$350$		0			0
$351$	−4.62132	−	8.00436i	−0.246668	−	0.427241i
$352$	−12.3960	+	7.15685i	−0.660711	+	0.381462i
$353$	−2.59808	−	1.50000i	−0.138282	−	0.0798369i	0.429263	−	0.903179i	$-0.358773\pi$
$353$	−2.59808	−	1.50000i	−0.138282	−	0.0798369i	−0.567545	+	0.823343i	$0.692107\pi$
$354$	0.349242	+	0.604906i	0.0185620	+	0.0321504i
$355$		0			0
$356$	−8.20101			−0.434653
$357$		−	1.00000i		−	0.0529256i
$358$	5.46783	+	3.15685i	0.288984	+	0.166845i
$359$	3.55025	+	6.14922i	0.187375	+	0.324543i	0.944374	−	0.328873i	$-0.106669\pi$
$359$	3.55025	+	6.14922i	0.187375	+	0.324543i	−0.756999	+	0.653416i	$0.773335\pi$
$360$		0			0
$361$	−0.242641	−	0.420266i	−0.0127706	−	0.0221193i
$362$	−4.41717	+	2.55025i	−0.232161	+	0.134038i
$363$	−0.174080	+	0.100505i	−0.00913682	+	0.00527515i
$364$	2.89949			0.151975
$365$		0			0
$366$	0.242641	−	0.420266i	0.0126830	−	0.0219677i
$367$	20.9692	−	12.1066i	1.09459	−	0.631959i	0.159792	−	0.987151i	$-0.448918\pi$
$367$	20.9692	−	12.1066i	1.09459	−	0.631959i	0.934794	+	0.355191i	$0.115584\pi$
$368$		−	12.0000i		−	0.625543i
$369$	10.5858	−	18.3351i	0.551074	−	0.954488i
$370$		0			0
$371$	−2.41421			−0.125340
$372$	4.20703	+	0.286797i	0.218125	+	0.0148697i
$373$			10.0000i			0.517780i	0.965907	+	0.258890i	$0.0833568\pi$
$373$			10.0000i			0.517780i	−0.965907	+	0.258890i	$0.916643\pi$
$374$	7.82843			0.404798
$375$		0			0
$376$	−15.3137			−0.789744
$377$	−22.6398	+	13.0711i	−1.16601	+	0.673194i
$378$	−0.358719	−	0.207107i	−0.0184505	−	0.0106524i
$379$	3.69239	−	6.39540i	0.189665	−	0.328510i	−0.755473	−	0.655179i	$-0.772593\pi$
$379$	3.69239	−	6.39540i	0.189665	−	0.328510i	0.945139	+	0.326669i	$0.105926\pi$
$380$		0			0
$381$	−1.84315	−	3.19242i	−0.0944272	−	0.163553i
$382$	7.49706	−	4.32843i	0.383583	−	0.221462i
$383$	4.41717	−	2.55025i	0.225707	−	0.130312i	−0.382883	−	0.923797i	$-0.625069\pi$
$383$	4.41717	−	2.55025i	0.225707	−	0.130312i	0.608590	+	0.793485i	$0.291735\pi$
$384$	−2.18629	+	3.78677i	−0.111569	+	0.193243i
$385$		0			0
$386$	−1.47918	+	2.56202i	−0.0752885	+	0.130404i
$387$		−	30.8284i		−	1.56710i
$388$		−	9.45584i		−	0.480048i
$389$	−5.57107	+	9.64937i	−0.282464	+	0.489243i	−0.971991	−	0.235018i	$-0.924485\pi$
$389$	−5.57107	+	9.64937i	−0.282464	+	0.489243i	0.689527	+	0.724260i	$0.257819\pi$
$390$		0			0
$391$	−11.6569	+	20.1903i	−0.589512	+	1.02107i
$392$	−9.37769	+	5.41421i	−0.473645	+	0.273459i
$393$	−4.75039	+	2.74264i	−0.239626	+	0.138348i
$394$	−2.79289	−	4.83743i	−0.140704	−	0.243706i
$395$		0			0
$396$	−8.38478	+	14.5229i	−0.421351	+	0.729801i
$397$	−28.9991	−	16.7426i	−1.45542	−	0.840289i	−0.456642	−	0.889650i	$-0.650948\pi$
$397$	−28.9991	−	16.7426i	−1.45542	−	0.840289i	−0.998781	+	0.0493613i	$0.984281\pi$
$398$	6.60554	−	3.81371i	0.331106	−	0.191164i
$399$	0.757359			0.0379154
$400$		0			0
$401$	−26.8284			−1.33975			−0.669874	−	0.742475i	$-0.733652\pi$
$401$	−26.8284			−1.33975			−0.669874	+	0.742475i	$0.733652\pi$
$402$		−	0.556349i		−	0.0277482i
$403$	11.8887	−	17.6924i	0.592220	−	0.881321i
$404$	−15.5147			−0.771886
$405$		0			0
$406$	−0.585786	+	1.01461i	−0.0290721	+	0.0503543i
$407$		−	3.24264i		−	0.160732i
$408$	3.31552	−	1.91421i	0.164142	−	0.0947677i
$409$	10.3284	−	17.8894i	0.510708	−	0.884572i	−0.489215	−	0.872163i	$-0.662717\pi$
$409$	10.3284	−	17.8894i	0.510708	−	0.884572i	0.999923	−	0.0124088i	$-0.00394995\pi$
$410$		0			0
$411$	3.92893			0.193800
$412$	3.27946	−	1.89340i	0.161567	−	0.0932810i
$413$	−1.46037	+	0.843146i	−0.0718602	+	0.0414885i
$414$	2.34315	+	4.05845i	0.115159	+	0.199462i
$415$		0			0
$416$	8.44975	+	14.6354i	0.414283	+	0.717559i
$417$		0			0
$418$			5.92893i			0.289994i
$419$	−28.0000			−1.36789			−0.683945	−	0.729534i	$-0.739737\pi$
$419$	−28.0000			−1.36789			−0.683945	+	0.729534i	$0.739737\pi$
$420$		0			0
$421$	15.5711	+	26.9699i	0.758887	+	1.31443i	0.943418	+	0.331605i	$0.107590\pi$
$421$	15.5711	+	26.9699i	0.758887	+	1.31443i	−0.184531	+	0.982827i	$0.559077\pi$
$422$	3.73578	+	2.15685i	0.181855	+	0.104994i
$423$	−23.6544	+	13.6569i	−1.15011	+	0.664019i
$424$	−4.62132	−	8.00436i	−0.224431	−	0.388726i
$425$		0			0
$426$	0.0121933			0.000590768
$427$	1.01461	+	0.585786i	0.0491005	+	0.0283482i
$428$	19.6575	+	11.3492i	0.950179	+	0.548586i
$429$	−2.57107	−	4.45322i	−0.124132	−	0.215003i
$430$		0			0
$431$	8.37868	−	14.5123i	0.403587	−	0.699033i	−0.590569	−	0.806987i	$-0.701097\pi$
$431$	8.37868	−	14.5123i	0.403587	−	0.699033i	0.994156	+	0.107954i	$0.0344300\pi$
$432$			7.24264i			0.348462i
$433$			27.1127i			1.30295i	0.758669	+	0.651477i	$0.225850\pi$
$433$			27.1127i			1.30295i	−0.758669	+	0.651477i	$0.774150\pi$
$434$	0.0649712	−	0.953065i	0.00311872	−	0.0457486i
$435$		0			0
$436$	19.7990			0.948200
$437$	−15.2913	−	8.82843i	−0.731481	−	0.422321i
$438$		−	0.313708i		−	0.0149896i
$439$	1.03553	+	1.79360i	0.0494233	+	0.0856037i	0.889679	−	0.456587i	$-0.150928\pi$
$439$	1.03553	+	1.79360i	0.0494233	+	0.0856037i	−0.840255	+	0.542191i	$0.817595\pi$
$440$		0			0
$441$	−9.65685	+	16.7262i	−0.459850	+	0.796484i
$442$		−	9.24264i		−	0.439628i
$443$	−4.11999	+	2.37868i	−0.195747	+	0.113014i	−0.594670	−	0.803970i	$-0.702717\pi$
$443$	−4.11999	+	2.37868i	−0.195747	+	0.113014i	0.398923	+	0.916984i	$0.369384\pi$
$444$	−0.378680	−	0.655892i	−0.0179713	−	0.0311273i
$445$		0			0
$446$	4.91421	−	8.51167i	0.232695	−	0.403039i
$447$	−0.358719	+	0.207107i	−0.0169668	+	0.00979581i
$448$	−1.49642	−	0.863961i	−0.0706994	−	0.0408183i
$449$	40.6274			1.91733			0.958663	−	0.284543i	$-0.0918420\pi$
$449$	40.6274			1.91733			0.958663	+	0.284543i	$0.0918420\pi$
$450$		0			0
$451$	12.1360	−	21.0202i	0.571464	−	0.989804i
$452$	26.3755	−	15.2279i	1.24060	−	0.716261i
$453$	−1.90613	−	1.10051i	−0.0895578	−	0.0517062i
$454$	−3.81371	−	6.60554i	−0.178986	−	0.310013i
$455$		0			0
$456$	1.44975	+	2.51104i	0.0678906	+	0.117590i
$457$			31.1127i			1.45539i	0.685901	+	0.727695i	$0.259409\pi$
$457$			31.1127i			1.45539i	−0.685901	+	0.727695i	$0.740591\pi$
$458$	1.96768	+	1.13604i	0.0919435	+	0.0530836i
$459$	7.03553	−	12.1859i	0.328391	−	0.568789i
$460$		0			0
$461$	−2.14214			−0.0997692			−0.0498846	−	0.998755i	$-0.515885\pi$
$461$	−2.14214			−0.0997692			−0.0498846	+	0.998755i	$0.515885\pi$
$462$	−0.199573	−	0.115224i	−0.00928499	−	0.00536069i
$463$		−	8.97056i		−	0.416897i	−0.978033	−	0.208449i	$-0.933159\pi$
$463$		−	8.97056i		−	0.416897i	0.978033	−	0.208449i	$-0.0668414\pi$
$464$	20.4853			0.951005
$465$		0			0
$466$	−3.79899			−0.175985
$467$			8.00000i			0.370196i	0.982720	+	0.185098i	$0.0592602\pi$
$467$			8.00000i			0.370196i	−0.982720	+	0.185098i	$0.940740\pi$
$468$	17.1464	+	9.89949i	0.792594	+	0.457604i
$469$	1.34315			0.0620207
$470$		0			0
$471$	−1.89949	+	3.29002i	−0.0875241	+	0.151596i
$472$	−5.59093	−	3.22792i	−0.257343	−	0.148577i
$473$		−	35.3431i		−	1.62508i
$474$	−0.579690	−	1.00405i	−0.0266260	−	0.0461176i
$475$		0			0
$476$	2.20711	+	3.82282i	0.101163	+	0.175219i
$477$	−14.2767	−	8.24264i	−0.653684	−	0.377405i
$478$	−7.62015	+	4.39949i	−0.348537	+	0.201228i
$479$	−7.86396	+	13.6208i	−0.359314	+	0.622349i	−0.987846	−	0.155434i	$-0.950322\pi$
$479$	−7.86396	+	13.6208i	−0.359314	+	0.622349i	0.628533	+	0.777783i	$0.283656\pi$
$480$		0			0
$481$	−3.82843			−0.174561
$482$	4.78645	+	2.76346i	0.218017	+	0.125872i
$483$	0.594346	−	0.343146i	0.0270437	−	0.0156137i
$484$	0.443651	−	0.768426i	0.0201659	−	0.0349284i
$485$		0			0
$486$	−2.14214	−	3.71029i	−0.0971692	−	0.168302i
$487$	−16.7877	+	9.69239i	−0.760724	+	0.439204i	−0.829556	−	0.558424i	$-0.811406\pi$
$487$	−16.7877	+	9.69239i	−0.760724	+	0.439204i	0.0688318	+	0.997628i	$0.478073\pi$
$488$			4.48528i			0.203039i
$489$	4.34315	−	7.52255i	0.196404	−	0.340181i
$490$		0			0
$491$	−0.792893	−	1.37333i	−0.0357828	−	0.0619776i	0.847579	−	0.530669i	$-0.178059\pi$
$491$	−0.792893	−	1.37333i	−0.0357828	−	0.0619776i	−0.883362	+	0.468691i	$0.844726\pi$
$492$		−	5.66905i		−	0.255580i
$493$	−34.4669	−	19.8995i	−1.55231	−	0.896228i
$494$	7.00000			0.314945
$495$		0			0
$496$	−15.0000	+	7.34847i	−0.673520	+	0.329956i
$497$			0.0294373i			0.00132044i
$498$		−	1.72792i		−	0.0774300i
$499$	−1.10660	+	1.91669i	−0.0495383	+	0.0858028i	−0.889731	−	0.456485i	$-0.849108\pi$
$499$	−1.10660	+	1.91669i	−0.0495383	+	0.0858028i	0.840193	+	0.542288i	$0.182442\pi$
$500$		0			0
$501$	−4.67157	−	8.09140i	−0.208710	−	0.361497i
$502$	2.30090	+	1.32843i	0.102694	+	0.0592906i
$503$	11.5916	+	6.69239i	0.516842	+	0.298399i	0.735642	−	0.677371i	$-0.236881\pi$
$503$	11.5916	+	6.69239i	0.516842	+	0.298399i	−0.218800	+	0.975770i	$0.570214\pi$
$504$	1.85786			0.0827559
$505$		0			0
$506$	2.68629	+	4.65279i	0.119420	+	0.206842i
$507$	−0.594346	+	0.343146i	−0.0263958	+	0.0152396i
$508$	14.0920	+	8.13604i	0.625233	+	0.360978i
$509$	−16.3995	−	28.4048i	−0.726895	−	1.25902i	−0.958189	−	0.286135i	$-0.907629\pi$
$509$	−16.3995	−	28.4048i	−0.726895	−	1.25902i	0.231294	−	0.972884i	$-0.425704\pi$
$510$		0			0
$511$	0.757359			0.0335036
$512$		−	22.7574i		−	1.00574i
$513$	9.22911	+	5.32843i	0.407475	+	0.235256i
$514$	4.62132	+	8.00436i	0.203838	+	0.353057i
$515$		0			0
$516$	−4.12742	−	7.14890i	−0.181699	−	0.314713i
$517$	−27.1185	+	15.6569i	−1.19267	+	0.688588i
$518$	−0.148586	+	0.0857864i	−0.00652851	+	0.00376924i
$519$	−3.44365			−0.151159
$520$		0			0
$521$	10.2279	−	17.7153i	0.448093	−	0.776121i	−0.550169	−	0.835054i	$-0.685437\pi$
$521$	10.2279	−	17.7153i	0.448093	−	0.776121i	0.998262	+	0.0589331i	$0.0187699\pi$
$522$	−6.92820	+	4.00000i	−0.303239	+	0.175075i
$523$		−	8.00000i		−	0.349816i	−0.984585	−	0.174908i	$-0.944037\pi$
$523$		−	8.00000i		−	0.349816i	0.984585	−	0.174908i	$-0.0559627\pi$
$524$	12.1066	−	20.9692i	0.528879	−	0.916046i
$525$		0			0
$526$	−9.65685			−0.421059
$527$	32.3762	+	2.20711i	1.41033	+	0.0961431i
$528$			4.02944i			0.175359i
$529$	7.00000			0.304348
$530$		0			0
$531$	−11.5147			−0.499696
$532$	−2.89525	+	1.67157i	−0.125525	+	0.0724719i
$533$	−24.8176	−	14.3284i	−1.07497	−	0.620633i
$534$	0.384776	−	0.666452i	0.0166509	−	0.0288402i
$535$		0			0
$536$	2.57107	+	4.45322i	0.111053	+	0.192350i
$537$	5.46783	−	3.15685i	0.235954	−	0.136228i
$538$	−9.38825	+	5.42031i	−0.404756	+	0.233686i
$539$	−11.0711	+	19.1757i	−0.476865	+	0.825954i
$540$		0			0
$541$	15.6421	−	27.0930i	0.672508	−	1.16482i	−0.304683	−	0.952454i	$-0.598550\pi$
$541$	15.6421	−	27.0930i	0.672508	−	1.16482i	0.977191	−	0.212364i	$-0.0681162\pi$
$542$			0.284271i			0.0122105i
$543$			5.10051i			0.218884i
$544$	−12.8640	+	22.2810i	−0.551538	+	0.955291i
$545$		0			0
$546$	−0.136039	+	0.235626i	−0.00582193	+	0.0100839i
$547$	17.0849	−	9.86396i	0.730497	−	0.421753i	−0.0881071	−	0.996111i	$-0.528082\pi$
$547$	17.0849	−	9.86396i	0.730497	−	0.421753i	0.818604	+	0.574358i	$0.194748\pi$
$548$	−15.0196	+	8.67157i	−0.641606	+	0.370431i
$549$	4.00000	+	6.92820i	0.170716	+	0.295689i
$550$		0			0
$551$	15.0711	−	26.1039i	0.642049	−	1.11206i
$552$	2.27541	+	1.31371i	0.0968479	+	0.0559151i
$553$	2.42400	−	1.39949i	0.103079	−	0.0595126i
$554$	−5.85786			−0.248877
$555$		0			0
$556$		0			0
$557$		−	27.5147i		−	1.16584i	−0.812531	−	0.582918i	$-0.801911\pi$
$557$		−	27.5147i		−	1.16584i	0.812531	−	0.582918i	$-0.198089\pi$
$558$	3.63818	−	5.41421i	0.154017	−	0.229202i
$559$	−41.7279			−1.76490
$560$		0			0
$561$	3.91421	−	6.77962i	0.165258	−	0.286236i
$562$		−	0.828427i		−	0.0349451i
$563$	11.4685	−	6.62132i	0.483338	−	0.279055i	−0.238468	−	0.971150i	$-0.576645\pi$
$563$	11.4685	−	6.62132i	0.483338	−	0.279055i	0.721807	+	0.692095i	$0.243312\pi$
$564$	−3.65685	+	6.33386i	−0.153981	+	0.266704i
$565$		0			0
$566$	−5.65685			−0.237775
$567$	2.68512	−	1.55025i	0.112764	−	0.0651045i
$568$	−0.0975997	+	0.0563492i	−0.00409519	+	0.00236436i
$569$	−6.57107	−	11.3814i	−0.275473	−	0.477134i	0.694781	−	0.719221i	$-0.255501\pi$
$569$	−6.57107	−	11.3814i	−0.275473	−	0.477134i	−0.970254	+	0.242087i	$0.922168\pi$
$570$		0			0
$571$	10.5503	+	18.2736i	0.441514	+	0.764725i	0.997802	−	0.0662645i	$-0.0211081\pi$
$571$	10.5503	+	18.2736i	0.441514	+	0.764725i	−0.556288	+	0.830990i	$0.687775\pi$
$572$	19.6575	+	11.3492i	0.821920	+	0.474536i
$573$		−	8.65685i		−	0.361645i
$574$	−1.28427			−0.0536044
$575$		0			0
$576$	−5.89949	−	10.2182i	−0.245812	−	0.425759i
$577$	−0.0254934	−	0.0147186i	−0.00106130	−	0.000612744i	0.499469	−	0.866332i	$-0.333528\pi$
$577$	−0.0254934	−	0.0147186i	−0.00106130	−	0.000612744i	−0.500531	+	0.865719i	$0.666862\pi$
$578$	6.08767	−	3.51472i	0.253214	−	0.146193i
$579$	1.47918	+	2.56202i	0.0614728	+	0.106474i
$580$		0			0
$581$	4.17157			0.173066
$582$	0.768426	+	0.443651i	0.0318523	+	0.0183899i
$583$	−16.3674	−	9.44975i	−0.677870	−	0.391369i
$584$	1.44975	+	2.51104i	0.0599910	+	0.103907i
$585$		0			0
$586$	−3.06497	+	5.30869i	−0.126613	+	0.219300i
$587$			31.6569i			1.30662i	0.757091	+	0.653309i	$0.226620\pi$
$587$			31.6569i			1.30662i	−0.757091	+	0.653309i	$0.773380\pi$
$588$			5.17157i			0.213272i
$589$	−1.67157	+	24.5204i	−0.0688760	+	1.01035i
$590$		0			0
$591$	−5.58579			−0.229769
$592$	2.59808	+	1.50000i	0.106780	+	0.0616496i
$593$		−	1.31371i		−	0.0539475i	−0.999636	−	0.0269738i	$-0.991413\pi$
$593$		−	1.31371i		−	0.0539475i	0.999636	−	0.0269738i	$-0.00858706\pi$
$594$	−1.62132	−	2.80821i	−0.0665236	−	0.115222i
$595$		0			0
$596$	0.914214	−	1.58346i	0.0374476	−	0.0648612i
$597$		−	7.62742i		−	0.312169i
$598$	5.49333	−	3.17157i	0.224639	−	0.129695i
$599$	7.55025	+	13.0774i	0.308495	+	0.534329i	0.978033	−	0.208449i	$-0.0668414\pi$
$599$	7.55025	+	13.0774i	0.308495	+	0.534329i	−0.669538	+	0.742777i	$0.733508\pi$
$600$		0			0
$601$	3.25736	−	5.64191i	0.132870	−	0.230138i	−0.791911	−	0.610636i	$-0.790914\pi$
$601$	3.25736	−	5.64191i	0.132870	−	0.230138i	0.924782	+	0.380498i	$0.124247\pi$
$602$	−1.61952	+	0.935029i	−0.0660066	+	0.0381089i
$603$	7.94282	+	4.58579i	0.323456	+	0.186748i
$604$	9.71573			0.395327
$605$		0			0
$606$	0.727922	−	1.26080i	0.0295698	−	0.0512164i
$607$	1.37333	−	0.792893i	0.0557418	−	0.0321825i	−0.471870	−	0.881668i	$-0.656421\pi$
$607$	1.37333	−	0.792893i	0.0557418	−	0.0321825i	0.527612	+	0.849486i	$0.323088\pi$
$608$	−16.8747	−	9.74264i	−0.684361	−	0.395116i
$609$	0.585786	+	1.01461i	0.0237373	+	0.0411141i
$610$		0			0
$611$	18.4853	+	32.0174i	0.747834	+	1.29529i
$612$			30.1421i			1.21842i
$613$	−10.6640	−	6.15685i	−0.430714	−	0.248673i	0.268937	−	0.963158i	$-0.413328\pi$
$613$	−10.6640	−	6.15685i	−0.430714	−	0.248673i	−0.699651	+	0.714485i	$0.746661\pi$
$614$	−2.32843	+	4.03295i	−0.0939677	+	0.162757i
$615$		0			0
$616$	2.12994			0.0858178
$617$	−28.8250	−	16.6421i	−1.16045	−	0.669987i	−0.209040	−	0.977907i	$-0.567034\pi$
$617$	−28.8250	−	16.6421i	−1.16045	−	0.669987i	−0.951412	+	0.307920i	$0.900367\pi$
$618$			0.355339i			0.0142938i
$619$	20.3431			0.817660			0.408830	−	0.912611i	$-0.365937\pi$
$619$	20.3431			0.817660			0.408830	+	0.912611i	$0.365937\pi$
$620$		0			0
$621$	9.65685			0.387516
$622$		−	4.68629i		−	0.187903i
$623$	1.60896	+	0.928932i	0.0644615	+	0.0372169i
$624$	4.75736			0.190447
$625$		0			0
$626$	0.378680	−	0.655892i	0.0151351	−	0.0262147i
$627$	5.13461	+	2.96447i	0.205056	+	0.118389i
$628$		−	16.7696i		−	0.669178i
$629$	−2.91421	−	5.04757i	−0.116197	−	0.201260i
$630$		0			0
$631$	−25.0061	−	43.3118i	−0.995477	−	1.72422i	−0.580013	−	0.814607i	$-0.696953\pi$
$631$	−25.0061	−	43.3118i	−0.995477	−	1.72422i	−0.415464	−	0.909610i	$-0.636381\pi$
$632$	9.28009	+	5.35786i	0.369142	+	0.213124i
$633$	3.73578	−	2.15685i	0.148484	−	0.0857273i
$634$	−1.62132	+	2.80821i	−0.0643909	+	0.111528i
$635$		0			0
$636$	−4.41421			−0.175035
$637$	22.6398	+	13.0711i	0.897020	+	0.517895i
$638$	−7.94282	+	4.58579i	−0.314459	+	0.181553i
$639$	−0.100505	+	0.174080i	−0.00397592	+	0.00688649i
$640$		0			0
$641$	6.98528	+	12.0989i	0.275902	+	0.477876i	0.970362	−	0.241655i	$-0.0776901\pi$
$641$	6.98528	+	12.0989i	0.275902	+	0.477876i	−0.694460	+	0.719531i	$0.744357\pi$
$642$	−1.84458	+	1.06497i	−0.0727999	+	0.0420311i
$643$			35.3137i			1.39264i	0.717733	+	0.696318i	$0.245180\pi$
$643$			35.3137i			1.39264i	−0.717733	+	0.696318i	$0.754820\pi$
$644$	−1.51472	+	2.62357i	−0.0596883	+	0.103383i
$645$		0			0
$646$	5.32843	+	9.22911i	0.209644	+	0.363114i
$647$			45.3137i			1.78147i	0.454527	+	0.890733i	$0.349808\pi$
$647$			45.3137i			1.78147i	−0.454527	+	0.890733i	$0.650192\pi$
$648$	10.2798	+	5.93503i	0.403828	+	0.233150i
$649$	−13.2010			−0.518185
$650$		0			0
$651$	−0.792893	−	0.532799i	−0.0310759	−	0.0208821i
$652$			38.3431i			1.50163i
$653$		−	6.14214i		−	0.240360i	−0.992752	−	0.120180i	$-0.961653\pi$
$653$		−	6.14214i		−	0.240360i	0.992752	−	0.120180i	$-0.0383472\pi$
$654$	−0.928932	+	1.60896i	−0.0363241	+	0.0629152i
$655$		0			0
$656$	11.2279	+	19.4473i	0.438377	+	0.759291i
$657$	4.47871	+	2.58579i	0.174731	+	0.100881i
$658$	1.43488	+	0.828427i	0.0559374	+	0.0322955i
$659$	1.65685			0.0645419			0.0322709	−	0.999479i	$-0.489726\pi$
$659$	1.65685			0.0645419			0.0322709	+	0.999479i	$0.489726\pi$
$660$		0			0
$661$	−2.42893	−	4.20703i	−0.0944745	−	0.163635i	0.814915	−	0.579581i	$-0.196784\pi$
$661$	−2.42893	−	4.20703i	−0.0944745	−	0.163635i	−0.909389	+	0.415946i	$0.863450\pi$
$662$	−3.31552	+	1.91421i	−0.128861	+	0.0743980i
$663$	−8.00436	−	4.62132i	−0.310864	−	0.179477i
$664$	7.98528	+	13.8309i	0.309889	+	0.536744i
$665$		0			0
$666$	−1.17157			−0.0453975
$667$		−	27.3137i		−	1.05759i
$668$	35.7172	+	20.6213i	1.38194	+	0.797863i
$669$	−4.91421	−	8.51167i	−0.189994	−	0.329080i
$670$		0			0
$671$	4.58579	+	7.94282i	0.177032	+	0.306629i
$672$	0.655892	−	0.378680i	0.0253016	−	0.0146079i
$673$	8.09140	−	4.67157i	0.311901	−	0.180076i	−0.335876	−	0.941906i	$-0.609032\pi$
$673$	8.09140	−	4.67157i	0.311901	−	0.180076i	0.647777	+	0.761830i	$0.275699\pi$
$674$	−3.85786			−0.148599
$675$		0			0
$676$	1.51472	−	2.62357i	0.0582584	−	0.100907i
$677$	33.4268	−	19.2990i	1.28470	−	0.741720i	0.306994	−	0.951711i	$-0.400677\pi$
$677$	33.4268	−	19.2990i	1.28470	−	0.741720i	0.977703	+	0.209991i	$0.0673435\pi$
$678$			2.85786i			0.109756i
$679$	−1.07107	+	1.85514i	−0.0411038	+	0.0711939i
$680$		0			0
$681$	−7.62742			−0.292283
$682$	4.17098	−	6.20711i	0.159715	−	0.237682i
$683$		−	1.37258i		−	0.0525204i	−0.999655	−	0.0262602i	$-0.991640\pi$
$683$		−	1.37258i		−	0.0525204i	0.999655	−	0.0262602i	$-0.00835985\pi$
$684$	−22.8284			−0.872867
$685$		0			0
$686$	2.37258			0.0905856
$687$	1.96768	−	1.13604i	0.0750716	−	0.0433426i
$688$	28.3177	+	16.3492i	1.07960	+	0.623309i
$689$	−11.1569	+	19.3242i	−0.425042	+	0.736195i
$690$		0			0
$691$	0.0355339	+	0.0615465i	0.00135177	+	0.00234134i	0.866700	−	0.498829i	$-0.166236\pi$
$691$	0.0355339	+	0.0615465i	0.00135177	+	0.00234134i	−0.865349	+	0.501170i	$0.832903\pi$
$692$	13.1645	−	7.60051i	0.500438	−	0.288928i
$693$	3.29002	−	1.89949i	0.124978	−	0.0721558i
$694$	−1.77208	+	3.06933i	−0.0672672	+	0.116510i
$695$		0			0
$696$	−2.24264	+	3.88437i	−0.0850071	+	0.147237i
$697$		−	43.6274i		−	1.65251i
$698$		−	11.2304i		−	0.425079i
$699$	−1.89949	+	3.29002i	−0.0718455	+	0.124440i
$700$		0			0
$701$	6.74264	−	11.6786i	0.254666	−	0.441094i	−0.710139	−	0.704062i	$-0.751368\pi$
$701$	6.74264	−	11.6786i	0.254666	−	0.441094i	0.964805	+	0.262967i	$0.0847011\pi$
$702$	−3.31552	+	1.91421i	−0.125136	+	0.0722473i
$703$	3.82282	−	2.20711i	0.144180	−	0.0832426i
$704$	−6.76346	−	11.7146i	−0.254907	−	0.441512i
$705$		0			0
$706$	−0.621320	+	1.07616i	−0.0233837	+	0.0405018i
$707$	3.04384	+	1.75736i	0.114475	+	0.0660923i
$708$	−2.67018	+	1.54163i	−0.100352	+	0.0579380i
$709$	−17.3137			−0.650230			−0.325115	−	0.945674i	$-0.605403\pi$
$709$	−17.3137			−0.650230			−0.325115	+	0.945674i	$0.605403\pi$
$710$		0			0
$711$	19.1127			0.716782
$712$			7.11270i			0.266560i
$713$	9.79796	+	20.0000i	0.366936	+	0.749006i
$714$	−0.414214			−0.0155016
$715$		0			0
$716$	−13.9350	+	24.1362i	−0.520776	+	0.902011i
$717$			8.79899i			0.328604i
$718$	2.54709	−	1.47056i	0.0950565	−	0.0548809i
$719$	−4.03553	+	6.98975i	−0.150500	+	0.260674i	−0.931411	−	0.363968i	$-0.881422\pi$
$719$	−4.03553	+	6.98975i	−0.150500	+	0.260674i	0.780911	+	0.624642i	$0.214755\pi$
$720$		0			0
$721$	−0.857864			−0.0319485
$722$	−0.174080	+	0.100505i	−0.00647858	+	0.00374041i
$723$	4.78645	−	2.76346i	0.178010	−	0.102774i
$724$	−11.2574	−	19.4983i	−0.418376	−	0.724649i
$725$		0			0
$726$	0.0416306	+	0.0721062i	0.00154506	+	0.00267611i
$727$	35.3690	+	20.4203i	1.31176	+	0.757347i	0.982388	−	0.186851i	$-0.0598283\pi$
$727$	35.3690	+	20.4203i	1.31176	+	0.757347i	0.329376	+	0.944199i	$0.393162\pi$
$728$		−	2.51472i		−	0.0932017i
$729$	18.1716			0.673021
$730$		0			0
$731$	−31.7635	−	55.0159i	−1.17481	−	2.03484i
$732$	1.85514	+	1.07107i	0.0685681	+	0.0395878i
$733$	13.5337	−	7.81371i	0.499880	−	0.288606i	−0.228784	−	0.973477i	$-0.573475\pi$
$733$	13.5337	−	7.81371i	0.499880	−	0.288606i	0.728664	+	0.684871i	$0.240142\pi$
$734$	−5.01472	−	8.68575i	−0.185097	−	0.320597i
$735$		0			0
$736$	−17.6569			−0.650840
$737$	9.10601	+	5.25736i	0.335424	+	0.193657i
$738$	−7.59466	−	4.38478i	−0.279563	−	0.161406i
$739$	22.9350	+	39.7246i	0.843679	+	1.46129i	0.886764	+	0.462223i	$0.152948\pi$
$739$	22.9350	+	39.7246i	0.843679	+	1.46129i	−0.0430851	+	0.999071i	$0.513719\pi$
$740$		0			0
$741$	3.50000	−	6.06218i	0.128576	−	0.222700i
$742$			1.00000i			0.0367112i
$743$			5.65685i			0.207530i	0.994602	+	0.103765i	$0.0330890\pi$
$743$			5.65685i			0.207530i	−0.994602	+	0.103765i	$0.966911\pi$
$744$	0.248737	−	3.64874i	0.00911915	−	0.133769i
$745$		0			0
$746$	4.14214			0.151654
$747$	24.6690	+	14.2426i	0.902591	+	0.521111i
$748$			34.5563i			1.26351i
$749$	−2.57107	−	4.45322i	−0.0939448	−	0.162717i
$750$		0			0
$751$	−3.62132	+	6.27231i	−0.132144	+	0.228880i	−0.924503	−	0.381175i	$-0.875519\pi$
$751$	−3.62132	+	6.27231i	−0.132144	+	0.228880i	0.792359	+	0.610055i	$0.208853\pi$
$752$		−	28.9706i		−	1.05645i
$753$	2.30090	−	1.32843i	0.0838496	−	0.0484106i
$754$	5.41421	+	9.37769i	0.197174	+	0.341515i
$755$		0			0
$756$	0.914214	−	1.58346i	0.0332496	−	0.0575900i
$757$	−20.2158	+	11.6716i	−0.734754	+	0.424211i	−0.820159	−	0.572136i	$-0.806115\pi$
$757$	−20.2158	+	11.6716i	−0.734754	+	0.424211i	0.0854047	+	0.996346i	$0.472782\pi$
$758$	−2.64906	−	1.52944i	−0.0962183	−	0.0555517i
$759$	5.37258			0.195012
$760$		0			0
$761$	−15.2279	+	26.3755i	−0.552012	+	0.956112i	0.446118	+	0.894974i	$0.352806\pi$
$761$	−15.2279	+	26.3755i	−0.552012	+	0.956112i	−0.998129	+	0.0611380i	$0.980527\pi$
$762$	−1.32234	+	0.763456i	−0.0479035	+	0.0276571i
$763$	−3.88437	−	2.24264i	−0.140624	−	0.0811890i
$764$	19.1066	+	33.0936i	0.691253	+	1.19728i
$765$		0			0
$766$	−1.05635	−	1.82965i	−0.0381674	−	0.0661080i
$767$			15.5858i			0.562770i
$768$	−1.42432	−	0.822330i	−0.0513957	−	0.0296733i
$769$	18.0563	−	31.2745i	0.651129	−	1.12779i	−0.331721	−	0.943378i	$-0.607629\pi$
$769$	18.0563	−	31.2745i	0.651129	−	1.12779i	0.982849	−	0.184410i	$-0.0590375\pi$
$770$		0			0
$771$	9.24264			0.332866
$772$	−11.3093	−	6.52944i	−0.407031	−	0.235000i
$773$			18.0000i			0.647415i	0.946157	+	0.323708i	$0.104929\pi$
$773$			18.0000i			0.647415i	−0.946157	+	0.323708i	$0.895071\pi$
$774$	−12.7696			−0.458992
$775$		0			0
$776$	−8.20101			−0.294399
$777$			0.171573i			0.00615514i
$778$	3.99690	+	2.30761i	0.143296	+	0.0827319i
$779$	33.0416			1.18384
$780$		0			0
$781$	−0.115224	+	0.199573i	−0.00412303	+	0.00714129i
$782$	8.36308	+	4.82843i	0.299063	+	0.172664i
$783$			16.4853i			0.589136i
$784$	−10.2426	−	17.7408i	−0.365809	−	0.633599i
$785$		0			0
$786$	1.13604	+	1.96768i	0.0405212	+	0.0701847i
$787$	36.7318	+	21.2071i	1.30935	+	0.755952i	0.981987	−	0.188948i	$-0.0605078\pi$
$787$	36.7318	+	21.2071i	1.30935	+	0.755952i	0.327360	+	0.944900i	$0.393841\pi$
$788$	21.3535	−	12.3284i	0.760686	−	0.439182i
$789$	−4.82843	+	8.36308i	−0.171897	+	0.297734i
$790$		0			0
$791$	−6.89949			−0.245318
$792$	12.5956	+	7.27208i	0.447565	+	0.258402i
$793$	9.37769	−	5.41421i	0.333012	−	0.192264i
$794$	−6.93503	+	12.0118i	−0.246115	+	0.426284i
$795$		0			0
$796$	16.8345	+	29.1583i	0.596684	+	1.03349i
$797$	−24.6435	+	14.2279i	−0.872917	+	0.503979i	−0.868316	−	0.496011i	$-0.834798\pi$
$797$	−24.6435	+	14.2279i	−0.872917	+	0.503979i	−0.00460050	+	0.999989i	$0.501464\pi$
$798$		−	0.313708i		−	0.0111052i
$799$	−28.1421	+	48.7436i	−0.995597	+	1.72442i
$800$		0			0
$801$	6.34315	+	10.9867i	0.224124	+	0.388194i
$802$			11.1127i			0.392403i
$803$	5.13461	+	2.96447i	0.181196	+	0.104614i
$804$	2.45584			0.0866109
$805$		0			0
$806$	−7.32843	−	4.92447i	−0.258133	−	0.173457i
$807$			10.8406i			0.381608i
$808$			13.4558i			0.473375i
$809$	−6.01472	+	10.4178i	−0.211466	+	0.366270i	−0.952174	−	0.305558i	$-0.901157\pi$
$809$	−6.01472	+	10.4178i	−0.211466	+	0.366270i	0.740707	+	0.671828i	$0.234491\pi$
$810$		0			0
$811$	6.86396	+	11.8887i	0.241026	+	0.417470i	0.961007	−	0.276524i	$-0.0891827\pi$
$811$	6.86396	+	11.8887i	0.241026	+	0.417470i	−0.719981	+	0.693994i	$0.755849\pi$
$812$	−4.47871	−	2.58579i	−0.157172	−	0.0907433i
$813$	0.246186	+	0.142136i	0.00863412	+	0.00498491i
$814$	−1.34315			−0.0470772
$815$		0			0
$816$	3.62132	+	6.27231i	0.126772	+	0.219575i
$817$	41.6668	−	24.0563i	1.45774	−	0.841625i
$818$	−7.41002	−	4.27817i	−0.259085	−	0.149583i
$819$	−2.24264	−	3.88437i	−0.0783642	−	0.135731i
$820$		0			0
$821$	8.48528			0.296138			0.148069	−	0.988977i	$-0.452694\pi$
$821$	8.48528			0.296138			0.148069	+	0.988977i	$0.452694\pi$
$822$		−	1.62742i		−	0.0567627i
$823$	−31.3616	−	18.1066i	−1.09320	−	0.631156i	−0.158770	−	0.987316i	$-0.550753\pi$
$823$	−31.3616	−	18.1066i	−1.09320	−	0.631156i	−0.934425	+	0.356159i	$0.884086\pi$
$824$	−1.64214	−	2.84426i	−0.0572065	−	0.0990846i
$825$		0			0
$826$	0.349242	+	0.604906i	0.0121517	+	0.0210474i
$827$	−31.9559	+	18.4497i	−1.11122	+	0.641561i	−0.939144	−	0.343524i	$-0.888379\pi$
$827$	−31.9559	+	18.4497i	−1.11122	+	0.641561i	−0.172072	+	0.985084i	$0.555046\pi$
$828$	−17.9149	+	10.3431i	−0.622584	+	0.359449i
$829$	−38.4264			−1.33460			−0.667302	−	0.744787i	$-0.732551\pi$
$829$	−38.4264			−1.33460			−0.667302	+	0.744787i	$0.732551\pi$
$830$		0			0
$831$	−2.92893	+	5.07306i	−0.101604	+	0.175982i
$832$	−13.8309	+	7.98528i	−0.479501	+	0.276840i
$833$			39.7990i			1.37895i
$834$		0			0
$835$		0			0
$836$	−26.1716			−0.905163
$837$	−5.91359	−	12.0711i	−0.204404	−	0.417237i
$838$			11.5980i			0.400646i
$839$	14.6274			0.504995			0.252497	−	0.967598i	$-0.418748\pi$
$839$	14.6274			0.504995			0.252497	+	0.967598i	$0.418748\pi$
$840$		0			0
$841$	17.6274			0.607842
$842$	11.1713	−	6.44975i	0.384988	−	0.222273i
$843$	−0.717439	−	0.414214i	−0.0247099	−	0.0142663i
$844$	−9.52082	+	16.4905i	−0.327720	+	0.567628i
$845$		0			0
$846$	5.65685	+	9.79796i	0.194487	+	0.336861i
$847$	−0.174080	+	0.100505i	−0.00598146	+	0.00345339i
$848$	15.1427	−	8.74264i	0.520002	−	0.300224i
$849$	−2.82843	+	4.89898i	−0.0970714	+	0.168133i
$850$		0			0
$851$	2.00000	−	3.46410i	0.0685591	−	0.118748i
$852$			0.0538239i			0.00184398i
$853$		−	15.5147i		−	0.531214i	−0.964081	−	0.265607i	$-0.914428\pi$
$853$		−	15.5147i		−	0.531214i	0.964081	−	0.265607i	$-0.0855723\pi$
$854$	0.242641	−	0.420266i	0.00830299	−	0.0143812i
$855$		0			0
$856$	9.84315	−	17.0488i	0.336432	−	0.582717i
$857$	16.8747	−	9.74264i	0.576430	−	0.332802i	−0.183283	−	0.983060i	$-0.558672\pi$
$857$	16.8747	−	9.74264i	0.576430	−	0.332802i	0.759714	+	0.650258i	$0.225339\pi$
$858$	−1.84458	+	1.06497i	−0.0629731	+	0.0363575i
$859$	−24.6924	−	42.7685i	−0.842493	−	1.45924i	−0.887780	−	0.460267i	$-0.847754\pi$
$859$	−24.6924	−	42.7685i	−0.842493	−	1.45924i	0.0452869	−	0.998974i	$-0.485580\pi$
$860$		0			0
$861$	−0.642136	+	1.11221i	−0.0218839	+	0.0379041i
$862$	−6.01119	−	3.47056i	−0.204742	−	0.118208i
$863$	−2.26485	+	1.30761i	−0.0770964	+	0.0445116i	−0.538053	−	0.842911i	$-0.680840\pi$
$863$	−2.26485	+	1.30761i	−0.0770964	+	0.0445116i	0.460956	+	0.887423i	$0.347507\pi$
$864$	10.6569			0.362554
$865$		0			0
$866$	11.2304			0.381626
$867$		−	7.02944i		−	0.238732i
$868$	4.20703	+	0.286797i	0.142796	+	0.00973451i
$869$	21.9117			0.743303
$870$		0			0
$871$	6.20711	−	10.7510i	0.210320	−	0.364285i
$872$		−	17.1716i		−	0.581503i
$873$	−12.6677	+	7.31371i	−0.428737	+	0.247532i
$874$	−3.65685	+	6.33386i	−0.123695	+	0.214246i
$875$		0			0
$876$	1.38478			0.0467873
$877$	−46.6168	+	26.9142i	−1.57414	+	0.908828i	−0.578483	+	0.815694i	$0.696355\pi$
$877$	−46.6168	+	26.9142i	−1.57414	+	0.908828i	−0.995654	+	0.0931343i	$0.970311\pi$
$878$	0.742932	−	0.428932i	0.0250728	−	0.0144758i
$879$	3.06497	+	5.30869i	0.103379	+	0.179058i
$880$		0			0
$881$	−5.84315	−	10.1206i	−0.196861	−	0.340973i	0.750648	−	0.660702i	$-0.229741\pi$
$881$	−5.84315	−	10.1206i	−0.196861	−	0.340973i	−0.947509	+	0.319729i	$0.896408\pi$
$882$	6.92820	+	4.00000i	0.233285	+	0.134687i
$883$		−	30.2843i		−	1.01915i	−0.860427	−	0.509573i	$-0.829803\pi$
$883$		−	30.2843i		−	1.01915i	0.860427	−	0.509573i	$-0.170197\pi$
$884$	40.7990			1.37222
$885$		0			0
$886$	0.985281	+	1.70656i	0.0331012	+	0.0573329i
$887$	−44.4495	−	25.6630i	−1.49247	−	0.861678i	−0.492507	−	0.870309i	$-0.663919\pi$
$887$	−44.4495	−	25.6630i	−1.49247	−	0.861678i	−0.999963	+	0.00863117i	$0.997253\pi$
$888$	−0.568852	+	0.328427i	−0.0190894	+	0.0110213i
$889$	−1.84315	−	3.19242i	−0.0618171	−	0.107070i
$890$		0			0
$891$	24.2721			0.813145
$892$	37.5723	+	21.6924i	1.25801	+	0.726315i
$893$	−36.9164	−	21.3137i	−1.23536	−	0.713236i
$894$	0.0857864	+	0.148586i	0.00286913	+	0.00496947i
$895$		0			0
$896$	−2.18629	+	3.78677i	−0.0730389	+	0.126507i
$897$		−	6.34315i		−	0.211791i
$898$		−	16.8284i		−	0.561572i
$899$	−34.1421	+	16.7262i	−1.13870	+	0.557849i
$900$		0			0
$901$	−33.9706			−1.13172
$902$	−8.70687	−	5.02691i	−0.289907	−	0.167378i
$903$			1.87006i			0.0622316i
$904$	−13.2071	−	22.8754i	−0.439262	−	0.760824i
$905$		0			0
$906$	−0.455844	+	0.789545i	−0.0151444	+	0.0262309i
$907$		−	32.6863i		−	1.08533i	−0.839949	−	0.542665i	$-0.817415\pi$
$907$		−	32.6863i		−	1.08533i	0.839949	−	0.542665i	$-0.182585\pi$
$908$	29.1583	−	16.8345i	0.967651	−	0.558673i
$909$	12.0000	+	20.7846i	0.398015	+	0.689382i
$910$		0			0
$911$	−0.479185	+	0.829972i	−0.0158761	+	0.0274982i	−0.873854	−	0.486188i	$-0.838387\pi$
$911$	−0.479185	+	0.829972i	−0.0158761	+	0.0274982i	0.857978	+	0.513686i	$0.171720\pi$
$912$	−4.75039	+	2.74264i	−0.157301	+	0.0908179i
$913$	28.2817	+	16.3284i	0.935987	+	0.540392i
$914$	12.8873			0.426274
$915$		0			0
$916$	−5.01472	+	8.68575i	−0.165691	+	0.286985i
$917$	−4.75039	+	2.74264i	−0.156872	+	0.0905700i
$918$	−5.04757	−	2.91421i	−0.166595	−	0.0961834i
$919$	−17.4497	−	30.2238i	−0.575614	−	0.996993i	−0.995975	−	0.0896356i	$-0.971430\pi$
$919$	−17.4497	−	30.2238i	−0.575614	−	0.996993i	0.420361	−	0.907357i	$-0.361904\pi$
$920$		0			0
$921$	2.32843	+	4.03295i	0.0767243	+	0.132890i
$922$			0.887302i			0.0292217i
$923$	0.235626	+	0.136039i	0.00775574	+	0.00447778i
$924$	0.508622	−	0.880959i	0.0167324	−	0.0289814i
$925$		0			0
$926$	−3.71573			−0.122106
$927$	−5.07306	−	2.92893i	−0.166621	−	0.0961988i
$928$		−	30.1421i		−	0.989464i
$929$	−7.51472			−0.246550			−0.123275	−	0.992373i	$-0.539340\pi$
$929$	−7.51472			−0.246550			−0.123275	+	0.992373i	$0.539340\pi$
$930$		0			0
$931$	−30.1421			−0.987869
$932$		−	16.7696i		−	0.549305i
$933$	−4.05845	−	2.34315i	−0.132868	−	0.0767111i
$934$	3.31371			0.108428
$935$		0			0
$936$	8.58579	−	14.8710i	0.280635	−	0.486074i
$937$	13.5847	+	7.84315i	0.443794	+	0.256224i	0.705206	−	0.709003i	$-0.250855\pi$
$937$	13.5847	+	7.84315i	0.443794	+	0.256224i	−0.261412	+	0.965227i	$0.584188\pi$
$938$		−	0.556349i		−	0.0181654i
$939$	−0.378680	−	0.655892i	−0.0123577	−	0.0214042i
$940$		0			0
$941$	17.5000	+	30.3109i	0.570484	+	0.988107i	0.996516	+	0.0833989i	$0.0265776\pi$
$941$	17.5000	+	30.3109i	0.570484	+	0.988107i	−0.426033	+	0.904708i	$0.640089\pi$
$942$	1.36277	+	0.786797i	0.0444015	+	0.0256352i
$943$	25.9298	−	14.9706i	0.844390	−	0.487509i
$944$	6.10660	−	10.5769i	0.198753	−	0.344250i
$945$		0			0
$946$	−14.6396			−0.475975
$947$	16.5415	+	9.55025i	0.537527	+	0.310342i	0.744076	−	0.668095i	$-0.232890\pi$
$947$	16.5415	+	9.55025i	0.537527	+	0.310342i	−0.206549	+	0.978436i	$0.566223\pi$
$948$	4.43210	−	2.55887i	0.143948	−	0.0831084i
$949$	3.50000	−	6.06218i	0.113615	−	0.196787i
$950$		0			0
$951$	1.62132	+	2.80821i	0.0525749	+	0.0910624i
$952$	3.31552	−	1.91421i	0.107456	−	0.0620400i
$953$			3.51472i			0.113853i	0.998378	+	0.0569265i	$0.0181301\pi$
$953$			3.51472i			0.113853i	−0.998378	+	0.0569265i	$0.981870\pi$
$954$	−3.41421	+	5.91359i	−0.110539	+	0.191460i
$955$		0			0
$956$	−19.4203	−	33.6370i	−0.628098	−	1.08790i
$957$			9.17157i			0.296475i
$958$	5.64191	+	3.25736i	0.182282	+	0.105241i
$959$	3.92893			0.126872
$960$		0			0
$961$	19.0000	−	24.4949i	0.612903	−	0.790158i
$962$			1.58579i			0.0511278i
$963$		−	35.1127i		−	1.13149i
$964$	−12.1985	+	21.1284i	−0.392887	+	0.680500i
$965$		0			0
$966$	−0.142136	−	0.246186i	−0.00457314	−	0.00792091i
$967$	−13.3746	−	7.72183i	−0.430098	−	0.248317i	0.269290	−	0.963059i	$-0.413211\pi$
$967$	−13.3746	−	7.72183i	−0.430098	−	0.248317i	−0.699388	+	0.714742i	$0.746544\pi$
$968$	−0.666452	−	0.384776i	−0.0214206	−	0.0123672i
$969$	10.6569			0.342347
$970$		0			0
$971$	0.349242	+	0.604906i	0.0112077	+	0.0194123i	0.871575	−	0.490262i	$-0.163099\pi$
$971$	0.349242	+	0.604906i	0.0112077	+	0.0194123i	−0.860367	+	0.509675i	$0.829766\pi$
$972$	16.3780	−	9.45584i	0.525325	−	0.303296i
$973$		0			0
$974$	4.01472	+	6.95370i	0.128640	+	0.222811i
$975$		0			0
$976$	−8.48528			−0.271607
$977$			0.485281i			0.0155255i	0.999970	+	0.00776276i	$0.00247099\pi$
$977$			0.485281i			0.0155255i	−0.999970	+	0.00776276i	$0.997529\pi$
$978$	−3.11594	−	1.79899i	−0.0996368	−	0.0575254i
$979$	7.27208	+	12.5956i	0.232417	+	0.402557i
$980$		0			0
$981$	−15.3137	−	26.5241i	−0.488929	−	0.846850i
$982$	−0.568852	+	0.328427i	−0.0181528	+	0.0104805i
$983$	−33.6370	+	19.4203i	−1.07285	+	0.619412i	−0.928959	−	0.370182i	$-0.879295\pi$
$983$	−33.6370	+	19.4203i	−1.07285	+	0.619412i	−0.143893	+	0.989593i	$0.545962\pi$
$984$	−4.91674			−0.156740
$985$		0			0
$986$	−8.24264	+	14.2767i	−0.262499	+	0.454662i
$987$	1.43488	−	0.828427i	0.0456727	−	0.0263691i
$988$			30.8995i			0.983044i
$989$	21.7990	−	37.7570i	0.693168	−	1.20060i
$990$		0			0
$991$	47.9411			1.52290			0.761450	−	0.648224i	$-0.224488\pi$
$991$	47.9411			1.52290			0.761450	+	0.648224i	$0.224488\pi$
$992$	10.8126	+	22.0711i	0.343299	+	0.700757i
$993$			3.82843i			0.121491i
$994$	0.0121933			0.000386748
$995$		0			0
$996$	7.62742			0.241684
$997$	−28.2307	+	16.2990i	−0.894075	+	0.516194i	−0.875273	−	0.483629i	$-0.839318\pi$
$997$	−28.2307	+	16.2990i	−0.894075	+	0.516194i	−0.0188015	+	0.999823i	$0.505985\pi$
$998$	0.793919	+	0.458369i	0.0251311	+	0.0145094i
$999$	−1.20711	+	2.09077i	−0.0381912	+	0.0661490i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.o.d.749.2		8
5.2	odd	4		31.2.c.a.5.2	✓	4
5.3	odd	4		775.2.e.e.501.1		4
5.4	even	2	inner	775.2.o.d.749.3		8
15.2	even	4		279.2.h.c.253.1		4
20.7	even	4		496.2.i.h.129.2		4
31.25	even	3	inner	775.2.o.d.149.2		8
155.2	odd	20		961.2.g.o.547.2		16
155.7	odd	60		961.2.g.o.338.1		16
155.12	even	60		961.2.g.r.844.2		16
155.17	even	60		961.2.g.r.732.1		16
155.22	even	60		961.2.d.i.374.1		8
155.27	even	20		961.2.g.r.235.1		16
155.37	even	12		961.2.c.a.521.2		4
155.42	even	60		961.2.d.i.388.1		8
155.47	odd	20		961.2.g.o.846.2		16
155.52	even	60		961.2.d.i.531.2		8
155.57	even	12		961.2.a.c.1.2		2
155.67	odd	12		961.2.a.a.1.2		2
155.72	odd	60		961.2.d.l.531.2		8
155.77	even	20		961.2.g.r.846.2		16
155.82	odd	60		961.2.d.l.388.1		8
155.87	odd	12		31.2.c.a.25.2	yes	4
155.92	even	4		961.2.c.a.439.2		4
155.97	odd	20		961.2.g.o.235.1		16
155.102	odd	60		961.2.d.l.374.1		8
155.107	odd	60		961.2.g.o.732.1		16
155.112	odd	60		961.2.g.o.844.2		16
155.117	even	60		961.2.g.r.338.1		16
155.118	odd	12		775.2.e.e.676.1		4
155.122	even	20		961.2.g.r.547.2		16
155.127	even	60		961.2.g.r.448.2		16
155.132	odd	20		961.2.g.o.816.1		16
155.137	even	60		961.2.d.i.628.2		8
155.142	odd	60		961.2.d.l.628.2		8
155.147	even	20		961.2.g.r.816.1		16
155.149	even	6	inner	775.2.o.d.149.3		8
155.152	odd	60		961.2.g.o.448.2		16
465.212	odd	12		8649.2.a.k.1.1		2
465.242	even	12		279.2.h.c.118.1		4
465.377	even	12		8649.2.a.l.1.1		2
620.87	even	12		496.2.i.h.273.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.c.a.5.2	✓	4	5.2	odd	4
31.2.c.a.25.2	yes	4	155.87	odd	12
279.2.h.c.118.1		4	465.242	even	12
279.2.h.c.253.1		4	15.2	even	4
496.2.i.h.129.2		4	20.7	even	4
496.2.i.h.273.2		4	620.87	even	12
775.2.e.e.501.1		4	5.3	odd	4
775.2.e.e.676.1		4	155.118	odd	12
775.2.o.d.149.2		8	31.25	even	3	inner
775.2.o.d.149.3		8	155.149	even	6	inner
775.2.o.d.749.2		8	1.1	even	1	trivial
775.2.o.d.749.3		8	5.4	even	2	inner
961.2.a.a.1.2		2	155.67	odd	12
961.2.a.c.1.2		2	155.57	even	12
961.2.c.a.439.2		4	155.92	even	4
961.2.c.a.521.2		4	155.37	even	12
961.2.d.i.374.1		8	155.22	even	60
961.2.d.i.388.1		8	155.42	even	60
961.2.d.i.531.2		8	155.52	even	60
961.2.d.i.628.2		8	155.137	even	60
961.2.d.l.374.1		8	155.102	odd	60
961.2.d.l.388.1		8	155.82	odd	60
961.2.d.l.531.2		8	155.72	odd	60
961.2.d.l.628.2		8	155.142	odd	60
961.2.g.o.235.1		16	155.97	odd	20
961.2.g.o.338.1		16	155.7	odd	60
961.2.g.o.448.2		16	155.152	odd	60
961.2.g.o.547.2		16	155.2	odd	20
961.2.g.o.732.1		16	155.107	odd	60
961.2.g.o.816.1		16	155.132	odd	20
961.2.g.o.844.2		16	155.112	odd	60
961.2.g.o.846.2		16	155.47	odd	20
961.2.g.r.235.1		16	155.27	even	20
961.2.g.r.338.1		16	155.117	even	60
961.2.g.r.448.2		16	155.127	even	60
961.2.g.r.547.2		16	155.122	even	20
961.2.g.r.732.1		16	155.17	even	60
961.2.g.r.816.1		16	155.147	even	20
961.2.g.r.844.2		16	155.12	even	60
961.2.g.r.846.2		16	155.77	even	20
8649.2.a.k.1.1		2	465.212	odd	12
8649.2.a.l.1.1		2	465.377	even	12

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.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.414214i q^{2} +(-0.358719 - 0.207107i) q^{3} +1.82843 q^{4} +(-0.0857864 + 0.148586i) q^{6} +(-0.358719 - 0.207107i) q^{7} -1.58579i q^{8} +(-1.41421 - 2.44949i) q^{9} +O(q^{10})\)	\(q-0.414214i q^{2} +(-0.358719 - 0.207107i) q^{3} +1.82843 q^{4} +(-0.0857864 + 0.148586i) q^{6} +(-0.358719 - 0.207107i) q^{7} -1.58579i q^{8} +(-1.41421 - 2.44949i) q^{9} +(-1.62132 - 2.80821i) q^{11} +(-0.655892 - 0.378680i) q^{12} +(-3.31552 + 1.91421i) q^{13} +(-0.0857864 + 0.148586i) q^{14} +3.00000 q^{16} +(-5.04757 - 2.91421i) q^{17} +(-1.01461 + 0.585786i) q^{18} +(2.20711 - 3.82282i) q^{19} +(0.0857864 + 0.148586i) q^{21} +(-1.16320 + 0.671573i) q^{22} -4.00000i q^{23} +(-0.328427 + 0.568852i) q^{24} +(0.792893 + 1.37333i) q^{26} +2.41421i q^{27} +(-0.655892 - 0.378680i) q^{28} +6.82843 q^{29} +(-5.00000 + 2.44949i) q^{31} -4.41421i q^{32} +1.34315i q^{33} +(-1.20711 + 2.09077i) q^{34} +(-2.58579 - 4.47871i) q^{36} +(0.866025 + 0.500000i) q^{37} +(-1.58346 - 0.914214i) q^{38} +1.58579 q^{39} +(3.74264 + 6.48244i) q^{41} +(0.0615465 - 0.0355339i) q^{42} +(9.43924 + 5.44975i) q^{43} +(-2.96447 - 5.13461i) q^{44} -1.65685 q^{46} -9.65685i q^{47} +(-1.07616 - 0.621320i) q^{48} +(-3.41421 - 5.91359i) q^{49} +(1.20711 + 2.09077i) q^{51} +(-6.06218 + 3.50000i) q^{52} +(5.04757 - 2.91421i) q^{53} +1.00000 q^{54} +(-0.328427 + 0.568852i) q^{56} +(-1.58346 + 0.914214i) q^{57} -2.82843i q^{58} +(2.03553 - 3.52565i) q^{59} -2.82843 q^{61} +(1.01461 + 2.07107i) q^{62} +1.17157i q^{63} +4.17157 q^{64} +0.556349 q^{66} +(-2.80821 + 1.62132i) q^{67} +(-9.22911 - 5.32843i) q^{68} +(-0.828427 + 1.43488i) q^{69} +(-0.0355339 - 0.0615465i) q^{71} +(-3.88437 + 2.24264i) q^{72} +(-1.58346 + 0.914214i) q^{73} +(0.207107 - 0.358719i) q^{74} +(4.03553 - 6.98975i) q^{76} +1.34315i q^{77} -0.656854i q^{78} +(-3.37868 + 5.85204i) q^{79} +(-3.74264 + 6.48244i) q^{81} +(2.68512 - 1.55025i) q^{82} +(-8.72180 + 5.03553i) q^{83} +(0.156854 + 0.271680i) q^{84} +(2.25736 - 3.90986i) q^{86} +(-2.44949 - 1.41421i) q^{87} +(-4.45322 + 2.57107i) q^{88} -4.48528 q^{89} +1.58579 q^{91} -7.31371i q^{92} +(2.30090 + 0.156854i) q^{93} -4.00000 q^{94} +(-0.914214 + 1.58346i) q^{96} -5.17157i q^{97} +(-2.44949 + 1.41421i) q^{98} +(-4.58579 + 7.94282i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 12 q^{6}+O(q^{10}) \) 8 * q - 8 * q^4 - 12 * q^6	\( 8 q - 8 q^{4} - 12 q^{6} + 4 q^{11} - 12 q^{14} + 24 q^{16} + 12 q^{19} + 12 q^{21} + 20 q^{24} + 12 q^{26} + 32 q^{29} - 40 q^{31} - 4 q^{34} - 32 q^{36} + 24 q^{39} - 4 q^{41} - 52 q^{44} + 32 q^{46} - 16 q^{49} + 4 q^{51} + 8 q^{54} + 20 q^{56} - 12 q^{59} + 56 q^{64} - 120 q^{66} + 16 q^{69} + 28 q^{71} - 4 q^{74} + 4 q^{76} - 44 q^{79} + 4 q^{81} - 44 q^{84} + 52 q^{86} + 32 q^{89} + 24 q^{91} - 32 q^{94} + 4 q^{96} - 48 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 - 12 * q^6 + 4 * q^11 - 12 * q^14 + 24 * q^16 + 12 * q^19 + 12 * q^21 + 20 * q^24 + 12 * q^26 + 32 * q^29 - 40 * q^31 - 4 * q^34 - 32 * q^36 + 24 * q^39 - 4 * q^41 - 52 * q^44 + 32 * q^46 - 16 * q^49 + 4 * q^51 + 8 * q^54 + 20 * q^56 - 12 * q^59 + 56 * q^64 - 120 * q^66 + 16 * q^69 + 28 * q^71 - 4 * q^74 + 4 * q^76 - 44 * q^79 + 4 * q^81 - 44 * q^84 + 52 * q^86 + 32 * q^89 + 24 * q^91 - 32 * q^94 + 4 * q^96 - 48 * q^99

Introduction

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