LMFDB - Embedded newform 1050.2.m.b.643.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(307,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("1050.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.m (of order $4$, 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:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.1698758656.6
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 $ x^8 + 18x^6 + 97x^4 + 176*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			643.4
Root			$3.16053i$ of defining polynomial
Character	$\chi$	$=$	1050.643
Dual form			1050.2.m.b.307.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} -1.00000i q^{6} +(-0.781409 + 2.52773i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} -1.00000i q^{6} +(-0.781409 + 2.52773i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +4.90685 q^{11} +(-0.707107 - 0.707107i) q^{12} +(3.41421 - 3.41421i) q^{13} +(1.23483 + 2.33991i) q^{14} -1.00000 q^{16} +(-2.74632 - 2.74632i) q^{17} +(-0.707107 - 0.707107i) q^{18} +1.26561 q^{19} +(1.23483 + 2.33991i) q^{21} +(3.46967 - 3.46967i) q^{22} +(1.05545 + 1.05545i) q^{23} -1.00000 q^{24} -4.82843i q^{26} +(-0.707107 - 0.707107i) q^{27} +(2.52773 + 0.781409i) q^{28} +4.76687i q^{29} -7.05545i q^{31} +(-0.707107 + 0.707107i) q^{32} +(3.46967 - 3.46967i) q^{33} -3.88388 q^{34} -1.00000 q^{36} +(4.74632 - 4.74632i) q^{37} +(0.894921 - 0.894921i) q^{38} -4.82843i q^{39} -5.44670i q^{41} +(2.52773 + 0.781409i) q^{42} +(7.58667 + 7.58667i) q^{43} -4.90685i q^{44} +1.49264 q^{46} +(-0.734390 - 0.734390i) q^{47} +(-0.707107 + 0.707107i) q^{48} +(-5.77880 - 3.95037i) q^{49} -3.88388 q^{51} +(-3.41421 - 3.41421i) q^{52} +(-1.26561 - 1.26561i) q^{53} -1.00000 q^{54} +(2.33991 - 1.23483i) q^{56} +(0.894921 - 0.894921i) q^{57} +(3.37069 + 3.37069i) q^{58} +1.39735 q^{59} -2.29721i q^{61} +(-4.98896 - 4.98896i) q^{62} +(2.52773 + 0.781409i) q^{63} +1.00000i q^{64} -4.90685i q^{66} +(-3.05545 + 3.05545i) q^{67} +(-2.74632 + 2.74632i) q^{68} +1.49264 q^{69} -13.0334 q^{71} +(-0.707107 + 0.707107i) q^{72} +(-5.04441 + 5.04441i) q^{73} -6.71231i q^{74} -1.26561i q^{76} +(-3.83425 + 12.4032i) q^{77} +(-3.41421 - 3.41421i) q^{78} +14.8063i q^{79} -1.00000 q^{81} +(-3.85140 - 3.85140i) q^{82} +(9.29809 - 9.29809i) q^{83} +(2.33991 - 1.23483i) q^{84} +10.7292 q^{86} +(3.37069 + 3.37069i) q^{87} +(-3.46967 - 3.46967i) q^{88} -15.3596 q^{89} +(5.96230 + 11.2981i) q^{91} +(1.05545 - 1.05545i) q^{92} +(-4.98896 - 4.98896i) q^{93} -1.03858 q^{94} +1.00000i q^{96} +(8.42614 + 8.42614i) q^{97} +(-6.87957 + 1.29289i) q^{98} -4.90685i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{7}+O(q^{10}) $ 8 * q - 4 * q^7	$ 8 q - 4 q^{7} + 8 q^{11} + 16 q^{13} - 8 q^{14} - 8 q^{16} - 12 q^{17} - 8 q^{19} - 8 q^{21} - 8 q^{22} - 16 q^{23} - 8 q^{24} + 8 q^{28} - 8 q^{33} + 16 q^{34} - 8 q^{36} + 28 q^{37} + 4 q^{38} + 8 q^{42} - 8 q^{46} - 24 q^{47} + 4 q^{49} + 16 q^{51} - 16 q^{52} + 8 q^{53} - 8 q^{54} + 4 q^{56} + 4 q^{57} + 12 q^{58} + 8 q^{59} + 4 q^{62} + 8 q^{63} - 12 q^{68} - 8 q^{69} + 8 q^{71} + 28 q^{73} + 44 q^{77} - 16 q^{78} - 8 q^{81} - 24 q^{82} + 16 q^{83} + 4 q^{84} + 8 q^{86} + 12 q^{87} + 8 q^{88} - 64 q^{89} - 8 q^{91} - 16 q^{92} + 4 q^{93} + 8 q^{94} + 28 q^{97}+O(q^{100}) $ 8 * q - 4 * q^7 + 8 * q^11 + 16 * q^13 - 8 * q^14 - 8 * q^16 - 12 * q^17 - 8 * q^19 - 8 * q^21 - 8 * q^22 - 16 * q^23 - 8 * q^24 + 8 * q^28 - 8 * q^33 + 16 * q^34 - 8 * q^36 + 28 * q^37 + 4 * q^38 + 8 * q^42 - 8 * q^46 - 24 * q^47 + 4 * q^49 + 16 * q^51 - 16 * q^52 + 8 * q^53 - 8 * q^54 + 4 * q^56 + 4 * q^57 + 12 * q^58 + 8 * q^59 + 4 * q^62 + 8 * q^63 - 12 * q^68 - 8 * q^69 + 8 * q^71 + 28 * q^73 + 44 * q^77 - 16 * q^78 - 8 * q^81 - 24 * q^82 + 16 * q^83 + 4 * q^84 + 8 * q^86 + 12 * q^87 + 8 * q^88 - 64 * q^89 - 8 * q^91 - 16 * q^92 + 4 * q^93 + 8 * q^94 + 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		−	1.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$		−	1.00000i		−	0.408248i
$7$	−0.781409	+	2.52773i	−0.295345	+	0.955391i
$7$	−0.781409	+	2.52773i	−0.295345	+	0.955391i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	4.90685			1.47947			0.739735	−	0.672898i	$-0.234951\pi$
$11$	4.90685			1.47947			0.739735	+	0.672898i	$0.234951\pi$
$12$	−0.707107	−	0.707107i	−0.204124	−	0.204124i
$13$	3.41421	−	3.41421i	0.946932	−	0.946932i	−0.0517287	−	0.998661i	$-0.516473\pi$
$13$	3.41421	−	3.41421i	0.946932	−	0.946932i	0.998661	+	0.0517287i	$0.0164731\pi$
$14$	1.23483	+	2.33991i	0.330023	+	0.625368i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−2.74632	−	2.74632i	−0.666080	−	0.666080i	0.290726	−	0.956806i	$-0.406103\pi$
$17$	−2.74632	−	2.74632i	−0.666080	−	0.666080i	−0.956806	+	0.290726i	$0.906103\pi$
$18$	−0.707107	−	0.707107i	−0.166667	−	0.166667i
$19$	1.26561			0.290351			0.145175	−	0.989406i	$-0.453625\pi$
$19$	1.26561			0.290351			0.145175	+	0.989406i	$0.453625\pi$
$20$		0			0
$21$	1.23483	+	2.33991i	0.269463	+	0.510611i
$22$	3.46967	−	3.46967i	0.739735	−	0.739735i
$23$	1.05545	+	1.05545i	0.220077	+	0.220077i	0.808531	−	0.588454i	$-0.200263\pi$
$23$	1.05545	+	1.05545i	0.220077	+	0.220077i	−0.588454	+	0.808531i	$0.700263\pi$
$24$	−1.00000			−0.204124
$25$		0			0
$26$		−	4.82843i		−	0.946932i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	2.52773	+	0.781409i	0.477695	+	0.147672i
$29$			4.76687i			0.885186i	0.896723	+	0.442593i	$0.145941\pi$
$29$			4.76687i			0.885186i	−0.896723	+	0.442593i	$0.854059\pi$
$30$		0			0
$31$		−	7.05545i		−	1.26720i	−0.773662	−	0.633598i	$-0.781577\pi$
$31$		−	7.05545i		−	1.26720i	0.773662	−	0.633598i	$-0.218423\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	3.46967	−	3.46967i	0.603991	−	0.603991i
$34$	−3.88388			−0.666080
$35$		0			0
$36$	−1.00000			−0.166667
$37$	4.74632	−	4.74632i	0.780290	−	0.780290i	−0.199590	−	0.979880i	$-0.563961\pi$
$37$	4.74632	−	4.74632i	0.780290	−	0.780290i	0.979880	+	0.199590i	$0.0639609\pi$
$38$	0.894921	−	0.894921i	0.145175	−	0.145175i
$39$		−	4.82843i		−	0.773167i
$40$		0			0
$41$		−	5.44670i		−	0.850631i	−0.905045	−	0.425316i	$-0.860163\pi$
$41$		−	5.44670i		−	0.850631i	0.905045	−	0.425316i	$-0.139837\pi$
$42$	2.52773	+	0.781409i	0.390037	+	0.120574i
$43$	7.58667	+	7.58667i	1.15696	+	1.15696i	0.985127	+	0.171830i	$0.0549680\pi$
$43$	7.58667	+	7.58667i	1.15696	+	1.15696i	0.171830	+	0.985127i	$0.445032\pi$
$44$		−	4.90685i		−	0.739735i
$45$		0			0
$46$	1.49264			0.220077
$47$	−0.734390	−	0.734390i	−0.107122	−	0.107122i	0.651514	−	0.758636i	$-0.274134\pi$
$47$	−0.734390	−	0.734390i	−0.107122	−	0.107122i	−0.758636	+	0.651514i	$0.774134\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$	−5.77880	−	3.95037i	−0.825543	−	0.564339i
$50$		0			0
$51$	−3.88388			−0.543852
$52$	−3.41421	−	3.41421i	−0.473466	−	0.473466i
$53$	−1.26561	−	1.26561i	−0.173845	−	0.173845i	0.614821	−	0.788666i	$-0.289228\pi$
$53$	−1.26561	−	1.26561i	−0.173845	−	0.173845i	−0.788666	+	0.614821i	$0.789228\pi$
$54$	−1.00000			−0.136083
$55$		0			0
$56$	2.33991	−	1.23483i	0.312684	−	0.165012i
$57$	0.894921	−	0.894921i	0.118535	−	0.118535i
$58$	3.37069	+	3.37069i	0.442593	+	0.442593i
$59$	1.39735			0.181919			0.0909594	−	0.995855i	$-0.471007\pi$
$59$	1.39735			0.181919			0.0909594	+	0.995855i	$0.471007\pi$
$60$		0			0
$61$		−	2.29721i		−	0.294127i	−0.989127	−	0.147064i	$-0.953018\pi$
$61$		−	2.29721i		−	0.294127i	0.989127	−	0.147064i	$-0.0469822\pi$
$62$	−4.98896	−	4.98896i	−0.633598	−	0.633598i
$63$	2.52773	+	0.781409i	0.318464	+	0.0984482i
$64$			1.00000i			0.125000i
$65$		0			0
$66$		−	4.90685i		−	0.603991i
$67$	−3.05545	+	3.05545i	−0.373283	+	0.373283i	−0.868672	−	0.495389i	$-0.835026\pi$
$67$	−3.05545	+	3.05545i	−0.373283	+	0.373283i	0.495389	+	0.868672i	$0.335026\pi$
$68$	−2.74632	+	2.74632i	−0.333040	+	0.333040i
$69$	1.49264			0.179692
$70$		0			0
$71$	−13.0334			−1.54678			−0.773388	−	0.633933i	$-0.781440\pi$
$71$	−13.0334			−1.54678			−0.773388	+	0.633933i	$0.781440\pi$
$72$	−0.707107	+	0.707107i	−0.0833333	+	0.0833333i
$73$	−5.04441	+	5.04441i	−0.590404	+	0.590404i	−0.937740	−	0.347337i	$-0.887086\pi$
$73$	−5.04441	+	5.04441i	−0.590404	+	0.590404i	0.347337	+	0.937740i	$0.387086\pi$
$74$		−	6.71231i		−	0.780290i
$75$		0			0
$76$		−	1.26561i		−	0.145175i
$77$	−3.83425	+	12.4032i	−0.436954	+	1.41347i
$78$	−3.41421	−	3.41421i	−0.386584	−	0.386584i
$79$			14.8063i			1.66584i	0.553391	+	0.832922i	$0.313334\pi$
$79$			14.8063i			1.66584i	−0.553391	+	0.832922i	$0.686666\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$	−3.85140	−	3.85140i	−0.425316	−	0.425316i
$83$	9.29809	−	9.29809i	1.02060	−	1.02060i	0.0208150	−	0.999783i	$-0.493374\pi$
$83$	9.29809	−	9.29809i	1.02060	−	1.02060i	0.999783	−	0.0208150i	$-0.00662610\pi$
$84$	2.33991	−	1.23483i	0.255305	−	0.134731i
$85$		0			0
$86$	10.7292			1.15696
$87$	3.37069	+	3.37069i	0.361376	+	0.361376i
$88$	−3.46967	−	3.46967i	−0.369868	−	0.369868i
$89$	−15.3596			−1.62812			−0.814060	−	0.580781i	$-0.802747\pi$
$89$	−15.3596			−1.62812			−0.814060	+	0.580781i	$0.802747\pi$
$90$		0			0
$91$	5.96230	+	11.2981i	0.625019	+	1.18436i
$92$	1.05545	−	1.05545i	0.110039	−	0.110039i
$93$	−4.98896	−	4.98896i	−0.517331	−	0.517331i
$94$	−1.03858			−0.107122
$95$		0			0
$96$			1.00000i			0.102062i
$97$	8.42614	+	8.42614i	0.855545	+	0.855545i	0.990810	−	0.135264i	$-0.0431884\pi$
$97$	8.42614	+	8.42614i	0.855545	+	0.855545i	−0.135264	+	0.990810i	$0.543188\pi$
$98$	−6.87957	+	1.29289i	−0.694941	+	0.130602i
$99$		−	4.90685i		−	0.493157i
$100$		0			0
$101$			18.1504i			1.80603i	0.429609	+	0.903015i	$0.358651\pi$
$101$			18.1504i			1.80603i	−0.429609	+	0.903015i	$0.641349\pi$
$102$	−2.74632	+	2.74632i	−0.271926	+	0.271926i
$103$	−8.36459	+	8.36459i	−0.824187	+	0.824187i	−0.986706	−	0.162518i	$-0.948038\pi$
$103$	−8.36459	+	8.36459i	−0.824187	+	0.824187i	0.162518	+	0.986706i	$0.448038\pi$
$104$	−4.82843			−0.473466
$105$		0			0
$106$	−1.78984			−0.173845
$107$	−3.77297	+	3.77297i	−0.364747	+	0.364747i	−0.865557	−	0.500810i	$-0.833036\pi$
$107$	−3.77297	+	3.77297i	−0.364747	+	0.364747i	0.500810	+	0.865557i	$0.333036\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$		−	0.0870500i		−	0.00833787i	−0.999991	−	0.00416894i	$-0.998673\pi$
$109$		−	0.0870500i		−	0.00833787i	0.999991	−	0.00416894i	$-0.00132702\pi$
$110$		0			0
$111$		−	6.71231i		−	0.637104i
$112$	0.781409	−	2.52773i	0.0738362	−	0.238848i
$113$	−2.03248	−	2.03248i	−0.191200	−	0.191200i	0.605014	−	0.796214i	$-0.293167\pi$
$113$	−2.03248	−	2.03248i	−0.191200	−	0.191200i	−0.796214	+	0.605014i	$0.793167\pi$
$114$		−	1.26561i		−	0.118535i
$115$		0			0
$116$	4.76687			0.442593
$117$	−3.41421	−	3.41421i	−0.315644	−	0.315644i
$118$	0.988072	−	0.988072i	0.0909594	−	0.0909594i
$119$	9.08794	−	4.79594i	0.833090	−	0.439643i
$120$		0			0
$121$	13.0772			1.18883
$122$	−1.62437	−	1.62437i	−0.147064	−	0.147064i
$123$	−3.85140	−	3.85140i	−0.347269	−	0.347269i
$124$	−7.05545			−0.633598
$125$		0			0
$126$	2.33991	−	1.23483i	0.208456	−	0.110008i
$127$	11.1761	−	11.1761i	0.991723	−	0.991723i	−0.00824340	−	0.999966i	$-0.502624\pi$
$127$	11.1761	−	11.1761i	0.991723	−	0.991723i	0.999966	+	0.00824340i	$0.00262398\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	10.7292			0.944651
$130$		0			0
$131$		−	12.8367i		−	1.12154i	−0.827970	−	0.560772i	$-0.810504\pi$
$131$		−	12.8367i		−	1.12154i	0.827970	−	0.560772i	$-0.189496\pi$
$132$	−3.46967	−	3.46967i	−0.301996	−	0.301996i
$133$	−0.988958	+	3.19912i	−0.0857536	+	0.277399i
$134$			4.32106i			0.373283i
$135$		0			0
$136$			3.88388i			0.333040i
$137$	3.62437	−	3.62437i	0.309651	−	0.309651i	−0.535123	−	0.844774i	$-0.679735\pi$
$137$	3.62437	−	3.62437i	0.309651	−	0.309651i	0.844774	+	0.535123i	$0.179735\pi$
$138$	1.05545	−	1.05545i	0.0898461	−	0.0898461i
$139$	3.90596			0.331299			0.165650	−	0.986185i	$-0.447028\pi$
$139$	3.90596			0.331299			0.165650	+	0.986185i	$0.447028\pi$
$140$		0			0
$141$	−1.03858			−0.0874646
$142$	−9.21598	+	9.21598i	−0.773388	+	0.773388i
$143$	16.7530	−	16.7530i	1.40096	−	1.40096i
$144$			1.00000i			0.0833333i
$145$		0			0
$146$			7.13387i			0.590404i
$147$	−6.87957	+	1.29289i	−0.567417	+	0.106636i
$148$	−4.74632	−	4.74632i	−0.390145	−	0.390145i
$149$			5.64124i			0.462148i	0.972936	+	0.231074i	$0.0742240\pi$
$149$			5.64124i			0.462148i	−0.972936	+	0.231074i	$0.925776\pi$
$150$		0			0
$151$	−11.7678			−0.957647			−0.478823	−	0.877911i	$-0.658937\pi$
$151$	−11.7678			−0.957647			−0.478823	+	0.877911i	$0.658937\pi$
$152$	−0.894921	−	0.894921i	−0.0725877	−	0.0725877i
$153$	−2.74632	+	2.74632i	−0.222027	+	0.222027i
$154$	6.05914	+	11.4816i	0.488259	+	0.925213i
$155$		0			0
$156$	−4.82843			−0.386584
$157$	13.7132	+	13.7132i	1.09443	+	1.09443i	0.995049	+	0.0993827i	$0.0316868\pi$
$157$	13.7132	+	13.7132i	1.09443	+	1.09443i	0.0993827	+	0.995049i	$0.468313\pi$
$158$	10.4697	+	10.4697i	0.832922	+	0.832922i
$159$	−1.78984			−0.141944
$160$		0			0
$161$	−3.49264	+	1.84316i	−0.275258	+	0.145261i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	7.21967	+	7.21967i	0.565488	+	0.565488i	0.930861	−	0.365373i	$-0.119059\pi$
$163$	7.21967	+	7.21967i	0.565488	+	0.565488i	−0.365373	+	0.930861i	$0.619059\pi$
$164$	−5.44670			−0.425316
$165$		0			0
$166$		−	13.1495i		−	1.02060i
$167$	6.73439	+	6.73439i	0.521123	+	0.521123i	0.917910	−	0.396788i	$-0.129875\pi$
$167$	6.73439	+	6.73439i	0.521123	+	0.521123i	−0.396788	+	0.917910i	$0.629875\pi$
$168$	0.781409	−	2.52773i	0.0602870	−	0.195018i
$169$		−	10.3137i		−	0.793362i
$170$		0			0
$171$		−	1.26561i		−	0.0967836i
$172$	7.58667	−	7.58667i	0.578478	−	0.578478i
$173$	−14.1605	+	14.1605i	−1.07661	+	1.07661i	−0.0797939	+	0.996811i	$0.525426\pi$
$173$	−14.1605	+	14.1605i	−1.07661	+	1.07661i	−0.996811	+	0.0797939i	$0.974574\pi$
$174$	4.76687			0.361376
$175$		0			0
$176$	−4.90685			−0.369868
$177$	0.988072	−	0.988072i	0.0742681	−	0.0742681i
$178$	−10.8609	+	10.8609i	−0.814060	+	0.814060i
$179$		−	3.28123i		−	0.245250i	−0.992453	−	0.122625i	$-0.960869\pi$
$179$		−	3.28123i		−	0.245250i	0.992453	−	0.122625i	$-0.0391313\pi$
$180$		0			0
$181$			19.3934i			1.44150i	0.693196	+	0.720749i	$0.256202\pi$
$181$			19.3934i			1.44150i	−0.693196	+	0.720749i	$0.743798\pi$
$182$	12.2049	+	3.77297i	0.904691	+	0.279671i
$183$	−1.62437	−	1.62437i	−0.120077	−	0.120077i
$184$		−	1.49264i		−	0.110039i
$185$		0			0
$186$	−7.05545			−0.517331
$187$	−13.4758	−	13.4758i	−0.985446	−	0.985446i
$188$	−0.734390	+	0.734390i	−0.0535609	+	0.0535609i
$189$	2.33991	−	1.23483i	0.170204	−	0.0898209i
$190$		0			0
$191$	−16.8453			−1.21888			−0.609441	−	0.792831i	$-0.708606\pi$
$191$	−16.8453			−1.21888			−0.609441	+	0.792831i	$0.708606\pi$
$192$	0.707107	+	0.707107i	0.0510310	+	0.0510310i
$193$	4.81370	+	4.81370i	0.346498	+	0.346498i	0.858803	−	0.512306i	$-0.171208\pi$
$193$	4.81370	+	4.81370i	0.346498	+	0.346498i	−0.512306	+	0.858803i	$0.671208\pi$
$194$	11.9164			0.855545
$195$		0			0
$196$	−3.95037	+	5.77880i	−0.282170	+	0.412772i
$197$	−13.0334	+	13.0334i	−0.928589	+	0.928589i	−0.997615	−	0.0690257i	$-0.978011\pi$
$197$	−13.0334	+	13.0334i	−0.928589	+	0.928589i	0.0690257	+	0.997615i	$0.478011\pi$
$198$	−3.46967	−	3.46967i	−0.246578	−	0.246578i
$199$	11.7509			0.832999			0.416499	−	0.909136i	$-0.363257\pi$
$199$	11.7509			0.832999			0.416499	+	0.909136i	$0.363257\pi$
$200$		0			0
$201$			4.32106i			0.304784i
$202$	12.8343	+	12.8343i	0.903015	+	0.903015i
$203$	−12.0494	−	3.72488i	−0.845699	−	0.261435i
$204$			3.88388i			0.271926i
$205$		0			0
$206$			11.8293i			0.824187i
$207$	1.05545	−	1.05545i	0.0733590	−	0.0733590i
$208$	−3.41421	+	3.41421i	−0.236733	+	0.236733i
$209$	6.21016			0.429566
$210$		0			0
$211$	16.5502			1.13937			0.569683	−	0.821864i	$-0.307066\pi$
$211$	16.5502			1.13937			0.569683	+	0.821864i	$0.307066\pi$
$212$	−1.26561	+	1.26561i	−0.0869224	+	0.0869224i
$213$	−9.21598	+	9.21598i	−0.631469	+	0.631469i
$214$			5.33579i			0.364747i
$215$		0			0
$216$			1.00000i			0.0680414i
$217$	17.8343	+	5.51319i	1.21067	+	0.374260i
$218$	−0.0615536	−	0.0615536i	−0.00416894	−	0.00416894i
$219$			7.13387i			0.482063i
$220$		0			0
$221$	−18.7530			−1.26147
$222$	−4.74632	−	4.74632i	−0.318552	−	0.318552i
$223$	8.26067	−	8.26067i	0.553175	−	0.553175i	−0.374181	−	0.927356i	$-0.622076\pi$
$223$	8.26067	−	8.26067i	0.553175	−	0.553175i	0.927356	+	0.374181i	$0.122076\pi$
$224$	−1.23483	−	2.33991i	−0.0825058	−	0.156342i
$225$		0			0
$226$	−2.87437			−0.191200
$227$	−5.91295	−	5.91295i	−0.392456	−	0.392456i	0.483106	−	0.875562i	$-0.339509\pi$
$227$	−5.91295	−	5.91295i	−0.392456	−	0.392456i	−0.875562	+	0.483106i	$0.839509\pi$
$228$	−0.894921	−	0.894921i	−0.0592676	−	0.0592676i
$229$	−9.31371			−0.615467			−0.307734	−	0.951473i	$-0.599571\pi$
$229$	−9.31371			−0.615467			−0.307734	+	0.951473i	$0.599571\pi$
$230$		0			0
$231$	6.05914	+	11.4816i	0.398662	+	0.755433i
$232$	3.37069	−	3.37069i	0.221297	−	0.221297i
$233$	−16.0563	−	16.0563i	−1.05189	−	1.05189i	−0.998578	−	0.0533076i	$-0.983024\pi$
$233$	−16.0563	−	16.0563i	−1.05189	−	1.05189i	−0.0533076	−	0.998578i	$-0.516976\pi$
$234$	−4.82843			−0.315644
$235$		0			0
$236$		−	1.39735i		−	0.0909594i
$237$	10.4697	+	10.4697i	0.680078	+	0.680078i
$238$	3.03490	−	9.81739i	0.196723	−	0.636367i
$239$			1.68592i			0.109053i	0.998512	+	0.0545267i	$0.0173650\pi$
$239$			1.68592i			0.109053i	−0.998512	+	0.0545267i	$0.982635\pi$
$240$		0			0
$241$		−	3.61574i		−	0.232910i	−0.993196	−	0.116455i	$-0.962847\pi$
$241$		−	3.61574i		−	0.232910i	0.993196	−	0.116455i	$-0.0371532\pi$
$242$	9.24695	−	9.24695i	0.594417	−	0.594417i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−2.29721			−0.147064
$245$		0			0
$246$	−5.44670			−0.347269
$247$	4.32106	−	4.32106i	0.274943	−	0.274943i
$248$	−4.98896	+	4.98896i	−0.316799	+	0.316799i
$249$		−	13.1495i		−	0.833315i
$250$		0			0
$251$			4.78896i			0.302276i	0.988513	+	0.151138i	$0.0482938\pi$
$251$			4.78896i			0.302276i	−0.988513	+	0.151138i	$0.951706\pi$
$252$	0.781409	−	2.52773i	0.0492241	−	0.159232i
$253$	5.17895	+	5.17895i	0.325598	+	0.325598i
$254$		−	15.8055i		−	0.991723i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−20.8113	−	20.8113i	−1.29817	−	1.29817i	−0.929599	−	0.368574i	$-0.879846\pi$
$257$	−20.8113	−	20.8113i	−1.29817	−	1.29817i	−0.368574	−	0.929599i	$-0.620154\pi$
$258$	7.58667	−	7.58667i	0.472326	−	0.472326i
$259$	8.28858	+	15.7062i	0.515027	+	0.975936i
$260$		0			0
$261$	4.76687			0.295062
$262$	−9.07689	−	9.07689i	−0.560772	−	0.560772i
$263$	−6.61827	−	6.61827i	−0.408100	−	0.408100i	0.472976	−	0.881076i	$-0.343180\pi$
$263$	−6.61827	−	6.61827i	−0.408100	−	0.408100i	−0.881076	+	0.472976i	$0.843180\pi$
$264$	−4.90685			−0.301996
$265$		0			0
$266$	1.56282	+	2.96142i	0.0958225	+	0.181576i
$267$	−10.8609	+	10.8609i	−0.664677	+	0.664677i
$268$	3.05545	+	3.05545i	0.186641	+	0.186641i
$269$	13.1192			0.799890			0.399945	−	0.916539i	$-0.369029\pi$
$269$	13.1192			0.799890			0.399945	+	0.916539i	$0.369029\pi$
$270$		0			0
$271$			18.0836i			1.09850i	0.835658	+	0.549250i	$0.185087\pi$
$271$			18.0836i			1.09850i	−0.835658	+	0.549250i	$0.814913\pi$
$272$	2.74632	+	2.74632i	0.166520	+	0.166520i
$273$	12.2049	+	3.77297i	0.738677	+	0.228351i
$274$		−	5.12563i		−	0.309651i
$275$		0			0
$276$		−	1.49264i		−	0.0898461i
$277$	−2.63541	+	2.63541i	−0.158347	+	0.158347i	−0.781834	−	0.623487i	$-0.785715\pi$
$277$	−2.63541	+	2.63541i	−0.158347	+	0.158347i	0.623487	+	0.781834i	$0.285715\pi$
$278$	2.76193	−	2.76193i	0.165650	−	0.165650i
$279$	−7.05545			−0.422399
$280$		0			0
$281$	20.4558			1.22029			0.610146	−	0.792289i	$-0.291111\pi$
$281$	20.4558			1.22029			0.610146	+	0.792289i	$0.291111\pi$
$282$	−0.734390	+	0.734390i	−0.0437323	+	0.0437323i
$283$	−10.7751	+	10.7751i	−0.640514	+	0.640514i	−0.950682	−	0.310168i	$-0.899615\pi$
$283$	−10.7751	+	10.7751i	−0.640514	+	0.640514i	0.310168	+	0.950682i	$0.399615\pi$
$284$			13.0334i			0.773388i
$285$		0			0
$286$		−	23.6924i		−	1.40096i
$287$	13.7678	+	4.25610i	0.812685	+	0.251229i
$288$	0.707107	+	0.707107i	0.0416667	+	0.0416667i
$289$		−	1.91548i		−	0.112675i
$290$		0			0
$291$	11.9164			0.698550
$292$	5.04441	+	5.04441i	0.295202	+	0.295202i
$293$	3.15965	−	3.15965i	0.184588	−	0.184588i	−0.608763	−	0.793352i	$-0.708334\pi$
$293$	3.15965	−	3.15965i	0.184588	−	0.184588i	0.793352	+	0.608763i	$0.208334\pi$
$294$	−3.95037	+	5.77880i	−0.230390	+	0.337027i
$295$		0			0
$296$	−6.71231			−0.390145
$297$	−3.46967	−	3.46967i	−0.201330	−	0.201330i
$298$	3.98896	+	3.98896i	0.231074	+	0.231074i
$299$	7.20708			0.416796
$300$		0			0
$301$	−25.1053	+	13.2487i	−1.44705	+	0.763645i
$302$	−8.32106	+	8.32106i	−0.478823	+	0.478823i
$303$	12.8343	+	12.8343i	0.737309	+	0.737309i
$304$	−1.26561			−0.0725877
$305$		0			0
$306$			3.88388i			0.222027i
$307$	−20.8011	−	20.8011i	−1.18718	−	1.18718i	−0.977843	−	0.209340i	$-0.932868\pi$
$307$	−20.8011	−	20.8011i	−1.18718	−	1.18718i	−0.209340	−	0.977843i	$-0.567132\pi$
$308$	12.4032	+	3.83425i	0.706736	+	0.218477i
$309$			11.8293i			0.672946i
$310$		0			0
$311$		−	11.4706i		−	0.650435i	−0.945639	−	0.325218i	$-0.894562\pi$
$311$		−	11.4706i		−	0.650435i	0.945639	−	0.325218i	$-0.105438\pi$
$312$	−3.41421	+	3.41421i	−0.193292	+	0.193292i
$313$	−0.612443	+	0.612443i	−0.0346173	+	0.0346173i	−0.724204	−	0.689586i	$-0.757792\pi$
$313$	−0.612443	+	0.612443i	−0.0346173	+	0.0346173i	0.689586	+	0.724204i	$0.257792\pi$
$314$	19.3934			1.09443
$315$		0			0
$316$	14.8063			0.832922
$317$	−7.03984	+	7.03984i	−0.395397	+	0.395397i	−0.876606	−	0.481209i	$-0.840198\pi$
$317$	−7.03984	+	7.03984i	−0.395397	+	0.395397i	0.481209	+	0.876606i	$0.340198\pi$
$318$	−1.26561	+	1.26561i	−0.0709719	+	0.0709719i
$319$			23.3903i			1.30961i
$320$		0			0
$321$			5.33579i			0.297815i
$322$	−1.16636	+	3.77297i	−0.0649986	+	0.210260i
$323$	−3.47577	−	3.47577i	−0.193397	−	0.193397i
$324$			1.00000i			0.0555556i
$325$		0			0
$326$	10.2102			0.565488
$327$	−0.0615536	−	0.0615536i	−0.00340392	−	0.00340392i
$328$	−3.85140	+	3.85140i	−0.212658	+	0.212658i
$329$	2.43020	−	1.28248i	0.133981	−	0.0707053i
$330$		0			0
$331$	10.1759			0.559317			0.279658	−	0.960100i	$-0.409779\pi$
$331$	10.1759			0.559317			0.279658	+	0.960100i	$0.409779\pi$
$332$	−9.29809	−	9.29809i	−0.510299	−	0.510299i
$333$	−4.74632	−	4.74632i	−0.260097	−	0.260097i
$334$	9.52387			0.521123
$335$		0			0
$336$	−1.23483	−	2.33991i	−0.0673657	−	0.127653i
$337$	−16.8137	+	16.8137i	−0.915901	+	0.915901i	−0.996728	−	0.0808276i	$-0.974244\pi$
$337$	−16.8137	+	16.8137i	−0.915901	+	0.915901i	0.0808276	+	0.996728i	$0.474244\pi$
$338$	−7.29289	−	7.29289i	−0.396681	−	0.396681i
$339$	−2.87437			−0.156114
$340$		0			0
$341$		−	34.6200i		−	1.87478i
$342$	−0.894921	−	0.894921i	−0.0483918	−	0.0483918i
$343$	14.5011	−	11.5204i	0.782984	−	0.622042i
$344$		−	10.7292i		−	0.578478i
$345$		0			0
$346$			20.0260i			1.07661i
$347$	7.83919	−	7.83919i	0.420830	−	0.420830i	−0.464659	−	0.885489i	$-0.653823\pi$
$347$	7.83919	−	7.83919i	0.420830	−	0.420830i	0.885489	+	0.464659i	$0.153823\pi$
$348$	3.37069	−	3.37069i	0.180688	−	0.180688i
$349$	−5.10838			−0.273445			−0.136723	−	0.990609i	$-0.543657\pi$
$349$	−5.10838			−0.273445			−0.136723	+	0.990609i	$0.543657\pi$
$350$		0			0
$351$	−4.82843			−0.257722
$352$	−3.46967	+	3.46967i	−0.184934	+	0.184934i
$353$	−12.0821	+	12.0821i	−0.643066	+	0.643066i	−0.951308	−	0.308242i	$-0.900259\pi$
$353$	−12.0821	+	12.0821i	−0.643066	+	0.643066i	0.308242	+	0.951308i	$0.400259\pi$
$354$		−	1.39735i		−	0.0742681i
$355$		0			0
$356$			15.3596i			0.814060i
$357$	3.03490	−	9.81739i	0.160624	−	0.519591i
$358$	−2.32018	−	2.32018i	−0.122625	−	0.122625i
$359$		−	3.90596i		−	0.206149i	−0.994674	−	0.103074i	$-0.967132\pi$
$359$		−	3.90596i		−	0.206149i	0.994674	−	0.103074i	$-0.0328680\pi$
$360$		0			0
$361$	−17.3982			−0.915696
$362$	13.7132	+	13.7132i	0.720749	+	0.720749i
$363$	9.24695	−	9.24695i	0.485339	−	0.485339i
$364$	11.2981	−	5.96230i	0.592181	−	0.312510i
$365$		0			0
$366$	−2.29721			−0.120077
$367$	3.98072	+	3.98072i	0.207792	+	0.207792i	0.803328	−	0.595536i	$-0.203060\pi$
$367$	3.98072	+	3.98072i	0.207792	+	0.207792i	−0.595536	+	0.803328i	$0.703060\pi$
$368$	−1.05545	−	1.05545i	−0.0550193	−	0.0550193i
$369$	−5.44670			−0.283544
$370$		0			0
$371$	4.18807	−	2.21016i	0.217434	−	0.114746i
$372$	−4.98896	+	4.98896i	−0.258665	+	0.258665i
$373$	8.95648	+	8.95648i	0.463749	+	0.463749i	0.899882	−	0.436133i	$-0.143652\pi$
$373$	8.95648	+	8.95648i	0.463749	+	0.463749i	−0.436133	+	0.899882i	$0.643652\pi$
$374$	−19.0576			−0.985446
$375$		0			0
$376$			1.03858i			0.0535609i
$377$	16.2751	+	16.2751i	0.838212	+	0.838212i
$378$	0.781409	−	2.52773i	0.0401913	−	0.130012i
$379$		−	14.0190i		−	0.720109i	−0.932931	−	0.360055i	$-0.882758\pi$
$379$		−	14.0190i		−	0.720109i	0.932931	−	0.360055i	$-0.117242\pi$
$380$		0			0
$381$		−	15.8055i		−	0.809738i
$382$	−11.9114	+	11.9114i	−0.609441	+	0.609441i
$383$	−7.00951	+	7.00951i	−0.358169	+	0.358169i	−0.863138	−	0.504968i	$-0.831504\pi$
$383$	−7.00951	+	7.00951i	−0.358169	+	0.358169i	0.504968	+	0.863138i	$0.331504\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	6.80760			0.346498
$387$	7.58667	−	7.58667i	0.385652	−	0.385652i
$388$	8.42614	−	8.42614i	0.427773	−	0.427773i
$389$			18.6560i			0.945895i	0.881091	+	0.472948i	$0.156810\pi$
$389$			18.6560i			0.945895i	−0.881091	+	0.472948i	$0.843190\pi$
$390$		0			0
$391$		−	5.79722i		−	0.293178i
$392$	1.29289	+	6.87957i	0.0653010	+	0.347471i
$393$	−9.07689	−	9.07689i	−0.457869	−	0.457869i
$394$			18.4320i			0.928589i
$395$		0			0
$396$	−4.90685			−0.246578
$397$	−19.3683	−	19.3683i	−0.972066	−	0.972066i	0.0275544	−	0.999620i	$-0.491228\pi$
$397$	−19.3683	−	19.3683i	−0.972066	−	0.972066i	−0.999620	+	0.0275544i	$0.991228\pi$
$398$	8.30913	−	8.30913i	0.416499	−	0.416499i
$399$	1.56282	+	2.96142i	0.0782387	+	0.148256i
$400$		0			0
$401$	−27.9099			−1.39375			−0.696877	−	0.717191i	$-0.745428\pi$
$401$	−27.9099			−1.39375			−0.696877	+	0.717191i	$0.745428\pi$
$402$	3.05545	+	3.05545i	0.152392	+	0.152392i
$403$	−24.0888	−	24.0888i	−1.19995	−	1.19995i
$404$	18.1504			0.903015
$405$		0			0
$406$	−11.1541	+	5.88629i	−0.553567	+	0.292132i
$407$	23.2895	−	23.2895i	1.15442	−	1.15442i
$408$	2.74632	+	2.74632i	0.135963	+	0.135963i
$409$	−18.3211			−0.905918			−0.452959	−	0.891531i	$-0.649632\pi$
$409$	−18.3211			−0.905918			−0.452959	+	0.891531i	$0.649632\pi$
$410$		0			0
$411$		−	5.12563i		−	0.252829i
$412$	8.36459	+	8.36459i	0.412094	+	0.412094i
$413$	−1.09190	+	3.53211i	−0.0537288	+	0.173804i
$414$		−	1.49264i		−	0.0733590i
$415$		0			0
$416$			4.82843i			0.236733i
$417$	2.76193	−	2.76193i	0.135252	−	0.135252i
$418$	4.39124	−	4.39124i	0.214783	−	0.214783i
$419$	−5.49605			−0.268500			−0.134250	−	0.990948i	$-0.542862\pi$
$419$	−5.49605			−0.268500			−0.134250	+	0.990948i	$0.542862\pi$
$420$		0			0
$421$	24.5863			1.19826			0.599132	−	0.800651i	$-0.295513\pi$
$421$	24.5863			1.19826			0.599132	+	0.800651i	$0.295513\pi$
$422$	11.7028	−	11.7028i	0.569683	−	0.569683i
$423$	−0.734390	+	0.734390i	−0.0357073	+	0.0357073i
$424$			1.78984i			0.0869224i
$425$		0			0
$426$			13.0334i			0.631469i
$427$	5.80671	+	1.79506i	0.281006	+	0.0868689i
$428$	3.77297	+	3.77297i	0.182374	+	0.182374i
$429$		−	23.6924i		−	1.14388i
$430$		0			0
$431$	22.8133			1.09888			0.549440	−	0.835533i	$-0.314841\pi$
$431$	22.8133			1.09888			0.549440	+	0.835533i	$0.314841\pi$
$432$	0.707107	+	0.707107i	0.0340207	+	0.0340207i
$433$	−17.1216	+	17.1216i	−0.822811	+	0.822811i	−0.986510	−	0.163700i	$-0.947657\pi$
$433$	−17.1216	+	17.1216i	−0.822811	+	0.822811i	0.163700	+	0.986510i	$0.447657\pi$
$434$	16.5091	−	8.71231i	0.792464	−	0.418204i
$435$		0			0
$436$	−0.0870500			−0.00416894
$437$	1.33579	+	1.33579i	0.0638996	+	0.0638996i
$438$	5.04441	+	5.04441i	0.241031	+	0.241031i
$439$	−35.8323			−1.71018			−0.855092	−	0.518476i	$-0.826500\pi$
$439$	−35.8323			−1.71018			−0.855092	+	0.518476i	$0.826500\pi$
$440$		0			0
$441$	−3.95037	+	5.77880i	−0.188113	+	0.275181i
$442$	−13.2604	+	13.2604i	−0.630733	+	0.630733i
$443$	−2.93109	−	2.93109i	−0.139260	−	0.139260i	0.634040	−	0.773300i	$-0.281395\pi$
$443$	−2.93109	−	2.93109i	−0.139260	−	0.139260i	−0.773300	+	0.634040i	$0.781395\pi$
$444$	−6.71231			−0.318552
$445$		0			0
$446$		−	11.6824i		−	0.553175i
$447$	3.98896	+	3.98896i	0.188671	+	0.188671i
$448$	−2.52773	−	0.781409i	−0.119424	−	0.0369181i
$449$		−	1.70279i		−	0.0803598i	−0.999192	−	0.0401799i	$-0.987207\pi$
$449$		−	1.70279i		−	0.0803598i	0.999192	−	0.0401799i	$-0.0127931\pi$
$450$		0			0
$451$		−	26.7261i		−	1.25848i
$452$	−2.03248	+	2.03248i	−0.0956000	+	0.0956000i
$453$	−8.32106	+	8.32106i	−0.390958	+	0.390958i
$454$	−8.36217			−0.392456
$455$		0			0
$456$	−1.26561			−0.0592676
$457$	5.34315	−	5.34315i	0.249942	−	0.249942i	−0.571005	−	0.820947i	$-0.693446\pi$
$457$	5.34315	−	5.34315i	0.249942	−	0.249942i	0.820947	+	0.571005i	$0.193446\pi$
$458$	−6.58579	+	6.58579i	−0.307734	+	0.307734i
$459$			3.88388i			0.181284i
$460$		0			0
$461$		−	0.858751i		−	0.0399960i	−0.999800	−	0.0199980i	$-0.993634\pi$
$461$		−	0.858751i		−	0.0399960i	0.999800	−	0.0199980i	$-0.00636599\pi$
$462$	12.4032	+	3.83425i	0.577048	+	0.178386i
$463$	20.3594	+	20.3594i	0.946180	+	0.946180i	0.998624	−	0.0524436i	$-0.0167010\pi$
$463$	20.3594	+	20.3594i	0.946180	+	0.946180i	−0.0524436	+	0.998624i	$0.516701\pi$
$464$		−	4.76687i		−	0.221297i
$465$		0			0
$466$	−22.7071			−1.05189
$467$	−8.77908	−	8.77908i	−0.406247	−	0.406247i	0.474181	−	0.880428i	$-0.342744\pi$
$467$	−8.77908	−	8.77908i	−0.406247	−	0.406247i	−0.880428	+	0.474181i	$0.842744\pi$
$468$	−3.41421	+	3.41421i	−0.157822	+	0.157822i
$469$	−5.33579	−	10.1109i	−0.246384	−	0.466878i
$470$		0			0
$471$	19.3934			0.893600
$472$	−0.988072	−	0.988072i	−0.0454797	−	0.0454797i
$473$	37.2267	+	37.2267i	1.71168	+	1.71168i
$474$	14.8063			0.680078
$475$		0			0
$476$	−4.79594	−	9.08794i	−0.219822	−	0.416545i
$477$	−1.26561	+	1.26561i	−0.0579483	+	0.0579483i
$478$	1.19213	+	1.19213i	0.0545267	+	0.0545267i
$479$	−1.17157			−0.0535305			−0.0267653	−	0.999642i	$-0.508521\pi$
$479$	−1.17157			−0.0535305			−0.0267653	+	0.999642i	$0.508521\pi$
$480$		0			0
$481$		−	32.4099i		−	1.47776i
$482$	−2.55672	−	2.55672i	−0.116455	−	0.116455i
$483$	−1.16636	+	3.77297i	−0.0530711	+	0.171676i
$484$		−	13.0772i		−	0.594417i
$485$		0			0
$486$			1.00000i			0.0453609i
$487$	−9.70737	+	9.70737i	−0.439883	+	0.439883i	−0.891972	−	0.452090i	$-0.850679\pi$
$487$	−9.70737	+	9.70737i	−0.439883	+	0.439883i	0.452090	+	0.891972i	$0.350679\pi$
$488$	−1.62437	+	1.62437i	−0.0735318	+	0.0735318i
$489$	10.2102			0.461719
$490$		0			0
$491$	−16.9381			−0.764405			−0.382202	−	0.924079i	$-0.624834\pi$
$491$	−16.9381			−0.764405			−0.382202	+	0.924079i	$0.624834\pi$
$492$	−3.85140	+	3.85140i	−0.173634	+	0.173634i
$493$	13.0913	−	13.0913i	0.589605	−	0.589605i
$494$		−	6.11091i		−	0.274943i
$495$		0			0
$496$			7.05545i			0.316799i
$497$	10.1844	−	32.9448i	0.456832	−	1.47778i
$498$	−9.29809	−	9.29809i	−0.416658	−	0.416658i
$499$		−	30.4117i		−	1.36141i	−0.732556	−	0.680706i	$-0.761673\pi$
$499$		−	30.4117i		−	1.36141i	0.732556	−	0.680706i	$-0.238327\pi$
$500$		0			0
$501$	9.52387			0.425495
$502$	3.38630	+	3.38630i	0.151138	+	0.151138i
$503$	4.75825	−	4.75825i	0.212160	−	0.212160i	−0.593025	−	0.805184i	$-0.702066\pi$
$503$	4.75825	−	4.75825i	0.212160	−	0.212160i	0.805184	+	0.593025i	$0.202066\pi$
$504$	−1.23483	−	2.33991i	−0.0550038	−	0.104228i
$505$		0			0
$506$	7.32414			0.325598
$507$	−7.29289	−	7.29289i	−0.323889	−	0.323889i
$508$	−11.1761	−	11.1761i	−0.495861	−	0.495861i
$509$	−40.3501			−1.78849			−0.894243	−	0.447581i	$-0.852286\pi$
$509$	−40.3501			−1.78849			−0.894243	+	0.447581i	$0.852286\pi$
$510$		0			0
$511$	−8.80915	−	16.6926i	−0.389694	−	0.738439i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−0.894921	−	0.894921i	−0.0395117	−	0.0395117i
$514$	−29.4316			−1.29817
$515$		0			0
$516$		−	10.7292i		−	0.472326i
$517$	−3.60354	−	3.60354i	−0.158484	−	0.158484i
$518$	16.9669	+	5.24505i	0.745482	+	0.230454i
$519$			20.0260i			0.879045i
$520$		0			0
$521$		−	8.96879i		−	0.392930i	−0.980511	−	0.196465i	$-0.937054\pi$
$521$		−	8.96879i		−	0.392930i	0.980511	−	0.196465i	$-0.0629462\pi$
$522$	3.37069	−	3.37069i	0.147531	−	0.147531i
$523$	8.40290	−	8.40290i	0.367433	−	0.367433i	−0.499107	−	0.866540i	$-0.666339\pi$
$523$	8.40290	−	8.40290i	0.367433	−	0.367433i	0.866540	+	0.499107i	$0.166339\pi$
$524$	−12.8367			−0.560772
$525$		0			0
$526$	−9.35965			−0.408100
$527$	−19.3765	+	19.3765i	−0.844054	+	0.844054i
$528$	−3.46967	+	3.46967i	−0.150998	+	0.150998i
$529$		−	20.7720i		−	0.903132i
$530$		0			0
$531$		−	1.39735i		−	0.0606396i
$532$	3.19912	+	0.988958i	0.138699	+	0.0428768i
$533$	−18.5962	−	18.5962i	−0.805490	−	0.805490i
$534$			15.3596i			0.664677i
$535$		0			0
$536$	4.32106			0.186641
$537$	−2.32018	−	2.32018i	−0.100123	−	0.100123i
$538$	9.27665	−	9.27665i	0.399945	−	0.399945i
$539$	−28.3557	−	19.3839i	−1.22137	−	0.834923i
$540$		0			0
$541$	27.1611			1.16775			0.583874	−	0.811844i	$-0.301536\pi$
$541$	27.1611			1.16775			0.583874	+	0.811844i	$0.301536\pi$
$542$	12.7870	+	12.7870i	0.549250	+	0.549250i
$543$	13.7132	+	13.7132i	0.588489	+	0.588489i
$544$	3.88388			0.166520
$545$		0			0
$546$	11.2981	−	5.96230i	0.483514	−	0.255163i
$547$	16.8471	−	16.8471i	0.720329	−	0.720329i	−0.248343	−	0.968672i	$-0.579886\pi$
$547$	16.8471	−	16.8471i	0.720329	−	0.720329i	0.968672	+	0.248343i	$0.0798861\pi$
$548$	−3.62437	−	3.62437i	−0.154825	−	0.154825i
$549$	−2.29721			−0.0980424
$550$		0			0
$551$			6.03300i			0.257015i
$552$	−1.05545	−	1.05545i	−0.0449231	−	0.0449231i
$553$	−37.4264	−	11.5698i	−1.59153	−	0.491998i
$554$			3.72704i			0.158347i
$555$		0			0
$556$		−	3.90596i		−	0.165650i
$557$	0.0529257	−	0.0529257i	0.00224253	−	0.00224253i	−0.705985	−	0.708227i	$-0.749495\pi$
$557$	0.0529257	−	0.0529257i	0.00224253	−	0.00224253i	0.708227	+	0.705985i	$0.249495\pi$
$558$	−4.98896	+	4.98896i	−0.211199	+	0.211199i
$559$	51.8050			2.19112
$560$		0			0
$561$	−19.0576			−0.804613
$562$	14.4645	−	14.4645i	0.610146	−	0.610146i
$563$	7.84316	−	7.84316i	0.330550	−	0.330550i	−0.522246	−	0.852795i	$-0.674906\pi$
$563$	7.84316	−	7.84316i	0.330550	−	0.330550i	0.852795	+	0.522246i	$0.174906\pi$
$564$			1.03858i			0.0437323i
$565$		0			0
$566$			15.2383i			0.640514i
$567$	0.781409	−	2.52773i	0.0328161	−	0.106155i
$568$	9.21598	+	9.21598i	0.386694	+	0.386694i
$569$		−	6.12311i		−	0.256694i	−0.991729	−	0.128347i	$-0.959033\pi$
$569$		−	6.12311i		−	0.256694i	0.991729	−	0.128347i	$-0.0409671\pi$
$570$		0			0
$571$	30.4896			1.27595			0.637974	−	0.770058i	$-0.279773\pi$
$571$	30.4896			1.27595			0.637974	+	0.770058i	$0.279773\pi$
$572$	−16.7530	−	16.7530i	−0.700479	−	0.700479i
$573$	−11.9114	+	11.9114i	−0.497607	+	0.497607i
$574$	12.7448	−	6.72576i	0.531957	−	0.280728i
$575$		0			0
$576$	1.00000			0.0416667
$577$	11.5444	+	11.5444i	0.480600	+	0.480600i	0.905323	−	0.424723i	$-0.139629\pi$
$577$	11.5444	+	11.5444i	0.480600	+	0.480600i	−0.424723	+	0.905323i	$0.639629\pi$
$578$	−1.35445	−	1.35445i	−0.0563376	−	0.0563376i
$579$	6.80760			0.282914
$580$		0			0
$581$	16.2374	+	30.7686i	0.673642	+	1.27650i
$582$	8.42614	−	8.42614i	0.349275	−	0.349275i
$583$	−6.21016	−	6.21016i	−0.257198	−	0.257198i
$584$	7.13387			0.295202
$585$		0			0
$586$		−	4.46841i		−	0.184588i
$587$	7.24478	+	7.24478i	0.299024	+	0.299024i	0.840632	−	0.541607i	$-0.182184\pi$
$587$	7.24478	+	7.24478i	0.299024	+	0.299024i	−0.541607	+	0.840632i	$0.682184\pi$
$588$	1.29289	+	6.87957i	0.0533180	+	0.283709i
$589$		−	8.92945i		−	0.367932i
$590$		0			0
$591$			18.4320i			0.758190i
$592$	−4.74632	+	4.74632i	−0.195072	+	0.195072i
$593$	6.67652	−	6.67652i	0.274172	−	0.274172i	−0.556605	−	0.830777i	$-0.687896\pi$
$593$	6.67652	−	6.67652i	0.274172	−	0.274172i	0.830777	+	0.556605i	$0.187896\pi$
$594$	−4.90685			−0.201330
$595$		0			0
$596$	5.64124			0.231074
$597$	8.30913	−	8.30913i	0.340070	−	0.340070i
$598$	5.09618	−	5.09618i	0.208398	−	0.208398i
$599$			2.62526i			0.107265i	0.998561	+	0.0536325i	$0.0170800\pi$
$599$			2.62526i			0.107265i	−0.998561	+	0.0536325i	$0.982920\pi$
$600$		0			0
$601$			11.7003i			0.477265i	0.971110	+	0.238632i	$0.0766991\pi$
$601$			11.7003i			0.477265i	−0.971110	+	0.238632i	$0.923301\pi$
$602$	−8.38387	+	27.1204i	−0.341701	+	1.10535i
$603$	3.05545	+	3.05545i	0.124428	+	0.124428i
$604$			11.7678i			0.478823i
$605$		0			0
$606$	18.1504			0.737309
$607$	−23.2749	−	23.2749i	−0.944697	−	0.944697i	0.0538519	−	0.998549i	$-0.482850\pi$
$607$	−23.2749	−	23.2749i	−0.944697	−	0.944697i	−0.998549	+	0.0538519i	$0.982850\pi$
$608$	−0.894921	+	0.894921i	−0.0362939	+	0.0362939i
$609$	−11.1541	+	5.88629i	−0.451985	+	0.238525i
$610$		0			0
$611$	−5.01473			−0.202874
$612$	2.74632	+	2.74632i	0.111013	+	0.111013i
$613$	−18.1372	−	18.1372i	−0.732554	−	0.732554i	0.238571	−	0.971125i	$-0.423321\pi$
$613$	−18.1372	−	18.1372i	−0.732554	−	0.732554i	−0.971125	+	0.238571i	$0.923321\pi$
$614$	−29.4172			−1.18718
$615$		0			0
$616$	11.4816	−	6.05914i	0.462607	−	0.244130i
$617$	−1.59063	+	1.59063i	−0.0640365	+	0.0640365i	−0.738400	−	0.674363i	$-0.764418\pi$
$617$	−1.59063	+	1.59063i	−0.0640365	+	0.0640365i	0.674363	+	0.738400i	$0.264418\pi$
$618$	8.36459	+	8.36459i	0.336473	+	0.336473i
$619$	39.2232			1.57651			0.788257	−	0.615346i	$-0.210984\pi$
$619$	39.2232			1.57651			0.788257	+	0.615346i	$0.210984\pi$
$620$		0			0
$621$		−	1.49264i		−	0.0598974i
$622$	−8.11091	−	8.11091i	−0.325218	−	0.325218i
$623$	12.0022	−	38.8250i	0.480856	−	1.55549i
$624$			4.82843i			0.193292i
$625$		0			0
$626$			0.866125i			0.0346173i
$627$	4.39124	−	4.39124i	0.175369	−	0.175369i
$628$	13.7132	−	13.7132i	0.547216	−	0.547216i
$629$	−26.0698			−1.03947
$630$		0			0
$631$	−1.69542			−0.0674935			−0.0337468	−	0.999430i	$-0.510744\pi$
$631$	−1.69542			−0.0674935			−0.0337468	+	0.999430i	$0.510744\pi$
$632$	10.4697	−	10.4697i	0.416461	−	0.416461i
$633$	11.7028	−	11.7028i	0.465144	−	0.465144i
$634$			9.95583i			0.395397i
$635$		0			0
$636$			1.78984i			0.0709719i
$637$	−33.2175	+	6.24264i	−1.31612	+	0.247342i
$638$	16.5395	+	16.5395i	0.654804	+	0.654804i
$639$			13.0334i			0.515592i
$640$		0			0
$641$	23.0043			0.908615			0.454308	−	0.890845i	$-0.349887\pi$
$641$	23.0043			0.908615			0.454308	+	0.890845i	$0.349887\pi$
$642$	3.77297	+	3.77297i	0.148907	+	0.148907i
$643$	13.9948	−	13.9948i	0.551900	−	0.551900i	−0.375089	−	0.926989i	$-0.622388\pi$
$643$	13.9948	−	13.9948i	0.551900	−	0.551900i	0.926989	+	0.375089i	$0.122388\pi$
$644$	1.84316	+	3.49264i	0.0726305	+	0.137629i
$645$		0			0
$646$	−4.91548			−0.193397
$647$	−5.22955	−	5.22955i	−0.205595	−	0.205595i	0.596797	−	0.802392i	$-0.296440\pi$
$647$	−5.22955	−	5.22955i	−0.205595	−	0.205595i	−0.802392	+	0.596797i	$0.796440\pi$
$648$	0.707107	+	0.707107i	0.0277778	+	0.0277778i
$649$	6.85656			0.269144
$650$		0			0
$651$	16.5091	−	8.71231i	0.647044	−	0.341462i
$652$	7.21967	−	7.21967i	0.282744	−	0.282744i
$653$	−1.74516	−	1.74516i	−0.0682933	−	0.0682933i	0.672135	−	0.740428i	$-0.265377\pi$
$653$	−1.74516	−	1.74516i	−0.0682933	−	0.0682933i	−0.740428	+	0.672135i	$0.765377\pi$
$654$	−0.0870500			−0.00340392
$655$		0			0
$656$			5.44670i			0.212658i
$657$	5.04441	+	5.04441i	0.196801	+	0.196801i
$658$	0.811559	−	2.62526i	0.0316379	−	0.102343i
$659$			21.4234i			0.834536i	0.908784	+	0.417268i	$0.137012\pi$
$659$			21.4234i			0.834536i	−0.908784	+	0.417268i	$0.862988\pi$
$660$		0			0
$661$		−	15.6881i		−	0.610196i	−0.952321	−	0.305098i	$-0.901311\pi$
$661$		−	15.6881i		−	0.610196i	0.952321	−	0.305098i	$-0.0986892\pi$
$662$	7.19543	−	7.19543i	0.279658	−	0.279658i
$663$	−13.2604	+	13.2604i	−0.514991	+	0.514991i
$664$	−13.1495			−0.510299
$665$		0			0
$666$	−6.71231			−0.260097
$667$	−5.03121	+	5.03121i	−0.194809	+	0.194809i
$668$	6.73439	−	6.73439i	0.260561	−	0.260561i
$669$		−	11.6824i		−	0.451666i
$670$		0			0
$671$		−	11.2720i		−	0.435153i
$672$	−2.52773	−	0.781409i	−0.0975092	−	0.0301435i
$673$	−26.0502	−	26.0502i	−1.00416	−	1.00416i	−0.999991	−	0.00417159i	$-0.998672\pi$
$673$	−26.0502	−	26.0502i	−1.00416	−	1.00416i	−0.00417159	−	0.999991i	$-0.501328\pi$
$674$			23.7782i			0.915901i
$675$		0			0
$676$	−10.3137			−0.396681
$677$	3.99149	+	3.99149i	0.153405	+	0.153405i	0.779637	−	0.626232i	$-0.215404\pi$
$677$	3.99149	+	3.99149i	0.153405	+	0.153405i	−0.626232	+	0.779637i	$0.715404\pi$
$678$	−2.03248	+	2.03248i	−0.0780571	+	0.0780571i
$679$	−27.8832	+	14.7147i	−1.07006	+	0.564699i
$680$		0			0
$681$	−8.36217			−0.320439
$682$	−24.4801	−	24.4801i	−0.937390	−	0.937390i
$683$	28.2530	+	28.2530i	1.08107	+	1.08107i	0.996410	+	0.0846629i	$0.0269813\pi$
$683$	28.2530	+	28.2530i	1.08107	+	1.08107i	0.0846629	+	0.996410i	$0.473019\pi$
$684$	−1.26561			−0.0483918
$685$		0			0
$686$	2.10767	−	18.3999i	0.0804713	−	0.702513i
$687$	−6.58579	+	6.58579i	−0.251263	+	0.251263i
$688$	−7.58667	−	7.58667i	−0.289239	−	0.289239i
$689$	−8.64213			−0.329239
$690$		0			0
$691$		−	2.45366i		−	0.0933418i	−0.998910	−	0.0466709i	$-0.985139\pi$
$691$		−	2.45366i		−	0.0933418i	0.998910	−	0.0466709i	$-0.0148612\pi$
$692$	14.1605	+	14.1605i	0.538303	+	0.538303i
$693$	12.4032	+	3.83425i	0.471158	+	0.145651i
$694$		−	11.0863i		−	0.420830i
$695$		0			0
$696$		−	4.76687i		−	0.180688i
$697$	−14.9584	+	14.9584i	−0.566588	+	0.566588i
$698$	−3.61217	+	3.61217i	−0.136723	+	0.136723i
$699$	−22.7071			−0.858861
$700$		0			0
$701$	−6.34833			−0.239773			−0.119887	−	0.992788i	$-0.538253\pi$
$701$	−6.34833			−0.239773			−0.119887	+	0.992788i	$0.538253\pi$
$702$	−3.41421	+	3.41421i	−0.128861	+	0.128861i
$703$	6.00699	−	6.00699i	0.226558	−	0.226558i
$704$			4.90685i			0.184934i
$705$		0			0
$706$			17.0867i			0.643066i
$707$	−45.8792	−	14.1829i	−1.72546	−	0.533401i
$708$	−0.988072	−	0.988072i	−0.0371340	−	0.0371340i
$709$		−	20.3645i		−	0.764805i	−0.923996	−	0.382402i	$-0.875097\pi$
$709$		−	20.3645i		−	0.764805i	0.923996	−	0.382402i	$-0.124903\pi$
$710$		0			0
$711$	14.8063			0.555281
$712$	10.8609	+	10.8609i	0.407030	+	0.407030i
$713$	7.44670	−	7.44670i	0.278881	−	0.278881i
$714$	−4.79594	−	9.08794i	−0.179484	−	0.340107i
$715$		0			0
$716$	−3.28123			−0.122625
$717$	1.19213	+	1.19213i	0.0445209	+	0.0445209i
$718$	−2.76193	−	2.76193i	−0.103074	−	0.103074i
$719$	25.9031			0.966021			0.483011	−	0.875614i	$-0.339543\pi$
$719$	25.9031			0.966021			0.483011	+	0.875614i	$0.339543\pi$
$720$		0			0
$721$	−14.6072	−	27.6795i	−0.544002	−	1.03084i
$722$	−12.3024	+	12.3024i	−0.457848	+	0.457848i
$723$	−2.55672	−	2.55672i	−0.0950853	−	0.0950853i
$724$	19.3934			0.720749
$725$		0			0
$726$		−	13.0772i		−	0.485339i
$727$	36.3373	+	36.3373i	1.34768	+	1.34768i	0.888180	+	0.459495i	$0.151970\pi$
$727$	36.3373	+	36.3373i	1.34768	+	1.34768i	0.459495	+	0.888180i	$0.348030\pi$
$728$	3.77297	−	12.2049i	0.139836	−	0.452345i
$729$			1.00000i			0.0370370i
$730$		0			0
$731$		−	41.6708i		−	1.54125i
$732$	−1.62437	+	1.62437i	−0.0600385	+	0.0600385i
$733$	−18.3535	+	18.3535i	−0.677904	+	0.677904i	−0.959525	−	0.281622i	$-0.909128\pi$
$733$	−18.3535	+	18.3535i	−0.677904	+	0.677904i	0.281622	+	0.959525i	$0.409128\pi$
$734$	5.62959			0.207792
$735$		0			0
$736$	−1.49264			−0.0550193
$737$	−14.9926	+	14.9926i	−0.552261	+	0.552261i
$738$	−3.85140	+	3.85140i	−0.141772	+	0.141772i
$739$		−	21.3934i		−	0.786968i	−0.919331	−	0.393484i	$-0.871270\pi$
$739$		−	21.3934i		−	0.786968i	0.919331	−	0.393484i	$-0.128730\pi$
$740$		0			0
$741$		−	6.11091i		−	0.224490i
$742$	1.39860	−	4.52423i	0.0513442	−	0.166090i
$743$	29.9264	+	29.9264i	1.09789	+	1.09789i	0.994657	+	0.103235i	$0.0329195\pi$
$743$	29.9264	+	29.9264i	1.09789	+	1.09789i	0.103235	+	0.994657i	$0.467081\pi$
$744$			7.05545i			0.258665i
$745$		0			0
$746$	12.6664			0.463749
$747$	−9.29809	−	9.29809i	−0.340199	−	0.340199i
$748$	−13.4758	+	13.4758i	−0.492723	+	0.492723i
$749$	−6.58881	−	12.4853i	−0.240750	−	0.456202i
$750$		0			0
$751$	−19.3081			−0.704563			−0.352281	−	0.935894i	$-0.614594\pi$
$751$	−19.3081			−0.704563			−0.352281	+	0.935894i	$0.614594\pi$
$752$	0.734390	+	0.734390i	0.0267804	+	0.0267804i
$753$	3.38630	+	3.38630i	0.123404	+	0.123404i
$754$	23.0165			0.838212
$755$		0			0
$756$	−1.23483	−	2.33991i	−0.0449104	−	0.0851018i
$757$	30.9872	−	30.9872i	1.12625	−	1.12625i	0.135465	−	0.990782i	$-0.456747\pi$
$757$	30.9872	−	30.9872i	1.12625	−	1.12625i	0.990782	−	0.135465i	$-0.0432529\pi$
$758$	−9.91295	−	9.91295i	−0.360055	−	0.360055i
$759$	7.32414			0.265849
$760$		0			0
$761$			47.3418i			1.71614i	0.513532	+	0.858070i	$0.328337\pi$
$761$			47.3418i			1.71614i	−0.513532	+	0.858070i	$0.671663\pi$
$762$	−11.1761	−	11.1761i	−0.404869	−	0.404869i
$763$	0.220039	+	0.0680216i	0.00796593	+	0.00246255i
$764$			16.8453i			0.609441i
$765$		0			0
$766$			9.91295i			0.358169i
$767$	4.77083	−	4.77083i	0.172265	−	0.172265i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	44.0520			1.58856			0.794278	−	0.607554i	$-0.207849\pi$
$769$	44.0520			1.58856			0.794278	+	0.607554i	$0.207849\pi$
$770$		0			0
$771$	−29.4316			−1.05995
$772$	4.81370	−	4.81370i	0.173249	−	0.173249i
$773$	−11.1336	+	11.1336i	−0.400448	+	0.400448i	−0.878391	−	0.477943i	$-0.841383\pi$
$773$	−11.1336	+	11.1336i	−0.400448	+	0.400448i	0.477943	+	0.878391i	$0.341383\pi$
$774$		−	10.7292i		−	0.385652i
$775$		0			0
$776$		−	11.9164i		−	0.427773i
$777$	16.9669	+	5.24505i	0.608683	+	0.188165i
$778$	13.1918	+	13.1918i	0.472948	+	0.472948i
$779$		−	6.89339i		−	0.246981i
$780$		0			0
$781$	−63.9528			−2.28841
$782$	−4.09925	−	4.09925i	−0.146589	−	0.146589i
$783$	3.37069	−	3.37069i	0.120459	−	0.120459i
$784$	5.77880	+	3.95037i	0.206386	+	0.141085i
$785$		0			0
$786$	−12.8367			−0.457869
$787$	−11.7098	−	11.7098i	−0.417409	−	0.417409i	0.466901	−	0.884310i	$-0.345370\pi$
$787$	−11.7098	−	11.7098i	−0.417409	−	0.417409i	−0.884310	+	0.466901i	$0.845370\pi$
$788$	13.0334	+	13.0334i	0.464295	+	0.464295i
$789$	−9.35965			−0.333212
$790$		0			0
$791$	6.72576	−	3.54936i	0.239141	−	0.126201i
$792$	−3.46967	+	3.46967i	−0.123289	+	0.123289i
$793$	−7.84316	−	7.84316i	−0.278519	−	0.278519i
$794$	−27.3909			−0.972066
$795$		0			0
$796$		−	11.7509i		−	0.416499i
$797$	−12.7255	−	12.7255i	−0.450760	−	0.450760i	0.444847	−	0.895607i	$-0.353258\pi$
$797$	−12.7255	−	12.7255i	−0.450760	−	0.450760i	−0.895607	+	0.444847i	$0.853258\pi$
$798$	3.19912	+	0.988958i	0.113247	+	0.0350088i
$799$			4.03374i			0.142703i
$800$		0			0
$801$			15.3596i			0.542706i
$802$	−19.7353	+	19.7353i	−0.696877	+	0.696877i
$803$	−24.7522	+	24.7522i	−0.873485	+	0.873485i
$804$	4.32106			0.152392
$805$		0			0
$806$	−34.0667			−1.19995
$807$	9.27665	−	9.27665i	0.326554	−	0.326554i
$808$	12.8343	−	12.8343i	0.451507	−	0.451507i
$809$			22.8744i			0.804220i	0.915591	+	0.402110i	$0.131723\pi$
$809$			22.8744i			0.804220i	−0.915591	+	0.402110i	$0.868277\pi$
$810$		0			0
$811$			0.722188i			0.0253595i	0.999920	+	0.0126797i	$0.00403619\pi$
$811$			0.722188i			0.0253595i	−0.999920	+	0.0126797i	$0.995964\pi$
$812$	−3.72488	+	12.0494i	−0.130718	+	0.422849i
$813$	12.7870	+	12.7870i	0.448461	+	0.448461i
$814$		−	32.9363i		−	1.15442i
$815$		0			0
$816$	3.88388			0.135963
$817$	9.60177	+	9.60177i	0.335923	+	0.335923i
$818$	−12.9549	+	12.9549i	−0.452959	+	0.452959i
$819$	11.2981	−	5.96230i	0.394787	−	0.208340i
$820$		0			0
$821$	21.2417			0.741341			0.370671	−	0.928764i	$-0.379128\pi$
$821$	21.2417			0.741341			0.370671	+	0.928764i	$0.379128\pi$
$822$	−3.62437	−	3.62437i	−0.126414	−	0.126414i
$823$	−10.3066	−	10.3066i	−0.359266	−	0.359266i	0.504276	−	0.863542i	$-0.331759\pi$
$823$	−10.3066	−	10.3066i	−0.359266	−	0.359266i	−0.863542	+	0.504276i	$0.831759\pi$
$824$	11.8293			0.412094
$825$		0			0
$826$	1.72549	+	3.26966i	0.0600374	+	0.113766i
$827$	26.1746	−	26.1746i	0.910181	−	0.910181i	−0.0861054	−	0.996286i	$-0.527442\pi$
$827$	26.1746	−	26.1746i	0.910181	−	0.910181i	0.996286	+	0.0861054i	$0.0274422\pi$
$828$	−1.05545	−	1.05545i	−0.0366795	−	0.0366795i
$829$	−21.0061			−0.729571			−0.364786	−	0.931092i	$-0.618858\pi$
$829$	−21.0061			−0.729571			−0.364786	+	0.931092i	$0.618858\pi$
$830$		0			0
$831$			3.72704i			0.129289i
$832$	3.41421	+	3.41421i	0.118367	+	0.118367i
$833$	5.02144	+	26.7194i	0.173983	+	0.925773i
$834$		−	3.90596i		−	0.135252i
$835$		0			0
$836$		−	6.21016i		−	0.214783i
$837$	−4.98896	+	4.98896i	−0.172444	+	0.172444i
$838$	−3.88629	+	3.88629i	−0.134250	+	0.134250i
$839$	50.2886			1.73615			0.868077	−	0.496430i	$-0.165356\pi$
$839$	50.2886			1.73615			0.868077	+	0.496430i	$0.165356\pi$
$840$		0			0
$841$	6.27692			0.216445
$842$	17.3851	−	17.3851i	0.599132	−	0.599132i
$843$	14.4645	−	14.4645i	0.498182	−	0.498182i
$844$		−	16.5502i		−	0.569683i
$845$		0			0
$846$			1.03858i			0.0357073i
$847$	−10.2186	+	33.0555i	−0.351116	+	1.13580i
$848$	1.26561	+	1.26561i	0.0434612	+	0.0434612i
$849$			15.2383i			0.522978i
$850$		0			0
$851$	10.0190			0.343448
$852$	9.21598	+	9.21598i	0.315734	+	0.315734i
$853$	13.1647	−	13.1647i	0.450751	−	0.450751i	−0.444853	−	0.895604i	$-0.646744\pi$
$853$	13.1647	−	13.1647i	0.450751	−	0.450751i	0.895604	+	0.444853i	$0.146744\pi$
$854$	5.37526	−	2.83667i	0.183938	−	0.0970688i
$855$		0			0
$856$	5.33579			0.182374
$857$	19.5839	+	19.5839i	0.668973	+	0.668973i	0.957478	−	0.288505i	$-0.0931583\pi$
$857$	19.5839	+	19.5839i	0.668973	+	0.668973i	−0.288505	+	0.957478i	$0.593158\pi$
$858$	−16.7530	−	16.7530i	−0.571939	−	0.571939i
$859$	7.58185			0.258689			0.129345	−	0.991600i	$-0.458713\pi$
$859$	7.58185			0.258689			0.129345	+	0.991600i	$0.458713\pi$
$860$		0			0
$861$	12.7448	−	6.72576i	0.434341	−	0.229213i
$862$	16.1315	−	16.1315i	0.549440	−	0.549440i
$863$	22.1829	+	22.1829i	0.755113	+	0.755113i	0.975429	−	0.220315i	$-0.0707086\pi$
$863$	22.1829	+	22.1829i	0.755113	+	0.755113i	−0.220315	+	0.975429i	$0.570709\pi$
$864$	1.00000			0.0340207
$865$		0			0
$866$			24.2136i			0.822811i
$867$	−1.35445	−	1.35445i	−0.0459994	−	0.0459994i
$868$	5.51319	−	17.8343i	0.187130	−	0.605334i
$869$			72.6525i			2.46457i
$870$		0			0
$871$			20.8639i			0.706948i
$872$	−0.0615536	+	0.0615536i	−0.00208447	+	0.00208447i
$873$	8.42614	−	8.42614i	0.285182	−	0.285182i
$874$	1.88909			0.0638996
$875$		0			0
$876$	7.13387			0.241031
$877$	5.71511	−	5.71511i	0.192985	−	0.192985i	−0.603999	−	0.796985i	$-0.706427\pi$
$877$	5.71511	−	5.71511i	0.192985	−	0.192985i	0.796985	+	0.603999i	$0.206427\pi$
$878$	−25.3373	+	25.3373i	−0.855092	+	0.855092i
$879$		−	4.46841i		−	0.150716i
$880$		0			0
$881$			31.8033i			1.07148i	0.844383	+	0.535740i	$0.179967\pi$
$881$			31.8033i			1.07148i	−0.844383	+	0.535740i	$0.820033\pi$
$882$	1.29289	+	6.87957i	0.0435340	+	0.231647i
$883$	16.9653	+	16.9653i	0.570929	+	0.570929i	0.932388	−	0.361459i	$-0.117721\pi$
$883$	16.9653	+	16.9653i	0.570929	+	0.570929i	−0.361459	+	0.932388i	$0.617721\pi$
$884$			18.7530i			0.630733i
$885$		0			0
$886$	−4.14519			−0.139260
$887$	7.70801	+	7.70801i	0.258810	+	0.258810i	0.824570	−	0.565760i	$-0.191417\pi$
$887$	7.70801	+	7.70801i	0.258810	+	0.258810i	−0.565760	+	0.824570i	$0.691417\pi$
$888$	−4.74632	+	4.74632i	−0.159276	+	0.159276i
$889$	19.5171	+	36.9834i	0.654583	+	1.24038i
$890$		0			0
$891$	−4.90685			−0.164386
$892$	−8.26067	−	8.26067i	−0.276588	−	0.276588i
$893$	−0.929451	−	0.929451i	−0.0311029	−	0.0311029i
$894$	5.64124			0.188671
$895$		0			0
$896$	−2.33991	+	1.23483i	−0.0781710	+	0.0412529i
$897$	5.09618	−	5.09618i	0.170156	−	0.170156i
$898$	−1.20406	−	1.20406i	−0.0401799	−	0.0401799i
$899$	33.6325			1.12171
$900$		0			0
$901$			6.95153i			0.231589i
$902$	−18.8982	−	18.8982i	−0.629242	−	0.629242i
$903$	−8.38387	+	27.1204i	−0.278998	+	0.902511i
$904$			2.87437i			0.0956000i
$905$		0			0
$906$			11.7678i			0.390958i
$907$	−0.997860	+	0.997860i	−0.0331334	+	0.0331334i	−0.723479	−	0.690346i	$-0.757458\pi$
$907$	−0.997860	+	0.997860i	−0.0331334	+	0.0331334i	0.690346	+	0.723479i	$0.257458\pi$
$908$	−5.91295	+	5.91295i	−0.196228	+	0.196228i
$909$	18.1504			0.602010
$910$		0			0
$911$	−21.9623			−0.727643			−0.363821	−	0.931469i	$-0.618528\pi$
$911$	−21.9623			−0.727643			−0.363821	+	0.931469i	$0.618528\pi$
$912$	−0.894921	+	0.894921i	−0.0296338	+	0.0296338i
$913$	45.6243	−	45.6243i	1.50995	−	1.50995i
$914$		−	7.55635i		−	0.249942i
$915$		0			0
$916$			9.31371i			0.307734i
$917$	32.4476	+	10.0307i	1.07151	+	0.331242i
$918$	2.74632	+	2.74632i	0.0906420	+	0.0906420i
$919$		−	32.6954i		−	1.07852i	−0.842138	−	0.539262i	$-0.818703\pi$
$919$		−	32.6954i		−	1.07852i	0.842138	−	0.539262i	$-0.181297\pi$
$920$		0			0
$921$	−29.4172			−0.969331
$922$	−0.607228	−	0.607228i	−0.0199980	−	0.0199980i
$923$	−44.4987	+	44.4987i	−1.46469	+	1.46469i
$924$	11.4816	−	6.05914i	0.377717	−	0.199331i
$925$		0			0
$926$	28.7925			0.946180
$927$	8.36459	+	8.36459i	0.274729	+	0.274729i
$928$	−3.37069	−	3.37069i	−0.110648	−	0.110648i
$929$	−10.8063			−0.354545			−0.177272	−	0.984162i	$-0.556727\pi$
$929$	−10.8063			−0.354545			−0.177272	+	0.984162i	$0.556727\pi$
$930$		0			0
$931$	−7.31371	−	4.99963i	−0.239697	−	0.163856i
$932$	−16.0563	+	16.0563i	−0.525943	+	0.525943i
$933$	−8.11091	−	8.11091i	−0.265539	−	0.265539i
$934$	−12.4155			−0.406247
$935$		0			0
$936$			4.82843i			0.157822i
$937$	3.51804	+	3.51804i	0.114929	+	0.114929i	0.762233	−	0.647303i	$-0.224103\pi$
$937$	3.51804	+	3.51804i	0.114929	+	0.114929i	−0.647303	+	0.762233i	$0.724103\pi$
$938$	−10.9225	−	3.37652i	−0.356631	−	0.110247i
$939$			0.866125i			0.0282649i
$940$		0			0
$941$		−	54.9021i		−	1.78976i	−0.446309	−	0.894879i	$-0.647262\pi$
$941$		−	54.9021i		−	1.78976i	0.446309	−	0.894879i	$-0.352738\pi$
$942$	13.7132	−	13.7132i	0.446800	−	0.446800i
$943$	5.74873	−	5.74873i	0.187204	−	0.187204i
$944$	−1.39735			−0.0454797
$945$		0			0
$946$	52.6464			1.71168
$947$	30.4494	−	30.4494i	0.989471	−	0.989471i	−0.0104740	−	0.999945i	$-0.503334\pi$
$947$	30.4494	−	30.4494i	0.989471	−	0.989471i	0.999945	+	0.0104740i	$0.00333405\pi$
$948$	10.4697	−	10.4697i	0.340039	−	0.340039i
$949$			34.4454i			1.11814i
$950$		0			0
$951$			9.95583i			0.322840i
$952$	−9.81739	−	3.03490i	−0.318183	−	0.0983616i
$953$	−40.3553	−	40.3553i	−1.30724	−	1.30724i	−0.923401	−	0.383836i	$-0.874603\pi$
$953$	−40.3553	−	40.3553i	−1.30724	−	1.30724i	−0.383836	−	0.923401i	$-0.625397\pi$
$954$			1.78984i			0.0579483i
$955$		0			0
$956$	1.68592			0.0545267
$957$	16.5395	+	16.5395i	0.534645	+	0.534645i
$958$	−0.828427	+	0.828427i	−0.0267653	+	0.0267653i
$959$	6.32930	+	11.9935i	0.204384	+	0.387291i
$960$		0			0
$961$	−18.7794			−0.605788
$962$	−22.9172	−	22.9172i	−0.738882	−	0.738882i
$963$	3.77297	+	3.77297i	0.121582	+	0.121582i
$964$	−3.61574			−0.116455
$965$		0			0
$966$	1.84316	+	3.49264i	0.0593026	+	0.112374i
$967$	−30.6566	+	30.6566i	−0.985849	+	0.985849i	−0.999901	−	0.0140521i	$-0.995527\pi$
$967$	−30.6566	+	30.6566i	−0.985849	+	0.985849i	0.0140521	+	0.999901i	$0.495527\pi$
$968$	−9.24695	−	9.24695i	−0.297208	−	0.297208i
$969$	−4.91548			−0.157908
$970$		0			0
$971$			46.5248i			1.49305i	0.665357	+	0.746525i	$0.268279\pi$
$971$			46.5248i			1.49305i	−0.665357	+	0.746525i	$0.731721\pi$
$972$	0.707107	+	0.707107i	0.0226805	+	0.0226805i
$973$	−3.05215	+	9.87321i	−0.0978475	+	0.316520i
$974$			13.7283i			0.439883i
$975$		0			0
$976$			2.29721i			0.0735318i
$977$	−42.6690	+	42.6690i	−1.36510	+	1.36510i	−0.497825	+	0.867278i	$0.665868\pi$
$977$	−42.6690	+	42.6690i	−1.36510	+	1.36510i	−0.867278	+	0.497825i	$0.834132\pi$
$978$	7.21967	−	7.21967i	0.230860	−	0.230860i
$979$	−75.3675			−2.40875
$980$		0			0
$981$	−0.0870500			−0.00277929
$982$	−11.9770	+	11.9770i	−0.382202	+	0.382202i
$983$	−1.34529	+	1.34529i	−0.0429079	+	0.0429079i	−0.728235	−	0.685327i	$-0.759659\pi$
$983$	−1.34529	+	1.34529i	−0.0429079	+	0.0429079i	0.685327	+	0.728235i	$0.259659\pi$
$984$			5.44670i			0.173634i
$985$		0			0
$986$		−	18.5140i		−	0.589605i
$987$	0.811559	−	2.62526i	0.0258322	−	0.0835629i
$988$	−4.32106	−	4.32106i	−0.137471	−	0.137471i
$989$			16.0147i			0.509239i
$990$		0			0
$991$	3.44975			0.109585			0.0547925	−	0.998498i	$-0.482550\pi$
$991$	3.44975			0.109585			0.0547925	+	0.998498i	$0.482550\pi$
$992$	4.98896	+	4.98896i	0.158400	+	0.158400i
$993$	7.19543	−	7.19543i	0.228340	−	0.228340i
$994$	−16.0940	−	30.4969i	−0.510472	−	0.967304i
$995$		0			0
$996$	−13.1495			−0.416658
$997$	−31.5368	−	31.5368i	−0.998780	−	0.998780i	0.00121964	−	0.999999i	$-0.499612\pi$
$997$	−31.5368	−	31.5368i	−0.998780	−	0.998780i	−0.999999	+	0.00121964i	$0.999612\pi$
$998$	−21.5043	−	21.5043i	−0.680706	−	0.680706i
$999$	−6.71231			−0.212368

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.m.b.643.4		8
5.2	odd	4		1050.2.m.a.307.3		8
5.3	odd	4		210.2.m.b.97.1	yes	8
5.4	even	2		210.2.m.a.13.2	✓	8
7.6	odd	2		1050.2.m.a.643.3		8
15.8	even	4		630.2.p.c.307.4		8
15.14	odd	2		630.2.p.b.433.3		8
20.3	even	4		1680.2.cz.a.97.1		8
20.19	odd	2		1680.2.cz.b.433.4		8
35.13	even	4		210.2.m.a.97.2	yes	8
35.27	even	4	inner	1050.2.m.b.307.4		8
35.34	odd	2		210.2.m.b.13.1	yes	8
105.83	odd	4		630.2.p.b.307.3		8
105.104	even	2		630.2.p.c.433.4		8
140.83	odd	4		1680.2.cz.b.97.4		8
140.139	even	2		1680.2.cz.a.433.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.m.a.13.2	✓	8	5.4	even	2
210.2.m.a.97.2	yes	8	35.13	even	4
210.2.m.b.13.1	yes	8	35.34	odd	2
210.2.m.b.97.1	yes	8	5.3	odd	4
630.2.p.b.307.3		8	105.83	odd	4
630.2.p.b.433.3		8	15.14	odd	2
630.2.p.c.307.4		8	15.8	even	4
630.2.p.c.433.4		8	105.104	even	2
1050.2.m.a.307.3		8	5.2	odd	4
1050.2.m.a.643.3		8	7.6	odd	2
1050.2.m.b.307.4		8	35.27	even	4	inner
1050.2.m.b.643.4		8	1.1	even	1	trivial
1680.2.cz.a.97.1		8	20.3	even	4
1680.2.cz.a.433.1		8	140.139	even	2
1680.2.cz.b.97.4		8	140.83	odd	4
1680.2.cz.b.433.4		8	20.19	odd	2

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} -1.00000i q^{6} +(-0.781409 + 2.52773i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} -1.00000i q^{6} +(-0.781409 + 2.52773i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +4.90685 q^{11} +(-0.707107 - 0.707107i) q^{12} +(3.41421 - 3.41421i) q^{13} +(1.23483 + 2.33991i) q^{14} -1.00000 q^{16} +(-2.74632 - 2.74632i) q^{17} +(-0.707107 - 0.707107i) q^{18} +1.26561 q^{19} +(1.23483 + 2.33991i) q^{21} +(3.46967 - 3.46967i) q^{22} +(1.05545 + 1.05545i) q^{23} -1.00000 q^{24} -4.82843i q^{26} +(-0.707107 - 0.707107i) q^{27} +(2.52773 + 0.781409i) q^{28} +4.76687i q^{29} -7.05545i q^{31} +(-0.707107 + 0.707107i) q^{32} +(3.46967 - 3.46967i) q^{33} -3.88388 q^{34} -1.00000 q^{36} +(4.74632 - 4.74632i) q^{37} +(0.894921 - 0.894921i) q^{38} -4.82843i q^{39} -5.44670i q^{41} +(2.52773 + 0.781409i) q^{42} +(7.58667 + 7.58667i) q^{43} -4.90685i q^{44} +1.49264 q^{46} +(-0.734390 - 0.734390i) q^{47} +(-0.707107 + 0.707107i) q^{48} +(-5.77880 - 3.95037i) q^{49} -3.88388 q^{51} +(-3.41421 - 3.41421i) q^{52} +(-1.26561 - 1.26561i) q^{53} -1.00000 q^{54} +(2.33991 - 1.23483i) q^{56} +(0.894921 - 0.894921i) q^{57} +(3.37069 + 3.37069i) q^{58} +1.39735 q^{59} -2.29721i q^{61} +(-4.98896 - 4.98896i) q^{62} +(2.52773 + 0.781409i) q^{63} +1.00000i q^{64} -4.90685i q^{66} +(-3.05545 + 3.05545i) q^{67} +(-2.74632 + 2.74632i) q^{68} +1.49264 q^{69} -13.0334 q^{71} +(-0.707107 + 0.707107i) q^{72} +(-5.04441 + 5.04441i) q^{73} -6.71231i q^{74} -1.26561i q^{76} +(-3.83425 + 12.4032i) q^{77} +(-3.41421 - 3.41421i) q^{78} +14.8063i q^{79} -1.00000 q^{81} +(-3.85140 - 3.85140i) q^{82} +(9.29809 - 9.29809i) q^{83} +(2.33991 - 1.23483i) q^{84} +10.7292 q^{86} +(3.37069 + 3.37069i) q^{87} +(-3.46967 - 3.46967i) q^{88} -15.3596 q^{89} +(5.96230 + 11.2981i) q^{91} +(1.05545 - 1.05545i) q^{92} +(-4.98896 - 4.98896i) q^{93} -1.03858 q^{94} +1.00000i q^{96} +(8.42614 + 8.42614i) q^{97} +(-6.87957 + 1.29289i) q^{98} -4.90685i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{7}+O(q^{10}) \) 8 * q - 4 * q^7	\( 8 q - 4 q^{7} + 8 q^{11} + 16 q^{13} - 8 q^{14} - 8 q^{16} - 12 q^{17} - 8 q^{19} - 8 q^{21} - 8 q^{22} - 16 q^{23} - 8 q^{24} + 8 q^{28} - 8 q^{33} + 16 q^{34} - 8 q^{36} + 28 q^{37} + 4 q^{38} + 8 q^{42} - 8 q^{46} - 24 q^{47} + 4 q^{49} + 16 q^{51} - 16 q^{52} + 8 q^{53} - 8 q^{54} + 4 q^{56} + 4 q^{57} + 12 q^{58} + 8 q^{59} + 4 q^{62} + 8 q^{63} - 12 q^{68} - 8 q^{69} + 8 q^{71} + 28 q^{73} + 44 q^{77} - 16 q^{78} - 8 q^{81} - 24 q^{82} + 16 q^{83} + 4 q^{84} + 8 q^{86} + 12 q^{87} + 8 q^{88} - 64 q^{89} - 8 q^{91} - 16 q^{92} + 4 q^{93} + 8 q^{94} + 28 q^{97}+O(q^{100}) \) 8 * q - 4 * q^7 + 8 * q^11 + 16 * q^13 - 8 * q^14 - 8 * q^16 - 12 * q^17 - 8 * q^19 - 8 * q^21 - 8 * q^22 - 16 * q^23 - 8 * q^24 + 8 * q^28 - 8 * q^33 + 16 * q^34 - 8 * q^36 + 28 * q^37 + 4 * q^38 + 8 * q^42 - 8 * q^46 - 24 * q^47 + 4 * q^49 + 16 * q^51 - 16 * q^52 + 8 * q^53 - 8 * q^54 + 4 * q^56 + 4 * q^57 + 12 * q^58 + 8 * q^59 + 4 * q^62 + 8 * q^63 - 12 * q^68 - 8 * q^69 + 8 * q^71 + 28 * q^73 + 44 * q^77 - 16 * q^78 - 8 * q^81 - 24 * q^82 + 16 * q^83 + 4 * q^84 + 8 * q^86 + 12 * q^87 + 8 * q^88 - 64 * q^89 - 8 * q^91 - 16 * q^92 + 4 * q^93 + 8 * q^94 + 28 * q^97

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