LMFDB - Embedded newform 196.3.g.b.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [196,3,Mod(67,196)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(196, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("196.67");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	196.g (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:	$5.34061318146$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			67.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	196.67
Dual form			196.3.g.b.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.73205i) q^{2} +(-2.12132 - 1.22474i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(2.82843 + 4.89898i) q^{5} +(4.24264 - 2.44949i) q^{6} +8.00000 q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.73205i) q^{2} +(-2.12132 - 1.22474i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(2.82843 + 4.89898i) q^{5} +(4.24264 - 2.44949i) q^{6} +8.00000 q^{8} +(-1.50000 - 2.59808i) q^{9} -11.3137 q^{10} +(15.0000 + 8.66025i) q^{11} +9.79796i q^{12} -14.1421 q^{13} -13.8564i q^{15} +(-8.00000 + 13.8564i) q^{16} +(-9.19239 + 15.9217i) q^{17} +6.00000 q^{18} +(-23.3345 + 13.4722i) q^{19} +(11.3137 - 19.5959i) q^{20} +(-30.0000 + 17.3205i) q^{22} +(-24.0000 + 13.8564i) q^{23} +(-16.9706 - 9.79796i) q^{24} +(-3.50000 + 6.06218i) q^{25} +(14.1421 - 24.4949i) q^{26} +29.3939i q^{27} +2.00000 q^{29} +(24.0000 + 13.8564i) q^{30} +(12.7279 + 7.34847i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(-21.2132 - 36.7423i) q^{33} +(-18.3848 - 31.8434i) q^{34} +(-6.00000 + 10.3923i) q^{36} +(15.0000 + 25.9808i) q^{37} -53.8888i q^{38} +(30.0000 + 17.3205i) q^{39} +(22.6274 + 39.1918i) q^{40} -24.0416 q^{41} -24.2487i q^{43} -69.2820i q^{44} +(8.48528 - 14.6969i) q^{45} -55.4256i q^{46} +(21.2132 - 12.2474i) q^{47} +(33.9411 - 19.5959i) q^{48} +(-7.00000 - 12.1244i) q^{50} +(39.0000 - 22.5167i) q^{51} +(28.2843 + 48.9898i) q^{52} +(-33.0000 + 57.1577i) q^{53} +(-50.9117 - 29.3939i) q^{54} +97.9796i q^{55} +66.0000 q^{57} +(-2.00000 + 3.46410i) q^{58} +(57.2756 + 33.0681i) q^{59} +(-48.0000 + 27.7128i) q^{60} +(22.6274 + 39.1918i) q^{61} +(-25.4558 + 14.6969i) q^{62} +64.0000 q^{64} +(-40.0000 - 69.2820i) q^{65} +84.8528 q^{66} +(-6.00000 - 3.46410i) q^{67} +73.5391 q^{68} +67.8823 q^{69} +48.4974i q^{71} +(-12.0000 - 20.7846i) q^{72} +(-9.19239 + 15.9217i) q^{73} -60.0000 q^{74} +(14.8492 - 8.57321i) q^{75} +(93.3381 + 53.8888i) q^{76} +(-60.0000 + 34.6410i) q^{78} +(18.0000 - 10.3923i) q^{79} -90.5097 q^{80} +(22.5000 - 38.9711i) q^{81} +(24.0416 - 41.6413i) q^{82} -154.318i q^{83} -104.000 q^{85} +(42.0000 + 24.2487i) q^{86} +(-4.24264 - 2.44949i) q^{87} +(120.000 + 69.2820i) q^{88} +(-12.0208 - 20.8207i) q^{89} +(16.9706 + 29.3939i) q^{90} +(96.0000 + 55.4256i) q^{92} +(-18.0000 - 31.1769i) q^{93} +48.9898i q^{94} +(-132.000 - 76.2102i) q^{95} +78.3837i q^{96} -83.4386 q^{97} -51.9615i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 8 q^{4} + 32 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 8 * q^4 + 32 * q^8 - 6 * q^9	$ 4 q - 4 q^{2} - 8 q^{4} + 32 q^{8} - 6 q^{9} + 60 q^{11} - 32 q^{16} + 24 q^{18} - 120 q^{22} - 96 q^{23} - 14 q^{25} + 8 q^{29} + 96 q^{30} - 64 q^{32} - 24 q^{36} + 60 q^{37} + 120 q^{39} - 28 q^{50} + 156 q^{51} - 132 q^{53} + 264 q^{57} - 8 q^{58} - 192 q^{60} + 256 q^{64} - 160 q^{65} - 24 q^{67} - 48 q^{72} - 240 q^{74} - 240 q^{78} + 72 q^{79} + 90 q^{81} - 416 q^{85} + 168 q^{86} + 480 q^{88} + 384 q^{92} - 72 q^{93} - 528 q^{95}+O(q^{100}) $ 4 * q - 4 * q^2 - 8 * q^4 + 32 * q^8 - 6 * q^9 + 60 * q^11 - 32 * q^16 + 24 * q^18 - 120 * q^22 - 96 * q^23 - 14 * q^25 + 8 * q^29 + 96 * q^30 - 64 * q^32 - 24 * q^36 + 60 * q^37 + 120 * q^39 - 28 * q^50 + 156 * q^51 - 132 * q^53 + 264 * q^57 - 8 * q^58 - 192 * q^60 + 256 * q^64 - 160 * q^65 - 24 * q^67 - 48 * q^72 - 240 * q^74 - 240 * q^78 + 72 * q^79 + 90 * q^81 - 416 * q^85 + 168 * q^86 + 480 * q^88 + 384 * q^92 - 72 * q^93 - 528 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.00000	+	1.73205i	−0.500000	+	0.866025i
$2$	−1.00000	+	1.73205i	−0.500000	+	0.866025i
$3$	−2.12132	−	1.22474i	−0.707107	−	0.408248i	0.102882	−	0.994694i	$-0.467194\pi$
$3$	−2.12132	−	1.22474i	−0.707107	−	0.408248i	−0.809989	+	0.586445i	$0.800527\pi$
$4$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$5$	2.82843	+	4.89898i	0.565685	+	0.979796i	0.996986	+	0.0775874i	$0.0247217\pi$
$5$	2.82843	+	4.89898i	0.565685	+	0.979796i	−0.431300	+	0.902209i	$0.641945\pi$
$6$	4.24264	−	2.44949i	0.707107	−	0.408248i
$7$		0			0
$7$		0			0
$8$	8.00000			1.00000
$9$	−1.50000	−	2.59808i	−0.166667	−	0.288675i
$10$	−11.3137			−1.13137
$11$	15.0000	+	8.66025i	1.36364	+	0.787296i	0.990106	−	0.140322i	$-0.0448138\pi$
$11$	15.0000	+	8.66025i	1.36364	+	0.787296i	0.373530	+	0.927618i	$0.378147\pi$
$12$			9.79796i			0.816497i
$13$	−14.1421			−1.08786			−0.543928	−	0.839132i	$-0.683064\pi$
$13$	−14.1421			−1.08786			−0.543928	+	0.839132i	$0.683064\pi$
$14$		0			0
$15$		−	13.8564i		−	0.923760i
$16$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$17$	−9.19239	+	15.9217i	−0.540729	+	0.936570i	0.458134	+	0.888883i	$0.348518\pi$
$17$	−9.19239	+	15.9217i	−0.540729	+	0.936570i	−0.998862	+	0.0476863i	$0.984815\pi$
$18$	6.00000			0.333333
$19$	−23.3345	+	13.4722i	−1.22813	+	0.709063i	−0.966639	−	0.256142i	$-0.917548\pi$
$19$	−23.3345	+	13.4722i	−1.22813	+	0.709063i	−0.261494	+	0.965205i	$0.584215\pi$
$20$	11.3137	−	19.5959i	0.565685	−	0.979796i
$21$		0			0
$22$	−30.0000	+	17.3205i	−1.36364	+	0.787296i
$23$	−24.0000	+	13.8564i	−1.04348	+	0.602452i	−0.920817	−	0.389996i	$-0.872476\pi$
$23$	−24.0000	+	13.8564i	−1.04348	+	0.602452i	−0.122662	+	0.992449i	$0.539143\pi$
$24$	−16.9706	−	9.79796i	−0.707107	−	0.408248i
$25$	−3.50000	+	6.06218i	−0.140000	+	0.242487i
$26$	14.1421	−	24.4949i	0.543928	−	0.942111i
$27$			29.3939i			1.08866i
$28$		0			0
$29$	2.00000			0.0689655			0.0344828	−	0.999405i	$-0.489022\pi$
$29$	2.00000			0.0689655			0.0344828	+	0.999405i	$0.489022\pi$
$30$	24.0000	+	13.8564i	0.800000	+	0.461880i
$31$	12.7279	+	7.34847i	0.410578	+	0.237047i	0.691038	−	0.722818i	$-0.257154\pi$
$31$	12.7279	+	7.34847i	0.410578	+	0.237047i	−0.280460	+	0.959866i	$0.590487\pi$
$32$	−16.0000	−	27.7128i	−0.500000	−	0.866025i
$33$	−21.2132	−	36.7423i	−0.642824	−	1.11340i
$34$	−18.3848	−	31.8434i	−0.540729	−	0.936570i
$35$		0			0
$36$	−6.00000	+	10.3923i	−0.166667	+	0.288675i
$37$	15.0000	+	25.9808i	0.405405	+	0.702183i	0.994369	−	0.105977i	$-0.0337970\pi$
$37$	15.0000	+	25.9808i	0.405405	+	0.702183i	−0.588963	+	0.808160i	$0.700464\pi$
$38$		−	53.8888i		−	1.41813i
$39$	30.0000	+	17.3205i	0.769231	+	0.444116i
$40$	22.6274	+	39.1918i	0.565685	+	0.979796i
$41$	−24.0416			−0.586381			−0.293191	−	0.956054i	$-0.594717\pi$
$41$	−24.0416			−0.586381			−0.293191	+	0.956054i	$0.594717\pi$
$42$		0			0
$43$		−	24.2487i		−	0.563924i	−0.959426	−	0.281962i	$-0.909015\pi$
$43$		−	24.2487i		−	0.563924i	0.959426	−	0.281962i	$-0.0909851\pi$
$44$		−	69.2820i		−	1.57459i
$45$	8.48528	−	14.6969i	0.188562	−	0.326599i
$46$		−	55.4256i		−	1.20490i
$47$	21.2132	−	12.2474i	0.451345	−	0.260584i	−0.257053	−	0.966397i	$-0.582752\pi$
$47$	21.2132	−	12.2474i	0.451345	−	0.260584i	0.708398	+	0.705813i	$0.249418\pi$
$48$	33.9411	−	19.5959i	0.707107	−	0.408248i
$49$		0			0
$50$	−7.00000	−	12.1244i	−0.140000	−	0.242487i
$51$	39.0000	−	22.5167i	0.764706	−	0.441503i
$52$	28.2843	+	48.9898i	0.543928	+	0.942111i
$53$	−33.0000	+	57.1577i	−0.622642	+	1.07845i	0.366350	+	0.930477i	$0.380607\pi$
$53$	−33.0000	+	57.1577i	−0.622642	+	1.07845i	−0.988992	+	0.147970i	$0.952726\pi$
$54$	−50.9117	−	29.3939i	−0.942809	−	0.544331i
$55$			97.9796i			1.78145i
$56$		0			0
$57$	66.0000			1.15789
$58$	−2.00000	+	3.46410i	−0.0344828	+	0.0597259i
$59$	57.2756	+	33.0681i	0.970774	+	0.560476i	0.899472	−	0.436978i	$-0.143951\pi$
$59$	57.2756	+	33.0681i	0.970774	+	0.560476i	0.0713017	+	0.997455i	$0.477285\pi$
$60$	−48.0000	+	27.7128i	−0.800000	+	0.461880i
$61$	22.6274	+	39.1918i	0.370941	+	0.642489i	0.989711	−	0.143084i	$-0.0457018\pi$
$61$	22.6274	+	39.1918i	0.370941	+	0.642489i	−0.618769	+	0.785573i	$0.712368\pi$
$62$	−25.4558	+	14.6969i	−0.410578	+	0.237047i
$63$		0			0
$64$	64.0000			1.00000
$65$	−40.0000	−	69.2820i	−0.615385	−	1.06588i
$66$	84.8528			1.28565
$67$	−6.00000	−	3.46410i	−0.0895522	−	0.0517030i	0.454555	−	0.890719i	$-0.349798\pi$
$67$	−6.00000	−	3.46410i	−0.0895522	−	0.0517030i	−0.544107	+	0.839016i	$0.683132\pi$
$68$	73.5391			1.08146
$69$	67.8823			0.983801
$70$		0			0
$71$			48.4974i			0.683062i	0.939870	+	0.341531i	$0.110945\pi$
$71$			48.4974i			0.683062i	−0.939870	+	0.341531i	$0.889055\pi$
$72$	−12.0000	−	20.7846i	−0.166667	−	0.288675i
$73$	−9.19239	+	15.9217i	−0.125923	+	0.218105i	−0.922093	−	0.386967i	$-0.873523\pi$
$73$	−9.19239	+	15.9217i	−0.125923	+	0.218105i	0.796170	+	0.605073i	$0.206856\pi$
$74$	−60.0000			−0.810811
$75$	14.8492	−	8.57321i	0.197990	−	0.114310i
$76$	93.3381	+	53.8888i	1.22813	+	0.709063i
$77$		0			0
$78$	−60.0000	+	34.6410i	−0.769231	+	0.444116i
$79$	18.0000	−	10.3923i	0.227848	−	0.131548i	−0.381731	−	0.924274i	$-0.624672\pi$
$79$	18.0000	−	10.3923i	0.227848	−	0.131548i	0.609579	+	0.792725i	$0.291339\pi$
$80$	−90.5097			−1.13137
$81$	22.5000	−	38.9711i	0.277778	−	0.481125i
$82$	24.0416	−	41.6413i	0.293191	−	0.507821i
$83$		−	154.318i		−	1.85925i	−0.368505	−	0.929626i	$-0.620130\pi$
$83$		−	154.318i		−	1.85925i	0.368505	−	0.929626i	$-0.379870\pi$
$84$		0			0
$85$	−104.000			−1.22353
$86$	42.0000	+	24.2487i	0.488372	+	0.281962i
$87$	−4.24264	−	2.44949i	−0.0487660	−	0.0281551i
$88$	120.000	+	69.2820i	1.36364	+	0.787296i
$89$	−12.0208	−	20.8207i	−0.135065	−	0.233940i	0.790557	−	0.612388i	$-0.209791\pi$
$89$	−12.0208	−	20.8207i	−0.135065	−	0.233940i	−0.925622	+	0.378448i	$0.876458\pi$
$90$	16.9706	+	29.3939i	0.188562	+	0.326599i
$91$		0			0
$92$	96.0000	+	55.4256i	1.04348	+	0.602452i
$93$	−18.0000	−	31.1769i	−0.193548	−	0.335236i
$94$			48.9898i			0.521168i
$95$	−132.000	−	76.2102i	−1.38947	−	0.802213i
$96$			78.3837i			0.816497i
$97$	−83.4386			−0.860192			−0.430096	−	0.902783i	$-0.641520\pi$
$97$	−83.4386			−0.860192			−0.430096	+	0.902783i	$0.641520\pi$
$98$		0			0
$99$		−	51.9615i		−	0.524864i
$100$	28.0000			0.280000
$101$	45.2548	−	78.3837i	0.448068	−	0.776076i	−0.550193	−	0.835038i	$-0.685446\pi$
$101$	45.2548	−	78.3837i	0.448068	−	0.776076i	0.998260	+	0.0589618i	$0.0187790\pi$
$102$			90.0666i			0.883006i
$103$	−38.1838	+	22.0454i	−0.370716	+	0.214033i	−0.673771	−	0.738940i	$-0.735327\pi$
$103$	−38.1838	+	22.0454i	−0.370716	+	0.214033i	0.303055	+	0.952973i	$0.401993\pi$
$104$	−113.137			−1.08786
$105$		0			0
$106$	−66.0000	−	114.315i	−0.622642	−	1.07845i
$107$	18.0000	−	10.3923i	0.168224	−	0.0971243i	−0.413524	−	0.910493i	$-0.635702\pi$
$107$	18.0000	−	10.3923i	0.168224	−	0.0971243i	0.581748	+	0.813369i	$0.302369\pi$
$108$	101.823	−	58.7878i	0.942809	−	0.544331i
$109$	93.0000	−	161.081i	0.853211	−	1.47780i	−0.0250838	−	0.999685i	$-0.507985\pi$
$109$	93.0000	−	161.081i	0.853211	−	1.47780i	0.878295	−	0.478119i	$-0.158681\pi$
$110$	−169.706	−	97.9796i	−1.54278	−	0.890724i
$111$		−	73.4847i		−	0.662024i
$112$		0			0
$113$	−12.0000			−0.106195			−0.0530973	−	0.998589i	$-0.516909\pi$
$113$	−12.0000			−0.106195			−0.0530973	+	0.998589i	$0.516909\pi$
$114$	−66.0000	+	114.315i	−0.578947	+	1.00277i
$115$	−135.765	−	78.3837i	−1.18056	−	0.681597i
$116$	−4.00000	−	6.92820i	−0.0344828	−	0.0597259i
$117$	21.2132	+	36.7423i	0.181309	+	0.314037i
$118$	−114.551	+	66.1362i	−0.970774	+	0.560476i
$119$		0			0
$120$		−	110.851i		−	0.923760i
$121$	89.5000	+	155.019i	0.739669	+	1.28115i
$122$	−90.5097			−0.741883
$123$	51.0000	+	29.4449i	0.414634	+	0.239389i
$124$		−	58.7878i		−	0.474095i
$125$	101.823			0.814587
$126$		0			0
$127$			145.492i			1.14561i	0.819692	+	0.572804i	$0.194144\pi$
$127$			145.492i			1.14561i	−0.819692	+	0.572804i	$0.805856\pi$
$128$	−64.0000	+	110.851i	−0.500000	+	0.866025i
$129$	−29.6985	+	51.4393i	−0.230221	+	0.398754i
$130$	160.000			1.23077
$131$	65.7609	−	37.9671i	0.501992	−	0.289825i	−0.227544	−	0.973768i	$-0.573070\pi$
$131$	65.7609	−	37.9671i	0.501992	−	0.289825i	0.729536	+	0.683943i	$0.239736\pi$
$132$	−84.8528	+	146.969i	−0.642824	+	1.11340i
$133$		0			0
$134$	12.0000	−	6.92820i	0.0895522	−	0.0517030i
$135$	−144.000	+	83.1384i	−1.06667	+	0.615840i
$136$	−73.5391	+	127.373i	−0.540729	+	0.936570i
$137$	−82.0000	+	142.028i	−0.598540	+	1.03670i	0.394497	+	0.918897i	$0.370919\pi$
$137$	−82.0000	+	142.028i	−0.598540	+	1.03670i	−0.993037	+	0.117805i	$0.962414\pi$
$138$	−67.8823	+	117.576i	−0.491900	+	0.851996i
$139$		−	85.7321i		−	0.616778i	−0.951260	−	0.308389i	$-0.900210\pi$
$139$		−	85.7321i		−	0.616778i	0.951260	−	0.308389i	$-0.0997898\pi$
$140$		0			0
$141$	−60.0000			−0.425532
$142$	−84.0000	−	48.4974i	−0.591549	−	0.341531i
$143$	−212.132	−	122.474i	−1.48344	−	0.856465i
$144$	48.0000			0.333333
$145$	5.65685	+	9.79796i	0.0390128	+	0.0675721i
$146$	−18.3848	−	31.8434i	−0.125923	−	0.218105i
$147$		0			0
$148$	60.0000	−	103.923i	0.405405	−	0.702183i
$149$	57.0000	+	98.7269i	0.382550	+	0.662597i	0.991426	−	0.130669i	$-0.0417125\pi$
$149$	57.0000	+	98.7269i	0.382550	+	0.662597i	−0.608876	+	0.793266i	$0.708379\pi$
$150$			34.2929i			0.228619i
$151$	−6.00000	−	3.46410i	−0.0397351	−	0.0229411i	0.480001	−	0.877268i	$-0.340636\pi$
$151$	−6.00000	−	3.46410i	−0.0397351	−	0.0229411i	−0.519736	+	0.854327i	$0.673970\pi$
$152$	−186.676	+	107.778i	−1.22813	+	0.709063i
$153$	55.1543			0.360486
$154$		0			0
$155$			83.1384i			0.536377i
$156$		−	138.564i		−	0.888231i
$157$	15.5563	−	26.9444i	0.0990850	−	0.171620i	−0.812221	−	0.583350i	$-0.801742\pi$
$157$	15.5563	−	26.9444i	0.0990850	−	0.171620i	0.911306	+	0.411729i	$0.135075\pi$
$158$			41.5692i			0.263096i
$159$	140.007	−	80.8332i	0.880548	−	0.508385i
$160$	90.5097	−	156.767i	0.565685	−	0.979796i
$161$		0			0
$162$	45.0000	+	77.9423i	0.277778	+	0.481125i
$163$	39.0000	−	22.5167i	0.239264	−	0.138139i	−0.375575	−	0.926792i	$-0.622555\pi$
$163$	39.0000	−	22.5167i	0.239264	−	0.138139i	0.614838	+	0.788653i	$0.289221\pi$
$164$	48.0833	+	83.2827i	0.293191	+	0.507821i
$165$	120.000	−	207.846i	0.727273	−	1.25967i
$166$	267.286	+	154.318i	1.61016	+	0.929626i
$167$		−	171.464i		−	1.02673i	−0.858170	−	0.513366i	$-0.828398\pi$
$167$		−	171.464i		−	1.02673i	0.858170	−	0.513366i	$-0.171602\pi$
$168$		0			0
$169$	31.0000			0.183432
$170$	104.000	−	180.133i	0.611765	−	1.05961i
$171$	70.0036	+	40.4166i	0.409378	+	0.236354i
$172$	−84.0000	+	48.4974i	−0.488372	+	0.281962i
$173$	52.3259	+	90.6311i	0.302462	+	0.523879i	0.976693	−	0.214641i	$-0.0688582\pi$
$173$	52.3259	+	90.6311i	0.302462	+	0.523879i	−0.674231	+	0.738520i	$0.735525\pi$
$174$	8.48528	−	4.89898i	0.0487660	−	0.0281551i
$175$		0			0
$176$	−240.000	+	138.564i	−1.36364	+	0.787296i
$177$	−81.0000	−	140.296i	−0.457627	−	0.792633i
$178$	48.0833			0.270131
$179$	−174.000	−	100.459i	−0.972067	−	0.561223i	−0.0722013	−	0.997390i	$-0.523002\pi$
$179$	−174.000	−	100.459i	−0.972067	−	0.561223i	−0.899866	+	0.436167i	$0.856336\pi$
$180$	−67.8823			−0.377124
$181$	302.642			1.67205			0.836027	−	0.548689i	$-0.184873\pi$
$181$	302.642			1.67205			0.836027	+	0.548689i	$0.184873\pi$
$182$		0			0
$183$		−	110.851i		−	0.605745i
$184$	−192.000	+	110.851i	−1.04348	+	0.602452i
$185$	−84.8528	+	146.969i	−0.458664	+	0.794429i
$186$	72.0000			0.387097
$187$	−275.772	+	159.217i	−1.47471	+	0.851427i
$188$	−84.8528	−	48.9898i	−0.451345	−	0.260584i
$189$		0			0
$190$	264.000	−	152.420i	1.38947	−	0.802213i
$191$	18.0000	−	10.3923i	0.0942408	−	0.0544100i	−0.452139	−	0.891948i	$-0.649339\pi$
$191$	18.0000	−	10.3923i	0.0942408	−	0.0544100i	0.546380	+	0.837538i	$0.316006\pi$
$192$	−135.765	−	78.3837i	−0.707107	−	0.408248i
$193$	−152.000	+	263.272i	−0.787565	+	1.36410i	0.139890	+	0.990167i	$0.455325\pi$
$193$	−152.000	+	263.272i	−0.787565	+	1.36410i	−0.927455	+	0.373935i	$0.878008\pi$
$194$	83.4386	−	144.520i	0.430096	−	0.744948i
$195$			195.959i			1.00492i
$196$		0			0
$197$	198.000			1.00508			0.502538	−	0.864555i	$-0.332400\pi$
$197$	198.000			1.00508			0.502538	+	0.864555i	$0.332400\pi$
$198$	90.0000	+	51.9615i	0.454545	+	0.262432i
$199$	250.316	+	144.520i	1.25787	+	0.726231i	0.972660	−	0.232235i	$-0.0746038\pi$
$199$	250.316	+	144.520i	1.25787	+	0.726231i	0.285209	+	0.958465i	$0.407937\pi$
$200$	−28.0000	+	48.4974i	−0.140000	+	0.242487i
$201$	8.48528	+	14.6969i	0.0422153	+	0.0731191i
$202$	90.5097	+	156.767i	0.448068	+	0.776076i
$203$		0			0
$204$	−156.000	−	90.0666i	−0.764706	−	0.441503i
$205$	−68.0000	−	117.779i	−0.331707	−	0.574534i
$206$		−	88.1816i		−	0.428066i
$207$	72.0000	+	41.5692i	0.347826	+	0.200817i
$208$	113.137	−	195.959i	0.543928	−	0.942111i
$209$	−466.690			−2.23297
$210$		0			0
$211$			48.4974i			0.229846i	0.993374	+	0.114923i	$0.0366621\pi$
$211$			48.4974i			0.229846i	−0.993374	+	0.114923i	$0.963338\pi$
$212$	264.000			1.24528
$213$	59.3970	−	102.879i	0.278859	−	0.482998i
$214$			41.5692i			0.194249i
$215$	118.794	−	68.5857i	0.552530	−	0.319003i
$216$			235.151i			1.08866i
$217$		0			0
$218$	186.000	+	322.161i	0.853211	+	1.47780i
$219$	39.0000	−	22.5167i	0.178082	−	0.102816i
$220$	339.411	−	195.959i	1.54278	−	0.890724i
$221$	130.000	−	225.167i	0.588235	−	1.01885i
$222$	127.279	+	73.4847i	0.573330	+	0.331012i
$223$			342.929i			1.53780i	0.639371	+	0.768898i	$0.279195\pi$
$223$			342.929i			1.53780i	−0.639371	+	0.768898i	$0.720805\pi$
$224$		0			0
$225$	21.0000			0.0933333
$226$	12.0000	−	20.7846i	0.0530973	−	0.0919673i
$227$	86.9741	+	50.2145i	0.383146	+	0.221209i	0.679186	−	0.733966i	$-0.262333\pi$
$227$	86.9741	+	50.2145i	0.383146	+	0.221209i	−0.296040	+	0.955175i	$0.595666\pi$
$228$	−132.000	−	228.631i	−0.578947	−	1.00277i
$229$	−185.262	−	320.883i	−0.809004	−	1.40124i	−0.913554	−	0.406717i	$-0.866674\pi$
$229$	−185.262	−	320.883i	−0.809004	−	1.40124i	0.104550	−	0.994520i	$-0.466660\pi$
$230$	271.529	−	156.767i	1.18056	−	0.681597i
$231$		0			0
$232$	16.0000			0.0689655
$233$	−20.0000	−	34.6410i	−0.0858369	−	0.148674i	0.819911	−	0.572492i	$-0.194023\pi$
$233$	−20.0000	−	34.6410i	−0.0858369	−	0.148674i	−0.905748	+	0.423818i	$0.860690\pi$
$234$	−84.8528			−0.362619
$235$	120.000	+	69.2820i	0.510638	+	0.294817i
$236$		−	264.545i		−	1.12095i
$237$	−50.9117			−0.214817
$238$		0			0
$239$		−	387.979i		−	1.62334i	−0.584113	−	0.811672i	$-0.698558\pi$
$239$		−	387.979i		−	1.62334i	0.584113	−	0.811672i	$-0.301442\pi$
$240$	192.000	+	110.851i	0.800000	+	0.461880i
$241$	178.898	−	309.860i	0.742315	−	1.28573i	−0.209123	−	0.977889i	$-0.567061\pi$
$241$	178.898	−	309.860i	0.742315	−	1.28573i	0.951439	−	0.307839i	$-0.0996057\pi$
$242$	−358.000			−1.47934
$243$	133.643	−	77.1589i	0.549972	−	0.317526i
$244$	90.5097	−	156.767i	0.370941	−	0.642489i
$245$		0			0
$246$	−102.000	+	58.8897i	−0.414634	+	0.239389i
$247$	330.000	−	190.526i	1.33603	−	0.771359i
$248$	101.823	+	58.7878i	0.410578	+	0.237047i
$249$	−189.000	+	327.358i	−0.759036	+	1.31469i
$250$	−101.823	+	176.363i	−0.407294	+	0.705453i
$251$			51.4393i			0.204937i	0.994736	+	0.102469i	$0.0326741\pi$
$251$			51.4393i			0.204937i	−0.994736	+	0.102469i	$0.967326\pi$
$252$		0			0
$253$	−480.000			−1.89723
$254$	−252.000	−	145.492i	−0.992126	−	0.572804i
$255$	220.617	+	127.373i	0.865166	+	0.499504i
$256$	−128.000	−	221.703i	−0.500000	−	0.866025i
$257$	−21.9203	−	37.9671i	−0.0852930	−	0.147732i	0.820223	−	0.572044i	$-0.193849\pi$
$257$	−21.9203	−	37.9671i	−0.0852930	−	0.147732i	−0.905516	+	0.424312i	$0.860516\pi$
$258$	−59.3970	−	102.879i	−0.230221	−	0.398754i
$259$		0			0
$260$	−160.000	+	277.128i	−0.615385	+	1.06588i
$261$	−3.00000	−	5.19615i	−0.0114943	−	0.0199086i
$262$			151.868i			0.579650i
$263$	246.000	+	142.028i	0.935361	+	0.540031i	0.888503	−	0.458871i	$-0.151746\pi$
$263$	246.000	+	142.028i	0.935361	+	0.540031i	0.0468581	+	0.998902i	$0.485079\pi$
$264$	−169.706	−	293.939i	−0.642824	−	1.11340i
$265$	−373.352			−1.40888
$266$		0			0
$267$			58.8897i			0.220561i
$268$			27.7128i			0.103406i
$269$	−83.4386	+	144.520i	−0.310181	+	0.537249i	−0.978401	−	0.206714i	$-0.933723\pi$
$269$	−83.4386	+	144.520i	−0.310181	+	0.537249i	0.668221	+	0.743963i	$0.267056\pi$
$270$		−	332.554i		−	1.23168i
$271$	−364.867	+	210.656i	−1.34637	+	0.777329i	−0.987734	−	0.156147i	$-0.950093\pi$
$271$	−364.867	+	210.656i	−1.34637	+	0.777329i	−0.358639	+	0.933476i	$0.616759\pi$
$272$	−147.078	−	254.747i	−0.540729	−	0.936570i
$273$		0			0
$274$	−164.000	−	284.056i	−0.598540	−	1.03670i
$275$	−105.000	+	60.6218i	−0.381818	+	0.220443i
$276$	−135.765	−	235.151i	−0.491900	−	0.851996i
$277$	−5.00000	+	8.66025i	−0.0180505	+	0.0312645i	−0.874910	−	0.484286i	$-0.839079\pi$
$277$	−5.00000	+	8.66025i	−0.0180505	+	0.0312645i	0.856859	+	0.515551i	$0.172413\pi$
$278$	148.492	+	85.7321i	0.534145	+	0.308389i
$279$		−	44.0908i		−	0.158032i
$280$		0			0
$281$	352.000			1.25267			0.626335	−	0.779554i	$-0.284554\pi$
$281$	352.000			1.25267			0.626335	+	0.779554i	$0.284554\pi$
$282$	60.0000	−	103.923i	0.212766	−	0.368521i
$283$	−61.5183	−	35.5176i	−0.217379	−	0.125504i	0.387357	−	0.921930i	$-0.373388\pi$
$283$	−61.5183	−	35.5176i	−0.217379	−	0.125504i	−0.604736	+	0.796426i	$0.706721\pi$
$284$	168.000	−	96.9948i	0.591549	−	0.341531i
$285$	186.676	+	323.333i	0.655004	+	1.13450i
$286$	424.264	−	244.949i	1.48344	−	0.856465i
$287$		0			0
$288$	−48.0000	+	83.1384i	−0.166667	+	0.288675i
$289$	−24.5000	−	42.4352i	−0.0847751	−	0.146835i
$290$	−22.6274			−0.0780256
$291$	177.000	+	102.191i	0.608247	+	0.351172i
$292$	73.5391			0.251846
$293$	401.637			1.37077			0.685387	−	0.728179i	$-0.259633\pi$
$293$	401.637			1.37077			0.685387	+	0.728179i	$0.259633\pi$
$294$		0			0
$295$			374.123i			1.26821i
$296$	120.000	+	207.846i	0.405405	+	0.702183i
$297$	−254.558	+	440.908i	−0.857099	+	1.48454i
$298$	−228.000			−0.765101
$299$	339.411	−	195.959i	1.13515	−	0.655382i
$300$	−59.3970	−	34.2929i	−0.197990	−	0.114310i
$301$		0			0
$302$	12.0000	−	6.92820i	0.0397351	−	0.0229411i
$303$	−192.000	+	110.851i	−0.633663	+	0.365846i
$304$		−	431.110i		−	1.41813i
$305$	−128.000	+	221.703i	−0.419672	+	0.726893i
$306$	−55.1543	+	95.5301i	−0.180243	+	0.312190i
$307$			565.832i			1.84310i	0.388258	+	0.921551i	$0.373077\pi$
$307$			565.832i			1.84310i	−0.388258	+	0.921551i	$0.626923\pi$
$308$		0			0
$309$	108.000			0.349515
$310$	−144.000	−	83.1384i	−0.464516	−	0.268189i
$311$	−16.9706	−	9.79796i	−0.0545677	−	0.0315047i	0.472468	−	0.881348i	$-0.343363\pi$
$311$	−16.9706	−	9.79796i	−0.0545677	−	0.0315047i	−0.527036	+	0.849843i	$0.676697\pi$
$312$	240.000	+	138.564i	0.769231	+	0.444116i
$313$	−219.910	−	380.896i	−0.702589	−	1.21692i	−0.967555	−	0.252661i	$-0.918694\pi$
$313$	−219.910	−	380.896i	−0.702589	−	1.21692i	0.264966	−	0.964258i	$-0.414639\pi$
$314$	31.1127	+	53.8888i	0.0990850	+	0.171620i
$315$		0			0
$316$	−72.0000	−	41.5692i	−0.227848	−	0.131548i
$317$	57.0000	+	98.7269i	0.179811	+	0.311441i	0.941816	−	0.336130i	$-0.109118\pi$
$317$	57.0000	+	98.7269i	0.179811	+	0.311441i	−0.762005	+	0.647571i	$0.775785\pi$
$318$			323.333i			1.01677i
$319$	30.0000	+	17.3205i	0.0940439	+	0.0542963i
$320$	181.019	+	313.535i	0.565685	+	0.979796i
$321$	−50.9117			−0.158603
$322$		0			0
$323$		−	495.367i		−	1.53364i
$324$	−180.000			−0.555556
$325$	49.4975	−	85.7321i	0.152300	−	0.263791i
$326$			90.0666i			0.276278i
$327$	−394.566	+	227.803i	−1.20662	+	0.696644i
$328$	−192.333			−0.586381
$329$		0			0
$330$	240.000	+	415.692i	0.727273	+	1.25967i
$331$	−465.000	+	268.468i	−1.40483	+	0.811081i	−0.994884	−	0.101027i	$-0.967787\pi$
$331$	−465.000	+	268.468i	−1.40483	+	0.811081i	−0.409950	+	0.912108i	$0.634454\pi$
$332$	−534.573	+	308.636i	−1.61016	+	0.929626i
$333$	45.0000	−	77.9423i	0.135135	−	0.234061i
$334$	296.985	+	171.464i	0.889176	+	0.513366i
$335$		−	39.1918i		−	0.116991i
$336$		0			0
$337$	450.000			1.33531			0.667656	−	0.744470i	$-0.267298\pi$
$337$	450.000			1.33531			0.667656	+	0.744470i	$0.267298\pi$
$338$	−31.0000	+	53.6936i	−0.0917160	+	0.158857i
$339$	25.4558	+	14.6969i	0.0750910	+	0.0433538i
$340$	208.000	+	360.267i	0.611765	+	1.05961i
$341$	127.279	+	220.454i	0.373253	+	0.646493i
$342$	−140.007	+	80.8332i	−0.409378	+	0.236354i
$343$		0			0
$344$		−	193.990i		−	0.563924i
$345$	192.000	+	332.554i	0.556522	+	0.963924i
$346$	−209.304			−0.604924
$347$	−27.0000	−	15.5885i	−0.0778098	−	0.0449235i	0.460590	−	0.887613i	$-0.347638\pi$
$347$	−27.0000	−	15.5885i	−0.0778098	−	0.0449235i	−0.538400	+	0.842689i	$0.680971\pi$
$348$			19.5959i			0.0563101i
$349$	−14.1421			−0.0405219			−0.0202609	−	0.999795i	$-0.506450\pi$
$349$	−14.1421			−0.0405219			−0.0202609	+	0.999795i	$0.506450\pi$
$350$		0			0
$351$		−	415.692i		−	1.18431i
$352$		−	554.256i		−	1.57459i
$353$	−147.785	+	255.972i	−0.418655	+	0.725132i	−0.995804	−	0.0915065i	$-0.970832\pi$
$353$	−147.785	+	255.972i	−0.418655	+	0.725132i	0.577149	+	0.816639i	$0.304165\pi$
$354$	324.000			0.915254
$355$	−237.588	+	137.171i	−0.669262	+	0.386398i
$356$	−48.0833	+	83.2827i	−0.135065	+	0.233940i
$357$		0			0
$358$	348.000	−	200.918i	0.972067	−	0.561223i
$359$	−66.0000	+	38.1051i	−0.183844	+	0.106142i	−0.589097	−	0.808062i	$-0.700517\pi$
$359$	−66.0000	+	38.1051i	−0.183844	+	0.106142i	0.405253	+	0.914204i	$0.367183\pi$
$360$	67.8823	−	117.576i	0.188562	−	0.326599i
$361$	182.500	−	316.099i	0.505540	−	0.875621i
$362$	−302.642	+	524.191i	−0.836027	+	1.44804i
$363$		−	438.459i		−	1.20788i
$364$		0			0
$365$	−104.000			−0.284932
$366$	192.000	+	110.851i	0.524590	+	0.302872i
$367$	−610.940	−	352.727i	−1.66469	−	0.961108i	−0.970431	−	0.241380i	$-0.922400\pi$
$367$	−610.940	−	352.727i	−1.66469	−	0.961108i	−0.694257	−	0.719727i	$-0.744267\pi$
$368$		−	443.405i		−	1.20490i
$369$	36.0624	+	62.4620i	0.0977302	+	0.169274i
$370$	−169.706	−	293.939i	−0.458664	−	0.794429i
$371$		0			0
$372$	−72.0000	+	124.708i	−0.193548	+	0.335236i
$373$	1.00000	+	1.73205i	0.00268097	+	0.00464357i	0.867363	−	0.497676i	$-0.165813\pi$
$373$	1.00000	+	1.73205i	0.00268097	+	0.00464357i	−0.864682	+	0.502320i	$0.832480\pi$
$374$		−	636.867i		−	1.70285i
$375$	−216.000	−	124.708i	−0.576000	−	0.332554i
$376$	169.706	−	97.9796i	0.451345	−	0.260584i
$377$	−28.2843			−0.0750246
$378$		0			0
$379$			509.223i			1.34360i	0.740734	+	0.671798i	$0.234478\pi$
$379$			509.223i			1.34360i	−0.740734	+	0.671798i	$0.765522\pi$
$380$			609.682i			1.60443i
$381$	178.191	−	308.636i	0.467693	−	0.810067i
$382$			41.5692i			0.108820i
$383$	80.6102	−	46.5403i	0.210470	−	0.121515i	−0.391060	−	0.920365i	$-0.627891\pi$
$383$	80.6102	−	46.5403i	0.210470	−	0.121515i	0.601530	+	0.798850i	$0.294558\pi$
$384$	271.529	−	156.767i	0.707107	−	0.408248i
$385$		0			0
$386$	−304.000	−	526.543i	−0.787565	−	1.36410i
$387$	−63.0000	+	36.3731i	−0.162791	+	0.0939873i
$388$	166.877	+	289.040i	0.430096	+	0.744948i
$389$	107.000	−	185.329i	0.275064	−	0.476425i	−0.695087	−	0.718926i	$-0.744634\pi$
$389$	107.000	−	185.329i	0.275064	−	0.476425i	0.970151	+	0.242500i	$0.0779675\pi$
$390$	−339.411	−	195.959i	−0.870285	−	0.502459i
$391$		−	509.494i		−	1.30305i
$392$		0			0
$393$	−186.000			−0.473282
$394$	−198.000	+	342.946i	−0.502538	+	0.870421i
$395$	101.823	+	58.7878i	0.257781	+	0.148830i
$396$	−180.000	+	103.923i	−0.454545	+	0.262432i
$397$	111.723	+	193.510i	0.281418	+	0.487430i	0.971734	−	0.236078i	$-0.0758620\pi$
$397$	111.723	+	193.510i	0.281418	+	0.487430i	−0.690316	+	0.723508i	$0.742529\pi$
$398$	−500.632	+	289.040i	−1.25787	+	0.726231i
$399$		0			0
$400$	−56.0000	−	96.9948i	−0.140000	−	0.242487i
$401$	−251.000	−	434.745i	−0.625935	−	1.08415i	−0.988359	−	0.152138i	$-0.951384\pi$
$401$	−251.000	−	434.745i	−0.625935	−	1.08415i	0.362424	−	0.932013i	$-0.381949\pi$
$402$	−33.9411			−0.0844307
$403$	−180.000	−	103.923i	−0.446650	−	0.257874i
$404$	−362.039			−0.896135
$405$	254.558			0.628539
$406$		0			0
$407$			519.615i			1.27670i
$408$	312.000	−	180.133i	0.764706	−	0.441503i
$409$	−127.986	+	221.679i	−0.312925	+	0.542002i	−0.978994	−	0.203888i	$-0.934642\pi$
$409$	−127.986	+	221.679i	−0.312925	+	0.542002i	0.666069	+	0.745890i	$0.267976\pi$
$410$	272.000			0.663415
$411$	347.897	−	200.858i	0.846464	−	0.488706i
$412$	152.735	+	88.1816i	0.370716	+	0.214033i
$413$		0			0
$414$	−144.000	+	83.1384i	−0.347826	+	0.200817i
$415$	756.000	−	436.477i	1.82169	−	1.05175i
$416$	226.274	+	391.918i	0.543928	+	0.942111i
$417$	−105.000	+	181.865i	−0.251799	+	0.436128i
$418$	466.690	−	808.332i	1.11648	−	1.93381i
$419$			17.1464i			0.0409223i	0.999791	+	0.0204611i	$0.00651343\pi$
$419$			17.1464i			0.0409223i	−0.999791	+	0.0204611i	$0.993487\pi$
$420$		0			0
$421$	−614.000			−1.45843			−0.729216	−	0.684283i	$-0.760115\pi$
$421$	−614.000			−1.45843			−0.729216	+	0.684283i	$0.760115\pi$
$422$	−84.0000	−	48.4974i	−0.199052	−	0.114923i
$423$	−63.6396	−	36.7423i	−0.150448	−	0.0868613i
$424$	−264.000	+	457.261i	−0.622642	+	1.07845i
$425$	−64.3467	−	111.452i	−0.151404	−	0.262239i
$426$	118.794	+	205.757i	0.278859	+	0.482998i
$427$		0			0
$428$	−72.0000	−	41.5692i	−0.168224	−	0.0971243i
$429$	300.000	+	519.615i	0.699301	+	1.21122i
$430$			274.343i			0.638007i
$431$	288.000	+	166.277i	0.668213	+	0.385793i	0.795399	−	0.606086i	$-0.207261\pi$
$431$	288.000	+	166.277i	0.668213	+	0.385793i	−0.127186	+	0.991879i	$0.540594\pi$
$432$	−407.294	−	235.151i	−0.942809	−	0.544331i
$433$	−202.233			−0.467050			−0.233525	−	0.972351i	$-0.575026\pi$
$433$	−202.233			−0.467050			−0.233525	+	0.972351i	$0.575026\pi$
$434$		0			0
$435$		−	27.7128i		−	0.0637076i
$436$	−744.000			−1.70642
$437$	373.352	−	646.665i	0.854353	−	1.47978i
$438$			90.0666i			0.205632i
$439$	526.087	−	303.737i	1.19838	−	0.691883i	0.238184	−	0.971220i	$-0.423448\pi$
$439$	526.087	−	303.737i	1.19838	−	0.691883i	0.960193	+	0.279337i	$0.0901146\pi$
$440$			783.837i			1.78145i
$441$		0			0
$442$	260.000	+	450.333i	0.588235	+	1.01885i
$443$	−66.0000	+	38.1051i	−0.148984	+	0.0860161i	−0.572639	−	0.819808i	$-0.694080\pi$
$443$	−66.0000	+	38.1051i	−0.148984	+	0.0860161i	0.423655	+	0.905824i	$0.360747\pi$
$444$	−254.558	+	146.969i	−0.573330	+	0.331012i
$445$	68.0000	−	117.779i	0.152809	−	0.264673i
$446$	−593.970	−	342.929i	−1.33177	−	0.768898i
$447$		−	279.242i		−	0.624702i
$448$		0			0
$449$	−642.000			−1.42984			−0.714922	−	0.699204i	$-0.753538\pi$
$449$	−642.000			−1.42984			−0.714922	+	0.699204i	$0.753538\pi$
$450$	−21.0000	+	36.3731i	−0.0466667	+	0.0808290i
$451$	−360.624	−	208.207i	−0.799611	−	0.461655i
$452$	24.0000	+	41.5692i	0.0530973	+	0.0919673i
$453$	8.48528	+	14.6969i	0.0187313	+	0.0324436i
$454$	−173.948	+	100.429i	−0.383146	+	0.221209i
$455$		0			0
$456$	528.000			1.15789
$457$	−76.0000	−	131.636i	−0.166302	−	0.288043i	0.770815	−	0.637059i	$-0.219849\pi$
$457$	−76.0000	−	131.636i	−0.166302	−	0.288043i	−0.937117	+	0.349016i	$0.886516\pi$
$458$	741.048			1.61801
$459$	−468.000	−	270.200i	−1.01961	−	0.588671i
$460$			627.069i			1.36319i
$461$	183.848			0.398802			0.199401	−	0.979918i	$-0.436100\pi$
$461$	183.848			0.398802			0.199401	+	0.979918i	$0.436100\pi$
$462$		0			0
$463$		−	96.9948i		−	0.209492i	−0.994499	−	0.104746i	$-0.966597\pi$
$463$		−	96.9948i		−	0.209492i	0.994499	−	0.104746i	$-0.0334030\pi$
$464$	−16.0000	+	27.7128i	−0.0344828	+	0.0597259i
$465$	101.823	−	176.363i	0.218975	−	0.379276i
$466$	80.0000			0.171674
$467$	−201.525	+	116.351i	−0.431532	+	0.249145i	−0.699999	−	0.714144i	$-0.746816\pi$
$467$	−201.525	+	116.351i	−0.431532	+	0.249145i	0.268467	+	0.963289i	$0.413483\pi$
$468$	84.8528	−	146.969i	0.181309	−	0.314037i
$469$		0			0
$470$	−240.000	+	138.564i	−0.510638	+	0.294817i
$471$	−66.0000	+	38.1051i	−0.140127	+	0.0809026i
$472$	458.205	+	264.545i	0.970774	+	0.560476i
$473$	210.000	−	363.731i	0.443975	−	0.768987i
$474$	50.9117	−	88.1816i	0.107409	−	0.186037i
$475$		−	188.611i		−	0.397075i
$476$		0			0
$477$	198.000			0.415094
$478$	672.000	+	387.979i	1.40586	+	0.811672i
$479$	784.889	+	453.156i	1.63860	+	0.946045i	0.981317	+	0.192400i	$0.0616271\pi$
$479$	784.889	+	453.156i	1.63860	+	0.946045i	0.657282	+	0.753645i	$0.271706\pi$
$480$	−384.000	+	221.703i	−0.800000	+	0.461880i
$481$	−212.132	−	367.423i	−0.441023	−	0.763874i
$482$	357.796	+	619.721i	0.742315	+	1.28573i
$483$		0			0
$484$	358.000	−	620.074i	0.739669	−	1.28115i
$485$	−236.000	−	408.764i	−0.486598	−	0.842812i
$486$			308.636i			0.635053i
$487$	−468.000	−	270.200i	−0.960986	−	0.554825i	−0.0645094	−	0.997917i	$-0.520548\pi$
$487$	−468.000	−	270.200i	−0.960986	−	0.554825i	−0.896476	+	0.443092i	$0.853882\pi$
$488$	181.019	+	313.535i	0.370941	+	0.642489i
$489$	−110.309			−0.225580
$490$		0			0
$491$			436.477i			0.888955i	0.895790	+	0.444477i	$0.146611\pi$
$491$			436.477i			0.888955i	−0.895790	+	0.444477i	$0.853389\pi$
$492$		−	235.559i		−	0.478778i
$493$	−18.3848	+	31.8434i	−0.0372916	+	0.0645910i
$494$			762.102i			1.54272i
$495$	254.558	−	146.969i	0.514259	−	0.296908i
$496$	−203.647	+	117.576i	−0.410578	+	0.237047i
$497$		0			0
$498$	−378.000	−	654.715i	−0.759036	−	1.31469i
$499$	690.000	−	398.372i	1.38277	−	0.798340i	0.390279	−	0.920697i	$-0.372378\pi$
$499$	690.000	−	398.372i	1.38277	−	0.798340i	0.992486	+	0.122356i	$0.0390451\pi$
$500$	−203.647	−	352.727i	−0.407294	−	0.705453i
$501$	−210.000	+	363.731i	−0.419162	+	0.726009i
$502$	−89.0955	−	51.4393i	−0.177481	−	0.102469i
$503$		−	137.171i		−	0.272707i	−0.990660	−	0.136353i	$-0.956462\pi$
$503$		−	137.171i		−	0.272707i	0.990660	−	0.136353i	$-0.0435382\pi$
$504$		0			0
$505$	512.000			1.01386
$506$	480.000	−	831.384i	0.948617	−	1.64305i
$507$	−65.7609	−	37.9671i	−0.129706	−	0.0748858i
$508$	504.000	−	290.985i	0.992126	−	0.572804i
$509$	230.517	+	399.267i	0.452882	+	0.784414i	0.998564	−	0.0535782i	$-0.0170626\pi$
$509$	230.517	+	399.267i	0.452882	+	0.784414i	−0.545682	+	0.837992i	$0.683729\pi$
$510$	−441.235	+	254.747i	−0.865166	+	0.499504i
$511$		0			0
$512$	512.000			1.00000
$513$	−396.000	−	685.892i	−0.771930	−	1.33702i
$514$	87.6812			0.170586
$515$	−216.000	−	124.708i	−0.419417	−	0.242151i
$516$	237.588			0.460442
$517$	424.264			0.820627
$518$		0			0
$519$		−	256.344i		−	0.493918i
$520$	−320.000	−	554.256i	−0.615385	−	1.06588i
$521$	−28.9914	+	50.2145i	−0.0556456	+	0.0963811i	−0.892506	−	0.451035i	$-0.851055\pi$
$521$	−28.9914	+	50.2145i	−0.0556456	+	0.0963811i	0.836861	+	0.547416i	$0.184388\pi$
$522$	12.0000			0.0229885
$523$	−231.224	+	133.497i	−0.442111	+	0.255253i	−0.704493	−	0.709711i	$-0.748825\pi$
$523$	−231.224	+	133.497i	−0.442111	+	0.255253i	0.262382	+	0.964964i	$0.415492\pi$
$524$	−263.044	−	151.868i	−0.501992	−	0.289825i
$525$		0			0
$526$	−492.000	+	284.056i	−0.935361	+	0.540031i
$527$	−234.000	+	135.100i	−0.444023	+	0.256357i
$528$	678.823			1.28565
$529$	119.500	−	206.980i	0.225898	−	0.391267i
$530$	373.352	−	646.665i	0.704438	−	1.22012i
$531$		−	198.409i		−	0.373651i
$532$		0			0
$533$	340.000			0.637899
$534$	−102.000	−	58.8897i	−0.191011	−	0.110280i
$535$	101.823	+	58.7878i	0.190324	+	0.109884i
$536$	−48.0000	−	27.7128i	−0.0895522	−	0.0517030i
$537$	246.073	+	426.211i	0.458237	+	0.793689i
$538$	−166.877	−	289.040i	−0.310181	−	0.537249i
$539$		0			0
$540$	576.000	+	332.554i	1.06667	+	0.615840i
$541$	281.000	+	486.706i	0.519409	+	0.899642i	0.999746	+	0.0225579i	$0.00718102\pi$
$541$	281.000	+	486.706i	0.519409	+	0.899642i	−0.480337	+	0.877084i	$0.659486\pi$
$542$		−	842.624i		−	1.55466i
$543$	−642.000	−	370.659i	−1.18232	−	0.682613i
$544$	588.313			1.08146
$545$	1052.17			1.93060
$546$		0			0
$547$			315.233i			0.576295i	0.957586	+	0.288147i	$0.0930393\pi$
$547$			315.233i			0.576295i	−0.957586	+	0.288147i	$0.906961\pi$
$548$	656.000			1.19708
$549$	67.8823	−	117.576i	0.123647	−	0.214163i
$550$		−	242.487i		−	0.440886i
$551$	−46.6690	+	26.9444i	−0.0846988	+	0.0489009i
$552$	543.058			0.983801
$553$		0			0
$554$	−10.0000	−	17.3205i	−0.0180505	−	0.0312645i
$555$	360.000	−	207.846i	0.648649	−	0.374497i
$556$	−296.985	+	171.464i	−0.534145	+	0.308389i
$557$	177.000	−	306.573i	0.317774	−	0.550400i	−0.662249	−	0.749283i	$-0.730398\pi$
$557$	177.000	−	306.573i	0.317774	−	0.550400i	0.980023	+	0.198883i	$0.0637314\pi$
$558$	76.3675	+	44.0908i	0.136859	+	0.0790158i
$559$			342.929i			0.613468i
$560$		0			0
$561$	780.000			1.39037
$562$	−352.000	+	609.682i	−0.626335	+	1.08484i
$563$	−239.709	−	138.396i	−0.425771	−	0.245819i	0.271772	−	0.962362i	$-0.412390\pi$
$563$	−239.709	−	138.396i	−0.425771	−	0.245819i	−0.697543	+	0.716542i	$0.745724\pi$
$564$	120.000	+	207.846i	0.212766	+	0.368521i
$565$	−33.9411	−	58.7878i	−0.0600728	−	0.104049i
$566$	123.037	−	71.0352i	0.217379	−	0.125504i
$567$		0			0
$568$			387.979i			0.683062i
$569$	491.000	+	850.437i	0.862917	+	1.49462i	0.869100	+	0.494636i	$0.164699\pi$
$569$	491.000	+	850.437i	0.862917	+	1.49462i	−0.00618290	+	0.999981i	$0.501968\pi$
$570$	−746.705			−1.31001
$571$	−69.0000	−	39.8372i	−0.120841	−	0.0697674i	0.438361	−	0.898799i	$-0.355559\pi$
$571$	−69.0000	−	39.8372i	−0.120841	−	0.0697674i	−0.559202	+	0.829031i	$0.688892\pi$
$572$			979.796i			1.71293i
$573$	−50.9117			−0.0888511
$574$		0			0
$575$		−	193.990i		−	0.337373i
$576$	−96.0000	−	166.277i	−0.166667	−	0.288675i
$577$	79.9031	−	138.396i	0.138480	−	0.239855i	−0.788441	−	0.615110i	$-0.789112\pi$
$577$	79.9031	−	138.396i	0.138480	−	0.239855i	0.926922	+	0.375255i	$0.122445\pi$
$578$	98.0000			0.169550
$579$	644.881	−	372.322i	1.11378	−	0.643044i
$580$	22.6274	−	39.1918i	0.0390128	−	0.0675721i
$581$		0			0
$582$	−354.000	+	204.382i	−0.608247	+	0.351172i
$583$	−990.000	+	571.577i	−1.69811	+	0.980406i
$584$	−73.5391	+	127.373i	−0.125923	+	0.218105i
$585$	−120.000	+	207.846i	−0.205128	+	0.355292i
$586$	−401.637	+	695.655i	−0.685387	+	1.18712i
$587$			531.539i			0.905518i	0.891633	+	0.452759i	$0.149560\pi$
$587$			531.539i			0.905518i	−0.891633	+	0.452759i	$0.850440\pi$
$588$		0			0
$589$	−396.000			−0.672326
$590$	−648.000	−	374.123i	−1.09831	−	0.634107i
$591$	−420.021	−	242.499i	−0.710696	−	0.410321i
$592$	−480.000			−0.810811
$593$	−348.604	−	603.799i	−0.587864	−	1.01821i	−0.994512	−	0.104626i	$-0.966635\pi$
$593$	−348.604	−	603.799i	−0.587864	−	1.01821i	0.406647	−	0.913585i	$-0.366698\pi$
$594$	−509.117	−	881.816i	−0.857099	−	1.48454i
$595$		0			0
$596$	228.000	−	394.908i	0.382550	−	0.662597i
$597$	−354.000	−	613.146i	−0.592965	−	1.02705i
$598$			783.837i			1.31076i
$599$	876.000	+	505.759i	1.46244	+	0.844339i	0.999124	−	0.0418557i	$-0.0133270\pi$
$599$	876.000	+	505.759i	1.46244	+	0.844339i	0.463314	+	0.886194i	$0.346660\pi$
$600$	118.794	−	68.5857i	0.197990	−	0.114310i
$601$	−816.001			−1.35774			−0.678870	−	0.734259i	$-0.737530\pi$
$601$	−816.001			−1.35774			−0.678870	+	0.734259i	$0.737530\pi$
$602$		0			0
$603$			20.7846i			0.0344687i
$604$			27.7128i			0.0458821i
$605$	−506.288	+	876.917i	−0.836840	+	1.44945i
$606$		−	443.405i		−	0.731691i
$607$	−127.279	+	73.4847i	−0.209686	+	0.121062i	−0.601165	−	0.799125i	$-0.705297\pi$
$607$	−127.279	+	73.4847i	−0.209686	+	0.121062i	0.391480	+	0.920187i	$0.371963\pi$
$608$	746.705	+	431.110i	1.22813	+	0.709063i
$609$		0			0
$610$	−256.000	−	443.405i	−0.419672	−	0.726893i
$611$	−300.000	+	173.205i	−0.490998	+	0.283478i
$612$	−110.309	−	191.060i	−0.180243	−	0.312190i
$613$	−369.000	+	639.127i	−0.601958	+	1.04262i	0.390567	+	0.920575i	$0.372279\pi$
$613$	−369.000	+	639.127i	−0.601958	+	1.04262i	−0.992524	+	0.122047i	$0.961054\pi$
$614$	−980.050	−	565.832i	−1.59617	−	0.921551i
$615$			333.131i			0.541676i
$616$		0			0
$617$	−754.000			−1.22204			−0.611021	−	0.791614i	$-0.709241\pi$
$617$	−754.000			−1.22204			−0.611021	+	0.791614i	$0.709241\pi$
$618$	−108.000	+	187.061i	−0.174757	+	0.302688i
$619$	680.944	+	393.143i	1.10007	+	0.635126i	0.936240	−	0.351362i	$-0.114281\pi$
$619$	680.944	+	393.143i	1.10007	+	0.635126i	0.163831	+	0.986488i	$0.447615\pi$
$620$	288.000	−	166.277i	0.464516	−	0.268189i
$621$	−407.294	−	705.453i	−0.655867	−	1.13600i
$622$	33.9411	−	19.5959i	0.0545677	−	0.0315047i
$623$		0			0
$624$	−480.000	+	277.128i	−0.769231	+	0.444116i
$625$	375.500	+	650.385i	0.600800	+	1.04062i
$626$	879.641			1.40518
$627$	990.000	+	571.577i	1.57895	+	0.911606i
$628$	−124.451			−0.198170
$629$	−551.543			−0.876857
$630$		0			0
$631$			48.4974i			0.0768580i	0.999261	+	0.0384290i	$0.0122353\pi$
$631$			48.4974i			0.0768580i	−0.999261	+	0.0384290i	$0.987765\pi$
$632$	144.000	−	83.1384i	0.227848	−	0.131548i
$633$	59.3970	−	102.879i	0.0938341	−	0.162525i
$634$	−228.000			−0.359621
$635$	−712.764	+	411.514i	−1.12246	+	0.648054i
$636$	−560.029	−	323.333i	−0.880548	−	0.508385i
$637$		0			0
$638$	−60.0000	+	34.6410i	−0.0940439	+	0.0542963i
$639$	126.000	−	72.7461i	0.197183	−	0.113844i
$640$	−724.077			−1.13137
$641$	−425.000	+	736.122i	−0.663027	+	1.14840i	0.316790	+	0.948496i	$0.397395\pi$
$641$	−425.000	+	736.122i	−0.663027	+	1.14840i	−0.979816	+	0.199900i	$0.935938\pi$
$642$	50.9117	−	88.1816i	0.0793017	−	0.137355i
$643$		−	565.832i		−	0.879988i	−0.898001	−	0.439994i	$-0.854981\pi$
$643$		−	565.832i		−	0.879988i	0.898001	−	0.439994i	$-0.145019\pi$
$644$		0			0
$645$	−336.000			−0.520930
$646$	858.000	+	495.367i	1.32817	+	0.766821i
$647$	−224.860	−	129.823i	−0.347542	−	0.200654i	0.316060	−	0.948739i	$-0.397640\pi$
$647$	−224.860	−	129.823i	−0.347542	−	0.200654i	−0.663602	+	0.748086i	$0.730973\pi$
$648$	180.000	−	311.769i	0.277778	−	0.481125i
$649$	572.756	+	992.043i	0.882522	+	1.52857i
$650$	98.9949	+	171.464i	0.152300	+	0.263791i
$651$		0			0
$652$	−156.000	−	90.0666i	−0.239264	−	0.138139i
$653$	29.0000	+	50.2295i	0.0444104	+	0.0769211i	0.887376	−	0.461046i	$-0.152526\pi$
$653$	29.0000	+	50.2295i	0.0444104	+	0.0769211i	−0.842966	+	0.537967i	$0.819192\pi$
$654$		−	911.210i		−	1.39329i
$655$	372.000	+	214.774i	0.567939	+	0.327900i
$656$	192.333	−	333.131i	0.293191	−	0.507821i
$657$	55.1543			0.0839488
$658$		0			0
$659$		−	1139.69i		−	1.72942i	−0.502269	−	0.864711i	$-0.667501\pi$
$659$		−	1139.69i		−	1.72942i	0.502269	−	0.864711i	$-0.332499\pi$
$660$	−960.000			−1.45455
$661$	−251.730	+	436.009i	−0.380832	+	0.659621i	−0.991181	−	0.132512i	$-0.957696\pi$
$661$	−251.730	+	436.009i	−0.380832	+	0.659621i	0.610349	+	0.792132i	$0.291029\pi$
$662$		−	1073.87i		−	1.62216i
$663$	−551.543	+	318.434i	−0.831890	+	0.480292i
$664$		−	1234.54i		−	1.85925i
$665$		0			0
$666$	90.0000	+	155.885i	0.135135	+	0.234061i
$667$	−48.0000	+	27.7128i	−0.0719640	+	0.0415484i
$668$	−593.970	+	342.929i	−0.889176	+	0.513366i
$669$	420.000	−	727.461i	0.627803	−	1.08739i
$670$	67.8823	+	39.1918i	0.101317	+	0.0584953i
$671$			783.837i			1.16816i
$672$		0			0
$673$	156.000			0.231798			0.115899	−	0.993261i	$-0.463025\pi$
$673$	156.000			0.231798			0.115899	+	0.993261i	$0.463025\pi$
$674$	−450.000	+	779.423i	−0.667656	+	1.15641i
$675$	−178.191	−	102.879i	−0.263987	−	0.152413i
$676$	−62.0000	−	107.387i	−0.0917160	−	0.158857i
$677$	−7.07107	−	12.2474i	−0.0104447	−	0.0180908i	0.860756	−	0.509018i	$-0.169991\pi$
$677$	−7.07107	−	12.2474i	−0.0104447	−	0.0180908i	−0.871201	+	0.490927i	$0.836658\pi$
$678$	−50.9117	+	29.3939i	−0.0750910	+	0.0433538i
$679$		0			0
$680$	−832.000			−1.22353
$681$	−123.000	−	213.042i	−0.180617	−	0.312837i
$682$	−509.117			−0.746506
$683$	1086.00	+	627.002i	1.59004	+	0.918012i	0.993298	+	0.115582i	$0.0368733\pi$
$683$	1086.00	+	627.002i	1.59004	+	0.918012i	0.596746	+	0.802430i	$0.296460\pi$
$684$		−	323.333i		−	0.472709i
$685$	−927.724			−1.35434
$686$		0			0
$687$			907.595i			1.32110i
$688$	336.000	+	193.990i	0.488372	+	0.281962i
$689$	466.690	−	808.332i	0.677345	−	1.17320i
$690$	−768.000			−1.11304
$691$	−290.621	+	167.790i	−0.420580	+	0.242822i	−0.695325	−	0.718695i	$-0.744740\pi$
$691$	−290.621	+	167.790i	−0.420580	+	0.242822i	0.274745	+	0.961517i	$0.411406\pi$
$692$	209.304	−	362.524i	0.302462	−	0.523879i
$693$		0			0
$694$	54.0000	−	31.1769i	0.0778098	−	0.0449235i
$695$	420.000	−	242.487i	0.604317	−	0.348902i
$696$	−33.9411	−	19.5959i	−0.0487660	−	0.0281551i
$697$	221.000	−	382.783i	0.317073	−	0.549187i
$698$	14.1421	−	24.4949i	0.0202609	−	0.0350930i
$699$			97.9796i			0.140171i
$700$		0			0
$701$	814.000			1.16120			0.580599	−	0.814190i	$-0.302818\pi$
$701$	814.000			1.16120			0.580599	+	0.814190i	$0.302818\pi$
$702$	720.000	+	415.692i	1.02564	+	0.592154i
$703$	−700.036	−	404.166i	−0.995783	−	0.574916i
$704$	960.000	+	554.256i	1.36364	+	0.787296i
$705$	−169.706	−	293.939i	−0.240717	−	0.416934i
$706$	−295.571	−	511.943i	−0.418655	−	0.725132i
$707$		0			0
$708$	−324.000	+	561.184i	−0.457627	+	0.792633i
$709$	−153.000	−	265.004i	−0.215797	−	0.373771i	0.737722	−	0.675105i	$-0.235902\pi$
$709$	−153.000	−	265.004i	−0.215797	−	0.373771i	−0.953519	+	0.301334i	$0.902568\pi$
$710$		−	548.686i		−	0.772797i
$711$	−54.0000	−	31.1769i	−0.0759494	−	0.0438494i
$712$	−96.1665	−	166.565i	−0.135065	−	0.233940i
$713$	−407.294			−0.571239
$714$		0			0
$715$		−	1385.64i		−	1.93796i
$716$			803.672i			1.12245i
$717$	−475.176	+	823.029i	−0.662728	+	1.14788i
$718$		−	152.420i		−	0.212285i
$719$	258.801	−	149.419i	0.359946	−	0.207815i	−0.309111	−	0.951026i	$-0.600032\pi$
$719$	258.801	−	149.419i	0.359946	−	0.207815i	0.669057	+	0.743211i	$0.266698\pi$
$720$	135.765	+	235.151i	0.188562	+	0.326599i
$721$		0			0
$722$	365.000	+	632.199i	0.505540	+	0.875621i
$723$	−759.000	+	438.209i	−1.04979	+	0.606098i
$724$	−605.283	−	1048.38i	−0.836027	−	1.44804i
$725$	−7.00000	+	12.1244i	−0.00965517	+	0.0167232i
$726$	759.433	+	438.459i	1.04605	+	0.603938i
$727$			377.221i			0.518874i	0.965760	+	0.259437i	$0.0835370\pi$
$727$			377.221i			0.518874i	−0.965760	+	0.259437i	$0.916463\pi$
$728$		0			0
$729$	−783.000			−1.07407
$730$	104.000	−	180.133i	0.142466	−	0.246758i
$731$	386.080	+	222.904i	0.528154	+	0.304930i
$732$	−384.000	+	221.703i	−0.524590	+	0.302872i
$733$	−214.960	−	372.322i	−0.293261	−	0.507943i	0.681318	−	0.731988i	$-0.261407\pi$
$733$	−214.960	−	372.322i	−0.293261	−	0.507943i	−0.974579	+	0.224045i	$0.928074\pi$
$734$	1221.88	−	705.453i	1.66469	−	0.961108i
$735$		0			0
$736$	768.000	+	443.405i	1.04348	+	0.602452i
$737$	−60.0000	−	103.923i	−0.0814111	−	0.141008i
$738$	−144.250			−0.195460
$739$	−867.000	−	500.563i	−1.17321	−	0.677351i	−0.218774	−	0.975776i	$-0.570206\pi$
$739$	−867.000	−	500.563i	−1.17321	−	0.677351i	−0.954433	+	0.298424i	$0.903539\pi$
$740$	678.823			0.917328
$741$	−933.381			−1.25962
$742$		0			0
$743$		−	436.477i		−	0.587452i	−0.955890	−	0.293726i	$-0.905105\pi$
$743$		−	436.477i		−	0.587452i	0.955890	−	0.293726i	$-0.0948953\pi$
$744$	−144.000	−	249.415i	−0.193548	−	0.335236i
$745$	−322.441	+	558.484i	−0.432806	+	0.749642i
$746$	−4.00000			−0.00536193
$747$	−400.930	+	231.477i	−0.536720	+	0.309875i
$748$	1103.09	+	636.867i	1.47471	+	0.851427i
$749$		0			0
$750$	432.000	−	249.415i	0.576000	−	0.332554i
$751$	−528.000	+	304.841i	−0.703063	+	0.405913i	−0.808487	−	0.588514i	$-0.799713\pi$
$751$	−528.000	+	304.841i	−0.703063	+	0.405913i	0.105424	+	0.994427i	$0.466380\pi$
$752$			391.918i			0.521168i
$753$	63.0000	−	109.119i	0.0836653	−	0.144913i
$754$	28.2843	−	48.9898i	0.0375123	−	0.0649732i
$755$		−	39.1918i		−	0.0519097i
$756$		0			0
$757$	786.000			1.03831			0.519155	−	0.854680i	$-0.326247\pi$
$757$	786.000			1.03831			0.519155	+	0.854680i	$0.326247\pi$
$758$	−882.000	−	509.223i	−1.16359	−	0.671798i
$759$	1018.23	+	587.878i	1.34155	+	0.774542i
$760$	−1056.00	−	609.682i	−1.38947	−	0.802213i
$761$	403.758	+	699.329i	0.530562	+	0.918961i	0.999364	+	0.0356576i	$0.0113526\pi$
$761$	403.758	+	699.329i	0.530562	+	0.918961i	−0.468802	+	0.883303i	$0.655314\pi$
$762$	356.382	+	617.271i	0.467693	+	0.810067i
$763$		0			0
$764$	−72.0000	−	41.5692i	−0.0942408	−	0.0544100i
$765$	156.000	+	270.200i	0.203922	+	0.353203i
$766$			186.161i			0.243030i
$767$	−810.000	−	467.654i	−1.05606	−	0.609718i
$768$			627.069i			0.816497i
$769$	926.310			1.20456			0.602282	−	0.798283i	$-0.294258\pi$
$769$	926.310			1.20456			0.602282	+	0.798283i	$0.294258\pi$
$770$		0			0
$771$			107.387i			0.139283i
$772$	1216.00			1.57513
$773$	659.024	−	1141.46i	0.852553	−	1.47667i	−0.0263436	−	0.999653i	$-0.508386\pi$
$773$	659.024	−	1141.46i	0.852553	−	1.47667i	0.878897	−	0.477012i	$-0.158280\pi$
$774$		−	145.492i		−	0.187975i
$775$	−89.0955	+	51.4393i	−0.114962	+	0.0663733i
$776$	−667.509			−0.860192
$777$		0			0
$778$	214.000	+	370.659i	0.275064	+	0.476425i
$779$	561.000	−	323.894i	0.720154	−	0.415781i
$780$	678.823	−	391.918i	0.870285	−	0.502459i
$781$	−420.000	+	727.461i	−0.537772	+	0.931449i
$782$	882.469	+	509.494i	1.12848	+	0.651527i
$783$			58.7878i			0.0750801i
$784$		0			0
$785$	176.000			0.224204
$786$	186.000	−	322.161i	0.236641	−	0.409875i
$787$	710.642	+	410.290i	0.902976	+	0.521334i	0.878165	−	0.478359i	$-0.158768\pi$
$787$	710.642	+	410.290i	0.902976	+	0.521334i	0.0248116	+	0.999692i	$0.492101\pi$
$788$	−396.000	−	685.892i	−0.502538	−	0.870421i
$789$	−347.897	−	602.574i	−0.440934	−	0.763719i
$790$	−203.647	+	117.576i	−0.257781	+	0.148830i
$791$		0			0
$792$		−	415.692i		−	0.524864i
$793$	−320.000	−	554.256i	−0.403531	−	0.698936i
$794$	−446.891			−0.562836
$795$	792.000	+	457.261i	0.996226	+	0.575172i
$796$		−	1156.16i		−	1.45246i
$797$	461.034			0.578461			0.289231	−	0.957259i	$-0.406601\pi$
$797$	461.034			0.578461			0.289231	+	0.957259i	$0.406601\pi$
$798$		0			0
$799$			450.333i			0.563621i
$800$	224.000			0.280000
$801$	−36.0624	+	62.4620i	−0.0450218	+	0.0779800i
$802$	1004.00			1.25187
$803$	−275.772	+	159.217i	−0.343427	+	0.198278i
$804$	33.9411	−	58.7878i	0.0422153	−	0.0731191i
$805$		0			0
$806$	360.000	−	207.846i	0.446650	−	0.257874i
$807$	354.000	−	204.382i	0.438662	−	0.253261i
$808$	362.039	−	627.069i	0.448068	−	0.776076i
$809$	72.0000	−	124.708i	0.0889988	−	0.154150i	−0.818089	−	0.575091i	$-0.804967\pi$
$809$	72.0000	−	124.708i	0.0889988	−	0.154150i	0.907088	+	0.420941i	$0.138300\pi$
$810$	−254.558	+	440.908i	−0.314270	+	0.544331i
$811$		−	17.1464i		−	0.0211423i	−0.999944	−	0.0105712i	$-0.996635\pi$
$811$		−	17.1464i		−	0.0211423i	0.999944	−	0.0105712i	$-0.00336497\pi$
$812$		0			0
$813$	1032.00			1.26937
$814$	−900.000	−	519.615i	−1.10565	−	0.638348i
$815$	220.617	+	127.373i	0.270696	+	0.156286i
$816$			720.533i			0.883006i
$817$	326.683	+	565.832i	0.399857	+	0.692573i
$818$	−255.973	−	443.358i	−0.312925	−	0.542002i
$819$		0			0
$820$	−272.000	+	471.118i	−0.331707	+	0.574534i
$821$	−657.000	−	1137.96i	−0.800244	−	1.38606i	−0.919456	−	0.393194i	$-0.871370\pi$
$821$	−657.000	−	1137.96i	−0.800244	−	1.38606i	0.119212	−	0.992869i	$-0.461963\pi$
$822$			803.433i			0.977412i
$823$	1212.00	+	699.749i	1.47266	+	0.850241i	0.999527	−	0.0307493i	$-0.00978936\pi$
$823$	1212.00	+	699.749i	1.47266	+	0.850241i	0.473134	+	0.880991i	$0.343123\pi$
$824$	−305.470	+	176.363i	−0.370716	+	0.214033i
$825$	296.985			0.359982
$826$		0			0
$827$		−	242.487i		−	0.293213i	−0.989195	−	0.146606i	$-0.953165\pi$
$827$		−	242.487i		−	0.293213i	0.989195	−	0.146606i	$-0.0468351\pi$
$828$		−	332.554i		−	0.401635i
$829$	−667.509	+	1156.16i	−0.805198	+	1.39464i	0.110960	+	0.993825i	$0.464607\pi$
$829$	−667.509	+	1156.16i	−0.805198	+	1.39464i	−0.916158	+	0.400818i	$0.868726\pi$
$830$			1745.91i			2.10350i
$831$	21.2132	−	12.2474i	0.0255273	−	0.0147382i
$832$	−905.097			−1.08786
$833$		0			0
$834$	−210.000	−	363.731i	−0.251799	−	0.436128i
$835$	840.000	−	484.974i	1.00599	−	0.580807i
$836$	933.381	+	1616.66i	1.11648	+	1.93381i
$837$	−216.000	+	374.123i	−0.258065	+	0.446981i
$838$	−29.6985	−	17.1464i	−0.0354397	−	0.0204611i
$839$			1200.25i			1.43057i	0.698832	+	0.715286i	$0.253704\pi$
$839$			1200.25i			1.43057i	−0.698832	+	0.715286i	$0.746296\pi$
$840$		0			0
$841$	−837.000			−0.995244
$842$	614.000	−	1063.48i	0.729216	−	1.26304i
$843$	−746.705	−	431.110i	−0.885771	−	0.511400i
$844$	168.000	−	96.9948i	0.199052	−	0.114923i
$845$	87.6812	+	151.868i	0.103765	+	0.179726i
$846$	127.279	−	73.4847i	0.150448	−	0.0868613i
$847$		0			0
$848$	−528.000	−	914.523i	−0.622642	−	1.07845i
$849$	87.0000	+	150.688i	0.102473	+	0.177489i
$850$	257.387			0.302808
$851$	−720.000	−	415.692i	−0.846063	−	0.488475i
$852$	−475.176			−0.557718
$853$	342.240			0.401219			0.200609	−	0.979671i	$-0.435708\pi$
$853$	342.240			0.401219			0.200609	+	0.979671i	$0.435708\pi$
$854$		0			0
$855$			457.261i			0.534809i
$856$	144.000	−	83.1384i	0.168224	−	0.0971243i
$857$	60.1041	−	104.103i	0.0701331	−	0.121474i	−0.828826	−	0.559506i	$-0.810991\pi$
$857$	60.1041	−	104.103i	0.0701331	−	0.121474i	0.898959	+	0.438032i	$0.144324\pi$
$858$	−1200.00			−1.39860
$859$	1372.49	−	792.410i	1.59778	−	0.922480i	0.605868	−	0.795565i	$-0.292826\pi$
$859$	1372.49	−	792.410i	1.59778	−	0.922480i	0.991914	−	0.126914i	$-0.0405073\pi$
$860$	−475.176	−	274.343i	−0.552530	−	0.319003i
$861$		0			0
$862$	−576.000	+	332.554i	−0.668213	+	0.385793i
$863$	−402.000	+	232.095i	−0.465817	+	0.268940i	−0.714487	−	0.699649i	$-0.753340\pi$
$863$	−402.000	+	232.095i	−0.465817	+	0.268940i	0.248670	+	0.968588i	$0.420007\pi$
$864$	814.587	−	470.302i	0.942809	−	0.544331i
$865$	−296.000	+	512.687i	−0.342197	+	0.592702i
$866$	202.233	−	350.277i	0.233525	−	0.404477i
$867$			120.025i			0.138437i
$868$		0			0
$869$	360.000			0.414269
$870$	48.0000	+	27.7128i	0.0551724	+	0.0318538i
$871$	84.8528	+	48.9898i	0.0974200	+	0.0562455i
$872$	744.000	−	1288.65i	0.853211	−	1.47780i
$873$	125.158	+	216.780i	0.143365	+	0.248316i
$874$	746.705	+	1293.33i	0.854353	+	1.47978i
$875$		0			0
$876$	−156.000	−	90.0666i	−0.178082	−	0.102816i
$877$	435.000	+	753.442i	0.496009	+	0.859113i	0.999989	−	0.00460215i	$-0.00146492\pi$
$877$	435.000	+	753.442i	0.496009	+	0.859113i	−0.503980	+	0.863715i	$0.668132\pi$
$878$			1214.95i			1.38377i
$879$	−852.000	−	491.902i	−0.969283	−	0.559616i
$880$	−1357.65	−	783.837i	−1.54278	−	0.890724i
$881$	807.516			0.916590			0.458295	−	0.888800i	$-0.348460\pi$
$881$	807.516			0.916590			0.458295	+	0.888800i	$0.348460\pi$
$882$		0			0
$883$			1406.43i			1.59278i	0.604783	+	0.796390i	$0.293260\pi$
$883$			1406.43i			1.59278i	−0.604783	+	0.796390i	$0.706740\pi$
$884$	−1040.00			−1.17647
$885$	458.205	−	793.635i	0.517746	−	0.896762i
$886$		−	152.420i		−	0.172032i
$887$	793.374	−	458.055i	0.894446	−	0.516409i	0.0190520	−	0.999818i	$-0.493935\pi$
$887$	793.374	−	458.055i	0.894446	−	0.516409i	0.875394	+	0.483410i	$0.160602\pi$
$888$		−	587.878i		−	0.662024i
$889$		0			0
$890$	136.000	+	235.559i	0.152809	+	0.264673i
$891$	675.000	−	389.711i	0.757576	−	0.437387i
$892$	1187.94	−	685.857i	1.33177	−	0.768898i
$893$	−330.000	+	571.577i	−0.369541	+	0.640064i
$894$	483.661	+	279.242i	0.541008	+	0.312351i
$895$		−	1136.56i		−	1.26990i
$896$		0			0
$897$	−960.000			−1.07023
$898$	642.000	−	1111.98i	0.714922	−	1.23828i
$899$	25.4558	+	14.6969i	0.0283157	+	0.0163481i
$900$	−42.0000	−	72.7461i	−0.0466667	−	0.0808290i
$901$	−606.698	−	1050.83i	−0.673360	−	1.16629i
$902$	721.249	−	416.413i	0.799611	−	0.461655i
$903$		0			0
$904$	−96.0000			−0.106195
$905$	856.000	+	1482.64i	0.945856	+	1.63827i
$906$	−33.9411			−0.0374626
$907$	−426.000	−	245.951i	−0.469680	−	0.271170i	0.246426	−	0.969162i	$-0.420744\pi$
$907$	−426.000	−	245.951i	−0.469680	−	0.271170i	−0.716106	+	0.697992i	$0.754077\pi$
$908$		−	401.716i		−	0.442419i
$909$	−271.529			−0.298712
$910$		0			0
$911$		−	48.4974i		−	0.0532354i	−0.999646	−	0.0266177i	$-0.991526\pi$
$911$		−	48.4974i		−	0.0532354i	0.999646	−	0.0266177i	$-0.00847367\pi$
$912$	−528.000	+	914.523i	−0.578947	+	1.00277i
$913$	1336.43	−	2314.77i	1.46378	−	2.53534i
$914$	304.000			0.332604
$915$	543.058	−	313.535i	0.593506	−	0.342661i
$916$	−741.048	+	1283.53i	−0.809004	+	1.40124i
$917$		0			0
$918$	936.000	−	540.400i	1.01961	−	0.588671i
$919$	−192.000	+	110.851i	−0.208923	+	0.120622i	−0.600811	−	0.799391i	$-0.705155\pi$
$919$	−192.000	+	110.851i	−0.208923	+	0.120622i	0.391888	+	0.920013i	$0.371822\pi$
$920$	−1086.12	−	627.069i	−1.18056	−	0.681597i
$921$	693.000	−	1200.31i	0.752443	−	1.30327i
$922$	−183.848	+	318.434i	−0.199401	+	0.345373i
$923$		−	685.857i		−	0.743074i
$924$		0			0
$925$	−210.000			−0.227027
$926$	168.000	+	96.9948i	0.181425	+	0.104746i
$927$	114.551	+	66.1362i	0.123572	+	0.0713444i
$928$	−32.0000	−	55.4256i	−0.0344828	−	0.0597259i
$929$	−546.594	−	946.728i	−0.588368	−	1.01908i	−0.994446	−	0.105245i	$-0.966437\pi$
$929$	−546.594	−	946.728i	−0.588368	−	1.01908i	0.406079	−	0.913838i	$-0.366896\pi$
$930$	203.647	+	352.727i	0.218975	+	0.379276i
$931$		0			0
$932$	−80.0000	+	138.564i	−0.0858369	+	0.148674i
$933$	24.0000	+	41.5692i	0.0257235	+	0.0445544i
$934$		−	465.403i		−	0.498290i
$935$	−1560.00	−	900.666i	−1.66845	−	0.963280i
$936$	169.706	+	293.939i	0.181309	+	0.314037i
$937$	1262.89			1.34780			0.673902	−	0.738821i	$-0.264617\pi$
$937$	1262.89			1.34780			0.673902	+	0.738821i	$0.264617\pi$
$938$		0			0
$939$			1077.34i			1.14732i
$940$		−	554.256i		−	0.589634i
$941$	−410.122	+	710.352i	−0.435836	+	0.754891i	−0.997363	−	0.0725677i	$-0.976881\pi$
$941$	−410.122	+	710.352i	−0.435836	+	0.754891i	0.561527	+	0.827458i	$0.310214\pi$
$942$		−	152.420i		−	0.161805i
$943$	576.999	−	333.131i	0.611876	−	0.353267i
$944$	−916.410	+	529.090i	−0.970774	+	0.560476i
$945$		0			0
$946$	420.000	+	727.461i	0.443975	+	0.768987i
$947$	165.000	−	95.2628i	0.174234	−	0.100594i	−0.410347	−	0.911930i	$-0.634592\pi$
$947$	165.000	−	95.2628i	0.174234	−	0.100594i	0.584581	+	0.811335i	$0.301259\pi$
$948$	101.823	+	176.363i	0.107409	+	0.186037i
$949$	130.000	−	225.167i	0.136986	−	0.237267i
$950$	326.683	+	188.611i	0.343877	+	0.198538i
$951$		−	279.242i		−	0.293630i
$952$		0			0
$953$	−642.000			−0.673662			−0.336831	−	0.941565i	$-0.609355\pi$
$953$	−642.000			−0.673662			−0.336831	+	0.941565i	$0.609355\pi$
$954$	−198.000	+	342.946i	−0.207547	+	0.359482i
$955$	101.823	+	58.7878i	0.106621	+	0.0615579i
$956$	−1344.00	+	775.959i	−1.40586	+	0.811672i
$957$	−42.4264	−	73.4847i	−0.0443327	−	0.0767865i
$958$	−1569.78	+	906.311i	−1.63860	+	0.946045i
$959$		0			0
$960$		−	886.810i		−	0.923760i
$961$	−372.500	−	645.189i	−0.387617	−	0.671372i
$962$	848.528			0.882046
$963$	−54.0000	−	31.1769i	−0.0560748	−	0.0323748i
$964$	−1431.18			−1.48463
$965$	−1719.68			−1.78206
$966$		0			0
$967$		−	1842.90i		−	1.90579i	−0.303295	−	0.952897i	$-0.598087\pi$
$967$		−	1842.90i		−	1.90579i	0.303295	−	0.952897i	$-0.401913\pi$
$968$	716.000	+	1240.15i	0.739669	+	1.28115i
$969$	−606.698	+	1050.83i	−0.626107	+	1.08445i
$970$	944.000			0.973196
$971$	−973.686	+	562.158i	−1.00277	+	0.578947i	−0.909066	−	0.416653i	$-0.863203\pi$
$971$	−973.686	+	562.158i	−1.00277	+	0.578947i	−0.0937007	+	0.995600i	$0.529870\pi$
$972$	−534.573	−	308.636i	−0.549972	−	0.317526i
$973$		0			0
$974$	936.000	−	540.400i	0.960986	−	0.554825i
$975$	−210.000	+	121.244i	−0.215385	+	0.124352i
$976$	−724.077			−0.741883
$977$	758.000	−	1312.89i	0.775844	−	1.34380i	−0.158474	−	0.987363i	$-0.550657\pi$
$977$	758.000	−	1312.89i	0.775844	−	1.34380i	0.934319	−	0.356439i	$-0.116009\pi$
$978$	110.309	−	191.060i	0.112790	−	0.195358i
$979$		−	416.413i		−	0.425346i
$980$		0			0
$981$	−558.000			−0.568807
$982$	−756.000	−	436.477i	−0.769857	−	0.444477i
$983$	−1472.20	−	849.973i	−1.49766	−	0.864672i	−0.497660	−	0.867372i	$-0.665807\pi$
$983$	−1472.20	−	849.973i	−1.49766	−	0.864672i	−0.999996	+	0.00269975i	$0.999141\pi$
$984$	408.000	+	235.559i	0.414634	+	0.239389i
$985$	560.029	+	969.998i	0.568557	+	0.984769i
$986$	−36.7696	−	63.6867i	−0.0372916	−	0.0645910i
$987$		0			0
$988$	−1320.00	−	762.102i	−1.33603	−	0.771359i
$989$	336.000	+	581.969i	0.339737	+	0.588442i
$990$			587.878i			0.593816i
$991$	792.000	+	457.261i	0.799193	+	0.461414i	0.843189	−	0.537618i	$-0.180676\pi$
$991$	792.000	+	457.261i	0.799193	+	0.461414i	−0.0439961	+	0.999032i	$0.514009\pi$
$992$		−	470.302i		−	0.474095i
$993$	1315.22			1.32449
$994$		0			0
$995$			1635.06i			1.64327i
$996$	1512.00			1.51807
$997$	461.034	−	798.534i	0.462421	−	0.800936i	−0.536660	−	0.843799i	$-0.680314\pi$
$997$	461.034	−	798.534i	0.462421	−	0.800936i	0.999081	+	0.0428620i	$0.0136476\pi$
$998$			1593.49i			1.59668i
$999$	−763.675	+	440.908i	−0.764440	+	0.441350i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.3.g.b.67.1		4
4.3	odd	2		196.3.g.f.67.2		4
7.2	even	3		196.3.g.f.79.2		4
7.3	odd	6		196.3.c.e.99.1	✓	4
7.4	even	3		196.3.c.e.99.2	yes	4
7.5	odd	6		196.3.g.f.79.1		4
7.6	odd	2	inner	196.3.g.b.67.2		4
28.3	even	6		196.3.c.e.99.4	yes	4
28.11	odd	6		196.3.c.e.99.3	yes	4
28.19	even	6	inner	196.3.g.b.79.2		4
28.23	odd	6	inner	196.3.g.b.79.1		4
28.27	even	2		196.3.g.f.67.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
196.3.c.e.99.1	✓	4	7.3	odd	6
196.3.c.e.99.2	yes	4	7.4	even	3
196.3.c.e.99.3	yes	4	28.11	odd	6
196.3.c.e.99.4	yes	4	28.3	even	6
196.3.g.b.67.1		4	1.1	even	1	trivial
196.3.g.b.67.2		4	7.6	odd	2	inner
196.3.g.b.79.1		4	28.23	odd	6	inner
196.3.g.b.79.2		4	28.19	even	6	inner
196.3.g.f.67.1		4	28.27	even	2
196.3.g.f.67.2		4	4.3	odd	2
196.3.g.f.79.1		4	7.5	odd	6
196.3.g.f.79.2		4	7.2	even	3

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:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	196.g (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{2} +(-2.12132 - 1.22474i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(2.82843 + 4.89898i) q^{5} +(4.24264 - 2.44949i) q^{6} +8.00000 q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.73205i) q^{2} +(-2.12132 - 1.22474i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(2.82843 + 4.89898i) q^{5} +(4.24264 - 2.44949i) q^{6} +8.00000 q^{8} +(-1.50000 - 2.59808i) q^{9} -11.3137 q^{10} +(15.0000 + 8.66025i) q^{11} +9.79796i q^{12} -14.1421 q^{13} -13.8564i q^{15} +(-8.00000 + 13.8564i) q^{16} +(-9.19239 + 15.9217i) q^{17} +6.00000 q^{18} +(-23.3345 + 13.4722i) q^{19} +(11.3137 - 19.5959i) q^{20} +(-30.0000 + 17.3205i) q^{22} +(-24.0000 + 13.8564i) q^{23} +(-16.9706 - 9.79796i) q^{24} +(-3.50000 + 6.06218i) q^{25} +(14.1421 - 24.4949i) q^{26} +29.3939i q^{27} +2.00000 q^{29} +(24.0000 + 13.8564i) q^{30} +(12.7279 + 7.34847i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(-21.2132 - 36.7423i) q^{33} +(-18.3848 - 31.8434i) q^{34} +(-6.00000 + 10.3923i) q^{36} +(15.0000 + 25.9808i) q^{37} -53.8888i q^{38} +(30.0000 + 17.3205i) q^{39} +(22.6274 + 39.1918i) q^{40} -24.0416 q^{41} -24.2487i q^{43} -69.2820i q^{44} +(8.48528 - 14.6969i) q^{45} -55.4256i q^{46} +(21.2132 - 12.2474i) q^{47} +(33.9411 - 19.5959i) q^{48} +(-7.00000 - 12.1244i) q^{50} +(39.0000 - 22.5167i) q^{51} +(28.2843 + 48.9898i) q^{52} +(-33.0000 + 57.1577i) q^{53} +(-50.9117 - 29.3939i) q^{54} +97.9796i q^{55} +66.0000 q^{57} +(-2.00000 + 3.46410i) q^{58} +(57.2756 + 33.0681i) q^{59} +(-48.0000 + 27.7128i) q^{60} +(22.6274 + 39.1918i) q^{61} +(-25.4558 + 14.6969i) q^{62} +64.0000 q^{64} +(-40.0000 - 69.2820i) q^{65} +84.8528 q^{66} +(-6.00000 - 3.46410i) q^{67} +73.5391 q^{68} +67.8823 q^{69} +48.4974i q^{71} +(-12.0000 - 20.7846i) q^{72} +(-9.19239 + 15.9217i) q^{73} -60.0000 q^{74} +(14.8492 - 8.57321i) q^{75} +(93.3381 + 53.8888i) q^{76} +(-60.0000 + 34.6410i) q^{78} +(18.0000 - 10.3923i) q^{79} -90.5097 q^{80} +(22.5000 - 38.9711i) q^{81} +(24.0416 - 41.6413i) q^{82} -154.318i q^{83} -104.000 q^{85} +(42.0000 + 24.2487i) q^{86} +(-4.24264 - 2.44949i) q^{87} +(120.000 + 69.2820i) q^{88} +(-12.0208 - 20.8207i) q^{89} +(16.9706 + 29.3939i) q^{90} +(96.0000 + 55.4256i) q^{92} +(-18.0000 - 31.1769i) q^{93} +48.9898i q^{94} +(-132.000 - 76.2102i) q^{95} +78.3837i q^{96} -83.4386 q^{97} -51.9615i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 8 q^{4} + 32 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 8 * q^4 + 32 * q^8 - 6 * q^9	\( 4 q - 4 q^{2} - 8 q^{4} + 32 q^{8} - 6 q^{9} + 60 q^{11} - 32 q^{16} + 24 q^{18} - 120 q^{22} - 96 q^{23} - 14 q^{25} + 8 q^{29} + 96 q^{30} - 64 q^{32} - 24 q^{36} + 60 q^{37} + 120 q^{39} - 28 q^{50} + 156 q^{51} - 132 q^{53} + 264 q^{57} - 8 q^{58} - 192 q^{60} + 256 q^{64} - 160 q^{65} - 24 q^{67} - 48 q^{72} - 240 q^{74} - 240 q^{78} + 72 q^{79} + 90 q^{81} - 416 q^{85} + 168 q^{86} + 480 q^{88} + 384 q^{92} - 72 q^{93} - 528 q^{95}+O(q^{100}) \) 4 * q - 4 * q^2 - 8 * q^4 + 32 * q^8 - 6 * q^9 + 60 * q^11 - 32 * q^16 + 24 * q^18 - 120 * q^22 - 96 * q^23 - 14 * q^25 + 8 * q^29 + 96 * q^30 - 64 * q^32 - 24 * q^36 + 60 * q^37 + 120 * q^39 - 28 * q^50 + 156 * q^51 - 132 * q^53 + 264 * q^57 - 8 * q^58 - 192 * q^60 + 256 * q^64 - 160 * q^65 - 24 * q^67 - 48 * q^72 - 240 * q^74 - 240 * q^78 + 72 * q^79 + 90 * q^81 - 416 * q^85 + 168 * q^86 + 480 * q^88 + 384 * q^92 - 72 * q^93 - 528 * q^95

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