LMFDB - Embedded newform 441.3.v.c.55.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,3,Mod(55,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("441.55");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	441.v (of order $14$, degree $6$, 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:	$12.0163796583$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{14})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			55.6
Character	$\chi$	$=$	441.55
Dual form			441.3.v.c.433.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.988314 + 1.23931i) q^{2} +(0.330967 + 1.45006i) q^{4} +(-1.75892 + 3.65243i) q^{5} +(5.32542 + 4.54311i) q^{7} +(-7.83679 - 3.77400i) q^{8} +O(q^{10})$	\(q+(-0.988314 + 1.23931i) q^{2} +(0.330967 + 1.45006i) q^{4} +(-1.75892 + 3.65243i) q^{5} +(5.32542 + 4.54311i) q^{7} +(-7.83679 - 3.77400i) q^{8} +(-2.78812 - 5.78959i) q^{10} +(-6.34573 + 7.95730i) q^{11} +(-18.6115 - 14.8421i) q^{13} +(-10.8935 + 2.10981i) q^{14} +(7.06213 - 3.40094i) q^{16} +(9.97642 + 2.27705i) q^{17} +27.1089i q^{19} +(-5.87839 - 1.34170i) q^{20} +(-3.58995 - 15.7286i) q^{22} +(-2.55547 - 11.1963i) q^{23} +(5.34080 + 6.69715i) q^{25} +(36.7879 - 8.39661i) q^{26} +(-4.82525 + 9.22581i) q^{28} +(-0.336228 + 1.47311i) q^{29} -30.5151i q^{31} +(4.97732 - 21.8071i) q^{32} +(-12.6818 + 10.1134i) q^{34} +(-25.9604 + 11.4598i) q^{35} +(0.274091 - 1.20087i) q^{37} +(-33.5963 - 26.7922i) q^{38} +(27.5685 - 21.9852i) q^{40} +(15.4080 - 31.9951i) q^{41} +(-52.8350 + 25.4440i) q^{43} +(-13.6388 - 6.56810i) q^{44} +(16.4012 + 7.89840i) q^{46} +(-54.7691 - 43.6769i) q^{47} +(7.72029 + 48.3880i) q^{49} -13.5782 q^{50} +(15.3622 - 31.9000i) q^{52} +(-10.9793 - 48.1034i) q^{53} +(-17.9018 - 37.1735i) q^{55} +(-24.5885 - 55.7016i) q^{56} +(-1.49334 - 1.87259i) q^{58} +(35.5147 + 73.7471i) q^{59} +(-87.2577 - 19.9160i) q^{61} +(37.8175 + 30.1585i) q^{62} +(41.6551 + 52.2338i) q^{64} +(86.9459 - 41.8709i) q^{65} -14.2041 q^{67} +15.2201i q^{68} +(11.4548 - 43.4987i) q^{70} +(5.77803 + 25.3152i) q^{71} +(59.6841 - 47.5965i) q^{73} +(1.21736 + 1.52652i) q^{74} +(-39.3096 + 8.97217i) q^{76} +(-69.9446 + 13.5466i) q^{77} -80.1687 q^{79} +31.7759i q^{80} +(24.4238 + 50.7166i) q^{82} +(-59.1097 + 47.1384i) q^{83} +(-25.8645 + 32.4330i) q^{85} +(20.6847 - 90.6254i) q^{86} +(79.7610 - 38.4109i) q^{88} +(73.7002 - 58.7739i) q^{89} +(-31.6844 - 163.595i) q^{91} +(15.3895 - 7.41118i) q^{92} +(108.258 - 24.7092i) q^{94} +(-99.0134 - 47.6824i) q^{95} +43.4868i q^{97} +(-67.5976 - 38.2547i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 32 q^{4} - 2 q^{7} - 12 q^{8}+O(q^{10}) $ 108 * q - 32 * q^4 - 2 * q^7 - 12 * q^8	$ 108 q - 32 q^{4} - 2 q^{7} - 12 q^{8} - 66 q^{11} + 2 q^{14} - 96 q^{16} + 98 q^{17} + 112 q^{20} - 116 q^{22} - 64 q^{23} + 130 q^{25} - 224 q^{26} - 204 q^{28} - 72 q^{29} + 220 q^{32} + 784 q^{34} + 376 q^{35} + 156 q^{37} + 280 q^{38} - 728 q^{40} + 196 q^{41} - 56 q^{43} + 840 q^{44} - 16 q^{46} - 266 q^{47} + 122 q^{49} + 244 q^{50} + 168 q^{52} - 148 q^{53} - 252 q^{55} - 686 q^{56} + 252 q^{58} - 700 q^{59} - 112 q^{61} - 392 q^{62} + 496 q^{64} + 12 q^{65} - 196 q^{67} + 898 q^{70} + 732 q^{71} + 126 q^{73} + 508 q^{74} - 210 q^{76} + 230 q^{77} + 136 q^{79} - 1960 q^{82} + 574 q^{83} - 480 q^{85} + 392 q^{86} - 108 q^{88} + 742 q^{89} + 152 q^{91} + 42 q^{92} + 98 q^{94} - 68 q^{95} + 508 q^{98}+O(q^{100}) $ 108 * q - 32 * q^4 - 2 * q^7 - 12 * q^8 - 66 * q^11 + 2 * q^14 - 96 * q^16 + 98 * q^17 + 112 * q^20 - 116 * q^22 - 64 * q^23 + 130 * q^25 - 224 * q^26 - 204 * q^28 - 72 * q^29 + 220 * q^32 + 784 * q^34 + 376 * q^35 + 156 * q^37 + 280 * q^38 - 728 * q^40 + 196 * q^41 - 56 * q^43 + 840 * q^44 - 16 * q^46 - 266 * q^47 + 122 * q^49 + 244 * q^50 + 168 * q^52 - 148 * q^53 - 252 * q^55 - 686 * q^56 + 252 * q^58 - 700 * q^59 - 112 * q^61 - 392 * q^62 + 496 * q^64 + 12 * q^65 - 196 * q^67 + 898 * q^70 + 732 * q^71 + 126 * q^73 + 508 * q^74 - 210 * q^76 + 230 * q^77 + 136 * q^79 - 1960 * q^82 + 574 * q^83 - 480 * q^85 + 392 * q^86 - 108 * q^88 + 742 * q^89 + 152 * q^91 + 42 * q^92 + 98 * q^94 - 68 * q^95 + 508 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{9}{14}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.988314	+	1.23931i	−0.494157	+	0.619654i	−0.964900	−	0.262617i	$-0.915414\pi$
$2$	−0.988314	+	1.23931i	−0.494157	+	0.619654i	0.470743	+	0.882270i	$0.343986\pi$
$3$		0			0
$3$		0			0
$4$	0.330967	+	1.45006i	0.0827418	+	0.362515i
$5$	−1.75892	+	3.65243i	−0.351783	+	0.730486i	−0.999507	−	0.0313895i	$-0.990007\pi$
$5$	−1.75892	+	3.65243i	−0.351783	+	0.730486i	0.647724	+	0.761875i	$0.275721\pi$
$6$		0			0
$7$	5.32542	+	4.54311i	0.760775	+	0.649016i
$7$	5.32542	+	4.54311i	0.760775	+	0.649016i
$8$	−7.83679	−	3.77400i	−0.979599	−	0.471750i
$9$		0			0
$10$	−2.78812	−	5.78959i	−0.278812	−	0.578959i
$11$	−6.34573	+	7.95730i	−0.576885	+	0.723391i	−0.981578	−	0.191062i	$-0.938807\pi$
$11$	−6.34573	+	7.95730i	−0.576885	+	0.723391i	0.404693	+	0.914452i	$0.367378\pi$
$12$		0			0
$13$	−18.6115	−	14.8421i	−1.43165	−	1.14170i	−0.966560	−	0.256440i	$-0.917450\pi$
$13$	−18.6115	−	14.8421i	−1.43165	−	1.14170i	−0.465090	−	0.885263i	$-0.653978\pi$
$14$	−10.8935	+	2.10981i	−0.778107	+	0.150701i
$15$		0			0
$16$	7.06213	−	3.40094i	0.441383	−	0.212559i
$17$	9.97642	+	2.27705i	0.586848	+	0.133944i	0.505628	−	0.862752i	$-0.331261\pi$
$17$	9.97642	+	2.27705i	0.586848	+	0.133944i	0.0812208	+	0.996696i	$0.474118\pi$
$18$		0			0
$19$			27.1089i			1.42679i	0.700764	+	0.713393i	$0.252843\pi$
$19$			27.1089i			1.42679i	−0.700764	+	0.713393i	$0.747157\pi$
$20$	−5.87839	−	1.34170i	−0.293919	−	0.0670852i
$21$		0			0
$22$	−3.58995	−	15.7286i	−0.163180	−	0.714937i
$23$	−2.55547	−	11.1963i	−0.111107	−	0.486794i	−0.999610	−	0.0279221i	$-0.991111\pi$
$23$	−2.55547	−	11.1963i	−0.111107	−	0.486794i	0.888503	−	0.458872i	$-0.151746\pi$
$24$		0			0
$25$	5.34080	+	6.69715i	0.213632	+	0.267886i
$26$	36.7879	−	8.39661i	1.41492	−	0.322946i
$27$		0			0
$28$	−4.82525	+	9.22581i	−0.172330	+	0.329493i
$29$	−0.336228	+	1.47311i	−0.0115941	+	0.0507969i	−0.980394	−	0.197047i	$-0.936865\pi$
$29$	−0.336228	+	1.47311i	−0.0115941	+	0.0507969i	0.968800	+	0.247844i	$0.0797220\pi$
$30$		0			0
$31$		−	30.5151i		−	0.984357i	−0.870494	−	0.492179i	$-0.836201\pi$
$31$		−	30.5151i		−	0.984357i	0.870494	−	0.492179i	$-0.163799\pi$
$32$	4.97732	−	21.8071i	0.155541	−	0.681471i
$33$		0			0
$34$	−12.6818	+	10.1134i	−0.372994	+	0.297453i
$35$	−25.9604	+	11.4598i	−0.741725	+	0.327422i
$36$		0			0
$37$	0.274091	−	1.20087i	0.00740787	−	0.0324560i	−0.971089	−	0.238718i	$-0.923273\pi$
$37$	0.274091	−	1.20087i	0.00740787	−	0.0324560i	0.978497	+	0.206262i	$0.0661299\pi$
$38$	−33.5963	−	26.7922i	−0.884113	−	0.705057i
$39$		0			0
$40$	27.5685	−	21.9852i	0.689213	−	0.549629i
$41$	15.4080	−	31.9951i	0.375806	−	0.780369i	−0.624194	−	0.781270i	$-0.714572\pi$
$41$	15.4080	−	31.9951i	0.375806	−	0.780369i	1.00000		0.000900421i	$0.000286613\pi$
$42$		0			0
$43$	−52.8350	+	25.4440i	−1.22872	+	0.591720i	−0.931727	−	0.363159i	$-0.881698\pi$
$43$	−52.8350	+	25.4440i	−1.22872	+	0.591720i	−0.296993	+	0.954880i	$0.595984\pi$
$44$	−13.6388	−	6.56810i	−0.309973	−	0.149275i
$45$		0			0
$46$	16.4012	+	7.89840i	0.356548	+	0.171704i
$47$	−54.7691	−	43.6769i	−1.16530	−	0.929296i	−0.166908	−	0.985972i	$-0.553378\pi$
$47$	−54.7691	−	43.6769i	−1.16530	−	0.929296i	−0.998393	+	0.0566760i	$0.981950\pi$
$48$		0			0
$49$	7.72029	+	48.3880i	0.157557	+	0.987510i
$50$	−13.5782			−0.271564
$51$		0			0
$52$	15.3622	−	31.9000i	0.295428	−	0.613462i
$53$	−10.9793	−	48.1034i	−0.207156	−	0.907612i	−0.966448	−	0.256862i	$-0.917312\pi$
$53$	−10.9793	−	48.1034i	−0.207156	−	0.907612i	0.759292	−	0.650750i	$-0.225546\pi$
$54$		0			0
$55$	−17.9018	−	37.1735i	−0.325488	−	0.675883i
$56$	−24.5885	−	55.7016i	−0.439081	−	0.994671i
$57$		0			0
$58$	−1.49334	−	1.87259i	−0.0257472	−	0.0322860i
$59$	35.5147	+	73.7471i	0.601944	+	1.24995i	0.949934	+	0.312452i	$0.101150\pi$
$59$	35.5147	+	73.7471i	0.601944	+	1.24995i	−0.347989	+	0.937499i	$0.613135\pi$
$60$		0			0
$61$	−87.2577	−	19.9160i	−1.43045	−	0.326492i	−0.564011	−	0.825767i	$-0.690742\pi$
$61$	−87.2577	−	19.9160i	−1.43045	−	0.326492i	−0.866443	+	0.499276i	$0.833600\pi$
$62$	37.8175	+	30.1585i	0.609960	+	0.486427i
$63$		0			0
$64$	41.6551	+	52.2338i	0.650861	+	0.816153i
$65$	86.9459	−	41.8709i	1.33763	−	0.644168i
$66$		0			0
$67$	−14.2041			−0.212001			−0.106000	−	0.994366i	$-0.533805\pi$
$67$	−14.2041			−0.212001			−0.106000	+	0.994366i	$0.533805\pi$
$68$			15.2201i			0.223824i
$69$		0			0
$70$	11.4548	−	43.4987i	0.163640	−	0.621410i
$71$	5.77803	+	25.3152i	0.0813808	+	0.356552i	0.999180	−	0.0404928i	$-0.0128928\pi$
$71$	5.77803	+	25.3152i	0.0813808	+	0.356552i	−0.917799	+	0.397045i	$0.870036\pi$
$72$		0			0
$73$	59.6841	−	47.5965i	0.817591	−	0.652007i	−0.122675	−	0.992447i	$-0.539147\pi$
$73$	59.6841	−	47.5965i	0.817591	−	0.652007i	0.940266	+	0.340440i	$0.110576\pi$
$74$	1.21736	+	1.52652i	0.0164508	+	0.0206287i
$75$		0			0
$76$	−39.3096	+	8.97217i	−0.517232	+	0.118055i
$77$	−69.9446	+	13.5466i	−0.908371	+	0.175930i
$78$		0			0
$79$	−80.1687			−1.01479			−0.507397	−	0.861713i	$-0.669392\pi$
$79$	−80.1687			−1.01479			−0.507397	+	0.861713i	$0.669392\pi$
$80$			31.7759i			0.397199i
$81$		0			0
$82$	24.4238	+	50.7166i	0.297851	+	0.618495i
$83$	−59.1097	+	47.1384i	−0.712165	+	0.567933i	−0.911152	−	0.412069i	$-0.864806\pi$
$83$	−59.1097	+	47.1384i	−0.712165	+	0.567933i	0.198987	+	0.980002i	$0.436235\pi$
$84$		0			0
$85$	−25.8645	+	32.4330i	−0.304288	+	0.381565i
$86$	20.6847	−	90.6254i	0.240519	−	1.05378i
$87$		0			0
$88$	79.7610	−	38.4109i	0.906375	−	0.436487i
$89$	73.7002	−	58.7739i	0.828092	−	0.660381i	−0.114834	−	0.993385i	$-0.536634\pi$
$89$	73.7002	−	58.7739i	0.828092	−	0.660381i	0.942926	+	0.333004i	$0.108062\pi$
$90$		0			0
$91$	−31.6844	−	163.595i	−0.348180	−	1.79774i
$92$	15.3895	−	7.41118i	0.167277	−	0.0805564i
$93$		0			0
$94$	108.258	−	24.7092i	1.15168	−	0.262864i
$95$	−99.0134	−	47.6824i	−1.04225	−	0.501920i
$96$		0			0
$97$			43.4868i			0.448318i	0.974553	+	0.224159i	$0.0719635\pi$
$97$			43.4868i			0.448318i	−0.974553	+	0.224159i	$0.928037\pi$
$98$	−67.5976	−	38.2547i	−0.689772	−	0.390354i
$99$		0			0
$100$	−7.94366	+	9.96103i	−0.0794366	+	0.0996103i
$101$	−46.1241	+	95.7777i	−0.456674	+	0.948294i	0.537776	+	0.843088i	$0.319265\pi$
$101$	−46.1241	+	95.7777i	−0.456674	+	0.948294i	−0.994450	+	0.105206i	$0.966450\pi$
$102$		0			0
$103$	24.9143	−	51.7351i	0.241887	−	0.502283i	−0.744316	−	0.667828i	$-0.767224\pi$
$103$	24.9143	−	51.7351i	0.241887	−	0.502283i	0.986202	+	0.165545i	$0.0529384\pi$
$104$	89.8399	+	186.554i	0.863845	+	1.79379i
$105$		0			0
$106$	70.4659	+	33.9346i	0.664773	+	0.320138i
$107$	78.0689	+	97.8953i	0.729616	+	0.914909i	0.998839	−	0.0481684i	$-0.0153384\pi$
$107$	78.0689	+	97.8953i	0.729616	+	0.914909i	−0.269223	+	0.963078i	$0.586767\pi$
$108$		0			0
$109$	80.3879	−	100.803i	0.737504	−	0.924800i	−0.261682	−	0.965154i	$-0.584277\pi$
$109$	80.3879	−	100.803i	0.737504	−	0.924800i	0.999185	+	0.0403539i	$0.0128485\pi$
$110$	63.7621	+	14.5533i	0.579655	+	0.132303i
$111$		0			0
$112$	53.0597	+	13.9726i	0.473747	+	0.124755i
$113$	25.0842	+	31.4546i	0.221984	+	0.278359i	0.880336	−	0.474351i	$-0.157317\pi$
$113$	25.0842	+	31.4546i	0.221984	+	0.278359i	−0.658352	+	0.752711i	$0.728746\pi$
$114$		0			0
$115$	45.3884	+	10.3596i	0.394682	+	0.0900835i
$116$	−2.24738			−0.0193740
$117$		0			0
$118$	−126.495	−	28.8716i	−1.07199	−	0.244675i
$119$	42.7838	+	57.4503i	0.359528	+	0.482775i
$120$		0			0
$121$	3.87479	+	16.9765i	0.0320230	+	0.140302i
$122$	110.920	−	88.4558i	0.909181	−	0.725048i
$123$		0			0
$124$	44.2487	−	10.0995i	0.356845	−	0.0814475i
$125$	−132.661	+	30.2790i	−1.06129	+	0.242232i
$126$		0			0
$127$	−32.4923	+	142.358i	−0.255845	+	1.12093i	0.669802	+	0.742540i	$0.266379\pi$
$127$	−32.4923	+	142.358i	−0.255845	+	1.12093i	−0.925647	+	0.378389i	$0.876478\pi$
$128$	−16.4305			−0.128363
$129$		0			0
$130$	−34.0389	+	149.134i	−0.261838	+	1.14719i
$131$	26.1072	+	54.2121i	0.199292	+	0.413833i	0.976533	−	0.215370i	$-0.0690957\pi$
$131$	26.1072	+	54.2121i	0.199292	+	0.413833i	−0.777241	+	0.629203i	$0.783381\pi$
$132$		0			0
$133$	−123.159	+	144.367i	−0.926007	+	1.08546i
$134$	14.0381	−	17.6032i	0.104762	−	0.131367i
$135$		0			0
$136$	−69.5896	−	55.4958i	−0.511688	−	0.408058i
$137$	−242.932	+	116.990i	−1.77323	+	0.853942i	−0.809472	+	0.587159i	$0.800246\pi$
$137$	−242.932	+	116.990i	−1.77323	+	0.853942i	−0.963757	+	0.266783i	$0.914039\pi$
$138$		0			0
$139$	27.5112	−	57.1276i	0.197922	−	0.410990i	−0.778260	−	0.627942i	$-0.783897\pi$
$139$	27.5112	−	57.1276i	0.197922	−	0.410990i	0.976182	+	0.216952i	$0.0696116\pi$
$140$	−25.2094	−	33.8513i	−0.180067	−	0.241795i
$141$		0			0
$142$	−37.0838	−	17.8586i	−0.261154	−	0.125765i
$143$	236.207	−	53.9126i	1.65179	−	0.377011i
$144$		0			0
$145$	−4.78904	−	3.81913i	−0.0330278	−	0.0263388i
$146$			121.007i			0.828817i
$147$		0			0
$148$	1.83205			0.0123787
$149$	−169.104	+	212.050i	−1.13493	+	1.42315i	−0.243551	+	0.969888i	$0.578312\pi$
$149$	−169.104	+	212.050i	−1.13493	+	1.42315i	−0.891376	+	0.453265i	$0.850259\pi$
$150$		0			0
$151$	14.5591	+	63.7876i	0.0964179	+	0.422434i	0.999982	−	0.00601879i	$-0.00191585\pi$
$151$	14.5591	+	63.7876i	0.0964179	+	0.422434i	−0.903564	+	0.428453i	$0.859059\pi$
$152$	102.309	−	212.447i	0.673087	−	1.39768i
$153$		0			0
$154$	52.3388	−	100.071i	0.339863	−	0.649813i
$155$	111.454	+	53.6735i	0.719059	+	0.346280i
$156$		0			0
$157$	127.401	+	264.551i	0.811472	+	1.68504i	0.724963	+	0.688788i	$0.241857\pi$
$157$	127.401	+	264.551i	0.811472	+	1.68504i	0.0865091	+	0.996251i	$0.472429\pi$
$158$	79.2319	−	99.3536i	0.501468	−	0.628820i
$159$		0			0
$160$	70.8941	+	56.5361i	0.443088	+	0.353351i
$161$	37.2568	−	71.2346i	0.231409	−	0.442451i
$162$		0			0
$163$	−19.6140	+	9.44561i	−0.120331	+	0.0579485i	−0.493081	−	0.869983i	$-0.664129\pi$
$163$	−19.6140	+	9.44561i	−0.120331	+	0.0579485i	0.372750	+	0.927932i	$0.378415\pi$
$164$	51.4945	+	11.7533i	0.313991	+	0.0716663i
$165$		0			0
$166$		−	119.843i		−	0.721944i
$167$	−90.3543	−	20.6228i	−0.541044	−	0.123490i	−0.0567390	−	0.998389i	$-0.518070\pi$
$167$	−90.3543	−	20.6228i	−0.541044	−	0.123490i	−0.484305	+	0.874899i	$0.660927\pi$
$168$		0			0
$169$	88.4911	+	387.705i	0.523616	+	2.29411i
$170$	−14.6322	−	64.1080i	−0.0860720	−	0.377106i
$171$		0			0
$172$	−54.3820	−	68.1928i	−0.316174	−	0.396470i
$173$	277.337	−	63.3004i	1.60311	−	0.365898i	0.674883	−	0.737924i	$-0.264194\pi$
$173$	277.337	−	63.3004i	1.60311	−	0.365898i	0.928222	+	0.372026i	$0.121337\pi$
$174$		0			0
$175$	−1.98387	+	59.9290i	−0.0113364	+	0.342452i
$176$	−17.7521	+	77.7769i	−0.100864	+	0.441914i
$177$		0			0
$178$			149.424i			0.839462i
$179$	−77.8280	+	340.987i	−0.434793	+	1.90495i	−0.00937604	+	0.999956i	$0.502985\pi$
$179$	−77.8280	+	340.987i	−0.434793	+	1.90495i	−0.425417	+	0.904997i	$0.639873\pi$
$180$		0			0
$181$	−141.931	+	113.187i	−0.784152	+	0.625340i	−0.931499	−	0.363745i	$-0.881498\pi$
$181$	−141.931	+	113.187i	−0.784152	+	0.625340i	0.147347	+	0.989085i	$0.452927\pi$
$182$	234.058	+	122.416i	1.28603	+	0.672616i
$183$		0			0
$184$	−22.2280	+	97.3871i	−0.120804	+	0.529278i
$185$	3.90400	+	3.11333i	0.0211027	+	0.0168288i
$186$		0			0
$187$	−81.4269	+	64.9358i	−0.435438	+	0.347250i
$188$	45.2075	−	93.8743i	0.240465	−	0.499331i
$189$		0			0
$190$	156.950	−	75.5829i	0.826050	−	0.397805i
$191$	−89.6102	−	43.1540i	−0.469163	−	0.225937i	0.184337	−	0.982863i	$-0.440986\pi$
$191$	−89.6102	−	43.1540i	−0.469163	−	0.225937i	−0.653501	+	0.756926i	$0.726700\pi$
$192$		0			0
$193$	−182.133	−	87.7105i	−0.943693	−	0.454458i	−0.102222	−	0.994762i	$-0.532595\pi$
$193$	−182.133	−	87.7105i	−0.943693	−	0.454458i	−0.841470	+	0.540303i	$0.818310\pi$
$194$	−53.8935	−	42.9787i	−0.277802	−	0.221539i
$195$		0			0
$196$	−67.6104	+	27.2097i	−0.344951	+	0.138825i
$197$	39.9281			0.202681			0.101340	−	0.994852i	$-0.467687\pi$
$197$	39.9281			0.202681			0.101340	+	0.994852i	$0.467687\pi$
$198$		0			0
$199$	91.5607	−	190.128i	0.460104	−	0.955416i	−0.533846	−	0.845582i	$-0.679254\pi$
$199$	91.5607	−	190.128i	0.460104	−	0.955416i	0.993950	−	0.109834i	$-0.0350320\pi$
$200$	−16.5797	−	72.6404i	−0.0828985	−	0.363202i
$201$		0			0
$202$	−73.1129	−	151.820i	−0.361945	−	0.751586i
$203$	−8.48306	+	6.31742i	−0.0417885	+	0.0311203i
$204$		0			0
$205$	89.7585	+	112.554i	0.437846	+	0.549042i
$206$	39.4925	+	82.0071i	0.191711	+	0.398092i
$207$		0			0
$208$	−181.914	−	41.5206i	−0.874585	−	0.199618i
$209$	−215.714	−	172.026i	−1.03212	−	0.823091i
$210$		0			0
$211$	−13.5143	−	16.9464i	−0.0640489	−	0.0803148i	0.748775	−	0.662824i	$-0.230642\pi$
$211$	−13.5143	−	16.9464i	−0.0640489	−	0.0803148i	−0.812824	+	0.582509i	$0.802071\pi$
$212$	66.1192	−	31.8413i	0.311883	−	0.150195i
$213$		0			0
$214$	−198.479			−0.927472
$215$		−	237.730i		−	1.10572i
$216$		0			0
$217$	138.633	−	162.506i	0.638863	−	0.748874i
$218$	45.4776	+	199.251i	0.208613	+	0.913993i
$219$		0			0
$220$	47.9790	−	38.2620i	0.218086	−	0.173918i
$221$	−151.879	−	190.451i	−0.687237	−	0.861768i
$222$		0			0
$223$	112.045	−	25.5736i	0.502445	−	0.114680i	0.0362160	−	0.999344i	$-0.488470\pi$
$223$	112.045	−	25.5736i	0.502445	−	0.114680i	0.466229	+	0.884664i	$0.345612\pi$
$224$	125.578	−	93.5194i	0.560617	−	0.417497i
$225$		0			0
$226$	−63.7729			−0.282181
$227$		−	20.0304i		−	0.0882395i	−0.999026	−	0.0441198i	$-0.985952\pi$
$227$		−	20.0304i		−	0.0882395i	0.999026	−	0.0441198i	$-0.0140483\pi$
$228$		0			0
$229$	−52.6712	−	109.373i	−0.230005	−	0.477610i	0.753742	−	0.657170i	$-0.228247\pi$
$229$	−52.6712	−	109.373i	−0.230005	−	0.477610i	−0.983747	+	0.179560i	$0.942533\pi$
$230$	−57.6967	+	46.0116i	−0.250855	+	0.200050i
$231$		0			0
$232$	8.19447	−	10.2755i	0.0353210	−	0.0442911i
$233$	4.82057	−	21.1203i	0.0206891	−	0.0906450i	−0.963529	−	0.267603i	$-0.913768\pi$
$233$	4.82057	−	21.1203i	0.0206891	−	0.0906450i	0.984218	+	0.176958i	$0.0566256\pi$
$234$		0			0
$235$	255.861	−	123.216i	1.08877	−	0.524325i
$236$	−95.1836	+	75.9064i	−0.403320	+	0.321637i
$237$		0			0
$238$	−113.482	−	3.75669i	−0.476817	−	0.0157844i
$239$	−282.974	+	136.273i	−1.18399	+	0.570180i	−0.919072	−	0.394090i	$-0.871060\pi$
$239$	−282.974	+	136.273i	−1.18399	+	0.570180i	−0.264920	+	0.964270i	$0.585345\pi$
$240$		0			0
$241$	−189.874	+	43.3374i	−0.787858	+	0.179823i	−0.597476	−	0.801887i	$-0.703830\pi$
$241$	−189.874	+	43.3374i	−0.787858	+	0.179823i	−0.190382	+	0.981710i	$0.560973\pi$
$242$	−24.8687	−	11.9761i	−0.102763	−	0.0494881i
$243$		0			0
$244$		−	133.121i		−	0.545576i
$245$	−190.313	−	56.9126i	−0.776788	−	0.232296i
$246$		0			0
$247$	402.355	−	504.537i	1.62897	−	2.04266i
$248$	−115.164	+	239.140i	−0.464371	+	0.964275i
$249$		0			0
$250$	93.5859	−	194.333i	0.374344	−	0.777332i
$251$	18.5853	+	38.5928i	0.0740451	+	0.153756i	0.934706	−	0.355423i	$-0.115663\pi$
$251$	18.5853	+	38.5928i	0.0740451	+	0.153756i	−0.860660	+	0.509179i	$0.829949\pi$
$252$		0			0
$253$	105.308	+	50.7138i	0.416238	+	0.200450i
$254$	−144.313	−	180.962i	−0.568160	−	0.712450i
$255$		0			0
$256$	−150.382	+	188.573i	−0.587429	+	0.736612i
$257$	−208.138	−	47.5061i	−0.809875	−	0.184849i	−0.202519	−	0.979278i	$-0.564913\pi$
$257$	−208.138	−	47.5061i	−0.809875	−	0.184849i	−0.607356	+	0.794430i	$0.707770\pi$
$258$		0			0
$259$	6.91535	−	5.14993i	0.0267002	−	0.0198839i
$260$	89.4916	+	112.219i	0.344199	+	0.431611i
$261$		0			0
$262$	−92.9876	−	21.2238i	−0.354914	−	0.0810069i
$263$	229.255			0.871693			0.435847	−	0.900021i	$-0.356449\pi$
$263$	229.255			0.871693			0.435847	+	0.900021i	$0.356449\pi$
$264$		0			0
$265$	195.006	+	44.5088i	0.735872	+	0.167958i
$266$	−57.1948	−	295.311i	−0.215018	−	1.11019i
$267$		0			0
$268$	−4.70108	−	20.5968i	−0.0175413	−	0.0768536i
$269$	181.876	−	145.042i	0.676121	−	0.539188i	−0.224130	−	0.974559i	$-0.571954\pi$
$269$	181.876	−	145.042i	0.676121	−	0.539188i	0.900251	+	0.435371i	$0.143383\pi$
$270$		0			0
$271$	285.500	−	65.1636i	1.05351	−	0.240456i	0.339508	−	0.940603i	$-0.389739\pi$
$271$	285.500	−	65.1636i	1.05351	−	0.240456i	0.713999	+	0.700147i	$0.246882\pi$
$272$	78.1989	−	17.8484i	0.287496	−	0.0656191i
$273$		0			0
$274$	95.1069	−	416.691i	0.347106	−	1.52077i
$275$	−87.1825			−0.317027
$276$		0			0
$277$	20.1310	−	88.1995i	0.0726749	−	0.318410i	−0.925504	−	0.378739i	$-0.876358\pi$
$277$	20.1310	−	88.1995i	0.0726749	−	0.318410i	0.998179	+	0.0603291i	$0.0192150\pi$
$278$	43.6090	+	90.5549i	0.156867	+	0.325737i
$279$		0			0
$280$	246.695	+	8.16653i	0.881054	+	0.0291662i
$281$	29.7810	−	37.3442i	0.105982	−	0.132897i	−0.726012	−	0.687683i	$-0.758628\pi$
$281$	29.7810	−	37.3442i	0.105982	−	0.132897i	0.831994	+	0.554785i	$0.187200\pi$
$282$		0			0
$283$	83.9603	+	66.9561i	0.296679	+	0.236594i	0.760504	−	0.649333i	$-0.224952\pi$
$283$	83.9603	+	66.9561i	0.296679	+	0.236594i	−0.463825	+	0.885927i	$0.653523\pi$
$284$	−34.7963	+	16.7570i	−0.122522	+	0.0590036i
$285$		0			0
$286$	−166.632	+	346.015i	−0.582630	+	1.20984i
$287$	227.412	−	100.387i	0.792376	−	0.349781i
$288$		0			0
$289$	−166.036	−	79.9587i	−0.574519	−	0.276674i
$290$	9.46615	−	2.16059i	0.0326419	−	0.00745030i
$291$		0			0
$292$	88.7714	+	70.7928i	0.304011	+	0.242441i
$293$			289.590i			0.988361i	0.869359	+	0.494181i	$0.164532\pi$
$293$			289.590i			0.988361i	−0.869359	+	0.494181i	$0.835468\pi$
$294$		0			0
$295$	−331.823			−1.12482
$296$	−6.68009	+	8.37657i	−0.0225679	+	0.0282992i
$297$		0			0
$298$	−95.6668	−	419.144i	−0.321030	−	1.40652i
$299$	−118.615	+	246.307i	−0.396707	+	0.823770i
$300$		0			0
$301$	−396.963	−	104.535i	−1.31882	−	0.347293i
$302$	−93.4414	−	44.9990i	−0.309409	−	0.149003i
$303$		0			0
$304$	92.1959	+	191.447i	0.303276	+	0.629759i
$305$	226.221	−	283.672i	0.741708	−	0.930072i
$306$		0			0
$307$	101.751	+	81.1433i	0.331435	+	0.264311i	0.775040	−	0.631912i	$-0.217729\pi$
$307$	101.751	+	81.1433i	0.331435	+	0.264311i	−0.443606	+	0.896222i	$0.646301\pi$
$308$	−42.7928	−	96.9405i	−0.138938	−	0.314742i
$309$		0			0
$310$	−176.670	+	85.0796i	−0.569902	+	0.274450i
$311$	429.740	+	98.0853i	1.38180	+	0.315387i	0.847898	−	0.530160i	$-0.177868\pi$
$311$	429.740	+	98.0853i	1.38180	+	0.315387i	0.533902	+	0.845546i	$0.320725\pi$
$312$		0			0
$313$		−	160.904i		−	0.514070i	−0.966402	−	0.257035i	$-0.917255\pi$
$313$		−	160.904i		−	0.514070i	0.966402	−	0.257035i	$-0.0827455\pi$
$314$	−453.772	−	103.571i	−1.44514	−	0.329843i
$315$		0			0
$316$	−26.5332	−	116.250i	−0.0839658	−	0.367878i
$317$	−131.702	−	577.026i	−0.415465	−	1.82027i	−0.557214	−	0.830369i	$-0.688130\pi$
$317$	−131.702	−	577.026i	−0.415465	−	1.82027i	0.141749	−	0.989903i	$-0.454728\pi$
$318$		0			0
$319$	−9.58837	−	12.0234i	−0.0300576	−	0.0376910i
$320$	−264.048	+	60.2672i	−0.825150	+	0.188335i
$321$		0			0
$322$	51.4601	+	116.575i	0.159814	+	0.362034i
$323$	−61.7285	+	270.450i	−0.191110	+	0.837307i
$324$		0			0
$325$		−	203.913i		−	0.627424i
$326$	7.67880	−	33.6430i	0.0235546	−	0.103199i
$327$		0			0
$328$	−241.499	+	192.589i	−0.736279	+	0.587163i
$329$	−93.2398	−	481.420i	−0.283404	−	1.46328i
$330$		0			0
$331$	−63.3603	+	277.600i	−0.191421	+	0.838669i	0.784428	+	0.620220i	$0.212957\pi$
$331$	−63.3603	+	277.600i	−0.191421	+	0.838669i	−0.975848	+	0.218449i	$0.929900\pi$
$332$	−87.9170	−	70.1114i	−0.264810	−	0.211179i
$333$		0			0
$334$	114.856	−	91.5949i	0.343882	−	0.274236i
$335$	24.9838	−	51.8793i	0.0745784	−	0.154864i
$336$		0			0
$337$	−200.244	+	96.4323i	−0.594195	+	0.286149i	−0.706713	−	0.707501i	$-0.749823\pi$
$337$	−200.244	+	96.4323i	−0.594195	+	0.286149i	0.112518	+	0.993650i	$0.464108\pi$
$338$	−567.943	−	273.507i	−1.68030	−	0.809192i
$339$		0			0
$340$	−55.5902	−	26.7708i	−0.163501	−	0.0787377i
$341$	242.817	+	193.640i	0.712075	+	0.567860i
$342$		0			0
$343$	−178.718	+	292.761i	−0.521044	+	0.853530i
$344$	510.082			1.48280
$345$		0			0
$346$	−195.648	+	406.267i	−0.565456	+	1.17418i
$347$	122.768	+	537.884i	0.353799	+	1.55010i	0.768326	+	0.640059i	$0.221090\pi$
$347$	122.768	+	537.884i	0.353799	+	1.55010i	−0.414526	+	0.910037i	$0.636053\pi$
$348$		0			0
$349$	159.047	+	330.264i	0.455721	+	0.946315i	0.994585	+	0.103922i	$0.0331392\pi$
$349$	159.047	+	330.264i	0.455721	+	0.946315i	−0.538864	+	0.842393i	$0.681146\pi$
$350$	−72.3098	−	61.6874i	−0.206599	−	0.176250i
$351$		0			0
$352$	141.941	+	177.988i	0.403240	+	0.505647i
$353$	−109.964	−	228.343i	−0.311513	−	0.646863i	0.685158	−	0.728395i	$-0.259733\pi$
$353$	−109.964	−	228.343i	−0.311513	−	0.646863i	−0.996671	+	0.0815313i	$0.974019\pi$
$354$		0			0
$355$	−102.625	−	23.4235i	−0.289085	−	0.0659817i
$356$	109.618	+	87.4175i	0.307916	+	0.245555i
$357$		0			0
$358$	−345.669	−	433.455i	−0.965555	−	1.21077i
$359$	−582.310	+	280.426i	−1.62203	+	0.781130i	−0.999998	−	0.00185886i	$-0.999408\pi$
$359$	−582.310	+	280.426i	−1.62203	+	0.781130i	−0.622035	+	0.782989i	$0.713694\pi$
$360$		0			0
$361$	−373.895			−1.03572
$362$		−	287.761i		−	0.794919i
$363$		0			0
$364$	226.736	−	100.089i	0.622901	−	0.274969i
$365$	68.8634	+	301.710i	0.188667	+	0.826603i
$366$		0			0
$367$	143.495	−	114.433i	0.390994	−	0.311807i	−0.408187	−	0.912899i	$-0.633839\pi$
$367$	143.495	−	114.433i	0.390994	−	0.311807i	0.799180	+	0.601091i	$0.205267\pi$
$368$	−56.1249	−	70.3784i	−0.152513	−	0.191246i
$369$		0			0
$370$	−7.71675	+	1.76130i	−0.0208561	+	0.00476027i
$371$	160.070	−	306.051i	0.431455	−	0.824936i
$372$		0			0
$373$	74.8378			0.200638			0.100319	−	0.994955i	$-0.468014\pi$
$373$	74.8378			0.200638			0.100319	+	0.994955i	$0.468014\pi$
$374$		−	165.090i		−	0.441417i
$375$		0			0
$376$	264.378	+	548.986i	0.703132	+	1.46007i
$377$	28.1218	−	22.4264i	0.0745937	−	0.0594865i
$378$		0			0
$379$	56.6054	−	70.9809i	0.149355	−	0.187285i	−0.701526	−	0.712644i	$-0.747498\pi$
$379$	56.6054	−	70.9809i	0.149355	−	0.187285i	0.850881	+	0.525359i	$0.176069\pi$
$380$	36.3722	−	159.357i	0.0957162	−	0.419360i
$381$		0			0
$382$	142.044	−	68.4048i	0.371843	−	0.179070i
$383$	299.807	−	239.088i	0.782786	−	0.624251i	−0.148345	−	0.988936i	$-0.547395\pi$
$383$	299.807	−	239.088i	0.782786	−	0.624251i	0.931131	+	0.364684i	$0.118823\pi$
$384$		0			0
$385$	73.5487	−	279.295i	0.191035	−	0.725441i
$386$	288.705	−	139.033i	0.747939	−	0.360189i
$387$		0			0
$388$	−63.0586	+	14.3927i	−0.162522	+	0.0370946i
$389$	−324.710	−	156.372i	−0.834730	−	0.401985i	−0.0328428	−	0.999461i	$-0.510456\pi$
$389$	−324.710	−	156.372i	−0.834730	−	0.401985i	−0.801887	+	0.597476i	$0.796170\pi$
$390$		0			0
$391$		−	117.518i		−	0.300556i
$392$	122.114	−	408.343i	0.311515	−	1.04169i
$393$		0			0
$394$	−39.4615	+	49.4831i	−0.100156	+	0.125592i
$395$	141.010	−	292.810i	0.356987	−	0.741292i
$396$		0			0
$397$	153.756	−	319.277i	0.387294	−	0.804225i	−0.612610	−	0.790385i	$-0.709880\pi$
$397$	153.756	−	319.277i	0.387294	−	0.804225i	0.999904	−	0.0138393i	$-0.00440532\pi$
$398$	145.136	+	301.378i	0.364663	+	0.757231i
$399$		0			0
$400$	60.4941	+	29.1324i	0.151235	+	0.0728310i
$401$	295.196	+	370.163i	0.736148	+	0.923101i	0.999130	−	0.0416999i	$-0.0132773\pi$
$401$	295.196	+	370.163i	0.736148	+	0.923101i	−0.262982	+	0.964801i	$0.584706\pi$
$402$		0			0
$403$	−452.909	+	567.930i	−1.12384	+	1.40926i
$404$	−154.149	−	35.1835i	−0.381557	−	0.0870880i
$405$		0			0
$406$	0.554710	−	16.7567i	0.00136628	−	0.0412727i
$407$	7.81639	+	9.80144i	0.0192049	+	0.0240822i
$408$		0			0
$409$	−83.5238	−	19.0638i	−0.204215	−	0.0466107i	0.119190	−	0.992871i	$-0.461970\pi$
$409$	−83.5238	−	19.0638i	−0.204215	−	0.0466107i	−0.323405	+	0.946261i	$0.604827\pi$
$410$	−228.198			−0.556581
$411$		0			0
$412$	83.2649	+	19.0047i	0.202099	+	0.0461279i
$413$	−145.910	+	554.082i	−0.353293	+	1.34160i
$414$		0			0
$415$	−68.2006	−	298.806i	−0.164339	−	0.720016i
$416$	−416.299	+	331.987i	−1.00072	+	0.798046i
$417$		0			0
$418$	426.386	−	97.3199i	1.02006	−	0.232823i
$419$	125.893	−	28.7344i	0.300462	−	0.0685784i	−0.0696323	−	0.997573i	$-0.522183\pi$
$419$	125.893	−	28.7344i	0.300462	−	0.0685784i	0.370094	+	0.928994i	$0.379325\pi$
$420$		0			0
$421$	52.7767	−	231.230i	0.125360	−	0.549240i	−0.872771	−	0.488130i	$-0.837679\pi$
$421$	52.7767	−	231.230i	0.125360	−	0.549240i	0.998131	−	0.0611093i	$-0.0194638\pi$
$422$	34.3582			0.0814175
$423$		0			0
$424$	−95.4999	+	418.413i	−0.225236	+	0.986822i
$425$	38.0323	+	78.9749i	0.0894878	+	0.185823i
$426$		0			0
$427$	−374.204	−	502.483i	−0.876355	−	1.17677i
$428$	−116.116	+	145.605i	−0.271299	+	0.340198i
$429$		0			0
$430$	294.620	+	234.952i	0.685163	+	0.546399i
$431$	−655.101	+	315.480i	−1.51996	+	0.731972i	−0.993021	−	0.117935i	$-0.962373\pi$
$431$	−655.101	+	315.480i	−1.51996	+	0.731972i	−0.526934	+	0.849906i	$0.676658\pi$
$432$		0			0
$433$	−130.725	+	271.454i	−0.301906	+	0.626914i	−0.995636	−	0.0933210i	$-0.970252\pi$
$433$	−130.725	+	271.454i	−0.301906	+	0.626914i	0.693730	+	0.720235i	$0.255966\pi$
$434$	64.3811	+	332.416i	0.148344	+	0.765935i
$435$		0			0
$436$	172.777	+	83.2049i	0.396277	+	0.190837i
$437$	303.519	−	69.2761i	0.694551	−	0.158527i
$438$		0			0
$439$	303.866	+	242.325i	0.692177	+	0.551993i	0.905164	−	0.425062i	$-0.139748\pi$
$439$	303.866	+	242.325i	0.692177	+	0.551993i	−0.212987	+	0.977055i	$0.568319\pi$
$440$			358.883i			0.815643i
$441$		0			0
$442$	386.132			0.873601
$443$	217.571	−	272.825i	0.491131	−	0.615859i	−0.473072	−	0.881024i	$-0.656855\pi$
$443$	217.571	−	272.825i	0.491131	−	0.615859i	0.964203	+	0.265165i	$0.0854265\pi$
$444$		0			0
$445$	85.0351	+	372.563i	0.191090	+	0.837220i
$446$	−79.0423	+	164.133i	−0.177225	+	0.368011i
$447$		0			0
$448$	−15.4730	+	467.411i	−0.0345380	+	1.04333i
$449$	−252.970	−	121.824i	−0.563408	−	0.271323i	0.130426	−	0.991458i	$-0.458366\pi$
$449$	−252.970	−	121.824i	−0.563408	−	0.271323i	−0.693834	+	0.720135i	$0.744080\pi$
$450$		0			0
$451$	156.819	+	325.639i	0.347715	+	0.722038i
$452$	−37.3090	+	46.7841i	−0.0825421	+	0.103505i
$453$		0			0
$454$	24.8238	+	19.7963i	0.0546779	+	0.0436042i
$455$	653.248	+	172.024i	1.43571	+	0.378075i
$456$		0			0
$457$	−266.755	+	128.463i	−0.583710	+	0.281100i	−0.702343	−	0.711838i	$-0.747863\pi$
$457$	−266.755	+	128.463i	−0.583710	+	0.281100i	0.118634	+	0.992938i	$0.462149\pi$
$458$	187.602	+	42.8190i	0.409612	+	0.0934912i
$459$		0			0
$460$			69.2446i			0.150532i
$461$	−536.799	−	122.521i	−1.16442	−	0.265772i	−0.403726	−	0.914880i	$-0.632285\pi$
$461$	−536.799	−	122.521i	−1.16442	−	0.265772i	−0.760696	+	0.649108i	$0.775142\pi$
$462$		0			0
$463$	101.698	+	445.568i	0.219650	+	0.962349i	0.957737	+	0.287644i	$0.0928721\pi$
$463$	101.698	+	445.568i	0.219650	+	0.962349i	−0.738087	+	0.674705i	$0.764271\pi$
$464$	2.63548	+	11.5468i	0.00567991	+	0.0248853i
$465$		0			0
$466$	21.4103	+	26.8476i	0.0459448	+	0.0576129i
$467$	501.820	−	114.537i	1.07456	−	0.245261i	0.351600	−	0.936150i	$-0.385638\pi$
$467$	501.820	−	114.537i	1.07456	−	0.245261i	0.722961	+	0.690889i	$0.242781\pi$
$468$		0			0
$469$	−75.6427	−	64.5306i	−0.161285	−	0.137592i
$470$	−100.169	+	438.867i	−0.213125	+	0.933760i
$471$		0			0
$472$		−	711.973i		−	1.50842i
$473$	132.811	−	581.884i	0.280785	−	1.23020i
$474$		0			0
$475$	−181.553	+	144.783i	−0.382216	+	0.304807i
$476$	−69.1464	+	81.0533i	−0.145266	+	0.170280i
$477$		0			0
$478$	110.783	−	485.372i	0.231764	−	1.01542i
$479$	454.008	+	362.059i	0.947825	+	0.755865i	0.969802	−	0.243893i	$-0.0784247\pi$
$479$	454.008	+	362.059i	0.947825	+	0.755865i	−0.0219772	+	0.999758i	$0.506996\pi$
$480$		0			0
$481$	−22.9248	+	18.2819i	−0.0476606	+	0.0380081i
$482$	133.947	−	278.143i	0.277897	−	0.577060i
$483$		0			0
$484$	−23.3346	+	11.2374i	−0.0482120	+	0.0232177i
$485$	−158.832	−	76.4897i	−0.327490	−	0.157711i
$486$		0			0
$487$	−84.6921	−	40.7856i	−0.173906	−	0.0837486i	0.344906	−	0.938637i	$-0.387911\pi$
$487$	−84.6921	−	40.7856i	−0.173906	−	0.0837486i	−0.518811	+	0.854889i	$0.673625\pi$
$488$	608.658	+	485.388i	1.24725	+	0.994648i
$489$		0			0
$490$	258.621	−	179.609i	0.527799	−	0.366548i
$491$	700.162			1.42599			0.712996	−	0.701168i	$-0.247338\pi$
$491$	700.162			1.42599			0.712996	+	0.701168i	$0.247338\pi$
$492$		0			0
$493$	−6.70871	+	13.9308i	−0.0136079	+	0.0282571i
$494$	227.623	+	997.282i	0.460776	+	2.01879i
$495$		0			0
$496$	−103.780	−	215.501i	−0.209234	−	0.434478i
$497$	−84.2394	+	161.065i	−0.169496	+	0.324073i
$498$		0			0
$499$	−401.262	−	503.167i	−0.804132	−	1.00835i	−0.999618	−	0.0276433i	$-0.991200\pi$
$499$	−401.262	−	503.167i	−0.804132	−	1.00835i	0.195486	−	0.980707i	$-0.437372\pi$
$500$	−87.8130	−	182.345i	−0.175626	−	0.364691i
$501$		0			0
$502$	−66.1965	−	15.1089i	−0.131866	−	0.0300975i
$503$	145.702	+	116.193i	0.289665	+	0.231000i	0.757531	−	0.652799i	$-0.226405\pi$
$503$	145.702	+	116.193i	0.289665	+	0.231000i	−0.467866	+	0.883800i	$0.654977\pi$
$504$		0			0
$505$	−268.693	−	336.930i	−0.532065	−	0.667188i
$506$	−166.928	+	80.3881i	−0.329896	+	0.158870i
$507$		0			0
$508$	−217.182			−0.427523
$509$			213.086i			0.418636i	0.977848	+	0.209318i	$0.0671243\pi$
$509$			213.086i			0.418636i	−0.977848	+	0.209318i	$0.932876\pi$
$510$		0			0
$511$	534.080	+	17.6800i	1.04517	+	0.0345989i
$512$	−99.6996	−	436.813i	−0.194726	−	0.853150i
$513$		0			0
$514$	264.580	−	210.996i	0.514748	−	0.410498i
$515$	145.137	+	181.996i	0.281819	+	0.353389i
$516$		0			0
$517$	695.101	−	158.652i	1.34449	−	0.306871i
$518$	−0.452196	+	13.6600i	−0.000872966	+	0.0263706i
$519$		0			0
$520$	−839.398			−1.61423
$521$		−	564.118i		−	1.08276i	−0.840778	−	0.541380i	$-0.817902\pi$
$521$		−	564.118i		−	1.08276i	0.840778	−	0.541380i	$-0.182098\pi$
$522$		0			0
$523$	88.4193	+	183.604i	0.169062	+	0.351060i	0.968236	−	0.250040i	$-0.0804437\pi$
$523$	88.4193	+	183.604i	0.169062	+	0.351060i	−0.799174	+	0.601100i	$0.794729\pi$
$524$	−69.9703	+	55.7995i	−0.133531	+	0.106488i
$525$		0			0
$526$	−226.576	+	284.118i	−0.430753	+	0.540148i
$527$	69.4844	−	304.431i	0.131849	−	0.577668i
$528$		0			0
$529$	357.787	−	172.301i	0.676346	−	0.325711i
$530$	−247.887	+	197.684i	−0.467712	+	0.372988i
$531$		0			0
$532$	−250.102	−	130.807i	−0.470117	−	0.245879i
$533$	−761.643	+	366.788i	−1.42897	+	0.688157i
$534$		0			0
$535$	−494.872	+	112.951i	−0.924995	+	0.211124i
$536$	111.314	+	53.6061i	0.207676	+	0.100011i
$537$		0			0
$538$			368.748i			0.685404i
$539$	−434.028	−	245.625i	−0.805248	−	0.455704i
$540$		0			0
$541$	453.131	−	568.208i	0.837580	−	1.05029i	−0.160418	−	0.987049i	$-0.551284\pi$
$541$	453.131	−	568.208i	0.837580	−	1.05029i	0.997998	−	0.0632435i	$-0.0201445\pi$
$542$	−201.407	+	418.225i	−0.371599	+	0.771633i
$543$		0			0
$544$	99.3117	−	206.223i	0.182558	−	0.379086i
$545$	226.781	+	470.915i	0.416112	+	0.864065i
$546$		0			0
$547$	279.320	+	134.513i	0.510640	+	0.245911i	0.671417	−	0.741080i	$-0.265686\pi$
$547$	279.320	+	134.513i	0.510640	+	0.245911i	−0.160778	+	0.986991i	$0.551400\pi$
$548$	−250.045	−	313.547i	−0.456287	−	0.572166i
$549$		0			0
$550$	86.1637	−	108.046i	0.156661	−	0.196447i
$551$	−39.9345	−	9.11479i	−0.0724764	−	0.0165423i
$552$		0			0
$553$	−426.932	−	364.215i	−0.772030	−	0.658617i
$554$	89.4105	+	112.117i	0.161391	+	0.202378i
$555$		0			0
$556$	91.9439	+	20.9856i	0.165367	+	0.0377439i
$557$	67.0557			0.120387			0.0601937	−	0.998187i	$-0.480828\pi$
$557$	67.0557			0.120387			0.0601937	+	0.998187i	$0.480828\pi$
$558$		0			0
$559$	1360.98	+	310.635i	2.43467	+	0.555697i
$560$	−144.361	+	169.220i	−0.257788	+	0.302179i
$561$		0			0
$562$	16.8479	+	73.8156i	0.0299785	+	0.131344i
$563$	50.3727	−	40.1709i	0.0894720	−	0.0713515i	−0.577732	−	0.816226i	$-0.696062\pi$
$563$	50.3727	−	40.1709i	0.0894720	−	0.0713515i	0.667204	+	0.744875i	$0.267491\pi$
$564$		0			0
$565$	−159.007	+	36.2922i	−0.281428	+	0.0642340i
$566$	−165.958	+	37.8789i	−0.293213	+	0.0669239i
$567$		0			0
$568$	50.2584	−	220.196i	0.0884831	−	0.387670i
$569$	278.849			0.490068			0.245034	−	0.969515i	$-0.421201\pi$
$569$	278.849			0.490068			0.245034	+	0.969515i	$0.421201\pi$
$570$		0			0
$571$	44.9547	−	196.959i	0.0787297	−	0.344937i	−0.920187	−	0.391480i	$-0.871963\pi$
$571$	44.9547	−	196.959i	0.0787297	−	0.344937i	0.998916	+	0.0465426i	$0.0148203\pi$
$572$	156.353	+	324.671i	0.273345	+	0.567606i
$573$		0			0
$574$	−100.344	+	381.047i	−0.174815	+	0.663845i
$575$	61.3348	−	76.9114i	0.106669	−	0.133759i
$576$		0			0
$577$	−183.274	−	146.156i	−0.317633	−	0.253304i	0.451674	−	0.892183i	$-0.350827\pi$
$577$	−183.274	−	146.156i	−0.317633	−	0.253304i	−0.769307	+	0.638879i	$0.779398\pi$
$578$	263.189	−	126.745i	0.455344	−	0.219282i
$579$		0			0
$580$	3.95296	−	8.20840i	0.00681545	−	0.0141524i
$581$	−528.939	−	17.5099i	−0.910395	−	0.0301374i
$582$		0			0
$583$	452.445	+	217.886i	0.776063	+	0.373732i
$584$	−647.361	+	147.756i	−1.10850	+	0.253007i
$585$		0			0
$586$	−358.891	−	286.206i	−0.612441	−	0.488406i
$587$		−	819.047i		−	1.39531i	−0.716434	−	0.697655i	$-0.754227\pi$
$587$		−	819.047i		−	1.39531i	0.716434	−	0.697655i	$-0.245773\pi$
$588$		0			0
$589$	827.231			1.40447
$590$	327.946	−	411.231i	0.555840	−	0.697002i
$591$		0			0
$592$	−2.14843	−	9.41289i	−0.00362910	−	0.0159001i
$593$	245.276	−	509.320i	0.413618	−	0.858887i	−0.585228	−	0.810869i	$-0.698995\pi$
$593$	245.276	−	509.320i	0.413618	−	0.858887i	0.998846	−	0.0480184i	$-0.0152906\pi$
$594$		0			0
$595$	−285.086	+	55.2145i	−0.479136	+	0.0927974i
$596$	−363.453	−	175.030i	−0.609821	−	0.293674i
$597$		0			0
$598$	−188.021	−	390.430i	−0.314417	−	0.652893i
$599$	145.984	−	183.059i	0.243713	−	0.305607i	−0.644897	−	0.764269i	$-0.723100\pi$
$599$	145.984	−	183.059i	0.243713	−	0.305607i	0.888611	+	0.458662i	$0.151671\pi$
$600$		0			0
$601$	−808.338	−	644.628i	−1.34499	−	1.07259i	−0.990497	−	0.137533i	$-0.956083\pi$
$601$	−808.338	−	644.628i	−1.34499	−	1.07259i	−0.354491	−	0.935059i	$-0.615346\pi$
$602$	521.876	−	388.646i	0.866903	−	0.645591i
$603$		0			0
$604$	−87.6774	+	42.2232i	−0.145161	+	0.0699059i
$605$	−68.8211	−	15.7080i	−0.113754	−	0.0259636i
$606$		0			0
$607$			1092.53i			1.79989i	0.436008	+	0.899943i	$0.356392\pi$
$607$			1092.53i			1.79989i	−0.436008	+	0.899943i	$0.643608\pi$
$608$	591.166	+	134.930i	0.972313	+	0.221924i
$609$		0			0
$610$	127.979	+	560.714i	0.209802	+	0.919203i
$611$	371.074	+	1625.78i	0.607323	+	2.66086i
$612$		0			0
$613$	423.418	+	530.949i	0.690731	+	0.866149i	0.996293	−	0.0860233i	$-0.0274159\pi$
$613$	423.418	+	530.949i	0.690731	+	0.866149i	−0.305563	+	0.952172i	$0.598845\pi$
$614$	−201.123	+	45.9050i	−0.327562	+	0.0747639i
$615$		0			0
$616$	599.266	+	157.809i	0.972835	+	0.256183i
$617$	67.5136	−	295.797i	0.109422	−	0.479411i	−0.890289	−	0.455396i	$-0.849498\pi$
$617$	67.5136	−	295.797i	0.109422	−	0.479411i	0.999712	−	0.0240153i	$-0.00764506\pi$
$618$		0			0
$619$			438.263i			0.708017i	0.935242	+	0.354009i	$0.115182\pi$
$619$			438.263i			0.708017i	−0.935242	+	0.354009i	$0.884818\pi$
$620$	−40.9422	+	179.379i	−0.0660358	+	0.289322i
$621$		0			0
$622$	−546.276	+	435.640i	−0.878257	+	0.700387i
$623$	659.501	+	21.8319i	1.05859	+	0.0350432i
$624$		0			0
$625$	75.0951	−	329.013i	0.120152	−	0.526421i
$626$	199.409	+	159.023i	0.318545	+	0.254031i
$627$		0			0
$628$	−341.450	+	272.297i	−0.543710	+	0.433594i
$629$	5.46890	−	11.3563i	0.00869460	−	0.0180545i
$630$		0			0
$631$	316.100	−	152.226i	0.500951	−	0.241245i	−0.166304	−	0.986074i	$-0.553183\pi$
$631$	316.100	−	152.226i	0.500951	−	0.241245i	0.667255	+	0.744829i	$0.267469\pi$
$632$	628.266	+	302.557i	0.994091	+	0.478729i
$633$		0			0
$634$	845.276	+	407.063i	1.33324	+	0.642056i
$635$	−462.801	−	369.071i	−0.728820	−	0.581215i
$636$		0			0
$637$	574.495	−	1015.16i	0.901877	−	1.59365i
$638$	24.3771			0.0382085
$639$		0			0
$640$	28.8999	−	60.0113i	0.0451561	−	0.0937677i
$641$	111.259	+	487.456i	0.173570	+	0.760461i	0.984510	+	0.175331i	$0.0560995\pi$
$641$	111.259	+	487.456i	0.173570	+	0.760461i	−0.810939	+	0.585130i	$0.801043\pi$
$642$		0			0
$643$	−304.497	−	632.295i	−0.473557	−	0.983352i	−0.991762	−	0.128095i	$-0.959114\pi$
$643$	−304.497	−	632.295i	−0.473557	−	0.983352i	0.518205	−	0.855257i	$-0.326601\pi$
$644$	115.625	+	30.4484i	0.179542	+	0.0472802i
$645$		0			0
$646$	−274.164	−	343.790i	−0.424402	−	0.532183i
$647$	38.6694	+	80.2979i	0.0597673	+	0.124108i	0.928713	−	0.370799i	$-0.120916\pi$
$647$	38.6694	+	80.2979i	0.0597673	+	0.124108i	−0.868946	+	0.494907i	$0.835202\pi$
$648$		0			0
$649$	−812.194	−	185.378i	−1.25145	−	0.285636i
$650$	252.710	+	201.530i	0.388785	+	0.310046i
$651$		0			0
$652$	−20.1883	−	25.3153i	−0.0309637	−	0.0388272i
$653$	120.704	−	58.1280i	0.184845	−	0.0890168i	−0.339172	−	0.940724i	$-0.610147\pi$
$653$	120.704	−	58.1280i	0.184845	−	0.0890168i	0.524017	+	0.851708i	$0.324433\pi$
$654$		0			0
$655$	−243.926			−0.372407
$656$		−	278.356i		−	0.424323i
$657$		0			0
$658$	688.778	+	360.242i	1.04678	+	0.547480i
$659$	−207.586	−	909.495i	−0.315002	−	1.38011i	−0.846200	−	0.532866i	$-0.821115\pi$
$659$	−207.586	−	909.495i	−0.315002	−	1.38011i	0.531198	−	0.847248i	$-0.321742\pi$
$660$		0			0
$661$	−833.082	+	664.361i	−1.26034	+	1.00508i	−0.261127	+	0.965304i	$0.584094\pi$
$661$	−833.082	+	664.361i	−1.26034	+	1.00508i	−0.999208	+	0.0397796i	$0.987334\pi$
$662$	−281.411	−	352.878i	−0.425092	−	0.533049i
$663$		0			0
$664$	641.131	−	146.334i	0.965559	−	0.220382i
$665$	−310.662	−	703.758i	−0.467161	−	1.05828i
$666$		0			0
$667$	17.3526			0.0260158
$668$		−	137.845i		−	0.206354i
$669$		0			0
$670$	39.6026	+	82.2356i	0.0591083	+	0.122740i
$671$	712.191	−	567.954i	1.06139	−	0.846429i
$672$		0			0
$673$	−280.425	+	351.642i	−0.416679	+	0.522499i	−0.945231	−	0.326402i	$-0.894164\pi$
$673$	−280.425	+	351.642i	−0.416679	+	0.522499i	0.528552	+	0.848901i	$0.322735\pi$
$674$	78.3945	−	343.469i	0.116312	−	0.509598i
$675$		0			0
$676$	−532.908	+	256.635i	−0.788326	+	0.379638i
$677$	528.559	−	421.512i	0.780737	−	0.622617i	−0.149841	−	0.988710i	$-0.547876\pi$
$677$	528.559	−	421.512i	0.780737	−	0.622617i	0.930578	+	0.366093i	$0.119305\pi$
$678$		0			0
$679$	−197.565	+	231.586i	−0.290965	+	0.341069i
$680$	325.097	−	156.558i	0.478084	−	0.230233i
$681$		0			0
$682$	−479.960	+	109.548i	−0.703754	+	0.160627i
$683$	−912.730	−	439.548i	−1.33635	−	0.643554i	−0.377120	−	0.926165i	$-0.623085\pi$
$683$	−912.730	−	439.548i	−1.33635	−	0.643554i	−0.959235	+	0.282610i	$0.908800\pi$
$684$		0			0
$685$		−	1093.07i		−	1.59572i
$686$	−186.191	−	510.826i	−0.271415	−	0.744645i
$687$		0			0
$688$	−286.594	+	359.377i	−0.416561	+	0.522351i
$689$	−509.617	+	1058.23i	−0.739648	+	1.53589i
$690$		0			0
$691$	−478.274	+	993.147i	−0.692148	+	1.43726i	0.197355	+	0.980332i	$0.436765\pi$
$691$	−478.274	+	993.147i	−0.692148	+	1.43726i	−0.889504	+	0.456928i	$0.848950\pi$
$692$	183.579	+	381.206i	0.265288	+	0.550875i
$693$		0			0
$694$	−787.937	−	379.450i	−1.13536	−	0.546758i
$695$	160.265	+	200.966i	0.230597	+	0.289159i
$696$		0			0
$697$	226.572	−	284.112i	0.325067	−	0.407621i
$698$	−566.486	−	129.297i	−0.811585	−	0.185239i
$699$		0			0
$700$	−87.5574	+	16.9578i	−0.125082	+	0.0242254i
$701$	−306.313	−	384.104i	−0.436965	−	0.547937i	0.513775	−	0.857925i	$-0.328246\pi$
$701$	−306.313	−	384.104i	−0.436965	−	0.547937i	−0.950741	+	0.309988i	$0.899675\pi$
$702$		0			0
$703$	32.5544	+	7.43033i	0.0463078	+	0.0105695i
$704$	−679.972			−0.965869
$705$		0			0
$706$	391.666	+	89.3952i	0.554767	+	0.126622i
$707$	−680.759	+	300.510i	−0.962884	+	0.425050i
$708$		0			0
$709$	277.513	+	1215.87i	0.391415	+	1.71490i	0.659672	+	0.751554i	$0.270695\pi$
$709$	277.513	+	1215.87i	0.391415	+	1.71490i	−0.268257	+	0.963347i	$0.586448\pi$
$710$	130.455	−	104.034i	0.183739	−	0.146527i
$711$		0			0
$712$	−799.386	+	182.455i	−1.12273	+	0.256256i
$713$	−341.654	+	77.9804i	−0.479179	+	0.109369i
$714$		0			0
$715$	−218.556	+	957.556i	−0.305672	+	1.33924i
$716$	−520.210			−0.726551
$717$		0			0
$718$	227.972	−	998.810i	0.317509	−	1.39110i
$719$	−74.7132	−	155.143i	−0.103913	−	0.215777i	0.842530	−	0.538650i	$-0.181065\pi$
$719$	−74.7132	−	155.143i	−0.103913	−	0.215777i	−0.946442	+	0.322873i	$0.895351\pi$
$720$		0			0
$721$	367.718	−	162.323i	0.510011	−	0.225136i
$722$	369.525	−	463.370i	0.511808	−	0.641787i
$723$		0			0
$724$	−211.102	−	168.348i	−0.291578	−	0.232525i
$725$	−11.6614	+	5.61582i	−0.0160847	+	0.00774597i
$726$		0			0
$727$	255.221	−	529.973i	0.351061	−	0.728986i	−0.648417	−	0.761285i	$-0.724569\pi$
$727$	255.221	−	529.973i	0.351061	−	0.728986i	0.999478	+	0.0322995i	$0.0102830\pi$
$728$	−369.102	+	1401.63i	−0.507008	+	1.92532i
$729$		0			0
$730$	−441.970	−	212.842i	−0.605439	−	0.291564i
$731$	−585.041	+	133.532i	−0.800330	+	0.182670i
$732$		0			0
$733$	176.130	+	140.459i	0.240287	+	0.191623i	0.736228	−	0.676734i	$-0.236605\pi$
$733$	176.130	+	140.459i	0.240287	+	0.191623i	−0.495941	+	0.868356i	$0.665177\pi$
$734$			290.930i			0.396362i
$735$		0			0
$736$	−256.877			−0.349018
$737$	90.1352	−	113.026i	0.122300	−	0.153359i
$738$		0			0
$739$	−251.513	−	1101.95i	−0.340342	−	1.49114i	−0.798353	−	0.602190i	$-0.794295\pi$
$739$	−251.513	−	1101.95i	−0.340342	−	1.49114i	0.458011	−	0.888947i	$-0.348562\pi$
$740$	−3.22243	+	6.69145i	−0.00435464	+	0.00904250i
$741$		0			0
$742$	221.092	+	500.851i	0.297968	+	0.675001i
$743$	346.171	+	166.707i	0.465910	+	0.224370i	0.652085	−	0.758146i	$-0.273895\pi$
$743$	346.171	+	166.707i	0.465910	+	0.224370i	−0.186174	+	0.982517i	$0.559609\pi$
$744$		0			0
$745$	−477.057	−	990.619i	−0.640345	−	1.32969i
$746$	−73.9633	+	92.7470i	−0.0991465	+	0.124326i
$747$		0			0
$748$	−121.111	−	96.5824i	−0.161912	−	0.129121i
$749$	−28.9992	+	876.010i	−0.0387172	+	1.16957i
$750$		0			0
$751$	−1000.05	+	481.599i	−1.33163	+	0.641277i	−0.958124	−	0.286353i	$-0.907557\pi$
$751$	−1000.05	+	481.599i	−1.33163	+	0.641277i	−0.373501	+	0.927630i	$0.621843\pi$
$752$	−535.329	−	122.185i	−0.711874	−	0.162481i
$753$		0			0
$754$			57.0159i			0.0756179i
$755$	−258.588	−	59.0210i	−0.342500	−	0.0781735i
$756$		0			0
$757$	−80.7934	−	353.979i	−0.106728	−	0.467607i	−0.999842	−	0.0177763i	$-0.994341\pi$
$757$	−80.7934	−	353.979i	−0.106728	−	0.467607i	0.893114	−	0.449831i	$-0.148516\pi$
$758$	32.0232	+	140.303i	0.0422470	+	0.185096i
$759$		0			0
$760$	595.995	+	747.354i	0.784204	+	0.983360i
$761$	815.631	−	186.162i	1.07179	−	0.244629i	0.350005	−	0.936748i	$-0.386180\pi$
$761$	815.631	−	186.162i	1.07179	−	0.244629i	0.721783	+	0.692119i	$0.243323\pi$
$762$		0			0
$763$	886.060	−	171.609i	1.16128	−	0.224913i
$764$	32.9179	−	144.223i	0.0430863	−	0.188773i
$765$		0			0
$766$			607.848i			0.793535i
$767$	433.584	−	1899.65i	0.565298	−	2.47673i
$768$		0			0
$769$	−852.466	+	679.819i	−1.10854	+	0.884030i	−0.993999	−	0.109389i	$-0.965111\pi$
$769$	−852.466	+	679.819i	−1.10854	+	0.884030i	−0.114539	+	0.993419i	$0.536539\pi$
$770$	273.443	+	367.181i	0.355121	+	0.476858i
$771$		0			0
$772$	66.9057	−	293.133i	0.0866654	−	0.379706i
$773$	−701.082	−	559.094i	−0.906962	−	0.723278i	0.0544132	−	0.998519i	$-0.482671\pi$
$773$	−701.082	−	559.094i	−0.906962	−	0.723278i	−0.961375	+	0.275240i	$0.911243\pi$
$774$		0			0
$775$	204.364	−	162.975i	0.263696	−	0.210290i
$776$	164.119	−	340.797i	0.211494	−	0.439172i
$777$		0			0
$778$	514.708	−	247.870i	0.661579	−	0.318600i
$779$	867.354	+	417.696i	1.11342	+	0.536195i
$780$		0			0
$781$	−238.107	−	114.666i	−0.304874	−	0.146820i
$782$	145.640	+	116.144i	0.186241	+	0.148522i
$783$		0			0
$784$	219.086	+	315.466i	0.279447	+	0.402380i
$785$	−1190.34			−1.51636
$786$		0			0
$787$	236.707	−	491.527i	0.300771	−	0.624558i	−0.694734	−	0.719267i	$-0.744478\pi$
$787$	236.707	−	491.527i	0.300771	−	0.624558i	0.995505	+	0.0947090i	$0.0301921\pi$
$788$	13.2149	+	57.8982i	0.0167702	+	0.0734748i
$789$		0			0
$790$	223.520	+	464.144i	0.282936	+	0.587523i
$791$	−9.31768	+	281.469i	−0.0117796	+	0.355840i
$792$		0			0
$793$	1328.40	+	1665.76i	1.67515	+	2.10058i
$794$	243.723	+	506.097i	0.306956	+	0.637402i
$795$		0			0
$796$	306.001	+	69.8427i	0.384423	+	0.0877420i
$797$	−941.701	−	750.982i	−1.18156	−	0.942261i	−0.182397	−	0.983225i	$-0.558386\pi$
$797$	−941.701	−	750.982i	−1.18156	−	0.942261i	−0.999161	+	0.0409642i	$0.986957\pi$
$798$		0			0
$799$	−446.945	−	560.452i	−0.559381	−	0.701442i
$800$	172.628	−	83.1334i	0.215785	−	0.103917i
$801$		0			0
$802$	−750.492			−0.935776
$803$			776.959i			0.967570i
$804$		0			0
$805$	194.648	+	261.374i	0.241798	+	0.324688i
$806$	−256.223	−	1122.59i	−0.317895	−	1.39279i
$807$		0			0
$808$	722.930	−	576.518i	0.894716	−	0.713512i
$809$	543.724	+	681.809i	0.672094	+	0.842780i	0.994599	−	0.103788i	$-0.0330964\pi$
$809$	543.724	+	681.809i	0.672094	+	0.842780i	−0.322505	+	0.946568i	$0.604525\pi$
$810$		0			0
$811$	557.712	−	127.294i	0.687684	−	0.156959i	0.135620	−	0.990761i	$-0.456697\pi$
$811$	557.712	−	127.294i	0.687684	−	0.156959i	0.552064	+	0.833801i	$0.313840\pi$
$812$	−11.9683	−	10.2101i	−0.0147392	−	0.0125740i
$813$		0			0
$814$	−19.8720			−0.0244128
$815$		−	88.2528i		−	0.108286i
$816$		0			0
$817$	−689.759	−	1432.30i	−0.844259	−	1.75312i
$818$	106.174	−	84.6707i	0.129797	−	0.103509i
$819$		0			0
$820$	−133.503	+	167.407i	−0.162808	+	0.204155i
$821$	−226.873	+	993.996i	−0.276338	+	1.21071i	0.626048	+	0.779785i	$0.284671\pi$
$821$	−226.873	+	993.996i	−0.276338	+	1.21071i	−0.902386	+	0.430930i	$0.858186\pi$
$822$		0			0
$823$	1211.28	−	583.321i	1.47178	−	0.708774i	0.485563	−	0.874202i	$-0.338615\pi$
$823$	1211.28	−	583.321i	1.47178	−	0.708774i	0.986222	+	0.165427i	$0.0529004\pi$
$824$	−390.497	+	311.411i	−0.473904	+	0.377926i
$825$		0			0
$826$	−542.472	−	728.434i	−0.656746	−	0.881882i
$827$	465.224	−	224.040i	0.562544	−	0.270907i	−0.130927	−	0.991392i	$-0.541795\pi$
$827$	465.224	−	224.040i	0.562544	−	0.270907i	0.693470	+	0.720485i	$0.256081\pi$
$828$		0			0
$829$	1043.40	−	238.149i	1.25863	−	0.287273i	0.459360	−	0.888250i	$-0.348079\pi$
$829$	1043.40	−	238.149i	1.25863	−	0.287273i	0.799266	+	0.600977i	$0.205222\pi$
$830$	437.717	+	210.793i	0.527369	+	0.253968i
$831$		0			0
$832$		−	1590.40i		−	1.91154i
$833$	−33.1611	+	500.319i	−0.0398093	+	0.600623i
$834$		0			0
$835$	234.249	−	293.739i	0.280538	−	0.351783i
$836$	178.054	−	369.733i	0.212983	−	0.442265i
$837$		0			0
$838$	−88.8116	+	184.419i	−0.105980	+	0.220071i
$839$	−17.1409	−	35.5935i	−0.0204302	−	0.0424237i	0.890504	−	0.454975i	$-0.150352\pi$
$839$	−17.1409	−	35.5935i	−0.0204302	−	0.0424237i	−0.910934	+	0.412552i	$0.864638\pi$
$840$		0			0
$841$	755.658	+	363.906i	0.898523	+	0.432706i
$842$	234.405	+	293.934i	0.278391	+	0.349091i
$843$		0			0
$844$	20.1006	−	25.2053i	0.0238158	−	0.0298641i
$845$	−1571.71	−	358.733i	−1.86002	−	0.424536i
$846$		0			0
$847$	−56.4915	+	108.011i	−0.0666959	+	0.127522i
$848$	−241.134	−	302.373i	−0.284356	−	0.356572i
$849$		0			0
$850$	−135.462	−	30.9183i	−0.159367	−	0.0363745i
$851$	−14.1457			−0.0166225
$852$		0			0
$853$	−1205.23	−	275.086i	−1.41293	−	0.322492i	−0.553118	−	0.833103i	$-0.686562\pi$
$853$	−1205.23	−	275.086i	−1.41293	−	0.322492i	−0.859812	+	0.510611i	$0.829419\pi$
$854$	992.561	+	32.8575i	1.16225	+	0.0384748i
$855$		0			0
$856$	−242.353	−	1061.82i	−0.283123	−	1.24044i
$857$	293.903	−	234.380i	0.342944	−	0.273489i	−0.436838	−	0.899540i	$-0.643902\pi$
$857$	293.903	−	234.380i	0.342944	−	0.273489i	0.779782	+	0.626052i	$0.215330\pi$
$858$		0			0
$859$	1018.22	−	232.401i	1.18535	−	0.270548i	0.415993	−	0.909368i	$-0.363434\pi$
$859$	1018.22	−	232.401i	1.18535	−	0.270548i	0.769357	+	0.638819i	$0.220577\pi$
$860$	344.723	−	78.6807i	0.400840	−	0.0914892i
$861$		0			0
$862$	256.469	−	1123.66i	0.297528	−	1.30355i
$863$	−278.390			−0.322584			−0.161292	−	0.986907i	$-0.551566\pi$
$863$	−278.390			−0.322584			−0.161292	+	0.986907i	$0.551566\pi$
$864$		0			0
$865$	−256.613	+	1124.29i	−0.296662	+	1.29976i
$866$	−207.217	−	430.290i	−0.239280	−	0.496871i
$867$		0			0
$868$	281.526	+	147.243i	0.324339	+	0.169635i
$869$	508.729	−	637.926i	0.585419	−	0.734092i
$870$		0			0
$871$	264.358	+	210.819i	0.303511	+	0.242042i
$872$	−1010.41	+	486.590i	−1.15873	+	0.558016i
$873$		0			0
$874$	−214.117	+	444.619i	−0.244986	+	0.508718i
$875$	−844.038	−	441.446i	−0.964615	−	0.504509i
$876$		0			0
$877$	−116.444	−	56.0764i	−0.132775	−	0.0639412i	0.366317	−	0.930490i	$-0.380619\pi$
$877$	−116.444	−	56.0764i	−0.132775	−	0.0639412i	−0.499092	+	0.866549i	$0.666333\pi$
$878$	−600.630	+	137.090i	−0.684089	+	0.156139i
$879$		0			0
$880$	−252.850	−	201.641i	−0.287330	−	0.229138i
$881$			821.345i			0.932287i	0.884709	+	0.466144i	$0.154357\pi$
$881$			821.345i			0.932287i	−0.884709	+	0.466144i	$0.845643\pi$
$882$		0			0
$883$	−1025.63			−1.16152			−0.580762	−	0.814073i	$-0.697245\pi$
$883$	−1025.63			−1.16152			−0.580762	+	0.814073i	$0.697245\pi$
$884$	225.898	−	283.268i	0.255541	−	0.320438i
$885$		0			0
$886$	123.086	+	539.274i	0.138923	+	0.608662i
$887$	−307.057	+	637.610i	−0.346175	+	0.718839i	−0.999261	−	0.0384447i	$-0.987760\pi$
$887$	−307.057	+	637.610i	−0.346175	+	0.718839i	0.653086	+	0.757284i	$0.273474\pi$
$888$		0			0
$889$	−819.783	+	610.500i	−0.922140	+	0.686727i
$890$	−545.761	−	262.825i	−0.613215	−	0.295309i
$891$		0			0
$892$	74.1665	+	154.008i	0.0831463	+	0.172655i
$893$	1184.04	−	1484.73i	1.32591	−	1.66264i
$894$		0			0
$895$	−1108.54	−	884.028i	−1.23859	−	0.987741i
$896$	−87.4995	−	74.6457i	−0.0976557	−	0.0833099i
$897$		0			0
$898$	400.992	−	193.107i	0.446539	−	0.215042i
$899$	44.9521	+	10.2600i	0.0500023	+	0.0114127i
$900$		0			0
$901$		−	504.901i		−	0.560378i
$902$	−558.554	−	127.486i	−0.619239	−	0.141337i
$903$		0			0
$904$	−77.8700	−	341.171i	−0.0861394	−	0.377401i
$905$	−163.760	−	717.480i	−0.180951	−	0.792796i
$906$		0			0
$907$	945.559	+	1185.69i	1.04251	+	1.30727i	0.950234	+	0.311537i	$0.100844\pi$
$907$	945.559	+	1185.69i	1.04251	+	1.30727i	0.0922792	+	0.995733i	$0.470585\pi$
$908$	29.0453	−	6.62940i	0.0319882	−	0.00730110i
$909$		0			0
$910$	−858.805	+	639.561i	−0.943742	+	0.702814i
$911$	−304.585	+	1334.47i	−0.334341	+	1.46484i	0.476291	+	0.879288i	$0.341981\pi$
$911$	−304.585	+	1334.47i	−0.334341	+	1.46484i	−0.810632	+	0.585556i	$0.800876\pi$
$912$		0			0
$913$		−	769.481i		−	0.842805i
$914$	104.434	−	457.553i	0.114260	−	0.500605i
$915$		0			0
$916$	141.165	−	112.575i	0.154110	−	0.122899i
$917$	−107.260	+	407.310i	−0.116968	+	0.444177i
$918$		0			0
$919$	−103.974	+	455.541i	−0.113138	+	0.495692i	0.886329	+	0.463056i	$0.153247\pi$
$919$	−103.974	+	455.541i	−0.113138	+	0.495692i	−0.999467	+	0.0326357i	$0.989610\pi$
$920$	−316.602	−	252.482i	−0.344133	−	0.274437i
$921$		0			0
$922$	682.367	−	544.169i	0.740094	−	0.590205i
$923$	268.194	−	556.912i	0.290568	−	0.603371i
$924$		0			0
$925$	9.50630	−	4.57799i	0.0102771	−	0.00494918i
$926$	−652.705	−	314.326i	−0.704865	−	0.339445i
$927$		0			0
$928$	30.4507	+	14.6643i	0.0328133	+	0.0158020i
$929$	247.589	+	197.446i	0.266512	+	0.212536i	0.747623	−	0.664124i	$-0.231195\pi$
$929$	247.589	+	197.446i	0.266512	+	0.212536i	−0.481111	+	0.876660i	$0.659767\pi$
$930$		0			0
$931$	−1311.75	+	209.289i	−1.40897	+	0.224800i
$932$	32.2212			0.0345721
$933$		0			0
$934$	−354.009	+	735.107i	−0.379025	+	0.787053i
$935$	−93.9502	−	411.623i	−0.100481	−	0.440238i
$936$		0			0
$937$	39.7667	+	82.5764i	0.0424405	+	0.0881285i	0.921111	−	0.389300i	$-0.127283\pi$
$937$	39.7667	+	82.5764i	0.0424405	+	0.0881285i	−0.878670	+	0.477429i	$0.841569\pi$
$938$	154.732	−	29.9679i	0.164959	−	0.0319488i
$939$		0			0
$940$	263.353	+	330.234i	0.280163	+	0.351313i
$941$	−39.2344	−	81.4711i	−0.0416944	−	0.0865793i	0.879081	−	0.476672i	$-0.158157\pi$
$941$	−39.2344	−	81.4711i	−0.0416944	−	0.0865793i	−0.920775	+	0.390093i	$0.872443\pi$
$942$		0			0
$943$	−397.601	−	90.7497i	−0.421634	−	0.0962351i
$944$	501.619	+	400.028i	0.531376	+	0.423758i
$945$		0			0
$946$	589.874	+	739.678i	0.623545	+	0.781901i
$947$	1035.42	−	498.634i	1.09337	−	0.526541i	0.201804	−	0.979426i	$-0.435320\pi$
$947$	1035.42	−	498.634i	1.09337	−	0.526541i	0.891569	+	0.452885i	$0.149605\pi$
$948$		0			0
$949$	−1817.24			−1.91490
$950$		−	368.091i		−	0.387464i
$951$		0			0
$952$	−118.470	−	611.692i	−0.124444	−	0.642534i
$953$	161.269	+	706.567i	0.169223	+	0.741414i	0.986310	+	0.164900i	$0.0527301\pi$
$953$	161.269	+	706.567i	0.169223	+	0.741414i	−0.817088	+	0.576514i	$0.804413\pi$
$954$		0			0
$955$	315.234	−	251.390i	0.330088	−	0.263236i
$956$	−291.259	−	365.228i	−0.304665	−	0.382037i
$957$		0			0
$958$	−897.405	+	204.827i	−0.936749	+	0.213807i
$959$	−1825.22	−	480.647i	−1.90325	−	0.501196i
$960$		0			0
$961$	29.8306			0.0310413
$962$		−	46.4791i		−	0.0483150i
$963$		0			0
$964$	−125.684	−	260.985i	−0.130377	−	0.270732i
$965$	640.712	−	510.951i	0.663951	−	0.529483i
$966$		0			0
$967$	16.6759	−	20.9109i	0.0172450	−	0.0216245i	−0.773134	−	0.634242i	$-0.781312\pi$
$967$	16.6759	−	20.9109i	0.0172450	−	0.0216245i	0.790379	+	0.612618i	$0.209884\pi$
$968$	33.7036	−	147.665i	0.0348178	−	0.152547i
$969$		0			0
$970$	251.771	−	121.246i	0.259557	−	0.124996i
$971$	−588.383	+	469.220i	−0.605956	+	0.483233i	−0.877748	−	0.479122i	$-0.840955\pi$
$971$	−588.383	+	469.220i	−0.605956	+	0.483233i	0.271793	+	0.962356i	$0.412384\pi$
$972$		0			0
$973$	406.046	−	179.242i	0.417314	−	0.184216i
$974$	134.248	−	64.6505i	0.137832	−	0.0663763i
$975$		0			0
$976$	−683.958	+	156.109i	−0.700777	+	0.159948i
$977$	1746.79	+	841.210i	1.78791	+	0.861014i	0.947984	+	0.318318i	$0.103118\pi$
$977$	1746.79	+	841.210i	1.78791	+	0.861014i	0.839929	+	0.542696i	$0.182596\pi$
$978$		0			0
$979$			959.417i			0.979997i
$980$	19.5395	−	294.802i	0.0199382	−	0.300818i
$981$		0			0
$982$	−691.980	+	867.716i	−0.704664	+	0.883621i
$983$	−9.01492	+	18.7197i	−0.00917083	+	0.0190434i	−0.905504	−	0.424338i	$-0.860507\pi$
$983$	−9.01492	+	18.7197i	−0.00917083	+	0.0190434i	0.896333	+	0.443381i	$0.146221\pi$
$984$		0			0
$985$	−70.2302	+	145.834i	−0.0712996	+	0.148055i
$986$	−10.6342	−	22.0821i	−0.0107852	−	0.0223957i
$987$		0			0
$988$	864.776	+	416.454i	0.875279	+	0.421512i
$989$	419.896	+	526.532i	0.424566	+	0.532389i
$990$		0			0
$991$	948.242	−	1189.06i	0.956853	−	1.19986i	−0.0229181	−	0.999737i	$-0.507296\pi$
$991$	948.242	−	1189.06i	0.956853	−	1.19986i	0.979772	−	0.200119i	$-0.0641329\pi$
$992$	−665.444	−	151.883i	−0.670811	−	0.153108i
$993$		0			0
$994$	−116.353	−	263.581i	−0.117056	−	0.265172i
$995$	533.380	+	668.838i	0.536061	+	0.672199i
$996$		0			0
$997$	1060.64	+	242.083i	1.06383	+	0.242812i	0.718397	−	0.695633i	$-0.244876\pi$
$997$	1060.64	+	242.083i	1.06383	+	0.242812i	0.345430	+	0.938445i	$0.387733\pi$
$998$	1020.15			1.02220
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.3.v.c.55.6		108
3.2	odd	2		147.3.j.a.55.13	✓	108
49.41	odd	14	inner	441.3.v.c.433.6		108
147.41	even	14		147.3.j.a.139.13	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.3.j.a.55.13	✓	108	3.2	odd	2
147.3.j.a.139.13	yes	108	147.41	even	14
441.3.v.c.55.6		108	1.1	even	1	trivial
441.3.v.c.433.6		108	49.41	odd	14	inner

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	441.v (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.988314 + 1.23931i) q^{2} +(0.330967 + 1.45006i) q^{4} +(-1.75892 + 3.65243i) q^{5} +(5.32542 + 4.54311i) q^{7} +(-7.83679 - 3.77400i) q^{8} +O(q^{10})\)	\(q+(-0.988314 + 1.23931i) q^{2} +(0.330967 + 1.45006i) q^{4} +(-1.75892 + 3.65243i) q^{5} +(5.32542 + 4.54311i) q^{7} +(-7.83679 - 3.77400i) q^{8} +(-2.78812 - 5.78959i) q^{10} +(-6.34573 + 7.95730i) q^{11} +(-18.6115 - 14.8421i) q^{13} +(-10.8935 + 2.10981i) q^{14} +(7.06213 - 3.40094i) q^{16} +(9.97642 + 2.27705i) q^{17} +27.1089i q^{19} +(-5.87839 - 1.34170i) q^{20} +(-3.58995 - 15.7286i) q^{22} +(-2.55547 - 11.1963i) q^{23} +(5.34080 + 6.69715i) q^{25} +(36.7879 - 8.39661i) q^{26} +(-4.82525 + 9.22581i) q^{28} +(-0.336228 + 1.47311i) q^{29} -30.5151i q^{31} +(4.97732 - 21.8071i) q^{32} +(-12.6818 + 10.1134i) q^{34} +(-25.9604 + 11.4598i) q^{35} +(0.274091 - 1.20087i) q^{37} +(-33.5963 - 26.7922i) q^{38} +(27.5685 - 21.9852i) q^{40} +(15.4080 - 31.9951i) q^{41} +(-52.8350 + 25.4440i) q^{43} +(-13.6388 - 6.56810i) q^{44} +(16.4012 + 7.89840i) q^{46} +(-54.7691 - 43.6769i) q^{47} +(7.72029 + 48.3880i) q^{49} -13.5782 q^{50} +(15.3622 - 31.9000i) q^{52} +(-10.9793 - 48.1034i) q^{53} +(-17.9018 - 37.1735i) q^{55} +(-24.5885 - 55.7016i) q^{56} +(-1.49334 - 1.87259i) q^{58} +(35.5147 + 73.7471i) q^{59} +(-87.2577 - 19.9160i) q^{61} +(37.8175 + 30.1585i) q^{62} +(41.6551 + 52.2338i) q^{64} +(86.9459 - 41.8709i) q^{65} -14.2041 q^{67} +15.2201i q^{68} +(11.4548 - 43.4987i) q^{70} +(5.77803 + 25.3152i) q^{71} +(59.6841 - 47.5965i) q^{73} +(1.21736 + 1.52652i) q^{74} +(-39.3096 + 8.97217i) q^{76} +(-69.9446 + 13.5466i) q^{77} -80.1687 q^{79} +31.7759i q^{80} +(24.4238 + 50.7166i) q^{82} +(-59.1097 + 47.1384i) q^{83} +(-25.8645 + 32.4330i) q^{85} +(20.6847 - 90.6254i) q^{86} +(79.7610 - 38.4109i) q^{88} +(73.7002 - 58.7739i) q^{89} +(-31.6844 - 163.595i) q^{91} +(15.3895 - 7.41118i) q^{92} +(108.258 - 24.7092i) q^{94} +(-99.0134 - 47.6824i) q^{95} +43.4868i q^{97} +(-67.5976 - 38.2547i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 32 q^{4} - 2 q^{7} - 12 q^{8}+O(q^{10}) \) 108 * q - 32 * q^4 - 2 * q^7 - 12 * q^8	\( 108 q - 32 q^{4} - 2 q^{7} - 12 q^{8} - 66 q^{11} + 2 q^{14} - 96 q^{16} + 98 q^{17} + 112 q^{20} - 116 q^{22} - 64 q^{23} + 130 q^{25} - 224 q^{26} - 204 q^{28} - 72 q^{29} + 220 q^{32} + 784 q^{34} + 376 q^{35} + 156 q^{37} + 280 q^{38} - 728 q^{40} + 196 q^{41} - 56 q^{43} + 840 q^{44} - 16 q^{46} - 266 q^{47} + 122 q^{49} + 244 q^{50} + 168 q^{52} - 148 q^{53} - 252 q^{55} - 686 q^{56} + 252 q^{58} - 700 q^{59} - 112 q^{61} - 392 q^{62} + 496 q^{64} + 12 q^{65} - 196 q^{67} + 898 q^{70} + 732 q^{71} + 126 q^{73} + 508 q^{74} - 210 q^{76} + 230 q^{77} + 136 q^{79} - 1960 q^{82} + 574 q^{83} - 480 q^{85} + 392 q^{86} - 108 q^{88} + 742 q^{89} + 152 q^{91} + 42 q^{92} + 98 q^{94} - 68 q^{95} + 508 q^{98}+O(q^{100}) \) 108 * q - 32 * q^4 - 2 * q^7 - 12 * q^8 - 66 * q^11 + 2 * q^14 - 96 * q^16 + 98 * q^17 + 112 * q^20 - 116 * q^22 - 64 * q^23 + 130 * q^25 - 224 * q^26 - 204 * q^28 - 72 * q^29 + 220 * q^32 + 784 * q^34 + 376 * q^35 + 156 * q^37 + 280 * q^38 - 728 * q^40 + 196 * q^41 - 56 * q^43 + 840 * q^44 - 16 * q^46 - 266 * q^47 + 122 * q^49 + 244 * q^50 + 168 * q^52 - 148 * q^53 - 252 * q^55 - 686 * q^56 + 252 * q^58 - 700 * q^59 - 112 * q^61 - 392 * q^62 + 496 * q^64 + 12 * q^65 - 196 * q^67 + 898 * q^70 + 732 * q^71 + 126 * q^73 + 508 * q^74 - 210 * q^76 + 230 * q^77 + 136 * q^79 - 1960 * q^82 + 574 * q^83 - 480 * q^85 + 392 * q^86 - 108 * q^88 + 742 * q^89 + 152 * q^91 + 42 * q^92 + 98 * q^94 - 68 * q^95 + 508 * q^98

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