LMFDB - Embedded newform 124.3.b.a.63.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,3,Mod(63,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("124.63");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	124.b (of order $2$, degree $1$, 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:	$3.37875527807$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			63.19
Character	$\chi$	$=$	124.63
Dual form			124.3.b.a.63.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.778186 - 1.84240i) q^{2} +5.21571i q^{3} +(-2.78885 - 2.86745i) q^{4} +3.92621 q^{5} +(9.60941 + 4.05879i) q^{6} +8.65127i q^{7} +(-7.45324 + 2.90676i) q^{8} -18.2037 q^{9} +O(q^{10})$	\(q+(0.778186 - 1.84240i) q^{2} +5.21571i q^{3} +(-2.78885 - 2.86745i) q^{4} +3.92621 q^{5} +(9.60941 + 4.05879i) q^{6} +8.65127i q^{7} +(-7.45324 + 2.90676i) q^{8} -18.2037 q^{9} +(3.05532 - 7.23364i) q^{10} +6.53793i q^{11} +(14.9558 - 14.5459i) q^{12} +11.5639 q^{13} +(15.9391 + 6.73230i) q^{14} +20.4780i q^{15} +(-0.444593 + 15.9938i) q^{16} +24.6638 q^{17} +(-14.1658 + 33.5384i) q^{18} -25.8919i q^{19} +(-10.9496 - 11.2582i) q^{20} -45.1226 q^{21} +(12.0455 + 5.08772i) q^{22} -8.45393i q^{23} +(-15.1608 - 38.8739i) q^{24} -9.58485 q^{25} +(8.99884 - 21.3053i) q^{26} -48.0036i q^{27} +(24.8071 - 24.1271i) q^{28} -30.8741 q^{29} +(37.7286 + 15.9357i) q^{30} -5.56776i q^{31} +(29.1210 + 13.2653i) q^{32} -34.0999 q^{33} +(19.1930 - 45.4404i) q^{34} +33.9667i q^{35} +(50.7673 + 52.1982i) q^{36} +14.6700 q^{37} +(-47.7032 - 20.1487i) q^{38} +60.3139i q^{39} +(-29.2630 + 11.4126i) q^{40} +41.0573 q^{41} +(-35.1137 + 83.1337i) q^{42} -84.0758i q^{43} +(18.7472 - 18.2333i) q^{44} -71.4714 q^{45} +(-15.5755 - 6.57873i) q^{46} -39.5261i q^{47} +(-83.4192 - 2.31887i) q^{48} -25.8445 q^{49} +(-7.45879 + 17.6591i) q^{50} +128.639i q^{51} +(-32.2500 - 33.1589i) q^{52} -47.9806 q^{53} +(-88.4418 - 37.3558i) q^{54} +25.6693i q^{55} +(-25.1472 - 64.4800i) q^{56} +135.045 q^{57} +(-24.0258 + 56.8823i) q^{58} +55.6676i q^{59} +(58.7197 - 57.1101i) q^{60} +79.6432 q^{61} +(-10.2580 - 4.33276i) q^{62} -157.485i q^{63} +(47.1015 - 43.3296i) q^{64} +45.4022 q^{65} +(-26.5361 + 62.8256i) q^{66} +121.488i q^{67} +(-68.7836 - 70.7222i) q^{68} +44.0932 q^{69} +(62.5802 + 26.4324i) q^{70} -54.6944i q^{71} +(135.676 - 52.9137i) q^{72} +35.9509 q^{73} +(11.4160 - 27.0280i) q^{74} -49.9918i q^{75} +(-74.2440 + 72.2089i) q^{76} -56.5614 q^{77} +(111.122 + 46.9354i) q^{78} -18.7646i q^{79} +(-1.74557 + 62.7952i) q^{80} +86.5403 q^{81} +(31.9502 - 75.6438i) q^{82} +38.9960i q^{83} +(125.840 + 129.387i) q^{84} +96.8352 q^{85} +(-154.901 - 65.4266i) q^{86} -161.030i q^{87} +(-19.0042 - 48.7287i) q^{88} -66.4860 q^{89} +(-55.6181 + 131.679i) q^{90} +100.042i q^{91} +(-24.2412 + 23.5768i) q^{92} +29.0399 q^{93} +(-72.8228 - 30.7587i) q^{94} -101.657i q^{95} +(-69.1879 + 151.887i) q^{96} +174.677 q^{97} +(-20.1118 + 47.6159i) q^{98} -119.014i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 2 q^{2} - 6 q^{4} - 4 q^{5} + 13 q^{8} - 82 q^{9}+O(q^{10}) $ 30 * q - 2 * q^2 - 6 * q^4 - 4 * q^5 + 13 * q^8 - 82 * q^9	$ 30 q - 2 q^{2} - 6 q^{4} - 4 q^{5} + 13 q^{8} - 82 q^{9} + q^{10} - 14 q^{12} + 12 q^{13} + 29 q^{14} + 50 q^{16} - 4 q^{17} - 34 q^{18} - 63 q^{20} - 16 q^{21} - 24 q^{22} - 20 q^{24} + 90 q^{25} + 38 q^{26} + 3 q^{28} - 4 q^{29} - 6 q^{30} + 118 q^{32} + 80 q^{33} + 4 q^{34} - 2 q^{36} + 76 q^{37} + 37 q^{38} - 180 q^{40} - 4 q^{41} - 38 q^{42} + 184 q^{44} - 20 q^{45} - 54 q^{46} - 172 q^{48} - 258 q^{49} - 31 q^{50} - 88 q^{52} - 132 q^{53} - 84 q^{54} - 28 q^{56} + 176 q^{57} + 164 q^{58} + 108 q^{60} - 100 q^{61} + 381 q^{64} - 104 q^{65} + 60 q^{66} + 214 q^{68} + 112 q^{69} + 45 q^{70} - 167 q^{72} - 132 q^{73} + 398 q^{74} - 317 q^{76} + 176 q^{77} - 188 q^{78} - 203 q^{80} + 158 q^{81} - 81 q^{82} + 176 q^{84} + 248 q^{85} - 78 q^{86} + 98 q^{88} - 20 q^{89} - 567 q^{90} - 260 q^{92} - 244 q^{94} - 90 q^{96} + 300 q^{97} - 371 q^{98}+O(q^{100}) $ 30 * q - 2 * q^2 - 6 * q^4 - 4 * q^5 + 13 * q^8 - 82 * q^9 + q^10 - 14 * q^12 + 12 * q^13 + 29 * q^14 + 50 * q^16 - 4 * q^17 - 34 * q^18 - 63 * q^20 - 16 * q^21 - 24 * q^22 - 20 * q^24 + 90 * q^25 + 38 * q^26 + 3 * q^28 - 4 * q^29 - 6 * q^30 + 118 * q^32 + 80 * q^33 + 4 * q^34 - 2 * q^36 + 76 * q^37 + 37 * q^38 - 180 * q^40 - 4 * q^41 - 38 * q^42 + 184 * q^44 - 20 * q^45 - 54 * q^46 - 172 * q^48 - 258 * q^49 - 31 * q^50 - 88 * q^52 - 132 * q^53 - 84 * q^54 - 28 * q^56 + 176 * q^57 + 164 * q^58 + 108 * q^60 - 100 * q^61 + 381 * q^64 - 104 * q^65 + 60 * q^66 + 214 * q^68 + 112 * q^69 + 45 * q^70 - 167 * q^72 - 132 * q^73 + 398 * q^74 - 317 * q^76 + 176 * q^77 - 188 * q^78 - 203 * q^80 + 158 * q^81 - 81 * q^82 + 176 * q^84 + 248 * q^85 - 78 * q^86 + 98 * q^88 - 20 * q^89 - 567 * q^90 - 260 * q^92 - 244 * q^94 - 90 * q^96 + 300 * q^97 - 371 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.778186	−	1.84240i	0.389093	−	0.921199i
$2$	0.778186	−	1.84240i	0.389093	−	0.921199i
$3$			5.21571i			1.73857i	0.494310	+	0.869285i	$0.335421\pi$
$3$			5.21571i			1.73857i	−0.494310	+	0.869285i	$0.664579\pi$
$4$	−2.78885	−	2.86745i	−0.697213	−	0.716864i
$5$	3.92621			0.785243			0.392621	−	0.919700i	$-0.371568\pi$
$5$	3.92621			0.785243			0.392621	+	0.919700i	$0.371568\pi$
$6$	9.60941	+	4.05879i	1.60157	+	0.676466i
$7$			8.65127i			1.23590i	0.786219	+	0.617948i	$0.212036\pi$
$7$			8.65127i			1.23590i	−0.786219	+	0.617948i	$0.787964\pi$
$8$	−7.45324	+	2.90676i	−0.931655	+	0.363345i
$9$	−18.2037			−2.02263
$10$	3.05532	−	7.23364i	0.305532	−	0.723364i
$11$			6.53793i			0.594357i	0.954822	+	0.297178i	$0.0960456\pi$
$11$			6.53793i			0.594357i	−0.954822	+	0.297178i	$0.903954\pi$
$12$	14.9558	−	14.5459i	1.24632	−	1.21215i
$13$	11.5639			0.889529			0.444764	−	0.895648i	$-0.353287\pi$
$13$	11.5639			0.889529			0.444764	+	0.895648i	$0.353287\pi$
$14$	15.9391	+	6.73230i	1.13851	+	0.480878i
$15$			20.4780i			1.36520i
$16$	−0.444593	+	15.9938i	−0.0277870	+	0.999614i
$17$	24.6638			1.45081			0.725405	−	0.688323i	$-0.241653\pi$
$17$	24.6638			1.45081			0.725405	+	0.688323i	$0.241653\pi$
$18$	−14.1658	+	33.5384i	−0.786991	+	1.86324i
$19$		−	25.8919i		−	1.36273i	−0.731942	−	0.681367i	$-0.761386\pi$
$19$		−	25.8919i		−	1.36273i	0.731942	−	0.681367i	$-0.238614\pi$
$20$	−10.9496	−	11.2582i	−0.547482	−	0.562912i
$21$	−45.1226			−2.14869
$22$	12.0455	+	5.08772i	0.547521	+	0.231260i
$23$		−	8.45393i		−	0.367562i	−0.982967	−	0.183781i	$-0.941166\pi$
$23$		−	8.45393i		−	0.367562i	0.982967	−	0.183781i	$-0.0588337\pi$
$24$	−15.1608	−	38.8739i	−0.631702	−	1.61975i
$25$	−9.58485			−0.383394
$26$	8.99884	−	21.3053i	0.346109	−	0.819433i
$27$		−	48.0036i		−	1.77791i
$28$	24.8071	−	24.1271i	0.885969	−	0.861683i
$29$	−30.8741			−1.06462			−0.532311	−	0.846549i	$-0.678676\pi$
$29$	−30.8741			−1.06462			−0.532311	+	0.846549i	$0.678676\pi$
$30$	37.7286	+	15.9357i	1.25762	+	0.531190i
$31$		−	5.56776i		−	0.179605i
$31$		−	5.56776i		−	0.179605i
$32$	29.1210	+	13.2653i	0.910031	+	0.414540i
$33$	−34.0999			−1.03333
$34$	19.1930	−	45.4404i	0.564500	−	1.33648i
$35$			33.9667i			0.970478i
$36$	50.7673	+	52.1982i	1.41020	+	1.44995i
$37$	14.6700			0.396487			0.198244	−	0.980153i	$-0.436476\pi$
$37$	14.6700			0.396487			0.198244	+	0.980153i	$0.436476\pi$
$38$	−47.7032	−	20.1487i	−1.25535	−	0.530230i
$39$			60.3139i			1.54651i
$40$	−29.2630	+	11.4126i	−0.731575	+	0.285314i
$41$	41.0573			1.00140			0.500699	−	0.865622i	$-0.333076\pi$
$41$	41.0573			1.00140			0.500699	+	0.865622i	$0.333076\pi$
$42$	−35.1137	+	83.1337i	−0.836041	+	1.97937i
$43$		−	84.0758i		−	1.95525i	−0.210351	−	0.977626i	$-0.567461\pi$
$43$		−	84.0758i		−	1.95525i	0.210351	−	0.977626i	$-0.432539\pi$
$44$	18.7472	−	18.2333i	0.426073	−	0.414394i
$45$	−71.4714			−1.58825
$46$	−15.5755	−	6.57873i	−0.338598	−	0.143016i
$47$		−	39.5261i		−	0.840981i	−0.907297	−	0.420491i	$-0.861858\pi$
$47$		−	39.5261i		−	0.840981i	0.907297	−	0.420491i	$-0.138142\pi$
$48$	−83.4192	−	2.31887i	−1.73790	−	0.0483097i
$49$	−25.8445			−0.527439
$50$	−7.45879	+	17.6591i	−0.149176	+	0.353182i
$51$			128.639i			2.52233i
$52$	−32.2500	−	33.1589i	−0.620191	−	0.637671i
$53$	−47.9806			−0.905295			−0.452647	−	0.891690i	$-0.649520\pi$
$53$	−47.9806			−0.905295			−0.452647	+	0.891690i	$0.649520\pi$
$54$	−88.4418	−	37.3558i	−1.63781	−	0.691773i
$55$			25.6693i			0.466714i
$56$	−25.1472	−	64.4800i	−0.449057	−	1.15143i
$57$	135.045			2.36921
$58$	−24.0258	+	56.8823i	−0.414237	+	0.980729i
$59$			55.6676i			0.943518i	0.881727	+	0.471759i	$0.156381\pi$
$59$			55.6676i			0.943518i	−0.881727	+	0.471759i	$0.843619\pi$
$60$	58.7197	−	57.1101i	0.978662	−	0.951836i
$61$	79.6432			1.30563			0.652813	−	0.757519i	$-0.273589\pi$
$61$	79.6432			1.30563			0.652813	+	0.757519i	$0.273589\pi$
$62$	−10.2580	−	4.33276i	−0.165452	−	0.0698832i
$63$		−	157.485i		−	2.49976i
$64$	47.1015	−	43.3296i	0.735960	−	0.677025i
$65$	45.4022			0.698496
$66$	−26.5361	+	62.8256i	−0.402062	+	0.951903i
$67$			121.488i			1.81326i	0.421930	+	0.906628i	$0.361353\pi$
$67$			121.488i			1.81326i	−0.421930	+	0.906628i	$0.638647\pi$
$68$	−68.7836	−	70.7222i	−1.01152	−	1.04003i
$69$	44.0932			0.639033
$70$	62.5802	+	26.4324i	0.894003	+	0.377606i
$71$		−	54.6944i		−	0.770344i	−0.922845	−	0.385172i	$-0.874142\pi$
$71$		−	54.6944i		−	0.770344i	0.922845	−	0.385172i	$-0.125858\pi$
$72$	135.676	−	52.9137i	1.88439	−	0.734913i
$73$	35.9509			0.492478			0.246239	−	0.969209i	$-0.420805\pi$
$73$	35.9509			0.492478			0.246239	+	0.969209i	$0.420805\pi$
$74$	11.4160	−	27.0280i	0.154270	−	0.365244i
$75$		−	49.9918i		−	0.666558i
$76$	−74.2440	+	72.2089i	−0.976895	+	0.950116i
$77$	−56.5614			−0.734563
$78$	111.122	+	46.9354i	1.42464	+	0.601736i
$79$		−	18.7646i		−	0.237527i	−0.992923	−	0.118763i	$-0.962107\pi$
$79$		−	18.7646i		−	0.237527i	0.992923	−	0.118763i	$-0.0378930\pi$
$80$	−1.74557	+	62.7952i	−0.0218196	+	0.784939i
$81$	86.5403			1.06840
$82$	31.9502	−	75.6438i	0.389637	−	0.922486i
$83$			38.9960i			0.469831i	0.972016	+	0.234916i	$0.0754814\pi$
$83$			38.9960i			0.469831i	−0.972016	+	0.234916i	$0.924519\pi$
$84$	125.840	+	129.387i	1.49810	+	1.54032i
$85$	96.8352			1.13924
$86$	−154.901	−	65.4266i	−1.80118	−	0.760775i
$87$		−	161.030i		−	1.85092i
$88$	−19.0042	−	48.7287i	−0.215957	−	0.553735i
$89$	−66.4860			−0.747034			−0.373517	−	0.927623i	$-0.621848\pi$
$89$	−66.4860			−0.747034			−0.373517	+	0.927623i	$0.621848\pi$
$90$	−55.6181	+	131.679i	−0.617979	+	1.46310i
$91$			100.042i			1.09937i
$92$	−24.2412	+	23.5768i	−0.263492	+	0.256269i
$93$	29.0399			0.312257
$94$	−72.8228	−	30.7587i	−0.774711	−	0.327220i
$95$		−	101.657i		−	1.07008i
$96$	−69.1879	+	151.887i	−0.720707	+	1.58215i
$97$	174.677			1.80079			0.900396	−	0.435072i	$-0.143277\pi$
$97$	174.677			1.80079			0.900396	+	0.435072i	$0.143277\pi$
$98$	−20.1118	+	47.6159i	−0.205223	+	0.485876i
$99$		−	119.014i		−	1.20216i
$100$	26.7307	+	27.4841i	0.267307	+	0.274841i
$101$	−112.512			−1.11398			−0.556989	−	0.830520i	$-0.688044\pi$
$101$	−112.512			−1.11398			−0.556989	+	0.830520i	$0.688044\pi$
$102$	237.004	+	100.105i	2.32357	+	0.981423i
$103$			142.709i			1.38553i	0.721164	+	0.692765i	$0.243607\pi$
$103$			142.709i			1.38553i	−0.721164	+	0.692765i	$0.756393\pi$
$104$	−86.1883	+	33.6134i	−0.828734	+	0.323206i
$105$	−177.161			−1.68725
$106$	−37.3378	+	88.3993i	−0.352244	+	0.833956i
$107$		−	56.5589i		−	0.528587i	−0.964442	−	0.264294i	$-0.914861\pi$
$107$		−	56.5589i		−	0.528587i	0.964442	−	0.264294i	$-0.0851388\pi$
$108$	−137.648	+	133.875i	−1.27452	+	1.23958i
$109$	−59.5407			−0.546245			−0.273123	−	0.961979i	$-0.588056\pi$
$109$	−59.5407			−0.546245			−0.273123	+	0.961979i	$0.588056\pi$
$110$	47.2930	+	19.9755i	0.429937	+	0.181595i
$111$			76.5147i			0.689321i
$112$	−138.367	−	3.84629i	−1.23542	−	0.0343419i
$113$	−16.3776			−0.144935			−0.0724675	−	0.997371i	$-0.523087\pi$
$113$	−16.3776			−0.144935			−0.0724675	+	0.997371i	$0.523087\pi$
$114$	105.090	−	248.806i	0.921843	−	2.18251i
$115$		−	33.1919i		−	0.288625i
$116$	86.1032	+	88.5299i	0.742269	+	0.763189i
$117$	−210.505			−1.79919
$118$	102.562	+	43.3197i	0.869168	+	0.367116i
$119$			213.373i			1.79305i
$120$	−59.5247	−	152.627i	−0.496039	−	1.27189i
$121$	78.2555			0.646740
$122$	61.9772	−	146.734i	0.508010	−	1.20274i
$123$			214.143i			1.74100i
$124$	−15.9653	+	15.5277i	−0.128753	+	0.125223i
$125$	−135.787			−1.08630
$126$	−290.150	−	122.552i	−2.30277	−	0.972639i
$127$		−	184.392i		−	1.45191i	−0.687745	−	0.725953i	$-0.741399\pi$
$127$		−	184.392i		−	1.45191i	0.687745	−	0.725953i	$-0.258601\pi$
$128$	−43.1766	−	120.498i	−0.337317	−	0.941391i
$129$	438.515			3.39934
$130$	35.3314	−	83.6490i	0.271780	−	0.643454i
$131$			15.3740i			0.117358i	0.998277	+	0.0586792i	$0.0186889\pi$
$131$			15.3740i			0.117358i	−0.998277	+	0.0586792i	$0.981311\pi$
$132$	95.0997	+	97.7800i	0.720453	+	0.740758i
$133$	223.998			1.68420
$134$	223.829	+	94.5404i	1.67037	+	0.705525i
$135$		−	188.473i		−	1.39609i
$136$	−183.825	+	71.6917i	−1.35165	+	0.527145i
$137$	−232.797			−1.69925			−0.849623	−	0.527391i	$-0.823170\pi$
$137$	−232.797			−1.69925			−0.849623	+	0.527391i	$0.823170\pi$
$138$	34.3127	−	81.2373i	0.248643	−	0.588676i
$139$			14.2342i			0.102405i	0.998688	+	0.0512023i	$0.0163053\pi$
$139$			14.2342i			0.102405i	−0.998688	+	0.0512023i	$0.983695\pi$
$140$	97.3981	−	94.7283i	0.695701	−	0.676631i
$141$	206.157			1.46211
$142$	−100.769	−	42.5624i	−0.709640	−	0.299736i
$143$			75.6038i			0.528698i
$144$	8.09321	−	291.146i	0.0562029	−	2.02185i
$145$	−121.218			−0.835987
$146$	27.9765	−	66.2359i	0.191620	−	0.453670i
$147$		−	134.798i		−	0.916991i
$148$	−40.9126	−	42.0657i	−0.276436	−	0.284227i
$149$	−22.0900			−0.148255			−0.0741274	−	0.997249i	$-0.523617\pi$
$149$	−22.0900			−0.148255			−0.0741274	+	0.997249i	$0.523617\pi$
$150$	−92.1048	−	38.9029i	−0.614032	−	0.259353i
$151$			64.7700i			0.428940i	0.976731	+	0.214470i	$0.0688025\pi$
$151$			64.7700i			0.428940i	−0.976731	+	0.214470i	$0.931198\pi$
$152$	75.2617	+	192.979i	0.495143	+	1.26960i
$153$	−448.971			−2.93445
$154$	−44.0153	+	104.209i	−0.285813	+	0.676679i
$155$		−	21.8602i		−	0.141034i
$156$	172.947	−	168.207i	1.10864	−	1.07825i
$157$	46.2089			0.294324			0.147162	−	0.989112i	$-0.452986\pi$
$157$	46.2089			0.294324			0.147162	+	0.989112i	$0.452986\pi$
$158$	−34.5718	−	14.6023i	−0.218809	−	0.0924199i
$159$		−	250.253i		−	1.57392i
$160$	114.335	+	52.0823i	0.714595	+	0.325515i
$161$	73.1372			0.454268
$162$	67.3444	−	159.442i	0.415706	−	0.984207i
$163$		−	18.4556i		−	0.113225i	−0.998396	−	0.0566123i	$-0.981970\pi$
$163$		−	18.4556i		−	0.113225i	0.998396	−	0.0566123i	$-0.0180299\pi$
$164$	−114.503	−	117.730i	−0.698188	−	0.717866i
$165$	−133.884			−0.811416
$166$	71.8461	+	30.3461i	0.432808	+	0.182808i
$167$		−	25.3291i		−	0.151671i	−0.997120	−	0.0758357i	$-0.975838\pi$
$167$		−	25.3291i		−	0.151671i	0.997120	−	0.0758357i	$-0.0241624\pi$
$168$	336.309	−	131.161i	2.00184	−	0.780718i
$169$	−35.2768			−0.208738
$170$	75.3558	−	178.409i	0.443269	−	1.04946i
$171$			471.328i			2.75631i
$172$	−241.084	+	234.475i	−1.40165	+	1.36323i
$173$	−64.3830			−0.372156			−0.186078	−	0.982535i	$-0.559578\pi$
$173$	−64.3830			−0.372156			−0.186078	+	0.982535i	$0.559578\pi$
$174$	−296.682	−	125.311i	−1.70507	−	0.720181i
$175$		−	82.9212i		−	0.473835i
$176$	−104.566	−	2.90671i	−0.594127	−	0.0165154i
$177$	−290.346			−1.64037
$178$	−51.7385	+	122.494i	−0.290666	+	0.688166i
$179$			27.8015i			0.155316i	0.996980	+	0.0776578i	$0.0247442\pi$
$179$			27.8015i			0.155316i	−0.996980	+	0.0776578i	$0.975256\pi$
$180$	199.323	+	204.941i	1.10735	+	1.13856i
$181$	−272.019			−1.50287			−0.751435	−	0.659807i	$-0.770638\pi$
$181$	−272.019			−1.50287			−0.751435	+	0.659807i	$0.770638\pi$
$182$	184.318	+	77.8515i	1.01273	+	0.427755i
$183$			415.396i			2.26992i
$184$	24.5736	+	63.0091i	0.133552	+	0.342441i
$185$	57.5977			0.311339
$186$	22.5984	−	53.5029i	0.121497	−	0.287650i
$187$			161.250i			0.862298i
$188$	−113.339	+	110.233i	−0.602869	+	0.586343i
$189$	415.293			2.19732
$190$	−187.293	−	79.1083i	−0.985753	−	0.416359i
$191$		−	287.996i		−	1.50783i	−0.656971	−	0.753915i	$-0.728163\pi$
$191$		−	287.996i		−	1.50783i	0.656971	−	0.753915i	$-0.271837\pi$
$192$	225.995	+	245.668i	1.17706	+	1.27952i
$193$	−114.476			−0.593138			−0.296569	−	0.955011i	$-0.595842\pi$
$193$	−114.476			−0.593138			−0.296569	+	0.955011i	$0.595842\pi$
$194$	135.931	−	321.824i	0.700675	−	1.65889i
$195$			236.805i			1.21438i
$196$	72.0766	+	74.1080i	0.367738	+	0.378102i
$197$	−24.7476			−0.125622			−0.0628112	−	0.998025i	$-0.520007\pi$
$197$	−24.7476			−0.125622			−0.0628112	+	0.998025i	$0.520007\pi$
$198$	−219.271	−	92.6151i	−1.10743	−	0.467753i
$199$		−	101.989i		−	0.512506i	−0.966610	−	0.256253i	$-0.917512\pi$
$199$		−	101.989i		−	0.512506i	0.966610	−	0.256253i	$-0.0824880\pi$
$200$	71.4381	−	27.8609i	0.357191	−	0.139304i
$201$	−633.647			−3.15248
$202$	−87.5551	+	207.291i	−0.433441	+	1.02620i
$203$		−	267.100i		−	1.31576i
$204$	368.867	−	358.755i	1.80817	−	1.75861i
$205$	161.200			0.786340
$206$	262.928	+	111.055i	1.27635	+	0.539100i
$207$			153.892i			0.743441i
$208$	−5.14121	+	184.951i	−0.0247174	+	0.889185i
$209$	169.280			0.809950
$210$	−137.864	+	326.400i	−0.656495	+	1.55429i
$211$		−	115.364i		−	0.546748i	−0.961908	−	0.273374i	$-0.911860\pi$
$211$		−	115.364i		−	0.546748i	0.961908	−	0.273374i	$-0.0881396\pi$
$212$	133.811	+	137.582i	0.631184	+	0.648973i
$213$	285.271			1.33930
$214$	−104.204	−	44.0133i	−0.486934	−	0.205670i
$215$		−	330.100i		−	1.53535i
$216$	139.535	+	357.782i	0.645996	+	1.65640i
$217$	48.1683			0.221974
$218$	−46.3338	+	109.698i	−0.212540	+	0.503200i
$219$			187.510i			0.856209i
$220$	73.6055	−	71.5879i	0.334571	−	0.325399i
$221$	285.209			1.29054
$222$	140.970	+	59.5426i	0.635002	+	0.268210i
$223$		−	175.451i		−	0.786776i	−0.919372	−	0.393388i	$-0.871303\pi$
$223$		−	175.451i		−	0.786776i	0.919372	−	0.393388i	$-0.128697\pi$
$224$	−114.762	+	251.934i	−0.512328	+	1.12470i
$225$	174.479			0.775464
$226$	−12.7449	+	30.1741i	−0.0563932	+	0.133514i
$227$			163.716i			0.721216i	0.932718	+	0.360608i	$0.117431\pi$
$227$			163.716i			0.721216i	−0.932718	+	0.360608i	$0.882569\pi$
$228$	−376.621	−	387.235i	−1.65184	−	1.69840i
$229$	184.622			0.806209			0.403104	−	0.915154i	$-0.367931\pi$
$229$	184.622			0.806209			0.403104	+	0.915154i	$0.367931\pi$
$230$	−61.1527	−	25.8295i	−0.265881	−	0.112302i
$231$		−	295.008i		−	1.27709i
$232$	230.112	−	89.7435i	0.991860	−	0.386826i
$233$	−2.14707			−0.00921490			−0.00460745	−	0.999989i	$-0.501467\pi$
$233$	−2.14707			−0.00921490			−0.00460745	+	0.999989i	$0.501467\pi$
$234$	−163.812	+	387.834i	−0.700051	+	1.65741i
$235$		−	155.188i		−	0.660374i
$236$	159.624	−	155.249i	0.676374	−	0.657834i
$237$	97.8707			0.412957
$238$	393.118	+	166.044i	1.65175	+	0.697663i
$239$			253.795i			1.06190i	0.847402	+	0.530951i	$0.178165\pi$
$239$			253.795i			1.06190i	−0.847402	+	0.530951i	$0.821835\pi$
$240$	−327.521	−	9.10437i	−1.36467	−	0.0379349i
$241$	117.305			0.486742			0.243371	−	0.969933i	$-0.421747\pi$
$241$	117.305			0.486742			0.243371	+	0.969933i	$0.421747\pi$
$242$	60.8974	−	144.178i	0.251642	−	0.595776i
$243$			19.3364i			0.0795736i
$244$	−222.113	−	228.373i	−0.910300	−	0.935955i
$245$	−101.471			−0.414168
$246$	394.537	+	166.643i	1.60381	+	0.677411i
$247$		−	299.411i		−	1.21219i
$248$	16.1842	+	41.4979i	0.0652587	+	0.167330i
$249$	−203.392			−0.816835
$250$	−105.668	+	250.174i	−0.422672	+	1.00070i
$251$			90.3359i			0.359904i	0.983675	+	0.179952i	$0.0575943\pi$
$251$			90.3359i			0.359904i	−0.983675	+	0.179952i	$0.942406\pi$
$252$	−451.581	+	439.202i	−1.79199	+	1.74287i
$253$	55.2711			0.218463
$254$	−339.723	−	143.491i	−1.33749	−	0.564926i
$255$			505.064i			1.98064i
$256$	−255.605	−	14.2215i	−0.998456	−	0.0555526i
$257$	−214.427			−0.834346			−0.417173	−	0.908827i	$-0.636979\pi$
$257$	−214.427			−0.834346			−0.417173	+	0.908827i	$0.636979\pi$
$258$	341.246	−	807.919i	1.32266	−	3.13147i
$259$			126.914i			0.490017i
$260$	−126.620	−	130.189i	−0.487001	−	0.500726i
$261$	562.021			2.15334
$262$	28.3249	+	11.9638i	0.108110	+	0.0456634i
$263$			113.778i			0.432616i	0.976325	+	0.216308i	$0.0694016\pi$
$263$			113.778i			0.432616i	−0.976325	+	0.216308i	$0.930598\pi$
$264$	254.155	−	99.1204i	0.962708	−	0.375456i
$265$	−188.382			−0.710876
$266$	174.312	−	412.694i	0.655310	−	1.55148i
$267$		−	346.772i		−	1.29877i
$268$	348.362	−	338.813i	1.29986	−	1.26423i
$269$	−236.904			−0.880683			−0.440342	−	0.897830i	$-0.645143\pi$
$269$	−236.904			−0.880683			−0.440342	+	0.897830i	$0.645143\pi$
$270$	−347.241	−	146.667i	−1.28608	−	0.543210i
$271$		−	389.591i		−	1.43760i	−0.695214	−	0.718802i	$-0.744691\pi$
$271$		−	389.591i		−	1.43760i	0.695214	−	0.718802i	$-0.255309\pi$
$272$	−10.9653	+	394.468i	−0.0403137	+	1.45025i
$273$	−521.792			−1.91132
$274$	−181.159	+	428.904i	−0.661165	+	1.56534i
$275$		−	62.6650i		−	0.227873i
$276$	−122.970	−	126.435i	−0.445542	−	0.458099i
$277$	−382.387			−1.38046			−0.690230	−	0.723590i	$-0.742491\pi$
$277$	−382.387			−1.38046			−0.690230	+	0.723590i	$0.742491\pi$
$278$	26.2251	+	11.0769i	0.0943349	+	0.0398449i
$279$			101.354i			0.363275i
$280$	−98.7333	−	253.162i	−0.352619	−	0.904151i
$281$	422.451			1.50338			0.751692	−	0.659514i	$-0.229238\pi$
$281$	422.451			1.50338			0.751692	+	0.659514i	$0.229238\pi$
$282$	160.428	−	379.823i	0.568895	−	1.34689i
$283$			217.902i			0.769972i	0.922922	+	0.384986i	$0.125794\pi$
$283$			217.902i			0.769972i	−0.922922	+	0.384986i	$0.874206\pi$
$284$	−156.834	+	152.535i	−0.552232	+	0.537094i
$285$	530.215			1.86040
$286$	139.292	+	58.8338i	0.487035	+	0.205712i
$287$			355.198i			1.23762i
$288$	−530.109	−	241.477i	−1.84065	−	0.838461i
$289$	319.301			1.10485
$290$	−94.3302	+	223.332i	−0.325277	+	0.770110i
$291$			911.064i			3.13080i
$292$	−100.262	−	103.088i	−0.343363	−	0.353040i
$293$	−234.175			−0.799231			−0.399616	−	0.916683i	$-0.630856\pi$
$293$	−234.175			−0.799231			−0.399616	+	0.916683i	$0.630856\pi$
$294$	−248.351	−	104.898i	−0.844731	−	0.356795i
$295$			218.563i			0.740891i
$296$	−109.339	+	42.6423i	−0.369389	+	0.144062i
$297$	313.844			1.05671
$298$	−17.1901	+	40.6985i	−0.0576849	+	0.136572i
$299$		−	97.7601i		−	0.326957i
$300$	−143.349	+	139.420i	−0.477831	+	0.464733i
$301$	727.363			2.41649
$302$	119.332	+	50.4031i	0.395139	+	0.166898i
$303$		−	586.829i		−	1.93673i
$304$	414.111	+	11.5114i	1.36221	+	0.0378663i
$305$	312.696			1.02523
$306$	−349.383	+	827.182i	−1.14177	+	2.70321i
$307$		−	216.888i		−	0.706475i	−0.935534	−	0.353237i	$-0.885081\pi$
$307$		−	216.888i		−	0.706475i	0.935534	−	0.353237i	$-0.114919\pi$
$308$	157.741	+	162.187i	0.512147	+	0.526582i
$309$	−744.332			−2.40884
$310$	−40.2752	−	17.0113i	−0.129920	−	0.0548752i
$311$			18.0919i			0.0581732i	0.999577	+	0.0290866i	$0.00925985\pi$
$311$			18.0919i			0.0581732i	−0.999577	+	0.0290866i	$0.990740\pi$
$312$	−175.318	−	449.533i	−0.561917	−	1.44081i
$313$	401.383			1.28238			0.641188	−	0.767384i	$-0.278442\pi$
$313$	401.383			1.28238			0.641188	+	0.767384i	$0.278442\pi$
$314$	35.9591	−	85.1351i	0.114519	−	0.271131i
$315$		−	618.319i		−	1.96292i
$316$	−53.8066	+	52.3317i	−0.170274	+	0.165607i
$317$	−464.216			−1.46440			−0.732201	−	0.681088i	$-0.761507\pi$
$317$	−464.216			−1.46440			−0.732201	+	0.681088i	$0.761507\pi$
$318$	−461.066	−	194.743i	−1.44989	−	0.612401i
$319$		−	201.852i		−	0.632766i
$320$	184.930	−	170.121i	0.577907	−	0.531629i
$321$	294.995			0.918987
$322$	56.9144	−	134.748i	0.176753	−	0.418471i
$323$		−	638.593i		−	1.97707i
$324$	−241.348	−	248.150i	−0.744902	−	0.765896i
$325$	−110.838			−0.341040
$326$	−34.0026	−	14.3619i	−0.104302	−	0.0440549i
$327$		−	310.547i		−	0.949686i
$328$	−306.010	+	119.344i	−0.932957	+	0.363853i
$329$	341.951			1.03937
$330$	−104.186	+	246.667i	−0.315716	+	0.747475i
$331$		−	193.007i		−	0.583102i	−0.956555	−	0.291551i	$-0.905829\pi$
$331$		−	193.007i		−	0.583102i	0.956555	−	0.291551i	$-0.0941713\pi$
$332$	111.819	−	108.754i	0.336805	−	0.327573i
$333$	−267.048			−0.801947
$334$	−46.6663	−	19.7108i	−0.139719	−	0.0590142i
$335$			476.989i			1.42385i
$336$	20.0612	−	721.682i	0.0597058	−	2.14786i
$337$	273.953			0.812916			0.406458	−	0.913669i	$-0.366764\pi$
$337$	273.953			0.812916			0.406458	+	0.913669i	$0.366764\pi$
$338$	−27.4519	+	64.9938i	−0.0812186	+	0.192289i
$339$		−	85.4211i		−	0.251980i
$340$	−270.059	−	277.670i	−0.794291	−	0.816678i
$341$	36.4016			0.106750
$342$	868.374	+	366.781i	2.53910	+	1.07246i
$343$			200.324i			0.584036i
$344$	244.388	+	626.637i	0.710432	+	1.82162i
$345$	173.119			0.501796
$346$	−50.1019	+	118.619i	−0.144803	+	0.342829i
$347$			176.475i			0.508575i	0.967129	+	0.254287i	$0.0818409\pi$
$347$			176.475i			0.508575i	−0.967129	+	0.254287i	$0.918159\pi$
$348$	−461.747	+	449.090i	−1.32686	+	1.29049i
$349$	−554.994			−1.59024			−0.795121	−	0.606451i	$-0.792592\pi$
$349$	−554.994			−1.59024			−0.795121	+	0.606451i	$0.792592\pi$
$350$	−152.774	−	64.5281i	−0.436496	−	0.184366i
$351$		−	555.108i		−	1.58150i
$352$	−86.7274	+	190.391i	−0.246385	+	0.540883i
$353$	−104.065			−0.294801			−0.147401	−	0.989077i	$-0.547091\pi$
$353$	−104.065			−0.294801			−0.147401	+	0.989077i	$0.547091\pi$
$354$	−225.943	+	534.933i	−0.638258	+	1.51111i
$355$		−	214.742i		−	0.604907i
$356$	185.420	+	190.646i	0.520842	+	0.535521i
$357$	−1112.89			−3.11734
$358$	51.2214	+	21.6347i	0.143077	+	0.0604322i
$359$			581.122i			1.61872i	0.587310	+	0.809362i	$0.300187\pi$
$359$			581.122i			1.61872i	−0.587310	+	0.809362i	$0.699813\pi$
$360$	532.694	−	207.751i	1.47970	−	0.577085i
$361$	−309.393			−0.857044
$362$	−211.682	+	501.168i	−0.584756	+	1.38444i
$363$			408.158i			1.12440i
$364$	286.867	−	279.003i	0.788095	−	0.766492i
$365$	141.151			0.386715
$366$	765.324	+	323.255i	2.09105	+	0.883211i
$367$		−	421.408i		−	1.14825i	−0.818768	−	0.574125i	$-0.805342\pi$
$367$		−	421.408i		−	1.14825i	0.818768	−	0.574125i	$-0.194658\pi$
$368$	135.211	+	3.75855i	0.367420	+	0.0102135i
$369$	−747.393			−2.02546
$370$	44.8217	−	106.118i	0.121140	−	0.286805i
$371$		−	415.093i		−	1.11885i
$372$	−80.9879	−	83.2705i	−0.217709	−	0.223845i
$373$	196.092			0.525717			0.262858	−	0.964834i	$-0.415335\pi$
$373$	196.092			0.525717			0.262858	+	0.964834i	$0.415335\pi$
$374$	297.086	+	125.482i	0.794348	+	0.335514i
$375$		−	708.229i		−	1.88861i
$376$	114.893	+	294.598i	0.305567	+	0.783504i
$377$	−357.024			−0.947012
$378$	323.175	−	765.134i	0.854960	−	2.02416i
$379$			266.449i			0.703033i	0.936182	+	0.351516i	$0.114334\pi$
$379$			266.449i			0.703033i	−0.936182	+	0.351516i	$0.885666\pi$
$380$	−291.498	+	283.507i	−0.767099	+	0.746072i
$381$	961.736			2.52424
$382$	−530.602	−	224.114i	−1.38901	−	0.586686i
$383$		−	117.544i		−	0.306903i	−0.988156	−	0.153452i	$-0.950961\pi$
$383$		−	117.544i		−	0.306903i	0.988156	−	0.153452i	$-0.0490389\pi$
$384$	628.483	−	225.197i	1.63668	−	0.586450i
$385$	−222.072			−0.576810
$386$	−89.0833	+	210.909i	−0.230786	+	0.546398i
$387$			1530.49i			3.95475i
$388$	−487.148	−	500.878i	−1.25554	−	1.29092i
$389$	656.073			1.68656			0.843281	−	0.537472i	$-0.180621\pi$
$389$	656.073			1.68656			0.843281	+	0.537472i	$0.180621\pi$
$390$	436.289	+	184.278i	1.11869	+	0.472509i
$391$		−	208.506i		−	0.533262i
$392$	192.625	−	75.1239i	0.491391	−	0.191643i
$393$	−80.1862			−0.204036
$394$	−19.2582	+	45.5949i	−0.0488788	+	0.115723i
$395$		−	73.6738i		−	0.186516i
$396$	−341.268	+	331.913i	−0.861787	+	0.838164i
$397$	29.2365			0.0736435			0.0368218	−	0.999322i	$-0.488277\pi$
$397$	29.2365			0.0736435			0.0368218	+	0.999322i	$0.488277\pi$
$398$	−187.904	−	79.3662i	−0.472120	−	0.199412i
$399$			1168.31i			2.92810i
$400$	4.26135	−	153.298i	0.0106534	−	0.383246i
$401$	665.189			1.65883			0.829413	−	0.558636i	$-0.188675\pi$
$401$	665.189			1.65883			0.829413	+	0.558636i	$0.188675\pi$
$402$	−493.096	+	1167.43i	−1.22661	+	2.90406i
$403$		−	64.3849i		−	0.159764i
$404$	313.779	+	322.623i	0.776681	+	0.798571i
$405$	339.776			0.838952
$406$	−492.104	−	207.853i	−1.21208	−	0.511954i
$407$			95.9116i			0.235655i
$408$	−373.923	−	958.777i	−0.916478	−	2.34994i
$409$	263.757			0.644882			0.322441	−	0.946590i	$-0.395497\pi$
$409$	263.757			0.644882			0.322441	+	0.946590i	$0.395497\pi$
$410$	125.443	−	296.994i	0.305959	−	0.724375i
$411$		−	1214.20i		−	2.95426i
$412$	409.213	−	397.996i	0.993235	−	0.966009i
$413$	−481.595			−1.16609
$414$	283.531	+	119.757i	0.684857	+	0.289268i
$415$			153.107i			0.368931i
$416$	336.752	+	153.398i	0.809499	+	0.368745i
$417$	−74.2416			−0.178037
$418$	131.731	−	311.880i	0.315146	−	0.746125i
$419$			63.9922i			0.152726i	0.997080	+	0.0763630i	$0.0243308\pi$
$419$			63.9922i			0.152726i	−0.997080	+	0.0763630i	$0.975669\pi$
$420$	494.075	+	508.000i	1.17637	+	1.20952i
$421$	−468.113			−1.11191			−0.555954	−	0.831213i	$-0.687647\pi$
$421$	−468.113			−1.11191			−0.555954	+	0.831213i	$0.687647\pi$
$422$	−212.546	−	89.7745i	−0.503663	−	0.212736i
$423$			719.520i			1.70099i
$424$	357.611	−	139.468i	0.843422	−	0.328935i
$425$	−236.398			−0.556231
$426$	221.994	−	525.582i	0.521112	−	1.23376i
$427$			689.015i			1.61362i
$428$	−162.180	+	157.734i	−0.378925	+	0.368538i
$429$	−394.327			−0.919178
$430$	−608.175	−	256.879i	−1.41436	−	0.597393i
$431$		−	81.5606i		−	0.189236i	−0.995514	−	0.0946178i	$-0.969837\pi$
$431$		−	81.5606i		−	0.189236i	0.995514	−	0.0946178i	$-0.0301629\pi$
$432$	767.762	+	21.3421i	1.77723	+	0.0494029i
$433$	263.724			0.609062			0.304531	−	0.952502i	$-0.401500\pi$
$433$	263.724			0.609062			0.304531	+	0.952502i	$0.401500\pi$
$434$	37.4839	−	88.7450i	0.0863683	−	0.204482i
$435$		−	632.239i		−	1.45342i
$436$	166.050	+	170.730i	0.380850	+	0.391583i
$437$	−218.889			−0.500889
$438$	345.467	+	145.917i	0.788738	+	0.333145i
$439$			544.955i			1.24135i	0.784066	+	0.620677i	$0.213142\pi$
$439$			544.955i			1.24135i	−0.784066	+	0.620677i	$0.786858\pi$
$440$	−74.6145	−	191.319i	−0.169578	−	0.434817i
$441$	470.465			1.06681
$442$	221.945	−	525.467i	0.502139	−	1.18884i
$443$		−	237.733i		−	0.536644i	−0.963329	−	0.268322i	$-0.913531\pi$
$443$		−	237.733i		−	0.536644i	0.963329	−	0.268322i	$-0.0864691\pi$
$444$	219.402	−	213.388i	0.494149	−	0.480604i
$445$	−261.038			−0.586603
$446$	−323.251	−	136.534i	−0.724777	−	0.306129i
$447$		−	115.215i		−	0.257752i
$448$	374.856	+	407.488i	0.836732	+	0.909571i
$449$	−400.343			−0.891632			−0.445816	−	0.895125i	$-0.647086\pi$
$449$	−400.343			−0.891632			−0.445816	+	0.895125i	$0.647086\pi$
$450$	135.777	−	321.460i	0.301727	−	0.714356i
$451$			268.430i			0.595187i
$452$	45.6749	+	46.9622i	0.101051	+	0.103899i
$453$	−337.822			−0.745743
$454$	301.630	+	127.401i	0.664383	+	0.280620i
$455$			392.787i			0.863269i
$456$	−1006.52	+	392.544i	−2.20729	+	0.860841i
$457$	166.789			0.364965			0.182483	−	0.983209i	$-0.441587\pi$
$457$	166.789			0.364965			0.182483	+	0.983209i	$0.441587\pi$
$458$	143.670	−	340.147i	0.313690	−	0.742678i
$459$		−	1183.95i		−	2.57941i
$460$	−95.1763	+	92.5674i	−0.206905	+	0.201233i
$461$	2.56296			0.00555958			0.00277979	−	0.999996i	$-0.499115\pi$
$461$	2.56296			0.00555958			0.00277979	+	0.999996i	$0.499115\pi$
$462$	−543.522	−	229.571i	−1.17645	−	0.496907i
$463$		−	57.8677i		−	0.124984i	−0.998045	−	0.0624922i	$-0.980095\pi$
$463$		−	57.8677i		−	0.124984i	0.998045	−	0.0624922i	$-0.0199048\pi$
$464$	13.7264	−	493.794i	0.0295827	−	1.06421i
$465$	114.017			0.245197
$466$	−1.67082	+	3.95576i	−0.00358545	+	0.00848875i
$467$			546.103i			1.16939i	0.811255	+	0.584693i	$0.198785\pi$
$467$			546.103i			1.16939i	−0.811255	+	0.584693i	$0.801215\pi$
$468$	587.067	+	603.613i	1.25442	+	1.28977i
$469$	−1051.03			−2.24100
$470$	−285.918	−	120.765i	−0.608336	−	0.256947i
$471$			241.012i			0.511703i
$472$	−161.812	−	414.904i	−0.342823	−	0.879033i
$473$	549.682			1.16212
$474$	76.1616	−	180.317i	0.160679	−	0.380415i
$475$			248.170i			0.522464i
$476$	611.837	−	595.066i	1.28537	−	1.25014i
$477$	873.423			1.83107
$478$	467.591	+	197.499i	0.978223	+	0.413179i
$479$			670.219i			1.39920i	0.714532	+	0.699602i	$0.246640\pi$
$479$			670.219i			1.39920i	−0.714532	+	0.699602i	$0.753360\pi$
$480$	−271.646	+	596.340i	−0.565930	+	1.24237i
$481$	169.642			0.352687
$482$	91.2850	−	216.122i	0.189388	−	0.448386i
$483$			381.463i			0.789778i
$484$	−218.243	−	224.394i	−0.450916	−	0.463624i
$485$	685.818			1.41406
$486$	35.6253	+	15.0473i	0.0733030	+	0.0309615i
$487$		−	231.458i		−	0.475273i	−0.971354	−	0.237636i	$-0.923627\pi$
$487$		−	231.458i		−	0.475273i	0.971354	−	0.237636i	$-0.0763727\pi$
$488$	−593.599	+	231.504i	−1.21639	+	0.474393i
$489$	96.2592			0.196849
$490$	−78.9634	+	186.950i	−0.161150	+	0.381531i
$491$			590.808i			1.20327i	0.798770	+	0.601637i	$0.205485\pi$
$491$			590.808i			1.20327i	−0.798770	+	0.601637i	$0.794515\pi$
$492$	614.046	−	597.214i	1.24806	−	1.21385i
$493$	−761.470			−1.54456
$494$	−551.634	−	232.998i	−1.11667	−	0.471655i
$495$		−	467.275i		−	0.943990i
$496$	89.0498	+	2.47539i	0.179536	+	0.00499070i
$497$	473.177			0.952066
$498$	−158.277	+	374.729i	−0.317825	+	0.752467i
$499$		−	117.679i		−	0.235830i	−0.993024	−	0.117915i	$-0.962379\pi$
$499$		−	117.679i		−	0.235830i	0.993024	−	0.117915i	$-0.0376210\pi$
$500$	378.691	+	389.364i	0.757383	+	0.778729i
$501$	132.109			0.263691
$502$	166.435	+	70.2981i	0.331543	+	0.140036i
$503$		−	157.463i		−	0.313048i	−0.987674	−	0.156524i	$-0.949971\pi$
$503$		−	157.463i		−	0.313048i	0.987674	−	0.156524i	$-0.0500288\pi$
$504$	457.771	+	1173.77i	0.908276	+	2.32891i
$505$	−441.745			−0.874743
$506$	43.0112	−	101.831i	0.0850024	−	0.201248i
$507$		−	183.994i		−	0.362906i
$508$	−528.736	+	514.242i	−1.04082	+	1.01229i
$509$	−402.018			−0.789819			−0.394910	−	0.918720i	$-0.629224\pi$
$509$	−402.018			−0.789819			−0.394910	+	0.918720i	$0.629224\pi$
$510$	930.529	+	393.034i	1.82457	+	0.770655i
$511$			311.021i			0.608652i
$512$	−225.110	+	459.858i	−0.439667	+	0.898161i
$513$	−1242.91			−2.42282
$514$	−166.864	+	395.060i	−0.324638	+	0.768598i
$515$			560.308i			1.08798i
$516$	−1222.96	−	1257.42i	−2.37007	−	2.43687i
$517$	258.419			0.499843
$518$	233.827	+	98.7630i	0.451403	+	0.190662i
$519$		−	335.803i		−	0.647019i
$520$	−338.394	+	131.974i	−0.650757	+	0.253795i
$521$	−322.000			−0.618043			−0.309021	−	0.951055i	$-0.600001\pi$
$521$	−322.000			−0.618043			−0.309021	+	0.951055i	$0.600001\pi$
$522$	437.357	−	1035.47i	0.837848	−	1.98365i
$523$		−	363.423i		−	0.694882i	−0.937702	−	0.347441i	$-0.887051\pi$
$523$		−	363.423i		−	0.694882i	0.937702	−	0.347441i	$-0.112949\pi$
$524$	44.0841	−	42.8757i	0.0841300	−	0.0818239i
$525$	432.493			0.823796
$526$	209.625	+	88.5405i	0.398526	+	0.168328i
$527$		−	137.322i		−	0.260573i
$528$	15.1606	−	545.388i	0.0287132	−	1.03293i
$529$	457.531			0.864898
$530$	−146.596	+	347.075i	−0.276597	+	0.654858i
$531$		−	1013.35i		−	1.90839i
$532$	−624.699	−	642.305i	−1.17425	−	1.20734i
$533$	474.782			0.890772
$534$	−638.891	−	269.853i	−1.19643	−	0.505343i
$535$		−	222.062i		−	0.415069i
$536$	−353.137	−	905.480i	−0.658838	−	1.68933i
$537$	−145.005			−0.270027
$538$	−184.355	+	436.471i	−0.342668	+	0.811284i
$539$		−	168.970i		−	0.313487i
$540$	−540.436	+	525.622i	−1.00081	+	0.973375i
$541$	171.486			0.316979			0.158489	−	0.987361i	$-0.449338\pi$
$541$	171.486			0.316979			0.158489	+	0.987361i	$0.449338\pi$
$542$	−717.781	−	303.174i	−1.32432	−	0.559362i
$543$		−	1418.78i		−	2.61285i
$544$	718.233	+	327.172i	1.32028	+	0.601419i
$545$	−233.770			−0.428935
$546$	−406.051	+	961.347i	−0.743683	+	1.76071i
$547$			676.814i			1.23732i	0.785659	+	0.618660i	$0.212324\pi$
$547$			676.814i			1.23732i	−0.785659	+	0.618660i	$0.787676\pi$
$548$	649.236	+	667.534i	1.18474	+	1.21813i
$549$	−1449.80			−2.64080
$550$	−115.454	−	48.7650i	−0.209916	−	0.0886637i
$551$			799.389i			1.45080i
$552$	−328.637	+	128.169i	−0.595358	+	0.232189i
$553$	162.338			0.293558
$554$	−297.568	+	704.509i	−0.537127	+	1.27168i
$555$			300.413i			0.541285i
$556$	40.8160	−	39.6972i	0.0734101	−	0.0713978i
$557$	−958.265			−1.72040			−0.860202	−	0.509953i	$-0.829663\pi$
$557$	−958.265			−1.72040			−0.860202	+	0.509953i	$0.829663\pi$
$558$	186.734	+	78.8720i	0.334648	+	0.141348i
$559$		−	972.242i		−	1.73925i
$560$	−543.258	−	15.1014i	−0.970104	−	0.0269667i
$561$	−841.033			−1.49917
$562$	328.745	−	778.323i	0.584956	−	1.38492i
$563$			5.68452i			0.0100968i	0.999987	+	0.00504842i	$0.00160697\pi$
$563$			5.68452i			0.0100968i	−0.999987	+	0.00504842i	$0.998393\pi$
$564$	−574.941	−	591.146i	−1.01940	−	1.04813i
$565$	−64.3021			−0.113809
$566$	401.462	+	169.568i	0.709297	+	0.299591i
$567$			748.683i			1.32043i
$568$	158.984	+	407.651i	0.279901	+	0.717695i
$569$	−385.709			−0.677872			−0.338936	−	0.940809i	$-0.610067\pi$
$569$	−385.709			−0.677872			−0.338936	+	0.940809i	$0.610067\pi$
$570$	412.606	−	976.867i	0.723870	−	1.71380i
$571$			168.878i			0.295759i	0.989005	+	0.147879i	$0.0472447\pi$
$571$			168.878i			0.295759i	−0.989005	+	0.147879i	$0.952755\pi$
$572$	216.790	−	210.848i	0.379004	−	0.368615i
$573$	1502.10			2.62147
$574$	654.416	+	276.410i	1.14010	+	0.481551i
$575$			81.0296i			0.140921i
$576$	−857.419	+	788.757i	−1.48857	+	1.36937i
$577$	548.814			0.951151			0.475575	−	0.879675i	$-0.342240\pi$
$577$	548.814			0.951151			0.475575	+	0.879675i	$0.342240\pi$
$578$	248.475	−	588.279i	0.429888	−	1.01778i
$579$		−	597.072i		−	1.03121i
$580$	338.060	+	347.587i	0.582861	+	0.599289i
$581$	−337.365			−0.580663
$582$	1678.54	+	708.977i	2.88409	+	1.21817i
$583$		−	313.694i		−	0.538068i
$584$	−267.951	+	104.501i	−0.458820	+	0.178940i
$585$	−826.487			−1.41280
$586$	−182.232	+	431.443i	−0.310975	+	0.736251i
$587$		−	773.525i		−	1.31776i	−0.752248	−	0.658880i	$-0.771031\pi$
$587$		−	773.525i		−	1.31776i	0.752248	−	0.658880i	$-0.228969\pi$
$588$	−386.526	+	375.931i	−0.657357	+	0.639338i
$589$	−144.160			−0.244754
$590$	402.679	+	170.082i	0.682507	+	0.288275i
$591$		−	129.076i		−	0.218403i
$592$	−6.52219	+	234.630i	−0.0110172	+	0.396334i
$593$	650.330			1.09668			0.548339	−	0.836256i	$-0.315260\pi$
$593$	650.330			1.09668			0.548339	+	0.836256i	$0.315260\pi$
$594$	244.229	−	578.226i	0.411160	−	0.973444i
$595$			837.747i			1.40798i
$596$	61.6057	+	63.3420i	0.103365	+	0.106279i
$597$	531.944			0.891028
$598$	−180.113	−	76.0756i	−0.301192	−	0.127217i
$599$		−	865.743i		−	1.44531i	−0.691207	−	0.722657i	$-0.742921\pi$
$599$		−	865.743i		−	1.44531i	0.691207	−	0.722657i	$-0.257079\pi$
$600$	145.314	+	372.601i	0.242191	+	0.621001i
$601$	370.489			0.616455			0.308227	−	0.951313i	$-0.400264\pi$
$601$	370.489			0.616455			0.308227	+	0.951313i	$0.400264\pi$
$602$	566.024	−	1340.09i	0.940239	−	2.22607i
$603$		−	2211.53i		−	3.66754i
$604$	185.725	−	180.634i	0.307492	−	0.299063i
$605$	307.248			0.507848
$606$	−1081.17	−	456.662i	−1.78411	−	0.753568i
$607$			95.6391i			0.157560i	0.996892	+	0.0787802i	$0.0251025\pi$
$607$			95.6391i			0.157560i	−0.996892	+	0.0787802i	$0.974897\pi$
$608$	343.464	−	753.999i	0.564908	−	1.24013i
$609$	1393.12			2.28755
$610$	243.336	−	576.110i	0.398911	−	0.944443i
$611$		−	457.075i		−	0.748077i
$612$	1252.11	+	1287.40i	2.04594	+	2.10360i
$613$	242.601			0.395760			0.197880	−	0.980226i	$-0.436594\pi$
$613$	242.601			0.395760			0.197880	+	0.980226i	$0.436594\pi$
$614$	−399.593	−	168.779i	−0.650804	−	0.274884i
$615$			840.771i			1.36711i
$616$	421.565	−	164.410i	0.684359	−	0.266900i
$617$	765.408			1.24053			0.620265	−	0.784392i	$-0.287025\pi$
$617$	765.408			1.24053			0.620265	+	0.784392i	$0.287025\pi$
$618$	−579.228	+	1371.35i	−0.937263	+	2.21902i
$619$		−	802.370i		−	1.29624i	−0.761540	−	0.648118i	$-0.775556\pi$
$619$		−	802.370i		−	1.29624i	0.761540	−	0.648118i	$-0.224444\pi$
$620$	−62.6832	+	60.9650i	−0.101102	+	0.0983306i
$621$	−405.819			−0.653493
$622$	33.3324	+	14.0788i	0.0535890	+	0.0226348i
$623$		−	575.188i		−	0.923256i
$624$	−964.649	−	26.8151i	−1.54591	−	0.0429729i
$625$	−293.509			−0.469615
$626$	312.351	−	739.508i	0.498963	−	1.18132i
$627$			882.914i			1.40816i
$628$	−128.870	−	132.502i	−0.205207	−	0.210990i
$629$	361.818			0.575227
$630$	−1139.19	−	481.167i	−1.80824	−	0.763757i
$631$			491.387i			0.778742i	0.921081	+	0.389371i	$0.127308\pi$
$631$			491.387i			0.778742i	−0.921081	+	0.389371i	$0.872692\pi$
$632$	54.5442	+	139.857i	0.0863041	+	0.221293i
$633$	601.704			0.950560
$634$	−361.246	+	855.269i	−0.569789	+	1.34901i
$635$		−	723.962i		−	1.14010i
$636$	−717.589	+	697.919i	−1.12829	+	1.09736i
$637$	−298.863			−0.469173
$638$	−371.892	−	157.079i	−0.582903	−	0.246205i
$639$			995.639i			1.55812i
$640$	−169.520	−	473.101i	−0.264876	−	0.739220i
$641$	1124.15			1.75374			0.876872	−	0.480723i	$-0.159626\pi$
$641$	1124.15			1.75374			0.876872	+	0.480723i	$0.159626\pi$
$642$	229.561	−	543.497i	0.357571	−	0.846569i
$643$		−	293.775i		−	0.456881i	−0.973558	−	0.228441i	$-0.926637\pi$
$643$		−	293.775i		−	0.456881i	0.973558	−	0.228441i	$-0.0733627\pi$
$644$	−203.969	−	209.718i	−0.316722	−	0.325649i
$645$	1721.70			2.66931
$646$	−1176.54	−	496.944i	−1.82127	−	0.769263i
$647$		−	292.209i		−	0.451636i	−0.974169	−	0.225818i	$-0.927494\pi$
$647$		−	292.209i		−	0.451636i	0.974169	−	0.225818i	$-0.0725055\pi$
$648$	−645.005	+	251.552i	−0.995378	+	0.388198i
$649$	−363.950			−0.560787
$650$	−86.2526	+	204.208i	−0.132696	+	0.314166i
$651$			251.232i			0.385917i
$652$	−52.9207	+	51.4700i	−0.0811666	+	0.0789417i
$653$	−1201.94			−1.84064			−0.920322	−	0.391162i	$-0.872073\pi$
$653$	−1201.94			−1.84064			−0.920322	+	0.391162i	$0.872073\pi$
$654$	−572.152	−	241.664i	−0.874850	−	0.369516i
$655$			60.3614i			0.0921549i
$656$	−18.2538	+	656.663i	−0.0278259	+	1.00101i
$657$	−654.438			−0.996101
$658$	266.102	−	630.010i	0.404410	−	0.957462i
$659$			730.317i			1.10822i	0.832443	+	0.554110i	$0.186941\pi$
$659$			730.317i			1.10822i	−0.832443	+	0.554110i	$0.813059\pi$
$660$	373.382	+	383.905i	0.565730	+	0.581675i
$661$	1288.61			1.94948			0.974742	−	0.223333i	$-0.0716937\pi$
$661$	1288.61			1.94948			0.974742	+	0.223333i	$0.0716937\pi$
$662$	−355.595	−	150.195i	−0.537153	−	0.226881i
$663$			1487.57i			2.24369i
$664$	−113.352	−	290.646i	−0.170711	−	0.437720i
$665$	879.465			1.32250
$666$	−207.813	+	492.009i	−0.312032	+	0.738752i
$667$			261.007i			0.391315i
$668$	−72.6301	+	70.6392i	−0.108728	+	0.105747i
$669$	915.103			1.36787
$670$	878.802	+	371.186i	1.31165	+	0.554009i
$671$			520.701i			0.776007i
$672$	−1314.01	−	598.563i	−1.95538	−	0.890719i
$673$	−470.184			−0.698639			−0.349319	−	0.937004i	$-0.613587\pi$
$673$	−470.184			−0.698639			−0.349319	+	0.937004i	$0.613587\pi$
$674$	213.186	−	504.730i	0.316300	−	0.748857i
$675$			460.108i			0.681641i
$676$	98.3818	+	101.155i	0.145535	+	0.149637i
$677$	376.211			0.555703			0.277852	−	0.960624i	$-0.410378\pi$
$677$	376.211			0.555703			0.277852	+	0.960624i	$0.410378\pi$
$678$	−157.380	−	66.4735i	−0.232123	−	0.0980435i
$679$			1511.18i			2.22559i
$680$	−721.735	+	281.477i	−1.06138	+	0.413936i
$681$	−853.896			−1.25388
$682$	28.3272	−	67.0662i	0.0415355	−	0.0983376i
$683$			375.909i			0.550380i	0.961390	+	0.275190i	$0.0887407\pi$
$683$			375.909i			0.550380i	−0.961390	+	0.275190i	$0.911259\pi$
$684$	1351.51	−	1314.47i	1.97590	−	1.92173i
$685$	−914.009			−1.33432
$686$	369.077	+	155.890i	0.538013	+	0.227244i
$687$			962.934i			1.40165i
$688$	1344.69	+	37.3795i	1.95450	+	0.0543307i
$689$	−554.842			−0.805286
$690$	134.719	−	318.955i	0.195245	−	0.462253i
$691$			1252.58i			1.81270i	0.422528	+	0.906350i	$0.361143\pi$
$691$			1252.58i			1.81270i	−0.422528	+	0.906350i	$0.638857\pi$
$692$	179.555	+	184.615i	0.259472	+	0.266785i
$693$	1029.62			1.48575
$694$	325.138	+	137.331i	0.468498	+	0.197883i
$695$			55.8866i			0.0804124i
$696$	468.077	+	1200.20i	0.672524	+	1.72442i
$697$	1012.63			1.45284
$698$	−431.889	+	1022.52i	−0.618752	+	1.46493i
$699$		−	11.1985i		−	0.0160208i
$700$	−237.773	+	231.255i	−0.339675	+	0.330364i
$701$	−336.634			−0.480219			−0.240109	−	0.970746i	$-0.577183\pi$
$701$	−336.634			−0.480219			−0.240109	+	0.970746i	$0.577183\pi$
$702$	−1022.73	−	431.977i	−1.45688	−	0.615352i
$703$		−	379.836i		−	0.540307i
$704$	283.286	+	307.946i	0.402394	+	0.437423i
$705$	809.416			1.14811
$706$	−80.9818	+	191.729i	−0.114705	+	0.271570i
$707$		−	973.370i		−	1.37676i
$708$	809.733	+	832.554i	1.14369	+	1.17592i
$709$	−570.508			−0.804666			−0.402333	−	0.915493i	$-0.631801\pi$
$709$	−570.508			−0.804666			−0.402333	+	0.915493i	$0.631801\pi$
$710$	−395.640	−	167.109i	−0.557240	−	0.235365i
$711$			341.584i			0.480428i
$712$	495.536	−	193.259i	0.695977	−	0.271431i
$713$	−47.0695			−0.0660161
$714$	−866.037	+	2050.39i	−1.21294	+	2.87169i
$715$			296.836i			0.415156i
$716$	79.7195	−	77.5343i	0.111340	−	0.108288i
$717$	−1323.72			−1.84619
$718$	1070.66	+	452.221i	1.49117	+	0.629834i
$719$		−	634.534i		−	0.882523i	−0.897379	−	0.441261i	$-0.854531\pi$
$719$		−	634.534i		−	0.882523i	0.897379	−	0.441261i	$-0.145469\pi$
$720$	31.7757	−	1143.10i	0.0441329	−	1.58764i
$721$	−1234.62			−1.71237
$722$	−240.765	+	570.025i	−0.333470	+	0.789508i
$723$			611.829i			0.846236i
$724$	758.623	+	780.004i	1.04782	+	1.07735i
$725$	295.923			0.408170
$726$	751.990	+	317.623i	1.03580	+	0.437497i
$727$			623.891i			0.858172i	0.903264	+	0.429086i	$0.141164\pi$
$727$			623.891i			0.858172i	−0.903264	+	0.429086i	$0.858836\pi$
$728$	−290.799	−	745.639i	−0.399449	−	1.02423i
$729$	678.009			0.930054
$730$	109.842	−	260.056i	0.150468	−	0.356241i
$731$		−	2073.63i		−	2.83670i
$732$	1191.13	−	1158.48i	1.62722	−	1.58262i
$733$	−1298.91			−1.77205			−0.886023	−	0.463641i	$-0.846543\pi$
$733$	−1298.91			−1.77205			−0.886023	+	0.463641i	$0.846543\pi$
$734$	−776.400	−	327.933i	−1.05777	−	0.446776i
$735$		−	529.244i		−	0.720060i
$736$	112.144	−	246.187i	0.152369	−	0.334493i
$737$	−794.281			−1.07772
$738$	−581.611	+	1376.99i	−0.788090	+	1.86585i
$739$		−	341.533i		−	0.462156i	−0.972935	−	0.231078i	$-0.925775\pi$
$739$		−	341.533i		−	0.462156i	0.972935	−	0.231078i	$-0.0742253\pi$
$740$	−160.631	−	165.159i	−0.217070	−	0.223187i
$741$	1561.64			2.10748
$742$	−764.767	−	323.020i	−1.03068	−	0.435337i
$743$		−	907.895i		−	1.22193i	−0.791657	−	0.610965i	$-0.790781\pi$
$743$		−	907.895i		−	1.22193i	0.791657	−	0.610965i	$-0.209219\pi$
$744$	−216.441	+	84.4120i	−0.290915	+	0.113457i
$745$	−86.7300			−0.116416
$746$	152.596	−	361.280i	0.204553	−	0.484289i
$747$		−	709.870i		−	0.950294i
$748$	462.376	−	449.702i	0.618150	−	0.601206i
$749$	489.306			0.653279
$750$	−1304.84	−	551.133i	−1.73978	−	0.734845i
$751$			753.800i			1.00373i	0.864947	+	0.501864i	$0.167352\pi$
$751$			753.800i			1.00373i	−0.864947	+	0.501864i	$0.832648\pi$
$752$	632.174	+	17.5730i	0.840657	+	0.0233684i
$753$	−471.166			−0.625719
$754$	−277.831	+	657.779i	−0.368476	+	0.872386i
$755$			254.301i			0.336822i
$756$	−1158.19	−	1190.83i	−1.53200	−	1.57518i
$757$	275.607			0.364077			0.182039	−	0.983291i	$-0.441730\pi$
$757$	275.607			0.364077			0.182039	+	0.983291i	$0.441730\pi$
$758$	490.906	+	207.347i	0.647633	+	0.273545i
$759$			288.278i			0.379813i
$760$	295.494	+	757.676i	0.388807	+	0.996942i
$761$	−1145.09			−1.50471			−0.752357	−	0.658755i	$-0.771083\pi$
$761$	−1145.09			−1.50471			−0.752357	+	0.658755i	$0.771083\pi$
$762$	748.409	−	1771.90i	0.982164	−	2.32533i
$763$		−	515.103i		−	0.675103i
$764$	−825.815	+	803.178i	−1.08091	+	1.05128i
$765$	−1762.75			−2.30425
$766$	−216.562	−	91.4710i	−0.282719	−	0.119414i
$767$			643.733i			0.839287i
$768$	74.1751	−	1333.16i	0.0965822	−	1.73589i
$769$	−1124.31			−1.46204			−0.731021	−	0.682355i	$-0.760956\pi$
$769$	−1124.31			−1.46204			−0.731021	+	0.682355i	$0.760956\pi$
$770$	−172.813	+	409.145i	−0.224433	+	0.531357i
$771$		−	1118.39i		−	1.45057i
$772$	319.256	+	328.254i	0.413544	+	0.425199i
$773$	439.903			0.569085			0.284543	−	0.958663i	$-0.408158\pi$
$773$	439.903			0.569085			0.284543	+	0.958663i	$0.408158\pi$
$774$	2819.77	+	1191.00i	3.64311	+	1.53876i
$775$			53.3662i			0.0688596i
$776$	−1301.91	+	507.744i	−1.67772	+	0.654309i
$777$	−661.949			−0.851930
$778$	510.547	−	1208.75i	0.656230	−	1.55366i
$779$		−	1063.05i		−	1.36464i
$780$	679.028	−	660.415i	0.870548	−	0.846685i
$781$	357.588			0.457859
$782$	−384.150	−	162.256i	−0.491240	−	0.207489i
$783$			1482.07i			1.89281i
$784$	11.4903	−	413.353i	0.0146560	−	0.527236i
$785$	181.426			0.231116
$786$	−62.3997	+	147.735i	−0.0793890	+	0.187958i
$787$		−	314.843i		−	0.400055i	−0.979790	−	0.200027i	$-0.935897\pi$
$787$		−	314.843i		−	0.400055i	0.979790	−	0.200027i	$-0.0641031\pi$
$788$	69.0174	+	70.9626i	0.0875856	+	0.0900541i
$789$	−593.434			−0.752134
$790$	−135.736	−	57.3319i	−0.171818	−	0.0725720i
$791$		−	141.687i		−	0.179125i
$792$	345.946	+	887.041i	0.436800	+	1.12000i
$793$	920.984			1.16139
$794$	22.7514	−	53.8652i	0.0286542	−	0.0678403i
$795$		−	982.547i		−	1.23591i
$796$	−292.448	+	284.432i	−0.367397	+	0.357326i
$797$	1039.73			1.30456			0.652278	−	0.757979i	$-0.273813\pi$
$797$	1039.73			1.30456			0.652278	+	0.757979i	$0.273813\pi$
$798$	2152.49	+	909.163i	2.69736	+	1.13930i
$799$		−	974.863i		−	1.22010i
$800$	−279.120	−	127.146i	−0.348900	−	0.158932i
$801$	1210.29			1.51097
$802$	517.641	−	1225.54i	0.645438	−	1.52811i
$803$			235.044i			0.292708i
$804$	1767.15	+	1816.96i	2.19795	+	2.25989i
$805$	287.152			0.356711
$806$	−118.623	−	50.1034i	−0.147174	−	0.0621631i
$807$		−	1235.62i		−	1.53113i
$808$	838.577	−	327.045i	1.03784	−	0.404759i
$809$	−1011.26			−1.25001			−0.625007	−	0.780619i	$-0.714904\pi$
$809$	−1011.26			−1.25001			−0.625007	+	0.780619i	$0.714904\pi$
$810$	264.409	−	626.001i	0.326430	−	0.772841i
$811$		−	269.914i		−	0.332816i	−0.986057	−	0.166408i	$-0.946783\pi$
$811$		−	269.914i		−	0.332816i	0.986057	−	0.166408i	$-0.0532169\pi$
$812$	−765.897	+	744.902i	−0.943223	+	0.917367i
$813$	2031.99			2.49938
$814$	176.707	+	74.6370i	0.217085	+	0.0916917i
$815$		−	72.4607i		−	0.0889088i
$816$	−2057.43	−	57.1920i	−2.52136	−	0.0700882i
$817$	−2176.89			−2.66449
$818$	205.252	−	485.944i	0.250919	−	0.594064i
$819$		−	1821.13i		−	2.22361i
$820$	−449.562	−	462.233i	−0.548247	−	0.563699i
$821$	349.953			0.426252			0.213126	−	0.977025i	$-0.431635\pi$
$821$	349.953			0.426252			0.213126	+	0.977025i	$0.431635\pi$
$822$	−2237.04	−	944.874i	−2.72146	−	1.14948i
$823$		−	380.513i		−	0.462349i	−0.972912	−	0.231174i	$-0.925743\pi$
$823$		−	380.513i		−	0.462349i	0.972912	−	0.231174i	$-0.0742568\pi$
$824$	−414.823	−	1063.65i	−0.503425	−	1.29083i
$825$	326.843			0.396173
$826$	−374.771	+	887.290i	−0.453718	+	1.07420i
$827$			793.396i			0.959366i	0.877442	+	0.479683i	$0.159248\pi$
$827$			793.396i			0.959366i	−0.877442	+	0.479683i	$0.840752\pi$
$828$	441.279	−	429.183i	0.532946	−	0.518337i
$829$	280.913			0.338857			0.169429	−	0.985542i	$-0.445808\pi$
$829$	280.913			0.338857			0.169429	+	0.985542i	$0.445808\pi$
$830$	282.083	+	119.145i	0.339859	+	0.143549i
$831$		−	1994.42i		−	2.40003i
$832$	544.675	−	501.058i	0.654658	−	0.602233i
$833$	−637.423			−0.765214
$834$	−57.7738	+	136.783i	−0.0692731	+	0.164008i
$835$		−	99.4475i		−	0.119099i
$836$	−472.096	−	485.402i	−0.564708	−	0.580624i
$837$	−267.273			−0.319323
$838$	117.899	+	49.7978i	0.140691	+	0.0594246i
$839$		−	75.5411i		−	0.0900371i	−0.998986	−	0.0450185i	$-0.985665\pi$
$839$		−	75.5411i		−	0.0900371i	0.998986	−	0.0450185i	$-0.0143347\pi$
$840$	1320.42	−	514.964i	1.57193	−	0.613053i
$841$	112.207			0.133421
$842$	−364.279	+	862.450i	−0.432635	+	1.02429i
$843$			2203.38i			2.61374i
$844$	−330.800	+	321.733i	−0.391944	+	0.381200i
$845$	−138.504			−0.163910
$846$	1325.64	+	559.920i	1.56695	+	0.661844i
$847$			677.010i			0.799303i
$848$	21.3318	−	767.393i	0.0251555	−	0.904945i
$849$	−1136.51			−1.33865
$850$	−183.962	+	435.540i	−0.216426	+	0.512400i
$851$		−	124.019i		−	0.145734i
$852$	−795.578	−	818.000i	−0.933777	−	0.960094i
$853$	780.218			0.914676			0.457338	−	0.889293i	$-0.348803\pi$
$853$	780.218			0.914676			0.457338	+	0.889293i	$0.348803\pi$
$854$	1269.44	+	536.182i	1.48646	+	0.627847i
$855$			1850.54i			2.16437i
$856$	164.403	+	421.546i	0.192060	+	0.492461i
$857$	843.864			0.984672			0.492336	−	0.870405i	$-0.336143\pi$
$857$	843.864			0.984672			0.492336	+	0.870405i	$0.336143\pi$
$858$	−306.860	+	726.508i	−0.357646	+	0.846746i
$859$			629.065i			0.732323i	0.930551	+	0.366161i	$0.119328\pi$
$859$			629.065i			0.732323i	−0.930551	+	0.366161i	$0.880672\pi$
$860$	−946.546	+	920.600i	−1.10063	+	1.07046i
$861$	−1852.61			−2.15170
$862$	−150.267	−	63.4693i	−0.174324	−	0.0736303i
$863$			667.425i			0.773377i	0.922210	+	0.386689i	$0.126381\pi$
$863$			667.425i			0.773377i	−0.922210	+	0.386689i	$0.873619\pi$
$864$	636.782	−	1397.91i	0.737016	−	1.61796i
$865$	−252.781			−0.292233
$866$	205.226	−	485.884i	0.236982	−	0.561067i
$867$			1665.38i			1.92085i
$868$	−134.334	−	138.120i	−0.154763	−	0.159125i
$869$	122.682			0.141175
$870$	−1164.83	−	491.999i	−1.33889	−	0.565516i
$871$			1404.87i			1.61294i
$872$	443.771	−	173.071i	0.508912	−	0.198476i
$873$	−3179.76			−3.64233
$874$	−170.336	+	403.280i	−0.194892	+	0.461418i
$875$		−	1174.73i		−	1.34255i
$876$	537.676	−	522.937i	0.613785	−	0.596960i
$877$	−951.448			−1.08489			−0.542444	−	0.840092i	$-0.682501\pi$
$877$	−951.448			−1.08489			−0.542444	+	0.840092i	$0.682501\pi$
$878$	1004.02	+	424.076i	1.14353	+	0.483002i
$879$		−	1221.39i		−	1.38952i
$880$	−410.550	−	11.4124i	−0.466534	−	0.0129686i
$881$	−1316.28			−1.49408			−0.747038	−	0.664781i	$-0.768525\pi$
$881$	−1316.28			−1.49408			−0.747038	+	0.664781i	$0.768525\pi$
$882$	366.109	−	866.783i	0.415090	−	0.982748i
$883$		−	1523.50i		−	1.72537i	−0.505741	−	0.862686i	$-0.668781\pi$
$883$		−	1523.50i		−	1.72537i	0.505741	−	0.862686i	$-0.331219\pi$
$884$	−795.405	−	817.823i	−0.899779	−	0.925139i
$885$	−1139.96			−1.28809
$886$	−437.999	−	185.001i	−0.494356	−	0.208804i
$887$			146.421i			0.165074i	0.996588	+	0.0825371i	$0.0263023\pi$
$887$			146.421i			0.165074i	−0.996588	+	0.0825371i	$0.973698\pi$
$888$	−222.410	−	570.282i	−0.250462	−	0.642209i
$889$	1595.23			1.79440
$890$	−203.136	+	480.936i	−0.228243	+	0.540377i
$891$			565.794i			0.635010i
$892$	−503.098	+	489.307i	−0.564011	+	0.548551i
$893$	−1023.41			−1.14603
$894$	−212.272	−	89.6587i	−0.237440	−	0.100289i
$895$			109.155i			0.121960i
$896$	1042.46	−	373.532i	1.16346	−	0.416889i
$897$	509.889			0.568438
$898$	−311.541	+	737.590i	−0.346928	+	0.821370i
$899$			171.899i			0.191212i
$900$	−486.597	−	500.312i	−0.540664	−	0.555902i
$901$	−1183.38			−1.31341
$902$	494.554	+	208.888i	0.548286	+	0.231583i
$903$			3793.72i			4.20124i
$904$	122.066	−	47.6059i	0.135029	−	0.0526614i
$905$	−1068.01			−1.18012
$906$	−262.888	+	622.402i	−0.290163	+	0.686978i
$907$		−	119.399i		−	0.131642i	−0.997831	−	0.0658209i	$-0.979033\pi$
$907$		−	119.399i		−	0.131642i	0.997831	−	0.0658209i	$-0.0209666\pi$
$908$	469.448	−	456.580i	0.517013	−	0.502841i
$909$	2048.13			2.25316
$910$	723.670	+	305.661i	0.795242	+	0.335892i
$911$			1058.99i			1.16244i	0.813745	+	0.581222i	$0.197425\pi$
$911$			1058.99i			1.16244i	−0.813745	+	0.581222i	$0.802575\pi$
$912$	−60.0400	+	2159.89i	−0.0658333	+	2.36830i
$913$	−254.953			−0.279247
$914$	129.793	−	307.292i	0.142005	−	0.336206i
$915$			1630.93i			1.78244i
$916$	−514.883	−	529.395i	−0.562099	−	0.577942i
$917$	−133.004			−0.145043
$918$	−2181.31	−	921.333i	−2.37615	−	1.00363i
$919$		−	100.968i		−	0.109867i	−0.998490	−	0.0549337i	$-0.982505\pi$
$919$		−	100.968i		−	0.109867i	0.998490	−	0.0549337i	$-0.0174947\pi$
$920$	96.4810	+	247.387i	0.104871	+	0.268899i
$921$	1131.22			1.22826
$922$	1.99446	−	4.72200i	0.00216319	−	0.00512147i
$923$		−	632.480i		−	0.685244i
$924$	−845.922	+	822.734i	−0.915500	+	0.890405i
$925$	−140.610			−0.152011
$926$	−106.615	−	45.0319i	−0.115135	−	0.0486305i
$927$		−	2597.83i		−	2.80241i
$928$	−899.083	−	409.553i	−0.968840	−	0.441329i
$929$	983.253			1.05840			0.529200	−	0.848497i	$-0.322492\pi$
$929$	983.253			1.05840			0.529200	+	0.848497i	$0.322492\pi$
$930$	88.7262	−	210.064i	0.0954045	−	0.225875i
$931$			669.165i			0.718760i
$932$	5.98787	+	6.15663i	0.00642475	+	0.00660583i
$933$	−94.3619			−0.101138
$934$	1006.14	+	424.970i	1.07724	+	0.455000i
$935$			633.101i			0.677113i
$936$	1568.94	−	611.888i	1.67622	−	0.653726i
$937$	−680.134			−0.725863			−0.362931	−	0.931816i	$-0.618224\pi$
$937$	−680.134			−0.725863			−0.362931	+	0.931816i	$0.618224\pi$
$938$	−817.895	+	1936.41i	−0.871956	+	2.06440i
$939$			2093.50i			2.22950i
$940$	−444.995	+	432.797i	−0.473398	+	0.460422i
$941$	1293.59			1.37470			0.687349	−	0.726327i	$-0.258774\pi$
$941$	1293.59			1.37470			0.687349	+	0.726327i	$0.258774\pi$
$942$	444.040	+	187.552i	0.471380	+	0.199100i
$943$		−	347.095i		−	0.368076i
$944$	−890.337	−	24.7494i	−0.943154	−	0.0262176i
$945$	1630.53			1.72543
$946$	427.754	−	1012.73i	0.452172	−	1.07054i
$947$		−	868.799i		−	0.917422i	−0.888585	−	0.458711i	$-0.848311\pi$
$947$		−	868.799i		−	0.917422i	0.888585	−	0.458711i	$-0.151689\pi$
$948$	−272.947	−	280.640i	−0.287919	−	0.296034i
$949$	415.732			0.438074
$950$	457.228	+	193.123i	0.481293	+	0.203287i
$951$		−	2421.22i		−	2.54597i
$952$	−620.224	−	1590.32i	−0.651496	−	1.67050i
$953$	−528.049			−0.554092			−0.277046	−	0.960857i	$-0.589355\pi$
$953$	−528.049			−0.554092			−0.277046	+	0.960857i	$0.589355\pi$
$954$	679.685	−	1609.19i	0.712458	−	1.68678i
$955$		−	1130.73i		−	1.18401i
$956$	727.745	−	707.796i	0.761239	−	0.740373i
$957$	1052.80			1.10011
$958$	1234.81	+	521.555i	1.28895	+	0.544421i
$959$		−	2013.99i		−	2.10009i
$960$	887.303	+	964.544i	0.924274	+	1.00473i
$961$	−31.0000			−0.0322581
$962$	132.013	−	312.549i	0.137228	−	0.324895i
$963$			1029.58i			1.06914i
$964$	−327.146	−	336.367i	−0.339363	−	0.348928i
$965$	−449.456			−0.465757
$966$	702.806	+	296.849i	0.727542	+	0.307297i
$967$		−	330.210i		−	0.341479i	−0.985316	−	0.170740i	$-0.945384\pi$
$967$		−	330.210i		−	0.341479i	0.985316	−	0.170740i	$-0.0546157\pi$
$968$	−583.257	+	227.470i	−0.602538	+	0.234990i
$969$	3330.72			3.43727
$970$	533.694	−	1263.55i	0.550200	−	1.30263i
$971$			1118.47i			1.15188i	0.817493	+	0.575939i	$0.195363\pi$
$971$			1118.47i			1.15188i	−0.817493	+	0.575939i	$0.804637\pi$
$972$	55.4462	−	53.9263i	0.0570434	−	0.0554797i
$973$	−123.144			−0.126561
$974$	−426.437	−	180.117i	−0.437820	−	0.184925i
$975$		−	578.099i		−	0.592922i
$976$	−35.4088	+	1273.80i	−0.0362795	+	1.30512i
$977$	813.777			0.832935			0.416467	−	0.909151i	$-0.363268\pi$
$977$	813.777			0.832935			0.416467	+	0.909151i	$0.363268\pi$
$978$	74.9076	−	177.348i	0.0765926	−	0.181337i
$979$		−	434.680i		−	0.444005i
$980$	282.988	+	290.964i	0.288763	+	0.296902i
$981$	1083.86			1.10485
$982$	1088.50	+	459.758i	1.10845	+	0.468186i
$983$			405.192i			0.412199i	0.978531	+	0.206100i	$0.0660771\pi$
$983$			405.192i			0.412199i	−0.978531	+	0.206100i	$0.933923\pi$
$984$	−622.463	−	1596.06i	−0.632584	−	1.62201i
$985$	−97.1644			−0.0986440
$986$	−592.565	+	1402.93i	−0.600979	+	1.42285i
$987$			1783.52i			1.80701i
$988$	−858.548	+	835.014i	−0.868976	+	0.845156i
$989$	−710.771			−0.718676
$990$	−860.906	−	363.627i	−0.869602	−	0.367300i
$991$			126.749i			0.127900i	0.997953	+	0.0639501i	$0.0203698\pi$
$991$			126.749i			0.127900i	−0.997953	+	0.0639501i	$0.979630\pi$
$992$	73.8580	−	162.139i	0.0744536	−	0.163446i
$993$	1006.67			1.01376
$994$	368.219	−	871.779i	0.370442	−	0.877041i
$995$		−	400.429i		−	0.402442i
$996$	567.230	+	583.217i	0.569508	+	0.585559i
$997$	1405.20			1.40943			0.704713	−	0.709493i	$-0.251076\pi$
$997$	1405.20			1.40943			0.704713	+	0.709493i	$0.251076\pi$
$998$	−216.812	−	91.5762i	−0.217246	−	0.0917597i
$999$		−	704.215i		−	0.704920i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.3.b.a.63.19	✓	30
4.3	odd	2	inner	124.3.b.a.63.20	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.3.b.a.63.19	✓	30	1.1	even	1	trivial
124.3.b.a.63.20	yes	30	4.3	odd	2	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:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	124.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.778186 - 1.84240i) q^{2} +5.21571i q^{3} +(-2.78885 - 2.86745i) q^{4} +3.92621 q^{5} +(9.60941 + 4.05879i) q^{6} +8.65127i q^{7} +(-7.45324 + 2.90676i) q^{8} -18.2037 q^{9} +O(q^{10})\)	\(q+(0.778186 - 1.84240i) q^{2} +5.21571i q^{3} +(-2.78885 - 2.86745i) q^{4} +3.92621 q^{5} +(9.60941 + 4.05879i) q^{6} +8.65127i q^{7} +(-7.45324 + 2.90676i) q^{8} -18.2037 q^{9} +(3.05532 - 7.23364i) q^{10} +6.53793i q^{11} +(14.9558 - 14.5459i) q^{12} +11.5639 q^{13} +(15.9391 + 6.73230i) q^{14} +20.4780i q^{15} +(-0.444593 + 15.9938i) q^{16} +24.6638 q^{17} +(-14.1658 + 33.5384i) q^{18} -25.8919i q^{19} +(-10.9496 - 11.2582i) q^{20} -45.1226 q^{21} +(12.0455 + 5.08772i) q^{22} -8.45393i q^{23} +(-15.1608 - 38.8739i) q^{24} -9.58485 q^{25} +(8.99884 - 21.3053i) q^{26} -48.0036i q^{27} +(24.8071 - 24.1271i) q^{28} -30.8741 q^{29} +(37.7286 + 15.9357i) q^{30} -5.56776i q^{31} +(29.1210 + 13.2653i) q^{32} -34.0999 q^{33} +(19.1930 - 45.4404i) q^{34} +33.9667i q^{35} +(50.7673 + 52.1982i) q^{36} +14.6700 q^{37} +(-47.7032 - 20.1487i) q^{38} +60.3139i q^{39} +(-29.2630 + 11.4126i) q^{40} +41.0573 q^{41} +(-35.1137 + 83.1337i) q^{42} -84.0758i q^{43} +(18.7472 - 18.2333i) q^{44} -71.4714 q^{45} +(-15.5755 - 6.57873i) q^{46} -39.5261i q^{47} +(-83.4192 - 2.31887i) q^{48} -25.8445 q^{49} +(-7.45879 + 17.6591i) q^{50} +128.639i q^{51} +(-32.2500 - 33.1589i) q^{52} -47.9806 q^{53} +(-88.4418 - 37.3558i) q^{54} +25.6693i q^{55} +(-25.1472 - 64.4800i) q^{56} +135.045 q^{57} +(-24.0258 + 56.8823i) q^{58} +55.6676i q^{59} +(58.7197 - 57.1101i) q^{60} +79.6432 q^{61} +(-10.2580 - 4.33276i) q^{62} -157.485i q^{63} +(47.1015 - 43.3296i) q^{64} +45.4022 q^{65} +(-26.5361 + 62.8256i) q^{66} +121.488i q^{67} +(-68.7836 - 70.7222i) q^{68} +44.0932 q^{69} +(62.5802 + 26.4324i) q^{70} -54.6944i q^{71} +(135.676 - 52.9137i) q^{72} +35.9509 q^{73} +(11.4160 - 27.0280i) q^{74} -49.9918i q^{75} +(-74.2440 + 72.2089i) q^{76} -56.5614 q^{77} +(111.122 + 46.9354i) q^{78} -18.7646i q^{79} +(-1.74557 + 62.7952i) q^{80} +86.5403 q^{81} +(31.9502 - 75.6438i) q^{82} +38.9960i q^{83} +(125.840 + 129.387i) q^{84} +96.8352 q^{85} +(-154.901 - 65.4266i) q^{86} -161.030i q^{87} +(-19.0042 - 48.7287i) q^{88} -66.4860 q^{89} +(-55.6181 + 131.679i) q^{90} +100.042i q^{91} +(-24.2412 + 23.5768i) q^{92} +29.0399 q^{93} +(-72.8228 - 30.7587i) q^{94} -101.657i q^{95} +(-69.1879 + 151.887i) q^{96} +174.677 q^{97} +(-20.1118 + 47.6159i) q^{98} -119.014i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 2 q^{2} - 6 q^{4} - 4 q^{5} + 13 q^{8} - 82 q^{9}+O(q^{10}) \) 30 * q - 2 * q^2 - 6 * q^4 - 4 * q^5 + 13 * q^8 - 82 * q^9	\( 30 q - 2 q^{2} - 6 q^{4} - 4 q^{5} + 13 q^{8} - 82 q^{9} + q^{10} - 14 q^{12} + 12 q^{13} + 29 q^{14} + 50 q^{16} - 4 q^{17} - 34 q^{18} - 63 q^{20} - 16 q^{21} - 24 q^{22} - 20 q^{24} + 90 q^{25} + 38 q^{26} + 3 q^{28} - 4 q^{29} - 6 q^{30} + 118 q^{32} + 80 q^{33} + 4 q^{34} - 2 q^{36} + 76 q^{37} + 37 q^{38} - 180 q^{40} - 4 q^{41} - 38 q^{42} + 184 q^{44} - 20 q^{45} - 54 q^{46} - 172 q^{48} - 258 q^{49} - 31 q^{50} - 88 q^{52} - 132 q^{53} - 84 q^{54} - 28 q^{56} + 176 q^{57} + 164 q^{58} + 108 q^{60} - 100 q^{61} + 381 q^{64} - 104 q^{65} + 60 q^{66} + 214 q^{68} + 112 q^{69} + 45 q^{70} - 167 q^{72} - 132 q^{73} + 398 q^{74} - 317 q^{76} + 176 q^{77} - 188 q^{78} - 203 q^{80} + 158 q^{81} - 81 q^{82} + 176 q^{84} + 248 q^{85} - 78 q^{86} + 98 q^{88} - 20 q^{89} - 567 q^{90} - 260 q^{92} - 244 q^{94} - 90 q^{96} + 300 q^{97} - 371 q^{98}+O(q^{100}) \) 30 * q - 2 * q^2 - 6 * q^4 - 4 * q^5 + 13 * q^8 - 82 * q^9 + q^10 - 14 * q^12 + 12 * q^13 + 29 * q^14 + 50 * q^16 - 4 * q^17 - 34 * q^18 - 63 * q^20 - 16 * q^21 - 24 * q^22 - 20 * q^24 + 90 * q^25 + 38 * q^26 + 3 * q^28 - 4 * q^29 - 6 * q^30 + 118 * q^32 + 80 * q^33 + 4 * q^34 - 2 * q^36 + 76 * q^37 + 37 * q^38 - 180 * q^40 - 4 * q^41 - 38 * q^42 + 184 * q^44 - 20 * q^45 - 54 * q^46 - 172 * q^48 - 258 * q^49 - 31 * q^50 - 88 * q^52 - 132 * q^53 - 84 * q^54 - 28 * q^56 + 176 * q^57 + 164 * q^58 + 108 * q^60 - 100 * q^61 + 381 * q^64 - 104 * q^65 + 60 * q^66 + 214 * q^68 + 112 * q^69 + 45 * q^70 - 167 * q^72 - 132 * q^73 + 398 * q^74 - 317 * q^76 + 176 * q^77 - 188 * q^78 - 203 * q^80 + 158 * q^81 - 81 * q^82 + 176 * q^84 + 248 * q^85 - 78 * q^86 + 98 * q^88 - 20 * q^89 - 567 * q^90 - 260 * q^92 - 244 * q^94 - 90 * q^96 + 300 * q^97 - 371 * q^98

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