LMFDB - Embedded newform 207.4.i.b.82.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,4,Mod(55,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("207.55");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	207.i (of order $11$, degree $10$, 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:	$12.2133953712$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{11})$
Twist minimal:	no (minimal twist has level 69)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			82.2
Character	$\chi$	$=$	207.82
Dual form			207.4.i.b.154.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.56668 - 1.80804i) q^{2} +(0.323978 - 2.25332i) q^{4} +(-6.20398 + 13.5848i) q^{5} +(-24.5496 - 7.20842i) q^{7} +(-20.6825 + 13.2918i) q^{8} +O(q^{10})$	\(q+(-1.56668 - 1.80804i) q^{2} +(0.323978 - 2.25332i) q^{4} +(-6.20398 + 13.5848i) q^{5} +(-24.5496 - 7.20842i) q^{7} +(-20.6825 + 13.2918i) q^{8} +(34.2816 - 10.0660i) q^{10} +(11.9090 - 13.7437i) q^{11} +(86.3921 - 25.3670i) q^{13} +(25.4282 + 55.6801i) q^{14} +(38.9608 + 11.4399i) q^{16} +(-0.0854087 - 0.594031i) q^{17} +(-13.3171 + 92.6227i) q^{19} +(28.6010 + 18.3807i) q^{20} -43.5068 q^{22} +(110.140 - 6.01038i) q^{23} +(-64.2004 - 74.0912i) q^{25} +(-181.213 - 116.459i) q^{26} +(-24.1964 + 52.9828i) q^{28} +(10.2601 + 71.3608i) q^{29} +(219.303 - 140.937i) q^{31} +(41.3497 + 90.5432i) q^{32} +(-0.940226 + 1.08508i) q^{34} +(250.230 - 288.781i) q^{35} +(53.6514 + 117.480i) q^{37} +(188.330 - 121.032i) q^{38} +(-52.2534 - 363.430i) q^{40} +(93.5789 - 204.909i) q^{41} +(396.280 + 254.674i) q^{43} +(-27.1107 - 31.2874i) q^{44} +(-183.421 - 189.722i) q^{46} -194.164 q^{47} +(262.172 + 168.488i) q^{49} +(-33.3788 + 232.154i) q^{50} +(-29.1708 - 202.887i) q^{52} +(-468.220 - 137.482i) q^{53} +(112.823 + 247.047i) q^{55} +(603.560 - 177.221i) q^{56} +(112.949 - 130.350i) q^{58} +(133.372 - 39.1616i) q^{59} +(-317.541 + 204.071i) q^{61} +(-598.398 - 175.705i) q^{62} +(233.870 - 512.104i) q^{64} +(-191.369 + 1331.00i) q^{65} +(-202.983 - 234.255i) q^{67} -1.36621 q^{68} -914.160 q^{70} +(593.068 + 684.437i) q^{71} +(-45.8429 + 318.844i) q^{73} +(128.355 - 281.058i) q^{74} +(204.394 + 60.0155i) q^{76} +(-391.431 + 251.557i) q^{77} +(938.227 - 275.488i) q^{79} +(-397.122 + 458.303i) q^{80} +(-517.093 + 151.832i) q^{82} +(-438.077 - 959.255i) q^{83} +(8.59968 + 2.52509i) q^{85} +(-160.382 - 1115.48i) q^{86} +(-63.6285 + 442.546i) q^{88} +(797.225 + 512.346i) q^{89} -2303.75 q^{91} +(22.1398 - 250.128i) q^{92} +(304.192 + 351.056i) q^{94} +(-1175.64 - 755.540i) q^{95} +(-510.773 + 1118.44i) q^{97} +(-106.106 - 737.985i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 4 q^{2} - 28 q^{4} + 6 q^{5} - 4 q^{7} + 52 q^{8}+O(q^{10}) $ 60 * q - 4 * q^2 - 28 * q^4 + 6 * q^5 - 4 * q^7 + 52 * q^8	$ 60 q - 4 q^{2} - 28 q^{4} + 6 q^{5} - 4 q^{7} + 52 q^{8} - 78 q^{10} - 10 q^{11} + 50 q^{13} + 224 q^{14} + 260 q^{16} + 662 q^{17} - 4 q^{19} + 735 q^{20} + 622 q^{22} + 438 q^{23} - 754 q^{25} + 40 q^{26} + 672 q^{28} - 1302 q^{29} + 1528 q^{31} - 1588 q^{32} + 29 q^{34} - 950 q^{35} + 316 q^{37} - 3122 q^{38} - 1939 q^{40} + 1500 q^{41} - 1316 q^{43} + 2901 q^{44} - 1980 q^{46} + 1440 q^{47} - 2310 q^{49} - 195 q^{50} + 6189 q^{52} + 148 q^{53} - 606 q^{55} + 432 q^{56} - 2623 q^{58} - 5264 q^{59} + 1482 q^{61} + 2299 q^{62} - 6780 q^{64} + 1446 q^{65} + 388 q^{67} - 5604 q^{68} + 2984 q^{70} + 3316 q^{71} + 2072 q^{73} + 6556 q^{74} + 9841 q^{76} - 9338 q^{77} + 268 q^{79} - 7980 q^{80} + 7742 q^{82} + 3494 q^{83} - 3842 q^{85} + 4792 q^{86} - 7960 q^{88} + 2754 q^{89} - 5436 q^{91} + 17609 q^{92} - 10961 q^{94} + 2396 q^{95} - 5654 q^{97} - 14411 q^{98}+O(q^{100}) $ 60 * q - 4 * q^2 - 28 * q^4 + 6 * q^5 - 4 * q^7 + 52 * q^8 - 78 * q^10 - 10 * q^11 + 50 * q^13 + 224 * q^14 + 260 * q^16 + 662 * q^17 - 4 * q^19 + 735 * q^20 + 622 * q^22 + 438 * q^23 - 754 * q^25 + 40 * q^26 + 672 * q^28 - 1302 * q^29 + 1528 * q^31 - 1588 * q^32 + 29 * q^34 - 950 * q^35 + 316 * q^37 - 3122 * q^38 - 1939 * q^40 + 1500 * q^41 - 1316 * q^43 + 2901 * q^44 - 1980 * q^46 + 1440 * q^47 - 2310 * q^49 - 195 * q^50 + 6189 * q^52 + 148 * q^53 - 606 * q^55 + 432 * q^56 - 2623 * q^58 - 5264 * q^59 + 1482 * q^61 + 2299 * q^62 - 6780 * q^64 + 1446 * q^65 + 388 * q^67 - 5604 * q^68 + 2984 * q^70 + 3316 * q^71 + 2072 * q^73 + 6556 * q^74 + 9841 * q^76 - 9338 * q^77 + 268 * q^79 - 7980 * q^80 + 7742 * q^82 + 3494 * q^83 - 3842 * q^85 + 4792 * q^86 - 7960 * q^88 + 2754 * q^89 - 5436 * q^91 + 17609 * q^92 - 10961 * q^94 + 2396 * q^95 - 5654 * q^97 - 14411 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{7}{11}\right)$	$1$

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 $

$2$	−1.56668	−	1.80804i	−0.553905	−	0.639240i	0.407884	−	0.913034i	$-0.366267\pi$
$2$	−1.56668	−	1.80804i	−0.553905	−	0.639240i	−0.961788	+	0.273794i	$0.911721\pi$
$3$		0			0
$3$		0			0
$4$	0.323978	−	2.25332i	0.0404973	−	0.281665i
$5$	−6.20398	+	13.5848i	−0.554901	+	1.21506i	0.399554	+	0.916709i	$0.369165\pi$
$5$	−6.20398	+	13.5848i	−0.554901	+	1.21506i	−0.954455	+	0.298354i	$0.903562\pi$
$6$		0			0
$7$	−24.5496	−	7.20842i	−1.32555	−	0.389218i	−0.459060	−	0.888405i	$-0.651814\pi$
$7$	−24.5496	−	7.20842i	−1.32555	−	0.389218i	−0.866494	+	0.499187i	$0.833632\pi$
$8$	−20.6825	+	13.2918i	−0.914046	+	0.587422i
$9$		0			0
$10$	34.2816	−	10.0660i	1.08408	−	0.318314i
$11$	11.9090	−	13.7437i	0.326427	−	0.376716i	−0.568687	−	0.822554i	$-0.692549\pi$
$11$	11.9090	−	13.7437i	0.326427	−	0.376716i	0.895114	+	0.445837i	$0.147094\pi$
$12$		0			0
$13$	86.3921	−	25.3670i	1.84314	−	0.541196i	0.843149	−	0.537680i	$-0.180699\pi$
$13$	86.3921	−	25.3670i	1.84314	−	0.541196i	0.999994	−	0.00351590i	$-0.00111915\pi$
$14$	25.4282	+	55.6801i	0.485427	+	1.06294i
$15$		0			0
$16$	38.9608	+	11.4399i	0.608763	+	0.178749i
$17$	−0.0854087	−	0.594031i	−0.00121851	−	0.00847492i	0.989203	−	0.146551i	$-0.0468172\pi$
$17$	−0.0854087	−	0.594031i	−0.00121851	−	0.00847492i	−0.990422	+	0.138076i	$0.955908\pi$
$18$		0			0
$19$	−13.3171	+	92.6227i	−0.160798	+	1.11837i	0.736336	+	0.676616i	$0.236554\pi$
$19$	−13.3171	+	92.6227i	−0.160798	+	1.11837i	−0.897134	+	0.441758i	$0.854355\pi$
$20$	28.6010	+	18.3807i	0.319769	+	0.205503i
$21$		0			0
$22$	−43.5068			−0.421621
$23$	110.140	−	6.01038i	0.998514	−	0.0544891i
$23$	110.140	−	6.01038i	0.998514	−	0.0544891i
$24$		0			0
$25$	−64.2004	−	74.0912i	−0.513603	−	0.592730i
$26$	−181.213	−	116.459i	−1.36688	−	0.878440i
$27$		0			0
$28$	−24.1964	+	52.9828i	−0.163310	+	0.357600i
$29$	10.2601	+	71.3608i	0.0656986	+	0.456944i	0.995942	+	0.0900001i	$0.0286867\pi$
$29$	10.2601	+	71.3608i	0.0656986	+	0.456944i	−0.930243	+	0.366944i	$0.880404\pi$
$30$		0			0
$31$	219.303	−	140.937i	1.27058	−	0.816551i	0.280883	−	0.959742i	$-0.409373\pi$
$31$	219.303	−	140.937i	1.27058	−	0.816551i	0.989695	+	0.143191i	$0.0457363\pi$
$32$	41.3497	+	90.5432i	0.228427	+	0.500185i
$33$		0			0
$34$	−0.940226	+	1.08508i	−0.00474257	+	0.00547322i
$35$	250.230	−	288.781i	1.20848	−	1.39466i
$36$		0			0
$37$	53.6514	+	117.480i	0.238385	+	0.521990i	0.990577	−	0.136953i	$-0.0437311\pi$
$37$	53.6514	+	117.480i	0.238385	+	0.521990i	−0.752193	+	0.658943i	$0.771004\pi$
$38$	188.330	−	121.032i	0.803976	−	0.516684i
$39$		0			0
$40$	−52.2534	−	363.430i	−0.206550	−	1.43658i
$41$	93.5789	−	204.909i	0.356453	−	0.780523i	−0.643434	−	0.765501i	$-0.722491\pi$
$41$	93.5789	−	204.909i	0.356453	−	0.780523i	0.999887	−	0.0150215i	$-0.00478166\pi$
$42$		0			0
$43$	396.280	+	254.674i	1.40540	+	0.903195i	0.999940	−	0.0109185i	$-0.00347553\pi$
$43$	396.280	+	254.674i	1.40540	+	0.903195i	0.405458	+	0.914113i	$0.367112\pi$
$44$	−27.1107	−	31.2874i	−0.0928884	−	0.107199i
$45$		0			0
$46$	−183.421	−	189.722i	−0.587914	−	0.608109i
$47$	−194.164			−0.602589			−0.301294	−	0.953531i	$-0.597419\pi$
$47$	−194.164			−0.602589			−0.301294	+	0.953531i	$0.597419\pi$
$48$		0			0
$49$	262.172	+	168.488i	0.764350	+	0.491218i
$50$	−33.3788	+	232.154i	−0.0944094	+	0.656632i
$51$		0			0
$52$	−29.1708	−	202.887i	−0.0777935	−	0.541066i
$53$	−468.220	−	137.482i	−1.21349	−	0.356313i	−0.388494	−	0.921451i	$-0.627005\pi$
$53$	−468.220	−	137.482i	−1.21349	−	0.356313i	−0.824996	+	0.565139i	$0.808823\pi$
$54$		0			0
$55$	112.823	+	247.047i	0.276600	+	0.605669i
$56$	603.560	−	177.221i	1.44025	−	0.422896i
$57$		0			0
$58$	112.949	−	130.350i	0.255706	−	0.295100i
$59$	133.372	−	39.1616i	0.294298	−	0.0864138i	−0.131251	−	0.991349i	$-0.541899\pi$
$59$	133.372	−	39.1616i	0.294298	−	0.0864138i	0.425549	+	0.904935i	$0.360081\pi$
$60$		0			0
$61$	−317.541	+	204.071i	−0.666507	+	0.428338i	−0.829665	−	0.558262i	$-0.811468\pi$
$61$	−317.541	+	204.071i	−0.666507	+	0.428338i	0.163158	+	0.986600i	$0.447832\pi$
$62$	−598.398	−	175.705i	−1.22575	−	0.359913i
$63$		0			0
$64$	233.870	−	512.104i	0.456777	−	1.00020i
$65$	−191.369	+	1331.00i	−0.365175	+	2.53985i
$66$		0			0
$67$	−202.983	−	234.255i	−0.370124	−	0.427146i	0.539882	−	0.841741i	$-0.318469\pi$
$67$	−202.983	−	234.255i	−0.370124	−	0.427146i	−0.910006	+	0.414595i	$0.863923\pi$
$68$	−1.36621			−0.00243643
$69$		0			0
$70$	−914.160			−1.56090
$71$	593.068	+	684.437i	0.991327	+	1.14405i	0.989570	+	0.144054i	$0.0460139\pi$
$71$	593.068	+	684.437i	0.991327	+	1.14405i	0.00175727	+	0.999998i	$0.499441\pi$
$72$		0			0
$73$	−45.8429	+	318.844i	−0.0735000	+	0.511204i	0.919500	+	0.393090i	$0.128594\pi$
$73$	−45.8429	+	318.844i	−0.0735000	+	0.511204i	−0.993000	+	0.118114i	$0.962315\pi$
$74$	128.355	−	281.058i	0.201634	−	0.441518i
$75$		0			0
$76$	204.394	+	60.0155i	0.308495	+	0.0905822i
$77$	−391.431	+	251.557i	−0.579321	+	0.372307i
$78$		0			0
$79$	938.227	−	275.488i	1.33619	−	0.392340i	0.465880	−	0.884848i	$-0.345738\pi$
$79$	938.227	−	275.488i	1.33619	−	0.392340i	0.870308	+	0.492508i	$0.163920\pi$
$80$	−397.122	+	458.303i	−0.554995	+	0.640498i
$81$		0			0
$82$	−517.093	+	151.832i	−0.696382	+	0.204476i
$83$	−438.077	−	959.255i	−0.579340	−	1.26858i	−0.941673	−	0.336528i	$-0.890747\pi$
$83$	−438.077	−	959.255i	−0.579340	−	1.26858i	0.362334	−	0.932048i	$-0.381980\pi$
$84$		0			0
$85$	8.59968	+	2.52509i	0.0109737	+	0.00322217i
$86$	−160.382	−	1115.48i	−0.201099	−	1.39867i
$87$		0			0
$88$	−63.6285	+	442.546i	−0.0770775	+	0.536086i
$89$	797.225	+	512.346i	0.949503	+	0.610208i	0.921074	−	0.389388i	$-0.127313\pi$
$89$	797.225	+	512.346i	0.949503	+	0.610208i	0.0284286	+	0.999596i	$0.490950\pi$
$90$		0			0
$91$	−2303.75			−2.65383
$92$	22.1398	−	250.128i	0.0250895	−	0.283453i
$93$		0			0
$94$	304.192	+	351.056i	0.333777	+	0.385199i
$95$	−1175.64	−	755.540i	−1.26967	−	0.815966i
$96$		0			0
$97$	−510.773	+	1118.44i	−0.534651	+	1.17072i	0.428938	+	0.903334i	$0.358888\pi$
$97$	−510.773	+	1118.44i	−0.534651	+	1.17072i	−0.963589	+	0.267389i	$0.913839\pi$
$98$	−106.106	−	737.985i	−0.109371	−	0.760692i
$99$		0			0
$100$	−187.751	+	120.660i	−0.187751	+	0.120660i
$101$	403.082	+	882.627i	0.397111	+	0.869551i	0.997555	+	0.0698846i	$0.0222631\pi$
$101$	403.082	+	882.627i	0.397111	+	0.869551i	−0.600444	+	0.799667i	$0.705010\pi$
$102$		0			0
$103$	−253.616	+	292.688i	−0.242616	+	0.279994i	−0.863978	−	0.503530i	$-0.832034\pi$
$103$	−253.616	+	292.688i	−0.242616	+	0.279994i	0.621361	+	0.783524i	$0.286580\pi$
$104$	−1449.63	+	1672.96i	−1.36681	+	1.57738i
$105$		0			0
$106$	484.977	+	1061.95i	0.444388	+	0.973075i
$107$	389.393	−	250.248i	0.351814	−	0.226097i	−0.352783	−	0.935705i	$-0.614764\pi$
$107$	389.393	−	250.248i	0.351814	−	0.226097i	0.704596	+	0.709608i	$0.251128\pi$
$108$		0			0
$109$	−73.2071	−	509.167i	−0.0643300	−	0.447425i	−0.996374	−	0.0850801i	$-0.972885\pi$
$109$	−73.2071	−	509.167i	−0.0643300	−	0.447425i	0.932044	−	0.362345i	$-0.118024\pi$
$110$	269.915	−	591.031i	0.233958	−	0.512297i
$111$		0			0
$112$	−874.010	−	561.692i	−0.737376	−	0.473883i
$113$	805.052	+	929.080i	0.670203	+	0.773456i	0.984408	−	0.175899i	$-0.0562834\pi$
$113$	805.052	+	929.080i	0.670203	+	0.773456i	−0.314205	+	0.949355i	$0.601738\pi$
$114$		0			0
$115$	−601.658	+	1533.52i	−0.487869	+	1.24349i
$116$	164.123			0.131366
$117$		0			0
$118$	−279.758	−	179.789i	−0.218252	−	0.140262i
$119$	−2.18527	+	15.1989i	−0.00168339	+	0.0117082i
$120$		0			0
$121$	142.356	+	990.106i	0.106954	+	0.743881i
$122$	866.454	+	254.414i	0.642992	+	0.188800i
$123$		0			0
$124$	−246.527	−	539.820i	−0.178539	−	0.390945i
$125$	−386.369	+	113.448i	−0.276463	+	0.0811769i
$126$		0			0
$127$	−28.1636	+	32.5025i	−0.0196780	+	0.0227097i	−0.765503	−	0.643432i	$-0.777510\pi$
$127$	−28.1636	+	32.5025i	−0.0196780	+	0.0227097i	0.745825	+	0.666142i	$0.232055\pi$
$128$	−528.256	+	155.110i	−0.364779	+	0.107109i
$129$		0			0
$130$	2706.32	−	1739.24i	1.82584	−	1.17340i
$131$	1281.81	+	376.375i	0.854906	+	0.251023i	0.679683	−	0.733506i	$-0.262117\pi$
$131$	1281.81	+	376.375i	0.854906	+	0.251023i	0.175223	+	0.984529i	$0.443935\pi$
$132$		0			0
$133$	994.593	−	2177.86i	0.648437	−	1.41988i
$134$	−105.534	+	734.004i	−0.0680353	+	0.473196i
$135$		0			0
$136$	9.66222	+	11.1508i	0.00609212	+	0.00703068i
$137$	−284.337			−0.177318			−0.0886590	−	0.996062i	$-0.528258\pi$
$137$	−284.337			−0.177318			−0.0886590	+	0.996062i	$0.528258\pi$
$138$		0			0
$139$	1353.39			0.825847			0.412923	−	0.910766i	$-0.364508\pi$
$139$	1353.39			0.825847			0.412923	+	0.910766i	$0.364508\pi$
$140$	−569.647	−	657.408i	−0.343886	−	0.396865i
$141$		0			0
$142$	308.345	−	2144.59i	0.182224	−	1.26739i
$143$	680.205	−	1489.44i	0.397774	−	0.871003i
$144$		0			0
$145$	−1033.08	−	303.339i	−0.591672	−	0.173730i
$146$	648.306	−	416.641i	0.367494	−	0.236174i
$147$		0			0
$148$	282.102	−	82.8327i	0.156680	−	0.0460054i
$149$	711.054	−	820.600i	0.390952	−	0.451183i	−0.525819	−	0.850597i	$-0.676241\pi$
$149$	711.054	−	820.600i	0.390952	−	0.451183i	0.916771	+	0.399414i	$0.130786\pi$
$150$		0			0
$151$	−242.714	+	71.2672i	−0.130806	+	0.0384082i	−0.346480	−	0.938057i	$-0.612623\pi$
$151$	−242.714	+	71.2672i	−0.130806	+	0.0384082i	0.215674	+	0.976465i	$0.430805\pi$
$152$	−955.694	−	2092.68i	−0.509980	−	1.11670i
$153$		0			0
$154$	1068.07	+	313.615i	0.558882	+	0.164103i
$155$	554.058	+	3853.56i	0.287116	+	1.99694i
$156$		0			0
$157$	14.9262	−	103.814i	0.00758753	−	0.0527725i	−0.985676	−	0.168650i	$-0.946059\pi$
$157$	14.9262	−	103.814i	0.00758753	−	0.0527725i	0.993263	+	0.115878i	$0.0369682\pi$
$158$	−1968.00	−	1264.75i	−0.990920	−	0.636826i
$159$		0			0
$160$	−1486.55			−0.734511
$161$	−2747.23	−	646.384i	−1.34479	−	0.316411i
$162$		0			0
$163$	−943.638	−	1089.02i	−0.453444	−	0.523302i	0.482289	−	0.876012i	$-0.339806\pi$
$163$	−943.638	−	1089.02i	−0.453444	−	0.523302i	−0.935733	+	0.352710i	$0.885260\pi$
$164$	−431.408	−	277.249i	−0.205411	−	0.132009i
$165$		0			0
$166$	−1048.05	+	2294.91i	−0.490026	+	1.07301i
$167$	−172.683	−	1201.04i	−0.0800158	−	0.556522i	−0.989912	−	0.141686i	$-0.954748\pi$
$167$	−172.683	−	1201.04i	−0.0800158	−	0.556522i	0.909896	−	0.414837i	$-0.136161\pi$
$168$		0			0
$169$	4971.88	−	3195.23i	2.26303	−	1.45436i
$170$	−8.90745	−	19.5046i	−0.00401865	−	0.00879962i
$171$		0			0
$172$	702.248	−	810.437i	0.311313	−	0.359275i
$173$	632.321	−	729.737i	0.277887	−	0.320699i	−0.599599	−	0.800300i	$-0.704673\pi$
$173$	632.321	−	729.737i	0.277887	−	0.320699i	0.877486	+	0.479602i	$0.159219\pi$
$174$		0			0
$175$	1042.01	+	2281.69i	0.450108	+	0.985599i
$176$	621.211	−	399.228i	0.266054	−	0.170983i
$177$		0			0
$178$	−322.653	−	2244.10i	−0.135864	−	0.944958i
$179$	1716.04	−	3757.60i	0.716551	−	1.56903i	−0.102124	−	0.994772i	$-0.532564\pi$
$179$	1716.04	−	3757.60i	0.716551	−	1.56903i	0.818675	−	0.574257i	$-0.194709\pi$
$180$		0			0
$181$	788.779	+	506.918i	0.323920	+	0.208171i	0.692487	−	0.721431i	$-0.256515\pi$
$181$	788.779	+	506.918i	0.323920	+	0.208171i	−0.368567	+	0.929601i	$0.620151\pi$
$182$	3609.24	+	4165.28i	1.46997	+	1.69643i
$183$		0			0
$184$	−2198.09	+	1588.28i	−0.880680	+	0.636354i
$185$	−1928.80			−0.766530
$186$		0			0
$187$	−9.18131	−	5.90047i	−0.00359039	−	0.00230741i
$188$	−62.9048	+	437.513i	−0.0244032	+	0.169728i
$189$		0			0
$190$	475.806	+	3309.30i	0.181677	+	1.26359i
$191$	4791.85	+	1407.01i	1.81532	+	0.533026i	0.999006	−	0.0445805i	$-0.0141951\pi$
$191$	4791.85	+	1407.01i	1.81532	+	0.533026i	0.816315	+	0.577607i	$0.196013\pi$
$192$		0			0
$193$	1055.96	+	2312.23i	0.393833	+	0.862374i	0.997859	+	0.0654091i	$0.0208352\pi$
$193$	1055.96	+	2312.23i	0.393833	+	0.862374i	−0.604025	+	0.796965i	$0.706437\pi$
$194$	2822.40	−	828.732i	1.04452	−	0.306698i
$195$		0			0
$196$	464.595	−	536.171i	0.169313	−	0.195398i
$197$	−2279.68	+	669.375i	−0.824470	+	0.242086i	−0.666640	−	0.745380i	$-0.732268\pi$
$197$	−2279.68	+	669.375i	−0.824470	+	0.242086i	−0.157830	+	0.987466i	$0.550450\pi$
$198$		0			0
$199$	−1791.40	+	1151.26i	−0.638136	+	0.410105i	−0.819314	−	0.573345i	$-0.805645\pi$
$199$	−1791.40	+	1151.26i	−0.638136	+	0.410105i	0.181178	+	0.983450i	$0.442009\pi$
$200$	2312.63	+	679.050i	0.817639	+	0.240081i
$201$		0			0
$202$	964.328	−	2111.58i	0.335891	−	0.735498i
$203$	262.516	−	1825.84i	0.0907636	−	0.631275i
$204$		0			0
$205$	2203.09	+	2542.50i	0.750589	+	0.866225i
$206$	926.528			0.313370
$207$		0			0
$208$	3656.11			1.21878
$209$	1114.38	+	1286.07i	0.368821	+	0.425642i
$210$		0			0
$211$	463.459	−	3223.43i	0.151213	−	1.05171i	−0.762979	−	0.646423i	$-0.776264\pi$
$211$	463.459	−	3223.43i	0.151213	−	1.05171i	0.914191	−	0.405283i	$-0.132827\pi$
$212$	−461.484	+	1010.51i	−0.149504	+	0.327368i
$213$		0			0
$214$	−1062.51	−	311.982i	−0.339402	−	0.0996573i
$215$	−5918.21	+	3803.40i	−1.87730	+	1.20646i
$216$		0			0
$217$	−6399.73	+	1879.13i	−2.00204	+	0.587851i
$218$	−805.904	+	930.062i	−0.250379	+	0.288953i
$219$		0			0
$220$	593.228	−	174.187i	0.181797	−	0.0533805i
$221$	−22.4474	−	49.1530i	−0.00683248	−	0.0149610i
$222$		0			0
$223$	1829.28	+	537.124i	0.549316	+	0.161294i	0.544601	−	0.838695i	$-0.316681\pi$
$223$	1829.28	+	537.124i	0.549316	+	0.161294i	0.00471458	+	0.999989i	$0.498499\pi$
$224$	−362.446	−	2520.87i	−0.108111	−	0.751930i
$225$		0			0
$226$	418.559	−	2911.14i	0.123195	−	0.856842i
$227$	−808.647	−	519.686i	−0.236440	−	0.151950i	0.417056	−	0.908881i	$-0.363062\pi$
$227$	−808.647	−	519.686i	−0.236440	−	0.151950i	−0.653496	+	0.756930i	$0.726698\pi$
$228$		0			0
$229$	−2604.64			−0.751614			−0.375807	−	0.926698i	$-0.622634\pi$
$229$	−2604.64			−0.751614			−0.375807	+	0.926698i	$0.622634\pi$
$230$	3715.28	−	1314.72i	1.06512	−	0.376912i
$231$		0			0
$232$	−1160.72	−	1339.54i	−0.328470	−	0.379075i
$233$	−2990.76	−	1922.04i	−0.840906	−	0.540418i	0.0478199	−	0.998856i	$-0.484773\pi$
$233$	−2990.76	−	1922.04i	−0.840906	−	0.540418i	−0.888726	+	0.458438i	$0.848409\pi$
$234$		0			0
$235$	1204.59	−	2637.68i	0.334377	−	0.732184i
$236$	−45.0340	−	313.218i	−0.0124214	−	0.0863930i
$237$		0			0
$238$	30.9039	−	19.8607i	0.00841681	−	0.00540916i
$239$	1178.48	+	2580.50i	0.318951	+	0.698405i	0.999409	−	0.0343819i	$-0.0109463\pi$
$239$	1178.48	+	2580.50i	0.318951	+	0.698405i	−0.680458	+	0.732787i	$0.738219\pi$
$240$		0			0
$241$	−1650.02	+	1904.22i	−0.441024	+	0.508969i	−0.932127	−	0.362133i	$-0.882049\pi$
$241$	−1650.02	+	1904.22i	−0.441024	+	0.508969i	0.491102	+	0.871102i	$0.336594\pi$
$242$	1567.13	−	1808.56i	0.416276	−	0.480409i
$243$		0			0
$244$	356.961	+	781.636i	0.0936561	+	0.205078i
$245$	−3915.39	+	2516.27i	−1.02100	+	0.656157i
$246$		0			0
$247$	1199.07	+	8339.68i	0.308885	+	2.14835i
$248$	−2662.41	+	5829.87i	−0.681707	+	1.49273i
$249$		0			0
$250$	810.436	+	520.836i	0.205026	+	0.131762i
$251$	−1441.32	−	1663.37i	−0.362450	−	0.418290i	0.545009	−	0.838430i	$-0.316526\pi$
$251$	−1441.32	−	1663.37i	−0.362450	−	0.418290i	−0.907459	+	0.420140i	$0.861981\pi$
$252$		0			0
$253$	1229.05	−	1585.31i	0.305415	−	0.393943i
$254$	102.889			0.0254167
$255$		0			0
$256$	−2680.81	−	1722.85i	−0.654495	−	0.420619i
$257$	903.809	−	6286.13i	0.219370	−	1.52575i	−0.521003	−	0.853555i	$-0.674442\pi$
$257$	903.809	−	6286.13i	0.219370	−	1.52575i	0.740373	−	0.672196i	$-0.234649\pi$
$258$		0			0
$259$	−470.275	−	3270.83i	−0.112824	−	0.784709i
$260$	2937.16	+	862.429i	0.700597	+	0.205714i
$261$		0			0
$262$	−1327.69	−	2907.24i	−0.313073	−	0.685533i
$263$	−510.171	+	149.800i	−0.119614	+	0.0351219i	−0.340992	−	0.940066i	$-0.610763\pi$
$263$	−510.171	+	149.800i	−0.119614	+	0.0351219i	0.221378	+	0.975188i	$0.428945\pi$
$264$		0			0
$265$	4772.49	−	5507.75i	1.10631	−	1.27675i
$266$	−5495.87	+	1613.73i	−1.26682	+	0.371971i
$267$		0			0
$268$	−593.613	+	381.492i	−0.135301	+	0.0869527i
$269$	−1404.56	−	412.417i	−0.318356	−	0.0934777i	0.118651	−	0.992936i	$-0.462143\pi$
$269$	−1404.56	−	412.417i	−0.318356	−	0.0934777i	−0.437006	+	0.899458i	$0.643961\pi$
$270$		0			0
$271$	−747.137	+	1636.00i	−0.167474	+	0.366716i	−0.974697	−	0.223530i	$-0.928242\pi$
$271$	−747.137	+	1636.00i	−0.167474	+	0.366716i	0.807223	+	0.590246i	$0.200969\pi$
$272$	3.46808	−	24.1210i	0.000773100	−	0.00537703i
$273$		0			0
$274$	445.465	+	514.094i	0.0982173	+	0.113349i
$275$	−1782.85			−0.390945
$276$		0			0
$277$	−7250.75			−1.57276			−0.786381	−	0.617741i	$-0.788048\pi$
$277$	−7250.75			−1.57276			−0.786381	+	0.617741i	$0.788048\pi$
$278$	−2120.32	−	2446.98i	−0.457440	−	0.527914i
$279$		0			0
$280$	−1336.96	+	9298.74i	−0.285352	+	1.98466i
$281$	−72.3201	+	158.359i	−0.0153532	+	0.0336189i	−0.917153	−	0.398535i	$-0.869519\pi$
$281$	−72.3201	+	158.359i	−0.0153532	+	0.0336189i	0.901800	+	0.432154i	$0.142246\pi$
$282$		0			0
$283$	−507.071	−	148.889i	−0.106510	−	0.0312741i	0.228043	−	0.973651i	$-0.426767\pi$
$283$	−507.071	−	148.889i	−0.106510	−	0.0312741i	−0.334553	+	0.942377i	$0.608585\pi$
$284$	1734.40	−	1114.63i	0.362386	−	0.232891i
$285$		0			0
$286$	−3758.64	+	1103.64i	−0.777109	+	0.228180i
$287$	−3774.40	+	4355.88i	−0.776291	+	0.895888i
$288$		0			0
$289$	4713.64	−	1384.05i	0.959423	−	0.281712i
$290$	1070.05	+	2343.08i	0.216674	+	0.474451i
$291$		0			0
$292$	703.606	+	206.597i	0.141012	+	0.0414048i
$293$	891.325	+	6199.30i	0.177719	+	1.23607i	0.862023	+	0.506869i	$0.169197\pi$
$293$	891.325	+	6199.30i	0.177719	+	1.23607i	−0.684304	+	0.729197i	$0.739894\pi$
$294$		0			0
$295$	−295.435	+	2054.80i	−0.0583082	+	0.405542i
$296$	−2671.17	−	1716.66i	−0.524523	−	0.337090i
$297$		0			0
$298$	−2597.68			−0.504964
$299$	9362.78	−	3313.18i	1.81092	−	0.640823i
$300$		0			0
$301$	−7892.73	−	9108.69i	−1.51139	−	1.74424i
$302$	509.109	+	327.185i	0.0970064	+	0.0623422i
$303$		0			0
$304$	−1578.44	+	3456.31i	−0.297796	+	0.652082i
$305$	−802.252	−	5579.79i	−0.150613	−	1.04753i
$306$		0			0
$307$	3888.24	−	2498.82i	0.722846	−	0.464545i	−0.126780	−	0.991931i	$-0.540464\pi$
$307$	3888.24	−	2498.82i	0.722846	−	0.464545i	0.849626	+	0.527386i	$0.176828\pi$
$308$	440.024	+	963.518i	0.0814049	+	0.178252i
$309$		0			0
$310$	6099.38	−	7039.05i	1.11749	−	1.28965i
$311$	5887.92	−	6795.02i	1.07355	−	1.23894i	0.103859	−	0.994592i	$-0.466881\pi$
$311$	5887.92	−	6795.02i	1.07355	−	1.23894i	0.969688	−	0.244347i	$-0.0785736\pi$
$312$		0			0
$313$	513.456	+	1124.31i	0.0927229	+	0.203035i	0.950311	−	0.311302i	$-0.100765\pi$
$313$	513.456	+	1124.31i	0.0927229	+	0.203035i	−0.857588	+	0.514337i	$0.828038\pi$
$314$	−211.085	+	135.656i	−0.0379371	+	0.0243807i
$315$		0			0
$316$	−316.798	−	2203.38i	−0.0563965	−	0.392246i
$317$	−1012.88	+	2217.89i	−0.179460	+	0.392963i	−0.977888	−	0.209127i	$-0.932938\pi$
$317$	−1012.88	+	2217.89i	−0.179460	+	0.392963i	0.798428	+	0.602090i	$0.205665\pi$
$318$		0			0
$319$	1102.95	+	708.822i	0.193584	+	0.124409i
$320$	5505.91	+	6354.16i	0.961844	+	1.11003i
$321$		0			0
$322$	3135.33	+	5979.78i	0.542625	+	1.03491i
$323$	56.1581			0.00967406
$324$		0			0
$325$	−7425.88	−	4772.32i	−1.26743	−	0.814526i
$326$	−490.611	+	3412.28i	−0.0833511	+	0.579720i
$327$		0			0
$328$	788.173	+	5481.87i	0.132682	+	0.922822i
$329$	4766.64	+	1399.61i	0.798764	+	0.234538i
$330$		0			0
$331$	2197.00	+	4810.77i	0.364828	+	0.798863i	0.999656	+	0.0262094i	$0.00834368\pi$
$331$	2197.00	+	4810.77i	0.364828	+	0.798863i	−0.634828	+	0.772653i	$0.718929\pi$
$332$	−2303.43	+	676.349i	−0.380775	+	0.111806i
$333$		0			0
$334$	−1900.99	+	2193.86i	−0.311430	+	0.359410i
$335$	4441.61	−	1304.17i	0.724391	−	0.212700i
$336$		0			0
$337$	496.546	−	319.111i	0.0802629	−	0.0515818i	−0.499894	−	0.866087i	$-0.666628\pi$
$337$	496.546	−	319.111i	0.0802629	−	0.0515818i	0.580157	+	0.814505i	$0.302991\pi$
$338$	−13566.5	−	3983.47i	−2.18319	−	0.641042i
$339$		0			0
$340$	8.47595	−	18.5597i	0.00135198	−	0.00296042i
$341$	674.672	−	4692.45i	0.107142	−	0.745191i
$342$		0			0
$343$	525.367	+	606.306i	0.0827030	+	0.0954444i
$344$	−11581.1			−1.81516
$345$		0			0
$346$	−2310.04			−0.358926
$347$	−3399.03	−	3922.69i	−0.525848	−	0.606861i	0.429237	−	0.903192i	$-0.358782\pi$
$347$	−3399.03	−	3922.69i	−0.525848	−	0.606861i	−0.955085	+	0.296331i	$0.904237\pi$
$348$		0			0
$349$	−1535.45	+	10679.3i	−0.235504	+	1.63797i	0.438137	+	0.898908i	$0.355638\pi$
$349$	−1535.45	+	10679.3i	−0.235504	+	1.63797i	−0.673641	+	0.739058i	$0.735271\pi$
$350$	2492.90	−	5458.69i	0.380718	−	0.833655i
$351$		0			0
$352$	1736.83	+	509.979i	0.262992	+	0.0772216i
$353$	4252.41	−	2732.86i	0.641169	−	0.412054i	−0.179261	−	0.983802i	$-0.557371\pi$
$353$	4252.41	−	2732.86i	0.641169	−	0.412054i	0.820430	+	0.571747i	$0.193734\pi$
$354$		0			0
$355$	−12977.3	+	3810.49i	−1.94018	+	0.569690i
$356$	1412.76	−	1630.41i	0.210327	−	0.242730i
$357$		0			0
$358$	−9482.39	+	2784.28i	−1.39989	+	0.411044i
$359$	−1921.14	−	4206.71i	−0.282434	−	0.618445i	0.714243	−	0.699898i	$-0.246771\pi$
$359$	−1921.14	−	4206.71i	−0.282434	−	0.618445i	−0.996677	+	0.0814530i	$0.974044\pi$
$360$		0			0
$361$	−1820.45	−	534.532i	−0.265410	−	0.0779315i
$362$	−319.235	−	2220.33i	−0.0463497	−	0.322369i
$363$		0			0
$364$	−746.365	+	5191.08i	−0.107473	+	0.747491i
$365$	−4047.03	−	2600.87i	−0.580360	−	0.372975i
$366$		0			0
$367$	2474.30			0.351927			0.175964	−	0.984397i	$-0.443696\pi$
$367$	2474.30			0.351927			0.175964	+	0.984397i	$0.443696\pi$
$368$	4359.92	+	1025.83i	0.617599	+	0.145312i
$369$		0			0
$370$	3021.81	+	3487.35i	0.424585	+	0.489997i
$371$	10503.6	+	6750.25i	1.46986	+	0.944624i
$372$		0			0
$373$	2630.48	−	5759.95i	0.365151	−	0.799568i	−0.634494	−	0.772927i	$-0.718792\pi$
$373$	2630.48	−	5759.95i	0.365151	−	0.799568i	0.999645	−	0.0266409i	$-0.00848106\pi$
$374$	3.71586	+	25.8443i	0.000513750	+	0.00357321i
$375$		0			0
$376$	4015.79	−	2580.79i	0.550794	−	0.353974i
$377$	2696.60	+	5904.74i	0.368388	+	0.806657i
$378$		0			0
$379$	8559.02	−	9877.63i	1.16002	−	1.33873i	0.229145	−	0.973392i	$-0.426407\pi$
$379$	8559.02	−	9877.63i	1.16002	−	1.33873i	0.930874	−	0.365341i	$-0.119048\pi$
$380$	−2083.36	+	2404.32i	−0.281247	+	0.324577i
$381$		0			0
$382$	−4963.35	−	10868.2i	−0.664783	−	1.45567i
$383$	−6727.91	+	4323.76i	−0.897598	+	0.576851i	−0.906077	−	0.423113i	$-0.860937\pi$
$383$	−6727.91	+	4323.76i	−0.897598	+	0.576851i	0.00847901	+	0.999964i	$0.497301\pi$
$384$		0			0
$385$	−988.933	−	6878.18i	−0.130911	−	0.910505i
$386$	2526.27	−	5531.75i	0.333118	−	0.729427i
$387$		0			0
$388$	2354.72	+	1513.29i	0.308100	+	0.198004i
$389$	1734.38	+	2001.58i	0.226058	+	0.260885i	0.857436	−	0.514590i	$-0.172056\pi$
$389$	1734.38	+	2001.58i	0.226058	+	0.260885i	−0.631378	+	0.775475i	$0.717510\pi$
$390$		0			0
$391$	−12.9773	−	64.9134i	−0.00167849	−	0.00839593i
$392$	−7661.89			−0.987204
$393$		0			0
$394$	4781.79	+	3073.07i	0.611429	+	0.392942i
$395$	−2078.28	+	14454.8i	−0.264734	+	1.84126i
$396$		0			0
$397$	1866.31	+	12980.5i	0.235938	+	1.64098i	0.671629	+	0.740887i	$0.265595\pi$
$397$	1866.31	+	12980.5i	0.235938	+	1.64098i	−0.435692	+	0.900096i	$0.643496\pi$
$398$	4888.09	+	1435.27i	0.615623	+	0.180763i
$399$		0			0
$400$	−1653.70	−	3621.11i	−0.206713	−	0.452638i
$401$	−4087.03	+	1200.06i	−0.508969	+	0.149447i	−0.526127	−	0.850406i	$-0.676356\pi$
$401$	−4087.03	+	1200.06i	−0.508969	+	0.149447i	0.0171579	+	0.999853i	$0.494538\pi$
$402$		0			0
$403$	15370.9	−	17738.9i	1.89994	−	2.19265i
$404$	2119.43	−	622.321i	0.261004	−	0.0766377i
$405$		0			0
$406$	−3712.48	+	2385.86i	−0.453811	+	0.291646i
$407$	2253.54	+	661.700i	0.274457	+	0.0805879i
$408$		0			0
$409$	−2570.29	+	5628.15i	−0.310740	+	0.680426i	−0.998985	−	0.0450529i	$-0.985654\pi$
$409$	−2570.29	+	5628.15i	−0.310740	+	0.680426i	0.688245	+	0.725479i	$0.258382\pi$
$410$	1145.42	−	7966.58i	0.137972	−	0.959613i
$411$		0			0
$412$	577.354	+	666.302i	0.0690393	+	0.0796756i
$413$	−3556.53			−0.423742
$414$		0			0
$415$	15749.1			1.86288
$416$	5869.10	+	6773.30i	0.691721	+	0.798289i
$417$		0			0
$418$	579.385	−	4029.71i	0.0677958	−	0.471530i
$419$	−2879.50	+	6305.23i	−0.335735	+	0.735157i	−0.999923	−	0.0124088i	$-0.996050\pi$
$419$	−2879.50	+	6305.23i	−0.335735	+	0.735157i	0.664188	+	0.747565i	$0.268777\pi$
$420$		0			0
$421$	−7342.34	−	2155.91i	−0.849986	−	0.249578i	−0.172404	−	0.985026i	$-0.555154\pi$
$421$	−7342.34	−	2155.91i	−0.849986	−	0.249578i	−0.677581	+	0.735448i	$0.736972\pi$
$422$	−6554.19	+	4212.13i	−0.756050	+	0.485884i
$423$		0			0
$424$	11511.3	−	3380.03i	1.31849	−	0.387144i
$425$	−38.5292	+	44.4651i	−0.00439751	+	0.00507499i
$426$		0			0
$427$	9266.53	−	2720.90i	1.05021	−	0.308369i
$428$	−437.733	−	958.502i	−0.0494361	−	0.108250i
$429$		0			0
$430$	16148.7	+	4741.68i	1.81106	+	0.531776i
$431$	129.588	+	901.308i	0.0144827	+	0.100730i	0.995781	−	0.0917657i	$-0.0292511\pi$
$431$	129.588	+	901.308i	0.0144827	+	0.100730i	−0.981298	+	0.192495i	$0.938342\pi$
$432$		0			0
$433$	1458.62	−	10145.0i	0.161887	−	1.12595i	−0.733186	−	0.680028i	$-0.761968\pi$
$433$	1458.62	−	10145.0i	0.161887	−	1.12595i	0.895073	−	0.445920i	$-0.147123\pi$
$434$	13423.9	+	8627.00i	1.48472	+	0.954169i
$435$		0			0
$436$	−1171.03			−0.128629
$437$	−910.055	+	10281.5i	−0.0996198	+	1.12547i
$438$		0			0
$439$	−7912.91	−	9131.98i	−0.860279	−	0.992815i	−0.999997	−	0.00262371i	$-0.999165\pi$
$439$	−7912.91	−	9131.98i	−0.860279	−	0.992815i	0.139717	−	0.990191i	$-0.455381\pi$
$440$	−5617.16	−	3609.93i	−0.608608	−	0.391129i
$441$		0			0
$442$	−53.7029	+	117.593i	−0.00577915	+	0.0126546i
$443$	1547.83	+	10765.4i	0.166004	+	1.15458i	0.887042	+	0.461688i	$0.152756\pi$
$443$	1547.83	+	10765.4i	0.166004	+	1.15458i	−0.721038	+	0.692895i	$0.756335\pi$
$444$		0			0
$445$	−11906.1	+	7651.58i	−1.26832	+	0.815101i
$446$	−1894.74	−	4148.91i	−0.201163	−	0.440486i
$447$		0			0
$448$	−9432.87	+	10886.1i	−0.994780	+	1.14804i
$449$	6869.48	−	7927.80i	0.722029	−	0.833266i	−0.269521	−	0.962995i	$-0.586865\pi$
$449$	6869.48	−	7927.80i	0.722029	−	0.833266i	0.991549	+	0.129729i	$0.0414108\pi$
$450$		0			0
$451$	−1701.78	−	3726.38i	−0.177680	−	0.389065i
$452$	2354.33	−	1513.04i	0.244997	−	0.157450i
$453$		0			0
$454$	327.275	+	2276.25i	0.0338321	+	0.235308i
$455$	14292.4	−	31296.0i	1.47261	−	3.22457i
$456$		0			0
$457$	−16034.6	−	10304.8i	−1.64128	−	1.05479i	−0.939585	−	0.342317i	$-0.888788\pi$
$457$	−16034.6	−	10304.8i	−1.64128	−	1.05479i	−0.701700	−	0.712473i	$-0.747575\pi$
$458$	4080.64	+	4709.31i	0.416323	+	0.480462i
$459$		0			0
$460$	3260.60	+	1852.56i	0.330491	+	0.187774i
$461$	−12528.0			−1.26570			−0.632852	−	0.774273i	$-0.718116\pi$
$461$	−12528.0			−1.26570			−0.632852	+	0.774273i	$0.718116\pi$
$462$		0			0
$463$	12348.8	+	7936.09i	1.23952	+	0.796591i	0.985346	−	0.170568i	$-0.0545603\pi$
$463$	12348.8	+	7936.09i	1.23952	+	0.796591i	0.254173	+	0.967159i	$0.418197\pi$
$464$	−416.619	+	2897.65i	−0.0416833	+	0.289914i
$465$		0			0
$466$	1210.42	+	8418.65i	0.120325	+	0.836881i
$467$	7411.76	+	2176.29i	0.734422	+	0.215646i	0.627495	−	0.778621i	$-0.284080\pi$
$467$	7411.76	+	2176.29i	0.734422	+	0.215646i	0.106928	+	0.994267i	$0.465899\pi$
$468$		0			0
$469$	3294.54	+	7214.04i	0.324366	+	0.710264i
$470$	−6656.24	+	1954.45i	−0.653254	+	0.191813i
$471$		0			0
$472$	−2237.94	+	2582.72i	−0.218241	+	0.251863i
$473$	8219.45	−	2413.45i	0.799008	−	0.234610i
$474$		0			0
$475$	7717.49	−	4959.73i	0.745480	−	0.479091i
$476$	33.5400	+	9.84822i	0.00322963	+	0.000948304i
$477$		0			0
$478$	2819.37	−	6173.56i	0.269780	−	0.590736i
$479$	−302.726	+	2105.50i	−0.0288766	+	0.200841i	−0.999153	−	0.0411599i	$-0.986895\pi$
$479$	−302.726	+	2105.50i	−0.0288766	+	0.200841i	0.970276	+	0.242001i	$0.0778038\pi$
$480$		0			0
$481$	7615.18	+	8788.38i	0.721876	+	0.833089i
$482$	6027.96			0.569639
$483$		0			0
$484$	2277.14			0.213857
$485$	−12024.9	−	13877.5i	−1.12582	−	1.29927i
$486$		0			0
$487$	−471.362	+	3278.39i	−0.0438592	+	0.305048i	0.956070	+	0.293139i	$0.0946999\pi$
$487$	−471.362	+	3278.39i	−0.0438592	+	0.305048i	−0.999929	+	0.0119088i	$0.996209\pi$
$488$	3855.06	−	8441.40i	0.357603	−	0.783041i
$489$		0			0
$490$	10683.7	+	3137.01i	0.984979	+	0.289216i
$491$	−11948.9	+	7679.12i	−1.09827	+	0.705812i	−0.958705	−	0.284401i	$-0.908205\pi$
$491$	−11948.9	+	7679.12i	−1.09827	+	0.705812i	−0.139560	+	0.990214i	$0.544569\pi$
$492$		0			0
$493$	41.5142	−	12.1897i	0.00379251	−	0.00111358i
$494$	13200.0	−	15233.6i	1.20222	−	1.38743i
$495$		0			0
$496$	10156.5	−	2982.23i	0.919439	−	0.269972i
$497$	−9625.88	−	21077.7i	−0.868772	−	1.90235i
$498$		0			0
$499$	−18276.5	−	5366.45i	−1.63961	−	0.481434i	−0.673421	−	0.739259i	$-0.735176\pi$
$499$	−18276.5	−	5366.45i	−1.63961	−	0.481434i	−0.966192	+	0.257825i	$0.916994\pi$
$500$	130.460	+	907.368i	0.0116687	+	0.0811575i
$501$		0			0
$502$	−749.362	+	5211.93i	−0.0666248	+	0.463386i
$503$	−4003.94	−	2573.17i	−0.354924	−	0.228096i	0.351013	−	0.936371i	$-0.385837\pi$
$503$	−4003.94	−	2573.17i	−0.354924	−	0.228096i	−0.705937	+	0.708275i	$0.749474\pi$
$504$		0			0
$505$	−14491.0			−1.27692
$506$	−4791.85	+	261.492i	−0.420995	+	0.0229738i
$507$		0			0
$508$	64.1141	+	73.9916i	0.00559961	+	0.00646230i
$509$	8529.84	+	5481.80i	0.742787	+	0.477360i	0.856496	−	0.516154i	$-0.172637\pi$
$509$	8529.84	+	5481.80i	0.742787	+	0.477360i	−0.113709	+	0.993514i	$0.536273\pi$
$510$		0			0
$511$	3423.79	−	7497.05i	0.296398	−	0.649021i
$512$	1711.80	+	11905.8i	0.147757	+	1.02767i
$513$		0			0
$514$	−12781.6	+	8214.22i	−1.09683	+	0.704891i
$515$	−2402.69	−	5261.16i	−0.205583	−	0.450164i
$516$		0			0
$517$	−2312.29	+	2668.53i	−0.196701	+	0.227005i
$518$	−5177.04	+	5974.63i	−0.439124	+	0.506776i
$519$		0			0
$520$	−13733.4	−	30072.0i	−1.15817	−	2.53605i
$521$	11147.3	−	7163.92i	0.937372	−	0.602412i	0.0197236	−	0.999805i	$-0.493721\pi$
$521$	11147.3	−	7163.92i	0.937372	−	0.602412i	0.917649	+	0.397393i	$0.130085\pi$
$522$		0			0
$523$	−1793.08	−	12471.1i	−0.149915	−	1.04268i	−0.916355	−	0.400367i	$-0.868883\pi$
$523$	−1793.08	−	12471.1i	−0.149915	−	1.04268i	0.766439	−	0.642317i	$-0.222027\pi$
$524$	1263.37	−	2766.40i	0.105326	−	0.230631i
$525$		0			0
$526$	1070.12	+	687.724i	0.0887062	+	0.0570080i
$527$	−102.451	−	118.235i	−0.00846841	−	0.00977307i
$528$		0			0
$529$	12094.8	−	1323.97i	0.994062	−	0.108816i
$530$	−17435.2			−1.42894
$531$		0			0
$532$	−4585.18	−	2946.71i	−0.373670	−	0.240143i
$533$	2886.54	−	20076.3i	0.234578	−	1.63153i
$534$		0			0
$535$	983.784	+	6842.37i	0.0795004	+	0.552937i
$536$	7311.86	+	2146.96i	0.589225	+	0.173012i
$537$		0			0
$538$	1454.83	+	3185.64i	0.116584	+	0.255284i
$539$	5437.85	−	1596.70i	0.434554	−	0.127597i
$540$		0			0
$541$	−6618.65	+	7638.32i	−0.525985	+	0.607019i	−0.955119	−	0.296222i	$-0.904273\pi$
$541$	−6618.65	+	7638.32i	−0.525985	+	0.607019i	0.429134	+	0.903241i	$0.358819\pi$
$542$	4128.49	−	1212.23i	0.327184	−	0.0960699i
$543$		0			0
$544$	50.2538	−	32.2962i	0.00396069	−	0.00254538i
$545$	7371.11	+	2164.35i	0.579346	+	0.170111i
$546$		0			0
$547$	3136.47	−	6867.90i	0.245166	−	0.536838i	−0.746544	−	0.665336i	$-0.768288\pi$
$547$	3136.47	−	6867.90i	0.245166	−	0.536838i	0.991710	+	0.128498i	$0.0410156\pi$
$548$	−92.1191	+	640.702i	−0.00718090	+	0.0499443i
$549$		0			0
$550$	2793.15	+	3223.47i	0.216546	+	0.249908i
$551$	−6746.26			−0.521598
$552$		0			0
$553$	−25019.0			−1.92390
$554$	11359.6	+	13109.7i	0.871161	+	1.00537i
$555$		0			0
$556$	438.468	−	3049.61i	0.0334446	−	0.232612i
$557$	−9548.81	+	20909.0i	−0.726384	+	1.59056i	0.0783508	+	0.996926i	$0.475035\pi$
$557$	−9548.81	+	20909.0i	−0.726384	+	1.59056i	−0.804735	+	0.593634i	$0.797693\pi$
$558$		0			0
$559$	40695.8	+	11949.4i	3.07916	+	0.904122i
$560$	13052.8	−	8388.54i	0.984969	−	0.633001i
$561$		0			0
$562$	399.623	−	117.340i	0.0299948	−	0.00880726i
$563$	−8113.07	+	9362.99i	−0.607327	+	0.700893i	−0.973249	−	0.229753i	$-0.926208\pi$
$563$	−8113.07	+	9362.99i	−0.607327	+	0.700893i	0.365922	+	0.930646i	$0.380754\pi$
$564$		0			0
$565$	−17615.9	+	5172.50i	−1.31169	+	0.385148i
$566$	525.219	+	1150.07i	0.0390046	+	0.0854081i
$567$		0			0
$568$	−21363.5	−	6272.90i	−1.57816	−	0.463389i
$569$	2898.15	+	20157.1i	0.213527	+	1.48511i	0.761254	+	0.648454i	$0.224584\pi$
$569$	2898.15	+	20157.1i	0.213527	+	1.48511i	−0.547727	+	0.836657i	$0.684507\pi$
$570$		0			0
$571$	−1971.17	+	13709.8i	−0.144467	+	1.00479i	0.780612	+	0.625017i	$0.214908\pi$
$571$	−1971.17	+	13709.8i	−0.144467	+	1.00479i	−0.925079	+	0.379775i	$0.876001\pi$
$572$	−3135.82	−	2015.27i	−0.229222	−	0.147312i
$573$		0			0
$574$	13788.9			1.00268
$575$	−7516.37	−	7774.56i	−0.545138	−	0.563863i
$576$		0			0
$577$	5382.36	+	6211.57i	0.388337	+	0.448165i	0.915933	−	0.401330i	$-0.131452\pi$
$577$	5382.36	+	6211.57i	0.388337	+	0.448165i	−0.527596	+	0.849495i	$0.676907\pi$
$578$	−9887.19	−	6354.11i	−0.711510	−	0.457260i
$579$		0			0
$580$	−1018.21	+	2229.58i	−0.0728949	+	0.159618i
$581$	3839.91	+	26707.2i	0.274193	+	1.90706i
$582$		0			0
$583$	−7465.53	+	4797.80i	−0.530344	+	0.340831i
$584$	−3289.88	−	7203.83i	−0.233110	−	0.510439i
$585$		0			0
$586$	9812.20	−	11323.9i	0.691703	−	0.798268i
$587$	−2288.26	+	2640.79i	−0.160897	+	0.185685i	−0.830474	−	0.557058i	$-0.811930\pi$
$587$	−2288.26	+	2640.79i	−0.160897	+	0.185685i	0.669577	+	0.742743i	$0.266476\pi$
$588$		0			0
$589$	10133.5	+	22189.3i	0.708903	+	1.55228i
$590$	4178.02	−	2685.05i	0.291536	−	0.187359i
$591$		0			0
$592$	746.338	+	5190.89i	0.0518147	+	0.360379i
$593$	−4071.05	+	8914.36i	−0.281919	+	0.617317i	−0.996623	−	0.0821102i	$-0.973834\pi$
$593$	−4071.05	+	8914.36i	−0.281919	+	0.617317i	0.714704	+	0.699427i	$0.246561\pi$
$594$		0			0
$595$	−192.917	−	123.980i	−0.0132921	−	0.00854233i
$596$	−1618.71	−	1868.09i	−0.111250	−	0.128389i
$597$		0			0
$598$	−20658.9	−	11737.6i	−1.41271	−	0.802655i
$599$	14512.6			0.989932			0.494966	−	0.868912i	$-0.335180\pi$
$599$	14512.6			0.989932			0.494966	+	0.868912i	$0.335180\pi$
$600$		0			0
$601$	−6600.63	−	4241.97i	−0.447996	−	0.287909i	0.297125	−	0.954838i	$-0.403972\pi$
$601$	−6600.63	−	4241.97i	−0.447996	−	0.287909i	−0.745121	+	0.666929i	$0.767608\pi$
$602$	−4103.55	+	28540.8i	−0.277821	+	1.93229i
$603$		0			0
$604$	81.9538	+	570.001i	0.00552095	+	0.0383990i
$605$	−14333.6	−	4208.72i	−0.963211	−	0.282824i
$606$		0			0
$607$	−2314.74	−	5068.58i	−0.154782	−	0.338925i	0.816316	−	0.577605i	$-0.196013\pi$
$607$	−2314.74	−	5068.58i	−0.154782	−	0.338925i	−0.971098	+	0.238680i	$0.923285\pi$
$608$	−8937.01	+	2624.14i	−0.596124	+	0.175038i
$609$		0			0
$610$	−8831.63	+	10192.2i	−0.586201	+	0.676511i
$611$	−16774.2	+	4925.35i	−1.11066	+	0.326118i
$612$		0			0
$613$	−17346.3	+	11147.8i	−1.14292	+	0.734509i	−0.968217	−	0.250112i	$-0.919533\pi$
$613$	−17346.3	+	11147.8i	−1.14292	+	0.734509i	−0.174702	+	0.984621i	$0.555896\pi$
$614$	−10609.6	−	3115.26i	−0.697343	−	0.204759i
$615$		0			0
$616$	4752.11	−	10405.7i	0.310825	−	0.680611i
$617$	1812.82	−	12608.4i	0.118284	−	0.822684i	−0.841160	−	0.540786i	$-0.818127\pi$
$617$	1812.82	−	12608.4i	0.118284	−	0.822684i	0.959444	−	0.281898i	$-0.0909639\pi$
$618$		0			0
$619$	3851.20	+	4444.52i	0.250069	+	0.288595i	0.866881	−	0.498516i	$-0.166121\pi$
$619$	3851.20	+	4444.52i	0.250069	+	0.288595i	−0.616812	+	0.787111i	$0.711576\pi$
$620$	8862.80			0.574095
$621$		0			0
$622$	−21510.2			−1.38662
$623$	−15878.4	−	18324.6i	−1.02111	−	1.17843i
$624$		0			0
$625$	2599.86	−	18082.4i	0.166391	−	1.15728i
$626$	1228.39	−	2689.79i	0.0784284	−	0.171734i
$627$		0			0
$628$	−229.091	−	67.2671i	−0.0145569	−	0.00427429i
$629$	65.2045	−	41.9044i	0.00413335	−	0.00265634i
$630$		0			0
$631$	3599.35	−	1056.87i	0.227081	−	0.0666769i	−0.166213	−	0.986090i	$-0.553154\pi$
$631$	3599.35	−	1056.87i	0.227081	−	0.0666769i	0.393293	+	0.919413i	$0.371336\pi$
$632$	−15743.1	+	18168.6i	−0.990868	+	1.14352i
$633$		0			0
$634$	5596.90	−	1643.40i	0.350601	−	0.102946i
$635$	−266.814	−	584.242i	−0.0166743	−	0.0365117i
$636$		0			0
$637$	26923.6	+	7905.49i	1.67465	+	0.491722i
$638$	−446.385	−	3104.68i	−0.0276999	−	0.192657i
$639$		0			0
$640$	1170.15	−	8138.56i	0.0722721	−	0.502664i
$641$	15927.2	+	10235.8i	0.981416	+	0.630717i	0.929845	−	0.367952i	$-0.119941\pi$
$641$	15927.2	+	10235.8i	0.981416	+	0.630717i	0.0515707	+	0.998669i	$0.483577\pi$
$642$		0			0
$643$	−10695.9			−0.655994			−0.327997	−	0.944679i	$-0.606374\pi$
$643$	−10695.9			−0.655994			−0.327997	+	0.944679i	$0.606374\pi$
$644$	−2346.55	+	5980.96i	−0.143583	+	0.365967i
$645$		0			0
$646$	−87.9817	−	101.536i	−0.00535851	−	0.00618405i
$647$	−25256.8	−	16231.5i	−1.53469	−	0.986287i	−0.988936	−	0.148342i	$-0.952606\pi$
$647$	−25256.8	−	16231.5i	−1.53469	−	0.986287i	−0.545756	−	0.837944i	$-0.683757\pi$
$648$		0			0
$649$	1050.10	−	2299.40i	0.0635133	−	0.139075i
$650$	3005.40	+	20903.0i	0.181356	+	1.26136i
$651$		0			0
$652$	−2759.62	+	1773.50i	−0.165759	+	0.106527i
$653$	−8447.70	−	18497.9i	−0.506254	−	1.10854i	−0.974386	−	0.224883i	$-0.927800\pi$
$653$	−8447.70	−	18497.9i	−0.506254	−	1.10854i	0.468131	−	0.883659i	$-0.344927\pi$
$654$		0			0
$655$	−13065.3	+	15078.2i	−0.779397	+	0.899472i
$656$	5990.06	−	6912.90i	0.356513	−	0.411438i
$657$		0			0
$658$	−4937.24	−	10811.0i	−0.292513	−	0.640514i
$659$	10721.5	−	6890.26i	0.633761	−	0.407293i	−0.183939	−	0.982938i	$-0.558885\pi$
$659$	10721.5	−	6890.26i	0.633761	−	0.407293i	0.817700	+	0.575644i	$0.195249\pi$
$660$		0			0
$661$	2882.80	+	20050.3i	0.169634	+	1.17983i	0.879643	+	0.475635i	$0.157782\pi$
$661$	2882.80	+	20050.3i	0.169634	+	1.17983i	−0.710009	+	0.704192i	$0.751309\pi$
$662$	5256.08	−	11509.2i	0.308585	−	0.675707i
$663$		0			0
$664$	21810.8	+	14016.9i	1.27473	+	0.819221i
$665$	23415.3	+	27022.7i	1.36543	+	1.57578i
$666$		0			0
$667$	1558.96	+	7798.03i	0.0904994	+	0.452685i
$668$	−2762.27			−0.159993
$669$		0			0
$670$	−9316.58	−	5987.40i	−0.537210	−	0.345244i
$671$	−976.896	+	6794.46i	−0.0562037	+	0.390905i
$672$		0			0
$673$	−3559.53	−	24757.1i	−0.203878	−	1.41800i	−0.792637	−	0.609693i	$-0.791293\pi$
$673$	−3559.53	−	24757.1i	−0.203878	−	1.41800i	0.588760	−	0.808308i	$-0.299617\pi$
$674$	−1354.89	−	397.833i	−0.0774312	−	0.0227358i
$675$		0			0
$676$	−5589.10	−	12238.4i	−0.317996	−	0.696314i
$677$	−5616.27	+	1649.09i	−0.318835	+	0.0936183i	−0.437234	−	0.899348i	$-0.644042\pi$
$677$	−5616.27	+	1649.09i	−0.318835	+	0.0936183i	0.118399	+	0.992966i	$0.462224\pi$
$678$		0			0
$679$	20601.4	−	23775.3i	1.16438	−	1.34376i
$680$	−211.426	+	62.0802i	−0.0119233	+	0.00350098i
$681$		0			0
$682$	−9541.15	+	6131.72i	−0.535703	+	0.344275i
$683$	13136.8	+	3857.31i	0.735967	+	0.216099i	0.628173	−	0.778074i	$-0.283803\pi$
$683$	13136.8	+	3857.31i	0.735967	+	0.216099i	0.107794	+	0.994173i	$0.465621\pi$
$684$		0			0
$685$	1764.02	−	3862.67i	0.0983939	−	0.215453i
$686$	273.146	−	1899.77i	0.0152023	−	0.105734i
$687$		0			0
$688$	12526.0	+	14455.7i	0.694110	+	0.801046i
$689$	−43938.0			−2.42947
$690$		0			0
$691$	−26534.1			−1.46079			−0.730395	−	0.683025i	$-0.760664\pi$
$691$	−26534.1			−1.46079			−0.730395	+	0.683025i	$0.760664\pi$
$692$	−1439.47	−	1661.24i	−0.0790759	−	0.0912585i
$693$		0			0
$694$	−1767.21	+	12291.2i	−0.0966602	+	0.672287i
$695$	−8396.38	+	18385.5i	−0.458263	+	1.00346i
$696$		0			0
$697$	−129.715	−	38.0877i	−0.00704921	−	0.00206983i
$698$	21714.2	−	13954.9i	1.17750	−	0.756734i
$699$		0			0
$700$	5478.98	−	1608.77i	0.295837	−	0.0868656i
$701$	20390.0	−	23531.4i	1.09860	−	1.26786i	0.137850	−	0.990453i	$-0.455981\pi$
$701$	20390.0	−	23531.4i	1.09860	−	1.26786i	0.960754	−	0.277403i	$-0.0894738\pi$
$702$		0			0
$703$	−11595.8	+	3404.84i	−0.622111	+	0.182668i
$704$	−4253.05	−	9312.87i	−0.227688	−	0.498568i
$705$		0			0
$706$	−11603.3	−	3407.03i	−0.618548	−	0.181622i
$707$	−3533.17	−	24573.7i	−0.187947	−	1.30720i
$708$		0			0
$709$	1678.15	−	11671.8i	0.0888915	−	0.618254i	−0.895866	−	0.444324i	$-0.853444\pi$
$709$	1678.15	−	11671.8i	0.0888915	−	0.618254i	0.984758	−	0.173931i	$-0.0556468\pi$
$710$	27220.9	+	17493.8i	1.43885	+	0.924690i
$711$		0			0
$712$	−23298.6			−1.22634
$713$	23307.0	−	16841.0i	1.22420	−	0.884571i
$714$		0			0
$715$	16013.8	+	18480.9i	0.837598	+	0.966640i
$716$	−7911.11	−	5084.16i	−0.412922	−	0.265369i
$717$		0			0
$718$	−4596.11	+	10064.1i	−0.238893	+	0.523103i
$719$	4361.77	+	30336.8i	0.226240	+	1.57353i	0.713739	+	0.700411i	$0.247000\pi$
$719$	4361.77	+	30336.8i	0.226240	+	1.57353i	−0.487499	+	0.873123i	$0.662091\pi$
$720$		0			0
$721$	8335.99	−	5357.21i	0.430580	−	0.276717i
$722$	1885.60	+	4128.90i	0.0971951	+	0.212828i
$723$		0			0
$724$	1397.80	−	1613.14i	0.0717523	−	0.0828065i
$725$	4628.50	−	5341.58i	0.237101	−	0.273629i
$726$		0			0
$727$	6279.58	+	13750.4i	0.320353	+	0.701476i	0.999470	−	0.0325547i	$-0.0103643\pi$
$727$	6279.58	+	13750.4i	0.320353	+	0.701476i	−0.679117	+	0.734030i	$0.737637\pi$
$728$	47647.3	−	30621.0i	2.42572	−	1.55892i
$729$		0			0
$730$	1637.91	+	11391.9i	0.0830437	+	0.577582i
$731$	117.438	−	257.154i	0.00594201	−	0.0130112i
$732$		0			0
$733$	14.7481	+	9.47804i	0.000743157	+	0.000477598i	0.541012	−	0.841015i	$-0.318041\pi$
$733$	14.7481	+	9.47804i	0.000743157	+	0.000477598i	−0.540269	+	0.841492i	$0.681678\pi$
$734$	−3876.43	−	4473.64i	−0.194934	−	0.224966i
$735$		0			0
$736$	5098.46	+	9723.92i	0.255342	+	0.486995i
$737$	−5636.84			−0.281731
$738$		0			0
$739$	3958.52	+	2543.99i	0.197045	+	0.126633i	0.635443	−	0.772148i	$-0.280818\pi$
$739$	3958.52	+	2543.99i	0.197045	+	0.126633i	−0.438398	+	0.898781i	$0.644454\pi$
$740$	−624.889	+	4346.20i	−0.0310424	+	0.215905i
$741$		0			0
$742$	−4251.01	−	29566.4i	−0.210323	−	1.46283i
$743$	23181.2	+	6806.62i	1.14460	+	0.336084i	0.798430	−	0.602088i	$-0.205664\pi$
$743$	23181.2	+	6806.62i	1.14460	+	0.336084i	0.346168	+	0.938172i	$0.387483\pi$
$744$		0			0
$745$	6736.34	+	14750.5i	0.331276	+	0.725393i
$746$	−14535.4	+	4267.97i	−0.713375	+	0.209466i
$747$		0			0
$748$	−16.2702	+	18.7768i	−0.000795317	+	0.000917844i
$749$	−11363.3	+	3336.58i	−0.554349	+	0.162772i
$750$		0			0
$751$	12083.3	−	7765.48i	0.587119	−	0.377319i	−0.213096	−	0.977031i	$-0.568355\pi$
$751$	12083.3	−	7765.48i	0.587119	−	0.377319i	0.800216	+	0.599712i	$0.204718\pi$
$752$	−7564.78	−	2221.22i	−0.366834	−	0.107712i
$753$		0			0
$754$	6451.32	−	14126.4i	0.311596	−	0.682299i
$755$	537.639	−	3739.36i	0.0259162	−	0.180251i
$756$		0			0
$757$	−15247.1	−	17596.1i	−0.732057	−	0.844839i	0.260645	−	0.965435i	$-0.416065\pi$
$757$	−15247.1	−	17596.1i	−0.732057	−	0.844839i	−0.992702	+	0.120596i	$0.961519\pi$
$758$	−31268.4			−1.49831
$759$		0			0
$760$	34357.7			1.63985
$761$	−7041.96	−	8126.85i	−0.335441	−	0.387120i	0.562822	−	0.826578i	$-0.309716\pi$
$761$	−7041.96	−	8126.85i	−0.335441	−	0.387120i	−0.898263	+	0.439459i	$0.855170\pi$
$762$		0			0
$763$	−1873.08	+	13027.5i	−0.0888729	+	0.618124i
$764$	4722.91	−	10341.7i	0.223650	−	0.489726i
$765$		0			0
$766$	18358.0	+	5390.40i	0.865930	+	0.254260i
$767$	10528.9	−	6766.51i	0.495667	−	0.318546i
$768$		0			0
$769$	23472.5	−	6892.16i	1.10070	−	0.323196i	0.319572	−	0.947562i	$-0.396461\pi$
$769$	23472.5	−	6892.16i	1.10070	−	0.323196i	0.781132	+	0.624366i	$0.214643\pi$
$770$	−10886.7	+	12563.9i	−0.509519	+	0.588017i
$771$		0			0
$772$	5552.31	−	1630.31i	0.258850	−	0.0760051i
$773$	14355.7	+	31434.6i	0.667968	+	1.46265i	0.874907	+	0.484291i	$0.160923\pi$
$773$	14355.7	+	31434.6i	0.667968	+	1.46265i	−0.206939	+	0.978354i	$0.566350\pi$
$774$		0			0
$775$	−24521.5	−	7200.17i	−1.13657	−	0.333726i
$776$	−4302.02	−	29921.2i	−0.199012	−	1.38416i
$777$		0			0
$778$	901.730	−	6271.67i	0.0415535	−	0.289011i
$779$	17733.0	+	11396.3i	0.815599	+	0.524154i
$780$		0			0
$781$	16469.5			0.754579
$782$	−97.0350	+	125.162i	−0.00443729	+	0.00572351i
$783$		0			0
$784$	8286.96	+	9563.66i	0.377504	+	0.435662i
$785$	1317.70	+	846.832i	0.0599116	+	0.0385028i
$786$		0			0
$787$	1469.09	−	3216.86i	0.0665406	−	0.145704i	−0.873440	−	0.486932i	$-0.838116\pi$
$787$	1469.09	−	3216.86i	0.0665406	−	0.145704i	0.939980	+	0.341229i	$0.110843\pi$
$788$	769.748	+	5353.71i	0.0347984	+	0.242028i
$789$		0			0
$790$	29390.9	−	18888.4i	1.32365	−	0.850656i
$791$	−13066.5	−	28611.7i	−0.587348	−	1.28611i
$792$		0			0
$793$	−22256.3	+	25685.2i	−0.996653	+	1.15020i
$794$	20545.3	−	23710.6i	0.918295	−	1.05977i
$795$		0			0
$796$	2013.79	+	4409.59i	0.0896695	+	0.196349i
$797$	22486.0	−	14450.9i	0.999368	−	0.642255i	0.0647479	−	0.997902i	$-0.479376\pi$
$797$	22486.0	−	14450.9i	0.999368	−	0.642255i	0.934621	+	0.355647i	$0.115739\pi$
$798$		0			0
$799$	16.5833	+	115.339i	0.000734260	+	0.00510689i
$800$	4053.79	−	8876.56i	0.179154	−	0.392292i
$801$		0			0
$802$	8572.83	+	5509.43i	0.377453	+	0.242574i
$803$	3836.15	+	4427.16i	0.168586	+	0.194559i
$804$		0			0
$805$	25824.8	−	33310.4i	1.13069	−	1.45843i
$806$	−56154.0			−2.45402
$807$		0			0
$808$	−20068.5	−	12897.2i	−0.873770	−	0.561538i
$809$	−5060.26	+	35194.9i	−0.219913	+	1.52953i	0.518442	+	0.855113i	$0.326512\pi$
$809$	−5060.26	+	35194.9i	−0.219913	+	1.52953i	−0.738355	+	0.674413i	$0.764397\pi$
$810$		0			0
$811$	−5286.17	−	36766.1i	−0.228881	−	1.59190i	−0.702834	−	0.711354i	$-0.748082\pi$
$811$	−5286.17	−	36766.1i	−0.228881	−	1.59190i	0.473953	−	0.880550i	$-0.342827\pi$
$812$	−4029.15	−	1183.07i	−0.174132	−	0.0511299i
$813$		0			0
$814$	−2334.20	−	5111.18i	−0.100508	−	0.220082i
$815$	20648.4	−	6062.92i	0.887462	−	0.260582i
$816$		0			0
$817$	−28865.9	+	33313.0i	−1.23609	+	1.42653i
$818$	14202.8	−	4170.31i	0.607076	−	0.178254i
$819$		0			0
$820$	6442.83	−	4140.56i	0.274382	−	0.176335i
$821$	−18341.8	−	5385.65i	−0.779701	−	0.228941i	−0.132422	−	0.991193i	$-0.542275\pi$
$821$	−18341.8	−	5385.65i	−0.779701	−	0.228941i	−0.647280	+	0.762253i	$0.724093\pi$
$822$		0			0
$823$	−2916.75	+	6386.78i	−0.123538	+	0.270509i	−0.961289	−	0.275542i	$-0.911143\pi$
$823$	−2916.75	+	6386.78i	−0.123538	+	0.270509i	0.837751	+	0.546052i	$0.183870\pi$
$824$	1355.04	−	9424.54i	0.0572879	−	0.398446i
$825$		0			0
$826$	5571.95	+	6430.37i	0.234713	+	0.270873i
$827$	31410.3			1.32073			0.660365	−	0.750944i	$-0.270401\pi$
$827$	31410.3			1.32073			0.660365	+	0.750944i	$0.270401\pi$
$828$		0			0
$829$	14068.0			0.589389			0.294695	−	0.955592i	$-0.404782\pi$
$829$	14068.0			0.589389			0.294695	+	0.955592i	$0.404782\pi$
$830$	−24673.8	−	28475.1i	−1.03186	−	1.19083i
$831$		0			0
$832$	7213.98	−	50174.3i	0.300601	−	2.09072i
$833$	77.6952	−	170.129i	0.00323167	−	0.00707636i
$834$		0			0
$835$	17387.2	+	5105.35i	0.720611	+	0.211590i
$836$	3258.96	−	2094.41i	0.134825	−	0.0866466i
$837$		0			0
$838$	15911.4	−	4672.01i	0.655907	−	0.192592i
$839$	−10082.0	+	11635.3i	−0.414863	+	0.478777i	−0.924265	−	0.381751i	$-0.875321\pi$
$839$	−10082.0	+	11635.3i	−0.414863	+	0.478777i	0.509402	+	0.860528i	$0.329867\pi$
$840$		0			0
$841$	18414.0	−	5406.83i	0.755012	−	0.221691i
$842$	7605.12	+	16652.9i	0.311271	+	0.681588i
$843$		0			0
$844$	−7113.27	−	2088.64i	−0.290105	−	0.0851825i
$845$	12561.2	+	87365.2i	0.511384	+	3.55675i
$846$		0			0
$847$	3642.32	−	25332.9i	0.147759	−	1.02768i
$848$	−16669.5	−	10712.8i	−0.675037	−	0.433820i
$849$		0			0
$850$	140.758			0.00567994
$851$	6615.28	+	12616.8i	0.266473	+	0.508225i
$852$		0			0
$853$	−10122.8	−	11682.3i	−0.406327	−	0.468926i	0.515296	−	0.857012i	$-0.327682\pi$
$853$	−10122.8	−	11682.3i	−0.406327	−	0.468926i	−0.921623	+	0.388086i	$0.873136\pi$
$854$	−19437.2	−	12491.5i	−0.778837	−	0.500528i
$855$		0			0
$856$	−4727.37	+	10351.5i	−0.188760	+	0.413326i
$857$	−4882.18	−	33956.3i	−0.194600	−	1.35347i	−0.819640	−	0.572880i	$-0.805826\pi$
$857$	−4882.18	−	33956.3i	−0.194600	−	1.35347i	0.625040	−	0.780593i	$-0.285083\pi$
$858$		0			0
$859$	−25424.6	+	16339.4i	−1.00987	+	0.649001i	−0.937358	−	0.348366i	$-0.886737\pi$
$859$	−25424.6	+	16339.4i	−1.00987	+	0.649001i	−0.0725076	+	0.997368i	$0.523100\pi$
$860$	6652.91	+	14567.8i	0.263793	+	0.577627i
$861$		0			0
$862$	1426.58	−	1646.36i	0.0563684	−	0.0650526i
$863$	−12366.4	+	14271.6i	−0.487783	+	0.562932i	−0.945272	−	0.326283i	$-0.894204\pi$
$863$	−12366.4	+	14271.6i	−0.487783	+	0.562932i	0.457489	+	0.889216i	$0.348749\pi$
$864$		0			0
$865$	5990.44	+	13117.2i	0.235470	+	0.515606i
$866$	−20627.7	+	13256.6i	−0.809421	+	0.520183i
$867$		0			0
$868$	2160.91	+	15029.4i	0.0844999	+	0.587710i
$869$	7387.10	−	16175.5i	0.288366	−	0.631434i
$870$		0			0
$871$	−23478.4	−	15088.7i	−0.913360	−	0.586981i
$872$	8281.86	+	9557.78i	0.321628	+	0.371178i
$873$		0			0
$874$	20015.2	−	14462.4i	0.774628	−	0.559724i
$875$	10303.0			0.398063
$876$		0			0
$877$	8287.49	+	5326.05i	0.319098	+	0.205072i	0.690377	−	0.723449i	$-0.257445\pi$
$877$	8287.49	+	5326.05i	0.319098	+	0.205072i	−0.371280	+	0.928521i	$0.621081\pi$
$878$	−4114.04	+	28613.8i	−0.158135	+	1.09985i
$879$		0			0
$880$	1569.46	+	10915.8i	0.0601210	+	0.418151i
$881$	−14063.4	−	4129.40i	−0.537808	−	0.157915i	0.00153795	−	0.999999i	$-0.499510\pi$
$881$	−14063.4	−	4129.40i	−0.537808	−	0.157915i	−0.539346	+	0.842084i	$0.681329\pi$
$882$		0			0
$883$	13440.8	+	29431.4i	0.512254	+	1.12168i	0.972290	+	0.233780i	$0.0751095\pi$
$883$	13440.8	+	29431.4i	0.512254	+	1.12168i	−0.460035	+	0.887901i	$0.652163\pi$
$884$	−118.030	+	34.6567i	−0.00449070	+	0.00131859i
$885$		0			0
$886$	17039.4	−	19664.5i	0.646106	−	0.745646i
$887$	−19507.8	+	5728.00i	−0.738452	+	0.216829i	−0.629264	−	0.777192i	$-0.716643\pi$
$887$	−19507.8	+	5728.00i	−0.738452	+	0.216829i	−0.109189	+	0.994021i	$0.534825\pi$
$888$		0			0
$889$	925.696	−	594.909i	0.0349233	−	0.0224439i
$890$	32487.4	+	9539.17i	1.22357	+	0.359274i
$891$		0			0
$892$	1802.96	−	3947.93i	0.0676766	−	0.148191i
$893$	2585.70	−	17984.0i	0.0968950	−	0.673919i
$894$		0			0
$895$	40400.0	+	46624.1i	1.50885	+	1.74131i
$896$	14086.6			0.525222
$897$		0			0
$898$	−25096.1			−0.932592
$899$	12307.5	+	14203.6i	0.456593	+	0.526936i
$900$		0			0
$901$	−41.6783	+	289.879i	−0.00154107	+	0.0107184i
$902$	−4071.31	+	8914.93i	−0.150288	+	0.329085i
$903$		0			0
$904$	−28999.7	−	8515.07i	−1.06694	−	0.313282i
$905$	−11780.0	+	7570.52i	−0.432684	+	0.278069i
$906$		0			0
$907$	9614.15	−	2822.97i	0.351965	−	0.103346i	−0.100971	−	0.994889i	$-0.532195\pi$
$907$	9614.15	−	2822.97i	0.351965	−	0.103346i	0.452936	+	0.891543i	$0.350377\pi$
$908$	−1433.00	+	1653.77i	−0.0523743	+	0.0604432i
$909$		0			0
$910$	−78976.2	+	23189.5i	−2.87696	+	0.844752i
$911$	4300.59	+	9416.98i	0.156405	+	0.342479i	0.971571	−	0.236748i	$-0.0760816\pi$
$911$	4300.59	+	9416.98i	0.156405	+	0.342479i	−0.815166	+	0.579227i	$0.803354\pi$
$912$		0			0
$913$	−18400.7	−	5402.95i	−0.667005	−	0.195850i
$914$	6489.52	+	45135.6i	0.234851	+	1.63343i
$915$		0			0
$916$	−843.848	+	5869.09i	−0.0304383	+	0.211703i
$917$	−28755.0	−	18479.7i	−1.03552	−	0.665489i
$918$		0			0
$919$	−6733.25			−0.241686			−0.120843	−	0.992672i	$-0.538560\pi$
$919$	−6733.25			−0.241686			−0.120843	+	0.992672i	$0.538560\pi$
$920$	−7939.55	−	39714.2i	−0.284521	−	1.42320i
$921$		0			0
$922$	19627.4	+	22651.3i	0.701079	+	0.809088i
$923$	68598.5	+	44085.6i	2.44631	+	1.57215i
$924$		0			0
$925$	5259.81	−	11517.4i	0.186964	−	0.409393i
$926$	−4997.80	−	34760.5i	−0.177363	−	1.23359i
$927$		0			0
$928$	−6036.98	+	3879.73i	−0.213549	+	0.137240i
$929$	−18544.0	−	40605.7i	−0.654907	−	1.43405i	−0.887193	−	0.461399i	$-0.847348\pi$
$929$	−18544.0	−	40605.7i	−0.654907	−	1.43405i	0.232286	−	0.972648i	$-0.425379\pi$
$930$		0			0
$931$	−19097.2	+	22039.3i	−0.672271	+	0.775843i
$932$	−5299.92	+	6116.44i	−0.186271	+	0.214968i
$933$		0			0
$934$	−7677.02	−	16810.3i	−0.268951	−	0.588920i
$935$	137.117	−	88.1200i	0.00479596	−	0.00308217i
$936$		0			0
$937$	4725.21	+	32864.5i	0.164745	+	1.14582i	0.889539	+	0.456859i	$0.151026\pi$
$937$	4725.21	+	32864.5i	0.164745	+	1.14582i	−0.724794	+	0.688966i	$0.758065\pi$
$938$	7881.82	−	17258.8i	0.274361	−	0.600767i
$939$		0			0
$940$	−5553.27	−	3568.87i	−0.192689	−	0.123834i
$941$	5836.32	+	6735.48i	0.202188	+	0.233337i	0.847784	−	0.530342i	$-0.177936\pi$
$941$	5836.32	+	6735.48i	0.202188	+	0.233337i	−0.645596	+	0.763679i	$0.723391\pi$
$942$		0			0
$943$	9075.22	−	23131.2i	0.313393	−	0.798786i
$944$	5644.31			0.194604
$945$		0			0
$946$	−17240.9	−	11080.0i	−0.592546	−	0.380806i
$947$	−529.216	+	3680.78i	−0.0181597	+	0.126303i	−0.996885	−	0.0788732i	$-0.974868\pi$
$947$	−529.216	+	3680.78i	−0.0181597	+	0.126303i	0.978725	+	0.205177i	$0.0657769\pi$
$948$		0			0
$949$	4127.66	+	28708.5i	0.141190	+	0.982000i
$950$	−21058.2	−	6183.26i	−0.719179	−	0.211170i
$951$		0			0
$952$	−156.824	−	343.397i	−0.00533897	−	0.0116907i
$953$	−48515.1	+	14245.3i	−1.64906	+	0.484209i	−0.968611	−	0.248582i	$-0.920035\pi$
$953$	−48515.1	+	14245.3i	−1.64906	+	0.484209i	−0.680453	+	0.732791i	$0.738217\pi$
$954$		0			0
$955$	−48842.6	+	56367.4i	−1.65498	+	1.90995i
$956$	6196.50	−	1819.46i	0.209633	−	0.0615538i
$957$		0			0
$958$	4281.12	−	2751.31i	0.144381	−	0.0927878i
$959$	6980.37	+	2049.62i	0.235045	+	0.0690153i
$960$		0			0
$961$	15854.7	−	34717.0i	0.532198	−	1.16535i
$962$	3959.25	−	27537.2i	0.132694	−	0.922904i
$963$		0			0
$964$	3756.25	+	4334.94i	0.125498	+	0.144833i
$965$	−37962.4			−1.26638
$966$		0			0
$967$	−23535.5			−0.782678			−0.391339	−	0.920247i	$-0.627988\pi$
$967$	−23535.5			−0.782678			−0.391339	+	0.920247i	$0.627988\pi$
$968$	−16104.6	−	18585.7i	−0.534733	−	0.617114i
$969$		0			0
$970$	−6251.95	+	43483.3i	−0.206946	+	1.43934i
$971$	1253.95	−	2745.76i	0.0414429	−	0.0907474i	−0.887778	−	0.460272i	$-0.847752\pi$
$971$	1253.95	−	2745.76i	0.0414429	−	0.0907474i	0.929221	+	0.369524i	$0.120479\pi$
$972$		0			0
$973$	−33225.1	−	9755.77i	−1.09470	−	0.321434i
$974$	6665.96	−	4283.95i	0.219293	−	0.140931i
$975$		0			0
$976$	−14706.2	+	4318.13i	−0.482310	+	0.141619i
$977$	26353.1	−	30413.1i	0.862958	−	0.995907i	−0.137027	−	0.990567i	$-0.543755\pi$
$977$	26353.1	−	30413.1i	0.862958	−	0.995907i	0.999986	−	0.00533978i	$-0.00169971\pi$
$978$		0			0
$979$	16535.7	−	4855.31i	0.539818	−	0.158505i
$980$	4401.45	+	9637.84i	0.143469	+	0.314153i
$981$		0			0
$982$	32604.4	+	9573.50i	1.05952	+	0.311103i
$983$	−4970.48	−	34570.5i	−0.161275	−	1.12170i	−0.896233	−	0.443583i	$-0.853707\pi$
$983$	−4970.48	−	34570.5i	−0.161275	−	1.12170i	0.734958	−	0.678113i	$-0.237202\pi$
$984$		0			0
$985$	5049.76	−	35121.8i	0.163349	−	1.13612i
$986$	−87.0789	−	55.9622i	−0.00281253	−	0.00180751i
$987$		0			0
$988$	19180.4			0.617623
$989$	45177.1	+	25668.0i	1.45253	+	0.825274i
$990$		0			0
$991$	−3772.73	−	4353.97i	−0.120933	−	0.139564i	0.692054	−	0.721845i	$-0.256706\pi$
$991$	−3772.73	−	4353.97i	−0.120933	−	0.139564i	−0.812988	+	0.582281i	$0.802160\pi$
$992$	21829.0	+	14028.6i	0.698661	+	0.449002i
$993$		0			0
$994$	−23028.8	+	50426.1i	−0.734839	+	1.60907i
$995$	−4525.90	−	31478.3i	−0.144202	−	1.00294i
$996$		0			0
$997$	8457.92	−	5435.57i	0.268671	−	0.172664i	−0.399368	−	0.916791i	$-0.630770\pi$
$997$	8457.92	−	5435.57i	0.268671	−	0.172664i	0.668039	+	0.744126i	$0.267134\pi$
$998$	18930.6	+	41452.2i	0.600438	+	1.31477i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.4.i.b.82.2		60
3.2	odd	2		69.4.e.b.13.5	✓	60
23.16	even	11	inner	207.4.i.b.154.2		60
69.50	odd	22		1587.4.a.w.1.9		30
69.62	odd	22		69.4.e.b.16.5	yes	60
69.65	even	22		1587.4.a.v.1.9		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.4.e.b.13.5	✓	60	3.2	odd	2
69.4.e.b.16.5	yes	60	69.62	odd	22
207.4.i.b.82.2		60	1.1	even	1	trivial
207.4.i.b.154.2		60	23.16	even	11	inner
1587.4.a.v.1.9		30	69.65	even	22
1587.4.a.w.1.9		30	69.50	odd	22

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	207.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.56668 - 1.80804i) q^{2} +(0.323978 - 2.25332i) q^{4} +(-6.20398 + 13.5848i) q^{5} +(-24.5496 - 7.20842i) q^{7} +(-20.6825 + 13.2918i) q^{8} +O(q^{10})\)	\(q+(-1.56668 - 1.80804i) q^{2} +(0.323978 - 2.25332i) q^{4} +(-6.20398 + 13.5848i) q^{5} +(-24.5496 - 7.20842i) q^{7} +(-20.6825 + 13.2918i) q^{8} +(34.2816 - 10.0660i) q^{10} +(11.9090 - 13.7437i) q^{11} +(86.3921 - 25.3670i) q^{13} +(25.4282 + 55.6801i) q^{14} +(38.9608 + 11.4399i) q^{16} +(-0.0854087 - 0.594031i) q^{17} +(-13.3171 + 92.6227i) q^{19} +(28.6010 + 18.3807i) q^{20} -43.5068 q^{22} +(110.140 - 6.01038i) q^{23} +(-64.2004 - 74.0912i) q^{25} +(-181.213 - 116.459i) q^{26} +(-24.1964 + 52.9828i) q^{28} +(10.2601 + 71.3608i) q^{29} +(219.303 - 140.937i) q^{31} +(41.3497 + 90.5432i) q^{32} +(-0.940226 + 1.08508i) q^{34} +(250.230 - 288.781i) q^{35} +(53.6514 + 117.480i) q^{37} +(188.330 - 121.032i) q^{38} +(-52.2534 - 363.430i) q^{40} +(93.5789 - 204.909i) q^{41} +(396.280 + 254.674i) q^{43} +(-27.1107 - 31.2874i) q^{44} +(-183.421 - 189.722i) q^{46} -194.164 q^{47} +(262.172 + 168.488i) q^{49} +(-33.3788 + 232.154i) q^{50} +(-29.1708 - 202.887i) q^{52} +(-468.220 - 137.482i) q^{53} +(112.823 + 247.047i) q^{55} +(603.560 - 177.221i) q^{56} +(112.949 - 130.350i) q^{58} +(133.372 - 39.1616i) q^{59} +(-317.541 + 204.071i) q^{61} +(-598.398 - 175.705i) q^{62} +(233.870 - 512.104i) q^{64} +(-191.369 + 1331.00i) q^{65} +(-202.983 - 234.255i) q^{67} -1.36621 q^{68} -914.160 q^{70} +(593.068 + 684.437i) q^{71} +(-45.8429 + 318.844i) q^{73} +(128.355 - 281.058i) q^{74} +(204.394 + 60.0155i) q^{76} +(-391.431 + 251.557i) q^{77} +(938.227 - 275.488i) q^{79} +(-397.122 + 458.303i) q^{80} +(-517.093 + 151.832i) q^{82} +(-438.077 - 959.255i) q^{83} +(8.59968 + 2.52509i) q^{85} +(-160.382 - 1115.48i) q^{86} +(-63.6285 + 442.546i) q^{88} +(797.225 + 512.346i) q^{89} -2303.75 q^{91} +(22.1398 - 250.128i) q^{92} +(304.192 + 351.056i) q^{94} +(-1175.64 - 755.540i) q^{95} +(-510.773 + 1118.44i) q^{97} +(-106.106 - 737.985i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 4 q^{2} - 28 q^{4} + 6 q^{5} - 4 q^{7} + 52 q^{8}+O(q^{10}) \) 60 * q - 4 * q^2 - 28 * q^4 + 6 * q^5 - 4 * q^7 + 52 * q^8	\( 60 q - 4 q^{2} - 28 q^{4} + 6 q^{5} - 4 q^{7} + 52 q^{8} - 78 q^{10} - 10 q^{11} + 50 q^{13} + 224 q^{14} + 260 q^{16} + 662 q^{17} - 4 q^{19} + 735 q^{20} + 622 q^{22} + 438 q^{23} - 754 q^{25} + 40 q^{26} + 672 q^{28} - 1302 q^{29} + 1528 q^{31} - 1588 q^{32} + 29 q^{34} - 950 q^{35} + 316 q^{37} - 3122 q^{38} - 1939 q^{40} + 1500 q^{41} - 1316 q^{43} + 2901 q^{44} - 1980 q^{46} + 1440 q^{47} - 2310 q^{49} - 195 q^{50} + 6189 q^{52} + 148 q^{53} - 606 q^{55} + 432 q^{56} - 2623 q^{58} - 5264 q^{59} + 1482 q^{61} + 2299 q^{62} - 6780 q^{64} + 1446 q^{65} + 388 q^{67} - 5604 q^{68} + 2984 q^{70} + 3316 q^{71} + 2072 q^{73} + 6556 q^{74} + 9841 q^{76} - 9338 q^{77} + 268 q^{79} - 7980 q^{80} + 7742 q^{82} + 3494 q^{83} - 3842 q^{85} + 4792 q^{86} - 7960 q^{88} + 2754 q^{89} - 5436 q^{91} + 17609 q^{92} - 10961 q^{94} + 2396 q^{95} - 5654 q^{97} - 14411 q^{98}+O(q^{100}) \) 60 * q - 4 * q^2 - 28 * q^4 + 6 * q^5 - 4 * q^7 + 52 * q^8 - 78 * q^10 - 10 * q^11 + 50 * q^13 + 224 * q^14 + 260 * q^16 + 662 * q^17 - 4 * q^19 + 735 * q^20 + 622 * q^22 + 438 * q^23 - 754 * q^25 + 40 * q^26 + 672 * q^28 - 1302 * q^29 + 1528 * q^31 - 1588 * q^32 + 29 * q^34 - 950 * q^35 + 316 * q^37 - 3122 * q^38 - 1939 * q^40 + 1500 * q^41 - 1316 * q^43 + 2901 * q^44 - 1980 * q^46 + 1440 * q^47 - 2310 * q^49 - 195 * q^50 + 6189 * q^52 + 148 * q^53 - 606 * q^55 + 432 * q^56 - 2623 * q^58 - 5264 * q^59 + 1482 * q^61 + 2299 * q^62 - 6780 * q^64 + 1446 * q^65 + 388 * q^67 - 5604 * q^68 + 2984 * q^70 + 3316 * q^71 + 2072 * q^73 + 6556 * q^74 + 9841 * q^76 - 9338 * q^77 + 268 * q^79 - 7980 * q^80 + 7742 * q^82 + 3494 * q^83 - 3842 * q^85 + 4792 * q^86 - 7960 * q^88 + 2754 * q^89 - 5436 * q^91 + 17609 * q^92 - 10961 * q^94 + 2396 * q^95 - 5654 * q^97 - 14411 * q^98

Introduction

L-functions

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