LMFDB - Embedded newform 312.4.m.a.181.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [312,4,Mod(181,312)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(312, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("312.181");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	312.m (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:	$18.4085959218$
Analytic rank:	$0$
Dimension:	$84$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.27
Character	$\chi$	$=$	312.181
Dual form			312.4.m.a.181.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.61542 - 2.32173i) q^{2} -3.00000i q^{3} +(-2.78086 + 7.50112i) q^{4} +1.96149 q^{5} +(-6.96519 + 4.84625i) q^{6} -7.12715i q^{7} +(21.9078 - 5.66102i) q^{8} -9.00000 q^{9} +(-3.16863 - 4.55406i) q^{10} -39.6233 q^{11} +(22.5034 + 8.34259i) q^{12} +(14.7839 + 44.4796i) q^{13} +(-16.5473 + 11.5133i) q^{14} -5.88448i q^{15} +(-48.5336 - 41.7192i) q^{16} -20.3979 q^{17} +(14.5387 + 20.8956i) q^{18} +78.7892 q^{19} +(-5.45464 + 14.7134i) q^{20} -21.3814 q^{21} +(64.0081 + 91.9946i) q^{22} -108.309 q^{23} +(-16.9831 - 65.7235i) q^{24} -121.153 q^{25} +(79.3875 - 106.177i) q^{26} +27.0000i q^{27} +(53.4616 + 19.8196i) q^{28} +306.234i q^{29} +(-13.6622 + 9.50588i) q^{30} +122.283i q^{31} +(-18.4587 + 180.076i) q^{32} +118.870i q^{33} +(32.9512 + 47.3585i) q^{34} -13.9798i q^{35} +(25.0278 - 67.5101i) q^{36} +238.381 q^{37} +(-127.277 - 182.927i) q^{38} +(133.439 - 44.3517i) q^{39} +(42.9720 - 11.1040i) q^{40} +113.600i q^{41} +(34.5399 + 49.6419i) q^{42} +443.229i q^{43} +(110.187 - 297.219i) q^{44} -17.6534 q^{45} +(174.964 + 251.464i) q^{46} -435.239i q^{47} +(-125.157 + 145.601i) q^{48} +292.204 q^{49} +(195.712 + 281.284i) q^{50} +61.1938i q^{51} +(-374.759 - 12.7958i) q^{52} -496.774i q^{53} +(62.6867 - 43.6162i) q^{54} -77.7208 q^{55} +(-40.3469 - 156.140i) q^{56} -236.368i q^{57} +(710.993 - 494.696i) q^{58} +868.043 q^{59} +(44.1402 + 16.3639i) q^{60} +355.574i q^{61} +(283.909 - 197.538i) q^{62} +64.1443i q^{63} +(447.906 - 248.041i) q^{64} +(28.9985 + 87.2464i) q^{65} +(275.984 - 192.024i) q^{66} -792.201 q^{67} +(56.7239 - 153.007i) q^{68} +324.927i q^{69} +(-32.4574 + 22.5833i) q^{70} -208.138i q^{71} +(-197.170 + 50.9492i) q^{72} +1075.25i q^{73} +(-385.085 - 553.457i) q^{74} +363.458i q^{75} +(-219.102 + 591.007i) q^{76} +282.401i q^{77} +(-318.532 - 238.163i) q^{78} +1229.23 q^{79} +(-95.1983 - 81.8318i) q^{80} +81.0000 q^{81} +(263.749 - 183.511i) q^{82} -701.173 q^{83} +(59.4588 - 160.385i) q^{84} -40.0104 q^{85} +(1029.06 - 715.999i) q^{86} +918.703 q^{87} +(-868.061 + 224.308i) q^{88} +14.2857i q^{89} +(28.5176 + 40.9865i) q^{90} +(317.013 - 105.367i) q^{91} +(301.192 - 812.438i) q^{92} +366.850 q^{93} +(-1010.51 + 703.092i) q^{94} +154.544 q^{95} +(540.227 + 55.3760i) q^{96} +1169.53i q^{97} +(-472.031 - 678.418i) q^{98} +356.610 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52}+ \cdots + 2480 q^{95}+O(q^{100}) $ 84 * q - 756 * q^9 - 36 * q^10 + 12 * q^12 - 208 * q^14 - 148 * q^16 - 104 * q^17 + 620 * q^22 + 2188 * q^25 + 444 * q^26 - 204 * q^30 - 40 * q^38 - 1924 * q^40 + 192 * q^42 + 624 * q^48 - 3396 * q^49 - 1292 * q^52 - 1616 * q^55 + 608 * q^56 - 2120 * q^62 - 2856 * q^64 + 696 * q^65 - 396 * q^66 - 2536 * q^68 - 3936 * q^74 - 156 * q^78 + 3160 * q^79 + 6804 * q^81 + 4276 * q^82 - 2088 * q^87 + 1780 * q^88 + 324 * q^90 + 4792 * q^92 - 860 * q^94 + 2480 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$1$	$-1$	$-1$	$1$

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 $

$2$	−1.61542	−	2.32173i	−0.571136	−	0.820856i
$2$	−1.61542	−	2.32173i	−0.571136	−	0.820856i
$3$		−	3.00000i		−	0.577350i
$3$		−	3.00000i		−	0.577350i
$4$	−2.78086	+	7.50112i	−0.347608	+	0.937640i
$5$	1.96149			0.175441			0.0877206	−	0.996145i	$-0.472042\pi$
$5$	1.96149			0.175441			0.0877206	+	0.996145i	$0.472042\pi$
$6$	−6.96519	+	4.84625i	−0.473921	+	0.329745i
$7$		−	7.12715i		−	0.384830i	−0.981314	−	0.192415i	$-0.938368\pi$
$7$		−	7.12715i		−	0.384830i	0.981314	−	0.192415i	$-0.0616319\pi$
$8$	21.9078	−	5.66102i	0.968198	−	0.250184i
$9$	−9.00000			−0.333333
$10$	−3.16863	−	4.55406i	−0.100201	−	0.144012i
$11$	−39.6233			−1.08608			−0.543040	−	0.839707i	$-0.682727\pi$
$11$	−39.6233			−1.08608			−0.543040	+	0.839707i	$0.682727\pi$
$12$	22.5034	+	8.34259i	0.541347	+	0.200691i
$13$	14.7839	+	44.4796i	0.315409	+	0.948956i
$13$	14.7839	+	44.4796i	0.315409	+	0.948956i
$14$	−16.5473	+	11.5133i	−0.315890	+	0.219790i
$15$		−	5.88448i		−	0.101291i
$16$	−48.5336	−	41.7192i	−0.758338	−	0.651862i
$17$	−20.3979			−0.291013			−0.145507	−	0.989357i	$-0.546481\pi$
$17$	−20.3979			−0.291013			−0.145507	+	0.989357i	$0.546481\pi$
$18$	14.5387	+	20.8956i	0.190379	+	0.273619i
$19$	78.7892			0.951341			0.475671	−	0.879623i	$-0.342205\pi$
$19$	78.7892			0.951341			0.475671	+	0.879623i	$0.342205\pi$
$20$	−5.45464	+	14.7134i	−0.0609847	+	0.164501i
$21$	−21.3814			−0.222182
$22$	64.0081	+	91.9946i	0.620299	+	0.891515i
$23$	−108.309			−0.981912			−0.490956	−	0.871184i	$-0.663352\pi$
$23$	−108.309			−0.981912			−0.490956	+	0.871184i	$0.663352\pi$
$24$	−16.9831	−	65.7235i	−0.144444	−	0.558990i
$25$	−121.153			−0.969220
$26$	79.3875	−	106.177i	0.598814	−	0.800888i
$27$			27.0000i			0.192450i
$28$	53.4616	+	19.8196i	0.360832	+	0.133770i
$29$			306.234i			1.96091i	0.196753	+	0.980453i	$0.436960\pi$
$29$			306.234i			1.96091i	−0.196753	+	0.980453i	$0.563040\pi$
$30$	−13.6622	+	9.50588i	−0.0831453	+	0.0578509i
$31$			122.283i			0.708475i	0.935156	+	0.354237i	$0.115260\pi$
$31$			122.283i			0.708475i	−0.935156	+	0.354237i	$0.884740\pi$
$32$	−18.4587	+	180.076i	−0.101971	+	0.994787i
$33$			118.870i			0.627048i
$34$	32.9512	+	47.3585i	0.166208	+	0.238880i
$35$		−	13.9798i		−	0.0675150i
$36$	25.0278	−	67.5101i	0.115869	−	0.312547i
$37$	238.381			1.05918			0.529590	−	0.848254i	$-0.322346\pi$
$37$	238.381			1.05918			0.529590	+	0.848254i	$0.322346\pi$
$38$	−127.277	−	182.927i	−0.543345	−	0.780914i
$39$	133.439	−	44.3517i	0.547880	−	0.182101i
$40$	42.9720	−	11.1040i	0.169862	−	0.0438926i
$41$			113.600i			0.432716i	0.976314	+	0.216358i	$0.0694178\pi$
$41$			113.600i			0.432716i	−0.976314	+	0.216358i	$0.930582\pi$
$42$	34.5399	+	49.6419i	0.126896	+	0.182379i
$43$			443.229i			1.57190i	0.618289	+	0.785951i	$0.287826\pi$
$43$			443.229i			1.57190i	−0.618289	+	0.785951i	$0.712174\pi$
$44$	110.187	−	297.219i	0.377530	−	1.01835i
$45$	−17.6534			−0.0584804
$46$	174.964	+	251.464i	0.560805	+	0.806008i
$47$		−	435.239i		−	1.35077i	−0.737466	−	0.675384i	$-0.763978\pi$
$47$		−	435.239i		−	1.35077i	0.737466	−	0.675384i	$-0.236022\pi$
$48$	−125.157	+	145.601i	−0.376353	+	0.437826i
$49$	292.204			0.851906
$50$	195.712	+	281.284i	0.553556	+	0.795590i
$51$			61.1938i			0.168017i
$52$	−374.759	−	12.7958i	−0.999418	−	0.0341243i
$53$		−	496.774i		−	1.28749i	−0.765238	−	0.643747i	$-0.777379\pi$
$53$		−	496.774i		−	1.28749i	0.765238	−	0.643747i	$-0.222621\pi$
$54$	62.6867	−	43.6162i	0.157974	−	0.109915i
$55$	−77.7208			−0.190543
$56$	−40.3469	−	156.140i	−0.0962783	−	0.372591i
$57$		−	236.368i		−	0.549257i
$58$	710.993	−	494.696i	1.60962	−	1.11994i
$59$	868.043			1.91542			0.957708	−	0.287741i	$-0.0929042\pi$
$59$	868.043			1.91542			0.957708	+	0.287741i	$0.0929042\pi$
$60$	44.1402	+	16.3639i	0.0949745	+	0.0352096i
$61$			355.574i			0.746338i	0.927763	+	0.373169i	$0.121729\pi$
$61$			355.574i			0.746338i	−0.927763	+	0.373169i	$0.878271\pi$
$62$	283.909	−	197.538i	0.581556	−	0.404635i
$63$			64.1443i			0.128277i
$64$	447.906	−	248.041i	0.874816	−	0.484456i
$65$	28.9985	+	87.2464i	0.0553357	+	0.166486i
$66$	275.984	−	192.024i	0.514716	−	0.358130i
$67$	−792.201			−1.44452			−0.722260	−	0.691622i	$-0.756896\pi$
$67$	−792.201			−1.44452			−0.722260	+	0.691622i	$0.756896\pi$
$68$	56.7239	−	153.007i	0.101159	−	0.272866i
$69$			324.927i			0.566907i
$70$	−32.4574	+	22.5833i	−0.0554201	+	0.0385602i
$71$		−	208.138i		−	0.347907i	−0.984754	−	0.173954i	$-0.944346\pi$
$71$		−	208.138i		−	0.347907i	0.984754	−	0.173954i	$-0.0556542\pi$
$72$	−197.170	+	50.9492i	−0.322733	+	0.0833947i
$73$			1075.25i			1.72394i	0.506956	+	0.861972i	$0.330771\pi$
$73$			1075.25i			1.72394i	−0.506956	+	0.861972i	$0.669229\pi$
$74$	−385.085	−	553.457i	−0.604936	−	0.869434i
$75$			363.458i			0.559580i
$76$	−219.102	+	591.007i	−0.330694	+	0.892016i
$77$			282.401i			0.417956i
$78$	−318.532	−	238.163i	−0.462393	−	0.345726i
$79$	1229.23			1.75062			0.875312	−	0.483559i	$-0.160656\pi$
$79$	1229.23			1.75062			0.875312	+	0.483559i	$0.160656\pi$
$80$	−95.1983	−	81.8318i	−0.133044	−	0.114363i
$81$	81.0000			0.111111
$82$	263.749	−	183.511i	0.355197	−	0.247140i
$83$	−701.173			−0.927274			−0.463637	−	0.886025i	$-0.653456\pi$
$83$	−701.173			−0.927274			−0.463637	+	0.886025i	$0.653456\pi$
$84$	59.4588	−	160.385i	0.0772320	−	0.208326i
$85$	−40.0104			−0.0510558
$86$	1029.06	−	715.999i	1.29030	−	0.897769i
$87$	918.703			1.13213
$88$	−868.061	+	224.308i	−1.05154	+	0.271720i
$89$			14.2857i			0.0170144i	0.999964	+	0.00850718i	$0.00270795\pi$
$89$			14.2857i			0.0170144i	−0.999964	+	0.00850718i	$0.997292\pi$
$90$	28.5176	+	40.9865i	0.0334003	+	0.0480040i
$91$	317.013	−	105.367i	0.365186	−	0.121379i
$92$	301.192	−	812.438i	0.341320	−	0.920680i
$93$	366.850			0.409038
$94$	−1010.51	+	703.092i	−1.10879	+	0.771472i
$95$	154.544			0.166905
$96$	540.227	+	55.3760i	0.574341	+	0.0588728i
$97$			1169.53i			1.22420i	0.790779	+	0.612102i	$0.209676\pi$
$97$			1169.53i			1.22420i	−0.790779	+	0.612102i	$0.790324\pi$
$98$	−472.031	−	678.418i	−0.486554	−	0.699292i
$99$	356.610			0.362027
$100$	336.909	−	908.780i	0.336909	−	0.908780i
$101$			1116.09i			1.09956i	0.835311	+	0.549778i	$0.185288\pi$
$101$			1116.09i			1.09956i	−0.835311	+	0.549778i	$0.814712\pi$
$102$	142.076	−	98.8535i	0.137917	−	0.0959604i
$103$	−843.767			−0.807173			−0.403586	−	0.914942i	$-0.632237\pi$
$103$	−843.767			−0.807173			−0.403586	+	0.914942i	$0.632237\pi$
$104$	575.683	+	890.760i	0.542792	+	0.839867i
$105$	−41.9395			−0.0389798
$106$	−1153.38	+	802.497i	−1.05685	+	0.735334i
$107$			159.431i			0.144045i	0.997403	+	0.0720224i	$0.0229453\pi$
$107$			159.431i			0.144045i	−0.997403	+	0.0720224i	$0.977055\pi$
$108$	−202.530	−	75.0833i	−0.180449	−	0.0668971i
$109$	−2228.83			−1.95856			−0.979282	−	0.202499i	$-0.935094\pi$
$109$	−2228.83			−1.95856			−0.979282	+	0.202499i	$0.935094\pi$
$110$	125.551	+	180.447i	0.108826	+	0.156408i
$111$		−	715.144i		−	0.611518i
$112$	−297.339	+	345.906i	−0.250856	+	0.291831i
$113$	−1136.08			−0.945778			−0.472889	−	0.881122i	$-0.656789\pi$
$113$	−1136.08			−0.945778			−0.472889	+	0.881122i	$0.656789\pi$
$114$	−548.782	+	381.832i	−0.450861	+	0.313700i
$115$	−212.447			−0.172268
$116$	−2297.10	−	851.595i	−1.83862	−	0.681626i
$117$	−133.055	−	400.317i	−0.105136	−	0.316319i
$118$	−1402.25	−	2015.36i	−1.09396	−	1.57228i
$119$			145.379i			0.111991i
$120$	−33.3121	−	128.916i	−0.0253414	−	0.0980698i
$121$	239.007			0.179569
$122$	825.547	−	574.400i	0.612636	−	0.426260i
$123$	340.800			0.249829
$124$	−917.261	−	340.053i	−0.664294	−	0.246271i
$125$	−482.826			−0.345482
$126$	148.926	−	103.620i	0.105297	−	0.0732633i
$127$	528.851			0.369512			0.184756	−	0.982784i	$-0.440851\pi$
$127$	528.851			0.369512			0.184756	+	0.982784i	$0.440851\pi$
$128$	−1299.44	−	639.227i	−0.897307	−	0.441408i
$129$	1329.69			0.907538
$130$	155.718	−	208.266i	0.105057	−	0.140509i
$131$			2158.33i			1.43950i	0.694233	+	0.719750i	$0.255744\pi$
$131$			2158.33i			1.43950i	−0.694233	+	0.719750i	$0.744256\pi$
$132$	−891.658	−	330.561i	−0.587946	−	0.217967i
$133$		−	561.542i		−	0.366104i
$134$	1279.73	+	1839.28i	0.825017	+	1.18574i
$135$			52.9603i			0.0337637i
$136$	−446.875	+	115.473i	−0.281759	+	0.0728069i
$137$		−	744.898i		−	0.464532i	−0.972652	−	0.232266i	$-0.925386\pi$
$137$		−	744.898i		−	0.464532i	0.972652	−	0.232266i	$-0.0746140\pi$
$138$	754.392	−	524.892i	0.465349	−	0.323781i
$139$			1667.91i			1.01777i	0.860834	+	0.508885i	$0.169942\pi$
$139$			1667.91i			1.01777i	−0.860834	+	0.508885i	$0.830058\pi$
$140$	104.864	+	38.8760i	0.0633048	+	0.0234687i
$141$	−1305.72			−0.779866
$142$	−483.240	+	336.229i	−0.285581	+	0.198702i
$143$	−585.787	−	1762.43i	−0.342559	−	1.03064i
$144$	436.803	+	375.472i	0.252779	+	0.217287i
$145$			600.676i			0.344024i
$146$	2496.43	−	1736.97i	1.41511	−	0.984606i
$147$		−	876.611i		−	0.491848i
$148$	−662.906	+	1788.13i	−0.368179	+	0.993129i
$149$	−1913.47			−1.05207			−0.526033	−	0.850464i	$-0.676321\pi$
$149$	−1913.47			−1.05207			−0.526033	+	0.850464i	$0.676321\pi$
$150$	843.851	−	587.135i	0.459334	−	0.319596i
$151$		−	1642.21i		−	0.885043i	−0.896758	−	0.442522i	$-0.854084\pi$
$151$		−	1642.21i		−	0.885043i	0.896758	−	0.442522i	$-0.145916\pi$
$152$	1726.10	−	446.027i	0.921087	−	0.238010i
$153$	183.582			0.0970045
$154$	655.659	−	456.195i	0.343081	−	0.238710i
$155$			239.858i			0.124296i
$156$	−38.3875	+	1124.28i	−0.0197017	+	0.577014i
$157$			352.705i			0.179293i	0.995974	+	0.0896463i	$0.0285737\pi$
$157$			352.705i			0.179293i	−0.995974	+	0.0896463i	$0.971426\pi$
$158$	−1985.72	−	2853.94i	−0.999844	−	1.43701i
$159$	−1490.32			−0.743335
$160$	−36.2065	+	353.217i	−0.0178899	+	0.174527i
$161$			771.933i			0.377869i
$162$	−130.849	−	188.060i	−0.0634595	−	0.0912062i
$163$	702.565			0.337602			0.168801	−	0.985650i	$-0.446010\pi$
$163$	702.565			0.337602			0.168801	+	0.985650i	$0.446010\pi$
$164$	−852.128	−	315.906i	−0.405732	−	0.150415i
$165$			233.162i			0.110010i
$166$	1132.69	+	1627.93i	0.529599	+	0.761158i
$167$		−	2150.91i		−	0.996663i	−0.866987	−	0.498332i	$-0.833946\pi$
$167$		−	2150.91i		−	0.996663i	0.866987	−	0.498332i	$-0.166054\pi$
$168$	−468.421	+	121.041i	−0.215116	+	0.0555863i
$169$	−1759.87	+	1315.16i	−0.801034	+	0.598618i
$170$	64.6335	+	92.8934i	0.0291598	+	0.0419094i
$171$	−709.103			−0.317114
$172$	−3324.71	−	1232.56i	−1.47388	−	0.546405i
$173$		−	863.589i		−	0.379523i	−0.981830	−	0.189761i	$-0.939229\pi$
$173$		−	863.589i		−	0.379523i	0.981830	−	0.189761i	$-0.0607715\pi$
$174$	−1484.09	−	2132.98i	−0.646600	−	0.929315i
$175$			863.472i			0.372985i
$176$	1923.06	+	1653.05i	0.823615	+	0.707974i
$177$		−	2604.13i		−	1.10587i
$178$	33.1675	−	23.0773i	0.0139663	−	0.00971751i
$179$		−	71.4411i		−	0.0298310i	−0.999889	−	0.0149155i	$-0.995252\pi$
$179$		−	71.4411i		−	0.0298310i	0.999889	−	0.0149155i	$-0.00474793\pi$
$180$	49.0918	−	132.421i	0.0203282	−	0.0548336i
$181$		−	1287.38i		−	0.528676i	−0.964430	−	0.264338i	$-0.914847\pi$
$181$		−	1287.38i		−	0.528676i	0.964430	−	0.264338i	$-0.0851534\pi$
$182$	−756.741	−	565.806i	−0.308205	−	0.230442i
$183$	1066.72			0.430898
$184$	−2372.81	+	613.139i	−0.950685	+	0.245659i
$185$	467.583			0.185824
$186$	−592.615	−	851.726i	−0.233616	−	0.335761i
$187$	808.234			0.316064
$188$	3264.78	+	1210.34i	1.26653	+	0.469537i
$189$	192.433			0.0740605
$190$	−249.654	−	358.811i	−0.0953251	−	0.137004i
$191$	−891.876			−0.337874			−0.168937	−	0.985627i	$-0.554033\pi$
$191$	−891.876			−0.337874			−0.168937	+	0.985627i	$0.554033\pi$
$192$	−744.124	−	1343.72i	−0.279701	−	0.505075i
$193$			2859.21i			1.06638i	0.845997	+	0.533188i	$0.179006\pi$
$193$			2859.21i			1.06638i	−0.845997	+	0.533188i	$0.820994\pi$
$194$	2715.33	−	1889.28i	1.00490	−	0.699187i
$195$	261.739	−	86.9956i	0.0961207	−	0.0319481i
$196$	−812.578	+	2191.86i	−0.296129	+	0.798781i
$197$	−4253.86			−1.53845			−0.769226	−	0.638977i	$-0.779358\pi$
$197$	−4253.86			−1.53845			−0.769226	+	0.638977i	$0.779358\pi$
$198$	−576.073	−	827.952i	−0.206766	−	0.297172i
$199$	1669.44			0.594690			0.297345	−	0.954770i	$-0.403899\pi$
$199$	1669.44			0.594690			0.297345	+	0.954770i	$0.403899\pi$
$200$	−2654.19	+	685.847i	−0.938398	+	0.242483i
$201$			2376.60i			0.833993i
$202$	2591.26	−	1802.95i	0.902577	−	0.627996i
$203$	2182.58			0.754615
$204$	−459.022	−	170.172i	−0.157539	−	0.0584039i
$205$			222.826i			0.0759162i
$206$	1363.03	+	1959.00i	0.461005	+	0.662572i
$207$	974.780			0.327304
$208$	1138.14	−	2775.53i	0.379402	−	0.925232i
$209$	−3121.89			−1.03323
$210$	67.7498	+	97.3723i	0.0222628	+	0.0319968i
$211$		−	4935.05i		−	1.61016i	−0.593169	−	0.805078i	$-0.702124\pi$
$211$		−	4935.05i		−	1.61016i	0.593169	−	0.805078i	$-0.297876\pi$
$212$	3726.36	+	1381.46i	1.20721	+	0.447543i
$213$	−624.413			−0.200864
$214$	370.156	−	257.548i	0.118240	−	0.0822691i
$215$			869.390i			0.275776i
$216$	152.847	+	591.511i	0.0481479	+	0.186330i
$217$	871.531			0.272642
$218$	3600.49	+	5174.75i	1.11861	+	1.60770i
$219$	3225.74			0.995320
$220$	216.131	−	582.993i	0.0662343	−	0.178661i
$221$	−301.561	−	907.293i	−0.0917883	−	0.276159i
$222$	−1660.37	+	1155.26i	−0.501968	+	0.349260i
$223$		−	4519.69i		−	1.35722i	−0.734498	−	0.678611i	$-0.762582\pi$
$223$		−	4519.69i		−	1.35722i	0.734498	−	0.678611i	$-0.237418\pi$
$224$	1283.43	+	131.558i	0.382824	+	0.0392414i
$225$	1090.37			0.323073
$226$	1835.23	+	2637.66i	0.540168	+	0.776347i
$227$	3561.18			1.04125			0.520626	−	0.853785i	$-0.325699\pi$
$227$	3561.18			1.04125			0.520626	+	0.853785i	$0.325699\pi$
$228$	1773.02	+	657.306i	0.515006	+	0.190926i
$229$	1225.27			0.353573			0.176786	−	0.984249i	$-0.443430\pi$
$229$	1225.27			0.353573			0.176786	+	0.984249i	$0.443430\pi$
$230$	343.190	+	493.245i	0.0983883	+	0.141407i
$231$	847.203			0.241307
$232$	1733.60	+	6708.93i	0.490587	+	1.89855i
$233$	−5389.72			−1.51542			−0.757709	−	0.652593i	$-0.773681\pi$
$233$	−5389.72			−1.51542			−0.757709	+	0.652593i	$0.773681\pi$
$234$	−714.488	+	955.596i	−0.199605	+	0.266963i
$235$		−	853.718i		−	0.236980i
$236$	−2413.91	+	6511.29i	−0.665814	+	1.79597i
$237$		−	3687.69i		−	1.01072i
$238$	337.531	−	234.848i	0.0919281	−	0.0639619i
$239$		−	1979.91i		−	0.535856i	−0.963439	−	0.267928i	$-0.913661\pi$
$239$		−	1979.91i		−	0.535856i	0.963439	−	0.267928i	$-0.0863389\pi$
$240$	−245.495	+	285.595i	−0.0660278	+	0.0768128i
$241$			3797.63i			1.01505i	0.861637	+	0.507525i	$0.169439\pi$
$241$			3797.63i			1.01505i	−0.861637	+	0.507525i	$0.830561\pi$
$242$	−386.095	−	554.909i	−0.102558	−	0.147400i
$243$		−	243.000i		−	0.0641500i
$244$	−2667.20	−	988.803i	−0.699796	−	0.259433i
$245$	573.156			0.149459
$246$	−550.534	−	791.246i	−0.142686	−	0.205073i
$247$	1164.81	+	3504.51i	0.300062	+	0.902781i
$248$	692.248	+	2678.96i	0.177249	+	0.685944i
$249$			2103.52i			0.535362i
$250$	779.965	+	1120.99i	0.197317	+	0.283591i
$251$			4440.20i			1.11658i	0.829644	+	0.558292i	$0.188543\pi$
$251$			4440.20i			1.11658i	−0.829644	+	0.558292i	$0.811457\pi$
$252$	−481.154	−	178.377i	−0.120277	−	0.0445899i
$253$	4291.56			1.06643
$254$	−854.315	−	1227.85i	−0.211041	−	0.303316i
$255$			120.031i			0.0294771i
$256$	615.023	+	4049.56i	0.150152	+	0.988663i
$257$	4237.67			1.02856			0.514278	−	0.857624i	$-0.328060\pi$
$257$	4237.67			1.02856			0.514278	+	0.857624i	$0.328060\pi$
$258$	−2148.00	−	3087.17i	−0.518327	−	0.744957i
$259$		−	1698.98i		−	0.407604i
$260$	−735.087	−	25.0989i	−0.175339	−	0.00598681i
$261$		−	2756.11i		−	0.653635i
$262$	5011.07	−	3486.61i	1.18162	−	0.822150i
$263$	−1562.99			−0.366457			−0.183228	−	0.983070i	$-0.558655\pi$
$263$	−1562.99			−0.366457			−0.183228	+	0.983070i	$0.558655\pi$
$264$	672.925	+	2604.18i	0.156878	+	0.607107i
$265$		−	974.419i		−	0.225880i
$266$	−1303.75	+	907.124i	−0.300519	+	0.209095i
$267$	42.8570			0.00982324
$268$	2203.00	−	5942.40i	0.502126	−	1.35444i
$269$			1057.42i			0.239673i	0.992794	+	0.119837i	$0.0382371\pi$
$269$			1057.42i			0.239673i	−0.992794	+	0.119837i	$0.961763\pi$
$270$	122.960	−	85.5529i	0.0277151	−	0.0192836i
$271$			3139.09i			0.703638i	0.936068	+	0.351819i	$0.114437\pi$
$271$			3139.09i			0.703638i	−0.936068	+	0.351819i	$0.885563\pi$
$272$	989.986	+	850.985i	0.220686	+	0.189701i
$273$	−316.101	−	951.038i	−0.0700781	−	0.210840i
$274$	−1729.45	+	1203.32i	−0.381314	+	0.265311i
$275$	4800.46			1.05265
$276$	−2437.31	−	903.576i	−0.531555	−	0.197061i
$277$		−	1799.10i		−	0.390242i	−0.980779	−	0.195121i	$-0.937490\pi$
$277$		−	1799.10i		−	0.390242i	0.980779	−	0.195121i	$-0.0625100\pi$
$278$	3872.43	−	2694.36i	0.835442	−	0.581285i
$279$		−	1100.55i		−	0.236158i
$280$	−79.1402	−	306.268i	−0.0168912	−	0.0653679i
$281$		−	2289.86i		−	0.486126i	−0.970010	−	0.243063i	$-0.921848\pi$
$281$		−	2289.86i		−	0.486126i	0.970010	−	0.243063i	$-0.0781522\pi$
$282$	2109.27	+	3031.52i	0.445410	+	0.640158i
$283$		−	2069.31i		−	0.434655i	−0.976099	−	0.217328i	$-0.930266\pi$
$283$		−	2069.31i		−	0.434655i	0.976099	−	0.217328i	$-0.0697340\pi$
$284$	1561.27	+	578.802i	0.326212	+	0.120935i
$285$		−	463.633i		−	0.0963624i
$286$	−3145.60	+	4207.10i	−0.650360	+	0.869828i
$287$	809.645			0.166522
$288$	166.128	−	1620.68i	0.0339902	−	0.331596i
$289$	−4496.92			−0.915311
$290$	1394.61	−	970.342i	0.282394	−	0.196484i
$291$	3508.59			0.706795
$292$	−8065.54	−	2990.11i	−1.61644	−	0.599256i
$293$	3205.38			0.639114			0.319557	−	0.947567i	$-0.396466\pi$
$293$	3205.38			0.639114			0.319557	+	0.947567i	$0.396466\pi$
$294$	−2035.26	+	1416.09i	−0.403736	+	0.280912i
$295$	1702.66			0.336043
$296$	5222.42	−	1349.48i	1.02550	−	0.264990i
$297$		−	1069.83i		−	0.209016i
$298$	3091.06	+	4442.57i	0.600873	+	0.863594i
$299$	−1601.23	−	4817.54i	−0.309704	−	0.931791i
$300$	−2726.34	−	1010.73i	−0.524684	−	0.194514i
$301$	3158.96			0.604914
$302$	−3812.78	+	2652.86i	−0.726493	+	0.505480i
$303$	3348.27			0.634829
$304$	−3823.93	−	3287.02i	−0.721438	−	0.620143i
$305$			697.456i			0.130938i
$306$	−296.561	−	426.227i	−0.0554027	−	0.0796267i
$307$	3977.40			0.739420			0.369710	−	0.929147i	$-0.379457\pi$
$307$	3977.40			0.739420			0.369710	+	0.929147i	$0.379457\pi$
$308$	−2118.32	−	785.319i	−0.391892	−	0.145285i
$309$			2531.30i			0.466021i
$310$	556.885	−	387.470i	0.102029	−	0.0709897i
$311$	−9844.30			−1.79492			−0.897458	−	0.441100i	$-0.854588\pi$
$311$	−9844.30			−1.79492			−0.897458	+	0.441100i	$0.854588\pi$
$312$	2672.28	−	1727.05i	0.484898	−	0.313381i
$313$	1209.11			0.218349			0.109174	−	0.994023i	$-0.465179\pi$
$313$	1209.11			0.218349			0.109174	+	0.994023i	$0.465179\pi$
$314$	818.886	−	569.766i	0.147173	−	0.102400i
$315$			125.819i			0.0225050i
$316$	−3418.32	+	9220.61i	−0.608531	+	1.64146i
$317$	29.0546			0.00514784			0.00257392	−	0.999997i	$-0.499181\pi$
$317$	29.0546			0.00514784			0.00257392	+	0.999997i	$0.499181\pi$
$318$	2407.49	+	3460.13i	0.424545	+	0.610171i
$319$		−	12134.0i		−	2.12970i
$320$	878.564	−	486.531i	0.153479	−	0.0849935i
$321$	478.293			0.0831643
$322$	1792.22	−	1246.99i	0.310176	−	0.215814i
$323$	−1607.14			−0.276853
$324$	−225.250	+	607.591i	−0.0386231	+	0.104182i
$325$	−1791.11	−	5388.82i	−0.305701	−	0.919747i
$326$	−1134.94	−	1631.17i	−0.192817	−	0.277123i
$327$			6686.50i			1.13078i
$328$	643.092	+	2488.73i	0.108259	+	0.418955i
$329$	−3102.01			−0.519816
$330$	541.340	−	376.654i	0.0903024	−	0.0628307i
$331$	−5174.18			−0.859210			−0.429605	−	0.903017i	$-0.641347\pi$
$331$	−5174.18			−0.859210			−0.429605	+	0.903017i	$0.641347\pi$
$332$	1949.86	−	5259.58i	0.322328	−	0.869449i
$333$	−2145.43			−0.353060
$334$	−4993.84	+	3474.62i	−0.818117	+	0.569230i
$335$	−1553.90			−0.253428
$336$	1037.72	+	892.016i	0.168489	+	0.144832i
$337$	6593.59			1.06580			0.532901	−	0.846177i	$-0.321102\pi$
$337$	6593.59			1.06580			0.532901	+	0.846177i	$0.321102\pi$
$338$	5896.38	+	1961.41i	0.948879	+	0.315641i
$339$			3408.23i			0.546045i
$340$	111.263	−	300.123i	0.0177474	−	0.0478719i
$341$		−	4845.27i		−	0.769460i
$342$	1145.50	+	1646.35i	0.181115	+	0.260305i
$343$		−	4527.19i		−	0.712669i
$344$	2509.13	+	9710.18i	0.393265	+	1.52191i
$345$			637.341i			0.0994588i
$346$	−2005.02	+	1395.06i	−0.311533	+	0.216759i
$347$			1471.21i			0.227604i	0.993503	+	0.113802i	$0.0363030\pi$
$347$			1471.21i			0.227604i	−0.993503	+	0.113802i	$0.963697\pi$
$348$	−2554.79	+	6891.30i	−0.393537	+	1.06153i
$349$	2830.48			0.434132			0.217066	−	0.976157i	$-0.430351\pi$
$349$	2830.48			0.434132			0.217066	+	0.976157i	$0.430351\pi$
$350$	2004.75	−	1394.87i	0.306167	−	0.213025i
$351$	−1200.95	+	399.165i	−0.182627	+	0.0607005i
$352$	731.393	−	7135.20i	0.110748	−	1.08042i
$353$			2140.98i			0.322813i	0.986888	+	0.161407i	$0.0516031\pi$
$353$			2140.98i			0.322813i	−0.986888	+	0.161407i	$0.948397\pi$
$354$	−6046.08	+	4206.75i	−0.907756	+	0.631600i
$355$		−	408.261i		−	0.0610372i
$356$	−107.158	−	39.7265i	−0.0159533	−	0.00591432i
$357$	436.137			0.0646578
$358$	−165.867	+	115.407i	−0.0244870	+	0.0170376i
$359$		−	8556.42i		−	1.25791i	−0.777441	−	0.628956i	$-0.783483\pi$
$359$		−	8556.42i		−	1.25791i	0.777441	−	0.628956i	$-0.216517\pi$
$360$	−386.748	+	99.9364i	−0.0566206	+	0.0146309i
$361$	−651.259			−0.0949496
$362$	−2988.95	+	2079.66i	−0.433967	+	0.301946i
$363$		−	717.020i		−	0.103674i
$364$	−91.1978	+	2670.96i	−0.0131320	+	0.384606i
$365$			2109.09i			0.302451i
$366$	−1723.20	−	2476.64i	−0.246101	−	0.353705i
$367$	3384.19			0.481344			0.240672	−	0.970606i	$-0.422632\pi$
$367$	3384.19			0.481344			0.240672	+	0.970606i	$0.422632\pi$
$368$	5256.62	+	4518.56i	0.744621	+	0.640071i
$369$		−	1022.40i		−	0.144239i
$370$	−755.341	−	1085.60i	−0.106131	−	0.152535i
$371$	−3540.58			−0.495466
$372$	−1020.16	+	2751.78i	−0.142185	+	0.383531i
$373$			8794.40i			1.22080i	0.792095	+	0.610398i	$0.208991\pi$
$373$			8794.40i			1.22080i	−0.792095	+	0.610398i	$0.791009\pi$
$374$	−1305.63	−	1876.50i	−0.180515	−	0.259443i
$375$			1448.48i			0.199464i
$376$	−2463.89	−	9535.13i	−0.337941	−	1.30781i
$377$	−13621.2	+	4527.34i	−1.86081	+	0.618487i
$378$	−310.859	−	446.777i	−0.0422986	−	0.0607930i
$379$	−12072.7			−1.63623			−0.818117	−	0.575052i	$-0.804982\pi$
$379$	−12072.7			−1.63623			−0.818117	+	0.575052i	$0.804982\pi$
$380$	−429.767	+	1159.26i	−0.0580173	+	0.156496i
$381$		−	1586.55i		−	0.213338i
$382$	1440.75	+	2070.70i	0.192972	+	0.277346i
$383$			10016.6i			1.33636i	0.744001	+	0.668178i	$0.232926\pi$
$383$			10016.6i			1.33636i	−0.744001	+	0.668178i	$0.767074\pi$
$384$	−1917.68	+	3898.32i	−0.254847	+	0.518060i
$385$			553.928i			0.0733267i
$386$	6638.31	−	4618.81i	0.875340	−	0.609045i
$387$		−	3989.06i		−	0.523967i
$388$	−8772.79	−	3252.30i	−1.14786	−	0.425543i
$389$			3792.53i			0.494316i	0.968975	+	0.247158i	$0.0794967\pi$
$389$			3792.53i			0.494316i	−0.968975	+	0.247158i	$0.920503\pi$
$390$	−624.798	−	467.154i	−0.0811228	−	0.0606545i
$391$	2209.28			0.285750
$392$	6401.55	−	1654.17i	0.824814	−	0.213133i
$393$	6475.00			0.831096
$394$	6871.76	+	9876.32i	0.878665	+	1.26285i
$395$	2411.13			0.307132
$396$	−991.683	+	2674.97i	−0.125843	+	0.339451i
$397$	3697.88			0.467484			0.233742	−	0.972299i	$-0.424903\pi$
$397$	3697.88			0.467484			0.233742	+	0.972299i	$0.424903\pi$
$398$	−2696.84	−	3875.99i	−0.339649	−	0.488155i
$399$	−1684.63			−0.211370
$400$	5879.97	+	5054.38i	0.734996	+	0.631798i
$401$		−	625.662i		−	0.0779154i	−0.999241	−	0.0389577i	$-0.987596\pi$
$401$		−	625.662i		−	0.0779154i	0.999241	−	0.0389577i	$-0.0124038\pi$
$402$	5517.83	−	3839.20i	0.684588	−	0.476324i
$403$	−5439.11	+	1807.82i	−0.672311	+	0.223459i
$404$	−8371.93	−	3103.69i	−1.03099	−	0.382214i
$405$	158.881			0.0194935
$406$	−3525.77	−	5067.35i	−0.430988	−	0.619430i
$407$	−9445.46			−1.15035
$408$	346.419	+	1340.62i	0.0420351	+	0.162673i
$409$			5895.18i			0.712709i	0.934351	+	0.356354i	$0.115980\pi$
$409$			5895.18i			0.712709i	−0.934351	+	0.356354i	$0.884020\pi$
$410$	517.341	−	359.956i	0.0623163	−	0.0433585i
$411$	−2234.69			−0.268198
$412$	2346.40	−	6329.20i	0.280580	−	0.756838i
$413$		−	6186.67i		−	0.737109i
$414$	−1574.68	−	2263.18i	−0.186935	−	0.268669i
$415$	−1375.35			−0.162682
$416$	−8282.59	+	1841.19i	−0.976172	+	0.216999i
$417$	5003.72			0.587610
$418$	5043.15	+	7248.19i	0.590116	+	0.848135i
$419$		−	11124.1i		−	1.29701i	−0.761209	−	0.648506i	$-0.775394\pi$
$419$		−	11124.1i		−	1.29701i	0.761209	−	0.648506i	$-0.224606\pi$
$420$	116.628	−	314.593i	0.0135497	−	0.0365490i
$421$	13498.0			1.56260			0.781299	−	0.624157i	$-0.214557\pi$
$421$	13498.0			1.56260			0.781299	+	0.624157i	$0.214557\pi$
$422$	−11457.9	+	7972.16i	−1.32171	+	0.919617i
$423$			3917.15i			0.450256i
$424$	−2812.25	−	10883.2i	−0.322111	−	1.24655i
$425$	2471.26			0.282056
$426$	1008.69	+	1449.72i	0.114721	+	0.164881i
$427$	2534.23			0.287213
$428$	−1195.91	−	443.356i	−0.135062	−	0.0500711i
$429$	−5287.29	+	1757.36i	−0.595041	+	0.197777i
$430$	2018.49	−	1404.43i	0.226373	−	0.157506i
$431$			6562.32i			0.733401i	0.930339	+	0.366701i	$0.119513\pi$
$431$			6562.32i			0.733401i	−0.930339	+	0.366701i	$0.880487\pi$
$432$	1126.42	−	1310.41i	0.125451	−	0.145942i
$433$	2471.18			0.274266			0.137133	−	0.990553i	$-0.456211\pi$
$433$	2471.18			0.274266			0.137133	+	0.990553i	$0.456211\pi$
$434$	−1407.88	−	2023.46i	−0.155716	−	0.223800i
$435$	1802.03			0.198622
$436$	6198.08	−	16718.8i	0.680812	−	1.83643i
$437$	−8533.57			−0.934133
$438$	−5210.90	−	7489.29i	−0.568463	−	0.817014i
$439$	10095.1			1.09753			0.548764	−	0.835977i	$-0.315098\pi$
$439$	10095.1			1.09753			0.548764	+	0.835977i	$0.315098\pi$
$440$	−1702.69	+	439.979i	−0.184484	+	0.0476709i
$441$	−2629.83			−0.283969
$442$	−1619.34	+	2165.80i	−0.174263	+	0.233069i
$443$			3059.12i			0.328088i	0.986453	+	0.164044i	$0.0524539\pi$
$443$			3059.12i			0.328088i	−0.986453	+	0.164044i	$0.947546\pi$
$444$	5364.38	+	1988.72i	0.573384	+	0.212568i
$445$			28.0212i			0.00298502i
$446$	−10493.5	+	7301.17i	−1.11408	+	0.775158i
$447$			5740.42i			0.607411i
$448$	−1767.83	−	3192.29i	−0.186433	−	0.336655i
$449$		−	14487.4i		−	1.52273i	−0.648325	−	0.761364i	$-0.724530\pi$
$449$		−	14487.4i		−	1.52273i	0.648325	−	0.761364i	$-0.275470\pi$
$450$	−1761.41	−	2531.55i	−0.184519	−	0.265197i
$451$		−	4501.21i		−	0.469964i
$452$	3159.27	−	8521.84i	0.328760	−	0.886800i
$453$	−4926.64			−0.510980
$454$	−5752.79	−	8268.11i	−0.594696	−	0.854717i
$455$	621.818	−	206.677i	0.0640688	−	0.0212948i
$456$	−1338.08	−	5178.30i	−0.137415	−	0.531790i
$457$		−	17435.8i		−	1.78471i	−0.451332	−	0.892356i	$-0.649051\pi$
$457$		−	17435.8i		−	1.78471i	0.451332	−	0.892356i	$-0.350949\pi$
$458$	−1979.32	−	2844.75i	−0.201938	−	0.290232i
$459$		−	550.745i		−	0.0560056i
$460$	590.786	−	1593.59i	0.0598816	−	0.161525i
$461$	−11637.1			−1.17569			−0.587843	−	0.808975i	$-0.700023\pi$
$461$	−11637.1			−1.17569			−0.587843	+	0.808975i	$0.700023\pi$
$462$	−1368.59	−	1966.98i	−0.137819	−	0.198078i
$463$		−	7443.25i		−	0.747122i	−0.927606	−	0.373561i	$-0.878137\pi$
$463$		−	7443.25i		−	0.747122i	0.927606	−	0.373561i	$-0.121863\pi$
$464$	12775.8	−	14862.7i	1.27824	−	1.48703i
$465$	719.573			0.0717622
$466$	8706.64	+	12513.5i	0.865509	+	1.24394i
$467$			1670.75i			0.165553i	0.996568	+	0.0827763i	$0.0263787\pi$
$467$			1670.75i			0.165553i	−0.996568	+	0.0827763i	$0.973621\pi$
$468$	3372.83	+	115.163i	0.333139	+	0.0113748i
$469$			5646.13i			0.555894i
$470$	−1982.10	+	1379.11i	−0.194527	+	0.135348i
$471$	1058.12			0.103515
$472$	19016.9	−	4914.01i	1.85450	−	0.479207i
$473$		−	17562.2i		−	1.70721i
$474$	−8561.83	+	5957.16i	−0.829658	+	0.577260i
$475$	−9545.51			−0.922059
$476$	−1090.51	−	404.279i	−0.105007	−	0.0389288i
$477$			4470.97i			0.429165i
$478$	−4596.81	+	3198.37i	−0.439860	+	0.306046i
$479$			15019.1i			1.43265i	0.697764	+	0.716327i	$0.254178\pi$
$479$			15019.1i			1.43265i	−0.697764	+	0.716327i	$0.745822\pi$
$480$	1059.65	+	108.620i	0.100763	+	0.0103287i
$481$	3524.21	+	10603.1i	0.334075	+	1.00511i
$482$	8817.07	−	6134.75i	0.833209	−	0.579731i
$483$	2315.80			0.218163
$484$	−664.644	+	1792.82i	−0.0624196	+	0.168371i
$485$			2294.03i			0.214776i
$486$	−564.180	+	392.546i	−0.0526579	+	0.0366384i
$487$		−	10089.1i		−	0.938773i	−0.882993	−	0.469386i	$-0.844475\pi$
$487$		−	10089.1i		−	0.938773i	0.882993	−	0.469386i	$-0.155525\pi$
$488$	2012.91	+	7789.86i	0.186722	+	0.722603i
$489$		−	2107.70i		−	0.194915i
$490$	−925.885	−	1330.71i	−0.0853616	−	0.122685i
$491$			12881.4i			1.18397i	0.805949	+	0.591985i	$0.201656\pi$
$491$			12881.4i			1.18397i	−0.805949	+	0.591985i	$0.798344\pi$
$492$	−947.719	+	2556.38i	−0.0868424	+	0.234249i
$493$		−	6246.55i		−	0.570650i
$494$	6254.88	−	8365.63i	0.569677	−	0.761918i
$495$	699.487			0.0635144
$496$	5101.56	−	5934.85i	0.461828	−	0.537263i
$497$	−1483.43			−0.133885
$498$	4883.80	−	3398.06i	0.439455	−	0.305764i
$499$	−13395.7			−1.20175			−0.600874	−	0.799344i	$-0.705181\pi$
$499$	−13395.7			−1.20175			−0.600874	+	0.799344i	$0.705181\pi$
$500$	1342.67	−	3621.74i	0.120092	−	0.323938i
$501$	−6452.74			−0.575424
$502$	10308.9	−	7172.76i	0.916555	−	0.637721i
$503$	3123.84			0.276909			0.138454	−	0.990369i	$-0.455787\pi$
$503$	3123.84			0.276909			0.138454	+	0.990369i	$0.455787\pi$
$504$	363.122	+	1405.26i	0.0320928	+	0.124197i
$505$			2189.20i			0.192907i
$506$	−6932.65	−	9963.84i	−0.609079	−	0.875389i
$507$	3945.49	+	5279.62i	0.345613	+	0.462477i
$508$	−1470.66	+	3966.98i	−0.128445	+	0.346469i
$509$	18899.4			1.64578			0.822888	−	0.568203i	$-0.192361\pi$
$509$	18899.4			1.64578			0.822888	+	0.568203i	$0.192361\pi$
$510$	278.680	−	193.900i	0.0241964	−	0.0168354i
$511$	7663.43			0.663425
$512$	8408.48	−	7969.65i	0.725792	−	0.687914i
$513$			2127.31i			0.183086i
$514$	−6845.60	−	9838.73i	−0.587445	−	0.844295i
$515$	−1655.04			−0.141611
$516$	−3697.67	+	9974.14i	−0.315467	+	0.850944i
$517$			17245.6i			1.46704i
$518$	−3944.57	+	2744.56i	−0.334584	+	0.232797i
$519$	−2590.77			−0.219118
$520$	1129.20	+	1747.22i	0.0952281	+	0.147347i
$521$	16479.0			1.38571			0.692857	−	0.721075i	$-0.256352\pi$
$521$	16479.0			1.38571			0.692857	+	0.721075i	$0.256352\pi$
$522$	−6398.94	+	4452.26i	−0.536540	+	0.373315i
$523$			1172.62i			0.0980401i	0.998798	+	0.0490200i	$0.0156098\pi$
$523$			1172.62i			0.0980401i	−0.998798	+	0.0490200i	$0.984390\pi$
$524$	−16189.9	−	6002.03i	−1.34973	−	0.500382i
$525$	2590.42			0.215343
$526$	2524.88	+	3628.84i	0.209297	+	0.300808i
$527$		−	2494.33i		−	0.206176i
$528$	4959.15	−	5769.19i	0.408749	−	0.475514i
$529$	−436.182			−0.0358496
$530$	−2262.34	+	1574.09i	−0.185415	+	0.129008i
$531$	−7812.39			−0.638472
$532$	4212.20	+	1561.57i	0.343274	+	0.127261i
$533$	−5052.89	+	1679.45i	−0.410628	+	0.136483i
$534$	−69.2319	−	99.5024i	−0.00561040	−	0.00806346i
$535$			312.723i			0.0252714i
$536$	−17355.4	+	4484.67i	−1.39858	+	0.361396i
$537$	−214.323			−0.0172230
$538$	2455.05	−	1708.18i	0.196737	−	0.136886i
$539$	−11578.1			−0.925238
$540$	−397.262	−	147.275i	−0.0316582	−	0.0117365i
$541$	12163.0			0.966594			0.483297	−	0.875456i	$-0.339439\pi$
$541$	12163.0			0.966594			0.483297	+	0.875456i	$0.339439\pi$
$542$	7288.11	−	5070.93i	0.577585	−	0.401873i
$543$	−3862.15			−0.305231
$544$	376.519	−	3673.18i	0.0296748	−	0.289497i
$545$	−4371.84			−0.343613
$546$	−1697.42	+	2270.22i	−0.133045	+	0.177943i
$547$		−	7645.69i		−	0.597635i	−0.954310	−	0.298817i	$-0.903408\pi$
$547$		−	7645.69i		−	0.597635i	0.954310	−	0.298817i	$-0.0965922\pi$
$548$	5587.57	+	2071.46i	0.435564	+	0.161475i
$549$		−	3200.17i		−	0.248779i
$550$	−7754.75	−	11145.4i	−0.601206	−	0.864074i
$551$			24128.0i			1.86549i
$552$	1839.42	+	7118.44i	0.141831	+	0.548878i
$553$		−	8760.91i		−	0.673692i
$554$	−4177.01	+	2906.29i	−0.320333	+	0.222881i
$555$		−	1402.75i		−	0.107285i
$556$	−12511.2	−	4638.22i	−0.954302	−	0.353785i
$557$	−7827.70			−0.595459			−0.297729	−	0.954650i	$-0.596229\pi$
$557$	−7827.70			−0.595459			−0.297729	+	0.954650i	$0.596229\pi$
$558$	−2555.18	+	1777.85i	−0.193852	+	0.134878i
$559$	−19714.6	+	6552.65i	−1.49166	+	0.495792i
$560$	−583.227	+	678.492i	−0.0440105	+	0.0511992i
$561$		−	2424.70i		−	0.182480i
$562$	−5316.43	+	3699.07i	−0.399039	+	0.277644i
$563$			10807.8i			0.809050i	0.914527	+	0.404525i	$0.132563\pi$
$563$			10807.8i			0.809050i	−0.914527	+	0.404525i	$0.867437\pi$
$564$	3631.02	−	9794.33i	0.271088	−	0.731234i
$565$	−2228.40			−0.165929
$566$	−4804.37	+	3342.79i	−0.356789	+	0.248247i
$567$		−	577.299i		−	0.0427589i
$568$	−1178.27	−	4559.84i	−0.0870408	−	0.336843i
$569$	1092.63			0.0805015			0.0402508	−	0.999190i	$-0.487184\pi$
$569$	1092.63			0.0805015			0.0402508	+	0.999190i	$0.487184\pi$
$570$	−1076.43	+	748.961i	−0.0790996	+	0.0550360i
$571$			25324.4i			1.85603i	0.372540	+	0.928016i	$0.378487\pi$
$571$			25324.4i			1.85603i	−0.372540	+	0.928016i	$0.621513\pi$
$572$	14849.2	+	507.013i	1.08545	+	0.0370617i
$573$			2675.63i			0.195072i
$574$	−1307.91	−	1879.78i	−0.0951067	−	0.136691i
$575$	13121.9			0.951689
$576$	−4031.15	+	2232.37i	−0.291605	+	0.161485i
$577$		−	5334.07i		−	0.384853i	−0.981311	−	0.192427i	$-0.938364\pi$
$577$		−	5334.07i		−	0.384853i	0.981311	−	0.192427i	$-0.0616357\pi$
$578$	7264.40	+	10440.6i	0.522767	+	0.751338i
$579$	8577.63			0.615672
$580$	−4505.74	−	1670.40i	−0.322570	−	0.119585i
$581$			4997.36i			0.356842i
$582$	−5667.84	−	8146.00i	−0.403676	−	0.580177i
$583$			19683.8i			1.39832i
$584$	6086.98	+	23556.3i	0.431303	+	1.66912i
$585$	−260.987	−	785.218i	−0.0184452	−	0.0554953i
$586$	−5178.03	−	7442.04i	−0.365021	−	0.524621i
$587$	−9169.90			−0.644774			−0.322387	−	0.946608i	$-0.604485\pi$
$587$	−9169.90			−0.644774			−0.322387	+	0.946608i	$0.604485\pi$
$588$	6575.57	+	2437.74i	0.461177	+	0.170970i
$589$			9634.60i			0.674001i
$590$	−2750.50	−	3953.12i	−0.191926	−	0.275843i
$591$			12761.6i			0.888226i
$592$	−11569.5	−	9945.07i	−0.803216	−	0.690439i
$593$		−	11447.3i		−	0.792719i	−0.918095	−	0.396359i	$-0.870273\pi$
$593$		−	11447.3i		−	0.792719i	0.918095	−	0.396359i	$-0.129727\pi$
$594$	−2483.86	+	1728.22i	−0.171572	+	0.119377i
$595$			285.160i			0.0196478i
$596$	5321.11	−	14353.2i	0.365706	−	0.986459i
$597$		−	5008.32i		−	0.343345i
$598$	−8598.37	+	11499.9i	−0.587983	+	0.786401i
$599$	133.223			0.00908740			0.00454370	−	0.999990i	$-0.498554\pi$
$599$	133.223			0.00908740			0.00454370	+	0.999990i	$0.498554\pi$
$600$	2057.54	+	7962.57i	0.139998	+	0.541784i
$601$	22130.3			1.50202			0.751009	−	0.660292i	$-0.229567\pi$
$601$	22130.3			1.50202			0.751009	+	0.660292i	$0.229567\pi$
$602$	−5103.03	−	7334.24i	−0.345488	−	0.496547i
$603$	7129.81			0.481506
$604$	12318.4	+	4566.77i	0.829852	+	0.307648i
$605$	468.810			0.0315038
$606$	−5408.85	−	7773.78i	−0.362574	−	0.521103i
$607$	−17566.5			−1.17463			−0.587316	−	0.809357i	$-0.699816\pi$
$607$	−17566.5			−1.17463			−0.587316	+	0.809357i	$0.699816\pi$
$608$	−1454.34	+	14188.0i	−0.0970089	+	0.946382i
$609$		−	6547.73i		−	0.435677i
$610$	1619.31	−	1126.68i	0.107482	−	0.0747836i
$611$	19359.3	−	6434.53i	1.28182	−	0.426044i
$612$	−510.515	+	1377.07i	−0.0337195	+	0.0909553i
$613$	26186.1			1.72536			0.862681	−	0.505748i	$-0.168783\pi$
$613$	26186.1			1.72536			0.862681	+	0.505748i	$0.168783\pi$
$614$	−6425.15	−	9234.44i	−0.422309	−	0.606957i
$615$	668.477			0.0438303
$616$	1598.68	+	6186.79i	0.104566	+	0.404664i
$617$			23951.0i			1.56278i	0.624046	+	0.781388i	$0.285488\pi$
$617$			23951.0i			1.56278i	−0.624046	+	0.781388i	$0.714512\pi$
$618$	5877.00	−	4089.10i	0.382536	−	0.266162i
$619$	−5760.47			−0.374044			−0.187022	−	0.982356i	$-0.559883\pi$
$619$	−5760.47			−0.374044			−0.187022	+	0.982356i	$0.559883\pi$
$620$	−1799.20	−	667.011i	−0.116545	−	0.0432062i
$621$		−	2924.34i		−	0.188969i
$622$	15902.6	+	22855.8i	1.02514	+	1.47337i
$623$	101.816			0.00654763
$624$	−8326.59	−	3414.41i	−0.534183	−	0.219048i
$625$	14197.0			0.908609
$626$	−1953.22	−	2807.24i	−0.124707	−	0.179233i
$627$			9365.67i			0.596537i
$628$	−2645.68	−	980.825i	−0.168112	−	0.0623235i
$629$	−4862.49			−0.308236
$630$	292.117	−	203.249i	0.0184734	−	0.0128534i
$631$		−	1160.57i		−	0.0732194i	−0.999330	−	0.0366097i	$-0.988344\pi$
$631$		−	1160.57i		−	0.0732194i	0.999330	−	0.0366097i	$-0.0116558\pi$
$632$	26929.8	−	6958.70i	1.69495	−	0.437978i
$633$	−14805.1			−0.929624
$634$	−46.9352	−	67.4569i	−0.00294012	−	0.00422564i
$635$	1037.34			0.0648276
$636$	4144.38	−	11179.1i	0.258389	−	0.696981i
$637$	4319.91	+	12997.1i	0.268699	+	0.808421i
$638$	−28171.9	+	19601.5i	−1.74818	+	1.21635i
$639$			1873.24i			0.115969i
$640$	−2548.84	−	1253.84i	−0.157425	−	0.0774411i
$641$	17057.7			1.05108			0.525538	−	0.850770i	$-0.323864\pi$
$641$	17057.7			1.05108			0.525538	+	0.850770i	$0.323864\pi$
$642$	−772.643	−	1110.47i	−0.0474981	−	0.0682659i
$643$	−14838.5			−0.910066			−0.455033	−	0.890475i	$-0.650373\pi$
$643$	−14838.5			−0.910066			−0.455033	+	0.890475i	$0.650373\pi$
$644$	−5790.37	−	2146.64i	−0.354305	−	0.131350i
$645$	2608.17			0.159220
$646$	2596.20	+	3731.34i	0.158121	+	0.227256i
$647$	12658.0			0.769144			0.384572	−	0.923095i	$-0.374349\pi$
$647$	12658.0			0.769144			0.384572	+	0.923095i	$0.374349\pi$
$648$	1774.53	−	458.542i	0.107578	−	0.0277982i
$649$	−34394.7			−2.08030
$650$	−9618.00	+	12863.7i	−0.580383	+	0.776237i
$651$		−	2614.59i		−	0.157410i
$652$	−1953.74	+	5270.03i	−0.117353	+	0.316549i
$653$			16485.5i			0.987944i	0.869478	+	0.493972i	$0.164456\pi$
$653$			16485.5i			0.987944i	−0.869478	+	0.493972i	$0.835544\pi$
$654$	15524.3	−	10801.5i	0.928205	−	0.645828i
$655$			4233.56i			0.252548i
$656$	4739.30	−	5513.42i	0.282071	−	0.328145i
$657$		−	9677.21i		−	0.574648i
$658$	5011.04	+	7202.03i	0.296885	+	0.426694i
$659$			12672.0i			0.749059i	0.927215	+	0.374530i	$0.122196\pi$
$659$			12672.0i			0.749059i	−0.927215	+	0.374530i	$0.877804\pi$
$660$	−1748.98	−	648.393i	−0.103150	−	0.0382404i
$661$	10745.0			0.632271			0.316135	−	0.948714i	$-0.397615\pi$
$661$	10745.0			0.632271			0.316135	+	0.948714i	$0.397615\pi$
$662$	8358.45	+	12013.0i	0.490726	+	0.705287i
$663$	−2721.88	+	904.684i	−0.159440	+	0.0529940i
$664$	−15361.2	+	3969.35i	−0.897785	+	0.231989i
$665$		−	1101.46i		−	0.0642298i
$666$	3465.77	+	4981.11i	0.201645	+	0.289811i
$667$		−	33167.9i		−	1.92544i
$668$	16134.3	+	5981.40i	0.934511	+	0.346448i
$669$	−13559.1			−0.783593
$670$	2510.19	+	3607.73i	0.144742	+	0.208028i
$671$		−	14089.0i		−	0.810582i
$672$	394.673	−	3850.28i	0.0226560	−	0.221023i
$673$	−18235.1			−1.04444			−0.522222	−	0.852810i	$-0.674897\pi$
$673$	−18235.1			−1.04444			−0.522222	+	0.852810i	$0.674897\pi$
$674$	−10651.4	−	15308.5i	−0.608718	−	0.874870i
$675$		−	3271.12i		−	0.186527i
$676$	−4971.25	−	16858.3i	−0.282843	−	0.959166i
$677$		−	3337.54i		−	0.189471i	−0.995502	−	0.0947356i	$-0.969799\pi$
$677$		−	3337.54i		−	0.189471i	0.995502	−	0.0947356i	$-0.0302006\pi$
$678$	7912.98	−	5505.70i	0.448224	−	0.311866i
$679$	8335.42			0.471110
$680$	−876.541	+	226.500i	−0.0494321	+	0.0127733i
$681$		−	10683.6i		−	0.601167i
$682$	−11249.4	+	7827.12i	−0.631616	+	0.439466i
$683$	20013.4			1.12122			0.560609	−	0.828081i	$-0.310567\pi$
$683$	20013.4			1.12122			0.560609	+	0.828081i	$0.310567\pi$
$684$	1971.92	−	5319.07i	0.110231	−	0.297339i
$685$		−	1461.11i		−	0.0814981i
$686$	−10510.9	+	7313.30i	−0.584998	+	0.407031i
$687$		−	3675.81i		−	0.204135i
$688$	18491.1	−	21511.5i	1.02466	−	1.19203i
$689$	22096.3	−	7344.26i	1.22178	−	0.406087i
$690$	1479.73	−	1029.57i	0.0816414	−	0.0568045i
$691$	4659.99			0.256547			0.128274	−	0.991739i	$-0.459056\pi$
$691$	4659.99			0.256547			0.128274	+	0.991739i	$0.459056\pi$
$692$	6477.89	+	2401.52i	0.355856	+	0.131925i
$693$		−	2541.61i		−	0.139319i
$694$	3415.76	−	2376.62i	0.186830	−	0.129993i
$695$			3271.59i			0.178559i
$696$	20126.8	−	5200.79i	1.09613	−	0.283241i
$697$		−	2317.21i		−	0.125926i
$698$	−4572.40	−	6571.60i	−0.247948	−	0.356359i
$699$			16169.2i			0.874927i
$700$	−6477.01	−	2401.20i	−0.349725	−	0.129652i
$701$			34527.6i			1.86033i	0.367146	+	0.930163i	$0.380335\pi$
$701$			34527.6i			1.86033i	−0.367146	+	0.930163i	$0.619665\pi$
$702$	2866.79	+	2143.46i	0.154131	+	0.115242i
$703$	18781.9			1.00764
$704$	−17747.5	+	9828.21i	−0.950120	+	0.526157i
$705$	−2561.15			−0.136821
$706$	4970.79	−	3458.58i	0.264983	−	0.184370i
$707$	7954.54			0.423142
$708$	19533.9	+	7241.72i	1.03690	+	0.384408i
$709$	−89.4916			−0.00474038			−0.00237019	−	0.999997i	$-0.500754\pi$
$709$	−89.4916			−0.00474038			−0.00237019	+	0.999997i	$0.500754\pi$
$710$	−947.871	+	659.511i	−0.0501028	+	0.0348605i
$711$	−11063.1			−0.583541
$712$	80.8714	+	312.968i	0.00425672	+	0.0164733i
$713$		−	13244.4i		−	0.695660i
$714$	−704.544	−	1012.59i	−0.0369284	−	0.0530747i
$715$	−1149.02	−	3456.99i	−0.0600990	−	0.180817i
$716$	535.888	+	198.668i	0.0279708	+	0.0103695i
$717$	−5939.72			−0.309377
$718$	−19865.7	+	13822.2i	−1.03256	+	0.718439i
$719$	−26608.2			−1.38013			−0.690067	−	0.723745i	$-0.742419\pi$
$719$	−26608.2			−1.38013			−0.690067	+	0.723745i	$0.742419\pi$
$720$	856.785	+	736.486i	0.0443479	+	0.0381212i
$721$			6013.65i			0.310624i
$722$	1052.05	+	1512.05i	0.0542291	+	0.0779399i
$723$	11392.9			0.586039
$724$	9656.81	+	3580.03i	0.495708	+	0.183772i
$725$		−	37101.1i		−	1.90055i
$726$	−1664.73	+	1158.29i	−0.0851016	+	0.0592121i
$727$	−7882.87			−0.402145			−0.201073	−	0.979576i	$-0.564443\pi$
$727$	−7882.87			−0.402145			−0.201073	+	0.979576i	$0.564443\pi$
$728$	6348.58	−	4102.98i	0.323206	−	0.208883i
$729$	−729.000			−0.0370370
$730$	4896.73	−	3407.05i	0.248268	−	0.172741i
$731$		−	9040.96i		−	0.457445i
$732$	−2966.41	+	8001.61i	−0.149784	+	0.404028i
$733$	−11514.6			−0.580219			−0.290110	−	0.956993i	$-0.593692\pi$
$733$	−11514.6			−0.580219			−0.290110	+	0.956993i	$0.593692\pi$
$734$	−5466.88	−	7857.18i	−0.274913	−	0.395114i
$735$		−	1719.47i		−	0.0862905i
$736$	1999.24	−	19503.8i	0.100126	−	0.976793i
$737$	31389.6			1.56886
$738$	−2373.74	+	1651.60i	−0.118399	+	0.0823799i
$739$	−12266.7			−0.610607			−0.305304	−	0.952255i	$-0.598758\pi$
$739$	−12266.7			−0.610607			−0.305304	+	0.952255i	$0.598758\pi$
$740$	−1300.28	+	3507.40i	−0.0645938	+	0.174236i
$741$	10513.5	−	3494.44i	0.521221	−	0.173241i
$742$	5719.51	+	8220.28i	0.282978	+	0.406706i
$743$			9024.07i			0.445573i	0.974867	+	0.222787i	$0.0715153\pi$
$743$			9024.07i			0.445573i	−0.974867	+	0.222787i	$0.928485\pi$
$744$	8036.88	−	2076.74i	0.396030	−	0.102335i
$745$	−3753.26			−0.184576
$746$	20418.2	−	14206.6i	1.00210	−	0.697240i
$747$	6310.56			0.309091
$748$	−2247.59	+	6062.66i	−0.109866	+	0.296354i
$749$	1136.29			0.0554327
$750$	3362.98	−	2339.90i	0.163731	−	0.113921i
$751$	11628.6			0.565027			0.282514	−	0.959263i	$-0.408832\pi$
$751$	11628.6			0.565027			0.282514	+	0.959263i	$0.408832\pi$
$752$	−18157.8	+	21123.7i	−0.880514	+	1.02434i
$753$	13320.6			0.644660
$754$	32515.1	+	24311.2i	1.57047	+	1.17422i
$755$		−	3221.19i		−	0.155273i
$756$	−535.130	+	1443.46i	−0.0257440	+	0.0694421i
$757$		−	20413.1i		−	0.980090i	−0.871697	−	0.490045i	$-0.836980\pi$
$757$		−	20413.1i		−	0.980090i	0.871697	−	0.490045i	$-0.163020\pi$
$758$	19502.4	+	28029.5i	0.934512	+	1.34311i
$759$		−	12874.7i		−	0.615706i
$760$	3385.73	−	874.879i	0.161597	−	0.0417568i
$761$		−	7463.82i		−	0.355537i	−0.984072	−	0.177768i	$-0.943112\pi$
$761$		−	7463.82i		−	0.355537i	0.984072	−	0.177768i	$-0.0568878\pi$
$762$	−3683.55	+	2562.94i	−0.175119	+	0.121845i
$763$			15885.2i			0.753714i
$764$	2480.19	−	6690.07i	0.117448	−	0.316804i
$765$	360.094			0.0170186
$766$	23255.9	−	16181.0i	1.09696	−	0.763241i
$767$	12833.1	+	38610.2i	0.604140	+	1.81765i
$768$	12148.7	−	1845.07i	0.570805	−	0.0866903i
$769$			24780.4i			1.16203i	0.813892	+	0.581016i	$0.197345\pi$
$769$			24780.4i			1.16203i	−0.813892	+	0.581016i	$0.802655\pi$
$770$	1286.07	−	894.824i	0.0601906	−	0.0418795i
$771$		−	12713.0i		−	0.593837i
$772$	−21447.3	−	7951.07i	−0.999876	−	0.370680i
$773$	37842.9			1.76082			0.880410	−	0.474213i	$-0.157267\pi$
$773$	37842.9			1.76082			0.880410	+	0.474213i	$0.157267\pi$
$774$	−9261.52	+	6443.99i	−0.430101	+	0.299256i

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:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	312.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.61542 - 2.32173i) q^{2} -3.00000i q^{3} +(-2.78086 + 7.50112i) q^{4} +1.96149 q^{5} +(-6.96519 + 4.84625i) q^{6} -7.12715i q^{7} +(21.9078 - 5.66102i) q^{8} -9.00000 q^{9} +(-3.16863 - 4.55406i) q^{10} -39.6233 q^{11} +(22.5034 + 8.34259i) q^{12} +(14.7839 + 44.4796i) q^{13} +(-16.5473 + 11.5133i) q^{14} -5.88448i q^{15} +(-48.5336 - 41.7192i) q^{16} -20.3979 q^{17} +(14.5387 + 20.8956i) q^{18} +78.7892 q^{19} +(-5.45464 + 14.7134i) q^{20} -21.3814 q^{21} +(64.0081 + 91.9946i) q^{22} -108.309 q^{23} +(-16.9831 - 65.7235i) q^{24} -121.153 q^{25} +(79.3875 - 106.177i) q^{26} +27.0000i q^{27} +(53.4616 + 19.8196i) q^{28} +306.234i q^{29} +(-13.6622 + 9.50588i) q^{30} +122.283i q^{31} +(-18.4587 + 180.076i) q^{32} +118.870i q^{33} +(32.9512 + 47.3585i) q^{34} -13.9798i q^{35} +(25.0278 - 67.5101i) q^{36} +238.381 q^{37} +(-127.277 - 182.927i) q^{38} +(133.439 - 44.3517i) q^{39} +(42.9720 - 11.1040i) q^{40} +113.600i q^{41} +(34.5399 + 49.6419i) q^{42} +443.229i q^{43} +(110.187 - 297.219i) q^{44} -17.6534 q^{45} +(174.964 + 251.464i) q^{46} -435.239i q^{47} +(-125.157 + 145.601i) q^{48} +292.204 q^{49} +(195.712 + 281.284i) q^{50} +61.1938i q^{51} +(-374.759 - 12.7958i) q^{52} -496.774i q^{53} +(62.6867 - 43.6162i) q^{54} -77.7208 q^{55} +(-40.3469 - 156.140i) q^{56} -236.368i q^{57} +(710.993 - 494.696i) q^{58} +868.043 q^{59} +(44.1402 + 16.3639i) q^{60} +355.574i q^{61} +(283.909 - 197.538i) q^{62} +64.1443i q^{63} +(447.906 - 248.041i) q^{64} +(28.9985 + 87.2464i) q^{65} +(275.984 - 192.024i) q^{66} -792.201 q^{67} +(56.7239 - 153.007i) q^{68} +324.927i q^{69} +(-32.4574 + 22.5833i) q^{70} -208.138i q^{71} +(-197.170 + 50.9492i) q^{72} +1075.25i q^{73} +(-385.085 - 553.457i) q^{74} +363.458i q^{75} +(-219.102 + 591.007i) q^{76} +282.401i q^{77} +(-318.532 - 238.163i) q^{78} +1229.23 q^{79} +(-95.1983 - 81.8318i) q^{80} +81.0000 q^{81} +(263.749 - 183.511i) q^{82} -701.173 q^{83} +(59.4588 - 160.385i) q^{84} -40.0104 q^{85} +(1029.06 - 715.999i) q^{86} +918.703 q^{87} +(-868.061 + 224.308i) q^{88} +14.2857i q^{89} +(28.5176 + 40.9865i) q^{90} +(317.013 - 105.367i) q^{91} +(301.192 - 812.438i) q^{92} +366.850 q^{93} +(-1010.51 + 703.092i) q^{94} +154.544 q^{95} +(540.227 + 55.3760i) q^{96} +1169.53i q^{97} +(-472.031 - 678.418i) q^{98} +356.610 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52}+ \cdots + 2480 q^{95}+O(q^{100}) \) 84 * q - 756 * q^9 - 36 * q^10 + 12 * q^12 - 208 * q^14 - 148 * q^16 - 104 * q^17 + 620 * q^22 + 2188 * q^25 + 444 * q^26 - 204 * q^30 - 40 * q^38 - 1924 * q^40 + 192 * q^42 + 624 * q^48 - 3396 * q^49 - 1292 * q^52 - 1616 * q^55 + 608 * q^56 - 2120 * q^62 - 2856 * q^64 + 696 * q^65 - 396 * q^66 - 2536 * q^68 - 3936 * q^74 - 156 * q^78 + 3160 * q^79 + 6804 * q^81 + 4276 * q^82 - 2088 * q^87 + 1780 * q^88 + 324 * q^90 + 4792 * q^92 - 860 * q^94 + 2480 * q^95

Introduction

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