LMFDB - Embedded newform 312.4.m.a.181.14

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			181.14
Character	$\chi$	$=$	312.181
Dual form			312.4.m.a.181.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.47275 + 1.37314i) q^{2} +3.00000i q^{3} +(4.22898 - 6.79086i) q^{4} -19.0411 q^{5} +(-4.11942 - 7.41825i) q^{6} -2.83206i q^{7} +(-1.13242 + 22.5991i) q^{8} -9.00000 q^{9} +(47.0838 - 26.1460i) q^{10} -28.0565 q^{11} +(20.3726 + 12.6869i) q^{12} +(-43.7302 + 16.8721i) q^{13} +(3.88880 + 7.00296i) q^{14} -57.1232i q^{15} +(-28.2314 - 57.4368i) q^{16} -86.5449 q^{17} +(22.2547 - 12.3582i) q^{18} +82.3327 q^{19} +(-80.5243 + 129.305i) q^{20} +8.49617 q^{21} +(69.3767 - 38.5255i) q^{22} +81.3529 q^{23} +(-67.7972 - 3.39727i) q^{24} +237.562 q^{25} +(84.9661 - 101.768i) q^{26} -27.0000i q^{27} +(-19.2321 - 11.9767i) q^{28} -70.2306i q^{29} +(78.4380 + 141.251i) q^{30} -184.991i q^{31} +(148.678 + 103.261i) q^{32} -84.1695i q^{33} +(214.004 - 118.838i) q^{34} +53.9253i q^{35} +(-38.0608 + 61.1177i) q^{36} -62.8138 q^{37} +(-203.588 + 113.054i) q^{38} +(-50.6163 - 131.191i) q^{39} +(21.5626 - 430.310i) q^{40} +405.889i q^{41} +(-21.0089 + 11.6664i) q^{42} +257.891i q^{43} +(-118.650 + 190.528i) q^{44} +171.370 q^{45} +(-201.165 + 111.709i) q^{46} -200.387i q^{47} +(172.310 - 84.6943i) q^{48} +334.979 q^{49} +(-587.431 + 326.205i) q^{50} -259.635i q^{51} +(-70.3581 + 368.317i) q^{52} -121.850i q^{53} +(37.0747 + 66.7642i) q^{54} +534.226 q^{55} +(64.0018 + 3.20709i) q^{56} +246.998i q^{57} +(96.4364 + 173.663i) q^{58} +513.774 q^{59} +(-387.915 - 241.573i) q^{60} -54.0234i q^{61} +(254.018 + 457.436i) q^{62} +25.4885i q^{63} +(-509.435 - 51.1835i) q^{64} +(832.670 - 321.263i) q^{65} +(115.576 + 208.130i) q^{66} +438.409 q^{67} +(-365.997 + 587.714i) q^{68} +244.059i q^{69} +(-74.0469 - 133.344i) q^{70} +181.243i q^{71} +(10.1918 - 203.392i) q^{72} +922.359i q^{73} +(155.323 - 86.2521i) q^{74} +712.686i q^{75} +(348.183 - 559.109i) q^{76} +79.4576i q^{77} +(305.304 + 254.898i) q^{78} +158.535 q^{79} +(537.557 + 1093.66i) q^{80} +81.0000 q^{81} +(-557.341 - 1003.66i) q^{82} +324.617 q^{83} +(35.9301 - 57.6962i) q^{84} +1647.91 q^{85} +(-354.119 - 637.699i) q^{86} +210.692 q^{87} +(31.7719 - 634.051i) q^{88} -990.251i q^{89} +(-423.754 + 235.314i) q^{90} +(47.7828 + 123.846i) q^{91} +(344.040 - 552.456i) q^{92} +554.973 q^{93} +(275.159 + 495.507i) q^{94} -1567.70 q^{95} +(-309.783 + 446.034i) q^{96} -1573.51i q^{97} +(-828.320 + 459.973i) q^{98} +252.509 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 $

$2$	−2.47275	+	1.37314i	−0.874249	+	0.485478i
$2$	−2.47275	+	1.37314i	−0.874249	+	0.485478i
$3$			3.00000i			0.577350i
$3$			3.00000i			0.577350i
$4$	4.22898	−	6.79086i	0.528623	−	0.848857i
$5$	−19.0411			−1.70308			−0.851542	−	0.524286i	$-0.824332\pi$
$5$	−19.0411			−1.70308			−0.851542	+	0.524286i	$0.824332\pi$
$6$	−4.11942	−	7.41825i	−0.280291	−	0.504748i
$7$		−	2.83206i		−	0.152917i	−0.997073	−	0.0764583i	$-0.975639\pi$
$7$		−	2.83206i		−	0.152917i	0.997073	−	0.0764583i	$-0.0243612\pi$
$8$	−1.13242	+	22.5991i	−0.0500466	+	0.998747i
$9$	−9.00000			−0.333333
$10$	47.0838	−	26.1460i	1.48892	−	0.826809i
$11$	−28.0565			−0.769032			−0.384516	−	0.923118i	$-0.625632\pi$
$11$	−28.0565			−0.769032			−0.384516	+	0.923118i	$0.625632\pi$
$12$	20.3726	+	12.6869i	0.490088	+	0.305200i
$13$	−43.7302	+	16.8721i	−0.932968	+	0.359960i
$13$	−43.7302	+	16.8721i	−0.932968	+	0.359960i
$14$	3.88880	+	7.00296i	0.0742376	+	0.133687i
$15$		−	57.1232i		−	0.983276i
$16$	−28.2314	−	57.4368i	−0.441116	−	0.897450i
$17$	−86.5449			−1.23472			−0.617360	−	0.786681i	$-0.711798\pi$
$17$	−86.5449			−1.23472			−0.617360	+	0.786681i	$0.711798\pi$
$18$	22.2547	−	12.3582i	0.291416	−	0.161826i
$19$	82.3327			0.994127			0.497063	−	0.867714i	$-0.334412\pi$
$19$	82.3327			0.994127			0.497063	+	0.867714i	$0.334412\pi$
$20$	−80.5243	+	129.305i	−0.900289	+	1.44567i
$21$	8.49617			0.0882864
$22$	69.3767	−	38.5255i	0.672326	−	0.373348i
$23$	81.3529			0.737532			0.368766	−	0.929522i	$-0.379780\pi$
$23$	81.3529			0.737532			0.368766	+	0.929522i	$0.379780\pi$
$24$	−67.7972	−	3.39727i	−0.576627	−	0.0288944i
$25$	237.562			1.90049
$26$	84.9661	−	101.768i	0.640893	−	0.767630i
$27$		−	27.0000i		−	0.192450i
$28$	−19.2321	−	11.9767i	−0.129804	−	0.0808352i
$29$		−	70.2306i		−	0.449707i	−0.974393	−	0.224853i	$-0.927810\pi$
$29$		−	70.2306i		−	0.449707i	0.974393	−	0.224853i	$-0.0721903\pi$
$30$	78.4380	+	141.251i	0.477359	+	0.859628i
$31$		−	184.991i		−	1.07179i	−0.844286	−	0.535893i	$-0.819975\pi$
$31$		−	184.991i		−	1.07179i	0.844286	−	0.535893i	$-0.180025\pi$
$32$	148.678	+	103.261i	0.821338	+	0.570443i
$33$		−	84.1695i		−	0.444001i
$34$	214.004	−	118.838i	1.07945	−	0.599429i
$35$			53.9253i			0.260430i
$36$	−38.0608	+	61.1177i	−0.176208	+	0.282952i
$37$	−62.8138			−0.279095			−0.139548	−	0.990215i	$-0.544565\pi$
$37$	−62.8138			−0.279095			−0.139548	+	0.990215i	$0.544565\pi$
$38$	−203.588	+	113.054i	−0.869114	+	0.482626i
$39$	−50.6163	−	131.191i	−0.207823	−	0.538649i
$40$	21.5626	−	430.310i	0.0852335	−	1.70095i
$41$			405.889i			1.54608i	0.634359	+	0.773039i	$0.281264\pi$
$41$			405.889i			1.54608i	−0.634359	+	0.773039i	$0.718736\pi$
$42$	−21.0089	+	11.6664i	−0.0771843	+	0.0428611i
$43$			257.891i			0.914603i	0.889312	+	0.457302i	$0.151184\pi$
$43$			257.891i			0.914603i	−0.889312	+	0.457302i	$0.848816\pi$
$44$	−118.650	+	190.528i	−0.406528	+	0.652798i
$45$	171.370			0.567695
$46$	−201.165	+	111.709i	−0.644787	+	0.358056i
$47$		−	200.387i		−	0.621903i	−0.950426	−	0.310952i	$-0.899352\pi$
$47$		−	200.387i		−	0.621903i	0.950426	−	0.310952i	$-0.100648\pi$
$48$	172.310	−	84.6943i	0.518143	−	0.254679i
$49$	334.979			0.976617
$50$	−587.431	+	326.205i	−1.66151	+	0.922648i
$51$		−	259.635i		−	0.712866i
$52$	−70.3581	+	368.317i	−0.187633	+	0.982239i
$53$		−	121.850i		−	0.315798i	−0.987455	−	0.157899i	$-0.949528\pi$
$53$		−	121.850i		−	0.315798i	0.987455	−	0.157899i	$-0.0504721\pi$
$54$	37.0747	+	66.7642i	0.0934302	+	0.168249i
$55$	534.226			1.30973
$56$	64.0018	+	3.20709i	0.152725	+	0.00765295i
$57$			246.998i			0.573959i
$58$	96.4364	+	173.663i	0.218323	+	0.393156i
$59$	513.774			1.13369			0.566845	−	0.823825i	$-0.308164\pi$
$59$	513.774			1.13369			0.566845	+	0.823825i	$0.308164\pi$
$60$	−387.915	−	241.573i	−0.834661	−	0.519782i
$61$		−	54.0234i		−	0.113393i	−0.998391	−	0.0566966i	$-0.981943\pi$
$61$		−	54.0234i		−	0.113393i	0.998391	−	0.0566966i	$-0.0180568\pi$
$62$	254.018	+	457.436i	0.520328	+	0.937008i
$63$			25.4885i			0.0509722i
$64$	−509.435	−	51.1835i	−0.994991	−	0.0999677i
$65$	832.670	−	321.263i	1.58892	−	0.613042i
$66$	115.576	+	208.130i	0.215553	+	0.388167i
$67$	438.409			0.799405			0.399702	−	0.916645i	$-0.369113\pi$
$67$	438.409			0.799405			0.399702	+	0.916645i	$0.369113\pi$
$68$	−365.997	+	587.714i	−0.652701	+	1.04810i
$69$			244.059i			0.425815i
$70$	−74.0469	−	133.344i	−0.126433	−	0.227681i
$71$			181.243i			0.302952i	0.988461	+	0.151476i	$0.0484027\pi$
$71$			181.243i			0.302952i	−0.988461	+	0.151476i	$0.951597\pi$
$72$	10.1918	−	203.392i	0.0166822	−	0.332916i
$73$			922.359i			1.47882i	0.673255	+	0.739410i	$0.264896\pi$
$73$			922.359i			1.47882i	−0.673255	+	0.739410i	$0.735104\pi$
$74$	155.323	−	86.2521i	0.243999	−	0.135495i
$75$			712.686i			1.09725i
$76$	348.183	−	559.109i	0.525518	−	0.843871i
$77$			79.4576i			0.117598i
$78$	305.304	+	254.898i	0.443191	+	0.370020i
$79$	158.535			0.225780			0.112890	−	0.993607i	$-0.463989\pi$
$79$	158.535			0.225780			0.112890	+	0.993607i	$0.463989\pi$
$80$	537.557	+	1093.66i	0.751258	+	1.52843i
$81$	81.0000			0.111111
$82$	−557.341	−	1003.66i	−0.750586	−	1.35166i
$83$	324.617			0.429293			0.214646	−	0.976692i	$-0.431140\pi$
$83$	324.617			0.429293			0.214646	+	0.976692i	$0.431140\pi$
$84$	35.9301	−	57.6962i	0.0466702	−	0.0749426i
$85$	1647.91			2.10283
$86$	−354.119	−	637.699i	−0.444020	−	0.799591i
$87$	210.692			0.259638
$88$	31.7719	−	634.051i	0.0384874	−	0.768069i
$89$		−	990.251i		−	1.17940i	−0.807623	−	0.589699i	$-0.799246\pi$
$89$		−	990.251i		−	1.17940i	0.807623	−	0.589699i	$-0.200754\pi$
$90$	−423.754	+	235.314i	−0.496306	+	0.275603i
$91$	47.7828	+	123.846i	0.0550439	+	0.142666i
$92$	344.040	−	552.456i	0.389876	−	0.626060i
$93$	554.973			0.618796
$94$	275.159	+	495.507i	0.301920	+	0.543698i
$95$	−1567.70			−1.69308
$96$	−309.783	+	446.034i	−0.329345	+	0.474199i
$97$		−	1573.51i		−	1.64707i	−0.567264	−	0.823536i	$-0.691998\pi$
$97$		−	1573.51i		−	1.64707i	0.567264	−	0.823536i	$-0.308002\pi$
$98$	−828.320	+	459.973i	−0.853806	+	0.474126i
$99$	252.509			0.256344
$100$	1004.64	−	1613.25i	1.00464	−	1.61325i
$101$		−	541.440i		−	0.533419i	−0.963777	−	0.266709i	$-0.914064\pi$
$101$		−	541.440i		−	0.533419i	0.963777	−	0.266709i	$-0.0859364\pi$
$102$	356.515	+	642.012i	0.346080	+	0.623222i
$103$	−1900.29			−1.81787			−0.908937	−	0.416933i	$-0.863105\pi$
$103$	−1900.29			−1.81787			−0.908937	+	0.416933i	$0.863105\pi$
$104$	−331.773	−	1007.37i	−0.312817	−	0.949813i
$105$	−161.776			−0.150359
$106$	167.316	+	301.303i	0.153313	+	0.276086i
$107$			2061.70i			1.86273i	0.364092	+	0.931363i	$0.381380\pi$
$107$			2061.70i			1.86273i	−0.364092	+	0.931363i	$0.618620\pi$
$108$	−183.353	−	114.182i	−0.163363	−	0.101733i
$109$	2009.01			1.76540			0.882699	−	0.469939i	$-0.155724\pi$
$109$	2009.01			1.76540			0.882699	+	0.469939i	$0.155724\pi$
$110$	−1321.01	+	733.566i	−1.14503	+	0.635843i
$111$		−	188.442i		−	0.161136i
$112$	−162.664	+	79.9530i	−0.137235	+	0.0674540i
$113$	462.450			0.384988			0.192494	−	0.981298i	$-0.438342\pi$
$113$	462.450			0.384988			0.192494	+	0.981298i	$0.438342\pi$
$114$	−339.162	−	610.764i	−0.278645	−	0.501783i
$115$	−1549.04			−1.25608
$116$	−476.926	−	297.004i	−0.381737	−	0.237725i
$117$	393.572	−	151.849i	0.310989	−	0.119987i
$118$	−1270.43	+	705.483i	−0.991127	+	0.550381i
$119$			245.100i			0.188809i
$120$	1290.93	+	64.6877i	0.982044	+	0.0492096i
$121$	−543.833			−0.408589
$122$	74.1816	+	133.586i	0.0550499	+	0.0991340i
$123$	−1217.67			−0.892628
$124$	−1256.25	−	782.323i	−0.909793	−	0.566570i
$125$	−2143.30			−1.53362
$126$	−34.9992	−	63.0267i	−0.0247459	−	0.0445624i
$127$	−1541.00			−1.07671			−0.538353	−	0.842719i	$-0.680953\pi$
$127$	−1541.00			−1.07671			−0.538353	+	0.842719i	$0.680953\pi$
$128$	1329.99	−	572.961i	0.918402	−	0.395649i
$129$	−773.672			−0.528046
$130$	−1617.84	+	1937.77i	−1.09150	+	1.30734i
$131$		−	898.222i		−	0.599069i	−0.954086	−	0.299534i	$-0.903169\pi$
$131$		−	898.222i		−	0.599069i	0.954086	−	0.299534i	$-0.0968313\pi$
$132$	−571.583	−	355.951i	−0.376893	−	0.234709i
$133$		−	233.171i		−	0.152018i
$134$	−1084.07	+	601.996i	−0.698879	+	0.388093i
$135$			514.109i			0.327759i
$136$	98.0056	−	1955.83i	0.0617934	−	1.23317i
$137$		−	2844.60i		−	1.77395i	−0.461819	−	0.886974i	$-0.652803\pi$
$137$		−	2844.60i		−	1.77395i	0.461819	−	0.886974i	$-0.347197\pi$
$138$	−335.126	−	603.496i	−0.206724	−	0.372268i
$139$		−	1961.68i		−	1.19703i	−0.801111	−	0.598516i	$-0.795757\pi$
$139$		−	1961.68i		−	1.19703i	0.801111	−	0.598516i	$-0.204243\pi$
$140$	366.199	+	228.049i	0.221068	+	0.137669i
$141$	601.161			0.359056
$142$	−248.872	−	448.169i	−0.147077	−	0.264856i
$143$	1226.92	−	473.373i	0.717482	−	0.276821i
$144$	254.083	+	516.931i	0.147039	+	0.299150i
$145$			1337.27i			0.765889i
$146$	−1266.53	−	2280.76i	−0.717935	−	1.29286i
$147$			1004.94i			0.563850i
$148$	−265.639	+	426.560i	−0.147536	+	0.236912i
$149$	−310.758			−0.170861			−0.0854304	−	0.996344i	$-0.527227\pi$
$149$	−310.758			−0.170861			−0.0854304	+	0.996344i	$0.527227\pi$
$150$	−978.616	−	1762.29i	−0.532691	−	0.959271i
$151$		−	2270.36i		−	1.22357i	−0.791024	−	0.611785i	$-0.790452\pi$
$151$		−	2270.36i		−	1.22357i	0.791024	−	0.611785i	$-0.209548\pi$
$152$	−93.2355	+	1860.64i	−0.0497526	+	0.992881i
$153$	778.904			0.411573
$154$	−109.106	−	196.479i	−0.0570911	−	0.102810i
$155$			3522.42i			1.82534i
$156$	−1104.95	−	211.074i	−0.567096	−	0.108330i
$157$		−	1677.20i		−	0.852580i	−0.904586	−	0.426290i	$-0.859820\pi$
$157$		−	1677.20i		−	0.852580i	0.904586	−	0.426290i	$-0.140180\pi$
$158$	−392.019	+	217.691i	−0.197388	+	0.109611i
$159$	365.549			0.182326
$160$	−2830.99	−	1966.20i	−1.39881	−	0.971512i
$161$		−	230.396i		−	0.112781i
$162$	−200.293	+	111.224i	−0.0971388	+	0.0539420i
$163$	332.627			0.159837			0.0799183	−	0.996801i	$-0.474534\pi$
$163$	332.627			0.159837			0.0799183	+	0.996801i	$0.474534\pi$
$164$	2756.33	+	1716.50i	1.31240	+	0.817291i
$165$			1602.68i			0.756171i
$166$	−802.696	+	445.744i	−0.375309	+	0.208412i
$167$			960.805i			0.445205i	0.974909	+	0.222603i	$0.0714553\pi$
$167$			960.805i			0.445205i	−0.974909	+	0.222603i	$0.928545\pi$
$168$	−9.62126	+	192.005i	−0.00441843	+	0.0881758i
$169$	1627.66	−	1475.64i	0.740857	−	0.671663i
$170$	−4074.86	+	2262.80i	−1.83840	+	1.02088i
$171$	−740.994			−0.331376
$172$	1751.30	+	1090.61i	0.776367	+	0.483480i
$173$		−	3431.96i		−	1.50825i	−0.656731	−	0.754125i	$-0.728061\pi$
$173$		−	3431.96i		−	1.50825i	0.656731	−	0.754125i	$-0.271939\pi$
$174$	−520.988	+	289.309i	−0.226989	+	0.126049i
$175$		−	672.788i		−	0.290617i
$176$	792.076	+	1611.48i	0.339233	+	0.690168i
$177$			1541.32i			0.654536i
$178$	1359.75	+	2448.64i	0.572571	+	1.03109i
$179$			3102.57i			1.29551i	0.761847	+	0.647757i	$0.224293\pi$
$179$			3102.57i			1.29551i	−0.761847	+	0.647757i	$0.775707\pi$
$180$	724.718	−	1163.75i	0.300096	−	0.481892i
$181$		−	851.643i		−	0.349736i	−0.984592	−	0.174868i	$-0.944050\pi$
$181$		−	851.643i		−	0.349736i	0.984592	−	0.174868i	$-0.0559498\pi$
$182$	−288.213	−	240.629i	−0.117383	−	0.0980032i
$183$	162.070			0.0654676
$184$	−92.1260	+	1838.50i	−0.0369110	+	0.736608i
$185$	1196.04			0.475323
$186$	−1372.31	+	762.055i	−0.540982	+	0.300412i
$187$	2428.15			0.949539
$188$	−1360.80	−	847.433i	−0.527907	−	0.328752i
$189$	−76.4655			−0.0294288
$190$	3876.53	−	2152.67i	1.48017	−	0.821953i
$191$	1091.38			0.413454			0.206727	−	0.978399i	$-0.433719\pi$
$191$	1091.38			0.413454			0.206727	+	0.978399i	$0.433719\pi$
$192$	153.550	−	1528.31i	0.0577164	−	0.574458i
$193$			4462.90i			1.66449i	0.554407	+	0.832246i	$0.312945\pi$
$193$			4462.90i			1.66449i	−0.554407	+	0.832246i	$0.687055\pi$
$194$	2160.65	+	3890.90i	0.799617	+	1.43995i
$195$	963.789	+	2498.01i	0.353940	+	0.917365i
$196$	1416.62	−	2274.80i	0.516262	−	0.829008i
$197$	127.527			0.0461216			0.0230608	−	0.999734i	$-0.492659\pi$
$197$	127.527			0.0461216			0.0230608	+	0.999734i	$0.492659\pi$
$198$	−624.390	+	346.729i	−0.224109	+	0.124449i
$199$	251.192			0.0894800			0.0447400	−	0.998999i	$-0.485754\pi$
$199$	251.192			0.0894800			0.0447400	+	0.998999i	$0.485754\pi$
$200$	−269.021	+	5368.68i	−0.0951132	+	1.89811i
$201$			1315.23i			0.461537i
$202$	743.472	+	1338.85i	0.258963	+	0.466341i
$203$	−198.897			−0.0687677
$204$	−1763.14	−	1097.99i	−0.605121	−	0.376837i
$205$		−	7728.55i		−	2.63310i
$206$	4698.94	−	2609.36i	1.58927	−	0.882538i
$207$	−732.176			−0.245844
$208$	2203.65	+	2035.40i	0.734594	+	0.678507i
$209$	−2309.97			−0.764515
$210$	400.031	−	222.141i	0.131451	−	0.0729961i
$211$		−	1553.27i		−	0.506785i	−0.967363	−	0.253393i	$-0.918454\pi$
$211$		−	1553.27i		−	0.506785i	0.967363	−	0.253393i	$-0.0815465\pi$
$212$	−827.462	−	515.299i	−0.268068	−	0.166938i
$213$	−543.729			−0.174910
$214$	−2830.99	−	5098.06i	−0.904312	−	1.62849i
$215$		−	4910.51i		−	1.55765i
$216$	610.175	+	30.5755i	0.192209	+	0.00963146i
$217$	−523.905			−0.163894
$218$	−4967.78	+	2758.65i	−1.54340	+	0.857061i
$219$	−2767.08			−0.853798
$220$	2259.23	−	3627.85i	0.692351	−	1.11177i
$221$	3784.63	−	1460.20i	1.15195	−	0.444450i
$222$	258.756	+	465.969i	0.0782279	+	0.140873i
$223$			3227.16i			0.969087i	0.874767	+	0.484543i	$0.161014\pi$
$223$			3227.16i			0.969087i	−0.874767	+	0.484543i	$0.838986\pi$
$224$	292.441	−	421.064i	0.0872301	−	0.125596i
$225$	−2138.06			−0.633498
$226$	−1143.52	+	635.009i	−0.336576	+	0.186903i
$227$	−3741.71			−1.09404			−0.547018	−	0.837121i	$-0.684237\pi$
$227$	−3741.71			−1.09404			−0.547018	+	0.837121i	$0.684237\pi$
$228$	1677.33	+	1044.55i	0.487209	+	0.303408i
$229$	840.871			0.242648			0.121324	−	0.992613i	$-0.461286\pi$
$229$	840.871			0.242648			0.121324	+	0.992613i	$0.461286\pi$
$230$	3830.40	−	2127.05i	1.09813	−	0.609799i
$231$	−238.373			−0.0678951
$232$	1587.15	+	79.5309i	0.449143	+	0.0225063i
$233$	1164.24			0.327348			0.163674	−	0.986514i	$-0.447665\pi$
$233$	1164.24			0.327348			0.163674	+	0.986514i	$0.447665\pi$
$234$	−764.695	+	915.913i	−0.213631	+	0.255877i
$235$			3815.58i			1.05915i
$236$	2172.74	−	3488.96i	0.599294	−	0.962340i
$237$			475.606i			0.130354i
$238$	−336.556	−	606.071i	−0.0916626	−	0.165066i
$239$		−	5869.21i		−	1.58848i	−0.607601	−	0.794242i	$-0.707868\pi$
$239$		−	5869.21i		−	1.58848i	0.607601	−	0.794242i	$-0.292132\pi$
$240$	−3280.97	+	1612.67i	−0.882441	+	0.433739i
$241$			4566.64i			1.22059i	0.792173	+	0.610297i	$0.208950\pi$
$241$			4566.64i			1.22059i	−0.792173	+	0.610297i	$0.791050\pi$
$242$	1344.76	−	746.757i	0.357209	−	0.198361i
$243$			243.000i			0.0641500i
$244$	−366.865	−	228.464i	−0.0962547	−	0.0599422i
$245$	−6378.36			−1.66326
$246$	3010.98	−	1672.02i	0.780379	−	0.433351i
$247$	−3600.42	+	1389.13i	−0.927488	+	0.357846i
$248$	4180.62	+	209.488i	1.07044	+	0.0536392i
$249$			973.850i			0.247852i
$250$	5299.84	−	2943.04i	1.34076	−	0.744538i
$251$		−	3708.86i		−	0.932674i	−0.884607	−	0.466337i	$-0.845573\pi$
$251$		−	3708.86i		−	0.932674i	0.884607	−	0.466337i	$-0.154427\pi$
$252$	173.089	+	107.790i	0.0432681	+	0.0269451i
$253$	−2282.48			−0.567186
$254$	3810.51	−	2116.01i	0.941309	−	0.522717i
$255$			4943.72i			1.21407i
$256$	−2501.97	+	3243.05i	−0.610833	+	0.791760i
$257$	2558.76			0.621056			0.310528	−	0.950564i	$-0.399494\pi$
$257$	2558.76			0.621056			0.310528	+	0.950564i	$0.399494\pi$
$258$	1913.10	−	1062.36i	0.461644	−	0.256355i
$259$			177.892i			0.0426783i
$260$	1339.69	−	7013.15i	0.319555	−	1.67284i
$261$			632.076i			0.149902i
$262$	1233.38	+	2221.08i	0.290835	+	0.523735i
$263$	4193.20			0.983132			0.491566	−	0.870840i	$-0.336425\pi$
$263$	4193.20			0.983132			0.491566	+	0.870840i	$0.336425\pi$
$264$	1902.15	+	95.3156i	0.443445	+	0.0222207i
$265$			2320.14i			0.537831i
$266$	320.176	+	576.573i	0.0738016	+	0.132902i
$267$	2970.75			0.680925
$268$	1854.02	−	2977.17i	0.422584	−	0.678580i
$269$		−	475.756i		−	0.107834i	−0.998545	−	0.0539170i	$-0.982829\pi$
$269$		−	475.756i		−	0.107834i	0.998545	−	0.0539170i	$-0.0171706\pi$
$270$	−705.942	−	1271.26i	−0.159120	−	0.286543i
$271$			3254.66i			0.729544i	0.931097	+	0.364772i	$0.118853\pi$
$271$			3254.66i			0.729544i	−0.931097	+	0.364772i	$0.881147\pi$
$272$	2443.29	+	4970.86i	0.544655	+	1.10810i
$273$	−371.539	+	143.348i	−0.0823684	+	0.0317796i
$274$	3906.04	+	7033.99i	0.861213	+	1.55087i
$275$	−6665.16			−1.46154
$276$	1657.37	+	1032.12i	0.361456	+	0.225095i
$277$			8173.58i			1.77293i	0.462791	+	0.886467i	$0.346848\pi$
$277$			8173.58i			1.77293i	−0.462791	+	0.886467i	$0.653152\pi$
$278$	2693.66	+	4850.74i	0.581132	+	1.04650i
$279$			1664.92i			0.357262i
$280$	−1218.66	−	61.0664i	−0.260103	−	0.0130336i
$281$		−	1965.24i		−	0.417211i	−0.978000	−	0.208605i	$-0.933108\pi$
$281$		−	1965.24i		−	0.417211i	0.978000	−	0.208605i	$-0.0668924\pi$
$282$	−1486.52	+	825.477i	−0.313904	+	0.174314i
$283$			3637.36i			0.764024i	0.924157	+	0.382012i	$0.124769\pi$
$283$			3637.36i			0.764024i	−0.924157	+	0.382012i	$0.875231\pi$
$284$	1230.80	+	766.474i	0.257163	+	0.160147i
$285$		−	4703.10i		−	0.977501i
$286$	−2383.85	+	2855.26i	−0.492868	+	0.590332i
$287$	1149.50			0.236421
$288$	−1338.10	−	929.350i	−0.273779	−	0.190148i
$289$	2577.02			0.524532
$290$	−1836.25	−	3306.72i	−0.371822	−	0.669577i
$291$	4720.54			0.950938
$292$	6263.60	+	3900.64i	1.25531	+	0.781738i
$293$	−308.003			−0.0614121			−0.0307060	−	0.999528i	$-0.509776\pi$
$293$	−308.003			−0.0614121			−0.0307060	+	0.999528i	$0.509776\pi$
$294$	−1379.92	−	2484.96i	−0.273737	−	0.492945i
$295$	−9782.80			−1.93077
$296$	71.1319	−	1419.53i	0.0139678	−	0.278746i
$297$			757.526i			0.148000i
$298$	768.426	−	426.714i	0.149375	−	0.0829492i
$299$	−3557.58	+	1372.60i	−0.688094	+	0.265482i
$300$	4839.75	+	3013.93i	0.931409	+	0.580032i
$301$	730.360			0.139858
$302$	3117.52	+	5614.03i	0.594016	+	1.06971i
$303$	1624.32			0.307969
$304$	−2324.37	−	4728.92i	−0.438525	−	0.892179i
$305$			1028.66i			0.193118i
$306$	−1926.04	+	1069.54i	−0.359817	+	0.199810i
$307$	−6355.37			−1.18150			−0.590749	−	0.806855i	$-0.701168\pi$
$307$	−6355.37			−1.18150			−0.590749	+	0.806855i	$0.701168\pi$
$308$	539.585	+	336.025i	0.0998237	+	0.0621649i
$309$		−	5700.87i		−	1.04955i
$310$	−4836.78	−	8710.07i	−0.886163	−	1.59580i
$311$	5572.23			1.01599			0.507994	−	0.861361i	$-0.330387\pi$
$311$	5572.23			1.01599			0.507994	+	0.861361i	$0.330387\pi$
$312$	3022.10	−	995.319i	0.548375	−	0.180605i
$313$	6281.26			1.13431			0.567153	−	0.823613i	$-0.308045\pi$
$313$	6281.26			1.13431			0.567153	+	0.823613i	$0.308045\pi$
$314$	2303.03	+	4147.29i	0.413909	+	0.745367i
$315$		−	485.328i		−	0.0868099i
$316$	670.443	−	1076.59i	0.119353	−	0.191655i
$317$	9250.23			1.63894			0.819471	−	0.573121i	$-0.194267\pi$
$317$	9250.23			1.63894			0.819471	+	0.573121i	$0.194267\pi$
$318$	−903.910	+	501.949i	−0.159399	+	0.0885154i
$319$			1970.43i			0.345839i
$320$	9700.19	+	974.587i	1.69455	+	0.170253i
$321$	−6185.09			−1.07545
$322$	316.365	+	569.711i	0.0547527	+	0.0985986i
$323$	−7125.47			−1.22747
$324$	342.547	−	550.059i	0.0587358	−	0.0943174i
$325$	−10388.6	+	4008.17i	−1.77310	+	0.684103i
$326$	−822.504	+	456.743i	−0.139737	+	0.0775971i
$327$			6027.03i			1.01925i
$328$	−9172.70	−	459.638i	−1.54414	−	0.0773758i
$329$	−567.507			−0.0950993
$330$	−2200.70	−	3963.02i	−0.367104	−	0.661082i
$331$	7929.83			1.31681			0.658403	−	0.752665i	$-0.271232\pi$
$331$	7929.83			1.31681			0.658403	+	0.752665i	$0.271232\pi$
$332$	1372.80	−	2204.43i	0.226934	−	0.364408i
$333$	565.325			0.0930318
$334$	−1319.32	−	2375.83i	−0.216137	−	0.389220i
$335$	−8347.76			−1.36145
$336$	−239.859	−	487.993i	−0.0389446	−	0.0792327i
$337$	10771.2			1.74107			0.870537	−	0.492103i	$-0.163772\pi$
$337$	10771.2			1.74107			0.870537	+	0.492103i	$0.163772\pi$
$338$	−1998.54	+	5883.90i	−0.321616	+	0.946870i
$339$			1387.35i			0.222273i
$340$	6968.97	−	11190.7i	1.11160	−	1.78500i
$341$			5190.20i			0.824238i
$342$	1832.29	−	1017.49i	0.289705	−	0.160875i
$343$		−	1920.08i		−	0.302257i
$344$	−5828.08	−	292.042i	−0.913457	−	0.0457727i
$345$		−	4647.13i		−	0.725198i
$346$	4712.56	+	8486.39i	0.732222	+	1.31859i
$347$		−	11340.5i		−	1.75443i	−0.480097	−	0.877215i	$-0.659399\pi$
$347$		−	11340.5i		−	1.75443i	0.480097	−	0.877215i	$-0.340601\pi$
$348$	891.012	−	1430.78i	0.137251	−	0.220396i
$349$	−9723.74			−1.49140			−0.745702	−	0.666280i	$-0.767886\pi$
$349$	−9723.74			−1.49140			−0.745702	+	0.666280i	$0.767886\pi$
$350$	923.832	+	1663.64i	0.141088	+	0.254072i
$351$	455.547	+	1180.72i	0.0692744	+	0.179550i
$352$	−4171.38	−	2897.15i	−0.631635	−	0.438689i
$353$			462.908i			0.0697963i	0.999391	+	0.0348982i	$0.0111107\pi$
$353$			462.908i			0.0697963i	−0.999391	+	0.0348982i	$0.988889\pi$
$354$	−2116.45	−	3811.30i	−0.317763	−	0.572227i
$355$		−	3451.06i		−	0.515953i
$356$	−6724.65	−	4187.75i	−1.00114	−	0.623456i
$357$	−735.300			−0.109009
$358$	−4260.26	−	7671.87i	−0.628943	−	1.13260i
$359$			9586.17i			1.40930i	0.709555	+	0.704650i	$0.248896\pi$
$359$			9586.17i			1.40930i	−0.709555	+	0.704650i	$0.751104\pi$
$360$	−194.063	+	3872.79i	−0.0284112	+	0.566983i
$361$	−80.3333			−0.0117121
$362$	1169.42	+	2105.90i	0.169789	+	0.305756i
$363$		−	1631.50i		−	0.235899i
$364$	1043.10	+	199.258i	0.150201	+	0.0286922i
$365$		−	17562.7i		−	2.51856i
$366$	−400.759	+	222.545i	−0.0572350	+	0.0317831i
$367$	10913.6			1.55228			0.776138	−	0.630564i	$-0.217176\pi$
$367$	10913.6			1.55228			0.776138	+	0.630564i	$0.217176\pi$
$368$	−2296.71	−	4672.65i	−0.325338	−	0.661898i
$369$		−	3653.00i		−	0.515359i
$370$	−2957.51	+	1642.33i	−0.415551	+	0.230759i
$371$	−345.085			−0.0482908
$372$	2346.97	−	3768.74i	0.327109	−	0.525269i
$373$			9886.46i			1.37239i	0.727418	+	0.686195i	$0.240720\pi$
$373$			9886.46i			1.37239i	−0.727418	+	0.686195i	$0.759280\pi$
$374$	−6004.20	+	3334.18i	−0.830133	+	0.460980i
$375$		−	6429.89i		−	0.885435i
$376$	4528.56	+	226.923i	0.621124	+	0.0311241i
$377$	1184.94	+	3071.20i	0.161877	+	0.419562i
$378$	189.080	−	104.998i	0.0257281	−	0.0142870i
$379$	−5858.78			−0.794051			−0.397026	−	0.917807i	$-0.629958\pi$
$379$	−5858.78			−0.794051			−0.397026	+	0.917807i	$0.629958\pi$
$380$	−6629.78	+	10646.0i	−0.895001	+	1.43718i
$381$		−	4623.00i		−	0.621636i
$382$	−2698.72	+	1498.62i	−0.361461	+	0.200723i
$383$		−	5711.41i		−	0.761982i	−0.924579	−	0.380991i	$-0.875583\pi$
$383$		−	5711.41i		−	0.761982i	0.924579	−	0.380991i	$-0.124417\pi$
$384$	1718.88	+	3989.96i	0.228428	+	0.530239i
$385$		−	1512.96i		−	0.200279i
$386$	−6128.18	−	11035.6i	−0.808073	−	1.45518i
$387$		−	2321.01i		−	0.304868i
$388$	−10685.5	−	6654.36i	−1.39813	−	0.870680i
$389$			2371.13i			0.309051i	0.987989	+	0.154526i	$0.0493849\pi$
$389$			2371.13i			0.309051i	−0.987989	+	0.154526i	$0.950615\pi$
$390$	−5813.32	−	4853.53i	−0.754792	−	0.630175i
$391$	−7040.68			−0.910645
$392$	−379.339	+	7570.22i	−0.0488763	+	0.975393i
$393$	2694.66			0.345872
$394$	−315.343	+	175.113i	−0.0403217	+	0.0223910i
$395$	−3018.68			−0.384523
$396$	1067.85	−	1714.75i	0.135509	−	0.217599i
$397$	15051.3			1.90278			0.951390	−	0.307989i	$-0.0996562\pi$
$397$	15051.3			1.90278			0.951390	+	0.307989i	$0.0996562\pi$
$398$	−621.134	+	344.921i	−0.0782278	+	0.0434405i
$399$	699.512			0.0877679
$400$	−6706.71	−	13644.8i	−0.838339	−	1.70560i
$401$		−	1988.23i		−	0.247600i	−0.992307	−	0.123800i	$-0.960492\pi$
$401$		−	1988.23i		−	0.247600i	0.992307	−	0.123800i	$-0.0395081\pi$
$402$	−1805.99	−	3252.22i	−0.224066	−	0.403498i
$403$	3121.19	+	8089.70i	0.385800	+	0.999942i
$404$	−3676.84	−	2289.74i	−0.452796	−	0.281977i
$405$	−1542.33			−0.189232
$406$	491.823	−	273.113i	0.0601201	−	0.0333852i
$407$	1762.34			0.214633
$408$	5867.50	+	294.017i	0.711972	+	0.0356765i
$409$			2230.74i			0.269689i	0.990867	+	0.134845i	$0.0430535\pi$
$409$			2230.74i			0.269689i	−0.990867	+	0.134845i	$0.956946\pi$
$410$	10612.4	+	19110.8i	1.27831	+	2.30198i
$411$	8533.81			1.02419
$412$	−8036.29	+	12904.6i	−0.960969	+	1.54312i
$413$		−	1455.04i		−	0.173360i
$414$	1810.49	−	1005.38i	0.214929	−	0.119352i
$415$	−6181.05			−0.731122
$416$	−8243.95	−	2007.12i	−0.971618	−	0.236556i
$417$	5885.03			0.691106
$418$	5711.97	−	3171.90i	0.668377	−	0.371155i
$419$		−	13926.1i		−	1.62371i	−0.583860	−	0.811855i	$-0.698458\pi$
$419$		−	13926.1i		−	1.62371i	0.583860	−	0.811855i	$-0.301542\pi$
$420$	−684.148	+	1098.60i	−0.0794833	+	0.127633i
$421$	−2376.40			−0.275104			−0.137552	−	0.990495i	$-0.543923\pi$
$421$	−2376.40			−0.275104			−0.137552	+	0.990495i	$0.543923\pi$
$422$	2132.86	+	3840.86i	0.246033	+	0.443057i
$423$			1803.48i			0.207301i
$424$	2753.68	+	137.985i	0.315403	+	0.0158046i
$425$	−20559.8			−2.34658
$426$	1344.51	−	746.616i	0.152914	−	0.0849147i
$427$	−152.997			−0.0173397
$428$	14000.7	+	8718.87i	1.58119	+	0.984679i
$429$	1420.12	+	3680.75i	0.159823	+	0.414239i
$430$	6742.81	+	12142.5i	0.756203	+	1.36177i
$431$		−	150.457i		−	0.0168150i	−0.999965	−	0.00840748i	$-0.997324\pi$
$431$		−	150.457i		−	0.0168150i	0.999965	−	0.00840748i	$-0.00267622\pi$
$432$	−1550.79	+	762.249i	−0.172714	+	0.0848929i
$433$	−3807.80			−0.422612			−0.211306	−	0.977420i	$-0.567772\pi$
$433$	−3807.80			−0.422612			−0.211306	+	0.977420i	$0.567772\pi$
$434$	1295.49	−	719.394i	0.143284	−	0.0795668i
$435$	−4011.80			−0.442186
$436$	8496.07	−	13642.9i	0.933229	−	1.49857i
$437$	6698.00			0.733201
$438$	6842.29	−	3799.58i	0.746432	−	0.414500i
$439$	−13823.6			−1.50288			−0.751438	−	0.659804i	$-0.770639\pi$
$439$	−13823.6			−1.50288			−0.751438	+	0.659804i	$0.770639\pi$
$440$	−604.970	+	12073.0i	−0.0655473	+	1.30809i
$441$	−3014.82			−0.325539
$442$	−7353.39	+	8807.52i	−0.791323	+	0.947808i
$443$		−	2783.09i		−	0.298485i	−0.988801	−	0.149242i	$-0.952317\pi$
$443$		−	2783.09i		−	0.298485i	0.988801	−	0.149242i	$-0.0476834\pi$
$444$	−1279.68	−	796.916i	−0.136781	−	0.0851801i
$445$			18855.4i			2.00861i
$446$	−4431.33	−	7979.95i	−0.470470	−	0.847223i
$447$		−	932.273i		−	0.0986466i
$448$	−144.954	+	1442.75i	−0.0152867	+	0.152151i
$449$		−	5168.19i		−	0.543211i	−0.962409	−	0.271606i	$-0.912445\pi$
$449$		−	5168.19i		−	0.543211i	0.962409	−	0.271606i	$-0.0875547\pi$
$450$	5286.88	−	2935.85i	0.553835	−	0.307549i
$451$		−	11387.8i		−	1.18898i
$452$	1955.69	−	3140.43i	0.203514	−	0.326800i
$453$	6811.07			0.706429
$454$	9252.31	−	5137.89i	0.956459	−	0.531130i
$455$	−909.834	−	2358.17i	−0.0937444	−	0.242973i
$456$	−5581.92	−	279.707i	−0.573240	−	0.0287247i
$457$		−	13075.6i		−	1.33841i	−0.743079	−	0.669203i	$-0.766635\pi$
$457$		−	13075.6i		−	1.33841i	0.743079	−	0.669203i	$-0.233365\pi$
$458$	−2079.26	+	1154.63i	−0.212134	+	0.117800i
$459$			2336.71i			0.237622i
$460$	−6550.88	+	10519.3i	−0.663992	+	1.06623i
$461$	−12458.9			−1.25872			−0.629359	−	0.777114i	$-0.716683\pi$
$461$	−12458.9			−1.25872			−0.629359	+	0.777114i	$0.716683\pi$
$462$	589.436	−	327.319i	0.0593572	−	0.0329616i
$463$		−	4329.02i		−	0.434529i	−0.976113	−	0.217264i	$-0.930287\pi$
$463$		−	4329.02i		−	0.434529i	0.976113	−	0.217264i	$-0.0697134\pi$
$464$	−4033.82	+	1982.71i	−0.403589	+	0.198373i
$465$	−10567.3			−1.05386
$466$	−2878.88	+	1598.67i	−0.286184	+	0.158920i
$467$			13755.4i			1.36300i	0.731817	+	0.681501i	$0.238673\pi$
$467$			13755.4i			1.36300i	−0.731817	+	0.681501i	$0.761327\pi$
$468$	633.223	−	3314.86i	0.0625443	−	0.327413i
$469$		−	1241.60i		−	0.122242i
$470$	−5239.32	−	9434.97i	−0.514195	−	0.925963i
$471$	5031.60			0.492237
$472$	−581.810	+	11610.8i	−0.0567372	+	1.13227i
$473$		−	7235.51i		−	0.703359i
$474$	−653.074	−	1176.06i	−0.0632841	−	0.113962i
$475$	19559.1			1.88933
$476$	1664.44	+	1036.52i	0.160272	+	0.0998087i
$477$			1096.65i			0.105266i
$478$	8059.24	+	14513.1i	0.771174	+	1.38873i
$479$		−	8537.70i		−	0.814400i	−0.913339	−	0.407200i	$-0.866505\pi$
$479$		−	8537.70i		−	0.814400i	0.913339	−	0.407200i	$-0.133495\pi$
$480$	5898.60	−	8492.96i	0.560902	−	0.807601i
$481$	2746.86	−	1059.80i	0.260387	−	0.100463i
$482$	−6270.63	−	11292.2i	−0.592571	−	1.06710i
$483$	691.187			0.0651141
$484$	−2299.86	+	3693.09i	−0.215990	+	0.346834i
$485$			29961.3i			2.80510i
$486$	−333.673	−	600.878i	−0.0311434	−	0.0560831i
$487$			7301.19i			0.679360i	0.940541	+	0.339680i	$0.110319\pi$
$487$			7301.19i			0.679360i	−0.940541	+	0.339680i	$0.889681\pi$
$488$	1220.88	+	61.1774i	0.113251	+	0.00567494i
$489$			997.881i			0.0922817i
$490$	15772.1	−	8758.38i	1.45410	−	0.807476i
$491$			13177.7i			1.21120i	0.795769	+	0.605601i	$0.207067\pi$
$491$			13177.7i			1.21120i	−0.795769	+	0.605601i	$0.792933\pi$
$492$	−5149.49	+	8269.00i	−0.471863	+	0.757714i
$493$			6078.10i			0.555262i
$494$	6995.49	−	8378.84i	0.637129	−	0.763121i
$495$	−4808.03			−0.436575
$496$	−10625.3	+	5222.56i	−0.961874	+	0.472782i
$497$	513.291			0.0463264
$498$	−1337.23	−	2408.09i	−0.120327	−	0.216685i
$499$	−938.020			−0.0841514			−0.0420757	−	0.999114i	$-0.513397\pi$
$499$	−938.020			−0.0841514			−0.0420757	+	0.999114i	$0.513397\pi$
$500$	−9063.96	+	14554.8i	−0.810705	+	1.30182i
$501$	−2882.41			−0.257039
$502$	5092.78	+	9171.08i	0.452792	+	0.815389i
$503$	16687.1			1.47921			0.739603	−	0.673044i	$-0.235013\pi$
$503$	16687.1			1.47921			0.739603	+	0.673044i	$0.235013\pi$
$504$	−576.016	−	28.8638i	−0.0509083	−	0.00255098i
$505$			10309.6i			0.908457i
$506$	5643.99	−	3134.16i	0.495862	−	0.275356i
$507$	4426.93	+	4882.99i	0.387785	+	0.427734i
$508$	−6516.86	+	10464.7i	−0.569171	+	0.913969i
$509$	−663.007			−0.0577353			−0.0288677	−	0.999583i	$-0.509190\pi$
$509$	−663.007			−0.0577353			−0.0288677	+	0.999583i	$0.509190\pi$
$510$	−6788.41	−	12224.6i	−0.589404	−	1.06140i
$511$	2612.17			0.226136
$512$	1733.59	−	11454.8i	0.149638	−	0.988741i
$513$		−	2222.98i		−	0.191320i
$514$	−6327.18	+	3513.54i	−0.542957	+	0.301509i
$515$	36183.5			3.09599
$516$	−3271.84	+	5253.89i	−0.279137	+	0.448236i
$517$			5622.16i			0.478263i
$518$	−244.271	−	439.883i	−0.0207194	−	0.0373115i
$519$	10295.9			0.870789
$520$	6317.31	+	19181.4i	0.532754	+	1.61761i
$521$	6252.16			0.525743			0.262871	−	0.964831i	$-0.415331\pi$
$521$	6252.16			0.525743			0.262871	+	0.964831i	$0.415331\pi$
$522$	−867.927	−	1562.96i	−0.0727742	−	0.131052i
$523$		−	11560.3i		−	0.966534i	−0.875473	−	0.483267i	$-0.839450\pi$
$523$		−	11560.3i		−	0.966534i	0.875473	−	0.483267i	$-0.160550\pi$
$524$	−6099.69	−	3798.56i	−0.508524	−	0.316681i
$525$	2018.36			0.167788
$526$	−10368.7	+	5757.84i	−0.859502	+	0.477289i
$527$			16010.0i			1.32335i
$528$	−4834.43	+	2376.23i	−0.398469	+	0.195856i
$529$	−5548.71			−0.456046
$530$	−3185.88	−	5737.13i	−0.261105	−	0.470198i
$531$	−4623.96			−0.377896
$532$	−1583.43	−	986.074i	−0.129042	−	0.0803604i
$533$	−6848.20	−	17749.6i	−0.556526	−	1.44244i
$534$	−7345.93	+	4079.25i	−0.595298	+	0.330574i
$535$		−	39256.9i		−	3.17238i
$536$	−496.465	+	9907.62i	−0.0400075	+	0.798403i
$537$	−9307.70			−0.747965
$538$	653.278	+	1176.42i	0.0523510	+	0.0942737i
$539$	−9398.35			−0.751050
$540$	3491.24	+	2174.16i	0.278220	+	0.173261i
$541$	5360.74			0.426019			0.213009	−	0.977050i	$-0.431674\pi$
$541$	5360.74			0.426019			0.213009	+	0.977050i	$0.431674\pi$
$542$	−4469.10	−	8047.96i	−0.354178	−	0.637803i
$543$	2554.93			0.201920
$544$	−12867.3	−	8936.73i	−1.01412	−	0.704336i
$545$	−38253.7			−3.00662
$546$	721.886	−	864.639i	0.0565822	−	0.0677713i
$547$		−	11075.7i		−	0.865748i	−0.901454	−	0.432874i	$-0.857499\pi$
$547$		−	11075.7i		−	0.865748i	0.901454	−	0.432874i	$-0.142501\pi$
$548$	−19317.3	−	12029.8i	−1.50583	−	0.937749i
$549$			486.211i			0.0377978i
$550$	16481.3	−	9152.18i	1.27775	−	0.709546i
$551$		−	5782.27i		−	0.447066i
$552$	−5515.50	−	276.378i	−0.425281	−	0.0213106i
$553$		−	448.981i		−	0.0345255i
$554$	−11223.5	−	20211.2i	−0.860720	−	1.54999i
$555$			3588.13i			0.274428i
$556$	−13321.5	−	8295.90i	−1.01611	−	0.632778i
$557$	−6357.69			−0.483634			−0.241817	−	0.970322i	$-0.577743\pi$
$557$	−6357.69			−0.483634			−0.241817	+	0.970322i	$0.577743\pi$
$558$	−2286.16	−	4116.93i	−0.173443	−	0.312336i
$559$	−4351.16	−	11277.6i	−0.329221	−	0.853295i
$560$	3097.30	−	1522.39i	0.233723	−	0.114880i
$561$			7284.44i			0.548217i
$562$	2698.54	+	4859.54i	0.202547	+	0.364746i
$563$		−	2931.63i		−	0.219456i	−0.993962	−	0.109728i	$-0.965002\pi$
$563$		−	2931.63i		−	0.219456i	0.993962	−	0.109728i	$-0.0349979\pi$
$564$	2542.30	−	4082.40i	0.189805	−	0.304787i
$565$	−8805.55			−0.655667
$566$	−4994.60	−	8994.29i	−0.370917	−	0.667947i
$567$		−	229.396i		−	0.0169907i
$568$	−4095.93	−	205.244i	−0.302573	−	0.0151617i
$569$	21921.1			1.61508			0.807540	−	0.589813i	$-0.200799\pi$
$569$	21921.1			1.61508			0.807540	+	0.589813i	$0.200799\pi$
$570$	6458.01	+	11629.6i	0.474555	+	0.854579i
$571$		−	12573.2i		−	0.921491i	−0.887532	−	0.460746i	$-0.847582\pi$
$571$		−	12573.2i		−	0.921491i	0.887532	−	0.460746i	$-0.152418\pi$
$572$	1974.00	−	10333.7i	0.144296	−	0.755374i
$573$			3274.15i			0.238708i
$574$	−2842.42	+	1578.42i	−0.206691	+	0.114777i
$575$	19326.3			1.40168
$576$	4584.92	+	460.651i	0.331664	+	0.0333226i
$577$			23277.6i			1.67948i	0.542992	+	0.839738i	$0.317291\pi$
$577$			23277.6i			1.67948i	−0.542992	+	0.839738i	$0.682709\pi$
$578$	−6372.34	+	3538.61i	−0.458571	+	0.254648i
$579$	−13388.7			−0.960994
$580$	9081.18	+	5655.27i	0.650130	+	0.404866i
$581$		−	919.332i		−	0.0656460i
$582$	−11672.7	+	6481.95i	−0.831356	+	0.461659i
$583$			3418.67i			0.242859i
$584$	−20844.4	−	1044.50i	−1.47697	−	0.0740099i
$585$	−7494.03	+	2891.37i	−0.529641	+	0.204347i
$586$	761.614	−	422.931i	0.0536894	−	0.0298142i
$587$	5861.63			0.412156			0.206078	−	0.978536i	$-0.433930\pi$
$587$	5861.63			0.412156			0.206078	+	0.978536i	$0.433930\pi$
$588$	6824.39	+	4249.87i	0.478628	+	0.298064i
$589$		−	15230.8i		−	1.06549i
$590$	24190.4	−	13433.1i	1.68797	−	0.937345i
$591$			382.582i			0.0266283i
$592$	1773.33	+	3607.83i	0.123114	+	0.250474i
$593$			1078.02i			0.0746523i	0.999303	+	0.0373262i	$0.0118840\pi$
$593$			1078.02i			0.0746523i	−0.999303	+	0.0373262i	$0.988116\pi$
$594$	−1040.19	−	1873.17i	−0.0718509	−	0.129389i
$595$		−	4666.96i		−	0.321558i
$596$	−1314.19	+	2110.31i	−0.0903209	+	0.145036i
$597$			753.575i			0.0516613i
$598$	6912.24	−	8279.13i	0.472680	−	0.566152i
$599$	13150.3			0.897005			0.448502	−	0.893782i	$-0.351958\pi$
$599$	13150.3			0.897005			0.448502	+	0.893782i	$0.351958\pi$
$600$	−16106.0	−	807.062i	−1.09588	−	0.0549136i
$601$	11153.1			0.756980			0.378490	−	0.925605i	$-0.376443\pi$
$601$	11153.1			0.756980			0.378490	+	0.925605i	$0.376443\pi$
$602$	−1806.00	+	1002.89i	−0.122271	+	0.0678980i
$603$	−3945.68			−0.266468
$604$	−15417.7	−	9601.30i	−1.03864	−	0.646807i
$605$	10355.1			0.695862
$606$	−4016.54	+	2230.42i	−0.269242	+	0.149512i
$607$	11496.2			0.768728			0.384364	−	0.923182i	$-0.374421\pi$
$607$	11496.2			0.768728			0.384364	+	0.923182i	$0.374421\pi$
$608$	12241.1	+	8501.76i	0.816514	+	0.567092i
$609$		−	596.691i		−	0.0397030i
$610$	−1412.50	−	2543.63i	−0.0937546	−	0.168833i
$611$	3380.95	+	8762.96i	0.223860	+	0.580215i
$612$	3293.97	−	5289.43i	0.217567	−	0.349367i
$613$	6120.51			0.403271			0.201636	−	0.979461i	$-0.435374\pi$
$613$	6120.51			0.403271			0.201636	+	0.979461i	$0.435374\pi$
$614$	15715.2	−	8726.80i	1.03292	−	0.573591i
$615$	23185.7			1.52022
$616$	−1795.67	−	89.9797i	−0.117450	−	0.00588537i
$617$		−	22638.2i		−	1.47711i	−0.674191	−	0.738557i	$-0.735508\pi$
$617$		−	22638.2i		−	1.47711i	0.674191	−	0.738557i	$-0.264492\pi$
$618$	7828.08	+	14096.8i	0.509533	+	0.917568i
$619$	27610.9			1.79285			0.896427	−	0.443192i	$-0.146154\pi$
$619$	27610.9			1.79285			0.896427	+	0.443192i	$0.146154\pi$
$620$	23920.3	+	14896.3i	1.54945	+	0.964917i
$621$		−	2196.53i		−	0.141938i
$622$	−13778.7	+	7651.44i	−0.888226	+	0.493239i
$623$	−2804.44			−0.180349
$624$	−6106.20	+	6610.94i	−0.391736	+	0.424118i
$625$	11115.4			0.711386
$626$	−15532.0	+	8625.04i	−0.991666	+	0.550680i
$627$		−	6929.90i		−	0.441393i
$628$	−11389.6	−	7092.84i	−0.723719	−	0.450693i
$629$	5436.22			0.344605
$630$	666.423	+	1200.09i	0.0421443	+	0.0758935i
$631$			22149.7i			1.39741i	0.715410	+	0.698705i	$0.246240\pi$
$631$			22149.7i			1.39741i	−0.715410	+	0.698705i	$0.753760\pi$
$632$	−179.529	+	3582.75i	−0.0112995	+	0.225497i
$633$	4659.82			0.292593
$634$	−22873.5	+	12701.8i	−1.43284	+	0.795670i
$635$	29342.3			1.83372
$636$	1545.90	−	2482.39i	0.0963818	−	0.154769i
$637$	−14648.7	+	5651.81i	−0.911152	+	0.351543i
$638$	−2705.67	−	4872.37i	−0.167897	−	0.302349i
$639$		−	1631.19i		−	0.100984i
$640$	−25324.4	+	10909.8i	−1.56412	+	0.673824i
$641$	6671.81			0.411109			0.205554	−	0.978646i	$-0.434100\pi$
$641$	6671.81			0.411109			0.205554	+	0.978646i	$0.434100\pi$
$642$	15294.2	−	8492.98i	0.940207	−	0.522105i
$643$	−17866.6			−1.09579			−0.547894	−	0.836548i	$-0.684570\pi$
$643$	−17866.6			−1.09579			−0.547894	+	0.836548i	$0.684570\pi$
$644$	−1564.58	−	974.339i	−0.0957349	−	0.0596186i
$645$	14731.5			0.899307
$646$	17619.5	−	9784.26i	1.07311	−	0.595908i
$647$	19665.9			1.19497			0.597486	−	0.801879i	$-0.296166\pi$
$647$	19665.9			1.19497			0.597486	+	0.801879i	$0.296166\pi$
$648$	−91.7264	+	1830.52i	−0.00556073	+	0.110972i
$649$	−14414.7			−0.871844
$650$	20184.7	−	24176.2i	1.21801	−	1.45888i
$651$		−	1571.71i		−	0.0946242i
$652$	1406.67	−	2258.82i	0.0844932	−	0.135678i
$653$			18833.2i			1.12864i	0.825557	+	0.564319i	$0.190861\pi$
$653$			18833.2i			1.12864i	−0.825557	+	0.564319i	$0.809139\pi$
$654$	−8275.95	−	14903.3i	−0.494825	−	0.891081i
$655$			17103.1i			1.02026i
$656$	23312.9	−	11458.8i	1.38753	−	0.682000i
$657$		−	8301.23i		−	0.492940i
$658$	1403.30	−	779.266i	0.0831405	−	0.0461686i
$659$		−	20442.3i		−	1.20838i	−0.796842	−	0.604188i	$-0.793498\pi$
$659$		−	20442.3i		−	1.20838i	0.796842	−	0.604188i	$-0.206502\pi$
$660$	10883.5	+	6777.69i	0.641881	+	0.399729i
$661$	25515.2			1.50140			0.750701	−	0.660642i	$-0.229716\pi$
$661$	25515.2			1.50140			0.750701	+	0.660642i	$0.229716\pi$
$662$	−19608.5	+	10888.8i	−1.15122	+	0.639280i
$663$	4380.59	+	11353.9i	0.256603	+	0.665080i
$664$	−367.604	+	7336.03i	−0.0214846	+	0.428755i
$665$			4439.82i			0.258900i
$666$	−1397.91	+	776.269i	−0.0813330	+	0.0451649i
$667$		−	5713.46i		−	0.331673i
$668$	6524.68	+	4063.22i	0.377916	+	0.235346i
$669$	−9681.47			−0.559502
$670$	20641.9	−	11462.6i	1.19025	−	0.660956i
$671$			1515.71i			0.0872031i
$672$	1263.19	+	877.324i	0.0725130	+	0.0503623i
$673$	24925.2			1.42763			0.713815	−	0.700335i	$-0.246966\pi$
$673$	24925.2			1.42763			0.713815	+	0.700335i	$0.246966\pi$
$674$	−26634.4	+	14790.3i	−1.52213	+	0.845253i
$675$		−	6414.17i		−	0.365750i
$676$	−3137.52	−	17293.7i	−0.178512	−	0.983938i
$677$		−	14340.1i		−	0.814082i	−0.913410	−	0.407041i	$-0.866561\pi$
$677$		−	14340.1i		−	0.814082i	0.913410	−	0.407041i	$-0.133439\pi$
$678$	−1905.03	−	3430.57i	−0.107909	−	0.194322i
$679$	−4456.28			−0.251865
$680$	−1866.13	+	37241.2i	−0.105239	+	2.10020i
$681$		−	11225.1i		−	0.631642i
$682$	−7126.87	−	12834.1i	−0.400149	−	0.720589i
$683$	−6419.43			−0.359638			−0.179819	−	0.983700i	$-0.557551\pi$
$683$	−6419.43			−0.359638			−0.179819	+	0.983700i	$0.557551\pi$
$684$	−3133.65	+	5031.98i	−0.175173	+	0.281290i
$685$			54164.3i			3.02118i
$686$	2636.53	+	4747.87i	0.146739	+	0.264248i
$687$			2522.61i			0.140093i
$688$	14812.4	−	7280.62i	0.820811	−	0.403446i
$689$	2055.86	+	5328.50i	0.113675	+	0.294630i
$690$	6381.16	+	11491.2i	0.352067	+	0.634004i
$691$	−3199.00			−0.176115			−0.0880576	−	0.996115i	$-0.528066\pi$
$691$	−3199.00			−0.176115			−0.0880576	+	0.996115i	$0.528066\pi$
$692$	−23306.0	−	14513.7i	−1.28029	−	0.797295i
$693$		−	715.118i		−	0.0391993i
$694$	15572.0	+	28042.1i	0.851737	+	1.53381i
$695$			37352.4i			2.03864i
$696$	−238.593	+	4761.44i	−0.0129940	+	0.259313i
$697$		−	35127.6i		−	1.90897i
$698$	24044.4	−	13352.0i	1.30386	−	0.724043i
$699$			3492.73i			0.188995i
$700$	−4568.81	−	2845.21i	−0.246692	−	0.153627i
$701$			23873.0i			1.28626i	0.765756	+	0.643131i	$0.222365\pi$
$701$			23873.0i			1.28626i	−0.765756	+	0.643131i	$0.777635\pi$
$702$	−2747.74	−	2294.09i	−0.147730	−	0.123340i
$703$	−5171.63			−0.277456
$704$	14293.0	+	1436.03i	0.765180	+	0.0768784i
$705$	−11446.7			−0.611502
$706$	−635.637	−	1144.66i	−0.0338846	−	0.0610194i
$707$	−1533.39			−0.0815686
$708$	10466.9	+	6518.22i	0.555607	+	0.346002i
$709$	−5639.64			−0.298732			−0.149366	−	0.988782i	$-0.547723\pi$
$709$	−5639.64			−0.298732			−0.149366	+	0.988782i	$0.547723\pi$
$710$	4738.79	+	8533.61i	0.250484	+	0.451071i
$711$	−1426.82			−0.0752601
$712$	22378.7	+	1121.38i	1.17792	+	0.0590248i
$713$		−	15049.5i		−	0.790477i
$714$	1818.21	−	1009.67i	0.0953010	−	0.0529214i
$715$	−23361.8	+	9013.52i	−1.22193	+	0.471449i
$716$	21069.1	+	13120.7i	1.09971	+	0.684837i
$717$	17607.6			0.917112
$718$	−13163.1	−	23704.2i	−0.684184	−	1.23208i
$719$	−34340.6			−1.78121			−0.890603	−	0.454782i	$-0.849717\pi$
$719$	−34340.6			−1.78121			−0.890603	+	0.454782i	$0.849717\pi$
$720$	−4838.01	−	9842.92i	−0.250419	−	0.509478i
$721$			5381.72i			0.277983i
$722$	198.644	−	110.309i	0.0102393	−	0.00568597i
$723$	−13699.9			−0.704710
$724$	−5783.39	−	3601.58i	−0.296876	−	0.184878i
$725$		−	16684.1i		−	0.854666i
$726$	2240.27	+	4034.28i	0.114524	+	0.206235i
$727$	−34048.5			−1.73698			−0.868492	−	0.495703i	$-0.834911\pi$
$727$	−34048.5			−1.73698			−0.868492	+	0.495703i	$0.834911\pi$
$728$	−2852.92	+	939.599i	−0.145242	+	0.0478350i
$729$	−729.000			−0.0370370
$730$	24116.0	+	43428.1i	1.22270	+	2.20184i
$731$		−	22319.1i		−	1.12928i
$732$	685.392	−	1100.60i	0.0346077	−	0.0555727i
$733$	−19102.4			−0.962570			−0.481285	−	0.876564i	$-0.659830\pi$
$733$	−19102.4			−0.962570			−0.481285	+	0.876564i	$0.659830\pi$
$734$	−26986.6	+	14985.9i	−1.35707	+	0.753595i
$735$		−	19135.1i		−	0.960284i
$736$	12095.4	+	8400.59i	0.605763	+	0.420720i
$737$	−12300.2			−0.614768
$738$	5016.07	+	9032.95i	0.250195	+	0.450552i
$739$	−7293.49			−0.363052			−0.181526	−	0.983386i	$-0.558104\pi$
$739$	−7293.49			−0.363052			−0.181526	+	0.983386i	$0.558104\pi$
$740$	5058.04	−	8122.15i	0.251266	−	0.403481i
$741$	−4167.38	−	10801.3i	−0.206603	−	0.535485i
$742$	853.308	−	473.849i	0.0422182	−	0.0234441i
$743$			33749.8i			1.66643i	0.552948	+	0.833216i	$0.313503\pi$
$743$			33749.8i			1.66643i	−0.552948	+	0.833216i	$0.686497\pi$
$744$	−628.465	+	12541.9i	−0.0309686	+	0.618020i
$745$	5917.16			0.290990
$746$	−13575.5	−	24446.7i	−0.666265	−	1.19981i
$747$	−2921.55			−0.143098
$748$	10268.6	−	16489.2i	0.501948	−	0.806023i
$749$	5838.84			0.284842
$750$	8829.13	+	15899.5i	0.429859	+	0.774091i
$751$	32882.7			1.59775			0.798874	−	0.601499i	$-0.205430\pi$
$751$	32882.7			1.59775			0.798874	+	0.601499i	$0.205430\pi$
$752$	−11509.6	+	5657.21i	−0.558127	+	0.274332i
$753$	11126.6			0.538479
$754$	−7147.24	−	5967.22i	−0.345208	−	0.288214i
$755$			43230.0i			2.08384i
$756$	−323.371	+	519.266i	−0.0155567	+	0.0249809i
$757$		−	27470.3i		−	1.31892i	−0.751738	−	0.659462i	$-0.770784\pi$
$757$		−	27470.3i		−	1.31892i	0.751738	−	0.659462i	$-0.229216\pi$
$758$	14487.3	−	8044.92i	0.694199	−	0.385494i
$759$		−	6847.43i		−	0.327465i
$760$	1775.30	−	35428.6i	0.0847329	−	1.69096i
$761$			2117.52i			0.100867i	0.998727	+	0.0504336i	$0.0160603\pi$
$761$			2117.52i			0.100867i	−0.998727	+	0.0504336i	$0.983940\pi$
$762$	6348.02	+	11431.5i	0.301791	+	0.543465i
$763$		−	5689.63i		−	0.269959i
$764$	4615.43	−	7411.42i	0.218561	−	0.350963i
$765$	−14831.2			−0.700944
$766$	7842.55	+	14122.9i	0.369925	+	0.666162i
$767$	−22467.4	+	8668.45i	−1.05770	+	0.408083i
$768$	−9729.14	−	7505.91i	−0.457123	−	0.352664i
$769$		−	29856.9i		−	1.40009i	−0.714101	−	0.700043i	$-0.753164\pi$
$769$		−	29856.9i		−	1.40009i	0.714101	−	0.700043i	$-0.246836\pi$
$770$	2077.50	+	3741.16i	0.0972310	+	0.175094i
$771$			7676.29i			0.358567i
$772$	30306.9	+	18873.5i	1.41291	+	0.879888i
$773$	−8725.41			−0.405991			−0.202995	−	0.979180i	$-0.565068\pi$
$773$	−8725.41			−0.405991			−0.202995	+	0.979180i	$0.565068\pi$
$774$	3187.08	+	5739.29i	0.148007	+

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+(-2.47275 + 1.37314i) q^{2} +3.00000i q^{3} +(4.22898 - 6.79086i) q^{4} -19.0411 q^{5} +(-4.11942 - 7.41825i) q^{6} -2.83206i q^{7} +(-1.13242 + 22.5991i) q^{8} -9.00000 q^{9} +(47.0838 - 26.1460i) q^{10} -28.0565 q^{11} +(20.3726 + 12.6869i) q^{12} +(-43.7302 + 16.8721i) q^{13} +(3.88880 + 7.00296i) q^{14} -57.1232i q^{15} +(-28.2314 - 57.4368i) q^{16} -86.5449 q^{17} +(22.2547 - 12.3582i) q^{18} +82.3327 q^{19} +(-80.5243 + 129.305i) q^{20} +8.49617 q^{21} +(69.3767 - 38.5255i) q^{22} +81.3529 q^{23} +(-67.7972 - 3.39727i) q^{24} +237.562 q^{25} +(84.9661 - 101.768i) q^{26} -27.0000i q^{27} +(-19.2321 - 11.9767i) q^{28} -70.2306i q^{29} +(78.4380 + 141.251i) q^{30} -184.991i q^{31} +(148.678 + 103.261i) q^{32} -84.1695i q^{33} +(214.004 - 118.838i) q^{34} +53.9253i q^{35} +(-38.0608 + 61.1177i) q^{36} -62.8138 q^{37} +(-203.588 + 113.054i) q^{38} +(-50.6163 - 131.191i) q^{39} +(21.5626 - 430.310i) q^{40} +405.889i q^{41} +(-21.0089 + 11.6664i) q^{42} +257.891i q^{43} +(-118.650 + 190.528i) q^{44} +171.370 q^{45} +(-201.165 + 111.709i) q^{46} -200.387i q^{47} +(172.310 - 84.6943i) q^{48} +334.979 q^{49} +(-587.431 + 326.205i) q^{50} -259.635i q^{51} +(-70.3581 + 368.317i) q^{52} -121.850i q^{53} +(37.0747 + 66.7642i) q^{54} +534.226 q^{55} +(64.0018 + 3.20709i) q^{56} +246.998i q^{57} +(96.4364 + 173.663i) q^{58} +513.774 q^{59} +(-387.915 - 241.573i) q^{60} -54.0234i q^{61} +(254.018 + 457.436i) q^{62} +25.4885i q^{63} +(-509.435 - 51.1835i) q^{64} +(832.670 - 321.263i) q^{65} +(115.576 + 208.130i) q^{66} +438.409 q^{67} +(-365.997 + 587.714i) q^{68} +244.059i q^{69} +(-74.0469 - 133.344i) q^{70} +181.243i q^{71} +(10.1918 - 203.392i) q^{72} +922.359i q^{73} +(155.323 - 86.2521i) q^{74} +712.686i q^{75} +(348.183 - 559.109i) q^{76} +79.4576i q^{77} +(305.304 + 254.898i) q^{78} +158.535 q^{79} +(537.557 + 1093.66i) q^{80} +81.0000 q^{81} +(-557.341 - 1003.66i) q^{82} +324.617 q^{83} +(35.9301 - 57.6962i) q^{84} +1647.91 q^{85} +(-354.119 - 637.699i) q^{86} +210.692 q^{87} +(31.7719 - 634.051i) q^{88} -990.251i q^{89} +(-423.754 + 235.314i) q^{90} +(47.7828 + 123.846i) q^{91} +(344.040 - 552.456i) q^{92} +554.973 q^{93} +(275.159 + 495.507i) q^{94} -1567.70 q^{95} +(-309.783 + 446.034i) q^{96} -1573.51i q^{97} +(-828.320 + 459.973i) q^{98} +252.509 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

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