LMFDB - Embedded newform 74.5.d.a.43.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,5,Mod(31,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("74.31");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	74.d (of order $4$, degree $2$, 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:	$7.64937726820$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 727 x^{12} + 198453 x^{10} + 24875201 x^{8} + 1392846203 x^{6} + 29089700589 x^{4} + \cdots + 446074380544 $ x^14 + 727x^12 + 198453x^10 + 24875201x^8 + 1392846203x^6 + 29089700589x^4 + 220261242916x^2 + 446074380544
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.2
Root			$-13.3074i$ of defining polynomial
Character	$\chi$	$=$	74.43
Dual form			74.5.d.a.31.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 + 2.00000i) q^{2} -12.3074i q^{3} -8.00000i q^{4} +(10.7621 + 10.7621i) q^{5} +(24.6148 + 24.6148i) q^{6} +35.0611 q^{7} +(16.0000 + 16.0000i) q^{8} -70.4723 q^{9} +O(q^{10})$	\(q+(-2.00000 + 2.00000i) q^{2} -12.3074i q^{3} -8.00000i q^{4} +(10.7621 + 10.7621i) q^{5} +(24.6148 + 24.6148i) q^{6} +35.0611 q^{7} +(16.0000 + 16.0000i) q^{8} -70.4723 q^{9} -43.0483 q^{10} -142.240i q^{11} -98.4593 q^{12} +(-181.910 - 181.910i) q^{13} +(-70.1223 + 70.1223i) q^{14} +(132.453 - 132.453i) q^{15} -64.0000 q^{16} +(-88.0634 - 88.0634i) q^{17} +(140.945 - 140.945i) q^{18} +(13.8864 + 13.8864i) q^{19} +(86.0967 - 86.0967i) q^{20} -431.512i q^{21} +(284.479 + 284.479i) q^{22} +(79.7242 + 79.7242i) q^{23} +(196.919 - 196.919i) q^{24} -393.355i q^{25} +727.640 q^{26} -129.569i q^{27} -280.489i q^{28} +(420.383 - 420.383i) q^{29} +529.813i q^{30} +(-624.657 + 624.657i) q^{31} +(128.000 - 128.000i) q^{32} -1750.60 q^{33} +352.253 q^{34} +(377.331 + 377.331i) q^{35} +563.778i q^{36} +(-7.65345 + 1368.98i) q^{37} -55.5457 q^{38} +(-2238.84 + 2238.84i) q^{39} +344.387i q^{40} -1239.16i q^{41} +(863.024 + 863.024i) q^{42} +(607.562 + 607.562i) q^{43} -1137.92 q^{44} +(-758.428 - 758.428i) q^{45} -318.897 q^{46} +2971.58 q^{47} +787.674i q^{48} -1171.72 q^{49} +(786.710 + 786.710i) q^{50} +(-1083.83 + 1083.83i) q^{51} +(-1455.28 + 1455.28i) q^{52} +1041.64 q^{53} +(259.138 + 259.138i) q^{54} +(1530.80 - 1530.80i) q^{55} +(560.978 + 560.978i) q^{56} +(170.906 - 170.906i) q^{57} +1681.53i q^{58} +(1896.67 + 1896.67i) q^{59} +(-1059.63 - 1059.63i) q^{60} +(4012.39 - 4012.39i) q^{61} -2498.63i q^{62} -2470.84 q^{63} +512.000i q^{64} -3915.46i q^{65} +(3501.20 - 3501.20i) q^{66} -2338.93i q^{67} +(-704.507 + 704.507i) q^{68} +(981.198 - 981.198i) q^{69} -1509.32 q^{70} +3648.82 q^{71} +(-1127.56 - 1127.56i) q^{72} +9943.51i q^{73} +(-2722.65 - 2753.26i) q^{74} -4841.18 q^{75} +(111.091 - 111.091i) q^{76} -4987.09i q^{77} -8955.36i q^{78} +(6403.03 + 6403.03i) q^{79} +(-688.773 - 688.773i) q^{80} -7302.91 q^{81} +(2478.31 + 2478.31i) q^{82} -7154.52 q^{83} -3452.09 q^{84} -1895.49i q^{85} -2430.25 q^{86} +(-5173.82 - 5173.82i) q^{87} +(2275.84 - 2275.84i) q^{88} +(2259.76 - 2259.76i) q^{89} +3033.71 q^{90} +(-6377.97 - 6377.97i) q^{91} +(637.794 - 637.794i) q^{92} +(7687.91 + 7687.91i) q^{93} +(-5943.15 + 5943.15i) q^{94} +298.893i q^{95} +(-1575.35 - 1575.35i) q^{96} +(8558.26 + 8558.26i) q^{97} +(2343.43 - 2343.43i) q^{98} +10024.0i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 28 q^{2} - 12 q^{5} - 40 q^{6} + 48 q^{7} + 224 q^{8} - 346 q^{9}+O(q^{10}) $ 14 * q - 28 * q^2 - 12 * q^5 - 40 * q^6 + 48 * q^7 + 224 * q^8 - 346 * q^9	\( 14 q - 28 q^{2} - 12 q^{5} - 40 q^{6} + 48 q^{7} + 224 q^{8} - 346 q^{9} + 48 q^{10} + 160 q^{12} - 56 q^{13} - 96 q^{14} - 378 q^{15} - 896 q^{16} - 348 q^{17} + 692 q^{18} - 184 q^{19} - 96 q^{20} - 320 q^{22} - 502 q^{23} - 320 q^{24} + 224 q^{26} - 474 q^{29} - 630 q^{31} + 1792 q^{32} + 632 q^{33} + 1392 q^{34} + 1826 q^{35} - 2544 q^{37} + 736 q^{38} - 798 q^{39} - 224 q^{42} + 1936 q^{43} + 1280 q^{44} + 6162 q^{45} + 2008 q^{46} + 5716 q^{47} + 7862 q^{49} - 1372 q^{50} - 2422 q^{51} - 448 q^{52} - 20228 q^{53} - 656 q^{54} + 14006 q^{55} + 768 q^{56} - 2270 q^{57} - 4502 q^{59} + 3024 q^{60} - 11906 q^{61} - 2588 q^{63} - 1264 q^{66} - 2784 q^{68} + 21440 q^{69} - 7304 q^{70} - 11224 q^{71} - 5536 q^{72} + 4924 q^{74} - 18652 q^{75} - 1472 q^{76} + 20488 q^{79} + 768 q^{80} - 1706 q^{81} + 9808 q^{82} - 20224 q^{83} + 896 q^{84} - 7744 q^{86} + 19636 q^{87} - 2560 q^{88} + 13864 q^{89} - 24648 q^{90} - 6070 q^{91} - 4016 q^{92} - 13800 q^{93} - 11432 q^{94} + 2560 q^{96} + 16622 q^{97} - 15724 q^{98}+O(q^{100}) \) 14 * q - 28 * q^2 - 12 * q^5 - 40 * q^6 + 48 * q^7 + 224 * q^8 - 346 * q^9 + 48 * q^10 + 160 * q^12 - 56 * q^13 - 96 * q^14 - 378 * q^15 - 896 * q^16 - 348 * q^17 + 692 * q^18 - 184 * q^19 - 96 * q^20 - 320 * q^22 - 502 * q^23 - 320 * q^24 + 224 * q^26 - 474 * q^29 - 630 * q^31 + 1792 * q^32 + 632 * q^33 + 1392 * q^34 + 1826 * q^35 - 2544 * q^37 + 736 * q^38 - 798 * q^39 - 224 * q^42 + 1936 * q^43 + 1280 * q^44 + 6162 * q^45 + 2008 * q^46 + 5716 * q^47 + 7862 * q^49 - 1372 * q^50 - 2422 * q^51 - 448 * q^52 - 20228 * q^53 - 656 * q^54 + 14006 * q^55 + 768 * q^56 - 2270 * q^57 - 4502 * q^59 + 3024 * q^60 - 11906 * q^61 - 2588 * q^63 - 1264 * q^66 - 2784 * q^68 + 21440 * q^69 - 7304 * q^70 - 11224 * q^71 - 5536 * q^72 + 4924 * q^74 - 18652 * q^75 - 1472 * q^76 + 20488 * q^79 + 768 * q^80 - 1706 * q^81 + 9808 * q^82 - 20224 * q^83 + 896 * q^84 - 7744 * q^86 + 19636 * q^87 - 2560 * q^88 + 13864 * q^89 - 24648 * q^90 - 6070 * q^91 - 4016 * q^92 - 13800 * q^93 - 11432 * q^94 + 2560 * q^96 + 16622 * q^97 - 15724 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−2.00000	+	2.00000i	−0.500000	+	0.500000i
$2$	−2.00000	+	2.00000i	−0.500000	+	0.500000i
$3$		−	12.3074i		−	1.36749i	−0.729721	−	0.683745i	$-0.760350\pi$
$3$		−	12.3074i		−	1.36749i	0.729721	−	0.683745i	$-0.239650\pi$
$4$		−	8.00000i		−	0.500000i
$5$	10.7621	+	10.7621i	0.430483	+	0.430483i	0.888793	−	0.458309i	$-0.151545\pi$
$5$	10.7621	+	10.7621i	0.430483	+	0.430483i	−0.458309	+	0.888793i	$0.651545\pi$
$6$	24.6148	+	24.6148i	0.683745	+	0.683745i
$7$	35.0611			0.715534			0.357767	−	0.933811i	$-0.383538\pi$
$7$	35.0611			0.715534			0.357767	+	0.933811i	$0.383538\pi$
$8$	16.0000	+	16.0000i	0.250000	+	0.250000i
$9$	−70.4723			−0.870028
$10$	−43.0483			−0.430483
$11$		−	142.240i		−	1.17553i	−0.809030	−	0.587767i	$-0.800007\pi$
$11$		−	142.240i		−	1.17553i	0.809030	−	0.587767i	$-0.199993\pi$
$12$	−98.4593			−0.683745
$13$	−181.910	−	181.910i	−1.07639	−	1.07639i	−0.996830	−	0.0795603i	$-0.974648\pi$
$13$	−181.910	−	181.910i	−1.07639	−	1.07639i	−0.0795603	−	0.996830i	$-0.525352\pi$
$14$	−70.1223	+	70.1223i	−0.357767	+	0.357767i
$15$	132.453	−	132.453i	0.588681	−	0.588681i
$16$	−64.0000			−0.250000
$17$	−88.0634	−	88.0634i	−0.304718	−	0.304718i	0.538139	−	0.842856i	$-0.319128\pi$
$17$	−88.0634	−	88.0634i	−0.304718	−	0.304718i	−0.842856	+	0.538139i	$0.819128\pi$
$18$	140.945	−	140.945i	0.435014	−	0.435014i
$19$	13.8864	+	13.8864i	0.0384665	+	0.0384665i	0.726078	−	0.687612i	$-0.241341\pi$
$19$	13.8864	+	13.8864i	0.0384665	+	0.0384665i	−0.687612	+	0.726078i	$0.741341\pi$
$20$	86.0967	−	86.0967i	0.215242	−	0.215242i
$21$		−	431.512i		−	0.978485i
$22$	284.479	+	284.479i	0.587767	+	0.587767i
$23$	79.7242	+	79.7242i	0.150707	+	0.150707i	0.778434	−	0.627727i	$-0.216014\pi$
$23$	79.7242	+	79.7242i	0.150707	+	0.150707i	−0.627727	+	0.778434i	$0.716014\pi$
$24$	196.919	−	196.919i	0.341872	−	0.341872i
$25$		−	393.355i		−	0.629368i
$26$	727.640			1.07639
$27$		−	129.569i		−	0.177735i
$28$		−	280.489i		−	0.357767i
$29$	420.383	−	420.383i	0.499861	−	0.499861i	−0.411534	−	0.911395i	$-0.635007\pi$
$29$	420.383	−	420.383i	0.499861	−	0.499861i	0.911395	+	0.411534i	$0.135007\pi$
$30$			529.813i			0.588681i
$31$	−624.657	+	624.657i	−0.650007	+	0.650007i	−0.952995	−	0.302987i	$-0.902016\pi$
$31$	−624.657	+	624.657i	−0.650007	+	0.650007i	0.302987	+	0.952995i	$0.402016\pi$
$32$	128.000	−	128.000i	0.125000	−	0.125000i
$33$	−1750.60			−1.60753
$34$	352.253			0.304718
$35$	377.331	+	377.331i	0.308025	+	0.308025i
$36$			563.778i			0.435014i
$37$	−7.65345	+	1368.98i	−0.00559054	+	0.999984i
$37$	−7.65345	+	1368.98i	−0.00559054	+	0.999984i
$38$	−55.5457			−0.0384665
$39$	−2238.84	+	2238.84i	−1.47195	+	1.47195i
$40$			344.387i			0.215242i
$41$		−	1239.16i		−	0.737154i	−0.929597	−	0.368577i	$-0.879845\pi$
$41$		−	1239.16i		−	0.737154i	0.929597	−	0.368577i	$-0.120155\pi$
$42$	863.024	+	863.024i	0.489242	+	0.489242i
$43$	607.562	+	607.562i	0.328590	+	0.328590i	0.852050	−	0.523460i	$-0.175359\pi$
$43$	607.562	+	607.562i	0.328590	+	0.328590i	−0.523460	+	0.852050i	$0.675359\pi$
$44$	−1137.92			−0.587767
$45$	−758.428	−	758.428i	−0.374533	−	0.374533i
$46$	−318.897			−0.150707
$47$	2971.58			1.34521			0.672607	−	0.740000i	$-0.265175\pi$
$47$	2971.58			1.34521			0.672607	+	0.740000i	$0.265175\pi$
$48$			787.674i			0.341872i
$49$	−1171.72			−0.488012
$50$	786.710	+	786.710i	0.314684	+	0.314684i
$51$	−1083.83	+	1083.83i	−0.416698	+	0.416698i
$52$	−1455.28	+	1455.28i	−0.538195	+	0.538195i
$53$	1041.64			0.370822			0.185411	−	0.982661i	$-0.440638\pi$
$53$	1041.64			0.370822			0.185411	+	0.982661i	$0.440638\pi$
$54$	259.138	+	259.138i	0.0888676	+	0.0888676i
$55$	1530.80	−	1530.80i	0.506048	−	0.506048i
$56$	560.978	+	560.978i	0.178883	+	0.178883i
$57$	170.906	−	170.906i	0.0526026	−	0.0526026i
$58$			1681.53i			0.499861i
$59$	1896.67	+	1896.67i	0.544863	+	0.544863i	0.924951	−	0.380087i	$-0.124106\pi$
$59$	1896.67	+	1896.67i	0.544863	+	0.544863i	−0.380087	+	0.924951i	$0.624106\pi$
$60$	−1059.63	−	1059.63i	−0.294341	−	0.294341i
$61$	4012.39	−	4012.39i	1.07831	−	1.07831i	0.0816497	−	0.996661i	$-0.473981\pi$
$61$	4012.39	−	4012.39i	1.07831	−	1.07831i	0.996661	−	0.0816497i	$-0.0260189\pi$
$62$		−	2498.63i		−	0.650007i
$63$	−2470.84			−0.622534
$64$			512.000i			0.125000i
$65$		−	3915.46i		−	0.926736i
$66$	3501.20	−	3501.20i	0.803766	−	0.803766i
$67$		−	2338.93i		−	0.521037i	−0.965469	−	0.260518i	$-0.916107\pi$
$67$		−	2338.93i		−	0.521037i	0.965469	−	0.260518i	$-0.0838934\pi$
$68$	−704.507	+	704.507i	−0.152359	+	0.152359i
$69$	981.198	−	981.198i	0.206091	−	0.206091i
$70$	−1509.32			−0.308025
$71$	3648.82			0.723830			0.361915	−	0.932211i	$-0.382123\pi$
$71$	3648.82			0.723830			0.361915	+	0.932211i	$0.382123\pi$
$72$	−1127.56	−	1127.56i	−0.217507	−	0.217507i
$73$			9943.51i			1.86592i	0.359976	+	0.932962i	$0.382785\pi$
$73$			9943.51i			1.86592i	−0.359976	+	0.932962i	$0.617215\pi$
$74$	−2722.65	−	2753.26i	−0.497197	−	0.502787i
$75$	−4841.18			−0.860655
$76$	111.091	−	111.091i	0.0192333	−	0.0192333i
$77$		−	4987.09i		−	0.841135i
$78$		−	8955.36i		−	1.47195i
$79$	6403.03	+	6403.03i	1.02596	+	1.02596i	0.999654	+	0.0263085i	$0.00837522\pi$
$79$	6403.03	+	6403.03i	1.02596	+	1.02596i	0.0263085	+	0.999654i	$0.491625\pi$
$80$	−688.773	−	688.773i	−0.107621	−	0.107621i
$81$	−7302.91			−1.11308
$82$	2478.31	+	2478.31i	0.368577	+	0.368577i
$83$	−7154.52			−1.03854			−0.519271	−	0.854610i	$-0.673797\pi$
$83$	−7154.52			−1.03854			−0.519271	+	0.854610i	$0.673797\pi$
$84$	−3452.09			−0.489242
$85$		−	1895.49i		−	0.262352i
$86$	−2430.25			−0.328590
$87$	−5173.82	−	5173.82i	−0.683555	−	0.683555i
$88$	2275.84	−	2275.84i	0.293884	−	0.293884i
$89$	2259.76	−	2259.76i	0.285287	−	0.285287i	−0.549926	−	0.835213i	$-0.685344\pi$
$89$	2259.76	−	2259.76i	0.285287	−	0.285287i	0.835213	+	0.549926i	$0.185344\pi$
$90$	3033.71			0.374533
$91$	−6377.97	−	6377.97i	−0.770193	−	0.770193i
$92$	637.794	−	637.794i	0.0753537	−	0.0753537i
$93$	7687.91	+	7687.91i	0.888878	+	0.888878i
$94$	−5943.15	+	5943.15i	−0.672607	+	0.672607i
$95$			298.893i			0.0331184i
$96$	−1575.35	−	1575.35i	−0.170936	−	0.170936i
$97$	8558.26	+	8558.26i	0.909583	+	0.909583i	0.996238	−	0.0866556i	$-0.0276180\pi$
$97$	8558.26	+	8558.26i	0.909583	+	0.909583i	−0.0866556	+	0.996238i	$0.527618\pi$
$98$	2343.43	−	2343.43i	0.244006	−	0.244006i
$99$			10024.0i			1.02275i
$100$	−3146.84			−0.314684
$101$		−	12369.2i		−	1.21255i	−0.795256	−	0.606274i	$-0.792664\pi$
$101$		−	12369.2i		−	1.21255i	0.795256	−	0.606274i	$-0.207336\pi$
$102$		−	4335.33i		−	0.416698i
$103$	−5805.26	+	5805.26i	−0.547202	+	0.547202i	−0.925630	−	0.378429i	$-0.876465\pi$
$103$	−5805.26	+	5805.26i	−0.547202	+	0.547202i	0.378429	+	0.925630i	$0.376465\pi$
$104$		−	5821.12i		−	0.538195i
$105$	4643.97	−	4643.97i	0.421221	−	0.421221i
$106$	−2083.28	+	2083.28i	−0.185411	+	0.185411i
$107$	3685.46			0.321903			0.160951	−	0.986962i	$-0.448544\pi$
$107$	3685.46			0.321903			0.160951	+	0.986962i	$0.448544\pi$
$108$	−1036.55			−0.0888676
$109$	9605.82	+	9605.82i	0.808502	+	0.808502i	0.984407	−	0.175905i	$-0.0562851\pi$
$109$	9605.82	+	9605.82i	0.808502	+	0.808502i	−0.175905	+	0.984407i	$0.556285\pi$
$110$			6123.18i			0.506048i
$111$	16848.6	+	94.1941i	1.36747	+	0.00764500i
$112$	−2243.91			−0.178883
$113$	4922.36	−	4922.36i	0.385493	−	0.385493i	−0.487583	−	0.873076i	$-0.662121\pi$
$113$	4922.36	−	4922.36i	0.385493	−	0.385493i	0.873076	+	0.487583i	$0.162121\pi$
$114$			683.623i			0.0526026i
$115$			1716.00i			0.129754i
$116$	−3363.06	−	3363.06i	−0.249930	−	0.249930i
$117$	12819.6	+	12819.6i	0.936490	+	0.936490i
$118$	−7586.67			−0.544863
$119$	−3087.60	−	3087.60i	−0.218036	−	0.218036i
$120$	4238.51			0.294341
$121$	−5591.14			−0.381882
$122$			16049.6i			1.07831i
$123$	−15250.8			−1.00805
$124$	4997.26	+	4997.26i	0.325004	+	0.325004i
$125$	10959.6	−	10959.6i	0.701416	−	0.701416i
$126$	4941.68	−	4941.68i	0.311267	−	0.311267i
$127$	−23426.1			−1.45242			−0.726211	−	0.687472i	$-0.758721\pi$
$127$	−23426.1			−1.45242			−0.726211	+	0.687472i	$0.758721\pi$
$128$	−1024.00	−	1024.00i	−0.0625000	−	0.0625000i
$129$	7477.51	−	7477.51i	0.449343	−	0.449343i
$130$	7830.92	+	7830.92i	0.463368	+	0.463368i
$131$	−4160.42	+	4160.42i	−0.242435	+	0.242435i	−0.817857	−	0.575422i	$-0.804838\pi$
$131$	−4160.42	+	4160.42i	−0.242435	+	0.242435i	0.575422	+	0.817857i	$0.304838\pi$
$132$			14004.8i			0.803766i
$133$	486.874	+	486.874i	0.0275241	+	0.0275241i
$134$	4677.87	+	4677.87i	0.260518	+	0.260518i
$135$	1394.43	−	1394.43i	0.0765121	−	0.0765121i
$136$		−	2818.03i		−	0.152359i
$137$	−22901.6			−1.22018			−0.610092	−	0.792331i	$-0.708867\pi$
$137$	−22901.6			−1.22018			−0.610092	+	0.792331i	$0.708867\pi$
$138$			3924.79i			0.206091i
$139$			30870.3i			1.59776i	0.601492	+	0.798879i	$0.294573\pi$
$139$			30870.3i			1.59776i	−0.601492	+	0.798879i	$0.705427\pi$
$140$	3018.65	−	3018.65i	0.154013	−	0.154013i
$141$		−	36572.4i		−	1.83957i
$142$	−7297.65	+	7297.65i	−0.361915	+	0.361915i
$143$	−25874.8	+	25874.8i	−1.26533	+	1.26533i
$144$	4510.23			0.217507
$145$	9048.39			0.430364
$146$	−19887.0	−	19887.0i	−0.932962	−	0.932962i
$147$			14420.8i			0.667351i
$148$	10951.8	+	61.2276i	0.499992	+	0.00279527i
$149$	23301.1			1.04955			0.524776	−	0.851240i	$-0.324149\pi$
$149$	23301.1			1.04955			0.524776	+	0.851240i	$0.324149\pi$
$150$	9682.37	−	9682.37i	0.430327	−	0.430327i
$151$		−	20776.6i		−	0.911214i	−0.890181	−	0.455607i	$-0.849422\pi$
$151$		−	20776.6i		−	0.911214i	0.890181	−	0.455607i	$-0.150578\pi$
$152$			444.365i			0.0192333i
$153$	6206.03	+	6206.03i	0.265113	+	0.265113i
$154$	9974.17	+	9974.17i	0.420567	+	0.420567i
$155$	−13445.2			−0.559635
$156$	17910.7	+	17910.7i	0.735976	+	0.735976i
$157$	−44450.2			−1.80333			−0.901663	−	0.432440i	$-0.857653\pi$
$157$	−44450.2			−1.80333			−0.901663	+	0.432440i	$0.857653\pi$
$158$	−25612.1			−1.02596
$159$		−	12819.9i		−	0.507096i
$160$	2755.09			0.107621
$161$	2795.22	+	2795.22i	0.107836	+	0.107836i
$162$	14605.8	−	14605.8i	0.556540	−	0.556540i
$163$	9806.05	−	9806.05i	0.369079	−	0.369079i	−0.498063	−	0.867141i	$-0.665955\pi$
$163$	9806.05	−	9806.05i	0.369079	−	0.369079i	0.867141	+	0.498063i	$0.165955\pi$
$164$	−9913.25			−0.368577
$165$	−18840.1	−	18840.1i	−0.692016	−	0.692016i
$166$	14309.0	−	14309.0i	0.519271	−	0.519271i
$167$	25412.6	+	25412.6i	0.911207	+	0.911207i	0.996367	−	0.0851606i	$-0.0271403\pi$
$167$	25412.6	+	25412.6i	0.911207	+	0.911207i	−0.0851606	+	0.996367i	$0.527140\pi$
$168$	6904.19	−	6904.19i	0.244621	−	0.244621i
$169$			37621.5i			1.31723i
$170$	3790.98	+	3790.98i	0.131176	+	0.131176i
$171$	−978.607	−	978.607i	−0.0334669	−	0.0334669i
$172$	4860.50	−	4860.50i	0.164295	−	0.164295i
$173$		−	26725.9i		−	0.892977i	−0.894789	−	0.446489i	$-0.852674\pi$
$173$		−	26725.9i		−	0.892977i	0.894789	−	0.446489i	$-0.147326\pi$
$174$	20695.3			0.683555
$175$		−	13791.5i		−	0.450334i
$176$			9103.34i			0.293884i
$177$	23343.1	−	23343.1i	0.745095	−	0.745095i
$178$			9039.02i			0.285287i
$179$	29943.6	−	29943.6i	0.934542	−	0.934542i	−0.0634438	−	0.997985i	$-0.520208\pi$
$179$	29943.6	−	29943.6i	0.934542	−	0.934542i	0.997985	+	0.0634438i	$0.0202084\pi$
$180$	−6067.43	+	6067.43i	−0.187266	+	0.187266i
$181$	36299.1			1.10800			0.553999	−	0.832518i	$-0.313101\pi$
$181$	36299.1			1.10800			0.553999	+	0.832518i	$0.313101\pi$
$182$	25511.9			0.770193
$183$	−49382.2	−	49382.2i	−1.47458	−	1.47458i
$184$			2551.18i			0.0753537i
$185$	−14815.4	+	14650.7i	−0.432883	+	0.428070i
$186$	−30751.6			−0.888878
$187$	−12526.1	+	12526.1i	−0.358206	+	0.358206i
$188$		−	23772.6i		−	0.672607i
$189$		−	4542.84i		−	0.127176i
$190$	−597.787	−	597.787i	−0.0165592	−	0.0165592i
$191$	1331.07	+	1331.07i	0.0364867	+	0.0364867i	0.725115	−	0.688628i	$-0.241787\pi$
$191$	1331.07	+	1331.07i	0.0364867	+	0.0364867i	−0.688628	+	0.725115i	$0.741787\pi$
$192$	6301.39			0.170936
$193$	−47495.0	−	47495.0i	−1.27507	−	1.27507i	−0.943394	−	0.331675i	$-0.892386\pi$
$193$	−47495.0	−	47495.0i	−1.27507	−	1.27507i	−0.331675	−	0.943394i	$-0.607614\pi$
$194$	−34233.1			−0.909583
$195$	−48189.2			−1.26730
$196$			9373.73i			0.244006i
$197$	22672.3			0.584202			0.292101	−	0.956388i	$-0.405646\pi$
$197$	22672.3			0.584202			0.292101	+	0.956388i	$0.405646\pi$
$198$	−20047.9	−	20047.9i	−0.511374	−	0.511374i
$199$	−26429.3	+	26429.3i	−0.667389	+	0.667389i	−0.957111	−	0.289722i	$-0.906437\pi$
$199$	−26429.3	+	26429.3i	−0.667389	+	0.667389i	0.289722	+	0.957111i	$0.406437\pi$
$200$	6293.68	−	6293.68i	0.157342	−	0.157342i
$201$	−28786.2			−0.712512
$202$	24738.4	+	24738.4i	0.606274	+	0.606274i
$203$	14739.1	−	14739.1i	0.357667	−	0.357667i
$204$	8670.65	+	8670.65i	0.208349	+	0.208349i
$205$	13335.9	−	13335.9i	0.317333	−	0.317333i
$206$		−	23221.1i		−	0.547202i
$207$	−5618.35	−	5618.35i	−0.131120	−	0.131120i
$208$	11642.2	+	11642.2i	0.269098	+	0.269098i
$209$	1975.20	−	1975.20i	0.0452187	−	0.0452187i
$210$			18575.9i			0.421221i
$211$	48508.7			1.08957			0.544784	−	0.838576i	$-0.316612\pi$
$211$	48508.7			1.08957			0.544784	+	0.838576i	$0.316612\pi$
$212$		−	8333.12i		−	0.185411i
$213$		−	44907.6i		−	0.989829i
$214$	−7370.93	+	7370.93i	−0.160951	+	0.160951i
$215$			13077.3i			0.282905i
$216$	2073.10	−	2073.10i	0.0444338	−	0.0444338i
$217$	−21901.2	+	21901.2i	−0.465102	+	0.465102i
$218$	−38423.3			−0.808502
$219$	122379.			2.55163
$220$	−12246.4	−	12246.4i	−0.253024	−	0.253024i
$221$			32039.2i			0.655990i
$222$	−33885.5	+	33508.8i	−0.687557	+	0.679912i
$223$	37090.7			0.745856			0.372928	−	0.927860i	$-0.378354\pi$
$223$	37090.7			0.745856			0.372928	+	0.927860i	$0.378354\pi$
$224$	4487.83	−	4487.83i	0.0894417	−	0.0894417i
$225$			27720.6i			0.547568i
$226$			19689.4i			0.385493i
$227$	38853.5	+	38853.5i	0.754012	+	0.754012i	0.975225	−	0.221214i	$-0.0710018\pi$
$227$	38853.5	+	38853.5i	0.754012	+	0.754012i	−0.221214	+	0.975225i	$0.571002\pi$
$228$	−1367.25	−	1367.25i	−0.0263013	−	0.0263013i
$229$	−22098.2			−0.421391			−0.210695	−	0.977552i	$-0.567573\pi$
$229$	−22098.2			−0.421391			−0.210695	+	0.977552i	$0.567573\pi$
$230$	−3431.99	−	3431.99i	−0.0648770	−	0.0648770i
$231$	−61378.1			−1.15024
$232$	13452.3			0.249930
$233$			45800.4i			0.843641i	0.906679	+	0.421821i	$0.138609\pi$
$233$			45800.4i			0.843641i	−0.906679	+	0.421821i	$0.861391\pi$
$234$	−51278.4			−0.936490
$235$	31980.3	+	31980.3i	0.579092	+	0.579092i
$236$	15173.3	−	15173.3i	0.272432	−	0.272432i
$237$	78804.7	−	78804.7i	1.40299	−	1.40299i
$238$	12350.4			0.218036
$239$	36004.7	+	36004.7i	0.630323	+	0.630323i	0.948149	−	0.317826i	$-0.102953\pi$
$239$	36004.7	+	36004.7i	0.630323	+	0.630323i	−0.317826	+	0.948149i	$0.602953\pi$
$240$	−8477.01	+	8477.01i	−0.147170	+	0.147170i
$241$	34717.3	+	34717.3i	0.597739	+	0.597739i	0.939710	−	0.341971i	$-0.111095\pi$
$241$	34717.3	+	34717.3i	0.597739	+	0.597739i	−0.341971	+	0.939710i	$0.611095\pi$
$242$	11182.3	−	11182.3i	0.190941	−	0.190941i
$243$			79384.8i			1.34439i
$244$	−32099.2	−	32099.2i	−0.539155	−	0.539155i
$245$	−12610.1	−	12610.1i	−0.210081	−	0.210081i
$246$	30501.6	−	30501.6i	0.504025	−	0.504025i
$247$		−	5052.15i		−	0.0828100i
$248$	−19989.0			−0.325004
$249$			88053.6i			1.42020i
$250$			43838.5i			0.701416i
$251$	−43521.6	+	43521.6i	−0.690807	+	0.690807i	−0.962410	−	0.271602i	$-0.912447\pi$
$251$	−43521.6	+	43521.6i	−0.690807	+	0.690807i	0.271602	+	0.962410i	$0.412447\pi$
$252$			19766.7i			0.311267i
$253$	11340.0	−	11340.0i	0.177162	−	0.177162i
$254$	46852.2	−	46852.2i	0.726211	−	0.726211i
$255$	−23328.6			−0.358763
$256$	4096.00			0.0625000
$257$	−53578.0	−	53578.0i	−0.811185	−	0.811185i	0.173627	−	0.984812i	$-0.444451\pi$
$257$	−53578.0	−	53578.0i	−0.811185	−	0.811185i	−0.984812	+	0.173627i	$0.944451\pi$
$258$			29910.1i			0.449343i
$259$	−268.339	+	47998.0i	−0.00400022	+	0.715522i
$260$	−31323.7			−0.463368
$261$	−29625.3	+	29625.3i	−0.434893	+	0.434893i
$262$		−	16641.7i		−	0.242435i
$263$			26433.1i			0.382153i	0.981575	+	0.191077i	$0.0611979\pi$
$263$			26433.1i			0.382153i	−0.981575	+	0.191077i	$0.938802\pi$
$264$	−28009.6	−	28009.6i	−0.401883	−	0.401883i
$265$	11210.2	+	11210.2i	0.159633	+	0.159633i
$266$	−1947.49			−0.0275241
$267$	−27811.7	−	27811.7i	−0.390127	−	0.390127i
$268$	−18711.5			−0.260518
$269$	−120348.			−1.66316			−0.831578	−	0.555408i	$-0.812562\pi$
$269$	−120348.			−1.66316			−0.831578	+	0.555408i	$0.812562\pi$
$270$			5577.73i			0.0765121i
$271$	12124.6			0.165093			0.0825464	−	0.996587i	$-0.473695\pi$
$271$	12124.6			0.165093			0.0825464	+	0.996587i	$0.473695\pi$
$272$	5636.06	+	5636.06i	0.0761794	+	0.0761794i
$273$	−78496.3	+	78496.3i	−1.05323	+	1.05323i
$274$	45803.2	−	45803.2i	0.610092	−	0.610092i
$275$	−55950.7			−0.739844
$276$	−7849.59	−	7849.59i	−0.103045	−	0.103045i
$277$	4822.15	−	4822.15i	0.0628465	−	0.0628465i	−0.674985	−	0.737831i	$-0.735850\pi$
$277$	4822.15	−	4822.15i	0.0628465	−	0.0628465i	0.737831	+	0.674985i	$0.235850\pi$
$278$	−61740.6	−	61740.6i	−0.798879	−	0.798879i
$279$	44021.0	−	44021.0i	0.565525	−	0.565525i
$280$			12074.6i			0.154013i
$281$	75002.5	+	75002.5i	0.949868	+	0.949868i	0.998802	−	0.0489341i	$-0.0155824\pi$
$281$	75002.5	+	75002.5i	0.949868	+	0.949868i	−0.0489341	+	0.998802i	$0.515582\pi$
$282$	73144.8	+	73144.8i	0.919783	+	0.919783i
$283$	23758.4	−	23758.4i	0.296650	−	0.296650i	−0.543050	−	0.839700i	$-0.682731\pi$
$283$	23758.4	−	23758.4i	0.296650	−	0.296650i	0.839700	+	0.543050i	$0.182731\pi$
$284$		−	29190.6i		−	0.361915i
$285$	3678.60			0.0452890
$286$		−	103499.i		−	1.26533i
$287$		−	43446.2i		−	0.527459i
$288$	−9020.45	+	9020.45i	−0.108754	+	0.108754i
$289$		−	68010.7i		−	0.814294i
$290$	−18096.8	+	18096.8i	−0.215182	+	0.215182i
$291$	105330.	−	105330.i	1.24384	−	1.24384i
$292$	79548.0			0.932962
$293$	108751.			1.26677			0.633384	−	0.773837i	$-0.281665\pi$
$293$	108751.			1.26677			0.633384	+	0.773837i	$0.281665\pi$
$294$	−28841.6	−	28841.6i	−0.333675	−	0.333675i
$295$			40824.2i			0.469109i
$296$	−22026.1	+	21781.2i	−0.251394	+	0.248598i
$297$	−18429.9			−0.208934
$298$	−46602.2	+	46602.2i	−0.524776	+	0.524776i
$299$		−	29005.3i		−	0.324440i
$300$			38729.5i			0.430327i
$301$	21301.8	+	21301.8i	0.235117	+	0.235117i
$302$	41553.2	+	41553.2i	0.455607	+	0.455607i
$303$	−152233.			−1.65815
$304$	−888.730	−	888.730i	−0.00961663	−	0.00961663i
$305$	86363.4			0.928389
$306$	−24824.1			−0.265113
$307$		−	162258.i		−	1.72159i	−0.508952	−	0.860795i	$-0.669967\pi$
$307$		−	162258.i		−	1.72159i	0.508952	−	0.860795i	$-0.330033\pi$
$308$	−39896.7			−0.420567
$309$	71447.7	+	71447.7i	0.748293	+	0.748293i
$310$	26890.4	−	26890.4i	0.279817	−	0.279817i
$311$	88112.7	−	88112.7i	0.910999	−	0.910999i	−0.0853518	−	0.996351i	$-0.527201\pi$
$311$	88112.7	−	88112.7i	0.910999	−	0.910999i	0.996351	+	0.0853518i	$0.0272014\pi$
$312$	−71642.9			−0.735976
$313$	−88253.8	−	88253.8i	−0.900834	−	0.900834i	0.0946740	−	0.995508i	$-0.469819\pi$
$313$	−88253.8	−	88253.8i	−0.900834	−	0.900834i	−0.995508	+	0.0946740i	$0.969819\pi$
$314$	88900.3	−	88900.3i	0.901663	−	0.901663i
$315$	−26591.4	−	26591.4i	−0.267991	−	0.267991i
$316$	51224.2	−	51224.2i	0.512981	−	0.512981i
$317$			34320.2i			0.341532i	0.985312	+	0.170766i	$0.0546242\pi$
$317$			34320.2i			0.341532i	−0.985312	+	0.170766i	$0.945376\pi$
$318$	25639.8	+	25639.8i	0.253548	+	0.253548i
$319$	−59795.2	−	59795.2i	−0.587604	−	0.587604i
$320$	−5510.19	+	5510.19i	−0.0538104	+	0.0538104i
$321$		−	45358.5i		−	0.440199i
$322$	−11180.9			−0.107836
$323$		−	2445.77i		−	0.0234428i
$324$			58423.3i			0.556540i
$325$	−71555.2	+	71555.2i	−0.677446	+	0.677446i
$326$			39224.2i			0.369079i
$327$	118223.	−	118223.i	1.10562	−	1.10562i
$328$	19826.5	−	19826.5i	0.184289	−	0.184289i
$329$	104187.			0.962545
$330$	75360.5			0.692016
$331$	27326.2	+	27326.2i	0.249415	+	0.249415i	0.820731	−	0.571316i	$-0.193567\pi$
$331$	27326.2	+	27326.2i	0.249415	+	0.249415i	−0.571316	+	0.820731i	$0.693567\pi$
$332$			57236.1i			0.519271i
$333$	539.356	−	96475.0i	0.00486393	−	0.870014i
$334$	−101651.			−0.911207
$335$	25171.8	−	25171.8i	0.224298	−	0.224298i
$336$			27616.8i			0.244621i
$337$		−	129267.i		−	1.13822i	−0.822261	−	0.569110i	$-0.807288\pi$
$337$		−	129267.i		−	1.13822i	0.822261	−	0.569110i	$-0.192712\pi$
$338$	−75242.9	−	75242.9i	−0.658616	−	0.658616i
$339$	−60581.5	−	60581.5i	−0.527158	−	0.527158i
$340$	−15163.9			−0.131176
$341$	88851.0	+	88851.0i	0.764106	+	0.764106i
$342$	3914.43			0.0334669
$343$	−125264.			−1.06472
$344$			19442.0i			0.164295i
$345$	21119.5			0.177437
$346$	53451.8	+	53451.8i	0.446489	+	0.446489i
$347$	−58943.9	+	58943.9i	−0.489531	+	0.489531i	−0.908158	−	0.418627i	$-0.862511\pi$
$347$	−58943.9	+	58943.9i	−0.489531	+	0.489531i	0.418627	+	0.908158i	$0.362511\pi$
$348$	−41390.6	+	41390.6i	−0.341777	+	0.341777i
$349$	−199349.			−1.63668			−0.818340	−	0.574734i	$-0.805105\pi$
$349$	−199349.			−1.63668			−0.818340	+	0.574734i	$0.805105\pi$
$350$	27583.0	+	27583.0i	0.225167	+	0.225167i
$351$	−23569.9	+	23569.9i	−0.191313	+	0.191313i
$352$	−18206.7	−	18206.7i	−0.146942	−	0.146942i
$353$	−134420.	+	134420.i	−1.07873	+	1.07873i	−0.0821094	+	0.996623i	$0.526166\pi$
$353$	−134420.	+	134420.i	−1.07873	+	1.07873i	−0.996623	+	0.0821094i	$0.973834\pi$
$354$			93372.3i			0.745095i
$355$	39268.9	+	39268.9i	0.311596	+	0.311596i
$356$	−18078.0	−	18078.0i	−0.142643	−	0.142643i
$357$	−38000.4	+	38000.4i	−0.298161	+	0.298161i
$358$			119775.i			0.934542i
$359$	237450.			1.84240			0.921199	−	0.389091i	$-0.127211\pi$
$359$	237450.			1.84240			0.921199	+	0.389091i	$0.127211\pi$
$360$		−	24269.7i		−	0.187266i
$361$		−	129935.i		−	0.997041i
$362$	−72598.2	+	72598.2i	−0.553999	+	0.553999i
$363$			68812.4i			0.522220i
$364$	−51023.8	+	51023.8i	−0.385097	+	0.385097i
$365$	−107013.	+	107013.i	−0.803249	+	0.803249i
$366$	197529.			1.47458
$367$	−204541.			−1.51862			−0.759309	−	0.650730i	$-0.774463\pi$
$367$	−204541.			−1.51862			−0.759309	+	0.650730i	$0.774463\pi$
$368$	−5102.35	−	5102.35i	−0.0376769	−	0.0376769i
$369$			87326.2i			0.641345i
$370$	329.468	−	58932.2i	0.00240663	−	0.430477i
$371$	36521.1			0.265336
$372$	61503.3	−	61503.3i	0.444439	−	0.444439i
$373$			10556.7i			0.0758767i	0.999280	+	0.0379384i	$0.0120791\pi$
$373$			10556.7i			0.0758767i	−0.999280	+	0.0379384i	$0.987921\pi$
$374$		−	50104.4i		−	0.358206i
$375$	−134885.	−	134885.i	−0.959179	−	0.959179i
$376$	47545.2	+	47545.2i	0.336303	+	0.336303i
$377$	−152944.			−1.07609
$378$	9085.68	+	9085.68i	0.0635878	+	0.0635878i
$379$	130955.			0.911682			0.455841	−	0.890061i	$-0.349339\pi$
$379$	130955.			0.911682			0.455841	+	0.890061i	$0.349339\pi$
$380$	2391.15			0.0165592
$381$			288315.i			1.98617i
$382$	−5324.29			−0.0364867
$383$	−152787.	−	152787.i	−1.04157	−	1.04157i	−0.999098	−	0.0424733i	$-0.986476\pi$
$383$	−152787.	−	152787.i	−1.04157	−	1.04157i	−0.0424733	−	0.999098i	$-0.513524\pi$
$384$	−12602.8	+	12602.8i	−0.0854681	+	0.0854681i
$385$	53671.4	−	53671.4i	0.362094	−	0.362094i
$386$	189980.			1.27507
$387$	−42816.3	−	42816.3i	−0.285882	−	0.285882i
$388$	68466.1	−	68466.1i	0.454791	−	0.454791i
$389$	−112269.	−	112269.i	−0.741929	−	0.741929i	0.231020	−	0.972949i	$-0.425794\pi$
$389$	−112269.	−	112269.i	−0.741929	−	0.741929i	−0.972949	+	0.231020i	$0.925794\pi$
$390$	96378.3	−	96378.3i	0.633651	−	0.633651i
$391$		−	14041.6i		−	0.0918464i
$392$	−18747.5	−	18747.5i	−0.122003	−	0.122003i
$393$	51204.0	+	51204.0i	0.331527	+	0.331527i
$394$	−45344.6	+	45344.6i	−0.292101	+	0.292101i
$395$			137820.i			0.883319i
$396$	80191.6			0.511374
$397$			157029.i			0.996319i	0.867085	+	0.498160i	$0.165991\pi$
$397$			157029.i			0.996319i	−0.867085	+	0.498160i	$0.834009\pi$
$398$		−	105717.i		−	0.667389i
$399$	5992.15	−	5992.15i	0.0376389	−	0.0376389i
$400$			25174.7i			0.157342i
$401$	15819.3	−	15819.3i	0.0983779	−	0.0983779i	−0.656205	−	0.754583i	$-0.727839\pi$
$401$	15819.3	−	15819.3i	0.0983779	−	0.0983779i	0.754583	+	0.656205i	$0.227839\pi$
$402$	57572.4	−	57572.4i	0.356256	−	0.356256i
$403$	227263.			1.39932
$404$	−98953.6			−0.606274
$405$	−78594.5	−	78594.5i	−0.479162	−	0.479162i
$406$			58956.4i			0.357667i
$407$	194723.	+	1088.62i	1.17552	+	0.00657187i
$408$	−34682.6			−0.208349
$409$	38105.9	−	38105.9i	0.227795	−	0.227795i	−0.583976	−	0.811771i	$-0.698504\pi$
$409$	38105.9	−	38105.9i	0.227795	−	0.227795i	0.811771	+	0.583976i	$0.198504\pi$
$410$			53343.6i			0.317333i
$411$			281860.i			1.66859i
$412$	46442.1	+	46442.1i	0.273601	+	0.273601i
$413$	66499.4	+	66499.4i	0.389868	+	0.389868i
$414$	22473.4			0.131120
$415$	−76997.5	−	76997.5i	−0.447075	−	0.447075i
$416$	−46569.0			−0.269098
$417$	379933.			2.18492
$418$			7900.80i			0.0452187i
$419$	260486.			1.48374			0.741868	−	0.670546i	$-0.233940\pi$
$419$	260486.			1.48374			0.741868	+	0.670546i	$0.233940\pi$
$420$	−37151.7	−	37151.7i	−0.210611	−	0.210611i
$421$	−94783.8	+	94783.8i	−0.534774	+	0.534774i	−0.921989	−	0.387216i	$-0.873437\pi$
$421$	−94783.8	+	94783.8i	−0.534774	+	0.534774i	0.387216	+	0.921989i	$0.373437\pi$
$422$	−97017.3	+	97017.3i	−0.544784	+	0.544784i
$423$	−209414.			−1.17037
$424$	16666.2	+	16666.2i	0.0927056	+	0.0927056i
$425$	−34640.2	+	34640.2i	−0.191780	+	0.191780i
$426$	89815.1	+	89815.1i	0.494915	+	0.494915i
$427$	140679.	−	140679.i	0.771568	−	0.771568i
$428$		−	29483.7i		−	0.160951i
$429$	318452.	+	318452.i	1.73033	+	1.73033i
$430$	−26154.5	−	26154.5i	−0.141452	−	0.141452i
$431$	−67577.5	+	67577.5i	−0.363788	+	0.363788i	−0.865205	−	0.501418i	$-0.832812\pi$
$431$	−67577.5	+	67577.5i	−0.363788	+	0.363788i	0.501418	+	0.865205i	$0.332812\pi$
$432$			8292.42i			0.0444338i
$433$	−236655.			−1.26224			−0.631118	−	0.775687i	$-0.717404\pi$
$433$	−236655.			−1.26224			−0.631118	+	0.775687i	$0.717404\pi$
$434$		−	87604.8i		−	0.465102i
$435$		−	111362.i		−	0.588518i
$436$	76846.5	−	76846.5i	0.404251	−	0.404251i
$437$			2214.17i			0.0115944i
$438$	−244758.	+	244758.i	−1.27582	+	1.27582i
$439$	131517.	−	131517.i	0.682424	−	0.682424i	−0.278122	−	0.960546i	$-0.589712\pi$
$439$	131517.	−	131517.i	0.682424	−	0.682424i	0.960546	+	0.278122i	$0.0897120\pi$
$440$	48985.5			0.253024
$441$	82573.5			0.424584
$442$	−64078.4	−	64078.4i	−0.327995	−	0.327995i
$443$			190133.i			0.968835i	0.874837	+	0.484418i	$0.160968\pi$
$443$			190133.i			0.968835i	−0.874837	+	0.484418i	$0.839032\pi$
$444$	753.553	−	134789.i	0.00382250	−	0.683734i
$445$	48639.4			0.245622
$446$	−74181.4	+	74181.4i	−0.372928	+	0.372928i
$447$		−	286776.i		−	1.43525i
$448$			17951.3i			0.0894417i
$449$	−201365.	−	201365.i	−0.998831	−	0.998831i	0.00116876	−	0.999999i	$-0.499628\pi$
$449$	−201365.	−	201365.i	−0.998831	−	0.998831i	−0.999999	+	0.00116876i	$0.999628\pi$
$450$	−55441.3	−	55441.3i	−0.273784	−	0.273784i
$451$	−176257.			−0.866550
$452$	−39378.9	−	39378.9i	−0.192747	−	0.192747i
$453$	−255706.			−1.24608
$454$	−155414.			−0.754012
$455$		−	137281.i		−	0.663111i
$456$	5468.98			0.0263013
$457$	−88971.9	−	88971.9i	−0.426011	−	0.426011i	0.461256	−	0.887267i	$-0.347399\pi$
$457$	−88971.9	−	88971.9i	−0.426011	−	0.426011i	−0.887267	+	0.461256i	$0.847399\pi$
$458$	44196.3	−	44196.3i	0.210695	−	0.210695i
$459$	−11410.3	+	11410.3i	−0.0541591	+	0.0541591i
$460$	13728.0			0.0648770
$461$	−222424.	−	222424.i	−1.04660	−	1.04660i	−0.998860	−	0.0477366i	$-0.984799\pi$
$461$	−222424.	−	222424.i	−1.04660	−	1.04660i	−0.0477366	−	0.998860i	$-0.515201\pi$
$462$	122756.	−	122756.i	0.575121	−	0.575121i
$463$	−164606.	−	164606.i	−0.767861	−	0.767861i	0.209868	−	0.977730i	$-0.432696\pi$
$463$	−164606.	−	164606.i	−0.767861	−	0.767861i	−0.977730	+	0.209868i	$0.932696\pi$
$464$	−26904.5	+	26904.5i	−0.124965	+	0.124965i
$465$			165476.i			0.765295i
$466$	−91600.9	−	91600.9i	−0.421821	−	0.421821i
$467$	209613.	+	209613.i	0.961134	+	0.961134i	0.999272	−	0.0381387i	$-0.0121429\pi$
$467$	209613.	+	209613.i	0.961134	+	0.961134i	−0.0381387	+	0.999272i	$0.512143\pi$
$468$	102557.	−	102557.i	0.468245	−	0.468245i
$469$		−	82005.7i		−	0.372819i
$470$	−127921.			−0.579092
$471$			547066.i			2.46603i
$472$			60693.4i			0.272432i
$473$	86419.4	−	86419.4i	0.386268	−	0.386268i
$474$			315219.i			1.40299i
$475$	5462.29	−	5462.29i	0.0242096	−	0.0242096i
$476$	−24700.8	+	24700.8i	−0.109018	+	0.109018i
$477$	−73406.7			−0.322626
$478$	−144019.			−0.630323
$479$	−157711.	−	157711.i	−0.687373	−	0.687373i	0.274278	−	0.961650i	$-0.411561\pi$
$479$	−157711.	−	157711.i	−0.687373	−	0.687373i	−0.961650	+	0.274278i	$0.911561\pi$
$480$		−	33908.1i		−	0.147170i
$481$	250423.	−	247639.i	1.08239	−	1.07036i
$482$	−138869.			−0.597739
$483$	34401.9	−	34401.9i	0.147465	−	0.147465i
$484$			44729.1i			0.190941i
$485$			184209.i			0.783120i
$486$	−158770.	−	158770.i	−0.672195	−	0.672195i
$487$	13375.5	+	13375.5i	0.0563966	+	0.0563966i	0.734743	−	0.678346i	$-0.237303\pi$
$487$	13375.5	+	13375.5i	0.0563966	+	0.0563966i	−0.678346	+	0.734743i	$0.737303\pi$
$488$	128397.			0.539155
$489$	−120687.	−	120687.i	−0.504711	−	0.504711i
$490$	50440.4			0.210081
$491$	386204.			1.60197			0.800984	−	0.598686i	$-0.204310\pi$
$491$	386204.			1.60197			0.800984	+	0.598686i	$0.204310\pi$
$492$			122006.i			0.504025i
$493$	−74040.7			−0.304633
$494$	10104.3	+	10104.3i	0.0414050	+	0.0414050i
$495$	−107879.	+	107879.i	−0.440276	+	0.440276i
$496$	39978.1	−	39978.1i	0.162502	−	0.162502i
$497$	127932.			0.517924
$498$	−176107.	−	176107.i	−0.710098	−	0.710098i
$499$	−22816.0	+	22816.0i	−0.0916303	+	0.0916303i	−0.751436	−	0.659806i	$-0.770639\pi$
$499$	−22816.0	+	22816.0i	−0.0916303	+	0.0916303i	0.659806	+	0.751436i	$0.270639\pi$
$500$	−87677.0	−	87677.0i	−0.350708	−	0.350708i
$501$	312764.	−	312764.i	1.24607	−	1.24607i
$502$		−	174086.i		−	0.690807i
$503$	310068.	+	310068.i	1.22552	+	1.22552i	0.965640	+	0.259882i	$0.0836837\pi$
$503$	310068.	+	310068.i	1.22552	+	1.22552i	0.259882	+	0.965640i	$0.416316\pi$
$504$	−39533.4	−	39533.4i	−0.155634	−	0.155634i
$505$	133118.	−	133118.i	0.521981	−	0.521981i
$506$			45359.8i			0.177162i
$507$	463023.			1.80130
$508$			187409.i			0.726211i
$509$		−	308422.i		−	1.19045i	−0.803560	−	0.595224i	$-0.797063\pi$
$509$		−	308422.i		−	1.19045i	0.803560	−	0.595224i	$-0.202937\pi$
$510$	46657.1	−	46657.1i	0.179382	−	0.179382i
$511$			348631.i			1.33513i
$512$	−8192.00	+	8192.00i	−0.0312500	+	0.0312500i
$513$	1799.25	−	1799.25i	0.00683686	−	0.00683686i
$514$	214312.			0.811185
$515$	−124953.			−0.471122
$516$	−59820.1	−	59820.1i	−0.224671	−	0.224671i
$517$		−	422676.i		−	1.58135i
$518$	−95459.2	−	96532.6i	−0.355761	−	0.359761i
$519$	−328927.			−1.22114
$520$	62647.4	−	62647.4i	0.231684	−	0.231684i
$521$			312647.i			1.15181i	0.817518	+	0.575903i	$0.195349\pi$
$521$			312647.i			1.15181i	−0.817518	+	0.575903i	$0.804651\pi$
$522$		−	118501.i		−	0.434893i
$523$	206955.	+	206955.i	0.756611	+	0.756611i	0.975704	−	0.219093i	$-0.0703098\pi$
$523$	206955.	+	206955.i	0.756611	+	0.756611i	−0.219093	+	0.975704i	$0.570310\pi$
$524$	33283.4	+	33283.4i	0.121217	+	0.121217i
$525$	−169737.			−0.615827
$526$	−52866.3	−	52866.3i	−0.191077	−	0.191077i
$527$	110019.			0.396137
$528$	112039.			0.401883
$529$		−	267129.i		−	0.954575i
$530$	−44840.8			−0.159633
$531$	−133663.	−	133663.i	−0.474046	−	0.474046i
$532$	3894.99	−	3894.99i	0.0137620	−	0.0137620i
$533$	−225415.	+	225415.i	−0.793466	+	0.793466i
$534$	111247.			0.390127
$535$	39663.3	+	39663.3i	0.138574	+	0.138574i
$536$	37422.9	−	37422.9i	0.130259	−	0.130259i
$537$	−368529.	−	368529.i	−1.27798	−	1.27798i
$538$	240695.	−	240695.i	0.831578	−	0.831578i
$539$			166665.i			0.573675i
$540$	−11155.5	−	11155.5i	−0.0382560	−	0.0382560i
$541$	52416.1	+	52416.1i	0.179089	+	0.179089i	0.790959	−	0.611869i	$-0.209582\pi$
$541$	52416.1	+	52416.1i	0.179089	+	0.179089i	−0.611869	+	0.790959i	$0.709582\pi$
$542$	−24249.2	+	24249.2i	−0.0825464	+	0.0825464i
$543$		−	446748.i		−	1.51517i
$544$	−22544.2			−0.0761794
$545$			206757.i			0.696093i
$546$		−	313985.i		−	1.05323i
$547$	−270647.	+	270647.i	−0.904543	+	0.904543i	−0.995825	−	0.0912822i	$-0.970903\pi$
$547$	−270647.	+	270647.i	−0.904543	+	0.904543i	0.0912822	+	0.995825i	$0.470903\pi$
$548$			183213.i			0.610092i
$549$	−282763.	+	282763.i	−0.938161	+	0.938161i
$550$	111901.	−	111901.i	0.369922	−	0.369922i
$551$	11675.2			0.0384558
$552$	31398.4			0.103045
$553$	224498.	+	224498.i	0.734111	+	0.734111i
$554$			19288.6i			0.0628465i
$555$	180312.	+	182339.i	0.585381	+	0.591963i
$556$	246962.			0.798879
$557$	312727.	−	312727.i	1.00799	−	1.00799i	0.00801789	−	0.999968i	$-0.497448\pi$
$557$	312727.	−	312727.i	1.00799	−	1.00799i	0.999968	−	0.00801789i	$-0.00255220\pi$
$558$			176084.i			0.565525i
$559$		−	221043.i		−	0.707381i
$560$	−24149.2	−	24149.2i	−0.0770063	−	0.0770063i
$561$	154164.	+	154164.i	0.489843	+	0.489843i
$562$	−300010.			−0.949868
$563$	−262229.	−	262229.i	−0.827303	−	0.827303i	0.159840	−	0.987143i	$-0.448902\pi$
$563$	−262229.	−	262229.i	−0.827303	−	0.827303i	−0.987143	+	0.159840i	$0.948902\pi$
$564$	−292579.			−0.919783
$565$	105950.			0.331897
$566$			95033.6i			0.296650i
$567$	−256048.			−0.796446
$568$	58381.2	+	58381.2i	0.180957	+	0.180957i
$569$	72427.4	−	72427.4i	0.223706	−	0.223706i	−0.586351	−	0.810057i	$-0.699436\pi$
$569$	72427.4	−	72427.4i	0.223706	−	0.223706i	0.810057	+	0.586351i	$0.199436\pi$
$570$	−7357.21	+	7357.21i	−0.0226445	+	0.0226445i
$571$	187442.			0.574902			0.287451	−	0.957795i	$-0.407192\pi$
$571$	187442.			0.574902			0.287451	+	0.957795i	$0.407192\pi$
$572$	206999.	+	206999.i	0.632667	+	0.632667i
$573$	16382.0	−	16382.0i	0.0498952	−	0.0498952i
$574$	86892.5	+	86892.5i	0.263729	+	0.263729i
$575$	31359.9	−	31359.9i	0.0948505	−	0.0948505i
$576$		−	36081.8i		−	0.108754i
$577$	440676.	+	440676.i	1.32363	+	1.32363i	0.910813	+	0.412820i	$0.135456\pi$
$577$	440676.	+	440676.i	1.32363	+	1.32363i	0.412820	+	0.910813i	$0.364544\pi$
$578$	136021.	+	136021.i	0.407147	+	0.407147i
$579$	−584541.	+	584541.i	−1.74364	+	1.74364i
$580$		−	72387.1i		−	0.215182i
$581$	−250846.			−0.743112
$582$			421320.i			1.24384i
$583$		−	148163.i		−	0.435914i
$584$	−159096.	+	159096.i	−0.466481	+	0.466481i
$585$			275931.i			0.806286i
$586$	−217502.	+	217502.i	−0.633384	+	0.633384i
$587$	−254904.	+	254904.i	−0.739777	+	0.739777i	−0.972535	−	0.232758i	$-0.925225\pi$
$587$	−254904.	+	254904.i	−0.739777	+	0.739777i	0.232758	+	0.972535i	$0.425225\pi$
$588$	115366.			0.333675
$589$	−17348.5			−0.0500070
$590$	−81648.4	−	81648.4i	−0.234554	−	0.234554i
$591$		−	279037.i		−	0.798890i
$592$	489.821	−	87614.6i	0.00139763	−	0.249996i
$593$	−67949.6			−0.193231			−0.0966156	−	0.995322i	$-0.530802\pi$
$593$	−67949.6			−0.193231			−0.0966156	+	0.995322i	$0.530802\pi$
$594$	36859.7	−	36859.7i	0.104467	−	0.104467i
$595$		−	66458.1i		−	0.187721i
$596$		−	186409.i		−	0.524776i
$597$	325276.	+	325276.i	0.912648	+	0.912648i
$598$	58010.5	+	58010.5i	0.162220	+	0.162220i
$599$	288040.			0.802785			0.401393	−	0.915906i	$-0.368526\pi$
$599$	288040.			0.802785			0.401393	+	0.915906i	$0.368526\pi$
$600$	−77458.9	−	77458.9i	−0.215164	−	0.215164i
$601$	117937.			0.326513			0.163257	−	0.986584i	$-0.447800\pi$
$601$	117937.			0.326513			0.163257	+	0.986584i	$0.447800\pi$
$602$	−85207.3			−0.235117
$603$			164830.i			0.453316i
$604$	−166213.			−0.455607
$605$	−60172.3	−	60172.3i	−0.164394	−	0.164394i
$606$	304465.	−	304465.i	0.829073	−	0.829073i
$607$	−93551.7	+	93551.7i	−0.253907	+	0.253907i	−0.822570	−	0.568663i	$-0.807461\pi$
$607$	−93551.7	+	93551.7i	−0.253907	+	0.253907i	0.568663	+	0.822570i	$0.307461\pi$
$608$	3554.92			0.00961663
$609$	−181400.	−	181400.i	−0.489106	−	0.489106i
$610$	−172727.	+	172727.i	−0.464195	+	0.464195i
$611$	−540559.	−	540559.i	−1.44797	−	1.44797i
$612$	49648.2	−	49648.2i	0.132556	−	0.132556i
$613$			268669.i			0.714983i	0.933916	+	0.357492i	$0.116368\pi$
$613$			268669.i			0.714983i	−0.933916	+	0.357492i	$0.883632\pi$
$614$	324516.	+	324516.i	0.860795	+	0.860795i
$615$	−164130.	−	164130.i	−0.433949	−	0.433949i
$616$	79793.4	−	79793.4i	0.210284	−	0.210284i
$617$			484519.i			1.27274i	0.771383	+	0.636371i	$0.219565\pi$
$617$			484519.i			1.27274i	−0.771383	+	0.636371i	$0.780435\pi$
$618$	−285791.			−0.748293
$619$			172756.i			0.450870i	0.974258	+	0.225435i	$0.0723804\pi$
$619$			172756.i			0.450870i	−0.974258	+	0.225435i	$0.927620\pi$
$620$			107562.i			0.279817i
$621$	10329.8	−	10329.8i	0.0267860	−	0.0267860i
$622$			352451.i			0.910999i
$623$	79229.6	−	79229.6i	0.204132	−	0.204132i
$624$	143286.	−	143286.i	0.367988	−	0.367988i
$625$	−9950.31			−0.0254728
$626$	353015.			0.900834
$627$	−24309.6	−	24309.6i	−0.0618361	−	0.0618361i
$628$			355601.i			0.901663i
$629$	121231.	−	119883.i	0.306416	−	0.303009i
$630$	106365.			0.267991
$631$	−170631.	+	170631.i	−0.428549	+	0.428549i	−0.888134	−	0.459585i	$-0.847998\pi$
$631$	−170631.	+	170631.i	−0.428549	+	0.428549i	0.459585	+	0.888134i	$0.347998\pi$
$632$			204897.i			0.512981i
$633$		−	597016.i		−	1.48997i
$634$	−68640.4	−	68640.4i	−0.170766	−	0.170766i
$635$	−252114.	−	252114.i	−0.625243	−	0.625243i
$636$	−102559.			−0.253548
$637$	213147.	+	213147.i	0.525291	+	0.525291i
$638$	239181.			0.587604
$639$	−257141.			−0.629752
$640$		−	22040.7i		−	0.0538104i
$641$	300030.			0.730211			0.365105	−	0.930966i	$-0.381033\pi$
$641$	300030.			0.730211			0.365105	+	0.930966i	$0.381033\pi$
$642$	90717.0	+	90717.0i	0.220099	+	0.220099i
$643$	−131810.	+	131810.i	−0.318806	+	0.318806i	−0.848309	−	0.529502i	$-0.822379\pi$
$643$	−131810.	+	131810.i	−0.318806	+	0.318806i	0.529502	+	0.848309i	$0.322379\pi$
$644$	22361.8	−	22361.8i	0.0539181	−	0.0539181i
$645$	160947.			0.386869
$646$	4891.54	+	4891.54i	0.0117214	+	0.0117214i
$647$	164840.	−	164840.i	0.393780	−	0.393780i	−0.482253	−	0.876032i	$-0.660181\pi$
$647$	164840.	−	164840.i	0.393780	−	0.393780i	0.876032	+	0.482253i	$0.160181\pi$
$648$	−116847.	−	116847.i	−0.278270	−	0.278270i
$649$	269782.	−	269782.i	0.640505	−	0.640505i
$650$		−	286221.i		−	0.677446i
$651$	269547.	+	269547.i	0.636022	+	0.636022i
$652$	−78448.4	−	78448.4i	−0.184539	−	0.184539i
$653$	−398531.	+	398531.i	−0.934622	+	0.934622i	−0.997990	−	0.0633679i	$-0.979816\pi$
$653$	−398531.	+	398531.i	−0.934622	+	0.934622i	0.0633679	+	0.997990i	$0.479816\pi$
$654$			472891.i			1.10562i
$655$	−89549.5			−0.208728
$656$			79306.0i			0.184289i
$657$		−	700741.i		−	1.62341i
$658$	−208374.	+	208374.i	−0.481273	+	0.481273i
$659$		−	282645.i		−	0.650833i	−0.945571	−	0.325417i	$-0.894495\pi$
$659$		−	282645.i		−	0.650833i	0.945571	−	0.325417i	$-0.105505\pi$
$660$	−150721.	+	150721.i	−0.346008	+	0.346008i
$661$	411076.	−	411076.i	0.940848	−	0.940848i	−0.0574980	−	0.998346i	$-0.518312\pi$
$661$	411076.	−	411076.i	0.940848	−	0.940848i	0.998346	+	0.0574980i	$0.0183123\pi$
$662$	−109305.			−0.249415
$663$	394320.			0.897060
$664$	−114472.	−	114472.i	−0.259636	−	0.259636i
$665$			10479.5i			0.0236973i
$666$	191871.	+	194029.i	0.432575	+	0.437439i
$667$	67029.4			0.150665
$668$	203301.	−	203301.i	0.455603	−	0.455603i
$669$		−	456490.i		−	1.01995i
$670$			100687.i			0.224298i
$671$	−570722.	−	570722.i	−1.26759	−	1.26759i
$672$	−55233.5	−	55233.5i	−0.122311	−	0.122311i
$673$	−550661.			−1.21578			−0.607889	−	0.794022i	$-0.707983\pi$
$673$	−550661.			−1.21578			−0.607889	+	0.794022i	$0.707983\pi$
$674$	258533.	+	258533.i	0.569110	+	0.569110i
$675$	−50966.6			−0.111861
$676$	300972.			0.658616
$677$			37674.3i			0.0821992i	0.999155	+	0.0410996i	$0.0130861\pi$
$677$			37674.3i			0.0821992i	−0.999155	+	0.0410996i	$0.986914\pi$
$678$	242326.			0.527158
$679$	300063.	+	300063.i	0.650837	+	0.650837i
$680$	30327.8	−	30327.8i	0.0655879	−	0.0655879i
$681$	478185.	−	478185.i	1.03110	−	1.03110i
$682$	−355404.			−0.764106
$683$	57341.0	+	57341.0i	0.122920	+	0.122920i	0.765891	−	0.642971i	$-0.222298\pi$
$683$	57341.0	+	57341.0i	0.122920	+	0.122920i	−0.642971	+	0.765891i	$0.722298\pi$
$684$	−7828.86	+	7828.86i	−0.0167335	+	0.0167335i
$685$	−246469.	−	246469.i	−0.525269	−	0.525269i
$686$	250527.	−	250527.i	0.532361	−	0.532361i
$687$			271971.i			0.576247i
$688$	−38884.0	−	38884.0i	−0.0821474	−	0.0821474i
$689$	−189485.	−	189485.i	−0.399150	−	0.399150i
$690$	−42239.0	+	42239.0i	−0.0887187	+	0.0887187i
$691$			360431.i			0.754859i	0.926038	+	0.377429i	$0.123192\pi$
$691$			360431.i			0.754859i	−0.926038	+	0.377429i	$0.876808\pi$
$692$	−213807.			−0.446489
$693$			351451.i			0.731811i
$694$		−	235776.i		−	0.489531i
$695$	−332228.	+	332228.i	−0.687808	+	0.687808i
$696$		−	165562.i		−	0.341777i
$697$	−109124.	+	109124.i	−0.224624	+	0.224624i
$698$	398699.	−	398699.i	0.818340	−	0.818340i
$699$	563685.			1.15367
$700$	−110332.			−0.225167
$701$	−26111.7	−	26111.7i	−0.0531373	−	0.0531373i	0.680039	−	0.733176i	$-0.261963\pi$
$701$	−26111.7	−	26111.7i	−0.0531373	−	0.0531373i	−0.733176	+	0.680039i	$0.761963\pi$
$702$		−	94279.6i		−	0.191313i
$703$	−19116.5	+	18903.9i	−0.0386810	+	0.0382509i
$704$	72826.7			0.146942
$705$	393595.	−	393595.i	0.791902	−	0.791902i
$706$		−	537679.i		−	1.07873i
$707$		−	433678.i		−	0.867618i
$708$	−186745.	−	186745.i	−0.372547	−	0.372547i
$709$	−17996.5	−	17996.5i	−0.0358010	−	0.0358010i	0.688980	−	0.724781i	$-0.258059\pi$
$709$	−17996.5	−	17996.5i	−0.0358010	−	0.0358010i	−0.724781	+	0.688980i	$0.758059\pi$
$710$	−157076.			−0.311596
$711$	−451236.	−	451236.i	−0.892616	−	0.892616i
$712$	72312.2			0.142643
$713$	−99600.6			−0.195922
$714$		−	152002.i		−	0.298161i
$715$	−556934.			−1.08941
$716$	−239549.	−	239549.i	−0.467271	−	0.467271i
$717$	443124.	−	443124.i	0.861960	−	0.861960i
$718$	−474900.	+	474900.i	−0.921199	+	0.921199i
$719$	−838819.			−1.62260			−0.811298	−	0.584633i	$-0.801238\pi$
$719$	−838819.			−1.62260			−0.811298	+	0.584633i	$0.801238\pi$
$720$	48539.4	+	48539.4i	0.0936331	+	0.0936331i
$721$	−203539.	+	203539.i	−0.391541	+	0.391541i
$722$	259871.	+	259871.i	0.498520	+	0.498520i
$723$	427280.	−	427280.i	0.817402	−	0.817402i
$724$		−	290393.i		−	0.553999i
$725$	−165360.	−	165360.i	−0.314597	−	0.314597i
$726$	−137625.	−	137625.i	−0.261110	−	0.261110i
$727$	−653992.	+	653992.i	−1.23738	+	1.23738i	−0.276314	+	0.961068i	$0.589113\pi$
$727$	−653992.	+	653992.i	−1.23738	+	1.23738i	−0.961068	+	0.276314i	$0.910887\pi$
$728$		−	204095.i		−	0.385097i
$729$	385486.			0.725359
$730$		−	428051.i		−	0.803249i
$731$		−	107008.i		−	0.200254i
$732$	−395057.	+	395057.i	−0.737289	+	0.737289i
$733$		−	199044.i		−	0.370460i	−0.982695	−	0.185230i	$-0.940697\pi$
$733$		−	199044.i		−	0.370460i	0.982695	−	0.185230i	$-0.0593029\pi$
$734$	409082.	−	409082.i	0.759309	−	0.759309i
$735$	−155198.	+	155198.i	−0.287283	+	0.287283i
$736$	20409.4			0.0376769
$737$	−332689.			−0.612497
$738$	−174652.	−	174652.i	−0.320672	−	0.320672i
$739$			637184.i			1.16674i	0.812205	+	0.583372i	$0.198267\pi$
$739$			637184.i			1.16674i	−0.812205	+	0.583372i	$0.801733\pi$
$740$	117206.	+	118523.i	0.214035	+	0.216442i
$741$	−62178.9			−0.113242
$742$	−73042.2	+	73042.2i	−0.132668	+	0.132668i
$743$		−	296206.i		−	0.536557i	−0.963341	−	0.268279i	$-0.913545\pi$
$743$		−	296206.i		−	0.536557i	0.963341	−	0.268279i	$-0.0864548\pi$
$744$			246013.i			0.444439i
$745$	250768.	+	250768.i	0.451815	+	0.451815i
$746$	−21113.3	−	21113.3i	−0.0379384	−	0.0379384i
$747$	504195.			0.903561
$748$	100209.	+	100209.i	0.179103	+	0.179103i
$749$	129217.			0.230332
$750$	539538.			0.959179
$751$			318219.i			0.564218i	0.959382	+	0.282109i	$0.0910339\pi$
$751$			318219.i			0.564218i	−0.959382	+	0.282109i	$0.908966\pi$
$752$	−190181.			−0.336303
$753$	535638.	+	535638.i	0.944672	+	0.944672i
$754$	305887.	−	305887.i	0.538045	−	0.538045i
$755$	223599.	−	223599.i	0.392263	−	0.392263i
$756$	−36342.7			−0.0635878
$757$	690801.	+	690801.i	1.20548	+	1.20548i	0.972475	+	0.233009i	$0.0748570\pi$
$757$	690801.	+	690801.i	1.20548	+	1.20548i	0.233009	+	0.972475i	$0.425143\pi$
$758$	−261910.	+	261910.i	−0.455841	+	0.455841i
$759$	−139565.	−	139565.i	−0.242267	−	0.242267i
$760$	−4782.29	+	4782.29i	−0.00827960	+	0.00827960i
$761$			483055.i			0.834117i	0.908880	+	0.417059i	$0.136939\pi$
$761$			483055.i			0.834117i	−0.908880	+	0.417059i	$0.863061\pi$
$762$	−576630.	−	576630.i	−0.993086	−	0.993086i
$763$	336791.	+	336791.i	0.578511	+	0.578511i
$764$	10648.6	−	10648.6i	0.0182434	−	0.0182434i
$765$			133580.i			0.228253i
$766$	611148.			1.04157
$767$		−	690046.i		−	1.17297i
$768$		−	50411.1i		−	0.0854681i
$769$	−346196.	+	346196.i	−0.585422	+	0.585422i	−0.936388	−	0.350966i	$-0.885853\pi$
$769$	−346196.	+	346196.i	−0.585422	+	0.585422i	0.350966	+	0.936388i	$0.385853\pi$
$770$			214686.i			0.362094i
$771$	−659406.	+	659406.i	−1.10929	+	1.10929i
$772$	−379960.	+	379960.i	−0.637534	+	0.637534i
$773$	−124294.			−0.208014			−0.104007	−	0.994577i	$-0.533166\pi$
$773$	−124294.			−0.208014			−0.104007	+	0.994577i	$0.533166\pi$
$774$	171265.			0.285882
$775$	245712.	+	245712.i	0.409094	+	0.409094i
$776$			273864.i			0.454791i
$777$	590730.	+	3302.55i	0.978470	+	0.00547026i
$778$	449078.			0.741929
$779$	17207.4	−	17207.4i	0.0283558	−	0.0283558i
$780$			385513.i			0.633651i
$781$		−	519008.i		−	0.850887i
$782$	28083.1	+	28083.1i	0.0459232	+	0.0459232i
$783$	−54468.6	−	54468.6i	−0.0888429	−	0.0888429i
$784$	74989.8			0.122003
$785$	−478376.	−	478376.i	−0.776301	−	0.776301i
$786$	−204816.			−0.331527
$787$	708117.			1.14329			0.571644	−	0.820502i	$-0.306306\pi$
$787$	708117.			1.14329			0.571644	+	0.820502i	$0.306306\pi$
$788$		−	181378.i		−	0.292101i
$789$	325323.			0.522590
$790$	−275640.	−	275640.i	−0.441660	−	0.441660i
$791$	172584.	−	172584.i	0.275833	−	0.275833i
$792$	−160383.	+	160383.i	−0.255687	+	0.255687i
$793$	−1.45979e6			−2.32137
$794$	−314058.	−	314058.i	−0.498160	−	0.498160i
$795$	137969.	−	137969.i	0.218296	−	0.218296i
$796$	211434.	+	211434.i	0.333695	+	0.333695i
$797$	564747.	−	564747.i	0.889073	−	0.889073i	−0.105361	−	0.994434i	$-0.533600\pi$
$797$	564747.	−	564747.i	0.889073	−	0.889073i	0.994434	+	0.105361i	$0.0335997\pi$
$798$			23968.6i			0.0376389i
$799$	−261687.	−	261687.i	−0.409910	−	0.409910i
$800$	−50349.5	−	50349.5i	−0.0786710	−	0.0786710i
$801$	−159250.	+	159250.i	−0.248207	+	0.248207i
$802$			63277.1i			0.0983779i
$803$	1.41436e6			2.19346
$804$			230290.i			0.356256i
$805$			60164.8i			0.0928434i
$806$	−454525.	+	454525.i	−0.699662	+	0.699662i
$807$			1.48117e6i			2.27435i
$808$	197907.	−	197907.i	0.303137	−	0.303137i
$809$	−527837.	+	527837.i	−0.806497	+	0.806497i	−0.984102	−	0.177605i	$-0.943165\pi$
$809$	−527837.	+	527837.i	−0.806497	+	0.806497i	0.177605	+	0.984102i	$0.443165\pi$
$810$	314378.			0.479162
$811$	−74359.6			−0.113056			−0.0565282	−	0.998401i	$-0.518003\pi$
$811$	−74359.6			−0.113056			−0.0565282	+	0.998401i	$0.518003\pi$
$812$	−117913.	−	117913.i	−0.178834	−	0.178834i
$813$		−	149222.i		−	0.225763i
$814$	−391623.	+	387269.i	−0.591044	+	0.584472i
$815$	211067.			0.317764
$816$	69365.2	−	69365.2i	0.104175	−	0.104175i
$817$			16873.7i			0.0252794i
$818$			152423.i			0.227795i
$819$	449470.	+	449470.i	0.670090	+	0.670090i
$820$	−106687.	−	106687.i	−0.158666	−	0.158666i
$821$	−546995.			−0.811516			−0.405758	−	0.913980i	$-0.632992\pi$
$821$	−546995.			−0.811516			−0.405758	+	0.913980i	$0.632992\pi$
$822$	−563719.	−	563719.i	−0.834294	−	0.834294i
$823$	182458.			0.269379			0.134690	−	0.990888i	$-0.456996\pi$
$823$	182458.			0.269379			0.134690	+	0.990888i	$0.456996\pi$
$824$	−185768.			−0.273601
$825$			688608.i			1.01173i
$826$	−265997.			−0.389868
$827$	647411.	+	647411.i	0.946606	+	0.946606i	0.998645	−	0.0520393i	$-0.0165721\pi$
$827$	647411.	+	647411.i	0.946606	+	0.946606i	−0.0520393	+	0.998645i	$0.516572\pi$
$828$	−44946.8	+	44946.8i	−0.0655598	+	0.0655598i
$829$	172830.	−	172830.i	0.251484	−	0.251484i	−0.570095	−	0.821579i	$-0.693094\pi$
$829$	172830.	−	172830.i	0.251484	−	0.251484i	0.821579	+	0.570095i	$0.193094\pi$
$830$	307990.			0.447075
$831$	−59348.1	−	59348.1i	−0.0859419	−	0.0859419i
$832$	93137.9	−	93137.9i	0.134549	−	0.134549i
$833$	103185.	+	103185.i	0.148706	+	0.148706i
$834$	−759866.	+	759866.i	−1.09246	+	1.09246i
$835$			546986.i			0.784518i
$836$	−15801.6	−	15801.6i	−0.0226094	−	0.0226094i
$837$	80936.2	+	80936.2i	0.115529	+	0.115529i
$838$	−520973.	+	520973.i	−0.741868	+	0.741868i
$839$			163602.i			0.232415i	0.993225	+	0.116208i	$0.0370738\pi$
$839$			163602.i			0.232415i	−0.993225	+	0.116208i	$0.962926\pi$
$840$	148607.			0.210611
$841$			353837.i			0.500278i
$842$		−	379135.i		−	0.534774i
$843$	923087.	−	923087.i	1.29893	−	1.29893i
$844$		−	388069.i		−	0.544784i
$845$	−404885.	+	404885.i	−0.567046	+	0.567046i
$846$	418828.	−	418828.i	0.585187	−	0.585187i
$847$	−196032.			−0.273249
$848$	−66664.9			−0.0927056
$849$	−292404.	−	292404.i	−0.405666	−	0.405666i
$850$		−	138561.i		−	0.191780i
$851$	−109751.	+	108531.i	−0.151548	+	0.149863i
$852$	−359261.			−0.494915
$853$	−18724.3	+	18724.3i	−0.0257341	+	0.0257341i	−0.719857	−	0.694123i	$-0.755793\pi$
$853$	−18724.3	+	18724.3i	−0.0257341	+	0.0257341i	0.694123	+	0.719857i	$0.255793\pi$
$854$			562717.i			0.771568i
$855$		−	21063.7i		−	0.0288139i
$856$	58967.4	+	58967.4i	0.0804757	+	0.0804757i
$857$	346059.	+	346059.i	0.471181	+	0.471181i	0.902297	−	0.431116i	$-0.141880\pi$
$857$	346059.	+	346059.i	0.471181	+	0.471181i	−0.431116	+	0.902297i	$0.641880\pi$
$858$	−1.27381e6			−1.73033
$859$	51923.0	+	51923.0i	0.0703677	+	0.0703677i	0.741415	−	0.671047i	$-0.234155\pi$
$859$	51923.0	+	51923.0i	0.0703677	+	0.0703677i	−0.671047	+	0.741415i	$0.734155\pi$
$860$	104618.			0.141452
$861$	−534711.			−0.721294
$862$		−	270310.i		−	0.363788i
$863$	−157762.			−0.211826			−0.105913	−	0.994375i	$-0.533777\pi$
$863$	−157762.			−0.211826			−0.105913	+	0.994375i	$0.533777\pi$
$864$	−16584.8	−	16584.8i	−0.0222169	−	0.0222169i
$865$	287626.	−	287626.i	0.384412	−	0.384412i
$866$	473311.	−	473311.i	0.631118	−	0.631118i
$867$	−837035.			−1.11354
$868$	175210.	+	175210.i	0.232551	+	0.232551i
$869$	910765.	−	910765.i	1.20605	−	1.20605i
$870$	222725.	+	222725.i	0.294259	+	0.294259i
$871$	−425475.	+	425475.i	−0.560839	+	0.560839i
$872$			307386.i			0.404251i
$873$	−603120.	−	603120.i	−0.791362	−	0.791362i
$874$	−4428.33	−	4428.33i	−0.00579719	−	0.00579719i
$875$	384257.	−	384257.i	0.501887	−	0.501887i
$876$		−	979030.i		−	1.27582i
$877$	−76468.4			−0.0994220			−0.0497110	−	0.998764i	$-0.515830\pi$
$877$	−76468.4			−0.0994220			−0.0497110	+	0.998764i	$0.515830\pi$
$878$			526069.i			0.682424i
$879$		−	1.33844e6i		−	1.73229i
$880$	−97970.9	+	97970.9i	−0.126512	+	0.126512i
$881$		−	906881.i		−	1.16842i	−0.811603	−	0.584209i	$-0.801405\pi$
$881$		−	906881.i		−	1.16842i	0.811603	−	0.584209i	$-0.198595\pi$
$882$	−165147.	+	165147.i	−0.212292	+	0.212292i
$883$	57834.1	−	57834.1i	0.0741759	−	0.0741759i	−0.669046	−	0.743221i	$-0.733297\pi$
$883$	57834.1	−	57834.1i	0.0741759	−	0.0741759i	0.743221	+	0.669046i	$0.233297\pi$
$884$	256314.			0.327995
$885$	502440.			0.641502
$886$	−380266.	−	380266.i	−0.484418	−	0.484418i
$887$		−	461248.i		−	0.586256i	−0.956073	−	0.293128i	$-0.905304\pi$
$887$		−	461248.i		−	0.586256i	0.956073	−	0.293128i	$-0.0946962\pi$
$888$	268070.	+	271084.i	0.339956	+	0.343778i
$889$	−821347.			−1.03926
$890$	−97278.7	+	97278.7i	−0.122811	+	0.122811i
$891$			1.03876e6i			1.30846i
$892$		−	296726.i		−	0.372928i
$893$	41264.5	+	41264.5i	0.0517457	+	0.0517457i
$894$	573552.	+	573552.i	0.717626	+	0.717626i
$895$	644512.			0.804609
$896$	−35902.6	−	35902.6i	−0.0447208	−	0.0447208i
$897$	−356980.			−0.443668
$898$	805461.			0.998831
$899$			525190.i			0.649827i
$900$	221765.			0.273784
$901$	−91730.3	−	91730.3i	−0.112996	−	0.112996i
$902$	352514.	−	352514.i	0.433275	−	0.433275i
$903$	262170.	−	262170.i	0.321520	−	0.321520i
$904$	157516.			0.192747
$905$	390654.	+	390654.i	0.476974	+	0.476974i
$906$	511412.	−	511412.i	0.623038	−	0.623038i
$907$	301412.	+	301412.i	0.366392	+	0.366392i	0.866160	−	0.499768i	$-0.166581\pi$
$907$	301412.	+	301412.i	0.366392	+	0.366392i	−0.499768	+	0.866160i	$0.666581\pi$
$908$	310828.	−	310828.i	0.377006	−	0.377006i
$909$			871685.i			1.05495i
$910$	274561.	+	274561.i	0.331555	+	0.331555i
$911$	683769.	+	683769.i	0.823896	+	0.823896i	0.986664	−	0.162768i	$-0.0520423\pi$
$911$	683769.	+	683769.i	0.823896	+	0.823896i	−0.162768	+	0.986664i	$0.552042\pi$
$912$	−10938.0	+	10938.0i	−0.0131506	+	0.0131506i
$913$			1.01766e6i			1.22084i
$914$	355888.			0.426011
$915$		−	1.06291e6i		−	1.26956i
$916$			176785.i			0.210695i
$917$	−145869.	+	145869.i	−0.173470	+	0.173470i
$918$		−	45641.1i		−	0.0541591i
$919$	1.04857e6	−	1.04857e6i	1.24155	−	1.24155i	0.282198	−	0.959356i	$-0.408936\pi$
$919$	1.04857e6	−	1.04857e6i	1.24155	−	1.24155i	0.959356	−	0.282198i	$-0.0910635\pi$
$920$	−27456.0	+	27456.0i	−0.0324385	+	0.0324385i
$921$	−1.99698e6			−2.35426
$922$	889695.			1.04660
$923$	−663758.	−	663758.i	−0.779123	−	0.779123i
$924$			491025.i			0.575121i
$925$	538495.	+	3010.52i	0.629358	+	0.00351851i
$926$	658423.			0.767861
$927$	409110.	−	409110.i	0.476081	−	0.476081i
$928$		−	107618.i		−	0.124965i
$929$			42411.1i			0.0491414i	0.999698	+	0.0245707i	$0.00782189\pi$
$929$			42411.1i			0.0491414i	−0.999698	+	0.0245707i	$0.992178\pi$
$930$	−330952.	−	330952.i	−0.382647	−	0.382647i
$931$	−16270.9	−	16270.9i	−0.0187721	−	0.0187721i
$932$	366403.			0.421821
$933$	−1.08444e6	−	1.08444e6i	−1.24578	−	1.24578i
$934$	−838451.			−0.961134
$935$	−269614.			−0.308403
$936$			410227.i			0.468245i
$937$	15225.0			0.0173411			0.00867057	−	0.999962i	$-0.497240\pi$
$937$	15225.0			0.0173411			0.00867057	+	0.999962i	$0.497240\pi$
$938$	164011.	+	164011.i	0.186410	+	0.186410i
$939$	−1.08618e6	+	1.08618e6i	−1.23188	+	1.23188i
$940$	255843.	−	255843.i	0.289546	−	0.289546i
$941$	−46311.6			−0.0523011			−0.0261505	−	0.999658i	$-0.508325\pi$
$941$	−46311.6			−0.0523011			−0.0261505	+	0.999658i	$0.508325\pi$
$942$	−1.09413e6	−	1.09413e6i	−1.23301	−	1.23301i
$943$	98790.8	−	98790.8i	0.111095	−	0.111095i
$944$	−121387.	−	121387.i	−0.136216	−	0.136216i
$945$	48890.4	−	48890.4i	0.0547469	−	0.0547469i
$946$			345678.i			0.386268i
$947$	−1.05701e6	−	1.05701e6i	−1.17864	−	1.17864i	−0.980092	−	0.198546i	$-0.936378\pi$
$947$	−1.05701e6	−	1.05701e6i	−1.17864	−	1.17864i	−0.198546	−	0.980092i	$-0.563622\pi$
$948$	−630438.	−	630438.i	−0.701496	−	0.701496i
$949$	1.80882e6	−	1.80882e6i	2.00846	−	2.00846i
$950$			21849.2i			0.0242096i
$951$	422393.			0.467041
$952$		−	98803.3i		−	0.109018i
$953$			1.71773e6i			1.89134i	0.325125	+	0.945671i	$0.394594\pi$
$953$			1.71773e6i			1.89134i	−0.325125	+	0.945671i	$0.605406\pi$
$954$	146813.	−	146813.i	0.161313	−	0.161313i
$955$			28650.2i			0.0314139i
$956$	288038.	−	288038.i	0.315162	−	0.315162i
$957$	−735923.	+	735923.i	−0.803542	+	0.803542i
$958$	630846.			0.687373
$959$	−802957.			−0.873082
$960$	67816.1	+	67816.1i	0.0735852	+	0.0735852i
$961$			143128.i			0.154981i
$962$	−5568.95	+	996123.i	−0.00601760	+	1.07637i
$963$	−259723.			−0.280064
$964$	277738.	−	277738.i	0.298869	−	0.298869i
$965$		−	1.02229e6i		−	1.09779i
$966$			137608.i			0.147465i
$967$	−671054.	−	671054.i	−0.717637	−	0.717637i	0.250484	−	0.968121i	$-0.419410\pi$
$967$	−671054.	−	671054.i	−0.717637	−	0.717637i	−0.968121	+	0.250484i	$0.919410\pi$
$968$	−89458.2	−	89458.2i	−0.0954705	−	0.0954705i
$969$	−30101.1			−0.0320578
$970$	−368419.	−	368419.i	−0.391560	−	0.391560i
$971$	−238177.			−0.252616			−0.126308	−	0.991991i	$-0.540313\pi$
$971$	−238177.			−0.252616			−0.126308	+	0.991991i	$0.540313\pi$
$972$	635079.			0.672195
$973$			1.08235e6i			1.14325i
$974$	−53502.1			−0.0563966
$975$	880659.	+	880659.i	0.926400	+	0.926400i
$976$	−256793.	+	256793.i	−0.269578	+	0.269578i
$977$	108059.	−	108059.i	0.113206	−	0.113206i	−0.648234	−	0.761441i	$-0.724492\pi$
$977$	108059.	−	108059.i	0.113206	−	0.113206i	0.761441	+	0.648234i	$0.224492\pi$
$978$	482748.			0.504711
$979$	−321427.	−	321427.i	−0.335364	−	0.335364i
$980$	−100881.	+	100881.i	−0.105040	+	0.105040i
$981$	−676944.	−	676944.i	−0.703420	−	0.703420i
$982$	−772408.	+	772408.i	−0.800984	+	0.800984i
$983$		−	1.48107e6i		−	1.53274i	−0.642397	−	0.766372i	$-0.722060\pi$
$983$		−	1.48107e6i		−	1.53274i	0.642397	−	0.766372i	$-0.277940\pi$
$984$	−244013.	−	244013.i	−0.252013	−	0.252013i
$985$	244001.	+	244001.i	0.251489	+	0.251489i
$986$	148081.	−	148081.i	0.152316	−	0.152316i
$987$		−	1.28227e6i		−	1.31627i
$988$	−40417.2			−0.0414050
$989$			96874.8i			0.0990417i
$990$		−	431515.i		−	0.440276i
$991$	−921056.	+	921056.i	−0.937861	+	0.937861i	−0.998179	−	0.0603181i	$-0.980788\pi$
$991$	−921056.	+	921056.i	−0.937861	+	0.937861i	0.0603181	+	0.998179i	$0.480788\pi$
$992$			159912.i			0.162502i
$993$	336314.	−	336314.i	0.341072	−	0.341072i
$994$	−255864.	+	255864.i	−0.258962	+	0.258962i
$995$	−568868.			−0.574600
$996$	704428.			0.710098
$997$	151297.	+	151297.i	0.152209	+	0.152209i	0.779104	−	0.626895i	$-0.215674\pi$
$997$	151297.	+	151297.i	0.152209	+	0.152209i	−0.626895	+	0.779104i	$0.715674\pi$
$998$		−	91264.1i		−	0.0916303i
$999$	177377.	+	991.650i	0.177732	+	0.000993636i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.5.d.a.43.2	yes	14
37.31	odd	4	inner	74.5.d.a.31.6	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.5.d.a.31.6	✓	14	37.31	odd	4	inner
74.5.d.a.43.2	yes	14	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	74.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 + 2.00000i) q^{2} -12.3074i q^{3} -8.00000i q^{4} +(10.7621 + 10.7621i) q^{5} +(24.6148 + 24.6148i) q^{6} +35.0611 q^{7} +(16.0000 + 16.0000i) q^{8} -70.4723 q^{9} +O(q^{10})\)	\(q+(-2.00000 + 2.00000i) q^{2} -12.3074i q^{3} -8.00000i q^{4} +(10.7621 + 10.7621i) q^{5} +(24.6148 + 24.6148i) q^{6} +35.0611 q^{7} +(16.0000 + 16.0000i) q^{8} -70.4723 q^{9} -43.0483 q^{10} -142.240i q^{11} -98.4593 q^{12} +(-181.910 - 181.910i) q^{13} +(-70.1223 + 70.1223i) q^{14} +(132.453 - 132.453i) q^{15} -64.0000 q^{16} +(-88.0634 - 88.0634i) q^{17} +(140.945 - 140.945i) q^{18} +(13.8864 + 13.8864i) q^{19} +(86.0967 - 86.0967i) q^{20} -431.512i q^{21} +(284.479 + 284.479i) q^{22} +(79.7242 + 79.7242i) q^{23} +(196.919 - 196.919i) q^{24} -393.355i q^{25} +727.640 q^{26} -129.569i q^{27} -280.489i q^{28} +(420.383 - 420.383i) q^{29} +529.813i q^{30} +(-624.657 + 624.657i) q^{31} +(128.000 - 128.000i) q^{32} -1750.60 q^{33} +352.253 q^{34} +(377.331 + 377.331i) q^{35} +563.778i q^{36} +(-7.65345 + 1368.98i) q^{37} -55.5457 q^{38} +(-2238.84 + 2238.84i) q^{39} +344.387i q^{40} -1239.16i q^{41} +(863.024 + 863.024i) q^{42} +(607.562 + 607.562i) q^{43} -1137.92 q^{44} +(-758.428 - 758.428i) q^{45} -318.897 q^{46} +2971.58 q^{47} +787.674i q^{48} -1171.72 q^{49} +(786.710 + 786.710i) q^{50} +(-1083.83 + 1083.83i) q^{51} +(-1455.28 + 1455.28i) q^{52} +1041.64 q^{53} +(259.138 + 259.138i) q^{54} +(1530.80 - 1530.80i) q^{55} +(560.978 + 560.978i) q^{56} +(170.906 - 170.906i) q^{57} +1681.53i q^{58} +(1896.67 + 1896.67i) q^{59} +(-1059.63 - 1059.63i) q^{60} +(4012.39 - 4012.39i) q^{61} -2498.63i q^{62} -2470.84 q^{63} +512.000i q^{64} -3915.46i q^{65} +(3501.20 - 3501.20i) q^{66} -2338.93i q^{67} +(-704.507 + 704.507i) q^{68} +(981.198 - 981.198i) q^{69} -1509.32 q^{70} +3648.82 q^{71} +(-1127.56 - 1127.56i) q^{72} +9943.51i q^{73} +(-2722.65 - 2753.26i) q^{74} -4841.18 q^{75} +(111.091 - 111.091i) q^{76} -4987.09i q^{77} -8955.36i q^{78} +(6403.03 + 6403.03i) q^{79} +(-688.773 - 688.773i) q^{80} -7302.91 q^{81} +(2478.31 + 2478.31i) q^{82} -7154.52 q^{83} -3452.09 q^{84} -1895.49i q^{85} -2430.25 q^{86} +(-5173.82 - 5173.82i) q^{87} +(2275.84 - 2275.84i) q^{88} +(2259.76 - 2259.76i) q^{89} +3033.71 q^{90} +(-6377.97 - 6377.97i) q^{91} +(637.794 - 637.794i) q^{92} +(7687.91 + 7687.91i) q^{93} +(-5943.15 + 5943.15i) q^{94} +298.893i q^{95} +(-1575.35 - 1575.35i) q^{96} +(8558.26 + 8558.26i) q^{97} +(2343.43 - 2343.43i) q^{98} +10024.0i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 28 q^{2} - 12 q^{5} - 40 q^{6} + 48 q^{7} + 224 q^{8} - 346 q^{9}+O(q^{10}) \) 14 * q - 28 * q^2 - 12 * q^5 - 40 * q^6 + 48 * q^7 + 224 * q^8 - 346 * q^9	\( 14 q - 28 q^{2} - 12 q^{5} - 40 q^{6} + 48 q^{7} + 224 q^{8} - 346 q^{9} + 48 q^{10} + 160 q^{12} - 56 q^{13} - 96 q^{14} - 378 q^{15} - 896 q^{16} - 348 q^{17} + 692 q^{18} - 184 q^{19} - 96 q^{20} - 320 q^{22} - 502 q^{23} - 320 q^{24} + 224 q^{26} - 474 q^{29} - 630 q^{31} + 1792 q^{32} + 632 q^{33} + 1392 q^{34} + 1826 q^{35} - 2544 q^{37} + 736 q^{38} - 798 q^{39} - 224 q^{42} + 1936 q^{43} + 1280 q^{44} + 6162 q^{45} + 2008 q^{46} + 5716 q^{47} + 7862 q^{49} - 1372 q^{50} - 2422 q^{51} - 448 q^{52} - 20228 q^{53} - 656 q^{54} + 14006 q^{55} + 768 q^{56} - 2270 q^{57} - 4502 q^{59} + 3024 q^{60} - 11906 q^{61} - 2588 q^{63} - 1264 q^{66} - 2784 q^{68} + 21440 q^{69} - 7304 q^{70} - 11224 q^{71} - 5536 q^{72} + 4924 q^{74} - 18652 q^{75} - 1472 q^{76} + 20488 q^{79} + 768 q^{80} - 1706 q^{81} + 9808 q^{82} - 20224 q^{83} + 896 q^{84} - 7744 q^{86} + 19636 q^{87} - 2560 q^{88} + 13864 q^{89} - 24648 q^{90} - 6070 q^{91} - 4016 q^{92} - 13800 q^{93} - 11432 q^{94} + 2560 q^{96} + 16622 q^{97} - 15724 q^{98}+O(q^{100}) \) 14 * q - 28 * q^2 - 12 * q^5 - 40 * q^6 + 48 * q^7 + 224 * q^8 - 346 * q^9 + 48 * q^10 + 160 * q^12 - 56 * q^13 - 96 * q^14 - 378 * q^15 - 896 * q^16 - 348 * q^17 + 692 * q^18 - 184 * q^19 - 96 * q^20 - 320 * q^22 - 502 * q^23 - 320 * q^24 + 224 * q^26 - 474 * q^29 - 630 * q^31 + 1792 * q^32 + 632 * q^33 + 1392 * q^34 + 1826 * q^35 - 2544 * q^37 + 736 * q^38 - 798 * q^39 - 224 * q^42 + 1936 * q^43 + 1280 * q^44 + 6162 * q^45 + 2008 * q^46 + 5716 * q^47 + 7862 * q^49 - 1372 * q^50 - 2422 * q^51 - 448 * q^52 - 20228 * q^53 - 656 * q^54 + 14006 * q^55 + 768 * q^56 - 2270 * q^57 - 4502 * q^59 + 3024 * q^60 - 11906 * q^61 - 2588 * q^63 - 1264 * q^66 - 2784 * q^68 + 21440 * q^69 - 7304 * q^70 - 11224 * q^71 - 5536 * q^72 + 4924 * q^74 - 18652 * q^75 - 1472 * q^76 + 20488 * q^79 + 768 * q^80 - 1706 * q^81 + 9808 * q^82 - 20224 * q^83 + 896 * q^84 - 7744 * q^86 + 19636 * q^87 - 2560 * q^88 + 13864 * q^89 - 24648 * q^90 - 6070 * q^91 - 4016 * q^92 - 13800 * q^93 - 11432 * q^94 + 2560 * q^96 + 16622 * q^97 - 15724 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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