LMFDB - Embedded newform 37.3.d.a.31.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,3,Mod(6,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

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

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

chi := DirichletCharacter("37.6");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	37.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:	$1.00817697813$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 18 x^{10} + 8 x^{9} + 42 x^{8} - 268 x^{7} + 884 x^{6} + 704 x^{5} + 761 x^{4} + \cdots + 16 $ x^12 - 6x^11 + 18x^10 + 8x^9 + 42x^8 - 268x^7 + 884x^6 + 704x^5 + 761x^4 - 2054x^3 + 3042x^2 + 312*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.6
Root			$3.14278 + 3.14278i$ of defining polynomial
Character	$\chi$	$=$	37.31
Dual form			37.3.d.a.6.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.14278 + 2.14278i) q^{2} -3.31038i q^{3} +5.18304i q^{4} +(-1.68576 + 1.68576i) q^{5} +(7.09343 - 7.09343i) q^{6} -11.3827 q^{7} +(-2.53501 + 2.53501i) q^{8} -1.95861 q^{9} +O(q^{10})$	\(q+(2.14278 + 2.14278i) q^{2} -3.31038i q^{3} +5.18304i q^{4} +(-1.68576 + 1.68576i) q^{5} +(7.09343 - 7.09343i) q^{6} -11.3827 q^{7} +(-2.53501 + 2.53501i) q^{8} -1.95861 q^{9} -7.22443 q^{10} +8.99230i q^{11} +17.1578 q^{12} +(11.2153 - 11.2153i) q^{13} +(-24.3906 - 24.3906i) q^{14} +(5.58050 + 5.58050i) q^{15} +9.86824 q^{16} +(13.6287 - 13.6287i) q^{17} +(-4.19688 - 4.19688i) q^{18} +(-20.3046 + 20.3046i) q^{19} +(-8.73736 - 8.73736i) q^{20} +37.6809i q^{21} +(-19.2686 + 19.2686i) q^{22} +(-4.76511 + 4.76511i) q^{23} +(8.39183 + 8.39183i) q^{24} +19.3164i q^{25} +48.0641 q^{26} -23.3097i q^{27} -58.9968i q^{28} +(-23.4890 - 23.4890i) q^{29} +23.9156i q^{30} +(7.93911 + 7.93911i) q^{31} +(31.2855 + 31.2855i) q^{32} +29.7679 q^{33} +58.4066 q^{34} +(19.1884 - 19.1884i) q^{35} -10.1516i q^{36} +(-8.89633 + 35.9146i) q^{37} -87.0169 q^{38} +(-37.1270 - 37.1270i) q^{39} -8.54681i q^{40} -48.4830i q^{41} +(-80.7421 + 80.7421i) q^{42} +(15.1316 - 15.1316i) q^{43} -46.6075 q^{44} +(3.30175 - 3.30175i) q^{45} -20.4212 q^{46} -12.6355 q^{47} -32.6676i q^{48} +80.5650 q^{49} +(-41.3909 + 41.3909i) q^{50} +(-45.1161 - 45.1161i) q^{51} +(58.1296 + 58.1296i) q^{52} -30.3728 q^{53} +(49.9476 - 49.9476i) q^{54} +(-15.1588 - 15.1588i) q^{55} +(28.8551 - 28.8551i) q^{56} +(67.2160 + 67.2160i) q^{57} -100.664i q^{58} +(17.1857 - 17.1857i) q^{59} +(-28.9240 + 28.9240i) q^{60} +(-8.21628 - 8.21628i) q^{61} +34.0236i q^{62} +22.2942 q^{63} +94.6032i q^{64} +37.8127i q^{65} +(63.7862 + 63.7862i) q^{66} -90.5888i q^{67} +(70.6380 + 70.6380i) q^{68} +(15.7743 + 15.7743i) q^{69} +82.2332 q^{70} -48.8433 q^{71} +(4.96509 - 4.96509i) q^{72} +95.5783i q^{73} +(-96.0200 + 57.8942i) q^{74} +63.9447 q^{75} +(-105.240 - 105.240i) q^{76} -102.356i q^{77} -159.110i q^{78} +(-54.0174 + 54.0174i) q^{79} +(-16.6355 + 16.6355i) q^{80} -94.7914 q^{81} +(103.889 - 103.889i) q^{82} +108.449 q^{83} -195.302 q^{84} +45.9493i q^{85} +64.8473 q^{86} +(-77.7577 + 77.7577i) q^{87} +(-22.7955 - 22.7955i) q^{88} +(39.5228 + 39.5228i) q^{89} +14.1499 q^{90} +(-127.660 + 127.660i) q^{91} +(-24.6978 - 24.6978i) q^{92} +(26.2815 - 26.2815i) q^{93} +(-27.0752 - 27.0752i) q^{94} -68.4574i q^{95} +(103.567 - 103.567i) q^{96} +(-52.1160 + 52.1160i) q^{97} +(172.633 + 172.633i) q^{98} -17.6124i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 6 q^{5} + 6 q^{6} - 4 q^{7} + 36 q^{8} - 60 q^{9}+O(q^{10}) $ 12 * q - 6 * q^2 - 6 * q^5 + 6 * q^6 - 4 * q^7 + 36 * q^8 - 60 * q^9	$ 12 q - 6 q^{2} - 6 q^{5} + 6 q^{6} - 4 q^{7} + 36 q^{8} - 60 q^{9} - 16 q^{10} + 64 q^{12} + 14 q^{13} - 70 q^{14} - 2 q^{15} - 96 q^{16} + 2 q^{17} + 132 q^{18} + 14 q^{19} - 24 q^{20} + 22 q^{22} + 56 q^{23} - 84 q^{24} - 48 q^{26} + 60 q^{29} + 72 q^{31} + 208 q^{32} + 56 q^{33} + 112 q^{34} - 154 q^{35} - 66 q^{37} - 336 q^{38} - 46 q^{39} + 90 q^{42} + 70 q^{43} + 80 q^{44} + 232 q^{45} - 424 q^{46} - 384 q^{47} + 144 q^{49} - 34 q^{50} - 126 q^{51} + 328 q^{52} - 56 q^{53} - 194 q^{54} + 70 q^{55} + 16 q^{56} - 94 q^{57} + 184 q^{59} + 276 q^{60} + 132 q^{61} - 400 q^{63} + 614 q^{66} + 116 q^{68} + 368 q^{69} + 556 q^{70} + 68 q^{71} - 692 q^{72} - 382 q^{74} + 116 q^{75} + 12 q^{76} - 2 q^{79} + 4 q^{80} - 76 q^{81} + 374 q^{82} + 108 q^{83} - 1436 q^{84} + 140 q^{86} - 420 q^{87} - 788 q^{88} + 278 q^{89} - 664 q^{90} - 450 q^{91} + 652 q^{92} + 584 q^{93} + 118 q^{94} + 1584 q^{96} - 244 q^{97} + 416 q^{98}+O(q^{100}) $ 12 * q - 6 * q^2 - 6 * q^5 + 6 * q^6 - 4 * q^7 + 36 * q^8 - 60 * q^9 - 16 * q^10 + 64 * q^12 + 14 * q^13 - 70 * q^14 - 2 * q^15 - 96 * q^16 + 2 * q^17 + 132 * q^18 + 14 * q^19 - 24 * q^20 + 22 * q^22 + 56 * q^23 - 84 * q^24 - 48 * q^26 + 60 * q^29 + 72 * q^31 + 208 * q^32 + 56 * q^33 + 112 * q^34 - 154 * q^35 - 66 * q^37 - 336 * q^38 - 46 * q^39 + 90 * q^42 + 70 * q^43 + 80 * q^44 + 232 * q^45 - 424 * q^46 - 384 * q^47 + 144 * q^49 - 34 * q^50 - 126 * q^51 + 328 * q^52 - 56 * q^53 - 194 * q^54 + 70 * q^55 + 16 * q^56 - 94 * q^57 + 184 * q^59 + 276 * q^60 + 132 * q^61 - 400 * q^63 + 614 * q^66 + 116 * q^68 + 368 * q^69 + 556 * q^70 + 68 * q^71 - 692 * q^72 - 382 * q^74 + 116 * q^75 + 12 * q^76 - 2 * q^79 + 4 * q^80 - 76 * q^81 + 374 * q^82 + 108 * q^83 - 1436 * q^84 + 140 * q^86 - 420 * q^87 - 788 * q^88 + 278 * q^89 - 664 * q^90 - 450 * q^91 + 652 * q^92 + 584 * q^93 + 118 * q^94 + 1584 * q^96 - 244 * q^97 + 416 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	2.14278	+	2.14278i	1.07139	+	1.07139i	0.997248	+	0.0741443i	$0.0236225\pi$
$2$	2.14278	+	2.14278i	1.07139	+	1.07139i	0.0741443	+	0.997248i	$0.476377\pi$
$3$		−	3.31038i		−	1.10346i	−0.834023	−	0.551730i	$-0.813968\pi$
$3$		−	3.31038i		−	1.10346i	0.834023	−	0.551730i	$-0.186032\pi$
$4$			5.18304i			1.29576i
$5$	−1.68576	+	1.68576i	−0.337152	+	0.337152i	−0.855294	−	0.518143i	$-0.826624\pi$
$5$	−1.68576	+	1.68576i	−0.337152	+	0.337152i	0.518143	+	0.855294i	$0.326624\pi$
$6$	7.09343	−	7.09343i	1.18224	−	1.18224i
$7$	−11.3827			−1.62609			−0.813047	−	0.582198i	$-0.802193\pi$
$7$	−11.3827			−1.62609			−0.813047	+	0.582198i	$0.802193\pi$
$8$	−2.53501	+	2.53501i	−0.316876	+	0.316876i
$9$	−1.95861			−0.217624
$10$	−7.22443			−0.722443
$11$			8.99230i			0.817482i	0.912650	+	0.408741i	$0.134032\pi$
$11$			8.99230i			0.817482i	−0.912650	+	0.408741i	$0.865968\pi$
$12$	17.1578			1.42982
$13$	11.2153	−	11.2153i	0.862718	−	0.862718i	−0.128935	−	0.991653i	$-0.541156\pi$
$13$	11.2153	−	11.2153i	0.862718	−	0.862718i	0.991653	+	0.128935i	$0.0411559\pi$
$14$	−24.3906	−	24.3906i	−1.74218	−	1.74218i
$15$	5.58050	+	5.58050i	0.372033	+	0.372033i
$16$	9.86824			0.616765
$17$	13.6287	−	13.6287i	0.801687	−	0.801687i	−0.181672	−	0.983359i	$-0.558151\pi$
$17$	13.6287	−	13.6287i	0.801687	−	0.801687i	0.983359	+	0.181672i	$0.0581510\pi$
$18$	−4.19688	−	4.19688i	−0.233160	−	0.233160i
$19$	−20.3046	+	20.3046i	−1.06866	+	1.06866i	−0.0712029	+	0.997462i	$0.522684\pi$
$19$	−20.3046	+	20.3046i	−1.06866	+	1.06866i	−0.997462	+	0.0712029i	$0.977316\pi$
$20$	−8.73736	−	8.73736i	−0.436868	−	0.436868i
$21$			37.6809i			1.79433i
$22$	−19.2686	+	19.2686i	−0.875843	+	0.875843i
$23$	−4.76511	+	4.76511i	−0.207179	+	0.207179i	−0.803067	−	0.595888i	$-0.796800\pi$
$23$	−4.76511	+	4.76511i	−0.207179	+	0.207179i	0.595888	+	0.803067i	$0.296800\pi$
$24$	8.39183	+	8.39183i	0.349660	+	0.349660i
$25$			19.3164i			0.772658i
$26$	48.0641			1.84862
$27$		−	23.3097i		−	0.863321i
$28$		−	58.9968i		−	2.10703i
$29$	−23.4890	−	23.4890i	−0.809967	−	0.809967i	0.174661	−	0.984629i	$-0.444117\pi$
$29$	−23.4890	−	23.4890i	−0.809967	−	0.809967i	−0.984629	+	0.174661i	$0.944117\pi$
$30$			23.9156i			0.797187i
$31$	7.93911	+	7.93911i	0.256100	+	0.256100i	0.823466	−	0.567366i	$-0.192037\pi$
$31$	7.93911	+	7.93911i	0.256100	+	0.256100i	−0.567366	+	0.823466i	$0.692037\pi$
$32$	31.2855	+	31.2855i	0.977672	+	0.977672i
$33$	29.7679			0.902058
$34$	58.4066			1.71784
$35$	19.1884	−	19.1884i	0.548240	−	0.548240i
$36$		−	10.1516i		−	0.281988i
$37$	−8.89633	+	35.9146i	−0.240441	+	0.970664i
$37$	−8.89633	+	35.9146i	−0.240441	+	0.970664i
$38$	−87.0169			−2.28992
$39$	−37.1270	−	37.1270i	−0.951975	−	0.951975i
$40$		−	8.54681i		−	0.213670i
$41$		−	48.4830i		−	1.18251i	−0.806484	−	0.591256i	$-0.798632\pi$
$41$		−	48.4830i		−	1.18251i	0.806484	−	0.591256i	$-0.201368\pi$
$42$	−80.7421	+	80.7421i	−1.92243	+	1.92243i
$43$	15.1316	−	15.1316i	0.351897	−	0.351897i	−0.508918	−	0.860815i	$-0.669954\pi$
$43$	15.1316	−	15.1316i	0.351897	−	0.351897i	0.860815	+	0.508918i	$0.169954\pi$
$44$	−46.6075			−1.05926
$45$	3.30175	−	3.30175i	0.0733722	−	0.0733722i
$46$	−20.4212			−0.443939
$47$	−12.6355			−0.268841			−0.134421	−	0.990924i	$-0.542917\pi$
$47$	−12.6355			−0.268841			−0.134421	+	0.990924i	$0.542917\pi$
$48$		−	32.6676i		−	0.680575i
$49$	80.5650			1.64418
$50$	−41.3909	+	41.3909i	−0.827819	+	0.827819i
$51$	−45.1161	−	45.1161i	−0.884629	−	0.884629i
$52$	58.1296	+	58.1296i	1.11788	+	1.11788i
$53$	−30.3728			−0.573072			−0.286536	−	0.958069i	$-0.592504\pi$
$53$	−30.3728			−0.573072			−0.286536	+	0.958069i	$0.592504\pi$
$54$	49.9476	−	49.9476i	0.924955	−	0.924955i
$55$	−15.1588	−	15.1588i	−0.275615	−	0.275615i
$56$	28.8551	−	28.8551i	0.515270	−	0.515270i
$57$	67.2160	+	67.2160i	1.17923	+	1.17923i
$58$		−	100.664i		−	1.73558i
$59$	17.1857	−	17.1857i	0.291283	−	0.291283i	−0.546304	−	0.837587i	$-0.683966\pi$
$59$	17.1857	−	17.1857i	0.291283	−	0.291283i	0.837587	+	0.546304i	$0.183966\pi$
$60$	−28.9240	+	28.9240i	−0.482066	+	0.482066i
$61$	−8.21628	−	8.21628i	−0.134693	−	0.134693i	0.636546	−	0.771239i	$-0.280363\pi$
$61$	−8.21628	−	8.21628i	−0.134693	−	0.134693i	−0.771239	+	0.636546i	$0.780363\pi$
$62$			34.0236i			0.548767i
$63$	22.2942			0.353877
$64$			94.6032i			1.47818i
$65$			37.8127i			0.581734i
$66$	63.7862	+	63.7862i	0.966458	+	0.966458i
$67$		−	90.5888i		−	1.35207i	−0.736869	−	0.676036i	$-0.763696\pi$
$67$		−	90.5888i		−	1.35207i	0.736869	−	0.676036i	$-0.236304\pi$
$68$	70.6380	+	70.6380i	1.03879	+	1.03879i
$69$	15.7743	+	15.7743i	0.228613	+	0.228613i
$70$	82.2332			1.17476
$71$	−48.8433			−0.687934			−0.343967	−	0.938982i	$-0.611771\pi$
$71$	−48.8433			−0.687934			−0.343967	+	0.938982i	$0.611771\pi$
$72$	4.96509	−	4.96509i	0.0689596	−	0.0689596i
$73$			95.5783i			1.30929i	0.755936	+	0.654646i	$0.227182\pi$
$73$			95.5783i			1.30929i	−0.755936	+	0.654646i	$0.772818\pi$
$74$	−96.0200	+	57.8942i	−1.29757	+	0.782354i
$75$	63.9447			0.852597
$76$	−105.240	−	105.240i	−1.38473	−	1.38473i
$77$		−	102.356i		−	1.32930i
$78$		−	159.110i		−	2.03988i
$79$	−54.0174	+	54.0174i	−0.683765	+	0.683765i	−0.960846	−	0.277082i	$-0.910633\pi$
$79$	−54.0174	+	54.0174i	−0.683765	+	0.683765i	0.277082	+	0.960846i	$0.410633\pi$
$80$	−16.6355	+	16.6355i	−0.207943	+	0.207943i
$81$	−94.7914			−1.17026
$82$	103.889	−	103.889i	1.26693	−	1.26693i
$83$	108.449			1.30662			0.653309	−	0.757091i	$-0.273380\pi$
$83$	108.449			1.30662			0.653309	+	0.757091i	$0.273380\pi$
$84$	−195.302			−2.32502
$85$			45.9493i			0.540580i
$86$	64.8473			0.754039
$87$	−77.7577	+	77.7577i	−0.893766	+	0.893766i
$88$	−22.7955	−	22.7955i	−0.259040	−	0.259040i
$89$	39.5228	+	39.5228i	0.444077	+	0.444077i	0.893379	−	0.449303i	$-0.148328\pi$
$89$	39.5228	+	39.5228i	0.444077	+	0.444077i	−0.449303	+	0.893379i	$0.648328\pi$
$90$	14.1499			0.157221
$91$	−127.660	+	127.660i	−1.40286	+	1.40286i
$92$	−24.6978	−	24.6978i	−0.268454	−	0.268454i
$93$	26.2815	−	26.2815i	0.282596	−	0.282596i
$94$	−27.0752	−	27.0752i	−0.288034	−	0.288034i
$95$		−	68.4574i		−	0.720604i
$96$	103.567	−	103.567i	1.07882	−	1.07882i
$97$	−52.1160	+	52.1160i	−0.537279	+	0.537279i	−0.922729	−	0.385450i	$-0.874046\pi$
$97$	−52.1160	+	52.1160i	−0.537279	+	0.537279i	0.385450	+	0.922729i	$0.374046\pi$
$98$	172.633	+	172.633i	1.76156	+	1.76156i
$99$		−	17.6124i		−	0.177903i
$100$	−100.118			−1.00118
$101$		−	64.5591i		−	0.639199i	−0.947553	−	0.319599i	$-0.896452\pi$
$101$		−	64.5591i		−	0.639199i	0.947553	−	0.319599i	$-0.103548\pi$
$102$		−	193.348i		−	1.89557i
$103$	−20.5836	−	20.5836i	−0.199841	−	0.199841i	0.600091	−	0.799932i	$-0.295131\pi$
$103$	−20.5836	−	20.5836i	−0.199841	−	0.199841i	−0.799932	+	0.600091i	$0.795131\pi$
$104$			56.8619i			0.546749i
$105$	−63.5209	−	63.5209i	−0.604961	−	0.604961i
$106$	−65.0824	−	65.0824i	−0.613985	−	0.613985i
$107$	193.350			1.80701			0.903505	−	0.428577i	$-0.140985\pi$
$107$	193.350			1.80701			0.903505	+	0.428577i	$0.140985\pi$
$108$	120.815			1.11866
$109$	−48.6478	+	48.6478i	−0.446310	+	0.446310i	−0.894126	−	0.447816i	$-0.852202\pi$
$109$	−48.6478	+	48.6478i	−0.446310	+	0.446310i	0.447816	+	0.894126i	$0.352202\pi$
$110$		−	64.9642i		−	0.590584i
$111$	118.891	+	29.4502i	1.07109	+	0.265317i
$112$	−112.327			−1.00292
$113$	46.6319	+	46.6319i	0.412671	+	0.412671i	0.882668	−	0.469997i	$-0.155745\pi$
$113$	46.6319	+	46.6319i	0.412671	+	0.412671i	−0.469997	+	0.882668i	$0.655745\pi$
$114$			288.059i			2.52683i
$115$		−	16.0657i		−	0.139701i
$116$	121.745	−	121.745i	1.04952	−	1.04952i
$117$	−21.9665	+	21.9665i	−0.187748	+	0.187748i
$118$	73.6504			0.624156
$119$	−155.131	+	155.131i	−1.30362	+	1.30362i
$120$	−28.2932			−0.235777
$121$	40.1386			0.331724
$122$		−	35.2114i		−	0.288618i
$123$	−160.497			−1.30485
$124$	−41.1487	+	41.1487i	−0.331845	+	0.331845i
$125$	−74.7068	−	74.7068i	−0.597654	−	0.597654i
$126$	47.7717	+	47.7717i	0.379140	+	0.379140i
$127$	95.5448			0.752321			0.376161	−	0.926554i	$-0.377244\pi$
$127$	95.5448			0.752321			0.376161	+	0.926554i	$0.377244\pi$
$128$	−77.5722	+	77.5722i	−0.606033	+	0.606033i
$129$	−50.0912	−	50.0912i	−0.388304	−	0.388304i
$130$	−81.0244	+	81.0244i	−0.623265	+	0.623265i
$131$	−73.3280	−	73.3280i	−0.559756	−	0.559756i	0.369482	−	0.929238i	$-0.379535\pi$
$131$	−73.3280	−	73.3280i	−0.559756	−	0.559756i	−0.929238	+	0.369482i	$0.879535\pi$
$132$			154.288i			1.16885i
$133$	231.121	−	231.121i	1.73775	−	1.73775i
$134$	194.112	−	194.112i	1.44860	−	1.44860i
$135$	39.2945	+	39.2945i	0.291070	+	0.291070i
$136$			69.0975i			0.508070i
$137$	−20.9988			−0.153276			−0.0766381	−	0.997059i	$-0.524419\pi$
$137$	−20.9988			−0.153276			−0.0766381	+	0.997059i	$0.524419\pi$
$138$			67.6019i			0.489869i
$139$			39.8855i			0.286946i	0.989654	+	0.143473i	$0.0458271\pi$
$139$			39.8855i			0.286946i	−0.989654	+	0.143473i	$0.954173\pi$
$140$	99.4544	+	99.4544i	0.710388	+	0.710388i
$141$			41.8284i			0.296655i
$142$	−104.661	−	104.661i	−0.737047	−	0.737047i
$143$	100.852	+	100.852i	0.705256	+	0.705256i
$144$	−19.3281			−0.134223
$145$	79.1937			0.546163
$146$	−204.804	+	204.804i	−1.40276	+	1.40276i
$147$		−	266.701i		−	1.81429i
$148$	−186.147	−	46.1101i	−1.25775	−	0.311555i
$149$	117.520			0.788728			0.394364	−	0.918954i	$-0.370965\pi$
$149$	117.520			0.788728			0.394364	+	0.918954i	$0.370965\pi$
$150$	137.020	+	137.020i	0.913465	+	0.913465i
$151$			63.7104i			0.421923i	0.977494	+	0.210962i	$0.0676595\pi$
$151$			63.7104i			0.421923i	−0.977494	+	0.210962i	$0.932340\pi$
$152$		−	102.945i		−	0.677268i
$153$	−26.6933	+	26.6933i	−0.174466	+	0.174466i
$154$	219.327	−	219.327i	1.42420	−	1.42420i
$155$	−26.7668			−0.172689
$156$	192.431	−	192.431i	1.23353	−	1.23353i
$157$	−195.433			−1.24480			−0.622398	−	0.782701i	$-0.713841\pi$
$157$	−195.433			−1.24480			−0.622398	+	0.782701i	$0.713841\pi$
$158$	−231.495			−1.46516
$159$			100.546i			0.632362i
$160$	−105.480			−0.659248
$161$	54.2396	−	54.2396i	0.336892	−	0.336892i
$162$	−203.117	−	203.117i	−1.25381	−	1.25381i
$163$	−118.277	−	118.277i	−0.725627	−	0.725627i	0.244119	−	0.969745i	$-0.421501\pi$
$163$	−118.277	−	118.277i	−0.725627	−	0.725627i	−0.969745	+	0.244119i	$0.921501\pi$
$164$	251.290			1.53225
$165$	−50.1815	+	50.1815i	−0.304130	+	0.304130i
$166$	232.384	+	232.384i	1.39990	+	1.39990i
$167$	−25.3470	+	25.3470i	−0.151778	+	0.151778i	−0.778912	−	0.627133i	$-0.784228\pi$
$167$	−25.3470	+	25.3470i	−0.151778	+	0.151778i	0.627133	+	0.778912i	$0.284228\pi$
$168$	−95.5214	−	95.5214i	−0.568579	−	0.568579i
$169$		−	82.5674i		−	0.488564i
$170$	−98.4594	+	98.4594i	−0.579173	+	0.579173i
$171$	39.7689	−	39.7689i	0.232567	−	0.232567i
$172$	78.4275	+	78.4275i	0.455974	+	0.455974i
$173$		−	23.2527i		−	0.134409i	−0.997739	−	0.0672045i	$-0.978592\pi$
$173$		−	23.2527i		−	0.134409i	0.997739	−	0.0672045i	$-0.0214080\pi$
$174$	−333.236			−1.91515
$175$		−	219.872i		−	1.25641i
$176$			88.7381i			0.504194i
$177$	−56.8912	−	56.8912i	−0.321419	−	0.321419i
$178$			169.378i			0.951560i
$179$	105.284	+	105.284i	0.588180	+	0.588180i	0.937138	−	0.348958i	$-0.113465\pi$
$179$	105.284	+	105.284i	0.588180	+	0.588180i	−0.348958	+	0.937138i	$0.613465\pi$
$180$	17.1131	+	17.1131i	0.0950728	+	0.0950728i
$181$	−91.7238			−0.506761			−0.253381	−	0.967367i	$-0.581543\pi$
$181$	−91.7238			−0.506761			−0.253381	+	0.967367i	$0.581543\pi$
$182$	−547.097			−3.00603
$183$	−27.1990	+	27.1990i	−0.148628	+	0.148628i
$184$		−	24.1592i		−	0.131300i
$185$	−45.5462	−	75.5403i	−0.246196	−	0.408326i
$186$	112.631			0.605543
$187$	122.553	+	122.553i	0.655364	+	0.655364i
$188$		−	65.4905i		−	0.348354i
$189$			265.326i			1.40384i
$190$	146.689	−	146.689i	0.772049	−	0.772049i
$191$	−3.32876	+	3.32876i	−0.0174280	+	0.0174280i	−0.715767	−	0.698339i	$-0.753923\pi$
$191$	−3.32876	+	3.32876i	−0.0174280	+	0.0174280i	0.698339	+	0.715767i	$0.253923\pi$
$192$	313.173			1.63111
$193$	92.9050	−	92.9050i	0.481373	−	0.481373i	−0.424197	−	0.905570i	$-0.639444\pi$
$193$	92.9050	−	92.9050i	0.481373	−	0.481373i	0.905570	+	0.424197i	$0.139444\pi$
$194$	−223.347			−1.15127
$195$	125.174			0.641920
$196$			417.572i			2.13047i
$197$	131.535			0.667693			0.333846	−	0.942627i	$-0.391653\pi$
$197$	131.535			0.667693			0.333846	+	0.942627i	$0.391653\pi$
$198$	37.7396	−	37.7396i	0.190604	−	0.190604i
$199$	178.456	+	178.456i	0.896764	+	0.896764i	0.995149	−	0.0983842i	$-0.0313674\pi$
$199$	178.456	+	178.456i	0.896764	+	0.896764i	−0.0983842	+	0.995149i	$0.531367\pi$
$200$	−48.9673	−	48.9673i	−0.244836	−	0.244836i
$201$	−299.883			−1.49196
$202$	138.336	−	138.336i	0.684832	−	0.684832i
$203$	267.368	+	267.368i	1.31708	+	1.31708i
$204$	233.839	−	233.839i	1.14627	−	1.14627i
$205$	81.7306	+	81.7306i	0.398686	+	0.398686i
$206$		−	88.2123i		−	0.428215i
$207$	9.33301	−	9.33301i	0.0450870	−	0.0450870i
$208$	110.676	−	110.676i	0.532094	−	0.532094i
$209$	−182.585	−	182.585i	−0.873614	−	0.873614i
$210$		−	272.223i		−	1.29630i
$211$	141.212			0.669250			0.334625	−	0.942351i	$-0.391390\pi$
$211$	141.212			0.669250			0.334625	+	0.942351i	$0.391390\pi$
$212$		−	157.424i		−	0.742565i
$213$			161.690i			0.759108i
$214$	414.307	+	414.307i	1.93602	+	1.93602i
$215$			51.0163i			0.237285i
$216$	59.0901	+	59.0901i	0.273565	+	0.273565i
$217$	−90.3682	−	90.3682i	−0.416443	−	0.416443i
$218$	−208.483			−0.956345
$219$	316.400			1.44475
$220$	78.5689	−	78.5689i	0.357131	−	0.357131i
$221$		−	305.700i		−	1.38326i
$222$	191.652	+	317.863i	0.863296	+	1.43181i
$223$	−174.380			−0.781972			−0.390986	−	0.920397i	$-0.627866\pi$
$223$	−174.380			−0.781972			−0.390986	+	0.920397i	$0.627866\pi$
$224$	−356.112	−	356.112i	−1.58979	−	1.58979i
$225$		−	37.8334i		−	0.168149i
$226$			199.844i			0.884265i
$227$	212.734	−	212.734i	0.937155	−	0.937155i	−0.0609838	−	0.998139i	$-0.519424\pi$
$227$	212.734	−	212.734i	0.937155	−	0.937155i	0.998139	+	0.0609838i	$0.0194238\pi$
$228$	−348.384	+	348.384i	−1.52800	+	1.52800i
$229$	−436.418			−1.90575			−0.952877	−	0.303357i	$-0.901893\pi$
$229$	−436.418			−1.90575			−0.952877	+	0.303357i	$0.901893\pi$
$230$	34.4252	−	34.4252i	0.149675	−	0.149675i
$231$	−338.838			−1.46683
$232$	119.090			0.513318
$233$		−	22.2955i		−	0.0956890i	−0.998855	−	0.0478445i	$-0.984765\pi$
$233$		−	22.2955i		−	0.0956890i	0.998855	−	0.0478445i	$-0.0152352\pi$
$234$	−94.1389			−0.402303
$235$	21.3005	−	21.3005i	0.0906402	−	0.0906402i
$236$	89.0742	+	89.0742i	0.377433	+	0.377433i
$237$	178.818	+	178.818i	0.754507	+	0.754507i
$238$	−664.823			−2.79337
$239$	−148.456	+	148.456i	−0.621155	+	0.621155i	−0.945827	−	0.324672i	$-0.894746\pi$
$239$	−148.456	+	148.456i	−0.621155	+	0.621155i	0.324672	+	0.945827i	$0.394746\pi$
$240$	55.0697	+	55.0697i	0.229457	+	0.229457i
$241$	92.3863	−	92.3863i	0.383346	−	0.383346i	−0.488960	−	0.872306i	$-0.662624\pi$
$241$	92.3863	−	92.3863i	0.383346	−	0.383346i	0.872306	+	0.488960i	$0.162624\pi$
$242$	86.0083	+	86.0083i	0.355406	+	0.355406i
$243$			104.008i			0.428018i
$244$	42.5853	−	42.5853i	0.174530	−	0.174530i
$245$	−135.813	+	135.813i	−0.554339	+	0.554339i
$246$	−343.911	−	343.911i	−1.39801	−	1.39801i
$247$			455.446i			1.84391i
$248$	−40.2514			−0.162304
$249$		−	359.009i		−	1.44180i
$250$		−	320.161i		−	1.28064i
$251$	−309.817	−	309.817i	−1.23433	−	1.23433i	−0.962285	−	0.272045i	$-0.912300\pi$
$251$	−309.817	−	309.817i	−1.23433	−	1.23433i	−0.272045	−	0.962285i	$-0.587700\pi$
$252$			115.552i			0.458539i
$253$	−42.8493	−	42.8493i	−0.169365	−	0.169365i
$254$	204.732	+	204.732i	0.806031	+	0.806031i
$255$	152.110			0.596508
$256$	45.9721			0.179578
$257$	−343.948	+	343.948i	−1.33832	+	1.33832i	−0.440631	+	0.897688i	$0.645245\pi$
$257$	−343.948	+	343.948i	−1.33832	+	1.33832i	−0.897688	+	0.440631i	$0.854755\pi$
$258$		−	214.669i		−	0.832051i
$259$	101.264	−	408.803i	0.390980	−	1.57839i
$260$	−195.985			−0.753788
$261$	46.0059	+	46.0059i	0.176268	+	0.176268i
$262$		−	314.252i		−	1.19944i
$263$		−	495.928i		−	1.88566i	−0.333277	−	0.942829i	$-0.608154\pi$
$263$		−	495.928i		−	1.88566i	0.333277	−	0.942829i	$-0.391846\pi$
$264$	−75.4618	+	75.4618i	−0.285840	+	0.285840i
$265$	51.2013	−	51.2013i	0.193212	−	0.193212i
$266$	990.483			3.72362
$267$	130.836	−	130.836i	0.490021	−	0.490021i
$268$	469.526			1.75196
$269$	188.779			0.701781			0.350890	−	0.936417i	$-0.385879\pi$
$269$	188.779			0.701781			0.350890	+	0.936417i	$0.385879\pi$
$270$			168.399i			0.623700i
$271$	−82.1137			−0.303003			−0.151501	−	0.988457i	$-0.548411\pi$
$271$	−82.1137			−0.303003			−0.151501	+	0.988457i	$0.548411\pi$
$272$	134.491	−	134.491i	0.494452	−	0.494452i
$273$	422.604	+	422.604i	1.54800	+	1.54800i
$274$	−44.9960	−	44.9960i	−0.164219	−	0.164219i
$275$	−173.699			−0.631633
$276$	−81.7590	+	81.7590i	−0.296228	+	0.296228i
$277$	51.3783	+	51.3783i	0.185481	+	0.185481i	0.793739	−	0.608258i	$-0.208131\pi$
$277$	51.3783	+	51.3783i	0.185481	+	0.185481i	−0.608258	+	0.793739i	$0.708131\pi$
$278$	−85.4661	+	85.4661i	−0.307432	+	0.307432i
$279$	−15.5496	−	15.5496i	−0.0557335	−	0.0557335i
$280$			97.2855i			0.347448i
$281$	−313.583	+	313.583i	−1.11596	+	1.11596i	−0.123626	+	0.992329i	$0.539452\pi$
$281$	−313.583	+	313.583i	−1.11596	+	1.11596i	−0.992329	+	0.123626i	$0.960548\pi$
$282$	−89.6292	+	89.6292i	−0.317834	+	0.317834i
$283$	−361.126	−	361.126i	−1.27606	−	1.27606i	−0.942853	−	0.333209i	$-0.891868\pi$
$283$	−361.126	−	361.126i	−1.27606	−	1.27606i	−0.333209	−	0.942853i	$-0.608132\pi$
$284$		−	253.157i		−	0.891398i
$285$	−226.620			−0.795158
$286$			432.206i			1.51121i
$287$			551.866i			1.92288i
$288$	−61.2762	−	61.2762i	−0.212765	−	0.212765i
$289$		−	82.4817i		−	0.285404i
$290$	169.695	+	169.695i	0.585155	+	0.585155i
$291$	172.524	+	172.524i	0.592865	+	0.592865i
$292$	−495.386			−1.69653
$293$	286.578			0.978081			0.489040	−	0.872261i	$-0.337347\pi$
$293$	286.578			0.978081			0.489040	+	0.872261i	$0.337347\pi$
$294$	571.482	−	571.482i	1.94382	−	1.94382i
$295$			57.9418i			0.196413i
$296$	−68.4913	−	113.596i	−0.231390	−	0.383770i
$297$	209.607			0.705749
$298$	251.821	+	251.821i	0.845037	+	0.845037i
$299$			106.885i			0.357474i
$300$			331.428i			1.10476i
$301$	−172.237	+	172.237i	−0.572217	+	0.572217i
$302$	−136.518	+	136.518i	−0.452045	+	0.452045i
$303$	−213.715			−0.705330
$304$	−200.371	+	200.371i	−0.659115	+	0.659115i
$305$	27.7013			0.0908240
$306$	−114.396			−0.373843
$307$		−	122.178i		−	0.397975i	−0.980002	−	0.198988i	$-0.936235\pi$
$307$		−	122.178i		−	0.397975i	0.980002	−	0.198988i	$-0.0637653\pi$
$308$	530.517			1.72246
$309$	−68.1395	+	68.1395i	−0.220516	+	0.220516i
$310$	−57.3555	−	57.3555i	−0.185018	−	0.185018i
$311$	−0.744369	−	0.744369i	−0.00239347	−	0.00239347i	0.705909	−	0.708303i	$-0.250539\pi$
$311$	−0.744369	−	0.744369i	−0.00239347	−	0.00239347i	−0.708303	+	0.705909i	$0.750539\pi$
$312$	188.234			0.603315
$313$	126.842	−	126.842i	0.405245	−	0.405245i	−0.474832	−	0.880077i	$-0.657491\pi$
$313$	126.842	−	126.842i	0.405245	−	0.405245i	0.880077	+	0.474832i	$0.157491\pi$
$314$	−418.770	−	418.770i	−1.33366	−	1.33366i
$315$	−37.5827	+	37.5827i	−0.119310	+	0.119310i
$316$	−279.975	−	279.975i	−0.885995	−	0.885995i
$317$		−	223.653i		−	0.705529i	−0.935712	−	0.352764i	$-0.885242\pi$
$317$		−	223.653i		−	0.705529i	0.935712	−	0.352764i	$-0.114758\pi$
$318$	−215.447	+	215.447i	−0.677508	+	0.677508i
$319$	211.221	−	211.221i	0.662133	−	0.662133i
$320$	−159.478	−	159.478i	−0.498369	−	0.498369i
$321$		−	640.062i		−	1.99396i
$322$	232.448			0.721887
$323$			553.450i			1.71347i
$324$		−	491.308i		−	1.51638i
$325$	216.640	+	216.640i	0.666586	+	0.666586i
$326$		−	506.885i		−	1.55486i
$327$	161.043	+	161.043i	0.492485	+	0.492485i
$328$	122.905	+	122.905i	0.374709	+	0.374709i
$329$	143.826			0.437161
$330$	−215.056			−0.651686
$331$	−304.968	+	304.968i	−0.921353	+	0.921353i	−0.997125	−	0.0757717i	$-0.975858\pi$
$331$	−304.968	+	304.968i	−0.921353	+	0.921353i	0.0757717	+	0.997125i	$0.475858\pi$
$332$			562.098i			1.69307i
$333$	17.4245	−	70.3427i	0.0523257	−	0.211239i
$334$	−108.626			−0.325228
$335$	152.711	+	152.711i	0.455853	+	0.455853i
$336$			371.844i			1.10668i
$337$			414.657i			1.23044i	0.788357	+	0.615218i	$0.210932\pi$
$337$			414.657i			1.23044i	−0.788357	+	0.615218i	$0.789068\pi$
$338$	176.924	−	176.924i	0.523444	−	0.523444i
$339$	154.369	−	154.369i	0.455366	−	0.455366i
$340$	−238.157			−0.700463
$341$	−71.3908	+	71.3908i	−0.209357	+	0.209357i
$342$	170.432			0.498340
$343$	−359.293			−1.04750
$344$			76.7172i			0.223015i
$345$	−53.1834			−0.154155
$346$	49.8256	−	49.8256i	0.144005	−	0.144005i
$347$	−305.558	−	305.558i	−0.880570	−	0.880570i	0.113022	−	0.993592i	$-0.463947\pi$
$347$	−305.558	−	305.558i	−0.880570	−	0.880570i	−0.993592	+	0.113022i	$0.963947\pi$
$348$	−403.021	−	403.021i	−1.15811	−	1.15811i
$349$	450.038			1.28951			0.644753	−	0.764391i	$-0.276960\pi$
$349$	450.038			1.28951			0.644753	+	0.764391i	$0.276960\pi$
$350$	471.139	−	471.139i	1.34611	−	1.34611i
$351$	−261.426	−	261.426i	−0.744802	−	0.744802i
$352$	−281.329	+	281.329i	−0.799229	+	0.799229i
$353$	144.744	+	144.744i	0.410039	+	0.410039i	0.881752	−	0.471713i	$-0.156364\pi$
$353$	144.744	+	144.744i	0.410039	+	0.410039i	−0.471713	+	0.881752i	$0.656364\pi$
$354$		−	243.811i		−	0.688731i
$355$	82.3380	−	82.3380i	0.231938	−	0.231938i
$356$	−204.848	+	204.848i	−0.575417	+	0.575417i
$357$	513.541	+	513.541i	1.43849	+	1.43849i
$358$			451.202i			1.26034i
$359$	427.601			1.19109			0.595545	−	0.803322i	$-0.296936\pi$
$359$	427.601			1.19109			0.595545	+	0.803322i	$0.296936\pi$
$360$			16.7399i			0.0464997i
$361$		−	463.556i		−	1.28409i
$362$	−196.544	−	196.544i	−0.542940	−	0.542940i
$363$		−	132.874i		−	0.366044i
$364$	−661.669	−	661.669i	−1.81777	−	1.81777i
$365$	−161.122	−	161.122i	−0.441430	−	0.441430i
$366$	−116.563			−0.318479
$367$	−143.668			−0.391465			−0.195732	−	0.980657i	$-0.562708\pi$
$367$	−143.668			−0.391465			−0.195732	+	0.980657i	$0.562708\pi$
$368$	−47.0232	+	47.0232i	−0.127781	+	0.127781i
$369$			94.9594i			0.257343i
$370$	64.2709	−	259.462i	0.173705	−	0.701249i
$371$	345.724			0.931870
$372$	136.218	+	136.218i	0.366177	+	0.366177i
$373$		−	552.142i		−	1.48027i	−0.672456	−	0.740137i	$-0.734761\pi$
$373$		−	552.142i		−	1.48027i	0.672456	−	0.740137i	$-0.265239\pi$
$374$			525.210i			1.40430i
$375$	−247.308	+	247.308i	−0.659488	+	0.659488i
$376$	32.0311	−	32.0311i	0.0851892	−	0.0851892i
$377$	−526.875			−1.39755
$378$	−568.536	+	568.536i	−1.50406	+	1.50406i
$379$	178.106			0.469936			0.234968	−	0.972003i	$-0.424501\pi$
$379$	178.106			0.469936			0.234968	+	0.972003i	$0.424501\pi$
$380$	354.818			0.933731
$381$		−	316.290i		−	0.830156i
$382$	−14.2656			−0.0373445
$383$	198.495	−	198.495i	0.518263	−	0.518263i	−0.398782	−	0.917046i	$-0.630567\pi$
$383$	198.495	−	198.495i	0.518263	−	0.518263i	0.917046	+	0.398782i	$0.130567\pi$
$384$	256.793	+	256.793i	0.668733	+	0.668733i
$385$	172.548	+	172.548i	0.448177	+	0.448177i
$386$	398.151			1.03148
$387$	−29.6369	+	29.6369i	−0.0765810	+	0.0765810i
$388$	−270.120	−	270.120i	−0.696184	−	0.696184i
$389$	216.353	−	216.353i	0.556177	−	0.556177i	−0.372040	−	0.928217i	$-0.621341\pi$
$389$	216.353	−	216.353i	0.556177	−	0.556177i	0.928217	+	0.372040i	$0.121341\pi$
$390$	268.221	+	268.221i	0.687747	+	0.687747i
$391$			129.884i			0.332185i
$392$	−204.233	+	204.233i	−0.521002	+	0.521002i
$393$	−242.744	+	242.744i	−0.617668	+	0.617668i
$394$	281.852	+	281.852i	0.715361	+	0.715361i
$395$		−	182.121i		−	0.461065i
$396$	91.2860			0.230520
$397$		−	350.449i		−	0.882742i	−0.897325	−	0.441371i	$-0.854492\pi$
$397$		−	350.449i		−	0.882742i	0.897325	−	0.441371i	$-0.145508\pi$
$398$			764.786i			1.92157i
$399$	−765.097	−	765.097i	−1.91754	−	1.91754i
$400$			190.619i			0.476548i
$401$	−368.290	−	368.290i	−0.918429	−	0.918429i	0.0784858	−	0.996915i	$-0.474991\pi$
$401$	−368.290	−	368.290i	−0.918429	−	0.918429i	−0.996915	+	0.0784858i	$0.974991\pi$
$402$	−642.585	−	642.585i	−1.59847	−	1.59847i
$403$	178.079			0.441885
$404$	334.612			0.828249
$405$	159.795	−	159.795i	0.394556	−	0.394556i
$406$			1145.82i			2.82222i
$407$	−322.954	−	79.9985i	−0.793500	−	0.196556i
$408$	228.739			0.560635
$409$	76.1355	+	76.1355i	0.186150	+	0.186150i	0.794030	−	0.607879i	$-0.207979\pi$
$409$	76.1355	+	76.1355i	0.186150	+	0.186150i	−0.607879	+	0.794030i	$0.707979\pi$
$410$			350.262i			0.854298i
$411$			69.5141i			0.169134i
$412$	106.686	−	106.686i	0.258946	−	0.258946i
$413$	−195.619	+	195.619i	−0.473653	+	0.473653i
$414$	39.9972			0.0966117
$415$	−182.819	+	182.819i	−0.440529	+	0.440529i
$416$	701.755			1.68691
$417$	132.036			0.316634
$418$		−	782.482i		−	1.87197i
$419$	−520.617			−1.24252			−0.621261	−	0.783604i	$-0.713379\pi$
$419$	−520.617			−1.24252			−0.621261	+	0.783604i	$0.713379\pi$
$420$	329.232	−	329.232i	0.783885	−	0.783885i
$421$	357.058	+	357.058i	0.848119	+	0.848119i	0.989898	−	0.141779i	$-0.0452823\pi$
$421$	357.058	+	357.058i	0.848119	+	0.848119i	−0.141779	+	0.989898i	$0.545282\pi$
$422$	302.586	+	302.586i	0.717029	+	0.717029i
$423$	24.7481			0.0585062
$424$	76.9953	−	76.9953i	0.181593	−	0.181593i
$425$	263.258	+	263.258i	0.619429	+	0.619429i
$426$	−346.467	+	346.467i	−0.813302	+	0.813302i
$427$	93.5231	+	93.5231i	0.219024	+	0.219024i
$428$			1002.14i			2.34145i
$429$	333.857	−	333.857i	0.778222	−	0.778222i
$430$	−109.317	+	109.317i	−0.254225	+	0.254225i
$431$	456.044	+	456.044i	1.05811	+	1.05811i	0.998204	+	0.0599028i	$0.0190791\pi$
$431$	456.044	+	456.044i	1.05811	+	1.05811i	0.0599028	+	0.998204i	$0.480921\pi$
$432$		−	230.025i		−	0.532466i
$433$	610.781			1.41058			0.705290	−	0.708919i	$-0.250817\pi$
$433$	610.781			1.41058			0.705290	+	0.708919i	$0.250817\pi$
$434$		−	387.279i		−	0.892348i
$435$		−	262.161i		−	0.602669i
$436$	−252.143	−	252.143i	−0.578311	−	0.578311i
$437$		−	193.508i		−	0.442809i
$438$	677.977	+	677.977i	1.54789	+	1.54789i
$439$	−36.4343	−	36.4343i	−0.0829939	−	0.0829939i	0.664391	−	0.747385i	$-0.268691\pi$
$439$	−36.4343	−	36.4343i	−0.0829939	−	0.0829939i	−0.747385	+	0.664391i	$0.768691\pi$
$440$	76.8555			0.174672
$441$	−157.796			−0.357813
$442$	655.050	−	655.050i	1.48201	−	1.48201i
$443$			174.556i			0.394032i	0.980400	+	0.197016i	$0.0631252\pi$
$443$			174.556i			0.394032i	−0.980400	+	0.197016i	$0.936875\pi$
$444$	−152.642	+	616.216i	−0.343788	+	1.38787i
$445$	−133.252			−0.299442
$446$	−373.658	−	373.658i	−0.837799	−	0.837799i
$447$		−	389.037i		−	0.870330i
$448$		−	1076.84i		−	2.40365i
$449$	−375.147	+	375.147i	−0.835517	+	0.835517i	−0.988265	−	0.152748i	$-0.951188\pi$
$449$	−375.147	+	375.147i	−0.835517	+	0.835517i	0.152748	+	0.988265i	$0.451188\pi$
$450$	81.0688	−	81.0688i	0.180153	−	0.180153i
$451$	435.974			0.966682
$452$	−241.695	+	241.695i	−0.534723	+	0.534723i
$453$	210.906			0.465575
$454$	911.687			2.00812
$455$		−	430.409i		−	0.945954i
$456$	−340.786			−0.747338
$457$	−167.718	+	167.718i	−0.366998	+	0.366998i	−0.866381	−	0.499383i	$-0.833560\pi$
$457$	−167.718	+	167.718i	−0.366998	+	0.366998i	0.499383	+	0.866381i	$0.333560\pi$
$458$	−935.149	−	935.149i	−2.04181	−	2.04181i
$459$	−317.680	−	317.680i	−0.692113	−	0.692113i
$460$	83.2690			0.181019
$461$	−252.674	+	252.674i	−0.548099	+	0.548099i	−0.925891	−	0.377791i	$-0.876684\pi$
$461$	−252.674	+	252.674i	−0.548099	+	0.548099i	0.377791	+	0.925891i	$0.376684\pi$
$462$	−726.057	−	726.057i	−1.57155	−	1.57155i
$463$	−59.8736	+	59.8736i	−0.129317	+	0.129317i	−0.768803	−	0.639486i	$-0.779147\pi$
$463$	−59.8736	+	59.8736i	−0.129317	+	0.129317i	0.639486	+	0.768803i	$0.279147\pi$
$464$	−231.795	−	231.795i	−0.499559	−	0.499559i
$465$			88.6084i			0.190556i
$466$	47.7745	−	47.7745i	0.102520	−	0.102520i
$467$	−151.793	+	151.793i	−0.325039	+	0.325039i	−0.850696	−	0.525657i	$-0.823819\pi$
$467$	−151.793	+	151.793i	−0.325039	+	0.325039i	0.525657	+	0.850696i	$0.323819\pi$
$468$	−113.853	−	113.853i	−0.243276	−	0.243276i
$469$			1031.14i			2.19860i
$470$	91.2845			0.194222
$471$			646.957i			1.37358i
$472$			87.1316i			0.184601i
$473$	136.067	+	136.067i	0.287669	+	0.287669i
$474$			766.337i			1.61674i
$475$	−392.213	−	392.213i	−0.825712	−	0.825712i
$476$	−804.049	−	804.049i	−1.68918	−	1.68918i
$477$	59.4886			0.124714
$478$	−636.218			−1.33100
$479$	314.983	−	314.983i	0.657584	−	0.657584i	−0.297224	−	0.954808i	$-0.596061\pi$
$479$	314.983	−	314.983i	0.657584	−	0.657584i	0.954808	+	0.297224i	$0.0960608\pi$
$480$			349.178i			0.727453i
$481$	303.018	+	502.569i	0.629976	+	1.04484i
$482$	395.928			0.821427
$483$	−179.554	−	179.554i	−0.371747	−	0.371747i
$484$			208.040i			0.429835i
$485$		−	175.710i		−	0.362289i
$486$	−222.867	+	222.867i	−0.458575	+	0.458575i
$487$	35.8530	−	35.8530i	0.0736202	−	0.0736202i	−0.669338	−	0.742958i	$-0.733422\pi$
$487$	35.8530	−	35.8530i	0.0736202	−	0.0736202i	0.742958	+	0.669338i	$0.233422\pi$
$488$	41.6566			0.0853620
$489$	−391.542	+	391.542i	−0.800700	+	0.800700i
$490$	−582.036			−1.18783
$491$	478.697			0.974944			0.487472	−	0.873139i	$-0.337919\pi$
$491$	478.697			0.974944			0.487472	+	0.873139i	$0.337919\pi$
$492$		−	831.864i		−	1.69078i
$493$	−640.249			−1.29868
$494$	−975.923	+	975.923i	−1.97555	+	1.97555i
$495$	29.6903	+	29.6903i	0.0599804	+	0.0599804i
$496$	78.3450	+	78.3450i	0.157954	+	0.157954i
$497$	555.967			1.11865
$498$	769.278	−	769.278i	1.54473	−	1.54473i
$499$	76.7154	+	76.7154i	0.153738	+	0.153738i	0.779785	−	0.626047i	$-0.215328\pi$
$499$	76.7154	+	76.7154i	0.153738	+	0.153738i	−0.626047	+	0.779785i	$0.715328\pi$
$500$	387.209	−	387.209i	0.774417	−	0.774417i
$501$	83.9082	+	83.9082i	0.167481	+	0.167481i
$502$		−	1327.74i		−	2.64490i
$503$	−461.075	+	461.075i	−0.916650	+	0.916650i	−0.996784	−	0.0801345i	$-0.974465\pi$
$503$	−461.075	+	461.075i	−0.916650	+	0.916650i	0.0801345	+	0.996784i	$0.474465\pi$
$504$	−56.5160	+	56.5160i	−0.112135	+	0.112135i
$505$	108.831	+	108.831i	0.215507	+	0.215507i
$506$		−	183.634i		−	0.362912i
$507$	−273.329			−0.539111
$508$			495.213i			0.974828i
$509$			324.657i			0.637833i	0.947783	+	0.318917i	$0.103319\pi$
$509$			324.657i			0.637833i	−0.947783	+	0.318917i	$0.896681\pi$
$510$	325.938	+	325.938i	0.639094	+	0.639094i
$511$		−	1087.94i		−	2.12903i
$512$	408.797	+	408.797i	0.798432	+	0.798432i
$513$	473.294	+	473.294i	0.922601	+	0.922601i
$514$	−1474.01			−2.86773
$515$	69.3979			0.134753
$516$	259.625	−	259.625i	0.503149	−	0.503149i
$517$		−	113.622i		−	0.219773i
$518$	1092.96	−	658.990i	2.10997	−	1.27218i
$519$	−76.9754			−0.148315
$520$	−95.8553	−	95.8553i	−0.184337	−	0.184337i
$521$		−	203.368i		−	0.390342i	−0.980769	−	0.195171i	$-0.937474\pi$
$521$		−	203.368i		−	0.390342i	0.980769	−	0.195171i	$-0.0625262\pi$
$522$			197.162i			0.377704i
$523$	−480.568	+	480.568i	−0.918868	+	0.918868i	−0.996947	−	0.0780792i	$-0.975121\pi$
$523$	−480.568	+	480.568i	−0.918868	+	0.918868i	0.0780792	+	0.996947i	$0.475121\pi$
$524$	380.062	−	380.062i	0.725310	−	0.725310i
$525$	−727.861			−1.38640
$526$	1062.67	−	1062.67i	2.02028	−	2.02028i
$527$	216.399			0.410624
$528$	293.757			0.556358
$529$			483.587i			0.914154i
$530$	219.426			0.414012
$531$	−33.6601	+	33.6601i	−0.0633900	+	0.0633900i
$532$	1197.91	+	1197.91i	2.25171	+	2.25171i
$533$	−543.753	−	543.753i	−1.02017	−	1.02017i
$534$	560.704			1.05001
$535$	−325.942	+	325.942i	−0.609237	+	0.609237i
$536$	229.643	+	229.643i	0.428439	+	0.428439i
$537$	348.531	−	348.531i	0.649033	−	0.649033i
$538$	404.512	+	404.512i	0.751882	+	0.751882i
$539$			724.464i			1.34409i
$540$	−203.665	+	203.665i	−0.377157	+	0.377157i
$541$	−215.103	+	215.103i	−0.397602	+	0.397602i	−0.877386	−	0.479784i	$-0.840715\pi$
$541$	−215.103	+	215.103i	−0.397602	+	0.397602i	0.479784	+	0.877386i	$0.340715\pi$
$542$	−175.952	−	175.952i	−0.324635	−	0.324635i
$543$			303.641i			0.559191i
$544$	852.760			1.56757
$545$		−	164.017i		−	0.300948i
$546$			1811.10i			3.31703i
$547$	166.683	+	166.683i	0.304721	+	0.304721i	0.842858	−	0.538136i	$-0.180871\pi$
$547$	166.683	+	166.683i	0.304721	+	0.304721i	−0.538136	+	0.842858i	$0.680871\pi$
$548$		−	108.838i		−	0.198609i
$549$	16.0925	+	16.0925i	0.0293124	+	0.0293124i
$550$	−372.200	−	372.200i	−0.676727	−	0.676727i
$551$	953.873			1.73117
$552$	−79.9760			−0.144884
$553$	614.862	−	614.862i	1.11187	−	1.11187i
$554$			220.185i			0.397446i
$555$	−250.067	+	150.775i	−0.450571	+	0.271667i
$556$	−206.728			−0.371814
$557$	−603.615	−	603.615i	−1.08369	−	1.08369i	−0.996162	−	0.0875282i	$-0.972103\pi$
$557$	−603.615	−	603.615i	−1.08369	−	1.08369i	−0.0875282	−	0.996162i	$-0.527897\pi$
$558$		−	66.6390i		−	0.119425i
$559$		−	339.411i		−	0.607175i
$560$	189.356	−	189.356i	0.338135	−	0.338135i
$561$	405.697	−	405.697i	0.723168	−	0.723168i
$562$	−1343.88			−2.39125
$563$	100.160	−	100.160i	0.177903	−	0.177903i	−0.612538	−	0.790441i	$-0.709851\pi$
$563$	100.160	−	100.160i	0.177903	−	0.177903i	0.790441	+	0.612538i	$0.209851\pi$
$564$	−216.798			−0.384394
$565$	−157.220			−0.278266
$566$		−	1547.63i		−	2.73432i
$567$	1078.98			1.90296
$568$	123.818	−	123.818i	0.217990	−	0.217990i
$569$	91.2726	+	91.2726i	0.160409	+	0.160409i	0.782748	−	0.622339i	$-0.213817\pi$
$569$	91.2726	+	91.2726i	0.160409	+	0.160409i	−0.622339	+	0.782748i	$0.713817\pi$
$570$	−485.598	−	485.598i	−0.851925	−	0.851925i
$571$	−34.7778			−0.0609068			−0.0304534	−	0.999536i	$-0.509695\pi$
$571$	−34.7778			−0.0609068			−0.0304534	+	0.999536i	$0.509695\pi$
$572$	−522.718	+	522.718i	−0.913843	+	0.913843i
$573$	11.0195	+	11.0195i	0.0192312	+	0.0192312i
$574$	−1182.53	+	1182.53i	−2.06015	+	2.06015i
$575$	−92.0450	−	92.0450i	−0.160078	−	0.160078i
$576$		−	185.291i		−	0.321686i
$577$	−608.252	+	608.252i	−1.05416	+	1.05416i	−0.0557154	+	0.998447i	$0.517744\pi$
$577$	−608.252	+	608.252i	−1.05416	+	1.05416i	−0.998447	+	0.0557154i	$0.982256\pi$
$578$	176.740	−	176.740i	0.305779	−	0.305779i
$579$	−307.551	−	307.551i	−0.531176	−	0.531176i
$580$			410.464i			0.707697i
$581$	−1234.44			−2.12469
$582$			739.362i			1.27038i
$583$		−	273.122i		−	0.468476i
$584$	−242.291	−	242.291i	−0.414883	−	0.414883i
$585$		−	74.0604i		−	0.126599i
$586$	614.074	+	614.074i	1.04791	+	1.04791i
$587$	277.120	+	277.120i	0.472095	+	0.472095i	0.902592	−	0.430497i	$-0.141662\pi$
$587$	277.120	+	277.120i	0.472095	+	0.472095i	−0.430497	+	0.902592i	$0.641662\pi$
$588$	1382.32			2.35089
$589$	−322.401			−0.547371
$590$	−124.157	+	124.157i	−0.210435	+	0.210435i
$591$		−	435.432i		−	0.736772i
$592$	−87.7911	+	354.413i	−0.148296	+	0.598671i
$593$	−697.353			−1.17597			−0.587987	−	0.808870i	$-0.700079\pi$
$593$	−697.353			−1.17597			−0.587987	+	0.808870i	$0.700079\pi$
$594$	449.143	+	449.143i	0.756134	+	0.756134i
$595$		−	523.025i		−	0.879034i
$596$			609.114i			1.02200i
$597$	590.757	−	590.757i	0.989543	−	0.989543i
$598$	−229.031	+	229.031i	−0.382994	+	0.382994i
$599$	832.623			1.39002			0.695011	−	0.718999i	$-0.255400\pi$
$599$	832.623			1.39002			0.695011	+	0.718999i	$0.255400\pi$
$600$	−162.100	+	162.100i	−0.270167	+	0.270167i
$601$	−370.191			−0.615958			−0.307979	−	0.951393i	$-0.599653\pi$
$601$	−370.191			−0.615958			−0.307979	+	0.951393i	$0.599653\pi$
$602$	−738.135			−1.22614
$603$			177.428i			0.294243i
$604$	−330.214			−0.546712
$605$	−67.6639	+	67.6639i	−0.111841	+	0.111841i
$606$	−457.945	−	457.945i	−0.755685	−	0.755685i
$607$	419.734	+	419.734i	0.691488	+	0.691488i	0.962559	−	0.271071i	$-0.0873778\pi$
$607$	419.734	+	419.734i	0.691488	+	0.691488i	−0.271071	+	0.962559i	$0.587378\pi$
$608$	−1270.48			−2.08961
$609$	885.089	−	885.089i	1.45335	−	1.45335i
$610$	59.3580	+	59.3580i	0.0973081	+	0.0973081i
$611$	−141.712	+	141.712i	−0.231934	+	0.231934i
$612$	−138.353	−	138.353i	−0.226066	−	0.226066i
$613$			318.127i			0.518967i	0.965748	+	0.259484i	$0.0835523\pi$
$613$			318.127i			0.518967i	−0.965748	+	0.259484i	$0.916448\pi$
$614$	261.802	−	261.802i	0.426387	−	0.426387i
$615$	270.559	−	270.559i	0.439934	−	0.439934i
$616$	259.474	+	259.474i	0.421224	+	0.421224i
$617$		−	989.706i		−	1.60406i	−0.597282	−	0.802031i	$-0.703753\pi$
$617$		−	989.706i		−	1.60406i	0.597282	−	0.802031i	$-0.296247\pi$
$618$	−292.016			−0.472518
$619$		−	60.8926i		−	0.0983725i	−0.998790	−	0.0491863i	$-0.984337\pi$
$619$		−	60.8926i		−	0.0983725i	0.998790	−	0.0491863i	$-0.0156628\pi$
$620$		−	138.734i		−	0.223764i
$621$	111.073	+	111.073i	0.178862	+	0.178862i
$622$		−	3.19004i		−	0.00512868i
$623$	−449.875	−	449.875i	−0.722110	−	0.722110i
$624$	−366.378	−	366.378i	−0.587144	−	0.587144i
$625$	−231.036			−0.369657
$626$	543.589			0.868352
$627$	−604.427	+	604.427i	−0.963998	+	0.963998i
$628$		−	1012.94i		−	1.61296i
$629$	368.223	+	610.713i	0.585410	+	0.970927i
$630$	−161.063			−0.255656
$631$	−5.81267	−	5.81267i	−0.00921183	−	0.00921183i	0.702486	−	0.711698i	$-0.252073\pi$
$631$	−5.81267	−	5.81267i	−0.00921183	−	0.00921183i	−0.711698	+	0.702486i	$0.752073\pi$
$632$		−	273.869i		−	0.433337i
$633$		−	467.465i		−	0.738491i
$634$	479.239	−	479.239i	0.755898	−	0.755898i
$635$	−161.065	+	161.065i	−0.253646	+	0.253646i
$636$	−521.132			−0.819390
$637$	903.563	−	903.563i	1.41847	−	1.41847i
$638$	905.200			1.41881
$639$	95.6652			0.149711
$640$		−	261.536i		−	0.408650i
$641$	664.951			1.03737			0.518683	−	0.854967i	$-0.326423\pi$
$641$	664.951			1.03737			0.518683	+	0.854967i	$0.326423\pi$
$642$	1371.51	−	1371.51i	2.13632	−	2.13632i
$643$	323.506	+	323.506i	0.503120	+	0.503120i	0.912406	−	0.409286i	$-0.134222\pi$
$643$	323.506	+	323.506i	0.503120	+	0.503120i	−0.409286	+	0.912406i	$0.634222\pi$
$644$	281.126	+	281.126i	0.436532	+	0.436532i
$645$	168.883			0.261835
$646$	−1185.92	+	1185.92i	−1.83580	+	1.83580i
$647$	−41.3737	−	41.3737i	−0.0639470	−	0.0639470i	0.674410	−	0.738357i	$-0.264398\pi$
$647$	−41.3737	−	41.3737i	−0.0639470	−	0.0639470i	−0.738357	+	0.674410i	$0.764398\pi$
$648$	240.297	−	240.297i	0.370828	−	0.370828i
$649$	154.539	+	154.539i	0.238118	+	0.238118i
$650$			928.427i			1.42835i
$651$	−299.153	+	299.153i	−0.459528	+	0.459528i
$652$	613.035	−	613.035i	0.940238	−	0.940238i
$653$	−712.222	−	712.222i	−1.09069	−	1.09069i	−0.995455	−	0.0952378i	$-0.969639\pi$
$653$	−712.222	−	712.222i	−1.09069	−	1.09069i	−0.0952378	−	0.995455i	$-0.530361\pi$
$654$			690.159i			1.05529i
$655$	247.227			0.377445
$656$		−	478.442i		−	0.729332i
$657$		−	187.201i		−	0.284933i
$658$	308.188	+	308.188i	0.468371	+	0.468371i
$659$			783.451i			1.18885i	0.804152	+	0.594424i	$0.202620\pi$
$659$			783.451i			1.18885i	−0.804152	+	0.594424i	$0.797380\pi$
$660$	−260.093	−	260.093i	−0.394080	−	0.394080i
$661$	−192.114	−	192.114i	−0.290642	−	0.290642i	0.546692	−	0.837334i	$-0.315887\pi$
$661$	−192.114	−	192.114i	−0.290642	−	0.290642i	−0.837334	+	0.546692i	$0.815887\pi$
$662$	−1306.96			−1.97426
$663$	−1011.98			−1.52637
$664$	−274.920	+	274.920i	−0.414036	+	0.414036i
$665$			779.227i			1.17177i
$666$	188.066	−	113.392i	0.282381	−	0.170259i
$667$	223.856			0.335616
$668$	−131.375	−	131.375i	−0.196669	−	0.196669i
$669$			577.263i			0.862875i
$670$			654.452i			0.976795i
$671$	73.8833	−	73.8833i	0.110109	−	0.110109i
$672$	−1178.87	+	1178.87i	−1.75427	+	1.75427i
$673$	799.852			1.18849			0.594244	−	0.804285i	$-0.297452\pi$
$673$	799.852			1.18849			0.594244	+	0.804285i	$0.297452\pi$
$674$	−888.520	+	888.520i	−1.31828	+	1.31828i
$675$	450.260			0.667051
$676$	427.950			0.633063
$677$			544.372i			0.804095i	0.915619	+	0.402048i	$0.131701\pi$
$677$			544.372i			0.804095i	−0.915619	+	0.402048i	$0.868299\pi$
$678$	661.559			0.975751
$679$	593.219	−	593.219i	0.873666	−	0.873666i
$680$	−116.482	−	116.482i	−0.171297	−	0.171297i
$681$	−704.231	−	704.231i	−1.03411	−	1.03411i
$682$	−305.950			−0.448607
$683$	−177.675	+	177.675i	−0.260140	+	0.260140i	−0.825111	−	0.564971i	$-0.808887\pi$
$683$	−177.675	+	177.675i	−0.260140	+	0.260140i	0.564971	+	0.825111i	$0.308887\pi$
$684$	206.124	+	206.124i	0.301351	+	0.301351i
$685$	35.3990	−	35.3990i	0.0516773	−	0.0516773i
$686$	−769.888	−	769.888i	−1.12229	−	1.12229i
$687$			1444.71i			2.10292i
$688$	149.322	−	149.322i	0.217038	−	0.217038i
$689$	−340.641	+	340.641i	−0.494400	+	0.494400i
$690$	−113.961	−	113.961i	−0.165160	−	0.165160i
$691$			180.179i			0.260751i	0.991465	+	0.130375i	$0.0416182\pi$
$691$			180.179i			0.260751i	−0.991465	+	0.130375i	$0.958382\pi$
$692$	120.520			0.174162
$693$			200.476i			0.289288i
$694$		−	1309.49i		−	1.88687i
$695$	−67.2374	−	67.2374i	−0.0967444	−	0.0967444i
$696$		−	394.232i		−	0.566425i
$697$	−660.759	−	660.759i	−0.948005	−	0.948005i
$698$	964.333	+	964.333i	1.38157	+	1.38157i
$699$	−73.8067			−0.105589
$700$	1139.61			1.62801
$701$	319.838	−	319.838i	0.456259	−	0.456259i	−0.441166	−	0.897425i	$-0.645435\pi$
$701$	319.838	−	319.838i	0.456259	−	0.456259i	0.897425	+	0.441166i	$0.145435\pi$
$702$		−	1120.36i		−	1.59595i
$703$	−548.595	−	909.868i	−0.780363	−	1.29427i
$704$	−850.701			−1.20838
$705$	−70.5126	−	70.5126i	−0.100018	−	0.100018i
$706$			620.309i			0.878625i
$707$			734.854i			1.03940i
$708$	294.869	−	294.869i	0.416482	−	0.416482i
$709$	572.918	−	572.918i	0.808065	−	0.808065i	−0.176276	−	0.984341i	$-0.556405\pi$
$709$	572.918	−	572.918i	0.808065	−	0.808065i	0.984341	+	0.176276i	$0.0564050\pi$
$710$	352.865			0.496993
$711$	105.799	−	105.799i	0.148803	−	0.148803i
$712$	−200.381			−0.281434
$713$	−75.6615			−0.106117
$714$			2200.82i			3.08237i
$715$	−340.023			−0.475557
$716$	−545.692	+	545.692i	−0.762140	+	0.762140i
$717$	491.446	+	491.446i	0.685419	+	0.685419i
$718$	916.257	+	916.257i	1.27612	+	1.27612i
$719$	1228.64			1.70882			0.854409	−	0.519601i	$-0.173919\pi$
$719$	1228.64			1.70882			0.854409	+	0.519601i	$0.173919\pi$
$720$	32.5824	−	32.5824i	0.0452534	−	0.0452534i
$721$	234.296	+	234.296i	0.324960	+	0.324960i
$722$	993.300	−	993.300i	1.37576	−	1.37576i
$723$	−305.834	−	305.834i	−0.423006	−	0.423006i
$724$		−	475.408i		−	0.656641i
$725$	453.725	−	453.725i	0.625827	−	0.625827i
$726$	284.720	−	284.720i	0.392176	−	0.392176i
$727$	138.448	+	138.448i	0.190437	+	0.190437i	0.795885	−	0.605448i	$-0.207006\pi$
$727$	138.448	+	138.448i	0.190437	+	0.190437i	−0.605448	+	0.795885i	$0.707006\pi$
$728$		−	647.239i		−	0.889065i
$729$	−508.815			−0.697963
$730$		−	690.499i		−	0.945888i
$731$		−	412.446i		−	0.564222i
$732$	−140.974	−	140.974i	−0.192587	−	0.192587i
$733$			582.262i			0.794355i	0.917742	+	0.397178i	$0.130010\pi$
$733$			582.262i			0.794355i	−0.917742	+	0.397178i	$0.869990\pi$
$734$	−307.849	−	307.849i	−0.419412	−	0.419412i
$735$	449.593	+	449.593i	0.611691	+	0.611691i
$736$	−298.158			−0.405106
$737$	814.601			1.10529
$738$	−203.478	+	203.478i	−0.275715	+	0.275715i
$739$		−	316.855i		−	0.428761i	−0.976750	−	0.214381i	$-0.931227\pi$
$739$		−	316.855i		−	0.428761i	0.976750	−	0.214381i	$-0.0687733\pi$
$740$	391.529	−	236.068i	0.529093	−	0.319011i
$741$	1507.70			2.03468
$742$	740.811	+	740.811i	0.998398	+	0.998398i
$743$		−	234.300i		−	0.315343i	−0.987492	−	0.157672i	$-0.949601\pi$
$743$		−	234.300i		−	0.315343i	0.987492	−	0.157672i	$-0.0503987\pi$
$744$			133.247i			0.179096i
$745$	−198.111	+	198.111i	−0.265921	+	0.265921i
$746$	1183.12	−	1183.12i	1.58595	−	1.58595i
$747$	−212.410			−0.284351
$748$	−635.198	+	635.198i	−0.849195	+	0.849195i
$749$	−2200.84			−2.93837
$750$	−1059.85			−1.41314
$751$			859.767i			1.14483i	0.819964	+	0.572415i	$0.193993\pi$
$751$			859.767i			1.14483i	−0.819964	+	0.572415i	$0.806007\pi$
$752$	−124.690			−0.165812
$753$	−1025.61	+	1025.61i	−1.36203	+	1.36203i
$754$	−1128.98	−	1128.98i	−1.49732	−	1.49732i
$755$	−107.400	−	107.400i	−0.142252	−	0.142252i
$756$	−1375.20			−1.81904
$757$	−1.28811	+	1.28811i	−0.00170160	+	0.00170160i	−0.707957	−	0.706255i	$-0.750383\pi$
$757$	−1.28811	+	1.28811i	−0.00170160	+	0.00170160i	0.706255	+	0.707957i	$0.250383\pi$
$758$	381.642	+	381.642i	0.503486	+	0.503486i
$759$	−141.847	+	141.847i	−0.186887	+	0.186887i
$760$	173.540	+	173.540i	0.228342	+	0.228342i
$761$		−	650.720i		−	0.855085i	−0.903995	−	0.427543i	$-0.859379\pi$
$761$		−	650.720i		−	0.855085i	0.903995	−	0.427543i	$-0.140621\pi$
$762$	677.740	−	677.740i	0.889423	−	0.889423i
$763$	553.741	−	553.741i	0.725742	−	0.725742i
$764$	−17.2531	−	17.2531i	−0.0225826	−	0.0225826i
$765$		−	89.9969i		−	0.117643i
$766$	850.663			1.11053
$767$		−	385.486i		−	0.502590i
$768$		−	152.185i		−	0.198158i
$769$	−652.734	−	652.734i	−0.848809	−	0.848809i	0.141175	−	0.989985i	$-0.454912\pi$
$769$	−652.734	−	652.734i	−0.848809	−	0.848809i	−0.989985	+	0.141175i	$0.954912\pi$
$770$			739.466i			0.960345i
$771$	1138.60	+	1138.60i	1.47678	+	1.47678i
$772$	481.530	+	481.530i	0.623744	+	0.623744i
$773$	−635.534			−0.822165			−0.411083	−	0.911598i	$-0.634849\pi$
$773$	−635.534			−0.822165			−0.411083	+	0.911598i	$0.634849\pi$
$774$	−127.011			−0.164097
$775$	−153.355	+	153.355i	−0.197878	+	0.197878i
$776$		−	264.229i		−	0.340501i
$777$	−1353.29	−	335.222i	−1.74169	−	0.431431i
$778$	927.195			1.19177
$779$	984.429	+	984.429i	1.26371	+	1.26371i
$780$			648.784i			0.831774i
$781$		−	439.214i		−	0.562374i
$782$	−278.314	+	278.314i	−0.355900	+	0.355900i
$783$	−547.522	+	547.522i	−0.699262	+	0.699262i
$784$	795.034			1.01407
$785$	329.453	−	329.453i	0.419685	−	0.419685i
$786$	−1040.29			−1.32353
$787$	−1078.68			−1.37063			−0.685313	−	0.728249i	$-0.740335\pi$
$787$	−1078.68			−1.37063			−0.685313	+	0.728249i	$0.740335\pi$
$788$			681.754i			0.865170i
$789$	−1641.71			−2.08075
$790$	390.245	−	390.245i	0.493981	−	0.493981i
$791$	−530.795	−	530.795i	−0.671042	−	0.671042i
$792$	44.6476	+	44.6476i	0.0563732	+	0.0563732i
$793$	−184.297			−0.232404
$794$	750.936	−	750.936i	0.945763	−	0.945763i
$795$	−169.496	−	169.496i	−0.213202	−	0.213202i
$796$	−924.946	+	924.946i	−1.16199	+	1.16199i
$797$	340.050	+	340.050i	0.426662	+	0.426662i	0.887490	−	0.460828i	$-0.152447\pi$
$797$	340.050	+	340.050i	0.426662	+	0.426662i	−0.460828	+	0.887490i	$0.652447\pi$
$798$		−	3278.88i		−	4.10887i
$799$	−172.206	+	172.206i	−0.215526	+	0.215526i
$800$	−604.325	+	604.325i	−0.755406	+	0.755406i
$801$	−77.4099	−	77.4099i	−0.0966416	−	0.0966416i
$802$		−	1578.33i		−	1.96800i
$803$	−859.468			−1.07032
$804$		−	1554.31i		−	1.93322i
$805$			182.870i			0.227168i
$806$	381.586	+	381.586i	0.473432	+	0.473432i
$807$		−	624.930i		−	0.774387i
$808$	163.658	+	163.658i	0.202547	+	0.202547i
$809$	511.246	+	511.246i	0.631948	+	0.631948i	0.948556	−	0.316608i	$-0.102544\pi$
$809$	511.246	+	511.246i	0.631948	+	0.631948i	−0.316608	+	0.948556i	$0.602544\pi$
$810$	684.814			0.845449
$811$	−21.9707			−0.0270909			−0.0135455	−	0.999908i	$-0.504312\pi$
$811$	−21.9707			−0.0270909			−0.0135455	+	0.999908i	$0.504312\pi$
$812$	−1385.78	+	1385.78i	−1.70662	+	1.70662i
$813$			271.828i			0.334351i
$814$	−520.602	−	863.441i	−0.639560	−	1.06074i
$815$	398.773			0.489292
$816$	−445.216	−	445.216i	−0.545608	−	0.545608i
$817$			614.481i			0.752119i
$818$			326.284i			0.398880i
$819$	250.037	−	250.037i	0.305296	−	0.305296i
$820$	−423.613	+	423.613i	−0.516602	+	0.516602i
$821$	1087.85			1.32503			0.662515	−	0.749049i	$-0.269489\pi$
$821$	1087.85			1.32503			0.662515	+	0.749049i	$0.269489\pi$
$822$	−148.954	+	148.954i	−0.181209	+	0.181209i
$823$	1450.59			1.76257			0.881284	−	0.472586i	$-0.156680\pi$
$823$	1450.59			1.76257			0.881284	+	0.472586i	$0.156680\pi$
$824$	104.359			0.126649
$825$			575.010i			0.696982i
$826$	−838.338			−1.01494
$827$	149.442	−	149.442i	0.180704	−	0.180704i	−0.610958	−	0.791663i	$-0.709216\pi$
$827$	149.442	−	149.442i	0.180704	−	0.180704i	0.791663	+	0.610958i	$0.209216\pi$
$828$	48.3734	+	48.3734i	0.0584220	+	0.0584220i
$829$	−720.863	−	720.863i	−0.869558	−	0.869558i	0.122866	−	0.992423i	$-0.460792\pi$
$829$	−720.863	−	720.863i	−0.869558	−	0.869558i	−0.992423	+	0.122866i	$0.960792\pi$
$830$	−783.485			−0.943958
$831$	170.082	−	170.082i	0.204671	−	0.204671i
$832$	1061.01	+	1061.01i	1.27525	+	1.27525i
$833$	1097.99	−	1097.99i	1.31812	−	1.31812i
$834$	282.925	+	282.925i	0.339239	+	0.339239i
$835$		−	85.4578i		−	0.102345i
$836$	946.347	−	946.347i	1.13199	−	1.13199i
$837$	185.058	−	185.058i	0.221097	−	0.221097i
$838$	−1115.57	−	1115.57i	−1.33123	−	1.33123i
$839$		−	1290.69i		−	1.53837i	−0.639028	−	0.769183i	$-0.720663\pi$
$839$		−	1290.69i		−	1.53837i	0.639028	−	0.769183i	$-0.279337\pi$
$840$	322.052			0.383395
$841$			262.471i			0.312093i
$842$			1530.20i			1.81734i
$843$	1038.08	+	1038.08i	1.23141	+	1.23141i
$844$			731.907i			0.867188i
$845$	139.189	+	139.189i	0.164720	+	0.164720i
$846$	53.0299	+	53.0299i	0.0626830	+	0.0626830i
$847$	−456.884			−0.539414
$848$	−299.726			−0.353451
$849$	−1195.46	+	1195.46i	−1.40808	+	1.40808i
$850$			1128.21i			1.32730i
$851$	−128.745	−	213.529i	−0.151287	−	0.250915i
$852$	−838.046			−0.983622
$853$	406.507	+	406.507i	0.476562	+	0.476562i	0.904030	−	0.427469i	$-0.140595\pi$
$853$	406.507	+	406.507i	0.476562	+	0.476562i	−0.427469	+	0.904030i	$0.640595\pi$
$854$			400.800i			0.469321i
$855$			134.082i			0.156821i
$856$	−490.144	+	490.144i	−0.572598	+	0.572598i
$857$	−660.027	+	660.027i	−0.770159	+	0.770159i	−0.978134	−	0.207975i	$-0.933313\pi$
$857$	−660.027	+	660.027i	−0.770159	+	0.770159i	0.207975	+	0.978134i	$0.433313\pi$
$858$	1430.77			1.66756
$859$	88.3482	−	88.3482i	0.102850	−	0.102850i	−0.653809	−	0.756659i	$-0.726830\pi$
$859$	88.3482	−	88.3482i	0.102850	−	0.102850i	0.756659	+	0.653809i	$0.226830\pi$
$860$	−264.420			−0.307465
$861$	1826.88			2.12182
$862$			1954.41i			2.26729i
$863$	828.215			0.959693			0.479847	−	0.877352i	$-0.340692\pi$
$863$	828.215			0.959693			0.479847	+	0.877352i	$0.340692\pi$
$864$	729.255	−	729.255i	0.844045	−	0.844045i
$865$	39.1985	+	39.1985i	0.0453162	+	0.0453162i
$866$	1308.77	+	1308.77i	1.51128	+	1.51128i
$867$	−273.046			−0.314932
$868$	468.382	−	468.382i	0.539611	−	0.539611i
$869$	−485.741	−	485.741i	−0.558965	−	0.558965i
$870$	561.755	−	561.755i	0.645695	−	0.645695i
$871$	−1015.98	−	1015.98i	−1.16646	−	1.16646i
$872$		−	246.645i		−	0.282849i
$873$	102.075	−	102.075i	0.116925	−	0.116925i
$874$	414.645	−	414.645i	0.474422	−	0.474422i
$875$	850.362	+	850.362i	0.971843	+	0.971843i
$876$			1639.92i			1.87205i
$877$	−90.6556			−0.103370			−0.0516850	−	0.998663i	$-0.516459\pi$
$877$	−90.6556			−0.103370			−0.0516850	+	0.998663i	$0.516459\pi$
$878$		−	156.142i		−	0.177838i
$879$		−	948.681i		−	1.07927i
$880$	−149.591	−	149.591i	−0.169990	−	0.169990i
$881$			303.710i			0.344733i	0.985033	+	0.172367i	$0.0551414\pi$
$881$			303.710i			0.344733i	−0.985033	+	0.172367i	$0.944859\pi$
$882$	−338.122	−	338.122i	−0.383358	−	0.383358i
$883$	−351.287	−	351.287i	−0.397834	−	0.397834i	0.479634	−	0.877468i	$-0.340769\pi$
$883$	−351.287	−	351.287i	−0.397834	−	0.397834i	−0.877468	+	0.479634i	$0.840769\pi$
$884$	1584.46			1.79237
$885$	191.809			0.216734
$886$	−374.036	+	374.036i	−0.422163	+	0.422163i
$887$		−	874.951i		−	0.986416i	−0.869912	−	0.493208i	$-0.835824\pi$
$887$		−	874.951i		−	0.986416i	0.869912	−	0.493208i	$-0.164176\pi$
$888$	−376.045	+	226.732i	−0.423474	+	0.255329i
$889$	−1087.55			−1.22335
$890$	−285.530	−	285.530i	−0.320820	−	0.320820i
$891$		−	852.392i		−	0.956669i
$892$		−	903.818i		−	1.01325i
$893$	256.560	−	256.560i	0.287301	−	0.287301i
$894$	833.623	−	833.623i	0.932464	−	0.932464i
$895$	−354.967			−0.396612
$896$	882.978	−	882.978i	0.985467	−	0.985467i
$897$	353.829			0.394458
$898$	−1607.72			−1.79033
$899$		−	372.964i		−	0.414866i
$900$	196.092			0.217880
$901$	−413.942	+	413.942i	−0.459425	+	0.459425i
$902$	934.197	+	934.197i	1.03570	+	1.03570i
$903$	570.171	+	570.171i	0.631419	+	0.631419i
$904$	−236.424			−0.261531
$905$	154.624	−	154.624i	0.170855	−	0.170855i
$906$	451.925	+	451.925i	0.498814	+	0.498814i
$907$	493.559	−	493.559i	0.544166	−	0.544166i	−0.380581	−	0.924747i	$-0.624276\pi$
$907$	493.559	−	493.559i	0.544166	−	0.544166i	0.924747	+	0.380581i	$0.124276\pi$
$908$	1102.61	+	1102.61i	1.21433	+	1.21433i
$909$			126.446i			0.139105i
$910$	922.273	−	922.273i	1.01349	−	1.01349i
$911$	−1198.53	+	1198.53i	−1.31562	+	1.31562i	−0.398411	+	0.917207i	$0.630438\pi$
$911$	−1198.53	+	1198.53i	−1.31562	+	1.31562i	−0.917207	+	0.398411i	$0.869562\pi$
$912$	663.304	+	663.304i	0.727307	+	0.727307i
$913$			975.209i			1.06814i
$914$	−718.767			−0.786397
$915$		−	91.7019i		−	0.100221i
$916$		−	2261.97i		−	2.46940i
$917$	834.668	+	834.668i	0.910216	+	0.910216i
$918$		−	1361.44i		−	1.48305i
$919$	−146.139	−	146.139i	−0.159019	−	0.159019i	0.623113	−	0.782132i	$-0.285868\pi$
$919$	−146.139	−	146.139i	−0.159019	−	0.159019i	−0.782132	+	0.623113i	$0.785868\pi$
$920$	40.7265	+	40.7265i	0.0442679	+	0.0442679i
$921$	−404.457			−0.439149
$922$	−1082.85			−1.17446
$923$	−547.794	+	547.794i	−0.593493	+	0.593493i
$924$		−	1756.21i		−	1.90066i
$925$	−693.741	−	171.845i	−0.749991	−	0.185779i
$926$	−256.592			−0.277098
$927$	40.3153	+	40.3153i	0.0434901	+	0.0434901i
$928$		−	1469.73i		−	1.58376i
$929$			194.218i			0.209061i	0.994522	+	0.104531i	$0.0333341\pi$
$929$			194.218i			0.209061i	−0.994522	+	0.104531i	$0.966666\pi$
$930$	−189.869	+	189.869i	−0.204160	+	0.204160i
$931$	−1635.84	+	1635.84i	−1.75708	+	1.75708i
$932$	115.559			0.123990
$933$	−2.46414	+	2.46414i	−0.00264110	+	0.00264110i
$934$	−650.520			−0.696488
$935$	−413.190			−0.441914
$936$		−	111.370i		−	0.118985i
$937$	−301.447			−0.321715			−0.160858	−	0.986978i	$-0.551426\pi$
$937$	−301.447			−0.321715			−0.160858	+	0.986978i	$0.551426\pi$
$938$	−2209.51	+	2209.51i	−2.35556	+	2.35556i
$939$	−419.894	−	419.894i	−0.447172	−	0.447172i
$940$	110.401	+	110.401i	0.117448	+	0.117448i
$941$	352.176			0.374257			0.187129	−	0.982335i	$-0.440082\pi$
$941$	352.176			0.374257			0.187129	+	0.982335i	$0.440082\pi$
$942$	−1386.29	+	1386.29i	−1.47164	+	1.47164i
$943$	231.027	+	231.027i	0.244991	+	0.244991i
$944$	169.592	−	169.592i	0.179653	−	0.179653i
$945$	−447.276	−	447.276i	−0.473307	−	0.473307i
$946$			583.126i			0.616413i
$947$	−725.341	+	725.341i	−0.765936	+	0.765936i	−0.977388	−	0.211452i	$-0.932181\pi$
$947$	−725.341	+	725.341i	−0.765936	+	0.765936i	0.211452	+	0.977388i	$0.432181\pi$
$948$	−926.822	+	926.822i	−0.977660	+	0.977660i
$949$	1071.94	+	1071.94i	1.12955	+	1.12955i
$950$		−	1680.86i		−	1.76932i
$951$	−740.375			−0.778523
$952$		−	786.514i		−	0.826170i
$953$		−	1859.21i		−	1.95090i	−0.220226	−	0.975449i	$-0.570680\pi$
$953$		−	1859.21i		−	1.95090i	0.220226	−	0.975449i	$-0.429320\pi$
$954$	127.471	+	127.471i	0.133618	+	0.133618i
$955$		−	11.2230i		−	0.0117518i
$956$	−769.454	−	769.454i	−0.804868	−	0.804868i
$957$	−699.220	−	699.220i	−0.730637	−	0.730637i
$958$	1349.88			1.40906
$959$	239.023			0.249242
$960$	−527.933	+	527.933i	−0.549931	+	0.549931i
$961$		−	834.941i		−	0.868825i
$962$	−427.594	+	1726.20i	−0.444484	+	1.79439i
$963$	−378.698			−0.393248
$964$	478.842	+	478.842i	0.496724	+	0.496724i
$965$			313.231i			0.324591i
$966$		−	769.490i		−	0.796573i
$967$	793.793	−	793.793i	0.820882	−	0.820882i	−0.165353	−	0.986235i	$-0.552876\pi$
$967$	793.793	−	793.793i	0.820882	−	0.820882i	0.986235	+	0.165353i	$0.0528762\pi$
$968$	−101.751	+	101.751i	−0.105115	+	0.105115i
$969$	1832.13			1.89074
$970$	376.509	−	376.509i	0.388153	−	0.388153i
$971$	509.994			0.525226			0.262613	−	0.964901i	$-0.415416\pi$
$971$	509.994			0.525226			0.262613	+	0.964901i	$0.415416\pi$
$972$	−539.080			−0.554609
$973$		−	454.004i		−	0.466602i
$974$	153.650			0.157752
$975$	717.162	−	717.162i	0.735550	−	0.735550i
$976$	−81.0802	−	81.0802i	−0.0830740	−	0.0830740i
$977$	1175.03	+	1175.03i	1.20269	+	1.20269i	0.973346	+	0.229343i	$0.0736578\pi$
$977$	1175.03	+	1175.03i	1.20269	+	1.20269i	0.229343	+	0.973346i	$0.426342\pi$
$978$	−1677.98			−1.71573
$979$	−355.401	+	355.401i	−0.363024	+	0.363024i
$980$	−703.925	−	703.925i	−0.718291	−	0.718291i
$981$	95.2821	−	95.2821i	0.0971276	−	0.0971276i
$982$	1025.75	+	1025.75i	1.04455	+	1.04455i
$983$		−	1278.99i		−	1.30111i	−0.759460	−	0.650554i	$-0.774537\pi$
$983$		−	1278.99i		−	1.30111i	0.759460	−	0.650554i	$-0.225463\pi$
$984$	406.861	−	406.861i	0.413477	−	0.413477i
$985$	−221.737	+	221.737i	−0.225114	+	0.225114i
$986$	−1371.92	−	1371.92i	−1.39140	−	1.39140i
$987$		−	476.119i		−	0.482390i
$988$	−2360.60			−2.38927
$989$			144.207i			0.145811i
$990$			127.240i			0.128525i
$991$	866.605	+	866.605i	0.874475	+	0.874475i	0.992956	−	0.118481i	$-0.0378026\pi$
$991$	866.605	+	866.605i	0.874475	+	0.874475i	−0.118481	+	0.992956i	$0.537803\pi$
$992$			496.758i			0.500764i
$993$	1009.56	+	1009.56i	1.01668	+	1.01668i
$994$	1191.32	+	1191.32i	1.19851	+	1.19851i
$995$	−601.668			−0.604691
$996$	1860.76			1.86823
$997$	1374.79	−	1374.79i	1.37893	−	1.37893i	0.532496	−	0.846433i	$-0.321254\pi$
$997$	1374.79	−	1374.79i	1.37893	−	1.37893i	0.846433	−	0.532496i	$-0.178746\pi$
$998$			328.769i			0.329428i
$999$	837.156	+	207.371i	0.837994	+	0.207578i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.3.d.a.31.6	yes	12
3.2	odd	2		333.3.i.a.253.1		12
4.3	odd	2		592.3.k.e.401.5		12
37.6	odd	4	inner	37.3.d.a.6.6	✓	12
111.80	even	4		333.3.i.a.154.1		12
148.43	even	4		592.3.k.e.561.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.3.d.a.6.6	✓	12	37.6	odd	4	inner
37.3.d.a.31.6	yes	12	1.1	even	1	trivial
333.3.i.a.154.1		12	111.80	even	4
333.3.i.a.253.1		12	3.2	odd	2
592.3.k.e.401.5		12	4.3	odd	2
592.3.k.e.561.2		12	148.43	even	4

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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	37.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.14278 + 2.14278i) q^{2} -3.31038i q^{3} +5.18304i q^{4} +(-1.68576 + 1.68576i) q^{5} +(7.09343 - 7.09343i) q^{6} -11.3827 q^{7} +(-2.53501 + 2.53501i) q^{8} -1.95861 q^{9} +O(q^{10})\)	\(q+(2.14278 + 2.14278i) q^{2} -3.31038i q^{3} +5.18304i q^{4} +(-1.68576 + 1.68576i) q^{5} +(7.09343 - 7.09343i) q^{6} -11.3827 q^{7} +(-2.53501 + 2.53501i) q^{8} -1.95861 q^{9} -7.22443 q^{10} +8.99230i q^{11} +17.1578 q^{12} +(11.2153 - 11.2153i) q^{13} +(-24.3906 - 24.3906i) q^{14} +(5.58050 + 5.58050i) q^{15} +9.86824 q^{16} +(13.6287 - 13.6287i) q^{17} +(-4.19688 - 4.19688i) q^{18} +(-20.3046 + 20.3046i) q^{19} +(-8.73736 - 8.73736i) q^{20} +37.6809i q^{21} +(-19.2686 + 19.2686i) q^{22} +(-4.76511 + 4.76511i) q^{23} +(8.39183 + 8.39183i) q^{24} +19.3164i q^{25} +48.0641 q^{26} -23.3097i q^{27} -58.9968i q^{28} +(-23.4890 - 23.4890i) q^{29} +23.9156i q^{30} +(7.93911 + 7.93911i) q^{31} +(31.2855 + 31.2855i) q^{32} +29.7679 q^{33} +58.4066 q^{34} +(19.1884 - 19.1884i) q^{35} -10.1516i q^{36} +(-8.89633 + 35.9146i) q^{37} -87.0169 q^{38} +(-37.1270 - 37.1270i) q^{39} -8.54681i q^{40} -48.4830i q^{41} +(-80.7421 + 80.7421i) q^{42} +(15.1316 - 15.1316i) q^{43} -46.6075 q^{44} +(3.30175 - 3.30175i) q^{45} -20.4212 q^{46} -12.6355 q^{47} -32.6676i q^{48} +80.5650 q^{49} +(-41.3909 + 41.3909i) q^{50} +(-45.1161 - 45.1161i) q^{51} +(58.1296 + 58.1296i) q^{52} -30.3728 q^{53} +(49.9476 - 49.9476i) q^{54} +(-15.1588 - 15.1588i) q^{55} +(28.8551 - 28.8551i) q^{56} +(67.2160 + 67.2160i) q^{57} -100.664i q^{58} +(17.1857 - 17.1857i) q^{59} +(-28.9240 + 28.9240i) q^{60} +(-8.21628 - 8.21628i) q^{61} +34.0236i q^{62} +22.2942 q^{63} +94.6032i q^{64} +37.8127i q^{65} +(63.7862 + 63.7862i) q^{66} -90.5888i q^{67} +(70.6380 + 70.6380i) q^{68} +(15.7743 + 15.7743i) q^{69} +82.2332 q^{70} -48.8433 q^{71} +(4.96509 - 4.96509i) q^{72} +95.5783i q^{73} +(-96.0200 + 57.8942i) q^{74} +63.9447 q^{75} +(-105.240 - 105.240i) q^{76} -102.356i q^{77} -159.110i q^{78} +(-54.0174 + 54.0174i) q^{79} +(-16.6355 + 16.6355i) q^{80} -94.7914 q^{81} +(103.889 - 103.889i) q^{82} +108.449 q^{83} -195.302 q^{84} +45.9493i q^{85} +64.8473 q^{86} +(-77.7577 + 77.7577i) q^{87} +(-22.7955 - 22.7955i) q^{88} +(39.5228 + 39.5228i) q^{89} +14.1499 q^{90} +(-127.660 + 127.660i) q^{91} +(-24.6978 - 24.6978i) q^{92} +(26.2815 - 26.2815i) q^{93} +(-27.0752 - 27.0752i) q^{94} -68.4574i q^{95} +(103.567 - 103.567i) q^{96} +(-52.1160 + 52.1160i) q^{97} +(172.633 + 172.633i) q^{98} -17.6124i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 6 q^{5} + 6 q^{6} - 4 q^{7} + 36 q^{8} - 60 q^{9}+O(q^{10}) \) 12 * q - 6 * q^2 - 6 * q^5 + 6 * q^6 - 4 * q^7 + 36 * q^8 - 60 * q^9	\( 12 q - 6 q^{2} - 6 q^{5} + 6 q^{6} - 4 q^{7} + 36 q^{8} - 60 q^{9} - 16 q^{10} + 64 q^{12} + 14 q^{13} - 70 q^{14} - 2 q^{15} - 96 q^{16} + 2 q^{17} + 132 q^{18} + 14 q^{19} - 24 q^{20} + 22 q^{22} + 56 q^{23} - 84 q^{24} - 48 q^{26} + 60 q^{29} + 72 q^{31} + 208 q^{32} + 56 q^{33} + 112 q^{34} - 154 q^{35} - 66 q^{37} - 336 q^{38} - 46 q^{39} + 90 q^{42} + 70 q^{43} + 80 q^{44} + 232 q^{45} - 424 q^{46} - 384 q^{47} + 144 q^{49} - 34 q^{50} - 126 q^{51} + 328 q^{52} - 56 q^{53} - 194 q^{54} + 70 q^{55} + 16 q^{56} - 94 q^{57} + 184 q^{59} + 276 q^{60} + 132 q^{61} - 400 q^{63} + 614 q^{66} + 116 q^{68} + 368 q^{69} + 556 q^{70} + 68 q^{71} - 692 q^{72} - 382 q^{74} + 116 q^{75} + 12 q^{76} - 2 q^{79} + 4 q^{80} - 76 q^{81} + 374 q^{82} + 108 q^{83} - 1436 q^{84} + 140 q^{86} - 420 q^{87} - 788 q^{88} + 278 q^{89} - 664 q^{90} - 450 q^{91} + 652 q^{92} + 584 q^{93} + 118 q^{94} + 1584 q^{96} - 244 q^{97} + 416 q^{98}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^5 + 6 * q^6 - 4 * q^7 + 36 * q^8 - 60 * q^9 - 16 * q^10 + 64 * q^12 + 14 * q^13 - 70 * q^14 - 2 * q^15 - 96 * q^16 + 2 * q^17 + 132 * q^18 + 14 * q^19 - 24 * q^20 + 22 * q^22 + 56 * q^23 - 84 * q^24 - 48 * q^26 + 60 * q^29 + 72 * q^31 + 208 * q^32 + 56 * q^33 + 112 * q^34 - 154 * q^35 - 66 * q^37 - 336 * q^38 - 46 * q^39 + 90 * q^42 + 70 * q^43 + 80 * q^44 + 232 * q^45 - 424 * q^46 - 384 * q^47 + 144 * q^49 - 34 * q^50 - 126 * q^51 + 328 * q^52 - 56 * q^53 - 194 * q^54 + 70 * q^55 + 16 * q^56 - 94 * q^57 + 184 * q^59 + 276 * q^60 + 132 * q^61 - 400 * q^63 + 614 * q^66 + 116 * q^68 + 368 * q^69 + 556 * q^70 + 68 * q^71 - 692 * q^72 - 382 * q^74 + 116 * q^75 + 12 * q^76 - 2 * q^79 + 4 * q^80 - 76 * q^81 + 374 * q^82 + 108 * q^83 - 1436 * q^84 + 140 * q^86 - 420 * q^87 - 788 * q^88 + 278 * q^89 - 664 * q^90 - 450 * q^91 + 652 * q^92 + 584 * q^93 + 118 * q^94 + 1584 * q^96 - 244 * q^97 + 416 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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