LMFDB - Embedded newform 37.3.d.a.31.4

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			31.4
Root			$0.781387 + 0.781387i$ of defining polynomial
Character	$\chi$	$=$	37.31
Dual form			37.3.d.a.6.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.218613 - 0.218613i) q^{2} -3.27551i q^{3} -3.90442i q^{4} +(-3.73585 + 3.73585i) q^{5} +(-0.716071 + 0.716071i) q^{6} +11.2506 q^{7} +(-1.72801 + 1.72801i) q^{8} -1.72900 q^{9} +O(q^{10})$	\(q+(-0.218613 - 0.218613i) q^{2} -3.27551i q^{3} -3.90442i q^{4} +(-3.73585 + 3.73585i) q^{5} +(-0.716071 + 0.716071i) q^{6} +11.2506 q^{7} +(-1.72801 + 1.72801i) q^{8} -1.72900 q^{9} +1.63341 q^{10} +7.70157i q^{11} -12.7890 q^{12} +(-9.81667 + 9.81667i) q^{13} +(-2.45952 - 2.45952i) q^{14} +(12.2368 + 12.2368i) q^{15} -14.8621 q^{16} +(14.2611 - 14.2611i) q^{17} +(0.377981 + 0.377981i) q^{18} +(10.4494 - 10.4494i) q^{19} +(14.5863 + 14.5863i) q^{20} -36.8514i q^{21} +(1.68367 - 1.68367i) q^{22} +(-26.6243 + 26.6243i) q^{23} +(5.66012 + 5.66012i) q^{24} -2.91316i q^{25} +4.29211 q^{26} -23.8163i q^{27} -43.9269i q^{28} +(0.147829 + 0.147829i) q^{29} -5.35027i q^{30} +(13.0530 + 13.0530i) q^{31} +(10.1611 + 10.1611i) q^{32} +25.2266 q^{33} -6.23534 q^{34} +(-42.0304 + 42.0304i) q^{35} +6.75072i q^{36} +(-32.4717 - 17.7366i) q^{37} -4.56876 q^{38} +(32.1547 + 32.1547i) q^{39} -12.9112i q^{40} +1.12653i q^{41} +(-8.05620 + 8.05620i) q^{42} +(-26.2287 + 26.2287i) q^{43} +30.0701 q^{44} +(6.45927 - 6.45927i) q^{45} +11.6409 q^{46} -59.6171 q^{47} +48.6811i q^{48} +77.5753 q^{49} +(-0.636854 + 0.636854i) q^{50} +(-46.7125 - 46.7125i) q^{51} +(38.3284 + 38.3284i) q^{52} -19.1173 q^{53} +(-5.20655 + 5.20655i) q^{54} +(-28.7719 - 28.7719i) q^{55} +(-19.4411 + 19.4411i) q^{56} +(-34.2272 - 34.2272i) q^{57} -0.0646349i q^{58} +(38.1810 - 38.1810i) q^{59} +(47.7777 - 47.7777i) q^{60} +(-2.53695 - 2.53695i) q^{61} -5.70712i q^{62} -19.4522 q^{63} +55.0058i q^{64} -73.3472i q^{65} +(-5.51487 - 5.51487i) q^{66} +35.6412i q^{67} +(-55.6814 - 55.6814i) q^{68} +(87.2083 + 87.2083i) q^{69} +18.3768 q^{70} +133.243 q^{71} +(2.98772 - 2.98772i) q^{72} -103.942i q^{73} +(3.22129 + 10.9762i) q^{74} -9.54209 q^{75} +(-40.7988 - 40.7988i) q^{76} +86.6471i q^{77} -14.0589i q^{78} +(3.44977 - 3.44977i) q^{79} +(55.5227 - 55.5227i) q^{80} -93.5715 q^{81} +(0.246274 - 0.246274i) q^{82} -58.9414 q^{83} -143.883 q^{84} +106.555i q^{85} +11.4679 q^{86} +(0.484218 - 0.484218i) q^{87} +(-13.3084 - 13.3084i) q^{88} +(-7.78393 - 7.78393i) q^{89} -2.82416 q^{90} +(-110.443 + 110.443i) q^{91} +(103.952 + 103.952i) q^{92} +(42.7553 - 42.7553i) q^{93} +(13.0331 + 13.0331i) q^{94} +78.0748i q^{95} +(33.2828 - 33.2828i) q^{96} +(48.8026 - 48.8026i) q^{97} +(-16.9590 - 16.9590i) q^{98} -13.3160i 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 $

$2$	−0.218613	−	0.218613i	−0.109307	−	0.109307i	0.650338	−	0.759645i	$-0.274627\pi$
$2$	−0.218613	−	0.218613i	−0.109307	−	0.109307i	−0.759645	+	0.650338i	$0.774627\pi$
$3$		−	3.27551i		−	1.09184i	−0.837838	−	0.545919i	$-0.816181\pi$
$3$		−	3.27551i		−	1.09184i	0.837838	−	0.545919i	$-0.183819\pi$
$4$		−	3.90442i		−	0.976104i
$5$	−3.73585	+	3.73585i	−0.747170	+	0.747170i	−0.973947	−	0.226777i	$-0.927181\pi$
$5$	−3.73585	+	3.73585i	−0.747170	+	0.747170i	0.226777	+	0.973947i	$0.427181\pi$
$6$	−0.716071	+	0.716071i	−0.119345	+	0.119345i
$7$	11.2506			1.60722			0.803612	−	0.595153i	$-0.202909\pi$
$7$	11.2506			1.60722			0.803612	+	0.595153i	$0.202909\pi$
$8$	−1.72801	+	1.72801i	−0.216001	+	0.216001i
$9$	−1.72900			−0.192111
$10$	1.63341			0.163341
$11$			7.70157i			0.700143i	0.936723	+	0.350071i	$0.113843\pi$
$11$			7.70157i			0.700143i	−0.936723	+	0.350071i	$0.886157\pi$
$12$	−12.7890			−1.06575
$13$	−9.81667	+	9.81667i	−0.755129	+	0.755129i	−0.975432	−	0.220303i	$-0.929295\pi$
$13$	−9.81667	+	9.81667i	−0.755129	+	0.755129i	0.220303	+	0.975432i	$0.429295\pi$
$14$	−2.45952	−	2.45952i	−0.175680	−	0.175680i
$15$	12.2368	+	12.2368i	0.815789	+	0.815789i
$16$	−14.8621			−0.928883
$17$	14.2611	−	14.2611i	0.838890	−	0.838890i	−0.149823	−	0.988713i	$-0.547870\pi$
$17$	14.2611	−	14.2611i	0.838890	−	0.838890i	0.988713	+	0.149823i	$0.0478705\pi$
$18$	0.377981	+	0.377981i	0.0209990	+	0.0209990i
$19$	10.4494	−	10.4494i	0.549969	−	0.549969i	−0.376463	−	0.926432i	$-0.622860\pi$
$19$	10.4494	−	10.4494i	0.549969	−	0.549969i	0.926432	+	0.376463i	$0.122860\pi$
$20$	14.5863	+	14.5863i	0.729316	+	0.729316i
$21$		−	36.8514i		−	1.75483i
$22$	1.68367	−	1.68367i	0.0765302	−	0.0765302i
$23$	−26.6243	+	26.6243i	−1.15758	+	1.15758i	−0.172584	+	0.984995i	$0.555212\pi$
$23$	−26.6243	+	26.6243i	−1.15758	+	1.15758i	−0.984995	+	0.172584i	$0.944788\pi$
$24$	5.66012	+	5.66012i	0.235838	+	0.235838i
$25$		−	2.91316i		−	0.116526i
$26$	4.29211			0.165081
$27$		−	23.8163i		−	0.882084i
$28$		−	43.9269i		−	1.56882i
$29$	0.147829	+	0.147829i	0.00509757	+	0.00509757i	0.709651	−	0.704553i	$-0.248853\pi$
$29$	0.147829	+	0.147829i	0.00509757	+	0.00509757i	−0.704553	+	0.709651i	$0.748853\pi$
$30$		−	5.35027i		−	0.178342i
$31$	13.0530	+	13.0530i	0.421064	+	0.421064i	0.885570	−	0.464506i	$-0.153768\pi$
$31$	13.0530	+	13.0530i	0.421064	+	0.421064i	−0.464506	+	0.885570i	$0.653768\pi$
$32$	10.1611	+	10.1611i	0.317534	+	0.317534i
$33$	25.2266			0.764443
$34$	−6.23534			−0.183392
$35$	−42.0304	+	42.0304i	−1.20087	+	1.20087i
$36$			6.75072i			0.187520i
$37$	−32.4717	−	17.7366i	−0.877614	−	0.479368i
$37$	−32.4717	−	17.7366i	−0.877614	−	0.479368i
$38$	−4.56876			−0.120230
$39$	32.1547	+	32.1547i	0.824478	+	0.824478i
$40$		−	12.9112i		−	0.322779i
$41$			1.12653i			0.0274763i	0.999906	+	0.0137382i	$0.00437313\pi$
$41$			1.12653i			0.0274763i	−0.999906	+	0.0137382i	$0.995627\pi$
$42$	−8.05620	+	8.05620i	−0.191814	+	0.191814i
$43$	−26.2287	+	26.2287i	−0.609969	+	0.609969i	−0.942938	−	0.332969i	$-0.891950\pi$
$43$	−26.2287	+	26.2287i	−0.609969	+	0.609969i	0.332969	+	0.942938i	$0.391950\pi$
$44$	30.0701			0.683412
$45$	6.45927	−	6.45927i	0.143539	−	0.143539i
$46$	11.6409			0.253062
$47$	−59.6171			−1.26845			−0.634224	−	0.773149i	$-0.718680\pi$
$47$	−59.6171			−1.26845			−0.634224	+	0.773149i	$0.718680\pi$
$48$			48.6811i			1.01419i
$49$	77.5753			1.58317
$50$	−0.636854	+	0.636854i	−0.0127371	+	0.0127371i
$51$	−46.7125	−	46.7125i	−0.915932	−	0.915932i
$52$	38.3284	+	38.3284i	0.737084	+	0.737084i
$53$	−19.1173			−0.360705			−0.180352	−	0.983602i	$-0.557724\pi$
$53$	−19.1173			−0.360705			−0.180352	+	0.983602i	$0.557724\pi$
$54$	−5.20655	+	5.20655i	−0.0964177	+	0.0964177i
$55$	−28.7719	−	28.7719i	−0.523126	−	0.523126i
$56$	−19.4411	+	19.4411i	−0.347162	+	0.347162i
$57$	−34.2272	−	34.2272i	−0.600477	−	0.600477i
$58$		−	0.0646349i		−	0.00111440i
$59$	38.1810	−	38.1810i	0.647136	−	0.647136i	−0.305164	−	0.952300i	$-0.598711\pi$
$59$	38.1810	−	38.1810i	0.647136	−	0.647136i	0.952300	+	0.305164i	$0.0987113\pi$
$60$	47.7777	−	47.7777i	0.796295	−	0.796295i
$61$	−2.53695	−	2.53695i	−0.0415893	−	0.0415893i	0.686006	−	0.727596i	$-0.259362\pi$
$61$	−2.53695	−	2.53695i	−0.0415893	−	0.0415893i	−0.727596	+	0.686006i	$0.759362\pi$
$62$		−	5.70712i		−	0.0920503i
$63$	−19.4522			−0.308765
$64$			55.0058i			0.859466i
$65$		−	73.3472i		−	1.12842i
$66$	−5.51487	−	5.51487i	−0.0835586	−	0.0835586i
$67$			35.6412i			0.531958i	0.963979	+	0.265979i	$0.0856952\pi$
$67$			35.6412i			0.531958i	−0.963979	+	0.265979i	$0.914305\pi$
$68$	−55.6814	−	55.6814i	−0.818844	−	0.818844i
$69$	87.2083	+	87.2083i	1.26389	+	1.26389i
$70$	18.3768			0.262526
$71$	133.243			1.87666			0.938332	−	0.345736i	$-0.112371\pi$
$71$	133.243			1.87666			0.938332	+	0.345736i	$0.112371\pi$
$72$	2.98772	−	2.98772i	0.0414961	−	0.0414961i
$73$		−	103.942i		−	1.42387i	−0.702248	−	0.711933i	$-0.747820\pi$
$73$		−	103.942i		−	1.42387i	0.702248	−	0.711933i	$-0.252180\pi$
$74$	3.22129	+	10.9762i	0.0435310	+	0.148327i
$75$	−9.54209			−0.127228
$76$	−40.7988	−	40.7988i	−0.536827	−	0.536827i
$77$			86.6471i			1.12529i
$78$		−	14.0589i		−	0.180242i
$79$	3.44977	−	3.44977i	0.0436680	−	0.0436680i	−0.684936	−	0.728604i	$-0.740170\pi$
$79$	3.44977	−	3.44977i	0.0436680	−	0.0436680i	0.728604	+	0.684936i	$0.240170\pi$
$80$	55.5227	−	55.5227i	0.694034	−	0.694034i
$81$	−93.5715			−1.15520
$82$	0.246274	−	0.246274i	0.00300334	−	0.00300334i
$83$	−58.9414			−0.710137			−0.355069	−	0.934840i	$-0.615543\pi$
$83$	−58.9414			−0.710137			−0.355069	+	0.934840i	$0.615543\pi$
$84$	−143.883			−1.71290
$85$			106.555i			1.25359i
$86$	11.4679			0.133347
$87$	0.484218	−	0.484218i	0.00556572	−	0.00556572i
$88$	−13.3084	−	13.3084i	−0.151232	−	0.151232i
$89$	−7.78393	−	7.78393i	−0.0874599	−	0.0874599i	0.662023	−	0.749483i	$-0.269698\pi$
$89$	−7.78393	−	7.78393i	−0.0874599	−	0.0874599i	−0.749483	+	0.662023i	$0.769698\pi$
$90$	−2.82416			−0.0313796
$91$	−110.443	+	110.443i	−1.21366	+	1.21366i
$92$	103.952	+	103.952i	1.12992	+	1.12992i
$93$	42.7553	−	42.7553i	0.459734	−	0.459734i
$94$	13.0331	+	13.0331i	0.138650	+	0.138650i
$95$			78.0748i			0.821840i
$96$	33.2828	−	33.2828i	0.346696	−	0.346696i
$97$	48.8026	−	48.8026i	0.503119	−	0.503119i	−0.409287	−	0.912406i	$-0.634222\pi$
$97$	48.8026	−	48.8026i	0.503119	−	0.503119i	0.912406	+	0.409287i	$0.134222\pi$
$98$	−16.9590	−	16.9590i	−0.173051	−	0.173051i
$99$		−	13.3160i		−	0.134505i
$100$	−11.3742			−0.113742
$101$		−	110.263i		−	1.09171i	−0.837879	−	0.545856i	$-0.816205\pi$
$101$		−	110.263i		−	1.09171i	0.837879	−	0.545856i	$-0.183795\pi$
$102$			20.4239i			0.200235i
$103$	100.019	+	100.019i	0.971056	+	0.971056i	0.999593	−	0.0285367i	$-0.00908475\pi$
$103$	100.019	+	100.019i	0.971056	+	0.971056i	−0.0285367	+	0.999593i	$0.509085\pi$
$104$		−	33.9266i		−	0.326217i
$105$	137.671	+	137.671i	1.31116	+	1.31116i
$106$	4.17930	+	4.17930i	0.0394274	+	0.0394274i
$107$	76.9180			0.718860			0.359430	−	0.933172i	$-0.382971\pi$
$107$	76.9180			0.718860			0.359430	+	0.933172i	$0.382971\pi$
$108$	−92.9887			−0.861006
$109$	−48.3249	+	48.3249i	−0.443347	+	0.443347i	−0.893135	−	0.449788i	$-0.851500\pi$
$109$	−48.3249	+	48.3249i	−0.443347	+	0.443347i	0.449788	+	0.893135i	$0.351500\pi$
$110$			12.5798i			0.114362i
$111$	−58.0965	+	106.362i	−0.523392	+	0.958213i
$112$	−167.207			−1.49292
$113$	−144.948	−	144.948i	−1.28272	−	1.28272i	−0.939111	−	0.343613i	$-0.888349\pi$
$113$	−144.948	−	144.948i	−1.28272	−	1.28272i	−0.343613	−	0.939111i	$-0.611651\pi$
$114$			14.9650i			0.131272i
$115$		−	198.929i		−	1.72982i
$116$	0.577188	−	0.577188i	0.00497576	−	0.00497576i
$117$	16.9730	−	16.9730i	0.145068	−	0.145068i
$118$	−16.6937			−0.141472
$119$	160.446	−	160.446i	1.34828	−	1.34828i
$120$	−42.2907			−0.352423
$121$	61.6858			0.509800
$122$			1.10922i			0.00909197i
$123$	3.68996			0.0299997
$124$	50.9643	−	50.9643i	0.411003	−	0.411003i
$125$	−82.5131	−	82.5131i	−0.660105	−	0.660105i
$126$	4.25251	+	4.25251i	0.0337500	+	0.0337500i
$127$	14.0525			0.110649			0.0553247	−	0.998468i	$-0.482381\pi$
$127$	14.0525			0.110649			0.0553247	+	0.998468i	$0.482381\pi$
$128$	52.6694	−	52.6694i	0.411480	−	0.411480i
$129$	85.9124	+	85.9124i	0.665987	+	0.665987i
$130$	−16.0347	+	16.0347i	−0.123344	+	0.123344i
$131$	−54.1488	−	54.1488i	−0.413350	−	0.413350i	0.469554	−	0.882904i	$-0.344415\pi$
$131$	−54.1488	−	54.1488i	−0.413350	−	0.413350i	−0.882904	+	0.469554i	$0.844415\pi$
$132$		−	98.4952i		−	0.746176i
$133$	117.562	−	117.562i	0.883923	−	0.883923i
$134$	7.79164	−	7.79164i	0.0581465	−	0.0581465i
$135$	88.9741	+	88.9741i	0.659067	+	0.659067i
$136$			49.2867i			0.362402i
$137$	−145.695			−1.06346			−0.531732	−	0.846913i	$-0.678459\pi$
$137$	−145.695			−1.06346			−0.531732	+	0.846913i	$0.678459\pi$
$138$		−	38.1298i		−	0.276303i
$139$			207.337i			1.49164i	0.666150	+	0.745818i	$0.267941\pi$
$139$			207.337i			1.49164i	−0.666150	+	0.745818i	$0.732059\pi$
$140$	164.104	+	164.104i	1.17217	+	1.17217i
$141$			195.277i			1.38494i
$142$	−29.1287	−	29.1287i	−0.205132	−	0.205132i
$143$	−75.6038	−	75.6038i	−0.528698	−	0.528698i
$144$	25.6966			0.178448
$145$	−1.10454			−0.00761750
$146$	−22.7231	+	22.7231i	−0.155638	+	0.155638i
$147$		−	254.099i		−	1.72857i
$148$	−69.2511	+	126.783i	−0.467913	+	0.856643i
$149$	77.3044			0.518821			0.259411	−	0.965767i	$-0.416472\pi$
$149$	77.3044			0.518821			0.259411	+	0.965767i	$0.416472\pi$
$150$	2.08603	+	2.08603i	0.0139068	+	0.0139068i
$151$		−	132.472i		−	0.877295i	−0.898659	−	0.438648i	$-0.855458\pi$
$151$		−	132.472i		−	0.877295i	0.898659	−	0.438648i	$-0.144542\pi$
$152$			36.1133i			0.237588i
$153$	−24.6574	+	24.6574i	−0.161160	+	0.161160i
$154$	18.9422	−	18.9422i	0.123001	−	0.123001i
$155$	−97.5281			−0.629213
$156$	125.545	−	125.545i	0.804777	−	0.804777i
$157$	−202.716			−1.29118			−0.645592	−	0.763683i	$-0.723389\pi$
$157$	−202.716			−1.29118			−0.645592	+	0.763683i	$0.723389\pi$
$158$	−1.50833			−0.00954639
$159$			62.6191i			0.393831i
$160$	−75.9207			−0.474504
$161$	−299.539	+	299.539i	−1.86049	+	1.86049i
$162$	20.4560	+	20.4560i	0.126271	+	0.126271i
$163$	87.6897	+	87.6897i	0.537974	+	0.537974i	0.922933	−	0.384960i	$-0.125785\pi$
$163$	87.6897	+	87.6897i	0.537974	+	0.537974i	−0.384960	+	0.922933i	$0.625785\pi$
$164$	4.39844			0.0268197
$165$	−94.2428	+	94.2428i	−0.571169	+	0.571169i
$166$	12.8854	+	12.8854i	0.0776227	+	0.0776227i
$167$	103.285	−	103.285i	0.618473	−	0.618473i	−0.326667	−	0.945140i	$-0.605926\pi$
$167$	103.285	−	103.285i	0.618473	−	0.618473i	0.945140	+	0.326667i	$0.105926\pi$
$168$	63.6796	+	63.6796i	0.379045	+	0.379045i
$169$		−	23.7342i		−	0.140439i
$170$	23.2943	−	23.2943i	0.137025	−	0.137025i
$171$	−18.0670	+	18.0670i	−0.105655	+	0.105655i
$172$	102.408	+	102.408i	0.595393	+	0.595393i
$173$			189.584i			1.09586i	0.836525	+	0.547929i	$0.184584\pi$
$173$			189.584i			1.09586i	−0.836525	+	0.547929i	$0.815416\pi$
$174$	−0.211713			−0.00121674
$175$		−	32.7747i		−	0.187284i
$176$		−	114.462i		−	0.650351i
$177$	−125.062	−	125.062i	−0.706568	−	0.706568i
$178$			3.40334i			0.0191199i
$179$	−30.4073	−	30.4073i	−0.169873	−	0.169873i	0.617050	−	0.786924i	$-0.288328\pi$
$179$	−30.4073	−	30.4073i	−0.169873	−	0.169873i	−0.786924	+	0.617050i	$0.788328\pi$
$180$	−25.2197	−	25.2197i	−0.140109	−	0.140109i
$181$	159.524			0.881350			0.440675	−	0.897667i	$-0.354739\pi$
$181$	159.524			0.881350			0.440675	+	0.897667i	$0.354739\pi$
$182$	48.2887			0.265322
$183$	−8.30981	+	8.30981i	−0.0454088	+	0.0454088i
$184$		−	92.0142i		−	0.500077i
$185$	187.571	−	55.0482i	1.01390	−	0.297558i
$186$	−18.6937			−0.100504
$187$	109.833	+	109.833i	0.587343	+	0.587343i
$188$			232.770i			1.23814i
$189$		−	267.947i		−	1.41771i
$190$	17.0682	−	17.0682i	0.0898326	−	0.0898326i
$191$	92.2469	−	92.2469i	0.482968	−	0.482968i	−0.423110	−	0.906078i	$-0.639062\pi$
$191$	92.2469	−	92.2469i	0.482968	−	0.482968i	0.906078	+	0.423110i	$0.139062\pi$
$192$	180.172			0.938398
$193$	−136.779	+	136.779i	−0.708701	+	0.708701i	−0.966262	−	0.257561i	$-0.917081\pi$
$193$	−136.779	+	136.779i	−0.708701	+	0.708701i	0.257561	+	0.966262i	$0.417081\pi$
$194$	−21.3378			−0.109988
$195$	−240.250			−1.23205
$196$		−	302.886i		−	1.54534i
$197$	0.0302563			0.000153585			7.67927e−5	−	1.00000i	$-0.499976\pi$
$197$	0.0302563			0.000153585			7.67927e−5		1.00000i	$0.499976\pi$
$198$	−2.91105	+	2.91105i	−0.0147023	+	0.0147023i
$199$	−196.285	−	196.285i	−0.986355	−	0.986355i	0.0135535	−	0.999908i	$-0.495686\pi$
$199$	−196.285	−	196.285i	−0.986355	−	0.986355i	−0.999908	+	0.0135535i	$0.995686\pi$
$200$	5.03396	+	5.03396i	0.0251698	+	0.0251698i
$201$	116.743			0.580812
$202$	−24.1049	+	24.1049i	−0.119331	+	0.119331i
$203$	1.66317	+	1.66317i	0.00819293	+	0.00819293i
$204$	−182.385	+	182.385i	−0.894045	+	0.894045i
$205$	−4.20854	−	4.20854i	−0.0205295	−	0.0205295i
$206$		−	43.7309i		−	0.212286i
$207$	46.0333	−	46.0333i	0.222383	−	0.222383i
$208$	145.897	−	145.897i	0.701427	−	0.701427i
$209$	80.4768	+	80.4768i	0.385057	+	0.385057i
$210$		−	60.1936i		−	0.286636i
$211$	−73.8512			−0.350006			−0.175003	−	0.984568i	$-0.555993\pi$
$211$	−73.8512			−0.350006			−0.175003	+	0.984568i	$0.555993\pi$
$212$			74.6421i			0.352085i
$213$		−	436.440i		−	2.04901i
$214$	−16.8153	−	16.8153i	−0.0785762	−	0.0785762i
$215$		−	195.973i		−	0.911501i
$216$	41.1548	+	41.1548i	0.190531	+	0.190531i
$217$	146.854	+	146.854i	0.676745	+	0.676745i
$218$	21.1289			0.0969216
$219$	−340.464			−1.55463
$220$	−112.338	+	112.338i	−0.510625	+	0.510625i
$221$			279.994i			1.26694i
$222$	35.9527	−	10.5514i	0.161949	−	0.0475288i
$223$	251.842			1.12933			0.564667	−	0.825319i	$-0.309004\pi$
$223$	251.842			1.12933			0.564667	+	0.825319i	$0.309004\pi$
$224$	114.318	+	114.318i	0.510349	+	0.510349i
$225$			5.03684i			0.0223859i
$226$			63.3750i			0.280420i
$227$	137.677	−	137.677i	0.606507	−	0.606507i	−0.335525	−	0.942031i	$-0.608914\pi$
$227$	137.677	−	137.677i	0.606507	−	0.606507i	0.942031	+	0.335525i	$0.108914\pi$
$228$	−133.637	+	133.637i	−0.586128	+	0.586128i
$229$	85.2606			0.372317			0.186159	−	0.982520i	$-0.440396\pi$
$229$	85.2606			0.372317			0.186159	+	0.982520i	$0.440396\pi$
$230$	−43.4885	+	43.4885i	−0.189080	+	0.189080i
$231$	283.814			1.22863
$232$	−0.510902			−0.00220216
$233$			259.682i			1.11451i	0.830340	+	0.557257i	$0.188146\pi$
$233$			259.682i			1.11451i	−0.830340	+	0.557257i	$0.811854\pi$
$234$	−7.42104			−0.0317138
$235$	222.721	−	222.721i	0.947747	−	0.947747i
$236$	−149.075	−	149.075i	−0.631672	−	0.631672i
$237$	−11.2998	−	11.2998i	−0.0476784	−	0.0476784i
$238$	−70.1511			−0.294753
$239$	−152.545	+	152.545i	−0.638263	+	0.638263i	−0.950127	−	0.311864i	$-0.899047\pi$
$239$	−152.545	+	152.545i	−0.638263	+	0.638263i	0.311864	+	0.950127i	$0.399047\pi$
$240$	−181.865	−	181.865i	−0.757773	−	0.757773i
$241$	24.2367	−	24.2367i	0.100567	−	0.100567i	−0.655033	−	0.755600i	$-0.727345\pi$
$241$	24.2367	−	24.2367i	0.100567	−	0.100567i	0.755600	+	0.655033i	$0.227345\pi$
$242$	−13.4853	−	13.4853i	−0.0557245	−	0.0557245i
$243$			92.1484i			0.379212i
$244$	−9.90530	+	9.90530i	−0.0405955	+	0.0405955i
$245$	−289.810	+	289.810i	−1.18290	+	1.18290i
$246$	−0.806675	−	0.806675i	−0.00327916	−	0.00327916i
$247$			205.157i			0.830594i
$248$	−45.1114			−0.181901
$249$			193.063i			0.775355i
$250$			36.0769i			0.144308i
$251$	−79.9458	−	79.9458i	−0.318509	−	0.318509i	0.529685	−	0.848194i	$-0.322310\pi$
$251$	−79.9458	−	79.9458i	−0.318509	−	0.318509i	−0.848194	+	0.529685i	$0.822310\pi$
$252$			75.9495i			0.301387i
$253$	−205.049	−	205.049i	−0.810471	−	0.810471i
$254$	−3.07206	−	3.07206i	−0.0120947	−	0.0120947i
$255$	349.022			1.36871
$256$	196.995			0.769511
$257$	24.1358	−	24.1358i	0.0939135	−	0.0939135i	−0.658589	−	0.752503i	$-0.728846\pi$
$257$	24.1358	−	24.1358i	0.0939135	−	0.0939135i	0.752503	+	0.658589i	$0.228846\pi$
$258$		−	37.5632i		−	0.145594i
$259$	−365.325	−	199.547i	−1.41052	−	0.770452i
$260$	−286.378			−1.10145
$261$	−0.255597	−	0.255597i	−0.000979297	−	0.000979297i
$262$			23.6753i			0.0903637i
$263$			454.509i			1.72817i	0.503344	+	0.864086i	$0.332103\pi$
$263$			454.509i			1.72817i	−0.503344	+	0.864086i	$0.667897\pi$
$264$	−43.5918	+	43.5918i	−0.165121	+	0.165121i
$265$	71.4195	−	71.4195i	0.269508	−	0.269508i
$266$	−51.4011			−0.193237
$267$	−25.4964	+	25.4964i	−0.0954921	+	0.0954921i
$268$	139.158			0.519247
$269$	−4.03538			−0.0150014			−0.00750070	−	0.999972i	$-0.502388\pi$
$269$	−4.03538			−0.0150014			−0.00750070	+	0.999972i	$0.502388\pi$
$270$		−	38.9018i		−	0.144081i
$271$	168.099			0.620291			0.310145	−	0.950689i	$-0.399622\pi$
$271$	168.099			0.620291			0.310145	+	0.950689i	$0.399622\pi$
$272$	−211.951	+	211.951i	−0.779231	+	0.779231i
$273$	361.758	+	361.758i	1.32512	+	1.32512i
$274$	31.8508	+	31.8508i	0.116244	+	0.116244i
$275$	22.4359			0.0815850
$276$	340.498	−	340.498i	1.23369	−	1.23369i
$277$	−188.617	−	188.617i	−0.680929	−	0.680929i	0.279281	−	0.960209i	$-0.409904\pi$
$277$	−188.617	−	188.617i	−0.680929	−	0.680929i	−0.960209	+	0.279281i	$0.909904\pi$
$278$	45.3267	−	45.3267i	0.163046	−	0.163046i
$279$	−22.5686	−	22.5686i	−0.0808910	−	0.0808910i
$280$		−	145.258i		−	0.518779i
$281$	−26.2199	+	26.2199i	−0.0933091	+	0.0933091i	−0.752221	−	0.658911i	$-0.771017\pi$
$281$	−26.2199	+	26.2199i	−0.0933091	+	0.0933091i	0.658911	+	0.752221i	$0.271017\pi$
$282$	42.6901	−	42.6901i	0.151383	−	0.151383i
$283$	−16.4746	−	16.4746i	−0.0582142	−	0.0582142i	0.677400	−	0.735615i	$-0.263107\pi$
$283$	−16.4746	−	16.4746i	−0.0582142	−	0.0582142i	−0.735615	+	0.677400i	$0.763107\pi$
$284$		−	520.237i		−	1.83182i
$285$	255.735			0.897317
$286$			33.0560i			0.115580i
$287$			12.6741i			0.0441606i
$288$	−17.5685	−	17.5685i	−0.0610017	−	0.0610017i
$289$		−	117.759i		−	0.407471i
$290$	0.241466	+	0.241466i	0.000832643	+	0.000832643i
$291$	−159.853	−	159.853i	−0.549325	−	0.549325i
$292$	−405.834			−1.38984
$293$	479.133			1.63527			0.817633	−	0.575739i	$-0.195286\pi$
$293$	479.133			1.63527			0.817633	+	0.575739i	$0.195286\pi$
$294$	−55.5494	+	55.5494i	−0.188944	+	0.188944i
$295$			285.277i			0.967041i
$296$	86.7605	−	25.4624i	0.293110	−	0.0860217i
$297$	183.423			0.617585
$298$	−16.8998	−	16.8998i	−0.0567106	−	0.0567106i
$299$		−	522.724i		−	1.74824i
$300$			37.2563i			0.124188i
$301$	−295.087	+	295.087i	−0.980357	+	0.980357i
$302$	−28.9600	+	28.9600i	−0.0958942	+	0.0958942i
$303$	−361.168			−1.19197
$304$	−155.300	+	155.300i	−0.510857	+	0.510857i
$305$	18.9553			0.0621486
$306$	10.7809			0.0352316
$307$			168.729i			0.549605i	0.961501	+	0.274803i	$0.0886125\pi$
$307$			168.729i			0.549605i	−0.961501	+	0.274803i	$0.911387\pi$
$308$	338.306			1.09840
$309$	327.613	−	327.613i	1.06024	−	1.06024i
$310$	21.3209	+	21.3209i	0.0687772	+	0.0687772i
$311$	30.6844	+	30.6844i	0.0986638	+	0.0986638i	0.754716	−	0.656052i	$-0.227775\pi$
$311$	30.6844	+	30.6844i	0.0986638	+	0.0986638i	−0.656052	+	0.754716i	$0.727775\pi$
$312$	−111.127			−0.356177
$313$	176.319	−	176.319i	0.563318	−	0.563318i	−0.366930	−	0.930248i	$-0.619591\pi$
$313$	176.319	−	176.319i	0.563318	−	0.563318i	0.930248	+	0.366930i	$0.119591\pi$
$314$	44.3164	+	44.3164i	0.141135	+	0.141135i
$315$	72.6705	−	72.6705i	0.230700	−	0.230700i
$316$	−13.4693	−	13.4693i	−0.0426245	−	0.0426245i
$317$		−	183.518i		−	0.578921i	−0.957190	−	0.289461i	$-0.906524\pi$
$317$		−	183.518i		−	0.578921i	0.957190	−	0.289461i	$-0.0934759\pi$
$318$	13.6894	−	13.6894i	0.0430483	−	0.0430483i
$319$	−1.13852	+	1.13852i	−0.00356902	+	0.00356902i
$320$	−205.494	−	205.494i	−0.642167	−	0.642167i
$321$		−	251.946i		−	0.784879i
$322$	130.966			0.406727
$323$		−	298.040i		−	0.922726i
$324$			365.342i			1.12760i
$325$	28.5975	+	28.5975i	0.0879923	+	0.0879923i
$326$		−	38.3403i		−	0.117608i
$327$	158.289	+	158.289i	0.484064	+	0.484064i
$328$	−1.94665	−	1.94665i	−0.00593492	−	0.00593492i
$329$	−670.726			−2.03868
$330$	41.2055			0.124865
$331$	115.989	−	115.989i	0.350421	−	0.350421i	−0.509845	−	0.860266i	$-0.670297\pi$
$331$	115.989	−	115.989i	0.350421	−	0.350421i	0.860266	+	0.509845i	$0.170297\pi$
$332$			230.132i			0.693168i
$333$	56.1435	+	30.6665i	0.168599	+	0.0920917i
$334$	−45.1589			−0.135206
$335$	−133.150	−	133.150i	−0.397463	−	0.397463i
$336$			547.691i			1.63003i
$337$		−	273.766i		−	0.812363i	−0.913792	−	0.406181i	$-0.866860\pi$
$337$		−	273.766i		−	0.812363i	0.913792	−	0.406181i	$-0.133140\pi$
$338$	−5.18860	+	5.18860i	−0.0153509	+	0.0153509i
$339$	−474.779	+	474.779i	−1.40053	+	1.40053i
$340$	416.034			1.22363
$341$	−100.529	+	100.529i	−0.294805	+	0.294805i
$342$	7.89936			0.0230975
$343$	321.489			0.937285
$344$		−	90.6468i		−	0.263508i
$345$	−651.595			−1.88868
$346$	41.4455	−	41.4455i	0.119785	−	0.119785i
$347$	345.845	+	345.845i	0.996671	+	0.996671i	0.999994	−	0.00332334i	$-0.00105785\pi$
$347$	345.845	+	345.845i	0.996671	+	0.996671i	−0.00332334	+	0.999994i	$0.501058\pi$
$348$	−1.89059	−	1.89059i	−0.00543272	−	0.00543272i
$349$	−197.561			−0.566077			−0.283039	−	0.959109i	$-0.591342\pi$
$349$	−197.561			−0.566077			−0.283039	+	0.959109i	$0.591342\pi$
$350$	−7.16498	+	7.16498i	−0.0204714	+	0.0204714i
$351$	233.797	+	233.797i	0.666087	+	0.666087i
$352$	−78.2564	+	78.2564i	−0.222319	+	0.222319i
$353$	159.972	+	159.972i	0.453178	+	0.453178i	0.896408	−	0.443230i	$-0.146167\pi$
$353$	159.972	+	159.972i	0.453178	+	0.453178i	−0.443230	+	0.896408i	$0.646167\pi$
$354$			54.6806i			0.154465i
$355$	−497.776	+	497.776i	−1.40219	+	1.40219i
$356$	−30.3917	+	30.3917i	−0.0853700	+	0.0853700i
$357$	−525.542	−	525.542i	−1.47211	−	1.47211i
$358$			13.2949i			0.0371366i
$359$	600.472			1.67262			0.836312	−	0.548254i	$-0.184707\pi$
$359$	600.472			1.67262			0.836312	+	0.548254i	$0.184707\pi$
$360$			22.3234i			0.0620094i
$361$			142.620i			0.395069i
$362$	−34.8741	−	34.8741i	−0.0963374	−	0.0963374i
$363$		−	202.053i		−	0.556619i
$364$	431.216	+	431.216i	1.18466	+	1.18466i
$365$	388.312	+	388.312i	1.06387	+	1.06387i
$366$	3.63327			0.00992696
$367$	−88.9880			−0.242474			−0.121237	−	0.992624i	$-0.538686\pi$
$367$	−88.9880			−0.242474			−0.121237	+	0.992624i	$0.538686\pi$
$368$	395.694	−	395.694i	1.07526	−	1.07526i
$369$		−	1.94776i		−	0.00527849i
$370$	−53.0397	−	28.9712i	−0.143351	−	0.0783005i
$371$	−215.081			−0.579733
$372$	−166.934	−	166.934i	−0.448748	−	0.448748i
$373$		−	412.326i		−	1.10543i	−0.833370	−	0.552716i	$-0.813591\pi$
$373$		−	412.326i		−	1.10543i	0.833370	−	0.552716i	$-0.186409\pi$
$374$		−	48.0219i		−	0.128401i
$375$	−270.273	+	270.273i	−0.720728	+	0.720728i
$376$	103.019	−	103.019i	0.273987	−	0.273987i
$377$	−2.90239			−0.00769864
$378$	−58.5767	+	58.5767i	−0.154965	+	0.154965i
$379$	251.508			0.663610			0.331805	−	0.943348i	$-0.392342\pi$
$379$	251.508			0.663610			0.331805	+	0.943348i	$0.392342\pi$
$380$	304.837			0.802202
$381$		−	46.0291i		−	0.120811i
$382$	−40.3328			−0.105583
$383$	−98.8181	+	98.8181i	−0.258011	+	0.258011i	−0.824245	−	0.566234i	$-0.808400\pi$
$383$	−98.8181	+	98.8181i	−0.258011	+	0.258011i	0.566234	+	0.824245i	$0.308400\pi$
$384$	−172.519	−	172.519i	−0.449269	−	0.449269i
$385$	−323.700	−	323.700i	−0.840780	−	0.840780i
$386$	59.8035			0.154931
$387$	45.3493	−	45.3493i	0.117182	−	0.117182i
$388$	−190.545	−	190.545i	−0.491097	−	0.491097i
$389$	250.429	−	250.429i	0.643777	−	0.643777i	−0.307705	−	0.951482i	$-0.599561\pi$
$389$	250.429	−	250.429i	0.643777	−	0.643777i	0.951482	+	0.307705i	$0.0995609\pi$
$390$	52.5218	+	52.5218i	0.134671	+	0.134671i
$391$			759.385i			1.94216i
$392$	−134.051	+	134.051i	−0.341967	+	0.341967i
$393$	−177.365	+	177.365i	−0.451311	+	0.451311i
$394$	−0.00661444	−	0.00661444i	−1.67879e−5	−	1.67879e-5i
$395$			25.7756i			0.0652548i
$396$	−51.9912			−0.131291
$397$			68.4961i			0.172534i	0.996272	+	0.0862672i	$0.0274939\pi$
$397$			68.4961i			0.172534i	−0.996272	+	0.0862672i	$0.972506\pi$
$398$			85.8208i			0.215630i
$399$	−385.075	−	385.075i	−0.965101	−	0.965101i
$400$			43.2957i			0.108239i
$401$	−553.535	−	553.535i	−1.38039	−	1.38039i	−0.843923	−	0.536465i	$-0.819759\pi$
$401$	−553.535	−	553.535i	−1.38039	−	1.38039i	−0.536465	−	0.843923i	$-0.680241\pi$
$402$	−25.5216	−	25.5216i	−0.0634866	−	0.0634866i
$403$	−256.274			−0.635916
$404$	−430.512			−1.06562
$405$	349.569	−	349.569i	0.863134	−	0.863134i
$406$		−	0.727180i		−	0.00179108i
$407$	136.600	−	250.083i	0.335626	−	0.614455i
$408$	161.439			0.395685
$409$	−18.5631	−	18.5631i	−0.0453865	−	0.0453865i	0.684049	−	0.729436i	$-0.260217\pi$
$409$	−18.5631	−	18.5631i	−0.0453865	−	0.0453865i	−0.729436	+	0.684049i	$0.760217\pi$
$410$			1.84009i			0.00448802i
$411$			477.225i			1.16113i
$412$	390.515	−	390.515i	0.947852	−	0.947852i
$413$	429.558	−	429.558i	1.04009	−	1.04009i
$414$	−20.1270			−0.0486159
$415$	220.196	−	220.196i	0.530593	−	0.530593i
$416$	−199.496			−0.479559
$417$	679.137			1.62863
$418$		−	35.1866i		−	0.0841785i
$419$	205.899			0.491405			0.245702	−	0.969345i	$-0.420981\pi$
$419$	205.899			0.491405			0.245702	+	0.969345i	$0.420981\pi$
$420$	537.526	−	537.526i	1.27982	−	1.27982i
$421$	499.794	+	499.794i	1.18716	+	1.18716i	0.977849	+	0.209309i	$0.0671215\pi$
$421$	499.794	+	499.794i	1.18716	+	1.18716i	0.209309	+	0.977849i	$0.432878\pi$
$422$	16.1448	+	16.1448i	0.0382579	+	0.0382579i
$423$	103.078			0.243683
$424$	33.0350	−	33.0350i	0.0779126	−	0.0779126i
$425$	−41.5449	−	41.5449i	−0.0977527	−	0.0977527i
$426$	−95.4115	+	95.4115i	−0.223971	+	0.223971i
$427$	−28.5421	−	28.5421i	−0.0668434	−	0.0668434i
$428$		−	300.320i		−	0.701682i
$429$	−247.641	+	247.641i	−0.577253	+	0.577253i
$430$	−42.8422	+	42.8422i	−0.0996331	+	0.0996331i
$431$	−21.0539	−	21.0539i	−0.0488489	−	0.0488489i	0.682260	−	0.731109i	$-0.260997\pi$
$431$	−21.0539	−	21.0539i	−0.0488489	−	0.0488489i	−0.731109	+	0.682260i	$0.760997\pi$
$432$			353.961i			0.819354i
$433$	−411.255			−0.949782			−0.474891	−	0.880045i	$-0.657512\pi$
$433$	−411.255			−0.949782			−0.474891	+	0.880045i	$0.657512\pi$
$434$		−	64.2083i		−	0.147945i
$435$			3.61793i			0.00831708i
$436$	188.680	+	188.680i	0.432753	+	0.432753i
$437$			556.416i			1.27326i
$438$	74.4300	+	74.4300i	0.169931	+	0.169931i
$439$	−345.725	−	345.725i	−0.787529	−	0.787529i	0.193559	−	0.981089i	$-0.437997\pi$
$439$	−345.725	−	345.725i	−0.787529	−	0.787529i	−0.981089	+	0.193559i	$0.937997\pi$
$440$	99.4363			0.225992
$441$	−134.127			−0.304144
$442$	61.2103	−	61.2103i	0.138485	−	0.138485i
$443$		−	19.0700i		−	0.0430475i	−0.999768	−	0.0215237i	$-0.993148\pi$
$443$		−	19.0700i		−	0.0430475i	0.999768	−	0.0215237i	$-0.00685175\pi$
$444$	415.280	+	226.833i	0.935315	+	0.510885i
$445$	58.1592			0.130695
$446$	−55.0559	−	55.0559i	−0.123444	−	0.123444i
$447$		−	253.212i		−	0.566469i
$448$			618.847i			1.38135i
$449$	328.598	−	328.598i	0.731845	−	0.731845i	−0.239140	−	0.970985i	$-0.576866\pi$
$449$	328.598	−	328.598i	0.731845	−	0.731845i	0.970985	+	0.239140i	$0.0768656\pi$
$450$	1.10112	−	1.10112i	0.00244693	−	0.00244693i
$451$	−8.67604			−0.0192373
$452$	−565.937	+	565.937i	−1.25207	+	1.25207i
$453$	−433.913			−0.957864
$454$	−60.1961			−0.132590
$455$		−	825.198i		−	1.81362i
$456$	118.290			0.259407
$457$	−150.014	+	150.014i	−0.328258	+	0.328258i	−0.851924	−	0.523666i	$-0.824564\pi$
$457$	−150.014	+	150.014i	−0.328258	+	0.328258i	0.523666	+	0.851924i	$0.324564\pi$
$458$	−18.6391	−	18.6391i	−0.0406967	−	0.0406967i
$459$	−339.647	−	339.647i	−0.739971	−	0.739971i
$460$	−776.701			−1.68848
$461$	149.166	−	149.166i	0.323571	−	0.323571i	−0.526564	−	0.850135i	$-0.676520\pi$
$461$	149.166	−	149.166i	0.323571	−	0.323571i	0.850135	+	0.526564i	$0.176520\pi$
$462$	−62.0454	−	62.0454i	−0.134297	−	0.134297i
$463$	−350.817	+	350.817i	−0.757704	+	0.757704i	−0.975904	−	0.218200i	$-0.929981\pi$
$463$	−350.817	+	350.817i	−0.757704	+	0.757704i	0.218200	+	0.975904i	$0.429981\pi$
$464$	−2.19706	−	2.19706i	−0.00473505	−	0.00473505i
$465$			319.455i			0.686999i
$466$	56.7699	−	56.7699i	0.121824	−	0.121824i
$467$	489.317	−	489.317i	1.04779	−	1.04779i	0.0489897	−	0.998799i	$-0.484400\pi$
$467$	489.317	−	489.317i	1.04779	−	1.04779i	0.998799	−	0.0489897i	$-0.0156001\pi$
$468$	−66.2696	−	66.2696i	−0.141602	−	0.141602i
$469$			400.984i			0.854976i
$470$	−97.3793			−0.207190
$471$			663.999i			1.40976i
$472$			131.954i			0.279564i
$473$	−202.002	−	202.002i	−0.427065	−	0.427065i
$474$			4.94056i			0.0104231i
$475$	−30.4407	−	30.4407i	−0.0640858	−	0.0640858i
$476$	−626.447	−	626.447i	−1.31607	−	1.31607i
$477$	33.0538			0.0692952
$478$	66.6967			0.139533
$479$	−553.862	+	553.862i	−1.15629	+	1.15629i	−0.171022	+	0.985267i	$0.554707\pi$
$479$	−553.862	+	553.862i	−1.15629	+	1.15629i	−0.985267	+	0.171022i	$0.945293\pi$
$480$			248.679i			0.518082i
$481$	492.879	−	144.650i	1.02470	−	0.300727i
$482$	−10.5969			−0.0219853
$483$	981.143	+	981.143i	2.03135	+	2.03135i
$484$		−	240.847i		−	0.497618i
$485$			364.638i			0.751831i
$486$	20.1449	−	20.1449i	0.0414503	−	0.0414503i
$487$	−190.594	+	190.594i	−0.391363	+	0.391363i	−0.875173	−	0.483810i	$-0.839253\pi$
$487$	−190.594	+	190.594i	−0.391363	+	0.391363i	0.483810	+	0.875173i	$0.339253\pi$
$488$	8.76774			0.0179667
$489$	287.229	−	287.229i	0.587380	−	0.587380i
$490$	126.713			0.258597
$491$	51.2605			0.104400			0.0522001	−	0.998637i	$-0.483377\pi$
$491$	51.2605			0.104400			0.0522001	+	0.998637i	$0.483377\pi$
$492$		−	14.4071i		−	0.0292828i
$493$	4.21643			0.00855259
$494$	44.8500	−	44.8500i	0.0907894	−	0.0907894i
$495$	49.7465	+	49.7465i	0.100498	+	0.100498i
$496$	−193.995	−	193.995i	−0.391120	−	0.391120i
$497$	1499.06			3.01622
$498$	42.2062	−	42.2062i	0.0847514	−	0.0847514i
$499$	227.555	+	227.555i	0.456023	+	0.456023i	0.897347	−	0.441325i	$-0.145491\pi$
$499$	227.555	+	227.555i	0.456023	+	0.456023i	−0.441325	+	0.897347i	$0.645491\pi$
$500$	−322.166	+	322.166i	−0.644331	+	0.644331i
$501$	−338.311	−	338.311i	−0.675272	−	0.675272i
$502$			34.9544i			0.0696303i
$503$	−589.214	+	589.214i	−1.17140	+	1.17140i	−0.189524	+	0.981876i	$0.560695\pi$
$503$	−589.214	+	589.214i	−1.17140	+	1.17140i	−0.981876	+	0.189524i	$0.939305\pi$
$504$	33.6136	−	33.6136i	0.0666936	−	0.0666936i
$505$	411.926	+	411.926i	0.815694	+	0.815694i
$506$			89.6529i			0.177180i
$507$	−77.7416			−0.153336
$508$		−	54.8667i		−	0.108005i
$509$			736.290i			1.44654i	0.690564	+	0.723271i	$0.257362\pi$
$509$			736.290i			1.44654i	−0.690564	+	0.723271i	$0.742638\pi$
$510$	−76.3008	−	76.3008i	−0.149609	−	0.149609i
$511$		−	1169.41i		−	2.28847i
$512$	−253.743	−	253.743i	−0.495592	−	0.495592i
$513$	−248.866	−	248.866i	−0.485119	−	0.485119i
$514$	−10.5528			−0.0205307
$515$	−747.310			−1.45109
$516$	335.438	−	335.438i	0.650073	−	0.650073i
$517$		−	459.145i		−	0.888095i
$518$	36.2414	+	123.489i	0.0699640	+	0.238395i
$519$	620.984			1.19650
$520$	126.745	+	126.745i	0.243740	+	0.243740i
$521$			164.241i			0.315242i	0.987500	+	0.157621i	$0.0503824\pi$
$521$			164.241i			0.315242i	−0.987500	+	0.157621i	$0.949618\pi$
$522$			0.111754i			0.000214087i
$523$	152.326	−	152.326i	0.291253	−	0.291253i	−0.546322	−	0.837575i	$-0.683972\pi$
$523$	152.326	−	152.326i	0.291253	−	0.291253i	0.837575	+	0.546322i	$0.183972\pi$
$524$	−211.419	+	211.419i	−0.403472	+	0.403472i
$525$	−107.354			−0.204484
$526$	99.3618	−	99.3618i	0.188901	−	0.188901i
$527$	372.301			0.706453
$528$	−374.921			−0.710078
$529$		−	888.708i		−	1.67998i
$530$	−31.2265			−0.0589179
$531$	−66.0148	+	66.0148i	−0.124322	+	0.124322i
$532$	−459.010	−	459.010i	−0.862801	−	0.862801i
$533$	−11.0588	−	11.0588i	−0.0207482	−	0.0207482i
$534$	11.1477			0.0208758
$535$	−287.354	+	287.354i	−0.537111	+	0.537111i
$536$	−61.5883	−	61.5883i	−0.114904	−	0.114904i
$537$	−99.5997	+	99.5997i	−0.185474	+	0.185474i
$538$	0.882187	+	0.882187i	0.00163975	+	0.00163975i
$539$			597.452i			1.10845i
$540$	347.392	−	347.392i	0.643318	−	0.643318i
$541$	−520.525	+	520.525i	−0.962153	+	0.962153i	−0.999309	−	0.0371563i	$-0.988170\pi$
$541$	−520.525	+	520.525i	−0.962153	+	0.962153i	0.0371563	+	0.999309i	$0.488170\pi$
$542$	−36.7486	−	36.7486i	−0.0678019	−	0.0678019i
$543$		−	522.524i		−	0.962291i
$544$	289.817			0.532752
$545$		−	361.069i		−	0.662512i
$546$		−	158.170i		−	0.289689i
$547$	−288.132	−	288.132i	−0.526750	−	0.526750i	0.392852	−	0.919602i	$-0.371488\pi$
$547$	−288.132	−	288.132i	−0.526750	−	0.526750i	−0.919602	+	0.392852i	$0.871488\pi$
$548$			568.852i			1.03805i
$549$	4.38637	+	4.38637i	0.00798975	+	0.00798975i
$550$	−4.90478	−	4.90478i	−0.00891778	−	0.00891778i
$551$	3.08946			0.00560700
$552$	−301.394			−0.546003
$553$	38.8119	−	38.8119i	0.0701842	−	0.0701842i
$554$			82.4685i			0.148860i
$555$	−180.311	−	614.391i	−0.324885	−	1.10701i
$556$	809.532			1.45599
$557$	−2.94464	−	2.94464i	−0.00528661	−	0.00528661i	0.704459	−	0.709745i	$-0.251190\pi$
$557$	−2.94464	−	2.94464i	−0.00528661	−	0.00528661i	−0.709745	+	0.704459i	$0.751190\pi$
$558$			9.86758i			0.0176838i
$559$		−	514.956i		−	0.921210i
$560$	624.662	−	624.662i	1.11547	−	1.11547i
$561$	359.760	−	359.760i	0.641283	−	0.641283i
$562$	11.4640			0.0203986
$563$	42.4752	−	42.4752i	0.0754444	−	0.0754444i	−0.668378	−	0.743822i	$-0.733011\pi$
$563$	42.4752	−	42.4752i	0.0754444	−	0.0754444i	0.743822	+	0.668378i	$0.233011\pi$
$564$	762.441			1.35185
$565$	1083.01			1.91683
$566$			7.20314i			0.0127264i
$567$	−1052.73			−1.85667
$568$	−230.245	+	230.245i	−0.405362	+	0.405362i
$569$	643.671	+	643.671i	1.13123	+	1.13123i	0.989973	+	0.141259i	$0.0451149\pi$
$569$	643.671	+	643.671i	1.13123	+	1.13123i	0.141259	+	0.989973i	$0.454885\pi$
$570$	−55.9071	−	55.9071i	−0.0980826	−	0.0980826i
$571$	114.094			0.199814			0.0999072	−	0.994997i	$-0.468145\pi$
$571$	114.094			0.199814			0.0999072	+	0.994997i	$0.468145\pi$
$572$	−295.189	+	295.189i	−0.516064	+	0.516064i
$573$	−302.156	−	302.156i	−0.527323	−	0.527323i
$574$	2.77072	−	2.77072i	0.00482705	−	0.00482705i
$575$	77.5608	+	77.5608i	0.134888	+	0.134888i
$576$		−	95.1049i		−	0.165113i
$577$	232.362	−	232.362i	0.402706	−	0.402706i	−0.476479	−	0.879186i	$-0.658087\pi$
$577$	232.362	−	232.362i	0.402706	−	0.402706i	0.879186	+	0.476479i	$0.158087\pi$
$578$	−25.7437	+	25.7437i	−0.0445393	+	0.0445393i
$579$	448.023	+	448.023i	0.773787	+	0.773787i
$580$			4.31257i			0.00743547i
$581$	−663.124			−1.14135
$582$			69.8922i			0.120090i
$583$		−	147.234i		−	0.252545i
$584$	179.613	+	179.613i	0.307557	+	0.307557i
$585$			126.817i			0.216781i
$586$	−104.745	−	104.745i	−0.178745	−	0.178745i
$587$	456.415	+	456.415i	0.777539	+	0.777539i	0.979412	−	0.201873i	$-0.0647029\pi$
$587$	456.415	+	456.415i	0.777539	+	0.777539i	−0.201873	+	0.979412i	$0.564703\pi$
$588$	−992.109			−1.68726
$589$	272.792			0.463144
$590$	62.3653	−	62.3653i	0.105704	−	0.105704i
$591$		−	0.0991051i		−	0.000167690i
$592$	482.599	+	263.604i	0.815201	+	0.445277i
$593$	−745.309			−1.25684			−0.628422	−	0.777872i	$-0.716299\pi$
$593$	−745.309			−1.25684			−0.628422	+	0.777872i	$0.716299\pi$
$594$	−40.0986	−	40.0986i	−0.0675061	−	0.0675061i
$595$			1198.80i			2.01479i
$596$		−	301.829i		−	0.506424i
$597$	−642.933	+	642.933i	−1.07694	+	1.07694i
$598$	−114.274	+	114.274i	−0.191094	+	0.191094i
$599$	528.707			0.882650			0.441325	−	0.897347i	$-0.354509\pi$
$599$	528.707			0.882650			0.441325	+	0.897347i	$0.354509\pi$
$600$	16.4888	−	16.4888i	0.0274814	−	0.0274814i
$601$	−672.930			−1.11968			−0.559842	−	0.828599i	$-0.689138\pi$
$601$	−672.930			−1.11968			−0.559842	+	0.828599i	$0.689138\pi$
$602$	129.020			0.214319
$603$		−	61.6235i		−	0.102195i
$604$	−517.224			−0.856331
$605$	−230.449	+	230.449i	−0.380907	+	0.380907i
$606$	78.9560	+	78.9560i	0.130291	+	0.130291i
$607$	−593.981	−	593.981i	−0.978552	−	0.978552i	0.0212231	−	0.999775i	$-0.493244\pi$
$607$	−593.981	−	593.981i	−0.978552	−	0.978552i	−0.999775	+	0.0212231i	$0.993244\pi$
$608$	212.355			0.349268
$609$	5.44772	−	5.44772i	0.00894536	−	0.00894536i
$610$	−4.14388	−	4.14388i	−0.00679325	−	0.00679325i
$611$	585.242	−	585.242i	0.957842	−	0.957842i
$612$	96.2729	+	96.2729i	0.157309	+	0.157309i
$613$		−	958.508i		−	1.56364i	−0.623507	−	0.781818i	$-0.714293\pi$
$613$		−	958.508i		−	1.56364i	0.623507	−	0.781818i	$-0.285707\pi$
$614$	36.8863	−	36.8863i	0.0600755	−	0.0600755i
$615$	−13.7851	+	13.7851i	−0.0224149	+	0.0224149i
$616$	−149.727	−	149.727i	−0.243063	−	0.243063i
$617$			10.0614i			0.0163070i	0.999967	+	0.00815349i	$0.00259537\pi$
$617$			10.0614i			0.0163070i	−0.999967	+	0.00815349i	$0.997405\pi$
$618$	−143.241			−0.231782
$619$			222.362i			0.359228i	0.983737	+	0.179614i	$0.0574849\pi$
$619$			222.362i			0.359228i	−0.983737	+	0.179614i	$0.942515\pi$
$620$			380.790i			0.614178i
$621$	634.092	+	634.092i	1.02108	+	1.02108i
$622$		−	13.4161i		−	0.0215692i
$623$	−87.5737	−	87.5737i	−0.140568	−	0.140568i
$624$	−477.887	−	477.887i	−0.765844	−	0.765844i
$625$	689.342			1.10295
$626$	−77.0911			−0.123149
$627$	263.603	−	263.603i	0.420419	−	0.420419i
$628$			791.487i			1.26033i
$629$	−716.027	+	210.139i	−1.13836	+	0.334085i
$630$	−31.7735			−0.0504341
$631$	−289.961	−	289.961i	−0.459526	−	0.459526i	0.438974	−	0.898500i	$-0.355342\pi$
$631$	−289.961	−	289.961i	−0.459526	−	0.459526i	−0.898500	+	0.438974i	$0.855342\pi$
$632$			11.9225i			0.0188647i
$633$			241.901i			0.382149i
$634$	−40.1195	+	40.1195i	−0.0632799	+	0.0632799i
$635$	−52.4979	+	52.4979i	−0.0826739	+	0.0826739i
$636$	244.491			0.384420
$637$	−761.532	+	761.532i	−1.19550	+	1.19550i
$638$	0.497791			0.000780236
$639$	−230.377			−0.360527
$640$			393.530i			0.614891i
$641$	−557.472			−0.869691			−0.434845	−	0.900505i	$-0.643197\pi$
$641$	−557.472			−0.869691			−0.434845	+	0.900505i	$0.643197\pi$
$642$	−55.0788	+	55.0788i	−0.0857925	+	0.0857925i
$643$	213.369	+	213.369i	0.331833	+	0.331833i	0.853282	−	0.521449i	$-0.174608\pi$
$643$	213.369	+	213.369i	0.331833	+	0.331833i	−0.521449	+	0.853282i	$0.674608\pi$
$644$	1169.52	+	1169.52i	1.81603	+	1.81603i
$645$	−641.912			−0.995212
$646$	−65.1556	+	65.1556i	−0.100860	+	0.100860i
$647$	−478.321	−	478.321i	−0.739290	−	0.739290i	0.233150	−	0.972441i	$-0.425097\pi$
$647$	−478.321	−	478.321i	−0.739290	−	0.739290i	−0.972441	+	0.233150i	$0.925097\pi$
$648$	161.693	−	161.693i	0.249526	−	0.249526i
$649$	294.054	+	294.054i	0.453087	+	0.453087i
$650$		−	12.5036i		−	0.0192363i
$651$	481.021	−	481.021i	0.738896	−	0.738896i
$652$	342.377	−	342.377i	0.525118	−	0.525118i
$653$	−182.906	−	182.906i	−0.280101	−	0.280101i	0.553048	−	0.833149i	$-0.313464\pi$
$653$	−182.906	−	182.906i	−0.280101	−	0.280101i	−0.833149	+	0.553048i	$0.813464\pi$
$654$		−	69.2080i		−	0.105823i
$655$	404.584			0.617685
$656$		−	16.7426i		−	0.0255223i
$657$			179.716i			0.273540i
$658$	146.630	+	146.630i	0.222841	+	0.222841i
$659$		−	7.20367i		−	0.0109312i	−0.999985	−	0.00546561i	$-0.998260\pi$
$659$		−	7.20367i		−	0.0109312i	0.999985	−	0.00546561i	$-0.00173977\pi$
$660$	367.963	+	367.963i	0.557520	+	0.557520i
$661$	−378.724	−	378.724i	−0.572957	−	0.572957i	0.359997	−	0.932954i	$-0.382778\pi$
$661$	−378.724	−	378.724i	−0.572957	−	0.572957i	−0.932954	+	0.359997i	$0.882778\pi$
$662$	−50.7136			−0.0766067
$663$	917.123			1.38329
$664$	101.851	−	101.851i	0.153391	−	0.153391i
$665$			878.386i			1.32088i
$666$	−5.56960	−	18.9778i	−0.00836276	−	0.0284952i
$667$	−7.87172			−0.0118017
$668$	−403.267	−	403.267i	−0.603694	−	0.603694i
$669$		−	824.911i		−	1.23305i
$670$			58.2168i			0.0868907i
$671$	19.5385	−	19.5385i	0.0291185	−	0.0291185i
$672$	374.451	−	374.451i	0.557218	−	0.557218i
$673$	−588.989			−0.875169			−0.437584	−	0.899177i	$-0.644166\pi$
$673$	−588.989			−0.875169			−0.437584	+	0.899177i	$0.644166\pi$
$674$	−59.8489	+	59.8489i	−0.0887966	+	0.0887966i
$675$	−69.3805			−0.102786
$676$	−92.6680			−0.137083
$677$			461.489i			0.681668i	0.940124	+	0.340834i	$0.110709\pi$
$677$			461.489i			0.681668i	−0.940124	+	0.340834i	$0.889291\pi$
$678$	207.586			0.306174
$679$	549.057	−	549.057i	0.808625	−	0.808625i
$680$	−184.128	−	184.128i	−0.270776	−	0.270776i
$681$	−450.963	−	450.963i	−0.662207	−	0.662207i
$682$	43.9538			0.0644483
$683$	213.567	−	213.567i	0.312690	−	0.312690i	−0.533261	−	0.845951i	$-0.679034\pi$
$683$	213.567	−	213.567i	0.312690	−	0.312690i	0.845951	+	0.533261i	$0.179034\pi$
$684$	70.5410	+	70.5410i	0.103130	+	0.103130i
$685$	544.293	−	544.293i	0.794589	−	0.794589i
$686$	−70.2817	−	70.2817i	−0.102451	−	0.102451i
$687$		−	279.272i		−	0.406510i
$688$	389.814	−	389.814i	0.566590	−	0.566590i
$689$	187.669	−	187.669i	0.272378	−	0.272378i
$690$	142.447	+	142.447i	0.206445	+	0.206445i
$691$		−	312.616i		−	0.452411i	−0.974080	−	0.226205i	$-0.927368\pi$
$691$		−	312.616i		−	0.452411i	0.974080	−	0.226205i	$-0.0726320\pi$
$692$	740.213			1.06967
$693$		−	149.812i		−	0.216180i
$694$		−	151.213i		−	0.217885i
$695$	−774.582	−	774.582i	−1.11451	−	1.11451i
$696$			1.67347i			0.00240440i
$697$	16.0656	+	16.0656i	0.0230496	+	0.0230496i
$698$	43.1894	+	43.1894i	0.0618760	+	0.0618760i
$699$	850.592			1.21687
$700$	−127.966			−0.182809
$701$	−773.159	+	773.159i	−1.10294	+	1.10294i	−0.108882	+	0.994055i	$0.534727\pi$
$701$	−773.159	+	773.159i	−1.10294	+	1.10294i	−0.994055	+	0.108882i	$0.965273\pi$
$702$		−	102.222i		−	0.145615i
$703$	−524.647	+	153.973i	−0.746297	+	0.219023i
$704$	−423.631			−0.601749
$705$	−729.524	−	729.524i	−1.03479	−	1.03479i
$706$		−	69.9439i		−	0.0990707i
$707$		−	1240.52i		−	1.75463i
$708$	−488.296	+	488.296i	−0.689684	+	0.689684i
$709$	−734.143	+	734.143i	−1.03546	+	1.03546i	−0.0361149	+	0.999348i	$0.511498\pi$
$709$	−734.143	+	734.143i	−1.03546	+	1.03546i	−0.999348	+	0.0361149i	$0.988502\pi$
$710$	217.641			0.306537
$711$	−5.96464	+	5.96464i	−0.00838908	+	0.00838908i
$712$	26.9014			0.0377829
$713$	−695.054			−0.974831
$714$			229.781i			0.321822i
$715$	564.889			0.790055
$716$	−118.723	+	118.723i	−0.165814	+	0.165814i
$717$	499.663	+	499.663i	0.696880	+	0.696880i
$718$	−131.271	−	131.271i	−0.182829	−	0.182829i
$719$	378.724			0.526737			0.263368	−	0.964695i	$-0.415167\pi$
$719$	378.724			0.526737			0.263368	+	0.964695i	$0.415167\pi$
$720$	−95.9985	+	95.9985i	−0.133331	+	0.133331i
$721$	1125.27	+	1125.27i	1.56070	+	1.56070i
$722$	31.1786	−	31.1786i	0.0431837	−	0.0431837i
$723$	−79.3877	−	79.3877i	−0.109803	−	0.109803i
$724$		−	622.849i		−	0.860289i
$725$	0.430650	−	0.430650i	0.000594000	−	0.000594000i
$726$	−44.1714	+	44.1714i	−0.0608422	+	0.0608422i
$727$	69.2214	+	69.2214i	0.0952152	+	0.0952152i	0.753110	−	0.657895i	$-0.228553\pi$
$727$	69.2214	+	69.2214i	0.0952152	+	0.0952152i	−0.657895	+	0.753110i	$0.728553\pi$
$728$		−	381.694i		−	0.524305i
$729$	−540.310			−0.741166
$730$		−	169.780i		−	0.232576i
$731$			748.100i			1.02339i
$732$	32.4450	+	32.4450i	0.0443237	+	0.0443237i
$733$		−	538.938i		−	0.735250i	−0.929974	−	0.367625i	$-0.880171\pi$
$733$		−	538.938i		−	0.735250i	0.929974	−	0.367625i	$-0.119829\pi$
$734$	19.4539	+	19.4539i	0.0265040	+	0.0265040i
$735$	949.276	+	949.276i	1.29153	+	1.29153i
$736$	−541.065			−0.735142
$737$	−274.493			−0.372447
$738$	−0.425807	+	0.425807i	−0.000576974	+	0.000576974i
$739$		−	1141.55i		−	1.54473i	−0.635181	−	0.772364i	$-0.719074\pi$
$739$		−	1141.55i		−	1.54473i	0.635181	−	0.772364i	$-0.280926\pi$
$740$	−214.931	−	732.355i	−0.290447	−	0.989668i
$741$	671.994			0.906874
$742$	47.0195	+	47.0195i	0.0633687	+	0.0633687i
$743$		−	773.006i		−	1.04038i	−0.854049	−	0.520192i	$-0.825860\pi$
$743$		−	773.006i		−	1.04038i	0.854049	−	0.520192i	$-0.174140\pi$
$744$			147.763i			0.198606i
$745$	−288.798	+	288.798i	−0.387648	+	0.387648i
$746$	−90.1399	+	90.1399i	−0.120831	+	0.120831i
$747$	101.909			0.136425
$748$	428.834	−	428.834i	0.573307	−	0.573307i
$749$	865.372			1.15537
$750$	118.171			0.157561
$751$			990.458i			1.31885i	0.751770	+	0.659426i	$0.229201\pi$
$751$			990.458i			1.31885i	−0.751770	+	0.659426i	$0.770799\pi$
$752$	886.037			1.17824
$753$	−261.864	+	261.864i	−0.347761	+	0.347761i
$754$	0.634500	+	0.634500i	0.000841512	+	0.000841512i
$755$	494.894	+	494.894i	0.655489	+	0.655489i
$756$	−1046.18			−1.38383
$757$	551.325	−	551.325i	0.728302	−	0.728302i	−0.241979	−	0.970281i	$-0.577797\pi$
$757$	551.325	−	551.325i	0.728302	−	0.728302i	0.970281	+	0.241979i	$0.0777966\pi$
$758$	−54.9830	−	54.9830i	−0.0725369	−	0.0725369i
$759$	−671.641	+	671.641i	−0.884903	+	0.884903i
$760$	−134.914	−	134.914i	−0.177519	−	0.177519i
$761$			443.611i			0.582931i	0.956581	+	0.291466i	$0.0941429\pi$
$761$			443.611i			0.582931i	−0.956581	+	0.291466i	$0.905857\pi$
$762$	−10.0626	+	10.0626i	−0.0132055	+	0.0132055i
$763$	−543.682	+	543.682i	−0.712559	+	0.712559i
$764$	−360.170	−	360.170i	−0.471427	−	0.471427i
$765$		−	184.233i		−	0.240827i
$766$	43.2059			0.0564046
$767$			749.621i			0.977342i
$768$		−	645.260i		−	0.840182i
$769$	431.616	+	431.616i	0.561269	+	0.561269i	0.929668	−	0.368399i	$-0.120094\pi$
$769$	431.616	+	431.616i	0.561269	+	0.561269i	−0.368399	+	0.929668i	$0.620094\pi$
$770$			141.530i			0.183806i
$771$	−79.0571	−	79.0571i	−0.102538	−	0.102538i
$772$	534.044	+	534.044i	0.691766	+	0.691766i
$773$	−177.893			−0.230133			−0.115067	−	0.993358i	$-0.536708\pi$
$773$	−177.893			−0.230133			−0.115067	+	0.993358i	$0.536708\pi$
$774$	−19.8279			−0.0256174
$775$	38.0254	−	38.0254i	0.0490651	−	0.0490651i
$776$			168.663i			0.217349i
$777$	−653.619	+	1196.63i	−0.841208	+	1.54006i
$778$	−109.494			−0.140738
$779$	11.7716	+	11.7716i	0.0151111	+	0.0151111i
$780$			938.036i			1.20261i
$781$			1026.18i			1.31393i
$782$	166.012	−	166.012i	0.212291	−	0.212291i
$783$	3.52075	−	3.52075i	0.00449648	−	0.00449648i
$784$	−1152.93			−1.47058
$785$	757.316	−	757.316i	0.964734	−	0.964734i
$786$	77.5487			0.0986625
$787$	−1489.76			−1.89296			−0.946482	−	0.322757i	$-0.895390\pi$
$787$	−1489.76			−1.89296			−0.946482	+	0.322757i	$0.895390\pi$
$788$		−	0.118133i		−	0.000149915i
$789$	1488.75			1.88689
$790$	5.63490	−	5.63490i	0.00713278	−	0.00713278i
$791$	−1630.75	−	1630.75i	−2.06163	−	2.06163i
$792$	23.0102	+	23.0102i	0.0290532	+	0.0290532i
$793$	49.8088			0.0628106
$794$	14.9742	−	14.9742i	0.0188591	−	0.0188591i
$795$	−233.936	−	233.936i	−0.294259	−	0.294259i
$796$	−766.377	+	766.377i	−0.962785	+	0.962785i
$797$	337.060	+	337.060i	0.422911	+	0.422911i	0.886205	−	0.463294i	$-0.153333\pi$
$797$	337.060	+	337.060i	0.422911	+	0.422911i	−0.463294	+	0.886205i	$0.653333\pi$
$798$			168.365i			0.210984i
$799$	−850.207	+	850.207i	−1.06409	+	1.06409i
$800$	29.6009	−	29.6009i	0.0370011	−	0.0370011i
$801$	13.4584	+	13.4584i	0.0168020	+	0.0168020i
$802$			242.020i			0.301771i
$803$	800.518			0.996909
$804$		−	455.814i		−	0.566933i
$805$		−	2238.06i		−	2.78020i
$806$	56.0249	+	56.0249i	0.0695098	+	0.0695098i
$807$			13.2179i			0.0163791i
$808$	190.535	+	190.535i	0.235811	+	0.235811i
$809$	208.693	+	208.693i	0.257965	+	0.257965i	0.824226	−	0.566261i	$-0.191611\pi$
$809$	208.693	+	208.693i	0.257965	+	0.257965i	−0.566261	+	0.824226i	$0.691611\pi$
$810$	−152.841			−0.188693
$811$	1268.09			1.56362			0.781808	−	0.623519i	$-0.214298\pi$
$811$	1268.09			1.56362			0.781808	+	0.623519i	$0.214298\pi$
$812$	6.49369	−	6.49369i	0.00799716	−	0.00799716i
$813$		−	550.610i		−	0.677257i
$814$	−84.5340	+	24.8090i	−0.103850	+	0.0304779i
$815$	−655.191			−0.803916
$816$	694.248	+	694.248i	0.850794	+	0.850794i
$817$			548.148i			0.670928i
$818$			8.11626i			0.00992208i
$819$	190.956	−	190.956i	0.233157	−	0.233157i
$820$	−16.4319	+	16.4319i	−0.0200389	+	0.0200389i
$821$	−157.649			−0.192021			−0.0960104	−	0.995380i	$-0.530608\pi$
$821$	−157.649			−0.192021			−0.0960104	+	0.995380i	$0.530608\pi$
$822$	104.328	−	104.328i	0.126919	−	0.126919i
$823$	−458.522			−0.557135			−0.278567	−	0.960417i	$-0.589860\pi$
$823$	−458.522			−0.557135			−0.278567	+	0.960417i	$0.589860\pi$
$824$	−345.667			−0.419499
$825$		−	73.4890i		−	0.0890776i
$826$	−187.814			−0.227378
$827$	85.3094	−	85.3094i	0.103155	−	0.103155i	−0.653646	−	0.756801i	$-0.726761\pi$
$827$	85.3094	−	85.3094i	0.103155	−	0.103155i	0.756801	+	0.653646i	$0.226761\pi$
$828$	−179.733	−	179.733i	−0.217069	−	0.217069i
$829$	694.674	+	694.674i	0.837966	+	0.837966i	0.988591	−	0.150625i	$-0.0481286\pi$
$829$	694.674	+	694.674i	0.837966	+	0.837966i	−0.150625	+	0.988591i	$0.548129\pi$
$830$	−96.2756			−0.115995
$831$	−617.819	+	617.819i	−0.743464	+	0.743464i
$832$	−539.974	−	539.974i	−0.649008	−	0.649008i
$833$	1106.31	−	1106.31i	1.32810	−	1.32810i
$834$	−148.468	−	148.468i	−0.178020	−	0.178020i
$835$			771.714i			0.924209i
$836$	314.215	−	314.215i	0.375855	−	0.375855i
$837$	310.874	−	310.874i	0.371414	−	0.371414i
$838$	−45.0121	−	45.0121i	−0.0537138	−	0.0537138i
$839$			254.225i			0.303010i	0.988456	+	0.151505i	$0.0484119\pi$
$839$			254.225i			0.303010i	−0.988456	+	0.151505i	$0.951588\pi$
$840$	−475.795			−0.566423
$841$		−	840.956i		−	0.999948i
$842$		−	218.523i		−	0.259529i
$843$	85.8836	+	85.8836i	0.101878	+	0.101878i
$844$			288.346i			0.341642i
$845$	88.6673	+	88.6673i	0.104932	+	0.104932i
$846$	−22.5342	−	22.5342i	−0.0266361	−	0.0266361i
$847$	694.000			0.819363
$848$	284.124			0.335052
$849$	−53.9629	+	53.9629i	−0.0635605	+	0.0635605i
$850$			18.1645i			0.0213700i
$851$	1336.76	−	392.312i	1.57081	−	0.461002i
$852$	−1704.04			−2.00005
$853$	349.655	+	349.655i	0.409912	+	0.409912i	0.881708	−	0.471796i	$-0.156394\pi$
$853$	349.655	+	349.655i	0.409912	+	0.409912i	−0.471796	+	0.881708i	$0.656394\pi$
$854$			12.4794i			0.0146128i
$855$		−	134.991i		−	0.157884i
$856$	−132.915	+	132.915i	−0.155275	+	0.155275i
$857$	658.357	−	658.357i	0.768212	−	0.768212i	−0.209580	−	0.977792i	$-0.567210\pi$
$857$	658.357	−	658.357i	0.768212	−	0.768212i	0.977792	+	0.209580i	$0.0672096\pi$
$858$	108.275			0.126195
$859$	−352.857	+	352.857i	−0.410776	+	0.410776i	−0.882009	−	0.471233i	$-0.843809\pi$
$859$	−352.857	+	352.857i	−0.410776	+	0.410776i	0.471233	+	0.882009i	$0.343809\pi$
$860$	−765.159			−0.889720
$861$	41.5142			0.0482162
$862$			9.20530i			0.0106790i
$863$	1317.93			1.52715			0.763574	−	0.645721i	$-0.223443\pi$
$863$	1317.93			1.52715			0.763574	+	0.645721i	$0.223443\pi$
$864$	242.000	−	242.000i	0.280092	−	0.280092i
$865$	−708.256	−	708.256i	−0.818793	−	0.818793i
$866$	89.9059	+	89.9059i	0.103817	+	0.103817i
$867$	−385.722			−0.444893
$868$	573.378	−	573.378i	0.660574	−	0.660574i
$869$	26.5686	+	26.5686i	0.0305738	+	0.0305738i
$870$	0.790927	−	0.790927i	0.000909111	−	0.000909111i
$871$	−349.878	−	349.878i	−0.401697	−	0.401697i
$872$		−	167.012i		−	0.191527i
$873$	−84.3794	+	84.3794i	−0.0966545	+	0.0966545i
$874$	121.640	−	121.640i	0.139176	−	0.139176i
$875$	−928.320	−	928.320i	−1.06094	−	1.06094i
$876$			1329.31i			1.51748i
$877$	−392.877			−0.447978			−0.223989	−	0.974592i	$-0.571908\pi$
$877$	−392.877			−0.447978			−0.223989	+	0.974592i	$0.571908\pi$
$878$			151.160i			0.172164i
$879$		−	1569.41i		−	1.78545i
$880$	427.612	+	427.612i	0.485923	+	0.485923i
$881$			655.658i			0.744220i	0.928189	+	0.372110i	$0.121366\pi$
$881$			655.658i			0.744220i	−0.928189	+	0.372110i	$0.878634\pi$
$882$	29.3220	+	29.3220i	0.0332449	+	0.0332449i
$883$	1039.40	+	1039.40i	1.17712	+	1.17712i	0.980475	+	0.196644i	$0.0630045\pi$
$883$	1039.40	+	1039.40i	1.17712	+	1.17712i	0.196644	+	0.980475i	$0.436996\pi$
$884$	1093.21			1.23666
$885$	934.429			1.05585
$886$	−4.16896	+	4.16896i	−0.00470538	+	0.00470538i
$887$		−	918.986i		−	1.03606i	−0.855362	−	0.518030i	$-0.826665\pi$
$887$		−	918.986i		−	1.03606i	0.855362	−	0.518030i	$-0.173335\pi$
$888$	−83.4025	−	284.185i	−0.0939218	−	0.320028i
$889$	158.098			0.177838
$890$	−12.7144	−	12.7144i	−0.0142858	−	0.0142858i
$891$		−	720.648i		−	0.808808i
$892$		−	983.295i		−	1.10235i
$893$	−622.963	+	622.963i	−0.697607	+	0.697607i
$894$	−55.3554	+	55.3554i	−0.0619188	+	0.0619188i
$895$	227.195			0.253849
$896$	592.561	−	592.561i	0.661340	−	0.661340i
$897$	−1712.19			−1.90880
$898$	−143.672			−0.159991
$899$			3.85923i			0.00429281i
$900$	19.6659			0.0218510
$901$	−272.635	+	272.635i	−0.302591	+	0.302591i
$902$	1.89670	+	1.89670i	0.00210277	+	0.00210277i
$903$	966.563	+	966.563i	1.07039	+	1.07039i
$904$	500.943			0.554140
$905$	−595.959	+	595.959i	−0.658518	+	0.658518i
$906$	94.8590	+	94.8590i	0.104701	+	0.104701i
$907$	−710.651	+	710.651i	−0.783518	+	0.783518i	−0.980423	−	0.196905i	$-0.936911\pi$
$907$	−710.651	+	710.651i	−0.783518	+	0.783518i	0.196905	+	0.980423i	$0.436911\pi$
$908$	−537.549	−	537.549i	−0.592014	−	0.592014i
$909$			190.644i			0.209730i
$910$	−180.399	+	180.399i	−0.198241	+	0.198241i
$911$	−11.6971	+	11.6971i	−0.0128398	+	0.0128398i	−0.713498	−	0.700658i	$-0.752890\pi$
$911$	−11.6971	+	11.6971i	−0.0128398	+	0.0128398i	0.700658	+	0.713498i	$0.252890\pi$
$912$	508.689	+	508.689i	0.557773	+	0.557773i
$913$		−	453.941i		−	0.497198i
$914$	65.5900			0.0717614
$915$		−	62.0884i		−	0.0678562i
$916$		−	332.893i		−	0.363420i
$917$	−609.205	−	609.205i	−0.664346	−	0.664346i
$918$			148.503i			0.161768i
$919$	149.843	+	149.843i	0.163051	+	0.163051i	0.783917	−	0.620866i	$-0.213219\pi$
$919$	149.843	+	149.843i	0.163051	+	0.163051i	−0.620866	+	0.783917i	$0.713219\pi$
$920$	343.751	+	343.751i	0.373643	+	0.373643i
$921$	552.674			0.600080
$922$	−65.2195			−0.0707370
$923$	−1308.00	+	1308.00i	−1.41712	+	1.41712i
$924$		−	1108.13i		−	1.19927i
$925$	−51.6695	+	94.5952i	−0.0558589	+	0.102265i
$926$	153.386			0.165644
$927$	−172.932	−	172.932i	−0.186550	−	0.186550i
$928$			3.00422i			0.00323731i
$929$			101.624i			0.109391i	0.998503	+	0.0546954i	$0.0174188\pi$
$929$			101.624i			0.109391i	−0.998503	+	0.0546954i	$0.982581\pi$
$930$	69.8370	−	69.8370i	0.0750936	−	0.0750936i
$931$	810.616	−	810.616i	0.870694	−	0.870694i
$932$	1013.91			1.08788
$933$	100.507	−	100.507i	0.107725	−	0.107725i
$934$	−213.943			−0.229061
$935$	−820.640			−0.877689
$936$			58.6590i			0.0626699i
$937$	−356.537			−0.380510			−0.190255	−	0.981735i	$-0.560931\pi$
$937$	−356.537			−0.380510			−0.190255	+	0.981735i	$0.560931\pi$
$938$	87.6604	−	87.6604i	0.0934545	−	0.0934545i
$939$	−577.534	−	577.534i	−0.615052	−	0.615052i
$940$	−869.594	−	869.594i	−0.925100	−	0.925100i
$941$	−1240.49			−1.31827			−0.659136	−	0.752024i	$-0.729078\pi$
$941$	−1240.49			−1.31827			−0.659136	+	0.752024i	$0.729078\pi$
$942$	145.159	−	145.159i	0.154096	−	0.154096i
$943$	−29.9931	−	29.9931i	−0.0318060	−	0.0318060i
$944$	−567.451	+	567.451i	−0.601114	+	0.601114i
$945$	1001.01	+	1001.01i	1.05927	+	1.05927i
$946$			88.3206i			0.0933621i
$947$	192.085	−	192.085i	0.202835	−	0.202835i	−0.598378	−	0.801214i	$-0.704188\pi$
$947$	192.085	−	192.085i	0.202835	−	0.202835i	0.801214	+	0.598378i	$0.204188\pi$
$948$	−44.1190	+	44.1190i	−0.0465390	+	0.0465390i
$949$	1020.37	+	1020.37i	1.07520	+	1.07520i
$950$			13.3095i			0.0140100i
$951$	−601.116			−0.632088
$952$			554.504i			0.582462i
$953$			1174.61i			1.23254i	0.787535	+	0.616270i	$0.211357\pi$
$953$			1174.61i			1.23254i	−0.787535	+	0.616270i	$0.788643\pi$
$954$	−7.22600	−	7.22600i	−0.00757442	−	0.00757442i
$955$			689.241i			0.721718i
$956$	595.599	+	595.599i	0.623011	+	0.623011i
$957$	3.72924	+	3.72924i	0.00389680	+	0.00389680i
$958$	242.163			0.252780
$959$	−1639.15			−1.70923
$960$	−673.097	+	673.097i	−0.701143	+	0.701143i
$961$		−	620.239i		−	0.645409i
$962$	−139.372	−	76.1275i	−0.144878	−	0.0791346i
$963$	−132.991			−0.138101
$964$	−94.6302	−	94.6302i	−0.0981641	−	0.0981641i
$965$		−	1021.97i		−	1.05904i
$966$		−	428.982i		−	0.444081i
$967$	162.381	−	162.381i	0.167923	−	0.167923i	−0.618143	−	0.786066i	$-0.712115\pi$
$967$	162.381	−	162.381i	0.167923	−	0.167923i	0.786066	+	0.618143i	$0.212115\pi$
$968$	−106.594	+	106.594i	−0.110117	+	0.110117i
$969$	−976.236			−1.00747
$970$	79.7147	−	79.7147i	0.0821801	−	0.0821801i
$971$	1046.35			1.07760			0.538802	−	0.842432i	$-0.318877\pi$
$971$	1046.35			1.07760			0.538802	+	0.842432i	$0.318877\pi$
$972$	359.786			0.370150
$973$			2332.66i			2.39739i
$974$	83.3326			0.0855571
$975$	93.6715	−	93.6715i	0.0960734	−	0.0960734i
$976$	37.7045	+	37.7045i	0.0386316	+	0.0386316i
$977$	817.033	+	817.033i	0.836267	+	0.836267i	0.988365	−	0.152098i	$-0.0486030\pi$
$977$	817.033	+	817.033i	0.836267	+	0.836267i	−0.152098	+	0.988365i	$0.548603\pi$
$978$	−125.584			−0.128409
$979$	59.9485	−	59.9485i	0.0612344	−	0.0612344i
$980$	1131.54	+	1131.54i	1.15463	+	1.15463i
$981$	83.5535	−	83.5535i	0.0851718	−	0.0851718i
$982$	−11.2062	−	11.2062i	−0.0114116	−	0.0114116i
$983$		−	49.6673i		−	0.0505263i	−0.999681	−	0.0252631i	$-0.991958\pi$
$983$		−	49.6673i		−	0.0505263i	0.999681	−	0.0252631i	$-0.00804237\pi$
$984$	−6.37629	+	6.37629i	−0.00647997	+	0.00647997i
$985$	−0.113033	+	0.113033i	−0.000114754	+	0.000114754i
$986$	−0.921767	−	0.921767i	−0.000934855	−	0.000934855i
$987$			2196.97i			2.22591i
$988$	801.017			0.810746
$989$		−	1396.64i		−	1.41217i
$990$		−	21.7505i		−	0.0219702i
$991$	217.306	+	217.306i	0.219280	+	0.219280i	0.808195	−	0.588915i	$-0.200445\pi$
$991$	217.306	+	217.306i	0.219280	+	0.219280i	−0.588915	+	0.808195i	$0.700445\pi$
$992$			265.266i			0.267405i
$993$	−379.925	−	379.925i	−0.382603	−	0.382603i
$994$	−327.715	−	327.715i	−0.329693	−	0.329693i
$995$	1466.58			1.47395
$996$	753.800			0.756827
$997$	1340.03	−	1340.03i	1.34406	−	1.34406i	0.452084	−	0.891975i	$-0.350681\pi$
$997$	1340.03	−	1340.03i	1.34406	−	1.34406i	0.891975	−	0.452084i	$-0.149319\pi$
$998$		−	99.4932i		−	0.0996926i
$999$	−422.420	+	773.356i	−0.422843	+	0.774130i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.3.d.a.31.4	yes	12
3.2	odd	2		333.3.i.a.253.3		12
4.3	odd	2		592.3.k.e.401.4		12
37.6	odd	4	inner	37.3.d.a.6.4	✓	12
111.80	even	4		333.3.i.a.154.3		12
148.43	even	4		592.3.k.e.561.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.3.d.a.6.4	✓	12	37.6	odd	4	inner
37.3.d.a.31.4	yes	12	1.1	even	1	trivial
333.3.i.a.154.3		12	111.80	even	4
333.3.i.a.253.3		12	3.2	odd	2
592.3.k.e.401.4		12	4.3	odd	2
592.3.k.e.561.3		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)

\(f(q)\)	\(=\)	\(q+(-0.218613 - 0.218613i) q^{2} -3.27551i q^{3} -3.90442i q^{4} +(-3.73585 + 3.73585i) q^{5} +(-0.716071 + 0.716071i) q^{6} +11.2506 q^{7} +(-1.72801 + 1.72801i) q^{8} -1.72900 q^{9} +O(q^{10})\)	\(q+(-0.218613 - 0.218613i) q^{2} -3.27551i q^{3} -3.90442i q^{4} +(-3.73585 + 3.73585i) q^{5} +(-0.716071 + 0.716071i) q^{6} +11.2506 q^{7} +(-1.72801 + 1.72801i) q^{8} -1.72900 q^{9} +1.63341 q^{10} +7.70157i q^{11} -12.7890 q^{12} +(-9.81667 + 9.81667i) q^{13} +(-2.45952 - 2.45952i) q^{14} +(12.2368 + 12.2368i) q^{15} -14.8621 q^{16} +(14.2611 - 14.2611i) q^{17} +(0.377981 + 0.377981i) q^{18} +(10.4494 - 10.4494i) q^{19} +(14.5863 + 14.5863i) q^{20} -36.8514i q^{21} +(1.68367 - 1.68367i) q^{22} +(-26.6243 + 26.6243i) q^{23} +(5.66012 + 5.66012i) q^{24} -2.91316i q^{25} +4.29211 q^{26} -23.8163i q^{27} -43.9269i q^{28} +(0.147829 + 0.147829i) q^{29} -5.35027i q^{30} +(13.0530 + 13.0530i) q^{31} +(10.1611 + 10.1611i) q^{32} +25.2266 q^{33} -6.23534 q^{34} +(-42.0304 + 42.0304i) q^{35} +6.75072i q^{36} +(-32.4717 - 17.7366i) q^{37} -4.56876 q^{38} +(32.1547 + 32.1547i) q^{39} -12.9112i q^{40} +1.12653i q^{41} +(-8.05620 + 8.05620i) q^{42} +(-26.2287 + 26.2287i) q^{43} +30.0701 q^{44} +(6.45927 - 6.45927i) q^{45} +11.6409 q^{46} -59.6171 q^{47} +48.6811i q^{48} +77.5753 q^{49} +(-0.636854 + 0.636854i) q^{50} +(-46.7125 - 46.7125i) q^{51} +(38.3284 + 38.3284i) q^{52} -19.1173 q^{53} +(-5.20655 + 5.20655i) q^{54} +(-28.7719 - 28.7719i) q^{55} +(-19.4411 + 19.4411i) q^{56} +(-34.2272 - 34.2272i) q^{57} -0.0646349i q^{58} +(38.1810 - 38.1810i) q^{59} +(47.7777 - 47.7777i) q^{60} +(-2.53695 - 2.53695i) q^{61} -5.70712i q^{62} -19.4522 q^{63} +55.0058i q^{64} -73.3472i q^{65} +(-5.51487 - 5.51487i) q^{66} +35.6412i q^{67} +(-55.6814 - 55.6814i) q^{68} +(87.2083 + 87.2083i) q^{69} +18.3768 q^{70} +133.243 q^{71} +(2.98772 - 2.98772i) q^{72} -103.942i q^{73} +(3.22129 + 10.9762i) q^{74} -9.54209 q^{75} +(-40.7988 - 40.7988i) q^{76} +86.6471i q^{77} -14.0589i q^{78} +(3.44977 - 3.44977i) q^{79} +(55.5227 - 55.5227i) q^{80} -93.5715 q^{81} +(0.246274 - 0.246274i) q^{82} -58.9414 q^{83} -143.883 q^{84} +106.555i q^{85} +11.4679 q^{86} +(0.484218 - 0.484218i) q^{87} +(-13.3084 - 13.3084i) q^{88} +(-7.78393 - 7.78393i) q^{89} -2.82416 q^{90} +(-110.443 + 110.443i) q^{91} +(103.952 + 103.952i) q^{92} +(42.7553 - 42.7553i) q^{93} +(13.0331 + 13.0331i) q^{94} +78.0748i q^{95} +(33.2828 - 33.2828i) q^{96} +(48.8026 - 48.8026i) q^{97} +(-16.9590 - 16.9590i) q^{98} -13.3160i 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

Properties

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