LMFDB - Embedded newform 102.4.f.c.55.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [102,4,Mod(13,102)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(102, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("102.13");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 102 = 2 \cdot 3 \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	102.f (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:	$6.01819482059$
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} + 886x^{10} + 292945x^{8} + 42943904x^{6} + 2387634208x^{4} + 5944075264x^{2} + 2089586944 $ x^12 + 886x^10 + 292945x^8 + 42943904x^6 + 2387634208x^4 + 5944075264*x^2 + 2089586944
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			55.2
Root			$0.650232i$ of defining polynomial
Character	$\chi$	$=$	102.55
Dual form			102.4.f.c.13.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.00000i q^{2} +(-2.12132 + 2.12132i) q^{3} -4.00000 q^{4} +(2.87400 - 2.87400i) q^{5} +(-4.24264 - 4.24264i) q^{6} +(-23.5451 - 23.5451i) q^{7} -8.00000i q^{8} -9.00000i q^{9} +(5.74799 + 5.74799i) q^{10} +(3.61347 + 3.61347i) q^{11} +(8.48528 - 8.48528i) q^{12} +18.3446 q^{13} +(47.0903 - 47.0903i) q^{14} +12.1933i q^{15} +16.0000 q^{16} +(-25.1071 - 65.4418i) q^{17} +18.0000 q^{18} -66.8279i q^{19} +(-11.4960 + 11.4960i) q^{20} +99.8936 q^{21} +(-7.22694 + 7.22694i) q^{22} +(-113.738 - 113.738i) q^{23} +(16.9706 + 16.9706i) q^{24} +108.480i q^{25} +36.6892i q^{26} +(19.0919 + 19.0919i) q^{27} +(94.1806 + 94.1806i) q^{28} +(120.744 - 120.744i) q^{29} -24.3867 q^{30} +(-182.902 + 182.902i) q^{31} +32.0000i q^{32} -15.3307 q^{33} +(130.884 - 50.2142i) q^{34} -135.337 q^{35} +36.0000i q^{36} +(-217.684 + 217.684i) q^{37} +133.656 q^{38} +(-38.9148 + 38.9148i) q^{39} +(-22.9920 - 22.9920i) q^{40} +(-198.360 - 198.360i) q^{41} +199.787i q^{42} -328.331i q^{43} +(-14.4539 - 14.4539i) q^{44} +(-25.8660 - 25.8660i) q^{45} +(227.476 - 227.476i) q^{46} -55.5285 q^{47} +(-33.9411 + 33.9411i) q^{48} +765.747i q^{49} -216.961 q^{50} +(192.083 + 85.5628i) q^{51} -73.3785 q^{52} +233.093i q^{53} +(-38.1838 + 38.1838i) q^{54} +20.7702 q^{55} +(-188.361 + 188.361i) q^{56} +(141.763 + 141.763i) q^{57} +(241.488 + 241.488i) q^{58} -182.149i q^{59} -48.7734i q^{60} +(5.15108 + 5.15108i) q^{61} +(-365.803 - 365.803i) q^{62} +(-211.906 + 211.906i) q^{63} -64.0000 q^{64} +(52.7224 - 52.7224i) q^{65} -30.6613i q^{66} +314.116 q^{67} +(100.428 + 261.767i) q^{68} +482.549 q^{69} -270.675i q^{70} +(-67.9639 + 67.9639i) q^{71} -72.0000 q^{72} +(717.292 - 717.292i) q^{73} +(-435.368 - 435.368i) q^{74} +(-230.121 - 230.121i) q^{75} +267.312i q^{76} -170.159i q^{77} +(-77.8296 - 77.8296i) q^{78} +(7.15665 + 7.15665i) q^{79} +(45.9840 - 45.9840i) q^{80} -81.0000 q^{81} +(396.720 - 396.720i) q^{82} -66.0553i q^{83} -399.574 q^{84} +(-260.237 - 115.922i) q^{85} +656.661 q^{86} +512.273i q^{87} +(28.9078 - 28.9078i) q^{88} +1499.70 q^{89} +(51.7320 - 51.7320i) q^{90} +(-431.927 - 431.927i) q^{91} +(454.951 + 454.951i) q^{92} -775.986i q^{93} -111.057i q^{94} +(-192.063 - 192.063i) q^{95} +(-67.8823 - 67.8823i) q^{96} +(-143.219 + 143.219i) q^{97} -1531.49 q^{98} +(32.5212 - 32.5212i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 48 q^{4} + 16 q^{5} - 12 q^{7} + 32 q^{10} - 32 q^{11} - 68 q^{13} + 24 q^{14} + 192 q^{16} + 64 q^{17} + 216 q^{18} - 64 q^{20} - 168 q^{21} + 64 q^{22} - 112 q^{23} + 48 q^{28} - 296 q^{29} - 168 q^{30}+ \cdots - 288 q^{99}+O(q^{100}) $ 12 * q - 48 * q^4 + 16 * q^5 - 12 * q^7 + 32 * q^10 - 32 * q^11 - 68 * q^13 + 24 * q^14 + 192 * q^16 + 64 * q^17 + 216 * q^18 - 64 * q^20 - 168 * q^21 + 64 * q^22 - 112 * q^23 + 48 * q^28 - 296 * q^29 - 168 * q^30 + 520 * q^31 + 204 * q^33 + 144 * q^34 + 392 * q^35 - 828 * q^37 - 280 * q^38 + 312 * q^39 - 128 * q^40 + 8 * q^41 + 128 * q^44 - 144 * q^45 + 224 * q^46 - 2920 * q^47 + 752 * q^50 + 420 * q^51 + 272 * q^52 + 1156 * q^55 - 96 * q^56 + 312 * q^57 - 592 * q^58 - 1124 * q^61 + 1040 * q^62 - 108 * q^63 - 768 * q^64 + 3288 * q^65 - 2008 * q^67 - 256 * q^68 + 468 * q^69 - 2184 * q^71 - 864 * q^72 + 2456 * q^73 - 1656 * q^74 - 192 * q^75 + 624 * q^78 + 2652 * q^79 + 256 * q^80 - 972 * q^81 - 16 * q^82 + 672 * q^84 + 3444 * q^85 - 184 * q^86 - 256 * q^88 + 5304 * q^89 + 288 * q^90 - 1420 * q^91 + 448 * q^92 - 2920 * q^95 + 2688 * q^97 - 4168 * q^98 - 288 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/102\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			2.00000i			0.707107i
$2$			2.00000i			0.707107i
$3$	−2.12132	+	2.12132i	−0.408248	+	0.408248i
$3$	−2.12132	+	2.12132i	−0.408248	+	0.408248i
$4$	−4.00000			−0.500000
$5$	2.87400	−	2.87400i	0.257058	−	0.257058i	−0.566798	−	0.823857i	$-0.691818\pi$
$5$	2.87400	−	2.87400i	0.257058	−	0.257058i	0.823857	+	0.566798i	$0.191818\pi$
$6$	−4.24264	−	4.24264i	−0.288675	−	0.288675i
$7$	−23.5451	−	23.5451i	−1.27132	−	1.27132i	−0.945397	−	0.325921i	$-0.894326\pi$
$7$	−23.5451	−	23.5451i	−1.27132	−	1.27132i	−0.325921	−	0.945397i	$-0.605674\pi$
$8$		−	8.00000i		−	0.353553i
$9$		−	9.00000i		−	0.333333i
$10$	5.74799	+	5.74799i	0.181768	+	0.181768i
$11$	3.61347	+	3.61347i	0.0990457	+	0.0990457i	0.754893	−	0.655848i	$-0.227689\pi$
$11$	3.61347	+	3.61347i	0.0990457	+	0.0990457i	−0.655848	+	0.754893i	$0.727689\pi$
$12$	8.48528	−	8.48528i	0.204124	−	0.204124i
$13$	18.3446			0.391376			0.195688	−	0.980666i	$-0.437306\pi$
$13$	18.3446			0.391376			0.195688	+	0.980666i	$0.437306\pi$
$14$	47.0903	−	47.0903i	0.898958	−	0.898958i
$15$			12.1933i			0.209887i
$16$	16.0000			0.250000
$17$	−25.1071	−	65.4418i	−0.358198	−	0.933646i
$17$	−25.1071	−	65.4418i	−0.358198	−	0.933646i
$18$	18.0000			0.235702
$19$		−	66.8279i		−	0.806914i	−0.914998	−	0.403457i	$-0.867808\pi$
$19$		−	66.8279i		−	0.806914i	0.914998	−	0.403457i	$-0.132192\pi$
$20$	−11.4960	+	11.4960i	−0.128529	+	0.128529i
$21$	99.8936			1.03803
$22$	−7.22694	+	7.22694i	−0.0700359	+	0.0700359i
$23$	−113.738	−	113.738i	−1.03113	−	1.03113i	−0.999500	−	0.0316293i	$-0.989930\pi$
$23$	−113.738	−	113.738i	−1.03113	−	1.03113i	−0.0316293	−	0.999500i	$-0.510070\pi$
$24$	16.9706	+	16.9706i	0.144338	+	0.144338i
$25$			108.480i			0.867842i
$26$			36.6892i			0.276744i
$27$	19.0919	+	19.0919i	0.136083	+	0.136083i
$28$	94.1806	+	94.1806i	0.635659	+	0.635659i
$29$	120.744	−	120.744i	0.773157	−	0.773157i	−0.205500	−	0.978657i	$-0.565882\pi$
$29$	120.744	−	120.744i	0.773157	−	0.773157i	0.978657	+	0.205500i	$0.0658820\pi$
$30$	−24.3867			−0.148413
$31$	−182.902	+	182.902i	−1.05968	+	1.05968i	−0.0615791	+	0.998102i	$0.519614\pi$
$31$	−182.902	+	182.902i	−1.05968	+	1.05968i	−0.998102	+	0.0615791i	$0.980386\pi$
$32$			32.0000i			0.176777i
$33$	−15.3307			−0.0808704
$34$	130.884	−	50.2142i	0.660187	−	0.253284i
$35$	−135.337			−0.653605
$36$			36.0000i			0.166667i
$37$	−217.684	+	217.684i	−0.967216	+	0.967216i	−0.999479	−	0.0322632i	$-0.989729\pi$
$37$	−217.684	+	217.684i	−0.967216	+	0.967216i	0.0322632	+	0.999479i	$0.489729\pi$
$38$	133.656			0.570575
$39$	−38.9148	+	38.9148i	−0.159778	+	0.159778i
$40$	−22.9920	−	22.9920i	−0.0908838	−	0.0908838i
$41$	−198.360	−	198.360i	−0.755575	−	0.755575i	0.219938	−	0.975514i	$-0.429414\pi$
$41$	−198.360	−	198.360i	−0.755575	−	0.755575i	−0.975514	+	0.219938i	$0.929414\pi$
$42$			199.787i			0.733996i
$43$		−	328.331i		−	1.16442i	−0.813039	−	0.582209i	$-0.802189\pi$
$43$		−	328.331i		−	1.16442i	0.813039	−	0.582209i	$-0.197811\pi$
$44$	−14.4539	−	14.4539i	−0.0495228	−	0.0495228i
$45$	−25.8660	−	25.8660i	−0.0856860	−	0.0856860i
$46$	227.476	−	227.476i	0.729118	−	0.729118i
$47$	−55.5285			−0.172333			−0.0861666	−	0.996281i	$-0.527462\pi$
$47$	−55.5285			−0.172333			−0.0861666	+	0.996281i	$0.527462\pi$
$48$	−33.9411	+	33.9411i	−0.102062	+	0.102062i
$49$			765.747i			2.23250i
$50$	−216.961			−0.613657
$51$	192.083	+	85.5628i	0.527393	+	0.234925i
$52$	−73.3785			−0.195688
$53$			233.093i			0.604108i	0.953291	+	0.302054i	$0.0976723\pi$
$53$			233.093i			0.604108i	−0.953291	+	0.302054i	$0.902328\pi$
$54$	−38.1838	+	38.1838i	−0.0962250	+	0.0962250i
$55$	20.7702			0.0509210
$56$	−188.361	+	188.361i	−0.449479	+	0.449479i
$57$	141.763	+	141.763i	0.329421	+	0.329421i
$58$	241.488	+	241.488i	0.546705	+	0.546705i
$59$		−	182.149i		−	0.401928i	−0.979599	−	0.200964i	$-0.935593\pi$
$59$		−	182.149i		−	0.401928i	0.979599	−	0.200964i	$-0.0644075\pi$
$60$		−	48.7734i		−	0.104944i
$61$	5.15108	+	5.15108i	0.0108119	+	0.0108119i	0.712492	−	0.701680i	$-0.247566\pi$
$61$	5.15108	+	5.15108i	0.0108119	+	0.0108119i	−0.701680	+	0.712492i	$0.747566\pi$
$62$	−365.803	−	365.803i	−0.749308	−	0.749308i
$63$	−211.906	+	211.906i	−0.423773	+	0.423773i
$64$	−64.0000			−0.125000
$65$	52.7224	−	52.7224i	0.100606	−	0.100606i
$66$		−	30.6613i		−	0.0571840i
$67$	314.116			0.572767			0.286383	−	0.958115i	$-0.407547\pi$
$67$	314.116			0.572767			0.286383	+	0.958115i	$0.407547\pi$
$68$	100.428	+	261.767i	0.179099	+	0.466823i
$69$	482.549			0.841913
$70$		−	270.675i		−	0.462169i
$71$	−67.9639	+	67.9639i	−0.113603	+	0.113603i	−0.761623	−	0.648020i	$-0.775597\pi$
$71$	−67.9639	+	67.9639i	−0.113603	+	0.113603i	0.648020	+	0.761623i	$0.275597\pi$
$72$	−72.0000			−0.117851
$73$	717.292	−	717.292i	1.15004	−	1.15004i	0.163493	−	0.986545i	$-0.447724\pi$
$73$	717.292	−	717.292i	1.15004	−	1.15004i	0.986545	−	0.163493i	$-0.0522761\pi$
$74$	−435.368	−	435.368i	−0.683925	−	0.683925i
$75$	−230.121	−	230.121i	−0.354295	−	0.354295i
$76$			267.312i			0.403457i
$77$		−	170.159i		−	0.251837i
$78$	−77.8296	−	77.8296i	−0.112980	−	0.112980i
$79$	7.15665	+	7.15665i	0.0101922	+	0.0101922i	0.712185	−	0.701992i	$-0.247706\pi$
$79$	7.15665	+	7.15665i	0.0101922	+	0.0101922i	−0.701992	+	0.712185i	$0.747706\pi$
$80$	45.9840	−	45.9840i	0.0642645	−	0.0642645i
$81$	−81.0000			−0.111111
$82$	396.720	−	396.720i	0.534272	−	0.534272i
$83$		−	66.0553i		−	0.0873555i	−0.999046	−	0.0436778i	$-0.986093\pi$
$83$		−	66.0553i		−	0.0873555i	0.999046	−	0.0436778i	$-0.0139075\pi$
$84$	−399.574			−0.519013
$85$	−260.237	−	115.922i	−0.332079	−	0.147923i
$86$	656.661			0.823367
$87$			512.273i			0.631280i
$88$	28.9078	−	28.9078i	0.0350179	−	0.0350179i
$89$	1499.70			1.78616			0.893081	−	0.449897i	$-0.148539\pi$
$89$	1499.70			1.78616			0.893081	+	0.449897i	$0.148539\pi$
$90$	51.7320	−	51.7320i	0.0605892	−	0.0605892i
$91$	−431.927	−	431.927i	−0.497563	−	0.497563i
$92$	454.951	+	454.951i	0.515564	+	0.515564i
$93$		−	775.986i		−	0.865226i
$94$		−	111.057i		−	0.121858i
$95$	−192.063	−	192.063i	−0.207424	−	0.207424i
$96$	−67.8823	−	67.8823i	−0.0721688	−	0.0721688i
$97$	−143.219	+	143.219i	−0.149914	+	0.149914i	−0.778080	−	0.628166i	$-0.783806\pi$
$97$	−143.219	+	143.219i	−0.149914	+	0.149914i	0.628166	+	0.778080i	$0.283806\pi$
$98$	−1531.49			−1.57862
$99$	32.5212	−	32.5212i	0.0330152	−	0.0330152i
$100$		−	433.921i		−	0.433921i
$101$	493.172			0.485866			0.242933	−	0.970043i	$-0.421891\pi$
$101$	493.172			0.485866			0.242933	+	0.970043i	$0.421891\pi$
$102$	−171.126	+	384.167i	−0.166117	+	0.372923i
$103$	−1263.90			−1.20909			−0.604544	−	0.796572i	$-0.706645\pi$
$103$	−1263.90			−1.20909			−0.604544	+	0.796572i	$0.706645\pi$
$104$		−	146.757i		−	0.138372i
$105$	287.094	−	287.094i	0.266833	−	0.266833i
$106$	−466.185			−0.427169
$107$	1209.48	−	1209.48i	1.09275	−	1.09275i	0.0975185	−	0.995234i	$-0.468909\pi$
$107$	1209.48	−	1209.48i	1.09275	−	1.09275i	0.995234	−	0.0975185i	$-0.0310905\pi$
$108$	−76.3675	−	76.3675i	−0.0680414	−	0.0680414i
$109$	1217.82	+	1217.82i	1.07015	+	1.07015i	0.997346	+	0.0728014i	$0.0231939\pi$
$109$	1217.82	+	1217.82i	1.07015	+	1.07015i	0.0728014	+	0.997346i	$0.476806\pi$
$110$			41.5404i			0.0360066i
$111$		−	923.554i		−	0.789729i
$112$	−376.722	−	376.722i	−0.317830	−	0.317830i
$113$	−778.737	−	778.737i	−0.648296	−	0.648296i	0.304285	−	0.952581i	$-0.401582\pi$
$113$	−778.737	−	778.737i	−0.648296	−	0.648296i	−0.952581	+	0.304285i	$0.901582\pi$
$114$	−283.527	+	283.527i	−0.232936	+	0.232936i
$115$	−653.764			−0.530120
$116$	−482.975	+	482.975i	−0.386579	+	0.386579i
$117$		−	165.102i		−	0.130459i
$118$	364.298			0.284206
$119$	−949.686	+	2131.99i	−0.731576	+	1.64234i
$120$	97.5467			0.0742063
$121$		−	1304.89i		−	0.980380i
$122$	−10.3022	+	10.3022i	−0.00764519	+	0.00764519i
$123$	841.569			0.616925
$124$	731.607	−	731.607i	0.529841	−	0.529841i
$125$	671.022	+	671.022i	0.480144	+	0.480144i
$126$	−423.813	−	423.813i	−0.299653	−	0.299653i
$127$			611.357i			0.427159i	0.976926	+	0.213579i	$0.0685122\pi$
$127$			611.357i			0.427159i	−0.976926	+	0.213579i	$0.931488\pi$
$128$		−	128.000i		−	0.0883883i
$129$	696.494	+	696.494i	0.475371	+	0.475371i
$130$	105.445	+	105.445i	0.0711394	+	0.0711394i
$131$	−1375.17	+	1375.17i	−0.917171	+	0.917171i	−0.996823	−	0.0796522i	$-0.974619\pi$
$131$	−1375.17	+	1375.17i	−0.917171	+	0.917171i	0.0796522	+	0.996823i	$0.474619\pi$
$132$	61.3226			0.0404352
$133$	−1573.47	+	1573.47i	−1.02584	+	1.02584i
$134$			628.232i			0.405007i
$135$	109.740			0.0699624
$136$	−523.535	+	200.857i	−0.330094	+	0.126642i
$137$	2208.72			1.37740			0.688700	−	0.725046i	$-0.258182\pi$
$137$	2208.72			1.37740			0.688700	+	0.725046i	$0.258182\pi$
$138$			965.097i			0.595323i
$139$	−949.032	+	949.032i	−0.579107	+	0.579107i	−0.934657	−	0.355550i	$-0.884293\pi$
$139$	−949.032	+	949.032i	−0.579107	+	0.579107i	0.355550	+	0.934657i	$0.384293\pi$
$140$	541.349			0.326803
$141$	117.794	−	117.794i	0.0703547	−	0.0703547i
$142$	−135.928	−	135.928i	−0.0803297	−	0.0803297i
$143$	66.2877	+	66.2877i	0.0387641	+	0.0387641i
$144$		−	144.000i		−	0.0833333i
$145$		−	694.035i		−	0.397493i
$146$	1434.58	+	1434.58i	0.813199	+	0.813199i
$147$	−1624.40	−	1624.40i	−0.911414	−	0.911414i
$148$	870.735	−	870.735i	0.483608	−	0.483608i
$149$	10.3414			0.00568590			0.00284295	−	0.999996i	$-0.499095\pi$
$149$	10.3414			0.00568590			0.00284295	+	0.999996i	$0.499095\pi$
$150$	460.243	−	460.243i	0.250524	−	0.250524i
$151$			1952.58i			1.05231i	0.850389	+	0.526155i	$0.176367\pi$
$151$			1952.58i			1.05231i	−0.850389	+	0.526155i	$0.823633\pi$
$152$	−534.623			−0.285287
$153$	−588.976	+	225.964i	−0.311215	+	0.119399i
$154$	340.319			0.178076
$155$			1051.32i			0.544799i
$156$	155.659	−	155.659i	0.0798892	−	0.0798892i
$157$	−214.205			−0.108888			−0.0544440	−	0.998517i	$-0.517339\pi$
$157$	−214.205			−0.108888			−0.0544440	+	0.998517i	$0.517339\pi$
$158$	−14.3133	+	14.3133i	−0.00720699	+	0.00720699i
$159$	−494.464	−	494.464i	−0.246626	−	0.246626i
$160$	91.9679	+	91.9679i	0.0454419	+	0.0454419i
$161$			5355.94i			2.62179i
$162$		−	162.000i		−	0.0785674i
$163$	−1039.61	−	1039.61i	−0.499560	−	0.499560i	0.411741	−	0.911301i	$-0.364921\pi$
$163$	−1039.61	−	1039.61i	−0.499560	−	0.499560i	−0.911301	+	0.411741i	$0.864921\pi$
$164$	793.439	+	793.439i	0.377788	+	0.377788i
$165$	−44.0603	+	44.0603i	−0.0207884	+	0.0207884i
$166$	132.111			0.0617697
$167$	2766.20	−	2766.20i	1.28176	−	1.28176i	0.342101	−	0.939663i	$-0.388862\pi$
$167$	2766.20	−	2766.20i	1.28176	−	1.28176i	0.939663	−	0.342101i	$-0.111138\pi$
$168$		−	799.149i		−	0.366998i
$169$	−1860.47			−0.846825
$170$	231.844	−	520.475i	0.104598	−	0.234815i
$171$	−601.451			−0.268971
$172$			1313.32i			0.582209i
$173$	1142.19	−	1142.19i	0.501958	−	0.501958i	−0.410088	−	0.912046i	$-0.634502\pi$
$173$	1142.19	−	1142.19i	0.501958	−	0.501958i	0.912046	+	0.410088i	$0.134502\pi$
$174$	−1024.55			−0.446383
$175$	2554.18	−	2554.18i	1.10330	−	1.10330i
$176$	57.8155	+	57.8155i	0.0247614	+	0.0247614i
$177$	386.396	+	386.396i	0.164086	+	0.164086i
$178$			2999.41i			1.26301i
$179$			40.4870i			0.0169058i	0.999964	+	0.00845290i	$0.00269068\pi$
$179$			40.4870i			0.0169058i	−0.999964	+	0.00845290i	$0.997309\pi$
$180$	103.464	+	103.464i	0.0428430	+	0.0428430i
$181$	−1189.85	−	1189.85i	−0.488624	−	0.488624i	0.419248	−	0.907872i	$-0.362294\pi$
$181$	−1189.85	−	1189.85i	−0.488624	−	0.488624i	−0.907872	+	0.419248i	$0.862294\pi$
$182$	863.853	−	863.853i	0.351830	−	0.351830i
$183$	−21.8542			−0.00882791
$184$	−909.902	+	909.902i	−0.364559	+	0.364559i
$185$			1251.25i			0.497262i
$186$	1551.97			0.611807
$187$	145.748	−	327.196i	0.0569955	−	0.127952i
$188$	222.114			0.0861666
$189$		−	899.042i		−	0.346009i
$190$	384.127	−	384.127i	0.146671	−	0.146671i
$191$	−1691.14			−0.640663			−0.320332	−	0.947305i	$-0.603794\pi$
$191$	−1691.14			−0.640663			−0.320332	+	0.947305i	$0.603794\pi$
$192$	135.765	−	135.765i	0.0510310	−	0.0510310i
$193$	−2474.02	−	2474.02i	−0.922713	−	0.922713i	0.0745076	−	0.997220i	$-0.476261\pi$
$193$	−2474.02	−	2474.02i	−0.922713	−	0.922713i	−0.997220	+	0.0745076i	$0.976261\pi$
$194$	−286.438	−	286.438i	−0.106005	−	0.106005i
$195$			223.682i			0.0821447i
$196$		−	3062.99i		−	1.11625i
$197$	−3089.38	−	3089.38i	−1.11730	−	1.11730i	−0.992135	−	0.125170i	$-0.960052\pi$
$197$	−3089.38	−	3089.38i	−1.11730	−	1.11730i	−0.125170	−	0.992135i	$-0.539948\pi$
$198$	65.0425	+	65.0425i	0.0233453	+	0.0233453i
$199$	2374.63	−	2374.63i	0.845894	−	0.845894i	−0.143723	−	0.989618i	$-0.545908\pi$
$199$	2374.63	−	2374.63i	0.845894	−	0.845894i	0.989618	+	0.143723i	$0.0459076\pi$
$200$	867.842			0.306829
$201$	−666.341	+	666.341i	−0.233831	+	0.233831i
$202$			986.344i			0.343559i
$203$	−5685.86			−1.96586
$204$	−768.333	−	342.251i	−0.263697	−	0.117463i
$205$	−1140.17			−0.388454
$206$		−	2527.80i		−	0.854954i
$207$	−1023.64	+	1023.64i	−0.343710	+	0.343710i
$208$	293.514			0.0978439
$209$	241.481	−	241.481i	0.0799214	−	0.0799214i
$210$	574.188	+	574.188i	0.188680	+	0.188680i
$211$	−523.969	−	523.969i	−0.170955	−	0.170955i	0.616444	−	0.787399i	$-0.288573\pi$
$211$	−523.969	−	523.969i	−0.170955	−	0.170955i	−0.787399	+	0.616444i	$0.788573\pi$
$212$		−	932.370i		−	0.302054i
$213$		−	288.346i		−	0.0927567i
$214$	2418.95	+	2418.95i	0.772693	+	0.772693i
$215$	−943.621	−	943.621i	−0.299323	−	0.299323i
$216$	152.735	−	152.735i	0.0481125	−	0.0481125i
$217$	8612.89			2.69438
$218$	−2435.64	+	2435.64i	−0.756709	+	0.756709i
$219$			3043.21i			0.939002i
$220$	−83.0808			−0.0254605
$221$	−460.581	−	1200.51i	−0.140190	−	0.365406i
$222$	1847.11			0.558423
$223$			881.040i			0.264569i	0.991212	+	0.132284i	$0.0422312\pi$
$223$			881.040i			0.264569i	−0.991212	+	0.132284i	$0.957769\pi$
$224$	753.444	−	753.444i	0.224739	−	0.224739i
$225$	976.323			0.289281
$226$	1557.47	−	1557.47i	0.458414	−	0.458414i
$227$	−3868.14	−	3868.14i	−1.13100	−	1.13100i	−0.990011	−	0.140992i	$-0.954971\pi$
$227$	−3868.14	−	3868.14i	−1.13100	−	1.13100i	−0.140992	−	0.990011i	$-0.545029\pi$
$228$	−567.054	−	567.054i	−0.164711	−	0.164711i
$229$			4951.00i			1.42870i	0.699790	+	0.714348i	$0.253277\pi$
$229$			4951.00i			1.42870i	−0.699790	+	0.714348i	$0.746723\pi$
$230$		−	1307.53i		−	0.374852i
$231$	360.962	+	360.962i	0.102812	+	0.102812i
$232$	−965.951	−	965.951i	−0.273352	−	0.273352i
$233$	1249.74	−	1249.74i	0.351388	−	0.351388i	−0.509238	−	0.860626i	$-0.670073\pi$
$233$	1249.74	−	1249.74i	0.351388	−	0.351388i	0.860626	+	0.509238i	$0.170073\pi$
$234$	330.203			0.0922481
$235$	−159.589	+	159.589i	−0.0442996	+	0.0442996i
$236$			728.595i			0.200964i
$237$	−30.3631			−0.00832192
$238$	−4263.98	−	1899.37i	−1.16131	−	0.517303i
$239$	2643.27			0.715392			0.357696	−	0.933838i	$-0.383562\pi$
$239$	2643.27			0.715392			0.357696	+	0.933838i	$0.383562\pi$
$240$			195.093i			0.0524718i
$241$	2845.07	−	2845.07i	0.760444	−	0.760444i	−0.215958	−	0.976403i	$-0.569288\pi$
$241$	2845.07	−	2845.07i	0.760444	−	0.760444i	0.976403	+	0.215958i	$0.0692876\pi$
$242$	2609.77			0.693233
$243$	171.827	−	171.827i	0.0453609	−	0.0453609i
$244$	−20.6043	−	20.6043i	−0.00540597	−	0.00540597i
$245$	2200.76	+	2200.76i	0.573882	+	0.573882i
$246$			1683.14i			0.436232i
$247$		−	1225.93i		−	0.315807i
$248$	1463.21	+	1463.21i	0.374654	+	0.374654i
$249$	140.124	+	140.124i	0.0356627	+	0.0356627i
$250$	−1342.04	+	1342.04i	−0.339513	+	0.339513i
$251$	380.065			0.0955757			0.0477879	−	0.998858i	$-0.484783\pi$
$251$	380.065			0.0955757			0.0477879	+	0.998858i	$0.484783\pi$
$252$	847.625	−	847.625i	0.211886	−	0.211886i
$253$		−	821.976i		−	0.204258i
$254$	−1222.71			−0.302047
$255$	797.954	−	306.140i	0.195960	−	0.0751812i
$256$	256.000			0.0625000
$257$		−	5121.07i		−	1.24297i	−0.783426	−	0.621486i	$-0.786529\pi$
$257$		−	5121.07i		−	1.24297i	0.783426	−	0.621486i	$-0.213471\pi$
$258$	−1392.99	+	1392.99i	−0.336138	+	0.336138i
$259$	10250.8			2.45928
$260$	−210.890	+	210.890i	−0.0503031	+	0.0503031i
$261$	−1086.69	−	1086.69i	−0.257719	−	0.257719i
$262$	−2750.34	−	2750.34i	−0.648538	−	0.648538i
$263$			2525.04i			0.592016i	0.955185	+	0.296008i	$0.0956556\pi$
$263$			2525.04i			0.592016i	−0.955185	+	0.296008i	$0.904344\pi$
$264$			122.645i			0.0285920i
$265$	669.907	+	669.907i	0.155291	+	0.155291i
$266$	−3146.95	−	3146.95i	−0.725382	−	0.725382i
$267$	−3181.35	+	3181.35i	−0.729197	+	0.729197i
$268$	−1256.46			−0.286383
$269$	4090.68	−	4090.68i	0.927186	−	0.927186i	−0.0703371	−	0.997523i	$-0.522407\pi$
$269$	4090.68	−	4090.68i	0.927186	−	0.927186i	0.997523	+	0.0703371i	$0.0224075\pi$
$270$			219.480i			0.0494709i
$271$	−1478.94			−0.331511			−0.165755	−	0.986167i	$-0.553006\pi$
$271$	−1478.94			−0.331511			−0.165755	+	0.986167i	$0.553006\pi$
$272$	−401.714	−	1047.07i	−0.0895496	−	0.233411i
$273$	1832.51			0.406258
$274$			4417.45i			0.973970i
$275$	−391.990	+	391.990i	−0.0859560	+	0.0859560i
$276$	−1930.19			−0.420957
$277$	−4859.21	+	4859.21i	−1.05401	+	1.05401i	−0.0555587	+	0.998455i	$0.517694\pi$
$277$	−4859.21	+	4859.21i	−1.05401	+	1.05401i	−0.998455	+	0.0555587i	$0.982306\pi$
$278$	−1898.06	−	1898.06i	−0.409490	−	0.409490i
$279$	1646.12	+	1646.12i	0.353227	+	0.353227i
$280$			1082.70i			0.231084i
$281$			5263.80i			1.11748i	0.829343	+	0.558740i	$0.188715\pi$
$281$			5263.80i			1.11748i	−0.829343	+	0.558740i	$0.811285\pi$
$282$	235.587	+	235.587i	0.0497483	+	0.0497483i
$283$	1901.80	+	1901.80i	0.399471	+	0.399471i	0.878046	−	0.478576i	$-0.158847\pi$
$283$	1901.80	+	1901.80i	0.399471	+	0.399471i	−0.478576	+	0.878046i	$0.658847\pi$
$284$	271.856	−	271.856i	0.0568016	−	0.0568016i
$285$	814.855			0.169361
$286$	−132.575	+	132.575i	−0.0274103	+	0.0274103i
$287$			9340.82i			1.92115i
$288$	288.000			0.0589256
$289$	−3652.26	+	3286.11i	−0.743388	+	0.668861i
$290$	1388.07			0.281070
$291$		−	607.626i		−	0.122404i
$292$	−2869.17	+	2869.17i	−0.575019	+	0.575019i
$293$	−6076.26			−1.21153			−0.605767	−	0.795642i	$-0.707133\pi$
$293$	−6076.26			−1.21153			−0.605767	+	0.795642i	$0.707133\pi$
$294$	3248.79	−	3248.79i	0.644467	−	0.644467i
$295$	−523.495	−	523.495i	−0.103319	−	0.103319i
$296$	1741.47	+	1741.47i	0.341963	+	0.341963i
$297$			137.976i			0.0269568i
$298$			20.6828i			0.00402054i
$299$	−2086.48	−	2086.48i	−0.403559	−	0.403559i
$300$	920.486	+	920.486i	0.177148	+	0.177148i
$301$	−7730.59	+	7730.59i	−1.48034	+	1.48034i
$302$	−3905.16			−0.744096
$303$	−1046.18	+	1046.18i	−0.198354	+	0.198354i
$304$		−	1069.25i		−	0.201729i
$305$	29.6084			0.00555859
$306$	−451.928	−	1177.95i	−0.0844282	−	0.220062i
$307$	8431.56			1.56747			0.783737	−	0.621093i	$-0.213311\pi$
$307$	8431.56			1.56747			0.783737	+	0.621093i	$0.213311\pi$
$308$			680.637i			0.125919i
$309$	2681.14	−	2681.14i	0.493608	−	0.493608i
$310$	−2102.64			−0.385231
$311$	3483.80	−	3483.80i	0.635203	−	0.635203i	−0.314166	−	0.949368i	$-0.601725\pi$
$311$	3483.80	−	3483.80i	0.635203	−	0.635203i	0.949368	+	0.314166i	$0.101725\pi$
$312$	311.319	+	311.319i	0.0564902	+	0.0564902i
$313$	1862.01	+	1862.01i	0.336252	+	0.336252i	0.854955	−	0.518703i	$-0.173585\pi$
$313$	1862.01	+	1862.01i	0.336252	+	0.336252i	−0.518703	+	0.854955i	$0.673585\pi$
$314$		−	428.410i		−	0.0769954i
$315$			1218.04i			0.217868i
$316$	−28.6266	−	28.6266i	−0.00509611	−	0.00509611i
$317$	−7875.61	−	7875.61i	−1.39539	−	1.39539i	−0.812681	−	0.582709i	$-0.801993\pi$
$317$	−7875.61	−	7875.61i	−1.39539	−	1.39539i	−0.582709	−	0.812681i	$-0.698007\pi$
$318$	988.928	−	988.928i	0.174391	−	0.174391i
$319$	872.608			0.153156
$320$	−183.936	+	183.936i	−0.0321323	+	0.0321323i
$321$			5131.37i			0.892228i
$322$	−10711.9			−1.85388
$323$	−4373.34	+	1677.86i	−0.753372	+	0.289035i
$324$	324.000			0.0555556
$325$			1990.03i			0.339652i
$326$	2079.21	−	2079.21i	0.353242	−	0.353242i
$327$	−5166.78			−0.873772
$328$	−1586.88	+	1586.88i	−0.267136	+	0.267136i
$329$	1307.43	+	1307.43i	0.219090	+	0.219090i
$330$	−88.1205	−	88.1205i	−0.0146996	−	0.0146996i
$331$		−	10177.8i		−	1.69009i	−0.534695	−	0.845045i	$-0.679573\pi$
$331$		−	10177.8i		−	1.69009i	0.534695	−	0.845045i	$-0.320427\pi$
$332$			264.221i			0.0436778i
$333$	1959.15	+	1959.15i	0.322405	+	0.322405i
$334$	5532.39	+	5532.39i	0.906344	+	0.906344i
$335$	902.769	−	902.769i	0.147234	−	0.147234i
$336$	1598.30			0.259507
$337$	−5222.92	+	5222.92i	−0.844245	+	0.844245i	−0.989408	−	0.145163i	$-0.953629\pi$
$337$	−5222.92	+	5222.92i	−0.844245	+	0.844245i	0.145163	+	0.989408i	$0.453629\pi$
$338$		−	3720.95i		−	0.598796i
$339$	3303.90			0.529331
$340$	1040.95	+	463.687i	0.166039	+	0.0739617i
$341$	−1321.82			−0.209914
$342$		−	1202.90i		−	0.190192i
$343$	9953.64	−	9953.64i	1.56690	−	1.56690i
$344$	−2626.64			−0.411684
$345$	1386.84	−	1386.84i	0.216421	−	0.216421i
$346$	2284.37	+	2284.37i	0.354938	+	0.354938i
$347$	7248.96	+	7248.96i	1.12145	+	1.12145i	0.991523	+	0.129931i	$0.0414757\pi$
$347$	7248.96	+	7248.96i	1.12145	+	1.12145i	0.129931	+	0.991523i	$0.458524\pi$
$348$		−	2049.09i		−	0.315640i
$349$		−	11338.1i		−	1.73901i	−0.493924	−	0.869505i	$-0.664438\pi$
$349$		−	11338.1i		−	1.73901i	0.493924	−	0.869505i	$-0.335562\pi$
$350$	5108.37	+	5108.37i	0.780153	+	0.780153i
$351$	350.233	+	350.233i	0.0532595	+	0.0532595i
$352$	−115.631	+	115.631i	−0.0175090	+	0.0175090i
$353$	4609.39			0.694995			0.347497	−	0.937681i	$-0.387032\pi$
$353$	4609.39			0.694995			0.347497	+	0.937681i	$0.387032\pi$
$354$	−772.792	+	772.792i	−0.116027	+	0.116027i
$355$			390.656i			0.0584053i
$356$	−5998.82			−0.893081
$357$	−2508.04	−	6537.22i	−0.371819	−	0.969149i
$358$	−80.9740			−0.0119542
$359$			4521.15i			0.664673i	0.943161	+	0.332336i	$0.107837\pi$
$359$			4521.15i			0.664673i	−0.943161	+	0.332336i	$0.892163\pi$
$360$	−206.928	+	206.928i	−0.0302946	+	0.0302946i
$361$	2393.03			0.348889
$362$	2379.70	−	2379.70i	0.345509	−	0.345509i
$363$	2768.08	+	2768.08i	0.400238	+	0.400238i
$364$	1727.71	+	1727.71i	0.248781	+	0.248781i
$365$		−	4122.99i		−	0.591253i
$366$		−	43.7084i		−	0.00624227i
$367$	2778.51	+	2778.51i	0.395196	+	0.395196i	0.876535	−	0.481339i	$-0.159849\pi$
$367$	2778.51	+	2778.51i	0.395196	+	0.395196i	−0.481339	+	0.876535i	$0.659849\pi$
$368$	−1819.80	−	1819.80i	−0.257782	−	0.257782i
$369$	−1785.24	+	1785.24i	−0.251858	+	0.251858i
$370$	−2502.49			−0.351617
$371$	5488.20	−	5488.20i	0.768013	−	0.768013i
$372$			3103.95i			0.432613i
$373$	−9797.93			−1.36010			−0.680050	−	0.733165i	$-0.738042\pi$
$373$	−9797.93			−1.36010			−0.680050	+	0.733165i	$0.738042\pi$
$374$	654.392	+	291.496i	0.0904754	+	0.0403019i
$375$	−2846.90			−0.392036
$376$			444.228i			0.0609290i
$377$	2215.00	−	2215.00i	0.302595	−	0.302595i
$378$	1798.08			0.244665
$379$	7104.90	−	7104.90i	0.962940	−	0.962940i	−0.0363970	−	0.999337i	$-0.511588\pi$
$379$	7104.90	−	7104.90i	0.962940	−	0.962940i	0.999337	+	0.0363970i	$0.0115881\pi$
$380$	768.253	+	768.253i	0.103712	+	0.103712i
$381$	−1296.88	−	1296.88i	−0.174387	−	0.174387i
$382$		−	3382.28i		−	0.453017i
$383$		−	2856.38i		−	0.381081i	−0.981679	−	0.190541i	$-0.938976\pi$
$383$		−	2856.38i		−	0.381081i	0.981679	−	0.190541i	$-0.0610241\pi$
$384$	271.529	+	271.529i	0.0360844	+	0.0360844i
$385$	−489.037	−	489.037i	−0.0647368	−	0.0647368i
$386$	4948.03	−	4948.03i	0.652456	−	0.652456i
$387$	−2954.98			−0.388139
$388$	572.875	−	572.875i	0.0749571	−	0.0749571i
$389$			5479.16i			0.714150i	0.934076	+	0.357075i	$0.116226\pi$
$389$			5479.16i			0.714150i	−0.934076	+	0.357075i	$0.883774\pi$
$390$	−447.364			−0.0580851
$391$	−4587.58	+	10298.8i	−0.593360	+	1.33206i
$392$	6125.98			0.789308
$393$		−	5834.36i		−	0.748867i
$394$	6178.76	−	6178.76i	0.790054	−	0.790054i
$395$	41.1364			0.00523999
$396$	−130.085	+	130.085i	−0.0165076	+	0.0165076i
$397$	−7528.85	−	7528.85i	−0.951794	−	0.951794i	0.0470963	−	0.998890i	$-0.485003\pi$
$397$	−7528.85	−	7528.85i	−0.951794	−	0.951794i	−0.998890	+	0.0470963i	$0.985003\pi$
$398$	4749.26	+	4749.26i	0.598138	+	0.598138i
$399$		−	6675.68i		−	0.837599i
$400$			1735.68i			0.216961i
$401$	−1584.22	−	1584.22i	−0.197288	−	0.197288i	0.601549	−	0.798836i	$-0.294551\pi$
$401$	−1584.22	−	1584.22i	−0.197288	−	0.197288i	−0.798836	+	0.601549i	$0.794551\pi$
$402$	−1332.68	−	1332.68i	−0.165344	−	0.165344i
$403$	−3355.26	+	3355.26i	−0.414733	+	0.414733i
$404$	−1972.69			−0.242933
$405$	−232.794	+	232.794i	−0.0285620	+	0.0285620i
$406$		−	11371.7i		−	1.39007i
$407$	−1573.19			−0.191597
$408$	684.503	−	1536.67i	0.0830586	−	0.186462i
$409$	−5233.25			−0.632684			−0.316342	−	0.948645i	$-0.602455\pi$
$409$	−5233.25			−0.632684			−0.316342	+	0.948645i	$0.602455\pi$
$410$		−	2280.34i		−	0.274678i
$411$	−4685.41	+	4685.41i	−0.562322	+	0.562322i
$412$	5055.61			0.604544
$413$	−4288.72	+	4288.72i	−0.510979	+	0.510979i
$414$	−2047.28	−	2047.28i	−0.243039	−	0.243039i
$415$	−189.843	−	189.843i	−0.0224554	−	0.0224554i
$416$			587.028i			0.0691861i
$417$		−	4026.40i		−	0.472839i
$418$	482.961	+	482.961i	0.0565129	+	0.0565129i
$419$	12061.2	+	12061.2i	1.40627	+	1.40627i	0.777985	+	0.628283i	$0.216242\pi$
$419$	12061.2	+	12061.2i	1.40627	+	1.40627i	0.628283	+	0.777985i	$0.283758\pi$
$420$	−1148.38	+	1148.38i	−0.133417	+	0.133417i
$421$	1995.98			0.231065			0.115532	−	0.993304i	$-0.463143\pi$
$421$	1995.98			0.231065			0.115532	+	0.993304i	$0.463143\pi$
$422$	1047.94	−	1047.94i	0.120883	−	0.120883i
$423$			499.756i			0.0574444i
$424$	1864.74			0.213584
$425$	7099.15	−	2723.63i	0.810257	−	0.310860i
$426$	576.693			0.0655889
$427$		−	242.566i		−	0.0274908i
$428$	−4837.91	+	4837.91i	−0.546376	+	0.546376i
$429$	−281.235			−0.0316507
$430$	1887.24	−	1887.24i	0.211653	−	0.211653i
$431$	−10257.3	−	10257.3i	−1.14635	−	1.14635i	−0.987265	−	0.159087i	$-0.949145\pi$
$431$	−10257.3	−	10257.3i	−1.14635	−	1.14635i	−0.159087	−	0.987265i	$-0.550855\pi$
$432$	305.470	+	305.470i	0.0340207	+	0.0340207i
$433$		−	1017.03i		−	0.112876i	−0.998406	−	0.0564378i	$-0.982026\pi$
$433$		−	1017.03i		−	0.112876i	0.998406	−	0.0564378i	$-0.0179743\pi$
$434$			17225.8i			1.90522i
$435$	1472.27	+	1472.27i	0.162276	+	0.162276i
$436$	−4871.29	−	4871.29i	−0.535074	−	0.535074i
$437$	−7600.86	+	7600.86i	−0.832033	+	0.832033i
$438$	−6086.43			−0.663974
$439$	−1311.08	+	1311.08i	−0.142539	+	0.142539i	−0.774775	−	0.632237i	$-0.782137\pi$
$439$	−1311.08	+	1311.08i	−0.142539	+	0.142539i	0.632237	+	0.774775i	$0.282137\pi$
$440$		−	166.162i		−	0.0180033i
$441$	6891.73			0.744166
$442$	2401.01	−	921.161i	0.258381	−	0.0991294i
$443$	−4297.84			−0.460941			−0.230470	−	0.973079i	$-0.574026\pi$
$443$	−4297.84			−0.460941			−0.230470	+	0.973079i	$0.574026\pi$
$444$			3694.22i			0.394864i
$445$	4310.15	−	4310.15i	0.459147	−	0.459147i
$446$	−1762.08			−0.187078
$447$	−21.9374	+	21.9374i	−0.00232126	+	0.00232126i
$448$	1506.89	+	1506.89i	0.158915	+	0.158915i
$449$	−1352.33	−	1352.33i	−0.142139	−	0.142139i	0.632457	−	0.774596i	$-0.282047\pi$
$449$	−1352.33	−	1352.33i	−0.142139	−	0.142139i	−0.774596	+	0.632457i	$0.782047\pi$
$450$			1952.65i			0.204552i
$451$		−	1433.53i		−	0.149673i
$452$	3114.95	+	3114.95i	0.324148	+	0.324148i
$453$	−4142.05	−	4142.05i	−0.429604	−	0.429604i
$454$	7736.28	−	7736.28i	0.799740	−	0.799740i
$455$	−2482.71			−0.255805
$456$	1134.11	−	1134.11i	0.116468	−	0.116468i
$457$			2234.77i			0.228749i	0.993438	+	0.114374i	$0.0364863\pi$
$457$			2234.77i			0.228749i	−0.993438	+	0.114374i	$0.963514\pi$
$458$	−9902.01			−1.01024
$459$	770.065	−	1728.75i	0.0783084	−	0.175798i
$460$	2615.06			0.265060
$461$			149.634i			0.0151174i	0.999971	+	0.00755871i	$0.00240604\pi$
$461$			149.634i			0.0151174i	−0.999971	+	0.00755871i	$0.997594\pi$
$462$	−721.925	+	721.925i	−0.0726991	+	0.0726991i
$463$	−4732.09			−0.474987			−0.237494	−	0.971389i	$-0.576326\pi$
$463$	−4732.09			−0.474987			−0.237494	+	0.971389i	$0.576326\pi$
$464$	1931.90	−	1931.90i	0.193289	−	0.193289i
$465$	−2230.18	−	2230.18i	−0.222413	−	0.222413i
$466$	2499.49	+	2499.49i	0.248469	+	0.248469i
$467$			2749.01i			0.272396i	0.990682	+	0.136198i	$0.0434884\pi$
$467$			2749.01i			0.272396i	−0.990682	+	0.136198i	$0.956512\pi$
$468$			660.406i			0.0652293i
$469$	−7395.90	−	7395.90i	−0.728169	−	0.728169i
$470$	−319.177	−	319.177i	−0.0313246	−	0.0313246i
$471$	454.397	−	454.397i	0.0444533	−	0.0444533i
$472$	−1457.19			−0.142103
$473$	1186.41	−	1186.41i	0.115330	−	0.115330i
$474$		−	60.7262i		−	0.00588449i
$475$	7249.51			0.700274
$476$	3798.74	−	8527.95i	0.365788	−	0.821172i
$477$	2097.83			0.201369
$478$			5286.54i			0.505859i
$479$	−2976.64	+	2976.64i	−0.283938	+	0.283938i	−0.834677	−	0.550739i	$-0.814346\pi$
$479$	−2976.64	+	2976.64i	−0.283938	+	0.283938i	0.550739	+	0.834677i	$0.314346\pi$
$480$	−390.187			−0.0371031
$481$	−3993.33	+	3993.33i	−0.378545	+	0.378545i
$482$	5690.14	+	5690.14i	0.537715	+	0.537715i
$483$	−11361.7	−	11361.7i	−1.07034	−	1.07034i
$484$			5219.54i			0.490190i
$485$			823.221i			0.0770733i
$486$	343.654	+	343.654i	0.0320750	+	0.0320750i
$487$	11877.6	+	11877.6i	1.10519	+	1.10519i	0.993774	+	0.111414i	$0.0355380\pi$
$487$	11877.6	+	11877.6i	1.10519	+	1.10519i	0.111414	+	0.993774i	$0.464462\pi$
$488$	41.2086	−	41.2086i	0.00382260	−	0.00382260i
$489$	4410.68			0.407889
$490$	−4401.51	+	4401.51i	−0.405796	+	0.405796i
$491$			10904.6i			1.00228i	0.865367	+	0.501138i	$0.167085\pi$
$491$			10904.6i			1.00228i	−0.865367	+	0.501138i	$0.832915\pi$
$492$	−3366.28			−0.308462
$493$	−10933.2	−	4870.17i	−0.998799	−	0.444911i
$494$	2451.87			0.223309
$495$		−	186.932i		−	0.0169737i
$496$	−2926.43	+	2926.43i	−0.264920	+	0.264920i
$497$	3200.44			0.288852
$498$	−280.249	+	280.249i	−0.0252174	+	0.0252174i
$499$	1827.30	+	1827.30i	0.163930	+	0.163930i	0.784305	−	0.620375i	$-0.213020\pi$
$499$	1827.30	+	1827.30i	0.163930	+	0.163930i	−0.620375	+	0.784305i	$0.713020\pi$
$500$	−2684.09	−	2684.09i	−0.240072	−	0.240072i
$501$			11736.0i			1.04656i
$502$			760.131i			0.0675823i
$503$	7741.93	+	7741.93i	0.686274	+	0.686274i	0.961406	−	0.275133i	$-0.0887218\pi$
$503$	7741.93	+	7741.93i	0.686274	+	0.686274i	−0.275133	+	0.961406i	$0.588722\pi$
$504$	1695.25	+	1695.25i	0.149826	+	0.149826i
$505$	1417.38	−	1417.38i	0.124896	−	0.124896i
$506$	1643.95			0.144432
$507$	3946.66	−	3946.66i	0.345715	−	0.345715i
$508$		−	2445.43i		−	0.213579i
$509$	134.612			0.0117221			0.00586106	−	0.999983i	$-0.498134\pi$
$509$	134.612			0.0117221			0.00586106	+	0.999983i	$0.498134\pi$
$510$	612.279	+	1595.91i	0.0531611	+	0.138565i
$511$	−33777.5			−2.92413
$512$			512.000i			0.0441942i
$513$	1275.87	−	1275.87i	0.109807	−	0.109807i
$514$	10242.1			0.878913
$515$	−3632.45	+	3632.45i	−0.310806	+	0.310806i
$516$	−2785.98	−	2785.98i	−0.237686	−	0.237686i
$517$	−200.650	−	200.650i	−0.0170689	−	0.0170689i
$518$			20501.6i			1.73897i
$519$			4845.88i			0.409847i
$520$	−421.779	−	421.779i	−0.0355697	−	0.0355697i
$521$	11455.0	+	11455.0i	0.963248	+	0.963248i	0.999348	−	0.0361000i	$-0.0114935\pi$
$521$	11455.0	+	11455.0i	0.963248	+	0.963248i	−0.0361000	+	0.999348i	$0.511493\pi$
$522$	2173.39	−	2173.39i	0.182235	−	0.182235i
$523$	21230.4			1.77503			0.887516	−	0.460778i	$-0.152429\pi$
$523$	21230.4			1.77503			0.887516	+	0.460778i	$0.152429\pi$
$524$	5500.69	−	5500.69i	0.458585	−	0.458585i
$525$			10836.5i			0.900844i
$526$	−5050.07			−0.418619
$527$	16561.6	+	7377.29i	1.36894	+	0.609791i
$528$	−245.290			−0.0202176
$529$			13705.6i			1.12645i
$530$	−1339.81	+	1339.81i	−0.109807	+	0.109807i
$531$	−1639.34			−0.133976
$532$	6293.89	−	6293.89i	0.512922	−	0.512922i
$533$	−3638.84	−	3638.84i	−0.295714	−	0.295714i
$534$	−6362.71	−	6362.71i	−0.515620	−	0.515620i
$535$		−	6952.06i		−	0.561802i
$536$		−	2512.93i		−	0.202504i
$537$	−85.8859	−	85.8859i	−0.00690177	−	0.00690177i
$538$	8181.36	+	8181.36i	0.655620	+	0.655620i
$539$	−2767.00	+	2767.00i	−0.221119	+	0.221119i
$540$	−438.960			−0.0349812
$541$	−6203.13	+	6203.13i	−0.492964	+	0.492964i	−0.909239	−	0.416275i	$-0.863335\pi$
$541$	−6203.13	+	6203.13i	−0.492964	+	0.492964i	0.416275	+	0.909239i	$0.363335\pi$
$542$		−	2957.89i		−	0.234413i
$543$	5048.11			0.398960
$544$	2094.14	−	803.428i	0.165047	−	0.0633211i
$545$	7000.03			0.550180
$546$			3665.02i			0.287268i
$547$	−5805.91	+	5805.91i	−0.453826	+	0.453826i	−0.896622	−	0.442796i	$-0.853986\pi$
$547$	−5805.91	+	5805.91i	−0.453826	+	0.453826i	0.442796	+	0.896622i	$0.353986\pi$
$548$	−8834.89			−0.688700
$549$	46.3597	−	46.3597i	0.00360398	−	0.00360398i
$550$	−783.980	−	783.980i	−0.0607801	−	0.0607801i
$551$	−8069.06	−	8069.06i	−0.623872	−	0.623872i
$552$		−	3860.39i		−	0.297661i
$553$		−	337.009i		−	0.0259151i
$554$	−9718.43	−	9718.43i	−0.745301	−	0.745301i
$555$	−2654.29	−	2654.29i	−0.203006	−	0.203006i
$556$	3796.13	−	3796.13i	0.289553	−	0.289553i
$557$	644.069			0.0489948			0.0244974	−	0.999700i	$-0.492201\pi$
$557$	644.069			0.0489948			0.0244974	+	0.999700i	$0.492201\pi$
$558$	−3292.23	+	3292.23i	−0.249769	+	0.249769i
$559$		−	6023.10i		−	0.455725i
$560$	−2165.40			−0.163401
$561$	384.909	+	1003.27i	0.0289677	+	0.0755043i
$562$	−10527.6			−0.790178
$563$		−	22872.8i		−	1.71221i	−0.516805	−	0.856103i	$-0.672879\pi$
$563$		−	22872.8i		−	1.71221i	0.516805	−	0.856103i	$-0.327121\pi$
$564$	−471.175	+	471.175i	−0.0351774	+	0.0351774i
$565$	−4476.18			−0.333299
$566$	−3803.60	+	3803.60i	−0.282468	+	0.282468i
$567$	1907.16	+	1907.16i	0.141258	+	0.141258i
$568$	543.711	+	543.711i	0.0401648	+	0.0401648i
$569$		−	13513.0i		−	0.995599i	−0.867292	−	0.497800i	$-0.834142\pi$
$569$		−	13513.0i		−	0.995599i	0.867292	−	0.497800i	$-0.165858\pi$
$570$			1629.71i			0.119756i
$571$	−11974.6	−	11974.6i	−0.877622	−	0.877622i	0.115666	−	0.993288i	$-0.463100\pi$
$571$	−11974.6	−	11974.6i	−0.877622	−	0.877622i	−0.993288	+	0.115666i	$0.963100\pi$
$572$	−265.151	−	265.151i	−0.0193820	−	0.0193820i
$573$	3587.45	−	3587.45i	0.261550	−	0.261550i
$574$	−18681.6			−1.35846
$575$	12338.3	−	12338.3i	0.894857	−	0.894857i
$576$			576.000i			0.0416667i
$577$	18805.8			1.35684			0.678420	−	0.734674i	$-0.262665\pi$
$577$	18805.8			1.35684			0.678420	+	0.734674i	$0.262665\pi$
$578$	−6572.22	−	7304.53i	−0.472956	−	0.525655i
$579$	10496.4			0.753392
$580$			2776.14i			0.198746i
$581$	−1555.28	+	1555.28i	−0.111057	+	0.111057i
$582$	1215.25			0.0865530
$583$	−842.273	+	842.273i	−0.0598343	+	0.0598343i
$584$	−5738.34	−	5738.34i	−0.406600	−	0.406600i
$585$	−474.502	−	474.502i	−0.0335354	−	0.0335354i
$586$		−	12152.5i		−	0.856683i
$587$		−	8038.76i		−	0.565239i	−0.959232	−	0.282619i	$-0.908797\pi$
$587$		−	8038.76i		−	0.565239i	0.959232	−	0.282619i	$-0.0912034\pi$
$588$	6497.58	+	6497.58i	0.455707	+	0.455707i
$589$	12222.9	+	12222.9i	0.855072	+	0.855072i
$590$	1046.99	−	1046.99i	0.0730575	−	0.0730575i
$591$	13107.1			0.912276
$592$	−3482.94	+	3482.94i	−0.241804	+	0.241804i
$593$		−	8124.66i		−	0.562630i	−0.959615	−	0.281315i	$-0.909229\pi$
$593$		−	8124.66i		−	0.562630i	0.959615	−	0.281315i	$-0.0907706\pi$
$594$	−275.952			−0.0190613
$595$	3397.93	+	8856.72i	0.234120	+	0.610236i
$596$	−41.3656			−0.00284295
$597$			10074.7i			0.690670i
$598$	4172.95	−	4172.95i	0.285359	−	0.285359i
$599$	8419.51			0.574310			0.287155	−	0.957884i	$-0.407290\pi$
$599$	8419.51			0.574310			0.287155	+	0.957884i	$0.407290\pi$
$600$	−1840.97	+	1840.97i	−0.125262	+	0.125262i
$601$	14357.8	+	14357.8i	0.974488	+	0.974488i	0.999683	−	0.0251941i	$-0.00802038\pi$
$601$	14357.8	+	14357.8i	0.974488	+	0.974488i	−0.0251941	+	0.999683i	$0.508020\pi$
$602$	−15461.2	−	15461.2i	−1.04676	−	1.04676i
$603$		−	2827.04i		−	0.190922i
$604$		−	7810.33i		−	0.526155i
$605$	−3750.24	−	3750.24i	−0.252015	−	0.252015i
$606$	−2092.35	−	2092.35i	−0.140257	−	0.140257i
$607$	−3129.93	+	3129.93i	−0.209292	+	0.209292i	−0.803966	−	0.594675i	$-0.797281\pi$
$607$	−3129.93	+	3129.93i	−0.209292	+	0.209292i	0.594675	+	0.803966i	$0.297281\pi$
$608$	2138.49			0.142644
$609$	12061.5	−	12061.5i	0.802558	−	0.802558i
$610$			59.2167i			0.00393052i
$611$	−1018.65			−0.0674470
$612$	2355.91	−	903.856i	0.155608	−	0.0596997i
$613$	−8994.17			−0.592612			−0.296306	−	0.955093i	$-0.595755\pi$
$613$	−8994.17			−0.592612			−0.296306	+	0.955093i	$0.595755\pi$
$614$			16863.1i			1.10837i
$615$	2418.67	−	2418.67i	0.158586	−	0.158586i
$616$	−1361.27			−0.0890378
$617$	−14300.2	+	14300.2i	−0.933068	+	0.933068i	−0.997896	−	0.0648287i	$-0.979350\pi$
$617$	−14300.2	+	14300.2i	−0.933068	+	0.933068i	0.0648287	+	0.997896i	$0.479350\pi$
$618$	5362.28	+	5362.28i	0.349033	+	0.349033i
$619$	12830.8	+	12830.8i	0.833138	+	0.833138i	0.987945	−	0.154807i	$-0.0494754\pi$
$619$	12830.8	+	12830.8i	0.833138	+	0.833138i	−0.154807	+	0.987945i	$0.549475\pi$
$620$		−	4205.27i		−	0.272400i
$621$		−	4342.94i		−	0.280638i
$622$	6967.59	+	6967.59i	0.449156	+	0.449156i
$623$	−35310.7	−	35310.7i	−2.27078	−	2.27078i
$624$	−622.637	+	622.637i	−0.0399446	+	0.0399446i
$625$	−9703.01			−0.620992
$626$	−3724.02	+	3724.02i	−0.237766	+	0.237766i
$627$			1024.52i			0.0652555i
$628$	856.820			0.0544440
$629$	19711.0	+	8780.21i	1.24949	+	0.556582i
$630$	−2436.07			−0.154056
$631$		−	27551.9i		−	1.73823i	−0.494611	−	0.869115i	$-0.664689\pi$
$631$		−	27551.9i		−	1.73823i	0.494611	−	0.869115i	$-0.335311\pi$
$632$	57.2532	−	57.2532i	0.00360350	−	0.00360350i
$633$	2223.01			0.139584
$634$	15751.2	−	15751.2i	0.986690	−	0.986690i
$635$	1757.04	+	1757.04i	0.109805	+	0.109805i
$636$	1977.86	+	1977.86i	0.123313	+	0.123313i
$637$			14047.3i			0.873746i
$638$			1745.22i			0.108297i
$639$	611.675	+	611.675i	0.0378678	+	0.0378678i
$640$	−367.872	−	367.872i	−0.0227209	−	0.0227209i
$641$	17303.2	−	17303.2i	1.06620	−	1.06620i	0.0685532	−	0.997647i	$-0.478162\pi$
$641$	17303.2	−	17303.2i	1.06620	−	1.06620i	0.997647	−	0.0685532i	$-0.0218383\pi$
$642$	−10262.7			−0.630901
$643$	−7139.55	+	7139.55i	−0.437879	+	0.437879i	−0.891298	−	0.453418i	$-0.850204\pi$
$643$	−7139.55	+	7139.55i	−0.437879	+	0.437879i	0.453418	+	0.891298i	$0.350204\pi$
$644$		−	21423.8i		−	1.31089i
$645$	4003.45			0.244396
$646$	−3355.71	−	8746.68i	−0.204379	−	0.532715i
$647$	13578.2			0.825059			0.412529	−	0.910944i	$-0.364645\pi$
$647$	13578.2			0.825059			0.412529	+	0.910944i	$0.364645\pi$
$648$			648.000i			0.0392837i
$649$	658.189	−	658.189i	0.0398092	−	0.0398092i
$650$	−3980.06			−0.240170
$651$	−18270.7	+	18270.7i	−1.09998	+	1.09998i
$652$	4158.43	+	4158.43i	0.249780	+	0.249780i
$653$	−7028.19	−	7028.19i	−0.421186	−	0.421186i	0.464426	−	0.885612i	$-0.346261\pi$
$653$	−7028.19	−	7028.19i	−0.421186	−	0.421186i	−0.885612	+	0.464426i	$0.846261\pi$
$654$		−	10333.6i		−	0.617850i
$655$			7904.48i			0.471532i
$656$	−3173.76	−	3173.76i	−0.188894	−	0.188894i
$657$	−6455.63	−	6455.63i	−0.383346	−	0.383346i
$658$	−2614.85	+	2614.85i	−0.154920	+	0.154920i
$659$	−18058.7			−1.06748			−0.533739	−	0.845649i	$-0.679213\pi$
$659$	−18058.7			−1.06748			−0.533739	+	0.845649i	$0.679213\pi$
$660$	176.241	−	176.241i	0.0103942	−	0.0103942i
$661$		−	19648.0i		−	1.15615i	−0.815983	−	0.578076i	$-0.803804\pi$
$661$		−	19648.0i		−	1.15615i	0.815983	−	0.578076i	$-0.196196\pi$
$662$	20355.5			1.19507
$663$	3523.70	+	1569.62i	0.206409	+	0.0919441i
$664$	−528.442			−0.0308848
$665$			9044.31i			0.527404i
$666$	−3918.31	+	3918.31i	−0.227975	+	0.227975i
$667$	−27466.3			−1.59445
$668$	−11064.8	+	11064.8i	−0.640882	+	0.640882i
$669$	−1868.97	−	1868.97i	−0.108010	−	0.108010i
$670$	1805.54	+	1805.54i	0.104110	+	0.104110i
$671$			37.2265i			0.00214175i
$672$			3196.59i			0.183499i
$673$	−12645.2	−	12645.2i	−0.724272	−	0.724272i	0.245200	−	0.969472i	$-0.421146\pi$
$673$	−12645.2	−	12645.2i	−0.724272	−	0.724272i	−0.969472	+	0.245200i	$0.921146\pi$
$674$	−10445.8	−	10445.8i	−0.596971	−	0.596971i
$675$	−2071.09	+	2071.09i	−0.118098	+	0.118098i
$676$	7441.90			0.423413
$677$	18897.5	−	18897.5i	1.07281	−	1.07281i	0.0756765	−	0.997132i	$-0.475888\pi$
$677$	18897.5	−	18897.5i	1.07281	−	1.07281i	0.997132	−	0.0756765i	$-0.0241116\pi$
$678$			6607.80i			0.374294i
$679$	6744.22			0.381177
$680$	−927.375	+	2081.90i	−0.0522988	+	0.117408i
$681$	16411.1			0.923460
$682$		−	2643.64i		−	0.148431i
$683$	−17168.0	+	17168.0i	−0.961810	+	0.961810i	−0.999297	−	0.0374871i	$-0.988065\pi$
$683$	−17168.0	+	17168.0i	−0.961810	+	0.961810i	0.0374871	+	0.999297i	$0.488065\pi$
$684$	2405.80			0.134486
$685$	6347.86	−	6347.86i	0.354072	−	0.354072i
$686$	19907.3	+	19907.3i	1.10796	+	1.10796i
$687$	−10502.7	−	10502.7i	−0.583263	−	0.583263i
$688$		−	5253.29i		−	0.291104i
$689$			4275.99i			0.236433i
$690$	2773.69	+	2773.69i	0.153033	+	0.153033i
$691$	7875.63	+	7875.63i	0.433579	+	0.433579i	0.889844	−	0.456265i	$-0.150813\pi$
$691$	7875.63	+	7875.63i	0.433579	+	0.433579i	−0.456265	+	0.889844i	$0.650813\pi$
$692$	−4568.74	+	4568.74i	−0.250979	+	0.250979i
$693$	−1531.43			−0.0839457
$694$	−14497.9	+	14497.9i	−0.792988	+	0.792988i
$695$			5455.03i			0.297728i
$696$	4098.18			0.223191
$697$	−8000.78	+	17961.3i	−0.434794	+	0.976085i
$698$	22676.2			1.22967
$699$			5302.21i			0.286907i
$700$	−10216.7	+	10216.7i	−0.551652	+	0.551652i
$701$	1650.56			0.0889312			0.0444656	−	0.999011i	$-0.485841\pi$
$701$	1650.56			0.0889312			0.0444656	+	0.999011i	$0.485841\pi$
$702$	−700.467	+	700.467i	−0.0376601	+	0.0376601i
$703$	14547.4	+	14547.4i	0.780461	+	0.780461i
$704$	−231.262	−	231.262i	−0.0123807	−	0.0123807i
$705$		−	677.077i		−	0.0361705i
$706$			9218.78i			0.491435i
$707$	−11611.8	−	11611.8i	−0.617690	−	0.617690i
$708$	−1545.58	−	1545.58i	−0.0820432	−	0.0820432i
$709$	10017.4	−	10017.4i	0.530620	−	0.530620i	−0.390137	−	0.920757i	$-0.627572\pi$
$709$	10017.4	−	10017.4i	0.530620	−	0.530620i	0.920757	+	0.390137i	$0.127572\pi$
$710$	−781.312			−0.0412988
$711$	64.4099	−	64.4099i	0.00339741	−	0.00339741i
$712$		−	11997.6i		−	0.631503i
$713$	41605.7			2.18534
$714$	13074.4	−	5016.08i	0.685292	−	0.262916i
$715$	381.022			0.0199292
$716$		−	161.948i		−	0.00845290i
$717$	−5607.22	+	5607.22i	−0.292058	+	0.292058i
$718$	−9042.31			−0.469994
$719$	6926.60	−	6926.60i	0.359275	−	0.359275i	−0.504271	−	0.863546i	$-0.668239\pi$
$719$	6926.60	−	6926.60i	0.359275	−	0.359275i	0.863546	+	0.504271i	$0.168239\pi$
$720$	−413.856	−	413.856i	−0.0214215	−	0.0214215i
$721$	29758.8	+	29758.8i	1.53713	+	1.53713i
$722$			4786.06i			0.246702i
$723$			12070.6i			0.620900i
$724$	4759.40	+	4759.40i	0.244312	+	0.244312i
$725$	13098.3	+	13098.3i	0.670979	+	0.670979i
$726$	−5536.16	+	5536.16i	−0.283011	+	0.283011i
$727$	8021.85			0.409235			0.204618	−	0.978842i	$-0.434405\pi$
$727$	8021.85			0.409235			0.204618	+	0.978842i	$0.434405\pi$
$728$	−3455.41	+	3455.41i	−0.175915	+	0.175915i
$729$			729.000i			0.0370370i
$730$	8245.99			0.418079
$731$	−21486.6	+	8243.44i	−1.08715	+	0.417092i
$732$	87.4167			0.00441395
$733$		−	11391.4i		−	0.574014i	−0.957928	−	0.287007i	$-0.907340\pi$
$733$		−	11391.4i		−	0.574014i	0.957928	−	0.287007i	$-0.0926603\pi$
$734$	−5557.01	+	5557.01i	−0.279446	+	0.279446i
$735$	−9337.02			−0.468573
$736$	3639.61	−	3639.61i	0.182280	−	0.182280i
$737$	1135.05	+	1135.05i	0.0567301	+	0.0567301i
$738$	−3570.48	−	3570.48i	−0.178091	−	0.178091i
$739$		−	15410.0i		−	0.767072i	−0.923526	−	0.383536i	$-0.874706\pi$
$739$		−	15410.0i		−	0.767072i	0.923526	−	0.383536i	$-0.125294\pi$
$740$		−	5004.98i		−	0.248631i
$741$	2600.60	+	2600.60i	0.128928	+	0.128928i
$742$	10976.4	+	10976.4i	0.543067	+	0.543067i
$743$	−20464.1	+	20464.1i	−1.01044	+	1.01044i	−0.0104944	+	0.999945i	$0.503341\pi$
$743$	−20464.1	+	20464.1i	−1.01044	+	1.01044i	−0.999945	+	0.0104944i	$0.996659\pi$
$744$	−6207.89			−0.305904
$745$	29.7211	−	29.7211i	0.00146161	−	0.00146161i
$746$		−	19595.9i		−	0.961737i
$747$	−594.497			−0.0291185
$748$	−582.993	+	1308.78i	−0.0284978	+	0.0639758i
$749$	−56954.6			−2.77847
$750$		−	5693.81i		−	0.277211i
$751$	−6696.98	+	6696.98i	−0.325401	+	0.325401i	−0.850835	−	0.525433i	$-0.823903\pi$
$751$	−6696.98	+	6696.98i	−0.325401	+	0.325401i	0.525433	+	0.850835i	$0.323903\pi$
$752$	−888.455			−0.0430833
$753$	−806.240	+	806.240i	−0.0390186	+	0.0390186i
$754$	4430.00	+	4430.00i	0.213967	+	0.213967i
$755$	5611.71	+	5611.71i	0.270505	+	0.270505i
$756$			3596.17i			0.173004i
$757$			1463.59i			0.0702710i	0.999383	+	0.0351355i	$0.0111863\pi$
$757$			1463.59i			0.0702710i	−0.999383	+	0.0351355i	$0.988814\pi$
$758$	14209.8	+	14209.8i	0.680902	+	0.680902i
$759$	1743.67	+	1743.67i	0.0833879	+	0.0833879i
$760$	−1536.51	+	1536.51i	−0.0733354	+	0.0733354i
$761$	−37987.0			−1.80950			−0.904748	−	0.425947i	$-0.859941\pi$
$761$	−37987.0			−1.80950			−0.904748	+	0.425947i	$0.859941\pi$
$762$	2593.77	−	2593.77i	0.123310	−	0.123310i
$763$		−	57347.5i		−	2.72100i
$764$	6764.57			0.320332
$765$	−1043.30	+	2342.14i	−0.0493078	+	0.110693i
$766$	5712.75			0.269465
$767$		−	3341.45i		−	0.157305i
$768$	−543.058	+	543.058i	−0.0255155	+	0.0255155i
$769$	29701.4			1.39280			0.696398	−	0.717655i	$-0.254785\pi$
$769$	29701.4			1.39280			0.696398	+	0.717655i	$0.254785\pi$
$770$	978.075	−	978.075i	0.0457758	−	0.0457758i
$771$	10863.4	+	10863.4i	0.507441	+	0.507441i
$772$	9896.06	+	9896.06i	0.461356	+	0.461356i
$773$		−	22444.2i		−	1.04432i	−0.852847	−	0.522161i	$-0.825126\pi$
$773$		−	22444.2i		−	1.04432i	0.852847	−	0.522161i	$-0.174874\pi$
$774$		−	5909.95i		−	0.274456i
$775$	−19841.2	−	19841.2i	−0.919636	−	0.919636i
$776$	1145.75	+	1145.75i	0.0530027	+	0.0530027i
$777$	−21745.2	+	21745.2i	−1.00400	+	1.00400i
$778$	−10958.3			−0.504980
$779$	−13256.0	+	13256.0i	−0.609685	+	0.609685i
$780$		−	894.729i		−	0.0410723i
$781$	−491.171			−0.0225038
$782$	−20597.7	−	9175.16i	−0.941907	−	0.419569i
$783$	4610.45			0.210427
$784$			12252.0i			0.558125i
$785$	−615.624	+	615.624i	−0.0279905	+	0.0279905i
$786$	11668.7			0.529529
$787$	−28691.9	+	28691.9i	−1.29956	+	1.29956i	−0.370887	+	0.928678i	$0.620946\pi$
$787$	−28691.9	+	28691.9i	−1.29956	+	1.29956i	−0.928678	+	0.370887i	$0.879054\pi$
$788$	12357.5	+	12357.5i	0.558652	+	0.558652i
$789$	−5356.41	−	5356.41i	−0.241690	−	0.241690i
$790$			82.2728i			0.00370523i
$791$			36671.0i			1.64838i
$792$	−260.170	−	260.170i	−0.0116726	−	0.0116726i
$793$	94.4946	+	94.4946i	0.00423153	+	0.00423153i
$794$	15057.7	−	15057.7i	0.673020	−	0.673020i
$795$	−2842.18			−0.126794
$796$	−9498.52	+	9498.52i	−0.422947	+	0.422947i
$797$			10014.0i			0.445063i	0.974926	+	0.222531i	$0.0714319\pi$
$797$			10014.0i			0.445063i	−0.974926	+	0.222531i	$0.928568\pi$
$798$	13351.4			0.592272
$799$	1394.16	+	3633.88i	0.0617294	+	0.160898i
$800$	−3471.37			−0.153414
$801$		−	13497.3i		−	0.595387i
$802$	3168.44	−	3168.44i	0.139503	−	0.139503i
$803$	5183.83			0.227812
$804$	2665.36	−	2665.36i	0.116916	−	0.116916i
$805$	15393.0	+	15393.0i	0.673951	+	0.673951i
$806$	−6710.53	−	6710.53i	−0.293261	−	0.293261i
$807$			17355.3i			0.757044i
$808$		−	3945.38i		−	0.171780i
$809$	1953.83	+	1953.83i	0.0849111	+	0.0849111i	0.748287	−	0.663376i	$-0.230877\pi$
$809$	1953.83	+	1953.83i	0.0849111	+	0.0849111i	−0.663376	+	0.748287i	$0.730877\pi$
$810$	−465.588	−	465.588i	−0.0201964	−	0.0201964i
$811$	20783.4	−	20783.4i	0.899880	−	0.899880i	−0.0955448	−	0.995425i	$-0.530459\pi$
$811$	20783.4	−	20783.4i	0.899880	−	0.899880i	0.995425	+	0.0955448i	$0.0304593\pi$
$812$	22743.4			0.982929
$813$	3137.31	−	3137.31i	0.135339	−	0.135339i
$814$		−	3146.38i		−	0.135480i
$815$	−5975.65			−0.256832
$816$	3073.33	+	1369.01i	0.131848	+	0.0587313i
$817$	−21941.6			−0.939585
$818$		−	10466.5i		−	0.447375i
$819$	−3887.34	+	3887.34i	−0.165854	+	0.165854i
$820$	4560.68			0.194227
$821$	−28722.0	+	28722.0i	−1.22096	+	1.22096i	−0.253663	+	0.967293i	$0.581636\pi$
$821$	−28722.0	+	28722.0i	−1.22096	+	1.22096i	−0.967293	+	0.253663i	$0.918364\pi$
$822$	−9370.82	−	9370.82i	−0.397621	−	0.397621i
$823$	5700.12	+	5700.12i	0.241426	+	0.241426i	0.817440	−	0.576014i	$-0.195393\pi$
$823$	5700.12	+	5700.12i	0.241426	+	0.241426i	−0.576014	+	0.817440i	$0.695393\pi$
$824$			10111.2i			0.427477i
$825$		−	1663.07i		−	0.0701828i
$826$	−8577.44	−	8577.44i	−0.361316	−	0.361316i
$827$	−10098.5	−	10098.5i	−0.424617	−	0.424617i	0.462173	−	0.886790i	$-0.347070\pi$
$827$	−10098.5	−	10098.5i	−0.424617	−	0.424617i	−0.886790	+	0.462173i	$0.847070\pi$
$828$	4094.56	−	4094.56i	0.171855	−	0.171855i
$829$	−19975.7			−0.836894			−0.418447	−	0.908241i	$-0.637425\pi$
$829$	−19975.7			−0.836894			−0.418447	+	0.908241i	$0.637425\pi$
$830$	379.685	−	379.685i	0.0158784	−	0.0158784i
$831$		−	20615.9i		−	0.860599i
$832$	−1174.06			−0.0489220
$833$	50111.9	−	19225.7i	2.08436	−	0.799678i
$834$	8052.81			0.334348
$835$		−	15900.1i		−	0.658976i
$836$	−965.923	+	965.923i	−0.0399607	+	0.0399607i
$837$	−6983.88			−0.288409
$838$	−24122.3	+	24122.3i	−0.994382	+	0.994382i
$839$	−7066.95	−	7066.95i	−0.290796	−	0.290796i	0.546598	−	0.837395i	$-0.315922\pi$
$839$	−7066.95	−	7066.95i	−0.290796	−	0.290796i	−0.837395	+	0.546598i	$0.815922\pi$
$840$	−2296.75	−	2296.75i	−0.0943398	−	0.0943398i
$841$		−	4769.14i		−	0.195545i
$842$			3991.97i			0.163388i
$843$	−11166.2	−	11166.2i	−0.456210	−	0.456210i
$844$	2095.88	+	2095.88i	0.0854775	+	0.0854775i
$845$	−5347.00	+	5347.00i	−0.217683	+	0.217683i
$846$	−999.512			−0.0406193
$847$	−30723.7	+	30723.7i	−1.24637	+	1.24637i
$848$			3729.48i			0.151027i
$849$	−8068.65			−0.326166
$850$	5447.26	+	14198.3i	0.219811	+	0.572938i
$851$	49517.7			1.99465
$852$			1153.39i			0.0463783i
$853$	22955.7	−	22955.7i	0.921439	−	0.921439i	−0.0756925	−	0.997131i	$-0.524117\pi$
$853$	22955.7	−	22955.7i	0.921439	−	0.921439i	0.997131	+	0.0756925i	$0.0241167\pi$
$854$	485.131			0.0194389
$855$	−1728.57	+	1728.57i	−0.0691413	+	0.0691413i
$856$	−9675.81	−	9675.81i	−0.386346	−	0.386346i
$857$	−8498.19	−	8498.19i	−0.338731	−	0.338731i	0.517159	−	0.855890i	$-0.326990\pi$
$857$	−8498.19	−	8498.19i	−0.338731	−	0.338731i	−0.855890	+	0.517159i	$0.826990\pi$
$858$		−	562.470i		−	0.0223804i
$859$		−	17465.0i		−	0.693711i	−0.937919	−	0.346855i	$-0.887249\pi$
$859$		−	17465.0i		−	0.693711i	0.937919	−	0.346855i	$-0.112751\pi$
$860$	3774.48	+	3774.48i	0.149661	+	0.149661i
$861$	−19814.9	−	19814.9i	−0.784308	−	0.784308i
$862$	20514.6	−	20514.6i	0.810593	−	0.810593i
$863$	40272.5			1.58852			0.794259	−	0.607579i	$-0.207859\pi$
$863$	40272.5			1.58852			0.794259	+	0.607579i	$0.207859\pi$
$864$	−610.940	+	610.940i	−0.0240563	+	0.0240563i
$865$		−	6565.28i		−	0.258065i
$866$	2034.05			0.0798152
$867$	776.728	−	14718.5i	0.0304257	−	0.576548i
$868$	−34451.6			−1.34719
$869$			51.7207i			0.00201899i
$870$	−2944.54	+	2944.54i	−0.114746	+	0.114746i
$871$	5762.34			0.224167
$872$	9742.57	−	9742.57i	0.378354	−	0.378354i
$873$	1288.97	+	1288.97i	0.0499714	+	0.0499714i
$874$	−15201.7	−	15201.7i	−0.588336	−	0.588336i
$875$		−	31598.6i		−	1.22083i
$876$		−	12172.9i		−	0.469501i
$877$	−10434.9	−	10434.9i	−0.401782	−	0.401782i	0.477079	−	0.878861i	$-0.341696\pi$
$877$	−10434.9	−	10434.9i	−0.401782	−	0.401782i	−0.878861	+	0.477079i	$0.841696\pi$
$878$	−2622.16	−	2622.16i	−0.100790	−	0.100790i
$879$	12889.7	−	12889.7i	0.494606	−	0.494606i
$880$	332.323			0.0127302
$881$	−12015.0	+	12015.0i	−0.459474	+	0.459474i	−0.898483	−	0.439009i	$-0.855330\pi$
$881$	−12015.0	+	12015.0i	−0.459474	+	0.459474i	0.439009	+	0.898483i	$0.355330\pi$
$882$			13783.5i			0.526205i
$883$	5494.09			0.209389			0.104695	−	0.994504i	$-0.466613\pi$
$883$	5494.09			0.209389			0.104695	+	0.994504i	$0.466613\pi$
$884$	1842.32	+	4802.02i	0.0700950	+	0.182703i
$885$	2221.00			0.0843595
$886$		−	8595.68i		−	0.325934i
$887$	9566.03	−	9566.03i	0.362115	−	0.362115i	−0.502476	−	0.864591i	$-0.667578\pi$
$887$	9566.03	−	9566.03i	0.362115	−	0.362115i	0.864591	+	0.502476i	$0.167578\pi$
$888$	−7388.43			−0.279211
$889$	14394.5	−	14394.5i	0.543055	−	0.543055i
$890$	8620.29	+	8620.29i	0.324666	+	0.324666i
$891$	−292.691	−	292.691i	−0.0110051	−	0.0110051i
$892$		−	3524.16i		−	0.132284i
$893$			3710.85i			0.139058i
$894$	−43.8748	−	43.8748i	−0.00164138	−	0.00164138i
$895$	116.360	+	116.360i	0.00434578	+	0.00434578i
$896$	−3013.78	+	3013.78i	−0.112370	+	0.112370i
$897$	8852.17			0.329504
$898$	2704.66	−	2704.66i	0.100508	−	0.100508i
$899$			44168.5i			1.63860i
$900$	−3905.29			−0.144640
$901$	15254.0	−	5852.28i	0.564023	−	0.216390i
$902$	2867.07			0.105835
$903$		−	32798.1i		−	1.20870i
$904$	−6229.90	+	6229.90i	−0.229207	+	0.229207i
$905$	−6839.26			−0.251210
$906$	8284.10	−	8284.10i	0.303776	−	0.303776i
$907$	8569.84	+	8569.84i	0.313734	+	0.313734i	0.846354	−	0.532620i	$-0.178793\pi$
$907$	8569.84	+	8569.84i	0.313734	+	0.313734i	−0.532620	+	0.846354i	$0.678793\pi$
$908$	15472.6	+	15472.6i	0.565501	+	0.565501i
$909$		−	4438.55i		−	0.161955i
$910$		−	4965.43i		−	0.180882i
$911$	23063.0	+	23063.0i	0.838759	+	0.838759i	0.988696	−	0.149936i	$-0.0479069\pi$
$911$	23063.0	+	23063.0i	0.838759	+	0.838759i	−0.149936	+	0.988696i	$0.547907\pi$
$912$	2268.21	+	2268.21i	0.0823554	+	0.0823554i
$913$	238.689	−	238.689i	0.00865218	−	0.00865218i
$914$	−4469.54			−0.161750
$915$	−62.8088	+	62.8088i	−0.00226929	+	0.00226929i
$916$		−	19804.0i		−	0.714348i
$917$	64757.2			2.33203
$918$	3457.50	+	1540.13i	0.124308	+	0.0553724i
$919$	−46742.5			−1.67780			−0.838898	−	0.544289i	$-0.816800\pi$
$919$	−46742.5			−1.67780			−0.838898	+	0.544289i	$0.816800\pi$
$920$			5230.11i			0.187426i
$921$	−17886.0	+	17886.0i	−0.639918	+	0.639918i
$922$	−299.267			−0.0106896
$923$	−1246.77	+	1246.77i	−0.0444616	+	0.0444616i
$924$	−1443.85	−	1443.85i	−0.0514060	−	0.0514060i
$925$	−23614.4	−	23614.4i	−0.839391	−	0.839391i
$926$		−	9464.19i		−	0.335867i
$927$			11375.1i			0.403029i
$928$	3863.80	+	3863.80i	0.136676	+	0.136676i
$929$	7027.24	+	7027.24i	0.248177	+	0.248177i	0.820222	−	0.572045i	$-0.193850\pi$
$929$	7027.24	+	7027.24i	0.248177	+	0.248177i	−0.572045	+	0.820222i	$0.693850\pi$
$930$	4460.37	−	4460.37i	0.157270	−	0.157270i
$931$	51173.3			1.80144
$932$	−4998.97	+	4998.97i	−0.175694	+	0.175694i
$933$			14780.5i			0.518641i
$934$	−5498.02			−0.192613
$935$	−521.480	−	1359.24i	−0.0182398	−	0.0475421i
$936$	−1320.81			−0.0461241
$937$			18865.1i			0.657733i	0.944376	+	0.328867i	$0.106667\pi$
$937$			18865.1i			0.657733i	−0.944376	+	0.328867i	$0.893333\pi$
$938$	14791.8	−	14791.8i	0.514893	−	0.514893i
$939$	−7899.83			−0.274549
$940$	638.355	−	638.355i	0.0221498	−	0.0221498i
$941$	25499.6	+	25499.6i	0.883384	+	0.883384i	0.993877	−	0.110493i	$-0.0352429\pi$
$941$	25499.6	+	25499.6i	0.883384	+	0.883384i	−0.110493	+	0.993877i	$0.535243\pi$
$942$	908.795	+	908.795i	0.0314333	+	0.0314333i
$943$			45122.0i			1.55819i
$944$		−	2914.38i		−	0.100482i
$945$	−2583.84	−	2583.84i	−0.0889444	−	0.0889444i
$946$	2372.83	+	2372.83i	0.0815510	+	0.0815510i
$947$	36894.9	−	36894.9i	1.26602	−	1.26602i	0.317896	−	0.948126i	$-0.397024\pi$
$947$	36894.9	−	36894.9i	1.26602	−	1.26602i	0.948126	−	0.317896i	$-0.102976\pi$
$948$	121.452			0.00416096
$949$	13158.5	−	13158.5i	0.450097	−	0.450097i
$950$			14499.0i			0.495169i
$951$	33413.4			1.13933
$952$	17055.9	+	7597.49i	0.580656	+	0.258651i
$953$	−38749.7			−1.31713			−0.658566	−	0.752523i	$-0.728836\pi$
$953$	−38749.7			−1.31713			−0.658566	+	0.752523i	$0.728836\pi$
$954$			4195.67i			0.142390i
$955$	−4860.34	+	4860.34i	−0.164688	+	0.164688i
$956$	−10573.1			−0.357696
$957$	−1851.08	+	1851.08i	−0.0625256	+	0.0625256i
$958$	−5953.28	−	5953.28i	−0.200774	−	0.200774i
$959$	−52004.7	−	52004.7i	−1.75111	−	1.75111i
$960$		−	780.374i		−	0.0262359i
$961$		−	37115.1i		−	1.24585i
$962$	−7986.66	−	7986.66i	−0.267672	−	0.267672i
$963$	−10885.3	−	10885.3i	−0.364251	−	0.364251i
$964$	−11380.3	+	11380.3i	−0.380222	+	0.380222i
$965$	−14220.6			−0.474382
$966$	22723.3	−	22723.3i	0.756844	−	0.756844i
$967$		−	52687.2i		−	1.75213i	−0.482197	−	0.876063i	$-0.660161\pi$
$967$		−	52687.2i		−	1.75213i	0.482197	−	0.876063i	$-0.339839\pi$
$968$	−10439.1			−0.346617
$969$	5717.99	−	12836.5i	0.189565	−	0.425561i
$970$	−1646.44			−0.0544991
$971$			4339.06i			0.143406i	0.997426	+	0.0717030i	$0.0228434\pi$
$971$			4339.06i			0.143406i	−0.997426	+	0.0717030i	$0.977157\pi$
$972$	−687.308	+	687.308i	−0.0226805	+	0.0226805i
$973$	44690.2			1.47246
$974$	−23755.3	+	23755.3i	−0.781486	+	0.781486i
$975$	−4221.49	−	4221.49i	−0.138662	−	0.138662i
$976$	82.4173	+	82.4173i	0.00270298	+	0.00270298i
$977$			23529.5i			0.770498i	0.922813	+	0.385249i	$0.125884\pi$
$977$			23529.5i			0.770498i	−0.922813	+	0.385249i	$0.874116\pi$
$978$			8821.35i			0.288421i
$979$	5419.14	+	5419.14i	0.176911	+	0.176911i
$980$	−8803.02	−	8803.02i	−0.286941	−	0.286941i
$981$	10960.4	−	10960.4i	0.356716	−	0.356716i
$982$	−21809.2			−0.708717
$983$	−17689.6	+	17689.6i	−0.573967	+	0.573967i	−0.933235	−	0.359267i	$-0.883027\pi$
$983$	−17689.6	+	17689.6i	−0.573967	+	0.573967i	0.359267	+	0.933235i	$0.383027\pi$
$984$		−	6732.55i		−	0.218116i
$985$	−17757.7			−0.574425
$986$	9740.33	−	21866.5i	0.314600	−	0.706257i
$987$	−5546.94			−0.178886
$988$			4903.73i			0.157903i
$989$	−37343.6	+	37343.6i	−1.20066	+	1.20066i
$990$	373.864			0.0120022
$991$	−33982.5	+	33982.5i	−1.08929	+	1.08929i	−0.0936904	+	0.995601i	$0.529866\pi$
$991$	−33982.5	+	33982.5i	−1.08929	+	1.08929i	−0.995601	+	0.0936904i	$0.970134\pi$
$992$	−5852.86	−	5852.86i	−0.187327	−	0.187327i
$993$	21590.3	+	21590.3i	0.689976	+	0.689976i
$994$			6400.88i			0.204249i
$995$		−	13649.4i		−	0.434888i
$996$	−560.498	−	560.498i	−0.0178314	−	0.0178314i
$997$	19292.0	+	19292.0i	0.612823	+	0.612823i	0.943681	−	0.330858i	$-0.107338\pi$
$997$	19292.0	+	19292.0i	0.612823	+	0.612823i	−0.330858	+	0.943681i	$0.607338\pi$
$998$	−3654.59	+	3654.59i	−0.115916	+	0.115916i
$999$	−8311.99			−0.263243

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	102.4.f.c.55.2	yes	12
3.2	odd	2		306.4.g.g.55.3		12
17.8	even	8		1734.4.a.be.1.4		6
17.9	even	8		1734.4.a.bd.1.3		6
17.13	even	4	inner	102.4.f.c.13.2	✓	12
51.47	odd	4		306.4.g.g.217.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
102.4.f.c.13.2	✓	12	17.13	even	4	inner
102.4.f.c.55.2	yes	12	1.1	even	1	trivial
306.4.g.g.55.3		12	3.2	odd	2
306.4.g.g.217.3		12	51.47	odd	4
1734.4.a.bd.1.3		6	17.9	even	8
1734.4.a.be.1.4		6	17.8	even	8

Overview	Random
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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:	\( N \)	\(=\)	\( 102 = 2 \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	102.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} +(-2.12132 + 2.12132i) q^{3} -4.00000 q^{4} +(2.87400 - 2.87400i) q^{5} +(-4.24264 - 4.24264i) q^{6} +(-23.5451 - 23.5451i) q^{7} -8.00000i q^{8} -9.00000i q^{9} +(5.74799 + 5.74799i) q^{10} +(3.61347 + 3.61347i) q^{11} +(8.48528 - 8.48528i) q^{12} +18.3446 q^{13} +(47.0903 - 47.0903i) q^{14} +12.1933i q^{15} +16.0000 q^{16} +(-25.1071 - 65.4418i) q^{17} +18.0000 q^{18} -66.8279i q^{19} +(-11.4960 + 11.4960i) q^{20} +99.8936 q^{21} +(-7.22694 + 7.22694i) q^{22} +(-113.738 - 113.738i) q^{23} +(16.9706 + 16.9706i) q^{24} +108.480i q^{25} +36.6892i q^{26} +(19.0919 + 19.0919i) q^{27} +(94.1806 + 94.1806i) q^{28} +(120.744 - 120.744i) q^{29} -24.3867 q^{30} +(-182.902 + 182.902i) q^{31} +32.0000i q^{32} -15.3307 q^{33} +(130.884 - 50.2142i) q^{34} -135.337 q^{35} +36.0000i q^{36} +(-217.684 + 217.684i) q^{37} +133.656 q^{38} +(-38.9148 + 38.9148i) q^{39} +(-22.9920 - 22.9920i) q^{40} +(-198.360 - 198.360i) q^{41} +199.787i q^{42} -328.331i q^{43} +(-14.4539 - 14.4539i) q^{44} +(-25.8660 - 25.8660i) q^{45} +(227.476 - 227.476i) q^{46} -55.5285 q^{47} +(-33.9411 + 33.9411i) q^{48} +765.747i q^{49} -216.961 q^{50} +(192.083 + 85.5628i) q^{51} -73.3785 q^{52} +233.093i q^{53} +(-38.1838 + 38.1838i) q^{54} +20.7702 q^{55} +(-188.361 + 188.361i) q^{56} +(141.763 + 141.763i) q^{57} +(241.488 + 241.488i) q^{58} -182.149i q^{59} -48.7734i q^{60} +(5.15108 + 5.15108i) q^{61} +(-365.803 - 365.803i) q^{62} +(-211.906 + 211.906i) q^{63} -64.0000 q^{64} +(52.7224 - 52.7224i) q^{65} -30.6613i q^{66} +314.116 q^{67} +(100.428 + 261.767i) q^{68} +482.549 q^{69} -270.675i q^{70} +(-67.9639 + 67.9639i) q^{71} -72.0000 q^{72} +(717.292 - 717.292i) q^{73} +(-435.368 - 435.368i) q^{74} +(-230.121 - 230.121i) q^{75} +267.312i q^{76} -170.159i q^{77} +(-77.8296 - 77.8296i) q^{78} +(7.15665 + 7.15665i) q^{79} +(45.9840 - 45.9840i) q^{80} -81.0000 q^{81} +(396.720 - 396.720i) q^{82} -66.0553i q^{83} -399.574 q^{84} +(-260.237 - 115.922i) q^{85} +656.661 q^{86} +512.273i q^{87} +(28.9078 - 28.9078i) q^{88} +1499.70 q^{89} +(51.7320 - 51.7320i) q^{90} +(-431.927 - 431.927i) q^{91} +(454.951 + 454.951i) q^{92} -775.986i q^{93} -111.057i q^{94} +(-192.063 - 192.063i) q^{95} +(-67.8823 - 67.8823i) q^{96} +(-143.219 + 143.219i) q^{97} -1531.49 q^{98} +(32.5212 - 32.5212i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 48 q^{4} + 16 q^{5} - 12 q^{7} + 32 q^{10} - 32 q^{11} - 68 q^{13} + 24 q^{14} + 192 q^{16} + 64 q^{17} + 216 q^{18} - 64 q^{20} - 168 q^{21} + 64 q^{22} - 112 q^{23} + 48 q^{28} - 296 q^{29} - 168 q^{30}+ \cdots - 288 q^{99}+O(q^{100}) \) 12 * q - 48 * q^4 + 16 * q^5 - 12 * q^7 + 32 * q^10 - 32 * q^11 - 68 * q^13 + 24 * q^14 + 192 * q^16 + 64 * q^17 + 216 * q^18 - 64 * q^20 - 168 * q^21 + 64 * q^22 - 112 * q^23 + 48 * q^28 - 296 * q^29 - 168 * q^30 + 520 * q^31 + 204 * q^33 + 144 * q^34 + 392 * q^35 - 828 * q^37 - 280 * q^38 + 312 * q^39 - 128 * q^40 + 8 * q^41 + 128 * q^44 - 144 * q^45 + 224 * q^46 - 2920 * q^47 + 752 * q^50 + 420 * q^51 + 272 * q^52 + 1156 * q^55 - 96 * q^56 + 312 * q^57 - 592 * q^58 - 1124 * q^61 + 1040 * q^62 - 108 * q^63 - 768 * q^64 + 3288 * q^65 - 2008 * q^67 - 256 * q^68 + 468 * q^69 - 2184 * q^71 - 864 * q^72 + 2456 * q^73 - 1656 * q^74 - 192 * q^75 + 624 * q^78 + 2652 * q^79 + 256 * q^80 - 972 * q^81 - 16 * q^82 + 672 * q^84 + 3444 * q^85 - 184 * q^86 - 256 * q^88 + 5304 * q^89 + 288 * q^90 - 1420 * q^91 + 448 * q^92 - 2920 * q^95 + 2688 * q^97 - 4168 * q^98 - 288 * q^99

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