LMFDB - Embedded newform 115.7.d.a.91.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,7,Mod(91,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("115.91");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	115.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$26.4562196163$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.3
Character	$\chi$	$=$	115.91
Dual form			115.7.d.a.91.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-15.2752 q^{2} +41.9187 q^{3} +169.333 q^{4} -55.9017i q^{5} -640.318 q^{6} +492.500i q^{7} -1608.98 q^{8} +1028.18 q^{9} +O(q^{10})$	\(q-15.2752 q^{2} +41.9187 q^{3} +169.333 q^{4} -55.9017i q^{5} -640.318 q^{6} +492.500i q^{7} -1608.98 q^{8} +1028.18 q^{9} +853.912i q^{10} -2366.90i q^{11} +7098.21 q^{12} -416.688 q^{13} -7523.05i q^{14} -2343.33i q^{15} +13740.3 q^{16} -1660.38i q^{17} -15705.7 q^{18} -7404.26i q^{19} -9465.99i q^{20} +20645.0i q^{21} +36155.0i q^{22} +(10144.5 - 6717.44i) q^{23} -67446.5 q^{24} -3125.00 q^{25} +6365.00 q^{26} +12541.2 q^{27} +83396.3i q^{28} -28325.9 q^{29} +35794.9i q^{30} +35637.8 q^{31} -106911. q^{32} -99217.5i q^{33} +25362.7i q^{34} +27531.6 q^{35} +174105. q^{36} -50443.3i q^{37} +113102. i q^{38} -17467.0 q^{39} +89944.9i q^{40} +19384.6 q^{41} -315357. i q^{42} +18673.0i q^{43} -400794. i q^{44} -57477.0i q^{45} +(-154960. + 102610. i) q^{46} +199795. q^{47} +575975. q^{48} -124907. q^{49} +47735.1 q^{50} -69601.0i q^{51} -70558.9 q^{52} +10721.3i q^{53} -191570. q^{54} -132314. q^{55} -792423. i q^{56} -310377. i q^{57} +432685. q^{58} +99581.0 q^{59} -396802. i q^{60} +161973. i q^{61} -544376. q^{62} +506378. i q^{63} +753715. q^{64} +23293.6i q^{65} +1.51557e6i q^{66} +227909. i q^{67} -281157. i q^{68} +(425247. - 281587. i) q^{69} -420551. q^{70} +220934. q^{71} -1.65432e6 q^{72} +130581. q^{73} +770533. i q^{74} -130996. q^{75} -1.25378e6i q^{76} +1.16570e6 q^{77} +266813. q^{78} -905589. i q^{79} -768105. i q^{80} -223830. q^{81} -296104. q^{82} -1.02491e6i q^{83} +3.49587e6i q^{84} -92818.0 q^{85} -285234. i q^{86} -1.18739e6 q^{87} +3.80830e6i q^{88} -458389. i q^{89} +877975. i q^{90} -205219. i q^{91} +(1.71780e6 - 1.13748e6i) q^{92} +1.49389e6 q^{93} -3.05192e6 q^{94} -413911. q^{95} -4.48158e6 q^{96} -56712.1i q^{97} +1.90798e6 q^{98} -2.43360e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 20 q^{2} + 1584 q^{4} + 410 q^{6} - 1210 q^{8} + 12896 q^{9}+O(q^{10}) $ 48 * q - 20 * q^2 + 1584 * q^4 + 410 * q^6 - 1210 * q^8 + 12896 * q^9	$ 48 q - 20 q^{2} + 1584 q^{4} + 410 q^{6} - 1210 q^{8} + 12896 q^{9} + 4290 q^{12} - 1440 q^{13} + 65400 q^{16} + 4610 q^{18} + 26600 q^{23} + 14940 q^{24} - 150000 q^{25} + 47594 q^{26} + 16080 q^{27} + 131800 q^{29} - 1392 q^{31} - 225040 q^{32} + 5000 q^{35} + 658786 q^{36} - 236320 q^{39} - 351496 q^{41} + 382692 q^{46} + 395680 q^{47} + 1042550 q^{48} - 637848 q^{49} + 62500 q^{50} + 523890 q^{52} - 241250 q^{54} - 402000 q^{55} - 479130 q^{58} - 466312 q^{59} - 1124330 q^{62} + 837582 q^{64} + 1021060 q^{69} - 396000 q^{70} - 114336 q^{71} - 1960750 q^{72} - 498720 q^{73} + 3610400 q^{77} - 1104610 q^{78} + 972888 q^{81} + 124950 q^{82} - 246000 q^{85} - 2090960 q^{87} + 4913480 q^{92} + 3234320 q^{93} - 5550378 q^{94} - 1664000 q^{95} - 776990 q^{96} + 9993220 q^{98}+O(q^{100}) $ 48 * q - 20 * q^2 + 1584 * q^4 + 410 * q^6 - 1210 * q^8 + 12896 * q^9 + 4290 * q^12 - 1440 * q^13 + 65400 * q^16 + 4610 * q^18 + 26600 * q^23 + 14940 * q^24 - 150000 * q^25 + 47594 * q^26 + 16080 * q^27 + 131800 * q^29 - 1392 * q^31 - 225040 * q^32 + 5000 * q^35 + 658786 * q^36 - 236320 * q^39 - 351496 * q^41 + 382692 * q^46 + 395680 * q^47 + 1042550 * q^48 - 637848 * q^49 + 62500 * q^50 + 523890 * q^52 - 241250 * q^54 - 402000 * q^55 - 479130 * q^58 - 466312 * q^59 - 1124330 * q^62 + 837582 * q^64 + 1021060 * q^69 - 396000 * q^70 - 114336 * q^71 - 1960750 * q^72 - 498720 * q^73 + 3610400 * q^77 - 1104610 * q^78 + 972888 * q^81 + 124950 * q^82 - 246000 * q^85 - 2090960 * q^87 + 4913480 * q^92 + 3234320 * q^93 - 5550378 * q^94 - 1664000 * q^95 - 776990 * q^96 + 9993220 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−15.2752			−1.90940			−0.954702	−	0.297563i	$-0.903826\pi$
$2$	−15.2752			−1.90940			−0.954702	+	0.297563i	$0.903826\pi$
$3$	41.9187			1.55255			0.776273	−	0.630397i	$-0.217108\pi$
$3$	41.9187			1.55255			0.776273	+	0.630397i	$0.217108\pi$
$4$	169.333			2.64582
$5$		−	55.9017i		−	0.447214i
$5$		−	55.9017i		−	0.447214i
$6$	−640.318			−2.96444
$7$			492.500i			1.43586i	0.696116	+	0.717929i	$0.254910\pi$
$7$			492.500i			1.43586i	−0.696116	+	0.717929i	$0.745090\pi$
$8$	−1608.98			−3.14254
$9$	1028.18			1.41040
$10$			853.912i			0.853912i
$11$		−	2366.90i		−	1.77829i	−0.457627	−	0.889144i	$-0.651300\pi$
$11$		−	2366.90i		−	1.77829i	0.457627	−	0.889144i	$-0.348700\pi$
$12$	7098.21			4.10776
$13$	−416.688			−0.189662			−0.0948311	−	0.995493i	$-0.530231\pi$
$13$	−416.688			−0.189662			−0.0948311	+	0.995493i	$0.530231\pi$
$14$		−	7523.05i		−	2.74163i
$15$		−	2343.33i		−	0.694320i
$16$	13740.3			3.35456
$17$		−	1660.38i		−	0.337956i	−0.985620	−	0.168978i	$-0.945953\pi$
$17$		−	1660.38i		−	0.337956i	0.985620	−	0.168978i	$-0.0540467\pi$
$18$	−15705.7			−2.69302
$19$		−	7404.26i		−	1.07950i	−0.841827	−	0.539748i	$-0.818520\pi$
$19$		−	7404.26i		−	1.07950i	0.841827	−	0.539748i	$-0.181480\pi$
$20$		−	9465.99i		−	1.18325i
$21$			20645.0i			2.22924i
$22$			36155.0i			3.39547i
$23$	10144.5	−	6717.44i	0.833776	−	0.552103i
$23$	10144.5	−	6717.44i	0.833776	−	0.552103i
$24$	−67446.5			−4.87894
$25$	−3125.00			−0.200000
$26$	6365.00			0.362142
$27$	12541.2			0.637161
$28$			83396.3i			3.79903i
$29$	−28325.9			−1.16142			−0.580712	−	0.814109i	$-0.697226\pi$
$29$	−28325.9			−1.16142			−0.580712	+	0.814109i	$0.697226\pi$
$30$			35794.9i			1.32574i
$31$	35637.8			1.19626			0.598130	−	0.801399i	$-0.295910\pi$
$31$	35637.8			1.19626			0.598130	+	0.801399i	$0.295910\pi$
$32$	−106911.			−3.26267
$33$		−	99217.5i		−	2.76087i
$34$			25362.7i			0.645295i
$35$	27531.6			0.642136
$36$	174105.			3.73166
$37$		−	50443.3i		−	0.995859i	−0.867217	−	0.497930i	$-0.834094\pi$
$37$		−	50443.3i		−	0.995859i	0.867217	−	0.497930i	$-0.165906\pi$
$38$			113102.i			2.06119i
$39$	−17467.0			−0.294459
$40$			89944.9i			1.40539i
$41$	19384.6			0.281258			0.140629	−	0.990062i	$-0.455088\pi$
$41$	19384.6			0.281258			0.140629	+	0.990062i	$0.455088\pi$
$42$		−	315357.i		−	4.25651i
$43$			18673.0i			0.234859i	0.993081	+	0.117430i	$0.0374655\pi$
$43$			18673.0i			0.234859i	−0.993081	+	0.117430i	$0.962535\pi$
$44$		−	400794.i		−	4.70504i
$45$		−	57477.0i		−	0.630749i
$46$	−154960.	+	102610.i	−1.59201	+	1.05419i
$47$	199795.			1.92439			0.962193	−	0.272369i	$-0.0878073\pi$
$47$	199795.			1.92439			0.962193	+	0.272369i	$0.0878073\pi$
$48$	575975.			5.20811
$49$	−124907.			−1.06169
$50$	47735.1			0.381881
$51$		−	69601.0i		−	0.524692i
$52$	−70558.9			−0.501813
$53$			10721.3i			0.0720143i	0.999352	+	0.0360071i	$0.0114639\pi$
$53$			10721.3i			0.0720143i	−0.999352	+	0.0360071i	$0.988536\pi$
$54$	−191570.			−1.21660
$55$	−132314.			−0.795275
$56$		−	792423.i		−	4.51225i
$57$		−	310377.i		−	1.67597i
$58$	432685.			2.21763
$59$	99581.0			0.484865			0.242432	−	0.970168i	$-0.422055\pi$
$59$	99581.0			0.484865			0.242432	+	0.970168i	$0.422055\pi$
$60$		−	396802.i		−	1.83705i
$61$			161973.i			0.713596i	0.934182	+	0.356798i	$0.116132\pi$
$61$			161973.i			0.713596i	−0.934182	+	0.356798i	$0.883868\pi$
$62$	−544376.			−2.28415
$63$			506378.i			2.02513i
$64$	753715.			2.87520
$65$			23293.6i			0.0848195i
$66$			1.51557e6i			5.27162i
$67$			227909.i			0.757770i	0.925444	+	0.378885i	$0.123692\pi$
$67$			227909.i			0.757770i	−0.925444	+	0.378885i	$0.876308\pi$
$68$		−	281157.i		−	0.894173i
$69$	425247.	−	281587.i	1.29447	−	0.857165i
$70$	−420551.			−1.22610
$71$	220934.			0.617287			0.308644	−	0.951178i	$-0.400125\pi$
$71$	220934.			0.617287			0.308644	+	0.951178i	$0.400125\pi$
$72$	−1.65432e6			−4.43224
$73$	130581.			0.335670			0.167835	−	0.985815i	$-0.446322\pi$
$73$	130581.			0.335670			0.167835	+	0.985815i	$0.446322\pi$
$74$			770533.i			1.90150i
$75$	−130996.			−0.310509
$76$		−	1.25378e6i		−	2.85616i
$77$	1.16570e6			2.55337
$78$	266813.			0.562242
$79$		−	905589.i		−	1.83675i	−0.395712	−	0.918375i	$-0.629502\pi$
$79$		−	905589.i		−	1.83675i	0.395712	−	0.918375i	$-0.370498\pi$
$80$		−	768105.i		−	1.50021i
$81$	−223830.			−0.421176
$82$	−296104.			−0.537035
$83$		−	1.02491e6i		−	1.79246i	−0.443589	−	0.896230i	$-0.646295\pi$
$83$		−	1.02491e6i		−	1.79246i	0.443589	−	0.896230i	$-0.353705\pi$
$84$			3.49587e6i			5.89817i
$85$	−92818.0			−0.151139
$86$		−	285234.i		−	0.448441i
$87$	−1.18739e6			−1.80316
$88$			3.80830e6i			5.58835i
$89$		−	458389.i		−	0.650226i	−0.945675	−	0.325113i	$-0.894598\pi$
$89$		−	458389.i		−	0.650226i	0.945675	−	0.325113i	$-0.105402\pi$
$90$			877975.i			1.20435i
$91$		−	205219.i		−	0.272328i
$92$	1.71780e6	−	1.13748e6i	2.20602	−	1.46077i
$93$	1.49389e6			1.85725
$94$	−3.05192e6			−3.67443
$95$	−413911.			−0.482765
$96$	−4.48158e6			−5.06545
$97$		−	56712.1i		−	0.0621384i	−0.999517	−	0.0310692i	$-0.990109\pi$
$97$		−	56712.1i		−	0.0621384i	0.999517	−	0.0310692i	$-0.00989123\pi$
$98$	1.90798e6			2.02720
$99$		−	2.43360e6i		−	2.50809i
$100$	−529165.			−0.529165
$101$	−755494.			−0.733275			−0.366638	−	0.930364i	$-0.619491\pi$
$101$	−755494.			−0.733275			−0.366638	+	0.930364i	$0.619491\pi$
$102$			1.06317e6i			1.00185i
$103$			149734.i			0.137028i	0.997650	+	0.0685140i	$0.0218258\pi$
$103$			149734.i			0.137028i	−0.997650	+	0.0685140i	$0.978174\pi$
$104$	670443.			0.596022
$105$	1.15409e6			0.996945
$106$		−	163770.i		−	0.137504i
$107$			1.46624e6i			1.19689i	0.801163	+	0.598446i	$0.204215\pi$
$107$			1.46624e6i			1.19689i	−0.801163	+	0.598446i	$0.795785\pi$
$108$	2.12364e6			1.68582
$109$		−	1.56521e6i		−	1.20863i	−0.796745	−	0.604315i	$-0.793447\pi$
$109$		−	1.56521e6i		−	1.20863i	0.796745	−	0.604315i	$-0.206553\pi$
$110$	2.02113e6			1.51850
$111$		−	2.11452e6i		−	1.54612i
$112$			6.76709e6i			4.81668i
$113$			916803.i			0.635390i	0.948193	+	0.317695i	$0.102909\pi$
$113$			916803.i			0.635390i	−0.948193	+	0.317695i	$0.897091\pi$
$114$			4.74108e6i			3.20010i
$115$	−375516.	−	567098.i	−0.246908	−	0.372876i
$116$	−4.79651e6			−3.07292
$117$	−428430.			−0.267499
$118$	−1.52112e6			−0.925803
$119$	817736.			0.485257
$120$			3.77037e6i			2.18193i
$121$	−3.83066e6			−2.16231
$122$		−	2.47417e6i		−	1.36254i
$123$	812576.			0.436665
$124$	6.03465e6			3.16510
$125$			174693.i			0.0894427i
$126$		−	7.73505e6i		−	3.86680i
$127$	3.59890e6			1.75695			0.878474	−	0.477789i	$-0.158562\pi$
$127$	3.59890e6			1.75695			0.878474	+	0.477789i	$0.158562\pi$
$128$	−4.67086e6			−2.22724
$129$			782747.i			0.364630i
$130$		−	355815.i		−	0.161955i
$131$	1.60298e6			0.713042			0.356521	−	0.934287i	$-0.383963\pi$
$131$	1.60298e6			0.713042			0.356521	+	0.934287i	$0.383963\pi$
$132$		−	1.68008e7i		−	7.30479i
$133$	3.64660e6			1.55000
$134$		−	3.48136e6i		−	1.44689i
$135$		−	701077.i		−	0.284947i
$136$			2.67152e6i			1.06204i
$137$		−	4.09437e6i		−	1.59230i	−0.605099	−	0.796151i	$-0.706866\pi$
$137$		−	4.09437e6i		−	1.59230i	0.605099	−	0.796151i	$-0.293134\pi$
$138$	−6.49574e6	+	4.30130e6i	−2.47168	+	1.63668i
$139$	−1.14383e6			−0.425910			−0.212955	−	0.977062i	$-0.568309\pi$
$139$	−1.14383e6			−0.425910			−0.212955	+	0.977062i	$0.568309\pi$
$140$	4.66200e6			1.69898
$141$	8.37517e6			2.98770
$142$	−3.37482e6			−1.17865
$143$			986259.i			0.337274i
$144$	1.41275e7			4.73127
$145$			1.58347e6i			0.519404i
$146$	−1.99466e6			−0.640929
$147$	−5.23594e6			−1.64832
$148$		−	8.54170e6i		−	2.63487i
$149$			1.76542e6i			0.533690i	0.963739	+	0.266845i	$0.0859812\pi$
$149$			1.76542e6i			0.533690i	−0.963739	+	0.266845i	$0.914019\pi$
$150$	2.00100e6			0.592887
$151$	2.35710e6			0.684615			0.342308	−	0.939588i	$-0.388792\pi$
$151$	2.35710e6			0.684615			0.342308	+	0.939588i	$0.388792\pi$
$152$			1.19133e7i			3.39236i
$153$		−	1.70717e6i		−	0.476653i
$154$	−1.78063e7			−4.87542
$155$		−	1.99221e6i		−	0.534984i
$156$	−2.95774e6			−0.779087
$157$			6.47695e6i			1.67368i	0.547450	+	0.836838i	$0.315599\pi$
$157$			6.47695e6i			1.67368i	−0.547450	+	0.836838i	$0.684401\pi$
$158$			1.38331e7i			3.50710i
$159$			449422.i			0.111805i
$160$			5.97652e6i			1.45911i
$161$	3.30834e6	+	4.99619e6i	0.792742	+	1.19718i
$162$	3.41906e6			0.804195
$163$	2.40065e6			0.554327			0.277163	−	0.960823i	$-0.410606\pi$
$163$	2.40065e6			0.554327			0.277163	+	0.960823i	$0.410606\pi$
$164$	3.28244e6			0.744158
$165$	−5.54643e6			−1.23470
$166$			1.56557e7i			3.42253i
$167$	−7.59032e6			−1.62971			−0.814855	−	0.579664i	$-0.803184\pi$
$167$	−7.59032e6			−1.62971			−0.814855	+	0.579664i	$0.803184\pi$
$168$		−	3.32174e7i		−	7.00547i
$169$	−4.65318e6			−0.964028
$170$	1.41782e6			0.288585
$171$		−	7.61291e6i		−	1.52252i
$172$			3.16194e6i			0.621397i
$173$	−4.23020e6			−0.817000			−0.408500	−	0.912758i	$-0.633948\pi$
$173$	−4.23020e6			−0.817000			−0.408500	+	0.912758i	$0.633948\pi$
$174$	1.81376e7			3.44297
$175$		−	1.53906e6i		−	0.287172i
$176$		−	3.25219e7i		−	5.96538i
$177$	4.17431e6			0.752775
$178$			7.00200e6i			1.24154i
$179$	−3.33333e6			−0.581192			−0.290596	−	0.956846i	$-0.593854\pi$
$179$	−3.33333e6			−0.581192			−0.290596	+	0.956846i	$0.593854\pi$
$180$		−	9.73274e6i		−	1.66885i
$181$			6.71387e6i			1.13224i	0.824324	+	0.566118i	$0.191555\pi$
$181$			6.71387e6i			1.13224i	−0.824324	+	0.566118i	$0.808445\pi$
$182$			3.13476e6i			0.519985i
$183$			6.78969e6i			1.10789i
$184$	−1.63224e7	+	1.08082e7i	−2.62018	+	1.73501i
$185$	−2.81986e6			−0.445362
$186$	−2.28195e7			−3.54624
$187$	−3.92995e6			−0.600984
$188$	3.38319e7			5.09159
$189$			6.17656e6i			0.914874i
$190$	6.32258e6			0.921794
$191$		−	5.51209e6i		−	0.791073i	−0.918450	−	0.395536i	$-0.870559\pi$
$191$		−	5.51209e6i		−	0.791073i	0.918450	−	0.395536i	$-0.129441\pi$
$192$	3.15948e7			4.46387
$193$	−5.15026e6			−0.716403			−0.358202	−	0.933644i	$-0.616610\pi$
$193$	−5.15026e6			−0.716403			−0.358202	+	0.933644i	$0.616610\pi$
$194$			866290.i			0.118647i
$195$			976436.i			0.131686i
$196$	−2.11508e7			−2.80905
$197$	−3.65294e6			−0.477798			−0.238899	−	0.971044i	$-0.576786\pi$
$197$	−3.65294e6			−0.477798			−0.238899	+	0.971044i	$0.576786\pi$
$198$			3.71738e7i			4.78897i
$199$		−	106147.i		−	0.0134695i	−0.999977	−	0.00673473i	$-0.997856\pi$
$199$		−	106147.i		−	0.0134695i	0.999977	−	0.00673473i	$-0.00214375\pi$
$200$	5.02807e6			0.628509
$201$			9.55366e6i			1.17647i
$202$	1.15403e7			1.40012
$203$		−	1.39505e7i		−	1.66764i
$204$		−	1.17857e7i		−	1.38824i
$205$		−	1.08363e6i		−	0.125782i
$206$		−	2.28722e6i		−	0.261642i
$207$	1.04304e7	−	6.90674e6i	1.17596	−	0.778685i
$208$	−5.72541e6			−0.636234
$209$	−1.75252e7			−1.91965
$210$	−1.76290e7			−1.90357
$211$	−1.08484e6			−0.115483			−0.0577415	−	0.998332i	$-0.518390\pi$
$211$	−1.08484e6			−0.115483			−0.0577415	+	0.998332i	$0.518390\pi$
$212$			1.81546e6i			0.190537i
$213$	9.26127e6			0.958367
$214$		−	2.23972e7i		−	2.28535i
$215$	1.04385e6			0.105032
$216$	−2.01786e7			−2.00231
$217$			1.75516e7i			1.71766i
$218$			2.39090e7i			2.30776i
$219$	5.47380e6			0.521143
$220$	−2.24051e7			−2.10416
$221$			691860.i			0.0640975i
$222$			3.22998e7i			2.95216i
$223$	7.21326e6			0.650455			0.325227	−	0.945636i	$-0.394559\pi$
$223$	7.21326e6			0.650455			0.325227	+	0.945636i	$0.394559\pi$
$224$		−	5.26537e7i		−	4.68473i
$225$	−3.21306e6			−0.282080
$226$		−	1.40044e7i		−	1.21322i
$227$		−	533399.i		−	0.0456010i	−0.999740	−	0.0228005i	$-0.992742\pi$
$227$		−	533399.i		−	0.0456010i	0.999740	−	0.0228005i	$-0.00725825\pi$
$228$		−	5.25570e7i		−	4.43431i
$229$		−	5.00600e6i		−	0.416854i	−0.978038	−	0.208427i	$-0.933166\pi$
$229$		−	5.00600e6i		−	0.416854i	0.978038	−	0.208427i	$-0.0668344\pi$
$230$	5.73610e6	+	8.66255e6i	0.471447	+	0.711971i
$231$	4.88646e7			3.96423
$232$	4.55760e7			3.64982
$233$	1.45319e7			1.14883			0.574414	−	0.818565i	$-0.305230\pi$
$233$	1.45319e7			1.14883			0.574414	+	0.818565i	$0.305230\pi$
$234$	6.54437e6			0.510764
$235$		−	1.11689e7i		−	0.860611i
$236$	1.68623e7			1.28287
$237$		−	3.79612e7i		−	2.85164i
$238$	−1.24911e7			−0.926553
$239$	−7.42504e6			−0.543882			−0.271941	−	0.962314i	$-0.587666\pi$
$239$	−7.42504e6			−0.543882			−0.271941	+	0.962314i	$0.587666\pi$
$240$		−	3.21980e7i		−	2.32914i
$241$			2.39002e7i			1.70746i	0.520715	+	0.853731i	$0.325665\pi$
$241$			2.39002e7i			1.70746i	−0.520715	+	0.853731i	$0.674335\pi$
$242$	5.85143e7			4.12872
$243$	−1.85252e7			−1.29106
$244$			2.74273e7i			1.88805i
$245$			6.98250e6i			0.474802i
$246$	−1.24123e7			−0.833771
$247$			3.08527e6i			0.204740i
$248$	−5.73406e7			−3.75930
$249$		−	4.29628e7i		−	2.78288i
$250$		−	2.66847e6i		−	0.170782i
$251$			3.70571e6i			0.234342i	0.993112	+	0.117171i	$0.0373826\pi$
$251$			3.70571e6i			0.234342i	−0.993112	+	0.117171i	$0.962617\pi$
$252$			8.57464e7i			5.35814i
$253$	−1.58995e7	−	2.40112e7i	−0.981799	−	1.48269i
$254$	−5.49741e7			−3.35473
$255$	−3.89081e6			−0.234650
$256$	2.31107e7			1.37750
$257$	−1.36948e7			−0.806785			−0.403392	−	0.915027i	$-0.632169\pi$
$257$	−1.36948e7			−0.806785			−0.403392	+	0.915027i	$0.632169\pi$
$258$		−	1.19566e7i		−	0.696226i
$259$	2.48433e7			1.42991
$260$			3.94436e6i			0.224418i
$261$	−2.91242e7			−1.63807
$262$	−2.44859e7			−1.36148
$263$			1.26164e7i			0.693533i	0.937951	+	0.346766i	$0.112720\pi$
$263$			1.26164e7i			0.693533i	−0.937951	+	0.346766i	$0.887280\pi$
$264$			1.59639e8i			8.67617i
$265$	599337.			0.0322058
$266$	−5.57026e7			−2.95958
$267$		−	1.92151e7i		−	1.00951i
$268$			3.85925e7i			2.00493i
$269$	3.70047e6			0.190108			0.0950540	−	0.995472i	$-0.469698\pi$
$269$	3.70047e6			0.190108			0.0950540	+	0.995472i	$0.469698\pi$
$270$			1.07091e7i			0.544079i
$271$	2.53188e7			1.27214			0.636070	−	0.771632i	$-0.280559\pi$
$271$	2.53188e7			1.27214			0.636070	+	0.771632i	$0.280559\pi$
$272$		−	2.28141e7i		−	1.13370i
$273$		−	8.60250e6i		−	0.422802i
$274$			6.25424e7i			3.04035i
$275$			7.39657e6i			0.355658i
$276$	7.20082e7	−	4.76818e7i	3.42495	−	2.26791i
$277$	1.43034e7			0.672979			0.336489	−	0.941687i	$-0.390760\pi$
$277$	1.43034e7			0.672979			0.336489	+	0.941687i	$0.390760\pi$
$278$	1.74723e7			0.813235
$279$	3.66421e7			1.68720
$280$	−4.42978e7			−2.01794
$281$			1.21939e7i			0.549569i	0.961506	+	0.274785i	$0.0886066\pi$
$281$			1.21939e7i			0.549569i	−0.961506	+	0.274785i	$0.911393\pi$
$282$	−1.27933e8			−5.70472
$283$			3.40795e6i			0.150361i	0.997170	+	0.0751803i	$0.0239532\pi$
$283$			3.40795e6i			0.150361i	−0.997170	+	0.0751803i	$0.976047\pi$
$284$	3.74113e7			1.63323
$285$	−1.73506e7			−0.749515
$286$		−	1.50653e7i		−	0.643993i
$287$			9.54689e6i			0.403846i
$288$	−1.09924e8			−4.60166
$289$	2.13807e7			0.885786
$290$		−	2.41879e7i		−	0.991753i
$291$		−	2.37730e6i		−	0.0964727i
$292$	2.21117e7			0.888123
$293$			3.53708e7i			1.40618i	0.711099	+	0.703092i	$0.248198\pi$
$293$			3.53708e7i			1.40618i	−0.711099	+	0.703092i	$0.751802\pi$
$294$	7.99801e7			3.14731
$295$		−	5.56675e6i		−	0.216838i
$296$			8.11623e7i			3.12953i
$297$		−	2.96839e7i		−	1.13306i
$298$		−	2.69672e7i		−	1.01903i
$299$	−4.22711e6	+	2.79908e6i	−0.158136	+	0.104713i
$300$	−2.21819e7			−0.821553
$301$	−9.19643e6			−0.337225
$302$	−3.60052e7			−1.30721
$303$	−3.16694e7			−1.13844
$304$		−	1.01737e8i		−	3.62124i
$305$	9.05455e6			0.319130
$306$			2.60774e7i			0.910123i
$307$	−2.02835e7			−0.701014			−0.350507	−	0.936560i	$-0.613991\pi$
$307$	−2.02835e7			−0.701014			−0.350507	+	0.936560i	$0.613991\pi$
$308$	1.97391e8			6.75577
$309$			6.27667e6i			0.212742i
$310$			3.04315e7i			1.02150i
$311$	8.59936e6			0.285881			0.142940	−	0.989731i	$-0.454344\pi$
$311$	8.59936e6			0.285881			0.142940	+	0.989731i	$0.454344\pi$
$312$	2.81041e7			0.925351
$313$		−	3.77817e6i		−	0.123211i	−0.998101	−	0.0616054i	$-0.980378\pi$
$313$		−	3.77817e6i		−	0.123211i	0.998101	−	0.0616054i	$-0.0196220\pi$
$314$		−	9.89369e7i		−	3.19573i
$315$	2.83074e7			0.905667
$316$		−	1.53346e8i		−	4.85972i
$317$	−3.18247e7			−0.999048			−0.499524	−	0.866300i	$-0.666492\pi$
$317$	−3.18247e7			−0.999048			−0.499524	+	0.866300i	$0.666492\pi$
$318$		−	6.86503e6i		−	0.213482i
$319$			6.70448e7i			2.06535i
$320$		−	4.21340e7i		−	1.28583i
$321$			6.14631e7i			1.85823i
$322$	−5.05356e7	−	7.63179e7i	−1.51367	−	2.28591i
$323$	−1.22939e7			−0.364822
$324$	−3.79018e7			−1.11436
$325$	1.30215e6			0.0379324
$326$	−3.66705e7			−1.05843
$327$		−	6.56117e7i		−	1.87645i
$328$	−3.11894e7			−0.883865
$329$			9.83992e7i			2.76315i
$330$	8.47230e7			2.35754
$331$	−3.47101e7			−0.957132			−0.478566	−	0.878052i	$-0.658843\pi$
$331$	−3.47101e7			−0.957132			−0.478566	+	0.878052i	$0.658843\pi$
$332$		−	1.73550e8i		−	4.74254i
$333$		−	5.18648e7i		−	1.40456i
$334$	1.15944e8			3.11178
$335$	1.27405e7			0.338885
$336$			2.83668e8i			7.47811i
$337$			4.06064e7i			1.06098i	0.847693	+	0.530488i	$0.177991\pi$
$337$			4.06064e7i			1.06098i	−0.847693	+	0.530488i	$0.822009\pi$
$338$	7.10784e7			1.84072
$339$			3.84312e7i			0.986472i
$340$	−1.57171e7			−0.399886
$341$		−	8.43512e7i		−	2.12730i
$342$			1.16289e8i			2.90710i
$343$		−	3.57448e6i		−	0.0885788i
$344$		−	3.00445e7i		−	0.738056i
$345$	−1.57412e7	−	2.37720e7i	−0.383336	−	0.578907i
$346$	6.46172e7			1.55998
$347$	7.29687e6			0.174642			0.0873209	−	0.996180i	$-0.472169\pi$
$347$	7.29687e6			0.174642			0.0873209	+	0.996180i	$0.472169\pi$
$348$	−2.01064e8			−4.77085
$349$	1.73998e7			0.409325			0.204663	−	0.978833i	$-0.434390\pi$
$349$	1.73998e7			0.409325			0.204663	+	0.978833i	$0.434390\pi$
$350$			2.35095e7i			0.548327i
$351$	−5.22579e6			−0.120845
$352$			2.53048e8i			5.80197i
$353$	−3.68987e7			−0.838855			−0.419427	−	0.907789i	$-0.637769\pi$
$353$	−3.68987e7			−0.838855			−0.419427	+	0.907789i	$0.637769\pi$
$354$	−6.37636e7			−1.43735
$355$		−	1.23506e7i		−	0.276059i
$356$		−	7.76203e7i		−	1.72038i
$357$	3.42785e7			0.753384
$358$	5.09174e7			1.10973
$359$			3.56531e7i			0.770572i	0.922797	+	0.385286i	$0.125897\pi$
$359$			3.56531e7i			0.770572i	−0.922797	+	0.385286i	$0.874103\pi$
$360$			9.24795e7i			1.98216i
$361$	−7.77720e6			−0.165311
$362$		−	1.02556e8i		−	2.16190i
$363$	−1.60577e8			−3.35709
$364$		−	3.47502e7i		−	0.720532i
$365$		−	7.29972e6i		−	0.150116i
$366$		−	1.03714e8i		−	2.11541i
$367$			3.71977e7i			0.752519i	0.926514	+	0.376259i	$0.122790\pi$
$367$			3.71977e7i			0.752519i	−0.926514	+	0.376259i	$0.877210\pi$
$368$	1.39389e8	−	9.22995e7i	2.79695	−	1.85206i
$369$	1.99308e7			0.396685
$370$	4.30741e7			0.850376
$371$	−5.28022e6			−0.103402
$372$	2.52965e8			4.91396
$373$			2.17293e6i			0.0418715i	0.999781	+	0.0209357i	$0.00666454\pi$
$373$			2.17293e6i			0.0418715i	−0.999781	+	0.0209357i	$0.993335\pi$
$374$	6.00310e7			1.14752
$375$			7.32290e6i			0.138864i
$376$	−3.21467e8			−6.04747
$377$	1.18031e7			0.220278
$378$		−	9.43484e7i		−	1.74686i
$379$		−	7.54489e7i		−	1.38591i	−0.720981	−	0.692955i	$-0.756308\pi$
$379$		−	7.54489e7i		−	1.38591i	0.720981	−	0.692955i	$-0.243692\pi$
$380$	−7.00887e7			−1.27731
$381$	1.50861e8			2.72774
$382$			8.41985e7i			1.51048i
$383$		−	5.28867e7i		−	0.941348i	−0.882307	−	0.470674i	$-0.844011\pi$
$383$		−	5.28867e7i		−	0.941348i	0.882307	−	0.470674i	$-0.155989\pi$
$384$	−1.95797e8			−3.45789
$385$		−	6.51645e7i		−	1.14190i
$386$	7.86715e7			1.36790
$387$			1.91992e7i			0.331245i
$388$		−	9.60321e6i		−	0.164407i
$389$		−	7.23230e7i		−	1.22865i	−0.789054	−	0.614324i	$-0.789429\pi$
$389$		−	7.23230e7i		−	1.22865i	0.789054	−	0.614324i	$-0.210571\pi$
$390$		−	1.49153e7i		−	0.251442i
$391$	−1.11535e7	−	1.68438e7i	−0.186587	−	0.281780i
$392$	2.00973e8			3.33641
$393$	6.71950e7			1.10703
$394$	5.57995e7			0.912309
$395$	−5.06240e7			−0.821419
$396$		−	4.12088e8i		−	6.63598i
$397$	3.03224e7			0.484610			0.242305	−	0.970200i	$-0.422097\pi$
$397$	3.03224e7			0.484610			0.242305	+	0.970200i	$0.422097\pi$
$398$			1.62143e6i			0.0257186i
$399$	1.52861e8			2.40645
$400$	−4.29384e7			−0.670912
$401$			7.73441e7i			1.19948i	0.800194	+	0.599741i	$0.204730\pi$
$401$			7.73441e7i			1.19948i	−0.800194	+	0.599741i	$0.795270\pi$
$402$		−	1.45934e8i		−	2.24636i
$403$	−1.48498e7			−0.226885
$404$	−1.27930e8			−1.94012
$405$			1.25125e7i			0.188356i
$406$			2.13097e8i			3.18420i
$407$	−1.19394e8			−1.77093
$408$			1.11987e8i			1.64887i
$409$	−3.21457e7			−0.469844			−0.234922	−	0.972014i	$-0.575483\pi$
$409$	−3.21457e7			−0.469844			−0.234922	+	0.972014i	$0.575483\pi$
$410$			1.65527e7i			0.240169i
$411$		−	1.71631e8i		−	2.47212i
$412$			2.53549e7i			0.362552i
$413$			4.90436e7i			0.696197i
$414$	−1.59327e8	+	1.05502e8i	−2.24537	+	1.48682i
$415$	−5.72940e7			−0.801613
$416$	4.45486e7			0.618805
$417$	−4.79480e7			−0.661245
$418$	2.67701e8			3.66540
$419$			1.11082e8i			1.51008i	0.655676	+	0.755042i	$0.272384\pi$
$419$			1.11082e8i			1.51008i	−0.655676	+	0.755042i	$0.727616\pi$
$420$	1.95425e8			2.63774
$421$			9.64125e7i			1.29207i	0.763307	+	0.646036i	$0.223575\pi$
$421$			9.64125e7i			1.29207i	−0.763307	+	0.646036i	$0.776425\pi$
$422$	1.65712e7			0.220504
$423$	2.05426e8			2.71415
$424$		−	1.72503e7i		−	0.226308i
$425$			5.18868e6i			0.0675912i
$426$	−1.41468e8			−1.82991
$427$	−7.97715e7			−1.02462
$428$			2.48283e8i			3.16677i
$429$			4.13427e7i			0.523633i
$430$	−1.59451e7			−0.200549
$431$		−	7.68113e7i		−	0.959385i	−0.877437	−	0.479693i	$-0.840748\pi$
$431$		−	7.68113e7i		−	0.959385i	0.877437	−	0.479693i	$-0.159252\pi$
$432$	1.72320e8			2.13740
$433$		−	4.56123e6i		−	0.0561848i	−0.999605	−	0.0280924i	$-0.991057\pi$
$433$		−	4.56123e6i		−	0.0561848i	0.999605	−	0.0280924i	$-0.00894326\pi$
$434$		−	2.68105e8i		−	3.27971i
$435$			6.63770e7i			0.806399i
$436$		−	2.65042e8i		−	3.19782i
$437$	−4.97377e7	−	7.51129e7i	−0.595993	−	0.900057i
$438$	−8.36136e7			−0.995072
$439$	8.58431e7			1.01464			0.507320	−	0.861758i	$-0.330636\pi$
$439$	8.58431e7			1.01464			0.507320	+	0.861758i	$0.330636\pi$
$440$	2.12891e8			2.49919
$441$	−1.28427e8			−1.49741
$442$		−	1.05683e7i		−	0.122388i
$443$	−8.46082e7			−0.973198			−0.486599	−	0.873625i	$-0.661763\pi$
$443$	−8.46082e7			−0.973198			−0.486599	+	0.873625i	$0.661763\pi$
$444$		−	3.58057e8i		−	4.09075i
$445$	−2.56247e7			−0.290790
$446$	−1.10184e8			−1.24198
$447$			7.40041e7i			0.828578i
$448$			3.71204e8i			4.12837i
$449$	1.19572e8			1.32096			0.660479	−	0.750845i	$-0.270353\pi$
$449$	1.19572e8			1.32096			0.660479	+	0.750845i	$0.270353\pi$
$450$	4.90803e7			0.538604
$451$		−	4.58814e7i		−	0.500157i
$452$			1.55245e8i			1.68113i
$453$	9.88065e7			1.06290
$454$			8.14779e6i			0.0870707i
$455$	−1.14721e7			−0.121789
$456$			4.99392e8i			5.26680i
$457$		−	5.40238e6i		−	0.0566026i	−0.999599	−	0.0283013i	$-0.990990\pi$
$457$		−	5.40238e6i		−	0.0566026i	0.999599	−	0.0283013i	$-0.00900978\pi$
$458$			7.64678e7i			0.795943i
$459$		−	2.08232e7i		−	0.215333i
$460$	−6.35872e7	−	9.60282e7i	−0.653275	−	0.986564i
$461$	1.76741e8			1.80399			0.901994	−	0.431750i	$-0.142104\pi$
$461$	1.76741e8			1.80399			0.901994	+	0.431750i	$0.142104\pi$
$462$	−7.46418e8			−7.56931
$463$	−9.71163e7			−0.978473			−0.489237	−	0.872151i	$-0.662725\pi$
$463$	−9.71163e7			−0.978473			−0.489237	+	0.872151i	$0.662725\pi$
$464$	−3.89207e8			−3.89607
$465$		−	8.35111e7i		−	0.830587i
$466$	−2.21978e8			−2.19358
$467$			2.51253e7i			0.246695i	0.992364	+	0.123348i	$0.0393630\pi$
$467$			2.51253e7i			0.246695i	−0.992364	+	0.123348i	$0.960637\pi$
$468$	−7.25473e7			−0.707756
$469$	−1.12245e8			−1.08805
$470$			1.70608e8i			1.64325i
$471$			2.71506e8i			2.59846i
$472$	−1.60224e8			−1.52371
$473$	4.41971e7			0.417648
$474$			5.79865e8i			5.44493i
$475$			2.31383e7i			0.215899i
$476$	1.38469e8			1.28391
$477$			1.10234e7i			0.101569i
$478$	1.13419e8			1.03849
$479$			8.93574e6i			0.0813063i	0.999173	+	0.0406531i	$0.0129439\pi$
$479$			8.93574e6i			0.0813063i	−0.999173	+	0.0406531i	$0.987056\pi$
$480$			2.50528e8i			2.26534i
$481$			2.10191e7i			0.188877i
$482$		−	3.65082e8i		−	3.26023i
$483$	1.38681e8	+	2.09434e8i	1.23077	+	1.85868i
$484$	−6.48657e8			−5.72109
$485$	−3.17030e6			−0.0277892
$486$	2.82977e8			2.46515
$487$	−1.62154e7			−0.140391			−0.0701957	−	0.997533i	$-0.522362\pi$
$487$	−1.62154e7			−0.140391			−0.0701957	+	0.997533i	$0.522362\pi$
$488$		−	2.60611e8i		−	2.24251i
$489$	1.00632e8			0.860618
$490$		−	1.06659e8i		−	0.906590i
$491$	−3.21366e7			−0.271491			−0.135745	−	0.990744i	$-0.543343\pi$
$491$	−3.21366e7			−0.271491			−0.135745	+	0.990744i	$0.543343\pi$
$492$	1.37596e8			1.15534
$493$			4.70318e7i			0.392510i
$494$		−	4.71282e7i		−	0.390931i
$495$	−1.36042e8			−1.12165
$496$	4.89674e8			4.01293
$497$			1.08810e8i			0.886337i
$498$			6.56266e8i			5.31364i
$499$	6.99593e7			0.563046			0.281523	−	0.959554i	$-0.409160\pi$
$499$	6.99593e7			0.563046			0.281523	+	0.959554i	$0.409160\pi$
$500$			2.95812e7i			0.236650i
$501$	−3.18176e8			−2.53020
$502$		−	5.66056e7i		−	0.447454i
$503$		−	6.76574e7i		−	0.531633i	−0.964024	−	0.265816i	$-0.914359\pi$
$503$		−	6.76574e7i		−	0.531633i	0.964024	−	0.265816i	$-0.0856415\pi$
$504$		−	8.14754e8i		−	6.36407i
$505$			4.22334e7i			0.327931i
$506$	2.42869e8	+	3.66776e8i	1.87465	+	2.83106i
$507$	−1.95055e8			−1.49670
$508$	6.09412e8			4.64858
$509$	−2.24719e8			−1.70406			−0.852032	−	0.523490i	$-0.824630\pi$
$509$	−2.24719e8			−1.70406			−0.852032	+	0.523490i	$0.824630\pi$
$510$	5.94331e7			0.448041
$511$			6.43112e7i			0.481974i
$512$	−5.40862e7			−0.402974
$513$		−	9.28587e7i		−	0.687813i
$514$	2.09192e8			1.54048
$515$	8.37039e6			0.0612808
$516$			1.32545e8i			0.964747i
$517$		−	4.72896e8i		−	3.42211i
$518$	−3.79487e8			−2.73028
$519$	−1.77324e8			−1.26843
$520$		−	3.74789e7i		−	0.266549i
$521$			1.14937e7i			0.0812730i	0.999174	+	0.0406365i	$0.0129386\pi$
$521$			1.14937e7i			0.0812730i	−0.999174	+	0.0406365i	$0.987061\pi$
$522$	4.44879e8			3.12774
$523$			6.63858e7i			0.464056i	0.972709	+	0.232028i	$0.0745361\pi$
$523$			6.63858e7i			0.464056i	−0.972709	+	0.232028i	$0.925464\pi$
$524$	2.71437e8			1.88658
$525$		−	6.45155e7i		−	0.445847i
$526$		−	1.92718e8i		−	1.32423i
$527$		−	5.91723e7i		−	0.404284i
$528$		−	1.36328e9i		−	9.26152i
$529$	5.77879e7	−	1.36291e8i	0.390364	−	0.920661i
$530$	−9.15502e6			−0.0614938
$531$	1.02387e8			0.683852
$532$	6.17488e8			4.10104
$533$	−8.07731e6			−0.0533440
$534$			2.93515e8i			1.92755i
$535$	8.19655e7			0.535266
$536$		−	3.66702e8i		−	2.38132i
$537$	−1.39729e8			−0.902327
$538$	−5.65256e7			−0.362993
$539$			2.95642e8i			1.88799i
$540$		−	1.18715e8i		−	0.753920i
$541$	−2.05867e6			−0.0130015			−0.00650077	−	0.999979i	$-0.502069\pi$
$541$	−2.05867e6			−0.0130015			−0.00650077	+	0.999979i	$0.502069\pi$
$542$	−3.86750e8			−2.42903
$543$			2.81437e8i			1.75785i
$544$			1.77513e8i			1.10264i
$545$	−8.74980e7			−0.540516
$546$			1.31405e8i			0.807300i
$547$	1.26195e8			0.771044			0.385522	−	0.922699i	$-0.374021\pi$
$547$	1.26195e8			0.771044			0.385522	+	0.922699i	$0.374021\pi$
$548$		−	6.93311e8i		−	4.21295i
$549$			1.66537e8i			1.00645i
$550$		−	1.12984e8i		−	0.679094i
$551$			2.09733e8i			1.25375i
$552$	−6.84214e8	+	4.53068e8i	−4.06794	+	2.69368i
$553$	4.46002e8			2.63731
$554$	−2.18488e8			−1.28499
$555$	−1.18205e8			−0.691445
$556$	−1.93688e8			−1.12688
$557$			2.43041e8i			1.40642i	0.710984	+	0.703209i	$0.248250\pi$
$557$			2.43041e8i			1.40642i	−0.710984	+	0.703209i	$0.751750\pi$
$558$	−5.59716e8			−3.22155
$559$		−	7.78080e6i		−	0.0445439i
$560$	3.78292e8			2.15408
$561$	−1.64739e8			−0.933055
$562$		−	1.86264e8i		−	1.04935i
$563$			1.04469e8i			0.585414i	0.956202	+	0.292707i	$0.0945561\pi$
$563$			1.04469e8i			0.585414i	−0.956202	+	0.292707i	$0.905444\pi$
$564$	1.41819e9			7.90492
$565$	5.12508e7			0.284155
$566$		−	5.20573e7i		−	0.287099i
$567$		−	1.10236e8i		−	0.604749i
$568$	−3.55479e8			−1.93985
$569$		−	1.48184e8i		−	0.804388i	−0.915554	−	0.402194i	$-0.868248\pi$
$569$		−	1.48184e8i		−	0.804388i	0.915554	−	0.402194i	$-0.131752\pi$
$570$	2.65035e8			1.43113
$571$		−	2.00764e8i		−	1.07839i	−0.842179	−	0.539197i	$-0.818728\pi$
$571$		−	2.00764e8i		−	1.07839i	0.842179	−	0.539197i	$-0.181272\pi$
$572$			1.67006e8i			0.892368i
$573$		−	2.31060e8i		−	1.22818i
$574$		−	1.45831e8i		−	0.771106i
$575$	−3.17017e7	+	2.09920e7i	−0.166755	+	0.110421i
$576$	7.74955e8			4.05517
$577$	6.94880e7			0.361728			0.180864	−	0.983508i	$-0.442111\pi$
$577$	6.94880e7			0.361728			0.180864	+	0.983508i	$0.442111\pi$
$578$	−3.26595e8			−1.69132
$579$	−2.15893e8			−1.11225
$580$			2.68133e8i			1.37425i
$581$	5.04766e8			2.57372
$582$			3.63138e7i			0.184205i
$583$	2.53762e7			0.128062
$584$	−2.10103e8			−1.05486
$585$			2.39500e7i			0.119629i
$586$		−	5.40297e8i		−	2.68497i
$587$	−1.26631e8			−0.626074			−0.313037	−	0.949741i	$-0.601346\pi$
$587$	−1.26631e8			−0.626074			−0.313037	+	0.949741i	$0.601346\pi$
$588$	−8.86615e8			−4.36117
$589$		−	2.63872e8i		−	1.29136i
$590$			8.50334e7i			0.414032i
$591$	−1.53127e8			−0.741803
$592$		−	6.93105e8i		−	3.34067i
$593$	3.59832e8			1.72558			0.862792	−	0.505559i	$-0.168714\pi$
$593$	3.59832e8			1.72558			0.862792	+	0.505559i	$0.168714\pi$
$594$			4.53429e8i			2.16346i
$595$		−	4.57128e7i		−	0.217014i
$596$			2.98943e8i			1.41205i
$597$		−	4.44956e6i		−	0.0209119i
$598$	6.45701e7	−	4.27565e7i	0.301945	−	0.199940i
$599$	−3.80464e8			−1.77024			−0.885122	−	0.465360i	$-0.845925\pi$
$599$	−3.80464e8			−1.77024			−0.885122	+	0.465360i	$0.845925\pi$
$600$	2.10770e8			0.975789
$601$	−8.15589e7			−0.375706			−0.187853	−	0.982197i	$-0.560153\pi$
$601$	−8.15589e7			−0.375706			−0.187853	+	0.982197i	$0.560153\pi$
$602$	1.40478e8			0.643899
$603$			2.34332e8i			1.06876i
$604$	3.99134e8			1.81137
$605$			2.14141e8i			0.967015i
$606$	4.83757e8			2.17375
$607$	3.47086e8			1.55193			0.775964	−	0.630778i	$-0.217264\pi$
$607$	3.47086e8			1.55193			0.775964	+	0.630778i	$0.217264\pi$
$608$			7.91598e8i			3.52204i
$609$		−	5.84788e8i		−	2.58909i
$610$	−1.38310e8			−0.609348
$611$	−8.32523e7			−0.364983
$612$		−	2.89080e8i		−	1.26114i
$613$		−	3.12710e6i		−	0.0135756i	−0.999977	−	0.00678781i	$-0.997839\pi$
$613$		−	3.12710e6i		−	0.0135756i	0.999977	−	0.00678781i	$-0.00216064\pi$
$614$	3.09835e8			1.33852
$615$		−	4.54244e7i		−	0.195283i
$616$	−1.87559e9			−8.02408
$617$			2.59497e8i			1.10478i	0.833585	+	0.552392i	$0.186285\pi$
$617$			2.59497e8i			1.10478i	−0.833585	+	0.552392i	$0.813715\pi$
$618$		−	9.58775e7i		−	0.406211i
$619$			1.97994e8i			0.834797i	0.908724	+	0.417399i	$0.137058\pi$
$619$			1.97994e8i			0.834797i	−0.908724	+	0.417399i	$0.862942\pi$
$620$		−	3.37347e8i		−	1.41547i
$621$	1.27225e8	−	8.42451e7i	0.531250	−	0.351779i
$622$	−1.31357e8			−0.545862
$623$	2.25756e8			0.933632
$624$	−2.40002e8			−0.987782
$625$	9.76562e6			0.0400000
$626$			5.77125e7i			0.235259i
$627$	−7.34633e8			−2.98035
$628$			1.09676e9i			4.42826i
$629$	−8.37549e7			−0.336557
$630$	−4.32402e8			−1.72928
$631$		−	1.13862e7i		−	0.0453201i	−0.999743	−	0.0226600i	$-0.992786\pi$
$631$		−	1.13862e7i		−	0.0453201i	0.999743	−	0.0226600i	$-0.00721353\pi$
$632$			1.45708e9i			5.77207i
$633$	−4.54751e7			−0.179293
$634$	4.86129e8			1.90759
$635$		−	2.01185e8i		−	0.785731i
$636$			7.61019e7i			0.295818i
$637$	5.20472e7			0.201363
$638$		−	1.02412e9i		−	3.94358i
$639$	2.27160e8			0.870621
$640$			2.61109e8i			0.996052i
$641$		−	3.47081e8i		−	1.31782i	−0.752220	−	0.658912i	$-0.771017\pi$
$641$		−	3.47081e8i		−	1.31782i	0.752220	−	0.658912i	$-0.228983\pi$
$642$		−	9.38863e8i		−	3.54811i
$643$			4.46086e8i			1.67798i	0.544149	+	0.838989i	$0.316853\pi$
$643$			4.46086e8i			1.67798i	−0.544149	+	0.838989i	$0.683147\pi$
$644$	5.60210e8	+	8.46018e8i	2.09746	+	3.16754i
$645$	4.37569e7			0.163067
$646$	1.87792e8			0.696593
$647$	8.72850e6			0.0322275			0.0161138	−	0.999870i	$-0.494871\pi$
$647$	8.72850e6			0.0322275			0.0161138	+	0.999870i	$0.494871\pi$
$648$	3.60139e8			1.32356
$649$		−	2.35699e8i		−	0.862229i
$650$	−1.98906e7			−0.0724284
$651$			7.35741e8i			2.66675i
$652$	4.06509e8			1.46665
$653$	−2.36182e8			−0.848217			−0.424108	−	0.905611i	$-0.639412\pi$
$653$	−2.36182e8			−0.848217			−0.424108	+	0.905611i	$0.639412\pi$
$654$			1.00223e9i			3.58291i
$655$		−	8.96094e7i		−	0.318882i
$656$	2.66349e8			0.943496
$657$	1.34261e8			0.473428
$658$		−	1.50307e9i		−	5.27596i
$659$			3.25879e8i			1.13868i	0.822103	+	0.569338i	$0.192800\pi$
$659$			3.25879e8i			1.13868i	−0.822103	+	0.569338i	$0.807200\pi$
$660$	−9.39192e8			−3.26680
$661$		−	3.92394e8i		−	1.35868i	−0.733823	−	0.679340i	$-0.762266\pi$
$661$		−	3.92394e8i		−	1.35868i	0.733823	−	0.679340i	$-0.237734\pi$
$662$	5.30205e8			1.82755
$663$			2.90019e7i			0.0995143i
$664$			1.64906e9i			5.63289i
$665$		−	2.03851e8i		−	0.693183i
$666$			7.92246e8i			2.68187i
$667$	−2.87354e8	+	1.90278e8i	−0.968366	+	0.641225i
$668$	−1.28529e9			−4.31193
$669$	3.02371e8			1.00986
$670$	−1.94614e8			−0.647068
$671$	3.83374e8			1.26898
$672$		−	2.20718e9i		−	7.27326i
$673$	−3.78830e8			−1.24280			−0.621398	−	0.783495i	$-0.713435\pi$
$673$	−3.78830e8			−1.24280			−0.621398	+	0.783495i	$0.713435\pi$
$674$		−	6.20273e8i		−	2.02583i
$675$	−3.91914e7			−0.127432
$676$	−7.87936e8			−2.55065
$677$		−	6.24225e7i		−	0.201176i	−0.994928	−	0.100588i	$-0.967928\pi$
$677$		−	6.24225e7i		−	0.201176i	0.994928	−	0.100588i	$-0.0320723\pi$
$678$		−	5.87046e8i		−	1.88357i
$679$	2.79307e7			0.0892220
$680$	1.49343e8			0.474960
$681$		−	2.23594e7i		−	0.0707976i
$682$			1.28848e9i			4.06187i
$683$	−2.89343e8			−0.908136			−0.454068	−	0.890967i	$-0.650028\pi$
$683$	−2.89343e8			−0.908136			−0.454068	+	0.890967i	$0.650028\pi$
$684$		−	1.28912e9i		−	4.02832i
$685$	−2.28882e8			−0.712099
$686$			5.46009e7i			0.169133i
$687$		−	2.09845e8i		−	0.647185i
$688$			2.56572e8i			0.787850i
$689$		−	4.46742e6i		−	0.0136584i
$690$	2.40450e8	+	3.63123e8i	0.731943	+	1.10537i
$691$	3.31690e8			1.00531			0.502653	−	0.864488i	$-0.332357\pi$
$691$	3.31690e8			1.00531			0.502653	+	0.864488i	$0.332357\pi$
$692$	−7.16311e8			−2.16164
$693$	1.19855e9			3.60127
$694$	−1.11461e8			−0.333462
$695$			6.39422e7i			0.190473i
$696$	1.91049e9			5.66652
$697$		−	3.21857e7i		−	0.0950528i
$698$	−2.65786e8			−0.781568
$699$	6.09159e8			1.78361
$700$		−	2.60613e8i		−	0.759806i
$701$			3.46807e8i			1.00678i	0.864060	+	0.503389i	$0.167914\pi$
$701$			3.46807e8i			1.00678i	−0.864060	+	0.503389i	$0.832086\pi$
$702$	7.98251e7			0.230743
$703$	−3.73495e8			−1.07503
$704$		−	1.78397e9i		−	5.11293i
$705$		−	4.68186e8i		−	1.33614i
$706$	5.63636e8			1.60171
$707$		−	3.72081e8i		−	1.05288i
$708$	7.06848e8			1.99171
$709$		−	1.26936e8i		−	0.356161i	−0.984016	−	0.178081i	$-0.943011\pi$
$709$		−	1.26936e8i		−	0.356161i	0.984016	−	0.178081i	$-0.0569888\pi$
$710$			1.88658e8i			0.527109i
$711$		−	9.31109e8i		−	2.59055i
$712$			7.37540e8i			2.04336i
$713$	3.61530e8	−	2.39395e8i	0.997413	−	0.660459i
$714$	−5.23611e8			−1.43852
$715$	5.51336e7			0.150834
$716$	−5.64442e8			−1.53773
$717$	−3.11248e8			−0.844402
$718$		−	5.44609e8i		−	1.47133i
$719$	−1.82145e8			−0.490038			−0.245019	−	0.969518i	$-0.578794\pi$
$719$	−1.82145e8			−0.490038			−0.245019	+	0.969518i	$0.578794\pi$
$720$		−	7.89751e8i		−	2.11589i
$721$	−7.37440e7			−0.196753
$722$	1.18799e8			0.315645
$723$			1.00187e9i			2.65091i
$724$			1.13688e9i			2.99570i
$725$	8.85186e7			0.232285
$726$	2.45285e9			6.41003
$727$			4.24942e8i			1.10593i	0.833205	+	0.552964i	$0.186503\pi$
$727$			4.24942e8i			1.10593i	−0.833205	+	0.552964i	$0.813497\pi$
$728$			3.30193e8i			0.855803i
$729$	−6.13383e8			−1.58325
$730$			1.11505e8i			0.286632i
$731$	3.10042e7			0.0793722
$732$			1.14972e9i			2.93128i
$733$		−	2.50034e8i		−	0.634872i	−0.948280	−	0.317436i	$-0.897178\pi$
$733$		−	2.50034e8i		−	0.634872i	0.948280	−	0.317436i	$-0.102822\pi$
$734$		−	5.68203e8i		−	1.43686i
$735$			2.92698e8i			0.737152i
$736$	−1.08457e9	+	7.18170e8i	−2.72034	+	1.80133i
$737$	5.39439e8			1.34753
$738$	−3.04448e8			−0.757432
$739$	2.71279e8			0.672177			0.336088	−	0.941830i	$-0.390896\pi$
$739$	2.71279e8			0.672177			0.336088	+	0.941830i	$0.390896\pi$
$740$	−4.77495e8			−1.17835
$741$			1.29330e8i			0.317867i
$742$	8.06566e7			0.197437
$743$		−	4.67051e8i		−	1.13867i	−0.822105	−	0.569335i	$-0.807201\pi$
$743$		−	4.67051e8i		−	1.13867i	0.822105	−	0.569335i	$-0.192799\pi$
$744$	−2.40365e9			−5.83649
$745$	9.86899e7			0.238673
$746$		−	3.31919e7i		−	0.0799496i
$747$		−	1.05379e9i		−	2.52808i
$748$	−6.65470e8			−1.59010
$749$	−7.22125e8			−1.71857
$750$		−	1.11859e8i		−	0.265147i
$751$			2.64043e8i			0.623382i	0.950184	+	0.311691i	$0.100895\pi$
$751$			2.64043e8i			0.623382i	−0.950184	+	0.311691i	$0.899105\pi$
$752$	2.74525e9			6.45547
$753$			1.55339e8i			0.363827i
$754$	−1.80295e8			−0.420600
$755$		−	1.31766e8i		−	0.306169i
$756$			1.04589e9i			2.42060i
$757$		−	4.42774e8i		−	1.02069i	−0.859969	−	0.510346i	$-0.829517\pi$
$757$		−	4.42774e8i		−	1.02069i	0.859969	−	0.510346i	$-0.170483\pi$
$758$			1.15250e9i			2.64626i
$759$	−6.66488e8	−	1.00652e9i	−1.52429	−	2.30195i
$760$	6.65975e8			1.51711
$761$	2.17051e8			0.492501			0.246251	−	0.969206i	$-0.420801\pi$
$761$	2.17051e8			0.492501			0.246251	+	0.969206i	$0.420801\pi$
$762$	−2.30444e9			−5.20836
$763$	7.70866e8			1.73542
$764$		−	9.33378e8i		−	2.09304i
$765$	−9.54336e7			−0.213166
$766$			8.07857e8i			1.79741i
$767$	−4.14942e7			−0.0919605
$768$	9.68771e8			2.13864
$769$		−	3.30362e8i		−	0.726459i	−0.931700	−	0.363230i	$-0.881674\pi$
$769$		−	3.30362e8i		−	0.726459i	0.931700	−	0.363230i	$-0.118326\pi$
$770$			9.95403e8i			2.18035i
$771$	−5.74070e8			−1.25257
$772$	−8.72108e8			−1.89548
$773$		−	2.04911e8i		−	0.443637i	−0.975088	−	0.221818i	$-0.928801\pi$
$773$		−	2.04911e8i		−	0.443637i	0.975088	−	0.221818i	$-0.0711992\pi$
$774$		−	2.93272e8i		−	0.632481i
$775$	−1.11368e8			−0.239252
$776$			9.12487e7i			0.195273i
$777$	1.04140e9			2.22001
$778$			1.10475e9i			2.34599i
$779$		−	1.43528e8i		−	0.303616i
$780$			1.65343e8i			0.348418i
$781$		−	5.22929e8i		−	1.09771i
$782$	1.70372e8	+	2.57293e8i	0.356269	+	0.538031i
$783$	−3.55243e8			−0.740014
$784$	−1.71626e9			−3.56151
$785$	3.62073e8			0.748491
$786$	−1.02642e9			−2.11377
$787$			6.62821e8i			1.35979i	0.733310	+	0.679895i	$0.237975\pi$
$787$			6.62821e8i			1.35979i	−0.733310	+	0.679895i	$0.762025\pi$
$788$	−6.18563e8			−1.26417
$789$			5.28862e8i			1.07674i
$790$	7.73293e8			1.56842
$791$	−4.51525e8			−0.912331
$792$			3.91562e9i			7.88180i
$793$		−	6.74921e7i		−	0.135342i
$794$	−4.63182e8			−0.925316
$795$	2.51235e7			0.0500009
$796$		−	1.79742e7i		−	0.0356378i
$797$		−	8.83821e7i		−	0.174578i	−0.996183	−	0.0872890i	$-0.972180\pi$
$797$		−	8.83821e7i		−	0.174578i	0.996183	−	0.0872890i	$-0.0278204\pi$
$798$	−2.33498e9			−4.59489
$799$		−	3.31736e8i		−	0.650358i
$800$	3.34098e8			0.652534
$801$		−	4.71306e8i		−	0.917077i
$802$		−	1.18145e9i		−	2.29030i
$803$		−	3.09073e8i		−	0.596918i
$804$			1.61775e9i			3.11274i
$805$	2.79295e8	−	1.84942e8i	0.535397	−	0.354525i
$806$	2.26835e8			0.433216
$807$	1.55119e8			0.295151
$808$	1.21558e9			2.30435
$809$	8.41160e8			1.58867			0.794334	−	0.607481i	$-0.207820\pi$
$809$	8.41160e8			1.58867			0.794334	+	0.607481i	$0.207820\pi$
$810$		−	1.91131e8i		−	0.359647i
$811$	−3.86442e8			−0.724473			−0.362237	−	0.932086i	$-0.617987\pi$
$811$	−3.86442e8			−0.724473			−0.362237	+	0.932086i	$0.617987\pi$
$812$		−	2.36228e9i		−	4.41228i
$813$	1.06133e9			1.97505
$814$	1.82378e9			3.38141
$815$		−	1.34200e8i		−	0.247902i
$816$		−	9.56337e8i		−	1.76011i
$817$	1.38259e8			0.253530
$818$	4.91034e8			0.897122
$819$		−	2.11002e8i		−	0.384091i
$820$		−	1.83494e8i		−	0.332798i
$821$	−2.96260e8			−0.535357			−0.267678	−	0.963508i	$-0.586256\pi$
$821$	−2.96260e8			−0.535357			−0.267678	+	0.963508i	$0.586256\pi$
$822$			2.62170e9i			4.72028i
$823$	9.20558e8			1.65140			0.825699	−	0.564111i	$-0.190781\pi$
$823$	9.20558e8			1.65140			0.825699	+	0.564111i	$0.190781\pi$
$824$		−	2.40920e8i		−	0.430616i
$825$			3.10055e8i			0.552175i
$826$		−	7.49153e8i		−	1.32932i
$827$			2.30978e8i			0.408370i	0.978932	+	0.204185i	$0.0654544\pi$
$827$			2.30978e8i			0.408370i	−0.978932	+	0.204185i	$0.934546\pi$
$828$	1.76621e9	−	1.16954e9i	3.11137	−	2.06026i
$829$	8.05098e8			1.41314			0.706570	−	0.707643i	$-0.250241\pi$
$829$	8.05098e8			1.41314			0.706570	+	0.707643i	$0.250241\pi$
$830$	8.75179e8			1.53060
$831$	5.99582e8			1.04483
$832$	−3.14064e8			−0.545316
$833$			2.07393e8i			0.358805i
$834$	7.32417e8			1.26258
$835$			4.24312e8i			0.728829i
$836$	−2.96758e9			−5.07907
$837$	4.46943e8			0.762211
$838$		−	1.69680e9i		−	2.88336i
$839$			2.10569e8i			0.356541i	0.983982	+	0.178270i	$0.0570502\pi$
$839$			2.10569e8i			0.356541i	−0.983982	+	0.178270i	$0.942950\pi$
$840$	−1.85691e9			−3.13294
$841$	2.07536e8			0.348904
$842$		−	1.47272e9i		−	2.46709i
$843$			5.11152e8i			0.853232i
$844$	−1.83699e8			−0.305548
$845$			2.60121e8i			0.431127i
$846$	−3.13793e9			−5.18241
$847$		−	1.88660e9i		−	3.10477i
$848$			1.47313e8i			0.241576i
$849$			1.42857e8i			0.233442i
$850$		−	7.92584e7i		−	0.129059i
$851$	−3.38850e8	−	5.11724e8i	−0.549817	−	0.830323i
$852$	1.56824e9			2.53567
$853$	−1.21498e9			−1.95760			−0.978799	−	0.204821i	$-0.934339\pi$
$853$	−1.21498e9			−1.95760			−0.978799	+	0.204821i	$0.934339\pi$
$854$	1.21853e9			1.95642
$855$	−4.25575e8			−0.680891
$856$		−	2.35916e9i		−	3.76129i
$857$	4.27304e8			0.678883			0.339441	−	0.940627i	$-0.389762\pi$
$857$	4.27304e8			0.678883			0.339441	+	0.940627i	$0.389762\pi$
$858$		−	6.31520e8i		−	0.999828i
$859$	4.88323e8			0.770420			0.385210	−	0.922829i	$-0.374129\pi$
$859$	4.88323e8			0.770420			0.385210	+	0.922829i	$0.374129\pi$
$860$	1.76758e8			0.277897
$861$			4.00193e8i			0.626990i
$862$			1.17331e9i			1.83185i
$863$	9.75359e8			1.51751			0.758756	−	0.651375i	$-0.225807\pi$
$863$	9.75359e8			1.51751			0.758756	+	0.651375i	$0.225807\pi$
$864$	−1.34080e9			−2.07885
$865$			2.36475e8i			0.365374i
$866$			6.96739e7i			0.107279i
$867$	8.96252e8			1.37522
$868$			2.97206e9i			4.54463i
$869$	−2.14344e9			−3.26627
$870$		−	1.01392e9i		−	1.53974i
$871$		−	9.49670e7i		−	0.143720i
$872$			2.51840e9i			3.79817i
$873$		−	5.83102e7i		−	0.0876399i
$874$	7.59755e8	+	1.14737e9i	1.13799	+	1.71857i
$875$	−8.60361e7			−0.128427
$876$	9.26894e8			1.37885
$877$	−1.02984e9			−1.52677			−0.763383	−	0.645946i	$-0.776463\pi$
$877$	−1.02984e9			−1.52677			−0.763383	+	0.645946i	$0.776463\pi$
$878$	−1.31127e9			−1.93736
$879$			1.48270e9i			2.18316i
$880$	−1.81803e9			−2.66780
$881$			4.03304e8i			0.589801i	0.955528	+	0.294900i	$0.0952865\pi$
$881$			4.03304e8i			0.589801i	−0.955528	+	0.294900i	$0.904714\pi$
$882$	1.96175e9			2.85915
$883$	4.11312e8			0.597432			0.298716	−	0.954342i	$-0.403442\pi$
$883$	4.11312e8			0.597432			0.298716	+	0.954342i	$0.403442\pi$
$884$			1.17155e8i			0.169591i
$885$		−	2.33351e8i		−	0.336651i
$886$	1.29241e9			1.85823
$887$	−8.95965e8			−1.28387			−0.641933	−	0.766760i	$-0.721867\pi$
$887$	−8.95965e8			−1.28387			−0.641933	+	0.766760i	$0.721867\pi$
$888$			3.40222e9i			4.85874i
$889$			1.77246e9i			2.52273i
$890$	3.91424e8			0.555235
$891$			5.29784e8i			0.748972i
$892$	1.22144e9			1.72099
$893$		−	1.47934e9i		−	2.07737i
$894$		−	1.13043e9i		−	1.58209i
$895$			1.86339e8i			0.259917i
$896$		−	2.30040e9i		−	3.19800i
$897$	−1.77195e8	+	1.17334e8i	−0.245513	+	0.162572i
$898$	−1.82648e9			−2.52224
$899$	−1.00947e9			−1.38937
$900$	−5.44077e8			−0.746333
$901$	1.78014e7			0.0243377
$902$			7.00848e8i			0.955003i
$903$	−3.85503e8			−0.523557
$904$		−	1.47512e9i		−	1.99674i
$905$	3.75316e8			0.506351
$906$	−1.50929e9			−2.02950
$907$		−	4.45488e8i		−	0.597055i	−0.954401	−	0.298527i	$-0.903505\pi$
$907$		−	4.45488e8i		−	0.597055i	0.954401	−	0.298527i	$-0.0964954\pi$
$908$		−	9.03219e7i		−	0.120652i
$909$	−7.76784e8			−1.03421
$910$	1.75239e8			0.232544
$911$		−	3.88035e8i		−	0.513234i	−0.966513	−	0.256617i	$-0.917392\pi$
$911$		−	3.88035e8i		−	0.513234i	0.966513	−	0.256617i	$-0.0826079\pi$
$912$		−	4.26467e9i		−	5.62213i
$913$	−2.42585e9			−3.18751
$914$			8.25226e7i			0.108077i
$915$	3.79555e8			0.495464
$916$		−	8.47680e8i		−	1.10292i
$917$			7.89468e8i			1.02383i
$918$			3.18080e8i			0.411157i
$919$		−	1.11943e9i		−	1.44228i	−0.692788	−	0.721141i	$-0.743618\pi$
$919$		−	1.11943e9i		−	1.44228i	0.692788	−	0.721141i	$-0.256382\pi$
$920$	6.04199e8	+	9.12450e8i	0.775919	+	1.17178i
$921$	−8.50257e8			−1.08836
$922$	−2.69975e9			−3.44454
$923$	−9.20605e7			−0.117076
$924$	8.27438e9			10.4886
$925$			1.57635e8i			0.199172i
$926$	1.48347e9			1.86830
$927$			1.53954e8i			0.193264i
$928$	3.02836e9			3.78934
$929$	7.92626e8			0.988601			0.494300	−	0.869291i	$-0.335424\pi$
$929$	7.92626e8			0.988601			0.494300	+	0.869291i	$0.335424\pi$
$930$			1.27565e9i			1.58593i
$931$			9.24843e8i			1.14609i
$932$	2.46073e9			3.03960
$933$	3.60474e8			0.443843
$934$		−	3.83795e8i		−	0.471041i
$935$			2.19691e8i			0.268768i
$936$	6.89337e8			0.840628
$937$		−	1.26695e9i		−	1.54007i	−0.638004	−	0.770033i	$-0.720240\pi$
$937$		−	1.26695e9i		−	1.54007i	0.638004	−	0.770033i	$-0.279760\pi$
$938$	1.71457e9			2.07753
$939$		−	1.58376e8i		−	0.191290i
$940$		−	1.89126e9i		−	2.27703i
$941$		−	3.99541e8i		−	0.479504i	−0.970834	−	0.239752i	$-0.922934\pi$
$941$		−	3.99541e8i		−	0.479504i	0.970834	−	0.239752i	$-0.0770661\pi$
$942$		−	4.14731e9i		−	4.96151i
$943$	1.96648e8	−	1.30215e8i	0.234506	−	0.155283i
$944$	1.36827e9			1.62651
$945$	3.45280e8			0.409144
$946$	−6.75121e8			−0.797458
$947$	−9.33304e8			−1.09894			−0.549469	−	0.835514i	$-0.685170\pi$
$947$	−9.33304e8			−1.09894			−0.549469	+	0.835514i	$0.685170\pi$
$948$		−	6.42807e9i		−	7.54493i
$949$	−5.44116e7			−0.0636639
$950$		−	3.53443e8i		−	0.412239i
$951$	−1.33405e9			−1.55107
$952$	−1.31572e9			−1.52494
$953$			1.00011e9i			1.15550i	0.816215	+	0.577748i	$0.196068\pi$
$953$			1.00011e9i			1.15550i	−0.816215	+	0.577748i	$0.803932\pi$
$954$		−	1.68385e8i		−	0.193936i
$955$	−3.08135e8			−0.353779
$956$	−1.25730e9			−1.43902
$957$			2.81043e9i			3.20654i
$958$		−	1.36496e8i		−	0.155247i
$959$	2.01647e9			2.28632
$960$		−	1.76620e9i		−	1.99630i
$961$	3.82550e8			0.431040
$962$		−	3.21072e8i		−	0.360642i
$963$			1.50756e9i			1.68809i
$964$			4.04709e9i			4.51764i
$965$			2.87909e8i			0.320385i
$966$	−2.11839e9	−	3.19915e9i	−2.35003	−	3.54898i
$967$	3.30123e8			0.365087			0.182544	−	0.983198i	$-0.441567\pi$
$967$	3.30123e8			0.365087			0.182544	+	0.983198i	$0.441567\pi$
$968$	6.16347e9			6.79516
$969$	−5.15344e8			−0.566403
$970$	4.84271e7			0.0530607
$971$			1.29794e9i			1.41774i	0.705338	+	0.708871i	$0.250795\pi$
$971$			1.29794e9i			1.41774i	−0.705338	+	0.708871i	$0.749205\pi$
$972$	−3.13693e9			−3.41591
$973$		−	5.63337e8i		−	0.611547i
$974$	2.47694e8			0.268064
$975$	5.45845e7			0.0588918
$976$			2.22555e9i			2.39380i
$977$			4.91742e8i			0.527295i	0.964619	+	0.263647i	$0.0849255\pi$
$977$			4.91742e8i			0.527295i	−0.964619	+	0.263647i	$0.915074\pi$
$978$	−1.53718e9			−1.64327
$979$	−1.08496e9			−1.15629
$980$			1.18237e9i			1.25624i
$981$		−	1.60932e9i		−	1.70465i
$982$	4.90894e8			0.518386
$983$			8.73505e8i			0.919612i	0.888019	+	0.459806i	$0.152081\pi$
$983$			8.73505e8i			0.919612i	−0.888019	+	0.459806i	$0.847919\pi$
$984$	−1.30742e9			−1.37224
$985$			2.04206e8i			0.213678i
$986$		−	7.18422e8i		−	0.749461i
$987$			4.12477e9i			4.28991i
$988$			5.22437e8i			0.541705i
$989$	1.25435e8	+	1.89429e8i	0.129667	+	0.195820i
$990$	2.07808e9			2.14169
$991$	8.85257e8			0.909596			0.454798	−	0.890595i	$-0.349711\pi$
$991$	8.85257e8			0.909596			0.454798	+	0.890595i	$0.349711\pi$
$992$	−3.81008e9			−3.90301
$993$	−1.45500e9			−1.48599
$994$		−	1.66210e9i		−	1.69238i
$995$	−5.93382e6			−0.00602372
$996$		−	7.27500e9i		−	7.36300i
$997$	−9.40173e7			−0.0948686			−0.0474343	−	0.998874i	$-0.515104\pi$
$997$	−9.40173e7			−0.0948686			−0.0474343	+	0.998874i	$0.515104\pi$
$998$	−1.06864e9			−1.07508
$999$		−	6.32622e8i		−	0.634523i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.7.d.a.91.3	✓	48
23.22	odd	2	inner	115.7.d.a.91.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.7.d.a.91.3	✓	48	1.1	even	1	trivial
115.7.d.a.91.4	yes	48	23.22	odd	2	inner

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	115.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-15.2752 q^{2} +41.9187 q^{3} +169.333 q^{4} -55.9017i q^{5} -640.318 q^{6} +492.500i q^{7} -1608.98 q^{8} +1028.18 q^{9} +O(q^{10})\)	\(q-15.2752 q^{2} +41.9187 q^{3} +169.333 q^{4} -55.9017i q^{5} -640.318 q^{6} +492.500i q^{7} -1608.98 q^{8} +1028.18 q^{9} +853.912i q^{10} -2366.90i q^{11} +7098.21 q^{12} -416.688 q^{13} -7523.05i q^{14} -2343.33i q^{15} +13740.3 q^{16} -1660.38i q^{17} -15705.7 q^{18} -7404.26i q^{19} -9465.99i q^{20} +20645.0i q^{21} +36155.0i q^{22} +(10144.5 - 6717.44i) q^{23} -67446.5 q^{24} -3125.00 q^{25} +6365.00 q^{26} +12541.2 q^{27} +83396.3i q^{28} -28325.9 q^{29} +35794.9i q^{30} +35637.8 q^{31} -106911. q^{32} -99217.5i q^{33} +25362.7i q^{34} +27531.6 q^{35} +174105. q^{36} -50443.3i q^{37} +113102. i q^{38} -17467.0 q^{39} +89944.9i q^{40} +19384.6 q^{41} -315357. i q^{42} +18673.0i q^{43} -400794. i q^{44} -57477.0i q^{45} +(-154960. + 102610. i) q^{46} +199795. q^{47} +575975. q^{48} -124907. q^{49} +47735.1 q^{50} -69601.0i q^{51} -70558.9 q^{52} +10721.3i q^{53} -191570. q^{54} -132314. q^{55} -792423. i q^{56} -310377. i q^{57} +432685. q^{58} +99581.0 q^{59} -396802. i q^{60} +161973. i q^{61} -544376. q^{62} +506378. i q^{63} +753715. q^{64} +23293.6i q^{65} +1.51557e6i q^{66} +227909. i q^{67} -281157. i q^{68} +(425247. - 281587. i) q^{69} -420551. q^{70} +220934. q^{71} -1.65432e6 q^{72} +130581. q^{73} +770533. i q^{74} -130996. q^{75} -1.25378e6i q^{76} +1.16570e6 q^{77} +266813. q^{78} -905589. i q^{79} -768105. i q^{80} -223830. q^{81} -296104. q^{82} -1.02491e6i q^{83} +3.49587e6i q^{84} -92818.0 q^{85} -285234. i q^{86} -1.18739e6 q^{87} +3.80830e6i q^{88} -458389. i q^{89} +877975. i q^{90} -205219. i q^{91} +(1.71780e6 - 1.13748e6i) q^{92} +1.49389e6 q^{93} -3.05192e6 q^{94} -413911. q^{95} -4.48158e6 q^{96} -56712.1i q^{97} +1.90798e6 q^{98} -2.43360e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 20 q^{2} + 1584 q^{4} + 410 q^{6} - 1210 q^{8} + 12896 q^{9}+O(q^{10}) \) 48 * q - 20 * q^2 + 1584 * q^4 + 410 * q^6 - 1210 * q^8 + 12896 * q^9	\( 48 q - 20 q^{2} + 1584 q^{4} + 410 q^{6} - 1210 q^{8} + 12896 q^{9} + 4290 q^{12} - 1440 q^{13} + 65400 q^{16} + 4610 q^{18} + 26600 q^{23} + 14940 q^{24} - 150000 q^{25} + 47594 q^{26} + 16080 q^{27} + 131800 q^{29} - 1392 q^{31} - 225040 q^{32} + 5000 q^{35} + 658786 q^{36} - 236320 q^{39} - 351496 q^{41} + 382692 q^{46} + 395680 q^{47} + 1042550 q^{48} - 637848 q^{49} + 62500 q^{50} + 523890 q^{52} - 241250 q^{54} - 402000 q^{55} - 479130 q^{58} - 466312 q^{59} - 1124330 q^{62} + 837582 q^{64} + 1021060 q^{69} - 396000 q^{70} - 114336 q^{71} - 1960750 q^{72} - 498720 q^{73} + 3610400 q^{77} - 1104610 q^{78} + 972888 q^{81} + 124950 q^{82} - 246000 q^{85} - 2090960 q^{87} + 4913480 q^{92} + 3234320 q^{93} - 5550378 q^{94} - 1664000 q^{95} - 776990 q^{96} + 9993220 q^{98}+O(q^{100}) \) 48 * q - 20 * q^2 + 1584 * q^4 + 410 * q^6 - 1210 * q^8 + 12896 * q^9 + 4290 * q^12 - 1440 * q^13 + 65400 * q^16 + 4610 * q^18 + 26600 * q^23 + 14940 * q^24 - 150000 * q^25 + 47594 * q^26 + 16080 * q^27 + 131800 * q^29 - 1392 * q^31 - 225040 * q^32 + 5000 * q^35 + 658786 * q^36 - 236320 * q^39 - 351496 * q^41 + 382692 * q^46 + 395680 * q^47 + 1042550 * q^48 - 637848 * q^49 + 62500 * q^50 + 523890 * q^52 - 241250 * q^54 - 402000 * q^55 - 479130 * q^58 - 466312 * q^59 - 1124330 * q^62 + 837582 * q^64 + 1021060 * q^69 - 396000 * q^70 - 114336 * q^71 - 1960750 * q^72 - 498720 * q^73 + 3610400 * q^77 - 1104610 * q^78 + 972888 * q^81 + 124950 * q^82 - 246000 * q^85 - 2090960 * q^87 + 4913480 * q^92 + 3234320 * q^93 - 5550378 * q^94 - 1664000 * q^95 - 776990 * q^96 + 9993220 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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